LMFDB - Embedded newform 74.2.f.b.7.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [74,2,Mod(7,74)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(74, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([16]))

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

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

chi := DirichletCharacter("74.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 74 = 2 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	74.f (of order $9$, degree $6$, 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:	$0.590892974957$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 24x^{10} + 264x^{8} - 1687x^{6} + 6600x^{4} - 15000x^{2} + 15625 $ x^12 - 24x^10 + 264x^8 - 1687x^6 + 6600x^4 - 15000*x^2 + 15625
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			7.1
Root			$2.00752 + 0.984808i$ of defining polynomial
Character	$\chi$	$=$	74.7
Dual form			74.2.f.b.53.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.939693 + 0.342020i) q^{2} +(-2.04963 - 0.746005i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-0.326352 - 1.85083i) q^{5} +2.18117 q^{6} +(-0.711830 - 4.03699i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(1.34633 + 1.12971i) q^{9} +O(q^{10})$	\(q+(-0.939693 + 0.342020i) q^{2} +(-2.04963 - 0.746005i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-0.326352 - 1.85083i) q^{5} +2.18117 q^{6} +(-0.711830 - 4.03699i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(1.34633 + 1.12971i) q^{9} +(0.939693 + 1.62760i) q^{10} +(-1.67088 + 2.89404i) q^{11} +(-2.04963 + 0.746005i) q^{12} +(1.48512 - 1.24616i) q^{13} +(2.04963 + 3.55007i) q^{14} +(-0.711830 + 4.03699i) q^{15} +(0.173648 - 0.984808i) q^{16} +(3.40626 + 2.85819i) q^{17} +(-1.65152 - 0.601105i) q^{18} +(0.0932770 + 0.0339500i) q^{19} +(-1.43969 - 1.20805i) q^{20} +(-1.55262 + 8.80536i) q^{21} +(0.580289 - 3.29098i) q^{22} +(-4.76146 - 8.24709i) q^{23} +(1.67088 - 1.40203i) q^{24} +(1.37939 - 0.502055i) q^{25} +(-0.969343 + 1.67895i) q^{26} +(1.35504 + 2.34700i) q^{27} +(-3.14022 - 2.63496i) q^{28} +(-0.387288 + 0.670802i) q^{29} +(-0.711830 - 4.03699i) q^{30} +10.3914 q^{31} +(0.173648 + 0.984808i) q^{32} +(5.58365 - 4.68524i) q^{33} +(-4.17840 - 1.52081i) q^{34} +(-7.23948 + 2.63496i) q^{35} +1.75751 q^{36} +(-3.50302 - 4.97281i) q^{37} -0.0992633 q^{38} +(-3.97359 + 1.44627i) q^{39} +(1.76604 + 0.642788i) q^{40} +(4.36218 - 3.66031i) q^{41} +(-1.55262 - 8.80536i) q^{42} -1.11986 q^{43} +(0.580289 + 3.29098i) q^{44} +(1.65152 - 2.86052i) q^{45} +(7.29498 + 6.12122i) q^{46} +(3.55724 + 6.16132i) q^{47} +(-1.09059 + 1.88895i) q^{48} +(-9.21271 + 3.35315i) q^{49} +(-1.12449 + 0.943555i) q^{50} +(-4.84936 - 8.39933i) q^{51} +(0.336649 - 1.90923i) q^{52} +(0.142188 - 0.806388i) q^{53} +(-2.07604 - 1.74200i) q^{54} +(5.90168 + 2.14804i) q^{55} +(3.85205 + 1.40203i) q^{56} +(-0.165857 - 0.139170i) q^{57} +(0.134504 - 0.762808i) q^{58} +(1.40642 - 7.97622i) q^{59} +(2.04963 + 3.55007i) q^{60} +(-8.19737 + 6.87841i) q^{61} +(-9.76476 + 3.55408i) q^{62} +(3.60225 - 6.23929i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-2.79111 - 2.34202i) q^{65} +(-3.64447 + 6.31240i) q^{66} +(2.28630 + 12.9663i) q^{67} +4.44656 q^{68} +(3.60687 + 20.4556i) q^{69} +(5.90168 - 4.95210i) q^{70} +(2.79386 + 1.01688i) q^{71} +(-1.65152 + 0.601105i) q^{72} -2.55740 q^{73} +(4.99257 + 3.47481i) q^{74} -3.20177 q^{75} +(0.0932770 - 0.0339500i) q^{76} +(12.8726 + 4.68524i) q^{77} +(3.23930 - 2.71810i) q^{78} +(-0.943888 - 5.35305i) q^{79} -1.87939 q^{80} +(-1.94203 - 11.0138i) q^{81} +(-2.84721 + 4.93152i) q^{82} +(0.504249 + 0.423115i) q^{83} +(4.47060 + 7.74331i) q^{84} +(4.17840 - 7.23720i) q^{85} +(1.05232 - 0.383014i) q^{86} +(1.29422 - 1.08598i) q^{87} +(-1.67088 - 2.89404i) q^{88} +(0.612149 - 3.47167i) q^{89} +(-0.573568 + 3.25286i) q^{90} +(-6.08790 - 5.10835i) q^{91} +(-8.94862 - 3.25703i) q^{92} +(-21.2986 - 7.75206i) q^{93} +(-5.45001 - 4.57310i) q^{94} +(0.0323948 - 0.183720i) q^{95} +(0.378757 - 2.14804i) q^{96} +(-1.81012 - 3.13522i) q^{97} +(7.51027 - 6.30186i) q^{98} +(-5.51897 + 2.00874i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3 q^{3} - 6 q^{5} + 6 q^{7} - 6 q^{8} - 3 q^{9}+O(q^{10}) $ 12 * q - 3 * q^3 - 6 * q^5 + 6 * q^7 - 6 * q^8 - 3 * q^9	$ 12 q - 3 q^{3} - 6 q^{5} + 6 q^{7} - 6 q^{8} - 3 q^{9} + 3 q^{11} - 3 q^{12} - 6 q^{13} + 3 q^{14} + 6 q^{15} - 3 q^{17} + 6 q^{18} - 3 q^{19} - 6 q^{20} - 33 q^{21} - 3 q^{22} - 21 q^{23} - 3 q^{24} - 6 q^{25} + 3 q^{27} - 3 q^{28} + 6 q^{29} + 6 q^{30} + 42 q^{31} + 57 q^{33} - 3 q^{34} - 9 q^{35} + 24 q^{36} - 3 q^{37} + 42 q^{38} - 24 q^{39} + 12 q^{40} - 21 q^{41} - 33 q^{42} + 36 q^{43} - 3 q^{44} - 6 q^{45} + 3 q^{46} + 9 q^{47} - 12 q^{49} + 12 q^{50} + 3 q^{52} - 6 q^{53} - 27 q^{54} - 3 q^{56} - 36 q^{57} - 3 q^{58} - 6 q^{59} + 3 q^{60} - 18 q^{61} - 33 q^{62} + 36 q^{63} - 6 q^{64} + 3 q^{65} + 3 q^{66} - 27 q^{67} + 6 q^{68} - 12 q^{69} - 18 q^{71} + 6 q^{72} + 54 q^{73} + 3 q^{74} - 6 q^{75} - 3 q^{76} + 51 q^{77} - 33 q^{78} - 12 q^{79} - 36 q^{81} - 18 q^{82} - 6 q^{83} - 6 q^{84} + 3 q^{85} + 39 q^{87} + 3 q^{88} - 15 q^{89} - 15 q^{90} - 51 q^{91} - 6 q^{92} + 45 q^{93} - 12 q^{94} - 15 q^{95} + 6 q^{96} - 42 q^{97} + 51 q^{98} - 33 q^{99}+O(q^{100}) $ 12 * q - 3 * q^3 - 6 * q^5 + 6 * q^7 - 6 * q^8 - 3 * q^9 + 3 * q^11 - 3 * q^12 - 6 * q^13 + 3 * q^14 + 6 * q^15 - 3 * q^17 + 6 * q^18 - 3 * q^19 - 6 * q^20 - 33 * q^21 - 3 * q^22 - 21 * q^23 - 3 * q^24 - 6 * q^25 + 3 * q^27 - 3 * q^28 + 6 * q^29 + 6 * q^30 + 42 * q^31 + 57 * q^33 - 3 * q^34 - 9 * q^35 + 24 * q^36 - 3 * q^37 + 42 * q^38 - 24 * q^39 + 12 * q^40 - 21 * q^41 - 33 * q^42 + 36 * q^43 - 3 * q^44 - 6 * q^45 + 3 * q^46 + 9 * q^47 - 12 * q^49 + 12 * q^50 + 3 * q^52 - 6 * q^53 - 27 * q^54 - 3 * q^56 - 36 * q^57 - 3 * q^58 - 6 * q^59 + 3 * q^60 - 18 * q^61 - 33 * q^62 + 36 * q^63 - 6 * q^64 + 3 * q^65 + 3 * q^66 - 27 * q^67 + 6 * q^68 - 12 * q^69 - 18 * q^71 + 6 * q^72 + 54 * q^73 + 3 * q^74 - 6 * q^75 - 3 * q^76 + 51 * q^77 - 33 * q^78 - 12 * q^79 - 36 * q^81 - 18 * q^82 - 6 * q^83 - 6 * q^84 + 3 * q^85 + 39 * q^87 + 3 * q^88 - 15 * q^89 - 15 * q^90 - 51 * q^91 - 6 * q^92 + 45 * q^93 - 12 * q^94 - 15 * q^95 + 6 * q^96 - 42 * q^97 + 51 * q^98 - 33 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/74\mathbb{Z}\right)^\times$.

$n$	$39$
$\chi(n)$	$e\left(\frac{8}{9}\right)$

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 $

$2$	−0.939693	+	0.342020i	−0.664463	+	0.241845i
$2$	−0.939693	+	0.342020i	−0.664463	+	0.241845i
$3$	−2.04963	−	0.746005i	−1.18336	−	0.430706i	−0.325970	−	0.945380i	$-0.605691\pi$
$3$	−2.04963	−	0.746005i	−1.18336	−	0.430706i	−0.857386	+	0.514674i	$0.827913\pi$
$4$	0.766044	−	0.642788i	0.383022	−	0.321394i
$5$	−0.326352	−	1.85083i	−0.145949	−	0.827718i	−0.966600	−	0.256289i	$-0.917500\pi$
$5$	−0.326352	−	1.85083i	−0.145949	−	0.827718i	0.820651	−	0.571429i	$-0.193611\pi$
$6$	2.18117			0.890460
$7$	−0.711830	−	4.03699i	−0.269046	−	1.52584i	−0.757260	−	0.653113i	$-0.773463\pi$
$7$	−0.711830	−	4.03699i	−0.269046	−	1.52584i	0.488214	−	0.872724i	$-0.337649\pi$
$8$	−0.500000	+	0.866025i	−0.176777	+	0.306186i
$9$	1.34633	+	1.12971i	0.448778	+	0.376569i
$10$	0.939693	+	1.62760i	0.297157	+	0.514691i
$11$	−1.67088	+	2.89404i	−0.503788	+	0.872586i	0.496203	+	0.868207i	$0.334727\pi$
$11$	−1.67088	+	2.89404i	−0.503788	+	0.872586i	−0.999990	+	0.00437929i	$0.998606\pi$
$12$	−2.04963	+	0.746005i	−0.591678	+	0.215353i
$13$	1.48512	−	1.24616i	0.411898	−	0.345623i	−0.413173	−	0.910653i	$-0.635580\pi$
$13$	1.48512	−	1.24616i	0.411898	−	0.345623i	0.825071	+	0.565029i	$0.191135\pi$
$14$	2.04963	+	3.55007i	0.547787	+	0.948795i
$15$	−0.711830	+	4.03699i	−0.183794	+	1.04235i
$16$	0.173648	−	0.984808i	0.0434120	−	0.246202i
$17$	3.40626	+	2.85819i	0.826140	+	0.693214i	0.954401	−	0.298527i	$-0.0964952\pi$
$17$	3.40626	+	2.85819i	0.826140	+	0.693214i	−0.128261	+	0.991740i	$0.540940\pi$
$18$	−1.65152	−	0.601105i	−0.389268	−	0.141682i
$19$	0.0932770	+	0.0339500i	0.0213992	+	0.00778868i	0.352698	−	0.935737i	$-0.385264\pi$
$19$	0.0932770	+	0.0339500i	0.0213992	+	0.00778868i	−0.331298	+	0.943526i	$0.607487\pi$
$20$	−1.43969	−	1.20805i	−0.321925	−	0.270127i
$21$	−1.55262	+	8.80536i	−0.338810	+	1.92149i
$22$	0.580289	−	3.29098i	0.123718	−	0.701640i
$23$	−4.76146	−	8.24709i	−0.992833	−	1.71964i	−0.599913	−	0.800065i	$-0.704798\pi$
$23$	−4.76146	−	8.24709i	−0.992833	−	1.71964i	−0.392920	−	0.919573i	$-0.628535\pi$
$24$	1.67088	−	1.40203i	0.341066	−	0.286188i
$25$	1.37939	−	0.502055i	0.275877	−	0.100411i
$26$	−0.969343	+	1.67895i	−0.190104	+	0.329269i
$27$	1.35504	+	2.34700i	0.260777	+	0.451680i
$28$	−3.14022	−	2.63496i	−0.593445	−	0.497960i
$29$	−0.387288	+	0.670802i	−0.0719175	+	0.124565i	−0.899742	−	0.436423i	$-0.856245\pi$
$29$	−0.387288	+	0.670802i	−0.0719175	+	0.124565i	0.827824	+	0.560988i	$0.189579\pi$
$30$	−0.711830	−	4.03699i	−0.129962	−	0.737049i
$31$	10.3914			1.86636			0.933179	−	0.359413i	$-0.117023\pi$
$31$	10.3914			1.86636			0.933179	+	0.359413i	$0.117023\pi$
$32$	0.173648	+	0.984808i	0.0306970	+	0.174091i
$33$	5.58365	−	4.68524i	0.971988	−	0.815595i
$34$	−4.17840	−	1.52081i	−0.716590	−	0.260817i
$35$	−7.23948	+	2.63496i	−1.22370	+	0.445389i
$36$	1.75751			0.292919
$37$	−3.50302	−	4.97281i	−0.575894	−	0.817525i
$37$	−3.50302	−	4.97281i	−0.575894	−	0.817525i
$38$	−0.0992633			−0.0161026
$39$	−3.97359	+	1.44627i	−0.636284	+	0.231588i
$40$	1.76604	+	0.642788i	0.279236	+	0.101634i
$41$	4.36218	−	3.66031i	0.681259	−	0.571644i	−0.235115	−	0.971968i	$-0.575547\pi$
$41$	4.36218	−	3.66031i	0.681259	−	0.571644i	0.916374	+	0.400324i	$0.131102\pi$
$42$	−1.55262	−	8.80536i	−0.239575	−	1.35870i
$43$	−1.11986			−0.170777			−0.0853884	−	0.996348i	$-0.527213\pi$
$43$	−1.11986			−0.170777			−0.0853884	+	0.996348i	$0.527213\pi$
$44$	0.580289	+	3.29098i	0.0874818	+	0.496134i
$45$	1.65152	−	2.86052i	0.246194	−	0.426421i
$46$	7.29498	+	6.12122i	1.07559	+	0.902524i
$47$	3.55724	+	6.16132i	0.518877	+	0.898721i	0.999759	+	0.0219357i	$0.00698290\pi$
$47$	3.55724	+	6.16132i	0.518877	+	0.898721i	−0.480883	+	0.876785i	$0.659684\pi$
$48$	−1.09059	+	1.88895i	−0.157413	+	0.272647i
$49$	−9.21271	+	3.35315i	−1.31610	+	0.479022i
$50$	−1.12449	+	0.943555i	−0.159026	+	0.133439i
$51$	−4.84936	−	8.39933i	−0.679046	−	1.17614i
$52$	0.336649	−	1.90923i	0.0466848	−	0.264763i
$53$	0.142188	−	0.806388i	0.0195310	−	0.110766i	−0.973484	−	0.228756i	$-0.926534\pi$
$53$	0.142188	−	0.806388i	0.0195310	−	0.110766i	0.993015	+	0.117990i	$0.0376452\pi$
$54$	−2.07604	−	1.74200i	−0.282513	−	0.237057i
$55$	5.90168	+	2.14804i	0.795782	+	0.289641i
$56$	3.85205	+	1.40203i	0.514751	+	0.187354i
$57$	−0.165857	−	0.139170i	−0.0219682	−	0.0184335i
$58$	0.134504	−	0.762808i	0.0176612	−	0.100162i
$59$	1.40642	−	7.97622i	0.183101	−	1.03842i	−0.745271	−	0.666762i	$-0.767680\pi$
$59$	1.40642	−	7.97622i	0.183101	−	1.03842i	0.928372	−	0.371653i	$-0.121209\pi$
$60$	2.04963	+	3.55007i	0.264606	+	0.458312i
$61$	−8.19737	+	6.87841i	−1.04957	+	0.880691i	−0.993048	−	0.117711i	$-0.962444\pi$
$61$	−8.19737	+	6.87841i	−1.04957	+	0.880691i	−0.0565183	+	0.998402i	$0.518000\pi$
$62$	−9.76476	+	3.55408i	−1.24013	+	0.451369i
$63$	3.60225	−	6.23929i	0.453841	−	0.786076i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	−2.79111	−	2.34202i	−0.346195	−	0.290492i
$66$	−3.64447	+	6.31240i	−0.448603	+	0.777003i
$67$	2.28630	+	12.9663i	0.279317	+	1.58408i	0.724907	+	0.688846i	$0.241883\pi$
$67$	2.28630	+	12.9663i	0.279317	+	1.58408i	−0.445591	+	0.895237i	$0.647006\pi$
$68$	4.44656			0.539225
$69$	3.60687	+	20.4556i	0.434216	+	2.46256i
$70$	5.90168	−	4.95210i	0.705386	−	0.591889i
$71$	2.79386	+	1.01688i	0.331570	+	0.120682i	0.502440	−	0.864612i	$-0.332436\pi$
$71$	2.79386	+	1.01688i	0.331570	+	0.120682i	−0.170870	+	0.985294i	$0.554658\pi$
$72$	−1.65152	+	0.601105i	−0.194634	+	0.0708409i
$73$	−2.55740			−0.299321			−0.149660	−	0.988737i	$-0.547818\pi$
$73$	−2.55740			−0.299321			−0.149660	+	0.988737i	$0.547818\pi$
$74$	4.99257	+	3.47481i	0.580374	+	0.403938i
$75$	−3.20177			−0.369708
$76$	0.0932770	−	0.0339500i	0.0106996	−	0.00389434i
$77$	12.8726	+	4.68524i	1.46697	+	0.533932i
$78$	3.23930	−	2.71810i	0.366779	−	0.307764i
$79$	−0.943888	−	5.35305i	−0.106196	−	0.602265i	−0.990736	−	0.135802i	$-0.956639\pi$
$79$	−0.943888	−	5.35305i	−0.106196	−	0.602265i	0.884540	−	0.466464i	$-0.154472\pi$
$80$	−1.87939			−0.210122
$81$	−1.94203	−	11.0138i	−0.215781	−	1.22375i
$82$	−2.84721	+	4.93152i	−0.314422	+	0.544595i
$83$	0.504249	+	0.423115i	0.0553485	+	0.0464429i	0.670042	−	0.742323i	$-0.266276\pi$
$83$	0.504249	+	0.423115i	0.0553485	+	0.0464429i	−0.614694	+	0.788766i	$0.710720\pi$
$84$	4.47060	+	7.74331i	0.487782	+	0.844864i
$85$	4.17840	−	7.23720i	0.453211	−	0.784985i
$86$	1.05232	−	0.383014i	0.113475	−	0.0413015i
$87$	1.29422	−	1.08598i	0.138755	−	0.116429i
$88$	−1.67088	−	2.89404i	−0.178116	−	0.308506i
$89$	0.612149	−	3.47167i	0.0648877	−	0.367996i	−0.935022	−	0.354589i	$-0.884621\pi$
$89$	0.612149	−	3.47167i	0.0648877	−	0.367996i	0.999910	−	0.0134078i	$-0.00426798\pi$
$90$	−0.573568	+	3.25286i	−0.0604593	+	0.342882i
$91$	−6.08790	−	5.10835i	−0.638185	−	0.535501i
$92$	−8.94862	−	3.25703i	−0.932958	−	0.339569i
$93$	−21.2986	−	7.75206i	−2.20856	−	0.803852i
$94$	−5.45001	−	4.57310i	−0.562125	−	0.471679i
$95$	0.0323948	−	0.183720i	0.00332363	−	0.0188493i
$96$	0.378757	−	2.14804i	0.0386567	−	0.219233i
$97$	−1.81012	−	3.13522i	−0.183790	−	0.318334i	0.759378	−	0.650650i	$-0.225503\pi$
$97$	−1.81012	−	3.13522i	−0.183790	−	0.318334i	−0.943168	+	0.332316i	$0.892170\pi$
$98$	7.51027	−	6.30186i	0.758652	−	0.636584i
$99$	−5.51897	+	2.00874i	−0.554678	+	0.201886i
$100$	0.733956	−	1.27125i	0.0733956	−	0.127125i
$101$	−1.97406	−	3.41917i	−0.196426	−	0.340220i	0.750941	−	0.660369i	$-0.229600\pi$
$101$	−1.97406	−	3.41917i	−0.196426	−	0.340220i	−0.947367	+	0.320149i	$0.896267\pi$
$102$	7.42965	+	6.23421i	0.735645	+	0.617279i
$103$	0.989402	−	1.71369i	0.0974887	−	0.168855i	−0.813156	−	0.582046i	$-0.802252\pi$
$103$	0.989402	−	1.71369i	0.0974887	−	0.168855i	0.910645	+	0.413191i	$0.135586\pi$
$104$	0.336649	+	1.90923i	0.0330112	+	0.187216i
$105$	16.8040			1.63990
$106$	0.142188	+	0.806388i	0.0138105	+	0.0783233i
$107$	6.31896	−	5.30224i	0.610877	−	0.512587i	−0.284044	−	0.958811i	$-0.591676\pi$
$107$	6.31896	−	5.30224i	0.610877	−	0.512587i	0.894921	+	0.446225i	$0.147232\pi$
$108$	2.54664	+	0.926901i	0.245051	+	0.0891911i
$109$	8.25476	−	3.00449i	0.790663	−	0.287778i	0.0850513	−	0.996377i	$-0.472895\pi$
$109$	8.25476	−	3.00449i	0.790663	−	0.287778i	0.705612	+	0.708599i	$0.250672\pi$
$110$	−6.28044			−0.598816
$111$	3.47017	+	12.8057i	0.329374	+	1.21546i
$112$	−4.09926			−0.387344
$113$	−9.37522	+	3.41230i	−0.881946	+	0.321002i	−0.742995	−	0.669297i	$-0.766595\pi$
$113$	−9.37522	+	3.41230i	−0.881946	+	0.321002i	−0.138951	+	0.990299i	$0.544373\pi$
$114$	0.203453	+	0.0740509i	0.0190551	+	0.00693550i
$115$	−13.7101	+	11.5041i	−1.27847	+	1.07277i
$116$	0.134504	+	0.762808i	0.0124884	+	0.0708250i
$117$	3.40727			0.315002
$118$	1.40642	+	7.97622i	0.129472	+	0.734270i
$119$	9.11381	−	15.7856i	0.835462	−	1.44706i
$120$	−3.14022	−	2.63496i	−0.286661	−	0.240537i
$121$	−0.0836467	−	0.144880i	−0.00760425	−	0.0131709i
$122$	5.35046	−	9.26726i	0.484408	−	0.839018i
$123$	−11.6715	+	4.24807i	−1.05238	+	0.383036i
$124$	7.96030	−	6.67949i	0.714856	−	0.599836i
$125$	−6.07785	−	10.5271i	−0.543619	−	0.941576i
$126$	−1.25105	+	7.09506i	−0.111452	+	0.632078i
$127$	−2.91336	+	16.5225i	−0.258519	+	1.46613i	0.528356	+	0.849023i	$0.322808\pi$
$127$	−2.91336	+	16.5225i	−0.258519	+	1.46613i	−0.786876	+	0.617112i	$0.788303\pi$
$128$	0.766044	+	0.642788i	0.0677094	+	0.0568149i
$129$	2.29530	+	0.835420i	0.202090	+	0.0735546i
$130$	3.42381	+	1.24616i	0.300288	+	0.109296i
$131$	1.07527	+	0.902259i	0.0939468	+	0.0788307i	0.688551	−	0.725188i	$-0.258247\pi$
$131$	1.07527	+	0.902259i	0.0939468	+	0.0788307i	−0.594605	+	0.804018i	$0.702691\pi$
$132$	1.26571	−	7.17820i	0.110166	−	0.624782i
$133$	0.0706586	−	0.400725i	0.00612687	−	0.0347472i
$134$	−6.58315	−	11.4024i	−0.568698	−	0.985013i
$135$	3.90168	−	3.27390i	0.335803	−	0.281772i
$136$	−4.17840	+	1.52081i	−0.358295	+	0.130409i
$137$	−6.20963	+	10.7554i	−0.530525	+	0.918896i	0.468841	+	0.883283i	$0.344672\pi$
$137$	−6.20963	+	10.7554i	−0.530525	+	0.918896i	−0.999366	+	0.0356133i	$0.988662\pi$
$138$	−10.3856	−	17.9883i	−0.884078	−	1.53127i
$139$	14.0949	+	11.8270i	1.19551	+	1.00315i	0.999747	+	0.0225036i	$0.00716372\pi$
$139$	14.0949	+	11.8270i	1.19551	+	1.00315i	0.195766	+	0.980651i	$0.437281\pi$
$140$	−3.85205	+	6.67194i	−0.325557	+	0.563882i
$141$	−2.69466	−	15.2821i	−0.226931	−	1.28699i
$142$	−2.97316			−0.249502
$143$	1.12500	+	6.38018i	0.0940770	+	0.533537i
$144$	1.34633	−	1.12971i	0.112194	−	0.0941423i
$145$	1.36794	+	0.497888i	0.113601	+	0.0413473i
$146$	2.40317	−	0.874681i	0.198887	−	0.0723891i
$147$	21.3841			1.76373
$148$	−5.87993	−	1.55769i	−0.483327	−	0.128042i
$149$	12.4068			1.01640			0.508201	−	0.861238i	$-0.330311\pi$
$149$	12.4068			1.01640			0.508201	+	0.861238i	$0.330311\pi$
$150$	3.00868	−	1.09507i	0.245657	−	0.0894120i
$151$	11.7921	+	4.29198i	0.959628	+	0.349276i	0.773888	−	0.633323i	$-0.218309\pi$
$151$	11.7921	+	4.29198i	0.959628	+	0.349276i	0.185740	+	0.982599i	$0.440532\pi$
$152$	−0.0760401	+	0.0638052i	−0.00616767	+	0.00517529i
$153$	1.35704	+	7.69616i	0.109710	+	0.622198i
$154$	−13.6987			−1.10387
$155$	−3.39126	−	19.2328i	−0.272393	−	1.54482i
$156$	−2.11430	+	3.66208i	−0.169280	+	0.293201i
$157$	2.69131	+	2.25828i	0.214790	+	0.180230i	0.743834	−	0.668364i	$-0.233005\pi$
$157$	2.69131	+	2.25828i	0.214790	+	0.180230i	−0.529045	+	0.848594i	$0.677450\pi$
$158$	2.71782	+	4.70740i	0.216218	+	0.374500i
$159$	−0.893002	+	1.54672i	−0.0708197	+	0.122663i
$160$	1.76604	−	0.642788i	0.139618	−	0.0508168i
$161$	−29.9041	+	25.0925i	−2.35677	+	1.97756i
$162$	5.59184	+	9.68536i	0.439337	+	0.760954i
$163$	−0.415269	+	2.35511i	−0.0325264	+	0.184466i	−0.996742	−	0.0806519i	$-0.974300\pi$
$163$	−0.415269	+	2.35511i	−0.0325264	+	0.184466i	0.964216	+	0.265118i	$0.0854109\pi$
$164$	0.988827	−	5.60792i	0.0772144	−	0.437905i
$165$	−10.4938	−	8.80536i	−0.816943	−	0.685497i
$166$	−0.618553	−	0.225135i	−0.0480090	−	0.0174738i
$167$	14.6442	+	5.33004i	1.13320	+	0.412451i	0.839453	−	0.543433i	$-0.182876\pi$
$167$	14.6442	+	5.33004i	1.13320	+	0.412451i	0.293746	+	0.955884i	$0.405098\pi$
$168$	−6.84936	−	5.74729i	−0.528439	−	0.443413i
$169$	−1.60477	+	9.10110i	−0.123444	+	0.700085i
$170$	−1.45114	+	8.22984i	−0.111298	+	0.631200i
$171$	0.0872283	+	0.151084i	0.00667051	+	0.0115537i
$172$	−0.857861	+	0.719831i	−0.0654113	+	0.0548866i
$173$	16.7991	−	6.11436i	1.27721	−	0.464866i	0.387701	−	0.921785i	$-0.373269\pi$
$173$	16.7991	−	6.11436i	1.27721	−	0.464866i	0.889508	+	0.456919i	$0.151047\pi$
$174$	−0.844742	+	1.46314i	−0.0640397	+	0.110920i
$175$	−3.00868	−	5.21118i	−0.227435	−	0.393928i
$176$	2.55993	+	2.14804i	0.192962	+	0.161914i
$177$	−8.83294	+	15.2991i	−0.663925	+	1.14995i
$178$	0.612149	+	3.47167i	0.0458825	+	0.260213i
$179$	−20.4063			−1.52524			−0.762619	−	0.646848i	$-0.776087\pi$
$179$	−20.4063			−1.52524			−0.762619	+	0.646848i	$0.776087\pi$
$180$	−0.573568	−	3.25286i	−0.0427512	−	0.242454i
$181$	−14.0006	+	11.7479i	−1.04065	+	0.873212i	−0.992080	−	0.125607i	$-0.959912\pi$
$181$	−14.0006	+	11.7479i	−1.04065	+	0.873212i	−0.0485737	+	0.998820i	$0.515468\pi$
$182$	7.46791	+	2.71810i	0.553558	+	0.201479i
$183$	21.9329	−	7.98293i	1.62133	−	0.590115i
$184$	9.52292			0.702039
$185$	−8.06062	+	8.10640i	−0.592629	+	0.595994i
$186$	22.6655			1.66192
$187$	−13.9632	+	5.08218i	−1.02109	+	0.371646i
$188$	6.68542	+	2.43329i	0.487584	+	0.177466i
$189$	8.51024	−	7.14094i	0.619029	−	0.519427i
$190$	0.0323948	+	0.183720i	0.00235016	+	0.0133284i
$191$	5.76567			0.417189			0.208595	−	0.978002i	$-0.433111\pi$
$191$	5.76567			0.417189			0.208595	+	0.978002i	$0.433111\pi$
$192$	0.378757	+	2.14804i	0.0273344	+	0.155021i
$193$	0.179712	−	0.311271i	0.0129360	−	0.0224057i	−0.859485	−	0.511161i	$-0.829216\pi$
$193$	0.179712	−	0.311271i	0.0129360	−	0.0224057i	0.872421	+	0.488755i	$0.162549\pi$
$194$	2.77327	+	2.32705i	0.199109	+	0.167072i
$195$	3.97359	+	6.88246i	0.284555	+	0.492863i
$196$	−4.90198	+	8.49048i	−0.350141	+	0.606463i
$197$	−6.54591	+	2.38251i	−0.466376	+	0.169747i	−0.564510	−	0.825426i	$-0.690935\pi$
$197$	−6.54591	+	2.38251i	−0.466376	+	0.169747i	0.0981338	+	0.995173i	$0.468713\pi$
$198$	4.49911	−	3.77520i	0.319738	−	0.268292i
$199$	−5.58897	−	9.68037i	−0.396191	−	0.686223i	0.597061	−	0.802196i	$-0.296335\pi$
$199$	−5.58897	−	9.68037i	−0.396191	−	0.686223i	−0.993252	+	0.115972i	$0.963002\pi$
$200$	−0.254900	+	1.44561i	−0.0180242	+	0.102220i
$201$	4.98683	−	28.2817i	0.351744	−	1.99484i
$202$	3.02443	+	2.53780i	0.212798	+	0.178559i
$203$	2.98370	+	1.08598i	0.209415	+	0.0762208i
$204$	−9.11381	−	3.31716i	−0.638094	−	0.232247i
$205$	−8.19823	−	6.87913i	−0.572589	−	0.480459i
$206$	−0.343616	+	1.94874i	−0.0239408	+	0.135775i
$207$	2.90629	−	16.4824i	0.202001	−	1.14561i
$208$	−0.969343	−	1.67895i	−0.0672118	−	0.116414i
$209$	−0.254107	+	0.213221i	−0.0175770	+	0.0147488i
$210$	−15.7906	+	5.74729i	−1.08965	+	0.396601i
$211$	6.10513	−	10.5744i	0.420295	−	0.727972i	−0.575673	−	0.817680i	$-0.695260\pi$
$211$	6.10513	−	10.5744i	0.420295	−	0.727972i	0.995968	+	0.0897080i	$0.0285934\pi$
$212$	−0.409414	−	0.709125i	−0.0281187	−	0.0487029i
$213$	−4.96778	−	4.16846i	−0.340387	−	0.285618i
$214$	−4.12441	+	7.14368i	−0.281939	+	0.488332i
$215$	0.365468	+	2.07267i	0.0249247	+	0.141355i
$216$	−2.71008			−0.184397
$217$	−7.39693	−	41.9501i	−0.502137	−	2.84776i
$218$	−6.72934	+	5.64659i	−0.455769	+	0.382435i
$219$	5.24172	+	1.90783i	0.354203	+	0.128919i
$220$	5.90168	−	2.14804i	0.397891	−	0.144821i
$221$	8.62048			0.579876
$222$	−7.64070	−	10.8466i	−0.512810	−	0.727973i
$223$	−10.7545			−0.720177			−0.360088	−	0.932918i	$-0.617253\pi$
$223$	−10.7545			−0.720177			−0.360088	+	0.932918i	$0.617253\pi$
$224$	3.85205	−	1.40203i	0.257376	−	0.0936771i
$225$	2.42429	+	0.882369i	0.161619	+	0.0588246i
$226$	7.64275	−	6.41303i	0.508388	−	0.426588i
$227$	−0.514913	−	2.92021i	−0.0341759	−	0.193821i	0.962940	−	0.269716i	$-0.0869298\pi$
$227$	−0.514913	−	2.92021i	−0.0341759	−	0.193821i	−0.997116	+	0.0758946i	$0.975819\pi$
$228$	−0.216510			−0.0143388
$229$	−0.526610	−	2.98655i	−0.0347994	−	0.197357i	0.962452	−	0.271453i	$-0.0875041\pi$
$229$	−0.526610	−	2.98655i	−0.0347994	−	0.197357i	−0.997251	+	0.0740958i	$0.976393\pi$
$230$	8.94862	−	15.4995i	0.590055	−	1.02200i
$231$	−22.8888	−	19.2060i	−1.50597	−	1.26366i
$232$	−0.387288	−	0.670802i	−0.0254267	−	0.0440403i
$233$	0.144403	−	0.250113i	0.00946016	−	0.0163855i	−0.861257	−	0.508170i	$-0.830322\pi$
$233$	0.144403	−	0.250113i	0.00946016	−	0.0163855i	0.870717	+	0.491785i	$0.163655\pi$
$234$	−3.20178	+	1.16535i	−0.209307	+	0.0761815i
$235$	10.2427	−	8.59461i	0.668157	−	0.560651i
$236$	−4.04963	−	7.01417i	−0.263609	−	0.456583i
$237$	−2.05878	+	11.6759i	−0.133732	+	0.758433i
$238$	−3.16519	+	17.9507i	−0.205169	+	1.16357i
$239$	−3.85711	−	3.23650i	−0.249496	−	0.209352i	0.509460	−	0.860495i	$-0.329845\pi$
$239$	−3.85711	−	3.23650i	−0.249496	−	0.209352i	−0.758955	+	0.651143i	$0.774290\pi$
$240$	3.85205	+	1.40203i	0.248649	+	0.0905007i
$241$	16.3281	+	5.94293i	1.05178	+	0.382818i	0.809336	−	0.587347i	$-0.199827\pi$
$241$	16.3281	+	5.94293i	1.05178	+	0.382818i	0.242448	+	0.970164i	$0.422050\pi$
$242$	0.128154	+	0.107534i	0.00823807	+	0.00691256i
$243$	−2.82410	+	16.0162i	−0.181166	+	1.02744i
$244$	−1.85819	+	10.5383i	−0.118959	+	0.674648i
$245$	9.21271	+	15.9569i	0.588578	+	1.01945i
$246$	9.51468	−	7.98376i	0.606634	−	0.509026i
$247$	0.180835	−	0.0658185i	0.0115062	−	0.00418793i
$248$	−5.19572	+	8.99925i	−0.329928	+	0.571453i
$249$	−0.717878	−	1.24340i	−0.0454937	−	0.0787974i
$250$	9.31180	+	7.81353i	0.588930	+	0.494171i
$251$	0.877844	−	1.52047i	0.0554090	−	0.0959713i	−0.836990	−	0.547218i	$-0.815687\pi$
$251$	0.877844	−	1.52047i	0.0554090	−	0.0959713i	0.892399	+	0.451246i	$0.149020\pi$
$252$	−1.25105	−	7.09506i	−0.0788087	−	0.446947i
$253$	31.8232			2.00071
$254$	−2.91336	−	16.5225i	−0.182801	−	1.03671i
$255$	−13.9632	+	11.7165i	−0.874407	+	0.733715i
$256$	−0.939693	−	0.342020i	−0.0587308	−	0.0213763i
$257$	11.9849	−	4.36215i	0.747598	−	0.272103i	0.0600034	−	0.998198i	$-0.480889\pi$
$257$	11.9849	−	4.36215i	0.747598	−	0.272103i	0.687595	+	0.726095i	$0.258667\pi$
$258$	−2.44260			−0.152070
$259$	−17.5816	+	17.6815i	−1.09247	+	1.09867i
$260$	−3.64354			−0.225963
$261$	−1.27923	+	0.465601i	−0.0791823	+	0.0288200i
$262$	−1.31901	−	0.480082i	−0.0814890	−	0.0296596i
$263$	−20.1968	+	16.9472i	−1.24539	+	1.04501i	−0.248307	+	0.968681i	$0.579874\pi$
$263$	−20.1968	+	16.9472i	−1.24539	+	1.04501i	−0.997083	+	0.0763250i	$0.975681\pi$
$264$	1.26571	+	7.17820i	0.0778991	+	0.441788i
$265$	−1.53889			−0.0945334
$266$	0.0706586	+	0.400725i	0.00433235	+	0.0245700i
$267$	−3.84457	+	6.65898i	−0.235284	+	0.407523i
$268$	10.0860	+	8.46314i	0.616099	+	0.516968i
$269$	−6.80289	−	11.7829i	−0.414779	−	0.718419i	0.580626	−	0.814171i	$-0.302808\pi$
$269$	−6.80289	−	11.7829i	−0.414779	−	0.718419i	−0.995405	+	0.0957514i	$0.969475\pi$
$270$	−2.54664	+	4.41091i	−0.154984	+	0.268439i
$271$	4.05562	−	1.47612i	0.246361	−	0.0896682i	−0.215888	−	0.976418i	$-0.569265\pi$
$271$	4.05562	−	1.47612i	0.246361	−	0.0896682i	0.462249	+	0.886750i	$0.347042\pi$
$272$	3.40626	−	2.85819i	0.206535	−	0.173303i
$273$	8.66709	+	15.0118i	0.524556	+	0.908558i
$274$	2.15658	−	12.2306i	0.130284	−	0.738877i
$275$	−0.851812	+	4.83087i	−0.0513662	+	0.291312i
$276$	15.9116	+	13.3514i	0.957767	+	0.803662i
$277$	3.28276	+	1.19483i	0.197242	+	0.0717902i	0.438752	−	0.898608i	$-0.355421\pi$
$277$	3.28276	+	1.19483i	0.197242	+	0.0717902i	−0.241510	+	0.970398i	$0.577643\pi$
$278$	−17.2899	−	6.29302i	−1.03698	−	0.377430i
$279$	13.9903	+	11.7393i	0.837580	+	0.702813i
$280$	1.33780	−	7.58705i	0.0799490	−	0.453413i
$281$	−1.27419	+	7.22628i	−0.0760116	+	0.431083i	0.922925	+	0.384980i	$0.125792\pi$
$281$	−1.27419	+	7.22628i	−0.0760116	+	0.431083i	−0.998937	+	0.0461037i	$0.985320\pi$
$282$	7.75895	+	13.4389i	0.462039	+	0.800275i
$283$	10.7268	−	9.00087i	0.637643	−	0.535046i	−0.265650	−	0.964070i	$-0.585587\pi$
$283$	10.7268	−	9.00087i	0.637643	−	0.535046i	0.903294	+	0.429023i	$0.141142\pi$
$284$	2.79386	−	1.01688i	0.165785	−	0.0603408i
$285$	−0.203453	+	0.352391i	−0.0120515	+	0.0208739i
$286$	−3.23930	−	5.61063i	−0.191544	−	0.331764i
$287$	−17.8817	−	15.0046i	−1.05553	−	0.885691i
$288$	−0.878757	+	1.52205i	−0.0517812	+	0.0896877i
$289$	0.481334	+	2.72978i	0.0283138	+	0.160575i
$290$	−1.45573			−0.0854832
$291$	1.37119	+	7.77641i	0.0803807	+	0.455861i
$292$	−1.95908	+	1.64386i	−0.114646	+	0.0961998i
$293$	23.7505	+	8.64447i	1.38752	+	0.505015i	0.924449	−	0.381306i	$-0.124526\pi$
$293$	23.7505	+	8.64447i	1.38752	+	0.505015i	0.463070	+	0.886322i	$0.346748\pi$
$294$	−20.0945	+	7.31380i	−1.17194	+	0.426550i
$295$	−15.2216			−0.886238
$296$	6.05809	−	0.547303i	0.352119	−	0.0318113i
$297$	−9.05640			−0.525506
$298$	−11.6586	+	4.24337i	−0.675362	+	0.245812i
$299$	−17.3486	−	6.31436i	−1.00329	−	0.365169i
$300$	−2.45270	+	2.05806i	−0.141606	+	0.118822i
$301$	0.797148	+	4.52085i	0.0459469	+	0.260578i
$302$	−12.5489			−0.722108
$303$	1.49537	+	8.48069i	0.0859070	+	0.487203i
$304$	0.0496317	−	0.0859645i	0.00284657	−	0.00493040i
$305$	15.4060	+	12.9272i	0.882146	+	0.740209i
$306$	−3.90744	−	6.76789i	−0.223374	−	0.386895i
$307$	12.2995	−	21.3034i	0.701972	−	1.21585i	−0.265801	−	0.964028i	$-0.585637\pi$
$307$	12.2995	−	21.3034i	0.701972	−	1.21585i	0.967773	−	0.251823i	$-0.0810301\pi$
$308$	12.8726	−	4.68524i	0.733483	−	0.266966i
$309$	−3.30633	+	2.77434i	−0.188091	+	0.157827i
$310$	9.76476	+	16.9131i	0.554601	+	0.960597i
$311$	0.904212	−	5.12804i	0.0512732	−	0.290785i	−0.948380	−	0.317138i	$-0.897278\pi$
$311$	0.904212	−	5.12804i	0.0512732	−	0.290785i	0.999653	+	0.0263531i	$0.00838941\pi$
$312$	0.734290	−	4.16437i	0.0415710	−	0.235761i
$313$	5.54340	+	4.65147i	0.313332	+	0.262916i	0.785867	−	0.618395i	$-0.212217\pi$
$313$	5.54340	+	4.65147i	0.313332	+	0.262916i	−0.472536	+	0.881311i	$0.656661\pi$
$314$	−3.30138	−	1.20160i	−0.186308	−	0.0678104i
$315$	−12.7235	−	4.63097i	−0.716887	−	0.260926i
$316$	−4.16394	−	3.49396i	−0.234240	−	0.196550i
$317$	−2.31803	+	13.1462i	−0.130194	+	0.738365i	0.847893	+	0.530167i	$0.177871\pi$
$317$	−2.31803	+	13.1462i	−0.130194	+	0.738365i	−0.978087	+	0.208198i	$0.933240\pi$
$318$	0.310136	−	1.75887i	0.0173916	−	0.0986326i
$319$	−1.29422	−	2.24165i	−0.0724624	−	0.125508i
$320$	−1.43969	+	1.20805i	−0.0804813	+	0.0675318i
$321$	−16.9070	+	6.15366i	−0.943659	+	0.343464i
$322$	19.5185	−	33.8070i	1.08772	−	1.88399i
$323$	0.220690	+	0.382246i	0.0122795	+	0.0212688i
$324$	−8.56720	−	7.18874i	−0.475956	−	0.399374i
$325$	1.42291	−	2.46455i	0.0789288	−	0.136709i
$326$	−0.415269	−	2.35511i	−0.0229996	−	0.130437i
$327$	−19.1606			−1.05958
$328$	0.988827	+	5.60792i	0.0545988	+	0.309645i
$329$	22.3410	−	18.7463i	1.23170	−	1.03352i
$330$	12.8726	+	4.68524i	0.708612	+	0.257914i
$331$	4.29733	−	1.56410i	0.236203	−	0.0859708i	−0.221207	−	0.975227i	$-0.571000\pi$
$331$	4.29733	−	1.56410i	0.236203	−	0.0859708i	0.457410	+	0.889256i	$0.348777\pi$
$332$	0.658250			0.0361262
$333$	0.901584	−	10.6525i	0.0494065	−	0.583751i
$334$	−15.5840			−0.852717
$335$	23.2523	−	8.46314i	1.27041	−	0.462391i
$336$	8.40198	+	3.05807i	0.458366	+	0.166831i
$337$	2.49218	−	2.09118i	0.135757	−	0.113914i	−0.572380	−	0.819988i	$-0.693980\pi$
$337$	2.49218	−	2.09118i	0.135757	−	0.113914i	0.708138	+	0.706074i	$0.249536\pi$
$338$	−1.60477	−	9.10110i	−0.0872879	−	0.495035i
$339$	21.7613			1.18191
$340$	−1.45114	−	8.22984i	−0.0786993	−	0.446326i
$341$	−17.3628	+	30.0732i	−0.940248	+	1.62856i
$342$	−0.133641	−	0.112139i	−0.00722650	−	0.00606376i
$343$	5.74708	+	9.95424i	0.310313	+	0.537479i
$344$	0.559929	−	0.969826i	0.0301894	−	0.0522895i
$345$	36.6827	−	13.3514i	1.97493	−	0.718817i
$346$	−13.6947	+	11.4912i	−0.736233	+	0.617773i
$347$	−12.2387	−	21.1981i	−0.657008	−	1.13797i	−0.981386	−	0.192044i	$-0.938488\pi$
$347$	−12.2387	−	21.1981i	−0.657008	−	1.13797i	0.324379	−	0.945927i	$-0.394845\pi$
$348$	0.293376	−	1.66382i	0.0157266	−	0.0891899i
$349$	0.990209	−	5.61576i	0.0530047	−	0.300604i	−0.946768	−	0.321916i	$-0.895673\pi$
$349$	0.990209	−	5.61576i	0.0530047	−	0.300604i	0.999773	+	0.0213116i	$0.00678421\pi$
$350$	4.60956	+	3.86788i	0.246391	+	0.206747i
$351$	4.93713	+	1.79697i	0.263525	+	0.0959152i
$352$	−3.14022	−	1.14295i	−0.167374	−	0.0609192i
$353$	18.7175	+	15.7059i	0.996233	+	0.835939i	0.986458	−	0.164014i	$-0.0524441\pi$
$353$	18.7175	+	15.7059i	0.996233	+	0.835939i	0.00977486	+	0.999952i	$0.496889\pi$
$354$	3.06765	−	17.3975i	0.163044	−	0.924667i
$355$	0.970296	−	5.50282i	0.0514980	−	0.292059i
$356$	−1.76261	−	3.05294i	−0.0934184	−	0.161805i
$357$	−30.4561	+	25.5557i	−1.61191	+	1.35255i
$358$	19.1756	−	6.97936i	1.01346	−	0.368871i
$359$	−9.35461	+	16.2027i	−0.493717	+	0.855144i	−0.999974	−	0.00723934i	$-0.997696\pi$
$359$	−9.35461	+	16.2027i	−0.493717	+	0.855144i	0.506256	+	0.862383i	$0.331029\pi$
$360$	1.65152	+	2.86052i	0.0870429	+	0.150763i
$361$	−14.5473	−	12.2066i	−0.765647	−	0.642454i
$362$	9.13822	−	15.8279i	0.480294	−	0.831894i
$363$	0.0633635	+	0.359352i	0.00332572	+	0.0188611i
$364$	−7.94718			−0.416546
$365$	0.834611	+	4.73331i	0.0436855	+	0.247753i
$366$	−17.8799	+	15.0030i	−0.934597	+	0.784220i
$367$	−31.6892	−	11.5339i	−1.65416	−	0.602067i	−0.664735	−	0.747080i	$-0.731455\pi$
$367$	−31.6892	−	11.5339i	−1.65416	−	0.602067i	−0.989430	+	0.145013i	$0.953678\pi$
$368$	−8.94862	+	3.25703i	−0.466479	+	0.169784i
$369$	10.0080			0.520997
$370$	4.80196	−	10.3744i	0.249642	−	0.539340i
$371$	−3.35659			−0.174265
$372$	−21.2986	+	7.75206i	−1.10428	+	0.401926i
$373$	−29.5389	−	10.7513i	−1.52947	−	0.556681i	−0.565977	−	0.824421i	$-0.691501\pi$
$373$	−29.5389	−	10.7513i	−1.52947	−	0.556681i	−0.963491	+	0.267740i	$0.913723\pi$
$374$	11.3829	−	9.55137i	0.588595	−	0.493889i
$375$	4.60405	+	26.1109i	0.237752	+	1.34836i
$376$	−7.11448			−0.366901
$377$	0.260760	+	1.47885i	0.0134298	+	0.0761644i
$378$	−5.55466	+	9.62096i	−0.285701	+	0.494849i
$379$	5.33697	+	4.47825i	0.274142	+	0.230032i	0.769485	−	0.638665i	$-0.220513\pi$
$379$	5.33697	+	4.47825i	0.274142	+	0.230032i	−0.495343	+	0.868697i	$0.664958\pi$
$380$	−0.0932770	−	0.161560i	−0.00478501	−	0.00828788i
$381$	18.2972	−	31.6916i	0.937393	−	1.62361i
$382$	−5.41796	+	1.97198i	−0.277207	+	0.100895i
$383$	−2.20412	+	1.84948i	−0.112625	+	0.0945038i	−0.697361	−	0.716720i	$-0.745643\pi$
$383$	−2.20412	+	1.84948i	−0.112625	+	0.0945038i	0.584736	+	0.811224i	$0.301198\pi$
$384$	−1.09059	−	1.88895i	−0.0556537	−	0.0963951i
$385$	4.47060	−	25.3540i	0.227843	−	1.29216i
$386$	−0.0624134	+	0.353964i	−0.00317676	+	0.0180163i
$387$	−1.50770	−	1.26511i	−0.0766408	−	0.0643093i
$388$	−3.40192	−	1.23820i	−0.172706	−	0.0628599i
$389$	11.0993	+	4.03981i	0.562756	+	0.204827i	0.607705	−	0.794163i	$-0.292090\pi$
$389$	11.0993	+	4.03981i	0.562756	+	0.204827i	−0.0449488	+	0.998989i	$0.514312\pi$
$390$	−6.08790	−	5.10835i	−0.308273	−	0.258671i
$391$	7.35300	−	41.7009i	0.371857	−	2.10891i
$392$	1.70244	−	9.65502i	0.0859862	−	0.487652i
$393$	−1.53082	−	2.65146i	−0.0772196	−	0.133748i
$394$	5.33627	−	4.47766i	0.268837	−	0.225581i
$395$	−9.59957	+	3.49396i	−0.483007	+	0.175800i
$396$	−2.93658	+	5.08631i	−0.147569	+	0.255597i
$397$	15.6563	+	27.1174i	0.785765	+	1.36098i	0.928541	+	0.371230i	$0.121064\pi$
$397$	15.6563	+	27.1174i	0.785765	+	1.36098i	−0.142776	+	0.989755i	$0.545603\pi$
$398$	8.56279	+	7.18504i	0.429214	+	0.360153i
$399$	−0.443767	+	0.768626i	−0.0222161	+	0.0384794i
$400$	−0.254900	−	1.44561i	−0.0127450	−	0.0722805i
$401$	−14.0281			−0.700531			−0.350266	−	0.936650i	$-0.613909\pi$
$401$	−14.0281			−0.700531			−0.350266	+	0.936650i	$0.613909\pi$
$402$	4.98683	+	28.2817i	0.248720	+	1.41056i
$403$	15.4325	−	12.9494i	0.768749	−	0.645057i
$404$	−3.71001	−	1.35033i	−0.184580	−	0.0671817i
$405$	−19.7509	+	7.18874i	−0.981430	+	0.357211i
$406$	−3.17519			−0.157582
$407$	20.2446	−	1.82895i	1.00349	−	0.0906577i
$408$	9.69871			0.480158
$409$	0.0761808	−	0.0277275i	0.00376690	−	0.00137104i	−0.340136	−	0.940376i	$-0.610473\pi$
$409$	0.0761808	−	0.0277275i	0.00376690	−	0.00137104i	0.343903	+	0.939005i	$0.388251\pi$
$410$	10.0566	+	3.66031i	0.496661	+	0.180770i
$411$	20.7510	−	17.4122i	1.02357	−	0.858880i
$412$	−0.343616	−	1.94874i	−0.0169287	−	0.0960076i
$413$	−33.2010			−1.63372
$414$	2.90629	+	16.4824i	0.142836	+	0.810066i
$415$	0.618553	−	1.07136i	0.0303636	−	0.0525912i
$416$	1.48512	+	1.24616i	0.0728140	+	0.0610982i
$417$	−20.0663	−	34.7559i	−0.982652	−	1.70200i
$418$	0.165857	−	0.287272i	0.00811231	−	0.0140509i
$419$	−4.35652	+	1.58564i	−0.212830	+	0.0774637i	−0.446235	−	0.894916i	$-0.647235\pi$
$419$	−4.35652	+	1.58564i	−0.212830	+	0.0774637i	0.233405	+	0.972380i	$0.425013\pi$
$420$	12.8726	−	10.8014i	0.628118	−	0.527053i
$421$	9.66110	+	16.7335i	0.470853	+	0.815542i	0.999444	−	0.0333350i	$-0.0106128\pi$
$421$	9.66110	+	16.7335i	0.470853	+	0.815542i	−0.528591	+	0.848877i	$0.677279\pi$
$422$	−2.12029	+	12.0248i	−0.103214	+	0.585356i
$423$	−2.17126	+	12.3138i	−0.105570	+	0.598719i
$424$	0.627258	+	0.526332i	0.0304624	+	0.0255610i
$425$	6.13352	+	2.23242i	0.297519	+	0.108288i
$426$	6.09388	+	2.21799i	0.295250	+	0.107462i
$427$	33.6032	+	28.1964i	1.62617	+	1.36452i
$428$	1.43239	−	8.12350i	0.0692373	−	0.392664i
$429$	2.45381	−	13.9163i	0.118471	−	0.671884i
$430$	−1.05232	−	1.82268i	−0.0507475	−	0.0878972i
$431$	5.77729	−	4.84772i	0.278282	−	0.233507i	−0.492954	−	0.870055i	$-0.664083\pi$
$431$	5.77729	−	4.84772i	0.278282	−	0.233507i	0.771237	+	0.636549i	$0.219639\pi$
$432$	2.54664	−	0.926901i	0.122525	−	0.0445956i
$433$	−14.9169	+	25.8369i	−0.716863	+	1.24164i	0.245374	+	0.969428i	$0.421089\pi$
$433$	−14.9169	+	25.8369i	−0.716863	+	1.24164i	−0.962237	+	0.272214i	$0.912244\pi$
$434$	21.2986	+	36.8903i	1.02237	+	1.77079i
$435$	−2.43234	−	2.04097i	−0.116622	−	0.0978571i
$436$	4.39227	−	7.60763i	0.210351	−	0.364339i
$437$	−0.164146	−	0.930916i	−0.00785215	−	0.0445317i
$438$	−5.57812			−0.266533
$439$	3.81229	+	21.6206i	0.181951	+	1.03189i	0.929811	+	0.368038i	$0.119970\pi$
$439$	3.81229	+	21.6206i	0.181951	+	1.03189i	−0.747860	+	0.663856i	$0.768919\pi$
$440$	−4.81109	+	4.03699i	−0.229360	+	0.192456i
$441$	−16.1915	−	5.89321i	−0.771022	−	0.280629i
$442$	−8.10060	+	2.94838i	−0.385306	+	0.140240i
$443$	−34.6241			−1.64504			−0.822520	−	0.568736i	$-0.807433\pi$
$443$	−34.6241			−1.64504			−0.822520	+	0.568736i	$0.807433\pi$
$444$	10.8896	+	7.57915i	0.516800	+	0.359691i
$445$	−6.62526			−0.314068
$446$	10.1060	−	3.67827i	0.478531	−	0.174171i
$447$	−25.4293	−	9.25552i	−1.20277	−	0.437771i
$448$	−3.14022	+	2.63496i	−0.148361	+	0.124490i
$449$	−3.46279	−	19.6385i	−0.163419	−	0.926796i	−0.950679	−	0.310175i	$-0.899612\pi$
$449$	−3.46279	−	19.6385i	−0.163419	−	0.926796i	0.787260	−	0.616621i	$-0.211499\pi$
$450$	−2.57987			−0.121616
$451$	3.30441	+	18.7403i	0.155599	+	0.882444i
$452$	−4.98845	+	8.64025i	−0.234637	+	0.406403i
$453$	−20.9676	−	17.5939i	−0.985146	−	0.826635i
$454$	1.48263	+	2.56799i	0.0695834	+	0.120522i
$455$	−7.46791	+	12.9348i	−0.350101	+	0.606393i
$456$	0.203453	−	0.0740509i	0.00952757	−	0.00346775i
$457$	24.6964	−	20.7227i	1.15525	−	0.969368i	0.155418	−	0.987849i	$-0.450328\pi$
$457$	24.6964	−	20.7227i	1.15525	−	0.969368i	0.999829	+	0.0184812i	$0.00588309\pi$
$458$	1.51631	+	2.62633i	0.0708526	+	0.122720i
$459$	−2.09255	+	11.8674i	−0.0976719	+	0.553925i
$460$	−3.10782	+	17.6253i	−0.144903	+	0.821786i
$461$	5.61373	+	4.71048i	0.261458	+	0.219389i	0.764087	−	0.645113i	$-0.223190\pi$
$461$	5.61373	+	4.71048i	0.261458	+	0.219389i	−0.502630	+	0.864502i	$0.667634\pi$
$462$	28.0773	+	10.2193i	1.30627	+	0.475445i
$463$	−6.09514	−	2.21845i	−0.283265	−	0.103100i	0.196480	−	0.980508i	$-0.437049\pi$
$463$	−6.09514	−	2.21845i	−0.283265	−	0.103100i	−0.479745	+	0.877408i	$0.659271\pi$
$464$	0.593359	+	0.497888i	0.0275460	+	0.0231139i
$465$	−7.39693	+	41.9501i	−0.343025	+	1.94539i
$466$	−0.0501507	+	0.284419i	−0.00232318	+	0.0131754i
$467$	5.99288	+	10.3800i	0.277317	+	0.480328i	0.970717	−	0.240225i	$-0.0772214\pi$
$467$	5.99288	+	10.3800i	0.277317	+	0.480328i	−0.693400	+	0.720553i	$0.743888\pi$
$468$	2.61012	−	2.19015i	0.120653	−	0.101240i
$469$	50.7172	−	18.4596i	2.34190	−	0.852383i
$470$	−6.68542	+	11.5795i	−0.308375	+	0.534122i
$471$	−3.83151	−	6.63637i	−0.176547	−	0.305788i
$472$	6.20440	+	5.20611i	0.285580	+	0.239630i
$473$	1.87114	−	3.24091i	0.0860352	−	0.149017i
$474$	−2.05878	−	11.6759i	−0.0945630	−	0.536293i
$475$	0.145710			0.00668562
$476$	−3.16519	−	17.9507i	−0.145076	−	0.822769i
$477$	1.10241	−	0.925036i	0.0504761	−	0.0423545i
$478$	4.73144	+	1.72210i	0.216411	+	0.0787672i
$479$	−21.3237	+	7.76119i	−0.974305	+	0.354618i	−0.779623	−	0.626249i	$-0.784590\pi$
$479$	−21.3237	+	7.76119i	−0.974305	+	0.354618i	−0.194681	+	0.980867i	$0.562367\pi$
$480$	−4.09926			−0.187105
$481$	−11.3993	−	3.01988i	−0.519765	−	0.137694i
$482$	−17.3760			−0.791454
$483$	80.0114	−	29.1218i	3.64064	−	1.32509i
$484$	−0.157204	−	0.0572177i	−0.00714566	−	0.00260081i
$485$	−5.21204	+	4.37342i	−0.236666	+	0.198587i
$486$	−2.82410	−	16.0162i	−0.128104	−	0.726511i
$487$	12.3108			0.557856			0.278928	−	0.960312i	$-0.410021\pi$
$487$	12.3108			0.557856			0.278928	+	0.960312i	$0.410021\pi$
$488$	−1.85819	−	10.5383i	−0.0841165	−	0.477048i
$489$	2.60807	−	4.51731i	0.117941	−	0.204280i
$490$	−14.1147	−	11.8436i	−0.637637	−	0.535041i
$491$	−0.575398	−	0.996619i	−0.0259674	−	0.0449768i	0.852750	−	0.522320i	$-0.174933\pi$
$491$	−0.575398	−	0.996619i	−0.0259674	−	0.0449768i	−0.878717	+	0.477343i	$0.841600\pi$
$492$	−6.21026	+	10.7565i	−0.279980	+	0.484940i
$493$	−3.23649	+	1.17798i	−0.145764	+	0.0530538i
$494$	−0.147418	+	0.123698i	−0.00663264	+	0.00556545i
$495$	5.51897	+	9.55914i	0.248059	+	0.429652i
$496$	1.80445	−	10.2336i	0.0810224	−	0.459501i
$497$	2.11638	−	12.0026i	0.0949327	−	0.538390i
$498$	1.09985	+	0.922887i	0.0492856	+	0.0413555i
$499$	−26.2321	−	9.54769i	−1.17431	−	0.427413i	−0.320120	−	0.947377i	$-0.603723\pi$
$499$	−26.2321	−	9.54769i	−1.17431	−	0.427413i	−0.854189	+	0.519963i	$0.825946\pi$
$500$	−11.4226	−	4.15749i	−0.510835	−	0.185929i
$501$	−26.0389	−	21.8492i	−1.16333	−	0.976151i
$502$	−0.304872	+	1.72902i	−0.0136071	+	0.0771697i
$503$	−2.84222	+	16.1191i	−0.126728	+	0.718713i	0.853538	+	0.521031i	$0.174452\pi$
$503$	−2.84222	+	16.1191i	−0.126728	+	0.718713i	−0.980266	+	0.197682i	$0.936659\pi$
$504$	3.60225	+	6.23929i	0.160457	+	0.277920i
$505$	−5.68407	+	4.76950i	−0.252938	+	0.212240i
$506$	−29.9041	+	10.8842i	−1.32940	+	0.483861i
$507$	10.0787	−	17.4567i	0.447609	−	0.775281i
$508$	8.38869	+	14.5296i	0.372188	+	0.644648i
$509$	3.32007	+	2.78587i	0.147159	+	0.123481i	0.713395	−	0.700762i	$-0.247156\pi$
$509$	3.32007	+	2.78587i	0.147159	+	0.123481i	−0.566236	+	0.824243i	$0.691601\pi$
$510$	9.11381	−	15.7856i	0.403566	−	0.698997i
$511$	1.82043	+	10.3242i	0.0805311	+	0.456715i
$512$	1.00000			0.0441942
$513$	0.0467133	+	0.264924i	0.00206244	+	0.0116967i
$514$	−9.77019	+	8.19816i	−0.430944	+	0.361605i
$515$	−3.49466	−	1.27195i	−0.153993	−	0.0560488i
$516$	2.29530	−	0.835420i	0.101045	−	0.0367773i
$517$	−23.7748			−1.04561
$518$	10.4739	−	22.6284i	0.460196	−	0.994234i
$519$	−38.9932			−1.71161
$520$	3.42381	−	1.24616i	0.150144	−	0.0546479i
$521$	−1.75997	−	0.640577i	−0.0771057	−	0.0280642i	0.303179	−	0.952934i	$-0.401952\pi$
$521$	−1.75997	−	0.640577i	−0.0771057	−	0.0280642i	−0.380285	+	0.924869i	$0.624174\pi$
$522$	1.04284	−	0.875044i	0.0456437	−	0.0382996i
$523$	6.43474	+	36.4932i	0.281371	+	1.59574i	0.717966	+	0.696078i	$0.245073\pi$
$523$	6.43474	+	36.4932i	0.281371	+	1.59574i	−0.436595	+	0.899658i	$0.643816\pi$
$524$	1.40367			0.0613194
$525$	2.27911	+	12.9255i	0.0994686	+	0.564115i
$526$	13.1825	−	22.8328i	0.574786	−	0.995559i
$527$	35.3960	+	29.7007i	1.54187	+	1.29378i
$528$	−3.64447	−	6.31240i	−0.158605	−	0.274712i
$529$	−33.8430	+	58.6178i	−1.47144	+	2.54860i
$530$	1.44609	−	0.526332i	0.0628140	−	0.0228624i
$531$	10.9043	−	9.14980i	0.473207	−	0.397068i
$532$	−0.203453	−	0.352391i	−0.00882082	−	0.0152781i
$533$	1.91702	−	10.8720i	0.0830356	−	0.470918i
$534$	1.33520	−	7.57232i	0.0577799	−	0.327686i
$535$	−11.8758	−	9.96494i	−0.513434	−	0.430822i
$536$	−12.3723	−	4.50314i	−0.534401	−	0.194506i
$537$	41.8254	+	15.2232i	1.80490	+	0.656929i
$538$	10.4226	+	8.74563i	0.449352	+	0.377051i
$539$	5.68913	−	32.2646i	0.245048	−	1.38974i
$540$	0.884439	−	5.01590i	0.0380602	−	0.215850i
$541$	−7.75312	−	13.4288i	−0.333332	−	0.577349i	0.649831	−	0.760079i	$-0.274840\pi$
$541$	−7.75312	−	13.4288i	−0.333332	−	0.577349i	−0.983163	+	0.182730i	$0.941506\pi$
$542$	−3.30617	+	2.77421i	−0.142012	+	0.119162i
$543$	37.4600	−	13.6343i	1.60756	−	0.585104i
$544$	−2.22328	+	3.85083i	−0.0953223	+	0.165103i
$545$	−8.25476	−	14.2977i	−0.353595	−	0.612445i
$546$	−13.2787	−	11.1422i	−0.568278	−	0.476842i
$547$	20.5925	−	35.6673i	0.880472	−	1.52502i	0.0296544	−	0.999560i	$-0.490559\pi$
$547$	20.5925	−	35.6673i	0.880472	−	1.52502i	0.850817	−	0.525462i	$-0.176107\pi$
$548$	2.15658	+	12.2306i	0.0921247	+	0.522465i
$549$	−18.8070			−0.802663
$550$	−0.851812	−	4.83087i	−0.0363214	−	0.205989i
$551$	−0.0588988	+	0.0494220i	−0.00250917	+	0.00210545i
$552$	−19.5185	−	7.10415i	−0.830762	−	0.302373i
$553$	−20.9383	+	7.62092i	−0.890388	+	0.324075i
$554$	−3.49344			−0.148422
$555$	22.5687	−	10.6019i	0.957989	−	0.450024i
$556$	18.3996			0.780315
$557$	11.4686	−	4.17423i	0.485940	−	0.176868i	−0.0874196	−	0.996172i	$-0.527862\pi$
$557$	11.4686	−	4.17423i	0.485940	−	0.176868i	0.573359	+	0.819304i	$0.305640\pi$
$558$	−17.1617	−	6.24634i	−0.726512	−	0.264429i
$559$	−1.66312	+	1.39553i	−0.0703426	+	0.0590245i
$560$	1.33780	+	7.58705i	0.0565325	+	0.320611i
$561$	32.4107			1.36838
$562$	−1.27419	−	7.22628i	−0.0537484	−	0.304822i
$563$	5.70965	−	9.88940i	0.240633	−	0.416788i	−0.720262	−	0.693702i	$-0.755978\pi$
$563$	5.70965	−	9.88940i	0.240633	−	0.416788i	0.960895	+	0.276914i	$0.0893117\pi$
$564$	−11.8874	−	9.97471i	−0.500550	−	0.420011i
$565$	9.37522	+	16.2384i	0.394418	+	0.683153i
$566$	−7.00144	+	12.1268i	−0.294292	+	0.509729i
$567$	−43.0801	+	15.6799i	−1.80919	+	0.658493i
$568$	−2.27757	+	1.91111i	−0.0955648	+	0.0801884i
$569$	11.1732	+	19.3526i	0.468406	+	0.811303i	0.999348	−	0.0361049i	$-0.0114951\pi$
$569$	11.1732	+	19.3526i	0.468406	+	0.811303i	−0.530942	+	0.847408i	$0.678162\pi$
$570$	0.0706586	−	0.400725i	0.00295956	−	0.0167845i
$571$	−2.29253	+	13.0016i	−0.0959395	+	0.544100i	0.898516	+	0.438941i	$0.144646\pi$
$571$	−2.29253	+	13.0016i	−0.0959395	+	0.544100i	−0.994455	+	0.105159i	$0.966465\pi$
$572$	4.96290	+	4.16437i	0.207509	+	0.174121i
$573$	−11.8175	−	4.30122i	−0.493683	−	0.179686i
$574$	21.9352	+	7.98376i	0.915558	+	0.333236i
$575$	−10.7084	−	8.98540i	−0.446571	−	0.374717i
$576$	0.305189	−	1.73081i	0.0127162	−	0.0721172i
$577$	5.09708	−	28.9070i	0.212194	−	1.20341i	−0.673515	−	0.739174i	$-0.735216\pi$
$577$	5.09708	−	28.9070i	0.212194	−	1.20341i	0.885709	−	0.464241i	$-0.153673\pi$
$578$	−1.38595	−	2.40053i	−0.0576478	−	0.0998489i
$579$	−0.600553	+	0.503924i	−0.0249581	+	0.0209424i
$580$	1.36794	−	0.497888i	0.0568004	−	0.0206737i
$581$	1.34917	−	2.33683i	0.0559730	−	0.0969481i
$582$	−3.94819	−	6.83846i	−0.163658	−	0.283463i
$583$	2.09614	+	1.75887i	0.0868133	+	0.0728450i
$584$	1.27870	−	2.21477i	0.0529129	−	0.0916478i
$585$	−1.11197	−	6.30628i	−0.0459742	−	0.260733i
$586$	−25.2747			−1.04409
$587$	−3.68838	−	20.9178i	−0.152236	−	0.863371i	−0.961270	−	0.275609i	$-0.911120\pi$
$587$	−3.68838	−	20.9178i	−0.152236	−	0.863371i	0.809034	−	0.587762i	$-0.199991\pi$
$588$	16.3812	−	13.7455i	0.675549	−	0.566853i
$589$	0.969282	+	0.352790i	0.0399386	+	0.0145365i
$590$	14.3037	−	5.20611i	0.588872	−	0.214332i
$591$	15.1941			0.625000
$592$	−5.50555	+	2.58629i	−0.226277	+	0.106296i
$593$	31.4119			1.28993			0.644965	−	0.764212i	$-0.276872\pi$
$593$	31.4119			1.28993			0.644965	+	0.764212i	$0.276872\pi$
$594$	8.51024	−	3.09747i	0.349179	−	0.127091i
$595$	−32.1908	−	11.7165i	−1.31969	−	0.480329i
$596$	9.50414	−	7.97492i	0.389305	−	0.326666i
$597$	4.23372	+	24.0106i	0.173274	+	0.982688i
$598$	18.4620			0.754965
$599$	−3.52563	−	19.9949i	−0.144053	−	0.816967i	−0.968122	−	0.250478i	$-0.919412\pi$
$599$	−3.52563	−	19.9949i	−0.144053	−	0.816967i	0.824069	−	0.566490i	$-0.191699\pi$
$600$	1.60088	−	2.77281i	0.0653558	−	0.113200i
$601$	−34.1524	−	28.6573i	−1.39311	−	1.16896i	−0.964063	−	0.265672i	$-0.914406\pi$
$601$	−34.1524	−	28.6573i	−1.39311	−	1.16896i	−0.429044	−	0.903284i	$-0.641149\pi$
$602$	−2.29530	−	3.97557i	−0.0935493	−	0.162032i
$603$	−11.5700	+	20.0398i	−0.471166	+	0.816083i
$604$	11.7921	−	4.29198i	0.479814	−	0.174638i
$605$	−0.240851	+	0.202098i	−0.00979199	+	0.00821646i
$606$	−4.30576	−	7.45779i	−0.174910	−	0.302952i
$607$	−3.49184	+	19.8032i	−0.141730	+	0.803788i	0.828205	+	0.560425i	$0.189362\pi$
$607$	−3.49184	+	19.8032i	−0.141730	+	0.803788i	−0.969935	+	0.243364i	$0.921749\pi$
$608$	−0.0172369	+	0.0977553i	−0.000699048	+	0.00396450i
$609$	−5.30534	−	4.45171i	−0.214983	−	0.180393i
$610$	−18.8983	−	6.87841i	−0.765169	−	0.278499i
$611$	12.9609	+	4.71739i	0.524343	+	0.190845i
$612$	5.98655	+	5.02331i	0.241992	+	0.203055i
$613$	5.59486	−	31.7300i	0.225974	−	1.28156i	−0.634839	−	0.772644i	$-0.718934\pi$
$613$	5.59486	−	31.7300i	0.225974	−	1.28156i	0.860814	−	0.508920i	$-0.169955\pi$
$614$	−4.27159	+	24.2254i	−0.172387	+	0.977656i
$615$	11.6715	+	20.2156i	0.470639	+	0.815172i
$616$	−10.4938	+	8.80536i	−0.422808	+	0.354778i
$617$	−36.5834	+	13.3153i	−1.47279	+	0.536052i	−0.948857	−	0.315707i	$-0.897758\pi$
$617$	−36.5834	+	13.3153i	−1.47279	+	0.536052i	−0.523934	+	0.851759i	$0.675536\pi$
$618$	2.15806	−	3.73786i	0.0868097	−	0.150359i
$619$	13.1812	+	22.8305i	0.529796	+	0.917634i	0.999396	+	0.0347545i	$0.0110649\pi$
$619$	13.1812	+	22.8305i	0.529796	+	0.917634i	−0.469600	+	0.882879i	$0.655602\pi$
$620$	−14.9605	−	12.5533i	−0.600827	−	0.504154i
$621$	12.9039	−	22.3503i	0.517817	−	0.896885i
$622$	0.904212	+	5.12804i	0.0362556	+	0.205616i
$623$	−14.4508			−0.578961
$624$	0.734290	+	4.16437i	0.0293951	+	0.166708i
$625$	−11.8780	+	9.96686i	−0.475122	+	0.398674i
$626$	−6.79999	−	2.47499i	−0.271782	−	0.0989206i
$627$	0.679890	−	0.247460i	0.0271522	−	0.00988259i
$628$	3.51326			0.140194
$629$	2.28103	−	26.9510i	0.0909507	−	1.07461i
$630$	13.5400			0.539448
$631$	−38.8218	+	14.1300i	−1.54547	+	0.562506i	−0.967350	−	0.253445i	$-0.918436\pi$
$631$	−38.8218	+	14.1300i	−1.54547	+	0.562506i	−0.578122	+	0.815950i	$0.696214\pi$
$632$	5.10782	+	1.85910i	0.203178	+	0.0739509i
$633$	−20.4018	+	17.1192i	−0.810900	+	0.680426i
$634$	−2.31803	−	13.1462i	−0.0920608	−	0.522103i
$635$	31.5312			1.25128
$636$	0.310136	+	1.75887i	0.0122977	+	0.0697438i
$637$	−9.50340	+	16.4604i	−0.376538	+	0.652184i
$638$	1.98286	+	1.66382i	0.0785021	+	0.0658711i
$639$	2.61268	+	4.52530i	0.103356	+	0.179018i
$640$	0.939693	−	1.62760i	0.0371446	−	0.0643364i
$641$	41.1013	−	14.9596i	1.62340	−	0.590871i	0.639377	−	0.768893i	$-0.279192\pi$
$641$	41.1013	−	14.9596i	1.62340	−	0.590871i	0.984026	+	0.178023i	$0.0569701\pi$
$642$	13.7827	−	11.5651i	0.543961	−	0.456438i
$643$	1.65777	+	2.87133i	0.0653759	+	0.113234i	0.896861	−	0.442313i	$-0.145842\pi$
$643$	1.65777	+	2.87133i	0.0653759	+	0.113234i	−0.831485	+	0.555548i	$0.812509\pi$
$644$	−6.77870	+	38.4439i	−0.267118	+	1.51490i
$645$	0.797148	−	4.52085i	0.0313877	−	0.178008i
$646$	−0.338117	−	0.283714i	−0.0133030	−	0.0111626i
$647$	21.4630	+	7.81189i	0.843797	+	0.307117i	0.727509	−	0.686099i	$-0.240678\pi$
$647$	21.4630	+	7.81189i	0.843797	+	0.307117i	0.116288	+	0.993216i	$0.462900\pi$
$648$	10.5092	+	3.82505i	0.412841	+	0.150262i
$649$	20.7335	+	17.3975i	0.813863	+	0.682912i
$650$	−0.494171	+	2.80258i	−0.0193830	+	0.109926i
$651$	−16.1340	+	91.5004i	−0.632341	+	3.58618i
$652$	1.19572	+	2.07105i	0.0468280	+	0.0811084i
$653$	1.62966	−	1.36745i	0.0637735	−	0.0535124i	−0.610344	−	0.792137i	$-0.708969\pi$
$653$	1.62966	−	1.36745i	0.0637735	−	0.0535124i	0.674117	+	0.738624i	$0.264524\pi$
$654$	18.0051	−	6.55331i	0.704054	−	0.256255i
$655$	1.31901	−	2.28460i	0.0515382	−	0.0892667i
$656$	−2.84721	−	4.93152i	−0.111165	−	0.192543i
$657$	−3.44311	−	2.88911i	−0.134328	−	0.112715i
$658$	−14.5821	+	25.2569i	−0.568468	+	0.984615i
$659$	−1.48751	−	8.43610i	−0.0579452	−	0.328624i	0.942031	−	0.335526i	$-0.108914\pi$
$659$	−1.48751	−	8.43610i	−0.0579452	−	0.328624i	−0.999976	+	0.00690225i	$0.997803\pi$
$660$	−13.6987			−0.533222
$661$	0.139199	+	0.789436i	0.00541421	+	0.0307055i	0.987395	−	0.158274i	$-0.0505930\pi$
$661$	0.139199	+	0.789436i	0.00541421	+	0.0307055i	−0.981981	+	0.188980i	$0.939482\pi$
$662$	−3.50322	+	2.93955i	−0.136156	+	0.114249i
$663$	−17.6688	−	6.43092i	−0.686200	−	0.249756i
$664$	−0.618553	+	0.225135i	−0.0240045	+	0.00873692i
$665$	−0.764734			−0.0296551
$666$	2.79614	+	10.3184i	0.108348	+	0.399829i
$667$	7.37622			0.285609
$668$	14.6442	−	5.33004i	0.566599	−	0.206225i
$669$	22.0428	+	8.02294i	0.852225	+	0.310185i
$670$	−18.9554	+	15.9055i	−0.732312	+	0.614483i
$671$	−6.20962	−	35.2165i	−0.239720	−	1.35952i
$672$	−8.94120			−0.344914
$673$	7.47353	+	42.3845i	0.288083	+	1.63380i	0.694059	+	0.719918i	$0.255821\pi$
$673$	7.47353	+	42.3845i	0.288083	+	1.63380i	−0.405976	+	0.913884i	$0.633068\pi$
$674$	−1.62665	+	2.81744i	−0.0626563	+	0.108524i
$675$	3.04744	+	2.55711i	0.117296	+	0.0984231i
$676$	4.62075	+	8.00337i	0.177721	+	0.307822i
$677$	−9.99716	+	17.3156i	−0.384222	+	0.665492i	−0.991661	−	0.128874i	$-0.958864\pi$
$677$	−9.99716	+	17.3156i	−0.384222	+	0.665492i	0.607439	+	0.794367i	$0.292197\pi$
$678$	−20.4490	+	7.44281i	−0.785338	+	0.285840i
$679$	−11.3684	+	9.53918i	−0.436277	+	0.366080i
$680$	4.17840	+	7.23720i	0.160234	+	0.277534i
$681$	−1.12311	+	6.36949i	−0.0430378	+	0.244079i
$682$	6.03003	−	34.1980i	0.230902	−	1.30951i
$683$	28.2126	+	23.6732i	1.07953	+	0.905830i	0.995881	−	0.0906653i	$-0.0288993\pi$
$683$	28.2126	+	23.6732i	1.07953	+	0.905830i	0.0836451	+	0.996496i	$0.473344\pi$
$684$	0.163936	+	0.0596677i	0.00626823	+	0.00228145i
$685$	21.9330	+	7.98295i	0.838016	+	0.305013i
$686$	−8.80504	−	7.38831i	−0.336178	−	0.282087i
$687$	−1.14863	+	6.51419i	−0.0438228	+	0.248532i
$688$	−0.194461	+	1.10284i	−0.00741377	+	0.0420456i
$689$	−0.793725	−	1.37477i	−0.0302385	−	0.0523746i
$690$	−29.9041	+	25.0925i	−1.13843	+	0.955254i
$691$	−0.825837	+	0.300580i	−0.0314163	+	0.0114346i	−0.357681	−	0.933844i	$-0.616432\pi$
$691$	−0.825837	+	0.300580i	−0.0314163	+	0.0114346i	0.326264	+	0.945279i	$0.394210\pi$
$692$	8.93860	−	15.4821i	0.339794	−	0.588541i
$693$	12.0378	+	20.8501i	0.457280	+	0.792031i
$694$	18.7508	+	15.7338i	0.711770	+	0.597246i
$695$	17.2899	−	29.9471i	0.655845	−	1.13596i
$696$	0.293376	+	1.66382i	0.0111204	+	0.0630668i
$697$	25.3206			0.959087
$698$	0.990209	+	5.61576i	0.0374800	+	0.212559i
$699$	−0.482559	+	0.404915i	−0.0182521	+	0.0153153i
$700$	−5.65446	−	2.05806i	−0.213719	−	0.0777872i
$701$	19.5851	−	7.12840i	0.739719	−	0.269236i	0.0554462	−	0.998462i	$-0.482342\pi$
$701$	19.5851	−	7.12840i	0.739719	−	0.269236i	0.684273	+	0.729226i	$0.260120\pi$
$702$	−5.25399			−0.198299
$703$	−0.157924	−	0.582776i	−0.00595623	−	0.0219798i
$704$	3.34175			0.125947
$705$	−27.4053	+	9.97471i	−1.03214	+	0.375669i
$706$	−22.9604	−	8.35691i	−0.864127	−	0.314517i
$707$	−12.3979	+	10.4031i	−0.466273	+	0.391249i
$708$	3.06765	+	17.3975i	0.115289	+	0.653838i
$709$	−21.6348			−0.812512			−0.406256	−	0.913759i	$-0.633166\pi$
$709$	−21.6348			−0.812512			−0.406256	+	0.913759i	$0.633166\pi$
$710$	0.970296	+	5.50282i	0.0364146	+	0.206517i
$711$	4.77660	−	8.27331i	0.179136	−	0.310273i
$712$	2.70048	+	2.26597i	0.101205	+	0.0849209i
$713$	−49.4784	−	85.6991i	−1.85298	−	3.20946i
$714$	19.8788	−	34.4311i	0.743945	−	1.28855i
$715$	11.4415	−	4.16437i	0.427888	−	0.155738i
$716$	−15.6321	+	13.1169i	−0.584200	+	0.490202i
$717$	5.49121	+	9.51105i	0.205073	+	0.355197i
$718$	3.24882	−	18.4250i	0.121245	−	0.687614i
$719$	4.46063	−	25.2975i	0.166353	−	0.943437i	−0.781305	−	0.624150i	$-0.785445\pi$
$719$	4.46063	−	25.2975i	0.166353	−	0.943437i	0.947658	−	0.319287i	$-0.103443\pi$
$720$	−2.53028	−	2.12316i	−0.0942979	−	0.0791254i
$721$	−7.62245	−	2.77434i	−0.283875	−	0.103322i
$722$	17.8449	+	6.49501i	0.664118	+	0.241719i
$723$	−29.0331	−	24.3616i	−1.07975	−	0.906019i
$724$	−3.17367	+	17.9988i	−0.117949	+	0.668919i
$725$	−0.197439	+	1.11973i	−0.00733272	+	0.0415859i
$726$	−0.182448	−	0.316009i	−0.00677128	−	0.0117282i
$727$	20.4343	−	17.1464i	0.757868	−	0.635927i	−0.179703	−	0.983721i	$-0.557514\pi$
$727$	20.4343	−	17.1464i	0.757868	−	0.635927i	0.937571	+	0.347794i	$0.113069\pi$
$728$	7.46791	−	2.71810i	0.276779	−	0.100739i
$729$	0.961018	−	1.66453i	0.0355933	−	0.0616493i
$730$	−2.40317	−	4.16241i	−0.0889452	−	0.154058i
$731$	−3.81453	−	3.20077i	−0.141086	−	0.118385i
$732$	11.6703	−	20.2135i	0.431345	−	0.747112i
$733$	−1.97614	−	11.2073i	−0.0729906	−	0.413950i	−0.999308	−	0.0372052i	$-0.988154\pi$
$733$	−1.97614	−	11.2073i	−0.0729906	−	0.413950i	0.926317	−	0.376745i	$-0.122957\pi$
$734$	33.7230			1.24474
$735$	−6.97875	−	39.5785i	−0.257415	−	1.45987i
$736$	7.29498	−	6.12122i	0.268897	−	0.225631i
$737$	−41.3451	−	15.0484i	−1.52297	−	0.554314i
$738$	−9.40447	+	3.42295i	−0.346183	+	0.126000i
$739$	3.18059			0.117000			0.0584999	−	0.998287i	$-0.481368\pi$
$739$	3.18059			0.117000			0.0584999	+	0.998287i	$0.481368\pi$
$740$	−0.964102	+	11.3911i	−0.0354411	+	0.418746i
$741$	−0.419746			−0.0154197
$742$	3.15416	−	1.14802i	0.115793	−	0.0421452i
$743$	49.7669	+	18.1137i	1.82577	+	0.664527i	0.993996	+	0.109415i	$0.0348976\pi$
$743$	49.7669	+	18.1137i	1.82577	+	0.664527i	0.831776	+	0.555112i	$0.187325\pi$
$744$	17.3628	−	14.5691i	0.636551	−	0.534130i
$745$	−4.04897	−	22.9629i	−0.148343	−	0.841295i
$746$	31.4347			1.15091
$747$	0.200891	+	1.13931i	0.00735020	+	0.0416851i
$748$	−7.42965	+	12.8685i	−0.271655	+	0.470520i
$749$	−25.9031	−	21.7353i	−0.946478	−	0.794189i
$750$	−13.2568	−	22.9615i	−0.484071	−	0.838436i
$751$	3.21483	−	5.56825i	0.117311	−	0.203188i	−0.801390	−	0.598142i	$-0.795906\pi$
$751$	3.21483	−	5.56825i	0.117311	−	0.203188i	0.918701	+	0.394954i	$0.129239\pi$
$752$	6.68542	−	2.43329i	0.243792	−	0.0887331i
$753$	−2.93354	+	2.46153i	−0.106904	+	0.0897031i
$754$	−0.750829	−	1.30047i	−0.0273436	−	0.0473605i
$755$	4.09536	−	23.2259i	0.149045	−	0.845278i
$756$	1.92911	−	10.9405i	0.0701612	−	0.397904i
$757$	−24.3176	−	20.4049i	−0.883837	−	0.741627i	0.0831276	−	0.996539i	$-0.473509\pi$
$757$	−24.3176	−	20.4049i	−0.883837	−	0.741627i	−0.966964	+	0.254912i	$0.917954\pi$
$758$	−6.54676	−	2.38282i	−0.237789	−	0.0865481i
$759$	−65.2259	−	23.7403i	−2.36755	−	0.861718i
$760$	0.142909	+	0.119915i	0.00518384	+	0.00434976i
$761$	−4.00842	+	22.7329i	−0.145305	+	0.824065i	0.821817	+	0.569752i	$0.192961\pi$
$761$	−4.00842	+	22.7329i	−0.145305	+	0.824065i	−0.967122	+	0.254314i	$0.918150\pi$
$762$	−6.35454	+	36.0384i	−0.230201	+	1.30553i
$763$	−18.0051	−	31.1857i	−0.651827	−	1.12900i
$764$	4.41676	−	3.70610i	0.159793	−	0.134082i
$765$	13.8014	−	5.02331i	0.498992	−	0.181618i
$766$	1.43864	−	2.49179i	0.0519801	−	0.0900321i
$767$	−7.85096	−	13.5983i	−0.283482	−	0.491005i
$768$	1.67088	+	1.40203i	0.0602925	+	0.0505914i
$769$	−23.5799	+	40.8416i	−0.850312	+	1.47278i	0.0306140	+	0.999531i	$0.490254\pi$
$769$	−23.5799	+	40.8416i	−0.850312	+	1.47278i	−0.880926	+	0.473253i	$0.843080\pi$
$770$	4.47060	+	25.3540i	0.161109	+	0.913696i
$771$	−27.8188			−1.00187
$772$	−0.0624134	−	0.353964i	−0.00224631	−	0.0127394i
$773$	−3.06540	+	2.57218i	−0.110255	+	0.0925148i	−0.696248	−	0.717801i	$-0.745149\pi$
$773$	−3.06540	+	2.57218i	−0.110255	+	0.0925148i	0.585994	+	0.810316i	$0.300704\pi$
$774$	1.84947	+	0.673152i	0.0664778	+	0.0241960i
$775$	14.3338	−	5.21707i	0.514885	−	0.187403i
$776$	3.62024			0.129959
$777$	49.2263	−	23.1245i	1.76598	−	0.829587i
$778$	−11.8116			−0.423467
$779$	0.531159	−	0.193326i	0.0190308	−	0.00692663i
$780$	7.46791	+	2.71810i	0.267394	+	0.0973235i
$781$	−7.61108	+	6.38645i	−0.272346	+	0.228525i
$782$	7.35300	+	41.7009i	0.262943	+	1.49122i
$783$	−2.09916			−0.0750179
$784$	1.70244	+	9.65502i	0.0608014	+	0.344822i
$785$	3.30138	−	5.71816i	0.117831	−	0.204090i
$786$	2.34535	+	1.96798i	0.0836559	+	0.0701956i
$787$	−5.78344	−	10.0172i	−0.206157	−	0.357075i	0.744344	−	0.667797i	$-0.232763\pi$
$787$	−5.78344	−	10.0172i	−0.206157	−	0.357075i	−0.950501	+	0.310722i	$0.899429\pi$
$788$	−3.48300	+	6.03274i	−0.124077	+	0.214907i
$789$	54.0387	−	19.6685i	1.92383	−	0.700217i
$790$	7.82564	−	6.56649i	0.278424	−	0.233625i
$791$	20.4490	+	35.4186i	0.727081	+	1.25934i
$792$	1.01987	−	5.78394i	0.0362393	−	0.205523i
$793$	−3.60245	+	20.4305i	−0.127927	+	0.725509i
$794$	−23.9868	−	20.1273i	−0.851259	−	0.714291i
$795$	3.15416	+	1.14802i	0.111867	+	0.0407161i
$796$	−10.5038	−	3.82308i	−0.372298	−	0.135505i
$797$	−28.0792	−	23.5612i	−0.994615	−	0.834581i	−0.00838538	−	0.999965i	$-0.502669\pi$
$797$	−28.0792	−	23.5612i	−0.994615	−	0.834581i	−0.986229	+	0.165384i	$0.947114\pi$
$798$	0.154119	−	0.874049i	0.00545574	−	0.0309410i
$799$	−5.49335	+	31.1543i	−0.194341	+	1.10216i
$800$	0.733956	+	1.27125i	0.0259492	+	0.0449454i
$801$	4.74613	−	3.98248i	0.167696	−	0.140714i
$802$	13.1821	−	4.79790i	0.465477	−	0.169420i
$803$	4.27309	−	7.40121i	0.150794	−	0.261183i
$804$	−14.3590	−	24.8705i	−0.506403	−	0.877115i
$805$	56.2012	+	47.1584i	1.98083	+	1.66212i
$806$	−10.0729	+	17.4467i	−0.354802	+	0.614534i
$807$	5.15328	+	29.2257i	0.181404	+	1.02879i
$808$	3.94811			0.138894
$809$	−1.35385	−	7.67809i	−0.0475990	−	0.269947i	0.951715	−	0.306983i	$-0.0993195\pi$
$809$	−1.35385	−	7.67809i	−0.0475990	−	0.269947i	−0.999314	+	0.0370359i	$0.988208\pi$
$810$	16.1011	−	13.5104i	0.565734	−	0.474707i
$811$	27.9730	+	10.1813i	0.982265	+	0.357515i	0.782720	−	0.622374i	$-0.213832\pi$
$811$	27.9730	+	10.1813i	0.982265	+	0.357515i	0.199545	+	0.979889i	$0.436054\pi$
$812$	2.98370	−	1.08598i	0.104707	−	0.0381104i
$813$	−9.41372			−0.330154
$814$	−18.3982	+	8.64272i	−0.644856	+	0.302927i
$815$	4.49443			0.157433
$816$	−9.11381	+	3.31716i	−0.319047	+	0.116124i
$817$	−0.104457	−	0.0380192i	−0.00365449	−	0.00133012i
$818$	−0.0621032	+	0.0521107i	−0.00217139	+	0.00182201i
$819$	−2.42539	−	13.7551i	−0.0847501	−	0.480642i
$820$	−10.7020			−0.373731
$821$	6.80968	+	38.6196i	0.237659	+	1.34783i	0.836940	+	0.547294i	$0.184342\pi$
$821$	6.80968	+	38.6196i	0.237659	+	1.34783i	−0.599281	+	0.800539i	$0.704547\pi$
$822$	−13.5443	+	23.4594i	−0.472411	+	0.818240i
$823$	−9.28031	−	7.78710i	−0.323491	−	0.271441i	0.466550	−	0.884495i	$-0.345497\pi$
$823$	−9.28031	−	7.78710i	−0.323491	−	0.271441i	−0.790042	+	0.613053i	$0.789941\pi$
$824$	0.989402	+	1.71369i	0.0344674	+	0.0596994i
$825$	5.34975	−	9.26604i	0.186254	−	0.322602i
$826$	31.1987	−	11.3554i	1.08554	−	0.395105i
$827$	−10.7589	+	9.02779i	−0.374124	+	0.313927i	−0.810390	−	0.585890i	$-0.800745\pi$
$827$	−10.7589	+	9.02779i	−0.374124	+	0.313927i	0.436267	+	0.899817i	$0.356300\pi$
$828$	−8.36833	−	14.4944i	−0.290820	−	0.503714i
$829$	5.56767	−	31.5758i	0.193373	−	1.09667i	−0.721343	−	0.692578i	$-0.756475\pi$
$829$	5.56767	−	31.5758i	0.193373	−	1.09667i	0.914716	−	0.404096i	$-0.132414\pi$
$830$	−0.214821	+	1.21831i	−0.00745655	+	0.0422882i
$831$	−5.83710	−	4.89791i	−0.202487	−	0.169907i
$832$	−1.82177	−	0.663070i	−0.0631585	−	0.0229878i
$833$	−40.9649	−	14.9100i	−1.41935	−	0.516601i
$834$	30.7434	+	25.7968i	1.06456	+	0.893269i
$835$	5.08586	−	28.8433i	0.176003	−	0.998165i
$836$	−0.0576014	+	0.326674i	−0.00199219	+	0.0112982i
$837$	14.0808	+	24.3887i	0.486704	+	0.842996i
$838$	3.55146	−	2.98003i	0.122683	−	0.102944i
$839$	10.3875	−	3.78073i	0.358616	−	0.130525i	−0.156428	−	0.987689i	$-0.549998\pi$
$839$	10.3875	−	3.78073i	0.358616	−	0.130525i	0.515044	+	0.857164i	$0.327776\pi$
$840$	−8.40198	+	14.5527i	−0.289896	+	0.502114i
$841$	14.2000	+	24.5951i	0.489656	+	0.848109i
$842$	−14.8017	−	12.4201i	−0.510099	−	0.428024i
$843$	8.00245	−	13.8607i	0.275619	−	0.477386i
$844$	−2.12029	−	12.0248i	−0.0729834	−	0.413909i
$845$	17.3683			0.597489
$846$	−2.17126	−	12.3138i	−0.0746494	−	0.423358i
$847$	−0.525338	+	0.440811i	−0.0180508	+	0.0151464i
$848$	−0.769446	−	0.280056i	−0.0264229	−	0.00961715i
$849$	−28.7007	+	10.4462i	−0.985007	+	0.358513i
$850$	−6.52715			−0.223880
$851$	−24.3317	+	52.5676i	−0.834080	+	1.80199i
$852$	−6.48497			−0.222172
$853$	−48.0604	+	17.4925i	−1.64556	+	0.598933i	−0.987997	−	0.154471i	$-0.950633\pi$
$853$	−48.0604	+	17.4925i	−1.64556	+	0.598933i	−0.657558	+	0.753404i	$0.728411\pi$
$854$	−41.2204	−	15.0030i	−1.41053	−	0.513392i
$855$	0.251164	−	0.210751i	0.00858962	−	0.00720755i
$856$	1.43239	+	8.12350i	0.0489581	+	0.277655i
$857$	−11.4315			−0.390493			−0.195246	−	0.980754i	$-0.562551\pi$
$857$	−11.4315			−0.390493			−0.195246	+	0.980754i	$0.562551\pi$
$858$	2.45381	+	13.9163i	0.0837718	+	0.475094i
$859$	5.49634	−	9.51995i	0.187533	−	0.324816i	−0.756894	−	0.653537i	$-0.773284\pi$
$859$	5.49634	−	9.51995i	0.187533	−	0.324816i	0.944427	+	0.328721i	$0.106618\pi$
$860$	1.61225	+	1.35284i	0.0549773	+	0.0461314i
$861$	25.4575	+	44.0937i	0.867590	+	1.50271i
$862$	−3.77086	+	6.53132i	−0.128436	+	0.222458i
$863$	14.1266	−	5.14167i	0.480876	−	0.175024i	−0.0901969	−	0.995924i	$-0.528750\pi$
$863$	14.1266	−	5.14167i	0.480876	−	0.175024i	0.571073	+	0.820899i	$0.306527\pi$
$864$	−2.07604	+	1.74200i	−0.0706283	+	0.0592642i
$865$	−16.7991	−	29.0968i	−0.571185	−	0.989322i
$866$	5.18060	−	29.3806i	0.176044	−	0.998395i
$867$	1.04987	−	5.95412i	0.0356555	−	0.202213i
$868$	−32.6314	−	27.3810i	−1.10758	−	0.929371i
$869$	17.0691	+	6.21263i	0.579028	+	0.210749i
$870$	2.98370	+	1.08598i	0.101157	+	0.0368181i
$871$	19.5535	+	16.4074i	0.662546	+	0.555942i
$872$	−1.52542	+	8.65108i	−0.0516572	+	0.292962i
$873$	1.10486	−	6.26596i	0.0373938	−	0.212071i
$874$	0.472638	+	0.818634i	0.0159872	+	0.0276907i
$875$	−38.1715	+	32.0297i	−1.29043	+	1.08280i
$876$	5.24172	−	1.90783i	0.177101	−	0.0644596i
$877$	14.7236	−	25.5020i	0.497180	−	0.861141i	−0.502815	−	0.864394i	$-0.667702\pi$
$877$	14.7236	−	25.5020i	0.497180	−	0.861141i	0.999995	+	0.00325344i	$0.00103560\pi$
$878$	−10.9771	−	19.0128i	−0.370458	−	0.641652i
$879$	−42.2309	−	35.4360i	−1.42441	−	1.19523i
$880$	3.14022	−	5.43902i	0.105857	−	0.183349i
$881$	3.19146	+	18.0997i	0.107523	+	0.609793i	0.990183	+	0.139780i	$0.0446396\pi$
$881$	3.19146	+	18.0997i	0.107523	+	0.609793i	−0.882660	+	0.470013i	$0.844249\pi$
$882$	17.2306			0.580184
$883$	5.06999	+	28.7534i	0.170619	+	0.967628i	0.943080	+	0.332566i	$0.107914\pi$
$883$	5.06999	+	28.7534i	0.170619	+	0.967628i	−0.772461	+	0.635062i	$0.780975\pi$
$884$	6.60367	−	5.54114i	0.222106	−	0.186369i
$885$	31.1987	+	11.3554i	1.04873	+	0.381708i
$886$	32.5360	−	11.8421i	1.09307	−	0.397844i
$887$	−36.5446			−1.22705			−0.613524	−	0.789676i	$-0.710249\pi$
$887$	−36.5446			−1.22705			−0.613524	+	0.789676i	$0.710249\pi$
$888$	−12.8251	−	3.39760i	−0.430384	−	0.114016i
$889$	68.7749			2.30664
$890$	6.22571	−	2.26597i	0.208686	−	0.0759556i
$891$	35.1192	+	12.7823i	1.17654	+	0.428225i
$892$	−8.23845	+	6.91288i	−0.275844	+	0.231460i
$893$	0.122631	+	0.695478i	0.00410371	+	0.0232733i
$894$	27.0613			0.905066
$895$	6.65963	+	37.7686i	0.222607	+	1.26247i
$896$	2.04963	−	3.55007i	0.0684734	−	0.118599i
$897$	30.8476	+	25.8842i	1.02997	+	0.864249i
$898$	9.97070	+	17.2698i	0.332727	+	0.576299i
$899$	−4.02448	+	6.97060i	−0.134224	+	0.232482i
$900$	2.42429	−	0.882369i	0.0808096	−	0.0294123i
$901$	2.78914	−	2.34037i	0.0929198	−	0.0779689i
$902$	−9.51468	−	16.4799i	−0.316804	−	0.548721i
$903$	1.73872	−	9.86076i	0.0578609	−	0.328145i
$904$	1.73247	−	9.82533i	0.0576211	−	0.326785i
$905$	26.3125	+	22.0788i	0.874656	+	0.733923i
$906$	25.7206	+	9.36154i	0.854510	+	0.311016i
$907$	−17.1239	−	6.23258i	−0.568589	−	0.206949i	0.0416975	−	0.999130i	$-0.486723\pi$
$907$	−17.1239	−	6.23258i	−0.568589	−	0.206949i	−0.610286	+	0.792181i	$0.708946\pi$
$908$	−2.27152	−	1.90603i	−0.0753832	−	0.0632540i
$909$	1.20492	−	6.83345i	0.0399647	−	0.226651i
$910$	2.59358	−	14.7089i	0.0859763	−	0.487596i
$911$	26.2373	+	45.4443i	0.869280	+	1.50564i	0.862733	+	0.505659i	$0.168751\pi$
$911$	26.2373	+	45.4443i	0.869280	+	1.50564i	0.00654696	+	0.999979i	$0.497916\pi$
$912$	−0.165857	+	0.139170i	−0.00549206	+	0.00460839i
$913$	−2.06705	+	0.752344i	−0.0684093	+	0.0248990i
$914$	−16.1194	+	27.9196i	−0.533183	+	0.923499i
$915$	−21.9329	−	37.9889i	−0.725080	−	1.25588i
$916$	−2.32313	−	1.94933i	−0.0767582	−	0.0644078i
$917$	2.87700	−	4.98311i	0.0950068	−	0.164557i
$918$	−2.09255	−	11.8674i	−0.0690645	−	0.391684i
$919$	−44.3955			−1.46447			−0.732236	−	0.681051i	$-0.761523\pi$
$919$	−44.3955			−1.46447			−0.732236	+	0.681051i	$0.761523\pi$
$920$	−3.10782	−	17.6253i	−0.102462	−	0.581090i
$921$	−41.1020	+	34.4887i	−1.35436	+	1.13644i
$922$	−6.88626	−	2.50640i	−0.226787	−	0.0825437i
$923$	5.41641	−	1.97141i	0.178283	−	0.0648898i
$924$	−29.8793			−0.982955
$925$	−7.32864	−	5.10071i	−0.240964	−	0.167710i
$926$	6.48631			0.213153
$927$	3.26804	−	1.18947i	0.107336	−	0.0390673i
$928$	−0.727863	−	0.264920i	−0.0238933	−	0.00869644i
$929$	22.9234	−	19.2350i	0.752092	−	0.631080i	−0.183963	−	0.982933i	$-0.558893\pi$
$929$	22.9234	−	19.2350i	0.752092	−	0.631080i	0.936055	+	0.351853i	$0.114448\pi$
$930$	−7.39693	−	41.9501i	−0.242555	−	1.37560i
$931$	−0.973173			−0.0318945
$932$	−0.0501507	−	0.284419i	−0.00164274	−	0.00931644i
$933$	−5.67884	+	9.83605i	−0.185917	+	0.322018i
$934$	−9.18162	−	7.70429i	−0.300432	−	0.252092i
$935$	13.9632	+	24.1849i	0.456644	+	0.790931i
$936$	−1.70363	+	2.95078i	−0.0556850	+	0.0964492i
$937$	−9.34478	+	3.40122i	−0.305281	+	0.111113i	−0.490118	−	0.871656i	$-0.663046\pi$
$937$	−9.34478	+	3.40122i	−0.305281	+	0.111113i	0.184837	+	0.982769i	$0.440824\pi$
$938$	−41.3451	+	34.6926i	−1.34996	+	1.13275i
$939$	−7.89191	−	13.6692i	−0.257543	−	0.446077i
$940$	2.32182	−	13.1677i	0.0757295	−	0.429483i
$941$	2.14576	−	12.1692i	0.0699497	−	0.396704i	−0.929651	−	0.368442i	$-0.879891\pi$
$941$	2.14576	−	12.1692i	0.0699497	−	0.396704i	0.999601	−	0.0282626i	$-0.00899747\pi$
$942$	5.87021	+	4.92569i	0.191262	+	0.160488i
$943$	−50.9573	−	18.5469i	−1.65940	−	0.603971i
$944$	−7.61082	−	2.77011i	−0.247711	−	0.0901594i
$945$	−15.9940	−	13.4206i	−0.520285	−	0.436571i
$946$	−0.649841	+	3.68543i	−0.0211282	+	0.119824i
$947$	−4.86165	+	27.5718i	−0.157982	+	0.895962i	0.798026	+	0.602623i	$0.205878\pi$
$947$	−4.86165	+	27.5718i	−0.157982	+	0.895962i	−0.956008	+	0.293339i	$0.905233\pi$
$948$	5.92803	+	10.2676i	0.192533	+	0.333477i
$949$	−3.79804	+	3.18693i	−0.123290	+	0.103452i
$950$	−0.136922	+	0.0498357i	−0.00444235	+	0.00161688i
$951$	14.5583	−	25.2156i	0.472084	−	0.817673i
$952$	9.11381	+	15.7856i	0.295380	+	0.511614i
$953$	33.5552	+	28.1562i	1.08696	+	0.912068i	0.996480	−	0.0838307i	$-0.0267155\pi$
$953$	33.5552	+	28.1562i	1.08696	+	0.912068i	0.0904798	+	0.995898i	$0.471160\pi$
$954$	−0.719550	+	1.24630i	−0.0232963	+	0.0403504i
$955$	−1.88164	−	10.6713i	−0.0608884	−	0.345315i
$956$	−5.03510			−0.162847
$957$	0.980388	+	5.56006i	0.0316914	+	0.179731i
$958$	17.3832	−	14.5863i	0.561627	−	0.471261i
$959$	47.8396	+	17.4122i	1.54482	+	0.562269i
$960$	3.85205	−	1.40203i	0.124324	−	0.0452503i
$961$	76.9820			2.48329
$962$	11.7447	−	1.06105i	0.378665	−	0.0342096i
$963$	14.4974			0.467172
$964$	16.3281	−	5.94293i	0.525892	−	0.191409i
$965$	−0.634759	−	0.231033i	−0.0204336	−	0.00743723i
$966$	−65.2259	+	54.7310i	−2.09861	+	1.76094i
$967$	−9.60416	−	54.4679i	−0.308849	−	1.75157i	−0.604810	−	0.796370i	$-0.706751\pi$
$967$	−9.60416	−	54.4679i	−0.308849	−	1.75157i	0.295961	−	0.955200i	$-0.404360\pi$
$968$	0.167293			0.00537702
$969$	−0.167176	−	0.948100i	−0.00537046	−	0.0304574i
$970$	3.40192	−	5.89229i	0.109229	−	0.189190i
$971$	−42.2703	−	35.4690i	−1.35652	−	1.13825i	−0.977041	−	0.213053i	$-0.931659\pi$
$971$	−42.2703	−	35.4690i	−1.35652	−	1.13825i	−0.379477	−	0.925201i	$-0.623896\pi$
$972$	8.13166	+	14.0844i	0.260823	+	0.451759i
$973$	37.7123	−	65.3197i	1.20900	−	2.09405i
$974$	−11.5684	+	4.21055i	−0.370675	+	0.134915i
$975$	−4.75501	+	3.98992i	−0.152282	+	0.127780i
$976$	5.35046	+	9.26726i	0.171264	+	0.296638i
$977$	−4.43401	+	25.1465i	−0.141857	+	0.804509i	0.827981	+	0.560757i	$0.189490\pi$
$977$	−4.43401	+	25.1465i	−0.141857	+	0.804509i	−0.969837	+	0.243753i	$0.921621\pi$
$978$	−0.905773	+	5.13689i	−0.0289634	+	0.164260i
$979$	9.02433	+	7.57232i	0.288419	+	0.242012i
$980$	17.3142	+	6.30186i	0.553083	+	0.201306i
$981$	14.5079	+	5.28043i	0.463200	+	0.168591i
$982$	0.881561	+	0.739718i	0.0281318	+	0.0236053i
$983$	−5.43056	+	30.7982i	−0.173208	+	0.982311i	0.766984	+	0.641666i	$0.221757\pi$
$983$	−5.43056	+	30.7982i	−0.173208	+	0.982311i	−0.940192	+	0.340645i	$0.889355\pi$
$984$	2.15680	−	12.2318i	0.0687563	−	0.389937i
$985$	6.54591	+	11.3378i	0.208570	+	0.361254i
$986$	2.63841	−	2.21389i	0.0840240	−	0.0705045i
$987$	−59.7757	+	21.7566i	−1.90268	+	0.692519i
$988$	0.0962202	−	0.166658i	0.00306117	−	0.00530210i
$989$	5.33216	+	9.23557i	0.169553	+	0.293674i
$990$	−8.45556	−	7.09506i	−0.268735	−	0.225496i
$991$	3.80674	−	6.59347i	0.120925	−	0.209448i	−0.799208	−	0.601055i	$-0.794747\pi$
$991$	3.80674	−	6.59347i	0.120925	−	0.209448i	0.920133	+	0.391607i	$0.128081\pi$
$992$	1.80445	+	10.2336i	0.0572915	+	0.324916i
$993$	−9.97478			−0.316540
$994$	2.11638	+	12.0026i	0.0671276	+	0.380699i
$995$	−16.0928	+	13.5035i	−0.510176	+	0.428088i
$996$	−1.34917	−	0.491058i	−0.0427501	−	0.0155598i
$997$	−14.6618	+	5.33644i	−0.464342	+	0.169007i	−0.563588	−	0.826056i	$-0.690579\pi$
$997$	−14.6618	+	5.33644i	−0.464342	+	0.169007i	0.0992454	+	0.995063i	$0.468357\pi$
$998$	27.9156			0.883653
$999$	6.92443	−	14.9599i	0.219079	−	0.473311i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	74.2.f.b.7.1	✓	12
3.2	odd	2		666.2.x.g.451.1		12
4.3	odd	2		592.2.bc.d.81.2		12
37.4	even	18		2738.2.a.q.1.5		6
37.16	even	9	inner	74.2.f.b.53.1	yes	12
37.33	even	9		2738.2.a.t.1.5		6
111.53	odd	18		666.2.x.g.127.1		12
148.127	odd	18		592.2.bc.d.497.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.2.f.b.7.1	✓	12	1.1	even	1	trivial
74.2.f.b.53.1	yes	12	37.16	even	9	inner
592.2.bc.d.81.2		12	4.3	odd	2
592.2.bc.d.497.2		12	148.127	odd	18
666.2.x.g.127.1		12	111.53	odd	18
666.2.x.g.451.1		12	3.2	odd	2
2738.2.a.q.1.5		6	37.4	even	18
2738.2.a.t.1.5		6	37.33	even	9

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:	\( N \)	\(=\)	\( 74 = 2 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	74.f (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.939693 + 0.342020i) q^{2} +(-2.04963 - 0.746005i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-0.326352 - 1.85083i) q^{5} +2.18117 q^{6} +(-0.711830 - 4.03699i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(1.34633 + 1.12971i) q^{9} +O(q^{10})\)	\(q+(-0.939693 + 0.342020i) q^{2} +(-2.04963 - 0.746005i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-0.326352 - 1.85083i) q^{5} +2.18117 q^{6} +(-0.711830 - 4.03699i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(1.34633 + 1.12971i) q^{9} +(0.939693 + 1.62760i) q^{10} +(-1.67088 + 2.89404i) q^{11} +(-2.04963 + 0.746005i) q^{12} +(1.48512 - 1.24616i) q^{13} +(2.04963 + 3.55007i) q^{14} +(-0.711830 + 4.03699i) q^{15} +(0.173648 - 0.984808i) q^{16} +(3.40626 + 2.85819i) q^{17} +(-1.65152 - 0.601105i) q^{18} +(0.0932770 + 0.0339500i) q^{19} +(-1.43969 - 1.20805i) q^{20} +(-1.55262 + 8.80536i) q^{21} +(0.580289 - 3.29098i) q^{22} +(-4.76146 - 8.24709i) q^{23} +(1.67088 - 1.40203i) q^{24} +(1.37939 - 0.502055i) q^{25} +(-0.969343 + 1.67895i) q^{26} +(1.35504 + 2.34700i) q^{27} +(-3.14022 - 2.63496i) q^{28} +(-0.387288 + 0.670802i) q^{29} +(-0.711830 - 4.03699i) q^{30} +10.3914 q^{31} +(0.173648 + 0.984808i) q^{32} +(5.58365 - 4.68524i) q^{33} +(-4.17840 - 1.52081i) q^{34} +(-7.23948 + 2.63496i) q^{35} +1.75751 q^{36} +(-3.50302 - 4.97281i) q^{37} -0.0992633 q^{38} +(-3.97359 + 1.44627i) q^{39} +(1.76604 + 0.642788i) q^{40} +(4.36218 - 3.66031i) q^{41} +(-1.55262 - 8.80536i) q^{42} -1.11986 q^{43} +(0.580289 + 3.29098i) q^{44} +(1.65152 - 2.86052i) q^{45} +(7.29498 + 6.12122i) q^{46} +(3.55724 + 6.16132i) q^{47} +(-1.09059 + 1.88895i) q^{48} +(-9.21271 + 3.35315i) q^{49} +(-1.12449 + 0.943555i) q^{50} +(-4.84936 - 8.39933i) q^{51} +(0.336649 - 1.90923i) q^{52} +(0.142188 - 0.806388i) q^{53} +(-2.07604 - 1.74200i) q^{54} +(5.90168 + 2.14804i) q^{55} +(3.85205 + 1.40203i) q^{56} +(-0.165857 - 0.139170i) q^{57} +(0.134504 - 0.762808i) q^{58} +(1.40642 - 7.97622i) q^{59} +(2.04963 + 3.55007i) q^{60} +(-8.19737 + 6.87841i) q^{61} +(-9.76476 + 3.55408i) q^{62} +(3.60225 - 6.23929i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-2.79111 - 2.34202i) q^{65} +(-3.64447 + 6.31240i) q^{66} +(2.28630 + 12.9663i) q^{67} +4.44656 q^{68} +(3.60687 + 20.4556i) q^{69} +(5.90168 - 4.95210i) q^{70} +(2.79386 + 1.01688i) q^{71} +(-1.65152 + 0.601105i) q^{72} -2.55740 q^{73} +(4.99257 + 3.47481i) q^{74} -3.20177 q^{75} +(0.0932770 - 0.0339500i) q^{76} +(12.8726 + 4.68524i) q^{77} +(3.23930 - 2.71810i) q^{78} +(-0.943888 - 5.35305i) q^{79} -1.87939 q^{80} +(-1.94203 - 11.0138i) q^{81} +(-2.84721 + 4.93152i) q^{82} +(0.504249 + 0.423115i) q^{83} +(4.47060 + 7.74331i) q^{84} +(4.17840 - 7.23720i) q^{85} +(1.05232 - 0.383014i) q^{86} +(1.29422 - 1.08598i) q^{87} +(-1.67088 - 2.89404i) q^{88} +(0.612149 - 3.47167i) q^{89} +(-0.573568 + 3.25286i) q^{90} +(-6.08790 - 5.10835i) q^{91} +(-8.94862 - 3.25703i) q^{92} +(-21.2986 - 7.75206i) q^{93} +(-5.45001 - 4.57310i) q^{94} +(0.0323948 - 0.183720i) q^{95} +(0.378757 - 2.14804i) q^{96} +(-1.81012 - 3.13522i) q^{97} +(7.51027 - 6.30186i) q^{98} +(-5.51897 + 2.00874i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{3} - 6 q^{5} + 6 q^{7} - 6 q^{8} - 3 q^{9}+O(q^{10}) \) 12 * q - 3 * q^3 - 6 * q^5 + 6 * q^7 - 6 * q^8 - 3 * q^9	\( 12 q - 3 q^{3} - 6 q^{5} + 6 q^{7} - 6 q^{8} - 3 q^{9} + 3 q^{11} - 3 q^{12} - 6 q^{13} + 3 q^{14} + 6 q^{15} - 3 q^{17} + 6 q^{18} - 3 q^{19} - 6 q^{20} - 33 q^{21} - 3 q^{22} - 21 q^{23} - 3 q^{24} - 6 q^{25} + 3 q^{27} - 3 q^{28} + 6 q^{29} + 6 q^{30} + 42 q^{31} + 57 q^{33} - 3 q^{34} - 9 q^{35} + 24 q^{36} - 3 q^{37} + 42 q^{38} - 24 q^{39} + 12 q^{40} - 21 q^{41} - 33 q^{42} + 36 q^{43} - 3 q^{44} - 6 q^{45} + 3 q^{46} + 9 q^{47} - 12 q^{49} + 12 q^{50} + 3 q^{52} - 6 q^{53} - 27 q^{54} - 3 q^{56} - 36 q^{57} - 3 q^{58} - 6 q^{59} + 3 q^{60} - 18 q^{61} - 33 q^{62} + 36 q^{63} - 6 q^{64} + 3 q^{65} + 3 q^{66} - 27 q^{67} + 6 q^{68} - 12 q^{69} - 18 q^{71} + 6 q^{72} + 54 q^{73} + 3 q^{74} - 6 q^{75} - 3 q^{76} + 51 q^{77} - 33 q^{78} - 12 q^{79} - 36 q^{81} - 18 q^{82} - 6 q^{83} - 6 q^{84} + 3 q^{85} + 39 q^{87} + 3 q^{88} - 15 q^{89} - 15 q^{90} - 51 q^{91} - 6 q^{92} + 45 q^{93} - 12 q^{94} - 15 q^{95} + 6 q^{96} - 42 q^{97} + 51 q^{98} - 33 q^{99}+O(q^{100}) \) 12 * q - 3 * q^3 - 6 * q^5 + 6 * q^7 - 6 * q^8 - 3 * q^9 + 3 * q^11 - 3 * q^12 - 6 * q^13 + 3 * q^14 + 6 * q^15 - 3 * q^17 + 6 * q^18 - 3 * q^19 - 6 * q^20 - 33 * q^21 - 3 * q^22 - 21 * q^23 - 3 * q^24 - 6 * q^25 + 3 * q^27 - 3 * q^28 + 6 * q^29 + 6 * q^30 + 42 * q^31 + 57 * q^33 - 3 * q^34 - 9 * q^35 + 24 * q^36 - 3 * q^37 + 42 * q^38 - 24 * q^39 + 12 * q^40 - 21 * q^41 - 33 * q^42 + 36 * q^43 - 3 * q^44 - 6 * q^45 + 3 * q^46 + 9 * q^47 - 12 * q^49 + 12 * q^50 + 3 * q^52 - 6 * q^53 - 27 * q^54 - 3 * q^56 - 36 * q^57 - 3 * q^58 - 6 * q^59 + 3 * q^60 - 18 * q^61 - 33 * q^62 + 36 * q^63 - 6 * q^64 + 3 * q^65 + 3 * q^66 - 27 * q^67 + 6 * q^68 - 12 * q^69 - 18 * q^71 + 6 * q^72 + 54 * q^73 + 3 * q^74 - 6 * q^75 - 3 * q^76 + 51 * q^77 - 33 * q^78 - 12 * q^79 - 36 * q^81 - 18 * q^82 - 6 * q^83 - 6 * q^84 + 3 * q^85 + 39 * q^87 + 3 * q^88 - 15 * q^89 - 15 * q^90 - 51 * q^91 - 6 * q^92 + 45 * q^93 - 12 * q^94 - 15 * q^95 + 6 * q^96 - 42 * q^97 + 51 * q^98 - 33 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more