LMFDB - Embedded newform 370.2.o.a.231.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [370,2,Mod(71,370)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(370, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("370.71");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 370 = 2 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	370.o (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:	$2.95446487479$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 3 x^{17} + 21 x^{16} - 20 x^{15} + 180 x^{14} - 126 x^{13} + 1002 x^{12} - 270 x^{11} + \cdots + 81 $ x^18 - 3x^17 + 21x^16 - 20x^15 + 180x^14 - 126x^13 + 1002x^12 - 270x^11 + 3294x^10 - 1172x^9 + 6585x^8 - 1464x^7 + 8092x^6 - 2088x^5 + 5598x^4 + 180x^3 + 972x^2 - 162*x + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			231.1
Root			$-0.231777 + 0.401450i$ of defining polynomial
Character	$\chi$	$=$	370.231
Dual form			370.2.o.a.181.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.173648 + 0.984808i) q^{2} +(-0.568073 + 3.22170i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(0.766044 + 0.642788i) q^{5} -3.27140 q^{6} +(2.86114 + 2.40078i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-7.23759 - 2.63427i) q^{9} +O(q^{10})$	\(q+(0.173648 + 0.984808i) q^{2} +(-0.568073 + 3.22170i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(0.766044 + 0.642788i) q^{5} -3.27140 q^{6} +(2.86114 + 2.40078i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-7.23759 - 2.63427i) q^{9} +(-0.500000 + 0.866025i) q^{10} +(1.39558 + 2.41722i) q^{11} +(-0.568073 - 3.22170i) q^{12} +(0.121034 - 0.0440529i) q^{13} +(-1.86748 + 3.23457i) q^{14} +(-2.50604 + 2.10282i) q^{15} +(0.766044 - 0.642788i) q^{16} +(2.07002 + 0.753426i) q^{17} +(1.33745 - 7.58507i) q^{18} +(1.30452 - 7.39828i) q^{19} +(-0.939693 - 0.342020i) q^{20} +(-9.35995 + 7.85393i) q^{21} +(-2.13815 + 1.79412i) q^{22} +(3.69271 - 6.39596i) q^{23} +(3.07411 - 1.11889i) q^{24} +(0.173648 + 0.984808i) q^{25} +(0.0644010 + 0.111546i) q^{26} +(7.69120 - 13.3215i) q^{27} +(-3.50971 - 1.27743i) q^{28} +(0.575441 + 0.996693i) q^{29} +(-2.50604 - 2.10282i) q^{30} -3.31765 q^{31} +(0.766044 + 0.642788i) q^{32} +(-8.58035 + 3.12299i) q^{33} +(-0.382524 + 2.16940i) q^{34} +(0.648569 + 3.67822i) q^{35} +7.70208 q^{36} +(-6.05380 - 0.592906i) q^{37} +7.51241 q^{38} +(0.0731690 + 0.414962i) q^{39} +(0.173648 - 0.984808i) q^{40} +(0.471381 - 0.171569i) q^{41} +(-9.35995 - 7.85393i) q^{42} +6.17766 q^{43} +(-2.13815 - 1.79412i) q^{44} +(-3.85104 - 6.67020i) q^{45} +(6.94003 + 2.52596i) q^{46} +(-2.40517 + 4.16588i) q^{47} +(1.63570 + 2.83312i) q^{48} +(1.20684 + 6.84433i) q^{49} +(-0.939693 + 0.342020i) q^{50} +(-3.60324 + 6.24099i) q^{51} +(-0.0986681 + 0.0827923i) q^{52} +(-0.569301 + 0.477700i) q^{53} +(14.4547 + 5.26109i) q^{54} +(-0.484680 + 2.74876i) q^{55} +(0.648569 - 3.67822i) q^{56} +(23.0940 + 8.40553i) q^{57} +(-0.881627 + 0.739773i) q^{58} +(-3.87451 + 3.25110i) q^{59} +(1.63570 - 2.83312i) q^{60} +(11.5139 - 4.19070i) q^{61} +(-0.576104 - 3.26725i) q^{62} +(-14.3835 - 24.9129i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(0.121034 + 0.0440529i) q^{65} +(-4.56551 - 7.90769i) q^{66} +(2.14629 + 1.80095i) q^{67} -2.20287 q^{68} +(18.5082 + 15.5302i) q^{69} +(-3.50971 + 1.27743i) q^{70} +(-2.90187 + 16.4573i) q^{71} +(1.33745 + 7.58507i) q^{72} -14.8887 q^{73} +(-0.467332 - 6.06478i) q^{74} -3.27140 q^{75} +(1.30452 + 7.39828i) q^{76} +(-1.81026 + 10.2665i) q^{77} +(-0.395952 + 0.144115i) q^{78} +(-5.68086 - 4.76680i) q^{79} +1.00000 q^{80} +(20.8485 + 17.4940i) q^{81} +(0.250817 + 0.434427i) q^{82} +(6.22262 + 2.26485i) q^{83} +(6.10928 - 10.5816i) q^{84} +(1.10143 + 1.90774i) q^{85} +(1.07274 + 6.08380i) q^{86} +(-3.53794 + 1.28771i) q^{87} +(1.39558 - 2.41722i) q^{88} +(-10.8537 + 9.10737i) q^{89} +(5.90013 - 4.95080i) q^{90} +(0.452058 + 0.164536i) q^{91} +(-1.28247 + 7.27322i) q^{92} +(1.88467 - 10.6885i) q^{93} +(-4.52025 - 1.64524i) q^{94} +(5.75484 - 4.82888i) q^{95} +(-2.50604 + 2.10282i) q^{96} +(-1.06550 + 1.84551i) q^{97} +(-6.53078 + 2.37701i) q^{98} +(-3.73305 - 21.1712i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 6 q^{6} - 3 q^{7} - 9 q^{8} - 12 q^{9}+O(q^{10}) $ 18 * q - 6 * q^6 - 3 * q^7 - 9 * q^8 - 12 * q^9	$ 18 q - 6 q^{6} - 3 q^{7} - 9 q^{8} - 12 q^{9} - 9 q^{10} + 3 q^{11} + 9 q^{13} - 6 q^{17} + 6 q^{18} + 9 q^{19} - 6 q^{21} + 21 q^{23} + 6 q^{26} + 12 q^{27} - 3 q^{28} + 6 q^{29} - 30 q^{31} - 45 q^{33} - 15 q^{34} + 6 q^{35} + 24 q^{36} + 6 q^{37} - 12 q^{38} + 24 q^{39} + 15 q^{41} - 6 q^{42} - 12 q^{43} - 12 q^{45} + 24 q^{47} + 3 q^{48} + 33 q^{49} - 42 q^{51} - 12 q^{53} + 27 q^{54} + 6 q^{56} + 51 q^{57} - 15 q^{58} - 15 q^{59} + 3 q^{60} + 72 q^{61} - 57 q^{62} - 30 q^{63} - 9 q^{64} + 9 q^{65} - 3 q^{66} + 18 q^{67} + 24 q^{69} - 3 q^{70} + 6 q^{72} - 66 q^{73} - 24 q^{74} - 6 q^{75} + 9 q^{76} - 66 q^{77} + 6 q^{78} - 12 q^{79} + 18 q^{80} + 66 q^{81} + 45 q^{82} + 9 q^{83} + 42 q^{84} + 12 q^{86} + 48 q^{87} + 3 q^{88} + 6 q^{90} - 78 q^{91} + 18 q^{92} + 24 q^{94} - 3 q^{97} - 48 q^{98} - 96 q^{99}+O(q^{100}) $ 18 * q - 6 * q^6 - 3 * q^7 - 9 * q^8 - 12 * q^9 - 9 * q^10 + 3 * q^11 + 9 * q^13 - 6 * q^17 + 6 * q^18 + 9 * q^19 - 6 * q^21 + 21 * q^23 + 6 * q^26 + 12 * q^27 - 3 * q^28 + 6 * q^29 - 30 * q^31 - 45 * q^33 - 15 * q^34 + 6 * q^35 + 24 * q^36 + 6 * q^37 - 12 * q^38 + 24 * q^39 + 15 * q^41 - 6 * q^42 - 12 * q^43 - 12 * q^45 + 24 * q^47 + 3 * q^48 + 33 * q^49 - 42 * q^51 - 12 * q^53 + 27 * q^54 + 6 * q^56 + 51 * q^57 - 15 * q^58 - 15 * q^59 + 3 * q^60 + 72 * q^61 - 57 * q^62 - 30 * q^63 - 9 * q^64 + 9 * q^65 - 3 * q^66 + 18 * q^67 + 24 * q^69 - 3 * q^70 + 6 * q^72 - 66 * q^73 - 24 * q^74 - 6 * q^75 + 9 * q^76 - 66 * q^77 + 6 * q^78 - 12 * q^79 + 18 * q^80 + 66 * q^81 + 45 * q^82 + 9 * q^83 + 42 * q^84 + 12 * q^86 + 48 * q^87 + 3 * q^88 + 6 * q^90 - 78 * q^91 + 18 * q^92 + 24 * q^94 - 3 * q^97 - 48 * q^98 - 96 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/370\mathbb{Z}\right)^\times$.

$n$	$261$	$297$
$\chi(n)$	$e\left(\frac{4}{9}\right)$	$1$

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 $

$2$	0.173648	+	0.984808i	0.122788	+	0.696364i
$2$	0.173648	+	0.984808i	0.122788	+	0.696364i
$3$	−0.568073	+	3.22170i	−0.327977	+	1.86005i	0.159892	+	0.987134i	$0.448885\pi$
$3$	−0.568073	+	3.22170i	−0.327977	+	1.86005i	−0.487869	+	0.872917i	$0.662226\pi$
$4$	−0.939693	+	0.342020i	−0.469846	+	0.171010i
$5$	0.766044	+	0.642788i	0.342585	+	0.287463i
$5$	0.766044	+	0.642788i	0.342585	+	0.287463i
$6$	−3.27140			−1.33554
$7$	2.86114	+	2.40078i	1.08141	+	0.907411i	0.996037	−	0.0889377i	$-0.0283472\pi$
$7$	2.86114	+	2.40078i	1.08141	+	0.907411i	0.0853735	+	0.996349i	$0.472792\pi$
$8$	−0.500000	−	0.866025i	−0.176777	−	0.306186i
$9$	−7.23759	−	2.63427i	−2.41253	−	0.878089i
$10$	−0.500000	+	0.866025i	−0.158114	+	0.273861i
$11$	1.39558	+	2.41722i	0.420784	+	0.728818i	0.996016	−	0.0891713i	$-0.0284219\pi$
$11$	1.39558	+	2.41722i	0.420784	+	0.728818i	−0.575233	+	0.817990i	$0.695089\pi$
$12$	−0.568073	−	3.22170i	−0.163989	−	0.930026i
$13$	0.121034	−	0.0440529i	0.0335689	−	0.0122181i	−0.325181	−	0.945652i	$-0.605425\pi$
$13$	0.121034	−	0.0440529i	0.0335689	−	0.0122181i	0.358750	+	0.933434i	$0.383203\pi$
$14$	−1.86748	+	3.23457i	−0.499105	+	0.864475i
$15$	−2.50604	+	2.10282i	−0.647057	+	0.542945i
$16$	0.766044	−	0.642788i	0.191511	−	0.160697i
$17$	2.07002	+	0.753426i	0.502054	+	0.182733i	0.580617	−	0.814177i	$-0.302811\pi$
$17$	2.07002	+	0.753426i	0.502054	+	0.182733i	−0.0785639	+	0.996909i	$0.525033\pi$
$18$	1.33745	−	7.58507i	0.315240	−	1.78782i
$19$	1.30452	−	7.39828i	0.299276	−	1.69728i	−0.350017	−	0.936743i	$-0.613824\pi$
$19$	1.30452	−	7.39828i	0.299276	−	1.69728i	0.649293	−	0.760538i	$-0.275065\pi$
$20$	−0.939693	−	0.342020i	−0.210122	−	0.0764780i
$21$	−9.35995	+	7.85393i	−2.04251	+	1.71387i
$22$	−2.13815	+	1.79412i	−0.455856	+	0.382509i
$23$	3.69271	−	6.39596i	0.769983	−	1.33365i	−0.167588	−	0.985857i	$-0.553598\pi$
$23$	3.69271	−	6.39596i	0.769983	−	1.33365i	0.937571	−	0.347793i	$-0.113069\pi$
$24$	3.07411	−	1.11889i	0.627501	−	0.228392i
$25$	0.173648	+	0.984808i	0.0347296	+	0.196962i
$26$	0.0644010	+	0.111546i	0.0126301	+	0.0218759i
$27$	7.69120	−	13.3215i	1.48017	−	2.56373i
$28$	−3.50971	−	1.27743i	−0.663273	−	0.241412i
$29$	0.575441	+	0.996693i	0.106857	+	0.185081i	0.914495	−	0.404597i	$-0.132588\pi$
$29$	0.575441	+	0.996693i	0.106857	+	0.185081i	−0.807639	+	0.589678i	$0.799255\pi$
$30$	−2.50604	−	2.10282i	−0.457538	−	0.383920i
$31$	−3.31765			−0.595867			−0.297934	−	0.954587i	$-0.596297\pi$
$31$	−3.31765			−0.595867			−0.297934	+	0.954587i	$0.596297\pi$
$32$	0.766044	+	0.642788i	0.135419	+	0.113630i
$33$	−8.58035	+	3.12299i	−1.49365	+	0.543643i
$34$	−0.382524	+	2.16940i	−0.0656024	+	0.372049i
$35$	0.648569	+	3.67822i	0.109628	+	0.621732i
$36$	7.70208			1.28368
$37$	−6.05380	−	0.592906i	−0.995238	−	0.0974732i
$37$	−6.05380	−	0.592906i	−0.995238	−	0.0974732i
$38$	7.51241			1.21867
$39$	0.0731690	+	0.414962i	0.0117164	+	0.0664471i
$40$	0.173648	−	0.984808i	0.0274562	−	0.155712i
$41$	0.471381	−	0.171569i	0.0736174	−	0.0267945i	−0.304949	−	0.952369i	$-0.598639\pi$
$41$	0.471381	−	0.171569i	0.0736174	−	0.0267945i	0.378566	+	0.925574i	$0.376417\pi$
$42$	−9.35995	−	7.85393i	−1.44427	−	1.21189i
$43$	6.17766			0.942084			0.471042	−	0.882111i	$-0.343878\pi$
$43$	6.17766			0.942084			0.471042	+	0.882111i	$0.343878\pi$
$44$	−2.13815	−	1.79412i	−0.322339	−	0.270474i
$45$	−3.85104	−	6.67020i	−0.574079	−	0.994334i
$46$	6.94003	+	2.52596i	1.02325	+	0.372433i
$47$	−2.40517	+	4.16588i	−0.350831	+	0.607657i	−0.986395	−	0.164391i	$-0.947434\pi$
$47$	−2.40517	+	4.16588i	−0.350831	+	0.607657i	0.635565	+	0.772048i	$0.280767\pi$
$48$	1.63570	+	2.83312i	0.236093	+	0.408925i
$49$	1.20684	+	6.84433i	0.172406	+	0.977761i
$50$	−0.939693	+	0.342020i	−0.132893	+	0.0483690i
$51$	−3.60324	+	6.24099i	−0.504554	+	0.873913i
$52$	−0.0986681	+	0.0827923i	−0.0136828	+	0.0114812i
$53$	−0.569301	+	0.477700i	−0.0781995	+	0.0656172i	−0.681050	−	0.732237i	$-0.738476\pi$
$53$	−0.569301	+	0.477700i	−0.0781995	+	0.0656172i	0.602850	+	0.797855i	$0.294032\pi$
$54$	14.4547	+	5.26109i	1.96704	+	0.715943i
$55$	−0.484680	+	2.74876i	−0.0653543	+	0.370642i
$56$	0.648569	−	3.67822i	0.0866686	−	0.491522i
$57$	23.0940	+	8.40553i	3.05887	+	1.11334i
$58$	−0.881627	+	0.739773i	−0.115763	+	0.0971369i
$59$	−3.87451	+	3.25110i	−0.504418	+	0.423257i	−0.859160	−	0.511707i	$-0.829013\pi$
$59$	−3.87451	+	3.25110i	−0.504418	+	0.423257i	0.354742	+	0.934964i	$0.384569\pi$
$60$	1.63570	−	2.83312i	0.211168	−	0.365754i
$61$	11.5139	−	4.19070i	1.47420	−	0.536565i	0.524962	−	0.851126i	$-0.324080\pi$
$61$	11.5139	−	4.19070i	1.47420	−	0.536565i	0.949237	+	0.314561i	$0.101857\pi$
$62$	−0.576104	−	3.26725i	−0.0731652	−	0.414941i
$63$	−14.3835	−	24.9129i	−1.81215	−	3.13873i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	0.121034	+	0.0440529i	0.0150125	+	0.00546409i
$66$	−4.56551	−	7.90769i	−0.561975	−	0.973370i
$67$	2.14629	+	1.80095i	0.262211	+	0.220021i	0.764409	−	0.644731i	$-0.223031\pi$
$67$	2.14629	+	1.80095i	0.262211	+	0.220021i	−0.502198	+	0.864753i	$0.667475\pi$
$68$	−2.20287			−0.267137
$69$	18.5082	+	15.5302i	2.22812	+	1.86962i
$70$	−3.50971	+	1.27743i	−0.419491	+	0.152682i
$71$	−2.90187	+	16.4573i	−0.344388	+	1.95312i	−0.0450162	+	0.998986i	$0.514334\pi$
$71$	−2.90187	+	16.4573i	−0.344388	+	1.95312i	−0.299372	+	0.954136i	$0.596777\pi$
$72$	1.33745	+	7.58507i	0.157620	+	0.893909i
$73$	−14.8887			−1.74259			−0.871295	−	0.490760i	$-0.836719\pi$
$73$	−14.8887			−1.74259			−0.871295	+	0.490760i	$0.836719\pi$
$74$	−0.467332	−	6.06478i	−0.0543263	−	0.705017i
$75$	−3.27140			−0.377749
$76$	1.30452	+	7.39828i	0.149638	+	0.848641i
$77$	−1.81026	+	10.2665i	−0.206298	+	1.16998i
$78$	−0.395952	+	0.144115i	−0.0448327	+	0.0163178i
$79$	−5.68086	−	4.76680i	−0.639146	−	0.536307i	0.264610	−	0.964356i	$-0.414757\pi$
$79$	−5.68086	−	4.76680i	−0.639146	−	0.536307i	−0.903756	+	0.428048i	$0.859201\pi$
$80$	1.00000			0.111803
$81$	20.8485	+	17.4940i	2.31650	+	1.94377i
$82$	0.250817	+	0.434427i	0.0276981	+	0.0479745i
$83$	6.22262	+	2.26485i	0.683021	+	0.248599i	0.660144	−	0.751139i	$-0.270495\pi$
$83$	6.22262	+	2.26485i	0.683021	+	0.248599i	0.0228768	+	0.999738i	$0.492717\pi$
$84$	6.10928	−	10.5816i	0.666577	−	1.15454i
$85$	1.10143	+	1.90774i	0.119467	+	0.206924i
$86$	1.07274	+	6.08380i	0.115676	+	0.656033i
$87$	−3.53794	+	1.28771i	−0.379307	+	0.138057i
$88$	1.39558	−	2.41722i	0.148769	−	0.257676i
$89$	−10.8537	+	9.10737i	−1.15049	+	0.965380i	−0.999731	−	0.0231902i	$-0.992618\pi$
$89$	−10.8537	+	9.10737i	−1.15049	+	0.965380i	−0.150764	+	0.988570i	$0.548173\pi$
$90$	5.90013	−	4.95080i	0.621929	−	0.521860i
$91$	0.452058	+	0.164536i	0.0473886	+	0.0172480i
$92$	−1.28247	+	7.27322i	−0.133706	+	0.758286i
$93$	1.88467	−	10.6885i	0.195431	−	1.10834i
$94$	−4.52025	−	1.64524i	−0.466228	−	0.169693i
$95$	5.75484	−	4.82888i	0.590434	−	0.495433i
$96$	−2.50604	+	2.10282i	−0.255772	+	0.214618i
$97$	−1.06550	+	1.84551i	−0.108185	+	0.187383i	−0.915035	−	0.403374i	$-0.867837\pi$
$97$	−1.06550	+	1.84551i	−0.108185	+	0.187383i	0.806850	+	0.590757i	$0.201171\pi$
$98$	−6.53078	+	2.37701i	−0.659708	+	0.240114i
$99$	−3.73305	−	21.1712i	−0.375185	−	2.12778i
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$	7.33324	−	12.7015i	0.729684	−	1.26385i	−0.227332	−	0.973817i	$-0.573000\pi$
$101$	7.33324	−	12.7015i	0.729684	−	1.26385i	0.957017	−	0.290033i	$-0.0936663\pi$
$102$	−6.77187	−	2.46476i	−0.670515	−	0.244047i
$103$	−3.30893	−	5.73124i	−0.326039	−	0.564716i	0.655683	−	0.755036i	$-0.272381\pi$
$103$	−3.30893	−	5.73124i	−0.326039	−	0.564716i	−0.981722	+	0.190320i	$0.939047\pi$
$104$	−0.0986681	−	0.0827923i	−0.00967520	−	0.00811846i
$105$	−12.2186			−1.19241
$106$	−0.569301	−	0.477700i	−0.0552954	−	0.0463984i
$107$	16.5212	−	6.01321i	1.59716	−	0.581319i	0.618317	−	0.785929i	$-0.287815\pi$
$107$	16.5212	−	6.01321i	1.59716	−	0.581319i	0.978844	+	0.204610i	$0.0655927\pi$
$108$	−2.67112	+	15.1487i	−0.257029	+	1.45768i
$109$	−2.92824	−	16.6069i	−0.280475	−	1.59065i	−0.721015	−	0.692920i	$-0.756324\pi$
$109$	−2.92824	−	16.6069i	−0.280475	−	1.59065i	0.440540	−	0.897733i	$-0.354787\pi$
$110$	−2.79116			−0.266127
$111$	5.34917	−	19.1667i	0.507721	−	1.81922i
$112$	3.73496			0.352920
$113$	1.91673	+	10.8703i	0.180311	+	1.02259i	0.931833	+	0.362886i	$0.118209\pi$
$113$	1.91673	+	10.8703i	0.180311	+	1.02259i	−0.751523	+	0.659707i	$0.770680\pi$
$114$	−4.26760	+	24.2027i	−0.399697	+	2.26680i
$115$	6.94003	−	2.52596i	0.647161	−	0.235547i
$116$	−0.881627	−	0.739773i	−0.0818570	−	0.0686862i
$117$	−0.992043			−0.0917144
$118$	−3.87451	−	3.25110i	−0.356678	−	0.299288i
$119$	4.11381	+	7.12533i	0.377112	+	0.653178i
$120$	3.07411	+	1.11889i	0.280627	+	0.102140i
$121$	1.60471	−	2.77943i	0.145882	−	0.252676i
$122$	6.12640	+	10.6112i	0.554658	+	0.960696i
$123$	0.284965	+	1.61611i	0.0256944	+	0.145720i
$124$	3.11757	−	1.13470i	0.279966	−	0.101899i
$125$	−0.500000	+	0.866025i	−0.0447214	+	0.0774597i
$126$	22.0368	−	18.4910i	1.96319	−	1.64731i
$127$	3.37133	−	2.82888i	0.299157	−	0.251023i	−0.480836	−	0.876810i	$-0.659667\pi$
$127$	3.37133	−	2.82888i	0.299157	−	0.251023i	0.779993	+	0.625788i	$0.215222\pi$
$128$	−0.939693	−	0.342020i	−0.0830579	−	0.0302306i
$129$	−3.50936	+	19.9026i	−0.308982	+	1.75232i
$130$	−0.0223662	+	0.126845i	−0.00196165	+	0.0111251i
$131$	−6.45522	−	2.34951i	−0.563995	−	0.205278i	0.0442584	−	0.999020i	$-0.485908\pi$
$131$	−6.45522	−	2.34951i	−0.563995	−	0.205278i	−0.608254	+	0.793743i	$0.708130\pi$
$132$	6.99476	−	5.86930i	0.608816	−	0.510857i
$133$	21.4941	−	18.0357i	1.86377	−	1.56389i
$134$	−1.40089	+	2.42642i	−0.121019	+	0.209610i
$135$	14.4547	−	5.26109i	1.24406	−	0.452802i
$136$	−0.382524	−	2.16940i	−0.0328012	−	0.186025i
$137$	−0.133213	−	0.230732i	−0.0113812	−	0.0197127i	0.860279	−	0.509824i	$-0.170289\pi$
$137$	−0.133213	−	0.230732i	−0.0113812	−	0.0197127i	−0.871660	+	0.490111i	$0.836956\pi$
$138$	−12.0803	+	20.9238i	−1.02835	+	1.78115i
$139$	−8.76707	−	3.19095i	−0.743613	−	0.270653i	−0.0576973	−	0.998334i	$-0.518376\pi$
$139$	−8.76707	−	3.19095i	−0.743613	−	0.270653i	−0.685915	+	0.727681i	$0.740598\pi$
$140$	−1.86748	−	3.23457i	−0.157831	−	0.273371i
$141$	−12.0549	−	10.1153i	−1.01521	−	0.851861i
$142$	−16.7112			−1.40237
$143$	0.275399	+	0.231087i	0.0230300	+	0.0193245i
$144$	−7.23759	+	2.63427i	−0.603132	+	0.219522i
$145$	−0.199849	+	1.13340i	−0.0165965	+	0.0941235i
$146$	−2.58539	−	14.6625i	−0.213969	−	1.21348i
$147$	−22.7360			−1.87523
$148$	5.89149	−	1.51337i	0.484278	−	0.124398i
$149$	−14.8183			−1.21397			−0.606983	−	0.794715i	$-0.707620\pi$
$149$	−14.8183			−1.21397			−0.606983	+	0.794715i	$0.707620\pi$
$150$	−0.568073	−	3.22170i	−0.0463830	−	0.263051i
$151$	1.35048	−	7.65894i	0.109900	−	0.623276i	−0.879249	−	0.476362i	$-0.841955\pi$
$151$	1.35048	−	7.65894i	0.109900	−	0.623276i	0.989149	−	0.146913i	$-0.0469339\pi$
$152$	−7.05935	+	2.56939i	−0.572589	+	0.208405i
$153$	−12.9972	−	10.9060i	−1.05076	−	0.881695i
$154$	−10.4249			−0.840060
$155$	−2.54147	−	2.13254i	−0.204135	−	0.171290i
$156$	−0.210682	−	0.364911i	−0.0168680	−	0.0292163i
$157$	6.84585	+	2.49169i	0.546358	+	0.198858i	0.600428	−	0.799679i	$-0.294997\pi$
$157$	6.84585	+	2.49169i	0.546358	+	0.198858i	−0.0540695	+	0.998537i	$0.517219\pi$
$158$	3.70792	−	6.42230i	0.294986	−	0.510931i
$159$	−1.21560	−	2.10549i	−0.0964037	−	0.166976i
$160$	0.173648	+	0.984808i	0.0137281	+	0.0778559i
$161$	25.9207	−	9.43437i	2.04284	−	0.743532i
$162$	−13.6079	+	23.5696i	−1.06914	+	1.85180i
$163$	8.04745	−	6.75261i	0.630325	−	0.528905i	−0.270705	−	0.962662i	$-0.587257\pi$
$163$	8.04745	−	6.75261i	0.630325	−	0.528905i	0.901030	+	0.433757i	$0.142812\pi$
$164$	−0.384274	+	0.322444i	−0.0300067	+	0.0251786i
$165$	−8.58035	−	3.12299i	−0.667979	−	0.243125i
$166$	−1.14989	+	6.52137i	−0.0892490	+	0.506156i
$167$	1.84672	−	10.4733i	0.142904	−	0.810447i	−0.826123	−	0.563490i	$-0.809458\pi$
$167$	1.84672	−	10.4733i	0.142904	−	0.810447i	0.969026	−	0.246957i	$-0.0794307\pi$
$168$	11.4817	+	4.17899i	0.885831	+	0.322416i
$169$	−9.94587	+	8.34558i	−0.765067	+	0.641967i
$170$	−1.68750	+	1.41598i	−0.129425	+	0.108600i
$171$	−28.9306	+	50.1092i	−2.21238	+	3.83195i
$172$	−5.80510	+	2.11288i	−0.442635	+	0.161106i
$173$	4.18610	+	23.7405i	0.318263	+	1.80496i	0.553310	+	0.832976i	$0.313365\pi$
$173$	4.18610	+	23.7405i	0.318263	+	1.80496i	−0.235047	+	0.971984i	$0.575524\pi$
$174$	−1.88250	−	3.26058i	−0.142712	−	0.247184i
$175$	−1.86748	+	3.23457i	−0.141168	+	0.244510i
$176$	2.62283	+	0.954634i	0.197704	+	0.0719582i
$177$	−8.27307	−	14.3294i	−0.621842	−	1.07706i
$178$	−10.8537	−	9.10737i	−0.813523	−	0.682626i
$179$	15.9779			1.19425			0.597123	−	0.802149i	$-0.296310\pi$
$179$	15.9779			1.19425			0.597123	+	0.802149i	$0.296310\pi$
$180$	5.90013	+	4.95080i	0.439770	+	0.369011i
$181$	−12.7405	+	4.63716i	−0.946993	+	0.344677i	−0.768924	−	0.639341i	$-0.779207\pi$
$181$	−12.7405	+	4.63716i	−0.946993	+	0.344677i	−0.178070	+	0.984018i	$0.556985\pi$
$182$	−0.0835370	+	0.473762i	−0.00619217	+	0.0351175i
$183$	6.96049	+	39.4749i	0.514534	+	2.91807i
$184$	−7.38542			−0.544461
$185$	−4.25637	−	4.34550i	−0.312934	−	0.319487i
$186$	10.8534			0.795807
$187$	1.06769	+	6.05515i	0.0780770	+	0.442797i
$188$	0.835308	−	4.73727i	0.0609211	−	0.345501i
$189$	53.9878	−	19.6499i	3.92703	−	1.42932i
$190$	5.75484	+	4.82888i	0.417500	+	0.350324i
$191$	13.8006			0.998578			0.499289	−	0.866435i	$-0.333595\pi$
$191$	13.8006			0.998578			0.499289	+	0.866435i	$0.333595\pi$
$192$	−2.50604	−	2.10282i	−0.180858	−	0.151758i
$193$	−3.53788	−	6.12778i	−0.254662	−	0.441087i	0.710142	−	0.704059i	$-0.248631\pi$
$193$	−3.53788	−	6.12778i	−0.254662	−	0.441087i	−0.964804	+	0.262971i	$0.915298\pi$
$194$	−2.00249	−	0.728847i	−0.143770	−	0.0523282i
$195$	−0.210682	+	0.364911i	−0.0150872	+	0.0261318i
$196$	−3.47496	−	6.01880i	−0.248211	−	0.429914i
$197$	−2.62737	−	14.9006i	−0.187193	−	1.06162i	−0.923106	−	0.384546i	$-0.874358\pi$
$197$	−2.62737	−	14.9006i	−0.187193	−	1.06162i	0.735913	−	0.677076i	$-0.236753\pi$
$198$	20.2013	−	7.35266i	1.43564	−	0.522531i
$199$	0.350762	−	0.607538i	0.0248649	−	0.0430673i	−0.853325	−	0.521379i	$-0.825418\pi$
$199$	0.350762	−	0.607538i	0.0248649	−	0.0430673i	0.878190	+	0.478312i	$0.158751\pi$
$200$	0.766044	−	0.642788i	0.0541675	−	0.0454519i
$201$	−7.02138	+	5.89164i	−0.495250	+	0.415564i
$202$	13.7820	+	5.01623i	0.969697	+	0.352941i
$203$	−0.746426	+	4.23319i	−0.0523888	+	0.297112i
$204$	1.25139	−	7.09699i	0.0876149	−	0.496889i
$205$	0.471381	+	0.171569i	0.0329227	+	0.0119829i
$206$	5.06958	−	4.25388i	0.353214	−	0.296382i
$207$	−43.5750	+	36.5637i	−3.02867	+	2.54136i
$208$	0.0644010	−	0.111546i	0.00446541	−	0.00773431i
$209$	19.7038	−	7.17160i	1.36294	−	0.496070i
$210$	−2.12173	−	12.0329i	−0.146413	−	0.830351i
$211$	−5.73067	−	9.92581i	−0.394515	−	0.683321i	0.598524	−	0.801105i	$-0.295754\pi$
$211$	−5.73067	−	9.92581i	−0.394515	−	0.683321i	−0.993039	+	0.117784i	$0.962421\pi$
$212$	0.371585	−	0.643604i	0.0255206	−	0.0442029i
$213$	−51.3721	−	18.6979i	−3.51996	−	1.28116i
$214$	8.79072	+	15.2260i	0.600921	+	1.04083i
$215$	4.73236	+	3.97092i	0.322744	+	0.270815i
$216$	−15.3824			−1.04664
$217$	−9.49227	−	7.96496i	−0.644377	−	0.540697i
$218$	15.8461	−	5.76752i	1.07323	−	0.390625i
$219$	8.45787	−	47.9669i	0.571530	−	3.24131i
$220$	−0.484680	−	2.74876i	−0.0326771	−	0.185321i
$221$	0.283734			0.0190860
$222$	19.8044	+	1.93964i	1.32919	+	0.130180i
$223$	2.53554			0.169792			0.0848961	−	0.996390i	$-0.472944\pi$
$223$	2.53554			0.169792			0.0848961	+	0.996390i	$0.472944\pi$
$224$	0.648569	+	3.67822i	0.0433343	+	0.245761i
$225$	1.33745	−	7.58507i	0.0891635	−	0.505671i
$226$	−10.3723	+	3.77522i	−0.689958	+	0.251124i
$227$	−6.48265	−	5.43959i	−0.430268	−	0.361038i	0.401785	−	0.915734i	$-0.368390\pi$
$227$	−6.48265	−	5.43959i	−0.430268	−	0.361038i	−0.832053	+	0.554696i	$0.812834\pi$
$228$	−24.5761			−1.62759
$229$	3.30618	+	2.77421i	0.218479	+	0.183325i	0.745458	−	0.666553i	$-0.232231\pi$
$229$	3.30618	+	2.77421i	0.218479	+	0.183325i	−0.526979	+	0.849878i	$0.676675\pi$
$230$	3.69271	+	6.39596i	0.243490	+	0.421737i
$231$	−32.0472	−	11.6642i	−2.10855	−	0.767451i
$232$	0.575441	−	0.996693i	0.0377796	−	0.0654361i
$233$	−2.54309	−	4.40476i	−0.166603	−	0.288565i	0.770620	−	0.637295i	$-0.219947\pi$
$233$	−2.54309	−	4.40476i	−0.166603	−	0.288565i	−0.937223	+	0.348729i	$0.886613\pi$
$234$	−0.172267	−	0.976972i	−0.0112614	−	0.0638667i
$235$	−4.52025	+	1.64524i	−0.294869	+	0.107323i
$236$	2.52891	−	4.38020i	0.164618	−	0.285126i
$237$	18.5844	−	15.5941i	1.20718	−	1.01295i
$238$	−6.30272	+	5.28861i	−0.408545	+	0.342810i
$239$	11.6921	+	4.25558i	0.756300	+	0.275271i	0.691254	−	0.722611i	$-0.257058\pi$
$239$	11.6921	+	4.25558i	0.756300	+	0.275271i	0.0650459	+	0.997882i	$0.479281\pi$
$240$	−0.568073	+	3.22170i	−0.0366690	+	0.207960i
$241$	−5.05256	+	28.6545i	−0.325464	+	1.84580i	0.180931	+	0.983496i	$0.442089\pi$
$241$	−5.05256	+	28.6545i	−0.325464	+	1.84580i	−0.506395	+	0.862301i	$0.669022\pi$
$242$	3.01586	+	1.09768i	0.193867	+	0.0705618i
$243$	−32.8530	+	27.5670i	−2.10752	+	1.76842i
$244$	−9.38619	+	7.87595i	−0.600889	+	0.504206i
$245$	−3.47496	+	6.01880i	−0.222007	+	0.384527i
$246$	−1.54208	+	0.561271i	−0.0983193	+	0.0357853i
$247$	−0.168024	−	0.952913i	−0.0106911	−	0.0606324i
$248$	1.65882	+	2.87317i	0.105335	+	0.182446i
$249$	−10.8316	+	18.7608i	−0.686423	+	1.18892i
$250$	−0.939693	−	0.342020i	−0.0594314	−	0.0216313i
$251$	−7.37307	−	12.7705i	−0.465384	−	0.806069i	0.533835	−	0.845589i	$-0.320750\pi$
$251$	−7.37307	−	12.7705i	−0.465384	−	0.806069i	−0.999219	+	0.0395199i	$0.987417\pi$
$252$	22.0368	+	18.4910i	1.38818	+	1.16483i
$253$	20.6139			1.29599
$254$	3.37133	+	2.82888i	0.211536	+	0.177500i
$255$	−6.77187	+	2.46476i	−0.424071	+	0.154349i
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	−0.947054	−	5.37101i	−0.0590756	−	0.335034i	0.940918	−	0.338635i	$-0.109965\pi$
$257$	−0.947054	−	5.37101i	−0.0590756	−	0.335034i	−0.999994	+	0.00360034i	$0.998854\pi$
$258$	−20.2096			−1.25819
$259$	−15.8973	−	16.2303i	−0.987813	−	1.00850i
$260$	−0.128802			−0.00798796
$261$	−1.53925	−	8.72952i	−0.0952771	−	0.540344i
$262$	1.19288	−	6.76514i	0.0736962	−	0.417952i
$263$	4.17841	−	1.52082i	0.257652	−	0.0937775i	−0.209965	−	0.977709i	$-0.567335\pi$
$263$	4.17841	−	1.52082i	0.257652	−	0.0937775i	0.467617	+	0.883931i	$0.345113\pi$
$264$	6.99476	+	5.86930i	0.430498	+	0.361231i
$265$	−0.743170			−0.0456526
$266$	21.4941	+	18.0357i	1.31789	+	1.10584i
$267$	−23.1755	−	40.1412i	−1.41832	−	2.45660i
$268$	−2.63282	−	0.958267i	−0.160825	−	0.0585355i
$269$	−11.6861	+	20.2409i	−0.712513	+	1.23411i	0.251399	+	0.967884i	$0.419110\pi$
$269$	−11.6861	+	20.2409i	−0.712513	+	1.23411i	−0.963911	+	0.266224i	$0.914224\pi$
$270$	7.69120	+	13.3215i	0.468071	+	0.810723i
$271$	−0.740242	−	4.19812i	−0.0449665	−	0.255018i	0.954035	−	0.299695i	$-0.0968850\pi$
$271$	−0.740242	−	4.19812i	−0.0449665	−	0.255018i	−0.999001	+	0.0446777i	$0.985774\pi$
$272$	2.07002	−	0.753426i	0.125513	−	0.0456831i
$273$	−0.786887	+	1.36293i	−0.0476246	+	0.0824882i
$274$	0.204094	−	0.171255i	0.0123298	−	0.0103459i
$275$	−2.13815	+	1.79412i	−0.128936	+	0.108190i
$276$	−22.7036	−	8.26344i	−1.36660	−	0.497401i
$277$	−0.429931	+	2.43826i	−0.0258321	+	0.146501i	−0.994996	−	0.0999167i	$-0.968142\pi$
$277$	−0.429931	+	2.43826i	−0.0258321	+	0.146501i	0.969164	+	0.246418i	$0.0792535\pi$
$278$	1.62009	−	9.18798i	0.0971664	−	0.551058i
$279$	24.0118	+	8.73957i	1.43755	+	0.523224i
$280$	2.86114	−	2.40078i	0.170986	−	0.143474i
$281$	6.11934	−	5.13473i	0.365049	−	0.306312i	−0.441750	−	0.897138i	$-0.645642\pi$
$281$	6.11934	−	5.13473i	0.365049	−	0.306312i	0.806799	+	0.590826i	$0.201198\pi$
$282$	7.86829	−	13.6283i	0.468550	−	0.811553i
$283$	16.8124	−	6.11923i	0.999396	−	0.363750i	0.210044	−	0.977692i	$-0.432639\pi$
$283$	16.8124	−	6.11923i	0.999396	−	0.363750i	0.789351	+	0.613942i	$0.210417\pi$
$284$	−2.90187	−	16.4573i	−0.172194	−	0.976561i
$285$	12.2881	+	21.2835i	0.727882	+	1.26073i
$286$	−0.179754	+	0.311342i	−0.0106291	+	0.0184101i
$287$	1.76059	+	0.640802i	0.103924	+	0.0378254i
$288$	−3.85104	−	6.67020i	−0.226925	−	0.393045i
$289$	−9.30542	−	7.80818i	−0.547378	−	0.459305i
$290$	−1.15088			−0.0675821
$291$	−5.34039	−	4.48112i	−0.313059	−	0.262688i
$292$	13.9908	−	5.09223i	0.818749	−	0.298000i
$293$	−1.85262	+	10.5067i	−0.108231	+	0.613810i	0.881649	+	0.471905i	$0.156434\pi$
$293$	−1.85262	+	10.5067i	−0.108231	+	0.613810i	−0.989880	+	0.141904i	$0.954677\pi$
$294$	−3.94806	−	22.3905i	−0.230255	−	1.30584i
$295$	−5.05781			−0.294477
$296$	2.51343	+	5.53920i	0.146090	+	0.321959i
$297$	42.9348			2.49133
$298$	−2.57318	−	14.5932i	−0.149060	−	0.845363i
$299$	0.165184	−	0.936806i	0.00955284	−	0.0541769i
$300$	3.07411	−	1.11889i	0.177484	−	0.0645989i
$301$	17.6752	+	14.8312i	1.01878	+	0.854857i
$302$	7.77709			0.447522
$303$	36.7548	+	30.8409i	2.11151	+	1.77176i
$304$	−3.75620	−	6.50594i	−0.215433	−	0.373141i
$305$	11.5139	+	4.19070i	0.659282	+	0.239959i
$306$	8.48333	−	14.6936i	0.484960	−	0.839975i
$307$	7.16431	+	12.4090i	0.408889	+	0.708217i	0.994766	−	0.102184i	$-0.0325830\pi$
$307$	7.16431	+	12.4090i	0.408889	+	0.708217i	−0.585877	+	0.810400i	$0.699250\pi$
$308$	−1.81026	−	10.2665i	−0.103149	−	0.584988i
$309$	20.3441	−	7.40464i	1.15733	−	0.421235i
$310$	1.65882	−	2.87317i	0.0942149	−	0.163185i
$311$	−5.79379	+	4.86157i	−0.328536	+	0.275674i	−0.792103	−	0.610388i	$-0.791014\pi$
$311$	−5.79379	+	4.86157i	−0.328536	+	0.275674i	0.463567	+	0.886062i	$0.346569\pi$
$312$	0.322783	−	0.270847i	0.0182740	−	0.0153337i
$313$	−22.4683	−	8.17780i	−1.26998	−	0.462237i	−0.382877	−	0.923799i	$-0.625067\pi$
$313$	−22.4683	−	8.17780i	−1.26998	−	0.462237i	−0.887108	+	0.461563i	$0.847289\pi$
$314$	−1.26506	+	7.17452i	−0.0713916	+	0.404882i
$315$	4.99533	−	28.3299i	0.281455	−	1.59621i
$316$	6.96860	+	2.53636i	0.392014	+	0.142682i
$317$	5.36030	−	4.49783i	0.301065	−	0.252623i	−0.479723	−	0.877420i	$-0.659263\pi$
$317$	5.36030	−	4.49783i	0.301065	−	0.252623i	0.780787	+	0.624797i	$0.214818\pi$
$318$	1.86241	−	1.56275i	0.104439	−	0.0876347i
$319$	−1.60615	+	2.78193i	−0.0899271	+	0.155758i
$320$	−0.939693	+	0.342020i	−0.0525304	+	0.0191195i
$321$	9.98755	+	56.6422i	0.557451	+	3.16146i
$322$	13.7921	+	23.8887i	0.768605	+	1.33126i
$323$	8.27443	−	14.3317i	0.460401	−	0.797439i
$324$	−25.5745	−	9.30834i	−1.42080	−	0.517130i
$325$	0.0644010	+	0.111546i	0.00357233	+	0.00618745i
$326$	8.04745	+	6.75261i	0.445707	+	0.373992i
$327$	55.1660			3.05068
$328$	−0.384274	−	0.322444i	−0.0212180	−	0.0178040i
$329$	−16.8829	+	6.14489i	−0.930787	+	0.338779i
$330$	1.58558	−	8.99230i	0.0872835	−	0.495010i
$331$	−0.815922	−	4.62733i	−0.0448472	−	0.254341i	0.954139	−	0.299365i	$-0.0967747\pi$
$331$	−0.815922	−	4.62733i	−0.0448472	−	0.254341i	−0.998986	+	0.0450239i	$0.985664\pi$
$332$	−6.62197			−0.363428
$333$	42.2530	+	20.2385i	2.31545	+	1.10906i
$334$	10.6349			0.581913
$335$	0.486525	+	2.75922i	0.0265817	+	0.150752i
$336$	−2.12173	+	12.0329i	−0.115750	+	0.656450i
$337$	24.6454	−	8.97020i	1.34252	−	0.488638i	0.431916	−	0.901914i	$-0.357838\pi$
$337$	24.6454	−	8.97020i	1.34252	−	0.488638i	0.910606	+	0.413276i	$0.135615\pi$
$338$	−9.94587	−	8.34558i	−0.540984	−	0.453939i
$339$	−36.1098			−1.96121
$340$	−1.68750	−	1.41598i	−0.0915173	−	0.0767921i
$341$	−4.63005	−	8.01948i	−0.250731	−	0.434279i
$342$	−54.3717	−	19.7897i	−2.94008	−	1.07010i
$343$	0.0935412	−	0.162018i	0.00505075	−	0.00874816i
$344$	−3.08883	−	5.35001i	−0.166538	−	0.288453i
$345$	4.19546	+	23.7936i	0.225876	+	1.28101i
$346$	−22.6530	+	8.24500i	−1.21783	+	0.443254i
$347$	−5.67510	+	9.82956i	−0.304655	+	0.527679i	−0.977185	−	0.212392i	$-0.931875\pi$
$347$	−5.67510	+	9.82956i	−0.304655	+	0.527679i	0.672529	+	0.740071i	$0.265208\pi$
$348$	2.88416	−	2.42009i	0.154607	−	0.129731i
$349$	21.0997	−	17.7048i	1.12944	−	0.947715i	0.130400	−	0.991461i	$-0.458374\pi$
$349$	21.0997	−	17.7048i	1.12944	−	0.947715i	0.999043	+	0.0437467i	$0.0139294\pi$
$350$	−3.50971	−	1.27743i	−0.187602	−	0.0682816i
$351$	0.344046	−	1.95118i	0.0183638	−	0.104146i
$352$	−0.484680	+	2.74876i	−0.0258335	+	0.146509i
$353$	18.9587	+	6.90040i	1.00907	+	0.367271i	0.793075	−	0.609124i	$-0.208479\pi$
$353$	18.9587	+	6.90040i	1.00907	+	0.367271i	0.215994	+	0.976395i	$0.430701\pi$
$354$	12.6751	−	10.6357i	0.673673	−	0.565279i
$355$	−12.8015	+	10.7417i	−0.679434	+	0.570113i
$356$	7.08428	−	12.2703i	0.375466	−	0.650326i
$357$	−25.2926	+	9.20577i	−1.33863	+	0.487221i
$358$	2.77454	+	15.7352i	0.146639	+	0.831631i
$359$	14.2152	+	24.6215i	0.750250	+	1.29947i	0.947701	+	0.319158i	$0.103400\pi$
$359$	14.2152	+	24.6215i	0.750250	+	1.29947i	−0.197452	+	0.980313i	$0.563267\pi$
$360$	−3.85104	+	6.67020i	−0.202968	+	0.351550i
$361$	−35.1786	−	12.8040i	−1.85151	−	0.673893i
$362$	−6.77907	−	11.7417i	−0.356300	−	0.617130i
$363$	8.04292	+	6.74881i	0.422144	+	0.354221i
$364$	−0.481070			−0.0252149
$365$	−11.4054	−	9.57027i	−0.596986	−	0.500931i
$366$	−37.6665	+	13.7095i	−1.96886	+	0.716606i
$367$	−1.06425	+	6.03565i	−0.0555533	+	0.315059i	−0.999904	−	0.0138829i	$-0.995581\pi$
$367$	−1.06425	+	6.03565i	−0.0555533	+	0.315059i	0.944350	+	0.328941i	$0.106692\pi$
$368$	−1.28247	−	7.27322i	−0.0668531	−	0.379143i
$369$	−3.86362			−0.201132
$370$	3.54037	−	4.94629i	0.184055	−	0.257145i
$371$	−2.77571			−0.144108
$372$	1.88467	+	10.6885i	0.0977154	+	0.554172i
$373$	2.83810	−	16.0957i	0.146951	−	0.833402i	−0.818828	−	0.574038i	$-0.805376\pi$
$373$	2.83810	−	16.0957i	0.146951	−	0.833402i	0.965780	−	0.259364i	$-0.0835128\pi$
$374$	−5.77776	+	2.10293i	−0.298761	+	0.108740i
$375$	−2.50604	−	2.10282i	−0.129411	−	0.108589i
$376$	4.81035			0.248075
$377$	0.113555	+	0.0952842i	0.00584840	+	0.00490739i
$378$	28.7263	+	49.7554i	1.47752	+	2.55914i
$379$	−28.8542	−	10.5021i	−1.48214	−	0.539455i	−0.530772	−	0.847514i	$-0.678098\pi$
$379$	−28.8542	−	10.5021i	−1.48214	−	0.539455i	−0.951367	+	0.308060i	$0.900320\pi$
$380$	−3.75620	+	6.50594i	−0.192689	+	0.333747i
$381$	7.19865	+	12.4684i	0.368798	+	0.638777i
$382$	2.39645	+	13.5910i	0.122613	+	0.695374i
$383$	13.2893	−	4.83691i	0.679051	−	0.247154i	0.0206110	−	0.999788i	$-0.493439\pi$
$383$	13.2893	−	4.83691i	0.679051	−	0.247154i	0.658440	+	0.752633i	$0.271217\pi$
$384$	1.63570	−	2.83312i	0.0834715	−	0.144577i
$385$	−7.98592	+	6.70098i	−0.407000	+	0.341514i
$386$	5.42034	−	4.54821i	0.275888	−	0.231498i
$387$	−44.7113	−	16.2736i	−2.27280	−	0.827233i
$388$	0.370045	−	2.09863i	0.0187862	−	0.106542i
$389$	−1.30915	+	7.42458i	−0.0663768	+	0.376441i	0.933465	+	0.358668i	$0.116769\pi$
$389$	−1.30915	+	7.42458i	−0.0663768	+	0.376441i	−0.999842	+	0.0177735i	$0.994342\pi$
$390$	−0.395952	−	0.144115i	−0.0200498	−	0.00729753i
$391$	12.4629	−	10.4576i	0.630274	−	0.528863i
$392$	5.32394	−	4.46732i	0.268900	−	0.225634i
$393$	11.2365	−	19.4621i	0.566804	−	0.981734i
$394$	14.2180	−	5.17491i	0.716290	−	0.260708i
$395$	−1.28775	−	7.30317i	−0.0647935	−	0.367462i
$396$	10.7489	+	18.6176i	0.540151	+	0.935569i
$397$	−8.35453	+	14.4705i	−0.419302	+	0.726252i	−0.995869	−	0.0907974i	$-0.971058\pi$
$397$	−8.35453	+	14.4705i	−0.419302	+	0.726252i	0.576568	+	0.817050i	$0.304392\pi$
$398$	0.659218	+	0.239936i	0.0330436	+	0.0120269i
$399$	45.8954	+	79.4931i	2.29764	+	3.97963i
$400$	0.766044	+	0.642788i	0.0383022	+	0.0321394i
$401$	−13.5240			−0.675355			−0.337677	−	0.941262i	$-0.609641\pi$
$401$	−13.5240			−0.675355			−0.337677	+	0.941262i	$0.609641\pi$
$402$	−7.02138	−	5.89164i	−0.350195	−	0.293848i
$403$	−0.401549	+	0.146152i	−0.0200026	+	0.00728035i
$404$	−2.54681	+	14.4437i	−0.126708	+	0.718599i
$405$	4.72597	+	26.8023i	0.234835	+	1.33182i
$406$	−4.29850			−0.213331
$407$	−7.01538	−	15.4608i	−0.347740	−	0.766363i
$408$	7.20647			0.356774
$409$	−1.05166	−	5.96423i	−0.0520010	−	0.294912i	0.947705	−	0.319147i	$-0.103396\pi$
$409$	−1.05166	−	5.96423i	−0.0520010	−	0.294912i	−0.999706	+	0.0242344i	$0.992285\pi$
$410$	−0.0871077	+	0.494013i	−0.00430194	+	0.0243975i
$411$	0.819024	−	0.298100i	0.0403995	−	0.0147042i
$412$	5.06958	+	4.25388i	0.249760	+	0.209574i
$413$	−18.8907			−0.929552
$414$	−43.5750	−	36.5637i	−2.14159	−	1.79701i
$415$	3.31099	+	5.73479i	0.162530	+	0.281510i
$416$	0.121034	+	0.0440529i	0.00593420	+	0.00215987i
$417$	15.2606	−	26.4322i	0.747316	−	1.29439i
$418$	10.4842	+	18.1591i	0.512798	+	0.888192i
$419$	−1.24587	−	7.06566i	−0.0608646	−	0.345180i	−0.999999	−	0.00162935i	$-0.999481\pi$
$419$	−1.24587	−	7.06566i	−0.0608646	−	0.345180i	0.939134	−	0.343551i	$-0.111630\pi$
$420$	11.4817	−	4.17899i	0.560249	−	0.203914i
$421$	19.0972	−	33.0773i	0.930739	−	1.61209i	0.148677	−	0.988886i	$-0.452499\pi$
$421$	19.0972	−	33.0773i	0.930739	−	1.61209i	0.782062	−	0.623201i	$-0.214168\pi$
$422$	8.77989	−	7.36720i	0.427398	−	0.358630i
$423$	28.3817	−	23.8151i	1.37997	−	1.15793i
$424$	0.698351	+	0.254179i	0.0339149	+	0.0123440i
$425$	−0.382524	+	2.16940i	−0.0185551	+	0.105231i
$426$	9.49318	−	53.8385i	0.459946	−	2.60848i
$427$	43.0038	+	15.6521i	2.08110	+	0.757458i
$428$	−13.4682	+	11.3011i	−0.651009	+	0.546261i
$429$	−0.900940	+	0.755978i	−0.0434978	+	0.0364990i
$430$	−3.08883	+	5.35001i	−0.148957	+	0.258000i
$431$	−16.1526	+	5.87906i	−0.778043	+	0.283185i	−0.700356	−	0.713793i	$-0.746976\pi$
$431$	−16.1526	+	5.87906i	−0.778043	+	0.283185i	−0.0776867	+	0.996978i	$0.524753\pi$
$432$	−2.67112	−	15.1487i	−0.128515	−	0.728842i
$433$	2.35697	+	4.08240i	0.113269	+	0.196188i	0.917086	−	0.398688i	$-0.130535\pi$
$433$	2.35697	+	4.08240i	0.113269	+	0.196188i	−0.803818	+	0.594876i	$0.797201\pi$
$434$	6.19564	−	10.7312i	0.297400	−	0.515112i
$435$	−3.53794	−	1.28771i	−0.169631	−	0.0617408i
$436$	8.43154	+	14.6039i	0.403798	+	0.699398i
$437$	−42.5019	−	35.6633i	−2.03314	−	1.70601i
$438$	48.7069			2.32731
$439$	12.5892	+	10.5636i	0.600849	+	0.504172i	0.891718	−	0.452591i	$-0.149500\pi$
$439$	12.5892	+	10.5636i	0.600849	+	0.504172i	−0.290870	+	0.956763i	$0.593945\pi$
$440$	2.62283	−	0.954634i	0.125039	−	0.0455104i
$441$	9.29517	−	52.7155i	0.442627	−	2.51026i
$442$	0.0492699	+	0.279423i	0.00234353	+	0.0132908i
$443$	31.9231			1.51671			0.758357	−	0.651839i	$-0.226002\pi$
$443$	31.9231			1.51671			0.758357	+	0.651839i	$0.226002\pi$
$444$	1.52883	+	19.8404i	0.0725552	+	0.941581i
$445$	−14.1686			−0.671654
$446$	0.440291	+	2.49702i	0.0208484	+	0.118237i
$447$	8.41790	−	47.7403i	0.398153	−	2.25804i
$448$	−3.50971	+	1.27743i	−0.165818	+	0.0603529i
$449$	−26.2200	−	22.0012i	−1.23740	−	1.03830i	−0.997723	−	0.0674469i	$-0.978515\pi$
$449$	−26.2200	−	22.0012i	−1.23740	−	1.03830i	−0.239675	−	0.970853i	$-0.577041\pi$
$450$	7.70208			0.363079
$451$	1.07257	+	0.899993i	0.0505053	+	0.0423790i
$452$	−5.51900	−	9.55920i	−0.259592	−	0.449627i
$453$	23.9077	+	8.70168i	1.12328	+	0.408841i
$454$	4.23125	−	7.32873i	0.198582	−	0.343955i
$455$	0.240535	+	0.416619i	0.0112765	+	0.0195314i
$456$	−4.26760	−	24.2027i	−0.199849	−	1.13340i
$457$	−29.5711	+	10.7630i	−1.38328	+	0.503471i	−0.923170	−	0.384393i	$-0.874411\pi$
$457$	−29.5711	+	10.7630i	−1.38328	+	0.503471i	−0.460106	+	0.887864i	$0.652189\pi$
$458$	−2.15796	+	3.73769i	−0.100835	+	0.174651i
$459$	25.9577	−	21.7811i	1.21160	−	1.01666i
$460$	−5.65756	+	4.74726i	−0.263785	+	0.221342i
$461$	−9.05900	−	3.29721i	−0.421920	−	0.153566i	0.122330	−	0.992489i	$-0.460963\pi$
$461$	−9.05900	−	3.29721i	−0.421920	−	0.153566i	−0.544250	+	0.838923i	$0.683186\pi$
$462$	5.92209	−	33.5858i	0.275521	−	1.56256i
$463$	−4.21361	+	23.8966i	−0.195823	+	1.11057i	0.715419	+	0.698696i	$0.246236\pi$
$463$	−4.21361	+	23.8966i	−0.195823	+	1.11057i	−0.911242	+	0.411872i	$0.864875\pi$
$464$	1.08148	+	0.393625i	0.0502062	+	0.0182736i
$465$	8.31416	−	6.97641i	0.385560	−	0.323523i
$466$	3.89624	−	3.26933i	0.180490	−	0.151449i
$467$	−13.9136	+	24.0990i	−0.643842	+	1.11517i	0.340725	+	0.940163i	$0.389327\pi$
$467$	−13.9136	+	24.0990i	−0.643842	+	1.11517i	−0.984568	+	0.175005i	$0.944006\pi$
$468$	0.932216	−	0.339299i	0.0430917	−	0.0156841i
$469$	1.81715	+	10.3056i	0.0839082	+	0.475867i
$470$	−2.40517	−	4.16588i	−0.110942	−	0.192158i
$471$	−11.9164	+	20.6398i	−0.549079	+	0.951033i
$472$	4.75279	+	1.72987i	0.218765	+	0.0796239i
$473$	8.62142	+	14.9327i	0.396413	+	0.686608i
$474$	18.5844	+	15.5941i	0.853608	+	0.716262i
$475$	7.51241			0.344693
$476$	−6.30272	−	5.28861i	−0.288885	−	0.242403i
$477$	5.37876	−	1.95771i	0.246276	−	0.0896373i
$478$	−2.16062	+	12.2535i	−0.0988243	+	0.560460i
$479$	−2.71555	−	15.4006i	−0.124076	−	0.703673i	−0.981852	−	0.189648i	$-0.939265\pi$
$479$	−2.71555	−	15.4006i	−0.124076	−	0.703673i	0.857776	−	0.514024i	$-0.171846\pi$
$480$	−3.27140			−0.149318
$481$	−0.758836	+	0.194925i	−0.0346000	+	0.00888783i
$482$	−29.0965			−1.32531
$483$	15.6699	+	88.8682i	0.713004	+	4.04364i
$484$	−0.557309	+	3.16066i	−0.0253322	+	0.143666i
$485$	−2.00249	+	0.728847i	−0.0909284	+	0.0330952i
$486$	−32.8530	−	27.5670i	−1.49024	−	1.25046i
$487$	22.3960			1.01486			0.507431	−	0.861693i	$-0.330595\pi$
$487$	22.3960			1.01486			0.507431	+	0.861693i	$0.330595\pi$
$488$	−9.38619	−	7.87595i	−0.424893	−	0.356527i
$489$	17.1834	+	29.7625i	0.777059	+	1.34591i
$490$	−6.53078	−	2.37701i	−0.295031	−	0.107382i
$491$	10.3221	−	17.8784i	0.465831	−	0.806843i	−0.533408	−	0.845858i	$-0.679089\pi$
$491$	10.3221	−	17.8784i	0.465831	−	0.806843i	0.999239	+	0.0390153i	$0.0124221\pi$
$492$	−0.820523	−	1.42119i	−0.0369920	−	0.0640721i
$493$	0.440240	+	2.49673i	0.0198274	+	0.112447i
$494$	0.909259	−	0.330943i	0.0409095	−	0.0148898i
$495$	10.7489	−	18.6176i	0.483126	−	0.836799i
$496$	−2.54147	+	2.13254i	−0.114115	+	0.0957540i
$497$	−47.8131	+	40.1200i	−2.14471	+	1.79963i
$498$	−20.3567	−	7.40923i	−0.912205	−	0.332015i
$499$	−2.39473	+	13.5812i	−0.107203	+	0.607977i	0.883115	+	0.469157i	$0.155442\pi$
$499$	−2.39473	+	13.5812i	−0.107203	+	0.607977i	−0.990318	+	0.138820i	$0.955669\pi$
$500$	0.173648	−	0.984808i	0.00776578	−	0.0440419i
$501$	32.6927	+	11.8992i	1.46060	+	0.531616i
$502$	11.2962	−	9.47864i	0.504174	−	0.423052i
$503$	−16.3208	+	13.6948i	−0.727711	+	0.610622i	−0.929506	−	0.368806i	$-0.879767\pi$
$503$	−16.3208	+	13.6948i	−0.727711	+	0.610622i	0.201796	+	0.979428i	$0.435322\pi$
$504$	−14.3835	+	24.9129i	−0.640691	+	1.10971i
$505$	13.7820	−	5.01623i	0.613290	−	0.223219i
$506$	3.57957	+	20.3007i	0.159131	+	0.902478i
$507$	−21.2370	−	36.7835i	−0.943168	−	1.63361i
$508$	−2.20048	+	3.81134i	−0.0976304	+	0.169101i
$509$	11.6932	+	4.25597i	0.518291	+	0.188642i	0.587903	−	0.808932i	$-0.299954\pi$
$509$	11.6932	+	4.25597i	0.518291	+	0.188642i	−0.0696117	+	0.997574i	$0.522176\pi$
$510$	−3.60324	−	6.24099i	−0.159554	−	0.276356i
$511$	−42.5987	−	35.7445i	−1.88445	−	1.58125i
$512$	1.00000			0.0441942
$513$	−88.5232	−	74.2798i	−3.90839	−	3.27953i
$514$	5.12496	−	1.86533i	0.226052	−	0.0822763i
$515$	1.14918	−	6.51733i	0.0506389	−	0.287188i
$516$	−3.50936	−	19.9026i	−0.154491	−	0.876162i
$517$	−13.4265			−0.590495
$518$	13.2231	−	18.4742i	0.580991	−	0.811709i
$519$	−78.8630			−3.46170
$520$	−0.0223662	−	0.126845i	−0.000980824	−	0.00556253i
$521$	−4.37140	+	24.7914i	−0.191514	+	1.08613i	0.725781	+	0.687925i	$0.241478\pi$
$521$	−4.37140	+	24.7914i	−0.191514	+	1.08613i	−0.917296	+	0.398207i	$0.869633\pi$
$522$	8.32961	−	3.03173i	0.364577	−	0.132695i
$523$	8.20733	+	6.88677i	0.358882	+	0.301137i	0.804345	−	0.594163i	$-0.202517\pi$
$523$	8.20733	+	6.88677i	0.358882	+	0.301137i	−0.445463	+	0.895300i	$0.646961\pi$
$524$	6.86951			0.300096
$525$	−9.35995	−	7.85393i	−0.408502	−	0.342774i
$526$	2.22328	+	3.85084i	0.0969398	+	0.167905i
$527$	−6.86760	−	2.49960i	−0.299157	−	0.108884i
$528$	−4.56551	+	7.90769i	−0.198688	+	0.344138i
$529$	−15.7722	−	27.3183i	−0.685749	−	1.18775i
$530$	−0.129050	−	0.731880i	−0.00560558	−	0.0317908i
$531$	36.6064	−	13.3236i	1.58858	−	0.578196i
$532$	−14.0293	+	24.2994i	−0.608246	+	1.05351i
$533$	0.0494952	−	0.0415314i	0.00214388	−	0.00179893i
$534$	35.5070	−	29.7939i	1.53654	−	1.28931i
$535$	16.5212	+	6.01321i	0.714272	+	0.259974i
$536$	0.486525	−	2.75922i	0.0210147	−	0.119180i
$537$	−9.07663	+	51.4762i	−0.391686	+	2.22136i
$538$	−21.9626	−	7.99375i	−0.946876	−	0.344635i
$539$	−14.8600	+	12.4690i	−0.640065	+	0.537078i
$540$	−11.7836	+	9.88761i	−0.507085	+	0.425495i
$541$	6.75442	−	11.6990i	0.290395	−	0.502979i	−0.683508	−	0.729943i	$-0.739547\pi$
$541$	6.75442	−	11.6990i	0.290395	−	0.502979i	0.973903	+	0.226964i	$0.0728799\pi$
$542$	4.00580	−	1.45799i	0.172064	−	0.0626261i
$543$	−7.70202	−	43.6803i	−0.330525	−	1.87450i
$544$	1.10143	+	1.90774i	0.0472236	+	0.0817937i
$545$	8.43154	−	14.6039i	0.361168	−	0.625561i
$546$	−1.47886	−	0.538263i	−0.0632895	−	0.0230355i
$547$	12.4051	+	21.4862i	0.530402	+	0.918684i	0.999371	+	0.0354688i	$0.0112925\pi$
$547$	12.4051	+	21.4862i	0.530402	+	0.918684i	−0.468968	+	0.883215i	$0.655374\pi$
$548$	0.204094	+	0.171255i	0.00871847	+	0.00731567i
$549$	−94.3720			−4.02770
$550$	−2.13815	−	1.79412i	−0.0911712	−	0.0765017i
$551$	8.12448	−	2.95707i	0.346115	−	0.125975i
$552$	4.19546	−	23.7936i	0.178571	−	1.01272i
$553$	−4.80968	−	27.2770i	−0.204528	−	1.15994i
$554$	−2.47588			−0.105190
$555$	16.4178	−	11.2442i	0.696898	−	0.477289i
$556$	9.32972			0.395668
$557$	0.823619	+	4.67097i	0.0348978	+	0.197915i	0.997272	−	0.0738115i	$-0.0235163\pi$
$557$	0.823619	+	4.67097i	0.0348978	+	0.197915i	−0.962374	+	0.271727i	$0.912405\pi$
$558$	−4.43720	+	25.1646i	−0.187841	+	1.06530i
$559$	0.747708	−	0.272144i	0.0316247	−	0.0115104i
$560$	2.86114	+	2.40078i	0.120905	+	0.101452i
$561$	−20.1144			−0.849232
$562$	6.11934	+	5.13473i	0.258129	+	0.216596i
$563$	2.88612	+	4.99890i	0.121635	+	0.210678i	0.920413	−	0.390948i	$-0.127853\pi$
$563$	2.88612	+	4.99890i	0.121635	+	0.210678i	−0.798777	+	0.601627i	$0.794520\pi$
$564$	14.7876	+	5.38223i	0.622668	+	0.226633i
$565$	−5.51900	+	9.55920i	−0.232186	+	0.402158i
$566$	8.94571	+	15.4944i	0.376016	+	0.651279i
$567$	17.6513	+	100.105i	0.741285	+	4.20404i
$568$	15.7034	−	5.71556i	0.658899	−	0.239820i
$569$	−14.1090	+	24.4375i	−0.591480	+	1.02447i	0.402553	+	0.915396i	$0.368123\pi$
$569$	−14.1090	+	24.4375i	−0.591480	+	1.02447i	−0.994033	+	0.109077i	$0.965211\pi$
$570$	−18.8264	+	15.7972i	−0.788551	+	0.661673i
$571$	−24.9012	+	20.8946i	−1.04208	+	0.874412i	−0.992239	−	0.124345i	$-0.960317\pi$
$571$	−24.9012	+	20.8946i	−1.04208	+	0.874412i	−0.0498447	+	0.998757i	$0.515873\pi$
$572$	−0.337826	−	0.122959i	−0.0141252	−	0.00514116i
$573$	−7.83977	+	44.4615i	−0.327511	+	1.85741i
$574$	−0.325344	+	1.84512i	−0.0135796	+	0.0770137i
$575$	6.94003	+	2.52596i	0.289419	+	0.105340i
$576$	5.90013	−	4.95080i	0.245839	−	0.206283i
$577$	1.14402	−	0.959944i	0.0476260	−	0.0399630i	−0.618664	−	0.785656i	$-0.712326\pi$
$577$	1.14402	−	0.959944i	0.0476260	−	0.0399630i	0.666290	+	0.745693i	$0.267881\pi$
$578$	6.07368	−	10.5199i	0.252632	−	0.437571i
$579$	21.7517	−	7.91696i	0.903968	−	0.329018i
$580$	−0.199849	−	1.13340i	−0.00829826	−	0.0470618i
$581$	12.3664	+	21.4192i	0.513044	+	0.888619i
$582$	3.48569	−	6.03739i	0.144487	−	0.250258i
$583$	−1.94921	−	0.709455i	−0.0807281	−	0.0293826i
$584$	7.44435	+	12.8940i	0.308049	+	0.533557i
$585$	−0.759949	−	0.637673i	−0.0314200	−	0.0263645i
$586$	−10.6688			−0.440725
$587$	−21.2757	−	17.8525i	−0.878144	−	0.736850i	0.0876529	−	0.996151i	$-0.472063\pi$
$587$	−21.2757	−	17.8525i	−0.878144	−	0.736850i	−0.965797	+	0.259301i	$0.916508\pi$
$588$	21.3648	−	7.77616i	0.881070	−	0.320683i
$589$	−4.32793	+	24.5449i	−0.178329	+	1.01135i
$590$	−0.878280	−	4.98097i	−0.0361582	−	0.205063i
$591$	49.4977			2.03607
$592$	−5.01859	+	3.43711i	−0.206263	+	0.141264i
$593$	−8.97409			−0.368522			−0.184261	−	0.982877i	$-0.558989\pi$
$593$	−8.97409			−0.368522			−0.184261	+	0.982877i	$0.558989\pi$
$594$	7.45554	+	42.2825i	0.305905	+	1.73487i
$595$	−1.42871	+	8.10263i	−0.0585715	+	0.332175i
$596$	13.9247	−	5.06817i	0.570378	−	0.207600i
$597$	1.75805	+	1.47518i	0.0719522	+	0.0603750i
$598$	0.951257			0.0388998
$599$	−9.15670	−	7.68338i	−0.374133	−	0.313935i	0.436261	−	0.899820i	$-0.356302\pi$
$599$	−9.15670	−	7.68338i	−0.374133	−	0.313935i	−0.810394	+	0.585886i	$0.800747\pi$
$600$	1.63570	+	2.83312i	0.0667772	+	0.115662i
$601$	−19.3366	−	7.03793i	−0.788754	−	0.287083i	−0.0839362	−	0.996471i	$-0.526749\pi$
$601$	−19.3366	−	7.03793i	−0.788754	−	0.287083i	−0.704818	+	0.709388i	$0.748971\pi$
$602$	−11.5366	+	19.9820i	−0.470198	+	0.814408i
$603$	−10.7898	−	18.6884i	−0.439394	−	0.761052i
$604$	1.35048	+	7.65894i	0.0549502	+	0.311638i
$605$	3.01586	−	1.09768i	0.122612	−	0.0446272i
$606$	−23.9900	+	41.5519i	−0.974526	+	1.68793i
$607$	3.09935	−	2.60067i	0.125799	−	0.105558i	−0.577718	−	0.816237i	$-0.696057\pi$
$607$	3.09935	−	2.60067i	0.125799	−	0.105558i	0.703517	+	0.710679i	$0.251612\pi$
$608$	5.75484	−	4.82888i	0.233390	−	0.195837i
$609$	−13.2141	−	4.80953i	−0.535461	−	0.194892i
$610$	−2.12768	+	12.0666i	−0.0861471	+	0.488564i
$611$	−0.107589	+	0.610170i	−0.00435260	+	0.0246848i
$612$	15.9435	+	5.80294i	0.644476	+	0.234570i
$613$	12.7495	−	10.6981i	0.514946	−	0.432091i	−0.347920	−	0.937524i	$-0.613112\pi$
$613$	12.7495	−	10.6981i	0.514946	−	0.432091i	0.862866	+	0.505433i	$0.168667\pi$
$614$	−10.9764	+	9.21026i	−0.442970	+	0.371696i
$615$	−0.820523	+	1.42119i	−0.0330867	+	0.0573078i
$616$	9.79618	−	3.56552i	0.394699	−	0.143659i
$617$	−6.61864	−	37.5362i	−0.266457	−	1.51115i	−0.764855	−	0.644202i	$-0.777189\pi$
$617$	−6.61864	−	37.5362i	−0.266457	−	1.51115i	0.498399	−	0.866948i	$-0.333922\pi$
$618$	10.8249	+	18.7492i	0.435440	+	0.754203i
$619$	−3.00497	+	5.20475i	−0.120780	+	0.209197i	−0.920075	−	0.391741i	$-0.871873\pi$
$619$	−3.00497	+	5.20475i	−0.120780	+	0.209197i	0.799296	+	0.600938i	$0.205206\pi$
$620$	3.11757	+	1.13470i	0.125205	+	0.0455708i
$621$	−56.8027	−	98.3852i	−2.27942	−	3.94806i
$622$	−5.79379	−	4.86157i	−0.232310	−	0.194931i
$623$	−52.9190			−2.12015
$624$	0.322783	+	0.270847i	0.0129217	+	0.0108426i
$625$	−0.939693	+	0.342020i	−0.0375877	+	0.0136808i
$626$	4.15198	−	23.5470i	0.165946	−	0.941129i
$627$	11.9116	+	67.5538i	0.475702	+	2.69784i
$628$	−7.28520			−0.290711
$629$	−12.0848	−	5.78841i	−0.481851	−	0.230799i
$630$	28.7669			1.14610
$631$	−0.890164	−	5.04837i	−0.0354369	−	0.200972i	0.961949	−	0.273228i	$-0.0880914\pi$
$631$	−0.890164	−	5.04837i	−0.0354369	−	0.200972i	−0.997386	+	0.0722556i	$0.976980\pi$
$632$	−1.28775	+	7.30317i	−0.0512238	+	0.290504i
$633$	35.2334	−	12.8239i	1.40040	−	0.509705i
$634$	5.36030	+	4.49783i	0.212885	+	0.178632i
$635$	4.40096			0.174647
$636$	1.86241	+	1.56275i	0.0738495	+	0.0619671i
$637$	0.447581	+	0.775233i	0.0177338	+	0.0307159i
$638$	−3.01857	−	1.09867i	−0.119506	−	0.0434968i
$639$	64.3554	−	111.467i	2.54586	−	4.40956i
$640$	−0.500000	−	0.866025i	−0.0197642	−	0.0342327i
$641$	−2.11618	−	12.0015i	−0.0835841	−	0.474029i	−0.997653	−	0.0684704i	$-0.978188\pi$
$641$	−2.11618	−	12.0015i	−0.0835841	−	0.474029i	0.914069	−	0.405559i	$-0.132923\pi$
$642$	−54.0474	+	19.6716i	−2.13308	+	0.776377i
$643$	−18.9927	+	32.8963i	−0.749000	+	1.29731i	0.199303	+	0.979938i	$0.436132\pi$
$643$	−18.9927	+	32.8963i	−0.749000	+	1.29731i	−0.948303	+	0.317367i	$0.897201\pi$
$644$	−21.1308	+	17.7308i	−0.832668	+	0.698692i
$645$	−15.4815	+	12.9905i	−0.609582	+	0.511500i
$646$	15.5508	+	5.66004i	0.611839	+	0.222691i
$647$	3.35044	−	19.0013i	0.131719	−	0.747018i	−0.845369	−	0.534183i	$-0.820619\pi$
$647$	3.35044	−	19.0013i	0.131719	−	0.747018i	0.977088	−	0.212835i	$-0.0682696\pi$
$648$	4.72597	−	26.8023i	0.185654	−	1.05289i
$649$	−13.2658	−	4.82836i	−0.520729	−	0.189530i
$650$	−0.0986681	+	0.0827923i	−0.00387008	+	0.00324738i
$651$	31.0530	−	26.0566i	1.21706	−	1.02124i
$652$	−5.25260	+	9.09777i	−0.205708	+	0.356296i
$653$	−16.1866	+	5.89143i	−0.633429	+	0.230549i	−0.638723	−	0.769437i	$-0.720537\pi$
$653$	−16.1866	+	5.89143i	−0.633429	+	0.230549i	0.00529394	+	0.999986i	$0.498315\pi$
$654$	9.57947	+	54.3279i	0.374587	+	2.12439i
$655$	−3.43475	−	5.94917i	−0.134207	−	0.232453i
$656$	0.250817	−	0.434427i	0.00979275	−	0.0169615i
$657$	107.758	+	39.2208i	4.20405	+	1.53015i
$658$	−8.98322	−	15.5594i	−0.350203	−	0.606569i
$659$	−7.89694	−	6.62632i	−0.307621	−	0.258125i	0.475887	−	0.879507i	$-0.342127\pi$
$659$	−7.89694	−	6.62632i	−0.307621	−	0.258125i	−0.783508	+	0.621382i	$0.786572\pi$
$660$	9.13102			0.355424
$661$	17.1008	+	14.3492i	0.665142	+	0.558121i	0.911623	−	0.411027i	$-0.134830\pi$
$661$	17.1008	+	14.3492i	0.665142	+	0.558121i	−0.246481	+	0.969148i	$0.579274\pi$
$662$	4.41534	−	1.60705i	0.171607	−	0.0624599i
$663$	−0.161182	+	0.914107i	−0.00625978	+	0.0355010i
$664$	−1.14989	−	6.52137i	−0.0446245	−	0.253078i
$665$	28.0585			1.08806
$666$	−12.5939	+	45.1255i	−0.488004	+	1.74858i
$667$	8.49975			0.329112
$668$	1.84672	+	10.4733i	0.0714519	+	0.405224i
$669$	−1.44037	+	8.16875i	−0.0556880	+	0.315822i
$670$	−2.63282	+	0.958267i	−0.101715	+	0.0370211i
$671$	26.1984	+	21.9830i	1.01138	+	0.848646i
$672$	−12.2186			−0.471341
$673$	7.74356	+	6.49761i	0.298492	+	0.250465i	0.779716	−	0.626133i	$-0.215363\pi$
$673$	7.74356	+	6.49761i	0.298492	+	0.250465i	−0.481224	+	0.876598i	$0.659808\pi$
$674$	13.1136	+	22.7134i	0.505115	+	0.874886i
$675$	14.4547	+	5.26109i	0.556363	+	0.202499i
$676$	6.49171	−	11.2440i	0.249681	−	0.432460i
$677$	3.69494	+	6.39982i	0.142008	+	0.245965i	0.928253	−	0.371950i	$-0.121311\pi$
$677$	3.69494	+	6.39982i	0.142008	+	0.245965i	−0.786245	+	0.617915i	$0.787977\pi$
$678$	−6.27040	−	35.5612i	−0.240813	−	1.36572i
$679$	−7.47922	+	2.72221i	−0.287026	+	0.104469i
$680$	1.10143	−	1.90774i	0.0422381	−	0.0731585i
$681$	21.2073	−	17.7951i	0.812667	−	0.681909i
$682$	7.09364	−	5.95227i	0.271630	−	0.227924i
$683$	−25.5361	−	9.29439i	−0.977112	−	0.355640i	−0.196395	−	0.980525i	$-0.562924\pi$
$683$	−25.5361	−	9.29439i	−0.977112	−	0.355640i	−0.780717	+	0.624885i	$0.785146\pi$
$684$	10.0475	−	56.9821i	0.384175	−	2.17877i
$685$	0.0462644	−	0.262378i	0.00176767	−	0.0100250i
$686$	0.175800	+	0.0639859i	0.00671207	+	0.00244299i
$687$	−10.8158	+	9.07557i	−0.412650	+	0.346255i
$688$	4.73236	−	3.97092i	0.180419	−	0.151390i
$689$	−0.0478609	+	0.0828975i	−0.00182335	+	0.00315814i
$690$	−22.7036	+	8.26344i	−0.864312	+	0.314584i
$691$	0.285985	+	1.62190i	0.0108794	+	0.0617000i	0.989764	−	0.142713i	$-0.0455826\pi$
$691$	0.285985	+	1.62190i	0.0108794	+	0.0617000i	−0.978885	+	0.204413i	$0.934471\pi$
$692$	−12.0534	−	20.8771i	−0.458201	−	0.793627i
$693$	40.1466	−	69.5359i	1.52504	−	2.64145i
$694$	−10.6657	−	3.88200i	−0.404865	−	0.147359i
$695$	−4.66486	−	8.07977i	−0.176948	−	0.306483i
$696$	2.88416	+	2.42009i	0.109324	+	0.0917335i
$697$	1.10503			0.0418561
$698$	21.0997	+	17.7048i	0.798636	+	0.670136i
$699$	15.6355	−	5.69085i	0.591388	−	0.215248i
$700$	0.648569	−	3.67822i	0.0245136	−	0.139023i
$701$	−3.14142	−	17.8159i	−0.118650	−	0.672897i	−0.984878	−	0.173249i	$-0.944574\pi$
$701$	−3.14142	−	17.8159i	−0.118650	−	0.672897i	0.866228	−	0.499649i	$-0.166538\pi$
$702$	1.98128			0.0747787
$703$	−12.2838	+	44.0142i	−0.463291	+	1.66003i
$704$	−2.79116			−0.105196
$705$	−2.73263	−	15.4975i	−0.102917	−	0.583670i
$706$	−3.50342	+	19.8689i	−0.131853	+	0.747776i
$707$	51.4751	−	18.7354i	1.93592	−	0.704617i
$708$	12.6751	+	10.6357i	0.476359	+	0.399713i
$709$	−24.2016			−0.908910			−0.454455	−	0.890770i	$-0.650166\pi$
$709$	−24.2016			−0.908910			−0.454455	+	0.890770i	$0.650166\pi$
$710$	−12.8015	−	10.7417i	−0.480432	−	0.403130i
$711$	28.5587	+	49.4650i	1.07103	+	1.85508i
$712$	13.3141	+	4.84593i	0.498967	+	0.181609i
$713$	−12.2511	+	21.2196i	−0.458808	+	0.794679i
$714$	−13.4579	−	23.3098i	−0.503651	−	0.872348i
$715$	0.0624278	+	0.354046i	0.00233467	+	0.0132406i
$716$	−15.0143	+	5.46477i	−0.561112	+	0.204228i
$717$	−20.3522	+	35.2511i	−0.760067	+	1.31647i
$718$	−21.7790	+	18.2747i	−0.812783	+	0.682006i
$719$	29.1343	−	24.4466i	1.08653	−	0.911703i	0.0900789	−	0.995935i	$-0.471288\pi$
$719$	29.1343	−	24.4466i	1.08653	−	0.911703i	0.996446	+	0.0842319i	$0.0268436\pi$
$720$	−7.23759	−	2.63427i	−0.269729	−	0.0981733i
$721$	4.29214	−	24.3419i	0.159848	−	0.906541i
$722$	6.50074	−	36.8675i	0.241933	−	1.37207i
$723$	−89.4460	−	32.5557i	−3.32653	−	1.21076i
$724$	10.3861	−	8.71501i	0.385998	−	0.323891i
$725$	−0.881627	+	0.739773i	−0.0327428	+	0.0274745i
$726$	−5.24964	+	9.09265i	−0.194833	+	0.337460i
$727$	1.40394	−	0.510994i	0.0520694	−	0.0189517i	−0.315854	−	0.948808i	$-0.602291\pi$
$727$	1.40394	−	0.510994i	0.0520694	−	0.0189517i	0.367924	+	0.929856i	$0.380069\pi$
$728$	−0.0835370	−	0.473762i	−0.00309609	−	0.0175588i
$729$	−29.3260	−	50.7941i	−1.08615	−	1.88126i
$730$	7.44435	−	12.8940i	0.275528	−	0.477228i
$731$	12.7879	+	4.65440i	0.472976	+	0.172149i
$732$	−20.0419	−	34.7136i	−0.740771	−	1.28305i
$733$	9.62447	+	8.07589i	0.355488	+	0.298290i	0.802989	−	0.595994i	$-0.203242\pi$
$733$	9.62447	+	8.07589i	0.355488	+	0.298290i	−0.447501	+	0.894283i	$0.647686\pi$
$734$	−6.12876			−0.226217
$735$	−17.4168	−	14.6144i	−0.642427	−	0.539060i
$736$	6.94003	−	2.52596i	0.255813	−	0.0931082i
$737$	−1.35797	+	7.70143i	−0.0500214	+	0.283686i
$738$	−0.670911	−	3.80492i	−0.0246966	−	0.140061i
$739$	38.8039			1.42743			0.713713	−	0.700438i	$-0.247012\pi$
$739$	38.8039			1.42743			0.713713	+	0.700438i	$0.247012\pi$
$740$	5.48592	+	2.62767i	0.201667	+	0.0965951i
$741$	3.16545			0.116286
$742$	−0.481997	−	2.73354i	−0.0176947	−	0.100351i
$743$	−4.09700	+	23.2353i	−0.150305	+	0.852419i	0.812649	+	0.582753i	$0.198024\pi$
$743$	−4.09700	+	23.2353i	−0.150305	+	0.852419i	−0.962954	+	0.269666i	$0.913087\pi$
$744$	−10.1988	+	3.71207i	−0.373907	+	0.136091i
$745$	−11.3515	−	9.52505i	−0.415887	−	0.348971i
$746$	16.3440			0.598395
$747$	−39.0705	−	32.7841i	−1.42952	−	1.19951i
$748$	−3.07428	−	5.32481i	−0.112407	−	0.194694i
$749$	61.7058	+	22.4591i	2.25468	+	0.820637i
$750$	1.63570	−	2.83312i	0.0597274	−	0.103451i
$751$	9.61812	+	16.6591i	0.350970	+	0.607898i	0.986420	−	0.164244i	$-0.0525185\pi$
$751$	9.61812	+	16.6591i	0.350970	+	0.607898i	−0.635449	+	0.772142i	$0.719185\pi$
$752$	0.835308	+	4.73727i	0.0304606	+	0.172750i
$753$	45.3313	−	16.4992i	1.65197	−	0.601266i
$754$	−0.0741180	+	0.128376i	−0.00269922	+	0.00467518i
$755$	5.95760	−	4.99902i	0.216819	−	0.181933i
$756$	−44.0112	+	36.9298i	−1.60067	+	1.34312i
$757$	−7.75126	−	2.82123i	−0.281724	−	0.102539i	0.197293	−	0.980344i	$-0.436785\pi$
$757$	−7.75126	−	2.82123i	−0.281724	−	0.102539i	−0.479018	+	0.877805i	$0.659007\pi$
$758$	5.33204	−	30.2395i	0.193668	−	1.09835i
$759$	−11.7102	+	66.4119i	−0.425054	+	2.41060i
$760$	−7.05935	−	2.56939i	−0.256070	−	0.0932018i
$761$	3.93916	−	3.30535i	0.142794	−	0.119819i	−0.568592	−	0.822619i	$-0.692512\pi$
$761$	3.93916	−	3.30535i	0.142794	−	0.119819i	0.711387	+	0.702801i	$0.248067\pi$
$762$	−11.0290	+	9.25441i	−0.399538	+	0.335252i
$763$	31.4915	−	54.5448i	1.14007	−	1.97465i
$764$	−12.9683	+	4.72009i	−0.469178	+	0.170767i
$765$	−2.94623	−	16.7089i	−0.106521	−	0.604112i
$766$	7.07108	+	12.2475i	0.255489	+	0.442519i
$767$	−0.325728	+	0.564178i	−0.0117614	+	0.0203713i
$768$	3.07411	+	1.11889i	0.110928	+	0.0403743i
$769$	−3.75777	−	6.50865i	−0.135509	−	0.234708i	0.790283	−	0.612742i	$-0.209934\pi$
$769$	−3.75777	−	6.50865i	−0.135509	−	0.234708i	−0.925792	+	0.378034i	$0.876600\pi$
$770$	−7.98592	−	6.70098i	−0.287792	−	0.241487i
$771$	17.8418			0.642557
$772$	5.42034	+	4.54821i	0.195082	+	0.163694i
$773$	−0.00943445	+	0.00343386i	−0.000339334	+	0.000123507i	−0.342190	−	0.939631i	$-0.611169\pi$
$773$	−0.00943445	+	0.00343386i	−0.000339334	+	0.000123507i	0.341850	+	0.939754i	$0.388946\pi$
$774$	8.26232	−	46.8579i	0.296983	−	1.68427i
$775$	−0.576104	−	3.26725i	−0.0206943	−	0.117363i
$776$	2.13101			0.0764987
$777$	61.3199	−	41.9966i	2.19984	−	1.50662i
$778$	−7.53912			−0.270291
$779$	−0.654389	−	3.71122i	−0.0234459	−	0.132968i
$780$	0.0731690	−	0.414962i	0.00261987	−	0.0148580i
$781$	−43.8307	+	15.9531i	−1.56838	+	0.570845i
$782$	12.4629	+	10.4576i	0.445671	+	0.373963i
$783$	17.7033			0.632665
$784$	5.32394	+	4.46732i	0.190141	+	0.159547i
$785$	3.64260	+	6.30917i	0.130010	+	0.225184i
$786$	21.1176	+	7.68619i	0.753241	+	0.274157i
$787$	−17.1056	+	29.6277i	−0.609747	+	1.05611i	0.381534	+	0.924355i	$0.375396\pi$
$787$	−17.1056	+	29.6277i	−0.609747	+	1.05611i	−0.991282	+	0.131759i	$0.957938\pi$
$788$	7.56522	+	13.1033i	0.269500	+	0.466787i
$789$	2.52598	+	14.3255i	0.0899271	+	0.510002i
$790$	6.96860	−	2.53636i	0.247932	−	0.0902398i
$791$	−20.6133	+	35.7032i	−0.732923	+	1.26946i
$792$	−16.4682	+	13.8185i	−0.585173	+	0.491019i
$793$	1.20896	−	1.01444i	0.0429314	−	0.0360237i
$794$	−15.7014	−	5.71484i	−0.557221	−	0.202812i
$795$	0.422175	−	2.39427i	0.0149730	−	0.0849161i
$796$	−0.121819	+	0.690867i	−0.00431774	+	0.0244871i
$797$	−14.7927	−	5.38412i	−0.523986	−	0.190715i	0.0664650	−	0.997789i	$-0.478828\pi$
$797$	−14.7927	−	5.38412i	−0.523986	−	0.190715i	−0.590451	+	0.807073i	$0.701050\pi$
$798$	−70.3158	+	59.0020i	−2.48915	+	2.08865i
$799$	−8.11744	+	6.81134i	−0.287174	+	0.240968i
$800$	−0.500000	+	0.866025i	−0.0176777	+	0.0306186i
$801$	102.546	−	37.3237i	3.62329	−	1.31877i
$802$	−2.34841	−	13.3185i	−0.0829254	−	0.470293i
$803$	−20.7784	−	35.9892i	−0.733253	−	1.27003i
$804$	4.58288	−	7.93779i	0.161626	−	0.279944i
$805$	25.9207	+	9.43437i	0.913585	+	0.332518i
$806$	−0.213660	−	0.370070i	−0.00752585	−	0.0130352i
$807$	−58.5715	−	49.1474i	−2.06182	−	1.73007i
$808$	−14.6665			−0.515965
$809$	36.2866	+	30.4481i	1.27577	+	1.07050i	0.993812	+	0.111071i	$0.0354282\pi$
$809$	36.2866	+	30.4481i	1.27577	+	1.07050i	0.281958	+	0.959427i	$0.409016\pi$
$810$	−25.5745	+	9.30834i	−0.898595	+	0.327062i
$811$	4.28478	−	24.3002i	0.150459	−	0.853295i	−0.812362	−	0.583154i	$-0.801818\pi$
$811$	4.28478	−	24.3002i	0.150459	−	0.853295i	0.962821	−	0.270141i	$-0.0870705\pi$
$812$	−0.746426	−	4.23319i	−0.0261944	−	0.148556i
$813$	13.9456			0.489094
$814$	14.0077	−	9.59354i	0.490970	−	0.336253i
$815$	10.5052			0.367981
$816$	1.25139	+	7.09699i	0.0438074	+	0.248444i
$817$	8.05885	−	45.7040i	0.281943	−	1.59898i
$818$	5.69101	−	2.07136i	0.198981	−	0.0724233i
$819$	−2.83838	−	2.38168i	−0.0991810	−	0.0832227i
$820$	−0.501633			−0.0175178
$821$	−26.0806	−	21.8842i	−0.910218	−	0.763764i	0.0619421	−	0.998080i	$-0.480271\pi$
$821$	−26.0806	−	21.8842i	−0.910218	−	0.763764i	−0.972161	+	0.234316i	$0.924715\pi$
$822$	0.435794	+	0.754817i	0.0152000	+	0.0263273i
$823$	30.9636	+	11.2698i	1.07932	+	0.392842i	0.819656	−	0.572856i	$-0.194164\pi$
$823$	30.9636	+	11.2698i	1.07932	+	0.392842i	0.259669	+	0.965698i	$0.416387\pi$
$824$	−3.30893	+	5.73124i	−0.115272	+	0.199657i
$825$	−4.56551	−	7.90769i	−0.158951	−	0.275311i
$826$	−3.28034	−	18.6037i	−0.114138	−	0.647307i
$827$	−10.6509	+	3.87661i	−0.370368	+	0.134803i	−0.520497	−	0.853863i	$-0.674253\pi$
$827$	−10.6509	+	3.87661i	−0.370368	+	0.134803i	0.150129	+	0.988666i	$0.452031\pi$
$828$	28.4415	−	49.2622i	0.988412	−	1.71198i
$829$	22.4972	−	18.8774i	0.781361	−	0.655639i	−0.162230	−	0.986753i	$-0.551869\pi$
$829$	22.4972	−	18.8774i	0.781361	−	0.655639i	0.943591	+	0.331113i	$0.107424\pi$
$830$	−5.07272	+	4.25652i	−0.176077	+	0.147746i
$831$	−7.61112	−	2.77022i	−0.264027	−	0.0960979i
$832$	−0.0223662	+	0.126845i	−0.000775410	+	0.00439757i
$833$	−2.65851	+	15.0772i	−0.0921119	+	0.522392i
$834$	28.6806	+	10.4389i	0.993128	+	0.361469i
$835$	8.14677	−	6.83595i	0.281931	−	0.236568i
$836$	−16.0627	+	13.4782i	−0.555540	+	0.466153i
$837$	−25.5167	+	44.1962i	−0.881986	+	1.52764i
$838$	6.74198	−	2.45388i	0.232898	−	0.0847678i
$839$	−7.92798	−	44.9618i	−0.273704	−	1.55225i	−0.743048	−	0.669239i	$-0.766620\pi$
$839$	−7.92798	−	44.9618i	−0.273704	−	1.55225i	0.469343	−	0.883016i	$-0.344491\pi$
$840$	6.10928	+	10.5816i	0.210790	+	0.365099i
$841$	13.8377	−	23.9677i	0.477163	−	0.826471i
$842$	35.8909	+	13.0632i	1.23688	+	0.450189i
$843$	13.0664	+	22.6316i	0.450029	+	0.779473i
$844$	8.77989	+	7.36720i	0.302216	+	0.253590i
$845$	−12.9834			−0.446643
$846$	28.3817	+	23.8151i	0.975783	+	0.818779i
$847$	11.2641	−	4.09980i	0.387040	−	0.140871i
$848$	−0.129050	+	0.731880i	−0.00443160	+	0.0251328i
$849$	10.1636	+	57.6408i	0.348815	+	1.97823i
$850$	−2.20287			−0.0755578
$851$	−26.1471	+	36.5304i	−0.896312	+	1.25225i
$852$	54.6690			1.87293
$853$	−5.07113	−	28.7598i	−0.173632	−	0.984718i	−0.939711	−	0.341971i	$-0.888906\pi$
$853$	−5.07113	−	28.7598i	−0.173632	−	0.984718i	0.766078	−	0.642747i	$-0.222205\pi$
$854$	−7.94678	+	45.0684i	−0.271933	+	1.54221i
$855$	−54.3717	+	19.7897i	−1.85947	+	0.676793i
$856$	−13.4682	−	11.3011i	−0.460333	−	0.386265i
$857$	9.87888			0.337456			0.168728	−	0.985663i	$-0.446034\pi$
$857$	9.87888			0.337456			0.168728	+	0.985663i	$0.446034\pi$
$858$	−0.900940	−	0.755978i	−0.0307576	−	0.0258087i
$859$	14.5898	+	25.2703i	0.497798	+	0.862211i	0.999997	−	0.00254115i	$-0.000808874\pi$
$859$	14.5898	+	25.2703i	0.497798	+	0.862211i	−0.502199	+	0.864752i	$0.667476\pi$
$860$	−5.80510	−	2.11288i	−0.197952	−	0.0720487i
$861$	−3.06462	+	5.30807i	−0.104442	+	0.180899i
$862$	−8.59462	−	14.8863i	−0.292734	−	0.507030i
$863$	−0.797078	−	4.52045i	−0.0271329	−	0.153878i	0.968231	−	0.250056i	$-0.0804492\pi$
$863$	−0.797078	−	4.52045i	−0.0271329	−	0.153878i	−0.995364	+	0.0961784i	$0.969338\pi$
$864$	14.4547	−	5.26109i	0.491760	−	0.178986i
$865$	−12.0534	+	20.8771i	−0.409827	+	0.709842i
$866$	−3.61109	+	3.03007i	−0.122710	+	0.102966i
$867$	30.4418	−	25.5437i	1.03386	−	0.867509i
$868$	11.6440	+	4.23807i	0.395223	+	0.143849i
$869$	3.59431	−	20.3843i	0.121928	−	0.691491i
$870$	0.653785	−	3.70780i	0.0221654	−	0.125706i
$871$	0.339112	+	0.123427i	0.0114904	+	0.00418215i
$872$	−12.9179	+	10.8394i	−0.437454	+	0.367068i
$873$	12.5732	−	10.5502i	0.425539	−	0.357070i
$874$	27.7412	−	48.0491i	0.938358	−	1.62528i
$875$	−3.50971	+	1.27743i	−0.118650	+	0.0431850i
$876$	8.45787	+	47.9669i	0.285765	+	1.62065i
$877$	12.7066	+	22.0085i	0.429073	+	0.743176i	0.996791	−	0.0800472i	$-0.0255071\pi$
$877$	12.7066	+	22.0085i	0.429073	+	0.743176i	−0.567718	+	0.823223i	$0.692174\pi$
$878$	−8.21700	+	14.2323i	−0.277310	+	0.480316i
$879$	−32.7971	−	11.9372i	−1.10622	−	0.402631i
$880$	1.39558	+	2.41722i	0.0470450	+	0.0814844i
$881$	−23.8657	−	20.0257i	−0.804056	−	0.674683i	0.145125	−	0.989413i	$-0.453642\pi$
$881$	−23.8657	−	20.0257i	−0.804056	−	0.674683i	−0.949181	+	0.314730i	$0.898086\pi$
$882$	53.5288			1.80241
$883$	26.6265	+	22.3423i	0.896052	+	0.751877i	0.969415	−	0.245428i	$-0.0789286\pi$
$883$	26.6265	+	22.3423i	0.896052	+	0.751877i	−0.0733625	+	0.997305i	$0.523373\pi$
$884$	−0.266623	+	0.0970427i	−0.00896749	+	0.00326390i
$885$	2.87321	−	16.2948i	0.0965819	−	0.547743i
$886$	5.54340	+	31.4382i	0.186234	+	1.05619i
$887$	−5.42756			−0.182240			−0.0911199	−	0.995840i	$-0.529045\pi$
$887$	−5.42756			−0.182240			−0.0911199	+	0.995840i	$0.529045\pi$
$888$	−19.2735	+	4.95085i	−0.646775	+	0.166140i
$889$	16.4374			0.551292
$890$	−2.46034	−	13.9533i	−0.0824709	−	0.467716i
$891$	−13.1909	+	74.8096i	−0.441913	+	2.50622i
$892$	−2.38263	+	0.867205i	−0.0797762	+	0.0290362i
$893$	27.6828	+	23.2286i	0.926369	+	0.777316i
$894$	48.4768			1.62131
$895$	12.2398	+	10.2704i	0.409132	+	0.343302i
$896$	−1.86748	−	3.23457i	−0.0623881	−	0.108059i
$897$	2.92427	+	1.06435i	0.0976386	+	0.0355376i
$898$	17.1139	−	29.6421i	0.571098	−	0.989170i
$899$	−1.90911	−	3.30668i	−0.0636724	−	0.110284i
$900$	1.33745	+	7.58507i	0.0445817	+	0.252836i
$901$	−1.53838	+	0.559923i	−0.0512508	+	0.0186537i
$902$	−0.700070	+	1.21256i	−0.0233098	+	0.0403737i
$903$	−57.8226	+	48.5189i	−1.92421	+	1.61461i
$904$	8.45561	−	7.09510i	0.281229	−	0.235979i
$905$	−12.7405	−	4.63716i	−0.423508	−	0.154144i
$906$	−4.41796	+	25.0555i	−0.146777	+	0.832413i
$907$	2.97072	−	16.8478i	0.0986411	−	0.559421i	−0.894930	−	0.446207i	$-0.852774\pi$
$907$	2.97072	−	16.8478i	0.0986411	−	0.559421i	0.993571	−	0.113214i	$-0.0361145\pi$
$908$	7.95214	+	2.89434i	0.263901	+	0.0960522i
$909$	−86.5342	+	72.6108i	−2.87016	+	2.40835i
$910$	−0.368521	+	0.309226i	−0.0122164	+	0.0102507i
$911$	13.7956	−	23.8947i	0.457069	−	0.791667i	−0.541736	−	0.840549i	$-0.682233\pi$
$911$	13.7956	−	23.8947i	0.457069	−	0.791667i	0.998805	+	0.0488824i	$0.0155660\pi$
$912$	23.0940	−	8.40553i	0.764719	−	0.278335i
$913$	3.20954	+	18.2022i	0.106220	+	0.602405i
$914$	−15.7344	−	27.2528i	−0.520449	−	0.901444i
$915$	−20.0419	+	34.7136i	−0.662565	+	1.14760i
$916$	−4.05563	−	1.47613i	−0.134002	−	0.0487727i
$917$	−12.8287	−	22.2199i	−0.423640	−	0.733765i
$918$	25.9577	+	21.7811i	0.856732	+	0.718884i
$919$	40.9662			1.35135			0.675676	−	0.737199i	$-0.263852\pi$
$919$	40.9662			1.35135			0.675676	+	0.737199i	$0.263852\pi$
$920$	−5.65756	−	4.74726i	−0.186524	−	0.156512i
$921$	−44.0478	+	16.0321i	−1.45143	+	0.528276i
$922$	1.67404	−	9.49393i	0.0551315	−	0.312666i
$923$	0.373766	+	2.11973i	0.0123027	+	0.0697719i
$924$	34.1040			1.12194
$925$	−0.467332	−	6.06478i	−0.0153658	−	0.199409i
$926$	−24.2652			−0.797404
$927$	8.85108	+	50.1970i	0.290708	+	1.64868i
$928$	−0.199849	+	1.13340i	−0.00656035	+	0.0372056i
$929$	1.28022	−	0.465962i	0.0420027	−	0.0152877i	−0.320933	−	0.947102i	$-0.603997\pi$
$929$	1.28022	−	0.465962i	0.0420027	−	0.0152877i	0.362936	+	0.931814i	$0.381774\pi$
$930$	8.31416	+	6.97641i	0.272632	+	0.228765i
$931$	52.2106			1.71113
$932$	3.89624	+	3.26933i	0.127625	+	0.107091i
$933$	−12.3712	−	21.4276i	−0.405016	−	0.701508i
$934$	−26.1489	−	9.51743i	−0.855619	−	0.311420i
$935$	−3.07428	+	5.32481i	−0.100540	+	0.174140i
$936$	0.496022	+	0.859135i	0.0162130	+	0.0280817i
$937$	2.29619	+	13.0224i	0.0750134	+	0.425422i	0.999068	+	0.0431617i	$0.0137431\pi$
$937$	2.29619	+	13.0224i	0.0750134	+	0.425422i	−0.924055	+	0.382260i	$0.875146\pi$
$938$	−9.83346	+	3.57909i	−0.321074	+	0.116861i
$939$	39.1101	−	67.7407i	1.27631	−	2.21063i
$940$	3.68494	−	3.09203i	0.120190	−	0.100851i
$941$	7.44963	−	6.25098i	0.242851	−	0.203776i	−0.513236	−	0.858248i	$-0.671553\pi$
$941$	7.44963	−	6.25098i	0.242851	−	0.203776i	0.756087	+	0.654472i	$0.227109\pi$
$942$	−22.3955	−	8.15131i	−0.729686	−	0.265584i
$943$	0.643327	−	3.64849i	0.0209496	−	0.118811i
$944$	−0.878280	+	4.98097i	−0.0285856	+	0.162117i
$945$	53.9878	+	19.6499i	1.75622	+	0.639213i
$946$	−13.2088	+	11.0835i	−0.429455	+	0.360355i
$947$	−4.60991	+	3.86817i	−0.149802	+	0.125699i	−0.714609	−	0.699525i	$-0.753395\pi$
$947$	−4.60991	+	3.86817i	−0.149802	+	0.125699i	0.564807	+	0.825223i	$0.308951\pi$
$948$	−12.1301	+	21.0099i	−0.393967	+	0.682371i
$949$	−1.80204	+	0.655890i	−0.0584968	+	0.0212911i
$950$	1.30452	+	7.39828i	0.0423241	+	0.240032i
$951$	11.4456	+	19.8244i	0.371150	+	0.642850i
$952$	4.11381	−	7.12533i	0.133329	−	0.230933i
$953$	−7.09932	−	2.58394i	−0.229970	−	0.0837021i	0.224465	−	0.974482i	$-0.427937\pi$
$953$	−7.09932	−	2.58394i	−0.229970	−	0.0837021i	−0.454435	+	0.890780i	$0.650159\pi$
$954$	2.86198	+	4.95709i	0.0926599	+	0.160492i
$955$	10.5719	+	8.87087i	0.342098	+	0.287055i
$956$	−12.4425			−0.402419
$957$	−8.05015	−	6.75488i	−0.260224	−	0.218354i
$958$	14.6951	−	5.34858i	0.474777	−	0.172805i
$959$	0.172796	−	0.979972i	0.00557986	−	0.0316450i
$960$	−0.568073	−	3.22170i	−0.0183345	−	0.103980i
$961$	−19.9932			−0.644942
$962$	−0.323734	−	0.713460i	−0.0104376	−	0.0230029i
$963$	−135.414			−4.36364
$964$	−5.05256	−	28.6545i	−0.162732	−	0.922899i
$965$	1.22869	−	6.96826i	0.0395530	−	0.224316i
$966$	−84.7971	+	30.8636i	−2.72830	+	0.993020i
$967$	38.5818	+	32.3740i	1.24071	+	1.04108i	0.997468	+	0.0711104i	$0.0226543\pi$
$967$	38.5818	+	32.3740i	1.24071	+	1.04108i	0.243239	+	0.969966i	$0.421790\pi$
$968$	−3.20941			−0.103154
$969$	41.4721	+	34.7992i	1.33228	+	1.11791i
$970$	−1.06550	−	1.84551i	−0.0342112	−	0.0592556i
$971$	−8.90771	−	3.24214i	−0.285862	−	0.104045i	0.195109	−	0.980781i	$-0.437494\pi$
$971$	−8.90771	−	3.24214i	−0.285862	−	0.104045i	−0.480972	+	0.876736i	$0.659716\pi$
$972$	21.4433	−	37.1409i	0.687794	−	1.19129i
$973$	−17.4230	−	30.1776i	−0.558557	−	0.967450i
$974$	3.88903	+	22.0558i	0.124613	+	0.706713i
$975$	−0.395952	+	0.144115i	−0.0126806	+	0.00461537i
$976$	6.12640	−	10.6112i	0.196101	−	0.339657i
$977$	−40.4013	+	33.9008i	−1.29255	+	1.08458i	−0.301173	+	0.953570i	$0.597378\pi$
$977$	−40.4013	+	33.9008i	−1.29255	+	1.08458i	−0.991381	+	0.131012i	$0.958177\pi$
$978$	−26.3264	+	22.0905i	−0.841827	+	0.706377i
$979$	−37.1618	−	13.5258i	−1.18770	−	0.432286i
$980$	1.20684	−	6.84433i	0.0385511	−	0.218634i
$981$	−22.5536	+	127.908i	−0.720080	+	4.08378i
$982$	19.3993	+	7.06075i	0.619055	+	0.225318i
$983$	−5.34815	+	4.48763i	−0.170580	+	0.143133i	−0.724081	−	0.689715i	$-0.757736\pi$
$983$	−5.34815	+	4.48763i	−0.170580	+	0.143133i	0.553501	+	0.832848i	$0.313291\pi$
$984$	1.25711	−	1.05484i	0.0400753	−	0.0336272i
$985$	7.56522	−	13.1033i	0.241048	−	0.417507i
$986$	−2.38235	+	0.867104i	−0.0758694	+	0.0276142i
$987$	−10.2063	−	57.8826i	−0.324869	−	1.84242i
$988$	0.483807	+	0.837978i	0.0153919	+	0.0266596i
$989$	22.8123	−	39.5121i	0.725389	−	1.25641i
$990$	20.2013	+	7.35266i	0.642039	+	0.233683i
$991$	1.59502	+	2.76266i	0.0506675	+	0.0877587i	0.890247	−	0.455478i	$-0.150532\pi$
$991$	1.59502	+	2.76266i	0.0506675	+	0.0877587i	−0.839579	+	0.543237i	$0.817198\pi$
$992$	−2.54147	−	2.13254i	−0.0806916	−	0.0677083i
$993$	15.3714			0.487796
$994$	−47.8131	−	40.1200i	−1.51654	−	1.27253i
$995$	0.659218	−	0.239936i	0.0208986	−	0.00760647i
$996$	3.76176	−	21.3340i	0.119196	−	0.675994i
$997$	−2.85660	−	16.2006i	−0.0904695	−	0.513078i	−0.996042	−	0.0888861i	$-0.971669\pi$
$997$	−2.85660	−	16.2006i	−0.0904695	−	0.513078i	0.905572	−	0.424192i	$-0.139442\pi$
$998$	−13.7907			−0.436537
$999$	−54.4594	+	76.0858i	−1.72302	+	2.40725i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	370.2.o.a.231.1	yes	18
37.33	even	9	inner	370.2.o.a.181.1	✓	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.o.a.181.1	✓	18	37.33	even	9	inner
370.2.o.a.231.1	yes	18	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:	\( N \)	\(=\)	\( 370 = 2 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	370.o (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.173648 + 0.984808i) q^{2} +(-0.568073 + 3.22170i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(0.766044 + 0.642788i) q^{5} -3.27140 q^{6} +(2.86114 + 2.40078i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-7.23759 - 2.63427i) q^{9} +O(q^{10})\)	\(q+(0.173648 + 0.984808i) q^{2} +(-0.568073 + 3.22170i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(0.766044 + 0.642788i) q^{5} -3.27140 q^{6} +(2.86114 + 2.40078i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-7.23759 - 2.63427i) q^{9} +(-0.500000 + 0.866025i) q^{10} +(1.39558 + 2.41722i) q^{11} +(-0.568073 - 3.22170i) q^{12} +(0.121034 - 0.0440529i) q^{13} +(-1.86748 + 3.23457i) q^{14} +(-2.50604 + 2.10282i) q^{15} +(0.766044 - 0.642788i) q^{16} +(2.07002 + 0.753426i) q^{17} +(1.33745 - 7.58507i) q^{18} +(1.30452 - 7.39828i) q^{19} +(-0.939693 - 0.342020i) q^{20} +(-9.35995 + 7.85393i) q^{21} +(-2.13815 + 1.79412i) q^{22} +(3.69271 - 6.39596i) q^{23} +(3.07411 - 1.11889i) q^{24} +(0.173648 + 0.984808i) q^{25} +(0.0644010 + 0.111546i) q^{26} +(7.69120 - 13.3215i) q^{27} +(-3.50971 - 1.27743i) q^{28} +(0.575441 + 0.996693i) q^{29} +(-2.50604 - 2.10282i) q^{30} -3.31765 q^{31} +(0.766044 + 0.642788i) q^{32} +(-8.58035 + 3.12299i) q^{33} +(-0.382524 + 2.16940i) q^{34} +(0.648569 + 3.67822i) q^{35} +7.70208 q^{36} +(-6.05380 - 0.592906i) q^{37} +7.51241 q^{38} +(0.0731690 + 0.414962i) q^{39} +(0.173648 - 0.984808i) q^{40} +(0.471381 - 0.171569i) q^{41} +(-9.35995 - 7.85393i) q^{42} +6.17766 q^{43} +(-2.13815 - 1.79412i) q^{44} +(-3.85104 - 6.67020i) q^{45} +(6.94003 + 2.52596i) q^{46} +(-2.40517 + 4.16588i) q^{47} +(1.63570 + 2.83312i) q^{48} +(1.20684 + 6.84433i) q^{49} +(-0.939693 + 0.342020i) q^{50} +(-3.60324 + 6.24099i) q^{51} +(-0.0986681 + 0.0827923i) q^{52} +(-0.569301 + 0.477700i) q^{53} +(14.4547 + 5.26109i) q^{54} +(-0.484680 + 2.74876i) q^{55} +(0.648569 - 3.67822i) q^{56} +(23.0940 + 8.40553i) q^{57} +(-0.881627 + 0.739773i) q^{58} +(-3.87451 + 3.25110i) q^{59} +(1.63570 - 2.83312i) q^{60} +(11.5139 - 4.19070i) q^{61} +(-0.576104 - 3.26725i) q^{62} +(-14.3835 - 24.9129i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(0.121034 + 0.0440529i) q^{65} +(-4.56551 - 7.90769i) q^{66} +(2.14629 + 1.80095i) q^{67} -2.20287 q^{68} +(18.5082 + 15.5302i) q^{69} +(-3.50971 + 1.27743i) q^{70} +(-2.90187 + 16.4573i) q^{71} +(1.33745 + 7.58507i) q^{72} -14.8887 q^{73} +(-0.467332 - 6.06478i) q^{74} -3.27140 q^{75} +(1.30452 + 7.39828i) q^{76} +(-1.81026 + 10.2665i) q^{77} +(-0.395952 + 0.144115i) q^{78} +(-5.68086 - 4.76680i) q^{79} +1.00000 q^{80} +(20.8485 + 17.4940i) q^{81} +(0.250817 + 0.434427i) q^{82} +(6.22262 + 2.26485i) q^{83} +(6.10928 - 10.5816i) q^{84} +(1.10143 + 1.90774i) q^{85} +(1.07274 + 6.08380i) q^{86} +(-3.53794 + 1.28771i) q^{87} +(1.39558 - 2.41722i) q^{88} +(-10.8537 + 9.10737i) q^{89} +(5.90013 - 4.95080i) q^{90} +(0.452058 + 0.164536i) q^{91} +(-1.28247 + 7.27322i) q^{92} +(1.88467 - 10.6885i) q^{93} +(-4.52025 - 1.64524i) q^{94} +(5.75484 - 4.82888i) q^{95} +(-2.50604 + 2.10282i) q^{96} +(-1.06550 + 1.84551i) q^{97} +(-6.53078 + 2.37701i) q^{98} +(-3.73305 - 21.1712i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 6 q^{6} - 3 q^{7} - 9 q^{8} - 12 q^{9}+O(q^{10}) \) 18 * q - 6 * q^6 - 3 * q^7 - 9 * q^8 - 12 * q^9	\( 18 q - 6 q^{6} - 3 q^{7} - 9 q^{8} - 12 q^{9} - 9 q^{10} + 3 q^{11} + 9 q^{13} - 6 q^{17} + 6 q^{18} + 9 q^{19} - 6 q^{21} + 21 q^{23} + 6 q^{26} + 12 q^{27} - 3 q^{28} + 6 q^{29} - 30 q^{31} - 45 q^{33} - 15 q^{34} + 6 q^{35} + 24 q^{36} + 6 q^{37} - 12 q^{38} + 24 q^{39} + 15 q^{41} - 6 q^{42} - 12 q^{43} - 12 q^{45} + 24 q^{47} + 3 q^{48} + 33 q^{49} - 42 q^{51} - 12 q^{53} + 27 q^{54} + 6 q^{56} + 51 q^{57} - 15 q^{58} - 15 q^{59} + 3 q^{60} + 72 q^{61} - 57 q^{62} - 30 q^{63} - 9 q^{64} + 9 q^{65} - 3 q^{66} + 18 q^{67} + 24 q^{69} - 3 q^{70} + 6 q^{72} - 66 q^{73} - 24 q^{74} - 6 q^{75} + 9 q^{76} - 66 q^{77} + 6 q^{78} - 12 q^{79} + 18 q^{80} + 66 q^{81} + 45 q^{82} + 9 q^{83} + 42 q^{84} + 12 q^{86} + 48 q^{87} + 3 q^{88} + 6 q^{90} - 78 q^{91} + 18 q^{92} + 24 q^{94} - 3 q^{97} - 48 q^{98} - 96 q^{99}+O(q^{100}) \) 18 * q - 6 * q^6 - 3 * q^7 - 9 * q^8 - 12 * q^9 - 9 * q^10 + 3 * q^11 + 9 * q^13 - 6 * q^17 + 6 * q^18 + 9 * q^19 - 6 * q^21 + 21 * q^23 + 6 * q^26 + 12 * q^27 - 3 * q^28 + 6 * q^29 - 30 * q^31 - 45 * q^33 - 15 * q^34 + 6 * q^35 + 24 * q^36 + 6 * q^37 - 12 * q^38 + 24 * q^39 + 15 * q^41 - 6 * q^42 - 12 * q^43 - 12 * q^45 + 24 * q^47 + 3 * q^48 + 33 * q^49 - 42 * q^51 - 12 * q^53 + 27 * q^54 + 6 * q^56 + 51 * q^57 - 15 * q^58 - 15 * q^59 + 3 * q^60 + 72 * q^61 - 57 * q^62 - 30 * q^63 - 9 * q^64 + 9 * q^65 - 3 * q^66 + 18 * q^67 + 24 * q^69 - 3 * q^70 + 6 * q^72 - 66 * q^73 - 24 * q^74 - 6 * q^75 + 9 * q^76 - 66 * q^77 + 6 * q^78 - 12 * q^79 + 18 * q^80 + 66 * q^81 + 45 * q^82 + 9 * q^83 + 42 * q^84 + 12 * q^86 + 48 * q^87 + 3 * q^88 + 6 * q^90 - 78 * q^91 + 18 * q^92 + 24 * q^94 - 3 * q^97 - 48 * q^98 - 96 * q^99

Introduction

L-functions

Modular forms

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