LMFDB - Embedded newform 98.2.e.b.71.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [98,2,Mod(15,98)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(98, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([10]))

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

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

chi := DirichletCharacter("98.15");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 98 = 2 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	98.e (of order $7$, 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:	$0.782533939809$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{7})$
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} + 37 x^{16} + 557 x^{14} + 4495 x^{12} + 21331 x^{10} + 60904 x^{8} + 101893 x^{6} + 91665 x^{4} + \cdots + 5103 $ x^18 + 37x^16 + 557x^14 + 4495x^12 + 21331x^10 + 60904x^8 + 101893x^6 + 91665x^4 + 36855x^2 + 5103
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			71.1
Root			$1.45077i$ of defining polynomial
Character	$\chi$	$=$	98.71
Dual form			98.2.e.b.29.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.900969 - 0.433884i) q^{2} +(-0.581491 + 2.54768i) q^{3} +(0.623490 - 0.781831i) q^{4} +(-0.504793 + 2.21164i) q^{5} +(0.581491 + 2.54768i) q^{6} +(-0.541999 - 2.58964i) q^{7} +(0.222521 - 0.974928i) q^{8} +(-3.44963 - 1.66125i) q^{9} +O(q^{10})$	\(q+(0.900969 - 0.433884i) q^{2} +(-0.581491 + 2.54768i) q^{3} +(0.623490 - 0.781831i) q^{4} +(-0.504793 + 2.21164i) q^{5} +(0.581491 + 2.54768i) q^{6} +(-0.541999 - 2.58964i) q^{7} +(0.222521 - 0.974928i) q^{8} +(-3.44963 - 1.66125i) q^{9} +(0.504793 + 2.21164i) q^{10} +(2.04387 - 0.984274i) q^{11} +(1.62930 + 2.04308i) q^{12} +(5.56864 - 2.68171i) q^{13} +(-1.61193 - 2.09802i) q^{14} +(-5.34103 - 2.57210i) q^{15} +(-0.222521 - 0.974928i) q^{16} +(-1.64372 - 2.06116i) q^{17} -3.82880 q^{18} -6.41513 q^{19} +(1.41440 + 1.77360i) q^{20} +(6.91274 + 0.125014i) q^{21} +(1.41440 - 1.77360i) q^{22} +(-3.11625 + 3.90766i) q^{23} +(2.35441 + 1.13382i) q^{24} +(-0.131708 - 0.0634274i) q^{25} +(3.85362 - 4.83228i) q^{26} +(1.35036 - 1.69330i) q^{27} +(-2.36259 - 1.19086i) q^{28} +(2.53592 + 3.17994i) q^{29} -5.92809 q^{30} -5.82721 q^{31} +(-0.623490 - 0.781831i) q^{32} +(1.31912 + 5.77946i) q^{33} +(-2.37524 - 1.14386i) q^{34} +(6.00096 + 0.108525i) q^{35} +(-3.44963 + 1.66125i) q^{36} +(-1.54059 - 1.93184i) q^{37} +(-5.77984 + 2.78342i) q^{38} +(3.59403 + 15.7465i) q^{39} +(2.04387 + 0.984274i) q^{40} +(0.0937760 - 0.410859i) q^{41} +(6.28240 - 2.88669i) q^{42} +(-1.93075 - 8.45917i) q^{43} +(0.504793 - 2.21164i) q^{44} +(5.41545 - 6.79076i) q^{45} +(-1.11218 + 4.87277i) q^{46} +(7.96296 - 3.83476i) q^{47} +2.61320 q^{48} +(-6.41247 + 2.80716i) q^{49} -0.146185 q^{50} +(6.20698 - 2.98913i) q^{51} +(1.37534 - 6.02576i) q^{52} +(0.276316 - 0.346490i) q^{53} +(0.481939 - 2.11151i) q^{54} +(1.14513 + 5.01716i) q^{55} +(-2.64532 - 0.0478395i) q^{56} +(3.73034 - 16.3437i) q^{57} +(3.66451 + 1.76473i) q^{58} +(0.798122 + 3.49680i) q^{59} +(-5.34103 + 2.57210i) q^{60} +(5.86420 + 7.35348i) q^{61} +(-5.25014 + 2.52833i) q^{62} +(-2.43235 + 9.83369i) q^{63} +(-0.900969 - 0.433884i) q^{64} +(3.11999 + 13.6696i) q^{65} +(3.69610 + 4.63477i) q^{66} +0.372255 q^{67} -2.63632 q^{68} +(-8.14339 - 10.2115i) q^{69} +(5.45377 - 2.50594i) q^{70} +(-8.51015 + 10.6714i) q^{71} +(-2.38722 + 2.99348i) q^{72} +(-9.54481 - 4.59654i) q^{73} +(-2.22622 - 1.07209i) q^{74} +(0.238180 - 0.298668i) q^{75} +(-3.99977 + 5.01555i) q^{76} +(-3.65669 - 4.75940i) q^{77} +(10.0703 + 12.6277i) q^{78} +7.15395 q^{79} +2.26852 q^{80} +(-3.63289 - 4.55549i) q^{81} +(-0.0937760 - 0.410859i) q^{82} +(4.26774 + 2.05523i) q^{83} +(4.40776 - 5.32665i) q^{84} +(5.38829 - 2.59486i) q^{85} +(-5.40984 - 6.78373i) q^{86} +(-9.57609 + 4.61160i) q^{87} +(-0.504793 - 2.21164i) q^{88} +(-2.30119 - 1.10820i) q^{89} +(1.93275 - 8.46794i) q^{90} +(-9.96287 - 12.9673i) q^{91} +(1.11218 + 4.87277i) q^{92} +(3.38847 - 14.8459i) q^{93} +(5.51054 - 6.91000i) q^{94} +(3.23832 - 14.1880i) q^{95} +(2.35441 - 1.13382i) q^{96} +0.652366 q^{97} +(-4.55946 + 5.31144i) q^{98} -8.68571 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 3 q^{2} - 5 q^{3} - 3 q^{4} + 5 q^{6} - q^{7} + 3 q^{8} - 10 q^{9}+O(q^{10}) $ 18 * q + 3 * q^2 - 5 * q^3 - 3 * q^4 + 5 * q^6 - q^7 + 3 * q^8 - 10 * q^9	\( 18 q + 3 q^{2} - 5 q^{3} - 3 q^{4} + 5 q^{6} - q^{7} + 3 q^{8} - 10 q^{9} + 7 q^{11} + 2 q^{12} - 10 q^{13} + q^{14} + 7 q^{15} - 3 q^{16} + q^{17} - 32 q^{18} - 44 q^{19} + 7 q^{20} - 5 q^{21} + 7 q^{22} + 21 q^{23} - 2 q^{24} + q^{25} + 3 q^{26} + 10 q^{27} - 8 q^{28} + 11 q^{29} - 24 q^{31} + 3 q^{32} - 14 q^{33} - q^{34} - 21 q^{35} - 10 q^{36} - 13 q^{37} - 19 q^{38} - 3 q^{39} + 7 q^{40} + 8 q^{41} + 61 q^{42} - 24 q^{43} + 98 q^{45} + 21 q^{46} + 40 q^{47} + 2 q^{48} - 43 q^{49} - 50 q^{50} + 36 q^{51} + 18 q^{52} + 10 q^{53} + 4 q^{54} + 49 q^{55} + q^{56} + 19 q^{57} + 24 q^{58} + 13 q^{59} + 7 q^{60} + 27 q^{61} - 11 q^{62} + 41 q^{63} - 3 q^{64} - 21 q^{66} - 86 q^{67} - 34 q^{68} - 91 q^{69} - 14 q^{70} + 3 q^{72} + 5 q^{73} + 13 q^{74} - 3 q^{75} - 2 q^{76} - 14 q^{77} + 38 q^{78} - 66 q^{79} - 2 q^{81} - 8 q^{82} + 55 q^{83} + 23 q^{84} - 49 q^{85} - 18 q^{86} - 110 q^{87} + 62 q^{89} + 21 q^{90} + 39 q^{91} - 21 q^{92} + 46 q^{93} + 23 q^{94} - 7 q^{95} - 2 q^{96} - 32 q^{97} - 48 q^{98} + 14 q^{99}+O(q^{100}) \) 18 * q + 3 * q^2 - 5 * q^3 - 3 * q^4 + 5 * q^6 - q^7 + 3 * q^8 - 10 * q^9 + 7 * q^11 + 2 * q^12 - 10 * q^13 + q^14 + 7 * q^15 - 3 * q^16 + q^17 - 32 * q^18 - 44 * q^19 + 7 * q^20 - 5 * q^21 + 7 * q^22 + 21 * q^23 - 2 * q^24 + q^25 + 3 * q^26 + 10 * q^27 - 8 * q^28 + 11 * q^29 - 24 * q^31 + 3 * q^32 - 14 * q^33 - q^34 - 21 * q^35 - 10 * q^36 - 13 * q^37 - 19 * q^38 - 3 * q^39 + 7 * q^40 + 8 * q^41 + 61 * q^42 - 24 * q^43 + 98 * q^45 + 21 * q^46 + 40 * q^47 + 2 * q^48 - 43 * q^49 - 50 * q^50 + 36 * q^51 + 18 * q^52 + 10 * q^53 + 4 * q^54 + 49 * q^55 + q^56 + 19 * q^57 + 24 * q^58 + 13 * q^59 + 7 * q^60 + 27 * q^61 - 11 * q^62 + 41 * q^63 - 3 * q^64 - 21 * q^66 - 86 * q^67 - 34 * q^68 - 91 * q^69 - 14 * q^70 + 3 * q^72 + 5 * q^73 + 13 * q^74 - 3 * q^75 - 2 * q^76 - 14 * q^77 + 38 * q^78 - 66 * q^79 - 2 * q^81 - 8 * q^82 + 55 * q^83 + 23 * q^84 - 49 * q^85 - 18 * q^86 - 110 * q^87 + 62 * q^89 + 21 * q^90 + 39 * q^91 - 21 * q^92 + 46 * q^93 + 23 * q^94 - 7 * q^95 - 2 * q^96 - 32 * q^97 - 48 * q^98 + 14 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$3$
$\chi(n)$	$e\left(\frac{4}{7}\right)$

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 $

$2$	0.900969	−	0.433884i	0.637081	−	0.306802i
$2$	0.900969	−	0.433884i	0.637081	−	0.306802i
$3$	−0.581491	+	2.54768i	−0.335724	+	1.47090i	0.472134	+	0.881527i	$0.343484\pi$
$3$	−0.581491	+	2.54768i	−0.335724	+	1.47090i	−0.807859	+	0.589376i	$0.799373\pi$
$4$	0.623490	−	0.781831i	0.311745	−	0.390916i
$5$	−0.504793	+	2.21164i	−0.225750	+	0.989077i	0.727313	+	0.686306i	$0.240769\pi$
$5$	−0.504793	+	2.21164i	−0.225750	+	0.989077i	−0.953063	+	0.302771i	$0.902088\pi$
$6$	0.581491	+	2.54768i	0.237393	+	1.04009i
$7$	−0.541999	−	2.58964i	−0.204856	−	0.978792i
$7$	−0.541999	−	2.58964i	−0.204856	−	0.978792i
$8$	0.222521	−	0.974928i	0.0786730	−	0.344689i
$9$	−3.44963	−	1.66125i	−1.14988	−	0.553751i
$10$	0.504793	+	2.21164i	0.159630	+	0.699383i
$11$	2.04387	−	0.984274i	0.616249	−	0.296770i	−0.0995973	−	0.995028i	$-0.531755\pi$
$11$	2.04387	−	0.984274i	0.616249	−	0.296770i	0.715846	+	0.698258i	$0.246041\pi$
$12$	1.62930	+	2.04308i	0.470339	+	0.589786i
$13$	5.56864	−	2.68171i	1.54446	−	0.743774i	0.548724	−	0.836003i	$-0.315114\pi$
$13$	5.56864	−	2.68171i	1.54446	−	0.743774i	0.995738	+	0.0922296i	$0.0293994\pi$
$14$	−1.61193	−	2.09802i	−0.430806	−	0.560720i
$15$	−5.34103	−	2.57210i	−1.37905	−	0.664114i
$16$	−0.222521	−	0.974928i	−0.0556302	−	0.243732i
$17$	−1.64372	−	2.06116i	−0.398661	−	0.499905i	0.541469	−	0.840720i	$-0.317868\pi$
$17$	−1.64372	−	2.06116i	−0.398661	−	0.499905i	−0.940130	+	0.340816i	$0.889297\pi$
$18$	−3.82880			−0.902457
$19$	−6.41513			−1.47173			−0.735866	−	0.677127i	$-0.763225\pi$
$19$	−6.41513			−1.47173			−0.735866	+	0.677127i	$0.763225\pi$
$20$	1.41440	+	1.77360i	0.316269	+	0.396589i
$21$	6.91274	+	0.125014i	1.50848	+	0.0272803i
$22$	1.41440	−	1.77360i	0.301551	−	0.378133i
$23$	−3.11625	+	3.90766i	−0.649784	+	0.814803i	−0.992188	−	0.124749i	$-0.960187\pi$
$23$	−3.11625	+	3.90766i	−0.649784	+	0.814803i	0.342404	+	0.939553i	$0.388759\pi$
$24$	2.35441	+	1.13382i	0.480592	+	0.231441i
$25$	−0.131708	−	0.0634274i	−0.0263417	−	0.0126855i
$26$	3.85362	−	4.83228i	0.755756	−	0.947689i
$27$	1.35036	−	1.69330i	0.259878	−	0.325876i
$28$	−2.36259	−	1.19086i	−0.446488	−	0.225052i
$29$	2.53592	+	3.17994i	0.470908	+	0.590501i	0.959393	−	0.282072i	$-0.0910217\pi$
$29$	2.53592	+	3.17994i	0.470908	+	0.590501i	−0.488485	+	0.872572i	$0.662450\pi$
$30$	−5.92809			−1.08232
$31$	−5.82721			−1.04660			−0.523299	−	0.852149i	$-0.675299\pi$
$31$	−5.82721			−1.04660			−0.523299	+	0.852149i	$0.675299\pi$
$32$	−0.623490	−	0.781831i	−0.110218	−	0.138210i
$33$	1.31912	+	5.77946i	0.229630	+	1.00608i
$34$	−2.37524	−	1.14386i	−0.407351	−	0.196170i
$35$	6.00096	+	0.108525i	1.01435	+	0.0183440i
$36$	−3.44963	+	1.66125i	−0.574938	+	0.276876i
$37$	−1.54059	−	1.93184i	−0.253272	−	0.317593i	0.638899	−	0.769290i	$-0.279390\pi$
$37$	−1.54059	−	1.93184i	−0.253272	−	0.317593i	−0.892171	+	0.451698i	$0.850819\pi$
$38$	−5.77984	+	2.78342i	−0.937613	+	0.451531i
$39$	3.59403	+	15.7465i	0.575506	+	2.52146i
$40$	2.04387	+	0.984274i	0.323164	+	0.155627i
$41$	0.0937760	−	0.410859i	0.0146453	−	0.0641654i	−0.967077	−	0.254483i	$-0.918095\pi$
$41$	0.0937760	−	0.410859i	0.0146453	−	0.0641654i	0.981723	+	0.190318i	$0.0609518\pi$
$42$	6.28240	−	2.88669i	0.969396	−	0.445426i
$43$	−1.93075	−	8.45917i	−0.294437	−	1.29001i	−0.878280	−	0.478146i	$-0.841309\pi$
$43$	−1.93075	−	8.45917i	−0.294437	−	1.29001i	0.583844	−	0.811866i	$-0.301548\pi$
$44$	0.504793	−	2.21164i	0.0761005	−	0.333418i
$45$	5.41545	−	6.79076i	0.807288	−	1.01231i
$46$	−1.11218	+	4.87277i	−0.163982	+	0.718451i
$47$	7.96296	−	3.83476i	1.16152	−	0.559357i	0.249044	−	0.968492i	$-0.419884\pi$
$47$	7.96296	−	3.83476i	1.16152	−	0.559357i	0.912474	+	0.409135i	$0.134169\pi$
$48$	2.61320			0.377183
$49$	−6.41247	+	2.80716i	−0.916068	+	0.401023i
$50$	−0.146185			−0.0206737
$51$	6.20698	−	2.98913i	0.869151	−	0.418561i
$52$	1.37534	−	6.02576i	0.190725	−	0.835622i
$53$	0.276316	−	0.346490i	0.0379550	−	0.0475940i	−0.762492	−	0.646998i	$-0.776024\pi$
$53$	0.276316	−	0.346490i	0.0379550	−	0.0475940i	0.800447	+	0.599404i	$0.204596\pi$
$54$	0.481939	−	2.11151i	0.0655836	−	0.287341i
$55$	1.14513	+	5.01716i	0.154410	+	0.676514i
$56$	−2.64532	−	0.0478395i	−0.353496	−	0.00639282i
$57$	3.73034	−	16.3437i	0.494096	−	2.16478i
$58$	3.66451	+	1.76473i	0.481174	+	0.231721i
$59$	0.798122	+	3.49680i	0.103907	+	0.455245i	0.999937	+	0.0112513i	$0.00358148\pi$
$59$	0.798122	+	3.49680i	0.103907	+	0.455245i	−0.896030	+	0.443993i	$0.853561\pi$
$60$	−5.34103	+	2.57210i	−0.689523	+	0.332057i
$61$	5.86420	+	7.35348i	0.750834	+	0.941517i	0.999634	−	0.0270383i	$-0.00860762\pi$
$61$	5.86420	+	7.35348i	0.750834	+	0.941517i	−0.248800	+	0.968555i	$0.580036\pi$
$62$	−5.25014	+	2.52833i	−0.666768	+	0.321099i
$63$	−2.43235	+	9.83369i	−0.306448	+	1.23893i
$64$	−0.900969	−	0.433884i	−0.112621	−	0.0542355i
$65$	3.11999	+	13.6696i	0.386987	+	1.69550i
$66$	3.69610	+	4.63477i	0.454959	+	0.570501i
$67$	0.372255			0.0454782			0.0227391	−	0.999741i	$-0.492761\pi$
$67$	0.372255			0.0454782			0.0227391	+	0.999741i	$0.492761\pi$
$68$	−2.63632			−0.319701
$69$	−8.14339	−	10.2115i	−0.980349	−	1.22932i
$70$	5.45377	−	2.50594i	0.651850	−	0.299517i
$71$	−8.51015	+	10.6714i	−1.00997	+	1.26646i	−0.0464226	+	0.998922i	$0.514782\pi$
$71$	−8.51015	+	10.6714i	−1.00997	+	1.26646i	−0.963547	+	0.267540i	$0.913789\pi$
$72$	−2.38722	+	2.99348i	−0.281336	+	0.352784i
$73$	−9.54481	−	4.59654i	−1.11714	−	0.537984i	−0.218129	−	0.975920i	$-0.569995\pi$
$73$	−9.54481	−	4.59654i	−1.11714	−	0.537984i	−0.899006	+	0.437936i	$0.855710\pi$
$74$	−2.22622	−	1.07209i	−0.258793	−	0.124628i
$75$	0.238180	−	0.298668i	0.0275026	−	0.0344872i
$76$	−3.99977	+	5.01555i	−0.458805	+	0.575324i
$77$	−3.65669	−	4.75940i	−0.416718	−	0.542384i
$78$	10.0703	+	12.6277i	1.14023	+	1.42981i
$79$	7.15395			0.804882			0.402441	−	0.915446i	$-0.368162\pi$
$79$	7.15395			0.804882			0.402441	+	0.915446i	$0.368162\pi$
$80$	2.26852			0.253628
$81$	−3.63289	−	4.55549i	−0.403654	−	0.506166i
$82$	−0.0937760	−	0.410859i	−0.0103558	−	0.0453718i
$83$	4.26774	+	2.05523i	0.468445	+	0.225591i	0.653188	−	0.757196i	$-0.273431\pi$
$83$	4.26774	+	2.05523i	0.468445	+	0.225591i	−0.184743	+	0.982787i	$0.559145\pi$
$84$	4.40776	−	5.32665i	0.480926	−	0.581185i
$85$	5.38829	−	2.59486i	0.584442	−	0.281453i
$86$	−5.40984	−	6.78373i	−0.583359	−	0.731509i
$87$	−9.57609	+	4.61160i	−1.02666	+	0.494415i
$88$	−0.504793	−	2.21164i	−0.0538111	−	0.235762i
$89$	−2.30119	−	1.10820i	−0.243926	−	0.117469i	0.307927	−	0.951410i	$-0.400365\pi$
$89$	−2.30119	−	1.10820i	−0.243926	−	0.117469i	−0.551853	+	0.833941i	$0.686079\pi$
$90$	1.93275	−	8.46794i	0.203730	−	0.892599i
$91$	−9.96287	−	12.9673i	−1.04439	−	1.35934i
$92$	1.11218	+	4.87277i	0.115953	+	0.508022i
$93$	3.38847	−	14.8459i	0.351368	−	1.53944i
$94$	5.51054	−	6.91000i	0.568369	−	0.712712i
$95$	3.23832	−	14.1880i	0.332244	−	1.45566i
$96$	2.35441	−	1.13382i	0.240296	−	0.115720i
$97$	0.652366			0.0662378			0.0331189	−	0.999451i	$-0.489456\pi$
$97$	0.652366			0.0662378			0.0331189	+	0.999451i	$0.489456\pi$
$98$	−4.55946	+	5.31144i	−0.460575	+	0.536536i
$99$	−8.68571			−0.872947
$100$	−0.131708	+	0.0634274i	−0.0131708	+	0.00634274i
$101$	−3.77926	+	16.5580i	−0.376050	+	1.64758i	0.333369	+	0.942797i	$0.391815\pi$
$101$	−3.77926	+	16.5580i	−0.376050	+	1.64758i	−0.709419	+	0.704787i	$0.751043\pi$
$102$	4.29537	−	5.38622i	0.425305	−	0.533315i
$103$	2.70247	−	11.8403i	0.266282	−	1.16666i	−0.648020	−	0.761624i	$-0.724402\pi$
$103$	2.70247	−	11.8403i	0.266282	−	1.16666i	0.914302	−	0.405034i	$-0.132740\pi$
$104$	−1.37534	−	6.02576i	−0.134863	−	0.590874i
$105$	−3.76599	+	15.2254i	−0.367523	+	1.48585i
$106$	0.0986162	−	0.432066i	0.00957845	−	0.0419659i
$107$	−1.04542	−	0.503448i	−0.101065	−	0.0486701i	0.382668	−	0.923886i	$-0.375005\pi$
$107$	−1.04542	−	0.503448i	−0.101065	−	0.0486701i	−0.483733	+	0.875216i	$0.660719\pi$
$108$	−0.481939	−	2.11151i	−0.0463746	−	0.203180i
$109$	3.02973	−	1.45904i	0.290195	−	0.139751i	−0.283123	−	0.959084i	$-0.591370\pi$
$109$	3.02973	−	1.45904i	0.290195	−	0.139751i	0.573318	+	0.819333i	$0.305656\pi$
$110$	3.20859	+	4.02345i	0.305927	+	0.383621i
$111$	5.81755	−	2.80158i	0.552177	−	0.265915i
$112$	−2.40411	+	1.10466i	−0.227167	+	0.104380i
$113$	5.57078	+	2.68275i	0.524055	+	0.252371i	0.677157	−	0.735839i	$-0.263212\pi$
$113$	5.57078	+	2.68275i	0.524055	+	0.252371i	−0.153102	+	0.988210i	$0.548926\pi$
$114$	−3.73034	−	16.3437i	−0.349379	−	1.53073i
$115$	−7.06929	−	8.86461i	−0.659214	−	0.826629i
$116$	4.06730			0.377639
$117$	−23.6647			−2.18781
$118$	2.23629	+	2.80422i	0.205867	+	0.258149i
$119$	−4.44677	+	5.37379i	−0.407635	+	0.492615i
$120$	−3.69610	+	4.63477i	−0.337407	+	0.423095i
$121$	−3.64979	+	4.57670i	−0.331799	+	0.416063i
$122$	8.47402	+	4.08087i	0.767202	+	0.369465i
$123$	0.992208	+	0.477822i	0.0894644	+	0.0430838i
$124$	−3.63321	+	4.55590i	−0.326272	+	0.409132i
$125$	−6.86523	+	8.60873i	−0.614045	+	0.769988i
$126$	2.07520	+	9.91521i	0.184874	+	0.883317i
$127$	12.0103	+	15.0604i	1.06574	+	1.33640i	0.938791	+	0.344486i	$0.111947\pi$
$127$	12.0103	+	15.0604i	1.06574	+	1.33640i	0.126948	+	0.991909i	$0.459482\pi$
$128$	−1.00000			−0.0883883
$129$	22.6740			1.99633
$130$	8.74201	+	10.9621i	0.766725	+	0.961443i
$131$	−1.26908	−	5.56021i	−0.110880	−	0.485798i	−0.999625	−	0.0273951i	$-0.991279\pi$
$131$	−1.26908	−	5.56021i	−0.110880	−	0.485798i	0.888744	−	0.458403i	$-0.151578\pi$
$132$	5.34103	+	2.57210i	0.464877	+	0.223873i
$133$	3.47700	+	16.6129i	0.301494	+	1.44052i
$134$	0.335390	−	0.161515i	0.0289733	−	0.0139528i
$135$	3.06333	+	3.84129i	0.263649	+	0.330606i
$136$	−2.37524	+	1.14386i	−0.203676	+	0.0980850i
$137$	−4.26790	−	18.6989i	−0.364632	−	1.59756i	−0.741278	−	0.671198i	$-0.765780\pi$
$137$	−4.26790	−	18.6989i	−0.364632	−	1.59756i	0.376646	−	0.926357i	$-0.377077\pi$
$138$	−11.7675	−	5.66695i	−1.00172	−	0.482403i
$139$	1.40588	−	6.15956i	0.119245	−	0.522447i	−0.879657	−	0.475608i	$-0.842228\pi$
$139$	1.40588	−	6.15956i	0.119245	−	0.522447i	0.998902	−	0.0468392i	$-0.0149149\pi$
$140$	3.82639	−	4.62408i	0.323389	−	0.390806i
$141$	5.13935	+	22.5170i	0.432811	+	1.89627i
$142$	−3.03724	+	13.3070i	−0.254879	+	1.11670i
$143$	8.74201	−	10.9621i	0.731043	−	0.916700i
$144$	−0.851988	+	3.73280i	−0.0709990	+	0.311067i
$145$	−8.31302	+	4.00334i	−0.690358	+	0.332459i
$146$	−10.5939			−0.876761
$147$	−3.42295	−	17.9693i	−0.282321	−	1.48208i
$148$	−2.47092			−0.203108
$149$	11.3390	−	5.46057i	0.928927	−	0.447347i	0.0926768	−	0.995696i	$-0.470458\pi$
$149$	11.3390	−	5.46057i	0.928927	−	0.447347i	0.836250	+	0.548349i	$0.184743\pi$
$150$	0.0850054	−	0.372433i	0.00694066	−	0.0304090i
$151$	3.48647	−	4.37189i	0.283725	−	0.355779i	−0.619463	−	0.785026i	$-0.712649\pi$
$151$	3.48647	−	4.37189i	0.283725	−	0.355779i	0.903187	+	0.429247i	$0.141221\pi$
$152$	−1.42750	+	6.25429i	−0.115786	+	0.507290i
$153$	2.24612	+	9.84087i	0.181588	+	0.795587i
$154$	−5.35959	−	2.70150i	−0.431888	−	0.217693i
$155$	2.94154	−	12.8877i	0.236270	−	1.03517i
$156$	14.5519	+	7.00785i	1.16509	+	0.561077i
$157$	−0.124743	−	0.546536i	−0.00995559	−	0.0436183i	0.969706	−	0.244274i	$-0.0785498\pi$
$157$	−0.124743	−	0.546536i	−0.00995559	−	0.0436183i	−0.979662	+	0.200656i	$0.935693\pi$
$158$	6.44549	−	3.10398i	0.512775	−	0.246940i
$159$	0.722069	+	0.905446i	0.0572638	+	0.0718065i
$160$	2.04387	−	0.984274i	0.161582	−	0.0778137i
$161$	11.8084	+	5.95203i	0.930635	+	0.469086i
$162$	−5.24967	−	2.52811i	−0.412453	−	0.198627i
$163$	4.23753	+	18.5658i	0.331909	+	1.45419i	0.815430	+	0.578856i	$0.196501\pi$
$163$	4.23753	+	18.5658i	0.331909	+	1.45419i	−0.483521	+	0.875333i	$0.660642\pi$
$164$	−0.262754	−	0.329484i	−0.0205177	−	0.0257283i
$165$	−13.4480			−1.04693
$166$	4.73683			0.367649
$167$	−3.23190	−	4.05267i	−0.250092	−	0.313605i	0.640900	−	0.767624i	$-0.278561\pi$
$167$	−3.23190	−	4.05267i	−0.250092	−	0.313605i	−0.890992	+	0.454019i	$0.849990\pi$
$168$	1.66011	−	6.71160i	0.128080	−	0.517812i
$169$	15.7128	−	19.7032i	1.20867	−	1.51563i
$170$	3.72881	−	4.67578i	0.285987	−	0.358616i
$171$	22.1298	+	10.6572i	1.69231	+	0.814974i
$172$	−7.81745	−	3.76469i	−0.596075	−	0.287055i
$173$	3.02589	−	3.79435i	0.230054	−	0.288479i	−0.653384	−	0.757027i	$-0.726651\pi$
$173$	3.02589	−	3.79435i	0.230054	−	0.288479i	0.883438	+	0.468548i	$0.155223\pi$
$174$	−6.62686	+	8.30982i	−0.502381	+	0.629966i
$175$	−0.0928684	+	0.375455i	−0.00702019	+	0.0283817i
$176$	−1.41440	−	1.77360i	−0.106614	−	0.133690i
$177$	−9.37282			−0.704505
$178$	−2.55413			−0.191440
$179$	8.33631	+	10.4534i	0.623085	+	0.781324i	0.988775	−	0.149413i	$-0.0477383\pi$
$179$	8.33631	+	10.4534i	0.623085	+	0.781324i	−0.365690	+	0.930737i	$0.619167\pi$
$180$	−1.93275	−	8.46794i	−0.144059	−	0.631163i
$181$	12.0759	+	5.81545i	0.897595	+	0.432259i	0.825020	−	0.565104i	$-0.191164\pi$
$181$	12.0759	+	5.81545i	0.897595	+	0.432259i	0.0725754	+	0.997363i	$0.476878\pi$
$182$	−14.6025	−	7.36039i	−1.08241	−	0.545588i
$183$	−22.1443	+	10.6641i	−1.63695	+	0.788315i
$184$	3.11625	+	3.90766i	0.229733	+	0.288077i
$185$	5.05022	−	2.43206i	0.371300	−	0.178809i
$186$	−3.38847	−	14.8459i	−0.248455	−	1.08855i
$187$	−5.38829	−	2.59486i	−0.394031	−	0.189755i
$188$	1.96669	−	8.61663i	0.143436	−	0.628432i
$189$	−5.11694	−	2.57919i	−0.372203	−	0.187608i
$190$	−3.23832	−	14.1880i	−0.234932	−	1.02931i
$191$	−3.05498	+	13.3847i	−0.221051	+	0.968486i	0.735638	+	0.677374i	$0.236882\pi$
$191$	−3.05498	+	13.3847i	−0.221051	+	0.968486i	−0.956689	+	0.291112i	$0.905975\pi$
$192$	1.62930	−	2.04308i	0.117585	−	0.147447i
$193$	−1.39421	+	6.10842i	−0.100357	+	0.439694i	0.899638	+	0.436636i	$0.143830\pi$
$193$	−1.39421	+	6.10842i	−0.100357	+	0.439694i	−0.999995	+	0.00305740i	$0.999027\pi$
$194$	0.587762	−	0.283051i	0.0421988	−	0.0203219i
$195$	−36.6399			−2.62384
$196$	−1.80338	+	6.76371i	−0.128813	+	0.483122i
$197$	−20.5511			−1.46421			−0.732104	−	0.681193i	$-0.761461\pi$
$197$	−20.5511			−1.46421			−0.732104	+	0.681193i	$0.761461\pi$
$198$	−7.82555	+	3.76859i	−0.556138	+	0.267822i
$199$	−0.767069	+	3.36075i	−0.0543761	+	0.238237i	−0.994812	−	0.101735i	$-0.967561\pi$
$199$	−0.767069	+	3.36075i	−0.0543761	+	0.238237i	0.940435	+	0.339972i	$0.110418\pi$
$200$	−0.0911450	+	0.114292i	−0.00644492	+	0.00808168i
$201$	−0.216463	+	0.948386i	−0.0152681	+	0.0668940i
$202$	3.77926	+	16.5580i	0.265908	+	1.16502i
$203$	6.86044	−	8.29064i	0.481509	−	0.581889i
$204$	1.53300	−	6.71650i	0.107331	−	0.470249i
$205$	0.861337	+	0.414798i	0.0601584	+	0.0289708i
$206$	−2.70247	−	11.8403i	−0.188290	−	0.824952i
$207$	17.2415	−	8.30309i	1.19837	−	0.577104i
$208$	−3.85362	−	4.83228i	−0.267200	−	0.335059i
$209$	−13.1117	+	6.31425i	−0.906954	+	0.436766i
$210$	3.21302	+	15.3516i	0.221719	+	1.05936i
$211$	9.64399	+	4.64430i	0.663920	+	0.319727i	0.735319	−	0.677721i	$-0.237032\pi$
$211$	9.64399	+	4.64430i	0.663920	+	0.319727i	−0.0713996	+	0.997448i	$0.522747\pi$
$212$	−0.0986162	−	0.432066i	−0.00677299	−	0.0296744i
$213$	−22.2387	−	27.8865i	−1.52377	−	1.91075i
$214$	−1.16033			−0.0793184
$215$	19.6833			1.34239
$216$	−1.35036	−	1.69330i	−0.0918806	−	0.115215i
$217$	3.15834	+	15.0904i	0.214402	+	1.02440i
$218$	2.09664	−	2.62910i	0.142002	−	0.178065i
$219$	17.2607	−	21.6443i	1.16637	−	1.46258i
$220$	4.63655	+	2.23285i	0.312596	+	0.150538i
$221$	−14.6807	−	7.06987i	−0.987533	−	0.475571i
$222$	4.02587	−	5.04828i	0.270199	−	0.338818i
$223$	6.51578	−	8.17053i	0.436329	−	0.547139i	−0.514243	−	0.857645i	$-0.671927\pi$
$223$	6.51578	−	8.17053i	0.436329	−	0.547139i	0.950572	+	0.310505i	$0.100498\pi$
$224$	−1.68673	+	2.03837i	−0.112700	+	0.136194i
$225$	0.348976	+	0.437602i	0.0232651	+	0.0291735i
$226$	6.18310			0.411294
$227$	10.6746			0.708501			0.354250	−	0.935151i	$-0.384736\pi$
$227$	10.6746			0.708501			0.354250	+	0.935151i	$0.384736\pi$
$228$	−10.4522	−	13.1066i	−0.692213	−	0.868008i
$229$	−1.79760	−	7.87578i	−0.118788	−	0.520446i	−0.998952	−	0.0457753i	$-0.985424\pi$
$229$	−1.79760	−	7.87578i	−0.118788	−	0.520446i	0.880163	−	0.474671i	$-0.157433\pi$
$230$	−10.2154	−	4.91949i	−0.673585	−	0.324381i
$231$	14.2518	−	6.54852i	0.937697	−	0.430861i
$232$	3.66451	−	1.76473i	0.240587	−	0.115861i
$233$	−1.61532	−	2.02555i	−0.105823	−	0.132698i	0.726099	−	0.687590i	$-0.241331\pi$
$233$	−1.61532	−	2.02555i	−0.105823	−	0.132698i	−0.831923	+	0.554891i	$0.812760\pi$
$234$	−21.3212	+	10.2677i	−1.39381	+	0.671223i
$235$	4.46148	+	19.5470i	0.291035	+	1.27511i
$236$	3.23153	+	1.55622i	0.210355	+	0.101301i
$237$	−4.15996	+	18.2260i	−0.270218	+	1.18390i
$238$	−1.67480	+	6.77100i	−0.108561	+	0.438899i
$239$	−0.924979	−	4.05260i	−0.0598319	−	0.262141i	0.936161	−	0.351571i	$-0.114352\pi$
$239$	−0.924979	−	4.05260i	−0.0598319	−	0.262141i	−0.995993	+	0.0894305i	$0.971495\pi$
$240$	−1.31912	+	5.77946i	−0.0851491	+	0.373063i
$241$	4.13182	−	5.18114i	0.266154	−	0.333747i	−0.630738	−	0.775996i	$-0.717248\pi$
$241$	4.13182	−	5.18114i	0.266154	−	0.333747i	0.896892	+	0.442249i	$0.145819\pi$
$242$	−1.30260	+	5.70705i	−0.0837341	+	0.366863i
$243$	19.5724	−	9.42558i	1.25557	−	0.604651i
$244$	9.40545			0.602122
$245$	−2.97147	−	15.5991i	−0.189840	−	0.996593i
$246$	1.10127			0.0702143
$247$	−35.7236	+	17.2036i	−2.27304	+	1.09464i
$248$	−1.29668	+	5.68111i	−0.0823391	+	0.360751i
$249$	−7.71772	+	9.67772i	−0.489091	+	0.613301i
$250$	−2.45017	+	10.7349i	−0.154963	+	0.678935i
$251$	−5.53382	−	24.2453i	−0.349292	−	1.53035i	−0.778793	−	0.627281i	$-0.784168\pi$
$251$	−5.53382	−	24.2453i	−0.349292	−	1.53035i	0.429501	−	0.903066i	$-0.358689\pi$
$252$	6.17174	+	8.03290i	0.388783	+	0.506025i
$253$	−2.52300	+	11.0540i	−0.158620	+	0.694958i
$254$	17.3554	+	8.35790i	1.08897	+	0.524421i
$255$	3.47764	+	15.2365i	0.217778	+	0.954148i
$256$	−0.900969	+	0.433884i	−0.0563106	+	0.0271177i
$257$	−11.7644	−	14.7520i	−0.733841	−	0.920207i	0.265191	−	0.964196i	$-0.414565\pi$
$257$	−11.7644	−	14.7520i	−0.733841	−	0.920207i	−0.999032	+	0.0439886i	$0.985993\pi$
$258$	20.4285	−	9.83787i	1.27183	−	0.612479i
$259$	−4.16777	+	5.03663i	−0.258973	+	0.312961i
$260$	12.6326	+	6.08352i	0.783439	+	0.377284i
$261$	−3.46529	−	15.1824i	−0.214496	−	0.939769i
$262$	−3.55589	−	4.45895i	−0.219684	−	0.275475i
$263$	−7.79421			−0.480612			−0.240306	−	0.970697i	$-0.577248\pi$
$263$	−7.79421			−0.480612			−0.240306	+	0.970697i	$0.577248\pi$
$264$	5.92809			0.364849
$265$	0.626829	+	0.786019i	0.0385058	+	0.0482848i
$266$	10.3407	+	13.4591i	0.634031	+	0.825230i
$267$	4.16145	−	5.21830i	0.254677	−	0.319355i
$268$	0.232097	−	0.291041i	0.0141776	−	0.0177781i
$269$	−1.12055	−	0.539629i	−0.0683212	−	0.0329018i	0.399411	−	0.916772i	$-0.369215\pi$
$269$	−1.12055	−	0.539629i	−0.0683212	−	0.0329018i	−0.467732	+	0.883870i	$0.654929\pi$
$270$	4.42664	+	2.13176i	0.269396	+	0.129734i
$271$	−12.9725	+	16.2670i	−0.788022	+	0.988148i	0.211919	+	0.977287i	$0.432029\pi$
$271$	−12.9725	+	16.2670i	−0.788022	+	0.988148i	−0.999941	+	0.0108611i	$0.996543\pi$
$272$	−1.64372	+	2.06116i	−0.0996652	+	0.124976i
$273$	38.8298	−	17.8418i	2.35009	−	1.07984i
$274$	−11.9584	−	14.9954i	−0.722433	−	0.905903i
$275$	−0.331624			−0.0199977
$276$	−13.0610			−0.786179
$277$	2.48978	+	3.12208i	0.149596	+	0.187588i	0.850983	−	0.525193i	$-0.176007\pi$
$277$	2.48978	+	3.12208i	0.149596	+	0.187588i	−0.701387	+	0.712781i	$0.747435\pi$
$278$	−1.40588	−	6.15956i	−0.0843191	−	0.369426i
$279$	20.1017	+	9.68048i	1.20346	+	0.579555i
$280$	1.44114	−	5.82635i	0.0861248	−	0.348191i
$281$	−22.9864	+	11.0697i	−1.37126	+	0.660362i	−0.967116	−	0.254335i	$-0.918143\pi$
$281$	−22.9864	+	11.0697i	−1.37126	+	0.660362i	−0.404140	+	0.914697i	$0.632429\pi$
$282$	14.4001	+	18.0572i	0.857515	+	1.07529i
$283$	2.52198	−	1.21452i	0.149916	−	0.0721958i	−0.357421	−	0.933943i	$-0.616344\pi$
$283$	2.52198	−	1.21452i	0.149916	−	0.0721958i	0.507338	+	0.861747i	$0.330630\pi$
$284$	3.03724	+	13.3070i	0.180227	+	0.789626i
$285$	34.2634	+	16.5004i	2.02959	+	0.977398i
$286$	3.11999	−	13.6696i	0.184489	−	0.808298i
$287$	−1.11480	−	0.0201608i	−0.0658048	−	0.00119005i
$288$	0.851988	+	3.73280i	0.0502039	+	0.219958i
$289$	2.23629	−	9.79783i	0.131547	−	0.576343i
$290$	−5.75279	+	7.21376i	−0.337815	+	0.423607i
$291$	−0.379345	+	1.66202i	−0.0222376	+	0.0974293i
$292$	−9.54481	+	4.59654i	−0.558568	+	0.268992i
$293$	1.32109			0.0771787			0.0385893	−	0.999255i	$-0.487714\pi$
$293$	1.32109			0.0771787			0.0385893	+	0.999255i	$0.487714\pi$
$294$	−10.8805	−	14.7046i	−0.634566	−	0.857589i
$295$	−8.13656			−0.473729
$296$	−2.22622	+	1.07209i	−0.129396	+	0.0623140i
$297$	1.09329	−	4.79001i	0.0634390	−	0.277945i
$298$	7.84683	−	9.83961i	0.454554	−	0.569993i
$299$	−6.87406	+	30.1172i	−0.397537	+	1.74173i
$300$	−0.0850054	−	0.372433i	−0.00490779	−	0.0215024i
$301$	−20.8598	+	9.58481i	−1.20234	+	0.552459i
$302$	1.24431	−	5.45166i	0.0716017	−	0.313708i
$303$	−39.9869	−	19.2567i	−2.29719	−	1.10627i
$304$	1.42750	+	6.25429i	0.0818728	+	0.358708i
$305$	−19.2235	+	9.25754i	−1.10073	+	0.530085i
$306$	6.29347	+	7.89177i	0.359774	+	0.451142i
$307$	10.2045	−	4.91424i	0.582403	−	0.280471i	−0.119394	−	0.992847i	$-0.538095\pi$
$307$	10.2045	−	4.91424i	0.582403	−	0.280471i	0.701798	+	0.712376i	$0.252381\pi$
$308$	−6.00096	−	0.108525i	−0.341936	−	0.00618378i
$309$	28.5938	+	13.7700i	1.62664	+	0.783350i
$310$	−2.94154	−	12.8877i	−0.167068	−	0.731973i
$311$	5.39367	+	6.76344i	0.305847	+	0.383520i	0.910874	−	0.412685i	$-0.135409\pi$
$311$	5.39367	+	6.76344i	0.305847	+	0.383520i	−0.605027	+	0.796205i	$0.706838\pi$
$312$	16.1514			0.914395
$313$	4.72084			0.266838			0.133419	−	0.991060i	$-0.457404\pi$
$313$	4.72084			0.266838			0.133419	+	0.991060i	$0.457404\pi$
$314$	−0.349523	−	0.438288i	−0.0197247	−	0.0247340i
$315$	−20.5208	−	10.3435i	−1.15622	−	0.582789i
$316$	4.46041	−	5.59318i	0.250918	−	0.314641i
$317$	9.78988	−	12.2761i	0.549854	−	0.689496i	−0.426792	−	0.904350i	$-0.640356\pi$
$317$	9.78988	−	12.2761i	0.549854	−	0.689496i	0.976646	+	0.214854i	$0.0689277\pi$
$318$	1.04342	+	0.502485i	0.0585121	+	0.0281779i
$319$	8.31302	+	4.00334i	0.465440	+	0.224144i
$320$	1.41440	−	1.77360i	0.0790673	−	0.0991473i
$321$	1.89053	−	2.37064i	0.105519	−	0.132316i
$322$	13.2215	+	0.239106i	0.736807	+	0.0133248i
$323$	10.5447	+	13.2226i	0.586722	+	0.735726i
$324$	−5.82670			−0.323705
$325$	−0.903530			−0.0501188
$326$	11.8733	+	14.8886i	0.657601	+	0.824606i
$327$	1.95541	+	8.56719i	0.108134	+	0.473767i
$328$	−0.379691	−	0.182850i	−0.0209649	−	0.0100962i
$329$	−14.2466	−	18.5428i	−0.785439	−	1.02230i
$330$	−12.1162	+	5.83487i	−0.666976	+	0.321199i
$331$	−12.3270	−	15.4576i	−0.677555	−	0.849628i	0.317571	−	0.948235i	$-0.397133\pi$
$331$	−12.3270	−	15.4576i	−0.677555	−	0.849628i	−0.995126	+	0.0986068i	$0.968561\pi$
$332$	4.26774	−	2.05523i	0.234222	−	0.112796i
$333$	2.10519	+	9.22344i	0.115364	+	0.505442i
$334$	−4.67023	−	2.24906i	−0.255544	−	0.123063i
$335$	−0.187912	+	0.823295i	−0.0102667	+	0.0449814i
$336$	−1.41635	−	6.76724i	−0.0772682	−	0.369183i
$337$	−1.00188	−	4.38952i	−0.0545758	−	0.239112i	0.940282	−	0.340398i	$-0.110562\pi$
$337$	−1.00188	−	4.38952i	−0.0545758	−	0.239112i	−0.994857	+	0.101285i	$0.967705\pi$
$338$	5.60782	−	24.5695i	0.305025	−	1.33640i
$339$	−10.0741	+	12.6326i	−0.547152	+	0.686107i
$340$	1.33080	−	5.83061i	0.0721727	−	0.316209i
$341$	−11.9100	+	5.73558i	−0.644965	+	0.310599i
$342$	24.5623			1.32817
$343$	10.7451	+	15.0845i	0.580181	+	0.814488i
$344$	−8.67672			−0.467817
$345$	26.6949	−	12.8556i	1.43720	−	0.692121i
$346$	1.07993	−	4.73148i	0.0580573	−	0.254366i
$347$	1.62544	−	2.03823i	0.0872579	−	0.109418i	−0.736286	−	0.676670i	$-0.763422\pi$
$347$	1.62544	−	2.03823i	0.0872579	−	0.109418i	0.823544	+	0.567252i	$0.191994\pi$
$348$	−2.36510	+	10.3622i	−0.126783	+	0.555471i
$349$	0.376110	+	1.64785i	0.0201327	+	0.0882072i	0.983996	−	0.178190i	$-0.0570240\pi$
$349$	0.376110	+	1.64785i	0.0201327	+	0.0882072i	−0.963863	+	0.266397i	$0.914167\pi$
$350$	0.0792322	+	0.378567i	0.00423514	+	0.0202353i
$351$	2.97873	−	13.0507i	0.158993	−	0.696593i
$352$	−2.04387	−	0.984274i	−0.108938	−	0.0524620i
$353$	5.47185	+	23.9737i	0.291237	+	1.27599i	0.882806	+	0.469738i	$0.155652\pi$
$353$	5.47185	+	23.9737i	0.291237	+	1.27599i	−0.591569	+	0.806255i	$0.701491\pi$
$354$	−8.44462	+	4.06672i	−0.448827	+	0.216144i
$355$	−19.3055	−	24.2083i	−1.02463	−	1.28484i
$356$	−2.30119	+	1.10820i	−0.121963	+	0.0587343i
$357$	−11.1049	−	14.4538i	−0.587736	−	0.764974i
$358$	12.0463	+	5.80120i	0.636668	+	0.306603i
$359$	−3.09536	−	13.5616i	−0.163367	−	0.715756i	−0.988550	−	0.150892i	$-0.951786\pi$
$359$	−3.09536	−	13.5616i	−0.163367	−	0.715756i	0.825184	−	0.564865i	$-0.191072\pi$
$360$	−5.41545	−	6.79076i	−0.285419	−	0.357904i
$361$	22.1540			1.16600
$362$	13.4032			0.704459
$363$	−9.53763	−	11.9598i	−0.500596	−	0.627727i
$364$	−16.3500	−	0.295683i	−0.856972	−	0.0154980i
$365$	14.9841	−	18.7894i	0.784302	−	0.983483i
$366$	−15.3243	+	19.2161i	−0.801015	+	1.00444i
$367$	−3.35262	−	1.61453i	−0.175005	−	0.0842780i	0.344330	−	0.938849i	$-0.388106\pi$
$367$	−3.35262	−	1.61453i	−0.175005	−	0.0842780i	−0.519335	+	0.854571i	$0.673820\pi$
$368$	4.50312	+	2.16859i	0.234741	+	0.113045i
$369$	−1.00603	+	1.26153i	−0.0523720	+	0.0656724i
$370$	3.49486	−	4.38242i	0.181689	−	0.227831i
$371$	−1.04705	−	0.527763i	−0.0543600	−	0.0274001i
$372$	−9.49429	−	11.9055i	−0.492256	−	0.617269i
$373$	15.9826			0.827549			0.413774	−	0.910379i	$-0.364210\pi$
$373$	15.9826			0.827549			0.413774	+	0.910379i	$0.364210\pi$
$374$	−5.98055			−0.309247
$375$	−17.9402	−	22.4963i	−0.926428	−	1.16170i
$376$	−1.96669	−	8.61663i	−0.101424	−	0.444369i
$377$	22.6493	+	10.9073i	1.16650	+	0.561756i
$378$	−5.72927	−	0.103611i	−0.294682	−	0.00532920i
$379$	8.48937	−	4.08827i	0.436070	−	0.210000i	−0.202952	−	0.979189i	$-0.565054\pi$
$379$	8.48937	−	4.08827i	0.436070	−	0.210000i	0.639022	+	0.769189i	$0.279339\pi$
$380$	−9.07356	−	11.3779i	−0.465464	−	0.583673i
$381$	−45.3530	+	21.8408i	−2.32350	+	1.11894i
$382$	3.05498	+	13.3847i	0.156306	+	0.684823i
$383$	11.6762	+	5.62296i	0.596626	+	0.287320i	0.707724	−	0.706489i	$-0.249722\pi$
$383$	11.6762	+	5.62296i	0.596626	+	0.287320i	−0.111097	+	0.993810i	$0.535437\pi$
$384$	0.581491	−	2.54768i	0.0296741	−	0.130011i
$385$	12.3720	−	5.68478i	0.630534	−	0.289723i
$386$	1.39421	+	6.10842i	0.0709633	+	0.310910i
$387$	−7.39246	+	32.3885i	−0.375780	+	1.64640i
$388$	0.406744	−	0.510040i	0.0206493	−	0.0258934i
$389$	−5.75642	+	25.2205i	−0.291862	+	1.27873i	0.590069	+	0.807353i	$0.299101\pi$
$389$	−5.75642	+	25.2205i	−0.291862	+	1.27873i	−0.881931	+	0.471379i	$0.843756\pi$
$390$	−33.0114	+	15.8974i	−1.67160	+	0.804999i
$391$	13.1766			0.666368
$392$	1.30987	+	6.87635i	0.0661585	+	0.347308i
$393$	14.9036			0.751787
$394$	−18.5159	+	8.91680i	−0.932819	+	0.449222i
$395$	−3.61127	+	15.8220i	−0.181703	+	0.796091i
$396$	−5.41545	+	6.79076i	−0.272137	+	0.341249i
$397$	7.16957	−	31.4119i	0.359830	−	1.57652i	−0.393785	−	0.919203i	$-0.628834\pi$
$397$	7.16957	−	31.4119i	0.359830	−	1.57652i	0.753615	−	0.657316i	$-0.228308\pi$
$398$	0.767069	+	3.36075i	0.0384497	+	0.168459i
$399$	−44.3462	−	0.801982i	−2.22008	−	0.0401493i
$400$	−0.0325293	+	0.142520i	−0.00162646	+	0.00712600i
$401$	−21.5905	−	10.3975i	−1.07818	−	0.519224i	−0.191446	−	0.981503i	$-0.561318\pi$
$401$	−21.5905	−	10.3975i	−1.07818	−	0.519224i	−0.886734	+	0.462279i	$0.847032\pi$
$402$	0.216463	+	0.948386i	0.0107962	+	0.0473012i
$403$	−32.4496	+	15.6269i	−1.61643	+	0.778433i
$404$	10.5892	+	13.2785i	0.526835	+	0.660630i
$405$	11.9090	−	5.73507i	0.591762	−	0.284978i
$406$	2.58387	−	10.4462i	0.128235	−	0.518439i
$407$	−5.05022	−	2.43206i	−0.250330	−	0.120553i
$408$	−1.53300	−	6.71650i	−0.0758947	−	0.332516i
$409$	−13.2330	−	16.5937i	−0.654331	−	0.820505i	0.338382	−	0.941009i	$-0.390120\pi$
$409$	−13.2330	−	16.5937i	−0.654331	−	0.820505i	−0.992713	+	0.120504i	$0.961549\pi$
$410$	0.956012			0.0472141
$411$	50.1206			2.47227
$412$	−7.57215	−	9.49517i	−0.373053	−	0.467793i
$413$	8.62287	−	3.96211i	0.424304	−	0.194963i
$414$	11.9315	−	14.9616i	0.586402	−	0.735325i
$415$	−6.69977	+	8.40124i	−0.328879	+	0.412401i
$416$	−5.56864	−	2.68171i	−0.273025	−	0.131482i
$417$	14.8751	+	7.16346i	0.728436	+	0.350796i
$418$	−9.07356	+	11.3779i	−0.443802	+	0.556511i
$419$	−1.32580	+	1.66250i	−0.0647694	+	0.0812183i	−0.813161	−	0.582039i	$-0.802255\pi$
$419$	−1.32580	+	1.66250i	−0.0647694	+	0.0812183i	0.748391	+	0.663257i	$0.230827\pi$
$420$	9.55565	+	12.4373i	0.466268	+	0.606876i
$421$	−14.4305	−	18.0953i	−0.703302	−	0.881913i	0.293963	−	0.955817i	$-0.405026\pi$
$421$	−14.4305	−	18.0953i	−0.703302	−	0.881913i	−0.997265	+	0.0739040i	$0.976454\pi$
$422$	10.7040			0.521064
$423$	−33.8398			−1.64535
$424$	−0.276316	−	0.346490i	−0.0134191	−	0.0168270i
$425$	0.0857577	+	0.375729i	0.00415986	+	0.0182255i
$426$	−32.1359	−	15.4758i	−1.55699	−	0.749806i
$427$	15.8645	−	19.1718i	0.767736	−	0.927786i
$428$	−1.04542	+	0.503448i	−0.0505323	+	0.0243351i
$429$	22.8446	+	28.6462i	1.10295	+	1.38305i
$430$	17.7341	−	8.54027i	0.855212	−	0.411848i
$431$	−8.80951	−	38.5970i	−0.424339	−	1.85915i	−0.506063	−	0.862496i	$-0.668900\pi$
$431$	−8.80951	−	38.5970i	−0.424339	−	1.85915i	0.0817239	−	0.996655i	$-0.473957\pi$
$432$	−1.95133	−	0.939712i	−0.0938835	−	0.0452119i
$433$	−3.01461	+	13.2079i	−0.144873	+	0.634730i	0.849390	+	0.527766i	$0.176970\pi$
$433$	−3.01461	+	13.2079i	−0.144873	+	0.634730i	−0.994263	+	0.106964i	$0.965887\pi$
$434$	9.39304	+	12.2256i	0.450880	+	0.586848i
$435$	−5.36527	−	23.5068i	−0.257245	−	1.12706i
$436$	0.748281	−	3.27843i	0.0358362	−	0.157008i
$437$	19.9912	−	25.0682i	0.956309	−	1.19917i
$438$	6.16028	−	26.9900i	0.294350	−	1.28963i
$439$	34.5039	−	16.6162i	1.64678	−	0.793048i	0.647254	−	0.762275i	$-0.275917\pi$
$439$	34.5039	−	16.6162i	1.64678	−	0.793048i	0.999526	−	0.0307729i	$-0.00979686\pi$
$440$	5.14619			0.245335
$441$	26.7841	+	0.969074i	1.27543	+	0.0461464i
$442$	−16.2944			−0.775044
$443$	−16.5975	+	7.99295i	−0.788573	+	0.379757i	−0.784416	−	0.620235i	$-0.787037\pi$
$443$	−16.5975	+	7.99295i	−0.788573	+	0.379757i	−0.00415647	+	0.999991i	$0.501323\pi$
$444$	1.43682	−	6.29510i	0.0681883	−	0.298752i
$445$	3.61256	−	4.53001i	0.171252	−	0.214743i
$446$	2.32546	−	10.1885i	0.110114	−	0.482439i
$447$	7.31826	+	32.0634i	0.346142	+	1.51655i
$448$	−0.635279	+	2.56835i	−0.0300141	+	0.121343i
$449$	−6.09815	+	26.7178i	−0.287790	+	1.26089i	0.599761	+	0.800179i	$0.295262\pi$
$449$	−6.09815	+	26.7178i	−0.287790	+	1.26089i	−0.887551	+	0.460710i	$0.847595\pi$
$450$	0.504285	+	0.242851i	0.0237722	+	0.0114481i
$451$	−0.212733	−	0.932043i	−0.0100172	−	0.0438882i
$452$	5.57078	−	2.68275i	0.262027	−	0.126186i
$453$	9.11082	+	11.4246i	0.428064	+	0.536775i
$454$	9.61752	−	4.63155i	0.451373	−	0.217370i
$455$	33.7082	−	15.4885i	1.58026	−	0.726113i
$456$	−15.1039	−	7.27363i	−0.707303	−	0.340619i
$457$	1.45705	+	6.38374i	0.0681578	+	0.298619i	0.997506	−	0.0705864i	$-0.0224870\pi$
$457$	1.45705	+	6.38374i	0.0681578	+	0.298619i	−0.929348	+	0.369205i	$0.879630\pi$
$458$	−5.03675	−	6.31589i	−0.235352	−	0.295122i
$459$	−5.70979			−0.266510
$460$	−11.3383			−0.528649
$461$	14.6775	+	18.4051i	0.683601	+	0.857209i	0.995680	−	0.0928471i	$-0.0295968\pi$
$461$	14.6775	+	18.4051i	0.683601	+	0.857209i	−0.312079	+	0.950056i	$0.601025\pi$
$462$	9.99910	−	12.0836i	0.465200	−	0.562181i
$463$	−1.95626	+	2.45307i	−0.0909149	+	0.114004i	−0.825208	−	0.564829i	$-0.808942\pi$
$463$	−1.95626	+	2.45307i	−0.0909149	+	0.114004i	0.734293	+	0.678832i	$0.237514\pi$
$464$	2.53592	−	3.17994i	0.117727	−	0.147625i
$465$	31.1233	+	14.9882i	1.44331	+	0.695061i
$466$	−2.33421	−	1.12410i	−0.108130	−	0.0520727i
$467$	−21.0590	+	26.4072i	−0.974495	+	1.22198i	0.000556262		1.00000i	$0.499823\pi$
$467$	−21.0590	+	26.4072i	−0.974495	+	1.22198i	−0.975052	+	0.221979i	$0.928748\pi$
$468$	−14.7547	+	18.5018i	−0.682037	+	0.855248i
$469$	−0.201762	−	0.964006i	−0.00931649	−	0.0445137i
$470$	12.5008	+	15.6755i	0.576618	+	0.723056i
$471$	1.46493			0.0675006
$472$	3.58673			0.165093
$473$	−12.2723	−	15.3890i	−0.564283	−	0.707588i
$474$	4.15996	+	18.2260i	0.191073	+	0.837146i
$475$	0.844927	+	0.406895i	0.0387679	+	0.0186696i
$476$	1.42888	+	6.82713i	0.0654928	+	0.312921i
$477$	−1.52880	+	0.736229i	−0.0699988	+	0.0337096i
$478$	−2.59173	−	3.24993i	−0.118543	−	0.148648i
$479$	26.3602	−	12.6944i	1.20443	−	0.580023i	0.279495	−	0.960147i	$-0.409833\pi$
$479$	26.3602	−	12.6944i	1.20443	−	0.580023i	0.924935	+	0.380124i	$0.124119\pi$
$480$	1.31912	+	5.77946i	0.0602095	+	0.263795i
$481$	−13.7596	−	6.62629i	−0.627385	−	0.302133i
$482$	1.47463	−	6.46078i	0.0671676	−	0.294280i
$483$	−22.0304	+	26.6231i	−1.00242	+	1.21139i
$484$	1.30260	+	5.70705i	0.0592089	+	0.259411i
$485$	−0.329310	+	1.44280i	−0.0149532	+	0.0655143i
$486$	13.5445	−	16.9843i	0.614393	−	0.770424i
$487$	−2.35825	+	10.3322i	−0.106862	+	0.468195i	0.892974	+	0.450108i	$0.148615\pi$
$487$	−2.35825	+	10.3322i	−0.106862	+	0.468195i	−0.999836	+	0.0180867i	$0.994243\pi$
$488$	8.47402	−	4.08087i	0.383601	−	0.184732i
$489$	−49.7639			−2.25040
$490$	−9.44542	−	12.7651i	−0.426701	−	0.576667i
$491$	−24.1721			−1.09087			−0.545437	−	0.838152i	$-0.683636\pi$
$491$	−24.1721			−1.09087			−0.545437	+	0.838152i	$0.683636\pi$
$492$	0.992208	−	0.477822i	0.0447322	−	0.0215419i
$493$	2.38603	−	10.4539i	0.107461	−	0.470819i
$494$	−24.7215	+	30.9997i	−1.11227	+	1.39474i
$495$	4.38449	−	19.2097i	0.197068	−	0.863412i
$496$	1.29668	+	5.68111i	0.0582225	+	0.255090i
$497$	32.2476	+	16.2544i	1.44650	+	0.729107i
$498$	−2.75442	+	12.0679i	−0.123429	+	0.540776i
$499$	23.7401	+	11.4326i	1.06275	+	0.511795i	0.881764	−	0.471691i	$-0.156356\pi$
$499$	23.7401	+	11.4326i	1.06275	+	0.511795i	0.180988	+	0.983485i	$0.442070\pi$
$500$	2.45017	+	10.7349i	0.109575	+	0.480080i
$501$	12.2042	−	5.87725i	0.545245	−	0.262576i
$502$	−15.5054	−	19.4432i	−0.692041	−	0.867792i
$503$	7.03178	−	3.38632i	0.313531	−	0.150989i	−0.270500	−	0.962720i	$-0.587189\pi$
$503$	7.03178	−	3.38632i	0.313531	−	0.150989i	0.584031	+	0.811731i	$0.301475\pi$
$504$	9.04589	+	4.55957i	0.402936	+	0.203100i
$505$	−34.7127	−	16.7167i	−1.54469	−	0.743885i
$506$	2.52300	+	11.0540i	0.112161	+	0.491409i
$507$	41.0605	+	51.4883i	1.82356	+	2.28668i
$508$	19.2630			0.854657
$509$	−8.11579			−0.359726			−0.179863	−	0.983692i	$-0.557565\pi$
$509$	−8.11579			−0.359726			−0.179863	+	0.983692i	$0.557565\pi$
$510$	9.74412	+	12.2187i	0.431477	+	0.541055i
$511$	−6.73011	+	27.2089i	−0.297722	+	1.20365i
$512$	−0.623490	+	0.781831i	−0.0275546	+	0.0345524i
$513$	−8.66276	+	10.8628i	−0.382470	+	0.479603i
$514$	−17.0000	−	8.18677i	−0.749838	−	0.361103i
$515$	24.8223	+	11.9538i	1.09380	+	0.526747i
$516$	14.1370	−	17.7272i	0.622346	−	0.780398i
$517$	12.5008	−	15.6755i	0.549784	−	0.689407i
$518$	−1.56972	+	6.34618i	−0.0689696	+	0.278835i
$519$	7.90726	+	9.91539i	0.347090	+	0.435237i
$520$	14.0211			0.614866
$521$	−24.0450			−1.05343			−0.526716	−	0.850041i	$-0.676577\pi$
$521$	−24.0450			−1.05343			−0.526716	+	0.850041i	$0.676577\pi$
$522$	−9.70953	−	12.1754i	−0.424974	−	0.532901i
$523$	3.29369	+	14.4306i	0.144023	+	0.631005i	0.994477	+	0.104956i	$0.0334702\pi$
$523$	3.29369	+	14.4306i	0.144023	+	0.631005i	−0.850454	+	0.526049i	$0.823673\pi$
$524$	−5.13841	−	2.47453i	−0.224472	−	0.108100i
$525$	−0.902536	−	0.454922i	−0.0393899	−	0.0198544i
$526$	−7.02234	+	3.38178i	−0.306189	+	0.147453i
$527$	9.57831	+	12.0108i	0.417238	+	0.523200i
$528$	5.34103	−	2.57210i	0.232438	−	0.111936i
$529$	−0.440780	−	1.93118i	−0.0191644	−	0.0839646i
$530$	0.905795	+	0.436208i	0.0393452	+	0.0189477i
$531$	3.05585	−	13.3885i	0.132613	−	0.581013i
$532$	15.1564	+	7.63954i	0.657111	+	0.331216i
$533$	−0.579603	−	2.53941i	−0.0251054	−	0.109994i
$534$	1.48521	−	6.50711i	0.0642711	−	0.281590i
$535$	1.64117	−	2.05796i	0.0709539	−	0.0889734i
$536$	0.0828345	−	0.362922i	0.00357791	−	0.0156758i
$537$	−31.4794	+	15.1597i	−1.35844	+	0.654189i
$538$	−1.24372			−0.0536205
$539$	−10.3432	+	12.0491i	−0.445514	+	0.518992i
$540$	4.91319			0.211430
$541$	32.5658	−	15.6829i	1.40011	−	0.674259i	0.426929	−	0.904285i	$-0.359595\pi$
$541$	32.5658	−	15.6829i	1.40011	−	0.674259i	0.973185	+	0.230026i	$0.0738810\pi$
$542$	−4.62982	+	20.2846i	−0.198868	+	0.871298i
$543$	−21.8379	+	27.3839i	−0.937155	+	1.17516i
$544$	−0.586637	+	2.57022i	−0.0251519	+	0.110197i
$545$	1.69749	+	7.43719i	0.0727125	+	0.318574i
$546$	27.2431	−	32.9226i	1.16590	−	1.40896i
$547$	2.82714	−	12.3865i	0.120880	−	0.529608i	−0.877837	−	0.478960i	$-0.841014\pi$
$547$	2.82714	−	12.3865i	0.120880	−	0.529608i	0.998717	−	0.0506486i	$-0.0161288\pi$
$548$	−17.2804	−	8.32180i	−0.738182	−	0.355490i
$549$	−8.01333	−	35.1087i	−0.342001	−	1.49840i
$550$	−0.298783	+	0.143886i	−0.0127402	+	0.00613533i
$551$	−16.2683	−	20.3998i	−0.693051	−	0.869059i
$552$	−11.7675	+	5.66695i	−0.500860	+	0.241201i
$553$	−3.87743	−	18.5262i	−0.164885	−	0.787812i
$554$	3.59783	+	1.73263i	0.152857	+	0.0736122i
$555$	3.25945	+	14.2806i	0.138356	+	0.606176i
$556$	−3.93919	−	4.93959i	−0.167059	−	0.209485i
$557$	−8.36124			−0.354277			−0.177139	−	0.984186i	$-0.556684\pi$
$557$	−8.36124			−0.354277			−0.177139	+	0.984186i	$0.556684\pi$
$558$	22.3112			0.944510
$559$	−33.4367	−	41.9284i	−1.41422	−	1.77338i
$560$	−1.22954	−	5.87465i	−0.0519573	−	0.248249i
$561$	9.74412	−	12.2187i	0.411397	−	0.515876i
$562$	−15.9071	+	19.9469i	−0.671001	+	0.841409i
$563$	−5.51200	−	2.65444i	−0.232303	−	0.111871i	0.314112	−	0.949386i	$-0.398293\pi$
$563$	−5.51200	−	2.65444i	−0.232303	−	0.111871i	−0.546415	+	0.837515i	$0.684008\pi$
$564$	20.8088	+	10.0210i	0.876208	+	0.421960i
$565$	−8.74537	+	10.9663i	−0.367920	+	0.461358i
$566$	1.74526	−	2.18849i	0.0733589	−	0.0919892i
$567$	−9.82807	+	11.8769i	−0.412740	+	0.498785i
$568$	8.51015	+	10.6714i	0.357078	+	0.447762i
$569$	−38.4165			−1.61050			−0.805251	−	0.592933i	$-0.797970\pi$
$569$	−38.4165			−1.61050			−0.805251	+	0.592933i	$0.797970\pi$
$570$	38.0295			1.59288
$571$	8.25821	+	10.3555i	0.345595	+	0.433363i	0.924003	−	0.382385i	$-0.124897\pi$
$571$	8.25821	+	10.3555i	0.345595	+	0.433363i	−0.578408	+	0.815748i	$0.696326\pi$
$572$	−3.11999	−	13.6696i	−0.130453	−	0.571553i
$573$	−32.3236	−	15.5662i	−1.35034	−	0.650288i
$574$	−1.01315	+	0.465531i	−0.0422881	+	0.0194309i
$575$	0.658289	−	0.317015i	0.0274526	−	0.0132205i
$576$	2.38722	+	2.99348i	0.0994674	+	0.124728i
$577$	11.0575	−	5.32502i	0.460331	−	0.221684i	−0.189321	−	0.981915i	$-0.560629\pi$
$577$	11.0575	−	5.32502i	0.460331	−	0.221684i	0.649652	+	0.760232i	$0.274915\pi$
$578$	−2.23629	−	9.79783i	−0.0930175	−	0.407536i
$579$	−14.7516	−	7.10398i	−0.613055	−	0.295231i
$580$	−2.05315	+	8.99542i	−0.0852522	+	0.373514i
$581$	3.00921	−	12.1658i	0.124843	−	0.504724i
$582$	0.379345	+	1.66202i	0.0157244	+	0.0688929i
$583$	0.223713	−	0.980150i	0.00926524	−	0.0405937i
$584$	−6.60521	+	8.28268i	−0.273326	+	0.342740i
$585$	11.9458	−	52.3380i	0.493898	−	2.16391i
$586$	1.19026	−	0.573198i	0.0491691	−	0.0236786i
$587$	1.62164			0.0669322			0.0334661	−	0.999440i	$-0.489345\pi$
$587$	1.62164			0.0669322			0.0334661	+	0.999440i	$0.489345\pi$
$588$	−16.1831	−	8.52748i	−0.667380	−	0.351667i
$589$	37.3824			1.54031
$590$	−7.33079	+	3.53032i	−0.301804	+	0.145341i
$591$	11.9503	−	52.3577i	0.491570	−	2.15371i
$592$	−1.54059	+	1.93184i	−0.0633179	+	0.0793981i
$593$	4.91324	−	21.5263i	0.201763	−	0.883980i	−0.768100	−	0.640330i	$-0.778798\pi$
$593$	4.91324	−	21.5263i	0.201763	−	0.883980i	0.969863	−	0.243651i	$-0.0783451\pi$
$594$	−1.09329	−	4.79001i	−0.0448582	−	0.196537i
$595$	−9.64021	−	12.5473i	−0.395210	−	0.514390i
$596$	2.80050	−	12.2698i	0.114713	−	0.502590i
$597$	−8.11607	−	3.90849i	−0.332169	−	0.159964i
$598$	6.87406	+	30.1172i	0.281101	+	1.23159i
$599$	31.6975	−	15.2647i	1.29513	−	0.623700i	0.345893	−	0.938274i	$-0.387576\pi$
$599$	31.6975	−	15.2647i	1.29513	−	0.623700i	0.949233	+	0.314574i	$0.101862\pi$
$600$	−0.238180	−	0.298668i	−0.00972365	−	0.0121931i
$601$	−40.3838	+	19.4478i	−1.64729	+	0.793293i	−0.647785	+	0.761823i	$0.724305\pi$
$601$	−40.3838	+	19.4478i	−1.64729	+	0.793293i	−0.999505	+	0.0314699i	$0.989981\pi$
$602$	−14.6353	+	17.6863i	−0.596490	+	0.720841i
$603$	−1.28414	−	0.618410i	−0.0522943	−	0.0251836i
$604$	−1.24431	−	5.45166i	−0.0506301	−	0.221825i
$605$	−8.27963	−	10.3823i	−0.336615	−	0.422102i
$606$	−44.3821			−1.80290
$607$	−32.0276			−1.29996			−0.649980	−	0.759951i	$-0.725223\pi$
$607$	−32.0276			−1.29996			−0.649980	+	0.759951i	$0.725223\pi$
$608$	3.99977	+	5.01555i	0.162212	+	0.203408i
$609$	17.1326	+	22.2991i	0.694249	+	0.903607i
$610$	−13.3031	+	16.6815i	−0.538625	+	0.675415i
$611$	34.0591	−	42.7088i	1.37788	−	1.72781i
$612$	9.09433	+	4.37960i	0.367617	+	0.177035i
$613$	12.9857	+	6.25360i	0.524489	+	0.252581i	0.677342	−	0.735668i	$-0.263132\pi$
$613$	12.9857	+	6.25360i	0.524489	+	0.252581i	−0.152853	+	0.988249i	$0.548846\pi$
$614$	7.06175	−	8.85516i	0.284989	−	0.357365i
$615$	−1.55763	+	1.95321i	−0.0628098	+	0.0787610i
$616$	−5.45377	+	2.50594i	−0.219738	+	0.100967i
$617$	−18.4529	−	23.1392i	−0.742886	−	0.931549i	0.256502	−	0.966544i	$-0.417430\pi$
$617$	−18.4529	−	23.1392i	−0.742886	−	0.931549i	−0.999388	+	0.0349946i	$0.988859\pi$
$618$	31.7367			1.27664
$619$	10.9561			0.440361			0.220181	−	0.975459i	$-0.429335\pi$
$619$	10.9561			0.440361			0.220181	+	0.975459i	$0.429335\pi$
$620$	−8.24201	−	10.3352i	−0.331007	−	0.415070i
$621$	2.40877	+	10.5535i	0.0966607	+	0.423498i
$622$	7.79407	+	3.75343i	0.312514	+	0.150499i
$623$	−1.62259	+	6.55991i	−0.0650076	+	0.262817i
$624$	14.5519	−	7.00785i	0.582544	−	0.280538i
$625$	−16.0296	−	20.1005i	−0.641186	−	0.804022i
$626$	4.25333	−	2.04830i	0.169997	−	0.0818663i
$627$	−8.46236	−	37.0760i	−0.337954	−	1.48067i
$628$	−0.505075	−	0.243231i	−0.0201547	−	0.00970599i
$629$	−1.44953	+	6.35081i	−0.0577966	+	0.253223i
$630$	−22.9765	−	0.415520i	−0.915404	−	0.0165547i
$631$	3.86535	+	16.9352i	0.153877	+	0.674180i	0.991736	+	0.128293i	$0.0409499\pi$
$631$	3.86535	+	16.9352i	0.153877	+	0.674180i	−0.837859	+	0.545887i	$0.816193\pi$
$632$	1.59190	−	6.97459i	0.0633225	−	0.277434i
$633$	−17.4401	+	21.8692i	−0.693181	+	0.869221i
$634$	3.49397	−	15.3081i	0.138763	−	0.607961i
$635$	−39.3710	+	18.9601i	−1.56239	+	0.752407i
$636$	1.15811			0.0459220
$637$	−28.1807	+	32.8285i	−1.11656	+	1.30071i
$638$	9.22675			0.365291
$639$	47.0848	−	22.6748i	1.86264	−	0.897002i
$640$	0.504793	−	2.21164i	0.0199537	−	0.0874229i
$641$	10.3664	−	12.9990i	0.409447	−	0.513430i	−0.533760	−	0.845636i	$-0.679221\pi$
$641$	10.3664	−	12.9990i	0.409447	−	0.513430i	0.943207	+	0.332206i	$0.107793\pi$
$642$	0.674721	−	2.95614i	0.0266291	−	0.116670i
$643$	0.609866	+	2.67200i	0.0240508	+	0.105373i	0.985529	−	0.169509i	$-0.0542182\pi$
$643$	0.609866	+	2.67200i	0.0240508	+	0.105373i	−0.961478	+	0.274882i	$0.911361\pi$
$644$	12.0159	−	5.52118i	0.473494	−	0.217565i
$645$	−11.4457	+	50.1468i	−0.450673	+	1.97453i
$646$	15.2375	+	7.33800i	0.599512	+	0.288710i
$647$	−3.92335	−	17.1893i	−0.154243	−	0.675783i	−0.991623	−	0.129162i	$-0.958771\pi$
$647$	−3.92335	−	17.1893i	−0.154243	−	0.675783i	0.837381	−	0.546620i	$-0.184086\pi$
$648$	−5.24967	+	2.52811i	−0.206227	+	0.0993135i
$649$	5.07306	+	6.36142i	0.199135	+	0.249708i
$650$	−0.814052	+	0.392027i	−0.0319298	+	0.0153766i
$651$	−40.2820	−	0.728483i	−1.57878	−	0.0285515i
$652$	17.1574	+	8.26258i	0.671936	+	0.323587i
$653$	7.74317	+	33.9250i	0.303014	+	1.32759i	0.865552	+	0.500819i	$0.166968\pi$
$653$	7.74317	+	33.9250i	0.303014	+	1.32759i	−0.562539	+	0.826771i	$0.690175\pi$
$654$	5.47893	+	6.87036i	0.214243	+	0.268652i
$655$	12.9378			0.505523
$656$	−0.421425			−0.0164539
$657$	25.2900	+	31.7127i	0.986658	+	1.23723i
$658$	−20.8811	−	10.5251i	−0.814031	−	0.410311i
$659$	−27.3299	+	34.2706i	−1.06462	+	1.33499i	−0.125239	+	0.992127i	$0.539970\pi$
$659$	−27.3299	+	34.2706i	−1.06462	+	1.33499i	−0.939383	+	0.342868i	$0.888602\pi$
$660$	−8.38469	+	10.5141i	−0.326374	+	0.409259i
$661$	−5.98806	−	2.88370i	−0.232909	−	0.112163i	0.313790	−	0.949492i	$-0.398401\pi$
$661$	−5.98806	−	2.88370i	−0.232909	−	0.112163i	−0.546698	+	0.837330i	$0.684116\pi$
$662$	−17.8131	−	8.57833i	−0.692325	−	0.333406i
$663$	26.5485	−	33.2907i	1.03106	−	1.29290i
$664$	2.95336	−	3.70340i	0.114613	−	0.143720i
$665$	−38.4970	−	0.696202i	−1.49285	−	0.0269975i
$666$	5.89861	+	7.39663i	0.228567	+	0.286613i
$667$	−20.3287			−0.787131
$668$	−5.18356			−0.200558
$669$	17.0270	+	21.3512i	0.658303	+	0.825486i
$670$	0.187912	+	0.823295i	0.00725966	+	0.0318067i
$671$	19.2235	+	9.25754i	0.742115	+	0.357384i
$672$	−4.21228	−	5.48254i	−0.162492	−	0.211494i
$673$	2.76926	−	1.33361i	0.106747	−	0.0514067i	−0.379748	−	0.925090i	$-0.623989\pi$
$673$	2.76926	−	1.33361i	0.106747	−	0.0514067i	0.486495	+	0.873683i	$0.338275\pi$
$674$	−2.80720	−	3.52012i	−0.108129	−	0.135590i
$675$	−0.285256	+	0.137372i	−0.0109795	+	0.00528745i
$676$	−5.60782	−	24.5695i	−0.215685	−	0.944979i
$677$	−5.13006	−	2.47051i	−0.197164	−	0.0949494i	0.332696	−	0.943034i	$-0.392042\pi$
$677$	−5.13006	−	2.47051i	−0.197164	−	0.0949494i	−0.529861	+	0.848085i	$0.677756\pi$
$678$	−3.59542	+	15.7525i	−0.138081	+	0.604973i
$679$	−0.353582	−	1.68939i	−0.0135692	−	0.0648330i
$680$	−1.33080	−	5.83061i	−0.0510338	−	0.223594i
$681$	−6.20721	+	27.1956i	−0.237861	+	1.04214i
$682$	−8.24201	+	10.3352i	−0.315603	+	0.395753i
$683$	−4.07125	+	17.8373i	−0.155782	+	0.682526i	0.835358	+	0.549706i	$0.185260\pi$
$683$	−4.07125	+	17.8373i	−0.155782	+	0.682526i	−0.991140	+	0.132820i	$0.957597\pi$
$684$	22.1298	−	10.6572i	0.846155	−	0.407487i
$685$	43.5097			1.66242
$686$	16.2259	+	8.92856i	0.619509	+	0.340894i
$687$	21.1102			0.805406
$688$	−7.81745	+	3.76469i	−0.298038	+	0.143527i
$689$	0.609519	−	2.67048i	0.0232208	−	0.101737i
$690$	18.4734	−	23.1650i	0.703272	−	0.881875i
$691$	−7.45629	+	32.6681i	−0.283651	+	1.24275i	0.609424	+	0.792845i	$0.291401\pi$
$691$	−7.45629	+	32.6681i	−0.283651	+	1.24275i	−0.893074	+	0.449909i	$0.851456\pi$
$692$	−1.07993	−	4.73148i	−0.0410527	−	0.179864i
$693$	4.70764	+	22.4929i	0.178829	+	0.854433i
$694$	0.580111	−	2.54163i	0.0220207	−	0.0964791i
$695$	12.9131	+	6.21861i	0.489821	+	0.235885i
$696$	2.36510	+	10.3622i	0.0896488	+	0.392777i
$697$	−1.00099	+	0.482051i	−0.0379151	+	0.0182590i
$698$	1.05384	+	1.32147i	0.0398883	+	0.0500184i
$699$	6.09975	−	2.93748i	0.230714	−	0.111106i
$700$	0.235640	+	0.306700i	0.00890635	+	0.0115922i
$701$	38.4598	+	18.5213i	1.45261	+	0.699538i	0.983045	−	0.183362i	$-0.0586980\pi$
$701$	38.4598	+	18.5213i	1.45261	+	0.699538i	0.469561	+	0.882900i	$0.344412\pi$
$702$	−2.97873	−	13.0507i	−0.112425	−	0.492566i
$703$	9.88310	+	12.3930i	0.372748	+	0.467411i
$704$	−2.26852			−0.0854981
$705$	−52.3938			−1.97326
$706$	15.3318	+	19.2254i	0.577019	+	0.723559i
$707$	44.9276	+	0.812498i	1.68968	+	0.0305571i
$708$	−5.84386	+	7.32797i	−0.219626	+	0.275402i
$709$	−7.62571	+	9.56233i	−0.286389	+	0.359121i	−0.904127	−	0.427263i	$-0.859478\pi$
$709$	−7.62571	+	9.56233i	−0.286389	+	0.359121i	0.617738	+	0.786384i	$0.288049\pi$
$710$	−27.8972	−	13.4346i	−1.04696	−	0.504191i
$711$	−24.6785	−	11.8845i	−0.925515	−	0.445705i
$712$	−1.59248	+	1.99690i	−0.0596806	+	0.0748371i
$713$	18.1591	−	22.7708i	0.680063	−	0.852772i
$714$	−16.2765	−	8.20413i	−0.609131	−	0.307032i
$715$	19.8314	+	24.8678i	0.741653	+	0.930004i
$716$	13.3704			0.499675
$717$	10.8626			0.405670
$718$	−8.67300	−	10.8756i	−0.323673	−	0.405874i
$719$	5.03069	+	22.0409i	0.187613	+	0.821987i	0.977870	+	0.209212i	$0.0670899\pi$
$719$	5.03069	+	22.0409i	0.187613	+	0.821987i	−0.790257	+	0.612775i	$0.790053\pi$
$720$	−7.82555	−	3.76859i	−0.291641	−	0.140447i
$721$	−32.1268	−	0.581000i	−1.19646	−	0.0216376i
$722$	19.9600	−	9.61224i	0.742835	−	0.357731i
$723$	10.7973	+	13.5393i	0.401555	+	0.503534i
$724$	12.0759	−	5.81545i	0.448798	−	0.216130i
$725$	−0.132306	−	0.579672i	−0.00491373	−	0.0215285i
$726$	−13.7823	−	6.63719i	−0.511508	−	0.246329i
$727$	5.97800	−	26.1913i	0.221712	−	0.971382i	−0.734478	−	0.678633i	$-0.762573\pi$
$727$	5.97800	−	26.1913i	0.221712	−	0.971382i	0.956189	−	0.292749i	$-0.0945702\pi$
$728$	−14.8591	+	6.82759i	−0.550715	+	0.253047i
$729$	8.74248	+	38.3033i	0.323796	+	1.41864i
$730$	5.34775	−	23.4300i	0.197929	−	0.867184i
$731$	−14.2621	+	17.8841i	−0.527503	+	0.661468i
$732$	−5.46919	+	23.9621i	−0.202147	+	0.885664i
$733$	24.9596	−	12.0199i	0.921904	−	0.443965i	0.0881533	−	0.996107i	$-0.471903\pi$
$733$	24.9596	−	12.0199i	0.921904	−	0.443965i	0.833750	+	0.552141i	$0.186189\pi$
$734$	−3.72112			−0.137349
$735$	41.4695	+	1.50041i	1.52963	+	0.0553434i
$736$	4.99808			0.184232
$737$	0.760839	−	0.366401i	0.0280259	−	0.0134965i
$738$	−0.359049	+	1.57310i	−0.0132168	+	0.0579065i
$739$	19.5301	−	24.4899i	0.718425	−	0.900877i	−0.279823	−	0.960052i	$-0.590276\pi$
$739$	19.5301	−	24.4899i	0.718425	−	0.900877i	0.998248	+	0.0591752i	$0.0188471\pi$
$740$	1.24730	−	5.46479i	0.0458517	−	0.200890i
$741$	−23.0562	−	101.016i	−0.846991	−	3.71091i
$742$	−1.17234	−	0.0212014i	−0.0430381	−	0.000778326i
$743$	10.0807	−	44.1664i	0.369825	−	1.62031i	−0.357430	−	0.933940i	$-0.616347\pi$
$743$	10.0807	−	44.1664i	0.369825	−	1.62031i	0.727255	−	0.686368i	$-0.240796\pi$
$744$	−13.7196	−	6.60703i	−0.502987	−	0.242226i
$745$	6.35299	+	27.8343i	0.232756	+	1.01977i
$746$	14.3998	−	6.93460i	0.527216	−	0.253894i
$747$	−11.3078	−	14.1796i	−0.413732	−	0.518804i
$748$	−5.38829	+	2.59486i	−0.197015	+	0.0948776i
$749$	−0.737132	+	2.98013i	−0.0269342	+	0.108892i
$750$	−25.9243	−	12.4845i	−0.946623	−	0.455870i
$751$	−3.58805	−	15.7203i	−0.130930	−	0.573641i	−0.997247	−	0.0741470i	$-0.976377\pi$
$751$	−3.58805	−	15.7203i	−0.130930	−	0.573641i	0.866318	−	0.499494i	$-0.166481\pi$
$752$	−5.51054	−	6.91000i	−0.200949	−	0.251982i
$753$	64.9870			2.36826
$754$	25.1388			0.915503
$755$	7.90912	+	9.91772i	0.287842	+	0.360943i
$756$	−5.20685	+	2.39249i	−0.189371	+	0.0870139i
$757$	−22.6223	+	28.3675i	−0.822222	+	1.03103i	0.176684	+	0.984268i	$0.443463\pi$
$757$	−22.6223	+	28.3675i	−0.822222	+	1.03103i	−0.998906	+	0.0467657i	$0.985109\pi$
$758$	5.87483	−	7.36680i	0.213383	−	0.267574i
$759$	−26.6949	−	12.8556i	−0.968963	−	0.466628i
$760$	−13.1117	−	6.31425i	−0.475611	−	0.229042i
$761$	23.1820	−	29.0692i	0.840345	−	1.05376i	−0.157459	−	0.987526i	$-0.550330\pi$
$761$	23.1820	−	29.0692i	0.840345	−	1.05376i	0.997804	−	0.0662338i	$-0.0210983\pi$
$762$	−31.3852	+	39.3558i	−1.13697	+	1.42571i
$763$	−5.42050	−	7.05511i	−0.196235	−	0.255412i
$764$	8.55987	+	10.7337i	0.309685	+	0.388333i
$765$	−22.8983			−0.827891
$766$	12.9596			0.468250
$767$	13.8219	+	17.3321i	0.499079	+	0.625825i
$768$	−0.581491	−	2.54768i	−0.0209828	−	0.0919314i
$769$	−8.29691	−	3.99558i	−0.299194	−	0.144084i	0.278264	−	0.960505i	$-0.410241\pi$
$769$	−8.29691	−	3.99558i	−0.299194	−	0.144084i	−0.577458	+	0.816420i	$0.695955\pi$
$770$	8.68023	−	10.4898i	0.312814	−	0.378026i
$771$	44.4243	−	21.3936i	1.59990	−	0.770473i
$772$	3.90648	+	4.89857i	0.140597	+	0.176304i
$773$	19.7655	−	9.51855i	0.710914	−	0.342358i	−0.0432316	−	0.999065i	$-0.513765\pi$
$773$	19.7655	−	9.51855i	0.710914	−	0.342358i	0.754146	+	0.656707i	$0.228051\pi$
$774$	7.39246	+	32.3885i	0.265716	+	1.16418i
$775$	0.767493	+	0.369605i	0.0275691	+	0.0132766i
$776$	0.145165	−	0.636010i	0.00521113	−	0.0228314i
$777$	−10.4082	−	13.5469i	−0.373392	−	0.485992i
$778$	5.75642	+	25.2205i	0.206378	+	0.904200i
$779$	−0.601585	+	2.63572i	−0.0215540	+	0.0944344i
$780$	−22.8446	+	28.6462i	−0.817968	+	1.02570i
$781$	−6.89004	+	30.1872i	−0.246545	+	1.08018i
$782$	11.8717	−	5.71710i	0.424530	−	0.204443i
$783$	8.80902			0.314809
$784$	4.16369	+	5.62705i	0.148703	+	0.200966i
$785$	1.27171			0.0453893
$786$	13.4277	−	6.46643i	0.478949	−	0.230650i
$787$	3.34870	−	14.6716i	0.119368	−	0.522987i	−0.879521	−	0.475861i	$-0.842137\pi$
$787$	3.34870	−	14.6716i	0.119368	−	0.522987i	0.998889	−	0.0471259i	$-0.0150062\pi$
$788$	−12.8134	+	16.0675i	−0.456459	+	0.572382i
$789$	4.53226	−	19.8571i	0.161353	−	0.706933i
$790$	3.61127	+	15.8220i	0.128483	+	0.562921i
$791$	3.92799	−	15.8804i	0.139663	−	0.564641i
$792$	−1.93275	+	8.46794i	−0.0686774	+	0.300895i
$793$	52.3756	+	25.2227i	1.85991	+	0.895686i
$794$	−7.16957	−	31.4119i	−0.254438	−	1.11477i
$795$	−2.36702	+	1.13990i	−0.0839495	+	0.0404280i
$796$	2.14928	+	2.69511i	0.0761792	+	0.0955257i
$797$	−20.3285	+	9.78967i	−0.720071	+	0.346768i	−0.757770	−	0.652521i	$-0.773711\pi$
$797$	−20.3285	+	9.78967i	−0.720071	+	0.346768i	0.0376996	+	0.999289i	$0.487997\pi$
$798$	−40.3025	+	18.5185i	−1.42669	+	0.655548i
$799$	−20.9929	−	10.1097i	−0.742677	−	0.357654i
$800$	0.0325293	+	0.142520i	0.00115008	+	0.00503884i
$801$	6.09727	+	7.64574i	0.215436	+	0.270149i
$802$	−23.9637			−0.846187
$803$	−24.0326			−0.848091
$804$	0.606515	+	0.760546i	0.0213902	+	0.0268224i
$805$	−19.1246	+	23.1115i	−0.674053	+	0.814574i
$806$	−22.4558	+	28.1587i	−0.790974	+	0.991849i
$807$	2.02639	−	2.54102i	0.0713324	−	0.0894480i
$808$	15.3019	+	7.36901i	0.538319	+	0.259241i
$809$	−48.2259	−	23.2244i	−1.69553	−	0.816525i	−0.994656	−	0.103243i	$-0.967078\pi$
$809$	−48.2259	−	23.2244i	−1.69553	−	0.816525i	−0.700876	−	0.713283i	$-0.747208\pi$
$810$	8.24128	−	10.3342i	0.289569	−	0.363108i
$811$	−30.3854	+	38.1021i	−1.06698	+	1.33795i	−0.128847	+	0.991665i	$0.541127\pi$
$811$	−30.3854	+	38.1021i	−1.06698	+	1.33795i	−0.938130	+	0.346282i	$0.887444\pi$
$812$	−2.20447	−	10.5328i	−0.0773618	−	0.369630i
$813$	−33.8996	−	42.5088i	−1.18891	−	1.49085i
$814$	−5.60532			−0.196467
$815$	−43.2001			−1.51323
$816$	−4.29537	−	5.38622i	−0.150368	−	0.188555i
$817$	12.3860	+	54.2667i	0.433332	+	1.89855i
$818$	−19.1223	−	9.20880i	−0.668595	−	0.321978i
$819$	12.8263	+	61.2832i	0.448186	+	2.14141i
$820$	0.861337	−	0.414798i	0.0300792	−	0.0144854i
$821$	−29.5987	−	37.1156i	−1.03300	−	1.29534i	−0.954430	−	0.298433i	$-0.903536\pi$
$821$	−29.5987	−	37.1156i	−1.03300	−	1.29534i	−0.0785703	−	0.996909i	$-0.525036\pi$
$822$	45.1571	−	21.7465i	1.57503	−	0.758496i
$823$	4.41213	+	19.3308i	0.153797	+	0.673829i	0.991761	+	0.128103i	$0.0408889\pi$
$823$	4.41213	+	19.3308i	0.153797	+	0.673829i	−0.837964	+	0.545726i	$0.816254\pi$
$824$	−10.9421	−	5.26942i	−0.381185	−	0.183569i
$825$	0.192836	−	0.844872i	0.00671370	−	0.0294147i
$826$	6.04985	−	7.31106i	0.210501	−	0.254384i
$827$	−6.93486	−	30.3836i	−0.241149	−	1.05654i	−0.939973	−	0.341248i	$-0.889150\pi$
$827$	−6.93486	−	30.3836i	−0.241149	−	1.05654i	0.698825	−	0.715293i	$-0.253707\pi$
$828$	4.25831	−	18.6569i	0.147986	−	0.648371i
$829$	−11.0774	+	13.8907i	−0.384735	+	0.482443i	−0.936056	−	0.351850i	$-0.885553\pi$
$829$	−11.0774	+	13.8907i	−0.384735	+	0.482443i	0.551321	+	0.834293i	$0.314124\pi$
$830$	−2.39112	+	10.4762i	−0.0829970	+	0.363633i
$831$	−9.40185	+	4.52769i	−0.326147	+	0.157064i
$832$	−6.18072			−0.214278
$833$	16.3263	+	8.60295i	0.565674	+	0.298074i
$834$	16.5101			0.571698
$835$	10.5945	−	5.10205i	0.366638	−	0.176564i
$836$	−3.23832	+	14.1880i	−0.112000	+	0.490702i
$837$	−7.86886	+	9.86723i	−0.271987	+	0.341061i
$838$	−0.473172	+	2.07310i	−0.0163454	+	0.0716140i
$839$	−6.45878	−	28.2978i	−0.222982	−	0.976947i	−0.955219	−	0.295898i	$-0.904381\pi$
$839$	−6.45878	−	28.2978i	−0.222982	−	0.976947i	0.732238	−	0.681049i	$-0.238476\pi$
$840$	14.0057	+	7.05954i	0.483241	+	0.243577i
$841$	2.77196	−	12.1448i	0.0955848	−	0.418785i
$842$	−20.8527	−	10.0422i	−0.718633	−	0.346075i
$843$	−14.8356	−	64.9990i	−0.510965	−	2.23868i
$844$	9.64399	−	4.64430i	0.331960	−	0.159863i
$845$	35.6447	+	44.6971i	1.22622	+	1.53763i
$846$	−30.4886	+	14.6825i	−1.04822	+	0.504796i
$847$	13.8302	+	6.97109i	0.475211	+	0.239529i
$848$	−0.399289	−	0.192287i	−0.0137116	−	0.00660317i
$849$	1.62770	+	7.13143i	0.0558626	+	0.244750i
$850$	0.240288	+	0.301311i	0.00824180	+	0.0103349i
$851$	12.3498			0.423347
$852$	−35.6681			−1.22197
$853$	−31.6955	−	39.7449i	−1.08523	−	1.36084i	−0.927701	−	0.373325i	$-0.878218\pi$
$853$	−31.6955	−	39.7449i	−1.08523	−	1.36084i	−0.157532	−	0.987514i	$-0.550354\pi$
$854$	5.97509	−	24.1565i	0.204463	−	0.826618i
$855$	−34.7408	+	43.5636i	−1.18811	+	1.48985i
$856$	−0.723453	+	0.907182i	−0.0247271	+	0.0310068i
$857$	40.8882	+	19.6907i	1.39671	+	0.672622i	0.972492	−	0.232936i	$-0.0748333\pi$
$857$	40.8882	+	19.6907i	1.39671	+	0.672622i	0.424222	+	0.905558i	$0.360548\pi$
$858$	33.0114	+	15.8974i	1.12699	+	0.542730i
$859$	20.0880	−	25.1895i	0.685393	−	0.859455i	−0.310446	−	0.950591i	$-0.600478\pi$
$859$	20.0880	−	25.1895i	0.685393	−	0.859455i	0.995838	+	0.0911360i	$0.0290498\pi$
$860$	12.2723	−	15.3890i	0.418483	−	0.524762i
$861$	0.699612	−	2.82844i	0.0238427	−	0.0963930i
$862$	−24.6837	−	30.9524i	−0.840730	−	1.05424i
$863$	32.2324			1.09720			0.548602	−	0.836084i	$-0.315160\pi$
$863$	32.2324			1.09720			0.548602	+	0.836084i	$0.315160\pi$
$864$	−2.16581			−0.0736825
$865$	6.86430	+	8.60756i	0.233393	+	0.292666i
$866$	3.01461	+	13.2079i	0.102441	+	0.448822i
$867$	23.6613	+	11.3947i	0.803581	+	0.386984i
$868$	13.7673	+	6.93941i	0.467294	+	0.235539i
$869$	14.6217	−	7.04145i	0.496008	−	0.238865i
$870$	−15.0332	−	18.8510i	−0.509672	−	0.639108i
$871$	2.07295	−	0.998281i	0.0702393	−	0.0338255i
$872$	−0.748281	−	3.27843i	−0.0253400	−	0.111022i
$873$	−2.25042	−	1.08375i	−0.0761652	−	0.0366792i
$874$	7.13477	−	31.2595i	0.241337	−	1.05737i
$875$	26.0145	+	13.1126i	0.879449	+	0.443286i
$876$	−6.16028	−	26.9900i	−0.208137	−	0.911906i
$877$	−2.02406	+	8.86797i	−0.0683475	+	0.299450i	−0.997536	−	0.0701562i	$-0.977650\pi$
$877$	−2.02406	+	8.86797i	−0.0683475	+	0.299450i	0.929189	+	0.369606i	$0.120507\pi$
$878$	23.8774	−	29.9413i	0.805824	−	1.01047i
$879$	−0.768200	+	3.36570i	−0.0259107	+	0.113522i
$880$	4.63655	−	2.23285i	0.156298	−	0.0752692i
$881$	10.2269			0.344554			0.172277	−	0.985049i	$-0.444888\pi$
$881$	10.2269			0.344554			0.172277	+	0.985049i	$0.444888\pi$
$882$	24.5521	−	10.7481i	0.826711	−	0.361906i
$883$	16.8330			0.566476			0.283238	−	0.959050i	$-0.408591\pi$
$883$	16.8330			0.566476			0.283238	+	0.959050i	$0.408591\pi$
$884$	−14.6807	+	7.06987i	−0.493766	+	0.237785i
$885$	4.73134	−	20.7294i	0.159042	−	0.696810i
$886$	−11.4859	+	14.4028i	−0.385875	+	0.483872i
$887$	−1.07817	+	4.72377i	−0.0362014	+	0.158609i	−0.989798	−	0.142479i	$-0.954493\pi$
$887$	−1.07817	+	4.72377i	−0.0362014	+	0.158609i	0.953596	+	0.301088i	$0.0973497\pi$
$888$	−1.43682	−	6.29510i	−0.0482164	−	0.211250i
$889$	32.4915	−	39.2650i	1.08973	−	1.31691i
$890$	1.28931	−	5.64883i	0.0432177	−	0.189349i
$891$	−11.9090	−	5.73507i	−0.398966	−	0.192132i
$892$	−2.32546	−	10.1885i	−0.0778620	−	0.341136i
$893$	−51.0835	+	24.6005i	−1.70944	+	0.823225i
$894$	20.5053	+	25.7128i	0.685800	+	0.859966i
$895$	−27.3273	+	13.1601i	−0.913452	+	0.439895i
$896$	0.541999	+	2.58964i	0.0181069	+	0.0865138i
$897$	−72.7319	−	35.0258i	−2.42845	−	1.16948i
$898$	6.09815	+	26.7178i	0.203498	+	0.891583i
$899$	−14.7773	−	18.5302i	−0.492852	−	0.618017i
$900$	0.559714			0.0186571
$901$	−1.16836			−0.0389236
$902$	−0.596064	−	0.747440i	−0.0198468	−	0.0248870i
$903$	−12.2893	−	58.7174i	−0.408961	−	1.95399i
$904$	3.85510	−	4.83414i	0.128219	−	0.160781i
$905$	−18.9575	+	23.7720i	−0.630170	+	0.790208i
$906$	13.1655	+	6.34018i	0.437395	+	0.210638i
$907$	−16.9685	−	8.17161i	−0.563431	−	0.271334i	0.130413	−	0.991460i	$-0.458370\pi$
$907$	−16.9685	−	8.17161i	−0.563431	−	0.271334i	−0.693843	+	0.720126i	$0.744084\pi$
$908$	6.65553	−	8.34577i	0.220872	−	0.276964i
$909$	40.5441	−	50.8407i	1.34476	−	1.68628i
$910$	23.6498	−	28.5801i	0.783984	−	0.947422i
$911$	−12.3583	−	15.4968i	−0.409447	−	0.513431i	0.533760	−	0.845636i	$-0.320779\pi$
$911$	−12.3583	−	15.4968i	−0.409447	−	0.513431i	−0.943207	+	0.332205i	$0.892207\pi$
$912$	−16.7640			−0.555112
$913$	10.7456			0.355627
$914$	4.08256	+	5.11937i	0.135039	+	0.169334i
$915$	−12.4070	−	54.3585i	−0.410162	−	1.79704i
$916$	−7.27832	−	3.50505i	−0.240482	−	0.115810i
$917$	−13.7111	+	6.30010i	−0.452781	+	0.208048i
$918$	−5.14434	+	2.47738i	−0.169789	+	0.0817658i
$919$	−12.6847	−	15.9061i	−0.418430	−	0.524695i	0.527286	−	0.849688i	$-0.323210\pi$
$919$	−12.6847	−	15.9061i	−0.418430	−	0.524695i	−0.945717	+	0.324993i	$0.894638\pi$
$920$	−10.2154	+	4.91949i	−0.336792	+	0.162191i
$921$	6.58607	+	28.8555i	0.217018	+	0.950820i
$922$	21.2097	+	10.2140i	0.698503	+	0.336381i
$923$	−18.7723	+	82.2469i	−0.617899	+	2.70719i
$924$	3.76599	−	15.2254i	0.123892	−	0.500879i
$925$	0.0803771	+	0.352155i	0.00264278	+	0.0115788i
$926$	−0.698180	+	3.05893i	−0.0229436	+	0.100523i
$927$	−28.9922	+	36.3551i	−0.952230	+	1.19406i
$928$	0.905059	−	3.96532i	0.0297100	−	0.130168i
$929$	8.62353	−	4.15287i	0.282929	−	0.136251i	−0.287038	−	0.957919i	$-0.592670\pi$
$929$	8.62353	−	4.15287i	0.282929	−	0.136251i	0.569966	+	0.821668i	$0.306956\pi$
$930$	34.5443			1.13275
$931$	41.1369	−	18.0083i	1.34821	−	0.590199i
$932$	−2.59078			−0.0848637
$933$	−20.3674	+	9.80845i	−0.666800	+	0.321114i
$934$	−7.51588	+	32.9292i	−0.245927	+	1.07748i
$935$	8.45889	−	10.6071i	0.276635	−	0.346890i
$936$	−5.26590	+	23.0714i	−0.172121	+	0.754113i
$937$	11.2692	+	49.3735i	0.368148	+	1.61296i	0.731862	+	0.681453i	$0.238651\pi$
$937$	11.2692	+	49.3735i	0.368148	+	1.61296i	−0.363714	+	0.931511i	$0.618491\pi$
$938$	−0.600048	−	0.780998i	−0.0195922	−	0.0255005i
$939$	−2.74513	+	12.0272i	−0.0895838	+	0.392492i
$940$	18.0641	+	8.69923i	0.589187	+	0.283738i
$941$	7.46059	+	32.6870i	0.243208	+	1.06557i	0.938076	+	0.346428i	$0.112606\pi$
$941$	7.46059	+	32.6870i	0.243208	+	1.06557i	−0.694868	+	0.719137i	$0.744537\pi$
$942$	1.31986	−	0.635611i	0.0430034	−	0.0207093i
$943$	1.31327	+	1.64679i	0.0427659	+	0.0536268i
$944$	3.23153	−	1.55622i	0.105177	−	0.0506507i
$945$	8.28724	−	10.0149i	0.269584	−	0.325784i
$946$	−17.7341	−	8.54027i	−0.576584	−	0.277668i
$947$	8.52136	+	37.3345i	0.276907	+	1.21321i	0.901681	+	0.432403i	$0.142334\pi$
$947$	8.52136	+	37.3345i	0.276907	+	1.21321i	−0.624774	+	0.780806i	$0.714809\pi$
$948$	11.6559	+	14.6161i	0.378567	+	0.474709i
$949$	−65.4782			−2.12551
$950$	0.937798			0.0304262
$951$	25.5829	+	32.0799i	0.829582	+	1.04026i
$952$	4.24956	+	5.53106i	0.137729	+	0.179263i
$953$	35.8905	−	45.0053i	1.16261	−	1.45786i	0.298604	−	0.954377i	$-0.403479\pi$
$953$	35.8905	−	45.0053i	1.16261	−	1.45786i	0.864003	−	0.503486i	$-0.167950\pi$
$954$	−1.05796	+	1.32664i	−0.0342527	+	0.0429515i
$955$	−28.0602	−	13.5131i	−0.908005	−	0.437272i
$956$	−3.74516	−	1.80357i	−0.121127	−	0.0583318i
$957$	−15.0332	+	18.8510i	−0.485953	+	0.609366i
$958$	18.2419	−	22.8746i	0.589367	−	0.739043i
$959$	−46.1103	+	21.1871i	−1.48898	+	0.684168i
$960$	3.69610	+	4.63477i	0.119291	+	0.149587i
$961$	2.95642			0.0953684
$962$	−15.2720			−0.492390
$963$	2.76996	+	3.47342i	0.0892606	+	0.111929i
$964$	−1.47463	−	6.46078i	−0.0474947	−	0.208088i
$965$	−12.8059	−	6.16698i	−0.412235	−	0.198522i
$966$	−8.29736	+	33.5452i	−0.266963	+	1.07930i
$967$	16.5206	−	7.95588i	0.531265	−	0.255844i	−0.148965	−	0.988842i	$-0.547594\pi$
$967$	16.5206	−	7.95588i	0.531265	−	0.255844i	0.680230	+	0.732999i	$0.261880\pi$
$968$	3.64979	+	4.57670i	0.117309	+	0.147101i
$969$	−39.8186	+	19.1756i	−1.27916	+	0.616010i
$970$	0.329310	+	1.44280i	0.0105735	+	0.0463256i
$971$	22.7969	+	10.9784i	0.731587	+	0.352314i	0.762308	−	0.647214i	$-0.224066\pi$
$971$	22.7969	+	10.9784i	0.731587	+	0.352314i	−0.0307210	+	0.999528i	$0.509780\pi$
$972$	4.83399	−	21.1791i	0.155050	−	0.679320i
$973$	−16.7130	−	0.302248i	−0.535796	−	0.00968964i
$974$	2.35825	+	10.3322i	0.0755632	+	0.331064i
$975$	0.525395	−	2.30190i	0.0168261	−	0.0737199i
$976$	5.86420	−	7.35348i	0.187709	−	0.235379i
$977$	7.45311	−	32.6542i	0.238446	−	1.04470i	−0.703963	−	0.710237i	$-0.748588\pi$
$977$	7.45311	−	32.6542i	0.238446	−	1.04470i	0.942409	−	0.334464i	$-0.108555\pi$
$978$	−44.8357	+	21.5917i	−1.43369	+	0.690428i
$979$	−5.79410			−0.185180
$980$	−14.0486	−	7.40272i	−0.448766	−	0.236471i
$981$	−12.8753			−0.411076
$982$	−21.7783	+	10.4879i	−0.694975	+	0.334682i
$983$	−0.352192	+	1.54305i	−0.0112332	+	0.0492157i	−0.980234	−	0.197842i	$-0.936607\pi$
$983$	−0.352192	+	1.54305i	−0.0112332	+	0.0492157i	0.969001	+	0.247058i	$0.0794638\pi$
$984$	0.686629	−	0.861006i	0.0218889	−	0.0274479i
$985$	10.3741	−	45.4518i	0.330545	−	1.44821i
$986$	−2.38603	−	10.4539i	−0.0759866	−	0.332919i
$987$	55.5253	−	25.5132i	1.76739	−	0.812095i
$988$	−8.82299	+	38.6560i	−0.280697	+	1.22981i
$989$	39.0723	+	18.8162i	1.24243	+	0.598321i
$990$	−4.38449	−	19.2097i	−0.139348	−	0.610524i
$991$	5.13551	−	2.47313i	0.163135	−	0.0785616i	−0.350535	−	0.936550i	$-0.614000\pi$
$991$	5.13551	−	2.47313i	0.163135	−	0.0785616i	0.513669	+	0.857988i	$0.328286\pi$
$992$	3.63321	+	4.55590i	0.115354	+	0.144650i
$993$	46.5491	−	22.4169i	1.47719	−	0.711378i
$994$	36.1066	+	0.652972i	1.14523	+	0.0207110i
$995$	−7.04557	−	3.39297i	−0.223360	−	0.107564i
$996$	2.75442	+	12.0679i	0.0872772	+	0.382387i
$997$	19.6631	+	24.6568i	0.622738	+	0.780889i	0.988727	−	0.149730i	$-0.0478406\pi$
$997$	19.6631	+	24.6568i	0.622738	+	0.780889i	−0.365989	+	0.930619i	$0.619269\pi$
$998$	26.3495			0.834079
$999$	−5.35155			−0.169315

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	98.2.e.b.71.1	yes	18
3.2	odd	2		882.2.u.g.757.2		18
4.3	odd	2		784.2.u.d.561.3		18
7.2	even	3		686.2.g.h.263.1		36
7.3	odd	6		686.2.g.g.275.1		36
7.4	even	3		686.2.g.h.275.3		36
7.5	odd	6		686.2.g.g.263.3		36
7.6	odd	2		686.2.e.b.491.3		18
49.12	odd	42		686.2.g.g.459.1		36
49.15	even	7		4802.2.a.d.1.9		9
49.17	odd	42		686.2.g.g.373.3		36
49.20	odd	14		686.2.e.b.197.3		18
49.29	even	7	inner	98.2.e.b.29.1	✓	18
49.32	even	21		686.2.g.h.373.1		36
49.34	odd	14		4802.2.a.c.1.1		9
49.37	even	21		686.2.g.h.459.3		36
147.29	odd	14		882.2.u.g.127.2		18
196.127	odd	14		784.2.u.d.225.3		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
98.2.e.b.29.1	✓	18	49.29	even	7	inner
98.2.e.b.71.1	yes	18	1.1	even	1	trivial
686.2.e.b.197.3		18	49.20	odd	14
686.2.e.b.491.3		18	7.6	odd	2
686.2.g.g.263.3		36	7.5	odd	6
686.2.g.g.275.1		36	7.3	odd	6
686.2.g.g.373.3		36	49.17	odd	42
686.2.g.g.459.1		36	49.12	odd	42
686.2.g.h.263.1		36	7.2	even	3
686.2.g.h.275.3		36	7.4	even	3
686.2.g.h.373.1		36	49.32	even	21
686.2.g.h.459.3		36	49.37	even	21
784.2.u.d.225.3		18	196.127	odd	14
784.2.u.d.561.3		18	4.3	odd	2
882.2.u.g.127.2		18	147.29	odd	14
882.2.u.g.757.2		18	3.2	odd	2
4802.2.a.c.1.1		9	49.34	odd	14
4802.2.a.d.1.9		9	49.15	even	7

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 98 = 2 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	98.e (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.900969 - 0.433884i) q^{2} +(-0.581491 + 2.54768i) q^{3} +(0.623490 - 0.781831i) q^{4} +(-0.504793 + 2.21164i) q^{5} +(0.581491 + 2.54768i) q^{6} +(-0.541999 - 2.58964i) q^{7} +(0.222521 - 0.974928i) q^{8} +(-3.44963 - 1.66125i) q^{9} +O(q^{10})\)	\(q+(0.900969 - 0.433884i) q^{2} +(-0.581491 + 2.54768i) q^{3} +(0.623490 - 0.781831i) q^{4} +(-0.504793 + 2.21164i) q^{5} +(0.581491 + 2.54768i) q^{6} +(-0.541999 - 2.58964i) q^{7} +(0.222521 - 0.974928i) q^{8} +(-3.44963 - 1.66125i) q^{9} +(0.504793 + 2.21164i) q^{10} +(2.04387 - 0.984274i) q^{11} +(1.62930 + 2.04308i) q^{12} +(5.56864 - 2.68171i) q^{13} +(-1.61193 - 2.09802i) q^{14} +(-5.34103 - 2.57210i) q^{15} +(-0.222521 - 0.974928i) q^{16} +(-1.64372 - 2.06116i) q^{17} -3.82880 q^{18} -6.41513 q^{19} +(1.41440 + 1.77360i) q^{20} +(6.91274 + 0.125014i) q^{21} +(1.41440 - 1.77360i) q^{22} +(-3.11625 + 3.90766i) q^{23} +(2.35441 + 1.13382i) q^{24} +(-0.131708 - 0.0634274i) q^{25} +(3.85362 - 4.83228i) q^{26} +(1.35036 - 1.69330i) q^{27} +(-2.36259 - 1.19086i) q^{28} +(2.53592 + 3.17994i) q^{29} -5.92809 q^{30} -5.82721 q^{31} +(-0.623490 - 0.781831i) q^{32} +(1.31912 + 5.77946i) q^{33} +(-2.37524 - 1.14386i) q^{34} +(6.00096 + 0.108525i) q^{35} +(-3.44963 + 1.66125i) q^{36} +(-1.54059 - 1.93184i) q^{37} +(-5.77984 + 2.78342i) q^{38} +(3.59403 + 15.7465i) q^{39} +(2.04387 + 0.984274i) q^{40} +(0.0937760 - 0.410859i) q^{41} +(6.28240 - 2.88669i) q^{42} +(-1.93075 - 8.45917i) q^{43} +(0.504793 - 2.21164i) q^{44} +(5.41545 - 6.79076i) q^{45} +(-1.11218 + 4.87277i) q^{46} +(7.96296 - 3.83476i) q^{47} +2.61320 q^{48} +(-6.41247 + 2.80716i) q^{49} -0.146185 q^{50} +(6.20698 - 2.98913i) q^{51} +(1.37534 - 6.02576i) q^{52} +(0.276316 - 0.346490i) q^{53} +(0.481939 - 2.11151i) q^{54} +(1.14513 + 5.01716i) q^{55} +(-2.64532 - 0.0478395i) q^{56} +(3.73034 - 16.3437i) q^{57} +(3.66451 + 1.76473i) q^{58} +(0.798122 + 3.49680i) q^{59} +(-5.34103 + 2.57210i) q^{60} +(5.86420 + 7.35348i) q^{61} +(-5.25014 + 2.52833i) q^{62} +(-2.43235 + 9.83369i) q^{63} +(-0.900969 - 0.433884i) q^{64} +(3.11999 + 13.6696i) q^{65} +(3.69610 + 4.63477i) q^{66} +0.372255 q^{67} -2.63632 q^{68} +(-8.14339 - 10.2115i) q^{69} +(5.45377 - 2.50594i) q^{70} +(-8.51015 + 10.6714i) q^{71} +(-2.38722 + 2.99348i) q^{72} +(-9.54481 - 4.59654i) q^{73} +(-2.22622 - 1.07209i) q^{74} +(0.238180 - 0.298668i) q^{75} +(-3.99977 + 5.01555i) q^{76} +(-3.65669 - 4.75940i) q^{77} +(10.0703 + 12.6277i) q^{78} +7.15395 q^{79} +2.26852 q^{80} +(-3.63289 - 4.55549i) q^{81} +(-0.0937760 - 0.410859i) q^{82} +(4.26774 + 2.05523i) q^{83} +(4.40776 - 5.32665i) q^{84} +(5.38829 - 2.59486i) q^{85} +(-5.40984 - 6.78373i) q^{86} +(-9.57609 + 4.61160i) q^{87} +(-0.504793 - 2.21164i) q^{88} +(-2.30119 - 1.10820i) q^{89} +(1.93275 - 8.46794i) q^{90} +(-9.96287 - 12.9673i) q^{91} +(1.11218 + 4.87277i) q^{92} +(3.38847 - 14.8459i) q^{93} +(5.51054 - 6.91000i) q^{94} +(3.23832 - 14.1880i) q^{95} +(2.35441 - 1.13382i) q^{96} +0.652366 q^{97} +(-4.55946 + 5.31144i) q^{98} -8.68571 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 3 q^{2} - 5 q^{3} - 3 q^{4} + 5 q^{6} - q^{7} + 3 q^{8} - 10 q^{9}+O(q^{10}) \) 18 * q + 3 * q^2 - 5 * q^3 - 3 * q^4 + 5 * q^6 - q^7 + 3 * q^8 - 10 * q^9	\( 18 q + 3 q^{2} - 5 q^{3} - 3 q^{4} + 5 q^{6} - q^{7} + 3 q^{8} - 10 q^{9} + 7 q^{11} + 2 q^{12} - 10 q^{13} + q^{14} + 7 q^{15} - 3 q^{16} + q^{17} - 32 q^{18} - 44 q^{19} + 7 q^{20} - 5 q^{21} + 7 q^{22} + 21 q^{23} - 2 q^{24} + q^{25} + 3 q^{26} + 10 q^{27} - 8 q^{28} + 11 q^{29} - 24 q^{31} + 3 q^{32} - 14 q^{33} - q^{34} - 21 q^{35} - 10 q^{36} - 13 q^{37} - 19 q^{38} - 3 q^{39} + 7 q^{40} + 8 q^{41} + 61 q^{42} - 24 q^{43} + 98 q^{45} + 21 q^{46} + 40 q^{47} + 2 q^{48} - 43 q^{49} - 50 q^{50} + 36 q^{51} + 18 q^{52} + 10 q^{53} + 4 q^{54} + 49 q^{55} + q^{56} + 19 q^{57} + 24 q^{58} + 13 q^{59} + 7 q^{60} + 27 q^{61} - 11 q^{62} + 41 q^{63} - 3 q^{64} - 21 q^{66} - 86 q^{67} - 34 q^{68} - 91 q^{69} - 14 q^{70} + 3 q^{72} + 5 q^{73} + 13 q^{74} - 3 q^{75} - 2 q^{76} - 14 q^{77} + 38 q^{78} - 66 q^{79} - 2 q^{81} - 8 q^{82} + 55 q^{83} + 23 q^{84} - 49 q^{85} - 18 q^{86} - 110 q^{87} + 62 q^{89} + 21 q^{90} + 39 q^{91} - 21 q^{92} + 46 q^{93} + 23 q^{94} - 7 q^{95} - 2 q^{96} - 32 q^{97} - 48 q^{98} + 14 q^{99}+O(q^{100}) \) 18 * q + 3 * q^2 - 5 * q^3 - 3 * q^4 + 5 * q^6 - q^7 + 3 * q^8 - 10 * q^9 + 7 * q^11 + 2 * q^12 - 10 * q^13 + q^14 + 7 * q^15 - 3 * q^16 + q^17 - 32 * q^18 - 44 * q^19 + 7 * q^20 - 5 * q^21 + 7 * q^22 + 21 * q^23 - 2 * q^24 + q^25 + 3 * q^26 + 10 * q^27 - 8 * q^28 + 11 * q^29 - 24 * q^31 + 3 * q^32 - 14 * q^33 - q^34 - 21 * q^35 - 10 * q^36 - 13 * q^37 - 19 * q^38 - 3 * q^39 + 7 * q^40 + 8 * q^41 + 61 * q^42 - 24 * q^43 + 98 * q^45 + 21 * q^46 + 40 * q^47 + 2 * q^48 - 43 * q^49 - 50 * q^50 + 36 * q^51 + 18 * q^52 + 10 * q^53 + 4 * q^54 + 49 * q^55 + q^56 + 19 * q^57 + 24 * q^58 + 13 * q^59 + 7 * q^60 + 27 * q^61 - 11 * q^62 + 41 * q^63 - 3 * q^64 - 21 * q^66 - 86 * q^67 - 34 * q^68 - 91 * q^69 - 14 * q^70 + 3 * q^72 + 5 * q^73 + 13 * q^74 - 3 * q^75 - 2 * q^76 - 14 * q^77 + 38 * q^78 - 66 * q^79 - 2 * q^81 - 8 * q^82 + 55 * q^83 + 23 * q^84 - 49 * q^85 - 18 * q^86 - 110 * q^87 + 62 * q^89 + 21 * q^90 + 39 * q^91 - 21 * q^92 + 46 * q^93 + 23 * q^94 - 7 * q^95 - 2 * q^96 - 32 * q^97 - 48 * q^98 + 14 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more