LMFDB - Embedded newform 400.2.j.d.307.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [400,2,Mod(43,400)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(400, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 3]))

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

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

chi := DirichletCharacter("400.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 400 = 2^{4} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	400.j (of order $4$, degree $2$, 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:	$3.19401608085$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$9$ over $\Q(i)$
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} + 2 x^{16} - 4 x^{15} - 5 x^{14} - 14 x^{13} - 10 x^{12} + 6 x^{11} + 37 x^{10} + 70 x^{9} + \cdots + 512 $ x^18 + 2x^16 - 4x^15 - 5x^14 - 14x^13 - 10x^12 + 6x^11 + 37x^10 + 70x^9 + 74x^8 + 24x^7 - 80x^6 - 224x^5 - 160x^4 - 256x^3 + 256*x^2 + 512
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{7} $
Twist minimal:	no (minimal twist has level 80)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			307.3
Root			$-1.37691 - 0.322680i$ of defining polynomial
Character	$\chi$	$=$	400.307
Dual form			400.2.j.d.43.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.687667 + 1.23576i) q^{2} +0.614566i q^{3} +(-1.05423 - 1.69959i) q^{4} +(-0.759459 - 0.422617i) q^{6} +(-2.83610 - 2.83610i) q^{7} +(2.82525 - 0.134028i) q^{8} +2.62231 q^{9} +O(q^{10})$	\(q+(-0.687667 + 1.23576i) q^{2} +0.614566i q^{3} +(-1.05423 - 1.69959i) q^{4} +(-0.759459 - 0.422617i) q^{6} +(-2.83610 - 2.83610i) q^{7} +(2.82525 - 0.134028i) q^{8} +2.62231 q^{9} +(1.95928 + 1.95928i) q^{11} +(1.04451 - 0.647893i) q^{12} +2.05493 q^{13} +(5.45504 - 1.55446i) q^{14} +(-1.77720 + 3.58351i) q^{16} +(4.06774 + 4.06774i) q^{17} +(-1.80327 + 3.24056i) q^{18} +(0.683479 + 0.683479i) q^{19} +(1.74297 - 1.74297i) q^{21} +(-3.76854 + 1.07388i) q^{22} +(4.95014 - 4.95014i) q^{23} +(0.0823693 + 1.73630i) q^{24} +(-1.41310 + 2.53941i) q^{26} +3.45528i q^{27} +(-1.83030 + 7.81010i) q^{28} +(-0.835439 + 0.835439i) q^{29} -2.35978i q^{31} +(-3.20625 - 4.66047i) q^{32} +(-1.20411 + 1.20411i) q^{33} +(-7.82401 + 2.22952i) q^{34} +(-2.76451 - 4.45685i) q^{36} +4.54384 q^{37} +(-1.31462 + 0.374613i) q^{38} +1.26289i q^{39} -5.07255i q^{41} +(0.955318 + 3.35248i) q^{42} +0.849753 q^{43} +(1.26444 - 5.39549i) q^{44} +(2.71316 + 9.52126i) q^{46} +(-2.72646 + 2.72646i) q^{47} +(-2.20230 - 1.09221i) q^{48} +9.08690i q^{49} +(-2.49989 + 2.49989i) q^{51} +(-2.16636 - 3.49253i) q^{52} +5.17605i q^{53} +(-4.26991 - 2.37608i) q^{54} +(-8.39280 - 7.63257i) q^{56} +(-0.420043 + 0.420043i) q^{57} +(-0.457903 - 1.60691i) q^{58} +(4.16328 - 4.16328i) q^{59} +(5.55706 + 5.55706i) q^{61} +(2.91613 + 1.62274i) q^{62} +(-7.43712 - 7.43712i) q^{63} +(7.96407 - 0.757328i) q^{64} +(-0.659968 - 2.31602i) q^{66} +1.73609 q^{67} +(2.62515 - 11.2018i) q^{68} +(3.04219 + 3.04219i) q^{69} +2.33526 q^{71} +(7.40868 - 0.351464i) q^{72} +(-4.39686 - 4.39686i) q^{73} +(-3.12465 + 5.61511i) q^{74} +(0.441090 - 1.88218i) q^{76} -11.1134i q^{77} +(-1.56063 - 0.868446i) q^{78} -14.0993 q^{79} +5.74343 q^{81} +(6.26848 + 3.48822i) q^{82} -2.75725i q^{83} +(-4.79982 - 1.12484i) q^{84} +(-0.584347 + 1.05009i) q^{86} +(-0.513433 - 0.513433i) q^{87} +(5.79805 + 5.27285i) q^{88} -11.6448 q^{89} +(-5.82797 - 5.82797i) q^{91} +(-13.6318 - 3.19462i) q^{92} +1.45024 q^{93} +(-1.49437 - 5.24417i) q^{94} +(2.86416 - 1.97045i) q^{96} +(3.52933 + 3.52933i) q^{97} +(-11.2293 - 6.24876i) q^{98} +(5.13783 + 5.13783i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 4 q^{2} - 4 q^{4} - 8 q^{6} - 2 q^{7} + 4 q^{8} - 10 q^{9}+O(q^{10}) $ 18 * q + 4 * q^2 - 4 * q^4 - 8 * q^6 - 2 * q^7 + 4 * q^8 - 10 * q^9	$ 18 q + 4 q^{2} - 4 q^{4} - 8 q^{6} - 2 q^{7} + 4 q^{8} - 10 q^{9} - 2 q^{11} - 4 q^{12} + 12 q^{14} + 6 q^{17} - 16 q^{18} + 2 q^{19} - 16 q^{21} - 4 q^{22} + 2 q^{23} + 4 q^{24} - 16 q^{26} + 4 q^{28} - 14 q^{29} + 4 q^{32} + 8 q^{33} - 28 q^{34} - 4 q^{36} - 8 q^{37} - 16 q^{38} - 28 q^{42} + 44 q^{43} + 44 q^{44} + 12 q^{46} + 38 q^{47} - 60 q^{48} + 8 q^{51} + 40 q^{52} - 4 q^{54} + 20 q^{56} - 24 q^{57} + 20 q^{58} - 10 q^{59} + 14 q^{61} - 6 q^{63} - 16 q^{64} + 4 q^{66} - 12 q^{67} - 36 q^{68} + 32 q^{69} + 24 q^{71} + 36 q^{72} - 14 q^{73} + 48 q^{74} - 16 q^{76} + 84 q^{78} + 16 q^{79} + 2 q^{81} + 28 q^{82} - 24 q^{84} - 36 q^{86} - 24 q^{87} + 96 q^{88} - 12 q^{89} - 52 q^{92} - 16 q^{93} + 28 q^{94} - 40 q^{96} - 18 q^{97} - 32 q^{98} - 22 q^{99}+O(q^{100}) $ 18 * q + 4 * q^2 - 4 * q^4 - 8 * q^6 - 2 * q^7 + 4 * q^8 - 10 * q^9 - 2 * q^11 - 4 * q^12 + 12 * q^14 + 6 * q^17 - 16 * q^18 + 2 * q^19 - 16 * q^21 - 4 * q^22 + 2 * q^23 + 4 * q^24 - 16 * q^26 + 4 * q^28 - 14 * q^29 + 4 * q^32 + 8 * q^33 - 28 * q^34 - 4 * q^36 - 8 * q^37 - 16 * q^38 - 28 * q^42 + 44 * q^43 + 44 * q^44 + 12 * q^46 + 38 * q^47 - 60 * q^48 + 8 * q^51 + 40 * q^52 - 4 * q^54 + 20 * q^56 - 24 * q^57 + 20 * q^58 - 10 * q^59 + 14 * q^61 - 6 * q^63 - 16 * q^64 + 4 * q^66 - 12 * q^67 - 36 * q^68 + 32 * q^69 + 24 * q^71 + 36 * q^72 - 14 * q^73 + 48 * q^74 - 16 * q^76 + 84 * q^78 + 16 * q^79 + 2 * q^81 + 28 * q^82 - 24 * q^84 - 36 * q^86 - 24 * q^87 + 96 * q^88 - 12 * q^89 - 52 * q^92 - 16 * q^93 + 28 * q^94 - 40 * q^96 - 18 * q^97 - 32 * q^98 - 22 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/400\mathbb{Z}\right)^\times$.

$n$	$101$	$177$	$351$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{4}\right)$	$-1$

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 $

$2$	−0.687667	+	1.23576i	−0.486254	+	0.873818i
$2$	−0.687667	+	1.23576i	−0.486254	+	0.873818i
$3$			0.614566i			0.354820i	0.984137	+	0.177410i	$0.0567718\pi$
$3$			0.614566i			0.354820i	−0.984137	+	0.177410i	$0.943228\pi$
$4$	−1.05423	−	1.69959i	−0.527114	−	0.849794i
$5$		0			0
$5$		0			0
$6$	−0.759459	−	0.422617i	−0.310048	−	0.172533i
$7$	−2.83610	−	2.83610i	−1.07194	−	1.07194i	−0.997203	−	0.0747413i	$-0.976187\pi$
$7$	−2.83610	−	2.83610i	−1.07194	−	1.07194i	−0.0747413	−	0.997203i	$-0.523813\pi$
$8$	2.82525	−	0.134028i	0.998877	−	0.0473862i
$9$	2.62231			0.874103
$10$		0			0
$11$	1.95928	+	1.95928i	0.590745	+	0.590745i	0.937833	−	0.347088i	$-0.112829\pi$
$11$	1.95928	+	1.95928i	0.590745	+	0.590745i	−0.347088	+	0.937833i	$0.612829\pi$
$12$	1.04451	−	0.647893i	0.301524	−	0.187031i
$13$	2.05493			0.569934			0.284967	−	0.958537i	$-0.408017\pi$
$13$	2.05493			0.569934			0.284967	+	0.958537i	$0.408017\pi$
$14$	5.45504	−	1.55446i	1.45792	−	0.415447i
$15$		0			0
$16$	−1.77720	+	3.58351i	−0.444301	+	0.895878i
$17$	4.06774	+	4.06774i	0.986571	+	0.986571i	0.999911	−	0.0133401i	$-0.00424641\pi$
$17$	4.06774	+	4.06774i	0.986571	+	0.986571i	−0.0133401	+	0.999911i	$0.504246\pi$
$18$	−1.80327	+	3.24056i	−0.425036	+	0.763806i
$19$	0.683479	+	0.683479i	0.156801	+	0.156801i	0.781147	−	0.624347i	$-0.214635\pi$
$19$	0.683479	+	0.683479i	0.156801	+	0.156801i	−0.624347	+	0.781147i	$0.714635\pi$
$20$		0			0
$21$	1.74297	−	1.74297i	0.380347	−	0.380347i
$22$	−3.76854	+	1.07388i	−0.803455	+	0.228951i
$23$	4.95014	−	4.95014i	1.03218	−	1.03218i	0.0327113	−	0.999465i	$-0.489586\pi$
$23$	4.95014	−	4.95014i	1.03218	−	1.03218i	0.999465	−	0.0327113i	$-0.0104142\pi$
$24$	0.0823693	+	1.73630i	0.0168136	+	0.354421i
$25$		0			0
$26$	−1.41310	+	2.53941i	−0.277133	+	0.498018i
$27$			3.45528i			0.664969i
$28$	−1.83030	+	7.81010i	−0.345895	+	1.47597i
$29$	−0.835439	+	0.835439i	−0.155137	+	0.155137i	−0.780408	−	0.625271i	$-0.784989\pi$
$29$	−0.835439	+	0.835439i	−0.155137	+	0.155137i	0.625271	+	0.780408i	$0.284989\pi$
$30$		0			0
$31$		−	2.35978i		−	0.423829i	−0.977288	−	0.211915i	$-0.932030\pi$
$31$		−	2.35978i		−	0.423829i	0.977288	−	0.211915i	$-0.0679698\pi$
$32$	−3.20625	−	4.66047i	−0.566791	−	0.823862i
$33$	−1.20411	+	1.20411i	−0.209608	+	0.209608i
$34$	−7.82401	+	2.22952i	−1.34181	+	0.382359i
$35$		0			0
$36$	−2.76451	−	4.45685i	−0.460752	−	0.742808i
$37$	4.54384			0.747002			0.373501	−	0.927630i	$-0.378157\pi$
$37$	4.54384			0.747002			0.373501	+	0.927630i	$0.378157\pi$
$38$	−1.31462	+	0.374613i	−0.213260	+	0.0607703i
$39$			1.26289i			0.202224i
$40$		0			0
$41$		−	5.07255i		−	0.792199i	−0.918208	−	0.396100i	$-0.870364\pi$
$41$		−	5.07255i		−	0.792199i	0.918208	−	0.396100i	$-0.129636\pi$
$42$	0.955318	+	3.35248i	0.147409	+	0.517299i
$43$	0.849753			0.129586			0.0647930	−	0.997899i	$-0.479361\pi$
$43$	0.849753			0.129586			0.0647930	+	0.997899i	$0.479361\pi$
$44$	1.26444	−	5.39549i	0.190621	−	0.813401i
$45$		0			0
$46$	2.71316	+	9.52126i	0.400034	+	1.40383i
$47$	−2.72646	+	2.72646i	−0.397696	+	0.397696i	−0.877419	−	0.479724i	$-0.840737\pi$
$47$	−2.72646	+	2.72646i	−0.397696	+	0.397696i	0.479724	+	0.877419i	$0.340737\pi$
$48$	−2.20230	−	1.09221i	−0.317875	−	0.157647i
$49$			9.08690i			1.29813i
$50$		0			0
$51$	−2.49989	+	2.49989i	−0.350055	+	0.350055i
$52$	−2.16636	−	3.49253i	−0.300420	−	0.484327i
$53$			5.17605i			0.710985i	0.934679	+	0.355492i	$0.115687\pi$
$53$			5.17605i			0.710985i	−0.934679	+	0.355492i	$0.884313\pi$
$54$	−4.26991	−	2.37608i	−0.581062	−	0.323344i
$55$		0			0
$56$	−8.39280	−	7.63257i	−1.12154	−	1.01994i
$57$	−0.420043	+	0.420043i	−0.0556360	+	0.0556360i
$58$	−0.457903	−	1.60691i	−0.0601256	−	0.210998i
$59$	4.16328	−	4.16328i	0.542013	−	0.542013i	−0.382105	−	0.924119i	$-0.624801\pi$
$59$	4.16328	−	4.16328i	0.542013	−	0.542013i	0.924119	+	0.382105i	$0.124801\pi$
$60$		0			0
$61$	5.55706	+	5.55706i	0.711509	+	0.711509i	0.966851	−	0.255342i	$-0.0821880\pi$
$61$	5.55706	+	5.55706i	0.711509	+	0.711509i	−0.255342	+	0.966851i	$0.582188\pi$
$62$	2.91613	+	1.62274i	0.370349	+	0.206088i
$63$	−7.43712	−	7.43712i	−0.936990	−	0.936990i
$64$	7.96407	−	0.757328i	0.995509	−	0.0946660i
$65$		0			0
$66$	−0.659968	−	2.31602i	−0.0812364	−	0.285082i
$67$	1.73609			0.212097			0.106048	−	0.994361i	$-0.466180\pi$
$67$	1.73609			0.212097			0.106048	+	0.994361i	$0.466180\pi$
$68$	2.62515	−	11.2018i	0.318347	−	1.35842i
$69$	3.04219	+	3.04219i	0.366237	+	0.366237i
$70$		0			0
$71$	2.33526			0.277144			0.138572	−	0.990352i	$-0.455749\pi$
$71$	2.33526			0.277144			0.138572	+	0.990352i	$0.455749\pi$
$72$	7.40868	−	0.351464i	0.873121	−	0.0414204i
$73$	−4.39686	−	4.39686i	−0.514613	−	0.514613i	0.401323	−	0.915936i	$-0.368550\pi$
$73$	−4.39686	−	4.39686i	−0.514613	−	0.514613i	−0.915936	+	0.401323i	$0.868550\pi$
$74$	−3.12465	+	5.61511i	−0.363233	+	0.652744i
$75$		0			0
$76$	0.441090	−	1.88218i	0.0505964	−	0.215900i
$77$		−	11.1134i		−	1.26649i
$78$	−1.56063	−	0.868446i	−0.176707	−	0.0983321i
$79$	−14.0993			−1.58629			−0.793146	−	0.609032i	$-0.791558\pi$
$79$	−14.0993			−1.58629			−0.793146	+	0.609032i	$0.791558\pi$
$80$		0			0
$81$	5.74343			0.638159
$82$	6.26848	+	3.48822i	0.692238	+	0.385210i
$83$		−	2.75725i		−	0.302648i	−0.988484	−	0.151324i	$-0.951646\pi$
$83$		−	2.75725i		−	0.302648i	0.988484	−	0.151324i	$-0.0483536\pi$
$84$	−4.79982	−	1.12484i	−0.523703	−	0.122730i
$85$		0			0
$86$	−0.584347	+	1.05009i	−0.0630117	+	0.113235i
$87$	−0.513433	−	0.513433i	−0.0550458	−	0.0550458i
$88$	5.79805	+	5.27285i	0.618074	+	0.562088i
$89$	−11.6448			−1.23435			−0.617173	−	0.786828i	$-0.711722\pi$
$89$	−11.6448			−1.23435			−0.617173	+	0.786828i	$0.711722\pi$
$90$		0			0
$91$	−5.82797	−	5.82797i	−0.610937	−	0.610937i
$92$	−13.6318	−	3.19462i	−1.42121	−	0.333062i
$93$	1.45024			0.150383
$94$	−1.49437	−	5.24417i	−0.154132	−	0.540894i
$95$		0			0
$96$	2.86416	−	1.97045i	0.292322	−	0.201109i
$97$	3.52933	+	3.52933i	0.358349	+	0.358349i	0.863204	−	0.504855i	$-0.168454\pi$
$97$	3.52933	+	3.52933i	0.358349	+	0.358349i	−0.504855	+	0.863204i	$0.668454\pi$
$98$	−11.2293	−	6.24876i	−1.13433	−	0.631220i
$99$	5.13783	+	5.13783i	0.516372	+	0.516372i
$100$		0			0
$101$	7.39467	−	7.39467i	0.735797	−	0.735797i	−0.235964	−	0.971762i	$-0.575825\pi$
$101$	7.39467	−	7.39467i	0.735797	−	0.735797i	0.971762	+	0.235964i	$0.0758249\pi$
$102$	−1.37019	−	4.80837i	−0.135669	−	0.476100i
$103$	−3.72605	+	3.72605i	−0.367139	+	0.367139i	−0.866433	−	0.499294i	$-0.833593\pi$
$103$	−3.72605	+	3.72605i	−0.367139	+	0.367139i	0.499294	+	0.866433i	$0.333593\pi$
$104$	5.80568	−	0.275419i	0.569294	−	0.0270070i
$105$		0			0
$106$	−6.39637	−	3.55939i	−0.621271	−	0.345719i
$107$		−	16.4605i		−	1.59130i	−0.605758	−	0.795649i	$-0.707130\pi$
$107$		−	16.4605i		−	1.59130i	0.605758	−	0.795649i	$-0.292870\pi$
$108$	5.87255	−	3.64266i	0.565087	−	0.350515i
$109$	12.8554	−	12.8554i	1.23133	−	1.23133i	0.267870	−	0.963455i	$-0.413680\pi$
$109$	12.8554	−	12.8554i	1.23133	−	1.23133i	0.963455	−	0.267870i	$-0.0863199\pi$
$110$		0			0
$111$			2.79249i			0.265051i
$112$	15.2035	−	5.12287i	1.43660	−	0.484065i
$113$	−0.863630	+	0.863630i	−0.0812435	+	0.0812435i	−0.746561	−	0.665317i	$-0.768296\pi$
$113$	−0.863630	+	0.863630i	−0.0812435	+	0.0812435i	0.665317	+	0.746561i	$0.268296\pi$
$114$	−0.230225	−	0.807924i	−0.0215625	−	0.0756690i
$115$		0			0
$116$	2.30065	+	0.539159i	0.213610	+	0.0500596i
$117$	5.38865			0.498181
$118$	2.28189	+	8.00779i	0.210065	+	0.737177i
$119$		−	23.0730i		−	2.11510i
$120$		0			0
$121$		−	3.32246i		−	0.302042i
$122$	−10.6886	+	3.04582i	−0.967703	+	0.275755i
$123$	3.11742			0.281088
$124$	−4.01066	+	2.48775i	−0.360168	+	0.223406i
$125$		0			0
$126$	14.3048	−	4.07627i	1.27437	−	0.363143i
$127$	−11.7944	+	11.7944i	−1.04659	+	1.04659i	−0.0477265	+	0.998860i	$0.515198\pi$
$127$	−11.7944	+	11.7944i	−1.04659	+	1.04659i	−0.998860	+	0.0477265i	$0.984802\pi$
$128$	−4.54075	+	10.3625i	−0.401349	+	0.915925i
$129$			0.522229i			0.0459797i
$130$		0			0
$131$	−15.9756	+	15.9756i	−1.39579	+	1.39579i	−0.584132	+	0.811659i	$0.698565\pi$
$131$	−15.9756	+	15.9756i	−1.39579	+	1.39579i	−0.811659	+	0.584132i	$0.801435\pi$
$132$	3.31589	+	0.777081i	0.288611	+	0.0676362i
$133$		−	3.87683i		−	0.336163i
$134$	−1.19385	+	2.14539i	−0.103133	+	0.185334i
$135$		0			0
$136$	12.0376	+	10.9472i	1.03221	+	0.938713i
$137$	1.29423	−	1.29423i	0.110573	−	0.110573i	−0.649655	−	0.760229i	$-0.725087\pi$
$137$	1.29423	−	1.29423i	0.110573	−	0.110573i	0.760229	+	0.649655i	$0.225087\pi$
$138$	−5.85144	+	1.66742i	−0.498108	+	0.141940i
$139$	−8.61413	+	8.61413i	−0.730641	+	0.730641i	−0.970747	−	0.240106i	$-0.922818\pi$
$139$	−8.61413	+	8.61413i	−0.730641	+	0.730641i	0.240106	+	0.970747i	$0.422818\pi$
$140$		0			0
$141$	−1.67559	−	1.67559i	−0.141110	−	0.141110i
$142$	−1.60588	+	2.88583i	−0.134762	+	0.242173i
$143$	4.02617	+	4.02617i	0.336685	+	0.336685i
$144$	−4.66037	+	9.39707i	−0.388364	+	0.783089i
$145$		0			0
$146$	8.45705	−	2.40991i	0.699911	−	0.199445i
$147$	−5.58450			−0.460602
$148$	−4.79025	−	7.72265i	−0.393756	−	0.634798i
$149$	−0.0806133	−	0.0806133i	−0.00660410	−	0.00660410i	0.703797	−	0.710401i	$-0.251486\pi$
$149$	−0.0806133	−	0.0806133i	−0.00660410	−	0.00660410i	−0.710401	+	0.703797i	$0.751486\pi$
$150$		0			0
$151$	−3.25198			−0.264643			−0.132321	−	0.991207i	$-0.542243\pi$
$151$	−3.25198			−0.264643			−0.132321	+	0.991207i	$0.542243\pi$
$152$	2.02260	+	1.83939i	0.164055	+	0.149194i
$153$	10.6669	+	10.6669i	0.862364	+	0.862364i
$154$	13.7336	+	7.64232i	1.10668	+	0.615836i
$155$		0			0
$156$	2.14639	−	1.33137i	0.171849	−	0.106595i
$157$			9.06652i			0.723587i	0.932258	+	0.361793i	$0.117835\pi$
$157$			9.06652i			0.723587i	−0.932258	+	0.361793i	$0.882165\pi$
$158$	9.69559	−	17.4234i	0.771340	−	1.38613i
$159$	−3.18102			−0.252271
$160$		0			0
$161$	−28.0782			−2.21287
$162$	−3.94956	+	7.09753i	−0.310307	+	0.557634i
$163$			3.93313i			0.308067i	0.988066	+	0.154033i	$0.0492263\pi$
$163$			3.93313i			0.308067i	−0.988066	+	0.154033i	$0.950774\pi$
$164$	−8.62125	+	5.34763i	−0.673206	+	0.417580i
$165$		0			0
$166$	3.40731	+	1.89607i	0.264459	+	0.147164i
$167$	−8.13216	−	8.13216i	−0.629285	−	0.629285i	0.318603	−	0.947888i	$-0.396786\pi$
$167$	−8.13216	−	8.13216i	−0.629285	−	0.629285i	−0.947888	+	0.318603i	$0.896786\pi$
$168$	4.69072	−	5.15793i	0.361897	−	0.397943i
$169$	−8.77728			−0.675175
$170$		0			0
$171$	1.79229	+	1.79229i	0.137060	+	0.137060i
$172$	−0.895834	−	1.44423i	−0.0683067	−	0.110121i
$173$	−6.86735			−0.522115			−0.261057	−	0.965323i	$-0.584071\pi$
$173$	−6.86735			−0.522115			−0.261057	+	0.965323i	$0.584071\pi$
$174$	0.987552	−	0.281411i	0.0748662	−	0.0213337i
$175$		0			0
$176$	−10.5031	+	3.53906i	−0.791703	+	0.266767i
$177$	2.55861	+	2.55861i	0.192317	+	0.192317i
$178$	8.00774	−	14.3902i	0.600205	−	1.07859i
$179$	15.7117	+	15.7117i	1.17435	+	1.17435i	0.981163	+	0.193183i	$0.0618811\pi$
$179$	15.7117	+	15.7117i	1.17435	+	1.17435i	0.193183	+	0.981163i	$0.438119\pi$
$180$		0			0
$181$	−13.9112	+	13.9112i	−1.03401	+	1.03401i	−0.0346142	+	0.999401i	$0.511020\pi$
$181$	−13.9112	+	13.9112i	−1.03401	+	1.03401i	−0.999401	+	0.0346142i	$0.988980\pi$
$182$	11.2097	−	3.19430i	0.830919	−	0.236777i
$183$	−3.41518	+	3.41518i	−0.252458	+	0.252458i
$184$	13.3219	−	14.6489i	0.982106	−	1.07993i
$185$		0			0
$186$	−0.997282	+	1.79216i	−0.0731243	+	0.131407i
$187$			15.9397i			1.16562i
$188$	7.50818	+	1.75955i	0.547591	+	0.128328i
$189$	9.79951	−	9.79951i	0.712810	−	0.712810i
$190$		0			0
$191$		−	10.3393i		−	0.748123i	−0.927404	−	0.374061i	$-0.877965\pi$
$191$		−	10.3393i		−	0.748123i	0.927404	−	0.374061i	$-0.122035\pi$
$192$	0.465428	+	4.89445i	0.0335894	+	0.353226i
$193$	−13.2080	+	13.2080i	−0.950734	+	0.950734i	−0.998842	−	0.0481079i	$-0.984681\pi$
$193$	−13.2080	+	13.2080i	−0.950734	+	0.950734i	0.0481079	+	0.998842i	$0.484681\pi$
$194$	−6.78843	+	1.93442i	−0.487381	+	0.138883i
$195$		0			0
$196$	15.4440	−	9.57968i	1.10314	−	0.684263i
$197$	−15.2437			−1.08607			−0.543036	−	0.839709i	$-0.682725\pi$
$197$	−15.2437			−1.08607			−0.543036	+	0.839709i	$0.682725\pi$
$198$	−9.88227	+	2.81604i	−0.702302	+	0.200127i
$199$			4.98761i			0.353562i	0.984250	+	0.176781i	$0.0565684\pi$
$199$			4.98761i			0.353562i	−0.984250	+	0.176781i	$0.943432\pi$
$200$		0			0
$201$			1.06694i			0.0752561i
$202$	4.05300	+	14.2231i	0.285168	+	1.00074i
$203$	4.73878			0.332597
$204$	6.88425	+	1.61333i	0.481994	+	0.112956i
$205$		0			0
$206$	−2.04224	−	7.16680i	−0.142290	−	0.499335i
$207$	12.9808	−	12.9808i	0.902228	−	0.902228i
$208$	−3.65202	+	7.36385i	−0.253222	+	0.510591i
$209$			2.67825i			0.185258i
$210$		0			0
$211$	10.3803	−	10.3803i	0.714608	−	0.714608i	−0.252887	−	0.967496i	$-0.581380\pi$
$211$	10.3803	−	10.3803i	0.714608	−	0.714608i	0.967496	+	0.252887i	$0.0813802\pi$
$212$	8.79715	−	5.45674i	0.604191	−	0.374770i
$213$			1.43517i			0.0983362i
$214$	20.3413	+	11.3193i	1.39050	+	0.773774i
$215$		0			0
$216$	0.463106	+	9.76203i	0.0315104	+	0.664222i
$217$	−6.69257	+	6.69257i	−0.454321	+	0.454321i
$218$	7.04603	+	24.7265i	0.477217	+	1.67469i
$219$	2.70216	−	2.70216i	0.182595	−	0.182595i
$220$		0			0
$221$	8.35890	+	8.35890i	0.562280	+	0.562280i
$222$	−3.45086	−	1.92030i	−0.231606	−	0.128882i
$223$	1.49853	+	1.49853i	0.100349	+	0.100349i	0.755499	−	0.655150i	$-0.227395\pi$
$223$	1.49853	+	1.49853i	0.100349	+	0.100349i	−0.655150	+	0.755499i	$0.727395\pi$
$224$	−4.12429	+	22.3108i	−0.275566	+	1.49070i
$225$		0			0
$226$	−0.473354	−	1.66113i	−0.0314870	−	0.110497i
$227$	15.6346			1.03771			0.518853	−	0.854864i	$-0.326359\pi$
$227$	15.6346			1.03771			0.518853	+	0.854864i	$0.326359\pi$
$228$	1.15672	+	0.271079i	0.0766057	+	0.0179526i
$229$	−9.74097	−	9.74097i	−0.643702	−	0.643702i	0.307762	−	0.951463i	$-0.400420\pi$
$229$	−9.74097	−	9.74097i	−0.643702	−	0.643702i	−0.951463	+	0.307762i	$0.900420\pi$
$230$		0			0
$231$	6.82992			0.449376
$232$	−2.24835	+	2.47230i	−0.147612	+	0.162314i
$233$	−0.509123	−	0.509123i	−0.0333538	−	0.0333538i	0.690233	−	0.723587i	$-0.257508\pi$
$233$	−0.509123	−	0.509123i	−0.0333538	−	0.0333538i	−0.723587	+	0.690233i	$0.757508\pi$
$234$	−3.70560	+	6.65910i	−0.242242	+	0.435319i
$235$		0			0
$236$	−11.4649	−	2.68681i	−0.746303	−	0.174897i
$237$		−	8.66493i		−	0.562848i
$238$	28.5128	+	15.8665i	1.84821	+	1.02847i
$239$	8.19486			0.530081			0.265041	−	0.964237i	$-0.414615\pi$
$239$	8.19486			0.530081			0.265041	+	0.964237i	$0.414615\pi$
$240$		0			0
$241$	5.66775			0.365092			0.182546	−	0.983197i	$-0.441566\pi$
$241$	5.66775			0.365092			0.182546	+	0.983197i	$0.441566\pi$
$242$	4.10578	+	2.28474i	0.263929	+	0.146869i
$243$			13.8956i			0.891400i
$244$	3.58630	−	15.3031i	0.229590	−	0.979683i
$245$		0			0
$246$	−2.14374	+	3.85239i	−0.136680	+	0.245620i
$247$	1.40450	+	1.40450i	0.0893661	+	0.0893661i
$248$	−0.316278	−	6.66697i	−0.0200837	−	0.423353i
$249$	1.69451			0.107385
$250$		0			0
$251$	14.7484	+	14.7484i	0.930911	+	0.930911i	0.997763	−	0.0668521i	$-0.0212956\pi$
$251$	14.7484	+	14.7484i	0.930911	+	0.930911i	−0.0668521	+	0.997763i	$0.521296\pi$
$252$	−4.79962	+	20.4805i	−0.302348	+	1.29015i
$253$	19.3974			1.21951
$254$	−6.46451	−	22.6858i	−0.405619	−	1.42343i
$255$		0			0
$256$	−9.68310	−	12.7373i	−0.605194	−	0.796078i
$257$	−3.61143	−	3.61143i	−0.225275	−	0.225275i	0.585440	−	0.810715i	$-0.300922\pi$
$257$	−3.61143	−	3.61143i	−0.225275	−	0.225275i	−0.810715	+	0.585440i	$0.800922\pi$
$258$	−0.645352	−	0.359120i	−0.0401779	−	0.0223578i
$259$	−12.8868	−	12.8868i	−0.800745	−	0.800745i
$260$		0			0
$261$	−2.19078	+	2.19078i	−0.135606	+	0.135606i
$262$	−8.75617	−	30.7279i	−0.540958	−	1.89838i
$263$	6.80041	−	6.80041i	0.419331	−	0.419331i	−0.465642	−	0.884973i	$-0.654177\pi$
$263$	6.80041	−	6.80041i	0.419331	−	0.419331i	0.884973	+	0.465642i	$0.154177\pi$
$264$	−3.24052	+	3.56328i	−0.199440	+	0.219305i
$265$		0			0
$266$	4.79084	+	2.66596i	0.293746	+	0.163461i
$267$		−	7.15650i		−	0.437970i
$268$	−1.83023	−	2.95063i	−0.111799	−	0.180238i
$269$	−1.20010	+	1.20010i	−0.0731711	+	0.0731711i	−0.742745	−	0.669574i	$-0.766477\pi$
$269$	−1.20010	+	1.20010i	−0.0731711	+	0.0731711i	0.669574	+	0.742745i	$0.266477\pi$
$270$		0			0
$271$		−	2.79591i		−	0.169840i	−0.996388	−	0.0849199i	$-0.972937\pi$
$271$		−	2.79591i		−	0.169840i	0.996388	−	0.0849199i	$-0.0270634\pi$
$272$	−21.8060	+	7.34759i	−1.32218	+	0.445513i
$273$	3.58167	−	3.58167i	0.216773	−	0.216773i
$274$	0.709364	+	2.48936i	0.0428543	+	0.150388i
$275$		0			0
$276$	1.96331	−	8.37764i	0.118177	−	0.504274i
$277$	−13.8115			−0.829852			−0.414926	−	0.909855i	$-0.636193\pi$
$277$	−13.8115			−0.829852			−0.414926	+	0.909855i	$0.636193\pi$
$278$	−4.72139	−	16.5687i	−0.283170	−	0.993724i
$279$		−	6.18807i		−	0.370470i
$280$		0			0
$281$			7.21718i			0.430541i	0.976554	+	0.215270i	$0.0690633\pi$
$281$			7.21718i			0.430541i	−0.976554	+	0.215270i	$0.930937\pi$
$282$	3.22289	−	0.918389i	0.191920	−	0.0546892i
$283$	−25.2988			−1.50386			−0.751930	−	0.659243i	$-0.770877\pi$
$283$	−25.2988			−1.50386			−0.751930	+	0.659243i	$0.770877\pi$
$284$	−2.46190	−	3.96898i	−0.146087	−	0.235515i
$285$		0			0
$286$	−7.74407	+	2.20674i	−0.457916	+	0.130487i
$287$	−14.3862	+	14.3862i	−0.849193	+	0.849193i
$288$	−8.40779	−	12.2212i	−0.495434	−	0.720140i
$289$			16.0930i			0.946644i
$290$		0			0
$291$	−2.16901	+	2.16901i	−0.127149	+	0.127149i
$292$	−2.83755	+	12.1081i	−0.166055	+	0.708575i
$293$		−	14.1276i		−	0.825344i	−0.910880	−	0.412672i	$-0.864596\pi$
$293$		−	14.1276i		−	0.825344i	0.910880	−	0.412672i	$-0.135404\pi$
$294$	3.84028	−	6.90113i	0.223969	−	0.402482i
$295$		0			0
$296$	12.8375	−	0.609004i	0.746163	−	0.0353976i
$297$	−6.76985	+	6.76985i	−0.392827	+	0.392827i
$298$	0.155054	−	0.0441840i	0.00898204	−	0.00255951i
$299$	10.1722	−	10.1722i	0.588272	−	0.588272i
$300$		0			0
$301$	−2.40998	−	2.40998i	−0.138909	−	0.138909i
$302$	2.23628	−	4.01869i	0.128683	−	0.231249i
$303$	4.54451	+	4.54451i	0.261076	+	0.261076i
$304$	−3.66393	+	1.23457i	−0.210141	+	0.0708076i
$305$		0			0
$306$	−20.5170	+	5.84648i	−1.17288	+	0.334221i
$307$	22.6081			1.29031			0.645156	−	0.764051i	$-0.276792\pi$
$307$	22.6081			1.29031			0.645156	+	0.764051i	$0.276792\pi$
$308$	−18.8882	+	11.7161i	−1.07626	+	0.667586i
$309$	−2.28990	−	2.28990i	−0.130268	−	0.130268i
$310$		0			0
$311$	−10.7903			−0.611859			−0.305929	−	0.952054i	$-0.598967\pi$
$311$	−10.7903			−0.611859			−0.305929	+	0.952054i	$0.598967\pi$
$312$	0.169263	+	3.56797i	0.00958263	+	0.201997i
$313$	−20.6842	−	20.6842i	−1.16914	−	1.16914i	−0.982412	−	0.186727i	$-0.940212\pi$
$313$	−20.6842	−	20.6842i	−1.16914	−	1.16914i	−0.186727	−	0.982412i	$-0.559788\pi$
$314$	−11.2041	−	6.23474i	−0.632283	−	0.351847i
$315$		0			0
$316$	14.8639	+	23.9629i	0.836157	+	1.34802i
$317$		−	23.8207i		−	1.33791i	−0.743305	−	0.668953i	$-0.766743\pi$
$317$		−	23.8207i		−	1.33791i	0.743305	−	0.668953i	$-0.233257\pi$
$318$	2.18748	−	3.93099i	0.122668	−	0.220439i
$319$	−3.27372			−0.183293
$320$		0			0
$321$	10.1161			0.564624
$322$	19.3084	−	34.6980i	1.07602	−	1.93365i
$323$			5.56042i			0.309390i
$324$	−6.05489	−	9.76146i	−0.336383	−	0.542304i
$325$		0			0
$326$	−4.86043	−	2.70469i	−0.269194	−	0.149799i
$327$	7.90050	+	7.90050i	0.436899	+	0.436899i
$328$	−0.679866	−	14.3312i	−0.0375393	−	0.791309i
$329$	15.4650			0.852615
$330$		0			0
$331$	−19.7688	−	19.7688i	−1.08659	−	1.08659i	−0.995877	−	0.0907155i	$-0.971085\pi$
$331$	−19.7688	−	19.7688i	−1.08659	−	1.08659i	−0.0907155	−	0.995877i	$-0.528915\pi$
$332$	−4.68619	+	2.90677i	−0.257188	+	0.159530i
$333$	11.9153			0.652957
$334$	15.6417	−	4.45722i	0.855873	−	0.243888i
$335$		0			0
$336$	3.14834	+	9.34356i	0.171756	+	0.509733i
$337$	−7.26955	−	7.26955i	−0.395998	−	0.395998i	0.480821	−	0.876819i	$-0.340339\pi$
$337$	−7.26955	−	7.26955i	−0.395998	−	0.395998i	−0.876819	+	0.480821i	$0.840339\pi$
$338$	6.03584	−	10.8467i	0.328307	−	0.589980i
$339$	−0.530758	−	0.530758i	−0.0288268	−	0.0288268i
$340$		0			0
$341$	4.62347	−	4.62347i	0.250375	−	0.250375i
$342$	−3.44735	+	0.982352i	−0.186411	+	0.0531195i
$343$	5.91866	−	5.91866i	0.319578	−	0.319578i
$344$	2.40076	−	0.113891i	0.129440	−	0.00614059i
$345$		0			0
$346$	4.72245	−	8.48642i	0.253880	−	0.456233i
$347$			23.4667i			1.25976i	0.776692	+	0.629880i	$0.216896\pi$
$347$			23.4667i			1.25976i	−0.776692	+	0.629880i	$0.783104\pi$
$348$	−0.331349	+	1.41390i	−0.0177622	+	0.0757930i
$349$	−23.2089	+	23.2089i	−1.24234	+	1.24234i	−0.283315	+	0.959027i	$0.591434\pi$
$349$	−23.2089	+	23.2089i	−1.24234	+	1.24234i	−0.959027	+	0.283315i	$0.908566\pi$
$350$		0			0
$351$			7.10035i			0.378988i
$352$	2.84921	−	15.4131i	0.151863	−	0.821521i
$353$	13.3220	−	13.3220i	0.709059	−	0.709059i	−0.257278	−	0.966337i	$-0.582826\pi$
$353$	13.3220	−	13.3220i	0.709059	−	0.709059i	0.966337	+	0.257278i	$0.0828256\pi$
$354$	−4.92131	+	1.40237i	−0.261565	+	0.0745351i
$355$		0			0
$356$	12.2763	+	19.7914i	0.650642	+	1.04894i
$357$	14.1799			0.750479
$358$	−30.2203	+	8.61154i	−1.59719	+	0.455134i
$359$			26.9902i			1.42449i	0.701932	+	0.712244i	$0.252321\pi$
$359$			26.9902i			1.42449i	−0.701932	+	0.712244i	$0.747679\pi$
$360$		0			0
$361$		−	18.0657i		−	0.950827i
$362$	−7.62473	−	26.7573i	−0.400747	−	1.40633i
$363$	2.04187			0.107170
$364$	−3.76114	+	16.0492i	−0.197137	+	0.841205i
$365$		0			0
$366$	−1.87185	−	6.56887i	−0.0978434	−	0.343360i
$367$	19.4758	−	19.4758i	1.01663	−	1.01663i	0.0167684	−	0.999859i	$-0.494662\pi$
$367$	19.4758	−	19.4758i	1.01663	−	1.01663i	0.999859	−	0.0167684i	$-0.00533781\pi$
$368$	8.94148	+	26.5363i	0.466107	+	1.38330i
$369$		−	13.3018i		−	0.692464i
$370$		0			0
$371$	14.6798	−	14.6798i	0.762136	−	0.762136i
$372$	−1.52889	−	2.46481i	−0.0792690	−	0.127795i
$373$			4.87069i			0.252195i	0.992018	+	0.126097i	$0.0402452\pi$
$373$			4.87069i			0.252195i	−0.992018	+	0.126097i	$0.959755\pi$
$374$	−19.6977	−	10.9612i	−1.01854	−	0.566789i
$375$		0			0
$376$	−7.33752	+	8.06836i	−0.378404	+	0.416094i
$377$	−1.71677	+	1.71677i	−0.0884180	+	0.0884180i
$378$	5.37109	+	18.8487i	0.276259	+	0.969472i
$379$	2.54450	−	2.54450i	0.130702	−	0.130702i	−0.638729	−	0.769432i	$-0.720540\pi$
$379$	2.54450	−	2.54450i	0.130702	−	0.130702i	0.769432	+	0.638729i	$0.220540\pi$
$380$		0			0
$381$	−7.24846	−	7.24846i	−0.371350	−	0.371350i
$382$	12.7769	+	7.10996i	0.653723	+	0.363777i
$383$	−0.193238	−	0.193238i	−0.00987399	−	0.00987399i	0.702153	−	0.712027i	$-0.252222\pi$
$383$	−0.193238	−	0.193238i	−0.00987399	−	0.00987399i	−0.712027	+	0.702153i	$0.752222\pi$
$384$	−6.36845	−	2.79059i	−0.324988	−	0.142407i
$385$		0			0
$386$	−7.23929	−	25.4047i	−0.368470	−	1.29307i
$387$	2.22831			0.113272
$388$	2.27769	−	9.71914i	0.115632	−	0.493414i
$389$	2.01528	+	2.01528i	0.102179	+	0.102179i	0.756348	−	0.654169i	$-0.226982\pi$
$389$	2.01528	+	2.01528i	0.102179	+	0.102179i	−0.654169	+	0.756348i	$0.726982\pi$
$390$		0			0
$391$	40.2718			2.03663
$392$	1.21790	+	25.6728i	0.0615134	+	1.29667i
$393$	−9.81803	−	9.81803i	−0.495254	−	0.495254i
$394$	10.4826	−	18.8377i	0.528107	−	0.949029i
$395$		0			0
$396$	3.31575	−	14.1487i	0.166623	−	0.710997i
$397$			21.5509i			1.08161i	0.841149	+	0.540804i	$0.181880\pi$
$397$			21.5509i			1.08161i	−0.841149	+	0.540804i	$0.818120\pi$
$398$	−6.16351	−	3.42981i	−0.308949	−	0.171921i
$399$	2.38257			0.119277
$400$		0			0
$401$	−10.3965			−0.519176			−0.259588	−	0.965719i	$-0.583587\pi$
$401$	−10.3965			−0.519176			−0.259588	+	0.965719i	$0.583587\pi$
$402$	−1.31849	−	0.733699i	−0.0657601	−	0.0365936i
$403$		−	4.84917i		−	0.241555i
$404$	−20.3636	−	4.77222i	−1.01313	−	0.237427i
$405$		0			0
$406$	−3.25870	+	5.85601i	−0.161726	+	0.290629i
$407$	8.90264	+	8.90264i	0.441288	+	0.441288i
$408$	−6.72776	+	7.39788i	−0.333074	+	0.366250i
$409$	−0.330732			−0.0163536			−0.00817682	−	0.999967i	$-0.502603\pi$
$409$	−0.330732			−0.0163536			−0.00817682	+	0.999967i	$0.502603\pi$
$410$		0			0
$411$	0.795389	+	0.795389i	0.0392337	+	0.0392337i
$412$	10.2609	+	2.40464i	0.505516	+	0.118468i
$413$	−23.6150			−1.16202
$414$	7.11475	+	24.9677i	0.349671	+	1.22709i
$415$		0			0
$416$	−6.58861	−	9.57691i	−0.323033	−	0.469547i
$417$	−5.29395	−	5.29395i	−0.259246	−	0.259246i
$418$	−3.30969	−	1.84174i	−0.161882	−	0.0900826i
$419$	−6.71354	−	6.71354i	−0.327978	−	0.327978i	0.523839	−	0.851817i	$-0.324499\pi$
$419$	−6.71354	−	6.71354i	−0.327978	−	0.327978i	−0.851817	+	0.523839i	$0.824499\pi$
$420$		0			0
$421$	2.99831	−	2.99831i	0.146129	−	0.146129i	−0.630258	−	0.776386i	$-0.717051\pi$
$421$	2.99831	−	2.99831i	0.146129	−	0.146129i	0.776386	+	0.630258i	$0.217051\pi$
$422$	5.68941	+	19.9658i	0.276956	+	0.971918i
$423$	−7.14963	+	7.14963i	−0.347627	+	0.347627i
$424$	0.693737	+	14.6236i	0.0336909	+	0.710186i
$425$		0			0
$426$	−1.77353	−	0.986918i	−0.0859279	−	0.0478163i
$427$		−	31.5208i		−	1.52540i
$428$	−27.9761	+	17.3531i	−1.35228	+	0.838796i
$429$	−2.47435	+	2.47435i	−0.119463	+	0.119463i
$430$		0			0
$431$		−	19.9548i		−	0.961191i	−0.876942	−	0.480596i	$-0.840420\pi$
$431$		−	19.9548i		−	0.961191i	0.876942	−	0.480596i	$-0.159580\pi$
$432$	−12.3820	−	6.14073i	−0.595731	−	0.295446i
$433$	16.1910	−	16.1910i	0.778092	−	0.778092i	−0.201414	−	0.979506i	$-0.564554\pi$
$433$	16.1910	−	16.1910i	0.778092	−	0.778092i	0.979506	+	0.201414i	$0.0645537\pi$
$434$	−3.66818	−	12.8727i	−0.176078	−	0.617909i
$435$		0			0
$436$	−35.4015	−	8.29636i	−1.69542	−	0.397324i
$437$	6.76664			0.323692
$438$	1.48105	+	5.19742i	0.0707672	+	0.248342i
$439$			29.3734i			1.40191i	0.713204	+	0.700957i	$0.247243\pi$
$439$			29.3734i			1.40191i	−0.713204	+	0.700957i	$0.752757\pi$
$440$		0			0
$441$			23.8287i			1.13470i
$442$	−16.0778	+	4.58150i	−0.764741	+	0.217920i
$443$	19.8713			0.944115			0.472057	−	0.881568i	$-0.343511\pi$
$443$	19.8713			0.944115			0.472057	+	0.881568i	$0.343511\pi$
$444$	4.74608	−	2.94392i	0.225239	−	0.139712i
$445$		0			0
$446$	−2.88232	+	0.821341i	−0.136482	+	0.0388916i
$447$	0.0495422	−	0.0495422i	0.00234326	−	0.00234326i
$448$	−24.7347	−	20.4390i	−1.16861	−	0.965654i
$449$		−	16.7577i		−	0.790844i	−0.918500	−	0.395422i	$-0.870598\pi$
$449$		−	16.7577i		−	0.790844i	0.918500	−	0.395422i	$-0.129402\pi$
$450$		0			0
$451$	9.93854	−	9.93854i	0.467987	−	0.467987i
$452$	2.37828	+	0.557352i	0.111865	+	0.0262156i
$453$		−	1.99856i		−	0.0939005i
$454$	−10.7514	+	19.3207i	−0.504588	+	0.906766i
$455$		0			0
$456$	−1.13043	+	1.24302i	−0.0529372	+	0.0582099i
$457$	5.00267	−	5.00267i	0.234015	−	0.234015i	−0.580351	−	0.814366i	$-0.697085\pi$
$457$	5.00267	−	5.00267i	0.234015	−	0.234015i	0.814366	+	0.580351i	$0.197085\pi$
$458$	18.7361	−	5.33901i	0.875480	−	0.249475i
$459$	−14.0552	+	14.0552i	−0.656039	+	0.656039i
$460$		0			0
$461$	2.71518	+	2.71518i	0.126459	+	0.126459i	0.767503	−	0.641045i	$-0.221499\pi$
$461$	2.71518	+	2.71518i	0.126459	+	0.126459i	−0.641045	+	0.767503i	$0.721499\pi$
$462$	−4.69671	+	8.44018i	−0.218511	+	0.392673i
$463$	−9.18551	−	9.18551i	−0.426887	−	0.426887i	0.460680	−	0.887566i	$-0.347606\pi$
$463$	−9.18551	−	9.18551i	−0.426887	−	0.426887i	−0.887566	+	0.460680i	$0.847606\pi$
$464$	−1.50906	−	4.47855i	−0.0700564	−	0.207912i
$465$		0			0
$466$	0.979263	−	0.279049i	0.0453635	−	0.0129267i
$467$	1.06405			0.0492385			0.0246193	−	0.999697i	$-0.492163\pi$
$467$	1.06405			0.0492385			0.0246193	+	0.999697i	$0.492163\pi$
$468$	−5.68087	−	9.15849i	−0.262598	−	0.423351i
$469$	−4.92371	−	4.92371i	−0.227356	−	0.227356i
$470$		0			0
$471$	−5.57197			−0.256743
$472$	11.2043	−	12.3203i	0.515720	−	0.567088i
$473$	1.66490	+	1.66490i	0.0765523	+	0.0765523i
$474$	10.7078	+	5.95858i	0.491826	+	0.273687i
$475$		0			0
$476$	−39.2146	+	24.3242i	−1.79740	+	1.11490i
$477$			13.5732i			0.621474i
$478$	−5.63533	+	10.1269i	−0.257754	+	0.463194i
$479$	15.8658			0.724926			0.362463	−	0.931998i	$-0.381936\pi$
$479$	15.8658			0.724926			0.362463	+	0.931998i	$0.381936\pi$
$480$		0			0
$481$	9.33725			0.425742
$482$	−3.89752	+	7.00400i	−0.177527	+	0.319024i
$483$		−	17.2559i		−	0.785170i
$484$	−5.64681	+	3.50263i	−0.256673	+	0.159210i
$485$		0			0
$486$	−17.1716	−	9.55551i	−0.778921	−	0.433447i
$487$	13.7947	+	13.7947i	0.625099	+	0.625099i	0.946831	−	0.321732i	$-0.104265\pi$
$487$	13.7947	+	13.7947i	0.625099	+	0.625099i	−0.321732	+	0.946831i	$0.604265\pi$
$488$	16.4449	+	14.9553i	0.744426	+	0.676994i
$489$	−2.41717			−0.109308
$490$		0			0
$491$	19.4471	+	19.4471i	0.877637	+	0.877637i	0.993290	−	0.115652i	$-0.0368958\pi$
$491$	19.4471	+	19.4471i	0.877637	+	0.877637i	−0.115652	+	0.993290i	$0.536896\pi$
$492$	−3.28647	−	5.29833i	−0.148166	−	0.238867i
$493$	−6.79669			−0.306108
$494$	−2.70146	+	0.769803i	−0.121544	+	0.0346351i
$495$		0			0
$496$	8.45630	+	4.19381i	0.379699	+	0.188308i
$497$	−6.62302	−	6.62302i	−0.297083	−	0.297083i
$498$	−1.16526	+	2.09402i	−0.0522166	+	0.0938353i
$499$	23.0141	+	23.0141i	1.03025	+	1.03025i	0.999528	+	0.0307258i	$0.00978185\pi$
$499$	23.0141	+	23.0141i	1.03025	+	1.03025i	0.0307258	+	0.999528i	$0.490218\pi$
$500$		0			0
$501$	4.99775	−	4.99775i	0.223283	−	0.223283i
$502$	−28.3675	+	8.08357i	−1.26611	+	0.360787i
$503$	−6.63364	+	6.63364i	−0.295780	+	0.295780i	−0.839358	−	0.543579i	$-0.817069\pi$
$503$	−6.63364	+	6.63364i	−0.295780	+	0.295780i	0.543579	+	0.839358i	$0.317069\pi$
$504$	−22.0085	−	20.0149i	−0.980337	−	0.891537i
$505$		0			0
$506$	−13.3390	+	23.9706i	−0.592989	+	1.06562i
$507$		−	5.39422i		−	0.239566i
$508$	32.4797	+	7.61165i	1.44105	+	0.337712i
$509$	8.04140	−	8.04140i	0.356429	−	0.356429i	−0.506066	−	0.862495i	$-0.668901\pi$
$509$	8.04140	−	8.04140i	0.356429	−	0.356429i	0.862495	+	0.506066i	$0.168901\pi$
$510$		0			0
$511$			24.9398i			1.10327i
$512$	22.3990	−	3.20705i	0.989905	−	0.141733i
$513$	−2.36161	+	2.36161i	−0.104268	+	0.104268i
$514$	6.94634	−	1.97942i	0.306390	−	0.0873084i
$515$		0			0
$516$	0.887575	−	0.550549i	0.0390733	−	0.0242366i
$517$	−10.6838			−0.469873
$518$	24.7868	−	7.06321i	1.08907	−	0.310340i
$519$		−	4.22044i		−	0.185257i
$520$		0			0
$521$			32.8549i			1.43940i	0.694285	+	0.719700i	$0.255721\pi$
$521$			32.8549i			1.43940i	−0.694285	+	0.719700i	$0.744279\pi$
$522$	−1.20076	−	4.21381i	−0.0525559	−	0.184434i
$523$	2.46341			0.107717			0.0538587	−	0.998549i	$-0.482848\pi$
$523$	2.46341			0.107717			0.0538587	+	0.998549i	$0.482848\pi$
$524$	43.9938	+	10.3100i	1.92188	+	0.450393i
$525$		0			0
$526$	3.72729	+	13.0801i	0.162518	+	0.570321i
$527$	9.59896	−	9.59896i	0.418137	−	0.418137i
$528$	−2.17499	−	6.45487i	−0.0946541	−	0.280912i
$529$		−	26.0078i		−	1.13078i
$530$		0			0
$531$	10.9174	−	10.9174i	0.473775	−	0.473775i
$532$	−6.58901	+	4.08706i	−0.285670	+	0.177197i
$533$		−	10.4237i		−	0.451501i
$534$	8.84375	+	4.92128i	0.382706	+	0.212965i
$535$		0			0
$536$	4.90487	−	0.232685i	0.211858	−	0.0100505i
$537$	−9.65586	+	9.65586i	−0.416681	+	0.416681i
$538$	−0.657770	−	2.30830i	−0.0283585	−	0.0995180i
$539$	−17.8038	+	17.8038i	−0.766863	+	0.766863i
$540$		0			0
$541$	−18.0772	−	18.0772i	−0.777198	−	0.777198i	0.202156	−	0.979353i	$-0.435205\pi$
$541$	−18.0772	−	18.0772i	−0.777198	−	0.777198i	−0.979353	+	0.202156i	$0.935205\pi$
$542$	3.45509	+	1.92266i	0.148409	+	0.0825852i
$543$	−8.54938	−	8.54938i	−0.366889	−	0.366889i
$544$	5.91535	−	31.9997i	0.253619	−	1.37198i
$545$		0			0
$546$	1.96311	+	6.88910i	0.0840133	+	0.294826i
$547$	−43.6742			−1.86738			−0.933688	−	0.358089i	$-0.883428\pi$
$547$	−43.6742			−1.86738			−0.933688	+	0.358089i	$0.883428\pi$
$548$	−3.56407	−	0.835243i	−0.152250	−	0.0356798i
$549$	14.5723	+	14.5723i	0.621932	+	0.621932i
$550$		0			0
$551$	−1.14201			−0.0486513
$552$	9.00269	+	8.18721i	0.383180	+	0.348471i
$553$	39.9869	+	39.9869i	1.70042	+	1.70042i
$554$	9.49770	−	17.0677i	0.403519	−	0.725139i
$555$		0			0
$556$	23.7217	+	5.55921i	1.00603	+	0.235763i
$557$			5.18948i			0.219885i	0.993938	+	0.109943i	$0.0350667\pi$
$557$			5.18948i			0.219885i	−0.993938	+	0.109943i	$0.964933\pi$
$558$	7.64700	+	4.25533i	0.323723	+	0.180143i
$559$	1.74618			0.0738555
$560$		0			0
$561$	−9.79597			−0.413586
$562$	−8.91874	−	4.96301i	−0.376214	−	0.209352i
$563$			11.3756i			0.479423i	0.970844	+	0.239711i	$0.0770528\pi$
$563$			11.3756i			0.479423i	−0.970844	+	0.239711i	$0.922947\pi$
$564$	−1.08136	+	4.61427i	−0.0455334	+	0.194296i
$565$		0			0
$566$	17.3972	−	31.2634i	0.731257	−	1.31410i
$567$	−16.2889	−	16.2889i	−0.684071	−	0.684071i
$568$	6.59768	−	0.312991i	0.276833	−	0.0131328i
$569$	−7.51787			−0.315165			−0.157583	−	0.987506i	$-0.550370\pi$
$569$	−7.51787			−0.315165			−0.157583	+	0.987506i	$0.550370\pi$
$570$		0			0
$571$	−7.76889	−	7.76889i	−0.325118	−	0.325118i	0.525609	−	0.850726i	$-0.323838\pi$
$571$	−7.76889	−	7.76889i	−0.325118	−	0.325118i	−0.850726	+	0.525609i	$0.823838\pi$
$572$	2.59833	−	11.0873i	0.108642	−	0.463585i
$573$	6.35416			0.265449
$574$	−7.88507	−	27.6710i	−0.329117	−	1.15496i
$575$		0			0
$576$	20.8843	−	1.98595i	0.870177	−	0.0827478i
$577$	9.84819	+	9.84819i	0.409986	+	0.409986i	0.881733	−	0.471748i	$-0.156377\pi$
$577$	9.84819	+	9.84819i	0.409986	+	0.409986i	−0.471748	+	0.881733i	$0.656377\pi$
$578$	−19.8871	−	11.0666i	−0.827195	−	0.460309i
$579$	−8.11720	−	8.11720i	−0.337339	−	0.337339i
$580$		0			0
$581$	−7.81984	+	7.81984i	−0.324421	+	0.324421i
$582$	−1.18883	−	4.17194i	−0.0492785	−	0.172932i
$583$	−10.1413	+	10.1413i	−0.420010	+	0.420010i
$584$	−13.0115	−	11.8329i	−0.538421	−	0.489650i
$585$		0			0
$586$	17.4584	+	9.71509i	0.721200	+	0.401327i
$587$			33.0447i			1.36390i	0.731398	+	0.681951i	$0.238868\pi$
$587$			33.0447i			1.36390i	−0.731398	+	0.681951i	$0.761132\pi$
$588$	5.88734	+	9.49136i	0.242790	+	0.391417i
$589$	1.61286	−	1.61286i	0.0664567	−	0.0664567i
$590$		0			0
$591$		−	9.36829i		−	0.385360i
$592$	−8.07532	+	16.2829i	−0.331894	+	0.669223i
$593$	−18.5424	+	18.5424i	−0.761445	+	0.761445i	−0.976584	−	0.215139i	$-0.930980\pi$
$593$	−18.5424	+	18.5424i	−0.761445	+	0.761445i	0.215139	+	0.976584i	$0.430980\pi$
$594$	−3.71054	−	13.0214i	−0.152245	−	0.534273i
$595$		0			0
$596$	−0.0520245	+	0.221994i	−0.00213101	+	0.00909324i
$597$	−3.06521			−0.125451
$598$	5.57535	+	19.5655i	0.227993	+	0.800092i
$599$		−	28.3117i		−	1.15678i	−0.815759	−	0.578392i	$-0.803681\pi$
$599$		−	28.3117i		−	1.15678i	0.815759	−	0.578392i	$-0.196319\pi$
$600$		0			0
$601$		−	41.7630i		−	1.70355i	−0.523909	−	0.851774i	$-0.675527\pi$
$601$		−	41.7630i		−	1.70355i	0.523909	−	0.851774i	$-0.324473\pi$
$602$	4.63543	−	1.32091i	0.188926	−	0.0538361i
$603$	4.55255			0.185394
$604$	3.42833	+	5.52703i	0.139497	+	0.224892i
$605$		0			0
$606$	−8.74106	+	2.49084i	−0.355081	+	0.101183i
$607$	−4.01973	+	4.01973i	−0.163156	+	0.163156i	−0.783963	−	0.620807i	$-0.786805\pi$
$607$	−4.01973	+	4.01973i	−0.163156	+	0.163156i	0.620807	+	0.783963i	$0.286805\pi$
$608$	0.993923	−	5.37674i	0.0403089	−	0.218055i
$609$			2.91229i			0.118012i
$610$		0			0
$611$	−5.60268	+	5.60268i	−0.226660	+	0.226660i
$612$	6.88396	−	29.3746i	0.278268	−	1.18740i
$613$			21.5230i			0.869305i	0.900598	+	0.434652i	$0.143129\pi$
$613$			21.5230i			0.869305i	−0.900598	+	0.434652i	$0.856871\pi$
$614$	−15.5468	+	27.9383i	−0.627419	+	1.12750i
$615$		0			0
$616$	−1.48951	−	31.3982i	−0.0600142	−	1.26507i
$617$	26.4655	−	26.4655i	1.06546	−	1.06546i	0.0677580	−	0.997702i	$-0.478415\pi$
$617$	26.4655	−	26.4655i	1.06546	−	1.06546i	0.997702	−	0.0677580i	$-0.0215846\pi$
$618$	4.40447	−	1.25509i	0.177174	−	0.0504872i
$619$	21.7935	−	21.7935i	0.875955	−	0.875955i	−0.117158	−	0.993113i	$-0.537378\pi$
$619$	21.7935	−	21.7935i	0.875955	−	0.875955i	0.993113	+	0.117158i	$0.0373784\pi$
$620$		0			0
$621$	17.1041	+	17.1041i	0.686365	+	0.686365i
$622$	7.42010	−	13.3342i	0.297519	−	0.534653i
$623$	33.0258	+	33.0258i	1.32315	+	1.32315i
$624$	−4.52557	−	2.24441i	−0.181168	−	0.0898482i
$625$		0			0
$626$	39.7846	−	11.3370i	1.59011	−	0.453116i
$627$	−1.64596			−0.0657334
$628$	15.4093	−	9.55818i	0.614900	−	0.381413i
$629$	18.4831	+	18.4831i	0.736971	+	0.736971i
$630$		0			0
$631$	−42.7412			−1.70150			−0.850751	−	0.525570i	$-0.823852\pi$
$631$	−42.7412			−1.70150			−0.850751	+	0.525570i	$0.823852\pi$
$632$	−39.8339	+	1.88970i	−1.58451	+	0.0751683i
$633$	6.37937	+	6.37937i	0.253557	+	0.253557i
$634$	29.4368	+	16.3807i	1.16909	+	0.650562i
$635$		0			0
$636$	3.35353	+	5.40643i	0.132976	+	0.214379i
$637$			18.6729i			0.739848i
$638$	2.25123	−	4.04554i	0.0891269	−	0.160165i
$639$	6.12376			0.242252
$640$		0			0
$641$	45.4930			1.79687			0.898433	−	0.439110i	$-0.144706\pi$
$641$	45.4930			1.79687			0.898433	+	0.439110i	$0.144706\pi$
$642$	−6.95648	+	12.5011i	−0.274551	+	0.493378i
$643$		−	31.3531i		−	1.23645i	−0.786002	−	0.618224i	$-0.787853\pi$
$643$		−	31.3531i		−	1.23645i	0.786002	−	0.618224i	$-0.212147\pi$
$644$	29.6008	+	47.7214i	1.16644	+	1.88048i
$645$		0			0
$646$	−6.87137	−	3.82372i	−0.270351	−	0.150442i
$647$	24.0355	+	24.0355i	0.944932	+	0.944932i	0.998561	−	0.0536292i	$-0.0170789\pi$
$647$	24.0355	+	24.0355i	0.944932	+	0.944932i	−0.0536292	+	0.998561i	$0.517079\pi$
$648$	16.2266	−	0.769783i	0.637442	−	0.0302399i
$649$	16.3141			0.640383
$650$		0			0
$651$	−4.11303	−	4.11303i	−0.161202	−	0.161202i
$652$	6.68471	−	4.14642i	0.261793	−	0.162387i
$653$	−15.4153			−0.603248			−0.301624	−	0.953427i	$-0.597529\pi$
$653$	−15.4153			−0.603248			−0.301624	+	0.953427i	$0.597529\pi$
$654$	−15.1961	+	4.33025i	−0.594213	+	0.169326i
$655$		0			0
$656$	18.1775	+	9.01495i	0.709714	+	0.351975i
$657$	−11.5299	−	11.5299i	−0.449825	−	0.449825i
$658$	−10.6348	+	19.1111i	−0.414587	+	0.745030i
$659$	−30.4355	−	30.4355i	−1.18560	−	1.18560i	−0.978272	−	0.207327i	$-0.933524\pi$
$659$	−30.4355	−	30.4355i	−1.18560	−	1.18560i	−0.207327	−	0.978272i	$-0.566476\pi$
$660$		0			0
$661$	−11.2208	+	11.2208i	−0.436437	+	0.436437i	−0.890811	−	0.454374i	$-0.849863\pi$
$661$	−11.2208	+	11.2208i	−0.436437	+	0.436437i	0.454374	+	0.890811i	$0.349863\pi$
$662$	38.0240	−	10.8352i	1.47784	−	0.421124i
$663$	−5.13709	+	5.13709i	−0.199508	+	0.199508i
$664$	−0.369550	−	7.78992i	−0.0143413	−	0.302308i
$665$		0			0
$666$	−8.19379	+	14.7246i	−0.317503	+	0.570565i
$667$			8.27109i			0.320258i
$668$	−5.24817	+	22.3945i	−0.203058	+	0.866469i
$669$	−0.920946	+	0.920946i	−0.0356058	+	0.0356058i
$670$		0			0
$671$			21.7757i			0.840640i
$672$	−13.7115	−	2.53465i	−0.528931	−	0.0977761i
$673$	29.2965	−	29.2965i	1.12930	−	1.12930i	0.139006	−	0.990291i	$-0.455609\pi$
$673$	29.2965	−	29.2965i	1.12930	−	1.12930i	0.990291	−	0.139006i	$-0.0443908\pi$
$674$	13.9825	−	3.98443i	0.538585	−	0.153474i
$675$		0			0
$676$	9.25326	+	14.9178i	0.355895	+	0.573760i
$677$	−2.74511			−0.105503			−0.0527516	−	0.998608i	$-0.516799\pi$
$677$	−2.74511			−0.105503			−0.0527516	+	0.998608i	$0.516799\pi$
$678$	1.02088	−	0.290907i	0.0392065	−	0.0111722i
$679$		−	20.0191i		−	0.768261i
$680$		0			0
$681$			9.60850i			0.368199i
$682$	2.53411	+	8.89292i	0.0970362	+	0.340528i
$683$	33.0796			1.26576			0.632878	−	0.774251i	$-0.281873\pi$
$683$	33.0796			1.26576			0.632878	+	0.774251i	$0.281873\pi$
$684$	1.15667	−	4.93565i	0.0442265	−	0.188719i
$685$		0			0
$686$	3.24401	+	11.3841i	0.123857	+	0.434648i
$687$	5.98647	−	5.98647i	0.228398	−	0.228398i
$688$	−1.51018	+	3.04510i	−0.0575752	+	0.116093i
$689$			10.6364i			0.405214i
$690$		0			0
$691$	−30.8216	+	30.8216i	−1.17251	+	1.17251i	−0.190899	+	0.981610i	$0.561140\pi$
$691$	−30.8216	+	30.8216i	−1.17251	+	1.17251i	−0.981610	+	0.190899i	$0.938860\pi$
$692$	7.23976	+	11.6717i	0.275214	+	0.443690i
$693$		−	29.1428i		−	1.10704i
$694$	−28.9994	−	16.1373i	−1.10080	−	0.612563i
$695$		0			0
$696$	−1.51939	−	1.38176i	−0.0575923	−	0.0523755i
$697$	20.6338	−	20.6338i	0.781561	−	0.781561i
$698$	−12.7207	−	44.6407i	−0.481487	−	1.68967i
$699$	0.312890	−	0.312890i	0.0118346	−	0.0118346i
$700$		0			0
$701$	−22.1242	−	22.1242i	−0.835619	−	0.835619i	0.152660	−	0.988279i	$-0.451216\pi$
$701$	−22.1242	−	22.1242i	−0.835619	−	0.835619i	−0.988279	+	0.152660i	$0.951216\pi$
$702$	−8.77436	−	4.88267i	−0.331167	−	0.184285i
$703$	3.10562	+	3.10562i	0.117131	+	0.117131i
$704$	17.0877	+	14.1200i	0.644015	+	0.532168i
$705$		0			0
$706$	7.30177	+	25.6240i	0.274806	+	0.964371i
$707$	−41.9440			−1.57747
$708$	1.65122	−	7.04595i	0.0620568	−	0.264803i
$709$	−7.09244	−	7.09244i	−0.266362	−	0.266362i	0.561270	−	0.827632i	$-0.310313\pi$
$709$	−7.09244	−	7.09244i	−0.266362	−	0.266362i	−0.827632	+	0.561270i	$0.810313\pi$
$710$		0			0
$711$	−36.9726			−1.38658
$712$	−32.8995	+	1.56073i	−1.23296	+	0.0584910i
$713$	−11.6812	−	11.6812i	−0.437466	−	0.437466i
$714$	−9.75103	+	17.5230i	−0.364923	+	0.655782i
$715$		0			0
$716$	10.1397	−	43.2671i	0.378938	−	1.61697i
$717$			5.03628i			0.188083i
$718$	−33.3535	−	18.5603i	−1.24474	−	0.692663i
$719$	30.2949			1.12981			0.564905	−	0.825156i	$-0.308913\pi$
$719$	30.2949			1.12981			0.564905	+	0.825156i	$0.308913\pi$
$720$		0			0
$721$	21.1349			0.787104
$722$	22.3250	+	12.4232i	0.830849	+	0.462343i
$723$			3.48320i			0.129542i
$724$	38.3090	+	8.97776i	1.42374	+	0.333656i
$725$		0			0
$726$	−1.40413	+	2.52327i	−0.0521120	+	0.0936473i
$727$	−15.9503	−	15.9503i	−0.591566	−	0.591566i	0.346489	−	0.938054i	$-0.387374\pi$
$727$	−15.9503	−	15.9503i	−0.591566	−	0.591566i	−0.938054	+	0.346489i	$0.887374\pi$
$728$	−17.2466	−	15.6844i	−0.639201	−	0.581301i
$729$	8.69055			0.321872
$730$		0			0
$731$	3.45657	+	3.45657i	0.127846	+	0.127846i
$732$	9.40479	+	2.20402i	0.347611	+	0.0814630i
$733$	−35.8535			−1.32428			−0.662140	−	0.749380i	$-0.730352\pi$
$733$	−35.8535			−1.32428			−0.662140	+	0.749380i	$0.730352\pi$
$734$	10.6746	+	37.4603i	0.394008	+	1.38269i
$735$		0			0
$736$	−38.9414	−	7.19856i	−1.43540	−	0.265342i
$737$	3.40147	+	3.40147i	0.125295	+	0.125295i
$738$	16.4379	+	9.14720i	0.605087	+	0.336713i
$739$	−21.4532	−	21.4532i	−0.789168	−	0.789168i	0.192190	−	0.981358i	$-0.438441\pi$
$739$	−21.4532	−	21.4532i	−0.789168	−	0.789168i	−0.981358	+	0.192190i	$0.938441\pi$
$740$		0			0
$741$	−0.863157	+	0.863157i	−0.0317089	+	0.0317089i
$742$	8.04595	+	28.2355i	0.295376	+	1.03656i
$743$	−13.0311	+	13.0311i	−0.478063	+	0.478063i	−0.904512	−	0.426449i	$-0.859765\pi$
$743$	−13.0311	+	13.0311i	−0.478063	+	0.478063i	0.426449	+	0.904512i	$0.359765\pi$
$744$	4.09729	−	0.194374i	0.150214	−	0.00712608i
$745$		0			0
$746$	−6.01903	−	3.34941i	−0.220372	−	0.122631i
$747$		−	7.23036i		−	0.264545i
$748$	27.0909	−	16.8040i	0.990540	−	0.614417i
$749$	−46.6836	+	46.6836i	−1.70578	+	1.70578i
$750$		0			0
$751$			22.4879i			0.820595i	0.911952	+	0.410297i	$0.134575\pi$
$751$			22.4879i			0.820595i	−0.911952	+	0.410297i	$0.865425\pi$
$752$	−4.92483	−	14.6158i	−0.179590	−	0.532983i
$753$	−9.06387	+	9.06387i	−0.330306	+	0.330306i
$754$	−0.940956	−	3.30208i	−0.0342676	−	0.120255i
$755$		0			0
$756$	−26.9861	−	6.32421i	−0.981474	−	0.230009i
$757$	−15.8781			−0.577100			−0.288550	−	0.957465i	$-0.593173\pi$
$757$	−15.8781			−0.577100			−0.288550	+	0.957465i	$0.593173\pi$
$758$	1.39464	+	4.89418i	0.0506555	+	0.177764i
$759$			11.9210i			0.432705i
$760$		0			0
$761$		−	19.5227i		−	0.707696i	−0.935303	−	0.353848i	$-0.884873\pi$
$761$		−	19.5227i		−	0.707696i	0.935303	−	0.353848i	$-0.115127\pi$
$762$	13.9419	−	3.97287i	0.505062	−	0.143922i
$763$	−72.9184			−2.63982
$764$	−17.5725	+	10.8999i	−0.635750	+	0.394346i
$765$		0			0
$766$	0.371680	−	0.105913i	0.0134293	−	0.00382680i
$767$	8.55524	−	8.55524i	0.308912	−	0.308912i
$768$	7.82788	−	5.95091i	0.282464	−	0.214735i
$769$		−	8.03843i		−	0.289873i	−0.989441	−	0.144937i	$-0.953702\pi$
$769$		−	8.03843i		−	0.289873i	0.989441	−	0.144937i	$-0.0462978\pi$
$770$		0			0
$771$	2.21946	−	2.21946i	0.0799320	−	0.0799320i
$772$	36.3725	+	8.52392i	1.30907	+	0.306783i
$773$			40.5118i			1.45711i	0.684988	+	0.728554i	$0.259807\pi$
$773$			40.5118i			1.45711i	−0.684988	+	0.728554i	$0.740193\pi$
$774$	−1.53234	+	2.75367i	−0.0550787	+	0.0989787i
$775$		0			0
$776$	10.4443	+	9.49821i	0.374928	+	0.340966i
$777$	7.91977	−	7.91977i	0.284120	−	0.284120i
$778$	−3.87625	+	1.10457i	−0.138970	+	0.0396008i
$779$	3.46698	−	3.46698i	0.124217	−	0.124217i
$780$		0			0
$781$	4.57542	+	4.57542i	0.163721	+	0.163721i
$782$	−27.6935	+	49.7664i	−0.990319	+	1.77964i
$783$	−2.88668	−	2.88668i	−0.103161	−	0.103161i
$784$	−32.5630	−	16.1493i	−1.16296	−	0.576760i
$785$		0			0
$786$	18.8843	−	5.38124i	0.673581	−	0.191943i
$787$	−15.8333			−0.564396			−0.282198	−	0.959356i	$-0.591063\pi$
$787$	−15.8333			−0.564396			−0.282198	+	0.959356i	$0.591063\pi$
$788$	16.0704	+	25.9081i	0.572484	+	0.922938i
$789$	4.17930	+	4.17930i	0.148787	+	0.148787i
$790$		0			0
$791$	4.89868			0.174177
$792$	15.2043	+	13.8270i	0.540260	+	0.491323i
$793$	11.4194	+	11.4194i	0.405513	+	0.405513i
$794$	−26.6318	−	14.8198i	−0.945128	−	0.525936i
$795$		0			0
$796$	8.47688	−	5.25808i	0.300455	−	0.186368i
$797$			10.2670i			0.363674i	0.983329	+	0.181837i	$0.0582044\pi$
$797$			10.2670i			0.363674i	−0.983329	+	0.181837i	$0.941796\pi$
$798$	−1.63841	+	2.94429i	−0.0579991	+	0.104227i
$799$	−22.1811			−0.784710
$800$		0			0
$801$	−30.5362			−1.07895
$802$	7.14932	−	12.8476i	0.252451	−	0.453665i
$803$		−	17.2293i		−	0.608010i
$804$	1.81336	−	1.12480i	0.0639522	−	0.0396686i
$805$		0			0
$806$	5.99244	+	3.33462i	0.211075	+	0.117457i
$807$	−0.737538	−	0.737538i	−0.0259626	−	0.0259626i
$808$	19.9007	−	21.8829i	0.700104	−	0.769837i
$809$	−9.16442			−0.322204			−0.161102	−	0.986938i	$-0.551505\pi$
$809$	−9.16442			−0.322204			−0.161102	+	0.986938i	$0.551505\pi$
$810$		0			0
$811$	−22.1702	−	22.1702i	−0.778502	−	0.778502i	0.201074	−	0.979576i	$-0.435557\pi$
$811$	−22.1702	−	22.1702i	−0.778502	−	0.778502i	−0.979576	+	0.201074i	$0.935557\pi$
$812$	−4.99575	−	8.05397i	−0.175317	−	0.282639i
$813$	1.71827			0.0602625
$814$	−17.1236	+	4.87952i	−0.600183	+	0.171027i
$815$		0			0
$816$	−4.51558	−	13.4012i	−0.158077	−	0.469136i
$817$	0.580788	+	0.580788i	0.0203192	+	0.0203192i
$818$	0.227433	−	0.408707i	0.00795202	−	0.0142901i
$819$	−15.2827	−	15.2827i	−0.534022	−	0.534022i
$820$		0			0
$821$	13.3258	−	13.3258i	0.465074	−	0.465074i	−0.435240	−	0.900314i	$-0.643337\pi$
$821$	13.3258	−	13.3258i	0.465074	−	0.465074i	0.900314	+	0.435240i	$0.143337\pi$
$822$	−1.52988	+	0.435951i	−0.0533606	+	0.0152055i
$823$	34.7796	−	34.7796i	1.21234	−	1.21234i	0.242084	−	0.970255i	$-0.422169\pi$
$823$	34.7796	−	34.7796i	1.21234	−	1.21234i	0.970255	−	0.242084i	$-0.0778308\pi$
$824$	−10.0276	+	11.0264i	−0.349329	+	0.384123i
$825$		0			0
$826$	16.2392	−	29.1825i	0.565035	−	1.01539i
$827$		−	16.5717i		−	0.576253i	−0.957592	−	0.288127i	$-0.906968\pi$
$827$		−	16.5717i		−	0.576253i	0.957592	−	0.288127i	$-0.0930324\pi$
$828$	−35.7468	−	8.37729i	−1.24229	−	0.291131i
$829$	−11.9869	+	11.9869i	−0.416321	+	0.416321i	−0.883933	−	0.467613i	$-0.845114\pi$
$829$	−11.9869	+	11.9869i	−0.416321	+	0.416321i	0.467613	+	0.883933i	$0.345114\pi$
$830$		0			0
$831$		−	8.48807i		−	0.294448i
$832$	16.3656	−	1.55625i	0.567374	−	0.0539534i
$833$	−36.9631	+	36.9631i	−1.28070	+	1.28070i
$834$	10.1826	−	2.90160i	0.352593	−	0.100474i
$835$		0			0
$836$	4.55192	−	2.82349i	0.157432	−	0.0976524i
$837$	8.15370			0.281833
$838$	12.9130	−	3.67968i	0.446073	−	0.127112i
$839$			4.44215i			0.153360i	0.997056	+	0.0766800i	$0.0244320\pi$
$839$			4.44215i			0.153360i	−0.997056	+	0.0766800i	$0.975568\pi$
$840$		0			0
$841$			27.6041i			0.951865i
$842$	1.64337	+	5.76704i	0.0566341	+	0.198745i
$843$	−4.43543			−0.152764
$844$	−28.5854	−	6.69902i	−0.983951	−	0.230590i
$845$		0			0
$846$	−3.91870	−	13.7518i	−0.134728	−	0.472797i
$847$	−9.42281	+	9.42281i	−0.323772	+	0.323772i
$848$	−18.5484	−	9.19888i	−0.636955	−	0.315891i
$849$		−	15.5478i		−	0.533599i
$850$		0			0
$851$	22.4926	−	22.4926i	0.771038	−	0.771038i
$852$	2.43920	−	1.51300i	0.0835655	−	0.0518344i
$853$			35.6748i			1.22148i	0.791830	+	0.610742i	$0.209129\pi$
$853$			35.6748i			1.22148i	−0.791830	+	0.610742i	$0.790871\pi$
$854$	38.9522	+	21.6758i	1.33292	+	0.741730i
$855$		0			0
$856$	−2.20618	−	46.5050i	−0.0754056	−	1.58951i
$857$	13.8568	−	13.8568i	0.473340	−	0.473340i	−0.429654	−	0.902994i	$-0.641364\pi$
$857$	13.8568	−	13.8568i	0.473340	−	0.473340i	0.902994	+	0.429654i	$0.141364\pi$
$858$	−1.35619	−	4.75924i	−0.0462994	−	0.162478i
$859$	−19.4217	+	19.4217i	−0.662660	+	0.662660i	−0.956006	−	0.293346i	$-0.905231\pi$
$859$	−19.4217	+	19.4217i	−0.662660	+	0.662660i	0.293346	+	0.956006i	$0.405231\pi$
$860$		0			0
$861$	−8.84130	−	8.84130i	−0.301311	−	0.301311i
$862$	24.6595	+	13.7223i	0.839906	+	0.467383i
$863$	−9.22041	−	9.22041i	−0.313866	−	0.313866i	0.532539	−	0.846405i	$-0.321238\pi$
$863$	−9.22041	−	9.22041i	−0.313866	−	0.313866i	−0.846405	+	0.532539i	$0.821238\pi$
$864$	16.1032	−	11.0785i	0.547842	−	0.376898i
$865$		0			0
$866$	8.87428	+	31.1424i	0.301560	+	1.05826i
$867$	−9.89018			−0.335888
$868$	18.4301	+	4.31911i	0.625559	+	0.146600i
$869$	−27.6244	−	27.6244i	−0.937093	−	0.937093i
$870$		0			0
$871$	3.56753			0.120881
$872$	34.5968	−	38.0427i	1.17159	−	1.28829i
$873$	9.25500	+	9.25500i	0.313234	+	0.313234i
$874$	−4.65319	+	8.36197i	−0.157396	+	0.282848i
$875$		0			0
$876$	−7.44125	−	1.74386i	−0.251417	−	0.0589197i
$877$		−	10.4267i		−	0.352084i	−0.984383	−	0.176042i	$-0.943670\pi$
$877$		−	10.4267i		−	0.352084i	0.984383	−	0.176042i	$-0.0563295\pi$
$878$	−36.2986	−	20.1991i	−1.22502	−	0.681686i
$879$	8.68236			0.292849
$880$		0			0
$881$	−12.7405			−0.429239			−0.214619	−	0.976698i	$-0.568851\pi$
$881$	−12.7405			−0.429239			−0.214619	+	0.976698i	$0.568851\pi$
$882$	−29.4466	−	16.3862i	−0.991519	−	0.551751i
$883$			27.9073i			0.939156i	0.882891	+	0.469578i	$0.155594\pi$
$883$			27.9073i			0.939156i	−0.882891	+	0.469578i	$0.844406\pi$
$884$	5.39449	−	23.0189i	0.181437	−	0.774209i
$885$		0			0
$886$	−13.6648	+	24.5563i	−0.459079	+	0.824984i
$887$	−41.7449	−	41.7449i	−1.40166	−	1.40166i	−0.794846	−	0.606811i	$-0.792448\pi$
$887$	−41.7449	−	41.7449i	−1.40166	−	1.40166i	−0.606811	−	0.794846i	$-0.707552\pi$
$888$	0.374273	+	7.88948i	0.0125598	+	0.264754i
$889$	66.9004			2.24377
$890$		0			0
$891$	11.2530	+	11.2530i	0.376989	+	0.376989i
$892$	0.967091	−	4.12668i	0.0323806	−	0.138171i
$893$	−3.72696			−0.124718
$894$	0.0271540	+	0.0952910i	0.000908164	+	0.00318701i
$895$		0			0
$896$	42.2671	−	16.5111i	1.41204	−	0.551597i
$897$	6.25148	+	6.25148i	0.208731	+	0.208731i
$898$	20.7086	+	11.5237i	0.691053	+	0.384551i
$899$	1.97145	+	1.97145i	0.0657516	+	0.0657516i
$900$		0			0
$901$	−21.0548	+	21.0548i	−0.701437	+	0.701437i
$902$	5.44729	+	19.1161i	0.181375	+	0.636496i
$903$	1.48109	−	1.48109i	0.0492877	−	0.0492877i
$904$	−2.32422	+	2.55572i	−0.0773024	+	0.0850021i
$905$		0			0
$906$	2.46975	+	1.37434i	0.0820519	+	0.0456595i
$907$		−	26.7614i		−	0.888597i	−0.895879	−	0.444298i	$-0.853453\pi$
$907$		−	26.7614i		−	0.888597i	0.895879	−	0.444298i	$-0.146547\pi$
$908$	−16.4825	−	26.5724i	−0.546990	−	0.881836i
$909$	19.3911	−	19.3911i	0.643163	−	0.643163i
$910$		0			0
$911$			19.2403i			0.637459i	0.947846	+	0.318729i	$0.103256\pi$
$911$			19.2403i			0.637459i	−0.947846	+	0.318729i	$0.896744\pi$
$912$	−0.758727	−	2.25173i	−0.0251240	−	0.0745622i
$913$	5.40222	−	5.40222i	0.178787	−	0.178787i
$914$	2.74195	+	9.62229i	0.0906957	+	0.318277i
$915$		0			0
$916$	−6.28643	+	26.8249i	−0.207709	+	0.886318i
$917$	90.6165			2.99242
$918$	−7.70361	−	27.0342i	−0.254257	−	0.892260i
$919$			42.6903i			1.40822i	0.710090	+	0.704111i	$0.248654\pi$
$919$			42.6903i			1.40822i	−0.710090	+	0.704111i	$0.751346\pi$
$920$		0			0
$921$			13.8942i			0.457828i
$922$	−5.22246	+	1.48819i	−0.171993	+	0.0490108i
$923$	4.79878			0.157954
$924$	−7.20030	−	11.6081i	−0.236873	−	0.381877i
$925$		0			0
$926$	17.6677	−	5.03456i	0.580597	−	0.165446i
$927$	−9.77085	+	9.77085i	−0.320917	+	0.320917i
$928$	6.57217	+	1.21491i	0.215742	+	0.0398812i
$929$			5.58037i			0.183086i	0.995801	+	0.0915430i	$0.0291799\pi$
$929$			5.58037i			0.183086i	−0.995801	+	0.0915430i	$0.970820\pi$
$930$		0			0
$931$	−6.21070	+	6.21070i	−0.203548	+	0.203548i
$932$	−0.328567	+	1.40203i	−0.0107626	+	0.0459251i
$933$		−	6.63132i		−	0.217100i
$934$	−0.731714	+	1.31492i	−0.0239424	+	0.0430255i
$935$		0			0
$936$	15.2243	−	0.722233i	0.497621	−	0.0236069i
$937$	−41.0680	+	41.0680i	−1.34163	+	1.34163i	−0.447197	+	0.894435i	$0.647578\pi$
$937$	−41.0680	+	41.0680i	−1.34163	+	1.34163i	−0.894435	+	0.447197i	$0.852422\pi$
$938$	9.47042	−	2.69867i	0.309220	−	0.0881149i
$939$	12.7118	−	12.7118i	0.414834	−	0.414834i
$940$		0			0
$941$	−31.5476	−	31.5476i	−1.02842	−	1.02842i	−0.999584	−	0.0288377i	$-0.990819\pi$
$941$	−31.5476	−	31.5476i	−1.02842	−	1.02842i	−0.0288377	−	0.999584i	$-0.509181\pi$
$942$	3.83166	−	6.88565i	0.124842	−	0.224347i
$943$	−25.1098	−	25.1098i	−0.817689	−	0.817689i
$944$	7.52017	+	22.3182i	0.244761	+	0.726394i
$945$		0			0
$946$	−3.20232	+	0.912529i	−0.104117	+	0.0296689i
$947$	34.7892			1.13050			0.565248	−	0.824921i	$-0.308780\pi$
$947$	34.7892			1.13050			0.565248	+	0.824921i	$0.308780\pi$
$948$	−14.7268	+	9.13482i	−0.478305	+	0.296685i
$949$	−9.03522	−	9.03522i	−0.293296	−	0.293296i
$950$		0			0
$951$	14.6394			0.474715
$952$	−3.09244	−	65.1870i	−0.100227	−	2.11272i
$953$	−26.7047	−	26.7047i	−0.865050	−	0.865050i	0.126870	−	0.991919i	$-0.459507\pi$
$953$	−26.7047	−	26.7047i	−0.865050	−	0.865050i	−0.991919	+	0.126870i	$0.959507\pi$
$954$	−16.7733	−	9.33383i	−0.543055	−	0.302194i
$955$		0			0
$956$	−8.63926	−	13.9279i	−0.279413	−	0.450460i
$957$		−	2.01191i		−	0.0650360i
$958$	−10.9104	+	19.6064i	−0.352498	+	0.633453i
$959$	−7.34112			−0.237057
$960$		0			0
$961$	25.4314			0.820369
$962$	−6.42092	+	11.5386i	−0.207019	+	0.372021i
$963$		−	43.1645i		−	1.39096i
$964$	−5.97510	−	9.63284i	−0.192445	−	0.310253i
$965$		0			0
$966$	21.3242	+	11.8663i	0.686096	+	0.381792i
$967$	12.8711	+	12.8711i	0.413906	+	0.413906i	0.883097	−	0.469191i	$-0.155454\pi$
$967$	12.8711	+	12.8711i	0.413906	+	0.413906i	−0.469191	+	0.883097i	$0.655454\pi$
$968$	−0.445304	−	9.38677i	−0.0143126	−	0.301702i
$969$	−3.41725			−0.109778
$970$		0			0
$971$	−23.9028	−	23.9028i	−0.767078	−	0.767078i	0.210513	−	0.977591i	$-0.432487\pi$
$971$	−23.9028	−	23.9028i	−0.767078	−	0.767078i	−0.977591	+	0.210513i	$0.932487\pi$
$972$	23.6167	−	14.6491i	0.757507	−	0.469870i
$973$	48.8610			1.56641
$974$	−26.5332	+	7.56087i	−0.850179	+	0.242266i
$975$		0			0
$976$	−29.7898	+	10.0378i	−0.953549	+	0.321301i
$977$	−2.71449	−	2.71449i	−0.0868441	−	0.0868441i	0.662350	−	0.749194i	$-0.269559\pi$
$977$	−2.71449	−	2.71449i	−0.0868441	−	0.0868441i	−0.749194	+	0.662350i	$0.769559\pi$
$978$	1.66221	−	2.98705i	0.0531515	−	0.0955155i
$979$	−22.8154	−	22.8154i	−0.729183	−	0.729183i
$980$		0			0
$981$	33.7109	−	33.7109i	1.07630	−	1.07630i
$982$	−37.4053	+	10.6589i	−1.19365	+	0.340141i
$983$	13.7542	−	13.7542i	0.438692	−	0.438692i	−0.452880	−	0.891572i	$-0.649603\pi$
$983$	13.7542	−	13.7542i	0.438692	−	0.438692i	0.891572	+	0.452880i	$0.149603\pi$
$984$	8.80748	−	0.417823i	0.280772	−	0.0133197i
$985$		0			0
$986$	4.67386	−	8.39911i	0.148846	−	0.267482i
$987$			9.50428i			0.302525i
$988$	0.906407	−	3.86773i	0.0288366	−	0.123049i
$989$	4.20640	−	4.20640i	0.133756	−	0.133756i
$990$		0			0
$991$			26.5971i			0.844883i	0.906390	+	0.422442i	$0.138827\pi$
$991$			26.5971i			0.844883i	−0.906390	+	0.422442i	$0.861173\pi$
$992$	−10.9977	+	7.56605i	−0.349177	+	0.240222i
$993$	12.1492	−	12.1492i	0.385545	−	0.385545i
$994$	12.7389	−	3.63006i	0.404054	−	0.115139i
$995$		0			0
$996$	−1.78640	−	2.87998i	−0.0566044	−	0.0912555i
$997$	25.4590			0.806295			0.403148	−	0.915135i	$-0.367916\pi$
$997$	25.4590			0.806295			0.403148	+	0.915135i	$0.367916\pi$
$998$	−44.2661	+	12.6140i	−1.40122	+	0.399289i
$999$			15.7002i			0.496733i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	400.2.j.d.307.3		18
4.3	odd	2		1600.2.j.d.1007.5		18
5.2	odd	4		80.2.s.b.3.3	yes	18
5.3	odd	4		400.2.s.d.243.7		18
5.4	even	2		80.2.j.b.67.7	yes	18
15.2	even	4		720.2.z.g.163.7		18
15.14	odd	2		720.2.bd.g.307.3		18
16.5	even	4		1600.2.s.d.207.5		18
16.11	odd	4		400.2.s.d.107.7		18
20.3	even	4		1600.2.s.d.943.5		18
20.7	even	4		320.2.s.b.303.5		18
20.19	odd	2		320.2.j.b.47.5		18
40.19	odd	2		640.2.j.c.607.5		18
40.27	even	4		640.2.s.c.223.5		18
40.29	even	2		640.2.j.d.607.5		18
40.37	odd	4		640.2.s.d.223.5		18
80.19	odd	4		640.2.s.d.287.5		18
80.27	even	4		80.2.j.b.43.7	✓	18
80.29	even	4		640.2.s.c.287.5		18
80.37	odd	4		320.2.j.b.143.5		18
80.43	even	4	inner	400.2.j.d.43.3		18
80.53	odd	4		1600.2.j.d.143.5		18
80.59	odd	4		80.2.s.b.27.3	yes	18
80.67	even	4		640.2.j.d.543.5		18
80.69	even	4		320.2.s.b.207.5		18
80.77	odd	4		640.2.j.c.543.5		18
240.59	even	4		720.2.z.g.667.7		18
240.107	odd	4		720.2.bd.g.523.3		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.2.j.b.43.7	✓	18	80.27	even	4
80.2.j.b.67.7	yes	18	5.4	even	2
80.2.s.b.3.3	yes	18	5.2	odd	4
80.2.s.b.27.3	yes	18	80.59	odd	4
320.2.j.b.47.5		18	20.19	odd	2
320.2.j.b.143.5		18	80.37	odd	4
320.2.s.b.207.5		18	80.69	even	4
320.2.s.b.303.5		18	20.7	even	4
400.2.j.d.43.3		18	80.43	even	4	inner
400.2.j.d.307.3		18	1.1	even	1	trivial
400.2.s.d.107.7		18	16.11	odd	4
400.2.s.d.243.7		18	5.3	odd	4
640.2.j.c.543.5		18	80.77	odd	4
640.2.j.c.607.5		18	40.19	odd	2
640.2.j.d.543.5		18	80.67	even	4
640.2.j.d.607.5		18	40.29	even	2
640.2.s.c.223.5		18	40.27	even	4
640.2.s.c.287.5		18	80.29	even	4
640.2.s.d.223.5		18	40.37	odd	4
640.2.s.d.287.5		18	80.19	odd	4
720.2.z.g.163.7		18	15.2	even	4
720.2.z.g.667.7		18	240.59	even	4
720.2.bd.g.307.3		18	15.14	odd	2
720.2.bd.g.523.3		18	240.107	odd	4
1600.2.j.d.143.5		18	80.53	odd	4
1600.2.j.d.1007.5		18	4.3	odd	2
1600.2.s.d.207.5		18	16.5	even	4
1600.2.s.d.943.5		18	20.3	even	4

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:	\( N \)	\(=\)	\( 400 = 2^{4} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	400.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.687667 + 1.23576i) q^{2} +0.614566i q^{3} +(-1.05423 - 1.69959i) q^{4} +(-0.759459 - 0.422617i) q^{6} +(-2.83610 - 2.83610i) q^{7} +(2.82525 - 0.134028i) q^{8} +2.62231 q^{9} +O(q^{10})\)	\(q+(-0.687667 + 1.23576i) q^{2} +0.614566i q^{3} +(-1.05423 - 1.69959i) q^{4} +(-0.759459 - 0.422617i) q^{6} +(-2.83610 - 2.83610i) q^{7} +(2.82525 - 0.134028i) q^{8} +2.62231 q^{9} +(1.95928 + 1.95928i) q^{11} +(1.04451 - 0.647893i) q^{12} +2.05493 q^{13} +(5.45504 - 1.55446i) q^{14} +(-1.77720 + 3.58351i) q^{16} +(4.06774 + 4.06774i) q^{17} +(-1.80327 + 3.24056i) q^{18} +(0.683479 + 0.683479i) q^{19} +(1.74297 - 1.74297i) q^{21} +(-3.76854 + 1.07388i) q^{22} +(4.95014 - 4.95014i) q^{23} +(0.0823693 + 1.73630i) q^{24} +(-1.41310 + 2.53941i) q^{26} +3.45528i q^{27} +(-1.83030 + 7.81010i) q^{28} +(-0.835439 + 0.835439i) q^{29} -2.35978i q^{31} +(-3.20625 - 4.66047i) q^{32} +(-1.20411 + 1.20411i) q^{33} +(-7.82401 + 2.22952i) q^{34} +(-2.76451 - 4.45685i) q^{36} +4.54384 q^{37} +(-1.31462 + 0.374613i) q^{38} +1.26289i q^{39} -5.07255i q^{41} +(0.955318 + 3.35248i) q^{42} +0.849753 q^{43} +(1.26444 - 5.39549i) q^{44} +(2.71316 + 9.52126i) q^{46} +(-2.72646 + 2.72646i) q^{47} +(-2.20230 - 1.09221i) q^{48} +9.08690i q^{49} +(-2.49989 + 2.49989i) q^{51} +(-2.16636 - 3.49253i) q^{52} +5.17605i q^{53} +(-4.26991 - 2.37608i) q^{54} +(-8.39280 - 7.63257i) q^{56} +(-0.420043 + 0.420043i) q^{57} +(-0.457903 - 1.60691i) q^{58} +(4.16328 - 4.16328i) q^{59} +(5.55706 + 5.55706i) q^{61} +(2.91613 + 1.62274i) q^{62} +(-7.43712 - 7.43712i) q^{63} +(7.96407 - 0.757328i) q^{64} +(-0.659968 - 2.31602i) q^{66} +1.73609 q^{67} +(2.62515 - 11.2018i) q^{68} +(3.04219 + 3.04219i) q^{69} +2.33526 q^{71} +(7.40868 - 0.351464i) q^{72} +(-4.39686 - 4.39686i) q^{73} +(-3.12465 + 5.61511i) q^{74} +(0.441090 - 1.88218i) q^{76} -11.1134i q^{77} +(-1.56063 - 0.868446i) q^{78} -14.0993 q^{79} +5.74343 q^{81} +(6.26848 + 3.48822i) q^{82} -2.75725i q^{83} +(-4.79982 - 1.12484i) q^{84} +(-0.584347 + 1.05009i) q^{86} +(-0.513433 - 0.513433i) q^{87} +(5.79805 + 5.27285i) q^{88} -11.6448 q^{89} +(-5.82797 - 5.82797i) q^{91} +(-13.6318 - 3.19462i) q^{92} +1.45024 q^{93} +(-1.49437 - 5.24417i) q^{94} +(2.86416 - 1.97045i) q^{96} +(3.52933 + 3.52933i) q^{97} +(-11.2293 - 6.24876i) q^{98} +(5.13783 + 5.13783i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 4 q^{2} - 4 q^{4} - 8 q^{6} - 2 q^{7} + 4 q^{8} - 10 q^{9}+O(q^{10}) \) 18 * q + 4 * q^2 - 4 * q^4 - 8 * q^6 - 2 * q^7 + 4 * q^8 - 10 * q^9	\( 18 q + 4 q^{2} - 4 q^{4} - 8 q^{6} - 2 q^{7} + 4 q^{8} - 10 q^{9} - 2 q^{11} - 4 q^{12} + 12 q^{14} + 6 q^{17} - 16 q^{18} + 2 q^{19} - 16 q^{21} - 4 q^{22} + 2 q^{23} + 4 q^{24} - 16 q^{26} + 4 q^{28} - 14 q^{29} + 4 q^{32} + 8 q^{33} - 28 q^{34} - 4 q^{36} - 8 q^{37} - 16 q^{38} - 28 q^{42} + 44 q^{43} + 44 q^{44} + 12 q^{46} + 38 q^{47} - 60 q^{48} + 8 q^{51} + 40 q^{52} - 4 q^{54} + 20 q^{56} - 24 q^{57} + 20 q^{58} - 10 q^{59} + 14 q^{61} - 6 q^{63} - 16 q^{64} + 4 q^{66} - 12 q^{67} - 36 q^{68} + 32 q^{69} + 24 q^{71} + 36 q^{72} - 14 q^{73} + 48 q^{74} - 16 q^{76} + 84 q^{78} + 16 q^{79} + 2 q^{81} + 28 q^{82} - 24 q^{84} - 36 q^{86} - 24 q^{87} + 96 q^{88} - 12 q^{89} - 52 q^{92} - 16 q^{93} + 28 q^{94} - 40 q^{96} - 18 q^{97} - 32 q^{98} - 22 q^{99}+O(q^{100}) \) 18 * q + 4 * q^2 - 4 * q^4 - 8 * q^6 - 2 * q^7 + 4 * q^8 - 10 * q^9 - 2 * q^11 - 4 * q^12 + 12 * q^14 + 6 * q^17 - 16 * q^18 + 2 * q^19 - 16 * q^21 - 4 * q^22 + 2 * q^23 + 4 * q^24 - 16 * q^26 + 4 * q^28 - 14 * q^29 + 4 * q^32 + 8 * q^33 - 28 * q^34 - 4 * q^36 - 8 * q^37 - 16 * q^38 - 28 * q^42 + 44 * q^43 + 44 * q^44 + 12 * q^46 + 38 * q^47 - 60 * q^48 + 8 * q^51 + 40 * q^52 - 4 * q^54 + 20 * q^56 - 24 * q^57 + 20 * q^58 - 10 * q^59 + 14 * q^61 - 6 * q^63 - 16 * q^64 + 4 * q^66 - 12 * q^67 - 36 * q^68 + 32 * q^69 + 24 * q^71 + 36 * q^72 - 14 * q^73 + 48 * q^74 - 16 * q^76 + 84 * q^78 + 16 * q^79 + 2 * q^81 + 28 * q^82 - 24 * q^84 - 36 * q^86 - 24 * q^87 + 96 * q^88 - 12 * q^89 - 52 * q^92 - 16 * q^93 + 28 * q^94 - 40 * q^96 - 18 * q^97 - 32 * q^98 - 22 * q^99

Introduction

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