LMFDB - Embedded newform 400.2.s.d.243.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [400,2,Mod(107,400)]

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, 1]))

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

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

chi := DirichletCharacter("400.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 400 = 2^{4} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	400.s (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			243.7
Root			$-1.37691 - 0.322680i$ of defining polynomial
Character	$\chi$	$=$	400.243
Dual form			400.2.s.d.107.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	1.23576	+	0.687667i	0.873818	+	0.486254i
$2$	1.23576	+	0.687667i	0.873818	+	0.486254i
$3$	−0.614566			−0.354820			−0.177410	−	0.984137i	$-0.556772\pi$
$3$	−0.614566			−0.354820			−0.177410	+	0.984137i	$0.556772\pi$
$4$	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	−0.0747413	+	0.997203i	$0.523813\pi$
$7$	−2.83610	+	2.83610i	−1.07194	+	1.07194i	−0.997203	+	0.0747413i	$0.976187\pi$
$8$	0.134028	+	2.82525i	0.0473862	+	0.998877i
$9$	−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	$0.612829\pi$
$12$	−0.647893	−	1.04451i	−0.187031	−	0.301524i
$13$			2.05493i			0.569934i	0.958537	+	0.284967i	$0.0919826\pi$
$13$			2.05493i			0.569934i	−0.958537	+	0.284967i	$0.908017\pi$
$14$	−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	−0.0133401	−	0.999911i	$-0.504246\pi$
$17$	4.06774	−	4.06774i	0.986571	−	0.986571i	0.999911	+	0.0133401i	$0.00424641\pi$
$18$	−3.24056	−	1.80327i	−0.763806	−	0.425036i
$19$	−0.683479	−	0.683479i	−0.156801	−	0.156801i	0.624347	−	0.781147i	$-0.285365\pi$
$19$	−0.683479	−	0.683479i	−0.156801	−	0.156801i	−0.781147	+	0.624347i	$0.785365\pi$
$20$		0			0
$21$	1.74297	−	1.74297i	0.380347	−	0.380347i
$22$	1.07388	+	3.76854i	0.228951	+	0.803455i
$23$	4.95014	+	4.95014i	1.03218	+	1.03218i	0.999465	+	0.0327113i	$0.0104142\pi$
$23$	4.95014	+	4.95014i	1.03218	+	1.03218i	0.0327113	+	0.999465i	$0.489586\pi$
$24$	−0.0823693	−	1.73630i	−0.0168136	−	0.354421i
$25$		0			0
$26$	−1.41310	+	2.53941i	−0.277133	+	0.498018i
$27$	3.45528			0.664969
$28$	−7.81010	−	1.83030i	−1.47597	−	0.345895i
$29$	0.835439	−	0.835439i	0.155137	−	0.155137i	−0.625271	−	0.780408i	$-0.715011\pi$
$29$	0.835439	−	0.835439i	0.155137	−	0.155137i	0.780408	+	0.625271i	$0.215011\pi$
$30$		0			0
$31$		−	2.35978i		−	0.423829i	−0.977288	−	0.211915i	$-0.932030\pi$
$31$		−	2.35978i		−	0.423829i	0.977288	−	0.211915i	$-0.0679698\pi$
$32$	−4.66047	+	3.20625i	−0.823862	+	0.566791i
$33$	−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
$37$		−	4.54384i		−	0.747002i	−0.927630	−	0.373501i	$-0.878157\pi$
$37$		−	4.54384i		−	0.747002i	0.927630	−	0.373501i	$-0.121843\pi$
$38$	−0.374613	−	1.31462i	−0.0607703	−	0.213260i
$39$		−	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	$-0.129636\pi$
$42$	3.35248	−	0.955318i	0.517299	−	0.147409i
$43$			0.849753i			0.129586i	0.997899	+	0.0647930i	$0.0206387\pi$
$43$			0.849753i			0.129586i	−0.997899	+	0.0647930i	$0.979361\pi$
$44$	−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	$-0.159263\pi$
$47$	2.72646	+	2.72646i	0.397696	+	0.397696i	−0.479724	+	0.877419i	$0.659263\pi$
$48$	1.09221	−	2.20230i	0.157647	−	0.317875i
$49$		−	9.08690i		−	1.29813i
$50$		0			0
$51$	−2.49989	+	2.49989i	−0.350055	+	0.350055i
$52$	−3.49253	+	2.16636i	−0.484327	+	0.300420i
$53$	−5.17605			−0.710985			−0.355492	−	0.934679i	$-0.615687\pi$
$53$	−5.17605			−0.710985			−0.355492	+	0.934679i	$0.615687\pi$
$54$	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
$58$	1.60691	−	0.457903i	0.210998	−	0.0601256i
$59$	−4.16328	+	4.16328i	−0.542013	+	0.542013i	−0.924119	−	0.382105i	$-0.875199\pi$
$59$	−4.16328	+	4.16328i	−0.542013	+	0.542013i	0.382105	+	0.924119i	$0.375199\pi$
$60$		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	$0.582188\pi$
$62$	1.62274	−	2.91613i	0.206088	−	0.370349i
$63$	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
$67$		−	1.73609i		−	0.212097i	−0.994361	−	0.106048i	$-0.966180\pi$
$67$		−	1.73609i		−	0.212097i	0.994361	−	0.106048i	$-0.0338198\pi$
$68$	11.2018	+	2.62515i	1.35842	+	0.318347i
$69$	−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	$0.455749\pi$
$72$	−0.351464	−	7.40868i	−0.0414204	−	0.873121i
$73$	4.39686	−	4.39686i	0.514613	−	0.514613i	−0.401323	−	0.915936i	$-0.631450\pi$
$73$	4.39686	−	4.39686i	0.514613	−	0.514613i	0.915936	+	0.401323i	$0.131450\pi$
$74$	3.12465	−	5.61511i	0.363233	−	0.652744i
$75$		0			0
$76$	0.441090	−	1.88218i	0.0505964	−	0.215900i
$77$	−11.1134			−1.26649
$78$	0.868446	−	1.56063i	0.0983321	−	0.176707i
$79$	14.0993			1.58629			0.793146	−	0.609032i	$-0.208442\pi$
$79$	14.0993			1.58629			0.793146	+	0.609032i	$0.208442\pi$
$80$		0			0
$81$	5.74343			0.638159
$82$	3.48822	−	6.26848i	0.385210	−	0.692238i
$83$	2.75725			0.302648			0.151324	−	0.988484i	$-0.451646\pi$
$83$	2.75725			0.302648			0.151324	+	0.988484i	$0.451646\pi$
$84$	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
$88$	−5.27285	+	5.79805i	−0.562088	+	0.618074i
$89$	11.6448			1.23435			0.617173	−	0.786828i	$-0.288278\pi$
$89$	11.6448			1.23435			0.617173	+	0.786828i	$0.288278\pi$
$90$		0			0
$91$	−5.82797	−	5.82797i	−0.610937	−	0.610937i
$92$	−3.19462	+	13.6318i	−0.333062	+	1.42121i
$93$			1.45024i			0.150383i
$94$	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	−0.504855	−	0.863204i	$-0.668454\pi$
$97$	3.52933	−	3.52933i	0.358349	−	0.358349i	0.863204	+	0.504855i	$0.168454\pi$
$98$	6.24876	−	11.2293i	0.631220	−	1.13433i
$99$	−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	$0.0758249\pi$
$102$	−4.80837	+	1.37019i	−0.476100	+	0.135669i
$103$	−3.72605	−	3.72605i	−0.367139	−	0.367139i	0.499294	−	0.866433i	$-0.333593\pi$
$103$	−3.72605	−	3.72605i	−0.367139	−	0.367139i	−0.866433	+	0.499294i	$0.833593\pi$
$104$	−5.80568	+	0.275419i	−0.569294	+	0.0270070i
$105$		0			0
$106$	−6.39637	−	3.55939i	−0.621271	−	0.345719i
$107$	−16.4605			−1.59130			−0.795649	−	0.605758i	$-0.792870\pi$
$107$	−16.4605			−1.59130			−0.795649	+	0.605758i	$0.792870\pi$
$108$	3.64266	+	5.87255i	0.350515	+	0.565087i
$109$	−12.8554	+	12.8554i	−1.23133	+	1.23133i	−0.267870	+	0.963455i	$0.586320\pi$
$109$	−12.8554	+	12.8554i	−1.23133	+	1.23133i	−0.963455	+	0.267870i	$0.913680\pi$
$110$		0			0
$111$			2.79249i			0.265051i
$112$	−5.12287	−	15.2035i	−0.484065	−	1.43660i
$113$	−0.863630	−	0.863630i	−0.0812435	−	0.0812435i	0.665317	−	0.746561i	$-0.268296\pi$
$113$	−0.863630	−	0.863630i	−0.0812435	−	0.0812435i	−0.746561	+	0.665317i	$0.768296\pi$
$114$	0.230225	+	0.807924i	0.0215625	+	0.0756690i
$115$		0			0
$116$	2.30065	+	0.539159i	0.213610	+	0.0500596i
$117$		−	5.38865i		−	0.498181i
$118$	−8.00779	+	2.28189i	−0.737177	+	0.210065i
$119$			23.0730i			2.11510i
$120$		0			0
$121$		−	3.32246i		−	0.302042i
$122$	3.04582	+	10.6886i	0.275755	+	0.967703i
$123$			3.11742i			0.281088i
$124$	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	0.998860	+	0.0477265i	$0.0151976\pi$
$127$	11.7944	+	11.7944i	1.04659	+	1.04659i	0.0477265	+	0.998860i	$0.484802\pi$
$128$	−10.3625	−	4.54075i	−0.915925	−	0.401349i
$129$		−	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	$0.801435\pi$
$132$	0.777081	−	3.31589i	0.0676362	−	0.288611i
$133$	3.87683			0.336163
$134$	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	$-0.274913\pi$
$137$	−1.29423	−	1.29423i	−0.110573	−	0.110573i	−0.760229	+	0.649655i	$0.774913\pi$
$138$	−1.66742	−	5.85144i	−0.141940	−	0.498108i
$139$	8.61413	−	8.61413i	0.730641	−	0.730641i	−0.240106	−	0.970747i	$-0.577182\pi$
$139$	8.61413	−	8.61413i	0.730641	−	0.730641i	0.970747	+	0.240106i	$0.0771821\pi$
$140$		0			0
$141$	−1.67559	−	1.67559i	−0.141110	−	0.141110i
$142$	2.88583	+	1.60588i	0.242173	+	0.134762i
$143$	−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
$147$			5.58450i			0.460602i
$148$	7.72265	−	4.79025i	0.634798	−	0.393756i
$149$	0.0806133	+	0.0806133i	0.00660410	+	0.00660410i	0.710401	−	0.703797i	$-0.248514\pi$
$149$	0.0806133	+	0.0806133i	0.00660410	+	0.00660410i	−0.703797	+	0.710401i	$0.748514\pi$
$150$		0			0
$151$	−3.25198			−0.264643			−0.132321	−	0.991207i	$-0.542243\pi$
$151$	−3.25198			−0.264643			−0.132321	+	0.991207i	$0.542243\pi$
$152$	1.83939	−	2.02260i	0.149194	−	0.164055i
$153$	−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
$157$	9.06652			0.723587			0.361793	−	0.932258i	$-0.382165\pi$
$157$	9.06652			0.723587			0.361793	+	0.932258i	$0.382165\pi$
$158$	17.4234	+	9.69559i	1.38613	+	0.771340i
$159$	3.18102			0.252271
$160$		0			0
$161$	−28.0782			−2.21287
$162$	7.09753	+	3.94956i	0.557634	+	0.310307i
$163$	−3.93313			−0.308067			−0.154033	−	0.988066i	$-0.549226\pi$
$163$	−3.93313			−0.308067			−0.154033	+	0.988066i	$0.549226\pi$
$164$	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	−0.947888	−	0.318603i	$-0.896786\pi$
$167$	−8.13216	+	8.13216i	−0.629285	+	0.629285i	0.318603	+	0.947888i	$0.396786\pi$
$168$	5.15793	+	4.69072i	0.397943	+	0.361897i
$169$	8.77728			0.675175
$170$		0			0
$171$	1.79229	+	1.79229i	0.137060	+	0.137060i
$172$	−1.44423	+	0.895834i	−0.110121	+	0.0683067i
$173$		−	6.86735i		−	0.522115i	−0.965323	−	0.261057i	$-0.915929\pi$
$173$		−	6.86735i		−	0.522115i	0.965323	−	0.261057i	$-0.0840712\pi$
$174$	−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
$178$	14.3902	+	8.00774i	1.07859	+	0.600205i
$179$	−15.7117	−	15.7117i	−1.17435	−	1.17435i	−0.981163	−	0.193183i	$-0.938119\pi$
$179$	−15.7117	−	15.7117i	−1.17435	−	1.17435i	−0.193183	−	0.981163i	$-0.561881\pi$
$180$		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	$0.988980\pi$
$182$	−3.19430	−	11.2097i	−0.236777	−	0.830919i
$183$	−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
$187$	15.9397			1.16562
$188$	−1.75955	+	7.50818i	−0.128328	+	0.547591i
$189$	−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	$-0.122035\pi$
$192$	4.89445	−	0.465428i	0.353226	−	0.0335894i
$193$	−13.2080	−	13.2080i	−0.950734	−	0.950734i	0.0481079	−	0.998842i	$-0.484681\pi$
$193$	−13.2080	−	13.2080i	−0.950734	−	0.950734i	−0.998842	+	0.0481079i	$0.984681\pi$
$194$	6.78843	−	1.93442i	0.487381	−	0.138883i
$195$		0			0
$196$	15.4440	−	9.57968i	1.10314	−	0.684263i
$197$			15.2437i			1.08607i	0.839709	+	0.543036i	$0.182725\pi$
$197$			15.2437i			1.08607i	−0.839709	+	0.543036i	$0.817275\pi$
$198$	−2.81604	−	9.88227i	−0.200127	−	0.702302i
$199$		−	4.98761i		−	0.353562i	−0.984250	−	0.176781i	$-0.943432\pi$
$199$		−	4.98761i		−	0.353562i	0.984250	−	0.176781i	$-0.0565684\pi$
$200$		0			0
$201$			1.06694i			0.0752561i
$202$	14.2231	−	4.05300i	1.00074	−	0.285168i
$203$			4.73878i			0.332597i
$204$	−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
$208$	−7.36385	−	3.65202i	−0.510591	−	0.253222i
$209$		−	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	$0.0813802\pi$
$212$	−5.45674	−	8.79715i	−0.374770	−	0.604191i
$213$	−1.43517			−0.0983362
$214$	−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
$218$	−24.7265	+	7.04603i	−1.67469	+	0.477217i
$219$	−2.70216	+	2.70216i	−0.182595	+	0.182595i
$220$		0			0
$221$	8.35890	+	8.35890i	0.562280	+	0.562280i
$222$	−1.92030	+	3.45086i	−0.128882	+	0.231606i
$223$	−1.49853	+	1.49853i	−0.100349	+	0.100349i	−0.755499	−	0.655150i	$-0.772605\pi$
$223$	−1.49853	+	1.49853i	−0.100349	+	0.100349i	0.655150	+	0.755499i	$0.272605\pi$
$224$	4.12429	−	22.3108i	0.275566	−	1.49070i
$225$		0			0
$226$	−0.473354	−	1.66113i	−0.0314870	−	0.110497i
$227$		−	15.6346i		−	1.03771i	−0.854864	−	0.518853i	$-0.826359\pi$
$227$		−	15.6346i		−	1.03771i	0.854864	−	0.518853i	$-0.173641\pi$
$228$	−0.271079	+	1.15672i	−0.0179526	+	0.0766057i
$229$	9.74097	+	9.74097i	0.643702	+	0.643702i	0.951463	−	0.307762i	$-0.0995800\pi$
$229$	9.74097	+	9.74097i	0.643702	+	0.643702i	−0.307762	+	0.951463i	$0.599580\pi$
$230$		0			0
$231$	6.82992			0.449376
$232$	2.47230	+	2.24835i	0.162314	+	0.147612i
$233$	0.509123	−	0.509123i	0.0333538	−	0.0333538i	−0.690233	−	0.723587i	$-0.742492\pi$
$233$	0.509123	−	0.509123i	0.0333538	−	0.0333538i	0.723587	+	0.690233i	$0.242492\pi$
$234$	3.70560	−	6.65910i	0.242242	−	0.435319i
$235$		0			0
$236$	−11.4649	−	2.68681i	−0.746303	−	0.174897i
$237$	−8.66493			−0.562848
$238$	−15.8665	+	28.5128i	−1.02847	+	1.84821i
$239$	−8.19486			−0.530081			−0.265041	−	0.964237i	$-0.585385\pi$
$239$	−8.19486			−0.530081			−0.265041	+	0.964237i	$0.585385\pi$
$240$		0			0
$241$	5.66775			0.365092			0.182546	−	0.983197i	$-0.441566\pi$
$241$	5.66775			0.365092			0.182546	+	0.983197i	$0.441566\pi$
$242$	2.28474	−	4.10578i	0.146869	−	0.263929i
$243$	−13.8956			−0.891400
$244$	−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
$248$	6.66697	−	0.316278i	0.423353	−	0.0200837i
$249$	−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	$0.521296\pi$
$252$	20.4805	+	4.79962i	1.29015	+	0.302348i
$253$			19.3974i			1.21951i
$254$	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	−0.810715	−	0.585440i	$-0.800922\pi$
$257$	−3.61143	+	3.61143i	−0.225275	+	0.225275i	0.585440	+	0.810715i	$0.300922\pi$
$258$	0.359120	−	0.645352i	0.0223578	−	0.0401779i
$259$	12.8868	+	12.8868i	0.800745	+	0.800745i
$260$		0			0
$261$	−2.19078	+	2.19078i	−0.135606	+	0.135606i
$262$	−30.7279	+	8.75617i	−1.89838	+	0.540958i
$263$	6.80041	+	6.80041i	0.419331	+	0.419331i	0.884973	−	0.465642i	$-0.154177\pi$
$263$	6.80041	+	6.80041i	0.419331	+	0.419331i	−0.465642	+	0.884973i	$0.654177\pi$
$264$	3.24052	−	3.56328i	0.199440	−	0.219305i
$265$		0			0
$266$	4.79084	+	2.66596i	0.293746	+	0.163461i
$267$	−7.15650			−0.437970
$268$	2.95063	−	1.83023i	0.180238	−	0.111799i
$269$	1.20010	−	1.20010i	0.0731711	−	0.0731711i	−0.669574	−	0.742745i	$-0.733523\pi$
$269$	1.20010	−	1.20010i	0.0731711	−	0.0731711i	0.742745	+	0.669574i	$0.233523\pi$
$270$		0			0
$271$		−	2.79591i		−	0.169840i	−0.996388	−	0.0849199i	$-0.972937\pi$
$271$		−	2.79591i		−	0.169840i	0.996388	−	0.0849199i	$-0.0270634\pi$
$272$	7.34759	+	21.8060i	0.445513	+	1.32218i
$273$	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
$277$			13.8115i			0.829852i	0.909855	+	0.414926i	$0.136193\pi$
$277$			13.8115i			0.829852i	−0.909855	+	0.414926i	$0.863807\pi$
$278$	16.5687	−	4.72139i	0.993724	−	0.283170i
$279$			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	$0.930937\pi$
$282$	−0.918389	−	3.22289i	−0.0546892	−	0.191920i
$283$		−	25.2988i		−	1.50386i	−0.659243	−	0.751930i	$-0.729123\pi$
$283$		−	25.2988i		−	1.50386i	0.659243	−	0.751930i	$-0.270877\pi$
$284$	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
$288$	12.2212	−	8.40779i	0.720140	−	0.495434i
$289$		−	16.0930i		−	0.946644i
$290$		0			0
$291$	−2.16901	+	2.16901i	−0.127149	+	0.127149i
$292$	12.1081	+	2.83755i	0.708575	+	0.166055i
$293$	14.1276			0.825344			0.412672	−	0.910880i	$-0.364596\pi$
$293$	14.1276			0.825344			0.412672	+	0.910880i	$0.364596\pi$
$294$	−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
$298$	0.0441840	+	0.155054i	0.00255951	+	0.00898204i
$299$	−10.1722	+	10.1722i	−0.588272	+	0.588272i
$300$		0			0
$301$	−2.40998	−	2.40998i	−0.138909	−	0.138909i
$302$	−4.01869	−	2.23628i	−0.231249	−	0.128683i
$303$	−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
$307$		−	22.6081i		−	1.29031i	−0.764051	−	0.645156i	$-0.776792\pi$
$307$		−	22.6081i		−	1.29031i	0.764051	−	0.645156i	$-0.223208\pi$
$308$	−11.7161	−	18.8882i	−0.667586	−	1.07626i
$309$	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	$0.598967\pi$
$312$	3.56797	−	0.169263i	0.201997	−	0.00958263i
$313$	20.6842	−	20.6842i	1.16914	−	1.16914i	0.186727	−	0.982412i	$-0.440212\pi$
$313$	20.6842	−	20.6842i	1.16914	−	1.16914i	0.982412	−	0.186727i	$-0.0597879\pi$
$314$	11.2041	+	6.23474i	0.632283	+	0.351847i
$315$		0			0
$316$	14.8639	+	23.9629i	0.836157	+	1.34802i
$317$	−23.8207			−1.33791			−0.668953	−	0.743305i	$-0.733257\pi$
$317$	−23.8207			−1.33791			−0.668953	+	0.743305i	$0.733257\pi$
$318$	3.93099	+	2.18748i	0.220439	+	0.122668i
$319$	3.27372			0.183293
$320$		0			0
$321$	10.1161			0.564624
$322$	−34.6980	−	19.3084i	−1.93365	−	1.07602i
$323$	−5.56042			−0.309390
$324$	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
$328$	14.3312	−	0.679866i	0.791309	−	0.0375393i
$329$	−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	$-0.528915\pi$
$332$	2.90677	+	4.68619i	0.159530	+	0.257188i
$333$			11.9153i			0.652957i
$334$	−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	−0.876819	−	0.480821i	$-0.840339\pi$
$337$	−7.26955	+	7.26955i	−0.395998	+	0.395998i	0.480821	+	0.876819i	$0.340339\pi$
$338$	10.8467	+	6.03584i	0.589980	+	0.328307i
$339$	0.530758	+	0.530758i	0.0288268	+	0.0288268i
$340$		0			0
$341$	4.62347	−	4.62347i	0.250375	−	0.250375i
$342$	0.982352	+	3.44735i	0.0531195	+	0.186411i
$343$	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
$347$	23.4667			1.25976			0.629880	−	0.776692i	$-0.283104\pi$
$347$	23.4667			1.25976			0.629880	+	0.776692i	$0.283104\pi$
$348$	−1.41390	−	0.331349i	−0.0757930	−	0.0177622i
$349$	23.2089	−	23.2089i	1.24234	−	1.24234i	0.283315	−	0.959027i	$-0.408566\pi$
$349$	23.2089	−	23.2089i	1.24234	−	1.24234i	0.959027	−	0.283315i	$-0.0914342\pi$
$350$		0			0
$351$			7.10035i			0.378988i
$352$	−15.4131	−	2.84921i	−0.821521	−	0.151863i
$353$	13.3220	+	13.3220i	0.709059	+	0.709059i	0.966337	−	0.257278i	$-0.0828256\pi$
$353$	13.3220	+	13.3220i	0.709059	+	0.709059i	−0.257278	+	0.966337i	$0.582826\pi$
$354$	4.92131	−	1.40237i	0.261565	−	0.0745351i
$355$		0			0
$356$	12.2763	+	19.7914i	0.650642	+	1.04894i
$357$		−	14.1799i		−	0.750479i
$358$	−8.61154	−	30.2203i	−0.455134	−	1.59719i
$359$		−	26.9902i		−	1.42449i	−0.701932	−	0.712244i	$-0.747679\pi$
$359$		−	26.9902i		−	1.42449i	0.701932	−	0.712244i	$-0.252321\pi$
$360$		0			0
$361$		−	18.0657i		−	0.950827i
$362$	−26.7573	+	7.62473i	−1.40633	+	0.400747i
$363$			2.04187i			0.107170i
$364$	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	−0.999859	−	0.0167684i	$-0.994662\pi$
$367$	−19.4758	−	19.4758i	−1.01663	−	1.01663i	−0.0167684	−	0.999859i	$-0.505338\pi$
$368$	−26.5363	+	8.94148i	−1.38330	+	0.466107i
$369$			13.3018i			0.692464i
$370$		0			0
$371$	14.6798	−	14.6798i	0.762136	−	0.762136i
$372$	−2.46481	+	1.52889i	−0.127795	+	0.0792690i
$373$	−4.87069			−0.252195			−0.126097	−	0.992018i	$-0.540245\pi$
$373$	−4.87069			−0.252195			−0.126097	+	0.992018i	$0.540245\pi$
$374$	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
$378$	−18.8487	+	5.37109i	−0.969472	+	0.276259i
$379$	−2.54450	+	2.54450i	−0.130702	+	0.130702i	−0.769432	−	0.638729i	$-0.779460\pi$
$379$	−2.54450	+	2.54450i	−0.130702	+	0.130702i	0.638729	+	0.769432i	$0.279460\pi$
$380$		0			0
$381$	−7.24846	−	7.24846i	−0.371350	−	0.371350i
$382$	7.10996	−	12.7769i	0.363777	−	0.653723i
$383$	0.193238	−	0.193238i	0.00987399	−	0.00987399i	−0.702153	−	0.712027i	$-0.747778\pi$
$383$	0.193238	−	0.193238i	0.00987399	−	0.00987399i	0.712027	+	0.702153i	$0.247778\pi$
$384$	6.36845	+	2.79059i	0.324988	+	0.142407i
$385$		0			0
$386$	−7.23929	−	25.4047i	−0.368470	−	1.29307i
$387$		−	2.22831i		−	0.113272i
$388$	9.71914	+	2.27769i	0.493414	+	0.115632i
$389$	−2.01528	−	2.01528i	−0.102179	−	0.102179i	0.654169	−	0.756348i	$-0.273018\pi$
$389$	−2.01528	−	2.01528i	−0.102179	−	0.102179i	−0.756348	+	0.654169i	$0.773018\pi$
$390$		0			0
$391$	40.2718			2.03663
$392$	25.6728	−	1.21790i	1.29667	−	0.0615134i
$393$	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
$397$	21.5509			1.08161			0.540804	−	0.841149i	$-0.318120\pi$
$397$	21.5509			1.08161			0.540804	+	0.841149i	$0.318120\pi$
$398$	3.42981	−	6.16351i	0.171921	−	0.308949i
$399$	−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	$0.583587\pi$
$402$	−0.733699	+	1.31849i	−0.0365936	+	0.0657601i
$403$	4.84917			0.241555
$404$	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
$408$	−7.39788	−	6.72776i	−0.366250	−	0.333074i
$409$	0.330732			0.0163536			0.00817682	−	0.999967i	$-0.497397\pi$
$409$	0.330732			0.0163536			0.00817682	+	0.999967i	$0.497397\pi$
$410$		0			0
$411$	0.795389	+	0.795389i	0.0392337	+	0.0392337i
$412$	2.40464	−	10.2609i	0.118468	−	0.505516i
$413$		−	23.6150i		−	1.16202i
$414$	−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
$418$	1.84174	−	3.30969i	0.0900826	−	0.161882i
$419$	6.71354	+	6.71354i	0.327978	+	0.327978i	0.851817	−	0.523839i	$-0.175501\pi$
$419$	6.71354	+	6.71354i	0.327978	+	0.327978i	−0.523839	+	0.851817i	$0.675501\pi$
$420$		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	$0.217051\pi$
$422$	19.9658	−	5.68941i	0.971918	−	0.276956i
$423$	−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
$427$	−31.5208			−1.52540
$428$	−17.3531	−	27.9761i	−0.838796	−	1.35228i
$429$	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	$-0.159580\pi$
$432$	−6.14073	+	12.3820i	−0.295446	+	0.595731i
$433$	16.1910	+	16.1910i	0.778092	+	0.778092i	0.979506	−	0.201414i	$-0.0645537\pi$
$433$	16.1910	+	16.1910i	0.778092	+	0.778092i	−0.201414	+	0.979506i	$0.564554\pi$
$434$	3.66818	+	12.8727i	0.176078	+	0.617909i
$435$		0			0
$436$	−35.4015	−	8.29636i	−1.69542	−	0.397324i
$437$		−	6.76664i		−	0.323692i
$438$	−5.19742	+	1.48105i	−0.248342	+	0.0707672i
$439$		−	29.3734i		−	1.40191i	−0.713204	−	0.700957i	$-0.752757\pi$
$439$		−	29.3734i		−	1.40191i	0.713204	−	0.700957i	$-0.247243\pi$
$440$		0			0
$441$			23.8287i			1.13470i
$442$	4.58150	+	16.0778i	0.217920	+	0.764741i
$443$			19.8713i			0.944115i	0.881568	+	0.472057i	$0.156489\pi$
$443$			19.8713i			0.944115i	−0.881568	+	0.472057i	$0.843511\pi$
$444$	−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
$448$	20.4390	−	24.7347i	0.965654	−	1.16861i
$449$			16.7577i			0.790844i	0.918500	+	0.395422i	$0.129402\pi$
$449$			16.7577i			0.790844i	−0.918500	+	0.395422i	$0.870598\pi$
$450$		0			0
$451$	9.93854	−	9.93854i	0.467987	−	0.467987i
$452$	0.557352	−	2.37828i	0.0262156	−	0.111865i
$453$	1.99856			0.0939005
$454$	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	$-0.302915\pi$
$457$	−5.00267	−	5.00267i	−0.234015	−	0.234015i	−0.814366	+	0.580351i	$0.802915\pi$
$458$	5.33901	+	18.7361i	0.249475	+	0.875480i
$459$	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	$0.721499\pi$
$462$	8.44018	+	4.69671i	0.392673	+	0.218511i
$463$	9.18551	−	9.18551i	0.426887	−	0.426887i	−0.460680	−	0.887566i	$-0.652394\pi$
$463$	9.18551	−	9.18551i	0.426887	−	0.426887i	0.887566	+	0.460680i	$0.152394\pi$
$464$	1.50906	+	4.47855i	0.0700564	+	0.207912i
$465$		0			0
$466$	0.979263	−	0.279049i	0.0453635	−	0.0129267i
$467$		−	1.06405i		−	0.0492385i	−0.999697	−	0.0246193i	$-0.992163\pi$
$467$		−	1.06405i		−	0.0492385i	0.999697	−	0.0246193i	$-0.00783735\pi$
$468$	9.15849	−	5.68087i	0.423351	−	0.262598i
$469$	4.92371	+	4.92371i	0.227356	+	0.227356i
$470$		0			0
$471$	−5.57197			−0.256743
$472$	−12.3203	−	11.2043i	−0.567088	−	0.515720i
$473$	−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
$477$	13.5732			0.621474
$478$	−10.1269	−	5.63533i	−0.463194	−	0.257754i
$479$	−15.8658			−0.724926			−0.362463	−	0.931998i	$-0.618064\pi$
$479$	−15.8658			−0.724926			−0.362463	+	0.931998i	$0.618064\pi$
$480$		0			0
$481$	9.33725			0.425742
$482$	7.00400	+	3.89752i	0.319024	+	0.177527i
$483$	17.2559			0.785170
$484$	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	−0.321732	−	0.946831i	$-0.604265\pi$
$487$	13.7947	−	13.7947i	0.625099	−	0.625099i	0.946831	+	0.321732i	$0.104265\pi$
$488$	−14.9553	+	16.4449i	−0.676994	+	0.744426i
$489$	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	$0.536896\pi$
$492$	−5.29833	+	3.28647i	−0.238867	+	0.148166i
$493$		−	6.79669i		−	0.306108i
$494$	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
$498$	−2.09402	−	1.16526i	−0.0938353	−	0.0522166i
$499$	−23.0141	−	23.0141i	−1.03025	−	1.03025i	−0.999528	−	0.0307258i	$-0.990218\pi$
$499$	−23.0141	−	23.0141i	−1.03025	−	1.03025i	−0.0307258	−	0.999528i	$-0.509782\pi$
$500$		0			0
$501$	4.99775	−	4.99775i	0.223283	−	0.223283i
$502$	8.08357	+	28.3675i	0.360787	+	1.26611i
$503$	−6.63364	−	6.63364i	−0.295780	−	0.295780i	0.543579	−	0.839358i	$-0.317069\pi$
$503$	−6.63364	−	6.63364i	−0.295780	−	0.295780i	−0.839358	+	0.543579i	$0.817069\pi$
$504$	22.0085	+	20.0149i	0.980337	+	0.891537i
$505$		0			0
$506$	−13.3390	+	23.9706i	−0.592989	+	1.06562i
$507$	−5.39422			−0.239566
$508$	−7.61165	+	32.4797i	−0.337712	+	1.44105i
$509$	−8.04140	+	8.04140i	−0.356429	+	0.356429i	−0.862495	−	0.506066i	$-0.831099\pi$
$509$	−8.04140	+	8.04140i	−0.356429	+	0.356429i	0.506066	+	0.862495i	$0.331099\pi$
$510$		0			0
$511$			24.9398i			1.10327i
$512$	−3.20705	−	22.3990i	−0.141733	−	0.989905i
$513$	−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
$517$			10.6838i			0.469873i
$518$	7.06321	+	24.7868i	0.310340	+	1.08907i
$519$			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	$0.744279\pi$
$522$	−4.21381	+	1.20076i	−0.184434	+	0.0525559i
$523$			2.46341i			0.107717i	0.998549	+	0.0538587i	$0.0171521\pi$
$523$			2.46341i			0.107717i	−0.998549	+	0.0538587i	$0.982848\pi$
$524$	−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
$528$	6.45487	−	2.17499i	0.280912	−	0.0946541i
$529$			26.0078i			1.13078i
$530$		0			0
$531$	10.9174	−	10.9174i	0.473775	−	0.473775i
$532$	4.08706	+	6.58901i	0.177197	+	0.285670i
$533$	10.4237			0.451501
$534$	−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
$538$	2.30830	−	0.657770i	0.0995180	−	0.0283585i
$539$	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	$0.935205\pi$
$542$	1.92266	−	3.45509i	0.0825852	−	0.148409i
$543$	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
$547$			43.6742i			1.86738i	0.358089	+	0.933688i	$0.383428\pi$
$547$			43.6742i			1.86738i	−0.358089	+	0.933688i	$0.616572\pi$
$548$	0.835243	−	3.56407i	0.0356798	−	0.152250i
$549$	−14.5723	−	14.5723i	−0.621932	−	0.621932i
$550$		0			0
$551$	−1.14201			−0.0486513
$552$	8.18721	−	9.00269i	0.348471	−	0.383180i
$553$	−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
$557$	5.18948			0.219885			0.109943	−	0.993938i	$-0.464933\pi$
$557$	5.18948			0.219885			0.109943	+	0.993938i	$0.464933\pi$
$558$	−4.25533	+	7.64700i	−0.180143	+	0.323723i
$559$	−1.74618			−0.0738555
$560$		0			0
$561$	−9.79597			−0.413586
$562$	−4.96301	+	8.91874i	−0.209352	+	0.376214i
$563$	−11.3756			−0.479423			−0.239711	−	0.970844i	$-0.577053\pi$
$563$	−11.3756			−0.479423			−0.239711	+	0.970844i	$0.577053\pi$
$564$	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
$568$	0.312991	+	6.59768i	0.0131328	+	0.276833i
$569$	7.51787			0.315165			0.157583	−	0.987506i	$-0.449630\pi$
$569$	7.51787			0.315165			0.157583	+	0.987506i	$0.449630\pi$
$570$		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	$0.823838\pi$
$572$	−11.0873	−	2.59833i	−0.463585	−	0.108642i
$573$			6.35416i			0.265449i
$574$	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	−0.471748	−	0.881733i	$-0.656377\pi$
$577$	9.84819	−	9.84819i	0.409986	−	0.409986i	0.881733	+	0.471748i	$0.156377\pi$
$578$	11.0666	−	19.8871i	0.460309	−	0.827195i
$579$	8.11720	+	8.11720i	0.337339	+	0.337339i
$580$		0			0
$581$	−7.81984	+	7.81984i	−0.324421	+	0.324421i
$582$	−4.17194	+	1.18883i	−0.172932	+	0.0492785i
$583$	−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
$587$	33.0447			1.36390			0.681951	−	0.731398i	$-0.261132\pi$
$587$	33.0447			1.36390			0.681951	+	0.731398i	$0.261132\pi$
$588$	−9.49136	+	5.88734i	−0.391417	+	0.242790i
$589$	−1.61286	+	1.61286i	−0.0664567	+	0.0664567i
$590$		0			0
$591$		−	9.36829i		−	0.385360i
$592$	16.2829	+	8.07532i	0.669223	+	0.331894i
$593$	−18.5424	−	18.5424i	−0.761445	−	0.761445i	0.215139	−	0.976584i	$-0.430980\pi$
$593$	−18.5424	−	18.5424i	−0.761445	−	0.761445i	−0.976584	+	0.215139i	$0.930980\pi$
$594$	3.71054	+	13.0214i	0.152245	+	0.534273i
$595$		0			0
$596$	−0.0520245	+	0.221994i	−0.00213101	+	0.00909324i
$597$			3.06521i			0.125451i
$598$	−19.5655	+	5.57535i	−0.800092	+	0.227993i
$599$			28.3117i			1.15678i	0.815759	+	0.578392i	$0.196319\pi$
$599$			28.3117i			1.15678i	−0.815759	+	0.578392i	$0.803681\pi$
$600$		0			0
$601$		−	41.7630i		−	1.70355i	−0.523909	−	0.851774i	$-0.675527\pi$
$601$		−	41.7630i		−	1.70355i	0.523909	−	0.851774i	$-0.324473\pi$
$602$	−1.32091	−	4.63543i	−0.0538361	−	0.188926i
$603$			4.55255i			0.185394i
$604$	−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	$-0.213195\pi$
$607$	4.01973	+	4.01973i	0.163156	+	0.163156i	−0.620807	+	0.783963i	$0.713195\pi$
$608$	5.37674	+	0.993923i	0.218055	+	0.0403089i
$609$		−	2.91229i		−	0.118012i
$610$		0			0
$611$	−5.60268	+	5.60268i	−0.226660	+	0.226660i
$612$	−29.3746	−	6.88396i	−1.18740	−	0.278268i
$613$	−21.5230			−0.869305			−0.434652	−	0.900598i	$-0.643129\pi$
$613$	−21.5230			−0.869305			−0.434652	+	0.900598i	$0.643129\pi$
$614$	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	−0.997702	−	0.0677580i	$-0.978415\pi$
$617$	−26.4655	−	26.4655i	−1.06546	−	1.06546i	−0.0677580	−	0.997702i	$-0.521585\pi$
$618$	1.25509	+	4.40447i	0.0504872	+	0.177174i
$619$	−21.7935	+	21.7935i	−0.875955	+	0.875955i	−0.993113	−	0.117158i	$-0.962622\pi$
$619$	−21.7935	+	21.7935i	−0.875955	+	0.875955i	0.117158	+	0.993113i	$0.462622\pi$
$620$		0			0
$621$	17.1041	+	17.1041i	0.686365	+	0.686365i
$622$	−13.3342	−	7.42010i	−0.534653	−	0.297519i
$623$	−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
$627$			1.64596i			0.0657334i
$628$	9.55818	+	15.4093i	0.381413	+	0.614900i
$629$	−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	$0.823852\pi$
$632$	1.88970	+	39.8339i	0.0751683	+	1.58451i
$633$	−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
$637$	18.6729			0.739848
$638$	4.04554	+	2.25123i	0.160165	+	0.0891269i
$639$	−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	$0.144706\pi$
$642$	12.5011	+	6.95648i	0.493378	+	0.274551i
$643$	31.3531			1.23645			0.618224	−	0.786002i	$-0.287853\pi$
$643$	31.3531			1.23645			0.618224	+	0.786002i	$0.287853\pi$
$644$	−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	−0.0536292	−	0.998561i	$-0.517079\pi$
$647$	24.0355	−	24.0355i	0.944932	−	0.944932i	0.998561	+	0.0536292i	$0.0170789\pi$
$648$	0.769783	+	16.2266i	0.0302399	+	0.637442i
$649$	−16.3141			−0.640383
$650$		0			0
$651$	−4.11303	−	4.11303i	−0.161202	−	0.161202i
$652$	−4.14642	−	6.68471i	−0.162387	−	0.261793i
$653$		−	15.4153i		−	0.603248i	−0.953427	−	0.301624i	$-0.902471\pi$
$653$		−	15.4153i		−	0.603248i	0.953427	−	0.301624i	$-0.0975288\pi$
$654$	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
$658$	−19.1111	−	10.6348i	−0.745030	−	0.414587i
$659$	30.4355	+	30.4355i	1.18560	+	1.18560i	0.978272	+	0.207327i	$0.0664763\pi$
$659$	30.4355	+	30.4355i	1.18560	+	1.18560i	0.207327	+	0.978272i	$0.433524\pi$
$660$		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	$0.349863\pi$
$662$	−10.8352	−	38.0240i	−0.421124	−	1.47784i
$663$	−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
$667$	8.27109			0.320258
$668$	−22.3945	−	5.24817i	−0.866469	−	0.203058i
$669$	0.920946	−	0.920946i	0.0356058	−	0.0356058i
$670$		0			0
$671$			21.7757i			0.840640i
$672$	−2.53465	+	13.7115i	−0.0977761	+	0.528931i
$673$	29.2965	+	29.2965i	1.12930	+	1.12930i	0.990291	+	0.139006i	$0.0443908\pi$
$673$	29.2965	+	29.2965i	1.12930	+	1.12930i	0.139006	+	0.990291i	$0.455609\pi$
$674$	−13.9825	+	3.98443i	−0.538585	+	0.153474i
$675$		0			0
$676$	9.25326	+	14.9178i	0.355895	+	0.573760i
$677$			2.74511i			0.105503i	0.998608	+	0.0527516i	$0.0167991\pi$
$677$			2.74511i			0.105503i	−0.998608	+	0.0527516i	$0.983201\pi$
$678$	0.290907	+	1.02088i	0.0111722	+	0.0392065i
$679$			20.0191i			0.768261i
$680$		0			0
$681$			9.60850i			0.368199i
$682$	8.89292	−	2.53411i	0.340528	−	0.0970362i
$683$			33.0796i			1.26576i	0.774251	+	0.632878i	$0.218127\pi$
$683$			33.0796i			1.26576i	−0.774251	+	0.632878i	$0.781873\pi$
$684$	−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
$688$	−3.04510	−	1.51018i	−0.116093	−	0.0575752i
$689$		−	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	$0.938860\pi$
$692$	11.6717	−	7.23976i	0.443690	−	0.275214i
$693$	29.1428			1.10704
$694$	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
$698$	44.6407	−	12.7207i	1.68967	−	0.481487i
$699$	−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	$0.951216\pi$
$702$	−4.88267	+	8.77436i	−0.184285	+	0.331167i
$703$	−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
$707$			41.9440i			1.57747i
$708$	7.04595	+	1.65122i	0.264803	+	0.0620568i
$709$	7.09244	+	7.09244i	0.266362	+	0.266362i	0.827632	−	0.561270i	$-0.189687\pi$
$709$	7.09244	+	7.09244i	0.266362	+	0.266362i	−0.561270	+	0.827632i	$0.689687\pi$
$710$		0			0
$711$	−36.9726			−1.38658
$712$	1.56073	+	32.8995i	0.0584910	+	1.23296i
$713$	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
$717$	5.03628			0.188083
$718$	18.5603	−	33.3535i	0.692663	−	1.24474i
$719$	−30.2949			−1.12981			−0.564905	−	0.825156i	$-0.691087\pi$
$719$	−30.2949			−1.12981			−0.564905	+	0.825156i	$0.691087\pi$
$720$		0			0
$721$	21.1349			0.787104
$722$	12.4232	−	22.3250i	0.462343	−	0.830849i
$723$	−3.48320			−0.129542
$724$	−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	−0.938054	−	0.346489i	$-0.887374\pi$
$727$	−15.9503	+	15.9503i	−0.591566	+	0.591566i	0.346489	+	0.938054i	$0.387374\pi$
$728$	15.6844	−	17.2466i	0.581301	−	0.639201i
$729$	−8.69055			−0.321872
$730$		0			0
$731$	3.45657	+	3.45657i	0.127846	+	0.127846i
$732$	2.20402	−	9.40479i	0.0814630	−	0.347611i
$733$		−	35.8535i		−	1.32428i	−0.749380	−	0.662140i	$-0.769648\pi$
$733$		−	35.8535i		−	1.32428i	0.749380	−	0.662140i	$-0.230352\pi$
$734$	−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
$738$	−9.14720	+	16.4379i	−0.336713	+	0.605087i
$739$	21.4532	+	21.4532i	0.789168	+	0.789168i	0.981358	−	0.192190i	$-0.0615590\pi$
$739$	21.4532	+	21.4532i	0.789168	+	0.789168i	−0.192190	+	0.981358i	$0.561559\pi$
$740$		0			0
$741$	−0.863157	+	0.863157i	−0.0317089	+	0.0317089i
$742$	28.2355	−	8.04595i	1.03656	−	0.295376i
$743$	−13.0311	−	13.0311i	−0.478063	−	0.478063i	0.426449	−	0.904512i	$-0.359765\pi$
$743$	−13.0311	−	13.0311i	−0.478063	−	0.478063i	−0.904512	+	0.426449i	$0.859765\pi$
$744$	−4.09729	+	0.194374i	−0.150214	+	0.00712608i
$745$		0			0
$746$	−6.01903	−	3.34941i	−0.220372	−	0.122631i
$747$	−7.23036			−0.264545
$748$	16.8040	+	27.0909i	0.614417	+	0.990540i
$749$	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	$0.865425\pi$
$752$	−14.6158	+	4.92483i	−0.532983	+	0.179590i
$753$	−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
$757$			15.8781i			0.577100i	0.957465	+	0.288550i	$0.0931731\pi$
$757$			15.8781i			0.577100i	−0.957465	+	0.288550i	$0.906827\pi$
$758$	−4.89418	+	1.39464i	−0.177764	+	0.0506555i
$759$		−	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	$-0.115127\pi$
$762$	−3.97287	−	13.9419i	−0.143922	−	0.505062i
$763$		−	72.9184i		−	2.63982i
$764$	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
$768$	5.95091	+	7.82788i	0.214735	+	0.282464i
$769$			8.03843i			0.289873i	0.989441	+	0.144937i	$0.0462978\pi$
$769$			8.03843i			0.289873i	−0.989441	+	0.144937i	$0.953702\pi$
$770$		0			0
$771$	2.21946	−	2.21946i	0.0799320	−	0.0799320i
$772$	8.52392	−	36.3725i	0.306783	−	1.30907i
$773$	−40.5118			−1.45711			−0.728554	−	0.684988i	$-0.759807\pi$
$773$	−40.5118			−1.45711			−0.728554	+	0.684988i	$0.759807\pi$
$774$	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
$778$	−1.10457	−	3.87625i	−0.0396008	−	0.138970i
$779$	−3.46698	+	3.46698i	−0.124217	+	0.124217i
$780$		0			0
$781$	4.57542	+	4.57542i	0.163721	+	0.163721i
$782$	49.7664	+	27.6935i	1.77964	+	0.990319i
$783$	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
$787$			15.8333i			0.564396i	0.959356	+	0.282198i	$0.0910635\pi$
$787$			15.8333i			0.564396i	−0.959356	+	0.282198i	$0.908937\pi$
$788$	−25.9081	+	16.0704i	−0.922938	+	0.572484i
$789$	−4.17930	−	4.17930i	−0.148787	−	0.148787i
$790$		0			0
$791$	4.89868			0.174177
$792$	13.8270	−	15.2043i	0.491323	−	0.540260i
$793$	−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
$797$	10.2670			0.363674			0.181837	−	0.983329i	$-0.441796\pi$
$797$	10.2670			0.363674			0.181837	+	0.983329i	$0.441796\pi$
$798$	−2.94429	−	1.63841i	−0.104227	−	0.0579991i
$799$	22.1811			0.784710
$800$		0			0
$801$	−30.5362			−1.07895
$802$	−12.8476	−	7.14932i	−0.453665	−	0.252451i
$803$	17.2293			0.608010
$804$	−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
$808$	21.8829	+	19.9007i	0.769837	+	0.700104i
$809$	9.16442			0.322204			0.161102	−	0.986938i	$-0.448495\pi$
$809$	9.16442			0.322204			0.161102	+	0.986938i	$0.448495\pi$
$810$		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	$0.935557\pi$
$812$	−8.05397	+	4.99575i	−0.282639	+	0.175317i
$813$			1.71827i			0.0602625i
$814$	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
$818$	0.408707	+	0.227433i	0.0142901	+	0.00795202i
$819$	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	$0.143337\pi$
$822$	0.435951	+	1.52988i	0.0152055	+	0.0533606i
$823$	34.7796	+	34.7796i	1.21234	+	1.21234i	0.970255	+	0.242084i	$0.0778308\pi$
$823$	34.7796	+	34.7796i	1.21234	+	1.21234i	0.242084	+	0.970255i	$0.422169\pi$
$824$	10.0276	−	11.0264i	0.349329	−	0.384123i
$825$		0			0
$826$	16.2392	−	29.1825i	0.565035	−	1.01539i
$827$	−16.5717			−0.576253			−0.288127	−	0.957592i	$-0.593032\pi$
$827$	−16.5717			−0.576253			−0.288127	+	0.957592i	$0.593032\pi$
$828$	8.37729	−	35.7468i	0.291131	−	1.24229i
$829$	11.9869	−	11.9869i	0.416321	−	0.416321i	−0.467613	−	0.883933i	$-0.654886\pi$
$829$	11.9869	−	11.9869i	0.416321	−	0.416321i	0.883933	+	0.467613i	$0.154886\pi$
$830$		0			0
$831$		−	8.48807i		−	0.294448i
$832$	−1.55625	−	16.3656i	−0.0539534	−	0.567374i
$833$	−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
$837$		−	8.15370i		−	0.281833i
$838$	3.67968	+	12.9130i	0.127112	+	0.446073i
$839$		−	4.44215i		−	0.153360i	−0.997056	−	0.0766800i	$-0.975568\pi$
$839$		−	4.44215i		−	0.153360i	0.997056	−	0.0766800i	$-0.0244320\pi$
$840$		0			0
$841$			27.6041i			0.951865i
$842$	5.76704	−	1.64337i	0.198745	−	0.0566341i
$843$		−	4.43543i		−	0.152764i
$844$	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
$848$	9.19888	−	18.5484i	0.315891	−	0.636955i
$849$			15.5478i			0.533599i
$850$		0			0
$851$	22.4926	−	22.4926i	0.771038	−	0.771038i
$852$	−1.51300	−	2.43920i	−0.0518344	−	0.0835655i
$853$	−35.6748			−1.22148			−0.610742	−	0.791830i	$-0.709129\pi$
$853$	−35.6748			−1.22148			−0.610742	+	0.791830i	$0.709129\pi$
$854$	−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	$-0.358636\pi$
$857$	−13.8568	−	13.8568i	−0.473340	−	0.473340i	−0.902994	+	0.429654i	$0.858636\pi$
$858$	4.75924	−	1.35619i	0.162478	−	0.0462994i
$859$	19.4217	−	19.4217i	0.662660	−	0.662660i	−0.293346	−	0.956006i	$-0.594769\pi$
$859$	19.4217	−	19.4217i	0.662660	−	0.662660i	0.956006	+	0.293346i	$0.0947690\pi$
$860$		0			0
$861$	−8.84130	−	8.84130i	−0.301311	−	0.301311i
$862$	13.7223	−	24.6595i	0.467383	−	0.839906i
$863$	9.22041	−	9.22041i	0.313866	−	0.313866i	−0.532539	−	0.846405i	$-0.678762\pi$
$863$	9.22041	−	9.22041i	0.313866	−	0.313866i	0.846405	+	0.532539i	$0.178762\pi$
$864$	−16.1032	+	11.0785i	−0.547842	+	0.376898i
$865$		0			0
$866$	8.87428	+	31.1424i	0.301560	+	1.05826i
$867$			9.89018i			0.335888i
$868$	−4.31911	+	18.4301i	−0.146600	+	0.625559i
$869$	27.6244	+	27.6244i	0.937093	+	0.937093i
$870$		0			0
$871$	3.56753			0.120881
$872$	−38.0427	−	34.5968i	−1.28829	−	1.17159i
$873$	−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
$877$	−10.4267			−0.352084			−0.176042	−	0.984383i	$-0.556330\pi$
$877$	−10.4267			−0.352084			−0.176042	+	0.984383i	$0.556330\pi$
$878$	20.1991	−	36.2986i	0.681686	−	1.22502i
$879$	−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	$0.568851\pi$
$882$	−16.3862	+	29.4466i	−0.551751	+	0.991519i
$883$	−27.9073			−0.939156			−0.469578	−	0.882891i	$-0.655594\pi$
$883$	−27.9073			−0.939156			−0.469578	+	0.882891i	$0.655594\pi$
$884$	−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	−0.606811	+	0.794846i	$0.707552\pi$
$887$	−41.7449	+	41.7449i	−1.40166	+	1.40166i	−0.794846	+	0.606811i	$0.792448\pi$
$888$	−7.88948	+	0.374273i	−0.264754	+	0.0125598i
$889$	−66.9004			−2.24377
$890$		0			0
$891$	11.2530	+	11.2530i	0.376989	+	0.376989i
$892$	−4.12668	−	0.967091i	−0.138171	−	0.0323806i
$893$		−	3.72696i		−	0.124718i
$894$	−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
$898$	−11.5237	+	20.7086i	−0.384551	+	0.691053i
$899$	−1.97145	−	1.97145i	−0.0657516	−	0.0657516i
$900$		0			0
$901$	−21.0548	+	21.0548i	−0.701437	+	0.701437i
$902$	19.1161	−	5.44729i	0.636496	−	0.181375i
$903$	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
$907$	−26.7614			−0.888597			−0.444298	−	0.895879i	$-0.646547\pi$
$907$	−26.7614			−0.888597			−0.444298	+	0.895879i	$0.646547\pi$
$908$	26.5724	−	16.4825i	0.881836	−	0.546990i
$909$	−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	$0.896744\pi$
$912$	−2.25173	+	0.758727i	−0.0745622	+	0.0251240i
$913$	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
$917$		−	90.6165i		−	2.99242i
$918$	27.0342	−	7.70361i	0.892260	−	0.254257i
$919$		−	42.6903i		−	1.40822i	−0.710090	−	0.704111i	$-0.751346\pi$
$919$		−	42.6903i		−	1.40822i	0.710090	−	0.704111i	$-0.248654\pi$
$920$		0			0
$921$			13.8942i			0.457828i
$922$	1.48819	+	5.22246i	0.0490108	+	0.171993i
$923$			4.79878i			0.157954i
$924$	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
$928$	−1.21491	+	6.57217i	−0.0398812	+	0.215742i
$929$		−	5.58037i		−	0.183086i	−0.995801	−	0.0915430i	$-0.970820\pi$
$929$		−	5.58037i		−	0.183086i	0.995801	−	0.0915430i	$-0.0291799\pi$
$930$		0			0
$931$	−6.21070	+	6.21070i	−0.203548	+	0.203548i
$932$	1.40203	+	0.328567i	0.0459251	+	0.0107626i
$933$	6.63132			0.217100
$934$	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	0.894435	+	0.447197i	$0.147578\pi$
$937$	41.0680	+	41.0680i	1.34163	+	1.34163i	0.447197	+	0.894435i	$0.352422\pi$
$938$	2.69867	+	9.47042i	0.0881149	+	0.309220i
$939$	−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	$-0.509181\pi$
$942$	−6.88565	−	3.83166i	−0.224347	−	0.124842i
$943$	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
$947$		−	34.7892i		−	1.13050i	−0.824921	−	0.565248i	$-0.808780\pi$
$947$		−	34.7892i		−	1.13050i	0.824921	−	0.565248i	$-0.191220\pi$
$948$	−9.13482	−	14.7268i	−0.296685	−	0.478305i
$949$	9.03522	+	9.03522i	0.293296	+	0.293296i
$950$		0			0
$951$	14.6394			0.474715
$952$	−65.1870	+	3.09244i	−2.11272	+	0.100227i
$953$	26.7047	−	26.7047i	0.865050	−	0.865050i	−0.126870	−	0.991919i	$-0.540493\pi$
$953$	26.7047	−	26.7047i	0.865050	−	0.865050i	0.991919	+	0.126870i	$0.0404931\pi$
$954$	16.7733	+	9.33383i	0.543055	+	0.302194i
$955$		0			0
$956$	−8.63926	−	13.9279i	−0.279413	−	0.450460i
$957$	−2.01191			−0.0650360
$958$	−19.6064	−	10.9104i	−0.633453	−	0.352498i
$959$	7.34112			0.237057
$960$		0			0
$961$	25.4314			0.820369
$962$	11.5386	+	6.42092i	0.372021	+	0.207019i
$963$	43.1645			1.39096
$964$	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	−0.469191	−	0.883097i	$-0.655454\pi$
$967$	12.8711	−	12.8711i	0.413906	−	0.413906i	0.883097	+	0.469191i	$0.155454\pi$
$968$	9.38677	−	0.445304i	0.301702	−	0.0143126i
$969$	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	$0.932487\pi$
$972$	−14.6491	−	23.6167i	−0.469870	−	0.757507i
$973$			48.8610i			1.56641i
$974$	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	−0.749194	−	0.662350i	$-0.769559\pi$
$977$	−2.71449	+	2.71449i	−0.0868441	+	0.0868441i	0.662350	+	0.749194i	$0.269559\pi$
$978$	2.98705	+	1.66221i	0.0955155	+	0.0531515i
$979$	22.8154	+	22.8154i	0.729183	+	0.729183i
$980$		0			0
$981$	33.7109	−	33.7109i	1.07630	−	1.07630i
$982$	10.6589	+	37.4053i	0.340141	+	1.19365i
$983$	13.7542	+	13.7542i	0.438692	+	0.438692i	0.891572	−	0.452880i	$-0.149603\pi$
$983$	13.7542	+	13.7542i	0.438692	+	0.438692i	−0.452880	+	0.891572i	$0.649603\pi$
$984$	−8.80748	+	0.417823i	−0.280772	+	0.0133197i
$985$		0			0
$986$	4.67386	−	8.39911i	0.148846	−	0.267482i
$987$	9.50428			0.302525
$988$	3.86773	+	0.906407i	0.123049	+	0.0288366i
$989$	−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	$0.861173\pi$
$992$	7.56605	+	10.9977i	0.240222	+	0.349177i
$993$	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
$997$		−	25.4590i		−	0.806295i	−0.915135	−	0.403148i	$-0.867916\pi$
$997$		−	25.4590i		−	0.806295i	0.915135	−	0.403148i	$-0.132084\pi$
$998$	−12.6140	−	44.2661i	−0.399289	−	1.40122i
$999$		−	15.7002i		−	0.496733i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.2.j.b.43.7	✓	18	80.59	odd	4
80.2.j.b.67.7	yes	18	5.3	odd	4
80.2.s.b.3.3	yes	18	5.4	even	2
80.2.s.b.27.3	yes	18	80.43	even	4
320.2.j.b.47.5		18	20.3	even	4
320.2.j.b.143.5		18	80.69	even	4
320.2.s.b.207.5		18	80.53	odd	4
320.2.s.b.303.5		18	20.19	odd	2
400.2.j.d.43.3		18	16.11	odd	4
400.2.j.d.307.3		18	5.2	odd	4
400.2.s.d.107.7		18	80.27	even	4	inner
400.2.s.d.243.7		18	1.1	even	1	trivial
640.2.j.c.543.5		18	80.29	even	4
640.2.j.c.607.5		18	40.3	even	4
640.2.j.d.543.5		18	80.19	odd	4
640.2.j.d.607.5		18	40.13	odd	4
640.2.s.c.223.5		18	40.19	odd	2
640.2.s.c.287.5		18	80.13	odd	4
640.2.s.d.223.5		18	40.29	even	2
640.2.s.d.287.5		18	80.3	even	4
720.2.z.g.163.7		18	15.14	odd	2
720.2.z.g.667.7		18	240.203	odd	4
720.2.bd.g.307.3		18	15.8	even	4
720.2.bd.g.523.3		18	240.59	even	4
1600.2.j.d.143.5		18	16.5	even	4
1600.2.j.d.1007.5		18	20.7	even	4
1600.2.s.d.207.5		18	80.37	odd	4
1600.2.s.d.943.5		18	4.3	odd	2

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.s (of order \(4\), degree \(2\), minimal)

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

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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