LMFDB - Embedded newform 1320.2.w.d.661.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1320,2,Mod(661,1320)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1320, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0, 0, 0]))

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

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

chi := DirichletCharacter("1320.661");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1320 = 2^{3} \cdot 3 \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1320.w (of order $2$, degree $1$, 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:	$10.5402530668$
Analytic rank:	$0$
Dimension:	$18$
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} + x^{16} + 16x^{10} - 16x^{9} + 32x^{8} + 128x^{2} + 512 $ x^18 + x^16 + 16x^10 - 16x^9 + 32x^8 + 128x^2 + 512
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{11} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			661.9
Root			$0.0805765 - 1.41192i$ of defining polynomial
Character	$\chi$	$=$	1320.661
Dual form			1320.2.w.d.661.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0805765 - 1.41192i) q^{2} -1.00000i q^{3} +(-1.98701 - 0.227534i) q^{4} +1.00000i q^{5} +(-1.41192 - 0.0805765i) q^{6} +1.10929 q^{7} +(-0.481366 + 2.78716i) q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+(0.0805765 - 1.41192i) q^{2} -1.00000i q^{3} +(-1.98701 - 0.227534i) q^{4} +1.00000i q^{5} +(-1.41192 - 0.0805765i) q^{6} +1.10929 q^{7} +(-0.481366 + 2.78716i) q^{8} -1.00000 q^{9} +(1.41192 + 0.0805765i) q^{10} -1.00000i q^{11} +(-0.227534 + 1.98701i) q^{12} -3.85979i q^{13} +(0.0893828 - 1.56623i) q^{14} +1.00000 q^{15} +(3.89646 + 0.904229i) q^{16} +1.10929 q^{17} +(-0.0805765 + 1.41192i) q^{18} -4.79786i q^{19} +(0.227534 - 1.98701i) q^{20} -1.10929i q^{21} +(-1.41192 - 0.0805765i) q^{22} +0.533975 q^{23} +(2.78716 + 0.481366i) q^{24} -1.00000 q^{25} +(-5.44970 - 0.311008i) q^{26} +1.00000i q^{27} +(-2.20418 - 0.252402i) q^{28} -2.68235i q^{29} +(0.0805765 - 1.41192i) q^{30} -7.40654 q^{31} +(1.59066 - 5.42861i) q^{32} -1.00000 q^{33} +(0.0893828 - 1.56623i) q^{34} +1.10929i q^{35} +(1.98701 + 0.227534i) q^{36} +2.36212i q^{37} +(-6.77418 - 0.386595i) q^{38} -3.85979 q^{39} +(-2.78716 - 0.481366i) q^{40} -3.93403 q^{41} +(-1.56623 - 0.0893828i) q^{42} -11.2135i q^{43} +(-0.227534 + 1.98701i) q^{44} -1.00000i q^{45} +(0.0430259 - 0.753929i) q^{46} -4.89887 q^{47} +(0.904229 - 3.89646i) q^{48} -5.76947 q^{49} +(-0.0805765 + 1.41192i) q^{50} -1.10929i q^{51} +(-0.878235 + 7.66946i) q^{52} +1.13531i q^{53} +(1.41192 + 0.0805765i) q^{54} +1.00000 q^{55} +(-0.533975 + 3.09178i) q^{56} -4.79786 q^{57} +(-3.78726 - 0.216134i) q^{58} -12.0787i q^{59} +(-1.98701 - 0.227534i) q^{60} +1.68834i q^{61} +(-0.596793 + 10.4574i) q^{62} -1.10929 q^{63} +(-7.53657 - 2.68329i) q^{64} +3.85979 q^{65} +(-0.0805765 + 1.41192i) q^{66} +6.44653i q^{67} +(-2.20418 - 0.252402i) q^{68} -0.533975i q^{69} +(1.56623 + 0.0893828i) q^{70} +13.0060 q^{71} +(0.481366 - 2.78716i) q^{72} -11.9142 q^{73} +(3.33512 + 0.190332i) q^{74} +1.00000i q^{75} +(-1.09168 + 9.53342i) q^{76} -1.10929i q^{77} +(-0.311008 + 5.44970i) q^{78} +3.44379 q^{79} +(-0.904229 + 3.89646i) q^{80} +1.00000 q^{81} +(-0.316990 + 5.55452i) q^{82} -2.71306i q^{83} +(-0.252402 + 2.20418i) q^{84} +1.10929i q^{85} +(-15.8326 - 0.903547i) q^{86} -2.68235 q^{87} +(2.78716 + 0.481366i) q^{88} +13.9410 q^{89} +(-1.41192 - 0.0805765i) q^{90} -4.28163i q^{91} +(-1.06102 - 0.121498i) q^{92} +7.40654i q^{93} +(-0.394734 + 6.91680i) q^{94} +4.79786 q^{95} +(-5.42861 - 1.59066i) q^{96} -19.1149 q^{97} +(-0.464884 + 8.14601i) q^{98} +1.00000i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 2 q^{4} - 2 q^{6} - 18 q^{9}+O(q^{10}) $ 18 * q - 2 * q^4 - 2 * q^6 - 18 * q^9	$ 18 q - 2 q^{4} - 2 q^{6} - 18 q^{9} + 2 q^{10} + 18 q^{15} + 2 q^{16} - 2 q^{22} + 2 q^{24} - 18 q^{25} + 32 q^{26} - 36 q^{31} - 18 q^{33} + 2 q^{36} - 40 q^{38} - 2 q^{40} - 36 q^{46} + 10 q^{49} + 2 q^{54} + 18 q^{55} + 28 q^{57} + 32 q^{58} - 2 q^{60} - 36 q^{62} - 2 q^{64} + 8 q^{71} + 28 q^{73} + 8 q^{79} + 18 q^{81} + 32 q^{82} - 48 q^{86} + 2 q^{88} - 28 q^{89} - 2 q^{90} - 68 q^{92} - 36 q^{94} - 28 q^{95} - 2 q^{96} - 52 q^{97} + 100 q^{98}+O(q^{100}) $ 18 * q - 2 * q^4 - 2 * q^6 - 18 * q^9 + 2 * q^10 + 18 * q^15 + 2 * q^16 - 2 * q^22 + 2 * q^24 - 18 * q^25 + 32 * q^26 - 36 * q^31 - 18 * q^33 + 2 * q^36 - 40 * q^38 - 2 * q^40 - 36 * q^46 + 10 * q^49 + 2 * q^54 + 18 * q^55 + 28 * q^57 + 32 * q^58 - 2 * q^60 - 36 * q^62 - 2 * q^64 + 8 * q^71 + 28 * q^73 + 8 * q^79 + 18 * q^81 + 32 * q^82 - 48 * q^86 + 2 * q^88 - 28 * q^89 - 2 * q^90 - 68 * q^92 - 36 * q^94 - 28 * q^95 - 2 * q^96 - 52 * q^97 + 100 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1320\mathbb{Z}\right)^\times$.

$n$	$661$	$881$	$991$	$1057$	$1201$
$\chi(n)$	$-1$	$1$	$1$	$1$	$1$

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 $

$2$	0.0805765	−	1.41192i	0.0569762	−	0.998376i
$2$	0.0805765	−	1.41192i	0.0569762	−	0.998376i
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	−1.98701	−	0.227534i	−0.993507	−	0.113767i
$5$			1.00000i			0.447214i
$5$			1.00000i			0.447214i
$6$	−1.41192	−	0.0805765i	−0.576412	−	0.0328952i
$7$	1.10929			0.419273			0.209636	−	0.977779i	$-0.432772\pi$
$7$	1.10929			0.419273			0.209636	+	0.977779i	$0.432772\pi$
$8$	−0.481366	+	2.78716i	−0.170189	+	0.985411i
$9$	−1.00000			−0.333333
$10$	1.41192	+	0.0805765i	0.446487	+	0.0254805i
$11$		−	1.00000i		−	0.301511i
$11$		−	1.00000i		−	0.301511i
$12$	−0.227534	+	1.98701i	−0.0656835	+	0.573602i
$13$		−	3.85979i		−	1.07051i	−0.844690	−	0.535256i	$-0.820215\pi$
$13$		−	3.85979i		−	1.07051i	0.844690	−	0.535256i	$-0.179785\pi$
$14$	0.0893828	−	1.56623i	0.0238886	−	0.418592i
$15$	1.00000			0.258199
$16$	3.89646	+	0.904229i	0.974114	+	0.226057i
$17$	1.10929			0.269043			0.134521	−	0.990911i	$-0.457050\pi$
$17$	1.10929			0.269043			0.134521	+	0.990911i	$0.457050\pi$
$18$	−0.0805765	+	1.41192i	−0.0189921	+	0.332792i
$19$		−	4.79786i		−	1.10071i	−0.834932	−	0.550353i	$-0.814493\pi$
$19$		−	4.79786i		−	1.10071i	0.834932	−	0.550353i	$-0.185507\pi$
$20$	0.227534	−	1.98701i	0.0508782	−	0.444310i
$21$		−	1.10929i		−	0.242067i
$22$	−1.41192	−	0.0805765i	−0.301022	−	0.0171790i
$23$	0.533975			0.111342			0.0556708	−	0.998449i	$-0.482270\pi$
$23$	0.533975			0.111342			0.0556708	+	0.998449i	$0.482270\pi$
$24$	2.78716	+	0.481366i	0.568928	+	0.0982585i
$25$	−1.00000			−0.200000
$26$	−5.44970	−	0.311008i	−1.06877	−	0.0609937i
$27$			1.00000i			0.192450i
$28$	−2.20418	−	0.252402i	−0.416551	−	0.0476995i
$29$		−	2.68235i		−	0.498100i	−0.968491	−	0.249050i	$-0.919882\pi$
$29$		−	2.68235i		−	0.498100i	0.968491	−	0.249050i	$-0.0801184\pi$
$30$	0.0805765	−	1.41192i	0.0147112	−	0.257779i
$31$	−7.40654			−1.33025			−0.665127	−	0.746731i	$-0.731622\pi$
$31$	−7.40654			−1.33025			−0.665127	+	0.746731i	$0.731622\pi$
$32$	1.59066	−	5.42861i	0.281191	−	0.959652i
$33$	−1.00000			−0.174078
$34$	0.0893828	−	1.56623i	0.0153290	−	0.268606i
$35$			1.10929i			0.187504i
$36$	1.98701	+	0.227534i	0.331169	+	0.0379224i
$37$			2.36212i			0.388331i	0.980969	+	0.194165i	$0.0621998\pi$
$37$			2.36212i			0.388331i	−0.980969	+	0.194165i	$0.937800\pi$
$38$	−6.77418	−	0.386595i	−1.09892	−	0.0627140i
$39$	−3.85979			−0.618061
$40$	−2.78716	−	0.481366i	−0.440689	−	0.0761107i
$41$	−3.93403			−0.614393			−0.307196	−	0.951646i	$-0.599391\pi$
$41$	−3.93403			−0.614393			−0.307196	+	0.951646i	$0.599391\pi$
$42$	−1.56623	−	0.0893828i	−0.241674	−	0.0137921i
$43$		−	11.2135i		−	1.71005i	−0.518588	−	0.855024i	$-0.673542\pi$
$43$		−	11.2135i		−	1.71005i	0.518588	−	0.855024i	$-0.326458\pi$
$44$	−0.227534	+	1.98701i	−0.0343021	+	0.299554i
$45$		−	1.00000i		−	0.149071i
$46$	0.0430259	−	0.753929i	0.00634382	−	0.111161i
$47$	−4.89887			−0.714574			−0.357287	−	0.933995i	$-0.616298\pi$
$47$	−4.89887			−0.714574			−0.357287	+	0.933995i	$0.616298\pi$
$48$	0.904229	−	3.89646i	0.130514	−	0.562405i
$49$	−5.76947			−0.824210
$50$	−0.0805765	+	1.41192i	−0.0113952	+	0.199675i
$51$		−	1.10929i		−	0.155332i
$52$	−0.878235	+	7.66946i	−0.121789	+	1.06356i
$53$			1.13531i			0.155947i	0.996955	+	0.0779736i	$0.0248450\pi$
$53$			1.13531i			0.155947i	−0.996955	+	0.0779736i	$0.975155\pi$
$54$	1.41192	+	0.0805765i	0.192137	+	0.0109651i
$55$	1.00000			0.134840
$56$	−0.533975	+	3.09178i	−0.0713555	+	0.413156i
$57$	−4.79786			−0.635492
$58$	−3.78726	−	0.216134i	−0.497291	−	0.0283798i
$59$		−	12.0787i		−	1.57251i	−0.617901	−	0.786256i	$-0.712017\pi$
$59$		−	12.0787i		−	1.57251i	0.617901	−	0.786256i	$-0.287983\pi$
$60$	−1.98701	−	0.227534i	−0.256523	−	0.0293746i
$61$			1.68834i			0.216170i	0.994142	+	0.108085i	$0.0344718\pi$
$61$			1.68834i			0.216170i	−0.994142	+	0.108085i	$0.965528\pi$
$62$	−0.596793	+	10.4574i	−0.0757927	+	1.32809i
$63$	−1.10929			−0.139758
$64$	−7.53657	−	2.68329i	−0.942072	−	0.335412i
$65$	3.85979			0.478748
$66$	−0.0805765	+	1.41192i	−0.00991828	+	0.173795i
$67$			6.44653i			0.787569i	0.919203	+	0.393785i	$0.128834\pi$
$67$			6.44653i			0.787569i	−0.919203	+	0.393785i	$0.871166\pi$
$68$	−2.20418	−	0.252402i	−0.267296	−	0.0306082i
$69$		−	0.533975i		−	0.0642831i
$70$	1.56623	+	0.0893828i	0.187200	+	0.0106833i
$71$	13.0060			1.54353			0.771763	−	0.635911i	$-0.219375\pi$
$71$	13.0060			1.54353			0.771763	+	0.635911i	$0.219375\pi$
$72$	0.481366	−	2.78716i	0.0567296	−	0.328470i
$73$	−11.9142			−1.39445			−0.697224	−	0.716853i	$-0.745582\pi$
$73$	−11.9142			−1.39445			−0.697224	+	0.716853i	$0.745582\pi$
$74$	3.33512	+	0.190332i	0.387700	+	0.0221256i
$75$			1.00000i			0.115470i
$76$	−1.09168	+	9.53342i	−0.125224	+	1.09356i
$77$		−	1.10929i		−	0.126416i
$78$	−0.311008	+	5.44970i	−0.0352147	+	0.617057i
$79$	3.44379			0.387457			0.193728	−	0.981055i	$-0.437942\pi$
$79$	3.44379			0.387457			0.193728	+	0.981055i	$0.437942\pi$
$80$	−0.904229	+	3.89646i	−0.101096	+	0.435637i
$81$	1.00000			0.111111
$82$	−0.316990	+	5.55452i	−0.0350057	+	0.613395i
$83$		−	2.71306i		−	0.297797i	−0.988852	−	0.148899i	$-0.952427\pi$
$83$		−	2.71306i		−	0.297797i	0.988852	−	0.148899i	$-0.0475728\pi$
$84$	−0.252402	+	2.20418i	−0.0275393	+	0.240496i
$85$			1.10929i			0.120320i
$86$	−15.8326	−	0.903547i	−1.70727	−	0.0974320i
$87$	−2.68235			−0.287578
$88$	2.78716	+	0.481366i	0.297113	+	0.0513138i
$89$	13.9410			1.47775			0.738873	−	0.673844i	$-0.235358\pi$
$89$	13.9410			1.47775			0.738873	+	0.673844i	$0.235358\pi$
$90$	−1.41192	−	0.0805765i	−0.148829	−	0.00849351i
$91$		−	4.28163i		−	0.448837i
$92$	−1.06102	−	0.121498i	−0.110619	−	0.0126670i
$93$			7.40654i			0.768022i
$94$	−0.394734	+	6.91680i	−0.0407137	+	0.713413i
$95$	4.79786			0.492250
$96$	−5.42861	−	1.59066i	−0.554055	−	0.162346i
$97$	−19.1149			−1.94082			−0.970412	−	0.241456i	$-0.922375\pi$
$97$	−19.1149			−1.94082			−0.970412	+	0.241456i	$0.922375\pi$
$98$	−0.464884	+	8.14601i	−0.0469603	+	0.822871i
$99$			1.00000i			0.100504i
$100$	1.98701	+	0.227534i	0.198701	+	0.0227534i
$101$			1.75360i			0.174490i	0.996187	+	0.0872448i	$0.0278062\pi$
$101$			1.75360i			0.174490i	−0.996187	+	0.0872448i	$0.972194\pi$
$102$	−1.56623	−	0.0893828i	−0.155080	−	0.00885022i
$103$	7.34041			0.723272			0.361636	−	0.932319i	$-0.382218\pi$
$103$	7.34041			0.723272			0.361636	+	0.932319i	$0.382218\pi$
$104$	10.7579	+	1.85797i	1.05490	+	0.182189i
$105$	1.10929			0.108256
$106$	1.60297	+	0.0914795i	0.155694	+	0.00888527i
$107$			4.82102i			0.466066i	0.972469	+	0.233033i	$0.0748650\pi$
$107$			4.82102i			0.466066i	−0.972469	+	0.233033i	$0.925135\pi$
$108$	0.227534	−	1.98701i	0.0218945	−	0.191201i
$109$		−	6.40843i		−	0.613816i	−0.951739	−	0.306908i	$-0.900706\pi$
$109$		−	6.40843i		−	0.613816i	0.951739	−	0.306908i	$-0.0992945\pi$
$110$	0.0805765	−	1.41192i	0.00768266	−	0.134621i
$111$	2.36212			0.224203
$112$	4.32231	+	1.00305i	0.408420	+	0.0947796i
$113$	−6.18727			−0.582050			−0.291025	−	0.956715i	$-0.593996\pi$
$113$	−6.18727			−0.582050			−0.291025	+	0.956715i	$0.593996\pi$
$114$	−0.386595	+	6.77418i	−0.0362079	+	0.634460i
$115$			0.533975i			0.0497935i
$116$	−0.610327	+	5.32987i	−0.0566675	+	0.494866i
$117$			3.85979i			0.356838i
$118$	−17.0541	−	0.973258i	−1.56996	−	0.0895957i
$119$	1.23053			0.112802
$120$	−0.481366	+	2.78716i	−0.0439425	+	0.254432i
$121$	−1.00000			−0.0909091
$122$	2.38379	+	0.136040i	0.215819	+	0.0123165i
$123$			3.93403i			0.354720i
$124$	14.7169	+	1.68524i	1.32162	+	0.151339i
$125$		−	1.00000i		−	0.0894427i
$126$	−0.0893828	+	1.56623i	−0.00796285	+	0.139531i
$127$	−0.205570			−0.0182414			−0.00912072	−	0.999958i	$-0.502903\pi$
$127$	−0.205570			−0.0182414			−0.00912072	+	0.999958i	$0.502903\pi$
$128$	−4.39586	+	10.4248i	−0.388542	+	0.921431i
$129$	−11.2135			−0.987297
$130$	0.311008	−	5.44970i	0.0272772	−	0.477970i
$131$		−	0.296752i		−	0.0259273i	−0.999916	−	0.0129637i	$-0.995873\pi$
$131$		−	0.296752i		−	0.0259273i	0.999916	−	0.0129637i	$-0.00412657\pi$
$132$	1.98701	+	0.227534i	0.172947	+	0.0198043i
$133$		−	5.32223i		−	0.461496i
$134$	9.10196	+	0.519439i	0.786290	+	0.0448727i
$135$	−1.00000			−0.0860663
$136$	−0.533975	+	3.09178i	−0.0457880	+	0.265118i
$137$	9.96720			0.851555			0.425778	−	0.904828i	$-0.360001\pi$
$137$	9.96720			0.851555			0.425778	+	0.904828i	$0.360001\pi$
$138$	−0.753929	−	0.0430259i	−0.0641787	−	0.00366260i
$139$		−	10.1021i		−	0.856846i	−0.903578	−	0.428423i	$-0.859069\pi$
$139$		−	10.1021i		−	0.856846i	0.903578	−	0.428423i	$-0.140931\pi$
$140$	0.252402	−	2.20418i	0.0213319	−	0.186287i
$141$			4.89887i			0.412559i
$142$	1.04798	−	18.3634i	0.0879442	−	1.54102i
$143$	−3.85979			−0.322772
$144$	−3.89646	−	0.904229i	−0.324705	−	0.0753524i
$145$	2.68235			0.222757
$146$	−0.960002	+	16.8218i	−0.0794503	+	1.39218i
$147$			5.76947i			0.475858i
$148$	0.537464	−	4.69357i	0.0441793	−	0.385809i
$149$			5.65265i			0.463083i	0.972825	+	0.231542i	$0.0743769\pi$
$149$			5.65265i			0.463083i	−0.972825	+	0.231542i	$0.925623\pi$
$150$	1.41192	+	0.0805765i	0.115282	+	0.00657904i
$151$	10.4793			0.852792			0.426396	−	0.904536i	$-0.359783\pi$
$151$	10.4793			0.852792			0.426396	+	0.904536i	$0.359783\pi$
$152$	13.3724	+	2.30953i	1.08465	+	0.187328i
$153$	−1.10929			−0.0896809
$154$	−1.56623	−	0.0893828i	−0.126210	−	0.00720267i
$155$		−	7.40654i		−	0.594907i
$156$	7.66946	+	0.878235i	0.614048	+	0.0703151i
$157$			2.14258i			0.170997i	0.996338	+	0.0854983i	$0.0272482\pi$
$157$			2.14258i			0.170997i	−0.996338	+	0.0854983i	$0.972752\pi$
$158$	0.277488	−	4.86234i	0.0220758	−	0.386827i
$159$	1.13531			0.0900362
$160$	5.42861	+	1.59066i	0.429169	+	0.125753i
$161$	0.592334			0.0466825
$162$	0.0805765	−	1.41192i	0.00633069	−	0.110931i
$163$		−	14.7976i		−	1.15904i	−0.814959	−	0.579519i	$-0.803240\pi$
$163$		−	14.7976i		−	1.15904i	0.814959	−	0.579519i	$-0.196760\pi$
$164$	7.81698	+	0.895128i	0.610404	+	0.0698978i
$165$		−	1.00000i		−	0.0778499i
$166$	−3.83061	−	0.218609i	−0.297313	−	0.0169673i
$167$	19.6194			1.51819			0.759096	−	0.650978i	$-0.225641\pi$
$167$	19.6194			1.51819			0.759096	+	0.650978i	$0.225641\pi$
$168$	3.09178	+	0.533975i	0.238536	+	0.0411971i
$169$	−1.89797			−0.145997
$170$	1.56623	+	0.0893828i	0.120124	+	0.00685535i
$171$			4.79786i			0.366902i
$172$	−2.55147	+	22.2815i	−0.194547	+	1.69895i
$173$		−	10.7400i		−	0.816545i	−0.912860	−	0.408272i	$-0.866131\pi$
$173$		−	10.7400i		−	0.816545i	0.912860	−	0.408272i	$-0.133869\pi$
$174$	−0.216134	+	3.78726i	−0.0163851	+	0.287111i
$175$	−1.10929			−0.0838546
$176$	0.904229	−	3.89646i	0.0681588	−	0.293706i
$177$	−12.0787			−0.907890
$178$	1.12332	−	19.6836i	0.0841963	−	1.47535i
$179$			2.41684i			0.180643i	0.995913	+	0.0903214i	$0.0287894\pi$
$179$			2.41684i			0.180643i	−0.995913	+	0.0903214i	$0.971211\pi$
$180$	−0.227534	+	1.98701i	−0.0169594	+	0.148103i
$181$			5.82247i			0.432780i	0.976307	+	0.216390i	$0.0694283\pi$
$181$			5.82247i			0.432780i	−0.976307	+	0.216390i	$0.930572\pi$
$182$	−6.04530	−	0.344999i	−0.448108	−	0.0255730i
$183$	1.68834			0.124806
$184$	−0.257038	+	1.48828i	−0.0189491	+	0.109717i
$185$	−2.36212			−0.173667
$186$	10.4574	+	0.596793i	0.766774	+	0.0437589i
$187$		−	1.10929i		−	0.0811194i
$188$	9.73413	+	1.11466i	0.709935	+	0.0812951i
$189$			1.10929i			0.0806891i
$190$	0.386595	−	6.77418i	0.0280465	−	0.491451i
$191$	4.15396			0.300570			0.150285	−	0.988643i	$-0.451981\pi$
$191$	4.15396			0.300570			0.150285	+	0.988643i	$0.451981\pi$
$192$	−2.68329	+	7.53657i	−0.193650	+	0.543905i
$193$	−12.2730			−0.883431			−0.441715	−	0.897155i	$-0.645630\pi$
$193$	−12.2730			−0.883431			−0.441715	+	0.897155i	$0.645630\pi$
$194$	−1.54021	+	26.9886i	−0.110581	+	1.93767i
$195$		−	3.85979i		−	0.276405i
$196$	11.4640	+	1.31275i	0.818859	+	0.0937681i
$197$		−	7.93158i		−	0.565102i	−0.959252	−	0.282551i	$-0.908819\pi$
$197$		−	7.93158i		−	0.565102i	0.959252	−	0.282551i	$-0.0911806\pi$
$198$	1.41192	+	0.0805765i	0.100341	+	0.00572632i
$199$	0.922025			0.0653606			0.0326803	−	0.999466i	$-0.489596\pi$
$199$	0.922025			0.0653606			0.0326803	+	0.999466i	$0.489596\pi$
$200$	0.481366	−	2.78716i	0.0340377	−	0.197082i
$201$	6.44653			0.454703
$202$	2.47593	+	0.141299i	0.174206	+	0.00994175i
$203$		−	2.97551i		−	0.208840i
$204$	−0.252402	+	2.20418i	−0.0176717	+	0.154323i
$205$		−	3.93403i		−	0.274765i
$206$	0.591464	−	10.3640i	0.0412092	−	0.722097i
$207$	−0.533975			−0.0371139
$208$	3.49013	−	15.0395i	0.241997	−	1.04280i
$209$	−4.79786			−0.331875
$210$	0.0893828	−	1.56623i	0.00616800	−	0.108080i
$211$		−	12.2179i		−	0.841115i	−0.907266	−	0.420558i	$-0.861834\pi$
$211$		−	12.2179i		−	0.841115i	0.907266	−	0.420558i	$-0.138166\pi$
$212$	0.258323	−	2.25588i	0.0177417	−	0.154935i
$213$		−	13.0060i		−	0.891155i
$214$	6.80688	+	0.388461i	0.465309	+	0.0265547i
$215$	11.2135			0.764757
$216$	−2.78716	−	0.481366i	−0.189643	−	0.0327528i
$217$	−8.21601			−0.557739
$218$	−9.04817	−	0.516369i	−0.612819	−	0.0349729i
$219$			11.9142i			0.805085i
$220$	−1.98701	−	0.227534i	−0.133965	−	0.0153404i
$221$		−	4.28163i		−	0.288014i
$222$	0.190332	−	3.33512i	0.0127742	−	0.223839i
$223$	−10.4962			−0.702879			−0.351440	−	0.936211i	$-0.614308\pi$
$223$	−10.4962			−0.702879			−0.351440	+	0.936211i	$0.614308\pi$
$224$	1.76450	−	6.02191i	0.117896	−	0.402356i
$225$	1.00000			0.0666667
$226$	−0.498549	+	8.73591i	−0.0331630	+	0.581104i
$227$			19.9398i			1.32345i	0.749746	+	0.661726i	$0.230176\pi$
$227$			19.9398i			1.32345i	−0.749746	+	0.661726i	$0.769824\pi$
$228$	9.53342	+	1.09168i	0.631366	+	0.0722982i
$229$		−	22.1880i		−	1.46622i	−0.680109	−	0.733111i	$-0.738068\pi$
$229$		−	22.1880i		−	1.46622i	0.680109	−	0.733111i	$-0.261932\pi$
$230$	0.753929	+	0.0430259i	0.0497126	+	0.00283704i
$231$	−1.10929			−0.0729860
$232$	7.47615	+	1.29119i	0.490834	+	0.0847710i
$233$	−3.60397			−0.236104			−0.118052	−	0.993007i	$-0.537665\pi$
$233$	−3.60397			−0.236104			−0.118052	+	0.993007i	$0.537665\pi$
$234$	5.44970	+	0.311008i	0.356258	+	0.0203312i
$235$		−	4.89887i		−	0.319567i
$236$	−2.74832	+	24.0005i	−0.178900	+	1.56230i
$237$		−	3.44379i		−	0.223698i
$238$	0.0991516	−	1.73740i	0.00642704	−	0.112619i
$239$	24.8117			1.60494			0.802469	−	0.596694i	$-0.203519\pi$
$239$	24.8117			1.60494			0.802469	+	0.596694i	$0.203519\pi$
$240$	3.89646	+	0.904229i	0.251515	+	0.0583677i
$241$	11.7834			0.759034			0.379517	−	0.925185i	$-0.376090\pi$
$241$	11.7834			0.759034			0.379517	+	0.925185i	$0.376090\pi$
$242$	−0.0805765	+	1.41192i	−0.00517965	+	0.0907614i
$243$		−	1.00000i		−	0.0641500i
$244$	0.384156	−	3.35476i	0.0245930	−	0.214766i
$245$		−	5.76947i		−	0.368598i
$246$	5.55452	+	0.316990i	0.354144	+	0.0202106i
$247$	−18.5187			−1.17832
$248$	3.56526	−	20.6432i	0.226394	−	1.31085i
$249$	−2.71306			−0.171933
$250$	−1.41192	−	0.0805765i	−0.0892974	−	0.00509610i
$251$			28.3697i			1.79068i	0.445385	+	0.895339i	$0.353067\pi$
$251$			28.3697i			1.79068i	−0.445385	+	0.895339i	$0.646933\pi$
$252$	2.20418	+	0.252402i	0.138850	+	0.0158998i
$253$		−	0.533975i		−	0.0335707i
$254$	−0.0165641	+	0.290248i	−0.00103933	+	0.0182118i
$255$	1.10929			0.0694665
$256$	14.3647	+	7.04657i	0.897796	+	0.440411i
$257$	−17.2750			−1.07759			−0.538793	−	0.842438i	$-0.681120\pi$
$257$	−17.2750			−1.07759			−0.538793	+	0.842438i	$0.681120\pi$
$258$	−0.903547	+	15.8326i	−0.0562524	+	0.985693i
$259$			2.62028i			0.162816i
$260$	−7.66946	−	0.878235i	−0.475640	−	0.0544658i
$261$			2.68235i			0.166033i
$262$	−0.418988	−	0.0239112i	−0.0258852	−	0.00147724i
$263$	−3.34321			−0.206151			−0.103076	−	0.994674i	$-0.532868\pi$
$263$	−3.34321			−0.206151			−0.103076	+	0.994674i	$0.532868\pi$
$264$	0.481366	−	2.78716i	0.0296260	−	0.171538i
$265$	−1.13531			−0.0697417
$266$	−7.51454	−	0.428846i	−0.460746	−	0.0262943i
$267$		−	13.9410i		−	0.853177i
$268$	1.46681	−	12.8094i	0.0895996	−	0.782456i
$269$			21.6071i			1.31741i	0.752403	+	0.658703i	$0.228894\pi$
$269$			21.6071i			1.31741i	−0.752403	+	0.658703i	$0.771106\pi$
$270$	−0.0805765	+	1.41192i	−0.00490373	+	0.0859265i
$271$	13.3858			0.813132			0.406566	−	0.913621i	$-0.366726\pi$
$271$	13.3858			0.813132			0.406566	+	0.913621i	$0.366726\pi$
$272$	4.32231	+	1.00305i	0.262078	+	0.0608190i
$273$	−4.28163			−0.259136
$274$	0.803122	−	14.0728i	0.0485184	−	0.850172i
$275$			1.00000i			0.0603023i
$276$	−0.121498	+	1.06102i	−0.00731331	+	0.0638657i
$277$			1.55071i			0.0931733i	0.998914	+	0.0465866i	$0.0148344\pi$
$277$			1.55071i			0.0931733i	−0.998914	+	0.0465866i	$0.985166\pi$
$278$	−14.2633	−	0.813989i	−0.855454	−	0.0488198i
$279$	7.40654			0.443418
$280$	−3.09178	−	0.533975i	−0.184769	−	0.0319111i
$281$	−0.400588			−0.0238971			−0.0119485	−	0.999929i	$-0.503803\pi$
$281$	−0.400588			−0.0238971			−0.0119485	+	0.999929i	$0.503803\pi$
$282$	6.91680	+	0.394734i	0.411889	+	0.0235061i
$283$		−	25.8493i		−	1.53658i	−0.640102	−	0.768290i	$-0.721108\pi$
$283$		−	25.8493i		−	1.53658i	0.640102	−	0.768290i	$-0.278892\pi$
$284$	−25.8431	−	2.95931i	−1.53350	−	0.175603i
$285$		−	4.79786i		−	0.284201i
$286$	−0.311008	+	5.44970i	−0.0183903	+	0.322247i
$287$	−4.36399			−0.257598
$288$	−1.59066	+	5.42861i	−0.0937304	+	0.319884i
$289$	−15.7695			−0.927616
$290$	0.216134	−	3.78726i	0.0126918	−	0.222395i
$291$			19.1149i			1.12054i
$292$	23.6736	+	2.71088i	1.38539	+	0.158642i
$293$		−	7.62504i		−	0.445459i	−0.974880	−	0.222730i	$-0.928503\pi$
$293$		−	7.62504i		−	0.445459i	0.974880	−	0.222730i	$-0.0714967\pi$
$294$	8.14601	+	0.464884i	0.475085	+	0.0271126i
$295$	12.0787			0.703249
$296$	−6.58363	−	1.13705i	−0.382666	−	0.0660895i
$297$	1.00000			0.0580259
$298$	7.98107	+	0.455471i	0.462331	+	0.0263847i
$299$		−	2.06103i		−	0.119193i
$300$	0.227534	−	1.98701i	0.0131367	−	0.114720i
$301$		−	12.4391i		−	0.716977i
$302$	0.844384	−	14.7959i	0.0485888	−	0.851407i
$303$	1.75360			0.100742
$304$	4.33836	−	18.6947i	0.248822	−	1.07221i
$305$	−1.68834			−0.0966741
$306$	−0.0893828	+	1.56623i	−0.00510967	+	0.0895352i
$307$			6.71091i			0.383012i	0.981491	+	0.191506i	$0.0613371\pi$
$307$			6.71091i			0.383012i	−0.981491	+	0.191506i	$0.938663\pi$
$308$	−0.252402	+	2.20418i	−0.0143819	+	0.125595i
$309$		−	7.34041i		−	0.417581i
$310$	−10.4574	−	0.596793i	−0.593941	−	0.0338955i
$311$	15.1336			0.858148			0.429074	−	0.903269i	$-0.358840\pi$
$311$	15.1336			0.858148			0.429074	+	0.903269i	$0.358840\pi$
$312$	1.85797	−	10.7579i	0.105187	−	0.609044i
$313$	15.2220			0.860398			0.430199	−	0.902734i	$-0.358443\pi$
$313$	15.2220			0.860398			0.430199	+	0.902734i	$0.358443\pi$
$314$	3.02515	+	0.172642i	0.170719	+	0.00974273i
$315$		−	1.10929i		−	0.0625015i
$316$	−6.84286	−	0.783581i	−0.384941	−	0.0440799i
$317$		−	33.4802i		−	1.88043i	−0.340578	−	0.940216i	$-0.610623\pi$
$317$		−	33.4802i		−	1.88043i	0.340578	−	0.940216i	$-0.389377\pi$
$318$	0.0914795	−	1.60297i	0.00512992	−	0.0898899i
$319$	−2.68235			−0.150183
$320$	2.68329	−	7.53657i	0.150001	−	0.421307i
$321$	4.82102			0.269083
$322$	0.0477282	−	0.836327i	0.00265979	−	0.0466067i
$323$		−	5.32223i		−	0.296137i
$324$	−1.98701	−	0.227534i	−0.110390	−	0.0126408i
$325$			3.85979i			0.214103i
$326$	−20.8930	−	1.19234i	−1.15716	−	0.0660376i
$327$	−6.40843			−0.354387
$328$	1.89371	−	10.9648i	0.104563	−	0.605430i
$329$	−5.43428			−0.299601
$330$	−1.41192	−	0.0805765i	−0.0777234	−	0.00443559i
$331$		−	32.9618i		−	1.81174i	−0.423553	−	0.905872i	$-0.639217\pi$
$331$		−	32.9618i		−	1.81174i	0.423553	−	0.905872i	$-0.360783\pi$
$332$	−0.617315	+	5.39089i	−0.0338796	+	0.295864i
$333$		−	2.36212i		−	0.129444i
$334$	1.58086	−	27.7009i	0.0865008	−	1.51573i
$335$	−6.44653			−0.352212
$336$	1.00305	−	4.32231i	0.0547210	−	0.235801i
$337$	12.0843			0.658274			0.329137	−	0.944282i	$-0.393242\pi$
$337$	12.0843			0.658274			0.329137	+	0.944282i	$0.393242\pi$
$338$	−0.152931	+	2.67977i	−0.00831837	+	0.145760i
$339$			6.18727i			0.336047i
$340$	0.252402	−	2.20418i	0.0136884	−	0.119538i
$341$			7.40654i			0.401086i
$342$	6.77418	+	0.386595i	0.366306	+	0.0209047i
$343$	−14.1651			−0.764842
$344$	31.2540	+	5.39782i	1.68510	+	0.291031i
$345$	0.533975			0.0287483
$346$	−15.1639	−	0.865389i	−0.815218	−	0.0465236i
$347$			12.9020i			0.692618i	0.938121	+	0.346309i	$0.112565\pi$
$347$			12.9020i			0.692618i	−0.938121	+	0.346309i	$0.887435\pi$
$348$	5.32987	+	0.610327i	0.285711	+	0.0327170i
$349$			30.5861i			1.63723i	0.574340	+	0.818617i	$0.305259\pi$
$349$			30.5861i			1.63723i	−0.574340	+	0.818617i	$0.694741\pi$
$350$	−0.0893828	+	1.56623i	−0.00477771	+	0.0837183i
$351$	3.85979			0.206020
$352$	−5.42861	−	1.59066i	−0.289346	−	0.0847823i
$353$	31.7526			1.69002			0.845009	−	0.534751i	$-0.179595\pi$
$353$	31.7526			1.69002			0.845009	+	0.534751i	$0.179595\pi$
$354$	−0.973258	+	17.0541i	−0.0517281	+	0.906415i
$355$			13.0060i			0.690286i
$356$	−27.7010	−	3.17207i	−1.46815	−	0.168119i
$357$		−	1.23053i		−	0.0651264i
$358$	3.41237	+	0.194740i	0.180349	+	0.0102923i
$359$	21.5000			1.13473			0.567363	−	0.823468i	$-0.307964\pi$
$359$	21.5000			1.13473			0.567363	+	0.823468i	$0.307964\pi$
$360$	2.78716	+	0.481366i	0.146896	+	0.0253702i
$361$	−4.01948			−0.211552
$362$	8.22083	+	0.469154i	0.432077	+	0.0246582i
$363$			1.00000i			0.0524864i
$364$	−0.974218	+	8.50766i	−0.0510629	+	0.445923i
$365$		−	11.9142i		−	0.623616i
$366$	0.136040	−	2.38379i	0.00711095	−	0.124603i
$367$	19.3760			1.01142			0.505710	−	0.862703i	$-0.331230\pi$
$367$	19.3760			1.01142			0.505710	+	0.862703i	$0.331230\pi$
$368$	2.08061	+	0.482836i	0.108459	+	0.0251696i
$369$	3.93403			0.204798
$370$	−0.190332	+	3.33512i	−0.00989487	+	0.173385i
$371$			1.25939i			0.0653844i
$372$	1.68524	−	14.7169i	0.0873757	−	0.763036i
$373$			25.4408i			1.31728i	0.752460	+	0.658638i	$0.228867\pi$
$373$			25.4408i			1.31728i	−0.752460	+	0.658638i	$0.771133\pi$
$374$	−1.56623	−	0.0893828i	−0.0809877	−	0.00462187i
$375$	−1.00000			−0.0516398
$376$	2.35815	−	13.6540i	0.121612	−	0.704149i
$377$	−10.3533			−0.533222
$378$	1.56623	+	0.0893828i	0.0805580	+	0.00459735i
$379$		−	1.23042i		−	0.0632022i	−0.999501	−	0.0316011i	$-0.989939\pi$
$379$		−	1.23042i		−	0.0632022i	0.999501	−	0.0316011i	$-0.0100606\pi$
$380$	−9.53342	−	1.09168i	−0.489054	−	0.0560019i
$381$			0.205570i			0.0105317i
$382$	0.334712	−	5.86505i	0.0171253	−	0.300082i
$383$	−36.3893			−1.85941			−0.929704	−	0.368308i	$-0.879937\pi$
$383$	−36.3893			−1.85941			−0.929704	+	0.368308i	$0.879937\pi$
$384$	10.4248	+	4.39586i	0.531988	+	0.224325i
$385$	1.10929			0.0565347
$386$	−0.988916	+	17.3285i	−0.0503345	+	0.881995i
$387$			11.2135i			0.570016i
$388$	37.9816	+	4.34930i	1.92822	+	0.220802i
$389$			22.6608i			1.14895i	0.818523	+	0.574474i	$0.194793\pi$
$389$			22.6608i			1.14895i	−0.818523	+	0.574474i	$0.805207\pi$
$390$	−5.44970	−	0.311008i	−0.275956	−	0.0157485i
$391$	0.592334			0.0299556
$392$	2.77723	−	16.0805i	0.140271	−	0.812186i
$393$	−0.296752			−0.0149691
$394$	−11.1987	−	0.639099i	−0.564184	−	0.0321973i
$395$			3.44379i			0.173276i
$396$	0.227534	−	1.98701i	0.0114340	−	0.0998513i
$397$			4.71284i			0.236531i	0.992982	+	0.118265i	$0.0377333\pi$
$397$			4.71284i			0.236531i	−0.992982	+	0.118265i	$0.962267\pi$
$398$	0.0742935	−	1.30182i	0.00372400	−	0.0652545i
$399$	−5.32223			−0.266445
$400$	−3.89646	−	0.904229i	−0.194823	−	0.0452114i
$401$	6.44647			0.321921			0.160961	−	0.986961i	$-0.448541\pi$
$401$	6.44647			0.321921			0.160961	+	0.986961i	$0.448541\pi$
$402$	0.519439	−	9.10196i	0.0259073	−	0.453965i
$403$			28.5877i			1.42405i
$404$	0.399004	−	3.48443i	0.0198512	−	0.173357i
$405$			1.00000i			0.0496904i
$406$	−4.20117	−	0.239756i	−0.208501	−	0.0118989i
$407$	2.36212			0.117086
$408$	3.09178	+	0.533975i	0.153066	+	0.0264357i
$409$	−19.1426			−0.946541			−0.473271	−	0.880917i	$-0.656927\pi$
$409$	−19.1426			−0.946541			−0.473271	+	0.880917i	$0.656927\pi$
$410$	−5.55452	−	0.316990i	−0.274318	−	0.0156550i
$411$		−	9.96720i		−	0.491646i
$412$	−14.5855	−	1.67020i	−0.718576	−	0.0822846i
$413$		−	13.3988i		−	0.659311i
$414$	−0.0430259	+	0.753929i	−0.00211461	+	0.0370536i
$415$	2.71306			0.133179
$416$	−20.9533	−	6.13960i	−1.02732	−	0.301019i
$417$	−10.1021			−0.494700
$418$	−0.386595	+	6.77418i	−0.0189090	+	0.331336i
$419$		−	33.3655i		−	1.63001i	−0.579452	−	0.815006i	$-0.696733\pi$
$419$		−	33.3655i		−	1.63001i	0.579452	−	0.815006i	$-0.303267\pi$
$420$	−2.20418	−	0.252402i	−0.107553	−	0.0123160i
$421$			27.6592i			1.34803i	0.738719	+	0.674013i	$0.235431\pi$
$421$			27.6592i			1.34803i	−0.738719	+	0.674013i	$0.764569\pi$
$422$	−17.2507	−	0.984476i	−0.839749	−	0.0479235i
$423$	4.89887			0.238191
$424$	−3.16430	−	0.546501i	−0.153672	−	0.0265404i
$425$	−1.10929			−0.0538085
$426$	−18.3634	−	1.04798i	−0.889707	−	0.0507746i
$427$			1.87286i			0.0906341i
$428$	1.09695	−	9.57945i	0.0530230	−	0.463040i
$429$			3.85979i			0.186352i
$430$	0.903547	−	15.8326i	0.0435729	−	0.763515i
$431$	28.8632			1.39029			0.695147	−	0.718868i	$-0.255339\pi$
$431$	28.8632			1.39029			0.695147	+	0.718868i	$0.255339\pi$
$432$	−0.904229	+	3.89646i	−0.0435047	+	0.187468i
$433$	22.0696			1.06060			0.530298	−	0.847811i	$-0.322080\pi$
$433$	22.0696			1.06060			0.530298	+	0.847811i	$0.322080\pi$
$434$	−0.662017	+	11.6003i	−0.0317778	+	0.556833i
$435$		−	2.68235i		−	0.128609i
$436$	−1.45814	+	12.7336i	−0.0698322	+	0.609831i
$437$		−	2.56194i		−	0.122554i
$438$	16.8218	+	0.960002i	0.803777	+	0.0458706i
$439$	21.8272			1.04175			0.520877	−	0.853631i	$-0.325605\pi$
$439$	21.8272			1.04175			0.520877	+	0.853631i	$0.325605\pi$
$440$	−0.481366	+	2.78716i	−0.0229482	+	0.132873i
$441$	5.76947			0.274737
$442$	−6.04530	−	0.344999i	−0.287546	−	0.0164099i
$443$		−	9.51341i		−	0.451996i	−0.974128	−	0.225998i	$-0.927436\pi$
$443$		−	9.51341i		−	0.451996i	0.974128	−	0.225998i	$-0.0725642\pi$
$444$	−4.69357	−	0.537464i	−0.222747	−	0.0255069i
$445$			13.9410i			0.660868i
$446$	−0.845749	+	14.8198i	−0.0400474	+	0.701737i
$447$	5.65265			0.267361
$448$	−8.36026	−	2.97656i	−0.394985	−	0.140629i
$449$	−0.914410			−0.0431537			−0.0215768	−	0.999767i	$-0.506869\pi$
$449$	−0.914410			−0.0431537			−0.0215768	+	0.999767i	$0.506869\pi$
$450$	0.0805765	−	1.41192i	0.00379841	−	0.0665584i
$451$			3.93403i			0.185246i
$452$	12.2942	+	1.40782i	0.578271	+	0.0662182i
$453$		−	10.4793i		−	0.492360i
$454$	28.1533	+	1.60668i	1.32130	+	0.0754052i
$455$	4.28163			0.200726
$456$	2.30953	−	13.3724i	0.108154	−	0.626221i
$457$	11.6844			0.546571			0.273286	−	0.961933i	$-0.411890\pi$
$457$	11.6844			0.546571			0.273286	+	0.961933i	$0.411890\pi$
$458$	−31.3275	−	1.78783i	−1.46384	−	0.0835397i
$459$			1.10929i			0.0517773i
$460$	0.121498	−	1.06102i	0.00566486	−	0.0494702i
$461$			40.9715i			1.90823i	0.299439	+	0.954115i	$0.403200\pi$
$461$			40.9715i			1.90823i	−0.299439	+	0.954115i	$0.596800\pi$
$462$	−0.0893828	+	1.56623i	−0.00415846	+	0.0728675i
$463$	13.3735			0.621521			0.310760	−	0.950488i	$-0.399416\pi$
$463$	13.3735			0.621521			0.310760	+	0.950488i	$0.399416\pi$
$464$	2.42546	−	10.4517i	0.112599	−	0.485206i
$465$	−7.40654			−0.343470
$466$	−0.290395	+	5.08851i	−0.0134523	+	0.235721i
$467$			40.4093i			1.86992i	0.354752	+	0.934961i	$0.384565\pi$
$467$			40.4093i			1.86992i	−0.354752	+	0.934961i	$0.615435\pi$
$468$	0.878235	−	7.66946i	0.0405964	−	0.354521i
$469$			7.15108i			0.330206i
$470$	−6.91680	−	0.394734i	−0.319048	−	0.0182077i
$471$	2.14258			0.0987249
$472$	33.6653	+	5.81427i	1.54957	+	0.267624i
$473$	−11.2135			−0.515599
$474$	−4.86234	−	0.277488i	−0.223335	−	0.0127455i
$475$			4.79786i			0.220141i
$476$	−2.44508	−	0.279987i	−0.112070	−	0.0128332i
$477$		−	1.13531i		−	0.0519824i
$478$	1.99924	−	35.0321i	0.0914432	−	1.60233i
$479$	22.5139			1.02868			0.514342	−	0.857585i	$-0.328036\pi$
$479$	22.5139			1.02868			0.514342	+	0.857585i	$0.328036\pi$
$480$	1.59066	−	5.42861i	0.0726033	−	0.247781i
$481$	9.11730			0.415713
$482$	0.949462	−	16.6371i	0.0432468	−	0.757801i
$483$		−	0.592334i		−	0.0269522i
$484$	1.98701	+	0.227534i	0.0903189	+	0.0103425i
$485$		−	19.1149i		−	0.867963i
$486$	−1.41192	−	0.0805765i	−0.0640458	−	0.00365502i
$487$	−14.3851			−0.651849			−0.325924	−	0.945396i	$-0.605676\pi$
$487$	−14.3851			−0.651849			−0.325924	+	0.945396i	$0.605676\pi$
$488$	−4.70568	−	0.812710i	−0.213016	−	0.0367897i
$489$	−14.7976			−0.669171
$490$	−8.14601	−	0.464884i	−0.367999	−	0.0210013i
$491$			2.28511i			0.103126i	0.998670	+	0.0515628i	$0.0164202\pi$
$491$			2.28511i			0.103126i	−0.998670	+	0.0515628i	$0.983580\pi$
$492$	0.895128	−	7.81698i	0.0403555	−	0.352417i
$493$		−	2.97551i		−	0.134010i
$494$	−1.49217	+	26.1469i	−0.0671361	+	1.17640i
$495$	−1.00000			−0.0449467
$496$	−28.8592	−	6.69720i	−1.29582	−	0.300713i
$497$	14.4274			0.647158
$498$	−0.218609	+	3.83061i	−0.00979610	+	0.171654i
$499$		−	20.1669i		−	0.902795i	−0.892323	−	0.451398i	$-0.850926\pi$
$499$		−	20.1669i		−	0.902795i	0.892323	−	0.451398i	$-0.149074\pi$
$500$	−0.227534	+	1.98701i	−0.0101756	+	0.0888620i
$501$		−	19.6194i		−	0.876529i
$502$	40.0556	+	2.28593i	1.78777	+	0.102026i
$503$	9.88520			0.440759			0.220380	−	0.975414i	$-0.429270\pi$
$503$	9.88520			0.440759			0.220380	+	0.975414i	$0.429270\pi$
$504$	0.533975	−	3.09178i	0.0237852	−	0.137719i
$505$	−1.75360			−0.0780341
$506$	−0.753929	−	0.0430259i	−0.0335162	−	0.00191273i
$507$			1.89797i			0.0842916i
$508$	0.408472	+	0.0467744i	0.0181230	+	0.00207528i
$509$		−	18.4339i		−	0.817070i	−0.912743	−	0.408535i	$-0.866040\pi$
$509$		−	18.4339i		−	0.817070i	0.912743	−	0.408535i	$-0.133960\pi$
$510$	0.0893828	−	1.56623i	0.00395794	−	0.0693537i
$511$	−13.2163			−0.584654
$512$	11.1066	−	19.7140i	0.490848	−	0.871245i
$513$	4.79786			0.211831
$514$	−1.39196	+	24.3909i	−0.0613967	+	1.07584i
$515$			7.34041i			0.323457i
$516$	22.2815	+	2.55147i	0.980887	+	0.112322i
$517$			4.89887i			0.215452i
$518$	3.69962	+	0.211133i	0.162552	+	0.00927666i
$519$	−10.7400			−0.471432
$520$	−1.85797	+	10.7579i	−0.0814774	+	0.471764i
$521$	−6.65531			−0.291574			−0.145787	−	0.989316i	$-0.546571\pi$
$521$	−6.65531			−0.291574			−0.145787	+	0.989316i	$0.546571\pi$
$522$	3.78726	+	0.216134i	0.165764	+	0.00945995i
$523$			20.6236i			0.901806i	0.892573	+	0.450903i	$0.148898\pi$
$523$			20.6236i			0.901806i	−0.892573	+	0.450903i	$0.851102\pi$
$524$	−0.0675212	+	0.589650i	−0.00294968	+	0.0257590i
$525$			1.10929i			0.0484135i
$526$	−0.269384	+	4.72033i	−0.0117457	+	0.205816i
$527$	−8.21601			−0.357895
$528$	−3.89646	−	0.904229i	−0.169571	−	0.0393515i
$529$	−22.7149			−0.987603
$530$	−0.0914795	+	1.60297i	−0.00397362	+	0.0696284i
$531$			12.0787i			0.524171i
$532$	−1.21099	+	10.5753i	−0.0525031	+	0.458499i
$533$			15.1845i			0.657715i
$534$	−19.6836	−	1.12332i	−0.851792	−	0.0486108i
$535$	−4.82102			−0.208431
$536$	−17.9675	−	3.10314i	−0.776080	−	0.134035i
$537$	2.41684			0.104294
$538$	30.5073	+	1.74102i	1.31527	+	0.0750607i
$539$			5.76947i			0.248509i
$540$	1.98701	+	0.227534i	0.0855075	+	0.00979152i
$541$		−	11.5706i		−	0.497460i	−0.968573	−	0.248730i	$-0.919987\pi$
$541$		−	11.5706i		−	0.497460i	0.968573	−	0.248730i	$-0.0800132\pi$
$542$	1.07858	−	18.8997i	0.0463292	−	0.811811i
$543$	5.82247			0.249866
$544$	1.76450	−	6.02191i	0.0756525	−	0.258187i
$545$	6.40843			0.274507
$546$	−0.344999	+	6.04530i	−0.0147646	+	0.258715i
$547$			17.0495i			0.728984i	0.931207	+	0.364492i	$0.118757\pi$
$547$			17.0495i			0.728984i	−0.931207	+	0.364492i	$0.881243\pi$
$548$	−19.8050	−	2.26788i	−0.846026	−	0.0968791i
$549$		−	1.68834i		−	0.0720566i
$550$	1.41192	+	0.0805765i	0.0602043	+	0.00343579i
$551$	−12.8696			−0.548261
$552$	1.48828	+	0.257038i	0.0633453	+	0.0109403i
$553$	3.82017			0.162450
$554$	2.18948	+	0.124951i	0.0930219	+	0.00530866i
$555$			2.36212i			0.100267i
$556$	−2.29857	+	20.0730i	−0.0974810	+	0.851283i
$557$		−	7.00000i		−	0.296600i	−0.988942	−	0.148300i	$-0.952620\pi$
$557$		−	7.00000i		−	0.296600i	0.988942	−	0.148300i	$-0.0473801\pi$
$558$	0.596793	−	10.4574i	0.0252642	−	0.442697i
$559$	−43.2819			−1.83063
$560$	−1.00305	+	4.32231i	−0.0423867	+	0.182651i
$561$	−1.10929			−0.0468343
$562$	−0.0322780	+	0.565596i	−0.00136156	+	0.0238582i
$563$		−	17.1369i		−	0.722234i	−0.932521	−	0.361117i	$-0.882396\pi$
$563$		−	17.1369i		−	0.722234i	0.932521	−	0.361117i	$-0.117604\pi$
$564$	1.11466	−	9.73413i	0.0469357	−	0.409881i
$565$		−	6.18727i		−	0.260301i
$566$	−36.4970	−	2.08284i	−1.53408	−	0.0875484i
$567$	1.10929			0.0465859
$568$	−6.26064	+	36.2498i	−0.262691	+	1.52101i
$569$	17.0090			0.713055			0.356528	−	0.934285i	$-0.383961\pi$
$569$	17.0090			0.713055			0.356528	+	0.934285i	$0.383961\pi$
$570$	−6.77418	−	0.386595i	−0.283739	−	0.0161927i
$571$			34.6935i			1.45188i	0.687758	+	0.725940i	$0.258595\pi$
$571$			34.6935i			1.45188i	−0.687758	+	0.725940i	$0.741405\pi$
$572$	7.66946	+	0.878235i	0.320676	+	0.0367208i
$573$		−	4.15396i		−	0.173534i
$574$	−0.351635	+	6.16159i	−0.0146770	+	0.257180i
$575$	−0.533975			−0.0222683
$576$	7.53657	+	2.68329i	0.314024	+	0.111804i
$577$	−22.9523			−0.955519			−0.477759	−	0.878491i	$-0.658551\pi$
$577$	−22.9523			−0.955519			−0.477759	+	0.878491i	$0.658551\pi$
$578$	−1.27065	+	22.2652i	−0.0528520	+	0.926109i
$579$			12.2730i			0.510049i
$580$	−5.32987	−	0.610327i	−0.221311	−	0.0253425i
$581$		−	3.00958i		−	0.124858i
$582$	26.9886	+	1.54021i	1.11871	+	0.0638438i
$583$	1.13531			0.0470199
$584$	5.73508	−	33.2067i	0.237319	−	1.37410i
$585$	−3.85979			−0.159583
$586$	−10.7659	−	0.614398i	−0.444736	−	0.0253806i
$587$			1.75446i			0.0724142i	0.999344	+	0.0362071i	$0.0115276\pi$
$587$			1.75446i			0.0724142i	−0.999344	+	0.0362071i	$0.988472\pi$
$588$	1.31275	−	11.4640i	0.0541370	−	0.472769i
$589$			35.5355i			1.46422i
$590$	0.973258	−	17.0541i	0.0400684	−	0.702106i
$591$	−7.93158			−0.326262
$592$	−2.13590	+	9.20391i	−0.0877849	+	0.378278i
$593$	−18.4126			−0.756115			−0.378057	−	0.925782i	$-0.623408\pi$
$593$	−18.4126			−0.756115			−0.378057	+	0.925782i	$0.623408\pi$
$594$	0.0805765	−	1.41192i	0.00330609	−	0.0579316i
$595$			1.23053i			0.0504467i
$596$	1.28617	−	11.2319i	0.0526837	−	0.460076i
$597$		−	0.922025i		−	0.0377360i
$598$	−2.91000	−	0.166071i	−0.118999	−	0.00679114i
$599$	18.7239			0.765038			0.382519	−	0.923948i	$-0.375057\pi$
$599$	18.7239			0.765038			0.382519	+	0.923948i	$0.375057\pi$
$600$	−2.78716	−	0.481366i	−0.113786	−	0.0196517i
$601$	42.3253			1.72648			0.863242	−	0.504791i	$-0.168430\pi$
$601$	42.3253			1.72648			0.863242	+	0.504791i	$0.168430\pi$
$602$	−17.5629	−	1.00230i	−0.715812	−	0.0408506i
$603$		−	6.44653i		−	0.262523i
$604$	−20.8225	−	2.38440i	−0.847256	−	0.0970198i
$605$		−	1.00000i		−	0.0406558i
$606$	0.141299	−	2.47593i	0.00573987	−	0.100578i
$607$	32.9914			1.33908			0.669539	−	0.742777i	$-0.266492\pi$
$607$	32.9914			1.33908			0.669539	+	0.742777i	$0.266492\pi$
$608$	−26.0457	−	7.63176i	−1.05629	−	0.309509i
$609$	−2.97551			−0.120574
$610$	−0.136040	+	2.38379i	−0.00550812	+	0.0965170i
$611$			18.9086i			0.764961i
$612$	2.20418	+	0.252402i	0.0890986	+	0.0102027i
$613$			35.9397i			1.45159i	0.687911	+	0.725795i	$0.258528\pi$
$613$			35.9397i			1.45159i	−0.687911	+	0.725795i	$0.741472\pi$
$614$	9.47524	+	0.540741i	0.382390	+	0.0218225i
$615$	−3.93403			−0.158636
$616$	3.09178	+	0.533975i	0.124571	+	0.0215145i
$617$	−5.13014			−0.206532			−0.103266	−	0.994654i	$-0.532929\pi$
$617$	−5.13014			−0.206532			−0.103266	+	0.994654i	$0.532929\pi$
$618$	−10.3640	−	0.591464i	−0.416903	−	0.0237922i
$619$		−	30.6167i		−	1.23059i	−0.788297	−	0.615295i	$-0.789037\pi$
$619$		−	30.6167i		−	1.23059i	0.788297	−	0.615295i	$-0.210963\pi$
$620$	−1.68524	+	14.7169i	−0.0676809	+	0.591045i
$621$			0.533975i			0.0214277i
$622$	1.21941	−	21.3674i	0.0488940	−	0.856754i
$623$	15.4647			0.619579
$624$	−15.0395	−	3.49013i	−0.602062	−	0.139717i
$625$	1.00000			0.0400000
$626$	1.22653	−	21.4922i	0.0490222	−	0.859001i
$627$			4.79786i			0.191608i
$628$	0.487511	−	4.25734i	0.0194538	−	0.169886i
$629$			2.62028i			0.104478i
$630$	−1.56623	−	0.0893828i	−0.0624000	−	0.00356110i
$631$	18.7668			0.747096			0.373548	−	0.927611i	$-0.378141\pi$
$631$	18.7668			0.747096			0.373548	+	0.927611i	$0.378141\pi$
$632$	−1.65772	+	9.59841i	−0.0659407	+	0.381804i
$633$	−12.2179			−0.485618
$634$	−47.2712	−	2.69771i	−1.87738	−	0.107140i
$635$		−	0.205570i		−	0.00815782i
$636$	−2.25588	−	0.258323i	−0.0894516	−	0.0102432i
$637$			22.2689i			0.882328i
$638$	−0.216134	+	3.78726i	−0.00855684	+	0.149939i
$639$	−13.0060			−0.514509
$640$	−10.4248	−	4.39586i	−0.412076	−	0.173761i
$641$	−7.01696			−0.277153			−0.138577	−	0.990352i	$-0.544253\pi$
$641$	−7.01696			−0.277153			−0.138577	+	0.990352i	$0.544253\pi$
$642$	0.388461	−	6.80688i	0.0153313	−	0.268646i
$643$		−	14.4766i		−	0.570901i	−0.958393	−	0.285450i	$-0.907857\pi$
$643$		−	14.4766i		−	0.570901i	0.958393	−	0.285450i	$-0.0921432\pi$
$644$	−1.17698	−	0.134776i	−0.0463794	−	0.00531094i
$645$		−	11.2135i		−	0.441533i
$646$	−7.51454	−	0.428846i	−0.295656	−	0.0168727i
$647$	−18.5693			−0.730033			−0.365017	−	0.931001i	$-0.618937\pi$
$647$	−18.5693			−0.730033			−0.365017	+	0.931001i	$0.618937\pi$
$648$	−0.481366	+	2.78716i	−0.0189099	+	0.109490i
$649$	−12.0787			−0.474130
$650$	5.44970	+	0.311008i	0.213755	+	0.0121987i
$651$			8.21601i			0.322011i
$652$	−3.36697	+	29.4031i	−0.131861	+	1.15151i
$653$		−	9.60926i		−	0.376039i	−0.982165	−	0.188020i	$-0.939793\pi$
$653$		−	9.60926i		−	0.376039i	0.982165	−	0.188020i	$-0.0602069\pi$
$654$	−0.516369	+	9.04817i	−0.0201916	+	0.353811i
$655$	0.296752			0.0115950
$656$	−15.3288	−	3.55727i	−0.598489	−	0.138888i
$657$	11.9142			0.464816
$658$	−0.437875	+	7.67275i	−0.0170701	+	0.299115i
$659$			15.1640i			0.590707i	0.955388	+	0.295354i	$0.0954375\pi$
$659$			15.1640i			0.590707i	−0.955388	+	0.295354i	$0.904563\pi$
$660$	−0.227534	+	1.98701i	−0.00885677	+	0.0773444i
$661$			15.3449i			0.596846i	0.954434	+	0.298423i	$0.0964607\pi$
$661$			15.3449i			0.596846i	−0.954434	+	0.298423i	$0.903539\pi$
$662$	−46.5393	−	2.65594i	−1.80880	−	0.103226i
$663$	−4.28163			−0.166285
$664$	7.56175	+	1.30598i	0.293453	+	0.0506817i
$665$	5.32223			0.206387
$666$	−3.33512	−	0.190332i	−0.129233	−	0.00737520i
$667$		−	1.43231i		−	0.0554593i
$668$	−38.9840	−	4.46408i	−1.50834	−	0.172721i
$669$			10.4962i			0.405807i
$670$	−0.519439	+	9.10196i	−0.0200677	+	0.351640i
$671$	1.68834			0.0651777
$672$	−6.02191	−	1.76450i	−0.232300	−	0.0680672i
$673$	−26.2662			−1.01249			−0.506244	−	0.862390i	$-0.668966\pi$
$673$	−26.2662			−1.01249			−0.506244	+	0.862390i	$0.668966\pi$
$674$	0.973710	−	17.0620i	0.0375059	−	0.657204i
$675$		−	1.00000i		−	0.0384900i
$676$	3.77129	+	0.431853i	0.145049	+	0.0166097i
$677$		−	23.0202i		−	0.884740i	−0.896833	−	0.442370i	$-0.854138\pi$
$677$		−	23.0202i		−	0.884740i	0.896833	−	0.442370i	$-0.145862\pi$
$678$	8.73591	+	0.498549i	0.335501	+	0.0191466i
$679$	−21.2040			−0.813735
$680$	−3.09178	−	0.533975i	−0.118564	−	0.0204770i
$681$	19.9398			0.764095
$682$	10.4574	+	0.596793i	0.400435	+	0.0228524i
$683$			34.2805i			1.31171i	0.754888	+	0.655854i	$0.227691\pi$
$683$			34.2805i			1.31171i	−0.754888	+	0.655854i	$0.772309\pi$
$684$	1.09168	−	9.53342i	0.0417414	−	0.364520i
$685$			9.96720i			0.380827i
$686$	−1.14137	+	19.9999i	−0.0435778	+	0.763599i
$687$	−22.1880			−0.846524
$688$	10.1396	−	43.6931i	0.386569	−	1.66578i
$689$	4.38207			0.166943
$690$	0.0430259	−	0.753929i	0.00163797	−	0.0287016i
$691$		−	41.1950i		−	1.56713i	−0.621309	−	0.783566i	$-0.713399\pi$
$691$		−	41.1950i		−	1.56713i	0.621309	−	0.783566i	$-0.286601\pi$
$692$	−2.44371	+	21.3405i	−0.0928960	+	0.811243i
$693$			1.10929i			0.0421385i
$694$	18.2166	+	1.03960i	0.691493	+	0.0394627i
$695$	10.1021			0.383193
$696$	1.29119	−	7.47615i	0.0489426	−	0.283383i
$697$	−4.36399			−0.165298
$698$	43.1849	+	2.46452i	1.63457	+	0.0932833i
$699$			3.60397i			0.136315i
$700$	2.20418	+	0.252402i	0.0833101	+	0.00953990i
$701$		−	27.4610i		−	1.03719i	−0.855021	−	0.518594i	$-0.826456\pi$
$701$		−	27.4610i		−	1.03719i	0.855021	−	0.518594i	$-0.173544\pi$
$702$	0.311008	−	5.44970i	0.0117382	−	0.205686i
$703$	11.3331			0.427438
$704$	−2.68329	+	7.53657i	−0.101130	+	0.284045i
$705$	−4.89887			−0.184502
$706$	2.55851	−	44.8320i	0.0962908	−	1.68727i
$707$			1.94525i			0.0731587i
$708$	24.0005	+	2.74832i	0.901996	+	0.103288i
$709$			31.3070i			1.17576i	0.808948	+	0.587880i	$0.200037\pi$
$709$			31.3070i			1.17576i	−0.808948	+	0.587880i	$0.799963\pi$
$710$	18.3634	+	1.04798i	0.689164	+	0.0393298i
$711$	−3.44379			−0.129152
$712$	−6.71074	+	38.8560i	−0.251496	+	1.45619i
$713$	−3.95491			−0.148112
$714$	−1.73740	−	0.0991516i	−0.0650206	−	0.00371065i
$715$		−	3.85979i		−	0.144348i
$716$	0.549914	−	4.80229i	0.0205512	−	0.179470i
$717$		−	24.8117i		−	0.926612i
$718$	1.73239	−	30.3562i	0.0646524	−	1.13288i
$719$	−32.3409			−1.20611			−0.603057	−	0.797698i	$-0.706051\pi$
$719$	−32.3409			−1.20611			−0.603057	+	0.797698i	$0.706051\pi$
$720$	0.904229	−	3.89646i	0.0336986	−	0.145212i
$721$	8.14265			0.303248
$722$	−0.323876	+	5.67517i	−0.0120534	+	0.211208i
$723$		−	11.7834i		−	0.438228i
$724$	1.32481	−	11.5693i	0.0492362	−	0.429971i
$725$			2.68235i			0.0996200i
$726$	1.41192	+	0.0805765i	0.0524011	+	0.00299047i
$727$	−48.5576			−1.80090			−0.900451	−	0.434957i	$-0.856764\pi$
$727$	−48.5576			−1.80090			−0.900451	+	0.434957i	$0.856764\pi$
$728$	11.9336	+	2.06103i	0.442289	+	0.0763869i
$729$	−1.00000			−0.0370370
$730$	−16.8218	−	0.960002i	−0.622603	−	0.0355313i
$731$		−	12.4391i		−	0.460076i
$732$	−3.35476	−	0.384156i	−0.123995	−	0.0141988i
$733$			26.8562i			0.991955i	0.868335	+	0.495978i	$0.165190\pi$
$733$			26.8562i			0.991955i	−0.868335	+	0.495978i	$0.834810\pi$
$734$	1.56125	−	27.3573i	0.0576269	−	1.00978i
$735$	−5.76947			−0.212810
$736$	0.849372	−	2.89874i	0.0313083	−	0.106849i
$737$	6.44653			0.237461
$738$	0.316990	−	5.55452i	0.0116686	−	0.204465i
$739$		−	5.69031i		−	0.209321i	−0.994508	−	0.104661i	$-0.966624\pi$
$739$		−	5.69031i		−	0.209321i	0.994508	−	0.104661i	$-0.0333756\pi$
$740$	4.69357	+	0.537464i	0.172539	+	0.0197576i
$741$			18.5187i			0.680303i
$742$	1.77816	+	0.101477i	0.0652782	+	0.00372535i
$743$	−21.3939			−0.784866			−0.392433	−	0.919781i	$-0.628366\pi$
$743$	−21.3939			−0.784866			−0.392433	+	0.919781i	$0.628366\pi$
$744$	−20.6432	−	3.56526i	−0.756818	−	0.130709i
$745$	−5.65265			−0.207097
$746$	35.9203	+	2.04993i	1.31514	+	0.0750533i
$747$			2.71306i			0.0992657i
$748$	−0.252402	+	2.20418i	−0.00922873	+	0.0805928i
$749$			5.34792i			0.195409i
$750$	−0.0805765	+	1.41192i	−0.00294224	+	0.0515559i
$751$	0.0564198			0.00205879			0.00102939	−	0.999999i	$-0.499672\pi$
$751$	0.0564198			0.00205879			0.00102939	+	0.999999i	$0.499672\pi$
$752$	−19.0882	−	4.42970i	−0.696077	−	0.161535i
$753$	28.3697			1.03385
$754$	−0.834233	+	14.6180i	−0.0303810	+	0.532356i
$755$			10.4793i			0.381380i
$756$	0.252402	−	2.20418i	0.00917977	−	0.0801652i
$757$		−	18.4756i		−	0.671508i	−0.941950	−	0.335754i	$-0.891009\pi$
$757$		−	18.4756i		−	0.671508i	0.941950	−	0.335754i	$-0.108991\pi$
$758$	−1.73724	−	0.0991425i	−0.0630995	−	0.00360102i
$759$	−0.533975			−0.0193821
$760$	−2.30953	+	13.3724i	−0.0837754	+	0.485069i
$761$	41.0714			1.48884			0.744418	−	0.667714i	$-0.232727\pi$
$761$	41.0714			1.48884			0.744418	+	0.667714i	$0.232727\pi$
$762$	0.290248	+	0.0165641i	0.0105146	+	0.000600056i
$763$		−	7.10882i		−	0.257357i
$764$	−8.25399	−	0.945170i	−0.298619	−	0.0341950i
$765$		−	1.10929i		−	0.0401065i
$766$	−2.93212	+	51.3787i	−0.105942	+	1.85639i
$767$	−46.6212			−1.68339
$768$	7.04657	−	14.3647i	0.254271	−	0.518343i
$769$	−40.1555			−1.44804			−0.724021	−	0.689778i	$-0.757708\pi$
$769$	−40.1555			−1.44804			−0.724021	+	0.689778i	$0.757708\pi$
$770$	0.0893828	−	1.56623i	0.00322113	−	0.0564429i
$771$			17.2750i			0.622145i
$772$	24.3867	+	2.79253i	0.877695	+	0.100505i
$773$			31.6221i			1.13737i	0.822556	+	0.568684i	$0.192547\pi$
$773$			31.6221i			1.13737i	−0.822556	+	0.568684i	$0.807453\pi$
$774$	15.8326	+	0.903547i	0.569090	+	0.0324773i
$775$	7.40654			0.266051
$776$	9.20127	−	53.2764i	0.330306	−	1.91251i
$777$	2.62028			0.0940021
$778$	31.9951	+	1.82593i	1.14708	+	0.0654626i
$779$			18.8749i			0.676265i
$780$	−0.878235	+	7.66946i	−0.0314458	+	0.274611i
$781$		−	13.0060i		−	0.465390i
$782$	0.0477282	−	0.836327i	0.00170676	−	0.0299070i
$783$	2.68235			0.0958594
$784$	−22.4805	−	5.21692i	−0.802875	−	0.186319i
$785$	−2.14258			−0.0764720
$786$	−0.0239112	+	0.418988i	−0.000852884	+	0.0149448i
$787$			39.8478i			1.42042i	0.703989	+	0.710210i	$0.251400\pi$
$787$			39.8478i			1.42042i	−0.703989	+	0.710210i	$0.748600\pi$
$788$	−1.80471	+	15.7602i	−0.0642900	+	0.561433i
$789$			3.34321i			0.119021i
$790$	4.86234	+	0.277488i	0.172994	+	0.00987259i
$791$	−6.86349			−0.244038
$792$	−2.78716	−	0.481366i	−0.0990376	−	0.0171046i
$793$	6.51664			0.231413
$794$	6.65414	+	0.379744i	0.236147	+	0.0134766i
$795$			1.13531i			0.0402654i
$796$	−1.83208	−	0.209792i	−0.0649363	−	0.00743590i
$797$			30.6821i			1.08681i	0.839469	+	0.543407i	$0.182866\pi$
$797$			30.6821i			1.08681i	−0.839469	+	0.543407i	$0.817134\pi$
$798$	−0.428846	+	7.51454i	−0.0151810	+	0.266012i
$799$	−5.43428			−0.192251
$800$	−1.59066	+	5.42861i	−0.0562382	+	0.191930i
$801$	−13.9410			−0.492582
$802$	0.519434	−	9.10188i	0.0183418	−	0.321398i
$803$			11.9142i			0.420442i
$804$	−12.8094	−	1.46681i	−0.451751	−	0.0517303i
$805$			0.592334i			0.0208770i
$806$	40.3634	+	2.30349i	1.42174	+	0.0811371i
$807$	21.6071			0.760604
$808$	−4.88757	−	0.844123i	−0.171944	−	0.0296961i
$809$	−28.0006			−0.984449			−0.492224	−	0.870468i	$-0.663816\pi$
$809$	−28.0006			−0.984449			−0.492224	+	0.870468i	$0.663816\pi$
$810$	1.41192	+	0.0805765i	0.0496097	+	0.00283117i
$811$		−	31.9277i		−	1.12113i	−0.828109	−	0.560567i	$-0.810583\pi$
$811$		−	31.9277i		−	1.12113i	0.828109	−	0.560567i	$-0.189417\pi$
$812$	−0.677031	+	5.91238i	−0.0237591	+	0.207484i
$813$		−	13.3858i		−	0.469462i
$814$	0.190332	−	3.33512i	0.00667112	−	0.116896i
$815$	14.7976			0.518338
$816$	1.00305	−	4.32231i	0.0351139	−	0.151311i
$817$	−53.8010			−1.88226
$818$	−1.54244	+	27.0278i	−0.0539303	+	0.945004i
$819$			4.28163i			0.149612i
$820$	−0.895128	+	7.81698i	−0.0312592	+	0.272981i
$821$			30.2311i			1.05507i	0.849532	+	0.527536i	$0.176884\pi$
$821$			30.2311i			1.05507i	−0.849532	+	0.527536i	$0.823116\pi$
$822$	−14.0728	−	0.803122i	−0.490847	−	0.0280121i
$823$	−1.53246			−0.0534184			−0.0267092	−	0.999643i	$-0.508503\pi$
$823$	−1.53246			−0.0534184			−0.0267092	+	0.999643i	$0.508503\pi$
$824$	−3.53342	+	20.4589i	−0.123093	+	0.712720i
$825$	1.00000			0.0348155
$826$	−18.9180	−	1.07963i	−0.658240	−	0.0375650i
$827$		−	29.2197i		−	1.01607i	−0.861337	−	0.508035i	$-0.830372\pi$
$827$		−	29.2197i		−	1.01607i	0.861337	−	0.508035i	$-0.169628\pi$
$828$	1.06102	+	0.121498i	0.0368729	+	0.00422234i
$829$			21.7095i			0.754002i	0.926213	+	0.377001i	$0.123045\pi$
$829$			21.7095i			0.754002i	−0.926213	+	0.377001i	$0.876955\pi$
$830$	0.218609	−	3.83061i	0.00758802	−	0.132963i
$831$	1.55071			0.0537936
$832$	−10.3569	+	29.0896i	−0.359062	+	1.00850i
$833$	−6.40003			−0.221748
$834$	−0.813989	+	14.2633i	−0.0281861	+	0.493897i
$835$			19.6194i			0.678956i
$836$	9.53342	+	1.09168i	0.329720	+	0.0377565i
$837$		−	7.40654i		−	0.256007i
$838$	−47.1093	−	2.68848i	−1.62736	−	0.0928719i
$839$	−44.7521			−1.54501			−0.772507	−	0.635006i	$-0.780998\pi$
$839$	−44.7521			−1.54501			−0.772507	+	0.635006i	$0.780998\pi$
$840$	−0.533975	+	3.09178i	−0.0184239	+	0.106676i
$841$	21.8050			0.751896
$842$	39.0524	+	2.22868i	1.34584	+	0.0768054i
$843$			0.400588i			0.0137970i
$844$	−2.77999	+	24.2772i	−0.0956913	+	0.835654i
$845$		−	1.89797i		−	0.0652920i
$846$	0.394734	−	6.91680i	0.0135712	−	0.237804i
$847$	−1.10929			−0.0381157
$848$	−1.02658	+	4.42370i	−0.0352530	+	0.151910i
$849$	−25.8493			−0.887145
$850$	−0.0893828	+	1.56623i	−0.00306580	+	0.0537211i
$851$			1.26132i			0.0432374i
$852$	−2.95931	+	25.8431i	−0.101384	+	0.885369i
$853$			11.4901i			0.393413i	0.980462	+	0.196706i	$0.0630246\pi$
$853$			11.4901i			0.393413i	−0.980462	+	0.196706i	$0.936975\pi$
$854$	2.64432	+	0.150909i	0.0904869	+	0.00516398i
$855$	−4.79786			−0.164083
$856$	−13.4370	−	2.32068i	−0.459267	−	0.0793191i
$857$	−35.9738			−1.22884			−0.614421	−	0.788978i	$-0.710610\pi$
$857$	−35.9738			−1.22884			−0.614421	+	0.788978i	$0.710610\pi$
$858$	5.44970	+	0.311008i	0.186050	+	0.0106176i
$859$		−	42.4735i		−	1.44918i	−0.689183	−	0.724588i	$-0.742030\pi$
$859$		−	42.4735i		−	1.44918i	0.689183	−	0.724588i	$-0.257970\pi$
$860$	−22.2815	−	2.55147i	−0.759792	−	0.0870043i
$861$			4.36399i			0.148724i
$862$	2.32570	−	40.7525i	0.0792136	−	1.38803i
$863$	23.1283			0.787297			0.393648	−	0.919261i	$-0.371213\pi$
$863$	23.1283			0.787297			0.393648	+	0.919261i	$0.371213\pi$
$864$	5.42861	+	1.59066i	0.184685	+	0.0541153i
$865$	10.7400			0.365170
$866$	1.77829	−	31.1604i	0.0604287	−	1.05887i
$867$			15.7695i			0.535559i
$868$	16.3253	+	1.86942i	0.554118	+	0.0634524i
$869$		−	3.44379i		−	0.116823i
$870$	−3.78726	−	0.216134i	−0.128400	−	0.00732764i
$871$	24.8822			0.843103
$872$	17.8614	+	3.08480i	0.604862	+	0.104465i
$873$	19.1149			0.646941
$874$	−3.61725	−	0.206432i	−0.122355	−	0.00698267i
$875$		−	1.10929i		−	0.0375009i
$876$	2.71088	−	23.6736i	0.0915923	−	0.799858i
$877$			27.7216i			0.936090i	0.883705	+	0.468045i	$0.155042\pi$
$877$			27.7216i			0.936090i	−0.883705	+	0.468045i	$0.844958\pi$
$878$	1.75876	−	30.8182i	0.0593552	−	1.04006i
$879$	−7.62504			−0.257186
$880$	3.89646	+	0.904229i	0.131350	+	0.0304815i
$881$	−4.00917			−0.135072			−0.0675361	−	0.997717i	$-0.521514\pi$
$881$	−4.00917			−0.135072			−0.0675361	+	0.997717i	$0.521514\pi$
$882$	0.464884	−	8.14601i	0.0156534	−	0.274290i
$883$			8.72477i			0.293612i	0.989165	+	0.146806i	$0.0468993\pi$
$883$			8.72477i			0.293612i	−0.989165	+	0.146806i	$0.953101\pi$
$884$	−0.974218	+	8.50766i	−0.0327665	+	0.286144i
$885$		−	12.0787i		−	0.406021i
$886$	−13.4321	−	0.766557i	−0.451261	−	0.0257530i
$887$	−20.3233			−0.682391			−0.341195	−	0.939992i	$-0.610832\pi$
$887$	−20.3233			−0.682391			−0.341195	+	0.939992i	$0.610832\pi$
$888$	−1.13705	+	6.58363i	−0.0381568	+	0.220932i
$889$	−0.228038			−0.00764814
$890$	19.6836	+	1.12332i	0.659795	+	0.0376537i
$891$		−	1.00000i		−	0.0335013i
$892$	20.8562	+	2.38825i	0.698316	+	0.0799646i
$893$			23.5041i			0.786535i
$894$	0.455471	−	7.98107i	0.0152332	−	0.266927i
$895$	−2.41684			−0.0807859
$896$	−4.87629	+	11.5641i	−0.162905	+	0.386331i
$897$	−2.06103			−0.0688159
$898$	−0.0736800	+	1.29107i	−0.00245873	+	0.0430836i
$899$			19.8669i			0.662599i
$900$	−1.98701	−	0.227534i	−0.0662338	−	0.00758448i
$901$			1.25939i			0.0419565i
$902$	5.55452	+	0.316990i	0.184945	+	0.0105546i
$903$	−12.4391			−0.413947
$904$	2.97834	−	17.2449i	0.0990583	−	0.573559i
$905$	−5.82247			−0.193545
$906$	−14.7959	−	0.844384i	−0.491560	−	0.0280528i
$907$		−	28.5645i		−	0.948468i	−0.880399	−	0.474234i	$-0.842725\pi$
$907$		−	28.5645i		−	0.948468i	0.880399	−	0.474234i	$-0.157275\pi$
$908$	4.53699	−	39.6207i	0.150565	−	1.31486i
$909$		−	1.75360i		−	0.0581632i
$910$	0.344999	−	6.04530i	0.0114366	−	0.200400i
$911$	26.2768			0.870589			0.435295	−	0.900288i	$-0.356644\pi$
$911$	26.2768			0.870589			0.435295	+	0.900288i	$0.356644\pi$
$912$	−18.6947	−	4.33836i	−0.619042	−	0.143658i
$913$	−2.71306			−0.0897892
$914$	0.941485	−	16.4973i	0.0311415	−	0.545684i
$915$			1.68834i			0.0558148i
$916$	−5.04853	+	44.0878i	−0.166808	+	1.45670i
$917$		−	0.329184i		−	0.0108706i
$918$	1.56623	+	0.0893828i	0.0516932	+	0.00295007i
$919$	−15.9484			−0.526088			−0.263044	−	0.964784i	$-0.584726\pi$
$919$	−15.9484			−0.526088			−0.263044	+	0.964784i	$0.584726\pi$
$920$	−1.48828	−	0.257038i	−0.0490671	−	0.00847428i
$921$	6.71091			0.221132
$922$	57.8483	+	3.30133i	1.90513	+	0.108724i
$923$		−	50.2003i		−	1.65236i
$924$	2.20418	+	0.252402i	0.0725122	+	0.00830342i
$925$		−	2.36212i		−	0.0776661i
$926$	1.07759	−	18.8823i	0.0354119	−	0.620511i
$927$	−7.34041			−0.241091
$928$	−14.5614	−	4.26670i	−0.478003	−	0.140061i
$929$	37.8391			1.24146			0.620731	−	0.784024i	$-0.286836\pi$
$929$	37.8391			1.24146			0.620731	+	0.784024i	$0.286836\pi$
$930$	−0.596793	+	10.4574i	−0.0195696	+	0.342912i
$931$			27.6811i			0.907212i
$932$	7.16115	+	0.820028i	0.234571	+	0.0268609i
$933$		−	15.1336i		−	0.495452i
$934$	57.0546	+	3.25604i	1.86688	+	0.106541i
$935$	1.10929			0.0362777
$936$	−10.7579	−	1.85797i	−0.351632	−	0.0607297i
$937$	32.3622			1.05723			0.528613	−	0.848863i	$-0.322712\pi$
$937$	32.3622			1.05723			0.528613	+	0.848863i	$0.322712\pi$
$938$	10.0967	+	0.576209i	0.329670	+	0.0188139i
$939$		−	15.2220i		−	0.496751i
$940$	−1.11466	+	9.73413i	−0.0363563	+	0.317492i
$941$		−	45.6044i		−	1.48666i	−0.668925	−	0.743330i	$-0.733245\pi$
$941$		−	45.6044i		−	1.48666i	0.668925	−	0.743330i	$-0.266755\pi$
$942$	0.172642	−	3.02515i	0.00562497	−	0.0985646i
$943$	−2.10068			−0.0684075
$944$	10.9219	−	47.0641i	0.355478	−	1.53181i
$945$	−1.10929			−0.0360853
$946$	−0.903547	+	15.8326i	−0.0293769	+	0.514761i
$947$		−	17.4628i		−	0.567463i	−0.958904	−	0.283732i	$-0.908428\pi$
$947$		−	17.4628i		−	0.567463i	0.958904	−	0.283732i	$-0.0915725\pi$
$948$	−0.783581	+	6.84286i	−0.0254495	+	0.222246i
$949$			45.9862i			1.49277i
$950$	6.77418	+	0.386595i	0.219783	+	0.0125428i
$951$	−33.4802			−1.08567
$952$	−0.592334	+	3.42968i	−0.0191977	+	0.111157i
$953$	51.0904			1.65498			0.827490	−	0.561481i	$-0.189768\pi$
$953$	51.0904			1.65498			0.827490	+	0.561481i	$0.189768\pi$
$954$	−1.60297	−	0.0914795i	−0.0518980	−	0.00296176i
$955$			4.15396i			0.134419i
$956$	−49.3013	−	5.64553i	−1.59452	−	0.182589i
$957$			2.68235i			0.0867081i
$958$	1.81409	−	31.7877i	0.0586105	−	1.02701i
$959$	11.0565			0.357034
$960$	−7.53657	−	2.68329i	−0.243242	−	0.0866029i
$961$	23.8568			0.769573
$962$	0.734640	−	12.8729i	0.0236857	−	0.415038i
$963$		−	4.82102i		−	0.155355i
$964$	−23.4137	−	2.68112i	−0.754106	−	0.0863531i
$965$		−	12.2730i		−	0.395082i
$966$	−0.836327	−	0.0477282i	−0.0269084	−	0.00153563i
$967$	−47.2549			−1.51961			−0.759807	−	0.650148i	$-0.774707\pi$
$967$	−47.2549			−1.51961			−0.759807	+	0.650148i	$0.774707\pi$
$968$	0.481366	−	2.78716i	0.0154717	−	0.0895829i
$969$	−5.32223			−0.170975
$970$	−26.9886	−	1.54021i	−0.866553	−	0.0494532i
$971$		−	26.5400i		−	0.851710i	−0.904791	−	0.425855i	$-0.859973\pi$
$971$		−	26.5400i		−	0.851710i	0.904791	−	0.425855i	$-0.140027\pi$
$972$	−0.227534	+	1.98701i	−0.00729817	+	0.0637335i
$973$		−	11.2061i		−	0.359252i
$974$	−1.15910	+	20.3105i	−0.0371398	+	0.650790i
$975$	3.85979			0.123612
$976$	−1.52665	+	6.57854i	−0.0488667	+	0.210574i
$977$	30.8413			0.986699			0.493350	−	0.869831i	$-0.335772\pi$
$977$	30.8413			0.986699			0.493350	+	0.869831i	$0.335772\pi$
$978$	−1.19234	+	20.8930i	−0.0381268	+	0.668084i
$979$		−	13.9410i		−	0.445557i
$980$	−1.31275	+	11.4640i	−0.0419344	+	0.366205i
$981$			6.40843i			0.204605i
$982$	3.22639	+	0.184126i	0.102958	+	0.00587571i
$983$	−25.8204			−0.823544			−0.411772	−	0.911287i	$-0.635090\pi$
$983$	−25.8204			−0.823544			−0.411772	+	0.911287i	$0.635090\pi$
$984$	−10.9648	−	1.89371i	−0.349545	−	0.0603693i
$985$	7.93158			0.252721
$986$	−4.20117	−	0.239756i	−0.133793	−	0.00763539i
$987$			5.43428i			0.172975i
$988$	36.7970	+	4.21365i	1.17067	+	0.134054i
$989$		−	5.98775i		−	0.190399i
$990$	−0.0805765	+	1.41192i	−0.00256089	+	0.0448736i
$991$	−34.0696			−1.08226			−0.541128	−	0.840940i	$-0.682003\pi$
$991$	−34.0696			−1.08226			−0.541128	+	0.840940i	$0.682003\pi$
$992$	−11.7813	+	40.2072i	−0.374056	+	1.27658i
$993$	−32.9618			−1.04601
$994$	1.16251	−	20.3703i	0.0368726	−	0.646107i
$995$			0.922025i			0.0292302i
$996$	5.39089	+	0.617315i	0.170817	+	0.0195604i
$997$		−	39.8148i		−	1.26095i	−0.776210	−	0.630474i	$-0.782860\pi$
$997$		−	39.8148i		−	1.26095i	0.776210	−	0.630474i	$-0.217140\pi$
$998$	−28.4740	−	1.62498i	−0.901329	−	0.0514378i
$999$	−2.36212			−0.0747343

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1320.2.w.d.661.9	✓	18
4.3	odd	2		5280.2.w.d.2641.13		18
8.3	odd	2		5280.2.w.d.2641.4		18
8.5	even	2	inner	1320.2.w.d.661.10	yes	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1320.2.w.d.661.9	✓	18	1.1	even	1	trivial
1320.2.w.d.661.10	yes	18	8.5	even	2	inner
5280.2.w.d.2641.4		18	8.3	odd	2
5280.2.w.d.2641.13		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:	\( N \)	\(=\)	\( 1320 = 2^{3} \cdot 3 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1320.w (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0805765 - 1.41192i) q^{2} -1.00000i q^{3} +(-1.98701 - 0.227534i) q^{4} +1.00000i q^{5} +(-1.41192 - 0.0805765i) q^{6} +1.10929 q^{7} +(-0.481366 + 2.78716i) q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+(0.0805765 - 1.41192i) q^{2} -1.00000i q^{3} +(-1.98701 - 0.227534i) q^{4} +1.00000i q^{5} +(-1.41192 - 0.0805765i) q^{6} +1.10929 q^{7} +(-0.481366 + 2.78716i) q^{8} -1.00000 q^{9} +(1.41192 + 0.0805765i) q^{10} -1.00000i q^{11} +(-0.227534 + 1.98701i) q^{12} -3.85979i q^{13} +(0.0893828 - 1.56623i) q^{14} +1.00000 q^{15} +(3.89646 + 0.904229i) q^{16} +1.10929 q^{17} +(-0.0805765 + 1.41192i) q^{18} -4.79786i q^{19} +(0.227534 - 1.98701i) q^{20} -1.10929i q^{21} +(-1.41192 - 0.0805765i) q^{22} +0.533975 q^{23} +(2.78716 + 0.481366i) q^{24} -1.00000 q^{25} +(-5.44970 - 0.311008i) q^{26} +1.00000i q^{27} +(-2.20418 - 0.252402i) q^{28} -2.68235i q^{29} +(0.0805765 - 1.41192i) q^{30} -7.40654 q^{31} +(1.59066 - 5.42861i) q^{32} -1.00000 q^{33} +(0.0893828 - 1.56623i) q^{34} +1.10929i q^{35} +(1.98701 + 0.227534i) q^{36} +2.36212i q^{37} +(-6.77418 - 0.386595i) q^{38} -3.85979 q^{39} +(-2.78716 - 0.481366i) q^{40} -3.93403 q^{41} +(-1.56623 - 0.0893828i) q^{42} -11.2135i q^{43} +(-0.227534 + 1.98701i) q^{44} -1.00000i q^{45} +(0.0430259 - 0.753929i) q^{46} -4.89887 q^{47} +(0.904229 - 3.89646i) q^{48} -5.76947 q^{49} +(-0.0805765 + 1.41192i) q^{50} -1.10929i q^{51} +(-0.878235 + 7.66946i) q^{52} +1.13531i q^{53} +(1.41192 + 0.0805765i) q^{54} +1.00000 q^{55} +(-0.533975 + 3.09178i) q^{56} -4.79786 q^{57} +(-3.78726 - 0.216134i) q^{58} -12.0787i q^{59} +(-1.98701 - 0.227534i) q^{60} +1.68834i q^{61} +(-0.596793 + 10.4574i) q^{62} -1.10929 q^{63} +(-7.53657 - 2.68329i) q^{64} +3.85979 q^{65} +(-0.0805765 + 1.41192i) q^{66} +6.44653i q^{67} +(-2.20418 - 0.252402i) q^{68} -0.533975i q^{69} +(1.56623 + 0.0893828i) q^{70} +13.0060 q^{71} +(0.481366 - 2.78716i) q^{72} -11.9142 q^{73} +(3.33512 + 0.190332i) q^{74} +1.00000i q^{75} +(-1.09168 + 9.53342i) q^{76} -1.10929i q^{77} +(-0.311008 + 5.44970i) q^{78} +3.44379 q^{79} +(-0.904229 + 3.89646i) q^{80} +1.00000 q^{81} +(-0.316990 + 5.55452i) q^{82} -2.71306i q^{83} +(-0.252402 + 2.20418i) q^{84} +1.10929i q^{85} +(-15.8326 - 0.903547i) q^{86} -2.68235 q^{87} +(2.78716 + 0.481366i) q^{88} +13.9410 q^{89} +(-1.41192 - 0.0805765i) q^{90} -4.28163i q^{91} +(-1.06102 - 0.121498i) q^{92} +7.40654i q^{93} +(-0.394734 + 6.91680i) q^{94} +4.79786 q^{95} +(-5.42861 - 1.59066i) q^{96} -19.1149 q^{97} +(-0.464884 + 8.14601i) q^{98} +1.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 2 q^{4} - 2 q^{6} - 18 q^{9}+O(q^{10}) \) 18 * q - 2 * q^4 - 2 * q^6 - 18 * q^9	\( 18 q - 2 q^{4} - 2 q^{6} - 18 q^{9} + 2 q^{10} + 18 q^{15} + 2 q^{16} - 2 q^{22} + 2 q^{24} - 18 q^{25} + 32 q^{26} - 36 q^{31} - 18 q^{33} + 2 q^{36} - 40 q^{38} - 2 q^{40} - 36 q^{46} + 10 q^{49} + 2 q^{54} + 18 q^{55} + 28 q^{57} + 32 q^{58} - 2 q^{60} - 36 q^{62} - 2 q^{64} + 8 q^{71} + 28 q^{73} + 8 q^{79} + 18 q^{81} + 32 q^{82} - 48 q^{86} + 2 q^{88} - 28 q^{89} - 2 q^{90} - 68 q^{92} - 36 q^{94} - 28 q^{95} - 2 q^{96} - 52 q^{97} + 100 q^{98}+O(q^{100}) \) 18 * q - 2 * q^4 - 2 * q^6 - 18 * q^9 + 2 * q^10 + 18 * q^15 + 2 * q^16 - 2 * q^22 + 2 * q^24 - 18 * q^25 + 32 * q^26 - 36 * q^31 - 18 * q^33 + 2 * q^36 - 40 * q^38 - 2 * q^40 - 36 * q^46 + 10 * q^49 + 2 * q^54 + 18 * q^55 + 28 * q^57 + 32 * q^58 - 2 * q^60 - 36 * q^62 - 2 * q^64 + 8 * q^71 + 28 * q^73 + 8 * q^79 + 18 * q^81 + 32 * q^82 - 48 * q^86 + 2 * q^88 - 28 * q^89 - 2 * q^90 - 68 * q^92 - 36 * q^94 - 28 * q^95 - 2 * q^96 - 52 * q^97 + 100 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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