LMFDB - Embedded newform 666.2.x.g.145.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [666,2,Mod(127,666)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(666, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("666.127");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 666 = 2 \cdot 3^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	666.x (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.31803677462$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 24x^{10} + 264x^{8} - 1687x^{6} + 6600x^{4} - 15000x^{2} + 15625 $ x^12 - 24x^10 + 264x^8 - 1687x^6 + 6600x^4 - 15000*x^2 + 15625
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 74)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			145.2
Root			$-2.20976 - 0.342020i$ of defining polynomial
Character	$\chi$	$=$	666.145
Dual form			666.2.x.g.271.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.766044 - 0.642788i) q^{2} +(0.173648 + 0.984808i) q^{4} +(1.43969 + 0.524005i) q^{5} +(4.53424 + 1.65033i) q^{7} +(0.500000 - 0.866025i) q^{8} +O(q^{10})$	\(q+(-0.766044 - 0.642788i) q^{2} +(0.173648 + 0.984808i) q^{4} +(1.43969 + 0.524005i) q^{5} +(4.53424 + 1.65033i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-0.766044 - 1.32683i) q^{10} +(-0.546896 + 0.947252i) q^{11} +(0.307284 + 1.74269i) q^{13} +(-2.41262 - 4.17878i) q^{14} +(-0.939693 + 0.342020i) q^{16} +(-0.511542 + 2.90110i) q^{17} +(-0.632167 + 0.530451i) q^{19} +(-0.266044 + 1.50881i) q^{20} +(1.02783 - 0.374099i) q^{22} +(-0.121620 - 0.210653i) q^{23} +(-2.03209 - 1.70513i) q^{25} +(0.884789 - 1.53250i) q^{26} +(-0.837893 + 4.75193i) q^{28} +(-2.78587 + 4.82526i) q^{29} -5.73495 q^{31} +(0.939693 + 0.342020i) q^{32} +(2.25665 - 1.89356i) q^{34} +(5.66313 + 4.75193i) q^{35} +(5.84038 - 1.69999i) q^{37} +0.825235 q^{38} +(1.17365 - 0.984808i) q^{40} +(-0.505653 - 2.86770i) q^{41} +4.37987 q^{43} +(-1.02783 - 0.374099i) q^{44} +(-0.0422383 + 0.239545i) q^{46} +(1.13249 + 1.96153i) q^{47} +(12.4734 + 10.4664i) q^{49} +(0.460637 + 2.61240i) q^{50} +(-1.66286 + 0.605232i) q^{52} +(5.77859 - 2.10324i) q^{53} +(-1.28373 + 1.07717i) q^{55} +(3.69634 - 3.10160i) q^{56} +(5.23571 - 1.90564i) q^{58} +(8.29301 - 3.01841i) q^{59} +(-2.04075 - 11.5737i) q^{61} +(4.39322 + 3.68635i) q^{62} +(-0.500000 - 0.866025i) q^{64} +(-0.470787 + 2.66996i) q^{65} +(-8.44220 - 3.07271i) q^{67} -2.94585 q^{68} +(-1.28373 - 7.28038i) q^{70} +(0.933535 - 0.783329i) q^{71} +8.79418 q^{73} +(-5.56672 - 2.45185i) q^{74} +(-0.632167 - 0.530451i) q^{76} +(-4.04303 + 3.39251i) q^{77} +(-2.02379 - 0.736599i) q^{79} -1.53209 q^{80} +(-1.45597 + 2.52181i) q^{82} +(-0.884528 + 5.01641i) q^{83} +(-2.25665 + 3.90864i) q^{85} +(-3.35518 - 2.81533i) q^{86} +(0.546896 + 0.947252i) q^{88} +(8.43486 - 3.07004i) q^{89} +(-1.48272 + 8.40891i) q^{91} +(0.186333 - 0.156352i) q^{92} +(0.393310 - 2.23057i) q^{94} +(-1.18809 + 0.432428i) q^{95} +(-2.17954 - 3.77507i) q^{97} +(-2.82750 - 16.0355i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{5} + 6 q^{7} + 6 q^{8}+O(q^{10}) $ 12 * q + 6 * q^5 + 6 * q^7 + 6 * q^8	$ 12 q + 6 q^{5} + 6 q^{7} + 6 q^{8} - 3 q^{11} - 6 q^{13} - 3 q^{14} + 3 q^{17} - 3 q^{19} + 6 q^{20} - 3 q^{22} + 21 q^{23} - 6 q^{25} - 3 q^{28} - 6 q^{29} + 42 q^{31} - 3 q^{34} + 9 q^{35} - 3 q^{37} - 42 q^{38} + 12 q^{40} + 21 q^{41} + 36 q^{43} + 3 q^{44} + 3 q^{46} - 9 q^{47} - 12 q^{49} - 12 q^{50} + 3 q^{52} + 6 q^{53} + 3 q^{56} - 3 q^{58} + 6 q^{59} - 18 q^{61} + 33 q^{62} - 6 q^{64} - 3 q^{65} - 27 q^{67} - 6 q^{68} + 18 q^{71} + 54 q^{73} - 3 q^{74} - 3 q^{76} - 51 q^{77} - 12 q^{79} - 18 q^{82} + 6 q^{83} + 3 q^{85} + 3 q^{88} + 15 q^{89} - 51 q^{91} + 6 q^{92} - 12 q^{94} + 15 q^{95} - 42 q^{97} - 51 q^{98}+O(q^{100}) $ 12 * q + 6 * q^5 + 6 * q^7 + 6 * q^8 - 3 * q^11 - 6 * q^13 - 3 * q^14 + 3 * q^17 - 3 * q^19 + 6 * q^20 - 3 * q^22 + 21 * q^23 - 6 * q^25 - 3 * q^28 - 6 * q^29 + 42 * q^31 - 3 * q^34 + 9 * q^35 - 3 * q^37 - 42 * q^38 + 12 * q^40 + 21 * q^41 + 36 * q^43 + 3 * q^44 + 3 * q^46 - 9 * q^47 - 12 * q^49 - 12 * q^50 + 3 * q^52 + 6 * q^53 + 3 * q^56 - 3 * q^58 + 6 * q^59 - 18 * q^61 + 33 * q^62 - 6 * q^64 - 3 * q^65 - 27 * q^67 - 6 * q^68 + 18 * q^71 + 54 * q^73 - 3 * q^74 - 3 * q^76 - 51 * q^77 - 12 * q^79 - 18 * q^82 + 6 * q^83 + 3 * q^85 + 3 * q^88 + 15 * q^89 - 51 * q^91 + 6 * q^92 - 12 * q^94 + 15 * q^95 - 42 * q^97 - 51 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/666\mathbb{Z}\right)^\times$.

$n$	$371$	$631$
$\chi(n)$	$1$	$e\left(\frac{2}{9}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.766044	−	0.642788i	−0.541675	−	0.454519i
$2$	−0.766044	−	0.642788i	−0.541675	−	0.454519i
$3$		0			0
$3$		0			0
$4$	0.173648	+	0.984808i	0.0868241	+	0.492404i
$5$	1.43969	+	0.524005i	0.643850	+	0.234342i	0.643248	−	0.765658i	$-0.277586\pi$
$5$	1.43969	+	0.524005i	0.643850	+	0.234342i	0.000601695		1.00000i	$0.499808\pi$
$6$		0			0
$7$	4.53424	+	1.65033i	1.71378	+	0.623765i	0.997272	−	0.0738128i	$-0.0235167\pi$
$7$	4.53424	+	1.65033i	1.71378	+	0.623765i	0.716509	+	0.697578i	$0.245739\pi$
$8$	0.500000	−	0.866025i	0.176777	−	0.306186i
$9$		0			0
$10$	−0.766044	−	1.32683i	−0.242245	−	0.419580i
$11$	−0.546896	+	0.947252i	−0.164895	+	0.285607i	−0.936618	−	0.350352i	$-0.886062\pi$
$11$	−0.546896	+	0.947252i	−0.164895	+	0.285607i	0.771723	+	0.635959i	$0.219395\pi$
$12$		0			0
$13$	0.307284	+	1.74269i	0.0852253	+	0.483337i	0.997308	+	0.0733298i	$0.0233626\pi$
$13$	0.307284	+	1.74269i	0.0852253	+	0.483337i	−0.912082	+	0.410007i	$0.865526\pi$
$14$	−2.41262	−	4.17878i	−0.644799	−	1.11682i
$15$		0			0
$16$	−0.939693	+	0.342020i	−0.234923	+	0.0855050i
$17$	−0.511542	+	2.90110i	−0.124067	+	0.703619i	0.857791	+	0.513999i	$0.171837\pi$
$17$	−0.511542	+	2.90110i	−0.124067	+	0.703619i	−0.981858	+	0.189620i	$0.939274\pi$
$18$		0			0
$19$	−0.632167	+	0.530451i	−0.145029	+	0.121694i	−0.712416	−	0.701758i	$-0.752399\pi$
$19$	−0.632167	+	0.530451i	−0.145029	+	0.121694i	0.567387	+	0.823451i	$0.307954\pi$
$20$	−0.266044	+	1.50881i	−0.0594893	+	0.337381i
$21$		0			0
$22$	1.02783	−	0.374099i	0.219134	−	0.0797582i
$23$	−0.121620	−	0.210653i	−0.0253596	−	0.0439241i	0.853067	−	0.521801i	$-0.174740\pi$
$23$	−0.121620	−	0.210653i	−0.0253596	−	0.0439241i	−0.878427	+	0.477877i	$0.841406\pi$
$24$		0			0
$25$	−2.03209	−	1.70513i	−0.406418	−	0.341025i
$26$	0.884789	−	1.53250i	0.173521	−	0.300548i
$27$		0			0
$28$	−0.837893	+	4.75193i	−0.158347	+	0.898030i
$29$	−2.78587	+	4.82526i	−0.517322	+	0.896028i	0.482475	+	0.875910i	$0.339738\pi$
$29$	−2.78587	+	4.82526i	−0.517322	+	0.896028i	−0.999798	+	0.0201189i	$0.993596\pi$
$30$		0			0
$31$	−5.73495			−1.03003			−0.515013	−	0.857182i	$-0.672213\pi$
$31$	−5.73495			−1.03003			−0.515013	+	0.857182i	$0.672213\pi$
$32$	0.939693	+	0.342020i	0.166116	+	0.0604612i
$33$		0			0
$34$	2.25665	−	1.89356i	0.387013	−	0.324742i
$35$	5.66313	+	4.75193i	0.957243	+	0.803223i
$36$		0			0
$37$	5.84038	−	1.69999i	0.960152	−	0.279477i
$37$	5.84038	−	1.69999i	0.960152	−	0.279477i
$38$	0.825235			0.133871
$39$		0			0
$40$	1.17365	−	0.984808i	0.185570	−	0.155712i
$41$	−0.505653	−	2.86770i	−0.0789697	−	0.447859i	−0.998496	−	0.0548301i	$-0.982538\pi$
$41$	−0.505653	−	2.86770i	−0.0789697	−	0.447859i	0.919526	−	0.393029i	$-0.128573\pi$
$42$		0			0
$43$	4.37987			0.667924			0.333962	−	0.942587i	$-0.391614\pi$
$43$	4.37987			0.667924			0.333962	+	0.942587i	$0.391614\pi$
$44$	−1.02783	−	0.374099i	−0.154951	−	0.0563975i
$45$		0			0
$46$	−0.0422383	+	0.239545i	−0.00622770	+	0.0353191i
$47$	1.13249	+	1.96153i	0.165191	+	0.286119i	0.936723	−	0.350071i	$-0.113843\pi$
$47$	1.13249	+	1.96153i	0.165191	+	0.286119i	−0.771532	+	0.636190i	$0.780509\pi$
$48$		0			0
$49$	12.4734	+	10.4664i	1.78192	+	1.49521i
$50$	0.460637	+	2.61240i	0.0651439	+	0.369450i
$51$		0			0
$52$	−1.66286	+	0.605232i	−0.230597	+	0.0839305i
$53$	5.77859	−	2.10324i	0.793751	−	0.288902i	0.0868564	−	0.996221i	$-0.472318\pi$
$53$	5.77859	−	2.10324i	0.793751	−	0.288902i	0.706894	+	0.707319i	$0.250096\pi$
$54$		0			0
$55$	−1.28373	+	1.07717i	−0.173098	+	0.145246i
$56$	3.69634	−	3.10160i	0.493945	−	0.414469i
$57$		0			0
$58$	5.23571	−	1.90564i	0.687483	−	0.250223i
$59$	8.29301	−	3.01841i	1.07966	−	0.392963i	0.259878	−	0.965642i	$-0.416318\pi$
$59$	8.29301	−	3.01841i	1.07966	−	0.392963i	0.819780	+	0.572678i	$0.194096\pi$
$60$		0			0
$61$	−2.04075	−	11.5737i	−0.261292	−	1.48186i	−0.779390	−	0.626539i	$-0.784471\pi$
$61$	−2.04075	−	11.5737i	−0.261292	−	1.48186i	0.518098	−	0.855321i	$-0.326640\pi$
$62$	4.39322	+	3.68635i	0.557940	+	0.468167i
$63$		0			0
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	−0.470787	+	2.66996i	−0.0583939	+	0.331168i
$66$		0			0
$67$	−8.44220	−	3.07271i	−1.03138	−	0.375391i	−0.229773	−	0.973244i	$-0.573798\pi$
$67$	−8.44220	−	3.07271i	−1.03138	−	0.375391i	−0.801606	+	0.597853i	$0.796021\pi$
$68$	−2.94585			−0.357237
$69$		0			0
$70$	−1.28373	−	7.28038i	−0.153435	−	0.870172i
$71$	0.933535	−	0.783329i	0.110790	−	0.0929640i	−0.585710	−	0.810521i	$-0.699184\pi$
$71$	0.933535	−	0.783329i	0.110790	−	0.0929640i	0.696500	+	0.717557i	$0.254740\pi$
$72$		0			0
$73$	8.79418			1.02928			0.514640	−	0.857406i	$-0.327925\pi$
$73$	8.79418			1.02928			0.514640	+	0.857406i	$0.327925\pi$
$74$	−5.56672	−	2.45185i	−0.647119	−	0.285022i
$75$		0			0
$76$	−0.632167	−	0.530451i	−0.0725145	−	0.0608469i
$77$	−4.04303	+	3.39251i	−0.460746	+	0.386612i
$78$		0			0
$79$	−2.02379	−	0.736599i	−0.227694	−	0.0828739i	0.225654	−	0.974208i	$-0.427548\pi$
$79$	−2.02379	−	0.736599i	−0.227694	−	0.0828739i	−0.453348	+	0.891334i	$0.649770\pi$
$80$	−1.53209			−0.171293
$81$		0			0
$82$	−1.45597	+	2.52181i	−0.160785	+	0.278488i
$83$	−0.884528	+	5.01641i	−0.0970895	+	0.550622i	0.896997	+	0.442036i	$0.145744\pi$
$83$	−0.884528	+	5.01641i	−0.0970895	+	0.550622i	−0.994087	+	0.108586i	$0.965368\pi$
$84$		0			0
$85$	−2.25665	+	3.90864i	−0.244768	+	0.423951i
$86$	−3.35518	−	2.81533i	−0.361798	−	0.303584i
$87$		0			0
$88$	0.546896	+	0.947252i	0.0582993	+	0.100977i
$89$	8.43486	−	3.07004i	0.894093	−	0.325423i	0.146210	−	0.989254i	$-0.453292\pi$
$89$	8.43486	−	3.07004i	0.894093	−	0.325423i	0.747883	+	0.663830i	$0.231070\pi$
$90$		0			0
$91$	−1.48272	+	8.40891i	−0.155431	+	0.881494i
$92$	0.186333	−	0.156352i	0.0194266	−	0.0163008i
$93$		0			0
$94$	0.393310	−	2.23057i	0.0405669	−	0.230066i
$95$	−1.18809	+	0.432428i	−0.121895	+	0.0443661i
$96$		0			0
$97$	−2.17954	−	3.77507i	−0.221298	−	0.383300i	0.733904	−	0.679253i	$-0.237696\pi$
$97$	−2.17954	−	3.77507i	−0.221298	−	0.383300i	−0.955203	+	0.295953i	$0.904363\pi$
$98$	−2.82750	−	16.0355i	−0.285620	−	1.61983i
$99$		0			0
$100$	1.32635	−	2.29731i	0.132635	−	0.229731i
$101$	−2.19444	−	3.80089i	−0.218355	−	0.378203i	0.735950	−	0.677036i	$-0.236736\pi$
$101$	−2.19444	−	3.80089i	−0.218355	−	0.378203i	−0.954305	+	0.298833i	$0.903403\pi$
$102$		0			0
$103$	−6.32262	+	10.9511i	−0.622987	+	1.07904i	0.365940	+	0.930638i	$0.380748\pi$
$103$	−6.32262	+	10.9511i	−0.622987	+	1.07904i	−0.988927	+	0.148406i	$0.952586\pi$
$104$	1.66286	+	0.605232i	0.163057	+	0.0593478i
$105$		0			0
$106$	−5.77859	−	2.10324i	−0.561266	−	0.204284i
$107$	−3.27495	−	18.5731i	−0.316601	−	1.79553i	−0.563098	−	0.826390i	$-0.690391\pi$
$107$	−3.27495	−	18.5731i	−0.316601	−	1.79553i	0.246497	−	0.969144i	$-0.420721\pi$
$108$		0			0
$109$	−6.44574	−	5.40862i	−0.617390	−	0.518052i	0.279592	−	0.960119i	$-0.409801\pi$
$109$	−6.44574	−	5.40862i	−0.617390	−	0.518052i	−0.896982	+	0.442067i	$0.854245\pi$
$110$	1.67579			0.159780
$111$		0			0
$112$	−4.82524			−0.455942
$113$	4.89090	+	4.10395i	0.460097	+	0.386067i	0.843167	−	0.537652i	$-0.180689\pi$
$113$	4.89090	+	4.10395i	0.460097	+	0.386067i	−0.383070	+	0.923719i	$0.625133\pi$
$114$		0			0
$115$	−0.0647129	−	0.367005i	−0.00603451	−	0.0342234i
$116$	−5.23571	−	1.90564i	−0.486124	−	0.176935i
$117$		0			0
$118$	−8.29301	−	3.01841i	−0.763433	−	0.277867i
$119$	−7.10721	+	12.3100i	−0.651517	+	1.12846i
$120$		0			0
$121$	4.90181	+	8.49018i	0.445619	+	0.771835i
$122$	−5.87612	+	10.1777i	−0.531999	+	0.921449i
$123$		0			0
$124$	−0.995863	−	5.64782i	−0.0894312	−	0.507189i
$125$	−5.86231	−	10.1538i	−0.524341	−	0.908185i
$126$		0			0
$127$	4.46592	−	1.62546i	0.396287	−	0.144237i	−0.136187	−	0.990683i	$-0.543485\pi$
$127$	4.46592	−	1.62546i	0.396287	−	0.144237i	0.532474	+	0.846447i	$0.321263\pi$
$128$	−0.173648	+	0.984808i	−0.0153485	+	0.0870455i
$129$		0			0
$130$	2.07686	−	1.74269i	0.182153	−	0.152844i
$131$	−3.12341	+	17.7137i	−0.272893	+	1.54765i	0.472682	+	0.881233i	$0.343286\pi$
$131$	−3.12341	+	17.7137i	−0.272893	+	1.54765i	−0.745575	+	0.666422i	$0.767825\pi$
$132$		0			0
$133$	−3.74181	+	1.36191i	−0.324456	+	0.118092i
$134$	4.49200	+	7.78037i	0.388050	+	0.672122i
$135$		0			0
$136$	2.25665	+	1.89356i	0.193506	+	0.162371i
$137$	11.0546	−	19.1471i	0.944456	−	1.63585i	0.187619	−	0.982242i	$-0.439923\pi$
$137$	11.0546	−	19.1471i	0.944456	−	1.63585i	0.756837	−	0.653603i	$-0.226744\pi$
$138$		0			0
$139$	−0.462854	+	2.62497i	−0.0392587	+	0.222647i	−0.998125	−	0.0612114i	$-0.980504\pi$
$139$	−0.462854	+	2.62497i	−0.0392587	+	0.222647i	0.958866	+	0.283859i	$0.0916147\pi$
$140$	−3.69634	+	6.40226i	−0.312398	+	0.541089i
$141$		0			0
$142$	−1.21864			−0.102266
$143$	−1.81882	−	0.661998i	−0.152098	−	0.0553590i
$144$		0			0
$145$	−6.53925	+	5.48708i	−0.543055	+	0.455678i
$146$	−6.73673	−	5.65279i	−0.557536	−	0.467828i
$147$		0			0
$148$	2.68834	+	5.45645i	0.220980	+	0.448517i
$149$	−6.13622			−0.502699			−0.251349	−	0.967896i	$-0.580874\pi$
$149$	−6.13622			−0.502699			−0.251349	+	0.967896i	$0.580874\pi$
$150$		0			0
$151$	−0.334584	+	0.280749i	−0.0272281	+	0.0228471i	−0.656300	−	0.754500i	$-0.727879\pi$
$151$	−0.334584	+	0.280749i	−0.0272281	+	0.0228471i	0.629072	+	0.777347i	$0.283435\pi$
$152$	0.143301	+	0.812698i	0.0116232	+	0.0659185i
$153$		0			0
$154$	5.27780			0.425298
$155$	−8.25656	−	3.00514i	−0.663183	−	0.241379i
$156$		0			0
$157$	1.05255	−	5.96930i	0.0840025	−	0.476402i	−0.913565	−	0.406693i	$-0.866682\pi$
$157$	1.05255	−	5.96930i	0.0840025	−	0.476402i	0.997567	−	0.0697089i	$-0.0222070\pi$
$158$	1.07684	+	1.86513i	0.0856684	+	0.148382i
$159$		0			0
$160$	1.17365	+	0.984808i	0.0927850	+	0.0778559i
$161$	−0.203810	−	1.15586i	−0.0160625	−	0.0910948i
$162$		0			0
$163$	−12.9066	+	4.69763i	−1.01093	+	0.367947i	−0.793788	−	0.608194i	$-0.791894\pi$
$163$	−12.9066	+	4.69763i	−1.01093	+	0.367947i	−0.217137	+	0.976141i	$0.569672\pi$
$164$	2.73633	−	0.995941i	0.213671	−	0.0777699i
$165$		0			0
$166$	3.90207	−	3.27423i	0.302859	−	0.254129i
$167$	−18.2471	+	15.3112i	−1.41201	+	1.18481i	−0.456543	+	0.889701i	$0.650913\pi$
$167$	−18.2471	+	15.3112i	−1.41201	+	1.18481i	−0.955463	+	0.295112i	$0.904643\pi$
$168$		0			0
$169$	9.27344	−	3.37526i	0.713342	−	0.259635i
$170$	4.24112	−	1.54364i	0.325279	−	0.118392i
$171$		0			0
$172$	0.760556	+	4.31333i	0.0579919	+	0.328888i
$173$	−16.4280	−	13.7847i	−1.24899	−	1.04803i	−0.996766	−	0.0803630i	$-0.974392\pi$
$173$	−16.4280	−	13.7847i	−1.24899	−	1.04803i	−0.252229	−	0.967668i	$-0.581164\pi$
$174$		0			0
$175$	−6.39996	−	11.0851i	−0.483791	−	0.837951i
$176$	0.189935	−	1.07717i	0.0143169	−	0.0811951i
$177$		0			0
$178$	−8.43486	−	3.07004i	−0.632220	−	0.230109i
$179$	−11.5247			−0.861400			−0.430700	−	0.902495i	$-0.641733\pi$
$179$	−11.5247			−0.861400			−0.430700	+	0.902495i	$0.641733\pi$
$180$		0			0
$181$	−3.08553	−	17.4989i	−0.229346	−	1.30068i	−0.854201	−	0.519943i	$-0.825953\pi$
$181$	−3.08553	−	17.4989i	−0.229346	−	1.30068i	0.624855	−	0.780740i	$-0.285158\pi$
$182$	6.54097	−	5.48853i	0.484849	−	0.406837i
$183$		0			0
$184$	−0.243241			−0.0179320
$185$	9.29916	+	0.612921i	0.683688	+	0.0450629i
$186$		0			0
$187$	−2.46831	−	2.07116i	−0.180501	−	0.151458i
$188$	−1.73508	+	1.45590i	−0.126544	+	0.106183i
$189$		0			0
$190$	1.18809	+	0.432428i	0.0861928	+	0.0313716i
$191$	25.9113			1.87487			0.937437	−	0.348155i	$-0.113192\pi$
$191$	25.9113			1.87487			0.937437	+	0.348155i	$0.113192\pi$
$192$		0			0
$193$	−5.45149	+	9.44225i	−0.392407	+	0.679668i	−0.992766	−	0.120062i	$-0.961691\pi$
$193$	−5.45149	+	9.44225i	−0.392407	+	0.679668i	0.600360	+	0.799730i	$0.295024\pi$
$194$	−0.756945	+	4.29285i	−0.0543455	+	0.308209i
$195$		0			0
$196$	−8.14145	+	14.1014i	−0.581532	+	1.00724i
$197$	4.93573	+	4.14157i	0.351656	+	0.295075i	0.801455	−	0.598055i	$-0.204060\pi$
$197$	4.93573	+	4.14157i	0.351656	+	0.295075i	−0.449798	+	0.893130i	$0.648504\pi$
$198$		0			0
$199$	−9.42779	−	16.3294i	−0.668318	−	1.15756i	−0.978374	−	0.206843i	$-0.933681\pi$
$199$	−9.42779	−	16.3294i	−0.668318	−	1.15756i	0.310056	−	0.950718i	$-0.399652\pi$
$200$	−2.49273	+	0.907278i	−0.176262	+	0.0641542i
$201$		0			0
$202$	−0.762122	+	4.32221i	−0.0536227	+	0.304110i
$203$	−20.5950	+	17.2813i	−1.44549	+	1.21291i
$204$		0			0
$205$	0.774705	−	4.39357i	0.0541077	−	0.306860i
$206$	11.8826	−	4.32493i	0.827903	−	0.301332i
$207$		0			0
$208$	−0.884789	−	1.53250i	−0.0613491	−	0.106260i
$209$	−0.156741	−	0.888923i	−0.0108420	−	0.0614881i
$210$		0			0
$211$	0.707251	−	1.22499i	0.0486891	−	0.0843321i	−0.840654	−	0.541573i	$-0.817829\pi$
$211$	0.707251	−	1.22499i	0.0486891	−	0.0843321i	0.889343	+	0.457241i	$0.151162\pi$
$212$	3.07472	+	5.32558i	0.211173	+	0.365762i
$213$		0			0
$214$	−9.42983	+	16.3330i	−0.644610	+	1.11650i
$215$	6.30567	+	2.29507i	0.430043	+	0.156523i
$216$		0			0
$217$	−26.0036	−	9.46454i	−1.76524	−	0.642495i
$218$	1.46113	+	8.28649i	0.0989603	+	0.561232i
$219$		0			0
$220$	−1.28373	−	1.07717i	−0.0865489	−	0.0726231i
$221$	−5.21291			−0.350659
$222$		0			0
$223$	−12.1750			−0.815302			−0.407651	−	0.913138i	$-0.633652\pi$
$223$	−12.1750			−0.815302			−0.407651	+	0.913138i	$0.633652\pi$
$224$	3.69634	+	3.10160i	0.246972	+	0.207234i
$225$		0			0
$226$	−1.10868	−	6.28761i	−0.0737480	−	0.418246i
$227$	−20.0154	−	7.28501i	−1.32847	−	0.483523i	−0.422306	−	0.906453i	$-0.638779\pi$
$227$	−20.0154	−	7.28501i	−1.32847	−	0.483523i	−0.906162	+	0.422930i	$0.861002\pi$
$228$		0			0
$229$	2.67775	+	0.974622i	0.176951	+	0.0644048i	0.428976	−	0.903316i	$-0.358874\pi$
$229$	2.67775	+	0.974622i	0.176951	+	0.0644048i	−0.252025	+	0.967721i	$0.581097\pi$
$230$	−0.186333	+	0.322739i	−0.0122865	+	0.0212808i
$231$		0			0
$232$	2.78587	+	4.82526i	0.182901	+	0.316794i
$233$	11.7583	−	20.3659i	0.770310	−	1.33422i	−0.167083	−	0.985943i	$-0.553435\pi$
$233$	11.7583	−	20.3659i	0.770310	−	1.33422i	0.937393	−	0.348273i	$-0.113232\pi$
$234$		0			0
$235$	0.602587	+	3.41744i	0.0393084	+	0.222929i
$236$	4.41262	+	7.64288i	0.287237	+	0.497509i
$237$		0			0
$238$	13.3572	−	4.86162i	0.865818	−	0.315132i
$239$	−1.39581	+	7.91601i	−0.0902872	+	0.512044i	0.905803	+	0.423700i	$0.139269\pi$
$239$	−1.39581	+	7.91601i	−0.0902872	+	0.512044i	−0.996090	+	0.0883447i	$0.971842\pi$
$240$		0			0
$241$	14.1349	−	11.8606i	0.910511	−	0.764010i	−0.0617048	−	0.998094i	$-0.519654\pi$
$241$	14.1349	−	11.8606i	0.910511	−	0.764010i	0.972216	+	0.234085i	$0.0752093\pi$
$242$	1.70238	−	9.65468i	0.109433	−	0.620626i
$243$		0			0
$244$	11.0435	−	4.01950i	0.706987	−	0.257322i
$245$	12.4734	+	21.6046i	0.796898	+	1.38027i
$246$		0			0
$247$	−1.11867	−	0.938675i	−0.0711792	−	0.0597265i
$248$	−2.86747	+	4.96661i	−0.182085	+	0.315380i
$249$		0			0
$250$	−2.03596	+	11.5465i	−0.128765	+	0.730265i
$251$	11.6472	−	20.1736i	0.735167	−	1.27335i	−0.219483	−	0.975616i	$-0.570437\pi$
$251$	11.6472	−	20.1736i	0.735167	−	1.27335i	0.954650	−	0.297731i	$-0.0962297\pi$
$252$		0			0
$253$	0.266055			0.0167267
$254$	−4.46592	−	1.62546i	−0.280217	−	0.101991i
$255$		0			0
$256$	0.766044	−	0.642788i	0.0478778	−	0.0401742i
$257$	3.26092	+	2.73624i	0.203411	+	0.170682i	0.738803	−	0.673922i	$-0.235392\pi$
$257$	3.26092	+	2.73624i	0.203411	+	0.170682i	−0.535392	+	0.844604i	$0.679836\pi$
$258$		0			0
$259$	29.2872	+	1.93036i	1.81982	+	0.119947i
$260$	−2.71115			−0.168139
$261$		0			0
$262$	13.7788	−	11.5618i	0.851259	−	0.714291i
$263$	1.19565	+	6.78086i	0.0737269	+	0.418126i	0.999225	+	0.0393727i	$0.0125359\pi$
$263$	1.19565	+	6.78086i	0.0737269	+	0.418126i	−0.925498	+	0.378753i	$0.876353\pi$
$264$		0			0
$265$	9.42150			0.578758
$266$	3.74181	+	1.36191i	0.229425	+	0.0835040i
$267$		0			0
$268$	1.56006	−	8.84751i	0.0952955	−	0.540448i
$269$	4.83783	+	8.37936i	0.294968	+	0.510899i	0.974977	−	0.222304i	$-0.0713578\pi$
$269$	4.83783	+	8.37936i	0.294968	+	0.510899i	−0.680010	+	0.733203i	$0.738024\pi$
$270$		0			0
$271$	5.87002	+	4.92553i	0.356578	+	0.299205i	0.803425	−	0.595406i	$-0.203009\pi$
$271$	5.87002	+	4.92553i	0.356578	+	0.299205i	−0.446847	+	0.894610i	$0.647453\pi$
$272$	−0.511542	−	2.90110i	−0.0310168	−	0.175905i
$273$		0			0
$274$	−20.7758	+	7.56177i	−1.25511	+	0.456823i
$275$	2.72652	−	0.992374i	0.164416	−	0.0598424i
$276$		0			0
$277$	3.07917	−	2.58373i	0.185009	−	0.155241i	−0.545579	−	0.838059i	$-0.683690\pi$
$277$	3.07917	−	2.58373i	0.185009	−	0.155241i	0.730589	+	0.682818i	$0.239246\pi$
$278$	2.04187	−	1.71333i	0.122463	−	0.102759i
$279$		0			0
$280$	6.94686	−	2.52845i	0.415154	−	0.151104i
$281$	−6.57717	+	2.39389i	−0.392361	+	0.142808i	−0.530664	−	0.847582i	$-0.678057\pi$
$281$	−6.57717	+	2.39389i	−0.392361	+	0.142808i	0.138303	+	0.990390i	$0.455835\pi$
$282$		0			0
$283$	−0.816946	−	4.63313i	−0.0485624	−	0.275411i	0.950851	−	0.309648i	$-0.100211\pi$
$283$	−0.816946	−	4.63313i	−0.0485624	−	0.275411i	−0.999414	+	0.0342367i	$0.989100\pi$
$284$	0.933535	+	0.783329i	0.0553951	+	0.0464820i
$285$		0			0
$286$	0.967776	+	1.67624i	0.0572258	+	0.0991179i
$287$	2.43989	−	13.8373i	0.144022	−	0.816791i
$288$		0			0
$289$	7.82009	+	2.84628i	0.460005	+	0.167428i
$290$	8.53639			0.501274
$291$		0			0
$292$	1.52709	+	8.66057i	0.0893663	+	0.506822i
$293$	10.9016	−	9.14751i	0.636877	−	0.534403i	−0.266180	−	0.963923i	$-0.585762\pi$
$293$	10.9016	−	9.14751i	0.636877	−	0.534403i	0.903057	+	0.429520i	$0.141317\pi$
$294$		0			0
$295$	13.5210			0.787226
$296$	1.44795	−	5.90791i	0.0841605	−	0.343390i
$297$		0			0
$298$	4.70062	+	3.94429i	0.272299	+	0.228486i
$299$	0.329731	−	0.276678i	0.0190689	−	0.0160007i
$300$		0			0
$301$	19.8594	+	7.22822i	1.14468	+	0.416628i
$302$	0.436768			0.0251332
$303$		0			0
$304$	0.412618	−	0.714675i	0.0236652	−	0.0409894i
$305$	3.12662	−	17.7319i	0.179030	−	1.01533i
$306$		0			0
$307$	−0.401308	+	0.695086i	−0.0229039	+	0.0396707i	−0.877250	−	0.480034i	$-0.840624\pi$
$307$	−0.401308	+	0.695086i	−0.0229039	+	0.0396707i	0.854346	+	0.519704i	$0.173958\pi$
$308$	−4.04303	−	3.39251i	−0.230373	−	0.193306i
$309$		0			0
$310$	4.39322	+	7.60929i	0.249518	+	0.432179i
$311$	−2.32051	+	0.844598i	−0.131584	+	0.0478928i	−0.406973	−	0.913440i	$-0.633416\pi$
$311$	−2.32051	+	0.844598i	−0.131584	+	0.0478928i	0.275389	+	0.961333i	$0.411193\pi$
$312$		0			0
$313$	−3.09856	+	17.5728i	−0.175141	+	0.993273i	0.762840	+	0.646587i	$0.223804\pi$
$313$	−3.09856	+	17.5728i	−0.175141	+	0.993273i	−0.937981	+	0.346686i	$0.887307\pi$
$314$	−4.64329	+	3.89618i	−0.262036	+	0.219874i
$315$		0			0
$316$	0.373981	−	2.12095i	0.0210381	−	0.119313i
$317$	3.32609	−	1.21060i	0.186812	−	0.0679940i	−0.246920	−	0.969036i	$-0.579419\pi$
$317$	3.32609	−	1.21060i	0.186812	−	0.0679940i	0.433732	+	0.901042i	$0.357196\pi$
$318$		0			0
$319$	−3.04716	−	5.27783i	−0.170608	−	0.295502i
$320$	−0.266044	−	1.50881i	−0.0148723	−	0.0843452i
$321$		0			0
$322$	−0.586847	+	1.01645i	−0.0327037	+	0.0566445i
$323$	−1.21551	−	2.10533i	−0.0676328	−	0.117143i
$324$		0			0
$325$	2.34708	−	4.06527i	0.130193	−	0.225501i
$326$	12.9066	+	4.69763i	0.714832	+	0.260178i
$327$		0			0
$328$	−2.73633	−	0.995941i	−0.151088	−	0.0549917i
$329$	1.89782	+	10.7630i	0.104630	+	0.593386i
$330$		0			0
$331$	2.93110	+	2.45948i	0.161108	+	0.135185i	0.719778	−	0.694205i	$-0.244244\pi$
$331$	2.93110	+	2.45948i	0.161108	+	0.135185i	−0.558670	+	0.829390i	$0.688688\pi$
$332$	−5.09379			−0.279558
$333$		0			0
$334$	23.8199			1.30337
$335$	−10.5441	−	8.84751i	−0.576083	−	0.483391i
$336$		0			0
$337$	−3.71542	−	21.0712i	−0.202392	−	1.14782i	−0.901492	−	0.432797i	$-0.857527\pi$
$337$	−3.71542	−	21.0712i	−0.202392	−	1.14782i	0.699100	−	0.715024i	$-0.253584\pi$
$338$	−9.27344	−	3.37526i	−0.504409	−	0.183590i
$339$		0			0
$340$	−4.24112	−	1.54364i	−0.230007	−	0.0837157i
$341$	3.13642	−	5.43244i	0.169847	−	0.294183i
$342$		0			0
$343$	22.3961	+	38.7912i	1.20927	+	2.09453i
$344$	2.18994	−	3.79308i	0.118073	−	0.204509i
$345$		0			0
$346$	3.72392	+	21.1194i	0.200199	+	1.13538i
$347$	−12.8181	−	22.2016i	−0.688113	−	1.19185i	−0.972448	−	0.233122i	$-0.925106\pi$
$347$	−12.8181	−	22.2016i	−0.688113	−	1.19185i	0.284334	−	0.958725i	$-0.408227\pi$
$348$		0			0
$349$	−14.5983	+	5.31334i	−0.781428	+	0.284417i	−0.701768	−	0.712406i	$-0.747606\pi$
$349$	−14.5983	+	5.31334i	−0.781428	+	0.284417i	−0.0796600	+	0.996822i	$0.525383\pi$
$350$	−2.22268	+	12.6055i	−0.118807	+	0.673790i
$351$		0			0
$352$	−0.837893	+	0.703076i	−0.0446599	+	0.0374741i
$353$	0.235520	−	1.33570i	0.0125355	−	0.0710923i	−0.977898	−	0.209081i	$-0.932953\pi$
$353$	0.235520	−	1.33570i	0.0125355	−	0.0710923i	0.990434	+	0.137989i	$0.0440638\pi$
$354$		0			0
$355$	1.75447	−	0.638576i	0.0931177	−	0.0338921i
$356$	4.48810	+	7.77361i	0.237869	+	0.412000i
$357$		0			0
$358$	8.82847	+	7.40796i	0.466599	+	0.391523i
$359$	−11.1573	+	19.3251i	−0.588862	+	1.01994i	0.405519	+	0.914086i	$0.367091\pi$
$359$	−11.1573	+	19.3251i	−0.588862	+	1.01994i	−0.994382	+	0.105853i	$0.966243\pi$
$360$		0			0
$361$	−3.18106	+	18.0407i	−0.167424	+	0.949509i
$362$	−8.88443	+	15.3883i	−0.466955	+	0.808790i
$363$		0			0
$364$	−8.53863			−0.447546
$365$	12.6609	+	4.60819i	0.662702	+	0.241204i
$366$		0			0
$367$	5.53730	−	4.64635i	0.289045	−	0.242538i	−0.486722	−	0.873557i	$-0.661808\pi$
$367$	5.53730	−	4.64635i	0.289045	−	0.242538i	0.775767	+	0.631019i	$0.217363\pi$
$368$	0.186333	+	0.156352i	0.00971329	+	0.00815042i
$369$		0			0
$370$	−6.72959	−	6.44691i	−0.349855	−	0.335159i
$371$	29.6725			1.54052
$372$		0			0
$373$	−8.98788	+	7.54173i	−0.465375	+	0.390496i	−0.845104	−	0.534602i	$-0.820462\pi$
$373$	−8.98788	+	7.54173i	−0.465375	+	0.390496i	0.379729	+	0.925098i	$0.376017\pi$
$374$	0.559520	+	3.17320i	0.0289321	+	0.164082i
$375$		0			0
$376$	2.26498			0.116808
$377$	−9.26501	−	3.37219i	−0.477172	−	0.173677i
$378$		0			0
$379$	−0.480627	+	2.72577i	−0.0246881	+	0.140013i	−0.994660	−	0.103202i	$-0.967091\pi$
$379$	−0.480627	+	2.72577i	−0.0246881	+	0.140013i	0.969972	+	0.243216i	$0.0782022\pi$
$380$	−0.632167	−	1.09495i	−0.0324295	−	0.0561695i
$381$		0			0
$382$	−19.8492	−	16.6554i	−1.01557	−	0.852167i
$383$	−3.38122	−	19.1758i	−0.172772	−	0.979840i	−0.940684	−	0.339284i	$-0.889815\pi$
$383$	−3.38122	−	19.1758i	−0.172772	−	0.979840i	0.767912	−	0.640556i	$-0.221296\pi$
$384$		0			0
$385$	−7.59842	+	2.76560i	−0.387251	+	0.140948i
$386$	10.2454	−	3.72904i	0.521479	−	0.189803i
$387$		0			0
$388$	3.33924	−	2.80196i	0.169524	−	0.142248i
$389$	1.79849	−	1.50911i	0.0911870	−	0.0765150i	−0.596055	−	0.802944i	$-0.703266\pi$
$389$	1.79849	−	1.50911i	0.0911870	−	0.0765150i	0.687242	+	0.726429i	$0.258821\pi$
$390$		0			0
$391$	0.673338	−	0.245075i	0.0340522	−	0.0123940i
$392$	15.3009	−	5.56908i	0.772813	−	0.281281i
$393$		0			0
$394$	−1.11884	−	6.34525i	−0.0563663	−	0.319669i
$395$	−2.52765	−	2.12095i	−0.127180	−	0.106717i
$396$		0			0
$397$	−1.13774	−	1.97062i	−0.0571015	−	0.0989026i	0.836062	−	0.548635i	$-0.184853\pi$
$397$	−1.13774	−	1.97062i	−0.0571015	−	0.0989026i	−0.893163	+	0.449733i	$0.851519\pi$
$398$	−3.27424	+	18.5691i	−0.164123	+	0.930786i
$399$		0			0
$400$	2.49273	+	0.907278i	0.124636	+	0.0453639i
$401$	−17.5482			−0.876316			−0.438158	−	0.898898i	$-0.644369\pi$
$401$	−17.5482			−0.876316			−0.438158	+	0.898898i	$0.644369\pi$
$402$		0			0
$403$	−1.76226	−	9.99426i	−0.0877843	−	0.497850i
$404$	3.36208	−	2.82112i	0.167270	−	0.140356i
$405$		0			0
$406$	26.8849			1.33428
$407$	−1.58376	+	6.46203i	−0.0785040	+	0.320311i
$408$		0			0
$409$	17.3730	+	14.5777i	0.859041	+	0.720821i	0.961761	−	0.273889i	$-0.0883102\pi$
$409$	17.3730	+	14.5777i	0.859041	+	0.720821i	−0.102720	+	0.994710i	$0.532755\pi$
$410$	−3.41759	+	2.86770i	−0.168783	+	0.141626i
$411$		0			0
$412$	−11.8826	−	4.32493i	−0.585416	−	0.213074i
$413$	42.5838			2.09541
$414$		0			0
$415$	−3.90207	+	6.75859i	−0.191545	+	0.331766i
$416$	−0.307284	+	1.74269i	−0.0150658	+	0.0854426i
$417$		0			0
$418$	−0.451318	+	0.781706i	−0.0220747	+	0.0382345i
$419$	−14.4180	−	12.0981i	−0.704365	−	0.591032i	0.218647	−	0.975804i	$-0.429836\pi$
$419$	−14.4180	−	12.0981i	−0.704365	−	0.591032i	−0.923012	+	0.384772i	$0.874280\pi$
$420$		0			0
$421$	8.96330	+	15.5249i	0.436844	+	0.756637i	0.997444	−	0.0714502i	$-0.0227627\pi$
$421$	8.96330	+	15.5249i	0.436844	+	0.756637i	−0.560600	+	0.828087i	$0.689429\pi$
$422$	−1.32920	+	0.483788i	−0.0647043	+	0.0235504i
$423$		0			0
$424$	1.06784	−	6.05602i	0.0518589	−	0.294107i
$425$	5.98623	−	5.02304i	0.290375	−	0.243653i
$426$		0			0
$427$	9.84712	−	55.8458i	0.476536	−	2.70257i
$428$	17.7223	−	6.45039i	0.856639	−	0.311791i
$429$		0			0
$430$	−3.35518	−	5.81133i	−0.161801	−	0.280247i
$431$	−2.12908	−	12.0746i	−0.102554	−	0.581613i	−0.992169	−	0.124902i	$-0.960138\pi$
$431$	−2.12908	−	12.0746i	−0.102554	−	0.581613i	0.889615	−	0.456711i	$-0.150973\pi$
$432$		0			0
$433$	−10.5573	+	18.2858i	−0.507351	+	0.878758i	0.492613	+	0.870249i	$0.336042\pi$
$433$	−10.5573	+	18.2858i	−0.507351	+	0.878758i	−0.999964	+	0.00850909i	$0.997291\pi$
$434$	13.8362	+	23.9651i	0.664161	+	1.15036i
$435$		0			0
$436$	4.20716	−	7.28702i	0.201486	−	0.348985i
$437$	0.188625	+	0.0686540i	0.00902318	+	0.00328417i
$438$		0			0
$439$	22.6396	+	8.24015i	1.08053	+	0.393281i	0.820105	−	0.572213i	$-0.193915\pi$
$439$	22.6396	+	8.24015i	1.08053	+	0.393281i	0.260425	+	0.965494i	$0.416137\pi$
$440$	0.290997	+	1.65033i	0.0138728	+	0.0786763i
$441$		0			0
$442$	3.99332	+	3.35080i	0.189943	+	0.159381i
$443$	−19.2348			−0.913871			−0.456936	−	0.889500i	$-0.651053\pi$
$443$	−19.2348			−0.913871			−0.456936	+	0.889500i	$0.651053\pi$
$444$		0			0
$445$	13.7523			0.651923
$446$	9.32663	+	7.82597i	0.441629	+	0.370570i
$447$		0			0
$448$	−0.837893	−	4.75193i	−0.0395867	−	0.224508i
$449$	−6.19008	−	2.25301i	−0.292128	−	0.106326i	0.191799	−	0.981434i	$-0.438568\pi$
$449$	−6.19008	−	2.25301i	−0.292128	−	0.106326i	−0.483927	+	0.875108i	$0.660790\pi$
$450$		0			0
$451$	2.99297	+	1.08935i	0.140934	+	0.0512956i
$452$	−3.19231	+	5.52924i	−0.150153	+	0.260073i
$453$		0			0
$454$	10.6500	+	18.4463i	0.499828	+	0.865727i
$455$	−6.54097	+	11.3293i	−0.306646	+	0.531126i
$456$		0			0
$457$	−5.03427	−	28.5507i	−0.235493	−	1.33555i	−0.841573	−	0.540144i	$-0.818370\pi$
$457$	−5.03427	−	28.5507i	−0.235493	−	1.33555i	0.606080	−	0.795404i	$-0.292741\pi$
$458$	−1.42480	−	2.46783i	−0.0665766	−	0.115314i
$459$		0			0
$460$	0.350192	−	0.127459i	0.0163278	−	0.00594283i
$461$	−6.22553	+	35.3067i	−0.289952	+	1.64440i	0.397089	+	0.917780i	$0.370020\pi$
$461$	−6.22553	+	35.3067i	−0.289952	+	1.64440i	−0.687041	+	0.726618i	$0.741091\pi$
$462$		0			0
$463$	−14.2350	+	11.9446i	−0.661556	+	0.555111i	−0.910553	−	0.413393i	$-0.864344\pi$
$463$	−14.2350	+	11.9446i	−0.661556	+	0.555111i	0.248997	+	0.968504i	$0.419899\pi$
$464$	0.967521	−	5.48708i	0.0449160	−	0.254731i
$465$		0			0
$466$	−22.0983	+	8.04313i	−1.02369	+	0.372591i
$467$	−0.823127	−	1.42570i	−0.0380898	−	0.0659734i	0.846352	−	0.532624i	$-0.178794\pi$
$467$	−0.823127	−	1.42570i	−0.0380898	−	0.0659734i	−0.884442	+	0.466650i	$0.845461\pi$
$468$		0			0
$469$	−33.2080	−	27.8648i	−1.53340	−	1.28668i
$470$	1.73508	−	3.00524i	0.0800332	−	0.138622i
$471$		0			0
$472$	1.53249	−	8.69116i	0.0705384	−	0.400043i
$473$	−2.39533	+	4.14884i	−0.110138	+	0.190764i
$474$		0			0
$475$	2.18911			0.100443
$476$	−13.3572	−	4.86162i	−0.612226	−	0.222832i
$477$		0			0
$478$	6.15757	−	5.16681i	0.281640	−	0.236324i
$479$	26.1002	+	21.9007i	1.19255	+	1.00067i	0.999811	+	0.0194166i	$0.00618087\pi$
$479$	26.1002	+	21.9007i	1.19255	+	1.00067i	0.192737	+	0.981250i	$0.438264\pi$
$480$		0			0
$481$	4.75723	+	9.65562i	0.216911	+	0.440258i
$482$	−18.4519			−0.840459
$483$		0			0
$484$	−7.51001	+	6.30164i	−0.341364	+	0.286438i
$485$	−1.15971	−	6.57703i	−0.0526596	−	0.298647i
$486$		0			0
$487$	−31.0898			−1.40881			−0.704407	−	0.709796i	$-0.748787\pi$
$487$	−31.0898			−1.40881			−0.704407	+	0.709796i	$0.748787\pi$
$488$	−11.0435	−	4.01950i	−0.499915	−	0.181954i
$489$		0			0
$490$	4.33197	−	24.5678i	0.195699	−	1.10986i
$491$	17.5270	+	30.3576i	0.790981	+	1.37002i	0.925360	+	0.379089i	$0.123763\pi$
$491$	17.5270	+	30.3576i	0.790981	+	1.37002i	−0.134379	+	0.990930i	$0.542904\pi$
$492$		0			0
$493$	−12.5735	−	10.5504i	−0.566280	−	0.475165i
$494$	0.253582	+	1.43813i	0.0114092	+	0.0647047i
$495$		0			0
$496$	5.38909	−	1.96147i	0.241977	−	0.0880725i
$497$	5.52562	−	2.01116i	0.247858	−	0.0902129i
$498$		0			0
$499$	−26.9427	+	22.6076i	−1.20612	+	1.01205i	−0.206686	+	0.978407i	$0.566268\pi$
$499$	−26.9427	+	22.6076i	−1.20612	+	1.01205i	−0.999434	+	0.0336472i	$0.989288\pi$
$500$	8.98158	−	7.53644i	0.401669	−	0.337040i
$501$		0			0
$502$	−21.8897	+	7.96718i	−0.976983	+	0.355593i
$503$	4.35300	−	1.58436i	0.194091	−	0.0706432i	−0.243146	−	0.969990i	$-0.578179\pi$
$503$	4.35300	−	1.58436i	0.194091	−	0.0706432i	0.437237	+	0.899346i	$0.355957\pi$
$504$		0			0
$505$	−1.16764	−	6.62201i	−0.0519593	−	0.294676i
$506$	−0.203810	−	0.171017i	−0.00906045	−	0.00760262i
$507$		0			0
$508$	2.37627	+	4.11582i	0.105430	+	0.182610i
$509$	4.14162	−	23.4883i	0.183574	−	1.04110i	−0.744199	−	0.667958i	$-0.767169\pi$
$509$	4.14162	−	23.4883i	0.183574	−	1.04110i	0.927774	−	0.373144i	$-0.121720\pi$
$510$		0			0
$511$	39.8749	+	14.5133i	1.76396	+	0.642029i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	−0.739191	−	4.19216i	−0.0326043	−	0.184908i
$515$	−14.8411	+	12.4531i	−0.653976	+	0.548751i
$516$		0			0
$517$	−2.47742			−0.108957
$518$	−21.1945	−	20.3042i	−0.931233	−	0.892115i
$519$		0			0
$520$	2.07686	+	1.74269i	0.0910765	+	0.0764222i
$521$	−14.8610	+	12.4698i	−0.651071	+	0.546313i	−0.907396	−	0.420278i	$-0.861933\pi$
$521$	−14.8610	+	12.4698i	−0.651071	+	0.546313i	0.256325	+	0.966591i	$0.417488\pi$
$522$		0			0
$523$	−1.82296	−	0.663503i	−0.0797125	−	0.0290130i	0.301856	−	0.953353i	$-0.402394\pi$
$523$	−1.82296	−	0.663503i	−0.0797125	−	0.0290130i	−0.381569	+	0.924341i	$0.624616\pi$
$524$	−17.9870			−0.785765
$525$		0			0
$526$	3.44273	−	5.96299i	0.150110	−	0.259999i
$527$	2.93366	−	16.6376i	0.127792	−	0.724747i
$528$		0			0
$529$	11.4704	−	19.8673i	0.498714	−	0.863798i
$530$	−7.21729	−	6.05602i	−0.313499	−	0.263057i
$531$		0			0
$532$	−1.99098	−	3.44847i	−0.0863198	−	0.149510i
$533$	4.84214	−	1.76240i	0.209737	−	0.0763379i
$534$		0			0
$535$	5.01751	−	28.4557i	0.216926	−	1.23025i
$536$	−6.88214	+	5.77480i	−0.297263	+	0.249434i
$537$		0			0
$538$	1.68016	−	9.52866i	0.0724368	−	0.410810i
$539$	−16.7360	+	6.09141i	−0.720872	+	0.262376i
$540$		0			0
$541$	2.15605	+	3.73439i	0.0926958	+	0.160554i	0.908645	−	0.417570i	$-0.137118\pi$
$541$	2.15605	+	3.73439i	0.0926958	+	0.160554i	−0.815949	+	0.578124i	$0.803785\pi$
$542$	−1.33063	−	7.54635i	−0.0571553	−	0.324144i
$543$		0			0
$544$	−1.47293	+	2.55118i	−0.0631511	+	0.109381i
$545$	−6.44574	−	11.1644i	−0.276105	−	0.478228i
$546$		0			0
$547$	−8.75830	+	15.1698i	−0.374478	+	0.648615i	−0.990249	−	0.139311i	$-0.955511\pi$
$547$	−8.75830	+	15.1698i	−0.374478	+	0.648615i	0.615771	+	0.787925i	$0.288845\pi$
$548$	20.7758	+	7.56177i	0.887498	+	0.323023i
$549$		0			0
$550$	−2.72652	−	0.992374i	−0.116259	−	0.0423150i
$551$	−0.798433	−	4.52814i	−0.0340144	−	0.192905i
$552$		0			0
$553$	−7.96071	−	6.67983i	−0.338524	−	0.284055i
$554$	−4.01957			−0.170775
$555$		0			0
$556$	−2.66547			−0.113041
$557$	−17.4740	−	14.6624i	−0.740398	−	0.621268i	0.192546	−	0.981288i	$-0.438325\pi$
$557$	−17.4740	−	14.6624i	−0.740398	−	0.621268i	−0.932945	+	0.360020i	$0.882770\pi$
$558$		0			0
$559$	1.34586	+	7.63278i	0.0569240	+	0.322832i
$560$	−6.94686	−	2.52845i	−0.293558	−	0.106846i
$561$		0			0
$562$	6.57717	+	2.39389i	0.277441	+	0.100980i
$563$	−13.2921	+	23.0226i	−0.560195	+	0.970287i	0.437284	+	0.899324i	$0.355941\pi$
$563$	−13.2921	+	23.0226i	−0.560195	+	0.970287i	−0.997479	+	0.0709631i	$0.977393\pi$
$564$		0			0
$565$	4.89090	+	8.47128i	0.205762	+	0.356389i
$566$	−2.35230	+	4.07430i	−0.0988746	+	0.171256i
$567$		0			0
$568$	−0.211615	−	1.20013i	−0.00887918	−	0.0503563i
$569$	−6.98492	−	12.0982i	−0.292823	−	0.507184i	0.681653	−	0.731676i	$-0.261261\pi$
$569$	−6.98492	−	12.0982i	−0.292823	−	0.507184i	−0.974476	+	0.224491i	$0.927928\pi$
$570$		0			0
$571$	−20.6390	+	7.51199i	−0.863717	+	0.314367i	−0.735620	−	0.677395i	$-0.763109\pi$
$571$	−20.6390	+	7.51199i	−0.863717	+	0.314367i	−0.128097	+	0.991762i	$0.540887\pi$
$572$	0.336105	−	1.90615i	0.0140533	−	0.0797000i
$573$		0			0
$574$	−10.7635	+	9.03167i	−0.449261	+	0.376975i
$575$	−0.112046	+	0.635443i	−0.00467263	+	0.0264998i
$576$		0			0
$577$	−29.6115	+	10.7777i	−1.23274	+	0.448682i	−0.874536	−	0.484961i	$-0.838834\pi$
$577$	−29.6115	+	10.7777i	−1.23274	+	0.448682i	−0.358207	+	0.933642i	$0.616612\pi$
$578$	−4.16098	−	7.20703i	−0.173074	−	0.299773i
$579$		0			0
$580$	−6.53925	−	5.48708i	−0.271528	−	0.227839i
$581$	−12.2894	+	21.2858i	−0.509849	+	0.883085i
$582$		0			0
$583$	−1.16800	+	6.62403i	−0.0483734	+	0.274339i
$584$	4.39709	−	7.61598i	0.181953	−	0.315151i
$585$		0			0
$586$	−14.2310			−0.587877
$587$	−39.3494	−	14.3220i	−1.62412	−	0.591133i	−0.639963	−	0.768406i	$-0.721050\pi$
$587$	−39.3494	−	14.3220i	−1.62412	−	0.591133i	−0.984162	+	0.177273i	$0.943273\pi$
$588$		0			0
$589$	3.62544	−	3.04211i	0.149384	−	0.125348i
$590$	−10.3577	−	8.69116i	−0.426421	−	0.357809i
$591$		0			0
$592$	−4.90673	+	3.59500i	−0.201665	+	0.147754i
$593$	30.7471			1.26263			0.631316	−	0.775525i	$-0.282515\pi$
$593$	30.7471			1.26263			0.631316	+	0.775525i	$0.282515\pi$
$594$		0			0
$595$	−16.6827	+	13.9985i	−0.683925	+	0.573881i
$596$	−1.06554	−	6.04300i	−0.0436463	−	0.247531i
$597$		0			0
$598$	−0.430434			−0.0176017
$599$	28.2700	+	10.2894i	1.15508	+	0.420415i	0.847337	−	0.531055i	$-0.178204\pi$
$599$	28.2700	+	10.2894i	1.15508	+	0.420415i	0.307742	+	0.951470i	$0.400427\pi$
$600$		0			0
$601$	5.27054	−	29.8907i	0.214990	−	1.21927i	−0.665935	−	0.746010i	$-0.731967\pi$
$601$	5.27054	−	29.8907i	0.214990	−	1.21927i	0.880924	−	0.473257i	$-0.156922\pi$
$602$	−10.5670	−	18.3025i	−0.430677	−	0.745954i
$603$		0			0
$604$	−0.334584	−	0.280749i	−0.0136140	−	0.0114235i
$605$	2.60820	+	14.7918i	0.106038	+	0.601373i
$606$		0			0
$607$	1.08095	−	0.393434i	0.0438744	−	0.0159690i	−0.319990	−	0.947421i	$-0.603679\pi$
$607$	1.08095	−	0.393434i	0.0438744	−	0.0159690i	0.363864	+	0.931452i	$0.381457\pi$
$608$	−0.775468	+	0.282247i	−0.0314494	+	0.0114466i
$609$		0			0
$610$	−13.7930	+	11.5737i	−0.558462	+	0.468605i
$611$	−3.07036	+	2.57634i	−0.124213	+	0.104227i
$612$		0			0
$613$	14.5282	−	5.28784i	0.586789	−	0.213574i	−0.0315273	−	0.999503i	$-0.510037\pi$
$613$	14.5282	−	5.28784i	0.586789	−	0.213574i	0.618317	+	0.785929i	$0.287815\pi$
$614$	0.754213	−	0.274511i	0.0304375	−	0.0110784i
$615$		0			0
$616$	0.916481	+	5.19762i	0.0369261	+	0.209418i
$617$	−16.0733	−	13.4871i	−0.647086	−	0.542970i	0.259099	−	0.965851i	$-0.416574\pi$
$617$	−16.0733	−	13.4871i	−0.647086	−	0.542970i	−0.906185	+	0.422881i	$0.861019\pi$
$618$		0			0
$619$	−15.4275	−	26.7212i	−0.620084	−	1.07402i	−0.989470	−	0.144741i	$-0.953765\pi$
$619$	−15.4275	−	26.7212i	−0.620084	−	1.07402i	0.369386	−	0.929276i	$-0.379568\pi$
$620$	1.52575	−	8.65296i	0.0612756	−	0.347511i
$621$		0			0
$622$	2.32051	+	0.844598i	0.0930441	+	0.0338653i
$623$	43.3122			1.73527
$624$		0			0
$625$	−0.816085	−	4.62825i	−0.0326434	−	0.185130i
$626$	13.6692	−	11.4698i	0.546331	−	0.458426i
$627$		0			0
$628$	6.06139			0.241876
$629$	1.94425	+	17.8131i	0.0775222	+	0.710255i
$630$		0			0
$631$	4.47641	+	3.75615i	0.178203	+	0.149530i	0.727526	−	0.686080i	$-0.240670\pi$
$631$	4.47641	+	3.75615i	0.178203	+	0.149530i	−0.549323	+	0.835610i	$0.685114\pi$
$632$	−1.64981	+	1.38435i	−0.0656258	+	0.0550666i
$633$		0			0
$634$	−3.32609	−	1.21060i	−0.132096	−	0.0480790i
$635$	7.28131			0.288950
$636$		0			0
$637$	−14.4069	+	24.9535i	−0.570824	+	0.988695i
$638$	−1.05827	+	6.00173i	−0.0418972	+	0.237611i
$639$		0			0
$640$	−0.766044	+	1.32683i	−0.0302806	+	0.0524475i
$641$	−22.8599	−	19.1817i	−0.902912	−	0.757633i	0.0678451	−	0.997696i	$-0.478388\pi$
$641$	−22.8599	−	19.1817i	−0.902912	−	0.757633i	−0.970757	+	0.240062i	$0.922832\pi$
$642$		0			0
$643$	−7.18117	−	12.4382i	−0.283198	−	0.490513i	0.688973	−	0.724787i	$-0.258062\pi$
$643$	−7.18117	−	12.4382i	−0.283198	−	0.490513i	−0.972171	+	0.234274i	$0.924729\pi$
$644$	1.10291	−	0.401427i	0.0434608	−	0.0158184i
$645$		0			0
$646$	−0.422142	+	2.39409i	−0.0166090	+	0.0941941i
$647$	−7.11852	+	5.97315i	−0.279858	+	0.234829i	−0.771902	−	0.635742i	$-0.780694\pi$
$647$	−7.11852	+	5.97315i	−0.279858	+	0.234829i	0.492044	+	0.870570i	$0.336250\pi$
$648$		0			0
$649$	−1.67622	+	9.50632i	−0.0657974	+	0.373156i
$650$	−4.41108	+	1.60550i	−0.173017	+	0.0629729i
$651$		0			0
$652$	−6.86747	−	11.8948i	−0.268951	−	0.465837i
$653$	7.38987	+	41.9101i	0.289188	+	1.64007i	0.689930	+	0.723876i	$0.257641\pi$
$653$	7.38987	+	41.9101i	0.289188	+	1.64007i	−0.400742	+	0.916191i	$0.631248\pi$
$654$		0			0
$655$	−13.7788	+	23.8656i	−0.538383	+	0.932507i
$656$	1.45597	+	2.52181i	0.0568460	+	0.0984602i
$657$		0			0
$658$	5.46454	−	9.46486i	0.213030	−	0.368979i
$659$	10.3196	+	3.75603i	0.401995	+	0.146314i	0.535102	−	0.844788i	$-0.320273\pi$
$659$	10.3196	+	3.75603i	0.401995	+	0.146314i	−0.133107	+	0.991102i	$0.542495\pi$
$660$		0			0
$661$	−31.5074	−	11.4678i	−1.22550	−	0.446044i	−0.353444	−	0.935456i	$-0.614989\pi$
$661$	−31.5074	−	11.4678i	−1.22550	−	0.446044i	−0.872053	+	0.489412i	$0.837212\pi$
$662$	−0.664426	−	3.76815i	−0.0258237	−	0.146453i
$663$		0			0
$664$	3.90207	+	3.27423i	0.151430	+	0.127065i
$665$	−6.10071			−0.236575
$666$		0			0
$667$	1.35527			0.0524764
$668$	−18.2471	−	15.3112i	−0.706003	−	0.592407i
$669$		0			0
$670$	2.39014	+	13.5552i	0.0923393	+	0.523682i
$671$	12.0793	+	4.39650i	0.466316	+	0.169725i
$672$		0			0
$673$	41.1753	+	14.9866i	1.58719	+	0.577691i	0.976752	−	0.214372i	$-0.0687704\pi$
$673$	41.1753	+	14.9866i	1.58719	+	0.577691i	0.610440	+	0.792063i	$0.290993\pi$
$674$	−10.6981	+	18.5297i	−0.412076	+	0.713737i
$675$		0			0
$676$	4.93430	+	8.54645i	0.189781	+	0.328710i
$677$	−1.08790	+	1.88429i	−0.0418113	+	0.0724192i	−0.886174	−	0.463353i	$-0.846646\pi$
$677$	−1.08790	+	1.88429i	−0.0418113	+	0.0724192i	0.844362	+	0.535772i	$0.179979\pi$
$678$		0			0
$679$	−3.65244	−	20.7140i	−0.140168	−	0.794931i
$680$	2.25665	+	3.90864i	0.0865387	+	0.149889i
$681$		0			0
$682$	−5.89454	+	2.14544i	−0.225714	+	0.0821531i
$683$	5.50558	−	31.2237i	0.210665	−	1.19474i	−0.677607	−	0.735424i	$-0.736983\pi$
$683$	5.50558	−	31.2237i	0.210665	−	1.19474i	0.888272	−	0.459318i	$-0.151906\pi$
$684$		0			0
$685$	25.9484	−	21.7733i	0.991436	−	0.831913i
$686$	7.77808	−	44.1117i	0.296968	−	1.68419i
$687$		0			0
$688$	−4.11573	+	1.49800i	−0.156911	+	0.0571109i
$689$	5.44097	+	9.42403i	0.207284	+	0.359027i
$690$		0			0
$691$	19.5271	+	16.3852i	0.742847	+	0.623323i	0.933601	−	0.358315i	$-0.116649\pi$
$691$	19.5271	+	16.3852i	0.742847	+	0.623323i	−0.190754	+	0.981638i	$0.561093\pi$
$692$	10.7226	−	18.5721i	0.407612	−	0.706004i
$693$		0			0
$694$	−4.45169	+	25.2468i	−0.168984	+	0.958355i
$695$	−2.04187	+	3.53662i	−0.0774525	+	0.134152i
$696$		0			0
$697$	8.57813			0.324920
$698$	14.5983	+	5.31334i	0.552553	+	0.201113i
$699$		0			0
$700$	9.80531	−	8.22763i	0.370606	−	0.310975i
$701$	13.7802	+	11.5629i	0.520470	+	0.436726i	0.864796	−	0.502124i	$-0.167448\pi$
$701$	13.7802	+	11.5629i	0.520470	+	0.436726i	−0.344325	+	0.938850i	$0.611892\pi$
$702$		0			0
$703$	−2.79033	+	4.17272i	−0.105239	+	0.157377i
$704$	1.09379			0.0412238
$705$		0			0
$706$	−1.03899	+	0.871818i	−0.0391030	+	0.0328113i
$707$	−3.67742	−	20.8557i	−0.138304	−	0.784359i
$708$		0			0
$709$	27.8902			1.04744			0.523719	−	0.851891i	$-0.324544\pi$
$709$	27.8902			1.04744			0.523719	+	0.851891i	$0.324544\pi$
$710$	−1.75447	−	0.638576i	−0.0658442	−	0.0239653i
$711$		0			0
$712$	1.55870	−	8.83982i	0.0584147	−	0.331286i
$713$	0.697487	+	1.20808i	0.0261211	+	0.0452430i
$714$		0			0
$715$	−2.27166	−	1.90615i	−0.0849551	−	0.0712858i
$716$	−2.00125	−	11.3497i	−0.0747903	−	0.424157i
$717$		0			0
$718$	20.9690	−	7.63208i	0.782555	−	0.284827i
$719$	−25.7753	+	9.38145i	−0.961257	+	0.349869i	−0.774526	−	0.632542i	$-0.782012\pi$
$719$	−25.7753	+	9.38145i	−0.961257	+	0.349869i	−0.186731	+	0.982411i	$0.559789\pi$
$720$		0			0
$721$	−46.7412	+	39.2205i	−1.74073	+	1.46065i
$722$	14.0332	−	11.7752i	0.522260	−	0.438228i
$723$		0			0
$724$	16.6973	−	6.07731i	0.620549	−	0.225861i
$725$	13.8888	−	5.05511i	0.515817	−	0.187742i
$726$		0			0
$727$	1.76832	+	10.0286i	0.0655832	+	0.371941i	0.999881	+	0.0154465i	$0.00491696\pi$
$727$	1.76832	+	10.0286i	0.0655832	+	0.371941i	−0.934298	+	0.356494i	$0.883972\pi$
$728$	6.54097	+	5.48853i	0.242425	+	0.203418i
$729$		0			0
$730$	−6.73673	−	11.6684i	−0.249338	−	0.431865i
$731$	−2.24049	+	12.7064i	−0.0828673	+	0.469964i
$732$		0			0
$733$	33.0879	+	12.0430i	1.22213	+	0.444819i	0.870895	−	0.491469i	$-0.163540\pi$
$733$	33.0879	+	12.0430i	1.22213	+	0.444819i	0.351234	+	0.936288i	$0.385762\pi$
$734$	−7.22844			−0.266807
$735$		0			0
$736$	−0.0422383	−	0.239545i	−0.00155693	−	0.00882976i
$737$	7.52763	−	6.31643i	0.277284	−	0.232669i
$738$		0			0
$739$	−8.78122			−0.323022			−0.161511	−	0.986871i	$-0.551637\pi$
$739$	−8.78122			−0.323022			−0.161511	+	0.986871i	$0.551637\pi$
$740$	1.01117	+	9.26431i	0.0371714	+	0.340563i
$741$		0			0
$742$	−22.7305	−	19.0731i	−0.834462	−	0.700197i
$743$	−11.2952	+	9.47778i	−0.414380	+	0.347706i	−0.826020	−	0.563640i	$-0.809400\pi$
$743$	−11.2952	+	9.47778i	−0.414380	+	0.347706i	0.411640	+	0.911346i	$0.364956\pi$
$744$		0			0
$745$	−8.83427	−	3.21541i	−0.323663	−	0.117804i
$746$	11.7328			0.429570
$747$		0			0
$748$	1.61107	−	2.79046i	0.0589067	−	0.102029i
$749$	15.8024	−	89.6198i	0.577407	−	3.27464i
$750$		0			0
$751$	17.4428	−	30.2118i	0.636496	−	1.10244i	−0.349700	−	0.936862i	$-0.613716\pi$
$751$	17.4428	−	30.2118i	0.636496	−	1.10244i	0.986196	−	0.165582i	$-0.0529503\pi$
$752$	−1.73508	−	1.45590i	−0.0632718	−	0.0530914i
$753$		0			0
$754$	4.92981	+	8.53868i	0.179533	+	0.310960i
$755$	−0.628812	+	0.228869i	−0.0228848	+	0.00832939i
$756$		0			0
$757$	9.03260	−	51.2264i	0.328296	−	1.86186i	−0.157129	−	0.987578i	$-0.550224\pi$
$757$	9.03260	−	51.2264i	0.328296	−	1.86186i	0.485425	−	0.874278i	$-0.338665\pi$
$758$	2.12027	−	1.77912i	0.0770117	−	0.0646205i
$759$		0			0
$760$	−0.219549	+	1.24513i	−0.00796389	+	0.0451655i
$761$	5.60441	−	2.03984i	0.203160	−	0.0739441i	−0.238436	−	0.971158i	$-0.576635\pi$
$761$	5.60441	−	2.03984i	0.203160	−	0.0739441i	0.441596	+	0.897214i	$0.354413\pi$
$762$		0			0
$763$	−20.3005	−	35.1616i	−0.734929	−	1.27293i
$764$	4.49945	+	25.5176i	0.162784	+	0.923195i
$765$		0			0
$766$	−9.73583	+	16.8629i	−0.351770	+	0.609283i
$767$	7.80847	+	13.5247i	0.281948	+	0.488348i
$768$		0			0
$769$	−18.5451	+	32.1210i	−0.668753	+	1.15831i	0.309500	+	0.950900i	$0.399838\pi$
$769$	−18.5451	+	32.1210i	−0.668753	+	1.15831i	−0.978253	+	0.207415i	$0.933495\pi$
$770$	7.59842	+	2.76560i	0.273828	+	0.0996652i
$771$		0			0
$772$	−10.2454	−	3.72904i	−0.368742	−	0.134211i
$773$	0.552148	+	3.13139i	0.0198594	+	0.112628i	0.993126	−	0.117050i	$-0.0373438\pi$
$773$	0.552148	+	3.13139i	0.0198594	+	0.112628i	−0.973267	+	0.229678i	$0.926233\pi$
$774$		0			0
$775$	11.6539	+	9.77880i	0.418621	+	0.351265i
$776$	−4.35907			−0.156482
$777$		0			0
$778$	−2.34776			−0.0841713
$779$	1.84083	+	1.54464i	0.0659546	+	0.0553425i
$780$		0			0
$781$	0.231463	+	1.31269i	0.00828240	+	0.0469718i
$782$	−0.673338	−	0.245075i	−0.0240785	−	0.00876386i
$783$		0			0
$784$	−15.3009	−	5.56908i	−0.546461	−	0.198896i
$785$	4.64329	−	8.04242i	0.165726	−	0.287046i
$786$		0			0
$787$	2.62525	+	4.54707i	0.0935802	+	0.162086i	0.909015	−	0.416763i	$-0.136836\pi$
$787$	2.62525	+	4.54707i	0.0935802	+	0.162086i	−0.815435	+	0.578849i	$0.803502\pi$
$788$	−3.22157	+	5.57992i	−0.114764	+	0.198777i
$789$		0			0
$790$	0.572972	+	3.24949i	0.0203854	+	0.115612i
$791$	15.4036	+	26.6799i	0.547690	+	0.948627i
$792$		0			0
$793$	19.5423	−	7.11283i	0.693968	−	0.252584i
$794$	−0.395132	+	2.24091i	−0.0140227	+	0.0795268i
$795$		0			0
$796$	14.4442	−	12.1201i	0.511961	−	0.429587i
$797$	−4.62443	+	26.2264i	−0.163806	+	0.928988i	0.786482	+	0.617614i	$0.211900\pi$
$797$	−4.62443	+	26.2264i	−0.163806	+	0.928988i	−0.950287	+	0.311375i	$0.899211\pi$
$798$		0			0
$799$	−6.26992	+	2.28206i	−0.221814	+	0.0807336i
$800$	−1.32635	−	2.29731i	−0.0468936	−	0.0812221i
$801$		0			0
$802$	13.4427	+	11.2798i	0.474679	+	0.398303i
$803$	−4.80950	+	8.33030i	−0.169724	+	0.293970i
$804$		0			0
$805$	0.312255	−	1.77089i	0.0110055	−	0.0624155i
$806$	−5.07422	+	8.78881i	−0.178732	+	0.309573i
$807$		0			0
$808$	−4.38889			−0.154401
$809$	−14.5826	−	5.30762i	−0.512696	−	0.186606i	0.0726995	−	0.997354i	$-0.476839\pi$
$809$	−14.5826	−	5.30762i	−0.512696	−	0.186606i	−0.585396	+	0.810748i	$0.699061\pi$
$810$		0			0
$811$	25.0817	−	21.0460i	0.880737	−	0.739026i	−0.0855938	−	0.996330i	$-0.527279\pi$
$811$	25.0817	−	21.0460i	0.880737	−	0.739026i	0.966330	+	0.257304i	$0.0828343\pi$
$812$	−20.5950	−	17.2813i	−0.722744	−	0.606454i
$813$		0			0
$814$	5.36694	−	3.93218i	0.188111	−	0.137823i
$815$	−21.0432			−0.737110
$816$		0			0
$817$	−2.76881	+	2.32331i	−0.0968684	+	0.0812822i
$818$	−3.93815	−	22.3343i	−0.137694	−	0.780902i
$819$		0			0
$820$	4.46135			0.155797
$821$	−11.4303	−	4.16028i	−0.398920	−	0.145195i	0.134767	−	0.990877i	$-0.456972\pi$
$821$	−11.4303	−	4.16028i	−0.398920	−	0.145195i	−0.533686	+	0.845682i	$0.679194\pi$
$822$		0			0
$823$	3.78732	−	21.4790i	0.132018	−	0.748709i	−0.844873	−	0.534968i	$-0.820324\pi$
$823$	3.78732	−	21.4790i	0.132018	−	0.748709i	0.976890	−	0.213742i	$-0.0685651\pi$
$824$	6.32262	+	10.9511i	0.220259	+	0.381500i
$825$		0			0
$826$	−32.6211	−	27.3724i	−1.13503	−	0.952406i
$827$	2.00178	+	11.3526i	0.0696086	+	0.394770i	0.999628	+	0.0272604i	$0.00867834\pi$
$827$	2.00178	+	11.3526i	0.0696086	+	0.394770i	−0.930020	+	0.367509i	$0.880211\pi$
$828$		0			0
$829$	9.86084	−	3.58905i	0.342481	−	0.124653i	−0.165053	−	0.986285i	$-0.552779\pi$
$829$	9.86084	−	3.58905i	0.342481	−	0.124653i	0.507534	+	0.861632i	$0.330557\pi$
$830$	7.33349	−	2.66917i	0.254549	−	0.0926484i
$831$		0			0
$832$	1.35558	−	1.13746i	0.0469961	−	0.0394344i
$833$	−36.7448	+	30.8326i	−1.27313	+	1.06829i
$834$		0			0
$835$	−34.2934	+	12.4818i	−1.18677	+	0.431950i
$836$	0.848200	−	0.308720i	0.0293356	−	0.0106773i
$837$		0			0
$838$	3.26829	+	18.5354i	0.112901	+	0.640295i
$839$	21.1557	+	17.7517i	0.730375	+	0.612857i	0.930234	−	0.366968i	$-0.119604\pi$
$839$	21.1557	+	17.7517i	0.730375	+	0.612857i	−0.199859	+	0.979825i	$0.564048\pi$
$840$		0			0
$841$	−1.02209	−	1.77032i	−0.0352446	−	0.0610455i
$842$	3.11292	−	17.6543i	0.107278	−	0.608406i
$843$		0			0
$844$	1.32920	+	0.483788i	0.0457528	+	0.0166527i
$845$	15.1196			0.520129
$846$		0			0
$847$	8.21439	+	46.5861i	0.282250	+	1.60072i
$848$	−4.71075	+	3.95279i	−0.161768	+	0.135739i
$849$		0			0
$850$	−7.81447			−0.268034
$851$	−1.06842	−	1.02354i	−0.0366249	−	0.0350864i
$852$		0			0
$853$	15.8103	+	13.2664i	0.541334	+	0.454233i	0.871994	−	0.489517i	$-0.162827\pi$
$853$	15.8103	+	13.2664i	0.541334	+	0.454233i	−0.330660	+	0.943750i	$0.607271\pi$
$854$	−43.4403	+	36.4508i	−1.48650	+	1.24732i
$855$		0			0
$856$	−17.7223	−	6.45039i	−0.605735	−	0.220470i
$857$	−31.3189			−1.06983			−0.534917	−	0.844905i	$-0.679657\pi$
$857$	−31.3189			−1.06983			−0.534917	+	0.844905i	$0.679657\pi$
$858$		0			0
$859$	−22.7736	+	39.4450i	−0.777025	+	1.34585i	0.156624	+	0.987658i	$0.449939\pi$
$859$	−22.7736	+	39.4450i	−0.777025	+	1.34585i	−0.933649	+	0.358189i	$0.883394\pi$
$860$	−1.16524	+	6.60840i	−0.0397344	+	0.225345i
$861$		0			0
$862$	−6.13043	+	10.6182i	−0.208803	+	0.361658i
$863$	38.4587	+	32.2707i	1.30915	+	1.09851i	0.988486	+	0.151314i	$0.0483503\pi$
$863$	38.4587	+	32.2707i	1.30915	+	1.09851i	0.320664	+	0.947193i	$0.396094\pi$
$864$		0			0
$865$	−16.4280	−	28.4541i	−0.558567	−	0.967467i
$866$	19.8412	−	7.22161i	0.674232	−	0.245400i
$867$		0			0
$868$	4.80527	−	27.2521i	0.163102	−	0.924995i
$869$	1.80455	−	1.51419i	0.0612151	−	0.0513655i
$870$		0			0
$871$	2.76064	−	15.6564i	0.0935407	−	0.530496i
$872$	−7.90687	+	2.87787i	−0.267761	+	0.0974569i
$873$		0			0
$874$	−0.100365	−	0.173838i	−0.00339491	−	0.00588016i
$875$	−9.82398	−	55.7146i	−0.332111	−	1.88350i
$876$		0			0
$877$	−15.8566	+	27.4644i	−0.535439	+	0.927408i	0.463702	+	0.885991i	$0.346521\pi$
$877$	−15.8566	+	27.4644i	−0.535439	+	0.927408i	−0.999142	+	0.0414174i	$0.986813\pi$
$878$	−12.0463	−	20.8648i	−0.406543	−	0.704153i
$879$		0			0
$880$	0.837893	−	1.45127i	0.0282454	−	0.0489224i
$881$	27.9167	+	10.1609i	0.940538	+	0.342328i	0.766378	−	0.642390i	$-0.222057\pi$
$881$	27.9167	+	10.1609i	0.940538	+	0.342328i	0.174160	+	0.984717i	$0.444279\pi$
$882$		0			0
$883$	−14.6477	−	5.33132i	−0.492934	−	0.179413i	0.0835793	−	0.996501i	$-0.473365\pi$
$883$	−14.6477	−	5.33132i	−0.492934	−	0.179413i	−0.576513	+	0.817088i	$0.695587\pi$
$884$	−0.905213	−	5.13372i	−0.0304456	−	0.172666i
$885$		0			0
$886$	14.7347	+	12.3639i	0.495021	+	0.415372i
$887$	39.8038			1.33648			0.668240	−	0.743946i	$-0.267048\pi$
$887$	39.8038			1.33648			0.668240	+	0.743946i	$0.267048\pi$
$888$		0			0
$889$	22.9321			0.769118
$890$	−10.5349	−	8.83982i	−0.353130	−	0.296312i
$891$		0			0
$892$	−2.11418	−	11.9901i	−0.0707878	−	0.401458i
$893$	−1.75642	−	0.639285i	−0.0587764	−	0.0213929i
$894$		0			0
$895$	−16.5921	−	6.03903i	−0.554612	−	0.201862i
$896$	−2.41262	+	4.17878i	−0.0805999	+	0.139603i
$897$		0			0
$898$	3.29367	+	5.70481i	0.109911	+	0.190372i
$899$	15.9768	−	27.6726i	0.532856	−	0.922933i
$900$		0			0
$901$	3.14570	+	17.8401i	0.104798	+	0.594341i
$902$	−1.59253	−	2.75834i	−0.0530253	−	0.0918426i
$903$		0			0
$904$	5.99957	−	2.18367i	0.199543	−	0.0726276i
$905$	4.72730	−	26.8099i	0.157141	−	0.891190i
$906$		0			0
$907$	34.4417	−	28.9000i	1.14362	−	0.959610i	0.144067	−	0.989568i	$-0.453982\pi$
$907$	34.4417	−	28.9000i	1.14362	−	0.959610i	0.999551	+	0.0299580i	$0.00953737\pi$
$908$	3.69870	−	20.9763i	0.122746	−	0.696124i
$909$		0			0
$910$	12.2930	−	4.47429i	0.407509	−	0.148321i
$911$	−7.10212	−	12.3012i	−0.235304	−	0.407558i	0.724057	−	0.689740i	$-0.242275\pi$
$911$	−7.10212	−	12.3012i	−0.235304	−	0.407558i	−0.959361	+	0.282182i	$0.908942\pi$
$912$		0			0
$913$	−4.26805	−	3.58132i	−0.141252	−	0.118524i
$914$	−14.4956	+	25.1071i	−0.479472	+	0.830469i
$915$		0			0
$916$	−0.494828	+	2.80631i	−0.0163496	+	0.0927231i
$917$	−43.3957	+	75.1636i	−1.43305	+	2.48212i
$918$		0			0
$919$	46.2177			1.52458			0.762291	−	0.647235i	$-0.224075\pi$
$919$	46.2177			1.52458			0.762291	+	0.647235i	$0.224075\pi$
$920$	−0.350192	−	0.127459i	−0.0115455	−	0.00420221i
$921$		0			0
$922$	27.4638	−	23.0448i	0.904471	−	0.758941i
$923$	1.65196	+	1.38616i	0.0543750	+	0.0456261i
$924$		0			0
$925$	−14.7669	−	6.50404i	−0.485532	−	0.213851i
$926$	18.5824			0.610657
$927$		0			0
$928$	−4.26819	+	3.58144i	−0.140110	+	0.117567i
$929$	9.34083	+	52.9745i	0.306463	+	1.73804i	0.616539	+	0.787325i	$0.288534\pi$
$929$	9.34083	+	52.9745i	0.306463	+	1.73804i	−0.310076	+	0.950712i	$0.600355\pi$
$930$		0			0
$931$	−13.4372			−0.440387
$932$	22.0983	+	8.04313i	0.723855	+	0.263462i
$933$		0			0
$934$	−0.285869	+	1.62124i	−0.00935392	+	0.0530487i
$935$	−2.46831	−	4.27524i	−0.0807223	−	0.139815i
$936$		0			0
$937$	−30.8185	−	25.8598i	−1.00680	−	0.844803i	−0.0188857	−	0.999822i	$-0.506012\pi$
$937$	−30.8185	−	25.8598i	−1.00680	−	0.844803i	−0.987912	+	0.155018i	$0.950456\pi$
$938$	7.52763	+	42.6913i	0.245786	+	1.39392i
$939$		0			0
$940$	−3.26088	+	1.18686i	−0.106358	+	0.0387112i
$941$	−1.65197	+	0.601267i	−0.0538526	+	0.0196007i	−0.368806	−	0.929506i	$-0.620233\pi$
$941$	−1.65197	+	0.601267i	−0.0538526	+	0.0196007i	0.314953	+	0.949107i	$0.398011\pi$
$942$		0			0
$943$	−0.542591	+	0.455288i	−0.0176692	+	0.0148262i
$944$	−6.76052	+	5.67275i	−0.220036	+	0.184632i
$945$		0			0
$946$	4.50175	−	1.63850i	0.146365	−	0.0532724i
$947$	47.7122	−	17.3658i	1.55044	−	0.564313i	0.581917	−	0.813248i	$-0.302303\pi$
$947$	47.7122	−	17.3658i	1.55044	−	0.564313i	0.968520	+	0.248935i	$0.0800804\pi$
$948$		0			0
$949$	2.70231	+	15.3256i	0.0877207	+	0.497489i
$950$	−1.67695	−	1.40713i	−0.0544075	−	0.0456533i
$951$		0			0
$952$	7.10721	+	12.3100i	0.230346	+	0.398971i
$953$	−4.28306	+	24.2904i	−0.138742	+	0.786845i	0.833439	+	0.552612i	$0.186369\pi$
$953$	−4.28306	+	24.2904i	−0.138742	+	0.786845i	−0.972181	+	0.234233i	$0.924742\pi$
$954$		0			0
$955$	37.3043	+	13.5776i	1.20714	+	0.439362i
$956$	−8.03813			−0.259972
$957$		0			0
$958$	−5.91643	−	33.5538i	−0.191151	−	1.08407i
$959$	81.7230	−	68.5738i	2.63897	−	2.21436i
$960$		0			0
$961$	1.88962			0.0609556
$962$	2.56227	−	10.4545i	0.0826107	−	0.337067i
$963$		0			0
$964$	14.1349	+	11.8606i	0.455256	+	0.382005i
$965$	−12.7963	+	10.7373i	−0.411926	+	0.345647i
$966$		0			0
$967$	29.2331	+	10.6400i	0.940073	+	0.342158i	0.766194	−	0.642609i	$-0.222148\pi$
$967$	29.2331	+	10.6400i	0.940073	+	0.342158i	0.173878	+	0.984767i	$0.444370\pi$
$968$	9.80362			0.315100
$969$		0			0
$970$	−3.33924	+	5.78374i	−0.107217	+	0.185705i
$971$	−3.59887	+	20.4102i	−0.115493	+	0.654995i	0.871011	+	0.491263i	$0.163464\pi$
$971$	−3.59887	+	20.4102i	−0.115493	+	0.654995i	−0.986505	+	0.163732i	$0.947647\pi$
$972$		0			0
$973$	−6.43076	+	11.1384i	−0.206161	+	0.357081i
$974$	23.8162	+	19.9842i	0.763120	+	0.640334i
$975$		0			0
$976$	5.87612	+	10.1777i	0.188090	+	0.325781i
$977$	−25.9583	+	9.44805i	−0.830480	+	0.302270i	−0.722056	−	0.691835i	$-0.756803\pi$
$977$	−25.9583	+	9.44805i	−0.830480	+	0.302270i	−0.108424	+	0.994105i	$0.534580\pi$
$978$		0			0
$979$	−1.70489	+	9.66893i	−0.0544886	+	0.309020i
$980$	−19.1104	+	16.0355i	−0.610459	+	0.512236i
$981$		0			0
$982$	6.08705	−	34.5214i	0.194246	−	1.10162i
$983$	−29.9156	+	10.8884i	−0.954159	+	0.347285i	−0.771742	−	0.635936i	$-0.780614\pi$
$983$	−29.9156	+	10.8884i	−0.954159	+	0.347285i	−0.182417	+	0.983221i	$0.558392\pi$
$984$		0			0
$985$	4.93573	+	8.54894i	0.157265	+	0.272392i
$986$	2.85017	+	16.1641i	0.0907680	+	0.514771i
$987$		0			0
$988$	0.730160	−	1.26467i	0.0232295	−	0.0402346i
$989$	−0.532682	−	0.922632i	−0.0169383	−	0.0293380i
$990$		0			0
$991$	−0.0451636	+	0.0782257i	−0.00143467	+	0.00248492i	−0.866742	−	0.498757i	$-0.833790\pi$
$991$	−0.0451636	+	0.0782257i	−0.00143467	+	0.00248492i	0.865307	+	0.501242i	$0.167123\pi$
$992$	−5.38909	−	1.96147i	−0.171104	−	0.0622767i
$993$		0			0
$994$	−5.52562	−	2.01116i	−0.175262	−	0.0637902i
$995$	−5.01642	−	28.4495i	−0.159031	−	0.901911i
$996$		0			0
$997$	35.7709	+	30.0153i	1.13288	+	0.950595i	0.999182	−	0.0404277i	$-0.0128720\pi$
$997$	35.7709	+	30.0153i	1.13288	+	0.950595i	0.133693	+	0.991023i	$0.457316\pi$
$998$	35.1712			1.11332
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	666.2.x.g.145.2		12
3.2	odd	2		74.2.f.b.71.1	yes	12
12.11	even	2		592.2.bc.d.145.2		12
37.12	even	9	inner	666.2.x.g.271.2		12
111.44	odd	18		2738.2.a.t.1.1		6
111.86	odd	18		74.2.f.b.49.1	✓	12
111.104	odd	18		2738.2.a.q.1.1		6
444.419	even	18		592.2.bc.d.49.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.2.f.b.49.1	✓	12	111.86	odd	18
74.2.f.b.71.1	yes	12	3.2	odd	2
592.2.bc.d.49.2		12	444.419	even	18
592.2.bc.d.145.2		12	12.11	even	2
666.2.x.g.145.2		12	1.1	even	1	trivial
666.2.x.g.271.2		12	37.12	even	9	inner
2738.2.a.q.1.1		6	111.104	odd	18
2738.2.a.t.1.1		6	111.44	odd	18

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:	\( N \)	\(=\)	\( 666 = 2 \cdot 3^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	666.x (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.766044 - 0.642788i) q^{2} +(0.173648 + 0.984808i) q^{4} +(1.43969 + 0.524005i) q^{5} +(4.53424 + 1.65033i) q^{7} +(0.500000 - 0.866025i) q^{8} +O(q^{10})\)	\(q+(-0.766044 - 0.642788i) q^{2} +(0.173648 + 0.984808i) q^{4} +(1.43969 + 0.524005i) q^{5} +(4.53424 + 1.65033i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-0.766044 - 1.32683i) q^{10} +(-0.546896 + 0.947252i) q^{11} +(0.307284 + 1.74269i) q^{13} +(-2.41262 - 4.17878i) q^{14} +(-0.939693 + 0.342020i) q^{16} +(-0.511542 + 2.90110i) q^{17} +(-0.632167 + 0.530451i) q^{19} +(-0.266044 + 1.50881i) q^{20} +(1.02783 - 0.374099i) q^{22} +(-0.121620 - 0.210653i) q^{23} +(-2.03209 - 1.70513i) q^{25} +(0.884789 - 1.53250i) q^{26} +(-0.837893 + 4.75193i) q^{28} +(-2.78587 + 4.82526i) q^{29} -5.73495 q^{31} +(0.939693 + 0.342020i) q^{32} +(2.25665 - 1.89356i) q^{34} +(5.66313 + 4.75193i) q^{35} +(5.84038 - 1.69999i) q^{37} +0.825235 q^{38} +(1.17365 - 0.984808i) q^{40} +(-0.505653 - 2.86770i) q^{41} +4.37987 q^{43} +(-1.02783 - 0.374099i) q^{44} +(-0.0422383 + 0.239545i) q^{46} +(1.13249 + 1.96153i) q^{47} +(12.4734 + 10.4664i) q^{49} +(0.460637 + 2.61240i) q^{50} +(-1.66286 + 0.605232i) q^{52} +(5.77859 - 2.10324i) q^{53} +(-1.28373 + 1.07717i) q^{55} +(3.69634 - 3.10160i) q^{56} +(5.23571 - 1.90564i) q^{58} +(8.29301 - 3.01841i) q^{59} +(-2.04075 - 11.5737i) q^{61} +(4.39322 + 3.68635i) q^{62} +(-0.500000 - 0.866025i) q^{64} +(-0.470787 + 2.66996i) q^{65} +(-8.44220 - 3.07271i) q^{67} -2.94585 q^{68} +(-1.28373 - 7.28038i) q^{70} +(0.933535 - 0.783329i) q^{71} +8.79418 q^{73} +(-5.56672 - 2.45185i) q^{74} +(-0.632167 - 0.530451i) q^{76} +(-4.04303 + 3.39251i) q^{77} +(-2.02379 - 0.736599i) q^{79} -1.53209 q^{80} +(-1.45597 + 2.52181i) q^{82} +(-0.884528 + 5.01641i) q^{83} +(-2.25665 + 3.90864i) q^{85} +(-3.35518 - 2.81533i) q^{86} +(0.546896 + 0.947252i) q^{88} +(8.43486 - 3.07004i) q^{89} +(-1.48272 + 8.40891i) q^{91} +(0.186333 - 0.156352i) q^{92} +(0.393310 - 2.23057i) q^{94} +(-1.18809 + 0.432428i) q^{95} +(-2.17954 - 3.77507i) q^{97} +(-2.82750 - 16.0355i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{5} + 6 q^{7} + 6 q^{8}+O(q^{10}) \) 12 * q + 6 * q^5 + 6 * q^7 + 6 * q^8	\( 12 q + 6 q^{5} + 6 q^{7} + 6 q^{8} - 3 q^{11} - 6 q^{13} - 3 q^{14} + 3 q^{17} - 3 q^{19} + 6 q^{20} - 3 q^{22} + 21 q^{23} - 6 q^{25} - 3 q^{28} - 6 q^{29} + 42 q^{31} - 3 q^{34} + 9 q^{35} - 3 q^{37} - 42 q^{38} + 12 q^{40} + 21 q^{41} + 36 q^{43} + 3 q^{44} + 3 q^{46} - 9 q^{47} - 12 q^{49} - 12 q^{50} + 3 q^{52} + 6 q^{53} + 3 q^{56} - 3 q^{58} + 6 q^{59} - 18 q^{61} + 33 q^{62} - 6 q^{64} - 3 q^{65} - 27 q^{67} - 6 q^{68} + 18 q^{71} + 54 q^{73} - 3 q^{74} - 3 q^{76} - 51 q^{77} - 12 q^{79} - 18 q^{82} + 6 q^{83} + 3 q^{85} + 3 q^{88} + 15 q^{89} - 51 q^{91} + 6 q^{92} - 12 q^{94} + 15 q^{95} - 42 q^{97} - 51 q^{98}+O(q^{100}) \) 12 * q + 6 * q^5 + 6 * q^7 + 6 * q^8 - 3 * q^11 - 6 * q^13 - 3 * q^14 + 3 * q^17 - 3 * q^19 + 6 * q^20 - 3 * q^22 + 21 * q^23 - 6 * q^25 - 3 * q^28 - 6 * q^29 + 42 * q^31 - 3 * q^34 + 9 * q^35 - 3 * q^37 - 42 * q^38 + 12 * q^40 + 21 * q^41 + 36 * q^43 + 3 * q^44 + 3 * q^46 - 9 * q^47 - 12 * q^49 - 12 * q^50 + 3 * q^52 + 6 * q^53 + 3 * q^56 - 3 * q^58 + 6 * q^59 - 18 * q^61 + 33 * q^62 - 6 * q^64 - 3 * q^65 - 27 * q^67 - 6 * q^68 + 18 * q^71 + 54 * q^73 - 3 * q^74 - 3 * q^76 - 51 * q^77 - 12 * q^79 - 18 * q^82 + 6 * q^83 + 3 * q^85 + 3 * q^88 + 15 * q^89 - 51 * q^91 + 6 * q^92 - 12 * q^94 + 15 * q^95 - 42 * q^97 - 51 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more