LMFDB - Embedded newform 387.2.bc.a.233.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [387,2,Mod(26,387)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(387, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([21, 17]))

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

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

chi := DirichletCharacter("387.26");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 387 = 3^{2} \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	387.bc (of order $42$, degree $12$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.09021055822$
Analytic rank:	$0$
Dimension:	$168$
Relative dimension:	$14$ over $\Q(\zeta_{42})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{42}]$

Embedding invariants

Embedding label			233.14
Character	$\chi$	$=$	387.233
Dual form			387.2.bc.a.98.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.29434 + 1.10489i) q^{2} +(2.79621 + 3.50634i) q^{4} +(-1.32170 + 1.22636i) q^{5} +(1.58722 + 0.916379i) q^{7} +(1.40801 + 6.16890i) q^{8} +O(q^{10})$	\(q+(2.29434 + 1.10489i) q^{2} +(2.79621 + 3.50634i) q^{4} +(-1.32170 + 1.22636i) q^{5} +(1.58722 + 0.916379i) q^{7} +(1.40801 + 6.16890i) q^{8} +(-4.38743 + 1.35334i) q^{10} +(-3.45109 - 2.75215i) q^{11} +(-1.81261 - 0.559116i) q^{13} +(2.62911 + 3.85619i) q^{14} +(-1.58962 + 6.96458i) q^{16} +(4.31300 - 4.64831i) q^{17} +(5.13830 + 2.01663i) q^{19} +(-7.99580 - 1.20517i) q^{20} +(-4.87713 - 10.1275i) q^{22} +(0.527656 - 3.50077i) q^{23} +(-0.130713 + 1.74425i) q^{25} +(-3.54097 - 3.28554i) q^{26} +(1.22506 + 8.12771i) q^{28} +(-2.51149 + 1.71231i) q^{29} +(0.00904218 + 0.120660i) q^{31} +(-3.45193 + 4.32858i) q^{32} +(15.0314 - 5.89938i) q^{34} +(-3.22164 + 0.735318i) q^{35} +(6.38100 - 3.68407i) q^{37} +(9.56082 + 10.3041i) q^{38} +(-9.42627 - 6.42672i) q^{40} +(-5.02184 + 10.4279i) q^{41} +(-4.75929 - 4.51100i) q^{43} -19.7963i q^{44} +(5.07860 - 7.44894i) q^{46} +(-3.82660 + 3.05161i) q^{47} +(-1.82050 - 3.15319i) q^{49} +(-2.22711 + 3.85747i) q^{50} +(-3.10799 - 7.91903i) q^{52} +(-4.20133 - 13.6204i) q^{53} +(7.93645 - 0.594755i) q^{55} +(-3.41824 + 11.0817i) q^{56} +(-7.65413 + 1.15367i) q^{58} +(-1.95031 - 0.445145i) q^{59} +(1.19896 + 0.0898498i) q^{61} +(-0.112570 + 0.286824i) q^{62} +(0.169954 - 0.0818456i) q^{64} +(3.08141 - 1.48393i) q^{65} +(4.79149 - 12.2085i) q^{67} +(28.3586 + 2.12518i) q^{68} +(-8.20398 - 1.87250i) q^{70} +(3.32988 - 0.501898i) q^{71} +(-4.23488 + 13.7291i) q^{73} +(18.7107 - 1.40217i) q^{74} +(7.29677 + 23.6556i) q^{76} +(-2.95561 - 7.53077i) q^{77} +(-2.64605 + 4.58310i) q^{79} +(-6.44008 - 11.1546i) q^{80} +(-23.0436 + 18.3766i) q^{82} +(-4.21282 + 6.17907i) q^{83} +11.4330i q^{85} +(-5.93524 - 15.6083i) q^{86} +(12.1186 - 25.1645i) q^{88} +(-5.09764 - 3.47551i) q^{89} +(-2.36464 - 2.54847i) q^{91} +(13.7503 - 7.93875i) q^{92} +(-12.1512 + 2.77344i) q^{94} +(-9.26442 + 3.63602i) q^{95} +(-8.33191 + 10.4479i) q^{97} +(-0.692888 - 9.24595i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 168 q - 24 q^{4} - 6 q^{7}+O(q^{10}) $ 168 * q - 24 * q^4 - 6 * q^7	$ 168 q - 24 q^{4} - 6 q^{7} + 8 q^{10} + 26 q^{13} - 8 q^{16} + 24 q^{19} + 14 q^{25} + 32 q^{31} - 48 q^{34} - 78 q^{37} - 244 q^{40} - 32 q^{43} - 92 q^{46} + 54 q^{49} + 76 q^{52} - 96 q^{55} - 20 q^{58} - 96 q^{64} - 18 q^{67} + 140 q^{70} + 10 q^{73} - 16 q^{76} - 168 q^{88} - 38 q^{91} - 112 q^{94} - 40 q^{97}+O(q^{100}) $ 168 * q - 24 * q^4 - 6 * q^7 + 8 * q^10 + 26 * q^13 - 8 * q^16 + 24 * q^19 + 14 * q^25 + 32 * q^31 - 48 * q^34 - 78 * q^37 - 244 * q^40 - 32 * q^43 - 92 * q^46 + 54 * q^49 + 76 * q^52 - 96 * q^55 - 20 * q^58 - 96 * q^64 - 18 * q^67 + 140 * q^70 + 10 * q^73 - 16 * q^76 - 168 * q^88 - 38 * q^91 - 112 * q^94 - 40 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/387\mathbb{Z}\right)^\times$.

$n$	$46$	$173$
$\chi(n)$	$e\left(\frac{29}{42}\right)$	$-1$

Coefficient data

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

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

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

$2$	2.29434	+	1.10489i	1.62234	+	0.781279i	0.999999	−	0.00146600i	$-0.000466643\pi$
$2$	2.29434	+	1.10489i	1.62234	+	0.781279i	0.622343	+	0.782745i	$0.286181\pi$
$3$		0			0
$3$		0			0
$4$	2.79621	+	3.50634i	1.39811	+	1.75317i
$5$	−1.32170	+	1.22636i	−0.591083	+	0.548445i	−0.917986	−	0.396613i	$-0.870186\pi$
$5$	−1.32170	+	1.22636i	−0.591083	+	0.548445i	0.326903	+	0.945058i	$0.393995\pi$
$6$		0			0
$7$	1.58722	+	0.916379i	0.599911	+	0.346359i	0.769007	−	0.639241i	$-0.220751\pi$
$7$	1.58722	+	0.916379i	0.599911	+	0.346359i	−0.169095	+	0.985600i	$0.554085\pi$
$8$	1.40801	+	6.16890i	0.497807	+	2.18104i
$9$		0			0
$10$	−4.38743	+	1.35334i	−1.38743	+	0.427965i
$11$	−3.45109	−	2.75215i	−1.04054	−	0.829805i	−0.0548735	−	0.998493i	$-0.517476\pi$
$11$	−3.45109	−	2.75215i	−1.04054	−	0.829805i	−0.985670	+	0.168688i	$0.946047\pi$
$12$		0			0
$13$	−1.81261	−	0.559116i	−0.502727	−	0.155071i	0.0330109	−	0.999455i	$-0.489490\pi$
$13$	−1.81261	−	0.559116i	−0.502727	−	0.155071i	−0.535738	+	0.844384i	$0.679967\pi$
$14$	2.62911	+	3.85619i	0.702658	+	1.03061i
$15$		0			0
$16$	−1.58962	+	6.96458i	−0.397405	+	1.74114i
$17$	4.31300	−	4.64831i	1.04606	−	1.12738i	0.0543929	−	0.998520i	$-0.482678\pi$
$17$	4.31300	−	4.64831i	1.04606	−	1.12738i	0.991663	−	0.128860i	$-0.0411319\pi$
$18$		0			0
$19$	5.13830	+	2.01663i	1.17881	+	0.462647i	0.872181	−	0.489183i	$-0.162705\pi$
$19$	5.13830	+	2.01663i	1.17881	+	0.462647i	0.306625	+	0.951830i	$0.400800\pi$
$20$	−7.99580	−	1.20517i	−1.78792	−	0.269485i
$21$		0			0
$22$	−4.87713	−	10.1275i	−1.03981	−	2.15918i
$23$	0.527656	−	3.50077i	0.110024	−	0.729960i	−0.863996	−	0.503498i	$-0.832046\pi$
$23$	0.527656	−	3.50077i	0.110024	−	0.729960i	0.974020	−	0.226462i	$-0.0727159\pi$
$24$		0			0
$25$	−0.130713	+	1.74425i	−0.0261427	+	0.348850i
$26$	−3.54097	−	3.28554i	−0.694442	−	0.644348i
$27$		0			0
$28$	1.22506	+	8.12771i	0.231514	+	1.53599i
$29$	−2.51149	+	1.71231i	−0.466372	+	0.317967i	−0.773606	−	0.633667i	$-0.781549\pi$
$29$	−2.51149	+	1.71231i	−0.466372	+	0.317967i	0.307234	+	0.951634i	$0.400597\pi$
$30$		0			0
$31$	0.00904218	+	0.120660i	0.00162402	+	0.0216711i	0.997957	−	0.0638901i	$-0.0203507\pi$
$31$	0.00904218	+	0.120660i	0.00162402	+	0.0216711i	−0.996333	+	0.0855612i	$0.972732\pi$
$32$	−3.45193	+	4.32858i	−0.610221	+	0.765193i
$33$		0			0
$34$	15.0314	−	5.89938i	2.57786	−	1.01173i
$35$	−3.22164	+	0.735318i	−0.544556	+	0.124291i
$36$		0			0
$37$	6.38100	−	3.68407i	1.04903	−	0.605658i	0.126653	−	0.991947i	$-0.459577\pi$
$37$	6.38100	−	3.68407i	1.04903	−	0.605658i	0.922378	+	0.386289i	$0.126243\pi$
$38$	9.56082	+	10.3041i	1.55097	+	1.67155i
$39$		0			0
$40$	−9.42627	−	6.42672i	−1.49042	−	1.01615i
$41$	−5.02184	+	10.4279i	−0.784279	+	1.62857i	−0.00654465	+	0.999979i	$0.502083\pi$
$41$	−5.02184	+	10.4279i	−0.784279	+	1.62857i	−0.777734	+	0.628593i	$0.783631\pi$
$42$		0			0
$43$	−4.75929	−	4.51100i	−0.725785	−	0.687921i
$43$	−4.75929	−	4.51100i	−0.725785	−	0.687921i
$44$		−	19.7963i		−	2.98441i
$45$		0			0
$46$	5.07860	−	7.44894i	0.748798	−	1.09829i
$47$	−3.82660	+	3.05161i	−0.558167	+	0.445124i	−0.861497	−	0.507762i	$-0.830473\pi$
$47$	−3.82660	+	3.05161i	−0.558167	+	0.445124i	0.303330	+	0.952886i	$0.401902\pi$
$48$		0			0
$49$	−1.82050	−	3.15319i	−0.260071	−	0.450456i
$50$	−2.22711	+	3.85747i	−0.314961	+	0.545529i
$51$		0			0
$52$	−3.10799	−	7.91903i	−0.431001	−	1.09817i
$53$	−4.20133	−	13.6204i	−0.577097	−	1.87090i	−0.483613	−	0.875282i	$-0.660676\pi$
$53$	−4.20133	−	13.6204i	−0.577097	−	1.87090i	−0.0934838	−	0.995621i	$-0.529800\pi$
$54$		0			0
$55$	7.93645	−	0.594755i	1.07015	−	0.0801967i
$56$	−3.41824	+	11.0817i	−0.456781	+	1.48085i
$57$		0			0
$58$	−7.65413	+	1.15367i	−1.00504	+	0.151485i
$59$	−1.95031	−	0.445145i	−0.253908	−	0.0579529i	0.0936720	−	0.995603i	$-0.470139\pi$
$59$	−1.95031	−	0.445145i	−0.253908	−	0.0579529i	−0.347580	+	0.937650i	$0.612997\pi$
$60$		0			0
$61$	1.19896	+	0.0898498i	0.153511	+	0.0115041i	0.151264	−	0.988493i	$-0.451666\pi$
$61$	1.19896	+	0.0898498i	0.153511	+	0.0115041i	0.00224730	+	0.999997i	$0.499285\pi$
$62$	−0.112570	+	0.286824i	−0.0142964	+	0.0364267i
$63$		0			0
$64$	0.169954	−	0.0818456i	0.0212443	−	0.0102307i
$65$	3.08141	−	1.48393i	0.382202	−	0.184059i
$66$		0			0
$67$	4.79149	−	12.2085i	0.585374	−	1.49151i	−0.264428	−	0.964406i	$-0.585183\pi$
$67$	4.79149	−	12.2085i	0.585374	−	1.49151i	0.849801	−	0.527103i	$-0.176722\pi$
$68$	28.3586	+	2.12518i	3.43899	+	0.257716i
$69$		0			0
$70$	−8.20398	−	1.87250i	−0.980563	−	0.223807i
$71$	3.32988	−	0.501898i	0.395184	−	0.0595644i	0.0515556	−	0.998670i	$-0.483582\pi$
$71$	3.32988	−	0.501898i	0.395184	−	0.0595644i	0.343628	+	0.939106i	$0.388344\pi$
$72$		0			0
$73$	−4.23488	+	13.7291i	−0.495655	+	1.60687i	0.269481	+	0.963006i	$0.413148\pi$
$73$	−4.23488	+	13.7291i	−0.495655	+	1.60687i	−0.765136	+	0.643869i	$0.777328\pi$
$74$	18.7107	−	1.40217i	2.17507	−	0.162999i
$75$		0			0
$76$	7.29677	+	23.6556i	0.836997	+	2.71348i
$77$	−2.95561	−	7.53077i	−0.336823	−	0.858211i
$78$		0			0
$79$	−2.64605	+	4.58310i	−0.297704	+	0.515639i	−0.975610	−	0.219509i	$-0.929554\pi$
$79$	−2.64605	+	4.58310i	−0.297704	+	0.515639i	0.677906	+	0.735149i	$0.262888\pi$
$80$	−6.44008	−	11.1546i	−0.720023	−	1.24712i
$81$		0			0
$82$	−23.0436	+	18.3766i	−2.54474	+	2.02936i
$83$	−4.21282	+	6.17907i	−0.462417	+	0.678241i	−0.984646	−	0.174565i	$-0.944148\pi$
$83$	−4.21282	+	6.17907i	−0.462417	+	0.678241i	0.522229	+	0.852805i	$0.325101\pi$
$84$		0			0
$85$			11.4330i			1.24008i
$86$	−5.93524	−	15.6083i	−0.640013	−	1.68308i
$87$		0			0
$88$	12.1186	−	25.1645i	1.29185	−	2.68255i
$89$	−5.09764	−	3.47551i	−0.540349	−	0.368404i	0.262178	−	0.965020i	$-0.415559\pi$
$89$	−5.09764	−	3.47551i	−0.540349	−	0.368404i	−0.802527	+	0.596616i	$0.796512\pi$
$90$		0			0
$91$	−2.36464	−	2.54847i	−0.247882	−	0.267153i
$92$	13.7503	−	7.93875i	1.43357	−	0.827672i
$93$		0			0
$94$	−12.1512	+	2.77344i	−1.25330	+	0.286058i
$95$	−9.26442	+	3.63602i	−0.950510	+	0.373048i
$96$		0			0
$97$	−8.33191	+	10.4479i	−0.845977	+	1.06082i	0.151402	+	0.988472i	$0.451621\pi$
$97$	−8.33191	+	10.4479i	−0.845977	+	1.06082i	−0.997379	+	0.0723495i	$0.976950\pi$
$98$	−0.692888	−	9.24595i	−0.0699923	−	0.933982i
$99$		0			0
$100$	−6.48144	+	4.41897i	−0.648144	+	0.441897i
$101$	−0.599364	−	3.97652i	−0.0596389	−	0.395679i	−0.998657	−	0.0518105i	$-0.983501\pi$
$101$	−0.599364	−	3.97652i	−0.0596389	−	0.395679i	0.939018	−	0.343868i	$-0.111737\pi$
$102$		0			0
$103$	1.41863	+	1.31630i	0.139782	+	0.129699i	0.746965	−	0.664863i	$-0.231510\pi$
$103$	1.41863	+	1.31630i	0.139782	+	0.129699i	−0.607183	+	0.794562i	$0.707701\pi$
$104$	0.896956	−	11.9690i	0.0879538	−	1.17366i
$105$		0			0
$106$	5.40981	−	35.8918i	0.525448	−	3.48612i
$107$	7.91144	+	16.4283i	0.764828	+	1.58818i	0.808048	+	0.589116i	$0.200524\pi$
$107$	7.91144	+	16.4283i	0.764828	+	1.58818i	−0.0432204	+	0.999066i	$0.513762\pi$
$108$		0			0
$109$	−4.06436	−	0.612604i	−0.389295	−	0.0586768i	−0.0485214	−	0.998822i	$-0.515451\pi$
$109$	−4.06436	−	0.612604i	−0.389295	−	0.0586768i	−0.340774	+	0.940145i	$0.610689\pi$
$110$	18.8660	+	7.40437i	1.79881	+	0.705979i
$111$		0			0
$112$	−8.90527	+	9.59759i	−0.841469	+	0.906887i
$113$	−3.50138	+	15.3405i	−0.329382	+	1.44312i	0.490930	+	0.871199i	$0.336657\pi$
$113$	−3.50138	+	15.3405i	−0.329382	+	1.44312i	−0.820312	+	0.571916i	$0.806200\pi$
$114$		0			0
$115$	3.59580	+	5.27407i	0.335310	+	0.491809i
$116$	−13.0266	−	4.01817i	−1.20949	−	0.373078i
$117$		0			0
$118$	−3.98283	−	3.17620i	−0.366649	−	0.292393i
$119$	11.1053	−	3.42552i	1.01802	−	0.314017i
$120$		0			0
$121$	1.88795	+	8.27165i	0.171632	+	0.751968i
$122$	2.65155	+	1.53087i	0.240060	+	0.138599i
$123$		0			0
$124$	−0.397790	+	0.369095i	−0.0357226	+	0.0331457i
$125$	−7.58712	−	9.51395i	−0.678613	−	0.850953i
$126$		0			0
$127$	−14.4557	−	6.96149i	−1.28273	−	0.617732i	−0.336643	−	0.941632i	$-0.609292\pi$
$127$	−14.4557	−	6.96149i	−1.28273	−	0.617732i	−0.946091	+	0.323900i	$0.895006\pi$
$128$	11.5533			1.02118
$129$		0			0
$130$	8.70937			0.763863
$131$	−0.193497	−	0.0931834i	−0.0169059	−	0.00814147i	0.425412	−	0.905000i	$-0.360129\pi$
$131$	−0.193497	−	0.0931834i	−0.0169059	−	0.00814147i	−0.442318	+	0.896858i	$0.645844\pi$
$132$		0			0
$133$	6.30758	+	7.90946i	0.546937	+	0.685837i
$134$	24.4824	−	22.7164i	2.11496	−	1.96240i
$135$		0			0
$136$	34.7477	+	20.0616i	2.97959	+	1.72027i
$137$	2.41324	+	10.5731i	0.206177	+	0.903320i	0.967084	+	0.254459i	$0.0818972\pi$
$137$	2.41324	+	10.5731i	0.206177	+	0.903320i	−0.760907	+	0.648861i	$0.775246\pi$
$138$		0			0
$139$	0.334312	−	0.103122i	0.0283560	−	0.00874666i	−0.280545	−	0.959841i	$-0.590515\pi$
$139$	0.334312	−	0.103122i	0.0283560	−	0.00874666i	0.308901	+	0.951094i	$0.400039\pi$
$140$	−11.5867	−	9.24006i	−0.979252	−	0.780928i
$141$		0			0
$142$	8.19441	+	2.52764i	0.687660	+	0.212115i
$143$	4.71671	+	6.91814i	0.394431	+	0.578524i
$144$		0			0
$145$	1.21954	−	5.34315i	0.101277	−	0.443725i
$146$	−24.8855	+	26.8202i	−2.05954	+	2.21966i
$147$		0			0
$148$	30.7603	+	12.0725i	2.52848	+	0.992355i
$149$	8.03717	+	1.21141i	0.658431	+	0.0992425i	0.469755	−	0.882797i	$-0.344342\pi$
$149$	8.03717	+	1.21141i	0.658431	+	0.0992425i	0.188676	+	0.982039i	$0.439580\pi$
$150$		0			0
$151$	2.00229	+	4.15781i	0.162944	+	0.338358i	0.966415	−	0.256987i	$-0.0827298\pi$
$151$	2.00229	+	4.15781i	0.162944	+	0.338358i	−0.803470	+	0.595345i	$0.797016\pi$
$152$	−5.20563	+	34.5371i	−0.422232	+	2.80133i
$153$		0			0
$154$	1.53954	−	20.5438i	0.124060	−	1.65546i
$155$	−0.159923	−	0.148387i	−0.0128453	−	0.0119187i
$156$		0			0
$157$	−1.37226	−	9.10435i	−0.109518	−	0.726606i	−0.974432	−	0.224685i	$-0.927865\pi$
$157$	−1.37226	−	9.10435i	−0.109518	−	0.726606i	0.864913	−	0.501921i	$-0.167373\pi$
$158$	−11.1348	+	7.59157i	−0.885836	+	0.603953i
$159$		0			0
$160$	−0.745980	−	9.95441i	−0.0589749	−	0.786965i
$161$	4.04553	−	5.07294i	0.318833	−	0.399803i
$162$		0			0
$163$	−0.573962	+	0.225264i	−0.0449562	+	0.0176440i	−0.387713	−	0.921780i	$-0.626735\pi$
$163$	−0.573962	+	0.225264i	−0.0449562	+	0.0176440i	0.342756	+	0.939424i	$0.388639\pi$
$164$	−50.6061	+	11.5505i	−3.95167	+	0.901943i
$165$		0			0
$166$	−16.4928	+	9.52215i	−1.28009	+	0.739062i
$167$	14.5067	+	15.6345i	1.12256	+	1.20984i	0.975334	+	0.220733i	$0.0708450\pi$
$167$	14.5067	+	15.6345i	1.12256	+	1.20984i	0.147229	+	0.989102i	$0.452965\pi$
$168$		0			0
$169$	−7.76816	−	5.29624i	−0.597551	−	0.407403i
$170$	−12.6322	+	26.2311i	−0.968848	+	2.01183i
$171$		0			0
$172$	2.50912	−	29.3014i	0.191318	−	2.23421i
$173$		−	18.8698i		−	1.43464i	−0.696743	−	0.717320i	$-0.745368\pi$
$173$		−	18.8698i		−	1.43464i	0.696743	−	0.717320i	$-0.254632\pi$
$174$		0			0
$175$	−1.80586	+	2.64872i	−0.136511	+	0.200224i
$176$	24.6535	−	19.6605i	1.85833	−	1.48197i
$177$		0			0
$178$	−7.85564	−	13.6064i	−0.588805	−	1.01984i
$179$	7.63851	−	13.2303i	0.570929	−	0.988879i	−0.425542	−	0.904939i	$-0.639916\pi$
$179$	7.63851	−	13.2303i	0.570929	−	0.988879i	0.996471	−	0.0839397i	$-0.0267503\pi$
$180$		0			0
$181$	−1.76991	−	4.50965i	−0.131556	−	0.335200i	0.849883	−	0.526971i	$-0.176672\pi$
$181$	−1.76991	−	4.50965i	−0.131556	−	0.335200i	−0.981440	+	0.191771i	$0.938577\pi$
$182$	−2.60948	−	8.45974i	−0.193428	−	0.627078i
$183$		0			0
$184$	22.3388	−	1.67406i	1.64684	−	0.123414i
$185$	−3.91579	+	12.6947i	−0.287894	+	0.933330i
$186$		0			0
$187$	−27.6774	+	4.17170i	−2.02397	+	0.305065i
$188$	−21.4000	−	4.88441i	−1.56076	−	0.356232i
$189$		0			0
$190$	−25.2731	−	1.89396i	−1.83351	−	0.137402i
$191$	−0.927107	+	2.36223i	−0.0670831	+	0.170925i	−0.960484	−	0.278336i	$-0.910217\pi$
$191$	−0.927107	+	2.36223i	−0.0670831	+	0.170925i	0.893401	+	0.449261i	$0.148313\pi$
$192$		0			0
$193$	2.93959	−	1.41563i	0.211596	−	0.101899i	−0.325084	−	0.945685i	$-0.605393\pi$
$193$	2.93959	−	1.41563i	0.211596	−	0.101899i	0.536680	+	0.843786i	$0.319678\pi$
$194$	−30.6600	+	14.7651i	−2.20126	+	1.06007i
$195$		0			0
$196$	5.96567	−	15.2003i	0.426120	−	1.08574i
$197$	−10.4054	−	0.779780i	−0.741357	−	0.0555570i	−0.301303	−	0.953528i	$-0.597422\pi$
$197$	−10.4054	−	0.779780i	−0.741357	−	0.0555570i	−0.440054	+	0.897971i	$0.645041\pi$
$198$		0			0
$199$	26.3803	+	6.02112i	1.87005	+	0.426826i	0.998035	−	0.0626583i	$-0.0199578\pi$
$199$	26.3803	+	6.02112i	1.87005	+	0.426826i	0.872012	+	0.489484i	$0.162815\pi$
$200$	−10.9442	+	1.64957i	−0.773868	+	0.116642i
$201$		0			0
$202$	3.01849	−	9.78572i	0.212380	−	0.688521i
$203$	−5.55540	+	0.416320i	−0.389913	+	0.0292199i
$204$		0			0
$205$	−6.15105	−	19.9412i	−0.429608	−	1.39276i
$206$	1.80045	+	4.58747i	0.125443	+	0.319624i
$207$		0			0
$208$	6.77536	−	11.7353i	0.469787	−	0.813695i
$209$	−12.1826	−	21.1010i	−0.842691	−	1.45958i
$210$		0			0
$211$	−9.01359	+	7.18810i	−0.620521	+	0.494849i	−0.882555	−	0.470210i	$-0.844178\pi$
$211$	−9.01359	+	7.18810i	−0.620521	+	0.494849i	0.262033	+	0.965059i	$0.415607\pi$
$212$	36.0099	−	52.8168i	2.47317	−	3.62747i
$213$		0			0
$214$			46.4333i			3.17412i
$215$	11.8225	+	0.125596i	0.806287	+	0.00856555i
$216$		0			0
$217$	−0.0962180	+	0.199799i	−0.00653171	+	0.0135632i
$218$	−8.64815	−	5.89621i	−0.585727	−	0.399342i
$219$		0			0
$220$	24.2774	+	26.1648i	1.63678	+	1.76403i
$221$	−10.4167	+	6.01410i	−0.700704	+	0.404552i
$222$		0			0
$223$	27.8951	−	6.36688i	1.86799	−	0.426358i	0.870198	−	0.492703i	$-0.163991\pi$
$223$	27.8951	−	6.36688i	1.86799	−	0.426358i	0.997797	+	0.0663453i	$0.0211339\pi$
$224$	−9.44558	+	3.70712i	−0.631109	+	0.247692i
$225$		0			0
$226$	−24.9830	+	31.3277i	−1.66184	+	2.08389i
$227$	0.381737	+	5.09393i	0.0253368	+	0.338096i	0.995439	+	0.0953995i	$0.0304128\pi$
$227$	0.381737	+	5.09393i	0.0253368	+	0.338096i	−0.970102	+	0.242696i	$0.921968\pi$
$228$		0			0
$229$	−21.3471	+	14.5542i	−1.41066	+	0.961771i	−0.411938	+	0.911212i	$0.635148\pi$
$229$	−21.3471	+	14.5542i	−1.41066	+	0.961771i	−0.998721	+	0.0505595i	$0.983900\pi$
$230$	2.42269	+	16.0735i	0.159747	+	1.05985i
$231$		0			0
$232$	−14.0993	−	13.0822i	−0.925661	−	0.858888i
$233$	0.441240	−	5.88794i	0.0289066	−	0.385732i	−0.963922	−	0.266185i	$-0.914237\pi$
$233$	0.441240	−	5.88794i	0.0289066	−	0.385732i	0.992829	−	0.119547i	$-0.0381442\pi$
$234$		0			0
$235$	1.31525	−	8.72612i	0.0857975	−	0.569230i
$236$	−3.89265	−	8.08317i	−0.253390	−	0.526169i
$237$		0			0
$238$	29.2641	+	4.41085i	1.89691	+	0.285913i
$239$	18.3763	+	7.21218i	1.18867	+	0.466517i	0.875517	−	0.483187i	$-0.160521\pi$
$239$	18.3763	+	7.21218i	1.18867	+	0.466517i	0.313149	+	0.949704i	$0.398616\pi$
$240$		0			0
$241$	−11.3932	+	12.2790i	−0.733901	+	0.790957i	−0.984172	−	0.177219i	$-0.943290\pi$
$241$	−11.3932	+	12.2790i	−0.733901	+	0.790957i	0.250270	+	0.968176i	$0.419481\pi$
$242$	−4.80771	+	21.0640i	−0.309051	+	1.35404i
$243$		0			0
$244$	3.03751	+	4.45521i	0.194457	+	0.285216i
$245$	6.27311	+	1.93500i	0.400774	+	0.123623i
$246$		0			0
$247$	−8.18619	−	6.52827i	−0.520875	−	0.415384i
$248$	−0.731605	+	0.225670i	−0.0464570	+	0.0143301i
$249$		0			0
$250$	−6.89550	−	30.2112i	−0.436110	−	1.91072i
$251$	14.9423	+	8.62692i	0.943148	+	0.544527i	0.890946	−	0.454110i	$-0.150043\pi$
$251$	14.9423	+	8.62692i	0.943148	+	0.544527i	0.0522021	+	0.998637i	$0.483376\pi$
$252$		0			0
$253$	−11.4556	+	10.6293i	−0.720209	+	0.668257i
$254$	−25.4745	−	31.9440i	−1.59841	−	2.00435i
$255$		0			0
$256$	26.1673	+	12.6015i	1.63545	+	0.787593i
$257$	−9.01528			−0.562358			−0.281179	−	0.959655i	$-0.590725\pi$
$257$	−9.01528			−0.562358			−0.281179	+	0.959655i	$0.590725\pi$
$258$		0			0
$259$	13.5040			0.839100
$260$	13.8194	+	6.65509i	0.857045	+	0.412731i
$261$		0			0
$262$	−0.340990	−	0.427588i	−0.0210664	−	0.0264165i
$263$	8.69492	−	8.06771i	0.536152	−	0.497476i	−0.364984	−	0.931014i	$-0.618925\pi$
$263$	8.69492	−	8.06771i	0.536152	−	0.497476i	0.901135	+	0.433538i	$0.142735\pi$
$264$		0			0
$265$	22.2564	+	12.8497i	1.36720	+	0.789353i
$266$	5.73261	+	25.1162i	0.351489	+	1.53997i
$267$		0			0
$268$	56.2053	−	17.3370i	3.43328	−	1.05903i
$269$	6.08481	+	4.85248i	0.370998	+	0.295861i	0.791185	−	0.611577i	$-0.209464\pi$
$269$	6.08481	+	4.85248i	0.370998	+	0.295861i	−0.420188	+	0.907437i	$0.638036\pi$
$270$		0			0
$271$	−9.68655	−	2.98791i	−0.588416	−	0.181502i	−0.0137713	−	0.999905i	$-0.504384\pi$
$271$	−9.68655	−	2.98791i	−0.588416	−	0.181502i	−0.574645	+	0.818403i	$0.694860\pi$
$272$	25.5175	+	37.4273i	1.54722	+	2.26936i
$273$		0			0
$274$	−6.14537	+	26.9246i	−0.371255	+	1.62657i
$275$	5.25155	−	5.65982i	0.316680	−	0.341300i
$276$		0			0
$277$	−19.6264	−	7.70278i	−1.17923	−	0.462815i	−0.306908	−	0.951739i	$-0.599294\pi$
$277$	−19.6264	−	7.70278i	−1.17923	−	0.462815i	−0.872327	+	0.488924i	$0.837390\pi$
$278$	0.880964	+	0.132784i	0.0528367	+	0.00796385i
$279$		0			0
$280$	−9.07221	−	18.8386i	−0.542168	−	1.12582i
$281$	−0.249540	+	1.65559i	−0.0148863	+	0.0987641i	−0.995040	−	0.0994742i	$-0.968284\pi$
$281$	−0.249540	+	1.65559i	−0.0148863	+	0.0987641i	0.980154	+	0.198238i	$0.0635220\pi$
$282$		0			0
$283$	0.0823720	−	1.09918i	0.00489651	−	0.0653393i	−0.994220	−	0.107360i	$-0.965760\pi$
$283$	0.0823720	−	1.09918i	0.00489651	−	0.0653393i	0.999117	+	0.0420203i	$0.0133794\pi$
$284$	11.0709	+	10.2723i	0.656936	+	0.609547i
$285$		0			0
$286$	3.17790	+	21.0840i	0.187913	+	1.24672i
$287$	−17.5267	+	11.9495i	−1.03457	+	0.705356i
$288$		0			0
$289$	−1.73439	−	23.1438i	−0.102023	−	1.36140i
$290$	8.70166	−	10.9115i	0.510979	−	0.640748i
$291$		0			0
$292$	−59.9807	+	23.5407i	−3.51010	+	1.37761i
$293$	0.670707	−	0.153085i	0.0391831	−	0.00894330i	−0.202884	−	0.979203i	$-0.565032\pi$
$293$	0.670707	−	0.153085i	0.0391831	−	0.00894330i	0.242068	+	0.970259i	$0.422174\pi$
$294$		0			0
$295$	3.12364	−	1.80343i	0.181865	−	0.105000i
$296$	31.7112	+	34.1766i	1.84318	+	1.98647i
$297$		0			0
$298$	17.1015	+	11.6596i	0.990664	+	0.675423i
$299$	−2.91377	+	6.05050i	−0.168507	+	0.349909i
$300$		0			0
$301$	−3.42023	−	11.5213i	−0.197139	−	0.664074i
$302$			11.7517i			0.676237i
$303$		0			0
$304$	−22.2129	+	32.5804i	−1.27400	+	1.86861i
$305$	−1.69486	+	1.35161i	−0.0970474	+	0.0773927i
$306$		0			0
$307$	6.61410	+	11.4560i	0.377487	+	0.653826i	0.990696	−	0.136095i	$-0.0434551\pi$
$307$	6.61410	+	11.4560i	0.377487	+	0.653826i	−0.613209	+	0.789920i	$0.710122\pi$
$308$	18.1409	−	31.4210i	1.03368	−	1.79038i
$309$		0			0
$310$	−0.202966	−	0.517148i	−0.0115277	−	0.0293721i
$311$	−0.404597	−	1.31167i	−0.0229426	−	0.0743780i	0.943378	−	0.331721i	$-0.107629\pi$
$311$	−0.404597	−	1.31167i	−0.0229426	−	0.0743780i	−0.966320	+	0.257343i	$0.917153\pi$
$312$		0			0
$313$	−2.21586	+	0.166055i	−0.125248	+	0.00938601i	−0.137206	−	0.990542i	$-0.543812\pi$
$313$	−2.21586	+	0.166055i	−0.125248	+	0.00938601i	0.0119588	+	0.999928i	$0.496193\pi$
$314$	6.91092	−	22.4046i	0.390006	−	1.26437i
$315$		0			0
$316$	−23.4689	+	3.53736i	−1.32023	+	0.198992i
$317$	5.17390	+	1.18091i	0.290595	+	0.0663264i	0.365333	−	0.930877i	$-0.380955\pi$
$317$	5.17390	+	1.18091i	0.290595	+	0.0663264i	−0.0747383	+	0.997203i	$0.523812\pi$
$318$		0			0
$319$	13.3799	+	1.00269i	0.749131	+	0.0561396i
$320$	−0.124257	+	0.316601i	−0.00694616	+	0.0176985i
$321$		0			0
$322$	14.8869	−	7.16914i	0.829614	−	0.399521i
$323$	31.5354	−	15.1866i	1.75468	−	0.845007i
$324$		0			0
$325$	1.21217	−	3.08856i	0.0672391	−	0.171322i
$326$	−1.56576	−	0.117337i	−0.0867192	−	0.00649871i
$327$		0			0
$328$	−71.3998	−	16.2965i	−3.94239	−	0.899826i
$329$	−8.87008	+	1.33695i	−0.489023	+	0.0737084i
$330$		0			0
$331$	9.64856	−	31.2799i	0.530333	−	1.71930i	−0.152114	−	0.988363i	$-0.548608\pi$
$331$	9.64856	−	31.2799i	0.530333	−	1.71930i	0.682447	−	0.730935i	$-0.260916\pi$
$332$	−33.4459	+	2.50642i	−1.83558	+	0.137558i
$333$		0			0
$334$	16.0088	+	51.8993i	0.875963	+	2.83980i
$335$	8.63913	+	22.0121i	0.472006	+	1.20265i
$336$		0			0
$337$	7.79997	−	13.5100i	0.424892	−	0.735934i	−0.571519	−	0.820589i	$-0.693646\pi$
$337$	7.79997	−	13.5100i	0.424892	−	0.735934i	0.996410	+	0.0846551i	$0.0269788\pi$
$338$	−11.9710	−	20.7344i	−0.651137	−	1.12780i
$339$		0			0
$340$	−40.0879	+	31.9690i	−2.17407	+	1.73376i
$341$	0.300868	−	0.441292i	0.0162929	−	0.0238973i
$342$		0			0
$343$		−	19.5024i		−	1.05303i
$344$	21.1268	−	35.7111i	1.13908	−	1.92542i
$345$		0			0
$346$	20.8491	−	43.2936i	1.12085	−	2.32748i
$347$	−4.51194	−	3.07619i	−0.242214	−	0.165139i	0.436129	−	0.899884i	$-0.356349\pi$
$347$	−4.51194	−	3.07619i	−0.242214	−	0.165139i	−0.678343	+	0.734746i	$0.737302\pi$
$348$		0			0
$349$	6.03814	+	6.50757i	0.323214	+	0.348342i	0.873667	−	0.486524i	$-0.161735\pi$
$349$	6.03814	+	6.50757i	0.323214	+	0.348342i	−0.550453	+	0.834866i	$0.685545\pi$
$350$	−7.06982	+	4.08176i	−0.377898	+	0.218179i
$351$		0			0
$352$	23.8258	−	5.43809i	1.26992	−	0.289851i
$353$	16.1375	−	6.33351i	0.858914	−	0.337099i	0.105319	−	0.994438i	$-0.466414\pi$
$353$	16.1375	−	6.33351i	0.858914	−	0.337099i	0.753594	+	0.657340i	$0.228318\pi$
$354$		0			0
$355$	−3.78560	+	4.74699i	−0.200919	+	0.251944i
$356$	−2.06776	−	27.5924i	−0.109591	−	1.46239i
$357$		0			0
$358$	32.1434	−	21.9150i	1.69883	−	1.15824i
$359$	1.29815	+	8.61269i	0.0685140	+	0.454560i	0.996614	+	0.0822283i	$0.0262037\pi$
$359$	1.29815	+	8.61269i	0.0685140	+	0.454560i	−0.928100	+	0.372332i	$0.878558\pi$
$360$		0			0
$361$	8.40730	+	7.80084i	0.442490	+	0.410570i
$362$	0.921925	−	12.3022i	0.0484553	−	0.646591i
$363$		0			0
$364$	2.32379	−	15.4173i	0.121799	−	0.808087i
$365$	−11.2396	−	23.3393i	−0.588309	−	1.22164i
$366$		0			0
$367$	25.5757	+	3.85492i	1.33504	+	0.201225i	0.777479	−	0.628909i	$-0.216498\pi$
$367$	25.5757	+	3.85492i	1.33504	+	0.201225i	0.557563	+	0.830135i	$0.311736\pi$
$368$	23.5426	+	9.23978i	1.22724	+	0.481657i
$369$		0			0
$370$	−23.0104	+	24.7993i	−1.19625	+	1.28926i
$371$	5.81302	−	25.4685i	0.301797	−	1.32226i
$372$		0			0
$373$	7.60181	+	11.1498i	0.393607	+	0.577315i	0.970979	−	0.239166i	$-0.0768741\pi$
$373$	7.60181	+	11.1498i	0.393607	+	0.577315i	−0.577372	+	0.816481i	$0.695922\pi$
$374$	−68.1106	−	21.0093i	−3.52191	−	1.08637i
$375$		0			0
$376$	−24.2130	−	19.3092i	−1.24869	−	0.995798i
$377$	5.50973	−	1.69953i	0.283765	−	0.0875300i
$378$		0			0
$379$	2.74073	+	12.0079i	0.140782	+	0.616805i	0.995254	+	0.0973086i	$0.0310234\pi$
$379$	2.74073	+	12.0079i	0.140782	+	0.616805i	−0.854472	+	0.519497i	$0.826119\pi$
$380$	−38.6544	−	22.3171i	−1.98293	−	1.14485i
$381$		0			0
$382$	−4.73711	+	4.39540i	−0.242372	+	0.224888i
$383$	−1.76924	−	2.21855i	−0.0904039	−	0.113363i	0.734572	−	0.678531i	$-0.237383\pi$
$383$	−1.76924	−	2.21855i	−0.0904039	−	0.113363i	−0.824976	+	0.565168i	$0.808811\pi$
$384$		0			0
$385$	13.1419	+	6.32879i	0.669772	+	0.322545i
$386$	8.30854			0.422893
$387$		0			0
$388$	−59.9316			−3.04257
$389$	3.71791	+	1.79045i	0.188506	+	0.0907795i	0.525756	−	0.850636i	$-0.323783\pi$
$389$	3.71791	+	1.79045i	0.188506	+	0.0907795i	−0.337250	+	0.941415i	$0.609497\pi$
$390$		0			0
$391$	−13.9969	−	17.5515i	−0.707851	−	0.887617i
$392$	16.8885	−	15.6702i	0.852996	−	0.791465i
$393$		0			0
$394$	−23.0120	−	13.2860i	−1.15933	−	0.669339i
$395$	−2.12324	−	9.30252i	−0.106832	−	0.468060i
$396$		0			0
$397$	9.22614	−	2.84589i	0.463047	−	0.142831i	−0.0544496	−	0.998517i	$-0.517340\pi$
$397$	9.22614	−	2.84589i	0.463047	−	0.142831i	0.517496	+	0.855686i	$0.326864\pi$
$398$	53.8725	+	42.9619i	2.70039	+	2.15349i
$399$		0			0
$400$	−11.9402	−	3.68306i	−0.597009	−	0.184153i
$401$	−19.8170	−	29.0662i	−0.989615	−	1.45150i	−0.889724	−	0.456500i	$-0.849103\pi$
$401$	−19.8170	−	29.0662i	−0.989615	−	1.45150i	−0.0998911	−	0.994998i	$-0.531849\pi$
$402$		0			0
$403$	0.0510727	−	0.223764i	0.00254411	−	0.0111465i
$404$	12.2671	−	13.2208i	0.610310	−	0.657758i
$405$		0			0
$406$	−13.2060	−	5.18296i	−0.655401	−	0.257226i
$407$	−32.1606	−	4.84742i	−1.59414	−	0.240278i
$408$		0			0
$409$	−10.9531	−	22.7444i	−0.541597	−	1.12464i	−0.974746	−	0.223316i	$-0.928312\pi$
$409$	−10.9531	−	22.7444i	−0.541597	−	1.12464i	0.433149	−	0.901323i	$-0.357403\pi$
$410$	7.92037	−	52.5482i	0.391159	−	2.59517i
$411$		0			0
$412$	−0.648592	+	8.65486i	−0.0319538	+	0.426394i
$413$	−2.68764	−	2.49376i	−0.132250	−	0.122710i
$414$		0			0
$415$	−2.00968	−	13.3333i	−0.0986511	−	0.654507i
$416$	8.67718	−	5.91600i	0.425434	−	0.290056i
$417$		0			0
$418$	−4.63676	−	61.8733i	−0.226791	−	3.02632i
$419$	−17.1050	+	21.4489i	−0.835632	+	1.04785i	0.162498	+	0.986709i	$0.448045\pi$
$419$	−17.1050	+	21.4489i	−0.835632	+	1.04785i	−0.998129	+	0.0611400i	$0.980526\pi$
$420$		0			0
$421$	−23.1305	+	9.07807i	−1.12731	+	0.442438i	−0.854408	−	0.519603i	$-0.826080\pi$
$421$	−23.1305	+	9.07807i	−1.12731	+	0.442438i	−0.272905	+	0.962041i	$0.587985\pi$
$422$	−28.6223	+	6.53286i	−1.39331	+	0.318015i
$423$		0			0
$424$	78.1073	−	45.0952i	3.79322	−	2.19002i
$425$	7.54404	+	8.13054i	0.365940	+	0.394389i
$426$		0			0
$427$	1.82068	+	1.24132i	0.0881086	+	0.0600715i
$428$	−35.4811	+	73.6772i	−1.71504	+	3.56132i
$429$		0			0
$430$	26.9860	+	13.3508i	1.30138	+	0.643831i
$431$		−	17.5547i		−	0.845582i	−0.906227	−	0.422791i	$-0.861050\pi$
$431$		−	17.5547i		−	0.845582i	0.906227	−	0.422791i	$-0.138950\pi$
$432$		0			0
$433$	−0.868375	+	1.27367i	−0.0417314	+	0.0612088i	−0.846537	−	0.532329i	$-0.821317\pi$
$433$	−0.868375	+	1.27367i	−0.0417314	+	0.0612088i	0.804806	+	0.593538i	$0.202269\pi$
$434$	−0.441513	+	0.352095i	−0.0211933	+	0.0169011i
$435$		0			0
$436$	−9.21682	−	15.9640i	−0.441406	−	0.764537i
$437$	9.77101	−	16.9239i	0.467411	−	0.809579i
$438$		0			0
$439$	−12.2583	−	31.2335i	−0.585055	−	1.49070i	−0.850186	−	0.526483i	$-0.823510\pi$
$439$	−12.2583	−	31.2335i	−0.585055	−	1.49070i	0.265131	−	0.964212i	$-0.414585\pi$
$440$	14.8436	+	48.1218i	0.707641	+	2.29411i
$441$		0			0
$442$	−30.5444	+	2.28899i	−1.45285	+	0.108876i
$443$	3.46918	−	11.2468i	0.164826	−	0.534352i	−0.835049	−	0.550176i	$-0.814561\pi$
$443$	3.46918	−	11.2468i	0.164826	−	0.534352i	0.999875	+	0.0158234i	$0.00503695\pi$
$444$		0			0
$445$	10.9998	−	1.65795i	0.521441	−	0.0785946i
$446$	71.0355	+	16.2134i	3.36363	+	0.767726i
$447$		0			0
$448$	0.344756	+	0.0258359i	0.0162882	+	0.00122063i
$449$	−8.88416	+	22.6365i	−0.419269	+	1.06828i	0.552743	+	0.833352i	$0.313581\pi$
$449$	−8.88416	+	22.6365i	−0.419269	+	1.06828i	−0.972013	+	0.234929i	$0.924514\pi$
$450$		0			0
$451$	46.0301	−	22.1669i	2.16747	−	1.04380i
$452$	−63.5797	+	30.6184i	−2.99054	+	1.44017i
$453$		0			0
$454$	−4.75242	+	12.1090i	−0.223042	+	0.568302i
$455$	6.25070	+	0.468425i	0.293037	+	0.0219601i
$456$		0			0
$457$	1.30337	+	0.297485i	0.0609689	+	0.0139157i	0.252897	−	0.967493i	$-0.418617\pi$
$457$	1.30337	+	0.297485i	0.0609689	+	0.0139157i	−0.191928	+	0.981409i	$0.561474\pi$
$458$	−65.0585	+	9.80599i	−3.03998	+	0.458204i
$459$		0			0
$460$	−8.43806	+	27.3555i	−0.393427	+	1.27546i
$461$	1.15538	−	0.0865835i	0.0538112	−	0.00403259i	−0.0477973	−	0.998857i	$-0.515220\pi$
$461$	1.15538	−	0.0865835i	0.0538112	−	0.00403259i	0.101608	+	0.994824i	$0.467601\pi$
$462$		0			0
$463$	6.20100	+	20.1031i	0.288185	+	0.934272i	0.977701	+	0.210002i	$0.0673469\pi$
$463$	6.20100	+	20.1031i	0.288185	+	0.934272i	−0.689516	+	0.724270i	$0.742177\pi$
$464$	−7.93317	−	20.2134i	−0.368288	−	0.938383i
$465$		0			0
$466$	7.51791	−	13.0214i	0.348260	−	0.603205i
$467$	7.63542	+	13.2249i	0.353325	+	0.611977i	0.986830	−	0.161762i	$-0.0517177\pi$
$467$	7.63542	+	13.2249i	0.353325	+	0.611977i	−0.633505	+	0.773739i	$0.718384\pi$
$468$		0			0
$469$	18.7928	−	14.9867i	0.867770	−	0.692023i
$470$	12.6591	−	18.5675i	0.583920	−	0.856453i
$471$		0			0
$472$		−	12.6580i		−	0.582633i
$473$	4.00978	+	28.6662i	0.184370	+	1.31807i
$474$		0			0
$475$	−4.18916	+	8.69887i	−0.192212	+	0.399132i
$476$	43.0638	+	29.3604i	1.97382	+	1.34573i
$477$		0			0
$478$	34.1928	+	36.8511i	1.56394	+	1.68553i
$479$	20.3515	−	11.7499i	0.929882	−	0.536868i	0.0431079	−	0.999070i	$-0.486274\pi$
$479$	20.3515	−	11.7499i	0.929882	−	0.536868i	0.886774	+	0.462203i	$0.152941\pi$
$480$		0			0
$481$	−13.6261	+	3.11007i	−0.621296	+	0.141807i
$482$	−39.7068	+	15.5838i	−1.80860	+	0.709822i
$483$		0			0
$484$	−23.7241	+	29.7491i	−1.07837	+	1.35223i
$485$	−1.80057	−	24.0269i	−0.0817596	−	1.09101i
$486$		0			0
$487$	−0.0577699	+	0.0393869i	−0.00261781	+	0.00178479i	−0.564628	−	0.825345i	$-0.690980\pi$
$487$	−0.0577699	+	0.0393869i	−0.00261781	+	0.00178479i	0.562010	+	0.827130i	$0.310028\pi$
$488$	1.13388	+	7.52279i	0.0513283	+	0.340541i
$489$		0			0
$490$	12.2547	+	11.3707i	0.553609	+	0.513674i
$491$	−1.51304	+	20.1902i	−0.0682827	+	0.911170i	0.852909	+	0.522060i	$0.174836\pi$
$491$	−1.51304	+	20.1902i	−0.0682827	+	0.911170i	−0.921191	+	0.389110i	$0.872783\pi$
$492$		0			0
$493$	−2.87274	+	19.0594i	−0.129381	+	0.858390i
$494$	−11.5688	−	24.0229i	−0.520507	−	1.08084i
$495$		0			0
$496$	−0.854716	−	0.128828i	−0.0383779	−	0.00578454i
$497$	5.74516	+	2.25481i	0.257706	+	0.101142i
$498$		0			0
$499$	−1.34184	+	1.44616i	−0.0600690	+	0.0647390i	−0.762371	−	0.647140i	$-0.775965\pi$
$499$	−1.34184	+	1.44616i	−0.0600690	+	0.0647390i	0.702302	+	0.711879i	$0.252155\pi$
$500$	12.1439	−	53.2061i	0.543093	−	2.37945i
$501$		0			0
$502$	24.7508	+	36.3027i	1.10468	+	1.62027i
$503$	5.38540	+	1.66118i	0.240123	+	0.0740682i	0.412481	−	0.910966i	$-0.364662\pi$
$503$	5.38540	+	1.66118i	0.240123	+	0.0740682i	−0.172358	+	0.985034i	$0.555139\pi$
$504$		0			0
$505$	5.66883	+	4.52074i	0.252260	+	0.201170i
$506$	−38.0273	+	11.7299i	−1.69052	+	0.521456i
$507$		0			0
$508$	−16.0118	−	70.1524i	−0.710410	−	3.11251i
$509$	−15.9487	−	9.20799i	−0.706914	−	0.408137i	0.103003	−	0.994681i	$-0.467155\pi$
$509$	−15.9487	−	9.20799i	−0.706914	−	0.408137i	−0.809917	+	0.586544i	$0.800488\pi$
$510$		0			0
$511$	−19.3028	+	17.9104i	−0.853904	+	0.792307i
$512$	31.7065	+	39.7587i	1.40124	+	1.75710i
$513$		0			0
$514$	−20.6841	−	9.96093i	−0.912336	−	0.439358i
$515$	−3.48927			−0.153755
$516$		0			0
$517$	21.6045			0.950163
$518$	30.9828	+	14.9205i	1.36131	+	0.655571i
$519$		0			0
$520$	13.4929	+	16.9195i	0.591701	+	0.741970i
$521$	8.11225	−	7.52707i	0.355404	−	0.329767i	−0.482183	−	0.876070i	$-0.660156\pi$
$521$	8.11225	−	7.52707i	0.355404	−	0.329767i	0.837587	+	0.546304i	$0.183966\pi$
$522$		0			0
$523$	30.2045	+	17.4386i	1.32075	+	0.762537i	0.983849	−	0.179002i	$-0.0572870\pi$
$523$	30.2045	+	17.4386i	1.32075	+	0.762537i	0.336904	+	0.941539i	$0.390620\pi$
$524$	−0.214327	−	0.939028i	−0.00936292	−	0.0410216i
$525$		0			0
$526$	28.8631	−	8.90308i	1.25849	−	0.388193i
$527$	0.599861	+	0.478374i	0.0261304	+	0.0208383i
$528$		0			0
$529$	10.0012	+	3.08497i	0.434836	+	0.134129i
$530$	36.8661	+	54.0726i	1.60136	+	2.34877i
$531$		0			0
$532$	−10.0959	+	44.2331i	−0.437713	+	1.91775i
$533$	14.9331	−	16.0940i	0.646822	−	0.697109i
$534$		0			0
$535$	−30.6036	−	12.0110i	−1.32311	−	0.519282i
$536$	82.0597	+	12.3685i	3.54444	+	0.534238i
$537$		0			0
$538$	8.59914	+	17.8563i	0.370735	+	0.769840i
$539$	−2.39537	+	15.8922i	−0.103176	+	0.684528i
$540$		0			0
$541$	2.50234	−	33.3915i	0.107584	−	1.43561i	−0.638430	−	0.769680i	$-0.720416\pi$
$541$	2.50234	−	33.3915i	0.107584	−	1.43561i	0.746014	−	0.665930i	$-0.231965\pi$
$542$	−18.9229	−	17.5579i	−0.812808	−	0.754176i
$543$		0			0
$544$	5.23241	+	34.7148i	0.224338	+	1.48838i
$545$	6.12315	−	4.17469i	0.262287	−	0.178824i
$546$		0			0
$547$	−0.262484	−	3.50260i	−0.0112230	−	0.149761i	−1.00000		0.000361166i	$-0.999885\pi$
$547$	−0.262484	−	3.50260i	−0.0112230	−	0.149761i	0.988777	−	0.149399i	$-0.0477340\pi$
$548$	−30.3249	+	38.0262i	−1.29542	+	1.62440i
$549$		0			0
$550$	18.3023	−	7.18313i	0.780414	−	0.306290i
$551$	−16.3579	+	3.73358i	−0.696869	+	0.159056i
$552$		0			0
$553$	−8.39972	+	4.84958i	−0.357192	+	0.206225i
$554$	−36.5188	−	39.3579i	−1.55153	−	1.67216i
$555$		0			0
$556$	1.29639	+	0.883862i	0.0549791	+	0.0374841i
$557$	11.1378	−	23.1279i	0.471924	−	0.979961i	−0.520123	−	0.854092i	$-0.674114\pi$
$557$	11.1378	−	23.1279i	0.471924	−	0.979961i	0.992047	−	0.125869i	$-0.0401719\pi$
$558$		0			0
$559$	6.10456	+	10.8377i	0.258195	+	0.458385i
$560$		−	23.6062i		−	0.997546i
$561$		0			0
$562$	−2.40178	+	3.52276i	−0.101313	+	0.148599i
$563$	−3.67624	+	2.93171i	−0.154935	+	0.123557i	−0.697889	−	0.716206i	$-0.745877\pi$
$563$	−3.67624	+	2.93171i	−0.154935	+	0.123557i	0.542954	+	0.839762i	$0.317306\pi$
$564$		0			0
$565$	−14.1852	−	24.5696i	−0.596778	−	1.03365i
$566$	1.40346	−	2.43087i	0.0589920	−	0.102177i
$567$		0			0
$568$	7.78467	+	19.8350i	0.326638	+	0.832259i
$569$	−1.81309	−	5.87789i	−0.0760087	−	0.246414i	0.909592	−	0.415502i	$-0.136394\pi$
$569$	−1.81309	−	5.87789i	−0.0760087	−	0.246414i	−0.985601	+	0.169088i	$0.945918\pi$
$570$		0			0
$571$	−17.3006	+	1.29650i	−0.724006	+	0.0542567i	−0.431635	−	0.902048i	$-0.642063\pi$
$571$	−17.3006	+	1.29650i	−0.724006	+	0.0542567i	−0.292371	+	0.956305i	$0.594444\pi$
$572$	−11.0684	+	35.8830i	−0.462794	+	1.50034i
$573$		0			0
$574$	−53.4151	+	8.05103i	−2.22950	+	0.336043i
$575$	6.03724	+	1.37796i	0.251770	+	0.0574649i
$576$		0			0
$577$	10.9210	+	0.818416i	0.454647	+	0.0340711i	0.300086	−	0.953912i	$-0.402985\pi$
$577$	10.9210	+	0.818416i	0.454647	+	0.0340711i	0.154561	+	0.987983i	$0.450604\pi$
$578$	21.5922	−	55.0160i	0.898117	−	2.28837i
$579$		0			0
$580$	22.1450	−	10.6645i	0.919522	−	0.442818i
$581$	−12.3490	+	5.94697i	−0.512324	+	0.246722i
$582$		0			0
$583$	−22.9862	+	58.5679i	−0.951991	+	2.42563i
$584$	−90.6565	−	6.79377i	−3.75139	−	0.281128i
$585$		0			0
$586$	1.70797	+	0.389833i	0.0705557	+	0.0161039i
$587$	−3.24140	+	0.488563i	−0.133787	+	0.0201651i	−0.215594	−	0.976483i	$-0.569169\pi$
$587$	−3.24140	+	0.488563i	−0.133787	+	0.0201651i	0.0818073	+	0.996648i	$0.473931\pi$
$588$		0			0
$589$	−0.196865	+	0.638219i	−0.00811166	+	0.0262974i
$590$	9.15928	−	0.686393i	0.377082	−	0.0282584i
$591$		0			0
$592$	15.5147	+	50.2973i	0.637648	+	2.06721i
$593$	7.55289	+	19.2444i	0.310160	+	0.790274i	0.997928	+	0.0643438i	$0.0204954\pi$
$593$	7.55289	+	19.2444i	0.310160	+	0.790274i	−0.687768	+	0.725931i	$0.741409\pi$
$594$		0			0
$595$	−10.4769	+	18.1466i	−0.429513	+	0.743938i
$596$	18.2260	+	31.5684i	0.746568	+	1.29309i
$597$		0			0
$598$	−13.3703	+	10.6625i	−0.546753	+	0.436021i
$599$	−14.3600	+	21.0623i	−0.586734	+	0.860581i	−0.998719	−	0.0506097i	$-0.983884\pi$
$599$	−14.3600	+	21.0623i	−0.586734	+	0.860581i	0.411984	+	0.911191i	$0.364836\pi$
$600$		0			0
$601$			9.40913i			0.383806i	0.981414	+	0.191903i	$0.0614660\pi$
$601$			9.40913i			0.383806i	−0.981414	+	0.191903i	$0.938534\pi$
$602$	4.88260	−	30.2126i	0.199000	−	1.23138i
$603$		0			0
$604$	−8.97985	+	18.6468i	−0.365385	+	0.758729i
$605$	−12.6393	−	8.61736i	−0.513862	−	0.350345i
$606$		0			0
$607$	−17.3759	−	18.7268i	−0.705266	−	0.760096i	0.274207	−	0.961671i	$-0.411585\pi$
$607$	−17.3759	−	18.7268i	−0.705266	−	0.760096i	−0.979473	+	0.201575i	$0.935394\pi$
$608$	−26.4662	+	15.2803i	−1.07335	+	0.619697i
$609$		0			0
$610$	−5.38196	+	1.22840i	−0.217909	+	0.0497364i
$611$	8.64234	−	3.39187i	0.349632	−	0.137220i
$612$		0			0
$613$	−26.1466	+	32.7868i	−1.05605	+	1.32425i	−0.112270	+	0.993678i	$0.535812\pi$
$613$	−26.1466	+	32.7868i	−1.05605	+	1.32425i	−0.943782	+	0.330569i	$0.892759\pi$
$614$	2.51735	+	33.5917i	0.101592	+	1.35565i
$615$		0			0
$616$	42.2950	−	28.8363i	1.70412	−	1.16185i
$617$	4.30522	+	28.5633i	0.173322	+	1.14991i	0.891155	+	0.453699i	$0.149896\pi$
$617$	4.30522	+	28.5633i	0.173322	+	1.14991i	−0.717833	+	0.696215i	$0.754866\pi$
$618$		0			0
$619$	10.6373	+	9.86998i	0.427550	+	0.396708i	0.864383	−	0.502835i	$-0.167710\pi$
$619$	10.6373	+	9.86998i	0.427550	+	0.396708i	−0.436833	+	0.899543i	$0.643900\pi$
$620$	0.0731162	−	0.975667i	0.00293642	−	0.0391837i
$621$		0			0
$622$	0.520976	−	3.45645i	0.0208892	−	0.138591i
$623$	−4.90617	−	10.1878i	−0.196562	−	0.408164i
$624$		0			0
$625$	13.0474	+	1.96658i	0.521897	+	0.0786633i
$626$	−5.26740	−	2.06730i	−0.210528	−	0.0826260i
$627$		0			0
$628$	28.0858	−	30.2693i	1.12075	−	1.20788i
$629$	10.3966	−	45.5503i	0.414538	−	1.81621i
$630$		0			0
$631$	−26.1754	−	38.3923i	−1.04203	−	1.52837i	−0.835164	−	0.550002i	$-0.814627\pi$
$631$	−26.1754	−	38.3923i	−1.04203	−	1.52837i	−0.206863	−	0.978370i	$-0.566325\pi$
$632$	−31.9984	−	9.87019i	−1.27283	−	0.392615i
$633$		0			0
$634$	10.5659	+	8.42601i	0.419625	+	0.334640i
$635$	27.6434	−	8.52686i	1.09700	−	0.338378i
$636$		0			0
$637$	1.53685	+	6.73338i	0.0608922	+	0.266786i
$638$	29.5902	+	17.0839i	1.17149	+	0.676358i
$639$		0			0
$640$	−15.2700	+	14.1685i	−0.603601	+	0.560060i
$641$	11.7590	+	14.7453i	0.464451	+	0.582403i	0.957803	−	0.287427i	$-0.0927998\pi$
$641$	11.7590	+	14.7453i	0.464451	+	0.582403i	−0.493352	+	0.869830i	$0.664228\pi$
$642$		0			0
$643$	−21.1176	−	10.1697i	−0.832795	−	0.401053i	−0.0316324	−	0.999500i	$-0.510071\pi$
$643$	−21.1176	−	10.1697i	−0.832795	−	0.401053i	−0.801163	+	0.598447i	$0.795785\pi$
$644$	29.0996			1.14669
$645$		0			0
$646$	89.1325			3.50687
$647$	−15.8153	−	7.61625i	−0.621764	−	0.299426i	0.0963541	−	0.995347i	$-0.469282\pi$
$647$	−15.8153	−	7.61625i	−0.621764	−	0.299426i	−0.718118	+	0.695921i	$0.754996\pi$
$648$		0			0
$649$	5.50558	+	6.90378i	0.216113	+	0.270997i
$650$	6.19366	−	5.74688i	0.242935	−	0.225411i
$651$		0			0
$652$	−2.39477	−	1.38262i	−0.0937865	−	0.0541477i
$653$	6.48043	+	28.3926i	0.253599	+	1.11109i	0.927958	+	0.372685i	$0.121563\pi$
$653$	6.48043	+	28.3926i	0.253599	+	1.11109i	−0.674359	+	0.738404i	$0.735580\pi$
$654$		0			0
$655$	0.370022	−	0.114137i	0.0144580	−	0.00445969i
$656$	−64.6435	−	51.5514i	−2.52390	−	2.01275i
$657$		0			0
$658$	−21.8282	−	6.73309i	−0.850950	−	0.262483i
$659$	19.4033	+	28.4594i	0.755845	+	1.10862i	0.990630	+	0.136573i	$0.0436089\pi$
$659$	19.4033	+	28.4594i	0.755845	+	1.10862i	−0.234785	+	0.972047i	$0.575439\pi$
$660$		0			0
$661$	2.96558	−	12.9931i	0.115348	−	0.505372i	−0.883939	−	0.467603i	$-0.845118\pi$
$661$	2.96558	−	12.9931i	0.115348	−	0.505372i	0.999287	−	0.0377689i	$-0.0120251\pi$
$662$	56.6980	−	61.1060i	2.20363	−	2.37495i
$663$		0			0
$664$	−44.0498	−	17.2883i	−1.70946	−	0.670914i
$665$	−18.0366	−	2.71858i	−0.699430	−	0.105422i
$666$		0			0
$667$	4.66918	+	9.69565i	0.180791	+	0.375417i
$668$	−14.2561	+	94.5830i	−0.551585	+	3.65953i
$669$		0			0
$670$	−4.50002	+	60.0486i	−0.173851	+	2.31988i
$671$	−3.89045	−	3.60981i	−0.150189	−	0.139355i
$672$		0			0
$673$	−1.45834	−	9.67546i	−0.0562149	−	0.372962i	−0.999195	−	0.0401129i	$-0.987228\pi$
$673$	−1.45834	−	9.67546i	−0.0562149	−	0.372962i	0.942980	−	0.332849i	$-0.108010\pi$
$674$	32.8229	−	22.3782i	1.26429	−	0.861978i
$675$		0			0
$676$	−3.15101	−	42.0473i	−0.121193	−	1.61720i
$677$	−22.5796	+	28.3139i	−0.867805	+	1.08819i	0.127542	+	0.991833i	$0.459291\pi$
$677$	−22.5796	+	28.3139i	−0.867805	+	1.08819i	−0.995347	+	0.0963598i	$0.969280\pi$
$678$		0			0
$679$	−22.7988	+	8.94785i	−0.874936	+	0.343387i
$680$	−70.5289	+	16.0978i	−2.70466	+	0.617321i
$681$		0			0
$682$	1.17787	−	0.680046i	0.0451032	−	0.0260403i
$683$	6.58437	+	7.09626i	0.251944	+	0.271531i	0.846342	−	0.532640i	$-0.178800\pi$
$683$	6.58437	+	7.09626i	0.251944	+	0.271531i	−0.594398	+	0.804171i	$0.702610\pi$
$684$		0			0
$685$	−16.1560	−	11.0150i	−0.617289	−	0.420861i
$686$	21.5481	−	44.7450i	0.822709	−	1.70837i
$687$		0			0
$688$	38.9827	−	25.9757i	1.48620	−	0.990314i
$689$			27.0374i			1.03004i
$690$		0			0
$691$	18.5527	−	27.2118i	0.705778	−	1.03519i	−0.291136	−	0.956682i	$-0.594033\pi$
$691$	18.5527	−	27.2118i	0.705778	−	1.03519i	0.996914	−	0.0785042i	$-0.0250144\pi$
$692$	66.1638	−	52.7639i	2.51517	−	2.00578i
$693$		0			0
$694$	−6.95305	−	12.0430i	−0.263934	−	0.457148i
$695$	−0.315397	+	0.546283i	−0.0119637	+	0.0207217i
$696$		0			0
$697$	26.8131	+	68.3187i	1.01562	+	2.58776i
$698$	6.66336	+	21.6021i	0.252212	+	0.817650i
$699$		0			0
$700$	−14.3369	+	1.07440i	−0.541884	+	0.0406086i
$701$	1.42877	−	4.63197i	0.0539640	−	0.174947i	−0.924579	−	0.380991i	$-0.875583\pi$
$701$	1.42877	−	4.63197i	0.0539640	−	0.174947i	0.978543	+	0.206044i	$0.0660590\pi$
$702$		0			0
$703$	40.2169	−	6.06172i	1.51681	−	0.228622i
$704$	−0.811779	−	0.185283i	−0.0305951	−	0.00698313i
$705$		0			0
$706$	44.0228	+	3.29905i	1.65682	+	0.124162i
$707$	2.69268	−	6.86084i	0.101269	−	0.258028i
$708$		0			0
$709$	−41.6841	+	20.0740i	−1.56548	+	0.753895i	−0.997602	−	0.0692180i	$-0.977950\pi$
$709$	−41.6841	+	20.0740i	−1.56548	+	0.753895i	−0.567878	+	0.823113i	$0.692235\pi$
$710$	−13.9304	+	6.70852i	−0.522798	+	0.251766i
$711$		0			0
$712$	14.2626	−	36.3404i	0.534512	−	1.36192i
$713$	0.427172	+	0.0320121i	0.0159977	+	0.00119886i
$714$		0			0
$715$	−14.7182	−	3.35934i	−0.550430	−	0.125632i
$716$	67.7488	−	10.2115i	2.53189	−	0.381622i
$717$		0			0
$718$	−6.53771	+	21.1947i	−0.243985	+	0.790981i
$719$	−42.7992	+	3.20735i	−1.59614	+	0.119614i	−0.842877	−	0.538106i	$-0.819140\pi$
$719$	−42.7992	+	3.20735i	−1.59614	+	0.119614i	−0.753262	+	0.657720i	$0.771521\pi$
$720$		0			0
$721$	1.04545	+	3.38925i	0.0389345	+	0.126222i
$722$	10.6701	+	27.1869i	0.397099	+	1.01179i
$723$		0			0
$724$	10.8633	−	18.8159i	0.403733	−	0.699286i
$725$	−2.65840	−	4.60449i	−0.0987306	−	0.171006i
$726$		0			0
$727$	17.1647	−	13.6884i	0.636602	−	0.507673i	−0.251178	−	0.967941i	$-0.580818\pi$
$727$	17.1647	−	13.6884i	0.636602	−	0.507673i	0.887780	+	0.460268i	$0.152247\pi$
$728$	12.3919	−	18.1755i	0.459273	−	0.673629i
$729$		0			0
$730$		−	65.9669i		−	2.44155i
$731$	−41.4953	+	2.66670i	−1.53476	+	0.0986314i
$732$		0			0
$733$	−12.7942	+	26.5675i	−0.472565	+	0.981291i	0.519371	+	0.854549i	$0.326166\pi$
$733$	−12.7942	+	26.5675i	−0.472565	+	0.981291i	−0.991936	+	0.126742i	$0.959548\pi$
$734$	54.4201	+	37.1030i	2.00868	+	1.36950i
$735$		0			0
$736$	13.3319	+	14.3684i	0.491421	+	0.529626i
$737$	−50.1356	+	28.9458i	−1.84677	+	1.06623i
$738$		0			0
$739$	18.3660	−	4.19191i	0.675603	−	0.154202i	0.129065	−	0.991636i	$-0.458803\pi$
$739$	18.3660	−	4.19191i	0.675603	−	0.154202i	0.546538	+	0.837434i	$0.315945\pi$
$740$	−55.4612	+	21.7669i	−2.03879	+	0.800168i
$741$		0			0
$742$	41.4770	−	52.0105i	1.52267	−	1.90937i
$743$	−2.43033	−	32.4305i	−0.0891602	−	1.18976i	−0.844913	−	0.534903i	$-0.820348\pi$
$743$	−2.43033	−	32.4305i	−0.0891602	−	1.18976i	0.755753	−	0.654857i	$-0.227271\pi$
$744$		0			0
$745$	−12.1084	+	8.25535i	−0.443617	+	0.302453i
$746$	5.12175	+	33.9806i	0.187521	+	1.24412i
$747$		0			0
$748$	−92.0193	−	85.3815i	−3.36456	−	3.12186i
$749$	−2.49737	+	33.3251i	−0.0912520	+	1.21767i
$750$		0			0
$751$	6.57574	−	43.6272i	0.239952	−	1.59198i	−0.466698	−	0.884417i	$-0.654557\pi$
$751$	6.57574	−	43.6272i	0.239952	−	1.59198i	0.706651	−	0.707563i	$-0.250205\pi$
$752$	−15.1704	−	31.5016i	−0.553206	−	1.14874i
$753$		0			0
$754$	14.5190	+	2.18838i	0.528750	+	0.0796962i
$755$	−7.74541	−	3.03985i	−0.281884	−	0.110631i
$756$		0			0
$757$	−16.7890	+	18.0942i	−0.610206	+	0.657646i	−0.960268	−	0.279081i	$-0.909970\pi$
$757$	−16.7890	+	18.0942i	−0.610206	+	0.657646i	0.350061	+	0.936727i	$0.386161\pi$
$758$	−6.97933	+	30.5784i	−0.253501	+	1.11066i
$759$		0			0
$760$	−35.4747	−	52.0318i	−1.28680	−	1.88739i
$761$	−5.29294	−	1.63266i	−0.191869	−	0.0591837i	0.197332	−	0.980337i	$-0.436772\pi$
$761$	−5.29294	−	1.63266i	−0.191869	−	0.0591837i	−0.389200	+	0.921153i	$0.627249\pi$
$762$		0			0
$763$	−5.88964	−	4.69683i	−0.213219	−	0.170037i
$764$	−10.8752	+	3.35455i	−0.393450	+	0.121363i
$765$		0			0
$766$	−1.60796	−	7.04494i	−0.0580980	−	0.254544i
$767$	3.28626	+	1.89732i	0.118660	+	0.0685083i
$768$		0			0
$769$	−5.74982	+	5.33505i	−0.207344	+	0.192387i	−0.777008	−	0.629491i	$-0.783264\pi$
$769$	−5.74982	+	5.33505i	−0.207344	+	0.192387i	0.569664	+	0.821877i	$0.307073\pi$
$770$	23.1593	+	29.0408i	0.834602	+	1.04656i
$771$		0			0
$772$	13.1834	+	6.34880i	0.474481	+	0.228498i
$773$	30.5190			1.09769			0.548845	−	0.835924i	$-0.315068\pi$
$773$	30.5190			1.09769			0.548845	+	0.835924i	$0.315068\pi$
$774$		0			0
$775$	−0.211642			−0.00760241
$776$	−76.1834	−	36.6880i	−2.73482	−	1.31702i
$777$		0			0
$778$	6.55189	+	8.21581i	0.234897	+	0.294551i
$779$	−46.8330	+	43.4547i	−1.67797	+	1.55693i
$780$		0			0
$781$	−12.8730	−	7.43224i	−0.460633	−	0.265946i
$782$	−12.7210	−	55.7341i	−0.454900	−	1.99305i
$783$		0			0
$784$	24.8546	−	7.66662i	0.887663	−	0.273808i
$785$	12.9789	+	10.3504i	0.463238	+	0.369420i
$786$		0			0
$787$	16.9234	+	5.22017i	0.603254	+	0.186079i	0.581313	−	0.813680i	$-0.302539\pi$
$787$	16.9234	+	5.22017i	0.603254	+	0.186079i	0.0219408	+	0.999759i	$0.493015\pi$
$788$	−26.3617	−	38.6654i	−0.939095	−	1.37740i
$789$		0			0
$790$	5.40688	−	23.6891i	0.192368	−	0.842819i
$791$	−19.6152	+	21.1401i	−0.697436	+	0.751657i
$792$		0			0
$793$	−2.12301	−	0.833221i	−0.0753904	−	0.0295886i
$794$	24.3123	+	3.66449i	0.862811	+	0.130048i
$795$		0			0
$796$	52.6527	+	109.335i	1.86623	+	3.87526i
$797$	6.34549	−	42.0996i	0.224769	−	1.49124i	−0.537104	−	0.843516i	$-0.680482\pi$
$797$	6.34549	−	42.0996i	0.224769	−	1.49124i	0.761872	−	0.647727i	$-0.224280\pi$
$798$		0			0
$799$	−2.31929	+	30.9488i	−0.0820507	+	1.09489i
$800$	−7.09892	−	6.58683i	−0.250985	−	0.232880i
$801$		0			0
$802$	−13.3518	−	88.5835i	−0.471469	−	3.12799i
$803$	52.3997	−	35.7255i	1.84914	−	1.26072i
$804$		0			0
$805$	0.874261	+	11.6662i	0.0308136	+	0.411180i
$806$	0.364414	−	0.456961i	0.0128359	−	0.0160958i
$807$		0			0
$808$	23.6869	−	9.29641i	0.833301	−	0.327046i
$809$	19.4572	−	4.44099i	0.684080	−	0.156137i	0.133663	−	0.991027i	$-0.457326\pi$
$809$	19.4572	−	4.44099i	0.684080	−	0.156137i	0.550417	+	0.834890i	$0.314469\pi$
$810$		0			0
$811$	−12.0826	+	6.97588i	−0.424277	+	0.244956i	−0.696905	−	0.717163i	$-0.745440\pi$
$811$	−12.0826	+	6.97588i	−0.424277	+	0.244956i	0.272629	+	0.962119i	$0.412107\pi$
$812$	−16.9938	−	18.3150i	−0.596367	−	0.642731i
$813$		0			0
$814$	−68.4313	−	46.6557i	−2.39852	−	1.63528i
$815$	0.482353	−	1.00162i	0.0168961	−	0.0350851i
$816$		0			0
$817$	−15.3576	−	32.7766i	−0.537295	−	1.14671i
$818$		−	64.2854i		−	2.24769i
$819$		0			0
$820$	52.7211	−	77.3276i	1.84110	−	2.70040i
$821$	10.5748	−	8.43311i	0.369063	−	0.294318i	−0.421343	−	0.906901i	$-0.638441\pi$
$821$	10.5748	−	8.43311i	0.369063	−	0.294318i	0.790406	+	0.612584i	$0.209870\pi$
$822$		0			0
$823$	4.25281	+	7.36609i	0.148244	+	0.256766i	0.930578	−	0.366093i	$-0.119305\pi$
$823$	4.25281	+	7.36609i	0.148244	+	0.256766i	−0.782335	+	0.622858i	$0.785971\pi$
$824$	−6.12267	+	10.6048i	−0.213293	+	0.369435i
$825$		0			0
$826$	−3.41100	−	8.69109i	−0.118684	−	0.302402i
$827$	7.96183	+	25.8116i	0.276860	+	0.897558i	0.982063	+	0.188552i	$0.0603796\pi$
$827$	7.96183	+	25.8116i	0.276860	+	0.897558i	−0.705203	+	0.709005i	$0.749144\pi$
$828$		0			0
$829$	16.7188	−	1.25290i	0.580668	−	0.0435151i	0.218841	−	0.975760i	$-0.429772\pi$
$829$	16.7188	−	1.25290i	0.580668	−	0.0435151i	0.361827	+	0.932245i	$0.382153\pi$
$830$	10.1210	−	32.8116i	0.351307	−	1.13891i
$831$		0			0
$832$	−0.353822	+	0.0533300i	−0.0122666	+	0.00184889i
$833$	−22.5088	−	5.13749i	−0.779884	−	0.178003i
$834$		0			0
$835$	−38.3471	−	2.87372i	−1.32706	−	0.0994492i
$836$	39.9219	−	101.719i	1.38073	−	3.51804i
$837$		0			0
$838$	−62.9434	+	30.3119i	−2.17434	+	1.04711i
$839$	36.0428	−	17.3573i	1.24433	−	0.599240i	0.308347	−	0.951274i	$-0.400224\pi$
$839$	36.0428	−	17.3573i	1.24433	−	0.599240i	0.935987	+	0.352034i	$0.114510\pi$
$840$		0			0
$841$	−7.21929	+	18.3945i	−0.248941	+	0.634292i
$842$	−63.0996	−	4.72866i	−2.17455	−	0.162960i
$843$		0			0
$844$	−50.4079	−	11.5053i	−1.73511	−	0.396028i
$845$	16.7623	−	2.52651i	0.576641	−	0.0869147i
$846$		0			0
$847$	−4.58339	+	14.8590i	−0.157487	+	0.510560i
$848$	101.539	−	7.60927i	3.48685	−	0.261304i
$849$		0			0
$850$	8.32518	+	26.9896i	0.285551	+	0.925735i
$851$	−9.53011	−	24.2823i	−0.326688	−	0.832387i
$852$		0			0
$853$	1.53783	−	2.66359i	0.0526542	−	0.0911997i	−0.838497	−	0.544906i	$-0.816565\pi$
$853$	1.53783	−	2.66359i	0.0526542	−	0.0911997i	0.891151	+	0.453707i	$0.149899\pi$
$854$	2.80572	+	4.85965i	0.0960098	+	0.166294i
$855$		0			0
$856$	−90.2050	+	71.9361i	−3.08315	+	2.45873i
$857$	−21.1534	+	31.0264i	−0.722587	+	1.05984i	0.272627	+	0.962120i	$0.412107\pi$
$857$	−21.1534	+	31.0264i	−0.722587	+	1.05984i	−0.995214	+	0.0977203i	$0.968845\pi$
$858$		0			0
$859$			47.3719i			1.61631i	0.588972	+	0.808154i	$0.299533\pi$
$859$			47.3719i			1.61631i	−0.588972	+	0.808154i	$0.700467\pi$
$860$	32.6178	+	41.8049i	1.11226	+	1.42553i
$861$		0			0
$862$	19.3961	−	40.2765i	0.660635	−	1.37182i
$863$	−34.2876	−	23.3769i	−1.16716	−	0.795759i	−0.184807	−	0.982775i	$-0.559166\pi$
$863$	−34.2876	−	23.3769i	−1.16716	−	0.795759i	−0.982357	+	0.187016i	$0.940119\pi$
$864$		0			0
$865$	23.1411	+	24.9402i	0.786822	+	0.847992i
$866$	−3.39962	+	1.96277i	−0.115524	+	0.0666977i
$867$		0			0
$868$	−0.969609	+	0.221307i	−0.0329107	+	0.00751165i
$869$	21.7452	−	8.53435i	0.737654	−	0.289508i
$870$		0			0
$871$	−15.5111	+	19.4503i	−0.525573	+	0.659048i
$872$	−1.94357	−	25.9352i	−0.0658177	−	0.878276i
$873$		0			0
$874$	41.1171	−	28.0332i	1.39081	−	0.948236i
$875$	−3.32401	−	22.0534i	−0.112372	−	0.745540i
$876$		0			0
$877$	28.3672	+	26.3209i	0.957892	+	0.888794i	0.993870	−	0.110559i	$-0.0352641\pi$
$877$	28.3672	+	26.3209i	0.957892	+	0.888794i	−0.0359779	+	0.999353i	$0.511455\pi$
$878$	6.38519	−	85.2044i	0.215490	−	2.87551i
$879$		0			0
$880$	−8.47372	+	56.2195i	−0.285649	+	1.89516i
$881$	−6.72334	−	13.9612i	−0.226515	−	0.470364i	0.756475	−	0.654023i	$-0.226920\pi$
$881$	−6.72334	−	13.9612i	−0.226515	−	0.470364i	−0.982990	+	0.183659i	$0.941206\pi$
$882$		0			0
$883$	21.2064	+	3.19636i	0.713653	+	0.107566i	0.495827	−	0.868422i	$-0.334865\pi$
$883$	21.2064	+	3.19636i	0.713653	+	0.107566i	0.217827	+	0.975987i	$0.430103\pi$
$884$	−50.2149	−	19.7079i	−1.68891	−	0.662848i
$885$		0			0
$886$	20.3860	−	21.9709i	0.684882	−	0.738127i
$887$	−0.453585	+	1.98728i	−0.0152299	+	0.0667265i	−0.981972	−	0.189027i	$-0.939467\pi$
$887$	−0.453585	+	1.98728i	−0.0152299	+	0.0667265i	0.966742	+	0.255754i	$0.0823237\pi$
$888$		0			0
$889$	−16.5649	−	24.2963i	−0.555570	−	0.814871i
$890$	27.0691	+	8.34972i	0.907360	+	0.279883i
$891$		0			0
$892$	100.325	+	80.0066i	3.35913	+	2.67882i
$893$	−25.8162	+	7.96325i	−0.863906	+	0.266480i
$894$		0			0
$895$	6.12927	+	26.8541i	0.204879	+	0.897633i
$896$	18.3376	+	10.5872i	0.612615	+	0.353694i
$897$		0			0
$898$	−45.3942	+	42.1196i	−1.51482	+	1.40555i
$899$	−0.229315	−	0.287552i	−0.00764810	−	0.00959041i
$900$		0			0
$901$	−81.4320	−	39.2156i	−2.71289	−	1.30646i
$902$	130.101			4.33188
$903$		0			0
$904$	−99.5642			−3.31146
$905$	7.86976	+	3.78987i	0.261600	+	0.125980i
$906$		0			0
$907$	−21.1633	−	26.5380i	−0.702716	−	0.881179i	0.294507	−	0.955649i	$-0.404845\pi$
$907$	−21.1633	−	26.5380i	−0.702716	−	0.881179i	−0.997223	+	0.0744709i	$0.976273\pi$
$908$	−16.7936	+	15.5822i	−0.557316	+	0.517114i
$909$		0			0
$910$	13.8237	+	7.98109i	0.458250	+	0.264571i
$911$	−0.166308	−	0.728643i	−0.00551003	−	0.0241410i	0.972098	−	0.234574i	$-0.0753696\pi$
$911$	−0.166308	−	0.728643i	−0.00551003	−	0.0241410i	−0.977608	+	0.210433i	$0.932513\pi$
$912$		0			0
$913$	31.5446	−	9.73021i	1.04397	−	0.322023i
$914$	2.66167	+	2.12261i	0.0880403	+	0.0702098i
$915$		0			0
$916$	−110.723	−	34.1536i	−3.65840	−	1.12847i
$917$	−0.221731	−	0.325219i	−0.00732219	−	0.0107397i
$918$		0			0
$919$	2.08417	−	9.13137i	0.0687506	−	0.301216i	−0.928849	−	0.370458i	$-0.879201\pi$
$919$	2.08417	−	9.13137i	0.0687506	−	0.301216i	0.997600	+	0.0692417i	$0.0220580\pi$
$920$	−27.4723	+	29.6081i	−0.905734	+	0.976149i
$921$		0			0
$922$	2.74649	+	1.07792i	0.0904508	+	0.0354993i
$923$	−6.31639	−	0.952042i	−0.207906	−	0.0313368i
$924$		0			0
$925$	5.59186	+	11.6116i	0.183859	+	0.381788i
$926$	−7.98467	+	52.9748i	−0.262393	+	1.74086i
$927$		0			0
$928$	1.25763	−	16.7820i	0.0412839	−	0.550895i
$929$	12.3532	+	11.4621i	0.405294	+	0.376058i	0.856314	−	0.516456i	$-0.172749\pi$
$929$	12.3532	+	11.4621i	0.405294	+	0.376058i	−0.451019	+	0.892514i	$0.648939\pi$
$930$		0			0
$931$	−2.99542	−	19.8733i	−0.0981710	−	0.651322i
$932$	21.8789	−	14.9168i	0.716668	−	0.488616i
$933$		0			0
$934$	2.90607	+	38.7788i	0.0950895	+	1.26888i
$935$	31.4653	−	39.4562i	1.02902	−	1.29036i
$936$		0			0
$937$	23.7330	−	9.31453i	0.775325	−	0.304293i	0.0555094	−	0.998458i	$-0.482322\pi$
$937$	23.7330	−	9.31453i	0.775325	−	0.304293i	0.719815	+	0.694166i	$0.244226\pi$
$938$	59.6757	−	13.6206i	1.94848	−	0.444728i
$939$		0			0
$940$	34.2745	−	19.7884i	1.11791	−	0.645426i
$941$	9.11755	+	9.82638i	0.297224	+	0.320331i	0.863952	−	0.503574i	$-0.167982\pi$
$941$	9.11755	+	9.82638i	0.297224	+	0.320331i	−0.566729	+	0.823904i	$0.691791\pi$
$942$		0			0
$943$	33.8560	+	23.0826i	1.10250	+	0.751674i
$944$	6.20049	−	12.8755i	0.201809	−	0.419061i
$945$		0			0
$946$	−22.4733	+	70.2003i	−0.730671	+	2.28241i
$947$			15.6761i			0.509406i	0.967019	+	0.254703i	$0.0819777\pi$
$947$			15.6761i			0.509406i	−0.967019	+	0.254703i	$0.918022\pi$
$948$		0			0
$949$	15.3524	−	22.5178i	0.498359	−	0.730958i
$950$	−19.2227	+	15.3296i	−0.623666	+	0.497357i
$951$		0			0
$952$	36.7681	+	63.6842i	1.19166	+	2.06402i
$953$	−22.0859	+	38.2539i	−0.715432	+	1.23917i	0.247360	+	0.968924i	$0.420437\pi$
$953$	−22.0859	+	38.2539i	−0.715432	+	1.23917i	−0.962793	+	0.270242i	$0.912896\pi$
$954$		0			0
$955$	−1.67159	−	4.25913i	−0.0540913	−	0.137822i
$956$	26.0958	+	84.6005i	0.843998	+	2.73617i
$957$		0			0
$958$	59.6756	−	4.47207i	1.92803	−	0.144486i
$959$	−5.85863	+	18.9932i	−0.189185	+	0.613323i
$960$		0			0
$961$	30.6393	−	4.61813i	0.988364	−	0.148972i
$962$	−34.6991	−	7.91985i	−1.11875	−	0.255346i
$963$		0			0
$964$	−74.9121	−	5.61388i	−2.41276	−	0.180811i
$965$	−2.14919	+	5.47604i	−0.0691848	+	0.176280i
$966$		0			0
$967$	1.13821	−	0.548133i	0.0366024	−	0.0176268i	−0.415493	−	0.909596i	$-0.636391\pi$
$967$	1.13821	−	0.548133i	0.0366024	−	0.0176268i	0.452095	+	0.891970i	$0.350677\pi$
$968$	−48.3688	+	23.2932i	−1.55463	+	0.748671i
$969$		0			0
$970$	22.4161	−	57.1153i	0.719738	−	1.83386i
$971$	−12.5075	−	0.937310i	−0.401386	−	0.0300797i	−0.127492	−	0.991840i	$-0.540693\pi$
$971$	−12.5075	−	0.937310i	−0.401386	−	0.0300797i	−0.273894	+	0.961760i	$0.588312\pi$
$972$		0			0
$973$	0.625124	+	0.142680i	0.0200406	+	0.00457413i
$974$	−0.176062	+	0.0265371i	−0.00564139	+	0.000850303i
$975$		0			0
$976$	−2.53166	+	8.20744i	−0.0810365	+	0.262714i
$977$	47.7656	−	3.57954i	1.52816	−	0.114520i	0.716059	−	0.698040i	$-0.245944\pi$
$977$	47.7656	−	3.57954i	1.52816	−	0.114520i	0.812099	+	0.583520i	$0.198325\pi$
$978$		0			0
$979$	8.02728	+	26.0238i	0.256553	+	0.831725i
$980$	10.7562	+	27.4063i	0.343594	+	0.875463i
$981$		0			0
$982$	−25.7795	+	44.6513i	−0.822656	+	1.42488i
$983$	26.9311	+	46.6461i	0.858970	+	1.48778i	0.872913	+	0.487876i	$0.162228\pi$
$983$	26.9311	+	46.6461i	0.858970	+	1.48778i	−0.0139432	+	0.999903i	$0.504438\pi$
$984$		0			0
$985$	14.7092	−	11.7302i	0.468674	−	0.373755i
$986$	−27.6496	+	40.5545i	−0.880543	+	1.29152i
$987$		0			0
$988$		−	46.9580i		−	1.49393i
$989$	−18.3032	+	14.2809i	−0.582009	+	0.454106i
$990$		0			0
$991$	−16.8995	+	35.0922i	−0.536830	+	1.11474i	0.439458	+	0.898263i	$0.355171\pi$
$991$	−16.8995	+	35.0922i	−0.536830	+	1.11474i	−0.976288	+	0.216476i	$0.930544\pi$
$992$	−0.553498	−	0.377368i	−0.0175736	−	0.0119815i
$993$		0			0
$994$	10.6900	+	11.5211i	0.339067	+	0.365427i
$995$	−42.2509	+	24.3936i	−1.33944	+	0.773329i
$996$		0			0
$997$	−33.7291	+	7.69845i	−1.06821	+	0.243812i	−0.720263	−	0.693701i	$-0.755979\pi$
$997$	−33.7291	+	7.69845i	−1.06821	+	0.243812i	−0.347949	+	0.937514i	$0.613122\pi$
$998$	−4.67649	+	1.83539i	−0.148032	+	0.0580981i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	387.2.bc.a.233.14	yes	168
3.2	odd	2	inner	387.2.bc.a.233.1	yes	168
43.12	odd	42	inner	387.2.bc.a.98.1	✓	168
129.98	even	42	inner	387.2.bc.a.98.14	yes	168

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
387.2.bc.a.98.1	✓	168	43.12	odd	42	inner
387.2.bc.a.98.14	yes	168	129.98	even	42	inner
387.2.bc.a.233.1	yes	168	3.2	odd	2	inner
387.2.bc.a.233.14	yes	168	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 387 = 3^{2} \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	387.bc (of order \(42\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(2.29434 + 1.10489i) q^{2} +(2.79621 + 3.50634i) q^{4} +(-1.32170 + 1.22636i) q^{5} +(1.58722 + 0.916379i) q^{7} +(1.40801 + 6.16890i) q^{8} +O(q^{10})\)	\(q+(2.29434 + 1.10489i) q^{2} +(2.79621 + 3.50634i) q^{4} +(-1.32170 + 1.22636i) q^{5} +(1.58722 + 0.916379i) q^{7} +(1.40801 + 6.16890i) q^{8} +(-4.38743 + 1.35334i) q^{10} +(-3.45109 - 2.75215i) q^{11} +(-1.81261 - 0.559116i) q^{13} +(2.62911 + 3.85619i) q^{14} +(-1.58962 + 6.96458i) q^{16} +(4.31300 - 4.64831i) q^{17} +(5.13830 + 2.01663i) q^{19} +(-7.99580 - 1.20517i) q^{20} +(-4.87713 - 10.1275i) q^{22} +(0.527656 - 3.50077i) q^{23} +(-0.130713 + 1.74425i) q^{25} +(-3.54097 - 3.28554i) q^{26} +(1.22506 + 8.12771i) q^{28} +(-2.51149 + 1.71231i) q^{29} +(0.00904218 + 0.120660i) q^{31} +(-3.45193 + 4.32858i) q^{32} +(15.0314 - 5.89938i) q^{34} +(-3.22164 + 0.735318i) q^{35} +(6.38100 - 3.68407i) q^{37} +(9.56082 + 10.3041i) q^{38} +(-9.42627 - 6.42672i) q^{40} +(-5.02184 + 10.4279i) q^{41} +(-4.75929 - 4.51100i) q^{43} -19.7963i q^{44} +(5.07860 - 7.44894i) q^{46} +(-3.82660 + 3.05161i) q^{47} +(-1.82050 - 3.15319i) q^{49} +(-2.22711 + 3.85747i) q^{50} +(-3.10799 - 7.91903i) q^{52} +(-4.20133 - 13.6204i) q^{53} +(7.93645 - 0.594755i) q^{55} +(-3.41824 + 11.0817i) q^{56} +(-7.65413 + 1.15367i) q^{58} +(-1.95031 - 0.445145i) q^{59} +(1.19896 + 0.0898498i) q^{61} +(-0.112570 + 0.286824i) q^{62} +(0.169954 - 0.0818456i) q^{64} +(3.08141 - 1.48393i) q^{65} +(4.79149 - 12.2085i) q^{67} +(28.3586 + 2.12518i) q^{68} +(-8.20398 - 1.87250i) q^{70} +(3.32988 - 0.501898i) q^{71} +(-4.23488 + 13.7291i) q^{73} +(18.7107 - 1.40217i) q^{74} +(7.29677 + 23.6556i) q^{76} +(-2.95561 - 7.53077i) q^{77} +(-2.64605 + 4.58310i) q^{79} +(-6.44008 - 11.1546i) q^{80} +(-23.0436 + 18.3766i) q^{82} +(-4.21282 + 6.17907i) q^{83} +11.4330i q^{85} +(-5.93524 - 15.6083i) q^{86} +(12.1186 - 25.1645i) q^{88} +(-5.09764 - 3.47551i) q^{89} +(-2.36464 - 2.54847i) q^{91} +(13.7503 - 7.93875i) q^{92} +(-12.1512 + 2.77344i) q^{94} +(-9.26442 + 3.63602i) q^{95} +(-8.33191 + 10.4479i) q^{97} +(-0.692888 - 9.24595i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 168 q - 24 q^{4} - 6 q^{7}+O(q^{10}) \) 168 * q - 24 * q^4 - 6 * q^7	\( 168 q - 24 q^{4} - 6 q^{7} + 8 q^{10} + 26 q^{13} - 8 q^{16} + 24 q^{19} + 14 q^{25} + 32 q^{31} - 48 q^{34} - 78 q^{37} - 244 q^{40} - 32 q^{43} - 92 q^{46} + 54 q^{49} + 76 q^{52} - 96 q^{55} - 20 q^{58} - 96 q^{64} - 18 q^{67} + 140 q^{70} + 10 q^{73} - 16 q^{76} - 168 q^{88} - 38 q^{91} - 112 q^{94} - 40 q^{97}+O(q^{100}) \) 168 * q - 24 * q^4 - 6 * q^7 + 8 * q^10 + 26 * q^13 - 8 * q^16 + 24 * q^19 + 14 * q^25 + 32 * q^31 - 48 * q^34 - 78 * q^37 - 244 * q^40 - 32 * q^43 - 92 * q^46 + 54 * q^49 + 76 * q^52 - 96 * q^55 - 20 * q^58 - 96 * q^64 - 18 * q^67 + 140 * q^70 + 10 * q^73 - 16 * q^76 - 168 * q^88 - 38 * q^91 - 112 * q^94 - 40 * q^97

Introduction

L-functions

Modular forms

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