LMFDB - Embedded newform 1674.2.q.a.1115.23

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1674,2,Mod(557,1674)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1674.557"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1674, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1674 = 2 \cdot 3^{3} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1674.q (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$13.3669572984$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 558)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1115.23
Character	$\chi$	$=$	1674.1115
Dual form			1674.2.q.a.557.23

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-1.92707 + 1.11259i) q^{5} +(0.556441 - 0.963784i) q^{7} +1.00000i q^{8} -2.22519 q^{10} +(0.510234 - 0.883751i) q^{11} +(2.77056 - 1.59958i) q^{13} +(0.963784 - 0.556441i) q^{14} +(-0.500000 + 0.866025i) q^{16} +4.61929 q^{17} +2.48701 q^{19} +(-1.92707 - 1.11259i) q^{20} +(0.883751 - 0.510234i) q^{22} +(1.93084 + 3.34431i) q^{23} +(-0.0242726 + 0.0420413i) q^{25} +3.19916 q^{26} +1.11288 q^{28} +(2.06180 - 3.57113i) q^{29} +(-4.17770 - 3.68060i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(4.00043 + 2.30965i) q^{34} +2.47637i q^{35} +9.83752i q^{37} +(2.15382 + 1.24351i) q^{38} +(-1.11259 - 1.92707i) q^{40} +(-9.95860 + 5.74960i) q^{41} +(5.89094 + 3.40113i) q^{43} +1.02047 q^{44} +3.86168i q^{46} +(8.88791 + 5.13144i) q^{47} +(2.88075 + 4.98960i) q^{49} +(-0.0420413 + 0.0242726i) q^{50} +(2.77056 + 1.59958i) q^{52} +9.85277 q^{53} +2.27073i q^{55} +(0.963784 + 0.556441i) q^{56} +(3.57113 - 2.06180i) q^{58} +(-5.10909 + 2.94973i) q^{59} +(1.55017 + 0.894989i) q^{61} +(-1.77769 - 5.27635i) q^{62} -1.00000 q^{64} +(-3.55937 + 6.16501i) q^{65} +(-1.63010 - 2.82341i) q^{67} +(2.30965 + 4.00043i) q^{68} +(-1.23818 + 2.14460i) q^{70} +1.19637i q^{71} -6.14833i q^{73} +(-4.91876 + 8.51955i) q^{74} +(1.24351 + 2.15382i) q^{76} +(-0.567830 - 0.983510i) q^{77} +(2.18886 + 1.26374i) q^{79} -2.22519i q^{80} -11.4992 q^{82} +(1.01481 - 1.75771i) q^{83} +(-8.90169 + 5.13940i) q^{85} +(3.40113 + 5.89094i) q^{86} +(0.883751 + 0.510234i) q^{88} +5.33213 q^{89} -3.56029i q^{91} +(-1.93084 + 3.34431i) q^{92} +(5.13144 + 8.88791i) q^{94} +(-4.79264 + 2.76703i) q^{95} +(1.06005 - 1.83605i) q^{97} +5.76149i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 32 q^{4} - 12 q^{5} - 4 q^{7} - 32 q^{16} - 8 q^{19} - 12 q^{20} + 44 q^{25} - 8 q^{28} + 8 q^{31} - 36 q^{38} - 24 q^{41} + 48 q^{47} - 36 q^{49} + 12 q^{59} - 64 q^{64} + 16 q^{67} - 12 q^{70}+ \cdots - 16 q^{97}+O(q^{100}) $ 64 * q + 32 * q^4 - 12 * q^5 - 4 * q^7 - 32 * q^16 - 8 * q^19 - 12 * q^20 + 44 * q^25 - 8 * q^28 + 8 * q^31 - 36 * q^38 - 24 * q^41 + 48 * q^47 - 36 * q^49 + 12 * q^59 - 64 * q^64 + 16 * q^67 - 12 * q^70 - 4 * q^76 + 180 * q^95 - 16 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1674\mathbb{Z}\right)^\times$.

$n$	$1055$	$1243$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−1.92707	+	1.11259i	−0.861811	+	0.497567i	−0.864618	−	0.502429i	$-0.832440\pi$
$5$	−1.92707	+	1.11259i	−0.861811	+	0.497567i	0.00280731	+	0.999996i	$0.499106\pi$
$6$		0			0
$7$	0.556441	−	0.963784i	0.210315	−	0.364276i	−0.741498	−	0.670955i	$-0.765884\pi$
$7$	0.556441	−	0.963784i	0.210315	−	0.364276i	0.951813	+	0.306679i	$0.0992178\pi$
$8$			1.00000i			0.353553i
$9$		0			0
$10$	−2.22519			−0.703666
$11$	0.510234	−	0.883751i	0.153841	−	0.266461i	−0.778795	−	0.627278i	$-0.784169\pi$
$11$	0.510234	−	0.883751i	0.153841	−	0.266461i	0.932636	+	0.360817i	$0.117502\pi$
$12$		0			0
$13$	2.77056	−	1.59958i	0.768414	−	0.443644i	−0.0638944	−	0.997957i	$-0.520352\pi$
$13$	2.77056	−	1.59958i	0.768414	−	0.443644i	0.832309	+	0.554313i	$0.187019\pi$
$14$	0.963784	−	0.556441i	0.257582	−	0.148715i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	4.61929			1.12034			0.560172	−	0.828377i	$-0.310735\pi$
$17$	4.61929			1.12034			0.560172	+	0.828377i	$0.310735\pi$
$18$		0			0
$19$	2.48701			0.570560			0.285280	−	0.958444i	$-0.407913\pi$
$19$	2.48701			0.570560			0.285280	+	0.958444i	$0.407913\pi$
$20$	−1.92707	−	1.11259i	−0.430906	−	0.248783i
$21$		0			0
$22$	0.883751	−	0.510234i	0.188416	−	0.108782i
$23$	1.93084	+	3.34431i	0.402608	+	0.697338i	0.994040	−	0.109017i	$-0.0347704\pi$
$23$	1.93084	+	3.34431i	0.402608	+	0.697338i	−0.591432	+	0.806355i	$0.701437\pi$
$24$		0			0
$25$	−0.0242726	+	0.0420413i	−0.00485451	+	0.00840826i
$26$	3.19916			0.627408
$27$		0			0
$28$	1.11288			0.210315
$29$	2.06180	−	3.57113i	0.382866	−	0.663143i	−0.608605	−	0.793473i	$-0.708270\pi$
$29$	2.06180	−	3.57113i	0.382866	−	0.663143i	0.991471	+	0.130330i	$0.0416038\pi$
$30$		0			0
$31$	−4.17770	−	3.68060i	−0.750337	−	0.661056i
$31$	−4.17770	−	3.68060i	−0.750337	−	0.661056i
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$		0			0
$34$	4.00043	+	2.30965i	0.686067	+	0.396101i
$35$			2.47637i			0.418583i
$36$		0			0
$37$			9.83752i			1.61728i	0.588304	+	0.808640i	$0.299796\pi$
$37$			9.83752i			1.61728i	−0.588304	+	0.808640i	$0.700204\pi$
$38$	2.15382	+	1.24351i	0.349395	+	0.201723i
$39$		0			0
$40$	−1.11259	−	1.92707i	−0.175916	−	0.304696i
$41$	−9.95860	+	5.74960i	−1.55527	+	0.897937i	−0.557574	+	0.830127i	$0.688268\pi$
$41$	−9.95860	+	5.74960i	−1.55527	+	0.897937i	−0.997698	+	0.0678092i	$0.978399\pi$
$42$		0			0
$43$	5.89094	+	3.40113i	0.898360	+	0.518668i	0.876668	−	0.481097i	$-0.159761\pi$
$43$	5.89094	+	3.40113i	0.898360	+	0.518668i	0.0216919	+	0.999765i	$0.493095\pi$
$44$	1.02047			0.153841
$45$		0			0
$46$			3.86168i			0.569374i
$47$	8.88791	+	5.13144i	1.29644	+	0.748497i	0.979787	−	0.200046i	$-0.0641091\pi$
$47$	8.88791	+	5.13144i	1.29644	+	0.748497i	0.316649	+	0.948543i	$0.397442\pi$
$48$		0			0
$49$	2.88075	+	4.98960i	0.411535	+	0.712800i
$50$	−0.0420413	+	0.0242726i	−0.00594554	+	0.00343266i
$51$		0			0
$52$	2.77056	+	1.59958i	0.384207	+	0.221822i
$53$	9.85277			1.35338			0.676691	−	0.736267i	$-0.263413\pi$
$53$	9.85277			1.35338			0.676691	+	0.736267i	$0.263413\pi$
$54$		0			0
$55$			2.27073i			0.306185i
$56$	0.963784	+	0.556441i	0.128791	+	0.0743575i
$57$		0			0
$58$	3.57113	−	2.06180i	0.468913	−	0.270727i
$59$	−5.10909	+	2.94973i	−0.665146	+	0.384022i	−0.794235	−	0.607611i	$-0.792128\pi$
$59$	−5.10909	+	2.94973i	−0.665146	+	0.384022i	0.129089	+	0.991633i	$0.458795\pi$
$60$		0			0
$61$	1.55017	+	0.894989i	0.198478	+	0.114592i	0.595946	−	0.803025i	$-0.296777\pi$
$61$	1.55017	+	0.894989i	0.198478	+	0.114592i	−0.397467	+	0.917616i	$0.630111\pi$
$62$	−1.77769	−	5.27635i	−0.225767	−	0.670096i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−3.55937	+	6.16501i	−0.441485	+	0.764675i
$66$		0			0
$67$	−1.63010	−	2.82341i	−0.199148	−	0.344935i	0.749104	−	0.662452i	$-0.230484\pi$
$67$	−1.63010	−	2.82341i	−0.199148	−	0.344935i	−0.948252	+	0.317517i	$0.897151\pi$
$68$	2.30965	+	4.00043i	0.280086	+	0.485123i
$69$		0			0
$70$	−1.23818	+	2.14460i	−0.147991	+	0.256329i
$71$			1.19637i			0.141983i	0.997477	+	0.0709913i	$0.0226163\pi$
$71$			1.19637i			0.141983i	−0.997477	+	0.0709913i	$0.977384\pi$
$72$		0			0
$73$		−	6.14833i		−	0.719608i	−0.933028	−	0.359804i	$-0.882844\pi$
$73$		−	6.14833i		−	0.719608i	0.933028	−	0.359804i	$-0.117156\pi$
$74$	−4.91876	+	8.51955i	−0.571795	+	0.990377i
$75$		0			0
$76$	1.24351	+	2.15382i	0.142640	+	0.247060i
$77$	−0.567830	−	0.983510i	−0.0647102	−	0.112081i
$78$		0			0
$79$	2.18886	+	1.26374i	0.246266	+	0.142182i	0.618053	−	0.786136i	$-0.287922\pi$
$79$	2.18886	+	1.26374i	0.246266	+	0.142182i	−0.371787	+	0.928318i	$0.621255\pi$
$80$		−	2.22519i		−	0.248783i
$81$		0			0
$82$	−11.4992			−1.26987
$83$	1.01481	−	1.75771i	0.111390	−	0.192933i	−0.804941	−	0.593355i	$-0.797803\pi$
$83$	1.01481	−	1.75771i	0.111390	−	0.192933i	0.916331	+	0.400422i	$0.131136\pi$
$84$		0			0
$85$	−8.90169	+	5.13940i	−0.965524	+	0.557446i
$86$	3.40113	+	5.89094i	0.366754	+	0.635236i
$87$		0			0
$88$	0.883751	+	0.510234i	0.0942081	+	0.0543911i
$89$	5.33213			0.565204			0.282602	−	0.959237i	$-0.408802\pi$
$89$	5.33213			0.565204			0.282602	+	0.959237i	$0.408802\pi$
$90$		0			0
$91$		−	3.56029i		−	0.373220i
$92$	−1.93084	+	3.34431i	−0.201304	+	0.348669i
$93$		0			0
$94$	5.13144	+	8.88791i	0.529267	+	0.916718i
$95$	−4.79264	+	2.76703i	−0.491715	+	0.283892i
$96$		0			0
$97$	1.06005	−	1.83605i	0.107631	−	0.186423i	−0.807179	−	0.590307i	$-0.799007\pi$
$97$	1.06005	−	1.83605i	0.107631	−	0.186423i	0.914810	+	0.403884i	$0.132340\pi$
$98$			5.76149i			0.581999i
$99$		0			0
$100$	−0.0485451			−0.00485451
$101$	−1.98249	−	1.14459i	−0.197265	−	0.113891i	0.398114	−	0.917336i	$-0.369665\pi$
$101$	−1.98249	−	1.14459i	−0.197265	−	0.113891i	−0.595379	+	0.803445i	$0.702998\pi$
$102$		0			0
$103$	−0.608600	−	1.05413i	−0.0599671	−	0.103866i	0.834483	−	0.551033i	$-0.185766\pi$
$103$	−0.608600	−	1.05413i	−0.0599671	−	0.103866i	−0.894450	+	0.447167i	$0.852433\pi$
$104$	1.59958	+	2.77056i	0.156852	+	0.271675i
$105$		0			0
$106$	8.53275	+	4.92639i	0.828774	+	0.478493i
$107$		−	10.3952i		−	1.00494i	−0.864594	−	0.502472i	$-0.832424\pi$
$107$		−	10.3952i		−	1.00494i	0.864594	−	0.502472i	$-0.167576\pi$
$108$		0			0
$109$	−11.6174			−1.11275			−0.556373	−	0.830933i	$-0.687807\pi$
$109$	−11.6174			−1.11275			−0.556373	+	0.830933i	$0.687807\pi$
$110$	−1.13536	+	1.96651i	−0.108253	+	0.187499i
$111$		0			0
$112$	0.556441	+	0.963784i	0.0525787	+	0.0910690i
$113$	14.5565	−	8.40422i	1.36936	−	0.790602i	0.378517	−	0.925595i	$-0.376434\pi$
$113$	14.5565	−	8.40422i	1.36936	−	0.790602i	0.990847	+	0.134992i	$0.0431010\pi$
$114$		0			0
$115$	−7.44172	−	4.29648i	−0.693944	−	0.400649i
$116$	4.12359			0.382866
$117$		0			0
$118$	−5.89947			−0.543090
$119$	2.57036	−	4.45200i	0.235625	−	0.408114i
$120$		0			0
$121$	4.97932	+	8.62444i	0.452666	+	0.784040i
$122$	0.894989	+	1.55017i	0.0810285	+	0.140345i
$123$		0			0
$124$	1.09865	−	5.45829i	0.0986615	−	0.490169i
$125$		−	11.2340i		−	1.00480i
$126$		0			0
$127$		−	2.30229i		−	0.204295i	−0.994769	−	0.102147i	$-0.967429\pi$
$127$		−	2.30229i		−	0.204295i	0.994769	−	0.102147i	$-0.0325713\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$		0			0
$130$	−6.16501	+	3.55937i	−0.540707	+	0.312177i
$131$	4.64203	−	2.68008i	0.405576	−	0.234159i	−0.283311	−	0.959028i	$-0.591433\pi$
$131$	4.64203	−	2.68008i	0.405576	−	0.234159i	0.688887	+	0.724869i	$0.258100\pi$
$132$		0			0
$133$	1.38388	−	2.39694i	0.119997	−	0.207841i
$134$		−	3.26020i		−	0.281638i
$135$		0			0
$136$			4.61929i			0.396101i
$137$	6.98169	−	12.0926i	0.596486	−	1.03314i	−0.396849	−	0.917884i	$-0.629896\pi$
$137$	6.98169	−	12.0926i	0.596486	−	1.03314i	0.993335	−	0.115260i	$-0.0367703\pi$
$138$		0			0
$139$	−6.56075	+	3.78785i	−0.556476	+	0.321281i	−0.751730	−	0.659471i	$-0.770780\pi$
$139$	−6.56075	+	3.78785i	−0.556476	+	0.321281i	0.195254	+	0.980753i	$0.437447\pi$
$140$	−2.14460	+	1.23818i	−0.181252	+	0.104646i
$141$		0			0
$142$	−0.598183	+	1.03608i	−0.0501984	+	0.0869462i
$143$		−	3.26464i		−	0.273003i
$144$		0			0
$145$			9.17576i			0.762005i
$146$	3.07417	−	5.32461i	0.254420	−	0.440668i
$147$		0			0
$148$	−8.51955	+	4.91876i	−0.700302	+	0.404320i
$149$	−4.53497	+	2.61827i	−0.371519	+	0.214497i	−0.674122	−	0.738620i	$-0.735478\pi$
$149$	−4.53497	+	2.61827i	−0.371519	+	0.214497i	0.302603	+	0.953117i	$0.402144\pi$
$150$		0			0
$151$	−8.53103	−	4.92539i	−0.694245	−	0.400823i	0.110955	−	0.993825i	$-0.464609\pi$
$151$	−8.53103	−	4.92539i	−0.694245	−	0.400823i	−0.805200	+	0.593003i	$0.797942\pi$
$152$			2.48701i			0.201723i
$153$		0			0
$154$		−	1.13566i		−	0.0915140i
$155$	12.1457	+	2.44470i	0.975568	+	0.196363i
$156$		0			0
$157$	6.67621	+	11.5635i	0.532819	+	0.922870i	0.999265	+	0.0383206i	$0.0122008\pi$
$157$	6.67621	+	11.5635i	0.532819	+	0.922870i	−0.466446	+	0.884550i	$0.654466\pi$
$158$	1.26374	+	2.18886i	0.100538	+	0.174136i
$159$		0			0
$160$	1.11259	−	1.92707i	0.0879582	−	0.152348i
$161$	4.29760			0.338698
$162$		0			0
$163$	−13.6554			−1.06957			−0.534787	−	0.844987i	$-0.679608\pi$
$163$	−13.6554			−1.06957			−0.534787	+	0.844987i	$0.679608\pi$
$164$	−9.95860	−	5.74960i	−0.777636	−	0.448968i
$165$		0			0
$166$	1.75771	−	1.01481i	0.136424	−	0.0787647i
$167$	−3.02979	−	5.24776i	−0.234453	−	0.406084i	0.724661	−	0.689106i	$-0.241996\pi$
$167$	−3.02979	−	5.24776i	−0.234453	−	0.406084i	−0.959113	+	0.283022i	$0.908663\pi$
$168$		0			0
$169$	−1.38268	+	2.39487i	−0.106360	+	0.184221i
$170$	−10.2788			−0.788347
$171$		0			0
$172$			6.80227i			0.518668i
$173$	12.7432	+	7.35730i	0.968849	+	0.559365i	0.898885	−	0.438184i	$-0.144378\pi$
$173$	12.7432	+	7.35730i	0.968849	+	0.559365i	0.0699640	+	0.997550i	$0.477712\pi$
$174$		0			0
$175$	0.0270125	+	0.0467870i	0.00204195	+	0.00353676i
$176$	0.510234	+	0.883751i	0.0384603	+	0.0666152i
$177$		0			0
$178$	4.61776	+	2.66606i	0.346116	+	0.199830i
$179$	13.1686			0.984269			0.492135	−	0.870519i	$-0.336217\pi$
$179$	13.1686			0.984269			0.492135	+	0.870519i	$0.336217\pi$
$180$		0			0
$181$			0.183146i			0.0136132i	0.999977	+	0.00680658i	$0.00216662\pi$
$181$			0.183146i			0.0136132i	−0.999977	+	0.00680658i	$0.997833\pi$
$182$	1.78014	−	3.08330i	0.131953	−	0.228550i
$183$		0			0
$184$	−3.34431	+	1.93084i	−0.246546	+	0.142343i
$185$	−10.9452	−	18.9576i	−0.804704	−	1.39379i
$186$		0			0
$187$	2.35692	−	4.08230i	0.172355	−	0.298528i
$188$			10.2629i			0.748497i
$189$		0			0
$190$	−5.53407			−0.401483
$191$	−0.0556007	−	0.0321011i	−0.00402313	−	0.00232275i	0.497987	−	0.867184i	$-0.334073\pi$
$191$	−0.0556007	−	0.0321011i	−0.00402313	−	0.00232275i	−0.502010	+	0.864862i	$0.667406\pi$
$192$		0			0
$193$	−1.25910	−	2.18083i	−0.0906320	−	0.156979i	0.817145	−	0.576432i	$-0.195555\pi$
$193$	−1.25910	−	2.18083i	−0.0906320	−	0.156979i	−0.907777	+	0.419453i	$0.862222\pi$
$194$	1.83605	−	1.06005i	0.131821	−	0.0761068i
$195$		0			0
$196$	−2.88075	+	4.98960i	−0.205768	+	0.356400i
$197$	−18.4548			−1.31485			−0.657426	−	0.753519i	$-0.728355\pi$
$197$	−18.4548			−1.31485			−0.657426	+	0.753519i	$0.728355\pi$
$198$		0			0
$199$		−	26.1593i		−	1.85439i	−0.374583	−	0.927194i	$-0.622214\pi$
$199$		−	26.1593i		−	1.85439i	0.374583	−	0.927194i	$-0.377786\pi$
$200$	−0.0420413	−	0.0242726i	−0.00297277	−	0.00171633i
$201$		0			0
$202$	−1.14459	−	1.98249i	−0.0805333	−	0.139488i
$203$	−2.29453	−	3.97425i	−0.161045	−	0.278938i
$204$		0			0
$205$	12.7939	−	22.1597i	0.893567	−	1.54770i
$206$		−	1.21720i		−	0.0848063i
$207$		0			0
$208$			3.19916i			0.221822i
$209$	1.26896	−	2.19790i	0.0877756	−	0.152032i
$210$		0			0
$211$	7.05862	+	12.2259i	0.485936	+	0.841665i	0.999869	−	0.0161647i	$-0.00514561\pi$
$211$	7.05862	+	12.2259i	0.485936	+	0.841665i	−0.513934	+	0.857830i	$0.671812\pi$
$212$	4.92639	+	8.53275i	0.338346	+	0.586032i
$213$		0			0
$214$	5.19761	−	9.00252i	0.355301	−	0.615400i
$215$	−15.1363			−1.03229
$216$		0			0
$217$	−5.87195	+	1.97836i	−0.398614	+	0.134300i
$218$	−10.0610	−	5.80870i	−0.681415	−	0.393415i
$219$		0			0
$220$	−1.96651	+	1.13536i	−0.132582	+	0.0765463i
$221$	12.7980	−	7.38894i	0.860888	−	0.497034i
$222$		0			0
$223$	−24.9380	−	14.3979i	−1.66997	−	0.964158i	−0.967650	−	0.252297i	$-0.918814\pi$
$223$	−24.9380	−	14.3979i	−1.66997	−	0.964158i	−0.702320	−	0.711861i	$-0.747853\pi$
$224$			1.11288i			0.0743575i
$225$		0			0
$226$	16.8084			1.11808
$227$	12.7248	+	7.34666i	0.844573	+	0.487615i	0.858816	−	0.512284i	$-0.171200\pi$
$227$	12.7248	+	7.34666i	0.844573	+	0.487615i	−0.0142427	+	0.999899i	$0.504534\pi$
$228$		0			0
$229$	6.07989	−	3.51023i	0.401771	−	0.231962i	−0.285477	−	0.958386i	$-0.592152\pi$
$229$	6.07989	−	3.51023i	0.401771	−	0.231962i	0.687248	+	0.726423i	$0.258819\pi$
$230$	−4.29648	−	7.44172i	−0.283302	−	0.490693i
$231$		0			0
$232$	3.57113	+	2.06180i	0.234456	+	0.135364i
$233$			2.04882i			0.134223i	0.997745	+	0.0671113i	$0.0213783\pi$
$233$			2.04882i			0.134223i	−0.997745	+	0.0671113i	$0.978622\pi$
$234$		0			0
$235$	−22.8368			−1.48971
$236$	−5.10909	−	2.94973i	−0.332573	−	0.192011i
$237$		0			0
$238$	4.45200	−	2.57036i	0.288580	−	0.166612i
$239$	−7.43679	−	12.8809i	−0.481046	−	0.833196i	0.518718	−	0.854946i	$-0.326410\pi$
$239$	−7.43679	−	12.8809i	−0.481046	−	0.833196i	−0.999763	+	0.0217497i	$0.993076\pi$
$240$		0			0
$241$	11.0795	+	6.39675i	0.713693	+	0.412051i	0.812427	−	0.583063i	$-0.198146\pi$
$241$	11.0795	+	6.39675i	0.713693	+	0.412051i	−0.0987341	+	0.995114i	$0.531479\pi$
$242$			9.95865i			0.640166i
$243$		0			0
$244$			1.78998i			0.114592i
$245$	−11.1028	−	6.41020i	−0.709331	−	0.409533i
$246$		0			0
$247$	6.89041	−	3.97818i	0.438426	−	0.253126i
$248$	3.68060	−	4.17770i	0.233719	−	0.265284i
$249$		0			0
$250$	5.61698	−	9.72889i	0.355249	−	0.615309i
$251$	26.7812			1.69042			0.845208	−	0.534437i	$-0.179476\pi$
$251$	26.7812			1.69042			0.845208	+	0.534437i	$0.179476\pi$
$252$		0			0
$253$	3.94072			0.247751
$254$	1.15114	−	1.99384i	0.0722291	−	0.125104i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−6.66716	+	3.84929i	−0.415886	+	0.240112i	−0.693316	−	0.720634i	$-0.743851\pi$
$257$	−6.66716	+	3.84929i	−0.415886	+	0.240112i	0.277430	+	0.960746i	$0.410517\pi$
$258$		0			0
$259$	9.48125	+	5.47400i	0.589136	+	0.340138i
$260$	−7.11873			−0.441485
$261$		0			0
$262$	5.36015			0.331151
$263$	−8.91249	+	15.4369i	−0.549567	+	0.951879i	0.448737	+	0.893664i	$0.351874\pi$
$263$	−8.91249	+	15.4369i	−0.549567	+	0.951879i	−0.998304	+	0.0582147i	$0.981459\pi$
$264$		0			0
$265$	−18.9870	+	10.9621i	−1.16636	+	0.673398i
$266$	2.39694	−	1.38388i	0.146966	−	0.0848509i
$267$		0			0
$268$	1.63010	−	2.82341i	0.0995741	−	0.172467i
$269$	−31.1931			−1.90188			−0.950938	−	0.309383i	$-0.899878\pi$
$269$	−31.1931			−1.90188			−0.950938	+	0.309383i	$0.899878\pi$
$270$		0			0
$271$		−	29.8901i		−	1.81569i	−0.419301	−	0.907847i	$-0.637725\pi$
$271$		−	29.8901i		−	1.81569i	0.419301	−	0.907847i	$-0.362275\pi$
$272$	−2.30965	+	4.00043i	−0.140043	+	0.242561i
$273$		0			0
$274$	12.0926	−	6.98169i	0.730543	−	0.421779i
$275$	0.0247693	+	0.0429018i	0.00149365	+	0.00258707i
$276$		0			0
$277$	−2.47722	−	1.43022i	−0.148842	−	0.0859337i	0.423730	−	0.905789i	$-0.360721\pi$
$277$	−2.47722	−	1.43022i	−0.148842	−	0.0859337i	−0.572571	+	0.819855i	$0.694054\pi$
$278$	−7.57570			−0.454360
$279$		0			0
$280$	−2.47637			−0.147991
$281$	−18.7340	−	10.8161i	−1.11758	−	0.645235i	−0.176797	−	0.984247i	$-0.556574\pi$
$281$	−18.7340	−	10.8161i	−1.11758	−	0.645235i	−0.940782	+	0.339013i	$0.889907\pi$
$282$		0			0
$283$	−3.83801	−	6.64763i	−0.228146	−	0.395161i	0.729113	−	0.684394i	$-0.239933\pi$
$283$	−3.83801	−	6.64763i	−0.228146	−	0.395161i	−0.957259	+	0.289233i	$0.906600\pi$
$284$	−1.03608	+	0.598183i	−0.0614803	+	0.0354956i
$285$		0			0
$286$	1.63232	−	2.82726i	0.0965211	−	0.167180i
$287$			12.7972i			0.755398i
$288$		0			0
$289$	4.33788			0.255169
$290$	−4.58788	+	7.94644i	−0.269410	+	0.466631i
$291$		0			0
$292$	5.32461	−	3.07417i	0.311599	−	0.179902i
$293$	−12.5129	+	7.22431i	−0.731010	+	0.422049i	−0.818792	−	0.574091i	$-0.805356\pi$
$293$	−12.5129	+	7.22431i	−0.731010	+	0.422049i	0.0877814	+	0.996140i	$0.472022\pi$
$294$		0			0
$295$	6.56371	−	11.3687i	0.382154	−	0.661910i
$296$	−9.83752			−0.571795
$297$		0			0
$298$	−5.23653			−0.303344
$299$	10.6990	+	6.17708i	0.618740	+	0.357230i
$300$		0			0
$301$	6.55592	−	3.78506i	0.377877	−	0.218167i
$302$	−4.92539	−	8.53103i	−0.283424	−	0.490905i
$303$		0			0
$304$	−1.24351	+	2.15382i	−0.0713200	+	0.123530i
$305$	−3.98303			−0.228068
$306$		0			0
$307$	33.7966			1.92887			0.964436	−	0.264317i	$-0.0851465\pi$
$307$	33.7966			1.92887			0.964436	+	0.264317i	$0.0851465\pi$
$308$	0.567830	−	0.983510i	0.0323551	−	0.0560407i
$309$		0			0
$310$	9.29616	+	8.19003i	0.527986	+	0.465162i
$311$	−12.3453	+	7.12756i	−0.700038	+	0.404167i	−0.807361	−	0.590057i	$-0.799105\pi$
$311$	−12.3453	+	7.12756i	−0.700038	+	0.404167i	0.107324	+	0.994224i	$0.465772\pi$
$312$		0			0
$313$	−7.96020	−	4.59583i	−0.449937	−	0.259771i	0.257866	−	0.966181i	$-0.416981\pi$
$313$	−7.96020	−	4.59583i	−0.449937	−	0.259771i	−0.707804	+	0.706409i	$0.750314\pi$
$314$			13.3524i			0.753520i
$315$		0			0
$316$			2.52748i			0.142182i
$317$	−6.43584	−	3.71574i	−0.361473	−	0.208696i	0.308254	−	0.951304i	$-0.400255\pi$
$317$	−6.43584	−	3.71574i	−0.361473	−	0.208696i	−0.669727	+	0.742608i	$0.733589\pi$
$318$		0			0
$319$	−2.10399	−	3.64423i	−0.117801	−	0.204037i
$320$	1.92707	−	1.11259i	0.107726	−	0.0621959i
$321$		0			0
$322$	3.72183	+	2.14880i	0.207409	+	0.119748i
$323$	11.4882			0.639223
$324$		0			0
$325$			0.155304i			0.00861470i
$326$	−11.8259	−	6.82771i	−0.654978	−	0.378152i
$327$		0			0
$328$	−5.74960	−	9.95860i	−0.317469	−	0.549872i
$329$	9.89119	−	5.71068i	0.545319	−	0.314840i
$330$		0			0
$331$	23.7405	+	13.7066i	1.30489	+	0.753381i	0.981239	−	0.192794i	$-0.0617549\pi$
$331$	23.7405	+	13.7066i	1.30489	+	0.753381i	0.323655	+	0.946175i	$0.395088\pi$
$332$	2.02962			0.111390
$333$		0			0
$334$		−	6.05959i		−	0.331566i
$335$	6.28262	+	3.62727i	0.343256	+	0.198179i
$336$		0			0
$337$	−2.96074	+	1.70938i	−0.161282	+	0.0931160i	−0.578468	−	0.815705i	$-0.696349\pi$
$337$	−2.96074	+	1.70938i	−0.161282	+	0.0931160i	0.417187	+	0.908821i	$0.363016\pi$
$338$	−2.39487	+	1.38268i	−0.130264	+	0.0752077i
$339$		0			0
$340$	−8.90169	−	5.13940i	−0.482762	−	0.278723i
$341$	−5.38434	+	1.81407i	−0.291578	+	0.0982377i
$342$		0			0
$343$	14.2020			0.766838
$344$	−3.40113	+	5.89094i	−0.183377	+	0.317618i
$345$		0			0
$346$	7.35730	+	12.7432i	0.395531	+	0.685080i
$347$	7.11555	+	12.3245i	0.381983	+	0.661613i	0.991346	−	0.131278i	$-0.0419081\pi$
$347$	7.11555	+	12.3245i	0.381983	+	0.661613i	−0.609363	+	0.792891i	$0.708575\pi$
$348$		0			0
$349$	12.1759	−	21.0892i	0.651759	−	1.12888i	−0.330937	−	0.943653i	$-0.607365\pi$
$349$	12.1759	−	21.0892i	0.651759	−	1.12888i	0.982696	−	0.185227i	$-0.0593020\pi$
$350$			0.0540250i			0.00288776i
$351$		0			0
$352$			1.02047i			0.0543911i
$353$	−13.1781	+	22.8251i	−0.701400	+	1.21486i	0.266576	+	0.963814i	$0.414108\pi$
$353$	−13.1781	+	22.8251i	−0.701400	+	1.21486i	−0.967975	+	0.251046i	$0.919226\pi$
$354$		0			0
$355$	−1.33107	−	2.30548i	−0.0706458	−	0.122362i
$356$	2.66606	+	4.61776i	0.141301	+	0.244741i
$357$		0			0
$358$	11.4044	+	6.58431i	0.602739	+	0.347992i
$359$		−	16.3382i		−	0.862297i	−0.902281	−	0.431149i	$-0.858108\pi$
$359$		−	16.3382i		−	0.862297i	0.902281	−	0.431149i	$-0.141892\pi$
$360$		0			0
$361$	−12.8148			−0.674461
$362$	−0.0915732	+	0.158609i	−0.00481298	+	0.00833633i
$363$		0			0
$364$	3.08330	−	1.78014i	0.161609	−	0.0933049i
$365$	6.84059	+	11.8483i	0.358053	+	0.620166i
$366$		0			0
$367$	−8.01274	−	4.62616i	−0.418262	−	0.241483i	0.276072	−	0.961137i	$-0.410967\pi$
$367$	−8.01274	−	4.62616i	−0.418262	−	0.241483i	−0.694333	+	0.719654i	$0.744301\pi$
$368$	−3.86168			−0.201304
$369$		0			0
$370$		−	21.8903i		−	1.13802i
$371$	5.48249	−	9.49594i	0.284636	−	0.493005i
$372$		0			0
$373$	4.49388	+	7.78363i	0.232684	+	0.403021i	0.958597	−	0.284766i	$-0.0919157\pi$
$373$	4.49388	+	7.78363i	0.232684	+	0.403021i	−0.725913	+	0.687787i	$0.758582\pi$
$374$	4.08230	−	2.35692i	0.211091	−	0.121873i
$375$		0			0
$376$	−5.13144	+	8.88791i	−0.264634	+	0.458359i
$377$		−	13.1920i		−	0.679425i
$378$		0			0
$379$	−23.1494			−1.18910			−0.594552	−	0.804057i	$-0.702670\pi$
$379$	−23.1494			−1.18910			−0.594552	+	0.804057i	$0.702670\pi$
$380$	−4.79264	−	2.76703i	−0.245857	−	0.141946i
$381$		0			0
$382$	−0.0321011	−	0.0556007i	−0.00164244	−	0.00284478i
$383$	3.83913	+	6.64957i	0.196170	+	0.339777i	0.947284	−	0.320396i	$-0.103816\pi$
$383$	3.83913	+	6.64957i	0.196170	+	0.339777i	−0.751113	+	0.660174i	$0.770483\pi$
$384$		0			0
$385$	2.18849	+	1.26353i	0.111536	+	0.0643953i
$386$		−	2.51820i		−	0.128173i
$387$		0			0
$388$	2.12009			0.107631
$389$	−8.96129	+	15.5214i	−0.454355	+	0.786967i	−0.998651	−	0.0519269i	$-0.983464\pi$
$389$	−8.96129	+	15.5214i	−0.454355	+	0.786967i	0.544295	+	0.838894i	$0.316797\pi$
$390$		0			0
$391$	8.91912	+	15.4484i	0.451059	+	0.781258i
$392$	−4.98960	+	2.88075i	−0.252013	+	0.145500i
$393$		0			0
$394$	−15.9823	−	9.22741i	−0.805179	−	0.464870i
$395$	−5.62410			−0.282979
$396$		0			0
$397$	−28.6115			−1.43597			−0.717984	−	0.696060i	$-0.754935\pi$
$397$	−28.6115			−1.43597			−0.717984	+	0.696060i	$0.754935\pi$
$398$	13.0797	−	22.6547i	0.655625	−	1.13558i
$399$		0			0
$400$	−0.0242726	−	0.0420413i	−0.00121363	−	0.00210207i
$401$	−7.63116	−	13.2176i	−0.381082	−	0.660053i	0.610135	−	0.792297i	$-0.291115\pi$
$401$	−7.63116	−	13.2176i	−0.381082	−	0.660053i	−0.991217	+	0.132244i	$0.957782\pi$
$402$		0			0
$403$	−17.4620	−	3.51475i	−0.869843	−	0.175082i
$404$		−	2.28919i		−	0.113891i
$405$		0			0
$406$		−	4.58907i		−	0.227752i
$407$	8.69392	+	5.01944i	0.430941	+	0.248804i
$408$		0			0
$409$	−24.7600	+	14.2952i	−1.22430	+	0.706852i	−0.965832	−	0.259167i	$-0.916552\pi$
$409$	−24.7600	+	14.2952i	−1.22430	+	0.706852i	−0.258471	+	0.966019i	$0.583219\pi$
$410$	22.1597	−	12.7939i	1.09439	−	0.631847i
$411$		0			0
$412$	0.608600	−	1.05413i	0.0299836	−	0.0519330i
$413$			6.56541i			0.323063i
$414$		0			0
$415$			4.51629i			0.221696i
$416$	−1.59958	+	2.77056i	−0.0784259	+	0.135838i
$417$		0			0
$418$	2.19790	−	1.26896i	0.107503	−	0.0620667i
$419$	−7.33646	+	4.23571i	−0.358409	+	0.206928i	−0.668383	−	0.743817i	$-0.733013\pi$
$419$	−7.33646	+	4.23571i	−0.358409	+	0.206928i	0.309973	+	0.950745i	$0.399680\pi$
$420$		0			0
$421$	−13.1893	+	22.8445i	−0.642807	+	1.11337i	0.341996	+	0.939701i	$0.388897\pi$
$421$	−13.1893	+	22.8445i	−0.642807	+	1.11337i	−0.984803	+	0.173673i	$0.944436\pi$
$422$			14.1172i			0.687217i
$423$		0			0
$424$			9.85277i			0.478493i
$425$	−0.112122	+	0.194201i	−0.00543872	+	0.00942014i
$426$		0			0
$427$	1.72515	−	0.996017i	0.0834859	−	0.0482006i
$428$	9.00252	−	5.19761i	0.435153	−	0.251236i
$429$		0			0
$430$	−13.1084	−	7.56816i	−0.632145	−	0.364969i
$431$		−	20.6052i		−	0.992519i	−0.868174	−	0.496260i	$-0.834706\pi$
$431$		−	20.6052i		−	0.992519i	0.868174	−	0.496260i	$-0.165294\pi$
$432$		0			0
$433$		−	24.4623i		−	1.17558i	−0.809012	−	0.587792i	$-0.799997\pi$
$433$		−	24.4623i		−	1.17558i	0.809012	−	0.587792i	$-0.200003\pi$
$434$	−6.07443	−	1.22266i	−0.291582	−	0.0586898i
$435$		0			0
$436$	−5.80870	−	10.0610i	−0.278186	−	0.481833i
$437$	4.80203	+	8.31736i	0.229712	+	0.397873i
$438$		0			0
$439$	7.15542	−	12.3935i	0.341509	−	0.591512i	−0.643204	−	0.765695i	$-0.722395\pi$
$439$	7.15542	−	12.3935i	0.341509	−	0.591512i	0.984713	+	0.174183i	$0.0557285\pi$
$440$	−2.27073			−0.108253
$441$		0			0
$442$	14.7779			0.702912
$443$	−4.39636	−	2.53824i	−0.208877	−	0.120595i	0.391912	−	0.920003i	$-0.371814\pi$
$443$	−4.39636	−	2.53824i	−0.208877	−	0.120595i	−0.600789	+	0.799407i	$0.705147\pi$
$444$		0			0
$445$	−10.2754	+	5.93249i	−0.487099	+	0.281227i
$446$	−14.3979	−	24.9380i	−0.681762	−	1.18085i
$447$		0			0
$448$	−0.556441	+	0.963784i	−0.0262894	+	0.0455345i
$449$	−34.1185			−1.61015			−0.805076	−	0.593172i	$-0.797875\pi$
$449$	−34.1185			−1.61015			−0.805076	+	0.593172i	$0.797875\pi$
$450$		0			0
$451$			11.7346i			0.552559i
$452$	14.5565	+	8.40422i	0.684682	+	0.395301i
$453$		0			0
$454$	7.34666	+	12.7248i	0.344796	+	0.597204i
$455$	3.96115	+	6.86092i	0.185702	+	0.321645i
$456$		0			0
$457$	5.09131	+	2.93947i	0.238161	+	0.137503i	0.614331	−	0.789048i	$-0.289426\pi$
$457$	5.09131	+	2.93947i	0.238161	+	0.137503i	−0.376170	+	0.926551i	$0.622759\pi$
$458$	7.02046			0.328044
$459$		0			0
$460$		−	8.59296i		−	0.400649i
$461$	19.7473	−	34.2032i	0.919721	−	1.59300i	0.119883	−	0.992788i	$-0.461748\pi$
$461$	19.7473	−	34.2032i	0.919721	−	1.59300i	0.799838	−	0.600216i	$-0.204919\pi$
$462$		0			0
$463$	20.0463	−	11.5738i	0.931633	−	0.537878i	0.0443051	−	0.999018i	$-0.485893\pi$
$463$	20.0463	−	11.5738i	0.931633	−	0.537878i	0.887328	+	0.461140i	$0.152559\pi$
$464$	2.06180	+	3.57113i	0.0957164	+	0.165786i
$465$		0			0
$466$	−1.02441	+	1.77433i	−0.0474549	+	0.0821943i
$467$		−	6.12670i		−	0.283510i	−0.989902	−	0.141755i	$-0.954725\pi$
$467$		−	6.12670i		−	0.283510i	0.989902	−	0.141755i	$-0.0452745\pi$
$468$		0			0
$469$	−3.62821			−0.167535
$470$	−19.7773	−	11.4184i	−0.912257	−	0.526692i
$471$		0			0
$472$	−2.94973	−	5.10909i	−0.135772	−	0.235165i
$473$	6.01151	−	3.47075i	0.276409	−	0.159585i
$474$		0			0
$475$	−0.0603662	+	0.104557i	−0.00276979	+	0.00479742i
$476$	5.14073			0.235625
$477$		0			0
$478$		−	14.8736i		−	0.680302i
$479$	6.48652	+	3.74499i	0.296377	+	0.171113i	0.640814	−	0.767696i	$-0.278597\pi$
$479$	6.48652	+	3.74499i	0.296377	+	0.171113i	−0.344437	+	0.938809i	$0.611930\pi$
$480$		0			0
$481$	15.7359	+	27.2554i	0.717496	+	1.24274i
$482$	6.39675	+	11.0795i	0.291364	+	0.504657i
$483$		0			0
$484$	−4.97932	+	8.62444i	−0.226333	+	0.392020i
$485$			4.71760i			0.214215i
$486$		0			0
$487$		−	9.68519i		−	0.438878i	−0.975626	−	0.219439i	$-0.929577\pi$
$487$		−	9.68519i		−	0.438878i	0.975626	−	0.219439i	$-0.0704227\pi$
$488$	−0.894989	+	1.55017i	−0.0405142	+	0.0701727i
$489$		0			0
$490$	−6.41020	−	11.1028i	−0.289583	−	0.501573i
$491$	8.25821	+	14.3036i	0.372688	+	0.645514i	0.989978	−	0.141221i	$-0.0451029\pi$
$491$	8.25821	+	14.3036i	0.372688	+	0.645514i	−0.617290	+	0.786736i	$0.711770\pi$
$492$		0			0
$493$	9.52404	−	16.4961i	0.428941	−	0.742948i
$494$	7.95636			0.357974
$495$		0			0
$496$	5.27635	−	1.77769i	0.236915	−	0.0798207i
$497$	1.15304	+	0.665707i	0.0517208	+	0.0298610i
$498$		0			0
$499$	16.5265	−	9.54159i	0.739829	−	0.427140i	−0.0821782	−	0.996618i	$-0.526188\pi$
$499$	16.5265	−	9.54159i	0.739829	−	0.427140i	0.822007	+	0.569477i	$0.192854\pi$
$500$	9.72889	−	5.61698i	0.435089	−	0.251199i
$501$		0			0
$502$	23.1932	+	13.3906i	1.03516	+	0.597652i
$503$			7.99974i			0.356691i	0.983968	+	0.178345i	$0.0570744\pi$
$503$			7.99974i			0.356691i	−0.983968	+	0.178345i	$0.942926\pi$
$504$		0			0
$505$	5.09386			0.226674
$506$	3.41276	+	1.97036i	0.151716	+	0.0875932i
$507$		0			0
$508$	1.99384	−	1.15114i	0.0884622	−	0.0510737i
$509$	−8.01549	−	13.8832i	−0.355280	−	0.615363i	0.631886	−	0.775062i	$-0.282281\pi$
$509$	−8.01549	−	13.8832i	−0.355280	−	0.615363i	−0.987166	+	0.159698i	$0.948948\pi$
$510$		0			0
$511$	−5.92566	−	3.42118i	−0.262136	−	0.151344i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	−7.69857			−0.339569
$515$	2.34563	+	1.35425i	0.103361	+	0.0596753i
$516$		0			0
$517$	9.06982	−	5.23646i	0.398890	−	0.230299i
$518$	5.47400	+	9.48125i	0.240514	+	0.416582i
$519$		0			0
$520$	−6.16501	−	3.55937i	−0.270353	−	0.156089i
$521$		−	33.5039i		−	1.46783i	−0.679241	−	0.733915i	$-0.737691\pi$
$521$		−	33.5039i		−	1.46783i	0.679241	−	0.733915i	$-0.262309\pi$
$522$		0			0
$523$		−	37.4112i		−	1.63588i	−0.575304	−	0.817940i	$-0.695116\pi$
$523$		−	37.4112i		−	1.63588i	0.575304	−	0.817940i	$-0.304884\pi$
$524$	4.64203	+	2.68008i	0.202788	+	0.117080i
$525$		0			0
$526$	−15.4369	+	8.91249i	−0.673080	+	0.388603i
$527$	−19.2980	−	17.0018i	−0.840635	−	0.740610i
$528$		0			0
$529$	4.04370	−	7.00390i	0.175813	−	0.304517i
$530$	−21.9243			−0.952329
$531$		0			0
$532$	2.76775			0.119997
$533$	−18.3939	+	31.8592i	−0.796729	+	1.37997i
$534$		0			0
$535$	11.5656	+	20.0323i	0.500026	+	0.866071i
$536$	2.82341	−	1.63010i	0.121953	−	0.0704095i
$537$		0			0
$538$	−27.0140	−	15.5965i	−1.16466	−	0.672414i
$539$	5.87942			0.253244
$540$		0			0
$541$	30.6235			1.31661			0.658303	−	0.752753i	$-0.271275\pi$
$541$	30.6235			1.31661			0.658303	+	0.752753i	$0.271275\pi$
$542$	14.9451	−	25.8856i	0.641945	−	1.11188i
$543$		0			0
$544$	−4.00043	+	2.30965i	−0.171517	+	0.0990253i
$545$	22.3875	−	12.9255i	0.958977	−	0.553665i
$546$		0			0
$547$	1.58488	−	2.74509i	0.0677645	−	0.117372i	−0.830152	−	0.557536i	$-0.811747\pi$
$547$	1.58488	−	2.74509i	0.0677645	−	0.117372i	0.897917	+	0.440165i	$0.145080\pi$
$548$	13.9634			0.596486
$549$		0			0
$550$			0.0495387i			0.00211234i
$551$	5.12771	−	8.88146i	0.218448	−	0.378363i
$552$		0			0
$553$	2.43594	−	1.40639i	0.103587	−	0.0598058i
$554$	−1.43022	−	2.47722i	−0.0607643	−	0.105247i
$555$		0			0
$556$	−6.56075	−	3.78785i	−0.278238	−	0.160641i
$557$	−2.07470			−0.0879079			−0.0439539	−	0.999034i	$-0.513995\pi$
$557$	−2.07470			−0.0879079			−0.0439539	+	0.999034i	$0.513995\pi$
$558$		0			0
$559$	21.7616			0.920416
$560$	−2.14460	−	1.23818i	−0.0906258	−	0.0523228i
$561$		0			0
$562$	−10.8161	−	18.7340i	−0.456250	−	0.790248i
$563$	−37.5837	+	21.6990i	−1.58397	+	0.914503i	−0.589693	+	0.807627i	$0.700751\pi$
$563$	−37.5837	+	21.6990i	−1.58397	+	0.914503i	−0.994272	+	0.106876i	$0.965915\pi$
$564$		0			0
$565$	−18.7009	+	32.3910i	−0.786755	+	1.36270i
$566$		−	7.67602i		−	0.322647i
$567$		0			0
$568$	−1.19637			−0.0501984
$569$	−17.6206	+	30.5197i	−0.738693	+	1.27945i	0.214391	+	0.976748i	$0.431223\pi$
$569$	−17.6206	+	30.5197i	−0.738693	+	1.27945i	−0.953084	+	0.302706i	$0.902110\pi$
$570$		0			0
$571$	31.1820	−	18.0029i	1.30492	−	0.753399i	0.323680	−	0.946167i	$-0.395080\pi$
$571$	31.1820	−	18.0029i	1.30492	−	0.753399i	0.981244	+	0.192768i	$0.0617465\pi$
$572$	2.82726	−	1.63232i	0.118214	−	0.0682508i
$573$		0			0
$574$	−6.39862	+	11.0827i	−0.267073	+	0.462585i
$575$	−0.187466			−0.00781786
$576$		0			0
$577$	−32.1410			−1.33805			−0.669023	−	0.743242i	$-0.733287\pi$
$577$	−32.1410			−1.33805			−0.669023	+	0.743242i	$0.733287\pi$
$578$	3.75671	+	2.16894i	0.156259	+	0.0902160i
$579$		0			0
$580$	−7.94644	+	4.58788i	−0.329958	+	0.190501i
$581$	−1.12937	−	1.95612i	−0.0468540	−	0.0811534i
$582$		0			0
$583$	5.02722	−	8.70740i	0.208206	−	0.360623i
$584$	6.14833			0.254420
$585$		0			0
$586$	−14.4486			−0.596867
$587$	6.41401	−	11.1094i	0.264734	−	0.458533i	−0.702760	−	0.711427i	$-0.748049\pi$
$587$	6.41401	−	11.1094i	0.264734	−	0.458533i	0.967494	+	0.252894i	$0.0813824\pi$
$588$		0			0
$589$	−10.3900	−	9.15371i	−0.428112	−	0.377172i
$590$	11.3687	−	6.56371i	0.468041	−	0.270223i
$591$		0			0
$592$	−8.51955	−	4.91876i	−0.350151	−	0.202160i
$593$		−	23.3171i		−	0.957519i	−0.877946	−	0.478760i	$-0.841087\pi$
$593$		−	23.3171i		−	0.957519i	0.877946	−	0.478760i	$-0.158913\pi$
$594$		0			0
$595$			11.4391i			0.468956i
$596$	−4.53497	−	2.61827i	−0.185760	−	0.107248i
$597$		0			0
$598$	6.17708	+	10.6990i	0.252599	+	0.437515i
$599$	22.1736	−	12.8019i	0.905988	−	0.523073i	0.0268500	−	0.999639i	$-0.491452\pi$
$599$	22.1736	−	12.8019i	0.905988	−	0.523073i	0.879138	+	0.476567i	$0.158119\pi$
$600$		0			0
$601$	5.37109	+	3.10100i	0.219091	+	0.126492i	0.605529	−	0.795823i	$-0.292961\pi$
$601$	5.37109	+	3.10100i	0.219091	+	0.126492i	−0.386438	+	0.922315i	$0.626295\pi$
$602$	7.57012			0.308535
$603$		0			0
$604$		−	9.85078i		−	0.400823i
$605$	−19.1910	−	11.0799i	−0.780225	−	0.450463i
$606$		0			0
$607$	−15.6728	−	27.1461i	−0.636141	−	1.10183i	−0.986272	−	0.165127i	$-0.947197\pi$
$607$	−15.6728	−	27.1461i	−0.636141	−	1.10183i	0.350132	−	0.936700i	$-0.386137\pi$
$608$	−2.15382	+	1.24351i	−0.0873488	+	0.0504308i
$609$		0			0
$610$	−3.44941	−	1.99152i	−0.139663	−	0.0806342i
$611$	32.8326			1.32827
$612$		0			0
$613$			40.9491i			1.65392i	0.562261	+	0.826960i	$0.309932\pi$
$613$			40.9491i			1.65392i	−0.562261	+	0.826960i	$0.690068\pi$
$614$	29.2687	+	16.8983i	1.18119	+	0.681959i
$615$		0			0
$616$	0.983510	−	0.567830i	0.0396267	−	0.0228785i
$617$	−34.9638	+	20.1863i	−1.40759	+	0.812671i	−0.995155	−	0.0983164i	$-0.968654\pi$
$617$	−34.9638	+	20.1863i	−1.40759	+	0.812671i	−0.412433	+	0.910988i	$0.635321\pi$
$618$		0			0
$619$	17.5241	+	10.1175i	0.704353	+	0.406659i	0.808967	−	0.587854i	$-0.200027\pi$
$619$	17.5241	+	10.1175i	0.704353	+	0.406659i	−0.104614	+	0.994513i	$0.533361\pi$
$620$	3.95569	+	11.7409i	0.158864	+	0.471524i
$621$		0			0
$622$	−14.2551			−0.571578
$623$	2.96701	−	5.13902i	0.118871	−	0.205890i
$624$		0			0
$625$	12.3775	+	21.4384i	0.495098	+	0.857536i
$626$	−4.59583	−	7.96020i	−0.183686	−	0.318154i
$627$		0			0
$628$	−6.67621	+	11.5635i	−0.266410	+	0.461435i
$629$			45.4424i			1.81191i
$630$		0			0
$631$			32.7799i			1.30495i	0.757811	+	0.652475i	$0.226269\pi$
$631$			32.7799i			1.30495i	−0.757811	+	0.652475i	$0.773731\pi$
$632$	−1.26374	+	2.18886i	−0.0502688	+	0.0870681i
$633$		0			0
$634$	−3.71574	−	6.43584i	−0.147571	−	0.255600i
$635$	2.56151	+	4.43666i	0.101650	+	0.176063i
$636$		0			0
$637$	15.9625	+	9.21598i	0.632459	+	0.365150i
$638$		−	4.20799i		−	0.166596i
$639$		0			0
$640$	2.22519			0.0879582
$641$	−10.6439	+	18.4357i	−0.420408	+	0.728167i	−0.995979	−	0.0895841i	$-0.971446\pi$
$641$	−10.6439	+	18.4357i	−0.420408	+	0.728167i	0.575572	+	0.817751i	$0.304780\pi$
$642$		0			0
$643$	40.7748	−	23.5413i	1.60800	−	0.928379i	0.618182	−	0.786035i	$-0.287869\pi$
$643$	40.7748	−	23.5413i	1.60800	−	0.928379i	0.989817	−	0.142344i	$-0.0454639\pi$
$644$	2.14880	+	3.72183i	0.0846745	+	0.146661i
$645$		0			0
$646$	9.94911	+	5.74412i	0.391443	+	0.225999i
$647$	29.5056			1.15998			0.579992	−	0.814622i	$-0.303055\pi$
$647$	29.5056			1.15998			0.579992	+	0.814622i	$0.303055\pi$
$648$		0			0
$649$			6.02021i			0.236314i
$650$	−0.0776519	+	0.134497i	−0.00304576	+	0.00527541i
$651$		0			0
$652$	−6.82771	−	11.8259i	−0.267394	−	0.463139i
$653$	−9.32930	+	5.38627i	−0.365084	+	0.210781i	−0.671308	−	0.741178i	$-0.734267\pi$
$653$	−9.32930	+	5.38627i	−0.365084	+	0.210781i	0.306225	+	0.951959i	$0.400934\pi$
$654$		0			0
$655$	−5.96367	+	10.3294i	−0.233020	+	0.403602i
$656$		−	11.4992i		−	0.448968i
$657$		0			0
$658$	11.4214			0.445251
$659$	1.37174	+	0.791977i	0.0534356	+	0.0308510i	0.526480	−	0.850188i	$-0.323512\pi$
$659$	1.37174	+	0.791977i	0.0534356	+	0.0308510i	−0.473044	+	0.881039i	$0.656845\pi$
$660$		0			0
$661$	−16.1220	−	27.9242i	−0.627075	−	1.08613i	−0.988136	−	0.153583i	$-0.950919\pi$
$661$	−16.1220	−	27.9242i	−0.627075	−	1.08613i	0.361061	−	0.932542i	$-0.382415\pi$
$662$	13.7066	+	23.7405i	0.532721	+	0.922700i
$663$		0			0
$664$	1.75771	+	1.01481i	0.0682122	+	0.0393823i
$665$			6.15876i			0.238827i
$666$		0			0
$667$	15.9240			0.616580
$668$	3.02979	−	5.24776i	0.117226	−	0.203042i
$669$		0			0
$670$	3.62727	+	6.28262i	0.140134	+	0.242719i
$671$	1.58189	−	0.913307i	0.0610683	−	0.0352578i
$672$		0			0
$673$	−7.10562	−	4.10243i	−0.273902	−	0.158137i	0.356758	−	0.934197i	$-0.383882\pi$
$673$	−7.10562	−	4.10243i	−0.273902	−	0.158137i	−0.630659	+	0.776060i	$0.717215\pi$
$674$	−3.41877			−0.131686
$675$		0			0
$676$	−2.76535			−0.106360
$677$	−3.99517	+	6.91983i	−0.153547	+	0.265951i	−0.932529	−	0.361095i	$-0.882403\pi$
$677$	−3.99517	+	6.91983i	−0.153547	+	0.265951i	0.778982	+	0.627046i	$0.215736\pi$
$678$		0			0
$679$	−1.17971	−	2.04331i	−0.0452729	−	0.0784150i
$680$	−5.13940	−	8.90169i	−0.197087	−	0.341364i
$681$		0			0
$682$	−5.57001	−	1.12113i	−0.213287	−	0.0429304i
$683$			19.0681i			0.729619i	0.931082	+	0.364809i	$0.118866\pi$
$683$			19.0681i			0.729619i	−0.931082	+	0.364809i	$0.881134\pi$
$684$		0			0
$685$			31.0711i			1.18717i
$686$	12.2993	+	7.10102i	0.469590	+	0.271118i
$687$		0			0
$688$	−5.89094	+	3.40113i	−0.224590	+	0.129667i
$689$	27.2977	−	15.7603i	1.03996	−	0.600420i
$690$		0			0
$691$	−12.0546	+	20.8792i	−0.458580	+	0.794284i	−0.998886	−	0.0471845i	$-0.984975\pi$
$691$	−12.0546	+	20.8792i	−0.458580	+	0.794284i	0.540306	+	0.841469i	$0.318308\pi$
$692$			14.7146i			0.559365i
$693$		0			0
$694$			14.2311i			0.540205i
$695$	8.42867	−	14.5989i	0.319718	−	0.553768i
$696$		0			0
$697$	−46.0017	+	26.5591i	−1.74244	+	1.00600i
$698$	21.0892	−	12.1759i	0.798239	−	0.460863i
$699$		0			0
$700$	−0.0270125	+	0.0467870i	−0.00102098	+	0.00176838i
$701$			24.8694i			0.939303i	0.882852	+	0.469651i	$0.155620\pi$
$701$			24.8694i			0.939303i	−0.882852	+	0.469651i	$0.844380\pi$
$702$		0			0
$703$			24.4661i			0.922755i
$704$	−0.510234	+	0.883751i	−0.0192302	+	0.0333076i
$705$		0			0
$706$	−22.8251	+	13.1781i	−0.859036	+	0.495964i
$707$	−2.20628	+	1.27380i	−0.0829757	+	0.0479060i
$708$		0			0
$709$	11.2903	+	6.51847i	0.424017	+	0.244806i	0.696794	−	0.717271i	$-0.254609\pi$
$709$	11.2903	+	6.51847i	0.424017	+	0.244806i	−0.272778	+	0.962077i	$0.587942\pi$
$710$		−	2.66214i		−	0.0999083i
$711$		0			0
$712$			5.33213i			0.199830i
$713$	4.24263	−	21.0782i	0.158888	−	0.789385i
$714$		0			0
$715$	3.63222	+	6.29119i	0.135837	+	0.235277i
$716$	6.58431	+	11.4044i	0.246067	+	0.426201i
$717$		0			0
$718$	8.16910	−	14.1493i	0.304868	−	0.528047i
$719$	−15.1422			−0.564708			−0.282354	−	0.959310i	$-0.591115\pi$
$719$	−15.1422			−0.564708			−0.282354	+	0.959310i	$0.591115\pi$
$720$		0			0
$721$	−1.35460			−0.0504479
$722$	−11.0979	−	6.40738i	−0.413022	−	0.238458i
$723$		0			0
$724$	−0.158609	+	0.0915732i	−0.00589467	+	0.00340329i
$725$	0.100090	+	0.173361i	0.00371725	+	0.00643847i
$726$		0			0
$727$	−13.4296	+	23.2608i	−0.498077	+	0.862695i	−0.999998	−	0.00221912i	$-0.999294\pi$
$727$	−13.4296	+	23.2608i	−0.498077	+	0.862695i	0.501921	+	0.864914i	$0.332627\pi$
$728$	3.56029			0.131953
$729$		0			0
$730$			13.6812i			0.506364i
$731$	27.2120	+	15.7108i	1.00647	+	0.581086i
$732$		0			0
$733$	−16.7337	−	28.9836i	−0.618073	−	1.07053i	−0.989837	−	0.142207i	$-0.954580\pi$
$733$	−16.7337	−	28.9836i	−0.618073	−	1.07053i	0.371764	−	0.928327i	$-0.378753\pi$
$734$	−4.62616	−	8.01274i	−0.170755	−	0.295756i
$735$		0			0
$736$	−3.34431	−	1.93084i	−0.123273	−	0.0711717i
$737$	−3.32692			−0.122549
$738$		0			0
$739$			18.4729i			0.679537i	0.940509	+	0.339769i	$0.110349\pi$
$739$			18.4729i			0.679537i	−0.940509	+	0.339769i	$0.889651\pi$
$740$	10.9452	−	18.9576i	0.402352	−	0.696894i
$741$		0			0
$742$	9.49594	−	5.48249i	0.348607	−	0.201268i
$743$	−17.6305	−	30.5369i	−0.646799	−	1.12029i	−0.983883	−	0.178814i	$-0.942774\pi$
$743$	−17.6305	−	30.5369i	−0.646799	−	1.12029i	0.337084	−	0.941475i	$-0.390559\pi$
$744$		0			0
$745$	5.82613	−	10.0912i	0.213453	−	0.369711i
$746$			8.98776i			0.329065i
$747$		0			0
$748$	4.71384			0.172355
$749$	−10.0187	−	5.78432i	−0.366077	−	0.211355i
$750$		0			0
$751$	−0.496728	−	0.860358i	−0.0181259	−	0.0313949i	0.856820	−	0.515615i	$-0.172437\pi$
$751$	−0.496728	−	0.860358i	−0.0181259	−	0.0313949i	−0.874946	+	0.484220i	$0.839103\pi$
$752$	−8.88791	+	5.13144i	−0.324109	+	0.187124i
$753$		0			0
$754$	6.59602	−	11.4246i	0.240213	−	0.416061i
$755$	21.9198			0.797744
$756$		0			0
$757$		−	11.9119i		−	0.432946i	−0.976289	−	0.216473i	$-0.930545\pi$
$757$		−	11.9119i		−	0.432946i	0.976289	−	0.216473i	$-0.0694553\pi$
$758$	−20.0479	−	11.5747i	−0.728174	−	0.420412i
$759$		0			0
$760$	−2.76703	−	4.79264i	−0.100371	−	0.173847i
$761$	26.4497	+	45.8122i	0.958800	+	1.66069i	0.725422	+	0.688305i	$0.241645\pi$
$761$	26.4497	+	45.8122i	0.958800	+	1.66069i	0.233378	+	0.972386i	$0.425022\pi$
$762$		0			0
$763$	−6.46440	+	11.1967i	−0.234027	+	0.405347i
$764$		−	0.0642022i		−	0.00232275i
$765$		0			0
$766$			7.67826i			0.277427i
$767$	−9.43668	+	16.3448i	−0.340739	+	0.590177i
$768$		0			0
$769$	−13.1731	−	22.8165i	−0.475036	−	0.822786i	0.524556	−	0.851376i	$-0.324231\pi$
$769$	−13.1731	−	22.8165i	−0.475036	−	0.822786i	−0.999591	+	0.0285904i	$0.990898\pi$
$770$	1.26353	+	2.18849i	0.0455343	+	0.0788678i
$771$		0			0
$772$	1.25910	−	2.18083i	0.0453160	−	0.0784896i
$773$	−41.3321			−1.48661			−0.743305	−	0.668952i	$-0.766743\pi$
$773$	−41.3321			−1.48661			−0.743305	+	0.668952i	$0.766743\pi$
$774$		0			0
$775$	0.256141	−	0.0862982i	0.00920085	−	0.00309992i
$776$	1.83605	+	1.06005i	0.0659105	+	0.0380534i
$777$		0			0
$778$	−15.5214	+	8.96129i	−0.556469	+	0.321278i
$779$	−24.7672	+	14.2993i	−0.887376	+	0.512327i
$780$		0			0
$781$	1.05729	+	0.610426i	0.0378328	+	0.0218428i
$782$			17.8382i			0.637894i
$783$		0			0
$784$	−5.76149			−0.205768
$785$	−25.7310	−	14.8558i	−0.918379	−	0.530226i
$786$		0			0
$787$	1.17396	−	0.677787i	0.0418472	−	0.0241605i	−0.478930	−	0.877853i	$-0.658975\pi$
$787$	1.17396	−	0.677787i	0.0418472	−	0.0241605i	0.520778	+	0.853692i	$0.325642\pi$
$788$	−9.22741	−	15.9823i	−0.328713	−	0.569347i
$789$		0			0
$790$	−4.87062	−	2.81205i	−0.173289	−	0.100048i
$791$		−	18.7058i		−	0.665102i
$792$		0			0
$793$	5.72643			0.203352
$794$	−24.7782	−	14.3057i	−0.879347	−	0.507691i
$795$		0			0
$796$	22.6547	−	13.0797i	0.802973	−	0.463597i
$797$	4.91284	+	8.50928i	0.174022	+	0.301414i	0.939822	−	0.341664i	$-0.110990\pi$
$797$	4.91284	+	8.50928i	0.174022	+	0.301414i	−0.765801	+	0.643078i	$0.777657\pi$
$798$		0			0
$799$	41.0559	+	23.7036i	1.45245	+	0.838574i
$800$		−	0.0485451i		−	0.00171633i
$801$		0			0
$802$		−	15.2623i		−	0.538931i
$803$	−5.43359	−	3.13709i	−0.191747	−	0.110705i
$804$		0			0
$805$	−8.28176	+	4.78148i	−0.291894	+	0.168525i
$806$	−13.3651	−	11.7749i	−0.470767	−	0.414751i
$807$		0			0
$808$	1.14459	−	1.98249i	0.0402666	−	0.0697438i
$809$	32.6168			1.14674			0.573372	−	0.819295i	$-0.305635\pi$
$809$	32.6168			1.14674			0.573372	+	0.819295i	$0.305635\pi$
$810$		0			0
$811$	50.1843			1.76221			0.881105	−	0.472921i	$-0.156800\pi$
$811$	50.1843			1.76221			0.881105	+	0.472921i	$0.156800\pi$
$812$	2.29453	−	3.97425i	0.0805224	−	0.139469i
$813$		0			0
$814$	5.01944	+	8.69392i	0.175931	+	0.304722i
$815$	26.3149	−	15.1929i	0.921771	−	0.532185i
$816$		0			0
$817$	14.6508	+	8.45867i	0.512568	+	0.295931i
$818$	−28.5904			−0.999640
$819$		0			0
$820$	25.5879			0.893567
$821$	−11.0576	+	19.1523i	−0.385912	+	0.668420i	−0.991895	−	0.127058i	$-0.959447\pi$
$821$	−11.0576	+	19.1523i	−0.385912	+	0.668420i	0.605983	+	0.795478i	$0.292780\pi$
$822$		0			0
$823$	−28.0176	+	16.1759i	−0.976631	+	0.563858i	−0.901251	−	0.433297i	$-0.857350\pi$
$823$	−28.0176	+	16.1759i	−0.976631	+	0.563858i	−0.0753796	+	0.997155i	$0.524017\pi$
$824$	1.05413	−	0.608600i	0.0367222	−	0.0212016i
$825$		0			0
$826$	−3.28270	+	5.68581i	−0.114220	+	0.197835i
$827$	15.7673			0.548282			0.274141	−	0.961690i	$-0.411607\pi$
$827$	15.7673			0.548282			0.274141	+	0.961690i	$0.411607\pi$
$828$		0			0
$829$			8.39199i			0.291466i	0.989324	+	0.145733i	$0.0465540\pi$
$829$			8.39199i			0.291466i	−0.989324	+	0.145733i	$0.953446\pi$
$830$	−2.25814	+	3.91122i	−0.0783814	+	0.135760i
$831$		0			0
$832$	−2.77056	+	1.59958i	−0.0960518	+	0.0554555i
$833$	13.3070	+	23.0484i	0.461061	+	0.798581i
$834$		0			0
$835$	11.6772	+	6.74186i	0.404107	+	0.233312i
$836$	2.53792			0.0877756
$837$		0			0
$838$	−8.47141			−0.292640
$839$	−27.8508	−	16.0797i	−0.961516	−	0.555131i	−0.0648765	−	0.997893i	$-0.520665\pi$
$839$	−27.8508	−	16.0797i	−0.961516	−	0.555131i	−0.896639	+	0.442762i	$0.853999\pi$
$840$		0			0
$841$	5.99800	+	10.3888i	0.206828	+	0.358236i
$842$	−22.8445	+	13.1893i	−0.787275	+	0.454533i
$843$		0			0
$844$	−7.05862	+	12.2259i	−0.242968	+	0.420833i
$845$		−	6.15343i		−	0.211684i
$846$		0			0
$847$	11.0828			0.380809
$848$	−4.92639	+	8.53275i	−0.169173	+	0.293016i
$849$		0			0
$850$	−0.194201	+	0.112122i	−0.00666104	+	0.00384576i
$851$	−32.8998	+	18.9947i	−1.12779	+	0.651130i
$852$		0			0
$853$	3.42036	−	5.92425i	0.117111	−	0.202842i	−0.801511	−	0.597981i	$-0.795970\pi$
$853$	3.42036	−	5.92425i	0.117111	−	0.202842i	0.918622	+	0.395138i	$0.129303\pi$
$854$	1.99203			0.0681660
$855$		0			0
$856$	10.3952			0.355301
$857$	33.3784	+	19.2710i	1.14018	+	0.658285i	0.946476	−	0.322774i	$-0.104615\pi$
$857$	33.3784	+	19.2710i	1.14018	+	0.658285i	0.193707	+	0.981059i	$0.437949\pi$
$858$		0			0
$859$	−16.4040	+	9.47085i	−0.559697	+	0.323141i	−0.753024	−	0.657993i	$-0.771406\pi$
$859$	−16.4040	+	9.47085i	−0.559697	+	0.323141i	0.193327	+	0.981134i	$0.438072\pi$
$860$	−7.56816	−	13.1084i	−0.258072	−	0.446994i
$861$		0			0
$862$	10.3026	−	17.8447i	0.350909	−	0.607792i
$863$	1.15240			0.0392282			0.0196141	−	0.999808i	$-0.493756\pi$
$863$	1.15240			0.0392282			0.0196141	+	0.999808i	$0.493756\pi$
$864$		0			0
$865$	−32.7427			−1.11329
$866$	12.2312	−	21.1850i	0.415631	−	0.719895i
$867$		0			0
$868$	−4.64928	−	4.09608i	−0.157807	−	0.139030i
$869$	2.23366	−	1.28960i	0.0757716	−	0.0437468i
$870$		0			0
$871$	−9.03256	−	5.21495i	−0.306057	−	0.176702i
$872$		−	11.6174i		−	0.393415i
$873$		0			0
$874$			9.60405i			0.324862i
$875$	−10.8271	−	6.25103i	−0.366023	−	0.211323i
$876$		0			0
$877$	−28.7645	−	49.8216i	−0.971309	−	1.68236i	−0.691613	−	0.722268i	$-0.743100\pi$
$877$	−28.7645	−	49.8216i	−0.971309	−	1.68236i	−0.279696	−	0.960089i	$-0.590234\pi$
$878$	12.3935	−	7.15542i	0.418262	−	0.241484i
$879$		0			0
$880$	−1.96651	−	1.13536i	−0.0662910	−	0.0382731i
$881$	1.62120			0.0546197			0.0273098	−	0.999627i	$-0.491306\pi$
$881$	1.62120			0.0546197			0.0273098	+	0.999627i	$0.491306\pi$
$882$		0			0
$883$			23.7417i			0.798971i	0.916739	+	0.399486i	$0.130811\pi$
$883$			23.7417i			0.798971i	−0.916739	+	0.399486i	$0.869189\pi$
$884$	12.7980	+	7.38894i	0.430444	+	0.248517i
$885$		0			0
$886$	−2.53824	−	4.39636i	−0.0852738	−	0.147698i
$887$	−3.06497	+	1.76956i	−0.102912	+	0.0594160i	−0.550572	−	0.834787i	$-0.685591\pi$
$887$	−3.06497	+	1.76956i	−0.102912	+	0.0594160i	0.447661	+	0.894203i	$0.352257\pi$
$888$		0			0
$889$	−2.21890	−	1.28109i	−0.0744197	−	0.0429662i
$890$	−11.8650			−0.397715
$891$		0			0
$892$		−	28.7959i		−	0.964158i
$893$	22.1044	+	12.7620i	0.739694	+	0.427063i
$894$		0			0
$895$	−25.3768	+	14.6513i	−0.848254	+	0.489740i
$896$	−0.963784	+	0.556441i	−0.0321978	+	0.0185894i
$897$		0			0
$898$	−29.5475	−	17.0592i	−0.986012	−	0.569274i
$899$	−21.7575	+	7.33047i	−0.725653	+	0.244485i
$900$		0			0
$901$	45.5129			1.51625
$902$	−5.86728	+	10.1624i	−0.195359	+	0.338372i
$903$		0			0
$904$	8.40422	+	14.5565i	0.279520	+	0.484143i
$905$	−0.203767	−	0.352936i	−0.00677346	−	0.0117320i
$906$		0			0
$907$	−18.0502	+	31.2639i	−0.599347	+	1.03810i	0.393570	+	0.919295i	$0.371240\pi$
$907$	−18.0502	+	31.2639i	−0.599347	+	1.03810i	−0.992918	+	0.118805i	$0.962094\pi$
$908$			14.6933i			0.487615i
$909$		0			0
$910$			7.92231i			0.262622i
$911$	23.2080	−	40.1975i	0.768916	−	1.33180i	−0.169235	−	0.985576i	$-0.554130\pi$
$911$	23.2080	−	40.1975i	0.768916	−	1.33180i	0.938151	−	0.346226i	$-0.112537\pi$
$912$		0			0
$913$	−1.03558	−	1.79368i	−0.0342728	−	0.0593622i
$914$	2.93947	+	5.09131i	0.0972290	+	0.168406i
$915$		0			0
$916$	6.07989	+	3.51023i	0.200885	+	0.115981i
$917$		−	5.96522i		−	0.196989i
$918$		0			0
$919$	−56.6374			−1.86829			−0.934147	−	0.356888i	$-0.883838\pi$
$919$	−56.6374			−1.86829			−0.934147	+	0.356888i	$0.883838\pi$
$920$	4.29648	−	7.44172i	0.141651	−	0.245346i
$921$		0			0
$922$	34.2032	−	19.7473i	1.12642	−	0.650341i
$923$	1.91369	+	3.31460i	0.0629897	+	0.109101i
$924$		0			0
$925$	−0.413582	−	0.238782i	−0.0135985	−	0.00785110i
$926$	23.1475			0.760675
$927$		0			0
$928$			4.12359i			0.135364i
$929$	24.5733	−	42.5622i	0.806224	−	1.39642i	−0.109237	−	0.994016i	$-0.534841\pi$
$929$	24.5733	−	42.5622i	0.806224	−	1.39642i	0.915461	−	0.402406i	$-0.131826\pi$
$930$		0			0
$931$	7.16446	+	12.4092i	0.234806	+	0.406695i
$932$	−1.77433	+	1.02441i	−0.0581201	+	0.0335557i
$933$		0			0
$934$	3.06335	−	5.30588i	0.100236	−	0.173614i
$935$			10.4892i			0.343033i
$936$		0			0
$937$	3.03674			0.0992059			0.0496029	−	0.998769i	$-0.484204\pi$
$937$	3.03674			0.0992059			0.0496029	+	0.998769i	$0.484204\pi$
$938$	−3.14212	−	1.81411i	−0.102594	−	0.0592327i
$939$		0			0
$940$	−11.4184	−	19.7773i	−0.372427	−	0.645063i
$941$	11.1294	+	19.2767i	0.362809	+	0.628404i	0.988422	−	0.151730i	$-0.0484843\pi$
$941$	11.1294	+	19.2767i	0.362809	+	0.628404i	−0.625613	+	0.780134i	$0.715151\pi$
$942$		0			0
$943$	−38.4569	−	22.2031i	−1.25233	−	0.723033i
$944$		−	5.89947i		−	0.192011i
$945$		0			0
$946$	6.94149			0.225687
$947$	−25.6560	+	44.4375i	−0.833708	+	1.44403i	0.0613692	+	0.998115i	$0.480453\pi$
$947$	−25.6560	+	44.4375i	−0.833708	+	1.44403i	−0.895078	+	0.445910i	$0.852880\pi$
$948$		0			0
$949$	−9.83476	−	17.0343i	−0.319250	−	0.552957i
$950$	−0.104557	+	0.0603662i	−0.00339229	+	0.00195854i
$951$		0			0
$952$	4.45200	+	2.57036i	0.144290	+	0.0833060i
$953$	−28.3831			−0.919417			−0.459709	−	0.888070i	$-0.652046\pi$
$953$	−28.3831			−0.919417			−0.459709	+	0.888070i	$0.652046\pi$
$954$		0			0
$955$	0.142862			0.00462290
$956$	7.43679	−	12.8809i	0.240523	−	0.416598i
$957$		0			0
$958$	3.74499	+	6.48652i	0.120995	+	0.209570i
$959$	−7.76980	−	13.4577i	−0.250900	−	0.434571i
$960$		0			0
$961$	3.90631	+	30.7529i	0.126010	+	0.992029i
$962$			31.4718i			1.01469i
$963$		0			0
$964$			12.7935i			0.412051i
$965$	4.85274	+	2.80173i	0.156215	+	0.0901910i
$966$		0			0
$967$	5.33559	−	3.08050i	0.171581	−	0.0990624i	−0.411750	−	0.911297i	$-0.635082\pi$
$967$	5.33559	−	3.08050i	0.171581	−	0.0990624i	0.583331	+	0.812234i	$0.301749\pi$
$968$	−8.62444	+	4.97932i	−0.277200	+	0.160042i
$969$		0			0
$970$	−2.35880	+	4.08556i	−0.0757365	+	0.131179i
$971$		−	25.5833i		−	0.821007i	−0.911859	−	0.410504i	$-0.865353\pi$
$971$		−	25.5833i		−	0.821007i	0.911859	−	0.410504i	$-0.134647\pi$
$972$		0			0
$973$			8.43086i			0.270281i
$974$	4.84260	−	8.38762i	0.155167	−	0.268757i
$975$		0			0
$976$	−1.55017	+	0.894989i	−0.0496196	+	0.0286479i
$977$	27.8940	−	16.1046i	0.892408	−	0.515232i	0.0176784	−	0.999844i	$-0.494373\pi$
$977$	27.8940	−	16.1046i	0.892408	−	0.515232i	0.874729	+	0.484612i	$0.161039\pi$
$978$		0			0
$979$	2.72063	−	4.71227i	0.0869517	−	0.150605i
$980$		−	12.8204i		−	0.409533i
$981$		0			0
$982$			16.5164i			0.527060i
$983$	−7.45474	+	12.9120i	−0.237769	+	0.411829i	−0.960074	−	0.279747i	$-0.909750\pi$
$983$	−7.45474	+	12.9120i	−0.237769	+	0.411829i	0.722305	+	0.691575i	$0.243083\pi$
$984$		0			0
$985$	35.5637	−	20.5327i	1.13315	−	0.654227i
$986$	16.4961	−	9.52404i	0.525344	−	0.303307i
$987$		0			0
$988$	6.89041	+	3.97818i	0.219213	+	0.126563i
$989$			26.2682i			0.835280i
$990$		0			0
$991$		−	45.0132i		−	1.42989i	−0.699181	−	0.714945i	$-0.746452\pi$
$991$		−	45.0132i		−	1.42989i	0.699181	−	0.714945i	$-0.253548\pi$
$992$	5.45829	+	1.09865i	0.173301	+	0.0348821i
$993$		0			0
$994$	0.665707	+	1.15304i	0.0211149	+	0.0365722i
$995$	29.1047	+	50.4108i	0.922681	+	1.59813i
$996$		0			0
$997$	7.75035	−	13.4240i	0.245456	−	0.425142i	−0.716804	−	0.697275i	$-0.754396\pi$
$997$	7.75035	−	13.4240i	0.245456	−	0.425142i	0.962260	+	0.272133i	$0.0877290\pi$
$998$	19.0832			0.604068
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1674.2.q.a.1115.23		64
3.2	odd	2		558.2.q.a.371.15	yes	64
9.4	even	3		558.2.q.a.185.2	✓	64
9.5	odd	6	inner	1674.2.q.a.557.26		64
31.30	odd	2	inner	1674.2.q.a.1115.26		64
93.92	even	2		558.2.q.a.371.2	yes	64
279.185	even	6	inner	1674.2.q.a.557.23		64
279.247	odd	6		558.2.q.a.185.15	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
558.2.q.a.185.2	✓	64	9.4	even	3
558.2.q.a.185.15	yes	64	279.247	odd	6
558.2.q.a.371.2	yes	64	93.92	even	2
558.2.q.a.371.15	yes	64	3.2	odd	2
1674.2.q.a.557.23		64	279.185	even	6	inner
1674.2.q.a.557.26		64	9.5	odd	6	inner
1674.2.q.a.1115.23		64	1.1	even	1	trivial
1674.2.q.a.1115.26		64	31.30	odd	2	inner

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1674 = 2 \cdot 3^{3} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1674.q (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-1.92707 + 1.11259i) q^{5} +(0.556441 - 0.963784i) q^{7} +1.00000i q^{8} -2.22519 q^{10} +(0.510234 - 0.883751i) q^{11} +(2.77056 - 1.59958i) q^{13} +(0.963784 - 0.556441i) q^{14} +(-0.500000 + 0.866025i) q^{16} +4.61929 q^{17} +2.48701 q^{19} +(-1.92707 - 1.11259i) q^{20} +(0.883751 - 0.510234i) q^{22} +(1.93084 + 3.34431i) q^{23} +(-0.0242726 + 0.0420413i) q^{25} +3.19916 q^{26} +1.11288 q^{28} +(2.06180 - 3.57113i) q^{29} +(-4.17770 - 3.68060i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(4.00043 + 2.30965i) q^{34} +2.47637i q^{35} +9.83752i q^{37} +(2.15382 + 1.24351i) q^{38} +(-1.11259 - 1.92707i) q^{40} +(-9.95860 + 5.74960i) q^{41} +(5.89094 + 3.40113i) q^{43} +1.02047 q^{44} +3.86168i q^{46} +(8.88791 + 5.13144i) q^{47} +(2.88075 + 4.98960i) q^{49} +(-0.0420413 + 0.0242726i) q^{50} +(2.77056 + 1.59958i) q^{52} +9.85277 q^{53} +2.27073i q^{55} +(0.963784 + 0.556441i) q^{56} +(3.57113 - 2.06180i) q^{58} +(-5.10909 + 2.94973i) q^{59} +(1.55017 + 0.894989i) q^{61} +(-1.77769 - 5.27635i) q^{62} -1.00000 q^{64} +(-3.55937 + 6.16501i) q^{65} +(-1.63010 - 2.82341i) q^{67} +(2.30965 + 4.00043i) q^{68} +(-1.23818 + 2.14460i) q^{70} +1.19637i q^{71} -6.14833i q^{73} +(-4.91876 + 8.51955i) q^{74} +(1.24351 + 2.15382i) q^{76} +(-0.567830 - 0.983510i) q^{77} +(2.18886 + 1.26374i) q^{79} -2.22519i q^{80} -11.4992 q^{82} +(1.01481 - 1.75771i) q^{83} +(-8.90169 + 5.13940i) q^{85} +(3.40113 + 5.89094i) q^{86} +(0.883751 + 0.510234i) q^{88} +5.33213 q^{89} -3.56029i q^{91} +(-1.93084 + 3.34431i) q^{92} +(5.13144 + 8.88791i) q^{94} +(-4.79264 + 2.76703i) q^{95} +(1.06005 - 1.83605i) q^{97} +5.76149i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 32 q^{4} - 12 q^{5} - 4 q^{7} - 32 q^{16} - 8 q^{19} - 12 q^{20} + 44 q^{25} - 8 q^{28} + 8 q^{31} - 36 q^{38} - 24 q^{41} + 48 q^{47} - 36 q^{49} + 12 q^{59} - 64 q^{64} + 16 q^{67} - 12 q^{70}+ \cdots - 16 q^{97}+O(q^{100}) \) 64 * q + 32 * q^4 - 12 * q^5 - 4 * q^7 - 32 * q^16 - 8 * q^19 - 12 * q^20 + 44 * q^25 - 8 * q^28 + 8 * q^31 - 36 * q^38 - 24 * q^41 + 48 * q^47 - 36 * q^49 + 12 * q^59 - 64 * q^64 + 16 * q^67 - 12 * q^70 - 4 * q^76 + 180 * q^95 - 16 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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