LMFDB - Embedded newform 1890.2.bi.a.899.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1890,2,Mod(719,1890)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1890, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5, 3, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1890.719"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1890.bi (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [48,-48] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$15.0917259820$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 630)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			899.5
Character	$\chi$	$=$	1890.899
Dual form			1890.2.bi.a.719.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000 q^{2} +1.00000 q^{4} +(-1.67933 - 1.47644i) q^{5} +(-2.41546 + 1.07960i) q^{7} -1.00000 q^{8} +(1.67933 + 1.47644i) q^{10} +(-5.13649 + 2.96556i) q^{11} +(-2.57957 - 4.46794i) q^{13} +(2.41546 - 1.07960i) q^{14} +1.00000 q^{16} +(-1.62025 - 0.935454i) q^{17} +(-1.51165 + 0.872754i) q^{19} +(-1.67933 - 1.47644i) q^{20} +(5.13649 - 2.96556i) q^{22} +(3.20885 - 5.55790i) q^{23} +(0.640274 + 4.95884i) q^{25} +(2.57957 + 4.46794i) q^{26} +(-2.41546 + 1.07960i) q^{28} +(2.16663 + 1.25090i) q^{29} -4.36743i q^{31} -1.00000 q^{32} +(1.62025 + 0.935454i) q^{34} +(5.65031 + 1.75328i) q^{35} +(-1.17895 + 0.680668i) q^{37} +(1.51165 - 0.872754i) q^{38} +(1.67933 + 1.47644i) q^{40} +(3.79398 + 6.57136i) q^{41} +(4.07460 + 2.35247i) q^{43} +(-5.13649 + 2.96556i) q^{44} +(-3.20885 + 5.55790i) q^{46} +9.74722i q^{47} +(4.66893 - 5.21547i) q^{49} +(-0.640274 - 4.95884i) q^{50} +(-2.57957 - 4.46794i) q^{52} +(-0.628956 + 1.08938i) q^{53} +(13.0043 + 2.60357i) q^{55} +(2.41546 - 1.07960i) q^{56} +(-2.16663 - 1.25090i) q^{58} +1.30033 q^{59} -11.4604i q^{61} +4.36743i q^{62} +1.00000 q^{64} +(-2.26470 + 11.3117i) q^{65} +15.0907i q^{67} +(-1.62025 - 0.935454i) q^{68} +(-5.65031 - 1.75328i) q^{70} +2.88706i q^{71} +(1.79824 - 3.11464i) q^{73} +(1.17895 - 0.680668i) q^{74} +(-1.51165 + 0.872754i) q^{76} +(9.20540 - 12.7086i) q^{77} +8.42064 q^{79} +(-1.67933 - 1.47644i) q^{80} +(-3.79398 - 6.57136i) q^{82} +(-2.43978 - 1.40861i) q^{83} +(1.33980 + 3.96313i) q^{85} +(-4.07460 - 2.35247i) q^{86} +(5.13649 - 2.96556i) q^{88} +(-8.92096 - 15.4516i) q^{89} +(11.0544 + 8.00725i) q^{91} +(3.20885 - 5.55790i) q^{92} -9.74722i q^{94} +(3.82713 + 0.766222i) q^{95} +(1.23514 - 2.13933i) q^{97} +(-4.66893 + 5.21547i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 48 q^{2} + 48 q^{4} + 3 q^{7} - 48 q^{8} - 6 q^{11} - 3 q^{14} + 48 q^{16} + 6 q^{22} - 3 q^{23} - 18 q^{25} + 3 q^{28} + 3 q^{29} - 48 q^{32} + 12 q^{35} + 3 q^{41} - 6 q^{44} + 3 q^{46} + 3 q^{49}+ \cdots - 3 q^{98}+O(q^{100}) $ 48 * q - 48 * q^2 + 48 * q^4 + 3 * q^7 - 48 * q^8 - 6 * q^11 - 3 * q^14 + 48 * q^16 + 6 * q^22 - 3 * q^23 - 18 * q^25 + 3 * q^28 + 3 * q^29 - 48 * q^32 + 12 * q^35 + 3 * q^41 - 6 * q^44 + 3 * q^46 + 3 * q^49 + 18 * q^50 - 42 * q^55 - 3 * q^56 - 3 * q^58 + 48 * q^64 - 12 * q^65 - 12 * q^70 - 18 * q^73 + 12 * q^77 - 3 * q^82 - 9 * q^83 - 33 * q^85 + 6 * q^88 + 33 * q^89 - 3 * q^92 - 24 * q^97 - 3 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1890\mathbb{Z}\right)^\times$.

$n$	$757$	$1081$	$1541$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$		0			0
$3$		0			0
$4$	1.00000			0.500000
$5$	−1.67933	−	1.47644i	−0.751018	−	0.660282i
$5$	−1.67933	−	1.47644i	−0.751018	−	0.660282i
$6$		0			0
$7$	−2.41546	+	1.07960i	−0.912959	+	0.408050i
$7$	−2.41546	+	1.07960i	−0.912959	+	0.408050i
$8$	−1.00000			−0.353553
$9$		0			0
$10$	1.67933	+	1.47644i	0.531050	+	0.466890i
$11$	−5.13649	+	2.96556i	−1.54871	+	0.894149i	−0.550471	+	0.834854i	$0.685552\pi$
$11$	−5.13649	+	2.96556i	−1.54871	+	0.894149i	−0.998241	+	0.0592945i	$0.981115\pi$
$12$		0			0
$13$	−2.57957	−	4.46794i	−0.715444	−	1.23918i	−0.962788	−	0.270257i	$-0.912891\pi$
$13$	−2.57957	−	4.46794i	−0.715444	−	1.23918i	0.247344	−	0.968928i	$-0.420442\pi$
$14$	2.41546	−	1.07960i	0.645560	−	0.288535i
$15$		0			0
$16$	1.00000			0.250000
$17$	−1.62025	−	0.935454i	−0.392969	−	0.226881i	0.290477	−	0.956882i	$-0.406186\pi$
$17$	−1.62025	−	0.935454i	−0.392969	−	0.226881i	−0.683446	+	0.730001i	$0.739519\pi$
$18$		0			0
$19$	−1.51165	+	0.872754i	−0.346797	+	0.200224i	−0.663274	−	0.748377i	$-0.730833\pi$
$19$	−1.51165	+	0.872754i	−0.346797	+	0.200224i	0.316476	+	0.948600i	$0.397500\pi$
$20$	−1.67933	−	1.47644i	−0.375509	−	0.330141i
$21$		0			0
$22$	5.13649	−	2.96556i	1.09510	−	0.632259i
$23$	3.20885	−	5.55790i	0.669092	−	1.15890i	−0.309066	−	0.951041i	$-0.600016\pi$
$23$	3.20885	−	5.55790i	0.669092	−	1.15890i	0.978158	−	0.207861i	$-0.0666503\pi$
$24$		0			0
$25$	0.640274	+	4.95884i	0.128055	+	0.991767i
$26$	2.57957	+	4.46794i	0.505895	+	0.876236i
$27$		0			0
$28$	−2.41546	+	1.07960i	−0.456480	+	0.204025i
$29$	2.16663	+	1.25090i	0.402333	+	0.232287i	0.687490	−	0.726194i	$-0.258712\pi$
$29$	2.16663	+	1.25090i	0.402333	+	0.232287i	−0.285157	+	0.958481i	$0.592046\pi$
$30$		0			0
$31$		−	4.36743i		−	0.784413i	−0.919877	−	0.392207i	$-0.871712\pi$
$31$		−	4.36743i		−	0.784413i	0.919877	−	0.392207i	$-0.128288\pi$
$32$	−1.00000			−0.176777
$33$		0			0
$34$	1.62025	+	0.935454i	0.277871	+	0.160429i
$35$	5.65031	+	1.75328i	0.955077	+	0.296358i
$36$		0			0
$37$	−1.17895	+	0.680668i	−0.193818	+	0.111901i	−0.593769	−	0.804636i	$-0.702361\pi$
$37$	−1.17895	+	0.680668i	−0.193818	+	0.111901i	0.399950	+	0.916537i	$0.369027\pi$
$38$	1.51165	−	0.872754i	0.245223	−	0.141579i
$39$		0			0
$40$	1.67933	+	1.47644i	0.265525	+	0.233445i
$41$	3.79398	+	6.57136i	0.592520	+	1.02627i	0.993892	+	0.110359i	$0.0352002\pi$
$41$	3.79398	+	6.57136i	0.592520	+	1.02627i	−0.401372	+	0.915915i	$0.631467\pi$
$42$		0			0
$43$	4.07460	+	2.35247i	0.621370	+	0.358748i	0.777402	−	0.629004i	$-0.216537\pi$
$43$	4.07460	+	2.35247i	0.621370	+	0.358748i	−0.156032	+	0.987752i	$0.549870\pi$
$44$	−5.13649	+	2.96556i	−0.774356	+	0.447074i
$45$		0			0
$46$	−3.20885	+	5.55790i	−0.473120	+	0.819467i
$47$			9.74722i			1.42178i	0.703304	+	0.710889i	$0.251707\pi$
$47$			9.74722i			1.42178i	−0.703304	+	0.710889i	$0.748293\pi$
$48$		0			0
$49$	4.66893	−	5.21547i	0.666990	−	0.745067i
$50$	−0.640274	−	4.95884i	−0.0905484	−	0.701285i
$51$		0			0
$52$	−2.57957	−	4.46794i	−0.357722	−	0.619592i
$53$	−0.628956	+	1.08938i	−0.0863938	+	0.149638i	−0.905984	−	0.423311i	$-0.860868\pi$
$53$	−0.628956	+	1.08938i	−0.0863938	+	0.149638i	0.819591	+	0.572950i	$0.194201\pi$
$54$		0			0
$55$	13.0043	+	2.60357i	1.75350	+	0.351065i
$56$	2.41546	−	1.07960i	0.322780	−	0.144268i
$57$		0			0
$58$	−2.16663	−	1.25090i	−0.284492	−	0.164252i
$59$	1.30033			0.169289			0.0846443	−	0.996411i	$-0.473025\pi$
$59$	1.30033			0.169289			0.0846443	+	0.996411i	$0.473025\pi$
$60$		0			0
$61$		−	11.4604i		−	1.46735i	−0.679499	−	0.733677i	$-0.737803\pi$
$61$		−	11.4604i		−	1.46735i	0.679499	−	0.733677i	$-0.262197\pi$
$62$			4.36743i			0.554664i
$63$		0			0
$64$	1.00000			0.125000
$65$	−2.26470	+	11.3117i	−0.280901	+	1.40304i
$66$		0			0
$67$			15.0907i			1.84362i	0.387641	+	0.921810i	$0.373290\pi$
$67$			15.0907i			1.84362i	−0.387641	+	0.921810i	$0.626710\pi$
$68$	−1.62025	−	0.935454i	−0.196485	−	0.113440i
$69$		0			0
$70$	−5.65031	−	1.75328i	−0.675341	−	0.209557i
$71$			2.88706i			0.342631i	0.985216	+	0.171315i	$0.0548017\pi$
$71$			2.88706i			0.342631i	−0.985216	+	0.171315i	$0.945198\pi$
$72$		0			0
$73$	1.79824	−	3.11464i	0.210468	−	0.364541i	−0.741393	−	0.671071i	$-0.765835\pi$
$73$	1.79824	−	3.11464i	0.210468	−	0.364541i	0.951861	+	0.306530i	$0.0991680\pi$
$74$	1.17895	−	0.680668i	0.137050	−	0.0791260i
$75$		0			0
$76$	−1.51165	+	0.872754i	−0.173399	+	0.100112i
$77$	9.20540	−	12.7086i	1.04905	−	1.44827i
$78$		0			0
$79$	8.42064			0.947396			0.473698	−	0.880687i	$-0.342919\pi$
$79$	8.42064			0.947396			0.473698	+	0.880687i	$0.342919\pi$
$80$	−1.67933	−	1.47644i	−0.187754	−	0.165071i
$81$		0			0
$82$	−3.79398	−	6.57136i	−0.418975	−	0.725686i
$83$	−2.43978	−	1.40861i	−0.267801	−	0.154615i	0.360087	−	0.932919i	$-0.382747\pi$
$83$	−2.43978	−	1.40861i	−0.267801	−	0.154615i	−0.627888	+	0.778304i	$0.716080\pi$
$84$		0			0
$85$	1.33980	+	3.96313i	0.145321	+	0.429862i
$86$	−4.07460	−	2.35247i	−0.439375	−	0.253673i
$87$		0			0
$88$	5.13649	−	2.96556i	0.547552	−	0.316129i
$89$	−8.92096	−	15.4516i	−0.945620	−	1.63786i	−0.754506	−	0.656293i	$-0.772123\pi$
$89$	−8.92096	−	15.4516i	−0.945620	−	1.63786i	−0.191113	−	0.981568i	$-0.561210\pi$
$90$		0			0
$91$	11.0544	+	8.00725i	1.15882	+	0.839388i
$92$	3.20885	−	5.55790i	0.334546	−	0.579451i
$93$		0			0
$94$		−	9.74722i		−	1.00535i
$95$	3.82713	+	0.766222i	0.392655	+	0.0786127i
$96$		0			0
$97$	1.23514	−	2.13933i	0.125410	−	0.217216i	−0.796483	−	0.604661i	$-0.793309\pi$
$97$	1.23514	−	2.13933i	0.125410	−	0.217216i	0.921893	+	0.387444i	$0.126642\pi$
$98$	−4.66893	+	5.21547i	−0.471633	+	0.526842i
$99$		0			0
$100$	0.640274	+	4.95884i	0.0640274	+	0.495884i
$101$	6.90957	+	11.9677i	0.687528	+	1.19083i	0.972635	+	0.232337i	$0.0746373\pi$
$101$	6.90957	+	11.9677i	0.687528	+	1.19083i	−0.285108	+	0.958496i	$0.592029\pi$
$102$		0			0
$103$	−0.712859	+	1.23471i	−0.0702400	+	0.121659i	−0.899006	−	0.437935i	$-0.855710\pi$
$103$	−0.712859	+	1.23471i	−0.0702400	+	0.121659i	0.828766	+	0.559595i	$0.189043\pi$
$104$	2.57957	+	4.46794i	0.252948	+	0.438118i
$105$		0			0
$106$	0.628956	−	1.08938i	0.0610896	−	0.105810i
$107$	1.67000	+	2.89252i	0.161445	+	0.279630i	0.935387	−	0.353626i	$-0.115051\pi$
$107$	1.67000	+	2.89252i	0.161445	+	0.279630i	−0.773942	+	0.633256i	$0.781718\pi$
$108$		0			0
$109$	4.42125	−	7.65783i	0.423479	−	0.733487i	−0.572798	−	0.819696i	$-0.694142\pi$
$109$	4.42125	−	7.65783i	0.423479	−	0.733487i	0.996277	+	0.0862097i	$0.0274755\pi$
$110$	−13.0043	−	2.60357i	−1.23991	−	0.248240i
$111$		0			0
$112$	−2.41546	+	1.07960i	−0.228240	+	0.102013i
$113$	8.87845	+	15.3779i	0.835215	+	1.44663i	0.893855	+	0.448355i	$0.147990\pi$
$113$	8.87845	+	15.3779i	0.835215	+	1.44663i	−0.0586408	+	0.998279i	$0.518677\pi$
$114$		0			0
$115$	−13.5946	+	4.59586i	−1.26770	+	0.428566i
$116$	2.16663	+	1.25090i	0.201166	+	0.116143i
$117$		0			0
$118$	−1.30033			−0.119705
$119$	4.92358	+	0.510329i	0.451344	+	0.0467817i
$120$		0			0
$121$	12.0891	−	20.9388i	1.09900	−	1.90353i
$122$			11.4604i			1.03758i
$123$		0			0
$124$		−	4.36743i		−	0.392207i
$125$	6.24617	−	9.27283i	0.558675	−	0.829387i
$126$		0			0
$127$		−	8.49642i		−	0.753936i	−0.926226	−	0.376968i	$-0.876967\pi$
$127$		−	8.49642i		−	0.753936i	0.926226	−	0.376968i	$-0.123033\pi$
$128$	−1.00000			−0.0883883
$129$		0			0
$130$	2.26470	−	11.3117i	0.198627	−	0.992102i
$131$	1.98718	−	3.44190i	0.173621	−	0.300720i	−0.766062	−	0.642766i	$-0.777787\pi$
$131$	1.98718	−	3.44190i	0.173621	−	0.300720i	0.939683	+	0.342046i	$0.111120\pi$
$132$		0			0
$133$	2.70912	−	3.74009i	0.234911	−	0.324307i
$134$		−	15.0907i		−	1.30364i
$135$		0			0
$136$	1.62025	+	0.935454i	0.138936	+	0.0802145i
$137$	−4.85327	−	8.40611i	−0.414643	−	0.718182i	0.580748	−	0.814083i	$-0.302760\pi$
$137$	−4.85327	−	8.40611i	−0.414643	−	0.718182i	−0.995391	+	0.0959011i	$0.969427\pi$
$138$		0			0
$139$	−17.4411	+	10.0696i	−1.47933	+	0.854092i	−0.999726	−	0.0233924i	$-0.992553\pi$
$139$	−17.4411	+	10.0696i	−1.47933	+	0.854092i	−0.479605	+	0.877485i	$0.659220\pi$
$140$	5.65031	+	1.75328i	0.477539	+	0.148179i
$141$		0			0
$142$		−	2.88706i		−	0.242276i
$143$	26.4999	+	15.2997i	2.21603	+	1.27943i
$144$		0			0
$145$	−1.79160	−	5.29956i	−0.148784	−	0.440105i
$146$	−1.79824	+	3.11464i	−0.148823	+	0.257769i
$147$		0			0
$148$	−1.17895	+	0.680668i	−0.0969092	+	0.0559506i
$149$	2.64213	+	1.52543i	0.216452	+	0.124968i	0.604306	−	0.796752i	$-0.293450\pi$
$149$	2.64213	+	1.52543i	0.216452	+	0.124968i	−0.387855	+	0.921721i	$0.626784\pi$
$150$		0			0
$151$	8.45186	+	14.6390i	0.687803	+	1.19131i	0.972547	+	0.232706i	$0.0747578\pi$
$151$	8.45186	+	14.6390i	0.687803	+	1.19131i	−0.284745	+	0.958603i	$0.591909\pi$
$152$	1.51165	−	0.872754i	0.122611	−	0.0707897i
$153$		0			0
$154$	−9.20540	+	12.7086i	−0.741792	+	1.02408i
$155$	−6.44823	+	7.33434i	−0.517934	+	0.589108i
$156$		0			0
$157$	−4.95836			−0.395720			−0.197860	−	0.980230i	$-0.563399\pi$
$157$	−4.95836			−0.395720			−0.197860	+	0.980230i	$0.563399\pi$
$158$	−8.42064			−0.669910
$159$		0			0
$160$	1.67933	+	1.47644i	0.132762	+	0.116723i
$161$	−1.75056	+	16.8892i	−0.137964	+	1.33105i
$162$		0			0
$163$	−5.11733	+	2.95449i	−0.400820	+	0.231413i	−0.686838	−	0.726811i	$-0.741002\pi$
$163$	−5.11733	+	2.95449i	−0.400820	+	0.231413i	0.286018	+	0.958224i	$0.407668\pi$
$164$	3.79398	+	6.57136i	0.296260	+	0.513137i
$165$		0			0
$166$	2.43978	+	1.40861i	0.189364	+	0.109329i
$167$	9.07327	−	5.23846i	0.702111	−	0.405364i	−0.106022	−	0.994364i	$-0.533811\pi$
$167$	9.07327	−	5.23846i	0.702111	−	0.405364i	0.808133	+	0.589000i	$0.200478\pi$
$168$		0			0
$169$	−6.80835	+	11.7924i	−0.523720	+	0.907109i
$170$	−1.33980	−	3.96313i	−0.102758	−	0.303958i
$171$		0			0
$172$	4.07460	+	2.35247i	0.310685	+	0.179374i
$173$		−	8.60028i		−	0.653867i	−0.945047	−	0.326933i	$-0.893985\pi$
$173$		−	8.60028i		−	0.653867i	0.945047	−	0.326933i	$-0.106015\pi$
$174$		0			0
$175$	−6.90012	−	11.2866i	−0.521600	−	0.853190i
$176$	−5.13649	+	2.96556i	−0.387178	+	0.223537i
$177$		0			0
$178$	8.92096	+	15.4516i	0.668654	+	1.15814i
$179$	2.31384	+	1.33590i	0.172945	+	0.0998497i	0.583974	−	0.811773i	$-0.301497\pi$
$179$	2.31384	+	1.33590i	0.172945	+	0.0998497i	−0.411029	+	0.911622i	$0.634830\pi$
$180$		0			0
$181$			7.92990i			0.589425i	0.955586	+	0.294712i	$0.0952238\pi$
$181$			7.92990i			0.589425i	−0.955586	+	0.294712i	$0.904776\pi$
$182$	−11.0544	−	8.00725i	−0.819410	−	0.593537i
$183$		0			0
$184$	−3.20885	+	5.55790i	−0.236560	+	0.409734i
$185$	2.98481	+	0.597583i	0.219447	+	0.0439352i
$186$		0			0
$187$	11.0966			0.811461
$188$			9.74722i			0.710889i
$189$		0			0
$190$	−3.82713	−	0.766222i	−0.277649	−	0.0555876i
$191$		−	11.8760i		−	0.859321i	−0.902991	−	0.429660i	$-0.858633\pi$
$191$		−	11.8760i		−	0.859321i	0.902991	−	0.429660i	$-0.141367\pi$
$192$		0			0
$193$			15.3218i			1.10288i	0.834213	+	0.551442i	$0.185922\pi$
$193$			15.3218i			1.10288i	−0.834213	+	0.551442i	$0.814078\pi$
$194$	−1.23514	+	2.13933i	−0.0886781	+	0.153595i
$195$		0			0
$196$	4.66893	−	5.21547i	0.333495	−	0.372534i
$197$	−9.02678			−0.643131			−0.321566	−	0.946887i	$-0.604209\pi$
$197$	−9.02678			−0.643131			−0.321566	+	0.946887i	$0.604209\pi$
$198$		0			0
$199$	10.4835	+	6.05268i	0.743159	+	0.429063i	0.823217	−	0.567727i	$-0.192177\pi$
$199$	10.4835	+	6.05268i	0.743159	+	0.429063i	−0.0800578	+	0.996790i	$0.525510\pi$
$200$	−0.640274	−	4.95884i	−0.0452742	−	0.350643i
$201$		0			0
$202$	−6.90957	−	11.9677i	−0.486155	−	0.842046i
$203$	−6.58389	−	0.682419i	−0.462098	−	0.0478965i
$204$		0			0
$205$	3.33087	−	16.6370i	0.232638	−	1.16198i
$206$	0.712859	−	1.23471i	0.0496672	−	0.0860261i
$207$		0			0
$208$	−2.57957	−	4.46794i	−0.178861	−	0.309796i
$209$	5.17640	−	8.96579i	0.358059	−	0.620177i
$210$		0			0
$211$	4.28556	+	7.42280i	0.295030	+	0.511007i	0.974992	−	0.222241i	$-0.0713370\pi$
$211$	4.28556	+	7.42280i	0.295030	+	0.511007i	−0.679962	+	0.733247i	$0.738004\pi$
$212$	−0.628956	+	1.08938i	−0.0431969	+	0.0748192i
$213$		0			0
$214$	−1.67000	−	2.89252i	−0.114159	−	0.197729i
$215$	−3.36931	−	9.96644i	−0.229785	−	0.679706i
$216$		0			0
$217$	4.71508	+	10.5494i	0.320080	+	0.716138i
$218$	−4.42125	+	7.65783i	−0.299445	+	0.518653i
$219$		0			0
$220$	13.0043	+	2.60357i	0.876750	+	0.175533i
$221$			9.65227i			0.649282i
$222$		0			0
$223$	−10.2042	+	17.6741i	−0.683322	+	1.18355i	0.290639	+	0.956833i	$0.406132\pi$
$223$	−10.2042	+	17.6741i	−0.683322	+	1.18355i	−0.973961	+	0.226716i	$0.927201\pi$
$224$	2.41546	−	1.07960i	0.161390	−	0.0721338i
$225$		0			0
$226$	−8.87845	−	15.3779i	−0.590586	−	1.02292i
$227$	19.9142	−	11.4974i	1.32175	−	0.763112i	0.337741	−	0.941239i	$-0.390337\pi$
$227$	19.9142	−	11.4974i	1.32175	−	0.763112i	0.984008	+	0.178127i	$0.0570037\pi$
$228$		0			0
$229$	−18.0144	−	10.4006i	−1.19043	−	0.687292i	−0.232022	−	0.972710i	$-0.574534\pi$
$229$	−18.0144	−	10.4006i	−1.19043	−	0.687292i	−0.958403	+	0.285418i	$0.907868\pi$
$230$	13.5946	−	4.59586i	0.896401	−	0.303042i
$231$		0			0
$232$	−2.16663	−	1.25090i	−0.142246	−	0.0821258i
$233$	13.6638	+	23.6663i	0.895143	+	1.55043i	0.833627	+	0.552327i	$0.186260\pi$
$233$	13.6638	+	23.6663i	0.895143	+	1.55043i	0.0615156	+	0.998106i	$0.480407\pi$
$234$		0			0
$235$	14.3911	−	16.3688i	0.938774	−	1.06778i
$236$	1.30033			0.0846443
$237$		0			0
$238$	−4.92358	−	0.510329i	−0.319148	−	0.0330797i
$239$	15.6608	−	9.04177i	1.01301	−	0.584864i	0.100941	−	0.994892i	$-0.467815\pi$
$239$	15.6608	−	9.04177i	1.01301	−	0.584864i	0.912073	+	0.410029i	$0.134481\pi$
$240$		0			0
$241$	2.31790	−	1.33824i	0.149309	−	0.0862037i	−0.423484	−	0.905903i	$-0.639193\pi$
$241$	2.31790	−	1.33824i	0.149309	−	0.0862037i	0.572793	+	0.819700i	$0.305860\pi$
$242$	−12.0891	+	20.9388i	−0.777114	+	1.34600i
$243$		0			0
$244$		−	11.4604i		−	0.733677i
$245$	−15.5410	+	1.86510i	−0.992875	+	0.119157i
$246$		0			0
$247$	7.79883	+	4.50266i	0.496228	+	0.286497i
$248$			4.36743i			0.277332i
$249$		0			0
$250$	−6.24617	+	9.27283i	−0.395043	+	0.586465i
$251$	−0.220993			−0.0139490			−0.00697448	−	0.999976i	$-0.502220\pi$
$251$	−0.220993			−0.0139490			−0.00697448	+	0.999976i	$0.502220\pi$
$252$		0			0
$253$			38.0642i			2.39307i
$254$			8.49642i			0.533113i
$255$		0			0
$256$	1.00000			0.0625000
$257$	14.7049	+	8.48987i	0.917265	+	0.529583i	0.882762	−	0.469821i	$-0.155682\pi$
$257$	14.7049	+	8.48987i	0.917265	+	0.529583i	0.0345037	+	0.999405i	$0.489015\pi$
$258$		0			0
$259$	2.11287	−	2.91692i	0.131287	−	0.181249i
$260$	−2.26470	+	11.3117i	−0.140450	+	0.701522i
$261$		0			0
$262$	−1.98718	+	3.44190i	−0.122768	+	0.212641i
$263$	−5.28060	−	9.14626i	−0.325615	−	0.563983i	0.656021	−	0.754742i	$-0.272238\pi$
$263$	−5.28060	−	9.14626i	−0.325615	−	0.563983i	−0.981637	+	0.190760i	$0.938905\pi$
$264$		0			0
$265$	2.66463	−	0.900818i	0.163687	−	0.0553368i
$266$	−2.70912	+	3.74009i	−0.166107	+	0.229319i
$267$		0			0
$268$			15.0907i			0.921810i
$269$	−1.54717	+	2.67977i	−0.0943324	+	0.163388i	−0.909330	−	0.416076i	$-0.863405\pi$
$269$	−1.54717	+	2.67977i	−0.0943324	+	0.163388i	0.814997	+	0.579465i	$0.196738\pi$
$270$		0			0
$271$	15.2570	−	8.80863i	0.926797	−	0.535086i	0.0409997	−	0.999159i	$-0.486946\pi$
$271$	15.2570	−	8.80863i	0.926797	−	0.535086i	0.885797	+	0.464073i	$0.153612\pi$
$272$	−1.62025	−	0.935454i	−0.0982423	−	0.0567202i
$273$		0			0
$274$	4.85327	+	8.40611i	0.293197	+	0.507831i
$275$	−17.9945	−	23.5723i	−1.08511	−	1.42146i
$276$		0			0
$277$	−2.43071	+	1.40337i	−0.146047	+	0.0843204i	−0.571243	−	0.820781i	$-0.693539\pi$
$277$	−2.43071	+	1.40337i	−0.146047	+	0.0843204i	0.425196	+	0.905101i	$0.360205\pi$
$278$	17.4411	−	10.0696i	1.04605	−	0.603934i
$279$		0			0
$280$	−5.65031	−	1.75328i	−0.337671	−	0.104778i
$281$	−6.77309	−	3.91045i	−0.404049	−	0.233278i	0.284181	−	0.958771i	$-0.408278\pi$
$281$	−6.77309	−	3.91045i	−0.404049	−	0.233278i	−0.688229	+	0.725493i	$0.741612\pi$
$282$		0			0
$283$	26.6702			1.58538			0.792691	−	0.609624i	$-0.208679\pi$
$283$	26.6702			1.58538			0.792691	+	0.609624i	$0.208679\pi$
$284$			2.88706i			0.171315i
$285$		0			0
$286$	−26.4999	−	15.2997i	−1.56697	−	0.904691i
$287$	−16.2587	−	11.7769i	−0.959718	−	0.695169i
$288$		0			0
$289$	−6.74985	−	11.6911i	−0.397050	−	0.687711i
$290$	1.79160	+	5.29956i	0.105206	+	0.311201i
$291$		0			0
$292$	1.79824	−	3.11464i	0.105234	−	0.182270i
$293$	28.0362	−	16.1867i	1.63789	−	0.945638i	0.656335	−	0.754469i	$-0.272106\pi$
$293$	28.0362	−	16.1867i	1.63789	−	0.945638i	0.981557	−	0.191168i	$-0.0612277\pi$
$294$		0			0
$295$	−2.18368	−	1.91986i	−0.127139	−	0.111778i
$296$	1.17895	−	0.680668i	0.0685252	−	0.0395630i
$297$		0			0
$298$	−2.64213	−	1.52543i	−0.153054	−	0.0883660i
$299$	−33.1098			−1.91479
$300$		0			0
$301$	−12.3818	−	1.28337i	−0.713673	−	0.0739722i
$302$	−8.45186	−	14.6390i	−0.486350	−	0.842383i
$303$		0			0
$304$	−1.51165	+	0.872754i	−0.0866993	+	0.0500559i
$305$	−16.9205	+	19.2457i	−0.968867	+	1.10201i
$306$		0			0
$307$	1.43218			0.0817386			0.0408693	−	0.999165i	$-0.486987\pi$
$307$	1.43218			0.0817386			0.0408693	+	0.999165i	$0.486987\pi$
$308$	9.20540	−	12.7086i	0.524526	−	0.724137i
$309$		0			0
$310$	6.44823	−	7.33434i	0.366235	−	0.416562i
$311$	−10.0729			−0.571182			−0.285591	−	0.958352i	$-0.592190\pi$
$311$	−10.0729			−0.571182			−0.285591	+	0.958352i	$0.592190\pi$
$312$		0			0
$313$	15.5516			0.879031			0.439516	−	0.898235i	$-0.355150\pi$
$313$	15.5516			0.879031			0.439516	+	0.898235i	$0.355150\pi$
$314$	4.95836			0.279816
$315$		0			0
$316$	8.42064			0.473698
$317$	−27.9352			−1.56899			−0.784497	−	0.620132i	$-0.787079\pi$
$317$	−27.9352			−1.56899			−0.784497	+	0.620132i	$0.787079\pi$
$318$		0			0
$319$	−14.8385			−0.830797
$320$	−1.67933	−	1.47644i	−0.0938772	−	0.0825353i
$321$		0			0
$322$	1.75056	−	16.8892i	0.0975550	−	0.941197i
$323$	3.26568			0.181708
$324$		0			0
$325$	20.5042	−	15.6524i	1.13737	−	0.868237i
$326$	5.11733	−	2.95449i	0.283422	−	0.163634i
$327$		0			0
$328$	−3.79398	−	6.57136i	−0.209487	−	0.362843i
$329$	−10.5231	−	23.5440i	−0.580157	−	1.29803i
$330$		0			0
$331$	−2.18531			−0.120116			−0.0600578	−	0.998195i	$-0.519128\pi$
$331$	−2.18531			−0.120116			−0.0600578	+	0.998195i	$0.519128\pi$
$332$	−2.43978	−	1.40861i	−0.133900	−	0.0773075i
$333$		0			0
$334$	−9.07327	+	5.23846i	−0.496467	+	0.286636i
$335$	22.2804	−	25.3422i	1.21731	−	1.38459i
$336$		0			0
$337$	0.212414	−	0.122637i	0.0115709	−	0.00668047i	−0.494203	−	0.869346i	$-0.664540\pi$
$337$	0.212414	−	0.122637i	0.0115709	−	0.00668047i	0.505774	+	0.862666i	$0.331207\pi$
$338$	6.80835	−	11.7924i	0.370326	−	0.641423i
$339$		0			0
$340$	1.33980	+	3.96313i	0.0726607	+	0.214931i
$341$	12.9519	+	22.4333i	0.701382	+	1.21483i
$342$		0			0
$343$	−5.64700	+	17.6383i	−0.304909	+	0.952381i
$344$	−4.07460	−	2.35247i	−0.219688	−	0.126837i
$345$		0			0
$346$			8.60028i			0.462354i
$347$	6.03454			0.323951			0.161976	−	0.986795i	$-0.448213\pi$
$347$	6.03454			0.323951			0.161976	+	0.986795i	$0.448213\pi$
$348$		0			0
$349$	6.70174	+	3.86925i	0.358736	+	0.207116i	0.668526	−	0.743689i	$-0.266925\pi$
$349$	6.70174	+	3.86925i	0.358736	+	0.207116i	−0.309790	+	0.950805i	$0.600259\pi$
$350$	6.90012	+	11.2866i	0.368827	+	0.603297i
$351$		0			0
$352$	5.13649	−	2.96556i	0.273776	−	0.158065i
$353$	−12.4114	+	7.16571i	−0.660591	+	0.381392i	−0.792502	−	0.609869i	$-0.791222\pi$
$353$	−12.4114	+	7.16571i	−0.660591	+	0.381392i	0.131911	+	0.991262i	$0.457889\pi$
$354$		0			0
$355$	4.26256	−	4.84831i	0.226233	−	0.257322i
$356$	−8.92096	−	15.4516i	−0.472810	−	0.818931i
$357$		0			0
$358$	−2.31384	−	1.33590i	−0.122290	−	0.0706044i
$359$	14.4007	−	8.31423i	0.760039	−	0.438808i	−0.0692710	−	0.997598i	$-0.522067\pi$
$359$	14.4007	−	8.31423i	0.760039	−	0.438808i	0.829310	+	0.558789i	$0.188734\pi$
$360$		0			0
$361$	−7.97660	+	13.8159i	−0.419821	+	0.727151i
$362$		−	7.92990i		−	0.416786i
$363$		0			0
$364$	11.0544	+	8.00725i	0.579411	+	0.419694i
$365$	−7.61839	+	2.57551i	−0.398765	+	0.134808i
$366$		0			0
$367$	16.5694	+	28.6990i	0.864914	+	1.49807i	0.867133	+	0.498077i	$0.165960\pi$
$367$	16.5694	+	28.6990i	0.864914	+	1.49807i	−0.00221888	+	0.999998i	$0.500706\pi$
$368$	3.20885	−	5.55790i	0.167273	−	0.289725i
$369$		0			0
$370$	−2.98481	−	0.597583i	−0.155173	−	0.0310668i
$371$	0.343121	−	3.31039i	0.0178140	−	0.171867i
$372$		0			0
$373$	−18.2835	−	10.5560i	−0.946682	−	0.546567i	−0.0546330	−	0.998507i	$-0.517399\pi$
$373$	−18.2835	−	10.5560i	−0.946682	−	0.546567i	−0.892048	+	0.451940i	$0.850732\pi$
$374$	−11.0966			−0.573790
$375$		0			0
$376$		−	9.74722i		−	0.502674i
$377$		−	12.9072i		−	0.664753i
$378$		0			0
$379$	−12.8226			−0.658651			−0.329325	−	0.944217i	$-0.606821\pi$
$379$	−12.8226			−0.658651			−0.329325	+	0.944217i	$0.606821\pi$
$380$	3.82713	+	0.766222i	0.196327	+	0.0393064i
$381$		0			0
$382$			11.8760i			0.607631i
$383$	14.1368	+	8.16190i	0.722358	+	0.417054i	0.815620	−	0.578588i	$-0.196396\pi$
$383$	14.1368	+	8.16190i	0.722358	+	0.417054i	−0.0932617	+	0.995642i	$0.529729\pi$
$384$		0			0
$385$	−34.2222	+	7.75063i	−1.74413	+	0.395008i
$386$		−	15.3218i		−	0.779857i
$387$		0			0
$388$	1.23514	−	2.13933i	0.0627049	−	0.108608i
$389$	9.64090	−	5.56618i	0.488813	−	0.282216i	−0.235269	−	0.971930i	$-0.575597\pi$
$389$	9.64090	−	5.56618i	0.488813	−	0.282216i	0.724082	+	0.689714i	$0.242264\pi$
$390$		0			0
$391$	−10.3983	+	6.00347i	−0.525865	+	0.303608i
$392$	−4.66893	+	5.21547i	−0.235816	+	0.263421i
$393$		0			0
$394$	9.02678			0.454763
$395$	−14.1410	−	12.4325i	−0.711511	−	0.625549i
$396$		0			0
$397$	−10.7572	−	18.6321i	−0.539891	−	0.935118i	−0.998909	−	0.0466914i	$-0.985132\pi$
$397$	−10.7572	−	18.6321i	−0.539891	−	0.935118i	0.459019	−	0.888427i	$-0.348201\pi$
$398$	−10.4835	−	6.05268i	−0.525493	−	0.303393i
$399$		0			0
$400$	0.640274	+	4.95884i	0.0320137	+	0.247942i
$401$	−11.7705	−	6.79568i	−0.587789	−	0.339360i	0.176434	−	0.984312i	$-0.443544\pi$
$401$	−11.7705	−	6.79568i	−0.587789	−	0.339360i	−0.764223	+	0.644953i	$0.776877\pi$
$402$		0			0
$403$	−19.5134	+	11.2661i	−0.972033	+	0.561204i
$404$	6.90957	+	11.9677i	0.343764	+	0.595416i
$405$		0			0
$406$	6.58389	+	0.682419i	0.326753	+	0.0338679i
$407$	4.03712	−	6.99249i	0.200113	−	0.346605i
$408$		0			0
$409$			6.31246i			0.312131i	0.987747	+	0.156066i	$0.0498811\pi$
$409$			6.31246i			0.312131i	−0.987747	+	0.156066i	$0.950119\pi$
$410$	−3.33087	+	16.6370i	−0.164500	+	0.821644i
$411$		0			0
$412$	−0.712859	+	1.23471i	−0.0351200	+	0.0608297i
$413$	−3.14090	+	1.40384i	−0.154554	+	0.0690783i
$414$		0			0
$415$	2.01747	+	5.96770i	0.0990337	+	0.292943i
$416$	2.57957	+	4.46794i	0.126474	+	0.219059i
$417$		0			0
$418$	−5.17640	+	8.96579i	−0.253186	+	0.438531i
$419$	−10.2076	−	17.6802i	−0.498676	−	0.863732i	0.501323	−	0.865260i	$-0.332847\pi$
$419$	−10.2076	−	17.6802i	−0.498676	−	0.863732i	−0.999999	+	0.00152816i	$0.999514\pi$
$420$		0			0
$421$	−15.4045	+	26.6814i	−0.750769	+	1.30037i	0.196681	+	0.980467i	$0.436984\pi$
$421$	−15.4045	+	26.6814i	−0.750769	+	1.30037i	−0.947450	+	0.319903i	$0.896350\pi$
$422$	−4.28556	−	7.42280i	−0.208618	−	0.361336i
$423$		0			0
$424$	0.628956	−	1.08938i	0.0305448	−	0.0529052i
$425$	3.60135	−	8.63352i	0.174691	−	0.418787i
$426$		0			0
$427$	12.3726	+	27.6822i	0.598754	+	1.33963i
$428$	1.67000	+	2.89252i	0.0807224	+	0.139815i
$429$		0			0
$430$	3.36931	+	9.96644i	0.162482	+	0.480625i
$431$	−29.8217	−	17.2176i	−1.43646	−	0.829342i	−0.438860	−	0.898556i	$-0.644618\pi$
$431$	−29.8217	−	17.2176i	−1.43646	−	0.829342i	−0.997602	+	0.0692140i	$0.977951\pi$
$432$		0			0
$433$	−5.86503			−0.281855			−0.140928	−	0.990020i	$-0.545008\pi$
$433$	−5.86503			−0.281855			−0.140928	+	0.990020i	$0.545008\pi$
$434$	−4.71508	−	10.5494i	−0.226331	−	0.506386i
$435$		0			0
$436$	4.42125	−	7.65783i	0.211739	−	0.366743i
$437$			11.2022i			0.535872i
$438$		0			0
$439$		−	0.0933769i		−	0.00445664i	−0.999998	−	0.00222832i	$-0.999291\pi$
$439$		−	0.0933769i		−	0.00445664i	0.999998	−	0.00222832i	$-0.000709296\pi$
$440$	−13.0043	−	2.60357i	−0.619956	−	0.124120i
$441$		0			0
$442$		−	9.65227i		−	0.459112i
$443$	−1.69982			−0.0807610			−0.0403805	−	0.999184i	$-0.512857\pi$
$443$	−1.69982			−0.0807610			−0.0403805	+	0.999184i	$0.512857\pi$
$444$		0			0
$445$	−7.83203	+	39.1194i	−0.371274	+	1.85444i
$446$	10.2042	−	17.6741i	0.483182	−	0.836895i
$447$		0			0
$448$	−2.41546	+	1.07960i	−0.114120	+	0.0510063i
$449$			1.98554i			0.0937035i	0.998902	+	0.0468518i	$0.0149188\pi$
$449$			1.98554i			0.0937035i	−0.998902	+	0.0468518i	$0.985081\pi$
$450$		0			0
$451$	−38.9755	−	22.5025i	−1.83528	−	1.05960i
$452$	8.87845	+	15.3779i	0.417607	+	0.723317i
$453$		0			0
$454$	−19.9142	+	11.4974i	−0.934618	+	0.539602i
$455$	−6.74183	−	29.7680i	−0.316062	−	1.39554i
$456$		0			0
$457$		−	24.5551i		−	1.14864i	−0.818631	−	0.574320i	$-0.805266\pi$
$457$		−	24.5551i		−	1.14864i	0.818631	−	0.574320i	$-0.194734\pi$
$458$	18.0144	+	10.4006i	0.841758	+	0.485989i
$459$		0			0
$460$	−13.5946	+	4.59586i	−0.633851	+	0.214283i
$461$	−16.3946	+	28.3963i	−0.763574	+	1.32255i	0.177423	+	0.984135i	$0.443224\pi$
$461$	−16.3946	+	28.3963i	−0.763574	+	1.32255i	−0.940997	+	0.338415i	$0.890109\pi$
$462$		0			0
$463$	19.1444	−	11.0530i	0.889717	−	0.513678i	0.0158669	−	0.999874i	$-0.494949\pi$
$463$	19.1444	−	11.0530i	0.889717	−	0.513678i	0.873850	+	0.486196i	$0.161616\pi$
$464$	2.16663	+	1.25090i	0.100583	+	0.0580717i
$465$		0			0
$466$	−13.6638	−	23.6663i	−0.632962	−	1.09632i
$467$	−30.9099	+	17.8459i	−1.43034	+	0.825808i	−0.997146	−	0.0754924i	$-0.975947\pi$
$467$	−30.9099	+	17.8459i	−1.43034	+	0.825808i	−0.433195	+	0.901300i	$0.642614\pi$
$468$		0			0
$469$	−16.2919	−	36.4510i	−0.752290	−	1.68315i
$470$	−14.3911	+	16.3688i	−0.663814	+	0.755034i
$471$		0			0
$472$	−1.30033			−0.0598526
$473$	−27.9055			−1.28310
$474$		0			0
$475$	−5.29572	−	6.93724i	−0.242984	−	0.318303i
$476$	4.92358	+	0.510329i	0.225672	+	0.0233909i
$477$		0			0
$478$	−15.6608	+	9.04177i	−0.716309	+	0.413561i
$479$	1.92319	+	3.33106i	0.0878727	+	0.152200i	0.906612	−	0.421966i	$-0.138660\pi$
$479$	1.92319	+	3.33106i	0.0878727	+	0.152200i	−0.818739	+	0.574166i	$0.805326\pi$
$480$		0			0
$481$	6.08237	+	3.51166i	0.277332	+	0.160118i
$482$	−2.31790	+	1.33824i	−0.105578	+	0.0609552i
$483$		0			0
$484$	12.0891	−	20.9388i	0.549502	−	0.951766i
$485$	−5.23279	+	1.76903i	−0.237609	+	0.0803273i
$486$		0			0
$487$	−17.1992	−	9.92995i	−0.779369	−	0.449969i	0.0568378	−	0.998383i	$-0.481898\pi$
$487$	−17.1992	−	9.92995i	−0.779369	−	0.449969i	−0.836207	+	0.548415i	$0.815232\pi$
$488$			11.4604i			0.518788i
$489$		0			0
$490$	15.5410	−	1.86510i	0.702069	−	0.0842568i
$491$	−7.14924	+	4.12761i	−0.322641	+	0.186277i	−0.652569	−	0.757729i	$-0.726309\pi$
$491$	−7.14924	+	4.12761i	−0.322641	+	0.186277i	0.329928	+	0.944006i	$0.392975\pi$
$492$		0			0
$493$	−2.34032	−	4.05356i	−0.105403	−	0.182563i
$494$	−7.79883	−	4.50266i	−0.350886	−	0.202584i
$495$		0			0
$496$		−	4.36743i		−	0.196103i
$497$	−3.11687	−	6.97358i	−0.139811	−	0.312808i
$498$		0			0
$499$	−15.9868	+	27.6900i	−0.715668	+	1.23957i	0.247033	+	0.969007i	$0.420544\pi$
$499$	−15.9868	+	27.6900i	−0.715668	+	1.23957i	−0.962701	+	0.270567i	$0.912789\pi$
$500$	6.24617	−	9.27283i	0.279337	−	0.414693i
$501$		0			0
$502$	0.220993			0.00986341
$503$			3.78755i			0.168878i	0.996429	+	0.0844392i	$0.0269099\pi$
$503$			3.78755i			0.168878i	−0.996429	+	0.0844392i	$0.973090\pi$
$504$		0			0
$505$	6.06616	−	30.2992i	0.269940	−	1.34830i
$506$		−	38.0642i		−	1.69216i
$507$		0			0
$508$		−	8.49642i		−	0.376968i
$509$	6.04054	−	10.4625i	0.267742	−	0.463743i	−0.700536	−	0.713617i	$-0.747056\pi$
$509$	6.04054	−	10.4625i	0.267742	−	0.463743i	0.968278	+	0.249874i	$0.0803891\pi$
$510$		0			0
$511$	−0.981013	+	9.46467i	−0.0433974	+	0.418693i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	−14.7049	−	8.48987i	−0.648605	−	0.374472i
$515$	3.02009	−	1.02099i	0.133081	−	0.0449900i
$516$		0			0
$517$	−28.9059	−	50.0665i	−1.27128	−	2.20192i
$518$	−2.11287	+	2.91692i	−0.0928340	+	0.128162i
$519$		0			0
$520$	2.26470	−	11.3117i	0.0993135	−	0.496051i
$521$	19.2169	−	33.2847i	0.841910	−	1.45823i	−0.0463687	−	0.998924i	$-0.514765\pi$
$521$	19.2169	−	33.2847i	0.841910	−	1.45823i	0.888278	−	0.459306i	$-0.151902\pi$
$522$		0			0
$523$	5.25006	+	9.09336i	0.229569	+	0.397625i	0.957680	−	0.287834i	$-0.0929350\pi$
$523$	5.25006	+	9.09336i	0.229569	+	0.397625i	−0.728111	+	0.685459i	$0.759602\pi$
$524$	1.98718	−	3.44190i	0.0868104	−	0.150360i
$525$		0			0
$526$	5.28060	+	9.14626i	0.230245	+	0.398796i
$527$	−4.08553	+	7.07634i	−0.177968	+	0.308250i
$528$		0			0
$529$	−9.09349	−	15.7504i	−0.395369	−	0.684799i
$530$	−2.66463	+	0.900818i	−0.115744	+	0.0391290i
$531$		0			0
$532$	2.70912	−	3.74009i	0.117455	−	0.162153i
$533$	19.5737	−	33.9026i	0.847829	−	1.46848i
$534$		0			0
$535$	1.46615	−	7.32313i	0.0633872	−	0.316607i
$536$		−	15.0907i		−	0.651818i
$537$		0			0
$538$	1.54717	−	2.67977i	0.0667031	−	0.115533i
$539$	−8.51515	+	40.6352i	−0.366773	+	1.75028i
$540$		0			0
$541$	17.0100	+	29.4622i	0.731316	+	1.26668i	0.956321	+	0.292319i	$0.0944270\pi$
$541$	17.0100	+	29.4622i	0.731316	+	1.26668i	−0.225004	+	0.974358i	$0.572240\pi$
$542$	−15.2570	+	8.80863i	−0.655344	+	0.378363i
$543$		0			0
$544$	1.62025	+	0.935454i	0.0694678	+	0.0401072i
$545$	−18.7310	+	6.33230i	−0.802348	+	0.271246i
$546$		0			0
$547$	−22.5807	−	13.0370i	−0.965482	−	0.557422i	−0.0676264	−	0.997711i	$-0.521543\pi$
$547$	−22.5807	−	13.0370i	−0.965482	−	0.557422i	−0.897856	+	0.440289i	$0.854876\pi$
$548$	−4.85327	−	8.40611i	−0.207321	−	0.359091i
$549$		0			0
$550$	17.9945	+	23.5723i	0.767287	+	1.00512i
$551$	−4.36692			−0.186037
$552$		0			0
$553$	−20.3398	+	9.09093i	−0.864934	+	0.386586i
$554$	2.43071	−	1.40337i	0.103271	−	0.0596235i
$555$		0			0
$556$	−17.4411	+	10.0696i	−0.739666	+	0.427046i
$557$	−9.87249	+	17.0997i	−0.418311	+	0.724535i	−0.995770	−	0.0918842i	$-0.970711\pi$
$557$	−9.87249	+	17.0997i	−0.418311	+	0.724535i	0.577459	+	0.816420i	$0.304044\pi$
$558$		0			0
$559$		−	24.2734i		−	1.02666i
$560$	5.65031	+	1.75328i	0.238769	+	0.0740894i
$561$		0			0
$562$	6.77309	+	3.91045i	0.285706	+	0.164952i
$563$			26.5207i			1.11771i	0.829264	+	0.558857i	$0.188760\pi$
$563$			26.5207i			1.11771i	−0.829264	+	0.558857i	$0.811240\pi$
$564$		0			0
$565$	7.79471	−	38.9330i	0.327926	−	1.63793i
$566$	−26.6702			−1.12103
$567$		0			0
$568$		−	2.88706i		−	0.121138i
$569$		−	4.44062i		−	0.186160i	−0.995659	−	0.0930802i	$-0.970329\pi$
$569$		−	4.44062i		−	0.186160i	0.995659	−	0.0930802i	$-0.0296713\pi$
$570$		0			0
$571$	34.4566			1.44196			0.720982	−	0.692954i	$-0.243691\pi$
$571$	34.4566			1.44196			0.720982	+	0.692954i	$0.243691\pi$
$572$	26.4999	+	15.2997i	1.10802	+	0.639713i
$573$		0			0
$574$	16.2587	+	11.7769i	0.678623	+	0.491559i
$575$	29.6152	+	12.3536i	1.23504	+	0.515181i
$576$		0			0
$577$	10.7016	−	18.5357i	0.445513	−	0.771651i	−0.552575	−	0.833463i	$-0.686355\pi$
$577$	10.7016	−	18.5357i	0.445513	−	0.771651i	0.998088	+	0.0618122i	$0.0196880\pi$
$578$	6.74985	+	11.6911i	0.280757	+	0.486285i
$579$		0			0
$580$	−1.79160	−	5.29956i	−0.0743920	−	0.220052i
$581$	7.41394	+	0.768454i	0.307582	+	0.0318809i
$582$		0			0
$583$		−	7.46082i		−	0.308996i
$584$	−1.79824	+	3.11464i	−0.0744116	+	0.128885i
$585$		0			0
$586$	−28.0362	+	16.1867i	−1.15816	+	0.668667i
$587$	−4.73587	−	2.73426i	−0.195470	−	0.112855i	0.399071	−	0.916920i	$-0.369333\pi$
$587$	−4.73587	−	2.73426i	−0.195470	−	0.112855i	−0.594541	+	0.804065i	$0.702666\pi$
$588$		0			0
$589$	3.81169	+	6.60204i	0.157058	+	0.272032i
$590$	2.18368	+	1.91986i	0.0899007	+	0.0790392i
$591$		0			0
$592$	−1.17895	+	0.680668i	−0.0484546	+	0.0279753i
$593$	5.02625	−	2.90190i	0.206403	−	0.119167i	−0.393236	−	0.919438i	$-0.628644\pi$
$593$	5.02625	−	2.90190i	0.206403	−	0.119167i	0.599639	+	0.800271i	$0.295311\pi$
$594$		0			0
$595$	−7.51483	−	8.12636i	−0.308078	−	0.333148i
$596$	2.64213	+	1.52543i	0.108226	+	0.0624842i
$597$		0			0
$598$	33.1098			1.35396
$599$			18.0350i			0.736888i	0.929650	+	0.368444i	$0.120109\pi$
$599$			18.0350i			0.736888i	−0.929650	+	0.368444i	$0.879891\pi$
$600$		0			0
$601$	2.29768	+	1.32656i	0.0937242	+	0.0541117i	0.546130	−	0.837701i	$-0.316101\pi$
$601$	2.29768	+	1.32656i	0.0937242	+	0.0541117i	−0.452405	+	0.891812i	$0.649434\pi$
$602$	12.3818	+	1.28337i	0.504643	+	0.0523062i
$603$		0			0
$604$	8.45186	+	14.6390i	0.343901	+	0.595654i
$605$	−51.2163	+	17.3145i	−2.08224	+	0.703933i
$606$		0			0
$607$	4.83260	−	8.37031i	0.196149	−	0.339740i	−0.751128	−	0.660157i	$-0.770490\pi$
$607$	4.83260	−	8.37031i	0.196149	−	0.339740i	0.947277	+	0.320417i	$0.103823\pi$
$608$	1.51165	−	0.872754i	0.0613057	−	0.0353949i
$609$		0			0
$610$	16.9205	−	19.2457i	0.685093	−	0.779237i
$611$	43.5500	−	25.1436i	1.76185	−	1.01720i
$612$		0			0
$613$	−0.262890	−	0.151780i	−0.0106180	−	0.00613033i	0.494682	−	0.869074i	$-0.335285\pi$
$613$	−0.262890	−	0.151780i	−0.0106180	−	0.00613033i	−0.505300	+	0.862944i	$0.668618\pi$
$614$	−1.43218			−0.0577979
$615$		0			0
$616$	−9.20540	+	12.7086i	−0.370896	+	0.512042i
$617$	3.49093	+	6.04647i	0.140540	+	0.243422i	0.927700	−	0.373327i	$-0.121783\pi$
$617$	3.49093	+	6.04647i	0.140540	+	0.243422i	−0.787160	+	0.616748i	$0.788450\pi$
$618$		0			0
$619$	15.3880	−	8.88428i	0.618497	−	0.357089i	−0.157787	−	0.987473i	$-0.550436\pi$
$619$	15.3880	−	8.88428i	0.618497	−	0.357089i	0.776284	+	0.630384i	$0.217102\pi$
$620$	−6.44823	+	7.33434i	−0.258967	+	0.294554i
$621$		0			0
$622$	10.0729			0.403887
$623$	38.2297	+	27.6916i	1.53164	+	1.10944i
$624$		0			0
$625$	−24.1801	+	6.35003i	−0.967204	+	0.254001i
$626$	−15.5516			−0.621569
$627$		0			0
$628$	−4.95836			−0.197860
$629$	2.54693			0.101553
$630$		0			0
$631$	12.0365			0.479167			0.239583	−	0.970876i	$-0.422989\pi$
$631$	12.0365			0.479167			0.239583	+	0.970876i	$0.422989\pi$
$632$	−8.42064			−0.334955
$633$		0			0
$634$	27.9352			1.10945
$635$	−12.5444	+	14.2683i	−0.497810	+	0.566219i
$636$		0			0
$637$	−35.3462	−	7.40685i	−1.40047	−	0.293470i
$638$	14.8385			0.587462
$639$		0			0
$640$	1.67933	+	1.47644i	0.0663812	+	0.0583613i
$641$	14.6690	−	8.46918i	0.579392	−	0.334512i	−0.181499	−	0.983391i	$-0.558095\pi$
$641$	14.6690	−	8.46918i	0.579392	−	0.334512i	0.760892	+	0.648879i	$0.224762\pi$
$642$		0			0
$643$	−12.5911	−	21.8084i	−0.496545	−	0.860041i	0.503447	−	0.864026i	$-0.332065\pi$
$643$	−12.5911	−	21.8084i	−0.496545	−	0.860041i	−0.999992	+	0.00398491i	$0.998732\pi$
$644$	−1.75056	+	16.8892i	−0.0689818	+	0.665527i
$645$		0			0
$646$	−3.26568			−0.128487
$647$	21.6450	+	12.4967i	0.850951	+	0.491297i	0.860972	−	0.508653i	$-0.169856\pi$
$647$	21.6450	+	12.4967i	0.850951	+	0.491297i	−0.0100203	+	0.999950i	$0.503190\pi$
$648$		0			0
$649$	−6.67914	+	3.85621i	−0.262179	+	0.151369i
$650$	−20.5042	+	15.6524i	−0.804240	+	0.613936i
$651$		0			0
$652$	−5.11733	+	2.95449i	−0.200410	+	0.115707i
$653$	−10.8541	+	18.7998i	−0.424753	+	0.735694i	−0.996397	−	0.0848077i	$-0.972972\pi$
$653$	−10.8541	+	18.7998i	−0.424753	+	0.735694i	0.571644	+	0.820502i	$0.306306\pi$
$654$		0			0
$655$	−8.41887	+	2.84612i	−0.328952	+	0.111207i
$656$	3.79398	+	6.57136i	0.148130	+	0.256569i
$657$		0			0
$658$	10.5231	+	23.5440i	0.410233	+	0.917842i
$659$	6.26940	+	3.61964i	0.244221	+	0.141001i	0.617115	−	0.786873i	$-0.288301\pi$
$659$	6.26940	+	3.61964i	0.244221	+	0.141001i	−0.372894	+	0.927874i	$0.621635\pi$
$660$		0			0
$661$			27.7010i			1.07744i	0.842484	+	0.538721i	$0.181092\pi$
$661$			27.7010i			1.07744i	−0.842484	+	0.538721i	$0.818908\pi$
$662$	2.18531			0.0849345
$663$		0			0
$664$	2.43978	+	1.40861i	0.0946820	+	0.0546646i
$665$	−10.0715	+	2.28099i	−0.390556	+	0.0884528i
$666$		0			0
$667$	13.9048	−	8.02793i	0.538396	−	0.310843i
$668$	9.07327	−	5.23846i	0.351055	−	0.202682i
$669$		0			0
$670$	−22.2804	+	25.3422i	−0.860768	+	0.979054i
$671$	33.9865	+	58.8663i	1.31203	+	2.27251i
$672$		0			0
$673$	40.2514	+	23.2391i	1.55158	+	0.895803i	0.998014	+	0.0629944i	$0.0200650\pi$
$673$	40.2514	+	23.2391i	1.55158	+	0.895803i	0.553562	+	0.832808i	$0.313268\pi$
$674$	−0.212414	+	0.122637i	−0.00818187	+	0.00472381i
$675$		0			0
$676$	−6.80835	+	11.7924i	−0.261860	+	0.453554i
$677$		−	1.40767i		−	0.0541012i	−0.999634	−	0.0270506i	$-0.991388\pi$
$677$		−	1.40767i		−	0.0541012i	0.999634	−	0.0270506i	$-0.00861152\pi$
$678$		0			0
$679$	−0.673822	+	6.50094i	−0.0258589	+	0.249483i
$680$	−1.33980	−	3.96313i	−0.0513789	−	0.151979i
$681$		0			0
$682$	−12.9519	−	22.4333i	−0.495952	−	0.859015i
$683$	−18.2234	+	31.5639i	−0.697300	+	1.20776i	0.272099	+	0.962269i	$0.412282\pi$
$683$	−18.2234	+	31.5639i	−0.697300	+	1.20776i	−0.969399	+	0.245490i	$0.921051\pi$
$684$		0			0
$685$	−4.26086	+	21.2821i	−0.162799	+	0.813149i
$686$	5.64700	−	17.6383i	0.215604	−	0.673435i
$687$		0			0
$688$	4.07460	+	2.35247i	0.155343	+	0.0896871i
$689$	6.48974			0.247240
$690$		0			0
$691$			41.4523i			1.57692i	0.615086	+	0.788460i	$0.289121\pi$
$691$			41.4523i			1.57692i	−0.615086	+	0.788460i	$0.710879\pi$
$692$		−	8.60028i		−	0.326933i
$693$		0			0
$694$	−6.03454			−0.229068
$695$	44.1563	+	8.84046i	1.67495	+	0.335338i
$696$		0			0
$697$		−	14.1964i		−	0.537726i
$698$	−6.70174	−	3.86925i	−0.253665	−	0.146453i
$699$		0			0
$700$	−6.90012	−	11.2866i	−0.260800	−	0.426595i
$701$			9.85600i			0.372256i	0.982526	+	0.186128i	$0.0595939\pi$
$701$			9.85600i			0.372256i	−0.982526	+	0.186128i	$0.940406\pi$
$702$		0			0
$703$	1.18811	−	2.05787i	0.0448105	−	0.0776140i
$704$	−5.13649	+	2.96556i	−0.193589	+	0.111769i
$705$		0			0
$706$	12.4114	−	7.16571i	0.467108	−	0.269685i
$707$	−29.6102	−	21.4480i	−1.11360	−	0.806636i
$708$		0			0
$709$	4.54234			0.170591			0.0852957	−	0.996356i	$-0.472817\pi$
$709$	4.54234			0.170591			0.0852957	+	0.996356i	$0.472817\pi$
$710$	−4.26256	+	4.84831i	−0.159971	+	0.181954i
$711$		0			0
$712$	8.92096	+	15.4516i	0.334327	+	0.579071i
$713$	−24.2737	−	14.0144i	−0.909058	−	0.524845i
$714$		0			0
$715$	−21.9129	−	64.8186i	−0.819496	−	2.42408i
$716$	2.31384	+	1.33590i	0.0864724	+	0.0499248i
$717$		0			0
$718$	−14.4007	+	8.31423i	−0.537428	+	0.310284i
$719$	20.9595	+	36.3030i	0.781659	+	1.35387i	0.930975	+	0.365083i	$0.118960\pi$
$719$	20.9595	+	36.3030i	0.781659	+	1.35387i	−0.149316	+	0.988790i	$0.547707\pi$
$720$		0			0
$721$	0.388894	−	3.75199i	0.0144832	−	0.139732i
$722$	7.97660	−	13.8159i	0.296858	−	0.514174i
$723$		0			0
$724$			7.92990i			0.294712i
$725$	−4.81579	+	11.5449i	−0.178854	+	0.428766i
$726$		0			0
$727$	5.40633	−	9.36404i	0.200510	−	0.347293i	−0.748183	−	0.663492i	$-0.769074\pi$
$727$	5.40633	−	9.36404i	0.200510	−	0.347293i	0.948693	+	0.316199i	$0.102407\pi$
$728$	−11.0544	−	8.00725i	−0.409705	−	0.296769i
$729$		0			0
$730$	7.61839	−	2.57551i	0.281969	−	0.0953240i
$731$	−4.40125	−	7.62319i	−0.162786	−	0.281954i
$732$		0			0
$733$	6.82458	−	11.8205i	0.252072	−	0.436601i	−0.712024	−	0.702155i	$-0.752221\pi$
$733$	6.82458	−	11.8205i	0.252072	−	0.436601i	0.964096	+	0.265554i	$0.0855548\pi$
$734$	−16.5694	−	28.6990i	−0.611586	−	1.05930i
$735$		0			0
$736$	−3.20885	+	5.55790i	−0.118280	+	0.204867i
$737$	−44.7523	−	77.5132i	−1.64847	−	2.85524i
$738$		0			0
$739$	15.6035	−	27.0261i	0.573985	−	0.994171i	−0.422166	−	0.906519i	$-0.638730\pi$
$739$	15.6035	−	27.0261i	0.573985	−	0.994171i	0.996151	−	0.0876529i	$-0.0279366\pi$
$740$	2.98481	+	0.597583i	0.109724	+	0.0219676i
$741$		0			0
$742$	−0.343121	+	3.31039i	−0.0125964	+	0.121528i
$743$	3.52550	+	6.10635i	0.129338	+	0.224020i	0.923420	−	0.383790i	$-0.125381\pi$
$743$	3.52550	+	6.10635i	0.129338	+	0.224020i	−0.794082	+	0.607810i	$0.792048\pi$
$744$		0			0
$745$	−2.18479	−	6.46263i	−0.0800445	−	0.236773i
$746$	18.2835	+	10.5560i	0.669405	+	0.386481i
$747$		0			0
$748$	11.0966			0.405731
$749$	−7.15658	−	5.18385i	−0.261496	−	0.189414i
$750$		0			0
$751$	16.2419	−	28.1318i	0.592675	−	1.02654i	−0.401196	−	0.915992i	$-0.631405\pi$
$751$	16.2419	−	28.1318i	0.592675	−	1.02654i	0.993871	−	0.110550i	$-0.0352613\pi$
$752$			9.74722i			0.355444i
$753$		0			0
$754$			12.9072i			0.470051i
$755$	7.42019	−	37.0624i	0.270048	−	1.34884i
$756$		0			0
$757$			4.96180i			0.180340i	0.995926	+	0.0901699i	$0.0287410\pi$
$757$			4.96180i			0.180340i	−0.995926	+	0.0901699i	$0.971259\pi$
$758$	12.8226			0.465736
$759$		0			0
$760$	−3.82713	−	0.766222i	−0.138824	−	0.0277938i
$761$	14.0123	−	24.2700i	0.507944	−	0.879785i	−0.492014	−	0.870588i	$-0.663739\pi$
$761$	14.0123	−	24.2700i	0.507944	−	0.879785i	0.999958	−	0.00919753i	$-0.00292771\pi$
$762$		0			0
$763$	−2.41197	+	23.2704i	−0.0873193	+	0.842444i
$764$		−	11.8760i		−	0.429660i
$765$		0			0
$766$	−14.1368	−	8.16190i	−0.510784	−	0.294902i
$767$	−3.35429	−	5.80981i	−0.121117	−	0.209780i
$768$		0			0
$769$	22.5043	−	12.9928i	0.811524	−	0.468534i	−0.0359606	−	0.999353i	$-0.511449\pi$
$769$	22.5043	−	12.9928i	0.811524	−	0.468534i	0.847485	+	0.530819i	$0.178116\pi$
$770$	34.2222	−	7.75063i	1.23328	−	0.279313i
$771$		0			0
$772$			15.3218i			0.551442i
$773$	44.5726	+	25.7340i	1.60317	+	0.925589i	0.990849	+	0.134977i	$0.0430960\pi$
$773$	44.5726	+	25.7340i	1.60317	+	0.925589i	0.612318	+	0.790612i	$0.290237\pi$
$774$		0			0
$775$	21.6574	−	2.79635i	0.777955	−	0.100448i
$776$	−1.23514	+	2.13933i	−0.0443391	+	0.0767975i
$777$		0			0
$778$	−9.64090	+	5.56618i	−0.345643	+	0.199557i
$779$	−11.4704	−	6.62242i	−0.410969	−	0.237273i
$780$		0			0
$781$	−8.56173	−	14.8294i	−0.306363	−	0.530636i
$782$	10.3983	−	6.00347i	0.371843	−	0.214684i
$783$		0			0
$784$	4.66893	−	5.21547i	0.166747	−	0.186267i
$785$	8.32670	+	7.32069i	0.297193	+	0.261287i
$786$		0			0
$787$	14.4239			0.514156			0.257078	−	0.966391i	$-0.417240\pi$
$787$	14.4239			0.514156			0.257078	+	0.966391i	$0.417240\pi$
$788$	−9.02678			−0.321566
$789$		0			0
$790$	14.1410	+	12.4325i	0.503115	+	0.442330i
$791$	−38.0476	−	27.5597i	−1.35282	−	0.979909i
$792$		0			0
$793$	−51.2044	+	29.5629i	−1.81832	+	1.04981i
$794$	10.7572	+	18.6321i	0.381760	+	0.661228i
$795$		0			0
$796$	10.4835	+	6.05268i	0.371580	+	0.214532i
$797$	18.3241	−	10.5794i	0.649072	−	0.374742i	−0.139029	−	0.990288i	$-0.544398\pi$
$797$	18.3241	−	10.5794i	0.649072	−	0.374742i	0.788101	+	0.615546i	$0.211065\pi$
$798$		0			0
$799$	9.11807	−	15.7930i	0.322574	−	0.558715i
$800$	−0.640274	−	4.95884i	−0.0226371	−	0.175321i
$801$		0			0
$802$	11.7705	+	6.79568i	0.415629	+	0.239964i
$803$			21.3311i			0.752758i
$804$		0			0
$805$	27.8756	−	25.7779i	0.982484	−	0.908550i
$806$	19.5134	−	11.2661i	0.687331	−	0.396831i
$807$		0			0
$808$	−6.90957	−	11.9677i	−0.243078	−	0.421023i
$809$	−14.1543	−	8.17201i	−0.497640	−	0.287312i	0.230099	−	0.973167i	$-0.426095\pi$
$809$	−14.1543	−	8.17201i	−0.497640	−	0.287312i	−0.727738	+	0.685855i	$0.759428\pi$
$810$		0			0
$811$			2.77152i			0.0973212i	0.998815	+	0.0486606i	$0.0154953\pi$
$811$			2.77152i			0.0973212i	−0.998815	+	0.0486606i	$0.984505\pi$
$812$	−6.58389	−	0.682419i	−0.231049	−	0.0239482i
$813$		0			0
$814$	−4.03712	+	6.99249i	−0.141501	+	0.245087i
$815$	12.9558	+	2.59385i	0.453821	+	0.0908586i
$816$		0			0
$817$	−8.21251			−0.287319
$818$		−	6.31246i		−	0.220710i
$819$		0			0
$820$	3.33087	−	16.6370i	0.116319	−	0.580990i
$821$			41.5518i			1.45017i	0.688660	+	0.725085i	$0.258199\pi$
$821$			41.5518i			1.45017i	−0.688660	+	0.725085i	$0.741801\pi$
$822$		0			0
$823$			40.0405i			1.39572i	0.716232	+	0.697862i	$0.245865\pi$
$823$			40.0405i			1.39572i	−0.716232	+	0.697862i	$0.754135\pi$
$824$	0.712859	−	1.23471i	0.0248336	−	0.0430131i
$825$		0			0
$826$	3.14090	−	1.40384i	0.109286	−	0.0488458i
$827$	44.7684			1.55675			0.778376	−	0.627799i	$-0.216044\pi$
$827$	44.7684			1.55675			0.778376	+	0.627799i	$0.216044\pi$
$828$		0			0
$829$	12.4094	+	7.16460i	0.430998	+	0.248837i	0.699772	−	0.714367i	$-0.253285\pi$
$829$	12.4094	+	7.16460i	0.430998	+	0.248837i	−0.268774	+	0.963203i	$0.586618\pi$
$830$	−2.01747	−	5.96770i	−0.0700274	−	0.207142i
$831$		0			0
$832$	−2.57957	−	4.46794i	−0.0894305	−	0.154898i
$833$	−12.4437	+	4.08282i	−0.431148	+	0.141461i
$834$		0			0
$835$	−22.9712	−	4.59903i	−0.794952	−	0.159156i
$836$	5.17640	−	8.96579i	0.179030	−	0.310088i
$837$		0			0
$838$	10.2076	+	17.6802i	0.352617	+	0.610751i
$839$	−6.70519	+	11.6137i	−0.231489	+	0.400951i	−0.958246	−	0.285943i	$-0.907693\pi$
$839$	−6.70519	+	11.6137i	−0.231489	+	0.400951i	0.726758	+	0.686894i	$0.241026\pi$
$840$		0			0
$841$	−11.3705	−	19.6942i	−0.392086	−	0.679112i
$842$	15.4045	−	26.6814i	0.530874	−	0.919501i
$843$		0			0
$844$	4.28556	+	7.42280i	0.147515	+	0.255503i
$845$	28.8442	−	9.75121i	0.992270	−	0.335452i
$846$		0			0
$847$	−6.59508	+	63.6284i	−0.226609	+	2.18630i
$848$	−0.628956	+	1.08938i	−0.0215984	+	0.0374096i
$849$		0			0
$850$	−3.60135	+	8.63352i	−0.123525	+	0.296127i
$851$			8.73666i			0.299489i
$852$		0			0
$853$	−6.92038	+	11.9865i	−0.236949	+	0.410408i	−0.959837	−	0.280557i	$-0.909481\pi$
$853$	−6.92038	+	11.9865i	−0.236949	+	0.410408i	0.722888	+	0.690965i	$0.242814\pi$
$854$	−12.3726	−	27.6822i	−0.423383	−	0.947264i
$855$		0			0
$856$	−1.67000	−	2.89252i	−0.0570793	−	0.0988643i
$857$	9.97559	−	5.75941i	0.340760	−	0.196738i	−0.319848	−	0.947469i	$-0.603632\pi$
$857$	9.97559	−	5.75941i	0.340760	−	0.196738i	0.660608	+	0.750731i	$0.270299\pi$
$858$		0			0
$859$	0.710391	+	0.410145i	0.0242382	+	0.0139940i	0.512070	−	0.858944i	$-0.328879\pi$
$859$	0.710391	+	0.410145i	0.0242382	+	0.0139940i	−0.487832	+	0.872938i	$0.662212\pi$
$860$	−3.36931	−	9.96644i	−0.114892	−	0.339853i
$861$		0			0
$862$	29.8217	+	17.2176i	1.01573	+	0.586433i
$863$	0.390428	+	0.676242i	0.0132903	+	0.0230195i	0.872594	−	0.488446i	$-0.162436\pi$
$863$	0.390428	+	0.676242i	0.0132903	+	0.0230195i	−0.859304	+	0.511466i	$0.829103\pi$
$864$		0			0
$865$	−12.6978	+	14.4427i	−0.431737	+	0.491066i
$866$	5.86503			0.199302
$867$		0			0
$868$	4.71508	+	10.5494i	0.160040	+	0.358069i
$869$	−43.2526	+	24.9719i	−1.46724	+	0.847114i
$870$		0			0
$871$	67.4244	−	38.9275i	2.28459	−	1.31901i
$872$	−4.42125	+	7.65783i	−0.149722	+	0.259327i
$873$		0			0
$874$		−	11.2022i		−	0.378919i
$875$	−5.07646	+	29.1415i	−0.171616	+	0.985164i
$876$		0			0
$877$	24.1988	+	13.9712i	0.817137	+	0.471774i	0.849428	−	0.527704i	$-0.176947\pi$
$877$	24.1988	+	13.9712i	0.817137	+	0.471774i	−0.0322912	+	0.999479i	$0.510280\pi$
$878$			0.0933769i			0.00315132i
$879$		0			0
$880$	13.0043	+	2.60357i	0.438375	+	0.0877663i
$881$	−32.6360			−1.09953			−0.549767	−	0.835318i	$-0.685284\pi$
$881$	−32.6360			−1.09953			−0.549767	+	0.835318i	$0.685284\pi$
$882$		0			0
$883$		−	45.5409i		−	1.53257i	−0.642499	−	0.766287i	$-0.722102\pi$
$883$		−	45.5409i		−	1.53257i	0.642499	−	0.766287i	$-0.277898\pi$
$884$			9.65227i			0.324641i
$885$		0			0
$886$	1.69982			0.0571066
$887$	−15.8391	−	9.14469i	−0.531824	−	0.307049i	0.209935	−	0.977715i	$-0.432675\pi$
$887$	−15.8391	−	9.14469i	−0.531824	−	0.307049i	−0.741759	+	0.670667i	$0.766008\pi$
$888$		0			0
$889$	9.17274	+	20.5228i	0.307644	+	0.688313i
$890$	7.83203	−	39.1194i	0.262530	−	1.31129i
$891$		0			0
$892$	−10.2042	+	17.6741i	−0.341661	+	0.591774i
$893$	−8.50692	−	14.7344i	−0.284673	−	0.493069i
$894$		0			0
$895$	−1.91333	−	5.65965i	−0.0639556	−	0.189181i
$896$	2.41546	−	1.07960i	0.0806950	−	0.0360669i
$897$		0			0
$898$		−	1.98554i		−	0.0662584i
$899$	5.46323	−	9.46260i	0.182209	−	0.315595i
$900$		0			0
$901$	2.03814	−	1.17672i	0.0679002	−	0.0392022i
$902$	38.9755	+	22.5025i	1.29774	+	0.749252i
$903$		0			0
$904$	−8.87845	−	15.3779i	−0.295293	−	0.511462i
$905$	11.7080	−	13.3169i	0.389187	−	0.442668i
$906$		0			0
$907$	25.0843	−	14.4825i	0.832912	−	0.480882i	−0.0219368	−	0.999759i	$-0.506983\pi$
$907$	25.0843	−	14.4825i	0.832912	−	0.480882i	0.854849	+	0.518877i	$0.173650\pi$
$908$	19.9142	−	11.4974i	0.660874	−	0.381556i
$909$		0			0
$910$	6.74183	+	29.7680i	0.223489	+	0.986799i
$911$	47.8771	+	27.6419i	1.58624	+	0.915816i	0.993919	+	0.110114i	$0.0351217\pi$
$911$	47.8771	+	27.6419i	1.58624	+	0.915816i	0.592321	+	0.805702i	$0.298212\pi$
$912$		0			0
$913$	16.7092			0.552995
$914$			24.5551i			0.812211i
$915$		0			0
$916$	−18.0144	−	10.4006i	−0.595213	−	0.343646i
$917$	−1.08409	+	10.4591i	−0.0357998	+	0.345391i
$918$		0			0
$919$	−5.45039	−	9.44036i	−0.179792	−	0.311409i	0.762017	−	0.647557i	$-0.224209\pi$
$919$	−5.45039	−	9.44036i	−0.179792	−	0.311409i	−0.941809	+	0.336148i	$0.890876\pi$
$920$	13.5946	−	4.59586i	0.448200	−	0.151521i
$921$		0			0
$922$	16.3946	−	28.3963i	0.539929	−	0.935184i
$923$	12.8992	−	7.44736i	0.424583	−	0.245133i
$924$		0			0
$925$	−4.13017	−	5.41041i	−0.135799	−	0.177893i
$926$	−19.1444	+	11.0530i	−0.629125	+	0.363225i
$927$		0			0
$928$	−2.16663	−	1.25090i	−0.0711231	−	0.0410629i
$929$	−28.3585			−0.930411			−0.465205	−	0.885203i	$-0.654020\pi$
$929$	−28.3585			−0.930411			−0.465205	+	0.885203i	$0.654020\pi$
$930$		0			0
$931$	−2.50598	+	11.9588i	−0.0821303	+	0.391934i
$932$	13.6638	+	23.6663i	0.447572	+	0.775217i
$933$		0			0
$934$	30.9099	−	17.8459i	1.01140	−	0.583934i
$935$	−18.6348	−	16.3834i	−0.609422	−	0.535793i
$936$		0			0
$937$	−7.70498			−0.251711			−0.125855	−	0.992049i	$-0.540168\pi$
$937$	−7.70498			−0.251711			−0.125855	+	0.992049i	$0.540168\pi$
$938$	16.2919	+	36.4510i	0.531950	+	1.19017i
$939$		0			0
$940$	14.3911	−	16.3688i	0.469387	−	0.533890i
$941$	44.4748			1.44984			0.724919	−	0.688834i	$-0.241877\pi$
$941$	44.4748			1.44984			0.724919	+	0.688834i	$0.241877\pi$
$942$		0			0
$943$	48.6973			1.58580
$944$	1.30033			0.0423222
$945$		0			0
$946$	27.9055			0.907287
$947$	48.7565			1.58437			0.792187	−	0.610279i	$-0.208942\pi$
$947$	48.7565			1.58437			0.792187	+	0.610279i	$0.208942\pi$
$948$		0			0
$949$	−18.5547			−0.602311
$950$	5.29572	+	6.93724i	0.171816	+	0.225074i
$951$		0			0
$952$	−4.92358	−	0.510329i	−0.159574	−	0.0165398i
$953$	−52.5200			−1.70129			−0.850644	−	0.525742i	$-0.823788\pi$
$953$	−52.5200			−1.70129			−0.850644	+	0.525742i	$0.823788\pi$
$954$		0			0
$955$	−17.5342	+	19.9438i	−0.567394	+	0.645365i
$956$	15.6608	−	9.04177i	0.506507	−	0.292432i
$957$		0			0
$958$	−1.92319	−	3.33106i	−0.0621354	−	0.107622i
$959$	20.7981	+	15.0651i	0.671606	+	0.486476i
$960$		0			0
$961$	11.9256			0.384696
$962$	−6.08237	−	3.51166i	−0.196104	−	0.113220i
$963$		0			0
$964$	2.31790	−	1.33824i	0.0746546	−	0.0431018i
$965$	22.6216	−	25.7302i	0.728215	−	0.828286i
$966$		0			0
$967$	−22.4676	+	12.9717i	−0.722510	+	0.417141i	−0.815676	−	0.578509i	$-0.803635\pi$
$967$	−22.4676	+	12.9717i	−0.722510	+	0.417141i	0.0931658	+	0.995651i	$0.470301\pi$
$968$	−12.0891	+	20.9388i	−0.388557	+	0.673000i
$969$		0			0
$970$	5.23279	−	1.76903i	0.168015	−	0.0568000i
$971$	−22.7435	−	39.3929i	−0.729875	−	1.26418i	−0.956936	−	0.290299i	$-0.906245\pi$
$971$	−22.7435	−	39.3929i	−0.729875	−	1.26418i	0.227061	−	0.973880i	$-0.427088\pi$
$972$		0			0
$973$	31.2571	−	43.1521i	1.00206	−	1.38339i
$974$	17.1992	+	9.92995i	0.551097	+	0.318176i
$975$		0			0
$976$		−	11.4604i		−	0.366838i
$977$	−46.0077			−1.47192			−0.735958	−	0.677027i	$-0.763268\pi$
$977$	−46.0077			−1.47192			−0.735958	+	0.677027i	$0.763268\pi$
$978$		0			0
$979$	91.6449	+	52.9112i	2.92898	+	1.69105i
$980$	−15.5410	+	1.86510i	−0.496438	+	0.0595785i
$981$		0			0
$982$	7.14924	−	4.12761i	0.228141	−	0.131717i
$983$	26.7395	−	15.4381i	0.852858	−	0.492398i	−0.00875587	−	0.999962i	$-0.502787\pi$
$983$	26.7395	−	15.4381i	0.852858	−	0.492398i	0.861614	+	0.507564i	$0.169454\pi$
$984$		0			0
$985$	15.1589	+	13.3275i	0.483003	+	0.424648i
$986$	2.34032	+	4.05356i	0.0745311	+	0.129092i
$987$		0			0
$988$	7.79883	+	4.50266i	0.248114	+	0.143249i
$989$	26.1496	−	15.0975i	0.831508	−	0.480071i
$990$		0			0
$991$	−12.4227	+	21.5168i	−0.394621	+	0.683504i	−0.993053	−	0.117670i	$-0.962457\pi$
$991$	−12.4227	+	21.5168i	−0.394621	+	0.683504i	0.598432	+	0.801174i	$0.295791\pi$
$992$			4.36743i			0.138666i
$993$		0			0
$994$	3.11687	+	6.97358i	0.0988610	+	0.221189i
$995$	−8.66891	−	25.6427i	−0.274823	−	0.812929i
$996$		0			0
$997$	14.0068	+	24.2604i	0.443599	+	0.768336i	0.997953	−	0.0639447i	$-0.0203681\pi$
$997$	14.0068	+	24.2604i	0.443599	+	0.768336i	−0.554354	+	0.832281i	$0.687035\pi$
$998$	15.9868	−	27.6900i	0.506054	−	0.876511i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1890.2.bi.a.899.5		48
3.2	odd	2		630.2.bi.b.479.18	yes	48
5.4	even	2		1890.2.bi.b.899.22		48
7.5	odd	6		1890.2.r.b.89.14		48
9.4	even	3		630.2.r.b.59.2	yes	48
9.5	odd	6		1890.2.r.a.1529.14		48
15.14	odd	2		630.2.bi.a.479.7	yes	48
21.5	even	6		630.2.r.a.299.23	yes	48
35.19	odd	6		1890.2.r.a.89.14		48
45.4	even	6		630.2.r.a.59.23	✓	48
45.14	odd	6		1890.2.r.b.1529.14		48
63.5	even	6		1890.2.bi.b.719.22		48
63.40	odd	6		630.2.bi.a.509.7	yes	48
105.89	even	6		630.2.r.b.299.2	yes	48
315.194	even	6	inner	1890.2.bi.a.719.5		48
315.229	odd	6		630.2.bi.b.509.18	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.r.a.59.23	✓	48	45.4	even	6
630.2.r.a.299.23	yes	48	21.5	even	6
630.2.r.b.59.2	yes	48	9.4	even	3
630.2.r.b.299.2	yes	48	105.89	even	6
630.2.bi.a.479.7	yes	48	15.14	odd	2
630.2.bi.a.509.7	yes	48	63.40	odd	6
630.2.bi.b.479.18	yes	48	3.2	odd	2
630.2.bi.b.509.18	yes	48	315.229	odd	6
1890.2.r.a.89.14		48	35.19	odd	6
1890.2.r.a.1529.14		48	9.5	odd	6
1890.2.r.b.89.14		48	7.5	odd	6
1890.2.r.b.1529.14		48	45.14	odd	6
1890.2.bi.a.719.5		48	315.194	even	6	inner
1890.2.bi.a.899.5		48	1.1	even	1	trivial
1890.2.bi.b.719.22		48	63.5	even	6
1890.2.bi.b.899.22		48	5.4	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1890.bi (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{4} +(-1.67933 - 1.47644i) q^{5} +(-2.41546 + 1.07960i) q^{7} -1.00000 q^{8} +(1.67933 + 1.47644i) q^{10} +(-5.13649 + 2.96556i) q^{11} +(-2.57957 - 4.46794i) q^{13} +(2.41546 - 1.07960i) q^{14} +1.00000 q^{16} +(-1.62025 - 0.935454i) q^{17} +(-1.51165 + 0.872754i) q^{19} +(-1.67933 - 1.47644i) q^{20} +(5.13649 - 2.96556i) q^{22} +(3.20885 - 5.55790i) q^{23} +(0.640274 + 4.95884i) q^{25} +(2.57957 + 4.46794i) q^{26} +(-2.41546 + 1.07960i) q^{28} +(2.16663 + 1.25090i) q^{29} -4.36743i q^{31} -1.00000 q^{32} +(1.62025 + 0.935454i) q^{34} +(5.65031 + 1.75328i) q^{35} +(-1.17895 + 0.680668i) q^{37} +(1.51165 - 0.872754i) q^{38} +(1.67933 + 1.47644i) q^{40} +(3.79398 + 6.57136i) q^{41} +(4.07460 + 2.35247i) q^{43} +(-5.13649 + 2.96556i) q^{44} +(-3.20885 + 5.55790i) q^{46} +9.74722i q^{47} +(4.66893 - 5.21547i) q^{49} +(-0.640274 - 4.95884i) q^{50} +(-2.57957 - 4.46794i) q^{52} +(-0.628956 + 1.08938i) q^{53} +(13.0043 + 2.60357i) q^{55} +(2.41546 - 1.07960i) q^{56} +(-2.16663 - 1.25090i) q^{58} +1.30033 q^{59} -11.4604i q^{61} +4.36743i q^{62} +1.00000 q^{64} +(-2.26470 + 11.3117i) q^{65} +15.0907i q^{67} +(-1.62025 - 0.935454i) q^{68} +(-5.65031 - 1.75328i) q^{70} +2.88706i q^{71} +(1.79824 - 3.11464i) q^{73} +(1.17895 - 0.680668i) q^{74} +(-1.51165 + 0.872754i) q^{76} +(9.20540 - 12.7086i) q^{77} +8.42064 q^{79} +(-1.67933 - 1.47644i) q^{80} +(-3.79398 - 6.57136i) q^{82} +(-2.43978 - 1.40861i) q^{83} +(1.33980 + 3.96313i) q^{85} +(-4.07460 - 2.35247i) q^{86} +(5.13649 - 2.96556i) q^{88} +(-8.92096 - 15.4516i) q^{89} +(11.0544 + 8.00725i) q^{91} +(3.20885 - 5.55790i) q^{92} -9.74722i q^{94} +(3.82713 + 0.766222i) q^{95} +(1.23514 - 2.13933i) q^{97} +(-4.66893 + 5.21547i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 48 q^{2} + 48 q^{4} + 3 q^{7} - 48 q^{8} - 6 q^{11} - 3 q^{14} + 48 q^{16} + 6 q^{22} - 3 q^{23} - 18 q^{25} + 3 q^{28} + 3 q^{29} - 48 q^{32} + 12 q^{35} + 3 q^{41} - 6 q^{44} + 3 q^{46} + 3 q^{49}+ \cdots - 3 q^{98}+O(q^{100}) \) 48 * q - 48 * q^2 + 48 * q^4 + 3 * q^7 - 48 * q^8 - 6 * q^11 - 3 * q^14 + 48 * q^16 + 6 * q^22 - 3 * q^23 - 18 * q^25 + 3 * q^28 + 3 * q^29 - 48 * q^32 + 12 * q^35 + 3 * q^41 - 6 * q^44 + 3 * q^46 + 3 * q^49 + 18 * q^50 - 42 * q^55 - 3 * q^56 - 3 * q^58 + 48 * q^64 - 12 * q^65 - 12 * q^70 - 18 * q^73 + 12 * q^77 - 3 * q^82 - 9 * q^83 - 33 * q^85 + 6 * q^88 + 33 * q^89 - 3 * q^92 - 24 * q^97 - 3 * q^98

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