LMFDB - Embedded newform 1674.2.q.a.557.7

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			557.7
Character	$\chi$	$=$	1674.557
Dual form			1674.2.q.a.1115.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(1.01733 + 0.587355i) q^{5} +(-0.902070 - 1.56243i) q^{7} +1.00000i q^{8} -1.17471 q^{10} +(0.983467 + 1.70342i) q^{11} +(1.16275 + 0.671312i) q^{13} +(1.56243 + 0.902070i) q^{14} +(-0.500000 - 0.866025i) q^{16} -7.80596 q^{17} -5.46712 q^{19} +(1.01733 - 0.587355i) q^{20} +(-1.70342 - 0.983467i) q^{22} +(0.563435 - 0.975899i) q^{23} +(-1.81003 - 3.13506i) q^{25} -1.34262 q^{26} -1.80414 q^{28} +(-0.743867 - 1.28842i) q^{29} +(1.81256 + 5.26447i) q^{31} +(0.866025 + 0.500000i) q^{32} +(6.76016 - 3.90298i) q^{34} -2.11934i q^{35} +7.70366i q^{37} +(4.73466 - 2.73356i) q^{38} +(-0.587355 + 1.01733i) q^{40} +(-3.93719 - 2.27314i) q^{41} +(-3.17930 + 1.83557i) q^{43} +1.96693 q^{44} +1.12687i q^{46} +(3.00693 - 1.73605i) q^{47} +(1.87254 - 3.24333i) q^{49} +(3.13506 + 1.81003i) q^{50} +(1.16275 - 0.671312i) q^{52} +2.37364 q^{53} +2.31058i q^{55} +(1.56243 - 0.902070i) q^{56} +(1.28842 + 0.743867i) q^{58} +(-11.9439 - 6.89581i) q^{59} +(-7.41504 + 4.28107i) q^{61} +(-4.20196 - 3.65288i) q^{62} -1.00000 q^{64} +(0.788596 + 1.36589i) q^{65} +(-7.88815 + 13.6627i) q^{67} +(-3.90298 + 6.76016i) q^{68} +(1.05967 + 1.83540i) q^{70} +4.04211i q^{71} +5.76852i q^{73} +(-3.85183 - 6.67157i) q^{74} +(-2.73356 + 4.73466i) q^{76} +(1.77431 - 3.07320i) q^{77} +(4.74613 - 2.74018i) q^{79} -1.17471i q^{80} +4.54627 q^{82} +(2.95973 + 5.12641i) q^{83} +(-7.94123 - 4.58487i) q^{85} +(1.83557 - 3.17930i) q^{86} +(-1.70342 + 0.983467i) q^{88} -4.83620 q^{89} -2.42228i q^{91} +(-0.563435 - 0.975899i) q^{92} +(-1.73605 + 3.00693i) q^{94} +(-5.56185 - 3.21114i) q^{95} +(-7.34334 - 12.7190i) q^{97} +3.74508i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/1674\mathbb{Z}\right)^\times$.

$n$	$1055$	$1243$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$

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
$5$	1.01733	+	0.587355i	0.454963	+	0.262673i	0.709924	−	0.704278i	$-0.248729\pi$
$5$	1.01733	+	0.587355i	0.454963	+	0.262673i	−0.254961	+	0.966951i	$0.582063\pi$
$6$		0			0
$7$	−0.902070	−	1.56243i	−0.340951	−	0.590544i	0.643659	−	0.765312i	$-0.277416\pi$
$7$	−0.902070	−	1.56243i	−0.340951	−	0.590544i	−0.984610	+	0.174769i	$0.944082\pi$
$8$			1.00000i			0.353553i
$9$		0			0
$10$	−1.17471			−0.371476
$11$	0.983467	+	1.70342i	0.296527	+	0.513599i	0.975339	−	0.220713i	$-0.0708383\pi$
$11$	0.983467	+	1.70342i	0.296527	+	0.513599i	−0.678812	+	0.734312i	$0.737505\pi$
$12$		0			0
$13$	1.16275	+	0.671312i	0.322488	+	0.186188i	0.652501	−	0.757788i	$-0.273720\pi$
$13$	1.16275	+	0.671312i	0.322488	+	0.186188i	−0.330013	+	0.943976i	$0.607053\pi$
$14$	1.56243	+	0.902070i	0.417577	+	0.241088i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−7.80596			−1.89322			−0.946612	−	0.322375i	$-0.895519\pi$
$17$	−7.80596			−1.89322			−0.946612	+	0.322375i	$0.895519\pi$
$18$		0			0
$19$	−5.46712			−1.25424			−0.627121	−	0.778922i	$-0.715767\pi$
$19$	−5.46712			−1.25424			−0.627121	+	0.778922i	$0.715767\pi$
$20$	1.01733	−	0.587355i	0.227482	−	0.131337i
$21$		0			0
$22$	−1.70342	−	0.983467i	−0.363169	−	0.209676i
$23$	0.563435	−	0.975899i	0.117484	−	0.203489i	−0.801286	−	0.598282i	$-0.795850\pi$
$23$	0.563435	−	0.975899i	0.117484	−	0.203489i	0.918770	+	0.394793i	$0.129184\pi$
$24$		0			0
$25$	−1.81003	−	3.13506i	−0.362006	−	0.627012i
$26$	−1.34262			−0.263310
$27$		0			0
$28$	−1.80414			−0.340951
$29$	−0.743867	−	1.28842i	−0.138133	−	0.239253i	0.788657	−	0.614833i	$-0.210777\pi$
$29$	−0.743867	−	1.28842i	−0.138133	−	0.239253i	−0.926790	+	0.375580i	$0.877443\pi$
$30$		0			0
$31$	1.81256	+	5.26447i	0.325546	+	0.945526i
$31$	1.81256	+	5.26447i	0.325546	+	0.945526i
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$		0			0
$34$	6.76016	−	3.90298i	1.15936	−	0.669356i
$35$		−	2.11934i		−	0.358234i
$36$		0			0
$37$			7.70366i			1.26647i	0.773958	+	0.633237i	$0.218274\pi$
$37$			7.70366i			1.26647i	−0.773958	+	0.633237i	$0.781726\pi$
$38$	4.73466	−	2.73356i	0.768064	−	0.443442i
$39$		0			0
$40$	−0.587355	+	1.01733i	−0.0928689	+	0.160854i
$41$	−3.93719	−	2.27314i	−0.614886	−	0.355004i	0.159989	−	0.987119i	$-0.448854\pi$
$41$	−3.93719	−	2.27314i	−0.614886	−	0.355004i	−0.774875	+	0.632114i	$0.782187\pi$
$42$		0			0
$43$	−3.17930	+	1.83557i	−0.484838	+	0.279921i	−0.722431	−	0.691443i	$-0.756975\pi$
$43$	−3.17930	+	1.83557i	−0.484838	+	0.279921i	0.237592	+	0.971365i	$0.423642\pi$
$44$	1.96693			0.296527
$45$		0			0
$46$			1.12687i			0.166148i
$47$	3.00693	−	1.73605i	0.438605	−	0.253229i	−0.264401	−	0.964413i	$-0.585174\pi$
$47$	3.00693	−	1.73605i	0.438605	−	0.253229i	0.703006	+	0.711184i	$0.251841\pi$
$48$		0			0
$49$	1.87254	−	3.24333i	0.267505	−	0.463333i
$50$	3.13506	+	1.81003i	0.443365	+	0.255977i
$51$		0			0
$52$	1.16275	−	0.671312i	0.161244	−	0.0930942i
$53$	2.37364			0.326044			0.163022	−	0.986622i	$-0.447876\pi$
$53$	2.37364			0.326044			0.163022	+	0.986622i	$0.447876\pi$
$54$		0			0
$55$			2.31058i			0.311558i
$56$	1.56243	−	0.902070i	0.208789	−	0.120544i
$57$		0			0
$58$	1.28842	+	0.743867i	0.169177	+	0.0976745i
$59$	−11.9439	−	6.89581i	−1.55496	−	0.897758i	−0.997726	−	0.0674045i	$-0.978528\pi$
$59$	−11.9439	−	6.89581i	−1.55496	−	0.897758i	−0.557237	−	0.830354i	$-0.688138\pi$
$60$		0			0
$61$	−7.41504	+	4.28107i	−0.949398	+	0.548135i	−0.892894	−	0.450267i	$-0.851329\pi$
$61$	−7.41504	+	4.28107i	−0.949398	+	0.548135i	−0.0565044	+	0.998402i	$0.517995\pi$
$62$	−4.20196	−	3.65288i	−0.533649	−	0.463916i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	0.788596	+	1.36589i	0.0978133	+	0.169418i
$66$		0			0
$67$	−7.88815	+	13.6627i	−0.963691	+	1.66916i	−0.250598	+	0.968091i	$0.580627\pi$
$67$	−7.88815	+	13.6627i	−0.963691	+	1.66916i	−0.713093	+	0.701070i	$0.752706\pi$
$68$	−3.90298	+	6.76016i	−0.473306	+	0.819790i
$69$		0			0
$70$	1.05967	+	1.83540i	0.126655	+	0.219373i
$71$			4.04211i			0.479710i	0.970809	+	0.239855i	$0.0770999\pi$
$71$			4.04211i			0.479710i	−0.970809	+	0.239855i	$0.922900\pi$
$72$		0			0
$73$			5.76852i			0.675154i	0.941298	+	0.337577i	$0.109607\pi$
$73$			5.76852i			0.675154i	−0.941298	+	0.337577i	$0.890393\pi$
$74$	−3.85183	−	6.67157i	−0.447766	−	0.775554i
$75$		0			0
$76$	−2.73356	+	4.73466i	−0.313561	+	0.543103i
$77$	1.77431	−	3.07320i	0.202202	−	0.350224i
$78$		0			0
$79$	4.74613	−	2.74018i	0.533982	−	0.308294i	−0.208655	−	0.977989i	$-0.566908\pi$
$79$	4.74613	−	2.74018i	0.533982	−	0.308294i	0.742636	+	0.669695i	$0.233575\pi$
$80$		−	1.17471i		−	0.131337i
$81$		0			0
$82$	4.54627			0.502052
$83$	2.95973	+	5.12641i	0.324873	+	0.562697i	0.981487	−	0.191530i	$-0.0613451\pi$
$83$	2.95973	+	5.12641i	0.324873	+	0.562697i	−0.656614	+	0.754227i	$0.728012\pi$
$84$		0			0
$85$	−7.94123	−	4.58487i	−0.861347	−	0.497299i
$86$	1.83557	−	3.17930i	0.197934	−	0.342832i
$87$		0			0
$88$	−1.70342	+	0.983467i	−0.181585	+	0.104838i
$89$	−4.83620			−0.512636			−0.256318	−	0.966593i	$-0.582509\pi$
$89$	−4.83620			−0.512636			−0.256318	+	0.966593i	$0.582509\pi$
$90$		0			0
$91$		−	2.42228i		−	0.253924i
$92$	−0.563435	−	0.975899i	−0.0587422	−	0.101744i
$93$		0			0
$94$	−1.73605	+	3.00693i	−0.179060	+	0.310141i
$95$	−5.56185	−	3.21114i	−0.570634	−	0.329456i
$96$		0			0
$97$	−7.34334	−	12.7190i	−0.745604	−	1.29142i	−0.949912	−	0.312517i	$-0.898828\pi$
$97$	−7.34334	−	12.7190i	−0.745604	−	1.29142i	0.204309	−	0.978907i	$-0.434505\pi$
$98$			3.74508i			0.378310i
$99$		0			0
$100$	−3.62006			−0.362006
$101$	2.31529	−	1.33673i	0.230380	−	0.133010i	−0.380367	−	0.924836i	$-0.624202\pi$
$101$	2.31529	−	1.33673i	0.230380	−	0.133010i	0.610747	+	0.791826i	$0.290869\pi$
$102$		0			0
$103$	3.70947	−	6.42499i	0.365505	−	0.633073i	−0.623352	−	0.781941i	$-0.714230\pi$
$103$	3.70947	−	6.42499i	0.365505	−	0.633073i	0.988857	+	0.148868i	$0.0475630\pi$
$104$	−0.671312	+	1.16275i	−0.0658275	+	0.114017i
$105$		0			0
$106$	−2.05563	+	1.18682i	−0.199660	+	0.115274i
$107$			6.24767i			0.603985i	0.953310	+	0.301992i	$0.0976517\pi$
$107$			6.24767i			0.603985i	−0.953310	+	0.301992i	$0.902348\pi$
$108$		0			0
$109$	−3.56111			−0.341092			−0.170546	−	0.985350i	$-0.554553\pi$
$109$	−3.56111			−0.341092			−0.170546	+	0.985350i	$0.554553\pi$
$110$	−1.15529	−	2.00102i	−0.110152	−	0.190790i
$111$		0			0
$112$	−0.902070	+	1.56243i	−0.0852376	+	0.147636i
$113$	−5.26672	−	3.04074i	−0.495451	−	0.286049i	0.231382	−	0.972863i	$-0.425675\pi$
$113$	−5.26672	−	3.04074i	−0.495451	−	0.286049i	−0.726833	+	0.686814i	$0.759009\pi$
$114$		0			0
$115$	1.14640	−	0.661873i	0.106902	−	0.0617200i
$116$	−1.48773			−0.138133
$117$		0			0
$118$	13.7916			1.26962
$119$	7.04153	+	12.1963i	0.645496	+	1.11803i
$120$		0			0
$121$	3.56558	−	6.17577i	0.324144	−	0.561434i
$122$	4.28107	−	7.41504i	0.387590	−	0.671326i
$123$		0			0
$124$	5.46544	+	1.06251i	0.490811	+	0.0954160i
$125$		−	10.1261i		−	0.905703i
$126$		0			0
$127$			18.7437i			1.66323i	0.555351	+	0.831616i	$0.312584\pi$
$127$			18.7437i			1.66323i	−0.555351	+	0.831616i	$0.687416\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$		0			0
$130$	−1.36589	−	0.788596i	−0.119796	−	0.0691645i
$131$	7.30906	+	4.21989i	0.638596	+	0.368693i	0.784073	−	0.620668i	$-0.213139\pi$
$131$	7.30906	+	4.21989i	0.638596	+	0.368693i	−0.145478	+	0.989362i	$0.546472\pi$
$132$		0			0
$133$	4.93172	+	8.54200i	0.427635	+	0.740685i
$134$		−	15.7763i		−	1.36286i
$135$		0			0
$136$		−	7.80596i		−	0.669356i
$137$	0.153160	+	0.265280i	0.0130853	+	0.0226644i	0.872494	−	0.488625i	$-0.162501\pi$
$137$	0.153160	+	0.265280i	0.0130853	+	0.0226644i	−0.859409	+	0.511289i	$0.829168\pi$
$138$		0			0
$139$	−10.0275	−	5.78940i	−0.850525	−	0.491051i	0.0103032	−	0.999947i	$-0.496720\pi$
$139$	−10.0275	−	5.78940i	−0.850525	−	0.491051i	−0.860828	+	0.508896i	$0.830054\pi$
$140$	−1.83540	−	1.05967i	−0.155120	−	0.0895585i
$141$		0			0
$142$	−2.02105	−	3.50057i	−0.169603	−	0.293761i
$143$			2.64085i			0.220839i
$144$		0			0
$145$		−	1.74766i		−	0.145135i
$146$	−2.88426	−	4.99569i	−0.238703	−	0.413446i
$147$		0			0
$148$	6.67157	+	3.85183i	0.548399	+	0.316618i
$149$	−14.9210	−	8.61466i	−1.22238	−	0.705741i	−0.256954	−	0.966424i	$-0.582719\pi$
$149$	−14.9210	−	8.61466i	−1.22238	−	0.705741i	−0.965425	+	0.260683i	$0.916052\pi$
$150$		0			0
$151$	−15.4514	+	8.92086i	−1.25742	+	0.725969i	−0.972571	−	0.232605i	$-0.925275\pi$
$151$	−15.4514	+	8.92086i	−1.25742	+	0.725969i	−0.284844	+	0.958574i	$0.591942\pi$
$152$		−	5.46712i		−	0.443442i
$153$		0			0
$154$			3.54863i			0.285957i
$155$	−1.24814	+	6.42031i	−0.100253	+	0.515692i
$156$		0			0
$157$	6.38199	−	11.0539i	0.509338	−	0.882200i	−0.490603	−	0.871383i	$-0.663224\pi$
$157$	6.38199	−	11.0539i	0.509338	−	0.882200i	0.999941	−	0.0108168i	$-0.00344316\pi$
$158$	−2.74018	+	4.74613i	−0.217997	+	0.377582i
$159$		0			0
$160$	0.587355	+	1.01733i	0.0464345	+	0.0804269i
$161$	−2.03303			−0.160226
$162$		0			0
$163$	−9.52863			−0.746340			−0.373170	−	0.927763i	$-0.621729\pi$
$163$	−9.52863			−0.746340			−0.373170	+	0.927763i	$0.621729\pi$
$164$	−3.93719	+	2.27314i	−0.307443	+	0.177502i
$165$		0			0
$166$	−5.12641	−	2.95973i	−0.397887	−	0.229720i
$167$	5.21593	−	9.03426i	0.403621	−	0.699092i	−0.590539	−	0.807009i	$-0.701085\pi$
$167$	5.21593	−	9.03426i	0.403621	−	0.699092i	0.994160	+	0.107917i	$0.0344181\pi$
$168$		0			0
$169$	−5.59868	−	9.69720i	−0.430668	−	0.745938i
$170$	9.16974			0.703287
$171$		0			0
$172$			3.67114i			0.279921i
$173$	−6.50221	+	3.75405i	−0.494354	+	0.285415i	−0.726379	−	0.687295i	$-0.758798\pi$
$173$	−6.50221	+	3.75405i	−0.494354	+	0.285415i	0.232025	+	0.972710i	$0.425465\pi$
$174$		0			0
$175$	−3.26555	+	5.65609i	−0.246852	+	0.427560i
$176$	0.983467	−	1.70342i	0.0741316	−	0.128400i
$177$		0			0
$178$	4.18827	−	2.41810i	0.313924	−	0.181244i
$179$	−21.9809			−1.64293			−0.821467	−	0.570257i	$-0.806844\pi$
$179$	−21.9809			−1.64293			−0.821467	+	0.570257i	$0.806844\pi$
$180$		0			0
$181$			12.5475i			0.932646i	0.884614	+	0.466323i	$0.154422\pi$
$181$			12.5475i			0.932646i	−0.884614	+	0.466323i	$0.845578\pi$
$182$	1.21114	+	2.09776i	0.0897757	+	0.155496i
$183$		0			0
$184$	0.975899	+	0.563435i	0.0719442	+	0.0415370i
$185$	−4.52478	+	7.83715i	−0.332669	+	0.576199i
$186$		0			0
$187$	−7.67691	−	13.2968i	−0.561391	−	0.972358i
$188$		−	3.47210i		−	0.253229i
$189$		0			0
$190$	6.42227			0.465921
$191$	16.0388	−	9.26002i	1.16053	−	0.670032i	0.209098	−	0.977895i	$-0.432947\pi$
$191$	16.0388	−	9.26002i	1.16053	−	0.670032i	0.951431	+	0.307863i	$0.0996138\pi$
$192$		0			0
$193$	−5.55289	+	9.61788i	−0.399705	+	0.692310i	−0.993689	−	0.112167i	$-0.964221\pi$
$193$	−5.55289	+	9.61788i	−0.399705	+	0.692310i	0.593984	+	0.804477i	$0.297554\pi$
$194$	12.7190	+	7.34334i	0.913174	+	0.527221i
$195$		0			0
$196$	−1.87254	−	3.24333i	−0.133753	−	0.231667i
$197$	−11.3186			−0.806414			−0.403207	−	0.915109i	$-0.632105\pi$
$197$	−11.3186			−0.806414			−0.403207	+	0.915109i	$0.632105\pi$
$198$		0			0
$199$		−	2.76824i		−	0.196236i	−0.995175	−	0.0981178i	$-0.968718\pi$
$199$		−	2.76824i		−	0.196236i	0.995175	−	0.0981178i	$-0.0312822\pi$
$200$	3.13506	−	1.81003i	0.221682	−	0.127988i
$201$		0			0
$202$	−1.33673	+	2.31529i	−0.0940523	+	0.162903i
$203$	−1.34204	+	2.32448i	−0.0941928	+	0.163147i
$204$		0			0
$205$	−2.67028	−	4.62505i	−0.186500	−	0.323028i
$206$			7.41894i			0.516902i
$207$		0			0
$208$		−	1.34262i		−	0.0930942i
$209$	−5.37673	−	9.31277i	−0.371916	−	0.644178i
$210$		0			0
$211$	1.35629	−	2.34917i	0.0933710	−	0.161723i	−0.815557	−	0.578677i	$-0.803569\pi$
$211$	1.35629	−	2.34917i	0.0933710	−	0.161723i	0.908928	+	0.416954i	$0.136902\pi$
$212$	1.18682	−	2.05563i	0.0815110	−	0.141181i
$213$		0			0
$214$	−3.12383	−	5.41064i	−0.213541	−	0.369864i
$215$	−4.31252			−0.294111
$216$		0			0
$217$	6.59031	−	7.58093i	0.447379	−	0.514627i
$218$	3.08401	−	1.78055i	0.208876	−	0.120594i
$219$		0			0
$220$	2.00102	+	1.15529i	0.134909	+	0.0778895i
$221$	−9.07635	−	5.24024i	−0.610542	−	0.352496i
$222$		0			0
$223$	5.59744	−	3.23168i	0.374832	−	0.216410i	−0.300735	−	0.953708i	$-0.597232\pi$
$223$	5.59744	−	3.23168i	0.374832	−	0.216410i	0.675567	+	0.737298i	$0.263899\pi$
$224$		−	1.80414i		−	0.120544i
$225$		0			0
$226$	6.08149			0.404534
$227$	−15.1524	+	8.74823i	−1.00570	+	0.580640i	−0.909929	−	0.414763i	$-0.863864\pi$
$227$	−15.1524	+	8.74823i	−1.00570	+	0.580640i	−0.0957693	+	0.995404i	$0.530531\pi$
$228$		0			0
$229$	−23.3070	−	13.4563i	−1.54017	−	0.889216i	−0.998827	−	0.0484115i	$-0.984584\pi$
$229$	−23.3070	−	13.4563i	−1.54017	−	0.889216i	−0.541339	−	0.840804i	$-0.682083\pi$
$230$	−0.661873	+	1.14640i	−0.0436426	+	0.0755912i
$231$		0			0
$232$	1.28842	−	0.743867i	0.0845886	−	0.0488373i
$233$			7.95864i			0.521388i	0.965421	+	0.260694i	$0.0839514\pi$
$233$			7.95864i			0.521388i	−0.965421	+	0.260694i	$0.916049\pi$
$234$		0			0
$235$	4.07871			0.266065
$236$	−11.9439	+	6.89581i	−0.777481	+	0.448879i
$237$		0			0
$238$	−12.1963	−	7.04153i	−0.790568	−	0.456434i
$239$	−8.56671	+	14.8380i	−0.554135	+	0.959789i	0.443836	+	0.896108i	$0.353617\pi$
$239$	−8.56671	+	14.8380i	−0.554135	+	0.959789i	−0.997970	+	0.0636810i	$0.979716\pi$
$240$		0			0
$241$	16.8288	−	9.71610i	1.08404	−	0.625869i	0.152055	−	0.988372i	$-0.451411\pi$
$241$	16.8288	−	9.71610i	1.08404	−	0.625869i	0.931983	+	0.362503i	$0.118078\pi$
$242$			7.13117i			0.458409i
$243$		0			0
$244$			8.56215i			0.548135i
$245$	3.80997	−	2.19969i	0.243410	−	0.140533i
$246$		0			0
$247$	−6.35687	−	3.67014i	−0.404478	−	0.233525i
$248$	−5.26447	+	1.81256i	−0.334294	+	0.115098i
$249$		0			0
$250$	5.06303	+	8.76943i	0.320214	+	0.554627i
$251$	20.3397			1.28383			0.641914	−	0.766776i	$-0.278141\pi$
$251$	20.3397			1.28383			0.641914	+	0.766776i	$0.278141\pi$
$252$		0			0
$253$	2.21648			0.139349
$254$	−9.37183	−	16.2325i	−0.588041	−	1.01852i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	16.1234	+	9.30883i	1.00575	+	0.580669i	0.909944	−	0.414732i	$-0.136125\pi$
$257$	16.1234	+	9.30883i	1.00575	+	0.580669i	0.0958037	+	0.995400i	$0.469458\pi$
$258$		0			0
$259$	12.0364	−	6.94924i	0.747908	−	0.431805i
$260$	1.57719			0.0978133
$261$		0			0
$262$	−8.43978			−0.521411
$263$	15.9965	+	27.7068i	0.986388	+	1.70847i	0.635599	+	0.772019i	$0.280753\pi$
$263$	15.9965	+	27.7068i	0.986388	+	1.70847i	0.350789	+	0.936455i	$0.385914\pi$
$264$		0			0
$265$	2.41477	+	1.39417i	0.148338	+	0.0856430i
$266$	−8.54200	−	4.93172i	−0.523743	−	0.302383i
$267$		0			0
$268$	7.88815	+	13.6627i	0.481845	+	0.834580i
$269$	12.1011			0.737817			0.368909	−	0.929466i	$-0.379732\pi$
$269$	12.1011			0.737817			0.368909	+	0.929466i	$0.379732\pi$
$270$		0			0
$271$		−	12.6409i		−	0.767878i	−0.923358	−	0.383939i	$-0.874567\pi$
$271$		−	12.6409i		−	0.767878i	0.923358	−	0.383939i	$-0.125433\pi$
$272$	3.90298	+	6.76016i	0.236653	+	0.409895i
$273$		0			0
$274$	−0.265280	−	0.153160i	−0.0160262	−	0.00925271i
$275$	3.56021	−	6.16646i	0.214689	−	0.371852i
$276$		0			0
$277$	14.1651	−	8.17823i	0.851099	−	0.491382i	−0.00992236	−	0.999951i	$-0.503158\pi$
$277$	14.1651	−	8.17823i	0.851099	−	0.491382i	0.861022	+	0.508568i	$0.169825\pi$
$278$	11.5788			0.694450
$279$		0			0
$280$	2.11934			0.126655
$281$	16.0630	−	9.27399i	0.958240	−	0.553240i	0.0626088	−	0.998038i	$-0.480058\pi$
$281$	16.0630	−	9.27399i	0.958240	−	0.553240i	0.895631	+	0.444798i	$0.146725\pi$
$282$		0			0
$283$	−3.99581	+	6.92095i	−0.237526	+	0.411408i	−0.960004	−	0.279987i	$-0.909670\pi$
$283$	−3.99581	+	6.92095i	−0.237526	+	0.411408i	0.722478	+	0.691394i	$0.243003\pi$
$284$	3.50057	+	2.02105i	0.207720	+	0.119927i
$285$		0			0
$286$	−1.32043	−	2.28705i	−0.0780785	−	0.135236i
$287$			8.20212i			0.484156i
$288$		0			0
$289$	43.9331			2.58430
$290$	0.873828	+	1.51351i	0.0513129	+	0.0888766i
$291$		0			0
$292$	4.99569	+	2.88426i	0.292350	+	0.168789i
$293$	8.93235	+	5.15710i	0.521834	+	0.301281i	0.737684	−	0.675146i	$-0.235919\pi$
$293$	8.93235	+	5.15710i	0.521834	+	0.301281i	−0.215851	+	0.976426i	$0.569253\pi$
$294$		0			0
$295$	−8.10057	−	14.0306i	−0.471634	−	0.816893i
$296$	−7.70366			−0.447766
$297$		0			0
$298$	17.2293			0.998068
$299$	1.31026	−	0.756482i	0.0757746	−	0.0437485i
$300$		0			0
$301$	5.73590	+	3.31162i	0.330612	+	0.190879i
$302$	8.92086	−	15.4514i	0.513338	−	0.889127i
$303$		0			0
$304$	2.73356	+	4.73466i	0.156780	+	0.271552i
$305$	−10.0580			−0.575922
$306$		0			0
$307$	−6.94163			−0.396180			−0.198090	−	0.980184i	$-0.563474\pi$
$307$	−6.94163			−0.396180			−0.198090	+	0.980184i	$0.563474\pi$
$308$	−1.77431	−	3.07320i	−0.101101	−	0.175112i
$309$		0			0
$310$	−2.12924	−	6.18422i	−0.120932	−	0.351240i
$311$	21.2573	+	12.2729i	1.20539	+	0.695933i	0.961749	−	0.273932i	$-0.0883242\pi$
$311$	21.2573	+	12.2729i	1.20539	+	0.695933i	0.243643	+	0.969865i	$0.421658\pi$
$312$		0			0
$313$	12.6751	−	7.31799i	0.716441	−	0.413637i	−0.0970006	−	0.995284i	$-0.530925\pi$
$313$	12.6751	−	7.31799i	0.716441	−	0.413637i	0.813441	+	0.581647i	$0.197592\pi$
$314$			12.7640i			0.720313i
$315$		0			0
$316$		−	5.48036i		−	0.308294i
$317$	−7.15880	+	4.13313i	−0.402078	+	0.232140i	−0.687380	−	0.726298i	$-0.741239\pi$
$317$	−7.15880	+	4.13313i	−0.402078	+	0.232140i	0.285302	+	0.958438i	$0.407906\pi$
$318$		0			0
$319$	1.46314	−	2.53423i	0.0819200	−	0.141890i
$320$	−1.01733	−	0.587355i	−0.0568704	−	0.0328341i
$321$		0			0
$322$	1.76066	−	1.01652i	0.0981177	−	0.0566483i
$323$	42.6761			2.37456
$324$		0			0
$325$		−	4.86038i		−	0.269605i
$326$	8.25203	−	4.76431i	0.457038	−	0.263871i
$327$		0			0
$328$	2.27314	−	3.93719i	0.125513	−	0.217395i
$329$	−5.42492	−	3.13208i	−0.299085	−	0.172677i
$330$		0			0
$331$	1.33427	−	0.770341i	0.0733381	−	0.0423418i	−0.462883	−	0.886420i	$-0.653185\pi$
$331$	1.33427	−	0.770341i	0.0733381	−	0.0423418i	0.536221	+	0.844078i	$0.319852\pi$
$332$	5.91947			0.324873
$333$		0			0
$334$			10.4319i			0.570806i
$335$	−16.0497	+	9.26628i	−0.876887	+	0.506271i
$336$		0			0
$337$	−3.46215	−	1.99887i	−0.188595	−	0.108886i	0.402729	−	0.915319i	$-0.368062\pi$
$337$	−3.46215	−	1.99887i	−0.188595	−	0.108886i	−0.591325	+	0.806433i	$0.701395\pi$
$338$	9.69720	+	5.59868i	0.527458	+	0.304528i
$339$		0			0
$340$	−7.94123	+	4.58487i	−0.430673	+	0.248649i
$341$	−7.18498	+	8.26498i	−0.389088	+	0.447574i
$342$		0			0
$343$	−19.3856			−1.04673
$344$	−1.83557	−	3.17930i	−0.0989672	−	0.171416i
$345$		0			0
$346$	3.75405	−	6.50221i	0.201819	−	0.349561i
$347$	−11.6581	+	20.1924i	−0.625839	+	1.08398i	0.362539	+	0.931969i	$0.381910\pi$
$347$	−11.6581	+	20.1924i	−0.625839	+	1.08398i	−0.988378	+	0.152016i	$0.951423\pi$
$348$		0			0
$349$	−3.69037	−	6.39191i	−0.197541	−	0.342151i	0.750190	−	0.661223i	$-0.229962\pi$
$349$	−3.69037	−	6.39191i	−0.197541	−	0.342151i	−0.947731	+	0.319072i	$0.896629\pi$
$350$		−	6.53109i		−	0.349102i
$351$		0			0
$352$			1.96693i			0.104838i
$353$	−9.02014	−	15.6233i	−0.480094	−	0.831547i	0.519646	−	0.854382i	$-0.326064\pi$
$353$	−9.02014	−	15.6233i	−0.480094	−	0.831547i	−0.999739	+	0.0228353i	$0.992731\pi$
$354$		0			0
$355$	−2.37415	+	4.11215i	−0.126007	+	0.218250i
$356$	−2.41810	+	4.18827i	−0.128159	+	0.221978i
$357$		0			0
$358$	19.0361	−	10.9905i	1.00609	−	0.580865i
$359$			18.0531i			0.952804i	0.879228	+	0.476402i	$0.158059\pi$
$359$			18.0531i			0.952804i	−0.879228	+	0.476402i	$0.841941\pi$
$360$		0			0
$361$	10.8894			0.573125
$362$	−6.27374	−	10.8664i	−0.329740	−	0.571127i
$363$		0			0
$364$	−2.09776	−	1.21114i	−0.109952	−	0.0634810i
$365$	−3.38817	+	5.86848i	−0.177345	+	0.307170i
$366$		0			0
$367$	4.58982	−	2.64994i	0.239587	−	0.138326i	−0.375400	−	0.926863i	$-0.622495\pi$
$367$	4.58982	−	2.64994i	0.239587	−	0.138326i	0.614987	+	0.788537i	$0.289161\pi$
$368$	−1.12687			−0.0587422
$369$		0			0
$370$		−	9.04956i		−	0.470464i
$371$	−2.14119	−	3.70865i	−0.111165	−	0.192543i
$372$		0			0
$373$	−12.2848	+	21.2778i	−0.636081	+	1.10172i	0.350204	+	0.936673i	$0.386112\pi$
$373$	−12.2848	+	21.2778i	−0.636081	+	1.10172i	−0.986285	+	0.165051i	$0.947221\pi$
$374$	13.2968	+	7.67691i	0.687561	+	0.396964i
$375$		0			0
$376$	1.73605	+	3.00693i	0.0895299	+	0.155070i
$377$		−	1.99747i		−	0.102875i
$378$		0			0
$379$	10.4838			0.538515			0.269257	−	0.963068i	$-0.413222\pi$
$379$	10.4838			0.538515			0.269257	+	0.963068i	$0.413222\pi$
$380$	−5.56185	+	3.21114i	−0.285317	+	0.164728i
$381$		0			0
$382$	−9.26002	+	16.0388i	−0.473784	+	0.820618i
$383$	15.5799	−	26.9851i	0.796094	−	1.37887i	−0.126049	−	0.992024i	$-0.540230\pi$
$383$	15.5799	−	26.9851i	0.796094	−	1.37887i	0.922142	−	0.386851i	$-0.126437\pi$
$384$		0			0
$385$	3.61012	−	2.08430i	0.183989	−	0.106226i
$386$		−	11.1058i		−	0.565269i
$387$		0			0
$388$	−14.6867			−0.745604
$389$	−11.8464	−	20.5186i	−0.600637	−	1.04033i	−0.992725	−	0.120406i	$-0.961580\pi$
$389$	−11.8464	−	20.5186i	−0.600637	−	1.04033i	0.392087	−	0.919928i	$-0.371753\pi$
$390$		0			0
$391$	−4.39816	+	7.61783i	−0.222424	+	0.385250i
$392$	3.24333	+	1.87254i	0.163813	+	0.0945775i
$393$		0			0
$394$	9.80217	−	5.65928i	0.493826	−	0.285111i
$395$	6.43783			0.323923
$396$		0			0
$397$	17.6682			0.886740			0.443370	−	0.896339i	$-0.353783\pi$
$397$	17.6682			0.886740			0.443370	+	0.896339i	$0.353783\pi$
$398$	1.38412	+	2.39737i	0.0693798	+	0.120169i
$399$		0			0
$400$	−1.81003	+	3.13506i	−0.0905014	+	0.156753i
$401$	12.2178	−	21.1619i	0.610130	−	1.05678i	−0.381089	−	0.924539i	$-0.624451\pi$
$401$	12.2178	−	21.1619i	0.610130	−	1.05678i	0.991218	−	0.132237i	$-0.0422160\pi$
$402$		0			0
$403$	−1.42655	+	7.33803i	−0.0710614	+	0.365534i
$404$		−	2.67347i		−	0.133010i
$405$		0			0
$406$		−	2.68408i		−	0.133209i
$407$	−13.1225	+	7.57630i	−0.650460	+	0.375543i
$408$		0			0
$409$	13.7946	+	7.96432i	0.682100	+	0.393810i	0.800646	−	0.599138i	$-0.204490\pi$
$409$	13.7946	+	7.96432i	0.682100	+	0.393810i	−0.118546	+	0.992949i	$0.537823\pi$
$410$	4.62505	+	2.67028i	0.228415	+	0.131876i
$411$		0			0
$412$	−3.70947	−	6.42499i	−0.182752	−	0.316536i
$413$			24.8820i			1.22436i
$414$		0			0
$415$			6.95366i			0.341342i
$416$	0.671312	+	1.16275i	0.0329138	+	0.0570083i
$417$		0			0
$418$	9.31277	+	5.37673i	0.455503	+	0.262985i
$419$	25.3252	+	14.6215i	1.23722	+	0.714309i	0.968525	−	0.248917i	$-0.0800746\pi$
$419$	25.3252	+	14.6215i	1.23722	+	0.714309i	0.268694	+	0.963226i	$0.413408\pi$
$420$		0			0
$421$	14.7078	+	25.4747i	0.716816	+	1.24156i	0.962255	+	0.272149i	$0.0877345\pi$
$421$	14.7078	+	25.4747i	0.716816	+	1.24156i	−0.245439	+	0.969412i	$0.578932\pi$
$422$			2.71258i			0.132046i
$423$		0			0
$424$			2.37364i			0.115274i
$425$	14.1290	+	24.4722i	0.685358	+	1.18708i
$426$		0			0
$427$	13.3778	+	7.72366i	0.647396	+	0.373774i
$428$	5.41064	+	3.12383i	0.261533	+	0.150996i
$429$		0			0
$430$	3.73475	−	2.15626i	0.180106	−	0.103984i
$431$			8.87309i			0.427402i	0.976899	+	0.213701i	$0.0685518\pi$
$431$			8.87309i			0.427402i	−0.976899	+	0.213701i	$0.931448\pi$
$432$		0			0
$433$		−	14.2778i		−	0.686146i	−0.939309	−	0.343073i	$-0.888532\pi$
$433$		−	14.2778i		−	0.686146i	0.939309	−	0.343073i	$-0.111468\pi$
$434$	−1.91691	+	9.86043i	−0.0920148	+	0.473316i
$435$		0			0
$436$	−1.78055	+	3.08401i	−0.0852731	+	0.147697i
$437$	−3.08037	+	5.33535i	−0.147354	+	0.255225i
$438$		0			0
$439$	−1.94281	−	3.36504i	−0.0927250	−	0.160604i	0.815932	−	0.578148i	$-0.196224\pi$
$439$	−1.94281	−	3.36504i	−0.0927250	−	0.160604i	−0.908657	+	0.417544i	$0.862891\pi$
$440$	−2.31058			−0.110152
$441$		0			0
$442$	10.4805			0.498505
$443$	−13.3810	+	7.72551i	−0.635749	+	0.367050i	−0.782975	−	0.622053i	$-0.786299\pi$
$443$	−13.3810	+	7.72551i	−0.635749	+	0.367050i	0.147226	+	0.989103i	$0.452965\pi$
$444$		0			0
$445$	−4.92000	−	2.84056i	−0.233230	−	0.134656i
$446$	−3.23168	+	5.59744i	−0.153025	+	0.265046i
$447$		0			0
$448$	0.902070	+	1.56243i	0.0426188	+	0.0738180i
$449$	−18.1349			−0.855837			−0.427919	−	0.903817i	$-0.640753\pi$
$449$	−18.1349			−0.855837			−0.427919	+	0.903817i	$0.640753\pi$
$450$		0			0
$451$		−	8.94223i		−	0.421073i
$452$	−5.26672	+	3.04074i	−0.247726	+	0.143025i
$453$		0			0
$454$	8.74823	−	15.1524i	0.410575	−	0.711136i
$455$	1.42274	−	2.46426i	0.0666990	−	0.115526i
$456$		0			0
$457$	5.36316	−	3.09642i	0.250878	−	0.144844i	−0.369288	−	0.929315i	$-0.620398\pi$
$457$	5.36316	−	3.09642i	0.250878	−	0.144844i	0.620166	+	0.784470i	$0.287065\pi$
$458$	26.9126			1.25754
$459$		0			0
$460$		−	1.32375i		−	0.0617200i
$461$	11.2038	+	19.4055i	0.521812	+	0.903805i	0.999678	+	0.0253724i	$0.00807714\pi$
$461$	11.2038	+	19.4055i	0.521812	+	0.903805i	−0.477866	+	0.878433i	$0.658590\pi$
$462$		0			0
$463$	−25.1537	−	14.5225i	−1.16899	−	0.674919i	−0.215551	−	0.976493i	$-0.569155\pi$
$463$	−25.1537	−	14.5225i	−1.16899	−	0.674919i	−0.953443	+	0.301574i	$0.902488\pi$
$464$	−0.743867	+	1.28842i	−0.0345332	+	0.0598132i
$465$		0			0
$466$	−3.97932	−	6.89239i	−0.184339	−	0.319284i
$467$			7.70867i			0.356715i	0.983966	+	0.178357i	$0.0570783\pi$
$467$			7.70867i			0.356715i	−0.983966	+	0.178357i	$0.942922\pi$
$468$		0			0
$469$	28.4627			1.31428
$470$	−3.53226	+	2.03935i	−0.162931	+	0.0940684i
$471$		0			0
$472$	6.89581	−	11.9439i	0.317405	−	0.549762i
$473$	−6.25347	−	3.61044i	−0.287535	−	0.166008i
$474$		0			0
$475$	9.89564	+	17.1398i	0.454043	+	0.786426i
$476$	14.0831			0.645496
$477$		0			0
$478$		−	17.1334i		−	0.783665i
$479$	29.7081	−	17.1520i	1.35740	−	0.783693i	0.368124	−	0.929777i	$-0.380000\pi$
$479$	29.7081	−	17.1520i	1.35740	−	0.783693i	0.989272	+	0.146083i	$0.0466668\pi$
$480$		0			0
$481$	−5.17156	+	8.95740i	−0.235803	+	0.408422i
$482$	−9.71610	+	16.8288i	−0.442556	+	0.766530i
$483$		0			0
$484$	−3.56558	−	6.17577i	−0.162072	−	0.280717i
$485$		−	17.2526i		−	0.783400i
$486$		0			0
$487$			35.5009i			1.60870i	0.594155	+	0.804351i	$0.297487\pi$
$487$			35.5009i			1.60870i	−0.594155	+	0.804351i	$0.702513\pi$
$488$	−4.28107	−	7.41504i	−0.193795	−	0.335663i
$489$		0			0
$490$	−2.19969	+	3.80997i	−0.0993718	+	0.172117i
$491$	13.2552	−	22.9586i	0.598197	−	1.03611i	−0.394890	−	0.918728i	$-0.629217\pi$
$491$	13.2552	−	22.9586i	0.598197	−	1.03611i	0.993087	−	0.117379i	$-0.0374492\pi$
$492$		0			0
$493$	5.80660	+	10.0573i	0.261516	+	0.452959i
$494$	7.34028			0.330255
$495$		0			0
$496$	3.65288	−	4.20196i	0.164019	−	0.188674i
$497$	6.31552	−	3.64626i	0.283290	−	0.163557i
$498$		0			0
$499$	10.9204	+	6.30488i	0.488863	+	0.282245i	0.724103	−	0.689692i	$-0.242254\pi$
$499$	10.9204	+	6.30488i	0.488863	+	0.282245i	−0.235240	+	0.971937i	$0.575588\pi$
$500$	−8.76943	−	5.06303i	−0.392181	−	0.226426i
$501$		0			0
$502$	−17.6147	+	10.1698i	−0.786181	+	0.453902i
$503$			0.806606i			0.0359648i	0.999838	+	0.0179824i	$0.00572428\pi$
$503$			0.806606i			0.0359648i	−0.999838	+	0.0179824i	$0.994276\pi$
$504$		0			0
$505$	3.14055			0.139753
$506$	−1.91953	+	1.10824i	−0.0853335	+	0.0492673i
$507$		0			0
$508$	16.2325	+	9.37183i	0.720200	+	0.415808i
$509$	10.3509	−	17.9284i	0.458797	−	0.794661i	−0.540100	−	0.841601i	$-0.681614\pi$
$509$	10.3509	−	17.9284i	0.458797	−	0.794661i	0.998898	+	0.0469402i	$0.0149470\pi$
$510$		0			0
$511$	9.01292	−	5.20361i	0.398708	−	0.230194i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	−18.6177			−0.821189
$515$	7.54749	−	4.35755i	0.332582	−	0.192016i
$516$		0			0
$517$	5.91443	+	3.41470i	0.260116	+	0.150178i
$518$	−6.94924	+	12.0364i	−0.305332	+	0.528851i
$519$		0			0
$520$	−1.36589	+	0.788596i	−0.0598982	+	0.0345822i
$521$		−	2.62461i		−	0.114986i	−0.998346	−	0.0574932i	$-0.981689\pi$
$521$		−	2.62461i		−	0.114986i	0.998346	−	0.0574932i	$-0.0183108\pi$
$522$		0			0
$523$			23.7535i			1.03867i	0.854571	+	0.519334i	$0.173820\pi$
$523$			23.7535i			1.03867i	−0.854571	+	0.519334i	$0.826180\pi$
$524$	7.30906	−	4.21989i	0.319298	−	0.184347i
$525$		0			0
$526$	−27.7068	−	15.9965i	−1.20807	−	0.697482i
$527$	−14.1488	−	41.0942i	−0.616331	−	1.79009i
$528$		0			0
$529$	10.8651	+	18.8189i	0.472395	+	0.818212i
$530$	−2.78833			−0.121117
$531$		0			0
$532$	9.86345			0.427635
$533$	−3.05197	−	5.28616i	−0.132195	−	0.228969i
$534$		0			0
$535$	−3.66960	+	6.35593i	−0.158650	+	0.274791i
$536$	−13.6627	−	7.88815i	−0.590137	−	0.340716i
$537$		0			0
$538$	−10.4799	+	6.05055i	−0.451819	+	0.260858i
$539$	7.36632			0.317290
$540$		0			0
$541$	−38.4480			−1.65301			−0.826504	−	0.562930i	$-0.809674\pi$
$541$	−38.4480			−1.65301			−0.826504	+	0.562930i	$0.809674\pi$
$542$	6.32044	+	10.9473i	0.271486	+	0.470228i
$543$		0			0
$544$	−6.76016	−	3.90298i	−0.289840	−	0.167339i
$545$	−3.62282	−	2.09163i	−0.155184	−	0.0895958i
$546$		0			0
$547$	4.64707	+	8.04896i	0.198694	+	0.344149i	0.948105	−	0.317956i	$-0.102997\pi$
$547$	4.64707	+	8.04896i	0.198694	+	0.344149i	−0.749411	+	0.662105i	$0.769663\pi$
$548$	0.306319			0.0130853
$549$		0			0
$550$			7.12042i			0.303616i
$551$	4.06681	+	7.04392i	0.173252	+	0.300081i
$552$		0			0
$553$	−8.56269	−	4.94367i	−0.364123	−	0.210226i
$554$	−8.17823	+	14.1651i	−0.347460	+	0.601818i
$555$		0			0
$556$	−10.0275	+	5.78940i	−0.425262	+	0.245525i
$557$	28.3323			1.20048			0.600239	−	0.799821i	$-0.295072\pi$
$557$	28.3323			1.20048			0.600239	+	0.799821i	$0.295072\pi$
$558$		0			0
$559$	−4.92895			−0.208473
$560$	−1.83540	+	1.05967i	−0.0775599	+	0.0447793i
$561$		0			0
$562$	−9.27399	+	16.0630i	−0.391200	+	0.677578i
$563$	−9.46217	−	5.46299i	−0.398783	−	0.230238i	0.287176	−	0.957878i	$-0.407284\pi$
$563$	−9.46217	−	5.46299i	−0.398783	−	0.230238i	−0.685959	+	0.727640i	$0.740617\pi$
$564$		0			0
$565$	−3.57199	−	6.18687i	−0.150275	−	0.260283i
$566$		−	7.99162i		−	0.335913i
$567$		0			0
$568$	−4.04211			−0.169603
$569$	6.03697	+	10.4563i	0.253083	+	0.438353i	0.964373	−	0.264546i	$-0.0852221\pi$
$569$	6.03697	+	10.4563i	0.253083	+	0.438353i	−0.711290	+	0.702899i	$0.751889\pi$
$570$		0			0
$571$	−0.598343	−	0.345454i	−0.0250399	−	0.0144568i	0.487428	−	0.873163i	$-0.337935\pi$
$571$	−0.598343	−	0.345454i	−0.0250399	−	0.0144568i	−0.512468	+	0.858707i	$0.671269\pi$
$572$	2.28705	+	1.32043i	0.0956262	+	0.0552098i
$573$		0			0
$574$	−4.10106	−	7.10324i	−0.171175	−	0.296484i
$575$	−4.07934			−0.170120
$576$		0			0
$577$	17.4717			0.727356			0.363678	−	0.931525i	$-0.381521\pi$
$577$	17.4717			0.727356			0.363678	+	0.931525i	$0.381521\pi$
$578$	−38.0471	+	21.9665i	−1.58255	+	0.913687i
$579$		0			0
$580$	−1.51351	−	0.873828i	−0.0628453	−	0.0362837i
$581$	5.33978	−	9.24877i	0.221531	−	0.383704i
$582$		0			0
$583$	2.33439	+	4.04329i	0.0966807	+	0.167456i
$584$	−5.76852			−0.238703
$585$		0			0
$586$	−10.3142			−0.426075
$587$	−13.6193	−	23.5893i	−0.562129	−	0.973636i	−0.997310	−	0.0732929i	$-0.976649\pi$
$587$	−13.6193	−	23.5893i	−0.562129	−	0.973636i	0.435182	−	0.900343i	$-0.356684\pi$
$588$		0			0
$589$	−9.90950	−	28.7815i	−0.408314	−	1.18592i
$590$	14.0306	+	8.10057i	0.577631	+	0.333495i
$591$		0			0
$592$	6.67157	−	3.85183i	0.274200	−	0.158309i
$593$		−	0.888587i		−	0.0364899i	−0.999834	−	0.0182449i	$-0.994192\pi$
$593$		−	0.888587i		−	0.0364899i	0.999834	−	0.0182449i	$-0.00580787\pi$
$594$		0			0
$595$			16.5435i			0.678217i
$596$	−14.9210	+	8.61466i	−0.611189	+	0.352870i
$597$		0			0
$598$	−0.756482	+	1.31026i	−0.0309348	+	0.0535807i
$599$	−26.2900	−	15.1785i	−1.07418	−	0.620178i	−0.144859	−	0.989452i	$-0.546273\pi$
$599$	−26.2900	−	15.1785i	−1.07418	−	0.620178i	−0.929320	+	0.369274i	$0.879606\pi$
$600$		0			0
$601$	−12.1949	+	7.04074i	−0.497441	+	0.287198i	−0.727656	−	0.685942i	$-0.759390\pi$
$601$	−12.1949	+	7.04074i	−0.497441	+	0.287198i	0.230215	+	0.973140i	$0.426057\pi$
$602$	−6.62325			−0.269943
$603$		0			0
$604$			17.8417i			0.725969i
$605$	7.25474	−	4.18852i	0.294947	−	0.170288i
$606$		0			0
$607$	19.4234	−	33.6423i	0.788371	−	1.36550i	−0.138593	−	0.990349i	$-0.544258\pi$
$607$	19.4234	−	33.6423i	0.788371	−	1.36550i	0.926964	−	0.375149i	$-0.122409\pi$
$608$	−4.73466	−	2.73356i	−0.192016	−	0.110860i
$609$		0			0
$610$	8.71052	−	5.02902i	0.352678	−	0.203619i
$611$	4.66172			0.188593
$612$		0			0
$613$		−	10.2447i		−	0.413778i	−0.978364	−	0.206889i	$-0.933666\pi$
$613$		−	10.2447i		−	0.413778i	0.978364	−	0.206889i	$-0.0663338\pi$
$614$	6.01163	−	3.47082i	0.242610	−	0.140071i
$615$		0			0
$616$	3.07320	+	1.77431i	0.123823	+	0.0714891i
$617$	29.4907	+	17.0265i	1.18725	+	0.685460i	0.957681	−	0.287832i	$-0.0929346\pi$
$617$	29.4907	+	17.0265i	1.18725	+	0.685460i	0.229570	+	0.973292i	$0.426268\pi$
$618$		0			0
$619$	−19.9729	+	11.5314i	−0.802780	+	0.463485i	−0.844442	−	0.535646i	$-0.820068\pi$
$619$	−19.9729	+	11.5314i	−0.802780	+	0.463485i	0.0416622	+	0.999132i	$0.486735\pi$
$620$	4.93608	+	4.29107i	0.198238	+	0.172334i
$621$		0			0
$622$	−24.5458			−0.984198
$623$	4.36259	+	7.55623i	0.174784	+	0.302734i
$624$		0			0
$625$	−3.10255	+	5.37378i	−0.124102	+	0.214951i
$626$	−7.31799	+	12.6751i	−0.292486	+	0.506600i
$627$		0			0
$628$	−6.38199	−	11.0539i	−0.254669	−	0.441100i
$629$		−	60.1345i		−	2.39772i
$630$		0			0
$631$		−	19.3017i		−	0.768387i	−0.923253	−	0.384194i	$-0.874480\pi$
$631$		−	19.3017i		−	0.768387i	0.923253	−	0.384194i	$-0.125520\pi$
$632$	2.74018	+	4.74613i	0.108999	+	0.188791i
$633$		0			0
$634$	4.13313	−	7.15880i	0.164148	−	0.284312i
$635$	−11.0092	+	19.0685i	−0.436886	+	0.756709i
$636$		0			0
$637$	4.35457	−	2.51411i	0.172534	−	0.0996128i
$638$			2.92628i			0.115852i
$639$		0			0
$640$	1.17471			0.0464345
$641$	−23.1194	−	40.0440i	−0.913161	−	1.58164i	−0.809571	−	0.587022i	$-0.800300\pi$
$641$	−23.1194	−	40.0440i	−0.913161	−	1.58164i	−0.103590	−	0.994620i	$-0.533033\pi$
$642$		0			0
$643$	22.3679	+	12.9141i	0.882105	+	0.509284i	0.871352	−	0.490658i	$-0.163244\pi$
$643$	22.3679	+	12.9141i	0.882105	+	0.509284i	0.0107534	+	0.999942i	$0.496577\pi$
$644$	−1.01652	+	1.76066i	−0.0400564	+	0.0693797i
$645$		0			0
$646$	−36.9586	+	21.3381i	−1.45412	+	0.839535i
$647$	−33.5018			−1.31709			−0.658547	−	0.752540i	$-0.728829\pi$
$647$	−33.5018			−1.31709			−0.658547	+	0.752540i	$0.728829\pi$
$648$		0			0
$649$		−	27.1272i		−	1.06484i
$650$	2.43019	+	4.20921i	0.0953198	+	0.165099i
$651$		0			0
$652$	−4.76431	+	8.25203i	−0.186585	+	0.323175i
$653$	9.36830	+	5.40879i	0.366610	+	0.211662i	0.671976	−	0.740573i	$-0.265446\pi$
$653$	9.36830	+	5.40879i	0.366610	+	0.211662i	−0.305366	+	0.952235i	$0.598779\pi$
$654$		0			0
$655$	4.95714	+	8.58602i	0.193692	+	0.335484i
$656$			4.54627i			0.177502i
$657$		0			0
$658$	6.26415			0.244202
$659$	25.1726	−	14.5334i	0.980584	−	0.566140i	0.0781375	−	0.996943i	$-0.475103\pi$
$659$	25.1726	−	14.5334i	0.980584	−	0.566140i	0.902446	+	0.430802i	$0.141769\pi$
$660$		0			0
$661$	−0.0255919	+	0.0443264i	−0.000995409	+	0.00172410i	−0.866523	−	0.499138i	$-0.833650\pi$
$661$	−0.0255919	+	0.0443264i	−0.000995409	+	0.00172410i	0.865527	+	0.500862i	$0.166984\pi$
$662$	−0.770341	+	1.33427i	−0.0299401	+	0.0518579i
$663$		0			0
$664$	−5.12641	+	2.95973i	−0.198943	+	0.114860i
$665$			11.5867i			0.449312i
$666$		0			0
$667$	−1.67648			−0.0649137
$668$	−5.21593	−	9.03426i	−0.201811	−	0.349546i
$669$		0			0
$670$	9.26628	−	16.0497i	0.357988	−	0.620053i
$671$	−14.5849	−	8.42059i	−0.563044	−	0.325073i
$672$		0			0
$673$	−6.48140	+	3.74204i	−0.249840	+	0.144245i	−0.619691	−	0.784846i	$-0.712742\pi$
$673$	−6.48140	+	3.74204i	−0.249840	+	0.144245i	0.369851	+	0.929091i	$0.379409\pi$
$674$	3.99775			0.153987
$675$		0			0
$676$	−11.1974			−0.430668
$677$	−1.57692	−	2.73130i	−0.0606059	−	0.104972i	0.834131	−	0.551567i	$-0.185970\pi$
$677$	−1.57692	−	2.73130i	−0.0606059	−	0.104972i	−0.894736	+	0.446595i	$0.852637\pi$
$678$		0			0
$679$	−13.2484	+	22.9469i	−0.508428	+	0.880623i
$680$	4.58487	−	7.94123i	0.175822	−	0.304532i
$681$		0			0
$682$	2.08988	−	10.7502i	0.0800258	−	0.411645i
$683$			26.3397i			1.00786i	0.863744	+	0.503931i	$0.168113\pi$
$683$			26.3397i			1.00786i	−0.863744	+	0.503931i	$0.831887\pi$
$684$		0			0
$685$			0.359836i			0.0137486i
$686$	16.7884	−	9.69281i	0.640986	−	0.370073i
$687$		0			0
$688$	3.17930	+	1.83557i	0.121210	+	0.0699804i
$689$	2.75994	+	1.59345i	0.105145	+	0.0607056i
$690$		0			0
$691$	0.667745	+	1.15657i	0.0254022	+	0.0439979i	0.878447	−	0.477840i	$-0.158580\pi$
$691$	0.667745	+	1.15657i	0.0254022	+	0.0439979i	−0.853045	+	0.521838i	$0.825247\pi$
$692$			7.50810i			0.285415i
$693$		0			0
$694$		−	23.3162i		−	0.885070i
$695$	−6.80086	−	11.7794i	−0.257971	−	0.446820i
$696$		0			0
$697$	30.7336	+	17.7440i	1.16412	+	0.672103i
$698$	6.39191	+	3.69037i	0.241937	+	0.139683i
$699$		0			0
$700$	3.26555	+	5.65609i	0.123426	+	0.213780i
$701$		−	42.5935i		−	1.60873i	−0.594132	−	0.804367i	$-0.702504\pi$
$701$		−	42.5935i		−	1.60873i	0.594132	−	0.804367i	$-0.297496\pi$
$702$		0			0
$703$		−	42.1168i		−	1.58847i
$704$	−0.983467	−	1.70342i	−0.0370658	−	0.0641999i
$705$		0			0
$706$	15.6233	+	9.02014i	0.587992	+	0.339477i
$707$	−4.17711	−	2.41166i	−0.157096	−	0.0906997i
$708$		0			0
$709$	−37.0728	+	21.4040i	−1.39230	+	0.803845i	−0.993570	−	0.113223i	$-0.963882\pi$
$709$	−37.0728	+	21.4040i	−1.39230	+	0.803845i	−0.398730	+	0.917068i	$0.630549\pi$
$710$		−	4.74830i		−	0.178201i
$711$		0			0
$712$		−	4.83620i		−	0.181244i
$713$	6.15885	+	1.19731i	0.230651	+	0.0448396i
$714$		0			0
$715$	−1.55112	+	2.68661i	−0.0580085	+	0.100474i
$716$	−10.9905	+	19.0361i	−0.410733	+	0.711411i
$717$		0			0
$718$	−9.02653	−	15.6344i	−0.336867	−	0.583471i
$719$	1.31866			0.0491778			0.0245889	−	0.999698i	$-0.492172\pi$
$719$	1.31866			0.0491778			0.0245889	+	0.999698i	$0.492172\pi$
$720$		0			0
$721$	−13.3848			−0.498476
$722$	−9.43047	+	5.44469i	−0.350966	+	0.202630i
$723$		0			0
$724$	10.8664	+	6.27374i	0.403848	+	0.233162i
$725$	−2.69284	+	4.66414i	−0.100010	+	0.173222i
$726$		0			0
$727$	−1.99610	−	3.45735i	−0.0740314	−	0.128226i	0.826633	−	0.562741i	$-0.190253\pi$
$727$	−1.99610	−	3.45735i	−0.0740314	−	0.128226i	−0.900665	+	0.434515i	$0.856920\pi$
$728$	2.42228			0.0897757
$729$		0			0
$730$		−	6.77633i		−	0.250803i
$731$	24.8175	−	14.3284i	0.917907	−	0.529954i
$732$		0			0
$733$	18.6015	−	32.2188i	0.687063	−	1.19003i	−0.285721	−	0.958313i	$-0.592233\pi$
$733$	18.6015	−	32.2188i	0.687063	−	1.19003i	0.972784	−	0.231715i	$-0.0744336\pi$
$734$	−2.64994	+	4.58982i	−0.0978109	+	0.169414i
$735$		0			0
$736$	0.975899	−	0.563435i	0.0359721	−	0.0207685i
$737$	−31.0309			−1.14304
$738$		0			0
$739$			25.2235i			0.927861i	0.885871	+	0.463931i	$0.153561\pi$
$739$			25.2235i			0.927861i	−0.885871	+	0.463931i	$0.846439\pi$
$740$	4.52478	+	7.83715i	0.166334	+	0.288099i
$741$		0			0
$742$	3.70865	+	2.14119i	0.136149	+	0.0786055i
$743$	−3.33907	+	5.78344i	−0.122499	+	0.212174i	−0.920752	−	0.390147i	$-0.872424\pi$
$743$	−3.33907	+	5.78344i	−0.122499	+	0.212174i	0.798254	+	0.602321i	$0.205757\pi$
$744$		0			0
$745$	−10.1197	−	17.5279i	−0.370758	−	0.642172i
$746$		−	24.5695i		−	0.899554i
$747$		0			0
$748$	−15.3538			−0.561391
$749$	9.76155	−	5.63583i	0.356679	−	0.205929i
$750$		0			0
$751$	13.6753	−	23.6864i	0.499020	−	0.864328i	−0.500980	−	0.865459i	$-0.667027\pi$
$751$	13.6753	−	23.6864i	0.499020	−	0.864328i	0.999999	+	0.00113141i	$0.000360139\pi$
$752$	−3.00693	−	1.73605i	−0.109651	−	0.0633072i
$753$		0			0
$754$	0.998734	+	1.72986i	0.0363717	+	0.0629977i
$755$	−20.9588			−0.762770
$756$		0			0
$757$		−	0.676092i		−	0.0245730i	−0.999925	−	0.0122865i	$-0.996089\pi$
$757$		−	0.676092i		−	0.0245730i	0.999925	−	0.0122865i	$-0.00391101\pi$
$758$	−9.07921	+	5.24188i	−0.329772	+	0.190394i
$759$		0			0
$760$	3.21114	−	5.56185i	0.116480	−	0.201750i
$761$	11.3364	−	19.6352i	0.410943	−	0.711774i	−0.584050	−	0.811718i	$-0.698533\pi$
$761$	11.3364	−	19.6352i	0.410943	−	0.711774i	0.994993	+	0.0999434i	$0.0318662\pi$
$762$		0			0
$763$	3.21237	+	5.56399i	0.116296	+	0.201430i
$764$		−	18.5200i		−	0.670032i
$765$		0			0
$766$			31.1597i			1.12585i
$767$	−9.25848	−	16.0362i	−0.334304	−	0.579032i
$768$		0			0
$769$	−0.835355	+	1.44688i	−0.0301237	+	0.0521757i	−0.880694	−	0.473685i	$-0.842923\pi$
$769$	−0.835355	+	1.44688i	−0.0301237	+	0.0521757i	0.850571	+	0.525861i	$0.176257\pi$
$770$	−2.08430	+	3.61012i	−0.0751131	+	0.130100i
$771$		0			0
$772$	5.55289	+	9.61788i	0.199853	+	0.346155i
$773$	−5.56061			−0.200001			−0.100001	−	0.994987i	$-0.531884\pi$
$773$	−5.56061			−0.200001			−0.100001	+	0.994987i	$0.531884\pi$
$774$		0			0
$775$	13.2236	−	15.2113i	0.475007	−	0.546407i
$776$	12.7190	−	7.34334i	0.456587	−	0.263611i
$777$		0			0
$778$	20.5186	+	11.8464i	0.735628	+	0.424715i
$779$	21.5251	+	12.4275i	0.771216	+	0.445262i
$780$		0			0
$781$	−6.88539	+	3.97528i	−0.246379	+	0.142247i
$782$		−	8.79631i		−	0.314556i
$783$		0			0
$784$	−3.74508			−0.133753
$785$	12.9852	−	7.49699i	0.463460	−	0.267579i
$786$		0			0
$787$	−21.2594	−	12.2741i	−0.757815	−	0.437525i	0.0706959	−	0.997498i	$-0.477478\pi$
$787$	−21.2594	−	12.2741i	−0.757815	−	0.437525i	−0.828511	+	0.559973i	$0.810811\pi$
$788$	−5.65928	+	9.80217i	−0.201604	+	0.349188i
$789$		0			0
$790$	−5.57533	+	3.21892i	−0.198361	+	0.114524i
$791$			10.9719i			0.390114i
$792$		0			0
$793$	−11.4957			−0.408226
$794$	−15.3011	+	8.83409i	−0.543015	+	0.313510i
$795$		0			0
$796$	−2.39737	−	1.38412i	−0.0849725	−	0.0490589i
$797$	−22.4889	+	38.9520i	−0.796599	+	1.37975i	0.125220	+	0.992129i	$0.460036\pi$
$797$	−22.4889	+	38.9520i	−0.796599	+	1.37975i	−0.921819	+	0.387621i	$0.873297\pi$
$798$		0			0
$799$	−23.4719	+	13.5515i	−0.830378	+	0.479419i
$800$		−	3.62006i		−	0.127988i
$801$		0			0
$802$			24.4357i			0.862853i
$803$	−9.82619	+	5.67315i	−0.346759	+	0.200201i
$804$		0			0
$805$	−2.06826	−	1.19411i	−0.0728967	−	0.0420869i
$806$	−2.43359	−	7.06820i	−0.0857196	−	0.248967i
$807$		0			0
$808$	1.33673	+	2.31529i	0.0470261	+	0.0814517i
$809$	10.3792			0.364914			0.182457	−	0.983214i	$-0.441595\pi$
$809$	10.3792			0.364914			0.182457	+	0.983214i	$0.441595\pi$
$810$		0			0
$811$	−52.3342			−1.83770			−0.918851	−	0.394604i	$-0.870882\pi$
$811$	−52.3342			−1.83770			−0.918851	+	0.394604i	$0.870882\pi$
$812$	1.34204	+	2.32448i	0.0470964	+	0.0815734i
$813$		0			0
$814$	7.57630	−	13.1225i	0.265549	−	0.459945i
$815$	−9.69374	−	5.59668i	−0.339557	−	0.196043i
$816$		0			0
$817$	17.3816	−	10.0353i	0.608105	−	0.351089i
$818$	−15.9286			−0.556932
$819$		0			0
$820$	−5.34055			−0.186500
$821$	3.44252	+	5.96262i	0.120145	+	0.208097i	0.919825	−	0.392330i	$-0.128331\pi$
$821$	3.44252	+	5.96262i	0.120145	+	0.208097i	−0.799680	+	0.600427i	$0.794997\pi$
$822$		0			0
$823$	33.0096	+	19.0581i	1.15064	+	0.664324i	0.949044	−	0.315144i	$-0.102053\pi$
$823$	33.0096	+	19.0581i	1.15064	+	0.664324i	0.201599	+	0.979468i	$0.435386\pi$
$824$	6.42499	+	3.70947i	0.223825	+	0.129225i
$825$		0			0
$826$	−12.4410	−	21.5485i	−0.432878	−	0.749767i
$827$	−55.2657			−1.92178			−0.960889	−	0.276934i	$-0.910682\pi$
$827$	−55.2657			−1.92178			−0.960889	+	0.276934i	$0.910682\pi$
$828$		0			0
$829$		−	54.3149i		−	1.88644i	−0.332175	−	0.943218i	$-0.607783\pi$
$829$		−	54.3149i		−	1.88644i	0.332175	−	0.943218i	$-0.392217\pi$
$830$	−3.47683	−	6.02204i	−0.120682	−	0.209028i
$831$		0			0
$832$	−1.16275	−	0.671312i	−0.0403110	−	0.0232736i
$833$	−14.6170	+	25.3173i	−0.506448	+	0.877193i
$834$		0			0
$835$	10.6126	−	6.12721i	0.367265	−	0.212041i
$836$	−10.7535			−0.371916
$837$		0			0
$838$	−29.2431			−1.01019
$839$	−18.7510	+	10.8259i	−0.647356	+	0.373751i	−0.787443	−	0.616388i	$-0.788595\pi$
$839$	−18.7510	+	10.8259i	−0.647356	+	0.373751i	0.140086	+	0.990139i	$0.455262\pi$
$840$		0			0
$841$	13.3933	−	23.1979i	0.461839	−	0.799928i
$842$	−25.4747	−	14.7078i	−0.877916	−	0.506865i
$843$		0			0
$844$	−1.35629	−	2.34917i	−0.0466855	−	0.0808616i
$845$		−	13.1536i		−	0.452499i
$846$		0			0
$847$	−12.8656			−0.442068
$848$	−1.18682	−	2.05563i	−0.0407555	−	0.0705906i
$849$		0			0
$850$	−24.4722	−	14.1290i	−0.839389	−	0.484621i
$851$	7.51799	+	4.34052i	0.257713	+	0.148791i
$852$		0			0
$853$	15.0534	+	26.0732i	0.515418	+	0.892730i	0.999840	+	0.0178957i	$0.00569667\pi$
$853$	15.0534	+	26.0732i	0.515418	+	0.892730i	−0.484422	+	0.874835i	$0.660970\pi$
$854$	−15.4473			−0.528596
$855$		0			0
$856$	−6.24767			−0.213541
$857$	−12.4523	+	7.18935i	−0.425363	+	0.245584i	−0.697369	−	0.716712i	$-0.745646\pi$
$857$	−12.4523	+	7.18935i	−0.425363	+	0.245584i	0.272006	+	0.962296i	$0.412313\pi$
$858$		0			0
$859$	47.2286	+	27.2674i	1.61142	+	0.930353i	0.989042	+	0.147634i	$0.0471659\pi$
$859$	47.2286	+	27.2674i	1.61142	+	0.930353i	0.622376	+	0.782718i	$0.286167\pi$
$860$	−2.15626	+	3.73475i	−0.0735278	+	0.127354i
$861$		0			0
$862$	−4.43654	−	7.68432i	−0.151109	−	0.261729i
$863$	−7.05428			−0.240131			−0.120065	−	0.992766i	$-0.538310\pi$
$863$	−7.05428			−0.240131			−0.120065	+	0.992766i	$0.538310\pi$
$864$		0			0
$865$	−8.81984			−0.299883
$866$	7.13889	+	12.3649i	0.242589	+	0.420177i
$867$		0			0
$868$	−3.27012	−	9.49784i	−0.110995	−	0.322378i
$869$	9.33533	+	5.38976i	0.316680	+	0.182835i
$870$		0			0
$871$	−18.3438	+	10.5908i	−0.621557	+	0.358856i
$872$		−	3.56111i		−	0.120594i
$873$		0			0
$874$		−	6.16074i		−	0.208390i
$875$	−15.8213	+	9.13442i	−0.534857	+	0.308800i
$876$		0			0
$877$	9.05222	−	15.6789i	0.305672	−	0.529439i	−0.671739	−	0.740788i	$-0.734452\pi$
$877$	9.05222	−	15.6789i	0.305672	−	0.529439i	0.977411	+	0.211349i	$0.0677857\pi$
$878$	3.36504	+	1.94281i	0.113565	+	0.0655665i
$879$		0			0
$880$	2.00102	−	1.15529i	0.0674543	−	0.0389448i
$881$	2.33807			0.0787717			0.0393859	−	0.999224i	$-0.487460\pi$
$881$	2.33807			0.0787717			0.0393859	+	0.999224i	$0.487460\pi$
$882$		0			0
$883$			4.54048i			0.152799i	0.997077	+	0.0763996i	$0.0243425\pi$
$883$			4.54048i			0.152799i	−0.997077	+	0.0763996i	$0.975658\pi$
$884$	−9.07635	+	5.24024i	−0.305271	+	0.176248i
$885$		0			0
$886$	7.72551	−	13.3810i	0.259543	−	0.449542i
$887$	−0.549808	−	0.317432i	−0.0184607	−	0.0106583i	0.490741	−	0.871305i	$-0.336726\pi$
$887$	−0.549808	−	0.317432i	−0.0184607	−	0.0106583i	−0.509202	+	0.860647i	$0.670059\pi$
$888$		0			0
$889$	29.2857	−	16.9081i	0.982211	−	0.567080i
$890$	5.68113			0.190432
$891$		0			0
$892$		−	6.46337i		−	0.216410i
$893$	−16.4392	+	9.49118i	−0.550117	+	0.317610i
$894$		0			0
$895$	−22.3618	−	12.9106i	−0.747474	−	0.431554i
$896$	−1.56243	−	0.902070i	−0.0521972	−	0.0301361i
$897$		0			0
$898$	15.7053	−	9.06743i	0.524091	−	0.302584i
$899$	5.43452	−	6.25140i	0.181251	−	0.208496i
$900$		0			0
$901$	−18.5285			−0.617275
$902$	4.47111	+	7.74419i	0.148872	+	0.257853i
$903$		0			0
$904$	3.04074	−	5.26672i	0.101134	−	0.175169i
$905$	−7.36982	+	12.7649i	−0.244981	+	0.424320i
$906$		0			0
$907$	−12.3213	−	21.3412i	−0.409123	−	0.708622i	0.585669	−	0.810550i	$-0.300832\pi$
$907$	−12.3213	−	21.3412i	−0.409123	−	0.708622i	−0.994792	+	0.101929i	$0.967499\pi$
$908$			17.4965i			0.580640i
$909$		0			0
$910$			2.84548i			0.0943267i
$911$	−3.09235	−	5.35611i	−0.102454	−	0.177456i	0.810241	−	0.586097i	$-0.199336\pi$
$911$	−3.09235	−	5.35611i	−0.102454	−	0.177456i	−0.912695	+	0.408641i	$0.866003\pi$
$912$		0			0
$913$	−5.82161	+	10.0833i	−0.192667	+	0.333709i
$914$	−3.09642	+	5.36316i	−0.102421	+	0.177398i
$915$		0			0
$916$	−23.3070	+	13.4563i	−0.770083	+	0.444608i
$917$		−	15.2265i		−	0.502825i
$918$		0			0
$919$	19.9961			0.659609			0.329805	−	0.944049i	$-0.393017\pi$
$919$	19.9961			0.659609			0.329805	+	0.944049i	$0.393017\pi$
$920$	0.661873	+	1.14640i	0.0218213	+	0.0377956i
$921$		0			0
$922$	−19.4055	−	11.2038i	−0.639087	−	0.368977i
$923$	−2.71351	+	4.69994i	−0.0893164	+	0.154701i
$924$		0			0
$925$	24.1515	−	13.9438i	0.794095	−	0.458471i
$926$	29.0450			0.954479
$927$		0			0
$928$		−	1.48773i		−	0.0488373i
$929$	−15.0929	−	26.1416i	−0.495181	−	0.857679i	0.504803	−	0.863234i	$-0.331565\pi$
$929$	−15.0929	−	26.1416i	−0.495181	−	0.857679i	−0.999985	+	0.00555525i	$0.998232\pi$
$930$		0			0
$931$	−10.2374	+	17.7317i	−0.335517	+	0.581132i
$932$	6.89239	+	3.97932i	0.225768	+	0.130347i
$933$		0			0
$934$	−3.85434	−	6.67590i	−0.126118	−	0.218442i
$935$		−	18.0363i		−	0.589849i
$936$		0			0
$937$	−22.0554			−0.720520			−0.360260	−	0.932852i	$-0.617312\pi$
$937$	−22.0554			−0.720520			−0.360260	+	0.932852i	$0.617312\pi$
$938$	−24.6494	+	14.2313i	−0.804831	+	0.464669i
$939$		0			0
$940$	2.03935	−	3.53226i	0.0665164	−	0.115210i
$941$	−26.5389	+	45.9668i	−0.865145	+	1.49848i	0.00175808	+	0.999998i	$0.499440\pi$
$941$	−26.5389	+	45.9668i	−0.865145	+	1.49848i	−0.866903	+	0.498477i	$0.833893\pi$
$942$		0			0
$943$	−4.43670	+	2.56153i	−0.144479	+	0.0834150i
$944$			13.7916i			0.448879i
$945$		0			0
$946$	7.22089			0.234771
$947$	10.7448	+	18.6106i	0.349160	+	0.604762i	0.986100	−	0.166150i	$-0.0531337\pi$
$947$	10.7448	+	18.6106i	0.349160	+	0.604762i	−0.636941	+	0.770913i	$0.719800\pi$
$948$		0			0
$949$	−3.87248	+	6.70732i	−0.125706	+	0.217729i
$950$	−17.1398	−	9.89564i	−0.556087	−	0.321057i
$951$		0			0
$952$	−12.1963	+	7.04153i	−0.395284	+	0.228217i
$953$	16.9059			0.547635			0.273818	−	0.961782i	$-0.411714\pi$
$953$	16.9059			0.547635			0.273818	+	0.961782i	$0.411714\pi$
$954$		0			0
$955$	21.7557			0.703997
$956$	8.56671	+	14.8380i	0.277067	+	0.479895i
$957$		0			0
$958$	−17.1520	+	29.7081i	−0.554155	+	0.959824i
$959$	0.276321	−	0.478603i	0.00892288	−	0.0154549i
$960$		0			0
$961$	−24.4292	+	19.0844i	−0.788040	+	0.615624i
$962$		−	10.3431i		−	0.333475i
$963$		0			0
$964$		−	19.4322i		−	0.625869i
$965$	−11.2982	+	6.52303i	−0.363702	+	0.209984i
$966$		0			0
$967$	−9.00191	−	5.19725i	−0.289482	−	0.167132i	0.348226	−	0.937410i	$-0.386784\pi$
$967$	−9.00191	−	5.19725i	−0.289482	−	0.167132i	−0.637708	+	0.770278i	$0.720117\pi$
$968$	6.17577	+	3.56558i	0.198497	+	0.114602i
$969$		0			0
$970$	8.62629	+	14.9412i	0.276974	+	0.479732i
$971$		−	8.52436i		−	0.273560i	−0.990601	−	0.136780i	$-0.956325\pi$
$971$		−	8.52436i		−	0.273560i	0.990601	−	0.136780i	$-0.0436753\pi$
$972$		0			0
$973$			20.8898i			0.669696i
$974$	−17.7505	−	30.7447i	−0.568762	−	0.985124i
$975$		0			0
$976$	7.41504	+	4.28107i	0.237350	+	0.137034i
$977$	−48.7020	−	28.1181i	−1.55811	−	0.899578i	−0.997438	−	0.0715430i	$-0.977208\pi$
$977$	−48.7020	−	28.1181i	−1.55811	−	0.899578i	−0.560677	−	0.828035i	$-0.689459\pi$
$978$		0			0
$979$	−4.75624	−	8.23805i	−0.152010	−	0.263289i
$980$		−	4.39938i		−	0.140533i
$981$		0			0
$982$			26.5103i			0.845978i
$983$	29.9167	+	51.8172i	0.954195	+	1.65271i	0.736201	+	0.676763i	$0.236618\pi$
$983$	29.9167	+	51.8172i	0.954195	+	1.65271i	0.217994	+	0.975950i	$0.430049\pi$
$984$		0			0
$985$	−11.5147	−	6.64801i	−0.366889	−	0.211823i
$986$	−10.0573	−	5.80660i	−0.320290	−	0.184920i
$987$		0			0
$988$	−6.35687	+	3.67014i	−0.202239	+	0.116763i
$989$			4.13690i			0.131546i
$990$		0			0
$991$			38.4776i			1.22228i	0.791522	+	0.611140i	$0.209289\pi$
$991$			38.4776i			1.22228i	−0.791522	+	0.611140i	$0.790711\pi$
$992$	−1.06251	+	5.46544i	−0.0337347	+	0.173528i
$993$		0			0
$994$	−3.64626	+	6.31552i	−0.115652	+	0.200316i
$995$	1.62594	−	2.81621i	0.0515458	−	0.0892800i
$996$		0			0
$997$	−16.1241	−	27.9278i	−0.510656	−	0.884482i	−0.999924	−	0.0123487i	$-0.996069\pi$
$997$	−16.1241	−	27.9278i	−0.510656	−	0.884482i	0.489268	−	0.872134i	$-0.337264\pi$
$998$	−12.6098			−0.399155
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1674.2.q.a.557.7		64
3.2	odd	2		558.2.q.a.185.32	yes	64
9.2	odd	6	inner	1674.2.q.a.1115.5		64
9.7	even	3		558.2.q.a.371.17	yes	64
31.30	odd	2	inner	1674.2.q.a.557.5		64
93.92	even	2		558.2.q.a.185.17	✓	64
279.61	odd	6		558.2.q.a.371.32	yes	64
279.92	even	6	inner	1674.2.q.a.1115.7		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
558.2.q.a.185.17	✓	64	93.92	even	2
558.2.q.a.185.32	yes	64	3.2	odd	2
558.2.q.a.371.17	yes	64	9.7	even	3
558.2.q.a.371.32	yes	64	279.61	odd	6
1674.2.q.a.557.5		64	31.30	odd	2	inner
1674.2.q.a.557.7		64	1.1	even	1	trivial
1674.2.q.a.1115.5		64	9.2	odd	6	inner
1674.2.q.a.1115.7		64	279.92	even	6	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)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(1.01733 + 0.587355i) q^{5} +(-0.902070 - 1.56243i) q^{7} +1.00000i q^{8} -1.17471 q^{10} +(0.983467 + 1.70342i) q^{11} +(1.16275 + 0.671312i) q^{13} +(1.56243 + 0.902070i) q^{14} +(-0.500000 - 0.866025i) q^{16} -7.80596 q^{17} -5.46712 q^{19} +(1.01733 - 0.587355i) q^{20} +(-1.70342 - 0.983467i) q^{22} +(0.563435 - 0.975899i) q^{23} +(-1.81003 - 3.13506i) q^{25} -1.34262 q^{26} -1.80414 q^{28} +(-0.743867 - 1.28842i) q^{29} +(1.81256 + 5.26447i) q^{31} +(0.866025 + 0.500000i) q^{32} +(6.76016 - 3.90298i) q^{34} -2.11934i q^{35} +7.70366i q^{37} +(4.73466 - 2.73356i) q^{38} +(-0.587355 + 1.01733i) q^{40} +(-3.93719 - 2.27314i) q^{41} +(-3.17930 + 1.83557i) q^{43} +1.96693 q^{44} +1.12687i q^{46} +(3.00693 - 1.73605i) q^{47} +(1.87254 - 3.24333i) q^{49} +(3.13506 + 1.81003i) q^{50} +(1.16275 - 0.671312i) q^{52} +2.37364 q^{53} +2.31058i q^{55} +(1.56243 - 0.902070i) q^{56} +(1.28842 + 0.743867i) q^{58} +(-11.9439 - 6.89581i) q^{59} +(-7.41504 + 4.28107i) q^{61} +(-4.20196 - 3.65288i) q^{62} -1.00000 q^{64} +(0.788596 + 1.36589i) q^{65} +(-7.88815 + 13.6627i) q^{67} +(-3.90298 + 6.76016i) q^{68} +(1.05967 + 1.83540i) q^{70} +4.04211i q^{71} +5.76852i q^{73} +(-3.85183 - 6.67157i) q^{74} +(-2.73356 + 4.73466i) q^{76} +(1.77431 - 3.07320i) q^{77} +(4.74613 - 2.74018i) q^{79} -1.17471i q^{80} +4.54627 q^{82} +(2.95973 + 5.12641i) q^{83} +(-7.94123 - 4.58487i) q^{85} +(1.83557 - 3.17930i) q^{86} +(-1.70342 + 0.983467i) q^{88} -4.83620 q^{89} -2.42228i q^{91} +(-0.563435 - 0.975899i) q^{92} +(-1.73605 + 3.00693i) q^{94} +(-5.56185 - 3.21114i) q^{95} +(-7.34334 - 12.7190i) q^{97} +3.74508i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 32 q^{4} - 12 q^{5} - 4 q^{7} - 32 q^{16} - 8 q^{19} - 12 q^{20} + 44 q^{25} - 8 q^{28} + 8 q^{31} - 36 q^{38} - 24 q^{41} + 48 q^{47} - 36 q^{49} + 12 q^{59} - 64 q^{64} + 16 q^{67} - 12 q^{70}+ \cdots - 16 q^{97}+O(q^{100}) \) 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

Related objects

Downloads

Learn more