LMFDB - Embedded newform 405.3.g.h.163.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [405,3,Mod(82,405)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(405, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 1])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("405.82"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 405 = 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	405.g (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [20,2] 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:	$11.0354507066$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 2 x^{19} + 2 x^{18} + 8 x^{17} + 245 x^{16} - 440 x^{15} + 422 x^{14} + 1724 x^{13} + \cdots + 11449 $ x^20 - 2x^19 + 2x^18 + 8x^17 + 245x^16 - 440x^15 + 422x^14 + 1724x^13 + 15070x^12 - 18240x^11 + 13542x^10 + 50064x^9 + 293818x^8 - 191648x^7 + 30530x^6 - 134164x^5 + 859529x^4 - 948950x^3 + 540800x^2 - 111280*x + 11449
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{3}\cdot 3^{4} $
Twist minimal:	no (minimal twist has level 45)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			163.2
Root			$-1.76130 - 1.76130i$ of defining polynomial
Character	$\chi$	$=$	405.163
Dual form			405.3.g.h.82.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.76130 + 1.76130i) q^{2} -2.20434i q^{4} +(4.13877 - 2.80545i) q^{5} +(0.0481814 - 0.0481814i) q^{7} +(-3.16269 - 3.16269i) q^{8} +(-2.34837 + 12.2309i) q^{10} -9.24583 q^{11} +(9.25335 + 9.25335i) q^{13} +0.169724i q^{14} +19.9582 q^{16} +(13.6029 - 13.6029i) q^{17} -5.80704i q^{19} +(-6.18418 - 9.12327i) q^{20} +(16.2847 - 16.2847i) q^{22} +(-32.0648 - 32.0648i) q^{23} +(9.25886 - 23.2223i) q^{25} -32.5958 q^{26} +(-0.106208 - 0.106208i) q^{28} -7.35801i q^{29} +16.7073 q^{31} +(-22.5017 + 22.5017i) q^{32} +47.9175i q^{34} +(0.0642412 - 0.334583i) q^{35} +(36.0680 - 36.0680i) q^{37} +(10.2279 + 10.2279i) q^{38} +(-21.9624 - 4.21687i) q^{40} +62.3133 q^{41} +(-7.10279 - 7.10279i) q^{43} +20.3810i q^{44} +112.951 q^{46} +(32.6843 - 32.6843i) q^{47} +48.9954i q^{49} +(24.5937 + 57.2089i) q^{50} +(20.3975 - 20.3975i) q^{52} +(28.0258 + 28.0258i) q^{53} +(-38.2664 + 25.9388i) q^{55} -0.304766 q^{56} +(12.9596 + 12.9596i) q^{58} +18.8804i q^{59} -5.39094 q^{61} +(-29.4265 + 29.4265i) q^{62} +0.568692i q^{64} +(64.2573 + 12.3376i) q^{65} +(35.0738 - 35.0738i) q^{67} +(-29.9854 - 29.9854i) q^{68} +(0.476152 + 0.702448i) q^{70} +56.4200 q^{71} +(-54.7135 - 54.7135i) q^{73} +127.053i q^{74} -12.8007 q^{76} +(-0.445478 + 0.445478i) q^{77} +47.3071i q^{79} +(82.6026 - 55.9919i) q^{80} +(-109.752 + 109.752i) q^{82} +(-43.9426 - 43.9426i) q^{83} +(18.1370 - 94.4615i) q^{85} +25.0203 q^{86} +(29.2417 + 29.2417i) q^{88} +59.1599i q^{89} +0.891679 q^{91} +(-70.6817 + 70.6817i) q^{92} +115.134i q^{94} +(-16.2914 - 24.0340i) q^{95} +(109.991 - 109.991i) q^{97} +(-86.2954 - 86.2954i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 2 q^{2} + 2 q^{5} + 2 q^{7} - 12 q^{8} - 4 q^{10} - 8 q^{11} + 2 q^{13} - 28 q^{16} + 14 q^{17} + 114 q^{20} - 14 q^{22} - 82 q^{23} + 8 q^{25} - 56 q^{26} - 44 q^{28} + 4 q^{31} + 14 q^{32} + 176 q^{35}+ \cdots - 938 q^{98}+O(q^{100}) $ 20 * q + 2 * q^2 + 2 * q^5 + 2 * q^7 - 12 * q^8 - 4 * q^10 - 8 * q^11 + 2 * q^13 - 28 * q^16 + 14 * q^17 + 114 * q^20 - 14 * q^22 - 82 * q^23 + 8 * q^25 - 56 * q^26 - 44 * q^28 + 4 * q^31 + 14 * q^32 + 176 * q^35 - 46 * q^37 - 330 * q^38 - 30 * q^40 + 28 * q^41 + 2 * q^43 - 68 * q^46 - 64 * q^47 + 458 * q^50 + 74 * q^52 - 304 * q^53 + 112 * q^55 + 192 * q^56 - 30 * q^58 - 92 * q^61 - 50 * q^62 + 326 * q^65 + 80 * q^67 - 626 * q^68 + 102 * q^70 + 124 * q^71 - 4 * q^73 + 96 * q^76 - 338 * q^77 + 722 * q^80 + 52 * q^82 - 370 * q^83 + 98 * q^85 + 328 * q^86 + 210 * q^88 + 76 * q^91 - 388 * q^92 + 360 * q^95 - 292 * q^97 - 938 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/405\mathbb{Z}\right)^\times$.

$n$	$82$	$326$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$

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 $

$2$	−1.76130	+	1.76130i	−0.880649	+	0.880649i	−0.993601	−	0.112951i	$-0.963970\pi$
$2$	−1.76130	+	1.76130i	−0.880649	+	0.880649i	0.112951	+	0.993601i	$0.463970\pi$
$3$		0			0
$3$		0			0
$4$		−	2.20434i		−	0.551086i
$5$	4.13877	−	2.80545i	0.827754	−	0.561091i
$5$	4.13877	−	2.80545i	0.827754	−	0.561091i
$6$		0			0
$7$	0.0481814	−	0.0481814i	0.00688306	−	0.00688306i	−0.703657	−	0.710540i	$-0.748451\pi$
$7$	0.0481814	−	0.0481814i	0.00688306	−	0.00688306i	0.710540	+	0.703657i	$0.248451\pi$
$8$	−3.16269	−	3.16269i	−0.395336	−	0.395336i
$9$		0			0
$10$	−2.34837	+	12.2309i	−0.234837	+	1.22309i
$11$	−9.24583			−0.840530			−0.420265	−	0.907401i	$-0.638063\pi$
$11$	−9.24583			−0.840530			−0.420265	+	0.907401i	$0.638063\pi$
$12$		0			0
$13$	9.25335	+	9.25335i	0.711796	+	0.711796i	0.966911	−	0.255115i	$-0.0821133\pi$
$13$	9.25335	+	9.25335i	0.711796	+	0.711796i	−0.255115	+	0.966911i	$0.582113\pi$
$14$			0.169724i			0.0121231i
$15$		0			0
$16$	19.9582			1.24739
$17$	13.6029	−	13.6029i	0.800170	−	0.800170i	−0.182952	−	0.983122i	$-0.558565\pi$
$17$	13.6029	−	13.6029i	0.800170	−	0.800170i	0.983122	+	0.182952i	$0.0585652\pi$
$18$		0			0
$19$		−	5.80704i		−	0.305634i	−0.988255	−	0.152817i	$-0.951166\pi$
$19$		−	5.80704i		−	0.305634i	0.988255	−	0.152817i	$-0.0488345\pi$
$20$	−6.18418	−	9.12327i	−0.309209	−	0.456163i
$21$		0			0
$22$	16.2847	−	16.2847i	0.740212	−	0.740212i
$23$	−32.0648	−	32.0648i	−1.39412	−	1.39412i	−0.815834	−	0.578286i	$-0.803722\pi$
$23$	−32.0648	−	32.0648i	−1.39412	−	1.39412i	−0.578286	−	0.815834i	$-0.696278\pi$
$24$		0			0
$25$	9.25886	−	23.2223i	0.370354	−	0.928891i
$26$	−32.5958			−1.25368
$27$		0			0
$28$	−0.106208	−	0.106208i	−0.00379316	−	0.00379316i
$29$		−	7.35801i		−	0.253724i	−0.991920	−	0.126862i	$-0.959509\pi$
$29$		−	7.35801i		−	0.253724i	0.991920	−	0.126862i	$-0.0404906\pi$
$30$		0			0
$31$	16.7073			0.538944			0.269472	−	0.963008i	$-0.413151\pi$
$31$	16.7073			0.538944			0.269472	+	0.963008i	$0.413151\pi$
$32$	−22.5017	+	22.5017i	−0.703177	+	0.703177i
$33$		0			0
$34$			47.9175i			1.40934i
$35$	0.0642412	−	0.334583i	0.00183546	−	0.00955951i
$36$		0			0
$37$	36.0680	−	36.0680i	0.974810	−	0.974810i	−0.0248806	−	0.999690i	$-0.507921\pi$
$37$	36.0680	−	36.0680i	0.974810	−	0.974810i	0.999690	+	0.0248806i	$0.00792055\pi$
$38$	10.2279	+	10.2279i	0.269156	+	0.269156i
$39$		0			0
$40$	−21.9624	−	4.21687i	−0.549061	−	0.105422i
$41$	62.3133			1.51984			0.759919	−	0.650018i	$-0.225239\pi$
$41$	62.3133			1.51984			0.759919	+	0.650018i	$0.225239\pi$
$42$		0			0
$43$	−7.10279	−	7.10279i	−0.165181	−	0.165181i	0.619676	−	0.784857i	$-0.287264\pi$
$43$	−7.10279	−	7.10279i	−0.165181	−	0.165181i	−0.784857	+	0.619676i	$0.787264\pi$
$44$			20.3810i			0.463204i
$45$		0			0
$46$	112.951			2.45546
$47$	32.6843	−	32.6843i	0.695410	−	0.695410i	−0.268007	−	0.963417i	$-0.586365\pi$
$47$	32.6843	−	32.6843i	0.695410	−	0.695410i	0.963417	+	0.268007i	$0.0863650\pi$
$48$		0			0
$49$			48.9954i			0.999905i
$50$	24.5937	+	57.2089i	0.491874	+	1.14418i
$51$		0			0
$52$	20.3975	−	20.3975i	0.392260	−	0.392260i
$53$	28.0258	+	28.0258i	0.528789	+	0.528789i	0.920211	−	0.391423i	$-0.128017\pi$
$53$	28.0258	+	28.0258i	0.528789	+	0.528789i	−0.391423	+	0.920211i	$0.628017\pi$
$54$		0			0
$55$	−38.2664	+	25.9388i	−0.695753	+	0.471614i
$56$	−0.304766			−0.00544225
$57$		0			0
$58$	12.9596	+	12.9596i	0.223442	+	0.223442i
$59$			18.8804i			0.320007i	0.987116	+	0.160004i	$0.0511506\pi$
$59$			18.8804i			0.320007i	−0.987116	+	0.160004i	$0.948849\pi$
$60$		0			0
$61$	−5.39094			−0.0883761			−0.0441881	−	0.999023i	$-0.514070\pi$
$61$	−5.39094			−0.0883761			−0.0441881	+	0.999023i	$0.514070\pi$
$62$	−29.4265	+	29.4265i	−0.474621	+	0.474621i
$63$		0			0
$64$			0.568692i			0.00888582i
$65$	64.2573	+	12.3376i	0.988574	+	0.189810i
$66$		0			0
$67$	35.0738	−	35.0738i	0.523489	−	0.523489i	−0.395134	−	0.918623i	$-0.629302\pi$
$67$	35.0738	−	35.0738i	0.523489	−	0.523489i	0.918623	+	0.395134i	$0.129302\pi$
$68$	−29.9854	−	29.9854i	−0.440962	−	0.440962i
$69$		0			0
$70$	0.476152	+	0.702448i	0.00680217	+	0.0100350i
$71$	56.4200			0.794648			0.397324	−	0.917678i	$-0.369939\pi$
$71$	56.4200			0.794648			0.397324	+	0.917678i	$0.369939\pi$
$72$		0			0
$73$	−54.7135	−	54.7135i	−0.749500	−	0.749500i	0.224885	−	0.974385i	$-0.427799\pi$
$73$	−54.7135	−	54.7135i	−0.749500	−	0.749500i	−0.974385	+	0.224885i	$0.927799\pi$
$74$			127.053i			1.71693i
$75$		0			0
$76$	−12.8007			−0.168430
$77$	−0.445478	+	0.445478i	−0.00578542	+	0.00578542i
$78$		0			0
$79$			47.3071i			0.598825i	0.954124	+	0.299412i	$0.0967906\pi$
$79$			47.3071i			0.598825i	−0.954124	+	0.299412i	$0.903209\pi$
$80$	82.6026	−	55.9919i	1.03253	−	0.699899i
$81$		0			0
$82$	−109.752	+	109.752i	−1.33844	+	1.33844i
$83$	−43.9426	−	43.9426i	−0.529429	−	0.529429i	0.390973	−	0.920402i	$-0.372138\pi$
$83$	−43.9426	−	43.9426i	−0.529429	−	0.529429i	−0.920402	+	0.390973i	$0.872138\pi$
$84$		0			0
$85$	18.1370	−	94.4615i	0.213376	−	1.11131i
$86$	25.0203			0.290933
$87$		0			0
$88$	29.2417	+	29.2417i	0.332292	+	0.332292i
$89$			59.1599i			0.664718i	0.943153	+	0.332359i	$0.107844\pi$
$89$			59.1599i			0.664718i	−0.943153	+	0.332359i	$0.892156\pi$
$90$		0			0
$91$	0.891679			0.00979867
$92$	−70.6817	+	70.6817i	−0.768280	+	0.768280i
$93$		0			0
$94$			115.134i			1.22482i
$95$	−16.2914	−	24.0340i	−0.171488	−	0.252990i
$96$		0			0
$97$	109.991	−	109.991i	1.13393	−	1.13393i	0.144411	−	0.989518i	$-0.453871\pi$
$97$	109.991	−	109.991i	1.13393	−	1.13393i	0.989518	−	0.144411i	$-0.0461289\pi$
$98$	−86.2954	−	86.2954i	−0.880566	−	0.880566i
$99$		0			0
$100$	−51.1898	−	20.4097i	−0.511898	−	0.204097i
$101$	−55.2105			−0.546639			−0.273319	−	0.961923i	$-0.588122\pi$
$101$	−55.2105			−0.546639			−0.273319	+	0.961923i	$0.588122\pi$
$102$		0			0
$103$	−64.6560	−	64.6560i	−0.627729	−	0.627729i	0.319767	−	0.947496i	$-0.396395\pi$
$103$	−64.6560	−	64.6560i	−0.627729	−	0.627729i	−0.947496	+	0.319767i	$0.896395\pi$
$104$		−	58.5309i		−	0.562797i
$105$		0			0
$106$	−98.7236			−0.931354
$107$	−14.6336	+	14.6336i	−0.136762	+	0.136762i	−0.772174	−	0.635411i	$-0.780831\pi$
$107$	−14.6336	+	14.6336i	−0.136762	+	0.136762i	0.635411	+	0.772174i	$0.280831\pi$
$108$		0			0
$109$			112.055i			1.02803i	0.857781	+	0.514015i	$0.171843\pi$
$109$			112.055i			1.02803i	−0.857781	+	0.514015i	$0.828157\pi$
$110$	21.7126	−	113.084i	0.197388	−	1.02804i
$111$		0			0
$112$	0.961617	−	0.961617i	0.00858586	−	0.00858586i
$113$	26.2214	+	26.2214i	0.232048	+	0.232048i	0.813547	−	0.581499i	$-0.197534\pi$
$113$	26.2214	+	26.2214i	0.232048	+	0.232048i	−0.581499	+	0.813547i	$0.697534\pi$
$114$		0			0
$115$	−222.665	−	42.7525i	−1.93622	−	0.371761i
$116$	−16.2196			−0.139824
$117$		0			0
$118$	−33.2541	−	33.2541i	−0.281814	−	0.281814i
$119$		−	1.31081i		−	0.0110152i
$120$		0			0
$121$	−35.5146			−0.293509
$122$	9.49506	−	9.49506i	0.0778284	−	0.0778284i
$123$		0			0
$124$		−	36.8285i		−	0.297004i
$125$	−26.8287	−	122.087i	−0.214629	−	0.976696i
$126$		0			0
$127$	151.793	−	151.793i	1.19522	−	1.19522i	0.219643	−	0.975580i	$-0.429511\pi$
$127$	151.793	−	151.793i	1.19522	−	1.19522i	0.975580	−	0.219643i	$-0.0704892\pi$
$128$	−91.0083	−	91.0083i	−0.711002	−	0.711002i
$129$		0			0
$130$	−134.907	+	91.4460i	−1.03774	+	0.703431i
$131$	1.50290			0.0114725			0.00573624	−	0.999984i	$-0.498174\pi$
$131$	1.50290			0.0114725			0.00573624	+	0.999984i	$0.498174\pi$
$132$		0			0
$133$	−0.279792	−	0.279792i	−0.00210370	−	0.00210370i
$134$			123.551i			0.922021i
$135$		0			0
$136$	−86.0434			−0.632672
$137$	−49.3914	+	49.3914i	−0.360521	+	0.360521i	−0.864005	−	0.503484i	$-0.832051\pi$
$137$	−49.3914	+	49.3914i	−0.360521	+	0.360521i	0.503484	+	0.864005i	$0.332051\pi$
$138$		0			0
$139$		−	122.782i		−	0.883322i	−0.897182	−	0.441661i	$-0.854389\pi$
$139$		−	122.782i		−	0.883322i	0.897182	−	0.441661i	$-0.145611\pi$
$140$	−0.737535	−	0.141610i	−0.00526811	−	0.00101150i
$141$		0			0
$142$	−99.3724	+	99.3724i	−0.699806	+	0.699806i
$143$	−85.5549	−	85.5549i	−0.598286	−	0.598286i
$144$		0			0
$145$	−20.6426	−	30.4531i	−0.142362	−	0.210021i
$146$	192.734			1.32009
$147$		0			0
$148$	−79.5061	−	79.5061i	−0.537204	−	0.537204i
$149$		−	26.5685i		−	0.178312i	−0.996018	−	0.0891560i	$-0.971583\pi$
$149$		−	26.5685i		−	0.178312i	0.996018	−	0.0891560i	$-0.0284170\pi$
$150$		0			0
$151$	98.4829			0.652204			0.326102	−	0.945335i	$-0.394265\pi$
$151$	98.4829			0.652204			0.326102	+	0.945335i	$0.394265\pi$
$152$	−18.3659	+	18.3659i	−0.120828	+	0.120828i
$153$		0			0
$154$		−	1.56924i		−	0.0101899i
$155$	69.1476	−	46.8715i	0.446113	−	0.302397i
$156$		0			0
$157$	−122.114	+	122.114i	−0.777796	+	0.777796i	−0.979456	−	0.201659i	$-0.935367\pi$
$157$	−122.114	+	122.114i	−0.777796	+	0.777796i	0.201659	+	0.979456i	$0.435367\pi$
$158$	−83.3220	−	83.3220i	−0.527354	−	0.527354i
$159$		0			0
$160$	−30.0019	+	156.257i	−0.187512	+	0.976604i
$161$	−3.08985			−0.0191916
$162$		0			0
$163$	−65.0824	−	65.0824i	−0.399278	−	0.399278i	0.478700	−	0.877978i	$-0.341108\pi$
$163$	−65.0824	−	65.0824i	−0.399278	−	0.399278i	−0.877978	+	0.478700i	$0.841108\pi$
$164$		−	137.360i		−	0.837560i
$165$		0			0
$166$	154.792			0.932482
$167$	−141.256	+	141.256i	−0.845845	+	0.845845i	−0.989612	−	0.143766i	$-0.954079\pi$
$167$	−141.256	+	141.256i	−0.845845	+	0.845845i	0.143766	+	0.989612i	$0.454079\pi$
$168$		0			0
$169$			2.24880i			0.0133065i
$170$	134.430	+	198.320i	0.790767	+	1.16659i
$171$		0			0
$172$	−15.6570	+	15.6570i	−0.0910290	+	0.0910290i
$173$	24.4507	+	24.4507i	0.141334	+	0.141334i	0.774234	−	0.632900i	$-0.218136\pi$
$173$	24.4507	+	24.4507i	0.141334	+	0.141334i	−0.632900	+	0.774234i	$0.718136\pi$
$174$		0			0
$175$	−0.672777	−	1.56499i	−0.00384444	−	0.00894278i
$176$	−184.531			−1.04847
$177$		0			0
$178$	−104.198	−	104.198i	−0.585383	−	0.585383i
$179$		−	185.962i		−	1.03890i	−0.854502	−	0.519448i	$-0.826138\pi$
$179$		−	185.962i		−	1.03890i	0.854502	−	0.519448i	$-0.173862\pi$
$180$		0			0
$181$	−97.7851			−0.540249			−0.270125	−	0.962825i	$-0.587065\pi$
$181$	−97.7851			−0.540249			−0.270125	+	0.962825i	$0.587065\pi$
$182$	−1.57051	+	1.57051i	−0.00862919	+	0.00862919i
$183$		0			0
$184$			202.822i			1.10229i
$185$	48.0901	−	250.464i	0.259946	−	1.35386i
$186$		0			0
$187$	−125.770	+	125.770i	−0.672567	+	0.672567i
$188$	−72.0473	−	72.0473i	−0.383231	−	0.383231i
$189$		0			0
$190$	71.0251	+	13.6371i	0.373816	+	0.0717741i
$191$	136.418			0.714231			0.357115	−	0.934060i	$-0.383760\pi$
$191$	136.418			0.714231			0.357115	+	0.934060i	$0.383760\pi$
$192$		0			0
$193$	65.3098	+	65.3098i	0.338393	+	0.338393i	0.855762	−	0.517369i	$-0.173089\pi$
$193$	65.3098	+	65.3098i	0.338393	+	0.338393i	−0.517369	+	0.855762i	$0.673089\pi$
$194$			387.454i			1.99719i
$195$		0			0
$196$	108.003			0.551033
$197$	−170.623	+	170.623i	−0.866107	+	0.866107i	−0.992039	−	0.125932i	$-0.959808\pi$
$197$	−170.623	+	170.623i	−0.866107	+	0.866107i	0.125932	+	0.992039i	$0.459808\pi$
$198$		0			0
$199$			36.4196i			0.183013i	0.995804	+	0.0915066i	$0.0291683\pi$
$199$			36.4196i			0.183013i	−0.995804	+	0.0915066i	$0.970832\pi$
$200$	−102.728	+	44.1619i	−0.513638	+	0.220809i
$201$		0			0
$202$	97.2422	−	97.2422i	0.481397	−	0.481397i
$203$	−0.354519	−	0.354519i	−0.00174640	−	0.00174640i
$204$		0			0
$205$	257.901	−	174.817i	1.25805	−	0.852767i
$206$	227.757			1.10562
$207$		0			0
$208$	184.681	+	184.681i	0.887887	+	0.887887i
$209$			53.6910i			0.256895i
$210$		0			0
$211$	−193.607			−0.917567			−0.458784	−	0.888548i	$-0.651715\pi$
$211$	−193.607			−0.917567			−0.458784	+	0.888548i	$0.651715\pi$
$212$	61.7784	−	61.7784i	0.291408	−	0.291408i
$213$		0			0
$214$		−	51.5481i		−	0.240879i
$215$	−49.3234	−	9.47028i	−0.229411	−	0.0440478i
$216$		0			0
$217$	0.804980	−	0.804980i	0.00370959	−	0.00370959i
$218$	−197.363	−	197.363i	−0.905334	−	0.905334i
$219$		0			0
$220$	57.1779	+	84.3522i	0.259900	+	0.383419i
$221$	251.745			1.13912
$222$		0			0
$223$	−67.7006	−	67.7006i	−0.303590	−	0.303590i	0.538826	−	0.842417i	$-0.318868\pi$
$223$	−67.7006	−	67.7006i	−0.303590	−	0.303590i	−0.842417	+	0.538826i	$0.818868\pi$
$224$			2.16833i			0.00968002i
$225$		0			0
$226$	−92.3675			−0.408706
$227$	−232.952	+	232.952i	−1.02622	+	1.02622i	−0.0265741	+	0.999647i	$0.508460\pi$
$227$	−232.952	+	232.952i	−1.02622	+	1.02622i	−0.999647	+	0.0265741i	$0.991540\pi$
$228$		0			0
$229$		−	415.987i		−	1.81654i	−0.418386	−	0.908269i	$-0.637404\pi$
$229$		−	415.987i		−	1.81654i	0.418386	−	0.908269i	$-0.362596\pi$
$230$	467.479	−	316.879i	2.03252	−	1.37774i
$231$		0			0
$232$	−23.2711	+	23.2711i	−0.100306	+	0.100306i
$233$	−22.0213	−	22.0213i	−0.0945121	−	0.0945121i	0.658270	−	0.752782i	$-0.271289\pi$
$233$	−22.0213	−	22.0213i	−0.0945121	−	0.0945121i	−0.752782	+	0.658270i	$0.771289\pi$
$234$		0			0
$235$	43.5785	−	226.967i	0.185441	−	0.965817i
$236$	41.6190			0.176352
$237$		0			0
$238$	2.30873	+	2.30873i	0.00970056	+	0.00970056i
$239$			308.942i			1.29265i	0.763064	+	0.646323i	$0.223694\pi$
$239$			308.942i			1.29265i	−0.763064	+	0.646323i	$0.776306\pi$
$240$		0			0
$241$	25.7138			0.106696			0.0533481	−	0.998576i	$-0.483011\pi$
$241$	25.7138			0.106696			0.0533481	+	0.998576i	$0.483011\pi$
$242$	62.5517	−	62.5517i	0.258478	−	0.258478i
$243$		0			0
$244$			11.8835i			0.0487028i
$245$	137.454	+	202.781i	0.561038	+	0.827676i
$246$		0			0
$247$	53.7346	−	53.7346i	0.217549	−	0.217549i
$248$	−52.8399	−	52.8399i	−0.213064	−	0.213064i
$249$		0			0
$250$	262.285	+	167.778i	1.04914	+	0.671113i
$251$	275.877			1.09911			0.549556	−	0.835457i	$-0.314797\pi$
$251$	275.877			1.09911			0.549556	+	0.835457i	$0.314797\pi$
$252$		0			0
$253$	296.465	+	296.465i	1.17180	+	1.17180i
$254$			534.707i			2.10514i
$255$		0			0
$256$	318.311			1.24340
$257$	4.52408	−	4.52408i	0.0176034	−	0.0176034i	−0.698250	−	0.715854i	$-0.746038\pi$
$257$	4.52408	−	4.52408i	0.0176034	−	0.0176034i	0.715854	+	0.698250i	$0.246038\pi$
$258$		0			0
$259$		−	3.47561i		−	0.0134194i
$260$	27.1964	−	141.645i	0.104602	−	0.544789i
$261$		0			0
$262$	−2.64705	+	2.64705i	−0.0101032	+	0.0101032i
$263$	150.253	+	150.253i	0.571304	+	0.571304i	0.932493	−	0.361189i	$-0.117629\pi$
$263$	150.253	+	150.253i	0.571304	+	0.571304i	−0.361189	+	0.932493i	$0.617629\pi$
$264$		0			0
$265$	194.617	+	37.3673i	0.734405	+	0.141009i
$266$	0.985593			0.00370524
$267$		0			0
$268$	−77.3147	−	77.3147i	−0.288488	−	0.288488i
$269$			349.046i			1.29757i	0.760973	+	0.648784i	$0.224722\pi$
$269$			349.046i			1.29757i	−0.760973	+	0.648784i	$0.775278\pi$
$270$		0			0
$271$	−202.277			−0.746409			−0.373205	−	0.927749i	$-0.621741\pi$
$271$	−202.277			−0.746409			−0.373205	+	0.927749i	$0.621741\pi$
$272$	271.490	−	271.490i	0.998124	−	0.998124i
$273$		0			0
$274$		−	173.986i		−	0.634985i
$275$	−85.6059	+	214.709i	−0.311294	+	0.780761i
$276$		0			0
$277$	171.573	−	171.573i	0.619397	−	0.619397i	−0.325980	−	0.945377i	$-0.605694\pi$
$277$	171.573	−	171.573i	0.619397	−	0.619397i	0.945377	+	0.325980i	$0.105694\pi$
$278$	216.255	+	216.255i	0.777897	+	0.777897i
$279$		0			0
$280$	−1.26136	+	0.855006i	−0.00450484	+	0.00305359i
$281$	−280.320			−0.997579			−0.498789	−	0.866723i	$-0.666222\pi$
$281$	−280.320			−0.997579			−0.498789	+	0.866723i	$0.666222\pi$
$282$		0			0
$283$	272.825	+	272.825i	0.964047	+	0.964047i	0.999376	−	0.0353287i	$-0.0112478\pi$
$283$	272.825	+	272.825i	0.964047	+	0.964047i	−0.0353287	+	0.999376i	$0.511248\pi$
$284$		−	124.369i		−	0.437919i
$285$		0			0
$286$	301.375			1.05376
$287$	3.00235	−	3.00235i	0.0104611	−	0.0104611i
$288$		0			0
$289$		−	81.0774i		−	0.280545i
$290$	89.9947	+	17.2793i	0.310327	+	0.0595839i
$291$		0			0
$292$	−120.607	+	120.607i	−0.413039	+	0.413039i
$293$	−29.8714	−	29.8714i	−0.101950	−	0.101950i	0.654292	−	0.756242i	$-0.272967\pi$
$293$	−29.8714	−	29.8714i	−0.101950	−	0.101950i	−0.756242	+	0.654292i	$0.772967\pi$
$294$		0			0
$295$	52.9682	+	78.1418i	0.179553	+	0.264888i
$296$	−228.143			−0.770755
$297$		0			0
$298$	46.7950	+	46.7950i	0.157030	+	0.157030i
$299$		−	593.413i		−	1.98466i
$300$		0			0
$301$	−0.684445			−0.00227390
$302$	−173.458	+	173.458i	−0.574363	+	0.574363i
$303$		0			0
$304$		−	115.898i		−	0.381245i
$305$	−22.3119	+	15.1240i	−0.0731537	+	0.0495870i
$306$		0			0
$307$	−85.1111	+	85.1111i	−0.277235	+	0.277235i	−0.832004	−	0.554769i	$-0.812806\pi$
$307$	−85.1111	+	85.1111i	−0.277235	+	0.277235i	0.554769	+	0.832004i	$0.312806\pi$
$308$	0.981985	+	0.981985i	0.00318826	+	0.00318826i
$309$		0			0
$310$	−39.2348	+	204.344i	−0.126564	+	0.659174i
$311$	−454.186			−1.46040			−0.730202	−	0.683231i	$-0.760574\pi$
$311$	−454.186			−1.46040			−0.730202	+	0.683231i	$0.760574\pi$
$312$		0			0
$313$	210.100	+	210.100i	0.671245	+	0.671245i	0.958003	−	0.286758i	$-0.0925777\pi$
$313$	210.100	+	210.100i	0.671245	+	0.671245i	−0.286758	+	0.958003i	$0.592578\pi$
$314$		−	430.158i		−	1.36993i
$315$		0			0
$316$	104.281			0.330004
$317$	−62.5145	+	62.5145i	−0.197207	+	0.197207i	−0.798801	−	0.601595i	$-0.794532\pi$
$317$	−62.5145	+	62.5145i	−0.197207	+	0.197207i	0.601595	+	0.798801i	$0.294532\pi$
$318$		0			0
$319$			68.0309i			0.213263i
$320$	1.59544	+	2.35369i	0.00498575	+	0.00735527i
$321$		0			0
$322$	5.44215	−	5.44215i	0.0169011	−	0.0169011i
$323$	−78.9926	−	78.9926i	−0.244559	−	0.244559i
$324$		0			0
$325$	300.559	−	129.208i	0.924797	−	0.397564i
$326$	229.259			0.703248
$327$		0			0
$328$	−197.078	−	197.078i	−0.600846	−	0.600846i
$329$		−	3.14955i		−	0.00957310i
$330$		0			0
$331$	−446.304			−1.34835			−0.674175	−	0.738572i	$-0.735500\pi$
$331$	−446.304			−1.34835			−0.674175	+	0.738572i	$0.735500\pi$
$332$	−96.8645	+	96.8645i	−0.291761	+	0.291761i
$333$		0			0
$334$		−	497.589i		−	1.48979i
$335$	46.7645	−	243.560i	0.139596	−	0.727046i
$336$		0			0
$337$	20.7140	−	20.7140i	0.0614658	−	0.0614658i	−0.675706	−	0.737171i	$-0.736161\pi$
$337$	20.7140	−	20.7140i	0.0614658	−	0.0614658i	0.737171	+	0.675706i	$0.236161\pi$
$338$	−3.96080	−	3.96080i	−0.0117184	−	0.0117184i
$339$		0			0
$340$	−208.226	−	39.9801i	−0.612428	−	0.117589i
$341$	−154.473			−0.452999
$342$		0			0
$343$	4.72156	+	4.72156i	0.0137655	+	0.0137655i
$344$			44.9278i			0.130604i
$345$		0			0
$346$	−86.1300			−0.248931
$347$	238.766	−	238.766i	0.688085	−	0.688085i	−0.273723	−	0.961809i	$-0.588255\pi$
$347$	238.766	−	238.766i	0.688085	−	0.688085i	0.961809	+	0.273723i	$0.0882552\pi$
$348$		0			0
$349$			59.4572i			0.170365i	0.996365	+	0.0851823i	$0.0271473\pi$
$349$			59.4572i			0.170365i	−0.996365	+	0.0851823i	$0.972853\pi$
$350$	3.94137	+	1.57145i	0.0112611	+	0.00448985i
$351$		0			0
$352$	208.047	−	208.047i	0.591042	−	0.591042i
$353$	−376.586	−	376.586i	−1.06682	−	1.06682i	−0.997602	−	0.0692134i	$-0.977951\pi$
$353$	−376.586	−	376.586i	−1.06682	−	1.06682i	−0.0692134	−	0.997602i	$-0.522049\pi$
$354$		0			0
$355$	233.509	−	158.284i	0.657773	−	0.445870i
$356$	130.409			0.366316
$357$		0			0
$358$	327.535	+	327.535i	0.914902	+	0.914902i
$359$			342.196i			0.953192i	0.879122	+	0.476596i	$0.158130\pi$
$359$			342.196i			0.953192i	−0.879122	+	0.476596i	$0.841870\pi$
$360$		0			0
$361$	327.278			0.906588
$362$	172.229	−	172.229i	0.475770	−	0.475770i
$363$		0			0
$364$		−	1.96557i		−	0.00539991i
$365$	−379.943	−	72.9505i	−1.04094	−	0.199864i
$366$		0			0
$367$	−260.251	+	260.251i	−0.709131	+	0.709131i	−0.966352	−	0.257222i	$-0.917193\pi$
$367$	−260.251	+	260.251i	−0.709131	+	0.709131i	0.257222	+	0.966352i	$0.417193\pi$
$368$	−639.956	−	639.956i	−1.73901	−	1.73901i
$369$		0			0
$370$	356.441	+	525.843i	0.963354	+	1.42120i
$371$	2.70065			0.00727937
$372$		0			0
$373$	235.355	+	235.355i	0.630978	+	0.630978i	0.948313	−	0.317335i	$-0.102788\pi$
$373$	235.355	+	235.355i	0.630978	+	0.630978i	−0.317335	+	0.948313i	$0.602788\pi$
$374$		−	443.037i		−	1.18459i
$375$		0			0
$376$	−206.740			−0.549841
$377$	68.0862	−	68.0862i	0.180600	−	0.180600i
$378$		0			0
$379$			203.700i			0.537466i	0.963215	+	0.268733i	$0.0866049\pi$
$379$			203.700i			0.537466i	−0.963215	+	0.268733i	$0.913395\pi$
$380$	−52.9792	+	35.9118i	−0.139419	+	0.0945047i
$381$		0			0
$382$	−240.273	+	240.273i	−0.628986	+	0.628986i
$383$	−14.6312	−	14.6312i	−0.0382015	−	0.0382015i	0.687748	−	0.725949i	$-0.258599\pi$
$383$	−14.6312	−	14.6312i	−0.0382015	−	0.0382015i	−0.725949	+	0.687748i	$0.758599\pi$
$384$		0			0
$385$	−0.593963	+	3.09350i	−0.00154276	+	0.00803505i
$386$	−230.060			−0.596010
$387$		0			0
$388$	−242.458	−	242.458i	−0.624892	−	0.624892i
$389$			185.259i			0.476245i	0.971235	+	0.238123i	$0.0765320\pi$
$389$			185.259i			0.476245i	−0.971235	+	0.238123i	$0.923468\pi$
$390$		0			0
$391$	−872.347			−2.23107
$392$	154.957	−	154.957i	0.395299	−	0.395299i
$393$		0			0
$394$		−	601.036i		−	1.52547i
$395$	132.718	+	195.793i	0.335995	+	0.495680i
$396$		0			0
$397$	−236.474	+	236.474i	−0.595652	+	0.595652i	−0.939152	−	0.343501i	$-0.888387\pi$
$397$	−236.474	+	236.474i	−0.595652	+	0.595652i	0.343501	+	0.939152i	$0.388387\pi$
$398$	−64.1458	−	64.1458i	−0.161170	−	0.161170i
$399$		0			0
$400$	184.791	−	463.476i	0.461976	−	1.15869i
$401$	68.0750			0.169763			0.0848816	−	0.996391i	$-0.472949\pi$
$401$	68.0750			0.169763			0.0848816	+	0.996391i	$0.472949\pi$
$402$		0			0
$403$	154.598	+	154.598i	0.383618	+	0.383618i
$404$			121.703i			0.301245i
$405$		0			0
$406$	1.24883			0.00307593
$407$	−333.478	+	333.478i	−0.819357	+	0.819357i
$408$		0			0
$409$			377.022i			0.921814i	0.887448	+	0.460907i	$0.152476\pi$
$409$			377.022i			0.921814i	−0.887448	+	0.460907i	$0.847524\pi$
$410$	−146.335	+	762.145i	−0.356914	+	1.85889i
$411$		0			0
$412$	−142.524	+	142.524i	−0.345932	+	0.345932i
$413$	0.909687	+	0.909687i	0.00220263	+	0.00220263i
$414$		0			0
$415$	−305.147	−	58.5894i	−0.735295	−	0.141179i
$416$	−416.431			−1.00104
$417$		0			0
$418$	−94.5658	−	94.5658i	−0.226234	−	0.226234i
$419$		−	228.659i		−	0.545726i	−0.962053	−	0.272863i	$-0.912029\pi$
$419$		−	228.659i		−	0.545726i	0.962053	−	0.272863i	$-0.0879706\pi$
$420$		0			0
$421$	−409.788			−0.973368			−0.486684	−	0.873578i	$-0.661794\pi$
$421$	−409.788			−0.973368			−0.486684	+	0.873578i	$0.661794\pi$
$422$	340.999	−	340.999i	0.808055	−	0.808055i
$423$		0			0
$424$		−	177.274i		−	0.418098i
$425$	−189.943	−	441.837i	−0.446924	−	1.03962i
$426$		0			0
$427$	−0.259743	+	0.259743i	−0.000608298	+	0.000608298i
$428$	32.2574	+	32.2574i	0.0753677	+	0.0753677i
$429$		0			0
$430$	103.553	−	70.1932i	0.240821	−	0.163240i
$431$	46.4787			0.107839			0.0539196	−	0.998545i	$-0.482829\pi$
$431$	46.4787			0.107839			0.0539196	+	0.998545i	$0.482829\pi$
$432$		0			0
$433$	−430.638	−	430.638i	−0.994544	−	0.994544i	0.00544093	−	0.999985i	$-0.498268\pi$
$433$	−430.638	−	430.638i	−0.994544	−	0.994544i	−0.999985	+	0.00544093i	$0.998268\pi$
$434$			2.83562i			0.00653369i
$435$		0			0
$436$	247.008			0.566533
$437$	−186.201	+	186.201i	−0.426090	+	0.426090i
$438$		0			0
$439$		−	387.208i		−	0.882024i	−0.897501	−	0.441012i	$-0.854620\pi$
$439$		−	387.208i		−	0.882024i	0.897501	−	0.441012i	$-0.145380\pi$
$440$	203.061	+	38.9885i	0.461502	+	0.0886101i
$441$		0			0
$442$	−443.397	+	443.397i	−1.00316	+	1.00316i
$443$	518.766	+	518.766i	1.17103	+	1.17103i	0.981965	+	0.189065i	$0.0605456\pi$
$443$	518.766	+	518.766i	1.17103	+	1.17103i	0.189065	+	0.981965i	$0.439454\pi$
$444$		0			0
$445$	165.970	+	244.849i	0.372967	+	0.550223i
$446$	238.482			0.534713
$447$		0			0
$448$	0.0274004	+	0.0274004i	6.11616e−5	+	6.11616e-5i
$449$		−	141.098i		−	0.314250i	−0.987579	−	0.157125i	$-0.949777\pi$
$449$		−	141.098i		−	0.314250i	0.987579	−	0.157125i	$-0.0502226\pi$
$450$		0			0
$451$	−576.139			−1.27747
$452$	57.8010	−	57.8010i	0.127878	−	0.127878i
$453$		0			0
$454$		−	820.596i		−	1.80748i
$455$	3.69046	−	2.50156i	0.00811089	−	0.00549794i
$456$		0			0
$457$	519.210	−	519.210i	1.13613	−	1.13613i	0.146989	−	0.989138i	$-0.453042\pi$
$457$	519.210	−	519.210i	1.13613	−	1.13613i	0.989138	−	0.146989i	$-0.0469581\pi$
$458$	732.678	+	732.678i	1.59973	+	1.59973i
$459$		0			0
$460$	−94.2412	+	490.830i	−0.204872	+	1.06702i
$461$	642.082			1.39280			0.696402	−	0.717652i	$-0.254783\pi$
$461$	642.082			1.39280			0.696402	+	0.717652i	$0.254783\pi$
$462$		0			0
$463$	−196.256	−	196.256i	−0.423879	−	0.423879i	0.462658	−	0.886537i	$-0.346896\pi$
$463$	−196.256	−	196.256i	−0.423879	−	0.423879i	−0.886537	+	0.462658i	$0.846896\pi$
$464$		−	146.853i		−	0.316493i
$465$		0			0
$466$	77.5722			0.166464
$467$	−57.4439	+	57.4439i	−0.123006	+	0.123006i	−0.765930	−	0.642924i	$-0.777721\pi$
$467$	−57.4439	+	57.4439i	−0.123006	+	0.123006i	0.642924	+	0.765930i	$0.277721\pi$
$468$		0			0
$469$		−	3.37981i		−	0.00720642i
$470$	323.002	+	476.511i	0.687238	+	1.01385i
$471$		0			0
$472$	59.7130	−	59.7130i	0.126510	−	0.126510i
$473$	65.6712	+	65.6712i	0.138840	+	0.138840i
$474$		0			0
$475$	−134.853	−	53.7666i	−0.283900	−	0.113193i
$476$	−2.88948			−0.00607034
$477$		0			0
$478$	−544.139	−	544.139i	−1.13837	−	1.13837i
$479$			484.198i			1.01085i	0.862870	+	0.505426i	$0.168665\pi$
$479$			484.198i			1.01085i	−0.862870	+	0.505426i	$0.831335\pi$
$480$		0			0
$481$	667.499			1.38773
$482$	−45.2896	+	45.2896i	−0.0939618	+	0.0939618i
$483$		0			0
$484$			78.2863i			0.161748i
$485$	146.653	−	763.803i	0.302378	−	1.57485i
$486$		0			0
$487$	−162.179	+	162.179i	−0.333017	+	0.333017i	−0.853731	−	0.520714i	$-0.825666\pi$
$487$	−162.179	+	162.179i	−0.333017	+	0.333017i	0.520714	+	0.853731i	$0.325666\pi$
$488$	17.0499	+	17.0499i	0.0349383	+	0.0349383i
$489$		0			0
$490$	−599.255	−	115.059i	−1.22297	−	0.234815i
$491$	790.045			1.60905			0.804527	−	0.593916i	$-0.202419\pi$
$491$	790.045			1.60905			0.804527	+	0.593916i	$0.202419\pi$
$492$		0			0
$493$	−100.090	−	100.090i	−0.203023	−	0.203023i
$494$			189.285i			0.383168i
$495$		0			0
$496$	333.448			0.672274
$497$	2.71840	−	2.71840i	0.00546961	−	0.00546961i
$498$		0			0
$499$			487.702i			0.977359i	0.872463	+	0.488680i	$0.162521\pi$
$499$			487.702i			0.977359i	−0.872463	+	0.488680i	$0.837479\pi$
$500$	−269.121	+	59.1396i	−0.538243	+	0.118279i
$501$		0			0
$502$	−485.902	+	485.902i	−0.967931	+	0.967931i
$503$	346.274	+	346.274i	0.688418	+	0.688418i	0.961882	−	0.273465i	$-0.0881696\pi$
$503$	346.274	+	346.274i	0.688418	+	0.688418i	−0.273465	+	0.961882i	$0.588170\pi$
$504$		0			0
$505$	−228.504	+	154.891i	−0.452483	+	0.306714i
$506$	−1044.33			−2.06389
$507$		0			0
$508$	−334.605	−	334.605i	−0.658670	−	0.658670i
$509$		−	418.212i		−	0.821635i	−0.911718	−	0.410818i	$-0.865243\pi$
$509$		−	418.212i		−	0.821635i	0.911718	−	0.410818i	$-0.134757\pi$
$510$		0			0
$511$	−5.27235			−0.0103177
$512$	−196.607	+	196.607i	−0.383998	+	0.383998i
$513$		0			0
$514$			15.9365i			0.0310049i
$515$	−448.986	−	86.2070i	−0.871818	−	0.167392i
$516$		0			0
$517$	−302.193	+	302.193i	−0.584513	+	0.584513i
$518$	6.12159	+	6.12159i	0.0118177	+	0.0118177i
$519$		0			0
$520$	−164.206	−	242.246i	−0.315780	−	0.465858i
$521$	−17.3149			−0.0332341			−0.0166170	−	0.999862i	$-0.505290\pi$
$521$	−17.3149			−0.0332341			−0.0166170	+	0.999862i	$0.505290\pi$
$522$		0			0
$523$	577.571	+	577.571i	1.10434	+	1.10434i	0.993880	+	0.110462i	$0.0352329\pi$
$523$	577.571	+	577.571i	1.10434	+	1.10434i	0.110462	+	0.993880i	$0.464767\pi$
$524$		−	3.31290i		−	0.00632232i
$525$		0			0
$526$	−529.280			−1.00624
$527$	227.267	−	227.267i	0.431247	−	0.431247i
$528$		0			0
$529$			1527.30i			2.88714i
$530$	−408.594	+	276.964i	−0.770932	+	0.522574i
$531$		0			0
$532$	−0.616757	+	0.616757i	−0.00115932	+	0.00115932i
$533$	576.607	+	576.607i	1.08181	+	1.08181i
$534$		0			0
$535$	−19.5112	+	101.619i	−0.0364695	+	0.189942i
$536$	−221.855			−0.413909
$537$		0			0
$538$	−614.774	−	614.774i	−1.14270	−	1.14270i
$539$		−	453.003i		−	0.840451i
$540$		0			0
$541$	846.162			1.56407			0.782035	−	0.623234i	$-0.214182\pi$
$541$	846.162			1.56407			0.782035	+	0.623234i	$0.214182\pi$
$542$	356.270	−	356.270i	0.657325	−	0.657325i
$543$		0			0
$544$			612.175i			1.12532i
$545$	314.366	+	463.771i	0.576819	+	0.850957i
$546$		0			0
$547$	−48.3435	+	48.3435i	−0.0883794	+	0.0883794i	−0.749914	−	0.661535i	$-0.769905\pi$
$547$	−48.3435	+	48.3435i	−0.0883794	+	0.0883794i	0.661535	+	0.749914i	$0.269905\pi$
$548$	108.876	+	108.876i	0.198678	+	0.198678i
$549$		0			0
$550$	−227.389	−	528.944i	−0.413435	−	0.961717i
$551$	−42.7283			−0.0775468
$552$		0			0
$553$	2.27933	+	2.27933i	0.00412175	+	0.00412175i
$554$			604.382i			1.09094i
$555$		0			0
$556$	−270.653			−0.486786
$557$	367.003	−	367.003i	0.658893	−	0.658893i	−0.296225	−	0.955118i	$-0.595728\pi$
$557$	367.003	−	367.003i	0.658893	−	0.658893i	0.955118	+	0.296225i	$0.0957279\pi$
$558$		0			0
$559$		−	131.449i		−	0.235151i
$560$	1.28214	−	6.67768i	0.00228954	−	0.0119244i
$561$		0			0
$562$	493.726	−	493.726i	0.878517	−	0.878517i
$563$	222.509	+	222.509i	0.395221	+	0.395221i	0.876543	−	0.481323i	$-0.159843\pi$
$563$	222.509	+	222.509i	0.395221	+	0.395221i	−0.481323	+	0.876543i	$0.659843\pi$
$564$		0			0
$565$	182.088	+	34.9615i	0.322279	+	0.0618788i
$566$	−961.053			−1.69797
$567$		0			0
$568$	−178.439	−	178.439i	−0.314153	−	0.314153i
$569$		−	1019.36i		−	1.79149i	−0.444569	−	0.895745i	$-0.646643\pi$
$569$		−	1019.36i		−	1.79149i	0.444569	−	0.895745i	$-0.353357\pi$
$570$		0			0
$571$	−886.192			−1.55200			−0.776000	−	0.630733i	$-0.782754\pi$
$571$	−886.192			−1.55200			−0.776000	+	0.630733i	$0.782754\pi$
$572$	−188.592	+	188.592i	−0.329707	+	0.329707i
$573$		0			0
$574$			10.5761i			0.0184252i
$575$	−1041.50	+	447.733i	−1.81130	+	0.778667i
$576$		0			0
$577$	194.509	−	194.509i	0.337105	−	0.337105i	−0.518172	−	0.855277i	$-0.673387\pi$
$577$	194.509	−	194.509i	0.337105	−	0.337105i	0.855277	+	0.518172i	$0.173387\pi$
$578$	142.801	+	142.801i	0.247061	+	0.247061i
$579$		0			0
$580$	−67.1291	+	45.5033i	−0.115740	+	0.0784539i
$581$	−4.23443			−0.00728818
$582$		0			0
$583$	−259.122	−	259.122i	−0.444463	−	0.444463i
$584$			346.084i			0.592609i
$585$		0			0
$586$	105.225			0.179565
$587$	567.866	−	567.866i	0.967404	−	0.967404i	−0.0320810	−	0.999485i	$-0.510213\pi$
$587$	567.866	−	567.866i	0.967404	−	0.967404i	0.999485	+	0.0320810i	$0.0102135\pi$
$588$		0			0
$589$		−	97.0198i		−	0.164720i
$590$	−230.924	−	44.3383i	−0.391396	−	0.0751496i
$591$		0			0
$592$	719.853	−	719.853i	1.21597	−	1.21597i
$593$	572.308	+	572.308i	0.965106	+	0.965106i	0.999411	−	0.0343049i	$-0.0109217\pi$
$593$	572.308	+	572.308i	0.965106	+	0.965106i	−0.0343049	+	0.999411i	$0.510922\pi$
$594$		0			0
$595$	−3.67743	−	5.42516i	−0.00618055	−	0.00911791i
$596$	−58.5660			−0.0982652
$597$		0			0
$598$	1045.18	+	1045.18i	1.74779	+	1.74779i
$599$		−	303.915i		−	0.507371i	−0.967287	−	0.253685i	$-0.918357\pi$
$599$		−	303.915i		−	0.507371i	0.967287	−	0.253685i	$-0.0816428\pi$
$600$		0			0
$601$	104.190			0.173360			0.0866801	−	0.996236i	$-0.472374\pi$
$601$	104.190			0.173360			0.0866801	+	0.996236i	$0.472374\pi$
$602$	1.20551	−	1.20551i	0.00200251	−	0.00200251i
$603$		0			0
$604$		−	217.090i		−	0.359420i
$605$	−146.987	+	99.6345i	−0.242953	+	0.164685i
$606$		0			0
$607$	207.492	−	207.492i	0.341831	−	0.341831i	−0.515224	−	0.857055i	$-0.672291\pi$
$607$	207.492	−	207.492i	0.341831	−	0.341831i	0.857055	+	0.515224i	$0.172291\pi$
$608$	130.668	+	130.668i	0.214915	+	0.214915i
$609$		0			0
$610$	12.6599	−	65.9358i	0.0207540	−	0.108092i
$611$	604.878			0.989980
$612$		0			0
$613$	610.767	+	610.767i	0.996357	+	0.996357i	0.999993	−	0.00363596i	$-0.00115736\pi$
$613$	610.767	+	610.767i	0.996357	+	0.996357i	−0.00363596	+	0.999993i	$0.501157\pi$
$614$		−	299.812i		−	0.488293i
$615$		0			0
$616$	2.81781			0.00457437
$617$	−712.152	+	712.152i	−1.15422	+	1.15422i	−0.168519	+	0.985698i	$0.553898\pi$
$617$	−712.152	+	712.152i	−1.15422	+	1.15422i	−0.985698	+	0.168519i	$0.946102\pi$
$618$		0			0
$619$			218.751i			0.353395i	0.984265	+	0.176697i	$0.0565414\pi$
$619$			218.751i			0.353395i	−0.984265	+	0.176697i	$0.943459\pi$
$620$	−103.321	−	152.425i	−0.166646	−	0.245847i
$621$		0			0
$622$	799.956	−	799.956i	1.28610	−	1.28610i
$623$	2.85041	+	2.85041i	0.00457529	+	0.00457529i
$624$		0			0
$625$	−453.547	−	430.023i	−0.725675	−	0.688037i
$626$	−740.096			−1.18226
$627$		0			0
$628$	269.181	+	269.181i	0.428632	+	0.428632i
$629$		−	981.257i		−	1.56003i
$630$		0			0
$631$	−427.714			−0.677835			−0.338917	−	0.940816i	$-0.610061\pi$
$631$	−427.714			−0.677835			−0.338917	+	0.940816i	$0.610061\pi$
$632$	149.618	−	149.618i	0.236737	−	0.236737i
$633$		0			0
$634$		−	220.214i		−	0.347340i
$635$	202.389	−	1054.09i	0.318722	−	1.65998i
$636$		0			0
$637$	−453.371	+	453.371i	−0.711728	+	0.711728i
$638$	−119.823	−	119.823i	−0.187810	−	0.187810i
$639$		0			0
$640$	−631.982	−	121.343i	−0.987472	−	0.189598i
$641$	513.823			0.801596			0.400798	−	0.916166i	$-0.368733\pi$
$641$	513.823			0.801596			0.400798	+	0.916166i	$0.368733\pi$
$642$		0			0
$643$	−137.617	−	137.617i	−0.214023	−	0.214023i	0.591951	−	0.805974i	$-0.298358\pi$
$643$	−137.617	−	137.617i	−0.214023	−	0.214023i	−0.805974	+	0.591951i	$0.798358\pi$
$644$			6.81109i			0.0105762i
$645$		0			0
$646$	278.259			0.430741
$647$	−139.726	+	139.726i	−0.215960	+	0.215960i	−0.806794	−	0.590833i	$-0.798799\pi$
$647$	−139.726	+	139.726i	−0.215960	+	0.215960i	0.590833	+	0.806794i	$0.298799\pi$
$648$		0			0
$649$		−	174.565i		−	0.268976i
$650$	−301.800	+	756.948i	−0.464308	+	1.16454i
$651$		0			0
$652$	−143.464	+	143.464i	−0.220037	+	0.220037i
$653$	−455.677	−	455.677i	−0.697820	−	0.697820i	0.266120	−	0.963940i	$-0.414258\pi$
$653$	−455.677	−	455.677i	−0.697820	−	0.697820i	−0.963940	+	0.266120i	$0.914258\pi$
$654$		0			0
$655$	6.22014	−	4.21631i	0.00949640	−	0.00643711i
$656$	1243.66			1.89583
$657$		0			0
$658$	5.54730	+	5.54730i	0.00843054	+	0.00843054i
$659$		−	242.718i		−	0.368312i	−0.982897	−	0.184156i	$-0.941045\pi$
$659$		−	242.718i		−	0.368312i	0.982897	−	0.184156i	$-0.0589552\pi$
$660$		0			0
$661$	662.727			1.00261			0.501307	−	0.865270i	$-0.332853\pi$
$661$	662.727			1.00261			0.501307	+	0.865270i	$0.332853\pi$
$662$	786.074	−	786.074i	1.18742	−	1.18742i
$663$		0			0
$664$			277.953i			0.418605i
$665$	−1.94294	−	0.373051i	−0.00292171	−	0.000560979i
$666$		0			0
$667$	−235.933	+	235.933i	−0.353722	+	0.353722i
$668$	311.377	+	311.377i	0.466133	+	0.466133i
$669$		0			0
$670$	346.616	+	511.349i	0.517337	+	0.763207i
$671$	49.8438			0.0742828
$672$		0			0
$673$	342.339	+	342.339i	0.508676	+	0.508676i	0.914120	−	0.405444i	$-0.132883\pi$
$673$	342.339	+	342.339i	0.508676	+	0.508676i	−0.405444	+	0.914120i	$0.632883\pi$
$674$			72.9670i			0.108260i
$675$		0			0
$676$	4.95712			0.00733302
$677$	−311.125	+	311.125i	−0.459564	+	0.459564i	−0.898512	−	0.438948i	$-0.855351\pi$
$677$	−311.125	+	311.125i	−0.459564	+	0.459564i	0.438948	+	0.898512i	$0.355351\pi$
$678$		0			0
$679$		−	10.5991i		−	0.0156098i
$680$	−356.114	+	241.391i	−0.523697	+	0.354987i
$681$		0			0
$682$	272.072	−	272.072i	0.398933	−	0.398933i
$683$	−336.034	−	336.034i	−0.491998	−	0.491998i	0.416938	−	0.908935i	$-0.363103\pi$
$683$	−336.034	−	336.034i	−0.491998	−	0.491998i	−0.908935	+	0.416938i	$0.863103\pi$
$684$		0			0
$685$	−65.8544	+	342.985i	−0.0961379	+	0.500708i
$686$	−16.6321			−0.0242451
$687$		0			0
$688$	−141.759	−	141.759i	−0.206045	−	0.206045i
$689$			518.665i			0.752779i
$690$		0			0
$691$	930.107			1.34603			0.673015	−	0.739629i	$-0.264999\pi$
$691$	930.107			1.34603			0.673015	+	0.739629i	$0.264999\pi$
$692$	53.8977	−	53.8977i	0.0778869	−	0.0778869i
$693$		0			0
$694$			841.075i			1.21192i
$695$	−344.459	−	508.166i	−0.495624	−	0.731174i
$696$		0			0
$697$	847.641	−	847.641i	1.21613	−	1.21613i
$698$	−104.722	−	104.722i	−0.150031	−	0.150031i
$699$		0			0
$700$	−3.44977	+	1.48303i	−0.00492824	+	0.00211862i
$701$	−1057.58			−1.50868			−0.754338	−	0.656486i	$-0.772042\pi$
$701$	−1057.58			−1.50868			−0.754338	+	0.656486i	$0.772042\pi$
$702$		0			0
$703$	−209.448	−	209.448i	−0.297935	−	0.297935i
$704$		−	5.25803i		−	0.00746880i
$705$		0			0
$706$	1326.56			1.87898
$707$	−2.66012	+	2.66012i	−0.00376255	+	0.00376255i
$708$		0			0
$709$		−	520.480i		−	0.734105i	−0.930200	−	0.367053i	$-0.880367\pi$
$709$		−	520.480i		−	0.734105i	0.930200	−	0.367053i	$-0.119633\pi$
$710$	−132.495	+	690.065i	−0.186613	+	0.971922i
$711$		0			0
$712$	187.104	−	187.104i	0.262787	−	0.262787i
$713$	−535.715	−	535.715i	−0.751353	−	0.751353i
$714$		0			0
$715$	−594.112	−	114.072i	−0.830926	−	0.159541i
$716$	−409.925			−0.572520
$717$		0			0
$718$	−602.709	−	602.709i	−0.839428	−	0.839428i
$719$		−	1211.89i		−	1.68553i	−0.538285	−	0.842763i	$-0.680928\pi$
$719$		−	1211.89i		−	1.68553i	0.538285	−	0.842763i	$-0.319072\pi$
$720$		0			0
$721$	−6.23044			−0.00864139
$722$	−576.435	+	576.435i	−0.798386	+	0.798386i
$723$		0			0
$724$			215.552i			0.297724i
$725$	−170.870	−	68.1268i	−0.235682	−	0.0939680i
$726$		0			0
$727$	147.356	−	147.356i	0.202691	−	0.202691i	−0.598461	−	0.801152i	$-0.704221\pi$
$727$	147.356	−	147.356i	0.202691	−	0.202691i	0.801152	+	0.598461i	$0.204221\pi$
$728$	−2.82010	−	2.82010i	−0.00387377	−	0.00387377i
$729$		0			0
$730$	797.680	−	540.705i	1.09271	−	0.740692i
$731$	−193.237			−0.264346
$732$		0			0
$733$	−518.014	−	518.014i	−0.706704	−	0.706704i	0.259136	−	0.965841i	$-0.416562\pi$
$733$	−518.014	−	518.014i	−0.706704	−	0.706704i	−0.965841	+	0.259136i	$0.916562\pi$
$734$		−	916.759i		−	1.24899i
$735$		0			0
$736$	1443.02			1.96063
$737$	−324.286	+	324.286i	−0.440009	+	0.440009i
$738$		0			0
$739$			1243.93i			1.68326i	0.540056	+	0.841629i	$0.318403\pi$
$739$			1243.93i			1.68326i	−0.540056	+	0.841629i	$0.681597\pi$
$740$	−552.109	−	106.007i	−0.746093	−	0.143253i
$741$		0			0
$742$	−4.75664	+	4.75664i	−0.00641057	+	0.00641057i
$743$	907.482	+	907.482i	1.22138	+	1.22138i	0.967143	+	0.254232i	$0.0818227\pi$
$743$	907.482	+	907.482i	1.22138	+	1.22138i	0.254232	+	0.967143i	$0.418177\pi$
$744$		0			0
$745$	−74.5367	−	109.961i	−0.100049	−	0.147599i
$746$	−829.060			−1.11134
$747$		0			0
$748$	277.240	+	277.240i	0.370642	+	0.370642i
$749$			1.41013i			0.00188269i
$750$		0			0
$751$	940.549			1.25240			0.626198	−	0.779664i	$-0.284610\pi$
$751$	940.549			1.25240			0.626198	+	0.779664i	$0.284610\pi$
$752$	652.321	−	652.321i	0.867448	−	0.867448i
$753$		0			0
$754$			239.840i			0.318090i
$755$	407.598	−	276.289i	0.539865	−	0.365946i
$756$		0			0
$757$	872.169	−	872.169i	1.15214	−	1.15214i	0.166015	−	0.986123i	$-0.446910\pi$
$757$	872.169	−	872.169i	1.15214	−	1.15214i	0.986123	−	0.166015i	$-0.0530901\pi$
$758$	−358.776	−	358.776i	−0.473319	−	0.473319i
$759$		0			0
$760$	−24.4875	+	127.537i	−0.0322204	+	0.167811i
$761$	459.612			0.603958			0.301979	−	0.953315i	$-0.402353\pi$
$761$	459.612			0.603958			0.301979	+	0.953315i	$0.402353\pi$
$762$		0			0
$763$	5.39899	+	5.39899i	0.00707600	+	0.00707600i
$764$		−	300.712i		−	0.393602i
$765$		0			0
$766$	51.5397			0.0672842
$767$	−174.707	+	174.707i	−0.227780	+	0.227780i
$768$		0			0
$769$			895.323i			1.16427i	0.813093	+	0.582134i	$0.197782\pi$
$769$			895.323i			1.16427i	−0.813093	+	0.582134i	$0.802218\pi$
$770$	−4.40242	−	6.49472i	−0.00571743	−	0.00843469i
$771$		0			0
$772$	143.965	−	143.965i	0.186483	−	0.186483i
$773$	94.0446	+	94.0446i	0.121662	+	0.121662i	0.765316	−	0.643654i	$-0.222583\pi$
$773$	94.0446	+	94.0446i	0.121662	+	0.121662i	−0.643654	+	0.765316i	$0.722583\pi$
$774$		0			0
$775$	154.690	−	387.981i	0.199600	−	0.500620i
$776$	−695.735			−0.896566
$777$		0			0
$778$	−326.297	−	326.297i	−0.419405	−	0.419405i
$779$		−	361.856i		−	0.464514i
$780$		0			0
$781$	−521.650			−0.667926
$782$	1536.46	−	1536.46i	1.96479	−	1.96479i
$783$		0			0
$784$			977.861i			1.24727i
$785$	−162.817	+	847.987i	−0.207410	+	1.08024i
$786$		0			0
$787$	−658.819	+	658.819i	−0.837127	+	0.837127i	−0.988480	−	0.151353i	$-0.951637\pi$
$787$	−658.819	+	658.819i	−0.837127	+	0.837127i	0.151353	+	0.988480i	$0.451637\pi$
$788$	376.112	+	376.112i	0.477299	+	0.477299i
$789$		0			0
$790$	−578.607	−	111.095i	−0.732413	−	0.140626i
$791$	2.52677			0.00319440
$792$		0			0
$793$	−49.8843	−	49.8843i	−0.0629058	−	0.0629058i
$794$		−	833.001i		−	1.04912i
$795$		0			0
$796$	80.2813			0.100856
$797$	−119.799	+	119.799i	−0.150313	+	0.150313i	−0.778258	−	0.627945i	$-0.783896\pi$
$797$	−119.799	+	119.799i	−0.150313	+	0.150313i	0.627945	+	0.778258i	$0.283896\pi$
$798$		0			0
$799$		−	889.201i		−	1.11289i
$800$	314.200	+	730.879i	0.392750	+	0.913599i
$801$		0			0
$802$	−119.900	+	119.900i	−0.149502	+	0.149502i
$803$	505.872	+	505.872i	0.629978	+	0.629978i
$804$		0			0
$805$	−12.7882	+	8.66844i	−0.0158860	+	0.0107682i
$806$	−544.587			−0.675666
$807$		0			0
$808$	174.614	+	174.614i	0.216106	+	0.216106i
$809$			1540.82i			1.90459i	0.305175	+	0.952296i	$0.401285\pi$
$809$			1540.82i			1.90459i	−0.305175	+	0.952296i	$0.598715\pi$
$810$		0			0
$811$	−895.419			−1.10409			−0.552046	−	0.833813i	$-0.686153\pi$
$811$	−895.419			−1.10409			−0.552046	+	0.833813i	$0.686153\pi$
$812$	−0.781482	+	0.781482i	−0.000962417	+	0.000962417i
$813$		0			0
$814$		−	1174.71i		−	1.44313i
$815$	−451.947	−	86.7755i	−0.554536	−	0.106473i
$816$		0			0
$817$	−41.2462	+	41.2462i	−0.0504850	+	0.0504850i
$818$	−664.048	−	664.048i	−0.811795	−	0.811795i
$819$		0			0
$820$	−385.357	−	568.501i	−0.469947	−	0.693294i
$821$	644.536			0.785063			0.392531	−	0.919739i	$-0.371599\pi$
$821$	644.536			0.785063			0.392531	+	0.919739i	$0.371599\pi$
$822$		0			0
$823$	−154.651	−	154.651i	−0.187911	−	0.187911i	0.606881	−	0.794792i	$-0.292420\pi$
$823$	−154.651	−	154.651i	−0.187911	−	0.187911i	−0.794792	+	0.606881i	$0.792420\pi$
$824$			408.974i			0.496327i
$825$		0			0
$826$	−3.20446			−0.00387949
$827$	−982.768	+	982.768i	−1.18835	+	1.18835i	−0.210831	+	0.977522i	$0.567617\pi$
$827$	−982.768	+	982.768i	−1.18835	+	1.18835i	−0.977522	+	0.210831i	$0.932383\pi$
$828$		0			0
$829$			763.031i			0.920424i	0.887809	+	0.460212i	$0.152227\pi$
$829$			763.031i			0.920424i	−0.887809	+	0.460212i	$0.847773\pi$
$830$	640.649	−	434.262i	0.771866	−	0.523207i
$831$		0			0
$832$	−5.26231	+	5.26231i	−0.00632489	+	0.00632489i
$833$	666.479	+	666.479i	0.800094	+	0.800094i
$834$		0			0
$835$	−188.339	+	980.915i	−0.225556	+	1.17475i
$836$	118.353			0.141571
$837$		0			0
$838$	402.737	+	402.737i	0.480593	+	0.480593i
$839$			1092.90i			1.30262i	0.758812	+	0.651309i	$0.225780\pi$
$839$			1092.90i			1.30262i	−0.758812	+	0.651309i	$0.774220\pi$
$840$		0			0
$841$	786.860			0.935624
$842$	721.758	−	721.758i	0.857195	−	0.857195i
$843$		0			0
$844$			426.775i			0.505658i
$845$	6.30890	+	9.30726i	0.00746615	+	0.0110145i
$846$		0			0
$847$	−1.71114	+	1.71114i	−0.00202024	+	0.00202024i
$848$	559.346	+	559.346i	0.659606	+	0.659606i
$849$		0			0
$850$	1112.75	+	443.661i	1.30912	+	0.521955i
$851$	−2313.02			−2.71800
$852$		0			0
$853$	1162.51	+	1162.51i	1.36285	+	1.36285i	0.870259	+	0.492594i	$0.163951\pi$
$853$	1162.51	+	1162.51i	1.36285	+	1.36285i	0.492594	+	0.870259i	$0.336049\pi$
$854$		−	0.914971i		−	0.00107140i
$855$		0			0
$856$	92.5628			0.108134
$857$	232.961	−	232.961i	0.271833	−	0.271833i	−0.558005	−	0.829838i	$-0.688433\pi$
$857$	232.961	−	232.961i	0.271833	−	0.271833i	0.829838	+	0.558005i	$0.188433\pi$
$858$		0			0
$859$			1572.39i			1.83049i	0.402894	+	0.915247i	$0.368004\pi$
$859$			1572.39i			1.83049i	−0.402894	+	0.915247i	$0.631996\pi$
$860$	−20.8757	+	108.726i	−0.0242741	+	0.126425i
$861$		0			0
$862$	−81.8629	+	81.8629i	−0.0949686	+	0.0949686i
$863$	458.505	+	458.505i	0.531292	+	0.531292i	0.920957	−	0.389665i	$-0.127409\pi$
$863$	458.505	+	458.505i	0.531292	+	0.531292i	−0.389665	+	0.920957i	$0.627409\pi$
$864$		0			0
$865$	169.791	+	32.6006i	0.196290	+	0.0376885i
$866$	1516.96			1.75169
$867$		0			0
$868$	−1.77445	−	1.77445i	−0.00204430	−	0.00204430i
$869$		−	437.394i		−	0.503330i
$870$		0			0
$871$	649.100			0.745235
$872$	354.396	−	354.396i	0.406418	−	0.406418i
$873$		0			0
$874$		−	655.913i		−	0.750472i
$875$	−7.17497	−	4.58968i	−0.00819996	−	0.00524535i
$876$		0			0
$877$	762.595	−	762.595i	0.869549	−	0.869549i	−0.122873	−	0.992422i	$-0.539211\pi$
$877$	762.595	−	762.595i	0.869549	−	0.869549i	0.992422	+	0.122873i	$0.0392109\pi$
$878$	681.989	+	681.989i	0.776753	+	0.776753i
$879$		0			0
$880$	−763.730	+	517.692i	−0.867875	+	0.588286i
$881$	1585.15			1.79927			0.899633	−	0.436647i	$-0.143834\pi$
$881$	1585.15			1.79927			0.899633	+	0.436647i	$0.143834\pi$
$882$		0			0
$883$	−1004.45	−	1004.45i	−1.13755	−	1.13755i	−0.988889	−	0.148657i	$-0.952505\pi$
$883$	−1004.45	−	1004.45i	−1.13755	−	1.13755i	−0.148657	−	0.988889i	$-0.547495\pi$
$884$		−	554.931i		−	0.627750i
$885$		0			0
$886$	−1827.40			−2.06253
$887$	221.378	−	221.378i	0.249580	−	0.249580i	−0.571218	−	0.820798i	$-0.693529\pi$
$887$	221.378	−	221.378i	0.249580	−	0.249580i	0.820798	+	0.571218i	$0.193529\pi$
$888$		0			0
$889$		−	14.6272i		−	0.0164536i
$890$	−723.576	−	138.929i	−0.813006	−	0.156100i
$891$		0			0
$892$	−149.235	+	149.235i	−0.167304	+	0.167304i
$893$	−189.799	−	189.799i	−0.212541	−	0.212541i
$894$		0			0
$895$	−521.709	−	769.655i	−0.582915	−	0.859950i
$896$	−8.76982			−0.00978775
$897$		0			0
$898$	248.516	+	248.516i	0.276744	+	0.276744i
$899$		−	122.932i		−	0.136743i
$900$		0			0
$901$	762.464			0.846242
$902$	1014.75	−	1014.75i	1.12500	−	1.12500i
$903$		0			0
$904$		−	165.860i		−	0.183474i
$905$	−404.710	+	274.332i	−0.447194	+	0.303129i
$906$		0			0
$907$	262.068	−	262.068i	0.288940	−	0.288940i	−0.547721	−	0.836661i	$-0.684505\pi$
$907$	262.068	−	262.068i	0.288940	−	0.288940i	0.836661	+	0.547721i	$0.184505\pi$
$908$	513.506	+	513.506i	0.565536	+	0.565536i
$909$		0			0
$910$	−2.09399	+	10.9060i	−0.00230109	+	0.0119846i
$911$	−980.168			−1.07593			−0.537963	−	0.842969i	$-0.680806\pi$
$911$	−980.168			−1.07593			−0.537963	+	0.842969i	$0.680806\pi$
$912$		0			0
$913$	406.286	+	406.286i	0.445001	+	0.445001i
$914$			1828.97i			2.00106i
$915$		0			0
$916$	−916.979			−1.00107
$917$	0.0724117	−	0.0724117i	7.89659e−5	−	7.89659e-5i
$918$		0			0
$919$		−	1321.17i		−	1.43762i	−0.695205	−	0.718811i	$-0.744687\pi$
$919$		−	1321.17i		−	1.43762i	0.695205	−	0.718811i	$-0.255313\pi$
$920$	569.007	+	839.433i	0.618486	+	0.912427i
$921$		0			0
$922$	−1130.90	+	1130.90i	−1.22657	+	1.22657i
$923$	522.074	+	522.074i	0.565627	+	0.565627i
$924$		0			0
$925$	−503.632	−	1171.53i	−0.544467	−	1.26652i
$926$	691.330			0.746577
$927$		0			0
$928$	165.567	+	165.567i	0.178413	+	0.178413i
$929$			776.302i			0.835632i	0.908532	+	0.417816i	$0.137204\pi$
$929$			776.302i			0.835632i	−0.908532	+	0.417816i	$0.862796\pi$
$930$		0			0
$931$	284.518			0.305605
$932$	−48.5425	+	48.5425i	−0.0520842	+	0.0520842i
$933$		0			0
$934$		−	202.352i		−	0.216651i
$935$	−167.691	+	873.376i	−0.179349	+	0.934092i
$936$		0			0
$937$	295.586	−	295.586i	0.315459	−	0.315459i	−0.531561	−	0.847020i	$-0.678394\pi$
$937$	295.586	−	295.586i	0.315459	−	0.315459i	0.847020	+	0.531561i	$0.178394\pi$
$938$	5.95286	+	5.95286i	0.00634633	+	0.00634633i
$939$		0			0
$940$	−500.313	−	96.0620i	−0.532248	−	0.102194i
$941$	97.6040			0.103724			0.0518618	−	0.998654i	$-0.483484\pi$
$941$	97.6040			0.103724			0.0518618	+	0.998654i	$0.483484\pi$
$942$		0			0
$943$	−1998.06	−	1998.06i	−2.11884	−	2.11884i
$944$			376.820i			0.399174i
$945$		0			0
$946$	−231.333			−0.244538
$947$	129.645	−	129.645i	0.136900	−	0.136900i	−0.635336	−	0.772236i	$-0.719138\pi$
$947$	129.645	−	129.645i	0.136900	−	0.136900i	0.772236	+	0.635336i	$0.219138\pi$
$948$		0			0
$949$		−	1012.57i		−	1.06698i
$950$	332.215	−	142.817i	0.349700	−	0.150333i
$951$		0			0
$952$	−4.14570	+	4.14570i	−0.00435472	+	0.00435472i
$953$	−16.8810	−	16.8810i	−0.0177135	−	0.0177135i	0.698195	−	0.715908i	$-0.253987\pi$
$953$	−16.8810	−	16.8810i	−0.0177135	−	0.0177135i	−0.715908	+	0.698195i	$0.753987\pi$
$954$		0			0
$955$	564.603	−	382.714i	0.591207	−	0.400748i
$956$	681.014			0.712358
$957$		0			0
$958$	−852.817	−	852.817i	−0.890206	−	0.890206i
$959$			4.75950i			0.00496298i
$960$		0			0
$961$	−681.867			−0.709539
$962$	−1175.66	+	1175.66i	−1.22210	+	1.22210i
$963$		0			0
$964$		−	56.6819i		−	0.0587987i
$965$	453.526	+	87.0787i	0.469975	+	0.0902370i
$966$		0			0
$967$	−850.051	+	850.051i	−0.879060	+	0.879060i	−0.993437	−	0.114377i	$-0.963513\pi$
$967$	−850.051	+	850.051i	−0.879060	+	0.879060i	0.114377	+	0.993437i	$0.463513\pi$
$968$	112.322	+	112.322i	0.116035	+	0.116035i
$969$		0			0
$970$	1086.99	+	1603.58i	1.12060	+	1.65318i
$971$	−608.975			−0.627163			−0.313582	−	0.949561i	$-0.601529\pi$
$971$	−608.975			−0.627163			−0.313582	+	0.949561i	$0.601529\pi$
$972$		0			0
$973$	−5.91580	−	5.91580i	−0.00607996	−	0.00607996i
$974$		−	571.291i		−	0.586541i
$975$		0			0
$976$	−107.594			−0.110240
$977$	−62.4068	+	62.4068i	−0.0638760	+	0.0638760i	−0.738323	−	0.674447i	$-0.764382\pi$
$977$	−62.4068	+	62.4068i	−0.0638760	+	0.0638760i	0.674447	+	0.738323i	$0.264382\pi$
$978$		0			0
$979$		−	546.982i		−	0.558715i
$980$	446.998	−	302.996i	0.456120	−	0.309180i
$981$		0			0
$982$	−1391.51	+	1391.51i	−1.41701	+	1.41701i
$983$	−1009.48	−	1009.48i	−1.02693	−	1.02693i	−0.999627	−	0.0273061i	$-0.991307\pi$
$983$	−1009.48	−	1009.48i	−1.02693	−	1.02693i	−0.0273061	−	0.999627i	$-0.508693\pi$
$984$		0			0
$985$	−227.495	+	1184.85i	−0.230959	+	1.20289i
$986$	352.577			0.357584
$987$		0			0
$988$	−118.449	−	118.449i	−0.119888	−	0.119888i
$989$			455.499i			0.460565i
$990$		0			0
$991$	14.7275			0.0148613			0.00743063	−	0.999972i	$-0.497635\pi$
$991$	14.7275			0.0148613			0.00743063	+	0.999972i	$0.497635\pi$
$992$	−375.941	+	375.941i	−0.378973	+	0.378973i
$993$		0			0
$994$			9.57581i			0.00963361i
$995$	102.174	+	150.732i	0.102687	+	0.151490i
$996$		0			0
$997$	−163.070	+	163.070i	−0.163561	+	0.163561i	−0.784142	−	0.620581i	$-0.786897\pi$
$997$	−163.070	+	163.070i	−0.163561	+	0.163561i	0.620581	+	0.784142i	$0.286897\pi$
$998$	−858.989	−	858.989i	−0.860710	−	0.860710i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	405.3.g.h.163.2		20
3.2	odd	2		405.3.g.g.163.9		20
5.2	odd	4	inner	405.3.g.h.82.2		20
9.2	odd	6		135.3.l.a.118.2		40
9.4	even	3		45.3.k.a.43.2	yes	40
9.5	odd	6		135.3.l.a.73.9		40
9.7	even	3		45.3.k.a.13.9	yes	40
15.2	even	4		405.3.g.g.82.9		20
45.2	even	12		135.3.l.a.37.9		40
45.4	even	6		225.3.o.b.43.9		40
45.7	odd	12		45.3.k.a.22.2	yes	40
45.13	odd	12		225.3.o.b.7.2		40
45.22	odd	12		45.3.k.a.7.9	✓	40
45.32	even	12		135.3.l.a.127.2		40
45.34	even	6		225.3.o.b.193.2		40
45.43	odd	12		225.3.o.b.157.9		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.3.k.a.7.9	✓	40	45.22	odd	12
45.3.k.a.13.9	yes	40	9.7	even	3
45.3.k.a.22.2	yes	40	45.7	odd	12
45.3.k.a.43.2	yes	40	9.4	even	3
135.3.l.a.37.9		40	45.2	even	12
135.3.l.a.73.9		40	9.5	odd	6
135.3.l.a.118.2		40	9.2	odd	6
135.3.l.a.127.2		40	45.32	even	12
225.3.o.b.7.2		40	45.13	odd	12
225.3.o.b.43.9		40	45.4	even	6
225.3.o.b.157.9		40	45.43	odd	12
225.3.o.b.193.2		40	45.34	even	6
405.3.g.g.82.9		20	15.2	even	4
405.3.g.g.163.9		20	3.2	odd	2
405.3.g.h.82.2		20	5.2	odd	4	inner
405.3.g.h.163.2		20	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 405 = 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	405.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.76130 + 1.76130i) q^{2} -2.20434i q^{4} +(4.13877 - 2.80545i) q^{5} +(0.0481814 - 0.0481814i) q^{7} +(-3.16269 - 3.16269i) q^{8} +(-2.34837 + 12.2309i) q^{10} -9.24583 q^{11} +(9.25335 + 9.25335i) q^{13} +0.169724i q^{14} +19.9582 q^{16} +(13.6029 - 13.6029i) q^{17} -5.80704i q^{19} +(-6.18418 - 9.12327i) q^{20} +(16.2847 - 16.2847i) q^{22} +(-32.0648 - 32.0648i) q^{23} +(9.25886 - 23.2223i) q^{25} -32.5958 q^{26} +(-0.106208 - 0.106208i) q^{28} -7.35801i q^{29} +16.7073 q^{31} +(-22.5017 + 22.5017i) q^{32} +47.9175i q^{34} +(0.0642412 - 0.334583i) q^{35} +(36.0680 - 36.0680i) q^{37} +(10.2279 + 10.2279i) q^{38} +(-21.9624 - 4.21687i) q^{40} +62.3133 q^{41} +(-7.10279 - 7.10279i) q^{43} +20.3810i q^{44} +112.951 q^{46} +(32.6843 - 32.6843i) q^{47} +48.9954i q^{49} +(24.5937 + 57.2089i) q^{50} +(20.3975 - 20.3975i) q^{52} +(28.0258 + 28.0258i) q^{53} +(-38.2664 + 25.9388i) q^{55} -0.304766 q^{56} +(12.9596 + 12.9596i) q^{58} +18.8804i q^{59} -5.39094 q^{61} +(-29.4265 + 29.4265i) q^{62} +0.568692i q^{64} +(64.2573 + 12.3376i) q^{65} +(35.0738 - 35.0738i) q^{67} +(-29.9854 - 29.9854i) q^{68} +(0.476152 + 0.702448i) q^{70} +56.4200 q^{71} +(-54.7135 - 54.7135i) q^{73} +127.053i q^{74} -12.8007 q^{76} +(-0.445478 + 0.445478i) q^{77} +47.3071i q^{79} +(82.6026 - 55.9919i) q^{80} +(-109.752 + 109.752i) q^{82} +(-43.9426 - 43.9426i) q^{83} +(18.1370 - 94.4615i) q^{85} +25.0203 q^{86} +(29.2417 + 29.2417i) q^{88} +59.1599i q^{89} +0.891679 q^{91} +(-70.6817 + 70.6817i) q^{92} +115.134i q^{94} +(-16.2914 - 24.0340i) q^{95} +(109.991 - 109.991i) q^{97} +(-86.2954 - 86.2954i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 2 q^{2} + 2 q^{5} + 2 q^{7} - 12 q^{8} - 4 q^{10} - 8 q^{11} + 2 q^{13} - 28 q^{16} + 14 q^{17} + 114 q^{20} - 14 q^{22} - 82 q^{23} + 8 q^{25} - 56 q^{26} - 44 q^{28} + 4 q^{31} + 14 q^{32} + 176 q^{35}+ \cdots - 938 q^{98}+O(q^{100}) \) 20 * q + 2 * q^2 + 2 * q^5 + 2 * q^7 - 12 * q^8 - 4 * q^10 - 8 * q^11 + 2 * q^13 - 28 * q^16 + 14 * q^17 + 114 * q^20 - 14 * q^22 - 82 * q^23 + 8 * q^25 - 56 * q^26 - 44 * q^28 + 4 * q^31 + 14 * q^32 + 176 * q^35 - 46 * q^37 - 330 * q^38 - 30 * q^40 + 28 * q^41 + 2 * q^43 - 68 * q^46 - 64 * q^47 + 458 * q^50 + 74 * q^52 - 304 * q^53 + 112 * q^55 + 192 * q^56 - 30 * q^58 - 92 * q^61 - 50 * q^62 + 326 * q^65 + 80 * q^67 - 626 * q^68 + 102 * q^70 + 124 * q^71 - 4 * q^73 + 96 * q^76 - 338 * q^77 + 722 * q^80 + 52 * q^82 - 370 * q^83 + 98 * q^85 + 328 * q^86 + 210 * q^88 + 76 * q^91 - 388 * q^92 + 360 * q^95 - 292 * q^97 - 938 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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