LMFDB - Embedded newform 1805.2.b.m.1084.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1805,2,Mod(1084,1805)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1805, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

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

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

chi := DirichletCharacter("1805.1084");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1805 = 5 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1805.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$14.4129975648$
Analytic rank:	$0$
Dimension:	$40$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1084.7
Character	$\chi$	$=$	1805.1084
Dual form			1805.2.b.m.1084.34

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.96724i q^{2} -3.10308i q^{3} -1.87002 q^{4} +(-2.04586 - 0.902473i) q^{5} -6.10450 q^{6} +2.84392i q^{7} -0.255698i q^{8} -6.62912 q^{9} +O(q^{10})$	\(q-1.96724i q^{2} -3.10308i q^{3} -1.87002 q^{4} +(-2.04586 - 0.902473i) q^{5} -6.10450 q^{6} +2.84392i q^{7} -0.255698i q^{8} -6.62912 q^{9} +(-1.77538 + 4.02469i) q^{10} -0.295824 q^{11} +5.80283i q^{12} -2.61871i q^{13} +5.59466 q^{14} +(-2.80045 + 6.34847i) q^{15} -4.24306 q^{16} +7.09714i q^{17} +13.0411i q^{18} +(3.82580 + 1.68764i) q^{20} +8.82491 q^{21} +0.581957i q^{22} -2.66459i q^{23} -0.793451 q^{24} +(3.37108 + 3.69267i) q^{25} -5.15162 q^{26} +11.2615i q^{27} -5.31819i q^{28} -1.25311 q^{29} +(12.4890 + 5.50915i) q^{30} +1.74251 q^{31} +7.83571i q^{32} +0.917968i q^{33} +13.9618 q^{34} +(2.56656 - 5.81826i) q^{35} +12.3966 q^{36} +0.722118i q^{37} -8.12606 q^{39} +(-0.230760 + 0.523122i) q^{40} -10.1012 q^{41} -17.3607i q^{42} -4.02118i q^{43} +0.553198 q^{44} +(13.5623 + 5.98261i) q^{45} -5.24189 q^{46} +2.94767i q^{47} +13.1666i q^{48} -1.08787 q^{49} +(7.26435 - 6.63172i) q^{50} +22.0230 q^{51} +4.89704i q^{52} -6.98387i q^{53} +22.1540 q^{54} +(0.605215 + 0.266974i) q^{55} +0.727184 q^{56} +2.46517i q^{58} -8.84124 q^{59} +(5.23690 - 11.8718i) q^{60} +6.62954 q^{61} -3.42793i q^{62} -18.8527i q^{63} +6.92858 q^{64} +(-2.36331 + 5.35751i) q^{65} +1.80586 q^{66} -1.93900i q^{67} -13.2718i q^{68} -8.26846 q^{69} +(-11.4459 - 5.04903i) q^{70} -15.7012 q^{71} +1.69505i q^{72} +3.05470i q^{73} +1.42058 q^{74} +(11.4587 - 10.4608i) q^{75} -0.841300i q^{77} +15.9859i q^{78} +8.06734 q^{79} +(8.68071 + 3.82925i) q^{80} +15.0579 q^{81} +19.8714i q^{82} +13.8489i q^{83} -16.5028 q^{84} +(6.40498 - 14.5198i) q^{85} -7.91061 q^{86} +3.88851i q^{87} +0.0756416i q^{88} +0.551256 q^{89} +(11.7692 - 26.6802i) q^{90} +7.44739 q^{91} +4.98285i q^{92} -5.40716i q^{93} +5.79876 q^{94} +24.3149 q^{96} +6.60229i q^{97} +2.14010i q^{98} +1.96106 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 48 q^{4} + 6 q^{5} + 20 q^{6} - 52 q^{9}+O(q^{10}) $ 40 * q - 48 * q^4 + 6 * q^5 + 20 * q^6 - 52 * q^9	$ 40 q - 48 q^{4} + 6 q^{5} + 20 q^{6} - 52 q^{9} + 20 q^{11} + 40 q^{16} - 18 q^{20} - 92 q^{24} - 26 q^{25} + 76 q^{26} + 40 q^{30} + 4 q^{35} + 156 q^{36} - 80 q^{39} - 48 q^{44} - 22 q^{45} - 72 q^{49} - 32 q^{54} - 40 q^{55} + 80 q^{61} - 72 q^{64} + 16 q^{66} - 100 q^{74} - 66 q^{80} + 40 q^{81} + 44 q^{85} + 380 q^{96} - 128 q^{99}+O(q^{100}) $ 40 * q - 48 * q^4 + 6 * q^5 + 20 * q^6 - 52 * q^9 + 20 * q^11 + 40 * q^16 - 18 * q^20 - 92 * q^24 - 26 * q^25 + 76 * q^26 + 40 * q^30 + 4 * q^35 + 156 * q^36 - 80 * q^39 - 48 * q^44 - 22 * q^45 - 72 * q^49 - 32 * q^54 - 40 * q^55 + 80 * q^61 - 72 * q^64 + 16 * q^66 - 100 * q^74 - 66 * q^80 + 40 * q^81 + 44 * q^85 + 380 * q^96 - 128 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1805\mathbb{Z}\right)^\times$.

$n$	$362$	$1446$
$\chi(n)$	$-1$	$1$

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 $

$2$		−	1.96724i		−	1.39105i	−0.718503	−	0.695523i	$-0.755173\pi$
$2$		−	1.96724i		−	1.39105i	0.718503	−	0.695523i	$-0.244827\pi$
$3$		−	3.10308i		−	1.79157i	−0.444492	−	0.895783i	$-0.646616\pi$
$3$		−	3.10308i		−	1.79157i	0.444492	−	0.895783i	$-0.353384\pi$
$4$	−1.87002			−0.935011
$5$	−2.04586	−	0.902473i	−0.914936	−	0.403598i
$5$	−2.04586	−	0.902473i	−0.914936	−	0.403598i
$6$	−6.10450			−2.49215
$7$			2.84392i			1.07490i	0.843296	+	0.537450i	$0.180612\pi$
$7$			2.84392i			1.07490i	−0.843296	+	0.537450i	$0.819388\pi$
$8$		−	0.255698i		−	0.0904028i
$9$	−6.62912			−2.20971
$10$	−1.77538	+	4.02469i	−0.561424	+	1.27272i
$11$	−0.295824			−0.0891944			−0.0445972	−	0.999005i	$-0.514200\pi$
$11$	−0.295824			−0.0891944			−0.0445972	+	0.999005i	$0.514200\pi$
$12$			5.80283i			1.67513i
$13$		−	2.61871i		−	0.726298i	−0.931731	−	0.363149i	$-0.881702\pi$
$13$		−	2.61871i		−	0.726298i	0.931731	−	0.363149i	$-0.118298\pi$
$14$	5.59466			1.49524
$15$	−2.80045	+	6.34847i	−0.723073	+	1.63917i
$16$	−4.24306			−1.06077
$17$			7.09714i			1.72131i	0.509189	+	0.860655i	$0.329945\pi$
$17$			7.09714i			1.72131i	−0.509189	+	0.860655i	$0.670055\pi$
$18$			13.0411i			3.07381i
$19$		0			0
$19$		0			0
$20$	3.82580	+	1.68764i	0.855475	+	0.377369i
$21$	8.82491			1.92575
$22$			0.581957i			0.124074i
$23$		−	2.66459i		−	0.555606i	−0.960638	−	0.277803i	$-0.910394\pi$
$23$		−	2.66459i		−	0.555606i	0.960638	−	0.277803i	$-0.0896063\pi$
$24$	−0.793451			−0.161963
$25$	3.37108	+	3.69267i	0.674217	+	0.738533i
$26$	−5.15162			−1.01031
$27$			11.2615i			2.16727i
$28$		−	5.31819i		−	1.00504i
$29$	−1.25311			−0.232697			−0.116349	−	0.993208i	$-0.537119\pi$
$29$	−1.25311			−0.232697			−0.116349	+	0.993208i	$0.537119\pi$
$30$	12.4890	+	5.50915i	2.28016	+	1.00583i
$31$	1.74251			0.312964			0.156482	−	0.987681i	$-0.449985\pi$
$31$	1.74251			0.312964			0.156482	+	0.987681i	$0.449985\pi$
$32$			7.83571i			1.38517i
$33$			0.917968i			0.159798i
$34$	13.9618			2.39442
$35$	2.56656	−	5.81826i	0.433828	−	0.983465i
$36$	12.3966			2.06610
$37$			0.722118i			0.118716i	0.998237	+	0.0593578i	$0.0189053\pi$
$37$			0.722118i			0.118716i	−0.998237	+	0.0593578i	$0.981095\pi$
$38$		0			0
$39$	−8.12606			−1.30121
$40$	−0.230760	+	0.523122i	−0.0364864	+	0.0827128i
$41$	−10.1012			−1.57754			−0.788768	−	0.614691i	$-0.789281\pi$
$41$	−10.1012			−1.57754			−0.788768	+	0.614691i	$0.789281\pi$
$42$		−	17.3607i		−	2.67881i
$43$		−	4.02118i		−	0.613224i	−0.951835	−	0.306612i	$-0.900805\pi$
$43$		−	4.02118i		−	0.613224i	0.951835	−	0.306612i	$-0.0991953\pi$
$44$	0.553198			0.0833978
$45$	13.5623	+	5.98261i	2.02174	+	0.891834i
$46$	−5.24189			−0.772874
$47$			2.94767i			0.429962i	0.976618	+	0.214981i	$0.0689689\pi$
$47$			2.94767i			0.429962i	−0.976618	+	0.214981i	$0.931031\pi$
$48$			13.1666i			1.90043i
$49$	−1.08787			−0.155410
$50$	7.26435	−	6.63172i	1.02733	−	0.937867i
$51$	22.0230			3.08384
$52$			4.89704i			0.679097i
$53$		−	6.98387i		−	0.959308i	−0.877458	−	0.479654i	$-0.840762\pi$
$53$		−	6.98387i		−	0.959308i	0.877458	−	0.479654i	$-0.159238\pi$
$54$	22.1540			3.01478
$55$	0.605215	+	0.266974i	0.0816072	+	0.0359987i
$56$	0.727184			0.0971740
$57$		0			0
$58$			2.46517i			0.323692i
$59$	−8.84124			−1.15103			−0.575516	−	0.817791i	$-0.695199\pi$
$59$	−8.84124			−1.15103			−0.575516	+	0.817791i	$0.695199\pi$
$60$	5.23690	−	11.8718i	0.676081	−	1.53264i
$61$	6.62954			0.848826			0.424413	−	0.905469i	$-0.360480\pi$
$61$	6.62954			0.848826			0.424413	+	0.905469i	$0.360480\pi$
$62$		−	3.42793i		−	0.435348i
$63$		−	18.8527i		−	2.37522i
$64$	6.92858			0.866073
$65$	−2.36331	+	5.35751i	−0.293133	+	0.664517i
$66$	1.80586			0.222286
$67$		−	1.93900i		−	0.236886i	−0.992961	−	0.118443i	$-0.962210\pi$
$67$		−	1.93900i		−	0.236886i	0.992961	−	0.118443i	$-0.0377903\pi$
$68$		−	13.2718i		−	1.60944i
$69$	−8.26846			−0.995405
$70$	−11.4459	−	5.04903i	−1.36805	−	0.603475i
$71$	−15.7012			−1.86340			−0.931698	−	0.363235i	$-0.881672\pi$
$71$	−15.7012			−1.86340			−0.931698	+	0.363235i	$0.881672\pi$
$72$			1.69505i			0.199764i
$73$			3.05470i			0.357526i	0.983892	+	0.178763i	$0.0572095\pi$
$73$			3.05470i			0.357526i	−0.983892	+	0.178763i	$0.942791\pi$
$74$	1.42058			0.165139
$75$	11.4587	−	10.4608i	1.32313	−	1.20790i
$76$		0			0
$77$		−	0.841300i		−	0.0958751i
$78$			15.9859i			1.81005i
$79$	8.06734			0.907647			0.453823	−	0.891092i	$-0.350060\pi$
$79$	8.06734			0.907647			0.453823	+	0.891092i	$0.350060\pi$
$80$	8.68071	+	3.82925i	0.970533	+	0.428123i
$81$	15.0579			1.67310
$82$			19.8714i			2.19443i
$83$			13.8489i			1.52011i	0.649857	+	0.760057i	$0.274829\pi$
$83$			13.8489i			1.52011i	−0.649857	+	0.760057i	$0.725171\pi$
$84$	−16.5028			−1.80060
$85$	6.40498	−	14.5198i	0.694717	−	1.57489i
$86$	−7.91061			−0.853023
$87$			3.88851i			0.416892i
$88$			0.0756416i			0.00806343i
$89$	0.551256			0.0584330			0.0292165	−	0.999573i	$-0.490699\pi$
$89$	0.551256			0.0584330			0.0292165	+	0.999573i	$0.490699\pi$
$90$	11.7692	−	26.6802i	1.24058	−	2.81234i
$91$	7.44739			0.780698
$92$			4.98285i			0.519498i
$93$		−	5.40716i		−	0.560696i
$94$	5.79876			0.598097
$95$		0			0
$96$	24.3149			2.48163
$97$			6.60229i			0.670361i	0.942154	+	0.335180i	$0.108797\pi$
$97$			6.60229i			0.670361i	−0.942154	+	0.335180i	$0.891203\pi$
$98$			2.14010i			0.216183i
$99$	1.96106			0.197094
$100$	−6.30400	−	6.90537i	−0.630400	−	0.690537i
$101$	−5.15989			−0.513428			−0.256714	−	0.966487i	$-0.582640\pi$
$101$	−5.15989			−0.513428			−0.256714	+	0.966487i	$0.582640\pi$
$102$		−	43.3245i		−	4.28976i
$103$			5.91869i			0.583186i	0.956542	+	0.291593i	$0.0941853\pi$
$103$			5.91869i			0.583186i	−0.956542	+	0.291593i	$0.905815\pi$
$104$	−0.669597			−0.0656594
$105$	−18.0545	−	7.96425i	−1.76194	−	0.777231i
$106$	−13.7389			−1.33444
$107$			3.73476i			0.361052i	0.983570	+	0.180526i	$0.0577801\pi$
$107$			3.73476i			0.361052i	−0.983570	+	0.180526i	$0.942220\pi$
$108$		−	21.0592i		−	2.02642i
$109$	8.67647			0.831055			0.415528	−	0.909581i	$-0.363597\pi$
$109$	8.67647			0.831055			0.415528	+	0.909581i	$0.363597\pi$
$110$	0.525200	−	1.19060i	0.0500759	−	0.113519i
$111$	2.24079			0.212687
$112$		−	12.0669i		−	1.14022i
$113$		−	11.8569i		−	1.11540i	−0.830042	−	0.557701i	$-0.811683\pi$
$113$		−	11.8569i		−	1.11540i	0.830042	−	0.557701i	$-0.188317\pi$
$114$		0			0
$115$	−2.40472	+	5.45139i	−0.224242	+	0.508344i
$116$	2.34335			0.217574
$117$			17.3597i			1.60491i
$118$			17.3928i			1.60114i
$119$	−20.1837			−1.85024
$120$	1.62329	+	0.716068i	0.148185	+	0.0653678i
$121$	−10.9125			−0.992044
$122$		−	13.0419i		−	1.18076i
$123$			31.3447i			2.82626i
$124$	−3.25854			−0.292625
$125$	−3.56424	−	10.5970i	−0.318795	−	0.947824i
$126$	−37.0877			−3.30404
$127$			11.3533i			1.00745i	0.863865	+	0.503723i	$0.168037\pi$
$127$			11.3533i			1.00745i	−0.863865	+	0.503723i	$0.831963\pi$
$128$			2.04126i			0.180424i
$129$	−12.4780			−1.09863
$130$	10.5395	+	4.64919i	0.924374	+	0.407761i
$131$	12.5054			1.09260			0.546299	−	0.837590i	$-0.316036\pi$
$131$	12.5054			1.09260			0.546299	+	0.837590i	$0.316036\pi$
$132$		−	1.71662i		−	0.149413i
$133$		0			0
$134$	−3.81447			−0.329520
$135$	10.1632	−	23.0394i	0.874707	−	1.98292i
$136$	1.81472			0.155611
$137$		−	14.5356i		−	1.24186i	−0.783866	−	0.620930i	$-0.786755\pi$
$137$		−	14.5356i		−	1.24186i	0.783866	−	0.620930i	$-0.213245\pi$
$138$			16.2660i			1.38466i
$139$	−21.7752			−1.84695			−0.923473	−	0.383663i	$-0.874662\pi$
$139$	−21.7752			−1.84695			−0.923473	+	0.383663i	$0.874662\pi$
$140$	−4.79952	+	10.8803i	−0.405634	+	0.919551i
$141$	9.14686			0.770305
$142$			30.8881i			2.59207i
$143$			0.774677i			0.0647818i
$144$	28.1278			2.34398
$145$	2.56369	+	1.13090i	0.212903	+	0.0939161i
$146$	6.00932			0.497335
$147$			3.37575i			0.278427i
$148$		−	1.35038i		−	0.111000i
$149$	−16.9257			−1.38660			−0.693302	−	0.720647i	$-0.743845\pi$
$149$	−16.9257			−1.38660			−0.693302	+	0.720647i	$0.743845\pi$
$150$	−20.5788	−	22.5419i	−1.68025	−	1.84054i
$151$	−16.4525			−1.33889			−0.669444	−	0.742863i	$-0.733467\pi$
$151$	−16.4525			−1.33889			−0.669444	+	0.742863i	$0.733467\pi$
$152$		0			0
$153$		−	47.0478i		−	3.80359i
$154$	−1.65504			−0.133367
$155$	−3.56494	−	1.57257i	−0.286342	−	0.126312i
$156$	15.1959			1.21665
$157$		−	6.09304i		−	0.486277i	−0.969992	−	0.243139i	$-0.921823\pi$
$157$		−	6.09304i		−	0.486277i	0.969992	−	0.243139i	$-0.0781770\pi$
$158$		−	15.8704i		−	1.26258i
$159$	−21.6715			−1.71866
$160$	7.07152	−	16.0308i	0.559053	−	1.26734i
$161$	7.57789			0.597221
$162$		−	29.6225i		−	2.32736i
$163$			4.98787i			0.390680i	0.980736	+	0.195340i	$0.0625811\pi$
$163$			4.98787i			0.390680i	−0.980736	+	0.195340i	$0.937419\pi$
$164$	18.8894			1.47501
$165$	0.828441	−	1.87803i	0.0644941	−	0.146205i
$166$	27.2441			2.11455
$167$		−	15.9975i		−	1.23792i	−0.785422	−	0.618961i	$-0.787554\pi$
$167$		−	15.9975i		−	1.23792i	0.785422	−	0.618961i	$-0.212446\pi$
$168$		−	2.25651i		−	0.174094i
$169$	6.14238			0.472491
$170$	−28.5638	−	12.6001i	−2.19074	−	0.966384i
$171$		0			0
$172$			7.51969i			0.573371i
$173$			1.89170i			0.143823i	0.997411	+	0.0719116i	$0.0229100\pi$
$173$			1.89170i			0.143823i	−0.997411	+	0.0719116i	$0.977090\pi$
$174$	7.64962			0.579916
$175$	−10.5016	+	9.58709i	−0.793849	+	0.724716i
$176$	1.25520			0.0946144
$177$			27.4351i			2.06215i
$178$		−	1.08445i		−	0.0812830i
$179$	1.93323			0.144496			0.0722480	−	0.997387i	$-0.476983\pi$
$179$	1.93323			0.144496			0.0722480	+	0.997387i	$0.476983\pi$
$180$	−25.3617	−	11.1876i	−1.89035	−	0.833875i
$181$	2.95409			0.219576			0.109788	−	0.993955i	$-0.464983\pi$
$181$	2.95409			0.219576			0.109788	+	0.993955i	$0.464983\pi$
$182$		−	14.6508i		−	1.08599i
$183$		−	20.5720i		−	1.52073i
$184$	−0.681331			−0.0502284
$185$	0.651692	−	1.47735i	0.0479134	−	0.108617i
$186$	−10.6372			−0.779955
$187$		−	2.09951i		−	0.153531i
$188$		−	5.51221i		−	0.402019i
$189$	−32.0267			−2.32960
$190$		0			0
$191$	−14.3187			−1.03607			−0.518033	−	0.855360i	$-0.673336\pi$
$191$	−14.3187			−1.03607			−0.518033	+	0.855360i	$0.673336\pi$
$192$		−	21.5000i		−	1.55163i
$193$			18.2682i			1.31497i	0.753466	+	0.657487i	$0.228381\pi$
$193$			18.2682i			1.31497i	−0.753466	+	0.657487i	$0.771619\pi$
$194$	12.9883			0.932503
$195$	16.6248	+	7.33355i	1.19053	+	0.525167i
$196$	2.03434			0.145310
$197$			17.1912i			1.22482i	0.790540	+	0.612410i	$0.209800\pi$
$197$			17.1912i			1.22482i	−0.790540	+	0.612410i	$0.790200\pi$
$198$		−	3.85786i		−	0.274166i
$199$	−5.28601			−0.374715			−0.187358	−	0.982292i	$-0.559992\pi$
$199$	−5.28601			−0.374715			−0.187358	+	0.982292i	$0.559992\pi$
$200$	0.944207	−	0.861979i	0.0667655	−	0.0609511i
$201$	−6.01687			−0.424397
$202$			10.1507i			0.714203i
$203$		−	3.56375i		−	0.250126i
$204$	−41.1835			−2.88342
$205$	20.6655	+	9.11602i	1.44334	+	0.636690i
$206$	11.6435			0.811239
$207$			17.6639i			1.22773i
$208$			11.1113i			0.770432i
$209$		0			0
$210$	−15.6676	+	35.5176i	−1.08116	+	2.45094i
$211$	−22.3385			−1.53784			−0.768921	−	0.639344i	$-0.779206\pi$
$211$	−22.3385			−1.53784			−0.768921	+	0.639344i	$0.779206\pi$
$212$			13.0600i			0.896964i
$213$			48.7223i			3.33840i
$214$	7.34715			0.502241
$215$	−3.62900	+	8.22676i	−0.247496	+	0.561061i
$216$	2.87953			0.195928
$217$			4.95556i			0.336405i
$218$		−	17.0687i		−	1.15604i
$219$	9.47899			0.640531
$220$	−1.13177	−	0.499246i	−0.0763036	−	0.0336592i
$221$	18.5853			1.25018
$222$		−	4.40817i		−	0.295857i
$223$			8.49587i			0.568926i	0.958687	+	0.284463i	$0.0918152\pi$
$223$			8.49587i			0.568926i	−0.958687	+	0.284463i	$0.908185\pi$
$224$	−22.2841			−1.48892
$225$	−22.3473	−	24.4791i	−1.48982	−	1.63194i
$226$	−23.3253			−1.55158
$227$		−	13.2798i		−	0.881411i	−0.897652	−	0.440706i	$-0.854728\pi$
$227$		−	13.2798i		−	0.881411i	0.897652	−	0.440706i	$-0.145272\pi$
$228$		0			0
$229$	15.7600			1.04145			0.520725	−	0.853724i	$-0.325662\pi$
$229$	15.7600			1.04145			0.520725	+	0.853724i	$0.325662\pi$
$230$	10.7242	+	4.73066i	0.707131	+	0.311931i
$231$	−2.61063			−0.171767
$232$			0.320418i			0.0210365i
$233$			8.38097i			0.549056i	0.961579	+	0.274528i	$0.0885216\pi$
$233$			8.38097i			0.549056i	−0.961579	+	0.274528i	$0.911478\pi$
$234$	34.1507			2.23250
$235$	2.66019	−	6.03052i	0.173532	−	0.393388i
$236$	16.5333			1.07623
$237$		−	25.0336i		−	1.62611i
$238$			39.7061i			2.57376i
$239$	−3.99353			−0.258320			−0.129160	−	0.991624i	$-0.541228\pi$
$239$	−3.99353			−0.258320			−0.129160	+	0.991624i	$0.541228\pi$
$240$	11.8825	−	26.9370i	0.767011	−	1.73877i
$241$	−14.1034			−0.908483			−0.454241	−	0.890879i	$-0.650090\pi$
$241$	−14.1034			−0.908483			−0.454241	+	0.890879i	$0.650090\pi$
$242$			21.4675i			1.37998i
$243$		−	12.9416i		−	0.830201i
$244$	−12.3974			−0.793662
$245$	2.22563	+	0.981773i	0.142190	+	0.0627232i
$246$	61.6625			3.93146
$247$		0			0
$248$		−	0.445556i		−	0.0282929i
$249$	42.9743			2.72338
$250$	−20.8468	+	7.01170i	−1.31847	+	0.443459i
$251$	14.9564			0.944041			0.472021	−	0.881587i	$-0.343525\pi$
$251$	14.9564			0.944041			0.472021	+	0.881587i	$0.343525\pi$
$252$			35.2549i			2.22085i
$253$			0.788252i			0.0495570i
$254$	22.3347			1.40140
$255$	−45.0560	−	19.8752i	−2.82152	−	1.24463i
$256$	17.8728			1.11705
$257$		−	8.64742i		−	0.539411i	−0.962943	−	0.269706i	$-0.913074\pi$
$257$		−	8.64742i		−	0.539411i	0.962943	−	0.269706i	$-0.0869264\pi$
$258$			24.5473i			1.52825i
$259$	−2.05365			−0.127607
$260$	4.41944	−	10.0187i	0.274082	−	0.621330i
$261$	8.30704			0.514193
$262$		−	24.6010i		−	1.51986i
$263$			15.3655i			0.947476i	0.880666	+	0.473738i	$0.157096\pi$
$263$			15.3655i			0.947476i	−0.880666	+	0.473738i	$0.842904\pi$
$264$	0.234722			0.0144462
$265$	−6.30276	+	14.2880i	−0.387175	+	0.877706i
$266$		0			0
$267$		−	1.71059i		−	0.104687i
$268$			3.62597i			0.221491i
$269$	16.5642			1.00993			0.504967	−	0.863139i	$-0.331505\pi$
$269$	16.5642			1.00993			0.504967	+	0.863139i	$0.331505\pi$
$270$	−45.3240	−	19.9934i	−2.75833	−	1.21676i
$271$	6.71990			0.408205			0.204103	−	0.978950i	$-0.434572\pi$
$271$	6.71990			0.408205			0.204103	+	0.978950i	$0.434572\pi$
$272$		−	30.1136i		−	1.82591i
$273$		−	23.1099i		−	1.39867i
$274$	−28.5949			−1.72748
$275$	−0.997249	−	1.09238i	−0.0601364	−	0.0658730i
$276$	15.4622			0.930715
$277$			7.71506i			0.463553i	0.972769	+	0.231777i	$0.0744538\pi$
$277$			7.71506i			0.463553i	−0.972769	+	0.231777i	$0.925546\pi$
$278$			42.8369i			2.56919i
$279$	−11.5513			−0.691560
$280$	−1.48772	−	0.656263i	−0.0889080	−	0.0392192i
$281$	13.7574			0.820696			0.410348	−	0.911929i	$-0.365407\pi$
$281$	13.7574			0.820696			0.410348	+	0.911929i	$0.365407\pi$
$282$		−	17.9940i		−	1.07153i
$283$		−	16.5978i		−	0.986639i	−0.869848	−	0.493320i	$-0.835783\pi$
$283$		−	16.5978i		−	0.986639i	0.869848	−	0.493320i	$-0.164217\pi$
$284$	29.3617			1.74230
$285$		0			0
$286$	1.52397			0.0901144
$287$		−	28.7269i		−	1.69569i
$288$		−	51.9439i		−	3.06083i
$289$	−33.3694			−1.96291
$290$	2.22475	−	5.04339i	0.130642	−	0.296158i
$291$	20.4874			1.20100
$292$		−	5.71236i		−	0.334290i
$293$			7.39839i			0.432219i	0.976369	+	0.216109i	$0.0693367\pi$
$293$			7.39839i			0.432219i	−0.976369	+	0.216109i	$0.930663\pi$
$294$	6.64090			0.387305
$295$	18.0879	+	7.97898i	1.05312	+	0.464554i
$296$	0.184644			0.0107322
$297$		−	3.33142i		−	0.193309i
$298$			33.2968i			1.92883i
$299$	−6.97779			−0.403536
$300$	−21.4279	+	19.5618i	−1.23714	+	1.12940i
$301$	11.4359			0.659154
$302$			32.3660i			1.86245i
$303$			16.0116i			0.919841i
$304$		0			0
$305$	−13.5631	−	5.98298i	−0.776622	−	0.342585i
$306$	−92.5542			−5.29097
$307$		−	13.8884i		−	0.792656i	−0.918109	−	0.396328i	$-0.870284\pi$
$307$		−	13.8884i		−	0.792656i	0.918109	−	0.396328i	$-0.129716\pi$
$308$			1.57325i			0.0896442i
$309$	18.3662			1.04482
$310$	−3.09362	+	7.01307i	−0.175706	+	0.398316i
$311$	26.4251			1.49843			0.749214	−	0.662328i	$-0.230431\pi$
$311$	26.4251			1.49843			0.749214	+	0.662328i	$0.230431\pi$
$312$			2.07782i			0.117633i
$313$		−	6.91198i		−	0.390688i	−0.980735	−	0.195344i	$-0.937418\pi$
$313$		−	6.91198i		−	0.390688i	0.980735	−	0.195344i	$-0.0625823\pi$
$314$	−11.9864			−0.676434
$315$	−17.0140	+	38.5700i	−0.958633	+	2.17317i
$316$	−15.0861			−0.848660
$317$			28.7345i			1.61389i	0.590628	+	0.806944i	$0.298880\pi$
$317$			28.7345i			1.61389i	−0.590628	+	0.806944i	$0.701120\pi$
$318$			42.6330i			2.39074i
$319$	0.370701			0.0207553
$320$	−14.1749	−	6.25286i	−0.792401	−	0.349545i
$321$	11.5893			0.646849
$322$		−	14.9075i		−	0.830763i
$323$		0			0
$324$	−28.1586			−1.56437
$325$	9.67001	−	8.82788i	0.536396	−	0.489683i
$326$	9.81232			0.543454
$327$		−	26.9238i		−	1.48889i
$328$			2.58284i			0.142614i
$329$	−8.38293			−0.462166
$330$	−3.69454	−	1.62974i	−0.203378	−	0.0897142i
$331$	8.13446			0.447110			0.223555	−	0.974691i	$-0.428234\pi$
$331$	8.13446			0.447110			0.223555	+	0.974691i	$0.428234\pi$
$332$		−	25.8977i		−	1.42132i
$333$		−	4.78701i		−	0.262327i
$334$	−31.4708			−1.72201
$335$	−1.74989	+	3.96692i	−0.0956069	+	0.216736i
$336$	−37.4447			−2.04277
$337$		−	6.76361i		−	0.368437i	−0.982885	−	0.184219i	$-0.941025\pi$
$337$		−	6.76361i		−	0.368437i	0.982885	−	0.184219i	$-0.0589754\pi$
$338$		−	12.0835i		−	0.657257i
$339$	−36.7929			−1.99832
$340$	−11.9774	+	27.1523i	−0.649568	+	1.47254i
$341$	−0.515478			−0.0279147
$342$		0			0
$343$			16.8136i			0.907850i
$344$	−1.02821			−0.0554371
$345$	16.9161	+	7.46206i	0.910733	+	0.401744i
$346$	3.72142			0.200065
$347$		−	15.5843i		−	0.836609i	−0.908307	−	0.418305i	$-0.862624\pi$
$347$		−	15.5843i		−	0.836609i	0.908307	−	0.418305i	$-0.137376\pi$
$348$		−	7.27160i		−	0.389799i
$349$	−5.80011			−0.310473			−0.155237	−	0.987877i	$-0.549614\pi$
$349$	−5.80011			−0.310473			−0.155237	+	0.987877i	$0.549614\pi$
$350$	18.8601	+	20.6592i	1.00811	+	1.10428i
$351$	29.4905			1.57409
$352$		−	2.31800i		−	0.123550i
$353$		−	31.7700i		−	1.69095i	−0.534016	−	0.845474i	$-0.679318\pi$
$353$		−	31.7700i		−	1.69095i	0.534016	−	0.845474i	$-0.320682\pi$
$354$	53.9714			2.86855
$355$	32.1226	+	14.1700i	1.70489	+	0.752063i
$356$	−1.03086			−0.0546355
$357$			62.6317i			3.31482i
$358$		−	3.80311i		−	0.201001i
$359$	−13.0256			−0.687464			−0.343732	−	0.939068i	$-0.611691\pi$
$359$	−13.0256			−0.687464			−0.343732	+	0.939068i	$0.611691\pi$
$360$	1.52974	−	3.46784i	0.0806243	−	0.182771i
$361$		0			0
$362$		−	5.81140i		−	0.305441i
$363$			33.8624i			1.77731i
$364$	−13.9268			−0.729961
$365$	2.75678	−	6.24949i	0.144297	−	0.327113i
$366$	−40.4700			−2.11540
$367$		−	11.9948i		−	0.626123i	−0.949733	−	0.313062i	$-0.898645\pi$
$367$		−	11.9948i		−	0.626123i	0.949733	−	0.313062i	$-0.101355\pi$
$368$			11.3060i			0.589368i
$369$	66.9618			3.48589
$370$	−2.90630	−	1.28203i	−0.151092	−	0.0666497i
$371$	19.8616			1.03116
$372$			10.1115i			0.524257i
$373$			26.0276i			1.34766i	0.738888	+	0.673829i	$0.235351\pi$
$373$			26.0276i			1.34766i	−0.738888	+	0.673829i	$0.764649\pi$
$374$	−4.13023			−0.213569
$375$	−32.8833	+	11.0601i	−1.69809	+	0.571142i
$376$	0.753712			0.0388697
$377$			3.28153i			0.169007i
$378$			63.0041i			3.24058i
$379$	6.45800			0.331725			0.165863	−	0.986149i	$-0.446959\pi$
$379$	6.45800			0.331725			0.165863	+	0.986149i	$0.446959\pi$
$380$		0			0
$381$	35.2304			1.80491
$382$			28.1683i			1.44122i
$383$			0.663150i			0.0338854i	0.999856	+	0.0169427i	$0.00539328\pi$
$383$			0.663150i			0.0338854i	−0.999856	+	0.0169427i	$0.994607\pi$
$384$	6.33421			0.323241
$385$	−0.759251	+	1.72118i	−0.0386950	+	0.0877196i
$386$	35.9379			1.82919
$387$			26.6569i			1.35505i
$388$		−	12.3464i		−	0.626795i
$389$	−31.6296			−1.60368			−0.801841	−	0.597537i	$-0.796146\pi$
$389$	−31.6296			−1.60368			−0.801841	+	0.597537i	$0.796146\pi$
$390$	14.4268	−	32.7049i	0.730531	−	1.65608i
$391$	18.9110			0.956371
$392$			0.278166i			0.0140495i
$393$		−	38.8052i		−	1.95746i
$394$	33.8191			1.70378
$395$	−16.5047	−	7.28056i	−0.830439	−	0.366325i
$396$	−3.66722			−0.184285
$397$		−	29.1694i		−	1.46397i	−0.681319	−	0.731986i	$-0.738593\pi$
$397$		−	29.1694i		−	1.46397i	0.681319	−	0.731986i	$-0.261407\pi$
$398$			10.3988i			0.521247i
$399$		0			0
$400$	−14.3037	−	15.6682i	−0.715186	−	0.783411i
$401$	−14.5778			−0.727981			−0.363990	−	0.931403i	$-0.618586\pi$
$401$	−14.5778			−0.727981			−0.363990	+	0.931403i	$0.618586\pi$
$402$			11.8366i			0.590357i
$403$		−	4.56313i		−	0.227306i
$404$	9.64911			0.480061
$405$	−30.8064	−	13.5894i	−1.53078	−	0.675261i
$406$	−7.01074			−0.347937
$407$		−	0.213620i		−	0.0105888i
$408$		−	5.63124i		−	0.278788i
$409$	25.9273			1.28202			0.641011	−	0.767532i	$-0.278515\pi$
$409$	25.9273			1.28202			0.641011	+	0.767532i	$0.278515\pi$
$410$	17.9334	−	40.6540i	0.885666	−	2.00776i
$411$	−45.1051			−2.22487
$412$		−	11.0681i		−	0.545285i
$413$		−	25.1438i		−	1.23724i
$414$	34.7491			1.70783
$415$	12.4983	−	28.3329i	0.613515	−	1.39081i
$416$	20.5194			1.00605
$417$			67.5702i			3.30893i
$418$		0			0
$419$	19.1795			0.936981			0.468491	−	0.883468i	$-0.344798\pi$
$419$	19.1795			0.936981			0.468491	+	0.883468i	$0.344798\pi$
$420$	33.7624	+	14.8933i	1.64744	+	0.726719i
$421$	−2.77299			−0.135147			−0.0675736	−	0.997714i	$-0.521526\pi$
$421$	−2.77299			−0.135147			−0.0675736	+	0.997714i	$0.521526\pi$
$422$			43.9450i			2.13921i
$423$		−	19.5405i		−	0.950090i
$424$	−1.78576			−0.0867242
$425$	−26.2074	+	23.9251i	−1.27124	+	1.16054i
$426$	95.8483			4.64386
$427$			18.8539i			0.912403i
$428$		−	6.98407i		−	0.337588i
$429$	2.40389			0.116061
$430$	16.1840	+	7.13911i	0.780461	+	0.344278i
$431$	7.17556			0.345634			0.172817	−	0.984954i	$-0.444713\pi$
$431$	7.17556			0.345634			0.172817	+	0.984954i	$0.444713\pi$
$432$		−	47.7831i		−	2.29897i
$433$			23.4728i			1.12803i	0.825763	+	0.564017i	$0.190745\pi$
$433$			23.4728i			1.12803i	−0.825763	+	0.564017i	$0.809255\pi$
$434$	9.74876			0.467956
$435$	3.50928	−	7.95535i	0.168257	−	0.381430i
$436$	−16.2252			−0.777046
$437$		0			0
$438$		−	18.6474i		−	0.891008i
$439$	13.7755			0.657468			0.328734	−	0.944423i	$-0.393378\pi$
$439$	13.7755			0.657468			0.328734	+	0.944423i	$0.393378\pi$
$440$	0.0682645	−	0.154752i	0.00325438	−	0.00737752i
$441$	7.21163			0.343411
$442$		−	36.5617i		−	1.73906i
$443$		−	1.10536i		−	0.0525173i	−0.999655	−	0.0262587i	$-0.991641\pi$
$443$		−	1.10536i		−	0.0525173i	0.999655	−	0.0262587i	$-0.00835935\pi$
$444$	−4.19033			−0.198864
$445$	−1.12779	−	0.497493i	−0.0534625	−	0.0235834i
$446$	16.7134			0.791402
$447$			52.5217i			2.48419i
$448$			19.7043i			0.930942i
$449$	−36.2183			−1.70925			−0.854624	−	0.519248i	$-0.826212\pi$
$449$	−36.2183			−1.70925			−0.854624	+	0.519248i	$0.826212\pi$
$450$	−48.1563	+	43.9625i	−2.27011	+	2.07241i
$451$	2.98817			0.140707
$452$			22.1727i			1.04291i
$453$			51.0535i			2.39870i
$454$	−26.1245			−1.22608
$455$	−15.2363	−	6.72106i	−0.714289	−	0.315088i
$456$		0			0
$457$			40.3095i			1.88560i	0.333358	+	0.942800i	$0.391818\pi$
$457$			40.3095i			1.88560i	−0.333358	+	0.942800i	$0.608182\pi$
$458$		−	31.0037i		−	1.44871i
$459$	−79.9243			−3.73055
$460$	4.49689	−	10.1942i	0.209668	−	0.475308i
$461$	−17.1122			−0.796993			−0.398497	−	0.917170i	$-0.630468\pi$
$461$	−17.1122			−0.796993			−0.398497	+	0.917170i	$0.630468\pi$
$462$			5.13572i			0.238935i
$463$		−	9.09776i		−	0.422809i	−0.977399	−	0.211404i	$-0.932196\pi$
$463$		−	9.09776i		−	0.422809i	0.977399	−	0.211404i	$-0.0678037\pi$
$464$	5.31703			0.246837
$465$	−4.87982	+	11.0623i	−0.226296	+	0.513001i
$466$	16.4874			0.763762
$467$			34.4216i			1.59284i	0.604744	+	0.796420i	$0.293275\pi$
$467$			34.4216i			1.59284i	−0.604744	+	0.796420i	$0.706725\pi$
$468$		−	32.4631i		−	1.50061i
$469$	5.51435			0.254629
$470$	−11.8635	−	5.23323i	−0.547220	−	0.241391i
$471$	−18.9072			−0.871198
$472$			2.26069i			0.104056i
$473$			1.18956i			0.0546961i
$474$	−49.2471			−2.26199
$475$		0			0
$476$	37.7439			1.72999
$477$			46.2970i			2.11979i
$478$			7.85621i			0.359335i
$479$	−28.4249			−1.29877			−0.649383	−	0.760461i	$-0.724973\pi$
$479$	−28.4249			−1.29877			−0.649383	+	0.760461i	$0.724973\pi$
$480$	−49.7448	−	21.9435i	−2.27053	−	1.00158i
$481$	1.89102			0.0862229
$482$			27.7448i			1.26374i
$483$		−	23.5148i		−	1.06996i
$484$	20.4066			0.927572
$485$	5.95839	−	13.5074i	0.270556	−	0.613337i
$486$	−25.4591			−1.15485
$487$		−	31.5734i		−	1.43073i	−0.698753	−	0.715363i	$-0.746261\pi$
$487$		−	31.5734i		−	1.43073i	0.698753	−	0.715363i	$-0.253739\pi$
$488$		−	1.69516i		−	0.0767363i
$489$	15.4778			0.699929
$490$	1.93138	−	4.37834i	0.0872509	−	0.197793i
$491$	2.94848			0.133063			0.0665316	−	0.997784i	$-0.478807\pi$
$491$	2.94848			0.133063			0.0665316	+	0.997784i	$0.478807\pi$
$492$		−	58.6153i		−	2.64258i
$493$		−	8.89351i		−	0.400544i
$494$		0			0
$495$	−4.01205	−	1.76980i	−0.180328	−	0.0795466i
$496$	−7.39359			−0.331982
$497$		−	44.6531i		−	2.00296i
$498$		−	84.5406i		−	3.78835i
$499$	1.21530			0.0544041			0.0272020	−	0.999630i	$-0.491340\pi$
$499$	1.21530			0.0544041			0.0272020	+	0.999630i	$0.491340\pi$
$500$	6.66520	+	19.8166i	0.298077	+	0.886226i
$501$	−49.6415			−2.21782
$502$		−	29.4228i		−	1.31321i
$503$			33.5439i			1.49565i	0.663897	+	0.747824i	$0.268902\pi$
$503$			33.5439i			1.49565i	−0.663897	+	0.747824i	$0.731098\pi$
$504$	−4.82059			−0.214726
$505$	10.5564	+	4.65666i	0.469754	+	0.207219i
$506$	1.55068			0.0689361
$507$		−	19.0603i		−	0.846498i
$508$		−	21.2310i		−	0.941973i
$509$	−31.8382			−1.41120			−0.705602	−	0.708608i	$-0.749323\pi$
$509$	−31.8382			−1.41120			−0.705602	+	0.708608i	$0.749323\pi$
$510$	−39.0992	+	88.6359i	−1.73134	+	3.92486i
$511$	−8.68732			−0.384304
$512$		−	31.0775i		−	1.37345i
$513$		0			0
$514$	−17.0115			−0.750346
$515$	5.34146	−	12.1088i	0.235373	−	0.533578i
$516$	23.3342			1.02723
$517$		−	0.871992i		−	0.0383502i
$518$			4.04001i			0.177508i
$519$	5.87010			0.257669
$520$	1.36990	+	0.604293i	0.0600742	+	0.0265000i
$521$	−34.6420			−1.51769			−0.758846	−	0.651270i	$-0.774237\pi$
$521$	−34.6420			−1.51769			−0.758846	+	0.651270i	$0.774237\pi$
$522$		−	16.3419i		−	0.715266i
$523$		−	31.4309i		−	1.37438i	−0.726480	−	0.687188i	$-0.758845\pi$
$523$		−	31.4309i		−	1.37438i	0.726480	−	0.687188i	$-0.241155\pi$
$524$	−23.3853			−1.02159
$525$	29.7495	+	32.5875i	1.29838	+	1.42223i
$526$	30.2275			1.31798
$527$			12.3669i			0.538709i
$528$		−	3.89499i		−	0.169508i
$529$	15.8999			0.691302
$530$	28.1079	+	12.3990i	1.22093	+	0.538579i
$531$	58.6097			2.54344
$532$		0			0
$533$			26.4520i			1.14576i
$534$	−3.36514			−0.145624
$535$	3.37052	−	7.64079i	0.145720	−	0.330340i
$536$	−0.495797			−0.0214152
$537$		−	5.99896i		−	0.258874i
$538$		−	32.5856i		−	1.40487i
$539$	0.321819			0.0138617
$540$	−19.0054	+	43.0842i	−0.817861	+	1.85405i
$541$	−39.3709			−1.69269			−0.846344	−	0.532636i	$-0.821202\pi$
$541$	−39.3709			−1.69269			−0.846344	+	0.532636i	$0.821202\pi$
$542$		−	13.2196i		−	0.567832i
$543$		−	9.16680i		−	0.393385i
$544$	−55.6112			−2.38431
$545$	−17.7508	−	7.83028i	−0.760363	−	0.335412i
$546$	−45.4626			−1.94562
$547$		−	2.76298i		−	0.118136i	−0.998254	−	0.0590682i	$-0.981187\pi$
$547$		−	2.76298i		−	0.118136i	0.998254	−	0.0590682i	$-0.0188129\pi$
$548$			27.1819i			1.16115i
$549$	−43.9481			−1.87566
$550$	−2.14897	+	1.96183i	−0.0916325	+	0.0836525i
$551$		0			0
$552$			2.11423i			0.0899875i
$553$			22.9429i			0.975630i
$554$	15.1774			0.644824
$555$	−4.58435	−	2.02226i	−0.194595	−	0.0858400i
$556$	40.7201			1.72692
$557$			5.58153i			0.236497i	0.992984	+	0.118249i	$0.0377279\pi$
$557$			5.58153i			0.236497i	−0.992984	+	0.118249i	$0.962272\pi$
$558$			22.7242i			0.961992i
$559$	−10.5303			−0.445383
$560$	−10.8901	+	24.6872i	−0.460189	+	1.04323i
$561$	−6.51495			−0.275061
$562$		−	27.0640i		−	1.14163i
$563$		−	24.0365i		−	1.01302i	−0.862235	−	0.506509i	$-0.830936\pi$
$563$		−	24.0365i		−	1.01302i	0.862235	−	0.506509i	$-0.169064\pi$
$564$	−17.1048			−0.720243
$565$	−10.7005	+	24.2575i	−0.450175	+	1.02052i
$566$	−32.6519			−1.37246
$567$			42.8235i			1.79842i
$568$			4.01477i			0.168456i
$569$	4.92199			0.206340			0.103170	−	0.994664i	$-0.467101\pi$
$569$	4.92199			0.206340			0.103170	+	0.994664i	$0.467101\pi$
$570$		0			0
$571$	−31.4861			−1.31765			−0.658826	−	0.752295i	$-0.728947\pi$
$571$	−31.4861			−1.31765			−0.658826	+	0.752295i	$0.728947\pi$
$572$		−	1.44866i		−	0.0605717i
$573$			44.4322i			1.85618i
$574$	−56.5125			−2.35879
$575$	9.83946	−	8.98258i	0.410334	−	0.374599i
$576$	−45.9304			−1.91377
$577$		−	29.2520i		−	1.21778i	−0.793256	−	0.608888i	$-0.791616\pi$
$577$		−	29.2520i		−	1.21778i	0.793256	−	0.608888i	$-0.208384\pi$
$578$			65.6455i			2.73049i
$579$	56.6878			2.35586
$580$	−4.79416	−	2.11481i	−0.199067	−	0.0878126i
$581$	−39.3851			−1.63397
$582$		−	40.3037i		−	1.67064i
$583$			2.06600i			0.0855650i
$584$	0.781080			0.0323213
$585$	15.6667	−	35.5156i	0.647738	−	1.46839i
$586$	14.5544			0.601236
$587$			24.0082i			0.990924i	0.868630	+	0.495462i	$0.165001\pi$
$587$			24.0082i			0.990924i	−0.868630	+	0.495462i	$0.834999\pi$
$588$		−	6.31273i		−	0.260333i
$589$		0			0
$590$	15.6965	−	35.5833i	0.646217	−	1.46494i
$591$	53.3456			2.19435
$592$		−	3.06399i		−	0.125929i
$593$			1.68162i			0.0690558i	0.999404	+	0.0345279i	$0.0109928\pi$
$593$			1.68162i			0.0690558i	−0.999404	+	0.0345279i	$0.989007\pi$
$594$	−6.55369			−0.268901
$595$	41.2930	+	18.2152i	1.69285	+	0.746752i
$596$	31.6513			1.29649
$597$			16.4029i			0.671327i
$598$			13.7270i			0.561337i
$599$	−42.2900			−1.72792			−0.863960	−	0.503560i	$-0.832023\pi$
$599$	−42.2900			−1.72792			−0.863960	+	0.503560i	$0.832023\pi$
$600$	−2.67479	−	2.92995i	−0.109198	−	0.119615i
$601$	−26.9576			−1.09962			−0.549811	−	0.835289i	$-0.685300\pi$
$601$	−26.9576			−1.09962			−0.549811	+	0.835289i	$0.685300\pi$
$602$		−	22.4971i		−	0.916914i
$603$			12.8539i			0.523450i
$604$	30.7666			1.25187
$605$	22.3254	+	9.84823i	0.907657	+	0.400387i
$606$	31.4986			1.27954
$607$		−	11.0115i		−	0.446944i	−0.974710	−	0.223472i	$-0.928261\pi$
$607$		−	11.0115i		−	0.446944i	0.974710	−	0.223472i	$-0.0717391\pi$
$608$		0			0
$609$	−11.0586			−0.448117
$610$	−11.7699	+	26.6819i	−0.476551	+	1.08032i
$611$	7.71908			0.312280
$612$			87.9805i			3.55640i
$613$			3.32175i			0.134164i	0.997747	+	0.0670822i	$0.0213690\pi$
$613$			3.32175i			0.134164i	−0.997747	+	0.0670822i	$0.978631\pi$
$614$	−27.3219			−1.10262
$615$	28.2878	−	64.1269i	1.14067	−	2.58585i
$616$	−0.215119			−0.00866738
$617$		−	11.0613i		−	0.445311i	−0.974897	−	0.222655i	$-0.928528\pi$
$617$		−	11.0613i		−	0.445311i	0.974897	−	0.222655i	$-0.0714725\pi$
$618$		−	36.1307i		−	1.45339i
$619$	−36.2777			−1.45812			−0.729062	−	0.684448i	$-0.760043\pi$
$619$	−36.2777			−1.45812			−0.729062	+	0.684448i	$0.760043\pi$
$620$	6.66651	+	2.94074i	0.267733	+	0.118103i
$621$	30.0073			1.20415
$622$		−	51.9844i		−	2.08438i
$623$			1.56773i			0.0628096i
$624$	34.4794			1.38028
$625$	−2.27157	+	24.8966i	−0.0908629	+	0.995863i
$626$	−13.5975			−0.543465
$627$		0			0
$628$			11.3941i			0.454674i
$629$	−5.12498			−0.204346
$630$	75.8763	+	33.4707i	3.02298	+	1.33350i
$631$	−1.73816			−0.0691950			−0.0345975	−	0.999401i	$-0.511015\pi$
$631$	−1.73816			−0.0691950			−0.0345975	+	0.999401i	$0.511015\pi$
$632$		−	2.06280i		−	0.0820538i
$633$			69.3181i			2.75515i
$634$	56.5275			2.24499
$635$	10.2461	−	23.2273i	0.406603	−	0.921749i
$636$	40.5262			1.60697
$637$			2.84881i			0.112874i
$638$		−	0.729257i		−	0.0288716i
$639$	104.086			4.11756
$640$	1.84218	−	4.17614i	0.0728187	−	0.165076i
$641$	−36.2439			−1.43155			−0.715774	−	0.698332i	$-0.753926\pi$
$641$	−36.2439			−1.43155			−0.715774	+	0.698332i	$0.753926\pi$
$642$		−	22.7988i		−	0.899798i
$643$		−	31.8707i		−	1.25686i	−0.777867	−	0.628429i	$-0.783698\pi$
$643$		−	31.8707i		−	1.25686i	0.777867	−	0.628429i	$-0.216302\pi$
$644$	−14.1708			−0.558408
$645$	25.5283	+	11.2611i	1.00518	+	0.443405i
$646$		0			0
$647$		−	21.1503i		−	0.831504i	−0.909478	−	0.415752i	$-0.863518\pi$
$647$		−	21.1503i		−	0.831504i	0.909478	−	0.415752i	$-0.136482\pi$
$648$		−	3.85028i		−	0.151253i
$649$	2.61545			0.102666
$650$	−17.3665	−	19.0232i	−0.681171	−	0.746151i
$651$	15.3775			0.602692
$652$		−	9.32743i		−	0.365290i
$653$		−	18.0859i		−	0.707758i	−0.935291	−	0.353879i	$-0.884863\pi$
$653$		−	18.0859i		−	0.707758i	0.935291	−	0.353879i	$-0.115137\pi$
$654$	−52.9655			−2.07112
$655$	−25.5842	−	11.2858i	−0.999658	−	0.440971i
$656$	42.8598			1.67340
$657$		−	20.2500i		−	0.790027i
$658$			16.4912i			0.642894i
$659$	11.0391			0.430024			0.215012	−	0.976611i	$-0.431021\pi$
$659$	11.0391			0.430024			0.215012	+	0.976611i	$0.431021\pi$
$660$	−1.54920	+	3.51196i	−0.0603026	+	0.136703i
$661$	14.9040			0.579698			0.289849	−	0.957072i	$-0.406395\pi$
$661$	14.9040			0.579698			0.289849	+	0.957072i	$0.406395\pi$
$662$		−	16.0024i		−	0.621951i
$663$		−	57.6718i		−	2.23979i
$664$	3.54113			0.137423
$665$		0			0
$666$	−9.41719			−0.364909
$667$			3.33904i			0.129288i
$668$			29.9156i			1.15747i
$669$	26.3634			1.01927
$670$	7.80387	+	3.44245i	0.301490	+	0.132994i
$671$	−1.96118			−0.0757105
$672$			69.1495i			2.66750i
$673$			1.42988i			0.0551178i	0.999620	+	0.0275589i	$0.00877339\pi$
$673$			1.42988i			0.0551178i	−0.999620	+	0.0275589i	$0.991227\pi$
$674$	−13.3056			−0.512513
$675$	−41.5849	+	37.9634i	−1.60060	+	1.46121i
$676$	−11.4864			−0.441784
$677$			4.76323i			0.183066i	0.995802	+	0.0915330i	$0.0291767\pi$
$677$			4.76323i			0.183066i	−0.995802	+	0.0915330i	$0.970823\pi$
$678$			72.3804i			2.77975i
$679$	−18.7764			−0.720571
$680$	−3.71267	−	1.63774i	−0.142374	−	0.0628044i
$681$	−41.2083			−1.57911
$682$			1.01407i			0.0388306i
$683$		−	44.7585i		−	1.71264i	−0.516450	−	0.856318i	$-0.672747\pi$
$683$		−	44.7585i		−	1.71264i	0.516450	−	0.856318i	$-0.327253\pi$
$684$		0			0
$685$	−13.1180	+	29.7378i	−0.501212	+	1.13622i
$686$	33.0764			1.26286
$687$		−	48.9046i		−	1.86583i
$688$			17.0621i			0.650486i
$689$	−18.2887			−0.696744
$690$	14.6796	−	33.2780i	0.558844	−	1.26687i
$691$	−19.5587			−0.744046			−0.372023	−	0.928223i	$-0.621336\pi$
$691$	−19.5587			−0.744046			−0.372023	+	0.928223i	$0.621336\pi$
$692$		−	3.53752i		−	0.134476i
$693$			5.57709i			0.211856i
$694$	−30.6580			−1.16376
$695$	44.5490	+	19.6515i	1.68984	+	0.745424i
$696$	0.994283			0.0376882
$697$		−	71.6893i		−	2.71543i
$698$			11.4102i			0.431882i
$699$	26.0069			0.983670
$700$	19.6383	−	17.9281i	0.742258	−	0.677617i
$701$	37.2131			1.40552			0.702760	−	0.711427i	$-0.251951\pi$
$701$	37.2131			1.40552			0.702760	+	0.711427i	$0.251951\pi$
$702$		−	58.0148i		−	2.18963i
$703$		0			0
$704$	−2.04964			−0.0772489
$705$	−18.7132	−	8.25480i	−0.704780	−	0.310894i
$706$	−62.4992			−2.35219
$707$		−	14.6743i		−	0.551884i
$708$		−	51.3042i		−	1.92813i
$709$	42.2853			1.58806			0.794030	−	0.607879i	$-0.207979\pi$
$709$	42.2853			1.58806			0.794030	+	0.607879i	$0.207979\pi$
$710$	27.8757	−	63.1927i	1.04615	−	2.37158i
$711$	−53.4794			−2.00563
$712$		−	0.140955i		−	0.00528251i
$713$		−	4.64309i		−	0.173885i
$714$	123.211			4.61107
$715$	0.699125	−	1.58488i	0.0261458	−	0.0592712i
$716$	−3.61517			−0.135105
$717$			12.3922i			0.462797i
$718$			25.6244i			0.956295i
$719$	−28.1334			−1.04920			−0.524600	−	0.851349i	$-0.675785\pi$
$719$	−28.1334			−1.04920			−0.524600	+	0.851349i	$0.675785\pi$
$720$	−57.5455	−	25.3846i	−2.14459	−	0.946027i
$721$	−16.8323			−0.626867
$722$		0			0
$723$			43.7642i			1.62761i
$724$	−5.52422			−0.205306
$725$	−4.22435	−	4.62732i	−0.156888	−	0.171855i
$726$	66.6153			2.47233
$727$		−	10.3337i		−	0.383254i	−0.981468	−	0.191627i	$-0.938624\pi$
$727$		−	10.3337i		−	0.383254i	0.981468	−	0.191627i	$-0.0613764\pi$
$728$		−	1.90428i		−	0.0705773i
$729$	5.01504			0.185742
$730$	−12.2942	−	5.42325i	−0.455030	−	0.200723i
$731$	28.5389			1.05555
$732$			38.4701i			1.42190i
$733$			0.823810i			0.0304281i	0.999884	+	0.0152141i	$0.00484297\pi$
$733$			0.823810i			0.0304281i	−0.999884	+	0.0152141i	$0.995157\pi$
$734$	−23.5966			−0.870967
$735$	3.04652	−	6.90631i	0.112373	−	0.254743i
$736$	20.8790			0.769610
$737$			0.573603i			0.0211289i
$738$		−	131.730i		−	4.84904i
$739$	−34.6161			−1.27337			−0.636687	−	0.771122i	$-0.719696\pi$
$739$	−34.6161			−1.27337			−0.636687	+	0.771122i	$0.719696\pi$
$740$	−1.21868	+	2.76268i	−0.0447995	+	0.101558i
$741$		0			0
$742$		−	39.0724i		−	1.43439i
$743$		−	33.8604i		−	1.24222i	−0.783724	−	0.621109i	$-0.786683\pi$
$743$		−	33.8604i		−	1.24222i	0.783724	−	0.621109i	$-0.213317\pi$
$744$	−1.38260			−0.0506885
$745$	34.6275	+	15.2749i	1.26865	+	0.559631i
$746$	51.2024			1.87465
$747$		−	91.8060i		−	3.35901i
$748$			3.92613i			0.143553i
$749$	−10.6213			−0.388095
$750$	21.7579	+	64.6893i	0.794485	+	2.36212i
$751$	−17.8196			−0.650247			−0.325124	−	0.945672i	$-0.605406\pi$
$751$	−17.8196			−0.650247			−0.325124	+	0.945672i	$0.605406\pi$
$752$		−	12.5071i		−	0.456089i
$753$		−	46.4110i		−	1.69131i
$754$	6.45555			0.235097
$755$	33.6596	+	14.8480i	1.22500	+	0.540372i
$756$	59.8907			2.17820
$757$			1.70824i			0.0620870i	0.999518	+	0.0310435i	$0.00988304\pi$
$757$			1.70824i			0.0620870i	−0.999518	+	0.0310435i	$0.990117\pi$
$758$		−	12.7044i		−	0.461445i
$759$	2.44601			0.0887846
$760$		0			0
$761$	2.70054			0.0978944			0.0489472	−	0.998801i	$-0.484413\pi$
$761$	2.70054			0.0978944			0.0489472	+	0.998801i	$0.484413\pi$
$762$		−	69.3065i		−	2.51071i
$763$			24.6752i			0.893302i
$764$	26.7763			0.968734
$765$	−42.4594	+	96.2533i	−1.53512	+	3.48004i
$766$	1.30457			0.0471362
$767$			23.1526i			0.835992i
$768$		−	55.4608i		−	2.00127i
$769$	−25.2710			−0.911296			−0.455648	−	0.890160i	$-0.650592\pi$
$769$	−25.2710			−0.911296			−0.455648	+	0.890160i	$0.650592\pi$
$770$	3.38597	+	1.49363i	0.122022	+	0.0538266i
$771$	−26.8337			−0.966391
$772$		−	34.1620i		−	1.22952i
$773$			44.9679i			1.61738i	0.588233	+	0.808692i	$0.299824\pi$
$773$			44.9679i			1.61738i	−0.588233	+	0.808692i	$0.700176\pi$
$774$	52.4404			1.88493
$775$	5.87416	+	6.43452i	0.211006	+	0.231135i
$776$	1.68819			0.0606025
$777$			6.37263i			0.228617i
$778$			62.2228i			2.23080i
$779$		0			0
$780$	−31.0887	−	13.7139i	−1.11315	−	0.491036i
$781$	4.64481			0.166204
$782$		−	37.2024i		−	1.33036i
$783$		−	14.1119i		−	0.504318i
$784$	4.61590			0.164854
$785$	−5.49880	+	12.4655i	−0.196261	+	0.444913i
$786$	−76.3390			−2.72292
$787$			2.87342i			0.102426i	0.998688	+	0.0512132i	$0.0163088\pi$
$787$			2.87342i			0.102426i	−0.998688	+	0.0512132i	$0.983691\pi$
$788$		−	32.1479i		−	1.14522i
$789$	47.6803			1.69747
$790$	−14.3226	+	32.4686i	−0.509575	+	1.15518i
$791$	33.7200			1.19895
$792$		−	0.501438i		−	0.0178178i
$793$		−	17.3608i		−	0.616501i
$794$	−57.3832			−2.03645
$795$	44.3369	+	19.5580i	1.57247	+	0.693650i
$796$	9.88496			0.350363
$797$			35.2445i			1.24842i	0.781255	+	0.624212i	$0.214580\pi$
$797$			35.2445i			1.24842i	−0.781255	+	0.624212i	$0.785420\pi$
$798$		0			0
$799$	−20.9200			−0.740097
$800$	−28.9347	+	26.4149i	−1.02300	+	0.933906i
$801$	−3.65434			−0.129120
$802$			28.6780i			1.01266i
$803$		−	0.903655i		−	0.0318893i
$804$	11.2517			0.396816
$805$	−15.5033	−	6.83884i	−0.546419	−	0.241037i
$806$	−8.97675			−0.316193
$807$		−	51.3999i		−	1.80936i
$808$			1.31937i			0.0464154i
$809$	19.6395			0.690487			0.345243	−	0.938513i	$-0.387796\pi$
$809$	19.6395			0.690487			0.345243	+	0.938513i	$0.387796\pi$
$810$	−26.7335	+	60.6035i	−0.939320	+	2.12939i
$811$	28.6430			1.00579			0.502897	−	0.864347i	$-0.332268\pi$
$811$	28.6430			1.00579			0.502897	+	0.864347i	$0.332268\pi$
$812$			6.66429i			0.233871i
$813$		−	20.8524i		−	0.731326i
$814$	−0.420242			−0.0147295
$815$	4.50142	−	10.2045i	0.157678	−	0.357447i
$816$	−93.4450			−3.27123
$817$		0			0
$818$		−	51.0051i		−	1.78335i
$819$	−49.3696			−1.72512
$820$	−38.6450	−	17.0472i	−1.34954	−	0.595313i
$821$	−23.4218			−0.817427			−0.408714	−	0.912663i	$-0.634022\pi$
$821$	−23.4218			−0.817427			−0.408714	+	0.912663i	$0.634022\pi$
$822$			88.7325i			3.09490i
$823$			8.33962i			0.290701i	0.989380	+	0.145350i	$0.0464310\pi$
$823$			8.33962i			0.290701i	−0.989380	+	0.145350i	$0.953569\pi$
$824$	1.51340			0.0527217
$825$	−3.38975	+	3.09455i	−0.118016	+	0.107738i
$826$	−49.4637			−1.72106
$827$		−	5.86827i		−	0.204060i	−0.994781	−	0.102030i	$-0.967466\pi$
$827$		−	5.86827i		−	0.204060i	0.994781	−	0.102030i	$-0.0325337\pi$
$828$		−	33.0319i		−	1.14794i
$829$	−12.1421			−0.421713			−0.210857	−	0.977517i	$-0.567625\pi$
$829$	−12.1421			−0.421713			−0.210857	+	0.977517i	$0.567625\pi$
$830$	−55.7375	−	24.5870i	−1.93468	−	0.853428i
$831$	23.9405			0.830486
$832$		−	18.1439i		−	0.629027i
$833$		−	7.72077i		−	0.267509i
$834$	132.927			4.60287
$835$	−14.4373	+	32.7286i	−0.499623	+	1.13262i
$836$		0			0
$837$			19.6233i			0.678279i
$838$		−	37.7307i		−	1.30338i
$839$	44.6011			1.53980			0.769900	−	0.638164i	$-0.220306\pi$
$839$	44.6011			1.53980			0.769900	+	0.638164i	$0.220306\pi$
$840$	−2.03644	+	4.61651i	−0.0702639	+	0.159285i
$841$	−27.4297			−0.945852
$842$			5.45512i			0.187996i
$843$		−	42.6903i		−	1.47033i
$844$	41.7734			1.43790
$845$	−12.5664	−	5.54333i	−0.432299	−	0.190696i
$846$	−38.4407			−1.32162
$847$		−	31.0342i		−	1.06635i
$848$			29.6330i			1.01760i
$849$	−51.5045			−1.76763
$850$	47.0663	+	51.5561i	1.61436	+	1.76836i
$851$	1.92415			0.0659591
$852$		−	91.1117i		−	3.12144i
$853$			11.5477i			0.395385i	0.980264	+	0.197693i	$0.0633448\pi$
$853$			11.5477i			0.395385i	−0.980264	+	0.197693i	$0.936655\pi$
$854$	37.0900			1.26920
$855$		0			0
$856$	0.954969			0.0326402
$857$			3.31493i			0.113236i	0.998396	+	0.0566179i	$0.0180317\pi$
$857$			3.31493i			0.113236i	−0.998396	+	0.0566179i	$0.981968\pi$
$858$		−	4.72902i		−	0.161446i
$859$	45.1590			1.54080			0.770402	−	0.637558i	$-0.220055\pi$
$859$	45.1590			1.54080			0.770402	+	0.637558i	$0.220055\pi$
$860$	6.78631	−	15.3842i	0.231411	−	0.524598i
$861$	−89.1418			−3.03795
$862$		−	14.1160i		−	0.480794i
$863$		−	33.7618i		−	1.14927i	−0.818411	−	0.574633i	$-0.805145\pi$
$863$		−	33.7618i		−	1.14927i	0.818411	−	0.574633i	$-0.194855\pi$
$864$	−88.2417			−3.00204
$865$	1.70721	−	3.87015i	0.0580468	−	0.131589i
$866$	46.1767			1.56915
$867$			103.548i			3.51668i
$868$		−	9.26701i		−	0.314543i
$869$	−2.38652			−0.0809570
$870$	−15.6501	−	6.90358i	−0.530587	−	0.234053i
$871$	−5.07766			−0.172050
$872$		−	2.21856i		−	0.0751298i
$873$		−	43.7674i		−	1.48130i
$874$		0			0
$875$	30.1370	−	10.1364i	1.01882	−	0.342673i
$876$	−17.7259			−0.598903
$877$			46.9447i			1.58521i	0.609736	+	0.792604i	$0.291275\pi$
$877$			46.9447i			1.58521i	−0.609736	+	0.792604i	$0.708725\pi$
$878$		−	27.0996i		−	0.914568i
$879$	22.9578			0.774348
$880$	−2.56797	−	1.13279i	−0.0865661	−	0.0381862i
$881$	−16.2541			−0.547613			−0.273807	−	0.961785i	$-0.588283\pi$
$881$	−16.2541			−0.547613			−0.273807	+	0.961785i	$0.588283\pi$
$882$		−	14.1870i		−	0.477700i
$883$		−	34.0553i		−	1.14605i	−0.819537	−	0.573027i	$-0.805769\pi$
$883$		−	34.0553i		−	1.14605i	0.819537	−	0.573027i	$-0.194231\pi$
$884$	−34.7550			−1.16894
$885$	24.7594	−	56.1284i	0.832280	−	1.88673i
$886$	−2.17451			−0.0730540
$887$			0.285914i			0.00960005i	0.999988	+	0.00480002i	$0.00152790\pi$
$887$			0.285914i			0.00960005i	−0.999988	+	0.00480002i	$0.998472\pi$
$888$		−	0.572966i		−	0.0192275i
$889$	−32.2880			−1.08290
$890$	−0.978687	+	2.21863i	−0.0328057	+	0.0743688i
$891$	−4.45450			−0.149231
$892$		−	15.8875i		−	0.531952i
$893$		0			0
$894$	103.323			3.45563
$895$	−3.95511	−	1.74468i	−0.132205	−	0.0583184i
$896$	−5.80518			−0.193938
$897$			21.6527i			0.722961i
$898$			71.2500i			2.37764i
$899$	−2.18356			−0.0728259
$900$	41.7900	+	45.7765i	1.39300	+	1.52588i
$901$	49.5655			1.65127
$902$		−	5.87844i		−	0.195731i
$903$		−	35.4865i		−	1.18092i
$904$	−3.03178			−0.100836
$905$	−6.04366	−	2.66599i	−0.200898	−	0.0886205i
$906$	100.434			3.33671
$907$		−	51.7442i		−	1.71814i	−0.511861	−	0.859068i	$-0.671044\pi$
$907$		−	51.7442i		−	1.71814i	0.511861	−	0.859068i	$-0.328956\pi$
$908$			24.8335i			0.824129i
$909$	34.2056			1.13453
$910$	−13.2219	+	29.9734i	−0.438303	+	0.993609i
$911$	21.7331			0.720050			0.360025	−	0.932943i	$-0.382768\pi$
$911$	21.7331			0.720050			0.360025	+	0.932943i	$0.382768\pi$
$912$		0			0
$913$		−	4.09684i		−	0.135586i
$914$	79.2984			2.62296
$915$	−18.5657	+	42.0875i	−0.613763	+	1.39137i
$916$	−29.4716			−0.973768
$917$			35.5642i			1.17443i
$918$			157.230i			5.18936i
$919$	−26.3182			−0.868158			−0.434079	−	0.900875i	$-0.642926\pi$
$919$	−26.3182			−0.868158			−0.434079	+	0.900875i	$0.642926\pi$
$920$	1.39391	+	0.614883i	0.0459558	+	0.0202721i
$921$	−43.0970			−1.42009
$922$			33.6637i			1.10865i
$923$			41.1170i			1.35338i
$924$	4.88193			0.160604
$925$	−2.66654	+	2.43432i	−0.0876754	+	0.0800400i
$926$	−17.8974			−0.588147
$927$		−	39.2357i		−	1.28867i
$928$		−	9.81903i		−	0.322325i
$929$	23.0700			0.756901			0.378451	−	0.925622i	$-0.376457\pi$
$929$	23.0700			0.756901			0.378451	+	0.925622i	$0.376457\pi$
$930$	21.7621	+	9.59975i	0.713609	+	0.314788i
$931$		0			0
$932$		−	15.6726i		−	0.513373i
$933$		−	81.9992i		−	2.68453i
$934$	67.7154			2.21571
$935$	−1.89475	+	4.29530i	−0.0619649	+	0.140471i
$936$	4.43884			0.145088
$937$			40.8628i			1.33493i	0.744641	+	0.667465i	$0.232621\pi$
$937$			40.8628i			1.33493i	−0.744641	+	0.667465i	$0.767379\pi$
$938$		−	10.8480i		−	0.354201i
$939$	−21.4484			−0.699943
$940$	−4.97462	+	11.2772i	−0.162254	+	0.367822i
$941$	−49.2781			−1.60642			−0.803210	−	0.595695i	$-0.796877\pi$
$941$	−49.2781			−1.60642			−0.803210	+	0.595695i	$0.796877\pi$
$942$			37.1949i			1.21188i
$943$			26.9155i			0.876489i
$944$	37.5139			1.22097
$945$	65.5222	+	28.9032i	2.13144	+	0.940223i
$946$	2.34015			0.0760849
$947$		−	14.4062i		−	0.468140i	−0.972220	−	0.234070i	$-0.924796\pi$
$947$		−	14.4062i		−	0.468140i	0.972220	−	0.234070i	$-0.0752044\pi$
$948$			46.8134i			1.52043i
$949$	7.99936			0.259670
$950$		0			0
$951$	89.1654			2.89139
$952$			5.16092i			0.167267i
$953$		−	46.6902i		−	1.51244i	−0.654316	−	0.756222i	$-0.727043\pi$
$953$		−	46.6902i		−	1.51244i	0.654316	−	0.756222i	$-0.272957\pi$
$954$	91.0771			2.94873
$955$	29.2941	+	12.9223i	0.947935	+	0.418155i
$956$	7.46798			0.241532
$957$		−	1.15032i		−	0.0371844i
$958$			55.9185i			1.80664i
$959$	41.3380			1.33487
$960$	−19.4031	+	43.9859i	−0.626234	+	1.41964i
$961$	−27.9637			−0.902053
$962$		−	3.72008i		−	0.119940i
$963$		−	24.7582i		−	0.797821i
$964$	26.3738			0.849441
$965$	16.4866	−	37.3742i	0.530721	−	1.20312i
$966$	−46.2592			−1.48837
$967$			15.6605i			0.503609i	0.967778	+	0.251804i	$0.0810240\pi$
$967$			15.6605i			0.503609i	−0.967778	+	0.251804i	$0.918976\pi$
$968$			2.79030i			0.0896836i
$969$		0			0
$970$	−26.5722	−	11.7216i	−0.853181	−	0.376357i
$971$	−44.2514			−1.42009			−0.710047	−	0.704154i	$-0.751327\pi$
$971$	−44.2514			−1.42009			−0.710047	+	0.704154i	$0.751327\pi$
$972$			24.2010i			0.776247i
$973$		−	61.9268i		−	1.98528i
$974$	−62.1123			−1.99021
$975$	−27.3936	−	30.0068i	−0.877299	−	0.960988i
$976$	−28.1296			−0.900405
$977$		−	38.3791i		−	1.22786i	−0.789362	−	0.613928i	$-0.789588\pi$
$977$		−	38.3791i		−	1.22786i	0.789362	−	0.613928i	$-0.210412\pi$
$978$		−	30.4485i		−	0.973634i
$979$	−0.163075			−0.00521190
$980$	−4.16198	−	1.83594i	−0.132949	−	0.0586469i
$981$	−57.5174			−1.83639
$982$		−	5.80036i		−	0.185097i
$983$		−	28.0361i		−	0.894213i	−0.894481	−	0.447107i	$-0.852454\pi$
$983$		−	28.0361i		−	0.894213i	0.894481	−	0.447107i	$-0.147546\pi$
$984$	8.01478			0.255502
$985$	15.5146	−	35.1707i	0.494335	−	1.12063i
$986$	−17.4956			−0.557175
$987$			26.0129i			0.828001i
$988$		0			0
$989$	−10.7148			−0.340711
$990$	−3.48162	+	7.89265i	−0.110653	+	0.250845i
$991$	−27.0434			−0.859062			−0.429531	−	0.903052i	$-0.641321\pi$
$991$	−27.0434			−0.859062			−0.429531	+	0.903052i	$0.641321\pi$
$992$			13.6538i			0.433509i
$993$		−	25.2419i		−	0.801027i
$994$	−87.8432			−2.78622
$995$	10.8144	+	4.77048i	0.342841	+	0.151234i
$996$	−80.3628			−2.54639
$997$			34.5872i			1.09539i	0.836679	+	0.547694i	$0.184494\pi$
$997$			34.5872i			1.09539i	−0.836679	+	0.547694i	$0.815506\pi$
$998$		−	2.39077i		−	0.0756786i
$999$	−8.13212			−0.257289

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1805.2.b.m.1084.7	✓	40
5.2	odd	4		9025.2.a.cv.1.33		40
5.3	odd	4		9025.2.a.cv.1.8		40
5.4	even	2	inner	1805.2.b.m.1084.34	yes	40
19.18	odd	2	inner	1805.2.b.m.1084.33	yes	40
95.18	even	4		9025.2.a.cv.1.34		40
95.37	even	4		9025.2.a.cv.1.7		40
95.94	odd	2	inner	1805.2.b.m.1084.8	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1805.2.b.m.1084.7	✓	40	1.1	even	1	trivial
1805.2.b.m.1084.8	yes	40	95.94	odd	2	inner
1805.2.b.m.1084.33	yes	40	19.18	odd	2	inner
1805.2.b.m.1084.34	yes	40	5.4	even	2	inner
9025.2.a.cv.1.7		40	95.37	even	4
9025.2.a.cv.1.8		40	5.3	odd	4
9025.2.a.cv.1.33		40	5.2	odd	4
9025.2.a.cv.1.34		40	95.18	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1805 = 5 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1805.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.96724i q^{2} -3.10308i q^{3} -1.87002 q^{4} +(-2.04586 - 0.902473i) q^{5} -6.10450 q^{6} +2.84392i q^{7} -0.255698i q^{8} -6.62912 q^{9} +O(q^{10})\)	\(q-1.96724i q^{2} -3.10308i q^{3} -1.87002 q^{4} +(-2.04586 - 0.902473i) q^{5} -6.10450 q^{6} +2.84392i q^{7} -0.255698i q^{8} -6.62912 q^{9} +(-1.77538 + 4.02469i) q^{10} -0.295824 q^{11} +5.80283i q^{12} -2.61871i q^{13} +5.59466 q^{14} +(-2.80045 + 6.34847i) q^{15} -4.24306 q^{16} +7.09714i q^{17} +13.0411i q^{18} +(3.82580 + 1.68764i) q^{20} +8.82491 q^{21} +0.581957i q^{22} -2.66459i q^{23} -0.793451 q^{24} +(3.37108 + 3.69267i) q^{25} -5.15162 q^{26} +11.2615i q^{27} -5.31819i q^{28} -1.25311 q^{29} +(12.4890 + 5.50915i) q^{30} +1.74251 q^{31} +7.83571i q^{32} +0.917968i q^{33} +13.9618 q^{34} +(2.56656 - 5.81826i) q^{35} +12.3966 q^{36} +0.722118i q^{37} -8.12606 q^{39} +(-0.230760 + 0.523122i) q^{40} -10.1012 q^{41} -17.3607i q^{42} -4.02118i q^{43} +0.553198 q^{44} +(13.5623 + 5.98261i) q^{45} -5.24189 q^{46} +2.94767i q^{47} +13.1666i q^{48} -1.08787 q^{49} +(7.26435 - 6.63172i) q^{50} +22.0230 q^{51} +4.89704i q^{52} -6.98387i q^{53} +22.1540 q^{54} +(0.605215 + 0.266974i) q^{55} +0.727184 q^{56} +2.46517i q^{58} -8.84124 q^{59} +(5.23690 - 11.8718i) q^{60} +6.62954 q^{61} -3.42793i q^{62} -18.8527i q^{63} +6.92858 q^{64} +(-2.36331 + 5.35751i) q^{65} +1.80586 q^{66} -1.93900i q^{67} -13.2718i q^{68} -8.26846 q^{69} +(-11.4459 - 5.04903i) q^{70} -15.7012 q^{71} +1.69505i q^{72} +3.05470i q^{73} +1.42058 q^{74} +(11.4587 - 10.4608i) q^{75} -0.841300i q^{77} +15.9859i q^{78} +8.06734 q^{79} +(8.68071 + 3.82925i) q^{80} +15.0579 q^{81} +19.8714i q^{82} +13.8489i q^{83} -16.5028 q^{84} +(6.40498 - 14.5198i) q^{85} -7.91061 q^{86} +3.88851i q^{87} +0.0756416i q^{88} +0.551256 q^{89} +(11.7692 - 26.6802i) q^{90} +7.44739 q^{91} +4.98285i q^{92} -5.40716i q^{93} +5.79876 q^{94} +24.3149 q^{96} +6.60229i q^{97} +2.14010i q^{98} +1.96106 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 48 q^{4} + 6 q^{5} + 20 q^{6} - 52 q^{9}+O(q^{10}) \) 40 * q - 48 * q^4 + 6 * q^5 + 20 * q^6 - 52 * q^9	\( 40 q - 48 q^{4} + 6 q^{5} + 20 q^{6} - 52 q^{9} + 20 q^{11} + 40 q^{16} - 18 q^{20} - 92 q^{24} - 26 q^{25} + 76 q^{26} + 40 q^{30} + 4 q^{35} + 156 q^{36} - 80 q^{39} - 48 q^{44} - 22 q^{45} - 72 q^{49} - 32 q^{54} - 40 q^{55} + 80 q^{61} - 72 q^{64} + 16 q^{66} - 100 q^{74} - 66 q^{80} + 40 q^{81} + 44 q^{85} + 380 q^{96} - 128 q^{99}+O(q^{100}) \) 40 * q - 48 * q^4 + 6 * q^5 + 20 * q^6 - 52 * q^9 + 20 * q^11 + 40 * q^16 - 18 * q^20 - 92 * q^24 - 26 * q^25 + 76 * q^26 + 40 * q^30 + 4 * q^35 + 156 * q^36 - 80 * q^39 - 48 * q^44 - 22 * q^45 - 72 * q^49 - 32 * q^54 - 40 * q^55 + 80 * q^61 - 72 * q^64 + 16 * q^66 - 100 * q^74 - 66 * q^80 + 40 * q^81 + 44 * q^85 + 380 * q^96 - 128 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

Properties

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