LMFDB - Embedded newform 1805.2.b.m.1084.2

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			1084.2
Character	$\chi$	$=$	1805.1084
Dual form			1805.2.b.m.1084.39

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.66900i q^{2} +1.76244i q^{3} -5.12357 q^{4} +(-0.705325 + 2.12191i) q^{5} +4.70394 q^{6} +2.20993i q^{7} +8.33681i q^{8} -0.106178 q^{9} +O(q^{10})$	\(q-2.66900i q^{2} +1.76244i q^{3} -5.12357 q^{4} +(-0.705325 + 2.12191i) q^{5} +4.70394 q^{6} +2.20993i q^{7} +8.33681i q^{8} -0.106178 q^{9} +(5.66339 + 1.88251i) q^{10} +2.86854 q^{11} -9.02996i q^{12} +4.83675i q^{13} +5.89830 q^{14} +(-3.73974 - 1.24309i) q^{15} +12.0038 q^{16} -2.06280i q^{17} +0.283389i q^{18} +(3.61378 - 10.8718i) q^{20} -3.89485 q^{21} -7.65613i q^{22} -4.40865i q^{23} -14.6931 q^{24} +(-4.00503 - 2.99328i) q^{25} +12.9093 q^{26} +5.10017i q^{27} -11.3227i q^{28} -8.08729 q^{29} +(-3.31781 + 9.98136i) q^{30} +3.97776 q^{31} -15.3646i q^{32} +5.05561i q^{33} -5.50563 q^{34} +(-4.68927 - 1.55872i) q^{35} +0.544010 q^{36} +9.05780i q^{37} -8.52446 q^{39} +(-17.6900 - 5.88015i) q^{40} +1.21984 q^{41} +10.3954i q^{42} +5.13320i q^{43} -14.6972 q^{44} +(0.0748899 - 0.225300i) q^{45} -11.7667 q^{46} +2.50131i q^{47} +21.1559i q^{48} +2.11623 q^{49} +(-7.98906 + 10.6894i) q^{50} +3.63556 q^{51} -24.7814i q^{52} -1.22600i q^{53} +13.6124 q^{54} +(-2.02325 + 6.08679i) q^{55} -18.4237 q^{56} +21.5850i q^{58} -0.244718 q^{59} +(19.1608 + 6.36905i) q^{60} +0.498155 q^{61} -10.6166i q^{62} -0.234645i q^{63} -17.0004 q^{64} +(-10.2632 - 3.41148i) q^{65} +13.4934 q^{66} -7.09797i q^{67} +10.5689i q^{68} +7.76996 q^{69} +(-4.16021 + 12.5157i) q^{70} -9.59683 q^{71} -0.885185i q^{72} -0.287288i q^{73} +24.1753 q^{74} +(5.27546 - 7.05861i) q^{75} +6.33926i q^{77} +22.7518i q^{78} -15.8865 q^{79} +(-8.46658 + 25.4710i) q^{80} -9.30726 q^{81} -3.25576i q^{82} -5.70094i q^{83} +19.9555 q^{84} +(4.37709 + 1.45495i) q^{85} +13.7005 q^{86} -14.2533i q^{87} +23.9144i q^{88} -16.6834 q^{89} +(-0.601327 - 0.199881i) q^{90} -10.6889 q^{91} +22.5880i q^{92} +7.01055i q^{93} +6.67600 q^{94} +27.0791 q^{96} -0.202690i q^{97} -5.64821i q^{98} -0.304575 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$		−	2.66900i		−	1.88727i	−0.330989	−	0.943634i	$-0.607382\pi$
$2$		−	2.66900i		−	1.88727i	0.330989	−	0.943634i	$-0.392618\pi$
$3$			1.76244i			1.01754i	0.860902	+	0.508771i	$0.169900\pi$
$3$			1.76244i			1.01754i	−0.860902	+	0.508771i	$0.830100\pi$
$4$	−5.12357			−2.56178
$5$	−0.705325	+	2.12191i	−0.315431	+	0.948949i
$5$	−0.705325	+	2.12191i	−0.315431	+	0.948949i
$6$	4.70394			1.92038
$7$			2.20993i			0.835274i	0.908614	+	0.417637i	$0.137142\pi$
$7$			2.20993i			0.835274i	−0.908614	+	0.417637i	$0.862858\pi$
$8$			8.33681i			2.94751i
$9$	−0.106178			−0.0353926
$10$	5.66339	+	1.88251i	1.79092	+	0.595303i
$11$	2.86854			0.864897			0.432448	−	0.901659i	$-0.357650\pi$
$11$	2.86854			0.864897			0.432448	+	0.901659i	$0.357650\pi$
$12$		−	9.02996i		−	2.60672i
$13$			4.83675i			1.34147i	0.741696	+	0.670736i	$0.234022\pi$
$13$			4.83675i			1.34147i	−0.741696	+	0.670736i	$0.765978\pi$
$14$	5.89830			1.57639
$15$	−3.73974	−	1.24309i	−0.965595	−	0.320964i
$16$	12.0038			3.00095
$17$		−	2.06280i		−	0.500304i	−0.968207	−	0.250152i	$-0.919519\pi$
$17$		−	2.06280i		−	0.500304i	0.968207	−	0.250152i	$-0.0804805\pi$
$18$			0.283389i			0.0667954i
$19$		0			0
$19$		0			0
$20$	3.61378	−	10.8718i	0.808065	−	2.43100i
$21$	−3.89485			−0.849926
$22$		−	7.65613i		−	1.63229i
$23$		−	4.40865i		−	0.919267i	−0.888109	−	0.459634i	$-0.847981\pi$
$23$		−	4.40865i		−	0.919267i	0.888109	−	0.459634i	$-0.152019\pi$
$24$	−14.6931			−2.99921
$25$	−4.00503	−	2.99328i	−0.801007	−	0.598655i
$26$	12.9093			2.53172
$27$			5.10017i			0.981529i
$28$		−	11.3227i		−	2.13979i
$29$	−8.08729			−1.50177			−0.750886	−	0.660432i	$-0.770373\pi$
$29$	−8.08729			−1.50177			−0.750886	+	0.660432i	$0.770373\pi$
$30$	−3.31781	+	9.98136i	−0.605746	+	1.82234i
$31$	3.97776			0.714427			0.357213	−	0.934023i	$-0.383727\pi$
$31$	3.97776			0.714427			0.357213	+	0.934023i	$0.383727\pi$
$32$		−	15.3646i		−	2.71610i
$33$			5.05561i			0.880069i
$34$	−5.50563			−0.944207
$35$	−4.68927	−	1.55872i	−0.792632	−	0.263471i
$36$	0.544010			0.0906683
$37$			9.05780i			1.48909i	0.667571	+	0.744546i	$0.267334\pi$
$37$			9.05780i			1.48909i	−0.667571	+	0.744546i	$0.732666\pi$
$38$		0			0
$39$	−8.52446			−1.36501
$40$	−17.6900	−	5.88015i	−2.79703	−	0.929734i
$41$	1.21984			0.190507			0.0952537	−	0.995453i	$-0.469634\pi$
$41$	1.21984			0.190507			0.0952537	+	0.995453i	$0.469634\pi$
$42$			10.3954i			1.60404i
$43$			5.13320i			0.782806i	0.920219	+	0.391403i	$0.128010\pi$
$43$			5.13320i			0.782806i	−0.920219	+	0.391403i	$0.871990\pi$
$44$	−14.6972			−2.21568
$45$	0.0748899	−	0.225300i	0.0111639	−	0.0335858i
$46$	−11.7667			−1.73490
$47$			2.50131i			0.364854i	0.983219	+	0.182427i	$0.0583953\pi$
$47$			2.50131i			0.364854i	−0.983219	+	0.182427i	$0.941605\pi$
$48$			21.1559i			3.05360i
$49$	2.11623			0.302318
$50$	−7.98906	+	10.6894i	−1.12982	+	1.51172i
$51$	3.63556			0.509080
$52$		−	24.7814i		−	3.43656i
$53$		−	1.22600i		−	0.168404i	−0.996449	−	0.0842018i	$-0.973166\pi$
$53$		−	1.22600i		−	0.168404i	0.996449	−	0.0842018i	$-0.0268340\pi$
$54$	13.6124			1.85241
$55$	−2.02325	+	6.08679i	−0.272815	+	0.820743i
$56$	−18.4237			−2.46197
$57$		0			0
$58$			21.5850i			2.83425i
$59$	−0.244718			−0.0318596			−0.0159298	−	0.999873i	$-0.505071\pi$
$59$	−0.244718			−0.0318596			−0.0159298	+	0.999873i	$0.505071\pi$
$60$	19.1608	+	6.36905i	2.47365	+	0.822241i
$61$	0.498155			0.0637823			0.0318911	−	0.999491i	$-0.489847\pi$
$61$	0.498155			0.0637823			0.0318911	+	0.999491i	$0.489847\pi$
$62$		−	10.6166i		−	1.34832i
$63$		−	0.234645i		−	0.0295625i
$64$	−17.0004			−2.12506
$65$	−10.2632	−	3.41148i	−1.27299	−	0.423142i
$66$	13.4934			1.66093
$67$		−	7.09797i		−	0.867155i	−0.901116	−	0.433578i	$-0.857251\pi$
$67$		−	7.09797i		−	0.867155i	0.901116	−	0.433578i	$-0.142749\pi$
$68$			10.5689i			1.28167i
$69$	7.76996			0.935393
$70$	−4.16021	+	12.5157i	−0.497241	+	1.49591i
$71$	−9.59683			−1.13893			−0.569467	−	0.822014i	$-0.692850\pi$
$71$	−9.59683			−1.13893			−0.569467	+	0.822014i	$0.692850\pi$
$72$		−	0.885185i		−	0.104320i
$73$		−	0.287288i		−	0.0336245i	−0.999859	−	0.0168122i	$-0.994648\pi$
$73$		−	0.287288i		−	0.0336245i	0.999859	−	0.0168122i	$-0.00535175\pi$
$74$	24.1753			2.81032
$75$	5.27546	−	7.05861i	0.609157	−	0.815058i
$76$		0			0
$77$			6.33926i			0.722425i
$78$			22.7518i			2.57613i
$79$	−15.8865			−1.78737			−0.893687	−	0.448691i	$-0.851890\pi$
$79$	−15.8865			−1.78737			−0.893687	+	0.448691i	$0.851890\pi$
$80$	−8.46658	+	25.4710i	−0.946593	+	2.84775i
$81$	−9.30726			−1.03414
$82$		−	3.25576i		−	0.359539i
$83$		−	5.70094i		−	0.625759i	−0.949793	−	0.312879i	$-0.898706\pi$
$83$		−	5.70094i		−	0.625759i	0.949793	−	0.312879i	$-0.101294\pi$
$84$	19.9555			2.17733
$85$	4.37709	+	1.45495i	0.474762	+	0.157811i
$86$	13.7005			1.47737
$87$		−	14.2533i		−	1.52812i
$88$			23.9144i			2.54929i
$89$	−16.6834			−1.76844			−0.884220	−	0.467072i	$-0.845309\pi$
$89$	−16.6834			−1.76844			−0.884220	+	0.467072i	$0.845309\pi$
$90$	−0.601327	−	0.199881i	−0.0633854	−	0.0210693i
$91$	−10.6889			−1.12050
$92$			22.5880i			2.35496i
$93$			7.01055i			0.726960i
$94$	6.67600			0.688577
$95$		0			0
$96$	27.0791			2.76375
$97$		−	0.202690i		−	0.0205801i	−0.999947	−	0.0102900i	$-0.996725\pi$
$97$		−	0.202690i		−	0.0205801i	0.999947	−	0.0102900i	$-0.00327548\pi$
$98$		−	5.64821i		−	0.570556i
$99$	−0.304575			−0.0306110
$100$	20.5201	+	15.3363i	2.05201	+	1.53363i
$101$	2.36522			0.235349			0.117674	−	0.993052i	$-0.462456\pi$
$101$	2.36522			0.235349			0.117674	+	0.993052i	$0.462456\pi$
$102$		−	9.70331i		−	0.960771i
$103$			1.07422i			0.105846i	0.998599	+	0.0529231i	$0.0168538\pi$
$103$			1.07422i			0.105846i	−0.998599	+	0.0529231i	$0.983146\pi$
$104$	−40.3230			−3.95400
$105$	2.74713	−	8.26454i	0.268093	−	0.806536i
$106$	−3.27219			−0.317823
$107$			0.186188i			0.0179994i	0.999960	+	0.00899972i	$0.00286474\pi$
$107$			0.186188i			0.0179994i	−0.999960	+	0.00899972i	$0.997135\pi$
$108$		−	26.1311i		−	2.51446i
$109$	13.1387			1.25846			0.629229	−	0.777220i	$-0.283371\pi$
$109$	13.1387			1.25846			0.629229	+	0.777220i	$0.283371\pi$
$110$	16.2457	+	5.40006i	1.54896	+	0.514875i
$111$	−15.9638			−1.51522
$112$			26.5275i			2.50662i
$113$			4.36458i			0.410586i	0.978701	+	0.205293i	$0.0658147\pi$
$113$			4.36458i			0.410586i	−0.978701	+	0.205293i	$0.934185\pi$
$114$		0			0
$115$	9.35478	+	3.10953i	0.872337	+	0.289965i
$116$	41.4358			3.84721
$117$		−	0.513556i		−	0.0474783i
$118$			0.653154i			0.0601277i
$119$	4.55864			0.417890
$120$	10.3634	−	31.1774i	0.946044	−	2.84610i
$121$	−2.77149			−0.251953
$122$		−	1.32958i		−	0.120374i
$123$			2.14989i			0.193849i
$124$	−20.3803			−1.83021
$125$	9.17632	−	6.38710i	0.820755	−	0.571280i
$126$	−0.626269			−0.0557925
$127$		−	3.40581i		−	0.302217i	−0.988517	−	0.151108i	$-0.951716\pi$
$127$		−	3.40581i		−	0.302217i	0.988517	−	0.151108i	$-0.0482843\pi$
$128$			14.6451i			1.29445i
$129$	−9.04694			−0.796538
$130$	−9.10524	+	27.3924i	−0.798582	+	2.40247i
$131$	0.573140			0.0500755			0.0250378	−	0.999687i	$-0.492029\pi$
$131$	0.573140			0.0500755			0.0250378	+	0.999687i	$0.492029\pi$
$132$		−	25.9028i		−	2.25455i
$133$		0			0
$134$	−18.9445			−1.63655
$135$	−10.8221	−	3.59728i	−0.931420	−	0.309604i
$136$	17.1972			1.47465
$137$			4.82207i			0.411977i	0.978554	+	0.205988i	$0.0660409\pi$
$137$			4.82207i			0.411977i	−0.978554	+	0.205988i	$0.933959\pi$
$138$		−	20.7380i		−	1.76534i
$139$	14.9925			1.27164			0.635822	−	0.771836i	$-0.280661\pi$
$139$	14.9925			1.27164			0.635822	+	0.771836i	$0.280661\pi$
$140$	24.0258	+	7.98618i	2.03055	+	0.674956i
$141$	−4.40840			−0.371254
$142$			25.6139i			2.14947i
$143$			13.8744i			1.16024i
$144$	−1.27454			−0.106212
$145$	5.70416	−	17.1605i	0.473705	−	1.42510i
$146$	−0.766771			−0.0634584
$147$			3.72971i			0.307622i
$148$		−	46.4082i		−	3.81473i
$149$	−12.6439			−1.03583			−0.517914	−	0.855433i	$-0.673291\pi$
$149$	−12.6439			−1.03583			−0.517914	+	0.855433i	$0.673291\pi$
$150$	−18.8394	−	14.0802i	−1.53823	−	1.14964i
$151$	11.0266			0.897328			0.448664	−	0.893701i	$-0.351900\pi$
$151$	11.0266			0.897328			0.448664	+	0.893701i	$0.351900\pi$
$152$		0			0
$153$			0.219024i			0.0177071i
$154$	16.9195			1.36341
$155$	−2.80561	+	8.44046i	−0.225352	+	0.677954i
$156$	43.6756			3.49685
$157$			22.4216i			1.78944i	0.446632	+	0.894718i	$0.352623\pi$
$157$			22.4216i			1.78944i	−0.446632	+	0.894718i	$0.647377\pi$
$158$			42.4011i			3.37325i
$159$	2.16074			0.171358
$160$	32.6023	+	10.8370i	2.57744	+	0.856741i
$161$	9.74279			0.767840
$162$			24.8411i			1.95170i
$163$		−	1.74791i		−	0.136907i	−0.997654	−	0.0684535i	$-0.978194\pi$
$163$		−	1.74791i		−	0.136907i	0.997654	−	0.0684535i	$-0.0218065\pi$
$164$	−6.24994			−0.488039
$165$	−10.7276	−	3.56585i	−0.835141	−	0.277601i
$166$	−15.2158			−1.18098
$167$			21.0484i			1.62877i	0.580324	+	0.814386i	$0.302926\pi$
$167$			21.0484i			1.62877i	−0.580324	+	0.814386i	$0.697074\pi$
$168$		−	32.4706i		−	2.50516i
$169$	−10.3941			−0.799549
$170$	3.88325	−	11.6825i	0.297832	−	0.896004i
$171$		0			0
$172$		−	26.3003i		−	2.00538i
$173$		−	11.6088i		−	0.882602i	−0.897359	−	0.441301i	$-0.854517\pi$
$173$		−	11.6088i		−	0.882602i	0.897359	−	0.441301i	$-0.145483\pi$
$174$	−38.0421			−2.88397
$175$	6.61492	−	8.85083i	0.500041	−	0.669060i
$176$	34.4334			2.59551
$177$		−	0.431300i		−	0.0324185i
$178$			44.5281i			3.33752i
$179$	3.98091			0.297547			0.148774	−	0.988871i	$-0.452467\pi$
$179$	3.98091			0.297547			0.148774	+	0.988871i	$0.452467\pi$
$180$	−0.383704	+	1.15434i	−0.0285996	+	0.0860396i
$181$	2.81859			0.209504			0.104752	−	0.994498i	$-0.466595\pi$
$181$	2.81859			0.209504			0.104752	+	0.994498i	$0.466595\pi$
$182$			28.5286i			2.11468i
$183$			0.877967i			0.0649012i
$184$	36.7541			2.70955
$185$	−19.2199	−	6.38869i	−1.41307	−	0.469706i
$186$	18.7112			1.37197
$187$		−	5.91723i		−	0.432711i
$188$		−	12.8156i		−	0.934676i
$189$	−11.2710			−0.819845
$190$		0			0
$191$	−19.8105			−1.43344			−0.716719	−	0.697362i	$-0.754357\pi$
$191$	−19.8105			−1.43344			−0.716719	+	0.697362i	$0.754357\pi$
$192$		−	29.9622i		−	2.16233i
$193$			5.52399i			0.397626i	0.980037	+	0.198813i	$0.0637086\pi$
$193$			5.52399i			0.397626i	−0.980037	+	0.198813i	$0.936291\pi$
$194$	−0.540981			−0.0388402
$195$	6.01251	−	18.0882i	0.430565	−	1.29532i
$196$	−10.8426			−0.774474
$197$		−	20.4993i		−	1.46051i	−0.683173	−	0.730257i	$-0.739400\pi$
$197$		−	20.4993i		−	1.46051i	0.683173	−	0.730257i	$-0.260600\pi$
$198$			0.812912i			0.0577712i
$199$	17.2575			1.22335			0.611677	−	0.791107i	$-0.290495\pi$
$199$	17.2575			1.22335			0.611677	+	0.791107i	$0.290495\pi$
$200$	24.9544	−	33.3892i	1.76454	−	2.36097i
$201$	12.5097			0.882367
$202$		−	6.31279i		−	0.444166i
$203$		−	17.8723i		−	1.25439i
$204$	−18.6270			−1.30415
$205$	−0.860385	+	2.58840i	−0.0600919	+	0.180782i
$206$	2.86710			0.199760
$207$			0.468101i			0.0325353i
$208$			58.0594i			4.02570i
$209$		0			0
$210$	−22.0581	−	7.33211i	−1.52215	−	0.505963i
$211$	−21.2379			−1.46207			−0.731037	−	0.682337i	$-0.760964\pi$
$211$	−21.2379			−1.46207			−0.731037	+	0.682337i	$0.760964\pi$
$212$			6.28148i			0.431414i
$213$		−	16.9138i		−	1.15891i
$214$	0.496935			0.0339698
$215$	−10.8922	−	3.62057i	−0.742843	−	0.246921i
$216$	−42.5192			−2.89306
$217$			8.79056i			0.596742i
$218$		−	35.0672i		−	2.37505i
$219$	0.506326			0.0342143
$220$	10.3663	−	31.1861i	0.698893	−	2.10257i
$221$	9.97726			0.671143
$222$			42.6074i			2.85962i
$223$			28.8555i			1.93231i	0.257967	+	0.966154i	$0.416947\pi$
$223$			28.8555i			1.93231i	−0.257967	+	0.966154i	$0.583053\pi$
$224$	33.9546			2.26869
$225$	0.425246	+	0.317820i	0.0283497	+	0.0211880i
$226$	11.6491			0.774885
$227$		−	8.42533i		−	0.559209i	−0.960115	−	0.279604i	$-0.909797\pi$
$227$		−	8.42533i		−	0.559209i	0.960115	−	0.279604i	$-0.0902033\pi$
$228$		0			0
$229$	−24.6658			−1.62996			−0.814981	−	0.579487i	$-0.803253\pi$
$229$	−24.6658			−1.62996			−0.814981	+	0.579487i	$0.803253\pi$
$230$	8.29934	−	24.9679i	0.547242	−	1.64633i
$231$	−11.1725			−0.735099
$232$		−	67.4221i		−	4.42648i
$233$		−	20.7240i		−	1.35768i	−0.734287	−	0.678839i	$-0.762484\pi$
$233$		−	20.7240i		−	1.35768i	0.734287	−	0.678839i	$-0.237516\pi$
$234$	−1.37068			−0.0896042
$235$	−5.30757	−	1.76424i	−0.346227	−	0.115086i
$236$	1.25383			0.0816175
$237$		−	27.9990i		−	1.81873i
$238$		−	12.1670i		−	0.788671i
$239$	−10.4341			−0.674924			−0.337462	−	0.941339i	$-0.609569\pi$
$239$	−10.4341			−0.674924			−0.337462	+	0.941339i	$0.609569\pi$
$240$	−44.8911	−	14.9218i	−2.89771	−	0.963198i
$241$	−20.0493			−1.29149			−0.645744	−	0.763554i	$-0.723452\pi$
$241$	−20.0493			−1.29149			−0.645744	+	0.763554i	$0.723452\pi$
$242$			7.39710i			0.475504i
$243$		−	1.10292i		−	0.0707524i
$244$	−2.55233			−0.163396
$245$	−1.49263	+	4.49045i	−0.0953604	+	0.286884i
$246$	5.73807			0.365846
$247$		0			0
$248$			33.1618i			2.10578i
$249$	10.0475			0.636736
$250$	−17.0472	−	24.4916i	−1.07816	−	1.54899i
$251$	−0.614289			−0.0387736			−0.0193868	−	0.999812i	$-0.506171\pi$
$251$	−0.614289			−0.0387736			−0.0193868	+	0.999812i	$0.506171\pi$
$252$			1.20222i			0.0757328i
$253$		−	12.6464i		−	0.795071i
$254$	−9.09012			−0.570365
$255$	−2.56425	+	7.71434i	−0.160580	+	0.483091i
$256$	5.08679			0.317924
$257$			10.1007i			0.630064i	0.949081	+	0.315032i	$0.102015\pi$
$257$			10.1007i			0.630064i	−0.949081	+	0.315032i	$0.897985\pi$
$258$			24.1463i			1.50328i
$259$	−20.0171			−1.24380
$260$	52.5840	+	17.4789i	3.26112	+	1.08400i
$261$	0.858691			0.0531517
$262$		−	1.52971i		−	0.0945060i
$263$			6.14445i			0.378883i	0.981892	+	0.189441i	$0.0606677\pi$
$263$			6.14445i			0.378883i	−0.981892	+	0.189441i	$0.939332\pi$
$264$	−42.1477			−2.59401
$265$	2.60146	+	0.864726i	0.159806	+	0.0531197i
$266$		0			0
$267$		−	29.4034i		−	1.79946i
$268$			36.3669i			2.22146i
$269$	23.0791			1.40716			0.703579	−	0.710617i	$-0.251584\pi$
$269$	23.0791			1.40716			0.703579	+	0.710617i	$0.251584\pi$
$270$	−9.60114	+	28.8843i	−0.584307	+	1.75784i
$271$	13.7769			0.836885			0.418443	−	0.908243i	$-0.362576\pi$
$271$	13.7769			0.836885			0.418443	+	0.908243i	$0.362576\pi$
$272$		−	24.7615i		−	1.50139i
$273$		−	18.8384i		−	1.14015i
$274$	12.8701			0.777511
$275$	−11.4886	−	8.58633i	−0.692788	−	0.517775i
$276$	−39.8099			−2.39628
$277$			18.2471i			1.09636i	0.836360	+	0.548181i	$0.184679\pi$
$277$			18.2471i			1.09636i	−0.836360	+	0.548181i	$0.815321\pi$
$278$		−	40.0149i		−	2.39993i
$279$	−0.422350			−0.0252855
$280$	12.9947	−	39.0936i	0.776582	−	2.33629i
$281$	20.3990			1.21690			0.608451	−	0.793591i	$-0.291791\pi$
$281$	20.3990			1.21690			0.608451	+	0.793591i	$0.291791\pi$
$282$			11.7660i			0.700656i
$283$		−	19.5454i		−	1.16186i	−0.813955	−	0.580928i	$-0.802690\pi$
$283$		−	19.5454i		−	1.16186i	0.813955	−	0.580928i	$-0.197310\pi$
$284$	49.1700			2.91770
$285$		0			0
$286$	37.0308			2.18968
$287$			2.69576i			0.159126i
$288$			1.63138i			0.0961299i
$289$	12.7448			0.749696
$290$	−45.8015	−	15.2244i	−2.68955	−	0.894009i
$291$	0.357229			0.0209411
$292$			1.47194i			0.0861386i
$293$		−	9.22402i		−	0.538873i	−0.963018	−	0.269436i	$-0.913163\pi$
$293$		−	9.22402i		−	0.538873i	0.963018	−	0.269436i	$-0.0868374\pi$
$294$	9.95461			0.580565
$295$	0.172606	−	0.519271i	0.0100495	−	0.0302331i
$296$	−75.5131			−4.38911
$297$			14.6300i			0.848921i
$298$			33.7466i			1.95489i
$299$	21.3235			1.23317
$300$	−27.0292	+	36.1653i	−1.56053	+	2.08800i
$301$	−11.3440			−0.653857
$302$		−	29.4299i		−	1.69350i
$303$			4.16855i			0.239477i
$304$		0			0
$305$	−0.351361	+	1.05704i	−0.0201189	+	0.0605261i
$306$	0.584576			0.0334180
$307$			7.75219i			0.442441i	0.975224	+	0.221220i	$0.0710040\pi$
$307$			7.75219i			0.442441i	−0.975224	+	0.221220i	$0.928996\pi$
$308$		−	32.4796i		−	1.85070i
$309$	−1.89325			−0.107703
$310$	22.5276	+	7.48818i	1.27948	+	0.425300i
$311$	24.8427			1.40870			0.704350	−	0.709853i	$-0.251239\pi$
$311$	24.8427			1.40870			0.704350	+	0.709853i	$0.251239\pi$
$312$		−	71.0667i		−	4.02336i
$313$		−	5.79256i		−	0.327415i	−0.986509	−	0.163707i	$-0.947655\pi$
$313$		−	5.79256i		−	0.327415i	0.986509	−	0.163707i	$-0.0523453\pi$
$314$	59.8432			3.37715
$315$	0.497897	+	0.165501i	0.0280533	+	0.00932493i
$316$	81.3957			4.57886
$317$		−	4.59924i		−	0.258319i	−0.991624	−	0.129159i	$-0.958772\pi$
$317$		−	4.59924i		−	0.258319i	0.991624	−	0.129159i	$-0.0412279\pi$
$318$		−	5.76702i		−	0.323398i
$319$	−23.1987			−1.29888
$320$	11.9908	−	36.0735i	0.670308	−	2.01657i
$321$	−0.328144			−0.0183152
$322$		−	26.0035i		−	1.44912i
$323$		0			0
$324$	47.6864			2.64924
$325$	14.4777	−	19.3713i	0.803080	−	1.07453i
$326$	−4.66518			−0.258380
$327$			23.1561i			1.28053i
$328$			10.1696i			0.561522i
$329$	−5.52771			−0.304753
$330$	−9.51725	+	28.6319i	−0.523908	+	1.57613i
$331$	−7.39548			−0.406493			−0.203246	−	0.979128i	$-0.565149\pi$
$331$	−7.39548			−0.406493			−0.203246	+	0.979128i	$0.565149\pi$
$332$			29.2091i			1.60306i
$333$		−	0.961738i		−	0.0527029i
$334$	56.1781			3.07393
$335$	15.0613	+	5.00637i	0.822886	+	0.273527i
$336$	−46.7531			−2.55059
$337$		−	16.6765i		−	0.908425i	−0.890893	−	0.454212i	$-0.849921\pi$
$337$		−	16.6765i		−	0.908425i	0.890893	−	0.454212i	$-0.150079\pi$
$338$			27.7420i			1.50896i
$339$	−7.69230			−0.417788
$340$	−22.4263	−	7.45452i	−1.21624	−	0.404278i
$341$	11.4104			0.617906
$342$		0			0
$343$			20.1462i			1.08779i
$344$	−42.7945			−2.30733
$345$	−5.48035	+	16.4872i	−0.295052	+	0.887640i
$346$	−30.9840			−1.66571
$347$			36.0300i			1.93419i	0.254417	+	0.967095i	$0.418116\pi$
$347$			36.0300i			1.93419i	−0.254417	+	0.967095i	$0.581884\pi$
$348$			73.0278i			3.91470i
$349$	23.6370			1.26526			0.632629	−	0.774455i	$-0.281976\pi$
$349$	23.6370			1.26526			0.632629	+	0.774455i	$0.281976\pi$
$350$	−23.6229	−	17.6552i	−1.26270	−	0.943712i
$351$	−24.6683			−1.31669
$352$		−	44.0739i		−	2.34914i
$353$		−	33.9305i		−	1.80594i	−0.429708	−	0.902968i	$-0.641383\pi$
$353$		−	33.9305i		−	1.80594i	0.429708	−	0.902968i	$-0.358617\pi$
$354$	−1.15114			−0.0611825
$355$	6.76888	−	20.3636i	0.359255	−	1.08079i
$356$	85.4786			4.53036
$357$			8.03432i			0.425221i
$358$		−	10.6251i		−	0.561551i
$359$	9.28731			0.490165			0.245083	−	0.969502i	$-0.421185\pi$
$359$	9.28731			0.490165			0.245083	+	0.969502i	$0.421185\pi$
$360$	1.87829	+	0.624343i	0.0989943	+	0.0329057i
$361$		0			0
$362$		−	7.52282i		−	0.395391i
$363$		−	4.88457i		−	0.256373i
$364$	54.7651			2.87047
$365$	0.609600	+	0.202631i	0.0319079	+	0.0106062i
$366$	2.34329			0.122486
$367$		−	11.4283i		−	0.596555i	−0.954479	−	0.298277i	$-0.903588\pi$
$367$		−	11.4283i		−	0.596555i	0.954479	−	0.298277i	$-0.0964120\pi$
$368$		−	52.9206i		−	2.75868i
$369$	−0.129520			−0.00674256
$370$	−17.0514	+	51.2978i	−0.886461	+	2.66685i
$371$	2.70936			0.140663
$372$		−	35.9190i		−	1.86231i
$373$			25.7467i			1.33312i	0.745454	+	0.666558i	$0.232233\pi$
$373$			25.7467i			1.33312i	−0.745454	+	0.666558i	$0.767767\pi$
$374$	−15.7931			−0.816642
$375$	11.2569	+	16.1727i	0.581302	+	0.835153i
$376$	−20.8529			−1.07541
$377$		−	39.1162i		−	2.01459i
$378$			30.0823i			1.54727i
$379$	−20.3628			−1.04597			−0.522984	−	0.852343i	$-0.675181\pi$
$379$	−20.3628			−1.04597			−0.522984	+	0.852343i	$0.675181\pi$
$380$		0			0
$381$	6.00252			0.307519
$382$			52.8742i			2.70528i
$383$			18.1004i			0.924886i	0.886649	+	0.462443i	$0.153027\pi$
$383$			18.1004i			0.924886i	−0.886649	+	0.462443i	$0.846973\pi$
$384$	−25.8110			−1.31716
$385$	−13.4514	−	4.47123i	−0.685545	−	0.227875i
$386$	14.7435			0.750426
$387$		−	0.545033i		−	0.0277056i
$388$			1.03850i			0.0527217i
$389$	30.3016			1.53635			0.768175	−	0.640239i	$-0.221165\pi$
$389$	30.3016			1.53635			0.768175	+	0.640239i	$0.221165\pi$
$390$	−48.2773	−	16.0474i	−2.44462	−	0.812591i
$391$	−9.09418			−0.459913
$392$			17.6426i			0.891084i
$393$			1.01012i			0.0509540i
$394$	−54.7126			−2.75638
$395$	11.2052	−	33.7098i	0.563793	−	1.69613i
$396$	1.56051			0.0784187
$397$		−	3.57059i		−	0.179203i	−0.995978	−	0.0896015i	$-0.971441\pi$
$397$		−	3.57059i		−	0.179203i	0.995978	−	0.0896015i	$-0.0285593\pi$
$398$		−	46.0604i		−	2.30880i
$399$		0			0
$400$	−48.0757	−	35.9307i	−2.40378	−	1.79654i
$401$	0.553079			0.0276194			0.0138097	−	0.999905i	$-0.495604\pi$
$401$	0.553079			0.0276194			0.0138097	+	0.999905i	$0.495604\pi$
$402$		−	33.3884i		−	1.66526i
$403$			19.2394i			0.958384i
$404$	−12.1184			−0.602912
$405$	6.56464	−	19.7492i	0.326200	−	0.981346i
$406$	−47.7012			−2.36737
$407$			25.9826i			1.28791i
$408$			30.3089i			1.50052i
$409$	−2.56270			−0.126718			−0.0633588	−	0.997991i	$-0.520181\pi$
$409$	−2.56270			−0.126718			−0.0633588	+	0.997991i	$0.520181\pi$
$410$	6.90844	+	2.29637i	0.341184	+	0.113410i
$411$	−8.49858			−0.419204
$412$		−	5.50385i		−	0.271155i
$413$		−	0.540810i		−	0.0266115i
$414$	1.24936			0.0614028
$415$	12.0969	+	4.02101i	0.593813	+	0.197384i
$416$	74.3146			3.64357
$417$			26.4232i			1.29395i
$418$		0			0
$419$	9.01138			0.440235			0.220117	−	0.975473i	$-0.429356\pi$
$419$	9.01138			0.440235			0.220117	+	0.975473i	$0.429356\pi$
$420$	−14.0751	+	42.3439i	−0.686796	+	2.06617i
$421$	8.61610			0.419923			0.209962	−	0.977710i	$-0.432666\pi$
$421$	8.61610			0.419923			0.209962	+	0.977710i	$0.432666\pi$
$422$			56.6839i			2.75933i
$423$		−	0.265584i		−	0.0129131i
$424$	10.2209			0.496371
$425$	−6.17454	+	8.26160i	−0.299509	+	0.400747i
$426$	−45.1429			−2.18718
$427$			1.10089i			0.0532756i
$428$		−	0.953945i		−	0.0461107i
$429$	−24.4527			−1.18059
$430$	−9.66332	+	29.0713i	−0.466007	+	1.40194i
$431$	−5.21526			−0.251210			−0.125605	−	0.992080i	$-0.540087\pi$
$431$	−5.21526			−0.251210			−0.125605	+	0.992080i	$0.540087\pi$
$432$			61.2215i			2.94552i
$433$		−	5.17272i		−	0.248585i	−0.992246	−	0.124293i	$-0.960334\pi$
$433$		−	5.17272i		−	0.248585i	0.992246	−	0.124293i	$-0.0396661\pi$
$434$	23.4620			1.12621
$435$	30.2443	+	10.0532i	1.45010	+	0.482015i
$436$	−67.3170			−3.22390
$437$		0			0
$438$		−	1.35138i		−	0.0645716i
$439$	−16.1031			−0.768560			−0.384280	−	0.923217i	$-0.625550\pi$
$439$	−16.1031			−0.768560			−0.384280	+	0.923217i	$0.625550\pi$
$440$	−50.7444	−	16.8675i	−2.41914	−	0.804124i
$441$	−0.224697			−0.0106998
$442$		−	26.6293i		−	1.26663i
$443$			12.1169i			0.575693i	0.957677	+	0.287846i	$0.0929393\pi$
$443$			12.1169i			0.575693i	−0.957677	+	0.287846i	$0.907061\pi$
$444$	81.7915			3.88165
$445$	11.7672	−	35.4008i	0.557820	−	1.67816i
$446$	77.0154			3.64678
$447$		−	22.2841i		−	1.05400i
$448$		−	37.5697i		−	1.77500i
$449$	−7.07384			−0.333835			−0.166918	−	0.985971i	$-0.553381\pi$
$449$	−7.07384			−0.333835			−0.166918	+	0.985971i	$0.553381\pi$
$450$	0.848262	−	1.13498i	0.0399874	−	0.0535036i
$451$	3.49916			0.164769
$452$		−	22.3622i		−	1.05183i
$453$			19.4336i			0.913069i
$454$	−22.4872			−1.05538
$455$	7.53911	−	22.6808i	0.353439	−	1.06329i
$456$		0			0
$457$			26.3810i			1.23405i	0.786942	+	0.617027i	$0.211663\pi$
$457$			26.3810i			1.23405i	−0.786942	+	0.617027i	$0.788337\pi$
$458$			65.8331i			3.07618i
$459$	10.5207			0.491062
$460$	−47.9298	−	15.9319i	−2.23474	−	0.742828i
$461$	−9.59005			−0.446653			−0.223327	−	0.974744i	$-0.571692\pi$
$461$	−9.59005			−0.446653			−0.223327	+	0.974744i	$0.571692\pi$
$462$			29.8195i			1.38733i
$463$			6.50235i			0.302190i	0.988519	+	0.151095i	$0.0482799\pi$
$463$			6.50235i			0.302190i	−0.988519	+	0.151095i	$0.951720\pi$
$464$	−97.0783			−4.50674
$465$	−14.8758	−	4.94471i	−0.689847	−	0.229305i
$466$	−55.3125			−2.56230
$467$		−	8.71364i		−	0.403219i	−0.979466	−	0.201610i	$-0.935383\pi$
$467$		−	8.71364i		−	0.403219i	0.979466	−	0.201610i	$-0.0646172\pi$
$468$			2.63124i			0.121629i
$469$	15.6860			0.724312
$470$	−4.70875	+	14.1659i	−0.217198	+	0.653424i
$471$	−39.5165			−1.82083
$472$		−	2.04017i		−	0.0939064i
$473$			14.7248i			0.677047i
$474$	−74.7293			−3.43243
$475$		0			0
$476$	−23.3565			−1.07054
$477$			0.130174i			0.00596025i
$478$			27.8486i			1.27376i
$479$	−27.3003			−1.24738			−0.623692	−	0.781670i	$-0.714368\pi$
$479$	−27.3003			−1.24738			−0.623692	+	0.781670i	$0.714368\pi$
$480$	−19.0995	+	57.4594i	−0.871770	+	2.62265i
$481$	−43.8103			−1.99758
$482$			53.5115i			2.43738i
$483$			17.1710i			0.781309i
$484$	14.1999			0.645450
$485$	0.430092	+	0.142963i	0.0195294	+	0.00649159i
$486$	−2.94370			−0.133529
$487$		−	35.5582i		−	1.61129i	−0.592395	−	0.805647i	$-0.701818\pi$
$487$		−	35.5582i		−	1.61129i	0.592395	−	0.805647i	$-0.298182\pi$
$488$			4.15302i			0.187999i
$489$	3.08058			0.139309
$490$	11.9850	+	3.98382i	0.541428	+	0.179971i
$491$	41.5813			1.87654			0.938269	−	0.345906i	$-0.112428\pi$
$491$	41.5813			1.87654			0.938269	+	0.345906i	$0.112428\pi$
$492$		−	11.0151i		−	0.496600i
$493$			16.6825i			0.751342i
$494$		0			0
$495$	0.214825	−	0.646283i	0.00965565	−	0.0290483i
$496$	47.7483			2.14396
$497$		−	21.2083i		−	0.951321i
$498$		−	26.8169i		−	1.20169i
$499$	27.1248			1.21427			0.607136	−	0.794598i	$-0.292318\pi$
$499$	27.1248			1.21427			0.607136	+	0.794598i	$0.292318\pi$
$500$	−47.0155	+	32.7248i	−2.10260	+	1.46350i
$501$	−37.0964			−1.65734
$502$			1.63954i			0.0731762i
$503$			34.8198i			1.55254i	0.630401	+	0.776269i	$0.282890\pi$
$503$			34.8198i			1.55254i	−0.630401	+	0.776269i	$0.717110\pi$
$504$	1.95619			0.0871358
$505$	−1.66825	+	5.01880i	−0.0742362	+	0.223334i
$506$	−33.7532			−1.50051
$507$		−	18.3190i		−	0.813575i
$508$			17.4499i			0.774215i
$509$	41.2656			1.82907			0.914533	−	0.404512i	$-0.132559\pi$
$509$	41.2656			1.82907			0.914533	+	0.404512i	$0.132559\pi$
$510$	20.5896	+	6.84398i	0.911722	+	0.303057i
$511$	0.634884			0.0280856
$512$			15.7135i			0.694443i
$513$		0			0
$514$	26.9588			1.18910
$515$	−2.27941	−	0.757675i	−0.100443	−	0.0333871i
$516$	46.3526			2.04056
$517$			7.17511i			0.315561i
$518$			53.4256i			2.34738i
$519$	20.4598			0.898085
$520$	28.4408	−	85.5620i	1.24721	−	3.75214i
$521$	33.5554			1.47009			0.735045	−	0.678018i	$-0.237161\pi$
$521$	33.5554			1.47009			0.735045	+	0.678018i	$0.237161\pi$
$522$		−	2.29185i		−	0.100311i
$523$			2.43983i			0.106687i	0.998576	+	0.0533433i	$0.0169877\pi$
$523$			2.43983i			0.106687i	−0.998576	+	0.0533433i	$0.983012\pi$
$524$	−2.93652			−0.128283
$525$	15.5990	+	11.6584i	0.680797	+	0.508813i
$526$	16.3995			0.715054
$527$		−	8.20534i		−	0.357430i
$528$			60.6866i			2.64105i
$529$	3.56380			0.154948
$530$	2.30795	−	6.94330i	0.100251	−	0.301598i
$531$	0.0259837			0.00112760
$532$		0			0
$533$			5.90007i			0.255560i
$534$	−78.4778			−3.39607
$535$	−0.395074	−	0.131323i	−0.0170805	−	0.00567758i
$536$	59.1744			2.55594
$537$			7.01609i			0.302767i
$538$		−	61.5981i		−	2.65568i
$539$	6.07048			0.261474
$540$	55.4479	+	18.4309i	2.38610	+	0.793140i
$541$	−27.7635			−1.19365			−0.596823	−	0.802373i	$-0.703571\pi$
$541$	−27.7635			−1.19365			−0.596823	+	0.802373i	$0.703571\pi$
$542$		−	36.7705i		−	1.57943i
$543$			4.96758i			0.213179i
$544$	−31.6941			−1.35887
$545$	−9.26704	+	27.8792i	−0.396957	+	1.19421i
$546$	−50.2798			−2.15177
$547$			25.2149i			1.07811i	0.842270	+	0.539056i	$0.181219\pi$
$547$			25.2149i			1.07811i	−0.842270	+	0.539056i	$0.818781\pi$
$548$		−	24.7062i		−	1.05540i
$549$	−0.0528931			−0.00225742
$550$	−22.9169	+	30.6631i	−0.977181	+	1.30748i
$551$		0			0
$552$			64.7767i			2.75708i
$553$		−	35.1080i		−	1.49295i
$554$	48.7015			2.06913
$555$	11.2597	−	33.8738i	0.477946	−	1.43786i
$556$	−76.8148			−3.25767
$557$			18.0110i			0.763151i	0.924338	+	0.381576i	$0.124618\pi$
$557$			18.0110i			0.763151i	−0.924338	+	0.381576i	$0.875382\pi$
$558$			1.12725i			0.0477205i
$559$	−24.8280			−1.05011
$560$	−56.2891	−	18.7105i	−2.37865	−	0.790664i
$561$	10.4287			0.440302
$562$		−	54.4450i		−	2.29662i
$563$		−	8.99696i		−	0.379177i	−0.981864	−	0.189588i	$-0.939285\pi$
$563$		−	8.99696i		−	0.379177i	0.981864	−	0.189588i	$-0.0607154\pi$
$564$	22.5867			0.951073
$565$	−9.26127	−	3.07845i	−0.389625	−	0.129511i
$566$	−52.1668			−2.19273
$567$		−	20.5684i		−	0.863790i
$568$		−	80.0069i		−	3.35701i
$569$	25.4166			1.06552			0.532759	−	0.846267i	$-0.321155\pi$
$569$	25.4166			1.06552			0.532759	+	0.846267i	$0.321155\pi$
$570$		0			0
$571$	16.9476			0.709233			0.354617	−	0.935012i	$-0.384611\pi$
$571$	16.9476			0.709233			0.354617	+	0.935012i	$0.384611\pi$
$572$		−	71.0864i		−	2.97227i
$573$		−	34.9147i		−	1.45858i
$574$	7.19499			0.300313
$575$	−13.1963	+	17.6568i	−0.550324	+	0.736339i
$576$	1.80507			0.0752113
$577$		−	25.1670i		−	1.04772i	−0.851805	−	0.523859i	$-0.824492\pi$
$577$		−	25.1670i		−	1.04772i	0.851805	−	0.523859i	$-0.175508\pi$
$578$		−	34.0160i		−	1.41488i
$579$	−9.73568			−0.404601
$580$	−29.2257	+	87.9231i	−1.21353	+	3.65081i
$581$	12.5986			0.522680
$582$		−	0.953444i		−	0.0395215i
$583$		−	3.51682i		−	0.145652i
$584$	2.39506			0.0991083
$585$	1.08972	+	0.362224i	0.0450544	+	0.0149761i
$586$	−24.6189			−1.01700
$587$			1.13849i			0.0469903i	0.999724	+	0.0234952i	$0.00747943\pi$
$587$			1.13849i			0.0469903i	−0.999724	+	0.0234952i	$0.992521\pi$
$588$		−	19.1094i		−	0.788060i
$589$		0			0
$590$	−1.38594	−	0.460685i	−0.0570581	−	0.0189661i
$591$	36.1287			1.48613
$592$			108.728i			4.46870i
$593$		−	5.56477i		−	0.228518i	−0.993451	−	0.114259i	$-0.963551\pi$
$593$		−	5.56477i		−	0.228518i	0.993451	−	0.114259i	$-0.0364494\pi$
$594$	39.0476			1.60214
$595$	−3.21532	+	9.67305i	−0.131815	+	0.396556i
$596$	64.7819			2.65357
$597$			30.4153i			1.24482i
$598$		−	56.9125i		−	2.32733i
$599$	−10.5181			−0.429758			−0.214879	−	0.976641i	$-0.568936\pi$
$599$	−10.5181			−0.429758			−0.214879	+	0.976641i	$0.568936\pi$
$600$	58.8463	+	43.9804i	2.40239	+	1.79549i
$601$	−36.9336			−1.50655			−0.753277	−	0.657703i	$-0.771528\pi$
$601$	−36.9336			−1.50655			−0.753277	+	0.657703i	$0.771528\pi$
$602$			30.2771i			1.23400i
$603$			0.753648i			0.0306909i
$604$	−56.4953			−2.29876
$605$	1.95480	−	5.88086i	0.0794739	−	0.239091i
$606$	11.1259			0.451958
$607$			31.6955i			1.28648i	0.765665	+	0.643240i	$0.222410\pi$
$607$			31.6955i			1.28648i	−0.765665	+	0.643240i	$0.777590\pi$
$608$		0			0
$609$	31.4988			1.27640
$610$	2.82125	+	0.937784i	0.114229	+	0.0379697i
$611$	−12.0982			−0.489441
$612$		−	1.12219i		−	0.0453617i
$613$		−	24.7004i		−	0.997641i	−0.866705	−	0.498820i	$-0.833767\pi$
$613$		−	24.7004i		−	0.997641i	0.866705	−	0.498820i	$-0.166233\pi$
$614$	20.6906			0.835004
$615$	−4.56189	−	1.51637i	−0.183953	−	0.0611460i
$616$	−52.8492			−2.12935
$617$			17.9984i			0.724589i	0.932064	+	0.362294i	$0.118006\pi$
$617$			17.9984i			0.724589i	−0.932064	+	0.362294i	$0.881994\pi$
$618$			5.05308i			0.203265i
$619$	−32.0927			−1.28991			−0.644957	−	0.764219i	$-0.723125\pi$
$619$	−32.0927			−1.28991			−0.644957	+	0.764219i	$0.723125\pi$
$620$	14.3747	−	43.2453i	0.577304	−	1.73677i
$621$	22.4849			0.902287
$622$		−	66.3052i		−	2.65860i
$623$		−	36.8691i		−	1.47713i
$624$	−102.326			−4.09632
$625$	7.08060	+	23.9763i	0.283224	+	0.959054i
$626$	−15.4603			−0.617920
$627$		0			0
$628$		−	114.878i		−	4.58415i
$629$	18.6845			0.744998
$630$	0.441723	−	1.32889i	0.0175987	−	0.0529442i
$631$	−6.97644			−0.277728			−0.138864	−	0.990311i	$-0.544345\pi$
$631$	−6.97644			−0.277728			−0.138864	+	0.990311i	$0.544345\pi$
$632$		−	132.443i		−	5.26829i
$633$		−	37.4304i		−	1.48772i
$634$	−12.2754			−0.487517
$635$	7.22684	+	2.40220i	0.286788	+	0.0953285i
$636$	−11.0707			−0.438982
$637$			10.2357i			0.405551i
$638$			61.9173i			2.45133i
$639$	1.01897			0.0403099
$640$	−31.0755	−	10.3295i	−1.22837	−	0.408310i
$641$	27.8888			1.10154			0.550770	−	0.834657i	$-0.314334\pi$
$641$	27.8888			1.10154			0.550770	+	0.834657i	$0.314334\pi$
$642$			0.875816i			0.0345657i
$643$			6.24974i			0.246466i	0.992378	+	0.123233i	$0.0393262\pi$
$643$			6.24974i			0.246466i	−0.992378	+	0.123233i	$0.960674\pi$
$644$	−49.9179			−1.96704
$645$	6.38103	−	19.1968i	0.251253	−	0.755874i
$646$		0			0
$647$		−	22.1840i		−	0.872142i	−0.899912	−	0.436071i	$-0.856370\pi$
$647$		−	22.1840i		−	0.872142i	0.899912	−	0.436071i	$-0.143630\pi$
$648$		−	77.5928i		−	3.04813i
$649$	−0.701984			−0.0275553
$650$	−51.7021	−	38.6411i	−2.02792	−	1.51563i
$651$	−15.4928			−0.607210
$652$			8.95554i			0.350726i
$653$			11.3373i			0.443664i	0.975085	+	0.221832i	$0.0712036\pi$
$653$			11.3373i			0.443664i	−0.975085	+	0.221832i	$0.928796\pi$
$654$	61.8036			2.41671
$655$	−0.404250	+	1.21615i	−0.0157954	+	0.0475191i
$656$	14.6428			0.571704
$657$			0.0305036i			0.00119006i
$658$			14.7535i			0.575150i
$659$	26.6149			1.03677			0.518385	−	0.855147i	$-0.326533\pi$
$659$	26.6149			1.03677			0.518385	+	0.855147i	$0.326533\pi$
$660$	54.9635	+	18.2699i	2.13945	+	0.711154i
$661$	45.7240			1.77846			0.889228	−	0.457465i	$-0.151242\pi$
$661$	45.7240			1.77846			0.889228	+	0.457465i	$0.151242\pi$
$662$			19.7386i			0.767161i
$663$			17.5843i			0.682917i
$664$	47.5276			1.84443
$665$		0			0
$666$	−2.56688			−0.0994646
$667$			35.6540i			1.38053i
$668$		−	107.843i		−	4.17256i
$669$	−50.8560			−1.96620
$670$	13.3620	−	40.1986i	0.516220	−	1.55301i
$671$	1.42898			0.0551651
$672$			59.8427i			2.30848i
$673$		−	25.6435i		−	0.988484i	−0.869324	−	0.494242i	$-0.835446\pi$
$673$		−	25.6435i		−	0.988484i	0.869324	−	0.494242i	$-0.164554\pi$
$674$	−44.5095			−1.71444
$675$	15.2662	−	20.4264i	0.587597	−	0.786211i
$676$	53.2550			2.04827
$677$			7.17287i			0.275676i	0.990455	+	0.137838i	$0.0440153\pi$
$677$			7.17287i			0.275676i	−0.990455	+	0.137838i	$0.955985\pi$
$678$			20.5307i			0.788479i
$679$	0.447931			0.0171900
$680$	−12.1296	+	36.4910i	−0.465149	+	1.39936i
$681$	14.8491			0.569019
$682$		−	30.4543i		−	1.16615i
$683$			6.25807i			0.239458i	0.992807	+	0.119729i	$0.0382026\pi$
$683$			6.25807i			0.239458i	−0.992807	+	0.119729i	$0.961797\pi$
$684$		0			0
$685$	−10.2320	−	3.40112i	−0.390945	−	0.129950i
$686$	53.7702			2.05296
$687$		−	43.4719i		−	1.65856i
$688$			61.6180i			2.34916i
$689$	5.92984			0.225909
$690$	44.0043	+	14.6270i	1.67522	+	0.556842i
$691$	−19.4240			−0.738925			−0.369463	−	0.929246i	$-0.620458\pi$
$691$	−19.4240			−0.738925			−0.369463	+	0.929246i	$0.620458\pi$
$692$			59.4786i			2.26104i
$693$		−	0.673089i		−	0.0255685i
$694$	96.1640			3.65034
$695$	−10.5745	+	31.8127i	−0.401115	+	1.20672i
$696$	118.827			4.50413
$697$		−	2.51630i		−	0.0953115i
$698$		−	63.0872i		−	2.38788i
$699$	36.5248			1.38149
$700$	−33.8920	+	45.3478i	−1.28100	+	1.71399i
$701$	9.49134			0.358483			0.179241	−	0.983805i	$-0.442636\pi$
$701$	9.49134			0.358483			0.179241	+	0.983805i	$0.442636\pi$
$702$			65.8396i			2.48496i
$703$		0			0
$704$	−48.7664			−1.83795
$705$	3.10935	−	9.35424i	0.117105	−	0.352301i
$706$	−90.5604			−3.40829
$707$			5.22697i			0.196580i
$708$			2.20980i			0.0830492i
$709$	21.9473			0.824246			0.412123	−	0.911128i	$-0.364787\pi$
$709$	21.9473			0.824246			0.412123	+	0.911128i	$0.364787\pi$
$710$	−54.3506	−	18.0661i	−2.03974	−	0.678011i
$711$	1.68680			0.0632599
$712$		−	139.086i		−	5.21248i
$713$		−	17.5366i		−	0.656749i
$714$	21.4436			0.802507
$715$	−29.4403	−	9.78596i	−1.10100	−	0.365974i
$716$	−20.3965			−0.762251
$717$		−	18.3894i		−	0.686764i
$718$		−	24.7878i		−	0.925074i
$719$	3.61331			0.134754			0.0673768	−	0.997728i	$-0.478537\pi$
$719$	3.61331			0.134754			0.0673768	+	0.997728i	$0.478537\pi$
$720$	0.898964	−	2.70446i	0.0335024	−	0.100789i
$721$	−2.37395			−0.0884105
$722$		0			0
$723$		−	35.3355i		−	1.31414i
$724$	−14.4412			−0.536704
$725$	32.3899	+	24.2075i	1.20293	+	0.899043i
$726$	−13.0369			−0.483845
$727$			41.1295i			1.52541i	0.646747	+	0.762705i	$0.276129\pi$
$727$			41.1295i			1.52541i	−0.646747	+	0.762705i	$0.723871\pi$
$728$		−	89.1109i		−	3.30267i
$729$	−25.9780			−0.962146
$730$	0.540823	−	1.62702i	0.0200167	−	0.0602188i
$731$	10.5888			0.391641
$732$		−	4.49832i		−	0.166263i
$733$			26.4052i			0.975297i	0.873040	+	0.487648i	$0.162145\pi$
$733$			26.4052i			0.975297i	−0.873040	+	0.487648i	$0.837855\pi$
$734$	−30.5023			−1.12586
$735$	−7.91413	−	2.63066i	−0.291917	−	0.0970333i
$736$	−67.7370			−2.49682
$737$		−	20.3608i		−	0.750000i
$738$			0.345690i			0.0127250i
$739$	16.0961			0.592106			0.296053	−	0.955172i	$-0.404330\pi$
$739$	16.0961			0.592106			0.296053	+	0.955172i	$0.404330\pi$
$740$	98.4743	+	32.7329i	3.61999	+	1.20328i
$741$		0			0
$742$		−	7.23129i		−	0.265469i
$743$		−	51.0206i		−	1.87176i	−0.352315	−	0.935882i	$-0.614605\pi$
$743$		−	51.0206i		−	1.87176i	0.352315	−	0.935882i	$-0.385395\pi$
$744$	−58.4456			−2.14272
$745$	8.91805	−	26.8293i	0.326732	−	0.982948i
$746$	68.7181			2.51595
$747$			0.605314i			0.0221473i
$748$			30.3173i			1.10851i
$749$	−0.411461			−0.0150345
$750$	43.1649	−	30.0446i	1.57616	−	1.09707i
$751$	7.88161			0.287604			0.143802	−	0.989606i	$-0.454067\pi$
$751$	7.88161			0.287604			0.143802	+	0.989606i	$0.454067\pi$
$752$			30.0253i			1.09491i
$753$		−	1.08264i		−	0.0394538i
$754$	−104.401			−3.80206
$755$	−7.77730	+	23.3974i	−0.283045	+	0.851518i
$756$	57.7478			2.10027
$757$		−	31.9261i		−	1.16037i	−0.814484	−	0.580186i	$-0.802980\pi$
$757$		−	31.9261i		−	1.16037i	0.814484	−	0.580186i	$-0.197020\pi$
$758$			54.3484i			1.97402i
$759$	22.2884			0.809019
$760$		0			0
$761$	21.6563			0.785039			0.392519	−	0.919744i	$-0.371604\pi$
$761$	21.6563			0.785039			0.392519	+	0.919744i	$0.371604\pi$
$762$		−	16.0207i		−	0.580370i
$763$			29.0355i			1.05116i
$764$	101.500			3.67216
$765$	−0.464751	−	0.154483i	−0.0168031	−	0.00558535i
$766$	48.3099			1.74551
$767$		−	1.18364i		−	0.0427388i
$768$			8.96514i			0.323502i
$769$	−14.8767			−0.536467			−0.268233	−	0.963354i	$-0.586440\pi$
$769$	−14.8767			−0.536467			−0.268233	+	0.963354i	$0.586440\pi$
$770$	−11.9337	+	35.9017i	−0.430062	+	1.29381i
$771$	−17.8018			−0.641117
$772$		−	28.3025i		−	1.01863i
$773$		−	1.66685i		−	0.0599524i	−0.999551	−	0.0299762i	$-0.990457\pi$
$773$		−	1.66685i		−	0.0599524i	0.999551	−	0.0299762i	$-0.00954314\pi$
$774$	−1.45469			−0.0522879
$775$	−15.9311	−	11.9065i	−0.572261	−	0.427695i
$776$	1.68979			0.0606599
$777$		−	35.2788i		−	1.26562i
$778$		−	80.8749i		−	2.89951i
$779$		0			0
$780$	−30.8055	+	92.6759i	−1.10301	+	3.31833i
$781$	−27.5289			−0.985060
$782$			24.2724i			0.867979i
$783$		−	41.2466i		−	1.47403i
$784$	25.4028			0.907242
$785$	−47.5766	−	15.8145i	−1.69808	−	0.564443i
$786$	2.69602			0.0961638
$787$			4.38273i			0.156228i	0.996944	+	0.0781138i	$0.0248898\pi$
$787$			4.38273i			0.156228i	−0.996944	+	0.0781138i	$0.975110\pi$
$788$			105.029i			3.74152i
$789$	−10.8292			−0.385530
$790$	−89.9716	−	29.9066i	−3.20104	−	1.06403i
$791$	−9.64541			−0.342951
$792$		−	2.53919i		−	0.0902261i
$793$			2.40945i			0.0855621i
$794$	−9.52992			−0.338204
$795$	−1.52402	+	4.58490i	−0.0540515	+	0.162610i
$796$	−88.4202			−3.13397
$797$			9.86857i			0.349563i	0.984607	+	0.174781i	$0.0559218\pi$
$797$			9.86857i			0.349563i	−0.984607	+	0.174781i	$0.944078\pi$
$798$		0			0
$799$	5.15972			0.182538
$800$	−45.9904	+	61.5356i	−1.62601	+	2.17561i
$801$	1.77141			0.0625897
$802$		−	1.47617i		−	0.0521253i
$803$		−	0.824096i		−	0.0290817i
$804$	−64.0944			−2.26043
$805$	−6.87183	+	20.6734i	−0.242200	+	0.728640i
$806$	51.3501			1.80873
$807$			40.6754i			1.43184i
$808$			19.7184i			0.693691i
$809$	40.4522			1.42222			0.711112	−	0.703079i	$-0.248192\pi$
$809$	40.4522			1.42222			0.711112	+	0.703079i	$0.248192\pi$
$810$	−52.7106	−	17.5210i	−1.85206	−	0.615626i
$811$	28.9125			1.01526			0.507628	−	0.861576i	$-0.330522\pi$
$811$	28.9125			1.01526			0.507628	+	0.861576i	$0.330522\pi$
$812$			91.5700i			3.21348i
$813$			24.2808i			0.851566i
$814$	69.3477			2.43064
$815$	3.70892	+	1.23285i	0.129918	+	0.0431847i
$816$	43.6406			1.52773
$817$		0			0
$818$			6.83986i			0.239150i
$819$	1.13492			0.0396573
$820$	4.40824	−	13.2618i	0.153942	−	0.463124i
$821$	−13.2912			−0.463866			−0.231933	−	0.972732i	$-0.574505\pi$
$821$	−13.2912			−0.463866			−0.231933	+	0.972732i	$0.574505\pi$
$822$			22.6827i			0.791151i
$823$			47.8247i			1.66706i	0.552471	+	0.833532i	$0.313685\pi$
$823$			47.8247i			1.66706i	−0.552471	+	0.833532i	$0.686315\pi$
$824$	−8.95558			−0.311982
$825$	15.1328	−	20.2479i	0.526858	−	0.704942i
$826$	−1.44342			−0.0502230
$827$			51.7917i			1.80098i	0.434882	+	0.900488i	$0.356790\pi$
$827$			51.7917i			1.80098i	−0.434882	+	0.900488i	$0.643210\pi$
$828$		−	2.39835i		−	0.0833484i
$829$	8.42434			0.292589			0.146295	−	0.989241i	$-0.453265\pi$
$829$	8.42434			0.292589			0.146295	+	0.989241i	$0.453265\pi$
$830$	10.7321	−	32.2866i	0.372516	−	1.12068i
$831$	−32.1593			−1.11559
$832$		−	82.2269i		−	2.85070i
$833$		−	4.36536i		−	0.151251i
$834$	70.5236			2.44203
$835$	−44.6628	−	14.8459i	−1.54562	−	0.513765i
$836$		0			0
$837$			20.2873i			0.701231i
$838$		−	24.0514i		−	0.830841i
$839$	23.7821			0.821051			0.410525	−	0.911849i	$-0.365345\pi$
$839$	23.7821			0.821051			0.410525	+	0.911849i	$0.365345\pi$
$840$	68.8999	+	22.9023i	2.37727	+	0.790205i
$841$	36.4042			1.25532
$842$		−	22.9964i		−	0.792508i
$843$			35.9519i			1.23825i
$844$	108.814			3.74552
$845$	7.33124	−	22.0555i	0.252202	−	0.758731i
$846$	−0.708844			−0.0243706
$847$		−	6.12478i		−	0.210450i
$848$		−	14.7166i		−	0.505371i
$849$	34.4476			1.18224
$850$	22.0502	+	16.4799i	0.756316	+	0.565255i
$851$	39.9327			1.36887
$852$			86.6589i			2.96889i
$853$		−	27.3430i		−	0.936205i	−0.883674	−	0.468102i	$-0.844938\pi$
$853$		−	27.3430i		−	0.936205i	0.883674	−	0.468102i	$-0.155062\pi$
$854$	2.93827			0.100545
$855$		0			0
$856$	−1.55221			−0.0530534
$857$			30.7007i			1.04872i	0.851498	+	0.524358i	$0.175695\pi$
$857$			30.7007i			1.04872i	−0.851498	+	0.524358i	$0.824305\pi$
$858$			65.2644i			2.22809i
$859$	36.8449			1.25713			0.628567	−	0.777756i	$-0.283642\pi$
$859$	36.8449			1.25713			0.628567	+	0.777756i	$0.283642\pi$
$860$	55.8070	+	18.5503i	1.90300	+	0.632559i
$861$	−4.75110			−0.161917
$862$			13.9195i			0.474102i
$863$			4.42788i			0.150727i	0.997156	+	0.0753634i	$0.0240117\pi$
$863$			4.42788i			0.150727i	−0.997156	+	0.0753634i	$0.975988\pi$
$864$	78.3620			2.66593
$865$	24.6329	+	8.18799i	0.837544	+	0.278400i
$866$	−13.8060			−0.469147
$867$			22.4620i			0.762848i
$868$		−	45.0390i		−	1.52872i
$869$	−45.5711			−1.54589
$870$	26.8321	−	80.7221i	0.909692	−	2.73674i
$871$	34.3311			1.16326
$872$			109.535i			3.70931i
$873$			0.0215212i			0.000728384i
$874$		0			0
$875$	14.1150	+	20.2790i	0.477175	+	0.685555i
$876$	−2.59419			−0.0876497
$877$			0.177859i			0.00600587i	0.999995	+	0.00300294i	$0.000955866\pi$
$877$			0.177859i			0.00600587i	−0.999995	+	0.00300294i	$0.999044\pi$
$878$			42.9792i			1.45048i
$879$	16.2567			0.548326
$880$	−24.2867	+	73.0647i	−0.818705	+	2.46301i
$881$	35.4916			1.19574			0.597871	−	0.801593i	$-0.296014\pi$
$881$	35.4916			1.19574			0.597871	+	0.801593i	$0.296014\pi$
$882$			0.599715i			0.0201935i
$883$			44.6775i			1.50352i	0.659438	+	0.751759i	$0.270794\pi$
$883$			44.6775i			1.50352i	−0.659438	+	0.751759i	$0.729206\pi$
$884$	−51.1192			−1.71932
$885$	0.915182	+	0.304207i	0.0307635	+	0.0102258i
$886$	32.3401			1.08649
$887$			34.5396i			1.15973i	0.814714	+	0.579863i	$0.196894\pi$
$887$			34.5396i			1.15973i	−0.814714	+	0.579863i	$0.803106\pi$
$888$		−	133.087i		−	4.46611i
$889$	7.52659			0.252434
$890$	−94.4847	−	31.4067i	−3.16713	−	1.05276i
$891$	−26.6982			−0.894424
$892$		−	147.843i		−	4.95015i
$893$		0			0
$894$	−59.4762			−1.98918
$895$	−2.80783	+	8.44714i	−0.0938555	+	0.282357i
$896$	−32.3645			−1.08122
$897$			37.5813i			1.25480i
$898$			18.8801i			0.630037i
$899$	−32.1693			−1.07291
$900$	−2.17878	−	1.62837i	−0.0726259	−	0.0542790i
$901$	−2.52899			−0.0842529
$902$		−	9.33927i		−	0.310964i
$903$		−	19.9931i		−	0.665327i
$904$	−36.3867			−1.21020
$905$	−1.98802	+	5.98081i	−0.0660841	+	0.198809i
$906$	51.8683			1.72321
$907$			30.4093i			1.00972i	0.863200	+	0.504862i	$0.168457\pi$
$907$			30.4093i			1.00972i	−0.863200	+	0.504862i	$0.831543\pi$
$908$			43.1677i			1.43257i
$909$	−0.251135			−0.00832961
$910$	−60.5352	−	20.1219i	−2.00672	−	0.667035i
$911$	−48.5898			−1.60985			−0.804926	−	0.593375i	$-0.797795\pi$
$911$	−48.5898			−1.60985			−0.804926	+	0.593375i	$0.797795\pi$
$912$		0			0
$913$		−	16.3534i		−	0.541217i
$914$	70.4110			2.32899
$915$	−1.86297	−	0.619251i	−0.0615879	−	0.0204718i
$916$	126.377			4.17561
$917$			1.26660i			0.0418268i
$918$		−	28.0797i		−	0.926767i
$919$	−46.0057			−1.51759			−0.758794	−	0.651331i	$-0.774211\pi$
$919$	−46.0057			−1.51759			−0.758794	+	0.651331i	$0.774211\pi$
$920$	−25.9235	+	77.9889i	−0.854674	+	2.57122i
$921$	−13.6627			−0.450202
$922$			25.5958i			0.842954i
$923$		−	46.4174i		−	1.52785i
$924$	57.2432			1.88316
$925$	27.1125	−	36.2768i	0.891453	−	1.19277i
$926$	17.3548			0.570313
$927$		−	0.114059i		−	0.00374618i
$928$			124.258i			4.07896i
$929$	−47.6797			−1.56432			−0.782161	−	0.623077i	$-0.785882\pi$
$929$	−47.6797			−1.56432			−0.782161	+	0.623077i	$0.785882\pi$
$930$	−13.1974	+	39.7035i	−0.432761	+	1.30193i
$931$		0			0
$932$			106.181i			3.47808i
$933$			43.7836i			1.43341i
$934$	−23.2567			−0.760983
$935$	12.5559	+	4.17357i	0.410620	+	0.136490i
$936$	4.28142			0.139942
$937$			32.4440i			1.05990i	0.848029	+	0.529950i	$0.177789\pi$
$937$			32.4440i			1.05990i	−0.848029	+	0.529950i	$0.822211\pi$
$938$		−	41.8659i		−	1.36697i
$939$	10.2090			0.333158
$940$	27.1937	+	9.03919i	0.886960	+	0.294826i
$941$	−22.9865			−0.749339			−0.374669	−	0.927159i	$-0.622244\pi$
$941$	−22.9865			−0.749339			−0.374669	+	0.927159i	$0.622244\pi$
$942$			105.470i			3.43639i
$943$		−	5.37786i		−	0.175127i
$944$	−2.93755			−0.0956092
$945$	7.94972	−	23.9161i	0.258604	−	0.777991i
$946$	39.3005			1.27777
$947$			19.5969i			0.636814i	0.947954	+	0.318407i	$0.103148\pi$
$947$			19.5969i			0.636814i	−0.947954	+	0.318407i	$0.896852\pi$
$948$			143.455i			4.65919i
$949$	1.38954			0.0451063
$950$		0			0
$951$	8.10586			0.262850
$952$			38.0045i			1.23173i
$953$		−	21.8067i		−	0.706387i	−0.935550	−	0.353194i	$-0.885096\pi$
$953$		−	21.8067i		−	0.706387i	0.935550	−	0.353194i	$-0.114904\pi$
$954$	0.347434			0.0112486
$955$	13.9728	−	42.0362i	0.452150	−	1.36026i
$956$	53.4597			1.72901
$957$		−	40.8862i		−	1.32166i
$958$			72.8646i			2.35415i
$959$	−10.6564			−0.344113
$960$	63.5772	+	21.1331i	2.05194	+	0.682067i
$961$	−15.1774			−0.489594
$962$			116.930i			3.76997i
$963$		−	0.0197690i		−	0.000637048i
$964$	102.724			3.30851
$965$	−11.7214	−	3.89621i	−0.377326	−	0.125423i
$966$	45.8295			1.47454
$967$			30.6010i			0.984063i	0.870577	+	0.492031i	$0.163745\pi$
$967$			30.6010i			0.984063i	−0.870577	+	0.492031i	$0.836255\pi$
$968$		−	23.1054i		−	0.742634i
$969$		0			0
$970$	0.381567	−	1.14791i	0.0122514	−	0.0368573i
$971$	24.6525			0.791136			0.395568	−	0.918437i	$-0.370548\pi$
$971$	24.6525			0.791136			0.395568	+	0.918437i	$0.370548\pi$
$972$			5.65089i			0.181252i
$973$			33.1322i			1.06217i
$974$	−94.9048			−3.04095
$975$	34.1407	+	25.5160i	1.09338	+	0.817168i
$976$	5.97976			0.191408
$977$		−	40.0301i		−	1.28067i	−0.768094	−	0.640337i	$-0.778795\pi$
$977$		−	40.0301i		−	1.28067i	0.768094	−	0.640337i	$-0.221205\pi$
$978$		−	8.22207i		−	0.262913i
$979$	−47.8570			−1.52952
$980$	7.64758	−	23.0071i	0.244293	−	0.734936i
$981$	−1.39504			−0.0445402
$982$		−	110.981i		−	3.54153i
$983$			18.0067i			0.574323i	0.957882	+	0.287162i	$0.0927117\pi$
$983$			18.0067i			0.574323i	−0.957882	+	0.287162i	$0.907288\pi$
$984$	−17.9232			−0.571372
$985$	43.4977	+	14.4586i	1.38595	+	0.460691i
$986$	44.5256			1.41798
$987$		−	9.74224i		−	0.310099i
$988$		0			0
$989$	22.6305			0.719608
$990$	−1.72493	−	0.573367i	−0.0548219	−	0.0182228i
$991$	47.2626			1.50135			0.750674	−	0.660673i	$-0.229729\pi$
$991$	47.2626			1.50135			0.750674	+	0.660673i	$0.229729\pi$
$992$		−	61.1166i		−	1.94045i
$993$		−	13.0341i		−	0.413623i
$994$	−56.6049			−1.79540
$995$	−12.1722	+	36.6190i	−0.385884	+	1.16090i
$996$	−51.4792			−1.63118
$997$		−	30.7551i		−	0.974024i	−0.873395	−	0.487012i	$-0.838087\pi$
$997$		−	30.7551i		−	0.974024i	0.873395	−	0.487012i	$-0.161913\pi$
$998$		−	72.3961i		−	2.29166i
$999$	−46.1964			−1.46159

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1805.2.b.m.1084.2	yes	40
5.2	odd	4		9025.2.a.cv.1.39		40
5.3	odd	4		9025.2.a.cv.1.2		40
5.4	even	2	inner	1805.2.b.m.1084.39	yes	40
19.18	odd	2	inner	1805.2.b.m.1084.40	yes	40
95.18	even	4		9025.2.a.cv.1.40		40
95.37	even	4		9025.2.a.cv.1.1		40
95.94	odd	2	inner	1805.2.b.m.1084.1	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1805.2.b.m.1084.1	✓	40	95.94	odd	2	inner
1805.2.b.m.1084.2	yes	40	1.1	even	1	trivial
1805.2.b.m.1084.39	yes	40	5.4	even	2	inner
1805.2.b.m.1084.40	yes	40	19.18	odd	2	inner
9025.2.a.cv.1.1		40	95.37	even	4
9025.2.a.cv.1.2		40	5.3	odd	4
9025.2.a.cv.1.39		40	5.2	odd	4
9025.2.a.cv.1.40		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)

\(f(q)\)	\(=\)	\(q-2.66900i q^{2} +1.76244i q^{3} -5.12357 q^{4} +(-0.705325 + 2.12191i) q^{5} +4.70394 q^{6} +2.20993i q^{7} +8.33681i q^{8} -0.106178 q^{9} +O(q^{10})\)	\(q-2.66900i q^{2} +1.76244i q^{3} -5.12357 q^{4} +(-0.705325 + 2.12191i) q^{5} +4.70394 q^{6} +2.20993i q^{7} +8.33681i q^{8} -0.106178 q^{9} +(5.66339 + 1.88251i) q^{10} +2.86854 q^{11} -9.02996i q^{12} +4.83675i q^{13} +5.89830 q^{14} +(-3.73974 - 1.24309i) q^{15} +12.0038 q^{16} -2.06280i q^{17} +0.283389i q^{18} +(3.61378 - 10.8718i) q^{20} -3.89485 q^{21} -7.65613i q^{22} -4.40865i q^{23} -14.6931 q^{24} +(-4.00503 - 2.99328i) q^{25} +12.9093 q^{26} +5.10017i q^{27} -11.3227i q^{28} -8.08729 q^{29} +(-3.31781 + 9.98136i) q^{30} +3.97776 q^{31} -15.3646i q^{32} +5.05561i q^{33} -5.50563 q^{34} +(-4.68927 - 1.55872i) q^{35} +0.544010 q^{36} +9.05780i q^{37} -8.52446 q^{39} +(-17.6900 - 5.88015i) q^{40} +1.21984 q^{41} +10.3954i q^{42} +5.13320i q^{43} -14.6972 q^{44} +(0.0748899 - 0.225300i) q^{45} -11.7667 q^{46} +2.50131i q^{47} +21.1559i q^{48} +2.11623 q^{49} +(-7.98906 + 10.6894i) q^{50} +3.63556 q^{51} -24.7814i q^{52} -1.22600i q^{53} +13.6124 q^{54} +(-2.02325 + 6.08679i) q^{55} -18.4237 q^{56} +21.5850i q^{58} -0.244718 q^{59} +(19.1608 + 6.36905i) q^{60} +0.498155 q^{61} -10.6166i q^{62} -0.234645i q^{63} -17.0004 q^{64} +(-10.2632 - 3.41148i) q^{65} +13.4934 q^{66} -7.09797i q^{67} +10.5689i q^{68} +7.76996 q^{69} +(-4.16021 + 12.5157i) q^{70} -9.59683 q^{71} -0.885185i q^{72} -0.287288i q^{73} +24.1753 q^{74} +(5.27546 - 7.05861i) q^{75} +6.33926i q^{77} +22.7518i q^{78} -15.8865 q^{79} +(-8.46658 + 25.4710i) q^{80} -9.30726 q^{81} -3.25576i q^{82} -5.70094i q^{83} +19.9555 q^{84} +(4.37709 + 1.45495i) q^{85} +13.7005 q^{86} -14.2533i q^{87} +23.9144i q^{88} -16.6834 q^{89} +(-0.601327 - 0.199881i) q^{90} -10.6889 q^{91} +22.5880i q^{92} +7.01055i q^{93} +6.67600 q^{94} +27.0791 q^{96} -0.202690i q^{97} -5.64821i q^{98} -0.304575 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 48 q^{4} + 6 q^{5} + 20 q^{6} - 52 q^{9}+O(q^{10}) \) 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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