LMFDB - Embedded newform 1805.2.b.k.1084.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1805,2,Mod(1084,1805)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage: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")

magma://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:traces = [24,0,0,-18,-3,-12,0,0,-12,-6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(10)] == traces)

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

Self dual:	no
Analytic conductor:	$14.4129975648$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	no (minimal twist has level 95)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1084.3
Character	$\chi$	$=$	1805.1084
Dual form			1805.2.b.k.1084.22

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.32462i q^{2} +1.14858i q^{3} -3.40387 q^{4} +(-2.01201 - 0.975617i) q^{5} +2.67001 q^{6} +0.143302i q^{7} +3.26348i q^{8} +1.68077 q^{9} +(-2.26794 + 4.67716i) q^{10} -2.81557 q^{11} -3.90962i q^{12} +1.70854i q^{13} +0.333123 q^{14} +(1.12057 - 2.31095i) q^{15} +0.778610 q^{16} -3.55886i q^{17} -3.90715i q^{18} +(6.84862 + 3.32088i) q^{20} -0.164594 q^{21} +6.54515i q^{22} +7.19394i q^{23} -3.74836 q^{24} +(3.09634 + 3.92590i) q^{25} +3.97171 q^{26} +5.37623i q^{27} -0.487782i q^{28} -7.57154 q^{29} +(-5.37209 - 2.60491i) q^{30} +4.84686 q^{31} +4.71698i q^{32} -3.23391i q^{33} -8.27302 q^{34} +(0.139808 - 0.288325i) q^{35} -5.72111 q^{36} -9.49127i q^{37} -1.96239 q^{39} +(3.18390 - 6.56614i) q^{40} -0.187320 q^{41} +0.382619i q^{42} +10.9943i q^{43} +9.58385 q^{44} +(-3.38171 - 1.63978i) q^{45} +16.7232 q^{46} +3.67032i q^{47} +0.894296i q^{48} +6.97946 q^{49} +(9.12623 - 7.19783i) q^{50} +4.08764 q^{51} -5.81566i q^{52} +1.64322i q^{53} +12.4977 q^{54} +(5.66495 + 2.74692i) q^{55} -0.467663 q^{56} +17.6010i q^{58} +5.36637 q^{59} +(-3.81429 + 7.86618i) q^{60} +10.1127 q^{61} -11.2671i q^{62} +0.240857i q^{63} +12.5224 q^{64} +(1.66688 - 3.43760i) q^{65} -7.51762 q^{66} -6.00805i q^{67} +12.1139i q^{68} -8.26281 q^{69} +(-0.670247 - 0.325001i) q^{70} +0.540979 q^{71} +5.48514i q^{72} +10.4674i q^{73} -22.0636 q^{74} +(-4.50920 + 3.55640i) q^{75} -0.403477i q^{77} +4.56183i q^{78} +11.6088 q^{79} +(-1.56657 - 0.759625i) q^{80} -1.13273 q^{81} +0.435449i q^{82} +7.59579i q^{83} +0.560257 q^{84} +(-3.47209 + 7.16046i) q^{85} +25.5576 q^{86} -8.69652i q^{87} -9.18856i q^{88} -1.44684 q^{89} +(-3.81188 + 7.86121i) q^{90} -0.244837 q^{91} -24.4873i q^{92} +5.56701i q^{93} +8.53210 q^{94} -5.41783 q^{96} -8.80212i q^{97} -16.2246i q^{98} -4.73232 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 18 q^{4} - 3 q^{5} - 12 q^{6} - 12 q^{9} - 6 q^{10} + 12 q^{11} - 24 q^{14} - 9 q^{15} + 6 q^{16} + 21 q^{20} + 6 q^{21} + 42 q^{24} - 3 q^{25} - 12 q^{26} - 36 q^{29} - 18 q^{30} + 42 q^{31} - 6 q^{34}+ \cdots - 120 q^{96}+O(q^{100}) $ 24 * q - 18 * q^4 - 3 * q^5 - 12 * q^6 - 12 * q^9 - 6 * q^10 + 12 * q^11 - 24 * q^14 - 9 * q^15 + 6 * q^16 + 21 * q^20 + 6 * q^21 + 42 * q^24 - 3 * q^25 - 12 * q^26 - 36 * q^29 - 18 * q^30 + 42 * q^31 - 6 * q^34 + 27 * q^35 - 6 * q^36 - 24 * q^39 + 12 * q^40 + 60 * q^41 + 30 * q^44 + 9 * q^45 + 6 * q^46 - 12 * q^49 + 18 * q^50 + 30 * q^51 + 24 * q^54 + 33 * q^55 + 18 * q^56 - 60 * q^59 - 42 * q^60 + 30 * q^61 + 18 * q^65 + 36 * q^66 - 66 * q^69 + 9 * q^70 + 96 * q^71 - 24 * q^74 + 36 * q^75 - 72 * q^79 - 42 * q^80 - 96 * q^81 + 54 * q^84 - 27 * q^85 + 108 * q^86 - 84 * q^89 - 93 * q^90 + 96 * q^91 - 36 * q^94 - 120 * q^96

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 $

$2$		−	2.32462i		−	1.64376i	−0.569663	−	0.821878i	$-0.692926\pi$
$2$		−	2.32462i		−	1.64376i	0.569663	−	0.821878i	$-0.307074\pi$
$3$			1.14858i			0.663133i	0.943432	+	0.331566i	$0.107577\pi$
$3$			1.14858i			0.663133i	−0.943432	+	0.331566i	$0.892423\pi$
$4$	−3.40387			−1.70194
$5$	−2.01201	−	0.975617i	−0.899797	−	0.436309i
$5$	−2.01201	−	0.975617i	−0.899797	−	0.436309i
$6$	2.67001			1.09003
$7$			0.143302i			0.0541631i	0.999633	+	0.0270816i	$0.00862138\pi$
$7$			0.143302i			0.0541631i	−0.999633	+	0.0270816i	$0.991379\pi$
$8$			3.26348i			1.15381i
$9$	1.68077			0.560255
$10$	−2.26794	+	4.67716i	−0.717186	+	1.47905i
$11$	−2.81557			−0.848927			−0.424463	−	0.905445i	$-0.639537\pi$
$11$	−2.81557			−0.848927			−0.424463	+	0.905445i	$0.639537\pi$
$12$		−	3.90962i		−	1.12861i
$13$			1.70854i			0.473864i	0.971526	+	0.236932i	$0.0761418\pi$
$13$			1.70854i			0.473864i	−0.971526	+	0.236932i	$0.923858\pi$
$14$	0.333123			0.0890310
$15$	1.12057	−	2.31095i	0.289331	−	0.596685i
$16$	0.778610			0.194653
$17$		−	3.55886i		−	0.863151i	−0.902077	−	0.431576i	$-0.857958\pi$
$17$		−	3.55886i		−	0.863151i	0.902077	−	0.431576i	$-0.142042\pi$
$18$		−	3.90715i		−	0.920923i
$19$		0			0
$19$		0			0
$20$	6.84862	+	3.32088i	1.53140	+	0.742571i
$21$	−0.164594			−0.0359173
$22$			6.54515i			1.39543i
$23$			7.19394i			1.50004i	0.661415	+	0.750020i	$0.269956\pi$
$23$			7.19394i			1.50004i	−0.661415	+	0.750020i	$0.730044\pi$
$24$	−3.74836			−0.765132
$25$	3.09634	+	3.92590i	0.619269	+	0.785179i
$26$	3.97171			0.778917
$27$			5.37623i			1.03466i
$28$		−	0.487782i		−	0.0921822i
$29$	−7.57154			−1.40600			−0.703000	−	0.711190i	$-0.748157\pi$
$29$	−7.57154			−1.40600			−0.703000	+	0.711190i	$0.748157\pi$
$30$	−5.37209	−	2.60491i	−0.980805	−	0.475589i
$31$	4.84686			0.870522			0.435261	−	0.900304i	$-0.356656\pi$
$31$	4.84686			0.870522			0.435261	+	0.900304i	$0.356656\pi$
$32$			4.71698i			0.833852i
$33$		−	3.23391i		−	0.562951i
$34$	−8.27302			−1.41881
$35$	0.139808	−	0.288325i	0.0236319	−	0.0487358i
$36$	−5.72111			−0.953519
$37$		−	9.49127i		−	1.56035i	−0.625559	−	0.780177i	$-0.715129\pi$
$37$		−	9.49127i		−	1.56035i	0.625559	−	0.780177i	$-0.284871\pi$
$38$		0			0
$39$	−1.96239			−0.314235
$40$	3.18390	−	6.56614i	0.503419	−	1.03820i
$41$	−0.187320			−0.0292545			−0.0146272	−	0.999893i	$-0.504656\pi$
$41$	−0.187320			−0.0292545			−0.0146272	+	0.999893i	$0.504656\pi$
$42$			0.382619i			0.0590393i
$43$			10.9943i			1.67662i	0.545196	+	0.838309i	$0.316455\pi$
$43$			10.9943i			1.67662i	−0.545196	+	0.838309i	$0.683545\pi$
$44$	9.58385			1.44482
$45$	−3.38171	−	1.63978i	−0.504116	−	0.244444i
$46$	16.7232			2.46570
$47$			3.67032i			0.535371i	0.963506	+	0.267685i	$0.0862587\pi$
$47$			3.67032i			0.535371i	−0.963506	+	0.267685i	$0.913741\pi$
$48$			0.894296i			0.129080i
$49$	6.97946			0.997066
$50$	9.12623	−	7.19783i	1.29064	−	1.01793i
$51$	4.08764			0.572384
$52$		−	5.81566i		−	0.806486i
$53$			1.64322i			0.225714i	0.993611	+	0.112857i	$0.0360002\pi$
$53$			1.64322i			0.225714i	−0.993611	+	0.112857i	$0.964000\pi$
$54$	12.4977			1.70072
$55$	5.66495	+	2.74692i	0.763862	+	0.370395i
$56$	−0.467663			−0.0624941
$57$		0			0
$58$			17.6010i			2.31112i
$59$	5.36637			0.698642			0.349321	−	0.937003i	$-0.386412\pi$
$59$	5.36637			0.698642			0.349321	+	0.937003i	$0.386412\pi$
$60$	−3.81429	+	7.86618i	−0.492423	+	1.01552i
$61$	10.1127			1.29480			0.647402	−	0.762148i	$-0.275855\pi$
$61$	10.1127			1.29480			0.647402	+	0.762148i	$0.275855\pi$
$62$		−	11.2671i		−	1.43093i
$63$			0.240857i			0.0303452i
$64$	12.5224			1.56530
$65$	1.66688	−	3.43760i	0.206751	−	0.426381i
$66$	−7.51762			−0.925355
$67$		−	6.00805i		−	0.734001i	−0.930221	−	0.367000i	$-0.880385\pi$
$67$		−	6.00805i		−	0.734001i	0.930221	−	0.367000i	$-0.119615\pi$
$68$			12.1139i			1.46903i
$69$	−8.26281			−0.994725
$70$	−0.670247	−	0.325001i	−0.0801098	−	0.0388450i
$71$	0.540979			0.0642024			0.0321012	−	0.999485i	$-0.489780\pi$
$71$	0.540979			0.0642024			0.0321012	+	0.999485i	$0.489780\pi$
$72$			5.48514i			0.646430i
$73$			10.4674i			1.22512i	0.790425	+	0.612559i	$0.209860\pi$
$73$			10.4674i			1.22512i	−0.790425	+	0.612559i	$0.790140\pi$
$74$	−22.0636			−2.56484
$75$	−4.50920	+	3.55640i	−0.520678	+	0.410657i
$76$		0			0
$77$		−	0.403477i		−	0.0459805i
$78$			4.56183i			0.516525i
$79$	11.6088			1.30610			0.653048	−	0.757317i	$-0.273490\pi$
$79$	11.6088			1.30610			0.653048	+	0.757317i	$0.273490\pi$
$80$	−1.56657	−	0.759625i	−0.175148	−	0.0849287i
$81$	−1.13273			−0.125859
$82$			0.435449i			0.0480873i
$83$			7.59579i			0.833746i	0.908965	+	0.416873i	$0.136874\pi$
$83$			7.59579i			0.833746i	−0.908965	+	0.416873i	$0.863126\pi$
$84$	0.560257			0.0611290
$85$	−3.47209	+	7.16046i	−0.376601	+	0.776661i
$86$	25.5576			2.75595
$87$		−	8.69652i		−	0.932365i
$88$		−	9.18856i		−	0.979504i
$89$	−1.44684			−0.153365			−0.0766823	−	0.997056i	$-0.524433\pi$
$89$	−1.44684			−0.153365			−0.0766823	+	0.997056i	$0.524433\pi$
$90$	−3.81188	+	7.86121i	−0.401807	+	0.828644i
$91$	−0.244837			−0.0256659
$92$		−	24.4873i		−	2.55297i
$93$			5.56701i			0.577272i
$94$	8.53210			0.880019
$95$		0			0
$96$	−5.41783			−0.552955
$97$		−	8.80212i		−	0.893720i	−0.894604	−	0.446860i	$-0.852542\pi$
$97$		−	8.80212i		−	0.893720i	0.894604	−	0.446860i	$-0.147458\pi$
$98$		−	16.2246i		−	1.63893i
$99$	−4.73232			−0.475616
$100$	−10.5396	−	13.3633i	−1.05396	−	1.33633i
$101$	−2.87795			−0.286367			−0.143183	−	0.989696i	$-0.545734\pi$
$101$	−2.87795			−0.286367			−0.143183	+	0.989696i	$0.545734\pi$
$102$		−	9.50222i		−	0.940860i
$103$			1.19966i			0.118206i	0.998252	+	0.0591032i	$0.0188241\pi$
$103$			1.19966i			0.118206i	−0.998252	+	0.0591032i	$0.981176\pi$
$104$	−5.57578			−0.546751
$105$	0.331164	+	0.160581i	0.0323183	+	0.0156711i
$106$	3.81987			0.371019
$107$			4.09536i			0.395913i	0.980211	+	0.197957i	$0.0634305\pi$
$107$			4.09536i			0.395913i	−0.980211	+	0.197957i	$0.936570\pi$
$108$		−	18.3000i		−	1.76092i
$109$	16.1941			1.55111			0.775555	−	0.631280i	$-0.217470\pi$
$109$	16.1941			1.55111			0.775555	+	0.631280i	$0.217470\pi$
$110$	6.38555	−	13.1689i	0.608839	−	1.25560i
$111$	10.9015			1.03472
$112$			0.111576i			0.0105430i
$113$			3.11845i			0.293359i	0.989184	+	0.146680i	$0.0468586\pi$
$113$			3.11845i			0.293359i	−0.989184	+	0.146680i	$0.953141\pi$
$114$		0			0
$115$	7.01853	−	14.4743i	0.654481	−	1.34973i
$116$	25.7726			2.39292
$117$			2.87166i			0.265485i
$118$		−	12.4748i		−	1.14840i
$119$	0.509993			0.0467509
$120$	7.54173	+	3.65697i	0.688463	+	0.333834i
$121$	−3.07255			−0.279323
$122$		−	23.5083i		−	2.12834i
$123$		−	0.215152i		−	0.0193996i
$124$	−16.4981			−1.48157
$125$	−2.39970	−	10.9198i	−0.214635	−	0.976694i
$126$	0.559902			0.0498801
$127$			8.16019i			0.724100i	0.932159	+	0.362050i	$0.117923\pi$
$127$			8.16019i			0.724100i	−0.932159	+	0.362050i	$0.882077\pi$
$128$		−	19.6760i		−	1.73913i
$129$	−12.6278			−1.11182
$130$	−7.99111	−	3.87487i	−0.700867	−	0.339849i
$131$	2.61996			0.228907			0.114453	−	0.993429i	$-0.463488\pi$
$131$	2.61996			0.228907			0.114453	+	0.993429i	$0.463488\pi$
$132$			11.0078i			0.958108i
$133$		0			0
$134$	−13.9665			−1.20652
$135$	5.24514	−	10.8170i	0.451430	−	0.930980i
$136$	11.6143			0.995916
$137$			12.3205i			1.05261i	0.850296	+	0.526305i	$0.176423\pi$
$137$			12.3205i			1.05261i	−0.850296	+	0.526305i	$0.823577\pi$
$138$			19.2079i			1.63509i
$139$	−7.95376			−0.674629			−0.337314	−	0.941392i	$-0.609519\pi$
$139$	−7.95376			−0.674629			−0.337314	+	0.941392i	$0.609519\pi$
$140$	−0.475889	+	0.981421i	−0.0402199	+	0.0829452i
$141$	−4.21565			−0.355022
$142$		−	1.25757i		−	0.105533i
$143$		−	4.81052i		−	0.402276i
$144$	1.30866			0.109055
$145$	15.2340	+	7.38692i	1.26511	+	0.613451i
$146$	24.3328			2.01380
$147$			8.01647i			0.661187i
$148$			32.3071i			2.65562i
$149$	4.19620			0.343766			0.171883	−	0.985117i	$-0.445015\pi$
$149$	4.19620			0.343766			0.171883	+	0.985117i	$0.445015\pi$
$150$	8.26728	+	10.4822i	0.675021	+	0.855868i
$151$	−2.86140			−0.232857			−0.116429	−	0.993199i	$-0.537145\pi$
$151$	−2.86140			−0.232857			−0.116429	+	0.993199i	$0.537145\pi$
$152$		0			0
$153$		−	5.98161i		−	0.483585i
$154$	−0.937933			−0.0755808
$155$	−9.75192	−	4.72868i	−0.783293	−	0.379817i
$156$	6.67974			0.534807
$157$			11.5244i			0.919744i	0.887985	+	0.459872i	$0.152105\pi$
$157$			11.5244i			0.919744i	−0.887985	+	0.459872i	$0.847895\pi$
$158$		−	26.9862i		−	2.14690i
$159$	−1.88737			−0.149678
$160$	4.60197	−	9.49060i	0.363817	−	0.750298i
$161$	−1.03091			−0.0812468
$162$			2.63318i			0.206882i
$163$			18.9195i			1.48189i	0.671567	+	0.740944i	$0.265621\pi$
$163$			18.9195i			1.48189i	−0.671567	+	0.740944i	$0.734379\pi$
$164$	0.637614			0.0497893
$165$	−3.15506	+	6.50665i	−0.245621	+	0.506542i
$166$	17.6573			1.37048
$167$		−	15.0690i		−	1.16607i	−0.812447	−	0.583036i	$-0.801865\pi$
$167$		−	15.0690i		−	1.16607i	0.812447	−	0.583036i	$-0.198135\pi$
$168$		−	0.537148i		−	0.0414419i
$169$	10.0809			0.775453
$170$	16.6454	+	8.07129i	1.27664	+	0.619040i
$171$		0			0
$172$		−	37.4233i		−	2.85350i
$173$			21.6950i			1.64944i	0.565542	+	0.824719i	$0.308667\pi$
$173$			21.6950i			1.64944i	−0.565542	+	0.824719i	$0.691333\pi$
$174$	−20.2161			−1.53258
$175$	−0.562589	+	0.443713i	−0.0425277	+	0.0335415i
$176$	−2.19223			−0.165246
$177$			6.16370i			0.463292i
$178$			3.36336i			0.252094i
$179$	−22.8790			−1.71006			−0.855028	−	0.518581i	$-0.826460\pi$
$179$	−22.8790			−1.71006			−0.855028	+	0.518581i	$0.826460\pi$
$180$	11.5109	+	5.58161i	0.857973	+	0.416029i
$181$	−11.5660			−0.859693			−0.429847	−	0.902902i	$-0.641432\pi$
$181$	−11.5660			−0.859693			−0.429847	+	0.902902i	$0.641432\pi$
$182$			0.569155i			0.0421886i
$183$			11.6153i			0.858627i
$184$	−23.4773			−1.73077
$185$	−9.25984	+	19.0965i	−0.680797	+	1.40400i
$186$	12.9412			0.948894
$187$			10.0202i			0.732752i
$188$		−	12.4933i		−	0.911167i
$189$	−0.770425			−0.0560402
$190$		0			0
$191$	7.28958			0.527455			0.263728	−	0.964597i	$-0.415048\pi$
$191$	7.28958			0.527455			0.263728	+	0.964597i	$0.415048\pi$
$192$			14.3830i			1.03800i
$193$		−	26.1862i		−	1.88493i	−0.334308	−	0.942464i	$-0.608503\pi$
$193$		−	26.1862i		−	1.88493i	0.334308	−	0.942464i	$-0.391497\pi$
$194$	−20.4616			−1.46906
$195$	3.94835	+	1.91454i	0.282747	+	0.137103i
$196$	−23.7572			−1.69694
$197$			2.28820i			0.163027i	0.996672	+	0.0815136i	$0.0259754\pi$
$197$			2.28820i			0.163027i	−0.996672	+	0.0815136i	$0.974025\pi$
$198$			11.0009i			0.781797i
$199$	12.2469			0.868159			0.434079	−	0.900875i	$-0.357074\pi$
$199$	12.2469			0.868159			0.434079	+	0.900875i	$0.357074\pi$
$200$	−12.8121	+	10.1049i	−0.905950	+	0.714521i
$201$	6.90073			0.486740
$202$			6.69015i			0.470717i
$203$		−	1.08502i		−	0.0761533i
$204$	−13.9138			−0.974161
$205$	0.376889	+	0.182753i	0.0263231	+	0.0127640i
$206$	2.78877			0.194302
$207$			12.0913i			0.840405i
$208$			1.33029i			0.0922388i
$209$		0			0
$210$	0.373289	−	0.769832i	0.0257594	−	0.0531234i
$211$	3.00309			0.206741			0.103371	−	0.994643i	$-0.467037\pi$
$211$	3.00309			0.206741			0.103371	+	0.994643i	$0.467037\pi$
$212$		−	5.59332i		−	0.384151i
$213$			0.621357i			0.0425747i
$214$	9.52016			0.650785
$215$	10.7262	−	22.1206i	0.731523	−	1.50861i
$216$	−17.5452			−1.19380
$217$			0.694565i			0.0471502i
$218$		−	37.6451i		−	2.54965i
$219$	−12.0227			−0.812416
$220$	−19.2828	−	9.35017i	−1.30004	−	0.630388i
$221$	6.08046			0.409016
$222$		−	25.3418i		−	1.70083i
$223$			2.19363i			0.146897i	0.997299	+	0.0734483i	$0.0234004\pi$
$223$			2.19363i			0.146897i	−0.997299	+	0.0734483i	$0.976600\pi$
$224$	−0.675953			−0.0451640
$225$	5.20423	+	6.59851i	0.346948	+	0.439901i
$226$	7.24922			0.482211
$227$			6.44357i			0.427675i	0.976869	+	0.213838i	$0.0685963\pi$
$227$			6.44357i			0.427675i	−0.976869	+	0.213838i	$0.931404\pi$
$228$		0			0
$229$	1.54321			0.101978			0.0509892	−	0.998699i	$-0.483763\pi$
$229$	1.54321			0.101978			0.0509892	+	0.998699i	$0.483763\pi$
$230$	−33.6472	−	16.3154i	−2.21863	−	1.07581i
$231$	0.463426			0.0304912
$232$		−	24.7096i		−	1.62226i
$233$			20.4612i			1.34046i	0.742155	+	0.670228i	$0.233804\pi$
$233$			20.4612i			1.34046i	−0.742155	+	0.670228i	$0.766196\pi$
$234$	6.67552			0.436392
$235$	3.58082	−	7.38470i	0.233587	−	0.481725i
$236$	−18.2665			−1.18904
$237$			13.3337i			0.866115i
$238$		−	1.18554i		−	0.0768472i
$239$	−6.24066			−0.403675			−0.201837	−	0.979419i	$-0.564691\pi$
$239$	−6.24066			−0.403675			−0.201837	+	0.979419i	$0.564691\pi$
$240$	0.872490	−	1.79933i	0.0563190	−	0.116146i
$241$	−26.3148			−1.69508			−0.847542	−	0.530728i	$-0.821919\pi$
$241$	−26.3148			−1.69508			−0.847542	+	0.530728i	$0.821919\pi$
$242$			7.14253i			0.459139i
$243$			14.8277i			0.951195i
$244$	−34.4225			−2.20368
$245$	−14.0427	−	6.80928i	−0.897157	−	0.435029i
$246$	−0.500147			−0.0318882
$247$		0			0
$248$			15.8176i			1.00442i
$249$	−8.72437			−0.552884
$250$	−25.3844	+	5.57839i	−1.60545	+	0.352808i
$251$	−10.7064			−0.675779			−0.337889	−	0.941186i	$-0.609713\pi$
$251$	−10.7064			−0.675779			−0.337889	+	0.941186i	$0.609713\pi$
$252$		−	0.819847i		−	0.0516455i
$253$		−	20.2551i		−	1.27342i
$254$	18.9694			1.19024
$255$	−8.22436	−	3.98797i	−0.515029	−	0.249736i
$256$	−20.6943			−1.29340
$257$			13.5240i			0.843603i	0.906688	+	0.421802i	$0.138602\pi$
$257$			13.5240i			0.843603i	−0.906688	+	0.421802i	$0.861398\pi$
$258$			29.3550i			1.82756i
$259$	1.36012			0.0845136
$260$	−5.67385	+	11.7011i	−0.351877	+	0.725674i
$261$	−12.7260			−0.787719
$262$		−	6.09042i		−	0.376267i
$263$		−	6.54056i		−	0.403308i	−0.979457	−	0.201654i	$-0.935368\pi$
$263$		−	6.54056i		−	0.403308i	0.979457	−	0.201654i	$-0.0646317\pi$
$264$	10.5538			0.649541
$265$	1.60315	−	3.30617i	0.0984810	−	0.203097i
$266$		0			0
$267$		−	1.66181i		−	0.101701i
$268$			20.4507i			1.24922i
$269$	−14.4220			−0.879327			−0.439663	−	0.898163i	$-0.644902\pi$
$269$	−14.4220			−0.879327			−0.439663	+	0.898163i	$0.644902\pi$
$270$	−25.1455	−	12.1930i	−1.53031	−	0.742041i
$271$	−2.18429			−0.132686			−0.0663431	−	0.997797i	$-0.521133\pi$
$271$	−2.18429			−0.132686			−0.0663431	+	0.997797i	$0.521133\pi$
$272$		−	2.77097i		−	0.168015i
$273$		−	0.281215i		−	0.0170199i
$274$	28.6405			1.73024
$275$	−8.71798	−	11.0536i	−0.525714	−	0.666560i
$276$	28.1256			1.69296
$277$		−	15.9746i		−	0.959823i	−0.877317	−	0.479911i	$-0.840669\pi$
$277$		−	15.9746i		−	0.959823i	0.877317	−	0.479911i	$-0.159331\pi$
$278$			18.4895i			1.10893i
$279$	8.14644			0.487714
$280$	0.940942	+	0.456260i	0.0562320	+	0.0272668i
$281$	−14.2569			−0.850496			−0.425248	−	0.905077i	$-0.639813\pi$
$281$	−14.2569			−0.850496			−0.425248	+	0.905077i	$0.639813\pi$
$282$			9.79980i			0.583569i
$283$			7.06732i			0.420108i	0.977690	+	0.210054i	$0.0673640\pi$
$283$			7.06732i			0.420108i	−0.977690	+	0.210054i	$0.932636\pi$
$284$	−1.84142			−0.109268
$285$		0			0
$286$	−11.1826			−0.661244
$287$		−	0.0268434i		−	0.00158451i
$288$			7.92814i			0.467170i
$289$	4.33449			0.254970
$290$	17.1718	−	35.4133i	1.00836	−	2.07954i
$291$	10.1099			0.592655
$292$		−	35.6298i		−	2.08507i
$293$		−	0.976745i		−	0.0570621i	−0.999593	−	0.0285310i	$-0.990917\pi$
$293$		−	0.976745i		−	0.0570621i	0.999593	−	0.0285310i	$-0.00908294\pi$
$294$	18.6353			1.08683
$295$	−10.7972	−	5.23552i	−0.628636	−	0.304824i
$296$	30.9745			1.80036
$297$		−	15.1372i		−	0.878347i
$298$		−	9.75458i		−	0.565068i
$299$	−12.2911			−0.710815
$300$	15.3488	−	12.1055i	0.886161	−	0.698913i
$301$	−1.57551			−0.0908108
$302$			6.65167i			0.382760i
$303$		−	3.30555i		−	0.189899i
$304$		0			0
$305$	−20.3469	−	9.86617i	−1.16506	−	0.564935i
$306$	−13.9050			−0.794896
$307$			28.4670i			1.62470i	0.583171	+	0.812350i	$0.301812\pi$
$307$			28.4670i			1.62470i	−0.583171	+	0.812350i	$0.698188\pi$
$308$			1.37339i			0.0782559i
$309$	−1.37791			−0.0783865
$310$	−10.9924	+	22.6695i	−0.624326	+	1.28754i
$311$	−25.5461			−1.44858			−0.724292	−	0.689493i	$-0.757833\pi$
$311$	−25.5461			−1.44858			−0.724292	+	0.689493i	$0.757833\pi$
$312$		−	6.40423i		−	0.362568i
$313$			14.9513i			0.845098i	0.906340	+	0.422549i	$0.138865\pi$
$313$			14.9513i			0.845098i	−0.906340	+	0.422549i	$0.861135\pi$
$314$	26.7898			1.51184
$315$	0.234984	−	0.484606i	0.0132399	−	0.0273045i
$316$	−39.5150			−2.22289
$317$			22.5401i			1.26598i	0.774160	+	0.632990i	$0.218173\pi$
$317$			22.5401i			1.26598i	−0.774160	+	0.632990i	$0.781827\pi$
$318$			4.38743i			0.246035i
$319$	21.3182			1.19359
$320$	−25.1952	−	12.2171i	−1.40845	−	0.682956i
$321$	−4.70384			−0.262543
$322$			2.39647i			0.133550i
$323$		0			0
$324$	3.85568			0.214204
$325$	−6.70755	+	5.29023i	−0.372068	+	0.293449i
$326$	43.9806			2.43586
$327$			18.6002i			1.02859i
$328$		−	0.611315i		−	0.0337542i
$329$	−0.525964			−0.0289973
$330$	15.1255	+	7.33432i	0.832632	+	0.403741i
$331$	−10.8681			−0.597365			−0.298682	−	0.954353i	$-0.596547\pi$
$331$	−10.8681			−0.597365			−0.298682	+	0.954353i	$0.596547\pi$
$332$		−	25.8551i		−	1.41898i
$333$		−	15.9526i		−	0.874196i
$334$	−35.0297			−1.91674
$335$	−5.86156	+	12.0882i	−0.320251	+	0.660451i
$336$	−0.128154			−0.00699140
$337$		−	7.70906i		−	0.419939i	−0.977708	−	0.209970i	$-0.932663\pi$
$337$		−	7.70906i		−	0.419939i	0.977708	−	0.209970i	$-0.0673365\pi$
$338$		−	23.4343i		−	1.27466i
$339$	−3.58179			−0.194536
$340$	11.8185	−	24.3733i	0.640951	−	1.32183i
$341$	−13.6467			−0.739010
$342$		0			0
$343$			2.00329i			0.108167i
$344$	−35.8797			−1.93450
$345$	16.6248	+	8.06134i	0.895051	+	0.434008i
$346$	50.4327			2.71128
$347$		−	20.2699i		−	1.08814i	−0.839039	−	0.544072i	$-0.816882\pi$
$347$		−	20.2699i		−	1.08814i	0.839039	−	0.544072i	$-0.183118\pi$
$348$			29.6019i			1.58683i
$349$	−19.0503			−1.01974			−0.509870	−	0.860252i	$-0.670306\pi$
$349$	−19.0503			−1.01974			−0.509870	+	0.860252i	$0.670306\pi$
$350$	1.03146	+	1.30781i	0.0551341	+	0.0699053i
$351$	−9.18551			−0.490286
$352$		−	13.2810i		−	0.707880i
$353$		−	18.1667i		−	0.966917i	−0.875367	−	0.483459i	$-0.839380\pi$
$353$		−	18.1667i		−	0.966917i	0.875367	−	0.483459i	$-0.160620\pi$
$354$	14.3283			0.761540
$355$	−1.08845	−	0.527788i	−0.0577691	−	0.0280121i
$356$	4.92486			0.261017
$357$			0.585767i			0.0310021i
$358$			53.1851i			2.81092i
$359$	16.1318			0.851406			0.425703	−	0.904863i	$-0.360027\pi$
$359$	16.1318			0.851406			0.425703	+	0.904863i	$0.360027\pi$
$360$	5.35139	−	11.0361i	0.282043	−	0.581656i
$361$		0			0
$362$			26.8866i			1.41313i
$363$		−	3.52907i		−	0.185228i
$364$	0.833396			0.0436818
$365$	10.2122	−	21.0605i	0.534530	−	1.10236i
$366$	27.0012			1.41137
$367$			32.2616i			1.68404i	0.539445	+	0.842021i	$0.318634\pi$
$367$			32.2616i			1.68404i	−0.539445	+	0.842021i	$0.681366\pi$
$368$			5.60127i			0.291987i
$369$	−0.314841			−0.0163900
$370$	44.3922	+	21.5256i	2.30784	+	1.11906i
$371$	−0.235477			−0.0122254
$372$		−	18.9494i		−	0.982480i
$373$		−	2.38037i		−	0.123251i	−0.998099	−	0.0616253i	$-0.980372\pi$
$373$		−	2.38037i		−	0.123251i	0.998099	−	0.0616253i	$-0.0196284\pi$
$374$	23.2933			1.20447
$375$	12.5422	−	2.75624i	0.647678	−	0.142332i
$376$	−11.9780			−0.617718
$377$		−	12.9363i		−	0.666253i
$378$			1.79095i			0.0921164i
$379$	−17.7215			−0.910291			−0.455145	−	0.890417i	$-0.650413\pi$
$379$	−17.7215			−0.910291			−0.455145	+	0.890417i	$0.650413\pi$
$380$		0			0
$381$	−9.37263			−0.480174
$382$		−	16.9455i		−	0.867009i
$383$		−	10.6646i		−	0.544934i	−0.962165	−	0.272467i	$-0.912160\pi$
$383$		−	10.6646i		−	0.544934i	0.962165	−	0.272467i	$-0.0878395\pi$
$384$	22.5994			1.15327
$385$	−0.393639	+	0.811799i	−0.0200617	+	0.0413731i
$386$	−60.8732			−3.09836
$387$			18.4789i			0.939333i
$388$			29.9613i			1.52105i
$389$	−22.7313			−1.15252			−0.576262	−	0.817265i	$-0.695489\pi$
$389$	−22.7313			−1.15252			−0.576262	+	0.817265i	$0.695489\pi$
$390$	4.45060	−	9.17843i	0.225365	−	0.464768i
$391$	25.6022			1.29476
$392$			22.7773i			1.15043i
$393$			3.00923i			0.151796i
$394$	5.31919			0.267977
$395$	−23.3570	−	11.3258i	−1.17522	−	0.569861i
$396$	16.1082			0.809468
$397$		−	20.4405i		−	1.02588i	−0.858425	−	0.512939i	$-0.828557\pi$
$397$		−	20.4405i		−	1.02588i	0.858425	−	0.512939i	$-0.171443\pi$
$398$		−	28.4694i		−	1.42704i
$399$		0			0
$400$	2.41084	+	3.05674i	0.120542	+	0.152837i
$401$	16.6972			0.833817			0.416908	−	0.908949i	$-0.363114\pi$
$401$	16.6972			0.833817			0.416908	+	0.908949i	$0.363114\pi$
$402$		−	16.0416i		−	0.800082i
$403$			8.28106i			0.412509i
$404$	9.79618			0.487378
$405$	2.27907	+	1.10511i	0.113248	+	0.0549135i
$406$	−2.52226			−0.125178
$407$			26.7233i			1.32463i
$408$			13.3399i			0.660424i
$409$	17.6846			0.874447			0.437224	−	0.899353i	$-0.355962\pi$
$409$	17.6846			0.874447			0.437224	+	0.899353i	$0.355962\pi$
$410$	0.424831	−	0.876126i	0.0209809	−	0.0432688i
$411$	−14.1511			−0.698021
$412$		−	4.08350i		−	0.201180i
$413$			0.769012i			0.0378406i
$414$	28.1078			1.38142
$415$	7.41058	−	15.2828i	0.363771	−	0.750202i
$416$	−8.05915			−0.395133
$417$		−	9.13552i		−	0.447369i
$418$		0			0
$419$	37.9339			1.85319			0.926596	−	0.376059i	$-0.122721\pi$
$419$	37.9339			1.85319			0.926596	+	0.376059i	$0.122721\pi$
$420$	−1.12724	−	0.546596i	−0.0550037	−	0.0266711i
$421$	11.5822			0.564481			0.282241	−	0.959344i	$-0.408922\pi$
$421$	11.5822			0.564481			0.282241	+	0.959344i	$0.408922\pi$
$422$		−	6.98106i		−	0.339833i
$423$			6.16894i			0.299944i
$424$	−5.36262			−0.260432
$425$	13.9717	−	11.0195i	0.677728	−	0.534523i
$426$	1.44442			0.0699825
$427$			1.44918i			0.0701306i
$428$		−	13.9401i		−	0.673819i
$429$	5.52526			0.266762
$430$	−51.4221	−	24.9345i	−2.47980	−	1.20245i
$431$	31.7898			1.53126			0.765629	−	0.643282i	$-0.222428\pi$
$431$	31.7898			1.53126			0.765629	+	0.643282i	$0.222428\pi$
$432$			4.18599i			0.201398i
$433$			4.08848i			0.196480i	0.995163	+	0.0982399i	$0.0313212\pi$
$433$			4.08848i			0.196480i	−0.995163	+	0.0982399i	$0.968679\pi$
$434$	1.61460			0.0775034
$435$	−8.48447	+	17.4975i	−0.406799	+	0.838939i
$436$	−55.1226			−2.63989
$437$		0			0
$438$			27.9481i			1.33541i
$439$	11.7557			0.561070			0.280535	−	0.959844i	$-0.409488\pi$
$439$	11.7557			0.561070			0.280535	+	0.959844i	$0.409488\pi$
$440$	−8.96451	+	18.4874i	−0.427366	+	0.881354i
$441$	11.7308			0.558611
$442$		−	14.1348i		−	0.672323i
$443$			7.88658i			0.374703i	0.982293	+	0.187351i	$0.0599903\pi$
$443$			7.88658i			0.374703i	−0.982293	+	0.187351i	$0.940010\pi$
$444$	−37.1072			−1.76103
$445$	2.91105	+	1.41156i	0.137997	+	0.0669144i
$446$	5.09937			0.241462
$447$			4.81967i			0.227962i
$448$			1.79449i			0.0847817i
$449$	1.16079			0.0547812			0.0273906	−	0.999625i	$-0.491280\pi$
$449$	1.16079			0.0547812			0.0273906	+	0.999625i	$0.491280\pi$
$450$	15.3390	−	12.0979i	0.723090	−	0.570299i
$451$	0.527413			0.0248349
$452$		−	10.6148i		−	0.499279i
$453$		−	3.28654i		−	0.154415i
$454$	14.9789			0.702994
$455$	0.492615	+	0.238867i	0.0230941	+	0.0111983i
$456$		0			0
$457$			38.6888i			1.80978i	0.425641	+	0.904892i	$0.360049\pi$
$457$			38.6888i			1.80978i	−0.425641	+	0.904892i	$0.639951\pi$
$458$		−	3.58739i		−	0.167628i
$459$	19.1333			0.893065
$460$	−23.8902	+	49.2685i	−1.11389	+	2.29716i
$461$	−24.4994			−1.14105			−0.570525	−	0.821280i	$-0.693260\pi$
$461$	−24.4994			−1.14105			−0.570525	+	0.821280i	$0.693260\pi$
$462$		−	1.07729i		−	0.0501201i
$463$			32.4849i			1.50970i	0.655895	+	0.754852i	$0.272291\pi$
$463$			32.4849i			1.50970i	−0.655895	+	0.754852i	$0.727709\pi$
$464$	−5.89528			−0.273681
$465$	5.43126	−	11.2009i	0.251869	−	0.519427i
$466$	47.5645			2.20338
$467$			14.7020i			0.680327i	0.940366	+	0.340163i	$0.110482\pi$
$467$			14.7020i			0.680327i	−0.940366	+	0.340163i	$0.889518\pi$
$468$		−	9.77475i		−	0.451838i
$469$	0.860967			0.0397558
$470$	−17.1666	−	8.32406i	−0.791838	−	0.383960i
$471$	−13.2366			−0.609912
$472$			17.5130i			0.806103i
$473$		−	30.9553i		−	1.42333i
$474$	30.9957			1.42368
$475$		0			0
$476$	−1.73595			−0.0795672
$477$			2.76187i			0.126457i
$478$			14.5072i			0.663543i
$479$	13.2196			0.604020			0.302010	−	0.953305i	$-0.402342\pi$
$479$	13.2196			0.604020			0.302010	+	0.953305i	$0.402342\pi$
$480$	10.9007	+	5.28572i	0.497547	+	0.241259i
$481$	16.2162			0.739396
$482$			61.1720i			2.78631i
$483$		−	1.18408i		−	0.0538774i
$484$	10.4586			0.475390
$485$	−8.58749	+	17.7099i	−0.389938	+	0.804166i
$486$	34.4687			1.56353
$487$		−	9.66071i		−	0.437769i	−0.975751	−	0.218884i	$-0.929758\pi$
$487$		−	9.66071i		−	0.437769i	0.975751	−	0.218884i	$-0.0702417\pi$
$488$			33.0027i			1.49396i
$489$	−21.7305			−0.982688
$490$	−15.8290	+	32.6441i	−0.715082	+	1.47471i
$491$	2.68634			0.121233			0.0606165	−	0.998161i	$-0.480693\pi$
$491$	2.68634			0.121233			0.0606165	+	0.998161i	$0.480693\pi$
$492$			0.732350i			0.0330169i
$493$			26.9461i			1.21359i
$494$		0			0
$495$	9.52145	+	4.61693i	0.427957	+	0.207515i
$496$	3.77382			0.169449
$497$			0.0775234i			0.00347740i
$498$			20.2809i			0.908807i
$499$	−2.35546			−0.105445			−0.0527224	−	0.998609i	$-0.516790\pi$
$499$	−2.35546			−0.105445			−0.0527224	+	0.998609i	$0.516790\pi$
$500$	8.16827	+	37.1695i	0.365296	+	1.66227i
$501$	17.3079			0.773260
$502$			24.8882i			1.11082i
$503$		−	13.7390i		−	0.612590i	−0.951937	−	0.306295i	$-0.900911\pi$
$503$		−	13.7390i		−	0.612590i	0.951937	−	0.306295i	$-0.0990894\pi$
$504$	−0.786032			−0.0350127
$505$	5.79045	+	2.80778i	0.257672	+	0.124944i
$506$	−47.0854			−2.09320
$507$			11.5787i			0.514228i
$508$		−	27.7763i		−	1.23237i
$509$	36.3796			1.61250			0.806249	−	0.591577i	$-0.201494\pi$
$509$	36.3796			1.61250			0.806249	+	0.591577i	$0.201494\pi$
$510$	−9.27052	+	19.1185i	−0.410506	+	0.846583i
$511$	−1.50000			−0.0663562
$512$			8.75464i			0.386904i
$513$		0			0
$514$	31.4382			1.38668
$515$	1.17041	−	2.41373i	0.0515745	−	0.106362i
$516$	42.9836			1.89225
$517$		−	10.3340i		−	0.454491i
$518$		−	3.16176i		−	0.138920i
$519$	−24.9184			−1.09380
$520$	11.2185	+	5.43983i	0.491965	+	0.238552i
$521$	0.580423			0.0254288			0.0127144	−	0.999919i	$-0.495953\pi$
$521$	0.580423			0.0254288			0.0127144	+	0.999919i	$0.495953\pi$
$522$			29.5831i			1.29482i
$523$			19.2463i			0.841582i	0.907158	+	0.420791i	$0.138247\pi$
$523$			19.2463i			0.841582i	−0.907158	+	0.420791i	$0.861753\pi$
$524$	−8.91801			−0.389585
$525$	−0.509639	−	0.646178i	−0.0222425	−	0.0282015i
$526$	−15.2043			−0.662941
$527$		−	17.2493i		−	0.751392i
$528$		−	2.51795i		−	0.109580i
$529$	−28.7528			−1.25012
$530$	−7.68561	−	3.72673i	−0.333841	−	0.161879i
$531$	9.01961			0.391418
$532$		0			0
$533$		−	0.320044i		−	0.0138626i
$534$	−3.86308			−0.167172
$535$	3.99550	−	8.23989i	0.172740	−	0.356241i
$536$	19.6072			0.846900
$537$		−	26.2783i		−	1.13399i
$538$			33.5258i			1.44540i
$539$	−19.6512			−0.846437
$540$	−17.8538	+	36.8198i	−0.768305	+	1.58447i
$541$	−31.9066			−1.37177			−0.685886	−	0.727709i	$-0.740585\pi$
$541$	−31.9066			−1.37177			−0.685886	+	0.727709i	$0.740585\pi$
$542$			5.07765i			0.218104i
$543$		−	13.2845i		−	0.570091i
$544$	16.7871			0.719741
$545$	−32.5826	−	15.7992i	−1.39568	−	0.676763i
$546$	−0.653720			−0.0279766
$547$			3.43452i			0.146849i	0.997301	+	0.0734246i	$0.0233928\pi$
$547$			3.43452i			0.146849i	−0.997301	+	0.0734246i	$0.976607\pi$
$548$		−	41.9374i		−	1.79148i
$549$	16.9972			0.725421
$550$	−25.6956	+	20.2660i	−1.09566	+	0.864146i
$551$		0			0
$552$		−	26.9655i		−	1.14773i
$553$			1.66357i			0.0707422i
$554$	−37.1350			−1.57772
$555$	−21.9338	−	10.6357i	−0.931040	−	0.451459i
$556$	27.0736			1.14818
$557$		−	6.83010i		−	0.289401i	−0.989476	−	0.144700i	$-0.953778\pi$
$557$		−	6.83010i		−	0.289401i	0.989476	−	0.144700i	$-0.0462218\pi$
$558$		−	18.9374i		−	0.801684i
$559$	−18.7842			−0.794488
$560$	0.108856	−	0.224493i	0.00460000	−	0.00948654i
$561$	−11.5090			−0.485912
$562$			33.1419i			1.39801i
$563$		−	12.5628i		−	0.529460i	−0.964323	−	0.264730i	$-0.914717\pi$
$563$		−	12.5628i		−	0.529460i	0.964323	−	0.264730i	$-0.0852828\pi$
$564$	14.3495			0.604225
$565$	3.04241	−	6.27434i	0.127995	−	0.263964i
$566$	16.4289			0.690556
$567$		−	0.162323i		−	0.00681692i
$568$			1.76547i			0.0740776i
$569$	−3.47978			−0.145880			−0.0729400	−	0.997336i	$-0.523238\pi$
$569$	−3.47978			−0.145880			−0.0729400	+	0.997336i	$0.523238\pi$
$570$		0			0
$571$	−0.621524			−0.0260100			−0.0130050	−	0.999915i	$-0.504140\pi$
$571$	−0.621524			−0.0260100			−0.0130050	+	0.999915i	$0.504140\pi$
$572$			16.3744i			0.684648i
$573$			8.37266i			0.349773i
$574$	−0.0624007			−0.00260456
$575$	−28.2426	+	22.2749i	−1.17780	+	0.928928i
$576$	21.0473			0.876969
$577$		−	3.85170i		−	0.160348i	−0.996781	−	0.0801742i	$-0.974452\pi$
$577$		−	3.85170i		−	0.160348i	0.996781	−	0.0801742i	$-0.0255477\pi$
$578$		−	10.0761i		−	0.419109i
$579$	30.0770			1.24996
$580$	−51.8546	−	25.1442i	−2.15315	−	1.04405i
$581$	−1.08849			−0.0451583
$582$		−	23.5018i		−	0.974180i
$583$		−	4.62661i		−	0.191615i
$584$	−34.1602			−1.41356
$585$	2.80163	−	5.77779i	0.115833	−	0.238882i
$586$	−2.27056			−0.0937961
$587$		−	40.4333i		−	1.66886i	−0.551113	−	0.834431i	$-0.685797\pi$
$587$		−	40.4333i		−	1.66886i	0.551113	−	0.834431i	$-0.314203\pi$
$588$		−	27.2871i		−	1.12530i
$589$		0			0
$590$	−12.1706	+	25.0994i	−0.501056	+	1.03332i
$591$	−2.62817			−0.108109
$592$		−	7.38999i		−	0.303727i
$593$		−	5.87362i		−	0.241201i	−0.992701	−	0.120600i	$-0.961518\pi$
$593$		−	5.87362i		−	0.241201i	0.992701	−	0.120600i	$-0.0384820\pi$
$594$	−35.1882			−1.44379
$595$	−1.02611	−	0.497557i	−0.0420664	−	0.0203979i
$596$	−14.2833			−0.585068
$597$			14.0665i			0.575704i
$598$			28.5723i			1.16841i
$599$	13.3107			0.543862			0.271931	−	0.962317i	$-0.412338\pi$
$599$	13.3107			0.543862			0.271931	+	0.962317i	$0.412338\pi$
$600$	−11.6062	−	14.7157i	−0.473822	−	0.600765i
$601$	5.16016			0.210487			0.105244	−	0.994446i	$-0.466438\pi$
$601$	5.16016			0.210487			0.105244	+	0.994446i	$0.466438\pi$
$602$			3.66246i			0.149271i
$603$		−	10.0981i		−	0.411228i
$604$	9.73983			0.396308
$605$	6.18200	+	2.99763i	0.251334	+	0.121871i
$606$	−7.68417			−0.312148
$607$		−	30.5069i		−	1.23824i	−0.785297	−	0.619119i	$-0.787490\pi$
$607$		−	30.5069i		−	1.23824i	0.785297	−	0.619119i	$-0.212510\pi$
$608$		0			0
$609$	1.24623			0.0504998
$610$	−22.9351	+	47.2989i	−0.928616	+	1.91508i
$611$	−6.27088			−0.253693
$612$			20.3607i			0.823031i
$613$		−	45.5007i		−	1.83776i	−0.394540	−	0.918879i	$-0.629096\pi$
$613$		−	45.5007i		−	1.83776i	0.394540	−	0.918879i	$-0.370904\pi$
$614$	66.1751			2.67061
$615$	−0.209906	+	0.432887i	−0.00846422	+	0.0174557i
$616$	1.31674			0.0530530
$617$		−	2.48247i		−	0.0999403i	−0.998751	−	0.0499701i	$-0.984087\pi$
$617$		−	2.48247i		−	0.0999403i	0.998751	−	0.0499701i	$-0.0159126\pi$
$618$			3.20312i			0.128848i
$619$	−23.4945			−0.944325			−0.472162	−	0.881512i	$-0.656526\pi$
$619$	−23.4945			−0.944325			−0.472162	+	0.881512i	$0.656526\pi$
$620$	33.1943	+	16.0958i	1.33312	+	0.646424i
$621$	−38.6763			−1.55203
$622$			59.3850i			2.38112i
$623$		−	0.207335i		−	0.00830670i
$624$	−1.52794			−0.0611666
$625$	−5.82531	+	24.3118i	−0.233012	+	0.972474i
$626$	34.7562			1.38914
$627$		0			0
$628$		−	39.2275i		−	1.56535i
$629$	−33.7781			−1.34682
$630$	−1.12653	−	0.546250i	−0.0448819	−	0.0217631i
$631$	−17.8197			−0.709392			−0.354696	−	0.934982i	$-0.615416\pi$
$631$	−17.8197			−0.709392			−0.354696	+	0.934982i	$0.615416\pi$
$632$			37.8852i			1.50699i
$633$			3.44929i			0.137097i
$634$	52.3974			2.08096
$635$	7.96122	−	16.4184i	0.315931	−	0.651543i
$636$	6.42437			0.254743
$637$			11.9247i			0.472474i
$638$		−	49.5568i		−	1.96197i
$639$	0.909259			0.0359697
$640$	−19.1962	+	39.5882i	−0.758796	+	1.56486i
$641$	37.4631			1.47970			0.739852	−	0.672770i	$-0.234896\pi$
$641$	37.4631			1.47970			0.739852	+	0.672770i	$0.234896\pi$
$642$			10.9347i			0.431557i
$643$		−	19.8886i		−	0.784331i	−0.919895	−	0.392165i	$-0.871726\pi$
$643$		−	19.8886i		−	0.784331i	0.919895	−	0.392165i	$-0.128274\pi$
$644$	3.50908			0.138277
$645$	25.4073	+	12.3199i	1.00041	+	0.485097i
$646$		0			0
$647$			23.0645i			0.906759i	0.891318	+	0.453380i	$0.149782\pi$
$647$			23.0645i			0.906759i	−0.891318	+	0.453380i	$0.850218\pi$
$648$		−	3.69665i		−	0.145218i
$649$	−15.1094			−0.593096
$650$	12.2978	+	15.5925i	0.482359	+	0.611589i
$651$	−0.797764			−0.0312668
$652$		−	64.3995i		−	2.52208i
$653$		−	26.9839i		−	1.05596i	−0.849256	−	0.527981i	$-0.822949\pi$
$653$		−	26.9839i		−	1.05596i	0.849256	−	0.527981i	$-0.177051\pi$
$654$	43.2384			1.69075
$655$	−5.27138	−	2.55608i	−0.205970	−	0.0998742i
$656$	−0.145849			−0.00569446
$657$			17.5933i			0.686379i
$658$			1.22267i			0.0476646i
$659$	−13.4880			−0.525418			−0.262709	−	0.964875i	$-0.584616\pi$
$659$	−13.4880			−0.525418			−0.262709	+	0.964875i	$0.584616\pi$
$660$	10.7394	−	22.1478i	0.418031	−	0.862102i
$661$	−21.9777			−0.854835			−0.427417	−	0.904054i	$-0.640577\pi$
$661$	−21.9777			−0.854835			−0.427417	+	0.904054i	$0.640577\pi$
$662$			25.2642i			0.981922i
$663$			6.98389i			0.271232i
$664$	−24.7887			−0.961988
$665$		0			0
$666$	−37.0838			−1.43697
$667$		−	54.4692i		−	2.10906i
$668$			51.2928i			1.98458i
$669$	−2.51956			−0.0974119
$670$	28.1006	+	13.6259i	1.08562	+	0.526415i
$671$	−28.4732			−1.09919
$672$		−	0.776386i		−	0.0299497i
$673$		−	23.1998i		−	0.894286i	−0.894462	−	0.447143i	$-0.852441\pi$
$673$		−	23.1998i		−	0.894286i	0.894462	−	0.447143i	$-0.147559\pi$
$674$	−17.9207			−0.690278
$675$	−21.1065	+	16.6467i	−0.812390	+	0.640730i
$676$	−34.3141			−1.31977
$677$		−	28.7294i		−	1.10416i	−0.833791	−	0.552081i	$-0.813834\pi$
$677$		−	28.7294i		−	1.10416i	0.833791	−	0.552081i	$-0.186166\pi$
$678$			8.32631i			0.319770i
$679$	1.26136			0.0484066
$680$	−23.3680	−	11.3311i	−0.896122	−	0.434527i
$681$	−7.40096			−0.283605
$682$			31.7234i			1.21475i
$683$			24.0010i			0.918374i	0.888340	+	0.459187i	$0.151859\pi$
$683$			24.0010i			0.918374i	−0.888340	+	0.459187i	$0.848141\pi$
$684$		0			0
$685$	12.0201	−	24.7889i	0.459264	−	0.947136i
$686$	4.65689			0.177801
$687$			1.77250i			0.0676252i
$688$			8.56028i			0.326358i
$689$	−2.80751			−0.106958
$690$	18.7396	−	38.6465i	0.713403	−	1.47125i
$691$	37.3866			1.42226			0.711128	−	0.703063i	$-0.248185\pi$
$691$	37.3866			1.42226			0.711128	+	0.703063i	$0.248185\pi$
$692$		−	73.8470i		−	2.80724i
$693$		−	0.678151i		−	0.0257608i
$694$	−47.1198			−1.78864
$695$	16.0030	+	7.75982i	0.607029	+	0.294347i
$696$	28.3809			1.07578
$697$			0.666647i			0.0252510i
$698$			44.2848i			1.67620i
$699$	−23.5013			−0.888900
$700$	1.91498	−	1.51034i	0.0723795	−	0.0570856i
$701$	−2.32624			−0.0878609			−0.0439304	−	0.999035i	$-0.513988\pi$
$701$	−2.32624			−0.0878609			−0.0439304	+	0.999035i	$0.513988\pi$
$702$			21.3528i			0.805911i
$703$		0			0
$704$	−35.2578			−1.32883
$705$	8.48192	+	4.11286i	0.319447	+	0.154899i
$706$	−42.2308			−1.58938
$707$		−	0.412416i		−	0.0155105i
$708$		−	20.9805i		−	0.788494i
$709$	24.3523			0.914568			0.457284	−	0.889321i	$-0.348822\pi$
$709$	24.3523			0.914568			0.457284	+	0.889321i	$0.348822\pi$
$710$	−1.22691	+	2.53024i	−0.0460451	+	0.0949584i
$711$	19.5117			0.731747
$712$		−	4.72173i		−	0.176954i
$713$			34.8680i			1.30582i
$714$	1.36169			0.0509599
$715$	−4.69322	+	9.67880i	−0.175517	+	0.361967i
$716$	77.8772			2.91041
$717$		−	7.16789i		−	0.267690i
$718$		−	37.5004i		−	1.39950i
$719$	−17.0622			−0.636311			−0.318155	−	0.948039i	$-0.603063\pi$
$719$	−17.0622			−0.636311			−0.318155	+	0.948039i	$0.603063\pi$
$720$	−2.63303	−	1.27675i	−0.0981274	−	0.0475817i
$721$	−0.171914			−0.00640242
$722$		0			0
$723$		−	30.2246i		−	1.12407i
$724$	39.3692			1.46314
$725$	−23.4441	−	29.7251i	−0.870692	−	1.10396i
$726$	−8.20376			−0.304470
$727$			14.6251i			0.542415i	0.962521	+	0.271207i	$0.0874229\pi$
$727$			14.6251i			0.542415i	−0.962521	+	0.271207i	$0.912577\pi$
$728$		−	0.799022i		−	0.0296137i
$729$	−20.4289			−0.756628
$730$	−48.9577	−	23.7395i	−1.81201	−	0.878638i
$731$	39.1273			1.44717
$732$		−	39.5370i		−	1.46133i
$733$			33.5260i			1.23831i	0.785268	+	0.619156i	$0.212525\pi$
$733$			33.5260i			1.23831i	−0.785268	+	0.619156i	$0.787475\pi$
$734$	74.9961			2.76816
$735$	7.82100	−	16.1292i	0.288482	−	0.594934i
$736$	−33.9337			−1.25081
$737$			16.9161i			0.623113i
$738$			0.731887i			0.0269411i
$739$	15.2098			0.559501			0.279751	−	0.960073i	$-0.409748\pi$
$739$	15.2098			0.559501			0.279751	+	0.960073i	$0.409748\pi$
$740$	31.5193	−	65.0021i	1.15867	−	2.38952i
$741$		0			0
$742$			0.547396i			0.0200955i
$743$			6.65799i			0.244258i	0.992514	+	0.122129i	$0.0389722\pi$
$743$			6.65799i			0.244258i	−0.992514	+	0.122129i	$0.961028\pi$
$744$	−18.1678			−0.666064
$745$	−8.44278	−	4.09388i	−0.309319	−	0.149988i
$746$	−5.53345			−0.202594
$747$			12.7667i			0.467110i
$748$		−	34.1076i		−	1.24710i
$749$	−0.586873			−0.0214439
$750$	−6.40723	−	29.1560i	−0.233959	−	1.06462i
$751$	7.81110			0.285031			0.142516	−	0.989793i	$-0.454481\pi$
$751$	7.81110			0.285031			0.142516	+	0.989793i	$0.454481\pi$
$752$			2.85774i			0.104211i
$753$		−	12.2971i		−	0.448131i
$754$	−30.0720			−1.09516
$755$	5.75715	+	2.79163i	0.209524	+	0.101598i
$756$	2.62243			0.0953769
$757$			18.3846i			0.668201i	0.942537	+	0.334100i	$0.108432\pi$
$757$			18.3846i			0.668201i	−0.942537	+	0.334100i	$0.891568\pi$
$758$			41.1958i			1.49630i
$759$	23.2645			0.844449
$760$		0			0
$761$	22.4779			0.814822			0.407411	−	0.913245i	$-0.366432\pi$
$761$	22.4779			0.814822			0.407411	+	0.913245i	$0.366432\pi$
$762$			21.7878i			0.789290i
$763$			2.32064i			0.0840129i
$764$	−24.8128			−0.897696
$765$	−5.83576	+	12.0350i	−0.210992	+	0.435128i
$766$	−24.7911			−0.895739
$767$			9.16866i			0.331061i
$768$		−	23.7691i		−	0.857694i
$769$	−5.51880			−0.199013			−0.0995065	−	0.995037i	$-0.531726\pi$
$769$	−5.51880			−0.199013			−0.0995065	+	0.995037i	$0.531726\pi$
$770$	1.88713	+	0.915063i	0.0680074	+	0.0329766i
$771$	−15.5334			−0.559421
$772$			89.1347i			3.20803i
$773$		−	33.1881i		−	1.19369i	−0.802356	−	0.596846i	$-0.796420\pi$
$773$		−	33.1881i		−	1.19369i	0.802356	−	0.596846i	$-0.203580\pi$
$774$	42.9564			1.54404
$775$	15.0076	+	19.0283i	0.539087	+	0.683516i
$776$	28.7255			1.03119
$777$			1.56220i			0.0560438i
$778$			52.8418i			1.89447i
$779$		0			0
$780$	−13.4397	−	6.51687i	−0.481218	−	0.233341i
$781$	−1.52317			−0.0545031
$782$		−	59.5156i		−	2.12827i
$783$		−	40.7064i		−	1.45473i
$784$	5.43428			0.194081
$785$	11.2434	−	23.1871i	0.401293	−	0.827583i
$786$	6.99533			0.249515
$787$			48.6451i			1.73401i	0.498300	+	0.867005i	$0.333958\pi$
$787$			48.6451i			1.73401i	−0.498300	+	0.867005i	$0.666042\pi$
$788$		−	7.78873i		−	0.277462i
$789$	7.51235			0.267447
$790$	−26.3281	+	54.2963i	−0.936713	+	1.93178i
$791$	−0.446881			−0.0158892
$792$		−	15.4438i		−	0.548772i
$793$			17.2780i			0.613561i
$794$	−47.5164			−1.68630
$795$	3.79740	+	1.84135i	0.134680	+	0.0653060i
$796$	−41.6869			−1.47755
$797$			1.06027i			0.0375567i	0.999824	+	0.0187784i	$0.00597769\pi$
$797$			1.06027i			0.0375567i	−0.999824	+	0.0187784i	$0.994022\pi$
$798$		0			0
$799$	13.0622			0.462106
$800$	−18.5184	+	14.6054i	−0.654723	+	0.516379i
$801$	−2.43180			−0.0859233
$802$		−	38.8146i		−	1.37059i
$803$		−	29.4718i		−	1.04004i
$804$	−23.4892			−0.828400
$805$	2.07419	+	1.00577i	0.0731056	+	0.0354487i
$806$	19.2503			0.678064
$807$		−	16.5648i		−	0.583110i
$808$		−	9.39213i		−	0.330414i
$809$	13.6192			0.478826			0.239413	−	0.970918i	$-0.423045\pi$
$809$	13.6192			0.478826			0.239413	+	0.970918i	$0.423045\pi$
$810$	2.56897	−	5.29797i	0.0902645	−	0.186152i
$811$	22.3947			0.786385			0.393192	−	0.919456i	$-0.371371\pi$
$811$	22.3947			0.786385			0.393192	+	0.919456i	$0.371371\pi$
$812$			3.69326i			0.129608i
$813$		−	2.50883i		−	0.0879886i
$814$	62.1217			2.17736
$815$	18.4582	−	38.0661i	0.646561	−	1.33340i
$816$	3.18268			0.111416
$817$		0			0
$818$		−	41.1100i		−	1.43738i
$819$	−0.411514			−0.0143795
$820$	−1.28288	−	0.622067i	−0.0448002	−	0.0217235i
$821$	−5.51937			−0.192627			−0.0963137	−	0.995351i	$-0.530705\pi$
$821$	−5.51937			−0.192627			−0.0963137	+	0.995351i	$0.530705\pi$
$822$			32.8959i			1.14738i
$823$		−	22.3523i		−	0.779154i	−0.920994	−	0.389577i	$-0.872621\pi$
$823$		−	22.3523i		−	0.779154i	0.920994	−	0.389577i	$-0.127379\pi$
$824$	−3.91508			−0.136388
$825$	12.6960	−	10.0133i	0.442017	−	0.348618i
$826$	1.78766			0.0622008
$827$			4.48687i			0.156024i	0.996952	+	0.0780118i	$0.0248572\pi$
$827$			4.48687i			0.156024i	−0.996952	+	0.0780118i	$0.975143\pi$
$828$		−	41.1573i		−	1.43032i
$829$	−27.0312			−0.938832			−0.469416	−	0.882977i	$-0.655535\pi$
$829$	−27.0312			−0.938832			−0.469416	+	0.882977i	$0.655535\pi$
$830$	−35.5267	−	17.2268i	−1.23315	−	0.597951i
$831$	18.3481			0.636490
$832$			21.3951i			0.741741i
$833$		−	24.8390i		−	0.860619i
$834$	−21.2367			−0.735365
$835$	−14.7015	+	30.3188i	−0.508767	+	1.04923i
$836$		0			0
$837$			26.0578i			0.900691i
$838$		−	88.1820i		−	3.04620i
$839$	10.1152			0.349214			0.174607	−	0.984638i	$-0.444135\pi$
$839$	10.1152			0.349214			0.174607	+	0.984638i	$0.444135\pi$
$840$	−0.524051	+	1.08075i	−0.0180815	+	0.0372893i
$841$	28.3283			0.976837
$842$		−	26.9242i		−	0.927870i
$843$		−	16.3752i		−	0.563991i
$844$	−10.2221			−0.351861
$845$	−20.2828	−	9.83508i	−0.697750	−	0.338337i
$846$	14.3405			0.493035
$847$		−	0.440303i		−	0.0151290i
$848$			1.27943i			0.0439358i
$849$	−8.11738			−0.278588
$850$	−25.6161	−	32.4790i	−0.878625	−	1.11402i
$851$	68.2796			2.34059
$852$		−	2.11502i		−	0.0724595i
$853$			27.6102i			0.945356i	0.881235	+	0.472678i	$0.156713\pi$
$853$			27.6102i			0.945356i	−0.881235	+	0.472678i	$0.843287\pi$
$854$	3.36879			0.115278
$855$		0			0
$856$	−13.3651			−0.456810
$857$			38.6174i			1.31915i	0.751640	+	0.659573i	$0.229263\pi$
$857$			38.6174i			1.31915i	−0.751640	+	0.659573i	$0.770737\pi$
$858$		−	12.8442i		−	0.438492i
$859$	−57.1723			−1.95069			−0.975346	−	0.220681i	$-0.929172\pi$
$859$	−57.1723			−1.95069			−0.975346	+	0.220681i	$0.929172\pi$
$860$	−36.5108	+	75.2959i	−1.24501	+	2.56757i
$861$	0.0308317			0.00105074
$862$		−	73.8992i		−	2.51702i
$863$		−	28.4419i		−	0.968173i	−0.875020	−	0.484087i	$-0.839152\pi$
$863$		−	28.4419i		−	0.968173i	0.875020	−	0.484087i	$-0.160848\pi$
$864$	−25.3596			−0.862750
$865$	21.1660	−	43.6505i	0.719665	−	1.48416i
$866$	9.50417			0.322965
$867$			4.97851i			0.169079i
$868$		−	2.36421i		−	0.0802466i
$869$	−32.6855			−1.10878
$870$	40.6750	+	19.7232i	1.37901	+	0.668679i
$871$	10.2650			0.347816
$872$			52.8490i			1.78969i
$873$		−	14.7943i		−	0.500711i
$874$		0			0
$875$	1.56483	−	0.343882i	0.0529008	−	0.0116253i
$876$	40.9236			1.38268
$877$			13.3300i			0.450121i	0.974345	+	0.225060i	$0.0722579\pi$
$877$			13.3300i			0.450121i	−0.974345	+	0.225060i	$0.927742\pi$
$878$		−	27.3276i		−	0.922263i
$879$	1.12187			0.0378397
$880$	4.41079	+	2.13878i	0.148688	+	0.0720982i
$881$	−28.1384			−0.948007			−0.474004	−	0.880523i	$-0.657192\pi$
$881$	−28.1384			−0.948007			−0.474004	+	0.880523i	$0.657192\pi$
$882$		−	27.2698i		−	0.918222i
$883$		−	35.6238i		−	1.19884i	−0.800436	−	0.599418i	$-0.795399\pi$
$883$		−	35.6238i		−	1.19884i	0.800436	−	0.599418i	$-0.204601\pi$
$884$	−20.6971			−0.696120
$885$	6.01341	−	12.4014i	0.202139	−	0.416869i
$886$	18.3333			0.615920
$887$		−	59.1722i		−	1.98681i	−0.114672	−	0.993403i	$-0.536582\pi$
$887$		−	59.1722i		−	1.98681i	0.114672	−	0.993403i	$-0.463418\pi$
$888$			35.5767i			1.19388i
$889$	−1.16937			−0.0392195
$890$	3.28135	−	6.76710i	0.109991	−	0.226834i
$891$	3.18929			0.106845
$892$		−	7.46685i		−	0.250009i
$893$		0			0
$894$	11.2039			0.374715
$895$	46.0327	+	22.3211i	1.53870	+	0.746113i
$896$	2.81961			0.0941964
$897$		−	14.1173i		−	0.471364i
$898$		−	2.69841i		−	0.0900470i
$899$	−36.6982			−1.22395
$900$	−17.7145	−	22.4605i	−0.590484	−	0.748683i
$901$	5.84800			0.194825
$902$		−	1.22604i		−	0.0408226i
$903$		−	1.80960i		−	0.0602196i
$904$	−10.1770			−0.338482
$905$	23.2709	+	11.2840i	0.773549	+	0.375092i
$906$	−7.63997			−0.253821
$907$		−	46.2445i		−	1.53552i	−0.640735	−	0.767762i	$-0.721370\pi$
$907$		−	46.2445i		−	1.53552i	0.640735	−	0.767762i	$-0.278630\pi$
$908$		−	21.9331i		−	0.727876i
$909$	−4.83716			−0.160438
$910$	0.555277	−	1.14514i	0.0184073	−	0.0379611i
$911$	48.8276			1.61773			0.808866	−	0.587994i	$-0.200082\pi$
$911$	48.8276			1.61773			0.808866	+	0.587994i	$0.200082\pi$
$912$		0			0
$913$		−	21.3865i		−	0.707790i
$914$	89.9368			2.97485
$915$	11.3321	−	23.3701i	0.374627	−	0.772590i
$916$	−5.25291			−0.173561
$917$			0.375446i			0.0123983i
$918$		−	44.4777i		−	1.46798i
$919$	9.60929			0.316981			0.158491	−	0.987360i	$-0.449337\pi$
$919$	9.60929			0.316981			0.158491	+	0.987360i	$0.449337\pi$
$920$	47.2364	+	22.9048i	1.55734	+	0.755149i
$921$	−32.6967			−1.07739
$922$			56.9519i			1.87561i
$923$			0.924285i			0.0304232i
$924$	−1.57744			−0.0518941
$925$	37.2617	−	29.3882i	1.22516	−	0.966279i
$926$	75.5153			2.48159
$927$			2.01635i			0.0662257i
$928$		−	35.7148i		−	1.17240i
$929$	−51.7174			−1.69679			−0.848396	−	0.529362i	$-0.822431\pi$
$929$	−51.7174			−1.69679			−0.848396	+	0.529362i	$0.822431\pi$
$930$	−26.0378	−	12.6256i	−0.853812	−	0.414011i
$931$		0			0
$932$		−	69.6473i		−	2.28137i
$933$		−	29.3417i		−	0.960604i
$934$	34.1766			1.11829
$935$	9.77591	−	20.1608i	0.319706	−	0.659328i
$936$	−9.37158			−0.306320
$937$			11.4894i			0.375341i	0.982232	+	0.187671i	$0.0600938\pi$
$937$			11.4894i			0.375341i	−0.982232	+	0.187671i	$0.939906\pi$
$938$		−	2.00142i		−	0.0653488i
$939$	−17.1728			−0.560412
$940$	−12.1887	+	25.1366i	−0.397550	+	0.819865i
$941$	26.4897			0.863540			0.431770	−	0.901984i	$-0.357889\pi$
$941$	26.4897			0.863540			0.431770	+	0.901984i	$0.357889\pi$
$942$			30.7702i			1.00255i
$943$		−	1.34757i		−	0.0438829i
$944$	4.17831			0.135992
$945$	1.55010	+	0.751640i	0.0504248	+	0.0244508i
$946$	−71.9594			−2.33960
$947$		−	14.7018i		−	0.477745i	−0.971051	−	0.238873i	$-0.923222\pi$
$947$		−	14.7018i		−	0.477745i	0.971051	−	0.238873i	$-0.0767778\pi$
$948$		−	45.3861i		−	1.47407i
$949$	−17.8840			−0.580539
$950$		0			0
$951$	−25.8892			−0.839513
$952$			1.66435i			0.0539419i
$953$			5.85051i			0.189517i	0.995500	+	0.0947583i	$0.0302078\pi$
$953$			5.85051i			0.189517i	−0.995500	+	0.0947583i	$0.969792\pi$
$954$	6.42031			0.207865
$955$	−14.6667	−	7.11184i	−0.474603	−	0.230134i
$956$	21.2424			0.687029
$957$			24.4857i			0.791510i
$958$		−	30.7306i		−	0.992862i
$959$	−1.76555			−0.0570127
$960$	14.0323	−	28.9387i	0.452890	−	0.933992i
$961$	−7.50793			−0.242191
$962$		−	37.6966i		−	1.21539i
$963$			6.88333i			0.221812i
$964$	89.5722			2.88493
$965$	−25.5477	+	52.6869i	−0.822411	+	1.69605i
$966$	−2.75254			−0.0885614
$967$			24.0705i			0.774054i	0.922068	+	0.387027i	$0.126498\pi$
$967$			24.0705i			0.774054i	−0.922068	+	0.387027i	$0.873502\pi$
$968$		−	10.0272i		−	0.322287i
$969$		0			0
$970$	41.1689	+	19.9627i	1.32185	+	0.640963i
$971$	52.6618			1.69000			0.844999	−	0.534768i	$-0.179601\pi$
$971$	52.6618			1.69000			0.844999	+	0.534768i	$0.179601\pi$
$972$		−	50.4715i		−	1.61887i
$973$		−	1.13979i		−	0.0365400i
$974$	−22.4575			−0.719585
$975$	−6.07625	−	7.70416i	−0.194596	−	0.246730i
$976$	7.87389			0.252037
$977$			6.50872i			0.208232i	0.994565	+	0.104116i	$0.0332014\pi$
$977$			6.50872i			0.208232i	−0.994565	+	0.104116i	$0.966799\pi$
$978$			50.5153i			1.61530i
$979$	4.07368			0.130195
$980$	47.7997	+	23.1779i	1.52691	+	0.740392i
$981$	27.2184			0.869017
$982$		−	6.24474i		−	0.199278i
$983$		−	1.24935i		−	0.0398480i	−0.999801	−	0.0199240i	$-0.993658\pi$
$983$		−	1.24935i		−	0.0398480i	0.999801	−	0.0199240i	$-0.00634243\pi$
$984$	0.702144			0.0223835
$985$	2.23240	−	4.60387i	0.0711302	−	0.146691i
$986$	62.6395			1.99485
$987$		−	0.604111i		−	0.0192291i
$988$		0			0
$989$	−79.0924			−2.51499
$990$	10.7326	−	22.1338i	0.341105	−	0.703458i
$991$	37.5958			1.19427			0.597134	−	0.802141i	$-0.296306\pi$
$991$	37.5958			1.19427			0.597134	+	0.802141i	$0.296306\pi$
$992$			22.8626i			0.725887i
$993$		−	12.4829i		−	0.396132i
$994$	0.180213			0.00571600
$995$	−24.6408	−	11.9483i	−0.781166	−	0.378785i
$996$	29.6966			0.940974
$997$		−	29.9308i		−	0.947918i	−0.880547	−	0.473959i	$-0.842825\pi$
$997$		−	29.9308i		−	0.947918i	0.880547	−	0.473959i	$-0.157175\pi$
$998$			5.47555i			0.173325i
$999$	51.0272			1.61443

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1805.2.b.k.1084.3		24
5.2	odd	4		9025.2.a.cu.1.22		24
5.3	odd	4		9025.2.a.cu.1.3		24
5.4	even	2	inner	1805.2.b.k.1084.22		24
19.9	even	9		95.2.p.a.24.7	yes	48
19.17	even	9		95.2.p.a.4.2	✓	48
19.18	odd	2		1805.2.b.l.1084.22		24
57.17	odd	18		855.2.da.b.289.7		48
57.47	odd	18		855.2.da.b.784.2		48
95.9	even	18		95.2.p.a.24.2	yes	48
95.17	odd	36		475.2.l.f.251.2		48
95.18	even	4		9025.2.a.ct.1.22		24
95.28	odd	36		475.2.l.f.176.7		48
95.37	even	4		9025.2.a.ct.1.3		24
95.47	odd	36		475.2.l.f.176.2		48
95.74	even	18		95.2.p.a.4.7	yes	48
95.93	odd	36		475.2.l.f.251.7		48
95.94	odd	2		1805.2.b.l.1084.3		24
285.74	odd	18		855.2.da.b.289.2		48
285.104	odd	18		855.2.da.b.784.7		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.p.a.4.2	✓	48	19.17	even	9
95.2.p.a.4.7	yes	48	95.74	even	18
95.2.p.a.24.2	yes	48	95.9	even	18
95.2.p.a.24.7	yes	48	19.9	even	9
475.2.l.f.176.2		48	95.47	odd	36
475.2.l.f.176.7		48	95.28	odd	36
475.2.l.f.251.2		48	95.17	odd	36
475.2.l.f.251.7		48	95.93	odd	36
855.2.da.b.289.2		48	285.74	odd	18
855.2.da.b.289.7		48	57.17	odd	18
855.2.da.b.784.2		48	57.47	odd	18
855.2.da.b.784.7		48	285.104	odd	18
1805.2.b.k.1084.3		24	1.1	even	1	trivial
1805.2.b.k.1084.22		24	5.4	even	2	inner
1805.2.b.l.1084.3		24	95.94	odd	2
1805.2.b.l.1084.22		24	19.18	odd	2
9025.2.a.ct.1.3		24	95.37	even	4
9025.2.a.ct.1.22		24	95.18	even	4
9025.2.a.cu.1.3		24	5.3	odd	4
9025.2.a.cu.1.22		24	5.2	odd	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 $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q-2.32462i q^{2} +1.14858i q^{3} -3.40387 q^{4} +(-2.01201 - 0.975617i) q^{5} +2.67001 q^{6} +0.143302i q^{7} +3.26348i q^{8} +1.68077 q^{9} +(-2.26794 + 4.67716i) q^{10} -2.81557 q^{11} -3.90962i q^{12} +1.70854i q^{13} +0.333123 q^{14} +(1.12057 - 2.31095i) q^{15} +0.778610 q^{16} -3.55886i q^{17} -3.90715i q^{18} +(6.84862 + 3.32088i) q^{20} -0.164594 q^{21} +6.54515i q^{22} +7.19394i q^{23} -3.74836 q^{24} +(3.09634 + 3.92590i) q^{25} +3.97171 q^{26} +5.37623i q^{27} -0.487782i q^{28} -7.57154 q^{29} +(-5.37209 - 2.60491i) q^{30} +4.84686 q^{31} +4.71698i q^{32} -3.23391i q^{33} -8.27302 q^{34} +(0.139808 - 0.288325i) q^{35} -5.72111 q^{36} -9.49127i q^{37} -1.96239 q^{39} +(3.18390 - 6.56614i) q^{40} -0.187320 q^{41} +0.382619i q^{42} +10.9943i q^{43} +9.58385 q^{44} +(-3.38171 - 1.63978i) q^{45} +16.7232 q^{46} +3.67032i q^{47} +0.894296i q^{48} +6.97946 q^{49} +(9.12623 - 7.19783i) q^{50} +4.08764 q^{51} -5.81566i q^{52} +1.64322i q^{53} +12.4977 q^{54} +(5.66495 + 2.74692i) q^{55} -0.467663 q^{56} +17.6010i q^{58} +5.36637 q^{59} +(-3.81429 + 7.86618i) q^{60} +10.1127 q^{61} -11.2671i q^{62} +0.240857i q^{63} +12.5224 q^{64} +(1.66688 - 3.43760i) q^{65} -7.51762 q^{66} -6.00805i q^{67} +12.1139i q^{68} -8.26281 q^{69} +(-0.670247 - 0.325001i) q^{70} +0.540979 q^{71} +5.48514i q^{72} +10.4674i q^{73} -22.0636 q^{74} +(-4.50920 + 3.55640i) q^{75} -0.403477i q^{77} +4.56183i q^{78} +11.6088 q^{79} +(-1.56657 - 0.759625i) q^{80} -1.13273 q^{81} +0.435449i q^{82} +7.59579i q^{83} +0.560257 q^{84} +(-3.47209 + 7.16046i) q^{85} +25.5576 q^{86} -8.69652i q^{87} -9.18856i q^{88} -1.44684 q^{89} +(-3.81188 + 7.86121i) q^{90} -0.244837 q^{91} -24.4873i q^{92} +5.56701i q^{93} +8.53210 q^{94} -5.41783 q^{96} -8.80212i q^{97} -16.2246i q^{98} -4.73232 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 18 q^{4} - 3 q^{5} - 12 q^{6} - 12 q^{9} - 6 q^{10} + 12 q^{11} - 24 q^{14} - 9 q^{15} + 6 q^{16} + 21 q^{20} + 6 q^{21} + 42 q^{24} - 3 q^{25} - 12 q^{26} - 36 q^{29} - 18 q^{30} + 42 q^{31} - 6 q^{34}+ \cdots - 120 q^{96}+O(q^{100}) \) 24 * q - 18 * q^4 - 3 * q^5 - 12 * q^6 - 12 * q^9 - 6 * q^10 + 12 * q^11 - 24 * q^14 - 9 * q^15 + 6 * q^16 + 21 * q^20 + 6 * q^21 + 42 * q^24 - 3 * q^25 - 12 * q^26 - 36 * q^29 - 18 * q^30 + 42 * q^31 - 6 * q^34 + 27 * q^35 - 6 * q^36 - 24 * q^39 + 12 * q^40 + 60 * q^41 + 30 * q^44 + 9 * q^45 + 6 * q^46 - 12 * q^49 + 18 * q^50 + 30 * q^51 + 24 * q^54 + 33 * q^55 + 18 * q^56 - 60 * q^59 - 42 * q^60 + 30 * q^61 + 18 * q^65 + 36 * q^66 - 66 * q^69 + 9 * q^70 + 96 * q^71 - 24 * q^74 + 36 * q^75 - 72 * q^79 - 42 * q^80 - 96 * q^81 + 54 * q^84 - 27 * q^85 + 108 * q^86 - 84 * q^89 - 93 * q^90 + 96 * q^91 - 36 * q^94 - 120 * q^96

Introduction

L-functions

Modular forms

Varieties

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Groups

Database

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