LMFDB - Embedded newform 1805.2.b.m.1084.18

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			1084.18
Character	$\chi$	$=$	1805.1084
Dual form			1805.2.b.m.1084.23

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.717155i q^{2} +1.56975i q^{3} +1.48569 q^{4} +(0.811198 + 2.08374i) q^{5} +1.12576 q^{6} +2.51917i q^{7} -2.49978i q^{8} +0.535883 q^{9} +O(q^{10})$	\(q-0.717155i q^{2} +1.56975i q^{3} +1.48569 q^{4} +(0.811198 + 2.08374i) q^{5} +1.12576 q^{6} +2.51917i q^{7} -2.49978i q^{8} +0.535883 q^{9} +(1.49436 - 0.581755i) q^{10} -5.85392 q^{11} +2.33216i q^{12} -0.791698i q^{13} +1.80664 q^{14} +(-3.27095 + 1.27338i) q^{15} +1.17865 q^{16} +0.651447i q^{17} -0.384311i q^{18} +(1.20519 + 3.09578i) q^{20} -3.95447 q^{21} +4.19817i q^{22} +4.88134i q^{23} +3.92403 q^{24} +(-3.68392 + 3.38064i) q^{25} -0.567770 q^{26} +5.55045i q^{27} +3.74270i q^{28} +4.83251 q^{29} +(0.913210 + 2.34578i) q^{30} -6.73907 q^{31} -5.84483i q^{32} -9.18920i q^{33} +0.467189 q^{34} +(-5.24929 + 2.04354i) q^{35} +0.796155 q^{36} -0.741957i q^{37} +1.24277 q^{39} +(5.20888 - 2.02782i) q^{40} +8.04494 q^{41} +2.83597i q^{42} +0.761041i q^{43} -8.69710 q^{44} +(0.434707 + 1.11664i) q^{45} +3.50068 q^{46} +11.3005i q^{47} +1.85018i q^{48} +0.653781 q^{49} +(2.42445 + 2.64194i) q^{50} -1.02261 q^{51} -1.17622i q^{52} +12.8983i q^{53} +3.98054 q^{54} +(-4.74869 - 12.1980i) q^{55} +6.29737 q^{56} -3.46566i q^{58} +2.14576 q^{59} +(-4.85961 + 1.89184i) q^{60} -6.75915 q^{61} +4.83296i q^{62} +1.34998i q^{63} -1.83436 q^{64} +(1.64969 - 0.642223i) q^{65} -6.59008 q^{66} -13.8808i q^{67} +0.967847i q^{68} -7.66249 q^{69} +(1.46554 + 3.76456i) q^{70} -6.05037 q^{71} -1.33959i q^{72} -11.1309i q^{73} -0.532098 q^{74} +(-5.30677 - 5.78283i) q^{75} -14.7470i q^{77} -0.891258i q^{78} -15.7669 q^{79} +(0.956114 + 2.45599i) q^{80} -7.10518 q^{81} -5.76948i q^{82} -3.26719i q^{83} -5.87511 q^{84} +(-1.35744 + 0.528452i) q^{85} +0.545785 q^{86} +7.58584i q^{87} +14.6335i q^{88} -1.07484 q^{89} +(0.800804 - 0.311752i) q^{90} +1.99442 q^{91} +7.25215i q^{92} -10.5787i q^{93} +8.10419 q^{94} +9.17493 q^{96} -10.1175i q^{97} -0.468863i q^{98} -3.13702 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$		−	0.717155i		−	0.507105i	−0.967322	−	0.253553i	$-0.918401\pi$
$2$		−	0.717155i		−	0.507105i	0.967322	−	0.253553i	$-0.0815991\pi$
$3$			1.56975i			0.906296i	0.891435	+	0.453148i	$0.149699\pi$
$3$			1.56975i			0.906296i	−0.891435	+	0.453148i	$0.850301\pi$
$4$	1.48569			0.742844
$5$	0.811198	+	2.08374i	0.362779	+	0.931875i
$5$	0.811198	+	2.08374i	0.362779	+	0.931875i
$6$	1.12576			0.459588
$7$			2.51917i			0.952157i	0.879403	+	0.476078i	$0.157942\pi$
$7$			2.51917i			0.952157i	−0.879403	+	0.476078i	$0.842058\pi$
$8$		−	2.49978i		−	0.883806i
$9$	0.535883			0.178628
$10$	1.49436	−	0.581755i	0.472559	−	0.183967i
$11$	−5.85392			−1.76502			−0.882512	−	0.470290i	$-0.844149\pi$
$11$	−5.85392			−1.76502			−0.882512	+	0.470290i	$0.844149\pi$
$12$			2.33216i			0.673237i
$13$		−	0.791698i		−	0.219577i	−0.993955	−	0.109789i	$-0.964983\pi$
$13$		−	0.791698i		−	0.219577i	0.993955	−	0.109789i	$-0.0350174\pi$
$14$	1.80664			0.482844
$15$	−3.27095	+	1.27338i	−0.844555	+	0.328785i
$16$	1.17865			0.294661
$17$			0.651447i			0.157999i	0.996875	+	0.0789996i	$0.0251726\pi$
$17$			0.651447i			0.157999i	−0.996875	+	0.0789996i	$0.974827\pi$
$18$		−	0.384311i		−	0.0905831i
$19$		0			0
$19$		0			0
$20$	1.20519	+	3.09578i	0.269488	+	0.692238i
$21$	−3.95447			−0.862936
$22$			4.19817i			0.895053i
$23$			4.88134i			1.01783i	0.860817	+	0.508915i	$0.169953\pi$
$23$			4.88134i			1.01783i	−0.860817	+	0.508915i	$0.830047\pi$
$24$	3.92403			0.800990
$25$	−3.68392	+	3.38064i	−0.736783	+	0.676129i
$26$	−0.567770			−0.111349
$27$			5.55045i			1.06819i
$28$			3.74270i			0.707304i
$29$	4.83251			0.897375			0.448687	−	0.893689i	$-0.351892\pi$
$29$	4.83251			0.897375			0.448687	+	0.893689i	$0.351892\pi$
$30$	0.913210	+	2.34578i	0.166729	+	0.428278i
$31$	−6.73907			−1.21037			−0.605186	−	0.796084i	$-0.706901\pi$
$31$	−6.73907			−1.21037			−0.605186	+	0.796084i	$0.706901\pi$
$32$		−	5.84483i		−	1.03323i
$33$		−	9.18920i		−	1.59963i
$34$	0.467189			0.0801222
$35$	−5.24929	+	2.04354i	−0.887292	+	0.345422i
$36$	0.796155			0.132693
$37$		−	0.741957i		−	0.121977i	−0.998138	−	0.0609885i	$-0.980575\pi$
$37$		−	0.741957i		−	0.121977i	0.998138	−	0.0609885i	$-0.0194253\pi$
$38$		0			0
$39$	1.24277			0.199002
$40$	5.20888	−	2.02782i	0.823597	−	0.320626i
$41$	8.04494			1.25641			0.628205	−	0.778048i	$-0.283790\pi$
$41$	8.04494			1.25641			0.628205	+	0.778048i	$0.283790\pi$
$42$			2.83597i			0.437600i
$43$			0.761041i			0.116058i	0.998315	+	0.0580289i	$0.0184815\pi$
$43$			0.761041i			0.116058i	−0.998315	+	0.0580289i	$0.981518\pi$
$44$	−8.69710			−1.31114
$45$	0.434707	+	1.11664i	0.0648023	+	0.166459i
$46$	3.50068			0.516147
$47$			11.3005i			1.64834i	0.566342	+	0.824171i	$0.308358\pi$
$47$			11.3005i			1.64834i	−0.566342	+	0.824171i	$0.691642\pi$
$48$			1.85018i			0.267050i
$49$	0.653781			0.0933973
$50$	2.42445	+	2.64194i	0.342869	+	0.373627i
$51$	−1.02261			−0.143194
$52$		−	1.17622i		−	0.163112i
$53$			12.8983i			1.77172i	0.463953	+	0.885860i	$0.346431\pi$
$53$			12.8983i			1.77172i	−0.463953	+	0.885860i	$0.653569\pi$
$54$	3.98054			0.541683
$55$	−4.74869	−	12.1980i	−0.640313	−	1.64478i
$56$	6.29737			0.841522
$57$		0			0
$58$		−	3.46566i		−	0.455064i
$59$	2.14576			0.279354			0.139677	−	0.990197i	$-0.455394\pi$
$59$	2.14576			0.279354			0.139677	+	0.990197i	$0.455394\pi$
$60$	−4.85961	+	1.89184i	−0.627373	+	0.244236i
$61$	−6.75915			−0.865421			−0.432710	−	0.901533i	$-0.642443\pi$
$61$	−6.75915			−0.865421			−0.432710	+	0.901533i	$0.642443\pi$
$62$			4.83296i			0.613787i
$63$			1.34998i			0.170082i
$64$	−1.83436			−0.229295
$65$	1.64969	−	0.642223i	0.204619	−	0.0796580i
$66$	−6.59008			−0.811183
$67$		−	13.8808i		−	1.69581i	−0.530152	−	0.847903i	$-0.677865\pi$
$67$		−	13.8808i		−	1.69581i	0.530152	−	0.847903i	$-0.322135\pi$
$68$			0.967847i			0.117369i
$69$	−7.66249			−0.922455
$70$	1.46554	+	3.76456i	0.175165	+	0.449950i
$71$	−6.05037			−0.718046			−0.359023	−	0.933329i	$-0.616890\pi$
$71$	−6.05037			−0.718046			−0.359023	+	0.933329i	$0.616890\pi$
$72$		−	1.33959i		−	0.157872i
$73$		−	11.1309i		−	1.30277i	−0.758746	−	0.651387i	$-0.774188\pi$
$73$		−	11.1309i		−	1.30277i	0.758746	−	0.651387i	$-0.225812\pi$
$74$	−0.532098			−0.0618552
$75$	−5.30677	−	5.78283i	−0.612773	−	0.667744i
$76$		0			0
$77$		−	14.7470i		−	1.68058i
$78$		−	0.891258i		−	0.100915i
$79$	−15.7669			−1.77391			−0.886955	−	0.461856i	$-0.847184\pi$
$79$	−15.7669			−1.77391			−0.886955	+	0.461856i	$0.847184\pi$
$80$	0.956114	+	2.45599i	0.106897	+	0.274588i
$81$	−7.10518			−0.789464
$82$		−	5.76948i		−	0.637132i
$83$		−	3.26719i		−	0.358621i	−0.983793	−	0.179310i	$-0.942613\pi$
$83$		−	3.26719i		−	0.358621i	0.983793	−	0.179310i	$-0.0573866\pi$
$84$	−5.87511			−0.641027
$85$	−1.35744	+	0.528452i	−0.147236	+	0.0573187i
$86$	0.545785			0.0588535
$87$			7.58584i			0.813287i
$88$			14.6335i			1.55994i
$89$	−1.07484			−0.113932			−0.0569662	−	0.998376i	$-0.518143\pi$
$89$	−1.07484			−0.113932			−0.0569662	+	0.998376i	$0.518143\pi$
$90$	0.800804	−	0.311752i	0.0844121	−	0.0328616i
$91$	1.99442			0.209072
$92$			7.25215i			0.756089i
$93$		−	10.5787i		−	1.09696i
$94$	8.10419			0.835883
$95$		0			0
$96$	9.17493			0.936412
$97$		−	10.1175i		−	1.02728i	−0.858005	−	0.513641i	$-0.828296\pi$
$97$		−	10.1175i		−	1.02728i	0.858005	−	0.513641i	$-0.171704\pi$
$98$		−	0.468863i		−	0.0473623i
$99$	−3.13702			−0.315282
$100$	−5.47315	+	5.02258i	−0.547315	+	0.502258i
$101$	5.63114			0.560320			0.280160	−	0.959953i	$-0.409613\pi$
$101$	5.63114			0.560320			0.280160	+	0.959953i	$0.409613\pi$
$102$			0.733370i			0.0726145i
$103$			0.459634i			0.0452891i	0.999744	+	0.0226446i	$0.00720861\pi$
$103$			0.459634i			0.0452891i	−0.999744	+	0.0226446i	$0.992791\pi$
$104$	−1.97907			−0.194064
$105$	−3.20786	−	8.24007i	−0.313055	−	0.804149i
$106$	9.25010			0.898449
$107$			5.11103i			0.494102i	0.969002	+	0.247051i	$0.0794616\pi$
$107$			5.11103i			0.494102i	−0.969002	+	0.247051i	$0.920538\pi$
$108$			8.24624i			0.793495i
$109$	10.1536			0.972537			0.486269	−	0.873809i	$-0.338358\pi$
$109$	10.1536			0.972537			0.486269	+	0.873809i	$0.338358\pi$
$110$	−8.74788	+	3.40555i	−0.834078	+	0.324706i
$111$	1.16469			0.110547
$112$			2.96921i			0.280564i
$113$			5.61000i			0.527745i	0.964558	+	0.263872i	$0.0849998\pi$
$113$			5.61000i			0.527745i	−0.964558	+	0.263872i	$0.915000\pi$
$114$		0			0
$115$	−10.1714	+	3.95973i	−0.948490	+	0.369247i
$116$	7.17960			0.666609
$117$		−	0.424257i		−	0.0392226i
$118$		−	1.53884i		−	0.141662i
$119$	−1.64111			−0.150440
$120$	3.18316	+	8.17665i	0.290582	+	0.746422i
$121$	23.2684			2.11531
$122$			4.84736i			0.438860i
$123$			12.6286i			1.13868i
$124$	−10.0122			−0.899118
$125$	−10.0328	−	4.93394i	−0.897357	−	0.441305i
$126$	0.968146			0.0862493
$127$		−	10.8609i		−	0.963747i	−0.876241	−	0.481873i	$-0.839956\pi$
$127$		−	10.8609i		−	0.963747i	0.876241	−	0.481873i	$-0.160044\pi$
$128$		−	10.3741i		−	0.916953i
$129$	−1.19465			−0.105183
$130$	−0.460574	−	1.18308i	−0.0403950	−	0.103763i
$131$	16.3484			1.42837			0.714184	−	0.699958i	$-0.246798\pi$
$131$	16.3484			1.42837			0.714184	+	0.699958i	$0.246798\pi$
$132$		−	13.6523i		−	1.18828i
$133$		0			0
$134$	−9.95467			−0.859952
$135$	−11.5657	+	4.50252i	−0.995416	+	0.387515i
$136$	1.62847			0.139641
$137$			18.3333i			1.56632i	0.621818	+	0.783162i	$0.286394\pi$
$137$			18.3333i			1.56632i	−0.621818	+	0.783162i	$0.713606\pi$
$138$			5.49519i			0.467782i
$139$	9.37358			0.795057			0.397529	−	0.917590i	$-0.369868\pi$
$139$	9.37358			0.795057			0.397529	+	0.917590i	$0.369868\pi$
$140$	−7.79880	+	3.03607i	−0.659119	+	0.256595i
$141$	−17.7389			−1.49389
$142$			4.33905i			0.364125i
$143$			4.63454i			0.387559i
$144$	0.631616			0.0526347
$145$	3.92012	+	10.0697i	0.325548	+	0.836241i
$146$	−7.98258			−0.660643
$147$			1.02627i			0.0846456i
$148$		−	1.10232i		−	0.0906099i
$149$	7.69847			0.630683			0.315342	−	0.948978i	$-0.397881\pi$
$149$	7.69847			0.630683			0.315342	+	0.948978i	$0.397881\pi$
$150$	−4.14719	+	3.80578i	−0.338617	+	0.310740i
$151$	−0.167275			−0.0136126			−0.00680631	−	0.999977i	$-0.502167\pi$
$151$	−0.167275			−0.0136126			−0.00680631	+	0.999977i	$0.502167\pi$
$152$		0			0
$153$			0.349100i			0.0282230i
$154$	−10.5759			−0.852231
$155$	−5.46672	−	14.0424i	−0.439097	−	1.12792i
$156$	1.84637			0.147828
$157$		−	14.8860i		−	1.18803i	−0.804453	−	0.594016i	$-0.797542\pi$
$157$		−	14.8860i		−	1.18803i	0.804453	−	0.594016i	$-0.202458\pi$
$158$			11.3073i			0.899559i
$159$	−20.2471			−1.60570
$160$	12.1791	−	4.74131i	0.962842	−	0.374834i
$161$	−12.2969			−0.969133
$162$			5.09552i			0.400342i
$163$			18.7516i			1.46874i	0.678751	+	0.734369i	$0.262522\pi$
$163$			18.7516i			1.46874i	−0.678751	+	0.734369i	$0.737478\pi$
$164$	11.9523			0.933316
$165$	19.1479	−	7.45425i	1.49066	−	0.580313i
$166$	−2.34308			−0.181859
$167$		−	11.1787i		−	0.865036i	−0.901625	−	0.432518i	$-0.857625\pi$
$167$		−	11.1787i		−	0.865036i	0.901625	−	0.432518i	$-0.142375\pi$
$168$			9.88530i			0.762668i
$169$	12.3732			0.951786
$170$	0.378982	+	0.973499i	0.0290666	+	0.0746639i
$171$		0			0
$172$			1.13067i			0.0862128i
$173$			5.09894i			0.387665i	0.981035	+	0.193833i	$0.0620919\pi$
$173$			5.09894i			0.387665i	−0.981035	+	0.193833i	$0.937908\pi$
$174$	5.44022			0.412422
$175$	−8.51642	−	9.28041i	−0.643781	−	0.701533i
$176$	−6.89970			−0.520084
$177$			3.36831i			0.253178i
$178$			0.770825i			0.0577757i
$179$	−0.474937			−0.0354984			−0.0177492	−	0.999842i	$-0.505650\pi$
$179$	−0.474937			−0.0354984			−0.0177492	+	0.999842i	$0.505650\pi$
$180$	0.645839	+	1.65898i	0.0481380	+	0.123653i
$181$	−1.41389			−0.105093			−0.0525466	−	0.998618i	$-0.516734\pi$
$181$	−1.41389			−0.105093			−0.0525466	+	0.998618i	$0.516734\pi$
$182$		−	1.43031i		−	0.106022i
$183$		−	10.6102i		−	0.784327i
$184$	12.2023			0.899564
$185$	1.54604	−	0.601874i	0.113667	−	0.0442506i
$186$	−7.58654			−0.556272
$187$		−	3.81352i		−	0.278872i
$188$			16.7890i			1.22446i
$189$	−13.9825			−1.01708
$190$		0			0
$191$	12.6109			0.912496			0.456248	−	0.889853i	$-0.349193\pi$
$191$	12.6109			0.912496			0.456248	+	0.889853i	$0.349193\pi$
$192$		−	2.87949i		−	0.207809i
$193$			12.6096i			0.907660i	0.891088	+	0.453830i	$0.149943\pi$
$193$			12.6096i			0.907660i	−0.891088	+	0.453830i	$0.850057\pi$
$194$	−7.25585			−0.520940
$195$	1.00813	+	2.58960i	0.0721937	+	0.185445i
$196$	0.971315			0.0693796
$197$		−	1.50078i		−	0.106926i	−0.998570	−	0.0534631i	$-0.982974\pi$
$197$		−	1.50078i		−	0.106926i	0.998570	−	0.0534631i	$-0.0170259\pi$
$198$			2.24973i			0.159881i
$199$	15.6650			1.11046			0.555231	−	0.831696i	$-0.312630\pi$
$199$	15.6650			1.11046			0.555231	+	0.831696i	$0.312630\pi$
$200$	8.45087	+	9.20898i	0.597567	+	0.651173i
$201$	21.7893			1.53690
$202$		−	4.03841i		−	0.284141i
$203$			12.1739i			0.854441i
$204$	−1.51928			−0.106371
$205$	6.52604	+	16.7635i	0.455798	+	1.17082i
$206$	0.329629			0.0229664
$207$			2.61583i			0.181813i
$208$		−	0.933131i		−	0.0647010i
$209$		0			0
$210$	−5.90941	+	2.30053i	−0.407788	+	0.158752i
$211$	17.8162			1.22652			0.613259	−	0.789882i	$-0.289858\pi$
$211$	17.8162			1.22652			0.613259	+	0.789882i	$0.289858\pi$
$212$			19.1629i			1.31611i
$213$		−	9.49757i		−	0.650763i
$214$	3.66540			0.250562
$215$	−1.58581	+	0.617355i	−0.108151	+	0.0421033i
$216$	13.8749			0.944068
$217$		−	16.9769i		−	1.15246i
$218$		−	7.28170i		−	0.493179i
$219$	17.4727			1.18070
$220$	−7.05507	−	18.1225i	−0.475653	−	1.22182i
$221$	0.515749			0.0346930
$222$		−	0.835262i		−	0.0560591i
$223$			18.4288i			1.23408i	0.786931	+	0.617041i	$0.211669\pi$
$223$			18.4288i			1.23408i	−0.786931	+	0.617041i	$0.788331\pi$
$224$	14.7241			0.983797
$225$	−1.97415	+	1.81163i	−0.131610	+	0.120775i
$226$	4.02325			0.267622
$227$			4.13839i			0.274674i	0.990524	+	0.137337i	$0.0438544\pi$
$227$			4.13839i			0.274674i	−0.990524	+	0.137337i	$0.956146\pi$
$228$		0			0
$229$	1.37089			0.0905907			0.0452953	−	0.998974i	$-0.485577\pi$
$229$	1.37089			0.0905907			0.0452953	+	0.998974i	$0.485577\pi$
$230$	2.83974	+	7.29449i	0.187247	+	0.480985i
$231$	23.1492			1.52310
$232$		−	12.0802i		−	0.793105i
$233$		−	1.01441i		−	0.0664564i	−0.999448	−	0.0332282i	$-0.989421\pi$
$233$		−	1.01441i		−	0.0664564i	0.999448	−	0.0332282i	$-0.0105788\pi$
$234$	−0.304258			−0.0198900
$235$	−23.5472	+	9.16690i	−1.53605	+	0.597983i
$236$	3.18793			0.207517
$237$		−	24.7500i		−	1.60769i
$238$			1.17693i			0.0762889i
$239$	−5.54538			−0.358701			−0.179351	−	0.983785i	$-0.557400\pi$
$239$	−5.54538			−0.358701			−0.179351	+	0.983785i	$0.557400\pi$
$240$	−3.85529	+	1.50086i	−0.248858	+	0.0968802i
$241$	−25.0078			−1.61089			−0.805445	−	0.592670i	$-0.798074\pi$
$241$	−25.0078			−1.61089			−0.805445	+	0.592670i	$0.798074\pi$
$242$		−	16.6871i		−	1.07268i
$243$			5.49800i			0.352697i
$244$	−10.0420			−0.642873
$245$	0.530346	+	1.36231i	0.0338825	+	0.0870346i
$246$	9.05664			0.577430
$247$		0			0
$248$			16.8462i			1.06973i
$249$	5.12867			0.325016
$250$	−3.53840	+	7.19505i	−0.223788	+	0.455055i
$251$	10.9588			0.691713			0.345857	−	0.938287i	$-0.387588\pi$
$251$	10.9588			0.691713			0.345857	+	0.938287i	$0.387588\pi$
$252$			2.00565i			0.126344i
$253$		−	28.5750i		−	1.79649i
$254$	−7.78894			−0.488721
$255$	−0.829538	−	2.13085i	−0.0519477	−	0.133439i
$256$	−11.1086			−0.694287
$257$		−	15.0295i		−	0.937514i	−0.883327	−	0.468757i	$-0.844702\pi$
$257$		−	15.0295i		−	0.937514i	0.883327	−	0.468757i	$-0.155298\pi$
$258$			0.856746i			0.0533387i
$259$	1.86912			0.116141
$260$	2.45092	−	0.954143i	0.152000	−	0.0591734i
$261$	2.58966			0.160296
$262$		−	11.7244i		−	0.724334i
$263$		−	14.8709i		−	0.916980i	−0.888700	−	0.458490i	$-0.848390\pi$
$263$		−	14.8709i		−	0.916980i	0.888700	−	0.458490i	$-0.151610\pi$
$264$	−22.9710			−1.41377
$265$	−26.8767	+	10.4631i	−1.65102	+	0.642742i
$266$		0			0
$267$		−	1.68722i		−	0.103256i
$268$		−	20.6225i		−	1.25972i
$269$	−3.34506			−0.203952			−0.101976	−	0.994787i	$-0.532516\pi$
$269$	−3.34506			−0.203952			−0.101976	+	0.994787i	$0.532516\pi$
$270$	3.22900	+	8.29439i	0.196511	+	0.504781i
$271$	9.34209			0.567492			0.283746	−	0.958900i	$-0.408423\pi$
$271$	9.34209			0.567492			0.283746	+	0.958900i	$0.408423\pi$
$272$			0.767825i			0.0465562i
$273$			3.13074i			0.189481i
$274$	13.1479			0.794291
$275$	21.5654	−	19.7900i	1.30044	−	1.19338i
$276$	−11.3841			−0.685240
$277$		−	2.79175i		−	0.167740i	−0.996477	−	0.0838700i	$-0.973272\pi$
$277$		−	2.79175i		−	0.167740i	0.996477	−	0.0838700i	$-0.0267280\pi$
$278$		−	6.72232i		−	0.403178i
$279$	−3.61135			−0.216206
$280$	5.10841	+	13.1221i	0.305286	+	0.784193i
$281$	27.7534			1.65563			0.827816	−	0.561000i	$-0.189583\pi$
$281$	27.7534			1.65563			0.827816	+	0.561000i	$0.189583\pi$
$282$			12.7215i			0.757557i
$283$		−	1.13648i		−	0.0675569i	−0.999429	−	0.0337784i	$-0.989246\pi$
$283$		−	1.13648i		−	0.0675569i	0.999429	−	0.0337784i	$-0.0107541\pi$
$284$	−8.98896			−0.533396
$285$		0			0
$286$	3.32368			0.196533
$287$			20.2666i			1.19630i
$288$		−	3.13215i		−	0.184563i
$289$	16.5756			0.975036
$290$	7.22152	−	2.81134i	0.424063	−	0.165087i
$291$	15.8820			0.931021
$292$		−	16.5370i		−	0.967757i
$293$			25.0362i			1.46263i	0.682041	+	0.731314i	$0.261092\pi$
$293$			25.0362i			1.46263i	−0.682041	+	0.731314i	$0.738908\pi$
$294$	0.735997			0.0429242
$295$	1.74064	+	4.47120i	0.101344	+	0.260323i
$296$	−1.85473			−0.107804
$297$		−	32.4919i		−	1.88537i
$298$		−	5.52100i		−	0.319823i
$299$	3.86454			0.223492
$300$	−7.88420	−	8.59148i	−0.455195	−	0.496030i
$301$	−1.91719			−0.110505
$302$			0.119962i			0.00690304i
$303$			8.83949i			0.507816i
$304$		0			0
$305$	−5.48301	−	14.0843i	−0.313956	−	0.806464i
$306$	0.250359			0.0143120
$307$		−	18.8926i		−	1.07826i	−0.842223	−	0.539130i	$-0.818753\pi$
$307$		−	18.8926i		−	1.07826i	0.842223	−	0.539130i	$-0.181247\pi$
$308$		−	21.9095i		−	1.24841i
$309$	−0.721512			−0.0410454
$310$	−10.0706	+	3.92049i	−0.571973	+	0.222669i
$311$	13.9570			0.791430			0.395715	−	0.918373i	$-0.370497\pi$
$311$	13.9570			0.791430			0.395715	+	0.918373i	$0.370497\pi$
$312$		−	3.10665i		−	0.175879i
$313$		−	0.212626i		−	0.0120183i	−0.999982	−	0.00600917i	$-0.998087\pi$
$313$		−	0.212626i		−	0.0120183i	0.999982	−	0.00600917i	$-0.00191279\pi$
$314$	−10.6756			−0.602457
$315$	−2.81300	+	1.09510i	−0.158495	+	0.0617019i
$316$	−23.4246			−1.31774
$317$			7.50284i			0.421402i	0.977551	+	0.210701i	$0.0675746\pi$
$317$			7.50284i			0.421402i	−0.977551	+	0.210701i	$0.932425\pi$
$318$			14.5203i			0.814261i
$319$	−28.2891			−1.58389
$320$	−1.48803	−	3.82233i	−0.0831834	−	0.213675i
$321$	−8.02305			−0.447803
$322$			8.81881i			0.491453i
$323$		0			0
$324$	−10.5561			−0.586449
$325$	2.67645	+	2.91655i	0.148463	+	0.161781i
$326$	13.4478			0.744805
$327$			15.9386i			0.881406i
$328$		−	20.1106i		−	1.11042i
$329$	−28.4678			−1.56948
$330$	−5.34586	−	13.7320i	−0.294280	−	0.755922i
$331$	3.22616			0.177326			0.0886629	−	0.996062i	$-0.471741\pi$
$331$	3.22616			0.177326			0.0886629	+	0.996062i	$0.471741\pi$
$332$		−	4.85403i		−	0.266399i
$333$		−	0.397602i		−	0.0217885i
$334$	−8.01688			−0.438664
$335$	28.9239	−	11.2600i	1.58028	−	0.615202i
$336$	−4.66092			−0.254274
$337$			34.5994i			1.88475i	0.334560	+	0.942375i	$0.391412\pi$
$337$			34.5994i			1.88475i	−0.334560	+	0.942375i	$0.608588\pi$
$338$		−	8.87352i		−	0.482656i
$339$	−8.80631			−0.478293
$340$	−2.01674	+	0.785115i	−0.109373	+	0.0425789i
$341$	39.4500			2.13634
$342$		0			0
$343$			19.2812i			1.04109i
$344$	1.90244			0.102572
$345$	−6.21579	−	15.9666i	−0.334647	−	0.859613i
$346$	3.65673			0.196587
$347$			0.0848311i			0.00455397i	0.999997	+	0.00227698i	$0.000724787\pi$
$347$			0.0848311i			0.00455397i	−0.999997	+	0.00227698i	$0.999275\pi$
$348$			11.2702i			0.604145i
$349$	17.8090			0.953295			0.476648	−	0.879094i	$-0.341852\pi$
$349$	17.8090			0.953295			0.476648	+	0.879094i	$0.341852\pi$
$350$	−6.65550	+	6.10760i	−0.355751	+	0.326465i
$351$	4.39428			0.234549
$352$			34.2152i			1.82368i
$353$		−	15.1330i		−	0.805451i	−0.915321	−	0.402725i	$-0.868063\pi$
$353$		−	15.1330i		−	0.805451i	0.915321	−	0.402725i	$-0.131937\pi$
$354$	2.41560			0.128388
$355$	−4.90804	−	12.6074i	−0.260492	−	0.669130i
$356$	−1.59687			−0.0846340
$357$		−	2.57613i		−	0.136343i
$358$			0.340603i			0.0180015i
$359$	−9.00023			−0.475014			−0.237507	−	0.971386i	$-0.576330\pi$
$359$	−9.00023			−0.475014			−0.237507	+	0.971386i	$0.576330\pi$
$360$	2.79135	−	1.08667i	0.147117	−	0.0572726i
$361$		0			0
$362$			1.01398i			0.0532934i
$363$			36.5256i			1.91710i
$364$	2.96309			0.155308
$365$	23.1939	−	9.02936i	1.21402	−	0.472618i
$366$	−7.60915			−0.397737
$367$		−	5.86064i		−	0.305923i	−0.988232	−	0.152962i	$-0.951119\pi$
$367$		−	5.86064i		−	0.305923i	0.988232	−	0.152962i	$-0.0488811\pi$
$368$			5.75337i			0.299915i
$369$	4.31115			0.224429
$370$	−0.431637	−	1.10875i	−0.0224397	−	0.0576413i
$371$	−32.4931			−1.68696
$372$		−	15.7166i		−	0.814867i
$373$		−	24.6228i		−	1.27492i	−0.770484	−	0.637460i	$-0.779985\pi$
$373$		−	24.6228i		−	1.27492i	0.770484	−	0.637460i	$-0.220015\pi$
$374$	−2.73489			−0.141418
$375$	7.74506	−	15.7489i	0.399953	−	0.813271i
$376$	28.2487			1.45681
$377$		−	3.82589i		−	0.197043i
$378$			10.0277i			0.515767i
$379$	−2.67753			−0.137536			−0.0687679	−	0.997633i	$-0.521907\pi$
$379$	−2.67753			−0.137536			−0.0687679	+	0.997633i	$0.521907\pi$
$380$		0			0
$381$	17.0489			0.873440
$382$		−	9.04401i		−	0.462732i
$383$		−	27.8484i		−	1.42299i	−0.702692	−	0.711494i	$-0.748019\pi$
$383$		−	27.8484i		−	1.42299i	0.702692	−	0.711494i	$-0.251981\pi$
$384$	16.2848			0.831031
$385$	30.7289	−	11.9628i	1.56609	−	0.609678i
$386$	9.04306			0.460280
$387$			0.407829i			0.0207311i
$388$		−	15.0315i		−	0.763110i
$389$	−14.8564			−0.753249			−0.376624	−	0.926366i	$-0.622915\pi$
$389$	−14.8564			−0.753249			−0.376624	+	0.926366i	$0.622915\pi$
$390$	1.85715	−	0.722986i	0.0940402	−	0.0366098i
$391$	−3.17994			−0.160816
$392$		−	1.63431i		−	0.0825451i
$393$			25.6630i			1.29452i
$394$	−1.07629			−0.0542229
$395$	−12.7900	−	32.8540i	−0.643537	−	1.65306i
$396$	−4.66063			−0.234205
$397$		−	11.1189i		−	0.558043i	−0.960285	−	0.279022i	$-0.909990\pi$
$397$		−	11.1189i		−	0.558043i	0.960285	−	0.279022i	$-0.0900101\pi$
$398$		−	11.2342i		−	0.563121i
$399$		0			0
$400$	−4.34203	+	3.98458i	−0.217102	+	0.199229i
$401$	−28.4510			−1.42078			−0.710388	−	0.703810i	$-0.751481\pi$
$401$	−28.4510			−1.42078			−0.710388	+	0.703810i	$0.751481\pi$
$402$		−	15.6263i		−	0.779371i
$403$			5.33531i			0.265771i
$404$	8.36612			0.416230
$405$	−5.76370	−	14.8053i	−0.286401	−	0.735683i
$406$	8.73059			0.433292
$407$			4.34336i			0.215292i
$408$			2.55630i			0.126556i
$409$	15.8493			0.783695			0.391847	−	0.920030i	$-0.371836\pi$
$409$	15.8493			0.783695			0.391847	+	0.920030i	$0.371836\pi$
$410$	12.0221	−	4.68018i	0.593728	−	0.231138i
$411$	−28.7788			−1.41955
$412$			0.682873i			0.0336428i
$413$			5.40554i			0.265989i
$414$	1.87595			0.0921981
$415$	6.80796	−	2.65034i	0.334190	−	0.130100i
$416$	−4.62734			−0.226874
$417$			14.7142i			0.720557i
$418$		0			0
$419$	10.2300			0.499769			0.249885	−	0.968276i	$-0.419607\pi$
$419$	10.2300			0.499769			0.249885	+	0.968276i	$0.419607\pi$
$420$	−4.76587	−	12.2422i	−0.232551	−	0.597357i
$421$	31.1606			1.51868			0.759338	−	0.650696i	$-0.225523\pi$
$421$	31.1606			1.51868			0.759338	+	0.650696i	$0.225523\pi$
$422$		−	12.7770i		−	0.621974i
$423$			6.05572i			0.294439i
$424$	32.2430			1.56586
$425$	−2.20231	−	2.39988i	−0.106828	−	0.116411i
$426$	−6.81123			−0.330005
$427$		−	17.0275i		−	0.824016i
$428$			7.59340i			0.367041i
$429$	−7.27506			−0.351243
$430$	0.442739	+	1.13727i	0.0213508	+	0.0548441i
$431$	−9.60728			−0.462767			−0.231383	−	0.972863i	$-0.574325\pi$
$431$	−9.60728			−0.462767			−0.231383	+	0.972863i	$0.574325\pi$
$432$			6.54202i			0.314753i
$433$		−	20.8460i		−	1.00179i	−0.865507	−	0.500897i	$-0.833004\pi$
$433$		−	20.8460i		−	1.00179i	0.865507	−	0.500897i	$-0.166996\pi$
$434$	−12.1751			−0.584421
$435$	−15.8069	+	6.15361i	−0.757882	+	0.295043i
$436$	15.0851			0.722443
$437$		0			0
$438$		−	12.5307i		−	0.598738i
$439$	−1.11124			−0.0530364			−0.0265182	−	0.999648i	$-0.508442\pi$
$439$	−1.11124			−0.0530364			−0.0265182	+	0.999648i	$0.508442\pi$
$440$	−30.4924	+	11.8707i	−1.45367	+	0.565912i
$441$	0.350350			0.0166833
$442$		−	0.369872i		−	0.0175930i
$443$		−	28.7487i		−	1.36589i	−0.730468	−	0.682947i	$-0.760698\pi$
$443$		−	28.7487i		−	1.36589i	0.730468	−	0.682947i	$-0.239302\pi$
$444$	1.73036			0.0821194
$445$	−0.871905	−	2.23968i	−0.0413322	−	0.106171i
$446$	13.2163			0.625810
$447$			12.0847i			0.571586i
$448$		−	4.62107i		−	0.218325i
$449$	31.9695			1.50873			0.754367	−	0.656452i	$-0.227944\pi$
$449$	31.9695			1.50873			0.754367	+	0.656452i	$0.227944\pi$
$450$	1.29922	+	1.41577i	0.0612458	+	0.0667401i
$451$	−47.0945			−2.21759
$452$			8.33472i			0.392032i
$453$		−	0.262580i		−	0.0123371i
$454$	2.96787			0.139289
$455$	1.61787	+	4.15585i	0.0758469	+	0.194829i
$456$		0			0
$457$			12.0035i			0.561498i	0.959781	+	0.280749i	$0.0905828\pi$
$457$			12.0035i			0.561498i	−0.959781	+	0.280749i	$0.909417\pi$
$458$		−	0.983138i		−	0.0459390i
$459$	−3.61583			−0.168772
$460$	−15.1116	+	5.88292i	−0.704580	+	0.274293i
$461$	−33.9752			−1.58238			−0.791191	−	0.611569i	$-0.790539\pi$
$461$	−33.9752			−1.58238			−0.791191	+	0.611569i	$0.790539\pi$
$462$		−	16.6015i		−	0.772374i
$463$		−	24.1005i		−	1.12004i	−0.828478	−	0.560022i	$-0.810793\pi$
$463$		−	24.1005i		−	1.12004i	0.828478	−	0.560022i	$-0.189207\pi$
$464$	5.69582			0.264422
$465$	22.0431	−	8.58138i	1.02223	−	0.397952i
$466$	−0.727492			−0.0337004
$467$		−	0.621098i		−	0.0287410i	−0.999897	−	0.0143705i	$-0.995426\pi$
$467$		−	0.621098i		−	0.0287410i	0.999897	−	0.0143705i	$-0.00457442\pi$
$468$		−	0.630314i		−	0.0291363i
$469$	34.9680			1.61467
$470$	6.57410	+	16.8870i	0.303240	+	0.778939i
$471$	23.3673			1.07671
$472$		−	5.36393i		−	0.246895i
$473$		−	4.45508i		−	0.204845i
$474$	−17.7496			−0.815267
$475$		0			0
$476$	−2.43817			−0.111753
$477$			6.91199i			0.316478i
$478$			3.97690i			0.181899i
$479$	−31.0733			−1.41978			−0.709888	−	0.704314i	$-0.751255\pi$
$479$	−31.0733			−1.41978			−0.709888	+	0.704314i	$0.751255\pi$
$480$	7.44268	+	19.1181i	0.339710	+	0.872620i
$481$	−0.587405			−0.0267834
$482$			17.9344i			0.816892i
$483$		−	19.3031i		−	0.878322i
$484$	34.5696			1.57134
$485$	21.0823	−	8.20733i	0.957298	−	0.372676i
$486$	3.94292			0.178855
$487$			37.2206i			1.68663i	0.537423	+	0.843313i	$0.319398\pi$
$487$			37.2206i			1.68663i	−0.537423	+	0.843313i	$0.680602\pi$
$488$			16.8964i			0.764864i
$489$	−29.4353			−1.33111
$490$	0.976986	−	0.380340i	0.0441357	−	0.0171820i
$491$	38.5493			1.73971			0.869853	−	0.493310i	$-0.164213\pi$
$491$	38.5493			1.73971			0.869853	+	0.493310i	$0.164213\pi$
$492$			18.7621i			0.845861i
$493$			3.14813i			0.141784i
$494$		0			0
$495$	−2.54474	−	6.53672i	−0.114378	−	0.293804i
$496$	−7.94298			−0.356650
$497$		−	15.2419i		−	0.683693i
$498$		−	3.67806i		−	0.164818i
$499$	5.38788			0.241194			0.120597	−	0.992702i	$-0.461519\pi$
$499$	5.38788			0.241194			0.120597	+	0.992702i	$0.461519\pi$
$500$	−14.9055	−	7.33030i	−0.666596	−	0.327821i
$501$	17.5478			0.783978
$502$		−	7.85916i		−	0.350771i
$503$		−	26.5719i		−	1.18478i	−0.805650	−	0.592392i	$-0.798184\pi$
$503$		−	26.5719i		−	1.18478i	0.805650	−	0.592392i	$-0.201816\pi$
$504$	3.37465			0.150319
$505$	4.56797	+	11.7338i	0.203272	+	0.522148i
$506$	−20.4927			−0.911012
$507$			19.4229i			0.862600i
$508$		−	16.1359i		−	0.715914i
$509$	−28.1487			−1.24767			−0.623836	−	0.781556i	$-0.714427\pi$
$509$	−28.1487			−1.24767			−0.623836	+	0.781556i	$0.714427\pi$
$510$	−1.52815	+	0.594908i	−0.0676676	+	0.0263430i
$511$	28.0406			1.24044
$512$		−	12.7817i		−	0.564876i
$513$		0			0
$514$	−10.7785			−0.475418
$515$	−0.957757	+	0.372854i	−0.0422038	+	0.0164299i
$516$	−1.77487			−0.0781343
$517$		−	66.1520i		−	2.90936i
$518$		−	1.34045i		−	0.0588958i
$519$	−8.00406			−0.351339
$520$	−1.60542	−	4.12386i	−0.0704022	−	0.180843i
$521$	9.50660			0.416492			0.208246	−	0.978077i	$-0.433225\pi$
$521$	9.50660			0.416492			0.208246	+	0.978077i	$0.433225\pi$
$522$		−	1.85719i		−	0.0812869i
$523$			17.3457i			0.758473i	0.925300	+	0.379237i	$0.123813\pi$
$523$			17.3457i			0.758473i	−0.925300	+	0.379237i	$0.876187\pi$
$524$	24.2887			1.06106
$525$	14.5679	−	13.3687i	0.635797	−	0.583456i
$526$	−10.6648			−0.465006
$527$		−	4.39015i		−	0.191238i
$528$		−	10.8308i		−	0.471350i
$529$	−0.827475			−0.0359772
$530$	7.50366	+	19.2748i	0.325938	+	0.837242i
$531$	1.14988			0.0499004
$532$		0			0
$533$		−	6.36916i		−	0.275879i
$534$	−1.21000			−0.0523619
$535$	−10.6500	+	4.14606i	−0.460442	+	0.179250i
$536$	−34.6989			−1.49876
$537$		−	0.745532i		−	0.0321721i
$538$			2.39893i			0.103425i
$539$	−3.82718			−0.164848
$540$	−17.1830	+	6.68933i	−0.739439	+	0.287863i
$541$	−18.5619			−0.798039			−0.399020	−	0.916942i	$-0.630649\pi$
$541$	−18.5619			−0.798039			−0.399020	+	0.916942i	$0.630649\pi$
$542$		−	6.69973i		−	0.287778i
$543$		−	2.21945i		−	0.0952456i
$544$	3.80760			0.163249
$545$	8.23656	+	21.1574i	0.352816	+	0.906283i
$546$	2.24523			0.0960870
$547$			5.56689i			0.238023i	0.992893	+	0.119011i	$0.0379725\pi$
$547$			5.56689i			0.238023i	−0.992893	+	0.119011i	$0.962027\pi$
$548$			27.2376i			1.16353i
$549$	−3.62211			−0.154588
$550$	−14.1925	−	15.4657i	−0.605171	−	0.659460i
$551$		0			0
$552$			19.1545i			0.815271i
$553$		−	39.7194i		−	1.68904i
$554$	−2.00212			−0.0850618
$555$	0.944792	+	2.42690i	0.0401042	+	0.103016i
$556$	13.9262			0.590603
$557$			25.5819i			1.08394i	0.840398	+	0.541970i	$0.182321\pi$
$557$			25.5819i			1.08394i	−0.840398	+	0.541970i	$0.817679\pi$
$558$			2.58990i			0.109639i
$559$	0.602515			0.0254837
$560$	−6.18705	+	2.40861i	−0.261451	+	0.101783i
$561$	5.98628			0.252741
$562$		−	19.9035i		−	0.839580i
$563$		−	12.8773i		−	0.542712i	−0.962479	−	0.271356i	$-0.912528\pi$
$563$		−	12.8773i		−	0.542712i	0.962479	−	0.271356i	$-0.0874720\pi$
$564$	−26.3545			−1.10972
$565$	−11.6898	+	4.55082i	−0.491792	+	0.191455i
$566$	−0.815034			−0.0342585
$567$		−	17.8992i		−	0.751694i
$568$			15.1246i			0.634614i
$569$	−11.4205			−0.478773			−0.239387	−	0.970924i	$-0.576946\pi$
$569$	−11.4205			−0.478773			−0.239387	+	0.970924i	$0.576946\pi$
$570$		0			0
$571$	11.1881			0.468208			0.234104	−	0.972212i	$-0.424784\pi$
$571$	11.1881			0.468208			0.234104	+	0.972212i	$0.424784\pi$
$572$			6.88547i			0.287896i
$573$			19.7960i			0.826991i
$574$	14.5343			0.606650
$575$	−16.5021	−	17.9824i	−0.688184	−	0.749920i
$576$	−0.983004			−0.0409585
$577$			0.256987i			0.0106985i	0.999986	+	0.00534924i	$0.00170273\pi$
$577$			0.256987i			0.0106985i	−0.999986	+	0.00534924i	$0.998297\pi$
$578$		−	11.8873i		−	0.494446i
$579$	−19.7940			−0.822609
$580$	5.82408	+	14.9604i	0.241832	+	0.621197i
$581$	8.23061			0.341463
$582$		−	11.3899i		−	0.472126i
$583$		−	75.5057i		−	3.12713i
$584$	−27.8248			−1.15140
$585$	0.884040	−	0.344156i	0.0365506	−	0.0142291i
$586$	17.9548			0.741706
$587$			2.50510i			0.103397i	0.998663	+	0.0516983i	$0.0164634\pi$
$587$			2.50510i			0.103397i	−0.998663	+	0.0516983i	$0.983537\pi$
$588$			1.52472i			0.0628785i
$589$		0			0
$590$	3.20655	−	1.24831i	0.132011	−	0.0513920i
$591$	2.35585			0.0969068
$592$		−	0.874504i		−	0.0359419i
$593$			27.9054i			1.14594i	0.819577	+	0.572969i	$0.194209\pi$
$593$			27.9054i			1.14594i	−0.819577	+	0.572969i	$0.805791\pi$
$594$	−23.3018			−0.956083
$595$	−1.33126	−	3.41963i	−0.0545764	−	0.140191i
$596$	11.4375			0.468499
$597$			24.5901i			1.00641i
$598$		−	2.77148i		−	0.113334i
$599$	−33.3364			−1.36209			−0.681045	−	0.732242i	$-0.738474\pi$
$599$	−33.3364			−1.36209			−0.681045	+	0.732242i	$0.738474\pi$
$600$	−14.4558	+	13.2658i	−0.590156	+	0.541572i
$601$	33.2223			1.35516			0.677582	−	0.735447i	$-0.263028\pi$
$601$	33.2223			1.35516			0.677582	+	0.735447i	$0.263028\pi$
$602$			1.37493i			0.0560378i
$603$		−	7.43847i		−	0.302918i
$604$	−0.248518			−0.0101121
$605$	18.8753	+	48.4852i	0.767389	+	1.97120i
$606$	6.33929			0.257516
$607$			20.6372i			0.837640i	0.908069	+	0.418820i	$0.137556\pi$
$607$			20.6372i			0.837640i	−0.908069	+	0.418820i	$0.862444\pi$
$608$		0			0
$609$	−19.1100			−0.774377
$610$	−10.1006	+	3.93217i	−0.408962	+	0.159209i
$611$	8.94655			0.361938
$612$			0.518653i			0.0209653i
$613$		−	27.6480i		−	1.11669i	−0.829608	−	0.558346i	$-0.811436\pi$
$613$		−	27.6480i		−	1.11669i	0.829608	−	0.558346i	$-0.188564\pi$
$614$	−13.5490			−0.546791
$615$	−26.3146	+	10.2443i	−1.06111	+	0.413088i
$616$	−36.8643			−1.48531
$617$			19.4964i			0.784896i	0.919774	+	0.392448i	$0.128372\pi$
$617$			19.4964i			0.784896i	−0.919774	+	0.392448i	$0.871628\pi$
$618$			0.517436i			0.0208143i
$619$	−26.9685			−1.08396			−0.541978	−	0.840392i	$-0.682325\pi$
$619$	−26.9685			−1.08396			−0.541978	+	0.840392i	$0.682325\pi$
$620$	−8.12184	−	20.8627i	−0.326181	−	0.837866i
$621$	−27.0937			−1.08723
$622$		−	10.0094i		−	0.401338i
$623$		−	2.70770i		−	0.108482i
$624$	1.46478			0.0586382
$625$	2.14249	−	24.9080i	0.0856996	−	0.996321i
$626$	−0.152486			−0.00609456
$627$		0			0
$628$		−	22.1159i		−	0.882522i
$629$	0.483346			0.0192723
$630$	0.785358	+	2.01736i	0.0312894	+	0.0803736i
$631$	−0.601618			−0.0239500			−0.0119750	−	0.999928i	$-0.503812\pi$
$631$	−0.601618			−0.0239500			−0.0119750	+	0.999928i	$0.503812\pi$
$632$			39.4137i			1.56779i
$633$			27.9670i			1.11159i
$634$	5.38070			0.213695
$635$	22.6312	−	8.81032i	0.898092	−	0.349627i
$636$	−30.0809			−1.19279
$637$		−	0.517597i		−	0.0205079i
$638$			20.2877i			0.803198i
$639$	−3.24229			−0.128263
$640$	21.6170	−	8.41548i	0.854486	−	0.332651i
$641$	7.42208			0.293154			0.146577	−	0.989199i	$-0.453174\pi$
$641$	7.42208			0.293154			0.146577	+	0.989199i	$0.453174\pi$
$642$			5.75377i			0.227083i
$643$		−	6.20548i		−	0.244720i	−0.992486	−	0.122360i	$-0.960954\pi$
$643$		−	6.20548i		−	0.244720i	0.992486	−	0.122360i	$-0.0390463\pi$
$644$	−18.2694			−0.719915
$645$	−0.969093	−	2.48933i	−0.0381580	−	0.0980171i
$646$		0			0
$647$			24.3051i			0.955530i	0.878488	+	0.477765i	$0.158553\pi$
$647$			24.3051i			0.955530i	−0.878488	+	0.477765i	$0.841447\pi$
$648$			17.7614i			0.697733i
$649$	−12.5611			−0.493067
$650$	2.09162	−	1.91943i	0.0820400	−	0.0752862i
$651$	26.6494			1.04447
$652$			27.8590i			1.09104i
$653$			1.38625i			0.0542483i	0.999632	+	0.0271242i	$0.00863495\pi$
$653$			1.38625i			0.0542483i	−0.999632	+	0.0271242i	$0.991365\pi$
$654$	11.4305			0.446966
$655$	13.2618	+	34.0658i	0.518182	+	1.33106i
$656$	9.48214			0.370215
$657$		−	5.96486i		−	0.232711i
$658$			20.4158i			0.795892i
$659$	30.4152			1.18481			0.592405	−	0.805641i	$-0.298179\pi$
$659$	30.4152			1.18481			0.592405	+	0.805641i	$0.298179\pi$
$660$	28.4478	−	11.0747i	1.10733	−	0.431082i
$661$	−18.4422			−0.717317			−0.358659	−	0.933469i	$-0.616766\pi$
$661$	−18.4422			−0.717317			−0.358659	+	0.933469i	$0.616766\pi$
$662$		−	2.31366i		−	0.0899228i
$663$			0.809598i			0.0314422i
$664$	−8.16726			−0.316951
$665$		0			0
$666$	−0.285143			−0.0110490
$667$			23.5891i			0.913374i
$668$		−	16.6081i		−	0.642587i
$669$	−28.9286			−1.11844
$670$	−8.07520	−	20.7429i	−0.311972	−	0.801368i
$671$	39.5675			1.52749
$672$			23.1132i			0.891611i
$673$			28.6496i			1.10436i	0.833724	+	0.552181i	$0.186204\pi$
$673$			28.6496i			1.10436i	−0.833724	+	0.552181i	$0.813796\pi$
$674$	24.8131			0.955767
$675$	−18.7641	−	20.4474i	−0.722231	−	0.787021i
$676$	18.3827			0.707028
$677$			5.02624i			0.193174i	0.995325	+	0.0965870i	$0.0307926\pi$
$677$			5.02624i			0.193174i	−0.995325	+	0.0965870i	$0.969207\pi$
$678$			6.31549i			0.242545i
$679$	25.4878			0.978133
$680$	1.32101	+	3.39331i	0.0506586	+	0.130128i
$681$	−6.49624			−0.248936
$682$		−	28.2918i		−	1.08335i
$683$			12.9236i			0.494509i	0.968951	+	0.247254i	$0.0795284\pi$
$683$			12.9236i			0.494509i	−0.968951	+	0.247254i	$0.920472\pi$
$684$		0			0
$685$	−38.2019	+	14.8720i	−1.45962	+	0.568228i
$686$	13.8276			0.527940
$687$			2.15195i			0.0821020i
$688$			0.896998i			0.0341977i
$689$	10.2116			0.389030
$690$	−11.4505	+	4.45769i	−0.435914	+	0.169701i
$691$	24.0901			0.916432			0.458216	−	0.888841i	$-0.348489\pi$
$691$	24.0901			0.916432			0.458216	+	0.888841i	$0.348489\pi$
$692$			7.57544i			0.287975i
$693$		−	7.90268i		−	0.300198i
$694$	0.0608371			0.00230934
$695$	7.60383	+	19.5321i	0.288430	+	0.740894i
$696$	18.9629			0.718788
$697$			5.24086i			0.198512i
$698$		−	12.7718i		−	0.483421i
$699$	1.59238			0.0602292
$700$	−12.6527	−	13.7878i	−0.478229	−	0.521130i
$701$	−6.98543			−0.263836			−0.131918	−	0.991261i	$-0.542114\pi$
$701$	−6.98543			−0.263836			−0.131918	+	0.991261i	$0.542114\pi$
$702$		−	3.15138i		−	0.118941i
$703$		0			0
$704$	10.7382			0.404712
$705$	−14.3898	−	36.9632i	−0.541949	−	1.39211i
$706$	−10.8527			−0.408448
$707$			14.1858i			0.533512i
$708$			5.00426i			0.188072i
$709$	0.256274			0.00962456			0.00481228	−	0.999988i	$-0.498468\pi$
$709$	0.256274			0.00962456			0.00481228	+	0.999988i	$0.498468\pi$
$710$	−9.04144	+	3.51983i	−0.339319	+	0.132097i
$711$	−8.44919			−0.316869
$712$			2.68685i			0.100694i
$713$		−	32.8957i		−	1.23195i
$714$	−1.84748			−0.0691404
$715$	−9.65715	+	3.75952i	−0.361157	+	0.140598i
$716$	−0.705608			−0.0263698
$717$		−	8.70487i		−	0.325089i
$718$			6.45456i			0.240882i
$719$	−18.5286			−0.690999			−0.345500	−	0.938419i	$-0.612291\pi$
$719$	−18.5286			−0.690999			−0.345500	+	0.938419i	$0.612291\pi$
$720$	0.512365	+	1.31612i	0.0190947	+	0.0490490i
$721$	−1.15790			−0.0431224
$722$		0			0
$723$		−	39.2559i		−	1.45994i
$724$	−2.10059			−0.0780679
$725$	−17.8026	+	16.3370i	−0.661171	+	0.606741i
$726$	26.1945			0.972170
$727$		−	35.1390i		−	1.30323i	−0.758548	−	0.651617i	$-0.774091\pi$
$727$		−	35.1390i		−	1.30323i	0.758548	−	0.651617i	$-0.225909\pi$
$728$		−	4.98561i		−	0.184779i
$729$	−29.9460			−1.10911
$730$	−6.47545	−	16.6336i	−0.239667	−	0.615637i
$731$	−0.495778			−0.0183370
$732$		−	15.7634i		−	0.582633i
$733$		−	34.9872i		−	1.29228i	−0.763217	−	0.646142i	$-0.776382\pi$
$733$		−	34.9872i		−	1.29228i	0.763217	−	0.646142i	$-0.223618\pi$
$734$	−4.20299			−0.155135
$735$	−2.13848	+	0.832510i	−0.0788791	+	0.0307076i
$736$	28.5306			1.05165
$737$			81.2569i			2.99314i
$738$		−	3.09176i		−	0.113809i
$739$	4.73129			0.174043			0.0870216	−	0.996206i	$-0.472265\pi$
$739$	4.73129			0.174043			0.0870216	+	0.996206i	$0.472265\pi$
$740$	2.29694	−	0.894197i	0.0844371	−	0.0328713i
$741$		0			0
$742$			23.3026i			0.855464i
$743$			6.77084i			0.248398i	0.992257	+	0.124199i	$0.0396361\pi$
$743$			6.77084i			0.248398i	−0.992257	+	0.124199i	$0.960364\pi$
$744$	−26.4443			−0.969496
$745$	6.24498	+	16.0416i	0.228798	+	0.587718i
$746$	−17.6584			−0.646519
$747$		−	1.75083i		−	0.0640596i
$748$		−	5.66570i		−	0.207159i
$749$	−12.8756			−0.470463
$750$	−11.2944	−	5.55441i	−0.412414	−	0.202818i
$751$	2.77014			0.101084			0.0505419	−	0.998722i	$-0.483905\pi$
$751$	2.77014			0.101084			0.0505419	+	0.998722i	$0.483905\pi$
$752$			13.3192i			0.485702i
$753$			17.2026i			0.626897i
$754$	−2.74376			−0.0999217
$755$	−0.135693	−	0.348557i	−0.00493837	−	0.0126853i
$756$	−20.7737			−0.755532
$757$			1.03606i			0.0376561i	0.999823	+	0.0188280i	$0.00599350\pi$
$757$			1.03606i			0.0376561i	−0.999823	+	0.0188280i	$0.994006\pi$
$758$			1.92021i			0.0697451i
$759$	44.8556			1.62815
$760$		0			0
$761$	32.4025			1.17459			0.587296	−	0.809373i	$-0.300193\pi$
$761$	32.4025			1.17459			0.587296	+	0.809373i	$0.300193\pi$
$762$		−	12.2267i		−	0.442926i
$763$			25.5786i			0.926008i
$764$	18.7359			0.677842
$765$	−0.727431	+	0.283189i	−0.0263003	+	0.0102387i
$766$	−19.9717			−0.721605
$767$		−	1.69879i		−	0.0613399i
$768$		−	17.4377i		−	0.629230i
$769$	−48.0188			−1.73160			−0.865801	−	0.500388i	$-0.833191\pi$
$769$	−48.0188			−1.73160			−0.865801	+	0.500388i	$0.833191\pi$
$770$	−8.57915	−	22.0374i	−0.309171	−	0.794173i
$771$	23.5925			0.849665
$772$			18.7340i			0.674250i
$773$		−	10.6208i		−	0.382004i	−0.981590	−	0.191002i	$-0.938826\pi$
$773$		−	10.6208i		−	0.382004i	0.981590	−	0.191002i	$-0.0611737\pi$
$774$	0.292477			0.0105129
$775$	24.8262	−	22.7824i	0.891783	−	0.818368i
$776$	−25.2916			−0.907917
$777$			2.93405i			0.105258i
$778$			10.6543i			0.381976i
$779$		0			0
$780$	1.49777	+	3.84734i	0.0536287	+	0.137757i
$781$	35.4184			1.26737
$782$			2.28051i			0.0815508i
$783$			26.8226i			0.958562i
$784$	0.770576			0.0275206
$785$	31.0185	−	12.0755i	1.10710	−	0.430992i
$786$	18.4043			0.656461
$787$		−	26.1251i		−	0.931259i	−0.884980	−	0.465629i	$-0.845828\pi$
$787$		−	26.1251i		−	0.931259i	0.884980	−	0.465629i	$-0.154172\pi$
$788$		−	2.22969i		−	0.0794295i
$789$	23.3436			0.831055
$790$	−23.5614	+	9.17244i	−0.838277	+	0.326341i
$791$	−14.1326			−0.502496
$792$			7.84185i			0.278648i
$793$			5.35120i			0.190027i
$794$	−7.97400			−0.282987
$795$	−16.4244	−	42.1897i	−0.582515	−	1.49631i
$796$	23.2733			0.824899
$797$		−	23.4923i		−	0.832139i	−0.909333	−	0.416069i	$-0.863407\pi$
$797$		−	23.4923i		−	0.832139i	0.909333	−	0.416069i	$-0.136593\pi$
$798$		0			0
$799$	−7.36165			−0.260437
$800$	19.7593	+	21.5319i	0.698597	+	0.761267i
$801$	−0.575987			−0.0203515
$802$			20.4038i			0.720483i
$803$			65.1594i			2.29943i
$804$	32.3722			1.14168
$805$	−9.97524	−	25.6236i	−0.351581	−	0.903112i
$806$	3.82624			0.134774
$807$		−	5.25091i		−	0.184841i
$808$		−	14.0766i		−	0.495214i
$809$	−18.6786			−0.656706			−0.328353	−	0.944555i	$-0.606494\pi$
$809$	−18.6786			−0.656706			−0.328353	+	0.944555i	$0.606494\pi$
$810$	−10.6177	+	4.13347i	−0.373069	+	0.145235i
$811$	16.1813			0.568202			0.284101	−	0.958794i	$-0.408305\pi$
$811$	16.1813			0.568202			0.284101	+	0.958794i	$0.408305\pi$
$812$			18.0866i			0.634717i
$813$			14.6648i			0.514315i
$814$	3.11486			0.109176
$815$	−39.0734	+	15.2112i	−1.36868	+	0.532827i
$816$	−1.20529			−0.0421937
$817$		0			0
$818$		−	11.3664i		−	0.397416i
$819$	1.06878			0.0373461
$820$	9.69566	+	24.9054i	0.338587	+	0.869734i
$821$	31.3762			1.09504			0.547519	−	0.836793i	$-0.315572\pi$
$821$	31.3762			1.09504			0.547519	+	0.836793i	$0.315572\pi$
$822$			20.6389i			0.719863i
$823$			12.2385i			0.426608i	0.976986	+	0.213304i	$0.0684225\pi$
$823$			12.2385i			0.426608i	−0.976986	+	0.213304i	$0.931578\pi$
$824$	1.14899			0.0400268
$825$	31.0654	+	33.8522i	1.08156	+	1.17858i
$826$	3.87661			0.134885
$827$		−	6.21619i		−	0.216158i	−0.994142	−	0.108079i	$-0.965530\pi$
$827$		−	6.21619i		−	0.216158i	0.994142	−	0.108079i	$-0.0344700\pi$
$828$			3.88630i			0.135058i
$829$	−52.2819			−1.81583			−0.907913	−	0.419158i	$-0.862325\pi$
$829$	−52.2819			−1.81583			−0.907913	+	0.419158i	$0.862325\pi$
$830$	−1.90070	−	4.88237i	−0.0659744	−	0.169469i
$831$	4.38235			0.152022
$832$			1.45226i			0.0503481i
$833$			0.425904i			0.0147567i
$834$	10.5524			0.365398
$835$	23.2935	−	9.06815i	0.806105	−	0.313816i
$836$		0			0
$837$		−	37.4049i		−	1.29290i
$838$		−	7.33651i		−	0.253436i
$839$	44.5398			1.53768			0.768842	−	0.639439i	$-0.220833\pi$
$839$	44.5398			1.53768			0.768842	+	0.639439i	$0.220833\pi$
$840$	−20.5984	+	8.01893i	−0.710711	+	0.276679i
$841$	−5.64685			−0.194719
$842$		−	22.3470i		−	0.770129i
$843$			43.5660i			1.50049i
$844$	26.4693			0.911112
$845$	10.0371	+	25.7825i	0.345287	+	0.886946i
$846$	4.34290			0.149312
$847$			58.6171i			2.01411i
$848$			15.2025i			0.522057i
$849$	1.78399			0.0612265
$850$	−1.72109	+	1.57940i	−0.0590327	+	0.0541730i
$851$	3.62174			0.124152
$852$		−	14.1104i		−	0.483415i
$853$		−	40.0057i		−	1.36977i	−0.728651	−	0.684885i	$-0.759852\pi$
$853$		−	40.0057i		−	1.36977i	0.728651	−	0.684885i	$-0.240148\pi$
$854$	−12.2113			−0.417863
$855$		0			0
$856$	12.7765			0.436690
$857$		−	27.8347i		−	0.950817i	−0.879765	−	0.475408i	$-0.842300\pi$
$857$		−	27.8347i		−	0.950817i	0.879765	−	0.475408i	$-0.157700\pi$
$858$			5.21735i			0.178117i
$859$	1.48811			0.0507737			0.0253869	−	0.999678i	$-0.491918\pi$
$859$	1.48811			0.0507737			0.0253869	+	0.999678i	$0.491918\pi$
$860$	−2.35602	+	0.917197i	−0.0803396	+	0.0312762i
$861$	−31.8135			−1.08420
$862$			6.88991i			0.234671i
$863$		−	13.3429i		−	0.454196i	−0.973872	−	0.227098i	$-0.927076\pi$
$863$		−	13.3429i		−	0.454196i	0.973872	−	0.227098i	$-0.0729238\pi$
$864$	32.4415			1.10368
$865$	−10.6248	+	4.13625i	−0.361256	+	0.140637i
$866$	−14.9498			−0.508015
$867$			26.0196i			0.883671i
$868$		−	25.2223i		−	0.856102i
$869$	92.2979			3.13099
$870$	4.41310	+	11.3360i	0.149618	+	0.384326i
$871$	−10.9894			−0.372361
$872$		−	25.3817i		−	0.859534i
$873$		−	5.42182i		−	0.183501i
$874$		0			0
$875$	12.4294	−	25.2742i	0.420192	−	0.854425i
$876$	25.9590			0.877074
$877$		−	0.167258i		−	0.00564790i	−0.999996	−	0.00282395i	$-0.999101\pi$
$877$		−	0.167258i		−	0.00564790i	0.999996	−	0.00282395i	$-0.000898892\pi$
$878$			0.796928i			0.0268950i
$879$	−39.3005			−1.32557
$880$	−5.59702	−	14.3772i	−0.188675	−	0.484654i
$881$	−28.5156			−0.960715			−0.480357	−	0.877073i	$-0.659493\pi$
$881$	−28.5156			−0.960715			−0.480357	+	0.877073i	$0.659493\pi$
$882$		−	0.251255i		−	0.00846021i
$883$			34.8335i			1.17224i	0.810224	+	0.586121i	$0.199346\pi$
$883$			34.8335i			1.17224i	−0.810224	+	0.586121i	$0.800654\pi$
$884$	0.766242			0.0257715
$885$	−7.01867	+	2.73237i	−0.235930	+	0.0918475i
$886$	−20.6173			−0.692652
$887$			25.7718i			0.865332i	0.901554	+	0.432666i	$0.142427\pi$
$887$			25.7718i			0.865332i	−0.901554	+	0.432666i	$0.857573\pi$
$888$		−	2.91146i		−	0.0977023i
$889$	27.3604			0.917638
$890$	−1.60620	+	0.625291i	−0.0538398	+	0.0209598i
$891$	41.5932			1.39342
$892$			27.3794i			0.916731i
$893$		0			0
$894$	8.66659			0.289854
$895$	−0.385268	−	0.989643i	−0.0128781	−	0.0330801i
$896$	26.1342			0.873083
$897$			6.06637i			0.202550i
$898$		−	22.9271i		−	0.765088i
$899$	−32.5666			−1.08616
$900$	−2.93297	+	2.69152i	−0.0977656	+	0.0897172i
$901$	−8.40257			−0.279930
$902$			33.7741i			1.12455i
$903$		−	3.00951i		−	0.100150i
$904$	14.0238			0.466424
$905$	−1.14694	−	2.94616i	−0.0381256	−	0.0979338i
$906$	−0.188310			−0.00625619
$907$		−	23.4162i		−	0.777521i	−0.921339	−	0.388761i	$-0.872903\pi$
$907$		−	23.4162i		−	0.777521i	0.921339	−	0.388761i	$-0.127097\pi$
$908$			6.14835i			0.204040i
$909$	3.01763			0.100089
$910$	2.98039	−	1.16026i	0.0987989	−	0.0384624i
$911$	−7.45626			−0.247037			−0.123518	−	0.992342i	$-0.539418\pi$
$911$	−7.45626			−0.247037			−0.123518	+	0.992342i	$0.539418\pi$
$912$		0			0
$913$			19.1259i			0.632974i
$914$	8.60834			0.284739
$915$	22.1088	−	8.60695i	0.730895	−	0.284537i
$916$	2.03671			0.0672948
$917$			41.1845i			1.36003i
$918$			2.59311i			0.0855854i
$919$	−40.0009			−1.31951			−0.659754	−	0.751481i	$-0.729340\pi$
$919$	−40.0009			−1.31951			−0.659754	+	0.751481i	$0.729340\pi$
$920$	9.89846	+	25.4263i	0.326342	+	0.838281i
$921$	29.6567			0.977223
$922$			24.3655i			0.802434i
$923$			4.79006i			0.157667i
$924$	34.3924			1.13143
$925$	2.50829	+	2.73331i	0.0824721	+	0.0898706i
$926$	−17.2838			−0.567981
$927$			0.246310i			0.00808989i
$928$		−	28.2452i		−	0.927194i
$929$	20.1755			0.661936			0.330968	−	0.943642i	$-0.392625\pi$
$929$	20.1755			0.661936			0.330968	+	0.943642i	$0.392625\pi$
$930$	−6.15419	−	15.8084i	−0.201804	−	0.518377i
$931$		0			0
$932$		−	1.50710i		−	0.0493667i
$933$			21.9090i			0.717270i
$934$	−0.445424			−0.0145747
$935$	7.94637	−	3.09352i	0.259874	−	0.101169i
$936$	−1.06055			−0.0346652
$937$			34.1398i			1.11530i	0.830077	+	0.557649i	$0.188297\pi$
$937$			34.1398i			1.11530i	−0.830077	+	0.557649i	$0.811703\pi$
$938$		−	25.0775i		−	0.818810i
$939$	0.333770			0.0108922
$940$	−34.9838	+	13.6192i	−1.14104	+	0.444208i
$941$	26.7549			0.872184			0.436092	−	0.899902i	$-0.356362\pi$
$941$	26.7549			0.872184			0.436092	+	0.899902i	$0.356362\pi$
$942$		−	16.7580i		−	0.546005i
$943$			39.2701i			1.27881i
$944$	2.52909			0.0823149
$945$	−11.3426	−	29.1359i	−0.368975	−	0.947792i
$946$	−3.19498			−0.103878
$947$			15.6563i			0.508763i	0.967104	+	0.254381i	$0.0818719\pi$
$947$			15.6563i			0.508763i	−0.967104	+	0.254381i	$0.918128\pi$
$948$		−	36.7708i		−	1.19426i
$949$	−8.81230			−0.286060
$950$		0			0
$951$	−11.7776			−0.381915
$952$			4.10241i			0.132960i
$953$			13.5072i			0.437541i	0.975776	+	0.218771i	$0.0702046\pi$
$953$			13.5072i			0.437541i	−0.975776	+	0.218771i	$0.929795\pi$
$954$	4.95697			0.160488
$955$	10.2300	+	26.2779i	0.331034	+	0.850332i
$956$	−8.23871			−0.266459
$957$		−	44.4069i		−	1.43547i
$958$			22.2844i			0.719977i
$959$	−46.1848			−1.49139
$960$	6.00010	−	2.33584i	0.193652	−	0.0753888i
$961$	14.4151			0.465003
$962$			0.421261i			0.0135820i
$963$			2.73892i			0.0882603i
$964$	−37.1537			−1.19664
$965$	−26.2751	+	10.2289i	−0.845826	+	0.329280i
$966$	−13.8433			−0.445402
$967$		−	21.9060i		−	0.704450i	−0.935915	−	0.352225i	$-0.885425\pi$
$967$		−	21.9060i		−	0.704450i	0.935915	−	0.352225i	$-0.114575\pi$
$968$		−	58.1659i		−	1.86952i
$969$		0			0
$970$	−5.88593	−	15.1193i	−0.188986	−	0.485451i
$971$	−30.9663			−0.993756			−0.496878	−	0.867821i	$-0.665520\pi$
$971$	−30.9663			−0.993756			−0.496878	+	0.867821i	$0.665520\pi$
$972$			8.16832i			0.261999i
$973$			23.6137i			0.757019i
$974$	26.6929			0.855297
$975$	−4.57825	+	4.20136i	−0.146621	+	0.134551i
$976$	−7.96664			−0.255006
$977$			9.89768i			0.316655i	0.987387	+	0.158327i	$0.0506101\pi$
$977$			9.89768i			0.316655i	−0.987387	+	0.158327i	$0.949390\pi$
$978$			21.1097i			0.675014i
$979$	6.29201			0.201093
$980$	0.787928	+	2.02396i	0.0251694	+	0.0646532i
$981$	5.44113			0.173722
$982$		−	27.6459i		−	0.882215i
$983$			10.3096i			0.328827i	0.986392	+	0.164413i	$0.0525731\pi$
$983$			10.3096i			0.328827i	−0.986392	+	0.164413i	$0.947427\pi$
$984$	31.5686			1.00637
$985$	3.12723	−	1.21743i	0.0996419	−	0.0387905i
$986$	2.25770			0.0718997
$987$		−	44.6873i		−	1.42241i
$988$		0			0
$989$	−3.71490			−0.118127
$990$	−4.68784	+	1.82497i	−0.148989	+	0.0580015i
$991$	20.4090			0.648314			0.324157	−	0.946003i	$-0.394919\pi$
$991$	20.4090			0.648314			0.324157	+	0.946003i	$0.394919\pi$
$992$			39.3887i			1.25059i
$993$			5.06426i			0.160710i
$994$	−10.9308			−0.346704
$995$	12.7074	+	32.6417i	0.402852	+	1.03481i
$996$	7.61961			0.241437
$997$			47.0764i			1.49092i	0.666549	+	0.745462i	$0.267771\pi$
$997$			47.0764i			1.49092i	−0.666549	+	0.745462i	$0.732229\pi$
$998$		−	3.86394i		−	0.122311i
$999$	4.11820			0.130294

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1805.2.b.m.1084.18	yes	40
5.2	odd	4		9025.2.a.cv.1.23		40
5.3	odd	4		9025.2.a.cv.1.18		40
5.4	even	2	inner	1805.2.b.m.1084.23	yes	40
19.18	odd	2	inner	1805.2.b.m.1084.24	yes	40
95.18	even	4		9025.2.a.cv.1.24		40
95.37	even	4		9025.2.a.cv.1.17		40
95.94	odd	2	inner	1805.2.b.m.1084.17	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1805.2.b.m.1084.17	✓	40	95.94	odd	2	inner
1805.2.b.m.1084.18	yes	40	1.1	even	1	trivial
1805.2.b.m.1084.23	yes	40	5.4	even	2	inner
1805.2.b.m.1084.24	yes	40	19.18	odd	2	inner
9025.2.a.cv.1.17		40	95.37	even	4
9025.2.a.cv.1.18		40	5.3	odd	4
9025.2.a.cv.1.23		40	5.2	odd	4
9025.2.a.cv.1.24		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)

\(f(q)\)	\(=\)	\(q-0.717155i q^{2} +1.56975i q^{3} +1.48569 q^{4} +(0.811198 + 2.08374i) q^{5} +1.12576 q^{6} +2.51917i q^{7} -2.49978i q^{8} +0.535883 q^{9} +O(q^{10})\)	\(q-0.717155i q^{2} +1.56975i q^{3} +1.48569 q^{4} +(0.811198 + 2.08374i) q^{5} +1.12576 q^{6} +2.51917i q^{7} -2.49978i q^{8} +0.535883 q^{9} +(1.49436 - 0.581755i) q^{10} -5.85392 q^{11} +2.33216i q^{12} -0.791698i q^{13} +1.80664 q^{14} +(-3.27095 + 1.27338i) q^{15} +1.17865 q^{16} +0.651447i q^{17} -0.384311i q^{18} +(1.20519 + 3.09578i) q^{20} -3.95447 q^{21} +4.19817i q^{22} +4.88134i q^{23} +3.92403 q^{24} +(-3.68392 + 3.38064i) q^{25} -0.567770 q^{26} +5.55045i q^{27} +3.74270i q^{28} +4.83251 q^{29} +(0.913210 + 2.34578i) q^{30} -6.73907 q^{31} -5.84483i q^{32} -9.18920i q^{33} +0.467189 q^{34} +(-5.24929 + 2.04354i) q^{35} +0.796155 q^{36} -0.741957i q^{37} +1.24277 q^{39} +(5.20888 - 2.02782i) q^{40} +8.04494 q^{41} +2.83597i q^{42} +0.761041i q^{43} -8.69710 q^{44} +(0.434707 + 1.11664i) q^{45} +3.50068 q^{46} +11.3005i q^{47} +1.85018i q^{48} +0.653781 q^{49} +(2.42445 + 2.64194i) q^{50} -1.02261 q^{51} -1.17622i q^{52} +12.8983i q^{53} +3.98054 q^{54} +(-4.74869 - 12.1980i) q^{55} +6.29737 q^{56} -3.46566i q^{58} +2.14576 q^{59} +(-4.85961 + 1.89184i) q^{60} -6.75915 q^{61} +4.83296i q^{62} +1.34998i q^{63} -1.83436 q^{64} +(1.64969 - 0.642223i) q^{65} -6.59008 q^{66} -13.8808i q^{67} +0.967847i q^{68} -7.66249 q^{69} +(1.46554 + 3.76456i) q^{70} -6.05037 q^{71} -1.33959i q^{72} -11.1309i q^{73} -0.532098 q^{74} +(-5.30677 - 5.78283i) q^{75} -14.7470i q^{77} -0.891258i q^{78} -15.7669 q^{79} +(0.956114 + 2.45599i) q^{80} -7.10518 q^{81} -5.76948i q^{82} -3.26719i q^{83} -5.87511 q^{84} +(-1.35744 + 0.528452i) q^{85} +0.545785 q^{86} +7.58584i q^{87} +14.6335i q^{88} -1.07484 q^{89} +(0.800804 - 0.311752i) q^{90} +1.99442 q^{91} +7.25215i q^{92} -10.5787i q^{93} +8.10419 q^{94} +9.17493 q^{96} -10.1175i q^{97} -0.468863i q^{98} -3.13702 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 48 q^{4} + 6 q^{5} + 20 q^{6} - 52 q^{9}+O(q^{10}) \) 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

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Database

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