LMFDB - Embedded newform 1805.2.b.m.1084.19

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			1084.19
Character	$\chi$	$=$	1805.1084
Dual form			1805.2.b.m.1084.22

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.113485i q^{2} +1.07621i q^{3} +1.98712 q^{4} +(-1.21941 - 1.87431i) q^{5} +0.122133 q^{6} +1.50555i q^{7} -0.452479i q^{8} +1.84178 q^{9} +O(q^{10})$	\(q-0.113485i q^{2} +1.07621i q^{3} +1.98712 q^{4} +(-1.21941 - 1.87431i) q^{5} +0.122133 q^{6} +1.50555i q^{7} -0.452479i q^{8} +1.84178 q^{9} +(-0.212706 + 0.138385i) q^{10} -0.314502 q^{11} +2.13855i q^{12} -5.17028i q^{13} +0.170857 q^{14} +(2.01714 - 1.31234i) q^{15} +3.92289 q^{16} -6.53710i q^{17} -0.209015i q^{18} +(-2.42312 - 3.72448i) q^{20} -1.62028 q^{21} +0.0356913i q^{22} -5.96878i q^{23} +0.486960 q^{24} +(-2.02607 + 4.57111i) q^{25} -0.586750 q^{26} +5.21075i q^{27} +2.99170i q^{28} -6.64674 q^{29} +(-0.148931 - 0.228916i) q^{30} -7.01474 q^{31} -1.35015i q^{32} -0.338469i q^{33} -0.741863 q^{34} +(2.82186 - 1.83588i) q^{35} +3.65984 q^{36} -1.92182i q^{37} +5.56429 q^{39} +(-0.848085 + 0.551758i) q^{40} +1.75303 q^{41} +0.183877i q^{42} -0.0943416i q^{43} -0.624953 q^{44} +(-2.24589 - 3.45207i) q^{45} -0.677368 q^{46} -0.794179i q^{47} +4.22184i q^{48} +4.73333 q^{49} +(0.518753 + 0.229929i) q^{50} +7.03526 q^{51} -10.2740i q^{52} -6.17127i q^{53} +0.591343 q^{54} +(0.383507 + 0.589474i) q^{55} +0.681228 q^{56} +0.754306i q^{58} +12.6295 q^{59} +(4.00831 - 2.60777i) q^{60} +7.61655 q^{61} +0.796068i q^{62} +2.77289i q^{63} +7.69256 q^{64} +(-9.69071 + 6.30470i) q^{65} -0.0384111 q^{66} +14.5501i q^{67} -12.9900i q^{68} +6.42364 q^{69} +(-0.208345 - 0.320239i) q^{70} +2.29699 q^{71} -0.833367i q^{72} -8.53778i q^{73} -0.218098 q^{74} +(-4.91945 - 2.18047i) q^{75} -0.473497i q^{77} -0.631464i q^{78} -8.30254 q^{79} +(-4.78362 - 7.35271i) q^{80} -0.0824966 q^{81} -0.198943i q^{82} -3.71479i q^{83} -3.21969 q^{84} +(-12.2525 + 7.97141i) q^{85} -0.0107064 q^{86} -7.15326i q^{87} +0.142305i q^{88} +2.77358 q^{89} +(-0.391758 + 0.254875i) q^{90} +7.78410 q^{91} -11.8607i q^{92} -7.54930i q^{93} -0.0901275 q^{94} +1.45304 q^{96} -6.44264i q^{97} -0.537163i q^{98} -0.579244 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$		−	0.113485i		−	0.0802461i	−0.999195	−	0.0401230i	$-0.987225\pi$
$2$		−	0.113485i		−	0.0802461i	0.999195	−	0.0401230i	$-0.0127750\pi$
$3$			1.07621i			0.621348i	0.950517	+	0.310674i	$0.100555\pi$
$3$			1.07621i			0.621348i	−0.950517	+	0.310674i	$0.899445\pi$
$4$	1.98712			0.993561
$5$	−1.21941	−	1.87431i	−0.545337	−	0.838217i
$5$	−1.21941	−	1.87431i	−0.545337	−	0.838217i
$6$	0.122133			0.0498607
$7$			1.50555i			0.569043i	0.958670	+	0.284521i	$0.0918347\pi$
$7$			1.50555i			0.569043i	−0.958670	+	0.284521i	$0.908165\pi$
$8$		−	0.452479i		−	0.159975i
$9$	1.84178			0.613927
$10$	−0.212706	+	0.138385i	−0.0672636	+	0.0437612i
$11$	−0.314502			−0.0948258			−0.0474129	−	0.998875i	$-0.515098\pi$
$11$	−0.314502			−0.0948258			−0.0474129	+	0.998875i	$0.515098\pi$
$12$			2.13855i			0.617346i
$13$		−	5.17028i		−	1.43398i	−0.697084	−	0.716989i	$-0.745520\pi$
$13$		−	5.17028i		−	1.43398i	0.697084	−	0.716989i	$-0.254480\pi$
$14$	0.170857			0.0456635
$15$	2.01714	−	1.31234i	0.520824	−	0.338844i
$16$	3.92289			0.980723
$17$		−	6.53710i		−	1.58548i	−0.609560	−	0.792740i	$-0.708654\pi$
$17$		−	6.53710i		−	1.58548i	0.609560	−	0.792740i	$-0.291346\pi$
$18$		−	0.209015i		−	0.0492652i
$19$		0			0
$19$		0			0
$20$	−2.42312	−	3.72448i	−0.541826	−	0.832819i
$21$	−1.62028			−0.353573
$22$			0.0356913i			0.00760940i
$23$		−	5.96878i		−	1.24458i	−0.782788	−	0.622288i	$-0.786203\pi$
$23$		−	5.96878i		−	1.24458i	0.782788	−	0.622288i	$-0.213797\pi$
$24$	0.486960			0.0994003
$25$	−2.02607	+	4.57111i	−0.405214	+	0.914222i
$26$	−0.586750			−0.115071
$27$			5.21075i			1.00281i
$28$			2.99170i			0.565379i
$29$	−6.64674			−1.23427			−0.617134	−	0.786858i	$-0.711706\pi$
$29$	−6.64674			−1.23427			−0.617134	+	0.786858i	$0.711706\pi$
$30$	−0.148931	−	0.228916i	−0.0271909	−	0.0417941i
$31$	−7.01474			−1.25988			−0.629942	−	0.776642i	$-0.716921\pi$
$31$	−7.01474			−1.25988			−0.629942	+	0.776642i	$0.716921\pi$
$32$		−	1.35015i		−	0.238675i
$33$		−	0.338469i		−	0.0589198i
$34$	−0.741863			−0.127228
$35$	2.82186	−	1.83588i	0.476981	−	0.310320i
$36$	3.65984			0.609974
$37$		−	1.92182i		−	0.315945i	−0.987444	−	0.157972i	$-0.949504\pi$
$37$		−	1.92182i		−	0.315945i	0.987444	−	0.157972i	$-0.0504957\pi$
$38$		0			0
$39$	5.56429			0.890999
$40$	−0.848085	+	0.551758i	−0.134094	+	0.0872406i
$41$	1.75303			0.273778			0.136889	−	0.990586i	$-0.456290\pi$
$41$	1.75303			0.273778			0.136889	+	0.990586i	$0.456290\pi$
$42$			0.183877i			0.0283729i
$43$		−	0.0943416i		−	0.0143870i	−0.999974	−	0.00719348i	$-0.997710\pi$
$43$		−	0.0943416i		−	0.0143870i	0.999974	−	0.00719348i	$-0.00228978\pi$
$44$	−0.624953			−0.0942152
$45$	−2.24589	−	3.45207i	−0.334797	−	0.514604i
$46$	−0.677368			−0.0998724
$47$		−	0.794179i		−	0.115843i	−0.998321	−	0.0579215i	$-0.981553\pi$
$47$		−	0.794179i		−	0.115843i	0.998321	−	0.0579215i	$-0.0184473\pi$
$48$			4.22184i			0.609370i
$49$	4.73333			0.676190
$50$	0.518753	+	0.229929i	0.0733627	+	0.0325168i
$51$	7.03526			0.985134
$52$		−	10.2740i		−	1.42474i
$53$		−	6.17127i		−	0.847689i	−0.905735	−	0.423844i	$-0.860680\pi$
$53$		−	6.17127i		−	0.847689i	0.905735	−	0.423844i	$-0.139320\pi$
$54$	0.591343			0.0804716
$55$	0.383507	+	0.589474i	0.0517121	+	0.0794846i
$56$	0.681228			0.0910329
$57$		0			0
$58$			0.754306i			0.0990452i
$59$	12.6295			1.64422			0.822109	−	0.569330i	$-0.192797\pi$
$59$	12.6295			1.64422			0.822109	+	0.569330i	$0.192797\pi$
$60$	4.00831	−	2.60777i	0.517470	−	0.336662i
$61$	7.61655			0.975199			0.487599	−	0.873067i	$-0.337873\pi$
$61$	7.61655			0.975199			0.487599	+	0.873067i	$0.337873\pi$
$62$			0.796068i			0.101101i
$63$			2.77289i			0.349351i
$64$	7.69256			0.961570
$65$	−9.69071	+	6.30470i	−1.20198	+	0.782002i
$66$	−0.0384111			−0.00472808
$67$			14.5501i			1.77758i	0.458314	+	0.888790i	$0.348454\pi$
$67$			14.5501i			1.77758i	−0.458314	+	0.888790i	$0.651546\pi$
$68$		−	12.9900i		−	1.57527i
$69$	6.42364			0.773315
$70$	−0.208345	−	0.320239i	−0.0249020	−	0.0382759i
$71$	2.29699			0.272602			0.136301	−	0.990667i	$-0.456479\pi$
$71$	2.29699			0.272602			0.136301	+	0.990667i	$0.456479\pi$
$72$		−	0.833367i		−	0.0982133i
$73$		−	8.53778i		−	0.999272i	−0.866236	−	0.499636i	$-0.833467\pi$
$73$		−	8.53778i		−	0.999272i	0.866236	−	0.499636i	$-0.166533\pi$
$74$	−0.218098			−0.0253533
$75$	−4.91945	−	2.18047i	−0.568050	−	0.251779i
$76$		0			0
$77$		−	0.473497i		−	0.0539600i
$78$		−	0.631464i		−	0.0714992i
$79$	−8.30254			−0.934109			−0.467054	−	0.884229i	$-0.654685\pi$
$79$	−8.30254			−0.934109			−0.467054	+	0.884229i	$0.654685\pi$
$80$	−4.78362	−	7.35271i	−0.534825	−	0.822058i
$81$	−0.0824966			−0.00916629
$82$		−	0.198943i		−	0.0219696i
$83$		−	3.71479i		−	0.407751i	−0.978997	−	0.203875i	$-0.934646\pi$
$83$		−	3.71479i		−	0.407751i	0.978997	−	0.203875i	$-0.0653537\pi$
$84$	−3.21969			−0.351297
$85$	−12.2525	+	7.97141i	−1.32897	+	0.864621i
$86$	−0.0107064			−0.00115450
$87$		−	7.15326i		−	0.766910i
$88$			0.142305i			0.0151698i
$89$	2.77358			0.293999			0.147000	−	0.989137i	$-0.453038\pi$
$89$	2.77358			0.293999			0.147000	+	0.989137i	$0.453038\pi$
$90$	−0.391758	+	0.254875i	−0.0412949	+	0.0268662i
$91$	7.78410			0.815995
$92$		−	11.8607i		−	1.23656i
$93$		−	7.54930i		−	0.782826i
$94$	−0.0901275			−0.00929594
$95$		0			0
$96$	1.45304			0.148300
$97$		−	6.44264i		−	0.654151i	−0.944998	−	0.327075i	$-0.893937\pi$
$97$		−	6.44264i		−	0.654151i	0.944998	−	0.327075i	$-0.106063\pi$
$98$		−	0.537163i		−	0.0542616i
$99$	−0.579244			−0.0582162
$100$	−4.02605	+	9.08335i	−0.402605	+	0.908335i
$101$	−9.46719			−0.942021			−0.471010	−	0.882128i	$-0.656111\pi$
$101$	−9.46719			−0.942021			−0.471010	+	0.882128i	$0.656111\pi$
$102$		−	0.798397i		−	0.0790531i
$103$			13.4778i			1.32800i	0.747731	+	0.664002i	$0.231143\pi$
$103$			13.4778i			1.32800i	−0.747731	+	0.664002i	$0.768857\pi$
$104$	−2.33944			−0.229401
$105$	1.97578	+	3.03690i	0.192817	+	0.296371i
$106$	−0.700347			−0.0680237
$107$		−	9.97967i		−	0.964771i	−0.875959	−	0.482385i	$-0.839770\pi$
$107$		−	9.97967i		−	0.964771i	0.875959	−	0.482385i	$-0.160230\pi$
$108$			10.3544i			0.996352i
$109$	8.18121			0.783618			0.391809	−	0.920047i	$-0.371849\pi$
$109$	8.18121			0.783618			0.391809	+	0.920047i	$0.371849\pi$
$110$	0.0668965	−	0.0435223i	0.00637833	−	0.00414969i
$111$	2.06827			0.196312
$112$			5.90610i			0.558074i
$113$			14.1535i			1.33145i	0.746198	+	0.665724i	$0.231877\pi$
$113$			14.1535i			1.33145i	−0.746198	+	0.665724i	$0.768123\pi$
$114$		0			0
$115$	−11.1873	+	7.27840i	−1.04323	+	0.678714i
$116$	−13.2079			−1.22632
$117$		−	9.52253i		−	0.880358i
$118$		−	1.43326i		−	0.131942i
$119$	9.84190			0.902206
$120$	−0.593805	−	0.912714i	−0.0542067	−	0.0833190i
$121$	−10.9011			−0.991008
$122$		−	0.864364i		−	0.0782559i
$123$			1.88663i			0.170111i
$124$	−13.9391			−1.25177
$125$	11.0383	−	1.77658i	0.987294	−	0.158902i
$126$	0.314681			0.0280340
$127$		−	18.5751i		−	1.64828i	−0.566388	−	0.824138i	$-0.691660\pi$
$127$		−	18.5751i		−	1.64828i	0.566388	−	0.824138i	$-0.308340\pi$
$128$		−	3.57329i		−	0.315837i
$129$	0.101531			0.00893930
$130$	0.715490	+	1.09975i	0.0627526	+	0.0964545i
$131$	18.3046			1.59928			0.799642	−	0.600477i	$-0.205023\pi$
$131$	18.3046			1.59928			0.799642	+	0.600477i	$0.205023\pi$
$132$		−	0.672578i		−	0.0585404i
$133$		0			0
$134$	1.65122			0.142644
$135$	9.76656	−	6.35405i	0.840572	−	0.546870i
$136$	−2.95790			−0.253638
$137$			2.57199i			0.219740i	0.993946	+	0.109870i	$0.0350434\pi$
$137$			2.57199i			0.219740i	−0.993946	+	0.109870i	$0.964957\pi$
$138$		−	0.728987i		−	0.0620555i
$139$	2.00421			0.169994			0.0849972	−	0.996381i	$-0.472912\pi$
$139$	2.00421			0.169994			0.0849972	+	0.996381i	$0.472912\pi$
$140$	5.60738	−	3.64812i	0.473910	−	0.308322i
$141$	0.854700			0.0719788
$142$		−	0.260674i		−	0.0218753i
$143$			1.62606i			0.135978i
$144$	7.22511			0.602093
$145$	8.10511	+	12.4580i	0.673093	+	1.03458i
$146$	−0.968911			−0.0801876
$147$			5.09404i			0.420149i
$148$		−	3.81888i		−	0.313910i
$149$	−8.49666			−0.696074			−0.348037	−	0.937481i	$-0.613152\pi$
$149$	−8.49666			−0.696074			−0.348037	+	0.937481i	$0.613152\pi$
$150$	−0.247451	+	0.558285i	−0.0202043	+	0.0455837i
$151$	16.1197			1.31180			0.655901	−	0.754847i	$-0.272289\pi$
$151$	16.1197			1.31180			0.655901	+	0.754847i	$0.272289\pi$
$152$		0			0
$153$		−	12.0399i		−	0.973369i
$154$	−0.0537348			−0.00433008
$155$	8.55385	+	13.1478i	0.687062	+	1.05606i
$156$	11.0569			0.885261
$157$		−	6.46789i		−	0.516194i	−0.966119	−	0.258097i	$-0.916905\pi$
$157$		−	6.46789i		−	0.516194i	0.966119	−	0.258097i	$-0.0830954\pi$
$158$			0.942215i			0.0749586i
$159$	6.64155			0.526709
$160$	−2.53059	+	1.64639i	−0.200061	+	0.130158i
$161$	8.98627			0.708218
$162$			0.00936214i			0.000735559i
$163$			17.1020i			1.33953i	0.742571	+	0.669767i	$0.233606\pi$
$163$			17.1020i			1.33953i	−0.742571	+	0.669767i	$0.766394\pi$
$164$	3.48349			0.272015
$165$	−0.634395	+	0.412733i	−0.0493876	+	0.0321312i
$166$	−0.421573			−0.0327204
$167$			0.904143i			0.0699647i	0.999388	+	0.0349823i	$0.0111375\pi$
$167$			0.904143i			0.0699647i	−0.999388	+	0.0349823i	$0.988863\pi$
$168$			0.733141i			0.0565631i
$169$	−13.7318			−1.05629
$170$	0.904637	+	1.39048i	0.0693825	+	0.106645i
$171$		0			0
$172$		−	0.187468i		−	0.0142943i
$173$		−	10.5529i		−	0.802326i	−0.916007	−	0.401163i	$-0.868606\pi$
$173$		−	10.5529i		−	0.802326i	0.916007	−	0.401163i	$-0.131394\pi$
$174$	−0.811788			−0.0615415
$175$	−6.88201	−	3.05034i	−0.520231	−	0.230584i
$176$	−1.23376			−0.0929979
$177$			13.5919i			1.02163i
$178$		−	0.314760i		−	0.0235923i
$179$	−2.54363			−0.190120			−0.0950601	−	0.995472i	$-0.530304\pi$
$179$	−2.54363			−0.190120			−0.0950601	+	0.995472i	$0.530304\pi$
$180$	−4.46286	−	6.85968i	−0.332642	−	0.511290i
$181$	6.28754			0.467349			0.233674	−	0.972315i	$-0.424925\pi$
$181$	6.28754			0.467349			0.233674	+	0.972315i	$0.424925\pi$
$182$		−	0.883379i		−	0.0654804i
$183$			8.19697i			0.605937i
$184$	−2.70075			−0.199102
$185$	−3.60208	+	2.34349i	−0.264830	+	0.172297i
$186$	−0.856733			−0.0628187
$187$			2.05593i			0.150344i
$188$		−	1.57813i		−	0.115097i
$189$	−7.84503			−0.570642
$190$		0			0
$191$	22.6478			1.63873			0.819367	−	0.573269i	$-0.194325\pi$
$191$	22.6478			1.63873			0.819367	+	0.573269i	$0.194325\pi$
$192$			8.27878i			0.597470i
$193$			8.73921i			0.629062i	0.949247	+	0.314531i	$0.101847\pi$
$193$			8.73921i			0.629062i	−0.949247	+	0.314531i	$0.898153\pi$
$194$	−0.731143			−0.0524930
$195$	−6.78516	−	10.4292i	−0.485895	−	0.746850i
$196$	9.40570			0.671836
$197$			19.9939i			1.42450i	0.701924	+	0.712252i	$0.252324\pi$
$197$			19.9939i			1.42450i	−0.701924	+	0.712252i	$0.747676\pi$
$198$			0.0657355i			0.00467162i
$199$	−2.87202			−0.203592			−0.101796	−	0.994805i	$-0.532459\pi$
$199$	−2.87202			−0.203592			−0.101796	+	0.994805i	$0.532459\pi$
$200$	2.06833	+	0.916754i	0.146253	+	0.0648243i
$201$	−15.6589			−1.10450
$202$			1.07439i			0.0755935i
$203$		−	10.0070i		−	0.702352i
$204$	13.9799			0.978790
$205$	−2.13767	−	3.28573i	−0.149301	−	0.229485i
$206$	1.52953			0.106567
$207$		−	10.9932i		−	0.764080i
$208$		−	20.2825i		−	1.40634i
$209$		0			0
$210$	0.344643	−	0.224222i	0.0237826	−	0.0154728i
$211$	−21.7010			−1.49396			−0.746979	−	0.664848i	$-0.768497\pi$
$211$	−21.7010			−1.49396			−0.746979	+	0.664848i	$0.768497\pi$
$212$		−	12.2631i		−	0.842230i
$213$			2.47203i			0.169381i
$214$	−1.13254			−0.0774191
$215$	−0.176825	+	0.115041i	−0.0120594	+	0.00784575i
$216$	2.35776			0.160425
$217$		−	10.5610i		−	0.716928i
$218$		−	0.928445i		−	0.0628822i
$219$	9.18841			0.620895
$220$	0.762075	+	1.17136i	0.0513791	+	0.0789728i
$221$	−33.7986			−2.27354
$222$		−	0.234718i		−	0.0157532i
$223$			10.3957i			0.696147i	0.937467	+	0.348074i	$0.113164\pi$
$223$			10.3957i			0.696147i	−0.937467	+	0.348074i	$0.886836\pi$
$224$	2.03271			0.135816
$225$	−3.73158	+	8.41898i	−0.248772	+	0.561266i
$226$	1.60621			0.106844
$227$			3.48770i			0.231487i	0.993279	+	0.115743i	$0.0369250\pi$
$227$			3.48770i			0.231487i	−0.993279	+	0.115743i	$0.963075\pi$
$228$		0			0
$229$	−14.2418			−0.941123			−0.470562	−	0.882367i	$-0.655949\pi$
$229$	−14.2418			−0.941123			−0.470562	+	0.882367i	$0.655949\pi$
$230$	0.825990	+	1.26960i	0.0544642	+	0.0837147i
$231$	0.509580			0.0335279
$232$			3.00751i			0.197453i
$233$			4.69025i			0.307269i	0.988128	+	0.153634i	$0.0490978\pi$
$233$			4.69025i			0.307269i	−0.988128	+	0.153634i	$0.950902\pi$
$234$	−1.08067			−0.0706453
$235$	−1.48854	+	0.968432i	−0.0971015	+	0.0631735i
$236$	25.0963			1.63363
$237$		−	8.93524i		−	0.580406i
$238$		−	1.11691i		−	0.0723985i
$239$	−11.4369			−0.739793			−0.369896	−	0.929073i	$-0.620607\pi$
$239$	−11.4369			−0.739793			−0.369896	+	0.929073i	$0.620607\pi$
$240$	7.91303	−	5.14816i	0.510784	−	0.332312i
$241$	23.9346			1.54176			0.770880	−	0.636980i	$-0.219817\pi$
$241$	23.9346			1.54176			0.770880	+	0.636980i	$0.219817\pi$
$242$			1.23711i			0.0795245i
$243$			15.5435i			0.997114i
$244$	15.1350			0.968919
$245$	−5.77188	−	8.87173i	−0.368752	−	0.566794i
$246$	0.214104			0.0136508
$247$		0			0
$248$			3.17402i			0.201550i
$249$	3.99787			0.253355
$250$	−0.201615	−	1.25268i	−0.0127513	−	0.0792265i
$251$	17.5359			1.10686			0.553429	−	0.832896i	$-0.313319\pi$
$251$	17.5359			1.10686			0.553429	+	0.832896i	$0.313319\pi$
$252$			5.51006i			0.347101i
$253$			1.87719i			0.118018i
$254$	−2.10800			−0.132268
$255$	−8.57888	−	13.1863i	−0.537230	−	0.825755i
$256$	14.9796			0.936226
$257$		−	20.9190i		−	1.30489i	−0.757836	−	0.652446i	$-0.773743\pi$
$257$		−	20.9190i		−	1.30489i	0.757836	−	0.652446i	$-0.226257\pi$
$258$		−	0.0115223i		−	0.000717344i
$259$	2.89338			0.179786
$260$	−19.2566	+	12.5282i	−1.19424	+	0.776966i
$261$	−12.2418			−0.757751
$262$		−	2.07730i		−	0.128336i
$263$			19.4145i			1.19715i	0.801067	+	0.598575i	$0.204266\pi$
$263$			19.4145i			1.19715i	−0.801067	+	0.598575i	$0.795734\pi$
$264$	−0.153150			−0.00942572
$265$	−11.5669	+	7.52532i	−0.710547	+	0.462277i
$266$		0			0
$267$			2.98494i			0.182676i
$268$			28.9129i			1.76613i
$269$	−3.01230			−0.183663			−0.0918317	−	0.995775i	$-0.529272\pi$
$269$	−3.01230			−0.183663			−0.0918317	+	0.995775i	$0.529272\pi$
$270$	−0.721090	−	1.10836i	−0.0438842	−	0.0674526i
$271$	19.1729			1.16467			0.582334	−	0.812949i	$-0.302139\pi$
$271$	19.1729			1.16467			0.582334	+	0.812949i	$0.302139\pi$
$272$		−	25.6443i		−	1.55492i
$273$			8.37729i			0.507017i
$274$	0.291882			0.0176333
$275$	0.637203	−	1.43762i	0.0384248	−	0.0866919i
$276$	12.7645			0.768335
$277$			20.7927i			1.24931i	0.780900	+	0.624656i	$0.214761\pi$
$277$			20.7927i			1.24931i	−0.780900	+	0.624656i	$0.785239\pi$
$278$		−	0.227447i		−	0.0136414i
$279$	−12.9196			−0.773477
$280$	−0.830697	−	1.27683i	−0.0496436	−	0.0763053i
$281$	−13.8711			−0.827482			−0.413741	−	0.910395i	$-0.635778\pi$
$281$	−13.8711			−0.827482			−0.413741	+	0.910395i	$0.635778\pi$
$282$		−	0.0969957i		−	0.00577601i
$283$			25.6745i			1.52619i	0.646287	+	0.763094i	$0.276321\pi$
$283$			25.6745i			1.52619i	−0.646287	+	0.763094i	$0.723679\pi$
$284$	4.56439			0.270847
$285$		0			0
$286$	0.184534			0.0109117
$287$			2.63927i			0.155791i
$288$		−	2.48668i		−	0.146529i
$289$	−25.7337			−1.51374
$290$	1.41380	−	0.919809i	0.0830213	−	0.0540131i
$291$	6.93360			0.406455
$292$		−	16.9656i		−	0.992837i
$293$		−	21.3740i		−	1.24868i	−0.781153	−	0.624340i	$-0.785368\pi$
$293$		−	21.3740i		−	1.24868i	0.781153	−	0.624340i	$-0.214632\pi$
$294$	0.578097			0.0337153
$295$	−15.4005	−	23.6716i	−0.896654	−	1.37821i
$296$	−0.869581			−0.0505434
$297$		−	1.63879i		−	0.0950923i
$298$			0.964244i			0.0558572i
$299$	−30.8603			−1.78470
$300$	−9.77555	−	4.33285i	−0.564392	−	0.250157i
$301$	0.142036			0.00818680
$302$		−	1.82934i		−	0.105267i
$303$		−	10.1886i		−	0.585322i
$304$		0			0
$305$	−9.28771	−	14.2758i	−0.531812	−	0.817428i
$306$	−1.36635			−0.0781090
$307$			29.9590i			1.70985i	0.518753	+	0.854924i	$0.326396\pi$
$307$			29.9590i			1.70985i	−0.518753	+	0.854924i	$0.673604\pi$
$308$		−	0.940896i		−	0.0536125i
$309$	−14.5049			−0.825152
$310$	1.49208	−	0.970735i	0.0847443	−	0.0551340i
$311$	−15.0057			−0.850898			−0.425449	−	0.904982i	$-0.639884\pi$
$311$	−15.0057			−0.850898			−0.425449	+	0.904982i	$0.639884\pi$
$312$		−	2.51772i		−	0.142538i
$313$			6.22859i			0.352061i	0.984385	+	0.176030i	$0.0563257\pi$
$313$			6.22859i			0.352061i	−0.984385	+	0.176030i	$0.943674\pi$
$314$	−0.734009			−0.0414225
$315$	5.19725	−	3.38129i	0.292832	−	0.190514i
$316$	−16.4982			−0.928094
$317$			25.3086i			1.42147i	0.703458	+	0.710737i	$0.251638\pi$
$317$			25.3086i			1.42147i	−0.703458	+	0.710737i	$0.748362\pi$
$318$		−	0.753717i		−	0.0422664i
$319$	2.09041			0.117041
$320$	−9.38040	−	14.4182i	−0.524380	−	0.806004i
$321$	10.7402			0.599458
$322$		−	1.01981i		−	0.0568317i
$323$		0			0
$324$	−0.163931			−0.00910727
$325$	23.6339	+	10.4754i	1.31097	+	0.581068i
$326$	1.94083			0.107492
$327$			8.80466i			0.486899i
$328$		−	0.793211i		−	0.0437978i
$329$	1.19567			0.0659196
$330$	0.0468390	+	0.0719943i	0.00257840	+	0.00396316i
$331$	20.8596			1.14654			0.573272	−	0.819365i	$-0.305674\pi$
$331$	20.8596			1.14654			0.573272	+	0.819365i	$0.305674\pi$
$332$		−	7.38173i		−	0.405125i
$333$		−	3.53957i		−	0.193967i
$334$	0.102607			0.00561439
$335$	27.2714	−	17.7426i	1.49000	−	0.969382i
$336$	−6.35617			−0.346758
$337$		−	22.3057i		−	1.21507i	−0.794294	−	0.607533i	$-0.792159\pi$
$337$		−	22.3057i		−	1.21507i	0.794294	−	0.607533i	$-0.207841\pi$
$338$			1.55836i			0.0847634i
$339$	−15.2321			−0.827292
$340$	−24.3473	+	15.8402i	−1.32042	+	0.859054i
$341$	2.20615			0.119470
$342$		0			0
$343$			17.6651i			0.953824i
$344$	−0.0426876			−0.00230156
$345$	−7.83306	−	12.0399i	−0.421718	−	0.648205i
$346$	−1.19760			−0.0643835
$347$			2.40870i			0.129306i	0.997908	+	0.0646529i	$0.0205940\pi$
$347$			2.40870i			0.129306i	−0.997908	+	0.0646529i	$0.979406\pi$
$348$		−	14.2144i		−	0.761971i
$349$	−15.5260			−0.831088			−0.415544	−	0.909573i	$-0.636409\pi$
$349$	−15.5260			−0.831088			−0.415544	+	0.909573i	$0.636409\pi$
$350$	−0.346168	+	0.781006i	−0.0185035	+	0.0417465i
$351$	26.9411			1.43801
$352$			0.424624i			0.0226325i
$353$		−	3.52309i		−	0.187515i	−0.995595	−	0.0937576i	$-0.970112\pi$
$353$		−	3.52309i		−	0.187515i	0.995595	−	0.0937576i	$-0.0298879\pi$
$354$	1.54248			0.0819819
$355$	−2.80097	−	4.30526i	−0.148660	−	0.228500i
$356$	5.51144			0.292106
$357$			10.5919i			0.560583i
$358$			0.288665i			0.0152564i
$359$	−10.8027			−0.570142			−0.285071	−	0.958506i	$-0.592017\pi$
$359$	−10.8027			−0.570142			−0.285071	+	0.958506i	$0.592017\pi$
$360$	−1.56199	+	1.01622i	−0.0823240	+	0.0535594i
$361$		0			0
$362$		−	0.713542i		−	0.0375029i
$363$		−	11.7318i		−	0.615760i
$364$	15.4679			0.810741
$365$	−16.0024	+	10.4111i	−0.837606	+	0.544940i
$366$	0.930234			0.0486241
$367$		−	15.5752i		−	0.813017i	−0.913647	−	0.406508i	$-0.866746\pi$
$367$		−	15.5752i		−	0.813017i	0.913647	−	0.406508i	$-0.133254\pi$
$368$		−	23.4149i		−	1.22059i
$369$	3.22871			0.168080
$370$	0.265951	+	0.408782i	0.0138261	+	0.0212516i
$371$	9.29113			0.482371
$372$		−	15.0014i		−	0.777785i
$373$		−	1.61712i		−	0.0837313i	−0.999123	−	0.0418657i	$-0.986670\pi$
$373$		−	1.61712i		−	0.0837313i	0.999123	−	0.0418657i	$-0.0133301\pi$
$374$	0.233317			0.0120645
$375$	1.91197	+	11.8795i	0.0987335	+	0.613453i
$376$	−0.359349			−0.0185320
$377$			34.3655i			1.76991i
$378$			0.890294i			0.0457918i
$379$	−18.0335			−0.926316			−0.463158	−	0.886276i	$-0.653284\pi$
$379$	−18.0335			−0.926316			−0.463158	+	0.886276i	$0.653284\pi$
$380$		0			0
$381$	19.9907			1.02415
$382$		−	2.57018i		−	0.131502i
$383$		−	26.2750i		−	1.34259i	−0.741191	−	0.671294i	$-0.765739\pi$
$383$		−	26.2750i		−	1.34259i	0.741191	−	0.671294i	$-0.234261\pi$
$384$	3.84559			0.196244
$385$	−0.887480	+	0.577388i	−0.0452301	+	0.0294264i
$386$	0.991770			0.0504798
$387$		−	0.173757i		−	0.00883254i
$388$		−	12.8023i		−	0.649938i
$389$	−9.94513			−0.504238			−0.252119	−	0.967696i	$-0.581127\pi$
$389$	−9.94513			−0.504238			−0.252119	+	0.967696i	$0.581127\pi$
$390$	−1.18356	+	0.770014i	−0.0599318	+	0.0389912i
$391$	−39.0185			−1.97325
$392$		−	2.14173i		−	0.108174i
$393$			19.6996i			0.993711i
$394$	2.26900			0.114311
$395$	10.1242	+	15.5615i	0.509405	+	0.782986i
$396$	−1.15103			−0.0578413
$397$			21.6194i			1.08505i	0.840040	+	0.542524i	$0.182531\pi$
$397$			21.6194i			1.08505i	−0.840040	+	0.542524i	$0.817469\pi$
$398$			0.325932i			0.0163375i
$399$		0			0
$400$	−7.94806	+	17.9320i	−0.397403	+	0.896599i
$401$	−10.1889			−0.508808			−0.254404	−	0.967098i	$-0.581879\pi$
$401$	−10.1889			−0.508808			−0.254404	+	0.967098i	$0.581879\pi$
$402$			1.77705i			0.0886314i
$403$			36.2682i			1.80665i
$404$	−18.8125			−0.935955
$405$	0.100597	+	0.154624i	0.00499872	+	0.00768334i
$406$	−1.13564			−0.0563610
$407$			0.604415i			0.0299597i
$408$		−	3.18331i		−	0.157597i
$409$	29.5673			1.46201			0.731003	−	0.682374i	$-0.239052\pi$
$409$	29.5673			1.46201			0.731003	+	0.682374i	$0.239052\pi$
$410$	−0.372881	+	0.242594i	−0.0184153	+	0.0119809i
$411$	−2.76799			−0.136535
$412$			26.7820i			1.31945i
$413$			19.0143i			0.935631i
$414$	−1.24756			−0.0613144
$415$	−6.96266	+	4.52985i	−0.341783	+	0.222362i
$416$	−6.98064			−0.342254
$417$			2.15694i			0.105626i
$418$		0			0
$419$	−38.4410			−1.87797			−0.938984	−	0.343961i	$-0.888231\pi$
$419$	−38.4410			−1.87797			−0.938984	+	0.343961i	$0.888231\pi$
$420$	3.92612	+	6.03469i	0.191575	+	0.294463i
$421$	−32.1388			−1.56635			−0.783175	−	0.621801i	$-0.786401\pi$
$421$	−32.1388			−1.56635			−0.783175	+	0.621801i	$0.786401\pi$
$422$			2.46274i			0.119884i
$423$		−	1.46270i		−	0.0711191i
$424$	−2.79237			−0.135609
$425$	29.8818	+	13.2446i	1.44948	+	0.642458i
$426$	0.280539			0.0135921
$427$			11.4671i			0.554930i
$428$		−	19.8308i		−	0.958558i
$429$	−1.74998			−0.0844897
$430$	0.0130555	+	0.0200670i	0.000629590	+	0.000967719i
$431$	−3.32723			−0.160267			−0.0801334	−	0.996784i	$-0.525535\pi$
$431$	−3.32723			−0.160267			−0.0801334	+	0.996784i	$0.525535\pi$
$432$			20.4412i			0.983479i
$433$		−	4.80891i		−	0.231101i	−0.993302	−	0.115551i	$-0.963137\pi$
$433$		−	4.80891i		−	0.231101i	0.993302	−	0.115551i	$-0.0368633\pi$
$434$	−1.19852			−0.0575307
$435$	−13.4074	+	8.72276i	−0.642836	+	0.418225i
$436$	16.2571			0.778572
$437$		0			0
$438$		−	1.04275i		−	0.0498244i
$439$	−2.48577			−0.118640			−0.0593198	−	0.998239i	$-0.518893\pi$
$439$	−2.48577			−0.118640			−0.0593198	+	0.998239i	$0.518893\pi$
$440$	0.266724	−	0.173529i	0.0127156	−	0.00827266i
$441$	8.71776			0.415132
$442$			3.83564i			0.182443i
$443$			5.25211i			0.249535i	0.992186	+	0.124768i	$0.0398185\pi$
$443$			5.25211i			0.249535i	−0.992186	+	0.124768i	$0.960181\pi$
$444$	4.10990			0.195047
$445$	−3.38214	−	5.19855i	−0.160329	−	0.246435i
$446$	1.17976			0.0558631
$447$		−	9.14415i		−	0.432504i
$448$			11.5815i			0.547175i
$449$	23.6384			1.11557			0.557783	−	0.829987i	$-0.311652\pi$
$449$	23.6384			1.11557			0.557783	+	0.829987i	$0.311652\pi$
$450$	0.955429	+	0.423479i	0.0450394	+	0.0199630i
$451$	−0.551333			−0.0259612
$452$			28.1247i			1.32287i
$453$			17.3481i			0.815085i
$454$	0.395802			0.0185759
$455$	−9.49202	−	14.5898i	−0.444993	−	0.683981i
$456$		0			0
$457$			17.5786i			0.822291i	0.911570	+	0.411145i	$0.134871\pi$
$457$			17.5786i			0.822291i	−0.911570	+	0.411145i	$0.865129\pi$
$458$			1.61623i			0.0755214i
$459$	34.0632			1.58993
$460$	−22.2306	+	14.4631i	−1.03651	+	0.674344i
$461$	3.04030			0.141601			0.0708004	−	0.997491i	$-0.477445\pi$
$461$	3.04030			0.141601			0.0708004	+	0.997491i	$0.477445\pi$
$462$		−	0.0578297i		−	0.00269048i
$463$			16.7690i			0.779321i	0.920959	+	0.389660i	$0.127408\pi$
$463$			16.7690i			0.779321i	−0.920959	+	0.389660i	$0.872592\pi$
$464$	−26.0744			−1.21048
$465$	−14.1497	+	9.20570i	−0.656178	+	0.426904i
$466$	0.532274			0.0246571
$467$			21.9836i			1.01728i	0.860980	+	0.508639i	$0.169851\pi$
$467$			21.9836i			1.01728i	−0.860980	+	0.508639i	$0.830149\pi$
$468$		−	18.9224i		−	0.874689i
$469$	−21.9059			−1.01152
$470$	0.109903	+	0.168927i	0.00506943	+	0.00779201i
$471$	6.96078			0.320736
$472$		−	5.71457i		−	0.263035i
$473$			0.0296706i			0.00136426i
$474$	−1.01402			−0.0465753
$475$		0			0
$476$	19.5571			0.896396
$477$		−	11.3661i		−	0.520419i
$478$			1.29792i			0.0593655i
$479$	−17.8638			−0.816219			−0.408109	−	0.912933i	$-0.633812\pi$
$479$	−17.8638			−0.816219			−0.408109	+	0.912933i	$0.633812\pi$
$480$	−1.77185	−	2.72344i	−0.0808735	−	0.124307i
$481$	−9.93634			−0.453058
$482$		−	2.71622i		−	0.123720i
$483$			9.67108i			0.440049i
$484$	−21.6618			−0.984627
$485$	−12.0755	+	7.85623i	−0.548320	+	0.356733i
$486$	1.76395			0.0800145
$487$			11.0841i			0.502270i	0.967952	+	0.251135i	$0.0808037\pi$
$487$			11.0841i			0.502270i	−0.967952	+	0.251135i	$0.919196\pi$
$488$		−	3.44633i		−	0.156008i
$489$	−18.4053			−0.832316
$490$	−1.00681	+	0.655022i	−0.0454830	+	0.0295909i
$491$	−9.61186			−0.433777			−0.216889	−	0.976196i	$-0.569591\pi$
$491$	−9.61186			−0.433777			−0.216889	+	0.976196i	$0.569591\pi$
$492$			3.74895i			0.169016i
$493$			43.4504i			1.95691i
$494$		0			0
$495$	0.706336	+	1.08568i	0.0317475	+	0.0487978i
$496$	−27.5181			−1.23560
$497$			3.45822i			0.155122i
$498$		−	0.453699i		−	0.0203307i
$499$	3.45169			0.154519			0.0772594	−	0.997011i	$-0.475383\pi$
$499$	3.45169			0.154519			0.0772594	+	0.997011i	$0.475383\pi$
$500$	21.9344	−	3.53028i	0.980937	−	0.157879i
$501$	−0.973043			−0.0434724
$502$		−	1.99007i		−	0.0888210i
$503$		−	34.6220i		−	1.54372i	−0.635793	−	0.771859i	$-0.719327\pi$
$503$		−	34.6220i		−	1.54372i	0.635793	−	0.771859i	$-0.280673\pi$
$504$	1.25467			0.0558876
$505$	11.5444	+	17.7444i	0.513719	+	0.789617i
$506$	0.213033			0.00947049
$507$		−	14.7783i		−	0.656326i
$508$		−	36.9110i		−	1.63766i
$509$	−35.2230			−1.56123			−0.780616	−	0.625011i	$-0.785094\pi$
$509$	−35.2230			−1.56123			−0.780616	+	0.625011i	$0.785094\pi$
$510$	−1.49644	+	0.973575i	−0.0662636	+	0.0431106i
$511$	12.8540			0.568628
$512$		−	8.84654i		−	0.390965i
$513$		0			0
$514$	−2.37399			−0.104712
$515$	25.2615	−	16.4349i	1.11315	−	0.724210i
$516$	0.201754			0.00888174
$517$			0.249771i			0.0109849i
$518$		−	0.328356i		−	0.0144271i
$519$	11.3571			0.498523
$520$	2.85274	+	4.38484i	0.125101	+	0.192288i
$521$	45.1472			1.97793			0.988967	−	0.148139i	$-0.0473282\pi$
$521$	45.1472			1.97793			0.988967	+	0.148139i	$0.0473282\pi$
$522$			1.38927i			0.0608065i
$523$		−	11.8077i		−	0.516315i	−0.966103	−	0.258158i	$-0.916885\pi$
$523$		−	11.8077i		−	0.516315i	0.966103	−	0.258158i	$-0.0831154\pi$
$524$	36.3735			1.58899
$525$	3.28280	−	7.40646i	0.143273	−	0.323245i
$526$	2.20326			0.0960665
$527$			45.8560i			1.99752i
$528$		−	1.32778i		−	0.0577840i
$529$	−12.6264			−0.548972
$530$	0.854011	+	1.31267i	0.0370959	+	0.0570186i
$531$	23.2607			1.00943
$532$		0			0
$533$		−	9.06368i		−	0.392592i
$534$	0.338747			0.0146590
$535$	−18.7050	+	12.1693i	−0.808687	+	0.526126i
$536$	6.58362			0.284369
$537$		−	2.73747i		−	0.118131i
$538$			0.341852i			0.0147383i
$539$	−1.48864			−0.0641203
$540$	19.4073	−	12.6263i	0.835159	−	0.543348i
$541$	16.4508			0.707274			0.353637	−	0.935383i	$-0.384945\pi$
$541$	16.4508			0.707274			0.353637	+	0.935383i	$0.384945\pi$
$542$		−	2.17583i		−	0.0934601i
$543$			6.76668i			0.290386i
$544$	−8.82605			−0.378414
$545$	−9.97626	−	15.3341i	−0.427336	−	0.656841i
$546$	0.950697			0.0406861
$547$		−	36.6728i		−	1.56802i	−0.620750	−	0.784009i	$-0.713172\pi$
$547$		−	36.6728i		−	1.56802i	0.620750	−	0.784009i	$-0.286828\pi$
$548$			5.11085i			0.218325i
$549$	14.0280			0.598701
$550$	−0.163149	−	0.0723130i	−0.00695668	−	0.00308344i
$551$		0			0
$552$		−	2.90656i		−	0.123711i
$553$		−	12.4999i		−	0.531548i
$554$	2.35966			0.100252
$555$	−2.52207	−	3.87658i	−0.107056	−	0.164552i
$556$	3.98260			0.168900
$557$			26.8747i			1.13872i	0.822089	+	0.569360i	$0.192809\pi$
$557$			26.8747i			1.13872i	−0.822089	+	0.569360i	$0.807191\pi$
$558$			1.46618i			0.0620685i
$559$	−0.487773			−0.0206306
$560$	11.0698	−	7.20196i	0.467786	−	0.304338i
$561$	−2.21260			−0.0934161
$562$			1.57417i			0.0664022i
$563$			3.21769i			0.135609i	0.997699	+	0.0678046i	$0.0215995\pi$
$563$			3.21769i			0.135609i	−0.997699	+	0.0678046i	$0.978401\pi$
$564$	1.69839			0.0715152
$565$	26.5280	−	17.2589i	1.11604	−	0.726089i
$566$	2.91367			0.122471
$567$		−	0.124202i		−	0.00521601i
$568$		−	1.03934i		−	0.0436096i
$569$	14.0358			0.588410			0.294205	−	0.955742i	$-0.404945\pi$
$569$	14.0358			0.588410			0.294205	+	0.955742i	$0.404945\pi$
$570$		0			0
$571$	−0.475134			−0.0198837			−0.00994187	−	0.999951i	$-0.503165\pi$
$571$	−0.475134			−0.0198837			−0.00994187	+	0.999951i	$0.503165\pi$
$572$			3.23118i			0.135103i
$573$			24.3736i			1.01822i
$574$	0.299518			0.0125017
$575$	27.2840	+	12.0932i	1.13782	+	0.504320i
$576$	14.1680			0.590334
$577$			6.46828i			0.269278i	0.990895	+	0.134639i	$0.0429874\pi$
$577$			6.46828i			0.269278i	−0.990895	+	0.134639i	$0.957013\pi$
$578$			2.92039i			0.121472i
$579$	−9.40518			−0.390866
$580$	16.1058	+	24.7556i	0.668758	+	1.02792i
$581$	5.59278			0.232028
$582$		−	0.786860i		−	0.0326164i
$583$			1.94087i			0.0803828i
$584$	−3.86316			−0.159859
$585$	−17.8482	+	11.6119i	−0.737931	+	0.480092i
$586$	−2.42563			−0.100202
$587$			16.8347i			0.694843i	0.937709	+	0.347421i	$0.112943\pi$
$587$			16.8347i			0.694843i	−0.937709	+	0.347421i	$0.887057\pi$
$588$			10.1225i			0.417444i
$589$		0			0
$590$	−2.68637	+	1.74773i	−0.110596	+	0.0719530i
$591$	−21.5175			−0.885112
$592$		−	7.53908i		−	0.309854i
$593$		−	15.1827i		−	0.623477i	−0.950168	−	0.311739i	$-0.899089\pi$
$593$		−	15.1827i		−	0.623477i	0.950168	−	0.311739i	$-0.100911\pi$
$594$	−0.185978			−0.00763078
$595$	−12.0013	−	18.4468i	−0.492007	−	0.756244i
$596$	−16.8839			−0.691591
$597$		−	3.09089i		−	0.126502i
$598$			3.50218i			0.143215i
$599$	21.5126			0.878982			0.439491	−	0.898247i	$-0.355159\pi$
$599$	21.5126			0.878982			0.439491	+	0.898247i	$0.355159\pi$
$600$	−0.986616	+	2.22595i	−0.0402784	+	0.0908740i
$601$	−26.0308			−1.06182			−0.530910	−	0.847428i	$-0.678150\pi$
$601$	−26.0308			−1.06182			−0.530910	+	0.847428i	$0.678150\pi$
$602$		−	0.0161189i		−	0.000656958i
$603$			26.7982i			1.09131i
$604$	32.0318			1.30335
$605$	13.2929	+	20.4320i	0.540434	+	0.830679i
$606$	−1.15626			−0.0469698
$607$			12.8904i			0.523204i	0.965176	+	0.261602i	$0.0842508\pi$
$607$			12.8904i			0.523204i	−0.965176	+	0.261602i	$0.915749\pi$
$608$		0			0
$609$	10.7696			0.436404
$610$	−1.62009	+	1.05402i	−0.0655954	+	0.0426759i
$611$	−4.10613			−0.166116
$612$		−	23.9248i		−	0.967101i
$613$		−	21.7499i		−	0.878472i	−0.898372	−	0.439236i	$-0.855249\pi$
$613$		−	21.7499i		−	0.878472i	0.898372	−	0.439236i	$-0.144751\pi$
$614$	3.39990			0.137209
$615$	3.53612	−	2.30057i	0.142590	−	0.0927681i
$616$	−0.214247			−0.00863227
$617$			18.5508i			0.746828i	0.927665	+	0.373414i	$0.121813\pi$
$617$			18.5508i			0.746828i	−0.927665	+	0.373414i	$0.878187\pi$
$618$			1.64608i			0.0662152i
$619$	−15.5031			−0.623121			−0.311561	−	0.950226i	$-0.600852\pi$
$619$	−15.5031			−0.623121			−0.311561	+	0.950226i	$0.600852\pi$
$620$	16.9975	+	26.1262i	0.682638	+	1.04926i
$621$	31.1018			1.24807
$622$			1.70293i			0.0682812i
$623$			4.17575i			0.167298i
$624$	21.8281			0.873823
$625$	−16.7901	−	18.5228i	−0.671603	−	0.740911i
$626$	0.706852			0.0282515
$627$		0			0
$628$		−	12.8525i		−	0.512870i
$629$	−12.5631			−0.500924
$630$	−0.383726	−	0.589810i	−0.0152880	−	0.0234986i
$631$	28.1737			1.12158			0.560789	−	0.827959i	$-0.310498\pi$
$631$	28.1737			1.12158			0.560789	+	0.827959i	$0.310498\pi$
$632$			3.75672i			0.149434i
$633$		−	23.3547i		−	0.928267i
$634$	2.87215			0.114068
$635$	−34.8156	+	22.6507i	−1.38161	+	0.898867i
$636$	13.1976			0.523318
$637$		−	24.4727i		−	0.969642i
$638$		−	0.237230i		−	0.00939204i
$639$	4.23055			0.167358
$640$	−6.69744	+	4.35731i	−0.264740	+	0.172238i
$641$	23.5724			0.931055			0.465528	−	0.885033i	$-0.345865\pi$
$641$	23.5724			0.931055			0.465528	+	0.885033i	$0.345865\pi$
$642$		−	1.21885i		−	0.0481042i
$643$		−	44.2053i		−	1.74329i	−0.490140	−	0.871644i	$-0.663054\pi$
$643$		−	44.2053i		−	1.74329i	0.490140	−	0.871644i	$-0.336946\pi$
$644$	17.8568			0.703657
$645$	−0.123808	−	0.190300i	−0.00487494	−	0.00749307i
$646$		0			0
$647$		−	21.2728i		−	0.836319i	−0.908374	−	0.418160i	$-0.862675\pi$
$647$		−	21.2728i		−	0.836319i	0.908374	−	0.418160i	$-0.137325\pi$
$648$			0.0373280i			0.00146638i
$649$	−3.97199			−0.155914
$650$	1.18880	−	2.68210i	0.0466284	−	0.105201i
$651$	11.3658			0.445461
$652$			33.9838i			1.33091i
$653$			27.6776i			1.08311i	0.840666	+	0.541555i	$0.182164\pi$
$653$			27.6776i			1.08311i	−0.840666	+	0.541555i	$0.817836\pi$
$654$	0.999198			0.0390717
$655$	−22.3209	−	34.3086i	−0.872149	−	1.34055i
$656$	6.87697			0.268500
$657$		−	15.7247i		−	0.613480i
$658$		−	0.135691i		−	0.00528979i
$659$	19.3063			0.752065			0.376033	−	0.926606i	$-0.377288\pi$
$659$	19.3063			0.752065			0.376033	+	0.926606i	$0.377288\pi$
$660$	−1.26062	+	0.820150i	−0.0490695	+	0.0319243i
$661$	19.9967			0.777781			0.388891	−	0.921284i	$-0.372858\pi$
$661$	19.9967			0.777781			0.388891	+	0.921284i	$0.372858\pi$
$662$		−	2.36725i		−	0.0920057i
$663$		−	36.3743i		−	1.41266i
$664$	−1.68086			−0.0652301
$665$		0			0
$666$	−0.401688			−0.0155651
$667$			39.6729i			1.53614i
$668$			1.79664i			0.0695141i
$669$	−11.1879			−0.432549
$670$	−2.01352	−	3.09490i	−0.0777891	−	0.119566i
$671$	−2.39542			−0.0924741
$672$			2.18761i			0.0843890i
$673$		−	24.0044i		−	0.925300i	−0.886541	−	0.462650i	$-0.846899\pi$
$673$		−	24.0044i		−	0.925300i	0.886541	−	0.462650i	$-0.153101\pi$
$674$	−2.53136			−0.0975043
$675$	−23.8189	−	10.5574i	−0.916791	−	0.406353i
$676$	−27.2868			−1.04949
$677$			18.1589i			0.697901i	0.937141	+	0.348951i	$0.113462\pi$
$677$			18.1589i			0.697901i	−0.937141	+	0.348951i	$0.886538\pi$
$678$			1.72861i			0.0663870i
$679$	9.69968			0.372240
$680$	3.60690	+	5.54402i	0.138318	+	0.212603i
$681$	−3.75348			−0.143834
$682$		−	0.250365i		−	0.00958696i
$683$		−	48.8671i		−	1.86985i	−0.354849	−	0.934924i	$-0.615468\pi$
$683$		−	48.8671i		−	1.86985i	0.354849	−	0.934924i	$-0.384532\pi$
$684$		0			0
$685$	4.82070	−	3.13631i	0.184190	−	0.119832i
$686$	2.00472			0.0765406
$687$		−	15.3271i		−	0.584765i
$688$		−	0.370092i		−	0.0141096i
$689$	−31.9072			−1.21557
$690$	−1.36635	+	0.888935i	−0.0520159	+	0.0338412i
$691$	18.9182			0.719682			0.359841	−	0.933014i	$-0.382831\pi$
$691$	18.9182			0.719682			0.359841	+	0.933014i	$0.382831\pi$
$692$		−	20.9700i		−	0.797159i
$693$		−	0.872078i		−	0.0331275i
$694$	0.273352			0.0103763
$695$	−2.44395	−	3.75650i	−0.0927044	−	0.142492i
$696$	−3.23670			−0.122687
$697$		−	11.4598i		−	0.434069i
$698$			1.76197i			0.0666915i
$699$	−5.04768			−0.190921
$700$	−13.6754	−	6.06140i	−0.516881	−	0.229099i
$701$	33.6317			1.27025			0.635126	−	0.772408i	$-0.280948\pi$
$701$	33.6317			1.27025			0.635126	+	0.772408i	$0.280948\pi$
$702$		−	3.05741i		−	0.115394i
$703$		0			0
$704$	−2.41932			−0.0911817
$705$	−1.04223	−	1.60197i	−0.0392527	−	0.0603338i
$706$	−0.399818			−0.0150474
$707$		−	14.2533i		−	0.536050i
$708$			27.0088i			1.01505i
$709$	−24.8928			−0.934868			−0.467434	−	0.884028i	$-0.654821\pi$
$709$	−24.8928			−0.934868			−0.467434	+	0.884028i	$0.654821\pi$
$710$	−0.488583	+	0.317869i	−0.0183362	+	0.0119294i
$711$	−15.2915			−0.573475
$712$		−	1.25499i		−	0.0470326i
$713$			41.8694i			1.56802i
$714$	1.20202			0.0449846
$715$	3.04774	−	1.98284i	0.113979	−	0.0741540i
$716$	−5.05451			−0.188896
$717$		−	12.3085i		−	0.459668i
$718$			1.22594i			0.0457517i
$719$	4.93432			0.184019			0.0920095	−	0.995758i	$-0.470671\pi$
$719$	4.93432			0.184019			0.0920095	+	0.995758i	$0.470671\pi$
$720$	−8.81038	−	13.5421i	−0.328344	−	0.504684i
$721$	−20.2914			−0.755691
$722$		0			0
$723$			25.7585i			0.957969i
$724$	12.4941			0.464340
$725$	13.4668	−	30.3830i	0.500143	−	1.12839i
$726$	−1.33139			−0.0494124
$727$		−	29.3061i		−	1.08690i	−0.839440	−	0.543452i	$-0.817117\pi$
$727$		−	29.3061i		−	1.08690i	0.839440	−	0.543452i	$-0.182883\pi$
$728$		−	3.52214i		−	0.130539i
$729$	−16.9755			−0.628721
$730$	1.18150	+	1.81604i	0.0437293	+	0.0672146i
$731$	−0.616720			−0.0228102
$732$			16.2884i			0.602036i
$733$		−	15.7183i		−	0.580567i	−0.956941	−	0.290284i	$-0.906250\pi$
$733$		−	15.7183i		−	0.580567i	0.956941	−	0.290284i	$-0.0937496\pi$
$734$	−1.76755			−0.0652414
$735$	9.54780	−	6.21173i	0.352176	−	0.229123i
$736$	−8.05874			−0.297049
$737$		−	4.57604i		−	0.168561i
$738$		−	0.366410i		−	0.0134877i
$739$	−5.49827			−0.202257			−0.101129	−	0.994873i	$-0.532245\pi$
$739$	−5.49827			−0.202257			−0.101129	+	0.994873i	$0.532245\pi$
$740$	−7.15777	+	4.65679i	−0.263125	+	0.171187i
$741$		0			0
$742$		−	1.05440i		−	0.0387084i
$743$			19.2065i			0.704618i	0.935884	+	0.352309i	$0.114603\pi$
$743$			19.2065i			0.704618i	−0.935884	+	0.352309i	$0.885397\pi$
$744$	−3.41590			−0.125233
$745$	10.3609	+	15.9254i	0.379595	+	0.583460i
$746$	−0.183519			−0.00671911
$747$		−	6.84182i		−	0.250329i
$748$			4.08538i			0.149376i
$749$	15.0248			0.548996
$750$	1.34814	−	0.216980i	0.0492272	−	0.00792298i
$751$	−13.7467			−0.501623			−0.250811	−	0.968036i	$-0.580697\pi$
$751$	−13.7467			−0.501623			−0.250811	+	0.968036i	$0.580697\pi$
$752$		−	3.11548i		−	0.113610i
$753$			18.8723i			0.687744i
$754$	3.89997			0.142029
$755$	−19.6565	−	30.2133i	−0.715374	−	1.09957i
$756$	−15.5890			−0.566967
$757$		−	29.9965i		−	1.09024i	−0.838357	−	0.545121i	$-0.816484\pi$
$757$		−	29.9965i		−	1.09024i	0.838357	−	0.545121i	$-0.183516\pi$
$758$			2.04653i			0.0743332i
$759$	−2.02024			−0.0733302
$760$		0			0
$761$	37.1297			1.34595			0.672976	−	0.739664i	$-0.265016\pi$
$761$	37.1297			1.34595			0.672976	+	0.739664i	$0.265016\pi$
$762$		−	2.26864i		−	0.0821843i
$763$			12.3172i			0.445912i
$764$	45.0038			1.62818
$765$	−22.5665	+	14.6816i	−0.815894	+	0.530814i
$766$	−2.98182			−0.107737
$767$		−	65.2980i		−	2.35777i
$768$			16.1211i			0.581722i
$769$	8.35052			0.301127			0.150564	−	0.988600i	$-0.451891\pi$
$769$	8.35052			0.301127			0.150564	+	0.988600i	$0.451891\pi$
$770$	0.0655249	+	0.100716i	0.00236135	+	0.00362954i
$771$	22.5131			0.810791
$772$			17.3659i			0.625011i
$773$		−	20.9026i		−	0.751816i	−0.926657	−	0.375908i	$-0.877331\pi$
$773$		−	20.9026i		−	0.751816i	0.926657	−	0.375908i	$-0.122669\pi$
$774$	−0.0197188			−0.000708777
$775$	14.2123	−	32.0651i	0.510523	−	1.15181i
$776$	−2.91516			−0.104648
$777$			3.11388i			0.111710i
$778$			1.12862i			0.0404631i
$779$		0			0
$780$	−13.4829	−	20.7241i	−0.482766	−	0.742041i
$781$	−0.722406			−0.0258497
$782$			4.42802i			0.158346i
$783$		−	34.6345i		−	1.23774i
$784$	18.5684			0.663155
$785$	−12.1228	+	7.88702i	−0.432682	+	0.281500i
$786$	2.23561			0.0797414
$787$			43.9642i			1.56716i	0.621294	+	0.783578i	$0.286607\pi$
$787$			43.9642i			1.56716i	−0.621294	+	0.783578i	$0.713393\pi$
$788$			39.7302i			1.41533i
$789$	−20.8940			−0.743846
$790$	1.76600	−	1.14895i	0.0628315	−	0.0408777i
$791$	−21.3087			−0.757651
$792$			0.262095i			0.00931316i
$793$		−	39.3797i		−	1.39841i
$794$	2.45348			0.0870708
$795$	−8.09879	−	12.4483i	−0.287234	−	0.441497i
$796$	−5.70706			−0.202281
$797$		−	16.3576i		−	0.579416i	−0.957115	−	0.289708i	$-0.906442\pi$
$797$		−	16.3576i		−	0.579416i	0.957115	−	0.289708i	$-0.0935582\pi$
$798$		0			0
$799$	−5.19163			−0.183667
$800$	6.17167	+	2.73549i	0.218202	+	0.0967143i
$801$	5.10833			0.180494
$802$			1.15629i			0.0408299i
$803$			2.68515i			0.0947568i
$804$	−31.1162			−1.09738
$805$	−10.9580	−	16.8431i	−0.386218	−	0.593640i
$806$	4.11590			0.144976
$807$		−	3.24186i		−	0.114119i
$808$			4.28370i			0.150700i
$809$	−6.79371			−0.238854			−0.119427	−	0.992843i	$-0.538106\pi$
$809$	−6.79371			−0.238854			−0.119427	+	0.992843i	$0.538106\pi$
$810$	0.0175475	−	0.0114163i	0.000616558	−	0.000401128i
$811$	10.6600			0.374324			0.187162	−	0.982329i	$-0.440071\pi$
$811$	10.6600			0.374324			0.187162	+	0.982329i	$0.440071\pi$
$812$		−	19.8851i		−	0.697829i
$813$			20.6339i			0.723664i
$814$	0.0685921			0.00240415
$815$	32.0545	−	20.8544i	1.12282	−	0.730498i
$816$	27.5986			0.966143
$817$		0			0
$818$		−	3.35544i		−	0.117320i
$819$	14.3366			0.500962
$820$	−4.24781	−	6.52914i	−0.148340	−	0.228008i
$821$	20.7381			0.723766			0.361883	−	0.932224i	$-0.382134\pi$
$821$	20.7381			0.723766			0.361883	+	0.932224i	$0.382134\pi$
$822$			0.314126i			0.0109564i
$823$			13.9819i			0.487377i	0.969854	+	0.243689i	$0.0783575\pi$
$823$			13.9819i			0.487377i	−0.969854	+	0.243689i	$0.921643\pi$
$824$	6.09840			0.212448
$825$	1.54718	+	0.685761i	0.0538658	+	0.0238751i
$826$	2.15784			0.0750807
$827$			33.1980i			1.15441i	0.816601	+	0.577203i	$0.195856\pi$
$827$			33.1980i			1.15441i	−0.816601	+	0.577203i	$0.804144\pi$
$828$		−	21.8448i		−	0.759159i
$829$	−8.68051			−0.301487			−0.150743	−	0.988573i	$-0.548167\pi$
$829$	−8.68051			−0.301487			−0.150743	+	0.988573i	$0.548167\pi$
$830$	0.514071	+	0.790158i	0.0178437	+	0.0274268i
$831$	−22.3772			−0.776257
$832$		−	39.7727i		−	1.37887i
$833$		−	30.9423i		−	1.07209i
$834$	0.244780			0.00847604
$835$	1.69464	−	1.10252i	0.0586455	−	0.0381543i
$836$		0			0
$837$		−	36.5521i		−	1.26342i
$838$			4.36249i			0.150700i
$839$	−12.2248			−0.422049			−0.211024	−	0.977481i	$-0.567680\pi$
$839$	−12.2248			−0.422049			−0.211024	+	0.977481i	$0.567680\pi$
$840$	1.37413	−	0.894001i	0.0474121	−	0.0308460i
$841$	15.1791			0.523418
$842$			3.64728i			0.125693i
$843$		−	14.9282i		−	0.514154i
$844$	−43.1225			−1.48434
$845$	16.7447	+	25.7377i	0.576037	+	0.885403i
$846$	−0.165995			−0.00570703
$847$		−	16.4121i		−	0.563926i
$848$		−	24.2092i		−	0.831348i
$849$	−27.6310			−0.948293
$850$	1.50307	−	3.39114i	0.0515548	−	0.116315i
$851$	−11.4709			−0.393218
$852$			4.91222i			0.168290i
$853$			19.6824i			0.673911i	0.941521	+	0.336956i	$0.109397\pi$
$853$			19.6824i			0.673911i	−0.941521	+	0.336956i	$0.890603\pi$
$854$	1.30134			0.0445310
$855$		0			0
$856$	−4.51559			−0.154340
$857$		−	45.3053i		−	1.54760i	−0.633430	−	0.773800i	$-0.718354\pi$
$857$		−	45.3053i		−	1.54760i	0.633430	−	0.773800i	$-0.281646\pi$
$858$			0.198596i			0.00677997i
$859$	−31.1076			−1.06138			−0.530689	−	0.847567i	$-0.678067\pi$
$859$	−31.1076			−1.06138			−0.530689	+	0.847567i	$0.678067\pi$
$860$	−0.351373	+	0.228601i	−0.0119817	+	0.00779523i
$861$	−2.84040			−0.0968006
$862$			0.377590i			0.0128608i
$863$			41.0858i			1.39858i	0.714839	+	0.699289i	$0.246500\pi$
$863$			41.0858i			1.39858i	−0.714839	+	0.699289i	$0.753500\pi$
$864$	7.03528			0.239345
$865$	−19.7795	+	12.8684i	−0.672523	+	0.437538i
$866$	−0.545740			−0.0185450
$867$		−	27.6947i		−	0.940561i
$868$		−	20.9860i		−	0.712311i
$869$	2.61116			0.0885777
$870$	0.989904	+	1.52154i	0.0335609	+	0.0515851i
$871$	75.2283			2.54901
$872$		−	3.70182i		−	0.125360i
$873$		−	11.8659i		−	0.401601i
$874$		0			0
$875$	2.67472	+	16.6186i	0.0904222	+	0.561813i
$876$	18.2585			0.616897
$877$			12.1276i			0.409520i	0.978812	+	0.204760i	$0.0656414\pi$
$877$			12.1276i			0.409520i	−0.978812	+	0.204760i	$0.934359\pi$
$878$			0.282098i			0.00952036i
$879$	23.0028			0.775865
$880$	1.50446	+	2.31244i	0.0507152	+	0.0779524i
$881$	−35.6584			−1.20136			−0.600680	−	0.799489i	$-0.705104\pi$
$881$	−35.6584			−1.20136			−0.600680	+	0.799489i	$0.705104\pi$
$882$		−	0.989336i		−	0.0333127i
$883$			1.13310i			0.0381318i	0.999818	+	0.0190659i	$0.00606923\pi$
$883$			1.13310i			0.0381318i	−0.999818	+	0.0190659i	$0.993931\pi$
$884$	−67.1620			−2.25890
$885$	25.4755	−	16.5741i	0.856348	−	0.557134i
$886$	0.596036			0.0200242
$887$			12.9644i			0.435301i	0.976027	+	0.217650i	$0.0698392\pi$
$887$			12.9644i			0.435301i	−0.976027	+	0.217650i	$0.930161\pi$
$888$		−	0.935848i		−	0.0314050i
$889$	27.9657			0.937940
$890$	−0.589958	+	0.383822i	−0.0197754	+	0.0128657i
$891$	0.0259453			0.000869201
$892$			20.6575i			0.691664i
$893$		0			0
$894$	−1.03773			−0.0347067
$895$	3.10174	+	4.76756i	0.103680	+	0.159362i
$896$	5.37975			0.179725
$897$		−	33.2120i		−	1.10892i
$898$		−	2.68261i		−	0.0895197i
$899$	46.6251			1.55503
$900$	−7.41510	+	16.7295i	−0.247170	+	0.557651i
$901$	−40.3422			−1.34399
$902$			0.0625680i			0.00208329i
$903$			0.152860i			0.00508685i
$904$	6.40416			0.212999
$905$	−7.66710	−	11.7848i	−0.254863	−	0.391740i
$906$	1.96875			0.0654073
$907$		−	8.58894i		−	0.285191i	−0.989781	−	0.142596i	$-0.954455\pi$
$907$		−	8.58894i		−	0.285191i	0.989781	−	0.142596i	$-0.0455448\pi$
$908$			6.93048i			0.229996i
$909$	−17.4365			−0.578332
$910$	−1.65573	+	1.07720i	−0.0548868	+	0.0357089i
$911$	−22.6445			−0.750246			−0.375123	−	0.926975i	$-0.622400\pi$
$911$	−22.6445			−0.750246			−0.375123	+	0.926975i	$0.622400\pi$
$912$		0			0
$913$			1.16831i			0.0386653i
$914$	1.99491			0.0659856
$915$	15.3637	−	9.99548i	0.507907	−	0.330440i
$916$	−28.3001			−0.935063
$917$			27.5585i			0.910061i
$918$		−	3.86567i		−	0.127586i
$919$	20.0503			0.661397			0.330698	−	0.943736i	$-0.392716\pi$
$919$	20.0503			0.661397			0.330698	+	0.943736i	$0.392716\pi$
$920$	3.29332	+	5.06204i	0.108578	+	0.166890i
$921$	−32.2420			−1.06241
$922$		−	0.345028i		−	0.0113629i
$923$		−	11.8761i		−	0.390906i
$924$	1.01260			0.0333120
$925$	8.78483	+	3.89374i	0.288844	+	0.128025i
$926$	1.90303			0.0625374
$927$			24.8231i			0.815298i
$928$			8.97408i			0.294588i
$929$	−59.6067			−1.95563			−0.977815	−	0.209468i	$-0.932827\pi$
$929$	−59.6067			−1.95563			−0.977815	+	0.209468i	$0.932827\pi$
$930$	1.04471	+	1.60578i	0.0342574	+	0.0526557i
$931$		0			0
$932$			9.32010i			0.305290i
$933$		−	16.1493i		−	0.528703i
$934$	2.49481			0.0816326
$935$	3.85345	−	2.50702i	0.126021	−	0.0819884i
$936$	−4.30874			−0.140836
$937$		−	1.03896i		−	0.0339415i	−0.999856	−	0.0169707i	$-0.994598\pi$
$937$		−	1.03896i		−	0.0339415i	0.999856	−	0.0169707i	$-0.00540222\pi$
$938$			2.48599i			0.0811705i
$939$	−6.70324			−0.218752
$940$	−2.95790	+	1.92439i	−0.0964762	+	0.0627667i
$941$	−2.96197			−0.0965574			−0.0482787	−	0.998834i	$-0.515374\pi$
$941$	−2.96197			−0.0965574			−0.0482787	+	0.998834i	$0.515374\pi$
$942$		−	0.789945i		−	0.0257378i
$943$		−	10.4635i		−	0.340738i
$944$	49.5441			1.61252
$945$	9.56632	+	14.7040i	0.311192	+	0.478321i
$946$	0.00336717			0.000109476
$947$			21.4691i			0.697653i	0.937187	+	0.348826i	$0.113420\pi$
$947$			21.4691i			0.697653i	−0.937187	+	0.348826i	$0.886580\pi$
$948$		−	17.7554i		−	0.576669i
$949$	−44.1427			−1.43293
$950$		0			0
$951$	−27.2373			−0.883230
$952$		−	4.45325i		−	0.144331i
$953$		−	20.2543i		−	0.656101i	−0.944660	−	0.328051i	$-0.893608\pi$
$953$		−	20.2543i		−	0.656101i	0.944660	−	0.328051i	$-0.106392\pi$
$954$	−1.28989			−0.0417616
$955$	−27.6169	−	42.4489i	−0.893663	−	1.37361i
$956$	−22.7265			−0.735029
$957$			2.24971i			0.0727229i
$958$			2.02728i			0.0654984i
$959$	−3.87225			−0.125041
$960$	15.5170	−	10.0952i	0.500809	−	0.325823i
$961$	18.2065			0.587307
$962$			1.12763i			0.0363561i
$963$		−	18.3804i		−	0.592299i
$964$	47.5609			1.53183
$965$	16.3800	−	10.6567i	0.527290	−	0.343051i
$966$	1.09752			0.0353122
$967$		−	61.2295i		−	1.96901i	−0.175363	−	0.984504i	$-0.556110\pi$
$967$		−	61.2295i		−	1.96901i	0.175363	−	0.984504i	$-0.443890\pi$
$968$			4.93251i			0.158537i
$969$		0			0
$970$	0.891564	+	1.37039i	0.0286264	+	0.0440005i
$971$	21.6739			0.695550			0.347775	−	0.937578i	$-0.386937\pi$
$971$	21.6739			0.695550			0.347775	+	0.937578i	$0.386937\pi$
$972$			30.8868i			0.990693i
$973$			3.01742i			0.0967341i
$974$	1.25788			0.0403052
$975$	−11.2736	+	25.4350i	−0.361045	+	0.814571i
$976$	29.8789			0.956400
$977$			22.5832i			0.722499i	0.932469	+	0.361250i	$0.117650\pi$
$977$			22.5832i			0.722499i	−0.932469	+	0.361250i	$0.882350\pi$
$978$			2.08873i			0.0667901i
$979$	−0.872296			−0.0278787
$980$	−11.4694	−	17.6292i	−0.366377	−	0.563144i
$981$	15.0680			0.481084
$982$			1.09080i			0.0348089i
$983$			4.45933i			0.142231i	0.997468	+	0.0711153i	$0.0226558\pi$
$983$			4.45933i			0.142231i	−0.997468	+	0.0711153i	$0.977344\pi$
$984$	0.853658			0.0272136
$985$	37.4747	−	24.3807i	1.19404	−	0.776835i
$986$	4.93097			0.157034
$987$			1.28679i			0.0409590i
$988$		0			0
$989$	−0.563104			−0.0179057
$990$	0.123209	−	0.0801586i	0.00391583	−	0.00254761i
$991$	24.5724			0.780568			0.390284	−	0.920695i	$-0.372377\pi$
$991$	24.5724			0.780568			0.390284	+	0.920695i	$0.372377\pi$
$992$			9.47093i			0.300702i
$993$			22.4492i			0.712403i
$994$	0.392456			0.0124480
$995$	3.50218	+	5.38306i	0.111027	+	0.170654i
$996$	7.94426			0.251723
$997$			37.5241i			1.18840i	0.804318	+	0.594199i	$0.202531\pi$
$997$			37.5241i			1.18840i	−0.804318	+	0.594199i	$0.797469\pi$
$998$		−	0.391715i		−	0.0123995i
$999$	10.0141			0.316832

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1805.2.b.m.1084.19	✓	40
5.2	odd	4		9025.2.a.cv.1.21		40
5.3	odd	4		9025.2.a.cv.1.20		40
5.4	even	2	inner	1805.2.b.m.1084.22	yes	40
19.18	odd	2	inner	1805.2.b.m.1084.21	yes	40
95.18	even	4		9025.2.a.cv.1.22		40
95.37	even	4		9025.2.a.cv.1.19		40
95.94	odd	2	inner	1805.2.b.m.1084.20	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1805.2.b.m.1084.19	✓	40	1.1	even	1	trivial
1805.2.b.m.1084.20	yes	40	95.94	odd	2	inner
1805.2.b.m.1084.21	yes	40	19.18	odd	2	inner
1805.2.b.m.1084.22	yes	40	5.4	even	2	inner
9025.2.a.cv.1.19		40	95.37	even	4
9025.2.a.cv.1.20		40	5.3	odd	4
9025.2.a.cv.1.21		40	5.2	odd	4
9025.2.a.cv.1.22		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)

\(f(q)\)	\(=\)	\(q-0.113485i q^{2} +1.07621i q^{3} +1.98712 q^{4} +(-1.21941 - 1.87431i) q^{5} +0.122133 q^{6} +1.50555i q^{7} -0.452479i q^{8} +1.84178 q^{9} +O(q^{10})\)	\(q-0.113485i q^{2} +1.07621i q^{3} +1.98712 q^{4} +(-1.21941 - 1.87431i) q^{5} +0.122133 q^{6} +1.50555i q^{7} -0.452479i q^{8} +1.84178 q^{9} +(-0.212706 + 0.138385i) q^{10} -0.314502 q^{11} +2.13855i q^{12} -5.17028i q^{13} +0.170857 q^{14} +(2.01714 - 1.31234i) q^{15} +3.92289 q^{16} -6.53710i q^{17} -0.209015i q^{18} +(-2.42312 - 3.72448i) q^{20} -1.62028 q^{21} +0.0356913i q^{22} -5.96878i q^{23} +0.486960 q^{24} +(-2.02607 + 4.57111i) q^{25} -0.586750 q^{26} +5.21075i q^{27} +2.99170i q^{28} -6.64674 q^{29} +(-0.148931 - 0.228916i) q^{30} -7.01474 q^{31} -1.35015i q^{32} -0.338469i q^{33} -0.741863 q^{34} +(2.82186 - 1.83588i) q^{35} +3.65984 q^{36} -1.92182i q^{37} +5.56429 q^{39} +(-0.848085 + 0.551758i) q^{40} +1.75303 q^{41} +0.183877i q^{42} -0.0943416i q^{43} -0.624953 q^{44} +(-2.24589 - 3.45207i) q^{45} -0.677368 q^{46} -0.794179i q^{47} +4.22184i q^{48} +4.73333 q^{49} +(0.518753 + 0.229929i) q^{50} +7.03526 q^{51} -10.2740i q^{52} -6.17127i q^{53} +0.591343 q^{54} +(0.383507 + 0.589474i) q^{55} +0.681228 q^{56} +0.754306i q^{58} +12.6295 q^{59} +(4.00831 - 2.60777i) q^{60} +7.61655 q^{61} +0.796068i q^{62} +2.77289i q^{63} +7.69256 q^{64} +(-9.69071 + 6.30470i) q^{65} -0.0384111 q^{66} +14.5501i q^{67} -12.9900i q^{68} +6.42364 q^{69} +(-0.208345 - 0.320239i) q^{70} +2.29699 q^{71} -0.833367i q^{72} -8.53778i q^{73} -0.218098 q^{74} +(-4.91945 - 2.18047i) q^{75} -0.473497i q^{77} -0.631464i q^{78} -8.30254 q^{79} +(-4.78362 - 7.35271i) q^{80} -0.0824966 q^{81} -0.198943i q^{82} -3.71479i q^{83} -3.21969 q^{84} +(-12.2525 + 7.97141i) q^{85} -0.0107064 q^{86} -7.15326i q^{87} +0.142305i q^{88} +2.77358 q^{89} +(-0.391758 + 0.254875i) q^{90} +7.78410 q^{91} -11.8607i q^{92} -7.54930i q^{93} -0.0901275 q^{94} +1.45304 q^{96} -6.44264i q^{97} -0.537163i q^{98} -0.579244 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 48 q^{4} + 6 q^{5} + 20 q^{6} - 52 q^{9}+O(q^{10}) \) 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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