LMFDB - Embedded newform 1045.2.f.b.626.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1045,2,Mod(626,1045)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1045, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1045.626");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1045 = 5 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1045.f (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:	$8.34436701122$
Analytic rank:	$0$
Dimension:	$40$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			626.16
Character	$\chi$	$=$	1045.626
Dual form			1045.2.f.b.626.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.863466 q^{2} +0.924425i q^{3} -1.25443 q^{4} +1.00000 q^{5} -0.798209i q^{6} +0.285490i q^{7} +2.81009 q^{8} +2.14544 q^{9} +O(q^{10})$	\(q-0.863466 q^{2} +0.924425i q^{3} -1.25443 q^{4} +1.00000 q^{5} -0.798209i q^{6} +0.285490i q^{7} +2.81009 q^{8} +2.14544 q^{9} -0.863466 q^{10} +(0.818744 + 3.21398i) q^{11} -1.15962i q^{12} -0.419046 q^{13} -0.246510i q^{14} +0.924425i q^{15} +0.0824425 q^{16} -2.73616i q^{17} -1.85251 q^{18} +(-2.97108 - 3.18946i) q^{19} -1.25443 q^{20} -0.263914 q^{21} +(-0.706957 - 2.77516i) q^{22} +7.54111 q^{23} +2.59771i q^{24} +1.00000 q^{25} +0.361832 q^{26} +4.75657i q^{27} -0.358126i q^{28} -2.67264 q^{29} -0.798209i q^{30} -3.45730i q^{31} -5.69136 q^{32} +(-2.97108 + 0.756867i) q^{33} +2.36258i q^{34} +0.285490i q^{35} -2.69130 q^{36} +1.21456i q^{37} +(2.56543 + 2.75399i) q^{38} -0.387377i q^{39} +2.81009 q^{40} +9.74248 q^{41} +0.227880 q^{42} +0.0617565i q^{43} +(-1.02705 - 4.03170i) q^{44} +2.14544 q^{45} -6.51149 q^{46} +2.51294 q^{47} +0.0762119i q^{48} +6.91850 q^{49} -0.863466 q^{50} +2.52937 q^{51} +0.525663 q^{52} +10.1781i q^{53} -4.10714i q^{54} +(0.818744 + 3.21398i) q^{55} +0.802250i q^{56} +(2.94842 - 2.74654i) q^{57} +2.30773 q^{58} +8.40673i q^{59} -1.15962i q^{60} +2.63798i q^{61} +2.98526i q^{62} +0.612500i q^{63} +4.74941 q^{64} -0.419046 q^{65} +(2.56543 - 0.653529i) q^{66} +11.1802i q^{67} +3.43231i q^{68} +6.97119i q^{69} -0.246510i q^{70} -2.61887i q^{71} +6.02886 q^{72} +7.15415i q^{73} -1.04873i q^{74} +0.924425i q^{75} +(3.72701 + 4.00095i) q^{76} +(-0.917557 + 0.233743i) q^{77} +0.334487i q^{78} -10.9113 q^{79} +0.0824425 q^{80} +2.03922 q^{81} -8.41230 q^{82} +14.5167i q^{83} +0.331061 q^{84} -2.73616i q^{85} -0.0533246i q^{86} -2.47066i q^{87} +(2.30074 + 9.03156i) q^{88} -13.9172i q^{89} -1.85251 q^{90} -0.119633i q^{91} -9.45977 q^{92} +3.19602 q^{93} -2.16984 q^{94} +(-2.97108 - 3.18946i) q^{95} -5.26123i q^{96} -19.2960i q^{97} -5.97388 q^{98} +(1.75656 + 6.89539i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 40 q^{4} + 40 q^{5} - 28 q^{9}+O(q^{10}) $ 40 * q + 40 * q^4 + 40 * q^5 - 28 * q^9	$ 40 q + 40 q^{4} + 40 q^{5} - 28 q^{9} - 4 q^{11} + 48 q^{16} + 40 q^{20} + 24 q^{23} + 40 q^{25} - 24 q^{26} + 24 q^{36} - 28 q^{38} - 60 q^{42} - 48 q^{44} - 28 q^{45} - 36 q^{49} - 4 q^{55} - 36 q^{58} - 40 q^{64} - 28 q^{66} + 8 q^{77} + 48 q^{80} + 80 q^{81} + 8 q^{82} + 4 q^{92} + 56 q^{93} - 16 q^{99}+O(q^{100}) $ 40 * q + 40 * q^4 + 40 * q^5 - 28 * q^9 - 4 * q^11 + 48 * q^16 + 40 * q^20 + 24 * q^23 + 40 * q^25 - 24 * q^26 + 24 * q^36 - 28 * q^38 - 60 * q^42 - 48 * q^44 - 28 * q^45 - 36 * q^49 - 4 * q^55 - 36 * q^58 - 40 * q^64 - 28 * q^66 + 8 * q^77 + 48 * q^80 + 80 * q^81 + 8 * q^82 + 4 * q^92 + 56 * q^93 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1045\mathbb{Z}\right)^\times$.

$n$	$496$	$761$	$837$
$\chi(n)$	$-1$	$-1$	$1$

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 $

$2$	−0.863466			−0.610562			−0.305281	−	0.952262i	$-0.598750\pi$
$2$	−0.863466			−0.610562			−0.305281	+	0.952262i	$0.598750\pi$
$3$			0.924425i			0.533717i	0.963736	+	0.266859i	$0.0859857\pi$
$3$			0.924425i			0.533717i	−0.963736	+	0.266859i	$0.914014\pi$
$4$	−1.25443			−0.627214
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$		−	0.798209i		−	0.325868i
$7$			0.285490i			0.107905i	0.998544	+	0.0539525i	$0.0171819\pi$
$7$			0.285490i			0.107905i	−0.998544	+	0.0539525i	$0.982818\pi$
$8$	2.81009			0.993515
$9$	2.14544			0.715146
$10$	−0.863466			−0.273052
$11$	0.818744	+	3.21398i	0.246860	+	0.969051i
$11$	0.818744	+	3.21398i	0.246860	+	0.969051i
$12$		−	1.15962i		−	0.334755i
$13$	−0.419046			−0.116223			−0.0581113	−	0.998310i	$-0.518508\pi$
$13$	−0.419046			−0.116223			−0.0581113	+	0.998310i	$0.518508\pi$
$14$		−	0.246510i		−	0.0658827i
$15$			0.924425i			0.238686i
$16$	0.0824425			0.0206106
$17$		−	2.73616i		−	0.663616i	−0.943347	−	0.331808i	$-0.892341\pi$
$17$		−	2.73616i		−	0.663616i	0.943347	−	0.331808i	$-0.107659\pi$
$18$	−1.85251			−0.436641
$19$	−2.97108	−	3.18946i	−0.681613	−	0.731713i
$19$	−2.97108	−	3.18946i	−0.681613	−	0.731713i
$20$	−1.25443			−0.280498
$21$	−0.263914			−0.0575907
$22$	−0.706957	−	2.77516i	−0.150724	−	0.591666i
$23$	7.54111			1.57243			0.786215	−	0.617953i	$-0.212038\pi$
$23$	7.54111			1.57243			0.786215	+	0.617953i	$0.212038\pi$
$24$			2.59771i			0.530256i
$25$	1.00000			0.200000
$26$	0.361832			0.0709611
$27$			4.75657i			0.915403i
$28$		−	0.358126i		−	0.0676794i
$29$	−2.67264			−0.496297			−0.248148	−	0.968722i	$-0.579822\pi$
$29$	−2.67264			−0.496297			−0.248148	+	0.968722i	$0.579822\pi$
$30$		−	0.798209i		−	0.145732i
$31$		−	3.45730i		−	0.620950i	−0.950582	−	0.310475i	$-0.899512\pi$
$31$		−	3.45730i		−	0.620950i	0.950582	−	0.310475i	$-0.100488\pi$
$32$	−5.69136			−1.00610
$33$	−2.97108	+	0.756867i	−0.517199	+	0.131754i
$34$			2.36258i			0.405179i
$35$			0.285490i			0.0482566i
$36$	−2.69130			−0.448549
$37$			1.21456i			0.199672i	0.995004	+	0.0998359i	$0.0318318\pi$
$37$			1.21456i			0.199672i	−0.995004	+	0.0998359i	$0.968168\pi$
$38$	2.56543	+	2.75399i	0.416167	+	0.446756i
$39$		−	0.387377i		−	0.0620300i
$40$	2.81009			0.444314
$41$	9.74248			1.52152			0.760760	−	0.649033i	$-0.224826\pi$
$41$	9.74248			1.52152			0.760760	+	0.649033i	$0.224826\pi$
$42$	0.227880			0.0351627
$43$			0.0617565i			0.00941777i	0.999989	+	0.00470889i	$0.00149889\pi$
$43$			0.0617565i			0.00941777i	−0.999989	+	0.00470889i	$0.998501\pi$
$44$	−1.02705	−	4.03170i	−0.154834	−	0.607802i
$45$	2.14544			0.319823
$46$	−6.51149			−0.960066
$47$	2.51294			0.366550			0.183275	−	0.983062i	$-0.441330\pi$
$47$	2.51294			0.366550			0.183275	+	0.983062i	$0.441330\pi$
$48$			0.0762119i			0.0110002i
$49$	6.91850			0.988357
$50$	−0.863466			−0.122112
$51$	2.52937			0.354183
$52$	0.525663			0.0728964
$53$			10.1781i			1.39807i	0.715088	+	0.699034i	$0.246386\pi$
$53$			10.1781i			1.39807i	−0.715088	+	0.699034i	$0.753614\pi$
$54$		−	4.10714i		−	0.558910i
$55$	0.818744	+	3.21398i	0.110399	+	0.433373i
$56$			0.802250i			0.107205i
$57$	2.94842	−	2.74654i	0.390528	−	0.363789i
$58$	2.30773			0.303020
$59$			8.40673i			1.09446i	0.836981	+	0.547232i	$0.184318\pi$
$59$			8.40673i			1.09446i	−0.836981	+	0.547232i	$0.815682\pi$
$60$		−	1.15962i		−	0.149707i
$61$			2.63798i			0.337758i	0.985637	+	0.168879i	$0.0540147\pi$
$61$			2.63798i			0.337758i	−0.985637	+	0.168879i	$0.945985\pi$
$62$			2.98526i			0.379128i
$63$			0.612500i			0.0771678i
$64$	4.74941			0.593676
$65$	−0.419046			−0.0519763
$66$	2.56543	−	0.653529i	0.315782	−	0.0804438i
$67$			11.1802i			1.36587i	0.730477	+	0.682937i	$0.239298\pi$
$67$			11.1802i			1.36587i	−0.730477	+	0.682937i	$0.760702\pi$
$68$			3.43231i			0.416229i
$69$			6.97119i			0.839233i
$70$		−	0.246510i		−	0.0294636i
$71$		−	2.61887i		−	0.310803i	−0.987851	−	0.155401i	$-0.950333\pi$
$71$		−	2.61887i		−	0.310803i	0.987851	−	0.155401i	$-0.0496671\pi$
$72$	6.02886			0.710509
$73$			7.15415i			0.837330i	0.908141	+	0.418665i	$0.137502\pi$
$73$			7.15415i			0.837330i	−0.908141	+	0.418665i	$0.862498\pi$
$74$		−	1.04873i		−	0.121912i
$75$			0.924425i			0.106743i
$76$	3.72701	+	4.00095i	0.427517	+	0.458940i
$77$	−0.917557	+	0.233743i	−0.104565	+	0.0266375i
$78$			0.334487i			0.0378732i
$79$	−10.9113			−1.22762			−0.613811	−	0.789453i	$-0.710364\pi$
$79$	−10.9113			−1.22762			−0.613811	+	0.789453i	$0.710364\pi$
$80$	0.0824425			0.00921735
$81$	2.03922			0.226580
$82$	−8.41230			−0.928983
$83$			14.5167i			1.59342i	0.604363	+	0.796709i	$0.293428\pi$
$83$			14.5167i			1.59342i	−0.604363	+	0.796709i	$0.706572\pi$
$84$	0.331061			0.0361217
$85$		−	2.73616i		−	0.296778i
$86$		−	0.0533246i		−	0.00575014i
$87$		−	2.47066i		−	0.264882i
$88$	2.30074	+	9.03156i	0.245260	+	0.962767i
$89$		−	13.9172i		−	1.47522i	−0.675226	−	0.737611i	$-0.735954\pi$
$89$		−	13.9172i		−	1.47522i	0.675226	−	0.737611i	$-0.264046\pi$
$90$	−1.85251			−0.195272
$91$		−	0.119633i		−	0.0125410i
$92$	−9.45977			−0.986249
$93$	3.19602			0.331411
$94$	−2.16984			−0.223802
$95$	−2.97108	−	3.18946i	−0.304827	−	0.327232i
$96$		−	5.26123i		−	0.536973i
$97$		−	19.2960i		−	1.95922i	−0.200920	−	0.979608i	$-0.564393\pi$
$97$		−	19.2960i		−	1.95922i	0.200920	−	0.979608i	$-0.435607\pi$
$98$	−5.97388			−0.603453
$99$	1.75656	+	6.89539i	0.176541	+	0.693013i
$100$	−1.25443			−0.125443
$101$			6.27231i			0.624119i	0.950063	+	0.312059i	$0.101019\pi$
$101$			6.27231i			0.624119i	−0.950063	+	0.312059i	$0.898981\pi$
$102$	−2.18403			−0.216251
$103$			13.7149i			1.35137i	0.737191	+	0.675684i	$0.236152\pi$
$103$			13.7149i			1.35137i	−0.737191	+	0.675684i	$0.763848\pi$
$104$	−1.17756			−0.115469
$105$	−0.263914			−0.0257553
$106$		−	8.78843i		−	0.853608i
$107$	−3.57005			−0.345130			−0.172565	−	0.984998i	$-0.555205\pi$
$107$	−3.57005			−0.345130			−0.172565	+	0.984998i	$0.555205\pi$
$108$		−	5.96677i		−	0.574153i
$109$	9.85614			0.944047			0.472024	−	0.881586i	$-0.343524\pi$
$109$	9.85614			0.944047			0.472024	+	0.881586i	$0.343524\pi$
$110$	−0.706957	−	2.77516i	−0.0674057	−	0.264601i
$111$	−1.12277			−0.106568
$112$			0.0235365i			0.00222399i
$113$			4.11217i			0.386840i	0.981116	+	0.193420i	$0.0619580\pi$
$113$			4.11217i			0.386840i	−0.981116	+	0.193420i	$0.938042\pi$
$114$	−2.54586	+	2.37155i	−0.238441	+	0.222116i
$115$	7.54111			0.703212
$116$	3.35263			0.311284
$117$	−0.899038			−0.0831161
$118$		−	7.25892i		−	0.668238i
$119$	0.781144			0.0716074
$120$			2.59771i			0.237138i
$121$	−9.65932	+	5.26285i	−0.878120	+	0.478441i
$122$		−	2.27780i		−	0.206222i
$123$			9.00620i			0.812061i
$124$			4.33693i			0.389468i
$125$	1.00000			0.0894427
$126$		−	0.528873i		−	0.0471157i
$127$	18.2607			1.62037			0.810187	−	0.586171i	$-0.199365\pi$
$127$	18.2607			1.62037			0.810187	+	0.586171i	$0.199365\pi$
$128$	7.28177			0.643623
$129$	−0.0570892			−0.00502643
$130$	0.361832			0.0317348
$131$		−	11.0127i		−	0.962180i	−0.876671	−	0.481090i	$-0.840241\pi$
$131$		−	11.0127i		−	0.962180i	0.876671	−	0.481090i	$-0.159759\pi$
$132$	3.72701	−	0.949435i	0.324394	−	0.0826377i
$133$	0.910558	−	0.848213i	0.0789554	−	0.0735494i
$134$		−	9.65369i		−	0.833951i
$135$			4.75657i			0.409381i
$136$		−	7.68884i		−	0.659312i
$137$	0.163904			0.0140033			0.00700164	−	0.999975i	$-0.497771\pi$
$137$	0.163904			0.0140033			0.00700164	+	0.999975i	$0.497771\pi$
$138$		−	6.01938i		−	0.512404i
$139$			16.5377i			1.40271i	0.712812	+	0.701355i	$0.247421\pi$
$139$			16.5377i			1.40271i	−0.712812	+	0.701355i	$0.752579\pi$
$140$		−	0.358126i		−	0.0302672i
$141$			2.32303i			0.195634i
$142$			2.26131i			0.189765i
$143$	−0.343091	−	1.34681i	−0.0286908	−	0.112626i
$144$	0.176875			0.0147396
$145$	−2.67264			−0.221951
$146$		−	6.17736i		−	0.511242i
$147$			6.39563i			0.527503i
$148$		−	1.52357i		−	0.125237i
$149$		−	17.8869i		−	1.46535i	−0.680577	−	0.732676i	$-0.738271\pi$
$149$		−	17.8869i		−	1.46535i	0.680577	−	0.732676i	$-0.261729\pi$
$150$		−	0.798209i		−	0.0651735i
$151$	3.24652			0.264198			0.132099	−	0.991237i	$-0.457828\pi$
$151$	3.24652			0.264198			0.132099	+	0.991237i	$0.457828\pi$
$152$	−8.34900	−	8.96266i	−0.677193	−	0.726968i
$153$		−	5.87025i		−	0.474582i
$154$	0.792279	−	0.201829i	0.0638437	−	0.0162638i
$155$		−	3.45730i		−	0.277697i
$156$			0.485936i			0.0389060i
$157$	−15.5202			−1.23865			−0.619323	−	0.785136i	$-0.712593\pi$
$157$	−15.5202			−1.23865			−0.619323	+	0.785136i	$0.712593\pi$
$158$	9.42156			0.749539
$159$	−9.40888			−0.746173
$160$	−5.69136			−0.449941
$161$			2.15291i			0.169673i
$162$	−1.76079			−0.138341
$163$	20.4847			1.60448			0.802241	−	0.597000i	$-0.203641\pi$
$163$	20.4847			1.60448			0.802241	+	0.597000i	$0.203641\pi$
$164$	−12.2212			−0.954318
$165$	−2.97108	+	0.756867i	−0.231299	+	0.0589220i
$166$		−	12.5347i		−	0.972881i
$167$	−8.05481			−0.623300			−0.311650	−	0.950197i	$-0.600882\pi$
$167$	−8.05481			−0.623300			−0.311650	+	0.950197i	$0.600882\pi$
$168$	−0.741620			−0.0572173
$169$	−12.8244			−0.986492
$170$			2.36258i			0.181201i
$171$	−6.37427	−	6.84279i	−0.487453	−	0.523281i
$172$		−	0.0774690i		−	0.00590696i
$173$	13.5272			1.02846			0.514228	−	0.857653i	$-0.328078\pi$
$173$	13.5272			1.02846			0.514228	+	0.857653i	$0.328078\pi$
$174$			2.13333i			0.161727i
$175$			0.285490i			0.0215810i
$176$	0.0674993	+	0.264968i	0.00508795	+	0.0199727i
$177$	−7.77140			−0.584134
$178$			12.0170i			0.900715i
$179$		−	15.9692i		−	1.19360i	−0.802391	−	0.596799i	$-0.796439\pi$
$179$		−	15.9692i		−	1.19360i	0.802391	−	0.596799i	$-0.203561\pi$
$180$	−2.69130			−0.200597
$181$		−	21.9473i		−	1.63133i	−0.578523	−	0.815666i	$-0.696371\pi$
$181$		−	21.9473i		−	1.63133i	0.578523	−	0.815666i	$-0.303629\pi$
$182$			0.103299i			0.00765705i
$183$	−2.43861			−0.180267
$184$	21.1912			1.56223
$185$			1.21456i			0.0892960i
$186$	−2.75965			−0.202347
$187$	8.79395	−	2.24021i	0.643077	−	0.163820i
$188$	−3.15230			−0.229905
$189$	−1.35795			−0.0987765
$190$	2.56543	+	2.75399i	0.186116	+	0.199795i
$191$	−14.9039			−1.07841			−0.539205	−	0.842174i	$-0.681275\pi$
$191$	−14.9039			−1.07841			−0.539205	+	0.842174i	$0.681275\pi$
$192$			4.39047i			0.316855i
$193$	14.3290			1.03142			0.515710	−	0.856763i	$-0.327528\pi$
$193$	14.3290			1.03142			0.515710	+	0.856763i	$0.327528\pi$
$194$			16.6615i			1.19622i
$195$		−	0.387377i		−	0.0277406i
$196$	−8.67875			−0.619911
$197$			21.3998i			1.52467i	0.647182	+	0.762336i	$0.275947\pi$
$197$			21.3998i			1.52467i	−0.647182	+	0.762336i	$0.724053\pi$
$198$	−1.51673	−	5.95393i	−0.107789	−	0.423128i
$199$	5.35992			0.379955			0.189977	−	0.981788i	$-0.439159\pi$
$199$	5.35992			0.379955			0.189977	+	0.981788i	$0.439159\pi$
$200$	2.81009			0.198703
$201$	−10.3352			−0.728991
$202$		−	5.41593i		−	0.381063i
$203$		−	0.763011i		−	0.0535529i
$204$	−3.17291			−0.222148
$205$	9.74248			0.680444
$206$		−	11.8423i		−	0.825095i
$207$	16.1790			1.12452
$208$	−0.0345472			−0.00239542
$209$	7.81831	−	12.1603i	0.540804	−	0.841149i
$210$	0.227880			0.0157252
$211$	16.0790			1.10692			0.553462	−	0.832875i	$-0.313307\pi$
$211$	16.0790			1.10692			0.553462	+	0.832875i	$0.313307\pi$
$212$		−	12.7677i		−	0.876888i
$213$	2.42095			0.165881
$214$	3.08262			0.210723
$215$			0.0617565i			0.00421176i
$216$			13.3664i			0.909467i
$217$	0.987023			0.0670035
$218$	−8.51044			−0.576400
$219$	−6.61348			−0.446898
$220$	−1.02705	−	4.03170i	−0.0692440	−	0.271817i
$221$			1.14658i			0.0771271i
$222$	0.969470			0.0650666
$223$			23.7630i			1.59129i	0.605765	+	0.795644i	$0.292867\pi$
$223$			23.7630i			1.59129i	−0.605765	+	0.795644i	$0.707133\pi$
$224$		−	1.62482i		−	0.108563i
$225$	2.14544			0.143029
$226$		−	3.55071i		−	0.236190i
$227$	−3.25234			−0.215865			−0.107933	−	0.994158i	$-0.534423\pi$
$227$	−3.25234			−0.215865			−0.107933	+	0.994158i	$0.534423\pi$
$228$	−3.69858	+	3.44534i	−0.244944	+	0.228173i
$229$	−14.7762			−0.976439			−0.488219	−	0.872721i	$-0.662353\pi$
$229$	−14.7762			−0.976439			−0.488219	+	0.872721i	$0.662353\pi$
$230$	−6.51149			−0.429355
$231$	−0.216078	−	0.848213i	−0.0142169	−	0.0558083i
$232$	−7.51035			−0.493078
$233$		−	25.4229i		−	1.66551i	−0.553644	−	0.832753i	$-0.686763\pi$
$233$		−	25.4229i		−	1.66551i	0.553644	−	0.832753i	$-0.313237\pi$
$234$	0.776288			0.0507475
$235$	2.51294			0.163926
$236$		−	10.5456i		−	0.686462i
$237$		−	10.0867i		−	0.655202i
$238$	−0.674491			−0.0437208
$239$		−	27.3076i		−	1.76638i	−0.469011	−	0.883192i	$-0.655390\pi$
$239$		−	27.3076i		−	1.76638i	0.469011	−	0.883192i	$-0.344610\pi$
$240$			0.0762119i			0.00491946i
$241$	−25.9387			−1.67086			−0.835429	−	0.549598i	$-0.814781\pi$
$241$	−25.9387			−1.67086			−0.835429	+	0.549598i	$0.814781\pi$
$242$	8.34049	−	4.54429i	0.536147	−	0.292118i
$243$			16.1548i			1.03633i
$244$		−	3.30915i		−	0.211847i
$245$	6.91850			0.442006
$246$		−	7.77654i		−	0.495814i
$247$	1.24502	+	1.33653i	0.0792188	+	0.0850415i
$248$		−	9.71531i		−	0.616923i
$249$	−13.4196			−0.850435
$250$	−0.863466			−0.0546104
$251$	−25.4969			−1.60935			−0.804676	−	0.593715i	$-0.797661\pi$
$251$	−25.4969			−1.60935			−0.804676	+	0.593715i	$0.797661\pi$
$252$		−	0.768337i		−	0.0484007i
$253$	6.17423	+	24.2370i	0.388171	+	1.52376i
$254$	−15.7675			−0.989339
$255$	2.52937			0.158395
$256$	−15.7864			−0.986648
$257$		−	2.63088i		−	0.164110i	−0.996628	−	0.0820549i	$-0.973852\pi$
$257$		−	2.63088i		−	0.164110i	0.996628	−	0.0820549i	$-0.0261483\pi$
$258$	0.0492946			0.00306895
$259$	−0.346743			−0.0215456
$260$	0.525663			0.0326002
$261$	−5.73398			−0.354925
$262$			9.50905i			0.587471i
$263$			11.6130i			0.716088i	0.933705	+	0.358044i	$0.116556\pi$
$263$			11.6130i			0.716088i	−0.933705	+	0.358044i	$0.883444\pi$
$264$	−8.34900	+	2.12686i	−0.513845	+	0.130899i
$265$			10.1781i			0.625235i
$266$	−0.786236	+	0.732403i	−0.0482072	+	0.0449065i
$267$	12.8654			0.787351
$268$		−	14.0247i		−	0.856695i
$269$		−	22.7940i		−	1.38978i	−0.719118	−	0.694888i	$-0.755454\pi$
$269$		−	22.7940i		−	1.38978i	0.719118	−	0.694888i	$-0.244546\pi$
$270$		−	4.10714i		−	0.249952i
$271$			9.35459i			0.568251i	0.958787	+	0.284125i	$0.0917032\pi$
$271$			9.35459i			0.568251i	−0.958787	+	0.284125i	$0.908297\pi$
$272$		−	0.225576i		−	0.0136775i
$273$	0.110592			0.00669334
$274$	−0.141526			−0.00854988
$275$	0.818744	+	3.21398i	0.0493721	+	0.193810i
$276$		−	8.74485i		−	0.526378i
$277$		−	9.57982i		−	0.575595i	−0.957691	−	0.287798i	$-0.907077\pi$
$277$		−	9.57982i		−	0.575595i	0.957691	−	0.287798i	$-0.0929231\pi$
$278$		−	14.2797i		−	0.856442i
$279$		−	7.41742i		−	0.444070i
$280$			0.802250i			0.0479436i
$281$	23.3350			1.39205			0.696026	−	0.718017i	$-0.254950\pi$
$281$	23.3350			1.39205			0.696026	+	0.718017i	$0.254950\pi$
$282$		−	2.00585i		−	0.119447i
$283$		−	32.5616i		−	1.93559i	−0.251749	−	0.967793i	$-0.581006\pi$
$283$		−	32.5616i		−	1.93559i	0.251749	−	0.967793i	$-0.418994\pi$
$284$			3.28519i			0.194940i
$285$	2.94842	−	2.74654i	0.174649	−	0.162691i
$286$	0.296248	+	1.16292i	0.0175175	+	0.0687649i
$287$			2.78138i			0.164179i
$288$	−12.2105			−0.719508
$289$	9.51345			0.559614
$290$	2.30773			0.135515
$291$	17.8377			1.04567
$292$		−	8.97437i		−	0.525185i
$293$	−21.8725			−1.27781			−0.638904	−	0.769286i	$-0.720612\pi$
$293$	−21.8725			−1.27781			−0.638904	+	0.769286i	$0.720612\pi$
$294$		−	5.52241i		−	0.322073i
$295$			8.40673i			0.489459i
$296$			3.41301i			0.198377i
$297$	−15.2875	+	3.89441i	−0.887072	+	0.225977i
$298$			15.4447i			0.894689i
$299$	−3.16007			−0.182752
$300$		−	1.15962i		−	0.0669509i
$301$	−0.0176308			−0.00101622
$302$	−2.80326			−0.161309
$303$	−5.79829			−0.333103
$304$	−0.244944	−	0.262947i	−0.0140485	−	0.0150811i
$305$			2.63798i			0.151050i
$306$			5.06876i			0.289762i
$307$	−13.1466			−0.750317			−0.375158	−	0.926961i	$-0.622412\pi$
$307$	−13.1466			−0.750317			−0.375158	+	0.926961i	$0.622412\pi$
$308$	1.15101	−	0.293213i	0.0655848	−	0.0167074i
$309$	−12.6784			−0.721249
$310$			2.98526i			0.169551i
$311$	−19.4254			−1.10151			−0.550756	−	0.834666i	$-0.685661\pi$
$311$	−19.4254			−1.10151			−0.550756	+	0.834666i	$0.685661\pi$
$312$		−	1.08856i		−	0.0616277i
$313$	15.7237			0.888757			0.444379	−	0.895839i	$-0.353425\pi$
$313$	15.7237			0.888757			0.444379	+	0.895839i	$0.353425\pi$
$314$	13.4011			0.756271
$315$			0.612500i			0.0345105i
$316$	13.6875			0.769981
$317$		−	2.48262i		−	0.139438i	−0.997567	−	0.0697189i	$-0.977790\pi$
$317$		−	2.48262i		−	0.139438i	0.997567	−	0.0697189i	$-0.0222102\pi$
$318$	8.12425			0.455585
$319$	−2.18821	−	8.58981i	−0.122516	−	0.480937i
$320$	4.74941			0.265500
$321$		−	3.30025i		−	0.184202i
$322$		−	1.85896i		−	0.103596i
$323$	−8.72687	+	8.12935i	−0.485576	+	0.452329i
$324$	−2.55805			−0.142114
$325$	−0.419046			−0.0232445
$326$	−17.6878			−0.979637
$327$			9.11127i			0.503854i
$328$	27.3772			1.51165
$329$			0.717419i			0.0395526i
$330$	2.56543	−	0.653529i	0.141222	−	0.0359756i
$331$			10.3625i			0.569575i	0.958591	+	0.284787i	$0.0919230\pi$
$331$			10.3625i			0.569575i	−0.958591	+	0.284787i	$0.908077\pi$
$332$		−	18.2102i		−	0.999414i
$333$			2.60576i			0.142795i
$334$	6.95505			0.380563
$335$			11.1802i			0.610838i
$336$	−0.0217577			−0.00118698
$337$	−7.00099			−0.381368			−0.190684	−	0.981651i	$-0.561071\pi$
$337$	−7.00099			−0.381368			−0.190684	+	0.981651i	$0.561071\pi$
$338$	11.0734			0.602315
$339$	−3.80139			−0.206463
$340$			3.43231i			0.186143i
$341$	11.1117	−	2.83064i	0.601732	−	0.153288i
$342$	5.50397	+	5.90851i	0.297620	+	0.319496i
$343$			3.97359i			0.214553i
$344$			0.173541i			0.00935670i
$345$			6.97119i			0.375316i
$346$	−11.6803			−0.627937
$347$		−	8.33222i		−	0.447297i	−0.974670	−	0.223648i	$-0.928203\pi$
$347$		−	8.33222i		−	0.447297i	0.974670	−	0.223648i	$-0.0717968\pi$
$348$			3.09926i			0.166138i
$349$			11.1985i			0.599444i	0.954027	+	0.299722i	$0.0968940\pi$
$349$			11.1985i			0.599444i	−0.954027	+	0.299722i	$0.903106\pi$
$350$		−	0.246510i		−	0.0131765i
$351$		−	1.99322i		−	0.106390i
$352$	−4.65976	−	18.2919i	−0.248366	−	0.974962i
$353$	−25.8509			−1.37590			−0.687952	−	0.725756i	$-0.741490\pi$
$353$	−25.8509			−1.37590			−0.687952	+	0.725756i	$0.741490\pi$
$354$	6.71033			0.356650
$355$		−	2.61887i		−	0.138995i
$356$			17.4581i			0.925279i
$357$			0.722110i			0.0382181i
$358$			13.7889i			0.728765i
$359$		−	12.0184i		−	0.634308i	−0.948374	−	0.317154i	$-0.897273\pi$
$359$		−	12.0184i		−	0.634308i	0.948374	−	0.317154i	$-0.102727\pi$
$360$	6.02886			0.317749
$361$	−1.34533	+	18.9523i	−0.0708069	+	0.997490i
$362$			18.9508i			0.996030i
$363$	−4.86511	−	8.92932i	−0.255352	−	0.468668i
$364$			0.150071i			0.00786588i
$365$			7.15415i			0.374465i
$366$	2.10566			0.110064
$367$	3.31693			0.173142			0.0865710	−	0.996246i	$-0.472409\pi$
$367$	3.31693			0.173142			0.0865710	+	0.996246i	$0.472409\pi$
$368$	0.621708			0.0324088
$369$	20.9019			1.08811
$370$		−	1.04873i		−	0.0545207i
$371$	−2.90574			−0.150858
$372$	−4.00917			−0.207866
$373$	−18.9618			−0.981803			−0.490902	−	0.871215i	$-0.663333\pi$
$373$	−18.9618			−0.981803			−0.490902	+	0.871215i	$0.663333\pi$
$374$	−7.59327	+	1.93434i	−0.392639	+	0.100023i
$375$			0.924425i			0.0477371i
$376$	7.06158			0.364173
$377$	1.11996			0.0576809
$378$	1.17254			0.0603092
$379$			16.8155i			0.863753i	0.901933	+	0.431876i	$0.142148\pi$
$379$			16.8155i			0.863753i	−0.901933	+	0.431876i	$0.857852\pi$
$380$	3.72701	+	4.00095i	0.191191	+	0.205244i
$381$			16.8806i			0.864822i
$382$	12.8690			0.658437
$383$		−	23.4062i		−	1.19600i	−0.801496	−	0.598000i	$-0.795962\pi$
$383$		−	23.4062i		−	1.19600i	0.801496	−	0.598000i	$-0.204038\pi$
$384$			6.73145i			0.343513i
$385$	−0.917557	+	0.233743i	−0.0467631	+	0.0119126i
$386$	−12.3726			−0.629747
$387$			0.132495i			0.00673508i
$388$			24.2055i			1.22885i
$389$	−10.9278			−0.554061			−0.277030	−	0.960861i	$-0.589350\pi$
$389$	−10.9278			−0.554061			−0.277030	+	0.960861i	$0.589350\pi$
$390$			0.334487i			0.0169374i
$391$		−	20.6337i		−	1.04349i
$392$	19.4416			0.981947
$393$	10.1804			0.513532
$394$		−	18.4780i		−	0.930907i
$395$	−10.9113			−0.549009
$396$	−2.20348	−	8.64977i	−0.110729	−	0.434667i
$397$	11.3605			0.570168			0.285084	−	0.958503i	$-0.407979\pi$
$397$	11.3605			0.570168			0.285084	+	0.958503i	$0.407979\pi$
$398$	−4.62811			−0.231986
$399$	0.784110	+	0.841743i	0.0392546	+	0.0421399i
$400$	0.0824425			0.00412213
$401$		−	35.4498i		−	1.77028i	−0.465325	−	0.885140i	$-0.654063\pi$
$401$		−	35.4498i		−	1.77028i	0.465325	−	0.885140i	$-0.345937\pi$
$402$	8.92411			0.445094
$403$			1.44877i			0.0721683i
$404$		−	7.86816i		−	0.391456i
$405$	2.03922			0.101330
$406$			0.658834i			0.0326974i
$407$	−3.90356	+	0.994410i	−0.193492	+	0.0492911i
$408$	7.10775			0.351886
$409$	15.0326			0.743313			0.371657	−	0.928370i	$-0.378790\pi$
$409$	15.0326			0.743313			0.371657	+	0.928370i	$0.378790\pi$
$410$	−8.41230			−0.415454
$411$			0.151517i			0.00747380i
$412$		−	17.2043i		−	0.847597i
$413$	−2.40003			−0.118098
$414$	−13.9700			−0.686588
$415$			14.5167i			0.712598i
$416$	2.38494			0.116931
$417$	−15.2879			−0.748651
$418$	−6.75084	+	10.5000i	−0.330194	+	0.513574i
$419$	−0.962258			−0.0470094			−0.0235047	−	0.999724i	$-0.507482\pi$
$419$	−0.962258			−0.0470094			−0.0235047	+	0.999724i	$0.507482\pi$
$420$	0.331061			0.0161541
$421$			8.70537i			0.424274i	0.977240	+	0.212137i	$0.0680423\pi$
$421$			8.70537i			0.424274i	−0.977240	+	0.212137i	$0.931958\pi$
$422$	−13.8837			−0.675846
$423$	5.39136			0.262137
$424$			28.6013i			1.38900i
$425$		−	2.73616i		−	0.132723i
$426$	−2.09041			−0.101281
$427$	−0.753115			−0.0364458
$428$	4.47837			0.216470
$429$	1.24502	−	0.317162i	0.0601102	−	0.0153127i
$430$		−	0.0533246i		−	0.00257154i
$431$	23.7218			1.14264			0.571320	−	0.820728i	$-0.306432\pi$
$431$	23.7218			1.14264			0.571320	+	0.820728i	$0.306432\pi$
$432$			0.392144i			0.0188670i
$433$		−	7.71823i		−	0.370914i	−0.982652	−	0.185457i	$-0.940623\pi$
$433$		−	7.71823i		−	0.370914i	0.982652	−	0.185457i	$-0.0593766\pi$
$434$	−0.852261			−0.0409098
$435$		−	2.47066i		−	0.118459i
$436$	−12.3638			−0.592119
$437$	−22.4053	−	24.0521i	−1.07179	−	1.15057i
$438$	5.71051			0.272859
$439$	16.4495			0.785090			0.392545	−	0.919733i	$-0.371595\pi$
$439$	16.4495			0.785090			0.392545	+	0.919733i	$0.371595\pi$
$440$	2.30074	+	9.03156i	0.109683	+	0.430563i
$441$	14.8432			0.706819
$442$		−	0.990029i		−	0.0470909i
$443$	−8.78802			−0.417531			−0.208766	−	0.977966i	$-0.566945\pi$
$443$	−8.78802			−0.417531			−0.208766	+	0.977966i	$0.566945\pi$
$444$	1.40843			0.0668411
$445$		−	13.9172i		−	0.659739i
$446$		−	20.5185i		−	0.971580i
$447$	16.5351			0.782084
$448$			1.35591i			0.0640605i
$449$			21.1724i			0.999188i	0.866260	+	0.499594i	$0.166517\pi$
$449$			21.1724i			0.999188i	−0.866260	+	0.499594i	$0.833483\pi$
$450$	−1.85251			−0.0873282
$451$	7.97659	+	31.3121i	0.375603	+	1.47443i
$452$		−	5.15842i		−	0.242631i
$453$			3.00116i			0.141007i
$454$	2.80828			0.131799
$455$		−	0.119633i		−	0.00560850i
$456$	8.28531	−	7.71802i	0.387995	−	0.361430i
$457$			17.5917i			0.822905i	0.911431	+	0.411453i	$0.134978\pi$
$457$			17.5917i			0.822905i	−0.911431	+	0.411453i	$0.865022\pi$
$458$	12.7587			0.596177
$459$	13.0147			0.607476
$460$	−9.45977			−0.441064
$461$			8.96166i			0.417386i	0.977981	+	0.208693i	$0.0669209\pi$
$461$			8.96166i			0.417386i	−0.977981	+	0.208693i	$0.933079\pi$
$462$	0.186576	+	0.732403i	0.00868029	+	0.0340745i
$463$	8.21384			0.381729			0.190865	−	0.981616i	$-0.438871\pi$
$463$	8.21384			0.381729			0.190865	+	0.981616i	$0.438871\pi$
$464$	−0.220339			−0.0102290
$465$	3.19602			0.148212
$466$			21.9518i			1.01690i
$467$	2.60310			0.120457			0.0602285	−	0.998185i	$-0.480817\pi$
$467$	2.60310			0.120457			0.0602285	+	0.998185i	$0.480817\pi$
$468$	1.12778			0.0521315
$469$	−3.19182			−0.147385
$470$	−2.16984			−0.100087
$471$		−	14.3473i		−	0.661087i
$472$			23.6236i			1.08737i
$473$	−0.198484	+	0.0505627i	−0.00912630	+	0.00232488i
$474$			8.70953i			0.400042i
$475$	−2.97108	−	3.18946i	−0.136323	−	0.146343i
$476$	−0.979889			−0.0449131
$477$			21.8365i			0.999823i
$478$			23.5792i			1.07849i
$479$			5.42770i			0.247998i	0.992282	+	0.123999i	$0.0395720\pi$
$479$			5.42770i			0.247998i	−0.992282	+	0.123999i	$0.960428\pi$
$480$		−	5.26123i		−	0.240141i
$481$		−	0.508955i		−	0.0232064i
$482$	22.3972			1.02016
$483$	−1.99020			−0.0905573
$484$	12.1169	−	6.60186i	0.550769	−	0.300085i
$485$		−	19.2960i		−	0.876188i
$486$		−	13.9491i		−	0.632745i
$487$			18.0629i			0.818508i	0.912420	+	0.409254i	$0.134211\pi$
$487$			18.0629i			0.818508i	−0.912420	+	0.409254i	$0.865789\pi$
$488$			7.41294i			0.335568i
$489$			18.9365i			0.856340i
$490$	−5.97388			−0.269872
$491$			3.41626i			0.154174i	0.997024	+	0.0770869i	$0.0245619\pi$
$491$			3.41626i			0.154174i	−0.997024	+	0.0770869i	$0.975438\pi$
$492$		−	11.2976i		−	0.509336i
$493$			7.31276i			0.329350i
$494$	−1.07503	−	1.15405i	−0.0483680	−	0.0519231i
$495$	1.75656	+	6.89539i	0.0789517	+	0.309925i
$496$		−	0.285029i		−	0.0127982i
$497$	0.747661			0.0335372
$498$	11.5874			0.519243
$499$	24.8994			1.11465			0.557325	−	0.830294i	$-0.311828\pi$
$499$	24.8994			1.11465			0.557325	+	0.830294i	$0.311828\pi$
$500$	−1.25443			−0.0560997
$501$		−	7.44607i		−	0.332666i
$502$	22.0157			0.982609
$503$		−	3.76317i		−	0.167792i	−0.996475	−	0.0838958i	$-0.973264\pi$
$503$		−	3.76317i		−	0.167792i	0.996475	−	0.0838958i	$-0.0267363\pi$
$504$			1.72118i			0.0766674i
$505$			6.27231i			0.279114i
$506$	−5.33124	−	20.9278i	−0.237002	−	0.930353i
$507$		−	11.8552i		−	0.526508i
$508$	−22.9067			−1.01632
$509$		−	20.6837i		−	0.916787i	−0.888749	−	0.458394i	$-0.848425\pi$
$509$		−	20.6837i		−	0.916787i	0.888749	−	0.458394i	$-0.151575\pi$
$510$	−2.18403			−0.0967103
$511$	−2.04244			−0.0903521
$512$	−0.932551			−0.0412133
$513$	15.1709	−	14.1322i	0.669812	−	0.623951i
$514$			2.27168i			0.100199i
$515$			13.7149i			0.604350i
$516$	0.0716143			0.00315264
$517$	2.05745	+	8.07654i	0.0904868	+	0.355206i
$518$	0.299401			0.0131549
$519$			12.5049i			0.548905i
$520$	−1.17756			−0.0516392
$521$		−	33.3317i		−	1.46029i	−0.683293	−	0.730144i	$-0.739453\pi$
$521$		−	33.3317i		−	1.46029i	0.683293	−	0.730144i	$-0.260547\pi$
$522$	4.95110			0.216704
$523$	−36.8461			−1.61117			−0.805584	−	0.592482i	$-0.798148\pi$
$523$	−36.8461			−1.61117			−0.805584	+	0.592482i	$0.798148\pi$
$524$			13.8146i			0.603492i
$525$	−0.263914			−0.0115181
$526$		−	10.0274i		−	0.437216i
$527$	−9.45972			−0.412072
$528$	−0.244944	+	0.0623980i	−0.0106598	+	0.00271553i
$529$	33.8683			1.47253
$530$		−	8.78843i		−	0.381745i
$531$			18.0361i			0.782701i
$532$	−1.14223	+	1.06402i	−0.0495219	+	0.0461312i
$533$	−4.08255			−0.176835
$534$	−11.1088			−0.480727
$535$	−3.57005			−0.154347
$536$			31.4172i			1.35702i
$537$	14.7624			0.637043
$538$			19.6819i			0.848545i
$539$	5.66447	+	22.2359i	0.243986	+	0.957768i
$540$		−	5.96677i		−	0.256769i
$541$		−	33.6821i		−	1.44811i	−0.689743	−	0.724054i	$-0.742277\pi$
$541$		−	33.6821i		−	1.44811i	0.689743	−	0.724054i	$-0.257723\pi$
$542$		−	8.07736i		−	0.346952i
$543$	20.2887			0.870670
$544$			15.5724i			0.667663i
$545$	9.85614			0.422191
$546$	−0.0954925			−0.00408670
$547$	21.0334			0.899323			0.449662	−	0.893199i	$-0.351545\pi$
$547$	21.0334			0.899323			0.449662	+	0.893199i	$0.351545\pi$
$548$	−0.205606			−0.00878305
$549$			5.65961i			0.241546i
$550$	−0.706957	−	2.77516i	−0.0301447	−	0.118333i
$551$	7.94064	+	8.52428i	0.338282	+	0.363147i
$552$			19.5896i			0.833791i
$553$		−	3.11507i		−	0.132466i
$554$			8.27184i			0.351437i
$555$	−1.12277			−0.0476588
$556$		−	20.7454i		−	0.879799i
$557$		−	16.2882i		−	0.690152i	−0.938575	−	0.345076i	$-0.887853\pi$
$557$		−	16.2882i		−	0.690152i	0.938575	−	0.345076i	$-0.112147\pi$
$558$			6.40469i			0.271132i
$559$		−	0.0258788i		−	0.00109456i
$560$			0.0235365i			0.000994598i
$561$	2.07091	+	8.12935i	0.0874338	+	0.343221i
$562$	−20.1490			−0.849934
$563$	9.87561			0.416207			0.208104	−	0.978107i	$-0.433271\pi$
$563$	9.87561			0.416207			0.208104	+	0.978107i	$0.433271\pi$
$564$		−	2.91407i		−	0.122704i
$565$			4.11217i			0.173000i
$566$			28.1158i			1.18180i
$567$			0.582175i			0.0244491i
$568$		−	7.35926i		−	0.308788i
$569$	34.7858			1.45830			0.729149	−	0.684355i	$-0.239916\pi$
$569$	34.7858			1.45830			0.729149	+	0.684355i	$0.239916\pi$
$570$	−2.54586	+	2.37155i	−0.106634	+	0.0993331i
$571$			20.2405i			0.847037i	0.905888	+	0.423518i	$0.139205\pi$
$571$			20.2405i			0.847037i	−0.905888	+	0.423518i	$0.860795\pi$
$572$	0.430383	+	1.68947i	0.0179952	+	0.0706403i
$573$		−	13.7776i		−	0.575566i
$574$		−	2.40162i		−	0.100242i
$575$	7.54111			0.314486
$576$	10.1896			0.424565
$577$	0.308647			0.0128491			0.00642456	−	0.999979i	$-0.497955\pi$
$577$	0.308647			0.0128491			0.00642456	+	0.999979i	$0.497955\pi$
$578$	−8.21453			−0.341679
$579$			13.2461i			0.550487i
$580$	3.35263			0.139210
$581$	−4.14438			−0.171938
$582$	−15.4023			−0.638445
$583$	−32.7122	+	8.33325i	−1.35480	+	0.345128i
$584$			20.1038i			0.831900i
$585$	−0.899038			−0.0371706
$586$	18.8862			0.780181
$587$	22.4405			0.926218			0.463109	−	0.886301i	$-0.346734\pi$
$587$	22.4405			0.926218			0.463109	+	0.886301i	$0.346734\pi$
$588$		−	8.02286i		−	0.330857i
$589$	−11.0269	+	10.2719i	−0.454357	+	0.423247i
$590$		−	7.25892i		−	0.298845i
$591$	−19.7825			−0.813743
$592$			0.100131i			0.00411536i
$593$			9.46067i			0.388503i	0.980952	+	0.194252i	$0.0622278\pi$
$593$			9.46067i			0.388503i	−0.980952	+	0.194252i	$0.937772\pi$
$594$	13.2002	−	3.36269i	0.541613	−	0.137973i
$595$	0.781144			0.0320238
$596$			22.4378i			0.919089i
$597$			4.95485i			0.202788i
$598$	2.72861			0.111581
$599$		−	1.87763i		−	0.0767181i	−0.999264	−	0.0383590i	$-0.987787\pi$
$599$		−	1.87763i		−	0.0767181i	0.999264	−	0.0383590i	$-0.0122131\pi$
$600$			2.59771i			0.106051i
$601$	−40.6076			−1.65642			−0.828210	−	0.560418i	$-0.810640\pi$
$601$	−40.6076			−1.65642			−0.828210	+	0.560418i	$0.810640\pi$
$602$	0.0152236			0.000620468
$603$			23.9863i			0.976800i
$604$	−4.07252			−0.165709
$605$	−9.65932	+	5.26285i	−0.392707	+	0.213965i
$606$	5.00662			0.203380
$607$	12.7418			0.517172			0.258586	−	0.965988i	$-0.416743\pi$
$607$	12.7418			0.517172			0.258586	+	0.965988i	$0.416743\pi$
$608$	16.9095	+	18.1524i	0.685771	+	0.736176i
$609$	0.705347			0.0285821
$610$		−	2.27780i		−	0.0922255i
$611$	−1.05304			−0.0426014
$612$			7.36381i			0.297664i
$613$		−	36.8280i		−	1.48747i	−0.668475	−	0.743734i	$-0.733053\pi$
$613$		−	36.8280i		−	1.48747i	0.668475	−	0.743734i	$-0.266947\pi$
$614$	11.3516			0.458115
$615$			9.00620i			0.363165i
$616$	−2.57842	+	0.656837i	−0.103887	+	0.0264647i
$617$	−9.39927			−0.378400			−0.189200	−	0.981939i	$-0.560590\pi$
$617$	−9.39927			−0.378400			−0.189200	+	0.981939i	$0.560590\pi$
$618$	10.9474			0.440367
$619$	10.0687			0.404695			0.202347	−	0.979314i	$-0.435143\pi$
$619$	10.0687			0.404695			0.202347	+	0.979314i	$0.435143\pi$
$620$			4.33693i			0.174175i
$621$			35.8698i			1.43941i
$622$	16.7731			0.672542
$623$	3.97322			0.159184
$624$		−	0.0319363i		−	0.00127848i
$625$	1.00000			0.0400000
$626$	−13.5769			−0.542642
$627$	11.2413	+	7.22744i	0.448936	+	0.288636i
$628$	19.4689			0.776896
$629$	3.32322			0.132505
$630$		−	0.528873i		−	0.0210708i
$631$	−1.63533			−0.0651013			−0.0325506	−	0.999470i	$-0.510363\pi$
$631$	−1.63533			−0.0651013			−0.0325506	+	0.999470i	$0.510363\pi$
$632$	−30.6618			−1.21966
$633$			14.8638i			0.590784i
$634$			2.14366i			0.0851355i
$635$	18.2607			0.724653
$636$	11.8028			0.468010
$637$	−2.89917			−0.114869
$638$	1.88944	+	7.41700i	0.0748037	+	0.293642i
$639$		−	5.61863i		−	0.222270i
$640$	7.28177			0.287837
$641$			28.3914i			1.12139i	0.828022	+	0.560696i	$0.189466\pi$
$641$			28.3914i			1.12139i	−0.828022	+	0.560696i	$0.810534\pi$
$642$			2.84965i			0.112467i
$643$	11.0504			0.435785			0.217892	−	0.975973i	$-0.430082\pi$
$643$	11.0504			0.435785			0.217892	+	0.975973i	$0.430082\pi$
$644$		−	2.70067i		−	0.106421i
$645$	−0.0570892			−0.00224789
$646$	7.53535	−	7.01941i	0.296474	−	0.276175i
$647$	−0.304025			−0.0119525			−0.00597623	−	0.999982i	$-0.501902\pi$
$647$	−0.304025			−0.0119525			−0.00597623	+	0.999982i	$0.501902\pi$
$648$	5.73038			0.225110
$649$	−27.0191	+	6.88296i	−1.06059	+	0.270180i
$650$	0.361832			0.0141922
$651$			0.912429i			0.0357609i
$652$	−25.6965			−1.00635
$653$	−33.1227			−1.29619			−0.648096	−	0.761559i	$-0.724434\pi$
$653$	−33.1227			−1.29619			−0.648096	+	0.761559i	$0.724434\pi$
$654$		−	7.86726i		−	0.307634i
$655$		−	11.0127i		−	0.430300i
$656$	0.803195			0.0313595
$657$			15.3488i			0.598813i
$658$		−	0.619466i		−	0.0241493i
$659$	7.22187			0.281324			0.140662	−	0.990058i	$-0.455077\pi$
$659$	7.22187			0.281324			0.140662	+	0.990058i	$0.455077\pi$
$660$	3.72701	−	0.949435i	0.145074	−	0.0369567i
$661$		−	33.4062i		−	1.29935i	−0.760213	−	0.649674i	$-0.774905\pi$
$661$		−	33.4062i		−	1.29935i	0.760213	−	0.649674i	$-0.225095\pi$
$662$		−	8.94766i		−	0.347761i
$663$	−1.05992			−0.0411640
$664$			40.7933i			1.58309i
$665$	0.910558	−	0.848213i	0.0353099	−	0.0328923i
$666$		−	2.24998i		−	0.0871849i
$667$	−20.1547			−0.780392
$668$	10.1042			0.390942
$669$	−21.9671			−0.849298
$670$		−	9.65369i		−	0.372954i
$671$	−8.47840	+	2.15983i	−0.327305	+	0.0833791i
$672$	1.50203			0.0579420
$673$	18.7855			0.724129			0.362064	−	0.932153i	$-0.382072\pi$
$673$	18.7855			0.724129			0.362064	+	0.932153i	$0.382072\pi$
$674$	6.04512			0.232849
$675$			4.75657i			0.183081i
$676$	16.0873			0.618741
$677$	36.0219			1.38444			0.692218	−	0.721689i	$-0.256634\pi$
$677$	36.0219			1.38444			0.692218	+	0.721689i	$0.256634\pi$
$678$	3.28237			0.126059
$679$	5.50882			0.211409
$680$		−	7.68884i		−	0.294853i
$681$		−	3.00655i		−	0.115211i
$682$	−9.59456	+	2.44416i	−0.367395	+	0.0935918i
$683$		−	22.1505i		−	0.847564i	−0.905764	−	0.423782i	$-0.860702\pi$
$683$		−	22.1505i		−	0.847564i	0.905764	−	0.423782i	$-0.139298\pi$
$684$	7.99606	+	8.58379i	0.305737	+	0.328209i
$685$	0.163904			0.00626246
$686$		−	3.43105i		−	0.130998i
$687$		−	13.6595i		−	0.521142i
$688$			0.00509136i			0.000194106i
$689$		−	4.26509i		−	0.162487i
$690$		−	6.01938i		−	0.229154i
$691$	46.9200			1.78492			0.892460	−	0.451126i	$-0.148978\pi$
$691$	46.9200			1.78492			0.892460	+	0.451126i	$0.148978\pi$
$692$	−16.9689			−0.645062
$693$	−1.96856	+	0.501481i	−0.0747795	+	0.0190497i
$694$			7.19458i			0.273103i
$695$			16.5377i			0.627311i
$696$		−	6.94276i		−	0.263164i
$697$		−	26.6570i		−	1.00970i
$698$		−	9.66956i		−	0.365998i
$699$	23.5015			0.888909
$700$		−	0.358126i		−	0.0135359i
$701$		−	0.369565i		−	0.0139583i	−0.999976	−	0.00697914i	$-0.997778\pi$
$701$		−	0.369565i		−	0.0139583i	0.999976	−	0.00697914i	$-0.00222155\pi$
$702$			1.72108i			0.0649580i
$703$	3.87378	−	3.60855i	0.146102	−	0.136099i
$704$	3.88855	+	15.2645i	0.146555	+	0.575302i
$705$			2.32303i			0.0874902i
$706$	22.3214			0.840076
$707$	−1.79068			−0.0673455
$708$	9.74865			0.366377
$709$	−24.3967			−0.916238			−0.458119	−	0.888891i	$-0.651477\pi$
$709$	−24.3967			−0.916238			−0.458119	+	0.888891i	$0.651477\pi$
$710$			2.26131i			0.0848653i
$711$	−23.4096			−0.877928
$712$		−	39.1086i		−	1.46566i
$713$		−	26.0719i		−	0.976399i
$714$		−	0.623517i		−	0.0233345i
$715$	−0.343091	−	1.34681i	−0.0128309	−	0.0503677i
$716$			20.0323i			0.748640i
$717$	25.2439			0.942750
$718$			10.3775i			0.387284i
$719$	−47.3952			−1.76754			−0.883771	−	0.467920i	$-0.845004\pi$
$719$	−47.3952			−1.76754			−0.883771	+	0.467920i	$0.845004\pi$
$720$	0.176875			0.00659175
$721$	−3.91546			−0.145819
$722$	1.16165	−	16.3647i	0.0432320	−	0.609030i
$723$		−	23.9784i		−	0.891766i
$724$			27.5313i			1.02319i
$725$	−2.67264			−0.0992594
$726$	4.20086	+	7.71016i	0.155908	+	0.286151i
$727$	−7.90775			−0.293282			−0.146641	−	0.989190i	$-0.546846\pi$
$727$	−7.90775			−0.293282			−0.146641	+	0.989190i	$0.546846\pi$
$728$		−	0.336180i		−	0.0124597i
$729$	−8.81627			−0.326529
$730$		−	6.17736i		−	0.228635i
$731$	0.168975			0.00624978
$732$	3.05906			0.113066
$733$		−	32.5236i		−	1.20129i	−0.799518	−	0.600643i	$-0.794911\pi$
$733$		−	32.5236i		−	1.20129i	0.799518	−	0.600643i	$-0.205089\pi$
$734$	−2.86405			−0.105714
$735$			6.39563i			0.235906i
$736$	−42.9191			−1.58202
$737$	−35.9328	+	9.15369i	−1.32360	+	0.337180i
$738$	−18.0481			−0.664358
$739$		−	46.6996i		−	1.71787i	−0.512082	−	0.858937i	$-0.671125\pi$
$739$		−	46.6996i		−	1.71787i	0.512082	−	0.858937i	$-0.328875\pi$
$740$		−	1.52357i		−	0.0560076i
$741$	−1.23552	+	1.15093i	−0.0453881	+	0.0422804i
$742$	2.50901			0.0921085
$743$	−5.69888			−0.209072			−0.104536	−	0.994521i	$-0.533336\pi$
$743$	−5.69888			−0.209072			−0.104536	+	0.994521i	$0.533336\pi$
$744$	8.98108			0.329262
$745$		−	17.8869i		−	0.655326i
$746$	16.3728			0.599452
$747$			31.1447i			1.13953i
$748$	−11.0314	+	2.81018i	−0.403347	+	0.102750i
$749$		−	1.01921i		−	0.0372412i
$750$		−	0.798209i		−	0.0291465i
$751$		−	33.8150i		−	1.23393i	−0.786992	−	0.616964i	$-0.788362\pi$
$751$		−	33.8150i		−	1.23393i	0.786992	−	0.616964i	$-0.211638\pi$
$752$	0.207173			0.00755483
$753$		−	23.5700i		−	0.858938i
$754$	−0.967047			−0.0352178
$755$	3.24652			0.118153
$756$	1.70345			0.0619540
$757$	−16.9966			−0.617753			−0.308876	−	0.951102i	$-0.599953\pi$
$757$	−16.9966			−0.617753			−0.308876	+	0.951102i	$0.599953\pi$
$758$		−	14.5196i		−	0.527375i
$759$	−22.4053	+	5.70762i	−0.813259	+	0.207173i
$760$	−8.34900	−	8.96266i	−0.302850	−	0.325110i
$761$			9.58612i			0.347497i	0.984790	+	0.173748i	$0.0555879\pi$
$761$			9.58612i			0.347497i	−0.984790	+	0.173748i	$0.944412\pi$
$762$		−	14.5759i		−	0.528027i
$763$			2.81383i			0.101867i
$764$	18.6959			0.676394
$765$		−	5.87025i		−	0.212240i
$766$			20.2104i			0.730233i
$767$		−	3.52281i		−	0.127201i
$768$		−	14.5933i		−	0.526591i
$769$			1.36265i			0.0491385i	0.999698	+	0.0245692i	$0.00782141\pi$
$769$			1.36265i			0.0491385i	−0.999698	+	0.0245692i	$0.992179\pi$
$770$	0.792279	−	0.201829i	0.0285518	−	0.00727341i
$771$	2.43205			0.0875883
$772$	−17.9746			−0.646921
$773$		−	20.3558i		−	0.732148i	−0.930586	−	0.366074i	$-0.880702\pi$
$773$		−	20.3558i		−	0.732148i	0.930586	−	0.366074i	$-0.119298\pi$
$774$		−	0.114405i		−	0.00411219i
$775$		−	3.45730i		−	0.124190i
$776$		−	54.2235i		−	1.94651i
$777$		−	0.320538i		−	0.0114992i
$778$	9.43577			0.338289
$779$	−28.9457	−	31.0733i	−1.03709	−	1.11332i
$780$			0.485936i			0.0173993i
$781$	8.41700	−	2.14419i	0.301184	−	0.0767250i
$782$			17.8164i			0.637115i
$783$		−	12.7126i		−	0.454312i
$784$	0.570378			0.0203706
$785$	−15.5202			−0.553939
$786$	−8.79040			−0.313543
$787$	−21.6286			−0.770975			−0.385487	−	0.922713i	$-0.625967\pi$
$787$	−21.6286			−0.770975			−0.385487	+	0.922713i	$0.625967\pi$
$788$		−	26.8445i		−	0.956295i
$789$	−10.7353			−0.382189
$790$	9.42156			0.335204
$791$	−1.17398			−0.0417420
$792$	4.93609	+	19.3766i	0.175396	+	0.688519i
$793$		−	1.10543i		−	0.0392551i
$794$	−9.80941			−0.348123
$795$	−9.40888			−0.333699
$796$	−6.72363			−0.238313
$797$			16.9815i			0.601516i	0.953700	+	0.300758i	$0.0972396\pi$
$797$			16.9815i			0.601516i	−0.953700	+	0.300758i	$0.902760\pi$
$798$	−0.677052	−	0.726816i	−0.0239674	−	0.0257290i
$799$		−	6.87580i		−	0.243248i
$800$	−5.69136			−0.201220
$801$		−	29.8585i		−	1.05500i
$802$			30.6097i			1.08087i
$803$	−22.9933	+	5.85742i	−0.811416	+	0.206704i
$804$	12.9648			0.457233
$805$			2.15291i			0.0758800i
$806$		−	1.25096i		−	0.0440633i
$807$	21.0714			0.741748
$808$			17.6257i			0.620071i
$809$		−	27.8406i		−	0.978825i	−0.872052	−	0.489412i	$-0.837211\pi$
$809$		−	27.8406i		−	0.978825i	0.872052	−	0.489412i	$-0.162789\pi$
$810$	−1.76079			−0.0618680
$811$	7.67428			0.269481			0.134740	−	0.990881i	$-0.456980\pi$
$811$	7.67428			0.269481			0.134740	+	0.990881i	$0.456980\pi$
$812$			0.957142i			0.0335891i
$813$	−8.64762			−0.303285
$814$	3.37059	−	0.858639i	0.118139	−	0.0300953i
$815$	20.4847			0.717546
$816$	0.208528			0.00729993
$817$	0.196970	−	0.183484i	0.00689110	−	0.00641928i
$818$	−12.9801			−0.453839
$819$		−	0.256666i		−	0.00896863i
$820$	−12.2212			−0.426784
$821$			43.8616i			1.53078i	0.643565	+	0.765391i	$0.277454\pi$
$821$			43.8616i			1.53078i	−0.643565	+	0.765391i	$0.722546\pi$
$822$		−	0.130830i		−	0.00456322i
$823$	−20.6693			−0.720487			−0.360243	−	0.932858i	$-0.617306\pi$
$823$	−20.6693			−0.720487			−0.360243	+	0.932858i	$0.617306\pi$
$824$			38.5400i			1.34261i
$825$	−2.97108	+	0.756867i	−0.103440	+	0.0263507i
$826$	2.07235			0.0721062
$827$	−46.7287			−1.62492			−0.812458	−	0.583020i	$-0.801871\pi$
$827$	−46.7287			−1.62492			−0.812458	+	0.583020i	$0.801871\pi$
$828$	−20.2954			−0.705312
$829$		−	3.18720i		−	0.110696i	−0.998467	−	0.0553480i	$-0.982373\pi$
$829$		−	3.18720i		−	0.110696i	0.998467	−	0.0553480i	$-0.0176268\pi$
$830$		−	12.5347i		−	0.435086i
$831$	8.85583			0.307205
$832$	−1.99022			−0.0689985
$833$		−	18.9301i		−	0.655889i
$834$	13.2006			0.457098
$835$	−8.05481			−0.278748
$836$	−9.80750	+	15.2543i	−0.339199	+	0.527580i
$837$	16.4449			0.568419
$838$	0.830877			0.0287022
$839$		−	26.5411i		−	0.916301i	−0.888875	−	0.458151i	$-0.848512\pi$
$839$		−	26.5411i		−	0.916301i	0.888875	−	0.458151i	$-0.151488\pi$
$840$	−0.741620			−0.0255883
$841$	−21.8570			−0.753689
$842$		−	7.51679i		−	0.259046i
$843$			21.5715i			0.742962i
$844$	−20.1699			−0.694277
$845$	−12.8244			−0.441173
$846$	−4.65525			−0.160051
$847$	−1.50249	−	2.75763i	−0.0516261	−	0.0947535i
$848$			0.839107i			0.0288151i
$849$	30.1008			1.03306
$850$			2.36258i			0.0810357i
$851$			9.15910i			0.313970i
$852$	−3.03691			−0.104043
$853$			9.53476i			0.326464i	0.986588	+	0.163232i	$0.0521919\pi$
$853$			9.53476i			0.326464i	−0.986588	+	0.163232i	$0.947808\pi$
$854$	0.650288			0.0222524
$855$	−6.37427	−	6.84279i	−0.217996	−	0.234019i
$856$	−10.0322			−0.342892
$857$	48.2839			1.64934			0.824672	−	0.565611i	$-0.191359\pi$
$857$	48.2839			1.64934			0.824672	+	0.565611i	$0.191359\pi$
$858$	−1.07503	+	0.273859i	−0.0367010	+	0.00934939i
$859$	3.97883			0.135756			0.0678780	−	0.997694i	$-0.478377\pi$
$859$	3.97883			0.135756			0.0678780	+	0.997694i	$0.478377\pi$
$860$		−	0.0774690i		−	0.00264167i
$861$	−2.57118			−0.0876254
$862$	−20.4830			−0.697653
$863$			13.3069i			0.452973i	0.974014	+	0.226486i	$0.0727239\pi$
$863$			13.3069i			0.452973i	−0.974014	+	0.226486i	$0.927276\pi$
$864$		−	27.0714i		−	0.920986i
$865$	13.5272			0.459940
$866$			6.66442i			0.226466i
$867$			8.79447i			0.298676i
$868$	−1.23815			−0.0420255
$869$	−8.93359	−	35.0688i	−0.303051	−	1.18963i
$870$			2.13333i			0.0723265i
$871$		−	4.68501i		−	0.158745i
$872$	27.6966			0.937925
$873$		−	41.3984i		−	1.40112i
$874$	19.3462	+	20.7681i	0.654394	+	0.702493i
$875$			0.285490i			0.00965131i
$876$	8.29613			0.280300
$877$	−2.91229			−0.0983411			−0.0491706	−	0.998790i	$-0.515658\pi$
$877$	−2.91229			−0.0983411			−0.0491706	+	0.998790i	$0.515658\pi$
$878$	−14.2035			−0.479346
$879$		−	20.2195i		−	0.681988i
$880$	0.0674993	+	0.264968i	0.00227540	+	0.00893209i
$881$	−4.59051			−0.154658			−0.0773291	−	0.997006i	$-0.524639\pi$
$881$	−4.59051			−0.154658			−0.0773291	+	0.997006i	$0.524639\pi$
$882$	−12.8166			−0.431557
$883$	−3.09847			−0.104272			−0.0521360	−	0.998640i	$-0.516603\pi$
$883$	−3.09847			−0.104272			−0.0521360	+	0.998640i	$0.516603\pi$
$884$		−	1.43830i		−	0.0483752i
$885$	−7.77140			−0.261233
$886$	7.58815			0.254929
$887$	−53.9299			−1.81079			−0.905395	−	0.424571i	$-0.860425\pi$
$887$	−53.9299			−1.81079			−0.905395	+	0.424571i	$0.860425\pi$
$888$	−3.15507			−0.105877
$889$			5.21324i			0.174846i
$890$			12.0170i			0.402812i
$891$	1.66960	+	6.55400i	0.0559336	+	0.219567i
$892$		−	29.8089i		−	0.998077i
$893$	−7.46616	−	8.01493i	−0.249845	−	0.268209i
$894$	−14.2775			−0.477511
$895$		−	15.9692i		−	0.533793i
$896$			2.07887i			0.0694501i
$897$		−	2.92125i		−	0.0975377i
$898$		−	18.2816i		−	0.610066i
$899$			9.24012i			0.308175i
$900$	−2.69130			−0.0897099
$901$	27.8489			0.927780
$902$	−6.88751	−	27.0369i	−0.229329	−	0.900232i
$903$		−	0.0162984i		−	0.000542376i
$904$			11.5555i			0.384332i
$905$		−	21.9473i		−	0.729554i
$906$		−	2.59140i		−	0.0860936i
$907$		−	2.40179i		−	0.0797502i	−0.999205	−	0.0398751i	$-0.987304\pi$
$907$		−	2.40179i		−	0.0797502i	0.999205	−	0.0398751i	$-0.0126960\pi$
$908$	4.07982			0.135394
$909$			13.4569i			0.446336i
$910$			0.103299i			0.00342434i
$911$		−	5.69493i		−	0.188681i	−0.995540	−	0.0943407i	$-0.969926\pi$
$911$		−	5.69493i		−	0.188681i	0.995540	−	0.0943407i	$-0.0300743\pi$
$912$	0.243075	−	0.226432i	0.00804902	−	0.00749791i
$913$	−46.6565	+	11.8855i	−1.54410	+	0.393352i
$914$		−	15.1898i		−	0.502435i
$915$	−2.43861			−0.0806180
$916$	18.5357			0.612436
$917$	3.14400			0.103824
$918$	−11.2378			−0.370902
$919$			41.7750i			1.37803i	0.724747	+	0.689015i	$0.241956\pi$
$919$			41.7750i			1.37803i	−0.724747	+	0.689015i	$0.758044\pi$
$920$	21.1912			0.698652
$921$		−	12.1531i		−	0.400457i
$922$		−	7.73808i		−	0.254840i
$923$			1.09743i			0.0361223i
$924$	0.271054	+	1.06402i	0.00891702	+	0.0350038i
$925$			1.21456i			0.0399344i
$926$	−7.09237			−0.233070
$927$			29.4245i			0.966426i
$928$	15.2110			0.499324
$929$	−40.9476			−1.34345			−0.671723	−	0.740802i	$-0.734446\pi$
$929$	−40.9476			−1.34345			−0.671723	+	0.740802i	$0.734446\pi$
$930$	−2.75965			−0.0904925
$931$	−20.5554	−	22.0663i	−0.673677	−	0.723193i
$932$			31.8911i			1.04463i
$933$		−	17.9573i		−	0.587896i
$934$	−2.24769			−0.0735466
$935$	8.79395	−	2.24021i	0.287593	−	0.0732627i
$936$	−2.52637			−0.0825771
$937$		−	11.8360i		−	0.386666i	−0.981133	−	0.193333i	$-0.938070\pi$
$937$		−	11.8360i		−	0.386666i	0.981133	−	0.193333i	$-0.0619298\pi$
$938$	2.75603			0.0899875
$939$			14.5354i			0.474345i
$940$	−3.15230			−0.102817
$941$	8.40698			0.274060			0.137030	−	0.990567i	$-0.456244\pi$
$941$	8.40698			0.274060			0.137030	+	0.990567i	$0.456244\pi$
$942$			12.3884i			0.403635i
$943$	73.4691			2.39248
$944$			0.693072i			0.0225576i
$945$	−1.35795			−0.0441742
$946$	0.171384	−	0.0436592i	0.00557218	−	0.00141948i
$947$	12.2038			0.396569			0.198285	−	0.980144i	$-0.436463\pi$
$947$	12.2038			0.396569			0.198285	+	0.980144i	$0.436463\pi$
$948$			12.6530i			0.410952i
$949$		−	2.99792i		−	0.0973166i
$950$	2.56543	+	2.75399i	0.0832335	+	0.0893512i
$951$	2.29500			0.0744204
$952$	2.19508			0.0711430
$953$	37.8910			1.22741			0.613706	−	0.789535i	$-0.289678\pi$
$953$	37.8910			1.22741			0.613706	+	0.789535i	$0.289678\pi$
$954$		−	18.8550i		−	0.610454i
$955$	−14.9039			−0.482280
$956$			34.2554i			1.10790i
$957$	7.94064	−	2.02283i	0.256684	−	0.0653889i
$958$		−	4.68663i		−	0.151418i
$959$			0.0467930i			0.00151102i
$960$			4.39047i			0.141702i
$961$	19.0471			0.614422
$962$			0.439465i			0.0141689i
$963$	−7.65933			−0.246818
$964$	32.5382			1.04799
$965$	14.3290			0.461265
$966$	1.71847			0.0552909
$967$		−	14.2006i		−	0.456660i	−0.973584	−	0.228330i	$-0.926674\pi$
$967$		−	14.2006i		−	0.456660i	0.973584	−	0.228330i	$-0.0733264\pi$
$968$	−27.1435	+	14.7891i	−0.872425	+	0.475338i
$969$	−7.51498	−	8.06734i	−0.241416	−	0.259160i
$970$			16.6615i			0.534967i
$971$		−	16.5201i		−	0.530155i	−0.964227	−	0.265077i	$-0.914602\pi$
$971$		−	16.5201i		−	0.530155i	0.964227	−	0.265077i	$-0.0853975\pi$
$972$		−	20.2651i		−	0.650002i
$973$	−4.72134			−0.151359
$974$		−	15.5967i		−	0.499750i
$975$		−	0.387377i		−	0.0124060i
$976$			0.217481i			0.00696141i
$977$			50.8851i			1.62796i	0.580893	+	0.813980i	$0.302703\pi$
$977$			50.8851i			1.62796i	−0.580893	+	0.813980i	$0.697297\pi$
$978$		−	16.3511i		−	0.522849i
$979$	44.7296	−	11.3946i	1.42956	−	0.364174i
$980$	−8.67875			−0.277232
$981$	21.1457			0.675132
$982$		−	2.94983i		−	0.0941327i
$983$		−	49.9366i		−	1.59273i	−0.604817	−	0.796365i	$-0.706754\pi$
$983$		−	49.9366i		−	1.59273i	0.604817	−	0.796365i	$-0.293246\pi$
$984$			25.3082i			0.806795i
$985$			21.3998i			0.681854i
$986$		−	6.31432i		−	0.201089i
$987$	−0.663200			−0.0211099
$988$	−1.56179	−	1.67658i	−0.0496871	−	0.0533392i
$989$			0.465712i			0.0148088i
$990$	−1.51673	−	5.95393i	−0.0482049	−	0.189228i
$991$			40.8792i			1.29857i	0.760545	+	0.649285i	$0.224932\pi$
$991$			40.8792i			1.29857i	−0.760545	+	0.649285i	$0.775068\pi$
$992$			19.6767i			0.624737i
$993$	−9.57936			−0.303992
$994$	−0.645579			−0.0204765
$995$	5.35992			0.169921
$996$	16.8340			0.533404
$997$		−	31.0466i		−	0.983257i	−0.870805	−	0.491629i	$-0.836402\pi$
$997$		−	31.0466i		−	0.983257i	0.870805	−	0.491629i	$-0.163598\pi$
$998$	−21.4998			−0.680564
$999$	−5.77713			−0.182780

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.2.f.b.626.16	yes	40
11.10	odd	2	inner	1045.2.f.b.626.26	yes	40
19.18	odd	2	inner	1045.2.f.b.626.25	yes	40
209.208	even	2	inner	1045.2.f.b.626.15	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.2.f.b.626.15	✓	40	209.208	even	2	inner
1045.2.f.b.626.16	yes	40	1.1	even	1	trivial
1045.2.f.b.626.25	yes	40	19.18	odd	2	inner
1045.2.f.b.626.26	yes	40	11.10	odd	2	inner

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:	\( N \)	\(=\)	\( 1045 = 5 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1045.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-0.863466 q^{2} +0.924425i q^{3} -1.25443 q^{4} +1.00000 q^{5} -0.798209i q^{6} +0.285490i q^{7} +2.81009 q^{8} +2.14544 q^{9} +O(q^{10})\)	\(q-0.863466 q^{2} +0.924425i q^{3} -1.25443 q^{4} +1.00000 q^{5} -0.798209i q^{6} +0.285490i q^{7} +2.81009 q^{8} +2.14544 q^{9} -0.863466 q^{10} +(0.818744 + 3.21398i) q^{11} -1.15962i q^{12} -0.419046 q^{13} -0.246510i q^{14} +0.924425i q^{15} +0.0824425 q^{16} -2.73616i q^{17} -1.85251 q^{18} +(-2.97108 - 3.18946i) q^{19} -1.25443 q^{20} -0.263914 q^{21} +(-0.706957 - 2.77516i) q^{22} +7.54111 q^{23} +2.59771i q^{24} +1.00000 q^{25} +0.361832 q^{26} +4.75657i q^{27} -0.358126i q^{28} -2.67264 q^{29} -0.798209i q^{30} -3.45730i q^{31} -5.69136 q^{32} +(-2.97108 + 0.756867i) q^{33} +2.36258i q^{34} +0.285490i q^{35} -2.69130 q^{36} +1.21456i q^{37} +(2.56543 + 2.75399i) q^{38} -0.387377i q^{39} +2.81009 q^{40} +9.74248 q^{41} +0.227880 q^{42} +0.0617565i q^{43} +(-1.02705 - 4.03170i) q^{44} +2.14544 q^{45} -6.51149 q^{46} +2.51294 q^{47} +0.0762119i q^{48} +6.91850 q^{49} -0.863466 q^{50} +2.52937 q^{51} +0.525663 q^{52} +10.1781i q^{53} -4.10714i q^{54} +(0.818744 + 3.21398i) q^{55} +0.802250i q^{56} +(2.94842 - 2.74654i) q^{57} +2.30773 q^{58} +8.40673i q^{59} -1.15962i q^{60} +2.63798i q^{61} +2.98526i q^{62} +0.612500i q^{63} +4.74941 q^{64} -0.419046 q^{65} +(2.56543 - 0.653529i) q^{66} +11.1802i q^{67} +3.43231i q^{68} +6.97119i q^{69} -0.246510i q^{70} -2.61887i q^{71} +6.02886 q^{72} +7.15415i q^{73} -1.04873i q^{74} +0.924425i q^{75} +(3.72701 + 4.00095i) q^{76} +(-0.917557 + 0.233743i) q^{77} +0.334487i q^{78} -10.9113 q^{79} +0.0824425 q^{80} +2.03922 q^{81} -8.41230 q^{82} +14.5167i q^{83} +0.331061 q^{84} -2.73616i q^{85} -0.0533246i q^{86} -2.47066i q^{87} +(2.30074 + 9.03156i) q^{88} -13.9172i q^{89} -1.85251 q^{90} -0.119633i q^{91} -9.45977 q^{92} +3.19602 q^{93} -2.16984 q^{94} +(-2.97108 - 3.18946i) q^{95} -5.26123i q^{96} -19.2960i q^{97} -5.97388 q^{98} +(1.75656 + 6.89539i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 40 q^{4} + 40 q^{5} - 28 q^{9}+O(q^{10}) \) 40 * q + 40 * q^4 + 40 * q^5 - 28 * q^9	\( 40 q + 40 q^{4} + 40 q^{5} - 28 q^{9} - 4 q^{11} + 48 q^{16} + 40 q^{20} + 24 q^{23} + 40 q^{25} - 24 q^{26} + 24 q^{36} - 28 q^{38} - 60 q^{42} - 48 q^{44} - 28 q^{45} - 36 q^{49} - 4 q^{55} - 36 q^{58} - 40 q^{64} - 28 q^{66} + 8 q^{77} + 48 q^{80} + 80 q^{81} + 8 q^{82} + 4 q^{92} + 56 q^{93} - 16 q^{99}+O(q^{100}) \) 40 * q + 40 * q^4 + 40 * q^5 - 28 * q^9 - 4 * q^11 + 48 * q^16 + 40 * q^20 + 24 * q^23 + 40 * q^25 - 24 * q^26 + 24 * q^36 - 28 * q^38 - 60 * q^42 - 48 * q^44 - 28 * q^45 - 36 * q^49 - 4 * q^55 - 36 * q^58 - 40 * q^64 - 28 * q^66 + 8 * q^77 + 48 * q^80 + 80 * q^81 + 8 * q^82 + 4 * q^92 + 56 * q^93 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more