LMFDB - Embedded newform 1445.2.b.i.579.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1445,2,Mod(579,1445)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1445, 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("1445.579");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1445 = 5 \cdot 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1445.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:	$11.5383830921$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	no (minimal twist has level 85)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			579.17
Character	$\chi$	$=$	1445.579
Dual form			1445.2.b.i.579.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+0.951739i q^{2} -2.47483i q^{3} +1.09419 q^{4} +(-2.23233 + 0.129310i) q^{5} +2.35540 q^{6} -0.533377i q^{7} +2.94486i q^{8} -3.12480 q^{9} +(-0.123069 - 2.12459i) q^{10} +4.67492 q^{11} -2.70795i q^{12} +3.92573i q^{13} +0.507636 q^{14} +(0.320020 + 5.52463i) q^{15} -0.614355 q^{16} -2.97399i q^{18} +1.00204 q^{19} +(-2.44260 + 0.141490i) q^{20} -1.32002 q^{21} +4.44930i q^{22} +5.73808i q^{23} +7.28805 q^{24} +(4.96656 - 0.577324i) q^{25} -3.73627 q^{26} +0.308860i q^{27} -0.583618i q^{28} +8.28676 q^{29} +(-5.25801 + 0.304576i) q^{30} -2.47907 q^{31} +5.30502i q^{32} -11.5697i q^{33} +(0.0689710 + 1.19067i) q^{35} -3.41914 q^{36} -4.09373i q^{37} +0.953679i q^{38} +9.71553 q^{39} +(-0.380800 - 6.57390i) q^{40} -0.814533 q^{41} -1.25631i q^{42} -6.43772i q^{43} +5.11527 q^{44} +(6.97557 - 0.404068i) q^{45} -5.46115 q^{46} -1.70505i q^{47} +1.52043i q^{48} +6.71551 q^{49} +(0.549461 + 4.72687i) q^{50} +4.29551i q^{52} +8.16327i q^{53} -0.293954 q^{54} +(-10.4359 + 0.604514i) q^{55} +1.57072 q^{56} -2.47988i q^{57} +7.88683i q^{58} +6.05714 q^{59} +(0.350164 + 6.04502i) q^{60} +1.13106 q^{61} -2.35943i q^{62} +1.66670i q^{63} -6.27771 q^{64} +(-0.507636 - 8.76352i) q^{65} +11.0113 q^{66} +7.68603i q^{67} +14.2008 q^{69} +(-1.13321 + 0.0656424i) q^{70} -6.94272 q^{71} -9.20211i q^{72} -12.0863i q^{73} +3.89616 q^{74} +(-1.42878 - 12.2914i) q^{75} +1.09642 q^{76} -2.49350i q^{77} +9.24665i q^{78} -1.48104 q^{79} +(1.37144 - 0.0794422i) q^{80} -8.61002 q^{81} -0.775222i q^{82} -16.1876i q^{83} -1.44436 q^{84} +6.12703 q^{86} -20.5083i q^{87} +13.7670i q^{88} +12.0717 q^{89} +(0.384567 + 6.63892i) q^{90} +2.09390 q^{91} +6.27857i q^{92} +6.13529i q^{93} +1.62276 q^{94} +(-2.23688 + 0.129573i) q^{95} +13.1290 q^{96} -0.228042i q^{97} +6.39141i q^{98} -14.6082 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 8 q^{4} + 8 q^{9} + 8 q^{15} - 8 q^{16} + 16 q^{19} - 32 q^{21} + 8 q^{25} - 48 q^{26} - 56 q^{30} + 8 q^{35} + 8 q^{36} + 56 q^{49} - 16 q^{50} - 24 q^{55} + 64 q^{59} - 88 q^{60} + 104 q^{64} - 16 q^{66}+ \cdots + 128 q^{94}+O(q^{100}) $ 24 * q - 8 * q^4 + 8 * q^9 + 8 * q^15 - 8 * q^16 + 16 * q^19 - 32 * q^21 + 8 * q^25 - 48 * q^26 - 56 * q^30 + 8 * q^35 + 8 * q^36 + 56 * q^49 - 16 * q^50 - 24 * q^55 + 64 * q^59 - 88 * q^60 + 104 * q^64 - 16 * q^66 + 32 * q^69 - 40 * q^70 - 48 * q^76 - 88 * q^81 + 96 * q^84 + 112 * q^89 + 128 * q^94

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1445\mathbb{Z}\right)^\times$.

$n$	$581$	$1157$
$\chi(n)$	$1$	$-1$

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 $

$2$			0.951739i			0.672981i	0.941687	+	0.336491i	$0.109240\pi$
$2$			0.951739i			0.672981i	−0.941687	+	0.336491i	$0.890760\pi$
$3$		−	2.47483i		−	1.42885i	−0.699714	−	0.714423i	$-0.746689\pi$
$3$		−	2.47483i		−	1.42885i	0.699714	−	0.714423i	$-0.253311\pi$
$4$	1.09419			0.547097
$5$	−2.23233	+	0.129310i	−0.998326	+	0.0578291i
$5$	−2.23233	+	0.129310i	−0.998326	+	0.0578291i
$6$	2.35540			0.961586
$7$		−	0.533377i		−	0.201598i	−0.994907	−	0.100799i	$-0.967860\pi$
$7$		−	0.533377i		−	0.201598i	0.994907	−	0.100799i	$-0.0321399\pi$
$8$			2.94486i			1.04117i
$9$	−3.12480			−1.04160
$10$	−0.123069	−	2.12459i	−0.0389179	−	0.671855i
$11$	4.67492			1.40954			0.704771	−	0.709435i	$-0.251050\pi$
$11$	4.67492			1.40954			0.704771	+	0.709435i	$0.251050\pi$
$12$		−	2.70795i		−	0.781717i
$13$			3.92573i			1.08880i	0.838825	+	0.544401i	$0.183243\pi$
$13$			3.92573i			1.08880i	−0.838825	+	0.544401i	$0.816757\pi$
$14$	0.507636			0.135671
$15$	0.320020	+	5.52463i	0.0826289	+	1.42645i
$16$	−0.614355			−0.153589
$17$		0			0
$17$		0			0
$18$		−	2.97399i		−	0.700977i
$19$	1.00204			0.229883			0.114942	−	0.993372i	$-0.463332\pi$
$19$	1.00204			0.229883			0.114942	+	0.993372i	$0.463332\pi$
$20$	−2.44260	+	0.141490i	−0.546181	+	0.0316381i
$21$	−1.32002			−0.288052
$22$			4.44930i			0.948595i
$23$			5.73808i			1.19647i	0.801320	+	0.598236i	$0.204132\pi$
$23$			5.73808i			1.19647i	−0.801320	+	0.598236i	$0.795868\pi$
$24$	7.28805			1.48767
$25$	4.96656	−	0.577324i	0.993312	−	0.115465i
$26$	−3.73627			−0.732743
$27$			0.308860i			0.0594402i
$28$		−	0.583618i		−	0.110293i
$29$	8.28676			1.53881			0.769406	−	0.638760i	$-0.220552\pi$
$29$	8.28676			1.53881			0.769406	+	0.638760i	$0.220552\pi$
$30$	−5.25801	+	0.304576i	−0.959977	+	0.0556077i
$31$	−2.47907			−0.445254			−0.222627	−	0.974904i	$-0.571463\pi$
$31$	−2.47907			−0.445254			−0.222627	+	0.974904i	$0.571463\pi$
$32$			5.30502i			0.937804i
$33$		−	11.5697i		−	2.01402i
$34$		0			0
$35$	0.0689710	+	1.19067i	0.0116582	+	0.201260i
$36$	−3.41914			−0.569856
$37$		−	4.09373i		−	0.673005i	−0.941683	−	0.336502i	$-0.890756\pi$
$37$		−	4.09373i		−	0.673005i	0.941683	−	0.336502i	$-0.109244\pi$
$38$			0.953679i			0.154707i
$39$	9.71553			1.55573
$40$	−0.380800	−	6.57390i	−0.0602098	−	1.03942i
$41$	−0.814533			−0.127209			−0.0636043	−	0.997975i	$-0.520260\pi$
$41$	−0.814533			−0.127209			−0.0636043	+	0.997975i	$0.520260\pi$
$42$		−	1.25631i		−	0.193854i
$43$		−	6.43772i		−	0.981743i	−0.871232	−	0.490872i	$-0.836678\pi$
$43$		−	6.43772i		−	0.981743i	0.871232	−	0.490872i	$-0.163322\pi$
$44$	5.11527			0.771156
$45$	6.97557	−	0.404068i	1.03986	−	0.0602348i
$46$	−5.46115			−0.805203
$47$		−	1.70505i		−	0.248707i	−0.992238	−	0.124354i	$-0.960314\pi$
$47$		−	1.70505i		−	0.248707i	0.992238	−	0.124354i	$-0.0396857\pi$
$48$			1.52043i			0.219455i
$49$	6.71551			0.959358
$50$	0.549461	+	4.72687i	0.0777056	+	0.668480i
$51$		0			0
$52$			4.29551i			0.595680i
$53$			8.16327i			1.12131i	0.828049	+	0.560656i	$0.189451\pi$
$53$			8.16327i			1.12131i	−0.828049	+	0.560656i	$0.810549\pi$
$54$	−0.293954			−0.0400021
$55$	−10.4359	+	0.604514i	−1.40718	+	0.0815126i
$56$	1.57072			0.209897
$57$		−	2.47988i		−	0.328468i
$58$			7.88683i			1.03559i
$59$	6.05714			0.788572			0.394286	−	0.918988i	$-0.370992\pi$
$59$	6.05714			0.788572			0.394286	+	0.918988i	$0.370992\pi$
$60$	0.350164	+	6.04502i	0.0452060	+	0.780408i
$61$	1.13106			0.144817			0.0724086	−	0.997375i	$-0.476931\pi$
$61$	1.13106			0.144817			0.0724086	+	0.997375i	$0.476931\pi$
$62$		−	2.35943i		−	0.299648i
$63$			1.66670i			0.209984i
$64$	−6.27771			−0.784713
$65$	−0.507636	−	8.76352i	−0.0629645	−	1.08698i
$66$	11.0113			1.35540
$67$			7.68603i			0.938998i	0.882933	+	0.469499i	$0.155565\pi$
$67$			7.68603i			0.938998i	−0.882933	+	0.469499i	$0.844435\pi$
$68$		0			0
$69$	14.2008			1.70957
$70$	−1.13321	+	0.0656424i	−0.135444	+	0.00784576i
$71$	−6.94272			−0.823949			−0.411975	−	0.911195i	$-0.635161\pi$
$71$	−6.94272			−0.823949			−0.411975	+	0.911195i	$0.635161\pi$
$72$		−	9.20211i		−	1.08448i
$73$		−	12.0863i		−	1.41459i	−0.706919	−	0.707295i	$-0.749915\pi$
$73$		−	12.0863i		−	1.41459i	0.706919	−	0.707295i	$-0.250085\pi$
$74$	3.89616			0.452920
$75$	−1.42878	−	12.2914i	−0.164981	−	1.41929i
$76$	1.09642			0.125768
$77$		−	2.49350i		−	0.284160i
$78$			9.24665i			1.04698i
$79$	−1.48104			−0.166630			−0.0833150	−	0.996523i	$-0.526551\pi$
$79$	−1.48104			−0.166630			−0.0833150	+	0.996523i	$0.526551\pi$
$80$	1.37144	−	0.0794422i	0.153332	−	0.00888191i
$81$	−8.61002			−0.956669
$82$		−	0.775222i		−	0.0856090i
$83$		−	16.1876i		−	1.77682i	−0.459048	−	0.888411i	$-0.651810\pi$
$83$		−	16.1876i		−	1.77682i	0.459048	−	0.888411i	$-0.348190\pi$
$84$	−1.44436			−0.157592
$85$		0			0
$86$	6.12703			0.660694
$87$		−	20.5083i		−	2.19872i
$88$			13.7670i			1.46757i
$89$	12.0717			1.27960			0.639800	−	0.768542i	$-0.279017\pi$
$89$	12.0717			1.27960			0.639800	+	0.768542i	$0.279017\pi$
$90$	0.384567	+	6.63892i	0.0405369	+	0.699804i
$91$	2.09390			0.219500
$92$			6.27857i			0.654586i
$93$			6.13529i			0.636199i
$94$	1.62276			0.167375
$95$	−2.23688	+	0.129573i	−0.229499	+	0.0132940i
$96$	13.1290			1.33998
$97$		−	0.228042i		−	0.0231542i	−0.999933	−	0.0115771i	$-0.996315\pi$
$97$		−	0.228042i		−	0.0231542i	0.999933	−	0.0115771i	$-0.00368519\pi$
$98$			6.39141i			0.645630i
$99$	−14.6082			−1.46818
$100$	5.43437	−	0.631704i	0.543437	−	0.0631704i
$101$	6.66539			0.663231			0.331616	−	0.943415i	$-0.392406\pi$
$101$	6.66539			0.663231			0.331616	+	0.943415i	$0.392406\pi$
$102$		0			0
$103$		−	0.350456i		−	0.0345315i	−0.999851	−	0.0172657i	$-0.994504\pi$
$103$		−	0.350456i		−	0.0345315i	0.999851	−	0.0172657i	$-0.00549613\pi$
$104$	−11.5607			−1.13362
$105$	2.94672	−	0.170692i	0.287570	−	0.0166578i
$106$	−7.76930			−0.754621
$107$		−	7.79876i		−	0.753935i	−0.926227	−	0.376967i	$-0.876967\pi$
$107$		−	7.79876i		−	0.753935i	0.926227	−	0.376967i	$-0.123033\pi$
$108$			0.337953i			0.0325195i
$109$	12.1781			1.16646			0.583228	−	0.812309i	$-0.301790\pi$
$109$	12.1781			1.16646			0.583228	+	0.812309i	$0.301790\pi$
$110$	−0.575339	−	9.93230i	−0.0548564	−	0.947007i
$111$	−10.1313			−0.961620
$112$			0.327683i			0.0309632i
$113$			17.8780i			1.68182i	0.541175	+	0.840910i	$0.317980\pi$
$113$			17.8780i			1.68182i	−0.541175	+	0.840910i	$0.682020\pi$
$114$	2.36020			0.221053
$115$	−0.741990	−	12.8093i	−0.0691910	−	1.19447i
$116$	9.06731			0.841879
$117$		−	12.2671i		−	1.13410i
$118$			5.76481i			0.530694i
$119$		0			0
$120$	−16.2693	+	0.942417i	−1.48518	+	0.0860305i
$121$	10.8549			0.986808
$122$			1.07647i			0.0974592i
$123$			2.01583i			0.181762i
$124$	−2.71258			−0.243597
$125$	−11.0123	+	1.93100i	−0.984972	+	0.172714i
$126$	−1.58626			−0.141315
$127$		−	12.3969i		−	1.10005i	−0.835148	−	0.550025i	$-0.814618\pi$
$127$		−	12.3969i		−	1.10005i	0.835148	−	0.550025i	$-0.185382\pi$
$128$			4.63531i			0.409707i
$129$	−15.9323			−1.40276
$130$	8.34058	−	0.483137i	0.731517	−	0.0423739i
$131$	10.0314			0.876446			0.438223	−	0.898866i	$-0.355608\pi$
$131$	10.0314			0.876446			0.438223	+	0.898866i	$0.355608\pi$
$132$		−	12.6594i		−	1.10186i
$133$		−	0.534465i		−	0.0463440i
$134$	−7.31509			−0.631928
$135$	−0.0399387	−	0.689477i	−0.00343737	−	0.0593407i
$136$		0			0
$137$			3.06808i			0.262124i	0.991374	+	0.131062i	$0.0418386\pi$
$137$			3.06808i			0.262124i	−0.991374	+	0.131062i	$0.958161\pi$
$138$			13.5154i			1.15051i
$139$	−12.2731			−1.04099			−0.520497	−	0.853864i	$-0.674253\pi$
$139$	−12.2731			−1.04099			−0.520497	+	0.853864i	$0.674253\pi$
$140$	0.0754676	+	1.30283i	0.00637817	+	0.110109i
$141$	−4.21972			−0.355364
$142$		−	6.60766i		−	0.554502i
$143$			18.3525i			1.53471i
$144$	1.91974			0.159978
$145$	−18.4987	+	1.07156i	−1.53624	+	0.0889882i
$146$	11.5030			0.951992
$147$		−	16.6198i		−	1.37078i
$148$		−	4.47933i		−	0.368199i
$149$	5.46544			0.447747			0.223873	−	0.974618i	$-0.428130\pi$
$149$	5.46544			0.447747			0.223873	+	0.974618i	$0.428130\pi$
$150$	11.6982	−	1.35983i	0.955155	−	0.111029i
$151$	−5.00780			−0.407529			−0.203765	−	0.979020i	$-0.565318\pi$
$151$	−5.00780			−0.407529			−0.203765	+	0.979020i	$0.565318\pi$
$152$			2.95087i			0.239347i
$153$		0			0
$154$	2.37316			0.191235
$155$	5.53409	−	0.320568i	0.444509	−	0.0257487i
$156$	10.6307			0.851135
$157$			10.9442i			0.873443i	0.899597	+	0.436721i	$0.143860\pi$
$157$			10.9442i			0.873443i	−0.899597	+	0.436721i	$0.856140\pi$
$158$		−	1.40956i		−	0.112139i
$159$	20.2027			1.60218
$160$	−0.685992	−	11.8425i	−0.0542324	−	0.936235i
$161$	3.06056			0.241206
$162$		−	8.19449i		−	0.643820i
$163$		−	7.38954i		−	0.578793i	−0.957209	−	0.289397i	$-0.906545\pi$
$163$		−	7.38954i		−	0.578793i	0.957209	−	0.289397i	$-0.0934547\pi$
$164$	−0.891256			−0.0695954
$165$	1.49607	+	25.8272i	0.116469	+	2.01065i
$166$	15.4064			1.19577
$167$			19.4979i			1.50879i	0.656419	+	0.754396i	$0.272070\pi$
$167$			19.4979i			1.50879i	−0.656419	+	0.754396i	$0.727930\pi$
$168$		−	3.88728i		−	0.299910i
$169$	−2.41138			−0.185491
$170$		0			0
$171$	−3.13117			−0.239447
$172$		−	7.04411i		−	0.537108i
$173$			13.2997i			1.01116i	0.862780	+	0.505579i	$0.168721\pi$
$173$			13.2997i			1.01116i	−0.862780	+	0.505579i	$0.831279\pi$
$174$	19.5186			1.47970
$175$	−0.307931	−	2.64905i	−0.0232774	−	0.200249i
$176$	−2.87206			−0.216490
$177$		−	14.9904i		−	1.12675i
$178$			11.4891i			0.861146i
$179$	10.1625			0.759582			0.379791	−	0.925072i	$-0.375996\pi$
$179$	10.1625			0.759582			0.379791	+	0.925072i	$0.375996\pi$
$180$	7.63262	−	0.442128i	0.568902	−	0.0329543i
$181$	−19.6193			−1.45829			−0.729145	−	0.684359i	$-0.760082\pi$
$181$	−19.6193			−1.45829			−0.729145	+	0.684359i	$0.760082\pi$
$182$			1.99284i			0.147719i
$183$		−	2.79918i		−	0.206921i
$184$	−16.8979			−1.24573
$185$	0.529360	+	9.13854i	0.0389193	+	0.671879i
$186$	−5.83919			−0.428150
$187$		0			0
$188$		−	1.86566i		−	0.136067i
$189$	0.164739			0.0119830
$190$	−0.123320	−	2.12892i	−0.00894658	−	0.154448i
$191$	−8.81287			−0.637677			−0.318838	−	0.947809i	$-0.603293\pi$
$191$	−8.81287			−0.637677			−0.318838	+	0.947809i	$0.603293\pi$
$192$			15.5363i			1.12123i
$193$			15.4624i			1.11301i	0.830845	+	0.556504i	$0.187858\pi$
$193$			15.4624i			1.11301i	−0.830845	+	0.556504i	$0.812142\pi$
$194$	0.217037			0.0155823
$195$	−21.6882	+	1.25631i	−1.55313	+	0.0899666i
$196$	7.34806			0.524862
$197$		−	0.230147i		−	0.0163973i	−0.999966	−	0.00819866i	$-0.997390\pi$
$197$		−	0.230147i		−	0.0163973i	0.999966	−	0.00819866i	$-0.00260974\pi$
$198$		−	13.9032i		−	0.988057i
$199$	−21.4615			−1.52137			−0.760684	−	0.649122i	$-0.775136\pi$
$199$	−21.4615			−1.52137			−0.760684	+	0.649122i	$0.775136\pi$
$200$	1.70014	+	14.6258i	0.120218	+	1.03420i
$201$	19.0216			1.34168
$202$			6.34371i			0.446342i
$203$		−	4.41997i		−	0.310221i
$204$		0			0
$205$	1.81830	−	0.105327i	0.126996	−	0.00735637i
$206$	0.333543			0.0232390
$207$		−	17.9304i		−	1.24625i
$208$		−	2.41179i		−	0.167228i
$209$	4.68445			0.324030
$210$	0.162454	+	2.80450i	0.0112104	+	0.193529i
$211$	−15.5447			−1.07014			−0.535071	−	0.844807i	$-0.679715\pi$
$211$	−15.5447			−1.07014			−0.535071	+	0.844807i	$0.679715\pi$
$212$			8.93219i			0.613465i
$213$			17.1821i			1.17730i
$214$	7.42238			0.507384
$215$	0.832461	+	14.3711i	0.0567734	+	0.980100i
$216$	−0.909551			−0.0618871
$217$			1.32228i			0.0897622i
$218$			11.5904i			0.785002i
$219$	−29.9115			−2.02123
$220$	−11.4189	+	0.661455i	−0.769865	+	0.0445953i
$221$		0			0
$222$		−	9.64235i		−	0.647152i
$223$		−	1.06955i		−	0.0716224i	−0.999359	−	0.0358112i	$-0.988599\pi$
$223$		−	1.06955i		−	0.0716224i	0.999359	−	0.0358112i	$-0.0114015\pi$
$224$	2.82958			0.189059
$225$	−15.5195	+	1.80402i	−1.03463	+	0.120268i
$226$	−17.0152			−1.13183
$227$			2.06789i			0.137251i	0.997642	+	0.0686255i	$0.0218614\pi$
$227$			2.06789i			0.137251i	−0.997642	+	0.0686255i	$0.978139\pi$
$228$		−	2.71347i		−	0.179704i
$229$	12.8134			0.846732			0.423366	−	0.905959i	$-0.360849\pi$
$229$	12.8134			0.846732			0.423366	+	0.905959i	$0.360849\pi$
$230$	12.1911	−	0.706181i	0.803856	−	0.0465642i
$231$	−6.17099			−0.406021
$232$			24.4034i			1.60216i
$233$		−	6.48391i		−	0.424775i	−0.977185	−	0.212388i	$-0.931876\pi$
$233$		−	6.48391i		−	0.424775i	0.977185	−	0.212388i	$-0.0681239\pi$
$234$	11.6751			0.763226
$235$	0.220480	+	3.80623i	0.0143825	+	0.248291i
$236$	6.62768			0.431425
$237$			3.66533i			0.238089i
$238$		0			0
$239$	1.26828			0.0820381			0.0410190	−	0.999158i	$-0.486940\pi$
$239$	1.26828			0.0820381			0.0410190	+	0.999158i	$0.486940\pi$
$240$	−0.196606	−	3.39409i	−0.0126909	−	0.219087i
$241$	2.49584			0.160771			0.0803856	−	0.996764i	$-0.474385\pi$
$241$	2.49584			0.160771			0.0803856	+	0.996764i	$0.474385\pi$
$242$			10.3310i			0.664103i
$243$			22.2350i			1.42637i
$244$	1.23760			0.0792290
$245$	−14.9912	+	0.868382i	−0.957753	+	0.0554789i
$246$	−1.91855			−0.122322
$247$			3.93374i			0.250298i
$248$		−	7.30052i		−	0.463584i
$249$	−40.0617			−2.53881
$250$	−1.83781	−	10.4809i	−0.116233	−	0.662867i
$251$	−17.3565			−1.09553			−0.547765	−	0.836632i	$-0.684521\pi$
$251$	−17.3565			−1.09553			−0.547765	+	0.836632i	$0.684521\pi$
$252$			1.82369i			0.114882i
$253$			26.8251i			1.68648i
$254$	11.7987			0.740313
$255$		0			0
$256$	−16.9670			−1.06044
$257$			15.5551i			0.970299i	0.874431	+	0.485149i	$0.161235\pi$
$257$			15.5551i			0.970299i	−0.874431	+	0.485149i	$0.838765\pi$
$258$		−	15.1634i		−	0.944030i
$259$	−2.18350			−0.135676
$260$	−0.555452	−	9.58898i	−0.0344477	−	0.594683i
$261$	−25.8945			−1.60283
$262$			9.54726i			0.589831i
$263$			9.04093i			0.557488i	0.960365	+	0.278744i	$0.0899181\pi$
$263$			9.04093i			0.557488i	−0.960365	+	0.278744i	$0.910082\pi$
$264$	34.0711			2.09693
$265$	−1.05559	−	18.2231i	−0.0648445	−	1.11943i
$266$	0.508671			0.0311886
$267$		−	29.8755i		−	1.82835i
$268$			8.41000i			0.513723i
$269$	−3.01989			−0.184126			−0.0920630	−	0.995753i	$-0.529346\pi$
$269$	−3.01989			−0.184126			−0.0920630	+	0.995753i	$0.529346\pi$
$270$	0.656202	−	0.0380112i	0.0399352	−	0.00231329i
$271$	−13.1638			−0.799642			−0.399821	−	0.916593i	$-0.630928\pi$
$271$	−13.1638			−0.799642			−0.399821	+	0.916593i	$0.630928\pi$
$272$		0			0
$273$		−	5.18205i		−	0.313632i
$274$	−2.92001			−0.176404
$275$	23.2183	−	2.69894i	1.40011	−	0.162752i
$276$	15.5384			0.935302
$277$			4.05137i			0.243423i	0.992566	+	0.121712i	$0.0388383\pi$
$277$			4.05137i			0.243423i	−0.992566	+	0.121712i	$0.961162\pi$
$278$		−	11.6808i		−	0.700569i
$279$	7.74660			0.463777
$280$	−3.50637	+	0.203110i	−0.209546	+	0.0121382i
$281$	14.2650			0.850976			0.425488	−	0.904964i	$-0.360102\pi$
$281$	14.2650			0.850976			0.425488	+	0.904964i	$0.360102\pi$
$282$		−	4.01607i		−	0.239154i
$283$		−	5.57411i		−	0.331346i	−0.986181	−	0.165673i	$-0.947020\pi$
$283$		−	5.57411i		−	0.331346i	0.986181	−	0.165673i	$-0.0529797\pi$
$284$	−7.59668			−0.450780
$285$	0.320673	+	5.53590i	0.0189950	+	0.327918i
$286$	−17.4668			−1.03283
$287$			0.434453i			0.0256450i
$288$		−	16.5771i		−	0.976817i
$289$		0			0
$290$	−1.01984	−	17.6060i	−0.0598873	−	1.03386i
$291$	−0.564367			−0.0330838
$292$		−	13.2247i		−	0.773917i
$293$			1.97120i			0.115159i	0.998341	+	0.0575795i	$0.0183383\pi$
$293$			1.97120i			0.115159i	−0.998341	+	0.0575795i	$0.981662\pi$
$294$	15.8177			0.922506
$295$	−13.5215	+	0.783248i	−0.787252	+	0.0456024i
$296$	12.0555			0.700710
$297$			1.44390i			0.0837834i
$298$			5.20168i			0.301325i
$299$	−22.5262			−1.30272
$300$	−1.56336	−	13.4492i	−0.0902607	−	0.776488i
$301$	−3.43373			−0.197917
$302$		−	4.76612i		−	0.274260i
$303$		−	16.4957i		−	0.947655i
$304$	−0.615608			−0.0353075
$305$	−2.52489	+	0.146257i	−0.144575	+	0.00837466i
$306$		0			0
$307$			1.69613i			0.0968034i	0.998828	+	0.0484017i	$0.0154128\pi$
$307$			1.69613i			0.0968034i	−0.998828	+	0.0484017i	$0.984587\pi$
$308$		−	2.72837i		−	0.155463i
$309$	−0.867321			−0.0493402
$310$	0.305097	+	5.26701i	0.0173284	+	0.299146i
$311$	10.8927			0.617666			0.308833	−	0.951116i	$-0.400062\pi$
$311$	10.8927			0.617666			0.308833	+	0.951116i	$0.400062\pi$
$312$			28.6109i			1.61977i
$313$		−	26.2916i		−	1.48609i	−0.669241	−	0.743045i	$-0.733381\pi$
$313$		−	26.2916i		−	1.48609i	0.669241	−	0.743045i	$-0.266619\pi$
$314$	−10.4160			−0.587811
$315$	−0.215521	−	3.72061i	−0.0121432	−	0.209633i
$316$	−1.62054			−0.0911627
$317$		−	25.0112i		−	1.40477i	−0.711797	−	0.702386i	$-0.752118\pi$
$317$		−	25.0112i		−	1.40477i	0.711797	−	0.702386i	$-0.247882\pi$
$318$			19.2277i			1.07824i
$319$	38.7399			2.16902
$320$	14.0139	−	0.811769i	0.783400	−	0.0453793i
$321$	−19.3006			−1.07726
$322$			2.91286i			0.162327i
$323$		0			0
$324$	−9.42103			−0.523390
$325$	2.26642	+	19.4974i	0.125718	+	1.08152i
$326$	7.03291			0.389517
$327$		−	30.1389i		−	1.66668i
$328$		−	2.39869i		−	0.132445i
$329$	−0.909436			−0.0501388
$330$	−24.5808	+	1.42387i	−1.35313	+	0.0783814i
$331$	−32.2873			−1.77467			−0.887335	−	0.461125i	$-0.847446\pi$
$331$	−32.2873			−1.77467			−0.887335	+	0.461125i	$0.847446\pi$
$332$		−	17.7124i		−	0.972094i
$333$			12.7921i			0.701002i
$334$	−18.5569			−1.01539
$335$	−0.993880	−	17.1577i	−0.0543015	−	0.937427i
$336$	0.810961			0.0442416
$337$		−	12.8636i		−	0.700723i	−0.936615	−	0.350361i	$-0.886059\pi$
$337$		−	12.8636i		−	0.700723i	0.936615	−	0.350361i	$-0.113941\pi$
$338$		−	2.29500i		−	0.124832i
$339$	44.2450			2.40306
$340$		0			0
$341$	−11.5895			−0.627604
$342$		−	2.98006i		−	0.161143i
$343$		−	7.31554i		−	0.395002i
$344$	18.9582			1.02216
$345$	−31.7008	+	1.83630i	−1.70671	+	0.0988632i
$346$	−12.6579			−0.680490
$347$			26.9376i			1.44609i	0.690802	+	0.723044i	$0.257257\pi$
$347$			26.9376i			1.44609i	−0.690802	+	0.723044i	$0.742743\pi$
$348$		−	22.4401i		−	1.20291i
$349$	−14.3193			−0.766496			−0.383248	−	0.923645i	$-0.625195\pi$
$349$	−14.3193			−0.766496			−0.383248	+	0.923645i	$0.625195\pi$
$350$	2.52120	−	0.293070i	0.134764	−	0.0156653i
$351$	−1.21250			−0.0647186
$352$			24.8006i			1.32187i
$353$			1.65351i			0.0880076i	0.999031	+	0.0440038i	$0.0140114\pi$
$353$			1.65351i			0.0880076i	−0.999031	+	0.0440038i	$0.985989\pi$
$354$	14.2670			0.758280
$355$	15.4984	−	0.897762i	0.822570	−	0.0476483i
$356$	13.2088			0.700065
$357$		0			0
$358$			9.67206i			0.511184i
$359$	17.3638			0.916427			0.458214	−	0.888842i	$-0.348489\pi$
$359$	17.3638			0.916427			0.458214	+	0.888842i	$0.348489\pi$
$360$	1.18992	+	20.5421i	0.0627145	+	1.08266i
$361$	−17.9959			−0.947154
$362$		−	18.6724i		−	0.981402i
$363$		−	26.8640i		−	1.41000i
$364$	2.29113			0.120088
$365$	1.56287	+	26.9805i	0.0818045	+	1.41222i
$366$	2.66409			0.139254
$367$			9.57097i			0.499601i	0.968297	+	0.249800i	$0.0803650\pi$
$367$			9.57097i			0.499601i	−0.968297	+	0.249800i	$0.919635\pi$
$368$		−	3.52522i		−	0.183765i
$369$	2.54525			0.132501
$370$	−8.69750	+	0.503812i	−0.452162	+	0.0261919i
$371$	4.35410			0.226054
$372$			6.71319i			0.348063i
$373$			14.4236i			0.746828i	0.927665	+	0.373414i	$0.121813\pi$
$373$			14.4236i			0.746828i	−0.927665	+	0.373414i	$0.878187\pi$
$374$		0			0
$375$	4.77890	+	27.2537i	0.246781	+	1.40737i
$376$	5.02114			0.258946
$377$			32.5316i			1.67546i
$378$			0.156789i			0.00806434i
$379$	9.51689			0.488850			0.244425	−	0.969668i	$-0.421401\pi$
$379$	9.51689			0.488850			0.244425	+	0.969668i	$0.421401\pi$
$380$	−2.44758	+	0.141778i	−0.125558	+	0.00727308i
$381$	−30.6804			−1.57180
$382$		−	8.38755i		−	0.429144i
$383$		−	27.7753i		−	1.41925i	−0.704579	−	0.709626i	$-0.748864\pi$
$383$		−	27.7753i		−	1.41925i	0.704579	−	0.709626i	$-0.251136\pi$
$384$	11.4716			0.585408
$385$	0.322434	+	5.56630i	0.0164328	+	0.283685i
$386$	−14.7162			−0.749033
$387$			20.1166i			1.02258i
$388$		−	0.249522i		−	0.0126676i
$389$	−21.0485			−1.06720			−0.533599	−	0.845737i	$-0.679161\pi$
$389$	−21.0485			−1.06720			−0.533599	+	0.845737i	$0.679161\pi$
$390$	−1.19568	−	20.6415i	−0.0605458	−	1.04523i
$391$		0			0
$392$			19.7763i			0.998852i
$393$		−	24.8260i		−	1.25231i
$394$	0.219040			0.0110351
$395$	3.30616	−	0.191513i	0.166351	−	0.00963607i
$396$	−15.9842			−0.803236
$397$		−	29.6505i		−	1.48812i	−0.668114	−	0.744059i	$-0.732898\pi$
$397$		−	29.6505i		−	1.48812i	0.668114	−	0.744059i	$-0.267102\pi$
$398$		−	20.4258i		−	1.02385i
$399$	−1.32271			−0.0662184
$400$	−3.05123	+	0.354682i	−0.152562	+	0.0177341i
$401$	−16.5656			−0.827245			−0.413622	−	0.910448i	$-0.635737\pi$
$401$	−16.5656			−0.827245			−0.413622	+	0.910448i	$0.635737\pi$
$402$			18.1036i			0.902928i
$403$		−	9.73217i		−	0.484794i
$404$	7.29322			0.362851
$405$	19.2204	−	1.11336i	0.955068	−	0.0553234i
$406$	4.20666			0.208773
$407$		−	19.1379i		−	0.948629i
$408$		0			0
$409$	19.3593			0.957257			0.478629	−	0.878017i	$-0.341134\pi$
$409$	19.3593			0.957257			0.478629	+	0.878017i	$0.341134\pi$
$410$	0.100244	+	1.73055i	0.00495069	+	0.0854657i
$411$	7.59298			0.374534
$412$		−	0.383467i		−	0.0188921i
$413$		−	3.23074i		−	0.158974i
$414$	17.0650			0.838700
$415$	2.09322	+	36.1361i	0.102752	+	1.77385i
$416$	−20.8261			−1.02108
$417$			30.3740i			1.48742i
$418$			4.45837i			0.218066i
$419$	−14.4016			−0.703565			−0.351783	−	0.936082i	$-0.614424\pi$
$419$	−14.4016			−0.703565			−0.351783	+	0.936082i	$0.614424\pi$
$420$	3.22428	−	0.186770i	0.157329	−	0.00911343i
$421$	26.7439			1.30342			0.651710	−	0.758468i	$-0.274052\pi$
$421$	26.7439			1.30342			0.651710	+	0.758468i	$0.274052\pi$
$422$		−	14.7945i		−	0.720185i
$423$			5.32795i			0.259054i
$424$	−24.0397			−1.16747
$425$		0			0
$426$	−16.3529			−0.792298
$427$		−	0.603281i		−	0.0291948i
$428$		−	8.53335i		−	0.412475i
$429$	45.4194			2.19287
$430$	−13.6775	+	0.792285i	−0.659589	+	0.0382074i
$431$	28.6183			1.37850			0.689248	−	0.724526i	$-0.257941\pi$
$431$	28.6183			1.37850			0.689248	+	0.724526i	$0.257941\pi$
$432$		−	0.189750i		−	0.00912935i
$433$		−	36.1924i		−	1.73930i	−0.493672	−	0.869648i	$-0.664346\pi$
$433$		−	36.1924i		−	1.73930i	0.493672	−	0.869648i	$-0.335654\pi$
$434$	−1.25847			−0.0604083
$435$	2.65193	+	45.7813i	0.127150	+	2.19505i
$436$	13.3252			0.638164
$437$			5.74978i			0.275049i
$438$		−	28.4679i		−	1.36025i
$439$	−32.4410			−1.54833			−0.774163	−	0.632986i	$-0.781829\pi$
$439$	−32.4410			−1.54833			−0.774163	+	0.632986i	$0.781829\pi$
$440$	−1.78021	−	30.7324i	−0.0848682	−	1.46511i
$441$	−20.9846			−0.999268
$442$		0			0
$443$			1.88468i			0.0895437i	0.998997	+	0.0447719i	$0.0142561\pi$
$443$			1.88468i			0.0895437i	−0.998997	+	0.0447719i	$0.985744\pi$
$444$	−11.0856			−0.526099
$445$	−26.9480	+	1.56099i	−1.27746	+	0.0739982i
$446$	1.01793			0.0482005
$447$		−	13.5261i		−	0.639761i
$448$			3.34839i			0.158196i
$449$	−2.00168			−0.0944652			−0.0472326	−	0.998884i	$-0.515040\pi$
$449$	−2.00168			−0.0944652			−0.0472326	+	0.998884i	$0.515040\pi$
$450$	−1.71696	−	14.7705i	−0.0809381	−	0.696289i
$451$	−3.80788			−0.179306
$452$			19.5620i			0.920118i
$453$			12.3935i			0.582297i
$454$	−1.96810			−0.0923673
$455$	−4.67426	+	0.270762i	−0.219133	+	0.0126935i
$456$	7.30290			0.341990
$457$		−	17.6583i		−	0.826022i	−0.910726	−	0.413011i	$-0.864477\pi$
$457$		−	17.6583i		−	0.826022i	0.910726	−	0.413011i	$-0.135523\pi$
$458$			12.1950i			0.569834i
$459$		0			0
$460$	−0.811881	−	14.0158i	−0.0378541	−	0.653490i
$461$	−31.8412			−1.48299			−0.741497	−	0.670957i	$-0.765884\pi$
$461$	−31.8412			−1.48299			−0.741497	+	0.670957i	$0.765884\pi$
$462$		−	5.87317i		−	0.273245i
$463$		−	15.7977i		−	0.734179i	−0.930186	−	0.367090i	$-0.880354\pi$
$463$		−	15.7977i		−	0.734179i	0.930186	−	0.367090i	$-0.119646\pi$
$464$	−5.09101			−0.236344
$465$	−0.793353	−	13.6960i	−0.0367909	−	0.635135i
$466$	6.17099			0.285866
$467$		−	8.86530i		−	0.410237i	−0.978737	−	0.205119i	$-0.934242\pi$
$467$		−	8.86530i		−	0.410237i	0.978737	−	0.205119i	$-0.0657580\pi$
$468$		−	13.4226i		−	0.620460i
$469$	4.09956			0.189300
$470$	−3.62254	+	0.209839i	−0.167095	+	0.00967917i
$471$	27.0851			1.24802
$472$			17.8374i			0.821035i
$473$		−	30.0958i		−	1.38381i
$474$	−3.48843			−0.160229
$475$	4.97668	−	0.578501i	0.228346	−	0.0265434i
$476$		0			0
$477$		−	25.5086i		−	1.16796i
$478$			1.20707i			0.0552101i
$479$	−11.9097			−0.544169			−0.272084	−	0.962273i	$-0.587713\pi$
$479$	−11.9097			−0.544169			−0.272084	+	0.962273i	$0.587713\pi$
$480$	−29.3083	+	1.69772i	−1.33774	+	0.0774898i
$481$	16.0709			0.732769
$482$			2.37539i			0.108196i
$483$		−	7.57438i		−	0.344646i
$484$	11.8773			0.539879
$485$	0.0294881	+	0.509065i	0.00133899	+	0.0231154i
$486$	−21.1619			−0.959922
$487$		−	26.7760i		−	1.21334i	−0.794955	−	0.606668i	$-0.792506\pi$
$487$		−	26.7760i		−	1.21334i	0.794955	−	0.606668i	$-0.207494\pi$
$488$			3.33081i			0.150779i
$489$	−18.2879			−0.827006
$490$	−0.826473	−	14.2677i	−0.0373362	−	0.644549i
$491$	−23.1191			−1.04335			−0.521676	−	0.853144i	$-0.674693\pi$
$491$	−23.1191			−1.04335			−0.521676	+	0.853144i	$0.674693\pi$
$492$			2.20571i			0.0994411i
$493$		0			0
$494$	−3.74389			−0.168446
$495$	32.6103	−	1.88898i	1.46572	−	0.0849035i
$496$	1.52303			0.0683860
$497$			3.70309i			0.166106i
$498$		−	38.1283i		−	1.70857i
$499$	−4.96635			−0.222324			−0.111162	−	0.993802i	$-0.535457\pi$
$499$	−4.96635			−0.222324			−0.111162	+	0.993802i	$0.535457\pi$
$500$	−12.0496	+	2.11289i	−0.538875	+	0.0944912i
$501$	48.2540			2.15583
$502$		−	16.5188i		−	0.737271i
$503$		−	23.3806i		−	1.04249i	−0.853407	−	0.521245i	$-0.825468\pi$
$503$		−	23.3806i		−	1.04249i	0.853407	−	0.521245i	$-0.174532\pi$
$504$	−4.90820			−0.218629
$505$	−14.8793	+	0.861901i	−0.662121	+	0.0383541i
$506$	−25.5305			−1.13497
$507$			5.96776i			0.265038i
$508$		−	13.5646i		−	0.601834i
$509$	−23.9562			−1.06184			−0.530921	−	0.847422i	$-0.678154\pi$
$509$	−23.9562			−1.06184			−0.530921	+	0.847422i	$0.678154\pi$
$510$		0			0
$511$	−6.44654			−0.285178
$512$		−	6.87755i		−	0.303948i
$513$			0.309490i			0.0136643i
$514$	−14.8044			−0.652993
$515$	0.0453175	+	0.782333i	0.00199693	+	0.0344737i
$516$	−17.4330			−0.767445
$517$		−	7.97098i		−	0.350563i
$518$		−	2.07812i		−	0.0913075i
$519$	32.9146			1.44479
$520$	25.8074	−	1.49492i	1.13173	−	0.0655565i
$521$	7.58483			0.332297			0.166149	−	0.986101i	$-0.446867\pi$
$521$	7.58483			0.332297			0.166149	+	0.986101i	$0.446867\pi$
$522$		−	24.6448i		−	1.07867i
$523$		−	17.3848i		−	0.760185i	−0.924948	−	0.380093i	$-0.875892\pi$
$523$		−	17.3848i		−	0.760185i	0.924948	−	0.380093i	$-0.124108\pi$
$524$	10.9763			0.479500
$525$	−6.55596	+	0.762079i	−0.286125	+	0.0332599i
$526$	−8.60461			−0.375179
$527$		0			0
$528$			7.10788i			0.309331i
$529$	−9.92555			−0.431546
$530$	17.3436	−	1.00465i	0.753358	−	0.0436391i
$531$	−18.9273			−0.821377
$532$		−	0.584808i		−	0.0253546i
$533$		−	3.19764i		−	0.138505i
$534$	28.4337			1.23045
$535$	1.00846	+	17.4094i	0.0435994	+	0.752673i
$536$	−22.6343			−0.977654
$537$		−	25.1505i		−	1.08533i
$538$		−	2.87415i		−	0.123913i
$539$	31.3945			1.35226
$540$	−0.0437006	−	0.754421i	−0.00188058	−	0.0324651i
$541$	−22.2354			−0.955974			−0.477987	−	0.878367i	$-0.658633\pi$
$541$	−22.2354			−0.955974			−0.477987	+	0.878367i	$0.658633\pi$
$542$		−	12.5285i		−	0.538144i
$543$			48.5545i			2.08367i
$544$		0			0
$545$	−27.1856	+	1.57475i	−1.16450	+	0.0674551i
$546$	4.93196			0.211068
$547$			40.1891i			1.71836i	0.511672	+	0.859181i	$0.329026\pi$
$547$			40.1891i			1.71836i	−0.511672	+	0.859181i	$0.670974\pi$
$548$			3.35707i			0.143407i
$549$	−3.53433			−0.150842
$550$	2.56869	+	22.0977i	0.109529	+	0.942250i
$551$	8.30365			0.353747
$552$			41.8194i			1.77995i
$553$			0.789953i			0.0335922i
$554$	−3.85585			−0.163819
$555$	22.6164	−	1.31008i	0.960011	−	0.0556097i
$556$	−13.4292			−0.569524
$557$		−	6.44000i		−	0.272872i	−0.990649	−	0.136436i	$-0.956435\pi$
$557$		−	6.44000i		−	0.272872i	0.990649	−	0.136436i	$-0.0435647\pi$
$558$			7.37274i			0.312113i
$559$	25.2728			1.06892
$560$	−0.0423727	−	0.731496i	−0.00179057	−	0.0309113i
$561$		0			0
$562$			13.5765i			0.572691i
$563$		−	19.8830i		−	0.837967i	−0.907994	−	0.418984i	$-0.862386\pi$
$563$		−	19.8830i		−	0.837967i	0.907994	−	0.418984i	$-0.137614\pi$
$564$	−4.61719			−0.194419
$565$	−2.31180	−	39.9095i	−0.0972582	−	1.67900i
$566$	5.30510			0.222990
$567$			4.59239i			0.192862i
$568$		−	20.4454i		−	0.857869i
$569$	−6.47627			−0.271499			−0.135750	−	0.990743i	$-0.543344\pi$
$569$	−6.47627			−0.271499			−0.135750	+	0.990743i	$0.543344\pi$
$570$	−5.26873	+	0.305197i	−0.220683	+	0.0127833i
$571$	36.5954			1.53147			0.765736	−	0.643155i	$-0.222375\pi$
$571$	36.5954			1.53147			0.765736	+	0.643155i	$0.222375\pi$
$572$			20.0812i			0.839636i
$573$			21.8104i			0.911142i
$574$	−0.413486			−0.0172586
$575$	3.31273	+	28.4985i	0.138150	+	1.18847i
$576$	19.6166			0.817357
$577$		−	19.2887i		−	0.802999i	−0.915859	−	0.401500i	$-0.868489\pi$
$577$		−	19.2887i		−	0.802999i	0.915859	−	0.401500i	$-0.131511\pi$
$578$		0			0
$579$	38.2669			1.59032
$580$	−20.2412	+	1.17249i	−0.840470	+	0.0486851i
$581$	−8.63411			−0.358203
$582$		−	0.537130i		−	0.0222647i
$583$			38.1626i			1.58053i
$584$	35.5924			1.47282
$585$	1.58626	+	27.3842i	0.0655838	+	1.13220i
$586$	−1.87607			−0.0774998
$587$			17.8880i			0.738316i	0.929367	+	0.369158i	$0.120354\pi$
$587$			17.8880i			0.738316i	−0.929367	+	0.369158i	$0.879646\pi$
$588$		−	18.1852i		−	0.749946i
$589$	−2.48412			−0.102357
$590$	−0.745447	−	12.8689i	−0.0306896	−	0.529806i
$591$	−0.569576			−0.0234292
$592$			2.51500i			0.103366i
$593$			22.6220i			0.928975i	0.885580	+	0.464487i	$0.153761\pi$
$593$			22.6220i			0.928975i	−0.885580	+	0.464487i	$0.846239\pi$
$594$	−1.37421			−0.0563847
$595$		0			0
$596$	5.98025			0.244961
$597$			53.1137i			2.17380i
$598$		−	21.4390i		−	0.876707i
$599$	17.4019			0.711023			0.355511	−	0.934672i	$-0.384307\pi$
$599$	17.4019			0.711023			0.355511	+	0.934672i	$0.384307\pi$
$600$	36.1965	−	4.20756i	1.47772	−	0.171773i
$601$	−21.5491			−0.879006			−0.439503	−	0.898241i	$-0.644845\pi$
$601$	−21.5491			−0.879006			−0.439503	+	0.898241i	$0.644845\pi$
$602$		−	3.26802i		−	0.133194i
$603$		−	24.0173i		−	0.978061i
$604$	−5.47951			−0.222958
$605$	−24.2317	+	1.40364i	−0.985157	+	0.0570663i
$606$	15.6996			0.637754
$607$			16.0617i			0.651925i	0.945383	+	0.325962i	$0.105688\pi$
$607$			16.0617i			0.651925i	−0.945383	+	0.325962i	$0.894312\pi$
$608$			5.31584i			0.215586i
$609$	−10.9387			−0.443258
$610$	−0.139199	−	2.40304i	−0.00563598	−	0.0972961i
$611$	6.69358			0.270793
$612$		0			0
$613$			15.6440i			0.631855i	0.948783	+	0.315928i	$0.102316\pi$
$613$			15.6440i			0.631855i	−0.948783	+	0.315928i	$0.897684\pi$
$614$	−1.61428			−0.0651469
$615$	−0.260667	−	4.50000i	−0.0105111	−	0.181457i
$616$	7.34301			0.295858
$617$			23.4218i			0.942926i	0.881886	+	0.471463i	$0.156274\pi$
$617$			23.4218i			0.942926i	−0.881886	+	0.471463i	$0.843726\pi$
$618$		−	0.825463i		−	0.0332050i
$619$	28.8903			1.16120			0.580600	−	0.814189i	$-0.302818\pi$
$619$	28.8903			1.16120			0.580600	+	0.814189i	$0.302818\pi$
$620$	6.05537	−	0.350764i	0.243189	−	0.0140870i
$621$	−1.77226			−0.0711185
$622$			10.3670i			0.415678i
$623$		−	6.43878i		−	0.257964i
$624$	−5.96879			−0.238943
$625$	24.3334	−	5.73462i	0.973336	−	0.229385i
$626$	25.0228			1.00011
$627$		−	11.5932i		−	0.462989i
$628$			11.9751i			0.477858i
$629$		0			0
$630$	3.54105	−	0.205119i	0.141079	−	0.00817215i
$631$	42.1314			1.67723			0.838613	−	0.544727i	$-0.183367\pi$
$631$	42.1314			1.67723			0.838613	+	0.544727i	$0.183367\pi$
$632$		−	4.36146i		−	0.173490i
$633$			38.4705i			1.52907i
$634$	23.8042			0.945384
$635$	1.60305	+	27.6740i	0.0636150	+	1.09821i
$636$	22.1057			0.876547
$637$			26.3633i			1.04455i
$638$			36.8703i			1.45971i
$639$	21.6946			0.858226
$640$	−0.599391	−	10.3475i	−0.0236930	−	0.409022i
$641$	−19.0113			−0.750903			−0.375451	−	0.926842i	$-0.622512\pi$
$641$	−19.0113			−0.750903			−0.375451	+	0.926842i	$0.622512\pi$
$642$		−	18.3692i		−	0.724973i
$643$			20.3390i			0.802092i	0.916058	+	0.401046i	$0.131353\pi$
$643$			20.3390i			0.802092i	−0.916058	+	0.401046i	$0.868647\pi$
$644$	3.34885			0.131963
$645$	35.5660	−	2.06020i	1.40041	−	0.0811204i
$646$		0			0
$647$		−	16.7736i		−	0.659440i	−0.944079	−	0.329720i	$-0.893046\pi$
$647$		−	16.7736i		−	0.659440i	0.944079	−	0.329720i	$-0.106954\pi$
$648$		−	25.3553i		−	0.996052i
$649$	28.3166			1.11153
$650$	−18.5564	+	2.15704i	−0.727842	+	0.0846060i
$651$	3.27242			0.128256
$652$		−	8.08558i		−	0.316656i
$653$			6.69796i			0.262111i	0.991375	+	0.131056i	$0.0418367\pi$
$653$			6.69796i			0.262111i	−0.991375	+	0.131056i	$0.958163\pi$
$654$	28.6844			1.12165
$655$	−22.3933	+	1.29716i	−0.874979	+	0.0506841i
$656$	0.500412			0.0195378
$657$			37.7672i			1.47344i
$658$		−	0.865546i		−	0.0337425i
$659$	−36.0525			−1.40440			−0.702202	−	0.711978i	$-0.747800\pi$
$659$	−36.0525			−1.40440			−0.702202	+	0.711978i	$0.747800\pi$
$660$	1.63699	+	28.2600i	0.0637197	+	1.10002i
$661$	44.7322			1.73988			0.869941	−	0.493156i	$-0.164157\pi$
$661$	44.7322			1.73988			0.869941	+	0.493156i	$0.164157\pi$
$662$		−	30.7291i		−	1.19432i
$663$		0			0
$664$	47.6704			1.84997
$665$	0.0691116	+	1.19310i	0.00268003	+	0.0462664i
$666$	−12.1747			−0.471761
$667$			47.5501i			1.84115i
$668$			21.3345i			0.825455i
$669$	−2.64696			−0.102337
$670$	16.3297	−	0.945914i	0.630870	−	0.0365438i
$671$	5.28761			0.204126
$672$		−	7.00274i		−	0.270136i
$673$			4.93857i			0.190368i	0.995460	+	0.0951839i	$0.0303439\pi$
$673$			4.93857i			0.190368i	−0.995460	+	0.0951839i	$0.969656\pi$
$674$	12.2427			0.471573
$675$	0.178312	+	1.53397i	0.00686325	+	0.0590426i
$676$	−2.63851			−0.101481
$677$			28.4568i			1.09368i	0.837236	+	0.546841i	$0.184170\pi$
$677$			28.4568i			1.09368i	−0.837236	+	0.546841i	$0.815830\pi$
$678$			42.1097i			1.61721i
$679$	−0.121633			−0.00466783
$680$		0			0
$681$	5.11770			0.196111
$682$		−	11.0301i		−	0.422366i
$683$		−	32.7689i		−	1.25387i	−0.779072	−	0.626934i	$-0.784310\pi$
$683$		−	32.7689i		−	1.25387i	0.779072	−	0.626934i	$-0.215690\pi$
$684$	−3.42611			−0.131000
$685$	−0.396733	−	6.84895i	−0.0151584	−	0.261685i
$686$	6.96249			0.265829
$687$		−	31.7110i		−	1.20985i
$688$			3.95505i			0.150785i
$689$	−32.0468			−1.22089
$690$	−1.74768	−	30.1709i	−0.0665331	−	1.14859i
$691$	6.64433			0.252762			0.126381	−	0.991982i	$-0.459664\pi$
$691$	6.64433			0.252762			0.126381	+	0.991982i	$0.459664\pi$
$692$			14.5525i			0.553201i
$693$			7.79168i			0.295982i
$694$	−25.6376			−0.973189
$695$	27.3976	−	1.58704i	1.03925	−	0.0601998i
$696$	60.3943			2.28924
$697$		0			0
$698$		−	13.6283i		−	0.515837i
$699$	−16.0466			−0.606938
$700$	−0.336936	−	2.89857i	−0.0127350	−	0.109556i
$701$	−24.2220			−0.914852			−0.457426	−	0.889248i	$-0.651228\pi$
$701$	−24.2220			−0.914852			−0.457426	+	0.889248i	$0.651228\pi$
$702$		−	1.15399i		−	0.0435544i
$703$		−	4.10207i		−	0.154713i
$704$	−29.3478			−1.10609
$705$	9.41979	−	0.545651i	0.354770	−	0.0205504i
$706$	−1.57371			−0.0592274
$707$		−	3.55517i		−	0.133706i
$708$		−	16.4024i		−	0.616440i
$709$	−1.21986			−0.0458128			−0.0229064	−	0.999738i	$-0.507292\pi$
$709$	−1.21986			−0.0458128			−0.0229064	+	0.999738i	$0.507292\pi$
$710$	0.854435	+	14.7504i	0.0320664	+	0.553574i
$711$	4.62795			0.173562
$712$			35.5496i			1.33228i
$713$		−	14.2251i		−	0.532734i
$714$		0			0
$715$	−2.37316	−	40.9687i	−0.0887511	−	1.53214i
$716$	11.1198			0.415565
$717$		−	3.13878i		−	0.117220i
$718$			16.5258i			0.616738i
$719$	−17.6361			−0.657715			−0.328858	−	0.944380i	$-0.606664\pi$
$719$	−17.6361			−0.657715			−0.328858	+	0.944380i	$0.606664\pi$
$720$	−4.28548	+	0.248241i	−0.159710	+	0.00925140i
$721$	−0.186925			−0.00696147
$722$		−	17.1274i		−	0.637416i
$723$		−	6.17679i		−	0.229717i
$724$	−21.4673			−0.797826
$725$	41.1566	−	4.78414i	1.52852	−	0.177678i
$726$	25.5676			0.948901
$727$			11.3177i			0.419751i	0.977728	+	0.209876i	$0.0673059\pi$
$727$			11.3177i			0.419751i	−0.977728	+	0.209876i	$0.932694\pi$
$728$			6.16624i			0.228536i
$729$	29.1977			1.08140
$730$	−25.6784	+	1.48745i	−0.950399	+	0.0550529i
$731$		0			0
$732$		−	3.06285i		−	0.113206i
$733$		−	2.54052i		−	0.0938362i	−0.998899	−	0.0469181i	$-0.985060\pi$
$733$		−	2.54052i		−	0.0938362i	0.998899	−	0.0469181i	$-0.0149400\pi$
$734$	−9.10906			−0.336222
$735$	2.14910	+	37.1007i	0.0792707	+	1.36848i
$736$	−30.4406			−1.12206
$737$			35.9316i			1.32356i
$738$			2.42242i			0.0891703i
$739$	−17.8767			−0.657606			−0.328803	−	0.944399i	$-0.606645\pi$
$739$	−17.8767			−0.657606			−0.328803	+	0.944399i	$0.606645\pi$
$740$	0.579222	+	9.99932i	0.0212926	+	0.367582i
$741$	9.73534			0.357637
$742$			4.14397i			0.152130i
$743$			11.9511i			0.438445i	0.975675	+	0.219223i	$0.0703521\pi$
$743$			11.9511i			0.438445i	−0.975675	+	0.219223i	$0.929648\pi$
$744$	−18.0676			−0.662390
$745$	−12.2007	+	0.706736i	−0.446997	+	0.0258928i
$746$	−13.7275			−0.502601
$747$			50.5831i			1.85074i
$748$		0			0
$749$	−4.15968			−0.151992
$750$	−25.9384	+	4.54827i	−0.947135	+	0.166079i
$751$	−26.7416			−0.975816			−0.487908	−	0.872895i	$-0.662240\pi$
$751$	−26.7416			−0.975816			−0.487908	+	0.872895i	$0.662240\pi$
$752$			1.04751i			0.0381987i
$753$			42.9544i			1.56534i
$754$	−30.9616			−1.12755
$755$	11.1791	−	0.647559i	0.406847	−	0.0235671i
$756$	0.180256			0.00655586
$757$			0.253468i			0.00921245i	0.999989	+	0.00460623i	$0.00146621\pi$
$757$			0.253468i			0.00921245i	−0.999989	+	0.00460623i	$0.998534\pi$
$758$			9.05760i			0.328987i
$759$	66.3876			2.40972
$760$	−0.381576	−	6.58730i	−0.0138412	−	0.238946i
$761$	−32.3234			−1.17172			−0.585860	−	0.810412i	$-0.699243\pi$
$761$	−32.3234			−1.17172			−0.585860	+	0.810412i	$0.699243\pi$
$762$		−	29.1997i		−	1.05779i
$763$		−	6.49555i		−	0.235155i
$764$	−9.64298			−0.348871
$765$		0			0
$766$	26.4348			0.955129
$767$			23.7787i			0.858599i
$768$			41.9905i			1.51520i
$769$	7.23844			0.261025			0.130512	−	0.991447i	$-0.458338\pi$
$769$	7.23844			0.261025			0.130512	+	0.991447i	$0.458338\pi$
$770$	−5.29766	+	0.306873i	−0.190915	+	0.0110589i
$771$	38.4962			1.38641
$772$			16.9188i			0.608923i
$773$			8.26832i			0.297391i	0.988883	+	0.148695i	$0.0475074\pi$
$773$			8.26832i			0.297391i	−0.988883	+	0.148695i	$0.952493\pi$
$774$	−19.1457			−0.688179
$775$	−12.3124	+	1.43123i	−0.442276	+	0.0514111i
$776$	0.671554			0.0241074
$777$			5.40381i			0.193860i
$778$		−	20.0326i		−	0.718205i
$779$	−0.816193			−0.0292432
$780$	−23.7311	+	1.37465i	−0.849711	+	0.0492204i
$781$	−32.4567			−1.16139
$782$		0			0
$783$			2.55945i			0.0914673i
$784$	−4.12571			−0.147347
$785$	−1.41519	−	24.4310i	−0.0505105	−	0.871981i
$786$	23.6279			0.842778
$787$		−	10.6654i		−	0.380182i	−0.981766	−	0.190091i	$-0.939122\pi$
$787$		−	10.6654i		−	0.380182i	0.981766	−	0.190091i	$-0.0608783\pi$
$788$		−	0.251826i		−	0.00897092i
$789$	22.3748			0.796564
$790$	0.182270	+	3.14660i	0.00648489	+	0.111951i
$791$	9.53572			0.339051
$792$		−	43.0192i		−	1.52862i
$793$			4.44023i			0.157677i
$794$	28.2196			1.00147
$795$	−45.0991	+	2.61241i	−1.59950	+	0.0926527i
$796$	−23.4831			−0.832335
$797$			22.6881i			0.803654i	0.915716	+	0.401827i	$0.131625\pi$
$797$			22.6881i			0.803654i	−0.915716	+	0.401827i	$0.868375\pi$
$798$		−	1.25888i		−	0.0445637i
$799$		0			0
$800$	3.06271	+	26.3477i	0.108283	+	0.931532i
$801$	−37.7217			−1.33283
$802$		−	15.7661i		−	0.556720i
$803$		−	56.5023i		−	1.99392i
$804$	20.8134			0.734030
$805$	−6.83217	+	0.395761i	−0.240802	+	0.0139487i
$806$	9.26248			0.326257
$807$			7.47373i			0.263088i
$808$			19.6287i			0.690534i
$809$	−18.9287			−0.665497			−0.332749	−	0.943016i	$-0.607976\pi$
$809$	−18.9287			−0.665497			−0.332749	+	0.943016i	$0.607976\pi$
$810$	1.05963	+	18.2928i	0.0372316	+	0.642743i
$811$	28.2619			0.992410			0.496205	−	0.868205i	$-0.334726\pi$
$811$	28.2619			0.992410			0.496205	+	0.868205i	$0.334726\pi$
$812$		−	4.83630i		−	0.169721i
$813$			32.5781i			1.14256i
$814$	18.2142			0.638409
$815$	0.955541	+	16.4959i	0.0334711	+	0.577825i
$816$		0			0
$817$		−	6.45084i		−	0.225686i
$818$			18.4250i			0.644216i
$819$	−6.54301			−0.228631
$820$	1.98957	−	0.115248i	0.0694789	−	0.00402464i
$821$	14.6133			0.510008			0.255004	−	0.966940i	$-0.417923\pi$
$821$	14.6133			0.510008			0.255004	+	0.966940i	$0.417923\pi$
$822$			7.22654i			0.252054i
$823$		−	19.4796i		−	0.679017i	−0.940603	−	0.339508i	$-0.889739\pi$
$823$		−	19.4796i		−	0.679017i	0.940603	−	0.339508i	$-0.110261\pi$
$824$	1.03205			0.0359530
$825$	−6.67943	−	57.4613i	−0.232548	−	2.00055i
$826$	3.07482			0.106987
$827$			9.75907i			0.339356i	0.985500	+	0.169678i	$0.0542728\pi$
$827$			9.75907i			0.339356i	−0.985500	+	0.169678i	$0.945727\pi$
$828$		−	19.6193i		−	0.681817i
$829$	5.96301			0.207104			0.103552	−	0.994624i	$-0.466979\pi$
$829$	5.96301			0.207104			0.103552	+	0.994624i	$0.466979\pi$
$830$	−34.3921	+	1.99220i	−1.19377	+	0.0691502i
$831$	10.0265			0.347814
$832$		−	24.6446i		−	0.854398i
$833$		0			0
$834$	−28.9081			−1.00100
$835$	−2.52127	−	43.5256i	−0.0872522	−	1.50627i
$836$	5.12569			0.177276
$837$		−	0.765686i		−	0.0264660i
$838$		−	13.7066i		−	0.473486i
$839$	22.6272			0.781178			0.390589	−	0.920565i	$-0.372271\pi$
$839$	22.6272			0.781178			0.390589	+	0.920565i	$0.372271\pi$
$840$	0.502664	+	8.67768i	0.0173435	+	0.299408i
$841$	39.6703			1.36794
$842$			25.4532i			0.877177i
$843$		−	35.3034i		−	1.21591i
$844$	−17.0089			−0.585471
$845$	5.38298	−	0.311815i	0.185180	−	0.0107268i
$846$	−5.07081			−0.174338
$847$		−	5.78975i		−	0.198938i
$848$		−	5.01515i		−	0.172221i
$849$	−13.7950			−0.473443
$850$		0			0
$851$	23.4901			0.805232
$852$			18.8005i			0.644095i
$853$		−	6.61276i		−	0.226417i	−0.993571	−	0.113208i	$-0.963887\pi$
$853$		−	6.61276i		−	0.226417i	0.993571	−	0.113208i	$-0.0361128\pi$
$854$	0.574166			0.0196476
$855$	6.98979	−	0.404891i	0.239046	−	0.0138470i
$856$	22.9663			0.784972
$857$		−	27.3305i		−	0.933592i	−0.884365	−	0.466796i	$-0.845408\pi$
$857$		−	27.3305i		−	0.933592i	0.884365	−	0.466796i	$-0.154592\pi$
$858$			43.2274i			1.47576i
$859$	−14.2440			−0.486000			−0.243000	−	0.970026i	$-0.578132\pi$
$859$	−14.2440			−0.486000			−0.243000	+	0.970026i	$0.578132\pi$
$860$	0.910873	+	15.7247i	0.0310605	+	0.536209i
$861$	1.07520			0.0366427
$862$			27.2372i			0.927701i
$863$		−	31.4670i		−	1.07115i	−0.844488	−	0.535574i	$-0.820095\pi$
$863$		−	31.4670i		−	1.07115i	0.844488	−	0.535574i	$-0.179905\pi$
$864$	−1.63851			−0.0557433
$865$	−1.71978	−	29.6893i	−0.0584744	−	1.00947i
$866$	34.4457			1.17051
$867$		0			0
$868$			1.44683i			0.0491086i
$869$	−6.92375			−0.234872
$870$	−43.5718	+	2.52395i	−1.47722	+	0.0855698i
$871$	−30.1733			−1.02238
$872$			35.8630i			1.21447i
$873$			0.712587i			0.0241174i
$874$	−5.47229			−0.185103
$875$	1.02995	+	5.87372i	0.0348187	+	0.198568i
$876$	−32.7289			−1.10581
$877$			5.57236i			0.188165i	0.995564	+	0.0940827i	$0.0299918\pi$
$877$			5.57236i			0.188165i	−0.995564	+	0.0940827i	$0.970008\pi$
$878$		−	30.8754i		−	1.04199i
$879$	4.87840			0.164544
$880$	6.41138	−	0.371386i	0.216128	−	0.0125194i
$881$	32.2473			1.08644			0.543219	−	0.839591i	$-0.317205\pi$
$881$	32.2473			1.08644			0.543219	+	0.839591i	$0.317205\pi$
$882$		−	19.9719i		−	0.672488i
$883$		−	38.2240i		−	1.28634i	−0.765724	−	0.643169i	$-0.777619\pi$
$883$		−	38.2240i		−	1.28634i	0.765724	−	0.643169i	$-0.222381\pi$
$884$		0			0
$885$	1.93841	+	33.4635i	0.0651589	+	1.12486i
$886$	−1.79372			−0.0602612
$887$		−	6.19540i		−	0.208021i	−0.994576	−	0.104011i	$-0.966832\pi$
$887$		−	6.19540i		−	0.208021i	0.994576	−	0.104011i	$-0.0331676\pi$
$888$		−	29.8353i		−	1.00121i
$889$	−6.61225			−0.221768
$890$	−1.48566	−	25.6475i	−0.0497994	−	0.859705i
$891$	−40.2512			−1.34847
$892$		−	1.17029i		−	0.0391844i
$893$		−	1.70853i		−	0.0571737i
$894$	12.8733			0.430547
$895$	−22.6860	+	1.31411i	−0.758311	+	0.0439260i
$896$	2.47237			0.0825960
$897$			55.7485i			1.86139i
$898$		−	1.90508i		−	0.0635733i
$899$	−20.5434			−0.685162
$900$	−16.9813	+	1.97395i	−0.566044	+	0.0657983i
$901$		0			0
$902$		−	3.62410i		−	0.120669i
$903$			8.49792i			0.282793i
$904$	−52.6482			−1.75105
$905$	43.7967	−	2.53697i	1.45585	−	0.0843317i
$906$	−11.7954			−0.391875
$907$			10.8314i			0.359652i	0.983698	+	0.179826i	$0.0575535\pi$
$907$			10.8314i			0.359652i	−0.983698	+	0.179826i	$0.942447\pi$
$908$			2.26268i			0.0750895i
$909$	−20.8280			−0.690822
$910$	−0.257694	−	4.44868i	−0.00854249	−	0.147472i
$911$	39.2943			1.30188			0.650939	−	0.759130i	$-0.274375\pi$
$911$	39.2943			1.30188			0.650939	+	0.759130i	$0.274375\pi$
$912$			1.52353i			0.0504490i
$913$		−	75.6759i		−	2.50451i
$914$	16.8061			0.555897
$915$	0.361962	+	6.24869i	0.0119661	+	0.206575i
$916$	14.0203			0.463244
$917$		−	5.35051i		−	0.176689i
$918$		0			0
$919$	−48.2620			−1.59202			−0.796008	−	0.605286i	$-0.793059\pi$
$919$	−48.2620			−1.59202			−0.796008	+	0.605286i	$0.793059\pi$
$920$	37.7215	−	2.18506i	1.24364	−	0.0720393i
$921$	4.19765			0.138317
$922$		−	30.3045i		−	0.998026i
$923$		−	27.2553i		−	0.897118i
$924$	−6.75226			−0.222133
$925$	−2.36341	−	20.3317i	−0.0777083	−	0.668504i
$926$	15.0352			0.494089
$927$			1.09511i			0.0359680i
$928$			43.9614i			1.44310i
$929$	23.3057			0.764636			0.382318	−	0.924031i	$-0.375126\pi$
$929$	23.3057			0.764636			0.382318	+	0.924031i	$0.375126\pi$
$930$	13.0350	−	0.755065i	0.427434	−	0.0247596i
$931$	6.72920			0.220541
$932$		−	7.09465i		−	0.232393i
$933$		−	26.9575i		−	0.882550i
$934$	8.43745			0.276082
$935$		0			0
$936$	36.1250			1.18078
$937$		−	9.72405i		−	0.317671i	−0.987305	−	0.158835i	$-0.949226\pi$
$937$		−	9.72405i		−	0.317671i	0.987305	−	0.158835i	$-0.0507739\pi$
$938$			3.90171i			0.127395i
$939$	−65.0674			−2.12339
$940$	0.241248	+	4.16475i	0.00786863	+	0.135839i
$941$	−14.1706			−0.461949			−0.230975	−	0.972960i	$-0.574191\pi$
$941$	−14.1706			−0.461949			−0.230975	+	0.972960i	$0.574191\pi$
$942$			25.7779i			0.839891i
$943$		−	4.67385i		−	0.152202i
$944$	−3.72123			−0.121116
$945$	−0.367751	+	0.0213024i	−0.0119630	+	0.000692967i
$946$	28.6434			0.931276
$947$			38.4870i			1.25066i	0.780360	+	0.625330i	$0.215036\pi$
$947$			38.4870i			1.25066i	−0.780360	+	0.625330i	$0.784964\pi$
$948$			4.01058i			0.130257i
$949$	47.4474			1.54021
$950$	0.550581	+	4.73650i	0.0178632	+	0.153672i
$951$	−61.8987			−2.00720
$952$		0			0
$953$		−	37.7984i		−	1.22441i	−0.790698	−	0.612206i	$-0.790282\pi$
$953$		−	37.7984i		−	1.22441i	0.790698	−	0.612206i	$-0.209718\pi$
$954$	24.2775			0.786013
$955$	19.6732	−	1.13959i	0.636609	−	0.0368763i
$956$	1.38774			0.0448828
$957$		−	95.8749i		−	3.09919i
$958$		−	11.3349i		−	0.366215i
$959$	1.63644			0.0528435
$960$	−2.00899	−	34.6820i	−0.0648400	−	1.11936i
$961$	−24.8542			−0.801749
$962$			15.2953i			0.493140i
$963$			24.3696i			0.785299i
$964$	2.73093			0.0879573
$965$	−1.99944	−	34.5171i	−0.0643643	−	1.11115i
$966$	7.20883			0.231940
$967$			4.79826i			0.154302i	0.997019	+	0.0771509i	$0.0245823\pi$
$967$			4.79826i			0.154302i	−0.997019	+	0.0771509i	$0.975418\pi$
$968$			31.9662i			1.02743i
$969$		0			0
$970$	−0.484497	+	0.0280650i	−0.0155563	+	0.000901113i
$971$	−36.4980			−1.17128			−0.585638	−	0.810573i	$-0.699156\pi$
$971$	−36.4980			−1.17128			−0.585638	+	0.810573i	$0.699156\pi$
$972$			24.3293i			0.780364i
$973$			6.54621i			0.209862i
$974$	25.4838			0.816552
$975$	48.2528	−	5.60901i	1.54533	−	0.179632i
$976$	−0.694872			−0.0222423
$977$		−	62.3221i		−	1.99386i	−0.0783005	−	0.996930i	$-0.524949\pi$
$977$		−	62.3221i		−	1.99386i	0.0783005	−	0.996930i	$-0.475051\pi$
$978$		−	17.4053i		−	0.556560i
$979$	56.4343			1.80365
$980$	−16.4033	+	0.950177i	−0.523983	+	0.0303523i
$981$	−38.0543			−1.21498
$982$		−	22.0034i		−	0.702156i
$983$		−	40.1721i		−	1.28129i	−0.767837	−	0.640645i	$-0.778667\pi$
$983$		−	40.1721i		−	1.28129i	0.767837	−	0.640645i	$-0.221333\pi$
$984$	−5.93635			−0.189244
$985$	0.0297603	+	0.513764i	0.000948243	+	0.0163699i
$986$		0			0
$987$			2.25070i			0.0716407i
$988$			4.30427i			0.136937i
$989$	36.9401			1.17463
$990$	1.79782	+	31.0364i	0.0571385	+	0.986403i
$991$	25.0802			0.796699			0.398349	−	0.917234i	$-0.369583\pi$
$991$	25.0802			0.796699			0.398349	+	0.917234i	$0.369583\pi$
$992$		−	13.1515i		−	0.417561i
$993$			79.9057i			2.53573i
$994$	−3.52438			−0.111786
$995$	47.9092	−	2.77519i	1.51882	−	0.0879794i
$996$	−43.8352			−1.38897
$997$		−	37.3646i		−	1.18335i	−0.806177	−	0.591674i	$-0.798467\pi$
$997$		−	37.3646i		−	1.18335i	0.806177	−	0.591674i	$-0.201533\pi$
$998$		−	4.72667i		−	0.149620i
$999$	1.26439			0.0400035

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1445.2.b.i.579.17		24
5.2	odd	4		7225.2.a.by.1.7		24
5.3	odd	4		7225.2.a.by.1.18		24
5.4	even	2	inner	1445.2.b.i.579.8		24
17.11	odd	16		85.2.m.a.19.2	yes	24
17.14	odd	16		85.2.m.a.9.5	yes	24
17.16	even	2	inner	1445.2.b.i.579.18		24
51.11	even	16		765.2.bh.b.19.5		24
51.14	even	16		765.2.bh.b.604.2		24
85.14	odd	16		85.2.m.a.9.2	✓	24
85.28	even	16		425.2.m.e.376.5		24
85.33	odd	4		7225.2.a.by.1.17		24
85.48	even	16		425.2.m.e.26.5		24
85.62	even	16		425.2.m.e.376.2		24
85.67	odd	4		7225.2.a.by.1.8		24
85.79	odd	16		85.2.m.a.19.5	yes	24
85.82	even	16		425.2.m.e.26.2		24
85.84	even	2	inner	1445.2.b.i.579.7		24
255.14	even	16		765.2.bh.b.604.5		24
255.164	even	16		765.2.bh.b.19.2		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
85.2.m.a.9.2	✓	24	85.14	odd	16
85.2.m.a.9.5	yes	24	17.14	odd	16
85.2.m.a.19.2	yes	24	17.11	odd	16
85.2.m.a.19.5	yes	24	85.79	odd	16
425.2.m.e.26.2		24	85.82	even	16
425.2.m.e.26.5		24	85.48	even	16
425.2.m.e.376.2		24	85.62	even	16
425.2.m.e.376.5		24	85.28	even	16
765.2.bh.b.19.2		24	255.164	even	16
765.2.bh.b.19.5		24	51.11	even	16
765.2.bh.b.604.2		24	51.14	even	16
765.2.bh.b.604.5		24	255.14	even	16
1445.2.b.i.579.7		24	85.84	even	2	inner
1445.2.b.i.579.8		24	5.4	even	2	inner
1445.2.b.i.579.17		24	1.1	even	1	trivial
1445.2.b.i.579.18		24	17.16	even	2	inner
7225.2.a.by.1.7		24	5.2	odd	4
7225.2.a.by.1.8		24	85.67	odd	4
7225.2.a.by.1.17		24	85.33	odd	4
7225.2.a.by.1.18		24	5.3	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1445 = 5 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1445.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+0.951739i q^{2} -2.47483i q^{3} +1.09419 q^{4} +(-2.23233 + 0.129310i) q^{5} +2.35540 q^{6} -0.533377i q^{7} +2.94486i q^{8} -3.12480 q^{9} +(-0.123069 - 2.12459i) q^{10} +4.67492 q^{11} -2.70795i q^{12} +3.92573i q^{13} +0.507636 q^{14} +(0.320020 + 5.52463i) q^{15} -0.614355 q^{16} -2.97399i q^{18} +1.00204 q^{19} +(-2.44260 + 0.141490i) q^{20} -1.32002 q^{21} +4.44930i q^{22} +5.73808i q^{23} +7.28805 q^{24} +(4.96656 - 0.577324i) q^{25} -3.73627 q^{26} +0.308860i q^{27} -0.583618i q^{28} +8.28676 q^{29} +(-5.25801 + 0.304576i) q^{30} -2.47907 q^{31} +5.30502i q^{32} -11.5697i q^{33} +(0.0689710 + 1.19067i) q^{35} -3.41914 q^{36} -4.09373i q^{37} +0.953679i q^{38} +9.71553 q^{39} +(-0.380800 - 6.57390i) q^{40} -0.814533 q^{41} -1.25631i q^{42} -6.43772i q^{43} +5.11527 q^{44} +(6.97557 - 0.404068i) q^{45} -5.46115 q^{46} -1.70505i q^{47} +1.52043i q^{48} +6.71551 q^{49} +(0.549461 + 4.72687i) q^{50} +4.29551i q^{52} +8.16327i q^{53} -0.293954 q^{54} +(-10.4359 + 0.604514i) q^{55} +1.57072 q^{56} -2.47988i q^{57} +7.88683i q^{58} +6.05714 q^{59} +(0.350164 + 6.04502i) q^{60} +1.13106 q^{61} -2.35943i q^{62} +1.66670i q^{63} -6.27771 q^{64} +(-0.507636 - 8.76352i) q^{65} +11.0113 q^{66} +7.68603i q^{67} +14.2008 q^{69} +(-1.13321 + 0.0656424i) q^{70} -6.94272 q^{71} -9.20211i q^{72} -12.0863i q^{73} +3.89616 q^{74} +(-1.42878 - 12.2914i) q^{75} +1.09642 q^{76} -2.49350i q^{77} +9.24665i q^{78} -1.48104 q^{79} +(1.37144 - 0.0794422i) q^{80} -8.61002 q^{81} -0.775222i q^{82} -16.1876i q^{83} -1.44436 q^{84} +6.12703 q^{86} -20.5083i q^{87} +13.7670i q^{88} +12.0717 q^{89} +(0.384567 + 6.63892i) q^{90} +2.09390 q^{91} +6.27857i q^{92} +6.13529i q^{93} +1.62276 q^{94} +(-2.23688 + 0.129573i) q^{95} +13.1290 q^{96} -0.228042i q^{97} +6.39141i q^{98} -14.6082 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 8 q^{4} + 8 q^{9} + 8 q^{15} - 8 q^{16} + 16 q^{19} - 32 q^{21} + 8 q^{25} - 48 q^{26} - 56 q^{30} + 8 q^{35} + 8 q^{36} + 56 q^{49} - 16 q^{50} - 24 q^{55} + 64 q^{59} - 88 q^{60} + 104 q^{64} - 16 q^{66}+ \cdots + 128 q^{94}+O(q^{100}) \) 24 * q - 8 * q^4 + 8 * q^9 + 8 * q^15 - 8 * q^16 + 16 * q^19 - 32 * q^21 + 8 * q^25 - 48 * q^26 - 56 * q^30 + 8 * q^35 + 8 * q^36 + 56 * q^49 - 16 * q^50 - 24 * q^55 + 64 * q^59 - 88 * q^60 + 104 * q^64 - 16 * q^66 + 32 * q^69 - 40 * q^70 - 48 * q^76 - 88 * q^81 + 96 * q^84 + 112 * q^89 + 128 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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