LMFDB - Embedded newform 140.2.u.a.117.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [140,2,Mod(17,140)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(140, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 2]))

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

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

chi := DirichletCharacter("140.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 140 = 2^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	140.u (of order $12$, degree $4$, 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:	$1.11790562830$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 52 x^{14} - 224 x^{13} + 802 x^{12} - 2264 x^{11} + 5402 x^{10} - 10642 x^{9} + \cdots + 196 $ x^16 - 8x^15 + 52x^14 - 224x^13 + 802x^12 - 2264x^11 + 5402x^10 - 10642x^9 + 17766x^8 - 24680x^7 + 28682x^6 - 27248x^5 + 20861x^4 - 12338x^3 + 5322x^2 - 1484*x + 196
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			117.1
Root			$0.500000 - 2.78727i$ of defining polynomial
Character	$\chi$	$=$	140.117
Dual form			140.2.u.a.73.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.837199 + 3.12447i) q^{3} +(2.23274 - 0.121977i) q^{5} +(-2.49857 + 0.870132i) q^{7} +(-6.46333 - 3.73161i) q^{9} +O(q^{10})$	\(q+(-0.837199 + 3.12447i) q^{3} +(2.23274 - 0.121977i) q^{5} +(-2.49857 + 0.870132i) q^{7} +(-6.46333 - 3.73161i) q^{9} +(0.615031 + 1.06527i) q^{11} +(2.44401 + 2.44401i) q^{13} +(-1.48813 + 7.07824i) q^{15} +(1.47727 + 0.395833i) q^{17} +(2.14670 - 3.71820i) q^{19} +(-0.626899 - 8.53519i) q^{21} +(-0.267786 - 0.999392i) q^{23} +(4.97024 - 0.544686i) q^{25} +(10.2086 - 10.2086i) q^{27} +3.02682i q^{29} +(4.67986 - 2.70192i) q^{31} +(-3.84329 + 1.02981i) q^{33} +(-5.47253 + 2.24755i) q^{35} +(-1.22510 + 0.328265i) q^{37} +(-9.68235 + 5.59011i) q^{39} +1.26012i q^{41} +(6.08857 - 6.08857i) q^{43} +(-14.8861 - 7.54332i) q^{45} +(1.43626 + 5.36018i) q^{47} +(5.48574 - 4.34818i) q^{49} +(-2.47354 + 4.28429i) q^{51} +(-12.0162 - 3.21972i) q^{53} +(1.50314 + 2.30344i) q^{55} +(9.82017 + 9.82017i) q^{57} +(1.71588 + 2.97199i) q^{59} +(-4.82171 - 2.78382i) q^{61} +(19.3961 + 3.69974i) q^{63} +(5.75495 + 5.15872i) q^{65} +(1.08405 - 4.04571i) q^{67} +3.34676 q^{69} -10.1297 q^{71} +(1.36024 - 5.07647i) q^{73} +(-2.45923 + 15.9854i) q^{75} +(-2.46362 - 2.12649i) q^{77} +(-4.35068 - 2.51187i) q^{79} +(12.1549 + 21.0530i) q^{81} +(-8.84600 - 8.84600i) q^{83} +(3.34664 + 0.703598i) q^{85} +(-9.45720 - 2.53405i) q^{87} +(-3.05790 + 5.29644i) q^{89} +(-8.23315 - 3.97993i) q^{91} +(4.52409 + 16.8841i) q^{93} +(4.33949 - 8.56361i) q^{95} +(-11.1946 + 11.1946i) q^{97} -9.18022i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 6 q^{5} + 2 q^{7}+O(q^{10}) $ 16 * q + 6 * q^5 + 2 * q^7	$ 16 q + 6 q^{5} + 2 q^{7} - 20 q^{15} + 18 q^{17} - 4 q^{21} - 16 q^{23} + 6 q^{25} - 12 q^{31} - 42 q^{33} - 40 q^{35} - 14 q^{37} + 28 q^{43} - 66 q^{45} - 6 q^{47} + 20 q^{51} - 10 q^{53} + 44 q^{57} + 60 q^{61} + 48 q^{63} + 34 q^{65} + 8 q^{67} - 8 q^{71} + 78 q^{73} + 96 q^{75} + 10 q^{77} + 24 q^{81} + 30 q^{87} - 64 q^{91} - 62 q^{93} + 2 q^{95}+O(q^{100}) $ 16 * q + 6 * q^5 + 2 * q^7 - 20 * q^15 + 18 * q^17 - 4 * q^21 - 16 * q^23 + 6 * q^25 - 12 * q^31 - 42 * q^33 - 40 * q^35 - 14 * q^37 + 28 * q^43 - 66 * q^45 - 6 * q^47 + 20 * q^51 - 10 * q^53 + 44 * q^57 + 60 * q^61 + 48 * q^63 + 34 * q^65 + 8 * q^67 - 8 * q^71 + 78 * q^73 + 96 * q^75 + 10 * q^77 + 24 * q^81 + 30 * q^87 - 64 * q^91 - 62 * q^93 + 2 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/140\mathbb{Z}\right)^\times$.

$n$	$57$	$71$	$101$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{5}{6}\right)$

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			0
$2$		0			0
$3$	−0.837199	+	3.12447i	−0.483357	+	1.80391i	0.103990	+	0.994578i	$0.466839\pi$
$3$	−0.837199	+	3.12447i	−0.483357	+	1.80391i	−0.587347	+	0.809335i	$0.699828\pi$
$4$		0			0
$5$	2.23274	−	0.121977i	0.998511	−	0.0545498i
$5$	2.23274	−	0.121977i	0.998511	−	0.0545498i
$6$		0			0
$7$	−2.49857	+	0.870132i	−0.944372	+	0.328879i
$7$	−2.49857	+	0.870132i	−0.944372	+	0.328879i
$8$		0			0
$9$	−6.46333	−	3.73161i	−2.15444	−	1.24387i
$10$		0			0
$11$	0.615031	+	1.06527i	0.185439	+	0.321190i	0.943724	−	0.330733i	$-0.107296\pi$
$11$	0.615031	+	1.06527i	0.185439	+	0.321190i	−0.758285	+	0.651923i	$0.773963\pi$
$12$		0			0
$13$	2.44401	+	2.44401i	0.677846	+	0.677846i	0.959512	−	0.281666i	$-0.0908871\pi$
$13$	2.44401	+	2.44401i	0.677846	+	0.677846i	−0.281666	+	0.959512i	$0.590887\pi$
$14$		0			0
$15$	−1.48813	+	7.07824i	−0.384234	+	1.82759i
$16$		0			0
$17$	1.47727	+	0.395833i	0.358290	+	0.0960036i	0.433474	−	0.901166i	$-0.357288\pi$
$17$	1.47727	+	0.395833i	0.358290	+	0.0960036i	−0.0751837	+	0.997170i	$0.523954\pi$
$18$		0			0
$19$	2.14670	−	3.71820i	0.492487	−	0.853013i	−0.507475	−	0.861666i	$-0.669421\pi$
$19$	2.14670	−	3.71820i	0.492487	−	0.853013i	0.999963	+	0.00865358i	$0.00275455\pi$
$20$		0			0
$21$	−0.626899	−	8.53519i	−0.136800	−	1.86253i
$22$		0			0
$23$	−0.267786	−	0.999392i	−0.0558373	−	0.208388i	0.932371	−	0.361503i	$-0.117736\pi$
$23$	−0.267786	−	0.999392i	−0.0558373	−	0.208388i	−0.988208	+	0.153115i	$0.951069\pi$
$24$		0			0
$25$	4.97024	−	0.544686i	0.994049	−	0.108937i
$26$		0			0
$27$	10.2086	−	10.2086i	1.96464	−	1.96464i
$28$		0			0
$29$			3.02682i			0.562066i	0.959698	+	0.281033i	$0.0906771\pi$
$29$			3.02682i			0.562066i	−0.959698	+	0.281033i	$0.909323\pi$
$30$		0			0
$31$	4.67986	−	2.70192i	0.840528	−	0.485279i	−0.0169154	−	0.999857i	$-0.505385\pi$
$31$	4.67986	−	2.70192i	0.840528	−	0.485279i	0.857444	+	0.514578i	$0.172051\pi$
$32$		0			0
$33$	−3.84329	+	1.02981i	−0.669032	+	0.179266i
$34$		0			0
$35$	−5.47253	+	2.24755i	−0.925026	+	0.379905i
$36$		0			0
$37$	−1.22510	+	0.328265i	−0.201405	+	0.0539664i	−0.358111	−	0.933679i	$-0.616579\pi$
$37$	−1.22510	+	0.328265i	−0.201405	+	0.0539664i	0.156706	+	0.987645i	$0.449912\pi$
$38$		0			0
$39$	−9.68235	+	5.59011i	−1.55042	+	0.895134i
$40$		0			0
$41$			1.26012i			0.196798i	0.995147	+	0.0983990i	$0.0313721\pi$
$41$			1.26012i			0.196798i	−0.995147	+	0.0983990i	$0.968628\pi$
$42$		0			0
$43$	6.08857	−	6.08857i	0.928498	−	0.928498i	−0.0691112	−	0.997609i	$-0.522016\pi$
$43$	6.08857	−	6.08857i	0.928498	−	0.928498i	0.997609	+	0.0691112i	$0.0220163\pi$
$44$		0			0
$45$	−14.8861	−	7.54332i	−2.21909	−	1.12449i
$46$		0			0
$47$	1.43626	+	5.36018i	0.209500	+	0.781863i	0.988031	+	0.154257i	$0.0492984\pi$
$47$	1.43626	+	5.36018i	0.209500	+	0.781863i	−0.778531	+	0.627606i	$0.784035\pi$
$48$		0			0
$49$	5.48574	−	4.34818i	0.783677	−	0.621168i
$50$		0			0
$51$	−2.47354	+	4.28429i	−0.346364	+	0.599920i
$52$		0			0
$53$	−12.0162	−	3.21972i	−1.65055	−	0.442263i	−0.690781	−	0.723065i	$-0.742733\pi$
$53$	−12.0162	−	3.21972i	−1.65055	−	0.442263i	−0.959766	+	0.280802i	$0.909400\pi$
$54$		0			0
$55$	1.50314	+	2.30344i	0.202684	+	0.310596i
$56$		0			0
$57$	9.82017	+	9.82017i	1.30071	+	1.30071i
$58$		0			0
$59$	1.71588	+	2.97199i	0.223389	+	0.386921i	0.955835	−	0.293904i	$-0.0949548\pi$
$59$	1.71588	+	2.97199i	0.223389	+	0.386921i	−0.732446	+	0.680825i	$0.761621\pi$
$60$		0			0
$61$	−4.82171	−	2.78382i	−0.617357	−	0.356431i	0.158482	−	0.987362i	$-0.449340\pi$
$61$	−4.82171	−	2.78382i	−0.617357	−	0.356431i	−0.775839	+	0.630930i	$0.782673\pi$
$62$		0			0
$63$	19.3961	+	3.69974i	2.44368	+	0.466123i
$64$		0			0
$65$	5.75495	+	5.15872i	0.713813	+	0.639861i
$66$		0			0
$67$	1.08405	−	4.04571i	0.132437	−	0.494263i	−0.867558	−	0.497336i	$-0.834312\pi$
$67$	1.08405	−	4.04571i	0.132437	−	0.494263i	0.999995	+	0.00307336i	$0.000978284\pi$
$68$		0			0
$69$	3.34676			0.402902
$70$		0			0
$71$	−10.1297			−1.20217			−0.601085	−	0.799185i	$-0.705265\pi$
$71$	−10.1297			−1.20217			−0.601085	+	0.799185i	$0.705265\pi$
$72$		0			0
$73$	1.36024	−	5.07647i	0.159204	−	0.594156i	−0.839505	−	0.543352i	$-0.817155\pi$
$73$	1.36024	−	5.07647i	0.159204	−	0.594156i	0.998709	−	0.0508042i	$-0.0161784\pi$
$74$		0			0
$75$	−2.45923	+	15.9854i	−0.283967	+	1.84583i
$76$		0			0
$77$	−2.46362	−	2.12649i	−0.280756	−	0.242336i
$78$		0			0
$79$	−4.35068	−	2.51187i	−0.489490	−	0.282607i	0.234873	−	0.972026i	$-0.424533\pi$
$79$	−4.35068	−	2.51187i	−0.489490	−	0.282607i	−0.724363	+	0.689419i	$0.757866\pi$
$80$		0			0
$81$	12.1549	+	21.0530i	1.35055	+	2.33922i
$82$		0			0
$83$	−8.84600	−	8.84600i	−0.970974	−	0.970974i	0.0286162	−	0.999590i	$-0.490890\pi$
$83$	−8.84600	−	8.84600i	−0.970974	−	0.970974i	−0.999590	+	0.0286162i	$0.990890\pi$
$84$		0			0
$85$	3.34664	+	0.703598i	0.362994	+	0.0763160i
$86$		0			0
$87$	−9.45720	−	2.53405i	−1.01392	−	0.271679i
$88$		0			0
$89$	−3.05790	+	5.29644i	−0.324137	+	0.561421i	−0.981337	−	0.192294i	$-0.938407\pi$
$89$	−3.05790	+	5.29644i	−0.324137	+	0.561421i	0.657201	+	0.753716i	$0.271740\pi$
$90$		0			0
$91$	−8.23315	−	3.97993i	−0.863068	−	0.417210i
$92$		0			0
$93$	4.52409	+	16.8841i	0.469126	+	1.75080i
$94$		0			0
$95$	4.33949	−	8.56361i	0.445222	−	0.878608i
$96$		0			0
$97$	−11.1946	+	11.1946i	−1.13664	+	1.13664i	−0.147592	+	0.989048i	$0.547152\pi$
$97$	−11.1946	+	11.1946i	−1.13664	+	1.13664i	−0.989048	+	0.147592i	$0.952848\pi$
$98$		0			0
$99$		−	9.18022i		−	0.922647i
$100$		0			0
$101$	14.1434	−	8.16571i	1.40732	−	0.812519i	0.412194	−	0.911096i	$-0.364762\pi$
$101$	14.1434	−	8.16571i	1.40732	−	0.812519i	0.995129	+	0.0985771i	$0.0314291\pi$
$102$		0			0
$103$	−5.75112	+	1.54101i	−0.566675	+	0.151840i	−0.530771	−	0.847515i	$-0.678098\pi$
$103$	−5.75112	+	1.54101i	−0.566675	+	0.151840i	−0.0359037	+	0.999355i	$0.511431\pi$
$104$		0			0
$105$	−2.44080	−	18.9804i	−0.238198	−	1.85230i
$106$		0			0
$107$	−10.5616	+	2.82996i	−1.02103	+	0.273583i	−0.730229	−	0.683202i	$-0.760587\pi$
$107$	−10.5616	+	2.82996i	−1.02103	+	0.273583i	−0.290796	+	0.956785i	$0.593920\pi$
$108$		0			0
$109$	5.63841	−	3.25534i	0.540062	−	0.311805i	−0.205042	−	0.978753i	$-0.565733\pi$
$109$	5.63841	−	3.25534i	0.540062	−	0.311805i	0.745104	+	0.666948i	$0.232400\pi$
$110$		0			0
$111$		−	4.10261i		−	0.389403i
$112$		0			0
$113$	−4.25688	+	4.25688i	−0.400454	+	0.400454i	−0.878393	−	0.477939i	$-0.841384\pi$
$113$	−4.25688	+	4.25688i	−0.400454	+	0.400454i	0.477939	+	0.878393i	$0.341384\pi$
$114$		0			0
$115$	−0.719799	−	2.19872i	−0.0671216	−	0.205031i
$116$		0			0
$117$	−6.67636	−	24.9165i	−0.617230	−	2.30353i
$118$		0			0
$119$	−4.03549	+	0.296402i	−0.369933	+	0.0271711i
$120$		0			0
$121$	4.74347	−	8.21594i	0.431225	−	0.746903i
$122$		0			0
$123$	−3.93721	−	1.05497i	−0.355006	−	0.0951237i
$124$		0			0
$125$	11.0308	−	1.82240i	0.986626	−	0.163000i
$126$		0			0
$127$	2.00309	+	2.00309i	0.177745	+	0.177745i	0.790372	−	0.612627i	$-0.209887\pi$
$127$	2.00309	+	2.00309i	0.177745	+	0.177745i	−0.612627	+	0.790372i	$0.709887\pi$
$128$		0			0
$129$	13.9262	+	24.1209i	1.22613	+	2.12373i
$130$		0			0
$131$	13.9636	+	8.06187i	1.22000	+	0.704369i	0.964918	−	0.262550i	$-0.0845635\pi$
$131$	13.9636	+	8.06187i	1.22000	+	0.704369i	0.255084	+	0.966919i	$0.417897\pi$
$132$		0			0
$133$	−2.12837	+	11.1581i	−0.184553	+	0.967530i
$134$		0			0
$135$	21.5479	−	24.0383i	1.85454	−	2.06889i
$136$		0			0
$137$	3.05017	−	11.3834i	0.260594	−	0.972550i	−0.704299	−	0.709904i	$-0.748738\pi$
$137$	3.05017	−	11.3834i	0.260594	−	0.972550i	0.964892	−	0.262646i	$-0.0845950\pi$
$138$		0			0
$139$	10.2015			0.865281			0.432641	−	0.901567i	$-0.357582\pi$
$139$	10.2015			0.865281			0.432641	+	0.901567i	$0.357582\pi$
$140$		0			0
$141$	−17.9502			−1.51168
$142$		0			0
$143$	−1.10038	+	4.10666i	−0.0920181	+	0.343416i
$144$		0			0
$145$	0.369203	+	6.75810i	0.0306606	+	0.561229i
$146$		0			0
$147$	8.99310	+	20.7803i	0.741738	+	1.71393i
$148$		0			0
$149$	−5.55085	−	3.20479i	−0.454744	−	0.262546i	0.255088	−	0.966918i	$-0.417896\pi$
$149$	−5.55085	−	3.20479i	−0.454744	−	0.262546i	−0.709831	+	0.704372i	$0.751229\pi$
$150$		0			0
$151$	−6.44980	−	11.1714i	−0.524877	−	0.909114i	−0.999580	−	0.0289682i	$-0.990778\pi$
$151$	−6.44980	−	11.1714i	−0.524877	−	0.909114i	0.474703	−	0.880146i	$-0.342555\pi$
$152$		0			0
$153$	−8.07098	−	8.07098i	−0.652500	−	0.652500i
$154$		0			0
$155$	10.1193	−	6.60352i	0.812805	−	0.530407i
$156$		0			0
$157$	4.22734	+	1.13271i	0.337378	+	0.0904002i	0.423531	−	0.905882i	$-0.360791\pi$
$157$	4.22734	+	1.13271i	0.337378	+	0.0904002i	−0.0861526	+	0.996282i	$0.527457\pi$
$158$		0			0
$159$	20.1198	−	34.8486i	1.59561	−	2.76367i
$160$		0			0
$161$	1.53869	+	2.26404i	0.121265	+	0.178432i
$162$		0			0
$163$	−3.85800	−	14.3983i	−0.302182	−	1.12776i	−0.935344	−	0.353740i	$-0.884910\pi$
$163$	−3.85800	−	14.3983i	−0.302182	−	1.12776i	0.633162	−	0.774020i	$-0.281757\pi$
$164$		0			0
$165$	−8.45546	+	2.76808i	−0.658256	+	0.215495i
$166$		0			0
$167$	−9.40827	+	9.40827i	−0.728034	+	0.728034i	−0.970228	−	0.242194i	$-0.922133\pi$
$167$	−9.40827	+	9.40827i	−0.728034	+	0.728034i	0.242194	+	0.970228i	$0.422133\pi$
$168$		0			0
$169$		−	1.05364i		−	0.0810491i
$170$		0			0
$171$	−27.7497	+	16.0213i	−2.12207	+	1.22518i
$172$		0			0
$173$	4.51104	−	1.20873i	0.342968	−	0.0918981i	−0.0832235	−	0.996531i	$-0.526522\pi$
$173$	4.51104	−	1.20873i	0.342968	−	0.0918981i	0.426192	+	0.904633i	$0.359855\pi$
$174$		0			0
$175$	−11.9446	+	5.68571i	−0.902925	+	0.429799i
$176$		0			0
$177$	−10.7224	+	2.87307i	−0.805948	+	0.215953i
$178$		0			0
$179$	−2.32710	+	1.34355i	−0.173936	+	0.100422i	−0.584440	−	0.811437i	$-0.698686\pi$
$179$	−2.32710	+	1.34355i	−0.173936	+	0.100422i	0.410505	+	0.911858i	$0.365353\pi$
$180$		0			0
$181$			13.7647i			1.02312i	0.859246	+	0.511562i	$0.170933\pi$
$181$			13.7647i			1.02312i	−0.859246	+	0.511562i	$0.829067\pi$
$182$		0			0
$183$	12.7347	−	12.7347i	0.941375	−	0.941375i
$184$		0			0
$185$	−2.69529	+	0.882363i	−0.198162	+	0.0648726i
$186$		0			0
$187$	0.486899	+	1.81713i	0.0356056	+	0.132882i
$188$		0			0
$189$	−16.6241	+	34.3897i	−1.20922	+	2.50148i
$190$		0			0
$191$	−3.82445	+	6.62413i	−0.276727	+	0.479305i	−0.970569	−	0.240822i	$-0.922583\pi$
$191$	−3.82445	+	6.62413i	−0.276727	+	0.479305i	0.693842	+	0.720127i	$0.255916\pi$
$192$		0			0
$193$	10.7192	+	2.87220i	0.771584	+	0.206745i	0.623071	−	0.782165i	$-0.285885\pi$
$193$	10.7192	+	2.87220i	0.771584	+	0.206745i	0.148513	+	0.988910i	$0.452551\pi$
$194$		0			0
$195$	−20.9363	+	13.6623i	−1.49928	+	0.978376i
$196$		0			0
$197$	−11.1833	−	11.1833i	−0.796777	−	0.796777i	0.185809	−	0.982586i	$-0.440510\pi$
$197$	−11.1833	−	11.1833i	−0.796777	−	0.796777i	−0.982586	+	0.185809i	$0.940510\pi$
$198$		0			0
$199$	6.41816	+	11.1166i	0.454971	+	0.788033i	0.998687	−	0.0512366i	$-0.0163163\pi$
$199$	6.41816	+	11.1166i	0.454971	+	0.788033i	−0.543715	+	0.839270i	$0.682983\pi$
$200$		0			0
$201$	11.7331	+	6.77414i	0.827592	+	0.477811i
$202$		0			0
$203$	−2.63373	−	7.56273i	−0.184852	−	0.530800i
$204$		0			0
$205$	0.153706	+	2.81352i	0.0107353	+	0.196505i
$206$		0			0
$207$	−1.99854	+	7.45867i	−0.138908	+	0.518413i
$208$		0			0
$209$	5.28116			0.365305
$210$		0			0
$211$	5.20941			0.358631			0.179315	−	0.983792i	$-0.442612\pi$
$211$	5.20941			0.358631			0.179315	+	0.983792i	$0.442612\pi$
$212$		0			0
$213$	8.48055	−	31.6498i	0.581077	−	2.16861i
$214$		0			0
$215$	12.8515	−	14.3368i	0.876466	−	0.977765i
$216$		0			0
$217$	−9.34196	+	10.8230i	−0.634173	+	0.734716i
$218$		0			0
$219$	14.7225	+	8.50004i	0.994854	+	0.574379i
$220$		0			0
$221$	2.64304	+	4.57788i	0.177790	+	0.307941i
$222$		0			0
$223$	3.58144	+	3.58144i	0.239831	+	0.239831i	0.816780	−	0.576949i	$-0.195757\pi$
$223$	3.58144	+	3.58144i	0.239831	+	0.239831i	−0.576949	+	0.816780i	$0.695757\pi$
$224$		0			0
$225$	−34.1569	−	15.0265i	−2.27713	−	1.00177i
$226$		0			0
$227$	24.6724	+	6.61096i	1.63757	+	0.438785i	0.956094	−	0.293059i	$-0.0946734\pi$
$227$	24.6724	+	6.61096i	1.63757	+	0.438785i	0.681472	+	0.731844i	$0.261340\pi$
$228$		0			0
$229$	−9.94027	+	17.2170i	−0.656871	+	1.13773i	0.324550	+	0.945869i	$0.394787\pi$
$229$	−9.94027	+	17.2170i	−0.656871	+	1.13773i	−0.981421	+	0.191866i	$0.938546\pi$
$230$		0			0
$231$	8.70668	−	5.91722i	0.572858	−	0.389325i
$232$		0			0
$233$	5.43438	+	20.2814i	0.356018	+	1.32868i	0.879199	+	0.476455i	$0.158078\pi$
$233$	5.43438	+	20.2814i	0.356018	+	1.32868i	−0.523181	+	0.852222i	$0.675255\pi$
$234$		0			0
$235$	3.86060	+	11.7927i	0.251838	+	0.769271i
$236$		0			0
$237$	11.4906	−	11.4906i	0.746397	−	0.746397i
$238$		0			0
$239$			17.8467i			1.15441i	0.816601	+	0.577203i	$0.195856\pi$
$239$			17.8467i			1.15441i	−0.816601	+	0.577203i	$0.804144\pi$
$240$		0			0
$241$	2.55328	−	1.47414i	0.164471	−	0.0949576i	−0.415505	−	0.909591i	$-0.636395\pi$
$241$	2.55328	−	1.47414i	0.164471	−	0.0949576i	0.579976	+	0.814633i	$0.303062\pi$
$242$		0			0
$243$	−34.1200	+	9.14242i	−2.18880	+	0.586487i
$244$		0			0
$245$	11.7178	−	10.3775i	0.748626	−	0.662993i
$246$		0			0
$247$	14.3339	−	3.84075i	0.912042	−	0.244381i
$248$		0			0
$249$	35.0449	−	20.2332i	2.22088	−	1.28223i
$250$		0			0
$251$			27.8935i			1.76062i	0.474397	+	0.880311i	$0.342666\pi$
$251$			27.8935i			1.76062i	−0.474397	+	0.880311i	$0.657334\pi$
$252$		0			0
$253$	0.899921	−	0.899921i	0.0565775	−	0.0565775i
$254$		0			0
$255$	−5.00017	+	9.86741i	−0.313123	+	0.617921i
$256$		0			0
$257$	−2.12823	−	7.94266i	−0.132755	−	0.495449i	0.867242	−	0.497887i	$-0.165891\pi$
$257$	−2.12823	−	7.94266i	−0.132755	−	0.495449i	−0.999997	+	0.00243792i	$0.999224\pi$
$258$		0			0
$259$	2.77537	−	1.88619i	0.172453	−	0.117202i
$260$		0			0
$261$	11.2949	−	19.5633i	0.699136	−	1.21094i
$262$		0			0
$263$	−0.826480	−	0.221455i	−0.0509629	−	0.0136555i	0.233248	−	0.972417i	$-0.425065\pi$
$263$	−0.826480	−	0.221455i	−0.0509629	−	0.0136555i	−0.284210	+	0.958762i	$0.591731\pi$
$264$		0			0
$265$	−27.2217	−	5.72310i	−1.67221	−	0.351567i
$266$		0			0
$267$	−13.9885	−	13.9885i	−0.856082	−	0.856082i
$268$		0			0
$269$	−15.2945	−	26.4909i	−0.932525	−	1.61518i	−0.778989	−	0.627038i	$-0.784267\pi$
$269$	−15.2945	−	26.4909i	−0.932525	−	1.61518i	−0.153536	−	0.988143i	$-0.549066\pi$
$270$		0			0
$271$	−22.5951	−	13.0453i	−1.37255	−	0.792444i	−0.381305	−	0.924449i	$-0.624525\pi$
$271$	−22.5951	−	13.0453i	−1.37255	−	0.792444i	−0.991249	+	0.132005i	$0.957859\pi$
$272$		0			0
$273$	19.3279	−	22.3922i	1.16978	−	1.35524i
$274$		0			0
$275$	3.63709	+	4.95963i	0.219325	+	0.299077i
$276$		0			0
$277$	−5.66094	+	21.1269i	−0.340133	+	1.26939i	0.558063	+	0.829798i	$0.311545\pi$
$277$	−5.66094	+	21.1269i	−0.340133	+	1.26939i	−0.898196	+	0.439595i	$0.855122\pi$
$278$		0			0
$279$	−40.3300			−2.41449
$280$		0			0
$281$	20.7731			1.23922			0.619609	−	0.784910i	$-0.287291\pi$
$281$	20.7731			1.23922			0.619609	+	0.784910i	$0.287291\pi$
$282$		0			0
$283$	1.91254	−	7.13770i	0.113689	−	0.424292i	−0.885497	−	0.464646i	$-0.846182\pi$
$283$	1.91254	−	7.13770i	0.113689	−	0.424292i	0.999185	+	0.0403536i	$0.0128484\pi$
$284$		0			0
$285$	23.1237	+	20.7280i	1.36973	+	1.22782i
$286$		0			0
$287$	−1.09647	−	3.14851i	−0.0647227	−	0.185850i
$288$		0			0
$289$	−12.6968	−	7.33050i	−0.746870	−	0.431206i
$290$		0			0
$291$	−25.6051	−	44.3493i	−1.50100	−	2.59980i
$292$		0			0
$293$	−9.60690	−	9.60690i	−0.561241	−	0.561241i	0.368419	−	0.929660i	$-0.379899\pi$
$293$	−9.60690	−	9.60690i	−0.561241	−	0.561241i	−0.929660	+	0.368419i	$0.879899\pi$
$294$		0			0
$295$	4.19363	+	6.42639i	0.244163	+	0.374159i
$296$		0			0
$297$	17.1534	+	4.59625i	0.995343	+	0.266701i
$298$		0			0
$299$	1.78805	−	3.09699i	0.103406	−	0.179104i
$300$		0			0
$301$	−9.91487	+	20.5106i	−0.571484	+	1.18221i
$302$		0			0
$303$	13.6727	+	51.0270i	0.785473	+	2.93143i
$304$		0			0
$305$	−11.1052	−	5.62740i	−0.635881	−	0.322224i
$306$		0			0
$307$	12.5009	−	12.5009i	0.713463	−	0.713463i	−0.253795	−	0.967258i	$-0.581679\pi$
$307$	12.5009	−	12.5009i	0.713463	−	0.713463i	0.967258	+	0.253795i	$0.0816788\pi$
$308$		0			0
$309$		−	19.2593i		−	1.09563i
$310$		0			0
$311$	−23.2048	+	13.3973i	−1.31582	+	0.759692i	−0.983054	−	0.183316i	$-0.941317\pi$
$311$	−23.2048	+	13.3973i	−1.31582	+	0.759692i	−0.332771	+	0.943008i	$0.607984\pi$
$312$		0			0
$313$	−25.9848	+	6.96262i	−1.46875	+	0.393550i	−0.902502	−	0.430685i	$-0.858272\pi$
$313$	−25.9848	+	6.96262i	−1.46875	+	0.393550i	−0.566248	+	0.824235i	$0.691605\pi$
$314$		0			0
$315$	43.7577	+	5.89467i	2.46547	+	0.332127i
$316$		0			0
$317$	18.7049	−	5.01197i	1.05057	−	0.281500i	0.308085	−	0.951359i	$-0.400312\pi$
$317$	18.7049	−	5.01197i	1.05057	−	0.281500i	0.742489	+	0.669859i	$0.233645\pi$
$318$		0			0
$319$	−3.22437	+	1.86159i	−0.180530	+	0.104229i
$320$		0			0
$321$		−	35.3685i		−	1.97408i
$322$		0			0
$323$	4.64304	−	4.64304i	0.258346	−	0.258346i
$324$		0			0
$325$	13.4785	+	10.8161i	0.747655	+	0.599969i
$326$		0			0
$327$	5.45073	+	20.3424i	0.301426	+	1.12494i
$328$		0			0
$329$	−8.25266	−	12.1431i	−0.454984	−	0.669469i
$330$		0			0
$331$	14.9161	−	25.8354i	0.819863	−	1.42004i	−0.0859200	−	0.996302i	$-0.527383\pi$
$331$	14.9161	−	25.8354i	0.819863	−	1.42004i	0.905783	−	0.423742i	$-0.139284\pi$
$332$		0			0
$333$	9.14318	+	2.44991i	0.501043	+	0.134254i
$334$		0			0
$335$	1.92691	−	9.16525i	0.105278	−	0.500751i
$336$		0			0
$337$	−10.8467	−	10.8467i	−0.590856	−	0.590856i	0.347007	−	0.937863i	$-0.387198\pi$
$337$	−10.8467	−	10.8467i	−0.590856	−	0.590856i	−0.937863	+	0.347007i	$0.887198\pi$
$338$		0			0
$339$	−9.73664	−	16.8644i	−0.528822	−	0.915946i
$340$		0			0
$341$	5.75653	+	3.32353i	0.311733	+	0.179979i
$342$		0			0
$343$	−9.92303	+	15.6376i	−0.535793	+	0.844349i
$344$		0			0
$345$	7.47244	−	0.408228i	0.402303	−	0.0219783i
$346$		0			0
$347$	8.47165	−	31.6166i	0.454782	−	1.69727i	−0.233946	−	0.972250i	$-0.575164\pi$
$347$	8.47165	−	31.6166i	0.454782	−	1.69727i	0.688728	−	0.725020i	$-0.258169\pi$
$348$		0			0
$349$	4.85034			0.259632			0.129816	−	0.991538i	$-0.458561\pi$
$349$	4.85034			0.259632			0.129816	+	0.991538i	$0.458561\pi$
$350$		0			0
$351$	49.8997			2.66345
$352$		0			0
$353$	−0.943907	+	3.52271i	−0.0502391	+	0.187495i	−0.986485	−	0.163850i	$-0.947609\pi$
$353$	−0.943907	+	3.52271i	−0.0502391	+	0.187495i	0.936246	+	0.351345i	$0.114275\pi$
$354$		0			0
$355$	−22.6169	+	1.23559i	−1.20038	+	0.0655782i
$356$		0			0
$357$	2.45241	−	12.8569i	0.129795	−	0.680460i
$358$		0			0
$359$	−2.82260	−	1.62963i	−0.148971	−	0.0860085i	0.423662	−	0.905821i	$-0.360745\pi$
$359$	−2.82260	−	1.62963i	−0.148971	−	0.0860085i	−0.572633	+	0.819812i	$0.694078\pi$
$360$		0			0
$361$	0.283347	+	0.490771i	0.0149130	+	0.0258301i
$362$		0			0
$363$	21.6992	+	21.6992i	1.13891	+	1.13891i
$364$		0			0
$365$	2.41784	−	11.5004i	0.126556	−	0.601956i
$366$		0			0
$367$	8.56115	+	2.29395i	0.446888	+	0.119743i	0.475243	−	0.879855i	$-0.342360\pi$
$367$	8.56115	+	2.29395i	0.446888	+	0.119743i	−0.0283547	+	0.999598i	$0.509027\pi$
$368$		0			0
$369$	4.70228	−	8.14458i	0.244791	−	0.423990i
$370$		0			0
$371$	32.8248	−	2.41094i	1.70418	−	0.125170i
$372$		0			0
$373$	5.00215	+	18.6683i	0.259002	+	0.966607i	0.965820	+	0.259213i	$0.0834630\pi$
$373$	5.00215	+	18.6683i	0.259002	+	0.966607i	−0.706819	+	0.707395i	$0.749870\pi$
$374$		0			0
$375$	−3.54096	+	35.9912i	−0.182855	+	1.85858i
$376$		0			0
$377$	−7.39757	+	7.39757i	−0.380994	+	0.380994i
$378$		0			0
$379$			30.0300i			1.54254i	0.636510	+	0.771268i	$0.280377\pi$
$379$			30.0300i			1.54254i	−0.636510	+	0.771268i	$0.719623\pi$
$380$		0			0
$381$	−7.93556	+	4.58160i	−0.406551	+	0.234722i
$382$		0			0
$383$	−9.99880	+	2.67917i	−0.510915	+	0.136899i	−0.505061	−	0.863084i	$-0.668530\pi$
$383$	−9.99880	+	2.67917i	−0.510915	+	0.136899i	−0.00585374	+	0.999983i	$0.501863\pi$
$384$		0			0
$385$	−5.76001	−	4.44738i	−0.293557	−	0.226660i
$386$		0			0
$387$	−62.0725	+	16.6323i	−3.15532	+	0.845467i
$388$		0			0
$389$	−30.0971	+	17.3765i	−1.52598	+	0.881026i	−0.526456	+	0.850202i	$0.676480\pi$
$389$	−30.0971	+	17.3765i	−1.52598	+	0.881026i	−0.999525	+	0.0308234i	$0.990187\pi$
$390$		0			0
$391$		−	1.58237i		−	0.0800238i
$392$		0			0
$393$	−36.8793	+	36.8793i	−1.86032	+	1.86032i
$394$		0			0
$395$	−10.0203	−	5.07766i	−0.504177	−	0.255485i
$396$		0			0
$397$	−4.67792	−	17.4582i	−0.234778	−	0.876204i	−0.978249	−	0.207435i	$-0.933488\pi$
$397$	−4.67792	−	17.4582i	−0.234778	−	0.876204i	0.743471	−	0.668768i	$-0.233178\pi$
$398$		0			0
$399$	−33.0813	−	15.9916i	−1.65614	−	0.800580i
$400$		0			0
$401$	−1.50000	+	2.59808i	−0.0749064	+	0.129742i	−0.901046	−	0.433724i	$-0.857199\pi$
$401$	−1.50000	+	2.59808i	−0.0749064	+	0.129742i	0.826139	+	0.563466i	$0.190532\pi$
$402$		0			0
$403$	18.0411	+	4.83411i	0.898694	+	0.240804i
$404$		0			0
$405$	29.7068	+	45.5232i	1.47614	+	2.26206i
$406$		0			0
$407$	−1.10316	−	1.10316i	−0.0546818	−	0.0546818i
$408$		0			0
$409$	−14.1982	−	24.5920i	−0.702057	−	1.21600i	−0.967743	−	0.251939i	$-0.918932\pi$
$409$	−14.1982	−	24.5920i	−0.702057	−	1.21600i	0.265686	−	0.964060i	$-0.414401\pi$
$410$		0			0
$411$	33.0135	+	19.0603i	1.62844	+	0.940177i
$412$		0			0
$413$	−6.87328	−	5.93270i	−0.338212	−	0.291929i
$414$		0			0
$415$	−20.8298	−	18.6718i	−1.02249	−	0.916562i
$416$		0			0
$417$	−8.54070	+	31.8743i	−0.418240	+	1.56089i
$418$		0			0
$419$	13.8024			0.674292			0.337146	−	0.941452i	$-0.390538\pi$
$419$	13.8024			0.674292			0.337146	+	0.941452i	$0.390538\pi$
$420$		0			0
$421$	−14.6964			−0.716257			−0.358128	−	0.933672i	$-0.616585\pi$
$421$	−14.6964			−0.716257			−0.358128	+	0.933672i	$0.616585\pi$
$422$		0			0
$423$	10.7191	−	40.0042i	0.521180	−	1.94507i
$424$		0			0
$425$	7.55799	+	1.16274i	0.366616	+	0.0564011i
$426$		0			0
$427$	14.4697	+	2.76004i	0.700238	+	0.133568i
$428$		0			0
$429$	−11.9099	−	6.87619i	−0.575016	−	0.331985i
$430$		0			0
$431$	8.38497	+	14.5232i	0.403890	+	0.699558i	0.994192	−	0.107625i	$-0.0343246\pi$
$431$	8.38497	+	14.5232i	0.403890	+	0.699558i	−0.590302	+	0.807183i	$0.700991\pi$
$432$		0			0
$433$	−0.621612	−	0.621612i	−0.0298728	−	0.0298728i	0.692013	−	0.721885i	$-0.256724\pi$
$433$	−0.621612	−	0.621612i	−0.0298728	−	0.0298728i	−0.721885	+	0.692013i	$0.756724\pi$
$434$		0			0
$435$	−21.4246	−	4.50431i	−1.02723	−	0.215965i
$436$		0			0
$437$	−4.29079	−	1.14971i	−0.205256	−	0.0549983i
$438$		0			0
$439$	3.19408	−	5.53232i	0.152445	−	0.264043i	−0.779681	−	0.626177i	$-0.784619\pi$
$439$	3.19408	−	5.53232i	0.152445	−	0.264043i	0.932126	+	0.362134i	$0.117952\pi$
$440$		0			0
$441$	−51.6818	+	7.63311i	−2.46104	+	0.363481i
$442$		0			0
$443$	−5.25381	−	19.6075i	−0.249616	−	0.931580i	−0.971007	−	0.239052i	$-0.923163\pi$
$443$	−5.25381	−	19.6075i	−0.249616	−	0.931580i	0.721391	−	0.692528i	$-0.243503\pi$
$444$		0			0
$445$	−6.18145	+	12.1986i	−0.293029	+	0.578267i
$446$		0			0
$447$	14.6604	−	14.6604i	0.693414	−	0.693414i
$448$		0			0
$449$			17.0506i			0.804669i	0.915493	+	0.402334i	$0.131801\pi$
$449$			17.0506i			0.804669i	−0.915493	+	0.402334i	$0.868199\pi$
$450$		0			0
$451$	−1.34236	+	0.775014i	−0.0632095	+	0.0364940i
$452$		0			0
$453$	40.3044	−	10.7995i	1.89367	−	0.507406i
$454$		0			0
$455$	−18.8679	−	7.88188i	−0.884542	−	0.369508i
$456$		0			0
$457$	16.0461	−	4.29955i	0.750607	−	0.201125i	0.136820	−	0.990596i	$-0.456312\pi$
$457$	16.0461	−	4.29955i	0.750607	−	0.201125i	0.613787	+	0.789471i	$0.289645\pi$
$458$		0			0
$459$	19.1217	−	11.0399i	0.892524	−	0.515299i
$460$		0			0
$461$		−	13.4410i		−	0.626011i	−0.949751	−	0.313006i	$-0.898664\pi$
$461$		−	13.4410i		−	0.626011i	0.949751	−	0.313006i	$-0.101336\pi$
$462$		0			0
$463$	7.10922	−	7.10922i	0.330393	−	0.330393i	−0.522342	−	0.852736i	$-0.674942\pi$
$463$	7.10922	−	7.10922i	0.330393	−	0.330393i	0.852736	+	0.522342i	$0.174942\pi$
$464$		0			0
$465$	12.1606	+	37.1460i	0.563934	+	1.72261i
$466$		0			0
$467$	−5.36906	−	20.0376i	−0.248451	−	0.927230i	−0.971618	−	0.236557i	$-0.923981\pi$
$467$	−5.36906	−	20.0376i	−0.248451	−	0.927230i	0.723167	−	0.690673i	$-0.242686\pi$
$468$		0			0
$469$	0.811739	+	11.0518i	0.0374826	+	0.510324i
$470$		0			0
$471$	−7.07824	+	12.2599i	−0.326148	+	0.564905i
$472$		0			0
$473$	10.2306	+	2.74128i	0.470404	+	0.126044i
$474$		0			0
$475$	8.64438	−	19.6496i	0.396631	−	0.901586i
$476$		0			0
$477$	65.6497	+	65.6497i	3.00589	+	3.00589i
$478$		0			0
$479$	16.5927	+	28.7394i	0.758139	+	1.31313i	0.943799	+	0.330521i	$0.107224\pi$
$479$	16.5927	+	28.7394i	0.758139	+	1.31313i	−0.185660	+	0.982614i	$0.559442\pi$
$480$		0			0
$481$	−3.79644	−	2.19187i	−0.173103	−	0.0999409i
$482$		0			0
$483$	−8.36212	+	2.91212i	−0.380490	+	0.132506i
$484$		0			0
$485$	−23.6292	+	26.3601i	−1.07294	+	1.19695i
$486$		0			0
$487$	0.722118	−	2.69498i	0.0327223	−	0.122121i	−0.947633	−	0.319362i	$-0.896531\pi$
$487$	0.722118	−	2.69498i	0.0327223	−	0.122121i	0.980355	+	0.197241i	$0.0631981\pi$
$488$		0			0
$489$	48.2169			2.18044
$490$		0			0
$491$	−15.7992			−0.713008			−0.356504	−	0.934294i	$-0.616031\pi$
$491$	−15.7992			−0.713008			−0.356504	+	0.934294i	$0.616031\pi$
$492$		0			0
$493$	−1.19811	+	4.47142i	−0.0539604	+	0.201383i
$494$		0			0
$495$	−1.11978	−	20.4970i	−0.0503302	−	0.921273i
$496$		0			0
$497$	25.3097	−	8.81415i	1.13530	−	0.395369i
$498$		0			0
$499$	−29.3154	−	16.9252i	−1.31234	−	0.757678i	−0.329853	−	0.944032i	$-0.606999\pi$
$499$	−29.3154	−	16.9252i	−1.31234	−	0.757678i	−0.982483	+	0.186355i	$0.940333\pi$
$500$		0			0
$501$	−21.5193	−	37.2725i	−0.961410	−	1.66521i
$502$		0			0
$503$	−5.02731	−	5.02731i	−0.224157	−	0.224157i	0.586090	−	0.810246i	$-0.300667\pi$
$503$	−5.02731	−	5.02731i	−0.224157	−	0.224157i	−0.810246	+	0.586090i	$0.800667\pi$
$504$		0			0
$505$	30.5826	−	19.9571i	1.36091	−	0.888078i
$506$		0			0
$507$	3.29206	+	0.882105i	0.146206	+	0.0391757i
$508$		0			0
$509$	−4.67261	+	8.09319i	−0.207110	+	0.358725i	−0.950803	−	0.309797i	$-0.899739\pi$
$509$	−4.67261	+	8.09319i	−0.207110	+	0.358725i	0.743693	+	0.668521i	$0.233072\pi$
$510$		0			0
$511$	1.01855	+	13.8675i	0.0450581	+	0.613463i
$512$		0			0
$513$	−16.0427	−	59.8722i	−0.708303	−	2.64342i
$514$		0			0
$515$	−12.6528	+	4.14217i	−0.557548	+	0.182526i
$516$		0			0
$517$	−4.82668	+	4.82668i	−0.212277	+	0.212277i
$518$		0			0
$519$			15.1066i			0.663105i
$520$		0			0
$521$	−33.0695	+	19.0927i	−1.44880	+	0.836466i	−0.998410	−	0.0563659i	$-0.982049\pi$
$521$	−33.0695	+	19.0927i	−1.44880	+	0.836466i	−0.450391	+	0.892832i	$0.648715\pi$
$522$		0			0
$523$	26.2493	−	7.03347i	1.14780	−	0.307552i	0.365717	−	0.930726i	$-0.380824\pi$
$523$	26.2493	−	7.03347i	1.14780	−	0.307552i	0.782083	+	0.623174i	$0.214157\pi$
$524$		0			0
$525$	−7.76484	−	42.0805i	−0.338885	−	1.83654i
$526$		0			0
$527$	7.98293	−	2.13902i	0.347742	−	0.0931771i
$528$		0			0
$529$	18.9915	−	10.9648i	0.825718	−	0.476728i
$530$		0			0
$531$		−	25.6120i		−	1.11146i
$532$		0			0
$533$	−3.07975	+	3.07975i	−0.133399	+	0.133399i
$534$		0			0
$535$	−23.2360	+	7.60684i	−1.00458	+	0.328872i
$536$		0			0
$537$	−2.24964	−	8.39577i	−0.0970792	−	0.362304i
$538$		0			0
$539$	8.00587	+	3.16950i	0.344837	+	0.136520i
$540$		0			0
$541$	10.8597	−	18.8096i	0.466896	−	0.808688i	−0.532389	−	0.846500i	$-0.678706\pi$
$541$	10.8597	−	18.8096i	0.466896	−	0.808688i	0.999285	+	0.0378121i	$0.0120388\pi$
$542$		0			0
$543$	−43.0075	−	11.5238i	−1.84563	−	0.494534i
$544$		0			0
$545$	12.1920	−	7.95608i	0.522249	−	0.340801i
$546$		0			0
$547$	−1.34474	−	1.34474i	−0.0574969	−	0.0574969i	0.677774	−	0.735271i	$-0.262945\pi$
$547$	−1.34474	−	1.34474i	−0.0574969	−	0.0574969i	−0.735271	+	0.677774i	$0.762945\pi$
$548$		0			0
$549$	20.7762	+	35.9855i	0.886708	+	1.53582i
$550$		0			0
$551$	11.2543	+	6.49768i	0.479450	+	0.276810i
$552$		0			0
$553$	13.0562	+	2.49042i	0.555204	+	0.105903i
$554$		0			0
$555$	−0.500425	−	9.16006i	−0.0212418	−	0.388823i
$556$		0			0
$557$	1.89708	−	7.07999i	0.0803818	−	0.299989i	−0.914018	−	0.405674i	$-0.867037\pi$
$557$	1.89708	−	7.07999i	0.0803818	−	0.299989i	0.994400	+	0.105685i	$0.0337035\pi$
$558$		0			0
$559$	29.7610			1.25876
$560$		0			0
$561$	−6.08521			−0.256918
$562$		0			0
$563$	−3.06760	+	11.4484i	−0.129284	+	0.482494i	−0.999956	−	0.00936989i	$-0.997017\pi$
$563$	−3.06760	+	11.4484i	−0.129284	+	0.482494i	0.870672	+	0.491863i	$0.163684\pi$
$564$		0			0
$565$	−8.98526	+	10.0237i	−0.378013	+	0.421702i
$566$		0			0
$567$	−48.6889	−	42.0260i	−2.04474	−	1.76493i
$568$		0			0
$569$	−10.9064	−	6.29679i	−0.457219	−	0.263975i	0.253655	−	0.967295i	$-0.418367\pi$
$569$	−10.9064	−	6.29679i	−0.457219	−	0.263975i	−0.710874	+	0.703319i	$0.751700\pi$
$570$		0			0
$571$	22.4679	+	38.9155i	0.940251	+	1.62856i	0.764991	+	0.644041i	$0.222743\pi$
$571$	22.4679	+	38.9155i	0.940251	+	1.62856i	0.175260	+	0.984522i	$0.443923\pi$
$572$		0			0
$573$	−17.4951	−	17.4951i	−0.730867	−	0.730867i
$574$		0			0
$575$	−1.87532	−	4.82136i	−0.0782061	−	0.201065i
$576$		0			0
$577$	−26.1700	−	7.01224i	−1.08947	−	0.291923i	−0.331002	−	0.943630i	$-0.607387\pi$
$577$	−26.1700	−	7.01224i	−1.08947	−	0.291923i	−0.758471	+	0.651707i	$0.774053\pi$
$578$		0			0
$579$	−17.9482	+	31.0872i	−0.745901	+	1.29194i
$580$		0			0
$581$	29.7996	+	14.4052i	1.23629	+	0.597628i
$582$		0			0
$583$	−3.96046	−	14.7806i	−0.164025	−	0.612151i
$584$		0			0
$585$	−17.9458	−	54.8177i	−0.741968	−	2.26643i
$586$		0			0
$587$	1.96674	−	1.96674i	0.0811759	−	0.0811759i	−0.665353	−	0.746529i	$-0.731719\pi$
$587$	1.96674	−	1.96674i	0.0811759	−	0.0811759i	0.746529	+	0.665353i	$0.231719\pi$
$588$		0			0
$589$		−	23.2009i		−	0.955975i
$590$		0			0
$591$	44.3045	−	25.5792i	1.82245	−	1.05219i
$592$		0			0
$593$	−14.6871	+	3.93539i	−0.603126	+	0.161607i	−0.547445	−	0.836842i	$-0.684400\pi$
$593$	−14.6871	+	3.93539i	−0.603126	+	0.161607i	−0.0556806	+	0.998449i	$0.517733\pi$
$594$		0			0
$595$	−8.97404	+	1.15402i	−0.367900	+	0.0473104i
$596$		0			0
$597$	−40.1067	+	10.7465i	−1.64146	+	0.439827i
$598$		0			0
$599$	−12.1470	+	7.01309i	−0.496314	+	0.286547i	−0.727190	−	0.686436i	$-0.759174\pi$
$599$	−12.1470	+	7.01309i	−0.496314	+	0.286547i	0.230876	+	0.972983i	$0.425841\pi$
$600$		0			0
$601$			19.9337i			0.813111i	0.913626	+	0.406555i	$0.133270\pi$
$601$			19.9337i			0.813111i	−0.913626	+	0.406555i	$0.866730\pi$
$602$		0			0
$603$	−22.1036	+	22.1036i	−0.900126	+	0.900126i
$604$		0			0
$605$	9.58878	−	18.9226i	0.389839	−	0.769314i
$606$		0			0
$607$	−0.496888	−	1.85441i	−0.0201681	−	0.0752683i	0.955108	−	0.296257i	$-0.0957384\pi$
$607$	−0.496888	−	1.85441i	−0.0201681	−	0.0752683i	−0.975276	+	0.220988i	$0.929072\pi$
$608$		0			0
$609$	25.8345	−	1.89751i	1.04687	−	0.0768909i
$610$		0			0
$611$	−9.59011	+	16.6106i	−0.387974	+	0.671991i
$612$		0			0
$613$	37.3779	+	10.0154i	1.50968	+	0.404517i	0.916328	−	0.400428i	$-0.131139\pi$
$613$	37.3779	+	10.0154i	1.50968	+	0.404517i	0.593349	+	0.804945i	$0.297805\pi$
$614$		0			0
$615$	−8.91944	−	1.87523i	−0.359667	−	0.0756165i
$616$		0			0
$617$	13.2837	+	13.2837i	0.534782	+	0.534782i	0.921992	−	0.387210i	$-0.126561\pi$
$617$	13.2837	+	13.2837i	0.534782	+	0.534782i	−0.387210	+	0.921992i	$0.626561\pi$
$618$		0			0
$619$	−9.82797	−	17.0225i	−0.395020	−	0.684194i	0.598084	−	0.801433i	$-0.295929\pi$
$619$	−9.82797	−	17.0225i	−0.395020	−	0.684194i	−0.993104	+	0.117239i	$0.962596\pi$
$620$		0			0
$621$	−12.9361	−	7.46865i	−0.519107	−	0.299706i
$622$		0			0
$623$	3.03179	−	15.8943i	0.121466	−	0.636792i
$624$		0			0
$625$	24.4066	−	5.41444i	0.976265	−	0.216578i
$626$		0			0
$627$	−4.42138	+	16.5008i	−0.176573	+	0.658979i
$628$		0			0
$629$	−1.93974			−0.0773425
$630$		0			0
$631$	−13.4687			−0.536182			−0.268091	−	0.963394i	$-0.586393\pi$
$631$	−13.4687			−0.536182			−0.268091	+	0.963394i	$0.586393\pi$
$632$		0			0
$633$	−4.36132	+	16.2767i	−0.173347	+	0.646939i
$634$		0			0
$635$	4.71670	+	4.22803i	0.187176	+	0.167784i
$636$		0			0
$637$	24.0342	+	2.78021i	0.952269	+	0.110156i
$638$		0			0
$639$	65.4714	+	37.7999i	2.59001	+	1.49534i
$640$		0			0
$641$	4.35542	+	7.54381i	0.172029	+	0.297962i	0.939129	−	0.343565i	$-0.111634\pi$
$641$	4.35542	+	7.54381i	0.172029	+	0.297962i	−0.767100	+	0.641527i	$0.778301\pi$
$642$		0			0
$643$	12.2173	+	12.2173i	0.481802	+	0.481802i	0.905707	−	0.423905i	$-0.139341\pi$
$643$	12.2173	+	12.2173i	0.481802	+	0.481802i	−0.423905	+	0.905707i	$0.639341\pi$
$644$		0			0
$645$	34.0358	+	52.1569i	1.34016	+	2.05368i
$646$		0			0
$647$	−7.03047	−	1.88381i	−0.276396	−	0.0740601i	0.117958	−	0.993019i	$-0.462365\pi$
$647$	−7.03047	−	1.88381i	−0.276396	−	0.0740601i	−0.394354	+	0.918958i	$0.629032\pi$
$648$		0			0
$649$	−2.11064	+	3.65574i	−0.0828499	+	0.143500i
$650$		0			0
$651$	−25.9952	−	38.2497i	−1.01883	−	1.49912i
$652$		0			0
$653$	7.45345	+	27.8167i	0.291676	+	1.08855i	0.943821	+	0.330456i	$0.107202\pi$
$653$	7.45345	+	27.8167i	0.291676	+	1.08855i	−0.652145	+	0.758094i	$0.726131\pi$
$654$		0			0
$655$	32.1604	+	16.2968i	1.25661	+	0.636769i
$656$		0			0
$657$	−27.7351	+	27.7351i	−1.08205	+	1.08205i
$658$		0			0
$659$			10.6895i			0.416403i	0.978086	+	0.208201i	$0.0667610\pi$
$659$			10.6895i			0.416403i	−0.978086	+	0.208201i	$0.933239\pi$
$660$		0			0
$661$	9.24885	−	5.33983i	0.359739	−	0.207695i	−0.309227	−	0.950988i	$-0.600070\pi$
$661$	9.24885	−	5.33983i	0.359739	−	0.207695i	0.668966	+	0.743293i	$0.266737\pi$
$662$		0			0
$663$	−16.5162	+	4.42550i	−0.641435	+	0.171872i
$664$		0			0
$665$	−3.39106	+	25.1727i	−0.131500	+	0.976157i
$666$		0			0
$667$	3.02498	−	0.810540i	0.117128	−	0.0313842i
$668$		0			0
$669$	−14.1885	+	8.19173i	−0.548559	+	0.316711i
$670$		0			0
$671$		−	6.84854i		−	0.264385i
$672$		0			0
$673$	29.8322	−	29.8322i	1.14995	−	1.14995i	0.163384	−	0.986563i	$-0.447759\pi$
$673$	29.8322	−	29.8322i	1.14995	−	1.14995i	0.986563	−	0.163384i	$-0.0522410\pi$
$674$		0			0
$675$	45.1786	−	56.2995i	1.73893	−	2.16697i
$676$		0			0
$677$	5.33980	+	19.9284i	0.205225	+	0.765911i	0.989381	+	0.145346i	$0.0464297\pi$
$677$	5.33980	+	19.9284i	0.205225	+	0.765911i	−0.784156	+	0.620564i	$0.786904\pi$
$678$		0			0
$679$	18.2298	−	37.7113i	0.699594	−	1.44723i
$680$		0			0
$681$	−41.3115	+	71.5536i	−1.58306	+	2.74194i
$682$		0			0
$683$	17.8149	+	4.77349i	0.681668	+	0.182653i	0.583005	−	0.812468i	$-0.301877\pi$
$683$	17.8149	+	4.77349i	0.681668	+	0.182653i	0.0986632	+	0.995121i	$0.468543\pi$
$684$		0			0
$685$	5.42172	−	25.7882i	0.207153	−	0.985317i
$686$		0			0
$687$	−45.4721	−	45.4721i	−1.73487	−	1.73487i
$688$		0			0
$689$	−21.4986	−	37.2366i	−0.819030	−	1.41860i
$690$		0			0
$691$	−3.62120	−	2.09070i	−0.137757	−	0.0795340i	0.429538	−	0.903049i	$-0.358677\pi$
$691$	−3.62120	−	2.09070i	−0.137757	−	0.0795340i	−0.567295	+	0.823515i	$0.692010\pi$
$692$		0			0
$693$	7.98801	+	22.9375i	0.303439	+	0.871322i
$694$		0			0
$695$	22.7773	−	1.24435i	0.863993	−	0.0472009i
$696$		0			0
$697$	−0.498798	+	1.86154i	−0.0188933	+	0.0705108i
$698$		0			0
$699$	−67.9182			−2.56890
$700$		0			0
$701$	−21.4571			−0.810424			−0.405212	−	0.914223i	$-0.632802\pi$
$701$	−21.4571			−0.810424			−0.405212	+	0.914223i	$0.632802\pi$
$702$		0			0
$703$	−1.40937	+	5.25985i	−0.0531555	+	0.198379i
$704$		0			0
$705$	−40.0780	+	2.18951i	−1.50943	+	0.0824616i
$706$		0			0
$707$	−28.2331	+	32.7093i	−1.06182	+	1.23016i
$708$		0			0
$709$	22.6370	+	13.0695i	0.850149	+	0.490834i	0.860701	−	0.509110i	$-0.170026\pi$
$709$	22.6370	+	13.0695i	0.850149	+	0.490834i	−0.0105520	+	0.999944i	$0.503359\pi$
$710$		0			0
$711$	18.7466	+	32.4701i	0.703052	+	1.21772i
$712$		0			0
$713$	−3.95348	−	3.95348i	−0.148059	−	0.148059i
$714$		0			0
$715$	−1.95593	+	9.30332i	−0.0731478	+	0.347925i
$716$		0			0
$717$	−55.7614	−	14.9412i	−2.08245	−	0.557990i
$718$		0			0
$719$	11.0172	−	19.0824i	0.410872	−	0.711652i	−0.584113	−	0.811672i	$-0.698558\pi$
$719$	11.0172	−	19.0824i	0.410872	−	0.711652i	0.994985	+	0.100021i	$0.0318909\pi$
$720$		0			0
$721$	13.0287	−	8.85456i	0.485215	−	0.329761i
$722$		0			0
$723$	2.46830	+	9.21180i	0.0917969	+	0.342591i
$724$		0			0
$725$	1.64867	+	15.0440i	0.0612299	+	0.558721i
$726$		0			0
$727$	6.19964	−	6.19964i	0.229932	−	0.229932i	−0.582732	−	0.812664i	$-0.698016\pi$
$727$	6.19964	−	6.19964i	0.229932	−	0.229932i	0.812664	+	0.582732i	$0.198016\pi$
$728$		0			0
$729$		−	41.3312i		−	1.53079i
$730$		0			0
$731$	11.4045	−	6.58439i	0.421811	−	0.243533i
$732$		0			0
$733$	−13.1895	+	3.53411i	−0.487164	+	0.130535i	−0.494036	−	0.869441i	$-0.664479\pi$
$733$	−13.1895	+	3.53411i	−0.487164	+	0.130535i	0.00687249	+	0.999976i	$0.497812\pi$
$734$		0			0
$735$	22.6140	+	45.3001i	0.834128	+	1.67092i
$736$		0			0
$737$	4.97648	−	1.33344i	0.183311	−	0.0491181i
$738$		0			0
$739$	−17.9456	+	10.3609i	−0.660141	+	0.381132i	−0.792331	−	0.610092i	$-0.791132\pi$
$739$	−17.9456	+	10.3609i	−0.660141	+	0.381132i	0.132190	+	0.991224i	$0.457799\pi$
$740$		0			0
$741$			48.0012i			1.76337i
$742$		0			0
$743$	−1.73501	+	1.73501i	−0.0636513	+	0.0636513i	−0.738216	−	0.674565i	$-0.764331\pi$
$743$	−1.73501	+	1.73501i	−0.0636513	+	0.0636513i	0.674565	+	0.738216i	$0.264331\pi$
$744$		0			0
$745$	−12.7845	−	6.47837i	−0.468388	−	0.237349i
$746$		0			0
$747$	24.1648	+	90.1844i	0.884145	+	3.29967i
$748$		0			0
$749$	23.9264	−	16.2608i	0.874252	−	0.594158i
$750$		0			0
$751$	−4.19292	+	7.26235i	−0.153002	+	0.265007i	−0.932330	−	0.361610i	$-0.882227\pi$
$751$	−4.19292	+	7.26235i	−0.153002	+	0.265007i	0.779328	+	0.626616i	$0.215561\pi$
$752$		0			0
$753$	−87.1524	−	23.3524i	−3.17601	−	0.851009i
$754$		0			0
$755$	−15.7634	−	24.1561i	−0.573688	−	0.879129i
$756$		0			0
$757$	−22.2101	−	22.2101i	−0.807241	−	0.807241i	0.176975	−	0.984215i	$-0.443369\pi$
$757$	−22.2101	−	22.2101i	−0.807241	−	0.807241i	−0.984215	+	0.176975i	$0.943369\pi$
$758$		0			0
$759$	2.05836	+	3.56519i	0.0747138	+	0.129408i
$760$		0			0
$761$	−20.3793	−	11.7660i	−0.738749	−	0.426517i	0.0828651	−	0.996561i	$-0.473593\pi$
$761$	−20.3793	−	11.7660i	−0.738749	−	0.426517i	−0.821614	+	0.570044i	$0.806926\pi$
$762$		0			0
$763$	−11.2554	+	13.0399i	−0.407473	+	0.472075i
$764$		0			0
$765$	−19.0049	−	17.0359i	−0.687122	−	0.615935i
$766$		0			0
$767$	−3.06995	+	11.4572i	−0.110849	+	0.413696i
$768$		0			0
$769$	5.77277			0.208171			0.104086	−	0.994568i	$-0.466808\pi$
$769$	5.77277			0.208171			0.104086	+	0.994568i	$0.466808\pi$
$770$		0			0
$771$	26.5983			0.957916
$772$		0			0
$773$	−10.2732	+	38.3400i	−0.369501	+	1.37899i	0.491715	+	0.870756i	$0.336370\pi$
$773$	−10.2732	+	38.3400i	−0.369501	+	1.37899i	−0.861216	+	0.508239i	$0.830297\pi$
$774$		0			0
$775$	21.7884	−	15.9783i	0.782661	−	0.573956i
$776$		0			0
$777$	3.56981	+	10.2507i	0.128066	+	0.367741i
$778$		0			0
$779$	4.68538	+	2.70510i	0.167871	+	0.0969204i
$780$		0			0
$781$	−6.23006	−	10.7908i	−0.222929	−	0.386125i
$782$		0			0
$783$	30.8995	+	30.8995i	1.10426	+	1.10426i
$784$		0			0
$785$	9.57670	+	2.01341i	0.341807	+	0.0718617i
$786$		0			0
$787$	−22.8135	−	6.11285i	−0.813212	−	0.217899i	−0.171835	−	0.985126i	$-0.554970\pi$
$787$	−22.8135	−	6.11285i	−0.813212	−	0.217899i	−0.641377	+	0.767226i	$0.721636\pi$
$788$		0			0
$789$	1.38386	−	2.39691i	0.0492666	−	0.0853322i
$790$		0			0
$791$	6.93208	−	14.3402i	0.246476	−	0.509878i
$792$		0			0
$793$	−4.98064	−	18.5880i	−0.176868	−	0.660079i
$794$		0			0
$795$	40.6716	−	80.2619i	1.44247	−	2.84660i
$796$		0			0
$797$	−0.0424381	+	0.0424381i	−0.00150323	+	0.00150323i	−0.707858	−	0.706355i	$-0.750338\pi$
$797$	−0.0424381	+	0.0424381i	−0.00150323	+	0.00150323i	0.706355	+	0.707858i	$0.250338\pi$
$798$		0			0
$799$			8.48695i			0.300247i
$800$		0			0
$801$	39.5284	−	22.8218i	1.39667	−	0.806367i
$802$		0			0
$803$	6.24438	−	1.67318i	0.220359	−	0.0590451i
$804$		0			0
$805$	3.71165	+	4.86733i	0.130818	+	0.171551i
$806$		0			0
$807$	95.5747	−	25.6092i	3.36439	−	0.901485i
$808$		0			0
$809$	−38.9718	+	22.5004i	−1.37018	+	0.791072i	−0.990950	−	0.134232i	$-0.957143\pi$
$809$	−38.9718	+	22.5004i	−1.37018	+	0.791072i	−0.379226	+	0.925304i	$0.623810\pi$
$810$		0			0
$811$			20.9653i			0.736191i	0.929788	+	0.368096i	$0.119990\pi$
$811$			20.9653i			0.736191i	−0.929788	+	0.368096i	$0.880010\pi$
$812$		0			0
$813$	59.6762	−	59.6762i	2.09293	−	2.09293i
$814$		0			0
$815$	−10.3702	−	31.6770i	−0.363251	−	1.10960i
$816$		0			0
$817$	−9.56815	−	35.7088i	−0.334747	−	1.24929i
$818$		0			0
$819$	38.3620	+	56.4464i	1.34048	+	1.97240i
$820$		0			0
$821$	25.0695	−	43.4216i	0.874931	−	1.51543i	0.0180958	−	0.999836i	$-0.494240\pi$
$821$	25.0695	−	43.4216i	0.874931	−	1.51543i	0.856836	−	0.515590i	$-0.172427\pi$
$822$		0			0
$823$	−39.9857	−	10.7141i	−1.39381	−	0.373471i	−0.517694	−	0.855566i	$-0.673209\pi$
$823$	−39.9857	−	10.7141i	−1.39381	−	0.373471i	−0.876119	+	0.482095i	$0.839876\pi$
$824$		0			0
$825$	−18.5412	+	7.21178i	−0.645521	+	0.251082i
$826$		0			0
$827$	−25.0625	−	25.0625i	−0.871507	−	0.871507i	0.121130	−	0.992637i	$-0.461348\pi$
$827$	−25.0625	−	25.0625i	−0.871507	−	0.871507i	−0.992637	+	0.121130i	$0.961348\pi$
$828$		0			0
$829$	22.9404	+	39.7339i	0.796752	+	1.38002i	0.921721	+	0.387854i	$0.126784\pi$
$829$	22.9404	+	39.7339i	0.796752	+	1.38002i	−0.124968	+	0.992161i	$0.539883\pi$
$830$		0			0
$831$	−61.2711	−	35.3749i	−2.12547	−	1.22714i
$832$		0			0
$833$	9.82506	−	4.25199i	0.340418	−	0.147323i
$834$		0			0
$835$	−19.8586	+	22.1538i	−0.687236	+	0.766664i
$836$		0			0
$837$	20.1920	−	75.3575i	0.697937	−	2.60474i
$838$		0			0
$839$	26.4488			0.913114			0.456557	−	0.889694i	$-0.349082\pi$
$839$	26.4488			0.913114			0.456557	+	0.889694i	$0.349082\pi$
$840$		0			0
$841$	19.8384			0.684082
$842$		0			0
$843$	−17.3912	+	64.9049i	−0.598985	+	2.23544i
$844$		0			0
$845$	−0.128520	−	2.35250i	−0.00442122	−	0.0809285i
$846$		0			0
$847$	−4.70296	+	24.6556i	−0.161596	+	0.847175i
$848$		0			0
$849$	20.7003	+	11.9513i	0.710434	+	0.410169i
$850$		0			0
$851$	0.656130	+	1.13645i	0.0224918	+	0.0389570i
$852$		0			0
$853$	−23.2354	−	23.2354i	−0.795566	−	0.795566i	0.186827	−	0.982393i	$-0.440180\pi$
$853$	−23.2354	−	23.2354i	−0.795566	−	0.795566i	−0.982393	+	0.186827i	$0.940180\pi$
$854$		0			0
$855$	−60.0035	+	39.1562i	−2.05208	+	1.33911i
$856$		0			0
$857$	37.7708	+	10.1207i	1.29023	+	0.345715i	0.837746	−	0.546060i	$-0.183873\pi$
$857$	37.7708	+	10.1207i	1.29023	+	0.345715i	0.452480	+	0.891775i	$0.350540\pi$
$858$		0			0
$859$	−8.13198	+	14.0850i	−0.277460	+	0.480574i	−0.970753	−	0.240082i	$-0.922826\pi$
$859$	−8.13198	+	14.0850i	−0.277460	+	0.480574i	0.693293	+	0.720656i	$0.256159\pi$
$860$		0			0
$861$	10.7554	−	0.789968i	0.366542	−	0.0269221i
$862$		0			0
$863$	−5.99898	−	22.3885i	−0.204208	−	0.762113i	−0.989690	−	0.143229i	$-0.954252\pi$
$863$	−5.99898	−	22.3885i	−0.204208	−	0.762113i	0.785482	−	0.618884i	$-0.212415\pi$
$864$		0			0
$865$	9.92455	−	3.24902i	0.337445	−	0.110470i
$866$		0			0
$867$	33.5337	−	33.5337i	1.13886	−	1.13886i
$868$		0			0
$869$		−	6.17951i		−	0.209625i
$870$		0			0
$871$	12.5372	−	7.23834i	0.424806	−	0.245262i
$872$		0			0
$873$	114.128	−	30.5806i	3.86266	−	1.03500i
$874$		0			0
$875$	−25.9756	+	14.1517i	−0.878135	+	0.478414i
$876$		0			0
$877$	35.3809	−	9.48029i	1.19473	−	0.320127i	0.393975	−	0.919121i	$-0.371099\pi$
$877$	35.3809	−	9.48029i	1.19473	−	0.320127i	0.800753	+	0.598994i	$0.204433\pi$
$878$		0			0
$879$	38.0593	−	21.9736i	1.28371	−	0.741150i
$880$		0			0
$881$		−	36.3165i		−	1.22353i	−0.791038	−	0.611767i	$-0.790459\pi$
$881$		−	36.3165i		−	1.22353i	0.791038	−	0.611767i	$-0.209541\pi$
$882$		0			0
$883$	0.463211	−	0.463211i	0.0155883	−	0.0155883i	−0.699270	−	0.714858i	$-0.746491\pi$
$883$	0.463211	−	0.463211i	0.0155883	−	0.0155883i	0.714858	+	0.699270i	$0.246491\pi$
$884$		0			0
$885$	−23.5899	+	7.72270i	−0.792967	+	0.259596i
$886$		0			0
$887$	9.02831	+	33.6941i	0.303141	+	1.13134i	0.934534	+	0.355874i	$0.115817\pi$
$887$	9.02831	+	33.6941i	0.303141	+	1.13134i	−0.631393	+	0.775463i	$0.717516\pi$
$888$		0			0
$889$	−6.74780	−	3.26191i	−0.226314	−	0.109401i
$890$		0			0
$891$	−14.9513	+	25.8965i	−0.500889	+	0.867565i
$892$		0			0
$893$	23.0134	+	6.16643i	0.770115	+	0.206352i
$894$		0			0
$895$	−5.03192	+	3.28365i	−0.168199	+	0.109760i
$896$		0			0
$897$	8.17951	+	8.17951i	0.273106	+	0.273106i
$898$		0			0
$899$	8.17823	+	14.1651i	0.272759	+	0.472433i
$900$		0			0
$901$	−16.4766	−	9.51278i	−0.548916	−	0.316917i
$902$		0			0
$903$	−55.7840	−	48.1502i	−1.85638	−	1.60234i
$904$		0			0
$905$	1.67898	+	30.7330i	0.0558113	+	1.02160i
$906$		0			0
$907$	−9.27896	+	34.6296i	−0.308103	+	1.14986i	0.622139	+	0.782907i	$0.286264\pi$
$907$	−9.27896	+	34.6296i	−0.308103	+	1.14986i	−0.930241	+	0.366948i	$0.880403\pi$
$908$		0			0
$909$	−121.885			−4.04267
$910$		0			0
$911$	−51.5115			−1.70665			−0.853325	−	0.521379i	$-0.825418\pi$
$911$	−51.5115			−1.70665			−0.853325	+	0.521379i	$0.825418\pi$
$912$		0			0
$913$	3.98277	−	14.8639i	0.131810	−	0.491923i
$914$		0			0
$915$	26.8799	−	29.9866i	0.888622	−	0.991326i
$916$		0			0
$917$	−41.9039	−	7.99302i	−1.38379	−	0.263953i
$918$		0			0
$919$	−29.9372	−	17.2843i	−0.987537	−	0.570155i	−0.0830000	−	0.996550i	$-0.526450\pi$
$919$	−29.9372	−	17.2843i	−0.987537	−	0.570155i	−0.904537	+	0.426395i	$0.859783\pi$
$920$		0			0
$921$	28.5929	+	49.5244i	0.942169	+	1.63188i
$922$		0			0
$923$	−24.7570	−	24.7570i	−0.814886	−	0.814886i
$924$		0			0
$925$	−5.91025	+	2.29885i	−0.194328	+	0.0755857i
$926$		0			0
$927$	42.9218	+	11.5009i	1.40974	+	0.377738i
$928$		0			0
$929$	9.82260	−	17.0132i	0.322269	−	0.558187i	−0.658687	−	0.752417i	$-0.728888\pi$
$929$	9.82260	−	17.0132i	0.322269	−	0.558187i	0.980956	+	0.194231i	$0.0622211\pi$
$930$		0			0
$931$	−4.39114	−	29.7313i	−0.143914	−	0.974404i
$932$		0			0
$933$	−22.4324	−	83.7190i	−0.734405	−	2.74084i
$934$		0			0
$935$	1.30877	+	3.99779i	0.0428013	+	0.130742i
$936$		0			0
$937$	−20.5897	+	20.5897i	−0.672636	+	0.672636i	−0.958323	−	0.285687i	$-0.907778\pi$
$937$	−20.5897	+	20.5897i	−0.672636	+	0.672636i	0.285687	+	0.958323i	$0.407778\pi$
$938$		0			0
$939$		−	87.0179i		−	2.83972i
$940$		0			0
$941$	−1.83153	+	1.05743i	−0.0597060	+	0.0344713i	−0.529556	−	0.848275i	$-0.677641\pi$
$941$	−1.83153	+	1.05743i	−0.0597060	+	0.0344713i	0.469850	+	0.882746i	$0.344308\pi$
$942$		0			0
$943$	1.25935	−	0.337443i	0.0410102	−	0.0109887i
$944$		0			0
$945$	−32.9224	+	78.8109i	−1.07097	+	2.56372i
$946$		0			0
$947$	−16.5894	+	4.44511i	−0.539082	+	0.144447i	−0.518079	−	0.855333i	$-0.673353\pi$
$947$	−16.5894	+	4.44511i	−0.539082	+	0.144447i	−0.0210032	+	0.999779i	$0.506686\pi$
$948$		0			0
$949$	15.7314	−	9.08252i	0.510662	−	0.294831i
$950$		0			0
$951$			62.6390i			2.03121i
$952$		0			0
$953$	−16.8460	+	16.8460i	−0.545694	+	0.545694i	−0.925192	−	0.379498i	$-0.876097\pi$
$953$	−16.8460	+	16.8460i	−0.545694	+	0.545694i	0.379498	+	0.925192i	$0.376097\pi$
$954$		0			0
$955$	−7.73099	+	15.2565i	−0.250169	+	0.493687i
$956$		0			0
$957$	−3.11704	−	11.6330i	−0.100760	−	0.376040i
$958$		0			0
$959$	2.28398	+	31.0963i	0.0737537	+	1.00415i
$960$		0			0
$961$	−0.899248	+	1.55754i	−0.0290080	+	0.0502433i
$962$		0			0
$963$	78.8232	+	21.1206i	2.54004	+	0.680602i
$964$		0			0
$965$	24.2835	+	5.10537i	0.781713	+	0.164348i
$966$		0			0
$967$	24.8080	+	24.8080i	0.797772	+	0.797772i	0.982744	−	0.184972i	$-0.0592193\pi$
$967$	24.8080	+	24.8080i	0.797772	+	0.797772i	−0.184972	+	0.982744i	$0.559219\pi$
$968$		0			0
$969$	10.6199	+	18.3942i	0.341160	+	0.590906i
$970$		0			0
$971$	−35.0396	−	20.2301i	−1.12447	−	0.649215i	−0.181935	−	0.983311i	$-0.558236\pi$
$971$	−35.0396	−	20.2301i	−1.12447	−	0.649215i	−0.942539	+	0.334095i	$0.891569\pi$
$972$		0			0
$973$	−25.4892	+	8.87667i	−0.817147	+	0.284573i
$974$		0			0
$975$	−45.0788	+	33.0580i	−1.44368	+	1.05870i
$976$		0			0
$977$	12.0231	−	44.8708i	0.384653	−	1.43554i	−0.454061	−	0.890971i	$-0.650025\pi$
$977$	12.0231	−	44.8708i	0.384653	−	1.43554i	0.838713	−	0.544573i	$-0.183308\pi$
$978$		0			0
$979$	−7.52282			−0.240430
$980$		0			0
$981$	−48.5906			−1.55138
$982$		0			0
$983$	−4.75681	+	17.7526i	−0.151719	+	0.566221i	0.847645	+	0.530563i	$0.178019\pi$
$983$	−4.75681	+	17.7526i	−0.151719	+	0.566221i	−0.999364	+	0.0356584i	$0.988647\pi$
$984$		0			0
$985$	−26.3335	−	23.6053i	−0.839055	−	0.752127i
$986$		0			0
$987$	44.8498	−	15.6190i	1.42758	−	0.497159i
$988$		0			0
$989$	−7.71530	−	4.45443i	−0.245332	−	0.141643i
$990$		0			0
$991$	−3.06942	−	5.31640i	−0.0975035	−	0.168881i	0.813147	−	0.582058i	$-0.197752\pi$
$991$	−3.06942	−	5.31640i	−0.0975035	−	0.168881i	−0.910651	+	0.413177i	$0.864419\pi$
$992$		0			0
$993$	68.2343	+	68.2343i	2.16535	+	2.16535i
$994$		0			0
$995$	15.6860	+	24.0375i	0.497281	+	0.762041i
$996$		0			0
$997$	7.08884	+	1.89945i	0.224506	+	0.0601561i	0.369318	−	0.929303i	$-0.379591\pi$
$997$	7.08884	+	1.89945i	0.224506	+	0.0601561i	−0.144812	+	0.989459i	$0.546258\pi$
$998$		0			0
$999$	−9.15541	+	15.8576i	−0.289664	+	0.501713i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	140.2.u.a.117.1	yes	16
3.2	odd	2		1260.2.dq.a.397.1		16
4.3	odd	2		560.2.ci.d.257.4		16
5.2	odd	4		700.2.bc.b.593.4		16
5.3	odd	4	inner	140.2.u.a.33.1	yes	16
5.4	even	2		700.2.bc.b.257.4		16
7.2	even	3		980.2.m.a.97.1		16
7.3	odd	6	inner	140.2.u.a.17.1	✓	16
7.4	even	3		980.2.v.a.717.4		16
7.5	odd	6		980.2.m.a.97.8		16
7.6	odd	2		980.2.v.a.117.4		16
15.8	even	4		1260.2.dq.a.1153.2		16
20.3	even	4		560.2.ci.d.33.4		16
21.17	even	6		1260.2.dq.a.577.2		16
28.3	even	6		560.2.ci.d.17.4		16
35.3	even	12	inner	140.2.u.a.73.1	yes	16
35.13	even	4		980.2.v.a.313.4		16
35.17	even	12		700.2.bc.b.493.4		16
35.18	odd	12		980.2.v.a.913.4		16
35.23	odd	12		980.2.m.a.293.8		16
35.24	odd	6		700.2.bc.b.157.4		16
35.33	even	12		980.2.m.a.293.1		16
105.38	odd	12		1260.2.dq.a.73.1		16
140.3	odd	12		560.2.ci.d.353.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.u.a.17.1	✓	16	7.3	odd	6	inner
140.2.u.a.33.1	yes	16	5.3	odd	4	inner
140.2.u.a.73.1	yes	16	35.3	even	12	inner
140.2.u.a.117.1	yes	16	1.1	even	1	trivial
560.2.ci.d.17.4		16	28.3	even	6
560.2.ci.d.33.4		16	20.3	even	4
560.2.ci.d.257.4		16	4.3	odd	2
560.2.ci.d.353.4		16	140.3	odd	12
700.2.bc.b.157.4		16	35.24	odd	6
700.2.bc.b.257.4		16	5.4	even	2
700.2.bc.b.493.4		16	35.17	even	12
700.2.bc.b.593.4		16	5.2	odd	4
980.2.m.a.97.1		16	7.2	even	3
980.2.m.a.97.8		16	7.5	odd	6
980.2.m.a.293.1		16	35.33	even	12
980.2.m.a.293.8		16	35.23	odd	12
980.2.v.a.117.4		16	7.6	odd	2
980.2.v.a.313.4		16	35.13	even	4
980.2.v.a.717.4		16	7.4	even	3
980.2.v.a.913.4		16	35.18	odd	12
1260.2.dq.a.73.1		16	105.38	odd	12
1260.2.dq.a.397.1		16	3.2	odd	2
1260.2.dq.a.577.2		16	21.17	even	6
1260.2.dq.a.1153.2		16	15.8	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 140 = 2^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	140.u (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.837199 + 3.12447i) q^{3} +(2.23274 - 0.121977i) q^{5} +(-2.49857 + 0.870132i) q^{7} +(-6.46333 - 3.73161i) q^{9} +O(q^{10})\)	\(q+(-0.837199 + 3.12447i) q^{3} +(2.23274 - 0.121977i) q^{5} +(-2.49857 + 0.870132i) q^{7} +(-6.46333 - 3.73161i) q^{9} +(0.615031 + 1.06527i) q^{11} +(2.44401 + 2.44401i) q^{13} +(-1.48813 + 7.07824i) q^{15} +(1.47727 + 0.395833i) q^{17} +(2.14670 - 3.71820i) q^{19} +(-0.626899 - 8.53519i) q^{21} +(-0.267786 - 0.999392i) q^{23} +(4.97024 - 0.544686i) q^{25} +(10.2086 - 10.2086i) q^{27} +3.02682i q^{29} +(4.67986 - 2.70192i) q^{31} +(-3.84329 + 1.02981i) q^{33} +(-5.47253 + 2.24755i) q^{35} +(-1.22510 + 0.328265i) q^{37} +(-9.68235 + 5.59011i) q^{39} +1.26012i q^{41} +(6.08857 - 6.08857i) q^{43} +(-14.8861 - 7.54332i) q^{45} +(1.43626 + 5.36018i) q^{47} +(5.48574 - 4.34818i) q^{49} +(-2.47354 + 4.28429i) q^{51} +(-12.0162 - 3.21972i) q^{53} +(1.50314 + 2.30344i) q^{55} +(9.82017 + 9.82017i) q^{57} +(1.71588 + 2.97199i) q^{59} +(-4.82171 - 2.78382i) q^{61} +(19.3961 + 3.69974i) q^{63} +(5.75495 + 5.15872i) q^{65} +(1.08405 - 4.04571i) q^{67} +3.34676 q^{69} -10.1297 q^{71} +(1.36024 - 5.07647i) q^{73} +(-2.45923 + 15.9854i) q^{75} +(-2.46362 - 2.12649i) q^{77} +(-4.35068 - 2.51187i) q^{79} +(12.1549 + 21.0530i) q^{81} +(-8.84600 - 8.84600i) q^{83} +(3.34664 + 0.703598i) q^{85} +(-9.45720 - 2.53405i) q^{87} +(-3.05790 + 5.29644i) q^{89} +(-8.23315 - 3.97993i) q^{91} +(4.52409 + 16.8841i) q^{93} +(4.33949 - 8.56361i) q^{95} +(-11.1946 + 11.1946i) q^{97} -9.18022i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 6 q^{5} + 2 q^{7}+O(q^{10}) \) 16 * q + 6 * q^5 + 2 * q^7	\( 16 q + 6 q^{5} + 2 q^{7} - 20 q^{15} + 18 q^{17} - 4 q^{21} - 16 q^{23} + 6 q^{25} - 12 q^{31} - 42 q^{33} - 40 q^{35} - 14 q^{37} + 28 q^{43} - 66 q^{45} - 6 q^{47} + 20 q^{51} - 10 q^{53} + 44 q^{57} + 60 q^{61} + 48 q^{63} + 34 q^{65} + 8 q^{67} - 8 q^{71} + 78 q^{73} + 96 q^{75} + 10 q^{77} + 24 q^{81} + 30 q^{87} - 64 q^{91} - 62 q^{93} + 2 q^{95}+O(q^{100}) \) 16 * q + 6 * q^5 + 2 * q^7 - 20 * q^15 + 18 * q^17 - 4 * q^21 - 16 * q^23 + 6 * q^25 - 12 * q^31 - 42 * q^33 - 40 * q^35 - 14 * q^37 + 28 * q^43 - 66 * q^45 - 6 * q^47 + 20 * q^51 - 10 * q^53 + 44 * q^57 + 60 * q^61 + 48 * q^63 + 34 * q^65 + 8 * q^67 - 8 * q^71 + 78 * q^73 + 96 * q^75 + 10 * q^77 + 24 * q^81 + 30 * q^87 - 64 * q^91 - 62 * q^93 + 2 * q^95

Introduction

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