LMFDB - Embedded newform 140.2.u.a.17.1

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			17.1
Root			$0.500000 + 1.78727i$ of defining polynomial
Character	$\chi$	$=$	140.17
Dual form			140.2.u.a.33.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.12447 + 0.837199i) q^{3} +(1.01073 - 1.99460i) q^{5} +(0.870132 - 2.49857i) q^{7} +(6.46333 - 3.73161i) q^{9} +O(q^{10})$	\(q+(-3.12447 + 0.837199i) q^{3} +(1.01073 - 1.99460i) q^{5} +(0.870132 - 2.49857i) q^{7} +(6.46333 - 3.73161i) q^{9} +(0.615031 - 1.06527i) q^{11} +(-2.44401 - 2.44401i) q^{13} +(-1.48813 + 7.07824i) q^{15} +(0.395833 + 1.47727i) q^{17} +(-2.14670 - 3.71820i) q^{19} +(-0.626899 + 8.53519i) q^{21} +(0.999392 + 0.267786i) q^{23} +(-2.95683 - 4.03201i) q^{25} +(-10.2086 + 10.2086i) q^{27} +3.02682i q^{29} +(4.67986 + 2.70192i) q^{31} +(-1.02981 + 3.84329i) q^{33} +(-4.10417 - 4.26096i) q^{35} +(0.328265 - 1.22510i) q^{37} +(9.68235 + 5.59011i) q^{39} -1.26012i q^{41} +(6.08857 - 6.08857i) q^{43} +(-0.910341 - 16.6634i) q^{45} +(5.36018 + 1.43626i) q^{47} +(-5.48574 - 4.34818i) q^{49} +(-2.47354 - 4.28429i) q^{51} +(3.21972 + 12.0162i) q^{53} +(-1.50314 - 2.30344i) q^{55} +(9.82017 + 9.82017i) q^{57} +(-1.71588 + 2.97199i) q^{59} +(-4.82171 + 2.78382i) q^{61} +(-3.69974 - 19.3961i) q^{63} +(-7.34506 + 2.40457i) q^{65} +(-4.04571 + 1.08405i) q^{67} -3.34676 q^{69} -10.1297 q^{71} +(5.07647 - 1.36024i) q^{73} +(12.6141 + 10.1224i) q^{75} +(-2.12649 - 2.46362i) q^{77} +(4.35068 - 2.51187i) q^{79} +(12.1549 - 21.0530i) q^{81} +(8.84600 + 8.84600i) q^{83} +(3.34664 + 0.703598i) q^{85} +(-2.53405 - 9.45720i) q^{87} +(3.05790 + 5.29644i) q^{89} +(-8.23315 + 3.97993i) q^{91} +(-16.8841 - 4.52409i) q^{93} +(-9.58605 + 0.523697i) q^{95} +(11.1946 - 11.1946i) q^{97} -9.18022i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/140\mathbb{Z}\right)^\times$.

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

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
$3$	−3.12447	+	0.837199i	−1.80391	+	0.483357i	−0.994578	−	0.103990i	$-0.966839\pi$
$3$	−3.12447	+	0.837199i	−1.80391	+	0.483357i	−0.809335	+	0.587347i	$0.800172\pi$
$4$		0			0
$5$	1.01073	−	1.99460i	0.452014	−	0.892011i
$5$	1.01073	−	1.99460i	0.452014	−	0.892011i
$6$		0			0
$7$	0.870132	−	2.49857i	0.328879	−	0.944372i
$7$	0.870132	−	2.49857i	0.328879	−	0.944372i
$8$		0			0
$9$	6.46333	−	3.73161i	2.15444	−	1.24387i
$10$		0			0
$11$	0.615031	−	1.06527i	0.185439	−	0.321190i	−0.758285	−	0.651923i	$-0.773963\pi$
$11$	0.615031	−	1.06527i	0.185439	−	0.321190i	0.943724	+	0.330733i	$0.107296\pi$
$12$		0			0
$13$	−2.44401	−	2.44401i	−0.677846	−	0.677846i	0.281666	−	0.959512i	$-0.409113\pi$
$13$	−2.44401	−	2.44401i	−0.677846	−	0.677846i	−0.959512	+	0.281666i	$0.909113\pi$
$14$		0			0
$15$	−1.48813	+	7.07824i	−0.384234	+	1.82759i
$16$		0			0
$17$	0.395833	+	1.47727i	0.0960036	+	0.358290i	0.997170	−	0.0751837i	$-0.0239543\pi$
$17$	0.395833	+	1.47727i	0.0960036	+	0.358290i	−0.901166	+	0.433474i	$0.857288\pi$
$18$		0			0
$19$	−2.14670	−	3.71820i	−0.492487	−	0.853013i	0.507475	−	0.861666i	$-0.330579\pi$
$19$	−2.14670	−	3.71820i	−0.492487	−	0.853013i	−0.999963	+	0.00865358i	$0.997245\pi$
$20$		0			0
$21$	−0.626899	+	8.53519i	−0.136800	+	1.86253i
$22$		0			0
$23$	0.999392	+	0.267786i	0.208388	+	0.0558373i	0.361503	−	0.932371i	$-0.382264\pi$
$23$	0.999392	+	0.267786i	0.208388	+	0.0558373i	−0.153115	+	0.988208i	$0.548931\pi$
$24$		0			0
$25$	−2.95683	−	4.03201i	−0.591367	−	0.806403i
$26$		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	0.857444	−	0.514578i	$-0.172051\pi$
$31$	4.67986	+	2.70192i	0.840528	+	0.485279i	−0.0169154	+	0.999857i	$0.505385\pi$
$32$		0			0
$33$	−1.02981	+	3.84329i	−0.179266	+	0.669032i
$34$		0			0
$35$	−4.10417	−	4.26096i	−0.693732	−	0.720233i
$36$		0			0
$37$	0.328265	−	1.22510i	0.0539664	−	0.201405i	−0.933679	−	0.358111i	$-0.883421\pi$
$37$	0.328265	−	1.22510i	0.0539664	−	0.201405i	0.987645	+	0.156706i	$0.0500875\pi$
$38$		0			0
$39$	9.68235	+	5.59011i	1.55042	+	0.895134i
$40$		0			0
$41$		−	1.26012i		−	0.196798i	−0.995147	−	0.0983990i	$-0.968628\pi$
$41$		−	1.26012i		−	0.196798i	0.995147	−	0.0983990i	$-0.0313721\pi$
$42$		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
$45$	−0.910341	−	16.6634i	−0.135706	−	2.48403i
$46$		0			0
$47$	5.36018	+	1.43626i	0.781863	+	0.209500i	0.627606	−	0.778531i	$-0.284035\pi$
$47$	5.36018	+	1.43626i	0.781863	+	0.209500i	0.154257	+	0.988031i	$0.450702\pi$
$48$		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
$53$	3.21972	+	12.0162i	0.442263	+	1.65055i	0.723065	+	0.690781i	$0.242733\pi$
$53$	3.21972	+	12.0162i	0.442263	+	1.65055i	−0.280802	+	0.959766i	$0.590600\pi$
$54$		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	$-0.905045\pi$
$59$	−1.71588	+	2.97199i	−0.223389	+	0.386921i	0.732446	+	0.680825i	$0.238379\pi$
$60$		0			0
$61$	−4.82171	+	2.78382i	−0.617357	+	0.356431i	−0.775839	−	0.630930i	$-0.782673\pi$
$61$	−4.82171	+	2.78382i	−0.617357	+	0.356431i	0.158482	+	0.987362i	$0.449340\pi$
$62$		0			0
$63$	−3.69974	−	19.3961i	−0.466123	−	2.44368i
$64$		0			0
$65$	−7.34506	+	2.40457i	−0.911042	+	0.298250i
$66$		0			0
$67$	−4.04571	+	1.08405i	−0.494263	+	0.132437i	−0.497336	−	0.867558i	$-0.665688\pi$
$67$	−4.04571	+	1.08405i	−0.494263	+	0.132437i	0.00307336	+	0.999995i	$0.499022\pi$
$68$		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
$73$	5.07647	−	1.36024i	0.594156	−	0.159204i	0.0508042	−	0.998709i	$-0.483822\pi$
$73$	5.07647	−	1.36024i	0.594156	−	0.159204i	0.543352	+	0.839505i	$0.317155\pi$
$74$		0			0
$75$	12.6141	+	10.1224i	1.45655	+	1.16884i
$76$		0			0
$77$	−2.12649	−	2.46362i	−0.242336	−	0.280756i
$78$		0			0
$79$	4.35068	−	2.51187i	0.489490	−	0.282607i	−0.234873	−	0.972026i	$-0.575467\pi$
$79$	4.35068	−	2.51187i	0.489490	−	0.282607i	0.724363	+	0.689419i	$0.242134\pi$
$80$		0			0
$81$	12.1549	−	21.0530i	1.35055	−	2.33922i
$82$		0			0
$83$	8.84600	+	8.84600i	0.970974	+	0.970974i	0.999590	−	0.0286162i	$-0.00911007\pi$
$83$	8.84600	+	8.84600i	0.970974	+	0.970974i	−0.0286162	+	0.999590i	$0.509110\pi$
$84$		0			0
$85$	3.34664	+	0.703598i	0.362994	+	0.0763160i
$86$		0			0
$87$	−2.53405	−	9.45720i	−0.271679	−	1.01392i
$88$		0			0
$89$	3.05790	+	5.29644i	0.324137	+	0.561421i	0.981337	−	0.192294i	$-0.0615929\pi$
$89$	3.05790	+	5.29644i	0.324137	+	0.561421i	−0.657201	+	0.753716i	$0.728260\pi$
$90$		0			0
$91$	−8.23315	+	3.97993i	−0.863068	+	0.417210i
$92$		0			0
$93$	−16.8841	−	4.52409i	−1.75080	−	0.469126i
$94$		0			0
$95$	−9.58605	+	0.523697i	−0.983508	+	0.0537302i
$96$		0			0
$97$	11.1946	−	11.1946i	1.13664	−	1.13664i	0.147592	−	0.989048i	$-0.452848\pi$
$97$	11.1946	−	11.1946i	1.13664	−	1.13664i	0.989048	−	0.147592i	$-0.0471523\pi$
$98$		0			0
$99$		−	9.18022i		−	0.922647i
$100$		0			0
$101$	14.1434	+	8.16571i	1.40732	+	0.812519i	0.995129	−	0.0985771i	$-0.0314291\pi$
$101$	14.1434	+	8.16571i	1.40732	+	0.812519i	0.412194	+	0.911096i	$0.364762\pi$
$102$		0			0
$103$	−1.54101	+	5.75112i	−0.151840	+	0.566675i	0.847515	+	0.530771i	$0.178098\pi$
$103$	−1.54101	+	5.75112i	−0.151840	+	0.566675i	−0.999355	+	0.0359037i	$0.988569\pi$
$104$		0			0
$105$	16.3906	+	9.87722i	1.59956	+	0.963918i
$106$		0			0
$107$	2.82996	−	10.5616i	0.273583	−	1.02103i	−0.683202	−	0.730229i	$-0.739413\pi$
$107$	2.82996	−	10.5616i	0.273583	−	1.02103i	0.956785	−	0.290796i	$-0.0939201\pi$
$108$		0			0
$109$	−5.63841	−	3.25534i	−0.540062	−	0.311805i	0.205042	−	0.978753i	$-0.434267\pi$
$109$	−5.63841	−	3.25534i	−0.540062	−	0.311805i	−0.745104	+	0.666948i	$0.767600\pi$
$110$		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
$115$	1.54424	−	1.72272i	0.144002	−	0.160645i
$116$		0			0
$117$	−24.9165	−	6.67636i	−2.30353	−	0.617230i
$118$		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
$123$	1.05497	+	3.93721i	0.0951237	+	0.355006i
$124$		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	0.255084	−	0.966919i	$-0.417897\pi$
$131$	13.9636	−	8.06187i	1.22000	−	0.704369i	0.964918	+	0.262550i	$0.0845635\pi$
$132$		0			0
$133$	−11.1581	+	2.12837i	−0.967530	+	0.184553i
$134$		0			0
$135$	10.0438	+	30.6801i	0.864435	+	2.64053i
$136$		0			0
$137$	−11.3834	+	3.05017i	−0.972550	+	0.260594i	−0.709904	−	0.704299i	$-0.751262\pi$
$137$	−11.3834	+	3.05017i	−0.972550	+	0.260594i	−0.262646	+	0.964892i	$0.584595\pi$
$138$		0			0
$139$	−10.2015			−0.865281			−0.432641	−	0.901567i	$-0.642418\pi$
$139$	−10.2015			−0.865281			−0.432641	+	0.901567i	$0.642418\pi$
$140$		0			0
$141$	−17.9502			−1.51168
$142$		0			0
$143$	−4.10666	+	1.10038i	−0.343416	+	0.0920181i
$144$		0			0
$145$	6.03728	+	3.05931i	0.501369	+	0.254062i
$146$		0			0
$147$	20.7803	+	8.99310i	1.71393	+	0.741738i
$148$		0			0
$149$	5.55085	−	3.20479i	0.454744	−	0.262546i	−0.255088	−	0.966918i	$-0.582104\pi$
$149$	5.55085	−	3.20479i	0.454744	−	0.262546i	0.709831	+	0.704372i	$0.248771\pi$
$150$		0			0
$151$	−6.44980	+	11.1714i	−0.524877	+	0.909114i	0.474703	+	0.880146i	$0.342555\pi$
$151$	−6.44980	+	11.1714i	−0.524877	+	0.909114i	−0.999580	+	0.0289682i	$0.990778\pi$
$152$		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
$157$	1.13271	+	4.22734i	0.0904002	+	0.337378i	0.996282	−	0.0861526i	$-0.0274573\pi$
$157$	1.13271	+	4.22734i	0.0904002	+	0.337378i	−0.905882	+	0.423531i	$0.860791\pi$
$158$		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
$163$	14.3983	+	3.85800i	1.12776	+	0.302182i	0.774020	−	0.633162i	$-0.218243\pi$
$163$	14.3983	+	3.85800i	1.12776	+	0.302182i	0.353740	+	0.935344i	$0.384910\pi$
$164$		0			0
$165$	6.62496	+	5.93860i	0.515752	+	0.462319i
$166$		0			0
$167$	9.40827	−	9.40827i	0.728034	−	0.728034i	−0.242194	−	0.970228i	$-0.577867\pi$
$167$	9.40827	−	9.40827i	0.728034	−	0.728034i	0.970228	+	0.242194i	$0.0778670\pi$
$168$		0			0
$169$		−	1.05364i		−	0.0810491i
$170$		0			0
$171$	−27.7497	−	16.0213i	−2.12207	−	1.22518i
$172$		0			0
$173$	1.20873	−	4.51104i	0.0918981	−	0.342968i	−0.904633	−	0.426192i	$-0.859855\pi$
$173$	1.20873	−	4.51104i	0.0918981	−	0.342968i	0.996531	+	0.0832235i	$0.0265215\pi$
$174$		0			0
$175$	−12.6471	+	3.87948i	−0.956032	+	0.293261i
$176$		0			0
$177$	2.87307	−	10.7224i	0.215953	−	0.805948i
$178$		0			0
$179$	2.32710	+	1.34355i	0.173936	+	0.100422i	0.584440	−	0.811437i	$-0.301314\pi$
$179$	2.32710	+	1.34355i	0.173936	+	0.100422i	−0.410505	+	0.911858i	$0.634647\pi$
$180$		0			0
$181$		−	13.7647i		−	1.02312i	−0.859246	−	0.511562i	$-0.829067\pi$
$181$		−	13.7647i		−	1.02312i	0.859246	−	0.511562i	$-0.170933\pi$
$182$		0			0
$183$	12.7347	−	12.7347i	0.941375	−	0.941375i
$184$		0			0
$185$	−2.11179	−	1.89301i	−0.155262	−	0.139177i
$186$		0			0
$187$	1.81713	+	0.486899i	0.132882	+	0.0356056i
$188$		0			0
$189$	16.6241	+	34.3897i	1.20922	+	2.50148i
$190$		0			0
$191$	−3.82445	−	6.62413i	−0.276727	−	0.479305i	0.693842	−	0.720127i	$-0.255916\pi$
$191$	−3.82445	−	6.62413i	−0.276727	−	0.479305i	−0.970569	+	0.240822i	$0.922583\pi$
$192$		0			0
$193$	−2.87220	−	10.7192i	−0.206745	−	0.771584i	−0.988910	−	0.148513i	$-0.952551\pi$
$193$	−2.87220	−	10.7192i	−0.206745	−	0.771584i	0.782165	−	0.623071i	$-0.214115\pi$
$194$		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	$-0.983684\pi$
$199$	−6.41816	+	11.1166i	−0.454971	+	0.788033i	0.543715	+	0.839270i	$0.317017\pi$
$200$		0			0
$201$	11.7331	−	6.77414i	0.827592	−	0.477811i
$202$		0			0
$203$	7.56273	+	2.63373i	0.530800	+	0.184852i
$204$		0			0
$205$	−2.51343	−	1.27365i	−0.175546	−	0.0889554i
$206$		0			0
$207$	7.45867	−	1.99854i	0.518413	−	0.138908i
$208$		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
$213$	31.6498	−	8.48055i	2.16861	−	0.581077i
$214$		0			0
$215$	−5.99031	−	18.2982i	−0.408536	−	1.24792i
$216$		0			0
$217$	10.8230	−	9.34196i	0.734716	−	0.634173i
$218$		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	0.576949	−	0.816780i	$-0.304243\pi$
$223$	−3.58144	−	3.58144i	−0.239831	−	0.239831i	−0.816780	+	0.576949i	$0.804243\pi$
$224$		0			0
$225$	−34.1569	−	15.0265i	−2.27713	−	1.00177i
$226$		0			0
$227$	6.61096	+	24.6724i	0.438785	+	1.63757i	0.731844	+	0.681472i	$0.238660\pi$
$227$	6.61096	+	24.6724i	0.438785	+	1.63757i	−0.293059	+	0.956094i	$0.594673\pi$
$228$		0			0
$229$	9.94027	+	17.2170i	0.656871	+	1.13773i	0.981421	+	0.191866i	$0.0614538\pi$
$229$	9.94027	+	17.2170i	0.656871	+	1.13773i	−0.324550	+	0.945869i	$0.605213\pi$
$230$		0			0
$231$	8.70668	+	5.91722i	0.572858	+	0.389325i
$232$		0			0
$233$	−20.2814	−	5.43438i	−1.32868	−	0.356018i	−0.476455	−	0.879199i	$-0.658078\pi$
$233$	−20.2814	−	5.43438i	−1.32868	−	0.356018i	−0.852222	+	0.523181i	$0.824745\pi$
$234$		0			0
$235$	8.28247	−	9.23973i	0.540289	−	0.602733i
$236$		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	0.579976	−	0.814633i	$-0.303062\pi$
$241$	2.55328	+	1.47414i	0.164471	+	0.0949576i	−0.415505	+	0.909591i	$0.636395\pi$
$242$		0			0
$243$	−9.14242	+	34.1200i	−0.586487	+	2.18880i
$244$		0			0
$245$	−14.2175	+	6.54699i	−0.908322	+	0.418272i
$246$		0			0
$247$	−3.84075	+	14.3339i	−0.244381	+	0.912042i
$248$		0			0
$249$	−35.0449	−	20.2332i	−2.22088	−	1.28223i
$250$		0			0
$251$		−	27.8935i		−	1.76062i	−0.474397	−	0.880311i	$-0.657334\pi$
$251$		−	27.8935i		−	1.76062i	0.474397	−	0.880311i	$-0.342666\pi$
$252$		0			0
$253$	0.899921	−	0.899921i	0.0565775	−	0.0565775i
$254$		0			0
$255$	−11.0455	+	0.603429i	−0.691697	+	0.0377882i
$256$		0			0
$257$	−7.94266	−	2.12823i	−0.495449	−	0.132755i	0.00243792	−	0.999997i	$-0.499224\pi$
$257$	−7.94266	−	2.12823i	−0.495449	−	0.132755i	−0.497887	+	0.867242i	$0.665891\pi$
$258$		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
$263$	0.221455	+	0.826480i	0.0136555	+	0.0509629i	0.972417	−	0.233248i	$-0.0749352\pi$
$263$	0.221455	+	0.826480i	0.0136555	+	0.0509629i	−0.958762	+	0.284210i	$0.908269\pi$
$264$		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	0.153536	−	0.988143i	$-0.450934\pi$
$269$	15.2945	−	26.4909i	0.932525	−	1.61518i	0.778989	−	0.627038i	$-0.215733\pi$
$270$		0			0
$271$	−22.5951	+	13.0453i	−1.37255	+	0.792444i	−0.991249	−	0.132005i	$-0.957859\pi$
$271$	−22.5951	+	13.0453i	−1.37255	+	0.792444i	−0.381305	+	0.924449i	$0.624525\pi$
$272$		0			0
$273$	22.3922	−	19.3279i	1.35524	−	1.16978i
$274$		0			0
$275$	−6.11371	+	0.669998i	−0.368671	+	0.0404024i
$276$		0			0
$277$	21.1269	−	5.66094i	1.26939	−	0.340133i	0.439595	−	0.898196i	$-0.355122\pi$
$277$	21.1269	−	5.66094i	1.26939	−	0.340133i	0.829798	+	0.558063i	$0.188455\pi$
$278$		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
$283$	7.13770	−	1.91254i	0.424292	−	0.113689i	−0.0403536	−	0.999185i	$-0.512848\pi$
$283$	7.13770	−	1.91254i	0.424292	−	0.113689i	0.464646	+	0.885497i	$0.346182\pi$
$284$		0			0
$285$	29.5129	−	9.66170i	1.74819	−	0.572310i
$286$		0			0
$287$	−3.14851	−	1.09647i	−0.185850	−	0.0647227i
$288$		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	0.929660	−	0.368419i	$-0.120101\pi$
$293$	9.60690	+	9.60690i	0.561241	+	0.561241i	−0.368419	+	0.929660i	$0.620101\pi$
$294$		0			0
$295$	4.19363	+	6.42639i	0.244163	+	0.374159i
$296$		0			0
$297$	4.59625	+	17.1534i	0.266701	+	0.995343i
$298$		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
$303$	−51.0270	−	13.6727i	−2.93143	−	0.785473i
$304$		0			0
$305$	0.679124	+	12.4311i	0.0388865	+	0.711801i
$306$		0			0
$307$	−12.5009	+	12.5009i	−0.713463	+	0.713463i	−0.967258	−	0.253795i	$-0.918321\pi$
$307$	−12.5009	+	12.5009i	−0.713463	+	0.713463i	0.253795	+	0.967258i	$0.418321\pi$
$308$		0			0
$309$		−	19.2593i		−	1.09563i
$310$		0			0
$311$	−23.2048	−	13.3973i	−1.31582	−	0.759692i	−0.332771	−	0.943008i	$-0.607984\pi$
$311$	−23.2048	−	13.3973i	−1.31582	−	0.759692i	−0.983054	+	0.183316i	$0.941317\pi$
$312$		0			0
$313$	−6.96262	+	25.9848i	−0.393550	+	1.46875i	0.430685	+	0.902502i	$0.358272\pi$
$313$	−6.96262	+	25.9848i	−0.393550	+	1.46875i	−0.824235	+	0.566248i	$0.808395\pi$
$314$		0			0
$315$	−42.4268	−	12.2248i	−2.39048	−	0.688790i
$316$		0			0
$317$	−5.01197	+	18.7049i	−0.281500	+	1.05057i	0.669859	+	0.742489i	$0.266355\pi$
$317$	−5.01197	+	18.7049i	−0.281500	+	1.05057i	−0.951359	+	0.308085i	$0.900312\pi$
$318$		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
$325$	−2.62775	+	17.0808i	−0.145761	+	0.947473i
$326$		0			0
$327$	20.3424	+	5.45073i	1.12494	+	0.301426i
$328$		0			0
$329$	8.25266	−	12.1431i	0.454984	−	0.669469i
$330$		0			0
$331$	14.9161	+	25.8354i	0.819863	+	1.42004i	0.905783	+	0.423742i	$0.139284\pi$
$331$	14.9161	+	25.8354i	0.819863	+	1.42004i	−0.0859200	+	0.996302i	$0.527383\pi$
$332$		0			0
$333$	−2.44991	−	9.14318i	−0.134254	−	0.501043i
$334$		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
$343$	−15.6376	+	9.92303i	−0.844349	+	0.535793i
$344$		0			0
$345$	−3.38268	+	6.67543i	−0.182118	+	0.359393i
$346$		0			0
$347$	−31.6166	+	8.47165i	−1.69727	+	0.454782i	−0.972250	−	0.233946i	$-0.924836\pi$
$347$	−31.6166	+	8.47165i	−1.69727	+	0.454782i	−0.725020	+	0.688728i	$0.758169\pi$
$348$		0			0
$349$	−4.85034			−0.259632			−0.129816	−	0.991538i	$-0.541439\pi$
$349$	−4.85034			−0.259632			−0.129816	+	0.991538i	$0.541439\pi$
$350$		0			0
$351$	49.8997			2.66345
$352$		0			0
$353$	−3.52271	+	0.943907i	−0.187495	+	0.0502391i	−0.351345	−	0.936246i	$-0.614275\pi$
$353$	−3.52271	+	0.943907i	−0.187495	+	0.0502391i	0.163850	+	0.986485i	$0.447609\pi$
$354$		0			0
$355$	−10.2384	+	20.2046i	−0.543398	+	1.07235i
$356$		0			0
$357$	−12.8569	+	2.45241i	−0.680460	+	0.129795i
$358$		0			0
$359$	2.82260	−	1.62963i	0.148971	−	0.0860085i	−0.423662	−	0.905821i	$-0.639255\pi$
$359$	2.82260	−	1.62963i	0.148971	−	0.0860085i	0.572633	+	0.819812i	$0.305922\pi$
$360$		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
$367$	2.29395	+	8.56115i	0.119743	+	0.446888i	0.999598	−	0.0283547i	$-0.00902681\pi$
$367$	2.29395	+	8.56115i	0.119743	+	0.446888i	−0.879855	+	0.475243i	$0.842360\pi$
$368$		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
$373$	−18.6683	−	5.00215i	−0.966607	−	0.259002i	−0.259213	−	0.965820i	$-0.583463\pi$
$373$	−18.6683	−	5.00215i	−0.966607	−	0.259002i	−0.707395	+	0.706819i	$0.750130\pi$
$374$		0			0
$375$	32.9397	−	14.9290i	1.70100	−	0.770931i
$376$		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
$383$	−2.67917	+	9.99880i	−0.136899	+	0.510915i	0.863084	+	0.505061i	$0.168530\pi$
$383$	−2.67917	+	9.99880i	−0.136899	+	0.510915i	−0.999983	+	0.00585374i	$0.998137\pi$
$384$		0			0
$385$	−7.06325	+	1.75141i	−0.359976	+	0.0892603i
$386$		0			0
$387$	16.6323	−	62.0725i	0.845467	−	3.15532i
$388$		0			0
$389$	30.0971	+	17.3765i	1.52598	+	0.881026i	0.999525	+	0.0308234i	$0.00981295\pi$
$389$	30.0971	+	17.3765i	1.52598	+	0.881026i	0.526456	+	0.850202i	$0.323520\pi$
$390$		0			0
$391$			1.58237i			0.0800238i
$392$		0			0
$393$	−36.8793	+	36.8793i	−1.86032	+	1.86032i
$394$		0			0
$395$	−0.612781	−	11.2167i	−0.0308323	−	0.564373i
$396$		0			0
$397$	−17.4582	−	4.67792i	−0.876204	−	0.234778i	−0.207435	−	0.978249i	$-0.566512\pi$
$397$	−17.4582	−	4.67792i	−0.876204	−	0.234778i	−0.668768	+	0.743471i	$0.733178\pi$
$398$		0			0
$399$	33.0813	−	15.9916i	1.65614	−	0.800580i
$400$		0			0
$401$	−1.50000	−	2.59808i	−0.0749064	−	0.129742i	0.826139	−	0.563466i	$-0.190532\pi$
$401$	−1.50000	−	2.59808i	−0.0749064	−	0.129742i	−0.901046	+	0.433724i	$0.857199\pi$
$402$		0			0
$403$	−4.83411	−	18.0411i	−0.240804	−	0.898694i
$404$		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	−0.265686	−	0.964060i	$-0.585599\pi$
$409$	14.1982	−	24.5920i	0.702057	−	1.21600i	0.967743	−	0.251939i	$-0.0810681\pi$
$410$		0			0
$411$	33.0135	−	19.0603i	1.62844	−	0.940177i
$412$		0			0
$413$	5.93270	+	6.87328i	0.291929	+	0.338212i
$414$		0			0
$415$	26.5851	−	8.70325i	1.30501	−	0.427226i
$416$		0			0
$417$	31.8743	−	8.54070i	1.56089	−	0.418240i
$418$		0			0
$419$	−13.8024			−0.674292			−0.337146	−	0.941452i	$-0.609462\pi$
$419$	−13.8024			−0.674292			−0.337146	+	0.941452i	$0.609462\pi$
$420$		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
$423$	40.0042	−	10.7191i	1.94507	−	0.521180i
$424$		0			0
$425$	4.78596	−	5.96404i	0.232153	−	0.289298i
$426$		0			0
$427$	2.76004	+	14.4697i	0.133568	+	0.700238i
$428$		0			0
$429$	11.9099	−	6.87619i	0.575016	−	0.331985i
$430$		0			0
$431$	8.38497	−	14.5232i	0.403890	−	0.699558i	−0.590302	−	0.807183i	$-0.700991\pi$
$431$	8.38497	−	14.5232i	0.403890	−	0.699558i	0.994192	+	0.107625i	$0.0343246\pi$
$432$		0			0
$433$	0.621612	+	0.621612i	0.0298728	+	0.0298728i	0.721885	−	0.692013i	$-0.243276\pi$
$433$	0.621612	+	0.621612i	0.0298728	+	0.0298728i	−0.692013	+	0.721885i	$0.743276\pi$
$434$		0			0
$435$	−21.4246	−	4.50431i	−1.02723	−	0.215965i
$436$		0			0
$437$	−1.14971	−	4.29079i	−0.0549983	−	0.205256i
$438$		0			0
$439$	−3.19408	−	5.53232i	−0.152445	−	0.264043i	0.779681	−	0.626177i	$-0.215381\pi$
$439$	−3.19408	−	5.53232i	−0.152445	−	0.264043i	−0.932126	+	0.362134i	$0.882048\pi$
$440$		0			0
$441$	−51.6818	−	7.63311i	−2.46104	−	0.363481i
$442$		0			0
$443$	19.6075	+	5.25381i	0.931580	+	0.249616i	0.692528	−	0.721391i	$-0.256497\pi$
$443$	19.6075	+	5.25381i	0.931580	+	0.249616i	0.239052	+	0.971007i	$0.423163\pi$
$444$		0			0
$445$	13.6550	−	0.745988i	0.647308	−	0.0353632i
$446$		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
$453$	10.7995	−	40.3044i	0.507406	−	1.89367i
$454$		0			0
$455$	−0.383177	+	20.4445i	−0.0179636	+	0.958451i
$456$		0			0
$457$	−4.29955	+	16.0461i	−0.201125	+	0.750607i	0.789471	+	0.613787i	$0.210355\pi$
$457$	−4.29955	+	16.0461i	−0.201125	+	0.750607i	−0.990596	+	0.136820i	$0.956312\pi$
$458$		0			0
$459$	−19.1217	−	11.0399i	−0.892524	−	0.515299i
$460$		0			0
$461$			13.4410i			0.626011i	0.949751	+	0.313006i	$0.101336\pi$
$461$			13.4410i			0.626011i	−0.949751	+	0.313006i	$0.898664\pi$
$462$		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
$465$	−26.0891	+	29.1044i	−1.20985	+	1.34968i
$466$		0			0
$467$	−20.0376	−	5.36906i	−0.927230	−	0.248451i	−0.236557	−	0.971618i	$-0.576019\pi$
$467$	−20.0376	−	5.36906i	−0.927230	−	0.248451i	−0.690673	+	0.723167i	$0.742686\pi$
$468$		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
$473$	−2.74128	−	10.2306i	−0.126044	−	0.470404i
$474$		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	0.185660	+	0.982614i	$0.440558\pi$
$479$	−16.5927	+	28.7394i	−0.758139	+	1.31313i	−0.943799	+	0.330521i	$0.892776\pi$
$480$		0			0
$481$	−3.79644	+	2.19187i	−0.173103	+	0.0999409i
$482$		0			0
$483$	−2.91212	+	8.36212i	−0.132506	+	0.380490i
$484$		0			0
$485$	−11.0140	−	33.6435i	−0.500118	−	1.52767i
$486$		0			0
$487$	−2.69498	+	0.722118i	−0.122121	+	0.0327223i	−0.319362	−	0.947633i	$-0.603469\pi$
$487$	−2.69498	+	0.722118i	−0.122121	+	0.0327223i	0.197241	+	0.980355i	$0.436802\pi$
$488$		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
$493$	−4.47142	+	1.19811i	−0.201383	+	0.0539604i
$494$		0			0
$495$	−18.3108	−	9.27876i	−0.823011	−	0.417049i
$496$		0			0
$497$	−8.81415	+	25.3097i	−0.395369	+	1.13530i
$498$		0			0
$499$	29.3154	−	16.9252i	1.31234	−	0.757678i	0.329853	−	0.944032i	$-0.393001\pi$
$499$	29.3154	−	16.9252i	1.31234	−	0.757678i	0.982483	+	0.186355i	$0.0596673\pi$
$500$		0			0
$501$	−21.5193	+	37.2725i	−0.961410	+	1.66521i
$502$		0			0
$503$	5.02731	+	5.02731i	0.224157	+	0.224157i	0.810246	−	0.586090i	$-0.199333\pi$
$503$	5.02731	+	5.02731i	0.224157	+	0.224157i	−0.586090	+	0.810246i	$0.699333\pi$
$504$		0			0
$505$	30.5826	−	19.9571i	1.36091	−	0.888078i
$506$		0			0
$507$	0.882105	+	3.29206i	0.0391757	+	0.146206i
$508$		0			0
$509$	4.67261	+	8.09319i	0.207110	+	0.358725i	0.950803	−	0.309797i	$-0.100261\pi$
$509$	4.67261	+	8.09319i	0.207110	+	0.358725i	−0.743693	+	0.668521i	$0.766928\pi$
$510$		0			0
$511$	1.01855	−	13.8675i	0.0450581	−	0.613463i
$512$		0			0
$513$	59.8722	+	16.0427i	2.64342	+	0.708303i
$514$		0			0
$515$	9.91362	+	8.88654i	0.436846	+	0.391588i
$516$		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	−0.450391	−	0.892832i	$-0.648715\pi$
$521$	−33.0695	−	19.0927i	−1.44880	−	0.836466i	−0.998410	+	0.0563659i	$0.982049\pi$
$522$		0			0
$523$	7.03347	−	26.2493i	0.307552	−	1.14780i	−0.623174	−	0.782083i	$-0.714157\pi$
$523$	7.03347	−	26.2493i	0.307552	−	1.14780i	0.930726	−	0.365717i	$-0.119176\pi$
$524$		0			0
$525$	36.2676	−	22.7095i	1.58285	−	0.991123i
$526$		0			0
$527$	−2.13902	+	7.98293i	−0.0931771	+	0.347742i
$528$		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
$535$	−18.2057	−	16.3196i	−0.787102	−	0.705557i
$536$		0			0
$537$	−8.39577	−	2.24964i	−0.362304	−	0.0970792i
$538$		0			0
$539$	−8.00587	+	3.16950i	−0.344837	+	0.136520i
$540$		0			0
$541$	10.8597	+	18.8096i	0.466896	+	0.808688i	0.999285	−	0.0378121i	$-0.0120388\pi$
$541$	10.8597	+	18.8096i	0.466896	+	0.808688i	−0.532389	+	0.846500i	$0.678706\pi$
$542$		0			0
$543$	11.5238	+	43.0075i	0.494534	+	1.84563i
$544$		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
$553$	−2.49042	−	13.0562i	−0.105903	−	0.555204i
$554$		0			0
$555$	8.18306	+	4.14665i	0.347351	+	0.176015i
$556$		0			0
$557$	−7.07999	+	1.89708i	−0.299989	+	0.0803818i	−0.405674	−	0.914018i	$-0.632963\pi$
$557$	−7.07999	+	1.89708i	−0.299989	+	0.0803818i	0.105685	+	0.994400i	$0.466296\pi$
$558$		0			0
$559$	−29.7610			−1.25876
$560$		0			0
$561$	−6.08521			−0.256918
$562$		0			0
$563$	−11.4484	+	3.06760i	−0.482494	+	0.129284i	−0.491863	−	0.870672i	$-0.663684\pi$
$563$	−11.4484	+	3.06760i	−0.482494	+	0.129284i	0.00936989	+	0.999956i	$0.497017\pi$
$564$		0			0
$565$	4.18819	+	12.7933i	0.176198	+	0.538220i
$566$		0			0
$567$	−42.0260	−	48.6889i	−1.76493	−	2.04474i
$568$		0			0
$569$	10.9064	−	6.29679i	0.457219	−	0.263975i	−0.253655	−	0.967295i	$-0.581633\pi$
$569$	10.9064	−	6.29679i	0.457219	−	0.263975i	0.710874	+	0.703319i	$0.248300\pi$
$570$		0			0
$571$	22.4679	−	38.9155i	0.940251	−	1.62856i	0.175260	−	0.984522i	$-0.443923\pi$
$571$	22.4679	−	38.9155i	0.940251	−	1.62856i	0.764991	−	0.644041i	$-0.222743\pi$
$572$		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
$577$	−7.01224	−	26.1700i	−0.291923	−	1.08947i	−0.943630	−	0.331002i	$-0.892613\pi$
$577$	−7.01224	−	26.1700i	−0.291923	−	1.08947i	0.651707	−	0.758471i	$-0.274053\pi$
$578$		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
$583$	14.7806	+	3.96046i	0.612151	+	0.164025i
$584$		0			0
$585$	−38.5006	+	42.9504i	−1.59180	+	1.77578i
$586$		0			0
$587$	−1.96674	+	1.96674i	−0.0811759	+	0.0811759i	−0.746529	−	0.665353i	$-0.768281\pi$
$587$	−1.96674	+	1.96674i	−0.0811759	+	0.0811759i	0.665353	+	0.746529i	$0.268281\pi$
$588$		0			0
$589$		−	23.2009i		−	0.955975i
$590$		0			0
$591$	44.3045	+	25.5792i	1.82245	+	1.05219i
$592$		0			0
$593$	−3.93539	+	14.6871i	−0.161607	+	0.603126i	0.836842	+	0.547445i	$0.184400\pi$
$593$	−3.93539	+	14.6871i	−0.161607	+	0.603126i	−0.998449	+	0.0556806i	$0.982267\pi$
$594$		0			0
$595$	4.67001	−	7.74959i	0.191452	−	0.317702i
$596$		0			0
$597$	10.7465	−	40.1067i	0.439827	−	1.64146i
$598$		0			0
$599$	12.1470	+	7.01309i	0.496314	+	0.286547i	0.727190	−	0.686436i	$-0.240826\pi$
$599$	12.1470	+	7.01309i	0.496314	+	0.286547i	−0.230876	+	0.972983i	$0.574159\pi$
$600$		0			0
$601$		−	19.9337i		−	0.813111i	−0.913626	−	0.406555i	$-0.866730\pi$
$601$		−	19.9337i		−	0.813111i	0.913626	−	0.406555i	$-0.133270\pi$
$602$		0			0
$603$	−22.1036	+	22.1036i	−0.900126	+	0.900126i
$604$		0			0
$605$	21.1819	−	1.15719i	0.861165	−	0.0470465i
$606$		0			0
$607$	−1.85441	−	0.496888i	−0.0752683	−	0.0201681i	0.220988	−	0.975276i	$-0.429072\pi$
$607$	−1.85441	−	0.496888i	−0.0752683	−	0.0201681i	−0.296257	+	0.955108i	$0.595738\pi$
$608$		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
$613$	−10.0154	−	37.3779i	−0.404517	−	1.50968i	−0.804945	−	0.593349i	$-0.797805\pi$
$613$	−10.0154	−	37.3779i	−0.404517	−	1.50968i	0.400428	−	0.916328i	$-0.368861\pi$
$614$		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	$-0.704071\pi$
$619$	9.82797	−	17.0225i	0.395020	−	0.684194i	0.993104	+	0.117239i	$0.0374045\pi$
$620$		0			0
$621$	−12.9361	+	7.46865i	−0.519107	+	0.299706i
$622$		0			0
$623$	15.8943	−	3.03179i	0.636792	−	0.121466i
$624$		0			0
$625$	−7.51427	+	23.8440i	−0.300571	+	0.953759i
$626$		0			0
$627$	16.5008	−	4.42138i	0.658979	−	0.176573i
$628$		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
$633$	−16.2767	+	4.36132i	−0.646939	+	0.173347i
$634$		0			0
$635$	6.01993	−	1.97076i	0.238894	−	0.0782073i
$636$		0			0
$637$	2.78021	+	24.0342i	0.110156	+	0.952269i
$638$		0			0
$639$	−65.4714	+	37.7999i	−2.59001	+	1.49534i
$640$		0			0
$641$	4.35542	−	7.54381i	0.172029	−	0.297962i	−0.767100	−	0.641527i	$-0.778301\pi$
$641$	4.35542	−	7.54381i	0.172029	−	0.297962i	0.939129	+	0.343565i	$0.111634\pi$
$642$		0			0
$643$	−12.2173	−	12.2173i	−0.481802	−	0.481802i	0.423905	−	0.905707i	$-0.360659\pi$
$643$	−12.2173	−	12.2173i	−0.481802	−	0.481802i	−0.905707	+	0.423905i	$0.860659\pi$
$644$		0			0
$645$	34.0358	+	52.1569i	1.34016	+	2.05368i
$646$		0			0
$647$	−1.88381	−	7.03047i	−0.0740601	−	0.276396i	0.918958	−	0.394354i	$-0.129032\pi$
$647$	−1.88381	−	7.03047i	−0.0740601	−	0.276396i	−0.993019	+	0.117958i	$0.962365\pi$
$648$		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
$653$	−27.8167	−	7.45345i	−1.08855	−	0.291676i	−0.330456	−	0.943821i	$-0.607202\pi$
$653$	−27.8167	−	7.45345i	−1.08855	−	0.291676i	−0.758094	+	0.652145i	$0.773869\pi$
$654$		0			0
$655$	−1.96673	−	36.0001i	−0.0768464	−	1.40664i
$656$		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	0.668966	−	0.743293i	$-0.266737\pi$
$661$	9.24885	+	5.33983i	0.359739	+	0.207695i	−0.309227	+	0.950988i	$0.600070\pi$
$662$		0			0
$663$	−4.42550	+	16.5162i	−0.171872	+	0.641435i
$664$		0			0
$665$	−7.03263	+	24.4071i	−0.272714	+	0.946468i
$666$		0			0
$667$	−0.810540	+	3.02498i	−0.0313842	+	0.117128i
$668$		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
$675$	71.3461	+	10.9761i	2.74611	+	0.422469i
$676$		0			0
$677$	19.9284	+	5.33980i	0.765911	+	0.205225i	0.620564	−	0.784156i	$-0.286904\pi$
$677$	19.9284	+	5.33980i	0.765911	+	0.205225i	0.145346	+	0.989381i	$0.453570\pi$
$678$		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
$683$	−4.77349	−	17.8149i	−0.182653	−	0.681668i	−0.995121	−	0.0986632i	$-0.968543\pi$
$683$	−4.77349	−	17.8149i	−0.182653	−	0.681668i	0.812468	−	0.583005i	$-0.198123\pi$
$684$		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	−0.567295	−	0.823515i	$-0.692010\pi$
$691$	−3.62120	+	2.09070i	−0.137757	+	0.0795340i	0.429538	+	0.903049i	$0.358677\pi$
$692$		0			0
$693$	−22.9375	−	7.98801i	−0.871322	−	0.303439i
$694$		0			0
$695$	−10.3110	+	20.3479i	−0.391119	+	0.771840i
$696$		0			0
$697$	1.86154	−	0.498798i	0.0705108	−	0.0188933i
$698$		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
$703$	−5.25985	+	1.40937i	−0.198379	+	0.0531555i
$704$		0			0
$705$	−18.1428	+	35.8033i	−0.683299	+	1.34843i
$706$		0			0
$707$	32.7093	−	28.2331i	1.23016	−	1.06182i
$708$		0			0
$709$	−22.6370	+	13.0695i	−0.850149	+	0.490834i	−0.860701	−	0.509110i	$-0.829974\pi$
$709$	−22.6370	+	13.0695i	−0.850149	+	0.490834i	0.0105520	+	0.999944i	$0.496641\pi$
$710$		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
$717$	−14.9412	−	55.7614i	−0.557990	−	2.08245i
$718$		0			0
$719$	−11.0172	−	19.0824i	−0.410872	−	0.711652i	0.584113	−	0.811672i	$-0.301442\pi$
$719$	−11.0172	−	19.0824i	−0.410872	−	0.711652i	−0.994985	+	0.100021i	$0.968109\pi$
$720$		0			0
$721$	13.0287	+	8.85456i	0.485215	+	0.329761i
$722$		0			0
$723$	−9.21180	−	2.46830i	−0.342591	−	0.0917969i
$724$		0			0
$725$	12.2042	−	8.94980i	0.453252	−	0.332387i
$726$		0			0
$727$	−6.19964	+	6.19964i	−0.229932	+	0.229932i	−0.812664	−	0.582732i	$-0.801984\pi$
$727$	−6.19964	+	6.19964i	−0.229932	+	0.229932i	0.582732	+	0.812664i	$0.301984\pi$
$728$		0			0
$729$		−	41.3312i		−	1.53079i
$730$		0			0
$731$	11.4045	+	6.58439i	0.421811	+	0.243533i
$732$		0			0
$733$	−3.53411	+	13.1895i	−0.130535	+	0.487164i	−0.999976	−	0.00687249i	$-0.997812\pi$
$733$	−3.53411	+	13.1895i	−0.130535	+	0.487164i	0.869441	+	0.494036i	$0.164479\pi$
$734$		0			0
$735$	38.9410	−	32.3587i	1.43636	−	1.19357i
$736$		0			0
$737$	−1.33344	+	4.97648i	−0.0491181	+	0.183311i
$738$		0			0
$739$	17.9456	+	10.3609i	0.660141	+	0.381132i	0.792331	−	0.610092i	$-0.208868\pi$
$739$	17.9456	+	10.3609i	0.660141	+	0.381132i	−0.132190	+	0.991224i	$0.542201\pi$
$740$		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
$745$	−0.781821	−	14.3109i	−0.0286437	−	0.524311i
$746$		0			0
$747$	90.1844	+	24.1648i	3.29967	+	0.884145i
$748$		0			0
$749$	−23.9264	−	16.2608i	−0.874252	−	0.594158i
$750$		0			0
$751$	−4.19292	−	7.26235i	−0.153002	−	0.265007i	0.779328	−	0.626616i	$-0.215561\pi$
$751$	−4.19292	−	7.26235i	−0.153002	−	0.265007i	−0.932330	+	0.361610i	$0.882227\pi$
$752$		0			0
$753$	23.3524	+	87.1524i	0.851009	+	3.17601i
$754$		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	−0.821614	−	0.570044i	$-0.806926\pi$
$761$	−20.3793	+	11.7660i	−0.738749	+	0.426517i	0.0828651	+	0.996561i	$0.473593\pi$
$762$		0			0
$763$	−13.0399	+	11.2554i	−0.472075	+	0.407473i
$764$		0			0
$765$	24.2560	−	7.94074i	0.876976	−	0.287098i
$766$		0			0
$767$	11.4572	−	3.06995i	0.413696	−	0.110849i
$768$		0			0
$769$	−5.77277			−0.208171			−0.104086	−	0.994568i	$-0.533192\pi$
$769$	−5.77277			−0.208171			−0.104086	+	0.994568i	$0.533192\pi$
$770$		0			0
$771$	26.5983			0.957916
$772$		0			0
$773$	−38.3400	+	10.2732i	−1.37899	+	0.369501i	−0.870756	−	0.491715i	$-0.836370\pi$
$773$	−38.3400	+	10.2732i	−1.37899	+	0.369501i	−0.508239	+	0.861216i	$0.669703\pi$
$774$		0			0
$775$	−2.94340	−	26.8584i	−0.105730	−	0.964782i
$776$		0			0
$777$	10.2507	+	3.56981i	0.367741	+	0.128066i
$778$		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
$787$	−6.11285	−	22.8135i	−0.217899	−	0.813212i	−0.985126	−	0.171835i	$-0.945030\pi$
$787$	−6.11285	−	22.8135i	−0.217899	−	0.813212i	0.767226	−	0.641377i	$-0.221636\pi$
$788$		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
$793$	18.5880	+	4.98064i	0.660079	+	0.176868i
$794$		0			0
$795$	−89.8446	+	4.90832i	−3.18646	+	0.174080i
$796$		0			0
$797$	0.0424381	−	0.0424381i	0.00150323	−	0.00150323i	−0.706355	−	0.707858i	$-0.749662\pi$
$797$	0.0424381	−	0.0424381i	0.00150323	−	0.00150323i	0.707858	+	0.706355i	$0.249662\pi$
$798$		0			0
$799$			8.48695i			0.300247i
$800$		0			0
$801$	39.5284	+	22.8218i	1.39667	+	0.806367i
$802$		0			0
$803$	1.67318	−	6.24438i	0.0590451	−	0.220359i
$804$		0			0
$805$	−2.96065	−	5.35741i	−0.104349	−	0.188824i
$806$		0			0
$807$	−25.6092	+	95.5747i	−0.901485	+	3.36439i
$808$		0			0
$809$	38.9718	+	22.5004i	1.37018	+	0.791072i	0.990950	−	0.134232i	$-0.0428568\pi$
$809$	38.9718	+	22.5004i	1.37018	+	0.791072i	0.379226	+	0.925304i	$0.376190\pi$
$810$		0			0
$811$		−	20.9653i		−	0.736191i	−0.929788	−	0.368096i	$-0.880010\pi$
$811$		−	20.9653i		−	0.736191i	0.929788	−	0.368096i	$-0.119990\pi$
$812$		0			0
$813$	59.6762	−	59.6762i	2.09293	−	2.09293i
$814$		0			0
$815$	22.2480	−	24.8193i	0.779313	−	0.869383i
$816$		0			0
$817$	−35.7088	−	9.56815i	−1.24929	−	0.334747i
$818$		0			0
$819$	−38.3620	+	56.4464i	−1.34048	+	1.97240i
$820$		0			0
$821$	25.0695	+	43.4216i	0.874931	+	1.51543i	0.856836	+	0.515590i	$0.172427\pi$
$821$	25.0695	+	43.4216i	0.874931	+	1.51543i	0.0180958	+	0.999836i	$0.494240\pi$
$822$		0			0
$823$	10.7141	+	39.9857i	0.373471	+	1.39381i	0.855566	+	0.517694i	$0.173209\pi$
$823$	10.7141	+	39.9857i	0.373471	+	1.39381i	−0.482095	+	0.876119i	$0.660124\pi$
$824$		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	0.124968	+	0.992161i	$0.460117\pi$
$829$	−22.9404	+	39.7339i	−0.796752	+	1.38002i	−0.921721	+	0.387854i	$0.873216\pi$
$830$		0			0
$831$	−61.2711	+	35.3749i	−2.12547	+	1.22714i
$832$		0			0
$833$	4.25199	−	9.82506i	0.147323	−	0.340418i
$834$		0			0
$835$	−9.25645	−	28.2750i	−0.320333	−	0.978496i
$836$		0			0
$837$	−75.3575	+	20.1920i	−2.60474	+	0.697937i
$838$		0			0
$839$	−26.4488			−0.913114			−0.456557	−	0.889694i	$-0.650918\pi$
$839$	−26.4488			−0.913114			−0.456557	+	0.889694i	$0.650918\pi$
$840$		0			0
$841$	19.8384			0.684082
$842$		0			0
$843$	−64.9049	+	17.3912i	−2.23544	+	0.598985i
$844$		0			0
$845$	−2.10158	−	1.06495i	−0.0722967	−	0.0366353i
$846$		0			0
$847$	24.6556	−	4.70296i	0.847175	−	0.161596i
$848$		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	0.982393	−	0.186827i	$-0.0598205\pi$
$853$	23.2354	+	23.2354i	0.795566	+	0.795566i	−0.186827	+	0.982393i	$0.559820\pi$
$854$		0			0
$855$	−60.0035	+	39.1562i	−2.05208	+	1.33911i
$856$		0			0
$857$	10.1207	+	37.7708i	0.345715	+	1.29023i	0.891775	+	0.452480i	$0.149460\pi$
$857$	10.1207	+	37.7708i	0.345715	+	1.29023i	−0.546060	+	0.837746i	$0.683873\pi$
$858$		0			0
$859$	8.13198	+	14.0850i	0.277460	+	0.480574i	0.970753	−	0.240082i	$-0.0771742\pi$
$859$	8.13198	+	14.0850i	0.277460	+	0.480574i	−0.693293	+	0.720656i	$0.743841\pi$
$860$		0			0
$861$	10.7554	+	0.789968i	0.366542	+	0.0269221i
$862$		0			0
$863$	22.3885	+	5.99898i	0.762113	+	0.204208i	0.618884	−	0.785482i	$-0.287585\pi$
$863$	22.3885	+	5.99898i	0.762113	+	0.204208i	0.143229	+	0.989690i	$0.454252\pi$
$864$		0			0
$865$	−7.77601	−	6.97040i	−0.264392	−	0.237001i
$866$		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
$873$	30.5806	−	114.128i	1.03500	−	3.86266i
$874$		0			0
$875$	−5.04488	+	29.1470i	−0.170548	+	0.985349i
$876$		0			0
$877$	−9.48029	+	35.3809i	−0.320127	+	1.19473i	0.598994	+	0.800753i	$0.295567\pi$
$877$	−9.48029	+	35.3809i	−0.320127	+	1.19473i	−0.919121	+	0.393975i	$0.871099\pi$
$878$		0			0
$879$	−38.0593	−	21.9736i	−1.28371	−	0.741150i
$880$		0			0
$881$			36.3165i			1.22353i	0.791038	+	0.611767i	$0.209541\pi$
$881$			36.3165i			1.22353i	−0.791038	+	0.611767i	$0.790459\pi$
$882$		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
$885$	−18.4830	−	16.5681i	−0.621300	−	0.556932i
$886$		0			0
$887$	33.6941	+	9.02831i	1.13134	+	0.303141i	0.775463	−	0.631393i	$-0.217516\pi$
$887$	33.6941	+	9.02831i	1.13134	+	0.303141i	0.355874	+	0.934534i	$0.384183\pi$
$888$		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
$893$	−6.16643	−	23.0134i	−0.206352	−	0.770115i
$894$		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
$903$	48.1502	+	55.7840i	1.60234	+	1.85638i
$904$		0			0
$905$	−27.4551	−	13.9125i	−0.912638	−	0.462467i
$906$		0			0
$907$	34.6296	−	9.27896i	1.14986	−	0.308103i	0.366948	−	0.930241i	$-0.380403\pi$
$907$	34.6296	−	9.27896i	1.14986	−	0.308103i	0.782907	+	0.622139i	$0.213736\pi$
$908$		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
$913$	14.8639	−	3.98277i	0.491923	−	0.131810i
$914$		0			0
$915$	−12.5292	−	38.2720i	−0.414202	−	1.26523i
$916$		0			0
$917$	−7.99302	−	41.9039i	−0.263953	−	1.38379i
$918$		0			0
$919$	29.9372	−	17.2843i	0.987537	−	0.570155i	0.0830000	−	0.996550i	$-0.473550\pi$
$919$	29.9372	−	17.2843i	0.987537	−	0.570155i	0.904537	+	0.426395i	$0.140217\pi$
$920$		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
$927$	11.5009	+	42.9218i	0.377738	+	1.40974i
$928$		0			0
$929$	−9.82260	−	17.0132i	−0.322269	−	0.558187i	0.658687	−	0.752417i	$-0.271112\pi$
$929$	−9.82260	−	17.0132i	−0.322269	−	0.558187i	−0.980956	+	0.194231i	$0.937779\pi$
$930$		0			0
$931$	−4.39114	+	29.7313i	−0.143914	+	0.974404i
$932$		0			0
$933$	83.7190	+	22.4324i	2.74084	+	0.734405i
$934$		0			0
$935$	2.80781	−	3.13232i	0.0918251	−	0.102438i
$936$		0			0
$937$	20.5897	−	20.5897i	0.672636	−	0.672636i	−0.285687	−	0.958323i	$-0.592222\pi$
$937$	20.5897	−	20.5897i	0.672636	−	0.672636i	0.958323	+	0.285687i	$0.0922217\pi$
$938$		0			0
$939$		−	87.0179i		−	2.83972i
$940$		0			0
$941$	−1.83153	−	1.05743i	−0.0597060	−	0.0344713i	0.469850	−	0.882746i	$-0.344308\pi$
$941$	−1.83153	−	1.05743i	−0.0597060	−	0.0344713i	−0.529556	+	0.848275i	$0.677641\pi$
$942$		0			0
$943$	0.337443	−	1.25935i	0.0109887	−	0.0410102i
$944$		0			0
$945$	85.3960	+	1.60052i	2.77793	+	0.0520649i
$946$		0			0
$947$	4.44511	−	16.5894i	0.144447	−	0.539082i	−0.855333	−	0.518079i	$-0.826647\pi$
$947$	4.44511	−	16.5894i	0.144447	−	0.539082i	0.999779	−	0.0210032i	$-0.00668601\pi$
$948$		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
$955$	−17.0780	+	0.932990i	−0.552630	+	0.0301908i
$956$		0			0
$957$	−11.6330	−	3.11704i	−0.376040	−	0.100760i
$958$		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
$963$	−21.1206	−	78.8232i	−0.680602	−	2.54004i
$964$		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	−0.942539	−	0.334095i	$-0.891569\pi$
$971$	−35.0396	+	20.2301i	−1.12447	+	0.649215i	−0.181935	+	0.983311i	$0.558236\pi$
$972$		0			0
$973$	−8.87667	+	25.4892i	−0.284573	+	0.817147i
$974$		0			0
$975$	−6.08971	−	55.5684i	−0.195027	−	1.77961i
$976$		0			0
$977$	−44.8708	+	12.0231i	−1.43554	+	0.384653i	−0.890971	−	0.454061i	$-0.849975\pi$
$977$	−44.8708	+	12.0231i	−1.43554	+	0.384653i	−0.544573	+	0.838713i	$0.683308\pi$
$978$		0			0
$979$	7.52282			0.240430
$980$		0			0
$981$	−48.5906			−1.55138
$982$		0			0
$983$	−17.7526	+	4.75681i	−0.566221	+	0.151719i	−0.530563	−	0.847645i	$-0.678019\pi$
$983$	−17.7526	+	4.75681i	−0.566221	+	0.151719i	−0.0356584	+	0.999364i	$0.511353\pi$
$984$		0			0
$985$	−33.6095	+	11.0028i	−1.07089	+	0.350580i
$986$		0			0
$987$	−15.6190	+	44.8498i	−0.497159	+	1.42758i
$988$		0			0
$989$	7.71530	−	4.45443i	0.245332	−	0.141643i
$990$		0			0
$991$	−3.06942	+	5.31640i	−0.0975035	+	0.168881i	−0.910651	−	0.413177i	$-0.864419\pi$
$991$	−3.06942	+	5.31640i	−0.0975035	+	0.168881i	0.813147	+	0.582058i	$0.197752\pi$
$992$		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
$997$	1.89945	+	7.08884i	0.0601561	+	0.224506i	0.989459	−	0.144812i	$-0.0462579\pi$
$997$	1.89945	+	7.08884i	0.0601561	+	0.224506i	−0.929303	+	0.369318i	$0.879591\pi$
$998$		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.17.1	✓	16
3.2	odd	2		1260.2.dq.a.577.2		16
4.3	odd	2		560.2.ci.d.17.4		16
5.2	odd	4		700.2.bc.b.493.4		16
5.3	odd	4	inner	140.2.u.a.73.1	yes	16
5.4	even	2		700.2.bc.b.157.4		16
7.2	even	3		980.2.v.a.117.4		16
7.3	odd	6		980.2.m.a.97.1		16
7.4	even	3		980.2.m.a.97.8		16
7.5	odd	6	inner	140.2.u.a.117.1	yes	16
7.6	odd	2		980.2.v.a.717.4		16
15.8	even	4		1260.2.dq.a.73.1		16
20.3	even	4		560.2.ci.d.353.4		16
21.5	even	6		1260.2.dq.a.397.1		16
28.19	even	6		560.2.ci.d.257.4		16
35.3	even	12		980.2.m.a.293.8		16
35.12	even	12		700.2.bc.b.593.4		16
35.13	even	4		980.2.v.a.913.4		16
35.18	odd	12		980.2.m.a.293.1		16
35.19	odd	6		700.2.bc.b.257.4		16
35.23	odd	12		980.2.v.a.313.4		16
35.33	even	12	inner	140.2.u.a.33.1	yes	16
105.68	odd	12		1260.2.dq.a.1153.2		16
140.103	odd	12		560.2.ci.d.33.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.u.a.17.1	✓	16	1.1	even	1	trivial
140.2.u.a.33.1	yes	16	35.33	even	12	inner
140.2.u.a.73.1	yes	16	5.3	odd	4	inner
140.2.u.a.117.1	yes	16	7.5	odd	6	inner
560.2.ci.d.17.4		16	4.3	odd	2
560.2.ci.d.33.4		16	140.103	odd	12
560.2.ci.d.257.4		16	28.19	even	6
560.2.ci.d.353.4		16	20.3	even	4
700.2.bc.b.157.4		16	5.4	even	2
700.2.bc.b.257.4		16	35.19	odd	6
700.2.bc.b.493.4		16	5.2	odd	4
700.2.bc.b.593.4		16	35.12	even	12
980.2.m.a.97.1		16	7.3	odd	6
980.2.m.a.97.8		16	7.4	even	3
980.2.m.a.293.1		16	35.18	odd	12
980.2.m.a.293.8		16	35.3	even	12
980.2.v.a.117.4		16	7.2	even	3
980.2.v.a.313.4		16	35.23	odd	12
980.2.v.a.717.4		16	7.6	odd	2
980.2.v.a.913.4		16	35.13	even	4
1260.2.dq.a.73.1		16	15.8	even	4
1260.2.dq.a.397.1		16	21.5	even	6
1260.2.dq.a.577.2		16	3.2	odd	2
1260.2.dq.a.1153.2		16	105.68	odd	12

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)

\(f(q)\)	\(=\)	\(q+(-3.12447 + 0.837199i) q^{3} +(1.01073 - 1.99460i) q^{5} +(0.870132 - 2.49857i) q^{7} +(6.46333 - 3.73161i) q^{9} +O(q^{10})\)	\(q+(-3.12447 + 0.837199i) q^{3} +(1.01073 - 1.99460i) q^{5} +(0.870132 - 2.49857i) q^{7} +(6.46333 - 3.73161i) q^{9} +(0.615031 - 1.06527i) q^{11} +(-2.44401 - 2.44401i) q^{13} +(-1.48813 + 7.07824i) q^{15} +(0.395833 + 1.47727i) q^{17} +(-2.14670 - 3.71820i) q^{19} +(-0.626899 + 8.53519i) q^{21} +(0.999392 + 0.267786i) q^{23} +(-2.95683 - 4.03201i) q^{25} +(-10.2086 + 10.2086i) q^{27} +3.02682i q^{29} +(4.67986 + 2.70192i) q^{31} +(-1.02981 + 3.84329i) q^{33} +(-4.10417 - 4.26096i) q^{35} +(0.328265 - 1.22510i) q^{37} +(9.68235 + 5.59011i) q^{39} -1.26012i q^{41} +(6.08857 - 6.08857i) q^{43} +(-0.910341 - 16.6634i) q^{45} +(5.36018 + 1.43626i) q^{47} +(-5.48574 - 4.34818i) q^{49} +(-2.47354 - 4.28429i) q^{51} +(3.21972 + 12.0162i) q^{53} +(-1.50314 - 2.30344i) q^{55} +(9.82017 + 9.82017i) q^{57} +(-1.71588 + 2.97199i) q^{59} +(-4.82171 + 2.78382i) q^{61} +(-3.69974 - 19.3961i) q^{63} +(-7.34506 + 2.40457i) q^{65} +(-4.04571 + 1.08405i) q^{67} -3.34676 q^{69} -10.1297 q^{71} +(5.07647 - 1.36024i) q^{73} +(12.6141 + 10.1224i) q^{75} +(-2.12649 - 2.46362i) q^{77} +(4.35068 - 2.51187i) q^{79} +(12.1549 - 21.0530i) q^{81} +(8.84600 + 8.84600i) q^{83} +(3.34664 + 0.703598i) q^{85} +(-2.53405 - 9.45720i) q^{87} +(3.05790 + 5.29644i) q^{89} +(-8.23315 + 3.97993i) q^{91} +(-16.8841 - 4.52409i) q^{93} +(-9.58605 + 0.523697i) q^{95} +(11.1946 - 11.1946i) q^{97} -9.18022i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 6 q^{5} + 2 q^{7}+O(q^{10}) \) 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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