LMFDB - Embedded newform 392.2.e.d.195.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [392,2,Mod(195,392)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("392.195"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(392, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 392 = 2^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	392.e (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,4,0,-4,0,0,0,4,8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(9)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.13013575923$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.1212153856.10
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{6} + 10x^{4} - 16x^{2} + 16 $ x^8 - 4x^6 + 10x^4 - 16*x^2 + 16
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			195.7
Root			$1.36145 + 0.382683i$ of defining polynomial
Character	$\chi$	$=$	392.195
Dual form			392.2.e.d.195.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.20711 + 0.736813i) q^{2} -1.84776i q^{3} +(0.914214 + 1.77882i) q^{4} +3.85077 q^{5} +(1.36145 - 2.23044i) q^{6} +(-0.207107 + 2.82083i) q^{8} -0.414214 q^{9} +(4.64829 + 2.83730i) q^{10} -4.24264 q^{11} +(3.28684 - 1.68925i) q^{12} -3.85077 q^{13} -7.11529i q^{15} +(-2.32843 + 3.25245i) q^{16} +0.317025i q^{17} +(-0.500000 - 0.305198i) q^{18} -2.93015i q^{19} +(3.52043 + 6.84984i) q^{20} +(-5.12132 - 3.12603i) q^{22} +2.94725i q^{23} +(5.21222 + 0.382683i) q^{24} +9.82843 q^{25} +(-4.64829 - 2.83730i) q^{26} -4.77791i q^{27} -2.94725i q^{29} +(5.24264 - 8.58892i) q^{30} -2.25573 q^{31} +(-5.20711 + 2.21044i) q^{32} +7.83938i q^{33} +(-0.233588 + 0.382683i) q^{34} +(-0.378680 - 0.736813i) q^{36} +7.11529i q^{37} +(2.15897 - 3.53701i) q^{38} +7.11529i q^{39} +(-0.797521 + 10.8624i) q^{40} -1.39942i q^{41} +5.41421 q^{43} +(-3.87868 - 7.54691i) q^{44} -1.59504 q^{45} +(-2.17157 + 3.55765i) q^{46} -7.70154 q^{47} +(6.00974 + 4.30237i) q^{48} +(11.8640 + 7.24171i) q^{50} +0.585786 q^{51} +(-3.52043 - 6.84984i) q^{52} -10.0625i q^{53} +(3.52043 - 5.76745i) q^{54} -16.3374 q^{55} -5.41421 q^{57} +(2.17157 - 3.55765i) q^{58} -0.131316i q^{59} +(12.6569 - 6.50490i) q^{60} -1.59504 q^{61} +(-2.72291 - 1.66205i) q^{62} +(-7.91421 - 1.16843i) q^{64} -14.8284 q^{65} +(-5.77615 + 9.46297i) q^{66} -2.00000 q^{67} +(-0.563932 + 0.289829i) q^{68} +5.44581 q^{69} +15.9570i q^{71} +(0.0857864 - 1.16843i) q^{72} -2.93015i q^{73} +(-5.24264 + 8.58892i) q^{74} -18.1606i q^{75} +(5.21222 - 2.67878i) q^{76} +(-5.24264 + 8.58892i) q^{78} -5.89450i q^{79} +(-8.96624 + 12.5244i) q^{80} -10.0711 q^{81} +(1.03111 - 1.68925i) q^{82} -3.82683i q^{83} +1.22079i q^{85} +(6.53553 + 3.98926i) q^{86} -5.44581 q^{87} +(0.878680 - 11.9678i) q^{88} +9.68714i q^{89} +(-1.92538 - 1.17525i) q^{90} +(-5.24264 + 2.69442i) q^{92} +4.16804i q^{93} +(-9.29658 - 5.67459i) q^{94} -11.2833i q^{95} +(4.08436 + 9.62148i) q^{96} +16.6298i q^{97} +1.75736 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{2} - 4 q^{4} + 4 q^{8} + 8 q^{9} + 4 q^{16} - 4 q^{18} - 24 q^{22} + 56 q^{25} + 8 q^{30} - 36 q^{32} - 20 q^{36} + 32 q^{43} - 48 q^{44} - 40 q^{46} + 44 q^{50} + 16 q^{51} - 32 q^{57} + 40 q^{58}+ \cdots + 48 q^{99}+O(q^{100}) $ 8 * q + 4 * q^2 - 4 * q^4 + 4 * q^8 + 8 * q^9 + 4 * q^16 - 4 * q^18 - 24 * q^22 + 56 * q^25 + 8 * q^30 - 36 * q^32 - 20 * q^36 + 32 * q^43 - 48 * q^44 - 40 * q^46 + 44 * q^50 + 16 * q^51 - 32 * q^57 + 40 * q^58 + 56 * q^60 - 52 * q^64 - 96 * q^65 - 16 * q^67 + 12 * q^72 - 8 * q^74 - 8 * q^78 - 24 * q^81 + 24 * q^86 + 24 * q^88 - 8 * q^92 + 48 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/392\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$297$
$\chi(n)$	$-1$	$-1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.20711	+	0.736813i	0.853553	+	0.521005i
$2$	1.20711	+	0.736813i	0.853553	+	0.521005i
$3$		−	1.84776i		−	1.06680i	−0.845862	−	0.533402i	$-0.820913\pi$
$3$		−	1.84776i		−	1.06680i	0.845862	−	0.533402i	$-0.179087\pi$
$4$	0.914214	+	1.77882i	0.457107	+	0.889412i
$5$	3.85077			1.72212			0.861058	−	0.508506i	$-0.169802\pi$
$5$	3.85077			1.72212			0.861058	+	0.508506i	$0.169802\pi$
$6$	1.36145	−	2.23044i	0.555811	−	0.910574i
$7$		0			0
$7$		0			0
$8$	−0.207107	+	2.82083i	−0.0732233	+	0.997316i
$9$	−0.414214			−0.138071
$10$	4.64829	+	2.83730i	1.46992	+	0.897232i
$11$	−4.24264			−1.27920			−0.639602	−	0.768706i	$-0.720901\pi$
$11$	−4.24264			−1.27920			−0.639602	+	0.768706i	$0.720901\pi$
$12$	3.28684	−	1.68925i	0.948828	−	0.487643i
$13$	−3.85077			−1.06801			−0.534006	−	0.845481i	$-0.679314\pi$
$13$	−3.85077			−1.06801			−0.534006	+	0.845481i	$0.679314\pi$
$14$		0			0
$15$		−	7.11529i		−	1.83716i
$16$	−2.32843	+	3.25245i	−0.582107	+	0.813112i
$17$			0.317025i			0.0768899i	0.999261	+	0.0384450i	$0.0122404\pi$
$17$			0.317025i			0.0768899i	−0.999261	+	0.0384450i	$0.987760\pi$
$18$	−0.500000	−	0.305198i	−0.117851	−	0.0719358i
$19$		−	2.93015i		−	0.672223i	−0.941822	−	0.336111i	$-0.890888\pi$
$19$		−	2.93015i		−	0.672223i	0.941822	−	0.336111i	$-0.109112\pi$
$20$	3.52043	+	6.84984i	0.787191	+	1.53167i
$21$		0			0
$22$	−5.12132	−	3.12603i	−1.09187	−	0.666472i
$23$			2.94725i			0.614544i	0.951622	+	0.307272i	$0.0994162\pi$
$23$			2.94725i			0.614544i	−0.951622	+	0.307272i	$0.900584\pi$
$24$	5.21222	+	0.382683i	1.06394	+	0.0781149i
$25$	9.82843			1.96569
$26$	−4.64829	−	2.83730i	−0.911605	−	0.556440i
$27$		−	4.77791i		−	0.919509i
$28$		0			0
$29$		−	2.94725i		−	0.547291i	−0.961831	−	0.273645i	$-0.911771\pi$
$29$		−	2.94725i		−	0.547291i	0.961831	−	0.273645i	$-0.0882295\pi$
$30$	5.24264	−	8.58892i	0.957171	−	1.56812i
$31$	−2.25573			−0.405141			−0.202570	−	0.979268i	$-0.564930\pi$
$31$	−2.25573			−0.405141			−0.202570	+	0.979268i	$0.564930\pi$
$32$	−5.20711	+	2.21044i	−0.920495	+	0.390754i
$33$			7.83938i			1.36466i
$34$	−0.233588	+	0.382683i	−0.0400601	+	0.0656297i
$35$		0			0
$36$	−0.378680	−	0.736813i	−0.0631133	−	0.122802i
$37$			7.11529i			1.16975i	0.811124	+	0.584874i	$0.198856\pi$
$37$			7.11529i			1.16975i	−0.811124	+	0.584874i	$0.801144\pi$
$38$	2.15897	−	3.53701i	0.350232	−	0.573778i
$39$			7.11529i			1.13936i
$40$	−0.797521	+	10.8624i	−0.126099	+	1.71749i
$41$		−	1.39942i		−	0.218552i	−0.994011	−	0.109276i	$-0.965147\pi$
$41$		−	1.39942i		−	0.218552i	0.994011	−	0.109276i	$-0.0348533\pi$
$42$		0			0
$43$	5.41421			0.825660			0.412830	−	0.910808i	$-0.364540\pi$
$43$	5.41421			0.825660			0.412830	+	0.910808i	$0.364540\pi$
$44$	−3.87868	−	7.54691i	−0.584733	−	1.13774i
$45$	−1.59504			−0.237775
$46$	−2.17157	+	3.55765i	−0.320181	+	0.524546i
$47$	−7.70154			−1.12338			−0.561692	−	0.827346i	$-0.689850\pi$
$47$	−7.70154			−1.12338			−0.561692	+	0.827346i	$0.689850\pi$
$48$	6.00974	+	4.30237i	0.867432	+	0.620994i
$49$		0			0
$50$	11.8640	+	7.24171i	1.67782	+	1.02413i
$51$	0.585786			0.0820265
$52$	−3.52043	−	6.84984i	−0.488195	−	0.949902i
$53$		−	10.0625i		−	1.38220i	−0.722761	−	0.691099i	$-0.757127\pi$
$53$		−	10.0625i		−	1.38220i	0.722761	−	0.691099i	$-0.242873\pi$
$54$	3.52043	−	5.76745i	0.479069	−	0.784850i
$55$	−16.3374			−2.20294
$56$		0			0
$57$	−5.41421			−0.717130
$58$	2.17157	−	3.55765i	0.285141	−	0.467142i
$59$		−	0.131316i		−	0.0170959i	−0.999963	−	0.00854796i	$-0.997279\pi$
$59$		−	0.131316i		−	0.0170959i	0.999963	−	0.00854796i	$-0.00272093\pi$
$60$	12.6569	−	6.50490i	1.63399	−	0.839779i
$61$	−1.59504			−0.204224			−0.102112	−	0.994773i	$-0.532560\pi$
$61$	−1.59504			−0.204224			−0.102112	+	0.994773i	$0.532560\pi$
$62$	−2.72291	−	1.66205i	−0.345809	−	0.211081i
$63$		0			0
$64$	−7.91421	−	1.16843i	−0.989277	−	0.146053i
$65$	−14.8284			−1.83924
$66$	−5.77615	+	9.46297i	−0.710995	+	1.16481i
$67$	−2.00000			−0.244339			−0.122169	−	0.992509i	$-0.538985\pi$
$67$	−2.00000			−0.244339			−0.122169	+	0.992509i	$0.538985\pi$
$68$	−0.563932	+	0.289829i	−0.0683868	+	0.0351469i
$69$	5.44581			0.655599
$70$		0			0
$71$			15.9570i			1.89375i	0.321597	+	0.946877i	$0.395780\pi$
$71$			15.9570i			1.89375i	−0.321597	+	0.946877i	$0.604220\pi$
$72$	0.0857864	−	1.16843i	0.0101100	−	0.137701i
$73$		−	2.93015i		−	0.342948i	−0.985189	−	0.171474i	$-0.945147\pi$
$73$		−	2.93015i		−	0.342948i	0.985189	−	0.171474i	$-0.0548530\pi$
$74$	−5.24264	+	8.58892i	−0.609445	+	0.998442i
$75$		−	18.1606i		−	2.09700i
$76$	5.21222	−	2.67878i	0.597883	−	0.307278i
$77$		0			0
$78$	−5.24264	+	8.58892i	−0.593612	+	0.972504i
$79$		−	5.89450i		−	0.663183i	−0.943423	−	0.331592i	$-0.892414\pi$
$79$		−	5.89450i		−	0.663183i	0.943423	−	0.331592i	$-0.107586\pi$
$80$	−8.96624	+	12.5244i	−1.00246	+	1.40027i
$81$	−10.0711			−1.11901
$82$	1.03111	−	1.68925i	0.113867	−	0.186546i
$83$		−	3.82683i		−	0.420050i	−0.977696	−	0.210025i	$-0.932646\pi$
$83$		−	3.82683i		−	0.420050i	0.977696	−	0.210025i	$-0.0673545\pi$
$84$		0			0
$85$			1.22079i			0.132413i
$86$	6.53553	+	3.98926i	0.704745	+	0.430173i
$87$	−5.44581			−0.583852
$88$	0.878680	−	11.9678i	0.0936676	−	1.27577i
$89$			9.68714i			1.02683i	0.858139	+	0.513417i	$0.171621\pi$
$89$			9.68714i			1.02683i	−0.858139	+	0.513417i	$0.828379\pi$
$90$	−1.92538	−	1.17525i	−0.202953	−	0.123882i
$91$		0			0
$92$	−5.24264	+	2.69442i	−0.546583	+	0.280912i
$93$			4.16804i			0.432206i
$94$	−9.29658	−	5.67459i	−0.958869	−	0.585290i
$95$		−	11.2833i		−	1.15765i
$96$	4.08436	+	9.62148i	0.416858	+	0.981988i
$97$			16.6298i			1.68850i	0.535947	+	0.844252i	$0.319955\pi$
$97$			16.6298i			1.68850i	−0.535947	+	0.844252i	$0.680045\pi$
$98$		0			0
$99$	1.75736			0.176621
$100$	8.98528	+	17.4830i	0.898528	+	1.74830i
$101$	−7.04085			−0.700591			−0.350295	−	0.936639i	$-0.613919\pi$
$101$	−7.04085			−0.700591			−0.350295	+	0.936639i	$0.613919\pi$
$102$	0.707107	+	0.431615i	0.0700140	+	0.0427363i
$103$	5.44581			0.536592			0.268296	−	0.963337i	$-0.413540\pi$
$103$	5.44581			0.536592			0.268296	+	0.963337i	$0.413540\pi$
$104$	0.797521	−	10.8624i	0.0782033	−	1.06514i
$105$		0			0
$106$	7.41421	−	12.1466i	0.720132	−	1.17978i
$107$	19.3137			1.86713			0.933563	−	0.358412i	$-0.116682\pi$
$107$	19.3137			1.86713			0.933563	+	0.358412i	$0.116682\pi$
$108$	8.49906	−	4.36803i	0.817822	−	0.420314i
$109$		−	2.94725i		−	0.282295i	−0.989989	−	0.141148i	$-0.954921\pi$
$109$		−	2.94725i		−	0.282295i	0.989989	−	0.141148i	$-0.0450793\pi$
$110$	−19.7210	−	12.0376i	−1.88033	−	1.14774i
$111$	13.1474			1.24789
$112$		0			0
$113$	1.41421			0.133038			0.0665190	−	0.997785i	$-0.478811\pi$
$113$	1.41421			0.133038			0.0665190	+	0.997785i	$0.478811\pi$
$114$	−6.53553	−	3.98926i	−0.612109	−	0.373629i
$115$			11.3492i			1.05832i
$116$	5.24264	−	2.69442i	0.486767	−	0.250170i
$117$	1.59504			0.147462
$118$	0.0967555	−	0.158513i	0.00890706	−	0.0145923i
$119$		0			0
$120$	20.0711	+	1.47363i	1.83223	+	0.134523i
$121$	7.00000			0.636364
$122$	−1.92538	−	1.17525i	−0.174316	−	0.106402i
$123$	−2.58579			−0.233153
$124$	−2.06222	−	4.01254i	−0.185193	−	0.360337i
$125$	18.5932			1.66302
$126$		0			0
$127$		−	17.1778i		−	1.52429i	−0.647408	−	0.762143i	$-0.724147\pi$
$127$		−	17.1778i		−	1.52429i	0.647408	−	0.762143i	$-0.275853\pi$
$128$	−8.69239	−	7.24171i	−0.768306	−	0.640083i
$129$		−	10.0042i		−	0.880817i
$130$	−17.8995	−	10.9258i	−1.56989	−	0.958254i
$131$			16.6298i			1.45296i	0.687190	+	0.726478i	$0.258844\pi$
$131$			16.6298i			1.45296i	−0.687190	+	0.726478i	$0.741156\pi$
$132$	−13.9449	+	7.16687i	−1.21375	+	0.623796i
$133$		0			0
$134$	−2.41421	−	1.47363i	−0.208556	−	0.127302i
$135$		−	18.3986i		−	1.58350i
$136$	−0.894276	−	0.0656581i	−0.0766835	−	0.00563014i
$137$	11.5563			0.987326			0.493663	−	0.869653i	$-0.335658\pi$
$137$	11.5563			0.987326			0.493663	+	0.869653i	$0.335658\pi$
$138$	6.57368	+	4.01254i	0.559588	+	0.341570i
$139$		−	14.4650i		−	1.22691i	−0.789730	−	0.613455i	$-0.789779\pi$
$139$		−	14.4650i		−	1.22691i	0.789730	−	0.613455i	$-0.210221\pi$
$140$		0			0
$141$			14.2306i			1.19843i
$142$	−11.7574	+	19.2619i	−0.986656	+	1.61642i
$143$	16.3374			1.36620
$144$	0.964466	−	1.34721i	0.0803722	−	0.112267i
$145$		−	11.3492i		−	0.942499i
$146$	2.15897	−	3.53701i	0.178678	−	0.292725i
$147$		0			0
$148$	−12.6569	+	6.50490i	−1.04039	+	0.534699i
$149$		−	14.2306i		−	1.16582i	−0.812538	−	0.582908i	$-0.801915\pi$
$149$		−	14.2306i		−	1.16582i	0.812538	−	0.582908i	$-0.198085\pi$
$150$	13.3809	−	21.9217i	1.09255	−	1.78990i
$151$			11.2833i			0.918225i	0.888378	+	0.459112i	$0.151833\pi$
$151$			11.2833i			0.918225i	−0.888378	+	0.459112i	$0.848167\pi$
$152$	8.26547	+	0.606854i	0.670418	+	0.0492224i
$153$		−	0.131316i		−	0.0106163i
$154$		0			0
$155$	−8.68629			−0.697700
$156$	−12.6569	+	6.50490i	−1.01336	+	0.520809i
$157$	1.59504			0.127298			0.0636491	−	0.997972i	$-0.479726\pi$
$157$	1.59504			0.127298			0.0636491	+	0.997972i	$0.479726\pi$
$158$	4.34315	−	7.11529i	0.345522	−	0.566062i
$159$	−18.5932			−1.47453
$160$	−20.0514	+	8.51189i	−1.58520	+	0.672924i
$161$		0			0
$162$	−12.1569	−	7.42049i	−0.955133	−	0.583009i
$163$	−2.58579			−0.202534			−0.101267	−	0.994859i	$-0.532290\pi$
$163$	−2.58579			−0.202534			−0.101267	+	0.994859i	$0.532290\pi$
$164$	2.48932	−	1.27937i	0.194383	−	0.0999017i
$165$			30.1876i			2.35010i
$166$	2.81966	−	4.61940i	0.218848	−	0.358535i
$167$	10.8916			0.842819			0.421409	−	0.906870i	$-0.361536\pi$
$167$	10.8916			0.842819			0.421409	+	0.906870i	$0.361536\pi$
$168$		0			0
$169$	1.82843			0.140648
$170$	−0.899495	+	1.47363i	−0.0689881	+	0.113022i
$171$			1.21371i			0.0928146i
$172$	4.94975	+	9.63093i	0.377415	+	0.734352i
$173$	20.1882			1.53488			0.767440	−	0.641120i	$-0.221530\pi$
$173$	20.1882			1.53488			0.767440	+	0.641120i	$0.221530\pi$
$174$	−6.57368	−	4.01254i	−0.498349	−	0.304190i
$175$		0			0
$176$	9.87868	−	13.7990i	0.744633	−	1.04014i
$177$	−0.242641			−0.0182380
$178$	−7.13761	+	11.6934i	−0.534986	+	0.876458i
$179$	13.6569			1.02076			0.510381	−	0.859949i	$-0.329505\pi$
$179$	13.6569			1.02076			0.510381	+	0.859949i	$0.329505\pi$
$180$	−1.45821	−	2.83730i	−0.108688	−	0.211480i
$181$	−11.5523			−0.858676			−0.429338	−	0.903144i	$-0.641253\pi$
$181$	−11.5523			−0.858676			−0.429338	+	0.903144i	$0.641253\pi$
$182$		0			0
$183$			2.94725i			0.217867i
$184$	−8.31371	−	0.610396i	−0.612895	−	0.0449990i
$185$			27.3994i			2.01444i
$186$	−3.07107	+	5.03127i	−0.225182	+	0.368911i
$187$		−	1.34502i		−	0.0983579i
$188$	−7.04085	−	13.6997i	−0.513507	−	0.999152i
$189$		0			0
$190$	8.31371	−	13.6202i	0.603140	−	0.988113i
$191$			10.0625i			0.728100i	0.931379	+	0.364050i	$0.118606\pi$
$191$			10.0625i			0.728100i	−0.931379	+	0.364050i	$0.881394\pi$
$192$	−2.15897	+	14.6236i	−0.155810	+	1.05536i
$193$	−6.58579			−0.474055			−0.237028	−	0.971503i	$-0.576173\pi$
$193$	−6.58579			−0.474055			−0.237028	+	0.971503i	$0.576173\pi$
$194$	−12.2531	+	20.0740i	−0.879719	+	1.44123i
$195$			27.3994i			1.96211i
$196$		0			0
$197$			1.72646i			0.123005i	0.998107	+	0.0615026i	$0.0195892\pi$
$197$			1.72646i			0.123005i	−0.998107	+	0.0615026i	$0.980411\pi$
$198$	2.12132	+	1.29484i	0.150756	+	0.0920206i
$199$	9.95727			0.705852			0.352926	−	0.935651i	$-0.385187\pi$
$199$	9.95727			0.705852			0.352926	+	0.935651i	$0.385187\pi$
$200$	−2.03553	+	27.7244i	−0.143934	+	1.96041i
$201$			3.69552i			0.260662i
$202$	−8.49906	−	5.18779i	−0.597992	−	0.365012i
$203$		0			0
$204$	0.535534	+	1.04201i	0.0374949	+	0.0729553i
$205$		−	5.38883i		−	0.376373i
$206$	6.57368	+	4.01254i	0.458010	+	0.279567i
$207$		−	1.22079i		−	0.0848509i
$208$	8.96624	−	12.5244i	0.621697	−	0.868413i
$209$			12.4316i			0.859910i
$210$		0			0
$211$	−14.9706			−1.03062			−0.515308	−	0.857005i	$-0.672322\pi$
$211$	−14.9706			−1.03062			−0.515308	+	0.857005i	$0.672322\pi$
$212$	17.8995	−	9.19932i	1.22934	−	0.631812i
$213$	29.4848			2.02026
$214$	23.3137	+	14.2306i	1.59369	+	0.972783i
$215$	20.8489			1.42188
$216$	13.4777	+	0.989538i	0.917041	+	0.0673295i
$217$		0			0
$218$	2.17157	−	3.55765i	0.147077	−	0.240954i
$219$	−5.41421			−0.365859
$220$	−14.9359	−	29.0614i	−1.00698	−	1.95932i
$221$		−	1.22079i		−	0.0821193i
$222$	15.8703	+	9.68714i	1.06514	+	0.650158i
$223$	5.44581			0.364678			0.182339	−	0.983236i	$-0.441633\pi$
$223$	5.44581			0.364678			0.182339	+	0.983236i	$0.441633\pi$
$224$		0			0
$225$	−4.07107			−0.271405
$226$	1.70711	+	1.04201i	0.113555	+	0.0693135i
$227$		−	21.8561i		−	1.45064i	−0.688412	−	0.725320i	$-0.741692\pi$
$227$		−	21.8561i		−	1.45064i	0.688412	−	0.725320i	$-0.258308\pi$
$228$	−4.94975	−	9.63093i	−0.327805	−	0.637824i
$229$	−23.3783			−1.54488			−0.772440	−	0.635087i	$-0.780964\pi$
$229$	−23.3783			−1.54488			−0.772440	+	0.635087i	$0.780964\pi$
$230$	−8.36223	+	13.6997i	−0.551389	+	0.903330i
$231$		0			0
$232$	8.31371	+	0.610396i	0.545822	+	0.0400744i
$233$	9.89949			0.648537			0.324269	−	0.945965i	$-0.394882\pi$
$233$	9.89949			0.648537			0.324269	+	0.945965i	$0.394882\pi$
$234$	1.92538	+	1.17525i	0.125866	+	0.0768283i
$235$	−29.6569			−1.93460
$236$	0.233588	−	0.120051i	0.0152053	−	0.00781466i
$237$	−10.8916			−0.707487
$238$		0			0
$239$			15.4514i			0.999467i	0.866179	+	0.499733i	$0.166569\pi$
$239$			15.4514i			0.999467i	−0.866179	+	0.499733i	$0.833431\pi$
$240$	23.1421	+	16.5674i	1.49382	+	1.06942i
$241$		−	18.3463i		−	1.18179i	−0.806749	−	0.590894i	$-0.798775\pi$
$241$		−	18.3463i		−	1.18179i	0.806749	−	0.590894i	$-0.201225\pi$
$242$	8.44975	+	5.15769i	0.543170	+	0.331549i
$243$			4.27518i			0.274253i
$244$	−1.45821	−	2.83730i	−0.0933522	−	0.181639i
$245$		0			0
$246$	−3.12132	−	1.90524i	−0.199008	−	0.121474i
$247$			11.2833i			0.717942i
$248$	0.467177	−	6.36304i	0.0296658	−	0.404053i
$249$	−7.07107			−0.448111
$250$	22.4439	+	13.6997i	1.41948	+	0.866444i
$251$			11.0322i			0.696344i	0.937431	+	0.348172i	$0.113197\pi$
$251$			11.0322i			0.696344i	−0.937431	+	0.348172i	$0.886803\pi$
$252$		0			0
$253$		−	12.5041i		−	0.786128i
$254$	12.6569	−	20.7355i	0.794162	−	1.30106i
$255$	2.25573			0.141259
$256$	−5.15685	−	15.1462i	−0.322303	−	0.946636i
$257$		−	15.3617i		−	0.958238i	−0.877750	−	0.479119i	$-0.840956\pi$
$257$		−	15.3617i		−	0.958238i	0.877750	−	0.479119i	$-0.159044\pi$
$258$	7.37120	−	12.0761i	0.458911	−	0.751825i
$259$		0			0
$260$	−13.5563	−	26.3772i	−0.840729	−	1.63584i
$261$			1.22079i			0.0755651i
$262$	−12.2531	+	20.0740i	−0.756997	+	1.24017i
$263$		0			0		1.00000			$0$
$263$		0			0		−1.00000			$\pi$
$264$	−22.1136	−	1.62359i	−1.36100	−	0.0999250i
$265$		−	38.7485i		−	2.38030i
$266$		0			0
$267$	17.8995			1.09543
$268$	−1.82843	−	3.55765i	−0.111689	−	0.217318i
$269$	14.7424			0.898859			0.449430	−	0.893316i	$-0.351627\pi$
$269$	14.7424			0.898859			0.449430	+	0.893316i	$0.351627\pi$
$270$	13.5563	−	22.2091i	0.825013	−	1.35160i
$271$	13.1474			0.798645			0.399322	−	0.916811i	$-0.369245\pi$
$271$	13.1474			0.798645			0.399322	+	0.916811i	$0.369245\pi$
$272$	−1.03111	−	0.738170i	−0.0625202	−	0.0447582i
$273$		0			0
$274$	13.9497	+	8.51487i	0.842735	+	0.514402i
$275$	−41.6985			−2.51451
$276$	4.97863	+	9.68714i	0.299679	+	0.583097i
$277$		−	30.1876i		−	1.81380i	−0.421347	−	0.906900i	$-0.638442\pi$
$277$		−	30.1876i		−	1.81380i	0.421347	−	0.906900i	$-0.361558\pi$
$278$	10.6580	−	17.4609i	0.639226	−	1.04723i
$279$	0.934353			0.0559383
$280$		0			0
$281$	3.07107			0.183205			0.0916023	−	0.995796i	$-0.470801\pi$
$281$	3.07107			0.183205			0.0916023	+	0.995796i	$0.470801\pi$
$282$	−10.4853	+	17.1778i	−0.624389	+	1.02293i
$283$			15.2848i			0.908587i	0.890852	+	0.454294i	$0.150108\pi$
$283$			15.2848i			0.908587i	−0.890852	+	0.454294i	$0.849892\pi$
$284$	−28.3848	+	14.5882i	−1.68433	+	0.865647i
$285$	−20.8489			−1.23498
$286$	19.7210	+	12.0376i	1.16613	+	0.711800i
$287$		0			0
$288$	2.15685	−	0.915594i	0.127094	−	0.0539519i
$289$	16.8995			0.994088
$290$	8.36223	−	13.6997i	0.491047	−	0.804473i
$291$	30.7279			1.80130
$292$	5.21222	−	2.67878i	0.305022	−	0.156764i
$293$	16.0638			0.938455			0.469228	−	0.883077i	$-0.344532\pi$
$293$	16.0638			0.938455			0.469228	+	0.883077i	$0.344532\pi$
$294$		0			0
$295$		−	0.505668i		−	0.0294412i
$296$	−20.0711	−	1.47363i	−1.16661	−	0.0856528i
$297$			20.2710i			1.17624i
$298$	10.4853	−	17.1778i	0.607396	−	0.995086i
$299$		−	11.3492i		−	0.656340i
$300$	32.3044	−	16.6026i	1.86510	−	0.958554i
$301$		0			0
$302$	−8.31371	+	13.6202i	−0.478400	+	0.783754i
$303$			13.0098i			0.747393i
$304$	9.53017	+	6.82264i	0.546593	+	0.391305i
$305$	−6.14214			−0.351698
$306$	0.0967555	−	0.158513i	0.00553114	−	0.00906157i
$307$			14.2024i			0.810575i	0.914189	+	0.405287i	$0.132829\pi$
$307$			14.2024i			0.810575i	−0.914189	+	0.405287i	$0.867171\pi$
$308$		0			0
$309$		−	10.0625i		−	0.572438i
$310$	−10.4853	−	6.40017i	−0.595524	−	0.363505i
$311$	−26.2947			−1.49104			−0.745518	−	0.666486i	$-0.767798\pi$
$311$	−26.2947			−1.49104			−0.745518	+	0.666486i	$0.767798\pi$
$312$	−20.0711	−	1.47363i	−1.13630	−	0.0834276i
$313$		−	15.9189i		−	0.899787i	−0.893082	−	0.449894i	$-0.851462\pi$
$313$		−	15.9189i		−	0.899787i	0.893082	−	0.449894i	$-0.148538\pi$
$314$	1.92538	+	1.17525i	0.108656	+	0.0663230i
$315$		0			0
$316$	10.4853	−	5.38883i	0.589843	−	0.303146i
$317$			8.33609i			0.468201i	0.972212	+	0.234101i	$0.0752145\pi$
$317$			8.33609i			0.468201i	−0.972212	+	0.234101i	$0.924785\pi$
$318$	−22.4439	−	13.6997i	−1.25859	−	0.768240i
$319$			12.5041i			0.700097i
$320$	−30.4758	−	4.49935i	−1.70365	−	0.251521i
$321$		−	35.6871i		−	1.99186i
$322$		0			0
$323$	0.928932			0.0516872
$324$	−9.20711	−	17.9147i	−0.511506	−	0.995259i
$325$	−37.8470			−2.09937
$326$	−3.12132	−	1.90524i	−0.172874	−	0.105522i
$327$	−5.44581			−0.301154
$328$	3.94753	+	0.289829i	0.217966	+	0.0160031i
$329$		0			0
$330$	−22.2426	+	36.4397i	−1.22442	+	2.00594i
$331$	11.0711			0.608521			0.304260	−	0.952589i	$-0.401591\pi$
$331$	11.0711			0.608521			0.304260	+	0.952589i	$0.401591\pi$
$332$	6.80726	−	3.49854i	0.373597	−	0.192008i
$333$		−	2.94725i		−	0.161508i
$334$	13.1474	+	8.02509i	0.719391	+	0.439113i
$335$	−7.70154			−0.420780
$336$		0			0
$337$	−14.1421			−0.770371			−0.385186	−	0.922839i	$-0.625863\pi$
$337$	−14.1421			−0.770371			−0.385186	+	0.922839i	$0.625863\pi$
$338$	2.20711	+	1.34721i	0.120051	+	0.0732785i
$339$		−	2.61313i		−	0.141926i
$340$	−2.17157	+	1.11606i	−0.117770	+	0.0605271i
$341$	9.57025			0.518258
$342$	−0.894276	+	1.46508i	−0.0483569	+	0.0792222i
$343$		0			0
$344$	−1.12132	+	15.2726i	−0.0604575	+	0.823443i
$345$	20.9706			1.12902
$346$	24.3693	+	14.8749i	1.31010	+	0.799681i
$347$	12.2426			0.657219			0.328610	−	0.944466i	$-0.393420\pi$
$347$	12.2426			0.657219			0.328610	+	0.944466i	$0.393420\pi$
$348$	−4.97863	−	9.68714i	−0.266883	−	0.519285i
$349$	−14.7424			−0.789142			−0.394571	−	0.918865i	$-0.629107\pi$
$349$	−14.7424			−0.789142			−0.394571	+	0.918865i	$0.629107\pi$
$350$		0			0
$351$			18.3986i			0.982046i
$352$	22.0919	−	9.37810i	1.17750	−	0.499854i
$353$		−	4.72352i		−	0.251407i	−0.992068	−	0.125704i	$-0.959881\pi$
$353$		−	4.72352i		−	0.251407i	0.992068	−	0.125704i	$-0.0401189\pi$
$354$	−0.292893	−	0.178781i	−0.0155671	−	0.00950209i
$355$			61.4469i			3.26126i
$356$	−17.2317	+	8.85611i	−0.913279	+	0.469373i
$357$		0			0
$358$	16.4853	+	10.0625i	0.871274	+	0.531822i
$359$			15.4514i			0.815493i	0.913095	+	0.407746i	$0.133685\pi$
$359$			15.4514i			0.815493i	−0.913095	+	0.407746i	$0.866315\pi$
$360$	0.330344	−	4.49935i	0.0174106	−	0.237136i
$361$	10.4142			0.548117
$362$	−13.9449	−	8.51189i	−0.732926	−	0.447375i
$363$		−	12.9343i		−	0.678875i
$364$		0			0
$365$		−	11.2833i		−	0.590597i
$366$	−2.17157	+	3.55765i	−0.113510	+	0.185961i
$367$	−30.4191			−1.58787			−0.793933	−	0.608005i	$-0.791970\pi$
$367$	−30.4191			−1.58787			−0.793933	+	0.608005i	$0.791970\pi$
$368$	−9.58579	−	6.86246i	−0.499694	−	0.357730i
$369$			0.579658i			0.0301758i
$370$	−20.1882	+	33.0740i	−1.04953	+	1.71943i
$371$		0			0
$372$	−7.41421	+	3.81048i	−0.384409	+	0.197564i
$373$		−	16.6722i		−	0.863252i	−0.902053	−	0.431626i	$-0.857940\pi$
$373$		−	16.6722i		−	0.863252i	0.902053	−	0.431626i	$-0.142060\pi$
$374$	0.991031	−	1.62359i	0.0512450	−	0.0839538i
$375$		−	34.3557i		−	1.77412i
$376$	1.59504	−	21.7248i	0.0822580	−	1.12037i
$377$			11.3492i			0.584513i
$378$		0			0
$379$	10.3848			0.533430			0.266715	−	0.963775i	$-0.414062\pi$
$379$	10.3848			0.533430			0.266715	+	0.963775i	$0.414062\pi$
$380$	20.0711	−	10.3154i	1.02962	−	0.529168i
$381$	−31.7405			−1.62612
$382$	−7.41421	+	12.1466i	−0.379344	+	0.621472i
$383$	33.9962			1.73713			0.868563	−	0.495578i	$-0.165044\pi$
$383$	33.9962			1.73713			0.868563	+	0.495578i	$0.165044\pi$
$384$	−13.3809	+	16.0614i	−0.682843	+	0.819632i
$385$		0			0
$386$	−7.94975	−	4.85249i	−0.404631	−	0.246985i
$387$	−2.24264			−0.114000
$388$	−29.5815	+	15.2032i	−1.50178	+	0.771826i
$389$			17.1778i			0.870951i	0.900201	+	0.435476i	$0.143420\pi$
$389$			17.1778i			0.870951i	−0.900201	+	0.435476i	$0.856580\pi$
$390$	−20.1882	+	33.0740i	−1.02227	+	1.67476i
$391$	−0.934353			−0.0472523
$392$		0			0
$393$	30.7279			1.55002
$394$	−1.27208	+	2.08402i	−0.0640864	+	0.104991i
$395$		−	22.6984i		−	1.14208i
$396$	1.60660	+	3.12603i	0.0807348	+	0.157089i
$397$	−27.8897			−1.39975			−0.699873	−	0.714267i	$-0.746760\pi$
$397$	−27.8897			−1.39975			−0.699873	+	0.714267i	$0.746760\pi$
$398$	12.0195	+	7.33664i	0.602482	+	0.367753i
$399$		0			0
$400$	−22.8848	+	31.9665i	−1.14424	+	1.59832i
$401$	−12.1421			−0.606349			−0.303175	−	0.952935i	$-0.598047\pi$
$401$	−12.1421			−0.606349			−0.303175	+	0.952935i	$0.598047\pi$
$402$	−2.72291	+	4.46088i	−0.135806	+	0.222489i
$403$	8.68629			0.432695
$404$	−6.43684	−	12.5244i	−0.320245	−	0.623114i
$405$	−38.7814			−1.92706
$406$		0			0
$407$		−	30.1876i		−	1.49635i
$408$	−0.121320	+	1.65241i	−0.00600625	+	0.0818063i
$409$		−	21.4847i		−	1.06235i	−0.847263	−	0.531174i	$-0.821751\pi$
$409$		−	21.4847i		−	1.06235i	0.847263	−	0.531174i	$-0.178249\pi$
$410$	3.97056	−	6.50490i	0.196092	−	0.321254i
$411$		−	21.3533i		−	1.05328i
$412$	4.97863	+	9.68714i	0.245280	+	0.477251i
$413$		0			0
$414$	0.899495	−	1.47363i	0.0442078	−	0.0724248i
$415$		−	14.7363i		−	0.723374i
$416$	20.0514	−	8.51189i	0.983099	−	0.417330i
$417$	−26.7279			−1.30887
$418$	−9.15975	+	15.0062i	−0.448018	+	0.733979i
$419$			9.94977i			0.486078i	0.970017	+	0.243039i	$0.0781443\pi$
$419$			9.94977i			0.486078i	−0.970017	+	0.243039i	$0.921856\pi$
$420$		0			0
$421$			7.62096i			0.371423i	0.982604	+	0.185712i	$0.0594590\pi$
$421$			7.62096i			0.371423i	−0.982604	+	0.185712i	$0.940541\pi$
$422$	−18.0711	−	11.0305i	−0.879686	−	0.536957i
$423$	3.19008			0.155107
$424$	28.3848	+	2.08402i	1.37849	+	0.101209i
$425$			3.11586i			0.151141i
$426$	35.5913	+	21.7248i	1.72440	+	1.05257i
$427$		0			0
$428$	17.6569	+	34.3557i	0.853476	+	1.66064i
$429$		−	30.1876i		−	1.45747i
$430$	25.1668	+	15.3617i	1.21365	+	0.740808i
$431$		−	18.9043i		−	0.910588i	−0.890341	−	0.455294i	$-0.849534\pi$
$431$		−	18.9043i		−	0.910588i	0.890341	−	0.455294i	$-0.150466\pi$
$432$	15.5399	+	11.1250i	0.747664	+	0.535253i
$433$			18.1606i			0.872741i	0.899767	+	0.436371i	$0.143736\pi$
$433$			18.1606i			0.872741i	−0.899767	+	0.436371i	$0.856264\pi$
$434$		0			0
$435$	−20.9706			−1.00546
$436$	5.24264	−	2.69442i	0.251077	−	0.129039i
$437$	8.63589			0.413111
$438$	−6.53553	−	3.98926i	−0.312280	−	0.190614i
$439$	−39.4421			−1.88247			−0.941233	−	0.337757i	$-0.890332\pi$
$439$	−39.4421			−1.88247			−0.941233	+	0.337757i	$0.890332\pi$
$440$	3.38359	−	46.0852i	0.161306	−	2.19703i
$441$		0			0
$442$	0.899495	−	1.47363i	0.0427846	−	0.0700932i
$443$	−1.02944			−0.0489100			−0.0244550	−	0.999701i	$-0.507785\pi$
$443$	−1.02944			−0.0489100			−0.0244550	+	0.999701i	$0.507785\pi$
$444$	12.0195	+	23.3868i	0.570420	+	1.10989i
$445$			37.3029i			1.76833i
$446$	6.57368	+	4.01254i	0.311273	+	0.189999i
$447$	−26.2947			−1.24370
$448$		0			0
$449$	36.2843			1.71236			0.856180	−	0.516677i	$-0.172831\pi$
$449$	36.2843			1.71236			0.856180	+	0.516677i	$0.172831\pi$
$450$	−4.91421	−	2.99962i	−0.231658	−	0.141403i
$451$			5.93723i			0.279573i
$452$	1.29289	+	2.51564i	0.0608126	+	0.118326i
$453$	20.8489			0.979566
$454$	16.1038	−	26.3826i	0.755791	−	1.23820i
$455$		0			0
$456$	1.12132	−	15.2726i	0.0525106	−	0.715205i
$457$	−24.0416			−1.12462			−0.562310	−	0.826927i	$-0.690087\pi$
$457$	−24.0416			−1.12462			−0.562310	+	0.826927i	$0.690087\pi$
$458$	−28.2201	−	17.2254i	−1.31864	−	0.804891i
$459$	1.51472			0.0707010
$460$	−20.1882	+	10.3756i	−0.941280	+	0.483764i
$461$	−25.6340			−1.19389			−0.596947	−	0.802280i	$-0.703620\pi$
$461$	−25.6340			−1.19389			−0.596947	+	0.802280i	$0.703620\pi$
$462$		0			0
$463$		−	12.5041i		−	0.581116i	−0.956857	−	0.290558i	$-0.906159\pi$
$463$		−	12.5041i		−	0.581116i	0.956857	−	0.290558i	$-0.0938409\pi$
$464$	9.58579	+	6.86246i	0.445009	+	0.318582i
$465$			16.0502i			0.744309i
$466$	11.9497	+	7.29408i	0.553561	+	0.337892i
$467$			23.8352i			1.10296i	0.834188	+	0.551480i	$0.185937\pi$
$467$			23.8352i			1.10296i	−0.834188	+	0.551480i	$0.814063\pi$
$468$	1.45821	+	2.83730i	0.0674057	+	0.131154i
$469$		0			0
$470$	−35.7990	−	21.8516i	−1.65128	−	1.00794i
$471$		−	2.94725i		−	0.135802i
$472$	0.370421	+	0.0271965i	0.0170500	+	0.00125182i
$473$	−22.9706			−1.05619
$474$	−13.1474	−	8.02509i	−0.603878	−	0.368604i
$475$		−	28.7988i		−	1.32138i
$476$		0			0
$477$			4.16804i			0.190842i
$478$	−11.3848	+	18.6515i	−0.520728	+	0.853098i
$479$	−8.63589			−0.394584			−0.197292	−	0.980345i	$-0.563215\pi$
$479$	−8.63589			−0.394584			−0.197292	+	0.980345i	$0.563215\pi$
$480$	15.7279	+	37.0501i	0.717878	+	1.69110i
$481$		−	27.3994i		−	1.24930i
$482$	13.5178	−	22.1459i	0.615718	−	1.00872i
$483$		0			0
$484$	6.39949	+	12.4518i	0.290886	+	0.565989i
$485$			64.0377i			2.90780i
$486$	−3.15000	+	5.16059i	−0.142887	+	0.234089i
$487$		−	23.7875i		−	1.07791i	−0.842334	−	0.538957i	$-0.818819\pi$
$487$		−	23.7875i		−	1.07791i	0.842334	−	0.538957i	$-0.181181\pi$
$488$	0.330344	−	4.49935i	0.0149540	−	0.203676i
$489$			4.77791i			0.216065i
$490$		0			0
$491$	−26.0000			−1.17336			−0.586682	−	0.809818i	$-0.699566\pi$
$491$	−26.0000			−1.17336			−0.586682	+	0.809818i	$0.699566\pi$
$492$	−2.36396	−	4.59966i	−0.106576	−	0.207369i
$493$	0.934353			0.0420812
$494$	−8.31371	+	13.6202i	−0.374051	+	0.612801i
$495$	6.76719			0.304162
$496$	5.25230	−	7.33664i	0.235835	−	0.329425i
$497$		0			0
$498$	−8.53553	−	5.21005i	−0.382486	−	0.233468i
$499$	−40.6274			−1.81873			−0.909366	−	0.415996i	$-0.863433\pi$
$499$	−40.6274			−1.81873			−0.909366	+	0.415996i	$0.863433\pi$
$500$	16.9981	+	33.0740i	0.760179	+	1.47911i
$501$		−	20.1251i		−	0.899123i
$502$	−8.12864	+	13.3170i	−0.362799	+	0.594367i
$503$	34.9306			1.55748			0.778739	−	0.627348i	$-0.215860\pi$
$503$	34.9306			1.55748			0.778739	+	0.627348i	$0.215860\pi$
$504$		0			0
$505$	−27.1127			−1.20650
$506$	9.21320	−	15.0938i	0.409577	−	0.671002i
$507$		−	3.37849i		−	0.150044i
$508$	30.5563	−	15.7042i	1.35572	−	0.696762i
$509$	6.10650			0.270666			0.135333	−	0.990800i	$-0.456790\pi$
$509$	6.10650			0.270666			0.135333	+	0.990800i	$0.456790\pi$
$510$	2.72291	+	1.66205i	0.120572	+	0.0735968i
$511$		0			0
$512$	4.93503	−	22.0827i	0.218100	−	0.975927i
$513$	−14.0000			−0.618115
$514$	11.3187	−	18.5432i	0.499247	−	0.817908i
$515$	20.9706			0.924073
$516$	17.7956	−	9.14594i	0.783409	−	0.402628i
$517$	32.6749			1.43704
$518$		0			0
$519$		−	37.3029i		−	1.63742i
$520$	3.07107	−	41.8285i	0.134675	−	1.83430i
$521$		−	45.5599i		−	1.99602i	−0.0630828	−	0.998008i	$-0.520093\pi$
$521$		−	45.5599i		−	1.99602i	0.0630828	−	0.998008i	$-0.479907\pi$
$522$	−0.899495	+	1.47363i	−0.0393698	+	0.0644988i
$523$		−	4.01254i		−	0.175456i	−0.996144	−	0.0877281i	$-0.972039\pi$
$523$		−	4.01254i		−	0.175456i	0.996144	−	0.0877281i	$-0.0279607\pi$
$524$	−29.5815	+	15.2032i	−1.29228	+	0.664156i
$525$		0			0
$526$		0			0
$527$		−	0.715123i		−	0.0311513i
$528$	−25.4972	−	18.2534i	−1.10962	−	0.794378i
$529$	14.3137			0.622335
$530$	28.5504	−	46.7736i	1.24015	−	2.03172i
$531$			0.0543929i			0.00236045i
$532$		0			0
$533$			5.38883i			0.233416i
$534$	21.6066	+	13.1886i	0.935009	+	0.570726i
$535$	74.3726			3.21541
$536$	0.414214	−	5.64167i	0.0178913	−	0.243683i
$537$		−	25.2346i		−	1.08895i
$538$	17.7956	+	10.8624i	0.767225	+	0.468311i
$539$		0			0
$540$	32.7279	−	16.8203i	1.40839	−	0.723830i
$541$			7.62096i			0.327651i	0.986489	+	0.163825i	$0.0523834\pi$
$541$			7.62096i			0.327651i	−0.986489	+	0.163825i	$0.947617\pi$
$542$	15.8703	+	9.68714i	0.681686	+	0.416098i
$543$			21.3459i			0.916040i
$544$	−0.700765	−	1.65078i	−0.0300451	−	0.0707768i
$545$		−	11.3492i		−	0.486146i
$546$		0			0
$547$	37.4142			1.59972			0.799858	−	0.600189i	$-0.204908\pi$
$547$	37.4142			1.59972			0.799858	+	0.600189i	$0.204908\pi$
$548$	10.5650	+	20.5567i	0.451313	+	0.878139i
$549$	0.660688			0.0281975
$550$	−50.3345	−	30.7240i	−2.14627	−	1.31007i
$551$	−8.63589			−0.367901
$552$	−1.12786	+	15.3617i	−0.0480051	+	0.653839i
$553$		0			0
$554$	22.2426	−	36.4397i	0.944999	−	1.54817i
$555$	50.6274			2.14901
$556$	25.7308	−	13.2241i	1.09123	−	0.560829i
$557$		−	7.62096i		−	0.322911i	−0.986880	−	0.161455i	$-0.948381\pi$
$557$		−	7.62096i		−	0.322911i	0.986880	−	0.161455i	$-0.0516188\pi$
$558$	1.12786	+	0.688444i	0.0477463	+	0.0291441i
$559$	−20.8489			−0.881814
$560$		0			0
$561$	−2.48528			−0.104929
$562$	3.70711	+	2.26280i	0.156375	+	0.0954506i
$563$			34.1020i			1.43723i	0.695410	+	0.718613i	$0.255223\pi$
$563$			34.1020i			1.43723i	−0.695410	+	0.718613i	$0.744777\pi$
$564$	−25.3137	+	13.0098i	−1.06590	+	0.547811i
$565$	5.44581			0.229107
$566$	−11.2620	+	18.4504i	−0.473379	+	0.775528i
$567$		0			0
$568$	−45.0122	−	3.30481i	−1.88867	−	0.138667i
$569$	13.1716			0.552181			0.276091	−	0.961132i	$-0.410961\pi$
$569$	13.1716			0.552181			0.276091	+	0.961132i	$0.410961\pi$
$570$	−25.1668	−	15.3617i	−1.05412	−	0.643432i
$571$	−34.3848			−1.43896			−0.719479	−	0.694514i	$-0.755619\pi$
$571$	−34.3848			−1.43896			−0.719479	+	0.694514i	$0.755619\pi$
$572$	14.9359	+	29.0614i	0.624501	+	1.21512i
$573$	18.5932			0.776740
$574$		0			0
$575$			28.9668i			1.20800i
$576$	3.27817	+	0.483979i	0.136591	+	0.0201658i
$577$			15.6244i			0.650451i	0.945637	+	0.325225i	$0.105440\pi$
$577$			15.6244i			0.650451i	−0.945637	+	0.325225i	$0.894560\pi$
$578$	20.3995	+	12.4518i	0.848507	+	0.517925i
$579$			12.1689i			0.505724i
$580$	20.1882	−	10.3756i	0.838269	−	0.430823i
$581$		0			0
$582$	37.0919	+	22.6407i	1.53751	+	0.938488i
$583$			42.6918i			1.76811i
$584$	8.26547	+	0.606854i	0.342028	+	0.0251118i
$585$	6.14214			0.253946
$586$	19.3907	+	11.8360i	0.801022	+	0.488940i
$587$		−	20.6968i		−	0.854247i	−0.904193	−	0.427124i	$-0.859527\pi$
$587$		−	20.6968i		−	0.854247i	0.904193	−	0.427124i	$-0.140473\pi$
$588$		0			0
$589$			6.60963i			0.272345i
$590$	0.372583	−	0.610396i	0.0153390	−	0.0251296i
$591$	3.19008			0.131222
$592$	−23.1421	−	16.5674i	−0.951136	−	0.680918i
$593$			42.5754i			1.74836i	0.485601	+	0.874181i	$0.338601\pi$
$593$			42.5754i			1.74836i	−0.485601	+	0.874181i	$0.661399\pi$
$594$	−14.9359	+	24.4692i	−0.612827	+	1.00398i
$595$		0			0
$596$	25.3137	−	13.0098i	1.03689	−	0.532902i
$597$		−	18.3986i		−	0.753006i
$598$	8.36223	−	13.6997i	0.341957	−	0.560222i
$599$			7.62096i			0.311384i	0.987806	+	0.155692i	$0.0497608\pi$
$599$			7.62096i			0.311384i	−0.987806	+	0.155692i	$0.950239\pi$
$600$	51.2279	+	3.76118i	2.09137	+	0.153549i
$601$			20.2166i			0.824651i	0.911037	+	0.412325i	$0.135283\pi$
$601$			20.2166i			0.824651i	−0.911037	+	0.412325i	$0.864717\pi$
$602$		0			0
$603$	0.828427			0.0337362
$604$	−20.0711	+	10.3154i	−0.816680	+	0.419727i
$605$	26.9554			1.09589
$606$	−9.58579	+	15.7042i	−0.389396	+	0.637940i
$607$	35.8649			1.45571			0.727857	−	0.685729i	$-0.240517\pi$
$607$	35.8649			1.45571			0.727857	+	0.685729i	$0.240517\pi$
$608$	6.47692	+	15.2576i	0.262674	+	0.618778i
$609$		0			0
$610$	−7.41421	−	4.52560i	−0.300193	−	0.183236i
$611$	29.6569			1.19979
$612$	0.233588	−	0.120051i	0.00944225	−	0.00485278i
$613$			30.6933i			1.23969i	0.784724	+	0.619845i	$0.212805\pi$
$613$			30.6933i			1.23969i	−0.784724	+	0.619845i	$0.787195\pi$
$614$	−10.4645	+	17.1438i	−0.422314	+	0.691869i
$615$	−9.95727			−0.401516
$616$		0			0
$617$	−23.1716			−0.932852			−0.466426	−	0.884560i	$-0.654459\pi$
$617$	−23.1716			−0.932852			−0.466426	+	0.884560i	$0.654459\pi$
$618$	7.41421	−	12.1466i	0.298243	−	0.488607i
$619$			28.3504i			1.13950i	0.821818	+	0.569750i	$0.192960\pi$
$619$			28.3504i			1.13950i	−0.821818	+	0.569750i	$0.807040\pi$
$620$	−7.94113	−	15.4514i	−0.318923	−	0.620542i
$621$	14.0817			0.565079
$622$	−31.7405	−	19.3743i	−1.27268	−	0.776838i
$623$		0			0
$624$	−23.1421	−	16.5674i	−0.926427	−	0.663229i
$625$	22.4558			0.898234
$626$	11.7292	−	19.2158i	0.468794	−	0.768016i
$627$	22.9706			0.917356
$628$	1.45821	+	2.83730i	0.0581888	+	0.113220i
$629$	−2.25573			−0.0899418
$630$		0			0
$631$			32.6292i			1.29895i	0.760383	+	0.649474i	$0.225011\pi$
$631$			32.6292i			1.29895i	−0.760383	+	0.649474i	$0.774989\pi$
$632$	16.6274	+	1.22079i	0.661403	+	0.0485605i
$633$			27.6620i			1.09947i
$634$	−6.14214	+	10.0625i	−0.243935	+	0.399635i
$635$		−	66.1479i		−	2.62500i
$636$	−16.9981	−	33.0740i	−0.674019	−	1.31147i
$637$		0			0
$638$	−9.21320	+	15.0938i	−0.364754	+	0.597570i
$639$		−	6.60963i		−	0.261473i
$640$	−33.4724	−	27.8862i	−1.32311	−	1.10230i
$641$	22.1421			0.874562			0.437281	−	0.899325i	$-0.355942\pi$
$641$	22.1421			0.874562			0.437281	+	0.899325i	$0.355942\pi$
$642$	26.2947	−	43.0781i	1.03777	−	1.70016i
$643$			25.0263i			0.986942i	0.869762	+	0.493471i	$0.164272\pi$
$643$			25.0263i			0.986942i	−0.869762	+	0.493471i	$0.835728\pi$
$644$		0			0
$645$		−	38.5237i		−	1.51687i
$646$	1.12132	+	0.684449i	0.0441178	+	0.0269293i
$647$	−33.0619			−1.29980			−0.649898	−	0.760021i	$-0.725189\pi$
$647$	−33.0619			−1.29980			−0.649898	+	0.760021i	$0.725189\pi$
$648$	2.08579	−	28.4088i	0.0819374	−	1.11600i
$649$			0.557127i			0.0218692i
$650$	−45.6854	−	27.8862i	−1.79193	−	1.09379i
$651$		0			0
$652$	−2.36396	−	4.59966i	−0.0925799	−	0.180137i
$653$			27.2404i			1.06600i	0.846116	+	0.532999i	$0.178935\pi$
$653$			27.2404i			1.06600i	−0.846116	+	0.532999i	$0.821065\pi$
$654$	−6.57368	−	4.01254i	−0.257051	−	0.156903i
$655$			64.0377i			2.50216i
$656$	4.55153	+	3.25844i	0.177708	+	0.127221i
$657$			1.21371i			0.0473513i
$658$		0			0
$659$	−33.6985			−1.31271			−0.656353	−	0.754454i	$-0.727902\pi$
$659$	−33.6985			−1.31271			−0.656353	+	0.754454i	$0.727902\pi$
$660$	−53.6985	+	27.5979i	−2.09021	+	1.07425i
$661$	13.8080			0.537070			0.268535	−	0.963270i	$-0.413460\pi$
$661$	13.8080			0.537070			0.268535	+	0.963270i	$0.413460\pi$
$662$	13.3640	+	8.15731i	0.519405	+	0.317043i
$663$	−2.25573			−0.0876052
$664$	10.7949	+	0.792563i	0.418922	+	0.0307574i
$665$		0			0
$666$	2.17157	−	3.55765i	0.0841467	−	0.137856i
$667$	8.68629			0.336335
$668$	9.95727	+	19.3743i	0.385258	+	0.749613i
$669$		−	10.0625i		−	0.389041i
$670$	−9.29658	−	5.67459i	−0.359158	−	0.219229i
$671$	6.76719			0.261244
$672$		0			0
$673$	−10.1005			−0.389346			−0.194673	−	0.980868i	$-0.562365\pi$
$673$	−10.1005			−0.389346			−0.194673	+	0.980868i	$0.562365\pi$
$674$	−17.0711	−	10.4201i	−0.657553	−	0.401368i
$675$		−	46.9593i		−	1.80747i
$676$	1.67157	+	3.25245i	0.0642913	+	0.125094i
$677$	−32.0142			−1.23040			−0.615202	−	0.788369i	$-0.710926\pi$
$677$	−32.0142			−1.23040			−0.615202	+	0.788369i	$0.710926\pi$
$678$	1.92538	−	3.15432i	0.0739440	−	0.121141i
$679$		0			0
$680$	−3.44365	−	0.252834i	−0.132058	−	0.00969575i
$681$	−40.3848			−1.54755
$682$	11.5523	+	7.05148i	0.442361	+	0.270015i
$683$	−17.0294			−0.651613			−0.325807	−	0.945436i	$-0.605636\pi$
$683$	−17.0294			−0.651613			−0.325807	+	0.945436i	$0.605636\pi$
$684$	−2.15897	+	1.10959i	−0.0825504	+	0.0424262i
$685$	44.5008			1.70029
$686$		0			0
$687$			43.1974i			1.64808i
$688$	−12.6066	+	17.6095i	−0.480622	+	0.671354i
$689$			38.7485i			1.47620i
$690$	25.3137	+	15.4514i	0.963676	+	0.588224i
$691$		−	31.9372i		−	1.21495i	−0.794340	−	0.607474i	$-0.792183\pi$
$691$		−	31.9372i		−	1.21495i	0.794340	−	0.607474i	$-0.207817\pi$
$692$	18.4563	+	35.9113i	0.701604	+	1.36514i
$693$		0			0
$694$	14.7782	+	9.02054i	0.560972	+	0.342415i
$695$		−	55.7016i		−	2.11288i
$696$	1.12786	−	15.3617i	0.0427516	−	0.582285i
$697$	0.443651			0.0168045
$698$	−17.7956	−	10.8624i	−0.673575	−	0.411147i
$699$		−	18.2919i		−	0.691862i
$700$		0			0
$701$			8.84175i			0.333948i	0.985961	+	0.166974i	$0.0533997\pi$
$701$			8.84175i			0.333948i	−0.985961	+	0.166974i	$0.946600\pi$
$702$	−13.5563	+	22.2091i	−0.511651	+	0.838229i
$703$	20.8489			0.786331
$704$	33.5772	+	4.95722i	1.26549	+	0.186832i
$705$			54.7987i			2.06384i
$706$	3.48035	−	5.70179i	0.130985	−	0.214590i
$707$		0			0
$708$	−0.221825	−	0.431615i	−0.00833671	−	0.0162211i
$709$		−	47.3655i		−	1.77885i	−0.457083	−	0.889424i	$-0.651106\pi$
$709$		−	47.3655i		−	1.77885i	0.457083	−	0.889424i	$-0.348894\pi$
$710$	−45.2749	+	74.1730i	−1.69914	+	2.78366i
$711$			2.44158i			0.0915665i
$712$	−27.3258	−	2.00627i	−1.02408	−	0.0751882i
$713$		−	6.64820i		−	0.248977i
$714$		0			0
$715$	62.9117			2.35276
$716$	12.4853	+	24.2931i	0.466597	+	0.907877i
$717$	28.5504			1.06624
$718$	−11.3848	+	18.6515i	−0.424876	+	0.696067i
$719$	−15.4031			−0.574438			−0.287219	−	0.957865i	$-0.592731\pi$
$719$	−15.4031			−0.574438			−0.287219	+	0.957865i	$0.592731\pi$
$720$	3.71394	−	5.18779i	0.138410	−	0.193338i
$721$		0			0
$722$	12.5711	+	7.67333i	0.467847	+	0.285572i
$723$	−33.8995			−1.26074
$724$	−10.5613	−	20.5495i	−0.392507	−	0.763717i
$725$		−	28.9668i		−	1.07580i
$726$	9.53017	−	15.6131i	0.353698	−	0.579456i
$727$	27.6161			1.02422			0.512112	−	0.858919i	$-0.328863\pi$
$727$	27.6161			1.02422			0.512112	+	0.858919i	$0.328863\pi$
$728$		0			0
$729$	−22.3137			−0.826434
$730$	8.31371	−	13.6202i	0.307704	−	0.504106i
$731$			1.71644i			0.0634849i
$732$	−5.24264	+	2.69442i	−0.193774	+	0.0995885i
$733$	34.6569			1.28008			0.640041	−	0.768340i	$-0.278917\pi$
$733$	34.6569			1.28008			0.640041	+	0.768340i	$0.278917\pi$
$734$	−36.7191	−	22.4132i	−1.35533	−	0.827287i
$735$		0			0
$736$	−6.51472	−	15.3467i	−0.240136	−	0.565685i
$737$	8.48528			0.312559
$738$	−0.427099	+	0.699709i	−0.0157217	+	0.0257566i
$739$	−15.7574			−0.579644			−0.289822	−	0.957081i	$-0.593596\pi$
$739$	−15.7574			−0.579644			−0.289822	+	0.957081i	$0.593596\pi$
$740$	−48.7386	+	25.0489i	−1.79167	+	0.920815i
$741$	20.8489			0.765903
$742$		0			0
$743$		−	38.0181i		−	1.39475i	−0.716708	−	0.697374i	$-0.754352\pi$
$743$		−	38.0181i		−	1.39475i	0.716708	−	0.697374i	$-0.245648\pi$
$744$	−11.7574	−	0.863230i	−0.431046	−	0.0316475i
$745$		−	54.7987i		−	2.00767i
$746$	12.2843	−	20.1251i	0.449759	−	0.736832i
$747$			1.58513i			0.0579968i
$748$	2.39256	−	1.22964i	0.0874807	−	0.0449601i
$749$		0			0
$750$	25.3137	−	41.4710i	0.924326	−	1.51431i
$751$		−	44.9239i		−	1.63930i	−0.572867	−	0.819648i	$-0.694169\pi$
$751$		−	44.9239i		−	1.63930i	0.572867	−	0.819648i	$-0.305831\pi$
$752$	17.9325	−	25.0489i	0.653930	−	0.913438i
$753$	20.3848			0.742863
$754$	−8.36223	+	13.6997i	−0.304534	+	0.498913i
$755$			43.4495i			1.58129i
$756$		0			0
$757$			43.9126i			1.59603i	0.602638	+	0.798015i	$0.294116\pi$
$757$			43.9126i			1.59603i	−0.602638	+	0.798015i	$0.705884\pi$
$758$	12.5355	+	7.65164i	0.455311	+	0.277920i
$759$	−23.1046			−0.838645
$760$	31.8284	+	2.33686i	1.15454	+	0.0847667i
$761$			44.0292i			1.59606i	0.602620	+	0.798028i	$0.294124\pi$
$761$			44.0292i			1.59606i	−0.602620	+	0.798028i	$0.705876\pi$
$762$	−38.3142	−	23.3868i	−1.38798	−	0.847215i
$763$		0			0
$764$	−17.8995	+	9.19932i	−0.647581	+	0.332820i
$765$		−	0.505668i		−	0.0182825i
$766$	41.0371	+	25.0489i	1.48273	+	0.905052i
$767$			0.505668i			0.0182586i
$768$	−27.9865	+	9.52862i	−1.00988	+	0.343835i
$769$			8.15640i			0.294127i	0.989127	+	0.147064i	$0.0469822\pi$
$769$			8.15640i			0.294127i	−0.989127	+	0.147064i	$0.953018\pi$
$770$		0			0
$771$	−28.3848			−1.02225
$772$	−6.02082	−	11.7150i	−0.216694	−	0.421630i
$773$	0.660688			0.0237633			0.0118816	−	0.999929i	$-0.496218\pi$
$773$	0.660688			0.0237633			0.0118816	+	0.999929i	$0.496218\pi$
$774$	−2.70711	−	1.65241i	−0.0973049	−	0.0593945i
$775$	−22.1703			−0.796379
$776$	−46.9100	−	3.44415i	−1.68397	−	0.123638i
$777$		0			0
$778$	−12.6569	+	20.7355i	−0.453770	+	0.743403i
$779$	−4.10051			−0.146916
$780$	−48.7386	+	25.0489i	−1.74512	+	0.896893i
$781$		−	67.7000i		−	2.42250i
$782$	−1.12786	−	0.688444i	−0.0403323	−	0.0246187i
$783$	−14.0817			−0.503239
$784$		0			0
$785$	6.14214			0.219222
$786$	37.0919	+	22.6407i	1.32302	+	0.807568i
$787$		−	10.3212i		−	0.367911i	−0.982935	−	0.183955i	$-0.941110\pi$
$787$		−	10.3212i		−	0.367911i	0.982935	−	0.183955i	$-0.0588902\pi$
$788$	−3.07107	+	1.57835i	−0.109402	+	0.0562265i
$789$		0			0
$790$	16.7245	−	27.3994i	0.595029	−	0.974826i
$791$		0			0
$792$	−0.363961	+	4.95722i	−0.0129328	+	0.176147i
$793$	6.14214			0.218114
$794$	−33.6659	−	20.5495i	−1.19476	−	0.729275i
$795$	−71.5980			−2.53932
$796$	9.10307	+	17.7122i	0.322650	+	0.627793i
$797$	8.36223			0.296205			0.148103	−	0.988972i	$-0.452683\pi$
$797$	8.36223			0.296205			0.148103	+	0.988972i	$0.452683\pi$
$798$		0			0
$799$		−	2.44158i		−	0.0863770i
$800$	−51.1777	+	21.7251i	−1.80940	+	0.768100i
$801$		−	4.01254i		−	0.141776i
$802$	−14.6569	−	8.94648i	−0.517552	−	0.315911i
$803$			12.4316i			0.438701i
$804$	−6.57368	+	3.37849i	−0.231836	+	0.119150i
$805$		0			0
$806$	10.4853	+	6.40017i	0.369328	+	0.225436i
$807$		−	27.2404i		−	0.958907i
$808$	1.45821	−	19.8611i	0.0512996	−	0.698710i
$809$	−20.9289			−0.735822			−0.367911	−	0.929861i	$-0.619927\pi$
$809$	−20.9289			−0.735822			−0.367911	+	0.929861i	$0.619927\pi$
$810$	−46.8132	−	28.5746i	−1.64485	−	1.00401i
$811$			30.8548i			1.08346i	0.840553	+	0.541729i	$0.182230\pi$
$811$			30.8548i			1.08346i	−0.840553	+	0.541729i	$0.817770\pi$
$812$		0			0
$813$		−	24.2931i		−	0.851997i
$814$	22.2426	−	36.4397i	0.779604	−	1.27721i
$815$	−9.95727			−0.348788
$816$	−1.36396	+	1.90524i	−0.0477482	+	0.0666968i
$817$		−	15.8645i		−	0.555027i
$818$	15.8302	−	25.9343i	0.553489	−	0.906771i
$819$		0			0
$820$	9.58579	−	4.92655i	0.334750	−	0.172042i
$821$		−	31.9141i		−	1.11381i	−0.830576	−	0.556905i	$-0.811989\pi$
$821$		−	31.9141i		−	1.11381i	0.830576	−	0.556905i	$-0.188011\pi$
$822$	15.7334	−	25.7758i	0.548766	−	0.899033i
$823$			21.8516i			0.761697i	0.924637	+	0.380849i	$0.124368\pi$
$823$			21.8516i			0.761697i	−0.924637	+	0.380849i	$0.875632\pi$
$824$	−1.12786	+	15.3617i	−0.0392910	+	0.535151i
$825$			77.0488i			2.68249i
$826$		0			0
$827$	9.65685			0.335802			0.167901	−	0.985804i	$-0.446301\pi$
$827$	9.65685			0.335802			0.167901	+	0.985804i	$0.446301\pi$
$828$	2.17157	−	1.11606i	0.0754674	−	0.0387859i
$829$	−41.9714			−1.45773			−0.728864	−	0.684658i	$-0.759951\pi$
$829$	−41.9714			−1.45773			−0.728864	+	0.684658i	$0.759951\pi$
$830$	10.8579	−	17.7882i	0.376882	−	0.617439i
$831$	−55.7795			−1.93497
$832$	30.4758	+	4.49935i	1.05656	+	0.155987i
$833$		0			0
$834$	−32.2635	−	19.6935i	−1.11719	−	0.681929i
$835$	41.9411			1.45143
$836$	−22.1136	+	11.3651i	−0.764814	+	0.393071i
$837$			10.7777i			0.372531i
$838$	−7.33112	+	12.0104i	−0.253249	+	0.414894i
$839$	−9.95727			−0.343763			−0.171882	−	0.985118i	$-0.554985\pi$
$839$	−9.95727			−0.343763			−0.171882	+	0.985118i	$0.554985\pi$
$840$		0			0
$841$	20.3137			0.700473
$842$	−5.61522	+	9.19932i	−0.193513	+	0.317029i
$843$		−	5.67459i		−	0.195443i
$844$	−13.6863	−	26.6300i	−0.471102	−	0.916642i
$845$	7.04085			0.242213
$846$	3.85077	+	2.35049i	0.132392	+	0.0808116i
$847$		0			0
$848$	32.7279	+	23.4299i	1.12388	+	0.804586i
$849$	28.2426			0.969285
$850$	−2.29581	+	3.76118i	−0.0787455	+	0.129007i
$851$	−20.9706			−0.718862
$852$	26.9554	+	52.4482i	0.923476	+	1.79685i
$853$	−13.8080			−0.472778			−0.236389	−	0.971658i	$-0.575964\pi$
$853$	−13.8080			−0.472778			−0.236389	+	0.971658i	$0.575964\pi$
$854$		0			0
$855$			4.67371i			0.159838i
$856$	−4.00000	+	54.4808i	−0.136717	+	1.86211i
$857$			35.9272i			1.22725i	0.789598	+	0.613625i	$0.210289\pi$
$857$			35.9272i			1.22725i	−0.789598	+	0.613625i	$0.789711\pi$
$858$	22.2426	−	36.4397i	0.759351	−	1.24403i
$859$		−	33.3910i		−	1.13929i	−0.821892	−	0.569643i	$-0.807082\pi$
$859$		−	33.3910i		−	1.13929i	0.821892	−	0.569643i	$-0.192918\pi$
$860$	19.0603	+	37.0865i	0.649952	+	1.26464i
$861$		0			0
$862$	13.9289	−	22.8195i	0.474421	−	0.777236i
$863$			17.6835i			0.601954i	0.953631	+	0.300977i	$0.0973127\pi$
$863$			17.6835i			0.601954i	−0.953631	+	0.300977i	$0.902687\pi$
$864$	10.5613	+	24.8791i	0.359302	+	0.846404i
$865$	77.7401			2.64324
$866$	−13.3809	+	21.9217i	−0.454703	+	0.744931i
$867$		−	31.2262i		−	1.06050i
$868$		0			0
$869$			25.0083i			0.848347i
$870$	−25.3137	−	15.4514i	−0.858215	−	0.523851i
$871$	7.70154			0.260957
$872$	8.31371	+	0.610396i	0.281538	+	0.0206706i
$873$		−	6.88830i		−	0.233134i
$874$	10.4244	+	6.36304i	0.352612	+	0.215233i
$875$		0			0
$876$	−4.94975	−	9.63093i	−0.167236	−	0.325399i
$877$		−	14.7363i		−	0.497608i	−0.968554	−	0.248804i	$-0.919962\pi$
$877$		−	14.7363i		−	0.497608i	0.968554	−	0.248804i	$-0.0800375\pi$
$878$	−47.6108	−	29.0614i	−1.60679	−	0.980775i
$879$		−	29.6820i		−	1.00115i
$880$	38.0405	−	53.1367i	1.28235	−	1.79124i
$881$		−	21.2220i		−	0.714988i	−0.933915	−	0.357494i	$-0.883631\pi$
$881$		−	21.2220i		−	0.714988i	0.933915	−	0.357494i	$-0.116369\pi$
$882$		0			0
$883$	−2.34315			−0.0788531			−0.0394266	−	0.999222i	$-0.512553\pi$
$883$	−2.34315			−0.0788531			−0.0394266	+	0.999222i	$0.512553\pi$
$884$	2.17157	−	1.11606i	0.0730379	−	0.0375373i
$885$	−0.934353			−0.0314079
$886$	−1.24264	−	0.758503i	−0.0417473	−	0.0254824i
$887$	−12.2130			−0.410072			−0.205036	−	0.978754i	$-0.565731\pi$
$887$	−12.2130			−0.410072			−0.205036	+	0.978754i	$0.565731\pi$
$888$	−2.72291	+	37.0865i	−0.0913747	+	1.24454i
$889$		0			0
$890$	−27.4853	+	45.0286i	−0.921309	+	1.50936i
$891$	42.7279			1.43144
$892$	4.97863	+	9.68714i	0.166697	+	0.324349i
$893$			22.5667i			0.755165i
$894$	−31.7405	−	19.3743i	−1.06156	−	0.647973i
$895$	52.5894			1.75787
$896$		0			0
$897$	−20.9706			−0.700187
$898$	43.7990	+	26.7347i	1.46159	+	0.892149i
$899$			6.64820i			0.221730i
$900$	−3.72183	−	7.24171i	−0.124061	−	0.241390i
$901$	3.19008			0.106277
$902$	−4.37462	+	7.16687i	−0.145659	+	0.238631i
$903$		0			0
$904$	−0.292893	+	3.98926i	−0.00974148	+	0.132681i
$905$	−44.4853			−1.47874
$906$	25.1668	+	15.3617i	0.836112	+	0.510359i
$907$	3.02944			0.100591			0.0502954	−	0.998734i	$-0.483984\pi$
$907$	3.02944			0.100591			0.0502954	+	0.998734i	$0.483984\pi$
$908$	38.8781	−	19.9811i	1.29022	−	0.663097i
$909$	2.91642			0.0967314
$910$		0			0
$911$		−	14.7363i		−	0.488234i	−0.969746	−	0.244117i	$-0.921502\pi$
$911$		−	14.7363i		−	0.488234i	0.969746	−	0.244117i	$-0.0784981\pi$
$912$	12.6066	−	17.6095i	0.417446	−	0.583107i
$913$			16.2359i			0.537329i
$914$	−29.0208	−	17.7142i	−0.959923	−	0.585933i
$915$			11.3492i			0.375193i
$916$	−21.3727	−	41.5858i	−0.706175	−	1.37403i
$917$		0			0
$918$	1.82843	+	1.11606i	0.0603471	+	0.0368356i
$919$			15.9570i			0.526374i	0.964745	+	0.263187i	$0.0847737\pi$
$919$			15.9570i			0.526374i	−0.964745	+	0.263187i	$0.915226\pi$
$920$	−32.0142	−	2.35049i	−1.05548	−	0.0774935i
$921$	26.2426			0.864724
$922$	−30.9430	−	18.8875i	−1.01905	−	0.622026i
$923$		−	61.4469i		−	2.02255i
$924$		0			0
$925$			69.9322i			2.29936i
$926$	9.21320	−	15.0938i	0.302765	−	0.496014i
$927$	−2.25573			−0.0740878
$928$	6.51472	+	15.3467i	0.213856	+	0.503779i
$929$			7.70806i			0.252893i	0.991973	+	0.126447i	$0.0403573\pi$
$929$			7.70806i			0.252893i	−0.991973	+	0.126447i	$0.959643\pi$
$930$	−11.8260	+	19.3743i	−0.387789	+	0.635307i
$931$		0			0
$932$	9.05025	+	17.6095i	0.296451	+	0.576817i
$933$			48.5863i			1.59064i
$934$	−17.5621	+	28.7716i	−0.574648	+	0.941435i
$935$		−	5.17938i		−	0.169384i
$936$	−0.330344	+	4.49935i	−0.0107976	+	0.147066i
$937$		−	17.9749i		−	0.587213i	−0.955926	−	0.293606i	$-0.905144\pi$
$937$		−	17.9749i		−	0.587213i	0.955926	−	0.293606i	$-0.0948555\pi$
$938$		0			0
$939$	−29.4142			−0.959897
$940$	−27.1127	−	52.7543i	−0.884319	−	1.72066i
$941$	−44.2272			−1.44176			−0.720882	−	0.693057i	$-0.756263\pi$
$941$	−44.2272			−1.44176			−0.720882	+	0.693057i	$0.756263\pi$
$942$	2.17157	−	3.55765i	0.0707537	−	0.115914i
$943$	4.12444			0.134310
$944$	0.427099	+	0.305760i	0.0139009	+	0.00995165i
$945$		0			0
$946$	−27.7279	−	16.9250i	−0.901513	−	0.550279i
$947$	−25.2132			−0.819319			−0.409660	−	0.912239i	$-0.634352\pi$
$947$	−25.2132			−0.819319			−0.409660	+	0.912239i	$0.634352\pi$
$948$	−9.95727	−	19.3743i	−0.323397	−	0.629247i
$949$			11.2833i			0.366273i
$950$	21.2193	−	34.7632i	0.688445	−	1.12787i
$951$	15.4031			0.499479
$952$		0			0
$953$	5.37258			0.174035			0.0870175	−	0.996207i	$-0.472266\pi$
$953$	5.37258			0.174035			0.0870175	+	0.996207i	$0.472266\pi$
$954$	−3.07107	+	5.03127i	−0.0994295	+	0.162893i
$955$			38.7485i			1.25387i
$956$	−27.4853	+	14.1259i	−0.888938	+	0.456863i
$957$	23.1046			0.746866
$958$	−10.4244	−	6.36304i	−0.336799	−	0.205580i
$959$		0			0
$960$	−8.31371	+	56.3120i	−0.268324	+	1.81746i
$961$	−25.9117			−0.835861
$962$	20.1882	−	33.0740i	0.650894	−	1.06635i
$963$	−8.00000			−0.257796
$964$	32.6348	−	16.7724i	1.05110	−	0.540203i
$965$	−25.3603			−0.816378
$966$		0			0
$967$			8.84175i			0.284332i	0.989843	+	0.142166i	$0.0454066\pi$
$967$			8.84175i			0.284332i	−0.989843	+	0.142166i	$0.954593\pi$
$968$	−1.44975	+	19.7458i	−0.0465966	+	0.634655i
$969$		−	1.71644i		−	0.0551401i
$970$	−47.1838	+	77.3003i	−1.51498	+	2.48196i
$971$		−	29.6955i		−	0.952973i	−0.879182	−	0.476486i	$-0.841910\pi$
$971$		−	29.6955i		−	0.952973i	0.879182	−	0.476486i	$-0.158090\pi$
$972$	−7.60478	+	3.90842i	−0.243924	+	0.125363i
$973$		0			0
$974$	17.5269	−	28.7140i	0.561598	−	0.920056i
$975$			69.9322i			2.23962i
$976$	3.71394	−	5.18779i	0.118880	−	0.166057i
$977$	3.75736			0.120209			0.0601043	−	0.998192i	$-0.480857\pi$
$977$	3.75736			0.120209			0.0601043	+	0.998192i	$0.480857\pi$
$978$	−3.52043	+	5.76745i	−0.112571	+	0.184423i
$979$		−	41.0990i		−	1.31353i
$980$		0			0
$981$			1.22079i			0.0389769i
$982$	−31.3848	−	19.1571i	−1.00153	−	0.611329i
$983$	2.25573			0.0719466			0.0359733	−	0.999353i	$-0.488547\pi$
$983$	2.25573			0.0719466			0.0359733	+	0.999353i	$0.488547\pi$
$984$	0.535534	−	7.29408i	0.0170722	−	0.232527i
$985$			6.64820i			0.211829i
$986$	1.12786	+	0.688444i	0.0359185	+	0.0219245i
$987$		0			0
$988$	−20.0711	+	10.3154i	−0.638546	+	0.328176i
$989$			15.9570i			0.507405i
$990$	8.16872	+	4.98615i	0.259619	+	0.158470i
$991$		−	36.0821i		−	1.14619i	−0.819490	−	0.573093i	$-0.805743\pi$
$991$		−	36.0821i		−	1.14619i	0.819490	−	0.573093i	$-0.194257\pi$
$992$	11.7458	−	4.98615i	0.372930	−	0.158310i
$993$		−	20.4567i		−	0.649173i
$994$		0			0
$995$	38.3431			1.21556
$996$	−6.46447	−	12.5782i	−0.204834	−	0.398555i
$997$	10.2309			0.324017			0.162008	−	0.986789i	$-0.448203\pi$
$997$	10.2309			0.324017			0.162008	+	0.986789i	$0.448203\pi$
$998$	−49.0416	−	29.9348i	−1.55239	−	0.947570i
$999$	33.9962			1.07559

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	392.2.e.d.195.7	yes	8
4.3	odd	2		1568.2.e.d.783.8		8
7.2	even	3		392.2.m.h.227.6		16
7.3	odd	6		392.2.m.h.19.2		16
7.4	even	3		392.2.m.h.19.1		16
7.5	odd	6		392.2.m.h.227.5		16
7.6	odd	2	inner	392.2.e.d.195.8	yes	8
8.3	odd	2	inner	392.2.e.d.195.5	✓	8
8.5	even	2		1568.2.e.d.783.7		8
28.3	even	6		1568.2.q.h.1391.2		16
28.11	odd	6		1568.2.q.h.1391.7		16
28.19	even	6		1568.2.q.h.815.8		16
28.23	odd	6		1568.2.q.h.815.1		16
28.27	even	2		1568.2.e.d.783.1		8
56.3	even	6		392.2.m.h.19.6		16
56.5	odd	6		1568.2.q.h.815.7		16
56.11	odd	6		392.2.m.h.19.5		16
56.13	odd	2		1568.2.e.d.783.2		8
56.19	even	6		392.2.m.h.227.1		16
56.27	even	2	inner	392.2.e.d.195.6	yes	8
56.37	even	6		1568.2.q.h.815.2		16
56.45	odd	6		1568.2.q.h.1391.1		16
56.51	odd	6		392.2.m.h.227.2		16
56.53	even	6		1568.2.q.h.1391.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
392.2.e.d.195.5	✓	8	8.3	odd	2	inner
392.2.e.d.195.6	yes	8	56.27	even	2	inner
392.2.e.d.195.7	yes	8	1.1	even	1	trivial
392.2.e.d.195.8	yes	8	7.6	odd	2	inner
392.2.m.h.19.1		16	7.4	even	3
392.2.m.h.19.2		16	7.3	odd	6
392.2.m.h.19.5		16	56.11	odd	6
392.2.m.h.19.6		16	56.3	even	6
392.2.m.h.227.1		16	56.19	even	6
392.2.m.h.227.2		16	56.51	odd	6
392.2.m.h.227.5		16	7.5	odd	6
392.2.m.h.227.6		16	7.2	even	3
1568.2.e.d.783.1		8	28.27	even	2
1568.2.e.d.783.2		8	56.13	odd	2
1568.2.e.d.783.7		8	8.5	even	2
1568.2.e.d.783.8		8	4.3	odd	2
1568.2.q.h.815.1		16	28.23	odd	6
1568.2.q.h.815.2		16	56.37	even	6
1568.2.q.h.815.7		16	56.5	odd	6
1568.2.q.h.815.8		16	28.19	even	6
1568.2.q.h.1391.1		16	56.45	odd	6
1568.2.q.h.1391.2		16	28.3	even	6
1568.2.q.h.1391.7		16	28.11	odd	6
1568.2.q.h.1391.8		16	56.53	even	6

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 392 = 2^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	392.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.20711 + 0.736813i) q^{2} -1.84776i q^{3} +(0.914214 + 1.77882i) q^{4} +3.85077 q^{5} +(1.36145 - 2.23044i) q^{6} +(-0.207107 + 2.82083i) q^{8} -0.414214 q^{9} +(4.64829 + 2.83730i) q^{10} -4.24264 q^{11} +(3.28684 - 1.68925i) q^{12} -3.85077 q^{13} -7.11529i q^{15} +(-2.32843 + 3.25245i) q^{16} +0.317025i q^{17} +(-0.500000 - 0.305198i) q^{18} -2.93015i q^{19} +(3.52043 + 6.84984i) q^{20} +(-5.12132 - 3.12603i) q^{22} +2.94725i q^{23} +(5.21222 + 0.382683i) q^{24} +9.82843 q^{25} +(-4.64829 - 2.83730i) q^{26} -4.77791i q^{27} -2.94725i q^{29} +(5.24264 - 8.58892i) q^{30} -2.25573 q^{31} +(-5.20711 + 2.21044i) q^{32} +7.83938i q^{33} +(-0.233588 + 0.382683i) q^{34} +(-0.378680 - 0.736813i) q^{36} +7.11529i q^{37} +(2.15897 - 3.53701i) q^{38} +7.11529i q^{39} +(-0.797521 + 10.8624i) q^{40} -1.39942i q^{41} +5.41421 q^{43} +(-3.87868 - 7.54691i) q^{44} -1.59504 q^{45} +(-2.17157 + 3.55765i) q^{46} -7.70154 q^{47} +(6.00974 + 4.30237i) q^{48} +(11.8640 + 7.24171i) q^{50} +0.585786 q^{51} +(-3.52043 - 6.84984i) q^{52} -10.0625i q^{53} +(3.52043 - 5.76745i) q^{54} -16.3374 q^{55} -5.41421 q^{57} +(2.17157 - 3.55765i) q^{58} -0.131316i q^{59} +(12.6569 - 6.50490i) q^{60} -1.59504 q^{61} +(-2.72291 - 1.66205i) q^{62} +(-7.91421 - 1.16843i) q^{64} -14.8284 q^{65} +(-5.77615 + 9.46297i) q^{66} -2.00000 q^{67} +(-0.563932 + 0.289829i) q^{68} +5.44581 q^{69} +15.9570i q^{71} +(0.0857864 - 1.16843i) q^{72} -2.93015i q^{73} +(-5.24264 + 8.58892i) q^{74} -18.1606i q^{75} +(5.21222 - 2.67878i) q^{76} +(-5.24264 + 8.58892i) q^{78} -5.89450i q^{79} +(-8.96624 + 12.5244i) q^{80} -10.0711 q^{81} +(1.03111 - 1.68925i) q^{82} -3.82683i q^{83} +1.22079i q^{85} +(6.53553 + 3.98926i) q^{86} -5.44581 q^{87} +(0.878680 - 11.9678i) q^{88} +9.68714i q^{89} +(-1.92538 - 1.17525i) q^{90} +(-5.24264 + 2.69442i) q^{92} +4.16804i q^{93} +(-9.29658 - 5.67459i) q^{94} -11.2833i q^{95} +(4.08436 + 9.62148i) q^{96} +16.6298i q^{97} +1.75736 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{2} - 4 q^{4} + 4 q^{8} + 8 q^{9} + 4 q^{16} - 4 q^{18} - 24 q^{22} + 56 q^{25} + 8 q^{30} - 36 q^{32} - 20 q^{36} + 32 q^{43} - 48 q^{44} - 40 q^{46} + 44 q^{50} + 16 q^{51} - 32 q^{57} + 40 q^{58}+ \cdots + 48 q^{99}+O(q^{100}) \) 8 * q + 4 * q^2 - 4 * q^4 + 4 * q^8 + 8 * q^9 + 4 * q^16 - 4 * q^18 - 24 * q^22 + 56 * q^25 + 8 * q^30 - 36 * q^32 - 20 * q^36 + 32 * q^43 - 48 * q^44 - 40 * q^46 + 44 * q^50 + 16 * q^51 - 32 * q^57 + 40 * q^58 + 56 * q^60 - 52 * q^64 - 96 * q^65 - 16 * q^67 + 12 * q^72 - 8 * q^74 - 8 * q^78 - 24 * q^81 + 24 * q^86 + 24 * q^88 - 8 * q^92 + 48 * q^99

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