LMFDB - Embedded newform 392.2.b.g.197.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [392,2,Mod(197,392)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(392, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("392.197");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$3.13013575923$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 8x^{10} + 27x^{8} + 14x^{6} + 25x^{4} - 42x^{2} + 16 $ x^12 + 8x^10 + 27x^8 + 14x^6 + 25x^4 - 42*x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			197.5
Root			$0.707107 - 0.164821i$ of defining polynomial
Character	$\chi$	$=$	392.197
Dual form			392.2.b.g.197.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.321037 - 1.37729i) q^{2} -2.86877i q^{3} +(-1.79387 + 0.884323i) q^{4} -3.19841i q^{5} +(-3.95113 + 0.920979i) q^{6} +(1.79387 + 2.18678i) q^{8} -5.22982 q^{9} +O(q^{10})$	\(q+(-0.321037 - 1.37729i) q^{2} -2.86877i q^{3} +(-1.79387 + 0.884323i) q^{4} -3.19841i q^{5} +(-3.95113 + 0.920979i) q^{6} +(1.79387 + 2.18678i) q^{8} -5.22982 q^{9} +(-4.40514 + 1.02681i) q^{10} -1.45212i q^{11} +(2.53692 + 5.14619i) q^{12} +1.14479i q^{13} -9.17548 q^{15} +(2.43594 - 3.17272i) q^{16} +5.58002 q^{17} +(1.67896 + 7.20299i) q^{18} -1.47444i q^{19} +(2.82843 + 5.73753i) q^{20} +(-2.00000 + 0.466185i) q^{22} +3.28415 q^{23} +(6.27337 - 5.14619i) q^{24} -5.22982 q^{25} +(1.57672 - 0.367521i) q^{26} +6.39682i q^{27} +3.59086i q^{29} +(2.94567 + 12.6373i) q^{30} -1.01237 q^{31} +(-5.15180 - 2.33645i) q^{32} -4.16580 q^{33} +(-1.79139 - 7.68532i) q^{34} +(9.38161 - 4.62485i) q^{36} +6.49511i q^{37} +(-2.03073 + 0.473349i) q^{38} +3.28415 q^{39} +(6.99423 - 5.73753i) q^{40} +7.39608 q^{41} -7.59434i q^{43} +(1.28415 + 2.60492i) q^{44} +16.7271i q^{45} +(-1.05433 - 4.52323i) q^{46} -11.9637 q^{47} +(-9.10180 - 6.98815i) q^{48} +(1.67896 + 7.20299i) q^{50} -16.0078i q^{51} +(-1.01237 - 2.05361i) q^{52} +11.0183i q^{53} +(8.81029 - 2.05361i) q^{54} -4.64449 q^{55} -4.22982 q^{57} +(4.94567 - 1.15280i) q^{58} -6.31671i q^{59} +(16.4596 - 8.11409i) q^{60} -3.19841i q^{61} +(0.325008 + 1.39433i) q^{62} +(-1.56406 + 7.84562i) q^{64} +3.66152 q^{65} +(1.33738 + 5.73753i) q^{66} -2.60492i q^{67} +(-10.0098 + 4.93454i) q^{68} -9.42145i q^{69} +12.4596 q^{71} +(-9.38161 - 11.4365i) q^{72} -9.21213 q^{73} +(8.94567 - 2.08517i) q^{74} +15.0031i q^{75} +(1.30388 + 2.64495i) q^{76} +(-1.05433 - 4.52323i) q^{78} -13.8913 q^{79} +(-10.1477 - 7.79114i) q^{80} +2.66152 q^{81} +(-2.37441 - 10.1866i) q^{82} -7.87125i q^{83} -17.8472i q^{85} +(-10.4596 + 2.43806i) q^{86} +10.3013 q^{87} +(3.17548 - 2.60492i) q^{88} +3.23027 q^{89} +(23.0381 - 5.37001i) q^{90} +(-5.89134 + 2.90425i) q^{92} +2.90425i q^{93} +(3.84080 + 16.4776i) q^{94} -4.71585 q^{95} +(-6.70272 + 14.7793i) q^{96} +0.401845 q^{97} +7.59434i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 2 q^{2} + 2 q^{4} - 2 q^{8} - 12 q^{9}+O(q^{10}) $ 12 * q - 2 * q^2 + 2 * q^4 - 2 * q^8 - 12 * q^9	$ 12 q - 2 q^{2} + 2 q^{4} - 2 q^{8} - 12 q^{9} - 16 q^{15} + 2 q^{16} + 22 q^{18} - 24 q^{22} + 32 q^{23} - 12 q^{25} - 8 q^{30} - 42 q^{32} + 42 q^{36} + 32 q^{39} + 8 q^{44} - 56 q^{46} + 22 q^{50} + 16 q^{58} + 96 q^{60} - 46 q^{64} + 8 q^{65} + 48 q^{71} - 42 q^{72} + 64 q^{74} - 56 q^{78} - 80 q^{79} - 4 q^{81} - 24 q^{86} - 56 q^{88} + 16 q^{92} - 64 q^{95}+O(q^{100}) $ 12 * q - 2 * q^2 + 2 * q^4 - 2 * q^8 - 12 * q^9 - 16 * q^15 + 2 * q^16 + 22 * q^18 - 24 * q^22 + 32 * q^23 - 12 * q^25 - 8 * q^30 - 42 * q^32 + 42 * q^36 + 32 * q^39 + 8 * q^44 - 56 * q^46 + 22 * q^50 + 16 * q^58 + 96 * q^60 - 46 * q^64 + 8 * q^65 + 48 * q^71 - 42 * q^72 + 64 * q^74 - 56 * q^78 - 80 * q^79 - 4 * q^81 - 24 * q^86 - 56 * q^88 + 16 * q^92 - 64 * q^95

Display 100 coefficients 10 coefficients

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 $

$2$	−0.321037	−	1.37729i	−0.227007	−	0.973893i
$2$	−0.321037	−	1.37729i	−0.227007	−	0.973893i
$3$		−	2.86877i		−	1.65628i	−0.560519	−	0.828141i	$-0.689399\pi$
$3$		−	2.86877i		−	1.65628i	0.560519	−	0.828141i	$-0.310601\pi$
$4$	−1.79387	+	0.884323i	−0.896935	+	0.442162i
$5$		−	3.19841i		−	1.43037i	−0.698934	−	0.715186i	$-0.746342\pi$
$5$		−	3.19841i		−	1.43037i	0.698934	−	0.715186i	$-0.253658\pi$
$6$	−3.95113	+	0.920979i	−1.61304	+	0.375988i
$7$		0			0
$7$		0			0
$8$	1.79387	+	2.18678i	0.634229	+	0.773145i
$9$	−5.22982			−1.74327
$10$	−4.40514	+	1.02681i	−1.39303	+	0.324705i
$11$		−	1.45212i		−	0.437832i	−0.975744	−	0.218916i	$-0.929748\pi$
$11$		−	1.45212i		−	0.437832i	0.975744	−	0.218916i	$-0.0702521\pi$
$12$	2.53692	+	5.14619i	0.732345	+	1.48558i
$13$			1.14479i			0.317509i	0.987318	+	0.158754i	$0.0507478\pi$
$13$			1.14479i			0.317509i	−0.987318	+	0.158754i	$0.949252\pi$
$14$		0			0
$15$	−9.17548			−2.36910
$16$	2.43594	−	3.17272i	0.608986	−	0.793181i
$17$	5.58002			1.35335			0.676676	−	0.736281i	$-0.263420\pi$
$17$	5.58002			1.35335			0.676676	+	0.736281i	$0.263420\pi$
$18$	1.67896	+	7.20299i	0.395735	+	1.69776i
$19$		−	1.47444i		−	0.338259i	−0.985594	−	0.169130i	$-0.945904\pi$
$19$		−	1.47444i		−	0.338259i	0.985594	−	0.169130i	$-0.0540956\pi$
$20$	2.82843	+	5.73753i	0.632456	+	1.28295i
$21$		0			0
$22$	−2.00000	+	0.466185i	−0.426401	+	0.0993910i
$23$	3.28415			0.684792			0.342396	−	0.939556i	$-0.388762\pi$
$23$	3.28415			0.684792			0.342396	+	0.939556i	$0.388762\pi$
$24$	6.27337	−	5.14619i	1.28055	−	1.05046i
$25$	−5.22982			−1.04596
$26$	1.57672	−	0.367521i	0.309220	−	0.0720768i
$27$			6.39682i			1.23107i
$28$		0			0
$29$			3.59086i			0.666806i	0.942784	+	0.333403i	$0.108197\pi$
$29$			3.59086i			0.666806i	−0.942784	+	0.333403i	$0.891803\pi$
$30$	2.94567	+	12.6373i	0.537803	+	2.30725i
$31$	−1.01237			−0.181827			−0.0909134	−	0.995859i	$-0.528979\pi$
$31$	−1.01237			−0.181827			−0.0909134	+	0.995859i	$0.528979\pi$
$32$	−5.15180	−	2.33645i	−0.910718	−	0.413029i
$33$	−4.16580			−0.725173
$34$	−1.79139	−	7.68532i	−0.307221	−	1.31802i
$35$		0			0
$36$	9.38161	−	4.62485i	1.56360	−	0.770808i
$37$			6.49511i			1.06779i	0.845551	+	0.533895i	$0.179272\pi$
$37$			6.49511i			1.06779i	−0.845551	+	0.533895i	$0.820728\pi$
$38$	−2.03073	+	0.473349i	−0.329428	+	0.0767873i
$39$	3.28415			0.525884
$40$	6.99423	−	5.73753i	1.10588	−	0.907183i
$41$	7.39608			1.15507			0.577536	−	0.816365i	$-0.304014\pi$
$41$	7.39608			1.15507			0.577536	+	0.816365i	$0.304014\pi$
$42$		0			0
$43$		−	7.59434i		−	1.15813i	−0.815283	−	0.579063i	$-0.803419\pi$
$43$		−	7.59434i		−	1.15813i	0.815283	−	0.579063i	$-0.196581\pi$
$44$	1.28415	+	2.60492i	0.193592	+	0.392707i
$45$			16.7271i			2.49353i
$46$	−1.05433	−	4.52323i	−0.155453	−	0.666914i
$47$	−11.9637			−1.74509			−0.872544	−	0.488535i	$-0.837531\pi$
$47$	−11.9637			−1.74509			−0.872544	+	0.488535i	$0.837531\pi$
$48$	−9.10180	−	6.98815i	−1.31373	−	1.00865i
$49$		0			0
$50$	1.67896	+	7.20299i	0.237441	+	1.01866i
$51$		−	16.0078i		−	2.24153i
$52$	−1.01237	−	2.05361i	−0.140390	−	0.284785i
$53$			11.0183i			1.51349i	0.653713	+	0.756743i	$0.273210\pi$
$53$			11.0183i			1.51349i	−0.653713	+	0.756743i	$0.726790\pi$
$54$	8.81029	−	2.05361i	1.19893	−	0.279461i
$55$	−4.64449			−0.626262
$56$		0			0
$57$	−4.22982			−0.560253
$58$	4.94567	−	1.15280i	0.649398	−	0.151370i
$59$		−	6.31671i		−	0.822365i	−0.911553	−	0.411183i	$-0.865116\pi$
$59$		−	6.31671i		−	0.822365i	0.911553	−	0.411183i	$-0.134884\pi$
$60$	16.4596	−	8.11409i	2.12493	−	1.04753i
$61$		−	3.19841i		−	0.409514i	−0.978813	−	0.204757i	$-0.934360\pi$
$61$		−	3.19841i		−	0.409514i	0.978813	−	0.204757i	$-0.0656404\pi$
$62$	0.325008	+	1.39433i	0.0412760	+	0.177080i
$63$		0			0
$64$	−1.56406	+	7.84562i	−0.195507	+	0.980702i
$65$	3.66152			0.454156
$66$	1.33738	+	5.73753i	0.164620	+	0.706241i
$67$		−	2.60492i		−	0.318242i	−0.987259	−	0.159121i	$-0.949134\pi$
$67$		−	2.60492i		−	0.318242i	0.987259	−	0.159121i	$-0.0508660\pi$
$68$	−10.0098	+	4.93454i	−1.21387	+	0.598401i
$69$		−	9.42145i		−	1.13421i
$70$		0			0
$71$	12.4596			1.47869			0.739343	−	0.673329i	$-0.235136\pi$
$71$	12.4596			1.47869			0.739343	+	0.673329i	$0.235136\pi$
$72$	−9.38161	−	11.4365i	−1.10563	−	1.34780i
$73$	−9.21213			−1.07820			−0.539099	−	0.842242i	$-0.681235\pi$
$73$	−9.21213			−1.07820			−0.539099	+	0.842242i	$0.681235\pi$
$74$	8.94567	−	2.08517i	1.03991	−	0.242396i
$75$			15.0031i			1.73241i
$76$	1.30388	+	2.64495i	0.149565	+	0.303397i
$77$		0			0
$78$	−1.05433	−	4.52323i	−0.119380	−	0.512155i
$79$	−13.8913			−1.56290			−0.781449	−	0.623970i	$-0.785519\pi$
$79$	−13.8913			−1.56290			−0.781449	+	0.623970i	$0.785519\pi$
$80$	−10.1477	−	7.79114i	−1.13454	−	0.871076i
$81$	2.66152			0.295725
$82$	−2.37441	−	10.1866i	−0.262210	−	1.12492i
$83$		−	7.87125i		−	0.863982i	−0.901878	−	0.431991i	$-0.857811\pi$
$83$		−	7.87125i		−	0.863982i	0.901878	−	0.431991i	$-0.142189\pi$
$84$		0			0
$85$		−	17.8472i		−	1.93580i
$86$	−10.4596	+	2.43806i	−1.12789	+	0.262903i
$87$	10.3013			1.10442
$88$	3.17548	−	2.60492i	0.338508	−	0.277686i
$89$	3.23027			0.342408			0.171204	−	0.985236i	$-0.445234\pi$
$89$	3.23027			0.342408			0.171204	+	0.985236i	$0.445234\pi$
$90$	23.0381	−	5.37001i	2.42843	−	0.566049i
$91$		0			0
$92$	−5.89134	+	2.90425i	−0.614214	+	0.302789i
$93$			2.90425i			0.301157i
$94$	3.84080	+	16.4776i	0.396148	+	1.69953i
$95$	−4.71585			−0.483836
$96$	−6.70272	+	14.7793i	−0.684093	+	1.50841i
$97$	0.401845			0.0408012			0.0204006	−	0.999792i	$-0.493506\pi$
$97$	0.401845			0.0408012			0.0204006	+	0.999792i	$0.493506\pi$
$98$		0			0
$99$			7.59434i			0.763260i
$100$	9.38161	−	4.62485i	0.938161	−	0.462485i
$101$		−	6.22304i		−	0.619216i	−0.950864	−	0.309608i	$-0.899802\pi$
$101$		−	6.22304i		−	0.619216i	0.950864	−	0.309608i	$-0.100198\pi$
$102$	−22.0474	+	5.13908i	−2.18302	+	0.508845i
$103$	7.31924			0.721186			0.360593	−	0.932723i	$-0.382574\pi$
$103$	7.31924			0.721186			0.360593	+	0.932723i	$0.382574\pi$
$104$	−2.50342	+	2.05361i	−0.245480	+	0.201373i
$105$		0			0
$106$	15.1755	−	3.53729i	1.47397	−	0.343572i
$107$			4.46966i			0.432099i	0.976382	+	0.216049i	$0.0693172\pi$
$107$			4.46966i			0.432099i	−0.976382	+	0.216049i	$0.930683\pi$
$108$	−5.65685	−	11.4751i	−0.544331	−	1.10419i
$109$		−	12.6373i		−	1.21044i	−0.796060	−	0.605218i	$-0.793086\pi$
$109$		−	12.6373i		−	1.21044i	0.796060	−	0.605218i	$-0.206914\pi$
$110$	1.49105	+	6.39682i	0.142166	+	0.609913i
$111$	18.6329			1.76856
$112$		0			0
$113$	−10.2298			−0.962340			−0.481170	−	0.876627i	$-0.659788\pi$
$113$	−10.2298			−0.962340			−0.481170	+	0.876627i	$0.659788\pi$
$114$	1.35793	+	5.82569i	0.127181	+	0.545626i
$115$		−	10.5040i		−	0.979507i
$116$	−3.17548	−	6.44154i	−0.294836	−	0.598082i
$117$		−	5.98706i		−	0.553504i
$118$	−8.69995	+	2.02790i	−0.800896	+	0.186683i
$119$		0			0
$120$	−16.4596	−	20.0648i	−1.50255	−	1.83166i
$121$	8.89134			0.808303
$122$	−4.40514	+	1.02681i	−0.398823	+	0.0929627i
$123$		−	21.2176i		−	1.91313i
$124$	1.81606	−	0.895261i	0.163087	−	0.0803968i
$125$			0.735042i			0.0657442i
$126$		0			0
$127$	15.0668			1.33696			0.668482	−	0.743728i	$-0.266944\pi$
$127$	15.0668			1.33696			0.668482	+	0.743728i	$0.266944\pi$
$128$	11.3078	−	0.364570i	0.999481	−	0.0322237i
$129$	−21.7864			−1.91818
$130$	−1.17548	−	5.04299i	−0.103097	−	0.442299i
$131$		−	4.92238i		−	0.430070i	−0.976606	−	0.215035i	$-0.931013\pi$
$131$		−	4.92238i		−	0.430070i	0.976606	−	0.215035i	$-0.0689866\pi$
$132$	7.47291	−	3.68392i	0.650434	−	0.320644i
$133$		0			0
$134$	−3.58774	+	0.836276i	−0.309934	+	0.0722433i
$135$	20.4596			1.76088
$136$	10.0098	+	12.2023i	0.858336	+	1.04634i
$137$	18.3510			1.56783			0.783914	−	0.620869i	$-0.213220\pi$
$137$	18.3510			1.56783			0.783914	+	0.620869i	$0.213220\pi$
$138$	−12.9761	+	3.02463i	−1.10460	+	0.257474i
$139$			17.0567i			1.44673i	0.690464	+	0.723366i	$0.257406\pi$
$139$			17.0567i			1.44673i	−0.690464	+	0.723366i	$0.742594\pi$
$140$		0			0
$141$			34.3211i			2.89036i
$142$	−4.00000	−	17.1606i	−0.335673	−	1.44008i
$143$	1.66238			0.139016
$144$	−12.7395	+	16.5928i	−1.06163	+	1.38273i
$145$	11.4850			0.953781
$146$	2.95743	+	12.6878i	0.244759	+	1.05005i
$147$		0			0
$148$	−5.74378	−	11.6514i	−0.472136	−	0.957738i
$149$			20.3985i			1.67111i	0.549405	+	0.835556i	$0.314854\pi$
$149$			20.3985i			1.67111i	−0.549405	+	0.835556i	$0.685146\pi$
$150$	20.6637	−	4.81655i	1.68718	−	0.393270i
$151$	4.71585			0.383771			0.191885	−	0.981417i	$-0.438540\pi$
$151$	4.71585			0.383771			0.191885	+	0.981417i	$0.438540\pi$
$152$	3.22428	−	2.64495i	0.261523	−	0.214534i
$153$	−29.1825			−2.35926
$154$		0			0
$155$			3.23797i			0.260080i
$156$	−5.89134	+	2.90425i	−0.471684	+	0.232526i
$157$			9.01170i			0.719212i	0.933104	+	0.359606i	$0.117089\pi$
$157$			9.01170i			0.719212i	−0.933104	+	0.359606i	$0.882911\pi$
$158$	4.45963	+	19.1324i	0.354789	+	1.52209i
$159$	31.6090			2.50676
$160$	−7.47291	+	16.4776i	−0.590786	+	1.30266i
$161$		0			0
$162$	−0.854446	−	3.66569i	−0.0671316	−	0.288004i
$163$		−	4.69009i		−	0.367356i	−0.982986	−	0.183678i	$-0.941200\pi$
$163$		−	4.69009i		−	0.367356i	0.982986	−	0.183678i	$-0.0588004\pi$
$164$	−13.2676	+	6.54052i	−1.03603	+	0.510729i
$165$			13.3239i			1.03727i
$166$	−10.8410	+	2.52696i	−0.841426	+	0.196130i
$167$	−13.9885			−1.08246			−0.541230	−	0.840875i	$-0.682041\pi$
$167$	−13.9885			−1.08246			−0.541230	+	0.840875i	$0.682041\pi$
$168$		0			0
$169$	11.6894			0.899188
$170$	−24.5808	+	5.72960i	−1.88526	+	0.439440i
$171$			7.71104i			0.589678i
$172$	6.71585	+	13.6233i	0.512079	+	1.03876i
$173$			7.54161i			0.573378i	0.958024	+	0.286689i	$0.0925546\pi$
$173$			7.54161i			0.573378i	−0.958024	+	0.286689i	$0.907445\pi$
$174$	−3.30711	−	14.1880i	−0.250711	−	1.07559i
$175$		0			0
$176$	−4.60719	−	3.53729i	−0.347280	−	0.266634i
$177$	−18.1212			−1.36207
$178$	−1.03704	−	4.44903i	−0.0777292	−	0.333469i
$179$			14.8894i			1.11288i	0.830887	+	0.556441i	$0.187834\pi$
$179$			14.8894i			1.11288i	−0.830887	+	0.556441i	$0.812166\pi$
$180$	−14.7922	−	30.0062i	−1.10254	−	2.23653i
$181$		−	16.4911i		−	1.22577i	−0.790170	−	0.612887i	$-0.790008\pi$
$181$		−	16.4911i		−	1.22577i	0.790170	−	0.612887i	$-0.209992\pi$
$182$		0			0
$183$	−9.17548			−0.678271
$184$	5.89134	+	7.18172i	0.434315	+	0.529444i
$185$	20.7740			1.52734
$186$	4.00000	−	0.932371i	0.293294	−	0.0683647i
$187$		−	8.10288i		−	0.592541i
$188$	21.4614	−	10.5798i	1.56523	−	0.771611i
$189$		0			0
$190$	1.51396	+	6.49511i	0.109834	+	0.471205i
$191$	2.35097			0.170110			0.0850550	−	0.996376i	$-0.472893\pi$
$191$	2.35097			0.170110			0.0850550	+	0.996376i	$0.472893\pi$
$192$	22.5072	+	4.48691i	1.62432	+	0.323815i
$193$	−9.55286			−0.687630			−0.343815	−	0.939037i	$-0.611719\pi$
$193$	−9.55286			−0.687630			−0.343815	+	0.939037i	$0.611719\pi$
$194$	−0.129007	−	0.553458i	−0.00926216	−	0.0397360i
$195$		−	10.5040i		−	0.752210i
$196$		0			0
$197$		−	12.0578i		−	0.859086i	−0.903046	−	0.429543i	$-0.858675\pi$
$197$		−	12.0578i		−	0.859086i	0.903046	−	0.429543i	$-0.141325\pi$
$198$	10.4596	−	2.43806i	0.743334	−	0.173266i
$199$	3.99447			0.283160			0.141580	−	0.989927i	$-0.454782\pi$
$199$	3.99447			0.283160			0.141580	+	0.989927i	$0.454782\pi$
$200$	−9.38161	−	11.4365i	−0.663380	−	0.808681i
$201$	−7.47291			−0.527099
$202$	−8.57095	+	1.99782i	−0.603050	+	0.140566i
$203$		0			0
$204$	14.1560	+	28.7159i	0.991121	+	2.01051i
$205$		−	23.6557i		−	1.65218i
$206$	−2.34974	−	10.0807i	−0.163714	−	0.702358i
$207$	−17.1755			−1.19378
$208$	3.63212	+	2.78866i	0.251842	+	0.193359i
$209$	−2.14107			−0.148101
$210$		0			0
$211$			6.44154i			0.443454i	0.975109	+	0.221727i	$0.0711694\pi$
$211$			6.44154i			0.443454i	−0.975109	+	0.221727i	$0.928831\pi$
$212$	−9.74378	−	19.7655i	−0.669205	−	1.35750i
$213$		−	35.7438i		−	2.44912i
$214$	6.15604	−	1.43493i	0.420818	−	0.0980896i
$215$	−24.2898			−1.65655
$216$	−13.9885	+	11.4751i	−0.951794	+	0.780779i
$217$		0			0
$218$	−17.4053	+	4.05705i	−1.17884	+	0.274778i
$219$			26.4275i			1.78580i
$220$	8.33161	−	4.10723i	0.561717	−	0.276909i
$221$			6.38797i			0.429702i
$222$	−5.98186	−	25.6630i	−0.401476	−	1.72239i
$223$	−19.2830			−1.29128			−0.645641	−	0.763641i	$-0.723410\pi$
$223$	−19.2830			−1.29128			−0.645641	+	0.763641i	$0.723410\pi$
$224$		0			0
$225$	27.3510			1.82340
$226$	3.28415	+	14.0895i	0.218458	+	0.937216i
$227$			9.68889i			0.643074i	0.946897	+	0.321537i	$0.104200\pi$
$227$			9.68889i			0.643074i	−0.946897	+	0.321537i	$0.895800\pi$
$228$	7.58774	−	3.74052i	0.502510	−	0.247722i
$229$			9.35925i			0.618477i	0.950985	+	0.309238i	$0.100074\pi$
$229$			9.35925i			0.618477i	−0.950985	+	0.309238i	$0.899926\pi$
$230$	−14.4671	+	3.37218i	−0.953935	+	0.222355i
$231$		0			0
$232$	−7.85244	+	6.44154i	−0.515538	+	0.422908i
$233$	16.9193			1.10842			0.554209	−	0.832378i	$-0.313021\pi$
$233$	16.9193			1.10842			0.554209	+	0.832378i	$0.313021\pi$
$234$	−8.24594	+	1.92207i	−0.539054	+	0.125650i
$235$			38.2649i			2.49613i
$236$	5.58601	+	11.3314i	0.363618	+	0.737608i
$237$			39.8510i			2.58860i
$238$		0			0
$239$	−4.71585			−0.305043			−0.152522	−	0.988300i	$-0.548739\pi$
$239$	−4.71585			−0.305043			−0.152522	+	0.988300i	$0.548739\pi$
$240$	−22.3510	+	29.1113i	−1.44275	+	1.87912i
$241$	8.88713			0.572470			0.286235	−	0.958159i	$-0.407596\pi$
$241$	8.88713			0.572470			0.286235	+	0.958159i	$0.407596\pi$
$242$	−2.85445	−	12.2460i	−0.183491	−	0.787201i
$243$			11.5552i			0.741265i
$244$	2.82843	+	5.73753i	0.181071	+	0.367308i
$245$		0			0
$246$	−29.2229	+	6.81163i	−1.86318	+	0.434294i
$247$	1.68793			0.107400
$248$	−1.81606	−	2.21383i	−0.115320	−	0.140578i
$249$	−22.5808			−1.43100
$250$	1.01237	−	0.235976i	0.0640278	−	0.0149244i
$251$		−	16.3974i		−	1.03500i	−0.855684	−	0.517499i	$-0.826863\pi$
$251$		−	16.3974i		−	1.03500i	0.855684	−	0.517499i	$-0.173137\pi$
$252$		0			0
$253$		−	4.76899i		−	0.299824i
$254$	−4.83700	−	20.7514i	−0.303501	−	1.30206i
$255$	−51.1994			−3.20623
$256$	−4.13235	−	15.4572i	−0.258272	−	0.966072i
$257$	12.7279			0.793946			0.396973	−	0.917830i	$-0.370061\pi$
$257$	12.7279			0.793946			0.396973	+	0.917830i	$0.370061\pi$
$258$	6.99423	+	30.0062i	0.435442	+	1.86811i
$259$		0			0
$260$	−6.56829	+	3.23797i	−0.407348	+	0.200810i
$261$		−	18.7795i		−	1.16242i
$262$	−6.77956	+	1.58026i	−0.418842	+	0.0976291i
$263$	21.8913			1.34988			0.674939	−	0.737874i	$-0.264170\pi$
$263$	21.8913			1.34988			0.674939	+	0.737874i	$0.264170\pi$
$264$	−7.47291	−	9.10972i	−0.459926	−	0.560664i
$265$	35.2412			2.16485
$266$		0			0
$267$		−	9.26689i		−	0.567125i
$268$	2.30359	+	4.67289i	0.140714	+	0.285442i
$269$			18.5176i			1.12904i	0.825420	+	0.564519i	$0.190938\pi$
$269$			18.5176i			1.12904i	−0.825420	+	0.564519i	$0.809062\pi$
$270$	−6.56829	−	28.1789i	−0.399734	−	1.71491i
$271$	13.9335			0.846397			0.423199	−	0.906037i	$-0.360907\pi$
$271$	13.9335			0.846397			0.423199	+	0.906037i	$0.360907\pi$
$272$	13.5926	−	17.7039i	0.824173	−	1.07345i
$273$		0			0
$274$	−5.89134	−	25.2747i	−0.355909	−	1.52690i
$275$			7.59434i			0.457956i
$276$	8.33161	+	16.9009i	0.501504	+	1.01731i
$277$		−	13.9226i		−	0.836527i	−0.908326	−	0.418264i	$-0.862639\pi$
$277$		−	13.9226i		−	0.836527i	0.908326	−	0.418264i	$-0.137361\pi$
$278$	23.4921	−	5.47584i	1.40896	−	0.328419i
$279$	5.29450			0.316973
$280$		0			0
$281$	1.43171			0.0854084			0.0427042	−	0.999088i	$-0.486403\pi$
$281$	1.43171			0.0854084			0.0427042	+	0.999088i	$0.486403\pi$
$282$	47.2702	−	11.0183i	2.81490	−	0.656133i
$283$		−	4.49907i		−	0.267442i	−0.991019	−	0.133721i	$-0.957307\pi$
$283$		−	4.49907i		−	0.267442i	0.991019	−	0.133721i	$-0.0426926\pi$
$284$	−22.3510	+	11.0183i	−1.32629	+	0.653818i
$285$			13.5287i			0.801370i
$286$	−0.533686	−	2.28959i	−0.0315575	−	0.135386i
$287$		0			0
$288$	26.9429	+	12.2192i	1.58763	+	0.720023i
$289$	14.1366			0.831564
$290$	−3.68712	−	15.8183i	−0.216515	−	0.928880i
$291$		−	1.15280i		−	0.0675783i
$292$	16.5254	−	8.14651i	0.967075	−	0.476738i
$293$			8.04068i			0.469741i	0.972027	+	0.234871i	$0.0754667\pi$
$293$			8.04068i			0.469741i	−0.972027	+	0.234871i	$0.924533\pi$
$294$		0			0
$295$	−20.2034			−1.17629
$296$	−14.2034	+	11.6514i	−0.825556	+	0.677223i
$297$	9.28897			0.539001
$298$	28.0947	−	6.54868i	1.62748	−	0.379355i
$299$			3.75967i			0.217428i
$300$	−13.2676	−	26.9136i	−0.766005	−	1.55386i
$301$		0			0
$302$	−1.51396	−	6.49511i	−0.0871187	−	0.373752i
$303$	−17.8524			−1.02560
$304$	−4.67798	−	3.59165i	−0.268301	−	0.205995i
$305$	−10.2298			−0.585758
$306$	9.36864	+	40.1928i	0.535570	+	2.29767i
$307$			11.9785i			0.683648i	0.939764	+	0.341824i	$0.111045\pi$
$307$			11.9785i			0.683648i	−0.939764	+	0.341824i	$0.888955\pi$
$308$		0			0
$309$		−	20.9972i		−	1.19449i
$310$	4.45963	−	1.03951i	0.253290	−	0.0590400i
$311$	21.6701			1.22880			0.614398	−	0.788996i	$-0.289399\pi$
$311$	21.6701			1.22880			0.614398	+	0.788996i	$0.289399\pi$
$312$	5.89134	+	7.18172i	0.333531	+	0.406585i
$313$	9.42081			0.532496			0.266248	−	0.963905i	$-0.414216\pi$
$313$	9.42081			0.532496			0.266248	+	0.963905i	$0.414216\pi$
$314$	12.4117	−	2.89309i	0.700435	−	0.163266i
$315$		0			0
$316$	24.9193	−	12.2844i	1.40182	−	0.691053i
$317$		−	9.15360i		−	0.514117i	−0.966396	−	0.257059i	$-0.917247\pi$
$317$		−	9.15360i		−	0.514117i	0.966396	−	0.257059i	$-0.0827534\pi$
$318$	−10.1477	−	43.5349i	−0.569053	−	2.44132i
$319$	5.21438			0.291949
$320$	25.0935	+	5.00249i	1.40277	+	0.279648i
$321$	12.8224			0.715678
$322$		0			0
$323$		−	8.22739i		−	0.457784i
$324$	−4.77442	+	2.35364i	−0.265246	+	0.130758i
$325$		−	5.98706i		−	0.332103i
$326$	−6.45963	+	1.50569i	−0.357766	+	0.0833926i
$327$	−36.2535			−2.00482
$328$	13.2676	+	16.1736i	0.732581	+	0.893039i
$329$		0			0
$330$	18.3510	−	4.27748i	1.01019	−	0.235467i
$331$		−	19.8788i		−	1.09264i	−0.837578	−	0.546318i	$-0.816029\pi$
$331$		−	19.8788i		−	1.09264i	0.837578	−	0.546318i	$-0.183971\pi$
$332$	6.96073	+	14.1200i	0.382020	+	0.774936i
$333$		−	33.9682i		−	1.86145i
$334$	4.49081	+	19.2662i	0.245726	+	1.05420i
$335$	−8.33161			−0.455204
$336$		0			0
$337$	−19.5529			−1.06511			−0.532556	−	0.846395i	$-0.678768\pi$
$337$	−19.5529			−1.06511			−0.532556	+	0.846395i	$0.678768\pi$
$338$	−3.75274	−	16.0998i	−0.204122	−	0.875713i
$339$			29.3469i			1.59391i
$340$	15.7827	+	32.0155i	0.855936	+	1.73629i
$341$			1.47008i			0.0796096i
$342$	10.6204	−	2.47553i	0.574283	−	0.133861i
$343$		0			0
$344$	16.6072	−	13.6233i	0.895400	−	0.734517i
$345$	−30.1336			−1.62234
$346$	10.3870	−	2.42113i	0.558409	−	0.130161i
$347$		−	31.0043i		−	1.66440i	−0.554479	−	0.832198i	$-0.687082\pi$
$347$		−	31.0043i		−	1.66440i	0.554479	−	0.832198i	$-0.312918\pi$
$348$	−18.4793	+	9.10972i	−0.990593	+	0.488332i
$349$		−	14.6735i		−	0.785453i	−0.919655	−	0.392726i	$-0.871532\pi$
$349$		−	14.6735i		−	0.785453i	0.919655	−	0.392726i	$-0.128468\pi$
$350$		0			0
$351$	−7.32304			−0.390875
$352$	−3.39281	+	7.48105i	−0.180837	+	0.398741i
$353$	25.6667			1.36610			0.683049	−	0.730372i	$-0.260653\pi$
$353$	25.6667			1.36610			0.683049	+	0.730372i	$0.260653\pi$
$354$	5.81756	+	24.9581i	0.309200	+	1.32651i
$355$		−	39.8510i		−	2.11507i
$356$	−5.79469	+	2.85661i	−0.307118	+	0.151400i
$357$		0			0
$358$	20.5070	−	4.78003i	1.08383	−	0.252633i
$359$	−4.20341			−0.221847			−0.110924	−	0.993829i	$-0.535381\pi$
$359$	−4.20341			−0.221847			−0.110924	+	0.993829i	$0.535381\pi$
$360$	−36.5785	+	30.0062i	−1.92786	+	1.58147i
$361$	16.8260			0.885581
$362$	−22.7131	+	5.29425i	−1.19377	+	0.278260i
$363$		−	25.5072i		−	1.33878i
$364$		0			0
$365$			29.4642i			1.54222i
$366$	2.94567	+	12.6373i	0.153973	+	0.660564i
$367$	−35.6035			−1.85849			−0.929244	−	0.369467i	$-0.879540\pi$
$367$	−35.6035			−1.85849			−0.929244	+	0.369467i	$0.879540\pi$
$368$	8.00000	−	10.4197i	0.417029	−	0.543164i
$369$	−38.6801			−2.01361
$370$	−6.66922	−	28.6119i	−0.346716	−	1.48746i
$371$		0			0
$372$	−2.56829	−	5.20985i	−0.133160	−	0.270118i
$373$		−	9.97884i		−	0.516684i	−0.966053	−	0.258342i	$-0.916824\pi$
$373$		−	9.97884i		−	0.516684i	0.966053	−	0.258342i	$-0.0831762\pi$
$374$	−11.1600	+	2.60132i	−0.577072	+	0.134511i
$375$	2.10866			0.108891
$376$	−21.4614	−	26.1621i	−1.10679	−	1.34921i
$377$	−4.11080			−0.211717
$378$		0			0
$379$			24.5283i			1.25993i	0.776622	+	0.629967i	$0.216932\pi$
$379$			24.5283i			1.25993i	−0.776622	+	0.629967i	$0.783068\pi$
$380$	8.45963	−	4.17034i	0.433970	−	0.213934i
$381$		−	43.2232i		−	2.21439i
$382$	−0.754747	−	3.23797i	−0.0386162	−	0.165669i
$383$	8.63896			0.441430			0.220715	−	0.975338i	$-0.429161\pi$
$383$	8.63896			0.441430			0.220715	+	0.975338i	$0.429161\pi$
$384$	−1.04587	−	32.4395i	−0.0533716	−	1.65542i
$385$		0			0
$386$	3.06682	+	13.1571i	0.156097	+	0.669678i
$387$			39.7170i			2.01893i
$388$	−0.720858	+	0.355361i	−0.0365960	+	0.0180407i
$389$		−	12.6373i		−	0.640738i	−0.947293	−	0.320369i	$-0.896193\pi$
$389$		−	12.6373i		−	0.640738i	0.947293	−	0.320369i	$-0.103807\pi$
$390$	−14.4671	+	3.37218i	−0.732572	+	0.170757i
$391$	18.3256			0.926765
$392$		0			0
$393$	−14.1212			−0.712318
$394$	−16.6072	+	3.87101i	−0.836658	+	0.195019i
$395$			44.4302i			2.23552i
$396$	−6.71585	−	13.6233i	−0.337484	−	0.684595i
$397$			1.87984i			0.0943463i	0.998887	+	0.0471732i	$0.0150213\pi$
$397$			1.87984i			0.0943463i	−0.998887	+	0.0471732i	$0.984979\pi$
$398$	−1.28237	−	5.50156i	−0.0642795	−	0.275768i
$399$		0			0
$400$	−12.7395	+	16.5928i	−0.636977	+	0.829638i
$401$	14.5808			0.728129			0.364065	−	0.931374i	$-0.381389\pi$
$401$	14.5808			0.728129			0.364065	+	0.931374i	$0.381389\pi$
$402$	2.39908	+	10.2924i	0.119655	+	0.513338i
$403$		−	1.15895i		−	0.0577316i
$404$	5.50318	+	11.1633i	0.273793	+	0.555396i
$405$		−	8.51263i		−	0.422996i
$406$		0			0
$407$	9.43171			0.467512
$408$	35.0055	−	28.7159i	1.73303	−	1.42165i
$409$	−30.1948			−1.49304			−0.746519	−	0.665364i	$-0.768276\pi$
$409$	−30.1948			−1.49304			−0.746519	+	0.665364i	$0.768276\pi$
$410$	−32.5808	+	7.59434i	−1.60905	+	0.375058i
$411$		−	52.6446i		−	2.59677i
$412$	−13.1298	+	6.47257i	−0.646857	+	0.318881i
$413$		0			0
$414$	5.51396	+	23.6557i	0.270996	+	1.16261i
$415$	−25.1755			−1.23582
$416$	2.67475	−	5.89775i	0.131141	−	0.289161i
$417$	48.9317			2.39620
$418$	0.687361	+	2.94887i	0.0336199	+	0.144234i
$419$		−	7.28773i		−	0.356029i	−0.984028	−	0.178014i	$-0.943033\pi$
$419$		−	7.28773i		−	0.356029i	0.984028	−	0.178014i	$-0.0569673\pi$
$420$		0			0
$421$		−	2.30560i		−	0.112368i	−0.998420	−	0.0561840i	$-0.982107\pi$
$421$		−	2.30560i		−	0.112368i	0.998420	−	0.0561840i	$-0.0178933\pi$
$422$	8.87189	−	2.06797i	0.431877	−	0.100667i
$423$	62.5681			3.04216
$424$	−24.0947	+	19.7655i	−1.17014	+	0.959897i
$425$	−29.1825			−1.41556
$426$	−49.2296	+	11.4751i	−2.38518	+	0.555969i
$427$		0			0
$428$	−3.95263	−	8.01800i	−0.191058	−	0.387565i
$429$		−	4.76899i		−	0.230249i
$430$	7.79792	+	33.4542i	0.376049	+	1.61330i
$431$	−2.36489			−0.113913			−0.0569563	−	0.998377i	$-0.518140\pi$
$431$	−2.36489			−0.113913			−0.0569563	+	0.998377i	$0.518140\pi$
$432$	20.2953	+	15.5823i	0.976460	+	0.749703i
$433$	−11.0832			−0.532624			−0.266312	−	0.963887i	$-0.585805\pi$
$433$	−11.0832			−0.532624			−0.266312	+	0.963887i	$0.585805\pi$
$434$		0			0
$435$		−	32.9479i		−	1.57973i
$436$	11.1755	+	22.6697i	0.535209	+	1.08568i
$437$		−	4.84227i		−	0.231637i
$438$	36.3983	−	8.48418i	1.73918	−	0.405390i
$439$	−6.66922			−0.318305			−0.159152	−	0.987254i	$-0.550876\pi$
$439$	−6.66922			−0.318305			−0.159152	+	0.987254i	$0.550876\pi$
$440$	−8.33161	−	10.1565i	−0.397194	−	0.484192i
$441$		0			0
$442$	8.79811	−	2.05077i	0.418483	−	0.0975454i
$443$			1.33883i			0.0636098i	0.999494	+	0.0318049i	$0.0101255\pi$
$443$			1.33883i			0.0636098i	−0.999494	+	0.0318049i	$0.989874\pi$
$444$	−33.4251	+	16.4776i	−1.58628	+	0.781990i
$445$		−	10.3317i		−	0.489771i
$446$	6.19054	+	26.5583i	0.293131	+	1.25757i
$447$	58.5186			2.76783
$448$		0			0
$449$	−4.35097			−0.205335			−0.102667	−	0.994716i	$-0.532738\pi$
$449$	−4.35097			−0.205335			−0.102667	+	0.994716i	$0.532738\pi$
$450$	−8.78067	−	37.6703i	−0.413925	−	1.77579i
$451$		−	10.7400i		−	0.505728i
$452$	18.3510	−	9.04646i	0.863157	−	0.425510i
$453$		−	13.5287i		−	0.635633i
$454$	13.3444	−	3.11049i	0.626286	−	0.145983i
$455$		0			0
$456$	−7.58774	−	9.24970i	−0.355329	−	0.433157i
$457$	−22.0125			−1.02970			−0.514850	−	0.857280i	$-0.672153\pi$
$457$	−22.0125			−1.02970			−0.514850	+	0.857280i	$0.672153\pi$
$458$	12.8904	−	3.00466i	0.602330	−	0.140399i
$459$			35.6943i			1.66607i
$460$	9.28897	+	18.8429i	0.433101	+	0.878555i
$461$			6.80657i			0.317014i	0.987358	+	0.158507i	$0.0506680\pi$
$461$			6.80657i			0.317014i	−0.987358	+	0.158507i	$0.949332\pi$
$462$		0			0
$463$	1.43171			0.0665370			0.0332685	−	0.999446i	$-0.489408\pi$
$463$	1.43171			0.0665370			0.0332685	+	0.999446i	$0.489408\pi$
$464$	11.3928	+	8.74714i	0.528898	+	0.406076i
$465$	9.28897			0.430766
$466$	−5.43171	−	23.3028i	−0.251619	−	1.07948i
$467$			33.7974i			1.56396i	0.623306	+	0.781978i	$0.285789\pi$
$467$			33.7974i			1.56396i	−0.623306	+	0.781978i	$0.714211\pi$
$468$	5.29450	+	10.7400i	0.244738	+	0.496458i
$469$		0			0
$470$	52.7019	−	12.2844i	2.43096	−	0.566639i
$471$	25.8524			1.19122
$472$	13.8133	−	11.3314i	0.635808	−	0.521568i
$473$	−11.0279			−0.507065
$474$	54.8865	−	12.7936i	2.52102	−	0.587631i
$475$			7.71104i			0.353807i
$476$		0			0
$477$		−	57.6239i		−	2.63842i
$478$	1.51396	+	6.49511i	0.0692470	+	0.297079i
$479$	21.9577			1.00327			0.501637	−	0.865078i	$-0.332731\pi$
$479$	21.9577			1.00327			0.501637	+	0.865078i	$0.332731\pi$
$480$	47.2702	+	21.4380i	2.15758	+	0.978508i
$481$	−7.43557			−0.339033
$482$	−2.85309	−	12.2402i	−0.129955	−	0.557525i
$483$		0			0
$484$	−15.9499	+	7.86282i	−0.724996	+	0.357401i
$485$		−	1.28526i		−	0.0583608i
$486$	15.9149	−	3.70964i	0.721912	−	0.168272i
$487$	−37.1227			−1.68219			−0.841094	−	0.540888i	$-0.818088\pi$
$487$	−37.1227			−1.68219			−0.841094	+	0.540888i	$0.818088\pi$
$488$	6.99423	−	5.73753i	0.316614	−	0.259726i
$489$	−13.4548			−0.608446
$490$		0			0
$491$		−	3.31071i		−	0.149410i	−0.997206	−	0.0747051i	$-0.976198\pi$
$491$		−	3.31071i		−	0.149410i	0.997206	−	0.0747051i	$-0.0238016\pi$
$492$	18.7632	+	38.0616i	0.845911	+	1.71595i
$493$			20.0371i			0.902424i
$494$	−0.541887	−	2.32477i	−0.0243807	−	0.104596i
$495$	24.2898			1.09175
$496$	−2.46607	+	3.21197i	−0.110730	+	0.144222i
$497$		0			0
$498$	7.24926	+	31.1003i	0.324847	+	1.39364i
$499$			24.5345i			1.09831i	0.835719	+	0.549157i	$0.185051\pi$
$499$			24.5345i			1.09831i	−0.835719	+	0.549157i	$0.814949\pi$
$500$	−0.650015	−	1.31857i	−0.0290696	−	0.0589683i
$501$			40.1296i			1.79286i
$502$	−22.5841	+	5.26418i	−1.00798	+	0.234952i
$503$	−3.68712			−0.164401			−0.0822003	−	0.996616i	$-0.526195\pi$
$503$	−3.68712			−0.164401			−0.0822003	+	0.996616i	$0.526195\pi$
$504$		0			0
$505$	−19.9038			−0.885708
$506$	−6.56829	+	1.53102i	−0.291996	+	0.0680622i
$507$		−	33.5343i		−	1.48931i
$508$	−27.0279	+	13.3239i	−1.19917	+	0.591154i
$509$		−	29.7567i		−	1.31894i	−0.751730	−	0.659471i	$-0.770780\pi$
$509$		−	29.7567i		−	1.31894i	0.751730	−	0.659471i	$-0.229220\pi$
$510$	16.4369	+	70.5165i	0.727837	+	3.12252i
$511$		0			0
$512$	−19.9624	+	10.6538i	−0.882221	+	0.470835i
$513$	9.43171			0.416420
$514$	−4.08613	−	17.5301i	−0.180232	−	0.773218i
$515$		−	23.4099i		−	1.03156i
$516$	39.0820	−	19.2662i	1.72049	−	0.848147i
$517$			17.3728i			0.764055i
$518$		0			0
$519$	21.6351			0.949676
$520$	6.56829	+	8.00696i	0.288039	+	0.351128i
$521$	−30.1948			−1.32286			−0.661430	−	0.750007i	$-0.730050\pi$
$521$	−30.1948			−1.32286			−0.661430	+	0.750007i	$0.730050\pi$
$522$	−25.8649	+	6.02892i	−1.13208	+	0.263879i
$523$			42.5324i			1.85981i	0.367796	+	0.929906i	$0.380112\pi$
$523$			42.5324i			1.85981i	−0.367796	+	0.929906i	$0.619888\pi$
$524$	4.35297	+	8.83011i	0.190161	+	0.385745i
$525$		0			0
$526$	−7.02792	−	30.1508i	−0.306432	−	1.31464i
$527$	−5.64903			−0.246076
$528$	−10.1477	+	13.2169i	−0.441620	+	0.575194i
$529$	−12.2144			−0.531060
$530$	−11.3137	−	48.5374i	−0.491436	−	2.10833i
$531$			33.0352i			1.43361i
$532$		0			0
$533$			8.46699i			0.366746i
$534$	−12.7632	+	2.97501i	−0.552319	+	0.128741i
$535$	14.2958			0.618062
$536$	5.69641	−	4.67289i	0.246047	−	0.201838i
$537$	42.7141			1.84325
$538$	25.5042	−	5.94483i	1.09956	−	0.256300i
$539$		0			0
$540$	−36.7019	+	18.0929i	−1.57940	+	0.778596i
$541$			5.20985i			0.223989i	0.993709	+	0.111994i	$0.0357239\pi$
$541$			5.20985i			0.223989i	−0.993709	+	0.111994i	$0.964276\pi$
$542$	−4.47315	−	19.1904i	−0.192138	−	0.824300i
$543$	−47.3091			−2.03023
$544$	−28.7471	−	13.0374i	−1.23252	−	0.558975i
$545$	−40.4193			−1.73137
$546$		0			0
$547$			37.1465i			1.58827i	0.607743	+	0.794134i	$0.292075\pi$
$547$			37.1465i			1.58827i	−0.607743	+	0.794134i	$0.707925\pi$
$548$	−32.9193	+	16.2282i	−1.40624	+	0.693234i
$549$			16.7271i			0.713895i
$550$	10.4596	−	2.43806i	0.446000	−	0.103959i
$551$	5.29450			0.225553
$552$	20.6027	−	16.9009i	0.876908	−	0.719348i
$553$		0			0
$554$	−19.1755	+	4.46966i	−0.814688	+	0.189898i
$555$		−	59.5958i		−	2.52970i
$556$	−15.0837	−	30.5976i	−0.639690	−	1.29763i
$557$			30.8182i			1.30581i	0.757440	+	0.652905i	$0.226450\pi$
$557$			30.8182i			1.30581i	−0.757440	+	0.652905i	$0.773550\pi$
$558$	−1.69973	−	7.29208i	−0.0719553	−	0.308698i
$559$	8.69396			0.367715
$560$		0			0
$561$	−23.2453			−0.981415
$562$	−0.459630	−	1.97188i	−0.0193883	−	0.0831786i
$563$			20.4289i			0.860976i	0.902596	+	0.430488i	$0.141659\pi$
$563$			20.4289i			0.860976i	−0.902596	+	0.430488i	$0.858341\pi$
$564$	−30.3510	−	61.5676i	−1.27801	−	2.59247i
$565$			32.7191i			1.37650i
$566$	−6.19654	+	1.44437i	−0.260460	+	0.0607113i
$567$		0			0
$568$	22.3510	+	27.2465i	0.937826	+	1.14324i
$569$	28.0125			1.17434			0.587172	−	0.809462i	$-0.300241\pi$
$569$	28.0125			1.17434			0.587172	+	0.809462i	$0.300241\pi$
$570$	18.6329	−	4.34320i	0.780448	−	0.181917i
$571$			14.5618i			0.609392i	0.952450	+	0.304696i	$0.0985549\pi$
$571$			14.5618i			0.609392i	−0.952450	+	0.304696i	$0.901445\pi$
$572$	−2.98210	+	1.47008i	−0.124688	+	0.0614673i
$573$		−	6.74437i		−	0.281750i
$574$		0			0
$575$	−17.1755			−0.716267
$576$	8.17972	−	41.0311i	0.340822	−	1.70963i
$577$	−20.3172			−0.845815			−0.422907	−	0.906173i	$-0.638990\pi$
$577$	−20.3172			−0.845815			−0.422907	+	0.906173i	$0.638990\pi$
$578$	−4.53837	−	19.4702i	−0.188771	−	0.809854i
$579$			27.4049i			1.13891i
$580$	−20.6027	+	10.1565i	−0.855480	+	0.421725i
$581$		0			0
$582$	−1.58774	+	0.370091i	−0.0658140	+	0.0153408i
$583$	16.0000			0.662652
$584$	−16.5254	−	20.1450i	−0.683825	−	0.833604i
$585$	−19.1491			−0.791717
$586$	11.0744	−	2.58135i	0.457478	−	0.106635i
$587$		−	8.05859i		−	0.332614i	−0.986074	−	0.166307i	$-0.946816\pi$
$587$		−	8.05859i		−	0.332614i	0.986074	−	0.166307i	$-0.0531842\pi$
$588$		0			0
$589$			1.49267i			0.0615046i
$590$	6.48604	+	27.8260i	0.267026	+	1.14558i
$591$	−34.5911			−1.42289
$592$	20.6072	+	15.8217i	0.846950	+	0.650269i
$593$	−26.0664			−1.07042			−0.535209	−	0.844720i	$-0.679767\pi$
$593$	−26.0664			−1.07042			−0.535209	+	0.844720i	$0.679767\pi$
$594$	−2.98210	−	12.7936i	−0.122357	−	0.524929i
$595$		0			0
$596$	−18.0389	−	36.5923i	−0.738902	−	1.49888i
$597$		−	11.4592i		−	0.468994i
$598$	5.17817	−	1.20699i	0.211751	−	0.0493576i
$599$	47.4876			1.94029			0.970144	−	0.242528i	$-0.0779766\pi$
$599$	47.4876			1.94029			0.970144	+	0.242528i	$0.0779766\pi$
$600$	−32.8086	+	26.9136i	−1.33940	+	1.09874i
$601$	2.00922			0.0819580			0.0409790	−	0.999160i	$-0.486952\pi$
$601$	2.00922			0.0819580			0.0409790	+	0.999160i	$0.486952\pi$
$602$		0			0
$603$			13.6233i			0.554782i
$604$	−8.45963	+	4.17034i	−0.344217	+	0.169689i
$605$		−	28.4381i		−	1.15617i
$606$	5.73129	+	24.5880i	0.232818	+	0.998821i
$607$	−41.5480			−1.68638			−0.843191	−	0.537614i	$-0.819326\pi$
$607$	−41.5480			−1.68638			−0.843191	+	0.537614i	$0.819326\pi$
$608$	−3.44495	+	7.59600i	−0.139711	+	0.308059i
$609$		0			0
$610$	3.28415	+	14.0895i	0.132971	+	0.570465i
$611$		−	13.6960i		−	0.554081i
$612$	52.3496	−	25.8067i	2.11611	−	1.04318i
$613$		−	35.0077i		−	1.41395i	−0.707239	−	0.706974i	$-0.750060\pi$
$613$		−	35.0077i		−	1.41395i	0.707239	−	0.706974i	$-0.249940\pi$
$614$	16.4979	−	3.84553i	0.665800	−	0.155193i
$615$	−67.8626			−2.73648
$616$		0			0
$617$	6.58078			0.264932			0.132466	−	0.991188i	$-0.457710\pi$
$617$	6.58078			0.264932			0.132466	+	0.991188i	$0.457710\pi$
$618$	−28.9193	+	6.74087i	−1.16330	+	0.271157i
$619$			0.391842i			0.0157495i	0.999969	+	0.00787473i	$0.00250663\pi$
$619$			0.391842i			0.0157495i	−0.999969	+	0.00787473i	$0.997493\pi$
$620$	−2.86341	−	5.80850i	−0.114997	−	0.233275i
$621$			21.0081i			0.843025i
$622$	−6.95688	−	29.8460i	−0.278946	−	1.19672i
$623$		0			0
$624$	8.00000	−	10.4197i	0.320256	−	0.417121i
$625$	−23.7981			−0.951924
$626$	−3.02443	−	12.9752i	−0.120880	−	0.518594i
$627$			6.14222i			0.245296i
$628$	−7.96925	−	16.1658i	−0.318008	−	0.645086i
$629$			36.2428i			1.44510i
$630$		0			0
$631$	23.4876			0.935025			0.467512	−	0.883987i	$-0.345150\pi$
$631$	23.4876			0.935025			0.467512	+	0.883987i	$0.345150\pi$
$632$	−24.9193	−	30.3774i	−0.991235	−	1.20835i
$633$	18.4793			0.734485
$634$	−12.6072	+	2.93864i	−0.500695	+	0.116708i
$635$		−	48.1898i		−	1.91236i
$636$	−56.7025	+	27.9526i	−2.24840	+	1.10839i
$637$		0			0
$638$	−1.67401	−	7.18172i	−0.0662746	−	0.284327i
$639$	−65.1616			−2.57775
$640$	−1.16604	−	36.1671i	−0.0460919	−	1.42963i
$641$	−15.9347			−0.629383			−0.314691	−	0.949194i	$-0.601901\pi$
$641$	−15.9347			−0.629383			−0.314691	+	0.949194i	$0.601901\pi$
$642$	−4.11647	−	17.6602i	−0.162464	−	0.696993i
$643$			44.8491i			1.76868i	0.466847	+	0.884338i	$0.345390\pi$
$643$			44.8491i			1.76868i	−0.466847	+	0.884338i	$0.654610\pi$
$644$		0			0
$645$			69.6817i			2.74372i
$646$	−11.3315	+	2.64129i	−0.445833	+	0.103920i
$647$	−23.9825			−0.942847			−0.471424	−	0.881907i	$-0.656260\pi$
$647$	−23.9825			−0.942847			−0.471424	+	0.881907i	$0.656260\pi$
$648$	4.77442	+	5.82017i	0.187557	+	0.228638i
$649$	−9.17264			−0.360058
$650$	−8.24594	+	1.92207i	−0.323432	+	0.0753897i
$651$		0			0
$652$	4.14756	+	8.41342i	0.162431	+	0.329495i
$653$			9.06564i			0.354766i	0.984142	+	0.177383i	$0.0567631\pi$
$653$			9.06564i			0.354766i	−0.984142	+	0.177383i	$0.943237\pi$
$654$	11.6387	+	49.9317i	0.455110	+	1.95248i
$655$	−15.7438			−0.615160
$656$	18.0164	−	23.4657i	0.703423	−	0.916182i
$657$	48.1778			1.87959
$658$		0			0
$659$		−	21.9578i		−	0.855354i	−0.903932	−	0.427677i	$-0.859332\pi$
$659$		−	21.9578i		−	0.855354i	0.903932	−	0.427677i	$-0.140668\pi$
$660$	−11.7827	−	23.9014i	−0.458640	−	0.930362i
$661$			26.0641i			1.01377i	0.862012	+	0.506887i	$0.169204\pi$
$661$			26.0641i			1.01377i	−0.862012	+	0.506887i	$0.830796\pi$
$662$	−27.3789	+	6.38182i	−1.06411	+	0.248036i
$663$	18.3256			0.711707
$664$	17.2127	−	14.1200i	0.667984	−	0.547963i
$665$		0			0
$666$	−46.7842	+	10.9051i	−1.81285	+	0.422562i
$667$			11.7929i			0.456624i
$668$	25.0935	−	12.3703i	0.970896	−	0.478622i
$669$			55.3183i			2.13873i
$670$	2.67475	+	11.4751i	0.103335	+	0.443320i
$671$	−4.64449			−0.179298
$672$		0			0
$673$	30.5683			1.17832			0.589161	−	0.808016i	$-0.299459\pi$
$673$	30.5683			1.17832			0.589161	+	0.808016i	$0.299459\pi$
$674$	6.27719	+	26.9300i	0.241788	+	1.03731i
$675$		−	33.4542i		−	1.28765i
$676$	−20.9694	+	10.3372i	−0.806514	+	0.397587i
$677$		−	11.9119i		−	0.457813i	−0.973448	−	0.228906i	$-0.926485\pi$
$677$		−	11.9119i		−	0.457813i	0.973448	−	0.228906i	$-0.0735149\pi$
$678$	40.4193	−	9.42145i	1.55229	−	0.361829i
$679$		0			0
$680$	39.0279	−	32.0155i	1.49665	−	1.22774i
$681$	27.7952			1.06511
$682$	2.02474	−	0.471951i	0.0775312	−	0.0180720i
$683$			18.9402i			0.724728i	0.932037	+	0.362364i	$0.118030\pi$
$683$			18.9402i			0.724728i	−0.932037	+	0.362364i	$0.881970\pi$
$684$	−6.81905	−	13.8326i	−0.260733	−	0.528903i
$685$		−	58.6939i		−	2.24258i
$686$		0			0
$687$	26.8495			1.02437
$688$	−24.0947	−	18.4994i	−0.918603	−	0.705283i
$689$	−12.6137			−0.480545
$690$	9.67401	+	41.5028i	0.368283	+	1.57999i
$691$		−	8.55765i		−	0.325549i	−0.986663	−	0.162774i	$-0.947956\pi$
$691$		−	8.55765i		−	0.325549i	0.986663	−	0.162774i	$-0.0520442\pi$
$692$	−6.66922	−	13.5287i	−0.253526	−	0.514283i
$693$		0			0
$694$	−42.7019	+	9.95351i	−1.62094	+	0.377830i
$695$	54.5544			2.06937
$696$	18.4793	+	22.5268i	0.700455	+	0.853877i
$697$	41.2702			1.56322
$698$	−20.2097	+	4.71072i	−0.764947	+	0.178304i
$699$		−	48.5374i		−	1.83585i
$700$		0			0
$701$		−	3.59086i		−	0.135625i	−0.997698	−	0.0678125i	$-0.978398\pi$
$701$		−	3.59086i		−	0.135625i	0.997698	−	0.0678125i	$-0.0216020\pi$
$702$	2.35097	+	10.0860i	0.0887315	+	0.380670i
$703$	9.57663			0.361190
$704$	11.3928	+	2.27120i	0.429383	+	0.0855992i
$705$	109.773			4.13429
$706$	−8.23995	−	35.3505i	−0.310114	−	1.33043i
$707$		0			0
$708$	32.5070	−	16.0250i	1.22169	−	0.602255i
$709$			36.8725i			1.38477i	0.721526	+	0.692387i	$0.243441\pi$
$709$			36.8725i			1.38477i	−0.721526	+	0.692387i	$0.756559\pi$
$710$	−54.8865	+	12.7936i	−2.05985	+	0.480136i
$711$	72.6491			2.72455
$712$	5.79469	+	7.06391i	0.217165	+	0.264731i
$713$	−3.32477			−0.124514
$714$		0			0
$715$		−	5.31698i		−	0.198844i
$716$	−13.1670	−	26.7096i	−0.492074	−	0.998184i
$717$			13.5287i			0.505238i
$718$	1.34945	+	5.78932i	0.0503610	+	0.216056i
$719$	43.9901			1.64055			0.820277	−	0.571966i	$-0.193819\pi$
$719$	43.9901			1.64055			0.820277	+	0.571966i	$0.193819\pi$
$720$	53.0704	+	40.7462i	1.97782	+	1.51852i
$721$		0			0
$722$	−5.40178	−	23.1744i	−0.201033	−	0.862461i
$723$		−	25.4951i		−	0.948172i
$724$	14.5835	+	29.5829i	0.541990	+	1.09944i
$725$		−	18.7795i		−	0.697455i
$726$	−35.1308	+	8.18874i	−1.30383	+	0.303913i
$727$	−50.1870			−1.86133			−0.930666	−	0.365870i	$-0.880772\pi$
$727$	−50.1870			−1.86133			−0.930666	+	0.365870i	$0.880772\pi$
$728$		0			0
$729$	41.1336			1.52347
$730$	40.5808	−	9.45908i	1.50196	−	0.350096i
$731$		−	42.3765i		−	1.56735i
$732$	16.4596	−	8.11409i	0.608365	−	0.299906i
$733$			6.30750i			0.232973i	0.993192	+	0.116486i	$0.0371632\pi$
$733$			6.30750i			0.232973i	−0.993192	+	0.116486i	$0.962837\pi$
$734$	11.4300	+	49.0365i	0.421890	+	1.80997i
$735$		0			0
$736$	−16.9193	−	7.67324i	−0.623652	−	0.282839i
$737$	−3.78267			−0.139336
$738$	12.4177	+	53.2738i	0.457103	+	1.96104i
$739$		−	34.4000i		−	1.26542i	−0.774387	−	0.632712i	$-0.781942\pi$
$739$		−	34.4000i		−	1.26542i	0.774387	−	0.632712i	$-0.218058\pi$
$740$	−37.2659	+	18.3709i	−1.36992	+	0.675329i
$741$		−	4.84227i		−	0.177885i
$742$		0			0
$743$	−9.93023			−0.364305			−0.182152	−	0.983270i	$-0.558306\pi$
$743$	−9.93023			−0.364305			−0.182152	+	0.983270i	$0.558306\pi$
$744$	−6.35097	+	5.20985i	−0.232838	+	0.191002i
$745$	65.2428			2.39031
$746$	−13.7438	+	3.20357i	−0.503195	+	0.117291i
$747$			41.1652i			1.50616i
$748$	7.16556	+	14.5355i	0.261999	+	0.531471i
$749$		0			0
$750$	−0.676959	−	2.90425i	−0.0247190	−	0.106048i
$751$	10.7717			0.393065			0.196532	−	0.980497i	$-0.437032\pi$
$751$	10.7717			0.393065			0.196532	+	0.980497i	$0.437032\pi$
$752$	−29.1430	+	37.9576i	−1.06273	+	1.38417i
$753$	−47.0404			−1.71425
$754$	1.31972	+	5.66177i	0.0480613	+	0.206190i
$755$		−	15.0832i		−	0.548935i
$756$		0			0
$757$			16.2090i			0.589127i	0.955632	+	0.294563i	$0.0951742\pi$
$757$			16.2090i			0.589127i	−0.955632	+	0.294563i	$0.904826\pi$
$758$	33.7827	−	7.87449i	1.22704	−	0.286014i
$759$	−13.6811			−0.496593
$760$	−8.45963	−	10.3126i	−0.306863	−	0.374076i
$761$	−5.37134			−0.194711			−0.0973554	−	0.995250i	$-0.531038\pi$
$761$	−5.37134			−0.194711			−0.0973554	+	0.995250i	$0.531038\pi$
$762$	−59.5310	+	13.8762i	−2.15658	+	0.502683i
$763$		0			0
$764$	−4.21733	+	2.07901i	−0.152578	+	0.0752161i
$765$			93.3374i			3.37462i
$766$	−2.77342	−	11.8984i	−0.100208	−	0.429906i
$767$	7.23133			0.261108
$768$	−44.3430	+	11.8547i	−1.60009	+	0.427771i
$769$	10.1872			0.367358			0.183679	−	0.982986i	$-0.441199\pi$
$769$	10.1872			0.367358			0.183679	+	0.982986i	$0.441199\pi$
$770$		0			0
$771$		−	36.5134i		−	1.31500i
$772$	17.1366	−	8.44781i	0.616759	−	0.304043i
$773$			51.3882i			1.84831i	0.382022	+	0.924153i	$0.375228\pi$
$773$			51.3882i			1.84831i	−0.382022	+	0.924153i	$0.624772\pi$
$774$	54.7019	−	12.7506i	1.96622	−	0.458312i
$775$	5.29450			0.190184
$776$	0.720858	+	0.878748i	0.0258773	+	0.0315452i
$777$		0			0
$778$	−17.4053	+	4.05705i	−0.624010	+	0.145452i
$779$		−	10.9051i		−	0.390714i
$780$	9.28897	+	18.8429i	0.332599	+	0.674684i
$781$		−	18.0929i		−	0.647416i
$782$	−5.88319	−	25.2397i	−0.210382	−	0.902570i
$783$	−22.9701			−0.820884
$784$		0			0
$785$	28.8231			1.02874
$786$	4.53341	+	19.4490i	0.161701	+	0.693721i
$787$		−	45.4326i		−	1.61950i	−0.586776	−	0.809749i	$-0.699603\pi$
$787$		−	45.4326i		−	1.61950i	0.586776	−	0.809749i	$-0.300397\pi$
$788$	10.6630	+	21.6302i	0.379855	+	0.770545i
$789$		−	62.8011i		−	2.23578i
$790$	61.1933	−	14.2637i	2.17716	−	0.507480i
$791$		0			0
$792$	−16.6072	+	13.6233i	−0.590111	+	0.484082i
$793$	3.66152			0.130024
$794$	2.58909	−	0.603497i	0.0918832	−	0.0214173i
$795$		−	101.099i		−	3.58560i
$796$	−7.16556	+	3.53240i	−0.253977	+	0.125203i
$797$		−	30.4917i		−	1.08007i	−0.841642	−	0.540036i	$-0.818410\pi$
$797$		−	30.4917i		−	1.08007i	0.841642	−	0.540036i	$-0.181590\pi$
$798$		0			0
$799$	−66.7578			−2.36172
$800$	26.9429	+	12.2192i	0.952577	+	0.432014i
$801$	−16.8937			−0.596910
$802$	−4.68097	−	20.0820i	−0.165291	−	0.709120i
$803$			13.3772i			0.472070i
$804$	13.4054	−	6.60847i	0.472773	−	0.233063i
$805$		0			0
$806$	−1.59622	+	0.372067i	−0.0562244	+	0.0131055i
$807$	53.1227			1.87001
$808$	13.6084	−	11.1633i	0.478744	−	0.392725i
$809$	−18.9068			−0.664727			−0.332363	−	0.943151i	$-0.607846\pi$
$809$	−18.9068			−0.664727			−0.332363	+	0.943151i	$0.607846\pi$
$810$	−11.7244	+	2.73287i	−0.411953	+	0.0960232i
$811$			34.8800i			1.22480i	0.790548	+	0.612401i	$0.209796\pi$
$811$			34.8800i			1.22480i	−0.790548	+	0.612401i	$0.790204\pi$
$812$		0			0
$813$		−	39.9718i		−	1.40187i
$814$	−3.02792	−	12.9902i	−0.106129	−	0.455307i
$815$	−15.0008			−0.525456
$816$	−50.7882	−	38.9940i	−1.77794	−	1.36506i
$817$	−11.1974			−0.391747
$818$	9.69365	+	41.5871i	0.338931	+	1.45406i
$819$		0			0
$820$	20.9193	+	42.4352i	0.730532	+	1.48190i
$821$			10.3509i			0.361249i	0.983552	+	0.180624i	$0.0578119\pi$
$821$			10.3509i			0.361249i	−0.983552	+	0.180624i	$0.942188\pi$
$822$	−72.5070	+	16.9009i	−2.52897	+	0.589485i
$823$	7.32304			0.255265			0.127633	−	0.991822i	$-0.459262\pi$
$823$	7.32304			0.255265			0.127633	+	0.991822i	$0.459262\pi$
$824$	13.1298	+	16.0056i	0.457397	+	0.557581i
$825$	21.7864			0.758504
$826$		0			0
$827$			33.6881i			1.17145i	0.810510	+	0.585725i	$0.199190\pi$
$827$			33.6881i			1.17145i	−0.810510	+	0.585725i	$0.800810\pi$
$828$	30.8106	−	15.1887i	1.07074	−	0.527843i
$829$		−	11.8848i		−	0.412777i	−0.978470	−	0.206388i	$-0.933829\pi$
$829$		−	11.8848i		−	0.412777i	0.978470	−	0.206388i	$-0.0661710\pi$
$830$	8.08226	+	34.6740i	0.280539	+	1.20355i
$831$	−39.9406			−1.38553
$832$	−8.98162	−	1.79052i	−0.311382	−	0.0620752i
$833$		0			0
$834$	−15.7089	−	67.3933i	−0.543954	−	2.33364i
$835$			44.7408i			1.54832i
$836$	3.84080	−	1.89339i	0.132837	−	0.0654844i
$837$		−	6.47594i		−	0.223841i
$838$	−10.0373	+	2.33963i	−0.346734	+	0.0808211i
$839$	53.8741			1.85994			0.929970	−	0.367635i	$-0.119832\pi$
$839$	53.8741			1.85994			0.929970	+	0.367635i	$0.119832\pi$
$840$		0			0
$841$	16.1057			0.555369
$842$	−3.17548	+	0.740182i	−0.109434	+	0.0255083i
$843$		−	4.10723i		−	0.141460i
$844$	−5.69641	−	11.5553i	−0.196078	−	0.397750i
$845$		−	37.3876i		−	1.28617i
$846$	−20.0867	−	86.1745i	−0.690593	−	2.96274i
$847$		0			0
$848$	34.9582	+	26.8401i	1.20047	+	0.921692i
$849$	−12.9068			−0.442959
$850$	9.36864	+	40.1928i	0.321342	+	1.37860i
$851$			21.3309i			0.731214i
$852$	31.6090	+	64.1197i	1.08291	+	2.19670i
$853$		−	31.6588i		−	1.08398i	−0.840386	−	0.541988i	$-0.817672\pi$
$853$		−	31.6588i		−	1.08398i	0.840386	−	0.541988i	$-0.182328\pi$
$854$		0			0
$855$	24.6630			0.843458
$856$	−9.77419	+	8.01800i	−0.334075	+	0.274050i
$857$	−3.02159			−0.103216			−0.0516078	−	0.998667i	$-0.516435\pi$
$857$	−3.02159			−0.103216			−0.0516078	+	0.998667i	$0.516435\pi$
$858$	−6.56829	+	1.53102i	−0.224238	+	0.0522682i
$859$			14.9274i			0.509315i	0.967031	+	0.254657i	$0.0819627\pi$
$859$			14.9274i			0.509315i	−0.967031	+	0.254657i	$0.918037\pi$
$860$	43.5728	−	21.4800i	1.48582	−	0.732463i
$861$		0			0
$862$	0.759216	+	3.25714i	0.0258590	+	0.110939i
$863$	−2.86341			−0.0974716			−0.0487358	−	0.998812i	$-0.515519\pi$
$863$	−2.86341			−0.0974716			−0.0487358	+	0.998812i	$0.515519\pi$
$864$	14.9458	−	32.9551i	0.508467	−	1.12116i
$865$	24.1212			0.820144
$866$	3.55811	+	15.2648i	0.120910	+	0.518719i
$867$		−	40.5546i		−	1.37730i
$868$		0			0
$869$			20.1719i			0.684286i
$870$	−45.3789	+	10.5775i	−1.53849	+	0.358610i
$871$	2.98210			0.101045
$872$	27.6351	−	22.6697i	0.935843	−	0.767694i
$873$	−2.10157			−0.0711275
$874$	−6.66922	+	1.55455i	−0.225590	+	0.0525833i
$875$		0			0
$876$	−23.3704	−	47.4074i	−0.789613	−	1.60175i
$877$		−	25.6275i		−	0.865381i	−0.901543	−	0.432690i	$-0.857564\pi$
$877$		−	25.6275i		−	0.865381i	0.901543	−	0.432690i	$-0.142436\pi$
$878$	2.14107	+	9.18547i	0.0722575	+	0.309995i
$879$	23.0668			0.778024
$880$	−11.3137	+	14.7357i	−0.381385	+	0.496739i
$881$	22.1882			0.747540			0.373770	−	0.927521i	$-0.378065\pi$
$881$	22.1882			0.747540			0.373770	+	0.927521i	$0.378065\pi$
$882$		0			0
$883$			26.5063i			0.892010i	0.895031	+	0.446005i	$0.147154\pi$
$883$			26.5063i			0.892010i	−0.895031	+	0.446005i	$0.852846\pi$
$884$	−5.64903	−	11.4592i	−0.189998	−	0.385415i
$885$			57.9588i			1.94827i
$886$	1.84396	−	0.429814i	0.0619492	−	0.0144399i
$887$	11.0064			0.369557			0.184779	−	0.982780i	$-0.440843\pi$
$887$	11.0064			0.369557			0.184779	+	0.982780i	$0.440843\pi$
$888$	33.4251	+	40.7462i	1.12167	+	1.36735i
$889$		0			0
$890$	−14.2298	+	3.31687i	−0.476984	+	0.111182i
$891$		−	3.86486i		−	0.129478i
$892$	34.5911	−	17.0524i	1.15820	−	0.570956i
$893$			17.6398i			0.590292i
$894$	−18.7866	−	80.5972i	−0.628319	−	2.69557i
$895$	47.6222			1.59184
$896$		0			0
$897$	10.7856			0.360121
$898$	1.39682	+	5.99255i	0.0466125	+	0.199974i
$899$		−	3.63528i		−	0.121243i
$900$	−49.0641	+	24.1871i	−1.63547	+	0.806237i
$901$			61.4825i			2.04828i
$902$	−14.7922	+	3.44794i	−0.492525	+	0.114804i
$903$		0			0
$904$	−18.3510	−	22.3704i	−0.610344	−	0.744029i
$905$	−52.7453			−1.75331
$906$	−18.6329	+	4.34320i	−0.619038	+	0.144293i
$907$			57.5895i			1.91223i	0.292995	+	0.956114i	$0.405348\pi$
$907$			57.5895i			1.91223i	−0.292995	+	0.956114i	$0.594652\pi$
$908$	−8.56811	−	17.3806i	−0.284343	−	0.576796i
$909$			32.5453i			1.07946i
$910$		0			0
$911$	2.77170			0.0918306			0.0459153	−	0.998945i	$-0.485380\pi$
$911$	2.77170			0.0918306			0.0459153	+	0.998945i	$0.485380\pi$
$912$	−10.3036	+	13.4200i	−0.341186	+	0.444382i
$913$	−11.4300			−0.378279
$914$	7.06682	+	30.3176i	0.233750	+	1.00282i
$915$			29.3469i			0.970180i
$916$	−8.27660	−	16.7893i	−0.273467	−	0.554734i
$917$		0			0
$918$	49.1616	−	11.4592i	1.62257	−	0.378210i
$919$	20.4596			0.674901			0.337450	−	0.941343i	$-0.390435\pi$
$919$	20.4596			0.674901			0.337450	+	0.941343i	$0.390435\pi$
$920$	22.9701	−	18.8429i	0.757301	−	0.621232i
$921$	34.3635			1.13231
$922$	9.37464	−	2.18516i	0.308737	−	0.0719644i
$923$			14.2637i			0.469496i
$924$		0			0
$925$		−	33.9682i		−	1.11687i
$926$	−0.459630	−	1.97188i	−0.0151044	−	0.0647999i
$927$	−38.2783			−1.25722
$928$	8.38986	−	18.4994i	0.275411	−	0.607272i
$929$	11.5442			0.378754			0.189377	−	0.981904i	$-0.439353\pi$
$929$	11.5442			0.378754			0.189377	+	0.981904i	$0.439353\pi$
$930$	−2.98210	−	12.7936i	−0.0977870	−	0.419520i
$931$		0			0
$932$	−30.3510	+	14.9621i	−0.994179	+	0.490100i
$933$		−	62.1663i		−	2.03523i
$934$	46.5489	−	10.8502i	1.52313	−	0.355029i
$935$	−25.9163			−0.847554
$936$	13.0924	−	10.7400i	0.427939	−	0.351049i
$937$	−46.4780			−1.51837			−0.759185	−	0.650874i	$-0.774402\pi$
$937$	−46.4780			−1.51837			−0.759185	+	0.650874i	$0.774402\pi$
$938$		0			0
$939$		−	27.0261i		−	0.881964i
$940$	−33.8385	−	68.6422i	−1.10369	−	2.23886i
$941$		−	39.6772i		−	1.29344i	−0.762728	−	0.646720i	$-0.776140\pi$
$941$		−	39.6772i		−	1.29344i	0.762728	−	0.646720i	$-0.223860\pi$
$942$	−8.29959	−	35.6064i	−0.270415	−	1.16012i
$943$	24.2898			0.790985
$944$	−20.0412	−	15.3871i	−0.652284	−	0.500809i
$945$		0			0
$946$	3.54037	+	15.1887i	0.115107	+	0.493827i
$947$		−	50.2561i		−	1.63310i	−0.577271	−	0.816552i	$-0.695882\pi$
$947$		−	50.2561i		−	1.63310i	0.577271	−	0.816552i	$-0.304118\pi$
$948$	−35.2412	−	71.4875i	−1.14458	−	2.32181i
$949$		−	10.5460i		−	0.342338i
$950$	10.6204	−	2.47553i	0.344570	−	0.0803167i
$951$	−26.2595			−0.851524
$952$		0			0
$953$	26.4596			0.857111			0.428556	−	0.903515i	$-0.359023\pi$
$953$	26.4596			0.857111			0.428556	+	0.903515i	$0.359023\pi$
$954$	−79.3650	+	18.4994i	−2.56954	+	0.598940i
$955$		−	7.51935i		−	0.243320i
$956$	8.45963	−	4.17034i	0.273604	−	0.134878i
$957$		−	14.9588i		−	0.483550i
$958$	−7.04923	−	30.2422i	−0.227750	−	0.977081i
$959$		0			0
$960$	14.3510	−	71.9873i	0.463175	−	2.32338i
$961$	−29.9751			−0.966939
$962$	2.38709	+	10.2410i	0.0769629	+	0.330182i
$963$		−	23.3755i		−	0.753265i
$964$	−15.9424	+	7.85909i	−0.513469	+	0.253124i
$965$			30.5539i			0.983566i
$966$		0			0
$967$	−6.98903			−0.224752			−0.112376	−	0.993666i	$-0.535846\pi$
$967$	−6.98903			−0.224752			−0.112376	+	0.993666i	$0.535846\pi$
$968$	15.9499	+	19.4434i	0.512649	+	0.624936i
$969$	−23.6024			−0.758220
$970$	−1.77018	+	0.412617i	−0.0568372	+	0.0132483i
$971$			26.3180i			0.844583i	0.906460	+	0.422292i	$0.138774\pi$
$971$			26.3180i			0.844583i	−0.906460	+	0.422292i	$0.861226\pi$
$972$	−10.2185	−	20.7285i	−0.327759	−	0.664866i
$973$		0			0
$974$	11.9177	+	51.1288i	0.381869	+	1.63827i
$975$	−17.1755			−0.550056
$976$	−10.1477	−	7.79114i	−0.324819	−	0.249388i
$977$	32.9193			1.05318			0.526590	−	0.850119i	$-0.323470\pi$
$977$	32.9193			1.05318			0.526590	+	0.850119i	$0.323470\pi$
$978$	4.31948	+	18.5312i	0.138122	+	0.592561i
$979$		−	4.69076i		−	0.149917i
$980$		0			0
$981$			66.0909i			2.11012i
$982$	−4.55982	+	1.06286i	−0.145510	+	0.0339172i
$983$	26.9646			0.860036			0.430018	−	0.902820i	$-0.358507\pi$
$983$	26.9646			0.860036			0.430018	+	0.902820i	$0.358507\pi$
$984$	46.3983	−	38.0616i	1.47912	−	1.21336i
$985$	−38.5659			−1.22881
$986$	27.5969	−	6.43264i	0.878865	−	0.204857i
$987$		0			0
$988$	−3.02792	+	1.49267i	−0.0963311	+	0.0474883i
$989$		−	24.9409i		−	0.793076i
$990$	−7.79792	−	33.4542i	−0.247834	−	1.06324i
$991$	−12.4596			−0.395793			−0.197897	−	0.980223i	$-0.563411\pi$
$991$	−12.4596			−0.395793			−0.197897	+	0.980223i	$0.563411\pi$
$992$	5.21552	+	2.36535i	0.165593	+	0.0750998i
$993$	−57.0275			−1.80971
$994$		0			0
$995$		−	12.7759i		−	0.405025i
$996$	40.5070	−	19.9687i	1.28351	−	0.632733i
$997$			44.8670i			1.42095i	0.703721	+	0.710477i	$0.251521\pi$
$997$			44.8670i			1.42095i	−0.703721	+	0.710477i	$0.748479\pi$
$998$	33.7911	−	7.87647i	1.06964	−	0.249325i
$999$	−41.5480			−1.31452

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	392.2.b.g.197.5	✓	12
4.3	odd	2		1568.2.b.g.785.12		12
7.2	even	3		392.2.p.h.165.4		24
7.3	odd	6		392.2.p.h.373.12		24
7.4	even	3		392.2.p.h.373.11		24
7.5	odd	6		392.2.p.h.165.3		24
7.6	odd	2	inner	392.2.b.g.197.6	yes	12
8.3	odd	2		1568.2.b.g.785.1		12
8.5	even	2	inner	392.2.b.g.197.8	yes	12
28.3	even	6		1568.2.t.h.177.2		24
28.11	odd	6		1568.2.t.h.177.12		24
28.19	even	6		1568.2.t.h.753.11		24
28.23	odd	6		1568.2.t.h.753.1		24
28.27	even	2		1568.2.b.g.785.2		12
56.3	even	6		1568.2.t.h.177.11		24
56.5	odd	6		392.2.p.h.165.12		24
56.11	odd	6		1568.2.t.h.177.1		24
56.13	odd	2	inner	392.2.b.g.197.7	yes	12
56.19	even	6		1568.2.t.h.753.2		24
56.27	even	2		1568.2.b.g.785.11		12
56.37	even	6		392.2.p.h.165.11		24
56.45	odd	6		392.2.p.h.373.3		24
56.51	odd	6		1568.2.t.h.753.12		24
56.53	even	6		392.2.p.h.373.4		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
392.2.b.g.197.5	✓	12	1.1	even	1	trivial
392.2.b.g.197.6	yes	12	7.6	odd	2	inner
392.2.b.g.197.7	yes	12	56.13	odd	2	inner
392.2.b.g.197.8	yes	12	8.5	even	2	inner
392.2.p.h.165.3		24	7.5	odd	6
392.2.p.h.165.4		24	7.2	even	3
392.2.p.h.165.11		24	56.37	even	6
392.2.p.h.165.12		24	56.5	odd	6
392.2.p.h.373.3		24	56.45	odd	6
392.2.p.h.373.4		24	56.53	even	6
392.2.p.h.373.11		24	7.4	even	3
392.2.p.h.373.12		24	7.3	odd	6
1568.2.b.g.785.1		12	8.3	odd	2
1568.2.b.g.785.2		12	28.27	even	2
1568.2.b.g.785.11		12	56.27	even	2
1568.2.b.g.785.12		12	4.3	odd	2
1568.2.t.h.177.1		24	56.11	odd	6
1568.2.t.h.177.2		24	28.3	even	6
1568.2.t.h.177.11		24	56.3	even	6
1568.2.t.h.177.12		24	28.11	odd	6
1568.2.t.h.753.1		24	28.23	odd	6
1568.2.t.h.753.2		24	56.19	even	6
1568.2.t.h.753.11		24	28.19	even	6
1568.2.t.h.753.12		24	56.51	odd	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-0.321037 - 1.37729i) q^{2} -2.86877i q^{3} +(-1.79387 + 0.884323i) q^{4} -3.19841i q^{5} +(-3.95113 + 0.920979i) q^{6} +(1.79387 + 2.18678i) q^{8} -5.22982 q^{9} +O(q^{10})\)	\(q+(-0.321037 - 1.37729i) q^{2} -2.86877i q^{3} +(-1.79387 + 0.884323i) q^{4} -3.19841i q^{5} +(-3.95113 + 0.920979i) q^{6} +(1.79387 + 2.18678i) q^{8} -5.22982 q^{9} +(-4.40514 + 1.02681i) q^{10} -1.45212i q^{11} +(2.53692 + 5.14619i) q^{12} +1.14479i q^{13} -9.17548 q^{15} +(2.43594 - 3.17272i) q^{16} +5.58002 q^{17} +(1.67896 + 7.20299i) q^{18} -1.47444i q^{19} +(2.82843 + 5.73753i) q^{20} +(-2.00000 + 0.466185i) q^{22} +3.28415 q^{23} +(6.27337 - 5.14619i) q^{24} -5.22982 q^{25} +(1.57672 - 0.367521i) q^{26} +6.39682i q^{27} +3.59086i q^{29} +(2.94567 + 12.6373i) q^{30} -1.01237 q^{31} +(-5.15180 - 2.33645i) q^{32} -4.16580 q^{33} +(-1.79139 - 7.68532i) q^{34} +(9.38161 - 4.62485i) q^{36} +6.49511i q^{37} +(-2.03073 + 0.473349i) q^{38} +3.28415 q^{39} +(6.99423 - 5.73753i) q^{40} +7.39608 q^{41} -7.59434i q^{43} +(1.28415 + 2.60492i) q^{44} +16.7271i q^{45} +(-1.05433 - 4.52323i) q^{46} -11.9637 q^{47} +(-9.10180 - 6.98815i) q^{48} +(1.67896 + 7.20299i) q^{50} -16.0078i q^{51} +(-1.01237 - 2.05361i) q^{52} +11.0183i q^{53} +(8.81029 - 2.05361i) q^{54} -4.64449 q^{55} -4.22982 q^{57} +(4.94567 - 1.15280i) q^{58} -6.31671i q^{59} +(16.4596 - 8.11409i) q^{60} -3.19841i q^{61} +(0.325008 + 1.39433i) q^{62} +(-1.56406 + 7.84562i) q^{64} +3.66152 q^{65} +(1.33738 + 5.73753i) q^{66} -2.60492i q^{67} +(-10.0098 + 4.93454i) q^{68} -9.42145i q^{69} +12.4596 q^{71} +(-9.38161 - 11.4365i) q^{72} -9.21213 q^{73} +(8.94567 - 2.08517i) q^{74} +15.0031i q^{75} +(1.30388 + 2.64495i) q^{76} +(-1.05433 - 4.52323i) q^{78} -13.8913 q^{79} +(-10.1477 - 7.79114i) q^{80} +2.66152 q^{81} +(-2.37441 - 10.1866i) q^{82} -7.87125i q^{83} -17.8472i q^{85} +(-10.4596 + 2.43806i) q^{86} +10.3013 q^{87} +(3.17548 - 2.60492i) q^{88} +3.23027 q^{89} +(23.0381 - 5.37001i) q^{90} +(-5.89134 + 2.90425i) q^{92} +2.90425i q^{93} +(3.84080 + 16.4776i) q^{94} -4.71585 q^{95} +(-6.70272 + 14.7793i) q^{96} +0.401845 q^{97} +7.59434i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 2 q^{2} + 2 q^{4} - 2 q^{8} - 12 q^{9}+O(q^{10}) \) 12 * q - 2 * q^2 + 2 * q^4 - 2 * q^8 - 12 * q^9	\( 12 q - 2 q^{2} + 2 q^{4} - 2 q^{8} - 12 q^{9} - 16 q^{15} + 2 q^{16} + 22 q^{18} - 24 q^{22} + 32 q^{23} - 12 q^{25} - 8 q^{30} - 42 q^{32} + 42 q^{36} + 32 q^{39} + 8 q^{44} - 56 q^{46} + 22 q^{50} + 16 q^{58} + 96 q^{60} - 46 q^{64} + 8 q^{65} + 48 q^{71} - 42 q^{72} + 64 q^{74} - 56 q^{78} - 80 q^{79} - 4 q^{81} - 24 q^{86} - 56 q^{88} + 16 q^{92} - 64 q^{95}+O(q^{100}) \) 12 * q - 2 * q^2 + 2 * q^4 - 2 * q^8 - 12 * q^9 - 16 * q^15 + 2 * q^16 + 22 * q^18 - 24 * q^22 + 32 * q^23 - 12 * q^25 - 8 * q^30 - 42 * q^32 + 42 * q^36 + 32 * q^39 + 8 * q^44 - 56 * q^46 + 22 * q^50 + 16 * q^58 + 96 * q^60 - 46 * q^64 + 8 * q^65 + 48 * q^71 - 42 * q^72 + 64 * q^74 - 56 * q^78 - 80 * q^79 - 4 * q^81 - 24 * q^86 - 56 * q^88 + 16 * q^92 - 64 * q^95

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