LMFDB - Embedded newform 351.2.e.c.118.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [351,2,Mod(118,351)] 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("351.118"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(351, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 351 = 3^{3} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	351.e (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$2.80274911095$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
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} - x^{11} - 3 x^{10} - x^{9} - 2 x^{8} + 9 x^{7} + 24 x^{6} + 27 x^{5} - 18 x^{4} - 27 x^{3} + \cdots + 729 $ x^12 - x^11 - 3x^10 - x^9 - 2x^8 + 9x^7 + 24x^6 + 27x^5 - 18x^4 - 27x^3 - 243x^2 - 243*x + 729
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 117)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			118.6
Root			$-1.29386 - 1.15149i$ of defining polynomial
Character	$\chi$	$=$	351.118
Dual form			351.2.e.c.235.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.10275 + 1.91002i) q^{2} +(-1.43212 + 2.48050i) q^{4} +(-1.80370 + 3.12410i) q^{5} +(0.540062 + 0.935414i) q^{7} -1.90608 q^{8} -7.95614 q^{10} +(-2.14415 - 3.71378i) q^{11} +(0.500000 - 0.866025i) q^{13} +(-1.19111 + 2.06306i) q^{14} +(0.762304 + 1.32035i) q^{16} +2.31911 q^{17} +1.50171 q^{19} +(-5.16624 - 8.94818i) q^{20} +(4.72893 - 8.19074i) q^{22} +(-3.54380 + 6.13804i) q^{23} +(-4.00668 - 6.93978i) q^{25} +2.20550 q^{26} -3.09373 q^{28} +(2.86719 + 4.96611i) q^{29} +(-1.22224 + 2.11699i) q^{31} +(-3.58735 + 6.21347i) q^{32} +(2.55740 + 4.42954i) q^{34} -3.89644 q^{35} +6.00066 q^{37} +(1.65602 + 2.86830i) q^{38} +(3.43801 - 5.95480i) q^{40} +(5.29070 - 9.16376i) q^{41} +(3.67650 + 6.36788i) q^{43} +12.2827 q^{44} -15.6317 q^{46} +(-0.992308 - 1.71873i) q^{47} +(2.91667 - 5.05181i) q^{49} +(8.83675 - 15.3057i) q^{50} +(1.43212 + 2.48050i) q^{52} +11.2772 q^{53} +15.4696 q^{55} +(-1.02940 - 1.78298i) q^{56} +(-6.32359 + 10.9528i) q^{58} +(1.84760 - 3.20014i) q^{59} +(0.840995 + 1.45665i) q^{61} -5.39132 q^{62} -12.7746 q^{64} +(1.80370 + 3.12410i) q^{65} +(2.46583 - 4.27094i) q^{67} +(-3.32124 + 5.75255i) q^{68} +(-4.29681 - 7.44229i) q^{70} -7.07217 q^{71} -3.54440 q^{73} +(6.61723 + 11.4614i) q^{74} +(-2.15063 + 3.72501i) q^{76} +(2.31595 - 4.01134i) q^{77} +(-2.03514 - 3.52496i) q^{79} -5.49988 q^{80} +23.3373 q^{82} +(-7.31845 - 12.6759i) q^{83} +(-4.18298 + 7.24513i) q^{85} +(-8.10853 + 14.0444i) q^{86} +(4.08693 + 7.07877i) q^{88} -6.03027 q^{89} +1.08012 q^{91} +(-10.1503 - 17.5808i) q^{92} +(2.18854 - 3.79066i) q^{94} +(-2.70864 + 4.69151i) q^{95} +(0.0682304 + 0.118178i) q^{97} +12.8654 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 2 q^{2} - 6 q^{4} - 3 q^{5} + 12 q^{8} - 12 q^{10} - 7 q^{11} + 6 q^{13} - 13 q^{14} - 6 q^{16} + 28 q^{17} - 6 q^{19} - 17 q^{20} + 3 q^{22} - 17 q^{23} - 3 q^{25} - 4 q^{26} + 30 q^{28} - 14 q^{29}+ \cdots + 34 q^{98}+O(q^{100}) $ 12 * q - 2 * q^2 - 6 * q^4 - 3 * q^5 + 12 * q^8 - 12 * q^10 - 7 * q^11 + 6 * q^13 - 13 * q^14 - 6 * q^16 + 28 * q^17 - 6 * q^19 - 17 * q^20 + 3 * q^22 - 17 * q^23 - 3 * q^25 - 4 * q^26 + 30 * q^28 - 14 * q^29 - 6 * q^31 - 9 * q^32 - 3 * q^34 + 26 * q^35 - 18 * q^37 + 4 * q^38 + 6 * q^40 + 4 * q^41 + 3 * q^43 + 26 * q^44 - 9 * q^47 + 21 * q^50 + 6 * q^52 + 56 * q^53 + 30 * q^55 - 16 * q^56 - 18 * q^58 - 17 * q^59 + 6 * q^61 - 8 * q^62 - 60 * q^64 + 3 * q^65 + 12 * q^67 - 22 * q^68 - 9 * q^70 - 2 * q^71 - 18 * q^73 + 27 * q^74 + 3 * q^76 - 15 * q^77 + 6 * q^79 - 48 * q^80 + 54 * q^82 - 28 * q^83 - 27 * q^85 + 6 * q^86 + 9 * q^88 - 18 * q^89 - 44 * q^92 + 24 * q^94 - 32 * q^95 + 34 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/351\mathbb{Z}\right)^\times$.

$n$	$28$	$326$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	1.10275	+	1.91002i	0.779763	+	1.35059i	0.932078	+	0.362257i	$0.117994\pi$
$2$	1.10275	+	1.91002i	0.779763	+	1.35059i	−0.152315	+	0.988332i	$0.548673\pi$
$3$		0			0
$3$		0			0
$4$	−1.43212	+	2.48050i	−0.716060	+	1.24025i
$5$	−1.80370	+	3.12410i	−0.806640	+	1.39714i	0.108538	+	0.994092i	$0.465383\pi$
$5$	−1.80370	+	3.12410i	−0.806640	+	1.39714i	−0.915178	+	0.403049i	$0.867950\pi$
$6$		0			0
$7$	0.540062	+	0.935414i	0.204124	+	0.353553i	0.949853	−	0.312696i	$-0.101232\pi$
$7$	0.540062	+	0.935414i	0.204124	+	0.353553i	−0.745729	+	0.666249i	$0.767899\pi$
$8$	−1.90608			−0.673902
$9$		0			0
$10$	−7.95614			−2.51595
$11$	−2.14415	−	3.71378i	−0.646485	−	1.11975i	−0.983956	−	0.178409i	$-0.942905\pi$
$11$	−2.14415	−	3.71378i	−0.646485	−	1.11975i	0.337471	−	0.941336i	$-0.390429\pi$
$12$		0			0
$13$	0.500000	−	0.866025i	0.138675	−	0.240192i
$13$	0.500000	−	0.866025i	0.138675	−	0.240192i
$14$	−1.19111	+	2.06306i	−0.318337	+	0.551376i
$15$		0			0
$16$	0.762304	+	1.32035i	0.190576	+	0.330087i
$17$	2.31911			0.562466			0.281233	−	0.959640i	$-0.409257\pi$
$17$	2.31911			0.562466			0.281233	+	0.959640i	$0.409257\pi$
$18$		0			0
$19$	1.50171			0.344517			0.172258	−	0.985052i	$-0.444894\pi$
$19$	1.50171			0.344517			0.172258	+	0.985052i	$0.444894\pi$
$20$	−5.16624	−	8.94818i	−1.15521	−	2.00087i
$21$		0			0
$22$	4.72893	−	8.19074i	1.00821	−	1.74627i
$23$	−3.54380	+	6.13804i	−0.738933	+	1.27987i	0.214043	+	0.976824i	$0.431337\pi$
$23$	−3.54380	+	6.13804i	−0.738933	+	1.27987i	−0.952976	+	0.303045i	$0.901997\pi$
$24$		0			0
$25$	−4.00668	−	6.93978i	−0.801337	−	1.38796i
$26$	2.20550			0.432535
$27$		0			0
$28$	−3.09373			−0.584661
$29$	2.86719	+	4.96611i	0.532423	+	0.922184i	0.999283	+	0.0378531i	$0.0120519\pi$
$29$	2.86719	+	4.96611i	0.532423	+	0.922184i	−0.466860	+	0.884331i	$0.654615\pi$
$30$		0			0
$31$	−1.22224	+	2.11699i	−0.219521	+	0.380222i	−0.954662	−	0.297693i	$-0.903783\pi$
$31$	−1.22224	+	2.11699i	−0.219521	+	0.380222i	0.735140	+	0.677915i	$0.237116\pi$
$32$	−3.58735	+	6.21347i	−0.634159	+	1.09840i
$33$		0			0
$34$	2.55740	+	4.42954i	0.438590	+	0.759660i
$35$	−3.89644			−0.658619
$36$		0			0
$37$	6.00066			0.986502			0.493251	−	0.869887i	$-0.335808\pi$
$37$	6.00066			0.986502			0.493251	+	0.869887i	$0.335808\pi$
$38$	1.65602	+	2.86830i	0.268641	+	0.465300i
$39$		0			0
$40$	3.43801	−	5.95480i	0.543597	−	0.941537i
$41$	5.29070	−	9.16376i	0.826268	−	1.43114i	−0.0746779	−	0.997208i	$-0.523793\pi$
$41$	5.29070	−	9.16376i	0.826268	−	1.43114i	0.900946	−	0.433931i	$-0.142874\pi$
$42$		0			0
$43$	3.67650	+	6.36788i	0.560661	+	0.971093i	0.997439	+	0.0715239i	$0.0227862\pi$
$43$	3.67650	+	6.36788i	0.560661	+	0.971093i	−0.436778	+	0.899569i	$0.643880\pi$
$44$	12.2827			1.85169
$45$		0			0
$46$	−15.6317			−2.30477
$47$	−0.992308	−	1.71873i	−0.144743	−	0.250702i	0.784534	−	0.620086i	$-0.212902\pi$
$47$	−0.992308	−	1.71873i	−0.144743	−	0.250702i	−0.929277	+	0.369384i	$0.879569\pi$
$48$		0			0
$49$	2.91667	−	5.05181i	0.416667	−	0.721688i
$50$	8.83675	−	15.3057i	1.24971	−	2.16455i
$51$		0			0
$52$	1.43212	+	2.48050i	0.198599	+	0.343984i
$53$	11.2772			1.54904			0.774520	−	0.632550i	$-0.217992\pi$
$53$	11.2772			1.54904			0.774520	+	0.632550i	$0.217992\pi$
$54$		0			0
$55$	15.4696			2.08592
$56$	−1.02940	−	1.78298i	−0.137560	−	0.238260i
$57$		0			0
$58$	−6.32359	+	10.9528i	−0.830328	+	1.43817i
$59$	1.84760	−	3.20014i	0.240537	−	0.416623i	−0.720330	−	0.693631i	$-0.756010\pi$
$59$	1.84760	−	3.20014i	0.240537	−	0.416623i	0.960867	+	0.277009i	$0.0893430\pi$
$60$		0			0
$61$	0.840995	+	1.45665i	0.107678	+	0.186504i	0.914829	−	0.403841i	$-0.132325\pi$
$61$	0.840995	+	1.45665i	0.107678	+	0.186504i	−0.807151	+	0.590345i	$0.798992\pi$
$62$	−5.39132			−0.684698
$63$		0			0
$64$	−12.7746			−1.59682
$65$	1.80370	+	3.12410i	0.223722	+	0.387497i
$66$		0			0
$67$	2.46583	−	4.27094i	0.301249	−	0.521778i	−0.675170	−	0.737662i	$-0.735930\pi$
$67$	2.46583	−	4.27094i	0.301249	−	0.521778i	0.976419	+	0.215884i	$0.0692633\pi$
$68$	−3.32124	+	5.75255i	−0.402759	+	0.697600i
$69$		0			0
$70$	−4.29681	−	7.44229i	−0.513567	−	0.889523i
$71$	−7.07217			−0.839313			−0.419656	−	0.907683i	$-0.637849\pi$
$71$	−7.07217			−0.839313			−0.419656	+	0.907683i	$0.637849\pi$
$72$		0			0
$73$	−3.54440			−0.414840			−0.207420	−	0.978252i	$-0.566507\pi$
$73$	−3.54440			−0.414840			−0.207420	+	0.978252i	$0.566507\pi$
$74$	6.61723	+	11.4614i	0.769237	+	1.33236i
$75$		0			0
$76$	−2.15063	+	3.72501i	−0.246695	+	0.427288i
$77$	2.31595	−	4.01134i	0.263927	−	0.457134i
$78$		0			0
$79$	−2.03514	−	3.52496i	−0.228971	−	0.396589i	0.728532	−	0.685011i	$-0.240203\pi$
$79$	−2.03514	−	3.52496i	−0.228971	−	0.396589i	−0.957503	+	0.288422i	$0.906869\pi$
$80$	−5.49988			−0.614905
$81$		0			0
$82$	23.3373			2.57717
$83$	−7.31845	−	12.6759i	−0.803304	−	1.39136i	−0.917430	−	0.397897i	$-0.869740\pi$
$83$	−7.31845	−	12.6759i	−0.803304	−	1.39136i	0.114126	−	0.993466i	$-0.463593\pi$
$84$		0			0
$85$	−4.18298	+	7.24513i	−0.453708	+	0.785844i
$86$	−8.10853	+	14.0444i	−0.874365	+	1.51444i
$87$		0			0
$88$	4.08693	+	7.07877i	0.435668	+	0.754599i
$89$	−6.03027			−0.639207			−0.319604	−	0.947551i	$-0.603550\pi$
$89$	−6.03027			−0.639207			−0.319604	+	0.947551i	$0.603550\pi$
$90$		0			0
$91$	1.08012			0.113228
$92$	−10.1503	−	17.5808i	−1.05824	−	1.83293i
$93$		0			0
$94$	2.18854	−	3.79066i	0.225730	−	0.390976i
$95$	−2.70864	+	4.69151i	−0.277901	+	0.481339i
$96$		0			0
$97$	0.0682304	+	0.118178i	0.00692775	+	0.0119992i	0.869468	−	0.493988i	$-0.164461\pi$
$97$	0.0682304	+	0.118178i	0.00692775	+	0.0119992i	−0.862541	+	0.505988i	$0.831128\pi$
$98$	12.8654			1.29960
$99$		0			0
$100$	22.9522			2.29522
$101$	−5.76417	−	9.98383i	−0.573556	−	0.993428i	−0.996197	−	0.0871309i	$-0.972230\pi$
$101$	−5.76417	−	9.98383i	−0.573556	−	0.993428i	0.422641	−	0.906297i	$-0.361103\pi$
$102$		0			0
$103$	−5.43445	+	9.41274i	−0.535472	+	0.927465i	0.463668	+	0.886009i	$0.346533\pi$
$103$	−5.43445	+	9.41274i	−0.535472	+	0.927465i	−0.999140	+	0.0414559i	$0.986800\pi$
$104$	−0.953042	+	1.65072i	−0.0934534	+	0.161866i
$105$		0			0
$106$	12.4359	+	21.5396i	1.20788	+	2.09212i
$107$	10.7559			1.03981			0.519905	−	0.854224i	$-0.325967\pi$
$107$	10.7559			1.03981			0.519905	+	0.854224i	$0.325967\pi$
$108$		0			0
$109$	6.01305			0.575946			0.287973	−	0.957639i	$-0.407019\pi$
$109$	6.01305			0.575946			0.287973	+	0.957639i	$0.407019\pi$
$110$	17.0591	+	29.5473i	1.62653	+	2.81723i
$111$		0			0
$112$	−0.823383	+	1.42614i	−0.0778023	+	0.134758i
$113$	−5.43613	+	9.41565i	−0.511388	+	0.885750i	0.488525	+	0.872550i	$0.337535\pi$
$113$	−5.43613	+	9.41565i	−0.511388	+	0.885750i	−0.999913	+	0.0132002i	$0.995798\pi$
$114$		0			0
$115$	−12.7839	−	22.1424i	−1.19211	−	2.06479i
$116$	−16.4246			−1.52499
$117$		0			0
$118$	8.14978			0.750248
$119$	1.25246	+	2.16932i	0.114813	+	0.198862i
$120$		0			0
$121$	−3.69475	+	6.39950i	−0.335887	+	0.581773i
$122$	−1.85482	+	3.21263i	−0.167927	+	0.290858i
$123$		0			0
$124$	−3.50080	−	6.06356i	−0.314381	−	0.544523i
$125$	10.8704			0.972281
$126$		0			0
$127$	1.94126			0.172259			0.0861293	−	0.996284i	$-0.472550\pi$
$127$	1.94126			0.172259			0.0861293	+	0.996284i	$0.472550\pi$
$128$	−6.91250	−	11.9728i	−0.610984	−	1.05826i
$129$		0			0
$130$	−3.97807	+	6.89022i	−0.348900	+	0.604312i
$131$	2.12838	−	3.68646i	0.185957	−	0.322087i	−0.757942	−	0.652322i	$-0.773795\pi$
$131$	2.12838	−	3.68646i	0.185957	−	0.322087i	0.943899	+	0.330235i	$0.107128\pi$
$132$		0			0
$133$	0.811018	+	1.40472i	0.0703242	+	0.121805i
$134$	10.8768			0.939610
$135$		0			0
$136$	−4.42041			−0.379047
$137$	−1.17422	−	2.03380i	−0.100320	−	0.173760i	0.811496	−	0.584357i	$-0.198653\pi$
$137$	−1.17422	−	2.03380i	−0.100320	−	0.173760i	−0.911817	+	0.410598i	$0.865320\pi$
$138$		0			0
$139$	−5.31461	+	9.20517i	−0.450779	+	0.780773i	−0.998435	−	0.0559314i	$-0.982187\pi$
$139$	−5.31461	+	9.20517i	−0.450779	+	0.780773i	0.547655	+	0.836704i	$0.315521\pi$
$140$	5.58017	−	9.66514i	0.471611	−	0.816854i
$141$		0			0
$142$	−7.79885	−	13.5080i	−0.654465	−	1.13357i
$143$	−4.28830			−0.358606
$144$		0			0
$145$	−20.6862			−1.71790
$146$	−3.90859	−	6.76987i	−0.323477	−	0.560278i
$147$		0			0
$148$	−8.59366	+	14.8847i	−0.706394	+	1.22351i
$149$	3.87302	−	6.70826i	0.317290	−	0.549562i	−0.662632	−	0.748945i	$-0.730561\pi$
$149$	3.87302	−	6.70826i	0.317290	−	0.549562i	0.979922	+	0.199383i	$0.0638939\pi$
$150$		0			0
$151$	−2.66826	−	4.62157i	−0.217140	−	0.376098i	0.736792	−	0.676119i	$-0.236340\pi$
$151$	−2.66826	−	4.62157i	−0.217140	−	0.376098i	−0.953932	+	0.300021i	$0.903006\pi$
$152$	−2.86239			−0.232171
$153$		0			0
$154$	10.2156			0.823200
$155$	−4.40912	−	7.63682i	−0.354149	−	0.613405i
$156$		0			0
$157$	1.49491	−	2.58926i	0.119307	−	0.206646i	−0.800186	−	0.599752i	$-0.795266\pi$
$157$	1.49491	−	2.58926i	0.119307	−	0.206646i	0.919493	+	0.393106i	$0.128599\pi$
$158$	4.48850	−	7.77431i	0.357086	−	0.618491i
$159$		0			0
$160$	−12.9410	−	22.4145i	−1.02308	−	1.77202i
$161$	−7.65548			−0.603336
$162$		0			0
$163$	−7.48075			−0.585937			−0.292969	−	0.956122i	$-0.594643\pi$
$163$	−7.48075			−0.585937			−0.292969	+	0.956122i	$0.594643\pi$
$164$	15.1538	+	26.2472i	1.18332	+	2.04956i
$165$		0			0
$166$	16.1409	−	27.9568i	1.25277	−	2.16987i
$167$	7.01589	−	12.1519i	0.542906	−	0.940341i	−0.455830	−	0.890067i	$-0.650657\pi$
$167$	7.01589	−	12.1519i	0.542906	−	0.940341i	0.998735	−	0.0502735i	$-0.0160093\pi$
$168$		0			0
$169$	−0.500000	−	0.866025i	−0.0384615	−	0.0666173i
$170$	−18.4511			−1.41514
$171$		0			0
$172$	−21.0608			−1.60587
$173$	8.45872	+	14.6509i	0.643104	+	1.11389i	0.984736	+	0.174055i	$0.0556872\pi$
$173$	8.45872	+	14.6509i	0.643104	+	1.11389i	−0.341632	+	0.939834i	$0.610979\pi$
$174$		0			0
$175$	4.32771	−	7.49582i	0.327144	−	0.566631i
$176$	3.26899	−	5.66205i	0.246409	−	0.426793i
$177$		0			0
$178$	−6.64988	−	11.5179i	−0.498430	−	0.863306i
$179$	17.5324			1.31043			0.655216	−	0.755441i	$-0.272577\pi$
$179$	17.5324			1.31043			0.655216	+	0.755441i	$0.272577\pi$
$180$		0			0
$181$	−4.80757			−0.357344			−0.178672	−	0.983909i	$-0.557180\pi$
$181$	−4.80757			−0.357344			−0.178672	+	0.983909i	$0.557180\pi$
$182$	1.19111	+	2.06306i	0.0882907	+	0.152924i
$183$		0			0
$184$	6.75478	−	11.6996i	0.497969	−	0.862507i
$185$	−10.8234	+	18.7467i	−0.795752	+	1.37828i
$186$		0			0
$187$	−4.97251	−	8.61264i	−0.363626	−	0.629819i
$188$	5.68441			0.414579
$189$		0			0
$190$	−11.9478			−0.866787
$191$	−13.1907	−	22.8469i	−0.954444	−	1.65315i	−0.735634	−	0.677379i	$-0.763116\pi$
$191$	−13.1907	−	22.8469i	−0.954444	−	1.65315i	−0.218810	−	0.975767i	$-0.570218\pi$
$192$		0			0
$193$	7.34991	−	12.7304i	0.529058	−	0.916356i	−0.470368	−	0.882471i	$-0.655879\pi$
$193$	7.34991	−	12.7304i	0.529058	−	0.916356i	0.999426	−	0.0338850i	$-0.0107880\pi$
$194$	−0.150482	+	0.260643i	−0.0108040	+	0.0187131i
$195$		0			0
$196$	8.35403	+	14.4696i	0.596717	+	1.03354i
$197$	−6.81721			−0.485706			−0.242853	−	0.970063i	$-0.578083\pi$
$197$	−6.81721			−0.485706			−0.242853	+	0.970063i	$0.578083\pi$
$198$		0			0
$199$	−12.5005			−0.886139			−0.443070	−	0.896487i	$-0.646111\pi$
$199$	−12.5005			−0.886139			−0.443070	+	0.896487i	$0.646111\pi$
$200$	7.63707	+	13.2278i	0.540023	+	0.935347i
$201$		0			0
$202$	12.7129	−	22.0194i	0.894475	−	1.54928i
$203$	−3.09692	+	5.36402i	−0.217361	+	0.376480i
$204$		0			0
$205$	19.0857	+	33.0574i	1.33300	+	2.30883i
$206$	−23.9714			−1.67016
$207$		0			0
$208$	1.52461			0.105713
$209$	−3.21990	−	5.57703i	−0.222725	−	0.385771i
$210$		0			0
$211$	2.37149	−	4.10754i	0.163260	−	0.282775i	−0.772776	−	0.634679i	$-0.781132\pi$
$211$	2.37149	−	4.10754i	0.163260	−	0.282775i	0.936036	+	0.351904i	$0.114466\pi$
$212$	−16.1503	+	27.9731i	−1.10921	+	1.92120i
$213$		0			0
$214$	11.8611	+	20.5439i	0.810805	+	1.40436i
$215$	−26.5252			−1.80901
$216$		0			0
$217$	−2.64035			−0.179238
$218$	6.63090	+	11.4850i	0.449101	+	0.777866i
$219$		0			0
$220$	−22.1544	+	38.3725i	−1.49365	+	2.58707i
$221$	1.15955	−	2.00840i	0.0780000	−	0.135100i
$222$		0			0
$223$	−7.44457	−	12.8944i	−0.498525	−	0.863471i	0.501473	−	0.865173i	$-0.332792\pi$
$223$	−7.44457	−	12.8944i	−0.498525	−	0.863471i	−0.999999	+	0.00170202i	$0.999458\pi$
$224$	−7.74956			−0.517789
$225$		0			0
$226$	−23.9788			−1.59505
$227$	−0.727113	−	1.25940i	−0.0482602	−	0.0835891i	0.840886	−	0.541212i	$-0.182034\pi$
$227$	−0.727113	−	1.25940i	−0.0482602	−	0.0835891i	−0.889146	+	0.457623i	$0.848701\pi$
$228$		0			0
$229$	5.51424	−	9.55095i	0.364391	−	0.631144i	−0.624287	−	0.781195i	$-0.714610\pi$
$229$	5.51424	−	9.55095i	0.364391	−	0.631144i	0.988678	+	0.150051i	$0.0479437\pi$
$230$	28.1949	−	48.8351i	1.85912	−	3.22009i
$231$		0			0
$232$	−5.46510	−	9.46583i	−0.358801	−	0.621462i
$233$	26.5412			1.73877			0.869386	−	0.494134i	$-0.164515\pi$
$233$	26.5412			1.73877			0.869386	+	0.494134i	$0.164515\pi$
$234$		0			0
$235$	7.15931			0.467022
$236$	5.29198	+	9.16597i	0.344478	+	0.596654i
$237$		0			0
$238$	−2.76230	+	4.78445i	−0.179054	+	0.310130i
$239$	−5.53531	+	9.58744i	−0.358049	+	0.620160i	−0.987635	−	0.156772i	$-0.949891\pi$
$239$	−5.53531	+	9.58744i	−0.358049	+	0.620160i	0.629586	+	0.776931i	$0.283225\pi$
$240$		0			0
$241$	5.96370	+	10.3294i	0.384156	+	0.665377i	0.991652	−	0.128946i	$-0.0411593\pi$
$241$	5.96370	+	10.3294i	0.384156	+	0.665377i	−0.607496	+	0.794323i	$0.707826\pi$
$242$	−16.2976			−1.04765
$243$		0			0
$244$	−4.81762			−0.308417
$245$	10.5216	+	18.2239i	0.672200	+	1.16428i
$246$		0			0
$247$	0.750857	−	1.30052i	0.0477759	−	0.0827502i
$248$	2.32970	−	4.03515i	0.147936	−	0.256232i
$249$		0			0
$250$	11.9874	+	20.7628i	0.758149	+	1.31315i
$251$	11.9196			0.752361			0.376181	−	0.926546i	$-0.377237\pi$
$251$	11.9196			0.752361			0.376181	+	0.926546i	$0.377237\pi$
$252$		0			0
$253$	30.3937			1.91084
$254$	2.14072	+	3.70784i	0.134321	+	0.232650i
$255$		0			0
$256$	2.47094	−	4.27979i	0.154434	−	0.267487i
$257$	7.22167	−	12.5083i	0.450476	−	0.780246i	−0.547940	−	0.836518i	$-0.684588\pi$
$257$	7.22167	−	12.5083i	0.450476	−	0.780246i	0.998416	+	0.0562712i	$0.0179211\pi$
$258$		0			0
$259$	3.24072	+	5.61310i	0.201369	+	0.348781i
$260$	−10.3325			−0.640793
$261$		0			0
$262$	9.38828			0.580010
$263$	−4.16501	−	7.21401i	−0.256826	−	0.444835i	0.708564	−	0.705646i	$-0.249343\pi$
$263$	−4.16501	−	7.21401i	−0.256826	−	0.444835i	−0.965390	+	0.260811i	$0.916010\pi$
$264$		0			0
$265$	−20.3407	+	35.2311i	−1.24952	+	2.16423i
$266$	−1.78870	+	3.09812i	−0.109672	+	0.189958i
$267$		0			0
$268$	7.06272	+	12.2330i	0.431424	+	0.747249i
$269$	−19.7008			−1.20118			−0.600588	−	0.799559i	$-0.705067\pi$
$269$	−19.7008			−1.20118			−0.600588	+	0.799559i	$0.705067\pi$
$270$		0			0
$271$	2.28480			0.138792			0.0693958	−	0.997589i	$-0.477893\pi$
$271$	2.28480			0.138792			0.0693958	+	0.997589i	$0.477893\pi$
$272$	1.76786	+	3.06203i	0.107193	+	0.185663i
$273$		0			0
$274$	2.58974	−	4.48556i	0.156452	−	0.270983i
$275$	−17.1819	+	29.7598i	−1.03610	+	1.79459i
$276$		0			0
$277$	8.58154	+	14.8637i	0.515615	+	0.893071i	0.999836	+	0.0181250i	$0.00576968\pi$
$277$	8.58154	+	14.8637i	0.515615	+	0.893071i	−0.484221	+	0.874946i	$0.660897\pi$
$278$	−23.4428			−1.40600
$279$		0			0
$280$	7.42695			0.443845
$281$	8.98863	+	15.5688i	0.536217	+	0.928755i	0.999103	+	0.0423371i	$0.0134803\pi$
$281$	8.98863	+	15.5688i	0.536217	+	0.928755i	−0.462887	+	0.886417i	$0.653186\pi$
$282$		0			0
$283$	4.57565	−	7.92525i	0.271994	−	0.471107i	−0.697378	−	0.716703i	$-0.745650\pi$
$283$	4.57565	−	7.92525i	0.271994	−	0.471107i	0.969372	+	0.245596i	$0.0789836\pi$
$284$	10.1282	−	17.5426i	0.600998	−	1.04096i
$285$		0			0
$286$	−4.72893	−	8.19074i	−0.279627	−	0.484329i
$287$	11.4292			0.674645
$288$		0			0
$289$	−11.6217			−0.683632
$290$	−22.8117	−	39.5111i	−1.33955	−	2.32017i
$291$		0			0
$292$	5.07600	−	8.79189i	0.297050	−	0.514506i
$293$	−1.80863	+	3.13263i	−0.105661	+	0.183010i	−0.914008	−	0.405696i	$-0.867029\pi$
$293$	−1.80863	+	3.13263i	−0.105661	+	0.183010i	0.808347	+	0.588706i	$0.200363\pi$
$294$		0			0
$295$	6.66505	+	11.5442i	0.388054	+	0.672129i
$296$	−11.4378			−0.664806
$297$		0			0
$298$	17.0839			0.989643
$299$	3.54380	+	6.13804i	0.204943	+	0.354972i
$300$		0			0
$301$	−3.97107	+	6.87810i	−0.228889	+	0.396447i
$302$	5.88486	−	10.1929i	0.338636	−	0.586534i
$303$		0			0
$304$	1.14476	+	1.98279i	0.0656566	+	0.113721i
$305$	−6.06762			−0.347431
$306$		0			0
$307$	−29.7837			−1.69985			−0.849923	−	0.526907i	$-0.823352\pi$
$307$	−29.7837			−1.69985			−0.849923	+	0.526907i	$0.823352\pi$
$308$	6.63343	+	11.4894i	0.377974	+	0.654671i
$309$		0			0
$310$	9.72433	−	16.8430i	0.552305	−	0.956620i
$311$	−8.46917	+	14.6690i	−0.480243	+	0.831805i	−0.999743	−	0.0226654i	$-0.992785\pi$
$311$	−8.46917	+	14.6690i	−0.480243	+	0.831805i	0.519500	+	0.854470i	$0.326118\pi$
$312$		0			0
$313$	−14.1018	−	24.4251i	−0.797084	−	1.38059i	−0.921508	−	0.388360i	$-0.873042\pi$
$313$	−14.1018	−	24.4251i	−0.797084	−	1.38059i	0.124424	−	0.992229i	$-0.460292\pi$
$314$	6.59406			0.372124
$315$		0			0
$316$	11.6583			0.655828
$317$	16.9186	+	29.3038i	0.950241	+	1.64587i	0.744901	+	0.667175i	$0.232497\pi$
$317$	16.9186	+	29.3038i	0.950241	+	1.64587i	0.205341	+	0.978691i	$0.434170\pi$
$318$		0			0
$319$	12.2954	−	21.2962i	0.688408	−	1.19236i
$320$	23.0416	−	39.9091i	1.28806	−	2.23099i
$321$		0			0
$322$	−8.44209	−	14.6221i	−0.470459	−	0.814859i
$323$	3.48263			0.193779
$324$		0			0
$325$	−8.01337			−0.444502
$326$	−8.24940	−	14.2884i	−0.456892	−	0.791360i
$327$		0			0
$328$	−10.0845	+	17.4669i	−0.556824	+	0.964448i
$329$	1.07181	−	1.85644i	0.0590911	−	0.102349i
$330$		0			0
$331$	−5.96014	−	10.3233i	−0.327599	−	0.567418i	0.654436	−	0.756118i	$-0.272906\pi$
$331$	−5.96014	−	10.3233i	−0.327599	−	0.567418i	−0.982035	+	0.188699i	$0.939573\pi$
$332$	41.9236			2.30086
$333$		0			0
$334$	30.9471			1.69335
$335$	8.89523	+	15.4070i	0.485998	+	0.841774i
$336$		0			0
$337$	4.59197	−	7.95352i	0.250141	−	0.433256i	−0.713424	−	0.700733i	$-0.752857\pi$
$337$	4.59197	−	7.95352i	0.250141	−	0.433256i	0.963564	+	0.267477i	$0.0861899\pi$
$338$	1.10275	−	1.91002i	0.0599818	−	0.103891i
$339$		0			0
$340$	−11.9811	−	20.7518i	−0.649764	−	1.12542i
$341$	10.4827			0.567669
$342$		0			0
$343$	13.8616			0.748455
$344$	−7.00772	−	12.1377i	−0.377831	−	0.654422i
$345$		0			0
$346$	−18.6557	+	32.3127i	−1.00294	+	1.73714i
$347$	−3.38728	+	5.86693i	−0.181838	+	0.314953i	−0.942507	−	0.334187i	$-0.891538\pi$
$347$	−3.38728	+	5.86693i	−0.181838	+	0.314953i	0.760668	+	0.649141i	$0.224871\pi$
$348$		0			0
$349$	17.4803	+	30.2768i	0.935700	+	1.62068i	0.773381	+	0.633942i	$0.218564\pi$
$349$	17.4803	+	30.2768i	0.935700	+	1.62068i	0.162319	+	0.986738i	$0.448103\pi$
$350$	19.0896			1.02038
$351$		0			0
$352$	30.7672			1.63990
$353$	−8.80119	−	15.2441i	−0.468440	−	0.811362i	0.530910	−	0.847429i	$-0.321850\pi$
$353$	−8.80119	−	15.2441i	−0.468440	−	0.811362i	−0.999349	+	0.0360669i	$0.988517\pi$
$354$		0			0
$355$	12.7561	−	22.0942i	0.677023	−	1.17264i
$356$	8.63607	−	14.9581i	0.457711	−	0.792778i
$357$		0			0
$358$	19.3339	+	33.4872i	1.02183	+	1.76986i
$359$	0.923928			0.0487631			0.0243815	−	0.999703i	$-0.492238\pi$
$359$	0.923928			0.0487631			0.0243815	+	0.999703i	$0.492238\pi$
$360$		0			0
$361$	−16.7449			−0.881308
$362$	−5.30156	−	9.18256i	−0.278644	−	0.482625i
$363$		0			0
$364$	−1.54687	+	2.67925i	−0.0810778	+	0.140431i
$365$	6.39303	−	11.0731i	0.334627	−	0.579590i
$366$		0			0
$367$	−12.4238	−	21.5187i	−0.648518	−	1.12327i	−0.983477	−	0.181034i	$-0.942056\pi$
$367$	−12.4238	−	21.5187i	−0.648518	−	1.12327i	0.334959	−	0.942233i	$-0.391278\pi$
$368$	−10.8058			−0.563292
$369$		0			0
$370$	−47.7420			−2.48199
$371$	6.09037	+	10.5488i	0.316196	+	0.547668i
$372$		0			0
$373$	−2.79864	+	4.84739i	−0.144908	+	0.250988i	−0.929339	−	0.369228i	$-0.879622\pi$
$373$	−2.79864	+	4.84739i	−0.144908	+	0.250988i	0.784431	+	0.620217i	$0.212955\pi$
$374$	10.9669	−	18.9952i	0.567084	−	0.982218i
$375$		0			0
$376$	1.89142	+	3.27604i	0.0975426	+	0.168949i
$377$	5.73438			0.295335
$378$		0			0
$379$	7.69687			0.395361			0.197681	−	0.980266i	$-0.436659\pi$
$379$	7.69687			0.395361			0.197681	+	0.980266i	$0.436659\pi$
$380$	−7.75821	−	13.4376i	−0.397988	−	0.689335i
$381$		0			0
$382$	29.0921	−	50.3890i	1.48848	−	2.57812i
$383$	10.7668	−	18.6487i	0.550159	−	0.952903i	−0.448104	−	0.893982i	$-0.647900\pi$
$383$	10.7668	−	18.6487i	0.550159	−	0.952903i	0.998263	−	0.0589217i	$-0.0187662\pi$
$384$		0			0
$385$	8.35455	+	14.4705i	0.425787	+	0.737486i
$386$	32.4205			1.65016
$387$		0			0
$388$	−0.390856			−0.0198427
$389$	3.06018	+	5.30039i	0.155157	+	0.268740i	0.933116	−	0.359575i	$-0.117078\pi$
$389$	3.06018	+	5.30039i	0.155157	+	0.268740i	−0.777959	+	0.628315i	$0.783745\pi$
$390$		0			0
$391$	−8.21844	+	14.2348i	−0.415625	+	0.719883i
$392$	−5.55941	+	9.62918i	−0.280793	+	0.486347i
$393$		0			0
$394$	−7.51769	−	13.0210i	−0.378736	−	0.655989i
$395$	14.6831			0.738789
$396$		0			0
$397$	−22.0318			−1.10574			−0.552871	−	0.833267i	$-0.686468\pi$
$397$	−22.0318			−1.10574			−0.552871	+	0.833267i	$0.686468\pi$
$398$	−13.7850	−	23.8763i	−0.690979	−	1.19681i
$399$		0			0
$400$	6.10862	−	10.5804i	0.305431	−	0.529022i
$401$	−3.50825	+	6.07647i	−0.175194	+	0.303445i	−0.940228	−	0.340545i	$-0.889389\pi$
$401$	−3.50825	+	6.07647i	−0.175194	+	0.303445i	0.765035	+	0.643989i	$0.222722\pi$
$402$		0			0
$403$	1.22224	+	2.11699i	0.0608842	+	0.105455i
$404$	33.0199			1.64280
$405$		0			0
$406$	−13.6605			−0.677960
$407$	−12.8663	−	22.2851i	−0.637759	−	1.10463i
$408$		0			0
$409$	−18.2267	+	31.5695i	−0.901251	+	1.56101i	−0.0753798	+	0.997155i	$0.524017\pi$
$409$	−18.2267	+	31.5695i	−0.901251	+	1.56101i	−0.825872	+	0.563858i	$0.809316\pi$
$410$	−42.0935	+	72.9081i	−2.07885	+	3.60068i
$411$		0			0
$412$	−15.5656	−	26.9603i	−0.766860	−	1.32824i
$413$	3.99128			0.196398
$414$		0			0
$415$	52.8012			2.59191
$416$	3.58735	+	6.21347i	0.175884	+	0.304640i
$417$		0			0
$418$	7.10149	−	12.3001i	0.347345	−	0.601620i
$419$	−2.74594	+	4.75612i	−0.134148	+	0.232351i	−0.925272	−	0.379305i	$-0.876163\pi$
$419$	−2.74594	+	4.75612i	−0.134148	+	0.232351i	0.791124	+	0.611656i	$0.209496\pi$
$420$		0			0
$421$	3.54583	+	6.14156i	0.172813	+	0.299321i	0.939402	−	0.342817i	$-0.111381\pi$
$421$	3.54583	+	6.14156i	0.172813	+	0.299321i	−0.766589	+	0.642138i	$0.778048\pi$
$422$	10.4607			0.509217
$423$		0			0
$424$	−21.4952			−1.04390
$425$	−9.29192	−	16.0941i	−0.450725	−	0.780678i
$426$		0			0
$427$	−0.908378	+	1.57336i	−0.0439595	+	0.0761401i
$428$	−15.4037	+	26.6800i	−0.744566	+	1.28963i
$429$		0			0
$430$	−29.2507	−	50.6638i	−1.41060	−	2.44322i
$431$	−6.55791			−0.315883			−0.157942	−	0.987448i	$-0.550486\pi$
$431$	−6.55791			−0.315883			−0.157942	+	0.987448i	$0.550486\pi$
$432$		0			0
$433$	12.0920			0.581104			0.290552	−	0.956859i	$-0.406161\pi$
$433$	12.0920			0.581104			0.290552	+	0.956859i	$0.406161\pi$
$434$	−2.91164	−	5.04312i	−0.139763	−	0.242077i
$435$		0			0
$436$	−8.61141	+	14.9154i	−0.412412	+	0.714318i
$437$	−5.32177	+	9.21757i	−0.254575	+	0.440936i
$438$		0			0
$439$	11.8761	+	20.5699i	0.566813	+	0.981750i	0.996878	+	0.0789517i	$0.0251573\pi$
$439$	11.8761	+	20.5699i	0.566813	+	0.981750i	−0.430065	+	0.902798i	$0.641509\pi$
$440$	−29.4864			−1.40571
$441$		0			0
$442$	5.11479			0.243286
$443$	7.86463	+	13.6219i	0.373660	+	0.647198i	0.990125	−	0.140184i	$-0.0447694\pi$
$443$	7.86463	+	13.6219i	0.373660	+	0.647198i	−0.616466	+	0.787382i	$0.711436\pi$
$444$		0			0
$445$	10.8768	−	18.8392i	0.515610	−	0.893063i
$446$	16.4190	−	28.4386i	0.777463	−	1.34661i
$447$		0			0
$448$	−6.89907	−	11.9495i	−0.325950	−	0.564562i
$449$	−17.3369			−0.818179			−0.409089	−	0.912494i	$-0.634154\pi$
$449$	−17.3369			−0.818179			−0.409089	+	0.912494i	$0.634154\pi$
$450$		0			0
$451$	−45.3762			−2.13668
$452$	−15.5704	−	26.9687i	−0.732369	−	1.26850i
$453$		0			0
$454$	1.60365	−	2.77760i	0.0752630	−	0.130359i
$455$	−1.94822	+	3.37442i	−0.0913340	+	0.158195i
$456$		0			0
$457$	2.99601	+	5.18925i	0.140148	+	0.242743i	0.927552	−	0.373694i	$-0.121909\pi$
$457$	2.99601	+	5.18925i	0.140148	+	0.242743i	−0.787404	+	0.616437i	$0.788576\pi$
$458$	24.3234			1.13656
$459$		0			0
$460$	73.2324			3.41448
$461$	−4.99213	−	8.64662i	−0.232507	−	0.402713i	0.726039	−	0.687654i	$-0.241359\pi$
$461$	−4.99213	−	8.64662i	−0.232507	−	0.402713i	−0.958545	+	0.284941i	$0.908026\pi$
$462$		0			0
$463$	2.56267	−	4.43868i	0.119098	−	0.206283i	−0.800313	−	0.599583i	$-0.795333\pi$
$463$	2.56267	−	4.43868i	0.119098	−	0.206283i	0.919410	+	0.393300i	$0.128667\pi$
$464$	−4.37134	+	7.57138i	−0.202934	+	0.351492i
$465$		0			0
$466$	29.2683	+	50.6942i	1.35583	+	2.34837i
$467$	−7.49976			−0.347047			−0.173524	−	0.984830i	$-0.555515\pi$
$467$	−7.49976			−0.347047			−0.173524	+	0.984830i	$0.555515\pi$
$468$		0			0
$469$	5.32679			0.245968
$470$	7.89494	+	13.6744i	0.364166	+	0.630755i
$471$		0			0
$472$	−3.52168	+	6.09974i	−0.162099	+	0.280763i
$473$	15.7659	−	27.3074i	0.724918	−	1.25559i
$474$		0			0
$475$	−6.01689	−	10.4216i	−0.276074	−	0.478174i
$476$	−7.17469			−0.328852
$477$		0			0
$478$	−24.4163			−1.11677
$479$	13.3053	+	23.0455i	0.607936	+	1.05298i	0.991580	+	0.129495i	$0.0413355\pi$
$479$	13.3053	+	23.0455i	0.607936	+	1.05298i	−0.383644	+	0.923481i	$0.625331\pi$
$480$		0			0
$481$	3.00033	−	5.19672i	0.136803	−	0.236950i
$482$	−13.1530	+	22.7816i	−0.599100	+	1.03767i
$483$		0			0
$484$	−10.5827	−	18.3297i	−0.481030	−	0.833168i
$485$	−0.492269			−0.0223528
$486$		0			0
$487$	−37.2926			−1.68989			−0.844945	−	0.534853i	$-0.820367\pi$
$487$	−37.2926			−1.68989			−0.844945	+	0.534853i	$0.820367\pi$
$488$	−1.60301	−	2.77649i	−0.0725647	−	0.125686i
$489$		0			0
$490$	−23.2054	+	40.1929i	−1.04831	+	1.81573i
$491$	−4.82831	+	8.36288i	−0.217899	+	0.377411i	−0.954165	−	0.299280i	$-0.903254\pi$
$491$	−4.82831	+	8.36288i	−0.217899	+	0.377411i	0.736267	+	0.676691i	$0.236587\pi$
$492$		0			0
$493$	6.64931	+	11.5169i	0.299470	+	0.518697i
$494$	3.31203			0.149015
$495$		0			0
$496$	−3.72688			−0.167342
$497$	−3.81941	−	6.61541i	−0.171324	−	0.296742i
$498$		0			0
$499$	−18.2175	+	31.5536i	−0.815526	+	1.41253i	0.0934229	+	0.995627i	$0.470219\pi$
$499$	−18.2175	+	31.5536i	−0.815526	+	1.41253i	−0.908949	+	0.416907i	$0.863114\pi$
$500$	−15.5678	+	26.9642i	−0.696212	+	1.20587i
$501$		0			0
$502$	13.1444	+	22.7668i	0.586663	+	1.01613i
$503$	−14.4772			−0.645504			−0.322752	−	0.946484i	$-0.604608\pi$
$503$	−14.4772			−0.645504			−0.322752	+	0.946484i	$0.604608\pi$
$504$		0			0
$505$	41.5874			1.85061
$506$	33.5167	+	58.0527i	1.49000	+	2.58076i
$507$		0			0
$508$	−2.78011	+	4.81529i	−0.123347	+	0.213644i
$509$	9.37473	−	16.2375i	0.415528	−	0.719715i	−0.579956	−	0.814648i	$-0.696930\pi$
$509$	9.37473	−	16.2375i	0.415528	−	0.719715i	0.995484	+	0.0949327i	$0.0302636\pi$
$510$		0			0
$511$	−1.91419	−	3.31548i	−0.0846789	−	0.146668i
$512$	−16.7507			−0.740282
$513$		0			0
$514$	31.8548			1.40506
$515$	−19.6042	−	33.9556i	−0.863866	−	1.49626i
$516$		0			0
$517$	−4.25531	+	7.37042i	−0.187148	+	0.324150i
$518$	−7.14742	+	12.3797i	−0.314040	+	0.543933i
$519$		0			0
$520$	−3.43801	−	5.95480i	−0.150767	−	0.261135i
$521$	−38.6095			−1.69151			−0.845756	−	0.533571i	$-0.820850\pi$
$521$	−38.6095			−1.69151			−0.845756	+	0.533571i	$0.820850\pi$
$522$		0			0
$523$	9.50729			0.415725			0.207862	−	0.978158i	$-0.433349\pi$
$523$	9.50729			0.415725			0.207862	+	0.978158i	$0.433349\pi$
$524$	6.09618	+	10.5589i	0.266313	+	0.461267i
$525$		0			0
$526$	9.18594	−	15.9105i	0.400526	−	0.693731i
$527$	−2.83451	+	4.90951i	−0.123473	+	0.213862i
$528$		0			0
$529$	−13.6170	−	23.5853i	−0.592044	−	1.02545i
$530$	−89.7228			−3.89731
$531$		0			0
$532$	−4.64590			−0.201425
$533$	−5.29070	−	9.16376i	−0.229166	−	0.396926i
$534$		0			0
$535$	−19.4004	+	33.6025i	−0.838752	+	1.45276i
$536$	−4.70007	+	8.14076i	−0.203012	+	0.351627i
$537$		0			0
$538$	−21.7250	−	37.6289i	−0.936633	−	1.62230i
$539$	−25.0151			−1.07748
$540$		0			0
$541$	−0.834277			−0.0358684			−0.0179342	−	0.999839i	$-0.505709\pi$
$541$	−0.834277			−0.0358684			−0.0179342	+	0.999839i	$0.505709\pi$
$542$	2.51956	+	4.36401i	0.108225	+	0.187450i
$543$		0			0
$544$	−8.31944	+	14.4097i	−0.356693	+	0.617810i
$545$	−10.8457	+	18.7854i	−0.464581	+	0.804678i
$546$		0			0
$547$	19.4741	+	33.7301i	0.832653	+	1.44220i	0.895927	+	0.444200i	$0.146512\pi$
$547$	19.4741	+	33.7301i	0.832653	+	1.44220i	−0.0632748	+	0.997996i	$0.520154\pi$
$548$	6.72648			0.287341
$549$		0			0
$550$	−75.7892			−3.23166
$551$	4.30569	+	7.45768i	0.183429	+	0.317708i
$552$		0			0
$553$	2.19820	−	3.80740i	0.0934770	−	0.161907i
$554$	−18.9266	+	32.7818i	−0.804114	+	1.39277i
$555$		0			0
$556$	−15.2223	−	26.3658i	−0.645570	−	1.11816i
$557$	33.4957			1.41926			0.709630	−	0.704575i	$-0.248862\pi$
$557$	33.4957			1.41926			0.709630	+	0.704575i	$0.248862\pi$
$558$		0			0
$559$	7.35300			0.310999
$560$	−2.97027	−	5.14467i	−0.125517	−	0.217402i
$561$		0			0
$562$	−19.8244	+	34.3369i	−0.836244	+	1.44842i
$563$	8.96646	−	15.5304i	0.377891	−	0.654527i	−0.612864	−	0.790189i	$-0.709983\pi$
$563$	8.96646	−	15.5304i	0.377891	−	0.654527i	0.990755	+	0.135661i	$0.0433159\pi$
$564$		0			0
$565$	−19.6103	−	33.9661i	−0.825012	−	1.42896i
$566$	20.1832			0.848363
$567$		0			0
$568$	13.4802			0.565615
$569$	14.2900	+	24.7510i	0.599069	+	1.03762i	0.992959	+	0.118460i	$0.0377957\pi$
$569$	14.2900	+	24.7510i	0.599069	+	1.03762i	−0.393890	+	0.919157i	$0.628871\pi$
$570$		0			0
$571$	8.40266	−	14.5538i	0.351640	−	0.609059i	−0.634897	−	0.772597i	$-0.718957\pi$
$571$	8.40266	−	14.5538i	0.351640	−	0.609059i	0.986537	+	0.163538i	$0.0522906\pi$
$572$	6.14136	−	10.6371i	0.256783	−	0.444761i
$573$		0			0
$574$	12.6036	+	21.8300i	0.526063	+	0.911168i
$575$	56.7955			2.36854
$576$		0			0
$577$	−5.34187			−0.222385			−0.111193	−	0.993799i	$-0.535467\pi$
$577$	−5.34187			−0.222385			−0.111193	+	0.993799i	$0.535467\pi$
$578$	−12.8159	−	22.1978i	−0.533071	−	0.923306i
$579$		0			0
$580$	29.6251	−	51.3122i	1.23012	−	2.13063i
$581$	7.90483	−	13.6916i	0.327947	−	0.568022i
$582$		0			0
$583$	−24.1800	−	41.8809i	−1.00143	−	1.73453i
$584$	6.75591			0.279562
$585$		0			0
$586$	−7.97785			−0.329562
$587$	−1.14969	−	1.99131i	−0.0474526	−	0.0821903i	0.841324	−	0.540532i	$-0.181777\pi$
$587$	−1.14969	−	1.99131i	−0.0474526	−	0.0821903i	−0.888776	+	0.458342i	$0.848444\pi$
$588$		0			0
$589$	−1.83546	+	3.17911i	−0.0756287	+	0.130993i
$590$	−14.6998	+	25.4608i	−0.605180	+	1.04820i
$591$		0			0
$592$	4.57432	+	7.92296i	0.188004	+	0.325632i
$593$	5.45698			0.224091			0.112046	−	0.993703i	$-0.464260\pi$
$593$	5.45698			0.224091			0.112046	+	0.993703i	$0.464260\pi$
$594$		0			0
$595$	−9.03626			−0.370451
$596$	11.0932	+	19.2141i	0.454397	+	0.787039i
$597$		0			0
$598$	−7.81585	+	13.5375i	−0.319614	+	0.553588i
$599$	−11.6453	+	20.1703i	−0.475815	+	0.824136i	−0.999616	−	0.0277047i	$-0.991180\pi$
$599$	−11.6453	+	20.1703i	−0.475815	+	0.824136i	0.523801	+	0.851841i	$0.324514\pi$
$600$		0			0
$601$	−11.5387	−	19.9857i	−0.470675	−	0.815232i	0.528763	−	0.848770i	$-0.322656\pi$
$601$	−11.5387	−	19.9857i	−0.470675	−	0.815232i	−0.999437	+	0.0335372i	$0.989323\pi$
$602$	−17.5164			−0.713916
$603$		0			0
$604$	15.2851			0.621941
$605$	−13.3285	−	23.0856i	−0.541879	−	0.938562i
$606$		0			0
$607$	16.9477	−	29.3542i	0.687885	−	1.19145i	−0.284636	−	0.958636i	$-0.591873\pi$
$607$	16.9477	−	29.3542i	0.687885	−	1.19145i	0.972521	−	0.232816i	$-0.0747940\pi$
$608$	−5.38717	+	9.33085i	−0.218478	+	0.378416i
$609$		0			0
$610$	−6.69107	−	11.5893i	−0.270914	−	0.469236i
$611$	−1.98462			−0.0802889
$612$		0			0
$613$	15.1947			0.613708			0.306854	−	0.951757i	$-0.400724\pi$
$613$	15.1947			0.613708			0.306854	+	0.951757i	$0.400724\pi$
$614$	−32.8440	−	56.8875i	−1.32548	−	2.29579i
$615$		0			0
$616$	−4.41439	+	7.64594i	−0.177861	+	0.308064i
$617$	−8.53434	+	14.7819i	−0.343580	+	0.595097i	−0.985095	−	0.172013i	$-0.944973\pi$
$617$	−8.53434	+	14.7819i	−0.343580	+	0.595097i	0.641515	+	0.767110i	$0.278306\pi$
$618$		0			0
$619$	19.3273	+	33.4759i	0.776830	+	1.34551i	0.933760	+	0.357899i	$0.116507\pi$
$619$	19.3273	+	33.4759i	0.776830	+	1.34551i	−0.156930	+	0.987610i	$0.550160\pi$
$620$	25.2576			1.01437
$621$		0			0
$622$	−37.3576			−1.49790
$623$	−3.25672	−	5.64080i	−0.130478	−	0.225994i
$624$		0			0
$625$	0.426392	−	0.738532i	0.0170557	−	0.0295413i
$626$	31.1017	−	53.8697i	1.24307	−	2.15306i
$627$		0			0
$628$	4.28179	+	7.41627i	0.170862	+	0.295941i
$629$	13.9162			0.554873
$630$		0			0
$631$	23.3989			0.931494			0.465747	−	0.884918i	$-0.345786\pi$
$631$	23.3989			0.931494			0.465747	+	0.884918i	$0.345786\pi$
$632$	3.87914	+	6.71888i	0.154304	+	0.267263i
$633$		0			0
$634$	−37.3139	+	64.6296i	−1.48193	+	2.56677i
$635$	−3.50145	+	6.06468i	−0.138951	+	0.240670i
$636$		0			0
$637$	−2.91667	−	5.05181i	−0.115563	−	0.200160i
$638$	54.2349			2.14718
$639$		0			0
$640$	49.8723			1.97138
$641$	15.6824	+	27.1628i	0.619419	+	1.07286i	0.989592	+	0.143902i	$0.0459650\pi$
$641$	15.6824	+	27.1628i	0.619419	+	1.07286i	−0.370173	+	0.928963i	$0.620702\pi$
$642$		0			0
$643$	15.0268	−	26.0272i	0.592599	−	1.02641i	−0.401282	−	0.915954i	$-0.631435\pi$
$643$	15.0268	−	26.0272i	0.592599	−	1.02641i	0.993881	−	0.110457i	$-0.0352313\pi$
$644$	10.9636	−	18.9895i	0.432025	−	0.748289i
$645$		0			0
$646$	3.84048	+	6.65190i	0.151102	+	0.261716i
$647$	−23.3783			−0.919096			−0.459548	−	0.888153i	$-0.651989\pi$
$647$	−23.3783			−0.919096			−0.459548	+	0.888153i	$0.651989\pi$
$648$		0			0
$649$	−15.8461			−0.622015
$650$	−8.83675	−	15.3057i	−0.346606	−	0.600339i
$651$		0			0
$652$	10.7133	−	18.5560i	0.419566	−	0.726710i
$653$	17.6818	−	30.6257i	0.691941	−	1.19848i	−0.279260	−	0.960215i	$-0.590089\pi$
$653$	17.6818	−	30.6257i	0.691941	−	1.19848i	0.971201	−	0.238261i	$-0.0765774\pi$
$654$		0			0
$655$	7.67791	+	13.2985i	0.300001	+	0.519617i
$656$	16.1325			0.629868
$657$		0			0
$658$	4.72778			0.184308
$659$	−10.7773	−	18.6668i	−0.419823	−	0.727155i	0.576098	−	0.817380i	$-0.304575\pi$
$659$	−10.7773	−	18.6668i	−0.419823	−	0.727155i	−0.995921	+	0.0902257i	$0.971241\pi$
$660$		0			0
$661$	25.0618	−	43.4083i	0.974790	−	1.68839i	0.294164	−	0.955755i	$-0.404959\pi$
$661$	25.0618	−	43.4083i	0.974790	−	1.68839i	0.680626	−	0.732631i	$-0.261708\pi$
$662$	13.1451	−	22.7680i	0.510899	−	0.884904i
$663$		0			0
$664$	13.9496	+	24.1614i	0.541348	+	0.937643i
$665$	−5.85134			−0.226905
$666$		0			0
$667$	−40.6429			−1.57370
$668$	20.0952	+	34.8059i	0.777506	+	1.34668i
$669$		0			0
$670$	−19.6185	+	33.9802i	−0.757927	+	1.31277i
$671$	3.60644	−	6.24653i	0.139225	−	0.241145i
$672$		0			0
$673$	−21.5733	−	37.3661i	−0.831591	−	1.44036i	−0.896776	−	0.442485i	$-0.854097\pi$
$673$	−21.5733	−	37.3661i	−0.831591	−	1.44036i	0.0651846	−	0.997873i	$-0.479236\pi$
$674$	20.2552			0.780201
$675$		0			0
$676$	2.86424			0.110163
$677$	−5.49875	−	9.52411i	−0.211334	−	0.366041i	0.740798	−	0.671728i	$-0.234447\pi$
$677$	−5.49875	−	9.52411i	−0.211334	−	0.366041i	−0.952132	+	0.305686i	$0.901114\pi$
$678$		0			0
$679$	−0.0736972	+	0.127647i	−0.00282824	+	0.00489866i
$680$	7.97310	−	13.8098i	0.305755	−	0.529582i
$681$		0			0
$682$	11.5598	+	20.0221i	0.442647	+	0.766687i
$683$	40.6682			1.55613			0.778063	−	0.628186i	$-0.216202\pi$
$683$	40.6682			1.55613			0.778063	+	0.628186i	$0.216202\pi$
$684$		0			0
$685$	8.47176			0.323689
$686$	15.2859	+	26.4759i	0.583618	+	1.01086i
$687$		0			0
$688$	−5.60522	+	9.70853i	−0.213697	+	0.370134i
$689$	5.63859	−	9.76632i	0.214813	−	0.372067i
$690$		0			0
$691$	8.12733	+	14.0770i	0.309178	+	0.535513i	0.978183	−	0.207746i	$-0.0666127\pi$
$691$	8.12733	+	14.0770i	0.309178	+	0.535513i	−0.669005	+	0.743258i	$0.733279\pi$
$692$	−48.4556			−1.84201
$693$		0			0
$694$	−14.9413			−0.567164
$695$	−19.1719	−	33.2068i	−0.727233	−	1.25961i
$696$		0			0
$697$	12.2697	−	21.2517i	0.464748	−	0.804967i
$698$	−38.5529	+	66.7756i	−1.45925	+	2.52749i
$699$		0			0
$700$	12.3956	+	21.4698i	0.468510	+	0.811483i
$701$	−21.6993			−0.819571			−0.409786	−	0.912182i	$-0.634396\pi$
$701$	−21.6993			−0.819571			−0.409786	+	0.912182i	$0.634396\pi$
$702$		0			0
$703$	9.01126			0.339866
$704$	27.3906	+	47.4420i	1.03232	+	1.78804i
$705$		0			0
$706$	19.4110	−	33.6209i	0.730544	−	1.26534i
$707$	6.22601	−	10.7838i	0.234153	−	0.405565i
$708$		0			0
$709$	−7.00438	−	12.1319i	−0.263055	−	0.455625i	0.703997	−	0.710203i	$-0.251397\pi$
$709$	−7.00438	−	12.1319i	−0.263055	−	0.455625i	−0.967052	+	0.254578i	$0.918063\pi$
$710$	56.2672			2.11167
$711$		0			0
$712$	11.4942			0.430763
$713$	−8.66276	−	15.0043i	−0.324423	−	0.561917i
$714$		0			0
$715$	7.73481	−	13.3971i	0.289266	−	0.501023i
$716$	−25.1085	+	43.4892i	−0.938348	+	1.62527i
$717$		0			0
$718$	1.01886	+	1.76472i	0.0380236	+	0.0658589i
$719$	−9.73722			−0.363137			−0.181569	−	0.983378i	$-0.558117\pi$
$719$	−9.73722			−0.363137			−0.181569	+	0.983378i	$0.558117\pi$
$720$		0			0
$721$	−11.7397			−0.437211
$722$	−18.4654	−	31.9830i	−0.687211	−	1.19029i
$723$		0			0
$724$	6.88502	−	11.9252i	0.255880	−	0.443197i
$725$	22.9758	−	39.7953i	0.853301	−	1.47796i
$726$		0			0
$727$	−5.44289	−	9.42737i	−0.201866	−	0.349642i	0.747264	−	0.664527i	$-0.231367\pi$
$727$	−5.44289	−	9.42737i	−0.201866	−	0.349642i	−0.949130	+	0.314886i	$0.898034\pi$
$728$	−2.05881			−0.0763044
$729$		0			0
$730$	28.1997			1.04372
$731$	8.52619	+	14.7678i	0.315353	+	0.546207i
$732$		0			0
$733$	−3.73133	+	6.46285i	−0.137820	+	0.238711i	−0.926671	−	0.375873i	$-0.877343\pi$
$733$	−3.73133	+	6.46285i	−0.137820	+	0.238711i	0.788851	+	0.614584i	$0.210676\pi$
$734$	27.4008	−	47.4595i	1.01138	−	1.75176i
$735$		0			0
$736$	−25.4257	−	44.0385i	−0.937203	−	1.62328i
$737$	−21.1484			−0.779011
$738$		0			0
$739$	−28.4029			−1.04482			−0.522408	−	0.852695i	$-0.674966\pi$
$739$	−28.4029			−1.04482			−0.522408	+	0.852695i	$0.674966\pi$
$740$	−31.0008	−	53.6950i	−1.13961	−	1.97387i
$741$		0			0
$742$	−13.4323	+	23.2655i	−0.493116	+	0.854103i
$743$	−0.712939	+	1.23485i	−0.0261552	+	0.0453021i	−0.878807	−	0.477178i	$-0.841660\pi$
$743$	−0.712939	+	1.23485i	−0.0261552	+	0.0453021i	0.852652	+	0.522480i	$0.174993\pi$
$744$		0			0
$745$	13.9715	+	24.1994i	0.511877	+	0.886598i
$746$	−12.3448			−0.451976
$747$		0			0
$748$	28.4849			1.04151
$749$	5.80884	+	10.0612i	0.212250	+	0.367628i
$750$		0			0
$751$	14.6709	−	25.4107i	0.535348	−	0.927250i	−0.463799	−	0.885941i	$-0.653514\pi$
$751$	14.6709	−	25.4107i	0.535348	−	0.927250i	0.999146	−	0.0413090i	$-0.0131528\pi$
$752$	1.51288	−	2.62039i	0.0551691	−	0.0955556i
$753$		0			0
$754$	6.32359	+	10.9528i	0.230292	+	0.398877i
$755$	19.2510			0.700616
$756$		0			0
$757$	15.3490			0.557868			0.278934	−	0.960310i	$-0.410019\pi$
$757$	15.3490			0.557868			0.278934	+	0.960310i	$0.410019\pi$
$758$	8.48773	+	14.7012i	0.308288	+	0.533971i
$759$		0			0
$760$	5.16290	−	8.94241i	0.187278	−	0.324375i
$761$	−7.47611	+	12.9490i	−0.271009	+	0.469401i	−0.969120	−	0.246588i	$-0.920691\pi$
$761$	−7.47611	+	12.9490i	−0.271009	+	0.469401i	0.698112	+	0.715989i	$0.254024\pi$
$762$		0			0
$763$	3.24742	+	5.62469i	0.117564	+	0.203628i
$764$	75.5626			2.73376
$765$		0			0
$766$	47.4925			1.71597
$767$	−1.84760	−	3.20014i	−0.0667131	−	0.115550i
$768$		0			0
$769$	−1.04194	+	1.80469i	−0.0375733	+	0.0650789i	−0.884201	−	0.467107i	$-0.845296\pi$
$769$	−1.04194	+	1.80469i	−0.0375733	+	0.0650789i	0.846627	+	0.532186i	$0.178629\pi$
$770$	−18.4260	+	31.9147i	−0.664026	+	1.15013i
$771$		0			0
$772$	21.0519	+	36.4630i	0.757675	+	1.31233i
$773$	5.99812			0.215737			0.107869	−	0.994165i	$-0.465597\pi$
$773$	5.99812			0.215737			0.107869	+	0.994165i	$0.465597\pi$
$774$		0			0
$775$	19.5886			0.703642
$776$	−0.130053	−	0.225258i	−0.00466862	−	0.00808629i
$777$		0			0
$778$	−6.74923	+	11.6900i	−0.241972	+	0.419107i
$779$	7.94511	−	13.7613i	0.284663	−	0.493051i
$780$		0			0
$781$	15.1638	+	26.2645i	0.542603	+	0.939816i
$782$	−36.2516			−1.29635
$783$		0			0
$784$	8.89355			0.317627
$785$	5.39275	+	9.34052i	0.192476	+	0.333377i
$786$		0			0
$787$	8.69989	−	15.0687i	0.310118	−	0.537139i	−0.668270	−	0.743919i	$-0.732965\pi$
$787$	8.69989	−	15.0687i	0.310118	−	0.537139i	0.978388	+	0.206779i	$0.0662982\pi$
$788$	9.76306	−	16.9101i	0.347795	−	0.602398i
$789$		0			0
$790$	16.1918	+	28.0451i	0.576080	+	0.997800i
$791$	−11.7434			−0.417547
$792$		0			0
$793$	1.68199			0.0597292
$794$	−24.2956	−	42.0811i	−0.862217	−	1.49340i
$795$		0			0
$796$	17.9023	−	31.0076i	0.634529	−	1.09904i
$797$	−1.97250	+	3.41647i	−0.0698696	+	0.121018i	−0.898844	−	0.438269i	$-0.855592\pi$
$797$	−1.97250	+	3.41647i	−0.0698696	+	0.121018i	0.828974	+	0.559287i	$0.188925\pi$
$798$		0			0
$799$	−2.30127	−	3.98591i	−0.0814130	−	0.141011i
$800$	57.4935			2.03270
$801$		0			0
$802$	−15.4749			−0.546438
$803$	7.59971	+	13.1631i	0.268188	+	0.464515i
$804$		0			0
$805$	13.8082	−	23.9165i	0.486675	−	0.842946i
$806$	−2.69566	+	4.66902i	−0.0949505	+	0.164459i
$807$		0			0
$808$	10.9870	+	19.0300i	0.386521	+	0.669474i
$809$	−37.3431			−1.31291			−0.656457	−	0.754364i	$-0.727946\pi$
$809$	−37.3431			−1.31291			−0.656457	+	0.754364i	$0.727946\pi$
$810$		0			0
$811$	−27.1179			−0.952240			−0.476120	−	0.879380i	$-0.657957\pi$
$811$	−27.1179			−0.952240			−0.476120	+	0.879380i	$0.657957\pi$
$812$	−8.87031	−	15.3638i	−0.311287	−	0.539165i
$813$		0			0
$814$	28.3767	−	49.1498i	0.994601	−	1.72270i
$815$	13.4930	−	23.3706i	0.472641	−	0.818638i
$816$		0			0
$817$	5.52105	+	9.56274i	0.193157	+	0.334558i
$818$	−80.3980			−2.81105
$819$		0			0
$820$	−109.332			−3.81804
$821$	−19.0569	−	33.0076i	−0.665092	−	1.15197i	−0.979260	−	0.202605i	$-0.935059\pi$
$821$	−19.0569	−	33.0076i	−0.665092	−	1.15197i	0.314169	−	0.949367i	$-0.398274\pi$
$822$		0			0
$823$	−11.3736	+	19.6997i	−0.396460	+	0.686688i	−0.993286	−	0.115682i	$-0.963095\pi$
$823$	−11.3736	+	19.6997i	−0.396460	+	0.686688i	0.596827	+	0.802370i	$0.296428\pi$
$824$	10.3585	−	17.9415i	0.360856	−	0.625021i
$825$		0			0
$826$	4.40139	+	7.62342i	0.153144	+	0.265253i
$827$	−50.3300			−1.75014			−0.875072	−	0.483992i	$-0.839186\pi$
$827$	−50.3300			−1.75014			−0.875072	+	0.483992i	$0.839186\pi$
$828$		0			0
$829$	21.3190			0.740438			0.370219	−	0.928945i	$-0.379283\pi$
$829$	21.3190			0.740438			0.370219	+	0.928945i	$0.379283\pi$
$830$	58.2266	+	100.851i	2.02107	+	3.50060i
$831$		0			0
$832$	−6.38729	+	11.0631i	−0.221440	+	0.383545i
$833$	6.76406	−	11.7157i	0.234361	−	0.405925i
$834$		0			0
$835$	25.3092	+	43.8367i	0.875859	+	1.51703i
$836$	18.4451			0.637938
$837$		0			0
$838$	−12.1124			−0.418415
$839$	−15.7723	−	27.3184i	−0.544520	−	0.943136i	−0.998637	−	0.0521939i	$-0.983379\pi$
$839$	−15.7723	−	27.3184i	−0.544520	−	0.943136i	0.454117	−	0.890942i	$-0.349955\pi$
$840$		0			0
$841$	−1.94153	+	3.36283i	−0.0669493	+	0.115960i
$842$	−7.82034	+	13.5452i	−0.269507	+	0.466799i
$843$		0			0
$844$	6.79252	+	11.7650i	0.233808	+	0.404968i
$845$	3.60740			0.124098
$846$		0			0
$847$	−7.98158			−0.274250
$848$	8.59664	+	14.8898i	0.295210	+	0.511318i
$849$		0			0
$850$	20.4934	−	35.4955i	0.702916	−	1.21749i
$851$	−21.2651	+	36.8322i	−0.728959	+	1.26259i
$852$		0			0
$853$	−17.8409	−	30.9014i	−0.610861	−	1.05804i	−0.991096	−	0.133153i	$-0.957490\pi$
$853$	−17.8409	−	30.9014i	−0.610861	−	1.05804i	0.380234	−	0.924890i	$-0.375843\pi$
$854$	−4.00686			−0.137112
$855$		0			0
$856$	−20.5016			−0.700730
$857$	16.5013	+	28.5812i	0.563675	+	0.976314i	0.997172	+	0.0751589i	$0.0239464\pi$
$857$	16.5013	+	28.5812i	0.563675	+	0.976314i	−0.433496	+	0.901155i	$0.642720\pi$
$858$		0			0
$859$	−6.12815	+	10.6143i	−0.209090	+	0.362154i	−0.951428	−	0.307871i	$-0.900383\pi$
$859$	−6.12815	+	10.6143i	−0.209090	+	0.362154i	0.742338	+	0.670025i	$0.233717\pi$
$860$	37.9873	−	65.7960i	1.29536	−	2.24362i
$861$		0			0
$862$	−7.23174	−	12.5257i	−0.246314	−	0.426628i
$863$	−33.7379			−1.14845			−0.574227	−	0.818696i	$-0.694697\pi$
$863$	−33.7379			−1.14845			−0.574227	+	0.818696i	$0.694697\pi$
$864$		0			0
$865$	−61.0280			−2.07502
$866$	13.3345	+	23.0960i	0.453123	+	0.784833i
$867$		0			0
$868$	3.78129	−	6.54939i	0.128345	−	0.222301i
$869$	−8.72728	+	15.1161i	−0.296053	+	0.512778i
$870$		0			0
$871$	−2.46583	−	4.27094i	−0.0835513	−	0.144715i
$872$	−11.4614			−0.388131
$873$		0			0
$874$	−23.4743			−0.794031
$875$	5.87071	+	10.1684i	0.198466	+	0.343753i
$876$		0			0
$877$	−16.3367	+	28.2961i	−0.551653	+	0.955491i	0.446503	+	0.894782i	$0.352669\pi$
$877$	−16.3367	+	28.2961i	−0.551653	+	0.955491i	−0.998156	+	0.0607085i	$0.980664\pi$
$878$	−26.1927	+	45.3670i	−0.883960	+	1.53106i
$879$		0			0
$880$	11.7926	+	20.4253i	0.397527	+	0.688537i
$881$	12.9456			0.436150			0.218075	−	0.975932i	$-0.430022\pi$
$881$	12.9456			0.436150			0.218075	+	0.975932i	$0.430022\pi$
$882$		0			0
$883$	−13.0620			−0.439570			−0.219785	−	0.975548i	$-0.570536\pi$
$883$	−13.0620			−0.439570			−0.219785	+	0.975548i	$0.570536\pi$
$884$	3.32124	+	5.75255i	0.111705	+	0.193479i
$885$		0			0
$886$	−17.3455	+	30.0432i	−0.582732	+	1.00932i
$887$	−4.42406	+	7.66270i	−0.148545	+	0.257288i	−0.930690	−	0.365809i	$-0.880792\pi$
$887$	−4.42406	+	7.66270i	−0.148545	+	0.257288i	0.782145	+	0.623097i	$0.214126\pi$
$888$		0			0
$889$	1.04840	+	1.81588i	0.0351621	+	0.0609026i
$890$	47.9776			1.60821
$891$		0			0
$892$	42.6461			1.42790
$893$	−1.49016	−	2.58104i	−0.0498664	−	0.0863711i
$894$		0			0
$895$	−31.6232	+	54.7730i	−1.05705	+	1.83086i
$896$	7.46635	−	12.9321i	0.249433	−	0.432031i
$897$		0			0
$898$	−19.1183	−	33.1138i	−0.637985	−	1.10502i
$899$	−14.0176			−0.467513
$900$		0			0
$901$	26.1530			0.871282
$902$	−50.0386	−	86.6695i	−1.66610	−	2.88578i
$903$		0			0
$904$	10.3617	−	17.9470i	0.344626	−	0.596909i
$905$	8.67143	−	15.0194i	0.288248	−	0.499260i
$906$		0			0
$907$	13.0067	+	22.5283i	0.431880	+	0.748039i	0.997035	−	0.0769462i	$-0.0245170\pi$
$907$	13.0067	+	22.5283i	0.431880	+	0.748039i	−0.565155	+	0.824985i	$0.691184\pi$
$908$	4.16525			0.138229
$909$		0			0
$910$	−8.59361			−0.284875
$911$	23.4978	+	40.6994i	0.778517	+	1.34843i	0.932796	+	0.360404i	$0.117361\pi$
$911$	23.4978	+	40.6994i	0.778517	+	1.34843i	−0.154279	+	0.988027i	$0.549305\pi$
$912$		0			0
$913$	−31.3837	+	54.3581i	−1.03865	+	1.79899i
$914$	−6.60772	+	11.4449i	−0.218564	+	0.378564i
$915$		0			0
$916$	15.7941	+	27.3562i	0.521852	+	0.903875i
$917$	4.59782			0.151833
$918$		0			0
$919$	−46.2304			−1.52500			−0.762500	−	0.646988i	$-0.776028\pi$
$919$	−46.2304			−1.52500			−0.762500	+	0.646988i	$0.776028\pi$
$920$	24.3672	+	42.2052i	0.803363	+	1.39147i
$921$		0			0
$922$	11.0102	−	19.0701i	0.362600	−	0.628042i
$923$	−3.53609	+	6.12468i	−0.116392	+	0.201596i
$924$		0			0
$925$	−24.0427	−	41.6432i	−0.790520	−	1.36922i
$926$	11.3040			0.371471
$927$		0			0
$928$	−41.1424			−1.35057
$929$	14.2698	+	24.7160i	0.468176	+	0.810905i	0.999339	−	0.0363651i	$-0.0115779\pi$
$929$	14.2698	+	24.7160i	0.468176	+	0.810905i	−0.531162	+	0.847270i	$0.678245\pi$
$930$		0			0
$931$	4.38000	−	7.58638i	0.143549	−	0.248633i
$932$	−38.0102	+	65.8356i	−1.24507	+	2.15652i
$933$		0			0
$934$	−8.27037	−	14.3247i	−0.270615	−	0.468718i
$935$	35.8757			1.17326
$936$		0			0
$937$	36.6972			1.19884			0.599422	−	0.800433i	$-0.295397\pi$
$937$	36.6972			1.19884			0.599422	+	0.800433i	$0.295397\pi$
$938$	5.87413	+	10.1743i	0.191797	+	0.332202i
$939$		0			0
$940$	−10.2530	+	17.7587i	−0.334416	+	0.579225i
$941$	21.6316	−	37.4671i	0.705171	−	1.22139i	−0.261458	−	0.965215i	$-0.584203\pi$
$941$	21.6316	−	37.4671i	0.705171	−	1.22139i	0.966630	−	0.256178i	$-0.0824633\pi$
$942$		0			0
$943$	37.4983	+	64.9490i	1.22111	+	2.11503i
$944$	5.63374			0.183363
$945$		0			0
$946$	69.5436			2.26106
$947$	−28.5717	−	49.4876i	−0.928454	−	1.60813i	−0.785909	−	0.618342i	$-0.787805\pi$
$947$	−28.5717	−	49.4876i	−0.928454	−	1.60813i	−0.142545	−	0.989788i	$-0.545529\pi$
$948$		0			0
$949$	−1.77220	+	3.06954i	−0.0575280	+	0.0996414i
$950$	13.2703	−	22.9848i	0.430544	−	0.745724i
$951$		0			0
$952$	−2.38729	−	4.13492i	−0.0773727	−	0.134013i
$953$	27.3044			0.884475			0.442237	−	0.896898i	$-0.354185\pi$
$953$	27.3044			0.884475			0.442237	+	0.896898i	$0.354185\pi$
$954$		0			0
$955$	95.1683			3.07957
$956$	−15.8545	−	27.4607i	−0.512770	−	0.888143i
$957$		0			0
$958$	−29.3449	+	50.8269i	−0.948091	+	1.64214i
$959$	1.26830	−	2.19676i	0.0409555	−	0.0709371i
$960$		0			0
$961$	12.5122	+	21.6718i	0.403621	+	0.699092i
$962$	13.2345			0.426696
$963$		0			0
$964$	−34.1629			−1.10031
$965$	26.5141	+	45.9238i	0.853519	+	1.47834i
$966$		0			0
$967$	19.6390	−	34.0157i	0.631547	−	1.09387i	−0.355689	−	0.934604i	$-0.615754\pi$
$967$	19.6390	−	34.0157i	0.631547	−	1.09387i	0.987236	−	0.159267i	$-0.0509130\pi$
$968$	7.04251	−	12.1980i	0.226355	−	0.392058i
$969$		0			0
$970$	−0.542850	−	0.940244i	−0.0174299	−	0.0301894i
$971$	36.9378			1.18539			0.592695	−	0.805427i	$-0.298064\pi$
$971$	36.9378			1.18539			0.592695	+	0.805427i	$0.298064\pi$
$972$		0			0
$973$	−11.4809			−0.368060
$974$	−41.1245	−	71.2297i	−1.31771	−	2.28235i
$975$		0			0
$976$	−1.28219	+	2.22081i	−0.0410418	+	0.0710865i
$977$	−26.4680	+	45.8438i	−0.846785	+	1.46667i	0.0372771	+	0.999305i	$0.488132\pi$
$977$	−26.4680	+	45.8438i	−0.846785	+	1.46667i	−0.884062	+	0.467370i	$0.845202\pi$
$978$		0			0
$979$	12.9298	+	22.3951i	0.413238	+	0.715749i
$980$	−60.2728			−1.92534
$981$		0			0
$982$	−21.2977			−0.679637
$983$	11.4293	+	19.7962i	0.364539	+	0.631400i	0.988702	−	0.149894i	$-0.0478932\pi$
$983$	11.4293	+	19.7962i	0.364539	+	0.631400i	−0.624163	+	0.781294i	$0.714560\pi$
$984$		0			0
$985$	12.2962	−	21.2977i	0.391790	−	0.678600i
$986$	−14.6651	+	25.4007i	−0.467031	+	0.808922i
$987$		0			0
$988$	2.15063	+	3.72501i	0.0684208	+	0.118508i
$989$	−52.1151			−1.65716
$990$		0			0
$991$	28.2013			0.895845			0.447923	−	0.894072i	$-0.352164\pi$
$991$	28.2013			0.895845			0.447923	+	0.894072i	$0.352164\pi$
$992$	−8.76922	−	15.1887i	−0.278423	−	0.482243i
$993$		0			0
$994$	8.42372	−	14.5903i	0.267184	−	0.462776i
$995$	22.5472	−	39.0530i	0.714796	−	1.23806i
$996$		0			0
$997$	0.838584	+	1.45247i	0.0265582	+	0.0460002i	0.878999	−	0.476824i	$-0.158212\pi$
$997$	0.838584	+	1.45247i	0.0265582	+	0.0460002i	−0.852441	+	0.522824i	$0.824879\pi$
$998$	−80.3574			−2.54367
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	351.2.e.c.118.6		12
3.2	odd	2		117.2.e.c.40.1	✓	12
9.2	odd	6		117.2.e.c.79.1	yes	12
9.4	even	3		1053.2.a.m.1.1		6
9.5	odd	6		1053.2.a.l.1.6		6
9.7	even	3	inner	351.2.e.c.235.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.2.e.c.40.1	✓	12	3.2	odd	2
117.2.e.c.79.1	yes	12	9.2	odd	6
351.2.e.c.118.6		12	1.1	even	1	trivial
351.2.e.c.235.6		12	9.7	even	3	inner
1053.2.a.l.1.6		6	9.5	odd	6
1053.2.a.m.1.1		6	9.4	even	3

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:	\( N \)	\(=\)	\( 351 = 3^{3} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	351.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.10275 + 1.91002i) q^{2} +(-1.43212 + 2.48050i) q^{4} +(-1.80370 + 3.12410i) q^{5} +(0.540062 + 0.935414i) q^{7} -1.90608 q^{8} -7.95614 q^{10} +(-2.14415 - 3.71378i) q^{11} +(0.500000 - 0.866025i) q^{13} +(-1.19111 + 2.06306i) q^{14} +(0.762304 + 1.32035i) q^{16} +2.31911 q^{17} +1.50171 q^{19} +(-5.16624 - 8.94818i) q^{20} +(4.72893 - 8.19074i) q^{22} +(-3.54380 + 6.13804i) q^{23} +(-4.00668 - 6.93978i) q^{25} +2.20550 q^{26} -3.09373 q^{28} +(2.86719 + 4.96611i) q^{29} +(-1.22224 + 2.11699i) q^{31} +(-3.58735 + 6.21347i) q^{32} +(2.55740 + 4.42954i) q^{34} -3.89644 q^{35} +6.00066 q^{37} +(1.65602 + 2.86830i) q^{38} +(3.43801 - 5.95480i) q^{40} +(5.29070 - 9.16376i) q^{41} +(3.67650 + 6.36788i) q^{43} +12.2827 q^{44} -15.6317 q^{46} +(-0.992308 - 1.71873i) q^{47} +(2.91667 - 5.05181i) q^{49} +(8.83675 - 15.3057i) q^{50} +(1.43212 + 2.48050i) q^{52} +11.2772 q^{53} +15.4696 q^{55} +(-1.02940 - 1.78298i) q^{56} +(-6.32359 + 10.9528i) q^{58} +(1.84760 - 3.20014i) q^{59} +(0.840995 + 1.45665i) q^{61} -5.39132 q^{62} -12.7746 q^{64} +(1.80370 + 3.12410i) q^{65} +(2.46583 - 4.27094i) q^{67} +(-3.32124 + 5.75255i) q^{68} +(-4.29681 - 7.44229i) q^{70} -7.07217 q^{71} -3.54440 q^{73} +(6.61723 + 11.4614i) q^{74} +(-2.15063 + 3.72501i) q^{76} +(2.31595 - 4.01134i) q^{77} +(-2.03514 - 3.52496i) q^{79} -5.49988 q^{80} +23.3373 q^{82} +(-7.31845 - 12.6759i) q^{83} +(-4.18298 + 7.24513i) q^{85} +(-8.10853 + 14.0444i) q^{86} +(4.08693 + 7.07877i) q^{88} -6.03027 q^{89} +1.08012 q^{91} +(-10.1503 - 17.5808i) q^{92} +(2.18854 - 3.79066i) q^{94} +(-2.70864 + 4.69151i) q^{95} +(0.0682304 + 0.118178i) q^{97} +12.8654 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 2 q^{2} - 6 q^{4} - 3 q^{5} + 12 q^{8} - 12 q^{10} - 7 q^{11} + 6 q^{13} - 13 q^{14} - 6 q^{16} + 28 q^{17} - 6 q^{19} - 17 q^{20} + 3 q^{22} - 17 q^{23} - 3 q^{25} - 4 q^{26} + 30 q^{28} - 14 q^{29}+ \cdots + 34 q^{98}+O(q^{100}) \) 12 * q - 2 * q^2 - 6 * q^4 - 3 * q^5 + 12 * q^8 - 12 * q^10 - 7 * q^11 + 6 * q^13 - 13 * q^14 - 6 * q^16 + 28 * q^17 - 6 * q^19 - 17 * q^20 + 3 * q^22 - 17 * q^23 - 3 * q^25 - 4 * q^26 + 30 * q^28 - 14 * q^29 - 6 * q^31 - 9 * q^32 - 3 * q^34 + 26 * q^35 - 18 * q^37 + 4 * q^38 + 6 * q^40 + 4 * q^41 + 3 * q^43 + 26 * q^44 - 9 * q^47 + 21 * q^50 + 6 * q^52 + 56 * q^53 + 30 * q^55 - 16 * q^56 - 18 * q^58 - 17 * q^59 + 6 * q^61 - 8 * q^62 - 60 * q^64 + 3 * q^65 + 12 * q^67 - 22 * q^68 - 9 * q^70 - 2 * q^71 - 18 * q^73 + 27 * q^74 + 3 * q^76 - 15 * q^77 + 6 * q^79 - 48 * q^80 + 54 * q^82 - 28 * q^83 - 27 * q^85 + 6 * q^86 + 9 * q^88 - 18 * q^89 - 44 * q^92 + 24 * q^94 - 32 * q^95 + 34 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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