LMFDB - Embedded newform 1008.2.r.m.673.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1008,2,Mod(337,1008)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1008, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1008.337");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1008 = 2^{4} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1008.r (of order $3$, degree $2$, not 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:	$8.04892052375$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.508277025.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 5x^{6} - 15x^{5} + 21x^{4} + 3x^{3} - 22x^{2} + 3x + 19 $ x^8 - 3x^7 + 5x^6 - 15x^5 + 21x^4 + 3x^3 - 22x^2 + 3*x + 19
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 504)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			673.2
Root			$-0.734668 - 0.348716i$ of defining polynomial
Character	$\chi$	$=$	1008.673
Dual form			1008.2.r.m.337.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.434663 - 1.67662i) q^{3} +(-1.21814 - 2.10988i) q^{5} +(0.500000 - 0.866025i) q^{7} +(-2.62214 - 1.45753i) q^{9} +O(q^{10})$	\(q+(0.434663 - 1.67662i) q^{3} +(-1.21814 - 2.10988i) q^{5} +(0.500000 - 0.866025i) q^{7} +(-2.62214 - 1.45753i) q^{9} +(0.379477 - 0.657274i) q^{11} +(-1.11414 - 1.92976i) q^{13} +(-4.06695 + 1.12527i) q^{15} -7.04904 q^{17} +1.37172 q^{19} +(-1.23467 - 1.21474i) q^{21} +(3.51814 + 6.09360i) q^{23} +(-0.467722 + 0.810117i) q^{25} +(-3.58348 + 3.76280i) q^{27} +(-0.418134 + 0.724229i) q^{29} +(-0.265332 - 0.459569i) q^{31} +(-0.937057 - 0.921933i) q^{33} -2.43628 q^{35} +4.53066 q^{37} +(-3.71975 + 1.02921i) q^{39} +(-4.42852 - 7.67042i) q^{41} +(3.70161 - 6.41137i) q^{43} +(0.118909 + 7.30786i) q^{45} +(-3.39762 + 5.88485i) q^{47} +(-0.500000 - 0.866025i) q^{49} +(-3.06396 + 11.8186i) q^{51} -0.607978 q^{53} -1.84902 q^{55} +(0.596236 - 2.29986i) q^{57} +(-0.581866 - 1.00782i) q^{59} +(-5.85680 + 10.1443i) q^{61} +(-2.57333 + 1.54207i) q^{63} +(-2.71436 + 4.70142i) q^{65} +(-0.152801 - 0.264659i) q^{67} +(11.7459 - 3.24994i) q^{69} -12.6192 q^{71} -10.1499 q^{73} +(1.15496 + 1.13632i) q^{75} +(-0.379477 - 0.657274i) q^{77} +(7.62453 - 13.2061i) q^{79} +(4.75120 + 7.64370i) q^{81} +(8.18909 - 14.1839i) q^{83} +(8.58671 + 14.8726i) q^{85} +(1.03251 + 1.01585i) q^{87} -9.63151 q^{89} -2.22829 q^{91} +(-0.885855 + 0.245105i) q^{93} +(-1.67094 - 2.89416i) q^{95} +(5.46718 - 9.46943i) q^{97} +(-1.95304 + 1.17036i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{3} + 4 q^{5} + 4 q^{7} + 10 q^{9}+O(q^{10}) $ 8 * q + 4 * q^3 + 4 * q^5 + 4 * q^7 + 10 * q^9	$ 8 q + 4 q^{3} + 4 q^{5} + 4 q^{7} + 10 q^{9} + 6 q^{11} - 3 q^{13} - 4 q^{15} - 16 q^{17} + 4 q^{19} - q^{21} + 5 q^{23} - 14 q^{25} - 5 q^{27} + q^{29} - 11 q^{31} + 8 q^{35} + 54 q^{37} + 12 q^{39} + 2 q^{41} + 11 q^{43} + 26 q^{45} - 7 q^{47} - 4 q^{49} - 17 q^{51} - 8 q^{53} - 12 q^{55} - 13 q^{57} - 9 q^{59} - 7 q^{61} + 5 q^{63} - 9 q^{65} + 12 q^{67} + 4 q^{69} + 24 q^{71} + 26 q^{73} + 23 q^{75} - 6 q^{77} + 22 q^{79} + 34 q^{81} + 6 q^{83} - 11 q^{85} - 37 q^{87} - 28 q^{89} - 6 q^{91} - 13 q^{93} + 23 q^{95} - q^{97} + 42 q^{99}+O(q^{100}) $ 8 * q + 4 * q^3 + 4 * q^5 + 4 * q^7 + 10 * q^9 + 6 * q^11 - 3 * q^13 - 4 * q^15 - 16 * q^17 + 4 * q^19 - q^21 + 5 * q^23 - 14 * q^25 - 5 * q^27 + q^29 - 11 * q^31 + 8 * q^35 + 54 * q^37 + 12 * q^39 + 2 * q^41 + 11 * q^43 + 26 * q^45 - 7 * q^47 - 4 * q^49 - 17 * q^51 - 8 * q^53 - 12 * q^55 - 13 * q^57 - 9 * q^59 - 7 * q^61 + 5 * q^63 - 9 * q^65 + 12 * q^67 + 4 * q^69 + 24 * q^71 + 26 * q^73 + 23 * q^75 - 6 * q^77 + 22 * q^79 + 34 * q^81 + 6 * q^83 - 11 * q^85 - 37 * q^87 - 28 * q^89 - 6 * q^91 - 13 * q^93 + 23 * q^95 - q^97 + 42 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times$.

$n$	$127$	$577$	$757$	$785$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$		0			0
$2$		0			0
$3$	0.434663	−	1.67662i	0.250953	−	0.967999i
$3$	0.434663	−	1.67662i	0.250953	−	0.967999i
$4$		0			0
$5$	−1.21814	−	2.10988i	−0.544768	−	0.943566i	−0.998621	−	0.0524895i	$-0.983284\pi$
$5$	−1.21814	−	2.10988i	−0.544768	−	0.943566i	0.453853	−	0.891076i	$-0.350049\pi$
$6$		0			0
$7$	0.500000	−	0.866025i	0.188982	−	0.327327i
$7$	0.500000	−	0.866025i	0.188982	−	0.327327i
$8$		0			0
$9$	−2.62214	−	1.45753i	−0.874045	−	0.485844i
$10$		0			0
$11$	0.379477	−	0.657274i	0.114417	−	0.198176i	−0.803130	−	0.595804i	$-0.796833\pi$
$11$	0.379477	−	0.657274i	0.114417	−	0.198176i	0.917546	+	0.397629i	$0.130167\pi$
$12$		0			0
$13$	−1.11414	−	1.92976i	−0.309008	−	0.535218i	0.669138	−	0.743139i	$-0.266664\pi$
$13$	−1.11414	−	1.92976i	−0.309008	−	0.535218i	−0.978146	+	0.207921i	$0.933330\pi$
$14$		0			0
$15$	−4.06695	+	1.12527i	−1.05008	+	0.290545i
$16$		0			0
$17$	−7.04904			−1.70964			−0.854822	−	0.518922i	$-0.826334\pi$
$17$	−7.04904			−1.70964			−0.854822	+	0.518922i	$0.826334\pi$
$18$		0			0
$19$	1.37172			0.314694			0.157347	−	0.987543i	$-0.449706\pi$
$19$	1.37172			0.314694			0.157347	+	0.987543i	$0.449706\pi$
$20$		0			0
$21$	−1.23467	−	1.21474i	−0.269427	−	0.265078i
$22$		0			0
$23$	3.51814	+	6.09360i	0.733583	+	1.27060i	0.955342	+	0.295502i	$0.0954870\pi$
$23$	3.51814	+	6.09360i	0.733583	+	1.27060i	−0.221759	+	0.975102i	$0.571180\pi$
$24$		0			0
$25$	−0.467722	+	0.810117i	−0.0935443	+	0.162023i
$26$		0			0
$27$	−3.58348	+	3.76280i	−0.689641	+	0.724151i
$28$		0			0
$29$	−0.418134	+	0.724229i	−0.0776455	+	0.134486i	−0.902234	−	0.431248i	$-0.858074\pi$
$29$	−0.418134	+	0.724229i	−0.0776455	+	0.134486i	0.824588	+	0.565733i	$0.191407\pi$
$30$		0			0
$31$	−0.265332	−	0.459569i	−0.0476551	−	0.0825411i	0.841214	−	0.540702i	$-0.181842\pi$
$31$	−0.265332	−	0.459569i	−0.0476551	−	0.0825411i	−0.888869	+	0.458161i	$0.848508\pi$
$32$		0			0
$33$	−0.937057	−	0.921933i	−0.163121	−	0.160488i
$34$		0			0
$35$	−2.43628			−0.411806
$36$		0			0
$37$	4.53066			0.744837			0.372418	−	0.928065i	$-0.378529\pi$
$37$	4.53066			0.744837			0.372418	+	0.928065i	$0.378529\pi$
$38$		0			0
$39$	−3.71975	+	1.02921i	−0.595637	+	0.164805i
$40$		0			0
$41$	−4.42852	−	7.67042i	−0.691618	−	1.19792i	−0.971307	−	0.237828i	$-0.923565\pi$
$41$	−4.42852	−	7.67042i	−0.691618	−	1.19792i	0.279689	−	0.960091i	$-0.409769\pi$
$42$		0			0
$43$	3.70161	−	6.41137i	0.564490	−	0.977725i	−0.432607	−	0.901583i	$-0.642406\pi$
$43$	3.70161	−	6.41137i	0.564490	−	0.977725i	0.997097	−	0.0761428i	$-0.0242605\pi$
$44$		0			0
$45$	0.118909	+	7.30786i	0.0177259	+	1.08939i
$46$		0			0
$47$	−3.39762	+	5.88485i	−0.495594	+	0.858394i	−0.999987	−	0.00508036i	$-0.998383\pi$
$47$	−3.39762	+	5.88485i	−0.495594	+	0.858394i	0.504393	+	0.863474i	$0.331716\pi$
$48$		0			0
$49$	−0.500000	−	0.866025i	−0.0714286	−	0.123718i
$50$		0			0
$51$	−3.06396	+	11.8186i	−0.429040	+	1.65493i
$52$		0			0
$53$	−0.607978			−0.0835122			−0.0417561	−	0.999128i	$-0.513295\pi$
$53$	−0.607978			−0.0835122			−0.0417561	+	0.999128i	$0.513295\pi$
$54$		0			0
$55$	−1.84902			−0.249322
$56$		0			0
$57$	0.596236	−	2.29986i	0.0789733	−	0.304624i
$58$		0			0
$59$	−0.581866	−	1.00782i	−0.0757525	−	0.131207i	0.825661	−	0.564167i	$-0.190803\pi$
$59$	−0.581866	−	1.00782i	−0.0757525	−	0.131207i	−0.901413	+	0.432960i	$0.857469\pi$
$60$		0			0
$61$	−5.85680	+	10.1443i	−0.749887	+	1.29884i	0.197990	+	0.980204i	$0.436559\pi$
$61$	−5.85680	+	10.1443i	−0.749887	+	1.29884i	−0.947876	+	0.318638i	$0.896775\pi$
$62$		0			0
$63$	−2.57333	+	1.54207i	−0.324209	+	0.194283i
$64$		0			0
$65$	−2.71436	+	4.70142i	−0.336676	+	0.583139i
$66$		0			0
$67$	−0.152801	−	0.264659i	−0.0186676	−	0.0323333i	0.856541	−	0.516080i	$-0.172609\pi$
$67$	−0.152801	−	0.264659i	−0.0186676	−	0.0323333i	−0.875208	+	0.483746i	$0.839276\pi$
$68$		0			0
$69$	11.7459	−	3.24994i	1.41404	−	0.391247i
$70$		0			0
$71$	−12.6192			−1.49763			−0.748813	−	0.662781i	$-0.769376\pi$
$71$	−12.6192			−1.49763			−0.748813	+	0.662781i	$0.769376\pi$
$72$		0			0
$73$	−10.1499			−1.18795			−0.593977	−	0.804482i	$-0.702443\pi$
$73$	−10.1499			−1.18795			−0.593977	+	0.804482i	$0.702443\pi$
$74$		0			0
$75$	1.15496	+	1.13632i	0.133363	+	0.131211i
$76$		0			0
$77$	−0.379477	−	0.657274i	−0.0432455	−	0.0749033i
$78$		0			0
$79$	7.62453	−	13.2061i	0.857827	−	1.48580i	−0.0161711	−	0.999869i	$-0.505148\pi$
$79$	7.62453	−	13.2061i	0.857827	−	1.48580i	0.873998	−	0.485930i	$-0.161519\pi$
$80$		0			0
$81$	4.75120	+	7.64370i	0.527911	+	0.849300i
$82$		0			0
$83$	8.18909	−	14.1839i	0.898869	−	1.55689i	0.0699272	−	0.997552i	$-0.477723\pi$
$83$	8.18909	−	14.1839i	0.898869	−	1.55689i	0.828942	−	0.559335i	$-0.188943\pi$
$84$		0			0
$85$	8.58671	+	14.8726i	0.931359	+	1.61316i
$86$		0			0
$87$	1.03251	+	1.01585i	0.110697	+	0.108910i
$88$		0			0
$89$	−9.63151			−1.02094			−0.510469	−	0.859896i	$-0.670528\pi$
$89$	−9.63151			−1.02094			−0.510469	+	0.859896i	$0.670528\pi$
$90$		0			0
$91$	−2.22829			−0.233588
$92$		0			0
$93$	−0.885855	+	0.245105i	−0.0918589	+	0.0254162i
$94$		0			0
$95$	−1.67094	−	2.89416i	−0.171435	−	0.296935i
$96$		0			0
$97$	5.46718	−	9.46943i	0.555108	−	0.961474i	−0.442788	−	0.896627i	$-0.646010\pi$
$97$	5.46718	−	9.46943i	0.555108	−	0.961474i	0.997895	−	0.0648479i	$-0.0206562\pi$
$98$		0			0
$99$	−1.95304	+	1.17036i	−0.196288	+	0.117626i
$100$		0			0
$101$	−0.750417	+	1.29976i	−0.0746693	+	0.129331i	−0.900942	−	0.433939i	$-0.857123\pi$
$101$	−0.750417	+	1.29976i	−0.0746693	+	0.129331i	0.826273	+	0.563270i	$0.190457\pi$
$102$		0			0
$103$	5.13229	+	8.88938i	0.505699	+	0.875897i	0.999978	+	0.00659356i	$0.00209881\pi$
$103$	5.13229	+	8.88938i	0.505699	+	0.875897i	−0.494279	+	0.869303i	$0.664568\pi$
$104$		0			0
$105$	−1.05896	+	4.08472i	−0.103344	+	0.398628i
$106$		0			0
$107$	7.84428			0.758335			0.379168	−	0.925328i	$-0.376210\pi$
$107$	7.84428			0.758335			0.379168	+	0.925328i	$0.376210\pi$
$108$		0			0
$109$	12.1754			1.16619			0.583096	−	0.812403i	$-0.301841\pi$
$109$	12.1754			1.16619			0.583096	+	0.812403i	$0.301841\pi$
$110$		0			0
$111$	1.96931	−	7.59622i	0.186919	−	0.721001i
$112$		0			0
$113$	−1.98586	−	3.43962i	−0.186814	−	0.323572i	0.757372	−	0.652984i	$-0.226483\pi$
$113$	−1.98586	−	3.43962i	−0.186814	−	0.323572i	−0.944186	+	0.329412i	$0.893150\pi$
$114$		0			0
$115$	8.57117	−	14.8457i	0.799266	−	1.38437i
$116$		0			0
$117$	0.108758	+	6.68398i	0.0100547	+	0.617935i
$118$		0			0
$119$	−3.52452	+	6.10465i	−0.323092	+	0.559612i
$120$		0			0
$121$	5.21199	+	9.02744i	0.473818	+	0.820676i
$122$		0			0
$123$	−14.7853	+	4.09091i	−1.33315	+	0.368865i
$124$		0			0
$125$	−9.90238			−0.885696
$126$		0			0
$127$	−15.7579			−1.39828			−0.699142	−	0.714983i	$-0.746435\pi$
$127$	−15.7579			−1.39828			−0.699142	+	0.714983i	$0.746435\pi$
$128$		0			0
$129$	−9.14051	−	8.99299i	−0.804777	−	0.791789i
$130$		0			0
$131$	−5.93789	−	10.2847i	−0.518796	−	0.898581i	−0.999761	−	0.0218413i	$-0.993047\pi$
$131$	−5.93789	−	10.2847i	−0.518796	−	0.898581i	0.480966	−	0.876739i	$-0.340286\pi$
$132$		0			0
$133$	0.685860	−	1.18794i	0.0594716	−	0.103008i
$134$		0			0
$135$	12.3042	+	2.97709i	1.05898	+	0.256227i
$136$		0			0
$137$	10.1869	−	17.6443i	0.870328	−	1.50745i	0.00867008	−	0.999962i	$-0.497240\pi$
$137$	10.1869	−	17.6443i	0.870328	−	1.50745i	0.861658	−	0.507490i	$-0.169426\pi$
$138$		0			0
$139$	−3.13489	−	5.42979i	−0.265898	−	0.460549i	0.701900	−	0.712275i	$-0.252335\pi$
$139$	−3.13489	−	5.42979i	−0.265898	−	0.460549i	−0.967799	+	0.251726i	$0.919002\pi$
$140$		0			0
$141$	8.38986	+	8.25446i	0.706554	+	0.695151i
$142$		0			0
$143$	−1.69117			−0.141423
$144$		0			0
$145$	2.03738			0.169195
$146$		0			0
$147$	−1.66933	+	0.461883i	−0.137684	+	0.0380955i
$148$		0			0
$149$	2.45679	+	4.25529i	0.201268	+	0.348607i	0.948937	−	0.315465i	$-0.102160\pi$
$149$	2.45679	+	4.25529i	0.201268	+	0.348607i	−0.747669	+	0.664071i	$0.768827\pi$
$150$		0			0
$151$	−2.80878	+	4.86494i	−0.228575	+	0.395903i	−0.957386	−	0.288811i	$-0.906740\pi$
$151$	−2.80878	+	4.86494i	−0.228575	+	0.395903i	0.728811	+	0.684715i	$0.240073\pi$
$152$		0			0
$153$	18.4835	+	10.2742i	1.49431	+	0.830621i
$154$		0			0
$155$	−0.646423	+	1.11964i	−0.0519220	+	0.0899315i
$156$		0			0
$157$	−10.3174	−	17.8702i	−0.823416	−	1.42620i	−0.903124	−	0.429379i	$-0.858732\pi$
$157$	−10.3174	−	17.8702i	−0.823416	−	1.42620i	0.0797087	−	0.996818i	$-0.474601\pi$
$158$		0			0
$159$	−0.264265	+	1.01935i	−0.0209576	+	0.0808397i
$160$		0			0
$161$	7.03629			0.554537
$162$		0			0
$163$	−4.95096			−0.387789			−0.193895	−	0.981022i	$-0.562112\pi$
$163$	−4.95096			−0.387789			−0.193895	+	0.981022i	$0.562112\pi$
$164$		0			0
$165$	−0.803702	+	3.10012i	−0.0625681	+	0.241344i
$166$		0			0
$167$	−0.485864	−	0.841542i	−0.0375973	−	0.0651205i	0.846614	−	0.532207i	$-0.178637\pi$
$167$	−0.485864	−	0.841542i	−0.0375973	−	0.0651205i	−0.884212	+	0.467086i	$0.845304\pi$
$168$		0			0
$169$	4.01736	−	6.95828i	0.309028	−	0.535252i
$170$		0			0
$171$	−3.59684	−	1.99933i	−0.275057	−	0.152892i
$172$		0			0
$173$	8.90960	−	15.4319i	0.677384	−	1.17326i	−0.298382	−	0.954447i	$-0.596447\pi$
$173$	8.90960	−	15.4319i	0.677384	−	1.17326i	0.975766	−	0.218817i	$-0.0702198\pi$
$174$		0			0
$175$	0.467722	+	0.810117i	0.0353564	+	0.0612391i
$176$		0			0
$177$	−1.94265	+	0.537508i	−0.146019	+	0.0404016i
$178$		0			0
$179$	10.6065			0.792764			0.396382	−	0.918086i	$-0.370266\pi$
$179$	10.6065			0.792764			0.396382	+	0.918086i	$0.370266\pi$
$180$		0			0
$181$	24.7360			1.83862			0.919308	−	0.393539i	$-0.128749\pi$
$181$	24.7360			1.83862			0.919308	+	0.393539i	$0.128749\pi$
$182$		0			0
$183$	14.4624	+	14.2290i	1.06909	+	1.05184i
$184$		0			0
$185$	−5.51898	−	9.55915i	−0.405763	−	0.702802i
$186$		0			0
$187$	−2.67495	+	4.63315i	−0.195612	+	0.338810i
$188$		0			0
$189$	1.46694	+	4.98479i	0.106704	+	0.362590i
$190$		0			0
$191$	9.25120	−	16.0235i	0.669393	−	1.15942i	−0.308681	−	0.951166i	$-0.599888\pi$
$191$	9.25120	−	16.0235i	0.669393	−	1.15942i	0.978074	−	0.208257i	$-0.0667791\pi$
$192$		0			0
$193$	−8.24505	−	14.2808i	−0.593492	−	1.02796i	−0.993758	−	0.111559i	$-0.964416\pi$
$193$	−8.24505	−	14.2808i	−0.593492	−	1.02796i	0.400266	−	0.916399i	$-0.368918\pi$
$194$		0			0
$195$	6.70268	+	6.59450i	0.479989	+	0.472242i
$196$		0			0
$197$	−8.68164			−0.618541			−0.309271	−	0.950974i	$-0.600085\pi$
$197$	−8.68164			−0.618541			−0.309271	+	0.950974i	$0.600085\pi$
$198$		0			0
$199$	19.2352			1.36355			0.681774	−	0.731563i	$-0.261209\pi$
$199$	19.2352			1.36355			0.681774	+	0.731563i	$0.261209\pi$
$200$		0			0
$201$	−0.510151	+	0.141152i	−0.0359833	+	0.00995613i
$202$		0			0
$203$	0.418134	+	0.724229i	0.0293472	+	0.0508309i
$204$		0			0
$205$	−10.7891	+	18.6873i	−0.753543	+	1.30518i
$206$		0			0
$207$	−0.343425	−	21.1061i	−0.0238697	−	1.46697i
$208$		0			0
$209$	0.520536	−	0.901595i	0.0360063	−	0.0623647i
$210$		0			0
$211$	11.3584	+	19.6734i	0.781946	+	1.35437i	0.930807	+	0.365512i	$0.119106\pi$
$211$	11.3584	+	19.6734i	0.781946	+	1.35437i	−0.148861	+	0.988858i	$0.547561\pi$
$212$		0			0
$213$	−5.48511	+	21.1577i	−0.375833	+	1.44970i
$214$		0			0
$215$	−18.0363			−1.23006
$216$		0			0
$217$	−0.530665			−0.0360239
$218$		0			0
$219$	−4.41178	+	17.0175i	−0.298120	+	1.14994i
$220$		0			0
$221$	7.85365	+	13.6029i	0.528294	+	0.915032i
$222$		0			0
$223$	7.76320	−	13.4462i	0.519862	−	0.900427i	−0.479871	−	0.877339i	$-0.659317\pi$
$223$	7.76320	−	13.4462i	0.519862	−	0.900427i	0.999733	−	0.0230886i	$-0.00734998\pi$
$224$		0			0
$225$	2.40720	−	1.44252i	0.160480	−	0.0961679i
$226$		0			0
$227$	1.13468	−	1.96533i	0.0753114	−	0.130443i	−0.825910	−	0.563802i	$-0.809338\pi$
$227$	1.13468	−	1.96533i	0.0753114	−	0.130443i	0.901222	+	0.433358i	$0.142672\pi$
$228$		0			0
$229$	−4.61037	−	7.98540i	−0.304662	−	0.527690i	0.672524	−	0.740075i	$-0.265210\pi$
$229$	−4.61037	−	7.98540i	−0.304662	−	0.527690i	−0.977186	+	0.212385i	$0.931877\pi$
$230$		0			0
$231$	−1.26695	+	0.350548i	−0.0833589	+	0.0230644i
$232$		0			0
$233$	−24.0842			−1.57781			−0.788905	−	0.614515i	$-0.789352\pi$
$233$	−24.0842			−1.57781			−0.788905	+	0.614515i	$0.789352\pi$
$234$		0			0
$235$	16.5551			1.07993
$236$		0			0
$237$	−18.8275	−	18.5237i	−1.22298	−	1.20324i
$238$		0			0
$239$	2.50000	+	4.33013i	0.161712	+	0.280093i	0.935483	−	0.353373i	$-0.114965\pi$
$239$	2.50000	+	4.33013i	0.161712	+	0.280093i	−0.773771	+	0.633465i	$0.781632\pi$
$240$		0			0
$241$	8.61761	−	14.9261i	0.555109	−	0.961477i	−0.442786	−	0.896627i	$-0.646010\pi$
$241$	8.61761	−	14.9261i	0.555109	−	0.961477i	0.997895	−	0.0648494i	$-0.0206567\pi$
$242$		0			0
$243$	14.8808	−	4.64354i	0.954602	−	0.297883i
$244$		0			0
$245$	−1.21814	+	2.10988i	−0.0778240	+	0.134795i
$246$		0			0
$247$	−1.52829	−	2.64708i	−0.0972430	−	0.168430i
$248$		0			0
$249$	−20.2216	−	19.8952i	−1.28149	−	1.26081i
$250$		0			0
$251$	−15.2725			−0.963994			−0.481997	−	0.876173i	$-0.660088\pi$
$251$	−15.2725			−0.963994			−0.481997	+	0.876173i	$0.660088\pi$
$252$		0			0
$253$	5.34022			0.335737
$254$		0			0
$255$	28.6681	−	7.93211i	1.79527	−	0.496728i
$256$		0			0
$257$	5.79524	+	10.0377i	0.361497	+	0.626131i	0.988207	−	0.153121i	$-0.0489324\pi$
$257$	5.79524	+	10.0377i	0.361497	+	0.626131i	−0.626710	+	0.779252i	$0.715599\pi$
$258$		0			0
$259$	2.26533	−	3.92367i	0.140761	−	0.243805i
$260$		0			0
$261$	2.15199	−	1.28958i	0.133205	−	0.0798232i
$262$		0			0
$263$	−4.05602	+	7.02523i	−0.250105	+	0.433194i	−0.963554	−	0.267512i	$-0.913798\pi$
$263$	−4.05602	+	7.02523i	−0.250105	+	0.433194i	0.713450	+	0.700707i	$0.247132\pi$
$264$		0			0
$265$	0.740601	+	1.28276i	0.0454948	+	0.0787992i
$266$		0			0
$267$	−4.18646	+	16.1484i	−0.256207	+	0.988267i
$268$		0			0
$269$	11.4598			0.698717			0.349358	−	0.936989i	$-0.386400\pi$
$269$	11.4598			0.698717			0.349358	+	0.936989i	$0.386400\pi$
$270$		0			0
$271$	3.30404			0.200706			0.100353	−	0.994952i	$-0.468003\pi$
$271$	3.30404			0.200706			0.100353	+	0.994952i	$0.468003\pi$
$272$		0			0
$273$	−0.968555	+	3.73600i	−0.0586196	+	0.226113i
$274$		0			0
$275$	0.354979	+	0.614842i	0.0214061	+	0.0370764i
$276$		0			0
$277$	5.12453	−	8.87595i	0.307903	−	0.533304i	−0.670000	−	0.742361i	$-0.733706\pi$
$277$	5.12453	−	8.87595i	0.307903	−	0.533304i	0.977903	+	0.209057i	$0.0670394\pi$
$278$		0			0
$279$	0.0259006	+	1.59178i	0.00155063	+	0.0952976i
$280$		0			0
$281$	0.861334	−	1.49188i	0.0513829	−	0.0889978i	−0.839190	−	0.543838i	$-0.816970\pi$
$281$	0.861334	−	1.49188i	0.0513829	−	0.0889978i	0.890573	+	0.454841i	$0.150304\pi$
$282$		0			0
$283$	12.0752	+	20.9148i	0.717795	+	1.24326i	0.961872	+	0.273501i	$0.0881817\pi$
$283$	12.0752	+	20.9148i	0.717795	+	1.24326i	−0.244077	+	0.969756i	$0.578485\pi$
$284$		0			0
$285$	−5.57872	+	1.54356i	−0.330455	+	0.0914326i
$286$		0			0
$287$	−8.85704			−0.522814
$288$		0			0
$289$	32.6890			1.92288
$290$		0			0
$291$	−13.5003	−	13.2824i	−0.791401	−	0.778628i
$292$		0			0
$293$	7.46533	+	12.9303i	0.436129	+	0.755398i	0.997387	−	0.0722432i	$-0.0230158\pi$
$293$	7.46533	+	12.9303i	0.436129	+	0.755398i	−0.561258	+	0.827641i	$0.689682\pi$
$294$		0			0
$295$	−1.41759	+	2.45533i	−0.0825351	+	0.142955i
$296$		0			0
$297$	1.11334	+	3.78323i	0.0646026	+	0.219525i
$298$		0			0
$299$	7.83944	−	13.5783i	0.453367	−	0.785254i
$300$		0			0
$301$	−3.70161	−	6.41137i	−0.213357	−	0.369545i
$302$		0			0
$303$	1.85303	+	1.82312i	0.106454	+	0.104736i
$304$		0			0
$305$	28.5376			1.63406
$306$		0			0
$307$	17.9563			1.02482			0.512411	−	0.858741i	$-0.328753\pi$
$307$	17.9563			1.02482			0.512411	+	0.858741i	$0.328753\pi$
$308$		0			0
$309$	17.1350	−	4.74103i	0.974774	−	0.269708i
$310$		0			0
$311$	10.8931	+	18.8673i	0.617689	+	1.06987i	0.989906	+	0.141723i	$0.0452643\pi$
$311$	10.8931	+	18.8673i	0.617689	+	1.06987i	−0.372217	+	0.928146i	$0.621402\pi$
$312$		0			0
$313$	−11.0624	+	19.1606i	−0.625284	+	1.08302i	0.363202	+	0.931710i	$0.381683\pi$
$313$	−11.0624	+	19.1606i	−0.625284	+	1.08302i	−0.988486	+	0.151313i	$0.951650\pi$
$314$		0			0
$315$	6.38825	+	3.55095i	0.359937	+	0.200074i
$316$		0			0
$317$	−2.86480	+	4.96197i	−0.160903	+	0.278692i	−0.935193	−	0.354139i	$-0.884774\pi$
$317$	−2.86480	+	4.96197i	−0.160903	+	0.278692i	0.774290	+	0.632831i	$0.218107\pi$
$318$		0			0
$319$	0.317344	+	0.549657i	0.0177679	+	0.0307749i
$320$		0			0
$321$	3.40962	−	13.1519i	0.190306	−	0.734068i
$322$		0			0
$323$	−9.66931			−0.538015
$324$		0			0
$325$	2.08444			0.115624
$326$		0			0
$327$	5.29219	−	20.4136i	0.292659	−	1.12887i
$328$		0			0
$329$	3.39762	+	5.88485i	0.187317	+	0.324442i
$330$		0			0
$331$	−15.8178	+	27.3973i	−0.869427	+	1.50589i	−0.00684339	+	0.999977i	$0.502178\pi$
$331$	−15.8178	+	27.3973i	−0.869427	+	1.50589i	−0.862583	+	0.505915i	$0.831155\pi$
$332$		0			0
$333$	−11.8800	−	6.60359i	−0.651021	−	0.361875i
$334$		0			0
$335$	−0.372266	+	0.644784i	−0.0203391	+	0.0352283i
$336$		0			0
$337$	−11.7771	−	20.3985i	−0.641539	−	1.11118i	−0.985089	−	0.172044i	$-0.944963\pi$
$337$	−11.7771	−	20.3985i	−0.641539	−	1.11118i	0.343550	−	0.939134i	$-0.388371\pi$
$338$		0			0
$339$	−6.63013	+	1.83447i	−0.360099	+	0.0996349i
$340$		0			0
$341$	−0.402751			−0.0218102
$342$		0			0
$343$	−1.00000			−0.0539949
$344$		0			0
$345$	−21.1651	−	20.8235i	−1.13949	−	1.12110i
$346$		0			0
$347$	−9.81359	−	16.9976i	−0.526821	−	0.912481i	−0.999512	−	0.0312526i	$-0.990050\pi$
$347$	−9.81359	−	16.9976i	−0.526821	−	0.912481i	0.472690	−	0.881229i	$-0.343283\pi$
$348$		0			0
$349$	13.0363	−	22.5795i	0.697816	−	1.20865i	−0.271406	−	0.962465i	$-0.587488\pi$
$349$	13.0363	−	22.5795i	0.697816	−	1.20865i	0.969222	−	0.246188i	$-0.0791782\pi$
$350$		0			0
$351$	11.2538	+	2.72293i	0.600683	+	0.145339i
$352$		0			0
$353$	−3.30878	+	5.73097i	−0.176108	+	0.305029i	−0.940544	−	0.339671i	$-0.889684\pi$
$353$	−3.30878	+	5.73097i	−0.176108	+	0.305029i	0.764436	+	0.644700i	$0.223018\pi$
$354$		0			0
$355$	15.3720	+	26.6250i	0.815859	+	1.41311i
$356$		0			0
$357$	8.70322	+	8.56276i	0.460623	+	0.453189i
$358$		0			0
$359$	23.0527			1.21668			0.608338	−	0.793678i	$-0.291836\pi$
$359$	23.0527			1.21668			0.608338	+	0.793678i	$0.291836\pi$
$360$		0			0
$361$	−17.1184			−0.900968
$362$		0			0
$363$	17.4011	−	4.81466i	0.913320	−	0.252704i
$364$		0			0
$365$	12.3640	+	21.4150i	0.647159	+	1.12091i
$366$		0			0
$367$	4.08931	−	7.08289i	0.213460	−	0.369724i	−0.739335	−	0.673338i	$-0.764860\pi$
$367$	4.08931	−	7.08289i	0.213460	−	0.369724i	0.952795	+	0.303614i	$0.0981933\pi$
$368$		0			0
$369$	0.432292	+	26.5676i	0.0225042	+	1.38305i
$370$		0			0
$371$	−0.303989	+	0.526524i	−0.0157823	+	0.0273358i
$372$		0			0
$373$	−7.75341	−	13.4293i	−0.401456	−	0.695343i	0.592446	−	0.805610i	$-0.298163\pi$
$373$	−7.75341	−	13.4293i	−0.401456	−	0.695343i	−0.993902	+	0.110268i	$0.964829\pi$
$374$		0			0
$375$	−4.30420	+	16.6026i	−0.222268	+	0.857353i
$376$		0			0
$377$	1.86345			0.0959723
$378$		0			0
$379$	−18.5814			−0.954461			−0.477231	−	0.878778i	$-0.658359\pi$
$379$	−18.5814			−0.954461			−0.477231	+	0.878778i	$0.658359\pi$
$380$		0			0
$381$	−6.84936	+	26.4200i	−0.350903	+	1.35354i
$382$		0			0
$383$	8.30959	+	14.3926i	0.424600	+	0.735429i	0.996383	−	0.0849761i	$-0.0270814\pi$
$383$	8.30959	+	14.3926i	0.424600	+	0.735429i	−0.571783	+	0.820405i	$0.693748\pi$
$384$		0			0
$385$	−0.924512	+	1.60130i	−0.0471175	+	0.0816099i
$386$		0			0
$387$	−19.0509	+	11.4163i	−0.968412	+	0.580322i
$388$		0			0
$389$	12.9112	−	22.3629i	0.654624	−	1.13384i	−0.327364	−	0.944898i	$-0.606160\pi$
$389$	12.9112	−	22.3629i	0.654624	−	1.13384i	0.981988	−	0.188944i	$-0.0605065\pi$
$390$		0			0
$391$	−24.7995	−	42.9541i	−1.25417	−	2.17228i
$392$		0			0
$393$	−19.8246	+	5.48522i	−1.00002	+	0.276693i
$394$		0			0
$395$	−37.1509			−1.86927
$396$		0			0
$397$	−0.729016			−0.0365883			−0.0182941	−	0.999833i	$-0.505824\pi$
$397$	−0.729016			−0.0365883			−0.0182941	+	0.999833i	$0.505824\pi$
$398$		0			0
$399$	−1.69362	−	1.66628i	−0.0847869	−	0.0834185i
$400$		0			0
$401$	8.67094	+	15.0185i	0.433006	+	0.749989i	0.997131	−	0.0757010i	$-0.0241195\pi$
$401$	8.67094	+	15.0185i	0.433006	+	0.749989i	−0.564124	+	0.825690i	$0.690786\pi$
$402$		0			0
$403$	−0.591238	+	1.02405i	−0.0294516	+	0.0510117i
$404$		0			0
$405$	10.3397	−	19.3355i	0.513781	−	0.960790i
$406$		0			0
$407$	1.71928	−	2.97789i	0.0852218	−	0.147608i
$408$		0			0
$409$	1.82351	+	3.15841i	0.0901668	+	0.156174i	0.907581	−	0.419877i	$-0.137927\pi$
$409$	1.82351	+	3.15841i	0.0901668	+	0.156174i	−0.817414	+	0.576050i	$0.804593\pi$
$410$		0			0
$411$	−25.1549	−	24.7490i	−1.24080	−	1.22078i
$412$		0			0
$413$	−1.16373			−0.0572635
$414$		0			0
$415$	−39.9018			−1.95870
$416$		0			0
$417$	−10.4663	+	2.89591i	−0.512539	+	0.141813i
$418$		0			0
$419$	0.117685	+	0.203836i	0.00574927	+	0.00995803i	0.868886	−	0.495013i	$-0.164837\pi$
$419$	0.117685	+	0.203836i	0.00574927	+	0.00995803i	−0.863136	+	0.504971i	$0.831503\pi$
$420$		0			0
$421$	−10.8985	+	18.8767i	−0.531158	+	0.919993i	0.468181	+	0.883633i	$0.344910\pi$
$421$	−10.8985	+	18.8767i	−0.531158	+	0.919993i	−0.999339	+	0.0363601i	$0.988424\pi$
$422$		0			0
$423$	17.4864	−	10.4787i	0.850217	−	0.509494i
$424$		0			0
$425$	3.29699	−	5.71055i	0.159927	−	0.277002i
$426$		0			0
$427$	5.85680	+	10.1443i	0.283431	+	0.490916i
$428$		0			0
$429$	−0.735089	+	2.83546i	−0.0354904	+	0.136897i
$430$		0			0
$431$	4.28806			0.206549			0.103274	−	0.994653i	$-0.467068\pi$
$431$	4.28806			0.206549			0.103274	+	0.994653i	$0.467068\pi$
$432$		0			0
$433$	−13.9263			−0.669257			−0.334628	−	0.942350i	$-0.608611\pi$
$433$	−13.9263			−0.669257			−0.334628	+	0.942350i	$0.608611\pi$
$434$		0			0
$435$	0.885573	−	3.41592i	0.0424600	−	0.163781i
$436$		0			0
$437$	4.82591	+	8.35871i	0.230854	+	0.399851i
$438$		0			0
$439$	−15.9397	+	27.6084i	−0.760762	+	1.31768i	0.181696	+	0.983355i	$0.441841\pi$
$439$	−15.9397	+	27.6084i	−0.760762	+	1.31768i	−0.942458	+	0.334324i	$0.891492\pi$
$440$		0			0
$441$	0.0488078	+	2.99960i	0.00232418	+	0.142838i
$442$		0			0
$443$	2.56216	−	4.43780i	0.121732	−	0.210846i	−0.798719	−	0.601705i	$-0.794488\pi$
$443$	2.56216	−	4.43780i	0.121732	−	0.210846i	0.920451	+	0.390858i	$0.127822\pi$
$444$		0			0
$445$	11.7325	+	20.3213i	0.556174	+	0.963322i
$446$		0			0
$447$	8.20239	−	2.26950i	0.387960	−	0.107344i
$448$		0			0
$449$	−33.9914			−1.60415			−0.802077	−	0.597221i	$-0.796272\pi$
$449$	−33.9914			−1.60415			−0.802077	+	0.597221i	$0.796272\pi$
$450$		0			0
$451$	−6.72209			−0.316531
$452$		0			0
$453$	6.93581	+	6.82387i	0.325873	+	0.320613i
$454$		0			0
$455$	2.71436	+	4.70142i	0.127251	+	0.220406i
$456$		0			0
$457$	−2.78826	+	4.82941i	−0.130429	+	0.225910i	−0.923842	−	0.382774i	$-0.874969\pi$
$457$	−2.78826	+	4.82941i	−0.130429	+	0.225910i	0.793413	+	0.608684i	$0.208302\pi$
$458$		0			0
$459$	25.2601	−	26.5241i	1.17904	−	1.23804i
$460$		0			0
$461$	−1.24904	+	2.16340i	−0.0581734	+	0.100759i	−0.893646	−	0.448774i	$-0.851861\pi$
$461$	−1.24904	+	2.16340i	−0.0581734	+	0.100759i	0.835472	+	0.549533i	$0.185194\pi$
$462$		0			0
$463$	−4.77517	−	8.27084i	−0.221921	−	0.384378i	0.733470	−	0.679722i	$-0.237899\pi$
$463$	−4.77517	−	8.27084i	−0.221921	−	0.384378i	−0.955391	+	0.295343i	$0.904566\pi$
$464$		0			0
$465$	1.59624	+	1.57047i	0.0740237	+	0.0728290i
$466$		0			0
$467$	−18.2128			−0.842787			−0.421393	−	0.906878i	$-0.638459\pi$
$467$	−18.2128			−0.842787			−0.421393	+	0.906878i	$0.638459\pi$
$468$		0			0
$469$	−0.305602			−0.0141114
$470$		0			0
$471$	−34.4462	+	9.53083i	−1.58720	+	0.439157i
$472$		0			0
$473$	−2.80935	−	4.86594i	−0.129174	−	0.223736i
$474$		0			0
$475$	−0.641583	+	1.11125i	−0.0294378	+	0.0509878i
$476$		0			0
$477$	1.59420	+	0.886147i	0.0729934	+	0.0405739i
$478$		0			0
$479$	−2.87648	+	4.98222i	−0.131430	+	0.227643i	−0.924228	−	0.381841i	$-0.875290\pi$
$479$	−2.87648	+	4.98222i	−0.131430	+	0.227643i	0.792798	+	0.609484i	$0.208623\pi$
$480$		0			0
$481$	−5.04782	−	8.74308i	−0.230161	−	0.398650i
$482$		0			0
$483$	3.05841	−	11.7972i	0.139163	−	0.536791i
$484$		0			0
$485$	−26.6391			−1.20962
$486$		0			0
$487$	−23.8918			−1.08264			−0.541321	−	0.840816i	$-0.682075\pi$
$487$	−23.8918			−1.08264			−0.541321	+	0.840816i	$0.682075\pi$
$488$		0			0
$489$	−2.15200	+	8.30090i	−0.0973167	+	0.375379i
$490$		0			0
$491$	7.31437	+	12.6689i	0.330093	+	0.571738i	0.982530	−	0.186105i	$-0.0595865\pi$
$491$	7.31437	+	12.6689i	0.330093	+	0.571738i	−0.652437	+	0.757843i	$0.726253\pi$
$492$		0			0
$493$	2.94744	−	5.10512i	0.132746	−	0.229923i
$494$		0			0
$495$	4.84839	+	2.69501i	0.217919	+	0.121132i
$496$		0			0
$497$	−6.30961	+	10.9286i	−0.283025	+	0.490213i
$498$		0			0
$499$	−11.9579	−	20.7117i	−0.535308	−	0.927181i	−0.999148	−	0.0412621i	$-0.986862\pi$
$499$	−11.9579	−	20.7117i	−0.535308	−	0.927181i	0.463840	−	0.885919i	$-0.346471\pi$
$500$		0			0
$501$	−1.62214	+	0.448825i	−0.0724717	+	0.0200520i
$502$		0			0
$503$	−7.57496			−0.337751			−0.168875	−	0.985637i	$-0.554014\pi$
$503$	−7.57496			−0.337751			−0.168875	+	0.985637i	$0.554014\pi$
$504$		0			0
$505$	3.65645			0.162710
$506$		0			0
$507$	−9.92021	−	9.76011i	−0.440572	−	0.433462i
$508$		0			0
$509$	3.50078	+	6.06353i	0.155169	+	0.268761i	0.933121	−	0.359563i	$-0.117074\pi$
$509$	3.50078	+	6.06353i	0.155169	+	0.268761i	−0.777951	+	0.628325i	$0.783741\pi$
$510$		0			0
$511$	−5.07494	+	8.79006i	−0.224502	+	0.388849i
$512$		0			0
$513$	−4.91553	+	5.16151i	−0.217026	+	0.227886i
$514$		0			0
$515$	12.5037	−	21.6570i	0.550978	−	0.954321i
$516$		0			0
$517$	2.57864	+	4.46633i	0.113408	+	0.196429i
$518$		0			0
$519$	−22.0008	−	21.6457i	−0.965727	−	0.950141i
$520$		0			0
$521$	42.4564			1.86005			0.930025	−	0.367497i	$-0.119785\pi$
$521$	42.4564			1.86005			0.930025	+	0.367497i	$0.119785\pi$
$522$		0			0
$523$	18.6096			0.813743			0.406871	−	0.913485i	$-0.366620\pi$
$523$	18.6096			0.813743			0.406871	+	0.913485i	$0.366620\pi$
$524$		0			0
$525$	1.56156	−	0.432065i	0.0681522	−	0.0188569i
$526$		0			0
$527$	1.87034	+	3.23952i	0.0814733	+	0.141116i
$528$		0			0
$529$	−13.2547	+	22.9577i	−0.576289	+	0.998163i
$530$		0			0
$531$	0.0567992	+	3.49074i	0.00246487	+	0.151485i
$532$		0			0
$533$	−9.86802	+	17.0919i	−0.427431	+	0.740333i
$534$		0			0
$535$	−9.55542	−	16.5505i	−0.413117	−	0.715539i
$536$		0			0
$537$	4.61024	−	17.7831i	0.198946	−	0.767395i
$538$		0			0
$539$	−0.758955			−0.0326905
$540$		0			0
$541$	−0.694443			−0.0298564			−0.0149282	−	0.999889i	$-0.504752\pi$
$541$	−0.694443			−0.0298564			−0.0149282	+	0.999889i	$0.504752\pi$
$542$		0			0
$543$	10.7518	−	41.4730i	0.461406	−	1.77978i
$544$		0			0
$545$	−14.8313	−	25.6886i	−0.635304	−	1.10038i
$546$		0			0
$547$	8.77655	−	15.2014i	0.375258	−	0.649966i	−0.615107	−	0.788443i	$-0.710887\pi$
$547$	8.77655	−	15.2014i	0.375258	−	0.649966i	0.990366	+	0.138477i	$0.0442207\pi$
$548$		0			0
$549$	30.1430	−	18.0632i	1.28647	−	0.770919i
$550$		0			0
$551$	−0.573562	+	0.993439i	−0.0244346	+	0.0423219i
$552$		0			0
$553$	−7.62453	−	13.2061i	−0.324228	−	0.561579i
$554$		0			0
$555$	−18.4260	+	5.09824i	−0.782140	+	0.216408i
$556$		0			0
$557$	14.2666			0.604495			0.302248	−	0.953229i	$-0.402263\pi$
$557$	14.2666			0.604495			0.302248	+	0.953229i	$0.402263\pi$
$558$		0			0
$559$	−16.4965			−0.697728
$560$		0			0
$561$	6.60535	+	6.49875i	0.278878	+	0.274377i
$562$		0			0
$563$	−16.8742	−	29.2270i	−0.711162	−	1.23177i	−0.964421	−	0.264371i	$-0.914836\pi$
$563$	−16.8742	−	29.2270i	−0.711162	−	1.23177i	0.253259	−	0.967399i	$-0.418498\pi$
$564$		0			0
$565$	−4.83811	+	8.37986i	−0.203541	+	0.352543i
$566$		0			0
$567$	8.99524	−	0.292808i	0.377764	−	0.0122968i
$568$		0			0
$569$	−19.9867	+	34.6180i	−0.837886	+	1.45126i	0.0537729	+	0.998553i	$0.482875\pi$
$569$	−19.9867	+	34.6180i	−0.837886	+	1.45126i	−0.891659	+	0.452708i	$0.850458\pi$
$570$		0			0
$571$	20.2266	+	35.0335i	0.846457	+	1.46611i	0.884350	+	0.466824i	$0.154602\pi$
$571$	20.2266	+	35.0335i	0.846457	+	1.46611i	−0.0378934	+	0.999282i	$0.512065\pi$
$572$		0			0
$573$	−22.8443	−	22.4756i	−0.954335	−	0.938932i
$574$		0			0
$575$	−6.58204			−0.274490
$576$		0			0
$577$	−31.6758			−1.31868			−0.659340	−	0.751845i	$-0.729164\pi$
$577$	−31.6758			−1.31868			−0.659340	+	0.751845i	$0.729164\pi$
$578$		0			0
$579$	−27.5274	+	7.61650i	−1.14400	+	0.316531i
$580$		0			0
$581$	−8.18909	−	14.1839i	−0.339741	−	0.588448i
$582$		0			0
$583$	−0.230714	+	0.399608i	−0.00955519	+	0.0165501i
$584$		0			0
$585$	13.9699	−	8.37148i	0.577584	−	0.346118i
$586$		0			0
$587$	7.65220	−	13.2540i	0.315840	−	0.547051i	−0.663776	−	0.747932i	$-0.731047\pi$
$587$	7.65220	−	13.2540i	0.315840	−	0.547051i	0.979616	+	0.200881i	$0.0643803\pi$
$588$		0			0
$589$	−0.363962	−	0.630400i	−0.0149968	−	0.0259752i
$590$		0			0
$591$	−3.77359	+	14.5558i	−0.155225	+	0.598748i
$592$		0			0
$593$	39.2583			1.61214			0.806072	−	0.591817i	$-0.201589\pi$
$593$	39.2583			1.61214			0.806072	+	0.591817i	$0.201589\pi$
$594$		0			0
$595$	17.1734			0.704041
$596$		0			0
$597$	8.36083	−	32.2502i	0.342186	−	1.31991i
$598$		0			0
$599$	8.77972	+	15.2069i	0.358730	+	0.621338i	0.987749	−	0.156052i	$-0.0498766\pi$
$599$	8.77972	+	15.2069i	0.358730	+	0.621338i	−0.629019	+	0.777390i	$0.716543\pi$
$600$		0			0
$601$	−9.12937	+	15.8125i	−0.372395	+	0.645007i	−0.989933	−	0.141534i	$-0.954797\pi$
$601$	−9.12937	+	15.8125i	−0.372395	+	0.645007i	0.617539	+	0.786541i	$0.288130\pi$
$602$		0			0
$603$	0.0149158	+	0.916686i	0.000607417	+	0.0373303i
$604$		0			0
$605$	12.6979	−	21.9933i	0.516241	−	0.894156i
$606$		0			0
$607$	−3.71415	−	6.43310i	−0.150753	−	0.261112i	0.780752	−	0.624842i	$-0.214836\pi$
$607$	−3.71415	−	6.43310i	−0.150753	−	0.261112i	−0.931504	+	0.363730i	$0.881503\pi$
$608$		0			0
$609$	1.39601	−	0.386258i	0.0565690	−	0.0156519i
$610$		0			0
$611$	15.1418			0.612570
$612$		0			0
$613$	−39.8772			−1.61062			−0.805312	−	0.592851i	$-0.798002\pi$
$613$	−39.8772			−1.61062			−0.805312	+	0.592851i	$0.798002\pi$
$614$		0			0
$615$	26.6419	+	26.2119i	1.07430	+	1.05697i
$616$		0			0
$617$	−0.187473	−	0.324713i	−0.00754739	−	0.0130725i	0.862227	−	0.506522i	$-0.169069\pi$
$617$	−0.187473	−	0.324713i	−0.00754739	−	0.0130725i	−0.869774	+	0.493450i	$0.835736\pi$
$618$		0			0
$619$	−6.95166	+	12.0406i	−0.279411	+	0.483954i	−0.971238	−	0.238109i	$-0.923472\pi$
$619$	−6.95166	+	12.0406i	−0.279411	+	0.483954i	0.691828	+	0.722063i	$0.256806\pi$
$620$		0			0
$621$	−35.5362	−	8.59823i	−1.42602	−	0.345035i
$622$		0			0
$623$	−4.81575	+	8.34113i	−0.192939	+	0.334180i
$624$		0			0
$625$	14.4011	+	24.9434i	0.576043	+	0.997736i
$626$		0			0
$627$	−1.28538	−	1.26463i	−0.0513331	−	0.0505046i
$628$		0			0
$629$	−31.9368			−1.27341
$630$		0			0
$631$	−28.6049			−1.13874			−0.569372	−	0.822080i	$-0.692813\pi$
$631$	−28.6049			−1.13874			−0.569372	+	0.822080i	$0.692813\pi$
$632$		0			0
$633$	37.9219	−	10.4925i	1.50726	−	0.417040i
$634$		0			0
$635$	19.1953	+	33.2472i	0.761740	+	1.31937i
$636$		0			0
$637$	−1.11414	+	1.92976i	−0.0441440	+	0.0764597i
$638$		0			0
$639$	33.0893	+	18.3929i	1.30899	+	0.727613i
$640$		0			0
$641$	10.9011	−	18.8812i	0.430566	−	0.745762i	−0.566356	−	0.824161i	$-0.691647\pi$
$641$	10.9011	−	18.8812i	0.430566	−	0.745762i	0.996922	+	0.0783986i	$0.0249807\pi$
$642$		0			0
$643$	−20.9205	−	36.2354i	−0.825025	−	1.42899i	−0.901900	−	0.431945i	$-0.857828\pi$
$643$	−20.9205	−	36.2354i	−0.825025	−	1.42899i	0.0768751	−	0.997041i	$-0.475506\pi$
$644$		0			0
$645$	−7.83971	+	30.2401i	−0.308688	+	1.19070i
$646$		0			0
$647$	−17.2614			−0.678615			−0.339308	−	0.940675i	$-0.610193\pi$
$647$	−17.2614			−0.678615			−0.339308	+	0.940675i	$0.610193\pi$
$648$		0			0
$649$	−0.883220			−0.0346694
$650$		0			0
$651$	−0.230660	+	0.889726i	−0.00904029	+	0.0348711i
$652$		0			0
$653$	−0.237661	−	0.411641i	−0.00930039	−	0.0161087i	0.861338	−	0.508033i	$-0.169627\pi$
$653$	−0.237661	−	0.411641i	−0.00930039	−	0.0161087i	−0.870638	+	0.491924i	$0.836294\pi$
$654$		0			0
$655$	−14.4663	+	25.0564i	−0.565247	+	0.979036i
$656$		0			0
$657$	26.6144	+	14.7938i	1.03833	+	0.577161i
$658$		0			0
$659$	18.2344	−	31.5828i	0.710310	−	1.23029i	−0.254431	−	0.967091i	$-0.581888\pi$
$659$	18.2344	−	31.5828i	0.710310	−	1.23029i	0.964741	−	0.263201i	$-0.0847784\pi$
$660$		0			0
$661$	−5.04982	−	8.74655i	−0.196415	−	0.340201i	0.750948	−	0.660361i	$-0.229597\pi$
$661$	−5.04982	−	8.74655i	−0.196415	−	0.340201i	−0.947364	+	0.320160i	$0.896263\pi$
$662$		0			0
$663$	26.2207	−	7.25494i	1.01833	−	0.281758i
$664$		0			0
$665$	−3.34189			−0.129593
$666$		0			0
$667$	−5.88422			−0.227838
$668$		0			0
$669$	−19.1699	−	18.8605i	−0.741152	−	0.729191i
$670$		0			0
$671$	4.44505	+	7.69905i	0.171599	+	0.297218i
$672$		0			0
$673$	9.51044	−	16.4726i	0.366600	−	0.634971i	−0.622431	−	0.782675i	$-0.713855\pi$
$673$	9.51044	−	16.4726i	0.366600	−	0.634971i	0.989032	+	0.147704i	$0.0471883\pi$
$674$		0			0
$675$	−1.37224	−	4.66298i	−0.0528175	−	0.179478i
$676$		0			0
$677$	22.6374	−	39.2091i	0.870024	−	1.50693i	0.00805435	−	0.999968i	$-0.497436\pi$
$677$	22.6374	−	39.2091i	0.870024	−	1.50693i	0.861970	−	0.506959i	$-0.169230\pi$
$678$		0			0
$679$	−5.46718	−	9.46943i	−0.209811	−	0.363403i
$680$		0			0
$681$	−2.80191	−	2.75669i	−0.107369	−	0.105637i
$682$		0			0
$683$	45.5318			1.74222			0.871112	−	0.491084i	$-0.163399\pi$
$683$	45.5318			1.74222			0.871112	+	0.491084i	$0.163399\pi$
$684$		0			0
$685$	−49.6363			−1.89651
$686$		0			0
$687$	−15.3925	+	4.25890i	−0.587259	+	0.162487i
$688$		0			0
$689$	0.677375	+	1.17325i	0.0258059	+	0.0446972i
$690$		0			0
$691$	−8.09446	+	14.0200i	−0.307928	+	0.533347i	−0.977909	−	0.209031i	$-0.932969\pi$
$691$	−8.09446	+	14.0200i	−0.307928	+	0.533347i	0.669981	+	0.742378i	$0.266302\pi$
$692$		0			0
$693$	0.0370429	+	2.27656i	0.00140714	+	0.0864795i
$694$		0			0
$695$	−7.63746	+	13.2285i	−0.289706	+	0.501785i
$696$		0			0
$697$	31.2168	+	54.0691i	1.18242	+	2.04801i
$698$		0			0
$699$	−10.4685	+	40.3802i	−0.395956	+	1.52732i
$700$		0			0
$701$	−2.61120			−0.0986238			−0.0493119	−	0.998783i	$-0.515703\pi$
$701$	−2.61120			−0.0986238			−0.0493119	+	0.998783i	$0.515703\pi$
$702$		0			0
$703$	6.21480			0.234396
$704$		0			0
$705$	7.19588	−	27.7567i	0.271013	−	1.04538i
$706$		0			0
$707$	0.750417	+	1.29976i	0.0282223	+	0.0488825i
$708$		0			0
$709$	−23.1702	+	40.1319i	−0.870175	+	1.50719i	−0.00835896	+	0.999965i	$0.502661\pi$
$709$	−23.1702	+	40.1319i	−0.870175	+	1.50719i	−0.861816	+	0.507222i	$0.830673\pi$
$710$		0			0
$711$	−39.2408	+	23.5151i	−1.47165	+	0.881886i
$712$		0			0
$713$	1.86696	−	3.23366i	0.0699180	−	0.121102i
$714$		0			0
$715$	2.06008	+	3.56816i	0.0770426	+	0.133442i
$716$		0			0
$717$	8.34665	−	2.30941i	0.311711	−	0.0862467i
$718$		0			0
$719$	46.2069			1.72323			0.861614	−	0.507564i	$-0.169454\pi$
$719$	46.2069			1.72323			0.861614	+	0.507564i	$0.169454\pi$
$720$		0			0
$721$	10.2646			0.382273
$722$		0			0
$723$	−21.2798	−	20.9363i	−0.791403	−	0.778630i
$724$		0			0
$725$	−0.391140	−	0.677475i	−0.0145266	−	0.0251608i
$726$		0			0
$727$	−9.72988	+	16.8526i	−0.360861	+	0.625030i	−0.988103	−	0.153795i	$-0.950851\pi$
$727$	−9.72988	+	16.8526i	−0.360861	+	0.625030i	0.627242	+	0.778825i	$0.284184\pi$
$728$		0			0
$729$	−1.31734	−	26.9678i	−0.0487905	−	0.998809i
$730$		0			0
$731$	−26.0928	+	45.1940i	−0.965077	+	1.67156i
$732$		0			0
$733$	−7.68617	−	13.3128i	−0.283895	−	0.491721i	0.688445	−	0.725288i	$-0.258293\pi$
$733$	−7.68617	−	13.3128i	−0.283895	−	0.491721i	−0.972341	+	0.233567i	$0.924960\pi$
$734$		0			0
$735$	3.00799	+	2.95945i	0.110951	+	0.109161i
$736$		0			0
$737$	−0.231938			−0.00854356
$738$		0			0
$739$	32.4962			1.19539			0.597696	−	0.801723i	$-0.296083\pi$
$739$	32.4962			1.19539			0.597696	+	0.801723i	$0.296083\pi$
$740$		0			0
$741$	−5.10246	+	1.41179i	−0.187443	+	0.0518632i
$742$		0			0
$743$	20.8664	+	36.1417i	0.765514	+	1.32591i	0.939974	+	0.341245i	$0.110849\pi$
$743$	20.8664	+	36.1417i	0.765514	+	1.32591i	−0.174460	+	0.984664i	$0.555818\pi$
$744$		0			0
$745$	5.98542	−	10.3671i	0.219289	−	0.379819i
$746$		0			0
$747$	−42.1464	+	25.2563i	−1.54206	+	0.924079i
$748$		0			0
$749$	3.92214	−	6.79335i	0.143312	−	0.248224i
$750$		0			0
$751$	5.02452	+	8.70273i	0.183347	+	0.317567i	0.943018	−	0.332741i	$-0.107973\pi$
$751$	5.02452	+	8.70273i	0.183347	+	0.317567i	−0.759671	+	0.650308i	$0.774640\pi$
$752$		0			0
$753$	−6.63841	+	25.6063i	−0.241917	+	0.933146i
$754$		0			0
$755$	13.6859			0.498081
$756$		0			0
$757$	−31.7989			−1.15575			−0.577876	−	0.816125i	$-0.696118\pi$
$757$	−31.7989			−1.15575			−0.577876	+	0.816125i	$0.696118\pi$
$758$		0			0
$759$	2.32120	−	8.95354i	0.0842541	−	0.324993i
$760$		0			0
$761$	27.4352	+	47.5192i	0.994526	+	1.72257i	0.587751	+	0.809042i	$0.300013\pi$
$761$	27.4352	+	47.5192i	0.994526	+	1.72257i	0.406775	+	0.913528i	$0.366653\pi$
$762$		0			0
$763$	6.08770	−	10.5442i	0.220389	−	0.381726i
$764$		0			0
$765$	−0.838196	−	51.5134i	−0.0303050	−	1.86247i
$766$		0			0
$767$	−1.29657	+	2.24572i	−0.0468163	+	0.0810882i
$768$		0			0
$769$	5.39041	+	9.33646i	0.194383	+	0.336681i	0.946698	−	0.322122i	$-0.104396\pi$
$769$	5.39041	+	9.33646i	0.194383	+	0.336681i	−0.752315	+	0.658804i	$0.771063\pi$
$770$		0			0
$771$	19.3483	−	5.35344i	0.696814	−	0.192800i
$772$		0			0
$773$	−47.4885			−1.70804			−0.854022	−	0.520237i	$-0.825844\pi$
$773$	−47.4885			−1.70804			−0.854022	+	0.520237i	$0.825844\pi$
$774$		0			0
$775$	0.496407			0.0178315
$776$		0			0
$777$	−5.59386	−	5.50359i	−0.200679	−	0.197440i
$778$		0			0
$779$	−6.07469	−	10.5217i	−0.217648	−	0.376978i
$780$		0			0
$781$	−4.78871	+	8.29428i	−0.171353	+	0.296793i
$782$		0			0
$783$	−1.22676	−	4.16861i	−0.0438407	−	0.148974i
$784$		0			0
$785$	−25.1360	+	43.5368i	−0.897141	+	1.55389i
$786$		0			0
$787$	−12.0563	−	20.8820i	−0.429759	−	0.744364i	0.567093	−	0.823654i	$-0.308068\pi$
$787$	−12.0563	−	20.8820i	−0.429759	−	0.744364i	−0.996852	+	0.0792896i	$0.974735\pi$
$788$		0			0
$789$	10.0157	+	9.85403i	0.356567	+	0.350813i
$790$		0			0
$791$	−3.97173			−0.141218
$792$		0			0
$793$	26.1013			0.926885
$794$		0			0
$795$	2.47262	−	0.684142i	0.0876946	−	0.0242640i
$796$		0			0
$797$	7.54620	+	13.0704i	0.267300	+	0.462978i	0.968164	−	0.250318i	$-0.0805351\pi$
$797$	7.54620	+	13.0704i	0.267300	+	0.462978i	−0.700863	+	0.713295i	$0.747202\pi$
$798$		0			0
$799$	23.9500	−	41.4826i	0.847289	−	1.46755i
$800$		0			0
$801$	25.2551	+	14.0382i	0.892346	+	0.496017i
$802$		0			0
$803$	−3.85165	+	6.67125i	−0.135922	+	0.235423i
$804$		0			0
$805$	−8.57117	−	14.8457i	−0.302094	−	0.523242i
$806$		0			0
$807$	4.98115	−	19.2138i	0.175345	−	0.676357i
$808$		0			0
$809$	20.1104			0.707043			0.353522	−	0.935426i	$-0.384984\pi$
$809$	20.1104			0.707043			0.353522	+	0.935426i	$0.384984\pi$
$810$		0			0
$811$	40.9770			1.43890			0.719448	−	0.694546i	$-0.244395\pi$
$811$	40.9770			1.43890			0.719448	+	0.694546i	$0.244395\pi$
$812$		0			0
$813$	1.43614	−	5.53964i	0.0503678	−	0.194284i
$814$		0			0
$815$	6.03095	+	10.4459i	0.211255	+	0.365904i
$816$		0			0
$817$	5.07757	−	8.79461i	0.177642	−	0.307684i
$818$		0			0
$819$	5.84288	+	3.24780i	0.204167	+	0.113487i
$820$		0			0
$821$	11.9427	−	20.6854i	0.416803	−	0.721925i	−0.578813	−	0.815461i	$-0.696484\pi$
$821$	11.9427	−	20.6854i	0.416803	−	0.721925i	0.995616	+	0.0935360i	$0.0298170\pi$
$822$		0			0
$823$	14.9451	+	25.8857i	0.520954	+	0.902319i	0.999703	+	0.0243673i	$0.00775714\pi$
$823$	14.9451	+	25.8857i	0.520954	+	0.902319i	−0.478749	+	0.877952i	$0.658910\pi$
$824$		0			0
$825$	1.18516	−	0.327918i	0.0412618	−	0.0114166i
$826$		0			0
$827$	44.7265			1.55529			0.777647	−	0.628702i	$-0.216413\pi$
$827$	44.7265			1.55529			0.777647	+	0.628702i	$0.216413\pi$
$828$		0			0
$829$	36.8943			1.28139			0.640695	−	0.767795i	$-0.278646\pi$
$829$	36.8943			1.28139			0.640695	+	0.767795i	$0.278646\pi$
$830$		0			0
$831$	−12.6542	−	12.4500i	−0.438969	−	0.431884i
$832$		0			0
$833$	3.52452	+	6.10465i	0.122117	+	0.211514i
$834$		0			0
$835$	−1.18370	+	2.05023i	−0.0409636	+	0.0709511i
$836$		0			0
$837$	2.68008	+	0.648464i	0.0926372	+	0.0224142i
$838$		0			0
$839$	0.918446	−	1.59080i	0.0317083	−	0.0549204i	−0.849736	−	0.527209i	$-0.823239\pi$
$839$	0.918446	−	1.59080i	0.0317083	−	0.0549204i	0.881444	+	0.472288i	$0.156572\pi$
$840$		0			0
$841$	14.1503	+	24.5091i	0.487942	+	0.845141i
$842$		0			0
$843$	−2.12692	−	2.09260i	−0.0732551	−	0.0720729i
$844$		0			0
$845$	−19.5748			−0.673394
$846$		0			0
$847$	10.4240			0.358172
$848$		0			0
$849$	40.3149	−	11.1546i	1.38360	−	0.382826i
$850$		0			0
$851$	15.9395	+	27.6081i	0.546400	+	0.946392i
$852$		0			0
$853$	26.0385	−	45.1000i	0.891542	−	1.54420i	0.0535152	−	0.998567i	$-0.482957\pi$
$853$	26.0385	−	45.1000i	0.891542	−	1.54420i	0.838027	−	0.545629i	$-0.183709\pi$
$854$		0			0
$855$	0.163110	+	10.0243i	0.00557825	+	0.342825i
$856$		0			0
$857$	9.46663	−	16.3967i	0.323374	−	0.560100i	−0.657808	−	0.753186i	$-0.728516\pi$
$857$	9.46663	−	16.3967i	0.323374	−	0.560100i	0.981182	+	0.193086i	$0.0618495\pi$
$858$		0			0
$859$	−4.00700	−	6.94033i	−0.136717	−	0.236801i	0.789535	−	0.613706i	$-0.210322\pi$
$859$	−4.00700	−	6.94033i	−0.136717	−	0.236801i	−0.926252	+	0.376905i	$0.876988\pi$
$860$		0			0
$861$	−3.84983	+	14.8499i	−0.131202	+	0.506084i
$862$		0			0
$863$	23.8647			0.812364			0.406182	−	0.913792i	$-0.366860\pi$
$863$	23.8647			0.812364			0.406182	+	0.913792i	$0.366860\pi$
$864$		0			0
$865$	−43.4125			−1.47607
$866$		0			0
$867$	14.2087	−	54.8071i	0.482552	−	1.86135i
$868$		0			0
$869$	−5.78667	−	10.0228i	−0.196299	−	0.340001i
$870$		0			0
$871$	−0.340485	+	0.589738i	−0.0115369	+	0.0199825i
$872$		0			0
$873$	−28.1377	+	16.8615i	−0.952316	+	0.570677i
$874$		0			0
$875$	−4.95119	+	8.57572i	−0.167381	+	0.289912i
$876$		0			0
$877$	17.0238	+	29.4861i	0.574853	+	0.995674i	0.996058	+	0.0887086i	$0.0282740\pi$
$877$	17.0238	+	29.4861i	0.574853	+	0.995674i	−0.421205	+	0.906965i	$0.638393\pi$
$878$		0			0
$879$	24.9242	−	6.89621i	0.840672	−	0.232604i
$880$		0			0
$881$	−38.8018			−1.30727			−0.653633	−	0.756812i	$-0.726756\pi$
$881$	−38.8018			−1.30727			−0.653633	+	0.756812i	$0.726756\pi$
$882$		0			0
$883$	42.0944			1.41659			0.708294	−	0.705917i	$-0.249465\pi$
$883$	42.0944			1.41659			0.708294	+	0.705917i	$0.249465\pi$
$884$		0			0
$885$	3.50050	+	3.44400i	0.117668	+	0.115769i
$886$		0			0
$887$	12.1168	+	20.9869i	0.406841	+	0.704670i	0.994534	−	0.104414i	$-0.0332968\pi$
$887$	12.1168	+	20.9869i	0.406841	+	0.704670i	−0.587692	+	0.809084i	$0.699964\pi$
$888$		0			0
$889$	−7.87893	+	13.6467i	−0.264251	+	0.457696i
$890$		0			0
$891$	6.82698	−	0.222228i	0.228712	−	0.00744491i
$892$		0			0
$893$	−4.66058	+	8.07236i	−0.155960	+	0.270131i
$894$		0			0
$895$	−12.9201	−	22.3783i	−0.431873	−	0.748025i
$896$		0			0
$897$	−19.3582	−	19.0458i	−0.646352	−	0.635920i
$898$		0			0
$899$	0.443778			0.0148008
$900$		0			0
$901$	4.28566			0.142776
$902$		0			0
$903$	−12.3584	+	3.41942i	−0.411262	+	0.113791i
$904$		0			0
$905$	−30.1319	−	52.1900i	−1.00162	−	1.73485i
$906$		0			0
$907$	−12.9424	+	22.4170i	−0.429747	+	0.744343i	−0.996851	−	0.0793031i	$-0.974731\pi$
$907$	−12.9424	+	22.4170i	−0.429747	+	0.744343i	0.567104	+	0.823646i	$0.308064\pi$
$908$		0			0
$909$	3.86214	−	2.31439i	0.128099	−	0.0767635i
$910$		0			0
$911$	−21.9571	+	38.0308i	−0.727471	+	1.26002i	0.230478	+	0.973078i	$0.425971\pi$
$911$	−21.9571	+	38.0308i	−0.727471	+	1.26002i	−0.957949	+	0.286939i	$0.907362\pi$
$912$		0			0
$913$	−6.21514	−	10.7649i	−0.205691	−	0.356268i
$914$		0			0
$915$	12.4042	−	47.8468i	0.410071	−	1.58177i
$916$		0			0
$917$	−11.8758			−0.392173
$918$		0			0
$919$	−41.4335			−1.36677			−0.683383	−	0.730060i	$-0.739492\pi$
$919$	−41.4335			−1.36677			−0.683383	+	0.730060i	$0.739492\pi$
$920$		0			0
$921$	7.80495	−	30.1060i	0.257182	−	0.992026i
$922$		0			0
$923$	14.0596	+	24.3520i	0.462779	+	0.801556i
$924$		0			0
$925$	−2.11909	+	3.67037i	−0.0696752	+	0.120681i
$926$		0			0
$927$	−0.500991	−	30.7896i	−0.0164547	−	1.01126i
$928$		0			0
$929$	1.56911	−	2.71778i	0.0514808	−	0.0891674i	−0.839137	−	0.543921i	$-0.816939\pi$
$929$	1.56911	−	2.71778i	0.0514808	−	0.0891674i	0.890617	+	0.454753i	$0.150273\pi$
$930$		0			0
$931$	−0.685860	−	1.18794i	−0.0224781	−	0.0389333i
$932$		0			0
$933$	36.3683	−	10.0626i	1.19064	−	0.329436i
$934$		0			0
$935$	13.0338			0.426252
$936$		0			0
$937$	10.2810			0.335866			0.167933	−	0.985798i	$-0.446291\pi$
$937$	10.2810			0.335866			0.167933	+	0.985798i	$0.446291\pi$
$938$		0			0
$939$	27.3168	+	26.8759i	0.891449	+	0.877062i
$940$		0			0
$941$	7.23844	+	12.5373i	0.235966	+	0.408706i	0.959553	−	0.281528i	$-0.0908411\pi$
$941$	7.23844	+	12.5373i	0.235966	+	0.408706i	−0.723587	+	0.690234i	$0.757508\pi$
$942$		0			0
$943$	31.1603	−	53.9713i	1.01472	−	1.75755i
$944$		0			0
$945$	8.73035	−	9.16722i	0.283998	−	0.298210i
$946$		0			0
$947$	14.8714	−	25.7580i	0.483256	−	0.837024i	−0.516559	−	0.856251i	$-0.672787\pi$
$947$	14.8714	−	25.7580i	0.483256	−	0.837024i	0.999815	+	0.0192278i	$0.00612078\pi$
$948$		0			0
$949$	11.3084	+	19.5868i	0.367088	+	0.635814i
$950$		0			0
$951$	7.07414	+	6.95997i	0.229395	+	0.225692i
$952$		0			0
$953$	19.4869			0.631242			0.315621	−	0.948885i	$-0.397787\pi$
$953$	19.4869			0.631242			0.315621	+	0.948885i	$0.397787\pi$
$954$		0			0
$955$	−45.0769			−1.45866
$956$		0			0
$957$	1.05951	−	0.293152i	0.0342490	−	0.00947626i
$958$		0			0
$959$	−10.1869	−	17.6443i	−0.328953	−	0.569763i
$960$		0			0
$961$	15.3592	−	26.6029i	0.495458	−	0.858158i
$962$		0			0
$963$	−20.5688	−	11.4333i	−0.662820	−	0.368433i
$964$		0			0
$965$	−20.0872	+	34.7921i	−0.646631	+	1.12000i
$966$		0			0
$967$	−6.94942	−	12.0368i	−0.223478	−	0.387076i	0.732384	−	0.680892i	$-0.238408\pi$
$967$	−6.94942	−	12.0368i	−0.223478	−	0.387076i	−0.955862	+	0.293817i	$0.905075\pi$
$968$		0			0
$969$	−4.20289	+	16.2118i	−0.135016	+	0.520798i
$970$		0			0
$971$	−19.2406			−0.617460			−0.308730	−	0.951150i	$-0.599904\pi$
$971$	−19.2406			−0.617460			−0.308730	+	0.951150i	$0.599904\pi$
$972$		0			0
$973$	−6.26978			−0.201000
$974$		0			0
$975$	0.906028	−	3.49482i	0.0290161	−	0.111924i
$976$		0			0
$977$	−2.44479	−	4.23450i	−0.0782158	−	0.135474i	0.824264	−	0.566205i	$-0.191589\pi$
$977$	−2.44479	−	4.23450i	−0.0782158	−	0.135474i	−0.902480	+	0.430731i	$0.858256\pi$
$978$		0			0
$979$	−3.65494	+	6.33054i	−0.116812	+	0.202325i
$980$		0			0
$981$	−31.9255	−	17.7460i	−1.01930	−	0.566587i
$982$		0			0
$983$	−14.9670	+	25.9236i	−0.477373	+	0.826834i	−0.999664	−	0.0259332i	$-0.991744\pi$
$983$	−14.9670	+	25.9236i	−0.477373	+	0.826834i	0.522291	+	0.852768i	$0.325078\pi$
$984$		0			0
$985$	10.5754	+	18.3172i	0.336962	+	0.583634i
$986$		0			0
$987$	11.3435	−	3.13860i	0.361068	−	0.0999029i
$988$		0			0
$989$	52.0912			1.65640
$990$		0			0
$991$	9.36157			0.297380			0.148690	−	0.988884i	$-0.452494\pi$
$991$	9.36157			0.297380			0.148690	+	0.988884i	$0.452494\pi$
$992$		0			0
$993$	39.0595	+	38.4291i	1.23952	+	1.21951i
$994$		0			0
$995$	−23.4311	−	40.5839i	−0.742817	−	1.28660i
$996$		0			0
$997$	23.8210	−	41.2592i	0.754420	−	1.30669i	−0.191242	−	0.981543i	$-0.561252\pi$
$997$	23.8210	−	41.2592i	0.754420	−	1.30669i	0.945662	−	0.325151i	$-0.105415\pi$
$998$		0			0
$999$	−16.2355	+	17.0480i	−0.513670	+	0.539375i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1008.2.r.m.673.2		8
3.2	odd	2		3024.2.r.l.2017.4		8
4.3	odd	2		504.2.r.d.169.3	✓	8
9.2	odd	6		9072.2.a.cl.1.1		4
9.4	even	3	inner	1008.2.r.m.337.2		8
9.5	odd	6		3024.2.r.l.1009.4		8
9.7	even	3		9072.2.a.ce.1.4		4
12.11	even	2		1512.2.r.d.505.4		8
36.7	odd	6		4536.2.a.x.1.4		4
36.11	even	6		4536.2.a.ba.1.1		4
36.23	even	6		1512.2.r.d.1009.4		8
36.31	odd	6		504.2.r.d.337.3	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.r.d.169.3	✓	8	4.3	odd	2
504.2.r.d.337.3	yes	8	36.31	odd	6
1008.2.r.m.337.2		8	9.4	even	3	inner
1008.2.r.m.673.2		8	1.1	even	1	trivial
1512.2.r.d.505.4		8	12.11	even	2
1512.2.r.d.1009.4		8	36.23	even	6
3024.2.r.l.1009.4		8	9.5	odd	6
3024.2.r.l.2017.4		8	3.2	odd	2
4536.2.a.x.1.4		4	36.7	odd	6
4536.2.a.ba.1.1		4	36.11	even	6
9072.2.a.ce.1.4		4	9.7	even	3
9072.2.a.cl.1.1		4	9.2	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:	\( N \)	\(=\)	\( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1008.r (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.434663 - 1.67662i) q^{3} +(-1.21814 - 2.10988i) q^{5} +(0.500000 - 0.866025i) q^{7} +(-2.62214 - 1.45753i) q^{9} +O(q^{10})\)	\(q+(0.434663 - 1.67662i) q^{3} +(-1.21814 - 2.10988i) q^{5} +(0.500000 - 0.866025i) q^{7} +(-2.62214 - 1.45753i) q^{9} +(0.379477 - 0.657274i) q^{11} +(-1.11414 - 1.92976i) q^{13} +(-4.06695 + 1.12527i) q^{15} -7.04904 q^{17} +1.37172 q^{19} +(-1.23467 - 1.21474i) q^{21} +(3.51814 + 6.09360i) q^{23} +(-0.467722 + 0.810117i) q^{25} +(-3.58348 + 3.76280i) q^{27} +(-0.418134 + 0.724229i) q^{29} +(-0.265332 - 0.459569i) q^{31} +(-0.937057 - 0.921933i) q^{33} -2.43628 q^{35} +4.53066 q^{37} +(-3.71975 + 1.02921i) q^{39} +(-4.42852 - 7.67042i) q^{41} +(3.70161 - 6.41137i) q^{43} +(0.118909 + 7.30786i) q^{45} +(-3.39762 + 5.88485i) q^{47} +(-0.500000 - 0.866025i) q^{49} +(-3.06396 + 11.8186i) q^{51} -0.607978 q^{53} -1.84902 q^{55} +(0.596236 - 2.29986i) q^{57} +(-0.581866 - 1.00782i) q^{59} +(-5.85680 + 10.1443i) q^{61} +(-2.57333 + 1.54207i) q^{63} +(-2.71436 + 4.70142i) q^{65} +(-0.152801 - 0.264659i) q^{67} +(11.7459 - 3.24994i) q^{69} -12.6192 q^{71} -10.1499 q^{73} +(1.15496 + 1.13632i) q^{75} +(-0.379477 - 0.657274i) q^{77} +(7.62453 - 13.2061i) q^{79} +(4.75120 + 7.64370i) q^{81} +(8.18909 - 14.1839i) q^{83} +(8.58671 + 14.8726i) q^{85} +(1.03251 + 1.01585i) q^{87} -9.63151 q^{89} -2.22829 q^{91} +(-0.885855 + 0.245105i) q^{93} +(-1.67094 - 2.89416i) q^{95} +(5.46718 - 9.46943i) q^{97} +(-1.95304 + 1.17036i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{3} + 4 q^{5} + 4 q^{7} + 10 q^{9}+O(q^{10}) \) 8 * q + 4 * q^3 + 4 * q^5 + 4 * q^7 + 10 * q^9	\( 8 q + 4 q^{3} + 4 q^{5} + 4 q^{7} + 10 q^{9} + 6 q^{11} - 3 q^{13} - 4 q^{15} - 16 q^{17} + 4 q^{19} - q^{21} + 5 q^{23} - 14 q^{25} - 5 q^{27} + q^{29} - 11 q^{31} + 8 q^{35} + 54 q^{37} + 12 q^{39} + 2 q^{41} + 11 q^{43} + 26 q^{45} - 7 q^{47} - 4 q^{49} - 17 q^{51} - 8 q^{53} - 12 q^{55} - 13 q^{57} - 9 q^{59} - 7 q^{61} + 5 q^{63} - 9 q^{65} + 12 q^{67} + 4 q^{69} + 24 q^{71} + 26 q^{73} + 23 q^{75} - 6 q^{77} + 22 q^{79} + 34 q^{81} + 6 q^{83} - 11 q^{85} - 37 q^{87} - 28 q^{89} - 6 q^{91} - 13 q^{93} + 23 q^{95} - q^{97} + 42 q^{99}+O(q^{100}) \) 8 * q + 4 * q^3 + 4 * q^5 + 4 * q^7 + 10 * q^9 + 6 * q^11 - 3 * q^13 - 4 * q^15 - 16 * q^17 + 4 * q^19 - q^21 + 5 * q^23 - 14 * q^25 - 5 * q^27 + q^29 - 11 * q^31 + 8 * q^35 + 54 * q^37 + 12 * q^39 + 2 * q^41 + 11 * q^43 + 26 * q^45 - 7 * q^47 - 4 * q^49 - 17 * q^51 - 8 * q^53 - 12 * q^55 - 13 * q^57 - 9 * q^59 - 7 * q^61 + 5 * q^63 - 9 * q^65 + 12 * q^67 + 4 * q^69 + 24 * q^71 + 26 * q^73 + 23 * q^75 - 6 * q^77 + 22 * q^79 + 34 * q^81 + 6 * q^83 - 11 * q^85 - 37 * q^87 - 28 * q^89 - 6 * q^91 - 13 * q^93 + 23 * q^95 - q^97 + 42 * q^99

Introduction

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Database

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