LMFDB - Embedded newform 968.2.i.q.753.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [968,2,Mod(9,968)] 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("968.9"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(968, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 0, 6])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 968 = 2^{3} \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	968.i (of order $5$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,-1,0,-3,0,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$7.72951891566$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.1305015625.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 5x^{6} - 9x^{5} + 29x^{4} + 36x^{3} + 80x^{2} + 64x + 256 $ x^8 - x^7 + 5x^6 - 9x^5 + 29x^4 + 36x^3 + 80x^2 + 64x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 88)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			753.1
Root			$-0.791563 - 2.43618i$ of defining polynomial
Character	$\chi$	$=$	968.753
Dual form			968.2.i.q.9.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.07234 - 1.50564i) q^{3} +(-0.173529 + 0.534068i) q^{5} +(-4.14468 + 3.01129i) q^{7} +(1.10058 + 3.38724i) q^{9} +(-0.965093 - 2.97025i) q^{13} +(1.16373 - 0.845498i) q^{15} +(-0.618034 + 1.90211i) q^{17} +(-3.23607 - 2.35114i) q^{19} +13.1231 q^{21} +6.56155 q^{23} +(3.78997 + 2.75357i) q^{25} +(0.444505 - 1.36804i) q^{27} +(2.52665 - 1.83572i) q^{29} +(-0.444505 - 1.36804i) q^{31} +(-0.889009 - 2.73609i) q^{35} +(2.78176 - 2.02107i) q^{37} +(-2.47214 + 7.60845i) q^{39} +(5.76271 + 4.18686i) q^{41} -1.12311 q^{43} -2.00000 q^{45} +(-6.47214 - 4.70228i) q^{47} +(5.94741 - 18.3042i) q^{49} +(4.14468 - 3.01129i) q^{51} +(-1.31215 - 4.03839i) q^{53} +(3.16625 + 9.74473i) q^{57} +(10.3617 - 7.52821i) q^{59} +(2.20116 - 6.77448i) q^{61} +(-14.7615 - 10.7249i) q^{63} +1.75379 q^{65} +5.43845 q^{67} +(-13.5978 - 9.87936i) q^{69} +(1.13862 - 3.50432i) q^{71} +(-2.52665 + 1.83572i) q^{73} +(-3.70820 - 11.4127i) q^{75} +(0.889009 + 2.73609i) q^{79} +(5.66312 - 4.11450i) q^{81} +(-2.81919 + 8.67659i) q^{83} +(-0.908612 - 0.660145i) q^{85} -8.00000 q^{87} -9.68466 q^{89} +(12.9443 + 9.40456i) q^{91} +(-1.13862 + 3.50432i) q^{93} +(1.81722 - 1.32029i) q^{95} +(3.53467 + 10.8786i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - q^{3} - 3 q^{5} - 2 q^{7} - 3 q^{9} - 2 q^{13} + 7 q^{15} + 4 q^{17} - 8 q^{19} + 72 q^{21} + 36 q^{23} - 3 q^{25} - 7 q^{27} - 2 q^{29} + 7 q^{31} + 14 q^{35} + 11 q^{37} + 16 q^{39} + 6 q^{41}+ \cdots - 27 q^{97}+O(q^{100}) $ 8 * q - q^3 - 3 * q^5 - 2 * q^7 - 3 * q^9 - 2 * q^13 + 7 * q^15 + 4 * q^17 - 8 * q^19 + 72 * q^21 + 36 * q^23 - 3 * q^25 - 7 * q^27 - 2 * q^29 + 7 * q^31 + 14 * q^35 + 11 * q^37 + 16 * q^39 + 6 * q^41 + 24 * q^43 - 16 * q^45 - 16 * q^47 - 22 * q^49 + 2 * q^51 - 8 * q^53 - 4 * q^57 + 5 * q^59 - 6 * q^61 - 20 * q^63 + 80 * q^65 + 60 * q^67 - 13 * q^69 + 5 * q^71 + 2 * q^73 + 24 * q^75 - 14 * q^79 + 14 * q^81 + 10 * q^83 + 6 * q^85 - 64 * q^87 - 28 * q^89 + 32 * q^91 - 5 * q^93 - 12 * q^95 - 27 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/968\mathbb{Z}\right)^\times$.

$n$	$485$	$727$	$849$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{5}\right)$

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
$3$	−2.07234	−	1.50564i	−1.19647	−	0.869283i	−0.202533	−	0.979275i	$-0.564917\pi$
$3$	−2.07234	−	1.50564i	−1.19647	−	0.869283i	−0.993932	+	0.109992i	$0.964917\pi$
$4$		0			0
$5$	−0.173529	+	0.534068i	−0.0776047	+	0.238843i	−0.982331	−	0.187150i	$-0.940075\pi$
$5$	−0.173529	+	0.534068i	−0.0776047	+	0.238843i	0.904727	+	0.425993i	$0.140075\pi$
$6$		0			0
$7$	−4.14468	+	3.01129i	−1.56654	+	1.13816i	−0.636166	+	0.771553i	$0.719480\pi$
$7$	−4.14468	+	3.01129i	−1.56654	+	1.13816i	−0.930376	+	0.366606i	$0.880520\pi$
$8$		0			0
$9$	1.10058	+	3.38724i	0.366860	+	1.12908i
$10$		0			0
$11$		0			0
$11$		0			0
$12$		0			0
$13$	−0.965093	−	2.97025i	−0.267669	−	0.823799i	−0.991067	−	0.133368i	$-0.957421\pi$
$13$	−0.965093	−	2.97025i	−0.267669	−	0.823799i	0.723398	−	0.690431i	$-0.242579\pi$
$14$		0			0
$15$	1.16373	−	0.845498i	0.300473	−	0.218307i
$16$		0			0
$17$	−0.618034	+	1.90211i	−0.149895	+	0.461330i	−0.997608	−	0.0691254i	$-0.977979\pi$
$17$	−0.618034	+	1.90211i	−0.149895	+	0.461330i	0.847713	+	0.530456i	$0.177979\pi$
$18$		0			0
$19$	−3.23607	−	2.35114i	−0.742405	−	0.539389i	0.151058	−	0.988525i	$-0.451732\pi$
$19$	−3.23607	−	2.35114i	−0.742405	−	0.539389i	−0.893463	+	0.449136i	$0.851732\pi$
$20$		0			0
$21$	13.1231			2.86370
$22$		0			0
$23$	6.56155			1.36818			0.684089	−	0.729398i	$-0.260200\pi$
$23$	6.56155			1.36818			0.684089	+	0.729398i	$0.260200\pi$
$24$		0			0
$25$	3.78997	+	2.75357i	0.757994	+	0.550715i
$26$		0			0
$27$	0.444505	−	1.36804i	0.0855450	−	0.263280i
$28$		0			0
$29$	2.52665	−	1.83572i	0.469186	−	0.340884i	−0.327938	−	0.944699i	$-0.606354\pi$
$29$	2.52665	−	1.83572i	0.469186	−	0.340884i	0.797124	+	0.603816i	$0.206354\pi$
$30$		0			0
$31$	−0.444505	−	1.36804i	−0.0798354	−	0.245708i	0.903171	−	0.429282i	$-0.141233\pi$
$31$	−0.444505	−	1.36804i	−0.0798354	−	0.245708i	−0.983006	+	0.183574i	$0.941233\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−0.889009	−	2.73609i	−0.150270	−	0.462483i
$36$		0			0
$37$	2.78176	−	2.02107i	0.457319	−	0.332262i	−0.335160	−	0.942161i	$-0.608790\pi$
$37$	2.78176	−	2.02107i	0.457319	−	0.332262i	0.792479	+	0.609900i	$0.208790\pi$
$38$		0			0
$39$	−2.47214	+	7.60845i	−0.395859	+	1.21833i
$40$		0			0
$41$	5.76271	+	4.18686i	0.899985	+	0.653877i	0.938462	−	0.345382i	$-0.112251\pi$
$41$	5.76271	+	4.18686i	0.899985	+	0.653877i	−0.0384774	+	0.999259i	$0.512251\pi$
$42$		0			0
$43$	−1.12311			−0.171272			−0.0856360	−	0.996326i	$-0.527292\pi$
$43$	−1.12311			−0.171272			−0.0856360	+	0.996326i	$0.527292\pi$
$44$		0			0
$45$	−2.00000			−0.298142
$46$		0			0
$47$	−6.47214	−	4.70228i	−0.944058	−	0.685898i	0.00533600	−	0.999986i	$-0.498301\pi$
$47$	−6.47214	−	4.70228i	−0.944058	−	0.685898i	−0.949394	+	0.314087i	$0.898301\pi$
$48$		0			0
$49$	5.94741	−	18.3042i	0.849629	−	2.61489i
$50$		0			0
$51$	4.14468	−	3.01129i	0.580371	−	0.421664i
$52$		0			0
$53$	−1.31215	−	4.03839i	−0.180238	−	0.554715i	0.819596	−	0.572942i	$-0.194198\pi$
$53$	−1.31215	−	4.03839i	−0.180238	−	0.554715i	−0.999834	+	0.0182268i	$0.994198\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	3.16625	+	9.74473i	0.419381	+	1.29072i
$58$		0			0
$59$	10.3617	−	7.52821i	1.34898	−	0.980090i	0.349917	−	0.936781i	$-0.386210\pi$
$59$	10.3617	−	7.52821i	1.34898	−	0.980090i	0.999062	−	0.0433092i	$-0.0137901\pi$
$60$		0			0
$61$	2.20116	−	6.77448i	0.281830	−	0.867383i	−0.705501	−	0.708709i	$-0.749278\pi$
$61$	2.20116	−	6.77448i	0.281830	−	0.867383i	0.987331	−	0.158674i	$-0.0507219\pi$
$62$		0			0
$63$	−14.7615	−	10.7249i	−1.85977	−	1.35120i
$64$		0			0
$65$	1.75379			0.217531
$66$		0			0
$67$	5.43845			0.664412			0.332206	−	0.943207i	$-0.392207\pi$
$67$	5.43845			0.664412			0.332206	+	0.943207i	$0.392207\pi$
$68$		0			0
$69$	−13.5978	−	9.87936i	−1.63698	−	1.18933i
$70$		0			0
$71$	1.13862	−	3.50432i	0.135130	−	0.415886i	−0.860481	−	0.509483i	$-0.829837\pi$
$71$	1.13862	−	3.50432i	0.135130	−	0.415886i	0.995610	+	0.0935972i	$0.0298366\pi$
$72$		0			0
$73$	−2.52665	+	1.83572i	−0.295721	+	0.214854i	−0.725746	−	0.687963i	$-0.758505\pi$
$73$	−2.52665	+	1.83572i	−0.295721	+	0.214854i	0.430024	+	0.902817i	$0.358505\pi$
$74$		0			0
$75$	−3.70820	−	11.4127i	−0.428187	−	1.31782i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	0.889009	+	2.73609i	0.100021	+	0.307834i	0.988530	−	0.151026i	$-0.0482578\pi$
$79$	0.889009	+	2.73609i	0.100021	+	0.307834i	−0.888508	+	0.458860i	$0.848258\pi$
$80$		0			0
$81$	5.66312	−	4.11450i	0.629235	−	0.457166i
$82$		0			0
$83$	−2.81919	+	8.67659i	−0.309447	+	0.952379i	0.668533	+	0.743682i	$0.266922\pi$
$83$	−2.81919	+	8.67659i	−0.309447	+	0.952379i	−0.977980	+	0.208697i	$0.933078\pi$
$84$		0			0
$85$	−0.908612	−	0.660145i	−0.0985528	−	0.0716028i
$86$		0			0
$87$	−8.00000			−0.857690
$88$		0			0
$89$	−9.68466			−1.02657			−0.513286	−	0.858218i	$-0.671572\pi$
$89$	−9.68466			−1.02657			−0.513286	+	0.858218i	$0.671572\pi$
$90$		0			0
$91$	12.9443	+	9.40456i	1.35693	+	0.985866i
$92$		0			0
$93$	−1.13862	+	3.50432i	−0.118070	+	0.363381i
$94$		0			0
$95$	1.81722	−	1.32029i	0.186443	−	0.135459i
$96$		0			0
$97$	3.53467	+	10.8786i	0.358892	+	1.10456i	0.953718	+	0.300701i	$0.0972207\pi$
$97$	3.53467	+	10.8786i	0.358892	+	1.10456i	−0.594827	+	0.803854i	$0.702779\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	0.618034	+	1.90211i	0.0614967	+	0.189267i	0.977085	−	0.212850i	$-0.0682745\pi$
$101$	0.618034	+	1.90211i	0.0614967	+	0.189267i	−0.915588	+	0.402117i	$0.868274\pi$
$102$		0			0
$103$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$103$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$104$		0			0
$105$	−2.27724	+	7.00864i	−0.222236	+	0.683973i
$106$		0			0
$107$	9.19797	+	6.68272i	0.889201	+	0.646043i	0.935670	−	0.352877i	$-0.114797\pi$
$107$	9.19797	+	6.68272i	0.889201	+	0.646043i	−0.0464683	+	0.998920i	$0.514797\pi$
$108$		0			0
$109$	4.24621			0.406713			0.203357	−	0.979105i	$-0.434815\pi$
$109$	4.24621			0.406713			0.203357	+	0.979105i	$0.434815\pi$
$110$		0			0
$111$	−8.80776			−0.835996
$112$		0			0
$113$	3.69037	+	2.68121i	0.347161	+	0.252227i	0.747677	−	0.664062i	$-0.231169\pi$
$113$	3.69037	+	2.68121i	0.347161	+	0.252227i	−0.400516	+	0.916290i	$0.631169\pi$
$114$		0			0
$115$	−1.13862	+	3.50432i	−0.106177	+	0.326779i
$116$		0			0
$117$	8.99878	−	6.53800i	0.831938	−	0.604438i
$118$		0			0
$119$	−3.16625	−	9.74473i	−0.290250	−	0.893298i
$120$		0			0
$121$		0			0
$122$		0			0
$123$	−5.63839	−	17.3532i	−0.508396	−	1.56468i
$124$		0			0
$125$	−4.39980	+	3.19664i	−0.393530	+	0.285916i
$126$		0			0
$127$	3.16625	−	9.74473i	0.280960	−	0.864705i	−0.706621	−	0.707592i	$-0.749781\pi$
$127$	3.16625	−	9.74473i	0.280960	−	0.864705i	0.987581	−	0.157113i	$-0.0502185\pi$
$128$		0			0
$129$	2.32746	+	1.69100i	0.204921	+	0.148884i
$130$		0			0
$131$	11.3693			0.993342			0.496671	−	0.867939i	$-0.334556\pi$
$131$	11.3693			0.993342			0.496671	+	0.867939i	$0.334556\pi$
$132$		0			0
$133$	20.4924			1.77692
$134$		0			0
$135$	0.653495	+	0.474792i	0.0562439	+	0.0408636i
$136$		0			0
$137$	−3.88173	+	11.9467i	−0.331639	+	1.02068i	0.636715	+	0.771099i	$0.280293\pi$
$137$	−3.88173	+	11.9467i	−0.331639	+	1.02068i	−0.968354	+	0.249580i	$0.919707\pi$
$138$		0			0
$139$	5.56352	−	4.04214i	0.471892	−	0.342850i	−0.326286	−	0.945271i	$-0.605797\pi$
$139$	5.56352	−	4.04214i	0.471892	−	0.342850i	0.798178	+	0.602421i	$0.205797\pi$
$140$		0			0
$141$	6.33251	+	19.4895i	0.533293	+	1.64131i
$142$		0			0
$143$		0			0
$144$		0			0
$145$	0.541951	+	1.66795i	0.0450065	+	0.138516i
$146$		0			0
$147$	−39.8847	+	28.9779i	−3.28963	+	2.39006i
$148$		0			0
$149$	3.78429	−	11.6468i	0.310021	−	0.954146i	−0.667735	−	0.744399i	$-0.732736\pi$
$149$	3.78429	−	11.6468i	0.310021	−	0.954146i	0.977756	−	0.209747i	$-0.0672640\pi$
$150$		0			0
$151$	12.4340	+	9.03386i	1.01187	+	0.735165i	0.964600	−	0.263717i	$-0.0849486\pi$
$151$	12.4340	+	9.03386i	1.01187	+	0.735165i	0.0472677	+	0.998882i	$0.484949\pi$
$152$		0			0
$153$	−7.12311			−0.575869
$154$		0			0
$155$	0.807764			0.0648812
$156$		0			0
$157$	6.92644	+	5.03235i	0.552790	+	0.401626i	0.828813	−	0.559525i	$-0.189017\pi$
$157$	6.92644	+	5.03235i	0.552790	+	0.401626i	−0.276023	+	0.961151i	$0.589017\pi$
$158$		0			0
$159$	−3.36115	+	10.3445i	−0.266556	+	0.820375i
$160$		0			0
$161$	−27.1955	+	19.7587i	−2.14331	+	1.55720i
$162$		0			0
$163$	−1.23607	−	3.80423i	−0.0968163	−	0.297970i	0.890906	−	0.454187i	$-0.150070\pi$
$163$	−1.23607	−	3.80423i	−0.0968163	−	0.297970i	−0.987723	+	0.156217i	$0.950070\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−2.47214	−	7.60845i	−0.191300	−	0.588760i	−1.00000		0.000538710i	$-0.999829\pi$
$167$	−2.47214	−	7.60845i	−0.191300	−	0.588760i	0.808700	−	0.588221i	$-0.200171\pi$
$168$		0			0
$169$	2.62624	−	1.90808i	0.202018	−	0.146775i
$170$		0			0
$171$	4.40232	−	13.5490i	0.336654	−	1.03611i
$172$		0			0
$173$	−3.43526	−	2.49586i	−0.261178	−	0.189757i	0.449488	−	0.893286i	$-0.351606\pi$
$173$	−3.43526	−	2.49586i	−0.261178	−	0.189757i	−0.710666	+	0.703529i	$0.751606\pi$
$174$		0			0
$175$	−24.0000			−1.81423
$176$		0			0
$177$	−32.8078			−2.46598
$178$		0			0
$179$	8.54448	+	6.20792i	0.638644	+	0.464002i	0.859384	−	0.511331i	$-0.170847\pi$
$179$	8.54448	+	6.20792i	0.638644	+	0.464002i	−0.220740	+	0.975333i	$0.570847\pi$
$180$		0			0
$181$	−4.22879	+	13.0149i	−0.314324	+	0.967389i	0.661708	+	0.749761i	$0.269832\pi$
$181$	−4.22879	+	13.0149i	−0.314324	+	0.967389i	−0.976032	+	0.217627i	$0.930168\pi$
$182$		0			0
$183$	−14.7615	+	10.7249i	−1.09120	+	0.792804i
$184$		0			0
$185$	0.596672	+	1.83637i	0.0438682	+	0.135012i
$186$		0			0
$187$		0			0
$188$		0			0
$189$	2.27724	+	7.00864i	0.165645	+	0.509803i
$190$		0			0
$191$	11.7805	−	8.55907i	0.852410	−	0.619312i	−0.0733993	−	0.997303i	$-0.523385\pi$
$191$	11.7805	−	8.55907i	0.852410	−	0.619312i	0.925810	+	0.377990i	$0.123385\pi$
$192$		0			0
$193$	0.270975	−	0.833976i	0.0195052	−	0.0600309i	−0.940830	−	0.338879i	$-0.889952\pi$
$193$	0.270975	−	0.833976i	0.0195052	−	0.0600309i	0.960335	+	0.278848i	$0.0899524\pi$
$194$		0			0
$195$	−3.63445	−	2.64058i	−0.260268	−	0.189096i
$196$		0			0
$197$	−18.4924			−1.31753			−0.658765	−	0.752349i	$-0.728921\pi$
$197$	−18.4924			−1.31753			−0.658765	+	0.752349i	$0.728921\pi$
$198$		0			0
$199$	20.4924			1.45267			0.726335	−	0.687341i	$-0.241222\pi$
$199$	20.4924			1.45267			0.726335	+	0.687341i	$0.241222\pi$
$200$		0			0
$201$	−11.2703	−	8.18836i	−0.794946	−	0.577562i
$202$		0			0
$203$	−4.94427	+	15.2169i	−0.347020	+	1.06802i
$204$		0			0
$205$	−3.23607	+	2.35114i	−0.226017	+	0.164211i
$206$		0			0
$207$	7.22152	+	22.2255i	0.501930	+	1.54478i
$208$		0			0
$209$		0			0
$210$		0			0
$211$	7.56857	+	23.2937i	0.521042	+	1.60360i	0.772012	+	0.635608i	$0.219251\pi$
$211$	7.56857	+	23.2937i	0.521042	+	1.60360i	−0.250970	+	0.967995i	$0.580749\pi$
$212$		0			0
$213$	−7.63586	+	5.54778i	−0.523201	+	0.380128i
$214$		0			0
$215$	0.194892	−	0.599815i	0.0132915	−	0.0409071i
$216$		0			0
$217$	5.96190	+	4.33158i	0.404720	+	0.294047i
$218$		0			0
$219$	8.00000			0.540590
$220$		0			0
$221$	6.24621			0.420166
$222$		0			0
$223$	−7.12563	−	5.17707i	−0.477168	−	0.346683i	0.323061	−	0.946378i	$-0.395288\pi$
$223$	−7.12563	−	5.17707i	−0.477168	−	0.346683i	−0.800228	+	0.599696i	$0.795288\pi$
$224$		0			0
$225$	−5.15584	+	15.8681i	−0.343723	+	1.05787i
$226$		0			0
$227$	12.0357	−	8.74442i	0.798835	−	0.580387i	−0.111737	−	0.993738i	$-0.535642\pi$
$227$	12.0357	−	8.74442i	0.798835	−	0.580387i	0.910572	+	0.413350i	$0.135642\pi$
$228$		0			0
$229$	0.715480	+	2.20202i	0.0472802	+	0.145514i	0.971910	−	0.235355i	$-0.0756251\pi$
$229$	0.715480	+	2.20202i	0.0472802	+	0.145514i	−0.924629	+	0.380868i	$0.875625\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−5.36741	−	16.5192i	−0.351631	−	1.08221i	−0.957937	−	0.286978i	$-0.907349\pi$
$233$	−5.36741	−	16.5192i	−0.351631	−	1.08221i	0.606306	−	0.795231i	$-0.292651\pi$
$234$		0			0
$235$	3.63445	−	2.64058i	0.237085	−	0.172252i
$236$		0			0
$237$	2.27724	−	7.00864i	0.147923	−	0.455260i
$238$		0			0
$239$	−10.6168	−	7.71357i	−0.686745	−	0.498949i	0.188844	−	0.982007i	$-0.439526\pi$
$239$	−10.6168	−	7.71357i	−0.686745	−	0.498949i	−0.875588	+	0.483058i	$0.839526\pi$
$240$		0			0
$241$	−20.8769			−1.34480			−0.672399	−	0.740188i	$-0.734736\pi$
$241$	−20.8769			−1.34480			−0.672399	+	0.740188i	$0.734736\pi$
$242$		0			0
$243$	−22.2462			−1.42710
$244$		0			0
$245$	8.74366	+	6.35264i	0.558612	+	0.405856i
$246$		0			0
$247$	−3.86037	+	11.8810i	−0.245630	+	0.755970i
$248$		0			0
$249$	18.9062	−	13.7361i	1.19813	−	0.870492i
$250$		0			0
$251$	−0.791563	−	2.43618i	−0.0499630	−	0.153770i	0.922962	−	0.384891i	$-0.125761\pi$
$251$	−0.791563	−	2.43618i	−0.0499630	−	0.153770i	−0.972925	+	0.231120i	$0.925761\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$	0.889009	+	2.73609i	0.0556719	+	0.171341i
$256$		0			0
$257$	−22.8517	+	16.6027i	−1.42545	+	1.03565i	−0.434606	+	0.900621i	$0.643112\pi$
$257$	−22.8517	+	16.6027i	−1.42545	+	1.03565i	−0.990842	+	0.135028i	$0.956888\pi$
$258$		0			0
$259$	−5.44350	+	16.7534i	−0.338242	+	1.04100i
$260$		0			0
$261$	8.99878	+	6.53800i	0.557011	+	0.404692i
$262$		0			0
$263$	−10.8769			−0.670698			−0.335349	−	0.942094i	$-0.608854\pi$
$263$	−10.8769			−0.670698			−0.335349	+	0.942094i	$0.608854\pi$
$264$		0			0
$265$	2.38447			0.146477
$266$		0			0
$267$	20.0699	+	14.5816i	1.22826	+	0.892382i
$268$		0			0
$269$	8.88073	−	27.3321i	0.541467	−	1.66647i	−0.187777	−	0.982212i	$-0.560128\pi$
$269$	8.88073	−	27.3321i	0.541467	−	1.66647i	0.729244	−	0.684254i	$-0.239872\pi$
$270$		0			0
$271$	3.63445	−	2.64058i	0.220777	−	0.160404i	−0.471899	−	0.881652i	$-0.656431\pi$
$271$	3.63445	−	2.64058i	0.220777	−	0.160404i	0.692676	+	0.721249i	$0.256431\pi$
$272$		0			0
$273$	−12.6650	−	38.9789i	−0.766521	−	2.35911i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	5.56231	+	17.1190i	0.334207	+	1.02858i	0.967112	+	0.254353i	$0.0818624\pi$
$277$	5.56231	+	17.1190i	0.334207	+	1.02858i	−0.632905	+	0.774229i	$0.718138\pi$
$278$		0			0
$279$	4.14468	−	3.01129i	0.248135	−	0.180281i
$280$		0			0
$281$	0.0760835	−	0.234161i	0.00453876	−	0.0139689i	−0.948761	−	0.315993i	$-0.897662\pi$
$281$	0.0760835	−	0.234161i	0.00453876	−	0.0139689i	0.953300	+	0.302024i	$0.0976624\pi$
$282$		0			0
$283$	16.1803	+	11.7557i	0.961821	+	0.698804i	0.953573	−	0.301162i	$-0.0973744\pi$
$283$	16.1803	+	11.7557i	0.961821	+	0.698804i	0.00824833	+	0.999966i	$0.497374\pi$
$284$		0			0
$285$	−5.75379			−0.340825
$286$		0			0
$287$	−36.4924			−2.15408
$288$		0			0
$289$	10.5172	+	7.64121i	0.618660	+	0.449483i
$290$		0			0
$291$	9.05426	−	27.8661i	0.530770	−	1.63354i
$292$		0			0
$293$	17.2881	−	12.5606i	1.00998	−	0.733796i	0.0457782	−	0.998952i	$-0.485423\pi$
$293$	17.2881	−	12.5606i	1.00998	−	0.733796i	0.964206	+	0.265155i	$0.0854232\pi$
$294$		0			0
$295$	2.22252	+	6.84022i	0.129400	+	0.398253i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−6.33251	−	19.4895i	−0.366218	−	1.12710i
$300$		0			0
$301$	4.65491	−	3.38199i	0.268305	−	0.194935i
$302$		0			0
$303$	1.58313	−	4.87236i	0.0909483	−	0.279910i
$304$		0			0
$305$	3.23607	+	2.35114i	0.185297	+	0.134626i
$306$		0			0
$307$	−0.492423			−0.0281040			−0.0140520	−	0.999901i	$-0.504473\pi$
$307$	−0.492423			−0.0281040			−0.0140520	+	0.999901i	$0.504473\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−21.2336	−	15.4271i	−1.20405	−	0.874793i	−0.209372	−	0.977836i	$-0.567142\pi$
$311$	−21.2336	−	15.4271i	−1.20405	−	0.874793i	−0.994677	+	0.103043i	$0.967142\pi$
$312$		0			0
$313$	3.33978	−	10.2788i	0.188776	−	0.580992i	−0.811217	−	0.584745i	$-0.801195\pi$
$313$	3.33978	−	10.2788i	0.188776	−	0.580992i	0.999993	+	0.00375303i	$0.00119463\pi$
$314$		0			0
$315$	8.28936	−	6.02257i	0.467052	−	0.339333i
$316$		0			0
$317$	−10.7562	−	33.1042i	−0.604128	−	1.85931i	−0.502678	−	0.864474i	$-0.667652\pi$
$317$	−10.7562	−	33.1042i	−0.604128	−	1.85931i	−0.101450	−	0.994841i	$-0.532348\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	−8.99953	−	27.6977i	−0.502305	−	1.54594i
$322$		0			0
$323$	6.47214	−	4.70228i	0.360119	−	0.261642i
$324$		0			0
$325$	4.52113	−	13.9146i	0.250787	−	0.771843i
$326$		0			0
$327$	−8.79959	−	6.39328i	−0.486619	−	0.353549i
$328$		0			0
$329$	40.9848			2.25957
$330$		0			0
$331$	6.06913			0.333590			0.166795	−	0.985992i	$-0.446658\pi$
$331$	6.06913			0.333590			0.166795	+	0.985992i	$0.446658\pi$
$332$		0			0
$333$	9.90739	+	7.19814i	0.542922	+	0.394456i
$334$		0			0
$335$	−0.943730	+	2.90450i	−0.0515615	+	0.158690i
$336$		0			0
$337$	26.4861	−	19.2433i	1.44279	−	1.04825i	0.455340	−	0.890317i	$-0.349518\pi$
$337$	26.4861	−	19.2433i	1.44279	−	1.04825i	0.987450	−	0.157931i	$-0.0504824\pi$
$338$		0			0
$339$	−3.61076	−	11.1128i	−0.196109	−	0.603563i
$340$		0			0
$341$		0			0
$342$		0			0
$343$	19.3873	+	59.6680i	1.04682	+	3.22177i
$344$		0			0
$345$	7.63586	−	5.54778i	0.411101	−	0.298682i
$346$		0			0
$347$	8.26269	−	25.4300i	0.443565	−	1.36515i	−0.440486	−	0.897760i	$-0.645194\pi$
$347$	8.26269	−	25.4300i	0.443565	−	1.36515i	0.884050	−	0.467392i	$-0.154806\pi$
$348$		0			0
$349$	−12.7451	−	9.25984i	−0.682229	−	0.495668i	0.191868	−	0.981421i	$-0.438546\pi$
$349$	−12.7451	−	9.25984i	−0.682229	−	0.495668i	−0.874096	+	0.485753i	$0.838546\pi$
$350$		0			0
$351$	−4.49242			−0.239788
$352$		0			0
$353$	13.0540			0.694793			0.347397	−	0.937718i	$-0.387066\pi$
$353$	13.0540			0.694793			0.347397	+	0.937718i	$0.387066\pi$
$354$		0			0
$355$	1.67396	+	1.21620i	0.0888447	+	0.0645494i
$356$		0			0
$357$	−8.11053	+	24.9616i	−0.429255	+	1.32111i
$358$		0			0
$359$	−23.0509	+	16.7474i	−1.21658	+	0.883895i	−0.995811	−	0.0914314i	$-0.970856\pi$
$359$	−23.0509	+	16.7474i	−1.21658	+	0.883895i	−0.220766	+	0.975327i	$0.570856\pi$
$360$		0			0
$361$	−0.927051	−	2.85317i	−0.0487922	−	0.150167i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−0.541951	−	1.66795i	−0.0283670	−	0.0873046i
$366$		0			0
$367$	4.79817	−	3.48608i	0.250463	−	0.181972i	−0.455469	−	0.890252i	$-0.650528\pi$
$367$	4.79817	−	3.48608i	0.250463	−	0.181972i	0.705932	+	0.708280i	$0.250528\pi$
$368$		0			0
$369$	−7.83955	+	24.1277i	−0.408111	+	1.25604i
$370$		0			0
$371$	17.5992	+	12.7866i	0.913704	+	0.663845i
$372$		0			0
$373$	−8.24621			−0.426973			−0.213486	−	0.976946i	$-0.568482\pi$
$373$	−8.24621			−0.426973			−0.213486	+	0.976946i	$0.568482\pi$
$374$		0			0
$375$	13.9309			0.719387
$376$		0			0
$377$	−7.89098	−	5.73313i	−0.406406	−	0.295271i
$378$		0			0
$379$	6.42995	−	19.7894i	0.330284	−	1.01651i	−0.638714	−	0.769444i	$-0.720533\pi$
$379$	6.42995	−	19.7894i	0.330284	−	1.01651i	0.968998	−	0.247067i	$-0.0794667\pi$
$380$		0			0
$381$	−21.2336	+	15.4271i	−1.08783	+	0.790356i
$382$		0			0
$383$	10.8323	+	33.3383i	0.553503	+	1.70351i	0.699863	+	0.714277i	$0.253244\pi$
$383$	10.8323	+	33.3383i	0.553503	+	1.70351i	−0.146360	+	0.989231i	$0.546756\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−1.23607	−	3.80423i	−0.0628329	−	0.193380i
$388$		0			0
$389$	0.454306	−	0.330072i	0.0230342	−	0.0167353i	−0.576209	−	0.817303i	$-0.695468\pi$
$389$	0.454306	−	0.330072i	0.0230342	−	0.0167353i	0.599243	+	0.800567i	$0.295468\pi$
$390$		0			0
$391$	−4.05526	+	12.4808i	−0.205083	+	0.631182i
$392$		0			0
$393$	−23.5611	−	17.1181i	−1.18850	−	0.863496i
$394$		0			0
$395$	−1.61553			−0.0812860
$396$		0			0
$397$	−22.4924			−1.12886			−0.564431	−	0.825480i	$-0.690904\pi$
$397$	−22.4924			−1.12886			−0.564431	+	0.825480i	$0.690904\pi$
$398$		0			0
$399$	−42.4673	−	30.8543i	−2.12602	−	1.54465i
$400$		0			0
$401$	−0.770201	+	2.37043i	−0.0384620	+	0.118374i	−0.968444	−	0.249231i	$-0.919822\pi$
$401$	−0.770201	+	2.37043i	−0.0384620	+	0.118374i	0.929982	+	0.367605i	$0.119822\pi$
$402$		0			0
$403$	−3.63445	+	2.64058i	−0.181045	+	0.131537i
$404$		0			0
$405$	1.21471	+	3.73848i	0.0603592	+	0.185767i
$406$		0			0
$407$		0			0
$408$		0			0
$409$	3.24234	+	9.97889i	0.160323	+	0.493424i	0.998661	−	0.0517265i	$-0.0164724\pi$
$409$	3.24234	+	9.97889i	0.160323	+	0.493424i	−0.838338	+	0.545151i	$0.816472\pi$
$410$		0			0
$411$	26.0318	−	18.9132i	1.28405	−	0.932920i
$412$		0			0
$413$	−20.2763	+	62.4041i	−0.997732	+	3.07070i
$414$		0			0
$415$	−4.14468	−	3.01129i	−0.203454	−	0.147818i
$416$		0			0
$417$	−17.6155			−0.862636
$418$		0			0
$419$	0.492423			0.0240564			0.0120282	−	0.999928i	$-0.496171\pi$
$419$	0.492423			0.0240564			0.0120282	+	0.999928i	$0.496171\pi$
$420$		0			0
$421$	24.6689	+	17.9230i	1.20229	+	0.873513i	0.994508	−	0.104662i	$-0.0333761\pi$
$421$	24.6689	+	17.9230i	1.20229	+	0.873513i	0.207780	+	0.978176i	$0.433376\pi$
$422$		0			0
$423$	8.80464	−	27.0979i	0.428096	−	1.31755i
$424$		0			0
$425$	−7.57994	+	5.50715i	−0.367681	+	0.267136i
$426$		0			0
$427$	11.2768	+	34.7064i	0.545722	+	1.67956i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−5.83328	−	17.9530i	−0.280979	−	0.864765i	−0.987575	−	0.157148i	$-0.949770\pi$
$431$	−5.83328	−	17.9530i	−0.280979	−	0.864765i	0.706596	−	0.707617i	$-0.250230\pi$
$432$		0			0
$433$	8.34529	−	6.06321i	0.401049	−	0.291379i	−0.368919	−	0.929461i	$-0.620272\pi$
$433$	8.34529	−	6.06321i	0.401049	−	0.291379i	0.769968	+	0.638082i	$0.220272\pi$
$434$		0			0
$435$	1.38823	−	4.27255i	0.0665608	−	0.204853i
$436$		0			0
$437$	−21.2336	−	15.4271i	−1.01574	−	0.737980i
$438$		0			0
$439$	28.4924			1.35987			0.679935	−	0.733273i	$-0.262008\pi$
$439$	28.4924			1.35987			0.679935	+	0.733273i	$0.262008\pi$
$440$		0			0
$441$	68.5464			3.26411
$442$		0			0
$443$	−19.1613	−	13.9215i	−0.910380	−	0.661430i	0.0307306	−	0.999528i	$-0.490217\pi$
$443$	−19.1613	−	13.9215i	−0.910380	−	0.661430i	−0.941111	+	0.338098i	$0.890217\pi$
$444$		0			0
$445$	1.68057	−	5.17227i	0.0796668	−	0.245189i
$446$		0			0
$447$	−25.3783	+	18.4384i	−1.20035	+	0.872107i
$448$		0			0
$449$	10.3664	+	31.9045i	0.489221	+	1.50567i	0.825773	+	0.564003i	$0.190739\pi$
$449$	10.3664	+	31.9045i	0.489221	+	1.50567i	−0.336552	+	0.941665i	$0.609261\pi$
$450$		0			0
$451$		0			0
$452$		0			0
$453$	−12.1658	−	37.4424i	−0.571599	−	1.75920i
$454$		0			0
$455$	−7.26889	+	5.28116i	−0.340771	+	0.247585i
$456$		0			0
$457$	10.4639	−	32.2044i	0.489478	−	1.50646i	−0.335910	−	0.941894i	$-0.609044\pi$
$457$	10.4639	−	32.2044i	0.489478	−	1.50646i	0.825388	−	0.564565i	$-0.190956\pi$
$458$		0			0
$459$	2.32746	+	1.69100i	0.108636	+	0.0789289i
$460$		0			0
$461$	7.12311			0.331756			0.165878	−	0.986146i	$-0.446954\pi$
$461$	7.12311			0.331756			0.165878	+	0.986146i	$0.446954\pi$
$462$		0			0
$463$	27.6847			1.28662			0.643308	−	0.765608i	$-0.277562\pi$
$463$	27.6847			1.28662			0.643308	+	0.765608i	$0.277562\pi$
$464$		0			0
$465$	−1.67396	−	1.21620i	−0.0776281	−	0.0564001i
$466$		0			0
$467$	−7.81819	+	24.0619i	−0.361783	+	1.11345i	0.590189	+	0.807265i	$0.299053\pi$
$467$	−7.81819	+	24.0619i	−0.361783	+	1.11345i	−0.951971	+	0.306187i	$0.900947\pi$
$468$		0			0
$469$	−22.5406	+	16.3767i	−1.04083	+	0.756207i
$470$		0			0
$471$	−6.77701	−	20.8575i	−0.312268	−	0.961063i
$472$		0			0
$473$		0			0
$474$		0			0
$475$	−5.79056	−	17.8215i	−0.265689	−	0.817706i
$476$		0			0
$477$	12.2348	−	8.88914i	0.560195	−	0.407006i
$478$		0			0
$479$	4.94427	−	15.2169i	0.225910	−	0.695278i	−0.772288	−	0.635272i	$-0.780888\pi$
$479$	4.94427	−	15.2169i	0.225910	−	0.695278i	0.998198	−	0.0600061i	$-0.0191120\pi$
$480$		0			0
$481$	−8.68774	−	6.31201i	−0.396127	−	0.287803i
$482$		0			0
$483$	86.1080			3.91805
$484$		0			0
$485$	−6.42329			−0.291667
$486$		0			0
$487$	11.2703	+	8.18836i	0.510707	+	0.371050i	0.813092	−	0.582136i	$-0.197783\pi$
$487$	11.2703	+	8.18836i	0.510707	+	0.371050i	−0.302385	+	0.953186i	$0.597783\pi$
$488$		0			0
$489$	−3.16625	+	9.74473i	−0.143183	+	0.440672i
$490$		0			0
$491$	24.4697	−	17.7783i	1.10430	−	0.802322i	0.122545	−	0.992463i	$-0.460894\pi$
$491$	24.4697	−	17.7783i	1.10430	−	0.802322i	0.981757	+	0.190141i	$0.0608944\pi$
$492$		0			0
$493$	1.93019	+	5.94050i	0.0869312	+	0.267547i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	5.83328	+	17.9530i	0.261658	+	0.805302i
$498$		0			0
$499$	−29.9214	+	21.7391i	−1.33946	+	0.973178i	−0.340001	+	0.940425i	$0.610427\pi$
$499$	−29.9214	+	21.7391i	−1.33946	+	0.973178i	−0.999463	+	0.0327527i	$0.989573\pi$
$500$		0			0
$501$	−6.33251	+	19.4895i	−0.282916	+	0.870724i
$502$		0			0
$503$	7.77913	+	5.65187i	0.346854	+	0.252004i	0.747548	−	0.664208i	$-0.231231\pi$
$503$	7.77913	+	5.65187i	0.346854	+	0.252004i	−0.400694	+	0.916212i	$0.631231\pi$
$504$		0			0
$505$	−1.12311			−0.0499775
$506$		0			0
$507$	−8.31534			−0.369297
$508$		0			0
$509$	−28.5585	−	20.7489i	−1.26583	−	0.919680i	−0.266803	−	0.963751i	$-0.585967\pi$
$509$	−28.5585	−	20.7489i	−1.26583	−	0.919680i	−0.999028	+	0.0440711i	$0.985967\pi$
$510$		0			0
$511$	4.94427	−	15.2169i	0.218722	−	0.673156i
$512$		0			0
$513$	−4.65491	+	3.38199i	−0.205519	+	0.149319i
$514$		0			0
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$	3.36115	+	10.3445i	0.147538	+	0.454075i
$520$		0			0
$521$	−11.0711	+	8.04364i	−0.485035	+	0.352398i	−0.803272	−	0.595613i	$-0.796909\pi$
$521$	−11.0711	+	8.04364i	−0.485035	+	0.352398i	0.318237	+	0.948011i	$0.396909\pi$
$522$		0			0
$523$	3.70820	−	11.4127i	0.162148	−	0.499042i	−0.836666	−	0.547713i	$-0.815499\pi$
$523$	3.70820	−	11.4127i	0.162148	−	0.499042i	0.998815	+	0.0486712i	$0.0154987\pi$
$524$		0			0
$525$	49.7362	+	36.1354i	2.17066	+	1.57708i
$526$		0			0
$527$	2.87689			0.125319
$528$		0			0
$529$	20.0540			0.871912
$530$		0			0
$531$	36.9037	+	26.8121i	1.60149	+	1.16355i
$532$		0			0
$533$	6.87446	−	21.1574i	0.297766	−	0.916429i
$534$		0			0
$535$	−5.16515	+	3.75270i	−0.223309	+	0.162243i
$536$		0			0
$537$	−8.36014	−	25.7299i	−0.360767	−	1.11033i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	−10.4639	−	32.2044i	−0.449876	−	1.38458i	−0.877047	−	0.480405i	$-0.840490\pi$
$541$	−10.4639	−	32.2044i	−0.449876	−	1.38458i	0.427170	−	0.904171i	$-0.359510\pi$
$542$		0			0
$543$	28.3593	−	20.6042i	1.21701	−	0.884211i
$544$		0			0
$545$	−0.736842	+	2.26777i	−0.0315629	+	0.0971405i
$546$		0			0
$547$	−20.8353	−	15.1377i	−0.890851	−	0.647241i	0.0452487	−	0.998976i	$-0.485592\pi$
$547$	−20.8353	−	15.1377i	−0.890851	−	0.647241i	−0.936100	+	0.351735i	$0.885592\pi$
$548$		0			0
$549$	25.3693			1.08274
$550$		0			0
$551$	−12.4924			−0.532195
$552$		0			0
$553$	−11.9238	−	8.66315i	−0.507052	−	0.368395i
$554$		0			0
$555$	1.52841	−	4.70395i	0.0648772	−	0.199672i
$556$		0			0
$557$	−16.3795	+	11.9004i	−0.694023	+	0.504237i	−0.877980	−	0.478697i	$-0.841109\pi$
$557$	−16.3795	+	11.9004i	−0.694023	+	0.504237i	0.183957	+	0.982934i	$0.441109\pi$
$558$		0			0
$559$	1.08390	+	3.33590i	0.0458441	+	0.141094i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	2.62430	+	8.07677i	0.110601	+	0.340395i	0.991004	−	0.133831i	$-0.0427279\pi$
$563$	2.62430	+	8.07677i	0.110601	+	0.340395i	−0.880403	+	0.474226i	$0.842728\pi$
$564$		0			0
$565$	−2.07234	+	1.50564i	−0.0871840	+	0.0633429i
$566$		0			0
$567$	−11.0819	+	34.1065i	−0.465396	+	1.43234i
$568$		0			0
$569$	−28.4152	−	20.6448i	−1.19123	−	0.865477i	−0.197833	−	0.980236i	$-0.563390\pi$
$569$	−28.4152	−	20.6448i	−1.19123	−	0.865477i	−0.993393	+	0.114759i	$0.963390\pi$
$570$		0			0
$571$	16.4924			0.690186			0.345093	−	0.938568i	$-0.387847\pi$
$571$	16.4924			0.690186			0.345093	+	0.938568i	$0.387847\pi$
$572$		0			0
$573$	−37.3002			−1.55824
$574$		0			0
$575$	24.8681	+	18.0677i	1.03707	+	0.753476i
$576$		0			0
$577$	3.53467	−	10.8786i	0.147150	−	0.452882i	−0.850131	−	0.526572i	$-0.823477\pi$
$577$	3.53467	−	10.8786i	0.147150	−	0.452882i	0.997281	+	0.0736891i	$0.0234772\pi$
$578$		0			0
$579$	−1.81722	+	1.32029i	−0.0755212	+	0.0548694i
$580$		0			0
$581$	−14.4430	−	44.4511i	−0.599198	−	1.84414i
$582$		0			0
$583$		0			0
$584$		0			0
$585$	1.93019	+	5.94050i	0.0798033	+	0.245609i
$586$		0			0
$587$	−6.87051	+	4.99172i	−0.283576	+	0.206030i	−0.720476	−	0.693480i	$-0.756077\pi$
$587$	−6.87051	+	4.99172i	−0.283576	+	0.206030i	0.436899	+	0.899510i	$0.356077\pi$
$588$		0			0
$589$	−1.77802	+	5.47218i	−0.0732620	+	0.225477i
$590$		0			0
$591$	38.3226	+	27.8430i	1.57638	+	1.14531i
$592$		0			0
$593$	21.3693			0.877533			0.438766	−	0.898601i	$-0.355416\pi$
$593$	21.3693			0.877533			0.438766	+	0.898601i	$0.355416\pi$
$594$		0			0
$595$	5.75379			0.235882
$596$		0			0
$597$	−42.4673	−	30.8543i	−1.73807	−	1.26278i
$598$		0			0
$599$	−4.94427	+	15.2169i	−0.202017	+	0.621746i	0.797805	+	0.602915i	$0.205994\pi$
$599$	−4.94427	+	15.2169i	−0.202017	+	0.621746i	−0.999823	+	0.0188306i	$0.994006\pi$
$600$		0			0
$601$	16.3795	−	11.9004i	0.668135	−	0.485428i	−0.201265	−	0.979537i	$-0.564505\pi$
$601$	16.3795	−	11.9004i	0.668135	−	0.485428i	0.869400	+	0.494108i	$0.164505\pi$
$602$		0			0
$603$	5.98545	+	18.4213i	0.243746	+	0.750174i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−3.66548	−	11.2812i	−0.148777	−	0.457889i	0.848700	−	0.528874i	$-0.177386\pi$
$607$	−3.66548	−	11.2812i	−0.148777	−	0.457889i	−0.997477	+	0.0709851i	$0.977386\pi$
$608$		0			0
$609$	33.1574	−	24.0903i	1.34361	−	0.976188i
$610$		0			0
$611$	−7.72074	+	23.7620i	−0.312348	+	0.961308i
$612$		0			0
$613$	−37.1029	−	26.9569i	−1.49857	−	1.08878i	−0.970945	−	0.239301i	$-0.923082\pi$
$613$	−37.1029	−	26.9569i	−1.49857	−	1.08878i	−0.527628	−	0.849476i	$-0.676918\pi$
$614$		0			0
$615$	10.2462			0.413167
$616$		0			0
$617$	30.4924			1.22758			0.613789	−	0.789470i	$-0.289644\pi$
$617$	30.4924			1.22758			0.613789	+	0.789470i	$0.289644\pi$
$618$		0			0
$619$	8.03424	+	5.83722i	0.322923	+	0.234618i	0.737422	−	0.675432i	$-0.236043\pi$
$619$	8.03424	+	5.83722i	0.322923	+	0.234618i	−0.414498	+	0.910050i	$0.636043\pi$
$620$		0			0
$621$	2.91664	−	8.97650i	0.117041	−	0.360214i
$622$		0			0
$623$	40.1398	−	29.1633i	1.60817	−	1.16840i
$624$		0			0
$625$	6.29447	+	19.3724i	0.251779	+	0.774895i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	2.12508	+	6.54032i	0.0847324	+	0.260779i
$630$		0			0
$631$	4.00142	−	2.90720i	0.159294	−	0.115734i	−0.505283	−	0.862954i	$-0.668612\pi$
$631$	4.00142	−	2.90720i	0.159294	−	0.115734i	0.664577	+	0.747220i	$0.268612\pi$
$632$		0			0
$633$	19.3873	−	59.6680i	0.770576	−	2.37159i
$634$		0			0
$635$	4.65491	+	3.38199i	0.184725	+	0.134210i
$636$		0			0
$637$	−60.1080			−2.38156
$638$		0			0
$639$	13.1231			0.519142
$640$		0			0
$641$	−5.90597	−	4.29094i	−0.233272	−	0.169482i	0.465009	−	0.885306i	$-0.346051\pi$
$641$	−5.90597	−	4.29094i	−0.233272	−	0.169482i	−0.698281	+	0.715824i	$0.746051\pi$
$642$		0			0
$643$	11.1793	−	34.4064i	0.440870	−	1.35686i	−0.446080	−	0.894993i	$-0.647180\pi$
$643$	11.1793	−	34.4064i	0.440870	−	1.35686i	0.886950	−	0.461865i	$-0.152820\pi$
$644$		0			0
$645$	−1.30699	+	0.949584i	−0.0514627	+	0.0373898i
$646$		0			0
$647$	2.91664	+	8.97650i	0.114665	+	0.352903i	0.991877	−	0.127201i	$-0.0405992\pi$
$647$	2.91664	+	8.97650i	0.114665	+	0.352903i	−0.877212	+	0.480103i	$0.840599\pi$
$648$		0			0
$649$		0			0
$650$		0			0
$651$	−5.83328	−	17.9530i	−0.228624	−	0.703633i
$652$		0			0
$653$	8.23343	−	5.98194i	0.322199	−	0.234091i	−0.414914	−	0.909861i	$-0.636188\pi$
$653$	8.23343	−	5.98194i	0.322199	−	0.234091i	0.737113	+	0.675769i	$0.236188\pi$
$654$		0			0
$655$	−1.97291	+	6.07199i	−0.0770880	+	0.237252i
$656$		0			0
$657$	−8.99878	−	6.53800i	−0.351076	−	0.255072i
$658$		0			0
$659$	−29.6155			−1.15366			−0.576829	−	0.816865i	$-0.695710\pi$
$659$	−29.6155			−1.15366			−0.576829	+	0.816865i	$0.695710\pi$
$660$		0			0
$661$	21.1922			0.824282			0.412141	−	0.911120i	$-0.364781\pi$
$661$	21.1922			0.824282			0.412141	+	0.911120i	$0.364781\pi$
$662$		0			0
$663$	−12.9443	−	9.40456i	−0.502714	−	0.365243i
$664$		0			0
$665$	−3.55604	+	10.9444i	−0.137897	+	0.424404i
$666$		0			0
$667$	16.5787	−	12.0451i	0.641931	−	0.466390i
$668$		0			0
$669$	6.97190	+	21.4573i	0.269549	+	0.829588i
$670$		0			0
$671$		0			0
$672$		0			0
$673$	15.2132	+	46.8215i	0.586427	+	1.80484i	0.593463	+	0.804862i	$0.297761\pi$
$673$	15.2132	+	46.8215i	0.586427	+	1.80484i	−0.00703553	+	0.999975i	$0.502239\pi$
$674$		0			0
$675$	5.45167	−	3.96087i	0.209835	−	0.152454i
$676$		0			0
$677$	−8.88073	+	27.3321i	−0.341314	+	1.05046i	0.622214	+	0.782848i	$0.286234\pi$
$677$	−8.88073	+	27.3321i	−0.341314	+	1.05046i	−0.963528	+	0.267609i	$0.913766\pi$
$678$		0			0
$679$	−47.4087	−	34.4444i	−1.81938	−	1.32186i
$680$		0			0
$681$	−38.1080			−1.46030
$682$		0			0
$683$	−42.7386			−1.63535			−0.817674	−	0.575681i	$-0.804737\pi$
$683$	−42.7386			−1.63535			−0.817674	+	0.575681i	$0.804737\pi$
$684$		0			0
$685$	−5.70679	−	4.14622i	−0.218045	−	0.158419i
$686$		0			0
$687$	1.83274	−	5.64059i	0.0699234	−	0.215202i
$688$		0			0
$689$	−10.7287	+	7.79484i	−0.408730	+	0.296960i
$690$		0			0
$691$	−14.5405	−	44.7510i	−0.553146	−	1.70241i	−0.700790	−	0.713367i	$-0.747169\pi$
$691$	−14.5405	−	44.7510i	−0.553146	−	1.70241i	0.147644	−	0.989041i	$-0.452831\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	1.19334	+	3.67273i	0.0452661	+	0.139315i
$696$		0			0
$697$	−11.5254	+	8.37371i	−0.436557	+	0.317177i
$698$		0			0
$699$	−13.7489	+	42.3148i	−0.520032	+	1.60049i
$700$		0			0
$701$	14.1639	+	10.2907i	0.534964	+	0.388674i	0.822211	−	0.569182i	$-0.192740\pi$
$701$	14.1639	+	10.2907i	0.534964	+	0.388674i	−0.287247	+	0.957856i	$0.592740\pi$
$702$		0			0
$703$	−13.7538			−0.518734
$704$		0			0
$705$	−11.5076			−0.433400
$706$		0			0
$707$	−8.28936	−	6.02257i	−0.311753	−	0.226502i
$708$		0			0
$709$	7.04799	−	21.6915i	0.264693	−	0.814640i	−0.727071	−	0.686562i	$-0.759119\pi$
$709$	7.04799	−	21.6915i	0.264693	−	0.814640i	0.991764	−	0.128078i	$-0.0408809\pi$
$710$		0			0
$711$	−8.28936	+	6.02257i	−0.310875	+	0.225864i
$712$		0			0
$713$	−2.91664	−	8.97650i	−0.109229	−	0.336172i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	10.3878	+	31.9703i	0.387938	+	1.19395i
$718$		0			0
$719$	21.3769	−	15.5312i	0.797224	−	0.579217i	−0.112875	−	0.993609i	$-0.536006\pi$
$719$	21.3769	−	15.5312i	0.797224	−	0.579217i	0.910098	+	0.414392i	$0.136006\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	43.2640	+	31.4331i	1.60901	+	1.16901i
$724$		0			0
$725$	14.6307			0.543370
$726$		0			0
$727$	−35.6847			−1.32347			−0.661735	−	0.749737i	$-0.730180\pi$
$727$	−35.6847			−1.32347			−0.661735	+	0.749737i	$0.730180\pi$
$728$		0			0
$729$	29.1124	+	21.1514i	1.07824	+	0.783384i
$730$		0			0
$731$	0.694117	−	2.13627i	0.0256729	−	0.0790129i
$732$		0			0
$733$	−5.76271	+	4.18686i	−0.212851	+	0.154645i	−0.689103	−	0.724664i	$-0.741995\pi$
$733$	−5.76271	+	4.18686i	−0.212851	+	0.154645i	0.476252	+	0.879309i	$0.341995\pi$
$734$		0			0
$735$	−8.55503	−	26.3297i	−0.315557	−	0.971185i
$736$		0			0
$737$		0			0
$738$		0			0
$739$	8.45758	+	26.0298i	0.311117	+	0.957520i	0.977323	+	0.211753i	$0.0679171\pi$
$739$	8.45758	+	26.0298i	0.311117	+	0.957520i	−0.666206	+	0.745768i	$0.732083\pi$
$740$		0			0
$741$	25.8885	−	18.8091i	0.951039	−	0.690971i
$742$		0			0
$743$	11.9709	−	36.8426i	0.439170	−	1.35163i	−0.449583	−	0.893238i	$-0.648428\pi$
$743$	11.9709	−	36.8426i	0.439170	−	1.35163i	0.888753	−	0.458387i	$-0.151572\pi$
$744$		0			0
$745$	5.56352	+	4.04214i	0.203832	+	0.148092i
$746$		0			0
$747$	−32.4924			−1.18884
$748$		0			0
$749$	−58.2462			−2.12827
$750$		0			0
$751$	−1.16373	−	0.845498i	−0.0424650	−	0.0308527i	0.566350	−	0.824165i	$-0.308355\pi$
$751$	−1.16373	−	0.845498i	−0.0424650	−	0.0308527i	−0.608815	+	0.793312i	$0.708355\pi$
$752$		0			0
$753$	−2.02763	+	6.24041i	−0.0738910	+	0.227413i
$754$		0			0
$755$	−6.98237	+	5.07299i	−0.254114	+	0.184625i
$756$		0			0
$757$	9.96463	+	30.6680i	0.362171	+	1.11465i	0.951734	+	0.306924i	$0.0992998\pi$
$757$	9.96463	+	30.6680i	0.362171	+	1.11465i	−0.589563	+	0.807722i	$0.700700\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	0.965093	+	2.97025i	0.0349846	+	0.107671i	0.967024	−	0.254686i	$-0.0819720\pi$
$761$	0.965093	+	2.97025i	0.0349846	+	0.107671i	−0.932039	+	0.362357i	$0.881972\pi$
$762$		0			0
$763$	−17.5992	+	12.7866i	−0.637133	+	0.462904i
$764$		0			0
$765$	1.23607	−	3.80423i	0.0446901	−	0.137542i
$766$		0			0
$767$	−32.3607	−	23.5114i	−1.16848	−	0.848948i
$768$		0			0
$769$	15.6155			0.563110			0.281555	−	0.959545i	$-0.409150\pi$
$769$	15.6155			0.563110			0.281555	+	0.959545i	$0.409150\pi$
$770$		0			0
$771$	72.3542			2.60577
$772$		0			0
$773$	7.06970	+	5.13644i	0.254280	+	0.184745i	0.707621	−	0.706592i	$-0.249768\pi$
$773$	7.06970	+	5.13644i	0.254280	+	0.184745i	−0.453342	+	0.891337i	$0.649768\pi$
$774$		0			0
$775$	2.08235	−	6.40882i	0.0748003	−	0.230212i
$776$		0			0
$777$	36.5054	−	26.5227i	1.30962	−	0.951496i
$778$		0			0
$779$	−8.80464	−	27.0979i	−0.315459	−	0.970883i
$780$		0			0
$781$		0			0
$782$		0			0
$783$	−1.38823	−	4.27255i	−0.0496115	−	0.152688i
$784$		0			0
$785$	−3.88956	+	2.82593i	−0.138824	+	0.100862i
$786$		0			0
$787$	14.2909	−	43.9828i	0.509414	−	1.56782i	−0.283806	−	0.958882i	$-0.591597\pi$
$787$	14.2909	−	43.9828i	0.509414	−	1.56782i	0.793221	−	0.608934i	$-0.208403\pi$
$788$		0			0
$789$	22.5406	+	16.3767i	0.802467	+	0.583027i
$790$		0			0
$791$	−23.3693			−0.830917
$792$		0			0
$793$	−22.2462			−0.789986
$794$		0			0
$795$	−4.94144	−	3.59016i	−0.175255	−	0.127330i
$796$		0			0
$797$	−10.7562	+	33.1042i	−0.381004	+	1.17261i	0.558334	+	0.829616i	$0.311441\pi$
$797$	−10.7562	+	33.1042i	−0.381004	+	1.17261i	−0.939338	+	0.342993i	$0.888559\pi$
$798$		0			0
$799$	12.9443	−	9.40456i	0.457935	−	0.332710i
$800$		0			0
$801$	−10.6587	−	32.8042i	−0.376608	−	1.15908i
$802$		0			0
$803$		0			0
$804$		0			0
$805$	−5.83328	−	17.9530i	−0.205596	−	0.632760i
$806$		0			0
$807$	−59.5562	+	43.2701i	−2.09648	+	1.52318i
$808$		0			0
$809$	1.35488	−	4.16988i	0.0476349	−	0.146605i	−0.924410	−	0.381400i	$-0.875442\pi$
$809$	1.35488	−	4.16988i	0.0476349	−	0.146605i	0.972045	+	0.234795i	$0.0754419\pi$
$810$		0			0
$811$	0.908612	+	0.660145i	0.0319057	+	0.0231808i	0.603624	−	0.797269i	$-0.293723\pi$
$811$	0.908612	+	0.660145i	0.0319057	+	0.0231808i	−0.571718	+	0.820450i	$0.693723\pi$
$812$		0			0
$813$	−11.5076			−0.403588
$814$		0			0
$815$	2.24621			0.0786813
$816$		0			0
$817$	3.63445	+	2.64058i	0.127153	+	0.0923822i
$818$		0			0
$819$	−17.6093	+	54.1958i	−0.615318	+	1.89375i
$820$		0			0
$821$	18.5951	−	13.5102i	0.648975	−	0.471508i	−0.213947	−	0.976845i	$-0.568632\pi$
$821$	18.5951	−	13.5102i	0.648975	−	0.471508i	0.862922	+	0.505338i	$0.168632\pi$
$822$		0			0
$823$	4.80410	+	14.7855i	0.167460	+	0.515390i	0.999209	−	0.0397620i	$-0.0126600\pi$
$823$	4.80410	+	14.7855i	0.167460	+	0.515390i	−0.831749	+	0.555152i	$0.812660\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	3.31842	+	10.2130i	0.115393	+	0.355142i	0.992029	−	0.126012i	$-0.0402177\pi$
$827$	3.31842	+	10.2130i	0.115393	+	0.355142i	−0.876636	+	0.481154i	$0.840218\pi$
$828$		0			0
$829$	−35.5408	+	25.8219i	−1.23438	+	0.896832i	−0.997211	−	0.0746352i	$-0.976221\pi$
$829$	−35.5408	+	25.8219i	−1.23438	+	0.896832i	−0.237173	+	0.971467i	$0.576221\pi$
$830$		0			0
$831$	14.2481	−	43.8513i	0.494263	−	1.52118i
$832$		0			0
$833$	31.1410	+	22.6253i	1.07897	+	0.783919i
$834$		0			0
$835$	4.49242			0.155467
$836$		0			0
$837$	−2.06913			−0.0715196
$838$		0			0
$839$	−0.653495	−	0.474792i	−0.0225611	−	0.0163916i	0.576448	−	0.817134i	$-0.304439\pi$
$839$	−0.653495	−	0.474792i	−0.0225611	−	0.0163916i	−0.599009	+	0.800743i	$0.704439\pi$
$840$		0			0
$841$	−5.94741	+	18.3042i	−0.205083	+	0.631181i
$842$		0			0
$843$	−0.510233	+	0.370706i	−0.0175734	+	0.0127678i
$844$		0			0
$845$	0.563313	+	1.73370i	0.0193786	+	0.0596411i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−15.8313	−	48.7236i	−0.543328	−	1.67219i
$850$		0			0
$851$	18.2527	−	13.2613i	0.625694	−	0.454593i
$852$		0			0
$853$	4.17407	−	12.8465i	0.142917	−	0.439855i	−0.853820	−	0.520569i	$-0.825720\pi$
$853$	4.17407	−	12.8465i	0.142917	−	0.439855i	0.996737	+	0.0807139i	$0.0257200\pi$
$854$		0			0
$855$	6.47214	+	4.70228i	0.221342	+	0.160815i
$856$		0			0
$857$	44.1080			1.50670			0.753349	−	0.657620i	$-0.228437\pi$
$857$	44.1080			1.50670			0.753349	+	0.657620i	$0.228437\pi$
$858$		0			0
$859$	−7.05398			−0.240679			−0.120339	−	0.992733i	$-0.538398\pi$
$859$	−7.05398			−0.240679			−0.120339	+	0.992733i	$0.538398\pi$
$860$		0			0
$861$	75.6247	+	54.9446i	2.57728	+	1.87251i
$862$		0			0
$863$	−1.08390	+	3.33590i	−0.0368964	+	0.113556i	−0.967808	−	0.251688i	$-0.919014\pi$
$863$	−1.08390	+	3.33590i	−0.0368964	+	0.113556i	0.930912	+	0.365244i	$0.119014\pi$
$864$		0			0
$865$	1.92908	−	1.40156i	0.0655906	−	0.0476544i
$866$		0			0
$867$	−10.2903	−	31.6704i	−0.349478	−	1.07558i
$868$		0			0
$869$		0			0
$870$		0			0
$871$	−5.24861	−	16.1535i	−0.177842	−	0.547342i
$872$		0			0
$873$	−32.9582	+	23.9456i	−1.11547	+	0.810435i
$874$		0			0
$875$	8.60975	−	26.4981i	0.291063	−	0.895799i
$876$		0			0
$877$	24.7807	+	18.0043i	0.836786	+	0.607961i	0.921471	−	0.388447i	$-0.126988\pi$
$877$	24.7807	+	18.0043i	0.836786	+	0.607961i	−0.0846848	+	0.996408i	$0.526988\pi$
$878$		0			0
$879$	−54.7386			−1.84629
$880$		0			0
$881$	−19.3002			−0.650240			−0.325120	−	0.945673i	$-0.605405\pi$
$881$	−19.3002			−0.650240			−0.325120	+	0.945673i	$0.605405\pi$
$882$		0			0
$883$	19.8148	+	14.3963i	0.666821	+	0.484474i	0.868959	−	0.494883i	$-0.164789\pi$
$883$	19.8148	+	14.3963i	0.666821	+	0.484474i	−0.202139	+	0.979357i	$0.564789\pi$
$884$		0			0
$885$	5.69311	−	17.5216i	0.191372	−	0.588982i
$886$		0			0
$887$	−7.77913	+	5.65187i	−0.261197	+	0.189771i	−0.710675	−	0.703521i	$-0.751610\pi$
$887$	−7.77913	+	5.65187i	−0.261197	+	0.189771i	0.449477	+	0.893292i	$0.351610\pi$
$888$		0			0
$889$	16.2211	+	49.9233i	0.544037	+	1.67437i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	9.88854	+	30.4338i	0.330908	+	1.01843i
$894$		0			0
$895$	−4.79817	+	3.48608i	−0.160385	+	0.116527i
$896$		0			0
$897$	−16.2211	+	49.9233i	−0.541605	+	1.66689i
$898$		0			0
$899$	−3.63445	−	2.64058i	−0.121216	−	0.0880683i
$900$		0			0
$901$	8.49242			0.282924
$902$		0			0
$903$	−14.7386			−0.490471
$904$		0			0
$905$	−6.21702	−	4.51693i	−0.206661	−	0.150148i
$906$		0			0
$907$	−5.09644	+	15.6852i	−0.169224	+	0.520819i	−0.999323	−	0.0367978i	$-0.988284\pi$
$907$	−5.09644	+	15.6852i	−0.169224	+	0.520819i	0.830098	+	0.557617i	$0.188284\pi$
$908$		0			0
$909$	−5.76271	+	4.18686i	−0.191137	+	0.138869i
$910$		0			0
$911$	7.02662	+	21.6257i	0.232802	+	0.716492i	0.997405	+	0.0719905i	$0.0229351\pi$
$911$	7.02662	+	21.6257i	0.232802	+	0.716492i	−0.764603	+	0.644502i	$0.777065\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$	−3.16625	−	9.74473i	−0.104673	−	0.322151i
$916$		0			0
$917$	−47.1222	+	34.2363i	−1.55611	+	1.13058i
$918$		0			0
$919$	−9.69365	+	29.8340i	−0.319764	+	0.984133i	0.653985	+	0.756508i	$0.273096\pi$
$919$	−9.69365	+	29.8340i	−0.319764	+	0.984133i	−0.973749	+	0.227625i	$0.926904\pi$
$920$		0			0
$921$	1.02047	+	0.741412i	0.0336255	+	0.0244304i
$922$		0			0
$923$	−11.5076			−0.378777
$924$		0			0
$925$	16.1080			0.529626
$926$		0			0
$927$		0			0
$928$		0			0
$929$	4.17407	−	12.8465i	0.136947	−	0.421479i	−0.858941	−	0.512075i	$-0.828877\pi$
$929$	4.17407	−	12.8465i	0.136947	−	0.421479i	0.995888	+	0.0905957i	$0.0288771\pi$
$930$		0			0
$931$	−62.2820	+	45.2506i	−2.04121	+	1.48303i
$932$		0			0
$933$	20.7755	+	63.9405i	0.680161	+	2.09332i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−9.92190	−	30.5365i	−0.324134	−	0.997583i	−0.971830	−	0.235684i	$-0.924267\pi$
$937$	−9.92190	−	30.5365i	−0.324134	−	0.997583i	0.647695	−	0.761899i	$-0.275733\pi$
$938$		0			0
$939$	−22.3974	+	16.2726i	−0.730910	+	0.531037i
$940$		0			0
$941$	4.86819	−	14.9827i	0.158698	−	0.488423i	−0.839818	−	0.542867i	$-0.817339\pi$
$941$	4.86819	−	14.9827i	0.158698	−	0.488423i	0.998517	+	0.0544439i	$0.0173386\pi$
$942$		0			0
$943$	37.8123	+	27.4723i	1.23134	+	0.894621i
$944$		0			0
$945$	−4.13826			−0.134618
$946$		0			0
$947$	−0.315342			−0.0102472			−0.00512361	−	0.999987i	$-0.501631\pi$
$947$	−0.315342			−0.0102472			−0.00512361	+	0.999987i	$0.501631\pi$
$948$		0			0
$949$	7.89098	+	5.73313i	0.256152	+	0.186105i
$950$		0			0
$951$	−27.5526	+	84.7980i	−0.893453	+	2.74976i
$952$		0			0
$953$	−13.1435	+	9.54928i	−0.425758	+	0.309332i	−0.779951	−	0.625841i	$-0.784756\pi$
$953$	−13.1435	+	9.54928i	−0.425758	+	0.309332i	0.354192	+	0.935173i	$0.384756\pi$
$954$		0			0
$955$	2.52686	+	7.77687i	0.0817672	+	0.251653i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−19.8865	−	61.2044i	−0.642170	−	1.97639i
$960$		0			0
$961$	23.4056	−	17.0051i	0.755018	−	0.548553i
$962$		0			0
$963$	−12.5128	+	38.5106i	−0.403221	+	1.24099i
$964$		0			0
$965$	0.398378	+	0.289439i	0.0128242	+	0.00931736i
$966$		0			0
$967$	−8.00000			−0.257263			−0.128631	−	0.991692i	$-0.541058\pi$
$967$	−8.00000			−0.257263			−0.128631	+	0.991692i	$0.541058\pi$
$968$		0			0
$969$	−20.4924			−0.658311
$970$		0			0
$971$	−28.7576	−	20.8936i	−0.922877	−	0.670509i	0.0213618	−	0.999772i	$-0.493200\pi$
$971$	−28.7576	−	20.8936i	−0.922877	−	0.670509i	−0.944238	+	0.329263i	$0.893200\pi$
$972$		0			0
$973$	−10.8870	+	33.5067i	−0.349021	+	1.07418i
$974$		0			0
$975$	−30.3197	+	22.0286i	−0.971009	+	0.705479i
$976$		0			0
$977$	10.2570	+	31.5677i	0.328149	+	1.00994i	0.969999	+	0.243109i	$0.0781674\pi$
$977$	10.2570	+	31.5677i	0.328149	+	1.00994i	−0.641850	+	0.766831i	$0.721833\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	4.67330	+	14.3829i	0.149207	+	0.459212i
$982$		0			0
$983$	−1.67396	+	1.21620i	−0.0533911	+	0.0387909i	−0.614161	−	0.789181i	$-0.710505\pi$
$983$	−1.67396	+	1.21620i	−0.0533911	+	0.0387909i	0.560770	+	0.827972i	$0.310505\pi$
$984$		0			0
$985$	3.20898	−	9.87622i	0.102247	−	0.314683i
$986$		0			0
$987$	−84.9345	−	61.7085i	−2.70350	−	1.96420i
$988$		0			0
$989$	−7.36932			−0.234331
$990$		0			0
$991$	28.4924			0.905092			0.452546	−	0.891741i	$-0.350516\pi$
$991$	28.4924			0.905092			0.452546	+	0.891741i	$0.350516\pi$
$992$		0			0
$993$	−12.5773	−	9.13794i	−0.399129	−	0.289984i
$994$		0			0
$995$	−3.55604	+	10.9444i	−0.112734	+	0.346959i
$996$		0			0
$997$	28.9254	−	21.0155i	0.916077	−	0.665569i	−0.0264672	−	0.999650i	$-0.508426\pi$
$997$	28.9254	−	21.0155i	0.916077	−	0.665569i	0.942545	+	0.334081i	$0.108426\pi$
$998$		0			0
$999$	−1.52841	−	4.70395i	−0.0483566	−	0.148826i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	968.2.i.q.753.1		8
11.2	odd	10		968.2.i.r.9.1		8
11.3	even	5		968.2.a.j.1.2		2
11.4	even	5	inner	968.2.i.q.729.2		8
11.5	even	5	inner	968.2.i.q.81.2		8
11.6	odd	10		968.2.i.r.81.2		8
11.7	odd	10		968.2.i.r.729.2		8
11.8	odd	10		88.2.a.b.1.2	✓	2
11.9	even	5	inner	968.2.i.q.9.1		8
11.10	odd	2		968.2.i.r.753.1		8
33.8	even	10		792.2.a.h.1.2		2
33.14	odd	10		8712.2.a.bb.1.2		2
44.3	odd	10		1936.2.a.r.1.1		2
44.19	even	10		176.2.a.d.1.1		2
55.8	even	20		2200.2.b.g.1849.4		4
55.19	odd	10		2200.2.a.o.1.1		2
55.52	even	20		2200.2.b.g.1849.1		4
77.41	even	10		4312.2.a.n.1.1		2
88.3	odd	10		7744.2.a.cl.1.2		2
88.19	even	10		704.2.a.p.1.2		2
88.69	even	10		7744.2.a.by.1.1		2
88.85	odd	10		704.2.a.m.1.1		2
132.107	odd	10		1584.2.a.t.1.2		2
176.19	even	20		2816.2.c.p.1409.1		4
176.85	odd	20		2816.2.c.w.1409.1		4
176.107	even	20		2816.2.c.p.1409.4		4
176.173	odd	20		2816.2.c.w.1409.4		4
220.19	even	10		4400.2.a.bp.1.2		2
220.63	odd	20		4400.2.b.v.4049.1		4
220.107	odd	20		4400.2.b.v.4049.4		4
264.107	odd	10		6336.2.a.cx.1.1		2
264.173	even	10		6336.2.a.cu.1.1		2
308.195	odd	10		8624.2.a.cb.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
88.2.a.b.1.2	✓	2	11.8	odd	10
176.2.a.d.1.1		2	44.19	even	10
704.2.a.m.1.1		2	88.85	odd	10
704.2.a.p.1.2		2	88.19	even	10
792.2.a.h.1.2		2	33.8	even	10
968.2.a.j.1.2		2	11.3	even	5
968.2.i.q.9.1		8	11.9	even	5	inner
968.2.i.q.81.2		8	11.5	even	5	inner
968.2.i.q.729.2		8	11.4	even	5	inner
968.2.i.q.753.1		8	1.1	even	1	trivial
968.2.i.r.9.1		8	11.2	odd	10
968.2.i.r.81.2		8	11.6	odd	10
968.2.i.r.729.2		8	11.7	odd	10
968.2.i.r.753.1		8	11.10	odd	2
1584.2.a.t.1.2		2	132.107	odd	10
1936.2.a.r.1.1		2	44.3	odd	10
2200.2.a.o.1.1		2	55.19	odd	10
2200.2.b.g.1849.1		4	55.52	even	20
2200.2.b.g.1849.4		4	55.8	even	20
2816.2.c.p.1409.1		4	176.19	even	20
2816.2.c.p.1409.4		4	176.107	even	20
2816.2.c.w.1409.1		4	176.85	odd	20
2816.2.c.w.1409.4		4	176.173	odd	20
4312.2.a.n.1.1		2	77.41	even	10
4400.2.a.bp.1.2		2	220.19	even	10
4400.2.b.v.4049.1		4	220.63	odd	20
4400.2.b.v.4049.4		4	220.107	odd	20
6336.2.a.cu.1.1		2	264.173	even	10
6336.2.a.cx.1.1		2	264.107	odd	10
7744.2.a.by.1.1		2	88.69	even	10
7744.2.a.cl.1.2		2	88.3	odd	10
8624.2.a.cb.1.2		2	308.195	odd	10
8712.2.a.bb.1.2		2	33.14	odd	10

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:	\( N \)	\(=\)	\( 968 = 2^{3} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	968.i (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.07234 - 1.50564i) q^{3} +(-0.173529 + 0.534068i) q^{5} +(-4.14468 + 3.01129i) q^{7} +(1.10058 + 3.38724i) q^{9} +(-0.965093 - 2.97025i) q^{13} +(1.16373 - 0.845498i) q^{15} +(-0.618034 + 1.90211i) q^{17} +(-3.23607 - 2.35114i) q^{19} +13.1231 q^{21} +6.56155 q^{23} +(3.78997 + 2.75357i) q^{25} +(0.444505 - 1.36804i) q^{27} +(2.52665 - 1.83572i) q^{29} +(-0.444505 - 1.36804i) q^{31} +(-0.889009 - 2.73609i) q^{35} +(2.78176 - 2.02107i) q^{37} +(-2.47214 + 7.60845i) q^{39} +(5.76271 + 4.18686i) q^{41} -1.12311 q^{43} -2.00000 q^{45} +(-6.47214 - 4.70228i) q^{47} +(5.94741 - 18.3042i) q^{49} +(4.14468 - 3.01129i) q^{51} +(-1.31215 - 4.03839i) q^{53} +(3.16625 + 9.74473i) q^{57} +(10.3617 - 7.52821i) q^{59} +(2.20116 - 6.77448i) q^{61} +(-14.7615 - 10.7249i) q^{63} +1.75379 q^{65} +5.43845 q^{67} +(-13.5978 - 9.87936i) q^{69} +(1.13862 - 3.50432i) q^{71} +(-2.52665 + 1.83572i) q^{73} +(-3.70820 - 11.4127i) q^{75} +(0.889009 + 2.73609i) q^{79} +(5.66312 - 4.11450i) q^{81} +(-2.81919 + 8.67659i) q^{83} +(-0.908612 - 0.660145i) q^{85} -8.00000 q^{87} -9.68466 q^{89} +(12.9443 + 9.40456i) q^{91} +(-1.13862 + 3.50432i) q^{93} +(1.81722 - 1.32029i) q^{95} +(3.53467 + 10.8786i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - q^{3} - 3 q^{5} - 2 q^{7} - 3 q^{9} - 2 q^{13} + 7 q^{15} + 4 q^{17} - 8 q^{19} + 72 q^{21} + 36 q^{23} - 3 q^{25} - 7 q^{27} - 2 q^{29} + 7 q^{31} + 14 q^{35} + 11 q^{37} + 16 q^{39} + 6 q^{41}+ \cdots - 27 q^{97}+O(q^{100}) \) 8 * q - q^3 - 3 * q^5 - 2 * q^7 - 3 * q^9 - 2 * q^13 + 7 * q^15 + 4 * q^17 - 8 * q^19 + 72 * q^21 + 36 * q^23 - 3 * q^25 - 7 * q^27 - 2 * q^29 + 7 * q^31 + 14 * q^35 + 11 * q^37 + 16 * q^39 + 6 * q^41 + 24 * q^43 - 16 * q^45 - 16 * q^47 - 22 * q^49 + 2 * q^51 - 8 * q^53 - 4 * q^57 + 5 * q^59 - 6 * q^61 - 20 * q^63 + 80 * q^65 + 60 * q^67 - 13 * q^69 + 5 * q^71 + 2 * q^73 + 24 * q^75 - 14 * q^79 + 14 * q^81 + 10 * q^83 + 6 * q^85 - 64 * q^87 - 28 * q^89 + 32 * q^91 - 5 * q^93 - 12 * q^95 - 27 * q^97

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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