LMFDB - Embedded newform 768.2.o.b.479.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [768,2,Mod(95,768)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(768, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 3, 4]))

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

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

chi := DirichletCharacter("768.95");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 768 = 2^{8} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	768.o (of order $8$, degree $4$, 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:	$6.13251087523$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{8})$
Twist minimal:	no (minimal twist has level 96)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			479.2
Character	$\chi$	$=$	768.479
Dual form			768.2.o.b.287.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.45336 - 0.942196i) q^{3} +(-0.348970 - 0.842489i) q^{5} +(-0.471834 - 0.471834i) q^{7} +(1.22453 + 2.73871i) q^{9} +O(q^{10})$	\(q+(-1.45336 - 0.942196i) q^{3} +(-0.348970 - 0.842489i) q^{5} +(-0.471834 - 0.471834i) q^{7} +(1.22453 + 2.73871i) q^{9} +(1.24185 + 2.99808i) q^{11} +(2.51698 + 1.04257i) q^{13} +(-0.286608 + 1.55324i) q^{15} +6.24340 q^{17} +(0.683586 - 1.65032i) q^{19} +(0.241187 + 1.13031i) q^{21} +(-5.69180 - 5.69180i) q^{23} +(2.94753 - 2.94753i) q^{25} +(0.800702 - 5.13409i) q^{27} +(-5.28905 - 2.19080i) q^{29} -5.07456i q^{31} +(1.01993 - 5.52737i) q^{33} +(-0.232859 + 0.562171i) q^{35} +(6.21892 - 2.57596i) q^{37} +(-2.67579 - 3.88672i) q^{39} +(-6.43169 + 6.43169i) q^{41} +(6.04703 - 2.50476i) q^{43} +(1.88000 - 1.98738i) q^{45} +8.94964i q^{47} -6.55474i q^{49} +(-9.07393 - 5.88250i) q^{51} +(4.63157 - 1.91846i) q^{53} +(2.09248 - 2.09248i) q^{55} +(-2.54843 + 1.75445i) q^{57} +(2.67262 - 1.10704i) q^{59} +(2.36352 - 5.70603i) q^{61} +(0.714438 - 1.86999i) q^{63} -2.48436i q^{65} +(3.39948 + 1.40811i) q^{67} +(2.90947 + 13.6350i) q^{69} +(7.71934 - 7.71934i) q^{71} +(0.0492824 + 0.0492824i) q^{73} +(-7.06098 + 1.50668i) q^{75} +(0.828653 - 2.00054i) q^{77} +10.1259 q^{79} +(-6.00103 + 6.70728i) q^{81} +(-3.65135 - 1.51244i) q^{83} +(-2.17876 - 5.25999i) q^{85} +(5.62276 + 8.16735i) q^{87} +(-4.09411 - 4.09411i) q^{89} +(-0.695680 - 1.67952i) q^{91} +(-4.78123 + 7.37518i) q^{93} -1.62893 q^{95} +4.72643 q^{97} +(-6.69018 + 7.07231i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 4 q^{3} - 8 q^{7} - 4 q^{9}+O(q^{10}) $ 56 * q + 4 * q^3 - 8 * q^7 - 4 * q^9	$ 56 q + 4 q^{3} - 8 q^{7} - 4 q^{9} + 8 q^{13} - 8 q^{15} + 8 q^{19} + 4 q^{21} - 8 q^{25} + 28 q^{27} - 8 q^{33} + 8 q^{37} - 28 q^{39} + 8 q^{43} + 4 q^{45} + 16 q^{51} + 24 q^{55} - 4 q^{57} + 40 q^{61} - 56 q^{67} + 4 q^{69} - 8 q^{73} - 16 q^{75} + 16 q^{79} + 48 q^{85} + 52 q^{87} - 40 q^{91} - 8 q^{93} - 16 q^{97} - 60 q^{99}+O(q^{100}) $ 56 * q + 4 * q^3 - 8 * q^7 - 4 * q^9 + 8 * q^13 - 8 * q^15 + 8 * q^19 + 4 * q^21 - 8 * q^25 + 28 * q^27 - 8 * q^33 + 8 * q^37 - 28 * q^39 + 8 * q^43 + 4 * q^45 + 16 * q^51 + 24 * q^55 - 4 * q^57 + 40 * q^61 - 56 * q^67 + 4 * q^69 - 8 * q^73 - 16 * q^75 + 16 * q^79 + 48 * q^85 + 52 * q^87 - 40 * q^91 - 8 * q^93 - 16 * q^97 - 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/768\mathbb{Z}\right)^\times$.

$n$	$257$	$511$	$517$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{7}{8}\right)$

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
$3$	−1.45336	−	0.942196i	−0.839100	−	0.543977i
$3$	−1.45336	−	0.942196i	−0.839100	−	0.543977i
$4$		0			0
$5$	−0.348970	−	0.842489i	−0.156064	−	0.376772i	0.826437	−	0.563030i	$-0.190364\pi$
$5$	−0.348970	−	0.842489i	−0.156064	−	0.376772i	−0.982501	+	0.186257i	$0.940364\pi$
$6$		0			0
$7$	−0.471834	−	0.471834i	−0.178337	−	0.178337i	0.612294	−	0.790630i	$-0.290247\pi$
$7$	−0.471834	−	0.471834i	−0.178337	−	0.178337i	−0.790630	+	0.612294i	$0.790247\pi$
$8$		0			0
$9$	1.22453	+	2.73871i	0.408178	+	0.912902i
$10$		0			0
$11$	1.24185	+	2.99808i	0.374431	+	0.903956i	0.992988	+	0.118216i	$0.0377176\pi$
$11$	1.24185	+	2.99808i	0.374431	+	0.903956i	−0.618557	+	0.785740i	$0.712282\pi$
$12$		0			0
$13$	2.51698	+	1.04257i	0.698086	+	0.289157i	0.703364	−	0.710830i	$-0.251680\pi$
$13$	2.51698	+	1.04257i	0.698086	+	0.289157i	−0.00527868	+	0.999986i	$0.501680\pi$
$14$		0			0
$15$	−0.286608	+	1.55324i	−0.0740019	+	0.401045i
$16$		0			0
$17$	6.24340			1.51425			0.757123	−	0.653272i	$-0.226604\pi$
$17$	6.24340			1.51425			0.757123	+	0.653272i	$0.226604\pi$
$18$		0			0
$19$	0.683586	−	1.65032i	0.156825	−	0.378610i	−0.825864	−	0.563869i	$-0.809312\pi$
$19$	0.683586	−	1.65032i	0.156825	−	0.378610i	0.982690	+	0.185259i	$0.0593123\pi$
$20$		0			0
$21$	0.241187	+	1.13031i	0.0526313	+	0.246653i
$22$		0			0
$23$	−5.69180	−	5.69180i	−1.18682	−	1.18682i	−0.977941	−	0.208881i	$-0.933018\pi$
$23$	−5.69180	−	5.69180i	−1.18682	−	1.18682i	−0.208881	−	0.977941i	$-0.566982\pi$
$24$		0			0
$25$	2.94753	−	2.94753i	0.589505	−	0.589505i
$26$		0			0
$27$	0.800702	−	5.13409i	0.154095	−	0.988056i
$28$		0			0
$29$	−5.28905	−	2.19080i	−0.982152	−	0.406821i	−0.166930	−	0.985969i	$-0.553385\pi$
$29$	−5.28905	−	2.19080i	−0.982152	−	0.406821i	−0.815222	+	0.579148i	$0.803385\pi$
$30$		0			0
$31$		−	5.07456i		−	0.911418i	−0.890129	−	0.455709i	$-0.849386\pi$
$31$		−	5.07456i		−	0.911418i	0.890129	−	0.455709i	$-0.150614\pi$
$32$		0			0
$33$	1.01993	−	5.52737i	0.177546	−	0.962191i
$34$		0			0
$35$	−0.232859	+	0.562171i	−0.0393604	+	0.0950243i
$36$		0			0
$37$	6.21892	−	2.57596i	1.02238	−	0.423485i	0.192426	−	0.981312i	$-0.438365\pi$
$37$	6.21892	−	2.57596i	1.02238	−	0.423485i	0.829958	+	0.557826i	$0.188365\pi$
$38$		0			0
$39$	−2.67579	−	3.88672i	−0.428469	−	0.622374i
$40$		0			0
$41$	−6.43169	+	6.43169i	−1.00446	+	1.00446i	−0.00447060	+	0.999990i	$0.501423\pi$
$41$	−6.43169	+	6.43169i	−1.00446	+	1.00446i	−0.999990	+	0.00447060i	$0.998577\pi$
$42$		0			0
$43$	6.04703	−	2.50476i	0.922163	−	0.381973i	0.129463	−	0.991584i	$-0.458675\pi$
$43$	6.04703	−	2.50476i	0.922163	−	0.381973i	0.792700	+	0.609612i	$0.208675\pi$
$44$		0			0
$45$	1.88000	−	1.98738i	0.280254	−	0.296262i
$46$		0			0
$47$			8.94964i			1.30544i	0.757600	+	0.652720i	$0.226372\pi$
$47$			8.94964i			1.30544i	−0.757600	+	0.652720i	$0.773628\pi$
$48$		0			0
$49$		−	6.55474i		−	0.936392i
$50$		0			0
$51$	−9.07393	−	5.88250i	−1.27060	−	0.823715i
$52$		0			0
$53$	4.63157	−	1.91846i	0.636195	−	0.263520i	−0.0411879	−	0.999151i	$-0.513114\pi$
$53$	4.63157	−	1.91846i	0.636195	−	0.263520i	0.677382	+	0.735631i	$0.263114\pi$
$54$		0			0
$55$	2.09248	−	2.09248i	0.282150	−	0.282150i
$56$		0			0
$57$	−2.54843	+	1.75445i	−0.337547	+	0.232382i
$58$		0			0
$59$	2.67262	−	1.10704i	0.347945	−	0.144124i	−0.201865	−	0.979413i	$-0.564700\pi$
$59$	2.67262	−	1.10704i	0.347945	−	0.144124i	0.549810	+	0.835290i	$0.314700\pi$
$60$		0			0
$61$	2.36352	−	5.70603i	0.302617	−	0.730583i	−0.697288	−	0.716791i	$-0.745610\pi$
$61$	2.36352	−	5.70603i	0.302617	−	0.730583i	0.999905	−	0.0137912i	$-0.00439002\pi$
$62$		0			0
$63$	0.714438	−	1.86999i	0.0900108	−	0.235597i
$64$		0			0
$65$		−	2.48436i		−	0.308146i
$66$		0			0
$67$	3.39948	+	1.40811i	0.415312	+	0.172028i	0.580548	−	0.814226i	$-0.302838\pi$
$67$	3.39948	+	1.40811i	0.415312	+	0.172028i	−0.165235	+	0.986254i	$0.552838\pi$
$68$		0			0
$69$	2.90947	+	13.6350i	0.350259	+	1.64147i
$70$		0			0
$71$	7.71934	−	7.71934i	0.916117	−	0.916117i	−0.0806272	−	0.996744i	$-0.525692\pi$
$71$	7.71934	−	7.71934i	0.916117	−	0.916117i	0.996744	+	0.0806272i	$0.0256923\pi$
$72$		0			0
$73$	0.0492824	+	0.0492824i	0.00576807	+	0.00576807i	0.709985	−	0.704217i	$-0.248702\pi$
$73$	0.0492824	+	0.0492824i	0.00576807	+	0.00576807i	−0.704217	+	0.709985i	$0.748702\pi$
$74$		0			0
$75$	−7.06098	+	1.50668i	−0.815331	+	0.173977i
$76$		0			0
$77$	0.828653	−	2.00054i	0.0944337	−	0.227983i
$78$		0			0
$79$	10.1259			1.13925			0.569625	−	0.821905i	$-0.307088\pi$
$79$	10.1259			1.13925			0.569625	+	0.821905i	$0.307088\pi$
$80$		0			0
$81$	−6.00103	+	6.70728i	−0.666781	+	0.745254i
$82$		0			0
$83$	−3.65135	−	1.51244i	−0.400787	−	0.166012i	0.173179	−	0.984890i	$-0.444596\pi$
$83$	−3.65135	−	1.51244i	−0.400787	−	0.166012i	−0.573966	+	0.818879i	$0.694596\pi$
$84$		0			0
$85$	−2.17876	−	5.25999i	−0.236320	−	0.570526i
$86$		0			0
$87$	5.62276	+	8.16735i	0.602823	+	0.875632i
$88$		0			0
$89$	−4.09411	−	4.09411i	−0.433974	−	0.433974i	0.456004	−	0.889978i	$-0.349280\pi$
$89$	−4.09411	−	4.09411i	−0.433974	−	0.433974i	−0.889978	+	0.456004i	$0.849280\pi$
$90$		0			0
$91$	−0.695680	−	1.67952i	−0.0729270	−	0.176061i
$92$		0			0
$93$	−4.78123	+	7.37518i	−0.495790	+	0.764771i
$94$		0			0
$95$	−1.62893			−0.167125
$96$		0			0
$97$	4.72643			0.479896			0.239948	−	0.970786i	$-0.422870\pi$
$97$	4.72643			0.479896			0.239948	+	0.970786i	$0.422870\pi$
$98$		0			0
$99$	−6.69018	+	7.07231i	−0.672389	+	0.710794i
$100$		0			0
$101$	2.70950	+	6.54131i	0.269605	+	0.650885i	0.999465	−	0.0327124i	$-0.0104145\pi$
$101$	2.70950	+	6.54131i	0.269605	+	0.650885i	−0.729859	+	0.683597i	$0.760415\pi$
$102$		0			0
$103$	4.68286	+	4.68286i	0.461416	+	0.461416i	0.899119	−	0.437703i	$-0.144208\pi$
$103$	4.68286	+	4.68286i	0.461416	+	0.461416i	−0.437703	+	0.899119i	$0.644208\pi$
$104$		0			0
$105$	0.868104	−	0.597641i	0.0847183	−	0.0583238i
$106$		0			0
$107$	−0.453771	−	1.09550i	−0.0438677	−	0.105906i	0.900427	−	0.435007i	$-0.143254\pi$
$107$	−0.453771	−	1.09550i	−0.0438677	−	0.105906i	−0.944295	+	0.329101i	$0.893254\pi$
$108$		0			0
$109$	−10.9543	−	4.53742i	−1.04923	−	0.434606i	−0.209614	−	0.977784i	$-0.567221\pi$
$109$	−10.9543	−	4.53742i	−1.04923	−	0.434606i	−0.839617	+	0.543178i	$0.817221\pi$
$110$		0			0
$111$	−11.4654	−	2.11563i	−1.08825	−	0.200806i
$112$		0			0
$113$	6.82755			0.642282			0.321141	−	0.947031i	$-0.395934\pi$
$113$	6.82755			0.642282			0.321141	+	0.947031i	$0.395934\pi$
$114$		0			0
$115$	−2.80901	+	6.78155i	−0.261941	+	0.632382i
$116$		0			0
$117$	0.226845	+	8.16994i	0.0209718	+	0.755311i
$118$		0			0
$119$	−2.94585	−	2.94585i	−0.270046	−	0.270046i
$120$		0			0
$121$	0.331857	−	0.331857i	0.0301688	−	0.0301688i
$122$		0			0
$123$	15.4075	−	3.28768i	1.38925	−	0.296440i
$124$		0			0
$125$	−7.72430	−	3.19951i	−0.690883	−	0.286173i
$126$		0			0
$127$			20.4851i			1.81776i	0.417059	+	0.908879i	$0.363061\pi$
$127$			20.4851i			1.81776i	−0.417059	+	0.908879i	$0.636939\pi$
$128$		0			0
$129$	−11.1485	−	2.05715i	−0.981572	−	0.181122i
$130$		0			0
$131$	−0.281165	+	0.678793i	−0.0245655	+	0.0593064i	−0.935686	−	0.352833i	$-0.885218\pi$
$131$	−0.281165	+	0.678793i	−0.0245655	+	0.0593064i	0.911121	+	0.412139i	$0.135218\pi$
$132$		0			0
$133$	−1.10122	+	0.456140i	−0.0954878	+	0.0395523i
$134$		0			0
$135$	−4.60483	+	1.11706i	−0.396321	+	0.0961414i
$136$		0			0
$137$	0.914012	−	0.914012i	0.0780893	−	0.0780893i	−0.666983	−	0.745073i	$-0.732415\pi$
$137$	0.914012	−	0.914012i	0.0780893	−	0.0780893i	0.745073	+	0.666983i	$0.232415\pi$
$138$		0			0
$139$	−6.07269	+	2.51539i	−0.515079	+	0.213353i	−0.625054	−	0.780582i	$-0.714923\pi$
$139$	−6.07269	+	2.51539i	−0.515079	+	0.213353i	0.109975	+	0.993934i	$0.464923\pi$
$140$		0			0
$141$	8.43231	−	13.0071i	0.710129	−	1.09539i
$142$		0			0
$143$			8.84084i			0.739308i
$144$		0			0
$145$			5.22049i			0.433538i
$146$		0			0
$147$	−6.17585	+	9.52643i	−0.509376	+	0.785727i
$148$		0			0
$149$	8.36760	−	3.46597i	0.685501	−	0.283944i	−0.0126235	−	0.999920i	$-0.504018\pi$
$149$	8.36760	−	3.46597i	0.685501	−	0.283944i	0.698124	+	0.715977i	$0.254018\pi$
$150$		0			0
$151$	−2.49354	+	2.49354i	−0.202921	+	0.202921i	−0.801250	−	0.598329i	$-0.795832\pi$
$151$	−2.49354	+	2.49354i	−0.202921	+	0.202921i	0.598329	+	0.801250i	$0.295832\pi$
$152$		0			0
$153$	7.64526	+	17.0988i	0.618083	+	1.38236i
$154$		0			0
$155$	−4.27526	+	1.77087i	−0.343397	+	0.142240i
$156$		0			0
$157$	−3.52366	+	8.50687i	−0.281219	+	0.678922i	−0.999865	−	0.0164542i	$-0.994762\pi$
$157$	−3.52366	+	8.50687i	−0.281219	+	0.678922i	0.718646	+	0.695376i	$0.244762\pi$
$158$		0			0
$159$	−8.53892	−	1.57562i	−0.677180	−	0.124955i
$160$		0			0
$161$			5.37117i			0.423308i
$162$		0			0
$163$	9.76152	+	4.04335i	0.764581	+	0.316700i	0.730675	−	0.682725i	$-0.239205\pi$
$163$	9.76152	+	4.04335i	0.764581	+	0.316700i	0.0339057	+	0.999425i	$0.489205\pi$
$164$		0			0
$165$	−5.01267	+	1.06961i	−0.390236	+	0.0832692i
$166$		0			0
$167$	3.05737	−	3.05737i	0.236587	−	0.236587i	−0.578848	−	0.815435i	$-0.696498\pi$
$167$	3.05737	−	3.05737i	0.236587	−	0.236587i	0.815435	+	0.578848i	$0.196498\pi$
$168$		0			0
$169$	−3.94413	−	3.94413i	−0.303395	−	0.303395i
$170$		0			0
$171$	5.35683	−	0.148736i	0.409647	−	0.0113742i
$172$		0			0
$173$	−7.23974	+	17.4783i	−0.550427	+	1.32885i	0.366732	+	0.930327i	$0.380477\pi$
$173$	−7.23974	+	17.4783i	−0.550427	+	1.32885i	−0.917159	+	0.398522i	$0.869523\pi$
$174$		0			0
$175$	−2.78149			−0.210261
$176$		0			0
$177$	−4.92733	−	0.909205i	−0.370361	−	0.0683400i
$178$		0			0
$179$	12.6819	+	5.25303i	0.947892	+	0.392630i	0.802438	−	0.596736i	$-0.203536\pi$
$179$	12.6819	+	5.25303i	0.947892	+	0.392630i	0.145454	+	0.989365i	$0.453536\pi$
$180$		0			0
$181$	−3.26250	−	7.87637i	−0.242500	−	0.585446i	0.755030	−	0.655690i	$-0.227622\pi$
$181$	−3.26250	−	7.87637i	−0.242500	−	0.585446i	−0.997530	+	0.0702439i	$0.977622\pi$
$182$		0			0
$183$	−8.81125	+	6.06605i	−0.651346	+	0.448415i
$184$		0			0
$185$	−4.34043	−	4.34043i	−0.319115	−	0.319115i
$186$		0			0
$187$	7.75334	+	18.7182i	0.566981	+	1.36881i
$188$		0			0
$189$	−2.80024	+	2.04464i	−0.203687	+	0.148726i
$190$		0			0
$191$	9.70190			0.702005			0.351002	−	0.936375i	$-0.385841\pi$
$191$	9.70190			0.702005			0.351002	+	0.936375i	$0.385841\pi$
$192$		0			0
$193$	−21.4271			−1.54235			−0.771177	−	0.636621i	$-0.780332\pi$
$193$	−21.4271			−1.54235			−0.771177	+	0.636621i	$0.780332\pi$
$194$		0			0
$195$	−2.34075	+	3.61067i	−0.167625	+	0.258566i
$196$		0			0
$197$	−5.50419	−	13.2883i	−0.392157	−	0.946751i	−0.989469	−	0.144742i	$-0.953765\pi$
$197$	−5.50419	−	13.2883i	−0.392157	−	0.946751i	0.597312	−	0.802009i	$-0.296235\pi$
$198$		0			0
$199$	6.75982	+	6.75982i	0.479191	+	0.479191i	0.904873	−	0.425682i	$-0.139966\pi$
$199$	6.75982	+	6.75982i	0.479191	+	0.479191i	−0.425682	+	0.904873i	$0.639966\pi$
$200$		0			0
$201$	−3.61397	−	5.24947i	−0.254909	−	0.370269i
$202$		0			0
$203$	1.46186	+	3.52925i	0.102603	+	0.247705i
$204$		0			0
$205$	7.66309	+	3.17416i	0.535213	+	0.221693i
$206$		0			0
$207$	8.61836	−	22.5580i	0.599017	−	1.56789i
$208$		0			0
$209$	5.79672			0.400967
$210$		0			0
$211$	2.53702	−	6.12491i	0.174656	−	0.421656i	−0.812175	−	0.583414i	$-0.801716\pi$
$211$	2.53702	−	6.12491i	0.174656	−	0.421656i	0.986830	+	0.161758i	$0.0517164\pi$
$212$		0			0
$213$	−18.4921	+	3.94588i	−1.26706	+	0.270368i
$214$		0			0
$215$	−4.22047	−	4.22047i	−0.287834	−	0.287834i
$216$		0			0
$217$	−2.39435	+	2.39435i	−0.162539	+	0.162539i
$218$		0			0
$219$	−0.0251916	−	0.118059i	−0.00170229	−	0.00797769i
$220$		0			0
$221$	15.7145	+	6.50917i	1.05707	+	0.437854i
$222$		0			0
$223$		−	8.81813i		−	0.590506i	−0.955419	−	0.295253i	$-0.904596\pi$
$223$		−	8.81813i		−	0.590506i	0.955419	−	0.295253i	$-0.0954039\pi$
$224$		0			0
$225$	11.6818	+	4.46306i	0.778784	+	0.297537i
$226$		0			0
$227$	9.49912	−	22.9329i	0.630479	−	1.52211i	−0.208543	−	0.978013i	$-0.566872\pi$
$227$	9.49912	−	22.9329i	0.630479	−	1.52211i	0.839022	−	0.544097i	$-0.183128\pi$
$228$		0			0
$229$	−17.9702	+	7.44351i	−1.18751	+	0.491881i	−0.886942	−	0.461881i	$-0.847175\pi$
$229$	−17.9702	+	7.44351i	−1.18751	+	0.491881i	−0.300563	+	0.953762i	$0.597175\pi$
$230$		0			0
$231$	−3.08924	+	2.12677i	−0.203257	+	0.139931i
$232$		0			0
$233$	0.551118	−	0.551118i	0.0361050	−	0.0361050i	−0.688824	−	0.724929i	$-0.741873\pi$
$233$	0.551118	−	0.551118i	0.0361050	−	0.0361050i	0.724929	+	0.688824i	$0.241873\pi$
$234$		0			0
$235$	7.53997	−	3.12316i	0.491854	−	0.203732i
$236$		0			0
$237$	−14.7166	−	9.54056i	−0.955945	−	0.619726i
$238$		0			0
$239$			1.64816i			0.106610i	0.998578	+	0.0533052i	$0.0169756\pi$
$239$			1.64816i			0.106610i	−0.998578	+	0.0533052i	$0.983024\pi$
$240$		0			0
$241$		−	18.3719i		−	1.18344i	−0.806145	−	0.591718i	$-0.798450\pi$
$241$		−	18.3719i		−	1.18344i	0.806145	−	0.591718i	$-0.201550\pi$
$242$		0			0
$243$	15.0413	−	4.09398i	0.964897	−	0.262629i
$244$		0			0
$245$	−5.52230	+	2.28741i	−0.352807	+	0.146137i
$246$		0			0
$247$	3.44115	−	3.44115i	0.218955	−	0.218955i
$248$		0			0
$249$	3.88172	+	5.63840i	0.245994	+	0.357319i
$250$		0			0
$251$	−26.5328	+	10.9903i	−1.67474	+	0.693699i	−0.999054	−	0.0434928i	$-0.986151\pi$
$251$	−26.5328	+	10.9903i	−1.67474	+	0.693699i	−0.675684	+	0.737192i	$0.736151\pi$
$252$		0			0
$253$	9.99614	−	24.1328i	0.628452	−	1.51722i
$254$		0			0
$255$	−1.78941	+	9.69750i	−0.112057	+	0.607281i
$256$		0			0
$257$			14.0179i			0.874413i	0.899361	+	0.437206i	$0.144032\pi$
$257$			14.0179i			0.874413i	−0.899361	+	0.437206i	$0.855968\pi$
$258$		0			0
$259$	−4.14972	−	1.71887i	−0.257851	−	0.106805i
$260$		0			0
$261$	−0.476679	−	17.1679i	−0.0295057	−	1.06266i
$262$		0			0
$263$	−17.6733	+	17.6733i	−1.08978	+	1.08978i	−0.0942329	+	0.995550i	$0.530040\pi$
$263$	−17.6733	+	17.6733i	−1.08978	+	1.08978i	−0.995550	+	0.0942329i	$0.969960\pi$
$264$		0			0
$265$	−3.23256	−	3.23256i	−0.198574	−	0.198574i
$266$		0			0
$267$	2.09278	+	9.80768i	0.128076	+	0.600220i
$268$		0			0
$269$	−6.87589	+	16.5999i	−0.419231	+	1.01211i	0.563340	+	0.826225i	$0.309516\pi$
$269$	−6.87589	+	16.5999i	−0.419231	+	1.01211i	−0.982571	+	0.185887i	$0.940484\pi$
$270$		0			0
$271$	−0.0752921			−0.00457367			−0.00228683	−	0.999997i	$-0.500728\pi$
$271$	−0.0752921			−0.00457367			−0.00228683	+	0.999997i	$0.500728\pi$
$272$		0			0
$273$	−0.571360	+	3.09642i	−0.0345803	+	0.187404i
$274$		0			0
$275$	12.4973	+	5.17655i	0.753616	+	0.312158i
$276$		0			0
$277$	6.16828	+	14.8915i	0.370616	+	0.894746i	0.993646	+	0.112548i	$0.0359013\pi$
$277$	6.16828	+	14.8915i	0.370616	+	0.894746i	−0.623030	+	0.782198i	$0.714099\pi$
$278$		0			0
$279$	13.8977	−	6.21397i	0.832035	−	0.372021i
$280$		0			0
$281$	−11.2880	−	11.2880i	−0.673386	−	0.673386i	0.285109	−	0.958495i	$-0.407970\pi$
$281$	−11.2880	−	11.2880i	−0.673386	−	0.673386i	−0.958495	+	0.285109i	$0.907970\pi$
$282$		0			0
$283$	−6.30429	−	15.2199i	−0.374751	−	0.904729i	−0.992931	−	0.118692i	$-0.962130\pi$
$283$	−6.30429	−	15.2199i	−0.374751	−	0.904729i	0.618180	−	0.786037i	$-0.287870\pi$
$284$		0			0
$285$	2.36743	+	1.53477i	0.140234	+	0.0909120i
$286$		0			0
$287$	6.06938			0.358264
$288$		0			0
$289$	21.9800			1.29294
$290$		0			0
$291$	−6.86923	−	4.45322i	−0.402681	−	0.261053i
$292$		0			0
$293$	−8.25342	−	19.9255i	−0.482170	−	1.16406i	−0.958576	−	0.284836i	$-0.908061\pi$
$293$	−8.25342	−	19.9255i	−0.482170	−	1.16406i	0.476406	−	0.879225i	$-0.341939\pi$
$294$		0			0
$295$	−1.86533	−	1.86533i	−0.108604	−	0.108604i
$296$		0			0
$297$	16.3868	−	3.97518i	0.950857	−	0.230663i
$298$		0			0
$299$	−8.39207	−	20.2603i	−0.485326	−	1.17168i
$300$		0			0
$301$	−4.03503	−	1.67136i	−0.232575	−	0.0963358i
$302$		0			0
$303$	2.22530	−	12.0598i	0.127840	−	0.692817i
$304$		0			0
$305$	−5.63207			−0.322491
$306$		0			0
$307$	−1.32663	+	3.20278i	−0.0757149	+	0.182792i	−0.957205	−	0.289410i	$-0.906541\pi$
$307$	−1.32663	+	3.20278i	−0.0757149	+	0.182792i	0.881490	+	0.472202i	$0.156541\pi$
$308$		0			0
$309$	−2.39373	−	11.2181i	−0.136175	−	0.638174i
$310$		0			0
$311$	5.22034	+	5.22034i	0.296018	+	0.296018i	0.839452	−	0.543434i	$-0.182876\pi$
$311$	5.22034	+	5.22034i	0.296018	+	0.296018i	−0.543434	+	0.839452i	$0.682876\pi$
$312$		0			0
$313$	3.87084	−	3.87084i	0.218793	−	0.218793i	−0.589197	−	0.807989i	$-0.700556\pi$
$313$	3.87084	−	3.87084i	0.218793	−	0.218793i	0.807989	+	0.589197i	$0.200556\pi$
$314$		0			0
$315$	−1.82477	+	0.0506660i	−0.102814	+	0.00285471i
$316$		0			0
$317$	27.3117	+	11.3129i	1.53398	+	0.635393i	0.980331	−	0.197360i	$-0.0632367\pi$
$317$	27.3117	+	11.3129i	1.53398	+	0.635393i	0.553644	+	0.832753i	$0.313237\pi$
$318$		0			0
$319$		−	18.5776i		−	1.04015i
$320$		0			0
$321$	−0.372681	+	2.01970i	−0.0208010	+	0.112729i
$322$		0			0
$323$	4.26790	−	10.3036i	0.237472	−	0.573309i
$324$		0			0
$325$	10.4919	−	4.34588i	0.581985	−	0.241066i
$326$		0			0
$327$	11.6455	+	16.9156i	0.643995	+	0.935436i
$328$		0			0
$329$	4.22275	−	4.22275i	0.232808	−	0.232808i
$330$		0			0
$331$	−9.20994	+	3.81488i	−0.506224	+	0.209685i	−0.621154	−	0.783689i	$-0.713336\pi$
$331$	−9.20994	+	3.81488i	−0.506224	+	0.209685i	0.114930	+	0.993374i	$0.463336\pi$
$332$		0			0
$333$	14.6701	+	13.8774i	0.803915	+	0.760479i
$334$		0			0
$335$		−	3.35541i		−	0.183326i
$336$		0			0
$337$			29.5659i			1.61056i	0.592895	+	0.805280i	$0.297985\pi$
$337$			29.5659i			1.61056i	−0.592895	+	0.805280i	$0.702015\pi$
$338$		0			0
$339$	−9.92291	−	6.43289i	−0.538939	−	0.349386i
$340$		0			0
$341$	15.2139	−	6.30182i	0.823881	−	0.341263i
$342$		0			0
$343$	−6.39559	+	6.39559i	−0.345330	+	0.345330i
$344$		0			0
$345$	10.4721	−	7.20942i	0.563796	−	0.388142i
$346$		0			0
$347$	−23.6365	+	9.79057i	−1.26888	+	0.525585i	−0.912622	−	0.408804i	$-0.865946\pi$
$347$	−23.6365	+	9.79057i	−1.26888	+	0.525585i	−0.356253	+	0.934389i	$0.615946\pi$
$348$		0			0
$349$	−10.2166	+	24.6651i	−0.546883	+	1.32029i	0.372902	+	0.927871i	$0.378363\pi$
$349$	−10.2166	+	24.6651i	−0.546883	+	1.32029i	−0.919785	+	0.392423i	$0.871637\pi$
$350$		0			0
$351$	7.36800	−	12.0876i	0.393274	−	0.645190i
$352$		0			0
$353$		−	17.7066i		−	0.942426i	−0.882020	−	0.471213i	$-0.843816\pi$
$353$		−	17.7066i		−	0.942426i	0.882020	−	0.471213i	$-0.156184\pi$
$354$		0			0
$355$	−9.19728	−	3.80964i	−0.488141	−	0.202195i
$356$		0			0
$357$	1.50583	+	7.05696i	0.0796968	+	0.373494i
$358$		0			0
$359$	7.15299	−	7.15299i	0.377520	−	0.377520i	−0.492686	−	0.870207i	$-0.663985\pi$
$359$	7.15299	−	7.15299i	0.377520	−	0.377520i	0.870207	+	0.492686i	$0.163985\pi$
$360$		0			0
$361$	11.1788	+	11.1788i	0.588355	+	0.588355i
$362$		0			0
$363$	−0.794983	+	0.169635i	−0.0417258	+	0.00890352i
$364$		0			0
$365$	0.0243218	−	0.0587180i	0.00127306	−	0.00307344i
$366$		0			0
$367$	−18.0884			−0.944205			−0.472102	−	0.881544i	$-0.656505\pi$
$367$	−18.0884			−0.944205			−0.472102	+	0.881544i	$0.656505\pi$
$368$		0			0
$369$	−25.4903	−	9.73868i	−1.32697	−	0.506975i
$370$		0			0
$371$	−3.09053	−	1.28014i	−0.160452	−	0.0664615i
$372$		0			0
$373$	4.46880	+	10.7886i	0.231386	+	0.558614i	0.996341	−	0.0854691i	$-0.0272389\pi$
$373$	4.46880	+	10.7886i	0.231386	+	0.558614i	−0.764955	+	0.644084i	$0.777239\pi$
$374$		0			0
$375$	8.21166	+	11.9279i	0.424048	+	0.615952i
$376$		0			0
$377$	−11.0284	−	11.0284i	−0.567992	−	0.567992i
$378$		0			0
$379$	−1.31108	−	3.16523i	−0.0673457	−	0.162587i	0.886623	−	0.462493i	$-0.153045\pi$
$379$	−1.31108	−	3.16523i	−0.0673457	−	0.162587i	−0.953969	+	0.299906i	$0.903045\pi$
$380$		0			0
$381$	19.3010	−	29.7723i	0.988819	−	1.52528i
$382$		0			0
$383$	9.44734			0.482737			0.241368	−	0.970434i	$-0.422404\pi$
$383$	9.44734			0.482737			0.241368	+	0.970434i	$0.422404\pi$
$384$		0			0
$385$	−1.97461			−0.100636
$386$		0			0
$387$	14.2646	+	13.4939i	0.725111	+	0.685932i
$388$		0			0
$389$	1.49354	+	3.60573i	0.0757256	+	0.182818i	0.957209	−	0.289397i	$-0.0934547\pi$
$389$	1.49354	+	3.60573i	0.0757256	+	0.182818i	−0.881484	+	0.472215i	$0.843455\pi$
$390$		0			0
$391$	−35.5362	−	35.5362i	−1.79714	−	1.79714i
$392$		0			0
$393$	1.04819	−	0.721620i	0.0528742	−	0.0364009i
$394$		0			0
$395$	−3.53363	−	8.53094i	−0.177796	−	0.429238i
$396$		0			0
$397$	35.3001	+	14.6218i	1.77166	+	0.733845i	0.994524	+	0.104512i	$0.0333281\pi$
$397$	35.3001	+	14.6218i	1.77166	+	0.733845i	0.777136	+	0.629333i	$0.216672\pi$
$398$		0			0
$399$	2.03025	+	0.374626i	0.101639	+	0.0187548i
$400$		0			0
$401$	−15.2403			−0.761063			−0.380531	−	0.924768i	$-0.624259\pi$
$401$	−15.2403			−0.761063			−0.380531	+	0.924768i	$0.624259\pi$
$402$		0			0
$403$	5.29058	−	12.7726i	0.263542	−	0.636248i
$404$		0			0
$405$	7.74499	+	2.71516i	0.384852	+	0.134917i
$406$		0			0
$407$	15.4459	+	15.4459i	0.765624	+	0.765624i
$408$		0			0
$409$	−10.0840	+	10.0840i	−0.498621	+	0.498621i	−0.911009	−	0.412387i	$-0.864695\pi$
$409$	−10.0840	+	10.0840i	−0.498621	+	0.498621i	0.412387	+	0.911009i	$0.364695\pi$
$410$		0			0
$411$	−2.18957	+	0.467214i	−0.108004	+	0.0230460i
$412$		0			0
$413$	−1.78337	−	0.738696i	−0.0877540	−	0.0363489i
$414$		0			0
$415$			3.60401i			0.176914i
$416$		0			0
$417$	11.1958	+	2.06588i	0.548262	+	0.101167i
$418$		0			0
$419$	−8.60540	+	20.7753i	−0.420401	+	1.01494i	0.561828	+	0.827254i	$0.310098\pi$
$419$	−8.60540	+	20.7753i	−0.420401	+	1.01494i	−0.982229	+	0.187684i	$0.939902\pi$
$420$		0			0
$421$	26.9768	−	11.1742i	1.31477	−	0.544596i	0.388498	−	0.921450i	$-0.372994\pi$
$421$	26.9768	−	11.1742i	1.31477	−	0.544596i	0.926273	+	0.376854i	$0.122994\pi$
$422$		0			0
$423$	−24.5104	+	10.9591i	−1.19174	+	0.532852i
$424$		0			0
$425$	18.4026	−	18.4026i	0.892656	−	0.892656i
$426$		0			0
$427$	−3.80749	+	1.57711i	−0.184257	+	0.0763219i
$428$		0			0
$429$	8.32980	−	12.8490i	0.402166	−	0.620353i
$430$		0			0
$431$		−	6.75028i		−	0.325150i	−0.986696	−	0.162575i	$-0.948020\pi$
$431$		−	6.75028i		−	0.325150i	0.986696	−	0.162575i	$-0.0519799\pi$
$432$		0			0
$433$		−	12.8840i		−	0.619163i	−0.950873	−	0.309582i	$-0.899811\pi$
$433$		−	12.8840i		−	0.619163i	0.950873	−	0.309582i	$-0.100189\pi$
$434$		0			0
$435$	4.91872	−	7.58727i	0.235835	−	0.363782i
$436$		0			0
$437$	−13.2841	+	5.50247i	−0.635467	+	0.263219i
$438$		0			0
$439$	12.4797	−	12.4797i	0.595625	−	0.595625i	−0.343521	−	0.939145i	$-0.611620\pi$
$439$	12.4797	−	12.4797i	0.595625	−	0.595625i	0.939145	+	0.343521i	$0.111620\pi$
$440$		0			0
$441$	17.9515	−	8.02651i	0.854834	−	0.382215i
$442$		0			0
$443$	11.4418	−	4.73933i	0.543614	−	0.225172i	−0.0939401	−	0.995578i	$-0.529946\pi$
$443$	11.4418	−	4.73933i	0.543614	−	0.225172i	0.637554	+	0.770406i	$0.279946\pi$
$444$		0			0
$445$	−2.02052	+	4.87796i	−0.0957817	+	0.231238i
$446$		0			0
$447$	−15.4268	−	2.84660i	−0.729663	−	0.134639i
$448$		0			0
$449$			28.4023i			1.34039i	0.742187	+	0.670193i	$0.233789\pi$
$449$			28.4023i			1.34039i	−0.742187	+	0.670193i	$0.766211\pi$
$450$		0			0
$451$	−27.2699	−	11.2956i	−1.28409	−	0.531887i
$452$		0			0
$453$	5.97342	−	1.27462i	0.280656	−	0.0598868i
$454$		0			0
$455$	−1.17220	+	1.17220i	−0.0549538	+	0.0549538i
$456$		0			0
$457$	2.18179	+	2.18179i	0.102060	+	0.102060i	0.756293	−	0.654233i	$-0.227008\pi$
$457$	2.18179	+	2.18179i	0.102060	+	0.102060i	−0.654233	+	0.756293i	$0.727008\pi$
$458$		0			0
$459$	4.99910	−	32.0542i	0.233338	−	1.49616i
$460$		0			0
$461$	2.67493	−	6.45785i	0.124584	−	0.300772i	−0.849266	−	0.527965i	$-0.822955\pi$
$461$	2.67493	−	6.45785i	0.124584	−	0.300772i	0.973850	+	0.227194i	$0.0729550\pi$
$462$		0			0
$463$	−14.4928			−0.673537			−0.336768	−	0.941588i	$-0.609334\pi$
$463$	−14.4928			−0.673537			−0.336768	+	0.941588i	$0.609334\pi$
$464$		0			0
$465$	7.88201	+	1.45441i	0.365520	+	0.0674467i
$466$		0			0
$467$	25.1292	+	10.4089i	1.16284	+	0.481665i	0.878821	−	0.477153i	$-0.158331\pi$
$467$	25.1292	+	10.4089i	1.16284	+	0.481665i	0.284022	+	0.958818i	$0.408331\pi$
$468$		0			0
$469$	−0.939596	−	2.26839i	−0.0433865	−	0.104744i
$470$		0			0
$471$	13.1363	−	9.04360i	0.605289	−	0.416707i
$472$		0			0
$473$	15.0190	+	15.0190i	0.690573	+	0.690573i
$474$		0			0
$475$	−2.84948	−	6.87926i	−0.130743	−	0.315642i
$476$		0			0
$477$	10.9256	+	10.3353i	0.500249	+	0.473220i
$478$		0			0
$479$	−17.4339			−0.796575			−0.398288	−	0.917261i	$-0.630395\pi$
$479$	−17.4339			−0.796575			−0.398288	+	0.917261i	$0.630395\pi$
$480$		0			0
$481$	18.3385			0.836165
$482$		0			0
$483$	5.06069	−	7.80627i	0.230270	−	0.355198i
$484$		0			0
$485$	−1.64938	−	3.98197i	−0.0748947	−	0.180812i
$486$		0			0
$487$	17.8550	+	17.8550i	0.809087	+	0.809087i	0.984496	−	0.175408i	$-0.0561245\pi$
$487$	17.8550	+	17.8550i	0.809087	+	0.809087i	−0.175408	+	0.984496i	$0.556125\pi$
$488$		0			0
$489$	−10.3774	−	15.0737i	−0.469283	−	0.681657i
$490$		0			0
$491$	5.45046	+	13.1586i	0.245976	+	0.593839i	0.997855	−	0.0654625i	$-0.0208523\pi$
$491$	5.45046	+	13.1586i	0.245976	+	0.593839i	−0.751879	+	0.659301i	$0.770852\pi$
$492$		0			0
$493$	−33.0217	−	13.6780i	−1.48722	−	0.616027i
$494$		0			0
$495$	8.29302	+	3.16838i	0.372743	+	0.142408i
$496$		0			0
$497$	−7.28450			−0.326754
$498$		0			0
$499$	0.698157	−	1.68550i	0.0312538	−	0.0754533i	−0.907482	−	0.420091i	$-0.861998\pi$
$499$	0.698157	−	1.68550i	0.0312538	−	0.0754533i	0.938736	+	0.344638i	$0.111998\pi$
$500$		0			0
$501$	−7.32412	+	1.56283i	−0.327218	+	0.0698222i
$502$		0			0
$503$	−10.2138	−	10.2138i	−0.455412	−	0.455412i	0.441734	−	0.897146i	$-0.354364\pi$
$503$	−10.2138	−	10.2138i	−0.455412	−	0.455412i	−0.897146	+	0.441734i	$0.854364\pi$
$504$		0			0
$505$	4.56545	−	4.56545i	0.203160	−	0.203160i
$506$		0			0
$507$	2.01612	+	9.44840i	0.0895389	+	0.419618i
$508$		0			0
$509$	−36.6825	−	15.1944i	−1.62592	−	0.673480i	−0.631157	−	0.775655i	$-0.717420\pi$
$509$	−36.6825	−	15.1944i	−1.62592	−	0.673480i	−0.994766	+	0.102175i	$0.967420\pi$
$510$		0			0
$511$		−	0.0465063i		−	0.00205732i
$512$		0			0
$513$	−7.92556	−	4.83101i	−0.349922	−	0.213294i
$514$		0			0
$515$	2.31108	−	5.57944i	0.101838	−	0.245859i
$516$		0			0
$517$	−26.8318	+	11.1141i	−1.18006	+	0.488797i
$518$		0			0
$519$	26.9899	−	18.5810i	1.18473	−	0.815617i
$520$		0			0
$521$	−0.526260	+	0.526260i	−0.0230559	+	0.0230559i	−0.718541	−	0.695485i	$-0.755190\pi$
$521$	−0.526260	+	0.526260i	−0.0230559	+	0.0230559i	0.695485	+	0.718541i	$0.255190\pi$
$522$		0			0
$523$	4.11152	−	1.70305i	0.179784	−	0.0744691i	−0.290975	−	0.956731i	$-0.593980\pi$
$523$	4.11152	−	1.70305i	0.179784	−	0.0744691i	0.470760	+	0.882261i	$0.343980\pi$
$524$		0			0
$525$	4.04252	+	2.62071i	0.176430	+	0.114377i
$526$		0			0
$527$		−	31.6825i		−	1.38011i
$528$		0			0
$529$			41.7931i			1.81709i
$530$		0			0
$531$	6.30456	+	5.96392i	0.273595	+	0.258812i
$532$		0			0
$533$	−22.8939	+	9.48297i	−0.991646	+	0.410753i
$534$		0			0
$535$	−0.764595	+	0.764595i	−0.0330563	+	0.0330563i
$536$		0			0
$537$	−13.4821	−	19.5834i	−0.581795	−	0.845087i
$538$		0			0
$539$	19.6517	−	8.13999i	0.846457	−	0.350614i
$540$		0			0
$541$	−2.79932	+	6.75816i	−0.120352	+	0.290556i	−0.972562	−	0.232645i	$-0.925262\pi$
$541$	−2.79932	+	6.75816i	−0.120352	+	0.290556i	0.852210	+	0.523201i	$0.175262\pi$
$542$		0			0
$543$	−2.67948	+	14.5212i	−0.114988	+	0.623162i
$544$		0			0
$545$			10.8123i			0.463148i
$546$		0			0
$547$	12.5442	+	5.19596i	0.536349	+	0.222163i	0.634382	−	0.773020i	$-0.281255\pi$
$547$	12.5442	+	5.19596i	0.536349	+	0.222163i	−0.0980322	+	0.995183i	$0.531255\pi$
$548$		0			0
$549$	18.5214	−	0.514259i	0.790472	−	0.0219481i
$550$		0			0
$551$	−7.23105	+	7.23105i	−0.308053	+	0.308053i
$552$		0			0
$553$	−4.77774	−	4.77774i	−0.203170	−	0.203170i
$554$		0			0
$555$	2.21869	+	10.3978i	0.0941783	+	0.441361i
$556$		0			0
$557$	4.26094	−	10.2868i	0.180542	−	0.435866i	−0.807537	−	0.589817i	$-0.799200\pi$
$557$	4.26094	−	10.2868i	0.180542	−	0.435866i	0.988078	+	0.153951i	$0.0491998\pi$
$558$		0			0
$559$	17.8317			0.754199
$560$		0			0
$561$	6.36780	−	34.5096i	0.268849	−	1.45699i
$562$		0			0
$563$	−16.5626	−	6.86044i	−0.698029	−	0.289133i	0.00531196	−	0.999986i	$-0.498309\pi$
$563$	−16.5626	−	6.86044i	−0.698029	−	0.289133i	−0.703341	+	0.710853i	$0.748309\pi$
$564$		0			0
$565$	−2.38261	−	5.75213i	−0.100237	−	0.241994i
$566$		0			0
$567$	5.99622	−	0.333236i	0.251817	−	0.0139946i
$568$		0			0
$569$	22.0173	+	22.0173i	0.923014	+	0.923014i	0.997241	−	0.0742272i	$-0.0236490\pi$
$569$	22.0173	+	22.0173i	0.923014	+	0.923014i	−0.0742272	+	0.997241i	$0.523649\pi$
$570$		0			0
$571$	−13.9626	−	33.7086i	−0.584315	−	1.41066i	−0.888866	−	0.458166i	$-0.848506\pi$
$571$	−13.9626	−	33.7086i	−0.584315	−	1.41066i	0.304551	−	0.952496i	$-0.401494\pi$
$572$		0			0
$573$	−14.1004	−	9.14108i	−0.589052	−	0.381874i
$574$		0			0
$575$	−33.5535			−1.39928
$576$		0			0
$577$	−24.0941			−1.00305			−0.501526	−	0.865143i	$-0.667228\pi$
$577$	−24.0941			−1.00305			−0.501526	+	0.865143i	$0.667228\pi$
$578$		0			0
$579$	31.1413	+	20.1885i	1.29419	+	0.839005i
$580$		0			0
$581$	1.00921	+	2.43645i	0.0418691	+	0.101081i
$582$		0			0
$583$	11.5034	+	11.5034i	0.476422	+	0.476422i
$584$		0			0
$585$	6.80392	−	3.04218i	0.281308	−	0.125779i
$586$		0			0
$587$	6.34332	+	15.3141i	0.261817	+	0.632082i	0.999051	−	0.0435555i	$-0.0138685\pi$
$587$	6.34332	+	15.3141i	0.261817	+	0.632082i	−0.737234	+	0.675637i	$0.763869\pi$
$588$		0			0
$589$	−8.37466	−	3.46890i	−0.345072	−	0.142933i
$590$		0			0
$591$	−4.52057	+	24.4987i	−0.185952	+	1.00774i
$592$		0			0
$593$	21.6814			0.890349			0.445174	−	0.895444i	$-0.353142\pi$
$593$	21.6814			0.890349			0.445174	+	0.895444i	$0.353142\pi$
$594$		0			0
$595$	−1.45383	+	3.50986i	−0.0596013	+	0.143890i
$596$		0			0
$597$	−3.45541	−	16.1935i	−0.141420	−	0.662758i
$598$		0			0
$599$	−17.5864	−	17.5864i	−0.718559	−	0.718559i	0.249751	−	0.968310i	$-0.419651\pi$
$599$	−17.5864	−	17.5864i	−0.718559	−	0.718559i	−0.968310	+	0.249751i	$0.919651\pi$
$600$		0			0
$601$	5.95620	−	5.95620i	0.242958	−	0.242958i	−0.575115	−	0.818073i	$-0.695043\pi$
$601$	5.95620	−	5.95620i	0.242958	−	0.242958i	0.818073	+	0.575115i	$0.195043\pi$
$602$		0			0
$603$	0.306380	+	11.0345i	0.0124768	+	0.449358i
$604$		0			0
$605$	−0.395394	−	0.163778i	−0.0160751	−	0.00665851i
$606$		0			0
$607$			0.123708i			0.00502116i	0.999997	+	0.00251058i	$0.000799143\pi$
$607$			0.123708i			0.00502116i	−0.999997	+	0.00251058i	$0.999201\pi$
$608$		0			0
$609$	1.20062	−	6.50665i	0.0486517	−	0.263663i
$610$		0			0
$611$	−9.33062	+	22.5261i	−0.377476	+	0.911308i
$612$		0			0
$613$	−22.5390	+	9.33597i	−0.910343	+	0.377076i	−0.788188	−	0.615435i	$-0.788980\pi$
$613$	−22.5390	+	9.33597i	−0.910343	+	0.377076i	−0.122155	+	0.992511i	$0.538980\pi$
$614$		0			0
$615$	−8.14659	−	11.8333i	−0.328502	−	0.477166i
$616$		0			0
$617$	−10.8400	+	10.8400i	−0.436403	+	0.436403i	−0.890799	−	0.454397i	$-0.849855\pi$
$617$	−10.8400	+	10.8400i	−0.436403	+	0.436403i	0.454397	+	0.890799i	$0.349855\pi$
$618$		0			0
$619$	−18.8328	+	7.80078i	−0.756952	+	0.313540i	−0.727575	−	0.686028i	$-0.759353\pi$
$619$	−18.8328	+	7.80078i	−0.756952	+	0.313540i	−0.0293776	+	0.999568i	$0.509353\pi$
$620$		0			0
$621$	−33.7796	+	24.6648i	−1.35553	+	0.989763i
$622$		0			0
$623$			3.86348i			0.154787i
$624$		0			0
$625$		−	13.2180i		−	0.528720i
$626$		0			0
$627$	−8.42474	−	5.46164i	−0.336452	−	0.218117i
$628$		0			0
$629$	38.8272	−	16.0827i	1.54814	−	0.641261i
$630$		0			0
$631$	−17.8628	+	17.8628i	−0.711107	+	0.711107i	−0.966767	−	0.255660i	$-0.917707\pi$
$631$	−17.8628	+	17.8628i	−0.711107	+	0.711107i	0.255660	+	0.966767i	$0.417707\pi$
$632$		0			0
$633$	−9.45808	+	6.51136i	−0.375925	+	0.258803i
$634$		0			0
$635$	17.2585	−	7.14869i	0.684881	−	0.283687i
$636$		0			0
$637$	6.83377	−	16.4982i	0.270764	−	0.653682i
$638$		0			0
$639$	30.5936	+	11.6884i	1.21026	+	0.462386i
$640$		0			0
$641$		−	35.0585i		−	1.38473i	−0.721548	−	0.692364i	$-0.756569\pi$
$641$		−	35.0585i		−	1.38473i	0.721548	−	0.692364i	$-0.243431\pi$
$642$		0			0
$643$	−25.3200	−	10.4879i	−0.998524	−	0.413602i	−0.177268	−	0.984163i	$-0.556726\pi$
$643$	−25.3200	−	10.4879i	−0.998524	−	0.413602i	−0.821256	+	0.570561i	$0.806726\pi$
$644$		0			0
$645$	2.15737	+	10.1104i	0.0849464	+	0.398096i
$646$		0			0
$647$	12.7202	−	12.7202i	0.500084	−	0.500084i	−0.411380	−	0.911464i	$-0.634953\pi$
$647$	12.7202	−	12.7202i	0.500084	−	0.500084i	0.911464	+	0.411380i	$0.134953\pi$
$648$		0			0
$649$	6.63797	+	6.63797i	0.260563	+	0.260563i
$650$		0			0
$651$	5.73581	−	1.22392i	0.224804	−	0.0479691i
$652$		0			0
$653$	9.79087	−	23.6372i	0.383146	−	0.924997i	−0.608207	−	0.793778i	$-0.708111\pi$
$653$	9.79087	−	23.6372i	0.383146	−	0.924997i	0.991353	−	0.131218i	$-0.0418889\pi$
$654$		0			0
$655$	0.669993			0.0261788
$656$		0			0
$657$	−0.0746221	+	0.195318i	−0.00291128	+	0.00762009i
$658$		0			0
$659$	−20.3402	−	8.42518i	−0.792341	−	0.328198i	−0.0504566	−	0.998726i	$-0.516068\pi$
$659$	−20.3402	−	8.42518i	−0.792341	−	0.328198i	−0.741884	+	0.670528i	$0.766068\pi$
$660$		0			0
$661$	1.08432	+	2.61778i	0.0421751	+	0.101820i	0.943563	−	0.331192i	$-0.107451\pi$
$661$	1.08432	+	2.61778i	0.0421751	+	0.101820i	−0.901388	+	0.433012i	$0.857451\pi$
$662$		0			0
$663$	−16.7060	−	24.2664i	−0.648808	−	0.942427i
$664$		0			0
$665$	0.768585	+	0.768585i	0.0298045	+	0.0298045i
$666$		0			0
$667$	17.6346	+	42.5738i	0.682816	+	1.64846i
$668$		0			0
$669$	−8.30840	+	12.8160i	−0.321221	+	0.495493i
$670$		0			0
$671$	20.0423			0.773724
$672$		0			0
$673$	6.03385			0.232588			0.116294	−	0.993215i	$-0.462899\pi$
$673$	6.03385			0.232588			0.116294	+	0.993215i	$0.462899\pi$
$674$		0			0
$675$	−12.7728	−	17.4930i	−0.491624	−	0.673304i
$676$		0			0
$677$	1.92640	+	4.65075i	0.0740377	+	0.178743i	0.956566	−	0.291517i	$-0.0941601\pi$
$677$	1.92640	+	4.65075i	0.0740377	+	0.178743i	−0.882528	+	0.470260i	$0.844160\pi$
$678$		0			0
$679$	−2.23009	−	2.23009i	−0.0855831	−	0.0855831i
$680$		0			0
$681$	−35.4130	+	24.3798i	−1.35703	+	0.934237i
$682$		0			0
$683$	5.29070	+	12.7729i	0.202443	+	0.488740i	0.992197	−	0.124684i	$-0.0397916\pi$
$683$	5.29070	+	12.7729i	0.202443	+	0.488740i	−0.789754	+	0.613424i	$0.789792\pi$
$684$		0			0
$685$	−1.08901	−	0.451082i	−0.0416088	−	0.0172349i
$686$		0			0
$687$	33.1305	+	6.11333i	1.26401	+	0.233238i
$688$		0			0
$689$	13.6577			0.520317
$690$		0			0
$691$	−11.3594	+	27.4241i	−0.432134	+	1.04326i	0.546464	+	0.837482i	$0.315973\pi$
$691$	−11.3594	+	27.4241i	−0.432134	+	1.04326i	−0.978598	+	0.205781i	$0.934027\pi$
$692$		0			0
$693$	6.49362	−	0.180300i	0.246672	−	0.00684904i
$694$		0			0
$695$	4.23838	+	4.23838i	0.160771	+	0.160771i
$696$		0			0
$697$	−40.1556	+	40.1556i	−1.52100	+	1.52100i
$698$		0			0
$699$	−1.32024	+	0.281714i	−0.0499359	+	0.0106554i
$700$		0			0
$701$	−21.6433	−	8.96496i	−0.817457	−	0.338602i	−0.0655321	−	0.997850i	$-0.520874\pi$
$701$	−21.6433	−	8.96496i	−0.817457	−	0.338602i	−0.751925	+	0.659249i	$0.770874\pi$
$702$		0			0
$703$		−	12.0241i		−	0.453498i
$704$		0			0
$705$	−13.9010	−	2.56504i	−0.523540	−	0.0966050i
$706$		0			0
$707$	1.80798	−	4.36485i	0.0679961	−	0.164157i
$708$		0			0
$709$	−4.37997	+	1.81424i	−0.164493	+	0.0681354i	−0.463411	−	0.886144i	$-0.653375\pi$
$709$	−4.37997	+	1.81424i	−0.164493	+	0.0681354i	0.298917	+	0.954279i	$0.403375\pi$
$710$		0			0
$711$	12.3995	+	27.7318i	0.465017	+	1.04002i
$712$		0			0
$713$	−28.8834	+	28.8834i	−1.08169	+	1.08169i
$714$		0			0
$715$	7.44831	−	3.08519i	0.278551	−	0.115380i
$716$		0			0
$717$	1.55289	−	2.39537i	0.0579936	−	0.0894568i
$718$		0			0
$719$			50.4878i			1.88288i	0.337182	+	0.941439i	$0.390526\pi$
$719$			50.4878i			1.88288i	−0.337182	+	0.941439i	$0.609474\pi$
$720$		0			0
$721$		−	4.41907i		−	0.164575i
$722$		0			0
$723$	−17.3099	+	26.7010i	−0.643762	+	0.993022i
$724$		0			0
$725$	−22.0471	+	9.13219i	−0.818807	+	0.339161i
$726$		0			0
$727$	−34.3899	+	34.3899i	−1.27545	+	1.27545i	−0.332267	+	0.943185i	$0.607814\pi$
$727$	−34.3899	+	34.3899i	−1.27545	+	1.27545i	−0.943185	+	0.332267i	$0.892186\pi$
$728$		0			0
$729$	−25.7178	−	8.22175i	−0.952509	−	0.304509i
$730$		0			0
$731$	37.7540	−	15.6382i	1.39638	−	0.578401i
$732$		0			0
$733$	−18.4767	+	44.6066i	−0.682451	+	1.64758i	0.0770104	+	0.997030i	$0.475463\pi$
$733$	−18.4767	+	44.6066i	−0.682451	+	1.64758i	−0.759461	+	0.650552i	$0.774537\pi$
$734$		0			0
$735$	10.1811	+	1.87864i	0.375536	+	0.0692948i
$736$		0			0
$737$			11.9406i			0.439837i
$738$		0			0
$739$	45.4385	+	18.8212i	1.67148	+	0.692350i	0.998865	−	0.0476402i	$-0.0151701\pi$
$739$	45.4385	+	18.8212i	1.67148	+	0.692350i	0.672617	+	0.739991i	$0.265170\pi$
$740$		0			0
$741$	−8.24348	+	1.75901i	−0.302832	+	0.0646188i
$742$		0			0
$743$	7.22016	−	7.22016i	0.264882	−	0.264882i	−0.562152	−	0.827034i	$-0.690026\pi$
$743$	7.22016	−	7.22016i	0.264882	−	0.264882i	0.827034	+	0.562152i	$0.190026\pi$
$744$		0			0
$745$	−5.84009	−	5.84009i	−0.213964	−	0.213964i
$746$		0			0
$747$	−0.329080	−	11.8520i	−0.0120404	−	0.433642i
$748$		0			0
$749$	−0.302790	+	0.731000i	−0.0110637	+	0.0267102i
$750$		0			0
$751$	−26.3211			−0.960472			−0.480236	−	0.877139i	$-0.659449\pi$
$751$	−26.3211			−0.960472			−0.480236	+	0.877139i	$0.659449\pi$
$752$		0			0
$753$	48.9168	+	9.02627i	1.78263	+	0.328935i
$754$		0			0
$755$	2.97095	+	1.23061i	0.108124	+	0.0447864i
$756$		0			0
$757$	6.71850	+	16.2199i	0.244188	+	0.589522i	0.997691	−	0.0679230i	$-0.0216372\pi$
$757$	6.71850	+	16.2199i	0.244188	+	0.589522i	−0.753503	+	0.657445i	$0.771637\pi$
$758$		0			0
$759$	−37.2659	+	25.6555i	−1.35267	+	0.931234i
$760$		0			0
$761$	8.55374	+	8.55374i	0.310073	+	0.310073i	0.844938	−	0.534865i	$-0.179637\pi$
$761$	8.55374	+	8.55374i	0.310073	+	0.310073i	−0.534865	+	0.844938i	$0.679637\pi$
$762$		0			0
$763$	3.02770	+	7.30953i	0.109610	+	0.264623i
$764$		0			0
$765$	11.7376	−	12.4080i	0.424374	−	0.448613i
$766$		0			0
$767$	7.88110			0.284570
$768$		0			0
$769$	−50.1936			−1.81003			−0.905014	−	0.425381i	$-0.860140\pi$
$769$	−50.1936			−1.81003			−0.905014	+	0.425381i	$0.860140\pi$
$770$		0			0
$771$	13.2076	−	20.3731i	0.475660	−	0.733720i
$772$		0			0
$773$	13.4148	+	32.3861i	0.482496	+	1.16485i	0.958420	+	0.285361i	$0.0921136\pi$
$773$	13.4148	+	32.3861i	0.482496	+	1.16485i	−0.475924	+	0.879486i	$0.657886\pi$
$774$		0			0
$775$	−14.9574	−	14.9574i	−0.537286	−	0.537286i
$776$		0			0
$777$	4.41155	+	6.40800i	0.158263	+	0.229886i
$778$		0			0
$779$	6.21775	+	15.0110i	0.222774	+	0.537824i
$780$		0			0
$781$	32.7295	+	13.5570i	1.17115	+	0.485107i
$782$		0			0
$783$	−15.4827	+	25.4003i	−0.553307	+	0.907732i
$784$		0			0
$785$	8.39659			0.299687
$786$		0			0
$787$	4.44921	−	10.7413i	0.158597	−	0.382887i	−0.824528	−	0.565821i	$-0.808559\pi$
$787$	4.44921	−	10.7413i	0.158597	−	0.382887i	0.983125	+	0.182934i	$0.0585593\pi$
$788$		0			0
$789$	42.3375	−	9.03404i	1.50725	−	0.321620i
$790$		0			0
$791$	−3.22147	−	3.22147i	−0.114542	−	0.114542i
$792$		0			0
$793$	11.8979	−	11.8979i	0.422506	−	0.422506i
$794$		0			0
$795$	1.65238	+	7.74379i	0.0586040	+	0.274644i
$796$		0			0
$797$	23.8387	+	9.87430i	0.844409	+	0.349766i	0.762590	−	0.646882i	$-0.223927\pi$
$797$	23.8387	+	9.87430i	0.844409	+	0.349766i	0.0818184	+	0.996647i	$0.473927\pi$
$798$		0			0
$799$			55.8762i			1.97676i
$800$		0			0
$801$	6.19918	−	16.2259i	0.219037	−	0.573315i
$802$		0			0
$803$	−0.0865516	+	0.208954i	−0.00305434	+	0.00737383i
$804$		0			0
$805$	4.52515	−	1.87438i	0.159491	−	0.0660632i
$806$		0			0
$807$	25.6335	−	17.6472i	0.902342	−	0.621212i
$808$		0			0
$809$	−4.78786	+	4.78786i	−0.168332	+	0.168332i	−0.786246	−	0.617914i	$-0.787978\pi$
$809$	−4.78786	+	4.78786i	−0.168332	+	0.168332i	0.617914	+	0.786246i	$0.287978\pi$
$810$		0			0
$811$	−27.1023	+	11.2261i	−0.951691	+	0.394203i	−0.803866	−	0.594810i	$-0.797227\pi$
$811$	−27.1023	+	11.2261i	−0.951691	+	0.394203i	−0.147825	+	0.989014i	$0.547227\pi$
$812$		0			0
$813$	0.109427	+	0.0709399i	0.00383777	+	0.00248797i
$814$		0			0
$815$		−	9.63498i		−	0.337499i
$816$		0			0
$817$		−	11.6918i		−	0.409044i
$818$		0			0
$819$	3.74783	−	3.96189i	0.130960	−	0.138440i
$820$		0			0
$821$	−14.6537	+	6.06977i	−0.511418	+	0.211836i	−0.623443	−	0.781869i	$-0.714266\pi$
$821$	−14.6537	+	6.06977i	−0.511418	+	0.211836i	0.112025	+	0.993705i	$0.464266\pi$
$822$		0			0
$823$	39.7738	−	39.7738i	1.38643	−	1.38643i	0.553735	−	0.832693i	$-0.313202\pi$
$823$	39.7738	−	39.7738i	1.38643	−	1.38643i	0.832693	−	0.553735i	$-0.186798\pi$
$824$		0			0
$825$	−13.2858	−	19.2983i	−0.462553	−	0.671881i
$826$		0			0
$827$	−26.7003	+	11.0596i	−0.928461	+	0.384581i	−0.795094	−	0.606486i	$-0.792579\pi$
$827$	−26.7003	+	11.0596i	−0.928461	+	0.384581i	−0.133366	+	0.991067i	$0.542579\pi$
$828$		0			0
$829$	2.13144	−	5.14575i	0.0740280	−	0.178719i	−0.882534	−	0.470249i	$-0.844164\pi$
$829$	2.13144	−	5.14575i	0.0740280	−	0.178719i	0.956562	+	0.291529i	$0.0941641\pi$
$830$		0			0
$831$	5.06599	−	27.4546i	0.175737	−	0.952388i
$832$		0			0
$833$		−	40.9239i		−	1.41793i
$834$		0			0
$835$	−3.64273	−	1.50887i	−0.126062	−	0.0522166i
$836$		0			0
$837$	−26.0532	−	4.06321i	−0.900532	−	0.140445i
$838$		0			0
$839$	0.866907	−	0.866907i	0.0299290	−	0.0299290i	−0.691984	−	0.721913i	$-0.743263\pi$
$839$	0.866907	−	0.866907i	0.0299290	−	0.0299290i	0.721913	+	0.691984i	$0.243263\pi$
$840$		0			0
$841$	2.66838	+	2.66838i	0.0920131	+	0.0920131i
$842$		0			0
$843$	5.77007	+	27.0411i	0.198732	+	0.931345i
$844$		0			0
$845$	−1.94650	+	4.69927i	−0.0669617	+	0.161660i
$846$		0			0
$847$	−0.313163			−0.0107604
$848$		0			0
$849$	−5.17769	+	28.0599i	−0.177698	+	0.963014i
$850$		0			0
$851$	−50.0587	−	20.7350i	−1.71599	−	0.710786i
$852$		0			0
$853$	−9.15951	−	22.1130i	−0.313616	−	0.757135i	−0.999565	−	0.0294859i	$-0.990613\pi$
$853$	−9.15951	−	22.1130i	−0.313616	−	0.757135i	0.685950	−	0.727649i	$-0.259387\pi$
$854$		0			0
$855$	−1.99468	−	4.46116i	−0.0682167	−	0.152569i
$856$		0			0
$857$	−0.411928	−	0.411928i	−0.0140712	−	0.0140712i	0.700036	−	0.714107i	$-0.253167\pi$
$857$	−0.411928	−	0.411928i	−0.0140712	−	0.0140712i	−0.714107	+	0.700036i	$0.753167\pi$
$858$		0			0
$859$	3.20564	+	7.73910i	0.109375	+	0.264055i	0.969085	−	0.246728i	$-0.0793556\pi$
$859$	3.20564	+	7.73910i	0.109375	+	0.264055i	−0.859710	+	0.510783i	$0.829356\pi$
$860$		0			0
$861$	−8.82102	−	5.71854i	−0.300620	−	0.194887i
$862$		0			0
$863$	10.6755			0.363398			0.181699	−	0.983354i	$-0.441840\pi$
$863$	10.6755			0.363398			0.181699	+	0.983354i	$0.441840\pi$
$864$		0			0
$865$	17.2517			0.586575
$866$		0			0
$867$	−31.9450	−	20.7095i	−1.08491	−	0.703331i
$868$		0			0
$869$	12.5748	+	30.3582i	0.426570	+	1.02983i
$870$		0			0
$871$	7.08838	+	7.08838i	0.240181	+	0.240181i
$872$		0			0
$873$	5.78768	+	12.9443i	0.195883	+	0.438098i
$874$		0			0
$875$	2.13495	+	5.15423i	0.0721745	+	0.174245i
$876$		0			0
$877$	−43.9222	−	18.1932i	−1.48315	−	0.614340i	−0.513335	−	0.858188i	$-0.671590\pi$
$877$	−43.9222	−	18.1932i	−1.48315	−	0.614340i	−0.969813	+	0.243848i	$0.921590\pi$
$878$		0			0
$879$	−6.77851	+	36.7354i	−0.228633	+	1.23905i
$880$		0			0
$881$	−22.6599			−0.763432			−0.381716	−	0.924280i	$-0.624667\pi$
$881$	−22.6599			−0.763432			−0.381716	+	0.924280i	$0.624667\pi$
$882$		0			0
$883$	−12.6776	+	30.6064i	−0.426635	+	1.02999i	0.553712	+	0.832708i	$0.313211\pi$
$883$	−12.6776	+	30.6064i	−0.426635	+	1.02999i	−0.980347	+	0.197280i	$0.936789\pi$
$884$		0			0
$885$	0.953498	+	4.46851i	0.0320515	+	0.150207i
$886$		0			0
$887$	14.9337	+	14.9337i	0.501426	+	0.501426i	0.911881	−	0.410455i	$-0.134630\pi$
$887$	14.9337	+	14.9337i	0.501426	+	0.501426i	−0.410455	+	0.911881i	$0.634630\pi$
$888$		0			0
$889$	9.66557	−	9.66557i	0.324173	−	0.324173i
$890$		0			0
$891$	−27.5613	−	9.66216i	−0.923340	−	0.323695i
$892$		0			0
$893$	14.7698	+	6.11785i	0.494253	+	0.204726i
$894$		0			0
$895$		−	12.5175i		−	0.418415i
$896$		0			0
$897$	−6.89239	+	37.3525i	−0.230130	+	1.24716i
$898$		0			0
$899$	−11.1173	+	26.8396i	−0.370784	+	0.895151i
$900$		0			0
$901$	28.9167	−	11.9777i	0.963355	−	0.399035i
$902$		0			0
$903$	4.28962	+	6.23089i	0.142749	+	0.207351i
$904$		0			0
$905$	−5.49724	+	5.49724i	−0.182734	+	0.182734i
$906$		0			0
$907$	41.6421	−	17.2487i	1.38270	−	0.572735i	0.437501	−	0.899218i	$-0.355864\pi$
$907$	41.6421	−	17.2487i	1.38270	−	0.572735i	0.945203	+	0.326483i	$0.105864\pi$
$908$		0			0
$909$	−14.5969	+	15.4306i	−0.484147	+	0.511800i
$910$		0			0
$911$		−	6.84174i		−	0.226677i	−0.993556	−	0.113339i	$-0.963846\pi$
$911$		−	6.84174i		−	0.226677i	0.993556	−	0.113339i	$-0.0361545\pi$
$912$		0			0
$913$		−	12.8253i		−	0.424454i
$914$		0			0
$915$	8.18544	+	5.30651i	0.270602	+	0.175428i
$916$		0			0
$917$	0.452941	−	0.187614i	0.0149574	−	0.00619557i
$918$		0			0
$919$	5.26082	−	5.26082i	0.173538	−	0.173538i	−0.614994	−	0.788532i	$-0.710841\pi$
$919$	5.26082	−	5.26082i	0.173538	−	0.173538i	0.788532	+	0.614994i	$0.210841\pi$
$920$		0			0
$921$	4.94572	−	3.40485i	0.162967	−	0.112194i
$922$		0			0
$923$	27.4774	−	11.3815i	0.904430	−	0.374627i
$924$		0			0
$925$	10.7377	−	25.9231i	0.353054	−	0.852347i
$926$		0			0
$927$	−7.09065	+	18.5593i	−0.232888	+	0.609568i
$928$		0			0
$929$		−	49.7721i		−	1.63297i	−0.577367	−	0.816485i	$-0.695920\pi$
$929$		−	49.7721i		−	1.63297i	0.577367	−	0.816485i	$-0.304080\pi$
$930$		0			0
$931$	−10.8175	−	4.48073i	−0.354528	−	0.146850i
$932$		0			0
$933$	−2.66847	−	12.5056i	−0.0873619	−	0.409416i
$934$		0			0
$935$	13.0642	−	13.0642i	0.427245	−	0.427245i
$936$		0			0
$937$	−5.73722	−	5.73722i	−0.187427	−	0.187427i	0.607156	−	0.794583i	$-0.292310\pi$
$937$	−5.73722	−	5.73722i	−0.187427	−	0.187427i	−0.794583	+	0.607156i	$0.792310\pi$
$938$		0			0
$939$	−9.27282	+	1.97865i	−0.302607	+	0.0645708i
$940$		0			0
$941$	13.9482	−	33.6739i	0.454698	−	1.09774i	−0.515817	−	0.856699i	$-0.672512\pi$
$941$	13.9482	−	33.6739i	0.454698	−	1.09774i	0.970515	−	0.241040i	$-0.0774884\pi$
$942$		0			0
$943$	73.2157			2.38423
$944$		0			0
$945$	2.69979	+	1.64565i	0.0878241	+	0.0535330i
$946$		0			0
$947$	−31.6414	−	13.1063i	−1.02821	−	0.425898i	−0.196143	−	0.980575i	$-0.562842\pi$
$947$	−31.6414	−	13.1063i	−1.02821	−	0.425898i	−0.832066	+	0.554677i	$0.812842\pi$
$948$		0			0
$949$	0.0726628	+	0.175423i	0.00235873	+	0.00569449i
$950$		0			0
$951$	−29.0349	−	42.1746i	−0.941520	−	1.36761i
$952$		0			0
$953$	−21.8401	−	21.8401i	−0.707470	−	0.707470i	0.258532	−	0.966003i	$-0.416761\pi$
$953$	−21.8401	−	21.8401i	−0.707470	−	0.707470i	−0.966003	+	0.258532i	$0.916761\pi$
$954$		0			0
$955$	−3.38567	−	8.17374i	−0.109558	−	0.264496i
$956$		0			0
$957$	−17.5038	+	27.0001i	−0.565817	+	0.872789i
$958$		0			0
$959$	−0.862524			−0.0278524
$960$		0			0
$961$	5.24886			0.169318
$962$		0			0
$963$	2.44460	−	2.58423i	0.0787760	−	0.0832755i
$964$		0			0
$965$	7.47741	+	18.0521i	0.240706	+	0.581117i
$966$		0			0
$967$	−9.23266	−	9.23266i	−0.296902	−	0.296902i	0.542897	−	0.839799i	$-0.317327\pi$
$967$	−9.23266	−	9.23266i	−0.296902	−	0.296902i	−0.839799	+	0.542897i	$0.817327\pi$
$968$		0			0
$969$	−15.9108	+	10.9537i	−0.511130	+	0.351884i
$970$		0			0
$971$	−22.6692	−	54.7283i	−0.727490	−	1.75632i	−0.650785	−	0.759262i	$-0.725560\pi$
$971$	−22.6692	−	54.7283i	−0.727490	−	1.75632i	−0.0767050	−	0.997054i	$-0.524440\pi$
$972$		0			0
$973$	4.05215	+	1.67846i	0.129906	+	0.0538088i
$974$		0			0
$975$	−19.3432	−	3.56926i	−0.619478	−	0.114308i
$976$		0			0
$977$	−13.4367			−0.429879			−0.214940	−	0.976627i	$-0.568955\pi$
$977$	−13.4367			−0.429879			−0.214940	+	0.976627i	$0.568955\pi$
$978$		0			0
$979$	7.19022	−	17.3587i	0.229800	−	0.554787i
$980$		0			0
$981$	−0.987262	−	35.5568i	−0.0315209	−	1.13524i
$982$		0			0
$983$	18.7274	+	18.7274i	0.597311	+	0.597311i	0.939596	−	0.342285i	$-0.111201\pi$
$983$	18.7274	+	18.7274i	0.597311	+	0.597311i	−0.342285	+	0.939596i	$0.611201\pi$
$984$		0			0
$985$	−9.27444	+	9.27444i	−0.295508	+	0.295508i
$986$		0			0
$987$	−10.1158	+	2.15854i	−0.321991	+	0.0687070i
$988$		0			0
$989$	−48.6751	−	20.1619i	−1.54778	−	0.641110i
$990$		0			0
$991$		−	17.5352i		−	0.557025i	−0.960433	−	0.278513i	$-0.910159\pi$
$991$		−	17.5352i		−	0.557025i	0.960433	−	0.278513i	$-0.0898414\pi$
$992$		0			0
$993$	16.9798	+	3.13315i	0.538837	+	0.0994276i
$994$		0			0
$995$	3.33609	−	8.05404i	0.105761	−	0.255330i
$996$		0			0
$997$	−11.6639	+	4.83134i	−0.369399	+	0.153010i	−0.559658	−	0.828724i	$-0.689067\pi$
$997$	−11.6639	+	4.83134i	−0.369399	+	0.153010i	0.190258	+	0.981734i	$0.439067\pi$
$998$		0			0
$999$	−8.24571	−	33.9910i	−0.260883	−	1.07543i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	768.2.o.b.479.2		56
3.2	odd	2	inner	768.2.o.b.479.1		56
4.3	odd	2		768.2.o.a.479.13		56
8.3	odd	2		384.2.o.a.239.2		56
8.5	even	2		96.2.o.a.83.7	yes	56
12.11	even	2		768.2.o.a.479.14		56
24.5	odd	2		96.2.o.a.83.8	yes	56
24.11	even	2		384.2.o.a.239.1		56
32.5	even	8		768.2.o.a.287.14		56
32.11	odd	8		96.2.o.a.59.8	yes	56
32.21	even	8		384.2.o.a.143.1		56
32.27	odd	8	inner	768.2.o.b.287.1		56
96.5	odd	8		768.2.o.a.287.13		56
96.11	even	8		96.2.o.a.59.7	✓	56
96.53	odd	8		384.2.o.a.143.2		56
96.59	even	8	inner	768.2.o.b.287.2		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
96.2.o.a.59.7	✓	56	96.11	even	8
96.2.o.a.59.8	yes	56	32.11	odd	8
96.2.o.a.83.7	yes	56	8.5	even	2
96.2.o.a.83.8	yes	56	24.5	odd	2
384.2.o.a.143.1		56	32.21	even	8
384.2.o.a.143.2		56	96.53	odd	8
384.2.o.a.239.1		56	24.11	even	2
384.2.o.a.239.2		56	8.3	odd	2
768.2.o.a.287.13		56	96.5	odd	8
768.2.o.a.287.14		56	32.5	even	8
768.2.o.a.479.13		56	4.3	odd	2
768.2.o.a.479.14		56	12.11	even	2
768.2.o.b.287.1		56	32.27	odd	8	inner
768.2.o.b.287.2		56	96.59	even	8	inner
768.2.o.b.479.1		56	3.2	odd	2	inner
768.2.o.b.479.2		56	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 768 = 2^{8} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	768.o (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.45336 - 0.942196i) q^{3} +(-0.348970 - 0.842489i) q^{5} +(-0.471834 - 0.471834i) q^{7} +(1.22453 + 2.73871i) q^{9} +O(q^{10})\)	\(q+(-1.45336 - 0.942196i) q^{3} +(-0.348970 - 0.842489i) q^{5} +(-0.471834 - 0.471834i) q^{7} +(1.22453 + 2.73871i) q^{9} +(1.24185 + 2.99808i) q^{11} +(2.51698 + 1.04257i) q^{13} +(-0.286608 + 1.55324i) q^{15} +6.24340 q^{17} +(0.683586 - 1.65032i) q^{19} +(0.241187 + 1.13031i) q^{21} +(-5.69180 - 5.69180i) q^{23} +(2.94753 - 2.94753i) q^{25} +(0.800702 - 5.13409i) q^{27} +(-5.28905 - 2.19080i) q^{29} -5.07456i q^{31} +(1.01993 - 5.52737i) q^{33} +(-0.232859 + 0.562171i) q^{35} +(6.21892 - 2.57596i) q^{37} +(-2.67579 - 3.88672i) q^{39} +(-6.43169 + 6.43169i) q^{41} +(6.04703 - 2.50476i) q^{43} +(1.88000 - 1.98738i) q^{45} +8.94964i q^{47} -6.55474i q^{49} +(-9.07393 - 5.88250i) q^{51} +(4.63157 - 1.91846i) q^{53} +(2.09248 - 2.09248i) q^{55} +(-2.54843 + 1.75445i) q^{57} +(2.67262 - 1.10704i) q^{59} +(2.36352 - 5.70603i) q^{61} +(0.714438 - 1.86999i) q^{63} -2.48436i q^{65} +(3.39948 + 1.40811i) q^{67} +(2.90947 + 13.6350i) q^{69} +(7.71934 - 7.71934i) q^{71} +(0.0492824 + 0.0492824i) q^{73} +(-7.06098 + 1.50668i) q^{75} +(0.828653 - 2.00054i) q^{77} +10.1259 q^{79} +(-6.00103 + 6.70728i) q^{81} +(-3.65135 - 1.51244i) q^{83} +(-2.17876 - 5.25999i) q^{85} +(5.62276 + 8.16735i) q^{87} +(-4.09411 - 4.09411i) q^{89} +(-0.695680 - 1.67952i) q^{91} +(-4.78123 + 7.37518i) q^{93} -1.62893 q^{95} +4.72643 q^{97} +(-6.69018 + 7.07231i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 4 q^{3} - 8 q^{7} - 4 q^{9}+O(q^{10}) \) 56 * q + 4 * q^3 - 8 * q^7 - 4 * q^9	\( 56 q + 4 q^{3} - 8 q^{7} - 4 q^{9} + 8 q^{13} - 8 q^{15} + 8 q^{19} + 4 q^{21} - 8 q^{25} + 28 q^{27} - 8 q^{33} + 8 q^{37} - 28 q^{39} + 8 q^{43} + 4 q^{45} + 16 q^{51} + 24 q^{55} - 4 q^{57} + 40 q^{61} - 56 q^{67} + 4 q^{69} - 8 q^{73} - 16 q^{75} + 16 q^{79} + 48 q^{85} + 52 q^{87} - 40 q^{91} - 8 q^{93} - 16 q^{97} - 60 q^{99}+O(q^{100}) \) 56 * q + 4 * q^3 - 8 * q^7 - 4 * q^9 + 8 * q^13 - 8 * q^15 + 8 * q^19 + 4 * q^21 - 8 * q^25 + 28 * q^27 - 8 * q^33 + 8 * q^37 - 28 * q^39 + 8 * q^43 + 4 * q^45 + 16 * q^51 + 24 * q^55 - 4 * q^57 + 40 * q^61 - 56 * q^67 + 4 * q^69 - 8 * q^73 - 16 * q^75 + 16 * q^79 + 48 * q^85 + 52 * q^87 - 40 * q^91 - 8 * q^93 - 16 * q^97 - 60 * q^99

Introduction

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