LMFDB - Embedded newform 768.2.o.b.479.1

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			479.1
Character	$\chi$	$=$	768.479
Dual form			768.2.o.b.287.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.69392 - 0.361451i) q^{3} +(0.348970 + 0.842489i) q^{5} +(-0.471834 - 0.471834i) q^{7} +(2.73871 + 1.22453i) q^{9} +O(q^{10})$	\(q+(-1.69392 - 0.361451i) q^{3} +(0.348970 + 0.842489i) q^{5} +(-0.471834 - 0.471834i) q^{7} +(2.73871 + 1.22453i) q^{9} +(-1.24185 - 2.99808i) q^{11} +(2.51698 + 1.04257i) q^{13} +(-0.286608 - 1.55324i) q^{15} -6.24340 q^{17} +(0.683586 - 1.65032i) q^{19} +(0.628703 + 0.969793i) q^{21} +(5.69180 + 5.69180i) q^{23} +(2.94753 - 2.94753i) q^{25} +(-4.19653 - 3.06417i) q^{27} +(5.28905 + 2.19080i) q^{29} -5.07456i q^{31} +(1.01993 + 5.52737i) q^{33} +(0.232859 - 0.562171i) q^{35} +(6.21892 - 2.57596i) q^{37} +(-3.88672 - 2.67579i) q^{39} +(6.43169 - 6.43169i) q^{41} +(6.04703 - 2.50476i) q^{43} +(-0.0759298 + 2.73466i) q^{45} -8.94964i q^{47} -6.55474i q^{49} +(10.5758 + 2.25668i) q^{51} +(-4.63157 + 1.91846i) q^{53} +(2.09248 - 2.09248i) q^{55} +(-1.75445 + 2.54843i) q^{57} +(-2.67262 + 1.10704i) q^{59} +(2.36352 - 5.70603i) q^{61} +(-0.714438 - 1.86999i) q^{63} +2.48436i q^{65} +(3.39948 + 1.40811i) q^{67} +(-7.58413 - 11.6987i) q^{69} +(-7.71934 + 7.71934i) q^{71} +(0.0492824 + 0.0492824i) q^{73} +(-6.05825 + 3.92748i) q^{75} +(-0.828653 + 2.00054i) q^{77} +10.1259 q^{79} +(6.00103 + 6.70728i) q^{81} +(3.65135 + 1.51244i) q^{83} +(-2.17876 - 5.25999i) q^{85} +(-8.16735 - 5.62276i) q^{87} +(4.09411 + 4.09411i) q^{89} +(-0.695680 - 1.67952i) q^{91} +(-1.83420 + 8.59588i) q^{93} +1.62893 q^{95} +4.72643 q^{97} +(0.270204 - 9.73155i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−1.69392	−	0.361451i	−0.977983	−	0.208684i
$3$	−1.69392	−	0.361451i	−0.977983	−	0.208684i
$4$		0			0
$5$	0.348970	+	0.842489i	0.156064	+	0.376772i	0.982501	−	0.186257i	$-0.0596357\pi$
$5$	0.348970	+	0.842489i	0.156064	+	0.376772i	−0.826437	+	0.563030i	$0.809636\pi$
$6$		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
$9$	2.73871	+	1.22453i	0.912902	+	0.408178i
$10$		0			0
$11$	−1.24185	−	2.99808i	−0.374431	−	0.903956i	−0.992988	−	0.118216i	$-0.962282\pi$
$11$	−1.24185	−	2.99808i	−0.374431	−	0.903956i	0.618557	−	0.785740i	$-0.287718\pi$
$12$		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	$-0.773396\pi$
$17$	−6.24340			−1.51425			−0.757123	+	0.653272i	$0.773396\pi$
$18$		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
$21$	0.628703	+	0.969793i	0.137194	+	0.211626i
$22$		0			0
$23$	5.69180	+	5.69180i	1.18682	+	1.18682i	0.977941	+	0.208881i	$0.0669821\pi$
$23$	5.69180	+	5.69180i	1.18682	+	1.18682i	0.208881	+	0.977941i	$0.433018\pi$
$24$		0			0
$25$	2.94753	−	2.94753i	0.589505	−	0.589505i
$26$		0			0
$27$	−4.19653	−	3.06417i	−0.807623	−	0.589699i
$28$		0			0
$29$	5.28905	+	2.19080i	0.982152	+	0.406821i	0.815222	−	0.579148i	$-0.196615\pi$
$29$	5.28905	+	2.19080i	0.982152	+	0.406821i	0.166930	+	0.985969i	$0.446615\pi$
$30$		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
$39$	−3.88672	−	2.67579i	−0.622374	−	0.428469i
$40$		0			0
$41$	6.43169	−	6.43169i	1.00446	−	1.00446i	0.00447060	−	0.999990i	$-0.498577\pi$
$41$	6.43169	−	6.43169i	1.00446	−	1.00446i	0.999990	−	0.00447060i	$-0.00142304\pi$
$42$		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
$45$	−0.0759298	+	2.73466i	−0.0113189	+	0.407658i
$46$		0			0
$47$		−	8.94964i		−	1.30544i	−0.757600	−	0.652720i	$-0.773628\pi$
$47$		−	8.94964i		−	1.30544i	0.757600	−	0.652720i	$-0.226372\pi$
$48$		0			0
$49$		−	6.55474i		−	0.936392i
$50$		0			0
$51$	10.5758	+	2.25668i	1.48091	+	0.315999i
$52$		0			0
$53$	−4.63157	+	1.91846i	−0.636195	+	0.263520i	−0.677382	−	0.735631i	$-0.736886\pi$
$53$	−4.63157	+	1.91846i	−0.636195	+	0.263520i	0.0411879	+	0.999151i	$0.486886\pi$
$54$		0			0
$55$	2.09248	−	2.09248i	0.282150	−	0.282150i
$56$		0			0
$57$	−1.75445	+	2.54843i	−0.232382	+	0.337547i
$58$		0			0
$59$	−2.67262	+	1.10704i	−0.347945	+	0.144124i	−0.549810	−	0.835290i	$-0.685300\pi$
$59$	−2.67262	+	1.10704i	−0.347945	+	0.144124i	0.201865	+	0.979413i	$0.435300\pi$
$60$		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
$69$	−7.58413	−	11.6987i	−0.913022	−	1.40836i
$70$		0			0
$71$	−7.71934	+	7.71934i	−0.916117	+	0.916117i	−0.996744	−	0.0806272i	$-0.974308\pi$
$71$	−7.71934	+	7.71934i	−0.916117	+	0.916117i	0.0806272	+	0.996744i	$0.474308\pi$
$72$		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
$75$	−6.05825	+	3.92748i	−0.699546	+	0.453506i
$76$		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	0.573966	−	0.818879i	$-0.305404\pi$
$83$	3.65135	+	1.51244i	0.400787	+	0.166012i	−0.173179	+	0.984890i	$0.555404\pi$
$84$		0			0
$85$	−2.17876	−	5.25999i	−0.236320	−	0.570526i
$86$		0			0
$87$	−8.16735	−	5.62276i	−0.875632	−	0.602823i
$88$		0			0
$89$	4.09411	+	4.09411i	0.433974	+	0.433974i	0.889978	−	0.456004i	$-0.150720\pi$
$89$	4.09411	+	4.09411i	0.433974	+	0.433974i	−0.456004	+	0.889978i	$0.650720\pi$
$90$		0			0
$91$	−0.695680	−	1.67952i	−0.0729270	−	0.176061i
$92$		0			0
$93$	−1.83420	+	8.59588i	−0.190198	+	0.891351i
$94$		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
$99$	0.270204	−	9.73155i	0.0271565	−	0.978058i
$100$		0			0
$101$	−2.70950	−	6.54131i	−0.269605	−	0.650885i	0.729859	−	0.683597i	$-0.239585\pi$
$101$	−2.70950	−	6.54131i	−0.269605	−	0.650885i	−0.999465	+	0.0327124i	$0.989585\pi$
$102$		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
$105$	−0.597641	+	0.868104i	−0.0583238	+	0.0847183i
$106$		0			0
$107$	0.453771	+	1.09550i	0.0438677	+	0.105906i	0.944295	−	0.329101i	$-0.106746\pi$
$107$	0.453771	+	1.09550i	0.0438677	+	0.105906i	−0.900427	+	0.435007i	$0.856746\pi$
$108$		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	$-0.604066\pi$
$113$	−6.82755			−0.642282			−0.321141	+	0.947031i	$0.604066\pi$
$114$		0			0
$115$	−2.80901	+	6.78155i	−0.261941	+	0.632382i
$116$		0			0
$117$	5.61662	+	5.93742i	0.519257	+	0.548915i
$118$		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
$123$	−13.2195	+	8.57000i	−1.19196	+	0.772731i
$124$		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	−0.911121	−	0.412139i	$-0.864782\pi$
$131$	0.281165	−	0.678793i	0.0245655	−	0.0593064i	0.935686	+	0.352833i	$0.114782\pi$
$132$		0			0
$133$	−1.10122	+	0.456140i	−0.0954878	+	0.0395523i
$134$		0			0
$135$	1.11706	−	4.60483i	0.0961414	−	0.396321i
$136$		0			0
$137$	−0.914012	+	0.914012i	−0.0780893	+	0.0780893i	−0.745073	−	0.666983i	$-0.767585\pi$
$137$	−0.914012	+	0.914012i	−0.0780893	+	0.0780893i	0.666983	+	0.745073i	$0.267585\pi$
$138$		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
$141$	−3.23485	+	15.1599i	−0.272424	+	1.27670i
$142$		0			0
$143$		−	8.84084i		−	0.739308i
$144$		0			0
$145$			5.22049i			0.433538i
$146$		0			0
$147$	−2.36922	+	11.1032i	−0.195410	+	0.915776i
$148$		0			0
$149$	−8.36760	+	3.46597i	−0.685501	+	0.283944i	−0.698124	−	0.715977i	$-0.745982\pi$
$149$	−8.36760	+	3.46597i	−0.685501	+	0.283944i	0.0126235	+	0.999920i	$0.495982\pi$
$150$		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
$153$	−17.0988	−	7.64526i	−1.38236	−	0.618083i
$154$		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
$165$	−4.30082	+	2.78816i	−0.334819	+	0.217058i
$166$		0			0
$167$	−3.05737	+	3.05737i	−0.236587	+	0.236587i	−0.815435	−	0.578848i	$-0.803502\pi$
$167$	−3.05737	+	3.05737i	−0.236587	+	0.236587i	0.578848	+	0.815435i	$0.303502\pi$
$168$		0			0
$169$	−3.94413	−	3.94413i	−0.303395	−	0.303395i
$170$		0			0
$171$	3.89302	−	3.68268i	0.297707	−	0.281621i
$172$		0			0
$173$	7.23974	−	17.4783i	0.550427	−	1.32885i	−0.366732	−	0.930327i	$-0.619523\pi$
$173$	7.23974	−	17.4783i	0.550427	−	1.32885i	0.917159	−	0.398522i	$-0.130477\pi$
$174$		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	−0.145454	−	0.989365i	$-0.546464\pi$
$179$	−12.6819	−	5.25303i	−0.947892	−	0.392630i	−0.802438	+	0.596736i	$0.796464\pi$
$180$		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
$183$	−6.06605	+	8.81125i	−0.448415	+	0.651346i
$184$		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
$189$	0.534288	+	3.42585i	0.0388637	+	0.249194i
$190$		0			0
$191$	−9.70190			−0.702005			−0.351002	−	0.936375i	$-0.614159\pi$
$191$	−9.70190			−0.702005			−0.351002	+	0.936375i	$0.614159\pi$
$192$		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
$195$	0.897972	−	4.20829i	0.0643051	−	0.301362i
$196$		0			0
$197$	5.50419	+	13.2883i	0.392157	+	0.946751i	0.989469	+	0.144742i	$0.0462354\pi$
$197$	5.50419	+	13.2883i	0.392157	+	0.946751i	−0.597312	+	0.802009i	$0.703765\pi$
$198$		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
$201$	−5.24947	−	3.61397i	−0.370269	−	0.254909i
$202$		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
$213$	15.8661	−	10.2858i	1.08713	−	0.704768i
$214$		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
$219$	−0.0656672	−	0.101294i	−0.00443738	−	0.00684478i
$220$		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	$0.433128\pi$
$227$	−9.49912	+	22.9329i	−0.630479	+	1.52211i	−0.839022	+	0.544097i	$0.816872\pi$
$228$		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
$231$	2.12677	−	3.08924i	0.139931	−	0.203257i
$232$		0			0
$233$	−0.551118	+	0.551118i	−0.0361050	+	0.0361050i	−0.724929	−	0.688824i	$-0.758127\pi$
$233$	−0.551118	+	0.551118i	−0.0361050	+	0.0361050i	0.688824	+	0.724929i	$0.258127\pi$
$234$		0			0
$235$	7.53997	−	3.12316i	0.491854	−	0.203732i
$236$		0			0
$237$	−17.1524	−	3.66001i	−1.11417	−	0.237743i
$238$		0			0
$239$		−	1.64816i		−	0.106610i	−0.998578	−	0.0533052i	$-0.983024\pi$
$239$		−	1.64816i		−	0.106610i	0.998578	−	0.0533052i	$-0.0169756\pi$
$240$		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
$243$	−7.74089	−	13.5307i	−0.496578	−	0.867992i
$244$		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
$249$	−5.63840	−	3.88172i	−0.357319	−	0.245994i
$250$		0			0
$251$	26.5328	−	10.9903i	1.67474	−	0.693699i	0.675684	−	0.737192i	$-0.263849\pi$
$251$	26.5328	−	10.9903i	1.67474	−	0.693699i	0.999054	+	0.0434928i	$0.0138486\pi$
$252$		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	$-0.855968\pi$
$257$		−	14.0179i		−	0.874413i	0.899361	−	0.437206i	$-0.144032\pi$
$258$		0			0
$259$	−4.14972	−	1.71887i	−0.257851	−	0.106805i
$260$		0			0
$261$	11.8025	+	12.4766i	0.730554	+	0.772281i
$262$		0			0
$263$	17.6733	−	17.6733i	1.08978	−	1.08978i	0.0942329	−	0.995550i	$-0.469960\pi$
$263$	17.6733	−	17.6733i	1.08978	−	1.08978i	0.995550	−	0.0942329i	$-0.0300398\pi$
$264$		0			0
$265$	−3.23256	−	3.23256i	−0.198574	−	0.198574i
$266$		0			0
$267$	−5.45526	−	8.41489i	−0.333856	−	0.514983i
$268$		0			0
$269$	6.87589	−	16.5999i	0.419231	−	1.01211i	−0.563340	−	0.826225i	$-0.690484\pi$
$269$	6.87589	−	16.5999i	0.419231	−	1.01211i	0.982571	−	0.185887i	$-0.0595160\pi$
$270$		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
$279$	6.21397	−	13.8977i	0.372021	−	0.832035i
$280$		0			0
$281$	11.2880	+	11.2880i	0.673386	+	0.673386i	0.958495	−	0.285109i	$-0.0920299\pi$
$281$	11.2880	+	11.2880i	0.673386	+	0.673386i	−0.285109	+	0.958495i	$0.592030\pi$
$282$		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
$285$	−2.75927	−	0.588778i	−0.163445	−	0.0348762i
$286$		0			0
$287$	−6.06938			−0.358264
$288$		0			0
$289$	21.9800			1.29294
$290$		0			0
$291$	−8.00618	−	1.70837i	−0.469331	−	0.100147i
$292$		0			0
$293$	8.25342	+	19.9255i	0.482170	+	1.16406i	0.958576	+	0.284836i	$0.0919391\pi$
$293$	8.25342	+	19.9255i	0.482170	+	1.16406i	−0.476406	+	0.879225i	$0.658061\pi$
$294$		0			0
$295$	−1.86533	−	1.86533i	−0.108604	−	0.108604i
$296$		0			0
$297$	−3.97518	+	16.3868i	−0.230663	+	0.950857i
$298$		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
$309$	−6.23975	−	9.62500i	−0.354967	−	0.547547i
$310$		0			0
$311$	−5.22034	−	5.22034i	−0.296018	−	0.296018i	0.543434	−	0.839452i	$-0.317124\pi$
$311$	−5.22034	−	5.22034i	−0.296018	−	0.296018i	−0.839452	+	0.543434i	$0.817124\pi$
$312$		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
$315$	1.32613	−	1.25448i	0.0747190	−	0.0706818i
$316$		0			0
$317$	−27.3117	−	11.3129i	−1.53398	−	0.635393i	−0.553644	−	0.832753i	$-0.686763\pi$
$317$	−27.3117	−	11.3129i	−1.53398	−	0.635393i	−0.980331	+	0.197360i	$0.936763\pi$
$318$		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
$327$	16.9156	+	11.6455i	0.935436	+	0.643995i
$328$		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
$333$	20.1861	+	0.560483i	1.10619	+	0.0307143i
$334$		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
$339$	11.5653	+	2.46782i	0.628141	+	0.134034i
$340$		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
$345$	7.20942	−	10.4721i	0.388142	−	0.563796i
$346$		0			0
$347$	23.6365	−	9.79057i	1.26888	−	0.525585i	0.356253	−	0.934389i	$-0.384054\pi$
$347$	23.6365	−	9.79057i	1.26888	−	0.525585i	0.912622	+	0.408804i	$0.134054\pi$
$348$		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	$0.156184\pi$
$353$			17.7066i			0.942426i	−0.882020	+	0.471213i	$0.843816\pi$
$354$		0			0
$355$	−9.19728	−	3.80964i	−0.488141	−	0.202195i
$356$		0			0
$357$	−3.92524	−	6.05480i	−0.207746	−	0.320454i
$358$		0			0
$359$	−7.15299	+	7.15299i	−0.377520	+	0.377520i	−0.870207	−	0.492686i	$-0.836015\pi$
$359$	−7.15299	+	7.15299i	−0.377520	+	0.377520i	0.492686	+	0.870207i	$0.336015\pi$
$360$		0			0
$361$	11.1788	+	11.1788i	0.588355	+	0.588355i
$362$		0			0
$363$	−0.682088	+	0.442188i	−0.0358003	+	0.0232089i
$364$		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
$375$	−11.9279	−	8.21166i	−0.615952	−	0.424048i
$376$		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
$381$	7.40436	−	34.7001i	0.379337	−	1.77774i
$382$		0			0
$383$	−9.44734			−0.482737			−0.241368	−	0.970434i	$-0.577596\pi$
$383$	−9.44734			−0.482737			−0.241368	+	0.970434i	$0.577596\pi$
$384$		0			0
$385$	−1.97461			−0.100636
$386$		0			0
$387$	19.6282	+	0.544992i	0.997758	+	0.0277035i
$388$		0			0
$389$	−1.49354	−	3.60573i	−0.0757256	−	0.182818i	0.881484	−	0.472215i	$-0.156545\pi$
$389$	−1.49354	−	3.60573i	−0.0757256	−	0.182818i	−0.957209	+	0.289397i	$0.906545\pi$
$390$		0			0
$391$	−35.5362	−	35.5362i	−1.79714	−	1.79714i
$392$		0			0
$393$	−0.721620	+	1.04819i	−0.0364009	+	0.0528742i
$394$		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	$-0.375741\pi$
$401$	15.2403			0.761063			0.380531	+	0.924768i	$0.375741\pi$
$402$		0			0
$403$	5.29058	−	12.7726i	0.263542	−	0.636248i
$404$		0			0
$405$	−3.55663	+	7.39644i	−0.176730	+	0.367532i
$406$		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
$411$	1.87863	−	1.21789i	0.0926660	−	0.0600741i
$412$		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	$-0.689902\pi$
$419$	8.60540	−	20.7753i	0.420401	−	1.01494i	0.982229	−	0.187684i	$-0.0600982\pi$
$420$		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
$423$	10.9591	−	24.5104i	0.532852	−	1.19174i
$424$		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
$429$	−3.19553	+	14.9756i	−0.154282	+	0.723031i
$430$		0			0
$431$			6.75028i			0.325150i	0.986696	+	0.162575i	$0.0519799\pi$
$431$			6.75028i			0.325150i	−0.986696	+	0.162575i	$0.948020\pi$
$432$		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
$435$	1.88695	−	8.84307i	0.0904723	−	0.423993i
$436$		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
$441$	8.02651	−	17.9515i	0.382215	−	0.854834i
$442$		0			0
$443$	−11.4418	+	4.73933i	−0.543614	+	0.225172i	−0.637554	−	0.770406i	$-0.720054\pi$
$443$	−11.4418	+	4.73933i	−0.543614	+	0.225172i	0.0939401	+	0.995578i	$0.470054\pi$
$444$		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	$-0.766211\pi$
$449$		−	28.4023i		−	1.34039i	0.742187	−	0.670193i	$-0.233789\pi$
$450$		0			0
$451$	−27.2699	−	11.2956i	−1.28409	−	0.531887i
$452$		0			0
$453$	5.12514	−	3.32256i	0.240800	−	0.156107i
$454$		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
$459$	26.2006	+	19.1308i	1.22294	+	0.892950i
$460$		0			0
$461$	−2.67493	+	6.45785i	−0.124584	+	0.300772i	−0.973850	−	0.227194i	$-0.927045\pi$
$461$	−2.67493	+	6.45785i	−0.124584	+	0.300772i	0.849266	+	0.527965i	$0.177045\pi$
$462$		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	−0.284022	−	0.958818i	$-0.591669\pi$
$467$	−25.1292	−	10.4089i	−1.16284	−	0.481665i	−0.878821	+	0.477153i	$0.841669\pi$
$468$		0			0
$469$	−0.939596	−	2.26839i	−0.0433865	−	0.104744i
$470$		0			0
$471$	9.04360	−	13.1363i	0.416707	−	0.605289i
$472$		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
$477$	−15.0337	−	0.417422i	−0.688347	−	0.0191125i
$478$		0			0
$479$	17.4339			0.796575			0.398288	−	0.917261i	$-0.369605\pi$
$479$	17.4339			0.796575			0.398288	+	0.917261i	$0.369605\pi$
$480$		0			0
$481$	18.3385			0.836165
$482$		0			0
$483$	−1.94141	+	9.09832i	−0.0883374	+	0.413988i
$484$		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
$489$	−15.0737	−	10.3774i	−0.681657	−	0.469283i
$490$		0			0
$491$	−5.45046	−	13.1586i	−0.245976	−	0.593839i	0.751879	−	0.659301i	$-0.229148\pi$
$491$	−5.45046	−	13.1586i	−0.245976	−	0.593839i	−0.997855	+	0.0654625i	$0.979148\pi$
$492$		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
$501$	6.28402	−	4.07384i	0.280750	−	0.182006i
$502$		0			0
$503$	10.2138	+	10.2138i	0.455412	+	0.455412i	0.897146	−	0.441734i	$-0.145636\pi$
$503$	10.2138	+	10.2138i	0.455412	+	0.455412i	−0.441734	+	0.897146i	$0.645636\pi$
$504$		0			0
$505$	4.56545	−	4.56545i	0.203160	−	0.203160i
$506$		0			0
$507$	5.25542	+	8.10664i	0.233401	+	0.360028i
$508$		0			0
$509$	36.6825	+	15.1944i	1.62592	+	0.673480i	0.994766	−	0.102175i	$-0.0325803\pi$
$509$	36.6825	+	15.1944i	1.62592	+	0.673480i	0.631157	+	0.775655i	$0.282580\pi$
$510$		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
$519$	−18.5810	+	26.9899i	−0.815617	+	1.18473i
$520$		0			0
$521$	0.526260	−	0.526260i	0.0230559	−	0.0230559i	−0.695485	−	0.718541i	$-0.744810\pi$
$521$	0.526260	−	0.526260i	0.0230559	−	0.0230559i	0.718541	+	0.695485i	$0.244810\pi$
$522$		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
$525$	4.71161	+	1.00537i	0.205632	+	0.0438780i
$526$		0			0
$527$			31.6825i			1.38011i
$528$		0			0
$529$			41.7931i			1.81709i
$530$		0			0
$531$	−8.67512	−	0.240871i	−0.376468	−	0.0104529i
$532$		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
$537$	19.5834	+	13.4821i	0.845087	+	0.581795i
$538$		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
$549$	13.4602	−	12.7329i	0.574468	−	0.543429i
$550$		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
$555$	−5.78348	−	8.92118i	−0.245495	−	0.378683i
$556$		0			0
$557$	−4.26094	+	10.2868i	−0.180542	+	0.435866i	−0.988078	−	0.153951i	$-0.950800\pi$
$557$	−4.26094	+	10.2868i	−0.180542	+	0.435866i	0.807537	+	0.589817i	$0.200800\pi$
$558$		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	0.703341	−	0.710853i	$-0.251691\pi$
$563$	16.5626	+	6.86044i	0.698029	+	0.289133i	−0.00531196	+	0.999986i	$0.501691\pi$
$564$		0			0
$565$	−2.38261	−	5.75213i	−0.100237	−	0.241994i
$566$		0			0
$567$	0.333236	−	5.99622i	0.0139946	−	0.251817i
$568$		0			0
$569$	−22.0173	−	22.0173i	−0.923014	−	0.923014i	0.0742272	−	0.997241i	$-0.476351\pi$
$569$	−22.0173	−	22.0173i	−0.923014	−	0.923014i	−0.997241	+	0.0742272i	$0.976351\pi$
$570$		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
$573$	16.4342	+	3.50676i	0.686549	+	0.146497i
$574$		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
$579$	36.2957	+	7.74483i	1.50840	+	0.321864i
$580$		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
$585$	−3.04218	+	6.80392i	−0.125779	+	0.281308i
$586$		0			0
$587$	−6.34332	−	15.3141i	−0.261817	−	0.632082i	0.737234	−	0.675637i	$-0.236131\pi$
$587$	−6.34332	−	15.3141i	−0.261817	−	0.632082i	−0.999051	+	0.0435555i	$0.986131\pi$
$588$		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	$-0.646858\pi$
$593$	−21.6814			−0.890349			−0.445174	+	0.895444i	$0.646858\pi$
$594$		0			0
$595$	−1.45383	+	3.50986i	−0.0596013	+	0.143890i
$596$		0			0
$597$	−9.00722	−	13.8939i	−0.368641	−	0.568640i
$598$		0			0
$599$	17.5864	+	17.5864i	0.718559	+	0.718559i	0.968310	−	0.249751i	$-0.0803487\pi$
$599$	17.5864	+	17.5864i	0.718559	+	0.718559i	−0.249751	+	0.968310i	$0.580349\pi$
$600$		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
$603$	7.58589	+	8.01918i	0.308922	+	0.326566i
$604$		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
$615$	−11.8333	−	8.14659i	−0.477166	−	0.328502i
$616$		0			0
$617$	10.8400	−	10.8400i	0.436403	−	0.436403i	−0.454397	−	0.890799i	$-0.650145\pi$
$617$	10.8400	−	10.8400i	0.436403	−	0.436403i	0.890799	+	0.454397i	$0.150145\pi$
$618$		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
$621$	−6.44519	−	41.3264i	−0.258636	−	1.65837i
$622$		0			0
$623$		−	3.86348i		−	0.154787i
$624$		0			0
$625$		−	13.2180i		−	0.528720i
$626$		0			0
$627$	9.81915	+	2.09523i	0.392139	+	0.0836753i
$628$		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
$633$	−6.51136	+	9.45808i	−0.258803	+	0.375925i
$634$		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	$0.243431\pi$
$641$			35.0585i			1.38473i	−0.721548	+	0.692364i	$0.756569\pi$
$642$		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
$645$	−5.62363	−	8.67461i	−0.221430	−	0.341562i
$646$		0			0
$647$	−12.7202	+	12.7202i	−0.500084	+	0.500084i	−0.911464	−	0.411380i	$-0.865047\pi$
$647$	−12.7202	+	12.7202i	−0.500084	+	0.500084i	0.411380	+	0.911464i	$0.365047\pi$
$648$		0			0
$649$	6.63797	+	6.63797i	0.260563	+	0.260563i
$650$		0			0
$651$	4.92127	−	3.19039i	0.192880	−	0.125041i
$652$		0			0
$653$	−9.79087	+	23.6372i	−0.383146	+	0.924997i	0.608207	+	0.793778i	$0.291889\pi$
$653$	−9.79087	+	23.6372i	−0.383146	+	0.924997i	−0.991353	+	0.131218i	$0.958111\pi$
$654$		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	0.741884	−	0.670528i	$-0.233932\pi$
$659$	20.3402	+	8.42518i	0.792341	+	0.328198i	0.0504566	+	0.998726i	$0.483932\pi$
$660$		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
$663$	24.2664	+	16.7060i	0.942427	+	0.648808i
$664$		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
$669$	−3.18732	+	14.9372i	−0.123229	+	0.577505i
$670$		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
$675$	−21.4011	+	3.33767i	−0.823729	+	0.128467i
$676$		0			0
$677$	−1.92640	−	4.65075i	−0.0740377	−	0.178743i	0.882528	−	0.470260i	$-0.155840\pi$
$677$	−1.92640	−	4.65075i	−0.0740377	−	0.178743i	−0.956566	+	0.291517i	$0.905840\pi$
$678$		0			0
$679$	−2.23009	−	2.23009i	−0.0855831	−	0.0855831i
$680$		0			0
$681$	24.3798	−	35.4130i	0.934237	−	1.35703i
$682$		0			0
$683$	−5.29070	−	12.7729i	−0.202443	−	0.488740i	0.789754	−	0.613424i	$-0.210208\pi$
$683$	−5.29070	−	12.7729i	−0.202443	−	0.488740i	−0.992197	+	0.124684i	$0.960208\pi$
$684$		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
$693$	−4.71917	+	4.46419i	−0.179267	+	0.169581i
$694$		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
$699$	1.13275	−	0.734346i	0.0428446	−	0.0277755i
$700$		0			0
$701$	21.6433	+	8.96496i	0.817457	+	0.338602i	0.751925	−	0.659249i	$-0.229126\pi$
$701$	21.6433	+	8.96496i	0.817457	+	0.338602i	0.0655321	+	0.997850i	$0.479126\pi$
$702$		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
$711$	27.7318	+	12.3995i	1.04002	+	0.465017i
$712$		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
$717$	−0.595728	+	2.79184i	−0.0222479	+	0.104263i
$718$		0			0
$719$		−	50.4878i		−	1.88288i	−0.337182	−	0.941439i	$-0.609474\pi$
$719$		−	50.4878i		−	1.88288i	0.337182	−	0.941439i	$-0.390526\pi$
$720$		0			0
$721$		−	4.41907i		−	0.164575i
$722$		0			0
$723$	−6.64053	+	31.1204i	−0.246964	+	1.15738i
$724$		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
$729$	8.22175	+	25.7178i	0.304509	+	0.952509i
$730$		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
$741$	−7.07283	+	4.58522i	−0.259827	+	0.168442i
$742$		0			0
$743$	−7.22016	+	7.22016i	−0.264882	+	0.264882i	−0.827034	−	0.562152i	$-0.809974\pi$
$743$	−7.22016	+	7.22016i	−0.264882	+	0.264882i	0.562152	+	0.827034i	$0.309974\pi$
$744$		0			0
$745$	−5.84009	−	5.84009i	−0.213964	−	0.213964i
$746$		0			0
$747$	8.14793	+	8.61332i	0.298117	+	0.315145i
$748$		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
$759$	−25.6555	+	37.2659i	−0.931234	+	1.35267i
$760$		0			0
$761$	−8.55374	−	8.55374i	−0.310073	−	0.310073i	0.534865	−	0.844938i	$-0.320363\pi$
$761$	−8.55374	−	8.55374i	−0.310073	−	0.310073i	−0.844938	+	0.534865i	$0.820363\pi$
$762$		0			0
$763$	3.02770	+	7.30953i	0.109610	+	0.264623i
$764$		0			0
$765$	0.474060	−	17.0735i	0.0171397	−	0.617295i
$766$		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
$771$	−5.06678	+	23.7452i	−0.182476	+	0.855161i
$772$		0			0
$773$	−13.4148	−	32.3861i	−0.482496	−	1.16485i	−0.958420	−	0.285361i	$-0.907886\pi$
$773$	−13.4148	−	32.3861i	−0.482496	−	1.16485i	0.475924	−	0.879486i	$-0.342114\pi$
$774$		0			0
$775$	−14.9574	−	14.9574i	−0.537286	−	0.537286i
$776$		0			0
$777$	6.40800	+	4.41155i	0.229886	+	0.158263i
$778$		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
$789$	−36.3251	+	23.5491i	−1.29321	+	0.838370i
$790$		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
$795$	4.30727	+	6.64409i	0.152763	+	0.235642i
$796$		0			0
$797$	−23.8387	−	9.87430i	−0.844409	−	0.349766i	−0.0818184	−	0.996647i	$-0.526073\pi$
$797$	−23.8387	−	9.87430i	−0.844409	−	0.349766i	−0.762590	+	0.646882i	$0.776073\pi$
$798$		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
$807$	−17.6472	+	25.6335i	−0.621212	+	0.902342i
$808$		0			0
$809$	4.78786	−	4.78786i	0.168332	−	0.168332i	−0.617914	−	0.786246i	$-0.712022\pi$
$809$	4.78786	−	4.78786i	0.168332	−	0.168332i	0.786246	+	0.617914i	$0.212022\pi$
$810$		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
$813$	0.127538	+	0.0272144i	0.00447297	+	0.000954450i
$814$		0			0
$815$			9.63498i			0.337499i
$816$		0			0
$817$		−	11.6918i		−	0.409044i
$818$		0			0
$819$	0.151368	−	5.45159i	0.00528921	−	0.190494i
$820$		0			0
$821$	14.6537	−	6.06977i	0.511418	−	0.211836i	−0.112025	−	0.993705i	$-0.535734\pi$
$821$	14.6537	−	6.06977i	0.511418	−	0.211836i	0.623443	+	0.781869i	$0.285734\pi$
$822$		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
$825$	19.2983	+	13.2858i	0.671881	+	0.462553i
$826$		0			0
$827$	26.7003	−	11.0596i	0.928461	−	0.384581i	0.133366	−	0.991067i	$-0.457421\pi$
$827$	26.7003	−	11.0596i	0.928461	−	0.384581i	0.795094	+	0.606486i	$0.207421\pi$
$828$		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
$837$	−15.5493	+	21.2955i	−0.537462	+	0.736082i
$838$		0			0
$839$	−0.866907	+	0.866907i	−0.0299290	+	0.0299290i	−0.721913	−	0.691984i	$-0.756737\pi$
$839$	−0.866907	+	0.866907i	−0.0299290	+	0.0299290i	0.691984	+	0.721913i	$0.256737\pi$
$840$		0			0
$841$	2.66838	+	2.66838i	0.0920131	+	0.0920131i
$842$		0			0
$843$	−15.0409	−	23.2010i	−0.518035	−	0.799085i
$844$		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
$855$	4.46116	+	1.99468i	0.152569	+	0.0682167i
$856$		0			0
$857$	0.411928	+	0.411928i	0.0140712	+	0.0140712i	0.714107	−	0.700036i	$-0.246833\pi$
$857$	0.411928	+	0.411928i	0.0140712	+	0.0140712i	−0.700036	+	0.714107i	$0.746833\pi$
$858$		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
$861$	10.2810	+	2.19378i	0.350376	+	0.0747639i
$862$		0			0
$863$	−10.6755			−0.363398			−0.181699	−	0.983354i	$-0.558160\pi$
$863$	−10.6755			−0.363398			−0.181699	+	0.983354i	$0.558160\pi$
$864$		0			0
$865$	17.2517			0.586575
$866$		0			0
$867$	−37.2323	−	7.94470i	−1.26448	−	0.269816i
$868$		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
$873$	12.9443	+	5.78768i	0.438098	+	0.195883i
$874$		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	$-0.375333\pi$
$881$	22.6599			0.763432			0.381716	+	0.924280i	$0.375333\pi$
$882$		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
$885$	2.48549	+	3.83394i	0.0835488	+	0.128876i
$886$		0			0
$887$	−14.9337	−	14.9337i	−0.501426	−	0.501426i	0.410455	−	0.911881i	$-0.365370\pi$
$887$	−14.9337	−	14.9337i	−0.501426	−	0.501426i	−0.911881	+	0.410455i	$0.865370\pi$
$888$		0			0
$889$	9.66557	−	9.66557i	0.324173	−	0.324173i
$890$		0			0
$891$	12.6566	−	26.3210i	0.424013	−	0.881787i
$892$		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
$903$	6.23089	+	4.28962i	0.207351	+	0.142749i
$904$		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
$909$	0.589539	−	21.2326i	0.0195538	−	0.704241i
$910$		0			0
$911$			6.84174i			0.226677i	0.993556	+	0.113339i	$0.0361545\pi$
$911$			6.84174i			0.226677i	−0.993556	+	0.113339i	$0.963846\pi$
$912$		0			0
$913$		−	12.8253i		−	0.424454i
$914$		0			0
$915$	−9.54025	−	2.03571i	−0.315391	−	0.0672986i
$916$		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
$921$	3.40485	−	4.94572i	0.112194	−	0.162967i
$922$		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	$0.304080\pi$
$929$			49.7721i			1.63297i	−0.577367	+	0.816485i	$0.695920\pi$
$930$		0			0
$931$	−10.8175	−	4.48073i	−0.354528	−	0.146850i
$932$		0			0
$933$	6.95593	+	10.7297i	0.227727	+	0.351275i
$934$		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
$939$	−7.95599	+	5.15776i	−0.259634	+	0.168317i
$940$		0			0
$941$	−13.9482	+	33.6739i	−0.454698	+	1.09774i	0.515817	+	0.856699i	$0.327488\pi$
$941$	−13.9482	+	33.6739i	−0.454698	+	1.09774i	−0.970515	+	0.241040i	$0.922512\pi$
$942$		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	0.832066	−	0.554677i	$-0.187158\pi$
$947$	31.6414	+	13.1063i	1.02821	+	0.425898i	0.196143	+	0.980575i	$0.437158\pi$
$948$		0			0
$949$	0.0726628	+	0.175423i	0.00235873	+	0.00569449i
$950$		0			0
$951$	42.1746	+	29.0349i	1.36761	+	0.941520i
$952$		0			0
$953$	21.8401	+	21.8401i	0.707470	+	0.707470i	0.966003	−	0.258532i	$-0.0832388\pi$
$953$	21.8401	+	21.8401i	0.707470	+	0.707470i	−0.258532	+	0.966003i	$0.583239\pi$
$954$		0			0
$955$	−3.38567	−	8.17374i	−0.109558	−	0.264496i
$956$		0			0
$957$	−6.71491	+	31.4690i	−0.217062	+	1.01725i
$958$		0			0
$959$	0.862524			0.0278524
$960$		0			0
$961$	5.24886			0.169318
$962$		0			0
$963$	−0.0987326	+	3.55592i	−0.00318162	+	0.114588i
$964$		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
$969$	10.9537	−	15.9108i	0.351884	−	0.511130i
$970$		0			0
$971$	22.6692	+	54.7283i	0.727490	+	1.75632i	0.650785	+	0.759262i	$0.274440\pi$
$971$	22.6692	+	54.7283i	0.727490	+	1.75632i	0.0767050	+	0.997054i	$0.475560\pi$
$972$		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	$-0.431045\pi$
$977$	13.4367			0.429879			0.214940	+	0.976627i	$0.431045\pi$
$978$		0			0
$979$	7.19022	−	17.3587i	0.229800	−	0.554787i
$980$		0			0
$981$	−24.4444	−	25.8406i	−0.780449	−	0.825026i
$982$		0			0
$983$	−18.7274	−	18.7274i	−0.597311	−	0.597311i	0.342285	−	0.939596i	$-0.388799\pi$
$983$	−18.7274	−	18.7274i	−0.597311	−	0.597311i	−0.939596	+	0.342285i	$0.888799\pi$
$984$		0			0
$985$	−9.27444	+	9.27444i	−0.295508	+	0.295508i
$986$		0			0
$987$	8.67930	−	5.62667i	0.276265	−	0.179099i
$988$		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
$999$	−33.9910	−	8.24571i	−1.07543	−	0.260883i

Twists

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

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

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)

\(f(q)\)	\(=\)	\(q+(-1.69392 - 0.361451i) q^{3} +(0.348970 + 0.842489i) q^{5} +(-0.471834 - 0.471834i) q^{7} +(2.73871 + 1.22453i) q^{9} +O(q^{10})\)	\(q+(-1.69392 - 0.361451i) q^{3} +(0.348970 + 0.842489i) q^{5} +(-0.471834 - 0.471834i) q^{7} +(2.73871 + 1.22453i) q^{9} +(-1.24185 - 2.99808i) q^{11} +(2.51698 + 1.04257i) q^{13} +(-0.286608 - 1.55324i) q^{15} -6.24340 q^{17} +(0.683586 - 1.65032i) q^{19} +(0.628703 + 0.969793i) q^{21} +(5.69180 + 5.69180i) q^{23} +(2.94753 - 2.94753i) q^{25} +(-4.19653 - 3.06417i) q^{27} +(5.28905 + 2.19080i) q^{29} -5.07456i q^{31} +(1.01993 + 5.52737i) q^{33} +(0.232859 - 0.562171i) q^{35} +(6.21892 - 2.57596i) q^{37} +(-3.88672 - 2.67579i) q^{39} +(6.43169 - 6.43169i) q^{41} +(6.04703 - 2.50476i) q^{43} +(-0.0759298 + 2.73466i) q^{45} -8.94964i q^{47} -6.55474i q^{49} +(10.5758 + 2.25668i) q^{51} +(-4.63157 + 1.91846i) q^{53} +(2.09248 - 2.09248i) q^{55} +(-1.75445 + 2.54843i) q^{57} +(-2.67262 + 1.10704i) q^{59} +(2.36352 - 5.70603i) q^{61} +(-0.714438 - 1.86999i) q^{63} +2.48436i q^{65} +(3.39948 + 1.40811i) q^{67} +(-7.58413 - 11.6987i) q^{69} +(-7.71934 + 7.71934i) q^{71} +(0.0492824 + 0.0492824i) q^{73} +(-6.05825 + 3.92748i) q^{75} +(-0.828653 + 2.00054i) q^{77} +10.1259 q^{79} +(6.00103 + 6.70728i) q^{81} +(3.65135 + 1.51244i) q^{83} +(-2.17876 - 5.25999i) q^{85} +(-8.16735 - 5.62276i) q^{87} +(4.09411 + 4.09411i) q^{89} +(-0.695680 - 1.67952i) q^{91} +(-1.83420 + 8.59588i) q^{93} +1.62893 q^{95} +4.72643 q^{97} +(0.270204 - 9.73155i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 4 q^{3} - 8 q^{7} - 4 q^{9}+O(q^{10}) \) 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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