LMFDB - Embedded newform 864.2.w.b.323.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [864,2,Mod(107,864)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(864, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 5, 4]))

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

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

chi := DirichletCharacter("864.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 864 = 2^{5} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	864.w (of order $8$, degree $4$, 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:	$6.89907473464$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$32$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			323.5
Character	$\chi$	$=$	864.323
Dual form			864.2.w.b.107.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.31642 + 0.516757i) q^{2} +(1.46592 - 1.36054i) q^{4} +(-2.69312 + 1.11553i) q^{5} +(0.0380585 + 0.0380585i) q^{7} +(-1.22670 + 2.54857i) q^{8} +O(q^{10})$	\(q+(-1.31642 + 0.516757i) q^{2} +(1.46592 - 1.36054i) q^{4} +(-2.69312 + 1.11553i) q^{5} +(0.0380585 + 0.0380585i) q^{7} +(-1.22670 + 2.54857i) q^{8} +(2.96882 - 2.86019i) q^{10} +(3.03924 - 1.25889i) q^{11} +(0.123691 - 0.298617i) q^{13} +(-0.0697680 - 0.0304340i) q^{14} +(0.297865 - 3.98889i) q^{16} -7.46409 q^{17} +(-1.56625 - 0.648761i) q^{19} +(-2.43019 + 5.29937i) q^{20} +(-3.35037 + 3.22778i) q^{22} +(2.75950 + 2.75950i) q^{23} +(2.47295 - 2.47295i) q^{25} +(-0.00851708 + 0.457023i) q^{26} +(0.107571 + 0.00401077i) q^{28} +(3.05231 - 7.36893i) q^{29} +0.333789i q^{31} +(1.66917 + 5.40498i) q^{32} +(9.82588 - 3.85712i) q^{34} +(-0.144951 - 0.0600408i) q^{35} +(0.638002 + 1.54027i) q^{37} +(2.39709 + 0.0446722i) q^{38} +(0.460662 - 8.23201i) q^{40} +(5.89478 - 5.89478i) q^{41} +(-1.45562 - 3.51419i) q^{43} +(2.74252 - 5.98045i) q^{44} +(-5.05866 - 2.20667i) q^{46} -6.87578i q^{47} -6.99710i q^{49} +(-1.97753 + 4.53336i) q^{50} +(-0.224958 - 0.606036i) q^{52} +(1.19539 + 2.88592i) q^{53} +(-6.78070 + 6.78070i) q^{55} +(-0.143681 + 0.0503082i) q^{56} +(-0.210175 + 11.2779i) q^{58} +(-4.07833 - 9.84595i) q^{59} +(11.3722 + 4.71053i) q^{61} +(-0.172488 - 0.439407i) q^{62} +(-4.99040 - 6.25267i) q^{64} +0.942191i q^{65} +(4.24516 - 10.2487i) q^{67} +(-10.9418 + 10.1552i) q^{68} +(0.221843 + 0.00413427i) q^{70} +(-3.99793 + 3.99793i) q^{71} +(-8.16699 - 8.16699i) q^{73} +(-1.63583 - 1.69795i) q^{74} +(-3.17867 + 1.17991i) q^{76} +(0.163580 + 0.0677572i) q^{77} -4.13365 q^{79} +(3.64753 + 11.0748i) q^{80} +(-4.71383 + 10.8062i) q^{82} +(2.38218 - 5.75109i) q^{83} +(20.1017 - 8.32638i) q^{85} +(3.73219 + 3.87394i) q^{86} +(-0.519866 + 9.29000i) q^{88} +(-7.59808 - 7.59808i) q^{89} +(0.0160724 - 0.00665741i) q^{91} +(7.79964 + 0.290809i) q^{92} +(3.55311 + 9.05142i) q^{94} +4.94180 q^{95} +6.88547 q^{97} +(3.61580 + 9.21113i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q+O(q^{10}) $ 128 * q	$ 128 q + 8 q^{10} + 32 q^{16} - 32 q^{22} + 64 q^{40} + 64 q^{46} + 40 q^{52} + 64 q^{55} + 64 q^{58} + 32 q^{61} + 96 q^{64} - 64 q^{67} - 48 q^{70} - 32 q^{76} - 32 q^{79} + 40 q^{82} + 40 q^{88} - 48 q^{91} + 72 q^{94}+O(q^{100}) $ 128 * q + 8 * q^10 + 32 * q^16 - 32 * q^22 + 64 * q^40 + 64 * q^46 + 40 * q^52 + 64 * q^55 + 64 * q^58 + 32 * q^61 + 96 * q^64 - 64 * q^67 - 48 * q^70 - 32 * q^76 - 32 * q^79 + 40 * q^82 + 40 * q^88 - 48 * q^91 + 72 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/864\mathbb{Z}\right)^\times$.

$n$	$325$	$353$	$703$
$\chi(n)$	$e\left(\frac{3}{8}\right)$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−1.31642	+	0.516757i	−0.930850	+	0.365403i
$2$	−1.31642	+	0.516757i	−0.930850	+	0.365403i
$3$		0			0
$3$		0			0
$4$	1.46592	−	1.36054i	0.732962	−	0.680270i
$5$	−2.69312	+	1.11553i	−1.20440	+	0.498878i	−0.892418	−	0.451210i	$-0.850993\pi$
$5$	−2.69312	+	1.11553i	−1.20440	+	0.498878i	−0.311981	+	0.950088i	$0.600993\pi$
$6$		0			0
$7$	0.0380585	+	0.0380585i	0.0143848	+	0.0143848i	0.714263	−	0.699878i	$-0.246762\pi$
$7$	0.0380585	+	0.0380585i	0.0143848	+	0.0143848i	−0.699878	+	0.714263i	$0.746762\pi$
$8$	−1.22670	+	2.54857i	−0.433705	+	0.901055i
$9$		0			0
$10$	2.96882	−	2.86019i	0.938823	−	0.904471i
$11$	3.03924	−	1.25889i	0.916365	−	0.379571i	0.125875	−	0.992046i	$-0.459826\pi$
$11$	3.03924	−	1.25889i	0.916365	−	0.379571i	0.790490	+	0.612475i	$0.209826\pi$
$12$		0			0
$13$	0.123691	−	0.298617i	0.0343057	−	0.0828214i	−0.905798	−	0.423710i	$-0.860728\pi$
$13$	0.123691	−	0.298617i	0.0343057	−	0.0828214i	0.940104	+	0.340888i	$0.110728\pi$
$14$	−0.0697680	−	0.0304340i	−0.0186463	−	0.00813382i
$15$		0			0
$16$	0.297865	−	3.98889i	0.0744663	−	0.997224i
$17$	−7.46409			−1.81031			−0.905154	−	0.425085i	$-0.860244\pi$
$17$	−7.46409			−1.81031			−0.905154	+	0.425085i	$0.860244\pi$
$18$		0			0
$19$	−1.56625	−	0.648761i	−0.359322	−	0.148836i	0.195717	−	0.980660i	$-0.437297\pi$
$19$	−1.56625	−	0.648761i	−0.359322	−	0.148836i	−0.555039	+	0.831824i	$0.687297\pi$
$20$	−2.43019	+	5.29937i	−0.543407	+	1.18498i
$21$		0			0
$22$	−3.35037	+	3.22778i	−0.714302	+	0.688166i
$23$	2.75950	+	2.75950i	0.575397	+	0.575397i	0.933631	−	0.358235i	$-0.116621\pi$
$23$	2.75950	+	2.75950i	0.575397	+	0.575397i	−0.358235	+	0.933631i	$0.616621\pi$
$24$		0			0
$25$	2.47295	−	2.47295i	0.494591	−	0.494591i
$26$	−0.00851708	+	0.457023i	−0.00167034	+	0.0896297i
$27$		0			0
$28$	0.107571	+	0.00401077i	0.0203290	+	0.000757965i
$29$	3.05231	−	7.36893i	0.566800	−	1.36838i	−0.337438	−	0.941348i	$-0.609560\pi$
$29$	3.05231	−	7.36893i	0.566800	−	1.36838i	0.904238	−	0.427029i	$-0.140440\pi$
$30$		0			0
$31$			0.333789i			0.0599503i	0.999551	+	0.0299752i	$0.00954282\pi$
$31$			0.333789i			0.0599503i	−0.999551	+	0.0299752i	$0.990457\pi$
$32$	1.66917	+	5.40498i	0.295071	+	0.955475i
$33$		0			0
$34$	9.82588	−	3.85712i	1.68512	−	0.661491i
$35$	−0.144951	−	0.0600408i	−0.0245012	−	0.0101487i
$36$		0			0
$37$	0.638002	+	1.54027i	0.104887	+	0.253219i	0.967606	−	0.252463i	$-0.0812407\pi$
$37$	0.638002	+	1.54027i	0.104887	+	0.253219i	−0.862720	+	0.505683i	$0.831241\pi$
$38$	2.39709	+	0.0446722i	0.388860	+	0.00724678i
$39$		0			0
$40$	0.460662	−	8.23201i	0.0728370	−	1.30160i
$41$	5.89478	−	5.89478i	0.920610	−	0.920610i	−0.0764629	−	0.997072i	$-0.524363\pi$
$41$	5.89478	−	5.89478i	0.920610	−	0.920610i	0.997072	+	0.0764629i	$0.0243627\pi$
$42$		0			0
$43$	−1.45562	−	3.51419i	−0.221981	−	0.535908i	0.773178	−	0.634189i	$-0.218666\pi$
$43$	−1.45562	−	3.51419i	−0.221981	−	0.535908i	−0.995159	+	0.0982803i	$0.968666\pi$
$44$	2.74252	−	5.98045i	0.413450	−	0.901586i
$45$		0			0
$46$	−5.05866	−	2.20667i	−0.745859	−	0.325356i
$47$		−	6.87578i		−	1.00294i	−0.865176	−	0.501468i	$-0.832794\pi$
$47$		−	6.87578i		−	1.00294i	0.865176	−	0.501468i	$-0.167206\pi$
$48$		0			0
$49$		−	6.99710i		−	0.999586i
$50$	−1.97753	+	4.53336i	−0.279665	+	0.641114i
$51$		0			0
$52$	−0.224958	−	0.606036i	−0.0311961	−	0.0840421i
$53$	1.19539	+	2.88592i	0.164199	+	0.396411i	0.984467	−	0.175567i	$-0.0561760\pi$
$53$	1.19539	+	2.88592i	0.164199	+	0.396411i	−0.820268	+	0.571979i	$0.806176\pi$
$54$		0			0
$55$	−6.78070	+	6.78070i	−0.914310	+	0.914310i
$56$	−0.143681	+	0.0503082i	−0.0192002	+	0.00672272i
$57$		0			0
$58$	−0.210175	+	11.2779i	−0.0275973	+	1.48086i
$59$	−4.07833	−	9.84595i	−0.530953	−	1.28183i	−0.930893	−	0.365292i	$-0.880969\pi$
$59$	−4.07833	−	9.84595i	−0.530953	−	1.28183i	0.399940	−	0.916541i	$-0.369031\pi$
$60$		0			0
$61$	11.3722	+	4.71053i	1.45606	+	0.603121i	0.963633	−	0.267231i	$-0.0861085\pi$
$61$	11.3722	+	4.71053i	1.45606	+	0.603121i	0.492431	+	0.870352i	$0.336109\pi$
$62$	−0.172488	−	0.439407i	−0.0219060	−	0.0558048i
$63$		0			0
$64$	−4.99040	−	6.25267i	−0.623800	−	0.781584i
$65$			0.942191i			0.116864i
$66$		0			0
$67$	4.24516	−	10.2487i	0.518629	−	1.25208i	−0.420117	−	0.907470i	$-0.638011\pi$
$67$	4.24516	−	10.2487i	0.518629	−	1.25208i	0.938746	−	0.344610i	$-0.111989\pi$
$68$	−10.9418	+	10.1552i	−1.32689	+	1.23150i
$69$		0			0
$70$	0.221843	+	0.00413427i	0.0265153	+	0.000494139i
$71$	−3.99793	+	3.99793i	−0.474467	+	0.474467i	−0.903357	−	0.428890i	$-0.858905\pi$
$71$	−3.99793	+	3.99793i	−0.474467	+	0.474467i	0.428890	+	0.903357i	$0.358905\pi$
$72$		0			0
$73$	−8.16699	−	8.16699i	−0.955874	−	0.955874i	0.0431930	−	0.999067i	$-0.486247\pi$
$73$	−8.16699	−	8.16699i	−0.955874	−	0.955874i	−0.999067	+	0.0431930i	$0.986247\pi$
$74$	−1.63583	−	1.69795i	−0.190161	−	0.197383i
$75$		0			0
$76$	−3.17867	+	1.17991i	−0.364618	+	0.135345i
$77$	0.163580	+	0.0677572i	0.0186417	+	0.00772165i
$78$		0			0
$79$	−4.13365			−0.465072			−0.232536	−	0.972588i	$-0.574702\pi$
$79$	−4.13365			−0.465072			−0.232536	+	0.972588i	$0.574702\pi$
$80$	3.64753	+	11.0748i	0.407806	+	1.23820i
$81$		0			0
$82$	−4.71383	+	10.8062i	−0.520556	+	1.19334i
$83$	2.38218	−	5.75109i	0.261478	−	0.631264i	−0.737552	−	0.675290i	$-0.764018\pi$
$83$	2.38218	−	5.75109i	0.261478	−	0.631264i	0.999030	+	0.0440260i	$0.0140184\pi$
$84$		0			0
$85$	20.1017	−	8.32638i	2.18033	−	0.903123i
$86$	3.73219	+	3.87394i	0.402453	+	0.417738i
$87$		0			0
$88$	−0.519866	+	9.29000i	−0.0554179	+	0.990317i
$89$	−7.59808	−	7.59808i	−0.805395	−	0.805395i	0.178538	−	0.983933i	$-0.442863\pi$
$89$	−7.59808	−	7.59808i	−0.805395	−	0.805395i	−0.983933	+	0.178538i	$0.942863\pi$
$90$		0			0
$91$	0.0160724	−	0.00665741i	0.00168485	−	0.000697886i
$92$	7.79964	+	0.290809i	0.813169	+	0.0303189i
$93$		0			0
$94$	3.55311	+	9.05142i	0.366475	+	0.933582i
$95$	4.94180			0.507018
$96$		0			0
$97$	6.88547			0.699114			0.349557	−	0.936915i	$-0.386332\pi$
$97$	6.88547			0.699114			0.349557	+	0.936915i	$0.386332\pi$
$98$	3.61580	+	9.21113i	0.365251	+	0.930464i
$99$		0			0
$100$	0.260611	−	6.98971i	0.0260611	−	0.698971i
$101$	16.3819	−	6.78560i	1.63006	−	0.675192i	0.634820	−	0.772660i	$-0.281074\pi$
$101$	16.3819	−	6.78560i	1.63006	−	0.675192i	0.995239	+	0.0974674i	$0.0310742\pi$
$102$		0			0
$103$	−4.17517	−	4.17517i	−0.411392	−	0.411392i	0.470831	−	0.882223i	$-0.343954\pi$
$103$	−4.17517	−	4.17517i	−0.411392	−	0.411392i	−0.882223	+	0.470831i	$0.843954\pi$
$104$	0.609313	+	0.681549i	0.0597481	+	0.0668314i
$105$		0			0
$106$	−3.06495	−	3.18136i	−0.297694	−	0.309001i
$107$	13.5990	−	5.63288i	1.31466	−	0.544551i	0.388421	−	0.921482i	$-0.373020\pi$
$107$	13.5990	−	5.63288i	1.31466	−	0.544551i	0.926242	+	0.376931i	$0.123020\pi$
$108$		0			0
$109$	0.712579	−	1.72032i	0.0682527	−	0.164777i	−0.886072	−	0.463547i	$-0.846577\pi$
$109$	0.712579	−	1.72032i	0.0682527	−	0.164777i	0.954325	+	0.298771i	$0.0965765\pi$
$110$	5.42227	−	12.4302i	0.516994	−	1.18518i
$111$		0			0
$112$	0.163148	−	0.140475i	0.0154160	−	0.0132736i
$113$	−5.29938			−0.498523			−0.249262	−	0.968436i	$-0.580188\pi$
$113$	−5.29938			−0.498523			−0.249262	+	0.968436i	$0.580188\pi$
$114$		0			0
$115$	−10.5100	−	4.35337i	−0.980060	−	0.405954i
$116$	−5.55127	−	14.9551i	−0.515422	−	1.38854i
$117$		0			0
$118$	10.4568	+	10.8539i	0.962623	+	0.999183i
$119$	−0.284072	−	0.284072i	−0.0260408	−	0.0260408i
$120$		0			0
$121$	−0.126014	+	0.126014i	−0.0114559	+	0.0114559i
$122$	−17.4048	−	0.324356i	−1.57576	−	0.0293658i
$123$		0			0
$124$	0.454134	+	0.489310i	0.0407824	+	0.0439413i
$125$	1.67632	−	4.04699i	0.149934	−	0.361974i
$126$		0			0
$127$			9.98032i			0.885610i	0.896618	+	0.442805i	$0.146017\pi$
$127$			9.98032i			0.885610i	−0.896618	+	0.442805i	$0.853983\pi$
$128$	9.80058	+	5.65232i	0.866257	+	0.499599i
$129$		0			0
$130$	−0.486884	−	1.24032i	−0.0427026	−	0.108783i
$131$	−15.0414	−	6.23037i	−1.31418	−	0.544350i	−0.388076	−	0.921627i	$-0.626860\pi$
$131$	−15.0414	−	6.23037i	−1.31418	−	0.544350i	−0.926100	+	0.377278i	$0.876860\pi$
$132$		0			0
$133$	−0.0349182	−	0.0842999i	−0.00302779	−	0.00730973i
$134$	−0.292312	+	15.6853i	−0.0252519	+	1.35501i
$135$		0			0
$136$	9.15622	−	19.0227i	0.785139	−	1.63119i
$137$	3.83745	−	3.83745i	0.327855	−	0.327855i	−0.523915	−	0.851770i	$-0.675529\pi$
$137$	3.83745	−	3.83745i	0.327855	−	0.327855i	0.851770	+	0.523915i	$0.175529\pi$
$138$		0			0
$139$	5.86851	+	14.1678i	0.497761	+	1.20170i	0.950687	+	0.310153i	$0.100380\pi$
$139$	5.86851	+	14.1678i	0.497761	+	1.20170i	−0.452926	+	0.891548i	$0.649620\pi$
$140$	−0.294175	+	0.109197i	−0.0248624	+	0.00922880i
$141$		0			0
$142$	3.19700	−	7.32891i	0.268286	−	0.615029i
$143$		−	1.06328i		−	0.0889161i
$144$		0			0
$145$			23.2503i			1.93084i
$146$	14.9715	+	6.53084i	1.23905	+	0.540496i
$147$		0			0
$148$	3.03087	+	1.38990i	0.249136	+	0.114249i
$149$	3.69293	+	8.91553i	0.302537	+	0.730388i	0.999906	+	0.0136768i	$0.00435359\pi$
$149$	3.69293	+	8.91553i	0.302537	+	0.730388i	−0.697370	+	0.716712i	$0.745646\pi$
$150$		0			0
$151$	−13.0693	+	13.0693i	−1.06356	+	1.06356i	−0.0657253	+	0.997838i	$0.520936\pi$
$151$	−13.0693	+	13.0693i	−1.06356	+	1.06356i	−0.997838	+	0.0657253i	$0.979064\pi$
$152$	3.57473	−	3.19585i	0.289949	−	0.259218i
$153$		0			0
$154$	−0.250355	−	0.00466560i	−0.0201742	−	0.000375965i
$155$	−0.372351	−	0.898934i	−0.0299079	−	0.0722041i
$156$		0			0
$157$	−10.4553	−	4.33071i	−0.834421	−	0.345628i	−0.0757694	−	0.997125i	$-0.524141\pi$
$157$	−10.4553	−	4.33071i	−0.834421	−	0.345628i	−0.758651	+	0.651497i	$0.774141\pi$
$158$	5.44161	−	2.13609i	0.432912	−	0.169938i
$159$		0			0
$160$	−10.5247	−	12.6943i	−0.832049	−	1.00357i
$161$			0.210045i			0.0165539i
$162$		0			0
$163$	−5.67045	+	13.6897i	−0.444144	+	1.07226i	0.530337	+	0.847787i	$0.322065\pi$
$163$	−5.67045	+	13.6897i	−0.444144	+	1.07226i	−0.974481	+	0.224471i	$0.927935\pi$
$164$	0.621218	−	16.6614i	0.0485090	−	1.30103i
$165$		0			0
$166$	−0.164031	+	8.80186i	−0.0127313	+	0.683157i
$167$	−17.9456	+	17.9456i	−1.38867	+	1.38867i	−0.560543	+	0.828125i	$0.689408\pi$
$167$	−17.9456	+	17.9456i	−1.38867	+	1.38867i	−0.828125	+	0.560543i	$0.810592\pi$
$168$		0			0
$169$	9.11852	+	9.11852i	0.701424	+	0.701424i
$170$	−22.1595	+	21.3487i	−1.69956	+	1.63737i
$171$		0			0
$172$	−6.91502	−	3.17110i	−0.527266	−	0.241794i
$173$	7.13683	+	2.95617i	0.542603	+	0.224754i	0.637113	−	0.770770i	$-0.280128\pi$
$173$	7.13683	+	2.95617i	0.542603	+	0.224754i	−0.0945098	+	0.995524i	$0.530128\pi$
$174$		0			0
$175$	0.188234			0.0142291
$176$	−4.11631	−	12.4982i	−0.310279	−	0.942086i
$177$		0			0
$178$	13.9286	+	6.07590i	1.04399	+	0.455408i
$179$	5.22075	−	12.6040i	0.390217	−	0.942067i	−0.599675	−	0.800244i	$-0.704703\pi$
$179$	5.22075	−	12.6040i	0.390217	−	0.942067i	0.989892	−	0.141823i	$-0.0452965\pi$
$180$		0			0
$181$	−0.940530	+	0.389580i	−0.0699091	+	0.0289573i	−0.417364	−	0.908739i	$-0.637046\pi$
$181$	−0.940530	+	0.389580i	−0.0699091	+	0.0289573i	0.347455	+	0.937697i	$0.387046\pi$
$182$	−0.0177178	+	0.0170695i	−0.00131333	+	0.00126527i
$183$		0			0
$184$	−10.4179	+	3.64769i	−0.768016	+	0.268912i
$185$	−3.43643	−	3.43643i	−0.252651	−	0.252651i
$186$		0			0
$187$	−22.6851	+	9.39650i	−1.65890	+	0.687140i
$188$	−9.35477	−	10.0794i	−0.682267	−	0.735114i
$189$		0			0
$190$	−6.50549	+	2.55371i	−0.471958	+	0.185266i
$191$	−5.85056			−0.423331			−0.211666	−	0.977342i	$-0.567889\pi$
$191$	−5.85056			−0.423331			−0.211666	+	0.977342i	$0.567889\pi$
$192$		0			0
$193$	12.9601			0.932891			0.466445	−	0.884550i	$-0.345534\pi$
$193$	12.9601			0.932891			0.466445	+	0.884550i	$0.345534\pi$
$194$	−9.06418	+	3.55812i	−0.650770	+	0.255458i
$195$		0			0
$196$	−9.51983	−	10.2572i	−0.679988	−	0.732659i
$197$	13.5069	−	5.59474i	0.962326	−	0.398609i	0.154476	−	0.987997i	$-0.450631\pi$
$197$	13.5069	−	5.59474i	0.962326	−	0.398609i	0.807850	+	0.589388i	$0.200631\pi$
$198$		0			0
$199$	−18.7847	−	18.7847i	−1.33161	−	1.33161i	−0.903929	−	0.427682i	$-0.859330\pi$
$199$	−18.7847	−	18.7847i	−1.33161	−	1.33161i	−0.427682	−	0.903929i	$-0.640670\pi$
$200$	3.26891	+	9.33607i	0.231147	+	0.660160i
$201$		0			0
$202$	−18.0589	+	17.3982i	−1.27062	+	1.22413i
$203$	0.396617	−	0.164284i	0.0278370	−	0.0115305i
$204$		0			0
$205$	−9.29955	+	22.4511i	−0.649509	+	1.56805i
$206$	7.65383	+	3.33873i	0.533268	+	0.232620i
$207$		0			0
$208$	−1.15431	−	0.582338i	−0.0800368	−	0.0403779i
$209$	−5.57692			−0.385764
$210$		0			0
$211$	−2.35533	−	0.975608i	−0.162147	−	0.0671636i	0.300133	−	0.953897i	$-0.402969\pi$
$211$	−2.35533	−	0.975608i	−0.162147	−	0.0671636i	−0.462281	+	0.886734i	$0.652969\pi$
$212$	5.67875	+	2.60417i	0.390018	+	0.178855i
$213$		0			0
$214$	−14.9911	+	14.4426i	−1.02477	+	0.987277i
$215$	7.84033	+	7.84033i	0.534706	+	0.534706i
$216$		0			0
$217$	−0.0127035	+	0.0127035i	−0.000862371	+	0.000862371i
$218$	−0.0490665	+	2.63289i	−0.00332320	+	0.178322i
$219$		0			0
$220$	−0.714580	+	19.1654i	−0.0481770	+	1.29213i
$221$	−0.923241	+	2.22890i	−0.0621039	+	0.149932i
$222$		0			0
$223$		−	9.95599i		−	0.666702i	−0.942803	−	0.333351i	$-0.891821\pi$
$223$		−	9.95599i		−	0.666702i	0.942803	−	0.333351i	$-0.108179\pi$
$224$	−0.142179	+	0.269232i	−0.00949975	+	0.0179888i
$225$		0			0
$226$	6.97621	−	2.73849i	0.464050	−	0.182162i
$227$	−19.2809	−	7.98641i	−1.27972	−	0.530077i	−0.363814	−	0.931472i	$-0.618525\pi$
$227$	−19.2809	−	7.98641i	−1.27972	−	0.530077i	−0.915905	+	0.401395i	$0.868525\pi$
$228$		0			0
$229$	−7.43755	−	17.9558i	−0.491487	−	1.18655i	−0.953963	−	0.299923i	$-0.903039\pi$
$229$	−7.43755	−	17.9558i	−0.491487	−	1.18655i	0.462476	−	0.886632i	$-0.346961\pi$
$230$	16.0852	+	0.299763i	1.06063	+	0.0197658i
$231$		0			0
$232$	15.0360	+	16.8185i	0.987158	+	1.10419i
$233$	−17.0409	+	17.0409i	−1.11639	+	1.11639i	−0.124121	+	0.992267i	$0.539611\pi$
$233$	−17.0409	+	17.0409i	−1.11639	+	1.11639i	−0.992267	+	0.124121i	$0.960389\pi$
$234$		0			0
$235$	7.67011	+	18.5173i	0.500343	+	1.20793i
$236$	−19.3743	−	8.88469i	−1.26116	−	0.578344i
$237$		0			0
$238$	0.520754	+	0.227162i	0.0337555	+	0.0147247i
$239$			12.8506i			0.831236i	0.909539	+	0.415618i	$0.136435\pi$
$239$			12.8506i			0.831236i	−0.909539	+	0.415618i	$0.863565\pi$
$240$		0			0
$241$		−	16.8642i		−	1.08632i	−0.839630	−	0.543159i	$-0.817228\pi$
$241$		−	16.8642i		−	1.08632i	0.839630	−	0.543159i	$-0.182772\pi$
$242$	0.100769	−	0.231007i	0.00647768	−	0.0148497i
$243$		0			0
$244$	23.0797	−	8.56708i	1.47752	−	0.548451i
$245$	7.80545	+	18.8440i	0.498672	+	1.20390i
$246$		0			0
$247$	−0.387462	+	0.387462i	−0.0246536	+	0.0246536i
$248$	−0.850685	−	0.409460i	−0.0540186	−	0.0260008i
$249$		0			0
$250$	−0.115427	+	6.19379i	−0.00730027	+	0.391730i
$251$	9.26264	+	22.3620i	0.584653	+	1.41148i	0.888553	+	0.458773i	$0.151711\pi$
$251$	9.26264	+	22.3620i	0.584653	+	1.41148i	−0.303901	+	0.952704i	$0.598289\pi$
$252$		0			0
$253$	11.8607	+	4.91287i	0.745677	+	0.308870i
$254$	−5.15740	−	13.1383i	−0.323604	−	0.824370i
$255$		0			0
$256$	−15.8226	−	2.37631i	−0.988910	−	0.148519i
$257$			7.94127i			0.495363i	0.968842	+	0.247681i	$0.0796686\pi$
$257$			7.94127i			0.495363i	−0.968842	+	0.247681i	$0.920331\pi$
$258$		0			0
$259$	−0.0343391	+	0.0829019i	−0.00213373	+	0.00515127i
$260$	1.28189	+	1.38118i	0.0794993	+	0.0856572i
$261$		0			0
$262$	23.0204	+	0.429008i	1.42221	+	0.0265042i
$263$	−9.04114	+	9.04114i	−0.557500	+	0.557500i	−0.928595	−	0.371095i	$-0.878983\pi$
$263$	−9.04114	+	9.04114i	−0.557500	+	0.557500i	0.371095	+	0.928595i	$0.378983\pi$
$264$		0			0
$265$	−6.43863	−	6.43863i	−0.395522	−	0.395522i
$266$	0.0895296	+	0.0929299i	0.00548941	+	0.00569790i
$267$		0			0
$268$	−7.72071	−	20.7995i	−0.471617	−	1.27053i
$269$	−11.8206	−	4.89625i	−0.720714	−	0.298530i	−0.00798417	−	0.999968i	$-0.502541\pi$
$269$	−11.8206	−	4.89625i	−0.720714	−	0.298530i	−0.712730	+	0.701439i	$0.752541\pi$
$270$		0			0
$271$	13.2128			0.802619			0.401310	−	0.915942i	$-0.368555\pi$
$271$	13.2128			0.802619			0.401310	+	0.915942i	$0.368555\pi$
$272$	−2.22329	+	29.7735i	−0.134807	+	1.80528i
$273$		0			0
$274$	−3.06866	+	7.03472i	−0.185385	+	0.424983i
$275$	4.40271	−	10.6291i	0.265493	−	0.640958i
$276$		0			0
$277$	3.35478	−	1.38959i	0.201569	−	0.0834926i	−0.279615	−	0.960112i	$-0.590207\pi$
$277$	3.35478	−	1.38959i	0.201569	−	0.0834926i	0.481184	+	0.876620i	$0.340207\pi$
$278$	−15.0468	−	15.6182i	−0.902445	−	0.936720i
$279$		0			0
$280$	0.330830	−	0.295766i	0.0197709	−	0.0176754i
$281$	0.768569	+	0.768569i	0.0458490	+	0.0458490i	0.729660	−	0.683811i	$-0.239679\pi$
$281$	0.768569	+	0.768569i	0.0458490	+	0.0458490i	−0.683811	+	0.729660i	$0.739679\pi$
$282$		0			0
$283$	−6.72644	+	2.78618i	−0.399845	+	0.165621i	−0.573539	−	0.819178i	$-0.694430\pi$
$283$	−6.72644	+	2.78618i	−0.399845	+	0.165621i	0.173694	+	0.984800i	$0.444430\pi$
$284$	−0.421320	+	11.3000i	−0.0250007	+	0.670532i
$285$		0			0
$286$	0.549459	+	1.39973i	0.0324902	+	0.0827675i
$287$	0.448693			0.0264855
$288$		0			0
$289$	38.7126			2.27721
$290$	−12.0148	−	30.6072i	−0.705532	−	1.79732i
$291$		0			0
$292$	−23.0837	−	0.860673i	−1.35087	−	0.0503671i
$293$	−0.940387	+	0.389521i	−0.0549380	+	0.0227561i	−0.409983	−	0.912093i	$-0.634465\pi$
$293$	−0.940387	+	0.389521i	−0.0549380	+	0.0227561i	0.355045	+	0.934849i	$0.384465\pi$
$294$		0			0
$295$	21.9668	+	21.9668i	1.27896	+	1.27896i
$296$	−4.70813	−	0.263466i	−0.273655	−	0.0153136i
$297$		0			0
$298$	−9.46861	−	9.82823i	−0.548502	−	0.569334i
$299$	1.16536	−	0.482708i	0.0673946	−	0.0279157i
$300$		0			0
$301$	0.0783458	−	0.189143i	0.00451578	−	0.0109020i
$302$	10.4510	−	23.9583i	0.601389	−	1.37865i
$303$		0			0
$304$	−3.05437	+	6.05436i	−0.175180	+	0.347241i
$305$	−35.8814			−2.05457
$306$		0			0
$307$	−25.7094	−	10.6492i	−1.46731	−	0.607780i	−0.501067	−	0.865409i	$-0.667059\pi$
$307$	−25.7094	−	10.6492i	−1.46731	−	0.607780i	−0.966244	+	0.257628i	$0.917059\pi$
$308$	0.331983	−	0.123231i	0.0189165	−	0.00702172i
$309$		0			0
$310$	0.954701	+	0.990960i	0.0542234	+	0.0562828i
$311$	11.5849	+	11.5849i	0.656919	+	0.656919i	0.954650	−	0.297731i	$-0.0962297\pi$
$311$	11.5849	+	11.5849i	0.656919	+	0.656919i	−0.297731	+	0.954650i	$0.596230\pi$
$312$		0			0
$313$	2.58789	−	2.58789i	0.146276	−	0.146276i	−0.630176	−	0.776452i	$-0.717017\pi$
$313$	2.58789	−	2.58789i	0.146276	−	0.146276i	0.776452	+	0.630176i	$0.217017\pi$
$314$	16.0014	+	0.298203i	0.903013	+	0.0168285i
$315$		0			0
$316$	−6.05961	+	5.62399i	−0.340880	+	0.316374i
$317$	−3.26479	+	7.88190i	−0.183369	+	0.442692i	−0.988657	−	0.150192i	$-0.952011\pi$
$317$	−3.26479	+	7.88190i	−0.183369	+	0.442692i	0.805288	+	0.592884i	$0.202011\pi$
$318$		0			0
$319$		−	26.2385i		−	1.46907i
$320$	20.4148	+	11.2723i	1.14122	+	0.630139i
$321$		0			0
$322$	−0.108542	−	0.276508i	−0.00604883	−	0.0154092i
$323$	11.6906	+	4.84241i	0.650483	+	0.269439i
$324$		0			0
$325$	−0.432583	−	1.04435i	−0.0239954	−	0.0579300i
$326$	0.390454	−	20.9516i	0.0216252	−	1.16040i
$327$		0			0
$328$	7.79210	+	22.2544i	0.430247	+	1.22879i
$329$	0.261682	−	0.261682i	0.0144270	−	0.0144270i
$330$		0			0
$331$	−0.602296	−	1.45407i	−0.0331052	−	0.0799230i	0.906462	−	0.422287i	$-0.138772\pi$
$331$	−0.602296	−	1.45407i	−0.0331052	−	0.0799230i	−0.939567	+	0.342364i	$0.888772\pi$
$332$	−4.33249	−	11.6717i	−0.237776	−	0.640568i
$333$		0			0
$334$	14.3504	−	32.8974i	0.785218	−	1.80006i
$335$			32.3366i			1.76674i
$336$		0			0
$337$			24.7531i			1.34839i	0.738554	+	0.674194i	$0.235509\pi$
$337$			24.7531i			1.34839i	−0.738554	+	0.674194i	$0.764491\pi$
$338$	−16.7159	−	7.29174i	−0.909223	−	0.396618i
$339$		0			0
$340$	18.1391	−	39.5550i	0.983733	−	2.14517i
$341$	0.420205	+	1.01447i	0.0227554	+	0.0549364i
$342$		0			0
$343$	0.532709	−	0.532709i	0.0287636	−	0.0287636i
$344$	10.7418	+	0.601107i	0.579157	+	0.0324095i
$345$		0			0
$346$	−10.9227	−	0.203555i	−0.587208	−	0.0109432i
$347$	−8.64929	−	20.8812i	−0.464318	−	1.12096i	−0.966607	−	0.256263i	$-0.917509\pi$
$347$	−8.64929	−	20.8812i	−0.464318	−	1.12096i	0.502289	−	0.864700i	$-0.332491\pi$
$348$		0			0
$349$	−33.3789	−	13.8260i	−1.78673	−	0.740089i	−0.990905	−	0.134566i	$-0.957036\pi$
$349$	−33.3789	−	13.8260i	−1.78673	−	0.740089i	−0.795828	−	0.605523i	$-0.792964\pi$
$350$	−0.247795	+	0.0972712i	−0.0132452	+	0.00519936i
$351$		0			0
$352$	11.8773	+	14.3257i	0.633063	+	0.763564i
$353$		−	10.5734i		−	0.562766i	−0.959596	−	0.281383i	$-0.909207\pi$
$353$		−	10.5734i		−	0.562766i	0.959596	−	0.281383i	$-0.0907931\pi$
$354$		0			0
$355$	6.30710	−	15.2267i	0.334746	−	0.808149i
$356$	−21.4757	−	0.800719i	−1.13821	−	0.0424380i
$357$		0			0
$358$	−0.359488	+	19.2900i	−0.0189995	+	1.01951i
$359$	22.9956	−	22.9956i	1.21366	−	1.21366i	0.243851	−	0.969813i	$-0.421589\pi$
$359$	22.9956	−	22.9956i	1.21366	−	1.21366i	0.969813	−	0.243851i	$-0.0784107\pi$
$360$		0			0
$361$	−11.4028	−	11.4028i	−0.600147	−	0.600147i
$362$	1.03681	−	0.998877i	0.0544938	−	0.0524998i
$363$		0			0
$364$	0.0145033	−	0.0316264i	0.000760177	−	0.00165767i
$365$	31.1052	+	12.8842i	1.62812	+	0.674389i
$366$		0			0
$367$	32.8908			1.71688			0.858442	−	0.512911i	$-0.171433\pi$
$367$	32.8908			1.71688			0.858442	+	0.512911i	$0.171433\pi$
$368$	11.8293	−	10.1854i	0.616647	−	0.530951i
$369$		0			0
$370$	6.29959	+	2.74799i	0.327500	+	0.142861i
$371$	−0.0643391	+	0.155328i	−0.00334032	+	0.00806424i
$372$		0			0
$373$	20.2662	−	8.39454i	1.04934	−	0.434653i	0.209687	−	0.977769i	$-0.432756\pi$
$373$	20.2662	−	8.39454i	1.04934	−	0.434653i	0.839658	+	0.543116i	$0.182756\pi$
$374$	25.0075	−	24.0925i	1.29311	−	1.24579i
$375$		0			0
$376$	17.5234	+	8.43454i	0.903700	+	0.434978i
$377$	−1.82294	−	1.82294i	−0.0938864	−	0.0938864i
$378$		0			0
$379$	9.65208	−	3.99802i	0.495794	−	0.205365i	−0.120753	−	0.992683i	$-0.538531\pi$
$379$	9.65208	−	3.99802i	0.495794	−	0.205365i	0.616547	+	0.787318i	$0.288531\pi$
$380$	7.24431	−	6.72352i	0.371625	−	0.344909i
$381$		0			0
$382$	7.70179	−	3.02332i	0.394058	−	0.154686i
$383$	−5.69346			−0.290922			−0.145461	−	0.989364i	$-0.546467\pi$
$383$	−5.69346			−0.290922			−0.145461	+	0.989364i	$0.546467\pi$
$384$		0			0
$385$	−0.516126			−0.0263042
$386$	−17.0610	+	6.69724i	−0.868381	+	0.340881i
$387$		0			0
$388$	10.0936	−	9.36796i	0.512424	−	0.475586i
$389$	1.64478	−	0.681292i	0.0833939	−	0.0345429i	−0.340597	−	0.940210i	$-0.610629\pi$
$389$	1.64478	−	0.681292i	0.0833939	−	0.0345429i	0.423990	+	0.905667i	$0.360629\pi$
$390$		0			0
$391$	−20.5972	−	20.5972i	−1.04164	−	1.04164i
$392$	17.8326	+	8.58337i	0.900682	+	0.433525i
$393$		0			0
$394$	−14.8896	+	14.3448i	−0.750128	+	0.722681i
$395$	11.1324	−	4.61119i	0.560132	−	0.232014i
$396$		0			0
$397$	3.91018	−	9.44001i	0.196246	−	0.473781i	−0.794870	−	0.606780i	$-0.792461\pi$
$397$	3.91018	−	9.44001i	0.196246	−	0.473781i	0.991116	+	0.133000i	$0.0424609\pi$
$398$	34.4357	+	15.0214i	1.72610	+	0.752955i
$399$		0			0
$400$	−9.12774	−	10.6010i	−0.456387	−	0.530048i
$401$	7.70571			0.384805			0.192402	−	0.981316i	$-0.438372\pi$
$401$	7.70571			0.384805			0.192402	+	0.981316i	$0.438372\pi$
$402$		0			0
$403$	0.0996751	+	0.0412868i	0.00496517	+	0.00205664i
$404$	14.7825	−	32.2354i	0.735458	−	1.60377i
$405$		0			0
$406$	−0.437219	+	0.421222i	−0.0216988	+	0.0209049i
$407$	3.87808	+	3.87808i	0.192229	+	0.192229i
$408$		0			0
$409$	12.8680	−	12.8680i	0.636282	−	0.636282i	−0.313354	−	0.949636i	$-0.601453\pi$
$409$	12.8680	−	12.8680i	0.636282	−	0.636282i	0.949636	+	0.313354i	$0.101453\pi$
$410$	0.640345	−	34.3607i	0.0316244	−	1.69695i
$411$		0			0
$412$	−11.8010	−	0.439998i	−0.581392	−	0.0216772i
$413$	0.219507	−	0.529937i	0.0108012	−	0.0260765i
$414$		0			0
$415$			18.1457i			0.890740i
$416$	1.82048	+	0.170105i	0.0892564	+	0.00834009i
$417$		0			0
$418$	7.34158	−	2.88192i	0.359088	−	0.140959i
$419$	31.6113	+	13.0938i	1.54432	+	0.639676i	0.982277	−	0.187435i	$-0.0600174\pi$
$419$	31.6113	+	13.0938i	1.54432	+	0.639676i	0.562038	+	0.827111i	$0.310017\pi$
$420$		0			0
$421$	−5.19481	−	12.5414i	−0.253179	−	0.611229i	0.745278	−	0.666754i	$-0.232317\pi$
$421$	−5.19481	−	12.5414i	−0.253179	−	0.611229i	−0.998457	+	0.0555247i	$0.982317\pi$
$422$	3.60475	+	0.0671781i	0.175477	+	0.00327018i
$423$		0			0
$424$	−8.82134	−	0.493640i	−0.428402	−	0.0239733i
$425$	−18.4583	+	18.4583i	−0.895361	+	0.895361i
$426$		0			0
$427$	0.253534	+	0.612085i	0.0122694	+	0.0296209i
$428$	12.2713	−	26.7593i	0.593156	−	1.29346i
$429$		0			0
$430$	−14.3727	−	6.26962i	−0.693114	−	0.302348i
$431$			35.4019i			1.70525i	0.522522	+	0.852626i	$0.324991\pi$
$431$			35.4019i			1.70525i	−0.522522	+	0.852626i	$0.675009\pi$
$432$		0			0
$433$			7.21929i			0.346937i	0.984839	+	0.173468i	$0.0554975\pi$
$433$			7.21929i			0.346937i	−0.984839	+	0.173468i	$0.944503\pi$
$434$	0.0101585	−	0.0232878i	0.000487625	−	0.00111785i
$435$		0			0
$436$	−1.29597	−	3.49135i	−0.0620659	−	0.167205i
$437$	−2.53181	−	6.11233i	−0.121113	−	0.292392i
$438$		0			0
$439$	−1.03963	+	1.03963i	−0.0496186	+	0.0496186i	−0.731481	−	0.681862i	$-0.761170\pi$
$439$	−1.03963	+	1.03963i	−0.0496186	+	0.0496186i	0.681862	+	0.731481i	$0.261170\pi$
$440$	−8.96317	−	25.5990i	−0.427303	−	1.22038i
$441$		0			0
$442$	0.0635722	−	3.41126i	0.00302382	−	0.162257i
$443$	−8.01237	−	19.3436i	−0.380679	−	0.919041i	−0.991835	−	0.127530i	$-0.959295\pi$
$443$	−8.01237	−	19.3436i	−0.380679	−	0.919041i	0.611156	−	0.791510i	$-0.290705\pi$
$444$		0			0
$445$	28.9384	+	11.9867i	1.37181	+	0.568223i
$446$	5.14483	+	13.1063i	0.243615	+	0.620599i
$447$		0			0
$448$	0.0480402	−	0.427894i	0.00226968	−	0.0202161i
$449$		−	14.3125i		−	0.675447i	−0.941245	−	0.337724i	$-0.890343\pi$
$449$		−	14.3125i		−	0.675447i	0.941245	−	0.337724i	$-0.109657\pi$
$450$		0			0
$451$	10.4947	−	25.3365i	0.494178	−	1.19305i
$452$	−7.76848	+	7.21001i	−0.365399	+	0.339130i
$453$		0			0
$454$	29.5088	+	0.549926i	1.38492	+	0.0258093i
$455$	−0.0358584	+	0.0358584i	−0.00168107	+	0.00168107i
$456$		0			0
$457$	−22.1556	−	22.1556i	−1.03640	−	1.03640i	−0.999312	−	0.0370849i	$-0.988193\pi$
$457$	−22.1556	−	22.1556i	−1.03640	−	1.03640i	−0.0370849	−	0.999312i	$-0.511807\pi$
$458$	19.0697	+	19.7940i	0.891071	+	0.924913i
$459$		0			0
$460$	−21.3298	+	7.91752i	−0.994505	+	0.369156i
$461$	24.7969	+	10.2712i	1.15490	+	0.478377i	0.876175	−	0.481993i	$-0.160087\pi$
$461$	24.7969	+	10.2712i	1.15490	+	0.478377i	0.278729	+	0.960370i	$0.410087\pi$
$462$		0			0
$463$	19.0735			0.886421			0.443210	−	0.896418i	$-0.353839\pi$
$463$	19.0735			0.886421			0.443210	+	0.896418i	$0.353839\pi$
$464$	−28.4847	−	14.3703i	−1.32237	−	0.667124i
$465$		0			0
$466$	13.6270	−	31.2390i	0.631258	−	1.44712i
$467$	−2.25504	+	5.44416i	−0.104351	+	0.251926i	−0.967428	−	0.253147i	$-0.918534\pi$
$467$	−2.25504	+	5.44416i	−0.104351	+	0.251926i	0.863077	+	0.505073i	$0.168534\pi$
$468$		0			0
$469$	0.551615	−	0.228486i	0.0254712	−	0.0105505i
$470$	−19.6660	−	20.4129i	−0.907127	−	0.941579i
$471$		0			0
$472$	30.0960	+	1.68416i	1.38528	+	0.0775199i
$473$	−8.84798	−	8.84798i	−0.406830	−	0.406830i
$474$		0			0
$475$	−5.47762	+	2.26890i	−0.251330	+	0.104104i
$476$	−0.802919	−	0.0299368i	−0.0368017	−	0.00137215i
$477$		0			0
$478$	−6.64064	−	16.9168i	−0.303736	−	0.773756i
$479$	−33.8588			−1.54705			−0.773524	−	0.633767i	$-0.781508\pi$
$479$	−33.8588			−1.54705			−0.773524	+	0.633767i	$0.781508\pi$
$480$		0			0
$481$	0.538867			0.0245702
$482$	8.71470	+	22.2004i	0.396944	+	1.01120i
$483$		0			0
$484$	−0.0132800	+	0.356175i	−0.000603634	+	0.0161898i
$485$	−18.5434	+	7.68093i	−0.842012	+	0.348773i
$486$		0			0
$487$	−15.2646	−	15.2646i	−0.691706	−	0.691706i	0.270901	−	0.962607i	$-0.412678\pi$
$487$	−15.2646	−	15.2646i	−0.691706	−	0.691706i	−0.962607	+	0.270901i	$0.912678\pi$
$488$	−25.9554	+	23.2045i	−1.17495	+	1.05042i
$489$		0			0
$490$	−20.0130	−	20.7731i	−0.904097	−	0.938434i
$491$	−9.18067	+	3.80276i	−0.414318	+	0.171616i	−0.580098	−	0.814547i	$-0.696986\pi$
$491$	−9.18067	+	3.80276i	−0.414318	+	0.171616i	0.165780	+	0.986163i	$0.446986\pi$
$492$		0			0
$493$	−22.7827	+	55.0024i	−1.02608	+	2.47718i
$494$	0.309839	−	0.710287i	0.0139403	−	0.0319573i
$495$		0			0
$496$	1.33145	+	0.0994242i	0.0597839	+	0.00446428i
$497$	−0.304310			−0.0136502
$498$		0			0
$499$	17.2082	+	7.12787i	0.770344	+	0.319087i	0.733012	−	0.680216i	$-0.238114\pi$
$499$	17.2082	+	7.12787i	0.770344	+	0.319087i	0.0373325	+	0.999303i	$0.488114\pi$
$500$	−3.04874	−	8.21328i	−0.136344	−	0.367309i
$501$		0			0
$502$	−23.7493	−	24.6512i	−1.05998	−	1.10024i
$503$	17.1384	+	17.1384i	0.764165	+	0.764165i	0.977072	−	0.212908i	$-0.0682933\pi$
$503$	17.1384	+	17.1384i	0.764165	+	0.764165i	−0.212908	+	0.977072i	$0.568293\pi$
$504$		0			0
$505$	−36.5488	+	36.5488i	−1.62640	+	1.62640i
$506$	−18.1525	−	0.338289i	−0.806975	−	0.0150388i
$507$		0			0
$508$	13.5786	+	14.6304i	0.602454	+	0.649119i
$509$	0.667909	−	1.61248i	0.0296046	−	0.0714717i	−0.908386	−	0.418133i	$-0.862685\pi$
$509$	0.667909	−	1.61248i	0.0296046	−	0.0714717i	0.937990	+	0.346661i	$0.112685\pi$
$510$		0			0
$511$		−	0.621646i		−	0.0275000i
$512$	22.0571	−	5.04820i	0.974795	−	0.223101i
$513$		0			0
$514$	−4.10371	−	10.4540i	−0.181007	−	0.461108i
$515$	15.9017	+	6.58672i	0.700715	+	0.290246i
$516$		0			0
$517$	−8.65588	−	20.8971i	−0.380685	−	0.919055i
$518$	0.00236451	−	0.126879i	0.000103891	−	0.00557473i
$519$		0			0
$520$	−2.40124	−	1.15579i	−0.105301	−	0.0506847i
$521$	−25.3672	+	25.3672i	−1.11136	+	1.11136i	−0.118389	+	0.992967i	$0.537773\pi$
$521$	−25.3672	+	25.3672i	−1.11136	+	1.11136i	−0.992967	+	0.118389i	$0.962227\pi$
$522$		0			0
$523$	15.8330	+	38.2243i	0.692329	+	1.67143i	0.740035	+	0.672569i	$0.234809\pi$
$523$	15.8330	+	38.2243i	0.692329	+	1.67143i	−0.0477056	+	0.998861i	$0.515191\pi$
$524$	−30.5263	+	11.3312i	−1.33355	+	0.495007i
$525$		0			0
$526$	7.22986	−	16.5740i	0.315237	−	0.722661i
$527$		−	2.49143i		−	0.108529i
$528$		0			0
$529$		−	7.77026i		−	0.337838i
$530$	11.8032	+	5.14874i	0.512696	+	0.223647i
$531$		0			0
$532$	−0.165881	−	0.0760697i	−0.00719184	−	0.00329804i
$533$	−1.03115	−	2.48941i	−0.0446640	−	0.107828i
$534$		0			0
$535$	−30.3400	+	30.3400i	−1.31171	+	1.31171i
$536$	20.9120	+	23.3912i	0.903261	+	1.01035i
$537$		0			0
$538$	18.0910	+	0.337144i	0.779960	+	0.0145353i
$539$	−8.80861	−	21.2659i	−0.379414	−	0.915986i
$540$		0			0
$541$	−31.7054	−	13.1328i	−1.36312	−	0.564623i	−0.423207	−	0.906033i	$-0.639096\pi$
$541$	−31.7054	−	13.1328i	−1.36312	−	0.564623i	−0.939914	+	0.341410i	$0.889096\pi$
$542$	−17.3936	+	6.82780i	−0.747118	+	0.293279i
$543$		0			0
$544$	−12.4589	−	40.3433i	−0.534169	−	1.72970i
$545$			5.42792i			0.232506i
$546$		0			0
$547$	12.9620	−	31.2932i	0.554217	−	1.33800i	−0.360068	−	0.932926i	$-0.617246\pi$
$547$	12.9620	−	31.2932i	0.554217	−	1.33800i	0.914285	−	0.405072i	$-0.132754\pi$
$548$	0.404407	−	10.8464i	0.0172754	−	0.463336i
$549$		0			0
$550$	−0.303160	+	16.2675i	−0.0129268	+	0.693647i
$551$	−9.56136	+	9.56136i	−0.407328	+	0.407328i
$552$		0			0
$553$	−0.157320	−	0.157320i	−0.00668994	−	0.00668994i
$554$	−3.69821	+	3.56290i	−0.157122	+	0.151373i
$555$		0			0
$556$	27.8787	+	12.7846i	1.18232	+	0.542189i
$557$	−6.94857	−	2.87819i	−0.294420	−	0.121953i	0.230584	−	0.973052i	$-0.425936\pi$
$557$	−6.94857	−	2.87819i	−0.294420	−	0.121953i	−0.525004	+	0.851100i	$0.675936\pi$
$558$		0			0
$559$	−1.22944			−0.0519999
$560$	−0.282672	+	0.560311i	−0.0119451	+	0.0236775i
$561$		0			0
$562$	−1.40892	−	0.614596i	−0.0594319	−	0.0259252i
$563$	−5.36452	+	12.9511i	−0.226087	+	0.545823i	−0.995695	−	0.0926943i	$-0.970452\pi$
$563$	−5.36452	+	12.9511i	−0.226087	+	0.545823i	0.769607	+	0.638518i	$0.220452\pi$
$564$		0			0
$565$	14.2718	−	5.91159i	0.600421	−	0.248703i
$566$	7.41504	−	7.14372i	0.311677	−	0.300273i
$567$		0			0
$568$	−5.28472	−	15.0933i	−0.221742	−	0.633300i
$569$	4.87882	+	4.87882i	0.204531	+	0.204531i	0.801938	−	0.597407i	$-0.203802\pi$
$569$	4.87882	+	4.87882i	0.204531	+	0.204531i	−0.597407	+	0.801938i	$0.703802\pi$
$570$		0			0
$571$	15.9469	−	6.60542i	0.667356	−	0.276428i	−0.0231740	−	0.999731i	$-0.507377\pi$
$571$	15.9469	−	6.60542i	0.667356	−	0.276428i	0.690530	+	0.723303i	$0.257377\pi$
$572$	−1.44664	−	1.55869i	−0.0604869	−	0.0651721i
$573$		0			0
$574$	−0.590668	+	0.231865i	−0.0246540	+	0.00967787i
$575$	13.6483			0.569172
$576$		0			0
$577$	−7.21616			−0.300413			−0.150206	−	0.988655i	$-0.547994\pi$
$577$	−7.21616			−0.300413			−0.150206	+	0.988655i	$0.547994\pi$
$578$	−50.9621	+	20.0050i	−2.11974	+	0.832099i
$579$		0			0
$580$	31.6330	+	34.0832i	1.31349	+	1.41523i
$581$	0.309540	−	0.128216i	0.0128419	−	0.00531928i
$582$		0			0
$583$	7.26613	+	7.26613i	0.300932	+	0.300932i
$584$	30.8326	−	10.7957i	1.27586	−	0.446728i
$585$		0			0
$586$	1.03666	−	0.998726i	0.0428239	−	0.0412570i
$587$	−25.0953	+	10.3948i	−1.03579	+	0.429039i	−0.834800	−	0.550553i	$-0.814417\pi$
$587$	−25.0953	+	10.3948i	−1.03579	+	0.429039i	−0.200993	+	0.979593i	$0.564417\pi$
$588$		0			0
$589$	0.216550	−	0.522797i	0.00892277	−	0.0215415i
$590$	−40.2691	−	17.5661i	−1.65785	−	0.723183i
$591$		0			0
$592$	6.33403	−	2.08613i	0.260327	−	0.0857394i
$593$	26.2174			1.07662			0.538309	−	0.842747i	$-0.319063\pi$
$593$	26.2174			1.07662			0.538309	+	0.842747i	$0.319063\pi$
$594$		0			0
$595$	1.08193	+	0.448150i	0.0443548	+	0.0183723i
$596$	17.5435	+	8.04510i	0.718609	+	0.329540i
$597$		0			0
$598$	−1.28466	+	1.23766i	−0.0525337	+	0.0506115i
$599$	−31.6309	−	31.6309i	−1.29240	−	1.29240i	−0.933296	−	0.359108i	$-0.883081\pi$
$599$	−31.6309	−	31.6309i	−1.29240	−	1.29240i	−0.359108	−	0.933296i	$-0.616919\pi$
$600$		0			0
$601$	20.5554	−	20.5554i	0.838473	−	0.838473i	−0.150185	−	0.988658i	$-0.547987\pi$
$601$	20.5554	−	20.5554i	0.838473	−	0.838473i	0.988658	+	0.150185i	$0.0479870\pi$
$602$	−0.00539471	+	0.289478i	−0.000219872	+	0.0117982i
$603$		0			0
$604$	−1.37730	+	36.9398i	−0.0560415	+	1.50306i
$605$	0.198799	−	0.479944i	0.00808234	−	0.0195125i
$606$		0			0
$607$		−	33.7590i		−	1.37024i	−0.728432	−	0.685118i	$-0.759751\pi$
$607$		−	33.7590i		−	1.37024i	0.728432	−	0.685118i	$-0.240249\pi$
$608$	0.892203	−	9.54844i	0.0361836	−	0.387241i
$609$		0			0
$610$	47.2351	−	18.5420i	1.91249	−	0.750744i
$611$	−2.05322	−	0.850473i	−0.0830645	−	0.0344065i
$612$		0			0
$613$	2.92982	+	7.07321i	0.118334	+	0.285684i	0.971937	−	0.235240i	$-0.0755875\pi$
$613$	2.92982	+	7.07321i	0.118334	+	0.285684i	−0.853603	+	0.520924i	$0.825587\pi$
$614$	39.3474	+	0.733277i	1.58793	+	0.0295926i
$615$		0			0
$616$	−0.373349	+	0.333778i	−0.0150426	+	0.0134483i
$617$	15.6232	−	15.6232i	0.628965	−	0.628965i	−0.318843	−	0.947808i	$-0.603294\pi$
$617$	15.6232	−	15.6232i	0.628965	−	0.628965i	0.947808	+	0.318843i	$0.103294\pi$
$618$		0			0
$619$	10.6086	+	25.6113i	0.426394	+	1.02941i	0.980422	+	0.196908i	$0.0630900\pi$
$619$	10.6086	+	25.6113i	0.426394	+	1.02941i	−0.554028	+	0.832498i	$0.686910\pi$
$620$	−1.76887	−	0.811171i	−0.0710397	−	0.0325774i
$621$		0			0
$622$	−21.2372	−	9.26401i	−0.851533	−	0.371453i
$623$		−	0.578343i		−	0.0231708i
$624$		0			0
$625$			30.2554i			1.21022i
$626$	−2.06944	+	4.74407i	−0.0827115	+	0.189611i
$627$		0			0
$628$	−21.2187	+	7.87630i	−0.846719	+	0.314299i
$629$	−4.76210	−	11.4967i	−0.189878	−	0.458405i
$630$		0			0
$631$	11.4381	−	11.4381i	0.455343	−	0.455343i	−0.441780	−	0.897123i	$-0.645653\pi$
$631$	11.4381	−	11.4381i	0.455343	−	0.455343i	0.897123	+	0.441780i	$0.145653\pi$
$632$	5.07076	−	10.5349i	0.201704	−	0.419055i
$633$		0			0
$634$	0.224806	−	12.0630i	0.00892818	−	0.479083i
$635$	−11.1333	−	26.8782i	−0.441812	−	1.06663i
$636$		0			0
$637$	−2.08945	−	0.865480i	−0.0827871	−	0.0342916i
$638$	13.5589	+	34.5409i	0.536803	+	1.36749i
$639$		0			0
$640$	−32.6994	−	4.28956i	−1.29256	−	0.169560i
$641$			15.1966i			0.600229i	0.953903	+	0.300115i	$0.0970249\pi$
$641$			15.1966i			0.600229i	−0.953903	+	0.300115i	$0.902975\pi$
$642$		0			0
$643$	0.170017	−	0.410458i	0.00670483	−	0.0161869i	−0.920492	−	0.390762i	$-0.872211\pi$
$643$	0.170017	−	0.410458i	0.00670483	−	0.0161869i	0.927196	+	0.374575i	$0.122211\pi$
$644$	0.285775	+	0.307910i	0.0112611	+	0.0121334i
$645$		0			0
$646$	−17.8921	−	0.333437i	−0.703956	−	0.0131189i
$647$	−5.93379	+	5.93379i	−0.233282	+	0.233282i	−0.814061	−	0.580779i	$-0.802748\pi$
$647$	−5.93379	+	5.93379i	−0.233282	+	0.233282i	0.580779	+	0.814061i	$0.302748\pi$
$648$		0			0
$649$	−24.7900	−	24.7900i	−0.973093	−	0.973093i
$650$	1.10914	+	1.15126i	0.0435039	+	0.0451561i
$651$		0			0
$652$	10.3129	+	27.7829i	0.403884	+	1.08806i
$653$	41.0347	+	16.9971i	1.60581	+	0.665149i	0.992222	−	0.124477i	$-0.0397253\pi$
$653$	41.0347	+	16.9971i	1.60581	+	0.665149i	0.613589	+	0.789626i	$0.289725\pi$
$654$		0			0
$655$	47.4585			1.85436
$656$	−21.7578	−	25.2695i	−0.849499	−	0.986608i
$657$		0			0
$658$	−0.209257	+	0.479709i	−0.00815770	+	0.0187010i
$659$	2.49348	−	6.01980i	0.0971323	−	0.234498i	−0.867843	−	0.496838i	$-0.834494\pi$
$659$	2.49348	−	6.01980i	0.0971323	−	0.234498i	0.964975	+	0.262340i	$0.0844942\pi$
$660$		0			0
$661$	0.149545	−	0.0619435i	0.00581662	−	0.00240932i	−0.379773	−	0.925080i	$-0.623998\pi$
$661$	0.149545	−	0.0619435i	0.00581662	−	0.00240932i	0.385590	+	0.922670i	$0.373998\pi$
$662$	1.54428	+	1.60293i	0.0600200	+	0.0622996i
$663$		0			0
$664$	11.7348	+	13.1260i	0.455399	+	0.509389i
$665$	0.188078	+	0.188078i	0.00729333	+	0.00729333i
$666$		0			0
$667$	28.7575	−	11.9117i	1.11349	−	0.461224i
$668$	−1.89118	+	50.7224i	−0.0731720	+	1.96251i
$669$		0			0
$670$	−16.7102	−	42.5685i	−0.645570	−	1.64457i
$671$	40.4929			1.56321
$672$		0			0
$673$	17.0544			0.657398			0.328699	−	0.944435i	$-0.393390\pi$
$673$	17.0544			0.657398			0.328699	+	0.944435i	$0.393390\pi$
$674$	−12.7914	−	32.5855i	−0.492705	−	1.25515i
$675$		0			0
$676$	25.7731	+	0.960950i	0.991275	+	0.0369596i
$677$	26.7156	−	11.0660i	1.02677	−	0.425300i	0.195221	−	0.980759i	$-0.437457\pi$
$677$	26.7156	−	11.0660i	1.02677	−	0.425300i	0.831544	+	0.555459i	$0.187457\pi$
$678$		0			0
$679$	0.262051	+	0.262051i	0.0100566	+	0.0100566i
$680$	−3.43842	+	61.4445i	−0.131857	+	2.35629i
$681$		0			0
$682$	−1.07740	−	1.11832i	−0.0412558	−	0.0428226i
$683$	−14.7014	+	6.08950i	−0.562532	+	0.233008i	−0.645784	−	0.763520i	$-0.723469\pi$
$683$	−14.7014	+	6.08950i	−0.562532	+	0.233008i	0.0832521	+	0.996529i	$0.473469\pi$
$684$		0			0
$685$	−6.05393	+	14.6155i	−0.231309	+	0.558429i
$686$	−0.425987	+	0.976549i	−0.0162643	+	0.0372848i
$687$		0			0
$688$	−14.4513	+	4.75958i	−0.550951	+	0.181457i
$689$	1.00964			0.0384643
$690$		0			0
$691$	−30.8550	−	12.7806i	−1.17378	−	0.486196i	−0.291340	−	0.956620i	$-0.594101\pi$
$691$	−30.8550	−	12.7806i	−1.17378	−	0.486196i	−0.882440	+	0.470424i	$0.844101\pi$
$692$	14.4840	−	5.37642i	0.550601	−	0.204381i
$693$		0			0
$694$	22.1766	+	23.0189i	0.841813	+	0.873785i
$695$	−31.6092	−	31.6092i	−1.19901	−	1.19901i
$696$		0			0
$697$	−43.9991	+	43.9991i	−1.66659	+	1.66659i
$698$	51.0854	+	0.952026i	1.93361	+	0.0360347i
$699$		0			0
$700$	0.275936	−	0.256099i	0.0104294	−	0.00967965i
$701$	−14.8370	+	35.8196i	−0.560384	+	1.35289i	0.349075	+	0.937095i	$0.386496\pi$
$701$	−14.8370	+	35.8196i	−0.560384	+	1.35289i	−0.909460	+	0.415792i	$0.863504\pi$
$702$		0			0
$703$		−	2.82636i		−	0.106598i
$704$	−23.0385	−	12.7210i	−0.868295	−	0.479440i
$705$		0			0
$706$	5.46389	+	13.9191i	0.205636	+	0.523851i
$707$	0.881720	+	0.365220i	0.0331605	+	0.0137355i
$708$		0			0
$709$	2.66021	+	6.42232i	0.0999064	+	0.241195i	0.965928	−	0.258811i	$-0.0833308\pi$
$709$	2.66021	+	6.42232i	0.0999064	+	0.241195i	−0.866021	+	0.500007i	$0.833331\pi$
$710$	−0.434292	+	23.3040i	−0.0162987	+	0.874582i
$711$		0			0
$712$	28.6848	−	10.0436i	1.07501	−	0.376401i
$713$	−0.921093	+	0.921093i	−0.0344952	+	0.0344952i
$714$		0			0
$715$	1.18612	+	2.86354i	0.0443583	+	0.107090i
$716$	−9.49502	−	25.5795i	−0.354845	−	0.955952i
$717$		0			0
$718$	−18.3888	+	42.1551i	−0.686262	+	1.57321i
$719$			8.45844i			0.315447i	0.987483	+	0.157723i	$0.0504154\pi$
$719$			8.45844i			0.315447i	−0.987483	+	0.157723i	$0.949585\pi$
$720$		0			0
$721$		−	0.317802i		−	0.0118355i
$722$	20.9033	+	9.11838i	0.777941	+	0.339351i
$723$		0			0
$724$	−0.848706	+	1.85072i	−0.0315419	+	0.0687816i
$725$	−10.6748	−	25.7713i	−0.396452	−	0.957120i
$726$		0			0
$727$	4.11274	−	4.11274i	0.152533	−	0.152533i	−0.626715	−	0.779248i	$-0.715601\pi$
$727$	4.11274	−	4.11274i	0.152533	−	0.152533i	0.779248	+	0.626715i	$0.215601\pi$
$728$	−0.00274921	+	0.0491283i	−0.000101892	+	0.00182081i
$729$		0			0
$730$	−47.6054	−	0.887174i	−1.76196	−	0.0328358i
$731$	10.8649	+	26.2302i	0.401853	+	0.970159i
$732$		0			0
$733$	−6.27451	−	2.59899i	−0.231754	−	0.0959958i	0.263784	−	0.964582i	$-0.415029\pi$
$733$	−6.27451	−	2.59899i	−0.231754	−	0.0959958i	−0.495539	+	0.868586i	$0.665029\pi$
$734$	−43.2981	+	16.9965i	−1.59816	+	0.627354i
$735$		0			0
$736$	−10.3090	+	19.5212i	−0.379994	+	0.719560i
$737$		−	36.4925i		−	1.34422i
$738$		0			0
$739$	0.883296	−	2.13247i	0.0324926	−	0.0784440i	−0.906800	−	0.421560i	$-0.861483\pi$
$739$	0.883296	−	2.13247i	0.0324926	−	0.0784440i	0.939293	+	0.343116i	$0.111483\pi$
$740$	−9.71295	−	0.362146i	−0.357055	−	0.0133128i
$741$		0			0
$742$	0.00443024	−	0.237725i	0.000162639	−	0.00872716i
$743$	−31.2132	+	31.2132i	−1.14510	+	1.14510i	−0.157597	+	0.987504i	$0.550375\pi$
$743$	−31.2132	+	31.2132i	−1.14510	+	1.14510i	−0.987504	+	0.157597i	$0.949625\pi$
$744$		0			0
$745$	−19.8910	−	19.8910i	−0.728750	−	0.728750i
$746$	−22.3409	+	21.5235i	−0.817959	+	0.788030i
$747$		0			0
$748$	−20.4704	+	44.6386i	−0.748472	+	1.63215i
$749$	0.731936	+	0.303178i	0.0267443	+	0.0110779i
$750$		0			0
$751$	0.150864			0.00550509			0.00275255	−	0.999996i	$-0.499124\pi$
$751$	0.150864			0.00550509			0.00275255	+	0.999996i	$0.499124\pi$
$752$	−27.4268	−	2.04806i	−1.00015	−	0.0746849i
$753$		0			0
$754$	3.34178	+	1.45774i	0.121700	+	0.0530878i
$755$	20.6180	−	49.7762i	0.750366	−	1.81154i
$756$		0			0
$757$	20.0153	−	8.29061i	0.727469	−	0.301327i	0.0119573	−	0.999929i	$-0.496194\pi$
$757$	20.0153	−	8.29061i	0.727469	−	0.301327i	0.715511	+	0.698601i	$0.246194\pi$
$758$	−10.6402	+	10.2509i	−0.386469	+	0.372328i
$759$		0			0
$760$	−6.06212	+	12.5945i	−0.219896	+	0.456851i
$761$	−21.6271	−	21.6271i	−0.783982	−	0.783982i	0.196518	−	0.980500i	$-0.437036\pi$
$761$	−21.6271	−	21.6271i	−0.783982	−	0.783982i	−0.980500	+	0.196518i	$0.937036\pi$
$762$		0			0
$763$	0.0925923	−	0.0383530i	0.00335207	−	0.00138847i
$764$	−8.57647	+	7.95991i	−0.310286	+	0.287979i
$765$		0			0
$766$	7.49498	−	2.94214i	0.270805	−	0.106304i
$767$	−3.44462			−0.124378
$768$		0			0
$769$	−35.5857			−1.28325			−0.641626	−	0.767018i	$-0.721740\pi$
$769$	−35.5857			−1.28325			−0.641626	+	0.767018i	$0.721740\pi$
$770$	0.679439	−	0.266712i	0.0244853	−	0.00961164i
$771$		0			0
$772$	18.9986	−	17.6328i	0.683773	−	0.634617i
$773$	8.20086	−	3.39691i	0.294964	−	0.122178i	−0.230294	−	0.973121i	$-0.573969\pi$
$773$	8.20086	−	3.39691i	0.294964	−	0.122178i	0.525258	+	0.850943i	$0.323969\pi$
$774$		0			0
$775$	0.825446	+	0.825446i	0.0296509	+	0.0296509i
$776$	−8.44643	+	17.5481i	−0.303209	+	0.629940i
$777$		0			0
$778$	−1.81316	+	1.74682i	−0.0650051	+	0.0626265i
$779$	−13.0570	+	5.40838i	−0.467815	+	0.193775i
$780$		0			0
$781$	−7.11769	+	17.1836i	−0.254691	+	0.614879i
$782$	37.7583	+	16.4708i	1.35023	+	0.588995i
$783$		0			0
$784$	−27.9107	−	2.08419i	−0.996811	−	0.0744355i
$785$	32.9883			1.17740
$786$		0			0
$787$	33.0252	+	13.6795i	1.17722	+	0.487621i	0.883573	−	0.468293i	$-0.155131\pi$
$787$	33.0252	+	13.6795i	1.17722	+	0.487621i	0.293648	+	0.955914i	$0.405131\pi$
$788$	12.1882	−	26.5781i	0.434187	−	0.946806i
$789$		0			0
$790$	−12.2720	+	11.8230i	−0.436620	+	0.420644i
$791$	−0.201686	−	0.201686i	−0.00717114	−	0.00717114i
$792$		0			0
$793$	2.81329	−	2.81329i	0.0999027	−	0.0999027i
$794$	−0.269246	+	14.4476i	−0.00955518	+	0.512727i
$795$		0			0
$796$	−53.0942	−	1.97961i	−1.88187	−	0.0701655i
$797$	13.3534	−	32.2380i	0.473003	−	1.14193i	−0.489827	−	0.871820i	$-0.662940\pi$
$797$	13.3534	−	32.2380i	0.473003	−	1.14193i	0.962829	−	0.270110i	$-0.0870601\pi$
$798$		0			0
$799$			51.3214i			1.81562i
$800$	17.4941	+	9.23848i	0.618509	+	0.326630i
$801$		0			0
$802$	−10.1439	+	3.98198i	−0.358195	+	0.140609i
$803$	−35.1028	−	14.5401i	−1.23875	−	0.513107i
$804$		0			0
$805$	−0.234311	−	0.565676i	−0.00825837	−	0.0199375i
$806$	−0.152550	−	0.00284291i	−0.00537333	−	0.000100137i
$807$		0			0
$808$	−2.80215	+	50.0743i	−0.0985791	+	1.76161i
$809$	21.2883	−	21.2883i	0.748456	−	0.748456i	−0.225733	−	0.974189i	$-0.572478\pi$
$809$	21.2883	−	21.2883i	0.748456	−	0.748456i	0.974189	+	0.225733i	$0.0724777\pi$
$810$		0			0
$811$	−6.81853	−	16.4614i	−0.239431	−	0.578038i	0.757793	−	0.652495i	$-0.226278\pi$
$811$	−6.81853	−	16.4614i	−0.239431	−	0.578038i	−0.997224	+	0.0744573i	$0.976278\pi$
$812$	0.357895	−	0.780441i	0.0125597	−	0.0273881i
$813$		0			0
$814$	−7.10921	−	3.10116i	−0.249178	−	0.108696i
$815$		−	43.1935i		−	1.51300i
$816$		0			0
$817$			6.44844i			0.225602i
$818$	−10.2901	+	23.5893i	−0.359784	+	0.824782i
$819$		0			0
$820$	16.9132	+	45.5640i	0.590634	+	1.59116i
$821$	−6.23247	−	15.0465i	−0.217515	−	0.525127i	0.777027	−	0.629467i	$-0.216727\pi$
$821$	−6.23247	−	15.0465i	−0.217515	−	0.525127i	−0.994542	+	0.104340i	$0.966727\pi$
$822$		0			0
$823$	−17.7479	+	17.7479i	−0.618652	+	0.618652i	−0.945186	−	0.326533i	$-0.894119\pi$
$823$	−17.7479	+	17.7479i	−0.618652	+	0.618652i	0.326533	+	0.945186i	$0.394119\pi$
$824$	15.7624	−	5.51902i	0.549110	−	0.192264i
$825$		0			0
$826$	−0.0151147	+	0.811051i	−0.000525909	+	0.0282201i
$827$	8.49078	+	20.4986i	0.295253	+	0.712804i	0.999994	+	0.00333994i	$0.00106314\pi$
$827$	8.49078	+	20.4986i	0.295253	+	0.712804i	−0.704741	+	0.709465i	$0.748937\pi$
$828$		0			0
$829$	23.6680	+	9.80362i	0.822025	+	0.340494i	0.753741	−	0.657172i	$-0.228248\pi$
$829$	23.6680	+	9.80362i	0.822025	+	0.340494i	0.0682842	+	0.997666i	$0.478248\pi$
$830$	−9.37695	−	23.8874i	−0.325479	−	0.829145i
$831$		0			0
$832$	−2.48442	+	0.716817i	−0.0861318	+	0.0248512i
$833$			52.2270i			1.80956i
$834$		0			0
$835$	28.3108	−	68.3482i	0.979734	−	2.36529i
$836$	−8.17535	+	7.58763i	−0.282750	+	0.262424i
$837$		0			0
$838$	−48.3802	−	0.901612i	−1.67126	−	0.0311457i
$839$	27.7267	−	27.7267i	0.957231	−	0.957231i	−0.0418908	−	0.999122i	$-0.513338\pi$
$839$	27.7267	−	27.7267i	0.957231	−	0.957231i	0.999122	+	0.0418908i	$0.0133382\pi$
$840$		0			0
$841$	−24.4785	−	24.4785i	−0.844085	−	0.844085i
$842$	13.3194	+	13.8253i	0.459017	+	0.476450i
$843$		0			0
$844$	−4.78008	+	1.77435i	−0.164537	+	0.0610755i
$845$	−34.7292	−	14.3853i	−1.19472	−	0.494869i
$846$		0			0
$847$	−0.00959183			−0.000329579
$848$	11.8677	−	3.90866i	0.407538	−	0.134224i
$849$		0			0
$850$	14.7604	−	33.8374i	0.506279	−	1.16061i
$851$	−2.48982	+	6.01096i	−0.0853500	+	0.206053i
$852$		0			0
$853$	−29.4430	+	12.1957i	−1.00811	+	0.417572i	−0.824764	−	0.565477i	$-0.808692\pi$
$853$	−29.4430	+	12.1957i	−1.00811	+	0.417572i	−0.183344	+	0.983049i	$0.558692\pi$
$854$	−0.650056	−	0.674745i	−0.0222445	−	0.0230893i
$855$		0			0
$856$	−2.32612	+	41.5678i	−0.0795053	+	1.42076i
$857$	−2.22501	−	2.22501i	−0.0760048	−	0.0760048i	0.668082	−	0.744087i	$-0.267115\pi$
$857$	−2.22501	−	2.22501i	−0.0760048	−	0.0760048i	−0.744087	+	0.668082i	$0.767115\pi$
$858$		0			0
$859$	10.3126	−	4.27163i	0.351862	−	0.145746i	−0.199750	−	0.979847i	$-0.564013\pi$
$859$	10.3126	−	4.27163i	0.351862	−	0.145746i	0.551612	+	0.834101i	$0.314013\pi$
$860$	22.1604	+	0.826249i	0.755664	+	0.0281749i
$861$		0			0
$862$	−18.2942	−	46.6038i	−0.623103	−	1.58733i
$863$	0.364624			0.0124120			0.00620598	−	0.999981i	$-0.498025\pi$
$863$	0.364624			0.0124120			0.00620598	+	0.999981i	$0.498025\pi$
$864$		0			0
$865$	−22.5180			−0.765636
$866$	−3.73062	−	9.50362i	−0.126772	−	0.322946i
$867$		0			0
$868$	−0.00133875	+	0.0359060i	−4.54402e−5	+	0.00121873i
$869$	−12.5631	+	5.20382i	−0.426175	+	0.176528i
$870$		0			0
$871$	−2.53535	−	2.53535i	−0.0859071	−	0.0859071i
$872$	3.51022	+	3.92637i	0.118871	+	0.132964i
$873$		0			0
$874$	6.49152	+	6.73806i	0.219579	+	0.227918i
$875$	0.217820	−	0.0902242i	0.00736368	−	0.00305013i
$876$		0			0
$877$	−20.9747	+	50.6373i	−0.708264	+	1.70990i	−0.00396924	+	0.999992i	$0.501263\pi$
$877$	−20.9747	+	50.6373i	−0.708264	+	1.70990i	−0.704295	+	0.709908i	$0.748737\pi$
$878$	0.831350	−	1.90582i	0.0280567	−	0.0643183i
$879$		0			0
$880$	25.0278	+	29.0672i	0.843686	+	0.979856i
$881$	8.52158			0.287099			0.143550	−	0.989643i	$-0.454148\pi$
$881$	8.52158			0.287099			0.143550	+	0.989643i	$0.454148\pi$
$882$		0			0
$883$	0.771103	+	0.319401i	0.0259497	+	0.0107487i	0.395621	−	0.918414i	$-0.370530\pi$
$883$	0.771103	+	0.319401i	0.0259497	+	0.0107487i	−0.369671	+	0.929163i	$0.620530\pi$
$884$	1.67911	+	4.52351i	0.0564745	+	0.152142i
$885$		0			0
$886$	20.5436	+	21.3238i	0.690175	+	0.716387i
$887$	−6.68514	−	6.68514i	−0.224465	−	0.224465i	0.585911	−	0.810376i	$-0.300737\pi$
$887$	−6.68514	−	6.68514i	−0.224465	−	0.224465i	−0.810376	+	0.585911i	$0.800737\pi$
$888$		0			0
$889$	−0.379836	+	0.379836i	−0.0127393	+	0.0127393i
$890$	−44.2893	−	0.825374i	−1.48458	−	0.0276666i
$891$		0			0
$892$	−13.5455	−	14.5947i	−0.453537	−	0.488667i
$893$	−4.46074	+	10.7692i	−0.149273	+	0.360377i
$894$		0			0
$895$			39.7679i			1.32930i
$896$	0.157876	+	0.588114i	0.00527428	+	0.0196475i
$897$		0			0
$898$	7.39607	+	18.8412i	0.246810	+	0.628740i
$899$	2.45967	+	1.01883i	0.0820347	+	0.0339799i
$900$		0			0
$901$	−8.92247	−	21.5407i	−0.297251	−	0.717626i
$902$	−0.722643	+	38.7768i	−0.0240614	+	1.29112i
$903$		0			0
$904$	6.50076	−	13.5058i	0.216212	−	0.449197i
$905$	2.09837	−	2.09837i	0.0697522	−	0.0697522i
$906$		0			0
$907$	−8.45548	−	20.4133i	−0.280760	−	0.677814i	0.719094	−	0.694913i	$-0.244557\pi$
$907$	−8.45548	−	20.4133i	−0.280760	−	0.677814i	−0.999854	+	0.0170988i	$0.994557\pi$
$908$	−39.1302	+	14.5250i	−1.29858	+	0.482028i
$909$		0			0
$910$	0.0286746	−	0.0657347i	0.000950554	−	0.00217909i
$911$			1.69648i			0.0562069i	0.999605	+	0.0281035i	$0.00894679\pi$
$911$			1.69648i			0.0562069i	−0.999605	+	0.0281035i	$0.991053\pi$
$912$		0			0
$913$		−	20.4778i		−	0.677718i
$914$	40.6152	+	17.7170i	1.34343	+	0.586028i
$915$		0			0
$916$	−35.3325	−	16.2028i	−1.16742	−	0.535356i
$917$	−0.335336	−	0.809573i	−0.0110738	−	0.0267344i
$918$		0			0
$919$	−37.0196	+	37.0196i	−1.22116	+	1.22116i	−0.253945	+	0.967219i	$0.581728\pi$
$919$	−37.0196	+	37.0196i	−1.22116	+	1.22116i	−0.967219	+	0.253945i	$0.918272\pi$
$920$	23.9875	−	21.4451i	0.790844	−	0.707024i
$921$		0			0
$922$	−37.9508	−	0.707250i	−1.24984	−	0.0232920i
$923$	0.699341	+	1.68836i	0.0230191	+	0.0555730i
$924$		0			0
$925$	5.38678	+	2.23128i	0.177116	+	0.0733639i
$926$	−25.1087	+	9.85637i	−0.825124	+	0.323900i
$927$		0			0
$928$	44.9238	+	4.19767i	1.47470	+	0.137795i
$929$		−	43.9949i		−	1.44342i	−0.692193	−	0.721712i	$-0.743355\pi$
$929$		−	43.9949i		−	1.44342i	0.692193	−	0.721712i	$-0.256645\pi$
$930$		0			0
$931$	−4.53945	+	10.9592i	−0.148774	+	0.359173i
$932$	−1.79585	+	48.1655i	−0.0588249	+	1.57771i
$933$		0			0
$934$	0.155277	−	8.33211i	0.00508082	−	0.272635i
$935$	50.6117	−	50.6117i	1.65518	−	1.65518i
$936$		0			0
$937$	7.93466	+	7.93466i	0.259214	+	0.259214i	0.824734	−	0.565520i	$-0.191325\pi$
$937$	7.93466	+	7.93466i	0.259214	+	0.259214i	−0.565520	+	0.824734i	$0.691325\pi$
$938$	−0.608085	+	0.585835i	−0.0198547	+	0.0191282i
$939$		0			0
$940$	36.4373	+	16.7094i	1.18845	+	0.545002i
$941$	35.0913	+	14.5353i	1.14394	+	0.473837i	0.872499	−	0.488616i	$-0.162498\pi$
$941$	35.0913	+	14.5353i	1.14394	+	0.473837i	0.271446	+	0.962454i	$0.412498\pi$
$942$		0			0
$943$	32.5333			1.05943
$944$	−40.4892	+	13.3352i	−1.31781	+	0.434025i
$945$		0			0
$946$	16.2199	+	7.07540i	0.527355	+	0.230041i
$947$	1.49823	−	3.61705i	0.0486860	−	0.117538i	−0.897665	−	0.440678i	$-0.854738\pi$
$947$	1.49823	−	3.61705i	0.0486860	−	0.117538i	0.946351	+	0.323139i	$0.104738\pi$
$948$		0			0
$949$	−3.44898	+	1.42862i	−0.111959	+	0.0463748i
$950$	6.03837	−	5.81743i	0.195911	−	0.188742i
$951$		0			0
$952$	1.07245	−	0.375505i	0.0347583	−	0.0121702i
$953$	−19.9810	−	19.9810i	−0.647248	−	0.647248i	0.305079	−	0.952327i	$-0.401317\pi$
$953$	−19.9810	−	19.9810i	−0.647248	−	0.647248i	−0.952327	+	0.305079i	$0.901317\pi$
$954$		0			0
$955$	15.7562	−	6.52645i	0.509860	−	0.211191i
$956$	17.4837	+	18.8380i	0.565465	+	0.609264i
$957$		0			0
$958$	44.5724	−	17.4968i	1.44007	−	0.565295i
$959$	0.292095			0.00943224
$960$		0			0
$961$	30.8886			0.996406
$962$	−0.709375	+	0.278463i	−0.0228712	+	0.00897802i
$963$		0			0
$964$	−22.9444	−	24.7216i	−0.738990	−	0.796230i
$965$	−34.9032	+	14.4574i	−1.12357	+	0.465399i
$966$		0			0
$967$	22.2824	+	22.2824i	0.716553	+	0.716553i	0.967898	−	0.251344i	$-0.0808726\pi$
$967$	22.2824	+	22.2824i	0.716553	+	0.716553i	−0.251344	+	0.967898i	$0.580873\pi$
$968$	−0.166574	−	0.475738i	−0.00535389	−	0.0152908i
$969$		0			0
$970$	20.4417	−	19.6938i	0.656344	−	0.632329i
$971$	49.0212	−	20.3053i	1.57317	−	0.651627i	0.585854	−	0.810417i	$-0.300759\pi$
$971$	49.0212	−	20.3053i	1.57317	−	0.651627i	0.987312	+	0.158790i	$0.0507593\pi$
$972$		0			0
$973$	−0.315860	+	0.762554i	−0.0101260	+	0.0244463i
$974$	27.9828	+	12.2066i	0.896626	+	0.391123i
$975$		0			0
$976$	22.1772	−	43.9595i	0.709874	−	1.40711i
$977$	−19.6379			−0.628273			−0.314137	−	0.949378i	$-0.601715\pi$
$977$	−19.6379			−0.628273			−0.314137	+	0.949378i	$0.601715\pi$
$978$		0			0
$979$	−32.6576	−	13.5272i	−1.04374	−	0.432331i
$980$	37.0802	+	17.0043i	1.18448	+	0.543182i
$981$		0			0
$982$	10.1205	−	9.75021i	0.322959	−	0.311142i
$983$	37.1087	+	37.1087i	1.18358	+	1.18358i	0.978809	+	0.204776i	$0.0656465\pi$
$983$	37.1087	+	37.1087i	1.18358	+	1.18358i	0.204776	+	0.978809i	$0.434353\pi$
$984$		0			0
$985$	−30.1346	+	30.1346i	−0.960168	+	0.960168i
$986$	1.56876	−	84.1794i	0.0499597	−	2.68082i
$987$		0			0
$988$	−0.0408325	+	1.09515i	−0.00129905	+	0.0348413i
$989$	5.68061	−	13.7142i	0.180633	−	0.436087i
$990$		0			0
$991$		−	54.6056i		−	1.73460i	−0.497783	−	0.867301i	$-0.665853\pi$
$991$		−	54.6056i		−	1.73460i	0.497783	−	0.867301i	$-0.334147\pi$
$992$	−1.80413	+	0.557153i	−0.0572811	+	0.0176896i
$993$		0			0
$994$	0.400600	−	0.157255i	0.0127063	−	0.00498781i
$995$	71.5442	+	29.6346i	2.26810	+	0.939479i
$996$		0			0
$997$	14.9638	+	36.1257i	0.473907	+	1.14411i	0.962422	+	0.271558i	$0.0875388\pi$
$997$	14.9638	+	36.1257i	0.473907	+	1.14411i	−0.488515	+	0.872556i	$0.662461\pi$
$998$	−26.3366	−	0.490808i	−0.833670	−	0.0155363i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.w.b.323.5	yes	128
3.2	odd	2	inner	864.2.w.b.323.28	yes	128
32.11	odd	8	inner	864.2.w.b.107.28	yes	128
96.11	even	8	inner	864.2.w.b.107.5	✓	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
864.2.w.b.107.5	✓	128	96.11	even	8	inner
864.2.w.b.107.28	yes	128	32.11	odd	8	inner
864.2.w.b.323.5	yes	128	1.1	even	1	trivial
864.2.w.b.323.28	yes	128	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:	\( N \)	\(=\)	\( 864 = 2^{5} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	864.w (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.31642 + 0.516757i) q^{2} +(1.46592 - 1.36054i) q^{4} +(-2.69312 + 1.11553i) q^{5} +(0.0380585 + 0.0380585i) q^{7} +(-1.22670 + 2.54857i) q^{8} +O(q^{10})\)	\(q+(-1.31642 + 0.516757i) q^{2} +(1.46592 - 1.36054i) q^{4} +(-2.69312 + 1.11553i) q^{5} +(0.0380585 + 0.0380585i) q^{7} +(-1.22670 + 2.54857i) q^{8} +(2.96882 - 2.86019i) q^{10} +(3.03924 - 1.25889i) q^{11} +(0.123691 - 0.298617i) q^{13} +(-0.0697680 - 0.0304340i) q^{14} +(0.297865 - 3.98889i) q^{16} -7.46409 q^{17} +(-1.56625 - 0.648761i) q^{19} +(-2.43019 + 5.29937i) q^{20} +(-3.35037 + 3.22778i) q^{22} +(2.75950 + 2.75950i) q^{23} +(2.47295 - 2.47295i) q^{25} +(-0.00851708 + 0.457023i) q^{26} +(0.107571 + 0.00401077i) q^{28} +(3.05231 - 7.36893i) q^{29} +0.333789i q^{31} +(1.66917 + 5.40498i) q^{32} +(9.82588 - 3.85712i) q^{34} +(-0.144951 - 0.0600408i) q^{35} +(0.638002 + 1.54027i) q^{37} +(2.39709 + 0.0446722i) q^{38} +(0.460662 - 8.23201i) q^{40} +(5.89478 - 5.89478i) q^{41} +(-1.45562 - 3.51419i) q^{43} +(2.74252 - 5.98045i) q^{44} +(-5.05866 - 2.20667i) q^{46} -6.87578i q^{47} -6.99710i q^{49} +(-1.97753 + 4.53336i) q^{50} +(-0.224958 - 0.606036i) q^{52} +(1.19539 + 2.88592i) q^{53} +(-6.78070 + 6.78070i) q^{55} +(-0.143681 + 0.0503082i) q^{56} +(-0.210175 + 11.2779i) q^{58} +(-4.07833 - 9.84595i) q^{59} +(11.3722 + 4.71053i) q^{61} +(-0.172488 - 0.439407i) q^{62} +(-4.99040 - 6.25267i) q^{64} +0.942191i q^{65} +(4.24516 - 10.2487i) q^{67} +(-10.9418 + 10.1552i) q^{68} +(0.221843 + 0.00413427i) q^{70} +(-3.99793 + 3.99793i) q^{71} +(-8.16699 - 8.16699i) q^{73} +(-1.63583 - 1.69795i) q^{74} +(-3.17867 + 1.17991i) q^{76} +(0.163580 + 0.0677572i) q^{77} -4.13365 q^{79} +(3.64753 + 11.0748i) q^{80} +(-4.71383 + 10.8062i) q^{82} +(2.38218 - 5.75109i) q^{83} +(20.1017 - 8.32638i) q^{85} +(3.73219 + 3.87394i) q^{86} +(-0.519866 + 9.29000i) q^{88} +(-7.59808 - 7.59808i) q^{89} +(0.0160724 - 0.00665741i) q^{91} +(7.79964 + 0.290809i) q^{92} +(3.55311 + 9.05142i) q^{94} +4.94180 q^{95} +6.88547 q^{97} +(3.61580 + 9.21113i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q+O(q^{10}) \) 128 * q	\( 128 q + 8 q^{10} + 32 q^{16} - 32 q^{22} + 64 q^{40} + 64 q^{46} + 40 q^{52} + 64 q^{55} + 64 q^{58} + 32 q^{61} + 96 q^{64} - 64 q^{67} - 48 q^{70} - 32 q^{76} - 32 q^{79} + 40 q^{82} + 40 q^{88} - 48 q^{91} + 72 q^{94}+O(q^{100}) \) 128 * q + 8 * q^10 + 32 * q^16 - 32 * q^22 + 64 * q^40 + 64 * q^46 + 40 * q^52 + 64 * q^55 + 64 * q^58 + 32 * q^61 + 96 * q^64 - 64 * q^67 - 48 * q^70 - 32 * q^76 - 32 * q^79 + 40 * q^82 + 40 * q^88 - 48 * q^91 + 72 * q^94

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