LMFDB - Embedded newform 864.2.v.a.109.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [864,2,Mod(109,864)]

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([0, 7, 0]))

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

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

chi := DirichletCharacter("864.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 864 = 2^{5} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	864.v (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			109.11
Character	$\chi$	$=$	864.109
Dual form			864.2.v.a.325.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.791979 + 1.17165i) q^{2} +(-0.745540 - 1.85585i) q^{4} +(2.17386 - 0.900442i) q^{5} +(-1.13840 + 1.13840i) q^{7} +(2.76486 + 0.596278i) q^{8} +O(q^{10})$	\(q+(-0.791979 + 1.17165i) q^{2} +(-0.745540 - 1.85585i) q^{4} +(2.17386 - 0.900442i) q^{5} +(-1.13840 + 1.13840i) q^{7} +(2.76486 + 0.596278i) q^{8} +(-0.666644 + 3.26014i) q^{10} +(-1.16219 - 2.80577i) q^{11} +(5.29700 + 2.19409i) q^{13} +(-0.432223 - 2.23541i) q^{14} +(-2.88834 + 2.76722i) q^{16} -1.37204i q^{17} +(-0.435446 - 0.180368i) q^{19} +(-3.29178 - 3.36303i) q^{20} +(4.20782 + 0.860429i) q^{22} +(-0.900399 - 0.900399i) q^{23} +(0.379330 - 0.379330i) q^{25} +(-6.76583 + 4.46858i) q^{26} +(2.96143 + 1.26398i) q^{28} +(2.18893 - 5.28455i) q^{29} +3.64689 q^{31} +(-0.954714 - 5.57571i) q^{32} +(1.60755 + 1.08662i) q^{34} +(-1.44966 + 3.49980i) q^{35} +(10.4431 - 4.32566i) q^{37} +(0.556192 - 0.367344i) q^{38} +(6.54733 - 1.19337i) q^{40} +(3.37936 + 3.37936i) q^{41} +(-0.290826 - 0.702117i) q^{43} +(-4.34062 + 4.24866i) q^{44} +(1.76805 - 0.341858i) q^{46} -9.15553i q^{47} +4.40807i q^{49} +(0.144022 + 0.744865i) q^{50} +(0.122770 - 11.4662i) q^{52} +(0.279738 + 0.675348i) q^{53} +(-5.05286 - 5.05286i) q^{55} +(-3.82633 + 2.46872i) q^{56} +(4.45807 + 6.74992i) q^{58} +(9.51130 - 3.93971i) q^{59} +(-3.14636 + 7.59599i) q^{61} +(-2.88826 + 4.27289i) q^{62} +(7.28891 + 3.29725i) q^{64} +13.4906 q^{65} +(2.00791 - 4.84753i) q^{67} +(-2.54629 + 1.02291i) q^{68} +(-2.95244 - 4.47026i) q^{70} +(3.53207 - 3.53207i) q^{71} +(-4.79474 - 4.79474i) q^{73} +(-3.20251 + 15.6615i) q^{74} +(-0.0100924 + 0.942593i) q^{76} +(4.51714 + 1.87106i) q^{77} +14.3012i q^{79} +(-3.78712 + 8.61632i) q^{80} +(-6.63581 + 1.28305i) q^{82} +(7.87490 + 3.26189i) q^{83} +(-1.23544 - 2.98262i) q^{85} +(1.05296 + 0.215314i) q^{86} +(-1.54027 - 8.45055i) q^{88} +(-1.44497 + 1.44497i) q^{89} +(-8.52789 + 3.53237i) q^{91} +(-0.999720 + 2.34229i) q^{92} +(10.7271 + 7.25099i) q^{94} -1.10901 q^{95} +8.99231 q^{97} +(-5.16473 - 3.49110i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q+O(q^{10}) $ 128 * q	$ 128 q - 8 q^{10} - 32 q^{16} + 32 q^{22} + 64 q^{40} + 64 q^{46} + 88 q^{52} - 64 q^{55} + 64 q^{58} - 32 q^{61} - 96 q^{64} + 64 q^{67} + 48 q^{70} + 32 q^{76} + 40 q^{82} + 40 q^{88} - 48 q^{91} + 24 q^{94}+O(q^{100}) $ 128 * q - 8 * q^10 - 32 * q^16 + 32 * q^22 + 64 * q^40 + 64 * q^46 + 88 * q^52 - 64 * q^55 + 64 * q^58 - 32 * q^61 - 96 * q^64 + 64 * q^67 + 48 * q^70 + 32 * q^76 + 40 * q^82 + 40 * q^88 - 48 * q^91 + 24 * q^94

Display 100 coefficients 10 coefficients

Character values

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

$n$	$325$	$353$	$703$
$\chi(n)$	$e\left(\frac{7}{8}\right)$	$1$	$1$

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 $

$2$	−0.791979	+	1.17165i	−0.560013	+	0.828484i
$2$	−0.791979	+	1.17165i	−0.560013	+	0.828484i
$3$		0			0
$3$		0			0
$4$	−0.745540	−	1.85585i	−0.372770	−	0.927924i
$5$	2.17386	−	0.900442i	0.972179	−	0.402690i	0.160656	−	0.987010i	$-0.448639\pi$
$5$	2.17386	−	0.900442i	0.972179	−	0.402690i	0.811523	+	0.584321i	$0.198639\pi$
$6$		0			0
$7$	−1.13840	+	1.13840i	−0.430276	+	0.430276i	−0.888722	−	0.458446i	$-0.848406\pi$
$7$	−1.13840	+	1.13840i	−0.430276	+	0.430276i	0.458446	+	0.888722i	$0.348406\pi$
$8$	2.76486	+	0.596278i	0.977526	+	0.210816i
$9$		0			0
$10$	−0.666644	+	3.26014i	−0.210811	+	1.03095i
$11$	−1.16219	−	2.80577i	−0.350413	−	0.845971i	−0.996569	−	0.0827662i	$-0.973625\pi$
$11$	−1.16219	−	2.80577i	−0.350413	−	0.845971i	0.646156	−	0.763205i	$-0.276375\pi$
$12$		0			0
$13$	5.29700	+	2.19409i	1.46912	+	0.608531i	0.966659	−	0.256066i	$-0.0824264\pi$
$13$	5.29700	+	2.19409i	1.46912	+	0.608531i	0.502465	+	0.864597i	$0.332426\pi$
$14$	−0.432223	−	2.23541i	−0.115516	−	0.597437i
$15$		0			0
$16$	−2.88834	+	2.76722i	−0.722085	+	0.691804i
$17$		−	1.37204i		−	0.332768i	−0.986061	−	0.166384i	$-0.946791\pi$
$17$		−	1.37204i		−	0.332768i	0.986061	−	0.166384i	$-0.0532092\pi$
$18$		0			0
$19$	−0.435446	−	0.180368i	−0.0998982	−	0.0413792i	0.332175	−	0.943218i	$-0.392218\pi$
$19$	−0.435446	−	0.180368i	−0.0998982	−	0.0413792i	−0.432073	+	0.901839i	$0.642218\pi$
$20$	−3.29178	−	3.36303i	−0.736064	−	0.751997i
$21$		0			0
$22$	4.20782	+	0.860429i	0.897109	+	0.183444i
$23$	−0.900399	−	0.900399i	−0.187746	−	0.187746i	0.606975	−	0.794721i	$-0.292383\pi$
$23$	−0.900399	−	0.900399i	−0.187746	−	0.187746i	−0.794721	+	0.606975i	$0.792383\pi$
$24$		0			0
$25$	0.379330	−	0.379330i	0.0758661	−	0.0758661i
$26$	−6.76583	+	4.46858i	−1.32689	+	0.876360i
$27$		0			0
$28$	2.96143	+	1.26398i	0.559658	+	0.238870i
$29$	2.18893	−	5.28455i	0.406475	−	0.981317i	−0.579583	−	0.814913i	$-0.696785\pi$
$29$	2.18893	−	5.28455i	0.406475	−	0.981317i	0.986058	−	0.166404i	$-0.0532155\pi$
$30$		0			0
$31$	3.64689			0.655001			0.327500	−	0.944851i	$-0.393794\pi$
$31$	3.64689			0.655001			0.327500	+	0.944851i	$0.393794\pi$
$32$	−0.954714	−	5.57571i	−0.168771	−	0.985655i
$33$		0			0
$34$	1.60755	+	1.08662i	0.275693	+	0.186355i
$35$	−1.44966	+	3.49980i	−0.245038	+	0.591573i
$36$		0			0
$37$	10.4431	−	4.32566i	1.71683	−	0.711134i	0.716927	−	0.697149i	$-0.245548\pi$
$37$	10.4431	−	4.32566i	1.71683	−	0.711134i	0.999902	−	0.0139853i	$-0.00445180\pi$
$38$	0.556192	−	0.367344i	0.0902263	−	0.0595911i
$39$		0			0
$40$	6.54733	−	1.19337i	1.03522	−	0.188689i
$41$	3.37936	+	3.37936i	0.527767	+	0.527767i	0.919906	−	0.392139i	$-0.128265\pi$
$41$	3.37936	+	3.37936i	0.527767	+	0.527767i	−0.392139	+	0.919906i	$0.628265\pi$
$42$		0			0
$43$	−0.290826	−	0.702117i	−0.0443506	−	0.107072i	0.900152	−	0.435576i	$-0.143455\pi$
$43$	−0.290826	−	0.702117i	−0.0443506	−	0.107072i	−0.944502	+	0.328505i	$0.893455\pi$
$44$	−4.34062	+	4.24866i	−0.654374	+	0.640509i
$45$		0			0
$46$	1.76805	−	0.341858i	0.260685	−	0.0504043i
$47$		−	9.15553i		−	1.33547i	−0.744398	−	0.667736i	$-0.767264\pi$
$47$		−	9.15553i		−	1.33547i	0.744398	−	0.667736i	$-0.232736\pi$
$48$		0			0
$49$			4.40807i			0.629725i
$50$	0.144022	+	0.744865i	0.0203678	+	0.105340i
$51$		0			0
$52$	0.122770	−	11.4662i	0.0170251	−	1.59008i
$53$	0.279738	+	0.675348i	0.0384250	+	0.0927662i	0.941927	−	0.335818i	$-0.109013\pi$
$53$	0.279738	+	0.675348i	0.0384250	+	0.0927662i	−0.903502	+	0.428584i	$0.859013\pi$
$54$		0			0
$55$	−5.05286	−	5.05286i	−0.681328	−	0.681328i
$56$	−3.82633	+	2.46872i	−0.511315	+	0.329897i
$57$		0			0
$58$	4.45807	+	6.74992i	0.585374	+	0.886308i
$59$	9.51130	−	3.93971i	1.23827	−	0.512906i	0.335094	−	0.942185i	$-0.391232\pi$
$59$	9.51130	−	3.93971i	1.23827	−	0.512906i	0.903172	+	0.429278i	$0.141232\pi$
$60$		0			0
$61$	−3.14636	+	7.59599i	−0.402850	+	0.972566i	0.584121	+	0.811667i	$0.301440\pi$
$61$	−3.14636	+	7.59599i	−0.402850	+	0.972566i	−0.986971	+	0.160899i	$0.948560\pi$
$62$	−2.88826	+	4.27289i	−0.366809	+	0.542657i
$63$		0			0
$64$	7.28891	+	3.29725i	0.911113	+	0.412156i
$65$	13.4906			1.67330
$66$		0			0
$67$	2.00791	−	4.84753i	0.245306	−	0.592221i	−0.752488	−	0.658606i	$-0.771147\pi$
$67$	2.00791	−	4.84753i	0.245306	−	0.592221i	0.997794	+	0.0663851i	$0.0211466\pi$
$68$	−2.54629	+	1.02291i	−0.308783	+	0.124046i
$69$		0			0
$70$	−2.95244	−	4.47026i	−0.352884	−	0.534299i
$71$	3.53207	−	3.53207i	0.419180	−	0.419180i	−0.465741	−	0.884921i	$-0.654212\pi$
$71$	3.53207	−	3.53207i	0.419180	−	0.419180i	0.884921	+	0.465741i	$0.154212\pi$
$72$		0			0
$73$	−4.79474	−	4.79474i	−0.561182	−	0.561182i	0.368461	−	0.929643i	$-0.379885\pi$
$73$	−4.79474	−	4.79474i	−0.561182	−	0.561182i	−0.929643	+	0.368461i	$0.879885\pi$
$74$	−3.20251	+	15.6615i	−0.372285	+	1.82061i
$75$		0			0
$76$	−0.0100924	+	0.942593i	−0.00115768	+	0.108123i
$77$	4.51714	+	1.87106i	0.514776	+	0.213227i
$78$		0			0
$79$			14.3012i			1.60902i	0.593942	+	0.804508i	$0.297571\pi$
$79$			14.3012i			1.60902i	−0.593942	+	0.804508i	$0.702429\pi$
$80$	−3.78712	+	8.61632i	−0.423413	+	0.963334i
$81$		0			0
$82$	−6.63581	+	1.28305i	−0.732803	+	0.141690i
$83$	7.87490	+	3.26189i	0.864383	+	0.358039i	0.770420	−	0.637537i	$-0.220047\pi$
$83$	7.87490	+	3.26189i	0.864383	+	0.358039i	0.0939626	+	0.995576i	$0.470047\pi$
$84$		0			0
$85$	−1.23544	−	2.98262i	−0.134002	−	0.323510i
$86$	1.05296	+	0.215314i	0.113544	+	0.0232179i
$87$		0			0
$88$	−1.54027	−	8.45055i	−0.164193	−	0.900831i
$89$	−1.44497	+	1.44497i	−0.153166	+	0.153166i	−0.779531	−	0.626364i	$-0.784542\pi$
$89$	−1.44497	+	1.44497i	−0.153166	+	0.153166i	0.626364	+	0.779531i	$0.284542\pi$
$90$		0			0
$91$	−8.52789	+	3.53237i	−0.893966	+	0.370293i
$92$	−0.999720	+	2.34229i	−0.104228	+	0.244200i
$93$		0			0
$94$	10.7271	+	7.25099i	1.10642	+	0.747882i
$95$	−1.10901			−0.113782
$96$		0			0
$97$	8.99231			0.913031			0.456515	−	0.889716i	$-0.349097\pi$
$97$	8.99231			0.913031			0.456515	+	0.889716i	$0.349097\pi$
$98$	−5.16473	−	3.49110i	−0.521716	−	0.352654i
$99$		0			0
$100$	−0.986785	−	0.421173i	−0.0986785	−	0.0421173i
$101$	−14.4378	+	5.98033i	−1.43662	+	0.595065i	−0.958975	−	0.283490i	$-0.908508\pi$
$101$	−14.4378	+	5.98033i	−1.43662	+	0.595065i	−0.477640	+	0.878556i	$0.658508\pi$
$102$		0			0
$103$	−7.43674	+	7.43674i	−0.732764	+	0.732764i	−0.971166	−	0.238403i	$-0.923376\pi$
$103$	−7.43674	+	7.43674i	−0.732764	+	0.732764i	0.238403	+	0.971166i	$0.423376\pi$
$104$	13.3372	+	9.22484i	1.30782	+	0.904570i
$105$		0			0
$106$	−1.01282	−	0.207105i	−0.0983737	−	0.0201158i
$107$	4.29647	+	10.3726i	0.415355	+	1.00276i	0.983676	+	0.179949i	$0.0575933\pi$
$107$	4.29647	+	10.3726i	0.415355	+	1.00276i	−0.568321	+	0.822807i	$0.692407\pi$
$108$		0			0
$109$	10.2468	+	4.24435i	0.981463	+	0.406535i	0.814967	−	0.579507i	$-0.196755\pi$
$109$	10.2468	+	4.24435i	0.981463	+	0.406535i	0.166496	+	0.986042i	$0.446755\pi$
$110$	9.92196	−	1.91844i	0.946022	−	0.182916i
$111$		0			0
$112$	0.137887	−	6.43831i	0.0130291	−	0.608363i
$113$		−	21.0084i		−	1.97630i	−0.153489	−	0.988150i	$-0.549051\pi$
$113$		−	21.0084i		−	1.97630i	0.153489	−	0.988150i	$-0.450949\pi$
$114$		0			0
$115$	−2.76810	−	1.14658i	−0.258126	−	0.106919i
$116$	−11.4393	−	0.122481i	−1.06211	−	0.0113721i
$117$		0			0
$118$	−2.91677	+	14.2641i	−0.268511	+	1.31312i
$119$	1.56193	+	1.56193i	0.143182	+	0.143182i
$120$		0			0
$121$	1.25651	−	1.25651i	0.114228	−	0.114228i
$122$	−6.40801	−	9.70230i	−0.580154	−	0.878405i
$123$		0			0
$124$	−2.71890	−	6.76807i	−0.244165	−	0.607791i
$125$	−4.01916	+	9.70312i	−0.359485	+	0.867873i
$126$		0			0
$127$	−16.8496			−1.49516			−0.747579	−	0.664173i	$-0.768784\pi$
$127$	−16.8496			−1.49516			−0.747579	+	0.664173i	$0.768784\pi$
$128$	−9.63589	+	5.92872i	−0.851700	+	0.524029i
$129$		0			0
$130$	−10.6843	+	15.8063i	−0.937071	+	1.38630i
$131$	−7.26316	+	17.5348i	−0.634585	+	1.53202i	0.199214	+	0.979956i	$0.436161\pi$
$131$	−7.26316	+	17.5348i	−0.634585	+	1.53202i	−0.833799	+	0.552068i	$0.813839\pi$
$132$		0			0
$133$	0.701045	−	0.290382i	0.0607883	−	0.0251793i
$134$	4.08940	+	6.19172i	0.353270	+	0.534883i
$135$		0			0
$136$	0.818116	−	3.79349i	0.0701528	−	0.325289i
$137$	9.61855	+	9.61855i	0.821768	+	0.821768i	0.986362	−	0.164593i	$-0.0526311\pi$
$137$	9.61855	+	9.61855i	0.821768	+	0.821768i	−0.164593	+	0.986362i	$0.552631\pi$
$138$		0			0
$139$	−7.39391	−	17.8505i	−0.627144	−	1.51406i	−0.843156	−	0.537668i	$-0.819305\pi$
$139$	−7.39391	−	17.8505i	−0.627144	−	1.51406i	0.216013	−	0.976391i	$-0.430695\pi$
$140$	7.57587	+	0.0811156i	0.640278	+	0.00685552i
$141$		0			0
$142$	1.34104	+	6.93569i	0.112537	+	0.582030i
$143$		−	17.4121i		−	1.45607i
$144$		0			0
$145$		−	13.4589i		−	1.11770i
$146$	9.41510	−	1.82044i	0.779199	−	0.150661i
$147$		0			0
$148$	−15.8135	−	16.1558i	−1.29986	−	1.32800i
$149$	−5.64285	−	13.6230i	−0.462280	−	1.11604i	−0.967459	−	0.253029i	$-0.918573\pi$
$149$	−5.64285	−	13.6230i	−0.462280	−	1.11604i	0.505178	−	0.863015i	$-0.331427\pi$
$150$		0			0
$151$	−5.30621	−	5.30621i	−0.431814	−	0.431814i	0.457431	−	0.889245i	$-0.348770\pi$
$151$	−5.30621	−	5.30621i	−0.431814	−	0.431814i	−0.889245	+	0.457431i	$0.848770\pi$
$152$	−1.09640	−	0.758338i	−0.0889297	−	0.0615094i
$153$		0			0
$154$	−5.76971	+	3.81068i	−0.464936	+	0.307073i
$155$	7.92782	−	3.28381i	0.636778	−	0.263762i
$156$		0			0
$157$	3.30883	−	7.98822i	0.264073	−	0.637529i	−0.735110	−	0.677948i	$-0.762869\pi$
$157$	3.30883	−	7.98822i	0.264073	−	0.637529i	0.999183	+	0.0404192i	$0.0128693\pi$
$158$	−16.7561	−	11.3263i	−1.33304	−	0.901070i
$159$		0			0
$160$	−7.09601	−	11.2611i	−0.560989	−	0.890271i
$161$	2.05004			0.161566
$162$		0			0
$163$	−6.00338	+	14.4934i	−0.470221	+	1.13521i	0.493845	+	0.869550i	$0.335591\pi$
$163$	−6.00338	+	14.4934i	−0.470221	+	1.13521i	−0.964066	+	0.265663i	$0.914409\pi$
$164$	3.75213	−	8.79102i	0.292992	−	0.686463i
$165$		0			0
$166$	−10.0586	+	6.64330i	−0.780695	+	0.515620i
$167$	7.23326	−	7.23326i	0.559726	−	0.559726i	−0.369503	−	0.929230i	$-0.620472\pi$
$167$	7.23326	−	7.23326i	0.559726	−	0.559726i	0.929230	+	0.369503i	$0.120472\pi$
$168$		0			0
$169$	14.0518	+	14.0518i	1.08091	+	1.08091i
$170$	4.47303	+	0.914661i	0.343066	+	0.0701513i
$171$		0			0
$172$	−1.08620	+	1.06319i	−0.0828219	+	0.0810671i
$173$	−15.6305	−	6.47436i	−1.18836	−	0.492236i	−0.301142	−	0.953579i	$-0.597368\pi$
$173$	−15.6305	−	6.47436i	−1.18836	−	0.492236i	−0.887222	+	0.461343i	$0.847368\pi$
$174$		0			0
$175$			0.863663i			0.0652868i
$176$	11.1210	+	4.88799i	0.838274	+	0.368446i
$177$		0			0
$178$	−0.548618	−	2.83739i	−0.0411206	−	0.212671i
$179$	−2.28703	−	0.947320i	−0.170941	−	0.0708060i	0.295572	−	0.955320i	$-0.404490\pi$
$179$	−2.28703	−	0.947320i	−0.170941	−	0.0708060i	−0.466513	+	0.884514i	$0.654490\pi$
$180$		0			0
$181$	−7.08921	−	17.1149i	−0.526937	−	1.27214i	−0.933521	−	0.358524i	$-0.883280\pi$
$181$	−7.08921	−	17.1149i	−0.526937	−	1.27214i	0.406584	−	0.913613i	$-0.366720\pi$
$182$	2.61520	−	12.7893i	0.193851	−	0.948005i
$183$		0			0
$184$	−1.95259	−	3.02637i	−0.143947	−	0.223107i
$185$	18.8067	−	18.8067i	1.38270	−	1.38270i
$186$		0			0
$187$	−3.84962	+	1.59457i	−0.281512	+	0.116606i
$188$	−16.9913	+	6.82582i	−1.23922	+	0.497824i
$189$		0			0
$190$	0.878311	−	1.29937i	0.0637194	−	0.0942664i
$191$	−3.56032			−0.257616			−0.128808	−	0.991670i	$-0.541115\pi$
$191$	−3.56032			−0.257616			−0.128808	+	0.991670i	$0.541115\pi$
$192$		0			0
$193$	12.0572			0.867899			0.433949	−	0.900937i	$-0.357120\pi$
$193$	12.0572			0.867899			0.433949	+	0.900937i	$0.357120\pi$
$194$	−7.12172	+	10.5359i	−0.511309	+	0.756431i
$195$		0			0
$196$	8.18071	−	3.28639i	0.584336	−	0.234742i
$197$	−15.8704	+	6.57373i	−1.13072	+	0.468359i	−0.868025	−	0.496521i	$-0.834611\pi$
$197$	−15.8704	+	6.57373i	−1.13072	+	0.468359i	−0.262693	+	0.964879i	$0.584611\pi$
$198$		0			0
$199$	16.0161	−	16.0161i	1.13535	−	1.13535i	0.146075	−	0.989274i	$-0.453336\pi$
$199$	16.0161	−	16.0161i	1.13535	−	1.13535i	0.989274	−	0.146075i	$-0.0466640\pi$
$200$	1.27498	−	0.822609i	0.0901548	−	0.0581673i
$201$		0			0
$202$	4.42756	−	21.6524i	0.311522	−	1.52346i
$203$	3.52407	+	8.50785i	0.247341	+	0.597134i
$204$		0			0
$205$	10.3892	+	4.30333i	0.725610	+	0.300558i
$206$	−2.82354	−	14.6030i	−0.196725	−	1.01744i
$207$		0			0
$208$	−21.3711	+	8.32068i	−1.48182	+	0.576935i
$209$			1.43138i			0.0990108i
$210$		0			0
$211$	5.74128	+	2.37812i	0.395246	+	0.163716i	0.571449	−	0.820638i	$-0.306382\pi$
$211$	5.74128	+	2.37812i	0.395246	+	0.163716i	−0.176203	+	0.984354i	$0.556382\pi$
$212$	1.04479	−	1.02265i	0.0717562	−	0.0702359i
$213$		0			0
$214$	−15.5558	−	3.18090i	−1.06337	−	0.217442i
$215$	−1.26443	−	1.26443i	−0.0862334	−	0.0862334i
$216$		0			0
$217$	−4.15164	+	4.15164i	−0.281831	+	0.281831i
$218$	−13.0881	+	8.64422i	−0.886440	+	0.585461i
$219$		0			0
$220$	−5.61023	+	13.1445i	−0.378242	+	0.886199i
$221$	3.01038	−	7.26769i	0.202500	−	0.488878i
$222$		0			0
$223$	−16.2386			−1.08742			−0.543709	−	0.839274i	$-0.682981\pi$
$223$	−16.2386			−1.08742			−0.543709	+	0.839274i	$0.682981\pi$
$224$	7.43426	+	5.26056i	0.496722	+	0.351486i
$225$		0			0
$226$	24.6145	+	16.6382i	1.63733	+	1.10675i
$227$	2.28158	−	5.50822i	0.151434	−	0.365594i	−0.829898	−	0.557915i	$-0.811602\pi$
$227$	2.28158	−	5.50822i	0.151434	−	0.365594i	0.981332	+	0.192321i	$0.0616016\pi$
$228$		0			0
$229$	−17.1593	+	7.10762i	−1.13392	+	0.469685i	−0.869111	−	0.494617i	$-0.835308\pi$
$229$	−17.1593	+	7.10762i	−1.13392	+	0.469685i	−0.264808	+	0.964301i	$0.585308\pi$
$230$	3.53567	−	2.33518i	0.233135	−	0.153977i
$231$		0			0
$232$	9.20316	−	13.3058i	0.604217	−	0.873571i
$233$	−4.96931	−	4.96931i	−0.325550	−	0.325550i	0.525341	−	0.850892i	$-0.323938\pi$
$233$	−4.96931	−	4.96931i	−0.325550	−	0.325550i	−0.850892	+	0.525341i	$0.823938\pi$
$234$		0			0
$235$	−8.24402	−	19.9028i	−0.537781	−	1.29832i
$236$	−14.4026	−	14.7143i	−0.937526	−	0.957820i
$237$		0			0
$238$	−3.06706	+	0.593026i	−0.198808	+	0.0384402i
$239$			5.43978i			0.351870i	0.984402	+	0.175935i	$0.0562948\pi$
$239$			5.43978i			0.351870i	−0.984402	+	0.175935i	$0.943705\pi$
$240$		0			0
$241$		−	3.47197i		−	0.223649i	−0.993728	−	0.111825i	$-0.964331\pi$
$241$		−	3.47197i		−	0.223649i	0.993728	−	0.111825i	$-0.0356695\pi$
$242$	0.477065	+	2.46733i	0.0306669	+	0.158606i
$243$		0			0
$244$	16.4427	+	0.176054i	1.05264	+	0.0112707i
$245$	3.96921	+	9.58252i	0.253584	+	0.612205i
$246$		0			0
$247$	−1.91082	−	1.91082i	−0.121582	−	0.121582i
$248$	10.0831	+	2.17456i	0.640280	+	0.138085i
$249$		0			0
$250$	−8.18559	−	12.3937i	−0.517702	−	0.783848i
$251$	−18.3761	+	7.61163i	−1.15989	+	0.480442i	−0.877838	−	0.478957i	$-0.841015\pi$
$251$	−18.3761	+	7.61163i	−1.15989	+	0.480442i	−0.282052	+	0.959399i	$0.591015\pi$
$252$		0			0
$253$	−1.47988	+	3.57275i	−0.0930393	+	0.224617i
$254$	13.3445	−	19.7419i	0.837309	−	1.23871i
$255$		0			0
$256$	0.685019	−	15.9853i	0.0428137	−	0.999083i
$257$	−0.252444			−0.0157470			−0.00787352	−	0.999969i	$-0.502506\pi$
$257$	−0.252444			−0.0157470			−0.00787352	+	0.999969i	$0.502506\pi$
$258$		0			0
$259$	−6.96408	+	16.8128i	−0.432727	+	1.04469i
$260$	−10.0578	−	25.0365i	−0.623757	−	1.55270i
$261$		0			0
$262$	−14.7924	−	22.3971i	−0.913880	−	1.38370i
$263$	0.736993	−	0.736993i	0.0454449	−	0.0454449i	−0.684019	−	0.729464i	$-0.739770\pi$
$263$	0.736993	−	0.736993i	0.0454449	−	0.0454449i	0.729464	+	0.684019i	$0.239770\pi$
$264$		0			0
$265$	1.21622	+	1.21622i	0.0747119	+	0.0747119i
$266$	−0.214985	+	1.05136i	−0.0131816	+	0.0644629i
$267$		0			0
$268$	−10.4933	−	0.112352i	−0.640978	−	0.00686302i
$269$	11.7788	+	4.87892i	0.718163	+	0.297473i	0.711678	−	0.702506i	$-0.247936\pi$
$269$	11.7788	+	4.87892i	0.718163	+	0.297473i	0.00648551	+	0.999979i	$0.497936\pi$
$270$		0			0
$271$		−	5.79934i		−	0.352285i	−0.984365	−	0.176142i	$-0.943638\pi$
$271$		−	5.79934i		−	0.352285i	0.984365	−	0.176142i	$-0.0563619\pi$
$272$	3.79673	+	3.96291i	0.230210	+	0.240287i
$273$		0			0
$274$	−18.8873	+	3.65192i	−1.14102	+	0.220620i
$275$	−1.50517	−	0.623461i	−0.0907650	−	0.0375961i
$276$		0			0
$277$	2.73705	+	6.60783i	0.164453	+	0.397026i	0.984527	−	0.175232i	$-0.0560676\pi$
$277$	2.73705	+	6.60783i	0.164453	+	0.397026i	−0.820074	+	0.572258i	$0.806068\pi$
$278$	26.7704	+	5.47410i	1.60558	+	0.328315i
$279$		0			0
$280$	−6.09496	+	8.81204i	−0.364244	+	0.526620i
$281$	−14.9553	+	14.9553i	−0.892161	+	0.892161i	−0.994726	−	0.102566i	$-0.967295\pi$
$281$	−14.9553	+	14.9553i	−0.892161	+	0.892161i	0.102566	+	0.994726i	$0.467295\pi$
$282$		0			0
$283$	−28.8306	+	11.9420i	−1.71380	+	0.709880i	−0.713847	+	0.700301i	$0.753049\pi$
$283$	−28.8306	+	11.9420i	−1.71380	+	0.709880i	−0.999954	+	0.00957841i	$0.996951\pi$
$284$	−9.18829	−	3.92169i	−0.545225	−	0.232709i
$285$		0			0
$286$	20.4010	+	13.7900i	1.20633	+	0.815421i
$287$	−7.69415			−0.454171
$288$		0			0
$289$	15.1175			0.889265
$290$	15.7691	+	10.6591i	0.925995	+	0.625926i
$291$		0			0
$292$	−5.32364	+	12.4730i	−0.311542	+	0.729926i
$293$	−8.68957	+	3.59934i	−0.507650	+	0.210276i	−0.621782	−	0.783190i	$-0.713591\pi$
$293$	−8.68957	+	3.59934i	−0.507650	+	0.210276i	0.114132	+	0.993466i	$0.463591\pi$
$294$		0			0
$295$	17.1287	−	17.1287i	0.997274	−	0.997274i
$296$	31.4529	−	5.73288i	1.82816	−	0.333217i
$297$		0			0
$298$	20.4305	+	4.17770i	1.18351	+	0.242008i
$299$	−2.79386	−	6.74498i	−0.161573	−	0.390072i
$300$		0			0
$301$	1.13037	+	0.468215i	0.0651535	+	0.0269874i
$302$	10.4194	−	2.01463i	0.599572	−	0.115929i
$303$		0			0
$304$	1.75683	−	0.684011i	0.100761	−	0.0392307i
$305$			19.3457i			1.10773i
$306$		0			0
$307$	15.1584	+	6.27880i	0.865134	+	0.358350i	0.770713	−	0.637182i	$-0.219900\pi$
$307$	15.1584	+	6.27880i	0.865134	+	0.358350i	0.0944206	+	0.995532i	$0.469900\pi$
$308$	0.104695	−	9.77807i	0.00596554	−	0.557157i
$309$		0			0
$310$	−2.43118	+	11.8894i	−0.138082	+	0.675270i
$311$	−0.739873	−	0.739873i	−0.0419544	−	0.0419544i	0.685818	−	0.727773i	$-0.259444\pi$
$311$	−0.739873	−	0.739873i	−0.0419544	−	0.0419544i	−0.727773	+	0.685818i	$0.759444\pi$
$312$		0			0
$313$	−14.0483	+	14.0483i	−0.794057	+	0.794057i	−0.982151	−	0.188094i	$-0.939769\pi$
$313$	−14.0483	+	14.0483i	−0.794057	+	0.794057i	0.188094	+	0.982151i	$0.439769\pi$
$314$	6.73889	+	10.2033i	0.380298	+	0.575805i
$315$		0			0
$316$	26.5409	−	10.6621i	1.49304	−	0.599793i
$317$	−10.6324	+	25.6688i	−0.597173	+	1.44170i	0.279277	+	0.960211i	$0.409905\pi$
$317$	−10.6324	+	25.6688i	−0.597173	+	1.44170i	−0.876450	+	0.481493i	$0.840095\pi$
$318$		0			0
$319$	−17.3712			−0.972600
$320$	18.8140	+	0.604516i	1.05174	+	0.0337935i
$321$		0			0
$322$	−1.62359	+	2.40193i	−0.0904789	+	0.133854i
$323$	−0.247471	+	0.597449i	−0.0137697	+	0.0332429i
$324$		0			0
$325$	2.84160	−	1.17703i	0.157624	−	0.0652898i
$326$	−12.2267	−	18.5124i	−0.677176	−	1.02530i
$327$		0			0
$328$	7.32842	+	11.3585i	0.404644	+	0.627168i
$329$	10.4227	+	10.4227i	0.574622	+	0.574622i
$330$		0			0
$331$	10.1989	+	24.6224i	0.560584	+	1.35337i	0.909300	+	0.416142i	$0.136618\pi$
$331$	10.1989	+	24.6224i	0.560584	+	1.35337i	−0.348715	+	0.937229i	$0.613382\pi$
$332$	0.182518	−	17.0465i	0.0100170	−	0.935547i
$333$		0			0
$334$	2.74628	+	14.2035i	0.150270	+	0.777178i
$335$		−	12.3459i		−	0.674526i
$336$		0			0
$337$		−	5.21363i		−	0.284005i	−0.989866	−	0.142002i	$-0.954646\pi$
$337$		−	5.21363i		−	0.284005i	0.989866	−	0.142002i	$-0.0453541\pi$
$338$	−27.5926	+	5.33512i	−1.50084	+	0.290192i
$339$		0			0
$340$	−4.61421	+	4.51645i	−0.250241	+	0.244939i
$341$	−4.23837	−	10.2323i	−0.229521	−	0.554112i
$342$		0			0
$343$	−12.9870	−	12.9870i	−0.701232	−	0.701232i
$344$	−0.385438	−	2.11467i	−0.0207814	−	0.114015i
$345$		0			0
$346$	19.9647	−	13.1859i	1.07331	−	0.708881i
$347$	−28.4977	+	11.8041i	−1.52984	+	0.633680i	−0.979533	−	0.201284i	$-0.935489\pi$
$347$	−28.4977	+	11.8041i	−1.52984	+	0.633680i	−0.550305	+	0.834964i	$0.685489\pi$
$348$		0			0
$349$	−6.28893	+	15.1828i	−0.336639	+	0.812718i	0.661395	+	0.750038i	$0.269965\pi$
$349$	−6.28893	+	15.1828i	−0.336639	+	0.812718i	−0.998034	+	0.0626799i	$0.980035\pi$
$350$	−1.01191	−	0.684002i	−0.0540890	−	0.0365615i
$351$		0			0
$352$	−14.5346	+	9.15873i	−0.774697	+	0.488162i
$353$	10.1322			0.539285			0.269643	−	0.962960i	$-0.413094\pi$
$353$	10.1322			0.539285			0.269643	+	0.962960i	$0.413094\pi$
$354$		0			0
$355$	4.49780	−	10.8586i	0.238718	−	0.576317i
$356$	3.75893	+	1.60436i	0.199223	+	0.0850309i
$357$		0			0
$358$	2.92121	−	1.92935i	0.154391	−	0.101969i
$359$	3.70820	−	3.70820i	0.195711	−	0.195711i	−0.602447	−	0.798159i	$-0.705808\pi$
$359$	3.70820	−	3.70820i	0.195711	−	0.195711i	0.798159	+	0.602447i	$0.205808\pi$
$360$		0			0
$361$	−13.2779	−	13.2779i	−0.698839	−	0.698839i
$362$	25.6672	+	5.24851i	1.34904	+	0.275856i
$363$		0			0
$364$	12.9134	+	13.1929i	0.676847	+	0.691498i
$365$	−14.7405	−	6.10570i	−0.771551	−	0.319587i
$366$		0			0
$367$			16.6849i			0.870945i	0.900202	+	0.435473i	$0.143419\pi$
$367$			16.6849i			0.870945i	−0.900202	+	0.435473i	$0.856581\pi$
$368$	5.09226	+	0.109059i	0.265452	+	0.00568510i
$369$		0			0
$370$	7.14043	+	36.9295i	0.371213	+	1.91987i
$371$	−1.08727	−	0.450364i	−0.0564484	−	0.0233817i
$372$		0			0
$373$	−9.12628	−	22.0328i	−0.472541	−	1.14081i	−0.963036	−	0.269371i	$-0.913184\pi$
$373$	−9.12628	−	22.0328i	−0.472541	−	1.14081i	0.490495	−	0.871444i	$-0.336816\pi$
$374$	1.18054	−	5.77328i	0.0610443	−	0.298529i
$375$		0			0
$376$	5.45924	−	25.3138i	0.281539	−	1.30546i
$377$	23.1896	−	23.1896i	1.19432	−	1.19432i
$378$		0			0
$379$	−11.3661	+	4.70797i	−0.583835	+	0.241832i	−0.654996	−	0.755632i	$-0.727330\pi$
$379$	−11.3661	+	4.70797i	−0.583835	+	0.241832i	0.0711608	+	0.997465i	$0.477330\pi$
$380$	0.826811	+	2.05815i	0.0424145	+	0.105581i
$381$		0			0
$382$	2.81970	−	4.17146i	0.144268	−	0.213430i
$383$	−31.7840			−1.62409			−0.812044	−	0.583596i	$-0.801645\pi$
$383$	−31.7840			−1.62409			−0.812044	+	0.583596i	$0.801645\pi$
$384$		0			0
$385$	11.5044			0.586319
$386$	−9.54907	+	14.1269i	−0.486035	+	0.719040i
$387$		0			0
$388$	−6.70413	−	16.6884i	−0.340350	−	0.847223i
$389$	−16.3082	+	6.75507i	−0.826858	+	0.342496i	−0.755658	−	0.654966i	$-0.772683\pi$
$389$	−16.3082	+	6.75507i	−0.826858	+	0.342496i	−0.0712000	+	0.997462i	$0.522683\pi$
$390$		0			0
$391$	−1.23538	+	1.23538i	−0.0624760	+	0.0624760i
$392$	−2.62843	+	12.1877i	−0.132756	+	0.615572i
$393$		0			0
$394$	4.86688	−	23.8008i	0.245190	−	1.19907i
$395$	12.8774	+	31.0889i	0.647934	+	1.56425i
$396$		0			0
$397$	9.48208	+	3.92761i	0.475892	+	0.197121i	0.607720	−	0.794152i	$-0.292084\pi$
$397$	9.48208	+	3.92761i	0.475892	+	0.197121i	−0.131827	+	0.991273i	$0.542084\pi$
$398$	6.08088	+	31.4496i	0.304807	+	1.57643i
$399$		0			0
$400$	−0.0459457	+	2.14532i	−0.00229728	+	0.107266i
$401$			9.46026i			0.472423i	0.971702	+	0.236211i	$0.0759058\pi$
$401$			9.46026i			0.472423i	−0.971702	+	0.236211i	$0.924094\pi$
$402$		0			0
$403$	19.3176	+	8.00161i	0.962278	+	0.398589i
$404$	21.8625	+	22.3358i	1.08770	+	1.11125i
$405$		0			0
$406$	−12.7592	−	2.60905i	−0.633230	−	0.129485i
$407$	−24.2736	−	24.2736i	−1.20320	−	1.20320i
$408$		0			0
$409$	0.357827	−	0.357827i	0.0176934	−	0.0176934i	−0.698205	−	0.715898i	$-0.746017\pi$
$409$	0.357827	−	0.357827i	0.0176934	−	0.0176934i	0.715898	+	0.698205i	$0.246017\pi$
$410$	−13.2700	+	8.76434i	−0.655359	+	0.432840i
$411$		0			0
$412$	19.3458	+	8.25707i	0.953101	+	0.406797i
$413$	−6.34272	+	15.3127i	−0.312105	+	0.753488i
$414$		0			0
$415$	20.0561			0.984513
$416$	7.17649	−	31.6293i	0.351856	−	1.55075i
$417$		0			0
$418$	−1.67708	−	1.13362i	−0.0820288	−	0.0554474i
$419$	−11.8267	+	28.5522i	−0.577773	+	1.39487i	0.317035	+	0.948414i	$0.397313\pi$
$419$	−11.8267	+	28.5522i	−0.577773	+	1.39487i	−0.894807	+	0.446453i	$0.852687\pi$
$420$		0			0
$421$	26.8221	−	11.1101i	1.30723	−	0.541473i	0.383156	−	0.923684i	$-0.374837\pi$
$421$	26.8221	−	11.1101i	1.30723	−	0.541473i	0.924075	+	0.382211i	$0.124837\pi$
$422$	−7.33330	+	4.84337i	−0.356979	+	0.235772i
$423$		0			0
$424$	0.370742	+	2.03404i	0.0180048	+	0.0987819i
$425$	−0.520456	−	0.520456i	−0.0252458	−	0.0252458i
$426$		0			0
$427$	−5.06547	−	12.2291i	−0.245135	−	0.591809i
$428$	16.0468	−	15.7068i	0.775649	−	0.759215i
$429$		0			0
$430$	2.48287	−	0.480071i	0.119735	−	0.0231511i
$431$			2.17909i			0.104963i	0.998622	+	0.0524815i	$0.0167130\pi$
$431$			2.17909i			0.104963i	−0.998622	+	0.0524815i	$0.983287\pi$
$432$		0			0
$433$			1.63528i			0.0785864i	0.999228	+	0.0392932i	$0.0125106\pi$
$433$			1.63528i			0.0785864i	−0.999228	+	0.0392932i	$0.987489\pi$
$434$	−1.57627	−	8.15228i	−0.0756633	−	0.391322i
$435$		0			0
$436$	0.237492	−	22.1808i	0.0113738	−	1.06227i
$437$	0.229673	+	0.554478i	0.0109867	+	0.0265243i
$438$		0			0
$439$	7.90859	+	7.90859i	0.377456	+	0.377456i	0.870184	−	0.492727i	$-0.164000\pi$
$439$	7.90859	+	7.90859i	0.377456	+	0.377456i	−0.492727	+	0.870184i	$0.664000\pi$
$440$	−10.9576	−	16.9834i	−0.522381	−	0.809650i
$441$		0			0
$442$	6.13106	+	9.28297i	0.291625	+	0.441546i
$443$	14.6031	−	6.04879i	0.693813	−	0.287387i	−0.00777498	−	0.999970i	$-0.502475\pi$
$443$	14.6031	−	6.04879i	0.693813	−	0.287387i	0.701588	+	0.712583i	$0.252475\pi$
$444$		0			0
$445$	−1.84005	+	4.44227i	−0.0872266	+	0.210584i
$446$	12.8606	−	19.0260i	0.608969	−	0.900908i
$447$		0			0
$448$	−12.0513	+	4.54412i	−0.569371	+	0.214689i
$449$	2.96863			0.140098			0.0700492	−	0.997544i	$-0.477684\pi$
$449$	2.96863			0.140098			0.0700492	+	0.997544i	$0.477684\pi$
$450$		0			0
$451$	5.55425	−	13.4092i	0.261540	−	0.631412i
$452$	−38.9883	+	15.6626i	−1.83386	+	0.736706i
$453$		0			0
$454$	4.64676	+	7.03561i	0.218083	+	0.330198i
$455$	−15.3577	+	15.3577i	−0.719982	+	0.719982i
$456$		0			0
$457$	−0.419581	−	0.419581i	−0.0196272	−	0.0196272i	0.697225	−	0.716852i	$-0.254418\pi$
$457$	−0.419581	−	0.419581i	−0.0196272	−	0.0196272i	−0.716852	+	0.697225i	$0.754418\pi$
$458$	5.26214	−	25.7338i	0.245884	−	1.20246i
$459$		0			0
$460$	−0.0641569	+	5.99199i	−0.00299133	+	0.279378i
$461$	−19.3447	−	8.01282i	−0.900971	−	0.373194i	−0.116378	−	0.993205i	$-0.537128\pi$
$461$	−19.3447	−	8.01282i	−0.900971	−	0.373194i	−0.784593	+	0.620011i	$0.787128\pi$
$462$		0			0
$463$			26.5615i			1.23442i	0.786800	+	0.617209i	$0.211737\pi$
$463$			26.5615i			1.23442i	−0.786800	+	0.617209i	$0.788263\pi$
$464$	8.30112	+	21.3208i	0.385370	+	0.989795i
$465$		0			0
$466$	9.75789	−	1.88672i	0.452026	−	0.0874005i
$467$	4.18753	+	1.73453i	0.193776	+	0.0802645i	0.477461	−	0.878653i	$-0.341557\pi$
$467$	4.18753	+	1.73453i	0.193776	+	0.0802645i	−0.283685	+	0.958917i	$0.591557\pi$
$468$		0			0
$469$	3.23264	+	7.80427i	0.149269	+	0.360368i
$470$	29.8483	+	6.10348i	1.37680	+	0.281533i
$471$		0			0
$472$	28.6466	−	5.22137i	1.31857	−	0.240333i
$473$	−1.63198	+	1.63198i	−0.0750386	+	0.0750386i
$474$		0			0
$475$	−0.233597	+	0.0967590i	−0.0107182	+	0.00443961i
$476$	1.73423	−	4.06320i	0.0794882	−	0.186236i
$477$		0			0
$478$	−6.37353	−	4.30819i	−0.291518	−	0.197052i
$479$	26.0009			1.18801			0.594005	−	0.804461i	$-0.297546\pi$
$479$	26.0009			1.18801			0.594005	+	0.804461i	$0.297546\pi$
$480$		0			0
$481$	64.8078			2.95498
$482$	4.06794	+	2.74972i	0.185290	+	0.125246i
$483$		0			0
$484$	−3.26868	−	1.39511i	−0.148576	−	0.0634143i
$485$	19.5480	−	8.09705i	0.887629	−	0.367668i
$486$		0			0
$487$	29.5458	−	29.5458i	1.33885	−	1.33885i	0.441667	−	0.897179i	$-0.354387\pi$
$487$	29.5458	−	29.5458i	1.33885	−	1.33885i	0.897179	−	0.441667i	$-0.145613\pi$
$488$	−13.2286	+	19.1257i	−0.598829	+	0.865781i
$489$		0			0
$490$	−14.3709	−	2.93862i	−0.649212	−	0.132753i
$491$	14.1215	+	34.0923i	0.637294	+	1.53856i	0.830271	+	0.557360i	$0.188185\pi$
$491$	14.1215	+	34.0923i	0.637294	+	1.53856i	−0.192978	+	0.981203i	$0.561815\pi$
$492$		0			0
$493$	−7.25061	−	3.00330i	−0.326551	−	0.135262i
$494$	3.75214	−	0.725488i	0.168817	−	0.0326412i
$495$		0			0
$496$	−10.5335	+	10.0917i	−0.472966	+	0.453132i
$497$			8.04185i			0.360726i
$498$		0			0
$499$	34.7185	+	14.3809i	1.55421	+	0.643776i	0.984072	−	0.177770i	$-0.0568884\pi$
$499$	34.7185	+	14.3809i	1.55421	+	0.643776i	0.570141	+	0.821547i	$0.306888\pi$
$500$	21.0039	+	0.224891i	0.939325	+	0.0100574i
$501$		0			0
$502$	5.63529	−	27.5587i	0.251515	−	1.23000i
$503$	−16.2601	−	16.2601i	−0.725002	−	0.725002i	0.244618	−	0.969620i	$-0.421338\pi$
$503$	−16.2601	−	16.2601i	−0.725002	−	0.725002i	−0.969620	+	0.244618i	$0.921338\pi$
$504$		0			0
$505$	−26.0008	+	26.0008i	−1.15702	+	1.15702i
$506$	−3.01398	−	4.56344i	−0.133988	−	0.202870i
$507$		0			0
$508$	12.5620	+	31.2703i	0.557350	+	1.38739i
$509$	−0.584208	+	1.41040i	−0.0258946	+	0.0625150i	−0.936298	−	0.351207i	$-0.885771\pi$
$509$	−0.584208	+	1.41040i	−0.0258946	+	0.0625150i	0.910403	+	0.413722i	$0.135771\pi$
$510$		0			0
$511$	10.9167			0.482927
$512$	18.1867	+	13.4626i	0.803748	+	0.594970i
$513$		0			0
$514$	0.199930	−	0.295777i	0.00881855	−	0.0130462i
$515$	−9.47007	+	22.8628i	−0.417301	+	1.00745i
$516$		0			0
$517$	−25.6883	+	10.6404i	−1.12977	+	0.467966i
$518$	−14.1833	−	21.4748i	−0.623180	−	0.943550i
$519$		0			0
$520$	37.2996	+	8.04413i	1.63570	+	0.352759i
$521$	0.163416	+	0.163416i	0.00715940	+	0.00715940i	0.710677	−	0.703518i	$-0.248389\pi$
$521$	0.163416	+	0.163416i	0.00715940	+	0.00715940i	−0.703518	+	0.710677i	$0.748389\pi$
$522$		0			0
$523$	12.2090	+	29.4752i	0.533864	+	1.28886i	0.928946	+	0.370216i	$0.120716\pi$
$523$	12.2090	+	29.4752i	0.533864	+	1.28886i	−0.395081	+	0.918646i	$0.629284\pi$
$524$	37.9569	+	0.406409i	1.65816	+	0.0177540i
$525$		0			0
$526$	0.279817	+	1.44718i	0.0122006	+	0.0631002i
$527$		−	5.00367i		−	0.217963i
$528$		0			0
$529$		−	21.3786i		−	0.929503i
$530$	−2.38821	+	0.461768i	−0.103737	+	0.0200579i
$531$		0			0
$532$	−1.06156	−	1.08454i	−0.0460246	−	0.0470208i
$533$	10.4859	+	25.3151i	0.454193	+	1.09652i
$534$		0			0
$535$	18.6798	+	18.6798i	0.807599	+	0.807599i
$536$	8.44208	−	12.2055i	0.364642	−	0.527197i
$537$		0			0
$538$	−15.0449	+	9.93661i	−0.648633	+	0.428398i
$539$	12.3680	−	5.12301i	0.532729	−	0.220664i
$540$		0			0
$541$	−8.77009	+	21.1729i	−0.377056	+	0.910293i	0.615459	+	0.788169i	$0.288971\pi$
$541$	−8.77009	+	21.1729i	−0.377056	+	0.910293i	−0.992515	+	0.122124i	$0.961029\pi$
$542$	6.79481	+	4.59295i	0.291862	+	0.197284i
$543$		0			0
$544$	−7.65009	+	1.30990i	−0.327995	+	0.0561617i
$545$	26.0968			1.11787
$546$		0			0
$547$	11.2969	−	27.2730i	0.483019	−	1.16611i	−0.475150	−	0.879905i	$-0.657606\pi$
$547$	11.2969	−	27.2730i	0.483019	−	1.16611i	0.958168	−	0.286205i	$-0.0923939\pi$
$548$	10.6796	−	25.0216i	0.456208	−	1.06887i
$549$		0			0
$550$	1.92254	−	1.26977i	0.0819773	−	0.0541430i
$551$	−1.90633	+	1.90633i	−0.0812122	+	0.0812122i
$552$		0			0
$553$	−16.2806	−	16.2806i	−0.692321	−	0.692321i
$554$	−9.90976	−	2.02638i	−0.421025	−	0.0860928i
$555$		0			0
$556$	−27.6153	+	27.0302i	−1.17115	+	1.14634i
$557$	−27.8164	−	11.5219i	−1.17862	−	0.488200i	−0.294586	−	0.955625i	$-0.595182\pi$
$557$	−27.8164	−	11.5219i	−1.17862	−	0.488200i	−0.884033	+	0.467425i	$0.845182\pi$
$558$		0			0
$559$		−	4.35721i		−	0.184291i
$560$	−5.49757	−	14.1201i	−0.232315	−	0.596684i
$561$		0			0
$562$	−5.67815	−	29.3668i	−0.239518	−	1.23876i
$563$	23.9806	+	9.93310i	1.01066	+	0.418630i	0.825696	−	0.564115i	$-0.190782\pi$
$563$	23.9806	+	9.93310i	1.01066	+	0.418630i	0.184966	+	0.982745i	$0.440782\pi$
$564$		0			0
$565$	−18.9168	−	45.6692i	−0.795836	−	1.92132i
$566$	8.84131	−	43.2373i	0.371628	−	1.81740i
$567$		0			0
$568$	11.8718	−	7.65959i	0.498129	−	0.321389i
$569$	−4.09869	+	4.09869i	−0.171826	+	0.171826i	−0.787781	−	0.615955i	$-0.788770\pi$
$569$	−4.09869	+	4.09869i	−0.171826	+	0.171826i	0.615955	+	0.787781i	$0.288770\pi$
$570$		0			0
$571$	21.9883	−	9.10786i	0.920182	−	0.381152i	0.128237	−	0.991744i	$-0.459068\pi$
$571$	21.9883	−	9.10786i	0.920182	−	0.381152i	0.791946	+	0.610592i	$0.209068\pi$
$572$	−32.3142	+	12.9814i	−1.35113	+	0.542781i
$573$		0			0
$574$	6.09360	−	9.01487i	0.254342	−	0.376274i
$575$	−0.683098			−0.0284871
$576$		0			0
$577$	−36.1747			−1.50597			−0.752987	−	0.658036i	$-0.771388\pi$
$577$	−36.1747			−1.50597			−0.752987	+	0.658036i	$0.771388\pi$
$578$	−11.9727	+	17.7125i	−0.498001	+	0.736742i
$579$		0			0
$580$	−24.9776	+	10.0341i	−1.03714	+	0.416645i
$581$	−12.6782	+	5.25147i	−0.525979	+	0.217868i
$582$		0			0
$583$	1.56976	−	1.56976i	0.0650129	−	0.0650129i
$584$	−10.3978	−	16.1158i	−0.430264	−	0.666876i
$585$		0			0
$586$	2.66478	−	13.0318i	0.110081	−	0.538337i
$587$	−10.4373	−	25.1978i	−0.430793	−	1.04003i	−0.979032	−	0.203704i	$-0.934702\pi$
$587$	−10.4373	−	25.1978i	−0.430793	−	1.04003i	0.548240	−	0.836321i	$-0.315298\pi$
$588$		0			0
$589$	−1.58802	−	0.657781i	−0.0654334	−	0.0271034i
$590$	6.50334	+	33.6345i	0.267738	+	1.38471i
$591$		0			0
$592$	−18.1931	+	41.3922i	−0.747731	+	1.70121i
$593$		−	11.4262i		−	0.469220i	−0.972090	−	0.234610i	$-0.924619\pi$
$593$		−	11.4262i		−	0.469220i	0.972090	−	0.234610i	$-0.0753813\pi$
$594$		0			0
$595$	4.80185	+	1.98899i	0.196857	+	0.0815408i
$596$	−21.0753	+	20.6288i	−0.863279	+	0.844988i
$597$		0			0
$598$	10.1154	+	2.06844i	0.413652	+	0.0845849i
$599$	3.62337	+	3.62337i	0.148047	+	0.148047i	0.777245	−	0.629198i	$-0.216617\pi$
$599$	3.62337	+	3.62337i	0.148047	+	0.148047i	−0.629198	+	0.777245i	$0.716617\pi$
$600$		0			0
$601$	−29.0115	+	29.0115i	−1.18341	+	1.18341i	−0.204549	+	0.978856i	$0.565573\pi$
$601$	−29.0115	+	29.0115i	−1.18341	+	1.18341i	−0.978856	+	0.204549i	$0.934427\pi$
$602$	−1.44381	+	0.953585i	−0.0588455	+	0.0388652i
$603$		0			0
$604$	−5.89153	+	13.8035i	−0.239723	+	0.561657i
$605$	1.60006	−	3.86289i	0.0650518	−	0.157049i
$606$		0			0
$607$	12.5298			0.508569			0.254284	−	0.967129i	$-0.418160\pi$
$607$	12.5298			0.508569			0.254284	+	0.967129i	$0.418160\pi$
$608$	−0.589951	+	2.60012i	−0.0239257	+	0.105449i
$609$		0			0
$610$	−22.6665	−	15.3214i	−0.917738	−	0.620345i
$611$	20.0881	−	48.4969i	0.812677	−	1.96197i
$612$		0			0
$613$	14.8631	−	6.15648i	0.600314	−	0.248658i	−0.0617671	−	0.998091i	$-0.519674\pi$
$613$	14.8631	−	6.15648i	0.600314	−	0.248658i	0.662081	+	0.749433i	$0.269674\pi$
$614$	−19.3617	+	12.7877i	−0.781374	+	0.516068i
$615$		0			0
$616$	11.3736	+	7.86669i	0.458255	+	0.316958i
$617$	−24.3889	−	24.3889i	−0.981862	−	0.981862i	0.0179765	−	0.999838i	$-0.494278\pi$
$617$	−24.3889	−	24.3889i	−0.981862	−	0.981862i	−0.999838	+	0.0179765i	$0.994278\pi$
$618$		0			0
$619$	−17.9672	−	43.3767i	−0.722163	−	1.74345i	−0.667095	−	0.744972i	$-0.732463\pi$
$619$	−17.9672	−	43.3767i	−0.722163	−	1.74345i	−0.0550673	−	0.998483i	$-0.517537\pi$
$620$	−12.0048	−	12.2646i	−0.482123	−	0.492559i
$621$		0			0
$622$	1.45284	−	0.280911i	0.0582535	−	0.0112635i
$623$		−	3.28992i		−	0.131808i
$624$		0			0
$625$			27.3945i			1.09578i
$626$	−5.33378	−	27.5857i	−0.213181	−	1.10255i
$627$		0			0
$628$	−17.2918	−	0.185145i	−0.690017	−	0.00738808i
$629$	−5.93497	−	14.3283i	−0.236643	−	0.571306i
$630$		0			0
$631$	−6.20470	−	6.20470i	−0.247005	−	0.247005i	0.572735	−	0.819740i	$-0.305882\pi$
$631$	−6.20470	−	6.20470i	−0.247005	−	0.247005i	−0.819740	+	0.572735i	$0.805882\pi$
$632$	−8.52751	+	39.5409i	−0.339206	+	1.57285i
$633$		0			0
$634$	−21.6543	−	32.7866i	−0.860003	−	1.30212i
$635$	−36.6286	+	15.1721i	−1.45356	+	0.602085i
$636$		0			0
$637$	−9.67171	+	23.3496i	−0.383207	+	0.925144i
$638$	13.7576	−	20.3530i	0.544669	−	0.805783i
$639$		0			0
$640$	−15.6086	+	21.5647i	−0.616984	+	0.852421i
$641$	−16.3098			−0.644197			−0.322099	−	0.946706i	$-0.604388\pi$
$641$	−16.3098			−0.644197			−0.322099	+	0.946706i	$0.604388\pi$
$642$		0			0
$643$	6.11409	−	14.7607i	0.241116	−	0.582106i	−0.756278	−	0.654250i	$-0.772984\pi$
$643$	6.11409	−	14.7607i	0.241116	−	0.582106i	0.997394	+	0.0721444i	$0.0229842\pi$
$644$	−1.52838	−	3.80456i	−0.0602268	−	0.149920i
$645$		0			0
$646$	−0.504011	−	0.763117i	−0.0198300	−	0.0300244i
$647$	28.6611	−	28.6611i	1.12678	−	1.12678i	0.136087	−	0.990697i	$-0.456547\pi$
$647$	28.6611	−	28.6611i	1.12678	−	1.12678i	0.990697	−	0.136087i	$-0.0434528\pi$
$648$		0			0
$649$	−22.1078	−	22.1078i	−0.867808	−	0.867808i
$650$	−0.871417	+	4.26155i	−0.0341798	+	0.167152i
$651$		0			0
$652$	31.3734	+	0.335918i	1.22868	+	0.0131556i
$653$	−16.8705	−	6.98799i	−0.660194	−	0.273461i	0.0273263	−	0.999627i	$-0.491301\pi$
$653$	−16.8705	−	6.98799i	−0.660194	−	0.273461i	−0.687520	+	0.726165i	$0.741301\pi$
$654$		0			0
$655$			44.6582i			1.74494i
$656$	−19.1122	−	0.409319i	−0.746204	−	0.0159812i
$657$		0			0
$658$	−20.4663	+	3.95723i	−0.797861	+	0.154269i
$659$	33.2906	+	13.7894i	1.29682	+	0.537160i	0.921011	−	0.389537i	$-0.127365\pi$
$659$	33.2906	+	13.7894i	1.29682	+	0.537160i	0.375808	+	0.926697i	$0.377365\pi$
$660$		0			0
$661$	−8.60025	−	20.7628i	−0.334511	−	0.807581i	−0.998223	−	0.0595926i	$-0.981020\pi$
$661$	−8.60025	−	20.7628i	−0.334511	−	0.807581i	0.663712	−	0.747988i	$-0.268980\pi$
$662$	−36.9263	−	7.55081i	−1.43518	−	0.293471i
$663$		0			0
$664$	19.8280	+	13.7143i	0.769476	+	0.532218i
$665$	1.26250	−	1.26250i	0.0489577	−	0.0489577i
$666$		0			0
$667$	−6.72912	+	2.78729i	−0.260553	+	0.107924i
$668$	−18.8165	−	8.03114i	−0.728033	−	0.310734i
$669$		0			0
$670$	14.4651	+	9.77766i	0.558834	+	0.377744i
$671$	24.9692			0.963927
$672$		0			0
$673$	4.18136			0.161179			0.0805897	−	0.996747i	$-0.474320\pi$
$673$	4.18136			0.161179			0.0805897	+	0.996747i	$0.474320\pi$
$674$	6.10857	+	4.12909i	0.235293	+	0.159046i
$675$		0			0
$676$	15.6019	−	36.5543i	0.600072	−	1.40593i
$677$	42.7076	−	17.6900i	1.64138	−	0.679884i	0.644948	−	0.764227i	$-0.276879\pi$
$677$	42.7076	−	17.6900i	1.64138	−	0.679884i	0.996437	+	0.0843427i	$0.0268790\pi$
$678$		0			0
$679$	−10.2369	+	10.2369i	−0.392855	+	0.392855i
$680$	−1.63735	−	8.98318i	−0.0627896	−	0.344489i
$681$		0			0
$682$	15.3454	+	3.13789i	0.587607	+	0.120156i
$683$	−6.12019	−	14.7754i	−0.234182	−	0.565366i	0.762479	−	0.647013i	$-0.223982\pi$
$683$	−6.12019	−	14.7754i	−0.234182	−	0.565366i	−0.996661	+	0.0816467i	$0.973982\pi$
$684$		0			0
$685$	29.5703	+	12.2484i	1.12982	+	0.467988i
$686$	25.5017	−	4.93083i	0.973658	−	0.188260i
$687$		0			0
$688$	2.78291	+	1.22317i	0.106098	+	0.0466330i
$689$			4.19109i			0.159668i
$690$		0			0
$691$	−5.16170	−	2.13805i	−0.196360	−	0.0813352i	0.282336	−	0.959316i	$-0.408891\pi$
$691$	−5.16170	−	2.13805i	−0.196360	−	0.0813352i	−0.478697	+	0.877980i	$0.658891\pi$
$692$	−0.362271	+	33.8347i	−0.0137715	+	1.28620i
$693$		0			0
$694$	8.73923	−	42.7381i	0.331737	−	1.62231i
$695$	−32.1466	−	32.1466i	−1.21939	−	1.21939i
$696$		0			0
$697$	4.63661	−	4.63661i	0.175624	−	0.175624i
$698$	−12.8083	−	19.3929i	−0.484801	−	0.734032i
$699$		0			0
$700$	1.60283	−	0.643895i	0.0605811	−	0.0243369i
$701$	−0.0119150	+	0.0287652i	−0.000450022	+	0.00108645i	−0.924104	−	0.382140i	$-0.875187\pi$
$701$	−0.0119150	+	0.0287652i	−0.000450022	+	0.00108645i	0.923654	+	0.383227i	$0.125187\pi$
$702$		0			0
$703$	−5.32760			−0.200934
$704$	0.780241	−	24.2830i	0.0294064	−	0.915200i
$705$		0			0
$706$	−8.02452	+	11.8715i	−0.302007	+	0.446789i
$707$	9.62802	−	23.2441i	0.362099	−	0.874184i
$708$		0			0
$709$	−26.8174	+	11.1081i	−1.00715	+	0.417175i	−0.824414	−	0.565988i	$-0.808495\pi$
$709$	−26.8174	+	11.1081i	−1.00715	+	0.417175i	−0.182735	+	0.983162i	$0.558495\pi$
$710$	9.16040	+	13.8697i	0.343784	+	0.520520i
$711$		0			0
$712$	−4.85674	+	3.13354i	−0.182014	+	0.117434i
$713$	−3.28366	−	3.28366i	−0.122974	−	0.122974i
$714$		0			0
$715$	−15.6786	−	37.8515i	−0.586346	−	1.41557i
$716$	−0.0530071	+	4.95065i	−0.00198097	+	0.185014i
$717$		0			0
$718$	1.40791	+	7.28154i	0.0525427	+	0.271745i
$719$			7.84582i			0.292600i	0.989240	+	0.146300i	$0.0467364\pi$
$719$			7.84582i			0.292600i	−0.989240	+	0.146300i	$0.953264\pi$
$720$		0			0
$721$		−	16.9320i		−	0.630582i
$722$	26.0730	−	5.04129i	0.970336	−	0.187618i
$723$		0			0
$724$	−26.4773	+	25.9163i	−0.984020	+	0.963172i
$725$	−1.17426	−	2.83492i	−0.0436110	−	0.105286i
$726$		0			0
$727$	−11.0377	−	11.0377i	−0.409367	−	0.409367i	0.472151	−	0.881518i	$-0.343478\pi$
$727$	−11.0377	−	11.0377i	−0.409367	−	0.409367i	−0.881518	+	0.472151i	$0.843478\pi$
$728$	−25.6847	+	4.68152i	−0.951939	+	0.173509i
$729$		0			0
$730$	18.8279	−	12.4351i	0.696852	−	0.460245i
$731$	−0.963331	+	0.399025i	−0.0356301	+	0.0147585i
$732$		0			0
$733$	−13.0754	+	31.5669i	−0.482952	+	1.16595i	0.475248	+	0.879852i	$0.342358\pi$
$733$	−13.0754	+	31.5669i	−0.482952	+	1.16595i	−0.958200	+	0.286098i	$0.907642\pi$
$734$	−19.5489	−	13.2141i	−0.721564	−	0.487741i
$735$		0			0
$736$	−4.16074	+	5.87999i	−0.153367	+	0.216739i
$737$	−15.9346			−0.586960
$738$		0			0
$739$	−6.90421	+	16.6682i	−0.253975	+	0.613151i	−0.998518	−	0.0544243i	$-0.982668\pi$
$739$	−6.90421	+	16.6682i	−0.253975	+	0.613151i	0.744543	+	0.667575i	$0.232668\pi$
$740$	−48.9236	−	20.8813i	−1.79847	−	0.767610i
$741$		0			0
$742$	1.38877	−	0.917229i	0.0509832	−	0.0336725i
$743$	−16.5040	+	16.5040i	−0.605472	+	0.605472i	−0.941759	−	0.336287i	$-0.890829\pi$
$743$	−16.5040	+	16.5040i	−0.605472	+	0.605472i	0.336287	+	0.941759i	$0.390829\pi$
$744$		0			0
$745$	−24.5335	−	24.5335i	−0.898838	−	0.898838i
$746$	33.0426	+	6.75667i	1.20978	+	0.247379i
$747$		0			0
$748$	5.82932	+	5.95550i	0.213141	+	0.217755i
$749$	−16.6993	−	6.91708i	−0.610180	−	0.252745i
$750$		0			0
$751$			16.8926i			0.616421i	0.951318	+	0.308211i	$0.0997301\pi$
$751$			16.8926i			0.616421i	−0.951318	+	0.308211i	$0.900270\pi$
$752$	25.3353	+	26.4443i	0.923885	+	0.964324i
$753$		0			0
$754$	8.80449	+	45.5358i	0.320640	+	1.65832i
$755$	−16.3129	−	6.75702i	−0.593687	−	0.245913i
$756$		0			0
$757$	4.13477	+	9.98223i	0.150281	+	0.362810i	0.981035	−	0.193829i	$-0.0620906\pi$
$757$	4.13477	+	9.98223i	0.150281	+	0.362810i	−0.830754	+	0.556639i	$0.812091\pi$
$758$	3.48556	−	17.0457i	0.126601	−	0.619127i
$759$		0			0
$760$	−3.06625	−	0.661277i	−0.111225	−	0.0239870i
$761$	11.6853	−	11.6853i	0.423590	−	0.423590i	−0.462848	−	0.886438i	$-0.653172\pi$
$761$	11.6853	−	11.6853i	0.423590	−	0.423590i	0.886438	+	0.462848i	$0.153172\pi$
$762$		0			0
$763$	−16.4968	+	6.83318i	−0.597223	+	0.247378i
$764$	2.65436	+	6.60741i	0.0960314	+	0.239048i
$765$		0			0
$766$	25.1723	−	37.2399i	0.909511	−	1.34553i
$767$	59.0255			2.13129
$768$		0			0
$769$	−10.8197			−0.390167			−0.195083	−	0.980787i	$-0.562498\pi$
$769$	−10.8197			−0.390167			−0.195083	+	0.980787i	$0.562498\pi$
$770$	−9.11124	+	13.4792i	−0.328346	+	0.485755i
$771$		0			0
$772$	−8.98915	−	22.3764i	−0.323527	−	0.805344i
$773$	−18.6929	+	7.74283i	−0.672335	+	0.278490i	−0.692619	−	0.721304i	$-0.743543\pi$
$773$	−18.6929	+	7.74283i	−0.672335	+	0.278490i	0.0202835	+	0.999794i	$0.493543\pi$
$774$		0			0
$775$	1.38338	−	1.38338i	0.0496924	−	0.0496924i
$776$	24.8625	+	5.36191i	0.892511	+	0.192481i
$777$		0			0
$778$	5.00114	−	24.4574i	0.179299	−	0.876841i
$779$	−0.862002	−	2.08106i	−0.0308844	−	0.0745616i
$780$		0			0
$781$	−14.0151	−	5.80525i	−0.501500	−	0.207728i
$782$	−0.469043	−	2.42584i	−0.0167729	−	0.0867477i
$783$		0			0
$784$	−12.1981	−	12.7320i	−0.435646	−	0.454715i
$785$		−	20.3447i		−	0.726132i
$786$		0			0
$787$	32.5894	+	13.4990i	1.16169	+	0.481187i	0.878437	−	0.477859i	$-0.158587\pi$
$787$	32.5894	+	13.4990i	1.16169	+	0.481187i	0.283251	+	0.959046i	$0.408587\pi$
$788$	24.0318	+	24.5520i	0.856099	+	0.874630i
$789$		0			0
$790$	−46.6240	−	9.53384i	−1.65881	−	0.339199i
$791$	23.9160	+	23.9160i	0.850355	+	0.850355i
$792$		0			0
$793$	−33.3326	+	33.3326i	−1.18367	+	1.18367i
$794$	−12.1114	+	7.99913i	−0.429818	+	0.283878i
$795$		0			0
$796$	−41.6640	−	17.7828i	−1.47674	−	0.630293i
$797$	17.1820	−	41.4810i	0.608617	−	1.46933i	−0.255888	−	0.966706i	$-0.582368\pi$
$797$	17.1820	−	41.4810i	0.608617	−	1.46933i	0.864505	−	0.502625i	$-0.167632\pi$
$798$		0			0
$799$	−12.5617			−0.444403
$800$	−2.47719	−	1.75288i	−0.0875818	−	0.0619738i
$801$		0			0
$802$	−11.0841	−	7.49232i	−0.391395	−	0.264563i
$803$	−7.88055	+	19.0253i	−0.278098	+	0.671389i
$804$		0			0
$805$	4.45649	−	1.84594i	0.157071	−	0.0650608i
$806$	−24.6742	+	16.2964i	−0.869113	+	0.574017i
$807$		0			0
$808$	−43.4844	+	7.92585i	−1.52978	+	0.278830i
$809$	26.1069	+	26.1069i	0.917871	+	0.917871i	0.996874	−	0.0790034i	$-0.0251738\pi$
$809$	26.1069	+	26.1069i	0.917871	+	0.917871i	−0.0790034	+	0.996874i	$0.525174\pi$
$810$		0			0
$811$	12.9197	+	31.1908i	0.453671	+	1.09526i	0.970916	+	0.239420i	$0.0769574\pi$
$811$	12.9197	+	31.1908i	0.453671	+	1.09526i	−0.517245	+	0.855837i	$0.673043\pi$
$812$	13.1619	−	12.8831i	0.461893	−	0.452107i
$813$		0			0
$814$	47.6644	−	9.21606i	1.67064	−	0.323023i
$815$			36.9124i			1.29298i
$816$		0			0
$817$			0.358190i			0.0125315i
$818$	0.135857	+	0.702639i	0.00475015	+	0.0245672i
$819$		0			0
$820$	0.240792	−	22.4890i	0.00840882	−	0.785350i
$821$	14.0571	+	33.9369i	0.490598	+	1.18441i	0.954417	+	0.298478i	$0.0964788\pi$
$821$	14.0571	+	33.9369i	0.490598	+	1.18441i	−0.463819	+	0.885930i	$0.653521\pi$
$822$		0			0
$823$	−14.7175	−	14.7175i	−0.513018	−	0.513018i	0.402432	−	0.915450i	$-0.368165\pi$
$823$	−14.7175	−	14.7175i	−0.513018	−	0.513018i	−0.915450	+	0.402432i	$0.868165\pi$
$824$	−24.9959	+	16.1272i	−0.870774	+	0.561817i
$825$		0			0
$826$	−12.9178	−	19.5588i	−0.449469	−	0.680537i
$827$	19.0944	−	7.90916i	0.663978	−	0.275029i	−0.0251336	−	0.999684i	$-0.508001\pi$
$827$	19.0944	−	7.90916i	0.663978	−	0.275029i	0.689111	+	0.724656i	$0.258001\pi$
$828$		0			0
$829$	12.7858	−	30.8677i	0.444070	−	1.07208i	−0.530438	−	0.847724i	$-0.677972\pi$
$829$	12.7858	−	30.8677i	0.444070	−	1.07208i	0.974507	−	0.224355i	$-0.0720276\pi$
$830$	−15.8840	+	23.4987i	−0.551341	+	0.815653i
$831$		0			0
$832$	31.3749	+	33.4581i	1.08773	+	1.15995i
$833$	6.04804			0.209552
$834$		0			0
$835$	9.21095	−	22.2372i	0.318758	−	0.769550i
$836$	2.65643	−	1.06715i	0.0918745	−	0.0369083i
$837$		0			0
$838$	−24.0868	−	36.4695i	−0.832064	−	1.25982i
$839$	8.22366	−	8.22366i	0.283912	−	0.283912i	−0.550755	−	0.834667i	$-0.685660\pi$
$839$	8.22366	−	8.22366i	0.283912	−	0.283912i	0.834667	+	0.550755i	$0.185660\pi$
$840$		0			0
$841$	−2.62898	−	2.62898i	−0.0906543	−	0.0906543i
$842$	−8.22539	+	40.2252i	−0.283466	+	1.38625i
$843$		0			0
$844$	0.133067	−	12.4279i	0.00458036	−	0.427787i
$845$	43.1996	+	17.8938i	1.48611	+	0.615567i
$846$		0			0
$847$			2.86084i			0.0982995i
$848$	−2.67681	−	1.17654i	−0.0919221	−	0.0404025i
$849$		0			0
$850$	1.02198	−	0.197604i	0.0350537	−	0.00677775i
$851$	−13.2977	−	5.50811i	−0.455841	−	0.188815i
$852$		0			0
$853$	−3.18696	−	7.69400i	−0.109119	−	0.263437i	0.859882	−	0.510493i	$-0.170537\pi$
$853$	−3.18696	−	7.69400i	−0.109119	−	0.263437i	−0.969001	+	0.247055i	$0.920537\pi$
$854$	18.3400	+	3.75024i	0.627583	+	0.128330i
$855$		0			0
$856$	5.69419	+	31.2406i	0.194623	+	1.06778i
$857$	−19.1857	+	19.1857i	−0.655372	+	0.655372i	−0.954282	−	0.298909i	$-0.903377\pi$
$857$	−19.1857	+	19.1857i	−0.655372	+	0.655372i	0.298909	+	0.954282i	$0.403377\pi$
$858$		0			0
$859$	−5.32393	+	2.20524i	−0.181650	+	0.0752419i	−0.471655	−	0.881783i	$-0.656343\pi$
$859$	−5.32393	+	2.20524i	−0.181650	+	0.0752419i	0.290005	+	0.957025i	$0.406343\pi$
$860$	−1.40391	+	3.28927i	−0.0478728	+	0.112163i
$861$		0			0
$862$	−2.55313	−	1.72579i	−0.0869600	−	0.0587806i
$863$	−10.7984			−0.367582			−0.183791	−	0.982965i	$-0.558837\pi$
$863$	−10.7984			−0.367582			−0.183791	+	0.982965i	$0.558837\pi$
$864$		0			0
$865$	−39.8082			−1.35352
$866$	−1.91598	−	1.29510i	−0.0651075	−	0.0440094i
$867$		0			0
$868$	10.8000	+	4.60959i	0.366576	+	0.156460i
$869$	40.1260	−	16.6207i	1.36118	−	0.563819i
$870$		0			0
$871$	21.2719	−	21.2719i	0.720770	−	0.720770i
$872$	25.8001	+	17.8450i	0.873701	+	0.604307i
$873$		0			0
$874$	−0.831552	−	0.170039i	−0.0281277	−	0.00575164i
$875$	−6.47064	−	15.6215i	−0.218747	−	0.528103i
$876$		0			0
$877$	−8.13374	−	3.36910i	−0.274657	−	0.113767i	0.241104	−	0.970499i	$-0.422491\pi$
$877$	−8.13374	−	3.36910i	−0.274657	−	0.113767i	−0.515761	+	0.856733i	$0.672491\pi$
$878$	−15.5296	+	3.00269i	−0.524097	+	0.101336i
$879$		0			0
$880$	28.5768	+	0.612019i	0.963322	+	0.0206311i
$881$			49.5671i			1.66996i	0.550281	+	0.834980i	$0.314521\pi$
$881$			49.5671i			1.66996i	−0.550281	+	0.834980i	$0.685479\pi$
$882$		0			0
$883$	28.9223	+	11.9800i	0.973314	+	0.403160i	0.811945	−	0.583734i	$-0.198409\pi$
$883$	28.9223	+	11.9800i	0.973314	+	0.403160i	0.161369	+	0.986894i	$0.448409\pi$
$884$	−15.7321	−	0.168445i	−0.529127	−	0.00566542i
$885$		0			0
$886$	−4.47824	+	21.9002i	−0.150449	+	0.735753i
$887$	23.0002	+	23.0002i	0.772270	+	0.772270i	0.978503	−	0.206233i	$-0.0661204\pi$
$887$	23.0002	+	23.0002i	0.772270	+	0.772270i	−0.206233	+	0.978503i	$0.566120\pi$
$888$		0			0
$889$	19.1816	−	19.1816i	0.643331	−	0.643331i
$890$	−3.74752	−	5.67408i	−0.125617	−	0.190196i
$891$		0			0
$892$	12.1065	+	30.1364i	0.405357	+	1.00904i
$893$	−1.65136	+	3.98674i	−0.0552607	+	0.133411i
$894$		0			0
$895$	−5.82469			−0.194698
$896$	4.22026	−	17.7188i	0.140989	−	0.591944i
$897$		0			0
$898$	−2.35109	+	3.47821i	−0.0784570	+	0.116069i
$899$	7.98280	−	19.2722i	0.266241	−	0.642763i
$900$		0			0
$901$	0.926603	−	0.383812i	0.0308696	−	0.0127866i
$902$	11.3120	+	17.1274i	0.376649	+	0.570280i
$903$		0			0
$904$	12.5268	−	58.0852i	0.416636	−	1.93188i
$905$	−30.8219	−	30.8219i	−1.02455	−	1.02455i
$906$		0			0
$907$	−18.4396	−	44.5170i	−0.612276	−	1.47816i	−0.860494	−	0.509460i	$-0.829845\pi$
$907$	−18.4396	−	44.5170i	−0.612276	−	1.47816i	0.248219	−	0.968704i	$-0.420155\pi$
$908$	−11.9234	−	0.127665i	−0.395693	−	0.00423672i
$909$		0			0
$910$	−5.83094	−	30.1569i	−0.193294	−	0.999693i
$911$			15.4598i			0.512207i	0.966649	+	0.256103i	$0.0824388\pi$
$911$			15.4598i			0.512207i	−0.966649	+	0.256103i	$0.917561\pi$
$912$		0			0
$913$		−	25.8861i		−	0.856704i
$914$	0.823902	−	0.159304i	0.0272522	−	0.00526931i
$915$		0			0
$916$	25.9836	+	26.5460i	0.858522	+	0.877106i
$917$	−11.6933	−	28.2301i	−0.386147	−	0.932240i
$918$		0			0
$919$	−2.58772	−	2.58772i	−0.0853611	−	0.0853611i	0.663137	−	0.748498i	$-0.269225\pi$
$919$	−2.58772	−	2.58772i	−0.0853611	−	0.0853611i	−0.748498	+	0.663137i	$0.769225\pi$
$920$	−6.96972	−	4.82070i	−0.229785	−	0.158934i
$921$		0			0
$922$	24.7088	−	16.3192i	0.813741	−	0.537446i
$923$	26.4591	−	10.9597i	0.870912	−	0.360743i
$924$		0			0
$925$	2.32052	−	5.60222i	0.0762981	−	0.184200i
$926$	−31.1208	−	21.0361i	−1.02269	−	0.691290i
$927$		0			0
$928$	−31.5549	−	7.15962i	−1.03584	−	0.235026i
$929$	17.3638			0.569689			0.284845	−	0.958574i	$-0.408058\pi$
$929$	17.3638			0.569689			0.284845	+	0.958574i	$0.408058\pi$
$930$		0			0
$931$	0.795074	−	1.91948i	0.0260575	−	0.0629084i
$932$	−5.51746	+	12.9271i	−0.180730	+	0.423441i
$933$		0			0
$934$	−5.34870	+	3.53262i	−0.175015	+	0.115591i
$935$	−6.93272	+	6.93272i	−0.226724	+	0.226724i
$936$		0			0
$937$	6.82794	+	6.82794i	0.223059	+	0.223059i	0.809785	−	0.586726i	$-0.199584\pi$
$937$	6.82794	+	6.82794i	0.223059	+	0.223059i	−0.586726	+	0.809785i	$0.699584\pi$
$938$	−11.7041	−	2.39329i	−0.382152	−	0.0781437i
$939$		0			0
$940$	−30.7904	+	30.1380i	−1.00427	+	0.982993i
$941$	45.4233	+	18.8150i	1.48076	+	0.613350i	0.969283	−	0.245948i	$-0.0790993\pi$
$941$	45.4233	+	18.8150i	1.48076	+	0.613350i	0.511475	+	0.859298i	$0.329099\pi$
$942$		0			0
$943$		−	6.08554i		−	0.198173i
$944$	−16.5698	+	37.6991i	−0.539302	+	1.22700i
$945$		0			0
$946$	−0.619622	−	3.20461i	−0.0201456	−	0.104191i
$947$	−44.5646	−	18.4593i	−1.44816	−	0.599846i	−0.486395	−	0.873739i	$-0.661688\pi$
$947$	−44.5646	−	18.4593i	−1.44816	−	0.599846i	−0.961760	+	0.273893i	$0.911688\pi$
$948$		0			0
$949$	−14.8777	−	35.9179i	−0.482949	−	1.16594i
$950$	0.0716358	−	0.350326i	0.00232417	−	0.0113661i
$951$		0			0
$952$	3.38718	+	5.24988i	0.109779	+	0.170149i
$953$	36.2629	−	36.2629i	1.17467	−	1.17467i	0.193589	−	0.981083i	$-0.437987\pi$
$953$	36.2629	−	36.2629i	1.17467	−	1.17467i	0.981083	−	0.193589i	$-0.0620128\pi$
$954$		0			0
$955$	−7.73963	+	3.20586i	−0.250449	+	0.103739i
$956$	10.0954	−	4.05557i	0.326508	−	0.131167i
$957$		0			0
$958$	−20.5921	+	30.4640i	−0.665302	+	0.984247i
$959$	−21.8996			−0.707175
$960$		0			0
$961$	−17.7002			−0.570974
$962$	−51.3264	+	75.9323i	−1.65483	+	2.44816i
$963$		0			0
$964$	−6.44344	+	2.58849i	−0.207529	+	0.0833696i
$965$	26.2107	−	10.8568i	0.843753	−	0.349494i
$966$		0			0
$967$	41.3477	−	41.3477i	1.32965	−	1.32965i	0.423983	−	0.905670i	$-0.360632\pi$
$967$	41.3477	−	41.3477i	1.32965	−	1.32965i	0.905670	−	0.423983i	$-0.139368\pi$
$968$	4.22331	−	2.72485i	0.135742	−	0.0875800i
$969$		0			0
$970$	−5.99467	+	29.3162i	−0.192477	+	0.941285i
$971$	3.32571	+	8.02897i	0.106727	+	0.257662i	0.968216	−	0.250114i	$-0.0804680\pi$
$971$	3.32571	+	8.02897i	0.106727	+	0.257662i	−0.861489	+	0.507775i	$0.830468\pi$
$972$		0			0
$973$	28.7383	+	11.9038i	0.921309	+	0.381619i
$974$	11.2178	+	58.0170i	0.359440	+	1.85898i
$975$		0			0
$976$	−11.9320	−	30.6465i	−0.381933	−	0.980969i
$977$		−	8.72467i		−	0.279127i	−0.990213	−	0.139563i	$-0.955430\pi$
$977$		−	8.72467i		−	0.279127i	0.990213	−	0.139563i	$-0.0445699\pi$
$978$		0			0
$979$	5.73358	+	2.37493i	0.183246	+	0.0759029i
$980$	14.8245	−	14.5104i	0.473551	−	0.463518i
$981$		0			0
$982$	−51.1282	−	10.4549i	−1.63157	−	0.333629i
$983$	−0.584357	−	0.584357i	−0.0186381	−	0.0186381i	0.697726	−	0.716364i	$-0.254195\pi$
$983$	−0.584357	−	0.584357i	−0.0186381	−	0.0186381i	−0.716364	+	0.697726i	$0.754195\pi$
$984$		0			0
$985$	−28.5807	+	28.5807i	−0.910657	+	0.910657i
$986$	9.26115	−	6.11665i	0.294935	−	0.194794i
$987$		0			0
$988$	−2.12160	+	4.97078i	−0.0674969	+	0.158141i
$989$	−0.370326	+	0.894045i	−0.0117757	+	0.0284290i
$990$		0			0
$991$	17.5113			0.556266			0.278133	−	0.960543i	$-0.410284\pi$
$991$	17.5113			0.556266			0.278133	+	0.960543i	$0.410284\pi$
$992$	−3.48174	−	20.3340i	−0.110545	−	0.645605i
$993$		0			0
$994$	−9.42226	−	6.36897i	−0.298856	−	0.202012i
$995$	20.3951	−	49.2382i	0.646569	−	1.56095i
$996$		0			0
$997$	−17.9933	+	7.45305i	−0.569852	+	0.236041i	−0.648956	−	0.760826i	$-0.724794\pi$
$997$	−17.9933	+	7.45305i	−0.569852	+	0.236041i	0.0791038	+	0.996866i	$0.474794\pi$
$998$	−44.3457	+	29.2887i	−1.40374	+	0.927117i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.v.a.109.11	✓	128
3.2	odd	2	inner	864.2.v.a.109.22	yes	128
32.5	even	8	inner	864.2.v.a.325.11	yes	128
96.5	odd	8	inner	864.2.v.a.325.22	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
864.2.v.a.109.11	✓	128	1.1	even	1	trivial
864.2.v.a.109.22	yes	128	3.2	odd	2	inner
864.2.v.a.325.11	yes	128	32.5	even	8	inner
864.2.v.a.325.22	yes	128	96.5	odd	8	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.v (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.791979 + 1.17165i) q^{2} +(-0.745540 - 1.85585i) q^{4} +(2.17386 - 0.900442i) q^{5} +(-1.13840 + 1.13840i) q^{7} +(2.76486 + 0.596278i) q^{8} +O(q^{10})\)	\(q+(-0.791979 + 1.17165i) q^{2} +(-0.745540 - 1.85585i) q^{4} +(2.17386 - 0.900442i) q^{5} +(-1.13840 + 1.13840i) q^{7} +(2.76486 + 0.596278i) q^{8} +(-0.666644 + 3.26014i) q^{10} +(-1.16219 - 2.80577i) q^{11} +(5.29700 + 2.19409i) q^{13} +(-0.432223 - 2.23541i) q^{14} +(-2.88834 + 2.76722i) q^{16} -1.37204i q^{17} +(-0.435446 - 0.180368i) q^{19} +(-3.29178 - 3.36303i) q^{20} +(4.20782 + 0.860429i) q^{22} +(-0.900399 - 0.900399i) q^{23} +(0.379330 - 0.379330i) q^{25} +(-6.76583 + 4.46858i) q^{26} +(2.96143 + 1.26398i) q^{28} +(2.18893 - 5.28455i) q^{29} +3.64689 q^{31} +(-0.954714 - 5.57571i) q^{32} +(1.60755 + 1.08662i) q^{34} +(-1.44966 + 3.49980i) q^{35} +(10.4431 - 4.32566i) q^{37} +(0.556192 - 0.367344i) q^{38} +(6.54733 - 1.19337i) q^{40} +(3.37936 + 3.37936i) q^{41} +(-0.290826 - 0.702117i) q^{43} +(-4.34062 + 4.24866i) q^{44} +(1.76805 - 0.341858i) q^{46} -9.15553i q^{47} +4.40807i q^{49} +(0.144022 + 0.744865i) q^{50} +(0.122770 - 11.4662i) q^{52} +(0.279738 + 0.675348i) q^{53} +(-5.05286 - 5.05286i) q^{55} +(-3.82633 + 2.46872i) q^{56} +(4.45807 + 6.74992i) q^{58} +(9.51130 - 3.93971i) q^{59} +(-3.14636 + 7.59599i) q^{61} +(-2.88826 + 4.27289i) q^{62} +(7.28891 + 3.29725i) q^{64} +13.4906 q^{65} +(2.00791 - 4.84753i) q^{67} +(-2.54629 + 1.02291i) q^{68} +(-2.95244 - 4.47026i) q^{70} +(3.53207 - 3.53207i) q^{71} +(-4.79474 - 4.79474i) q^{73} +(-3.20251 + 15.6615i) q^{74} +(-0.0100924 + 0.942593i) q^{76} +(4.51714 + 1.87106i) q^{77} +14.3012i q^{79} +(-3.78712 + 8.61632i) q^{80} +(-6.63581 + 1.28305i) q^{82} +(7.87490 + 3.26189i) q^{83} +(-1.23544 - 2.98262i) q^{85} +(1.05296 + 0.215314i) q^{86} +(-1.54027 - 8.45055i) q^{88} +(-1.44497 + 1.44497i) q^{89} +(-8.52789 + 3.53237i) q^{91} +(-0.999720 + 2.34229i) q^{92} +(10.7271 + 7.25099i) q^{94} -1.10901 q^{95} +8.99231 q^{97} +(-5.16473 - 3.49110i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q+O(q^{10}) \) 128 * q	\( 128 q - 8 q^{10} - 32 q^{16} + 32 q^{22} + 64 q^{40} + 64 q^{46} + 88 q^{52} - 64 q^{55} + 64 q^{58} - 32 q^{61} - 96 q^{64} + 64 q^{67} + 48 q^{70} + 32 q^{76} + 40 q^{82} + 40 q^{88} - 48 q^{91} + 24 q^{94}+O(q^{100}) \) 128 * q - 8 * q^10 - 32 * q^16 + 32 * q^22 + 64 * q^40 + 64 * q^46 + 88 * q^52 - 64 * q^55 + 64 * q^58 - 32 * q^61 - 96 * q^64 + 64 * q^67 + 48 * q^70 + 32 * q^76 + 40 * q^82 + 40 * q^88 - 48 * q^91 + 24 * q^94

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