LMFDB - Embedded newform 864.2.v.b.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.b.325.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.679990 + 1.24001i) q^{2} +(-1.07523 - 1.68638i) q^{4} +(-3.54476 + 1.46829i) q^{5} +(1.60611 - 1.60611i) q^{7} +(2.82227 - 0.186565i) q^{8} +O(q^{10})$	\(q+(-0.679990 + 1.24001i) q^{2} +(-1.07523 - 1.68638i) q^{4} +(-3.54476 + 1.46829i) q^{5} +(1.60611 - 1.60611i) q^{7} +(2.82227 - 0.186565i) q^{8} +(0.589716 - 5.39394i) q^{10} +(0.347249 + 0.838334i) q^{11} +(-5.66583 - 2.34686i) q^{13} +(0.899444 + 3.08372i) q^{14} +(-1.68777 + 3.62649i) q^{16} -0.593837i q^{17} +(5.16462 + 2.13925i) q^{19} +(6.28751 + 4.39907i) q^{20} +(-1.27566 - 0.139468i) q^{22} +(0.0201157 + 0.0201157i) q^{23} +(6.87390 - 6.87390i) q^{25} +(6.76283 - 5.42982i) q^{26} +(-4.43544 - 0.981580i) q^{28} +(2.80250 - 6.76583i) q^{29} +6.90566 q^{31} +(-3.34920 - 4.55882i) q^{32} +(0.736362 + 0.403803i) q^{34} +(-3.33503 + 8.05148i) q^{35} +(1.45330 - 0.601978i) q^{37} +(-6.16457 + 4.94948i) q^{38} +(-9.73032 + 4.80522i) q^{40} +(8.95213 + 8.95213i) q^{41} +(2.56146 + 6.18392i) q^{43} +(1.04038 - 1.48699i) q^{44} +(-0.0386221 + 0.0112651i) q^{46} -2.63414i q^{47} +1.84085i q^{49} +(3.84949 + 13.1979i) q^{50} +(2.13435 + 12.0782i) q^{52} +(2.47496 + 5.97509i) q^{53} +(-2.46183 - 2.46183i) q^{55} +(4.23322 - 4.83250i) q^{56} +(6.48400 + 8.07581i) q^{58} +(-7.46732 + 3.09307i) q^{59} +(-2.06985 + 4.99706i) q^{61} +(-4.69578 + 8.56306i) q^{62} +(7.93039 - 1.05307i) q^{64} +23.5299 q^{65} +(3.91146 - 9.44309i) q^{67} +(-1.00144 + 0.638510i) q^{68} +(-7.71609 - 9.61038i) q^{70} +(10.7650 - 10.7650i) q^{71} +(-4.07812 - 4.07812i) q^{73} +(-0.241775 + 2.21144i) q^{74} +(-1.94554 - 11.0097i) q^{76} +(1.90417 + 0.788734i) q^{77} +7.64704i q^{79} +(0.658016 - 15.3332i) q^{80} +(-17.1880 + 5.01333i) q^{82} +(2.67059 + 1.10620i) q^{83} +(0.871923 + 2.10501i) q^{85} +(-9.40986 - 1.02877i) q^{86} +(1.13643 + 2.30122i) q^{88} +(-3.74752 + 3.74752i) q^{89} +(-12.8692 + 5.33061i) q^{91} +(0.0122938 - 0.0555518i) q^{92} +(3.26635 + 1.79119i) q^{94} -21.4483 q^{95} +14.4996 q^{97} +(-2.28266 - 1.25176i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q+O(q^{10}) $ 128 * q	$ 128 q + 16 q^{10} - 32 q^{16} - 16 q^{22} - 32 q^{40} - 32 q^{46} - 80 q^{52} + 32 q^{55} - 32 q^{58} + 64 q^{61} + 48 q^{64} + 64 q^{67} - 96 q^{70} + 32 q^{76} - 80 q^{82} - 80 q^{88} + 96 q^{91} - 48 q^{94}+O(q^{100}) $ 128 * q + 16 * q^10 - 32 * q^16 - 16 * q^22 - 32 * q^40 - 32 * q^46 - 80 * q^52 + 32 * q^55 - 32 * q^58 + 64 * q^61 + 48 * q^64 + 64 * q^67 - 96 * q^70 + 32 * q^76 - 80 * q^82 - 80 * q^88 + 96 * q^91 - 48 * 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 $

$2$	−0.679990	+	1.24001i	−0.480825	+	0.876816i
$2$	−0.679990	+	1.24001i	−0.480825	+	0.876816i
$3$		0			0
$3$		0			0
$4$	−1.07523	−	1.68638i	−0.537614	−	0.843191i
$5$	−3.54476	+	1.46829i	−1.58526	+	0.656638i	−0.989236	−	0.146327i	$-0.953255\pi$
$5$	−3.54476	+	1.46829i	−1.58526	+	0.656638i	−0.596027	+	0.802964i	$0.703255\pi$
$6$		0			0
$7$	1.60611	−	1.60611i	0.607051	−	0.607051i	−0.335123	−	0.942174i	$-0.608778\pi$
$7$	1.60611	−	1.60611i	0.607051	−	0.607051i	0.942174	+	0.335123i	$0.108778\pi$
$8$	2.82227	−	0.186565i	0.997822	−	0.0659606i
$9$		0			0
$10$	0.589716	−	5.39394i	0.186484	−	1.70571i
$11$	0.347249	+	0.838334i	0.104700	+	0.252767i	0.967544	−	0.252702i	$-0.0813193\pi$
$11$	0.347249	+	0.838334i	0.104700	+	0.252767i	−0.862845	+	0.505469i	$0.831319\pi$
$12$		0			0
$13$	−5.66583	−	2.34686i	−1.57142	−	0.650903i	−0.584394	−	0.811470i	$-0.698668\pi$
$13$	−5.66583	−	2.34686i	−1.57142	−	0.650903i	−0.987025	+	0.160567i	$0.948668\pi$
$14$	0.899444	+	3.08372i	0.240387	+	0.824158i
$15$		0			0
$16$	−1.68777	+	3.62649i	−0.421943	+	0.906622i
$17$		−	0.593837i		−	0.144027i	−0.997404	−	0.0720134i	$-0.977058\pi$
$17$		−	0.593837i		−	0.144027i	0.997404	−	0.0720134i	$-0.0229424\pi$
$18$		0			0
$19$	5.16462	+	2.13925i	1.18484	+	0.490779i	0.886073	−	0.463546i	$-0.153423\pi$
$19$	5.16462	+	2.13925i	1.18484	+	0.490779i	0.298772	+	0.954325i	$0.403423\pi$
$20$	6.28751	+	4.39907i	1.40593	+	0.983663i
$21$		0			0
$22$	−1.27566	−	0.139468i	−0.271973	−	0.0297346i
$23$	0.0201157	+	0.0201157i	0.00419442	+	0.00419442i	0.709201	−	0.705006i	$-0.249056\pi$
$23$	0.0201157	+	0.0201157i	0.00419442	+	0.00419442i	−0.705006	+	0.709201i	$0.749056\pi$
$24$		0			0
$25$	6.87390	−	6.87390i	1.37478	−	1.37478i
$26$	6.76283	−	5.42982i	1.32630	−	1.06487i
$27$		0			0
$28$	−4.43544	−	0.981580i	−0.838219	−	0.185501i
$29$	2.80250	−	6.76583i	0.520411	−	1.25638i	−0.417237	−	0.908798i	$-0.637002\pi$
$29$	2.80250	−	6.76583i	0.520411	−	1.25638i	0.937648	−	0.347586i	$-0.112998\pi$
$30$		0			0
$31$	6.90566			1.24029			0.620147	−	0.784486i	$-0.287073\pi$
$31$	6.90566			1.24029			0.620147	+	0.784486i	$0.287073\pi$
$32$	−3.34920	−	4.55882i	−0.592060	−	0.805894i
$33$		0			0
$34$	0.736362	+	0.403803i	0.126285	+	0.0692517i
$35$	−3.33503	+	8.05148i	−0.563723	+	1.36095i
$36$		0			0
$37$	1.45330	−	0.601978i	0.238921	−	0.0989645i	−0.260010	−	0.965606i	$-0.583726\pi$
$37$	1.45330	−	0.601978i	0.238921	−	0.0989645i	0.498932	+	0.866641i	$0.333726\pi$
$38$	−6.16457	+	4.94948i	−1.00003	+	0.802912i
$39$		0			0
$40$	−9.73032	+	4.80522i	−1.53850	+	0.759772i
$41$	8.95213	+	8.95213i	1.39809	+	1.39809i	0.805524	+	0.592563i	$0.201884\pi$
$41$	8.95213	+	8.95213i	1.39809	+	1.39809i	0.592563	+	0.805524i	$0.298116\pi$
$42$		0			0
$43$	2.56146	+	6.18392i	0.390619	+	0.943039i	0.989805	+	0.142429i	$0.0454912\pi$
$43$	2.56146	+	6.18392i	0.390619	+	0.943039i	−0.599186	+	0.800610i	$0.704509\pi$
$44$	1.04038	−	1.48699i	0.156843	−	0.224173i
$45$		0			0
$46$	−0.0386221	+	0.0112651i	−0.00569452	+	0.00166095i
$47$		−	2.63414i		−	0.384229i	−0.981373	−	0.192115i	$-0.938465\pi$
$47$		−	2.63414i		−	0.384229i	0.981373	−	0.192115i	$-0.0615345\pi$
$48$		0			0
$49$			1.84085i			0.262979i
$50$	3.84949	+	13.1979i	0.544400	+	1.86646i
$51$		0			0
$52$	2.13435	+	12.0782i	0.295981	+	1.67494i
$53$	2.47496	+	5.97509i	0.339962	+	0.820741i	0.997719	+	0.0675106i	$0.0215056\pi$
$53$	2.47496	+	5.97509i	0.339962	+	0.820741i	−0.657756	+	0.753231i	$0.728494\pi$
$54$		0			0
$55$	−2.46183	−	2.46183i	−0.331953	−	0.331953i
$56$	4.23322	−	4.83250i	0.565687	−	0.645770i
$57$		0			0
$58$	6.48400	+	8.07581i	0.851390	+	1.06041i
$59$	−7.46732	+	3.09307i	−0.972163	+	0.402683i	−0.811517	−	0.584329i	$-0.801358\pi$
$59$	−7.46732	+	3.09307i	−0.972163	+	0.402683i	−0.160646	+	0.987012i	$0.551358\pi$
$60$		0			0
$61$	−2.06985	+	4.99706i	−0.265017	+	0.639808i	−0.999235	−	0.0391060i	$-0.987549\pi$
$61$	−2.06985	+	4.99706i	−0.265017	+	0.639808i	0.734218	+	0.678914i	$0.237549\pi$
$62$	−4.69578	+	8.56306i	−0.596365	+	1.08751i
$63$		0			0
$64$	7.93039	−	1.05307i	0.991298	−	0.131634i
$65$	23.5299			2.91852
$66$		0			0
$67$	3.91146	−	9.44309i	0.477860	−	1.15366i	−0.482750	−	0.875758i	$-0.660362\pi$
$67$	3.91146	−	9.44309i	0.477860	−	1.15366i	0.960610	−	0.277899i	$-0.0896380\pi$
$68$	−1.00144	+	0.638510i	−0.121442	+	0.0774307i
$69$		0			0
$70$	−7.71609	−	9.61038i	−0.922249	−	1.14866i
$71$	10.7650	−	10.7650i	1.27757	−	1.27757i	0.335549	−	0.942023i	$-0.391078\pi$
$71$	10.7650	−	10.7650i	1.27757	−	1.27757i	0.942023	−	0.335549i	$-0.108922\pi$
$72$		0			0
$73$	−4.07812	−	4.07812i	−0.477308	−	0.477308i	0.426962	−	0.904270i	$-0.359584\pi$
$73$	−4.07812	−	4.07812i	−0.477308	−	0.477308i	−0.904270	+	0.426962i	$0.859584\pi$
$74$	−0.241775	+	2.21144i	−0.0281058	+	0.257075i
$75$		0			0
$76$	−1.94554	−	11.0097i	−0.223168	−	1.26290i
$77$	1.90417	+	0.788734i	0.217000	+	0.0898845i
$78$		0			0
$79$			7.64704i			0.860359i	0.902743	+	0.430180i	$0.141550\pi$
$79$			7.64704i			0.860359i	−0.902743	+	0.430180i	$0.858450\pi$
$80$	0.658016	−	15.3332i	0.0735684	−	1.71430i
$81$		0			0
$82$	−17.1880	+	5.01333i	−1.89810	+	0.553630i
$83$	2.67059	+	1.10620i	0.293135	+	0.121421i	0.524405	−	0.851469i	$-0.324288\pi$
$83$	2.67059	+	1.10620i	0.293135	+	0.121421i	−0.231269	+	0.972890i	$0.574288\pi$
$84$		0			0
$85$	0.871923	+	2.10501i	0.0945734	+	0.228320i
$86$	−9.40986	−	1.02877i	−1.01469	−	0.110936i
$87$		0			0
$88$	1.13643	+	2.30122i	0.121144	+	0.245311i
$89$	−3.74752	+	3.74752i	−0.397236	+	0.397236i	−0.877257	−	0.480021i	$-0.840629\pi$
$89$	−3.74752	+	3.74752i	−0.397236	+	0.397236i	0.480021	+	0.877257i	$0.340629\pi$
$90$		0			0
$91$	−12.8692	+	5.33061i	−1.34906	+	0.558800i
$92$	0.0122938	−	0.0555518i	0.00128172	−	0.00579168i
$93$		0			0
$94$	3.26635	+	1.79119i	0.336898	+	0.184747i
$95$	−21.4483			−2.20055
$96$		0			0
$97$	14.4996			1.47221			0.736106	−	0.676866i	$-0.236662\pi$
$97$	14.4996			1.47221			0.736106	+	0.676866i	$0.236662\pi$
$98$	−2.28266	−	1.25176i	−0.230584	−	0.126447i
$99$		0			0
$100$	−18.9830	−	4.20102i	−1.89830	−	0.420102i
$101$	3.93445	−	1.62970i	0.391493	−	0.162162i	−0.178249	−	0.983985i	$-0.557043\pi$
$101$	3.93445	−	1.62970i	0.391493	−	0.162162i	0.569742	+	0.821824i	$0.307043\pi$
$102$		0			0
$103$	10.0464	−	10.0464i	0.989903	−	0.989903i	−0.0100468	−	0.999950i	$-0.503198\pi$
$103$	10.0464	−	10.0464i	0.989903	−	0.989903i	0.999950	+	0.0100468i	$0.00319804\pi$
$104$	−16.4283	−	5.56643i	−1.61093	−	0.545834i
$105$		0			0
$106$	−9.09209	−	0.994032i	−0.883102	−	0.0965489i
$107$	−2.72596	−	6.58106i	−0.263529	−	0.636215i	0.735623	−	0.677391i	$-0.236890\pi$
$107$	−2.72596	−	6.58106i	−0.263529	−	0.636215i	−0.999152	+	0.0411761i	$0.986890\pi$
$108$		0			0
$109$	3.05385	+	1.26495i	0.292506	+	0.121160i	0.524111	−	0.851650i	$-0.324398\pi$
$109$	3.05385	+	1.26495i	0.292506	+	0.121160i	−0.231605	+	0.972810i	$0.574398\pi$
$110$	4.72670	−	1.37866i	0.450673	−	0.131450i
$111$		0			0
$112$	3.11379	+	8.53527i	0.294225	+	0.806507i
$113$		−	0.622324i		−	0.0585433i	−0.999571	−	0.0292716i	$-0.990681\pi$
$113$		−	0.622324i		−	0.0585433i	0.999571	−	0.0292716i	$-0.00931879\pi$
$114$		0			0
$115$	−0.100841	−	0.0417697i	−0.00940347	−	0.00389505i
$116$	−14.4231	+	2.54872i	−1.33915	+	0.236643i
$117$		0			0
$118$	1.24228	−	11.3628i	0.114362	−	1.04603i
$119$	−0.953766	−	0.953766i	−0.0874316	−	0.0874316i
$120$		0			0
$121$	7.19595	−	7.19595i	0.654178	−	0.654178i
$122$	−4.78890	−	5.96457i	−0.433567	−	0.540007i
$123$		0			0
$124$	−7.42516	−	11.6456i	−0.666799	−	1.04580i
$125$	−6.93202	+	16.7354i	−0.620018	+	1.49686i
$126$		0			0
$127$	9.84939			0.873992			0.436996	−	0.899463i	$-0.356042\pi$
$127$	9.84939			0.873992			0.436996	+	0.899463i	$0.356042\pi$
$128$	−4.08677	+	10.5498i	−0.361223	+	0.932480i
$129$		0			0
$130$	−16.0001	+	29.1772i	−1.40330	+	2.55901i
$131$	3.55214	−	8.57563i	0.310352	−	0.749256i	−0.689340	−	0.724438i	$-0.742099\pi$
$131$	3.55214	−	8.57563i	0.310352	−	0.749256i	0.999692	−	0.0248182i	$-0.00790069\pi$
$132$		0			0
$133$	11.7308	−	4.85905i	1.01719	−	0.421333i
$134$	9.04973	+	11.2714i	0.781778	+	0.973704i
$135$		0			0
$136$	−0.110789	−	1.67597i	−0.00950010	−	0.143713i
$137$	−7.55484	−	7.55484i	−0.645454	−	0.645454i	0.306437	−	0.951891i	$-0.400863\pi$
$137$	−7.55484	−	7.55484i	−0.645454	−	0.645454i	−0.951891	+	0.306437i	$0.900863\pi$
$138$		0			0
$139$	2.37282	+	5.72849i	0.201260	+	0.485884i	0.991995	−	0.126273i	$-0.0403017\pi$
$139$	2.37282	+	5.72849i	0.201260	+	0.485884i	−0.790736	+	0.612158i	$0.790302\pi$
$140$	17.1638	−	3.03303i	1.45060	−	0.256338i
$141$		0			0
$142$	6.02857	+	20.6688i	0.505907	+	1.73448i
$143$		−	5.56480i		−	0.465352i
$144$		0			0
$145$			28.0981i			2.33342i
$146$	7.82998	−	2.28381i	0.648014	−	0.189010i
$147$		0			0
$148$	−2.57780	−	1.80356i	−0.211893	−	0.148252i
$149$	−7.03565	−	16.9856i	−0.576383	−	1.39151i	−0.896038	−	0.443977i	$-0.853567\pi$
$149$	−7.03565	−	16.9856i	−0.576383	−	1.39151i	0.319655	−	0.947534i	$-0.396433\pi$
$150$		0			0
$151$	−15.9489	−	15.9489i	−1.29790	−	1.29790i	−0.929775	−	0.368129i	$-0.879998\pi$
$151$	−15.9489	−	15.9489i	−1.29790	−	1.29790i	−0.368129	−	0.929775i	$-0.620002\pi$
$152$	14.9750	+	5.07401i	1.21464	+	0.411557i
$153$		0			0
$154$	−2.27285	+	1.82485i	−0.183152	+	0.147051i
$155$	−24.4789	+	10.1395i	−1.96619	+	0.814423i
$156$		0			0
$157$	0.0755402	−	0.182370i	0.00602876	−	0.0145547i	−0.920836	−	0.389949i	$-0.872493\pi$
$157$	0.0755402	−	0.182370i	0.00602876	−	0.0145547i	0.926865	+	0.375394i	$0.122493\pi$
$158$	−9.48237	−	5.19991i	−0.754377	−	0.413683i
$159$		0			0
$160$	18.5658	+	11.2423i	1.46775	+	0.888785i
$161$	0.0646160			0.00509245
$162$		0			0
$163$	−3.11179	+	7.51254i	−0.243735	+	0.588427i	−0.997648	−	0.0685466i	$-0.978164\pi$
$163$	−3.11179	+	7.51254i	−0.243735	+	0.588427i	0.753913	+	0.656974i	$0.228164\pi$
$164$	5.47114	−	24.7223i	0.427224	−	1.93049i
$165$		0			0
$166$	−3.18766	+	2.55935i	−0.247411	+	0.198644i
$167$	−2.05729	+	2.05729i	−0.159198	+	0.159198i	−0.782211	−	0.623013i	$-0.785908\pi$
$167$	−2.05729	+	2.05729i	−0.159198	+	0.159198i	0.623013	+	0.782211i	$0.285908\pi$
$168$		0			0
$169$	17.4015	+	17.4015i	1.33858	+	1.33858i
$170$	−3.20312	−	0.350195i	−0.245668	−	0.0268587i
$171$		0			0
$172$	7.67430	−	10.9687i	0.585160	−	0.836358i
$173$	10.0549	+	4.16489i	0.764462	+	0.316650i	0.730627	−	0.682777i	$-0.239228\pi$
$173$	10.0549	+	4.16489i	0.764462	+	0.316650i	0.0338350	+	0.999427i	$0.489228\pi$
$174$		0			0
$175$		−	22.0804i		−	1.66912i
$176$	−3.62629	−	0.155621i	−0.273342	−	0.0117303i
$177$		0			0
$178$	−2.09867	−	7.19522i	−0.157302	−	0.539305i
$179$	−6.17617	−	2.55825i	−0.461628	−	0.191213i	0.139734	−	0.990189i	$-0.455375\pi$
$179$	−6.17617	−	2.55825i	−0.461628	−	0.191213i	−0.601362	+	0.798976i	$0.705375\pi$
$180$		0			0
$181$	3.25743	+	7.86412i	0.242123	+	0.584536i	0.997493	−	0.0707622i	$-0.0225431\pi$
$181$	3.25743	+	7.86412i	0.242123	+	0.584536i	−0.755371	+	0.655298i	$0.772543\pi$
$182$	2.14096	−	19.5827i	0.158699	−	1.45157i
$183$		0			0
$184$	0.0605249	+	0.0530191i	0.00446195	+	0.00390862i
$185$	−4.26773	+	4.26773i	−0.313770	+	0.313770i
$186$		0			0
$187$	0.497834	−	0.206210i	0.0364052	−	0.0150795i
$188$	−4.44217	+	2.83230i	−0.323979	+	0.206567i
$189$		0			0
$190$	14.5847	−	26.5961i	1.05808	−	1.92948i
$191$	−10.9258			−0.790560			−0.395280	−	0.918561i	$-0.629352\pi$
$191$	−10.9258			−0.790560			−0.395280	+	0.918561i	$0.629352\pi$
$192$		0			0
$193$	−1.25358			−0.0902347			−0.0451174	−	0.998982i	$-0.514366\pi$
$193$	−1.25358			−0.0902347			−0.0451174	+	0.998982i	$0.514366\pi$
$194$	−9.85959	+	17.9796i	−0.707877	+	1.29086i
$195$		0			0
$196$	3.10438	−	1.97933i	0.221741	−	0.141381i
$197$	24.4641	−	10.1334i	1.74300	−	0.721973i	0.744474	−	0.667651i	$-0.232700\pi$
$197$	24.4641	−	10.1334i	1.74300	−	0.721973i	0.998523	−	0.0543220i	$-0.0172998\pi$
$198$		0			0
$199$	−10.5918	+	10.5918i	−0.750835	+	0.750835i	−0.974635	−	0.223800i	$-0.928154\pi$
$199$	−10.5918	+	10.5918i	−0.750835	+	0.750835i	0.223800	+	0.974635i	$0.428154\pi$
$200$	18.1176	−	20.6824i	1.28110	−	1.46247i
$201$		0			0
$202$	−0.654547	+	5.98692i	−0.0460537	+	0.421239i
$203$	−6.36553	−	15.3677i	−0.446773	−	1.07860i
$204$		0			0
$205$	−44.8774	−	18.5888i	−3.13437	−	1.29830i
$206$	5.62615	+	19.2891i	0.391992	+	1.34393i
$207$		0			0
$208$	18.0735	−	16.5861i	1.25317	−	1.15004i
$209$			5.07253i			0.350874i
$210$		0			0
$211$	15.0917	+	6.25117i	1.03895	+	0.430348i	0.835936	−	0.548827i	$-0.184925\pi$
$211$	15.0917	+	6.25117i	1.03895	+	0.430348i	0.203017	+	0.979175i	$0.434925\pi$
$212$	7.41513	−	10.5983i	0.509274	−	0.727895i
$213$		0			0
$214$	10.0142	+	1.09484i	0.684555	+	0.0748420i
$215$	−18.1595	−	18.1595i	−1.23847	−	1.23847i
$216$		0			0
$217$	11.0912	−	11.0912i	0.752921	−	0.752921i
$218$	−3.64513	+	2.92664i	−0.246879	+	0.198217i
$219$		0			0
$220$	−1.50456	+	6.79861i	−0.101437	+	0.458362i
$221$	−1.39366	+	3.36458i	−0.0937474	+	0.226326i
$222$		0			0
$223$	−14.6420			−0.980501			−0.490250	−	0.871582i	$-0.663095\pi$
$223$	−14.6420			−0.980501			−0.490250	+	0.871582i	$0.663095\pi$
$224$	−12.7011	−	1.94278i	−0.848629	−	0.129808i
$225$		0			0
$226$	0.771685	+	0.423174i	0.0513317	+	0.0281491i
$227$	5.96486	−	14.4004i	0.395902	−	0.955791i	−0.592726	−	0.805404i	$-0.701948\pi$
$227$	5.96486	−	14.4004i	0.395902	−	0.955791i	0.988627	−	0.150387i	$-0.0480518\pi$
$228$		0			0
$229$	1.61192	−	0.667680i	0.106519	−	0.0441215i	−0.328788	−	0.944404i	$-0.606640\pi$
$229$	1.61192	−	0.667680i	0.106519	−	0.0441215i	0.435306	+	0.900282i	$0.356640\pi$
$230$	0.120366	−	0.0966404i	0.00793667	−	0.00637228i
$231$		0			0
$232$	6.64713	−	19.6178i	0.436406	−	1.28797i
$233$	−12.0945	−	12.0945i	−0.792340	−	0.792340i	0.189534	−	0.981874i	$-0.439302\pi$
$233$	−12.0945	−	12.0945i	−0.792340	−	0.792340i	−0.981874	+	0.189534i	$0.939302\pi$
$234$		0			0
$235$	3.86767	+	9.33739i	0.252299	+	0.609104i
$236$	13.2452	+	9.26701i	0.862187	+	0.603231i
$237$		0			0
$238$	1.83123	−	0.534124i	0.118701	−	0.0346221i
$239$			22.9115i			1.48202i	0.671495	+	0.741009i	$0.265653\pi$
$239$			22.9115i			1.48202i	−0.671495	+	0.741009i	$0.734347\pi$
$240$		0			0
$241$		−	16.6684i		−	1.07371i	−0.843676	−	0.536853i	$-0.819613\pi$
$241$		−	16.6684i		−	1.07371i	0.843676	−	0.536853i	$-0.180387\pi$
$242$	4.02985	+	13.8162i	0.259048	+	0.888139i
$243$		0			0
$244$	10.6525	−	1.88242i	0.681957	−	0.120509i
$245$	−2.70289	−	6.52536i	−0.172682	−	0.416890i
$246$		0			0
$247$	−24.2413	−	24.2413i	−1.54244	−	1.54244i
$248$	19.4896	−	1.28835i	1.23759	−	0.0818106i
$249$		0			0
$250$	−16.0382	−	19.9756i	−1.01435	−	1.26337i
$251$	−2.62614	+	1.08778i	−0.165761	+	0.0686603i	−0.464021	−	0.885824i	$-0.653594\pi$
$251$	−2.62614	+	1.08778i	−0.165761	+	0.0686603i	0.298260	+	0.954485i	$0.403594\pi$
$252$		0			0
$253$	−0.00987852	+	0.0238489i	−0.000621057	+	0.00149937i
$254$	−6.69748	+	12.2133i	−0.420238	+	0.766330i
$255$		0			0
$256$	−10.3029	−	12.2414i	−0.643928	−	0.765086i
$257$	11.2410			0.701196			0.350598	−	0.936526i	$-0.385978\pi$
$257$	11.2410			0.701196			0.350598	+	0.936526i	$0.385978\pi$
$258$		0			0
$259$	1.36732	−	3.30100i	0.0849610	−	0.205114i
$260$	−25.2999	−	39.6803i	−1.56904	−	2.46087i
$261$		0			0
$262$	8.21841	+	10.2360i	0.507735	+	0.632383i
$263$	−17.3998	+	17.3998i	−1.07292	+	1.07292i	−0.0757955	+	0.997123i	$0.524150\pi$
$263$	−17.3998	+	17.3998i	−1.07292	+	1.07292i	−0.997123	+	0.0757955i	$0.975850\pi$
$264$		0			0
$265$	−17.5463	−	17.5463i	−1.07786	−	1.07786i
$266$	−1.95157	+	17.8503i	−0.119658	+	1.09448i
$267$		0			0
$268$	−20.1304	+	3.55726i	−1.22966	+	0.217294i
$269$	20.2847	+	8.40222i	1.23678	+	0.512292i	0.902708	−	0.430254i	$-0.141576\pi$
$269$	20.2847	+	8.40222i	1.23678	+	0.512292i	0.334075	+	0.942547i	$0.391576\pi$
$270$		0			0
$271$		−	4.06118i		−	0.246699i	−0.992363	−	0.123350i	$-0.960636\pi$
$271$		−	4.06118i		−	0.246699i	0.992363	−	0.123350i	$-0.0393637\pi$
$272$	2.15355	+	1.00226i	0.130578	+	0.0607711i
$273$		0			0
$274$	14.5053	−	4.23083i	0.876295	−	0.255594i
$275$	8.14958	+	3.37567i	0.491438	+	0.203560i
$276$		0			0
$277$	−5.72498	−	13.8213i	−0.343981	−	0.830443i	−0.997305	−	0.0733652i	$-0.976626\pi$
$277$	−5.72498	−	13.8213i	−0.343981	−	0.830443i	0.653324	−	0.757078i	$-0.273374\pi$
$278$	−8.71686	−	0.953008i	−0.522802	−	0.0571576i
$279$		0			0
$280$	−7.91023	+	23.3456i	−0.472726	+	1.39517i
$281$	5.96575	−	5.96575i	0.355887	−	0.355887i	−0.506408	−	0.862294i	$-0.669027\pi$
$281$	5.96575	−	5.96575i	0.355887	−	0.355887i	0.862294	+	0.506408i	$0.169027\pi$
$282$		0			0
$283$	−19.7761	+	8.19155i	−1.17557	+	0.486937i	−0.883030	−	0.469316i	$-0.844500\pi$
$283$	−19.7761	+	8.19155i	−1.17557	+	0.486937i	−0.292540	+	0.956253i	$0.594500\pi$
$284$	−29.7288	−	6.57909i	−1.76408	−	0.390397i
$285$		0			0
$286$	6.90039	+	3.78401i	0.408028	+	0.223753i
$287$	28.7561			1.69742
$288$		0			0
$289$	16.6474			0.979256
$290$	−34.8418	−	19.1064i	−2.04598	−	1.12197i
$291$		0			0
$292$	−2.49237	+	11.2622i	−0.145855	+	0.659070i
$293$	−11.8575	+	4.91155i	−0.692725	+	0.286936i	−0.701135	−	0.713029i	$-0.747323\pi$
$293$	−11.8575	+	4.91155i	−0.692725	+	0.286936i	0.00841001	+	0.999965i	$0.497323\pi$
$294$		0			0
$295$	21.9283	−	21.9283i	1.27672	−	1.27672i
$296$	3.98930	−	1.97008i	0.231873	−	0.114508i
$297$		0			0
$298$	25.8464	+	2.82577i	1.49724	+	0.163692i
$299$	−0.0667634	−	0.161181i	−0.00386103	−	0.00932135i
$300$		0			0
$301$	14.0460	+	5.81805i	0.809598	+	0.335347i
$302$	30.6218	−	8.93164i	1.76209	−	0.513958i
$303$		0			0
$304$	−16.4747	+	15.1189i	−0.944888	+	0.867126i
$305$		−	20.7525i		−	1.18828i
$306$		0			0
$307$	21.0702	+	8.72756i	1.20254	+	0.498108i	0.891819	−	0.452393i	$-0.149430\pi$
$307$	21.0702	+	8.72756i	1.20254	+	0.498108i	0.310721	+	0.950501i	$0.399430\pi$
$308$	−0.717311	−	4.05923i	−0.0408726	−	0.231296i
$309$		0			0
$310$	4.07238	−	37.2487i	0.231295	−	2.11558i
$311$	−2.17719	−	2.17719i	−0.123457	−	0.123457i	0.642679	−	0.766136i	$-0.277823\pi$
$311$	−2.17719	−	2.17719i	−0.123457	−	0.123457i	−0.766136	+	0.642679i	$0.777823\pi$
$312$		0			0
$313$	−9.67647	+	9.67647i	−0.546946	+	0.546946i	−0.925556	−	0.378610i	$-0.876402\pi$
$313$	−9.67647	+	9.67647i	−0.546946	+	0.546946i	0.378610	+	0.925556i	$0.376402\pi$
$314$	0.174773	+	0.217680i	0.00986303	+	0.0122844i
$315$		0			0
$316$	12.8958	−	8.22231i	0.725447	−	0.462541i
$317$	−2.56261	+	6.18669i	−0.143931	+	0.347479i	−0.979362	−	0.202116i	$-0.935218\pi$
$317$	−2.56261	+	6.18669i	−0.143931	+	0.347479i	0.835431	+	0.549596i	$0.185218\pi$
$318$		0			0
$319$	6.64519			0.372059
$320$	−26.5651	+	15.3770i	−1.48503	+	0.859598i
$321$		0			0
$322$	−0.0439382	+	0.0801242i	−0.00244858	+	0.00446515i
$323$	1.27037	−	3.06694i	0.0706852	−	0.170649i
$324$		0			0
$325$	−55.0785	+	22.8142i	−3.05520	+	1.26551i
$326$	−7.19960	−	8.96709i	−0.398749	−	0.496641i
$327$		0			0
$328$	26.9354	+	23.5951i	1.48726	+	1.30282i
$329$	−4.23071	−	4.23071i	−0.233247	−	0.233247i
$330$		0			0
$331$	8.91192	+	21.5153i	0.489844	+	1.18259i	0.954799	+	0.297253i	$0.0960704\pi$
$331$	8.91192	+	21.5153i	0.489844	+	1.18259i	−0.464955	+	0.885334i	$0.653930\pi$
$332$	−1.00602	−	5.69305i	−0.0552128	−	0.312447i
$333$		0			0
$334$	−1.15211	−	3.94998i	−0.0630408	−	0.216133i
$335$			39.2166i			2.14263i
$336$		0			0
$337$		−	11.4661i		−	0.624597i	−0.949984	−	0.312299i	$-0.898901\pi$
$337$		−	11.4661i		−	0.624597i	0.949984	−	0.312299i	$-0.101099\pi$
$338$	−33.4108	+	9.74510i	−1.81731	+	0.530064i
$339$		0			0
$340$	2.61233	−	3.73376i	0.141674	−	0.202492i
$341$	2.39799	+	5.78925i	0.129858	+	0.313505i
$342$		0			0
$343$	14.1993	+	14.1993i	0.766692	+	0.766692i
$344$	8.38284	+	16.9748i	0.451972	+	0.915220i
$345$		0			0
$346$	−12.0017	+	9.63608i	−0.645217	+	0.518039i
$347$	29.6276	−	12.2721i	1.59049	−	0.658803i	0.600460	−	0.799655i	$-0.294984\pi$
$347$	29.6276	−	12.2721i	1.59049	−	0.658803i	0.990031	+	0.140852i	$0.0449843\pi$
$348$		0			0
$349$	−10.9206	+	26.3647i	−0.584567	+	1.41127i	0.304065	+	0.952651i	$0.401656\pi$
$349$	−10.9206	+	26.3647i	−0.584567	+	1.41127i	−0.888633	+	0.458620i	$0.848344\pi$
$350$	27.3798	+	15.0145i	1.46351	+	0.802557i
$351$		0			0
$352$	2.65881	−	4.39079i	0.141715	−	0.234030i
$353$	−2.15781			−0.114849			−0.0574243	−	0.998350i	$-0.518289\pi$
$353$	−2.15781			−0.114849			−0.0574243	+	0.998350i	$0.518289\pi$
$354$		0			0
$355$	−22.3532	+	53.9654i	−1.18639	+	2.86419i
$356$	10.3492	+	2.29032i	0.548506	+	0.121386i
$357$		0			0
$358$	7.37198	−	5.91889i	0.389621	−	0.312823i
$359$	6.11399	−	6.11399i	0.322684	−	0.322684i	−0.527112	−	0.849796i	$-0.676725\pi$
$359$	6.11399	−	6.11399i	0.322684	−	0.322684i	0.849796	+	0.527112i	$0.176725\pi$
$360$		0			0
$361$	8.66183	+	8.66183i	0.455886	+	0.455886i
$362$	−11.9666	−	1.30830i	−0.628949	−	0.0687626i
$363$		0			0
$364$	22.8268	+	15.9708i	1.19645	+	0.837099i
$365$	20.4438	+	8.46810i	1.07008	+	0.443241i
$366$		0			0
$367$			10.3243i			0.538924i	0.963011	+	0.269462i	$0.0868459\pi$
$367$			10.3243i			0.538924i	−0.963011	+	0.269462i	$0.913154\pi$
$368$	−0.106900	+	0.0389987i	−0.00557256	+	0.00203295i
$369$		0			0
$370$	−2.38999	−	8.19402i	−0.124250	−	0.425987i
$371$	13.5717	+	5.62157i	0.704606	+	0.291857i
$372$		0			0
$373$	−3.33636	−	8.05469i	−0.172750	−	0.417056i	0.813664	−	0.581336i	$-0.197470\pi$
$373$	−3.33636	−	8.05469i	−0.172750	−	0.417056i	−0.986414	+	0.164280i	$0.947470\pi$
$374$	−0.0828210	+	0.757537i	−0.00428257	+	0.0391713i
$375$		0			0
$376$	−0.491438	−	7.43425i	−0.0253440	−	0.383392i
$377$	−31.7570	+	31.7570i	−1.63557	+	1.63557i
$378$		0			0
$379$	−5.51425	+	2.28408i	−0.283248	+	0.117325i	−0.519785	−	0.854297i	$-0.673988\pi$
$379$	−5.51425	+	2.28408i	−0.283248	+	0.117325i	0.236536	+	0.971623i	$0.423988\pi$
$380$	23.0618	+	36.1701i	1.18305	+	1.85549i
$381$		0			0
$382$	7.42941	−	13.5480i	0.380122	−	0.693176i
$383$	−9.23956			−0.472120			−0.236060	−	0.971739i	$-0.575856\pi$
$383$	−9.23956			−0.472120			−0.236060	+	0.971739i	$0.575856\pi$
$384$		0			0
$385$	−7.90791			−0.403024
$386$	0.852422	−	1.55445i	0.0433872	−	0.0791193i
$387$		0			0
$388$	−15.5904	−	24.4519i	−0.791482	−	1.24136i
$389$	34.6091	−	14.3355i	1.75475	−	0.726841i	0.757491	−	0.652845i	$-0.226425\pi$
$389$	34.6091	−	14.3355i	1.75475	−	0.726841i	0.997259	−	0.0739961i	$-0.0235752\pi$
$390$		0			0
$391$	0.0119455	−	0.0119455i	0.000604109	−	0.000604109i
$392$	0.343438	+	5.19537i	0.0173462	+	0.262406i
$393$		0			0
$394$	−4.06992	+	37.2263i	−0.205040	+	1.87543i
$395$	−11.2280	−	27.1069i	−0.564944	−	1.36390i
$396$		0			0
$397$	−15.6301	−	6.47420i	−0.784452	−	0.324931i	−0.0457415	−	0.998953i	$-0.514565\pi$
$397$	−15.6301	−	6.47420i	−0.784452	−	0.324931i	−0.738711	+	0.674023i	$0.764565\pi$
$398$	−5.93159	−	20.3363i	−0.297324	−	1.01936i
$399$		0			0
$400$	13.3265	+	36.5297i	0.666327	+	1.82648i
$401$			20.6019i			1.02881i	0.857548	+	0.514405i	$0.171987\pi$
$401$			20.6019i			1.02881i	−0.857548	+	0.514405i	$0.828013\pi$
$402$		0			0
$403$	−39.1263	−	16.2067i	−1.94902	−	0.807311i
$404$	−6.97873	−	4.88269i	−0.347205	−	0.242923i
$405$		0			0
$406$	23.3846	+	2.55662i	1.16056	+	0.126883i
$407$	1.00932	+	1.00932i	0.0500299	+	0.0500299i
$408$		0			0
$409$	−1.39644	+	1.39644i	−0.0690496	+	0.0690496i	−0.740788	−	0.671739i	$-0.765548\pi$
$409$	−1.39644	+	1.39644i	−0.0690496	+	0.0690496i	0.671739	+	0.740788i	$0.265548\pi$
$410$	53.5664	−	43.0080i	2.64546	−	2.12401i
$411$		0			0
$412$	−27.7443	−	6.13992i	−1.36686	−	0.302492i
$413$	−7.02552	+	16.9611i	−0.345703	+	0.834601i
$414$		0			0
$415$	−11.0908			−0.544426
$416$	8.27706	+	33.6896i	0.405816	+	1.65177i
$417$		0			0
$418$	−6.28996	−	3.44927i	−0.307652	−	0.168709i
$419$	−3.15556	+	7.61820i	−0.154159	+	0.372173i	−0.982024	−	0.188754i	$-0.939555\pi$
$419$	−3.15556	+	7.61820i	−0.154159	+	0.372173i	0.827865	+	0.560927i	$0.189555\pi$
$420$		0			0
$421$	−19.8735	+	8.23189i	−0.968577	+	0.401198i	−0.810182	−	0.586178i	$-0.800632\pi$
$421$	−19.8735	+	8.23189i	−0.968577	+	0.401198i	−0.158395	+	0.987376i	$0.550632\pi$
$422$	−18.0137	+	14.4630i	−0.876892	+	0.704048i
$423$		0			0
$424$	8.09975	+	16.4016i	0.393358	+	0.796530i
$425$	−4.08198	−	4.08198i	−0.198005	−	0.198005i
$426$		0			0
$427$	4.70141	+	11.3502i	0.227517	+	0.549275i
$428$	−8.16715	+	11.6732i	−0.394774	+	0.564243i
$429$		0			0
$430$	34.8662	−	10.1696i	1.68140	−	0.490423i
$431$			19.9125i			0.959153i	0.877500	+	0.479576i	$0.159210\pi$
$431$			19.9125i			0.959153i	−0.877500	+	0.479576i	$0.840790\pi$
$432$		0			0
$433$			4.68554i			0.225173i	0.993642	+	0.112586i	$0.0359135\pi$
$433$			4.68554i			0.225173i	−0.993642	+	0.112586i	$0.964086\pi$
$434$	6.21126	+	21.2951i	0.298150	+	1.02220i
$435$		0			0
$436$	−1.15040	−	6.51007i	−0.0550942	−	0.311776i
$437$	0.0608574	+	0.146923i	0.00291120	+	0.00702827i
$438$		0			0
$439$	19.8658	+	19.8658i	0.948142	+	0.948142i	0.998720	−	0.0505784i	$-0.0161065\pi$
$439$	19.8658	+	19.8658i	0.948142	+	0.948142i	−0.0505784	+	0.998720i	$0.516106\pi$
$440$	−7.40723	−	6.48864i	−0.353126	−	0.309334i
$441$		0			0
$442$	−3.22443	−	4.01602i	−0.153370	−	0.191023i
$443$	−8.20972	+	3.40058i	−0.390056	+	0.161566i	−0.569088	−	0.822277i	$-0.692703\pi$
$443$	−8.20972	+	3.40058i	−0.390056	+	0.161566i	0.179032	+	0.983843i	$0.442703\pi$
$444$		0			0
$445$	7.78161	−	18.7865i	0.368884	−	0.890564i
$446$	9.95641	−	18.1562i	0.471450	−	0.859719i
$447$		0			0
$448$	11.0457	−	14.4284i	0.521860	−	0.681677i
$449$	24.2045			1.14228			0.571141	−	0.820852i	$-0.306501\pi$
$449$	24.2045			1.14228			0.571141	+	0.820852i	$0.306501\pi$
$450$		0			0
$451$	−4.39625	+	10.6135i	−0.207011	+	0.499770i
$452$	−1.04948	+	0.669140i	−0.0493632	+	0.0314737i
$453$		0			0
$454$	13.8006	+	17.1886i	0.647694	+	0.806702i
$455$	37.7914	−	37.7914i	1.77169	−	1.77169i
$456$		0			0
$457$	12.5941	+	12.5941i	0.589128	+	0.589128i	0.937395	−	0.348267i	$-0.113230\pi$
$457$	12.5941	+	12.5941i	0.589128	+	0.589128i	−0.348267	+	0.937395i	$0.613230\pi$
$458$	−0.268164	+	2.45281i	−0.0125305	+	0.114612i
$459$		0			0
$460$	0.0379873	+	0.214968i	0.00177117	+	0.0100230i
$461$	15.2109	+	6.30054i	0.708440	+	0.293446i	0.707659	−	0.706554i	$-0.249751\pi$
$461$	15.2109	+	6.30054i	0.708440	+	0.293446i	0.000781253		1.00000i	$0.499751\pi$
$462$		0			0
$463$		−	33.7363i		−	1.56786i	−0.620849	−	0.783930i	$-0.713212\pi$
$463$		−	33.7363i		−	1.56786i	0.620849	−	0.783930i	$-0.286788\pi$
$464$	19.8062	+	21.5824i	0.919481	+	1.00194i
$465$		0			0
$466$	23.2215	−	6.77313i	1.07571	−	0.313759i
$467$	33.4989	+	13.8757i	1.55015	+	0.642091i	0.983343	−	0.181762i	$-0.0581801\pi$
$467$	33.4989	+	13.8757i	1.55015	+	0.642091i	0.566803	+	0.823853i	$0.308180\pi$
$468$		0			0
$469$	−8.88439	−	21.4488i	−0.410243	−	0.990414i
$470$	−14.2084	−	1.55339i	−0.655384	−	0.0716527i
$471$		0			0
$472$	−20.4977	+	10.1226i	−0.943484	+	0.465930i
$473$	−4.29472	+	4.29472i	−0.197472	+	0.197472i
$474$		0			0
$475$	50.2061	−	20.7960i	2.30361	−	0.954188i
$476$	−0.582899	+	2.63393i	−0.0267171	+	0.120726i
$477$		0			0
$478$	−28.4103	−	15.5796i	−1.29946	−	0.712592i
$479$	−30.0639			−1.37365			−0.686827	−	0.726821i	$-0.740997\pi$
$479$	−30.0639			−1.37365			−0.686827	+	0.726821i	$0.740997\pi$
$480$		0			0
$481$	−9.64693			−0.439862
$482$	20.6689	+	11.3343i	0.941443	+	0.516265i
$483$		0			0
$484$	−19.8724	−	4.39784i	−0.903292	−	0.199902i
$485$	−51.3976	+	21.2896i	−2.33384	+	0.966710i
$486$		0			0
$487$	−25.9500	+	25.9500i	−1.17590	+	1.17590i	−0.195127	+	0.980778i	$0.562512\pi$
$487$	−25.9500	+	25.9500i	−1.17590	+	1.17590i	−0.980778	+	0.195127i	$0.937488\pi$
$488$	−4.90939	+	14.4892i	−0.222238	+	0.655895i
$489$		0			0
$490$	9.92943	+	1.08558i	0.448566	+	0.0490414i
$491$	−7.04524	−	17.0087i	−0.317947	−	0.767592i	−0.999363	−	0.0356955i	$-0.988635\pi$
$491$	−7.04524	−	17.0087i	−0.317947	−	0.767592i	0.681416	−	0.731897i	$-0.261365\pi$
$492$		0			0
$493$	−4.01780	−	1.66423i	−0.180953	−	0.0749531i
$494$	46.5432	−	13.5755i	2.09408	−	0.610791i
$495$		0			0
$496$	−11.6552	+	25.0433i	−0.523333	+	1.12448i
$497$		−	34.5795i		−	1.55110i
$498$		0			0
$499$	−24.3749	−	10.0964i	−1.09117	−	0.451978i	−0.236757	−	0.971569i	$-0.576084\pi$
$499$	−24.3749	−	10.0964i	−1.09117	−	0.451978i	−0.854415	+	0.519591i	$0.826084\pi$
$500$	35.6757	−	6.30430i	1.59547	−	0.281937i
$501$		0			0
$502$	0.436892	−	3.99611i	0.0194995	−	0.178355i
$503$	−2.77268	−	2.77268i	−0.123628	−	0.123628i	0.642586	−	0.766214i	$-0.277862\pi$
$503$	−2.77268	−	2.77268i	−0.123628	−	0.123628i	−0.766214	+	0.642586i	$0.777862\pi$
$504$		0			0
$505$	−11.5538	+	11.5538i	−0.514138	+	0.514138i
$506$	−0.0228554	−	0.0284664i	−0.00101605	−	0.00126549i
$507$		0			0
$508$	−10.5903	−	16.6098i	−0.469870	−	0.736942i
$509$	−4.94920	+	11.9484i	−0.219369	+	0.529604i	−0.994802	−	0.101826i	$-0.967532\pi$
$509$	−4.94920	+	11.9484i	−0.219369	+	0.529604i	0.775433	+	0.631430i	$0.217532\pi$
$510$		0			0
$511$	−13.0998			−0.579501
$512$	22.1852	−	4.45158i	0.980457	−	0.196734i
$513$		0			0
$514$	−7.64378	+	13.9389i	−0.337153	+	0.614820i
$515$	−20.8611	+	50.3631i	−0.919249	+	2.21926i
$516$		0			0
$517$	2.20829	−	0.914703i	0.0971205	−	0.0402286i
$518$	3.16349	+	3.94013i	0.138996	+	0.173119i
$519$		0			0
$520$	66.4076	−	4.38984i	2.91216	−	0.192507i
$521$	10.6270	+	10.6270i	0.465580	+	0.465580i	0.900479	−	0.434899i	$-0.143216\pi$
$521$	10.6270	+	10.6270i	0.465580	+	0.465580i	−0.434899	+	0.900479i	$0.643216\pi$
$522$		0			0
$523$	−15.4746	−	37.3590i	−0.676657	−	1.63360i	−0.770064	−	0.637967i	$-0.779776\pi$
$523$	−15.4746	−	37.3590i	−0.676657	−	1.63360i	0.0934064	−	0.995628i	$-0.470224\pi$
$524$	−18.2812	+	3.23048i	−0.798616	+	0.141124i
$525$		0			0
$526$	−9.74417	−	33.4076i	−0.424866	−	1.45664i
$527$		−	4.10084i		−	0.178635i
$528$		0			0
$529$		−	22.9992i		−	0.999965i
$530$	33.6888	−	9.82619i	1.46335	−	0.426822i
$531$		0			0
$532$	−20.8075	−	14.5580i	−0.902119	−	0.631170i
$533$	−29.7118	−	71.7306i	−1.28696	−	3.10700i
$534$		0			0
$535$	19.3258	+	19.3258i	0.835525	+	0.835525i
$536$	9.27743	−	27.3807i	0.400724	−	1.18266i
$537$		0			0
$538$	−24.2122	+	19.4398i	−1.04386	+	0.838108i
$539$	−1.54325	+	0.639233i	−0.0664723	+	0.0275337i
$540$		0			0
$541$	−4.99043	+	12.0480i	−0.214555	+	0.517982i	−0.994113	−	0.108348i	$-0.965444\pi$
$541$	−4.99043	+	12.0480i	−0.214555	+	0.517982i	0.779558	+	0.626330i	$0.215444\pi$
$542$	5.03589	+	2.76156i	0.216310	+	0.118619i
$543$		0			0
$544$	−2.70720	+	1.98888i	−0.116070	+	0.0852725i
$545$	−12.6825			−0.543257
$546$		0			0
$547$	5.45215	−	13.1627i	0.233117	−	0.562795i	−0.763424	−	0.645898i	$-0.776483\pi$
$547$	5.45215	−	13.1627i	0.233117	−	0.562795i	0.996541	+	0.0831031i	$0.0264831\pi$
$548$	−4.61718	+	20.8635i	−0.197236	+	0.891246i
$549$		0			0
$550$	−9.72747	+	7.81010i	−0.414781	+	0.333024i
$551$	28.9477	−	28.9477i	1.23321	−	1.23321i
$552$		0			0
$553$	12.2820	+	12.2820i	0.522282	+	0.522282i
$554$	21.0315	+	2.29936i	0.893541	+	0.0976903i
$555$		0			0
$556$	7.10911	−	10.1609i	0.301493	−	0.430919i
$557$	−24.1244	−	9.99266i	−1.02218	−	0.423403i	−0.192299	−	0.981336i	$-0.561594\pi$
$557$	−24.1244	−	9.99266i	−1.02218	−	0.423403i	−0.829885	+	0.557934i	$0.811594\pi$
$558$		0			0
$559$		−	41.0484i		−	1.73616i
$560$	−23.5698	−	25.6835i	−0.996007	−	1.08533i
$561$		0			0
$562$	3.34091	+	11.4542i	0.140928	+	0.483166i
$563$	27.9136	+	11.5622i	1.17642	+	0.487288i	0.883309	−	0.468792i	$-0.155311\pi$
$563$	27.9136	+	11.5622i	1.17642	+	0.487288i	0.293108	+	0.956079i	$0.405311\pi$
$564$		0			0
$565$	0.913749	+	2.20599i	0.0384417	+	0.0928065i
$566$	3.29002	−	30.0927i	0.138290	−	1.26489i
$567$		0			0
$568$	28.3734	−	32.3901i	1.19052	−	1.35906i
$569$	7.42864	−	7.42864i	0.311425	−	0.311425i	−0.534037	−	0.845461i	$-0.679326\pi$
$569$	7.42864	−	7.42864i	0.311425	−	0.311425i	0.845461	+	0.534037i	$0.179326\pi$
$570$		0			0
$571$	−14.3745	+	5.95413i	−0.601556	+	0.249173i	−0.662613	−	0.748962i	$-0.730553\pi$
$571$	−14.3745	+	5.95413i	−0.601556	+	0.249173i	0.0610576	+	0.998134i	$0.480553\pi$
$572$	−9.38439	+	5.98343i	−0.392381	+	0.250180i
$573$		0			0
$574$	−19.5539	+	35.6577i	−0.816163	+	1.48833i
$575$	0.276547			0.0115328
$576$		0			0
$577$	28.4266			1.18342			0.591708	−	0.806153i	$-0.298454\pi$
$577$	28.4266			1.18342			0.591708	+	0.806153i	$0.298454\pi$
$578$	−11.3200	+	20.6428i	−0.470851	+	0.858628i
$579$		0			0
$580$	47.3841	−	30.2118i	1.96752	−	1.25448i
$581$	6.06592	−	2.51259i	0.251657	−	0.104240i
$582$		0			0
$583$	−4.14969	+	4.14969i	−0.171863	+	0.171863i
$584$	−12.2704	−	10.7487i	−0.507752	−	0.444785i
$585$		0			0
$586$	1.97265	−	18.0432i	0.0814896	−	0.745359i
$587$	−3.24243	−	7.82792i	−0.133829	−	0.323093i	0.842731	−	0.538334i	$-0.180946\pi$
$587$	−3.24243	−	7.82792i	−0.133829	−	0.323093i	−0.976561	+	0.215241i	$0.930946\pi$
$588$		0			0
$589$	35.6651	+	14.7730i	1.46956	+	0.608710i
$590$	12.2802	+	42.1023i	0.505568	+	1.73332i
$591$		0			0
$592$	−0.269778	+	6.28639i	−0.0110878	+	0.258369i
$593$			28.4410i			1.16793i	0.811779	+	0.583965i	$0.198500\pi$
$593$			28.4410i			1.16793i	−0.811779	+	0.583965i	$0.801500\pi$
$594$		0			0
$595$	4.78127	+	1.98047i	0.196013	+	0.0811912i
$596$	−21.0792	+	30.1281i	−0.863439	+	1.23410i
$597$		0			0
$598$	0.245264	+	0.0268146i	0.0100296	+	0.00109653i
$599$	30.7323	+	30.7323i	1.25569	+	1.25569i	0.953131	+	0.302559i	$0.0978410\pi$
$599$	30.7323	+	30.7323i	1.25569	+	1.25569i	0.302559	+	0.953131i	$0.402159\pi$
$600$		0			0
$601$	−8.09508	+	8.09508i	−0.330205	+	0.330205i	−0.852664	−	0.522459i	$-0.825015\pi$
$601$	−8.09508	+	8.09508i	−0.330205	+	0.330205i	0.522459	+	0.852664i	$0.325015\pi$
$602$	−16.7656	+	13.4609i	−0.683313	+	0.548626i
$603$		0			0
$604$	−9.74726	+	44.0447i	−0.396610	+	1.79215i
$605$	−14.9422	+	36.0736i	−0.607486	+	1.46660i
$606$		0			0
$607$	−27.7849			−1.12775			−0.563877	−	0.825859i	$-0.690691\pi$
$607$	−27.7849			−1.12775			−0.563877	+	0.825859i	$0.690691\pi$
$608$	−7.54485	−	30.7094i	−0.305984	−	1.24543i
$609$		0			0
$610$	25.7332	+	14.1115i	1.04191	+	0.571357i
$611$	−6.18197	+	14.9246i	−0.250096	+	0.603785i
$612$		0			0
$613$	−1.11196	+	0.460588i	−0.0449115	+	0.0186030i	−0.405026	−	0.914305i	$-0.632738\pi$
$613$	−1.11196	+	0.460588i	−0.0449115	+	0.0186030i	0.360115	+	0.932908i	$0.382738\pi$
$614$	−25.1497	+	20.1925i	−1.01496	+	0.814903i
$615$		0			0
$616$	5.52123	+	1.87077i	0.222457	+	0.0753753i
$617$	−5.18952	−	5.18952i	−0.208922	−	0.208922i	0.594887	−	0.803809i	$-0.297197\pi$
$617$	−5.18952	−	5.18952i	−0.208922	−	0.208922i	−0.803809	+	0.594887i	$0.797197\pi$
$618$		0			0
$619$	−12.4653	−	30.0938i	−0.501022	−	1.20957i	−0.948928	−	0.315493i	$-0.897830\pi$
$619$	−12.4653	−	30.0938i	−0.501022	−	1.20957i	0.447906	−	0.894080i	$-0.352170\pi$
$620$	43.4194	+	30.3785i	1.74377	+	1.22003i
$621$		0			0
$622$	4.18019	−	1.21926i	0.167610	−	0.0488879i
$623$			12.0378i			0.482285i
$624$		0			0
$625$		−	20.8952i		−	0.835807i
$626$	−5.41897	−	18.5788i	−0.216586	−	0.742557i
$627$		0			0
$628$	−0.388769	+	0.0686997i	−0.0155136	+	0.00274142i
$629$	−0.357477	−	0.863025i	−0.0142535	−	0.0344111i
$630$		0			0
$631$	−11.7055	−	11.7055i	−0.465990	−	0.465990i	0.434623	−	0.900613i	$-0.356882\pi$
$631$	−11.7055	−	11.7055i	−0.465990	−	0.465990i	−0.900613	+	0.434623i	$0.856882\pi$
$632$	1.42667	+	21.5820i	0.0567498	+	0.858486i
$633$		0			0
$634$	−5.92898	−	7.38454i	−0.235470	−	0.293278i
$635$	−34.9137	+	14.4617i	−1.38551	+	0.573896i
$636$		0			0
$637$	4.32022	−	10.4299i	0.171173	−	0.413249i
$638$	−4.51866	+	8.24007i	−0.178895	+	0.326227i
$639$		0			0
$640$	−1.00353	−	43.3970i	−0.0396680	−	1.71542i
$641$	9.09143			0.359090			0.179545	−	0.983750i	$-0.442537\pi$
$641$	9.09143			0.359090			0.179545	+	0.983750i	$0.442537\pi$
$642$		0			0
$643$	−2.60708	+	6.29406i	−0.102813	+	0.248213i	−0.966913	−	0.255108i	$-0.917889\pi$
$643$	−2.60708	+	6.29406i	−0.102813	+	0.248213i	0.864099	+	0.503322i	$0.167889\pi$
$644$	−0.0694769	−	0.108967i	−0.00273777	−	0.00429391i
$645$		0			0
$646$	2.93919	+	3.66076i	0.115641	+	0.144030i
$647$	−1.17619	+	1.17619i	−0.0462409	+	0.0462409i	−0.729849	−	0.683608i	$-0.760410\pi$
$647$	−1.17619	+	1.17619i	−0.0462409	+	0.0462409i	0.683608	+	0.729849i	$0.260410\pi$
$648$		0			0
$649$	−5.18604	−	5.18604i	−0.203570	−	0.203570i
$650$	9.16301	−	83.8110i	0.359403	−	3.28734i
$651$		0			0
$652$	16.0149	−	2.83001i	0.627192	−	0.110832i
$653$	21.8087	+	9.03346i	0.853440	+	0.353506i	0.766138	−	0.642676i	$-0.222176\pi$
$653$	21.8087	+	9.03346i	0.853440	+	0.353506i	0.0873015	+	0.996182i	$0.472176\pi$
$654$		0			0
$655$			35.6141i			1.39156i
$656$	−47.5739	+	17.3556i	−1.85745	+	0.677624i
$657$		0			0
$658$	8.12294	−	2.36926i	0.316665	−	0.0923635i
$659$	−3.84511	−	1.59270i	−0.149784	−	0.0620426i	0.306532	−	0.951860i	$-0.400831\pi$
$659$	−3.84511	−	1.59270i	−0.149784	−	0.0620426i	−0.456316	+	0.889818i	$0.650831\pi$
$660$		0			0
$661$	8.39703	+	20.2722i	0.326607	+	0.788498i	0.998840	+	0.0481584i	$0.0153352\pi$
$661$	8.39703	+	20.2722i	0.326607	+	0.788498i	−0.672233	+	0.740339i	$0.734665\pi$
$662$	−32.7391	−	3.57934i	−1.27244	−	0.139115i
$663$		0			0
$664$	7.74350	+	2.62374i	0.300506	+	0.101821i
$665$	−34.4483	+	34.4483i	−1.33585	+	1.33585i
$666$		0			0
$667$	0.192474	−	0.0797253i	0.00745262	−	0.00308698i
$668$	5.68143	+	1.25732i	0.219821	+	0.0486472i
$669$		0			0
$670$	−48.6288	−	26.6669i	−1.87869	−	1.03023i
$671$	−4.90796			−0.189470
$672$		0			0
$673$	21.0624			0.811897			0.405949	−	0.913896i	$-0.366941\pi$
$673$	21.0624			0.811897			0.405949	+	0.913896i	$0.366941\pi$
$674$	14.2180	+	7.79682i	0.547657	+	0.300322i
$675$		0			0
$676$	10.6350	−	48.0561i	0.409039	−	1.84831i
$677$	−23.4192	+	9.70057i	−0.900074	+	0.372823i	−0.784249	−	0.620447i	$-0.786951\pi$
$677$	−23.4192	+	9.70057i	−0.900074	+	0.372823i	−0.115826	+	0.993270i	$0.536951\pi$
$678$		0			0
$679$	23.2879	−	23.2879i	0.893708	−	0.893708i
$680$	2.85352	+	5.77823i	0.109428	+	0.221585i
$681$		0			0
$682$	−8.80931	−	0.963116i	−0.337326	−	0.0368796i
$683$	−9.64199	−	23.2778i	−0.368940	−	0.890701i	−0.993925	−	0.110064i	$-0.964895\pi$
$683$	−9.64199	−	23.2778i	−0.368940	−	0.890701i	0.624984	−	0.780637i	$-0.285105\pi$
$684$		0			0
$685$	37.8728	+	15.6874i	1.44704	+	0.599385i
$686$	−27.2627	+	7.95185i	−1.04089	+	0.303603i
$687$		0			0
$688$	−26.7491	−	1.14793i	−1.01980	−	0.0437643i
$689$		−	39.6622i		−	1.51101i
$690$		0			0
$691$	14.5099	+	6.01021i	0.551984	+	0.228639i	0.641201	−	0.767373i	$-0.278436\pi$
$691$	14.5099	+	6.01021i	0.551984	+	0.228639i	−0.0892171	+	0.996012i	$0.528436\pi$
$692$	−3.78774	−	21.4347i	−0.143988	−	0.814823i
$693$		0			0
$694$	−4.92892	+	45.0833i	−0.187099	+	1.71134i
$695$	−16.8221	−	16.8221i	−0.638100	−	0.638100i
$696$		0			0
$697$	5.31611	−	5.31611i	0.201362	−	0.201362i
$698$	−25.2665	−	31.4694i	−0.956350	−	1.19113i
$699$		0			0
$700$	−37.2360	+	23.7415i	−1.40739	+	0.897343i
$701$	15.0307	−	36.2872i	0.567700	−	1.37055i	−0.335789	−	0.941937i	$-0.609003\pi$
$701$	15.0307	−	36.2872i	0.567700	−	1.37055i	0.903489	−	0.428612i	$-0.140997\pi$
$702$		0			0
$703$	8.79353			0.331654
$704$	3.63665	+	6.28263i	0.137061	+	0.236786i
$705$		0			0
$706$	1.46729	−	2.67569i	0.0552221	−	0.100701i
$707$	3.70167	−	8.93662i	0.139216	−	0.336096i
$708$		0			0
$709$	−17.8505	+	7.39392i	−0.670389	+	0.277684i	−0.691803	−	0.722086i	$-0.743183\pi$
$709$	−17.8505	+	7.39392i	−0.670389	+	0.277684i	0.0214137	+	0.999771i	$0.493183\pi$
$710$	−51.7175	−	64.4141i	−1.94092	−	2.41742i
$711$		0			0
$712$	−9.87735	+	11.2757i	−0.370169	+	0.422573i
$713$	0.138912	+	0.138912i	0.00520231	+	0.00520231i
$714$		0			0
$715$	8.17072	+	19.7259i	0.305568	+	0.737706i
$716$	2.32659	+	13.1661i	0.0869488	+	0.492040i
$717$		0			0
$718$	3.42393	+	11.7388i	0.127780	+	0.438090i
$719$		−	15.1220i		−	0.563955i	−0.959421	−	0.281977i	$-0.909010\pi$
$719$		−	15.1220i		−	0.563955i	0.959421	−	0.281977i	$-0.0909903\pi$
$720$		0			0
$721$		−	32.2712i		−	1.20184i
$722$	−16.6307	+	4.85076i	−0.618930	+	0.180527i
$723$		0			0
$724$	9.75945	−	13.9490i	0.362707	−	0.518410i
$725$	−27.2435	−	65.7717i	−1.01180	−	2.44270i
$726$		0			0
$727$	−4.29348	−	4.29348i	−0.159236	−	0.159236i	0.622992	−	0.782228i	$-0.285917\pi$
$727$	−4.29348	−	4.29348i	−0.159236	−	0.159236i	−0.782228	+	0.622992i	$0.785917\pi$
$728$	−35.3259	+	17.4454i	−1.30927	+	0.646568i
$729$		0			0
$730$	−24.4021	+	19.5922i	−0.903161	+	0.725140i
$731$	3.67224	−	1.52109i	0.135823	−	0.0562597i
$732$		0			0
$733$	−3.86315	+	9.32647i	−0.142689	+	0.344481i	−0.979026	−	0.203734i	$-0.934692\pi$
$733$	−3.86315	+	9.32647i	−0.142689	+	0.344481i	0.836338	+	0.548215i	$0.184692\pi$
$734$	−12.8022	−	7.02042i	−0.472537	−	0.259128i
$735$		0			0
$736$	0.0243325	−	0.159076i	0.000896907	−	0.00586361i
$737$	9.27471			0.341638
$738$		0			0
$739$	−7.81425	+	18.8653i	−0.287452	+	0.693970i	−0.999970	−	0.00768326i	$-0.997554\pi$
$739$	−7.81425	+	18.8653i	−0.287452	+	0.693970i	0.712519	+	0.701653i	$0.247554\pi$
$740$	11.7858	+	2.60824i	0.433255	+	0.0958809i
$741$		0			0
$742$	−16.1994	+	13.0063i	−0.594698	+	0.477478i
$743$	30.2898	−	30.2898i	1.11122	−	1.11122i	0.118239	−	0.992985i	$-0.462275\pi$
$743$	30.2898	−	30.2898i	1.11122	−	1.11122i	0.992985	−	0.118239i	$-0.0377248\pi$
$744$		0			0
$745$	49.8793	+	49.8793i	1.82744	+	1.82744i
$746$	12.2565	+	1.34000i	0.448744	+	0.0490609i
$747$		0			0
$748$	−0.883033	−	0.617816i	−0.0322869	−	0.0225896i
$749$	−14.9481	−	6.19169i	−0.546190	−	0.226239i
$750$		0			0
$751$		−	24.7308i		−	0.902439i	−0.892413	−	0.451220i	$-0.850989\pi$
$751$		−	24.7308i		−	0.902439i	0.892413	−	0.451220i	$-0.149011\pi$
$752$	9.55269	+	4.44583i	0.348351	+	0.162123i
$753$		0			0
$754$	−17.7844	−	60.9732i	−0.647669	−	2.22051i
$755$	79.9526	+	33.1174i	2.90977	+	1.20527i
$756$		0			0
$757$	−0.536814	−	1.29598i	−0.0195109	−	0.0471034i	0.913824	−	0.406111i	$-0.133115\pi$
$757$	−0.536814	−	1.29598i	−0.0195109	−	0.0471034i	−0.933335	+	0.359007i	$0.883115\pi$
$758$	0.917367	−	8.39086i	0.0333203	−	0.304770i
$759$		0			0
$760$	−60.5330	+	4.00151i	−2.19576	+	0.145150i
$761$	32.7299	−	32.7299i	1.18646	−	1.18646i	0.208416	−	0.978040i	$-0.433169\pi$
$761$	32.7299	−	32.7299i	1.18646	−	1.18646i	0.978040	−	0.208416i	$-0.0668308\pi$
$762$		0			0
$763$	6.93645	−	2.87317i	0.251116	−	0.104016i
$764$	11.7477	+	18.4250i	0.425016	+	0.666593i
$765$		0			0
$766$	6.28281	−	11.4571i	0.227007	−	0.413962i
$767$	49.5676			1.78978
$768$		0			0
$769$	9.81757			0.354031			0.177015	−	0.984208i	$-0.443356\pi$
$769$	9.81757			0.354031			0.177015	+	0.984208i	$0.443356\pi$
$770$	5.37730	−	9.80585i	0.193784	−	0.353378i
$771$		0			0
$772$	1.34788	+	2.11402i	0.0485114	+	0.0760851i
$773$	−21.7629	+	9.01448i	−0.782756	+	0.324228i	−0.738027	−	0.674771i	$-0.764242\pi$
$773$	−21.7629	+	9.01448i	−0.782756	+	0.324228i	−0.0447290	+	0.998999i	$0.514242\pi$
$774$		0			0
$775$	47.4688	−	47.4688i	1.70513	−	1.70513i
$776$	40.9218	−	2.70512i	1.46901	−	0.0971081i
$777$		0			0
$778$	−5.75766	+	52.6635i	−0.206422	+	1.88808i
$779$	27.0834	+	65.3852i	0.970364	+	2.34267i
$780$		0			0
$781$	12.7628	+	5.28653i	0.456689	+	0.189167i
$782$	0.00668965	+	0.0229353i	0.000239221	+	0.000820163i
$783$		0			0
$784$	−6.67582	−	3.10693i	−0.238422	−	0.110962i
$785$			0.757372i			0.0270318i
$786$		0			0
$787$	−1.27278	−	0.527202i	−0.0453697	−	0.0187927i	0.359883	−	0.932997i	$-0.382817\pi$
$787$	−1.27278	−	0.527202i	−0.0453697	−	0.0187927i	−0.405253	+	0.914205i	$0.632817\pi$
$788$	−43.3933	−	30.3602i	−1.54582	−	1.08154i
$789$		0			0
$790$	41.2477	+	4.50958i	1.46753	+	0.160444i
$791$	−0.999518	−	0.999518i	−0.0355388	−	0.0355388i
$792$		0			0
$793$	23.4548	−	23.4548i	0.832906	−	0.832906i
$794$	18.6564	−	14.9790i	0.662089	−	0.531586i
$795$		0			0
$796$	29.2505	+	6.47325i	1.03676	+	0.229438i
$797$	−12.6159	+	30.4576i	−0.446879	+	1.07886i	0.526605	+	0.850110i	$0.323465\pi$
$797$	−12.6159	+	30.4576i	−0.446879	+	1.07886i	−0.973485	+	0.228753i	$0.926535\pi$
$798$		0			0
$799$	−1.56425			−0.0553393
$800$	−54.3589	−	8.31483i	−1.92188	−	0.293974i
$801$		0			0
$802$	−25.5465	−	14.0091i	−0.902077	−	0.494678i
$803$	2.00270	−	4.83495i	0.0706739	−	0.170622i
$804$		0			0
$805$	−0.229048	+	0.0948747i	−0.00807288	+	0.00334390i
$806$	46.7018	−	37.4965i	1.64500	−	1.32076i
$807$		0			0
$808$	10.8000	−	5.33349i	0.379944	−	0.187632i
$809$	−9.99600	−	9.99600i	−0.351441	−	0.351441i	0.509205	−	0.860645i	$-0.329940\pi$
$809$	−9.99600	−	9.99600i	−0.351441	−	0.351441i	−0.860645	+	0.509205i	$0.829940\pi$
$810$		0			0
$811$	10.7146	+	25.8674i	0.376241	+	0.908326i	0.992663	+	0.120910i	$0.0385813\pi$
$811$	10.7146	+	25.8674i	0.376241	+	0.908326i	−0.616423	+	0.787416i	$0.711419\pi$
$812$	−19.0715	+	27.2585i	−0.669279	+	0.956587i
$813$		0			0
$814$	−1.93788	+	0.565233i	−0.0679227	+	0.0198114i
$815$		−	31.1991i		−	1.09286i
$816$		0			0
$817$			37.4172i			1.30906i
$818$	−0.782029	−	2.68116i	−0.0273430	−	0.0937446i
$819$		0			0
$820$	16.9055	+	95.6676i	0.590367	+	3.34086i
$821$	8.20618	+	19.8115i	0.286398	+	0.691425i	0.999958	−	0.00916880i	$-0.00291856\pi$
$821$	8.20618	+	19.8115i	0.286398	+	0.691425i	−0.713560	+	0.700594i	$0.752919\pi$
$822$		0			0
$823$	2.41720	+	2.41720i	0.0842583	+	0.0842583i	0.747980	−	0.663722i	$-0.231024\pi$
$823$	2.41720	+	2.41720i	0.0842583	+	0.0842583i	−0.663722	+	0.747980i	$0.731024\pi$
$824$	26.4794	−	30.2280i	0.922452	−	1.05304i
$825$		0			0
$826$	−16.2546	−	20.2451i	−0.565569	−	0.704416i
$827$	26.3881	−	10.9303i	0.917605	−	0.380084i	0.126642	−	0.991949i	$-0.459580\pi$
$827$	26.3881	−	10.9303i	0.917605	−	0.380084i	0.790963	+	0.611864i	$0.209580\pi$
$828$		0			0
$829$	16.5480	−	39.9505i	0.574737	−	1.38754i	−0.322744	−	0.946486i	$-0.604605\pi$
$829$	16.5480	−	39.9505i	0.574737	−	1.38754i	0.897482	−	0.441052i	$-0.145395\pi$
$830$	7.54164	−	13.7527i	0.261774	−	0.477362i
$831$		0			0
$832$	−47.4036	−	12.6450i	−1.64343	−	0.438387i
$833$	1.09317			0.0378759
$834$		0			0
$835$	4.27190	−	10.3133i	0.147835	−	0.356905i
$836$	8.55422	−	5.45412i	0.295854	−	0.188635i
$837$		0			0
$838$	−7.30086	−	9.09321i	−0.252204	−	0.314120i
$839$	5.84028	−	5.84028i	0.201629	−	0.201629i	−0.599069	−	0.800698i	$-0.704462\pi$
$839$	5.84028	−	5.84028i	0.201629	−	0.201629i	0.800698	+	0.599069i	$0.204462\pi$
$840$		0			0
$841$	−17.4164	−	17.4164i	−0.600564	−	0.600564i
$842$	3.30622	−	30.2409i	0.113940	−	1.04217i
$843$		0			0
$844$	−5.68510	−	32.1717i	−0.195689	−	1.10740i
$845$	−87.2344	−	36.1337i	−3.00095	−	1.24304i
$846$		0			0
$847$		−	23.1149i		−	0.794238i
$848$	−25.8458	−	1.10916i	−0.887547	−	0.0380887i
$849$		0			0
$850$	7.83738	−	2.28597i	0.268820	−	0.0784082i
$851$	0.0413435	+	0.0171250i	0.00141724	+	0.000587038i
$852$		0			0
$853$	−15.4413	−	37.2785i	−0.528699	−	1.27639i	−0.932376	−	0.361491i	$-0.882268\pi$
$853$	−15.4413	−	37.2785i	−0.528699	−	1.27639i	0.403676	−	0.914902i	$-0.367732\pi$
$854$	−17.2712	−	1.88825i	−0.591009	−	0.0646146i
$855$		0			0
$856$	−8.92119	−	18.0649i	−0.304920	−	0.617447i
$857$	−27.5758	+	27.5758i	−0.941972	+	0.941972i	−0.998406	−	0.0564339i	$-0.982027\pi$
$857$	−27.5758	+	27.5758i	−0.941972	+	0.941972i	0.0564339	+	0.998406i	$0.482027\pi$
$858$		0			0
$859$	20.0077	−	8.28746i	0.682654	−	0.282764i	−0.0142820	−	0.999898i	$-0.504546\pi$
$859$	20.0077	−	8.28746i	0.682654	−	0.282764i	0.696936	+	0.717134i	$0.254546\pi$
$860$	−11.0983	+	50.1495i	−0.378448	+	1.71008i
$861$		0			0
$862$	−24.6917	−	13.5403i	−0.841001	−	0.461185i
$863$	25.5094			0.868351			0.434176	−	0.900828i	$-0.357040\pi$
$863$	25.5094			0.868351			0.434176	+	0.900828i	$0.357040\pi$
$864$		0			0
$865$	−41.7575			−1.41980
$866$	−5.81010	−	3.18612i	−0.197435	−	0.108269i
$867$		0			0
$868$	−30.6296	−	6.77846i	−1.03964	−	0.230076i
$869$	−6.41077	+	2.65543i	−0.217471	+	0.0900792i
$870$		0			0
$871$	−44.3233	+	44.3233i	−1.50184	+	1.50184i
$872$	8.85478	+	3.00028i	0.299861	+	0.101602i
$873$		0			0
$874$	−0.223567	−	0.0244425i	−0.00756228	−	0.000826779i
$875$	15.7452	+	38.0123i	0.532286	+	1.28505i
$876$		0			0
$877$	−15.7968	−	6.54325i	−0.533420	−	0.220950i	0.0996801	−	0.995020i	$-0.468218\pi$
$877$	−15.7968	−	6.54325i	−0.533420	−	0.220950i	−0.633101	+	0.774070i	$0.718218\pi$
$878$	−38.1422	+	11.1251i	−1.28724	+	0.375455i
$879$		0			0
$880$	13.0828	−	4.77279i	0.441021	−	0.160891i
$881$		−	30.9174i		−	1.04163i	−0.853669	−	0.520817i	$-0.825627\pi$
$881$		−	30.9174i		−	1.04163i	0.853669	−	0.520817i	$-0.174373\pi$
$882$		0			0
$883$	6.83747	+	2.83217i	0.230099	+	0.0953101i	0.494754	−	0.869033i	$-0.335258\pi$
$883$	6.83747	+	2.83217i	0.230099	+	0.0953101i	−0.264655	+	0.964343i	$0.585258\pi$
$884$	7.17247	−	1.26745i	0.241236	−	0.0426291i
$885$		0			0
$886$	1.36579	−	12.4925i	0.0458847	−	0.419692i
$887$	4.55771	+	4.55771i	0.153033	+	0.153033i	0.779471	−	0.626438i	$-0.215488\pi$
$887$	4.55771	+	4.55771i	0.153033	+	0.153033i	−0.626438	+	0.779471i	$0.715488\pi$
$888$		0			0
$889$	15.8192	−	15.8192i	0.530558	−	0.530558i
$890$	18.0039	+	22.4239i	0.603493	+	0.751649i
$891$		0			0
$892$	15.7435	+	24.6920i	0.527131	+	0.826750i
$893$	5.63510	−	13.6043i	0.188571	−	0.455252i
$894$		0			0
$895$	25.6493			0.857360
$896$	10.3803	+	23.5079i	0.346782	+	0.785343i
$897$		0			0
$898$	−16.4588	+	30.0137i	−0.549238	+	1.00157i
$899$	19.3531	−	46.7225i	0.645462	−	1.55828i
$900$		0			0
$901$	3.54823	−	1.46973i	0.118209	−	0.0489636i
$902$	−10.1714	−	12.6684i	−0.338670	−	0.421813i
$903$		0			0
$904$	−0.116104	−	1.75636i	−0.00386155	−	0.0584158i
$905$	−23.0936	−	23.0936i	−0.767656	−	0.767656i
$906$		0			0
$907$	3.85442	+	9.30540i	0.127984	+	0.308981i	0.974863	−	0.222805i	$-0.0715212\pi$
$907$	3.85442	+	9.30540i	0.127984	+	0.308981i	−0.846879	+	0.531786i	$0.821521\pi$
$908$	−30.6982	+	5.42472i	−1.01876	+	0.180026i
$909$		0			0
$910$	21.1638	+	72.5594i	0.701573	+	2.40532i
$911$			34.7146i			1.15015i	0.818102	+	0.575073i	$0.195026\pi$
$911$			34.7146i			1.15015i	−0.818102	+	0.575073i	$0.804974\pi$
$912$		0			0
$913$			2.62297i			0.0868077i
$914$	−24.1807	+	7.05291i	−0.799825	+	0.233289i
$915$		0			0
$916$	−2.85915	−	2.00041i	−0.0944688	−	0.0660954i
$917$	−8.06825	−	19.4785i	−0.266437	−	0.643236i
$918$		0			0
$919$	4.10915	+	4.10915i	0.135548	+	0.135548i	0.771626	−	0.636077i	$-0.219444\pi$
$919$	4.10915	+	4.10915i	0.135548	+	0.135548i	−0.636077	+	0.771626i	$0.719444\pi$
$920$	−0.292393	−	0.0990719i	−0.00963991	−	0.00326630i
$921$		0			0
$922$	−18.1559	+	14.5772i	−0.597934	+	0.480076i
$923$	−86.2567	+	35.7287i	−2.83917	+	1.17602i
$924$		0			0
$925$	5.85192	−	14.1278i	0.192410	−	0.464519i
$926$	41.8332	+	22.9404i	1.37472	+	0.753867i
$927$		0			0
$928$	−40.2303	+	9.88402i	−1.32063	+	0.324459i
$929$	−12.7028			−0.416766			−0.208383	−	0.978047i	$-0.566820\pi$
$929$	−12.7028			−0.416766			−0.208383	+	0.978047i	$0.566820\pi$
$930$		0			0
$931$	−3.93805	+	9.50728i	−0.129064	+	0.311589i
$932$	−7.39164	+	33.4004i	−0.242121	+	1.09407i
$933$		0			0
$934$	−39.9849	+	32.1035i	−1.30835	+	1.05046i
$935$	−1.46193	+	1.46193i	−0.0478101	+	0.0478101i
$936$		0			0
$937$	−13.6700	−	13.6700i	−0.446580	−	0.446580i	0.447636	−	0.894216i	$-0.352266\pi$
$937$	−13.6700	−	13.6700i	−0.446580	−	0.446580i	−0.894216	+	0.447636i	$0.852266\pi$
$938$	32.6379	+	3.56828i	1.06567	+	0.116509i
$939$		0			0
$940$	11.5878	−	16.5622i	0.377952	−	0.540199i
$941$	22.9410	+	9.50245i	0.747854	+	0.309771i	0.723866	−	0.689941i	$-0.242364\pi$
$941$	22.9410	+	9.50245i	0.747854	+	0.309771i	0.0239882	+	0.999712i	$0.492364\pi$
$942$		0			0
$943$			0.360157i			0.0117283i
$944$	1.38617	−	32.3006i	0.0451158	−	1.05129i
$945$		0			0
$946$	−2.40511	−	8.24585i	−0.0781969	−	0.268096i
$947$	−37.8206	−	15.6658i	−1.22900	−	0.509071i	−0.328743	−	0.944419i	$-0.606625\pi$
$947$	−37.8206	−	15.6658i	−1.22900	−	0.509071i	−0.900262	+	0.435349i	$0.856625\pi$
$948$		0			0
$949$	13.5352	+	32.6768i	0.439370	+	1.06073i
$950$	−8.35242	+	76.3969i	−0.270988	+	2.47864i
$951$		0			0
$952$	−2.86972	−	2.51384i	−0.0930082	−	0.0814741i
$953$	−28.3713	+	28.3713i	−0.919038	+	0.919038i	−0.996959	−	0.0779219i	$-0.975172\pi$
$953$	−28.3713	+	28.3713i	−0.919038	+	0.919038i	0.0779219	+	0.996959i	$0.475172\pi$
$954$		0			0
$955$	38.7292	−	16.0421i	1.25325	−	0.519112i
$956$	38.6375	−	24.6350i	1.24963	−	0.796753i
$957$		0			0
$958$	20.4431	−	37.2794i	0.660487	−	1.20444i
$959$	−24.2678			−0.783647
$960$		0			0
$961$	16.6882			0.538329
$962$	6.55981	−	11.9622i	0.211497	−	0.385678i
$963$		0			0
$964$	−28.1093	+	17.9223i	−0.905340	+	0.577239i
$965$	4.44364	−	1.84062i	0.143046	−	0.0592515i
$966$		0			0
$967$	4.94537	−	4.94537i	0.159032	−	0.159032i	−0.623106	−	0.782138i	$-0.714129\pi$
$967$	4.94537	−	4.94537i	0.159032	−	0.159032i	0.782138	+	0.623106i	$0.214129\pi$
$968$	18.9664	−	21.6514i	0.609603	−	0.695903i
$969$		0			0
$970$	8.55065	−	78.2100i	0.274545	−	2.51117i
$971$	−19.5243	−	47.1358i	−0.626564	−	1.51266i	−0.843865	−	0.536555i	$-0.819725\pi$
$971$	−19.5243	−	47.1358i	−0.626564	−	1.51266i	0.217301	−	0.976105i	$-0.430275\pi$
$972$		0			0
$973$	13.0116	+	5.38957i	0.417132	+	0.172782i
$974$	−14.5324	−	49.8238i	−0.465648	−	1.59646i
$975$		0			0
$976$	−14.6283	−	15.9402i	−0.468242	−	0.510233i
$977$			48.3431i			1.54663i	0.634020	+	0.773317i	$0.281404\pi$
$977$			48.3431i			1.54663i	−0.634020	+	0.773317i	$0.718596\pi$
$978$		0			0
$979$	−4.44299	−	1.84035i	−0.141999	−	0.0588178i
$980$	−8.09803	+	11.5744i	−0.258682	+	0.369729i
$981$		0			0
$982$	25.8816	+	2.82962i	0.825914	+	0.0902967i
$983$	−8.13455	−	8.13455i	−0.259452	−	0.259452i	0.565379	−	0.824831i	$-0.308730\pi$
$983$	−8.13455	−	8.13455i	−0.259452	−	0.259452i	−0.824831	+	0.565379i	$0.808730\pi$
$984$		0			0
$985$	−71.8407	+	71.8407i	−2.28904	+	2.28904i
$986$	4.79572	−	3.85044i	0.152727	−	0.122623i
$987$		0			0
$988$	−14.8152	+	66.9450i	−0.471334	+	2.12981i
$989$	−0.0728684	+	0.175920i	−0.00231708	+	0.00559392i
$990$		0			0
$991$	−22.2640			−0.707240			−0.353620	−	0.935389i	$-0.615049\pi$
$991$	−22.2640			−0.707240			−0.353620	+	0.935389i	$0.615049\pi$
$992$	−23.1284	−	31.4817i	−0.734329	−	0.999545i
$993$		0			0
$994$	42.8787	+	23.5137i	1.36003	+	0.745809i
$995$	21.9936	−	53.0973i	0.697244	−	1.68330i
$996$		0			0
$997$	53.6095	−	22.2058i	1.69783	−	0.703264i	0.697913	−	0.716183i	$-0.254112\pi$
$997$	53.6095	−	22.2058i	1.69783	−	0.703264i	0.999917	+	0.0129189i	$0.00411234\pi$
$998$	29.0943	−	23.3596i	0.920965	−	0.739435i
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
864.2.v.b.109.11	✓	128	1.1	even	1	trivial
864.2.v.b.109.22	yes	128	3.2	odd	2	inner
864.2.v.b.325.11	yes	128	32.5	even	8	inner
864.2.v.b.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)

\(f(q)\)	\(=\)	\(q+(-0.679990 + 1.24001i) q^{2} +(-1.07523 - 1.68638i) q^{4} +(-3.54476 + 1.46829i) q^{5} +(1.60611 - 1.60611i) q^{7} +(2.82227 - 0.186565i) q^{8} +O(q^{10})\)	\(q+(-0.679990 + 1.24001i) q^{2} +(-1.07523 - 1.68638i) q^{4} +(-3.54476 + 1.46829i) q^{5} +(1.60611 - 1.60611i) q^{7} +(2.82227 - 0.186565i) q^{8} +(0.589716 - 5.39394i) q^{10} +(0.347249 + 0.838334i) q^{11} +(-5.66583 - 2.34686i) q^{13} +(0.899444 + 3.08372i) q^{14} +(-1.68777 + 3.62649i) q^{16} -0.593837i q^{17} +(5.16462 + 2.13925i) q^{19} +(6.28751 + 4.39907i) q^{20} +(-1.27566 - 0.139468i) q^{22} +(0.0201157 + 0.0201157i) q^{23} +(6.87390 - 6.87390i) q^{25} +(6.76283 - 5.42982i) q^{26} +(-4.43544 - 0.981580i) q^{28} +(2.80250 - 6.76583i) q^{29} +6.90566 q^{31} +(-3.34920 - 4.55882i) q^{32} +(0.736362 + 0.403803i) q^{34} +(-3.33503 + 8.05148i) q^{35} +(1.45330 - 0.601978i) q^{37} +(-6.16457 + 4.94948i) q^{38} +(-9.73032 + 4.80522i) q^{40} +(8.95213 + 8.95213i) q^{41} +(2.56146 + 6.18392i) q^{43} +(1.04038 - 1.48699i) q^{44} +(-0.0386221 + 0.0112651i) q^{46} -2.63414i q^{47} +1.84085i q^{49} +(3.84949 + 13.1979i) q^{50} +(2.13435 + 12.0782i) q^{52} +(2.47496 + 5.97509i) q^{53} +(-2.46183 - 2.46183i) q^{55} +(4.23322 - 4.83250i) q^{56} +(6.48400 + 8.07581i) q^{58} +(-7.46732 + 3.09307i) q^{59} +(-2.06985 + 4.99706i) q^{61} +(-4.69578 + 8.56306i) q^{62} +(7.93039 - 1.05307i) q^{64} +23.5299 q^{65} +(3.91146 - 9.44309i) q^{67} +(-1.00144 + 0.638510i) q^{68} +(-7.71609 - 9.61038i) q^{70} +(10.7650 - 10.7650i) q^{71} +(-4.07812 - 4.07812i) q^{73} +(-0.241775 + 2.21144i) q^{74} +(-1.94554 - 11.0097i) q^{76} +(1.90417 + 0.788734i) q^{77} +7.64704i q^{79} +(0.658016 - 15.3332i) q^{80} +(-17.1880 + 5.01333i) q^{82} +(2.67059 + 1.10620i) q^{83} +(0.871923 + 2.10501i) q^{85} +(-9.40986 - 1.02877i) q^{86} +(1.13643 + 2.30122i) q^{88} +(-3.74752 + 3.74752i) q^{89} +(-12.8692 + 5.33061i) q^{91} +(0.0122938 - 0.0555518i) q^{92} +(3.26635 + 1.79119i) q^{94} -21.4483 q^{95} +14.4996 q^{97} +(-2.28266 - 1.25176i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q+O(q^{10}) \) 128 * q	\( 128 q + 16 q^{10} - 32 q^{16} - 16 q^{22} - 32 q^{40} - 32 q^{46} - 80 q^{52} + 32 q^{55} - 32 q^{58} + 64 q^{61} + 48 q^{64} + 64 q^{67} - 96 q^{70} + 32 q^{76} - 80 q^{82} - 80 q^{88} + 96 q^{91} - 48 q^{94}+O(q^{100}) \) 128 * q + 16 * q^10 - 32 * q^16 - 16 * q^22 - 32 * q^40 - 32 * q^46 - 80 * q^52 + 32 * q^55 - 32 * q^58 + 64 * q^61 + 48 * q^64 + 64 * q^67 - 96 * q^70 + 32 * q^76 - 80 * q^82 - 80 * q^88 + 96 * q^91 - 48 * q^94

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