LMFDB - Embedded newform 256.2.i.a.49.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [256,2,Mod(17,256)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(256, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([0, 7]))

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

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

chi := DirichletCharacter("256.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 256 = 2^{8} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	256.i (of order $16$, degree $8$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.04417029174$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$7$ over $\Q(\zeta_{16})$
Twist minimal:	no (minimal twist has level 64)
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			49.7
Character	$\chi$	$=$	256.49
Dual form			256.2.i.a.209.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.98137 - 0.593031i) q^{3} +(0.914126 + 1.36809i) q^{5} +(-2.65574 - 1.10004i) q^{7} +(5.76522 - 2.38803i) q^{9} +O(q^{10})$	\(q+(2.98137 - 0.593031i) q^{3} +(0.914126 + 1.36809i) q^{5} +(-2.65574 - 1.10004i) q^{7} +(5.76522 - 2.38803i) q^{9} +(-0.246413 + 1.23880i) q^{11} +(0.319413 - 0.478036i) q^{13} +(3.53666 + 3.53666i) q^{15} +(-3.38390 + 3.38390i) q^{17} +(-4.19561 - 2.80342i) q^{19} +(-8.57011 - 1.70470i) q^{21} +(-0.178010 - 0.429755i) q^{23} +(0.877384 - 2.11819i) q^{25} +(8.18962 - 5.47213i) q^{27} +(-1.02242 - 5.14005i) q^{29} +10.0065i q^{31} +3.83945i q^{33} +(-0.922728 - 4.63887i) q^{35} +(0.447703 - 0.299146i) q^{37} +(0.668798 - 1.61462i) q^{39} +(2.44115 + 5.89346i) q^{41} +(-3.80641 - 0.757142i) q^{43} +(8.53718 + 5.70436i) q^{45} +(5.99084 - 5.99084i) q^{47} +(0.893127 + 0.893127i) q^{49} +(-8.08188 + 12.0954i) q^{51} +(0.810472 - 4.07452i) q^{53} +(-1.92004 + 0.795307i) q^{55} +(-14.1712 - 5.86989i) q^{57} +(1.03615 + 1.55070i) q^{59} +(-6.47490 + 1.28794i) q^{61} -17.9379 q^{63} +0.945978 q^{65} +(-6.01983 + 1.19742i) q^{67} +(-0.785572 - 1.17569i) q^{69} +(4.20400 + 1.74136i) q^{71} +(-0.911379 + 0.377506i) q^{73} +(1.35965 - 6.83542i) q^{75} +(2.01715 - 3.01887i) q^{77} +(-0.152459 - 0.152459i) q^{79} +(7.93360 - 7.93360i) q^{81} +(5.16472 + 3.45096i) q^{83} +(-7.72277 - 1.53615i) q^{85} +(-6.09641 - 14.7180i) q^{87} +(1.48745 - 3.59102i) q^{89} +(-1.37414 + 0.918171i) q^{91} +(5.93418 + 29.8331i) q^{93} -8.30263i q^{95} +13.7742i q^{97} +(1.53767 + 7.73041i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 8 q^{3} - 8 q^{5} + 8 q^{7} - 8 q^{9}+O(q^{10}) $ 56 * q + 8 * q^3 - 8 * q^5 + 8 * q^7 - 8 * q^9	$ 56 q + 8 q^{3} - 8 q^{5} + 8 q^{7} - 8 q^{9} + 8 q^{11} - 8 q^{13} + 8 q^{15} - 8 q^{17} + 8 q^{19} - 8 q^{21} + 8 q^{23} - 8 q^{25} + 8 q^{27} - 8 q^{29} + 8 q^{35} - 8 q^{37} + 8 q^{39} - 8 q^{41} + 8 q^{43} - 8 q^{45} + 8 q^{47} - 8 q^{49} - 24 q^{51} - 8 q^{53} - 56 q^{55} - 8 q^{57} - 56 q^{59} - 8 q^{61} - 64 q^{63} - 16 q^{65} - 72 q^{67} - 8 q^{69} - 56 q^{71} - 8 q^{73} - 56 q^{75} - 8 q^{77} - 24 q^{79} - 8 q^{81} + 8 q^{83} - 8 q^{85} + 8 q^{87} - 8 q^{89} + 8 q^{91} + 16 q^{93} - 16 q^{99}+O(q^{100}) $ 56 * q + 8 * q^3 - 8 * q^5 + 8 * q^7 - 8 * q^9 + 8 * q^11 - 8 * q^13 + 8 * q^15 - 8 * q^17 + 8 * q^19 - 8 * q^21 + 8 * q^23 - 8 * q^25 + 8 * q^27 - 8 * q^29 + 8 * q^35 - 8 * q^37 + 8 * q^39 - 8 * q^41 + 8 * q^43 - 8 * q^45 + 8 * q^47 - 8 * q^49 - 24 * q^51 - 8 * q^53 - 56 * q^55 - 8 * q^57 - 56 * q^59 - 8 * q^61 - 64 * q^63 - 16 * q^65 - 72 * q^67 - 8 * q^69 - 56 * q^71 - 8 * q^73 - 56 * q^75 - 8 * q^77 - 24 * q^79 - 8 * q^81 + 8 * q^83 - 8 * q^85 + 8 * q^87 - 8 * q^89 + 8 * q^91 + 16 * q^93 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/256\mathbb{Z}\right)^\times$.

$n$	$5$	$255$
$\chi(n)$	$e\left(\frac{5}{16}\right)$	$1$

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			0
$2$		0			0
$3$	2.98137	−	0.593031i	1.72129	−	0.342386i	0.767088	−	0.641542i	$-0.221705\pi$
$3$	2.98137	−	0.593031i	1.72129	−	0.342386i	0.954204	+	0.299155i	$0.0967048\pi$
$4$		0			0
$5$	0.914126	+	1.36809i	0.408810	+	0.611827i	0.977553	−	0.210688i	$-0.0675704\pi$
$5$	0.914126	+	1.36809i	0.408810	+	0.611827i	−0.568744	+	0.822515i	$0.692570\pi$
$6$		0			0
$7$	−2.65574	−	1.10004i	−1.00378	−	0.415778i	−0.180596	−	0.983557i	$-0.557803\pi$
$7$	−2.65574	−	1.10004i	−1.00378	−	0.415778i	−0.823181	+	0.567779i	$0.807803\pi$
$8$		0			0
$9$	5.76522	−	2.38803i	1.92174	−	0.796011i
$10$		0			0
$11$	−0.246413	+	1.23880i	−0.0742963	+	0.373513i	−0.999989	−	0.00476447i	$-0.998483\pi$
$11$	−0.246413	+	1.23880i	−0.0742963	+	0.373513i	0.925692	+	0.378277i	$0.123483\pi$
$12$		0			0
$13$	0.319413	−	0.478036i	0.0885893	−	0.132583i	−0.784528	−	0.620093i	$-0.787095\pi$
$13$	0.319413	−	0.478036i	0.0885893	−	0.132583i	0.873117	+	0.487510i	$0.162095\pi$
$14$		0			0
$15$	3.53666	+	3.53666i	0.913162	+	0.913162i
$16$		0			0
$17$	−3.38390	+	3.38390i	−0.820715	+	0.820715i	−0.986211	−	0.165495i	$-0.947078\pi$
$17$	−3.38390	+	3.38390i	−0.820715	+	0.820715i	0.165495	+	0.986211i	$0.447078\pi$
$18$		0			0
$19$	−4.19561	−	2.80342i	−0.962539	−	0.643148i	−0.0282261	−	0.999602i	$-0.508986\pi$
$19$	−4.19561	−	2.80342i	−0.962539	−	0.643148i	−0.934313	+	0.356453i	$0.883986\pi$
$20$		0			0
$21$	−8.57011	−	1.70470i	−1.87015	−	0.371996i
$22$		0			0
$23$	−0.178010	−	0.429755i	−0.0371177	−	0.0896101i	0.904234	−	0.427038i	$-0.140443\pi$
$23$	−0.178010	−	0.429755i	−0.0371177	−	0.0896101i	−0.941351	+	0.337428i	$0.890443\pi$
$24$		0			0
$25$	0.877384	−	2.11819i	0.175477	−	0.423638i
$26$		0			0
$27$	8.18962	−	5.47213i	1.57609	−	1.05311i
$28$		0			0
$29$	−1.02242	−	5.14005i	−0.189858	−	0.954483i	−0.951773	−	0.306805i	$-0.900740\pi$
$29$	−1.02242	−	5.14005i	−0.189858	−	0.954483i	0.761914	−	0.647678i	$-0.224260\pi$
$30$		0			0
$31$			10.0065i			1.79722i	0.438743	+	0.898612i	$0.355424\pi$
$31$			10.0065i			1.79722i	−0.438743	+	0.898612i	$0.644576\pi$
$32$		0			0
$33$			3.83945i			0.668363i
$34$		0			0
$35$	−0.922728	−	4.63887i	−0.155969	−	0.784111i
$36$		0			0
$37$	0.447703	−	0.299146i	0.0736019	−	0.0491792i	−0.518225	−	0.855244i	$-0.673407\pi$
$37$	0.447703	−	0.299146i	0.0736019	−	0.0491792i	0.591827	+	0.806065i	$0.298407\pi$
$38$		0			0
$39$	0.668798	−	1.61462i	0.107093	−	0.258546i
$40$		0			0
$41$	2.44115	+	5.89346i	0.381244	+	0.920404i	0.991726	+	0.128374i	$0.0409757\pi$
$41$	2.44115	+	5.89346i	0.381244	+	0.920404i	−0.610482	+	0.792030i	$0.709024\pi$
$42$		0			0
$43$	−3.80641	−	0.757142i	−0.580472	−	0.115463i	−0.103883	−	0.994589i	$-0.533127\pi$
$43$	−3.80641	−	0.757142i	−0.580472	−	0.115463i	−0.476589	+	0.879126i	$0.658127\pi$
$44$		0			0
$45$	8.53718	+	5.70436i	1.27265	+	0.850355i
$46$		0			0
$47$	5.99084	−	5.99084i	0.873854	−	0.873854i	−0.119036	−	0.992890i	$-0.537980\pi$
$47$	5.99084	−	5.99084i	0.873854	−	0.873854i	0.992890	+	0.119036i	$0.0379804\pi$
$48$		0			0
$49$	0.893127	+	0.893127i	0.127590	+	0.127590i
$50$		0			0
$51$	−8.08188	+	12.0954i	−1.13169	+	1.69369i
$52$		0			0
$53$	0.810472	−	4.07452i	0.111327	−	0.559678i	−0.884353	−	0.466820i	$-0.845400\pi$
$53$	0.810472	−	4.07452i	0.111327	−	0.559678i	0.995679	−	0.0928581i	$-0.0296003\pi$
$54$		0			0
$55$	−1.92004	+	0.795307i	−0.258898	+	0.107239i
$56$		0			0
$57$	−14.1712	−	5.86989i	−1.87702	−	0.777486i
$58$		0			0
$59$	1.03615	+	1.55070i	0.134895	+	0.201884i	0.892767	−	0.450519i	$-0.148761\pi$
$59$	1.03615	+	1.55070i	0.134895	+	0.201884i	−0.757872	+	0.652403i	$0.773761\pi$
$60$		0			0
$61$	−6.47490	+	1.28794i	−0.829026	+	0.164903i	−0.591323	−	0.806435i	$-0.701394\pi$
$61$	−6.47490	+	1.28794i	−0.829026	+	0.164903i	−0.237702	+	0.971338i	$0.576394\pi$
$62$		0			0
$63$	−17.9379			−2.25996
$64$		0			0
$65$	0.945978			0.117334
$66$		0			0
$67$	−6.01983	+	1.19742i	−0.735439	+	0.146288i	−0.548579	−	0.836099i	$-0.684831\pi$
$67$	−6.01983	+	1.19742i	−0.735439	+	0.146288i	−0.186860	+	0.982387i	$0.559831\pi$
$68$		0			0
$69$	−0.785572	−	1.17569i	−0.0945718	−	0.141537i
$70$		0			0
$71$	4.20400	+	1.74136i	0.498924	+	0.206661i	0.617931	−	0.786232i	$-0.287971\pi$
$71$	4.20400	+	1.74136i	0.498924	+	0.206661i	−0.119007	+	0.992893i	$0.537971\pi$
$72$		0			0
$73$	−0.911379	+	0.377506i	−0.106669	+	0.0441837i	−0.435380	−	0.900247i	$-0.643386\pi$
$73$	−0.911379	+	0.377506i	−0.106669	+	0.0441837i	0.328711	+	0.944431i	$0.393386\pi$
$74$		0			0
$75$	1.35965	−	6.83542i	0.156999	−	0.789286i
$76$		0			0
$77$	2.01715	−	3.01887i	0.229875	−	0.344033i
$78$		0			0
$79$	−0.152459	−	0.152459i	−0.0171530	−	0.0171530i	0.698478	−	0.715631i	$-0.253861\pi$
$79$	−0.152459	−	0.152459i	−0.0171530	−	0.0171530i	−0.715631	+	0.698478i	$0.753861\pi$
$80$		0			0
$81$	7.93360	−	7.93360i	0.881511	−	0.881511i
$82$		0			0
$83$	5.16472	+	3.45096i	0.566902	+	0.378792i	0.805741	−	0.592267i	$-0.201767\pi$
$83$	5.16472	+	3.45096i	0.566902	+	0.378792i	−0.238840	+	0.971059i	$0.576767\pi$
$84$		0			0
$85$	−7.72277	−	1.53615i	−0.837652	−	0.166619i
$86$		0			0
$87$	−6.09641	−	14.7180i	−0.653604	−	1.57794i
$88$		0			0
$89$	1.48745	−	3.59102i	0.157669	−	0.380648i	−0.825228	−	0.564799i	$-0.808954\pi$
$89$	1.48745	−	3.59102i	0.157669	−	0.380648i	0.982898	+	0.184151i	$0.0589537\pi$
$90$		0			0
$91$	−1.37414	+	0.918171i	−0.144049	+	0.0962505i
$92$		0			0
$93$	5.93418	+	29.8331i	0.615345	+	3.09355i
$94$		0			0
$95$		−	8.30263i		−	0.851832i
$96$		0			0
$97$			13.7742i			1.39856i	0.714849	+	0.699279i	$0.246495\pi$
$97$			13.7742i			1.39856i	−0.714849	+	0.699279i	$0.753505\pi$
$98$		0			0
$99$	1.53767	+	7.73041i	0.154542	+	0.776936i
$100$		0			0
$101$	3.34129	−	2.23258i	0.332470	−	0.222150i	−0.378118	−	0.925757i	$-0.623429\pi$
$101$	3.34129	−	2.23258i	0.332470	−	0.222150i	0.710589	+	0.703608i	$0.248429\pi$
$102$		0			0
$103$	−3.02140	+	7.29430i	−0.297707	+	0.718728i	0.702270	+	0.711911i	$0.252170\pi$
$103$	−3.02140	+	7.29430i	−0.297707	+	0.718728i	−0.999977	+	0.00681740i	$0.997830\pi$
$104$		0			0
$105$	−5.50198	−	13.2830i	−0.536938	−	1.29628i
$106$		0			0
$107$	5.40913	+	1.07594i	0.522920	+	0.104015i	0.449490	−	0.893285i	$-0.351606\pi$
$107$	5.40913	+	1.07594i	0.522920	+	0.104015i	0.0734296	+	0.997300i	$0.476606\pi$
$108$		0			0
$109$	−3.62995	−	2.42545i	−0.347686	−	0.232316i	0.369448	−	0.929251i	$-0.379547\pi$
$109$	−3.62995	−	2.42545i	−0.347686	−	0.232316i	−0.717134	+	0.696935i	$0.754547\pi$
$110$		0			0
$111$	1.15736	−	1.15736i	0.109852	−	0.109852i
$112$		0			0
$113$	−11.6929	−	11.6929i	−1.09998	−	1.09998i	−0.994412	−	0.105567i	$-0.966334\pi$
$113$	−11.6929	−	11.6929i	−1.09998	−	1.09998i	−0.105567	−	0.994412i	$-0.533666\pi$
$114$		0			0
$115$	0.425218	−	0.636384i	0.0396518	−	0.0593431i
$116$		0			0
$117$	0.699923	−	3.51875i	0.0647079	−	0.325309i
$118$		0			0
$119$	12.7092	−	5.26432i	1.16505	−	0.482580i
$120$		0			0
$121$	8.68876	+	3.59900i	0.789888	+	0.327182i
$122$		0			0
$123$	10.7730	+	16.1229i	0.971366	+	1.45375i
$124$		0			0
$125$	11.7687	−	2.34095i	1.05263	−	0.209381i
$126$		0			0
$127$	21.9517			1.94790			0.973949	−	0.226767i	$-0.0728154\pi$
$127$	21.9517			1.94790			0.973949	+	0.226767i	$0.0728154\pi$
$128$		0			0
$129$	−11.7973			−1.03870
$130$		0			0
$131$	7.05871	−	1.40406i	0.616722	−	0.122674i	0.123164	−	0.992386i	$-0.460696\pi$
$131$	7.05871	−	1.40406i	0.616722	−	0.122674i	0.493558	+	0.869713i	$0.335696\pi$
$132$		0			0
$133$	8.05858	+	12.0605i	0.698768	+	1.04578i
$134$		0			0
$135$	14.9727	+	6.20189i	1.28864	+	0.533774i
$136$		0			0
$137$	10.2318	−	4.23815i	0.874161	−	0.362089i	0.0999315	−	0.994994i	$-0.468138\pi$
$137$	10.2318	−	4.23815i	0.874161	−	0.362089i	0.774229	+	0.632905i	$0.218138\pi$
$138$		0			0
$139$	0.752410	−	3.78262i	0.0638186	−	0.320838i	−0.935668	−	0.352882i	$-0.885202\pi$
$139$	0.752410	−	3.78262i	0.0638186	−	0.320838i	0.999486	+	0.0320443i	$0.0102018\pi$
$140$		0			0
$141$	14.3081	−	21.4136i	1.20496	−	1.80335i
$142$		0			0
$143$	0.513484	+	0.513484i	0.0429397	+	0.0429397i
$144$		0			0
$145$	6.09741	−	6.09741i	0.506362	−	0.506362i
$146$		0			0
$147$	3.19239	+	2.13309i	0.263304	+	0.175934i
$148$		0			0
$149$	21.8201	+	4.34028i	1.78757	+	0.355569i	0.974114	−	0.226059i	$-0.0725841\pi$
$149$	21.8201	+	4.34028i	1.78757	+	0.355569i	0.813455	+	0.581628i	$0.197584\pi$
$150$		0			0
$151$	−2.99065	−	7.22006i	−0.243375	−	0.587560i	0.754239	−	0.656600i	$-0.228006\pi$
$151$	−2.99065	−	7.22006i	−0.243375	−	0.587560i	−0.997614	+	0.0690406i	$0.978006\pi$
$152$		0			0
$153$	−11.4281	+	27.5898i	−0.923904	+	2.23050i
$154$		0			0
$155$	−13.6898	+	9.14722i	−1.09959	+	0.734723i
$156$		0			0
$157$	−4.09955	−	20.6098i	−0.327180	−	1.64484i	−0.697970	−	0.716127i	$-0.745913\pi$
$157$	−4.09955	−	20.6098i	−0.327180	−	1.64484i	0.370790	−	0.928717i	$-0.379087\pi$
$158$		0			0
$159$		−	12.6283i		−	1.00149i
$160$		0			0
$161$			1.33714i			0.105381i
$162$		0			0
$163$	−3.99966	−	20.1077i	−0.313278	−	1.57495i	−0.741293	−	0.671182i	$-0.765787\pi$
$163$	−3.99966	−	20.1077i	−0.313278	−	1.57495i	0.428015	−	0.903772i	$-0.359213\pi$
$164$		0			0
$165$	−5.25270	+	3.50974i	−0.408922	+	0.273233i
$166$		0			0
$167$	−5.57052	+	13.4484i	−0.431060	+	1.04067i	0.547886	+	0.836553i	$0.315433\pi$
$167$	−5.57052	+	13.4484i	−0.431060	+	1.04067i	−0.978946	+	0.204118i	$0.934567\pi$
$168$		0			0
$169$	4.84839	+	11.7051i	0.372953	+	0.900389i
$170$		0			0
$171$	−30.8833	−	6.14307i	−2.36170	−	0.469772i
$172$		0			0
$173$	−15.4616	−	10.3311i	−1.17552	−	0.785459i	−0.194796	−	0.980844i	$-0.562405\pi$
$173$	−15.4616	−	10.3311i	−1.17552	−	0.785459i	−0.980727	+	0.195384i	$0.937405\pi$
$174$		0			0
$175$	−4.66021	+	4.66021i	−0.352279	+	0.352279i
$176$		0			0
$177$	4.00874	+	4.00874i	0.301315	+	0.301315i
$178$		0			0
$179$	5.99376	−	8.97030i	0.447995	−	0.670472i	−0.536896	−	0.843648i	$-0.680403\pi$
$179$	5.99376	−	8.97030i	0.447995	−	0.670472i	0.984891	+	0.173177i	$0.0554032\pi$
$180$		0			0
$181$	0.698076	−	3.50946i	0.0518876	−	0.260856i	−0.946130	−	0.323786i	$-0.895044\pi$
$181$	0.698076	−	3.50946i	0.0518876	−	0.260856i	0.998018	+	0.0629294i	$0.0200443\pi$
$182$		0			0
$183$	−18.5403	+	7.67963i	−1.37054	+	0.567694i
$184$		0			0
$185$	0.818514	+	0.339039i	0.0601783	+	0.0249267i
$186$		0			0
$187$	−3.35814	−	5.02581i	−0.245572	−	0.367524i
$188$		0			0
$189$	−27.7691	+	5.52362i	−2.01991	+	0.401784i
$190$		0			0
$191$	0.722126			0.0522512			0.0261256	−	0.999659i	$-0.491683\pi$
$191$	0.722126			0.0522512			0.0261256	+	0.999659i	$0.491683\pi$
$192$		0			0
$193$	−5.30778			−0.382063			−0.191031	−	0.981584i	$-0.561183\pi$
$193$	−5.30778			−0.382063			−0.191031	+	0.981584i	$0.561183\pi$
$194$		0			0
$195$	2.82031	−	0.560994i	0.201966	−	0.0401736i
$196$		0			0
$197$	8.28629	+	12.4013i	0.590373	+	0.883556i	0.999583	−	0.0288843i	$-0.00919543\pi$
$197$	8.28629	+	12.4013i	0.590373	+	0.883556i	−0.409209	+	0.912441i	$0.634195\pi$
$198$		0			0
$199$	0.443861	+	0.183853i	0.0314644	+	0.0130330i	0.398360	−	0.917229i	$-0.369579\pi$
$199$	0.443861	+	0.183853i	0.0314644	+	0.0130330i	−0.366896	+	0.930262i	$0.619579\pi$
$200$		0			0
$201$	−17.2372	+	7.13989i	−1.21582	+	0.503609i
$202$		0			0
$203$	−2.93900	+	14.7753i	−0.206277	+	1.03703i
$204$		0			0
$205$	−5.83124	+	8.72707i	−0.407272	+	0.609525i
$206$		0			0
$207$	−2.05254	−	2.05254i	−0.142661	−	0.142661i
$208$		0			0
$209$	4.50673	−	4.50673i	0.311737	−	0.311737i
$210$		0			0
$211$	12.2014	+	8.15273i	0.839980	+	0.561257i	0.899475	−	0.436972i	$-0.143949\pi$
$211$	12.2014	+	8.15273i	0.839980	+	0.561257i	−0.0594948	+	0.998229i	$0.518949\pi$
$212$		0			0
$213$	13.5664	+	2.69852i	0.929551	+	0.184899i
$214$		0			0
$215$	−2.44370	−	5.89962i	−0.166659	−	0.402351i
$216$		0			0
$217$	11.0076	−	26.5748i	0.747246	−	1.80401i
$218$		0			0
$219$	−2.49328	+	1.66596i	−0.168480	+	0.112575i
$220$		0			0
$221$	0.536762	+	2.69848i	0.0361065	+	0.181520i
$222$		0			0
$223$			20.5439i			1.37572i	0.725843	+	0.687860i	$0.241450\pi$
$223$			20.5439i			1.37572i	−0.725843	+	0.687860i	$0.758550\pi$
$224$		0			0
$225$		−	14.3071i		−	0.953804i
$226$		0			0
$227$	−3.83215	−	19.2655i	−0.254348	−	1.27870i	−0.870931	−	0.491406i	$-0.836483\pi$
$227$	−3.83215	−	19.2655i	−0.254348	−	1.27870i	0.616582	−	0.787290i	$-0.288517\pi$
$228$		0			0
$229$	−18.1422	+	12.1223i	−1.19887	+	0.801061i	−0.984447	−	0.175680i	$-0.943788\pi$
$229$	−18.1422	+	12.1223i	−1.19887	+	0.801061i	−0.214425	+	0.976740i	$0.568788\pi$
$230$		0			0
$231$	4.22357	−	10.1966i	0.277891	−	0.670887i
$232$		0			0
$233$	−1.49754	−	3.61539i	−0.0981074	−	0.236852i	0.867204	−	0.497953i	$-0.165915\pi$
$233$	−1.49754	−	3.61539i	−0.0981074	−	0.236852i	−0.965312	+	0.261100i	$0.915915\pi$
$234$		0			0
$235$	13.6724	+	2.71960i	0.891887	+	0.177407i
$236$		0			0
$237$	−0.544950	−	0.364124i	−0.0353983	−	0.0236524i
$238$		0			0
$239$	−4.87803	+	4.87803i	−0.315534	+	0.315534i	−0.847049	−	0.531515i	$-0.821623\pi$
$239$	−4.87803	+	4.87803i	−0.315534	+	0.315534i	0.531515	+	0.847049i	$0.321623\pi$
$240$		0			0
$241$	1.70539	+	1.70539i	0.109854	+	0.109854i	0.759897	−	0.650043i	$-0.225249\pi$
$241$	1.70539	+	1.70539i	0.109854	+	0.109854i	−0.650043	+	0.759897i	$0.725249\pi$
$242$		0			0
$243$	2.53170	−	3.78895i	0.162409	−	0.243062i
$244$		0			0
$245$	−0.405444	+	2.03831i	−0.0259029	+	0.130223i
$246$		0			0
$247$	−2.68027	+	1.11020i	−0.170541	+	0.0706405i
$248$		0			0
$249$	17.4444	+	7.22572i	1.10550	+	0.457912i
$250$		0			0
$251$	0.380597	+	0.569604i	0.0240231	+	0.0359531i	0.843287	−	0.537464i	$-0.180618\pi$
$251$	0.380597	+	0.569604i	0.0240231	+	0.0359531i	−0.819264	+	0.573417i	$0.805618\pi$
$252$		0			0
$253$	0.576245	−	0.114622i	0.0362282	−	0.00720625i
$254$		0			0
$255$	−23.9354			−1.49889
$256$		0			0
$257$	24.3404			1.51831			0.759156	−	0.650908i	$-0.225612\pi$
$257$	24.3404			1.51831			0.759156	+	0.650908i	$0.225612\pi$
$258$		0			0
$259$	−1.51806	+	0.301960i	−0.0943275	+	0.0187629i
$260$		0			0
$261$	−18.1691	−	27.1919i	−1.12464	−	1.68314i
$262$		0			0
$263$	−9.60085	−	3.97680i	−0.592014	−	0.245220i	0.0665030	−	0.997786i	$-0.478816\pi$
$263$	−9.60085	−	3.97680i	−0.592014	−	0.245220i	−0.658517	+	0.752566i	$0.728816\pi$
$264$		0			0
$265$	6.31516	−	2.61583i	0.387937	−	0.160689i
$266$		0			0
$267$	2.30505	−	11.5883i	0.141067	−	0.709190i
$268$		0			0
$269$	−17.3303	+	25.9367i	−1.05665	+	1.58139i	−0.271136	+	0.962541i	$0.587399\pi$
$269$	−17.3303	+	25.9367i	−1.05665	+	1.58139i	−0.785513	+	0.618845i	$0.787601\pi$
$270$		0			0
$271$	−11.8443	−	11.8443i	−0.719491	−	0.719491i	0.249010	−	0.968501i	$-0.419895\pi$
$271$	−11.8443	−	11.8443i	−0.719491	−	0.719491i	−0.968501	+	0.249010i	$0.919895\pi$
$272$		0			0
$273$	−3.55231	+	3.55231i	−0.214996	+	0.214996i
$274$		0			0
$275$	2.40782	+	1.60885i	0.145197	+	0.0970176i
$276$		0			0
$277$	−25.5130	−	5.07485i	−1.53293	−	0.304918i	−0.644741	−	0.764401i	$-0.723035\pi$
$277$	−25.5130	−	5.07485i	−1.53293	−	0.304918i	−0.888187	+	0.459483i	$0.848035\pi$
$278$		0			0
$279$	23.8959	+	57.6898i	1.43061	+	3.45380i
$280$		0			0
$281$	−9.37710	+	22.6383i	−0.559391	+	1.35049i	0.350858	+	0.936429i	$0.385890\pi$
$281$	−9.37710	+	22.6383i	−0.559391	+	1.35049i	−0.910249	+	0.414061i	$0.864110\pi$
$282$		0			0
$283$	19.3155	−	12.9062i	1.14819	−	0.767195i	0.172210	−	0.985060i	$-0.444909\pi$
$283$	19.3155	−	12.9062i	1.14819	−	0.767195i	0.975979	+	0.217865i	$0.0699092\pi$
$284$		0			0
$285$	−4.92372	−	24.7532i	−0.291656	−	1.46625i
$286$		0			0
$287$		−	18.3369i		−	1.08239i
$288$		0			0
$289$		−	5.90150i		−	0.347147i
$290$		0			0
$291$	8.16852	+	41.0659i	0.478847	+	2.40733i
$292$		0			0
$293$	23.5455	−	15.7326i	1.37554	−	0.919109i	0.375573	−	0.926793i	$-0.377446\pi$
$293$	23.5455	−	15.7326i	1.37554	−	0.919109i	0.999970	+	0.00768446i	$0.00244606\pi$
$294$		0			0
$295$	−1.17433	+	2.83507i	−0.0683719	+	0.165064i
$296$		0			0
$297$	4.76086	+	11.4937i	0.276253	+	0.666934i
$298$		0			0
$299$	−0.262297	−	0.0521741i	−0.0151690	−	0.00301731i
$300$		0			0
$301$	9.27596	+	6.19800i	0.534657	+	0.357247i
$302$		0			0
$303$	8.63761	−	8.63761i	0.496218	−	0.496218i
$304$		0			0
$305$	−7.68088	−	7.68088i	−0.439806	−	0.439806i
$306$		0			0
$307$	6.01712	−	9.00525i	0.343415	−	0.513957i	−0.619054	−	0.785348i	$-0.712484\pi$
$307$	6.01712	−	9.00525i	0.343415	−	0.513957i	0.962469	+	0.271392i	$0.0874838\pi$
$308$		0			0
$309$	−4.68215	+	23.5388i	−0.266358	+	1.33907i
$310$		0			0
$311$	6.91332	−	2.86359i	0.392018	−	0.162379i	−0.177963	−	0.984037i	$-0.556951\pi$
$311$	6.91332	−	2.86359i	0.392018	−	0.162379i	0.569981	+	0.821658i	$0.306951\pi$
$312$		0			0
$313$	−20.9463	−	8.67625i	−1.18396	−	0.490411i	−0.298174	−	0.954511i	$-0.596378\pi$
$313$	−20.9463	−	8.67625i	−1.18396	−	0.490411i	−0.885783	+	0.464101i	$0.846378\pi$
$314$		0			0
$315$	−16.3975	−	24.5406i	−0.923894	−	1.38271i
$316$		0			0
$317$	−12.9479	+	2.57551i	−0.727229	+	0.144655i	−0.544802	−	0.838565i	$-0.683395\pi$
$317$	−12.9479	+	2.57551i	−0.727229	+	0.144655i	−0.182427	+	0.983219i	$0.558395\pi$
$318$		0			0
$319$	6.61944			0.370617
$320$		0			0
$321$	16.7647			0.935712
$322$		0			0
$323$	23.6840	−	4.71104i	1.31781	−	0.262129i
$324$		0			0
$325$	−0.732323	−	1.09600i	−0.0406220	−	0.0607951i
$326$		0			0
$327$	−12.2606	−	5.07850i	−0.678012	−	0.280842i
$328$		0			0
$329$	−22.5003	+	9.31994i	−1.24048	+	0.513825i
$330$		0			0
$331$	−0.994900	+	5.00170i	−0.0546846	+	0.274918i	−0.998447	−	0.0557056i	$-0.982259\pi$
$331$	−0.994900	+	5.00170i	−0.0546846	+	0.274918i	0.943763	+	0.330624i	$0.107259\pi$
$332$		0			0
$333$	1.86674	−	2.79377i	0.102297	−	0.153098i
$334$		0			0
$335$	−7.14106	−	7.14106i	−0.390158	−	0.390158i
$336$		0			0
$337$	−9.51763	+	9.51763i	−0.518459	+	0.518459i	−0.917105	−	0.398646i	$-0.869480\pi$
$337$	−9.51763	+	9.51763i	−0.518459	+	0.518459i	0.398646	+	0.917105i	$0.369480\pi$
$338$		0			0
$339$	−41.7952	−	27.9267i	−2.27000	−	1.51677i
$340$		0			0
$341$	−12.3961	−	2.46574i	−0.671286	−	0.133527i
$342$		0			0
$343$	6.31088	+	15.2358i	0.340755	+	0.822656i
$344$		0			0
$345$	0.890336	−	2.14946i	0.0479341	−	0.115723i
$346$		0			0
$347$	−24.8873	+	16.6292i	−1.33602	+	0.892701i	−0.998812	−	0.0487284i	$-0.984483\pi$
$347$	−24.8873	+	16.6292i	−1.33602	+	0.892701i	−0.337210	+	0.941430i	$0.609483\pi$
$348$		0			0
$349$	2.77238	+	13.9377i	0.148402	+	0.746067i	0.981276	+	0.192605i	$0.0616936\pi$
$349$	2.77238	+	13.9377i	0.148402	+	0.746067i	−0.832874	+	0.553462i	$0.813306\pi$
$350$		0			0
$351$		−	5.66280i		−	0.302258i
$352$		0			0
$353$		−	22.9803i		−	1.22312i	−0.791199	−	0.611558i	$-0.790543\pi$
$353$		−	22.9803i		−	1.22312i	0.791199	−	0.611558i	$-0.209457\pi$
$354$		0			0
$355$	1.46066	+	7.34326i	0.0775240	+	0.389740i
$356$		0			0
$357$	34.7689	−	23.2318i	1.84016	−	1.22956i
$358$		0			0
$359$	−2.63107	+	6.35196i	−0.138862	+	0.335244i	−0.977978	−	0.208710i	$-0.933073\pi$
$359$	−2.63107	+	6.35196i	−0.138862	+	0.335244i	0.839115	+	0.543954i	$0.183073\pi$
$360$		0			0
$361$	2.47302	+	5.97039i	0.130159	+	0.314231i
$362$		0			0
$363$	28.0387	+	5.57725i	1.47165	+	0.292730i
$364$		0			0
$365$	−1.34958	−	0.901757i	−0.0706400	−	0.0472001i
$366$		0			0
$367$	2.41091	−	2.41091i	0.125848	−	0.125848i	−0.641377	−	0.767226i	$-0.721637\pi$
$367$	2.41091	−	2.41091i	0.125848	−	0.125848i	0.767226	+	0.641377i	$0.221637\pi$
$368$		0			0
$369$	28.1476	+	28.1476i	1.46530	+	1.46530i
$370$		0			0
$371$	−6.63456	+	9.92931i	−0.344449	+	0.515504i
$372$		0			0
$373$	2.78301	−	13.9911i	0.144099	−	0.724433i	−0.839400	−	0.543515i	$-0.817093\pi$
$373$	2.78301	−	13.9911i	0.144099	−	0.724433i	0.983498	−	0.180918i	$-0.0579068\pi$
$374$		0			0
$375$	33.6987	−	13.9585i	1.74019	−	0.720812i
$376$		0			0
$377$	−2.78370	−	1.15305i	−0.143368	−	0.0593849i
$378$		0			0
$379$	−14.2902	−	21.3867i	−0.734036	−	1.09856i	−0.991223	−	0.132201i	$-0.957796\pi$
$379$	−14.2902	−	21.3867i	−0.734036	−	1.09856i	0.257187	−	0.966362i	$-0.417204\pi$
$380$		0			0
$381$	65.4461	−	13.0180i	3.35290	−	0.666934i
$382$		0			0
$383$	−21.5847			−1.10293			−0.551463	−	0.834199i	$-0.685930\pi$
$383$	−21.5847			−1.10293			−0.551463	+	0.834199i	$0.685930\pi$
$384$		0			0
$385$	5.97401			0.304464
$386$		0			0
$387$	−23.7529	+	4.72474i	−1.20743	+	0.240172i
$388$		0			0
$389$	3.94394	+	5.90253i	0.199966	+	0.299270i	0.917877	−	0.396864i	$-0.129902\pi$
$389$	3.94394	+	5.90253i	0.199966	+	0.299270i	−0.717911	+	0.696135i	$0.754902\pi$
$390$		0			0
$391$	2.05662	+	0.851878i	0.104007	+	0.0430813i
$392$		0			0
$393$	20.2119	−	8.37206i	1.01956	−	0.422315i
$394$		0			0
$395$	0.0692105	−	0.347944i	0.00348236	−	0.0175070i
$396$		0			0
$397$	−7.40790	+	11.0867i	−0.371792	+	0.556426i	−0.969439	−	0.245334i	$-0.921102\pi$
$397$	−7.40790	+	11.0867i	−0.371792	+	0.556426i	0.597647	+	0.801759i	$0.296102\pi$
$398$		0			0
$399$	31.1778	+	31.1778i	1.56084	+	1.56084i
$400$		0			0
$401$	−8.50260	+	8.50260i	−0.424600	+	0.424600i	−0.886784	−	0.462184i	$-0.847066\pi$
$401$	−8.50260	+	8.50260i	−0.424600	+	0.424600i	0.462184	+	0.886784i	$0.347066\pi$
$402$		0			0
$403$	4.78347	+	3.19622i	0.238282	+	0.159215i
$404$		0			0
$405$	18.1061	+	3.60154i	0.899702	+	0.178962i
$406$		0			0
$407$	0.260262	+	0.628329i	0.0129007	+	0.0311451i
$408$		0			0
$409$	10.8420	−	26.1750i	0.536104	−	1.29427i	−0.391320	−	0.920255i	$-0.627981\pi$
$409$	10.8420	−	26.1750i	0.536104	−	1.29427i	0.927423	−	0.374014i	$-0.122019\pi$
$410$		0			0
$411$	27.9914	−	18.7032i	1.38071	−	0.922563i
$412$		0			0
$413$	−1.04590	−	5.25807i	−0.0514651	−	0.258733i
$414$		0			0
$415$			10.2204i			0.501699i
$416$		0			0
$417$		−	11.7236i		−	0.574106i
$418$		0			0
$419$	4.06419	+	20.4320i	0.198549	+	0.998171i	0.943581	+	0.331142i	$0.107434\pi$
$419$	4.06419	+	20.4320i	0.198549	+	0.998171i	−0.745032	+	0.667028i	$0.767566\pi$
$420$		0			0
$421$	−18.4939	+	12.3572i	−0.901337	+	0.602254i	−0.917553	−	0.397614i	$-0.869838\pi$
$421$	−18.4939	+	12.3572i	−0.901337	+	0.602254i	0.0162157	+	0.999869i	$0.494838\pi$
$422$		0			0
$423$	20.2322	−	48.8449i	0.983723	−	2.37492i
$424$		0			0
$425$	4.19876	+	10.1367i	0.203670	+	0.491703i
$426$		0			0
$427$	18.6125	+	3.70225i	0.900720	+	0.179164i
$428$		0			0
$429$	1.83540	+	1.22637i	0.0886137	+	0.0592098i
$430$		0			0
$431$	−9.16945	+	9.16945i	−0.441677	+	0.441677i	−0.892575	−	0.450898i	$-0.851104\pi$
$431$	−9.16945	+	9.16945i	−0.441677	+	0.441677i	0.450898	+	0.892575i	$0.351104\pi$
$432$		0			0
$433$	9.06306	+	9.06306i	0.435543	+	0.435543i	0.890509	−	0.454966i	$-0.150349\pi$
$433$	9.06306	+	9.06306i	0.435543	+	0.435543i	−0.454966	+	0.890509i	$0.650349\pi$
$434$		0			0
$435$	14.5627	−	21.7946i	0.698226	−	1.04497i
$436$		0			0
$437$	−0.457921	+	2.30212i	−0.0219053	+	0.110125i
$438$		0			0
$439$	−37.3964	+	15.4901i	−1.78483	+	0.739301i	−0.793395	+	0.608707i	$0.791688\pi$
$439$	−37.3964	+	15.4901i	−1.78483	+	0.739301i	−0.991436	+	0.130594i	$0.958312\pi$
$440$		0			0
$441$	7.28190	+	3.01626i	0.346757	+	0.143631i
$442$		0			0
$443$	0.953921	+	1.42764i	0.0453222	+	0.0678294i	0.853439	−	0.521193i	$-0.174513\pi$
$443$	0.953921	+	1.42764i	0.0453222	+	0.0678294i	−0.808117	+	0.589023i	$0.799513\pi$
$444$		0			0
$445$	6.27255	−	1.24769i	0.297347	−	0.0591460i
$446$		0			0
$447$	67.6275			3.19867
$448$		0			0
$449$	−24.6119			−1.16151			−0.580754	−	0.814079i	$-0.697242\pi$
$449$	−24.6119			−1.16151			−0.580754	+	0.814079i	$0.697242\pi$
$450$		0			0
$451$	−7.90236	+	1.57188i	−0.372108	+	0.0740168i
$452$		0			0
$453$	−13.1979	−	19.7521i	−0.620093	−	0.928034i
$454$		0			0
$455$	−2.51227	−	1.04062i	−0.117777	−	0.0487849i
$456$		0			0
$457$	0.962960	−	0.398871i	0.0450454	−	0.0186584i	−0.360047	−	0.932934i	$-0.617239\pi$
$457$	0.962960	−	0.398871i	0.0450454	−	0.0186584i	0.405092	+	0.914276i	$0.367239\pi$
$458$		0			0
$459$	−9.19571	+	46.2300i	−0.429219	+	2.15783i
$460$		0			0
$461$	−7.72794	+	11.5657i	−0.359926	+	0.538667i	−0.966602	−	0.256282i	$-0.917502\pi$
$461$	−7.72794	+	11.5657i	−0.359926	+	0.538667i	0.606676	+	0.794949i	$0.292502\pi$
$462$		0			0
$463$	−8.29596	−	8.29596i	−0.385546	−	0.385546i	0.487549	−	0.873095i	$-0.337891\pi$
$463$	−8.29596	−	8.29596i	−0.385546	−	0.385546i	−0.873095	+	0.487549i	$0.837891\pi$
$464$		0			0
$465$	−35.3897	+	35.3897i	−1.64116	+	1.64116i
$466$		0			0
$467$	0.240041	+	0.160391i	0.0111078	+	0.00742199i	0.561112	−	0.827740i	$-0.310374\pi$
$467$	0.240041	+	0.160391i	0.0111078	+	0.00742199i	−0.550004	+	0.835162i	$0.685374\pi$
$468$		0			0
$469$	17.3043	+	3.44205i	0.799040	+	0.158939i
$470$		0			0
$471$	−24.4445	−	59.0143i	−1.12634	−	2.71924i
$472$		0			0
$473$	1.87590	−	4.52882i	0.0862539	−	0.208235i
$474$		0			0
$475$	−9.61934	+	6.42743i	−0.441365	+	0.294911i
$476$		0			0
$477$	−5.05753	−	25.4259i	−0.231568	−	1.16417i
$478$		0			0
$479$			27.3994i			1.25191i	0.779860	+	0.625954i	$0.215290\pi$
$479$			27.3994i			1.25191i	−0.779860	+	0.625954i	$0.784710\pi$
$480$		0			0
$481$		−	0.309569i		−	0.0141151i
$482$		0			0
$483$	0.792964	+	3.98650i	0.0360811	+	0.181392i
$484$		0			0
$485$	−18.8443	+	12.5913i	−0.855675	+	0.571744i
$486$		0			0
$487$	11.7477	−	28.3614i	0.532338	−	1.28518i	−0.397633	−	0.917544i	$-0.630168\pi$
$487$	11.7477	−	28.3614i	0.532338	−	1.28518i	0.929971	−	0.367633i	$-0.119832\pi$
$488$		0			0
$489$	−23.8489	−	57.5764i	−1.07849	−	2.60369i
$490$		0			0
$491$	−1.43618	−	0.285675i	−0.0648141	−	0.0128923i	0.162577	−	0.986696i	$-0.448019\pi$
$491$	−1.43618	−	0.285675i	−0.0648141	−	0.0128923i	−0.227391	+	0.973804i	$0.573019\pi$
$492$		0			0
$493$	20.8531	+	13.9336i	0.939178	+	0.627539i
$494$		0			0
$495$	−9.17024	+	9.17024i	−0.412172	+	0.412172i
$496$		0			0
$497$	−9.24919	−	9.24919i	−0.414883	−	0.414883i
$498$		0			0
$499$	−8.33594	+	12.4756i	−0.373168	+	0.558485i	−0.969760	−	0.244059i	$-0.921521\pi$
$499$	−8.33594	+	12.4756i	−0.373168	+	0.558485i	0.596592	+	0.802544i	$0.296521\pi$
$500$		0			0
$501$	−8.63244	+	43.3982i	−0.385669	+	1.93889i
$502$		0			0
$503$	9.56425	−	3.96164i	0.426449	−	0.176641i	−0.159128	−	0.987258i	$-0.550868\pi$
$503$	9.56425	−	3.96164i	0.426449	−	0.176641i	0.585577	+	0.810617i	$0.300868\pi$
$504$		0			0
$505$	6.10871	+	2.53031i	0.271834	+	0.112597i
$506$		0			0
$507$	21.3963	+	32.0218i	0.950242	+	1.42214i
$508$		0			0
$509$	−1.27790	+	0.254190i	−0.0566419	+	0.0112668i	−0.223330	−	0.974743i	$-0.571693\pi$
$509$	−1.27790	+	0.254190i	−0.0566419	+	0.0112668i	0.166688	+	0.986010i	$0.446693\pi$
$510$		0			0
$511$	2.83566			0.125442
$512$		0			0
$513$	−49.7011			−2.19436
$514$		0			0
$515$	−12.7412	+	2.53437i	−0.561443	+	0.111678i
$516$		0			0
$517$	5.94524	+	8.89768i	0.261471	+	0.391320i
$518$		0			0
$519$	−52.2233	−	21.6316i	−2.29235	−	0.949522i
$520$		0			0
$521$	−30.4733	+	12.6225i	−1.33506	+	0.553001i	−0.932095	−	0.362214i	$-0.882021\pi$
$521$	−30.4733	+	12.6225i	−1.33506	+	0.553001i	−0.402967	+	0.915215i	$0.632021\pi$
$522$		0			0
$523$	−0.709853	+	3.56867i	−0.0310397	+	0.156047i	−0.993197	−	0.116448i	$-0.962849\pi$
$523$	−0.709853	+	3.56867i	−0.0310397	+	0.156047i	0.962157	+	0.272496i	$0.0878490\pi$
$524$		0			0
$525$	−11.1302	+	16.6574i	−0.485760	+	0.726991i
$526$		0			0
$527$	−33.8610	−	33.8610i	−1.47501	−	1.47501i
$528$		0			0
$529$	16.1105	−	16.1105i	0.700455	−	0.700455i
$530$		0			0
$531$	9.67673	+	6.46579i	0.419934	+	0.280591i
$532$		0			0
$533$	3.59702	+	0.715492i	0.155804	+	0.0309914i
$534$		0			0
$535$	3.47264	+	8.38370i	0.150135	+	0.362459i
$536$		0			0
$537$	12.5499	−	30.2982i	0.541570	−	1.30747i
$538$		0			0
$539$	−1.32649	+	0.886330i	−0.0571358	+	0.0381769i
$540$		0			0
$541$	0.728776	+	3.66380i	0.0313325	+	0.157519i	0.993284	−	0.115701i	$-0.0369113\pi$
$541$	0.728776	+	3.66380i	0.0313325	+	0.157519i	−0.961952	+	0.273220i	$0.911911\pi$
$542$		0			0
$543$		−	10.8770i		−	0.466776i
$544$		0			0
$545$		−	7.18326i		−	0.307697i
$546$		0			0
$547$	−2.21811	−	11.1512i	−0.0948394	−	0.476790i	−0.998791	−	0.0491555i	$-0.984347\pi$
$547$	−2.21811	−	11.1512i	−0.0948394	−	0.476790i	0.903952	−	0.427635i	$-0.140653\pi$
$548$		0			0
$549$	−34.2536	+	22.8875i	−1.46191	+	0.976815i
$550$		0			0
$551$	−10.1200	+	24.4319i	−0.431128	+	1.04083i
$552$		0			0
$553$	0.237181	+	0.572605i	0.0100859	+	0.0243496i
$554$		0			0
$555$	2.64135	+	0.525397i	0.112119	+	0.0223019i
$556$		0			0
$557$	−15.2399	−	10.1830i	−0.645734	−	0.431466i	0.189107	−	0.981956i	$-0.439441\pi$
$557$	−15.2399	−	10.1830i	−0.645734	−	0.431466i	−0.834841	+	0.550491i	$0.814441\pi$
$558$		0			0
$559$	−1.57776	+	1.57776i	−0.0667321	+	0.0667321i
$560$		0			0
$561$	−12.9923	−	12.9923i	−0.548536	−	0.548536i
$562$		0			0
$563$	−2.21898	+	3.32093i	−0.0935187	+	0.139961i	−0.875279	−	0.483619i	$-0.839322\pi$
$563$	−2.21898	+	3.32093i	−0.0935187	+	0.139961i	0.781760	+	0.623579i	$0.214322\pi$
$564$		0			0
$565$	5.30813	−	26.6858i	0.223315	−	1.12268i
$566$		0			0
$567$	−29.7969	+	12.3423i	−1.25135	+	0.518327i
$568$		0			0
$569$	27.7449	+	11.4923i	1.16313	+	0.481783i	0.878915	−	0.476978i	$-0.158268\pi$
$569$	27.7449	+	11.4923i	1.16313	+	0.481783i	0.284213	+	0.958761i	$0.408268\pi$
$570$		0			0
$571$	−17.3752	−	26.0038i	−0.727128	−	1.08822i	−0.992280	−	0.124017i	$-0.960422\pi$
$571$	−17.3752	−	26.0038i	−0.727128	−	1.08822i	0.265152	−	0.964207i	$-0.414578\pi$
$572$		0			0
$573$	2.15292	−	0.428243i	0.0899396	−	0.0178901i
$574$		0			0
$575$	−1.06649			−0.0444756
$576$		0			0
$577$	−4.61192			−0.191997			−0.0959984	−	0.995381i	$-0.530604\pi$
$577$	−4.61192			−0.191997			−0.0959984	+	0.995381i	$0.530604\pi$
$578$		0			0
$579$	−15.8244	+	3.14768i	−0.657642	+	0.130813i
$580$		0			0
$581$	−9.91996	−	14.8463i	−0.411549	−	0.615927i
$582$		0			0
$583$	4.84781	+	2.00803i	0.200776	+	0.0831640i
$584$		0			0
$585$	5.45377	−	2.25903i	0.225486	−	0.0933992i
$586$		0			0
$587$	4.06182	−	20.4202i	0.167649	−	0.842831i	−0.801810	−	0.597579i	$-0.796129\pi$
$587$	4.06182	−	20.4202i	0.167649	−	0.842831i	0.969459	−	0.245252i	$-0.0788706\pi$
$588$		0			0
$589$	28.0525	−	41.9835i	1.15588	−	1.72990i
$590$		0			0
$591$	32.0588	+	32.0588i	1.31872	+	1.31872i
$592$		0			0
$593$	−3.69463	+	3.69463i	−0.151720	+	0.151720i	−0.778886	−	0.627166i	$-0.784215\pi$
$593$	−3.69463	+	3.69463i	−0.151720	+	0.151720i	0.627166	+	0.778886i	$0.284215\pi$
$594$		0			0
$595$	18.8199	+	12.5750i	0.771539	+	0.515526i
$596$		0			0
$597$	1.43234	+	0.284911i	0.0586218	+	0.0116606i
$598$		0			0
$599$	4.44136	+	10.7224i	0.181469	+	0.438105i	0.988270	−	0.152719i	$-0.0488028\pi$
$599$	4.44136	+	10.7224i	0.181469	+	0.438105i	−0.806801	+	0.590824i	$0.798803\pi$
$600$		0			0
$601$	−4.16840	+	10.0634i	−0.170033	+	0.410495i	−0.985809	−	0.167873i	$-0.946310\pi$
$601$	−4.16840	+	10.0634i	−0.170033	+	0.410495i	0.815776	+	0.578368i	$0.196310\pi$
$602$		0			0
$603$	−31.8462	+	21.2789i	−1.29688	+	0.866546i
$604$		0			0
$605$	3.01888	+	15.1769i	0.122735	+	0.617030i
$606$		0			0
$607$		−	29.1457i		−	1.18299i	−0.806310	−	0.591493i	$-0.798539\pi$
$607$		−	29.1457i		−	1.18299i	0.806310	−	0.591493i	$-0.201461\pi$
$608$		0			0
$609$			45.7937i			1.85565i
$610$		0			0
$611$	−0.950281	−	4.77739i	−0.0384443	−	0.193272i
$612$		0			0
$613$	−5.29850	+	3.54035i	−0.214005	+	0.142993i	−0.657953	−	0.753059i	$-0.728577\pi$
$613$	−5.29850	+	3.54035i	−0.214005	+	0.142993i	0.443948	+	0.896052i	$0.353577\pi$
$614$		0			0
$615$	−12.2096	+	29.4767i	−0.492340	+	1.18862i
$616$		0			0
$617$	3.88763	+	9.38556i	0.156510	+	0.377849i	0.982612	−	0.185673i	$-0.0594464\pi$
$617$	3.88763	+	9.38556i	0.156510	+	0.377849i	−0.826102	+	0.563521i	$0.809446\pi$
$618$		0			0
$619$	3.09719	+	0.616070i	0.124487	+	0.0247620i	0.256940	−	0.966427i	$-0.417286\pi$
$619$	3.09719	+	0.616070i	0.124487	+	0.0247620i	−0.132454	+	0.991189i	$0.542286\pi$
$620$		0			0
$621$	−3.80951	−	2.54544i	−0.152871	−	0.102145i
$622$		0			0
$623$	−7.90057	+	7.90057i	−0.316530	+	0.316530i
$624$		0			0
$625$	5.85477	+	5.85477i	0.234191	+	0.234191i
$626$		0			0
$627$	10.7636	−	16.1089i	0.429856	−	0.643326i
$628$		0			0
$629$	−0.502703	+	2.52726i	−0.0200441	+	0.100768i
$630$		0			0
$631$	29.9605	−	12.4100i	1.19271	−	0.494036i	0.304073	−	0.952649i	$-0.401653\pi$
$631$	29.9605	−	12.4100i	1.19271	−	0.494036i	0.888636	+	0.458613i	$0.151653\pi$
$632$		0			0
$633$	41.2117	+	17.0705i	1.63802	+	0.678490i
$634$		0			0
$635$	20.0666	+	30.0318i	0.796319	+	1.19178i
$636$		0			0
$637$	0.712223	−	0.141670i	0.0282193	−	0.00561317i
$638$		0			0
$639$	28.3954			1.12331
$640$		0			0
$641$	27.6811			1.09334			0.546668	−	0.837349i	$-0.315896\pi$
$641$	27.6811			1.09334			0.546668	+	0.837349i	$0.315896\pi$
$642$		0			0
$643$	−42.4514	+	8.44410i	−1.67412	+	0.333003i	−0.938733	−	0.344646i	$-0.887999\pi$
$643$	−42.4514	+	8.44410i	−1.67412	+	0.333003i	−0.735386	+	0.677649i	$0.762999\pi$
$644$		0			0
$645$	−10.7842	−	16.1397i	−0.424629	−	0.635502i
$646$		0			0
$647$	35.3075	+	14.6248i	1.38808	+	0.574962i	0.946630	−	0.322324i	$-0.104464\pi$
$647$	35.3075	+	14.6248i	1.38808	+	0.574962i	0.441451	+	0.897285i	$0.354464\pi$
$648$		0			0
$649$	−2.17633	+	0.901466i	−0.0854285	+	0.0353856i
$650$		0			0
$651$	17.0581	−	85.7570i	0.668560	−	3.36108i
$652$		0			0
$653$	13.3150	−	19.9272i	0.521055	−	0.779813i	−0.473853	−	0.880604i	$-0.657137\pi$
$653$	13.3150	−	19.9272i	0.521055	−	0.779813i	0.994908	+	0.100791i	$0.0321372\pi$
$654$		0			0
$655$	8.37343	+	8.37343i	0.327177	+	0.327177i
$656$		0			0
$657$	−4.35281	+	4.35281i	−0.169819	+	0.169819i
$658$		0			0
$659$	−17.2984	−	11.5584i	−0.673852	−	0.450253i	0.170988	−	0.985273i	$-0.445304\pi$
$659$	−17.2984	−	11.5584i	−0.673852	−	0.450253i	−0.844839	+	0.535020i	$0.820304\pi$
$660$		0			0
$661$	14.9381	+	2.97137i	0.581025	+	0.115573i	0.476848	−	0.878986i	$-0.341779\pi$
$661$	14.9381	+	2.97137i	0.581025	+	0.115573i	0.104177	+	0.994559i	$0.466779\pi$
$662$		0			0
$663$	3.20057	+	7.72685i	0.124300	+	0.300086i
$664$		0			0
$665$	−9.13327	+	22.0497i	−0.354173	+	0.855049i
$666$		0			0
$667$	−2.02696	+	1.35437i	−0.0784842	+	0.0524415i
$668$		0			0
$669$	12.1832	+	61.2489i	0.471028	+	2.36802i
$670$		0			0
$671$		−	8.33848i		−	0.321903i
$672$		0			0
$673$			33.8371i			1.30432i	0.758080	+	0.652162i	$0.226138\pi$
$673$			33.8371i			1.30432i	−0.758080	+	0.652162i	$0.773862\pi$
$674$		0			0
$675$	−4.40558	−	22.1483i	−0.169571	−	0.852490i
$676$		0			0
$677$	28.0419	−	18.7370i	1.07774	−	0.720121i	0.115768	−	0.993276i	$-0.463067\pi$
$677$	28.0419	−	18.7370i	1.07774	−	0.720121i	0.961970	+	0.273155i	$0.0880672\pi$
$678$		0			0
$679$	15.1522	−	36.5807i	0.581489	−	1.40384i
$680$		0			0
$681$	−22.8501	−	55.1649i	−0.875616	−	2.11392i
$682$		0			0
$683$	−14.0115	−	2.78707i	−0.536137	−	0.106644i	−0.0804066	−	0.996762i	$-0.525622\pi$
$683$	−14.0115	−	2.78707i	−0.536137	−	0.106644i	−0.455730	+	0.890118i	$0.650622\pi$
$684$		0			0
$685$	15.1513	+	10.1238i	0.578901	+	0.386809i
$686$		0			0
$687$	−46.8998	+	46.8998i	−1.78934	+	1.78934i
$688$		0			0
$689$	−1.68889	−	1.68889i	−0.0643415	−	0.0643415i
$690$		0			0
$691$	−10.9236	+	16.3483i	−0.415552	+	0.621918i	−0.978909	−	0.204296i	$-0.934510\pi$
$691$	−10.9236	+	16.3483i	−0.415552	+	0.621918i	0.563357	+	0.826214i	$0.309510\pi$
$692$		0			0
$693$	4.42013	−	22.2215i	0.167907	−	0.844125i
$694$		0			0
$695$	5.86275	−	2.42843i	0.222387	−	0.0921156i
$696$		0			0
$697$	−28.2035	−	11.6823i	−1.06828	−	0.442497i
$698$		0			0
$699$	−6.60877	−	9.89072i	−0.249967	−	0.374101i
$700$		0			0
$701$	11.0341	−	2.19482i	0.416753	−	0.0828974i	0.0177402	−	0.999843i	$-0.494353\pi$
$701$	11.0341	−	2.19482i	0.416753	−	0.0828974i	0.399013	+	0.916945i	$0.369353\pi$
$702$		0			0
$703$	−2.71702			−0.102474
$704$		0			0
$705$	42.3751			1.59594
$706$		0			0
$707$	−11.3295	+	2.25358i	−0.426091	+	0.0847548i
$708$		0			0
$709$	−23.4418	−	35.0831i	−0.880374	−	1.31757i	−0.947476	−	0.319827i	$-0.896375\pi$
$709$	−23.4418	−	35.0831i	−0.880374	−	1.31757i	0.0671017	−	0.997746i	$-0.478625\pi$
$710$		0			0
$711$	−1.24304	−	0.514884i	−0.0466176	−	0.0193097i
$712$		0			0
$713$	4.30035	−	1.78127i	0.161050	−	0.0667089i
$714$		0			0
$715$	−0.233101	+	1.17188i	−0.00871749	+	0.0438258i
$716$		0			0
$717$	−11.6504	+	17.4360i	−0.435091	+	0.651160i
$718$		0			0
$719$	9.10621	+	9.10621i	0.339604	+	0.339604i	0.856218	−	0.516614i	$-0.172808\pi$
$719$	9.10621	+	9.10621i	0.339604	+	0.339604i	−0.516614	+	0.856218i	$0.672808\pi$
$720$		0			0
$721$	16.0481	−	16.0481i	0.597663	−	0.597663i
$722$		0			0
$723$	6.09576	+	4.07305i	0.226704	+	0.151479i
$724$		0			0
$725$	−11.7847	−	2.34411i	−0.437671	−	0.0870582i
$726$		0			0
$727$	−8.28934	−	20.0122i	−0.307435	−	0.742213i	−0.999787	−	0.0206529i	$-0.993426\pi$
$727$	−8.28934	−	20.0122i	−0.307435	−	0.742213i	0.692352	−	0.721560i	$-0.256574\pi$
$728$		0			0
$729$	−7.57994	+	18.2996i	−0.280739	+	0.677763i
$730$		0			0
$731$	15.4426	−	10.3184i	0.571165	−	0.381640i
$732$		0			0
$733$	−1.86746	−	9.38837i	−0.0689763	−	0.346767i	0.930850	−	0.365401i	$-0.119068\pi$
$733$	−1.86746	−	9.38837i	−0.0689763	−	0.346767i	−0.999826	+	0.0186340i	$0.994068\pi$
$734$		0			0
$735$			6.31738i			0.233020i
$736$		0			0
$737$		−	7.75244i		−	0.285565i
$738$		0			0
$739$	3.72209	+	18.7122i	0.136919	+	0.688340i	0.986875	+	0.161486i	$0.0516287\pi$
$739$	3.72209	+	18.7122i	0.136919	+	0.688340i	−0.849956	+	0.526854i	$0.823371\pi$
$740$		0			0
$741$	−7.33247	+	4.89940i	−0.269365	+	0.179984i
$742$		0			0
$743$	2.74886	−	6.63633i	0.100846	−	0.243463i	−0.865402	−	0.501079i	$-0.832937\pi$
$743$	2.74886	−	6.63633i	0.100846	−	0.243463i	0.966248	+	0.257615i	$0.0829368\pi$
$744$		0			0
$745$	14.0084	+	33.8193i	0.513228	+	1.23904i
$746$		0			0
$747$	38.0168	+	7.56200i	1.39096	+	0.276679i
$748$		0			0
$749$	−13.1817	−	8.80771i	−0.481648	−	0.321827i
$750$		0			0
$751$	1.88191	−	1.88191i	0.0686719	−	0.0686719i	−0.671937	−	0.740609i	$-0.734537\pi$
$751$	1.88191	−	1.88191i	0.0686719	−	0.0686719i	0.740609	+	0.671937i	$0.234537\pi$
$752$		0			0
$753$	1.47249	+	1.47249i	0.0536606	+	0.0536606i
$754$		0			0
$755$	7.14383	−	10.6915i	0.259991	−	0.389104i
$756$		0			0
$757$	7.70412	−	38.7312i	0.280011	−	1.40771i	−0.543023	−	0.839718i	$-0.682720\pi$
$757$	7.70412	−	38.7312i	0.280011	−	1.40771i	0.823034	−	0.567992i	$-0.192280\pi$
$758$		0			0
$759$	1.65002	−	0.683463i	0.0598921	−	0.0248081i
$760$		0			0
$761$	−7.53878	−	3.12266i	−0.273280	−	0.113196i	0.241835	−	0.970317i	$-0.422251\pi$
$761$	−7.53878	−	3.12266i	−0.273280	−	0.113196i	−0.515115	+	0.857121i	$0.672251\pi$
$762$		0			0
$763$	6.97211	+	10.4345i	0.252407	+	0.377754i
$764$		0			0
$765$	−48.1919	+	9.58596i	−1.74238	+	0.346581i
$766$		0			0
$767$	1.07225			0.0387167
$768$		0			0
$769$	3.77877			0.136266			0.0681330	−	0.997676i	$-0.478296\pi$
$769$	3.77877			0.136266			0.0681330	+	0.997676i	$0.478296\pi$
$770$		0			0
$771$	72.5677	−	14.4346i	2.61346	−	0.519850i
$772$		0			0
$773$	−2.84091	−	4.25173i	−0.102181	−	0.152924i	0.776856	−	0.629678i	$-0.216813\pi$
$773$	−2.84091	−	4.25173i	−0.102181	−	0.152924i	−0.879037	+	0.476754i	$0.841813\pi$
$774$		0			0
$775$	21.1957	+	8.77956i	0.761373	+	0.315371i
$776$		0			0
$777$	−4.34681	+	1.80051i	−0.155941	+	0.0645929i
$778$		0			0
$779$	6.27971	−	31.5702i	0.224994	−	1.13112i
$780$		0			0
$781$	−3.19312	+	4.77884i	−0.114259	+	0.171000i
$782$		0			0
$783$	−36.5002	−	36.5002i	−1.30441	−	1.30441i
$784$		0			0
$785$	24.4485	−	24.4485i	0.872605	−	0.872605i
$786$		0			0
$787$	25.7884	+	17.2312i	0.919257	+	0.614228i	0.922596	−	0.385767i	$-0.126063\pi$
$787$	25.7884	+	17.2312i	0.919257	+	0.614228i	−0.00333965	+	0.999994i	$0.501063\pi$
$788$		0			0
$789$	−30.9820	−	6.16271i	−1.10299	−	0.219398i
$790$		0			0
$791$	18.1907	+	43.9162i	0.646786	+	1.56148i
$792$		0			0
$793$	−1.45249	+	3.50662i	−0.0515793	+	0.124524i
$794$		0			0
$795$	17.2765	−	11.5438i	0.612736	−	0.409417i
$796$		0			0
$797$	0.860359	+	4.32532i	0.0304755	+	0.153211i	0.993027	−	0.117889i	$-0.0376127\pi$
$797$	0.860359	+	4.32532i	0.0304755	+	0.153211i	−0.962551	+	0.271100i	$0.912613\pi$
$798$		0			0
$799$			40.5448i			1.43437i
$800$		0			0
$801$		−	24.2551i		−	0.857013i
$802$		0			0
$803$	−0.243079	−	1.22204i	−0.00857807	−	0.0431249i
$804$		0			0
$805$	−1.82932	+	1.22231i	−0.0644751	+	0.0430809i
$806$		0			0
$807$	−36.2868	+	87.6041i	−1.27736	+	3.08381i
$808$		0			0
$809$	−4.29079	−	10.3589i	−0.150856	−	0.364199i	0.830327	−	0.557276i	$-0.188153\pi$
$809$	−4.29079	−	10.3589i	−0.150856	−	0.364199i	−0.981184	+	0.193077i	$0.938153\pi$
$810$		0			0
$811$	−3.92167	−	0.780069i	−0.137709	−	0.0273919i	0.125755	−	0.992061i	$-0.459865\pi$
$811$	−3.92167	−	0.780069i	−0.137709	−	0.0273919i	−0.263463	+	0.964669i	$0.584865\pi$
$812$		0			0
$813$	−42.3363	−	28.2882i	−1.48480	−	0.992110i
$814$		0			0
$815$	23.8528	−	23.8528i	0.835528	−	0.835528i
$816$		0			0
$817$	13.8476	+	13.8476i	0.484467	+	0.484467i
$818$		0			0
$819$	−5.72960	+	8.57495i	−0.200208	+	0.299633i
$820$		0			0
$821$	−7.39036	+	37.1538i	−0.257925	+	1.29668i	0.606970	+	0.794725i	$0.292385\pi$
$821$	−7.39036	+	37.1538i	−0.257925	+	1.29668i	−0.864895	+	0.501953i	$0.832615\pi$
$822$		0			0
$823$	−13.1154	+	5.43259i	−0.457175	+	0.189368i	−0.599373	−	0.800470i	$-0.704583\pi$
$823$	−13.1154	+	5.43259i	−0.457175	+	0.189368i	0.142197	+	0.989838i	$0.454583\pi$
$824$		0			0
$825$	8.13270	+	3.36867i	0.283144	+	0.117282i
$826$		0			0
$827$	−13.3036	−	19.9102i	−0.462611	−	0.692347i	0.524674	−	0.851303i	$-0.324187\pi$
$827$	−13.3036	−	19.9102i	−0.462611	−	0.692347i	−0.987286	+	0.158956i	$0.949187\pi$
$828$		0			0
$829$	12.2166	−	2.43003i	0.424299	−	0.0843983i	0.0216779	−	0.999765i	$-0.493099\pi$
$829$	12.2166	−	2.43003i	0.424299	−	0.0843983i	0.402621	+	0.915367i	$0.368099\pi$
$830$		0			0
$831$	−79.0731			−2.74302
$832$		0			0
$833$	−6.04450			−0.209430
$834$		0			0
$835$	−23.4908	+	4.67260i	−0.812932	+	0.161702i
$836$		0			0
$837$	54.7570	+	81.9497i	1.89268	+	2.83259i
$838$		0			0
$839$	26.8826	+	11.1351i	0.928089	+	0.384427i	0.794953	−	0.606671i	$-0.207495\pi$
$839$	26.8826	+	11.1351i	0.928089	+	0.384427i	0.133136	+	0.991098i	$0.457495\pi$
$840$		0			0
$841$	1.41778	−	0.587262i	0.0488888	−	0.0202504i
$842$		0			0
$843$	−14.5314	+	73.0540i	−0.500486	+	2.51612i
$844$		0			0
$845$	−11.5815	+	17.3329i	−0.398415	+	0.596270i
$846$		0			0
$847$	−19.1161	−	19.1161i	−0.656836	−	0.656836i
$848$		0			0
$849$	49.9329	−	49.9329i	1.71369	−	1.71369i
$850$		0			0
$851$	−0.208255	−	0.139152i	−0.00713889	−	0.00477006i
$852$		0			0
$853$	29.6923	+	5.90616i	1.01664	+	0.202223i	0.675165	−	0.737666i	$-0.264072\pi$
$853$	29.6923	+	5.90616i	1.01664	+	0.202223i	0.341479	+	0.939889i	$0.389072\pi$
$854$		0			0
$855$	−19.8270	−	47.8665i	−0.678068	−	1.63700i
$856$		0			0
$857$	−0.425175	+	1.02646i	−0.0145237	+	0.0350633i	−0.930975	−	0.365083i	$-0.881041\pi$
$857$	−0.425175	+	1.02646i	−0.0145237	+	0.0350633i	0.916451	+	0.400146i	$0.131041\pi$
$858$		0			0
$859$	40.2028	−	26.8627i	1.37170	−	0.916543i	0.371773	−	0.928324i	$-0.378750\pi$
$859$	40.2028	−	26.8627i	1.37170	−	0.916543i	0.999931	+	0.0117809i	$0.00375007\pi$
$860$		0			0
$861$	−10.8743	−	54.6690i	−0.370596	−	1.86311i
$862$		0			0
$863$		−	54.0259i		−	1.83906i	−0.393018	−	0.919531i	$-0.628569\pi$
$863$		−	54.0259i		−	1.83906i	0.393018	−	0.919531i	$-0.371431\pi$
$864$		0			0
$865$		−	30.5967i		−	1.04032i
$866$		0			0
$867$	−3.49977	−	17.5945i	−0.118858	−	0.597542i
$868$		0			0
$869$	0.226435	−	0.151299i	0.00768127	−	0.00513246i
$870$		0			0
$871$	−1.35040	+	3.26016i	−0.0457567	+	0.110466i
$872$		0			0
$873$	32.8932	+	79.4113i	1.11327	+	2.68766i
$874$		0			0
$875$	−33.8299	−	6.72919i	−1.14366	−	0.227488i
$876$		0			0
$877$	25.7807	+	17.2261i	0.870552	+	0.581684i	0.908635	−	0.417590i	$-0.137125\pi$
$877$	25.7807	+	17.2261i	0.870552	+	0.581684i	−0.0380835	+	0.999275i	$0.512125\pi$
$878$		0			0
$879$	60.8679	−	60.8679i	2.05302	−	2.05302i
$880$		0			0
$881$	24.7406	+	24.7406i	0.833533	+	0.833533i	0.987998	−	0.154465i	$-0.0493655\pi$
$881$	24.7406	+	24.7406i	0.833533	+	0.833533i	−0.154465	+	0.987998i	$0.549365\pi$
$882$		0			0
$883$	17.5606	−	26.2813i	0.590962	−	0.884436i	−0.408639	−	0.912696i	$-0.633997\pi$
$883$	17.5606	−	26.2813i	0.590962	−	0.884436i	0.999601	+	0.0282597i	$0.00899652\pi$
$884$		0			0
$885$	−1.81981	+	9.14880i	−0.0611722	+	0.307534i
$886$		0			0
$887$	15.7202	−	6.51152i	0.527833	−	0.218635i	−0.102821	−	0.994700i	$-0.532787\pi$
$887$	15.7202	−	6.51152i	0.527833	−	0.218635i	0.630654	+	0.776064i	$0.282787\pi$
$888$		0			0
$889$	−58.2981	−	24.1479i	−1.95525	−	0.809893i
$890$		0			0
$891$	7.87321	+	11.7831i	0.263763	+	0.394749i
$892$		0			0
$893$	−41.9301	+	8.34041i	−1.40314	+	0.279101i
$894$		0			0
$895$	17.7512			0.593357
$896$		0			0
$897$	−0.812945			−0.0271434
$898$		0			0
$899$	51.4340	−	10.2309i	1.71542	−	0.341218i
$900$		0			0
$901$	11.0452	+	16.5303i	0.367968	+	0.550704i
$902$		0			0
$903$	31.3306	+	12.9776i	1.04262	+	0.431867i
$904$		0			0
$905$	5.43938	−	2.25306i	0.180811	−	0.0748944i
$906$		0			0
$907$	−7.39593	+	37.1818i	−0.245578	+	1.23460i	0.639365	+	0.768903i	$0.279197\pi$
$907$	−7.39593	+	37.1818i	−0.245578	+	1.23460i	−0.884943	+	0.465699i	$0.845803\pi$
$908$		0			0
$909$	13.9318	−	20.8504i	0.462088	−	0.691564i
$910$		0			0
$911$	30.6254	+	30.6254i	1.01467	+	1.01467i	0.999891	+	0.0147749i	$0.00470317\pi$
$911$	30.6254	+	30.6254i	1.01467	+	1.01467i	0.0147749	+	0.999891i	$0.495297\pi$
$912$		0			0
$913$	−5.54770	+	5.54770i	−0.183602	+	0.183602i
$914$		0			0
$915$	−27.4545	−	18.3445i	−0.907618	−	0.606451i
$916$		0			0
$917$	−20.2907	−	4.03606i	−0.670057	−	0.133283i
$918$		0			0
$919$	−3.89489	−	9.40310i	−0.128481	−	0.310180i	0.846529	−	0.532343i	$-0.178688\pi$
$919$	−3.89489	−	9.40310i	−0.128481	−	0.310180i	−0.975010	+	0.222163i	$0.928688\pi$
$920$		0			0
$921$	12.5988	−	30.4163i	0.415146	−	1.00225i
$922$		0			0
$923$	2.17524	−	1.45345i	0.0715990	−	0.0478409i
$924$		0			0
$925$	−0.240840	−	1.21079i	−0.00791878	−	0.0398104i
$926$		0			0
$927$			49.2684i			1.61819i
$928$		0			0
$929$		−	0.932872i		−	0.0306066i	−0.999883	−	0.0153033i	$-0.995129\pi$
$929$		−	0.932872i		−	0.0306066i	0.999883	−	0.0153033i	$-0.00487137\pi$
$930$		0			0
$931$	−1.24341	−	6.25102i	−0.0407510	−	0.204869i
$932$		0			0
$933$	18.9129	−	12.6372i	0.619182	−	0.413724i
$934$		0			0
$935$	3.80598	−	9.18845i	0.124469	−	0.300494i
$936$		0			0
$937$	9.77432	+	23.5973i	0.319313	+	0.770890i	0.999291	+	0.0376573i	$0.0119895\pi$
$937$	9.77432	+	23.5973i	0.319313	+	0.770890i	−0.679978	+	0.733233i	$0.738010\pi$
$938$		0			0
$939$	−67.5940	−	13.4453i	−2.20585	−	0.438770i
$940$		0			0
$941$	14.0830	+	9.40994i	0.459092	+	0.306755i	0.763525	−	0.645778i	$-0.223467\pi$
$941$	14.0830	+	9.40994i	0.459092	+	0.306755i	−0.304433	+	0.952534i	$0.598467\pi$
$942$		0			0
$943$	2.09819	−	2.09819i	0.0683266	−	0.0683266i
$944$		0			0
$945$	−32.9413	−	32.9413i	−1.07158	−	1.07158i
$946$		0			0
$947$	−13.0115	+	19.4731i	−0.422818	+	0.632791i	−0.980327	−	0.197379i	$-0.936757\pi$
$947$	−13.0115	+	19.4731i	−0.422818	+	0.632791i	0.557510	+	0.830171i	$0.311757\pi$
$948$		0			0
$949$	−0.110645	+	0.556252i	−0.00359170	+	0.0180567i
$950$		0			0
$951$	−37.0752	+	15.3571i	−1.20225	+	0.497987i
$952$		0			0
$953$	44.5204	+	18.4410i	1.44216	+	0.597361i	0.960320	−	0.278899i	$-0.0899695\pi$
$953$	44.5204	+	18.4410i	1.44216	+	0.597361i	0.481838	+	0.876261i	$0.339970\pi$
$954$		0			0
$955$	0.660114	+	0.987930i	0.0213608	+	0.0319687i
$956$		0			0
$957$	19.7350	−	3.92553i	0.637941	−	0.126894i
$958$		0			0
$959$	−31.8352			−1.02801
$960$		0			0
$961$	−69.1305			−2.23002
$962$		0			0
$963$	33.7542	−	6.71413i	1.08771	−	0.216360i
$964$		0			0
$965$	−4.85198	−	7.26150i	−0.156191	−	0.233756i
$966$		0			0
$967$	−25.4255	−	10.5316i	−0.817629	−	0.338673i	−0.0656353	−	0.997844i	$-0.520907\pi$
$967$	−25.4255	−	10.5316i	−0.817629	−	0.338673i	−0.751993	+	0.659171i	$0.770907\pi$
$968$		0			0
$969$	67.8169	−	28.0907i	2.17859	−	0.902402i
$970$		0			0
$971$	−3.37327	+	16.9586i	−0.108254	+	0.544227i	0.888154	+	0.459545i	$0.151988\pi$
$971$	−3.37327	+	16.9586i	−0.108254	+	0.544227i	−0.996408	+	0.0846822i	$0.973012\pi$
$972$		0			0
$973$	−6.15926	+	9.21798i	−0.197457	+	0.295515i
$974$		0			0
$975$	−2.83328	−	2.83328i	−0.0907377	−	0.0907377i
$976$		0			0
$977$	−26.1853	+	26.1853i	−0.837743	+	0.837743i	−0.988562	−	0.150818i	$-0.951809\pi$
$977$	−26.1853	+	26.1853i	−0.837743	+	0.837743i	0.150818	+	0.988562i	$0.451809\pi$
$978$		0			0
$979$	4.08204	+	2.72753i	0.130463	+	0.0871723i
$980$		0			0
$981$	−26.7195	−	5.31485i	−0.853089	−	0.169690i
$982$		0			0
$983$	0.628339	+	1.51695i	0.0200409	+	0.0483831i	0.933583	−	0.358361i	$-0.116664\pi$
$983$	0.628339	+	1.51695i	0.0200409	+	0.0483831i	−0.913542	+	0.406744i	$0.866664\pi$
$984$		0			0
$985$	−9.39134	+	22.6727i	−0.299233	+	0.722412i
$986$		0			0
$987$	−61.5547	+	41.1295i	−1.95931	+	1.30917i
$988$		0			0
$989$	0.352195	+	1.77060i	0.0111991	+	0.0563019i
$990$		0			0
$991$		−	0.482249i		−	0.0153191i	−0.999971	−	0.00765957i	$-0.997562\pi$
$991$		−	0.482249i		−	0.0153191i	0.999971	−	0.00765957i	$-0.00243814\pi$
$992$		0			0
$993$			15.5019i			0.491938i
$994$		0			0
$995$	0.154218	+	0.775305i	0.00488903	+	0.0245788i
$996$		0			0
$997$	−5.71075	+	3.81580i	−0.180861	+	0.120848i	−0.642705	−	0.766114i	$-0.722188\pi$
$997$	−5.71075	+	3.81580i	−0.180861	+	0.120848i	0.461844	+	0.886961i	$0.347188\pi$
$998$		0			0
$999$	2.02955	−	4.89978i	0.0642123	−	0.155022i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	256.2.i.a.49.7		56
4.3	odd	2		64.2.i.a.53.6	yes	56
8.3	odd	2		512.2.i.b.353.7		56
8.5	even	2		512.2.i.a.353.1		56
12.11	even	2		576.2.bd.a.181.2		56
64.3	odd	16		512.2.i.b.161.7		56
64.29	even	16	inner	256.2.i.a.209.7		56
64.35	odd	16		64.2.i.a.29.6	✓	56
64.61	even	16		512.2.i.a.161.1		56
192.35	even	16		576.2.bd.a.541.2		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
64.2.i.a.29.6	✓	56	64.35	odd	16
64.2.i.a.53.6	yes	56	4.3	odd	2
256.2.i.a.49.7		56	1.1	even	1	trivial
256.2.i.a.209.7		56	64.29	even	16	inner
512.2.i.a.161.1		56	64.61	even	16
512.2.i.a.353.1		56	8.5	even	2
512.2.i.b.161.7		56	64.3	odd	16
512.2.i.b.353.7		56	8.3	odd	2
576.2.bd.a.181.2		56	12.11	even	2
576.2.bd.a.541.2		56	192.35	even	16

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:	\( N \)	\(=\)	\( 256 = 2^{8} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	256.i (of order \(16\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.98137 - 0.593031i) q^{3} +(0.914126 + 1.36809i) q^{5} +(-2.65574 - 1.10004i) q^{7} +(5.76522 - 2.38803i) q^{9} +O(q^{10})\)	\(q+(2.98137 - 0.593031i) q^{3} +(0.914126 + 1.36809i) q^{5} +(-2.65574 - 1.10004i) q^{7} +(5.76522 - 2.38803i) q^{9} +(-0.246413 + 1.23880i) q^{11} +(0.319413 - 0.478036i) q^{13} +(3.53666 + 3.53666i) q^{15} +(-3.38390 + 3.38390i) q^{17} +(-4.19561 - 2.80342i) q^{19} +(-8.57011 - 1.70470i) q^{21} +(-0.178010 - 0.429755i) q^{23} +(0.877384 - 2.11819i) q^{25} +(8.18962 - 5.47213i) q^{27} +(-1.02242 - 5.14005i) q^{29} +10.0065i q^{31} +3.83945i q^{33} +(-0.922728 - 4.63887i) q^{35} +(0.447703 - 0.299146i) q^{37} +(0.668798 - 1.61462i) q^{39} +(2.44115 + 5.89346i) q^{41} +(-3.80641 - 0.757142i) q^{43} +(8.53718 + 5.70436i) q^{45} +(5.99084 - 5.99084i) q^{47} +(0.893127 + 0.893127i) q^{49} +(-8.08188 + 12.0954i) q^{51} +(0.810472 - 4.07452i) q^{53} +(-1.92004 + 0.795307i) q^{55} +(-14.1712 - 5.86989i) q^{57} +(1.03615 + 1.55070i) q^{59} +(-6.47490 + 1.28794i) q^{61} -17.9379 q^{63} +0.945978 q^{65} +(-6.01983 + 1.19742i) q^{67} +(-0.785572 - 1.17569i) q^{69} +(4.20400 + 1.74136i) q^{71} +(-0.911379 + 0.377506i) q^{73} +(1.35965 - 6.83542i) q^{75} +(2.01715 - 3.01887i) q^{77} +(-0.152459 - 0.152459i) q^{79} +(7.93360 - 7.93360i) q^{81} +(5.16472 + 3.45096i) q^{83} +(-7.72277 - 1.53615i) q^{85} +(-6.09641 - 14.7180i) q^{87} +(1.48745 - 3.59102i) q^{89} +(-1.37414 + 0.918171i) q^{91} +(5.93418 + 29.8331i) q^{93} -8.30263i q^{95} +13.7742i q^{97} +(1.53767 + 7.73041i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 8 q^{3} - 8 q^{5} + 8 q^{7} - 8 q^{9}+O(q^{10}) \) 56 * q + 8 * q^3 - 8 * q^5 + 8 * q^7 - 8 * q^9	\( 56 q + 8 q^{3} - 8 q^{5} + 8 q^{7} - 8 q^{9} + 8 q^{11} - 8 q^{13} + 8 q^{15} - 8 q^{17} + 8 q^{19} - 8 q^{21} + 8 q^{23} - 8 q^{25} + 8 q^{27} - 8 q^{29} + 8 q^{35} - 8 q^{37} + 8 q^{39} - 8 q^{41} + 8 q^{43} - 8 q^{45} + 8 q^{47} - 8 q^{49} - 24 q^{51} - 8 q^{53} - 56 q^{55} - 8 q^{57} - 56 q^{59} - 8 q^{61} - 64 q^{63} - 16 q^{65} - 72 q^{67} - 8 q^{69} - 56 q^{71} - 8 q^{73} - 56 q^{75} - 8 q^{77} - 24 q^{79} - 8 q^{81} + 8 q^{83} - 8 q^{85} + 8 q^{87} - 8 q^{89} + 8 q^{91} + 16 q^{93} - 16 q^{99}+O(q^{100}) \) 56 * q + 8 * q^3 - 8 * q^5 + 8 * q^7 - 8 * q^9 + 8 * q^11 - 8 * q^13 + 8 * q^15 - 8 * q^17 + 8 * q^19 - 8 * q^21 + 8 * q^23 - 8 * q^25 + 8 * q^27 - 8 * q^29 + 8 * q^35 - 8 * q^37 + 8 * q^39 - 8 * q^41 + 8 * q^43 - 8 * q^45 + 8 * q^47 - 8 * q^49 - 24 * q^51 - 8 * q^53 - 56 * q^55 - 8 * q^57 - 56 * q^59 - 8 * q^61 - 64 * q^63 - 16 * q^65 - 72 * q^67 - 8 * q^69 - 56 * q^71 - 8 * q^73 - 56 * q^75 - 8 * q^77 - 24 * q^79 - 8 * q^81 + 8 * q^83 - 8 * q^85 + 8 * q^87 - 8 * q^89 + 8 * q^91 + 16 * q^93 - 16 * q^99

Introduction

L-functions

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Database

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