LMFDB - Embedded newform 864.2.w.b.323.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("864.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 864 = 2^{5} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	864.w (of order $8$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.89907473464$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$32$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			323.9
Character	$\chi$	$=$	864.323
Dual form			864.2.w.b.107.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.919792 + 1.07424i) q^{2} +(-0.307965 - 1.97615i) q^{4} +(-1.92195 + 0.796096i) q^{5} +(0.893559 + 0.893559i) q^{7} +(2.40611 + 1.48682i) q^{8} +O(q^{10})$	\(q+(-0.919792 + 1.07424i) q^{2} +(-0.307965 - 1.97615i) q^{4} +(-1.92195 + 0.796096i) q^{5} +(0.893559 + 0.893559i) q^{7} +(2.40611 + 1.48682i) q^{8} +(0.912596 - 2.79687i) q^{10} +(-2.30882 + 0.956343i) q^{11} +(1.00666 - 2.43029i) q^{13} +(-1.78178 + 0.138004i) q^{14} +(-3.81032 + 1.21717i) q^{16} -0.737842 q^{17} +(-0.939857 - 0.389301i) q^{19} +(2.16509 + 3.55288i) q^{20} +(1.09629 - 3.35985i) q^{22} +(-2.03966 - 2.03966i) q^{23} +(-0.475427 + 0.475427i) q^{25} +(1.68479 + 3.31675i) q^{26} +(1.49062 - 2.04099i) q^{28} +(-1.71442 + 4.13897i) q^{29} +1.70471i q^{31} +(2.19717 - 5.21272i) q^{32} +(0.678661 - 0.792616i) q^{34} +(-2.42873 - 1.00601i) q^{35} +(-2.62443 - 6.33592i) q^{37} +(1.28267 - 0.651551i) q^{38} +(-5.80807 - 0.942088i) q^{40} +(-0.488988 + 0.488988i) q^{41} +(-2.31249 - 5.58284i) q^{43} +(2.60091 + 4.26804i) q^{44} +(4.06714 - 0.315012i) q^{46} -2.29883i q^{47} -5.40310i q^{49} +(-0.0734267 - 0.948015i) q^{50} +(-5.11262 - 1.24086i) q^{52} +(-4.28534 - 10.3457i) q^{53} +(3.67608 - 3.67608i) q^{55} +(0.821443 + 3.47856i) q^{56} +(-2.86932 - 5.64868i) q^{58} +(-4.69375 - 11.3317i) q^{59} +(-9.31495 - 3.85838i) q^{61} +(-1.83126 - 1.56797i) q^{62} +(3.57875 + 7.15490i) q^{64} +5.47228i q^{65} +(-4.83801 + 11.6800i) q^{67} +(0.227229 + 1.45808i) q^{68} +(3.31462 - 1.68371i) q^{70} +(7.02532 - 7.02532i) q^{71} +(-2.71338 - 2.71338i) q^{73} +(9.22020 + 3.00848i) q^{74} +(-0.479874 + 1.97719i) q^{76} +(-2.91761 - 1.20851i) q^{77} +1.95835 q^{79} +(6.35424 - 5.37271i) q^{80} +(-0.0755210 - 0.975055i) q^{82} +(-3.06174 + 7.39169i) q^{83} +(1.41809 - 0.587393i) q^{85} +(8.12429 + 2.65089i) q^{86} +(-6.97717 - 1.13172i) q^{88} +(-5.22765 - 5.22765i) q^{89} +(3.07111 - 1.27210i) q^{91} +(-3.40252 + 4.65881i) q^{92} +(2.46949 + 2.11445i) q^{94} +2.11627 q^{95} -4.63177 q^{97} +(5.80421 + 4.96973i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q+O(q^{10}) $ 128 * q	$ 128 q + 8 q^{10} + 32 q^{16} - 32 q^{22} + 64 q^{40} + 64 q^{46} + 40 q^{52} + 64 q^{55} + 64 q^{58} + 32 q^{61} + 96 q^{64} - 64 q^{67} - 48 q^{70} - 32 q^{76} - 32 q^{79} + 40 q^{82} + 40 q^{88} - 48 q^{91} + 72 q^{94}+O(q^{100}) $ 128 * q + 8 * q^10 + 32 * q^16 - 32 * q^22 + 64 * q^40 + 64 * q^46 + 40 * q^52 + 64 * q^55 + 64 * q^58 + 32 * q^61 + 96 * q^64 - 64 * q^67 - 48 * q^70 - 32 * q^76 - 32 * q^79 + 40 * q^82 + 40 * q^88 - 48 * q^91 + 72 * q^94

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−0.919792	+	1.07424i	−0.650391	+	0.759599i
$2$	−0.919792	+	1.07424i	−0.650391	+	0.759599i
$3$		0			0
$3$		0			0
$4$	−0.307965	−	1.97615i	−0.153982	−	0.988074i
$5$	−1.92195	+	0.796096i	−0.859520	+	0.356025i	−0.768520	−	0.639826i	$-0.779006\pi$
$5$	−1.92195	+	0.796096i	−0.859520	+	0.356025i	−0.0910004	+	0.995851i	$0.529006\pi$
$6$		0			0
$7$	0.893559	+	0.893559i	0.337734	+	0.337734i	0.855514	−	0.517780i	$-0.173241\pi$
$7$	0.893559	+	0.893559i	0.337734	+	0.337734i	−0.517780	+	0.855514i	$0.673241\pi$
$8$	2.40611	+	1.48682i	0.850689	+	0.525670i
$9$		0			0
$10$	0.912596	−	2.79687i	0.288588	−	0.884447i
$11$	−2.30882	+	0.956343i	−0.696134	+	0.288348i	−0.702553	−	0.711631i	$-0.747957\pi$
$11$	−2.30882	+	0.956343i	−0.696134	+	0.288348i	0.00641921	+	0.999979i	$0.497957\pi$
$12$		0			0
$13$	1.00666	−	2.43029i	0.279197	−	0.674040i	−0.720617	−	0.693333i	$-0.756141\pi$
$13$	1.00666	−	2.43029i	0.279197	−	0.674040i	0.999814	+	0.0192927i	$0.00614145\pi$
$14$	−1.78178	+	0.138004i	−0.476201	+	0.0368832i
$15$		0			0
$16$	−3.81032	+	1.21717i	−0.952579	+	0.304292i
$17$	−0.737842			−0.178953			−0.0894765	−	0.995989i	$-0.528519\pi$
$17$	−0.737842			−0.178953			−0.0894765	+	0.995989i	$0.528519\pi$
$18$		0			0
$19$	−0.939857	−	0.389301i	−0.215618	−	0.0893119i	0.272260	−	0.962224i	$-0.412229\pi$
$19$	−0.939857	−	0.389301i	−0.215618	−	0.0893119i	−0.487878	+	0.872912i	$0.662229\pi$
$20$	2.16509	+	3.55288i	0.484130	+	0.794448i
$21$		0			0
$22$	1.09629	−	3.35985i	0.233730	−	0.716322i
$23$	−2.03966	−	2.03966i	−0.425298	−	0.425298i	0.461725	−	0.887023i	$-0.347231\pi$
$23$	−2.03966	−	2.03966i	−0.425298	−	0.425298i	−0.887023	+	0.461725i	$0.847231\pi$
$24$		0			0
$25$	−0.475427	+	0.475427i	−0.0950854	+	0.0950854i
$26$	1.68479	+	3.31675i	0.330414	+	0.650468i
$27$		0			0
$28$	1.49062	−	2.04099i	0.281701	−	0.385711i
$29$	−1.71442	+	4.13897i	−0.318359	+	0.768587i	0.680982	+	0.732300i	$0.261553\pi$
$29$	−1.71442	+	4.13897i	−0.318359	+	0.768587i	−0.999341	+	0.0362870i	$0.988447\pi$
$30$		0			0
$31$			1.70471i			0.306174i	0.988213	+	0.153087i	$0.0489215\pi$
$31$			1.70471i			0.306174i	−0.988213	+	0.153087i	$0.951079\pi$
$32$	2.19717	−	5.21272i	0.388409	−	0.921487i
$33$		0			0
$34$	0.678661	−	0.792616i	0.116389	−	0.135933i
$35$	−2.42873	−	1.00601i	−0.410530	−	0.170047i
$36$		0			0
$37$	−2.62443	−	6.33592i	−0.431453	−	1.04162i	−0.978819	−	0.204726i	$-0.934370\pi$
$37$	−2.62443	−	6.33592i	−0.431453	−	1.04162i	0.547366	−	0.836893i	$-0.315630\pi$
$38$	1.28267	−	0.651551i	0.208077	−	0.105696i
$39$		0			0
$40$	−5.80807	−	0.942088i	−0.918336	−	0.148957i
$41$	−0.488988	+	0.488988i	−0.0763670	+	0.0763670i	−0.744259	−	0.667892i	$-0.767197\pi$
$41$	−0.488988	+	0.488988i	−0.0763670	+	0.0763670i	0.667892	+	0.744259i	$0.267197\pi$
$42$		0			0
$43$	−2.31249	−	5.58284i	−0.352651	−	0.851375i	−0.996291	−	0.0860466i	$-0.972577\pi$
$43$	−2.31249	−	5.58284i	−0.352651	−	0.851375i	0.643640	−	0.765328i	$-0.277423\pi$
$44$	2.60091	+	4.26804i	0.392102	+	0.643431i
$45$		0			0
$46$	4.06714	−	0.315012i	0.599667	−	0.0464460i
$47$		−	2.29883i		−	0.335319i	−0.985845	−	0.167660i	$-0.946379\pi$
$47$		−	2.29883i		−	0.335319i	0.985845	−	0.167660i	$-0.0536210\pi$
$48$		0			0
$49$		−	5.40310i		−	0.771872i
$50$	−0.0734267	−	0.948015i	−0.0103841	−	0.134070i
$51$		0			0
$52$	−5.11262	−	1.24086i	−0.708993	−	0.172077i
$53$	−4.28534	−	10.3457i	−0.588637	−	1.42109i	−0.884806	−	0.465959i	$-0.845709\pi$
$53$	−4.28534	−	10.3457i	−0.588637	−	1.42109i	0.296170	−	0.955135i	$-0.404291\pi$
$54$		0			0
$55$	3.67608	−	3.67608i	0.495682	−	0.495682i
$56$	0.821443	+	3.47856i	0.109770	+	0.464842i
$57$		0			0
$58$	−2.86932	−	5.64868i	−0.376760	−	0.741708i
$59$	−4.69375	−	11.3317i	−0.611074	−	1.47526i	−0.861823	−	0.507210i	$-0.830677\pi$
$59$	−4.69375	−	11.3317i	−0.611074	−	1.47526i	0.250749	−	0.968052i	$-0.419323\pi$
$60$		0			0
$61$	−9.31495	−	3.85838i	−1.19266	−	0.494015i	−0.304038	−	0.952660i	$-0.598335\pi$
$61$	−9.31495	−	3.85838i	−1.19266	−	0.494015i	−0.888620	+	0.458645i	$0.848335\pi$
$62$	−1.83126	−	1.56797i	−0.232570	−	0.199133i
$63$		0			0
$64$	3.57875	+	7.15490i	0.447343	+	0.894362i
$65$			5.47228i			0.678752i
$66$		0			0
$67$	−4.83801	+	11.6800i	−0.591057	+	1.42694i	0.291425	+	0.956594i	$0.405871\pi$
$67$	−4.83801	+	11.6800i	−0.591057	+	1.42694i	−0.882483	+	0.470345i	$0.844129\pi$
$68$	0.227229	+	1.45808i	0.0275556	+	0.176819i
$69$		0			0
$70$	3.31462	−	1.68371i	0.396173	−	0.201241i
$71$	7.02532	−	7.02532i	0.833752	−	0.833752i	−0.154276	−	0.988028i	$-0.549305\pi$
$71$	7.02532	−	7.02532i	0.833752	−	0.833752i	0.988028	+	0.154276i	$0.0493045\pi$
$72$		0			0
$73$	−2.71338	−	2.71338i	−0.317577	−	0.317577i	0.530259	−	0.847836i	$-0.322095\pi$
$73$	−2.71338	−	2.71338i	−0.317577	−	0.317577i	−0.847836	+	0.530259i	$0.822095\pi$
$74$	9.22020	+	3.00848i	1.07183	+	0.349729i
$75$		0			0
$76$	−0.479874	+	1.97719i	−0.0550453	+	0.226799i
$77$	−2.91761	−	1.20851i	−0.332493	−	0.137723i
$78$		0			0
$79$	1.95835			0.220331			0.110166	−	0.993913i	$-0.464862\pi$
$79$	1.95835			0.220331			0.110166	+	0.993913i	$0.464862\pi$
$80$	6.35424	−	5.37271i	0.710425	−	0.600687i
$81$		0			0
$82$	−0.0755210	−	0.975055i	−0.00833990	−	0.107677i
$83$	−3.06174	+	7.39169i	−0.336070	+	0.811344i	0.662016	+	0.749490i	$0.269701\pi$
$83$	−3.06174	+	7.39169i	−0.336070	+	0.811344i	−0.998085	+	0.0618537i	$0.980299\pi$
$84$		0			0
$85$	1.41809	−	0.587393i	0.153814	−	0.0637117i
$86$	8.12429	+	2.65089i	0.876065	+	0.285853i
$87$		0			0
$88$	−6.97717	−	1.13172i	−0.743769	−	0.120642i
$89$	−5.22765	−	5.22765i	−0.554130	−	0.554130i	0.373500	−	0.927630i	$-0.378157\pi$
$89$	−5.22765	−	5.22765i	−0.554130	−	0.554130i	−0.927630	+	0.373500i	$0.878157\pi$
$90$		0			0
$91$	3.07111	−	1.27210i	0.321940	−	0.133352i
$92$	−3.40252	+	4.65881i	−0.354738	+	0.485715i
$93$		0			0
$94$	2.46949	+	2.11445i	0.254708	+	0.218089i
$95$	2.11627			0.217125
$96$		0			0
$97$	−4.63177			−0.470285			−0.235142	−	0.971961i	$-0.575556\pi$
$97$	−4.63177			−0.470285			−0.235142	+	0.971961i	$0.575556\pi$
$98$	5.80421	+	4.96973i	0.586313	+	0.502019i
$99$		0			0
$100$	1.08593	+	0.793099i	0.108593	+	0.0793099i
$101$	−0.241528	+	0.100044i	−0.0240330	+	0.00995479i	−0.394668	−	0.918824i	$-0.629140\pi$
$101$	−0.241528	+	0.100044i	−0.0240330	+	0.00995479i	0.370635	+	0.928779i	$0.379140\pi$
$102$		0			0
$103$	11.7515	+	11.7515i	1.15791	+	1.15791i	0.984924	+	0.172987i	$0.0553418\pi$
$103$	11.7515	+	11.7515i	1.15791	+	1.15791i	0.172987	+	0.984924i	$0.444658\pi$
$104$	6.03553	−	4.35083i	0.591832	−	0.426634i
$105$		0			0
$106$	15.0554	+	4.91245i	1.46231	+	0.477139i
$107$	−14.2373	+	5.89730i	−1.37637	+	0.570113i	−0.943510	−	0.331345i	$-0.892497\pi$
$107$	−14.2373	+	5.89730i	−1.37637	+	0.570113i	−0.432865	+	0.901459i	$0.642497\pi$
$108$		0			0
$109$	6.92230	−	16.7119i	0.663036	−	1.60071i	−0.129984	−	0.991516i	$-0.541493\pi$
$109$	6.92230	−	16.7119i	0.663036	−	1.60071i	0.793020	−	0.609195i	$-0.208507\pi$
$110$	0.567746	+	7.33020i	0.0541325	+	0.698907i
$111$		0			0
$112$	−4.49235	−	2.31713i	−0.424487	−	0.218948i
$113$	9.94948			0.935968			0.467984	−	0.883737i	$-0.344980\pi$
$113$	9.94948			0.935968			0.467984	+	0.883737i	$0.344980\pi$
$114$		0			0
$115$	5.54388	+	2.29635i	0.516969	+	0.214136i
$116$	8.70719	+	2.11328i	0.808442	+	0.196213i
$117$		0			0
$118$	16.4902	+	5.38062i	1.51805	+	0.495326i
$119$	−0.659306	−	0.659306i	−0.0604384	−	0.0604384i
$120$		0			0
$121$	−3.36214	+	3.36214i	−0.305649	+	0.305649i
$122$	12.7126	−	6.45755i	1.15095	−	0.584639i
$123$		0			0
$124$	3.36875	−	0.524989i	0.302523	−	0.0471454i
$125$	4.51574	−	10.9020i	0.403900	−	0.975101i
$126$		0			0
$127$			4.46970i			0.396622i	0.980139	+	0.198311i	$0.0635456\pi$
$127$			4.46970i			0.396622i	−0.980139	+	0.198311i	$0.936454\pi$
$128$	−10.9778	−	2.73660i	−0.970305	−	0.241884i
$129$		0			0
$130$	−5.87852	−	5.03336i	−0.515580	−	0.441455i
$131$	1.60935	+	0.666616i	0.140610	+	0.0582425i	0.451879	−	0.892079i	$-0.350754\pi$
$131$	1.60935	+	0.666616i	0.140610	+	0.0582425i	−0.311269	+	0.950322i	$0.600754\pi$
$132$		0			0
$133$	−0.491954	−	1.18768i	−0.0426578	−	0.102985i
$134$	−8.09710	−	15.9403i	−0.699483	−	1.37704i
$135$		0			0
$136$	−1.77533	−	1.09704i	−0.152233	−	0.0940701i
$137$	−9.62190	+	9.62190i	−0.822054	+	0.822054i	−0.986402	−	0.164348i	$-0.947448\pi$
$137$	−9.62190	+	9.62190i	−0.822054	+	0.822054i	0.164348	+	0.986402i	$0.447448\pi$
$138$		0			0
$139$	4.54249	+	10.9665i	0.385289	+	0.930169i	0.990924	+	0.134426i	$0.0429192\pi$
$139$	4.54249	+	10.9665i	0.385289	+	0.930169i	−0.605635	+	0.795743i	$0.707081\pi$
$140$	−1.24007	+	5.10935i	−0.104805	+	0.431819i
$141$		0			0
$142$	1.08501	+	14.0087i	0.0910524	+	1.17558i
$143$			6.57379i			0.549728i
$144$		0			0
$145$		−	9.31971i		−	0.773960i
$146$	5.41055	−	0.419064i	0.447780	−	0.0346820i
$147$		0			0
$148$	−11.7125	+	7.13749i	−0.962760	+	0.586698i
$149$	−9.26518	−	22.3681i	−0.759033	−	1.83247i	−0.498125	−	0.867105i	$-0.665978\pi$
$149$	−9.26518	−	22.3681i	−0.759033	−	1.83247i	−0.260908	−	0.965364i	$-0.584022\pi$
$150$		0			0
$151$	−6.27877	+	6.27877i	−0.510959	+	0.510959i	−0.914820	−	0.403861i	$-0.867668\pi$
$151$	−6.27877	+	6.27877i	−0.510959	+	0.510959i	0.403861	+	0.914820i	$0.367668\pi$
$152$	−1.68258	−	2.33410i	−0.136475	−	0.189320i
$153$		0			0
$154$	3.98183	−	2.02262i	0.320865	−	0.162987i
$155$	−1.35711	−	3.27635i	−0.109006	−	0.263163i
$156$		0			0
$157$	13.5860	+	5.62752i	1.08428	+	0.449125i	0.852010	−	0.523526i	$-0.175384\pi$
$157$	13.5860	+	5.62752i	1.08428	+	0.449125i	0.232273	+	0.972651i	$0.425384\pi$
$158$	−1.80127	+	2.10373i	−0.143302	+	0.167364i
$159$		0			0
$160$	−0.0730241	+	11.7677i	−0.00577306	+	0.930320i
$161$		−	3.64511i		−	0.287275i
$162$		0			0
$163$	−7.83728	+	18.9209i	−0.613864	+	1.48200i	0.244860	+	0.969558i	$0.421258\pi$
$163$	−7.83728	+	18.9209i	−0.613864	+	1.48200i	−0.858724	+	0.512439i	$0.828742\pi$
$164$	1.11690	+	0.815720i	0.0872154	+	0.0636971i
$165$		0			0
$166$	−5.12426	−	10.0879i	−0.397719	−	0.782969i
$167$	4.23455	−	4.23455i	0.327679	−	0.327679i	−0.524024	−	0.851703i	$-0.675570\pi$
$167$	4.23455	−	4.23455i	0.327679	−	0.327679i	0.851703	+	0.524024i	$0.175570\pi$
$168$		0			0
$169$	4.29945	+	4.29945i	0.330727	+	0.330727i
$170$	−0.673352	+	2.06365i	−0.0516437	+	0.158274i
$171$		0			0
$172$	−10.3203	+	6.28913i	−0.786919	+	0.479542i
$173$	−10.1993	−	4.22468i	−0.775438	−	0.321197i	−0.0403649	−	0.999185i	$-0.512852\pi$
$173$	−10.1993	−	4.22468i	−0.775438	−	0.321197i	−0.735073	+	0.677988i	$0.762852\pi$
$174$		0			0
$175$	−0.849645			−0.0642271
$176$	7.63328	−	6.45418i	0.575380	−	0.486502i
$177$		0			0
$178$	10.4241	−	0.807377i	0.781318	−	0.0605154i
$179$	−4.98031	+	12.0235i	−0.372245	+	0.898680i	0.621124	+	0.783713i	$0.286676\pi$
$179$	−4.98031	+	12.0235i	−0.372245	+	0.898680i	−0.993369	+	0.114968i	$0.963324\pi$
$180$		0			0
$181$	−19.3135	+	7.99990i	−1.43556	+	0.594628i	−0.958717	−	0.284361i	$-0.908219\pi$
$181$	−19.3135	+	7.99990i	−1.43556	+	0.594628i	−0.476842	+	0.878989i	$0.658219\pi$
$182$	−1.45825	+	4.46917i	−0.108093	+	0.331277i
$183$		0			0
$184$	−1.87505	−	7.94025i	−0.138230	−	0.585363i
$185$	10.0880	+	10.0880i	0.741685	+	0.741685i
$186$		0			0
$187$	1.70354	−	0.705630i	0.124575	−	0.0516008i
$188$	−4.54283	+	0.707960i	−0.331320	+	0.0516333i
$189$		0			0
$190$	−1.94653	+	2.27338i	−0.141216	+	0.164928i
$191$	2.75815			0.199573			0.0997865	−	0.995009i	$-0.468184\pi$
$191$	2.75815			0.199573			0.0997865	+	0.995009i	$0.468184\pi$
$192$		0			0
$193$	−7.25597			−0.522296			−0.261148	−	0.965299i	$-0.584101\pi$
$193$	−7.25597			−0.522296			−0.261148	+	0.965299i	$0.584101\pi$
$194$	4.26026	−	4.97561i	0.305869	−	0.357228i
$195$		0			0
$196$	−10.6773	+	1.66397i	−0.762666	+	0.118855i
$197$	8.75653	−	3.62707i	0.623877	−	0.258418i	−0.0482721	−	0.998834i	$-0.515371\pi$
$197$	8.75653	−	3.62707i	0.623877	−	0.258418i	0.672149	+	0.740416i	$0.265371\pi$
$198$		0			0
$199$	0.366033	+	0.366033i	0.0259474	+	0.0259474i	0.719961	−	0.694014i	$-0.244159\pi$
$199$	0.366033	+	0.366033i	0.0259474	+	0.0259474i	−0.694014	+	0.719961i	$0.744159\pi$
$200$	−1.85080	+	0.437057i	−0.130872	+	0.0309046i
$201$		0			0
$202$	0.114685	−	0.351478i	0.00806919	−	0.0247299i
$203$	−5.23034	+	2.16648i	−0.367098	+	0.152057i
$204$		0			0
$205$	0.550526	−	1.32909i	0.0384504	−	0.0928276i
$206$	−23.4328	+	1.81495i	−1.63264	+	0.126453i
$207$		0			0
$208$	−0.877618	+	10.4854i	−0.0608518	+	0.727034i
$209$	2.54226			0.175852
$210$		0			0
$211$	19.3139	+	8.00007i	1.32962	+	0.550748i	0.930548	−	0.366171i	$-0.119331\pi$
$211$	19.3139	+	8.00007i	1.32962	+	0.550748i	0.399075	+	0.916918i	$0.369331\pi$
$212$	−19.1249	+	11.6546i	−1.31351	+	0.800440i
$213$		0			0
$214$	6.76030	−	20.7185i	0.462125	−	1.41629i
$215$	8.88895	+	8.88895i	0.606221	+	0.606221i
$216$		0			0
$217$	−1.52326	+	1.52326i	−0.103405	+	0.103405i
$218$	11.5855	+	22.8077i	0.784666	+	1.54473i
$219$		0			0
$220$	−8.39657	−	6.13237i	−0.566097	−	0.413444i
$221$	−0.742755	+	1.79317i	−0.0499631	+	0.120622i
$222$		0			0
$223$			11.6831i			0.782360i	0.920314	+	0.391180i	$0.127933\pi$
$223$			11.6831i			0.782360i	−0.920314	+	0.391180i	$0.872067\pi$
$224$	6.62118	−	2.69457i	0.442396	−	0.180038i
$225$		0			0
$226$	−9.15145	+	10.6881i	−0.608746	+	0.710961i
$227$	−7.29242	−	3.02062i	−0.484015	−	0.200486i	0.127313	−	0.991863i	$-0.459365\pi$
$227$	−7.29242	−	3.02062i	−0.484015	−	0.200486i	−0.611329	+	0.791377i	$0.709365\pi$
$228$		0			0
$229$	3.16767	+	7.64743i	0.209326	+	0.505357i	0.993317	−	0.115414i	$-0.0368196\pi$
$229$	3.16767	+	7.64743i	0.209326	+	0.505357i	−0.783992	+	0.620771i	$0.786820\pi$
$230$	−7.56604	+	3.84327i	−0.498890	+	0.253418i
$231$		0			0
$232$	−10.2790	+	7.40979i	−0.674847	+	0.486477i
$233$	−5.00534	+	5.00534i	−0.327911	+	0.327911i	−0.851792	−	0.523881i	$-0.824484\pi$
$233$	−5.00534	+	5.00534i	−0.327911	+	0.327911i	0.523881	+	0.851792i	$0.324484\pi$
$234$		0			0
$235$	1.83009	+	4.41823i	0.119382	+	0.288214i
$236$	−20.9476	+	12.7653i	−1.36357	+	0.830950i
$237$		0			0
$238$	1.31467	−	0.101825i	0.0852176	−	0.00660037i
$239$		−	0.263528i		−	0.0170462i	−0.999964	−	0.00852309i	$-0.997287\pi$
$239$		−	0.263528i		−	0.0170462i	0.999964	−	0.00852309i	$-0.00271302\pi$
$240$		0			0
$241$		−	25.1521i		−	1.62019i	−0.586301	−	0.810093i	$-0.699417\pi$
$241$		−	25.1521i		−	1.62019i	0.586301	−	0.810093i	$-0.300583\pi$
$242$	−0.519261	−	6.70420i	−0.0333793	−	0.430962i
$243$		0			0
$244$	−4.75605	+	19.5960i	−0.304475	+	1.25450i
$245$	4.30139	+	10.3845i	0.274806	+	0.663440i
$246$		0			0
$247$	−1.89223	+	1.89223i	−0.120400	+	0.120400i
$248$	−2.53459	+	4.10171i	−0.160946	+	0.260459i
$249$		0			0
$250$	7.55773	+	14.8785i	0.477993	+	0.940999i
$251$	11.2132	+	27.0711i	0.707772	+	1.70871i	0.705495	+	0.708715i	$0.250725\pi$
$251$	11.2132	+	27.0711i	0.707772	+	1.70871i	0.00227634	+	0.999997i	$0.499275\pi$
$252$		0			0
$253$	6.65981	+	2.75858i	0.418699	+	0.173431i
$254$	−4.80151	−	4.11120i	−0.301274	−	0.257959i
$255$		0			0
$256$	13.0370	−	9.27558i	0.814813	−	0.579724i
$257$			20.3777i			1.27113i	0.772049	+	0.635563i	$0.219232\pi$
$257$			20.3777i			1.27113i	−0.772049	+	0.635563i	$0.780768\pi$
$258$		0			0
$259$	3.31644	−	8.00660i	0.206074	−	0.497506i
$260$	10.8140	−	1.68527i	0.670657	−	0.104516i
$261$		0			0
$262$	−2.19637	+	1.11568i	−0.135692	+	0.0689267i
$263$	16.8072	−	16.8072i	1.03638	−	1.03638i	0.0370655	−	0.999313i	$-0.488199\pi$
$263$	16.8072	−	16.8072i	1.03638	−	1.03638i	0.999313	−	0.0370655i	$-0.0118010\pi$
$264$		0			0
$265$	16.4724	+	16.4724i	1.01189	+	1.01189i
$266$	1.72834	+	0.563946i	0.105972	+	0.0345777i
$267$		0			0
$268$	24.5713	+	5.96360i	1.50093	+	0.364285i
$269$	−5.35918	−	2.21985i	−0.326755	−	0.135346i	0.213275	−	0.976992i	$-0.431587\pi$
$269$	−5.35918	−	2.21985i	−0.326755	−	0.135346i	−0.540030	+	0.841646i	$0.681587\pi$
$270$		0			0
$271$	−23.2742			−1.41381			−0.706904	−	0.707310i	$-0.749909\pi$
$271$	−23.2742			−1.41381			−0.706904	+	0.707310i	$0.749909\pi$
$272$	2.81141	−	0.898077i	0.170467	−	0.0544539i
$273$		0			0
$274$	−1.48604	−	19.1863i	−0.0897750	−	1.15909i
$275$	0.643002	−	1.55234i	0.0387745	−	0.0936099i
$276$		0			0
$277$	−16.5264	+	6.84547i	−0.992977	+	0.411305i	−0.819217	−	0.573483i	$-0.805592\pi$
$277$	−16.5264	+	6.84547i	−0.992977	+	0.411305i	−0.173760	+	0.984788i	$0.555592\pi$
$278$	−15.9588	−	5.20723i	−0.957144	−	0.312309i
$279$		0			0
$280$	−4.34804	−	6.03166i	−0.259845	−	0.360461i
$281$	16.8395	+	16.8395i	1.00456	+	1.00456i	0.999990	+	0.00457241i	$0.00145545\pi$
$281$	16.8395	+	16.8395i	1.00456	+	1.00456i	0.00457241	+	0.999990i	$0.498545\pi$
$282$		0			0
$283$	14.1293	−	5.85256i	0.839901	−	0.347899i	0.0790867	−	0.996868i	$-0.474800\pi$
$283$	14.1293	−	5.85256i	0.839901	−	0.347899i	0.760815	+	0.648969i	$0.224800\pi$
$284$	−16.0466	−	11.7195i	−0.952191	−	0.695425i
$285$		0			0
$286$	−7.06180	−	6.04652i	−0.417573	−	0.357538i
$287$	−0.873879			−0.0515834
$288$		0			0
$289$	−16.4556			−0.967976
$290$	10.0116	+	8.57220i	0.587899	+	0.503377i
$291$		0			0
$292$	−4.52641	+	6.19766i	−0.264888	+	0.362691i
$293$	−11.4278	+	4.73354i	−0.667618	+	0.276537i	−0.690640	−	0.723198i	$-0.742671\pi$
$293$	−11.4278	+	4.73354i	−0.667618	+	0.276537i	0.0230220	+	0.999735i	$0.492671\pi$
$294$		0			0
$295$	18.0422	+	18.0422i	1.05046	+	1.05046i
$296$	3.10570	−	19.1470i	0.180515	−	1.11290i
$297$		0			0
$298$	32.5507	+	10.6210i	1.88561	+	0.615260i
$299$	−7.01020	+	2.90372i	−0.405410	+	0.167926i
$300$		0			0
$301$	2.92225	−	7.05494i	0.168436	−	0.406640i
$302$	−0.969715	−	12.5200i	−0.0558009	−	0.720447i
$303$		0			0
$304$	4.05499	+	0.339398i	0.232570	+	0.0194658i
$305$	20.9745			1.20100
$306$		0			0
$307$	−18.2939	−	7.57758i	−1.04409	−	0.432475i	−0.206310	−	0.978487i	$-0.566146\pi$
$307$	−18.2939	−	7.57758i	−1.04409	−	0.432475i	−0.837778	+	0.546011i	$0.816146\pi$
$308$	−1.48968	+	6.13781i	−0.0848824	+	0.349734i
$309$		0			0
$310$	4.76783	+	1.55571i	0.270795	+	0.0883582i
$311$	−0.879271	−	0.879271i	−0.0498589	−	0.0498589i	0.681738	−	0.731597i	$-0.261225\pi$
$311$	−0.879271	−	0.879271i	−0.0498589	−	0.0498589i	−0.731597	+	0.681738i	$0.761225\pi$
$312$		0			0
$313$	19.1529	−	19.1529i	1.08258	−	1.08258i	0.0863155	−	0.996268i	$-0.472491\pi$
$313$	19.1529	−	19.1529i	1.08258	−	1.08258i	0.996268	−	0.0863155i	$-0.0275093\pi$
$314$	−18.5416	+	9.41845i	−1.04636	+	0.531514i
$315$		0			0
$316$	−0.603103	−	3.86999i	−0.0339272	−	0.217704i
$317$	2.65048	−	6.39882i	0.148866	−	0.359394i	−0.831802	−	0.555072i	$-0.812691\pi$
$317$	2.65048	−	6.39882i	0.148866	−	0.359394i	0.980668	+	0.195678i	$0.0626908\pi$
$318$		0			0
$319$		−	11.1957i		−	0.626838i
$320$	−12.5741	−	10.9023i	−0.702916	−	0.609457i
$321$		0			0
$322$	3.91571	+	3.35275i	0.218214	+	0.186841i
$323$	0.693466	+	0.287243i	0.0385855	+	0.0159826i
$324$		0			0
$325$	0.676832	+	1.63402i	0.0375439	+	0.0906390i
$326$	−13.1168	−	25.8224i	−0.726473	−	1.43017i
$327$		0			0
$328$	−1.90359	+	0.449523i	−0.105108	+	0.0248208i
$329$	2.05414	−	2.05414i	0.113249	−	0.113249i
$330$		0			0
$331$	−9.57207	−	23.1090i	−0.526128	−	1.27019i	−0.934041	−	0.357165i	$-0.883743\pi$
$331$	−9.57207	−	23.1090i	−0.526128	−	1.27019i	0.407913	−	0.913021i	$-0.366257\pi$
$332$	15.5500	+	3.77407i	0.853416	+	0.207129i
$333$		0			0
$334$	0.653999	+	8.44381i	0.0357852	+	0.462025i
$335$		−	26.2998i		−	1.43691i
$336$		0			0
$337$		−	16.9874i		−	0.925364i	−0.886524	−	0.462682i	$-0.846887\pi$
$337$		−	16.9874i		−	0.925364i	0.886524	−	0.462682i	$-0.153113\pi$
$338$	−8.57323	+	0.664023i	−0.466322	+	0.0361181i
$339$		0			0
$340$	−1.59750	−	2.62146i	−0.0866365	−	0.142169i
$341$	−1.63028	−	3.93585i	−0.0882847	−	0.213138i
$342$		0			0
$343$	11.0829	−	11.0829i	0.598421	−	0.598421i
$344$	2.73656	−	16.8712i	0.147546	−	0.909633i
$345$		0			0
$346$	13.9195	−	7.07061i	0.748319	−	0.380118i
$347$	−3.71736	−	8.97450i	−0.199558	−	0.481777i	0.792144	−	0.610335i	$-0.208965\pi$
$347$	−3.71736	−	8.97450i	−0.199558	−	0.481777i	−0.991702	+	0.128558i	$0.958965\pi$
$348$		0			0
$349$	−3.48797	−	1.44476i	−0.186707	−	0.0773364i	0.287372	−	0.957819i	$-0.407219\pi$
$349$	−3.48797	−	1.44476i	−0.186707	−	0.0773364i	−0.474078	+	0.880483i	$0.657219\pi$
$350$	0.781496	−	0.912719i	0.0417727	−	0.0487869i
$351$		0			0
$352$	−0.0877231	+	14.1365i	−0.00467566	+	0.753475i
$353$			23.8874i			1.27140i	0.771937	+	0.635700i	$0.219288\pi$
$353$			23.8874i			1.27140i	−0.771937	+	0.635700i	$0.780712\pi$
$354$		0			0
$355$	−7.90945	+	19.0951i	−0.419790	+	1.01346i
$356$	−8.72067	+	11.9405i	−0.462195	+	0.632847i
$357$		0			0
$358$	−8.33525	−	16.4092i	−0.440532	−	0.867251i
$359$	7.02888	−	7.02888i	0.370970	−	0.370970i	−0.496860	−	0.867830i	$-0.665514\pi$
$359$	7.02888	−	7.02888i	0.370970	−	0.370970i	0.867830	+	0.496860i	$0.165514\pi$
$360$		0			0
$361$	−12.7033	−	12.7033i	−0.668592	−	0.668592i
$362$	9.17060	−	28.1055i	0.481996	−	1.47719i
$363$		0			0
$364$	−3.45965	−	5.67721i	−0.181335	−	0.297567i
$365$	7.37508	+	3.05486i	0.386029	+	0.159898i
$366$		0			0
$367$	−26.1654			−1.36583			−0.682913	−	0.730500i	$-0.739287\pi$
$367$	−26.1654			−1.36583			−0.682913	+	0.730500i	$0.739287\pi$
$368$	10.2544	+	5.28914i	0.534545	+	0.275715i
$369$		0			0
$370$	−20.1158	+	1.55803i	−1.04577	+	0.0809980i
$371$	5.41531	−	13.0737i	0.281149	−	0.678754i
$372$		0			0
$373$	−2.20450	+	0.913134i	−0.114145	+	0.0472803i	−0.439025	−	0.898475i	$-0.644676\pi$
$373$	−2.20450	+	0.913134i	−0.114145	+	0.0472803i	0.324880	+	0.945755i	$0.394676\pi$
$374$	−0.808891	+	2.47904i	−0.0418267	+	0.128188i
$375$		0			0
$376$	3.41795	−	5.53125i	0.176267	−	0.285253i
$377$	8.33305	+	8.33305i	0.429174	+	0.429174i
$378$		0			0
$379$	19.6054	−	8.12082i	1.00706	−	0.417139i	0.182680	−	0.983172i	$-0.441523\pi$
$379$	19.6054	−	8.12082i	1.00706	−	0.417139i	0.824382	+	0.566034i	$0.191523\pi$
$380$	−0.651738	−	4.18207i	−0.0334335	−	0.214536i
$381$		0			0
$382$	−2.53693	+	2.96291i	−0.129801	+	0.151596i
$383$	37.5793			1.92022			0.960108	−	0.279631i	$-0.0902121\pi$
$383$	37.5793			1.92022			0.960108	+	0.279631i	$0.0902121\pi$
$384$		0			0
$385$	6.56958			0.334817
$386$	6.67398	−	7.79462i	0.339697	−	0.396736i
$387$		0			0
$388$	1.42642	+	9.15305i	0.0724156	+	0.464676i
$389$	12.8477	−	5.32168i	0.651403	−	0.269820i	−0.0324129	−	0.999475i	$-0.510319\pi$
$389$	12.8477	−	5.32168i	0.651403	−	0.269820i	0.683816	+	0.729655i	$0.260319\pi$
$390$		0			0
$391$	1.50495	+	1.50495i	0.0761084	+	0.0761084i
$392$	8.03343	−	13.0005i	0.405750	−	0.656623i
$393$		0			0
$394$	−4.15785	+	12.7427i	−0.209470	+	0.641969i
$395$	−3.76384	+	1.55903i	−0.189379	+	0.0784435i
$396$		0			0
$397$	3.36696	−	8.12856i	0.168983	−	0.407961i	−0.816589	−	0.577220i	$-0.804137\pi$
$397$	3.36696	−	8.12856i	0.168983	−	0.407961i	0.985572	+	0.169259i	$0.0541375\pi$
$398$	−0.729880	+	0.0565314i	−0.0365856	+	0.00283366i
$399$		0			0
$400$	1.23285	−	2.39020i	0.0616427	−	0.119510i
$401$	−8.75174			−0.437041			−0.218520	−	0.975832i	$-0.570123\pi$
$401$	−8.75174			−0.437041			−0.218520	+	0.975832i	$0.570123\pi$
$402$		0			0
$403$	4.14292	+	1.71606i	0.206374	+	0.0854828i
$404$	0.272085	+	0.446486i	0.0135367	+	0.0222135i
$405$		0			0
$406$	2.48352	−	7.61133i	0.123255	−	0.377744i
$407$	12.1186	+	12.1186i	0.600698	+	0.600698i
$408$		0			0
$409$	−15.2190	+	15.2190i	−0.752530	+	0.752530i	−0.974951	−	0.222421i	$-0.928604\pi$
$409$	−15.2190	+	15.2190i	−0.752530	+	0.752530i	0.222421	+	0.974951i	$0.428604\pi$
$410$	0.921384	+	1.81388i	0.0455039	+	0.0895812i
$411$		0			0
$412$	19.6037	−	26.8418i	0.965803	−	1.32240i
$413$	5.93141	−	14.3197i	0.291866	−	0.704626i
$414$		0			0
$415$		−	16.6439i		−	0.817015i
$416$	−10.4566	−	10.5872i	−0.512677	−	0.519080i
$417$		0			0
$418$	−2.33835	+	2.73099i	−0.114372	+	0.133577i
$419$	0.923237	+	0.382417i	0.0451031	+	0.0186823i	0.405121	−	0.914263i	$-0.367229\pi$
$419$	0.923237	+	0.382417i	0.0451031	+	0.0186823i	−0.360018	+	0.932945i	$0.617229\pi$
$420$		0			0
$421$	−7.35619	−	17.7594i	−0.358519	−	0.865541i	−0.995509	−	0.0946690i	$-0.969821\pi$
$421$	−7.35619	−	17.7594i	−0.358519	−	0.865541i	0.636990	−	0.770872i	$-0.280179\pi$
$422$	−26.3587	+	13.3893i	−1.28312	+	0.651779i
$423$		0			0
$424$	5.07120	−	31.2645i	0.246279	−	1.51834i
$425$	0.350790	−	0.350790i	0.0170158	−	0.0170158i
$426$		0			0
$427$	−4.87577	−	11.7712i	−0.235955	−	0.569646i
$428$	16.0385	+	26.3189i	0.775251	+	1.27217i
$429$		0			0
$430$	−17.7248	+	1.37284i	−0.854767	+	0.0662043i
$431$			9.63403i			0.464055i	0.972709	+	0.232027i	$0.0745359\pi$
$431$			9.63403i			0.464055i	−0.972709	+	0.232027i	$0.925464\pi$
$432$		0			0
$433$		−	1.58110i		−	0.0759830i	−0.999278	−	0.0379915i	$-0.987904\pi$
$433$		−	1.58110i		−	0.0759830i	0.999278	−	0.0379915i	$-0.0120960\pi$
$434$	−0.235257	−	3.03741i	−0.0112927	−	0.145800i
$435$		0			0
$436$	−35.1570	−	8.53281i	−1.68372	−	0.408647i
$437$	1.12295	+	2.71103i	0.0537178	+	0.129686i
$438$		0			0
$439$	0.640531	−	0.640531i	0.0305709	−	0.0305709i	−0.691656	−	0.722227i	$-0.743119\pi$
$439$	0.640531	−	0.640531i	0.0305709	−	0.0305709i	0.722227	+	0.691656i	$0.243119\pi$
$440$	14.3107	−	3.37939i	0.682236	−	0.161106i
$441$		0			0
$442$	−1.24311	−	2.44724i	−0.0591285	−	0.116403i
$443$	1.16650	+	2.81617i	0.0554220	+	0.133801i	0.949165	−	0.314779i	$-0.101930\pi$
$443$	1.16650	+	2.81617i	0.0554220	+	0.133801i	−0.893743	+	0.448579i	$0.851930\pi$
$444$		0			0
$445$	14.2090	+	5.88555i	0.673570	+	0.279002i
$446$	−12.5504	−	10.7461i	−0.594280	−	0.508840i
$447$		0			0
$448$	−3.19551	+	9.59115i	−0.150973	+	0.453139i
$449$		−	21.7114i		−	1.02462i	−0.858800	−	0.512311i	$-0.828789\pi$
$449$		−	21.7114i		−	1.02462i	0.858800	−	0.512311i	$-0.171211\pi$
$450$		0			0
$451$	0.661342	−	1.59662i	0.0311414	−	0.0751820i
$452$	−3.06409	−	19.6616i	−0.144123	−	0.924805i
$453$		0			0
$454$	9.95237	−	5.05544i	0.467088	−	0.237263i
$455$	−4.88980	+	4.88980i	−0.229238	+	0.229238i
$456$		0			0
$457$	28.6343	+	28.6343i	1.33945	+	1.33945i	0.896588	+	0.442866i	$0.146038\pi$
$457$	28.6343	+	28.6343i	1.33945	+	1.33945i	0.442866	+	0.896588i	$0.353962\pi$
$458$	−11.1287	−	3.63122i	−0.520012	−	0.169676i
$459$		0			0
$460$	2.83061	−	11.6627i	0.131978	−	0.543777i
$461$	0.751268	+	0.311185i	0.0349900	+	0.0144934i	0.400110	−	0.916467i	$-0.368972\pi$
$461$	0.751268	+	0.311185i	0.0349900	+	0.0144934i	−0.365120	+	0.930961i	$0.618972\pi$
$462$		0			0
$463$	−18.5749			−0.863251			−0.431625	−	0.902053i	$-0.642060\pi$
$463$	−18.5749			−0.863251			−0.431625	+	0.902053i	$0.642060\pi$
$464$	1.49465	−	17.8575i	0.0693874	−	0.829014i
$465$		0			0
$466$	−0.773042	−	9.98079i	−0.0358105	−	0.462351i
$467$	−5.40928	+	13.0591i	−0.250311	+	0.604305i	−0.998229	−	0.0594862i	$-0.981054\pi$
$467$	−5.40928	+	13.0591i	−0.250311	+	0.604305i	0.747918	+	0.663791i	$0.231054\pi$
$468$		0			0
$469$	−14.7598	+	6.11372i	−0.681545	+	0.282305i
$470$	−6.42953	−	2.09791i	−0.296572	−	0.0967692i
$471$		0			0
$472$	5.55450	−	34.2441i	0.255667	−	1.57621i
$473$	10.6782	+	10.6782i	0.490985	+	0.490985i
$474$		0			0
$475$	0.631918	−	0.261749i	0.0289944	−	0.0120099i
$476$	−1.09984	+	1.50593i	−0.0504112	+	0.0690241i
$477$		0			0
$478$	0.283091	+	0.242391i	0.0129483	+	0.0110867i
$479$	19.0749			0.871553			0.435776	−	0.900055i	$-0.356474\pi$
$479$	19.0749			0.871553			0.435776	+	0.900055i	$0.356474\pi$
$480$		0			0
$481$	−18.0400			−0.822554
$482$	27.0192	+	23.1347i	1.23069	+	1.05375i
$483$		0			0
$484$	7.67950	+	5.60866i	0.349068	+	0.254939i
$485$	8.90201	−	3.68733i	0.404219	−	0.167433i
$486$		0			0
$487$	0.0797223	+	0.0797223i	0.00361256	+	0.00361256i	0.708911	−	0.705298i	$-0.249187\pi$
$487$	0.0797223	+	0.0797223i	0.00361256	+	0.00361256i	−0.705298	+	0.708911i	$0.749187\pi$
$488$	−16.6761	−	23.1333i	−0.754892	−	1.04720i
$489$		0			0
$490$	−15.1118	−	4.93085i	−0.682680	−	0.222753i
$491$	2.55287	−	1.05744i	0.115210	−	0.0477214i	−0.324334	−	0.945943i	$-0.605140\pi$
$491$	2.55287	−	1.05744i	0.115210	−	0.0477214i	0.439544	+	0.898221i	$0.355140\pi$
$492$		0			0
$493$	1.26497	−	3.05390i	0.0569713	−	0.137541i
$494$	−0.292242	−	3.77316i	−0.0131486	−	0.169762i
$495$		0			0
$496$	−2.07491	−	6.49547i	−0.0931663	−	0.291655i
$497$	12.5551			0.563172
$498$		0			0
$499$	10.7410	+	4.44905i	0.480831	+	0.199167i	0.609915	−	0.792467i	$-0.291204\pi$
$499$	10.7410	+	4.44905i	0.480831	+	0.199167i	−0.129084	+	0.991634i	$0.541204\pi$
$500$	−22.9346	−	5.56635i	−1.02566	−	0.248935i
$501$		0			0
$502$	−39.3946	−	12.8541i	−1.75827	−	0.573708i
$503$	13.8749	+	13.8749i	0.618651	+	0.618651i	0.945185	−	0.326534i	$-0.105881\pi$
$503$	13.8749	+	13.8749i	0.618651	+	0.618651i	−0.326534	+	0.945185i	$0.605881\pi$
$504$		0			0
$505$	0.384560	−	0.384560i	0.0171127	−	0.0171127i
$506$	−9.08901	+	4.61688i	−0.404056	+	0.205245i
$507$		0			0
$508$	8.83279	−	1.37651i	0.391892	−	0.0610728i
$509$	−0.459308	+	1.10887i	−0.0203585	+	0.0491497i	−0.933732	−	0.357973i	$-0.883468\pi$
$509$	−0.459308	+	1.10887i	−0.0203585	+	0.0491497i	0.913373	+	0.407123i	$0.133468\pi$
$510$		0			0
$511$		−	4.84913i		−	0.214513i
$512$	−2.02717	+	22.5364i	−0.0895892	+	0.995979i
$513$		0			0
$514$	−21.8904	−	18.7432i	−0.965546	−	0.826729i
$515$	−31.9411	−	13.2304i	−1.40749	−	0.583003i
$516$		0			0
$517$	2.19847	+	5.30758i	0.0966887	+	0.233427i
$518$	5.55054	+	10.9271i	0.243877	+	0.480107i
$519$		0			0
$520$	−8.13628	+	13.1669i	−0.356799	+	0.577407i
$521$	10.7919	−	10.7919i	0.472802	−	0.472802i	−0.430018	−	0.902820i	$-0.641493\pi$
$521$	10.7919	−	10.7919i	0.472802	−	0.472802i	0.902820	+	0.430018i	$0.141493\pi$
$522$		0			0
$523$	−5.60560	−	13.5331i	−0.245116	−	0.591762i	0.752661	−	0.658409i	$-0.228770\pi$
$523$	−5.60560	−	13.5331i	−0.245116	−	0.591762i	−0.997777	+	0.0666464i	$0.978770\pi$
$524$	0.821707	−	3.38561i	0.0358964	−	0.147901i
$525$		0			0
$526$	2.59577	+	33.5141i	0.113181	+	1.46128i
$527$		−	1.25780i		−	0.0547908i
$528$		0			0
$529$		−	14.6796i		−	0.638243i
$530$	−32.8464	+	2.54405i	−1.42676	+	0.110507i
$531$		0			0
$532$	−2.19553	+	1.33794i	−0.0951882	+	0.0580069i
$533$	0.696137	+	1.68062i	0.0301530	+	0.0727959i
$534$		0			0
$535$	22.6686	−	22.6686i	0.980048	−	0.980048i
$536$	−29.0068	+	20.9101i	−1.25290	+	0.903180i
$537$		0			0
$538$	7.31397	−	3.71523i	0.315328	−	0.160175i
$539$	5.16722	+	12.4748i	0.222568	+	0.537326i
$540$		0			0
$541$	35.8825	+	14.8630i	1.54271	+	0.639011i	0.981979	−	0.188988i	$-0.0605207\pi$
$541$	35.8825	+	14.8630i	1.54271	+	0.639011i	0.560730	+	0.827999i	$0.310521\pi$
$542$	21.4074	−	25.0020i	0.919528	−	1.07393i
$543$		0			0
$544$	−1.62117	+	3.84616i	−0.0695070	+	0.164903i
$545$			37.6302i			1.61190i
$546$		0			0
$547$	−3.04956	+	7.36230i	−0.130390	+	0.314789i	−0.975569	−	0.219695i	$-0.929494\pi$
$547$	−3.04956	+	7.36230i	−0.130390	+	0.314789i	0.845179	+	0.534484i	$0.179494\pi$
$548$	21.9775	+	16.0511i	0.938832	+	0.685668i
$549$		0			0
$550$	1.07616	+	2.11857i	0.0458874	+	0.0903361i
$551$	3.22261	−	3.22261i	0.137288	−	0.137288i
$552$		0			0
$553$	1.74990	+	1.74990i	0.0744134	+	0.0744134i
$554$	7.84723	−	24.0497i	0.333397	−	1.02177i
$555$		0			0
$556$	20.2726	−	12.3539i	0.859748	−	0.523923i
$557$	−39.6963	−	16.4428i	−1.68199	−	0.696702i	−0.682570	−	0.730820i	$-0.739138\pi$
$557$	−39.6963	−	16.4428i	−1.68199	−	0.696702i	−0.999418	+	0.0341181i	$0.989138\pi$
$558$		0			0
$559$	−15.8958			−0.672320
$560$	10.4787	+	0.877056i	0.442807	+	0.0370624i
$561$		0			0
$562$	−33.5785	+	2.60076i	−1.41642	+	0.109706i
$563$	−15.9730	+	38.5621i	−0.673180	+	1.62520i	0.102995	+	0.994682i	$0.467157\pi$
$563$	−15.9730	+	38.5621i	−0.673180	+	1.62520i	−0.776175	+	0.630518i	$0.782843\pi$
$564$		0			0
$565$	−19.1224	+	7.92074i	−0.804484	+	0.333228i
$566$	−6.70902	+	20.5614i	−0.282001	+	0.864259i
$567$		0			0
$568$	27.3491	−	6.45833i	1.14754	−	0.270985i
$569$	−1.66264	−	1.66264i	−0.0697017	−	0.0697017i	0.671397	−	0.741098i	$-0.265695\pi$
$569$	−1.66264	−	1.66264i	−0.0697017	−	0.0697017i	−0.741098	+	0.671397i	$0.765695\pi$
$570$		0			0
$571$	−13.7130	+	5.68011i	−0.573871	+	0.237705i	−0.650695	−	0.759339i	$-0.725522\pi$
$571$	−13.7130	+	5.68011i	−0.573871	+	0.237705i	0.0768234	+	0.997045i	$0.475522\pi$
$572$	12.9908	−	2.02450i	0.543172	−	0.0846485i
$573$		0			0
$574$	0.803787	−	0.938752i	0.0335494	−	0.0391827i
$575$	1.93942			0.0808794
$576$		0			0
$577$	−10.5206			−0.437980			−0.218990	−	0.975727i	$-0.570276\pi$
$577$	−10.5206			−0.437980			−0.218990	+	0.975727i	$0.570276\pi$
$578$	15.1357	−	17.6772i	0.629563	−	0.735274i
$579$		0			0
$580$	−18.4171	+	2.87014i	−0.764729	+	0.119176i
$581$	−9.34076	+	3.86907i	−0.387520	+	0.160516i
$582$		0			0
$583$	19.7881	+	19.7881i	0.819540	+	0.819540i
$584$	−2.49439	−	10.5630i	−0.103219	−	0.437100i
$585$		0			0
$586$	5.42625	−	16.6300i	0.224156	−	0.686979i
$587$	14.8140	−	6.13616i	0.611439	−	0.253266i	−0.0554048	−	0.998464i	$-0.517645\pi$
$587$	14.8140	−	6.13616i	0.611439	−	0.253266i	0.666844	+	0.745198i	$0.267645\pi$
$588$		0			0
$589$	0.663644	−	1.60218i	0.0273450	−	0.0660166i
$590$	−35.9767	+	2.78651i	−1.48114	+	0.114719i
$591$		0			0
$592$	17.7118	+	20.9475i	0.727949	+	0.860937i
$593$	−20.3738			−0.836653			−0.418327	−	0.908297i	$-0.637383\pi$
$593$	−20.3738			−0.836653			−0.418327	+	0.908297i	$0.637383\pi$
$594$		0			0
$595$	1.79202	+	0.742279i	0.0734657	+	0.0304305i
$596$	−41.3494	+	25.1980i	−1.69374	+	1.03215i
$597$		0			0
$598$	3.32865	−	10.2014i	0.136118	−	0.417167i
$599$	−8.08761	−	8.08761i	−0.330451	−	0.330451i	0.522307	−	0.852758i	$-0.325072\pi$
$599$	−8.08761	−	8.08761i	−0.330451	−	0.330451i	−0.852758	+	0.522307i	$0.825072\pi$
$600$		0			0
$601$	−16.9334	+	16.9334i	−0.690726	+	0.690726i	−0.962392	−	0.271666i	$-0.912426\pi$
$601$	−16.9334	+	16.9334i	−0.690726	+	0.690726i	0.271666	+	0.962392i	$0.412426\pi$
$602$	4.89081	+	9.62827i	0.199334	+	0.392419i
$603$		0			0
$604$	14.3414	+	10.4741i	0.583544	+	0.426186i
$605$	3.78526	−	9.13843i	0.153893	−	0.371530i
$606$		0			0
$607$		−	35.3664i		−	1.43548i	−0.696313	−	0.717738i	$-0.745177\pi$
$607$		−	35.3664i		−	1.43548i	0.696313	−	0.717738i	$-0.254823\pi$
$608$	−4.09435	+	4.04384i	−0.166048	+	0.164000i
$609$		0			0
$610$	−19.2922	+	22.5315i	−0.781117	+	0.912275i
$611$	−5.58683	−	2.31414i	−0.226019	−	0.0936201i
$612$		0			0
$613$	10.5466	+	25.4618i	0.425975	+	1.02839i	0.980552	+	0.196262i	$0.0628802\pi$
$613$	10.5466	+	25.4618i	0.425975	+	1.02839i	−0.554577	+	0.832133i	$0.687120\pi$
$614$	24.9667	−	12.6822i	1.00757	−	0.511810i
$615$		0			0
$616$	−5.22326	−	7.24578i	−0.210451	−	0.291941i
$617$	11.7366	−	11.7366i	0.472498	−	0.472498i	−0.430224	−	0.902722i	$-0.641565\pi$
$617$	11.7366	−	11.7366i	0.472498	−	0.472498i	0.902722	+	0.430224i	$0.141565\pi$
$618$		0			0
$619$	−16.1570	−	39.0066i	−0.649407	−	1.56781i	−0.813630	−	0.581383i	$-0.802512\pi$
$619$	−16.1570	−	39.0066i	−0.649407	−	1.56781i	0.164223	−	0.986423i	$-0.447488\pi$
$620$	−6.05661	+	3.69085i	−0.243239	+	0.148228i
$621$		0			0
$622$	1.75329	−	0.135798i	0.0703006	−	0.00544500i
$623$		−	9.34243i		−	0.374296i
$624$		0			0
$625$			21.1862i			0.847446i
$626$	2.95804	+	38.1913i	0.118227	+	1.52643i
$627$		0			0
$628$	6.93678	−	28.5811i	0.276808	−	1.14051i
$629$	1.93641	+	4.67491i	0.0772098	+	0.186401i
$630$		0			0
$631$	31.6963	−	31.6963i	1.26181	−	1.26181i	0.311597	−	0.950214i	$-0.399136\pi$
$631$	31.6963	−	31.6963i	1.26181	−	1.26181i	0.950214	−	0.311597i	$-0.100864\pi$
$632$	4.71201	+	2.91171i	0.187434	+	0.115822i
$633$		0			0
$634$	4.43596	+	8.73283i	0.176174	+	0.346825i
$635$	−3.55831	−	8.59052i	−0.141207	−	0.340905i
$636$		0			0
$637$	−13.1311	−	5.43908i	−0.520273	−	0.215504i
$638$	12.0268	+	10.2977i	0.476145	+	0.407690i
$639$		0			0
$640$	23.2772	−	3.47974i	0.920114	−	0.137549i
$641$		−	6.53709i		−	0.258200i	−0.991632	−	0.129100i	$-0.958791\pi$
$641$		−	6.53709i		−	0.258200i	0.991632	−	0.129100i	$-0.0412087\pi$
$642$		0			0
$643$	−6.85869	+	16.5584i	−0.270480	+	0.652998i	−0.999504	−	0.0314910i	$-0.989974\pi$
$643$	−6.85869	+	16.5584i	−0.270480	+	0.652998i	0.729024	+	0.684489i	$0.239974\pi$
$644$	−7.20328	+	1.12257i	−0.283849	+	0.0442353i
$645$		0			0
$646$	−0.946411	+	0.480742i	−0.0372360	+	0.0189145i
$647$	−25.1282	+	25.1282i	−0.987890	+	0.987890i	−0.999928	−	0.0120376i	$-0.996168\pi$
$647$	−25.1282	+	25.1282i	−0.987890	+	0.987890i	0.0120376	+	0.999928i	$0.496168\pi$
$648$		0			0
$649$	21.6740	+	21.6740i	0.850778	+	0.850778i
$650$	−2.37786	−	0.775879i	−0.0932675	−	0.0304325i
$651$		0			0
$652$	39.8040	+	9.66066i	1.55885	+	0.378341i
$653$	35.2170	+	14.5873i	1.37815	+	0.570847i	0.943985	−	0.329989i	$-0.107045\pi$
$653$	35.2170	+	14.5873i	1.37815	+	0.570847i	0.434161	+	0.900835i	$0.357045\pi$
$654$		0			0
$655$	−3.62378			−0.141593
$656$	1.26802	−	2.45838i	0.0495077	−	0.0959835i
$657$		0			0
$658$	0.317249	+	4.09602i	0.0123677	+	0.159680i
$659$	8.14855	−	19.6724i	0.317423	−	0.766326i	−0.681967	−	0.731383i	$-0.738875\pi$
$659$	8.14855	−	19.6724i	0.317423	−	0.766326i	0.999389	−	0.0349428i	$-0.0111249\pi$
$660$		0			0
$661$	3.17496	−	1.31511i	0.123492	−	0.0511519i	−0.320082	−	0.947390i	$-0.603710\pi$
$661$	3.17496	−	1.31511i	0.123492	−	0.0511519i	0.443574	+	0.896238i	$0.353710\pi$
$662$	33.6288	+	10.9728i	1.30702	+	0.426471i
$663$		0			0
$664$	−18.3570	+	13.2330i	−0.712389	+	0.513540i
$665$	1.89102	+	1.89102i	0.0733305	+	0.0733305i
$666$		0			0
$667$	11.9389	−	4.94526i	0.462276	−	0.191481i
$668$	−9.67218	−	7.06400i	−0.374228	−	0.273314i
$669$		0			0
$670$	28.2522	+	24.1904i	1.09148	+	0.934556i
$671$	25.1964			0.972698
$672$		0			0
$673$	26.4144			1.01820			0.509099	−	0.860708i	$-0.329979\pi$
$673$	26.4144			1.01820			0.509099	+	0.860708i	$0.329979\pi$
$674$	18.2485	+	15.6249i	0.702906	+	0.601848i
$675$		0			0
$676$	7.17227	−	9.82043i	0.275857	−	0.377709i
$677$	−27.1357	+	11.2400i	−1.04291	+	0.431987i	−0.837355	−	0.546659i	$-0.815899\pi$
$677$	−27.1357	+	11.2400i	−1.04291	+	0.431987i	−0.205553	+	0.978646i	$0.565899\pi$
$678$		0			0
$679$	−4.13876	−	4.13876i	−0.158831	−	0.158831i
$680$	4.28543	+	0.695112i	0.164339	+	0.0266563i
$681$		0			0
$682$	5.72755	+	1.86886i	0.219319	+	0.0715622i
$683$	−26.8532	+	11.1230i	−1.02751	+	0.425608i	−0.831813	−	0.555056i	$-0.812697\pi$
$683$	−26.8532	+	11.1230i	−1.02751	+	0.425608i	−0.195696	+	0.980665i	$0.562697\pi$
$684$		0			0
$685$	10.8328	−	26.1527i	0.413901	−	0.999244i
$686$	1.71168	+	22.0996i	0.0653524	+	0.843768i
$687$		0			0
$688$	15.6066	+	18.4577i	0.594994	+	0.703693i
$689$	−29.4570			−1.12222
$690$		0			0
$691$	−36.4143	−	15.0833i	−1.38526	−	0.573795i	−0.439381	−	0.898301i	$-0.644802\pi$
$691$	−36.4143	−	15.0833i	−1.38526	−	0.573795i	−0.945884	+	0.324506i	$0.894802\pi$
$692$	−5.20758	+	21.4564i	−0.197962	+	0.815648i
$693$		0			0
$694$	13.0599	+	4.26136i	0.495748	+	0.161759i
$695$	−17.4608	−	17.4608i	−0.662327	−	0.662327i
$696$		0			0
$697$	0.360796	−	0.360796i	0.0136661	−	0.0136661i
$698$	4.76022	−	2.41802i	0.180177	−	0.0915233i
$699$		0			0
$700$	0.261661	+	1.67902i	0.00988984	+	0.0634611i
$701$	11.6213	−	28.0563i	0.438930	−	1.05967i	−0.537389	−	0.843335i	$-0.680589\pi$
$701$	11.6213	−	28.0563i	0.438930	−	1.05967i	0.976319	−	0.216337i	$-0.0694109\pi$
$702$		0			0
$703$			6.97655i			0.263126i
$704$	−15.1052	−	13.0968i	−0.569298	−	0.493605i
$705$		0			0
$706$	−25.6607	−	21.9715i	−0.965754	−	0.826907i
$707$	−0.305216	−	0.126424i	−0.0114788	−	0.00475468i
$708$		0			0
$709$	−0.313401	−	0.756616i	−0.0117700	−	0.0284153i	0.917885	−	0.396846i	$-0.129895\pi$
$709$	−0.313401	−	0.756616i	−0.0117700	−	0.0284153i	−0.929655	+	0.368431i	$0.879895\pi$
$710$	−13.2376	−	26.0601i	−0.496798	−	0.978020i
$711$		0			0
$712$	−4.80574	−	20.3509i	−0.180103	−	0.762681i
$713$	3.47702	−	3.47702i	0.130215	−	0.130215i
$714$		0			0
$715$	−5.23337	−	12.6345i	−0.195717	−	0.472503i
$716$	25.2940	+	6.13900i	0.945281	+	0.229425i
$717$		0			0
$718$	1.08557	+	14.0158i	0.0405129	+	0.523064i
$719$			8.98451i			0.335066i	0.985866	+	0.167533i	$0.0535800\pi$
$719$			8.98451i			0.335066i	−0.985866	+	0.167533i	$0.946420\pi$
$720$		0			0
$721$			21.0013i			0.782131i
$722$	25.3306	−	1.96194i	0.942709	−	0.0730157i
$723$		0			0
$724$	21.7569	+	35.7026i	0.808587	+	1.32688i
$725$	−1.15270	−	2.78286i	−0.0428101	−	0.103353i
$726$		0			0
$727$	−21.5136	+	21.5136i	−0.797896	+	0.797896i	−0.982764	−	0.184867i	$-0.940815\pi$
$727$	−21.5136	+	21.5136i	−0.797896	+	0.797896i	0.184867	+	0.982764i	$0.440815\pi$
$728$	9.28082	+	1.50538i	0.343970	+	0.0557931i
$729$		0			0
$730$	−10.0652	+	5.11274i	−0.372529	+	0.189231i
$731$	1.70625	+	4.11925i	0.0631080	+	0.152356i
$732$		0			0
$733$	34.2259	+	14.1768i	1.26416	+	0.523633i	0.911184	−	0.411999i	$-0.135169\pi$
$733$	34.2259	+	14.1768i	1.26416	+	0.523633i	0.352977	+	0.935632i	$0.385169\pi$
$734$	24.0668	−	28.1079i	0.888321	−	1.03748i
$735$		0			0
$736$	−15.1137	+	6.15068i	−0.557097	+	0.226717i
$737$		−	31.5938i		−	1.16377i
$738$		0			0
$739$	−9.90083	+	23.9027i	−0.364208	+	0.879275i	0.630467	+	0.776216i	$0.282863\pi$
$739$	−9.90083	+	23.9027i	−0.364208	+	0.879275i	−0.994675	+	0.103060i	$0.967137\pi$
$740$	16.8286	−	23.0421i	0.618633	−	0.847046i
$741$		0			0
$742$	9.06330	+	17.8424i	0.332724	+	0.655016i
$743$	−26.1986	+	26.1986i	−0.961135	+	0.961135i	−0.999272	−	0.0381376i	$-0.987857\pi$
$743$	−26.1986	+	26.1986i	−0.961135	+	0.961135i	0.0381376	+	0.999272i	$0.487857\pi$
$744$		0			0
$745$	35.6144	+	35.6144i	1.30481	+	1.30481i
$746$	1.04676	−	3.20805i	0.0383246	−	0.117455i
$747$		0			0
$748$	−1.91906	−	3.14914i	−0.0701677	−	0.115144i
$749$	−17.9915	−	7.45232i	−0.657394	−	0.272302i
$750$		0			0
$751$	−18.2626			−0.666413			−0.333207	−	0.942854i	$-0.608131\pi$
$751$	−18.2626			−0.666413			−0.333207	+	0.942854i	$0.608131\pi$
$752$	2.79807	+	8.75928i	0.102035	+	0.319418i
$753$		0			0
$754$	−16.6163	+	1.28699i	−0.605131	+	0.0468693i
$755$	7.06895	−	17.0660i	0.257265	−	0.621094i
$756$		0			0
$757$	10.5714	−	4.37882i	0.384225	−	0.159151i	−0.182206	−	0.983260i	$-0.558324\pi$
$757$	10.5714	−	4.37882i	0.384225	−	0.159151i	0.566431	+	0.824109i	$0.308324\pi$
$758$	−9.30922	+	28.5303i	−0.338126	+	1.03627i
$759$		0			0
$760$	5.09199	+	3.14651i	0.184706	+	0.114136i
$761$	−11.1889	−	11.1889i	−0.405596	−	0.405596i	0.474604	−	0.880200i	$-0.342591\pi$
$761$	−11.1889	−	11.1889i	−0.405596	−	0.405596i	−0.880200	+	0.474604i	$0.842591\pi$
$762$		0			0
$763$	21.1186	−	8.74760i	0.764544	−	0.316684i
$764$	−0.849414	−	5.45052i	−0.0307307	−	0.197193i
$765$		0			0
$766$	−34.5652	+	40.3691i	−1.24889	+	1.45859i
$767$	−32.2643			−1.16500
$768$		0			0
$769$	−37.9130			−1.36718			−0.683589	−	0.729867i	$-0.739582\pi$
$769$	−37.9130			−1.36718			−0.683589	+	0.729867i	$0.739582\pi$
$770$	−6.04265	+	7.05728i	−0.217762	+	0.254327i
$771$		0			0
$772$	2.23458	+	14.3389i	0.0804244	+	0.516067i
$773$	−9.44761	+	3.91333i	−0.339807	+	0.140753i	−0.546060	−	0.837746i	$-0.683873\pi$
$773$	−9.44761	+	3.91333i	−0.339807	+	0.140753i	0.206253	+	0.978499i	$0.433873\pi$
$774$		0			0
$775$	−0.810463	−	0.810463i	−0.0291127	−	0.0291127i
$776$	−11.1445	−	6.88659i	−0.400066	−	0.247214i
$777$		0			0
$778$	−6.10045	+	18.6963i	−0.218712	+	0.670294i
$779$	0.649942	−	0.269215i	0.0232866	−	0.00964562i
$780$		0			0
$781$	−9.50155	+	22.9388i	−0.339992	+	0.820814i
$782$	−3.00091	+	0.232429i	−0.107312	+	0.00831166i
$783$		0			0
$784$	6.57648	+	20.5875i	0.234874	+	0.735269i
$785$	−30.5917			−1.09186
$786$		0			0
$787$	−30.0213	−	12.4352i	−1.07014	−	0.443268i	−0.223102	−	0.974795i	$-0.571618\pi$
$787$	−30.0213	−	12.4352i	−1.07014	−	0.443268i	−0.847041	+	0.531527i	$0.821618\pi$
$788$	−9.86433	−	16.1872i	−0.351402	−	0.576644i
$789$		0			0
$790$	1.78718	−	5.47724i	0.0635851	−	0.194871i
$791$	8.89045	+	8.89045i	0.316108	+	0.316108i
$792$		0			0
$793$	−18.7539	+	18.7539i	−0.665972	+	0.665972i
$794$	5.63509	+	11.0935i	0.199982	+	0.393693i
$795$		0			0
$796$	0.610610	−	0.836060i	0.0216425	−	0.0296334i
$797$	−7.58056	+	18.3011i	−0.268517	+	0.648258i	−0.999414	−	0.0342301i	$-0.989102\pi$
$797$	−7.58056	+	18.3011i	−0.268517	+	0.648258i	0.730897	+	0.682488i	$0.239102\pi$
$798$		0			0
$799$			1.69618i			0.0600064i
$800$	1.43367	+	3.52286i	0.0506880	+	0.124552i
$801$		0			0
$802$	8.04978	−	9.40143i	0.284248	−	0.331976i
$803$	8.85961	+	3.66977i	0.312649	+	0.129503i
$804$		0			0
$805$	2.90186	+	7.00571i	0.102277	+	0.246919i
$806$	−5.65408	+	2.87206i	−0.199156	+	0.101164i
$807$		0			0
$808$	−0.729892	−	0.118391i	−0.0256775	−	0.00416498i
$809$	−15.5598	+	15.5598i	−0.547055	+	0.547055i	−0.925588	−	0.378533i	$-0.876429\pi$
$809$	−15.5598	+	15.5598i	−0.547055	+	0.547055i	0.378533	+	0.925588i	$0.376429\pi$
$810$		0			0
$811$	−2.24453	−	5.41877i	−0.0788160	−	0.190279i	0.879560	−	0.475788i	$-0.157837\pi$
$811$	−2.24453	−	5.41877i	−0.0788160	−	0.190279i	−0.958376	+	0.285510i	$0.907837\pi$
$812$	5.89204	+	9.66873i	0.206770	+	0.339306i
$813$		0			0
$814$	−24.1649	+	1.87164i	−0.846978	+	0.0656011i
$815$		−	42.6041i		−	1.49236i
$816$		0			0
$817$			6.14732i			0.215068i
$818$	−2.35047	−	30.3471i	−0.0821824	−	1.06106i
$819$		0			0
$820$	−2.79602	−	0.678609i	−0.0976412	−	0.0236981i
$821$	−2.56167	−	6.18442i	−0.0894029	−	0.215838i	0.872853	−	0.487983i	$-0.162267\pi$
$821$	−2.56167	−	6.18442i	−0.0894029	−	0.215838i	−0.962256	+	0.272145i	$0.912267\pi$
$822$		0			0
$823$	18.6586	−	18.6586i	0.650397	−	0.650397i	−0.302691	−	0.953089i	$-0.597885\pi$
$823$	18.6586	−	18.6586i	0.650397	−	0.650397i	0.953089	+	0.302691i	$0.0978851\pi$
$824$	10.8031	+	45.7478i	0.376343	+	1.59370i
$825$		0			0
$826$	9.92706	+	19.5429i	0.345406	+	0.679983i
$827$	8.33091	+	20.1126i	0.289694	+	0.699384i	0.999990	−	0.00451985i	$-0.00143872\pi$
$827$	8.33091	+	20.1126i	0.289694	+	0.699384i	−0.710296	+	0.703904i	$0.751439\pi$
$828$		0			0
$829$	8.99503	+	3.72586i	0.312410	+	0.129405i	0.533379	−	0.845876i	$-0.320922\pi$
$829$	8.99503	+	3.72586i	0.312410	+	0.129405i	−0.220969	+	0.975281i	$0.570922\pi$
$830$	17.8794	+	15.3089i	0.620604	+	0.531380i
$831$		0			0
$832$	20.9910	−	1.49484i	0.727733	−	0.0518243i
$833$			3.98664i			0.138129i
$834$		0			0
$835$	−4.76747	+	11.5097i	−0.164985	+	0.398309i
$836$	−0.782927	−	5.02388i	−0.0270781	−	0.173755i
$837$		0			0
$838$	−1.25999	+	0.640030i	−0.0435257	+	0.0221095i
$839$	12.0311	−	12.0311i	0.415360	−	0.415360i	−0.468241	−	0.883601i	$-0.655112\pi$
$839$	12.0311	−	12.0311i	0.415360	−	0.415360i	0.883601	+	0.468241i	$0.155112\pi$
$840$		0			0
$841$	6.31427	+	6.31427i	0.217734	+	0.217734i
$842$	25.8440	+	8.43269i	0.890642	+	0.290610i
$843$		0			0
$844$	9.86133	−	40.6308i	0.339441	−	1.39857i
$845$	−11.6861	−	4.84054i	−0.402014	−	0.166520i
$846$		0			0
$847$	−6.00854			−0.206456
$848$	28.9210	+	34.2045i	0.993150	+	1.17459i
$849$		0			0
$850$	0.0541773	+	0.699485i	0.00185827	+	0.0239922i
$851$	−7.57019	+	18.2761i	−0.259503	+	0.626495i
$852$		0			0
$853$	−53.1307	+	22.0074i	−1.81916	+	0.753520i	−0.842510	+	0.538681i	$0.818923\pi$
$853$	−53.1307	+	22.0074i	−1.81916	+	0.753520i	−0.976649	+	0.214839i	$0.931077\pi$
$854$	17.1297	+	5.58929i	0.586166	+	0.191261i
$855$		0			0
$856$	−43.0248	−	6.97877i	−1.47056	−	0.238529i
$857$	2.93352	+	2.93352i	0.100207	+	0.100207i	0.755433	−	0.655226i	$-0.227427\pi$
$857$	2.93352	+	2.93352i	0.100207	+	0.100207i	−0.655226	+	0.755433i	$0.727427\pi$
$858$		0			0
$859$	−12.4657	+	5.16346i	−0.425324	+	0.176175i	−0.585069	−	0.810983i	$-0.698933\pi$
$859$	−12.4657	+	5.16346i	−0.425324	+	0.176175i	0.159745	+	0.987158i	$0.448933\pi$
$860$	14.8284	−	20.3034i	0.505644	−	0.692339i
$861$		0			0
$862$	−10.3492	−	8.86130i	−0.352496	−	0.301817i
$863$	−20.2856			−0.690531			−0.345265	−	0.938505i	$-0.612211\pi$
$863$	−20.2856			−0.690531			−0.345265	+	0.938505i	$0.612211\pi$
$864$		0			0
$865$	22.9657			0.780859
$866$	1.69848	+	1.45429i	0.0577166	+	0.0494187i
$867$		0			0
$868$	3.47929	+	2.54107i	0.118095	+	0.0862494i
$869$	−4.52147	+	1.87285i	−0.153380	+	0.0635322i
$870$		0			0
$871$	23.5155	+	23.5155i	0.796793	+	0.796793i
$872$	41.5034	−	29.9185i	1.40548	−	1.01317i
$873$		0			0
$874$	−3.94516	−	1.28728i	−0.133447	−	0.0435428i
$875$	13.7766	−	5.70647i	0.465735	−	0.192914i
$876$		0			0
$877$	11.0514	−	26.6804i	0.373178	−	0.900932i	−0.620029	−	0.784579i	$-0.712879\pi$
$877$	11.0514	−	26.6804i	0.373178	−	0.900932i	0.993208	−	0.116354i	$-0.0371207\pi$
$878$	0.0989259	+	1.27724i	0.00333859	+	0.0431046i
$879$		0			0
$880$	−9.53261	+	18.4814i	−0.321344	+	0.623008i
$881$	37.6011			1.26681			0.633407	−	0.773819i	$-0.281656\pi$
$881$	37.6011			1.26681			0.633407	+	0.773819i	$0.281656\pi$
$882$		0			0
$883$	25.1937	+	10.4356i	0.847836	+	0.351185i	0.763938	−	0.645289i	$-0.223263\pi$
$883$	25.1937	+	10.4356i	0.847836	+	0.351185i	0.0838975	+	0.996474i	$0.473263\pi$
$884$	3.77231	+	0.915560i	0.126876	+	0.0307936i
$885$		0			0
$886$	−4.09817	−	1.33720i	−0.137681	−	0.0449242i
$887$	−37.0506	−	37.0506i	−1.24404	−	1.24404i	−0.958311	−	0.285726i	$-0.907765\pi$
$887$	−37.0506	−	37.0506i	−1.24404	−	1.24404i	−0.285726	−	0.958311i	$-0.592235\pi$
$888$		0			0
$889$	−3.99394	+	3.99394i	−0.133953	+	0.133953i
$890$	−19.3918	+	9.85030i	−0.650013	+	0.330183i
$891$		0			0
$892$	23.0876	−	3.59799i	0.773029	−	0.120470i
$893$	−0.894939	+	2.16057i	−0.0299480	+	0.0723009i
$894$		0			0
$895$		−	27.0734i		−	0.904962i
$896$	−7.36395	−	12.2546i	−0.246012	−	0.409397i
$897$		0			0
$898$	23.3231	+	19.9699i	0.778303	+	0.666406i
$899$	−7.05572	−	2.92257i	−0.235321	−	0.0974733i
$900$		0			0
$901$	3.16190	+	7.63351i	0.105338	+	0.254309i
$902$	1.10685	+	2.17900i	0.0368541	+	0.0725527i
$903$		0			0
$904$	23.9396	+	14.7931i	0.796218	+	0.492010i
$905$	30.7508	−	30.7508i	1.02219	−	1.02219i
$906$		0			0
$907$	−16.2572	−	39.2484i	−0.539812	−	1.30322i	−0.924854	−	0.380322i	$-0.875813\pi$
$907$	−16.2572	−	39.2484i	−0.539812	−	1.30322i	0.385042	−	0.922899i	$-0.374187\pi$
$908$	−3.72338	+	15.3411i	−0.123565	+	0.509114i
$909$		0			0
$910$	−0.755199	−	9.75040i	−0.0250346	−	0.323223i
$911$			9.04684i			0.299735i	0.988706	+	0.149868i	$0.0478847\pi$
$911$			9.04684i			0.299735i	−0.988706	+	0.149868i	$0.952115\pi$
$912$		0			0
$913$		−	19.9941i		−	0.661709i
$914$	−57.0975	+	4.42238i	−1.88862	+	0.146279i
$915$		0			0
$916$	14.1369	−	8.61492i	0.467097	−	0.284645i
$917$	0.842391	+	2.03371i	0.0278182	+	0.0671591i
$918$		0			0
$919$	−22.4185	+	22.4185i	−0.739517	+	0.739517i	−0.972484	−	0.232968i	$-0.925156\pi$
$919$	−22.4185	+	22.4185i	−0.739517	+	0.739517i	0.232968	+	0.972484i	$0.425156\pi$
$920$	9.92494	+	13.7680i	0.327216	+	0.453918i
$921$		0			0
$922$	−1.02530	+	0.520813i	−0.0337664	+	0.0171521i
$923$	−10.0014	−	24.1456i	−0.329202	−	0.794763i
$924$		0			0
$925$	4.25999	+	1.76455i	0.140068	+	0.0580179i
$926$	17.0851	−	19.9539i	0.561451	−	0.655725i
$927$		0			0
$928$	17.8084	+	18.0308i	0.584589	+	0.591890i
$929$		−	11.8259i		−	0.387995i	−0.981002	−	0.193997i	$-0.937855\pi$
$929$		−	11.8259i		−	0.387995i	0.981002	−	0.193997i	$-0.0621453\pi$
$930$		0			0
$931$	−2.10344	+	5.07814i	−0.0689373	+	0.166429i
$932$	11.4328	+	8.34982i	0.374492	+	0.273507i
$933$		0			0
$934$	−9.05319	−	17.8225i	−0.296229	−	0.583171i
$935$	−2.71236	+	2.71236i	−0.0887038	+	0.0887038i
$936$		0			0
$937$	15.4720	+	15.4720i	0.505449	+	0.505449i	0.913126	−	0.407677i	$-0.133661\pi$
$937$	15.4720	+	15.4720i	0.505449	+	0.505449i	−0.407677	+	0.913126i	$0.633661\pi$
$938$	7.00839	−	21.4789i	0.228832	−	0.701310i
$939$		0			0
$940$	8.16748	−	4.97719i	0.266394	−	0.162338i
$941$	17.7076	+	7.33471i	0.577250	+	0.239105i	0.652155	−	0.758086i	$-0.273865\pi$
$941$	17.7076	+	7.33471i	0.577250	+	0.239105i	−0.0749046	+	0.997191i	$0.523865\pi$
$942$		0			0
$943$	1.99474			0.0649575
$944$	31.6772	+	37.4643i	1.03101	+	1.21936i
$945$		0			0
$946$	−21.2927	+	1.64918i	−0.692284	+	0.0536195i
$947$	10.6783	−	25.7798i	0.347000	−	0.837731i	−0.649972	−	0.759959i	$-0.725219\pi$
$947$	10.6783	−	25.7798i	0.347000	−	0.837731i	0.996971	−	0.0777726i	$-0.0247808\pi$
$948$		0			0
$949$	−9.32573	+	3.86285i	−0.302726	+	0.125393i
$950$	−0.300053	+	0.919583i	−0.00973500	+	0.0298352i
$951$		0			0
$952$	−0.606095	−	2.56663i	−0.0196437	−	0.0831849i
$953$	−8.95317	−	8.95317i	−0.290022	−	0.290022i	0.547067	−	0.837089i	$-0.315744\pi$
$953$	−8.95317	−	8.95317i	−0.290022	−	0.290022i	−0.837089	+	0.547067i	$0.815744\pi$
$954$		0			0
$955$	−5.30102	+	2.19575i	−0.171537	+	0.0710530i
$956$	−0.520769	+	0.0811572i	−0.0168429	+	0.00262481i
$957$		0			0
$958$	−17.5449	+	20.4909i	−0.566850	+	0.662031i
$959$	−17.1955			−0.555271
$960$		0			0
$961$	28.0940			0.906257
$962$	16.5931	−	19.3792i	0.534982	−	0.624811i
$963$		0			0
$964$	−49.7042	+	7.74595i	−1.60086	+	0.249480i
$965$	13.9456	−	5.77645i	0.448924	−	0.185950i
$966$		0			0
$967$	−20.3800	−	20.3800i	−0.655375	−	0.655375i	0.298907	−	0.954282i	$-0.403378\pi$
$967$	−20.3800	−	20.3800i	−0.655375	−	0.655375i	−0.954282	+	0.298907i	$0.903378\pi$
$968$	−13.0886	+	3.09079i	−0.420683	+	0.0993418i
$969$		0			0
$970$	−4.22693	+	12.9544i	−0.135719	+	0.415942i
$971$	40.1216	−	16.6189i	1.28756	−	0.533326i	0.369304	−	0.929309i	$-0.379596\pi$
$971$	40.1216	−	16.6189i	1.28756	−	0.533326i	0.918258	+	0.395983i	$0.129596\pi$
$972$		0			0
$973$	−5.74026	+	13.8582i	−0.184024	+	0.444274i
$974$	−0.158968	+	0.0123126i	−0.00509368	+	0.000394521i
$975$		0			0
$976$	40.1892	+	3.36379i	1.28643	+	0.107672i
$977$	−47.2334			−1.51113			−0.755564	−	0.655074i	$-0.772637\pi$
$977$	−47.2334			−1.51113			−0.755564	+	0.655074i	$0.772637\pi$
$978$		0			0
$979$	17.0691	+	7.07025i	0.545531	+	0.225966i
$980$	19.1966	−	11.6982i	0.613212	−	0.373686i
$981$		0			0
$982$	−1.21218	+	3.71501i	−0.0386822	+	0.118551i
$983$	2.15099	+	2.15099i	0.0686059	+	0.0686059i	0.740577	−	0.671971i	$-0.234552\pi$
$983$	2.15099	+	2.15099i	0.0686059	+	0.0686059i	−0.671971	+	0.740577i	$0.734552\pi$
$984$		0			0
$985$	−13.9421	+	13.9421i	−0.444231	+	0.444231i
$986$	2.11710	+	4.16783i	0.0674223	+	0.132731i
$987$		0			0
$988$	4.32206	+	3.15658i	0.137503	+	0.100424i
$989$	−6.67040	+	16.1038i	−0.212106	+	0.512070i
$990$		0			0
$991$			2.97265i			0.0944293i	0.998885	+	0.0472147i	$0.0150345\pi$
$991$			2.97265i			0.0944293i	−0.998885	+	0.0472147i	$0.984966\pi$
$992$	8.88615	+	3.74553i	0.282135	+	0.118921i
$993$		0			0
$994$	−11.5481	+	13.4871i	−0.366282	+	0.427785i
$995$	−0.994893	−	0.412098i	−0.0315402	−	0.0130644i
$996$		0			0
$997$	16.5018	+	39.8388i	0.522617	+	1.26171i	0.936272	+	0.351275i	$0.114252\pi$
$997$	16.5018	+	39.8388i	0.522617	+	1.26171i	−0.413655	+	0.910434i	$0.635748\pi$
$998$	−14.6588	+	7.44611i	−0.464015	+	0.235703i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.w.b.323.9	yes	128
3.2	odd	2	inner	864.2.w.b.323.24	yes	128
32.11	odd	8	inner	864.2.w.b.107.24	yes	128
96.11	even	8	inner	864.2.w.b.107.9	✓	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
864.2.w.b.107.9	✓	128	96.11	even	8	inner
864.2.w.b.107.24	yes	128	32.11	odd	8	inner
864.2.w.b.323.9	yes	128	1.1	even	1	trivial
864.2.w.b.323.24	yes	128	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 864 = 2^{5} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	864.w (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.919792 + 1.07424i) q^{2} +(-0.307965 - 1.97615i) q^{4} +(-1.92195 + 0.796096i) q^{5} +(0.893559 + 0.893559i) q^{7} +(2.40611 + 1.48682i) q^{8} +O(q^{10})\)	\(q+(-0.919792 + 1.07424i) q^{2} +(-0.307965 - 1.97615i) q^{4} +(-1.92195 + 0.796096i) q^{5} +(0.893559 + 0.893559i) q^{7} +(2.40611 + 1.48682i) q^{8} +(0.912596 - 2.79687i) q^{10} +(-2.30882 + 0.956343i) q^{11} +(1.00666 - 2.43029i) q^{13} +(-1.78178 + 0.138004i) q^{14} +(-3.81032 + 1.21717i) q^{16} -0.737842 q^{17} +(-0.939857 - 0.389301i) q^{19} +(2.16509 + 3.55288i) q^{20} +(1.09629 - 3.35985i) q^{22} +(-2.03966 - 2.03966i) q^{23} +(-0.475427 + 0.475427i) q^{25} +(1.68479 + 3.31675i) q^{26} +(1.49062 - 2.04099i) q^{28} +(-1.71442 + 4.13897i) q^{29} +1.70471i q^{31} +(2.19717 - 5.21272i) q^{32} +(0.678661 - 0.792616i) q^{34} +(-2.42873 - 1.00601i) q^{35} +(-2.62443 - 6.33592i) q^{37} +(1.28267 - 0.651551i) q^{38} +(-5.80807 - 0.942088i) q^{40} +(-0.488988 + 0.488988i) q^{41} +(-2.31249 - 5.58284i) q^{43} +(2.60091 + 4.26804i) q^{44} +(4.06714 - 0.315012i) q^{46} -2.29883i q^{47} -5.40310i q^{49} +(-0.0734267 - 0.948015i) q^{50} +(-5.11262 - 1.24086i) q^{52} +(-4.28534 - 10.3457i) q^{53} +(3.67608 - 3.67608i) q^{55} +(0.821443 + 3.47856i) q^{56} +(-2.86932 - 5.64868i) q^{58} +(-4.69375 - 11.3317i) q^{59} +(-9.31495 - 3.85838i) q^{61} +(-1.83126 - 1.56797i) q^{62} +(3.57875 + 7.15490i) q^{64} +5.47228i q^{65} +(-4.83801 + 11.6800i) q^{67} +(0.227229 + 1.45808i) q^{68} +(3.31462 - 1.68371i) q^{70} +(7.02532 - 7.02532i) q^{71} +(-2.71338 - 2.71338i) q^{73} +(9.22020 + 3.00848i) q^{74} +(-0.479874 + 1.97719i) q^{76} +(-2.91761 - 1.20851i) q^{77} +1.95835 q^{79} +(6.35424 - 5.37271i) q^{80} +(-0.0755210 - 0.975055i) q^{82} +(-3.06174 + 7.39169i) q^{83} +(1.41809 - 0.587393i) q^{85} +(8.12429 + 2.65089i) q^{86} +(-6.97717 - 1.13172i) q^{88} +(-5.22765 - 5.22765i) q^{89} +(3.07111 - 1.27210i) q^{91} +(-3.40252 + 4.65881i) q^{92} +(2.46949 + 2.11445i) q^{94} +2.11627 q^{95} -4.63177 q^{97} +(5.80421 + 4.96973i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q+O(q^{10}) \) 128 * q	\( 128 q + 8 q^{10} + 32 q^{16} - 32 q^{22} + 64 q^{40} + 64 q^{46} + 40 q^{52} + 64 q^{55} + 64 q^{58} + 32 q^{61} + 96 q^{64} - 64 q^{67} - 48 q^{70} - 32 q^{76} - 32 q^{79} + 40 q^{82} + 40 q^{88} - 48 q^{91} + 72 q^{94}+O(q^{100}) \) 128 * q + 8 * q^10 + 32 * q^16 - 32 * q^22 + 64 * q^40 + 64 * q^46 + 40 * q^52 + 64 * q^55 + 64 * q^58 + 32 * q^61 + 96 * q^64 - 64 * q^67 - 48 * q^70 - 32 * q^76 - 32 * q^79 + 40 * q^82 + 40 * q^88 - 48 * q^91 + 72 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more