LMFDB - Embedded newform 896.2.bh.a.81.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [896,2,Mod(81,896)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(896, base_ring=CyclotomicField(24))

chi = DirichletCharacter(H, H._module([0, 9, 16]))

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

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

chi := DirichletCharacter("896.81");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 896 = 2^{7} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	896.bh (of order $24$, 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:	$7.15459602111$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$30$ over $\Q(\zeta_{24})$
Twist minimal:	no (minimal twist has level 224)
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			81.20
Character	$\chi$	$=$	896.81
Dual form			896.2.bh.a.177.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.11575 - 0.856146i) q^{3} +(0.209020 - 0.272400i) q^{5} +(-1.04743 + 2.42958i) q^{7} +(-0.264542 + 0.987286i) q^{9} +O(q^{10})$	\(q+(1.11575 - 0.856146i) q^{3} +(0.209020 - 0.272400i) q^{5} +(-1.04743 + 2.42958i) q^{7} +(-0.264542 + 0.987286i) q^{9} +(-0.603027 + 4.58045i) q^{11} +(0.512123 - 1.23638i) q^{13} -0.482883i q^{15} +(6.17490 + 3.56508i) q^{17} +(-6.91367 + 0.910201i) q^{19} +(0.911403 + 3.60757i) q^{21} +(1.26848 - 4.73403i) q^{23} +(1.26358 + 4.71575i) q^{25} +(2.16468 + 5.22601i) q^{27} +(-2.69409 - 1.11593i) q^{29} +(-4.81036 + 8.33178i) q^{31} +(3.24870 + 5.62692i) q^{33} +(0.442885 + 0.793153i) q^{35} +(4.98877 - 6.50149i) q^{37} +(-0.487115 - 1.81794i) q^{39} +(-0.781419 - 0.781419i) q^{41} +(8.76180 - 3.62926i) q^{43} +(0.213642 + 0.278424i) q^{45} +(3.11860 - 1.80052i) q^{47} +(-4.80576 - 5.08966i) q^{49} +(9.94188 - 1.30887i) q^{51} +(0.408274 - 3.10115i) q^{53} +(1.12167 + 1.12167i) q^{55} +(-6.93466 + 6.93466i) q^{57} +(-0.303606 - 0.0399704i) q^{59} +(0.639509 + 4.85755i) q^{61} +(-2.12160 - 1.67685i) q^{63} +(-0.229745 - 0.397930i) q^{65} +(6.53355 - 5.01337i) q^{67} +(-2.63771 - 6.36800i) q^{69} +(-6.89237 + 6.89237i) q^{71} +(5.67527 - 1.52068i) q^{73} +(5.44722 + 4.17980i) q^{75} +(-10.4970 - 6.26282i) q^{77} +(6.48602 - 3.74471i) q^{79} +(4.23395 + 2.44447i) q^{81} +(1.84563 - 4.45575i) q^{83} +(2.26181 - 0.936871i) q^{85} +(-3.96134 + 1.06144i) q^{87} +(-4.55360 - 1.22013i) q^{89} +(2.46746 + 2.53927i) q^{91} +(1.76606 + 13.4146i) q^{93} +(-1.19716 + 2.07353i) q^{95} -3.11863 q^{97} +(-4.36268 - 1.80708i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 4 q^{3} - 4 q^{5} + 8 q^{7} - 4 q^{9}+O(q^{10}) $ 240 * q + 4 * q^3 - 4 * q^5 + 8 * q^7 - 4 * q^9	$ 240 q + 4 q^{3} - 4 q^{5} + 8 q^{7} - 4 q^{9} + 4 q^{11} - 16 q^{13} + 4 q^{19} - 8 q^{21} + 12 q^{23} - 4 q^{25} + 16 q^{27} - 16 q^{29} + 56 q^{31} - 8 q^{33} + 32 q^{35} - 4 q^{37} + 4 q^{39} - 16 q^{41} + 8 q^{45} + 28 q^{51} - 20 q^{53} + 16 q^{55} - 16 q^{57} + 36 q^{59} - 4 q^{61} + 16 q^{63} - 8 q^{65} - 36 q^{67} - 16 q^{69} - 48 q^{71} - 4 q^{73} - 16 q^{75} - 8 q^{77} + 96 q^{83} - 56 q^{85} + 4 q^{87} - 4 q^{89} + 56 q^{91} + 20 q^{93} + 8 q^{95} - 32 q^{97} - 8 q^{99}+O(q^{100}) $ 240 * q + 4 * q^3 - 4 * q^5 + 8 * q^7 - 4 * q^9 + 4 * q^11 - 16 * q^13 + 4 * q^19 - 8 * q^21 + 12 * q^23 - 4 * q^25 + 16 * q^27 - 16 * q^29 + 56 * q^31 - 8 * q^33 + 32 * q^35 - 4 * q^37 + 4 * q^39 - 16 * q^41 + 8 * q^45 + 28 * q^51 - 20 * q^53 + 16 * q^55 - 16 * q^57 + 36 * q^59 - 4 * q^61 + 16 * q^63 - 8 * q^65 - 36 * q^67 - 16 * q^69 - 48 * q^71 - 4 * q^73 - 16 * q^75 - 8 * q^77 + 96 * q^83 - 56 * q^85 + 4 * q^87 - 4 * q^89 + 56 * q^91 + 20 * q^93 + 8 * q^95 - 32 * q^97 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/896\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$645$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{3}{8}\right)$

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
$3$	1.11575	−	0.856146i	0.644179	−	0.494296i	−0.234245	−	0.972178i	$-0.575262\pi$
$3$	1.11575	−	0.856146i	0.644179	−	0.494296i	0.878424	+	0.477881i	$0.158595\pi$
$4$		0			0
$5$	0.209020	−	0.272400i	0.0934766	−	0.121821i	−0.744273	−	0.667875i	$-0.767204\pi$
$5$	0.209020	−	0.272400i	0.0934766	−	0.121821i	0.837750	+	0.546054i	$0.183871\pi$
$6$		0			0
$7$	−1.04743	+	2.42958i	−0.395893	+	0.918297i
$7$	−1.04743	+	2.42958i	−0.395893	+	0.918297i
$8$		0			0
$9$	−0.264542	+	0.987286i	−0.0881808	+	0.329095i
$10$		0			0
$11$	−0.603027	+	4.58045i	−0.181820	+	1.38106i	0.620521	+	0.784190i	$0.286921\pi$
$11$	−0.603027	+	4.58045i	−0.181820	+	1.38106i	−0.802340	+	0.596867i	$0.796412\pi$
$12$		0			0
$13$	0.512123	−	1.23638i	0.142037	−	0.342909i	−0.836812	−	0.547490i	$-0.815583\pi$
$13$	0.512123	−	1.23638i	0.142037	−	0.342909i	0.978850	+	0.204581i	$0.0655833\pi$
$14$		0			0
$15$		−	0.482883i		−	0.124680i
$16$		0			0
$17$	6.17490	+	3.56508i	1.49763	+	0.864659i	0.999996	−	0.00272606i	$-0.000867734\pi$
$17$	6.17490	+	3.56508i	1.49763	+	0.864659i	0.497637	+	0.867385i	$0.334201\pi$
$18$		0			0
$19$	−6.91367	+	0.910201i	−1.58610	+	0.208815i	−0.871386	−	0.490598i	$-0.836778\pi$
$19$	−6.91367	+	0.910201i	−1.58610	+	0.208815i	−0.714718	+	0.699413i	$0.753445\pi$
$20$		0			0
$21$	0.911403	+	3.60757i	0.198884	+	0.787236i
$22$		0			0
$23$	1.26848	−	4.73403i	0.264496	−	0.987113i	−0.698062	−	0.716038i	$-0.745954\pi$
$23$	1.26848	−	4.73403i	0.264496	−	0.987113i	0.962558	−	0.271076i	$-0.0873794\pi$
$24$		0			0
$25$	1.26358	+	4.71575i	0.252717	+	0.943151i
$26$		0			0
$27$	2.16468	+	5.22601i	0.416594	+	1.00575i
$28$		0			0
$29$	−2.69409	−	1.11593i	−0.500281	−	0.207223i	0.118250	−	0.992984i	$-0.462272\pi$
$29$	−2.69409	−	1.11593i	−0.500281	−	0.207223i	−0.618530	+	0.785761i	$0.712272\pi$
$30$		0			0
$31$	−4.81036	+	8.33178i	−0.863966	+	1.49643i	0.00410494	+	0.999992i	$0.498693\pi$
$31$	−4.81036	+	8.33178i	−0.863966	+	1.49643i	−0.868071	+	0.496441i	$0.834640\pi$
$32$		0			0
$33$	3.24870	+	5.62692i	0.565527	+	0.979521i
$34$		0			0
$35$	0.442885	+	0.793153i	0.0748612	+	0.134067i
$36$		0			0
$37$	4.98877	−	6.50149i	0.820148	−	1.06884i	−0.176276	−	0.984341i	$-0.556405\pi$
$37$	4.98877	−	6.50149i	0.820148	−	1.06884i	0.996424	−	0.0844969i	$-0.0269283\pi$
$38$		0			0
$39$	−0.487115	−	1.81794i	−0.0780009	−	0.291103i
$40$		0			0
$41$	−0.781419	−	0.781419i	−0.122037	−	0.122037i	0.643451	−	0.765488i	$-0.277502\pi$
$41$	−0.781419	−	0.781419i	−0.122037	−	0.122037i	−0.765488	+	0.643451i	$0.777502\pi$
$42$		0			0
$43$	8.76180	−	3.62926i	1.33616	−	0.553457i	0.403756	−	0.914867i	$-0.367705\pi$
$43$	8.76180	−	3.62926i	1.33616	−	0.553457i	0.932407	+	0.361410i	$0.117705\pi$
$44$		0			0
$45$	0.213642	+	0.278424i	0.0318479	+	0.0415050i
$46$		0			0
$47$	3.11860	−	1.80052i	0.454895	−	0.262634i	−0.255000	−	0.966941i	$-0.582076\pi$
$47$	3.11860	−	1.80052i	0.454895	−	0.262634i	0.709895	+	0.704307i	$0.248742\pi$
$48$		0			0
$49$	−4.80576	−	5.08966i	−0.686538	−	0.727094i
$50$		0			0
$51$	9.94188	−	1.30887i	1.39214	−	0.183279i
$52$		0			0
$53$	0.408274	−	3.10115i	0.0560807	−	0.425975i	−0.940257	−	0.340466i	$-0.889415\pi$
$53$	0.408274	−	3.10115i	0.0560807	−	0.425975i	0.996337	−	0.0855089i	$-0.0272516\pi$
$54$		0			0
$55$	1.12167	+	1.12167i	0.151246	+	0.151246i
$56$		0			0
$57$	−6.93466	+	6.93466i	−0.918519	+	0.918519i
$58$		0			0
$59$	−0.303606	−	0.0399704i	−0.0395261	−	0.00520371i	0.110737	−	0.993850i	$-0.464679\pi$
$59$	−0.303606	−	0.0399704i	−0.0395261	−	0.00520371i	−0.150263	+	0.988646i	$0.548012\pi$
$60$		0			0
$61$	0.639509	+	4.85755i	0.0818807	+	0.621946i	0.982354	+	0.187034i	$0.0598873\pi$
$61$	0.639509	+	4.85755i	0.0818807	+	0.621946i	−0.900473	+	0.434912i	$0.856779\pi$
$62$		0			0
$63$	−2.12160	−	1.67685i	−0.267297	−	0.211263i
$64$		0			0
$65$	−0.229745	−	0.397930i	−0.0284963	−	0.0493571i
$66$		0			0
$67$	6.53355	−	5.01337i	0.798200	−	0.612481i	−0.127025	−	0.991900i	$-0.540543\pi$
$67$	6.53355	−	5.01337i	0.798200	−	0.612481i	0.925225	+	0.379419i	$0.123876\pi$
$68$		0			0
$69$	−2.63771	−	6.36800i	−0.317543	−	0.766617i
$70$		0			0
$71$	−6.89237	+	6.89237i	−0.817974	+	0.817974i	−0.985814	−	0.167840i	$-0.946321\pi$
$71$	−6.89237	+	6.89237i	−0.817974	+	0.817974i	0.167840	+	0.985814i	$0.446321\pi$
$72$		0			0
$73$	5.67527	−	1.52068i	0.664240	−	0.177983i	0.0890811	−	0.996024i	$-0.471607\pi$
$73$	5.67527	−	1.52068i	0.664240	−	0.177983i	0.575159	+	0.818042i	$0.304940\pi$
$74$		0			0
$75$	5.44722	+	4.17980i	0.628991	+	0.482641i
$76$		0			0
$77$	−10.4970	−	6.26282i	−1.19624	−	0.713715i
$78$		0			0
$79$	6.48602	−	3.74471i	0.729734	−	0.421312i	−0.0885907	−	0.996068i	$-0.528236\pi$
$79$	6.48602	−	3.74471i	0.729734	−	0.421312i	0.818325	+	0.574756i	$0.194903\pi$
$80$		0			0
$81$	4.23395	+	2.44447i	0.470439	+	0.271608i
$82$		0			0
$83$	1.84563	−	4.45575i	0.202585	−	0.489082i	−0.789636	−	0.613576i	$-0.789731\pi$
$83$	1.84563	−	4.45575i	0.202585	−	0.489082i	0.992220	+	0.124493i	$0.0397306\pi$
$84$		0			0
$85$	2.26181	−	0.936871i	0.245327	−	0.101618i
$86$		0			0
$87$	−3.96134	+	1.06144i	−0.424700	+	0.113798i
$88$		0			0
$89$	−4.55360	−	1.22013i	−0.482680	−	0.129334i	0.00927015	−	0.999957i	$-0.497049\pi$
$89$	−4.55360	−	1.22013i	−0.482680	−	0.129334i	−0.491950	+	0.870623i	$0.663716\pi$
$90$		0			0
$91$	2.46746	+	2.53927i	0.258660	+	0.266188i
$92$		0			0
$93$	1.76606	+	13.4146i	0.183132	+	1.39103i
$94$		0			0
$95$	−1.19716	+	2.07353i	−0.122826	+	0.212740i
$96$		0			0
$97$	−3.11863			−0.316649			−0.158324	−	0.987387i	$-0.550609\pi$
$97$	−3.11863			−0.316649			−0.158324	+	0.987387i	$0.550609\pi$
$98$		0			0
$99$	−4.36268	−	1.80708i	−0.438466	−	0.181619i
$100$		0			0
$101$	1.09466	+	0.144115i	0.108923	+	0.0143400i	0.184790	−	0.982778i	$-0.440839\pi$
$101$	1.09466	+	0.144115i	0.108923	+	0.0143400i	−0.0758677	+	0.997118i	$0.524173\pi$
$102$		0			0
$103$	−6.04019	−	1.61846i	−0.595157	−	0.159472i	−0.0513481	−	0.998681i	$-0.516352\pi$
$103$	−6.04019	−	1.61846i	−0.595157	−	0.159472i	−0.543809	+	0.839209i	$0.683018\pi$
$104$		0			0
$105$	1.17320	+	0.505788i	0.114493	+	0.0493598i
$106$		0			0
$107$	2.61917	+	2.00976i	0.253205	+	0.194291i	0.727563	−	0.686041i	$-0.240653\pi$
$107$	2.61917	+	2.00976i	0.253205	+	0.194291i	−0.474358	+	0.880332i	$0.657320\pi$
$108$		0			0
$109$	0.942092	+	1.22776i	0.0902360	+	0.117598i	0.836289	−	0.548288i	$-0.184720\pi$
$109$	0.942092	+	1.22776i	0.0902360	+	0.117598i	−0.746053	+	0.665886i	$0.768054\pi$
$110$		0			0
$111$		−	11.5252i		−	1.09392i
$112$		0			0
$113$			14.9682i			1.40809i	0.710156	+	0.704044i	$0.248624\pi$
$113$			14.9682i			1.40809i	−0.710156	+	0.704044i	$0.751376\pi$
$114$		0			0
$115$	−1.02441	−	1.33504i	−0.0955270	−	0.124493i
$116$		0			0
$117$	1.08518	+	0.832686i	0.100325	+	0.0769818i
$118$		0			0
$119$	−15.1295	+	11.2683i	−1.38692	+	1.03296i
$120$		0			0
$121$	−9.99166	−	2.67726i	−0.908333	−	0.243387i
$122$		0			0
$123$	−1.54088	−	0.202860i	−0.138936	−	0.0182913i
$124$		0			0
$125$	3.13477	+	1.29846i	0.280382	+	0.116138i
$126$		0			0
$127$	2.95339			0.262071			0.131036	−	0.991378i	$-0.458170\pi$
$127$	2.95339			0.262071			0.131036	+	0.991378i	$0.458170\pi$
$128$		0			0
$129$	6.66882	−	11.5507i	0.587157	−	1.01699i
$130$		0			0
$131$	−0.520644	−	3.95468i	−0.0454888	−	0.345522i	−0.999021	−	0.0442318i	$-0.985916\pi$
$131$	−0.520644	−	3.95468i	−0.0454888	−	0.345522i	0.953532	−	0.301290i	$-0.0974173\pi$
$132$		0			0
$133$	5.03020	−	17.7507i	0.436174	−	1.53918i
$134$		0			0
$135$	1.87603	+	0.502681i	0.161463	+	0.0432639i
$136$		0			0
$137$	−9.65652	+	2.58746i	−0.825012	+	0.221061i	−0.646537	−	0.762883i	$-0.723783\pi$
$137$	−9.65652	+	2.58746i	−0.825012	+	0.221061i	−0.178476	+	0.983944i	$0.557117\pi$
$138$		0			0
$139$	2.62716	−	1.08821i	0.222833	−	0.0923005i	−0.268474	−	0.963287i	$-0.586519\pi$
$139$	2.62716	−	1.08821i	0.222833	−	0.0923005i	0.491307	+	0.870986i	$0.336519\pi$
$140$		0			0
$141$	1.93807	−	4.67892i	0.163215	−	0.394036i
$142$		0			0
$143$	5.35433	+	3.09132i	0.447751	+	0.258509i
$144$		0			0
$145$	−0.867099	+	0.500620i	−0.0720087	+	0.0415742i
$146$		0			0
$147$	−9.71953	−	1.56436i	−0.801653	−	0.129026i
$148$		0			0
$149$	−6.52564	−	5.00730i	−0.534601	−	0.410214i	0.305868	−	0.952074i	$-0.401054\pi$
$149$	−6.52564	−	5.00730i	−0.534601	−	0.410214i	−0.840469	+	0.541860i	$0.817720\pi$
$150$		0			0
$151$	11.3930	−	3.05275i	0.927150	−	0.248429i	0.236511	−	0.971629i	$-0.423996\pi$
$151$	11.3930	−	3.05275i	0.927150	−	0.248429i	0.690639	+	0.723200i	$0.257329\pi$
$152$		0			0
$153$	−5.15328	+	5.15328i	−0.416618	+	0.416618i
$154$		0			0
$155$	1.26412	+	3.05185i	0.101536	+	0.245131i
$156$		0			0
$157$	4.20045	−	3.22312i	0.335232	−	0.257233i	−0.427403	−	0.904061i	$-0.640572\pi$
$157$	4.20045	−	3.22312i	0.335232	−	0.257233i	0.762636	+	0.646828i	$0.223905\pi$
$158$		0			0
$159$	−2.19950	−	3.80965i	−0.174432	−	0.302125i
$160$		0			0
$161$	10.1731	+	8.04046i	0.801751	+	0.633677i
$162$		0			0
$163$	−3.06599	−	23.2885i	−0.240147	−	1.82410i	−0.508830	−	0.860867i	$-0.669922\pi$
$163$	−3.06599	−	23.2885i	−0.240147	−	1.82410i	0.268683	−	0.963229i	$-0.413412\pi$
$164$		0			0
$165$	2.21182	+	0.291191i	0.172190	+	0.0226692i
$166$		0			0
$167$	−8.79409	+	8.79409i	−0.680507	+	0.680507i	−0.960114	−	0.279607i	$-0.909796\pi$
$167$	−8.79409	+	8.79409i	−0.680507	+	0.680507i	0.279607	+	0.960114i	$0.409796\pi$
$168$		0			0
$169$	7.92603	+	7.92603i	0.609695	+	0.609695i
$170$		0			0
$171$	0.930329	−	7.06655i	0.0711440	−	0.540393i
$172$		0			0
$173$	−18.8057	+	2.47581i	−1.42977	+	0.188232i	−0.805323	−	0.592837i	$-0.798008\pi$
$173$	−18.8057	+	2.47581i	−1.42977	+	0.188232i	−0.624444	+	0.781069i	$0.714675\pi$
$174$		0			0
$175$	−12.7808	−	1.86946i	−0.966141	−	0.141318i
$176$		0			0
$177$	−0.372969	+	0.215334i	−0.0280341	+	0.0161855i
$178$		0			0
$179$	9.15999	+	11.9375i	0.684650	+	0.892253i	0.998359	−	0.0572661i	$-0.0182383\pi$
$179$	9.15999	+	11.9375i	0.684650	+	0.892253i	−0.313709	+	0.949519i	$0.601572\pi$
$180$		0			0
$181$	12.4039	−	5.13787i	0.921976	−	0.381895i	0.129347	−	0.991599i	$-0.458712\pi$
$181$	12.4039	−	5.13787i	0.921976	−	0.381895i	0.792629	+	0.609704i	$0.208712\pi$
$182$		0			0
$183$	4.87231	+	4.87231i	0.360171	+	0.360171i
$184$		0			0
$185$	−0.728254	−	2.71788i	−0.0535423	−	0.199823i
$186$		0			0
$187$	−20.0533	+	26.1340i	−1.46644	+	1.91110i
$188$		0			0
$189$	−14.9644	−	0.214618i	−1.08850	−	0.0156112i
$190$		0			0
$191$	−0.317769	−	0.550392i	−0.0229930	−	0.0398250i	0.854300	−	0.519780i	$-0.173986\pi$
$191$	−0.317769	−	0.550392i	−0.0229930	−	0.0398250i	−0.877293	+	0.479955i	$0.840653\pi$
$192$		0			0
$193$	−7.23923	+	12.5387i	−0.521091	+	0.902556i	0.478608	+	0.878029i	$0.341142\pi$
$193$	−7.23923	+	12.5387i	−0.521091	+	0.902556i	−0.999699	+	0.0245276i	$0.992192\pi$
$194$		0			0
$195$	−0.597024	−	0.247295i	−0.0427538	−	0.0177092i
$196$		0			0
$197$	−0.824258	−	1.98994i	−0.0587260	−	0.141777i	0.891793	−	0.452444i	$-0.149448\pi$
$197$	−0.824258	−	1.98994i	−0.0587260	−	0.141777i	−0.950519	+	0.310667i	$0.899448\pi$
$198$		0			0
$199$	−6.90967	−	25.7872i	−0.489814	−	1.82801i	−0.557330	−	0.830291i	$-0.688174\pi$
$199$	−6.90967	−	25.7872i	−0.489814	−	1.82801i	0.0675163	−	0.997718i	$-0.478493\pi$
$200$		0			0
$201$	2.99764	−	11.1873i	0.211437	−	0.789095i
$202$		0			0
$203$	5.53313	−	5.37666i	0.388350	−	0.377368i
$204$		0			0
$205$	−0.376191	+	0.0495265i	−0.0262743	+	0.00345908i
$206$		0			0
$207$	4.33827	+	2.50470i	0.301531	+	0.174089i
$208$		0			0
$209$		−	32.2166i		−	2.22847i
$210$		0			0
$211$	5.53193	−	13.3553i	0.380834	−	0.919414i	−0.610971	−	0.791653i	$-0.709221\pi$
$211$	5.53193	−	13.3553i	0.380834	−	0.919414i	0.991805	−	0.127761i	$-0.0407792\pi$
$212$		0			0
$213$	−1.78929	+	13.5910i	−0.122600	+	0.931243i
$214$		0			0
$215$	0.842782	−	3.14531i	0.0574773	−	0.214508i
$216$		0			0
$217$	−15.2042	−	20.4142i	−1.03213	−	1.38580i
$218$		0			0
$219$	5.03026	−	6.55556i	0.339913	−	0.442984i
$220$		0			0
$221$	7.57009	−	5.80873i	0.509219	−	0.390738i
$222$		0			0
$223$	14.1052			0.944555			0.472277	−	0.881450i	$-0.343432\pi$
$223$	14.1052			0.944555			0.472277	+	0.881450i	$0.343432\pi$
$224$		0			0
$225$	−4.99007			−0.332671
$226$		0			0
$227$	0.338923	−	0.260065i	0.0224951	−	0.0172611i	−0.597453	−	0.801904i	$-0.703820\pi$
$227$	0.338923	−	0.260065i	0.0224951	−	0.0172611i	0.619948	+	0.784643i	$0.287154\pi$
$228$		0			0
$229$	−12.1858	+	15.8808i	−0.805258	+	1.04943i	0.192419	+	0.981313i	$0.438367\pi$
$229$	−12.1858	+	15.8808i	−0.805258	+	1.04943i	−0.997677	+	0.0681200i	$0.978300\pi$
$230$		0			0
$231$	−17.0739	+	1.99917i	−1.12338	+	0.131536i
$232$		0			0
$233$	6.82750	−	25.4806i	0.447284	−	1.66929i	−0.262550	−	0.964918i	$-0.584563\pi$
$233$	6.82750	−	25.4806i	0.447284	−	1.66929i	0.709834	−	0.704369i	$-0.248770\pi$
$234$		0			0
$235$	0.161387	−	1.22585i	0.0105277	−	0.0799659i
$236$		0			0
$237$	4.03077	−	9.73114i	0.261827	−	0.632105i
$238$		0			0
$239$			3.92821i			0.254095i	0.991897	+	0.127047i	$0.0405500\pi$
$239$			3.92821i			0.254095i	−0.991897	+	0.127047i	$0.959450\pi$
$240$		0			0
$241$	1.21964	+	0.704160i	0.0785640	+	0.0453590i	0.538767	−	0.842455i	$-0.318890\pi$
$241$	1.21964	+	0.704160i	0.0785640	+	0.0453590i	−0.460203	+	0.887814i	$0.652224\pi$
$242$		0			0
$243$	−10.0077	+	1.31754i	−0.641997	+	0.0845205i
$244$		0			0
$245$	−2.39093	+	0.245250i	−0.152751	+	0.0156684i
$246$		0			0
$247$	−2.41530	+	9.01402i	−0.153682	+	0.573548i
$248$		0			0
$249$	−1.75551	−	6.55164i	−0.111251	−	0.415193i
$250$		0			0
$251$	−7.04925	−	17.0184i	−0.444944	−	1.07419i	−0.974191	−	0.225723i	$-0.927526\pi$
$251$	−7.04925	−	17.0184i	−0.444944	−	1.07419i	0.529247	−	0.848468i	$-0.322474\pi$
$252$		0			0
$253$	20.9190	+	8.66495i	1.31517	+	0.544761i
$254$		0			0
$255$	1.72152	−	2.98175i	0.107805	−	0.186725i
$256$		0			0
$257$	3.48995	+	6.04477i	0.217697	+	0.377062i	0.954103	−	0.299477i	$-0.0968122\pi$
$257$	3.48995	+	6.04477i	0.217697	+	0.377062i	−0.736407	+	0.676539i	$0.763479\pi$
$258$		0			0
$259$	10.5705	+	18.9305i	0.656819	+	1.17628i
$260$		0			0
$261$	1.81444	−	2.36463i	0.112311	−	0.146367i
$262$		0			0
$263$	−0.143989	−	0.537374i	−0.00887873	−	0.0331359i	0.961344	−	0.275349i	$-0.0887934\pi$
$263$	−0.143989	−	0.537374i	−0.00887873	−	0.0331359i	−0.970223	+	0.242213i	$0.922127\pi$
$264$		0			0
$265$	−0.759416	−	0.759416i	−0.0466505	−	0.0466505i
$266$		0			0
$267$	−6.12529	+	2.53718i	−0.374862	+	0.155273i
$268$		0			0
$269$	12.3712	+	16.1225i	0.754285	+	0.983003i	0.999907	+	0.0136376i	$0.00434113\pi$
$269$	12.3712	+	16.1225i	0.754285	+	0.983003i	−0.245622	+	0.969366i	$0.578992\pi$
$270$		0			0
$271$	16.4158	−	9.47769i	0.997191	−	0.575729i	0.0897752	−	0.995962i	$-0.471385\pi$
$271$	16.4158	−	9.47769i	0.997191	−	0.575729i	0.907416	+	0.420233i	$0.138052\pi$
$272$		0			0
$273$	4.92706	+	0.720684i	0.298199	+	0.0436178i
$274$		0			0
$275$	−22.3622	+	2.94404i	−1.34849	+	0.177533i
$276$		0			0
$277$	2.49116	−	18.9222i	0.149679	−	1.13693i	−0.737449	−	0.675403i	$-0.763970\pi$
$277$	2.49116	−	18.9222i	0.149679	−	1.13693i	0.887128	−	0.461524i	$-0.152697\pi$
$278$		0			0
$279$	−6.95331	−	6.95331i	−0.416284	−	0.416284i
$280$		0			0
$281$	9.35935	−	9.35935i	0.558332	−	0.558332i	−0.370500	−	0.928832i	$-0.620814\pi$
$281$	9.35935	−	9.35935i	0.558332	−	0.558332i	0.928832	+	0.370500i	$0.120814\pi$
$282$		0			0
$283$	1.32549	+	0.174504i	0.0787921	+	0.0103732i	0.169819	−	0.985475i	$-0.445682\pi$
$283$	1.32549	+	0.174504i	0.0787921	+	0.0103732i	−0.0910271	+	0.995848i	$0.529015\pi$
$284$		0			0
$285$	0.439520	+	3.33849i	0.0260349	+	0.197755i
$286$		0			0
$287$	2.71701	−	1.08004i	0.160380	−	0.0637526i
$288$		0			0
$289$	16.9196	+	29.3056i	0.995271	+	1.72386i
$290$		0			0
$291$	−3.47961	+	2.67000i	−0.203979	+	0.156518i
$292$		0			0
$293$	−9.09096	−	21.9475i	−0.531100	−	1.28219i	−0.930795	−	0.365540i	$-0.880884\pi$
$293$	−9.09096	−	21.9475i	−0.531100	−	1.28219i	0.399696	−	0.916648i	$-0.369116\pi$
$294$		0			0
$295$	−0.0743476	+	0.0743476i	−0.00432869	+	0.00432869i
$296$		0			0
$297$	−25.2428	+	6.76380i	−1.46474	+	0.392475i
$298$		0			0
$299$	−5.20342	−	3.99272i	−0.300922	−	0.230905i
$300$		0			0
$301$	−0.359824	+	25.0890i	−0.0207399	+	1.44610i
$302$		0			0
$303$	1.34475	−	0.776393i	0.0772539	−	0.0446026i
$304$		0			0
$305$	1.45687	+	0.841124i	0.0834201	+	0.0481626i
$306$		0			0
$307$	0.389081	−	0.939324i	0.0222060	−	0.0536101i	−0.912388	−	0.409327i	$-0.865763\pi$
$307$	0.389081	−	0.939324i	0.0222060	−	0.0536101i	0.934594	+	0.355717i	$0.115763\pi$
$308$		0			0
$309$	−8.12498	+	3.36548i	−0.462214	+	0.191455i
$310$		0			0
$311$	−25.4984	+	6.83228i	−1.44588	+	0.387423i	−0.894589	−	0.446889i	$-0.852532\pi$
$311$	−25.4984	+	6.83228i	−1.44588	+	0.387423i	−0.551292	+	0.834312i	$0.685865\pi$
$312$		0			0
$313$	11.7631	+	3.15191i	0.664889	+	0.178157i	0.575451	−	0.817836i	$-0.304826\pi$
$313$	11.7631	+	3.15191i	0.664889	+	0.178157i	0.0894376	+	0.995992i	$0.471493\pi$
$314$		0			0
$315$	−0.900231	+	0.227431i	−0.0507223	+	0.0128143i
$316$		0			0
$317$	−0.624831	−	4.74606i	−0.0350940	−	0.266565i	−0.999992	−	0.00394125i	$-0.998745\pi$
$317$	−0.624831	−	4.74606i	−0.0350940	−	0.266565i	0.964898	−	0.262624i	$-0.0845879\pi$
$318$		0			0
$319$	6.73607	−	11.6672i	0.377147	−	0.653239i
$320$		0			0
$321$	4.64300			0.259147
$322$		0			0
$323$	−45.9361	−	19.0274i	−2.55596	−	1.05871i
$324$		0			0
$325$	6.47755	+	0.852786i	0.359310	+	0.0473041i
$326$		0			0
$327$	2.10228	+	0.563304i	0.116256	+	0.0311508i
$328$		0			0
$329$	1.10800	+	9.46284i	0.0610859	+	0.521703i
$330$		0			0
$331$	8.37261	+	6.42453i	0.460200	+	0.353124i	0.812695	−	0.582690i	$-0.198000\pi$
$331$	8.37261	+	6.42453i	0.460200	+	0.353124i	−0.352494	+	0.935814i	$0.614666\pi$
$332$		0			0
$333$	5.09908	+	6.64526i	0.279428	+	0.364158i
$334$		0			0
$335$		−	2.82764i		−	0.154490i
$336$		0			0
$337$		−	14.2179i		−	0.774496i	−0.921976	−	0.387248i	$-0.873426\pi$
$337$		−	14.2179i		−	0.774496i	0.921976	−	0.387248i	$-0.126574\pi$
$338$		0			0
$339$	12.8150	+	16.7008i	0.696013	+	0.907061i
$340$		0			0
$341$	−35.2625	−	27.0579i	−1.90957	−	1.46527i
$342$		0			0
$343$	17.3995	−	6.34492i	0.939484	−	0.342594i
$344$		0			0
$345$	−2.28598	−	0.612527i	−0.123073	−	0.0329773i
$346$		0			0
$347$	2.49481	+	0.328447i	0.133928	+	0.0176320i	0.197192	−	0.980365i	$-0.436818\pi$
$347$	2.49481	+	0.328447i	0.133928	+	0.0176320i	−0.0632640	+	0.997997i	$0.520151\pi$
$348$		0			0
$349$	−15.0665	−	6.24076i	−0.806493	−	0.334060i	−0.0589393	−	0.998262i	$-0.518772\pi$
$349$	−15.0665	−	6.24076i	−0.806493	−	0.334060i	−0.747554	+	0.664201i	$0.768772\pi$
$350$		0			0
$351$	7.56990			0.404051
$352$		0			0
$353$	6.52315	−	11.2984i	0.347192	−	0.601354i	−0.638557	−	0.769574i	$-0.720469\pi$
$353$	6.52315	−	11.2984i	0.347192	−	0.601354i	0.985749	+	0.168220i	$0.0538019\pi$
$354$		0			0
$355$	0.436840	+	3.31813i	0.0231850	+	0.176108i
$356$		0			0
$357$	−7.23345	+	25.5256i	−0.382835	+	1.35096i
$358$		0			0
$359$	20.8565	+	5.58848i	1.10076	+	0.294949i	0.763076	−	0.646309i	$-0.223688\pi$
$359$	20.8565	+	5.58848i	1.10076	+	0.294949i	0.337688	+	0.941258i	$0.390355\pi$
$360$		0			0
$361$	28.6177	−	7.66809i	1.50620	−	0.403584i
$362$		0			0
$363$	−13.4403	+	5.56717i	−0.705435	+	0.292201i
$364$		0			0
$365$	0.772010	−	1.86380i	0.0404089	−	0.0975556i
$366$		0			0
$367$	20.4966	+	11.8337i	1.06992	+	0.617716i	0.928158	−	0.372186i	$-0.121391\pi$
$367$	20.4966	+	11.8337i	1.06992	+	0.617716i	0.141757	+	0.989901i	$0.454725\pi$
$368$		0			0
$369$	0.978202	−	0.564765i	0.0509232	−	0.0294005i
$370$		0			0
$371$	7.10686	+	4.24018i	0.368970	+	0.220139i
$372$		0			0
$373$	20.7316	+	15.9080i	1.07344	+	0.823683i	0.985027	−	0.172401i	$-0.0551524\pi$
$373$	20.7316	+	15.9080i	1.07344	+	0.823683i	0.0884173	+	0.996084i	$0.471819\pi$
$374$		0			0
$375$	4.60930	−	1.23506i	0.238023	−	0.0637781i
$376$		0			0
$377$	−2.75942	+	2.75942i	−0.142117	+	0.142117i
$378$		0			0
$379$	2.35938	+	5.69606i	0.121193	+	0.292587i	0.972820	−	0.231562i	$-0.0743836\pi$
$379$	2.35938	+	5.69606i	0.121193	+	0.292587i	−0.851627	+	0.524149i	$0.824384\pi$
$380$		0			0
$381$	3.29525	−	2.52854i	0.168821	−	0.129541i
$382$		0			0
$383$	7.65038	+	13.2509i	0.390916	+	0.677087i	0.992571	−	0.121670i	$-0.0388248\pi$
$383$	7.65038	+	13.2509i	0.390916	+	0.677087i	−0.601654	+	0.798757i	$0.705491\pi$
$384$		0			0
$385$	−3.90007	+	1.55032i	−0.198766	+	0.0790115i
$386$		0			0
$387$	1.26525	+	9.61050i	0.0643161	+	0.488529i
$388$		0			0
$389$	19.5632	+	2.57554i	0.991892	+	0.130585i	0.608968	−	0.793195i	$-0.291584\pi$
$389$	19.5632	+	2.57554i	0.991892	+	0.130585i	0.382924	+	0.923780i	$0.374917\pi$
$390$		0			0
$391$	24.7099	−	24.7099i	1.24964	−	1.24964i
$392$		0			0
$393$	−3.96669	−	3.96669i	−0.200093	−	0.200093i
$394$		0			0
$395$	0.335650	−	2.54951i	0.0168884	−	0.128280i
$396$		0			0
$397$	−11.7666	+	1.54910i	−0.590547	+	0.0777470i	−0.419877	−	0.907581i	$-0.637927\pi$
$397$	−11.7666	+	1.54910i	−0.590547	+	0.0777470i	−0.170670	+	0.985328i	$0.554593\pi$
$398$		0			0
$399$	−9.58475	−	24.1120i	−0.479838	−	1.20711i
$400$		0			0
$401$	−14.1367	+	8.16185i	−0.705955	+	0.407583i	−0.809561	−	0.587035i	$-0.800295\pi$
$401$	−14.1367	+	8.16185i	−0.705955	+	0.407583i	0.103607	+	0.994618i	$0.466962\pi$
$402$		0			0
$403$	7.83771	+	10.2143i	0.390424	+	0.508811i
$404$		0			0
$405$	1.55086	−	0.642385i	0.0770626	−	0.0319204i
$406$		0			0
$407$	26.7713	+	26.7713i	1.32701	+	1.32701i
$408$		0			0
$409$	−1.33600	−	4.98604i	−0.0660612	−	0.246544i	0.924997	−	0.379975i	$-0.124067\pi$
$409$	−1.33600	−	4.98604i	−0.0660612	−	0.246544i	−0.991058	+	0.133431i	$0.957401\pi$
$410$		0			0
$411$	−8.55903	+	11.1544i	−0.422186	+	0.550204i
$412$		0			0
$413$	0.415119	−	0.695769i	0.0204266	−	0.0342366i
$414$		0			0
$415$	−0.827974	−	1.43409i	−0.0406436	−	0.0703968i
$416$		0			0
$417$	1.99960	−	3.46340i	0.0979207	−	0.169604i
$418$		0			0
$419$	−5.67288	−	2.34979i	−0.277138	−	0.114795i	0.239785	−	0.970826i	$-0.422923\pi$
$419$	−5.67288	−	2.34979i	−0.277138	−	0.114795i	−0.516924	+	0.856031i	$0.672923\pi$
$420$		0			0
$421$	7.55578	+	18.2413i	0.368246	+	0.889025i	0.994038	+	0.109035i	$0.0347760\pi$
$421$	7.55578	+	18.2413i	0.368246	+	0.889025i	−0.625792	+	0.779990i	$0.715224\pi$
$422$		0			0
$423$	0.952630	+	3.55527i	0.0463185	+	0.172863i
$424$		0			0
$425$	−9.00955	+	33.6241i	−0.437027	+	1.63101i
$426$		0			0
$427$	−12.4717	−	3.53423i	−0.603547	−	0.171033i
$428$		0			0
$429$	8.62072	−	1.13494i	0.416212	−	0.0547954i
$430$		0			0
$431$	14.0942	+	8.13731i	0.678896	+	0.391961i	0.799439	−	0.600747i	$-0.205130\pi$
$431$	14.0942	+	8.13731i	0.678896	+	0.391961i	−0.120543	+	0.992708i	$0.538464\pi$
$432$		0			0
$433$			1.00886i			0.0484828i	0.999706	+	0.0242414i	$0.00771704\pi$
$433$			1.00886i			0.0484828i	−0.999706	+	0.0242414i	$0.992283\pi$
$434$		0			0
$435$	−0.538863	+	1.30093i	−0.0258365	+	0.0623749i
$436$		0			0
$437$	−4.46092	+	33.8841i	−0.213395	+	1.62089i
$438$		0			0
$439$	4.57061	−	17.0578i	0.218143	−	0.814122i	−0.766893	−	0.641775i	$-0.778198\pi$
$439$	4.57061	−	17.0578i	0.218143	−	0.814122i	0.985036	−	0.172347i	$-0.0551351\pi$
$440$		0			0
$441$	6.29628	−	3.39823i	0.299823	−	0.161820i
$442$		0			0
$443$	5.06598	−	6.60211i	0.240692	−	0.313676i	−0.657350	−	0.753585i	$-0.728323\pi$
$443$	5.06598	−	6.60211i	0.240692	−	0.313676i	0.898042	+	0.439909i	$0.144989\pi$
$444$		0			0
$445$	−1.28416	+	0.985369i	−0.0608749	+	0.0467109i
$446$		0			0
$447$	−11.5680			−0.547146
$448$		0			0
$449$	−27.0350			−1.27586			−0.637930	−	0.770094i	$-0.720209\pi$
$449$	−27.0350			−1.27586			−0.637930	+	0.770094i	$0.720209\pi$
$450$		0			0
$451$	4.05046	−	3.10803i	0.190729	−	0.146351i
$452$		0			0
$453$	10.0982	−	13.1602i	0.474453	−	0.618320i
$454$		0			0
$455$	1.20745	−	0.141379i	0.0566060	−	0.00662797i
$456$		0			0
$457$	3.71956	−	13.8816i	0.173994	−	0.649354i	−0.822727	−	0.568437i	$-0.807548\pi$
$457$	3.71956	−	13.8816i	0.173994	−	0.649354i	0.996721	−	0.0809171i	$-0.0257849\pi$
$458$		0			0
$459$	−5.26444	+	39.9874i	−0.245723	+	1.86645i
$460$		0			0
$461$	−12.5649	+	30.3344i	−0.585206	+	1.41281i	0.302833	+	0.953044i	$0.402068\pi$
$461$	−12.5649	+	30.3344i	−0.585206	+	1.41281i	−0.888039	+	0.459768i	$0.847932\pi$
$462$		0			0
$463$			16.4865i			0.766194i	0.923708	+	0.383097i	$0.125142\pi$
$463$			16.4865i			0.766194i	−0.923708	+	0.383097i	$0.874858\pi$
$464$		0			0
$465$	4.02327	+	2.32284i	0.186575	+	0.107719i
$466$		0			0
$467$	18.1302	−	2.38689i	0.838966	−	0.110452i	0.301216	−	0.953556i	$-0.402608\pi$
$467$	18.1302	−	2.38689i	0.838966	−	0.110452i	0.537750	+	0.843104i	$0.319274\pi$
$468$		0			0
$469$	5.33694	+	21.1250i	0.246437	+	0.975461i
$470$		0			0
$471$	1.92720	−	7.19239i	0.0888005	−	0.331408i
$472$		0			0
$473$	11.3400	+	42.3215i	0.521415	+	1.94595i
$474$		0			0
$475$	−13.0283	−	31.4530i	−0.597778	−	1.44316i
$476$		0			0
$477$	2.95371	+	1.22347i	0.135241	+	0.0560187i
$478$		0			0
$479$	−4.62770	+	8.01542i	−0.211445	+	0.366234i	−0.952167	−	0.305578i	$-0.901150\pi$
$479$	−4.62770	+	8.01542i	−0.211445	+	0.366234i	0.740722	+	0.671812i	$0.234484\pi$
$480$		0			0
$481$	−5.48341	−	9.49755i	−0.250022	−	0.433051i
$482$		0			0
$483$	18.2344	+	0.261517i	0.829695	+	0.0118994i
$484$		0			0
$485$	−0.651856	+	0.849515i	−0.0295993	+	0.0385745i
$486$		0			0
$487$	6.21158	+	23.1819i	0.281473	+	1.05047i	0.951378	+	0.308026i	$0.0996684\pi$
$487$	6.21158	+	23.1819i	0.281473	+	1.05047i	−0.669905	+	0.742447i	$0.733665\pi$
$488$		0			0
$489$	−23.3592	−	23.3592i	−1.05634	−	1.05634i
$490$		0			0
$491$	−0.0789814	+	0.0327151i	−0.00356438	+	0.00147641i	−0.384465	−	0.923140i	$-0.625614\pi$
$491$	−0.0789814	+	0.0327151i	−0.00356438	+	0.00147641i	0.380901	+	0.924616i	$0.375614\pi$
$492$		0			0
$493$	−12.6574	−	16.4954i	−0.570060	−	0.742916i
$494$		0			0
$495$	−1.40414	+	0.810680i	−0.0631113	+	0.0364373i
$496$		0			0
$497$	−9.52629	−	23.9649i	−0.427313	−	1.07497i
$498$		0			0
$499$	18.5928	−	2.44780i	0.832330	−	0.109578i	0.297695	−	0.954661i	$-0.403782\pi$
$499$	18.5928	−	2.44780i	0.832330	−	0.109578i	0.534636	+	0.845083i	$0.320449\pi$
$500$		0			0
$501$	−2.28299	+	17.3410i	−0.101997	+	0.774740i
$502$		0			0
$503$	14.5426	+	14.5426i	0.648424	+	0.648424i	0.952612	−	0.304188i	$-0.0983851\pi$
$503$	14.5426	+	14.5426i	0.648424	+	0.648424i	−0.304188	+	0.952612i	$0.598385\pi$
$504$		0			0
$505$	0.268063	−	0.268063i	0.0119286	−	0.0119286i
$506$		0			0
$507$	15.6293	+	2.05764i	0.694123	+	0.0913830i
$508$		0			0
$509$	−1.02130	−	7.75757i	−0.0452685	−	0.343848i	−0.999059	−	0.0433754i	$-0.986189\pi$
$509$	−1.02130	−	7.75757i	−0.0452685	−	0.343848i	0.953790	−	0.300473i	$-0.0971445\pi$
$510$		0			0
$511$	−2.24984	+	15.3814i	−0.0995271	+	0.680431i
$512$		0			0
$513$	−19.7226	−	34.1606i	−0.870775	−	1.50823i
$514$		0			0
$515$	−1.70339	+	1.30706i	−0.0750603	+	0.0575958i
$516$		0			0
$517$	6.36661	+	15.3703i	0.280003	+	0.675987i
$518$		0			0
$519$	−18.8628	+	18.8628i	−0.827984	+	0.827984i
$520$		0			0
$521$	−16.3735	+	4.38728i	−0.717338	+	0.192210i	−0.598984	−	0.800761i	$-0.704429\pi$
$521$	−16.3735	+	4.38728i	−0.717338	+	0.192210i	−0.118355	+	0.992971i	$0.537762\pi$
$522$		0			0
$523$	11.2399	+	8.62467i	0.491486	+	0.377131i	0.824564	−	0.565769i	$-0.191420\pi$
$523$	11.2399	+	8.62467i	0.491486	+	0.377131i	−0.333078	+	0.942899i	$0.608087\pi$
$524$		0			0
$525$	−15.8608	+	8.85642i	−0.692221	+	0.386526i
$526$		0			0
$527$	−59.4070	+	34.2986i	−2.58781	+	1.49407i
$528$		0			0
$529$	−0.883414	−	0.510040i	−0.0384093	−	0.0221756i
$530$		0			0
$531$	0.119779	−	0.289172i	0.00519796	−	0.0125490i
$532$		0			0
$533$	−1.36631	+	0.565944i	−0.0591814	+	0.0245138i
$534$		0			0
$535$	1.09492	−	0.293383i	0.0473375	−	0.0126840i
$536$		0			0
$537$	20.4405	+	5.47703i	0.882074	+	0.236351i
$538$		0			0
$539$	26.2109	−	18.9433i	1.12898	−	0.815947i
$540$		0			0
$541$	3.80057	+	28.8682i	0.163399	+	1.24114i	0.854911	+	0.518774i	$0.173612\pi$
$541$	3.80057	+	28.8682i	0.163399	+	1.24114i	−0.691512	+	0.722365i	$0.743055\pi$
$542$		0			0
$543$	9.44092	−	16.3522i	0.405149	−	0.701738i
$544$		0			0
$545$	0.531358			0.0227609
$546$		0			0
$547$	4.29183	+	1.77774i	0.183506	+	0.0760105i	0.472544	−	0.881307i	$-0.343336\pi$
$547$	4.29183	+	1.77774i	0.183506	+	0.0760105i	−0.289039	+	0.957317i	$0.593336\pi$
$548$		0			0
$549$	−4.96497	−	0.653651i	−0.211900	−	0.0278971i
$550$		0			0
$551$	19.6418	+	5.26300i	0.836768	+	0.224211i
$552$		0			0
$553$	2.30440	+	19.6807i	0.0979930	+	0.836907i
$554$		0			0
$555$	−3.13945	−	2.40899i	−0.133262	−	0.102256i
$556$		0			0
$557$	11.1436	+	14.5226i	0.472170	+	0.615344i	0.967349	−	0.253447i	$-0.0815643\pi$
$557$	11.1436	+	14.5226i	0.472170	+	0.615344i	−0.495179	+	0.868791i	$0.664898\pi$
$558$		0			0
$559$		−	12.6915i		−	0.536794i
$560$		0			0
$561$			46.3276i			1.95595i
$562$		0			0
$563$	−11.4122	−	14.8727i	−0.480968	−	0.626809i	0.488342	−	0.872652i	$-0.337602\pi$
$563$	−11.4122	−	14.8727i	−0.480968	−	0.626809i	−0.969310	+	0.245843i	$0.920935\pi$
$564$		0			0
$565$	4.07734	+	3.12865i	0.171535	+	0.131623i
$566$		0			0
$567$	−10.3738	+	7.72632i	−0.435660	+	0.324475i
$568$		0			0
$569$	19.4460	+	5.21054i	0.815218	+	0.218437i	0.642255	−	0.766491i	$-0.277999\pi$
$569$	19.4460	+	5.21054i	0.815218	+	0.218437i	0.172963	+	0.984928i	$0.444666\pi$
$570$		0			0
$571$	−10.5365	−	1.38716i	−0.440939	−	0.0580508i	−0.0932116	−	0.995646i	$-0.529713\pi$
$571$	−10.5365	−	1.38716i	−0.440939	−	0.0580508i	−0.347728	+	0.937596i	$0.613047\pi$
$572$		0			0
$573$	−0.825767	−	0.342044i	−0.0344969	−	0.0142891i
$574$		0			0
$575$	23.9274			0.997840
$576$		0			0
$577$	11.2377	−	19.4642i	0.467831	−	0.810307i	−0.531493	−	0.847062i	$-0.678369\pi$
$577$	11.2377	−	19.4642i	0.467831	−	0.810307i	0.999324	+	0.0367556i	$0.0117023\pi$
$578$		0			0
$579$	2.65779	+	20.1879i	0.110454	+	0.838981i
$580$		0			0
$581$	8.89245	+	9.15123i	0.368921	+	0.379657i
$582$		0			0
$583$	13.9584	+	3.74015i	0.578099	+	0.154901i
$584$		0			0
$585$	0.453648	−	0.121555i	0.0187560	−	0.00502566i
$586$		0			0
$587$	−16.4707	+	6.82238i	−0.679818	+	0.281590i	−0.695751	−	0.718283i	$-0.744928\pi$
$587$	−16.4707	+	6.82238i	−0.679818	+	0.281590i	0.0159330	+	0.999873i	$0.494928\pi$
$588$		0			0
$589$	25.6736	−	61.9816i	1.05786	−	2.55391i
$590$		0			0
$591$	−2.62334	−	1.51459i	−0.107910	−	0.0623018i
$592$		0			0
$593$	38.1447	−	22.0229i	1.56642	−	0.904371i	0.569834	−	0.821760i	$-0.307007\pi$
$593$	38.1447	−	22.0229i	1.56642	−	0.904371i	0.996582	−	0.0826113i	$-0.0263260\pi$
$594$		0			0
$595$	−0.0928863	+	6.47656i	−0.00380797	+	0.265513i
$596$		0			0
$597$	−29.7871	−	22.8565i	−1.21911	−	0.935453i
$598$		0			0
$599$	5.84720	−	1.56675i	0.238910	−	0.0640158i	−0.137377	−	0.990519i	$-0.543867\pi$
$599$	5.84720	−	1.56675i	0.238910	−	0.0640158i	0.376287	+	0.926503i	$0.377201\pi$
$600$		0			0
$601$	17.3615	−	17.3615i	0.708192	−	0.708192i	−0.257963	−	0.966155i	$-0.583051\pi$
$601$	17.3615	−	17.3615i	0.708192	−	0.708192i	0.966155	+	0.257963i	$0.0830513\pi$
$602$		0			0
$603$	3.22123	+	7.77673i	0.131179	+	0.316693i
$604$		0			0
$605$	−2.81774	+	2.16213i	−0.114558	+	0.0879031i
$606$		0			0
$607$	−13.3121	−	23.0572i	−0.540321	−	0.935863i	−0.998885	−	0.0472019i	$-0.984970\pi$
$607$	−13.3121	−	23.0572i	−0.540321	−	0.935863i	0.458565	−	0.888661i	$-0.348364\pi$
$608$		0			0
$609$	1.57039	−	10.7362i	0.0636354	−	0.435052i
$610$		0			0
$611$	−0.629016	−	4.77785i	−0.0254473	−	0.193291i
$612$		0			0
$613$	6.67545	+	0.878839i	0.269619	+	0.0354960i	0.264123	−	0.964489i	$-0.414917\pi$
$613$	6.67545	+	0.878839i	0.269619	+	0.0354960i	0.00549546	+	0.999985i	$0.498251\pi$
$614$		0			0
$615$	−0.377333	+	0.377333i	−0.0152156	+	0.0152156i
$616$		0			0
$617$	−10.4255	−	10.4255i	−0.419715	−	0.419715i	0.465391	−	0.885105i	$-0.345914\pi$
$617$	−10.4255	−	10.4255i	−0.419715	−	0.419715i	−0.885105	+	0.465391i	$0.845914\pi$
$618$		0			0
$619$	1.79860	−	13.6617i	0.0722919	−	0.549111i	−0.916525	−	0.399977i	$-0.869018\pi$
$619$	1.79860	−	13.6617i	0.0722919	−	0.549111i	0.988817	−	0.149134i	$-0.0476486\pi$
$620$		0			0
$621$	27.4860	−	3.61859i	1.10297	−	0.145209i
$622$		0			0
$623$	7.73401	−	9.78534i	0.309856	−	0.392041i
$624$		0			0
$625$	−20.1312	+	11.6228i	−0.805249	+	0.464911i
$626$		0			0
$627$	−27.5821	−	35.9457i	−1.10152	−	1.43553i
$628$		0			0
$629$	53.9835	−	22.3607i	2.15246	−	0.891579i
$630$		0			0
$631$	−26.7977	−	26.7977i	−1.06680	−	1.06680i	−0.997603	−	0.0691970i	$-0.977956\pi$
$631$	−26.7977	−	26.7977i	−1.06680	−	1.06680i	−0.0691970	−	0.997603i	$-0.522044\pi$
$632$		0			0
$633$	−5.26180	−	19.6373i	−0.209138	−	0.780512i
$634$		0			0
$635$	0.617319	−	0.804505i	0.0244975	−	0.0319258i
$636$		0			0
$637$	−8.75387	+	3.33519i	−0.346841	+	0.132145i
$638$		0			0
$639$	−4.98141	−	8.62806i	−0.197062	−	0.341321i
$640$		0			0
$641$	1.54544	−	2.67678i	0.0610411	−	0.105726i	−0.833890	−	0.551931i	$-0.813891\pi$
$641$	1.54544	−	2.67678i	0.0610411	−	0.105726i	0.894931	+	0.446204i	$0.147225\pi$
$642$		0			0
$643$	17.6646	+	7.31691i	0.696623	+	0.288551i	0.702757	−	0.711430i	$-0.251952\pi$
$643$	17.6646	+	7.31691i	0.696623	+	0.288551i	−0.00613319	+	0.999981i	$0.501952\pi$
$644$		0			0
$645$	−1.75251	−	4.23092i	−0.0690048	−	0.166592i
$646$		0			0
$647$	−7.29774	−	27.2355i	−0.286904	−	1.07074i	−0.947437	−	0.319943i	$-0.896336\pi$
$647$	−7.29774	−	27.2355i	−0.286904	−	1.07074i	0.660533	−	0.750797i	$-0.270330\pi$
$648$		0			0
$649$	0.366165	−	1.36655i	0.0143732	−	0.0536416i
$650$		0			0
$651$	−34.4417	−	9.76008i	−1.34987	−	0.382528i
$652$		0			0
$653$	28.7854	−	3.78967i	1.12646	−	0.148301i	0.455812	−	0.890076i	$-0.349349\pi$
$653$	28.7854	−	3.78967i	1.12646	−	0.148301i	0.670649	+	0.741775i	$0.266016\pi$
$654$		0			0
$655$	−1.18608	−	0.684784i	−0.0463440	−	0.0267567i
$656$		0			0
$657$			6.00540i			0.234293i
$658$		0			0
$659$	0.0474821	−	0.114632i	0.00184964	−	0.00446543i	−0.922952	−	0.384915i	$-0.874231\pi$
$659$	0.0474821	−	0.114632i	0.00184964	−	0.00446543i	0.924802	+	0.380450i	$0.124231\pi$
$660$		0			0
$661$	−1.76482	+	13.4052i	−0.0686437	+	0.521401i	0.922234	+	0.386633i	$0.126362\pi$
$661$	−1.76482	+	13.4052i	−0.0686437	+	0.521401i	−0.990877	+	0.134767i	$0.956971\pi$
$662$		0			0
$663$	3.47321	−	12.9622i	0.134888	−	0.503410i
$664$		0			0
$665$	−3.78389	−	5.08048i	−0.146733	−	0.197013i
$666$		0			0
$667$	−8.70025	+	11.3384i	−0.336875	+	0.439024i
$668$		0			0
$669$	15.7379	−	12.0761i	0.608463	−	0.466890i
$670$		0			0
$671$	−22.6354			−0.873830
$672$		0			0
$673$	−6.83887			−0.263619			−0.131810	−	0.991275i	$-0.542079\pi$
$673$	−6.83887			−0.263619			−0.131810	+	0.991275i	$0.542079\pi$
$674$		0			0
$675$	−21.9093	+	16.8116i	−0.843291	+	0.647080i
$676$		0			0
$677$	−28.3992	+	37.0105i	−1.09147	+	1.42243i	−0.194190	+	0.980964i	$0.562208\pi$
$677$	−28.3992	+	37.0105i	−1.09147	+	1.42243i	−0.897278	+	0.441465i	$0.854459\pi$
$678$		0			0
$679$	3.26656	−	7.57697i	0.125359	−	0.290777i
$680$		0			0
$681$	0.155500	−	0.580335i	0.00595878	−	0.0222385i
$682$		0			0
$683$	3.42423	−	26.0096i	0.131024	−	0.995230i	−0.792009	−	0.610510i	$-0.790965\pi$
$683$	3.42423	−	26.0096i	0.131024	−	0.995230i	0.923033	−	0.384720i	$-0.125702\pi$
$684$		0			0
$685$	−1.31358	+	3.17127i	−0.0501894	+	0.121168i
$686$		0			0
$687$			28.1518i			1.07406i
$688$		0			0
$689$	−3.62509	−	2.09295i	−0.138105	−	0.0797350i
$690$		0			0
$691$	−38.9179	+	5.12364i	−1.48051	+	0.194912i	−0.827083	−	0.562080i	$-0.810001\pi$
$691$	−38.9179	+	5.12364i	−1.48051	+	0.194912i	−0.653424	+	0.756992i	$0.726668\pi$
$692$		0			0
$693$	8.96008	−	8.70671i	0.340365	−	0.330740i
$694$		0			0
$695$	0.252702	−	0.943097i	0.00958554	−	0.0357737i
$696$		0			0
$697$	−2.03936	−	7.61100i	−0.0772464	−	0.288287i
$698$		0			0
$699$	−14.1973	−	34.2753i	−0.536991	−	1.29641i
$700$		0			0
$701$	−40.4854	−	16.7696i	−1.52911	−	0.633380i	−0.549722	−	0.835348i	$-0.685266\pi$
$701$	−40.4854	−	16.7696i	−1.52911	−	0.633380i	−0.979392	+	0.201968i	$0.935266\pi$
$702$		0			0
$703$	−28.5730	+	49.4899i	−1.07765	+	1.86655i
$704$		0			0
$705$	−0.869442	−	1.50592i	−0.0327451	−	0.0567162i
$706$		0			0
$707$	−1.49672	+	2.50862i	−0.0562901	+	0.0943463i
$708$		0			0
$709$	16.9117	−	22.0397i	0.635131	−	0.827719i	−0.359287	−	0.933227i	$-0.616980\pi$
$709$	16.9117	−	22.0397i	0.635131	−	0.827719i	0.994418	+	0.105508i	$0.0336469\pi$
$710$		0			0
$711$	1.98127	+	7.39419i	0.0743033	+	0.277304i
$712$		0			0
$713$	33.3411	+	33.3411i	1.24863	+	1.24863i
$714$		0			0
$715$	1.96124	−	0.812372i	0.0733462	−	0.0303810i
$716$		0			0
$717$	3.36312	+	4.38290i	0.125598	+	0.163683i
$718$		0			0
$719$	−23.5088	+	13.5728i	−0.876731	+	0.506181i	−0.869579	−	0.493793i	$-0.835610\pi$
$719$	−23.5088	+	13.5728i	−0.876731	+	0.506181i	−0.00715216	+	0.999974i	$0.502277\pi$
$720$		0			0
$721$	10.2589	−	12.9799i	0.382061	−	0.483397i
$722$		0			0
$723$	1.96368	−	0.258523i	0.0730301	−	0.00961459i
$724$		0			0
$725$	1.85824	−	14.1148i	0.0690134	−	0.524209i
$726$		0			0
$727$	0.315294	+	0.315294i	0.0116936	+	0.0116936i	0.712929	−	0.701236i	$-0.247368\pi$
$727$	0.315294	+	0.315294i	0.0116936	+	0.0116936i	−0.701236	+	0.712929i	$0.747368\pi$
$728$		0			0
$729$	−20.4092	+	20.4092i	−0.755895	+	0.755895i
$730$		0			0
$731$	67.0419	+	8.82623i	2.47963	+	0.326450i
$732$		0			0
$733$	−5.48629	−	41.6725i	−0.202641	−	1.53921i	−0.726358	−	0.687316i	$-0.758789\pi$
$733$	−5.48629	−	41.6725i	−0.202641	−	1.53921i	0.523718	−	0.851892i	$-0.324545\pi$
$734$		0			0
$735$	−2.45771	+	2.32062i	−0.0906539	+	0.0855973i
$736$		0			0
$737$	19.0236	+	32.9498i	0.700742	+	1.21372i
$738$		0			0
$739$	4.97125	−	3.81457i	0.182870	−	0.140321i	−0.513270	−	0.858227i	$-0.671566\pi$
$739$	4.97125	−	3.81457i	0.182870	−	0.140321i	0.696140	+	0.717906i	$0.254899\pi$
$740$		0			0
$741$	5.02244	+	12.1253i	0.184504	+	0.445432i
$742$		0			0
$743$	33.5287	−	33.5287i	1.23005	−	1.23005i	0.266105	−	0.963944i	$-0.414263\pi$
$743$	33.5287	−	33.5287i	1.23005	−	1.23005i	0.963944	−	0.266105i	$-0.0857369\pi$
$744$		0			0
$745$	−2.72798	+	0.730960i	−0.0999454	+	0.0267803i
$746$		0			0
$747$	3.91085	+	3.00090i	0.143091	+	0.109797i
$748$		0			0
$749$	−7.62630	+	4.25841i	−0.278659	+	0.155599i
$750$		0			0
$751$	−29.8096	+	17.2106i	−1.08777	+	0.628023i	−0.932981	−	0.359925i	$-0.882802\pi$
$751$	−29.8096	+	17.2106i	−1.08777	+	0.628023i	−0.154786	+	0.987948i	$0.549469\pi$
$752$		0			0
$753$	−22.4354	−	12.9531i	−0.817592	−	0.472037i
$754$		0			0
$755$	1.54980	−	3.74155i	0.0564030	−	0.136169i
$756$		0			0
$757$	13.8297	−	5.72847i	0.502650	−	0.208205i	−0.116926	−	0.993141i	$-0.537304\pi$
$757$	13.8297	−	5.72847i	0.502650	−	0.208205i	0.619577	+	0.784936i	$0.287304\pi$
$758$		0			0
$759$	30.7589	−	8.24182i	1.11648	−	0.299159i
$760$		0			0
$761$	46.8612	+	12.5564i	1.69872	+	0.455170i	0.972616	−	0.232419i	$-0.0746641\pi$
$761$	46.8612	+	12.5564i	1.69872	+	0.455170i	0.726100	+	0.687589i	$0.241331\pi$
$762$		0			0
$763$	−3.96972	+	1.00290i	−0.143714	+	0.0363073i
$764$		0			0
$765$	0.326616	+	2.48089i	0.0118088	+	0.0896969i
$766$		0			0
$767$	−0.204902	+	0.354901i	−0.00739858	+	0.0128147i
$768$		0			0
$769$	−29.8122			−1.07505			−0.537527	−	0.843246i	$-0.680641\pi$
$769$	−29.8122			−1.07505			−0.537527	+	0.843246i	$0.680641\pi$
$770$		0			0
$771$	9.06912	+	3.75655i	0.326616	+	0.135289i
$772$		0			0
$773$	−51.7245	−	6.80966i	−1.86040	−	0.244926i	−0.885035	−	0.465524i	$-0.845866\pi$
$773$	−51.7245	−	6.80966i	−1.86040	−	0.244926i	−0.975365	+	0.220597i	$0.929199\pi$
$774$		0			0
$775$	−45.3689	−	12.1566i	−1.62970	−	0.436677i
$776$		0			0
$777$	28.0013	+	12.0718i	1.00454	+	0.433075i
$778$		0			0
$779$	6.11372	+	4.69122i	0.219047	+	0.168080i
$780$		0			0
$781$	−27.4138	−	35.7264i	−0.980944	−	1.27839i
$782$		0			0
$783$		−	16.4950i		−	0.589483i
$784$		0			0
$785$		−	1.81790i		−	0.0648836i
$786$		0			0
$787$	25.6295	+	33.4010i	0.913592	+	1.19062i	0.981217	+	0.192905i	$0.0617909\pi$
$787$	25.6295	+	33.4010i	0.913592	+	1.19062i	−0.0676259	+	0.997711i	$0.521542\pi$
$788$		0			0
$789$	−0.620726	−	0.476300i	−0.0220984	−	0.0169567i
$790$		0			0
$791$	−36.3665	−	15.6782i	−1.29304	−	0.557452i
$792$		0			0
$793$	6.33327	+	1.69699i	0.224901	+	0.0602620i
$794$		0			0
$795$	−1.49749	−	0.197148i	−0.0531105	−	0.00699213i
$796$		0			0
$797$	−21.6418	−	8.96433i	−0.766592	−	0.317533i	−0.0351007	−	0.999384i	$-0.511175\pi$
$797$	−21.6418	−	8.96433i	−0.766592	−	0.317533i	−0.731491	+	0.681851i	$0.761175\pi$
$798$		0			0
$799$	25.6761			0.908354
$800$		0			0
$801$	2.40924	−	4.17292i	0.0851263	−	0.147443i
$802$		0			0
$803$	3.54307	+	26.9123i	0.125032	+	0.949714i
$804$		0			0
$805$	4.31660	−	1.09053i	0.152140	−	0.0384362i
$806$		0			0
$807$	27.6063	+	7.39710i	0.971789	+	0.260390i
$808$		0			0
$809$	4.98556	−	1.33588i	0.175283	−	0.0469669i	−0.170110	−	0.985425i	$-0.554412\pi$
$809$	4.98556	−	1.33588i	0.175283	−	0.0469669i	0.345393	+	0.938458i	$0.387746\pi$
$810$		0			0
$811$	15.1446	−	6.27312i	0.531801	−	0.220279i	−0.100591	−	0.994928i	$-0.532073\pi$
$811$	15.1446	−	6.27312i	0.531801	−	0.220279i	0.632392	+	0.774649i	$0.282073\pi$
$812$		0			0
$813$	10.2017	−	24.6291i	0.357789	−	0.863780i
$814$		0			0
$815$	−6.98465	−	4.03259i	−0.244661	−	0.141255i
$816$		0			0
$817$	−57.2728	+	33.0665i	−2.00372	+	1.15685i
$818$		0			0
$819$	−3.15973	+	1.76435i	−0.110410	+	0.0616513i
$820$		0			0
$821$	−14.7892	−	11.3482i	−0.516147	−	0.396053i	0.317579	−	0.948232i	$-0.397130\pi$
$821$	−14.7892	−	11.3482i	−0.516147	−	0.396053i	−0.833726	+	0.552178i	$0.813797\pi$
$822$		0			0
$823$	15.2617	−	4.08937i	0.531990	−	0.142546i	0.0171831	−	0.999852i	$-0.494530\pi$
$823$	15.2617	−	4.08937i	0.531990	−	0.142546i	0.514807	+	0.857306i	$0.327864\pi$
$824$		0			0
$825$	−22.4302	+	22.4302i	−0.780918	+	0.780918i
$826$		0			0
$827$	−6.24046	−	15.0658i	−0.217002	−	0.523889i	0.777466	−	0.628924i	$-0.216504\pi$
$827$	−6.24046	−	15.0658i	−0.217002	−	0.523889i	−0.994469	+	0.105035i	$0.966504\pi$
$828$		0			0
$829$	30.7112	−	23.5655i	1.06664	−	0.818464i	0.0826339	−	0.996580i	$-0.473667\pi$
$829$	30.7112	−	23.5655i	1.06664	−	0.818464i	0.984010	+	0.178116i	$0.0570001\pi$
$830$		0			0
$831$	−13.4207	−	23.2453i	−0.465558	−	0.806371i
$832$		0			0
$833$	−11.5301	−	48.5611i	−0.399493	−	1.68254i
$834$		0			0
$835$	0.557371	+	4.23365i	0.0192886	+	0.146512i
$836$		0			0
$837$	−53.9549	−	7.10330i	−1.86495	−	0.245526i
$838$		0			0
$839$	−35.7565	+	35.7565i	−1.23445	+	1.23445i	−0.272213	+	0.962237i	$0.587756\pi$
$839$	−35.7565	+	35.7565i	−1.23445	+	1.23445i	−0.962237	+	0.272213i	$0.912244\pi$
$840$		0			0
$841$	−14.4933	−	14.4933i	−0.499768	−	0.499768i
$842$		0			0
$843$	2.42974	−	18.4557i	0.0836845	−	0.635647i
$844$		0			0
$845$	3.81575	−	0.502354i	0.131266	−	0.0172815i
$846$		0			0
$847$	16.9702	−	21.4713i	0.583104	−	0.737764i
$848$		0			0
$849$	1.62832	−	0.940109i	0.0558837	−	0.0322644i
$850$		0			0
$851$	−24.4501	−	31.8640i	−0.838138	−	1.09228i
$852$		0			0
$853$	−38.6427	+	16.0063i	−1.32310	+	0.548046i	−0.928679	−	0.370883i	$-0.879055\pi$
$853$	−38.6427	+	16.0063i	−1.32310	+	0.548046i	−0.394421	+	0.918930i	$0.629055\pi$
$854$		0			0
$855$	−1.73047	−	1.73047i	−0.0591809	−	0.0591809i
$856$		0			0
$857$	−3.43843	−	12.8324i	−0.117455	−	0.438347i	0.882004	−	0.471242i	$-0.156194\pi$
$857$	−3.43843	−	12.8324i	−0.117455	−	0.438347i	−0.999459	+	0.0328950i	$0.989527\pi$
$858$		0			0
$859$	−7.98154	+	10.4017i	−0.272327	+	0.354903i	−0.909416	−	0.415887i	$-0.863471\pi$
$859$	−7.98154	+	10.4017i	−0.272327	+	0.354903i	0.637090	+	0.770789i	$0.280138\pi$
$860$		0			0
$861$	2.10683	−	3.53121i	0.0718007	−	0.120343i
$862$		0			0
$863$	−10.9924	−	19.0394i	−0.374185	−	0.648108i	0.616019	−	0.787731i	$-0.288744\pi$
$863$	−10.9924	−	19.0394i	−0.374185	−	0.648108i	−0.990205	+	0.139623i	$0.955411\pi$
$864$		0			0
$865$	−3.25635	+	5.64016i	−0.110719	+	0.191771i
$866$		0			0
$867$	43.9680	+	18.2121i	1.49323	+	0.618516i
$868$		0			0
$869$	13.2412	+	31.9670i	0.449176	+	1.08441i
$870$		0			0
$871$	−2.85242	−	10.6454i	−0.0966506	−	0.360705i
$872$		0			0
$873$	0.825009	−	3.07898i	0.0279223	−	0.104208i
$874$		0			0
$875$	−6.43820	+	6.25614i	−0.217651	+	0.211496i
$876$		0			0
$877$	14.2576	−	1.87705i	0.481446	−	0.0633835i	0.114103	−	0.993469i	$-0.463601\pi$
$877$	14.2576	−	1.87705i	0.481446	−	0.0633835i	0.367343	+	0.930085i	$0.380267\pi$
$878$		0			0
$879$	−28.9335	−	16.7048i	−0.975904	−	0.563439i
$880$		0			0
$881$			29.2633i			0.985907i	0.870056	+	0.492954i	$0.164083\pi$
$881$			29.2633i			0.985907i	−0.870056	+	0.492954i	$0.835917\pi$
$882$		0			0
$883$	−3.76447	+	9.08824i	−0.126685	+	0.305844i	−0.974478	−	0.224483i	$-0.927931\pi$
$883$	−3.76447	+	9.08824i	−0.126685	+	0.305844i	0.847793	+	0.530327i	$0.177931\pi$
$884$		0			0
$885$	−0.0193010	+	0.146606i	−0.000648797	+	0.00492810i
$886$		0			0
$887$	6.15443	−	22.9687i	0.206646	−	0.771212i	−0.782296	−	0.622907i	$-0.785952\pi$
$887$	6.15443	−	22.9687i	0.206646	−	0.771212i	0.988942	−	0.148305i	$-0.0473818\pi$
$888$		0			0
$889$	−3.09349	+	7.17552i	−0.103752	+	0.240659i
$890$		0			0
$891$	−13.7500	+	17.9193i	−0.460641	+	0.600319i
$892$		0			0
$893$	−19.9221	+	15.2868i	−0.666668	+	0.511553i
$894$		0			0
$895$	5.16641			0.172694
$896$		0			0
$897$	−9.22408			−0.307983
$898$		0			0
$899$	22.2572	−	17.0786i	0.742320	−	0.569602i
$900$		0			0
$901$	13.5769	−	17.6937i	0.452312	−	0.589464i
$902$		0			0
$903$	21.0783	+	28.3011i	0.701443	+	0.941801i
$904$		0			0
$905$	1.19311	−	4.45275i	0.0396604	−	0.148014i
$906$		0			0
$907$	4.03173	−	30.6240i	0.133871	−	1.01685i	−0.784219	−	0.620484i	$-0.786936\pi$
$907$	4.03173	−	30.6240i	0.133871	−	1.01685i	0.918091	−	0.396371i	$-0.129730\pi$
$908$		0			0
$909$	−0.431866	+	1.04262i	−0.0143241	+	0.0345814i
$910$		0			0
$911$			10.3192i			0.341889i	0.985281	+	0.170945i	$0.0546819\pi$
$911$			10.3192i			0.341889i	−0.985281	+	0.170945i	$0.945318\pi$
$912$		0			0
$913$	19.2964	+	11.1408i	0.638616	+	0.368705i
$914$		0			0
$915$	2.34563	−	0.308808i	0.0775441	−	0.0102089i
$916$		0			0
$917$	10.1536	+	2.87732i	0.335301	+	0.0950175i
$918$		0			0
$919$	2.14486	−	8.00475i	0.0707526	−	0.264052i	−0.921484	−	0.388416i	$-0.873022\pi$
$919$	2.14486	−	8.00475i	0.0707526	−	0.264052i	0.992237	+	0.124364i	$0.0396890\pi$
$920$		0			0
$921$	−0.370081	−	1.38116i	−0.0121946	−	0.0455108i
$922$		0			0
$923$	4.99181	+	12.0513i	0.164307	+	0.396673i
$924$		0			0
$925$	36.9631	+	15.3106i	1.21534	+	0.503410i
$926$		0			0
$927$	3.19577	−	5.53524i	0.104963	−	0.181801i
$928$		0			0
$929$	15.0662	+	26.0955i	0.494307	+	0.856166i	0.999978	−	0.00656082i	$-0.00208839\pi$
$929$	15.0662	+	26.0955i	0.494307	+	0.856166i	−0.505671	+	0.862726i	$0.668755\pi$
$930$		0			0
$931$	37.8581	+	30.8140i	1.24075	+	1.00989i
$932$		0			0
$933$	−22.6004	+	29.4535i	−0.739905	+	0.964263i
$934$		0			0
$935$	2.92736	+	10.9250i	0.0957348	+	0.357287i
$936$		0			0
$937$	35.8872	+	35.8872i	1.17238	+	1.17238i	0.981640	+	0.190743i	$0.0610896\pi$
$937$	35.8872	+	35.8872i	1.17238	+	1.17238i	0.190743	+	0.981640i	$0.438910\pi$
$938$		0			0
$939$	15.8232	−	6.55417i	0.516370	−	0.213887i
$940$		0			0
$941$	−21.1127	−	27.5147i	−0.688256	−	0.896952i	0.310302	−	0.950638i	$-0.399570\pi$
$941$	−21.1127	−	27.5147i	−0.688256	−	0.896952i	−0.998558	+	0.0536856i	$0.982903\pi$
$942$		0			0
$943$	−4.69047	+	2.70805i	−0.152743	+	0.0881861i
$944$		0			0
$945$	−3.18632	+	4.03145i	−0.103651	+	0.131143i
$946$		0			0
$947$	−13.1905	+	1.73656i	−0.428633	+	0.0564307i	−0.341757	−	0.939788i	$-0.611022\pi$
$947$	−13.1905	+	1.73656i	−0.428633	+	0.0564307i	−0.0868766	+	0.996219i	$0.527689\pi$
$948$		0			0
$949$	1.02630	−	7.79554i	0.0333152	−	0.253054i
$950$		0			0
$951$	−4.76047	−	4.76047i	−0.154369	−	0.154369i
$952$		0			0
$953$	11.8190	−	11.8190i	0.382855	−	0.382855i	−0.489275	−	0.872130i	$-0.662738\pi$
$953$	11.8190	−	11.8190i	0.382855	−	0.382855i	0.872130	+	0.489275i	$0.162738\pi$
$954$		0			0
$955$	−0.216347	−	0.0284826i	−0.00700082	−	0.000921676i
$956$		0			0
$957$	−2.47306	−	18.7848i	−0.0799427	−	0.607225i
$958$		0			0
$959$	3.82813	−	26.1715i	0.123617	−	0.845123i
$960$		0			0
$961$	−30.7791	−	53.3109i	−0.992873	−	1.71971i
$962$		0			0
$963$	−2.67709	+	2.05421i	−0.0862681	+	0.0661958i
$964$		0			0
$965$	1.90240	+	4.59281i	0.0612406	+	0.147848i
$966$		0			0
$967$	31.0513	−	31.0513i	0.998542	−	0.998542i	−0.00145736	−	0.999999i	$-0.500464\pi$
$967$	31.0513	−	31.0513i	0.998542	−	0.998542i	0.999999	+	0.00145736i	$0.000463891\pi$
$968$		0			0
$969$	−67.5435	+	18.0982i	−2.16981	+	0.581399i
$970$		0			0
$971$	−19.2767	−	14.7915i	−0.618619	−	0.474683i	0.251279	−	0.967915i	$-0.419149\pi$
$971$	−19.2767	−	14.7915i	−0.618619	−	0.474683i	−0.869898	+	0.493232i	$0.835815\pi$
$972$		0			0
$973$	−0.107891	+	7.52274i	−0.00345881	+	0.241168i
$974$		0			0
$975$	7.95745	−	4.59423i	0.254842	−	0.147133i
$976$		0			0
$977$	46.5949	+	26.9016i	1.49070	+	0.860657i	0.999943	−	0.0106383i	$-0.00338636\pi$
$977$	46.5949	+	26.9016i	1.49070	+	0.860657i	0.490759	+	0.871296i	$0.336720\pi$
$978$		0			0
$979$	8.33469	−	20.1217i	0.266378	−	0.643093i
$980$		0			0
$981$	−1.46137	+	0.605320i	−0.0466580	+	0.0193264i
$982$		0			0
$983$	−38.8676	+	10.4145i	−1.23968	+	0.332172i	−0.818343	−	0.574731i	$-0.805107\pi$
$983$	−38.8676	+	10.4145i	−1.23968	+	0.332172i	−0.421340	+	0.906903i	$0.638440\pi$
$984$		0			0
$985$	−0.714345	−	0.191408i	−0.0227609	−	0.00609877i
$986$		0			0
$987$	9.33782	+	9.60956i	0.297226	+	0.305876i
$988$		0			0
$989$	−6.06685	−	46.0823i	−0.192915	−	1.46533i
$990$		0			0
$991$	−19.8157	+	34.3218i	−0.629466	+	1.09027i	0.358193	+	0.933647i	$0.383393\pi$
$991$	−19.8157	+	34.3218i	−0.629466	+	1.09027i	−0.987659	+	0.156619i	$0.949940\pi$
$992$		0			0
$993$	14.8421			0.471000
$994$		0			0
$995$	−8.46871	−	3.50786i	−0.268476	−	0.111206i
$996$		0			0
$997$	10.0567	+	1.32399i	0.318500	+	0.0419313i	0.288081	−	0.957606i	$-0.406983\pi$
$997$	10.0567	+	1.32399i	0.318500	+	0.0419313i	0.0304187	+	0.999537i	$0.490316\pi$
$998$		0			0
$999$	44.7759	+	11.9977i	1.41665	+	0.379590i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	896.2.bh.a.81.20		240
4.3	odd	2		224.2.bd.a.221.3	yes	240
7.2	even	3	inner	896.2.bh.a.849.20		240
28.23	odd	6		224.2.bd.a.93.23	yes	240
32.11	odd	8		224.2.bd.a.53.23	✓	240
32.21	even	8	inner	896.2.bh.a.305.20		240
224.107	odd	24		224.2.bd.a.149.3	yes	240
224.149	even	24	inner	896.2.bh.a.177.20		240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
224.2.bd.a.53.23	✓	240	32.11	odd	8
224.2.bd.a.93.23	yes	240	28.23	odd	6
224.2.bd.a.149.3	yes	240	224.107	odd	24
224.2.bd.a.221.3	yes	240	4.3	odd	2
896.2.bh.a.81.20		240	1.1	even	1	trivial
896.2.bh.a.177.20		240	224.149	even	24	inner
896.2.bh.a.305.20		240	32.21	even	8	inner
896.2.bh.a.849.20		240	7.2	even	3	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:	\( N \)	\(=\)	\( 896 = 2^{7} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	896.bh (of order \(24\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.11575 - 0.856146i) q^{3} +(0.209020 - 0.272400i) q^{5} +(-1.04743 + 2.42958i) q^{7} +(-0.264542 + 0.987286i) q^{9} +O(q^{10})\)	\(q+(1.11575 - 0.856146i) q^{3} +(0.209020 - 0.272400i) q^{5} +(-1.04743 + 2.42958i) q^{7} +(-0.264542 + 0.987286i) q^{9} +(-0.603027 + 4.58045i) q^{11} +(0.512123 - 1.23638i) q^{13} -0.482883i q^{15} +(6.17490 + 3.56508i) q^{17} +(-6.91367 + 0.910201i) q^{19} +(0.911403 + 3.60757i) q^{21} +(1.26848 - 4.73403i) q^{23} +(1.26358 + 4.71575i) q^{25} +(2.16468 + 5.22601i) q^{27} +(-2.69409 - 1.11593i) q^{29} +(-4.81036 + 8.33178i) q^{31} +(3.24870 + 5.62692i) q^{33} +(0.442885 + 0.793153i) q^{35} +(4.98877 - 6.50149i) q^{37} +(-0.487115 - 1.81794i) q^{39} +(-0.781419 - 0.781419i) q^{41} +(8.76180 - 3.62926i) q^{43} +(0.213642 + 0.278424i) q^{45} +(3.11860 - 1.80052i) q^{47} +(-4.80576 - 5.08966i) q^{49} +(9.94188 - 1.30887i) q^{51} +(0.408274 - 3.10115i) q^{53} +(1.12167 + 1.12167i) q^{55} +(-6.93466 + 6.93466i) q^{57} +(-0.303606 - 0.0399704i) q^{59} +(0.639509 + 4.85755i) q^{61} +(-2.12160 - 1.67685i) q^{63} +(-0.229745 - 0.397930i) q^{65} +(6.53355 - 5.01337i) q^{67} +(-2.63771 - 6.36800i) q^{69} +(-6.89237 + 6.89237i) q^{71} +(5.67527 - 1.52068i) q^{73} +(5.44722 + 4.17980i) q^{75} +(-10.4970 - 6.26282i) q^{77} +(6.48602 - 3.74471i) q^{79} +(4.23395 + 2.44447i) q^{81} +(1.84563 - 4.45575i) q^{83} +(2.26181 - 0.936871i) q^{85} +(-3.96134 + 1.06144i) q^{87} +(-4.55360 - 1.22013i) q^{89} +(2.46746 + 2.53927i) q^{91} +(1.76606 + 13.4146i) q^{93} +(-1.19716 + 2.07353i) q^{95} -3.11863 q^{97} +(-4.36268 - 1.80708i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 4 q^{3} - 4 q^{5} + 8 q^{7} - 4 q^{9}+O(q^{10}) \) 240 * q + 4 * q^3 - 4 * q^5 + 8 * q^7 - 4 * q^9	\( 240 q + 4 q^{3} - 4 q^{5} + 8 q^{7} - 4 q^{9} + 4 q^{11} - 16 q^{13} + 4 q^{19} - 8 q^{21} + 12 q^{23} - 4 q^{25} + 16 q^{27} - 16 q^{29} + 56 q^{31} - 8 q^{33} + 32 q^{35} - 4 q^{37} + 4 q^{39} - 16 q^{41} + 8 q^{45} + 28 q^{51} - 20 q^{53} + 16 q^{55} - 16 q^{57} + 36 q^{59} - 4 q^{61} + 16 q^{63} - 8 q^{65} - 36 q^{67} - 16 q^{69} - 48 q^{71} - 4 q^{73} - 16 q^{75} - 8 q^{77} + 96 q^{83} - 56 q^{85} + 4 q^{87} - 4 q^{89} + 56 q^{91} + 20 q^{93} + 8 q^{95} - 32 q^{97} - 8 q^{99}+O(q^{100}) \) 240 * q + 4 * q^3 - 4 * q^5 + 8 * q^7 - 4 * q^9 + 4 * q^11 - 16 * q^13 + 4 * q^19 - 8 * q^21 + 12 * q^23 - 4 * q^25 + 16 * q^27 - 16 * q^29 + 56 * q^31 - 8 * q^33 + 32 * q^35 - 4 * q^37 + 4 * q^39 - 16 * q^41 + 8 * q^45 + 28 * q^51 - 20 * q^53 + 16 * q^55 - 16 * q^57 + 36 * q^59 - 4 * q^61 + 16 * q^63 - 8 * q^65 - 36 * q^67 - 16 * q^69 - 48 * q^71 - 4 * q^73 - 16 * q^75 - 8 * q^77 + 96 * q^83 - 56 * q^85 + 4 * q^87 - 4 * q^89 + 56 * q^91 + 20 * q^93 + 8 * q^95 - 32 * q^97 - 8 * q^99

Introduction

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Database

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