LMFDB - Embedded newform 920.2.bv.a.217.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [920,2,Mod(17,920)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(920, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([0, 0, 11, 14]))

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

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

chi := DirichletCharacter("920.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 920 = 2^{3} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	920.bv (of order $44$, degree $20$, 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:	$7.34623698596$
Analytic rank:	$0$
Dimension:	$720$
Relative dimension:	$36$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			217.10
Character	$\chi$	$=$	920.217
Dual form			920.2.bv.a.513.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.29943 + 0.282674i) q^{3} +(2.15500 + 0.596647i) q^{5} +(-3.34234 + 1.82505i) q^{7} +(-1.12027 + 0.511612i) q^{9} +O(q^{10})$	\(q+(-1.29943 + 0.282674i) q^{3} +(2.15500 + 0.596647i) q^{5} +(-3.34234 + 1.82505i) q^{7} +(-1.12027 + 0.511612i) q^{9} +(-3.02806 - 2.62382i) q^{11} +(0.995015 - 1.82223i) q^{13} +(-2.96893 - 0.166141i) q^{15} +(0.914193 + 0.684356i) q^{17} +(1.16265 - 8.08644i) q^{19} +(3.82725 - 3.31633i) q^{21} +(2.48057 - 4.10448i) q^{23} +(4.28802 + 2.57155i) q^{25} +(4.50484 - 3.37228i) q^{27} +(-0.306883 + 0.0441231i) q^{29} +(-1.90422 + 1.22377i) q^{31} +(4.67645 + 2.55353i) q^{33} +(-8.29164 + 1.93879i) q^{35} +(-3.82515 - 1.42671i) q^{37} +(-0.777857 + 2.64914i) q^{39} +(3.62052 - 7.92784i) q^{41} +(1.56526 + 7.19537i) q^{43} +(-2.71944 + 0.434114i) q^{45} +(5.78946 + 5.78946i) q^{47} +(4.05591 - 6.31112i) q^{49} +(-1.38138 - 0.630857i) q^{51} +(-3.62495 - 6.63861i) q^{53} +(-4.95995 - 7.46101i) q^{55} +(0.775038 + 10.8364i) q^{57} +(-4.24133 - 14.4446i) q^{59} +(1.02715 + 1.59828i) q^{61} +(2.81061 - 3.75454i) q^{63} +(3.23149 - 3.33324i) q^{65} +(13.2495 + 0.947622i) q^{67} +(-2.06311 + 6.03470i) q^{69} +(-3.82759 - 4.41728i) q^{71} +(-7.41840 - 9.90982i) q^{73} +(-6.29891 - 2.12944i) q^{75} +(14.9094 + 3.24334i) q^{77} +(-10.6834 + 3.13694i) q^{79} +(-2.48097 + 2.86319i) q^{81} +(-2.44923 + 6.56663i) q^{83} +(1.56176 + 2.02024i) q^{85} +(0.386302 - 0.144083i) q^{87} +(-9.37790 - 6.02681i) q^{89} +7.90648i q^{91} +(2.12848 - 2.12848i) q^{93} +(7.33027 - 16.7326i) q^{95} +(-5.04805 - 13.5343i) q^{97} +(4.73463 + 1.39021i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 720 q+O(q^{10}) $ 720 * q	$ 720 q - 20 q^{23} + 16 q^{25} - 24 q^{27} - 16 q^{31} + 88 q^{37} - 32 q^{41} + 56 q^{47} - 40 q^{55} + 88 q^{57} + 16 q^{73} - 140 q^{75} - 48 q^{77} + 40 q^{81} - 92 q^{85} - 88 q^{87} + 72 q^{93} - 248 q^{95}+O(q^{100}) $ 720 * q - 20 * q^23 + 16 * q^25 - 24 * q^27 - 16 * q^31 + 88 * q^37 - 32 * q^41 + 56 * q^47 - 40 * q^55 + 88 * q^57 + 16 * q^73 - 140 * q^75 - 48 * q^77 + 40 * q^81 - 92 * q^85 - 88 * q^87 + 72 * q^93 - 248 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/920\mathbb{Z}\right)^\times$.

$n$	$231$	$281$	$461$	$737$
$\chi(n)$	$1$	$e\left(\frac{3}{22}\right)$	$1$	$e\left(\frac{1}{4}\right)$

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
$3$	−1.29943	+	0.282674i	−0.750228	+	0.163202i	−0.571393	−	0.820677i	$-0.693597\pi$
$3$	−1.29943	+	0.282674i	−0.750228	+	0.163202i	−0.178836	+	0.983879i	$0.557233\pi$
$4$		0			0
$5$	2.15500	+	0.596647i	0.963744	+	0.266829i
$5$	2.15500	+	0.596647i	0.963744	+	0.266829i
$6$		0			0
$7$	−3.34234	+	1.82505i	−1.26328	+	0.689806i	−0.964391	−	0.264481i	$-0.914799\pi$
$7$	−3.34234	+	1.82505i	−1.26328	+	0.689806i	−0.298894	+	0.954286i	$0.596618\pi$
$8$		0			0
$9$	−1.12027	+	0.511612i	−0.373424	+	0.170537i
$10$		0			0
$11$	−3.02806	−	2.62382i	−0.912993	−	0.791113i	0.0654016	−	0.997859i	$-0.479167\pi$
$11$	−3.02806	−	2.62382i	−0.912993	−	0.791113i	−0.978395	+	0.206746i	$0.933713\pi$
$12$		0			0
$13$	0.995015	−	1.82223i	0.275968	−	0.505397i	−0.702530	−	0.711654i	$-0.747946\pi$
$13$	0.995015	−	1.82223i	0.275968	−	0.505397i	0.978498	+	0.206257i	$0.0661283\pi$
$14$		0			0
$15$	−2.96893	−	0.166141i	−0.766575	−	0.0428973i
$16$		0			0
$17$	0.914193	+	0.684356i	0.221724	+	0.165981i	0.704366	−	0.709837i	$-0.251232\pi$
$17$	0.914193	+	0.684356i	0.221724	+	0.165981i	−0.482641	+	0.875818i	$0.660322\pi$
$18$		0			0
$19$	1.16265	−	8.08644i	0.266731	−	1.85516i	−0.212098	−	0.977248i	$-0.568030\pi$
$19$	1.16265	−	8.08644i	0.266731	−	1.85516i	0.478830	−	0.877908i	$-0.341061\pi$
$20$		0			0
$21$	3.82725	−	3.31633i	0.835174	−	0.723683i
$22$		0			0
$23$	2.48057	−	4.10448i	0.517235	−	0.855844i
$23$	2.48057	−	4.10448i	0.517235	−	0.855844i
$24$		0			0
$25$	4.28802	+	2.57155i	0.857605	+	0.514309i
$26$		0			0
$27$	4.50484	−	3.37228i	0.866957	−	0.648996i
$28$		0			0
$29$	−0.306883	+	0.0441231i	−0.0569867	+	0.00819345i	−0.170749	−	0.985315i	$-0.554619\pi$
$29$	−0.306883	+	0.0441231i	−0.0569867	+	0.00819345i	0.113762	+	0.993508i	$0.463710\pi$
$30$		0			0
$31$	−1.90422	+	1.22377i	−0.342008	+	0.219795i	−0.700358	−	0.713792i	$-0.746976\pi$
$31$	−1.90422	+	1.22377i	−0.342008	+	0.219795i	0.358349	+	0.933588i	$0.383340\pi$
$32$		0			0
$33$	4.67645	+	2.55353i	0.814065	+	0.444513i
$34$		0			0
$35$	−8.29164	+	1.93879i	−1.40154	+	0.327715i
$36$		0			0
$37$	−3.82515	−	1.42671i	−0.628850	−	0.234549i	0.0147738	−	0.999891i	$-0.495297\pi$
$37$	−3.82515	−	1.42671i	−0.628850	−	0.234549i	−0.643624	+	0.765342i	$0.722570\pi$
$38$		0			0
$39$	−0.777857	+	2.64914i	−0.124557	+	0.424202i
$40$		0			0
$41$	3.62052	−	7.92784i	0.565431	−	1.23812i	−0.383764	−	0.923431i	$-0.625372\pi$
$41$	3.62052	−	7.92784i	0.565431	−	1.23812i	0.949195	−	0.314690i	$-0.101900\pi$
$42$		0			0
$43$	1.56526	+	7.19537i	0.238699	+	1.09728i	0.927934	+	0.372745i	$0.121583\pi$
$43$	1.56526	+	7.19537i	0.238699	+	1.09728i	−0.689235	+	0.724538i	$0.742053\pi$
$44$		0			0
$45$	−2.71944	+	0.434114i	−0.405390	+	0.0647139i
$46$		0			0
$47$	5.78946	+	5.78946i	0.844479	+	0.844479i	0.989438	−	0.144959i	$-0.0463049\pi$
$47$	5.78946	+	5.78946i	0.844479	+	0.844479i	−0.144959	+	0.989438i	$0.546305\pi$
$48$		0			0
$49$	4.05591	−	6.31112i	0.579415	−	0.901588i
$50$		0			0
$51$	−1.38138	−	0.630857i	−0.193432	−	0.0883376i
$52$		0			0
$53$	−3.62495	−	6.63861i	−0.497926	−	0.911883i	−0.998921	−	0.0464330i	$-0.985215\pi$
$53$	−3.62495	−	6.63861i	−0.497926	−	0.911883i	0.500996	−	0.865450i	$-0.332967\pi$
$54$		0			0
$55$	−4.95995	−	7.46101i	−0.668800	−	1.00604i
$56$		0			0
$57$	0.775038	+	10.8364i	0.102656	+	1.43532i
$58$		0			0
$59$	−4.24133	−	14.4446i	−0.552174	−	1.88053i	−0.467204	−	0.884150i	$-0.654738\pi$
$59$	−4.24133	−	14.4446i	−0.552174	−	1.88053i	−0.0849708	−	0.996383i	$-0.527080\pi$
$60$		0			0
$61$	1.02715	+	1.59828i	0.131513	+	0.204639i	0.900765	−	0.434308i	$-0.143007\pi$
$61$	1.02715	+	1.59828i	0.131513	+	0.204639i	−0.769251	+	0.638946i	$0.779371\pi$
$62$		0			0
$63$	2.81061	−	3.75454i	0.354104	−	0.473027i
$64$		0			0
$65$	3.23149	−	3.33324i	0.400816	−	0.413437i
$66$		0			0
$67$	13.2495	+	0.947622i	1.61868	+	0.115770i	0.851037	−	0.525105i	$-0.175974\pi$
$67$	13.2495	+	0.947622i	1.61868	+	0.115770i	0.767645	+	0.640876i	$0.221429\pi$
$68$		0			0
$69$	−2.06311	+	6.03470i	−0.248369	+	0.726492i
$70$		0			0
$71$	−3.82759	−	4.41728i	−0.454252	−	0.524234i	0.481713	−	0.876329i	$-0.340015\pi$
$71$	−3.82759	−	4.41728i	−0.454252	−	0.524234i	−0.935964	+	0.352095i	$0.885469\pi$
$72$		0			0
$73$	−7.41840	−	9.90982i	−0.868258	−	1.15986i	−0.985989	−	0.166811i	$-0.946653\pi$
$73$	−7.41840	−	9.90982i	−0.868258	−	1.15986i	0.117731	−	0.993046i	$-0.462438\pi$
$74$		0			0
$75$	−6.29891	−	2.12944i	−0.727336	−	0.245886i
$76$		0			0
$77$	14.9094	+	3.24334i	1.69908	+	0.369613i
$78$		0			0
$79$	−10.6834	+	3.13694i	−1.20198	+	0.352933i	−0.820610	−	0.571489i	$-0.806366\pi$
$79$	−10.6834	+	3.13694i	−1.20198	+	0.352933i	−0.381370	+	0.924422i	$0.624548\pi$
$80$		0			0
$81$	−2.48097	+	2.86319i	−0.275663	+	0.318132i
$82$		0			0
$83$	−2.44923	+	6.56663i	−0.268838	+	0.720781i	0.730447	+	0.682969i	$0.239312\pi$
$83$	−2.44923	+	6.56663i	−0.268838	+	0.720781i	−0.999285	+	0.0378124i	$0.987961\pi$
$84$		0			0
$85$	1.56176	+	2.02024i	0.169397	+	0.219125i
$86$		0			0
$87$	0.386302	−	0.144083i	0.0414159	−	0.0154473i
$88$		0			0
$89$	−9.37790	−	6.02681i	−0.994055	−	0.638841i	−0.0608359	−	0.998148i	$-0.519377\pi$
$89$	−9.37790	−	6.02681i	−0.994055	−	0.638841i	−0.933219	+	0.359307i	$0.883013\pi$
$90$		0			0
$91$			7.90648i			0.828824i
$92$		0			0
$93$	2.12848	−	2.12848i	0.220713	−	0.220713i
$94$		0			0
$95$	7.33027	−	16.7326i	0.752069	−	1.71672i
$96$		0			0
$97$	−5.04805	−	13.5343i	−0.512552	−	1.37420i	−0.893273	−	0.449515i	$-0.851597\pi$
$97$	−5.04805	−	13.5343i	−0.512552	−	1.37420i	0.380721	−	0.924690i	$-0.375676\pi$
$98$		0			0
$99$	4.73463	+	1.39021i	0.475848	+	0.139722i
$100$		0			0
$101$	−0.499208	−	1.09311i	−0.0496731	−	0.108769i	0.883168	−	0.469056i	$-0.155406\pi$
$101$	−0.499208	−	1.09311i	−0.0496731	−	0.108769i	−0.932841	+	0.360287i	$0.882679\pi$
$102$		0			0
$103$	−13.6637	+	0.977244i	−1.34632	+	0.0962907i	−0.725803	−	0.687902i	$-0.758532\pi$
$103$	−13.6637	+	0.977244i	−1.34632	+	0.0962907i	−0.620517	+	0.784193i	$0.713077\pi$
$104$		0			0
$105$	10.2264	−	4.86316i	0.997993	−	0.474596i
$106$		0			0
$107$	0.183456	−	0.843333i	0.0177353	−	0.0815281i	−0.967429	−	0.253144i	$-0.918535\pi$
$107$	0.183456	−	0.843333i	0.0177353	−	0.0815281i	0.985164	+	0.171616i	$0.0548989\pi$
$108$		0			0
$109$	−1.34283	−	9.33959i	−0.128620	−	0.894571i	−0.947306	−	0.320330i	$-0.896206\pi$
$109$	−1.34283	−	9.33959i	−0.128620	−	0.894571i	0.818686	−	0.574241i	$-0.194703\pi$
$110$		0			0
$111$	5.37382	+	0.772638i	0.510060	+	0.0733356i
$112$		0			0
$113$	−1.11079	+	15.5309i	−0.104494	+	1.46102i	0.626916	+	0.779087i	$0.284317\pi$
$113$	−1.11079	+	15.5309i	−0.104494	+	1.46102i	−0.731411	+	0.681937i	$0.761138\pi$
$114$		0			0
$115$	7.79455	−	7.36512i	0.726846	−	0.686801i
$116$		0			0
$117$	−0.182413	+	2.55046i	−0.0168640	+	0.235790i
$118$		0			0
$119$	−4.30453	−	0.618898i	−0.394595	−	0.0567343i
$120$		0			0
$121$	0.719199	+	5.00214i	0.0653817	+	0.454740i
$122$		0			0
$123$	−2.46363	+	11.3251i	−0.222138	+	1.02115i
$124$		0			0
$125$	7.70638	+	8.10011i	0.689279	+	0.724496i
$126$		0			0
$127$	14.8818	−	1.06437i	1.32055	−	0.0944475i	0.606803	−	0.794852i	$-0.292452\pi$
$127$	14.8818	−	1.06437i	1.32055	−	0.0944475i	0.713746	+	0.700405i	$0.246997\pi$
$128$		0			0
$129$	−4.06789	−	8.90744i	−0.358158	−	0.784257i
$130$		0			0
$131$	−2.10472	−	0.618002i	−0.183890	−	0.0539951i	0.188491	−	0.982075i	$-0.439640\pi$
$131$	−2.10472	−	0.618002i	−0.183890	−	0.0539951i	−0.372381	+	0.928080i	$0.621459\pi$
$132$		0			0
$133$	10.8722	+	29.1495i	0.942740	+	2.52758i
$134$		0			0
$135$	11.7200	−	4.57945i	1.00869	−	0.394137i
$136$		0			0
$137$	−0.339179	+	0.339179i	−0.0289780	+	0.0289780i	−0.721447	−	0.692469i	$-0.756523\pi$
$137$	−0.339179	+	0.339179i	−0.0289780	+	0.0289780i	0.692469	+	0.721447i	$0.256523\pi$
$138$		0			0
$139$			7.65052i			0.648909i	0.945901	+	0.324454i	$0.105181\pi$
$139$			7.65052i			0.648909i	−0.945901	+	0.324454i	$0.894819\pi$
$140$		0			0
$141$	−9.15955	−	5.88648i	−0.771373	−	0.495731i
$142$		0			0
$143$	−7.79418	+	2.90708i	−0.651782	+	0.243102i
$144$		0			0
$145$	−0.687658	−	0.0880156i	−0.0571069	−	0.00730930i
$146$		0			0
$147$	−3.48639	+	9.34738i	−0.287553	+	0.770959i
$148$		0			0
$149$	7.05925	−	8.14681i	0.578317	−	0.667413i	−0.388925	−	0.921269i	$-0.627154\pi$
$149$	7.05925	−	8.14681i	0.578317	−	0.667413i	0.967242	+	0.253856i	$0.0816991\pi$
$150$		0			0
$151$	−16.7495	+	4.91808i	−1.36305	+	0.400228i	−0.879838	−	0.475275i	$-0.842349\pi$
$151$	−16.7495	+	4.91808i	−1.36305	+	0.400228i	−0.483214	+	0.875503i	$0.660531\pi$
$152$		0			0
$153$	−1.37427	−	0.298954i	−0.111103	−	0.0241690i
$154$		0			0
$155$	−4.83375	+	1.50107i	−0.388256	+	0.120569i
$156$		0			0
$157$	−5.31698	−	7.10265i	−0.424341	−	0.566853i	0.536519	−	0.843888i	$-0.319739\pi$
$157$	−5.31698	−	7.10265i	−0.424341	−	0.566853i	−0.960860	+	0.277035i	$0.910648\pi$
$158$		0			0
$159$	6.58695	+	7.60175i	0.522379	+	0.602858i
$160$		0			0
$161$	−0.800004	+	18.2457i	−0.0630492	+	1.43797i
$162$		0			0
$163$	−10.1585	−	0.726550i	−0.795674	−	0.0569078i	−0.332418	−	0.943132i	$-0.607864\pi$
$163$	−10.1585	−	0.726550i	−0.795674	−	0.0569078i	−0.463256	+	0.886224i	$0.653319\pi$
$164$		0			0
$165$	8.55417	+	8.29304i	0.665941	+	0.645612i
$166$		0			0
$167$	−9.02044	+	12.0499i	−0.698023	+	0.932449i	−0.999781	−	0.0209354i	$-0.993336\pi$
$167$	−9.02044	+	12.0499i	−0.698023	+	0.932449i	0.301758	+	0.953384i	$0.402426\pi$
$168$		0			0
$169$	4.69785	+	7.31000i	0.361373	+	0.562307i
$170$		0			0
$171$	2.83462	+	9.65385i	0.216769	+	0.738248i
$172$		0			0
$173$	0.578232	+	8.08475i	0.0439622	+	0.614672i	0.970904	+	0.239468i	$0.0769729\pi$
$173$	0.578232	+	8.08475i	0.0439622	+	0.614672i	−0.926942	+	0.375204i	$0.877573\pi$
$174$		0			0
$175$	−19.0252	−	0.769094i	−1.43817	−	0.0581380i
$176$		0			0
$177$	9.59446	+	17.5709i	0.721164	+	1.32071i
$178$		0			0
$179$	2.93204	+	1.33902i	0.219151	+	0.100083i	0.521966	−	0.852967i	$-0.325199\pi$
$179$	2.93204	+	1.33902i	0.219151	+	0.100083i	−0.302814	+	0.953050i	$0.597926\pi$
$180$		0			0
$181$	−0.495956	+	0.771722i	−0.0368641	+	0.0573616i	−0.859197	−	0.511646i	$-0.829036\pi$
$181$	−0.495956	+	0.771722i	−0.0368641	+	0.0573616i	0.822332	+	0.569007i	$0.192672\pi$
$182$		0			0
$183$	−1.78651	−	1.78651i	−0.132062	−	0.132062i
$184$		0			0
$185$	−7.39194	−	5.35681i	−0.543466	−	0.393840i
$186$		0			0
$187$	−0.972596	−	4.47095i	−0.0711232	−	0.326948i
$188$		0			0
$189$	−8.90209	+	19.4929i	−0.647532	+	1.41790i
$190$		0			0
$191$	−3.96996	+	13.5205i	−0.287257	+	0.978306i	0.681815	+	0.731525i	$0.261191\pi$
$191$	−3.96996	+	13.5205i	−0.287257	+	0.978306i	−0.969071	+	0.246781i	$0.920627\pi$
$192$		0			0
$193$	−21.2771	−	7.93594i	−1.53156	−	0.571241i	−0.564418	−	0.825489i	$-0.690900\pi$
$193$	−21.2771	−	7.93594i	−1.53156	−	0.571241i	−0.967139	+	0.254247i	$0.918172\pi$
$194$		0			0
$195$	−3.25688	+	5.24478i	−0.233230	+	0.375586i
$196$		0			0
$197$	10.6190	+	5.79839i	0.756570	+	0.413118i	0.810735	−	0.585414i	$-0.199068\pi$
$197$	10.6190	+	5.79839i	0.756570	+	0.413118i	−0.0541649	+	0.998532i	$0.517250\pi$
$198$		0			0
$199$	17.1839	−	11.0434i	1.21813	−	0.782846i	0.236131	−	0.971721i	$-0.424120\pi$
$199$	17.1839	−	11.0434i	1.21813	−	0.782846i	0.982001	+	0.188875i	$0.0604841\pi$
$200$		0			0
$201$	−17.4847	+	2.51392i	−1.23328	+	0.177318i
$202$		0			0
$203$	0.945179	−	0.707552i	0.0663386	−	0.0496604i
$204$		0			0
$205$	12.5323	−	14.9243i	0.875297	−	1.04236i
$206$		0			0
$207$	−0.679017	+	5.86723i	−0.0471949	+	0.407801i
$208$		0			0
$209$	−24.7380	+	21.4356i	−1.71116	+	1.48273i
$210$		0			0
$211$	1.59798	−	11.1142i	0.110009	−	0.765132i	−0.857897	−	0.513821i	$-0.828229\pi$
$211$	1.59798	−	11.1142i	0.110009	−	0.765132i	0.967907	−	0.251310i	$-0.0808615\pi$
$212$		0			0
$213$	6.22236	+	4.65800i	0.426349	+	0.319161i
$214$		0			0
$215$	−0.919972	+	16.4399i	−0.0627415	+	1.12119i
$216$		0			0
$217$	4.13111	−	7.56556i	0.280438	−	0.513583i
$218$		0			0
$219$	12.4410	+	10.7802i	0.840683	+	0.728456i
$220$		0			0
$221$	2.15669	−	0.984929i	0.145075	−	0.0662535i
$222$		0			0
$223$	19.6490	−	10.7292i	1.31580	−	0.718480i	0.340682	−	0.940179i	$-0.389342\pi$
$223$	19.6490	−	10.7292i	1.31580	−	0.718480i	0.975115	+	0.221699i	$0.0711602\pi$
$224$		0			0
$225$	−6.11939	−	0.687030i	−0.407959	−	0.0458020i
$226$		0			0
$227$	−4.48863	+	0.976443i	−0.297921	+	0.0648088i	−0.359041	−	0.933322i	$-0.616896\pi$
$227$	−4.48863	+	0.976443i	−0.297921	+	0.0648088i	0.0611203	+	0.998130i	$0.480533\pi$
$228$		0			0
$229$	13.2340			0.874530			0.437265	−	0.899333i	$-0.355947\pi$
$229$	13.2340			0.874530			0.437265	+	0.899333i	$0.355947\pi$
$230$		0			0
$231$	−20.2906			−1.33502
$232$		0			0
$233$	14.5846	−	3.17269i	0.955469	−	0.207850i	0.292306	−	0.956325i	$-0.405577\pi$
$233$	14.5846	−	3.17269i	0.955469	−	0.207850i	0.663163	+	0.748475i	$0.269214\pi$
$234$		0			0
$235$	9.02200	+	15.9305i	0.588530	+	1.03919i
$236$		0			0
$237$	12.9957	−	7.09618i	0.844160	−	0.460946i
$238$		0			0
$239$	4.83456	−	2.20787i	0.312721	−	0.142815i	−0.252871	−	0.967500i	$-0.581375\pi$
$239$	4.83456	−	2.20787i	0.312721	−	0.142815i	0.565592	+	0.824685i	$0.308648\pi$
$240$		0			0
$241$	4.94388	+	4.28390i	0.318463	+	0.275950i	0.799392	−	0.600810i	$-0.205155\pi$
$241$	4.94388	+	4.28390i	0.318463	+	0.275950i	−0.480929	+	0.876760i	$0.659700\pi$
$242$		0			0
$243$	−5.67605	+	10.3949i	−0.364119	+	0.666833i
$244$		0			0
$245$	12.5060	−	11.1805i	0.798978	−	0.714295i
$246$		0			0
$247$	−13.5785	−	10.1648i	−0.863981	−	0.646768i
$248$		0			0
$249$	1.32639	−	9.22524i	0.0840565	−	0.584626i
$250$		0			0
$251$	0.738395	−	0.639823i	0.0466071	−	0.0403852i	−0.631246	−	0.775583i	$-0.717456\pi$
$251$	0.738395	−	0.639823i	0.0466071	−	0.0403852i	0.677853	+	0.735198i	$0.262911\pi$
$252$		0			0
$253$	−18.2807	+	5.92001i	−1.14930	+	0.372188i
$254$		0			0
$255$	−2.60048	−	2.18369i	−0.162848	−	0.136748i
$256$		0			0
$257$	12.6096	−	9.43943i	0.786565	−	0.588815i	−0.128692	−	0.991685i	$-0.541078\pi$
$257$	12.6096	−	9.43943i	0.786565	−	0.588815i	0.915258	+	0.402869i	$0.131987\pi$
$258$		0			0
$259$	15.3887	−	2.21257i	0.956210	−	0.137482i
$260$		0			0
$261$	0.321219	−	0.206435i	0.0198829	−	0.0127780i
$262$		0			0
$263$	−3.88059	−	2.11896i	−0.239288	−	0.130661i	0.355131	−	0.934816i	$-0.384436\pi$
$263$	−3.88059	−	2.11896i	−0.239288	−	0.130661i	−0.594419	+	0.804155i	$0.702618\pi$
$264$		0			0
$265$	−3.85086	−	16.4690i	−0.236556	−	1.01168i
$266$		0			0
$267$	13.8896	+	5.18055i	0.850029	+	0.317044i
$268$		0			0
$269$	−5.44716	+	18.5513i	−0.332119	+	1.13110i	0.609042	+	0.793138i	$0.291554\pi$
$269$	−5.44716	+	18.5513i	−0.332119	+	1.13110i	−0.941161	+	0.337957i	$0.890264\pi$
$270$		0			0
$271$	5.12469	−	11.2215i	0.311303	−	0.681658i	−0.687714	−	0.725981i	$-0.741386\pi$
$271$	5.12469	−	11.2215i	0.311303	−	0.681658i	0.999017	+	0.0443232i	$0.0141131\pi$
$272$		0			0
$273$	−2.23496	−	10.2739i	−0.135266	−	0.621807i
$274$		0			0
$275$	−6.23709	−	19.0378i	−0.376111	−	1.14802i
$276$		0			0
$277$	−10.3835	−	10.3835i	−0.623883	−	0.623883i	0.322639	−	0.946522i	$-0.395430\pi$
$277$	−10.3835	−	10.3835i	−0.623883	−	0.623883i	−0.946522	+	0.322639i	$0.895430\pi$
$278$		0			0
$279$	1.50715	−	2.34518i	0.0902309	−	0.140402i
$280$		0			0
$281$	−19.5140	−	8.91174i	−1.16411	−	0.531630i	−0.262817	−	0.964846i	$-0.584651\pi$
$281$	−19.5140	−	8.91174i	−1.16411	−	0.531630i	−0.901290	+	0.433216i	$0.857379\pi$
$282$		0			0
$283$	0.0990131	+	0.181329i	0.00588572	+	0.0107789i	0.880605	−	0.473851i	$-0.157136\pi$
$283$	0.0990131	+	0.181329i	0.00588572	+	0.0107789i	−0.874720	+	0.484629i	$0.838954\pi$
$284$		0			0
$285$	−4.79533	+	23.8149i	−0.284051	+	1.41067i
$286$		0			0
$287$	2.36773	+	33.1052i	0.139763	+	1.95414i
$288$		0			0
$289$	−4.42205	−	15.0601i	−0.260120	−	0.885889i
$290$		0			0
$291$	10.3854	+	16.1600i	0.608804	+	0.947318i
$292$		0			0
$293$	−3.02466	+	4.04047i	−0.176702	+	0.236047i	−0.880145	−	0.474706i	$-0.842554\pi$
$293$	−3.02466	+	4.04047i	−0.176702	+	0.236047i	0.703442	+	0.710752i	$0.251645\pi$
$294$		0			0
$295$	−0.521700	−	33.6588i	−0.0303746	−	1.95969i
$296$		0			0
$297$	−22.4892	−	1.60846i	−1.30495	−	0.0933322i
$298$		0			0
$299$	−5.01112	−	8.60420i	−0.289801	−	0.497594i
$300$		0			0
$301$	−18.3635	−	21.1927i	−1.05846	−	1.22152i
$302$		0			0
$303$	0.957683	+	1.27932i	0.0550175	+	0.0734947i
$304$		0			0
$305$	1.25990	+	4.05713i	0.0721416	+	0.232311i
$306$		0			0
$307$	2.92989	+	0.637358i	0.167217	+	0.0363759i	0.295394	−	0.955375i	$-0.404549\pi$
$307$	2.92989	+	0.637358i	0.167217	+	0.0363759i	−0.128177	+	0.991751i	$0.540913\pi$
$308$		0			0
$309$	17.4788	−	5.13223i	0.994333	−	0.291962i
$310$		0			0
$311$	3.98884	−	4.60337i	0.226187	−	0.261033i	−0.631301	−	0.775538i	$-0.717479\pi$
$311$	3.98884	−	4.60337i	0.226187	−	0.261033i	0.857488	+	0.514505i	$0.172024\pi$
$312$		0			0
$313$	4.16893	−	11.1773i	0.235642	−	0.631781i	−0.764272	−	0.644894i	$-0.776902\pi$
$313$	4.16893	−	11.1773i	0.235642	−	0.631781i	0.999914	+	0.0131134i	$0.00417423\pi$
$314$		0			0
$315$	8.29699	−	6.41407i	0.467482	−	0.361392i
$316$		0			0
$317$	21.7114	−	8.09795i	1.21944	−	0.454826i	0.344372	−	0.938833i	$-0.388092\pi$
$317$	21.7114	−	8.09795i	1.21944	−	0.454826i	0.875064	+	0.484007i	$0.160819\pi$
$318$		0			0
$319$	1.04503	+	0.671600i	0.0585104	+	0.0376024i
$320$		0			0
$321$			1.14771i			0.0640591i
$322$		0			0
$323$	6.59689	−	6.59689i	0.367061	−	0.367061i
$324$		0			0
$325$	8.95261	−	5.25506i	0.496601	−	0.291498i
$326$		0			0
$327$	4.38498	+	11.7566i	0.242490	+	0.650141i
$328$		0			0
$329$	−29.9164	−	8.78424i	−1.64934	−	0.484291i
$330$		0			0
$331$	−5.93915	−	13.0049i	−0.326445	−	0.714815i	0.673252	−	0.739413i	$-0.264897\pi$
$331$	−5.93915	−	13.0049i	−0.326445	−	0.714815i	−0.999697	+	0.0245976i	$0.992170\pi$
$332$		0			0
$333$	5.01513	−	0.358689i	0.274827	−	0.0196560i
$334$		0			0
$335$	27.9872	+	9.94739i	1.52910	+	0.543484i
$336$		0			0
$337$	−3.07554	+	14.1380i	−0.167535	+	0.770147i	0.814305	+	0.580437i	$0.197118\pi$
$337$	−3.07554	+	14.1380i	−0.167535	+	0.770147i	−0.981840	+	0.189710i	$0.939245\pi$
$338$		0			0
$339$	−2.94679	−	20.4954i	−0.160048	−	1.11316i
$340$		0			0
$341$	8.97704	+	1.29070i	0.486134	+	0.0698955i
$342$		0			0
$343$	−0.136389	+	1.90696i	−0.00736430	+	0.102966i
$344$		0			0
$345$	−8.04657	+	11.7738i	−0.433213	+	0.633880i
$346$		0			0
$347$	−2.31694	+	32.3950i	−0.124380	+	1.73906i	0.426513	+	0.904481i	$0.359742\pi$
$347$	−2.31694	+	32.3950i	−0.124380	+	1.73906i	−0.550893	+	0.834576i	$0.685713\pi$
$348$		0			0
$349$	34.5506	+	4.96763i	1.84945	+	0.265911i	0.975484	−	0.220072i	$-0.0706293\pi$
$349$	34.5506	+	4.96763i	1.84945	+	0.265911i	0.873968	+	0.485983i	$0.161538\pi$
$350$		0			0
$351$	−1.66270	−	11.5643i	−0.0887484	−	0.617259i
$352$		0			0
$353$	−3.58443	+	16.4774i	−0.190780	+	0.877002i	0.777841	+	0.628461i	$0.216315\pi$
$353$	−3.58443	+	16.4774i	−0.190780	+	0.877002i	−0.968621	+	0.248541i	$0.920049\pi$
$354$		0			0
$355$	−5.61290	−	11.8029i	−0.297902	−	0.626435i
$356$		0			0
$357$	5.76839	−	0.412564i	0.305296	−	0.0218352i
$358$		0			0
$359$	3.69381	+	8.08832i	0.194952	+	0.426885i	0.981712	−	0.190374i	$-0.0609701\pi$
$359$	3.69381	+	8.08832i	0.194952	+	0.426885i	−0.786760	+	0.617260i	$0.788243\pi$
$360$		0			0
$361$	−45.8084	−	13.4505i	−2.41097	−	0.707924i
$362$		0			0
$363$	−2.34853	−	6.29665i	−0.123266	−	0.330488i
$364$		0			0
$365$	−10.0740	−	25.7818i	−0.527295	−	1.34948i
$366$		0			0
$367$	3.71598	−	3.71598i	0.193973	−	0.193973i	−0.603438	−	0.797410i	$-0.706203\pi$
$367$	3.71598	−	3.71598i	0.193973	−	0.193973i	0.797410	+	0.603438i	$0.206203\pi$
$368$		0			0
$369$			10.7336i			0.558771i
$370$		0			0
$371$	24.2316	+	15.5727i	1.25804	+	0.808495i
$372$		0			0
$373$	−31.0462	+	11.5796i	−1.60751	+	0.599571i	−0.983350	−	0.181724i	$-0.941832\pi$
$373$	−31.0462	+	11.5796i	−1.60751	+	0.599571i	−0.624162	+	0.781295i	$0.714559\pi$
$374$		0			0
$375$	−12.3036	−	8.34716i	−0.635356	−	0.431045i
$376$		0			0
$377$	−0.224950	+	0.603116i	−0.0115855	+	0.0310620i
$378$		0			0
$379$	20.4037	−	23.5471i	1.04807	−	1.20953i	0.0708064	−	0.997490i	$-0.477443\pi$
$379$	20.4037	−	23.5471i	1.04807	−	1.20953i	0.977260	−	0.212043i	$-0.0680118\pi$
$380$		0			0
$381$	−19.0371	+	5.58979i	−0.975299	+	0.286374i
$382$		0			0
$383$	7.00559	+	1.52397i	0.357969	+	0.0778714i	0.387954	−	0.921679i	$-0.373182\pi$
$383$	7.00559	+	1.52397i	0.357969	+	0.0778714i	−0.0299844	+	0.999550i	$0.509546\pi$
$384$		0			0
$385$	30.1946	+	15.8850i	1.53886	+	0.809577i
$386$		0			0
$387$	−5.43475	−	7.25997i	−0.276264	−	0.369045i
$388$		0			0
$389$	17.2863	+	19.9494i	0.876449	+	1.01148i	0.999817	+	0.0191154i	$0.00608501\pi$
$389$	17.2863	+	19.9494i	0.876449	+	1.01148i	−0.123368	+	0.992361i	$0.539370\pi$
$390$		0			0
$391$	5.07665	−	2.05469i	0.256737	−	0.103910i
$392$		0			0
$393$	2.90964	+	0.208101i	0.146772	+	0.0104973i
$394$		0			0
$395$	−24.8944	+	0.385856i	−1.25257	+	0.0194145i
$396$		0			0
$397$	4.67317	−	6.24262i	0.234540	−	0.313308i	−0.667794	−	0.744346i	$-0.732761\pi$
$397$	4.67317	−	6.24262i	0.234540	−	0.313308i	0.902334	+	0.431037i	$0.141852\pi$
$398$		0			0
$399$	−22.3675	−	34.8046i	−1.11978	−	1.74241i
$400$		0			0
$401$	2.28523	+	7.78276i	0.114119	+	0.388653i	0.996668	−	0.0815676i	$-0.0259927\pi$
$401$	2.28523	+	7.78276i	0.114119	+	0.388653i	−0.882549	+	0.470220i	$0.844174\pi$
$402$		0			0
$403$	0.335264	+	4.68761i	0.0167007	+	0.233506i
$404$		0			0
$405$	−7.05479	+	4.68990i	−0.350555	+	0.233043i
$406$		0			0
$407$	7.83933	+	14.3567i	0.388581	+	0.711633i
$408$		0			0
$409$	−19.6046	−	8.95314i	−0.969387	−	0.442704i	−0.133164	−	0.991094i	$-0.542514\pi$
$409$	−19.6046	−	8.95314i	−0.969387	−	0.442704i	−0.836223	+	0.548390i	$0.815241\pi$
$410$		0			0
$411$	0.344863	−	0.536618i	0.0170109	−	0.0264694i
$412$		0			0
$413$	40.5382	+	40.5382i	1.99476	+	1.99476i
$414$		0			0
$415$	−9.19604	+	12.6897i	−0.451416	+	0.622915i
$416$		0			0
$417$	−2.16261	−	9.94134i	−0.105903	−	0.486830i
$418$		0			0
$419$	−7.43423	+	16.2787i	−0.363186	+	0.795266i	0.636526	+	0.771255i	$0.280371\pi$
$419$	−7.43423	+	16.2787i	−0.363186	+	0.795266i	−0.999712	+	0.0240106i	$0.992356\pi$
$420$		0			0
$421$	−3.07610	+	10.4762i	−0.149920	+	0.510580i	−0.999867	−	0.0162874i	$-0.994815\pi$
$421$	−3.07610	+	10.4762i	−0.149920	+	0.510580i	0.849948	+	0.526867i	$0.176633\pi$
$422$		0			0
$423$	−9.44773	−	3.52382i	−0.459364	−	0.171334i
$424$		0			0
$425$	2.16023	+	5.28542i	0.104786	+	0.256381i
$426$		0			0
$427$	−6.35003	−	3.46738i	−0.307299	−	0.167798i
$428$		0			0
$429$	9.30627	−	5.98077i	0.449311	−	0.288755i
$430$		0			0
$431$	39.9246	−	5.74030i	1.92310	−	0.276500i	0.927782	−	0.373124i	$-0.121713\pi$
$431$	39.9246	−	5.74030i	1.92310	−	0.276500i	0.995321	+	0.0966235i	$0.0308043\pi$
$432$		0			0
$433$	−2.41648	+	1.80895i	−0.116128	+	0.0869326i	−0.655763	−	0.754966i	$-0.727653\pi$
$433$	−2.41648	+	1.80895i	−0.116128	+	0.0869326i	0.539635	+	0.841899i	$0.318562\pi$
$434$		0			0
$435$	0.918445	−	0.0800128i	0.0440361	−	0.00383632i
$436$		0			0
$437$	−30.3066	−	24.8311i	−1.44976	−	1.18783i
$438$		0			0
$439$	−1.88426	+	1.63272i	−0.0899309	+	0.0779255i	−0.698666	−	0.715448i	$-0.746223\pi$
$439$	−1.88426	+	1.63272i	−0.0899309	+	0.0779255i	0.608735	+	0.793373i	$0.291677\pi$
$440$		0			0
$441$	−1.31488	+	9.14522i	−0.0626135	+	0.435487i
$442$		0			0
$443$	3.27779	+	2.45372i	0.155732	+	0.116580i	0.674302	−	0.738455i	$-0.264445\pi$
$443$	3.27779	+	2.45372i	0.155732	+	0.116580i	−0.518570	+	0.855035i	$0.673535\pi$
$444$		0			0
$445$	−16.6135	−	18.5831i	−0.787554	−	0.880921i
$446$		0			0
$447$	−6.87014	+	12.5817i	−0.324946	+	0.595095i
$448$		0			0
$449$	−1.84205	−	1.59614i	−0.0869315	−	0.0753266i	0.610311	−	0.792162i	$-0.291044\pi$
$449$	−1.84205	−	1.59614i	−0.0869315	−	0.0753266i	−0.697243	+	0.716835i	$0.745590\pi$
$450$		0			0
$451$	−31.7644	+	14.5063i	−1.49573	+	0.683076i
$452$		0			0
$453$	20.3746	−	11.1254i	0.957282	−	0.522715i
$454$		0			0
$455$	−4.71738	+	17.0384i	−0.221154	+	0.798774i
$456$		0			0
$457$	−25.0609	+	5.45167i	−1.17230	+	0.255018i	−0.756225	−	0.654312i	$-0.772958\pi$
$457$	−25.0609	+	5.45167i	−1.17230	+	0.255018i	−0.416076	+	0.909330i	$0.636595\pi$
$458$		0			0
$459$	6.42613			0.299946
$460$		0			0
$461$	26.1575			1.21828			0.609138	−	0.793064i	$-0.291516\pi$
$461$	26.1575			1.21828			0.609138	+	0.793064i	$0.291516\pi$
$462$		0			0
$463$	3.73181	−	0.811807i	0.173432	−	0.0377279i	−0.125011	−	0.992155i	$-0.539896\pi$
$463$	3.73181	−	0.811807i	0.173432	−	0.0377279i	0.298443	+	0.954428i	$0.403533\pi$
$464$		0			0
$465$	5.85682	−	3.31692i	0.271604	−	0.153818i
$466$		0			0
$467$	16.1009	−	8.79178i	0.745063	−	0.406835i	−0.0614050	−	0.998113i	$-0.519558\pi$
$467$	16.1009	−	8.79178i	0.745063	−	0.406835i	0.806468	+	0.591278i	$0.201376\pi$
$468$		0			0
$469$	−46.0137	+	21.0137i	−2.12471	+	0.970325i
$470$		0			0
$471$	8.91680	+	7.72645i	0.410864	+	0.356016i
$472$		0			0
$473$	14.1397	−	25.8949i	0.650144	−	1.19065i
$474$		0			0
$475$	25.7801	−	31.6850i	1.18287	−	1.45381i
$476$		0			0
$477$	7.45732	+	5.58248i	0.341447	+	0.255604i
$478$		0			0
$479$	−0.361817	+	2.51650i	−0.0165319	+	0.114982i	−0.996416	−	0.0845838i	$-0.973044\pi$
$479$	−0.361817	+	2.51650i	−0.0165319	+	0.114982i	0.979885	+	0.199565i	$0.0639530\pi$
$480$		0			0
$481$	−6.40587	+	5.55072i	−0.292083	+	0.253091i
$482$		0			0
$483$	−4.11805	−	23.9353i	−0.187378	−	1.08909i
$484$		0			0
$485$	−2.80331	−	32.1784i	−0.127292	−	1.46114i
$486$		0			0
$487$	14.7034	−	11.0068i	0.666274	−	0.498766i	−0.211787	−	0.977316i	$-0.567928\pi$
$487$	14.7034	−	11.0068i	0.666274	−	0.498766i	0.878060	+	0.478550i	$0.158837\pi$
$488$		0			0
$489$	13.4057	−	1.92744i	0.606225	−	0.0871620i
$490$		0			0
$491$	−0.758031	+	0.487157i	−0.0342094	+	0.0219851i	−0.557634	−	0.830087i	$-0.688291\pi$
$491$	−0.758031	+	0.487157i	−0.0342094	+	0.0219851i	0.523424	+	0.852072i	$0.324654\pi$
$492$		0			0
$493$	−0.310746	−	0.169680i	−0.0139953	−	0.00764201i
$494$		0			0
$495$	9.37364	+	5.82080i	0.421314	+	0.261626i
$496$		0			0
$497$	20.8549	+	7.77847i	0.935469	+	0.348912i
$498$		0			0
$499$	2.68518	−	9.14488i	0.120205	−	0.409381i	−0.877303	−	0.479938i	$-0.840659\pi$
$499$	2.68518	−	9.14488i	0.120205	−	0.409381i	0.997508	+	0.0705565i	$0.0224775\pi$
$500$		0			0
$501$	8.31527	−	18.2079i	0.371499	−	0.813469i
$502$		0			0
$503$	−0.115224	−	0.529676i	−0.00513758	−	0.0236171i	0.974507	−	0.224358i	$-0.0720286\pi$
$503$	−0.115224	−	0.529676i	−0.00513758	−	0.0236171i	−0.979644	+	0.200741i	$0.935665\pi$
$504$		0			0
$505$	−0.423589	−	2.65351i	−0.0188495	−	0.118080i
$506$		0			0
$507$	−8.17089	−	8.17089i	−0.362882	−	0.362882i
$508$		0			0
$509$	−9.41590	+	14.6514i	−0.417352	+	0.649413i	−0.984739	−	0.174039i	$-0.944318\pi$
$509$	−9.41590	+	14.6514i	−0.417352	+	0.649413i	0.567386	+	0.823452i	$0.307955\pi$
$510$		0			0
$511$	42.8808	+	19.5830i	1.89693	+	0.866300i
$512$		0			0
$513$	−22.0322	−	40.3489i	−0.972744	−	1.78145i
$514$		0			0
$515$	−30.0282	−	6.04642i	−1.32320	−	0.266437i
$516$		0			0
$517$	−2.34027	−	32.7213i	−0.102925	−	1.43908i
$518$		0			0
$519$	−3.03673	−	10.3421i	−0.133297	−	0.453970i
$520$		0			0
$521$	−23.5440	−	36.6352i	−1.03148	−	1.60502i	−0.768106	−	0.640322i	$-0.778801\pi$
$521$	−23.5440	−	36.6352i	−1.03148	−	1.60502i	−0.263375	−	0.964694i	$-0.584836\pi$
$522$		0			0
$523$	15.0003	−	20.0381i	0.655918	−	0.876204i	−0.342065	−	0.939676i	$-0.611126\pi$
$523$	15.0003	−	20.0381i	0.655918	−	0.876204i	0.997984	+	0.0634720i	$0.0202173\pi$
$524$		0			0
$525$	24.9394	−	4.37856i	1.08845	−	0.191096i
$526$		0			0
$527$	−2.57832	−	0.184405i	−0.112313	−	0.00803281i
$528$		0			0
$529$	−10.6935	−	20.3629i	−0.464936	−	0.885344i
$530$		0			0
$531$	12.1415	+	14.0120i	0.526896	+	0.608071i
$532$		0			0
$533$	−10.8439	−	14.4858i	−0.469702	−	0.627448i
$534$		0			0
$535$	0.898519	−	1.70792i	0.0388464	−	0.0738399i
$536$		0			0
$537$	−4.18850	−	0.911153i	−0.180747	−	0.0393192i
$538$		0			0
$539$	−28.8408	+	8.46842i	−1.24226	+	0.364760i
$540$		0			0
$541$	−4.08803	+	4.71784i	−0.175758	+	0.202836i	−0.836793	−	0.547520i	$-0.815572\pi$
$541$	−4.08803	+	4.71784i	−0.175758	+	0.202836i	0.661035	+	0.750355i	$0.270118\pi$
$542$		0			0
$543$	0.426315	−	1.14300i	0.0182949	−	0.0490506i
$544$		0			0
$545$	2.67864	−	20.9280i	0.114740	−	0.896456i
$546$		0			0
$547$	−22.5762	+	8.42049i	−0.965289	+	0.360034i	−0.782176	−	0.623058i	$-0.785890\pi$
$547$	−22.5762	+	8.42049i	−0.965289	+	0.360034i	−0.183113	+	0.983092i	$0.558617\pi$
$548$		0			0
$549$	−1.96839	−	1.26501i	−0.0840087	−	0.0539891i
$550$		0			0
$551$			2.53289i			0.107905i
$552$		0			0
$553$	29.9825	−	29.9825i	1.27499	−	1.27499i
$554$		0			0
$555$	11.1196	+	4.87131i	0.471999	+	0.206775i
$556$		0			0
$557$	6.63042	+	17.7768i	0.280940	+	0.753229i	0.998396	+	0.0566248i	$0.0180339\pi$
$557$	6.63042	+	17.7768i	0.280940	+	0.753229i	−0.717456	+	0.696604i	$0.754693\pi$
$558$		0			0
$559$	14.6691	+	4.30723i	0.620437	+	0.182177i
$560$		0			0
$561$	2.52765	+	5.53478i	0.106717	+	0.233678i
$562$		0			0
$563$	−35.4869	+	2.53807i	−1.49559	+	0.106967i	−0.795008	−	0.606600i	$-0.792533\pi$
$563$	−35.4869	+	2.53807i	−1.49559	+	0.106967i	−0.700587	+	0.713567i	$0.747079\pi$
$564$		0			0
$565$	−11.6602	+	32.8063i	−0.490549	+	1.38017i
$566$		0			0
$567$	3.06675	−	14.0976i	0.128792	−	0.592045i
$568$		0			0
$569$	1.43286	+	9.96577i	0.0600687	+	0.417787i	0.997562	+	0.0697840i	$0.0222310\pi$
$569$	1.43286	+	9.96577i	0.0600687	+	0.417787i	−0.937493	+	0.348003i	$0.886860\pi$
$570$		0			0
$571$	9.24080	+	1.32863i	0.386715	+	0.0556013i	0.332931	−	0.942951i	$-0.391962\pi$
$571$	9.24080	+	1.32863i	0.386715	+	0.0556013i	0.0537847	+	0.998553i	$0.482872\pi$
$572$		0			0
$573$	1.33682	−	18.6911i	0.0558463	−	0.780834i
$574$		0			0
$575$	21.1916	−	11.2212i	0.883751	−	0.467957i
$576$		0			0
$577$	−0.291655	+	4.07786i	−0.0121417	+	0.169764i	0.987763	+	0.155962i	$0.0498478\pi$
$577$	−0.291655	+	4.07786i	−0.0121417	+	0.169764i	−0.999905	+	0.0138014i	$0.995607\pi$
$578$		0			0
$579$	29.8914	+	4.29774i	1.24225	+	0.178608i
$580$		0			0
$581$	−3.79832	−	26.4179i	−0.157581	−	1.09600i
$582$		0			0
$583$	−6.44198	+	29.6133i	−0.266800	+	1.22646i
$584$		0			0
$585$	−1.91482	+	5.38740i	−0.0791682	+	0.222742i
$586$		0			0
$587$	13.5763	−	0.970994i	0.560353	−	0.0400772i	0.211709	−	0.977333i	$-0.432097\pi$
$587$	13.5763	−	0.970994i	0.560353	−	0.0400772i	0.348643	+	0.937255i	$0.386642\pi$
$588$		0			0
$589$	7.68198	+	16.8212i	0.316531	+	0.693105i
$590$		0			0
$591$	−15.4377	−	4.53292i	−0.635022	−	0.186459i
$592$		0			0
$593$	−7.22835	−	19.3800i	−0.296833	−	0.795840i	−0.996670	−	0.0815374i	$-0.974017\pi$
$593$	−7.22835	−	19.3800i	−0.296833	−	0.795840i	0.699837	−	0.714302i	$-0.253256\pi$
$594$		0			0
$595$	−8.90698	−	3.90201i	−0.365151	−	0.159967i
$596$		0			0
$597$	−19.2076	+	19.2076i	−0.786115	+	0.786115i
$598$		0			0
$599$		−	35.5964i		−	1.45443i	−0.686410	−	0.727215i	$-0.740814\pi$
$599$		−	35.5964i		−	1.45443i	0.686410	−	0.727215i	$-0.259186\pi$
$600$		0			0
$601$	11.5428	+	7.41810i	0.470840	+	0.302590i	0.754460	−	0.656346i	$-0.227899\pi$
$601$	11.5428	+	7.41810i	0.470840	+	0.302590i	−0.283620	+	0.958937i	$0.591535\pi$
$602$		0			0
$603$	−15.3278	+	5.71699i	−0.624198	+	0.232814i
$604$		0			0
$605$	−1.43464	+	11.2087i	−0.0583264	+	0.455698i
$606$		0			0
$607$	−10.7511	+	28.8248i	−0.436374	+	1.16996i	0.513708	+	0.857965i	$0.328271\pi$
$607$	−10.7511	+	28.8248i	−0.436374	+	1.16996i	−0.950082	+	0.311999i	$0.899001\pi$
$608$		0			0
$609$	−1.02819	+	1.18660i	−0.0416644	+	0.0480833i
$610$		0			0
$611$	16.3103	−	4.78915i	0.659846	−	0.193748i
$612$		0			0
$613$	−4.73824	−	1.03074i	−0.191376	−	0.0416313i	0.115856	−	0.993266i	$-0.463039\pi$
$613$	−4.73824	−	1.03074i	−0.191376	−	0.0416313i	−0.307232	+	0.951635i	$0.599403\pi$
$614$		0			0
$615$	−12.0662	+	22.9357i	−0.486557	+	0.924857i
$616$		0			0
$617$	−20.8926	−	27.9093i	−0.841105	−	1.12358i	−0.990864	−	0.134862i	$-0.956941\pi$
$617$	−20.8926	−	27.9093i	−0.841105	−	1.12358i	0.149759	−	0.988722i	$-0.452150\pi$
$618$		0			0
$619$	−22.5917	−	26.0722i	−0.908035	−	1.04793i	−0.998645	−	0.0520422i	$-0.983427\pi$
$619$	−22.5917	−	26.0722i	−0.908035	−	1.04793i	0.0906095	−	0.995886i	$-0.471118\pi$
$620$		0			0
$621$	−2.66689	−	26.8552i	−0.107018	−	1.07766i
$622$		0			0
$623$	42.3433	+	3.02846i	1.69645	+	0.121333i
$624$		0			0
$625$	11.7743	+	22.0537i	0.470972	+	0.882148i
$626$		0			0
$627$	26.0861	−	34.8469i	1.04178	−	1.39165i
$628$		0			0
$629$	−2.52055	−	3.92205i	−0.100501	−	0.156382i
$630$		0			0
$631$	−2.13576	−	7.27374i	−0.0850234	−	0.289563i	0.905995	−	0.423288i	$-0.139124\pi$
$631$	−2.13576	−	7.27374i	−0.0850234	−	0.289563i	−0.991018	+	0.133725i	$0.957306\pi$
$632$		0			0
$633$	1.06523	+	14.8938i	0.0423391	+	0.591977i
$634$		0			0
$635$	32.7054	+	6.58549i	1.29787	+	0.261337i
$636$		0			0
$637$	−7.46464	−	13.6705i	−0.295760	−	0.541644i
$638$		0			0
$639$	6.54788	+	2.99032i	0.259030	+	0.118295i
$640$		0			0
$641$	−11.3605	+	17.6772i	−0.448711	+	0.698208i	−0.989753	−	0.142787i	$-0.954394\pi$
$641$	−11.3605	+	17.6772i	−0.448711	+	0.698208i	0.541042	+	0.840995i	$0.318030\pi$
$642$		0			0
$643$	−27.1307	−	27.1307i	−1.06993	−	1.06993i	−0.997364	−	0.0725657i	$-0.976881\pi$
$643$	−27.1307	−	27.1307i	−1.06993	−	1.06993i	−0.0725657	−	0.997364i	$-0.523119\pi$
$644$		0			0
$645$	−3.45170	−	21.6226i	−0.135910	−	0.851389i
$646$		0			0
$647$	−1.22072	−	5.61156i	−0.0479915	−	0.220613i	0.946905	−	0.321513i	$-0.104191\pi$
$647$	−1.22072	−	5.61156i	−0.0479915	−	0.220613i	−0.994897	+	0.100900i	$0.967828\pi$
$648$		0			0
$649$	−25.0572	+	54.8677i	−0.983583	+	2.15375i
$650$		0			0
$651$	−3.22951	+	10.9987i	−0.126574	+	0.431073i
$652$		0			0
$653$	22.6614	+	8.45225i	0.886808	+	0.330762i	0.751258	−	0.660008i	$-0.229447\pi$
$653$	22.6614	+	8.45225i	0.886808	+	0.330762i	0.135550	+	0.990771i	$0.456720\pi$
$654$		0			0
$655$	−4.16694	−	2.58757i	−0.162816	−	0.101105i
$656$		0			0
$657$	13.3806	+	7.30637i	0.522027	+	0.285049i
$658$		0			0
$659$	−24.9517	+	16.0355i	−0.971980	+	0.624654i	−0.927289	−	0.374347i	$-0.877867\pi$
$659$	−24.9517	+	16.0355i	−0.971980	+	0.624654i	−0.0446917	+	0.999001i	$0.514231\pi$
$660$		0			0
$661$	29.5647	−	4.25076i	1.14993	−	0.165335i	0.459124	−	0.888372i	$-0.348163\pi$
$661$	29.5647	−	4.25076i	1.14993	−	0.165335i	0.690810	+	0.723037i	$0.257254\pi$
$662$		0			0
$663$	−2.52407	+	1.88949i	−0.0980266	+	0.0733818i
$664$		0			0
$665$	6.03760	+	69.3040i	0.234128	+	2.68749i
$666$		0			0
$667$	−0.580142	+	1.36905i	−0.0224632	+	0.0530097i
$668$		0			0
$669$	−22.4998	+	19.4962i	−0.869891	+	0.753765i
$670$		0			0
$671$	1.08333	−	7.53474i	0.0418216	−	0.290875i
$672$		0			0
$673$	−0.324162	−	0.242664i	−0.0124955	−	0.00935402i	0.593012	−	0.805194i	$-0.297939\pi$
$673$	−0.324162	−	0.242664i	−0.0124955	−	0.00935402i	−0.605507	+	0.795840i	$0.707030\pi$
$674$		0			0
$675$	27.9888	−	2.87602i	1.07729	−	0.110698i
$676$		0			0
$677$	−4.46427	+	8.17571i	−0.171576	+	0.314218i	−0.949291	−	0.314399i	$-0.898197\pi$
$677$	−4.46427	+	8.17571i	−0.171576	+	0.314218i	0.777715	+	0.628617i	$0.216379\pi$
$678$		0			0
$679$	41.5732	+	36.0234i	1.59543	+	1.38245i
$680$		0			0
$681$	5.55667	−	2.53765i	0.212932	−	0.0972428i
$682$		0			0
$683$	−9.79953	+	5.35095i	−0.374968	+	0.204748i	−0.655671	−	0.755046i	$-0.727614\pi$
$683$	−9.79953	+	5.35095i	−0.374968	+	0.204748i	0.280703	+	0.959795i	$0.409432\pi$
$684$		0			0
$685$	−0.933300	+	0.528559i	−0.0356595	+	0.0201952i
$686$		0			0
$687$	−17.1968	+	3.74093i	−0.656098	+	0.142725i
$688$		0			0
$689$	−15.7040			−0.598274
$690$		0			0
$691$	−9.56796			−0.363982			−0.181991	−	0.983300i	$-0.558254\pi$
$691$	−9.56796			−0.363982			−0.181991	+	0.983300i	$0.558254\pi$
$692$		0			0
$693$	−18.3619	+	3.99439i	−0.697512	+	0.151734i
$694$		0			0
$695$	−4.56466	+	16.4868i	−0.173147	+	0.625382i
$696$		0			0
$697$	8.73533	−	4.76985i	0.330874	−	0.180671i
$698$		0			0
$699$	−18.0549	+	8.24539i	−0.682899	+	0.311869i
$700$		0			0
$701$	3.79297	+	3.28663i	0.143259	+	0.124134i	0.723542	−	0.690280i	$-0.242513\pi$
$701$	3.79297	+	3.28663i	0.143259	+	0.124134i	−0.580283	+	0.814415i	$0.697058\pi$
$702$		0			0
$703$	−15.9843	+	29.2730i	−0.602859	+	1.10405i
$704$		0			0
$705$	−16.2266	−	18.1504i	−0.611131	−	0.683583i
$706$		0			0
$707$	3.66351	+	2.74247i	0.137781	+	0.103141i
$708$		0			0
$709$	3.98299	−	27.7023i	0.149584	−	1.04038i	−0.767317	−	0.641268i	$-0.778409\pi$
$709$	3.98299	−	27.7023i	0.149584	−	1.04038i	0.916901	−	0.399114i	$-0.130682\pi$
$710$		0			0
$711$	10.3635	−	8.97999i	0.388660	−	0.336776i
$712$		0			0
$713$	0.299379	+	10.8515i	0.0112118	+	0.406391i
$714$		0			0
$715$	−18.5309	+	1.61437i	−0.693018	+	0.0603741i
$716$		0			0
$717$	−5.65808	+	4.23558i	−0.211305	+	0.158181i
$718$		0			0
$719$	34.5693	−	4.97032i	1.28922	−	0.185361i	0.536610	−	0.843831i	$-0.319705\pi$
$719$	34.5693	−	4.97032i	1.28922	−	0.185361i	0.752608	+	0.658469i	$0.228796\pi$
$720$		0			0
$721$	43.8850	−	28.2032i	1.63436	−	1.05034i
$722$		0			0
$723$	−7.63519	−	4.16913i	−0.283956	−	0.155052i
$724$		0			0
$725$	−1.42939	−	0.599962i	−0.0530861	−	0.0222820i
$726$		0			0
$727$	24.1697	+	9.01485i	0.896406	+	0.334342i	0.755089	−	0.655622i	$-0.227594\pi$
$727$	24.1697	+	9.01485i	0.896406	+	0.334342i	0.141317	+	0.989964i	$0.454866\pi$
$728$		0			0
$729$	7.63934	−	26.0172i	0.282938	−	0.963600i
$730$		0			0
$731$	−3.49325	+	7.64915i	−0.129202	+	0.282914i
$732$		0			0
$733$	5.88234	+	27.0407i	0.217269	+	0.998770i	0.948534	+	0.316676i	$0.102567\pi$
$733$	5.88234	+	27.0407i	0.217269	+	0.998770i	−0.731265	+	0.682094i	$0.761070\pi$
$734$		0			0
$735$	−13.0902	+	18.0634i	−0.482841	+	0.666280i
$736$		0			0
$737$	−37.6338	−	37.6338i	−1.38626	−	1.38626i
$738$		0			0
$739$	16.6652	−	25.9316i	0.613041	−	0.953910i	−0.386460	−	0.922306i	$-0.626302\pi$
$739$	16.6652	−	25.9316i	0.613041	−	0.953910i	0.999500	−	0.0316038i	$-0.0100615\pi$
$740$		0			0
$741$	20.5177	+	9.37012i	0.753737	+	0.344220i
$742$		0			0
$743$	−22.3792	−	40.9844i	−0.821013	−	1.50357i	−0.863427	−	0.504473i	$-0.831687\pi$
$743$	−22.3792	−	40.9844i	−0.821013	−	1.50357i	0.0424143	−	0.999100i	$-0.486495\pi$
$744$		0			0
$745$	20.0734	−	13.3445i	0.735434	−	0.488904i
$746$		0			0
$747$	−0.615762	−	8.60947i	−0.0225295	−	0.315004i
$748$		0			0
$749$	0.925957	+	3.15352i	0.0338337	+	0.115227i
$750$		0			0
$751$	19.0370	+	29.6221i	0.694669	+	1.08093i	0.992011	+	0.126155i	$0.0402638\pi$
$751$	19.0370	+	29.6221i	0.694669	+	1.08093i	−0.297341	+	0.954771i	$0.596100\pi$
$752$		0			0
$753$	−0.778633	+	1.04013i	−0.0283750	+	0.0379045i
$754$		0			0
$755$	−39.0294	+	0.604943i	−1.42042	+	0.0220161i
$756$		0			0
$757$	12.2273	+	0.874515i	0.444409	+	0.0317848i	0.291751	−	0.956494i	$-0.405762\pi$
$757$	12.2273	+	0.874515i	0.444409	+	0.0317848i	0.152658	+	0.988279i	$0.451217\pi$
$758$		0			0
$759$	22.0812	−	12.8602i	0.801496	−	0.466794i
$760$		0			0
$761$	27.3665	+	31.5826i	0.992035	+	1.14487i	0.989450	+	0.144873i	$0.0462772\pi$
$761$	27.3665	+	31.5826i	0.992035	+	1.14487i	0.00258459	+	0.999997i	$0.499177\pi$
$762$		0			0
$763$	21.5334	+	28.7653i	0.779563	+	1.04137i
$764$		0			0
$765$	−2.78318	−	1.46420i	−0.100626	−	0.0529382i
$766$		0			0
$767$	−30.5417	−	6.64394i	−1.10280	−	0.239899i
$768$		0			0
$769$	7.98319	−	2.34408i	0.287881	−	0.0845295i	−0.134604	−	0.990900i	$-0.542976\pi$
$769$	7.98319	−	2.34408i	0.287881	−	0.0845295i	0.422485	+	0.906370i	$0.361158\pi$
$770$		0			0
$771$	−13.7171	+	15.8303i	−0.494008	+	0.570115i
$772$		0			0
$773$	−3.40538	+	9.13019i	−0.122483	+	0.328390i	−0.983692	−	0.179861i	$-0.942435\pi$
$773$	−3.40538	+	9.13019i	−0.122483	+	0.328390i	0.861209	+	0.508251i	$0.169708\pi$
$774$		0			0
$775$	−11.3123	+	0.350759i	−0.406351	+	0.0125996i
$776$		0			0
$777$	−19.3712	+	7.22509i	−0.694938	+	0.259199i
$778$		0			0
$779$	−59.8986	−	38.4945i	−2.14609	−	1.37921i
$780$		0			0
$781$			23.4187i			0.837987i
$782$		0			0
$783$	−1.23366	+	1.23366i	−0.0440875	+	0.0440875i
$784$		0			0
$785$	−7.22030	−	18.4786i	−0.257703	−	0.659528i
$786$		0			0
$787$	−8.27750	−	22.1928i	−0.295061	−	0.791089i	−0.996895	−	0.0787483i	$-0.974908\pi$
$787$	−8.27750	−	22.1928i	−0.295061	−	0.791089i	0.701833	−	0.712341i	$-0.252365\pi$
$788$		0			0
$789$	5.64155	+	1.65651i	0.200845	+	0.0589733i
$790$		0			0
$791$	−24.6321	−	53.9367i	−0.875816	−	1.91777i
$792$		0			0
$793$	3.93447	−	0.281399i	0.139717	−	0.00999276i
$794$		0			0
$795$	9.65930	+	20.3118i	0.342580	+	0.720386i
$796$		0			0
$797$	−5.53476	+	25.4429i	−0.196051	+	0.901234i	0.769015	+	0.639230i	$0.220747\pi$
$797$	−5.53476	+	25.4429i	−0.196051	+	0.901234i	−0.965067	+	0.262004i	$0.915617\pi$
$798$		0			0
$799$	1.33063	+	9.25473i	0.0470743	+	0.327409i
$800$		0			0
$801$	13.5892	+	1.95383i	0.480150	+	0.0690352i
$802$		0			0
$803$	−3.53831	+	49.4721i	−0.124864	+	1.74583i
$804$		0			0
$805$	−12.6103	+	38.8422i	−0.444454	+	1.36901i
$806$		0			0
$807$	1.83424	−	25.6460i	0.0645683	−	0.902782i
$808$		0			0
$809$	49.4049	+	7.10336i	1.73699	+	0.249741i	0.936763	−	0.349963i	$-0.113806\pi$
$809$	49.4049	+	7.10336i	1.73699	+	0.249741i	0.800222	+	0.599704i	$0.204715\pi$
$810$		0			0
$811$	2.43630	+	16.9449i	0.0855502	+	0.595015i	0.986828	+	0.161773i	$0.0517213\pi$
$811$	2.43630	+	16.9449i	0.0855502	+	0.595015i	−0.901278	+	0.433242i	$0.857370\pi$
$812$		0			0
$813$	−3.48716	+	16.0302i	−0.122300	+	0.562205i
$814$		0			0
$815$	−21.4580	−	7.62675i	−0.751642	−	0.267153i
$816$		0			0
$817$	60.0047	−	4.29162i	2.09930	−	0.150145i
$818$		0			0
$819$	−4.04504	−	8.85741i	−0.141345	−	0.309503i
$820$		0			0
$821$	2.63213	+	0.772863i	0.0918619	+	0.0269731i	0.327341	−	0.944906i	$-0.393848\pi$
$821$	2.63213	+	0.772863i	0.0918619	+	0.0269731i	−0.235479	+	0.971880i	$0.575666\pi$
$822$		0			0
$823$	−9.06892	−	24.3147i	−0.316123	−	0.847557i	−0.993697	−	0.112103i	$-0.964241\pi$
$823$	−9.06892	−	24.3147i	−0.316123	−	0.847557i	0.677574	−	0.735455i	$-0.263031\pi$
$824$		0			0
$825$	13.4862	+	22.9753i	0.469529	+	0.799897i
$826$		0			0
$827$	16.0012	−	16.0012i	0.556415	−	0.556415i	−0.371870	−	0.928285i	$-0.621283\pi$
$827$	16.0012	−	16.0012i	0.556415	−	0.556415i	0.928285	+	0.371870i	$0.121283\pi$
$828$		0			0
$829$		−	23.9593i		−	0.832142i	−0.909332	−	0.416071i	$-0.863407\pi$
$829$		−	23.9593i		−	0.832142i	0.909332	−	0.416071i	$-0.136593\pi$
$830$		0			0
$831$	16.4278	+	10.5575i	0.569874	+	0.366236i
$832$		0			0
$833$	8.02693	−	2.99389i	0.278117	−	0.103732i
$834$		0			0
$835$	−26.6286	+	20.5855i	−0.921519	+	0.712390i
$836$		0			0
$837$	−4.45132	+	11.9345i	−0.153860	+	0.412515i
$838$		0			0
$839$	−29.7238	+	34.3031i	−1.02618	+	1.18428i	−0.0434837	+	0.999054i	$0.513846\pi$
$839$	−29.7238	+	34.3031i	−1.02618	+	1.18428i	−0.982697	+	0.185221i	$0.940700\pi$
$840$		0			0
$841$	−27.7331	+	8.14316i	−0.956313	+	0.280799i
$842$		0			0
$843$	27.8763	+	6.06411i	0.960109	+	0.208859i
$844$		0			0
$845$	5.76236	+	18.5560i	0.198231	+	0.638345i
$846$		0			0
$847$	−11.5330	−	15.4062i	−0.396278	−	0.529365i
$848$		0			0
$849$	−0.179918	−	0.207636i	−0.00617477	−	0.00712607i
$850$		0			0
$851$	−15.3444	+	12.1612i	−0.526000	+	0.416880i
$852$		0			0
$853$	−39.1751	−	2.80186i	−1.34133	−	0.0959339i	−0.617860	−	0.786288i	$-0.712000\pi$
$853$	−39.1751	−	2.80186i	−1.34133	−	0.0959339i	−0.723471	+	0.690355i	$0.757455\pi$
$854$		0			0
$855$	0.348670	+	22.4953i	0.0119243	+	0.769322i
$856$		0			0
$857$	6.11026	−	8.16236i	0.208723	−	0.278821i	−0.683948	−	0.729531i	$-0.739738\pi$
$857$	6.11026	−	8.16236i	0.208723	−	0.278821i	0.892670	+	0.450710i	$0.148829\pi$
$858$		0			0
$859$	28.7906	+	44.7990i	0.982322	+	1.52852i	0.842746	+	0.538311i	$0.180937\pi$
$859$	28.7906	+	44.7990i	0.982322	+	1.52852i	0.139575	+	0.990211i	$0.455426\pi$
$860$		0			0
$861$	−12.4347	−	42.3487i	−0.423773	−	1.44324i
$862$		0			0
$863$	1.06495	+	14.8899i	0.0362512	+	0.506858i	0.982846	+	0.184431i	$0.0590441\pi$
$863$	1.06495	+	14.8899i	0.0362512	+	0.506858i	−0.946594	+	0.322427i	$0.895501\pi$
$864$		0			0
$865$	−3.57765	+	17.7676i	−0.121644	+	0.604117i
$866$		0			0
$867$	10.0033	+	18.3196i	0.339729	+	0.622167i
$868$		0			0
$869$	40.5808	+	18.5326i	1.37661	+	0.628676i
$870$		0			0
$871$	14.9102	−	23.2008i	0.505214	−	0.786128i
$872$		0			0
$873$	12.5795	+	12.5795i	0.425752	+	0.425752i
$874$		0			0
$875$	−40.5404	−	13.0087i	−1.37052	−	0.439776i
$876$		0			0
$877$	4.27741	+	19.6629i	0.144438	+	0.663970i	0.991241	+	0.132064i	$0.0421604\pi$
$877$	4.27741	+	19.6629i	0.144438	+	0.663970i	−0.846803	+	0.531906i	$0.821476\pi$
$878$		0			0
$879$	2.78820	−	6.10532i	0.0940438	−	0.205927i
$880$		0			0
$881$	−6.82542	+	23.2452i	−0.229954	+	0.783152i	0.760977	+	0.648779i	$0.224720\pi$
$881$	−6.82542	+	23.2452i	−0.229954	+	0.783152i	−0.990931	+	0.134373i	$0.957098\pi$
$882$		0			0
$883$	38.5086	+	14.3629i	1.29592	+	0.483352i	0.900382	−	0.435100i	$-0.143287\pi$
$883$	38.5086	+	14.3629i	1.29592	+	0.483352i	0.395534	+	0.918451i	$0.370560\pi$
$884$		0			0
$885$	10.1924	+	43.5898i	0.342613	+	1.46526i
$886$		0			0
$887$	−31.0189	−	16.9376i	−1.04151	−	0.568709i	−0.134981	−	0.990848i	$-0.543097\pi$
$887$	−31.0189	−	16.9376i	−1.04151	−	0.568709i	−0.906531	+	0.422140i	$0.861279\pi$
$888$		0			0
$889$	−47.7976	+	30.7176i	−1.60308	+	1.03024i
$890$		0			0
$891$	15.0250	−	2.16027i	0.503357	−	0.0723718i
$892$		0			0
$893$	53.5472	−	40.0850i	1.79189	−	1.34139i
$894$		0			0
$895$	5.51962	+	4.63498i	0.184501	+	0.154930i
$896$		0			0
$897$	8.94381	+	9.76407i	0.298625	+	0.326013i
$898$		0			0
$899$	0.530377	−	0.459574i	0.0176890	−	0.0153276i
$900$		0			0
$901$	1.22926	−	8.54973i	0.0409528	−	0.284833i
$902$		0			0
$903$	29.8528	+	22.3476i	0.993440	+	0.743680i
$904$		0			0
$905$	−1.52923	+	1.36715i	−0.0508333	+	0.0454455i
$906$		0			0
$907$	7.69395	−	14.0904i	0.255473	−	0.467865i	−0.718192	−	0.695845i	$-0.755030\pi$
$907$	7.69395	−	14.0904i	0.255473	−	0.467865i	0.973666	+	0.227980i	$0.0732121\pi$
$908$		0			0
$909$	1.11850	+	0.969185i	0.0370983	+	0.0321458i
$910$		0			0
$911$	−35.6199	+	16.2671i	−1.18014	+	0.538952i	−0.906223	−	0.422800i	$-0.861047\pi$
$911$	−35.6199	+	16.2671i	−1.18014	+	0.538952i	−0.273918	+	0.961753i	$0.588320\pi$
$912$		0			0
$913$	24.6461	−	13.4578i	0.815666	−	0.445388i
$914$		0			0
$915$	−2.78400	−	4.91583i	−0.0920363	−	0.162512i
$916$		0			0
$917$	8.16257	−	1.77566i	0.269552	−	0.0586374i
$918$		0			0
$919$	−28.2999			−0.933527			−0.466763	−	0.884382i	$-0.654580\pi$
$919$	−28.2999			−0.933527			−0.466763	+	0.884382i	$0.654580\pi$
$920$		0			0
$921$	−3.98736			−0.131388
$922$		0			0
$923$	−11.8578	+	2.57951i	−0.390305	+	0.0849057i
$924$		0			0
$925$	−12.7335	−	15.9543i	−0.418674	−	0.524574i
$926$		0			0
$927$	14.8071	−	8.08526i	0.486328	−	0.265555i
$928$		0			0
$929$	31.7471	−	14.4984i	1.04159	−	0.475678i	0.180204	−	0.983629i	$-0.442324\pi$
$929$	31.7471	−	14.4984i	1.04159	−	0.475678i	0.861386	+	0.507951i	$0.169597\pi$
$930$		0			0
$931$	−46.3188	−	40.1355i	−1.51804	−	1.31539i
$932$		0			0
$933$	−3.88198	+	7.10932i	−0.127090	+	0.232749i
$934$		0			0
$935$	0.571638	−	10.2152i	0.0186946	−	0.334072i
$936$		0			0
$937$	2.38013	+	1.78175i	0.0777556	+	0.0582071i	0.637448	−	0.770493i	$-0.279990\pi$
$937$	2.38013	+	1.78175i	0.0777556	+	0.0582071i	−0.559693	+	0.828700i	$0.689081\pi$
$938$		0			0
$939$	−2.25770	+	15.7027i	−0.0736773	+	0.512437i
$940$		0			0
$941$	11.0184	−	9.54750i	0.359190	−	0.311240i	−0.456507	−	0.889720i	$-0.650899\pi$
$941$	11.0184	−	9.54750i	0.359190	−	0.311240i	0.815696	+	0.578480i	$0.196354\pi$
$942$		0			0
$943$	−23.5587	−	34.5260i	−0.767177	−	1.12432i
$944$		0			0
$945$	−30.8144	+	36.6957i	−1.00239	+	1.19371i
$946$		0			0
$947$	−9.30615	+	6.96650i	−0.302409	+	0.226381i	−0.739696	−	0.672942i	$-0.765031\pi$
$947$	−9.30615	+	6.96650i	−0.302409	+	0.226381i	0.437286	+	0.899322i	$0.355940\pi$
$948$		0			0
$949$	−25.4394	+	3.65764i	−0.825799	+	0.118732i
$950$		0			0
$951$	−25.9235	+	16.6600i	−0.840627	+	0.540238i
$952$		0			0
$953$	15.5834	+	8.50917i	0.504795	+	0.275639i	0.711402	−	0.702785i	$-0.248060\pi$
$953$	15.5834	+	8.50917i	0.504795	+	0.275639i	−0.206607	+	0.978424i	$0.566242\pi$
$954$		0			0
$955$	−16.6222	+	26.7679i	−0.537882	+	0.866188i
$956$		0			0
$957$	−1.54779	−	0.577296i	−0.0500330	−	0.0186613i
$958$		0			0
$959$	0.514630	−	1.75267i	0.0166183	−	0.0565967i
$960$		0			0
$961$	−10.7494	+	23.5379i	−0.346755	+	0.759288i
$962$		0			0
$963$	0.225938	+	1.03862i	0.00728076	+	0.0334691i
$964$		0			0
$965$	−41.1171	−	29.7968i	−1.32361	−	0.959194i
$966$		0			0
$967$	−29.3910	−	29.3910i	−0.945151	−	0.945151i	0.0534214	−	0.998572i	$-0.482987\pi$
$967$	−29.3910	−	29.3910i	−0.945151	−	0.945151i	−0.998572	+	0.0534214i	$0.982987\pi$
$968$		0			0
$969$	−6.70745	+	10.4370i	−0.215474	+	0.335285i
$970$		0			0
$971$	44.2700	+	20.2175i	1.42069	+	0.648809i	0.969830	−	0.243784i	$-0.0783888\pi$
$971$	44.2700	+	20.2175i	1.42069	+	0.648809i	0.450864	+	0.892593i	$0.351116\pi$
$972$		0			0
$973$	−13.9626	−	25.5706i	−0.447621	−	0.819756i
$974$		0			0
$975$	−10.1478	+	9.35927i	−0.324991	+	0.299737i
$976$		0			0
$977$	2.34317	+	32.7618i	0.0749647	+	1.04814i	0.886163	+	0.463373i	$0.153361\pi$
$977$	2.34317	+	32.7618i	0.0749647	+	1.04814i	−0.811199	+	0.584771i	$0.801185\pi$
$978$		0			0
$979$	12.5835	+	42.8555i	0.402170	+	1.36967i
$980$		0			0
$981$	6.28258	+	9.77588i	0.200587	+	0.312120i
$982$		0			0
$983$	−16.1662	+	21.5955i	−0.515621	+	0.688788i	−0.980485	−	0.196593i	$-0.937012\pi$
$983$	−16.1662	+	21.5955i	−0.515621	+	0.688788i	0.464865	+	0.885382i	$0.346103\pi$
$984$		0			0
$985$	19.4242	+	18.8313i	0.618908	+	0.600015i
$986$		0			0
$987$	41.3574	+	2.95794i	1.31642	+	0.0941524i
$988$		0			0
$989$	33.4160	+	11.4241i	1.06257	+	0.363264i
$990$		0			0
$991$	−29.1042	−	33.5881i	−0.924527	−	1.06696i	−0.997573	−	0.0696324i	$-0.977817\pi$
$991$	−29.1042	−	33.5881i	−0.924527	−	1.06696i	0.0730458	−	0.997329i	$-0.476728\pi$
$992$		0			0
$993$	11.3937	+	15.2202i	0.361568	+	0.482998i
$994$		0			0
$995$	43.6202	−	13.5458i	1.38285	−	0.429431i
$996$		0			0
$997$	−38.9517	−	8.47342i	−1.23361	−	0.268356i	−0.451941	−	0.892048i	$-0.649268\pi$
$997$	−38.9517	−	8.47342i	−1.23361	−	0.268356i	−0.781670	+	0.623692i	$0.785632\pi$
$998$		0			0
$999$	−22.0429	+	6.47238i	−0.697407	+	0.204777i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	920.2.bv.a.217.10	yes	720
5.3	odd	4	inner	920.2.bv.a.33.10	✓	720
23.7	odd	22	inner	920.2.bv.a.697.10	yes	720
115.53	even	44	inner	920.2.bv.a.513.10	yes	720

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
920.2.bv.a.33.10	✓	720	5.3	odd	4	inner
920.2.bv.a.217.10	yes	720	1.1	even	1	trivial
920.2.bv.a.513.10	yes	720	115.53	even	44	inner
920.2.bv.a.697.10	yes	720	23.7	odd	22	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:	\( N \)	\(=\)	\( 920 = 2^{3} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	920.bv (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.29943 + 0.282674i) q^{3} +(2.15500 + 0.596647i) q^{5} +(-3.34234 + 1.82505i) q^{7} +(-1.12027 + 0.511612i) q^{9} +O(q^{10})\)	\(q+(-1.29943 + 0.282674i) q^{3} +(2.15500 + 0.596647i) q^{5} +(-3.34234 + 1.82505i) q^{7} +(-1.12027 + 0.511612i) q^{9} +(-3.02806 - 2.62382i) q^{11} +(0.995015 - 1.82223i) q^{13} +(-2.96893 - 0.166141i) q^{15} +(0.914193 + 0.684356i) q^{17} +(1.16265 - 8.08644i) q^{19} +(3.82725 - 3.31633i) q^{21} +(2.48057 - 4.10448i) q^{23} +(4.28802 + 2.57155i) q^{25} +(4.50484 - 3.37228i) q^{27} +(-0.306883 + 0.0441231i) q^{29} +(-1.90422 + 1.22377i) q^{31} +(4.67645 + 2.55353i) q^{33} +(-8.29164 + 1.93879i) q^{35} +(-3.82515 - 1.42671i) q^{37} +(-0.777857 + 2.64914i) q^{39} +(3.62052 - 7.92784i) q^{41} +(1.56526 + 7.19537i) q^{43} +(-2.71944 + 0.434114i) q^{45} +(5.78946 + 5.78946i) q^{47} +(4.05591 - 6.31112i) q^{49} +(-1.38138 - 0.630857i) q^{51} +(-3.62495 - 6.63861i) q^{53} +(-4.95995 - 7.46101i) q^{55} +(0.775038 + 10.8364i) q^{57} +(-4.24133 - 14.4446i) q^{59} +(1.02715 + 1.59828i) q^{61} +(2.81061 - 3.75454i) q^{63} +(3.23149 - 3.33324i) q^{65} +(13.2495 + 0.947622i) q^{67} +(-2.06311 + 6.03470i) q^{69} +(-3.82759 - 4.41728i) q^{71} +(-7.41840 - 9.90982i) q^{73} +(-6.29891 - 2.12944i) q^{75} +(14.9094 + 3.24334i) q^{77} +(-10.6834 + 3.13694i) q^{79} +(-2.48097 + 2.86319i) q^{81} +(-2.44923 + 6.56663i) q^{83} +(1.56176 + 2.02024i) q^{85} +(0.386302 - 0.144083i) q^{87} +(-9.37790 - 6.02681i) q^{89} +7.90648i q^{91} +(2.12848 - 2.12848i) q^{93} +(7.33027 - 16.7326i) q^{95} +(-5.04805 - 13.5343i) q^{97} +(4.73463 + 1.39021i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 720 q+O(q^{10}) \) 720 * q	\( 720 q - 20 q^{23} + 16 q^{25} - 24 q^{27} - 16 q^{31} + 88 q^{37} - 32 q^{41} + 56 q^{47} - 40 q^{55} + 88 q^{57} + 16 q^{73} - 140 q^{75} - 48 q^{77} + 40 q^{81} - 92 q^{85} - 88 q^{87} + 72 q^{93} - 248 q^{95}+O(q^{100}) \) 720 * q - 20 * q^23 + 16 * q^25 - 24 * q^27 - 16 * q^31 + 88 * q^37 - 32 * q^41 + 56 * q^47 - 40 * q^55 + 88 * q^57 + 16 * q^73 - 140 * q^75 - 48 * q^77 + 40 * q^81 - 92 * q^85 - 88 * q^87 + 72 * q^93 - 248 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

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Groups

Database

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