LMFDB - Embedded newform 920.2.bv.a.217.17

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			217.17
Character	$\chi$	$=$	920.217
Dual form			920.2.bv.a.513.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.507977 + 0.110504i) q^{3} +(-0.763385 + 2.10172i) q^{5} +(3.36669 - 1.83835i) q^{7} +(-2.48307 + 1.13398i) q^{9} +O(q^{10})$	\(q+(-0.507977 + 0.110504i) q^{3} +(-0.763385 + 2.10172i) q^{5} +(3.36669 - 1.83835i) q^{7} +(-2.48307 + 1.13398i) q^{9} +(-4.65203 - 4.03101i) q^{11} +(1.62061 - 2.96793i) q^{13} +(0.155534 - 1.15199i) q^{15} +(-2.47793 - 1.85495i) q^{17} +(0.331313 - 2.30434i) q^{19} +(-1.50706 + 1.30587i) q^{21} +(4.56894 + 1.45767i) q^{23} +(-3.83449 - 3.20885i) q^{25} +(2.38454 - 1.78504i) q^{27} +(7.35910 - 1.05808i) q^{29} +(0.738843 - 0.474826i) q^{31} +(2.80857 + 1.53359i) q^{33} +(1.29363 + 8.47921i) q^{35} +(-3.59784 - 1.34193i) q^{37} +(-0.495267 + 1.68673i) q^{39} +(-0.404350 + 0.885402i) q^{41} +(-2.19940 - 10.1105i) q^{43} +(-0.487775 - 6.08438i) q^{45} +(8.05055 + 8.05055i) q^{47} +(4.17056 - 6.48952i) q^{49} +(1.46371 + 0.668454i) q^{51} +(-1.86532 - 3.41608i) q^{53} +(12.0233 - 6.70007i) q^{55} +(0.0863379 + 1.20716i) q^{57} +(-0.365545 - 1.24493i) q^{59} +(-7.02794 - 10.9357i) q^{61} +(-6.27506 + 8.38249i) q^{63} +(5.00062 + 5.67175i) q^{65} +(0.964386 + 0.0689742i) q^{67} +(-2.48200 - 0.235581i) q^{69} +(0.390272 + 0.450398i) q^{71} +(-8.57000 - 11.4482i) q^{73} +(2.30242 + 1.20630i) q^{75} +(-23.0723 - 5.01908i) q^{77} +(16.1584 - 4.74455i) q^{79} +(4.34878 - 5.01876i) q^{81} +(-0.553188 + 1.48315i) q^{83} +(5.79021 - 3.79187i) q^{85} +(-3.62133 + 1.35069i) q^{87} +(-2.95246 - 1.89743i) q^{89} -12.9713i q^{91} +(-0.322846 + 0.322846i) q^{93} +(4.59016 + 2.45542i) q^{95} +(3.79504 + 10.1749i) q^{97} +(16.1224 + 4.73395i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−0.507977	+	0.110504i	−0.293281	+	0.0637994i	−0.356799	−	0.934181i	$-0.616132\pi$
$3$	−0.507977	+	0.110504i	−0.293281	+	0.0637994i	0.0635176	+	0.997981i	$0.479768\pi$
$4$		0			0
$5$	−0.763385	+	2.10172i	−0.341396	+	0.939920i
$5$	−0.763385	+	2.10172i	−0.341396	+	0.939920i
$6$		0			0
$7$	3.36669	−	1.83835i	1.27249	−	0.694831i	0.306120	−	0.951993i	$-0.400969\pi$
$7$	3.36669	−	1.83835i	1.27249	−	0.694831i	0.966368	+	0.257162i	$0.0827874\pi$
$8$		0			0
$9$	−2.48307	+	1.13398i	−0.827689	+	0.377993i
$10$		0			0
$11$	−4.65203	−	4.03101i	−1.40264	−	1.21539i	−0.945342	−	0.326080i	$-0.894272\pi$
$11$	−4.65203	−	4.03101i	−1.40264	−	1.21539i	−0.457297	−	0.889314i	$-0.651182\pi$
$12$		0			0
$13$	1.62061	−	2.96793i	0.449477	−	0.823156i	−0.550454	−	0.834865i	$-0.685545\pi$
$13$	1.62061	−	2.96793i	0.449477	−	0.823156i	0.999931	+	0.0117094i	$0.00372731\pi$
$14$		0			0
$15$	0.155534	−	1.15199i	0.0401587	−	0.297441i
$16$		0			0
$17$	−2.47793	−	1.85495i	−0.600985	−	0.449892i	0.254965	−	0.966950i	$-0.417936\pi$
$17$	−2.47793	−	1.85495i	−0.600985	−	0.449892i	−0.855950	+	0.517058i	$0.827027\pi$
$18$		0			0
$19$	0.331313	−	2.30434i	0.0760085	−	0.528651i	−0.915871	−	0.401472i	$-0.868499\pi$
$19$	0.331313	−	2.30434i	0.0760085	−	0.528651i	0.991880	−	0.127179i	$-0.0405922\pi$
$20$		0			0
$21$	−1.50706	+	1.30587i	−0.328867	+	0.284965i
$22$		0			0
$23$	4.56894	+	1.45767i	0.952689	+	0.303946i
$23$	4.56894	+	1.45767i	0.952689	+	0.303946i
$24$		0			0
$25$	−3.83449	−	3.20885i	−0.766898	−	0.641770i
$26$		0			0
$27$	2.38454	−	1.78504i	0.458904	−	0.343531i
$28$		0			0
$29$	7.35910	−	1.05808i	1.36655	−	0.196480i	0.580307	−	0.814398i	$-0.302933\pi$
$29$	7.35910	−	1.05808i	1.36655	−	0.196480i	0.786243	+	0.617917i	$0.212023\pi$
$30$		0			0
$31$	0.738843	−	0.474826i	0.132700	−	0.0852812i	−0.472607	−	0.881274i	$-0.656687\pi$
$31$	0.738843	−	0.474826i	0.132700	−	0.0852812i	0.605307	+	0.795992i	$0.293050\pi$
$32$		0			0
$33$	2.80857	+	1.53359i	0.488909	+	0.266964i
$34$		0			0
$35$	1.29363	+	8.47921i	0.218663	+	1.43325i
$36$		0			0
$37$	−3.59784	−	1.34193i	−0.591482	−	0.220611i	0.0358582	−	0.999357i	$-0.488584\pi$
$37$	−3.59784	−	1.34193i	−0.591482	−	0.220611i	−0.627340	+	0.778746i	$0.715856\pi$
$38$		0			0
$39$	−0.495267	+	1.68673i	−0.0793062	+	0.270092i
$40$		0			0
$41$	−0.404350	+	0.885402i	−0.0631488	+	0.138277i	−0.938575	−	0.345075i	$-0.887853\pi$
$41$	−0.404350	+	0.885402i	−0.0631488	+	0.138277i	0.875426	+	0.483352i	$0.160581\pi$
$42$		0			0
$43$	−2.19940	−	10.1105i	−0.335405	−	1.54183i	−0.768122	−	0.640304i	$-0.778809\pi$
$43$	−2.19940	−	10.1105i	−0.335405	−	1.54183i	0.432716	−	0.901530i	$-0.357555\pi$
$44$		0			0
$45$	−0.487775	−	6.08438i	−0.0727132	−	0.907006i
$46$		0			0
$47$	8.05055	+	8.05055i	1.17429	+	1.17429i	0.981176	+	0.193117i	$0.0618598\pi$
$47$	8.05055	+	8.05055i	1.17429	+	1.17429i	0.193117	+	0.981176i	$0.438140\pi$
$48$		0			0
$49$	4.17056	−	6.48952i	0.595795	−	0.927074i
$50$		0			0
$51$	1.46371	+	0.668454i	0.204960	+	0.0936022i
$52$		0			0
$53$	−1.86532	−	3.41608i	−0.256222	−	0.469235i	0.717628	−	0.696426i	$-0.245228\pi$
$53$	−1.86532	−	3.41608i	−0.256222	−	0.469235i	−0.973850	+	0.227191i	$0.927046\pi$
$54$		0			0
$55$	12.0233	−	6.70007i	1.62123	−	0.903437i
$56$		0			0
$57$	0.0863379	+	1.20716i	0.0114357	+	0.159892i
$58$		0			0
$59$	−0.365545	−	1.24493i	−0.0475899	−	0.162076i	0.932270	−	0.361764i	$-0.117825\pi$
$59$	−0.365545	−	1.24493i	−0.0475899	−	0.162076i	−0.979860	+	0.199688i	$0.936007\pi$
$60$		0			0
$61$	−7.02794	−	10.9357i	−0.899836	−	1.40017i	−0.916380	−	0.400309i	$-0.868903\pi$
$61$	−7.02794	−	10.9357i	−0.899836	−	1.40017i	0.0165445	−	0.999863i	$-0.494733\pi$
$62$		0			0
$63$	−6.27506	+	8.38249i	−0.790583	+	1.05609i
$64$		0			0
$65$	5.00062	+	5.67175i	0.620251	+	0.703494i
$66$		0			0
$67$	0.964386	+	0.0689742i	0.117818	+	0.00842654i	0.130124	−	0.991498i	$-0.458462\pi$
$67$	0.964386	+	0.0689742i	0.117818	+	0.00842654i	−0.0123054	+	0.999924i	$0.503917\pi$
$68$		0			0
$69$	−2.48200	−	0.235581i	−0.298797	−	0.0283607i
$70$		0			0
$71$	0.390272	+	0.450398i	0.0463167	+	0.0534524i	0.778435	−	0.627725i	$-0.216014\pi$
$71$	0.390272	+	0.450398i	0.0463167	+	0.0534524i	−0.732118	+	0.681177i	$0.761468\pi$
$72$		0			0
$73$	−8.57000	−	11.4482i	−1.00304	−	1.33991i	−0.939731	−	0.341913i	$-0.888925\pi$
$73$	−8.57000	−	11.4482i	−1.00304	−	1.33991i	−0.0633107	−	0.997994i	$-0.520166\pi$
$74$		0			0
$75$	2.30242	+	1.20630i	0.265861	+	0.139291i
$76$		0			0
$77$	−23.0723	−	5.01908i	−2.62933	−	0.571977i
$78$		0			0
$79$	16.1584	−	4.74455i	1.81797	−	0.533803i	0.818779	−	0.574108i	$-0.194651\pi$
$79$	16.1584	−	4.74455i	1.81797	−	0.533803i	0.999187	+	0.0403052i	$0.0128330\pi$
$80$		0			0
$81$	4.34878	−	5.01876i	0.483197	−	0.557640i
$82$		0			0
$83$	−0.553188	+	1.48315i	−0.0607202	+	0.162797i	−0.963767	−	0.266744i	$-0.914052\pi$
$83$	−0.553188	+	1.48315i	−0.0607202	+	0.162797i	0.903047	+	0.429542i	$0.141325\pi$
$84$		0			0
$85$	5.79021	−	3.79187i	0.628036	−	0.411286i
$86$		0			0
$87$	−3.62133	+	1.35069i	−0.388248	+	0.144809i
$88$		0			0
$89$	−2.95246	−	1.89743i	−0.312961	−	0.201128i	0.374725	−	0.927136i	$-0.377737\pi$
$89$	−2.95246	−	1.89743i	−0.312961	−	0.201128i	−0.687686	+	0.726008i	$0.741373\pi$
$90$		0			0
$91$		−	12.9713i		−	1.35977i
$92$		0			0
$93$	−0.322846	+	0.322846i	−0.0334775	+	0.0334775i
$94$		0			0
$95$	4.59016	+	2.45542i	0.470940	+	0.251921i
$96$		0			0
$97$	3.79504	+	10.1749i	0.385328	+	1.03310i	0.974360	+	0.224994i	$0.0722364\pi$
$97$	3.79504	+	10.1749i	0.385328	+	1.03310i	−0.589032	+	0.808110i	$0.700491\pi$
$98$		0			0
$99$	16.1224	+	4.73395i	1.62036	+	0.475780i
$100$		0			0
$101$	−3.20444	−	7.01675i	−0.318854	−	0.698193i	0.680550	−	0.732701i	$-0.261741\pi$
$101$	−3.20444	−	7.01675i	−0.318854	−	0.698193i	−0.999404	+	0.0345085i	$0.989013\pi$
$102$		0			0
$103$	−15.0450	+	1.07604i	−1.48242	+	0.106025i	−0.788950	−	0.614457i	$-0.789375\pi$
$103$	−15.0450	+	1.07604i	−1.48242	+	0.106025i	−0.693474	+	0.720482i	$0.743921\pi$
$104$		0			0
$105$	−1.59412	−	4.16430i	−0.155570	−	0.406394i
$106$		0			0
$107$	−0.199453	+	0.916872i	−0.0192819	+	0.0886374i	−0.985782	−	0.168028i	$-0.946260\pi$
$107$	−0.199453	+	0.916872i	−0.0192819	+	0.0886374i	0.966500	+	0.256665i	$0.0826238\pi$
$108$		0			0
$109$	1.50840	+	10.4911i	0.144478	+	1.00487i	0.925062	+	0.379816i	$0.124013\pi$
$109$	1.50840	+	10.4911i	0.144478	+	1.00487i	−0.780584	+	0.625051i	$0.785078\pi$
$110$		0			0
$111$	1.97591	+	0.284093i	0.187545	+	0.0269649i
$112$		0			0
$113$	−0.393708	+	5.50476i	−0.0370369	+	0.517844i	0.944742	+	0.327816i	$0.106312\pi$
$113$	−0.393708	+	5.50476i	−0.0370369	+	0.517844i	−0.981779	+	0.190028i	$0.939142\pi$
$114$		0			0
$115$	−6.55149	+	8.48988i	−0.610929	+	0.791685i
$116$		0			0
$117$	−0.658520	+	9.20731i	−0.0608802	+	0.851216i
$118$		0			0
$119$	−11.7524	−	1.68975i	−1.07735	−	0.154899i
$120$		0			0
$121$	3.82690	+	26.6167i	0.347900	+	2.41970i
$122$		0			0
$123$	0.107560	−	0.494446i	0.00969838	−	0.0445827i
$124$		0			0
$125$	9.67130	−	5.60945i	0.865028	−	0.501724i
$126$		0			0
$127$	−14.3670	+	1.02755i	−1.27486	+	0.0911801i	−0.692303	−	0.721607i	$-0.743404\pi$
$127$	−14.3670	+	1.02755i	−1.27486	+	0.0911801i	−0.582561	+	0.812787i	$0.697949\pi$
$128$		0			0
$129$	2.23449	+	4.89285i	0.196736	+	0.430792i
$130$		0			0
$131$	−3.76424	−	1.10528i	−0.328883	−	0.0965689i	0.113122	−	0.993581i	$-0.463915\pi$
$131$	−3.76424	−	1.10528i	−0.328883	−	0.0965689i	−0.442006	+	0.897012i	$0.645733\pi$
$132$		0			0
$133$	−3.12075	−	8.36704i	−0.270603	−	0.725515i
$134$		0			0
$135$	1.93135	+	6.37431i	0.166224	+	0.548613i
$136$		0			0
$137$	−5.36830	+	5.36830i	−0.458645	+	0.458645i	−0.898210	−	0.439566i	$-0.855132\pi$
$137$	−5.36830	+	5.36830i	−0.458645	+	0.458645i	0.439566	+	0.898210i	$0.355132\pi$
$138$		0			0
$139$		−	5.14143i		−	0.436091i	−0.975939	−	0.218045i	$-0.930032\pi$
$139$		−	5.14143i		−	0.436091i	0.975939	−	0.218045i	$-0.0699681\pi$
$140$		0			0
$141$	−4.97911	−	3.19988i	−0.419317	−	0.269479i
$142$		0			0
$143$	−19.5029	+	7.27420i	−1.63091	+	0.608299i
$144$		0			0
$145$	−3.39403	+	16.2745i	−0.281859	+	1.35152i
$146$		0			0
$147$	−1.40144	+	3.75739i	−0.115588	+	0.309905i
$148$		0			0
$149$	−6.96997	+	8.04377i	−0.571002	+	0.658971i	−0.965646	−	0.259863i	$-0.916323\pi$
$149$	−6.96997	+	8.04377i	−0.571002	+	0.658971i	0.394644	+	0.918834i	$0.370868\pi$
$150$		0			0
$151$	22.1884	−	6.51510i	1.80567	−	0.530191i	0.807452	−	0.589933i	$-0.200846\pi$
$151$	22.1884	−	6.51510i	1.80567	−	0.530191i	0.998214	+	0.0597416i	$0.0190277\pi$
$152$		0			0
$153$	8.25633	+	1.79605i	0.667484	+	0.145202i
$154$		0			0
$155$	0.433931	+	1.91532i	0.0348542	+	0.153842i
$156$		0			0
$157$	1.63758	+	2.18755i	0.130693	+	0.174585i	0.861114	−	0.508412i	$-0.169767\pi$
$157$	1.63758	+	2.18755i	0.130693	+	0.174585i	−0.730421	+	0.682997i	$0.760676\pi$
$158$		0			0
$159$	1.32503	+	1.52917i	0.105082	+	0.121271i
$160$		0			0
$161$	18.0619	−	3.49177i	1.42348	−	0.275190i
$162$		0			0
$163$	8.54996	+	0.611505i	0.669684	+	0.0478968i	0.402041	−	0.915621i	$-0.368301\pi$
$163$	8.54996	+	0.611505i	0.669684	+	0.0478968i	0.267643	+	0.963518i	$0.413755\pi$
$164$		0			0
$165$	−5.36721	+	4.73211i	−0.417837	+	0.368394i
$166$		0			0
$167$	−2.01670	+	2.69400i	−0.156057	+	0.208468i	−0.871755	−	0.489942i	$-0.837018\pi$
$167$	−2.01670	+	2.69400i	−0.156057	+	0.208468i	0.715698	+	0.698410i	$0.246109\pi$
$168$		0			0
$169$	0.846104	+	1.31656i	0.0650849	+	0.101274i
$170$		0			0
$171$	1.79039	+	6.09752i	0.136915	+	0.466289i
$172$		0			0
$173$	0.773016	+	10.8082i	0.0587713	+	0.821730i	0.938286	+	0.345859i	$0.112413\pi$
$173$	0.773016	+	10.8082i	0.0587713	+	0.821730i	−0.879515	+	0.475871i	$0.842133\pi$
$174$		0			0
$175$	−18.8085	−	3.75405i	−1.42179	−	0.283780i
$176$		0			0
$177$	0.323258	+	0.592003i	0.0242976	+	0.0444977i
$178$		0			0
$179$	−3.03960	−	1.38814i	−0.227190	−	0.103754i	0.298568	−	0.954388i	$-0.403491\pi$
$179$	−3.03960	−	1.38814i	−0.227190	−	0.103754i	−0.525758	+	0.850634i	$0.676218\pi$
$180$		0			0
$181$	6.10902	−	9.50582i	0.454080	−	0.706562i	−0.536439	−	0.843939i	$-0.680231\pi$
$181$	6.10902	−	9.50582i	0.454080	−	0.706562i	0.990519	+	0.137377i	$0.0438671\pi$
$182$		0			0
$183$	4.77847	+	4.77847i	0.353235	+	0.353235i
$184$		0			0
$185$	5.56690	−	6.53727i	0.409286	−	0.480629i
$186$		0			0
$187$	4.05006	+	18.6178i	0.296170	+	1.36147i
$188$		0			0
$189$	4.74645	−	10.3933i	0.345254	−	0.756000i
$190$		0			0
$191$	5.23311	−	17.8223i	0.378654	−	1.28958i	−0.521218	−	0.853424i	$-0.674522\pi$
$191$	5.23311	−	17.8223i	0.378654	−	1.28958i	0.899872	−	0.436154i	$-0.143660\pi$
$192$		0			0
$193$	−10.5591	−	3.93834i	−0.760060	−	0.283488i	−0.0606027	−	0.998162i	$-0.519302\pi$
$193$	−10.5591	−	3.93834i	−0.760060	−	0.283488i	−0.699458	+	0.714674i	$0.746575\pi$
$194$		0			0
$195$	−3.16695	−	2.32854i	−0.226790	−	0.166750i
$196$		0			0
$197$	−14.7185	−	8.03692i	−1.04865	−	0.572607i	−0.139995	−	0.990152i	$-0.544709\pi$
$197$	−14.7185	−	8.03692i	−1.04865	−	0.572607i	−0.908656	+	0.417545i	$0.862891\pi$
$198$		0			0
$199$	−3.44524	+	2.21412i	−0.244226	+	0.156955i	−0.657028	−	0.753866i	$-0.728187\pi$
$199$	−3.44524	+	2.21412i	−0.244226	+	0.156955i	0.412802	+	0.910821i	$0.364550\pi$
$200$		0			0
$201$	−0.497508	+	0.0715309i	−0.0350915	+	0.00504540i
$202$		0			0
$203$	22.8307	−	17.0908i	1.60240	−	1.19954i
$204$		0			0
$205$	−1.55220	−	1.52573i	−0.108410	−	0.106562i
$206$		0			0
$207$	−12.9979	+	1.56157i	−0.903419	+	0.108537i
$208$		0			0
$209$	−10.8301	+	9.38431i	−0.749131	+	0.649126i
$210$		0			0
$211$	−1.58651	+	11.0344i	−0.109220	+	0.759642i	0.859437	+	0.511241i	$0.170814\pi$
$211$	−1.58651	+	11.0344i	−0.109220	+	0.759642i	−0.968657	+	0.248401i	$0.920095\pi$
$212$		0			0
$213$	−0.248020	−	0.185665i	−0.0169940	−	0.0127216i
$214$		0			0
$215$	22.9284	+	3.09565i	1.56371	+	0.211122i
$216$		0			0
$217$	1.61456	−	2.95684i	0.109603	−	0.200723i
$218$		0			0
$219$	5.61843	+	4.86840i	0.379658	+	0.328976i
$220$		0			0
$221$	−9.52113	+	4.34815i	−0.640460	+	0.292488i
$222$		0			0
$223$	15.0035	−	8.19253i	1.00471	−	0.548612i	0.109371	−	0.994001i	$-0.465116\pi$
$223$	15.0035	−	8.19253i	1.00471	−	0.548612i	0.895337	+	0.445389i	$0.146934\pi$
$224$		0			0
$225$	13.1600	+	3.61956i	0.877337	+	0.241304i
$226$		0			0
$227$	6.15908	−	1.33983i	0.408793	−	0.0889274i	−0.00346661	−	0.999994i	$-0.501103\pi$
$227$	6.15908	−	1.33983i	0.408793	−	0.0889274i	0.412259	+	0.911067i	$0.364740\pi$
$228$		0			0
$229$	−2.15190			−0.142201			−0.0711007	−	0.997469i	$-0.522651\pi$
$229$	−2.15190			−0.142201			−0.0711007	+	0.997469i	$0.522651\pi$
$230$		0			0
$231$	12.2748			0.807626
$232$		0			0
$233$	14.2023	−	3.08952i	0.930422	−	0.202401i	0.278282	−	0.960499i	$-0.410235\pi$
$233$	14.2023	−	3.08952i	0.930422	−	0.202401i	0.652140	+	0.758099i	$0.273871\pi$
$234$		0			0
$235$	−23.0657	+	10.7744i	−1.50464	+	0.702842i
$236$		0			0
$237$	−7.68383	+	4.19569i	−0.499119	+	0.272539i
$238$		0			0
$239$	−8.01535	+	3.66049i	−0.518470	+	0.236777i	−0.657423	−	0.753522i	$-0.728354\pi$
$239$	−8.01535	+	3.66049i	−0.518470	+	0.236777i	0.138953	+	0.990299i	$0.455626\pi$
$240$		0			0
$241$	16.9524	+	14.6893i	1.09200	+	0.946221i	0.998778	−	0.0494244i	$-0.0157387\pi$
$241$	16.9524	+	14.6893i	1.09200	+	0.946221i	0.0932196	+	0.995646i	$0.470284\pi$
$242$		0			0
$243$	−5.93704	+	10.8729i	−0.380861	+	0.697496i
$244$		0			0
$245$	10.4554	+	13.7194i	0.667973	+	0.876498i
$246$		0			0
$247$	−6.30218	−	4.71775i	−0.400998	−	0.300183i
$248$		0			0
$249$	0.117113	−	0.814538i	0.00742173	−	0.0516192i
$250$		0			0
$251$	−4.92037	+	4.26353i	−0.310571	+	0.269112i	−0.796174	−	0.605068i	$-0.793146\pi$
$251$	−4.92037	+	4.26353i	−0.310571	+	0.269112i	0.485602	+	0.874180i	$0.338600\pi$
$252$		0			0
$253$	−15.3789	−	25.1986i	−0.966865	−	1.58422i
$254$		0			0
$255$	−2.52228	+	2.56603i	−0.157951	+	0.160691i
$256$		0			0
$257$	−11.7815	+	8.81954i	−0.734912	+	0.550148i	−0.899873	−	0.436152i	$-0.856341\pi$
$257$	−11.7815	+	8.81954i	−0.734912	+	0.550148i	0.164961	+	0.986300i	$0.447250\pi$
$258$		0			0
$259$	−14.5797	+	2.09625i	−0.905941	+	0.130255i
$260$		0			0
$261$	−17.0733	+	10.9723i	−1.05681	+	0.679170i
$262$		0			0
$263$	−5.49164	−	2.99866i	−0.338629	−	0.184905i	0.300932	−	0.953645i	$-0.402702\pi$
$263$	−5.49164	−	2.99866i	−0.338629	−	0.184905i	−0.639561	+	0.768740i	$0.720884\pi$
$264$		0			0
$265$	8.60363	−	1.31261i	0.528517	−	0.0806329i
$266$		0			0
$267$	1.70946	+	0.637595i	0.104617	+	0.0390202i
$268$		0			0
$269$	−5.62563	+	19.1591i	−0.343001	+	1.16815i	0.589736	+	0.807596i	$0.299232\pi$
$269$	−5.62563	+	19.1591i	−0.343001	+	1.16815i	−0.932737	+	0.360558i	$0.882586\pi$
$270$		0			0
$271$	−2.76415	+	6.05264i	−0.167910	+	0.367672i	−0.974817	−	0.223007i	$-0.928413\pi$
$271$	−2.76415	+	6.05264i	−0.167910	+	0.367672i	0.806907	+	0.590679i	$0.201140\pi$
$272$		0			0
$273$	1.43338	+	6.58915i	0.0867522	+	0.398794i
$274$		0			0
$275$	4.90326	+	30.3845i	0.295678	+	1.83225i
$276$		0			0
$277$	16.8085	+	16.8085i	1.00992	+	1.00992i	0.999950	+	0.00997335i	$0.00317467\pi$
$277$	16.8085	+	16.8085i	1.00992	+	1.00992i	0.00997335	+	0.999950i	$0.496825\pi$
$278$		0			0
$279$	−1.29615	+	2.01686i	−0.0775987	+	0.120746i
$280$		0			0
$281$	−24.8600	−	11.3532i	−1.48302	−	0.677274i	−0.500899	−	0.865506i	$-0.666997\pi$
$281$	−24.8600	−	11.3532i	−1.48302	−	0.677274i	−0.982125	+	0.188232i	$0.939724\pi$
$282$		0			0
$283$	−5.23614	−	9.58928i	−0.311256	−	0.570023i	0.674486	−	0.738288i	$-0.264365\pi$
$283$	−5.23614	−	9.58928i	−0.311256	−	0.570023i	−0.985742	+	0.168265i	$0.946184\pi$
$284$		0			0
$285$	−2.60303	−	0.740070i	−0.154190	−	0.0438380i
$286$		0			0
$287$	0.266361	+	3.72421i	0.0157228	+	0.219833i
$288$		0			0
$289$	−2.09019	−	7.11852i	−0.122952	−	0.418736i
$290$		0			0
$291$	−3.05216	−	4.74925i	−0.178921	−	0.278406i
$292$		0			0
$293$	−19.1130	+	25.5319i	−1.11659	+	1.49159i	−0.267342	+	0.963602i	$0.586145\pi$
$293$	−19.1130	+	25.5319i	−1.11659	+	1.49159i	−0.849250	+	0.527991i	$0.822946\pi$
$294$		0			0
$295$	2.89555	+	0.182087i	0.168586	+	0.0106015i
$296$		0			0
$297$	−18.2884	−	1.30801i	−1.06120	−	0.0758987i
$298$		0			0
$299$	11.7308	−	11.1980i	0.678407	−	0.647595i
$300$		0			0
$301$	−25.9913	−	29.9955i	−1.49811	−	1.72891i
$302$		0			0
$303$	2.40316	+	3.21025i	0.138058	+	0.184424i
$304$		0			0
$305$	28.3488	−	6.42266i	1.62325	−	0.367760i
$306$		0			0
$307$	8.58874	+	1.86837i	0.490185	+	0.106633i	0.450863	−	0.892593i	$-0.351116\pi$
$307$	8.58874	+	1.86837i	0.490185	+	0.106633i	0.0393224	+	0.999227i	$0.487480\pi$
$308$		0			0
$309$	7.52360	−	2.20913i	0.428002	−	0.125673i
$310$		0			0
$311$	−9.52587	+	10.9934i	−0.540163	+	0.623381i	−0.958563	−	0.284882i	$-0.908046\pi$
$311$	−9.52587	+	10.9934i	−0.540163	+	0.623381i	0.418400	+	0.908263i	$0.362591\pi$
$312$		0			0
$313$	9.02145	−	24.1874i	0.509922	−	1.36715i	−0.385817	−	0.922575i	$-0.626080\pi$
$313$	9.02145	−	24.1874i	0.509922	−	1.36715i	0.895739	−	0.444579i	$-0.146647\pi$
$314$		0			0
$315$	−12.8274	−	19.5875i	−0.722742	−	1.10363i
$316$		0			0
$317$	5.06568	−	1.88940i	0.284517	−	0.106119i	−0.203154	−	0.979147i	$-0.565119\pi$
$317$	5.06568	−	1.88940i	0.284517	−	0.106119i	0.487671	+	0.873027i	$0.337847\pi$
$318$		0			0
$319$	−38.4999	−	24.7424i	−2.15558	−	1.38531i
$320$		0			0
$321$		−	0.487791i		−	0.0272258i
$322$		0			0
$323$	−5.09540	+	5.09540i	−0.283516	+	0.283516i
$324$		0			0
$325$	−15.7379	+	6.18019i	−0.872979	+	0.342815i
$326$		0			0
$327$	−1.92554	−	5.16257i	−0.106483	−	0.285491i
$328$		0			0
$329$	41.9034	+	12.3039i	2.31021	+	0.678338i
$330$		0			0
$331$	−1.43208	−	3.13582i	−0.0787143	−	0.172360i	0.866183	−	0.499727i	$-0.166566\pi$
$331$	−1.43208	−	3.13582i	−0.0787143	−	0.172360i	−0.944898	+	0.327366i	$0.893839\pi$
$332$		0			0
$333$	10.4554	−	0.747785i	0.572952	−	0.0409783i
$334$		0			0
$335$	−0.881162	+	1.97422i	−0.0481430	+	0.107863i
$336$		0			0
$337$	−4.64388	+	21.3476i	−0.252968	+	1.16288i	0.658848	+	0.752276i	$0.271044\pi$
$337$	−4.64388	+	21.3476i	−0.252968	+	1.16288i	−0.911816	+	0.410599i	$0.865319\pi$
$338$		0			0
$339$	−0.408301	−	2.83980i	−0.0221759	−	0.154237i
$340$		0			0
$341$	−5.35114	−	0.769378i	−0.289781	−	0.0416642i
$342$		0			0
$343$	0.195416	−	2.73227i	0.0105515	−	0.147529i
$344$		0			0
$345$	2.38984	−	5.03663i	0.128665	−	0.271163i
$346$		0			0
$347$	1.20604	−	16.8627i	0.0647437	−	0.905236i	−0.856474	−	0.516189i	$-0.827350\pi$
$347$	1.20604	−	16.8627i	0.0647437	−	0.905236i	0.921218	−	0.389046i	$-0.127195\pi$
$348$		0			0
$349$	29.8898	+	4.29750i	1.59996	+	0.230040i	0.883790	−	0.467883i	$-0.154983\pi$
$349$	29.8898	+	4.29750i	1.59996	+	0.230040i	0.716172	+	0.697923i	$0.245892\pi$
$350$		0			0
$351$	−1.43347	−	9.97000i	−0.0765129	−	0.532159i
$352$		0			0
$353$	4.67014	−	21.4683i	0.248567	−	1.14264i	−0.668438	−	0.743767i	$-0.733037\pi$
$353$	4.67014	−	21.4683i	0.248567	−	1.14264i	0.917005	−	0.398875i	$-0.130599\pi$
$354$		0			0
$355$	−1.24454	+	0.476417i	−0.0660533	+	0.0252856i
$356$		0			0
$357$	6.15670	−	0.440336i	0.325847	−	0.0233051i
$358$		0			0
$359$	−3.72333	−	8.15297i	−0.196510	−	0.430297i	0.785567	−	0.618777i	$-0.212371\pi$
$359$	−3.72333	−	8.15297i	−0.196510	−	0.430297i	−0.982077	+	0.188480i	$0.939644\pi$
$360$		0			0
$361$	13.0302	+	3.82600i	0.685799	+	0.201369i
$362$		0			0
$363$	−4.88522	−	13.0978i	−0.256408	−	0.687455i
$364$		0			0
$365$	30.6031	−	9.27240i	1.60184	−	0.485340i
$366$		0			0
$367$	−2.97137	+	2.97137i	−0.155104	+	0.155104i	−0.780393	−	0.625289i	$-0.784981\pi$
$367$	−2.97137	+	2.97137i	−0.155104	+	0.155104i	0.625289	+	0.780393i	$0.284981\pi$
$368$		0			0
$369$		−	2.65703i		−	0.138320i
$370$		0			0
$371$	−12.5599	−	8.07177i	−0.652079	−	0.419065i
$372$		0			0
$373$	4.83473	−	1.80326i	0.250333	−	0.0933694i	−0.221165	−	0.975236i	$-0.570986\pi$
$373$	4.83473	−	1.80326i	0.250333	−	0.0933694i	0.471498	+	0.881867i	$0.343713\pi$
$374$		0			0
$375$	−4.29294	+	3.91819i	−0.221686	+	0.202334i
$376$		0			0
$377$	8.78594	−	23.5560i	0.452499	−	1.21320i
$378$		0			0
$379$	−6.58919	+	7.60433i	−0.338464	+	0.390608i	−0.899310	−	0.437312i	$-0.855931\pi$
$379$	−6.58919	+	7.60433i	−0.338464	+	0.390608i	0.560846	+	0.827920i	$0.310476\pi$
$380$		0			0
$381$	7.18456	−	2.10958i	0.368076	−	0.108077i
$382$		0			0
$383$	33.0381	+	7.18700i	1.68817	+	0.367239i	0.951173	−	0.308659i	$-0.0998801\pi$
$383$	33.0381	+	7.18700i	1.68817	+	0.367239i	0.736996	+	0.675897i	$0.236244\pi$
$384$		0			0
$385$	28.1618	−	44.6602i	1.43526	−	2.27609i
$386$		0			0
$387$	16.9263	+	22.6109i	0.860413	+	1.14938i
$388$		0			0
$389$	10.6285	+	12.2659i	0.538887	+	0.621908i	0.958257	−	0.285907i	$-0.0922948\pi$
$389$	10.6285	+	12.2659i	0.538887	+	0.621908i	−0.419371	+	0.907815i	$0.637749\pi$
$390$		0			0
$391$	−8.61757	−	12.0872i	−0.435809	−	0.611274i
$392$		0			0
$393$	2.03429	+	0.145495i	0.102616	+	0.00733926i
$394$		0			0
$395$	−2.36338	+	37.5825i	−0.118915	+	1.89098i
$396$		0			0
$397$	−16.0210	+	21.4016i	−0.804073	+	1.07412i	0.191626	+	0.981468i	$0.438624\pi$
$397$	−16.0210	+	21.4016i	−0.804073	+	1.07412i	−0.995699	+	0.0926479i	$0.970467\pi$
$398$		0			0
$399$	2.50986	+	3.90542i	0.125650	+	0.195515i
$400$		0			0
$401$	−4.16223	−	14.1753i	−0.207852	−	0.707879i	−0.995752	−	0.0920755i	$-0.970650\pi$
$401$	−4.16223	−	14.1753i	−0.207852	−	0.707879i	0.787900	−	0.615803i	$-0.211168\pi$
$402$		0			0
$403$	−0.211871	−	2.96234i	−0.0105540	−	0.147565i
$404$		0			0
$405$	7.22825	+	12.9712i	0.359175	+	0.644543i
$406$		0			0
$407$	11.3280	+	20.7456i	0.561506	+	1.02832i
$408$		0			0
$409$	20.4822	+	9.35391i	1.01278	+	0.462521i	0.851482	−	0.524384i	$-0.175704\pi$
$409$	20.4822	+	9.35391i	1.01278	+	0.462521i	0.161299	+	0.986906i	$0.448432\pi$
$410$		0			0
$411$	2.13376	−	3.32019i	0.105250	−	0.163773i
$412$		0			0
$413$	−3.51929	−	3.51929i	−0.173173	−	0.173173i
$414$		0			0
$415$	−2.69488	−	2.29486i	−0.132287	−	0.112650i
$416$		0			0
$417$	0.568148	+	2.61173i	0.0278223	+	0.127897i
$418$		0			0
$419$	13.4909	−	29.5409i	0.659072	−	1.44317i	−0.224313	−	0.974517i	$-0.572014\pi$
$419$	13.4909	−	29.5409i	0.659072	−	1.44317i	0.883385	−	0.468649i	$-0.155259\pi$
$420$		0			0
$421$	8.84338	−	30.1178i	0.431000	−	1.46785i	−0.402545	−	0.915400i	$-0.631874\pi$
$421$	8.84338	−	30.1178i	0.431000	−	1.46785i	0.833545	−	0.552451i	$-0.186307\pi$
$422$		0			0
$423$	−29.1192	−	10.8609i	−1.41582	−	0.528075i
$424$		0			0
$425$	3.54932	+	15.0641i	0.172167	+	0.730715i
$426$		0			0
$427$	−43.7645	−	23.8972i	−2.11791	−	1.15647i
$428$		0			0
$429$	9.10320	−	5.85027i	0.439507	−	0.282454i
$430$		0			0
$431$	37.4273	−	5.38123i	1.80281	−	0.259205i	0.842611	−	0.538522i	$-0.181017\pi$
$431$	37.4273	−	5.38123i	1.80281	−	0.259205i	0.960199	+	0.279317i	$0.0901082\pi$
$432$		0			0
$433$	−4.06538	+	3.04331i	−0.195370	+	0.146252i	−0.692484	−	0.721433i	$-0.743484\pi$
$433$	−4.06538	+	3.04331i	−0.195370	+	0.146252i	0.497114	+	0.867685i	$0.334393\pi$
$434$		0			0
$435$	−0.0743019	−	8.64214i	−0.00356251	−	0.414359i
$436$		0			0
$437$	4.87272	−	10.0454i	0.233094	−	0.480537i
$438$		0			0
$439$	12.4407	−	10.7799i	0.593761	−	0.514497i	−0.305337	−	0.952244i	$-0.598769\pi$
$439$	12.4407	−	10.7799i	0.593761	−	0.514497i	0.899098	+	0.437747i	$0.144224\pi$
$440$		0			0
$441$	−2.99680	+	20.8432i	−0.142705	+	0.992535i
$442$		0			0
$443$	−20.6930	−	15.4906i	−0.983155	−	0.735980i	−0.0185902	−	0.999827i	$-0.505918\pi$
$443$	−20.6930	−	15.4906i	−0.983155	−	0.735980i	−0.964565	+	0.263847i	$0.915009\pi$
$444$		0			0
$445$	6.24175	−	4.75679i	0.295887	−	0.225494i
$446$		0			0
$447$	2.65172	−	4.85626i	0.125422	−	0.229693i
$448$		0			0
$449$	−22.6561	−	19.6316i	−1.06921	−	0.926473i	−0.0717267	−	0.997424i	$-0.522851\pi$
$449$	−22.6561	−	19.6316i	−1.06921	−	0.926473i	−0.997480	+	0.0709517i	$0.977396\pi$
$450$		0			0
$451$	5.45011	−	2.48898i	0.256635	−	0.117201i
$452$		0			0
$453$	−10.5513	+	5.76143i	−0.495742	+	0.270695i
$454$		0			0
$455$	27.2622	+	9.90213i	1.27807	+	0.464219i
$456$		0			0
$457$	1.10637	−	0.240676i	0.0517538	−	0.0112584i	−0.186614	−	0.982433i	$-0.559751\pi$
$457$	1.10637	−	0.240676i	0.0517538	−	0.0112584i	0.238368	+	0.971175i	$0.423388\pi$
$458$		0			0
$459$	−9.21987			−0.430347
$460$		0			0
$461$	−23.2230			−1.08160			−0.540800	−	0.841151i	$-0.681879\pi$
$461$	−23.2230			−1.08160			−0.540800	+	0.841151i	$0.681879\pi$
$462$		0			0
$463$	9.76133	−	2.12345i	0.453647	−	0.0986849i	0.0200646	−	0.999799i	$-0.493613\pi$
$463$	9.76133	−	2.12345i	0.453647	−	0.0986849i	0.433583	+	0.901114i	$0.357249\pi$
$464$		0			0
$465$	−0.432077	−	0.924988i	−0.0200371	−	0.0428953i
$466$		0			0
$467$	11.3316	−	6.18752i	0.524363	−	0.286324i	−0.195185	−	0.980766i	$-0.562531\pi$
$467$	11.3316	−	6.18752i	0.524363	−	0.286324i	0.719548	+	0.694442i	$0.244349\pi$
$468$		0			0
$469$	3.37358	−	1.54066i	0.155778	−	0.0711413i
$470$		0			0
$471$	−1.07358	−	0.930266i	−0.0494681	−	0.0428644i
$472$		0			0
$473$	−30.5237	+	55.9000i	−1.40348	+	2.57029i
$474$		0			0
$475$	−8.66468	+	7.77281i	−0.397563	+	0.356641i
$476$		0			0
$477$	8.50549	+	6.36713i	0.389440	+	0.291531i
$478$		0			0
$479$	3.87034	−	26.9188i	0.176840	−	1.22995i	−0.687178	−	0.726489i	$-0.741151\pi$
$479$	3.87034	−	26.9188i	0.176840	−	1.22995i	0.864018	−	0.503461i	$-0.167940\pi$
$480$		0			0
$481$	−9.81345	+	8.50340i	−0.447455	+	0.387722i
$482$		0			0
$483$	−8.78918	+	3.76965i	−0.399922	+	0.171525i
$484$		0			0
$485$	−24.2819	+	0.208767i	−1.10258	+	0.00947961i
$486$		0			0
$487$	27.8197	−	20.8255i	1.26063	−	0.943695i	0.260864	−	0.965376i	$-0.415993\pi$
$487$	27.8197	−	20.8255i	1.26063	−	0.943695i	0.999765	+	0.0216805i	$0.00690165\pi$
$488$		0			0
$489$	−4.41076	+	0.634171i	−0.199461	+	0.0286782i
$490$		0			0
$491$	19.9462	−	12.8187i	0.900161	−	0.578498i	−0.00667722	−	0.999978i	$-0.502125\pi$
$491$	19.9462	−	12.8187i	0.900161	−	0.578498i	0.906838	+	0.421480i	$0.138489\pi$
$492$		0			0
$493$	−20.1980	−	11.0289i	−0.909671	−	0.496718i
$494$		0			0
$495$	−22.2570	+	30.2709i	−1.00038	+	1.36058i
$496$		0			0
$497$	2.14191	+	0.798891i	0.0960778	+	0.0358352i
$498$		0			0
$499$	−5.00821	+	17.0564i	−0.224198	+	0.763549i	0.768171	+	0.640245i	$0.221167\pi$
$499$	−5.00821	+	17.0564i	−0.224198	+	0.763549i	−0.992369	+	0.123304i	$0.960651\pi$
$500$		0			0
$501$	0.726741	−	1.59134i	0.0324684	−	0.0710959i
$502$		0			0
$503$	6.57740	+	30.2358i	0.293272	+	1.34815i	0.854054	+	0.520185i	$0.174137\pi$
$503$	6.57740	+	30.2358i	0.293272	+	1.34815i	−0.560782	+	0.827963i	$0.689500\pi$
$504$		0			0
$505$	17.1935	−	1.37837i	0.765101	−	0.0613368i
$506$		0			0
$507$	−0.575287	−	0.575287i	−0.0255494	−	0.0255494i
$508$		0			0
$509$	0.529040	−	0.823203i	0.0234493	−	0.0364878i	−0.829331	−	0.558758i	$-0.811278\pi$
$509$	0.529040	−	0.823203i	0.0234493	−	0.0364878i	0.852780	+	0.522270i	$0.174915\pi$
$510$		0			0
$511$	−49.8982	−	22.7878i	−2.20737	−	1.00807i
$512$		0			0
$513$	−3.32330	−	6.08618i	−0.146727	−	0.268711i
$514$		0			0
$515$	9.22356	−	32.4418i	0.406439	−	1.42956i
$516$		0			0
$517$	−4.99957	−	69.9032i	−0.219881	−	3.07434i
$518$		0			0
$519$	−1.58702	−	5.40489i	−0.0696624	−	0.237248i
$520$		0			0
$521$	10.5994	+	16.4930i	0.464368	+	0.722570i	0.991908	−	0.126960i	$-0.0405220\pi$
$521$	10.5994	+	16.4930i	0.464368	+	0.722570i	−0.527540	+	0.849530i	$0.676886\pi$
$522$		0			0
$523$	−6.08028	+	8.12230i	−0.265872	+	0.355163i	−0.913533	−	0.406766i	$-0.866657\pi$
$523$	−6.08028	+	8.12230i	−0.265872	+	0.355163i	0.647661	+	0.761929i	$0.275747\pi$
$524$		0			0
$525$	9.96913	−	0.171435i	0.435089	−	0.00748202i
$526$		0			0
$527$	−2.71158	−	0.193936i	−0.118118	−	0.00844798i
$528$		0			0
$529$	18.7504	+	13.3200i	0.815233	+	0.579133i
$530$		0			0
$531$	2.31940	+	2.67673i	0.100653	+	0.116160i
$532$		0			0
$533$	1.97252	+	2.63497i	0.0854392	+	0.114133i
$534$		0			0
$535$	−1.77475	−	1.11912i	−0.0767293	−	0.0483839i
$536$		0			0
$537$	1.69744	+	0.369256i	0.0732499	+	0.0159346i
$538$		0			0
$539$	−45.5609	+	13.3779i	−1.96245	+	0.576226i
$540$		0			0
$541$	−23.8141	+	27.4829i	−1.02385	+	1.18158i	−0.0406245	+	0.999174i	$0.512935\pi$
$541$	−23.8141	+	27.4829i	−1.02385	+	1.18158i	−0.983223	+	0.182408i	$0.941611\pi$
$542$		0			0
$543$	−2.05282	+	5.50381i	−0.0880948	+	0.236191i
$544$		0			0
$545$	−23.2009	−	4.83853i	−0.993819	−	0.207260i
$546$		0			0
$547$	−3.35257	+	1.25044i	−0.143345	+	0.0534650i	−0.420113	−	0.907472i	$-0.638010\pi$
$547$	−3.35257	+	1.25044i	−0.143345	+	0.0534650i	0.276768	+	0.960937i	$0.410737\pi$
$548$		0			0
$549$	29.8517	+	19.1845i	1.27404	+	0.818775i
$550$		0			0
$551$		−	17.3084i		−	0.737362i
$552$		0			0
$553$	45.6783	−	45.6783i	1.94244	−	1.94244i
$554$		0			0
$555$	−2.10547	+	3.93595i	−0.0893720	+	0.167072i
$556$		0			0
$557$	−4.39308	−	11.7783i	−0.186141	−	0.499063i	0.810040	−	0.586374i	$-0.199445\pi$
$557$	−4.39308	−	11.7783i	−0.186141	−	0.499063i	−0.996181	+	0.0873115i	$0.972172\pi$
$558$		0			0
$559$	−33.5716	−	9.85750i	−1.41993	−	0.416928i
$560$		0			0
$561$	−4.11468	−	9.00989i	−0.173722	−	0.380398i
$562$		0			0
$563$	1.63132	−	0.116674i	0.0687518	−	0.00491723i	−0.0369209	−	0.999318i	$-0.511755\pi$
$563$	1.63132	−	0.116674i	0.0687518	−	0.00491723i	0.105673	+	0.994401i	$0.466300\pi$
$564$		0			0
$565$	−11.2689	−	5.02971i	−0.474087	−	0.211602i
$566$		0			0
$567$	5.41474	−	24.8912i	0.227398	−	1.04533i
$568$		0			0
$569$	2.23822	+	15.5671i	0.0938309	+	0.652608i	0.981406	+	0.191945i	$0.0614794\pi$
$569$	2.23822	+	15.5671i	0.0938309	+	0.652608i	−0.887575	+	0.460663i	$0.847612\pi$
$570$		0			0
$571$	25.7858	+	3.70743i	1.07910	+	0.155151i	0.658863	−	0.752263i	$-0.271038\pi$
$571$	25.7858	+	3.70743i	1.07910	+	0.155151i	0.420237	+	0.907414i	$0.361947\pi$
$572$		0			0
$573$	−0.688867	+	9.63162i	−0.0287778	+	0.402367i
$574$		0			0
$575$	−12.8421	−	20.2505i	−0.535552	−	0.844503i
$576$		0			0
$577$	−0.195504	+	2.73350i	−0.00813894	+	0.113797i	−0.999897	−	0.0143244i	$-0.995440\pi$
$577$	−0.195504	+	2.73350i	−0.00813894	+	0.113797i	0.991758	+	0.128122i	$0.0408948\pi$
$578$		0			0
$579$	5.79898	+	0.833768i	0.240997	+	0.0346502i
$580$		0			0
$581$	0.864146	+	6.01026i	0.0358508	+	0.249348i
$582$		0			0
$583$	−5.09272	+	23.4109i	−0.210919	+	0.969578i
$584$		0			0
$585$	−18.8485	−	8.41274i	−0.779290	−	0.347824i
$586$		0			0
$587$	19.3809	−	1.38615i	0.799935	−	0.0572125i	0.334615	−	0.942355i	$-0.391394\pi$
$587$	19.3809	−	1.38615i	0.799935	−	0.0572125i	0.465320	+	0.885143i	$0.345939\pi$
$588$		0			0
$589$	−0.849369	−	1.85986i	−0.0349976	−	0.0766341i
$590$		0			0
$591$	8.36479	+	2.45612i	0.344081	+	0.101031i
$592$		0			0
$593$	8.99390	+	24.1136i	0.369335	+	0.990226i	0.980116	+	0.198426i	$0.0635830\pi$
$593$	8.99390	+	24.1136i	0.369335	+	0.990226i	−0.610781	+	0.791800i	$0.709144\pi$
$594$		0			0
$595$	12.5230	−	23.4105i	0.513394	−	0.959736i
$596$		0			0
$597$	1.50543	−	1.50543i	0.0616133	−	0.0616133i
$598$		0			0
$599$			13.4630i			0.550081i	0.961433	+	0.275041i	$0.0886913\pi$
$599$			13.4630i			0.550081i	−0.961433	+	0.275041i	$0.911309\pi$
$600$		0			0
$601$	36.5576	+	23.4941i	1.49122	+	0.958346i	0.995979	+	0.0895883i	$0.0285551\pi$
$601$	36.5576	+	23.4941i	1.49122	+	0.958346i	0.495237	+	0.868758i	$0.335081\pi$
$602$		0			0
$603$	−2.47285	+	0.922325i	−0.100702	+	0.0375600i
$604$		0			0
$605$	−58.8623	−	12.2757i	−2.39309	−	0.499077i
$606$		0			0
$607$	−7.88732	+	21.1467i	−0.320137	+	0.858319i	0.672816	+	0.739810i	$0.265084\pi$
$607$	−7.88732	+	21.1467i	−0.320137	+	0.858319i	−0.992953	+	0.118510i	$0.962188\pi$
$608$		0			0
$609$	−9.70886	+	11.2046i	−0.393423	+	0.454034i
$610$		0			0
$611$	36.9403	−	10.8466i	1.49444	−	0.438808i
$612$		0			0
$613$	46.2683	+	10.0650i	1.86876	+	0.406523i	0.996578	−	0.0826623i	$-0.0263423\pi$
$613$	46.2683	+	10.0650i	1.86876	+	0.406523i	0.872180	+	0.489186i	$0.162706\pi$
$614$		0			0
$615$	0.957080	+	0.603515i	0.0385932	+	0.0243361i
$616$		0			0
$617$	−13.5303	−	18.0743i	−0.544708	−	0.727645i	0.440738	−	0.897636i	$-0.354717\pi$
$617$	−13.5303	−	18.0743i	−0.544708	−	0.727645i	−0.985446	+	0.169991i	$0.945626\pi$
$618$		0			0
$619$	−18.3787	−	21.2102i	−0.738703	−	0.852508i	0.254720	−	0.967015i	$-0.418017\pi$
$619$	−18.3787	−	21.2102i	−0.738703	−	0.852508i	−0.993422	+	0.114507i	$0.963471\pi$
$620$		0			0
$621$	13.4968	−	4.67986i	0.541608	−	0.187796i
$622$		0			0
$623$	−13.4282	−	0.960402i	−0.537988	−	0.0384777i
$624$		0			0
$625$	4.40659	+	24.6086i	0.176264	+	0.984343i
$626$		0			0
$627$	4.46443	−	5.96378i	0.178292	−	0.238170i
$628$		0			0
$629$	6.42598	+	9.99902i	0.256221	+	0.398687i
$630$		0			0
$631$	−6.37957	−	21.7268i	−0.253967	−	0.864931i	−0.983488	−	0.180973i	$-0.942075\pi$
$631$	−6.37957	−	21.7268i	−0.253967	−	0.864931i	0.729521	−	0.683958i	$-0.239743\pi$
$632$		0			0
$633$	−0.413434	−	5.78056i	−0.0164325	−	0.229757i
$634$		0			0
$635$	8.80792	−	30.9799i	0.349532	−	1.22940i
$636$		0			0
$637$	−12.5016	−	22.8949i	−0.495331	−	0.907131i
$638$		0			0
$639$	−1.47981	−	0.675807i	−0.0585404	−	0.0267345i
$640$		0			0
$641$	16.3696	−	25.4716i	0.646560	−	1.00607i	−0.351009	−	0.936372i	$-0.614161\pi$
$641$	16.3696	−	25.4716i	0.646560	−	1.00607i	0.997568	−	0.0696945i	$-0.0222025\pi$
$642$		0			0
$643$	4.66290	+	4.66290i	0.183887	+	0.183887i	0.793047	−	0.609160i	$-0.208493\pi$
$643$	4.66290	+	4.66290i	0.183887	+	0.183887i	−0.609160	+	0.793047i	$0.708493\pi$
$644$		0			0
$645$	−11.9892	+	0.961155i	−0.472075	+	0.0378454i
$646$		0			0
$647$	3.67249	+	16.8821i	0.144380	+	0.663706i	0.991260	+	0.131921i	$0.0421146\pi$
$647$	3.67249	+	16.8821i	0.144380	+	0.663706i	−0.846880	+	0.531784i	$0.821522\pi$
$648$		0			0
$649$	−3.31780	+	7.26497i	−0.130235	+	0.285175i
$650$		0			0
$651$	−0.493417	+	1.68042i	−0.0193385	+	0.0658610i
$652$		0			0
$653$	−17.9633	−	6.69995i	−0.702957	−	0.262189i	−0.0275349	−	0.999621i	$-0.508766\pi$
$653$	−17.9633	−	6.69995i	−0.702957	−	0.262189i	−0.675422	+	0.737432i	$0.736038\pi$
$654$		0			0
$655$	5.19656	−	7.06765i	0.203047	−	0.276156i
$656$		0			0
$657$	34.2618	+	18.7084i	1.33668	+	0.729883i
$658$		0			0
$659$	−10.0086	+	6.43213i	−0.389879	+	0.250560i	−0.720865	−	0.693076i	$-0.756255\pi$
$659$	−10.0086	+	6.43213i	−0.389879	+	0.250560i	0.330986	+	0.943636i	$0.392619\pi$
$660$		0			0
$661$	17.0377	−	2.44965i	0.662689	−	0.0952803i	0.197240	−	0.980355i	$-0.436802\pi$
$661$	17.0377	−	2.44965i	0.662689	−	0.0952803i	0.465449	+	0.885075i	$0.345893\pi$
$662$		0			0
$663$	4.35603	−	3.26088i	0.169174	−	0.126642i
$664$		0			0
$665$	19.9675	−	0.171674i	0.774308	−	0.00665722i
$666$		0			0
$667$	35.1656	+	5.89288i	1.36162	+	0.228173i
$668$		0			0
$669$	−6.71613	+	5.81956i	−0.259661	+	0.224997i
$670$		0			0
$671$	−11.3876	+	79.2028i	−0.439615	+	3.05759i
$672$		0			0
$673$	−11.6651	−	8.73235i	−0.449655	−	0.336607i	0.350331	−	0.936626i	$-0.386069\pi$
$673$	−11.6651	−	8.73235i	−0.449655	−	0.336607i	−0.799986	+	0.600018i	$0.795160\pi$
$674$		0			0
$675$	−14.8714	−	0.806894i	−0.572400	−	0.0310574i
$676$		0			0
$677$	9.69683	−	17.7584i	0.372680	−	0.682512i	−0.622279	−	0.782795i	$-0.713793\pi$
$677$	9.69683	−	17.7584i	0.372680	−	0.682512i	0.994959	+	0.100284i	$0.0319750\pi$
$678$		0			0
$679$	31.4817	+	27.2791i	1.20816	+	1.04687i
$680$		0			0
$681$	−2.98062	+	1.36120i	−0.114218	+	0.0521614i
$682$		0			0
$683$	10.6223	−	5.80020i	0.406450	−	0.221939i	−0.262999	−	0.964796i	$-0.584712\pi$
$683$	10.6223	−	5.80020i	0.406450	−	0.221939i	0.669450	+	0.742857i	$0.266530\pi$
$684$		0			0
$685$	−7.18460	−	15.3808i	−0.274510	−	0.587668i
$686$		0			0
$687$	1.09312	−	0.237793i	0.0417050	−	0.00907236i
$688$		0			0
$689$	−13.1617			−0.501420
$690$		0			0
$691$	46.2881			1.76088			0.880442	−	0.474154i	$-0.157246\pi$
$691$	46.2881			1.76088			0.880442	+	0.474154i	$0.157246\pi$
$692$		0			0
$693$	62.9816	−	13.7008i	2.39247	−	0.520451i
$694$		0			0
$695$	10.8059	+	3.92489i	0.409890	+	0.148880i
$696$		0			0
$697$	2.64433	−	1.44391i	0.100161	−	0.0546920i
$698$		0			0
$699$	−6.87303	+	3.13881i	−0.259962	+	0.118721i
$700$		0			0
$701$	0.202167	+	0.175179i	0.00763574	+	0.00661641i	0.658670	−	0.752432i	$-0.271119\pi$
$701$	0.202167	+	0.175179i	0.00763574	+	0.00661641i	−0.651035	+	0.759048i	$0.725665\pi$
$702$		0			0
$703$	−4.28426	+	7.84604i	−0.161584	+	0.295919i
$704$		0			0
$705$	10.5262	−	8.02198i	0.396441	−	0.302125i
$706$		0			0
$707$	−23.6876	−	17.7323i	−0.890864	−	0.666892i
$708$		0			0
$709$	5.62954	−	39.1543i	0.211422	−	1.47047i	−0.556992	−	0.830518i	$-0.688045\pi$
$709$	5.62954	−	39.1543i	0.211422	−	1.47047i	0.768414	−	0.639954i	$-0.221046\pi$
$710$		0			0
$711$	−34.7423	+	30.1043i	−1.30294	+	1.12900i
$712$		0			0
$713$	4.06787	−	1.09246i	0.152343	−	0.0409128i
$714$		0			0
$715$	−0.400157	−	46.5427i	−0.0149650	−	1.74060i
$716$		0			0
$717$	3.66712	−	2.74517i	0.136951	−	0.102520i
$718$		0			0
$719$	35.8945	−	5.16085i	1.33864	−	0.192467i	0.564474	−	0.825451i	$-0.309079\pi$
$719$	35.8945	−	5.16085i	1.33864	−	0.192467i	0.774165	+	0.632984i	$0.218170\pi$
$720$		0			0
$721$	−48.6735	+	31.2806i	−1.81270	+	1.16495i
$722$		0			0
$723$	−10.2346	−	5.58854i	−0.380630	−	0.207840i
$724$		0			0
$725$	−31.6136	−	19.5570i	−1.17410	−	0.726330i
$726$		0			0
$727$	−26.5769	−	9.91265i	−0.985681	−	0.367640i	−0.195628	−	0.980678i	$-0.562674\pi$
$727$	−26.5769	−	9.91265i	−0.985681	−	0.367640i	−0.790053	+	0.613038i	$0.789947\pi$
$728$		0			0
$729$	−3.79837	+	12.9361i	−0.140680	+	0.479113i
$730$		0			0
$731$	−13.3045	+	29.1328i	−0.492085	+	1.07752i
$732$		0			0
$733$	−0.505579	−	2.32411i	−0.0186740	−	0.0858429i	0.966867	−	0.255282i	$-0.0821682\pi$
$733$	−0.505579	−	2.32411i	−0.0186740	−	0.0858429i	−0.985541	+	0.169439i	$0.945805\pi$
$734$		0			0
$735$	−6.82717	−	5.81377i	−0.251824	−	0.214444i
$736$		0			0
$737$	−4.20832	−	4.20832i	−0.155015	−	0.155015i
$738$		0			0
$739$	15.8221	−	24.6197i	0.582027	−	0.905652i	−0.417969	−	0.908461i	$-0.637258\pi$
$739$	15.8221	−	24.6197i	0.582027	−	0.905652i	0.999996	+	0.00280944i	$0.000894273\pi$
$740$		0			0
$741$	3.72269	+	1.70010i	0.136757	+	0.0624546i
$742$		0			0
$743$	−12.3689	−	22.6520i	−0.453772	−	0.831022i	0.546206	−	0.837651i	$-0.316072\pi$
$743$	−12.3689	−	22.6520i	−0.453772	−	0.831022i	−0.999978	+	0.00662905i	$0.997890\pi$
$744$		0			0
$745$	−11.5850	−	20.7894i	−0.424442	−	0.761666i
$746$		0			0
$747$	−0.308262	−	4.31007i	−0.0112787	−	0.157697i
$748$		0			0
$749$	1.01404	+	3.45349i	0.0370520	+	0.126188i
$750$		0			0
$751$	−19.2695	−	29.9839i	−0.703154	−	1.09413i	−0.990661	−	0.136350i	$-0.956463\pi$
$751$	−19.2695	−	29.9839i	−0.703154	−	1.09413i	0.287507	−	0.957779i	$-0.407174\pi$
$752$		0			0
$753$	2.02830	−	2.70950i	0.0739155	−	0.0987395i
$754$		0			0
$755$	−3.24534	+	51.6074i	−0.118110	+	1.87819i
$756$		0			0
$757$	1.64580	+	0.117710i	0.0598176	+	0.00427824i	0.101216	−	0.994864i	$-0.467727\pi$
$757$	1.64580	+	0.117710i	0.0598176	+	0.00427824i	−0.0413983	+	0.999143i	$0.513181\pi$
$758$		0			0
$759$	10.5967	+	11.1009i	0.384635	+	0.402936i
$760$		0			0
$761$	28.2711	+	32.6266i	1.02483	+	1.18271i	0.983004	+	0.183587i	$0.0587707\pi$
$761$	28.2711	+	32.6266i	1.02483	+	1.18271i	0.0418219	+	0.999125i	$0.486684\pi$
$762$		0			0
$763$	24.3647	+	32.5474i	0.882060	+	1.17829i
$764$		0			0
$765$	−10.0776	+	15.9814i	−0.364355	+	0.577810i
$766$		0			0
$767$	−4.28728	−	0.932640i	−0.154805	−	0.0336757i
$768$		0			0
$769$	−46.9788	+	13.7942i	−1.69410	+	0.497432i	−0.979388	−	0.201989i	$-0.935259\pi$
$769$	−46.9788	+	13.7942i	−1.69410	+	0.497432i	−0.714710	+	0.699421i	$0.753441\pi$
$770$		0			0
$771$	5.01016	−	5.78203i	0.180436	−	0.208235i
$772$		0			0
$773$	−9.03739	+	24.2302i	−0.325053	+	0.871499i	0.666930	+	0.745121i	$0.267608\pi$
$773$	−9.03739	+	24.2302i	−0.325053	+	0.871499i	−0.991982	+	0.126379i	$0.959665\pi$
$774$		0			0
$775$	−4.35673	−	0.550122i	−0.156498	−	0.0197610i
$776$		0			0
$777$	7.17453	−	2.67596i	0.257385	−	0.0959996i
$778$		0			0
$779$	1.90630	+	1.22510i	0.0683002	+	0.0438938i
$780$		0			0
$781$		−	3.66845i		−	0.131267i
$782$		0			0
$783$	15.6593	−	15.6593i	0.559618	−	0.559618i
$784$		0			0
$785$	−5.84772	+	1.77179i	−0.208714	+	0.0632381i
$786$		0			0
$787$	2.87575	+	7.71018i	0.102509	+	0.274838i	0.978072	−	0.208266i	$-0.0667819\pi$
$787$	2.87575	+	7.71018i	0.102509	+	0.274838i	−0.875563	+	0.483104i	$0.839509\pi$
$788$		0			0
$789$	3.12099	+	0.916406i	0.111110	+	0.0326249i
$790$		0			0
$791$	8.79418	+	19.2566i	0.312685	+	0.684684i
$792$		0			0
$793$	−43.8459	+	3.13592i	−1.55702	+	0.111360i
$794$		0			0
$795$	−4.22540	+	1.61751i	−0.149860	+	0.0573671i
$796$		0			0
$797$	−11.0964	+	51.0095i	−0.393056	+	1.80685i	0.175815	+	0.984423i	$0.443744\pi$
$797$	−11.0964	+	51.0095i	−0.393056	+	1.80685i	−0.568871	+	0.822426i	$0.692620\pi$
$798$		0			0
$799$	−5.01528	−	34.8820i	−0.177428	−	1.23404i
$800$		0			0
$801$	9.48281	+	1.36342i	0.335059	+	0.0481742i
$802$		0			0
$803$	−6.27979	+	87.8029i	−0.221609	+	3.09850i
$804$		0			0
$805$	−6.44944	+	40.6267i	−0.227313	+	1.43190i
$806$		0			0
$807$	0.740538	−	10.3541i	0.0260682	−	0.364480i
$808$		0			0
$809$	9.65659	+	1.38841i	0.339507	+	0.0488138i	0.309960	−	0.950750i	$-0.399684\pi$
$809$	9.65659	+	1.38841i	0.339507	+	0.0488138i	0.0295474	+	0.999563i	$0.490593\pi$
$810$		0			0
$811$	7.22737	+	50.2674i	0.253787	+	1.76513i	0.575031	+	0.818132i	$0.304990\pi$
$811$	7.22737	+	50.2674i	0.253787	+	1.76513i	−0.321243	+	0.946997i	$0.604101\pi$
$812$		0			0
$813$	0.735286	−	3.38005i	0.0257876	−	0.118544i
$814$		0			0
$815$	−7.81212	+	17.5028i	−0.273647	+	0.613098i
$816$		0			0
$817$	−24.0266	+	1.71842i	−0.840585	+	0.0601198i
$818$		0			0
$819$	14.7092	+	32.2087i	0.513982	+	1.12546i
$820$		0			0
$821$	−16.1221	−	4.73387i	−0.562665	−	0.165213i	−0.0119824	−	0.999928i	$-0.503814\pi$
$821$	−16.1221	−	4.73387i	−0.562665	−	0.165213i	−0.550682	+	0.834715i	$0.685632\pi$
$822$		0			0
$823$	4.98651	+	13.3693i	0.173819	+	0.466026i	0.994422	−	0.105472i	$-0.0336353\pi$
$823$	4.98651	+	13.3693i	0.173819	+	0.466026i	−0.820604	+	0.571498i	$0.806363\pi$
$824$		0			0
$825$	−5.84835	−	14.8928i	−0.203613	−	0.518501i
$826$		0			0
$827$	−36.2265	+	36.2265i	−1.25972	+	1.25972i	−0.308493	+	0.951227i	$0.599825\pi$
$827$	−36.2265	+	36.2265i	−1.25972	+	1.25972i	−0.951227	+	0.308493i	$0.900175\pi$
$828$		0			0
$829$		−	1.35750i		−	0.0471478i	−0.999722	−	0.0235739i	$-0.992495\pi$
$829$		−	1.35750i		−	0.0471478i	0.999722	−	0.0235739i	$-0.00750451\pi$
$830$		0			0
$831$	−10.3957	−	6.68093i	−0.360624	−	0.231759i
$832$		0			0
$833$	−22.3721	+	8.34436i	−0.775147	+	0.289115i
$834$		0			0
$835$	−4.12252	−	6.29510i	−0.142666	−	0.217851i
$836$		0			0
$837$	0.914215	−	2.45110i	0.0315999	−	0.0847226i
$838$		0			0
$839$	8.18293	−	9.44360i	0.282506	−	0.326029i	−0.596706	−	0.802460i	$-0.703524\pi$
$839$	8.18293	−	9.44360i	0.282506	−	0.326029i	0.879212	+	0.476431i	$0.158070\pi$
$840$		0			0
$841$	25.2115	−	7.40276i	0.869362	−	0.255268i
$842$		0			0
$843$	13.8829	+	3.02004i	0.478152	+	0.104016i
$844$		0			0
$845$	−3.41296	+	0.773233i	−0.117409	+	0.0266000i
$846$		0			0
$847$	61.8147	+	82.5748i	2.12398	+	2.83730i
$848$		0			0
$849$	3.71949	+	4.29252i	0.127653	+	0.147319i
$850$		0			0
$851$	−14.4822	−	11.3757i	−0.496444	−	0.389953i
$852$		0			0
$853$	34.1541	+	2.44275i	1.16941	+	0.0836381i	0.642504	−	0.766283i	$-0.277896\pi$
$853$	34.1541	+	2.44275i	1.16941	+	0.0836381i	0.526910	+	0.849921i	$0.323350\pi$
$854$		0			0
$855$	−14.1821	−	0.891840i	−0.485016	−	0.0305003i
$856$		0			0
$857$	1.88935	−	2.52388i	0.0645390	−	0.0862140i	−0.767110	−	0.641515i	$-0.778306\pi$
$857$	1.88935	−	2.52388i	0.0645390	−	0.0862140i	0.831649	+	0.555301i	$0.187397\pi$
$858$		0			0
$859$	−5.18395	−	8.06638i	−0.176874	−	0.275221i	0.741485	−	0.670969i	$-0.234122\pi$
$859$	−5.18395	−	8.06638i	−0.176874	−	0.275221i	−0.918359	+	0.395748i	$0.870485\pi$
$860$		0			0
$861$	−0.546844	−	1.86238i	−0.0186364	−	0.0634697i
$862$		0			0
$863$	−3.67783	−	51.4228i	−0.125195	−	1.75045i	−0.541022	−	0.841008i	$-0.681962\pi$
$863$	−3.67783	−	51.4228i	−0.125195	−	1.75045i	0.415827	−	0.909444i	$-0.363492\pi$
$864$		0			0
$865$	−23.3059	−	6.62613i	−0.792425	−	0.225295i
$866$		0			0
$867$	1.84839	+	3.38507i	0.0627746	+	0.114963i
$868$		0			0
$869$	−94.2948	−	43.0630i	−3.19873	−	1.46081i
$870$		0			0
$871$	1.76761	−	2.75045i	0.0598931	−	0.0931954i
$872$		0			0
$873$	−20.9614	−	20.9614i	−0.709437	−	0.709437i
$874$		0			0
$875$	22.2481	−	36.6645i	0.752123	−	1.23949i
$876$		0			0
$877$	9.63212	+	44.2781i	0.325254	+	1.49517i	0.791861	+	0.610702i	$0.209113\pi$
$877$	9.63212	+	44.2781i	0.325254	+	1.49517i	−0.466607	+	0.884465i	$0.654524\pi$
$878$		0			0
$879$	6.88759	−	15.0817i	0.232313	−	0.508693i
$880$		0			0
$881$	3.97830	−	13.5488i	0.134032	−	0.456472i	−0.864936	−	0.501882i	$-0.832641\pi$
$881$	3.97830	−	13.5488i	0.134032	−	0.456472i	0.998968	+	0.0454097i	$0.0144593\pi$
$882$		0			0
$883$	3.56722	+	1.33050i	0.120046	+	0.0447750i	0.408770	−	0.912638i	$-0.365958\pi$
$883$	3.56722	+	1.33050i	0.120046	+	0.0447750i	−0.288723	+	0.957413i	$0.593231\pi$
$884$		0			0
$885$	−1.49100	+	0.227473i	−0.0501193	+	0.00764643i
$886$		0			0
$887$	10.9743	+	5.99242i	0.368481	+	0.201206i	0.652811	−	0.757521i	$-0.273589\pi$
$887$	10.9743	+	5.99242i	0.368481	+	0.201206i	−0.284331	+	0.958726i	$0.591771\pi$
$888$		0			0
$889$	−46.4802	+	29.8710i	−1.55890	+	1.00184i
$890$		0			0
$891$	−40.4613	+	5.81745i	−1.35550	+	0.194892i
$892$		0			0
$893$	21.2184	−	15.8839i	0.710047	−	0.531535i
$894$		0			0
$895$	5.23786	−	5.32871i	0.175082	−	0.178119i
$896$		0			0
$897$	−4.72154	+	6.98460i	−0.157648	+	0.233209i
$898$		0			0
$899$	4.93482	−	4.27604i	0.164585	−	0.142614i
$900$		0			0
$901$	−1.71454	+	11.9249i	−0.0571196	+	0.397276i
$902$		0			0
$903$	16.5176	+	12.3649i	0.549672	+	0.411479i
$904$		0			0
$905$	15.3151	+	20.0961i	0.509091	+	0.668016i
$906$		0			0
$907$	−6.69043	+	12.2526i	−0.222152	+	0.406841i	−0.964856	−	0.262779i	$-0.915361\pi$
$907$	−6.69043	+	12.2526i	−0.222152	+	0.406841i	0.742704	+	0.669620i	$0.233543\pi$
$908$		0			0
$909$	15.9137	+	13.7893i	0.527824	+	0.457362i
$910$		0			0
$911$	3.18458	−	1.45435i	0.105510	−	0.0481848i	−0.361961	−	0.932193i	$-0.617893\pi$
$911$	3.18458	−	1.45435i	0.105510	−	0.0481848i	0.467471	+	0.884009i	$0.345165\pi$
$912$		0			0
$913$	8.55204	−	4.66977i	0.283031	−	0.154547i
$914$		0			0
$915$	−13.6908	+	6.39522i	−0.452605	+	0.211419i
$916$		0			0
$917$	−14.7049	+	3.19886i	−0.485599	+	0.105636i
$918$		0			0
$919$	20.2847			0.669132			0.334566	−	0.942372i	$-0.391410\pi$
$919$	20.2847			0.669132			0.334566	+	0.942372i	$0.391410\pi$
$920$		0			0
$921$	−4.56935			−0.150565
$922$		0			0
$923$	1.96923	−	0.428379i	0.0648179	−	0.0141003i
$924$		0			0
$925$	9.48985	+	16.6905i	0.312024	+	0.548781i
$926$		0			0
$927$	36.1374	−	19.7325i	1.18691	−	0.648101i
$928$		0			0
$929$	18.4941	−	8.44598i	0.606772	−	0.277104i	−0.0882427	−	0.996099i	$-0.528125\pi$
$929$	18.4941	−	8.44598i	0.606772	−	0.277104i	0.695015	+	0.718995i	$0.255398\pi$
$930$		0			0
$931$	−13.5723	−	11.7604i	−0.444813	−	0.385433i
$932$		0			0
$933$	3.62411	−	6.63707i	0.118648	−	0.217288i
$934$		0			0
$935$	−42.2213	−	5.70045i	−1.38078	−	0.186425i
$936$		0			0
$937$	−11.0695	−	8.28649i	−0.361623	−	0.270708i	0.402980	−	0.915209i	$-0.367974\pi$
$937$	−11.0695	−	8.28649i	−0.361623	−	0.270708i	−0.764604	+	0.644501i	$0.777065\pi$
$938$		0			0
$939$	−1.90989	+	13.2836i	−0.0623269	+	0.433493i
$940$		0			0
$941$	−16.8567	+	14.6064i	−0.549514	+	0.476156i	−0.884807	−	0.465957i	$-0.845710\pi$
$941$	−16.8567	+	14.6064i	−0.549514	+	0.476156i	0.335294	+	0.942114i	$0.391165\pi$
$942$		0			0
$943$	−3.13808	+	3.45594i	−0.102190	+	0.112541i
$944$		0			0
$945$	18.2204	+	17.9098i	0.592711	+	0.582606i
$946$		0			0
$947$	15.9776	−	11.9607i	0.519204	−	0.388671i	−0.307291	−	0.951616i	$-0.599422\pi$
$947$	15.9776	−	11.9607i	0.519204	−	0.388671i	0.826495	+	0.562945i	$0.190332\pi$
$948$		0			0
$949$	−47.8660	+	6.88210i	−1.55380	+	0.223402i
$950$		0			0
$951$	−2.36447	+	1.51955i	−0.0766730	+	0.0492748i
$952$		0			0
$953$	−5.60579	−	3.06099i	−0.181589	−	0.0991553i	0.385883	−	0.922548i	$-0.373897\pi$
$953$	−5.60579	−	3.06099i	−0.181589	−	0.0991553i	−0.567472	+	0.823392i	$0.692079\pi$
$954$		0			0
$955$	33.4627	+	24.6038i	1.08283	+	0.796161i
$956$		0			0
$957$	22.2912	+	8.31418i	0.720572	+	0.268759i
$958$		0			0
$959$	−8.20457	+	27.9422i	−0.264939	+	0.902300i
$960$		0			0
$961$	−12.5574	+	27.4969i	−0.405079	+	0.886998i
$962$		0			0
$963$	−0.544457	−	2.50283i	−0.0175449	−	0.0806526i
$964$		0			0
$965$	16.3379	−	19.1858i	0.525937	−	0.617614i
$966$		0			0
$967$	38.1800	+	38.1800i	1.22779	+	1.22779i	0.964800	+	0.262986i	$0.0847072\pi$
$967$	38.1800	+	38.1800i	1.22779	+	1.22779i	0.262986	+	0.964800i	$0.415293\pi$
$968$		0			0
$969$	2.02529	−	3.15141i	0.0650616	−	0.101238i
$970$		0			0
$971$	33.1508	+	15.1395i	1.06386	+	0.485849i	0.868913	−	0.494964i	$-0.164819\pi$
$971$	33.1508	+	15.1395i	1.06386	+	0.485849i	0.194948	+	0.980814i	$0.437546\pi$
$972$		0			0
$973$	−9.45175	−	17.3096i	−0.303009	−	0.554920i
$974$		0			0
$975$	7.31154	−	4.87849i	0.234157	−	0.156237i
$976$		0			0
$977$	−2.71760	−	37.9970i	−0.0869437	−	1.21563i	−0.834339	−	0.551252i	$-0.814150\pi$
$977$	−2.71760	−	37.9970i	−0.0869437	−	1.21563i	0.747395	−	0.664380i	$-0.231304\pi$
$978$		0			0
$979$	6.08638	+	20.7283i	0.194522	+	0.662480i
$980$		0			0
$981$	−15.6422	−	24.3397i	−0.499415	−	0.777106i
$982$		0			0
$983$	17.6116	−	23.5264i	0.561724	−	0.750375i	−0.426316	−	0.904574i	$-0.640189\pi$
$983$	17.6116	−	23.5264i	0.561724	−	0.750375i	0.988040	+	0.154199i	$0.0492798\pi$
$984$		0			0
$985$	28.1273	−	24.7990i	0.896210	−	0.790162i
$986$		0			0
$987$	−22.6456	−	1.61965i	−0.720818	−	0.0515539i
$988$		0			0
$989$	4.68887	−	49.4002i	0.149097	−	1.57083i
$990$		0			0
$991$	−25.6016	−	29.5458i	−0.813261	−	0.938553i	0.185769	−	0.982593i	$-0.440522\pi$
$991$	−25.6016	−	29.5458i	−0.813261	−	0.938553i	−0.999030	+	0.0440405i	$0.985977\pi$
$992$		0			0
$993$	1.07399	+	1.43468i	0.0340819	+	0.0455281i
$994$		0			0
$995$	−2.02343	−	8.93116i	−0.0641469	−	0.283137i
$996$		0			0
$997$	−11.8750	−	2.58324i	−0.376084	−	0.0818121i	0.0205501	−	0.999789i	$-0.493458\pi$
$997$	−11.8750	−	2.58324i	−0.376084	−	0.0818121i	−0.396634	+	0.917977i	$0.629822\pi$
$998$		0			0
$999$	−10.9746	+	3.22243i	−0.347220	+	0.101953i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	920.2.bv.a.217.17	yes	720
5.3	odd	4	inner	920.2.bv.a.33.17	✓	720
23.7	odd	22	inner	920.2.bv.a.697.17	yes	720
115.53	even	44	inner	920.2.bv.a.513.17	yes	720

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
920.2.bv.a.33.17	✓	720	5.3	odd	4	inner
920.2.bv.a.217.17	yes	720	1.1	even	1	trivial
920.2.bv.a.513.17	yes	720	115.53	even	44	inner
920.2.bv.a.697.17	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)

\(f(q)\)	\(=\)	\(q+(-0.507977 + 0.110504i) q^{3} +(-0.763385 + 2.10172i) q^{5} +(3.36669 - 1.83835i) q^{7} +(-2.48307 + 1.13398i) q^{9} +O(q^{10})\)	\(q+(-0.507977 + 0.110504i) q^{3} +(-0.763385 + 2.10172i) q^{5} +(3.36669 - 1.83835i) q^{7} +(-2.48307 + 1.13398i) q^{9} +(-4.65203 - 4.03101i) q^{11} +(1.62061 - 2.96793i) q^{13} +(0.155534 - 1.15199i) q^{15} +(-2.47793 - 1.85495i) q^{17} +(0.331313 - 2.30434i) q^{19} +(-1.50706 + 1.30587i) q^{21} +(4.56894 + 1.45767i) q^{23} +(-3.83449 - 3.20885i) q^{25} +(2.38454 - 1.78504i) q^{27} +(7.35910 - 1.05808i) q^{29} +(0.738843 - 0.474826i) q^{31} +(2.80857 + 1.53359i) q^{33} +(1.29363 + 8.47921i) q^{35} +(-3.59784 - 1.34193i) q^{37} +(-0.495267 + 1.68673i) q^{39} +(-0.404350 + 0.885402i) q^{41} +(-2.19940 - 10.1105i) q^{43} +(-0.487775 - 6.08438i) q^{45} +(8.05055 + 8.05055i) q^{47} +(4.17056 - 6.48952i) q^{49} +(1.46371 + 0.668454i) q^{51} +(-1.86532 - 3.41608i) q^{53} +(12.0233 - 6.70007i) q^{55} +(0.0863379 + 1.20716i) q^{57} +(-0.365545 - 1.24493i) q^{59} +(-7.02794 - 10.9357i) q^{61} +(-6.27506 + 8.38249i) q^{63} +(5.00062 + 5.67175i) q^{65} +(0.964386 + 0.0689742i) q^{67} +(-2.48200 - 0.235581i) q^{69} +(0.390272 + 0.450398i) q^{71} +(-8.57000 - 11.4482i) q^{73} +(2.30242 + 1.20630i) q^{75} +(-23.0723 - 5.01908i) q^{77} +(16.1584 - 4.74455i) q^{79} +(4.34878 - 5.01876i) q^{81} +(-0.553188 + 1.48315i) q^{83} +(5.79021 - 3.79187i) q^{85} +(-3.62133 + 1.35069i) q^{87} +(-2.95246 - 1.89743i) q^{89} -12.9713i q^{91} +(-0.322846 + 0.322846i) q^{93} +(4.59016 + 2.45542i) q^{95} +(3.79504 + 10.1749i) q^{97} +(16.1224 + 4.73395i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 720 q+O(q^{10}) \) 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

Representations

Groups

Database

Properties

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