LMFDB - Embedded newform 432.2.u.f.193.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [432,2,Mod(49,432)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(432, base_ring=CyclotomicField(18))

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

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

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

chi := DirichletCharacter("432.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 432 = 2^{4} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	432.u (of order $9$, degree $6$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.44953736732$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$5$ over $\Q(\zeta_{9})$
Twist minimal:	no (minimal twist has level 216)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			193.5
Character	$\chi$	$=$	432.193
Dual form			432.2.u.f.385.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.72136 - 0.192108i) q^{3} +(0.0709538 - 0.402399i) q^{5} +(2.76051 - 2.31635i) q^{7} +(2.92619 - 0.661376i) q^{9} +O(q^{10})$	\(q+(1.72136 - 0.192108i) q^{3} +(0.0709538 - 0.402399i) q^{5} +(2.76051 - 2.31635i) q^{7} +(2.92619 - 0.661376i) q^{9} +(-0.933014 - 5.29139i) q^{11} +(-6.08313 + 2.21408i) q^{13} +(0.0448332 - 0.706306i) q^{15} +(-1.42852 + 2.47428i) q^{17} +(2.71628 + 4.70473i) q^{19} +(4.30686 - 4.51759i) q^{21} +(-2.18286 - 1.83164i) q^{23} +(4.54157 + 1.65300i) q^{25} +(4.90998 - 1.70061i) q^{27} +(2.41013 + 0.877216i) q^{29} +(2.53550 + 2.12754i) q^{31} +(-2.62258 - 8.92917i) q^{33} +(-0.736226 - 1.27518i) q^{35} +(-0.462667 + 0.801362i) q^{37} +(-10.0459 + 4.97985i) q^{39} +(3.40030 - 1.23761i) q^{41} +(0.154105 + 0.873975i) q^{43} +(-0.0585128 - 1.22442i) q^{45} +(-7.89750 + 6.62679i) q^{47} +(1.03944 - 5.89495i) q^{49} +(-1.98368 + 4.53356i) q^{51} -4.56786 q^{53} -2.19545 q^{55} +(5.57952 + 7.57674i) q^{57} +(-1.06184 + 6.02201i) q^{59} +(-4.86002 + 4.07804i) q^{61} +(6.54581 - 8.60380i) q^{63} +(0.459322 + 2.60494i) q^{65} +(5.49728 - 2.00085i) q^{67} +(-4.10937 - 2.73357i) q^{69} +(5.61578 - 9.72681i) q^{71} +(3.59061 + 6.21912i) q^{73} +(8.13525 + 1.97294i) q^{75} +(-14.8323 - 12.4458i) q^{77} +(0.0666470 + 0.0242575i) q^{79} +(8.12516 - 3.87062i) q^{81} +(-15.4725 - 5.63155i) q^{83} +(0.894287 + 0.750396i) q^{85} +(4.31723 + 1.04700i) q^{87} +(3.42863 + 5.93857i) q^{89} +(-11.6640 + 20.2026i) q^{91} +(4.77323 + 3.17517i) q^{93} +(2.08591 - 0.759210i) q^{95} +(2.10988 + 11.9657i) q^{97} +(-6.22977 - 14.8665i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 3 q^{7} - 6 q^{9}+O(q^{10}) $ 30 * q - 3 * q^7 - 6 * q^9	$ 30 q - 3 q^{7} - 6 q^{9} + 3 q^{11} - 12 q^{13} - 15 q^{15} + 6 q^{17} + 9 q^{19} + 30 q^{21} + 12 q^{23} + 24 q^{25} + 15 q^{27} - 9 q^{29} - 27 q^{31} - 30 q^{33} + 18 q^{35} - 15 q^{37} + 21 q^{39} - 15 q^{41} + 30 q^{43} + 15 q^{45} + 18 q^{47} + 15 q^{49} + 6 q^{51} - 18 q^{53} - 54 q^{55} - 72 q^{57} + 12 q^{59} + 6 q^{61} + 54 q^{63} - 54 q^{65} + 45 q^{67} + 9 q^{69} - 36 q^{73} - 69 q^{75} + 12 q^{77} - 45 q^{79} - 30 q^{81} + 3 q^{83} + 57 q^{85} + 60 q^{87} + 36 q^{89} + 39 q^{91} + 30 q^{93} - 51 q^{95} - 84 q^{97} - 162 q^{99}+O(q^{100}) $ 30 * q - 3 * q^7 - 6 * q^9 + 3 * q^11 - 12 * q^13 - 15 * q^15 + 6 * q^17 + 9 * q^19 + 30 * q^21 + 12 * q^23 + 24 * q^25 + 15 * q^27 - 9 * q^29 - 27 * q^31 - 30 * q^33 + 18 * q^35 - 15 * q^37 + 21 * q^39 - 15 * q^41 + 30 * q^43 + 15 * q^45 + 18 * q^47 + 15 * q^49 + 6 * q^51 - 18 * q^53 - 54 * q^55 - 72 * q^57 + 12 * q^59 + 6 * q^61 + 54 * q^63 - 54 * q^65 + 45 * q^67 + 9 * q^69 - 36 * q^73 - 69 * q^75 + 12 * q^77 - 45 * q^79 - 30 * q^81 + 3 * q^83 + 57 * q^85 + 60 * q^87 + 36 * q^89 + 39 * q^91 + 30 * q^93 - 51 * q^95 - 84 * q^97 - 162 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/432\mathbb{Z}\right)^\times$.

$n$	$271$	$325$	$353$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{9}\right)$

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
$3$	1.72136	−	0.192108i	0.993830	−	0.110914i
$3$	1.72136	−	0.192108i	0.993830	−	0.110914i
$4$		0			0
$5$	0.0709538	−	0.402399i	0.0317315	−	0.179958i	−0.964823	−	0.262901i	$-0.915321\pi$
$5$	0.0709538	−	0.402399i	0.0317315	−	0.179958i	0.996554	+	0.0829427i	$0.0264318\pi$
$6$		0			0
$7$	2.76051	−	2.31635i	1.04338	−	0.875496i	0.0509944	−	0.998699i	$-0.483761\pi$
$7$	2.76051	−	2.31635i	1.04338	−	0.875496i	0.992382	+	0.123203i	$0.0393165\pi$
$8$		0			0
$9$	2.92619	−	0.661376i	0.975396	−	0.220459i
$10$		0			0
$11$	−0.933014	−	5.29139i	−0.281314	−	1.59541i	−0.718161	−	0.695877i	$-0.755016\pi$
$11$	−0.933014	−	5.29139i	−0.281314	−	1.59541i	0.436846	−	0.899536i	$-0.356095\pi$
$12$		0			0
$13$	−6.08313	+	2.21408i	−1.68716	+	0.614075i	−0.994263	−	0.106964i	$-0.965887\pi$
$13$	−6.08313	+	2.21408i	−1.68716	+	0.614075i	−0.692894	+	0.721039i	$0.743665\pi$
$14$		0			0
$15$	0.0448332	−	0.706306i	0.0115759	−	0.182367i
$16$		0			0
$17$	−1.42852	+	2.47428i	−0.346468	+	0.600100i	−0.985619	−	0.168981i	$-0.945952\pi$
$17$	−1.42852	+	2.47428i	−0.346468	+	0.600100i	0.639151	+	0.769081i	$0.279286\pi$
$18$		0			0
$19$	2.71628	+	4.70473i	0.623157	+	1.07934i	0.988894	+	0.148622i	$0.0474837\pi$
$19$	2.71628	+	4.70473i	0.623157	+	1.07934i	−0.365737	+	0.930718i	$0.619183\pi$
$20$		0			0
$21$	4.30686	−	4.51759i	0.939834	−	0.985819i
$22$		0			0
$23$	−2.18286	−	1.83164i	−0.455157	−	0.381922i	0.386188	−	0.922420i	$-0.373792\pi$
$23$	−2.18286	−	1.83164i	−0.455157	−	0.381922i	−0.841346	+	0.540498i	$0.818236\pi$
$24$		0			0
$25$	4.54157	+	1.65300i	0.908315	+	0.330599i
$26$		0			0
$27$	4.90998	−	1.70061i	0.944926	−	0.327283i
$28$		0			0
$29$	2.41013	+	0.877216i	0.447550	+	0.162895i	0.555956	−	0.831212i	$-0.312352\pi$
$29$	2.41013	+	0.877216i	0.447550	+	0.162895i	−0.108406	+	0.994107i	$0.534575\pi$
$30$		0			0
$31$	2.53550	+	2.12754i	0.455389	+	0.382117i	0.841431	−	0.540364i	$-0.181714\pi$
$31$	2.53550	+	2.12754i	0.455389	+	0.382117i	−0.386042	+	0.922481i	$0.626158\pi$
$32$		0			0
$33$	−2.62258	−	8.92917i	−0.456532	−	1.55437i
$34$		0			0
$35$	−0.736226	−	1.27518i	−0.124445	−	0.215545i
$36$		0			0
$37$	−0.462667	+	0.801362i	−0.0760619	+	0.131743i	−0.901548	−	0.432680i	$-0.857568\pi$
$37$	−0.462667	+	0.801362i	−0.0760619	+	0.131743i	0.825486	+	0.564423i	$0.190901\pi$
$38$		0			0
$39$	−10.0459	+	4.97985i	−1.60864	+	0.797415i
$40$		0			0
$41$	3.40030	−	1.23761i	0.531037	−	0.193282i	−0.0625644	−	0.998041i	$-0.519928\pi$
$41$	3.40030	−	1.23761i	0.531037	−	0.193282i	0.593601	+	0.804759i	$0.297706\pi$
$42$		0			0
$43$	0.154105	+	0.873975i	0.0235008	+	0.133280i	0.994301	−	0.106610i	$-0.0339997\pi$
$43$	0.154105	+	0.873975i	0.0235008	+	0.133280i	−0.970800	+	0.239890i	$0.922889\pi$
$44$		0			0
$45$	−0.0585128	−	1.22442i	−0.00872258	−	0.182526i
$46$		0			0
$47$	−7.89750	+	6.62679i	−1.15197	+	0.966617i	−0.999764	−	0.0217322i	$-0.993082\pi$
$47$	−7.89750	+	6.62679i	−1.15197	+	0.966617i	−0.152205	+	0.988349i	$0.548637\pi$
$48$		0			0
$49$	1.03944	−	5.89495i	0.148491	−	0.842136i
$50$		0			0
$51$	−1.98368	+	4.53356i	−0.277771	+	0.634826i
$52$		0			0
$53$	−4.56786			−0.627444			−0.313722	−	0.949515i	$-0.601576\pi$
$53$	−4.56786			−0.627444			−0.313722	+	0.949515i	$0.601576\pi$
$54$		0			0
$55$	−2.19545			−0.296034
$56$		0			0
$57$	5.57952	+	7.57674i	0.739026	+	1.00356i
$58$		0			0
$59$	−1.06184	+	6.02201i	−0.138240	+	0.783999i	0.834308	+	0.551298i	$0.185867\pi$
$59$	−1.06184	+	6.02201i	−0.138240	+	0.783999i	−0.972548	+	0.232701i	$0.925244\pi$
$60$		0			0
$61$	−4.86002	+	4.07804i	−0.622261	+	0.522139i	−0.898513	−	0.438946i	$-0.855352\pi$
$61$	−4.86002	+	4.07804i	−0.622261	+	0.522139i	0.276252	+	0.961085i	$0.410908\pi$
$62$		0			0
$63$	6.54581	−	8.60380i	0.824694	−	1.08398i
$64$		0			0
$65$	0.459322	+	2.60494i	0.0569719	+	0.323103i
$66$		0			0
$67$	5.49728	−	2.00085i	0.671599	−	0.244442i	0.0163631	−	0.999866i	$-0.494791\pi$
$67$	5.49728	−	2.00085i	0.671599	−	0.244442i	0.655236	+	0.755424i	$0.272569\pi$
$68$		0			0
$69$	−4.10937	−	2.73357i	−0.494709	−	0.329083i
$70$		0			0
$71$	5.61578	−	9.72681i	0.666470	−	1.15436i	−0.312414	−	0.949946i	$-0.601138\pi$
$71$	5.61578	−	9.72681i	0.666470	−	1.15436i	0.978884	−	0.204414i	$-0.0655290\pi$
$72$		0			0
$73$	3.59061	+	6.21912i	0.420249	+	0.727893i	0.995964	−	0.0897576i	$-0.0286092\pi$
$73$	3.59061	+	6.21912i	0.420249	+	0.727893i	−0.575714	+	0.817651i	$0.695276\pi$
$74$		0			0
$75$	8.13525	+	1.97294i	0.939378	+	0.227815i
$76$		0			0
$77$	−14.8323	−	12.4458i	−1.69030	−	1.41833i
$78$		0			0
$79$	0.0666470	+	0.0242575i	0.00749837	+	0.00272918i	0.345767	−	0.938321i	$-0.387619\pi$
$79$	0.0666470	+	0.0242575i	0.00749837	+	0.00272918i	−0.338268	+	0.941050i	$0.609841\pi$
$80$		0			0
$81$	8.12516	−	3.87062i	0.902796	−	0.430069i
$82$		0			0
$83$	−15.4725	−	5.63155i	−1.69833	−	0.618142i	−0.702699	−	0.711488i	$-0.748022\pi$
$83$	−15.4725	−	5.63155i	−1.69833	−	0.618142i	−0.995634	+	0.0933452i	$0.970244\pi$
$84$		0			0
$85$	0.894287	+	0.750396i	0.0969991	+	0.0813919i
$86$		0			0
$87$	4.31723	+	1.04700i	0.462856	+	0.112250i
$88$		0			0
$89$	3.42863	+	5.93857i	0.363434	+	0.629487i	0.988524	−	0.151066i	$-0.0482707\pi$
$89$	3.42863	+	5.93857i	0.363434	+	0.629487i	−0.625089	+	0.780553i	$0.714937\pi$
$90$		0			0
$91$	−11.6640	+	20.2026i	−1.22272	+	2.11781i
$92$		0			0
$93$	4.77323	+	3.17517i	0.494961	+	0.329250i
$94$		0			0
$95$	2.08591	−	0.759210i	0.214010	−	0.0778933i
$96$		0			0
$97$	2.10988	+	11.9657i	0.214226	+	1.21494i	0.882245	+	0.470791i	$0.156031\pi$
$97$	2.10988	+	11.9657i	0.214226	+	1.21494i	−0.668019	+	0.744144i	$0.732857\pi$
$98$		0			0
$99$	−6.22977	−	14.8665i	−0.626116	−	1.49414i
$100$		0			0
$101$	−13.4523	+	11.2879i	−1.33856	+	1.12318i	−0.356564	+	0.934271i	$0.616052\pi$
$101$	−13.4523	+	11.2879i	−1.33856	+	1.12318i	−0.981994	+	0.188913i	$0.939504\pi$
$102$		0			0
$103$	−0.584165	+	3.31296i	−0.0575595	+	0.326436i	−0.999968	−	0.00802867i	$-0.997444\pi$
$103$	−0.584165	+	3.31296i	−0.0575595	+	0.326436i	0.942408	+	0.334465i	$0.108555\pi$
$104$		0			0
$105$	−1.51229	−	2.05362i	−0.147584	−	0.200412i
$106$		0			0
$107$	6.12276			0.591910			0.295955	−	0.955202i	$-0.404362\pi$
$107$	6.12276			0.591910			0.295955	+	0.955202i	$0.404362\pi$
$108$		0			0
$109$	−1.31494			−0.125948			−0.0629742	−	0.998015i	$-0.520059\pi$
$109$	−1.31494			−0.125948			−0.0629742	+	0.998015i	$0.520059\pi$
$110$		0			0
$111$	−0.642470	+	1.46832i	−0.0609805	+	0.139367i
$112$		0			0
$113$	2.05736	−	11.6679i	0.193540	−	1.09762i	−0.720942	−	0.692995i	$-0.756291\pi$
$113$	2.05736	−	11.6679i	0.193540	−	1.09762i	0.914482	−	0.404626i	$-0.132598\pi$
$114$		0			0
$115$	−0.891930	+	0.748419i	−0.0831729	+	0.0697904i
$116$		0			0
$117$	−16.3361	+	10.5020i	−1.51027	+	0.970915i
$118$		0			0
$119$	1.78782	+	10.1392i	0.163889	+	0.929462i
$120$		0			0
$121$	−16.7917	+	6.11166i	−1.52651	+	0.555606i
$122$		0			0
$123$	5.61539	−	2.78360i	0.506323	−	0.250988i
$124$		0			0
$125$	2.00892	−	3.47956i	0.179684	−	0.311221i
$126$		0			0
$127$	−0.138097	−	0.239191i	−0.0122541	−	0.0212247i	0.859833	−	0.510575i	$-0.170567\pi$
$127$	−0.138097	−	0.239191i	−0.0122541	−	0.0212247i	−0.872087	+	0.489350i	$0.837234\pi$
$128$		0			0
$129$	0.433169	+	1.47482i	0.0381384	+	0.129851i
$130$		0			0
$131$	−7.82558	−	6.56644i	−0.683724	−	0.573713i	0.233368	−	0.972389i	$-0.425025\pi$
$131$	−7.82558	−	6.56644i	−0.683724	−	0.573713i	−0.917092	+	0.398676i	$0.869470\pi$
$132$		0			0
$133$	18.3961	+	6.69564i	1.59515	+	0.580586i
$134$		0			0
$135$	−0.335943	−	2.09644i	−0.0289134	−	0.180433i
$136$		0			0
$137$	−6.08304	−	2.21404i	−0.519709	−	0.189159i	0.0688286	−	0.997628i	$-0.478074\pi$
$137$	−6.08304	−	2.21404i	−0.519709	−	0.189159i	−0.588537	+	0.808470i	$0.700296\pi$
$138$		0			0
$139$	−15.4332	−	12.9500i	−1.30903	−	1.09840i	−0.988509	−	0.151160i	$-0.951699\pi$
$139$	−15.4332	−	12.9500i	−1.30903	−	1.09840i	−0.320516	−	0.947243i	$-0.603856\pi$
$140$		0			0
$141$	−12.3214	+	12.9243i	−1.03765	+	1.08842i
$142$		0			0
$143$	17.3912	+	30.1224i	1.45433	+	2.51896i
$144$		0			0
$145$	0.523999	−	0.907593i	0.0435157	−	0.0753715i
$146$		0			0
$147$	0.656785	−	10.3470i	0.0541707	−	0.853410i
$148$		0			0
$149$	9.16942	−	3.33740i	0.751188	−	0.273410i	0.0620826	−	0.998071i	$-0.480226\pi$
$149$	9.16942	−	3.33740i	0.751188	−	0.273410i	0.689106	+	0.724661i	$0.258004\pi$
$150$		0			0
$151$	−2.72982	−	15.4816i	−0.222150	−	1.25987i	−0.868059	−	0.496461i	$-0.834633\pi$
$151$	−2.72982	−	15.4816i	−0.222150	−	1.25987i	0.645909	−	0.763414i	$-0.276478\pi$
$152$		0			0
$153$	−2.54370	+	8.18499i	−0.205646	+	0.661717i
$154$		0			0
$155$	1.03602	−	0.869325i	0.0832153	−	0.0698259i
$156$		0			0
$157$	3.38362	−	19.1895i	0.270042	−	1.53149i	−0.484240	−	0.874935i	$-0.660904\pi$
$157$	3.38362	−	19.1895i	0.270042	−	1.53149i	0.754282	−	0.656551i	$-0.227985\pi$
$158$		0			0
$159$	−7.86296	+	0.877524i	−0.623573	+	0.0695922i
$160$		0			0
$161$	−10.2685			−0.809272
$162$		0			0
$163$	−14.7007			−1.15145			−0.575725	−	0.817644i	$-0.695280\pi$
$163$	−14.7007			−1.15145			−0.575725	+	0.817644i	$0.695280\pi$
$164$		0			0
$165$	−3.77917	+	0.421764i	−0.294208	+	0.0328343i
$166$		0			0
$167$	0.812805	−	4.60964i	0.0628967	−	0.356705i	−0.937075	−	0.349129i	$-0.886477\pi$
$167$	0.812805	−	4.60964i	0.0628967	−	0.356705i	0.999971	−	0.00757578i	$-0.00241147\pi$
$168$		0			0
$169$	22.1438	−	18.5808i	1.70337	−	1.42929i
$170$		0			0
$171$	11.0599	+	11.9705i	0.845775	+	0.915404i
$172$		0			0
$173$	0.660003	+	3.74306i	0.0501791	+	0.284580i	0.999564	−	0.0295362i	$-0.00940304\pi$
$173$	0.660003	+	3.74306i	0.0501791	+	0.284580i	−0.949385	+	0.314116i	$0.898292\pi$
$174$		0			0
$175$	16.3660	−	5.95673i	1.23715	−	0.450287i
$176$		0			0
$177$	−0.670942	+	10.5701i	−0.0504311	+	0.794495i
$178$		0			0
$179$	0.942243	−	1.63201i	0.0704265	−	0.121982i	−0.828662	−	0.559750i	$-0.810897\pi$
$179$	0.942243	−	1.63201i	0.0704265	−	0.121982i	0.899088	+	0.437767i	$0.144231\pi$
$180$		0			0
$181$	−4.64699	−	8.04882i	−0.345408	−	0.598264i	0.640020	−	0.768358i	$-0.278926\pi$
$181$	−4.64699	−	8.04882i	−0.345408	−	0.598264i	−0.985428	+	0.170094i	$0.945593\pi$
$182$		0			0
$183$	−7.58243	+	7.95344i	−0.560510	+	0.587935i
$184$		0			0
$185$	0.289639	+	0.243036i	0.0212947	+	0.0178684i
$186$		0			0
$187$	14.4252	+	5.25034i	1.05487	+	0.383943i
$188$		0			0
$189$	9.61486	−	16.0678i	0.699378	−	1.16876i
$190$		0			0
$191$	0.410875	+	0.149546i	0.0297299	+	0.0108208i	0.356842	−	0.934165i	$-0.383853\pi$
$191$	0.410875	+	0.149546i	0.0297299	+	0.0108208i	−0.327112	+	0.944985i	$0.606076\pi$
$192$		0			0
$193$	−3.21444	−	2.69724i	−0.231381	−	0.194152i	0.519725	−	0.854334i	$-0.326035\pi$
$193$	−3.21444	−	2.69724i	−0.231381	−	0.194152i	−0.751105	+	0.660182i	$0.770479\pi$
$194$		0			0
$195$	1.29109	+	4.39582i	0.0924569	+	0.314791i
$196$		0			0
$197$	12.4258	+	21.5220i	0.885299	+	1.53338i	0.845371	+	0.534180i	$0.179379\pi$
$197$	12.4258	+	21.5220i	0.885299	+	1.53338i	0.0399279	+	0.999203i	$0.487287\pi$
$198$		0			0
$199$	3.72980	−	6.46020i	0.264398	−	0.457951i	−0.703008	−	0.711182i	$-0.748160\pi$
$199$	3.72980	−	6.46020i	0.264398	−	0.457951i	0.967406	+	0.253231i	$0.0814933\pi$
$200$		0			0
$201$	9.07844	−	4.50026i	0.640344	−	0.317424i
$202$		0			0
$203$	8.68513	−	3.16113i	0.609577	−	0.221868i
$204$		0			0
$205$	−0.256748	−	1.45609i	−0.0179320	−	0.101698i
$206$		0			0
$207$	−7.59885	−	3.91602i	−0.528157	−	0.272182i
$208$		0			0
$209$	22.3602	−	18.7625i	1.54669	−	1.29783i
$210$		0			0
$211$	−3.26395	+	18.5108i	−0.224699	+	1.27433i	0.638559	+	0.769572i	$0.279531\pi$
$211$	−3.26395	+	18.5108i	−0.224699	+	1.27433i	−0.863259	+	0.504761i	$0.831580\pi$
$212$		0			0
$213$	7.79820	−	17.8222i	0.534324	−	1.22116i
$214$		0			0
$215$	0.362621			0.0247305
$216$		0			0
$217$	11.9274			0.809684
$218$		0			0
$219$	7.37550	+	10.0156i	0.498390	+	0.676791i
$220$		0			0
$221$	3.21166	−	18.2142i	0.216039	−	1.22522i
$222$		0			0
$223$	6.24421	−	5.23951i	0.418143	−	0.350864i	−0.409313	−	0.912394i	$-0.634232\pi$
$223$	6.24421	−	5.23951i	0.418143	−	0.350864i	0.827456	+	0.561530i	$0.189787\pi$
$224$		0			0
$225$	14.3828	+	1.83330i	0.958850	+	0.122220i
$226$		0			0
$227$	0.426443	+	2.41848i	0.0283040	+	0.160520i	0.995684	−	0.0928105i	$-0.0295851\pi$
$227$	0.426443	+	2.41848i	0.0283040	+	0.160520i	−0.967380	+	0.253331i	$0.918474\pi$
$228$		0			0
$229$	9.63795	−	3.50793i	0.636894	−	0.231810i	−0.00333520	−	0.999994i	$-0.501062\pi$
$229$	9.63795	−	3.50793i	0.636894	−	0.231810i	0.640229	+	0.768184i	$0.278839\pi$
$230$		0			0
$231$	−27.9227	−	18.5743i	−1.83718	−	1.22210i
$232$		0			0
$233$	7.67465	−	13.2929i	0.502783	−	0.870846i	−0.497212	−	0.867629i	$-0.665643\pi$
$233$	7.67465	−	13.2929i	0.502783	−	0.870846i	0.999995	−	0.00321665i	$-0.00102389\pi$
$234$		0			0
$235$	2.10626	+	3.64814i	0.137397	+	0.237979i
$236$		0			0
$237$	0.119384	+	0.0289526i	0.00775481	+	0.00188067i
$238$		0			0
$239$	16.2668	+	13.6495i	1.05221	+	0.882912i	0.993325	−	0.115352i	$-0.0367997\pi$
$239$	16.2668	+	13.6495i	1.05221	+	0.882912i	0.0588890	+	0.998265i	$0.481244\pi$
$240$		0			0
$241$	−25.8696	−	9.41577i	−1.66641	−	0.606523i	−0.675058	−	0.737765i	$-0.735881\pi$
$241$	−25.8696	−	9.41577i	−1.66641	−	0.606523i	−0.991350	+	0.131241i	$0.958104\pi$
$242$		0			0
$243$	13.2428	−	8.22366i	0.849525	−	0.527548i
$244$		0			0
$245$	−2.29837	−	0.836538i	−0.146838	−	0.0534445i
$246$		0			0
$247$	−26.9401	−	22.6055i	−1.71416	−	1.43835i
$248$		0			0
$249$	−27.7157	−	6.72154i	−1.75641	−	0.425960i
$250$		0			0
$251$	−6.10751	−	10.5785i	−0.385503	−	0.667710i	0.606336	−	0.795208i	$-0.292639\pi$
$251$	−6.10751	−	10.5785i	−0.385503	−	0.667710i	−0.991839	+	0.127498i	$0.959305\pi$
$252$		0			0
$253$	−7.65526	+	13.2593i	−0.481282	+	0.833604i
$254$		0			0
$255$	1.68355	+	1.11991i	0.105428	+	0.0701312i
$256$		0			0
$257$	−12.7499	+	4.64060i	−0.795319	+	0.289472i	−0.707545	−	0.706668i	$-0.750197\pi$
$257$	−12.7499	+	4.64060i	−0.795319	+	0.289472i	−0.0877736	+	0.996140i	$0.527975\pi$
$258$		0			0
$259$	0.579034	+	3.28387i	0.0359794	+	0.204050i
$260$		0			0
$261$	7.63267	+	0.972897i	0.472450	+	0.0602208i
$262$		0			0
$263$	3.81550	−	3.20159i	0.235274	−	0.197418i	−0.517526	−	0.855667i	$-0.673147\pi$
$263$	3.81550	−	3.20159i	0.235274	−	0.197418i	0.752800	+	0.658249i	$0.228703\pi$
$264$		0			0
$265$	−0.324107	+	1.83810i	−0.0199098	+	0.112914i
$266$		0			0
$267$	7.04277	+	9.56377i	0.431011	+	0.585293i
$268$		0			0
$269$	22.8793			1.39498			0.697488	−	0.716596i	$-0.254301\pi$
$269$	22.8793			1.39498			0.697488	+	0.716596i	$0.254301\pi$
$270$		0			0
$271$	12.1601			0.738671			0.369336	−	0.929296i	$-0.379585\pi$
$271$	12.1601			0.738671			0.369336	+	0.929296i	$0.379585\pi$
$272$		0			0
$273$	−16.1969	+	37.0168i	−0.980280	+	2.24036i
$274$		0			0
$275$	4.50930	−	25.5735i	0.271921	−	1.54214i
$276$		0			0
$277$	−4.50394	+	3.77925i	−0.270616	+	0.227073i	−0.767989	−	0.640463i	$-0.778742\pi$
$277$	−4.50394	+	3.77925i	−0.270616	+	0.227073i	0.497373	+	0.867537i	$0.334298\pi$
$278$		0			0
$279$	8.82645	+	4.54865i	0.528426	+	0.272321i
$280$		0			0
$281$	3.29717	+	18.6992i	0.196692	+	1.11550i	0.909988	+	0.414635i	$0.136091\pi$
$281$	3.29717	+	18.6992i	0.196692	+	1.11550i	−0.713296	+	0.700863i	$0.752798\pi$
$282$		0			0
$283$	1.56007	−	0.567819i	0.0927365	−	0.0337533i	−0.295235	−	0.955425i	$-0.595398\pi$
$283$	1.56007	−	0.567819i	0.0927365	−	0.0337533i	0.387972	+	0.921671i	$0.373176\pi$
$284$		0			0
$285$	3.44476	−	1.70760i	0.204050	−	0.101149i
$286$		0			0
$287$	6.51984	−	11.2927i	0.384854	−	0.666586i
$288$		0			0
$289$	4.41864	+	7.65330i	0.259920	+	0.450194i
$290$		0			0
$291$	5.93059	+	20.1920i	0.347657	+	1.18368i
$292$		0			0
$293$	19.6142	+	16.4583i	1.14587	+	0.961502i	0.999615	−	0.0277442i	$-0.00883239\pi$
$293$	19.6142	+	16.4583i	1.14587	+	0.961502i	0.146259	+	0.989246i	$0.453277\pi$
$294$		0			0
$295$	2.34791	+	0.854569i	0.136701	+	0.0497550i
$296$		0			0
$297$	−13.5797	−	24.3939i	−0.787974	−	1.41548i
$298$		0			0
$299$	17.3340	+	6.30906i	1.00245	+	0.364862i
$300$		0			0
$301$	2.44984	+	2.05566i	0.141206	+	0.118486i
$302$		0			0
$303$	−20.9879	+	22.0148i	−1.20572	+	1.26472i
$304$		0			0
$305$	1.29616	+	2.24502i	0.0742180	+	0.128549i
$306$		0			0
$307$	10.2102	−	17.6845i	0.582726	−	1.00931i	−0.412429	−	0.910990i	$-0.635320\pi$
$307$	10.2102	−	17.6845i	0.582726	−	1.00931i	0.995155	−	0.0983207i	$-0.0313471\pi$
$308$		0			0
$309$	−0.369113	+	5.81504i	−0.0209981	+	0.330806i
$310$		0			0
$311$	−13.9565	+	5.07976i	−0.791402	+	0.288047i	−0.705919	−	0.708293i	$-0.749466\pi$
$311$	−13.9565	+	5.07976i	−0.791402	+	0.288047i	−0.0854831	+	0.996340i	$0.527243\pi$
$312$		0			0
$313$	−5.70622	−	32.3616i	−0.322535	−	1.82919i	−0.526461	−	0.850200i	$-0.676481\pi$
$313$	−5.70622	−	32.3616i	−0.322535	−	1.82919i	0.203926	−	0.978986i	$-0.434630\pi$
$314$		0			0
$315$	−2.99771	−	3.24450i	−0.168902	−	0.182807i
$316$		0			0
$317$	−16.6536	+	13.9740i	−0.935357	+	0.784858i	−0.976771	−	0.214284i	$-0.931258\pi$
$317$	−16.6536	+	13.9740i	−0.935357	+	0.784858i	0.0414141	+	0.999142i	$0.486814\pi$
$318$		0			0
$319$	2.39300	−	13.5714i	0.133982	−	0.759852i
$320$		0			0
$321$	10.5395	−	1.17623i	0.588258	−	0.0656509i
$322$		0			0
$323$	−15.5211			−0.863616
$324$		0			0
$325$	−31.2868			−1.73548
$326$		0			0
$327$	−2.26349	+	0.252611i	−0.125171	+	0.0139694i
$328$		0			0
$329$	−6.45122	+	36.5867i	−0.355667	+	2.01709i
$330$		0			0
$331$	8.03858	−	6.74517i	0.441840	−	0.370748i	−0.394557	−	0.918871i	$-0.629102\pi$
$331$	8.03858	−	6.74517i	0.441840	−	0.370748i	0.836398	+	0.548123i	$0.184658\pi$
$332$		0			0
$333$	−0.823848	+	2.65093i	−0.0451466	+	0.145270i
$334$		0			0
$335$	−0.415086	−	2.35407i	−0.0226785	−	0.128616i
$336$		0			0
$337$	−21.5337	+	7.83763i	−1.17302	+	0.426943i	−0.853730	−	0.520716i	$-0.825665\pi$
$337$	−21.5337	+	7.83763i	−1.17302	+	0.426943i	−0.319285	+	0.947659i	$0.603443\pi$
$338$		0			0
$339$	1.29997	−	20.4799i	0.0706049	−	1.11231i
$340$		0			0
$341$	8.89196	−	15.4013i	0.481527	−	0.834029i
$342$		0			0
$343$	1.82722	+	3.16484i	0.0986606	+	0.170885i
$344$		0			0
$345$	−1.39156	+	1.45965i	−0.0749191	+	0.0785848i
$346$		0			0
$347$	−11.1357	−	9.34392i	−0.597793	−	0.501608i	0.292942	−	0.956130i	$-0.405366\pi$
$347$	−11.1357	−	9.34392i	−0.597793	−	0.501608i	−0.890735	+	0.454522i	$0.849810\pi$
$348$		0			0
$349$	5.34972	+	1.94714i	0.286364	+	0.104228i	0.481209	−	0.876606i	$-0.340198\pi$
$349$	5.34972	+	1.94714i	0.286364	+	0.104228i	−0.194844	+	0.980834i	$0.562420\pi$
$350$		0			0
$351$	−26.1028	+	21.2161i	−1.39326	+	1.13243i
$352$		0			0
$353$	−10.3509	−	3.76744i	−0.550925	−	0.200520i	0.0515322	−	0.998671i	$-0.483590\pi$
$353$	−10.3509	−	3.76744i	−0.550925	−	0.200520i	−0.602458	+	0.798151i	$0.705812\pi$
$354$		0			0
$355$	−3.51560	−	2.94994i	−0.186589	−	0.156566i
$356$		0			0
$357$	5.02532	+	17.1099i	0.265968	+	0.905549i
$358$		0			0
$359$	4.28815	+	7.42730i	0.226320	+	0.391998i	0.956715	−	0.291028i	$-0.0939972\pi$
$359$	4.28815	+	7.42730i	0.226320	+	0.391998i	−0.730395	+	0.683025i	$0.760664\pi$
$360$		0			0
$361$	−5.25635	+	9.10427i	−0.276650	+	0.479172i
$362$		0			0
$363$	−27.7305	+	13.7462i	−1.45547	+	0.721489i
$364$		0			0
$365$	2.75734	−	1.00359i	0.144326	−	0.0525302i
$366$		0			0
$367$	2.16636	+	12.2860i	0.113083	+	0.641326i	0.987681	+	0.156478i	$0.0500140\pi$
$367$	2.16636	+	12.2860i	0.113083	+	0.641326i	−0.874598	+	0.484848i	$0.838875\pi$
$368$		0			0
$369$	9.13138	−	5.87034i	0.475361	−	0.305598i
$370$		0			0
$371$	−12.6097	+	10.5808i	−0.654660	+	0.549325i
$372$		0			0
$373$	4.50699	−	25.5604i	0.233363	−	1.32347i	−0.612671	−	0.790338i	$-0.709905\pi$
$373$	4.50699	−	25.5604i	0.233363	−	1.32347i	0.846034	−	0.533129i	$-0.178984\pi$
$374$		0			0
$375$	2.78964	−	6.37552i	0.144056	−	0.329230i
$376$		0			0
$377$	−16.6034			−0.855117
$378$		0			0
$379$	21.7489			1.11717			0.558584	−	0.829448i	$-0.311345\pi$
$379$	21.7489			1.11717			0.558584	+	0.829448i	$0.311345\pi$
$380$		0			0
$381$	−0.283665	−	0.385204i	−0.0145326	−	0.0197346i
$382$		0			0
$383$	1.65979	−	9.41315i	0.0848114	−	0.480989i	−0.912586	−	0.408885i	$-0.865918\pi$
$383$	1.65979	−	9.41315i	0.0848114	−	0.480989i	0.997397	−	0.0721039i	$-0.0229713\pi$
$384$		0			0
$385$	−6.06057	+	5.08542i	−0.308875	+	0.259177i
$386$		0			0
$387$	1.02897	+	2.45549i	0.0523053	+	0.124820i
$388$		0			0
$389$	−3.45589	−	19.5993i	−0.175221	−	0.993726i	−0.937889	−	0.346936i	$-0.887222\pi$
$389$	−3.45589	−	19.5993i	−0.175221	−	0.993726i	0.762668	−	0.646790i	$-0.223889\pi$
$390$		0			0
$391$	7.65024	−	2.78446i	0.386889	−	0.140816i
$392$		0			0
$393$	−14.7321	−	9.79988i	−0.743138	−	0.494339i
$394$		0			0
$395$	0.0144901	−	0.0250975i	0.000729074	−	0.00126279i
$396$		0			0
$397$	3.53351	+	6.12022i	0.177342	+	0.307165i	0.940969	−	0.338492i	$-0.109917\pi$
$397$	3.53351	+	6.12022i	0.177342	+	0.307165i	−0.763627	+	0.645657i	$0.776583\pi$
$398$		0			0
$399$	32.9527	+	7.99159i	1.64970	+	0.400080i
$400$		0			0
$401$	25.8470	+	21.6882i	1.29074	+	1.08306i	0.991667	+	0.128824i	$0.0411202\pi$
$401$	25.8470	+	21.6882i	1.29074	+	1.08306i	0.299068	+	0.954232i	$0.403324\pi$
$402$		0			0
$403$	−20.1343	−	7.32828i	−1.00296	−	0.365048i
$404$		0			0
$405$	−0.981023	−	3.54419i	−0.0487474	−	0.176112i
$406$		0			0
$407$	4.67199	+	1.70047i	0.231582	+	0.0842890i
$408$		0			0
$409$	6.63889	+	5.57069i	0.328272	+	0.275453i	0.791995	−	0.610527i	$-0.209042\pi$
$409$	6.63889	+	5.57069i	0.328272	+	0.275453i	−0.463723	+	0.885980i	$0.653487\pi$
$410$		0			0
$411$	−10.8965	−	2.64258i	−0.537483	−	0.130349i
$412$		0			0
$413$	11.0178	+	19.0834i	0.542152	+	0.939035i
$414$		0			0
$415$	−3.36396	+	5.82656i	−0.165131	+	0.286014i
$416$		0			0
$417$	−29.0539	−	19.3268i	−1.42278	−	0.946437i
$418$		0			0
$419$	9.22863	−	3.35895i	0.450848	−	0.164095i	−0.106609	−	0.994301i	$-0.533999\pi$
$419$	9.22863	−	3.35895i	0.450848	−	0.164095i	0.557457	+	0.830206i	$0.311777\pi$
$420$		0			0
$421$	0.599574	+	3.40035i	0.0292215	+	0.165723i	0.995926	−	0.0901709i	$-0.0287413\pi$
$421$	0.599574	+	3.40035i	0.0292215	+	0.165723i	−0.966705	+	0.255894i	$0.917630\pi$
$422$		0			0
$423$	−18.7268	+	24.6145i	−0.910527	+	1.19680i
$424$		0			0
$425$	−10.5777	+	8.87576i	−0.513095	+	0.430538i
$426$		0			0
$427$	−3.96999	+	22.5150i	−0.192121	+	1.08957i
$428$		0			0
$429$	35.7233	+	48.5107i	1.72474	+	2.34212i
$430$		0			0
$431$	−24.7448			−1.19191			−0.595957	−	0.803016i	$-0.703227\pi$
$431$	−24.7448			−1.19191			−0.595957	+	0.803016i	$0.703227\pi$
$432$		0			0
$433$	−7.20492			−0.346246			−0.173123	−	0.984900i	$-0.555386\pi$
$433$	−7.20492			−0.346246			−0.173123	+	0.984900i	$0.555386\pi$
$434$		0			0
$435$	0.727637	−	1.66296i	0.0348875	−	0.0797329i
$436$		0			0
$437$	2.68810	−	15.2450i	0.128589	−	0.729267i
$438$		0			0
$439$	4.11157	−	3.45002i	0.196235	−	0.164660i	−0.539376	−	0.842065i	$-0.681340\pi$
$439$	4.11157	−	3.45002i	0.196235	−	0.164660i	0.735611	+	0.677405i	$0.236895\pi$
$440$		0			0
$441$	−0.857184	−	17.9372i	−0.0408183	−	0.854152i
$442$		0			0
$443$	−0.218121	−	1.23703i	−0.0103633	−	0.0587729i	0.979188	−	0.202957i	$-0.0650553\pi$
$443$	−0.218121	−	1.23703i	−0.0103633	−	0.0587729i	−0.989551	+	0.144184i	$0.953944\pi$
$444$		0			0
$445$	2.63295	−	0.958315i	0.124814	−	0.0454285i
$446$		0			0
$447$	15.1428	−	7.50639i	0.716229	−	0.355040i
$448$		0			0
$449$	1.75825	−	3.04537i	0.0829768	−	0.143720i	−0.821550	−	0.570136i	$-0.806891\pi$
$449$	1.75825	−	3.04537i	0.0829768	−	0.143720i	0.904527	+	0.426416i	$0.140224\pi$
$450$		0			0
$451$	−9.72118	−	16.8376i	−0.457752	−	0.792850i
$452$		0			0
$453$	−7.67316	−	26.1251i	−0.360517	−	1.22746i
$454$		0			0
$455$	7.30191	+	6.12703i	0.342319	+	0.287240i
$456$		0			0
$457$	2.47059	+	0.899221i	0.115569	+	0.0420638i	0.399158	−	0.916882i	$-0.369303\pi$
$457$	2.47059	+	0.899221i	0.115569	+	0.0420638i	−0.283588	+	0.958946i	$0.591525\pi$
$458$		0			0
$459$	−2.80624	+	14.5780i	−0.130984	+	0.680444i
$460$		0			0
$461$	12.6604	+	4.60803i	0.589656	+	0.214617i	0.619578	−	0.784935i	$-0.287304\pi$
$461$	12.6604	+	4.60803i	0.589656	+	0.214617i	−0.0299223	+	0.999552i	$0.509526\pi$
$462$		0			0
$463$	−10.8003	−	9.06249i	−0.501931	−	0.421170i	0.356348	−	0.934353i	$-0.384022\pi$
$463$	−10.8003	−	9.06249i	−0.501931	−	0.421170i	−0.858279	+	0.513183i	$0.828466\pi$
$464$		0			0
$465$	1.61637	−	1.69545i	0.0749572	−	0.0786248i
$466$		0			0
$467$	19.4700	+	33.7231i	0.900965	+	1.56052i	0.826243	+	0.563314i	$0.190474\pi$
$467$	19.4700	+	33.7231i	0.900965	+	1.56052i	0.0747223	+	0.997204i	$0.476193\pi$
$468$		0			0
$469$	10.5407	−	18.2570i	0.486722	−	0.843028i
$470$		0			0
$471$	2.13799	−	33.6821i	0.0985134	−	1.55199i
$472$		0			0
$473$	4.48076	−	1.63086i	0.206025	−	0.0749871i
$474$		0			0
$475$	4.55927	+	25.8569i	0.209194	+	1.18640i
$476$		0			0
$477$	−13.3664	+	3.02108i	−0.612007	+	0.138326i
$478$		0			0
$479$	15.7501	−	13.2159i	0.719640	−	0.603850i	−0.207646	−	0.978204i	$-0.566580\pi$
$479$	15.7501	−	13.2159i	0.719640	−	0.603850i	0.927286	+	0.374355i	$0.122136\pi$
$480$		0			0
$481$	1.04018	−	5.89917i	0.0474283	−	0.268979i
$482$		0			0
$483$	−17.6758	+	1.97266i	−0.804279	+	0.0897593i
$484$		0			0
$485$	4.96470			0.225435
$486$		0			0
$487$	−16.2004			−0.734111			−0.367055	−	0.930199i	$-0.619634\pi$
$487$	−16.2004			−0.734111			−0.367055	+	0.930199i	$0.619634\pi$
$488$		0			0
$489$	−25.3053	+	2.82413i	−1.14435	+	0.127711i
$490$		0			0
$491$	−0.431395	+	2.44656i	−0.0194686	+	0.110412i	−0.992993	−	0.118169i	$-0.962297\pi$
$491$	−0.431395	+	2.44656i	−0.0194686	+	0.110412i	0.973525	+	0.228581i	$0.0734086\pi$
$492$		0			0
$493$	−5.61341	+	4.71021i	−0.252815	+	0.212137i
$494$		0			0
$495$	−6.42430	+	1.45202i	−0.288751	+	0.0652634i
$496$		0			0
$497$	−7.02823	−	39.8591i	−0.315259	−	1.78792i
$498$		0			0
$499$	−20.8557	+	7.59086i	−0.933630	+	0.339813i	−0.763647	−	0.645634i	$-0.776593\pi$
$499$	−20.8557	+	7.59086i	−0.933630	+	0.339813i	−0.169982	+	0.985447i	$0.554371\pi$
$500$		0			0
$501$	0.513583	−	8.09102i	0.0229452	−	0.361480i
$502$		0			0
$503$	−12.8273	+	22.2176i	−0.571943	+	0.990634i	0.424424	+	0.905464i	$0.360477\pi$
$503$	−12.8273	+	22.2176i	−0.571943	+	0.990634i	−0.996366	+	0.0851702i	$0.972857\pi$
$504$		0			0
$505$	3.58773	+	6.21413i	0.159652	+	0.276525i
$506$		0			0
$507$	34.5479	−	36.2384i	1.53433	−	1.60940i
$508$		0			0
$509$	−26.3979	−	22.1505i	−1.17007	−	0.981804i	−0.170075	−	0.985431i	$-0.554401\pi$
$509$	−26.3979	−	22.1505i	−1.17007	−	0.981804i	−0.999993	+	0.00362752i	$0.998845\pi$
$510$		0			0
$511$	24.3176	+	8.85087i	1.07575	+	0.391540i
$512$		0			0
$513$	21.3378	+	18.4808i	0.942088	+	0.815948i
$514$		0			0
$515$	1.29168	+	0.470135i	0.0569184	+	0.0207166i
$516$		0			0
$517$	42.4334	+	35.6059i	1.86622	+	1.56594i
$518$		0			0
$519$	1.85518	+	6.31638i	0.0814333	+	0.277258i
$520$		0			0
$521$	1.28577	+	2.22701i	0.0563305	+	0.0975673i	0.892816	−	0.450422i	$-0.148727\pi$
$521$	1.28577	+	2.22701i	0.0563305	+	0.0975673i	−0.836485	+	0.547990i	$0.815393\pi$
$522$		0			0
$523$	−0.517332	+	0.896045i	−0.0226213	+	0.0391813i	−0.877114	−	0.480281i	$-0.840535\pi$
$523$	−0.517332	+	0.896045i	−0.0226213	+	0.0391813i	0.854493	+	0.519463i	$0.173868\pi$
$524$		0			0
$525$	27.0275	−	13.3977i	1.17958	−	0.584725i
$526$		0			0
$527$	−8.88613	+	3.23429i	−0.387086	+	0.140888i
$528$		0			0
$529$	−2.58393	−	14.6542i	−0.112345	−	0.637138i
$530$		0			0
$531$	0.875660	+	18.3238i	0.0380004	+	0.795186i
$532$		0			0
$533$	−17.9443	+	15.0570i	−0.777253	+	0.652193i
$534$		0			0
$535$	0.434433	−	2.46379i	0.0187822	−	0.106519i
$536$		0			0
$537$	1.30842	−	2.99030i	0.0564625	−	0.129041i
$538$		0			0
$539$	−32.1623			−1.38533
$540$		0			0
$541$	0.798944			0.0343493			0.0171746	−	0.999853i	$-0.494533\pi$
$541$	0.798944			0.0343493			0.0171746	+	0.999853i	$0.494533\pi$
$542$		0			0
$543$	−9.54540	−	12.9622i	−0.409632	−	0.556262i
$544$		0			0
$545$	−0.0933000	+	0.529131i	−0.00399653	+	0.0226655i
$546$		0			0
$547$	−28.1704	+	23.6378i	−1.20448	+	1.01068i	−0.204991	+	0.978764i	$0.565716\pi$
$547$	−28.1704	+	23.6378i	−1.20448	+	1.01068i	−0.999491	+	0.0319159i	$0.989839\pi$
$548$		0			0
$549$	−11.5242	+	15.1474i	−0.491841	+	0.646476i
$550$		0			0
$551$	2.41952	+	13.7218i	0.103075	+	0.584568i
$552$		0			0
$553$	0.240169	−	0.0874142i	0.0102130	−	0.00371723i
$554$		0			0
$555$	0.545264	+	0.362712i	0.0231452	+	0.0153963i
$556$		0			0
$557$	21.5747	−	37.3685i	0.914150	−	1.58335i	0.106010	−	0.994365i	$-0.466193\pi$
$557$	21.5747	−	37.3685i	0.914150	−	1.58335i	0.808141	−	0.588990i	$-0.200474\pi$
$558$		0			0
$559$	−2.87249	−	4.97530i	−0.121493	−	0.210433i
$560$		0			0
$561$	25.8396	+	6.26655i	1.09095	+	0.264574i
$562$		0			0
$563$	−26.5075	−	22.2424i	−1.11716	−	0.937406i	−0.118700	−	0.992930i	$-0.537873\pi$
$563$	−26.5075	−	22.2424i	−1.11716	−	0.937406i	−0.998457	+	0.0555243i	$0.982317\pi$
$564$		0			0
$565$	−4.54916	−	1.65576i	−0.191385	−	0.0696583i
$566$		0			0
$567$	13.4639	−	29.5056i	0.565432	−	1.23912i
$568$		0			0
$569$	−6.77707	−	2.46665i	−0.284110	−	0.103407i	0.196035	−	0.980597i	$-0.437193\pi$
$569$	−6.77707	−	2.46665i	−0.284110	−	0.103407i	−0.480144	+	0.877189i	$0.659416\pi$
$570$		0			0
$571$	17.1660	+	14.4040i	0.718375	+	0.602788i	0.926935	−	0.375221i	$-0.122433\pi$
$571$	17.1660	+	14.4040i	0.718375	+	0.602788i	−0.208560	+	0.978010i	$0.566878\pi$
$572$		0			0
$573$	0.735995	+	0.178491i	0.0307466	+	0.00745658i
$574$		0			0
$575$	−6.88592	−	11.9268i	−0.287163	−	0.497380i
$576$		0			0
$577$	−11.1264	+	19.2714i	−0.463197	+	0.802281i	−0.999118	−	0.0419873i	$-0.986631\pi$
$577$	−11.1264	+	19.2714i	−0.463197	+	0.802281i	0.535921	+	0.844268i	$0.319964\pi$
$578$		0			0
$579$	−6.05139	−	4.02541i	−0.251487	−	0.167290i
$580$		0			0
$581$	−55.7568	+	20.2938i	−2.31318	+	0.841929i
$582$		0			0
$583$	4.26188	+	24.1703i	0.176509	+	1.00103i
$584$		0			0
$585$	3.06691	+	7.31877i	0.126801	+	0.302594i
$586$		0			0
$587$	−1.98897	+	1.66894i	−0.0820934	+	0.0688845i	−0.682911	−	0.730502i	$-0.739286\pi$
$587$	−1.98897	+	1.66894i	−0.0820934	+	0.0688845i	0.600817	+	0.799386i	$0.294842\pi$
$588$		0			0
$589$	−3.12237	+	17.7078i	−0.128655	+	0.729638i
$590$		0			0
$591$	25.5238	+	34.6602i	1.04991	+	1.42573i
$592$		0			0
$593$	−42.9863			−1.76524			−0.882619	−	0.470089i	$-0.844222\pi$
$593$	−42.9863			−1.76524			−0.882619	+	0.470089i	$0.844222\pi$
$594$		0			0
$595$	4.20687			0.172465
$596$		0			0
$597$	5.17928	−	11.8369i	0.211974	−	0.484451i
$598$		0			0
$599$	3.07269	−	17.4261i	0.125547	−	0.712010i	−0.855435	−	0.517910i	$-0.826710\pi$
$599$	3.07269	−	17.4261i	0.125547	−	0.712010i	0.980982	−	0.194100i	$-0.0621786\pi$
$600$		0			0
$601$	1.91374	−	1.60582i	0.0780630	−	0.0655026i	−0.602921	−	0.797801i	$-0.705997\pi$
$601$	1.91374	−	1.60582i	0.0780630	−	0.0655026i	0.680984	+	0.732298i	$0.261552\pi$
$602$		0			0
$603$	14.7628	−	9.49062i	0.601186	−	0.386488i
$604$		0			0
$605$	1.26790	+	7.19059i	0.0515473	+	0.292339i
$606$		0			0
$607$	−17.4845	+	6.36382i	−0.709672	+	0.258299i	−0.671535	−	0.740973i	$-0.734365\pi$
$607$	−17.4845	+	6.36382i	−0.709672	+	0.258299i	−0.0381372	+	0.999273i	$0.512142\pi$
$608$		0			0
$609$	14.3430	−	7.10994i	0.581208	−	0.288109i
$610$		0			0
$611$	33.3693	−	57.7973i	1.34998	−	2.33823i
$612$		0			0
$613$	−15.9684	−	27.6582i	−0.644959	−	1.11710i	−0.984311	−	0.176443i	$-0.943541\pi$
$613$	−15.9684	−	27.6582i	−0.644959	−	1.11710i	0.339351	−	0.940660i	$-0.389792\pi$
$614$		0			0
$615$	−0.721683	−	2.45714i	−0.0291011	−	0.0990812i
$616$		0			0
$617$	−13.2872	−	11.1493i	−0.534924	−	0.448855i	0.334874	−	0.942263i	$-0.391306\pi$
$617$	−13.2872	−	11.1493i	−0.534924	−	0.448855i	−0.869798	+	0.493408i	$0.835751\pi$
$618$		0			0
$619$	−7.49484	−	2.72790i	−0.301243	−	0.109644i	0.186976	−	0.982364i	$-0.440131\pi$
$619$	−7.49484	−	2.72790i	−0.301243	−	0.109644i	−0.488219	+	0.872721i	$0.662353\pi$
$620$		0			0
$621$	−13.8327	−	5.28110i	−0.555087	−	0.211923i
$622$		0			0
$623$	23.2206	+	8.45159i	0.930312	+	0.338606i
$624$		0			0
$625$	17.2540	+	14.4778i	0.690160	+	0.579113i
$626$		0			0
$627$	34.8857	−	36.5926i	1.39320	−	1.46137i
$628$		0			0
$629$	−1.32186	−	2.28953i	−0.0527061	−	0.0912896i
$630$		0			0
$631$	18.2924	−	31.6833i	0.728208	−	1.26129i	−0.229432	−	0.973325i	$-0.573687\pi$
$631$	18.2924	−	31.6833i	0.728208	−	1.26129i	0.957640	−	0.287969i	$-0.0929798\pi$
$632$		0			0
$633$	−2.06237	+	32.4908i	−0.0819720	+	1.29139i
$634$		0			0
$635$	−0.106049	+	0.0385985i	−0.00420841	+	0.00153174i
$636$		0			0
$637$	6.72884	+	38.1612i	0.266606	+	1.51200i
$638$		0			0
$639$	9.99975	−	32.1766i	0.395584	−	1.27289i
$640$		0			0
$641$	29.9786	−	25.1551i	1.18408	−	0.993565i	0.184142	−	0.982900i	$-0.441049\pi$
$641$	29.9786	−	25.1551i	1.18408	−	0.993565i	0.999943	−	0.0106655i	$-0.00339499\pi$
$642$		0			0
$643$	3.97161	−	22.5241i	0.156625	−	0.888265i	−0.800660	−	0.599119i	$-0.795518\pi$
$643$	3.97161	−	22.5241i	0.156625	−	0.888265i	0.957285	−	0.289146i	$-0.0933712\pi$
$644$		0			0
$645$	0.624203	−	0.0696624i	0.0245780	−	0.00274295i
$646$		0			0
$647$	−8.83094			−0.347180			−0.173590	−	0.984818i	$-0.555537\pi$
$647$	−8.83094			−0.347180			−0.173590	+	0.984818i	$0.555537\pi$
$648$		0			0
$649$	32.8555			1.28969
$650$		0			0
$651$	20.5314	−	2.29135i	0.804688	−	0.0898050i
$652$		0			0
$653$	−1.57500	+	8.93227i	−0.0616345	+	0.349547i	0.938358	+	0.345665i	$0.112347\pi$
$653$	−1.57500	+	8.93227i	−0.0616345	+	0.349547i	−0.999992	+	0.00388158i	$0.998764\pi$
$654$		0			0
$655$	−3.19758	+	2.68309i	−0.124940	+	0.104837i
$656$		0			0
$657$	14.6200	+	15.8236i	0.570380	+	0.617337i
$658$		0			0
$659$	1.28317	+	7.27721i	0.0499851	+	0.283480i	0.999547	−	0.0301003i	$-0.00958267\pi$
$659$	1.28317	+	7.27721i	0.0499851	+	0.283480i	−0.949562	+	0.313580i	$0.898472\pi$
$660$		0			0
$661$	38.7918	−	14.1191i	1.50883	−	0.549168i	0.550499	−	0.834836i	$-0.314438\pi$
$661$	38.7918	−	14.1191i	1.50883	−	0.549168i	0.958329	+	0.285668i	$0.0922154\pi$
$662$		0			0
$663$	2.02933	−	31.9703i	0.0788128	−	1.24162i
$664$		0			0
$665$	3.99959	−	6.92750i	0.155098	−	0.268637i
$666$		0			0
$667$	−3.65423	−	6.32932i	−0.141493	−	0.245072i
$668$		0			0
$669$	9.74201	−	10.2187i	0.376648	−	0.395077i
$670$		0			0
$671$	26.1129	+	21.9114i	1.00808	+	0.845879i
$672$		0			0
$673$	13.4796	+	4.90619i	0.519602	+	0.189120i	0.588490	−	0.808505i	$-0.299723\pi$
$673$	13.4796	+	4.90619i	0.519602	+	0.189120i	−0.0688878	+	0.997624i	$0.521945\pi$
$674$		0			0
$675$	25.1101	+	0.392725i	0.966490	+	0.0151160i
$676$		0			0
$677$	4.87645	+	1.77488i	0.187417	+	0.0682143i	0.434024	−	0.900901i	$-0.357093\pi$
$677$	4.87645	+	1.77488i	0.187417	+	0.0682143i	−0.246607	+	0.969116i	$0.579316\pi$
$678$		0			0
$679$	33.5411	+	28.1443i	1.28719	+	1.08008i
$680$		0			0
$681$	1.19867	+	4.08116i	0.0459332	+	0.156390i
$682$		0			0
$683$	8.39380	+	14.5385i	0.321180	+	0.556300i	0.980732	−	0.195359i	$-0.0625872\pi$
$683$	8.39380	+	14.5385i	0.321180	+	0.556300i	−0.659552	+	0.751659i	$0.729254\pi$
$684$		0			0
$685$	−1.32254	+	2.29071i	−0.0505318	+	0.0875237i
$686$		0			0
$687$	15.9165	−	7.88995i	0.607253	−	0.301020i
$688$		0			0
$689$	27.7869	−	10.1136i	1.05860	−	0.385298i
$690$		0			0
$691$	−4.90860	−	27.8381i	−0.186732	−	1.05901i	−0.923710	−	0.383093i	$-0.874859\pi$
$691$	−4.90860	−	27.8381i	−0.186732	−	1.05901i	0.736978	−	0.675917i	$-0.236252\pi$
$692$		0			0
$693$	−51.6334	−	26.6089i	−1.96139	−	1.01079i
$694$		0			0
$695$	−6.30610	+	5.29145i	−0.239204	+	0.200716i
$696$		0			0
$697$	−1.79522	+	10.1812i	−0.0679990	+	0.385641i
$698$		0			0
$699$	10.6572	−	24.3563i	0.403092	−	0.921238i
$700$		0			0
$701$	−18.4343			−0.696256			−0.348128	−	0.937447i	$-0.613182\pi$
$701$	−18.4343			−0.696256			−0.348128	+	0.937447i	$0.613182\pi$
$702$		0			0
$703$	−5.02693			−0.189594
$704$		0			0
$705$	4.32647	+	5.87515i	0.162944	+	0.221271i
$706$		0			0
$707$	−10.9888	+	62.3205i	−0.413276	+	2.34381i
$708$		0			0
$709$	−0.254095	+	0.213211i	−0.00954274	+	0.00800731i	−0.647547	−	0.762026i	$-0.724205\pi$
$709$	−0.254095	+	0.213211i	−0.00954274	+	0.00800731i	0.638004	+	0.770033i	$0.279760\pi$
$710$		0			0
$711$	0.211065	+	0.0269034i	0.00791555	+	0.00100895i
$712$		0			0
$713$	−1.63776	−	9.28822i	−0.0613347	−	0.347846i
$714$		0			0
$715$	13.3552	−	4.86090i	0.499457	−	0.181787i
$716$		0			0
$717$	30.6233	+	20.3708i	1.14365	+	0.760760i
$718$		0			0
$719$	2.49107	−	4.31467i	0.0929014	−	0.160910i	−0.815829	−	0.578293i	$-0.803719\pi$
$719$	2.49107	−	4.31467i	0.0929014	−	0.160910i	0.908731	+	0.417383i	$0.137053\pi$
$720$		0			0
$721$	6.06137	+	10.4986i	0.225737	+	0.390989i
$722$		0			0
$723$	−46.3399	−	11.2382i	−1.72340	−	0.417953i
$724$		0			0
$725$	9.49575	+	7.96788i	0.352663	+	0.295920i
$726$		0			0
$727$	−27.4939	−	10.0070i	−1.01969	−	0.371138i	−0.222545	−	0.974922i	$-0.571436\pi$
$727$	−27.4939	−	10.0070i	−1.01969	−	0.371138i	−0.797148	+	0.603785i	$0.793659\pi$
$728$		0			0
$729$	21.2158	−	16.7000i	0.785771	−	0.618517i
$730$		0			0
$731$	−2.38260	−	0.867195i	−0.0881236	−	0.0320744i
$732$		0			0
$733$	−13.2376	−	11.1076i	−0.488941	−	0.410270i	0.364705	−	0.931123i	$-0.381170\pi$
$733$	−13.2376	−	11.1076i	−0.488941	−	0.410270i	−0.853647	+	0.520853i	$0.825614\pi$
$734$		0			0
$735$	−4.11704	−	0.998452i	−0.151859	−	0.0368284i
$736$		0			0
$737$	−15.7163	−	27.2214i	−0.578917	−	1.00271i
$738$		0			0
$739$	3.42221	−	5.92743i	0.125888	−	0.218044i	−0.796192	−	0.605044i	$-0.793155\pi$
$739$	3.42221	−	5.92743i	0.125888	−	0.218044i	0.922080	+	0.387000i	$0.126489\pi$
$740$		0			0
$741$	−50.7165	−	33.7368i	−1.86312	−	1.23935i
$742$		0			0
$743$	−4.10544	+	1.49426i	−0.150614	+	0.0548190i	−0.416227	−	0.909261i	$-0.636648\pi$
$743$	−4.10544	+	1.49426i	−0.150614	+	0.0548190i	0.265613	+	0.964080i	$0.414426\pi$
$744$		0			0
$745$	−0.692360	−	3.92657i	−0.0253661	−	0.143858i
$746$		0			0
$747$	−49.0002	−	6.24580i	−1.79282	−	0.228522i
$748$		0			0
$749$	16.9020	−	14.1824i	0.617584	−	0.518215i
$750$		0			0
$751$	−7.68869	+	43.6047i	−0.280564	+	1.59116i	0.440149	+	0.897925i	$0.354926\pi$
$751$	−7.68869	+	43.6047i	−0.280564	+	1.59116i	−0.720713	+	0.693234i	$0.756185\pi$
$752$		0			0
$753$	−12.5455	−	17.0362i	−0.457182	−	0.620833i
$754$		0			0
$755$	−6.42347			−0.233774
$756$		0			0
$757$	33.6789			1.22408			0.612040	−	0.790827i	$-0.290349\pi$
$757$	33.6789			1.22408			0.612040	+	0.790827i	$0.290349\pi$
$758$		0			0
$759$	−10.6303	+	24.2947i	−0.385854	+	0.881842i
$760$		0			0
$761$	−6.22770	+	35.3191i	−0.225754	+	1.28031i	0.635484	+	0.772114i	$0.280800\pi$
$761$	−6.22770	+	35.3191i	−0.225754	+	1.28031i	−0.861238	+	0.508201i	$0.830311\pi$
$762$		0			0
$763$	−3.62991	+	3.04586i	−0.131412	+	0.110267i
$764$		0			0
$765$	3.11315	+	1.60434i	0.112556	+	0.0580051i
$766$		0			0
$767$	−6.87388	−	38.9837i	−0.248201	−	1.40762i
$768$		0			0
$769$	−7.66524	+	2.78992i	−0.276416	+	0.100607i	−0.476509	−	0.879170i	$-0.658098\pi$
$769$	−7.66524	+	2.78992i	−0.276416	+	0.100607i	0.200093	+	0.979777i	$0.435876\pi$
$770$		0			0
$771$	−21.0558	+	10.4375i	−0.758305	+	0.375898i
$772$		0			0
$773$	−12.0555	+	20.8807i	−0.433605	+	0.751027i	−0.997181	−	0.0750381i	$-0.976092\pi$
$773$	−12.0555	+	20.8807i	−0.433605	+	0.751027i	0.563575	+	0.826065i	$0.309425\pi$
$774$		0			0
$775$	7.99834	+	13.8535i	0.287309	+	0.497633i
$776$		0			0
$777$	1.62759	+	5.54149i	0.0583893	+	0.198800i
$778$		0			0
$779$	15.0588	+	12.6358i	0.539536	+	0.452725i
$780$		0			0
$781$	−56.7079	−	20.6400i	−2.02917	−	0.738557i
$782$		0			0
$783$	13.3255	+	0.208412i	0.476215	+	0.00744804i
$784$		0			0
$785$	−7.48174	−	2.72313i	−0.267035	−	0.0971927i
$786$		0			0
$787$	27.1965	+	22.8206i	0.969450	+	0.813465i	0.982464	−	0.186451i	$-0.0596984\pi$
$787$	27.1965	+	22.8206i	0.969450	+	0.813465i	−0.0130148	+	0.999915i	$0.504143\pi$
$788$		0			0
$789$	5.95282	−	6.24409i	0.211926	−	0.222295i
$790$		0			0
$791$	−21.3474	−	36.9749i	−0.759028	−	1.31467i
$792$		0			0
$793$	20.5350	−	35.5677i	0.729220	−	1.26305i
$794$		0			0
$795$	−0.204792	+	3.22631i	−0.00726323	+	0.114425i
$796$		0			0
$797$	34.5360	−	12.5701i	1.22333	−	0.445256i	0.352021	−	0.935992i	$-0.385494\pi$
$797$	34.5360	−	12.5701i	1.22333	−	0.445256i	0.871308	+	0.490736i	$0.163272\pi$
$798$		0			0
$799$	−5.11474	−	29.0071i	−0.180947	−	1.02620i
$800$		0			0
$801$	13.9605	+	15.1098i	0.493268	+	0.533877i
$802$		0			0
$803$	29.5577	−	24.8019i	1.04307	−	0.875239i
$804$		0			0
$805$	−0.728590	+	4.13204i	−0.0256794	+	0.145635i
$806$		0			0
$807$	39.3836	−	4.39530i	1.38637	−	0.154722i
$808$		0			0
$809$	−37.0769			−1.30356			−0.651778	−	0.758410i	$-0.725977\pi$
$809$	−37.0769			−1.30356			−0.651778	+	0.758410i	$0.725977\pi$
$810$		0			0
$811$	10.9432			0.384267			0.192133	−	0.981369i	$-0.438459\pi$
$811$	10.9432			0.384267			0.192133	+	0.981369i	$0.438459\pi$
$812$		0			0
$813$	20.9319	−	2.33605i	0.734114	−	0.0819287i
$814$		0			0
$815$	−1.04307	+	5.91556i	−0.0365372	+	0.207213i
$816$		0			0
$817$	−3.69322	+	3.09898i	−0.129210	+	0.108420i
$818$		0			0
$819$	−20.7695	+	66.8310i	−0.725745	+	2.33526i
$820$		0			0
$821$	9.56522	+	54.2471i	0.333829	+	1.89324i	0.438504	+	0.898729i	$0.355509\pi$
$821$	9.56522	+	54.2471i	0.333829	+	1.89324i	−0.104675	+	0.994506i	$0.533380\pi$
$822$		0			0
$823$	2.61994	−	0.953582i	0.0913255	−	0.0332398i	−0.295953	−	0.955202i	$-0.595637\pi$
$823$	2.61994	−	0.953582i	0.0913255	−	0.0332398i	0.387279	+	0.921963i	$0.373415\pi$
$824$		0			0
$825$	2.84927	−	44.8876i	0.0991987	−	1.56278i
$826$		0			0
$827$	−13.3263	+	23.0819i	−0.463402	+	0.802636i	−0.999128	−	0.0417562i	$-0.986705\pi$
$827$	−13.3263	+	23.0819i	−0.463402	+	0.802636i	0.535726	+	0.844392i	$0.320038\pi$
$828$		0			0
$829$	−5.82918	−	10.0964i	−0.202456	−	0.350664i	0.746863	−	0.664978i	$-0.231559\pi$
$829$	−5.82918	−	10.0964i	−0.202456	−	0.350664i	−0.949319	+	0.314314i	$0.898226\pi$
$830$		0			0
$831$	−7.02690	+	7.37072i	−0.243760	+	0.255687i
$832$		0			0
$833$	13.1009	+	10.9929i	0.453918	+	0.380883i
$834$		0			0
$835$	−1.79725	−	0.654144i	−0.0621962	−	0.0226376i
$836$		0			0
$837$	16.0674	+	6.13426i	0.555369	+	0.212031i
$838$		0			0
$839$	−43.6936	−	15.9032i	−1.50847	−	0.549038i	−0.550233	−	0.835011i	$-0.685461\pi$
$839$	−43.6936	−	15.9032i	−1.50847	−	0.549038i	−0.958238	+	0.285973i	$0.907683\pi$
$840$		0			0
$841$	−17.1761	−	14.4124i	−0.592278	−	0.496980i
$842$		0			0
$843$	9.26788	+	31.5546i	0.319203	+	1.08680i
$844$		0			0
$845$	−5.90572	−	10.2290i	−0.203163	−	0.351889i
$846$		0			0
$847$	−32.1969	+	55.7666i	−1.10630	+	1.91616i
$848$		0			0
$849$	2.57637	−	1.27713i	0.0884206	−	0.0438308i
$850$		0			0
$851$	2.47774	−	0.901823i	0.0849358	−	0.0309141i
$852$		0			0
$853$	7.62116	+	43.2218i	0.260944	+	1.47988i	0.780342	+	0.625353i	$0.215045\pi$
$853$	7.62116	+	43.2218i	0.260944	+	1.47988i	−0.519399	+	0.854532i	$0.673844\pi$
$854$		0			0
$855$	5.60165	−	3.60116i	0.191572	−	0.123157i
$856$		0			0
$857$	35.2869	−	29.6092i	1.20538	−	1.01143i	0.205916	−	0.978570i	$-0.433983\pi$
$857$	35.2869	−	29.6092i	1.20538	−	1.01143i	0.999460	−	0.0328607i	$-0.0104618\pi$
$858$		0			0
$859$	6.61255	−	37.5016i	0.225617	−	1.27954i	−0.635885	−	0.771784i	$-0.719365\pi$
$859$	6.61255	−	37.5016i	0.225617	−	1.27954i	0.861502	−	0.507754i	$-0.169524\pi$
$860$		0			0
$861$	9.05359	−	20.6913i	0.308546	−	0.705159i
$862$		0			0
$863$	−52.4338			−1.78487			−0.892433	−	0.451179i	$-0.851003\pi$
$863$	−52.4338			−1.78487			−0.892433	+	0.451179i	$0.851003\pi$
$864$		0			0
$865$	1.55303			0.0528048
$866$		0			0
$867$	9.07634	+	12.3253i	0.308249	+	0.418588i
$868$		0			0
$869$	0.0661733	−	0.375288i	0.00224478	−	0.0127308i
$870$		0			0
$871$	−29.0106	+	24.3428i	−0.982988	+	0.824825i
$872$		0			0
$873$	14.0878	+	33.6186i	0.476798	+	1.13782i
$874$		0			0
$875$	−2.51420	−	14.2587i	−0.0849954	−	0.482033i
$876$		0			0
$877$	−29.8219	+	10.8543i	−1.00701	+	0.366523i	−0.792285	−	0.610151i	$-0.791109\pi$
$877$	−29.8219	+	10.8543i	−1.00701	+	0.366523i	−0.214728	+	0.976674i	$0.568886\pi$
$878$		0			0
$879$	36.9249	+	24.5626i	1.24545	+	0.828477i
$880$		0			0
$881$	−10.1586	+	17.5953i	−0.342253	+	0.592800i	−0.984851	−	0.173404i	$-0.944523\pi$
$881$	−10.1586	+	17.5953i	−0.342253	+	0.592800i	0.642597	+	0.766204i	$0.277857\pi$
$882$		0			0
$883$	25.3780	+	43.9560i	0.854038	+	1.47924i	0.877534	+	0.479514i	$0.159187\pi$
$883$	25.3780	+	43.9560i	0.854038	+	1.47924i	−0.0234958	+	0.999724i	$0.507480\pi$
$884$		0			0
$885$	4.20578	+	1.01997i	0.141376	+	0.0342860i
$886$		0			0
$887$	−21.4813	−	18.0250i	−0.721272	−	0.605219i	0.206465	−	0.978454i	$-0.433804\pi$
$887$	−21.4813	−	18.0250i	−0.721272	−	0.605219i	−0.927737	+	0.373235i	$0.878249\pi$
$888$		0			0
$889$	−0.935266	−	0.340409i	−0.0313678	−	0.0114169i
$890$		0			0
$891$	−28.0619	−	39.3820i	−0.940108	−	1.31935i
$892$		0			0
$893$	−52.6291	−	19.1554i	−1.76117	−	0.641012i
$894$		0			0
$895$	−0.589865	−	0.494955i	−0.0197170	−	0.0165445i
$896$		0			0
$897$	31.0501	+	7.53019i	1.03673	+	0.251426i
$898$		0			0
$899$	4.24457	+	7.35182i	0.141564	+	0.245197i
$900$		0			0
$901$	6.52531	−	11.3022i	0.217389	−	0.376530i
$902$		0			0
$903$	4.61197	+	3.06790i	0.153477	+	0.102093i
$904$		0			0
$905$	−3.56856	+	1.29885i	−0.118623	+	0.0431752i
$906$		0			0
$907$	−4.59509	−	26.0601i	−0.152578	−	0.865310i	−0.960967	−	0.276662i	$-0.910772\pi$
$907$	−4.59509	−	26.0601i	−0.152578	−	0.865310i	0.808390	−	0.588648i	$-0.200340\pi$
$908$		0			0
$909$	−31.8986	+	41.9275i	−1.05801	+	1.39065i
$910$		0			0
$911$	5.54481	−	4.65265i	0.183708	−	0.154149i	−0.546296	−	0.837592i	$-0.683963\pi$
$911$	5.54481	−	4.65265i	0.183708	−	0.154149i	0.730004	+	0.683443i	$0.239518\pi$
$912$		0			0
$913$	−15.3626	+	87.1256i	−0.508427	+	2.88343i
$914$		0			0
$915$	2.66245	+	3.61549i	0.0880180	+	0.119524i
$916$		0			0
$917$	−36.8128			−1.21566
$918$		0			0
$919$	9.10266			0.300269			0.150135	−	0.988666i	$-0.452029\pi$
$919$	9.10266			0.300269			0.150135	+	0.988666i	$0.452029\pi$
$920$		0			0
$921$	14.1781	−	32.4030i	0.467184	−	1.06772i
$922$		0			0
$923$	−12.6256	+	71.6032i	−0.415576	+	2.35685i
$924$		0			0
$925$	−3.42588	+	2.87466i	−0.112642	+	0.0945182i
$926$		0			0
$927$	0.481738	+	10.0807i	0.0158223	+	0.331094i
$928$		0			0
$929$	2.75571	+	15.6284i	0.0904120	+	0.512752i	0.996057	+	0.0887152i	$0.0282761\pi$
$929$	2.75571	+	15.6284i	0.0904120	+	0.512752i	−0.905645	+	0.424037i	$0.860613\pi$
$930$		0			0
$931$	30.5576	−	11.1221i	1.00148	−	0.364511i
$932$		0			0
$933$	−23.0484	+	11.4253i	−0.754570	+	0.374047i
$934$		0			0
$935$	3.13625	−	5.43215i	0.102566	−	0.177650i
$936$		0			0
$937$	9.66153	+	16.7343i	0.315628	+	0.546684i	0.979571	−	0.201099i	$-0.0644514\pi$
$937$	9.66153	+	16.7343i	0.315628	+	0.546684i	−0.663943	+	0.747784i	$0.731118\pi$
$938$		0			0
$939$	−16.0394	−	54.6099i	−0.523427	−	1.78213i
$940$		0			0
$941$	−30.6681	−	25.7336i	−0.999750	−	0.838890i	−0.0128002	−	0.999918i	$-0.504075\pi$
$941$	−30.6681	−	25.7336i	−0.999750	−	0.838890i	−0.986950	+	0.161028i	$0.948519\pi$
$942$		0			0
$943$	−9.68920	−	3.52658i	−0.315524	−	0.114841i
$944$		0			0
$945$	−5.78345	−	5.00908i	−0.188136	−	0.162945i
$946$		0			0
$947$	−8.37919	−	3.04978i	−0.272287	−	0.0991044i	0.202268	−	0.979330i	$-0.435169\pi$
$947$	−8.37919	−	3.04978i	−0.272287	−	0.0991044i	−0.474555	+	0.880226i	$0.657391\pi$
$948$		0			0
$949$	−35.6118	−	29.8818i	−1.15601	−	0.970006i
$950$		0			0
$951$	−25.9823	+	27.2536i	−0.842535	+	0.883759i
$952$		0			0
$953$	5.86354	+	10.1559i	0.189939	+	0.328983i	0.945230	−	0.326406i	$-0.105838\pi$
$953$	5.86354	+	10.1559i	0.189939	+	0.328983i	−0.755291	+	0.655390i	$0.772504\pi$
$954$		0			0
$955$	0.0893305	−	0.154725i	0.00289067	−	0.00500678i
$956$		0			0
$957$	1.51205	−	23.8210i	0.0488778	−	0.770024i
$958$		0			0
$959$	−21.9208	+	7.97852i	−0.707859	+	0.257640i
$960$		0			0
$961$	−3.48075	−	19.7403i	−0.112282	−	0.636784i
$962$		0			0
$963$	17.9164	−	4.04945i	0.577347	−	0.130492i
$964$		0			0
$965$	−1.31344	+	1.10211i	−0.0422813	+	0.0354782i
$966$		0			0
$967$	−8.87441	+	50.3293i	−0.285382	+	1.61848i	0.418537	+	0.908200i	$0.362543\pi$
$967$	−8.87441	+	50.3293i	−0.285382	+	1.61848i	−0.703919	+	0.710280i	$0.748568\pi$
$968$		0			0
$969$	−26.7174	+	2.98173i	−0.858288	+	0.0957869i
$970$		0			0
$971$	3.03597			0.0974291			0.0487145	−	0.998813i	$-0.484488\pi$
$971$	3.03597			0.0974291			0.0487145	+	0.998813i	$0.484488\pi$
$972$		0			0
$973$	−72.6001			−2.32745
$974$		0			0
$975$	−53.8561	+	6.01046i	−1.72477	+	0.192489i
$976$		0			0
$977$	−2.41298	+	13.6847i	−0.0771981	+	0.437812i	0.921571	+	0.388210i	$0.126907\pi$
$977$	−2.41298	+	13.6847i	−0.0771981	+	0.437812i	−0.998769	+	0.0496024i	$0.984205\pi$
$978$		0			0
$979$	28.2243	−	23.6830i	0.902053	−	0.756912i
$980$		0			0
$981$	−3.84776	+	0.869670i	−0.122850	+	0.0277664i
$982$		0			0
$983$	−1.31516	−	7.45863i	−0.0419470	−	0.237893i	0.956625	−	0.291324i	$-0.0940956\pi$
$983$	−1.31516	−	7.45863i	−0.0419470	−	0.237893i	−0.998572	+	0.0534303i	$0.982985\pi$
$984$		0			0
$985$	9.54211	−	3.47304i	0.304037	−	0.110660i
$986$		0			0
$987$	−4.07630	+	64.2183i	−0.129750	+	2.04409i
$988$		0			0
$989$	1.26441	−	2.19003i	0.0402060	−	0.0696388i
$990$		0			0
$991$	−23.1789	−	40.1470i	−0.736301	−	1.27531i	−0.954150	−	0.299329i	$-0.903237\pi$
$991$	−23.1789	−	40.1470i	−0.736301	−	1.27531i	0.217849	−	0.975983i	$-0.430096\pi$
$992$		0			0
$993$	12.5415	−	13.1552i	0.397993	−	0.417467i
$994$		0			0
$995$	−2.33493	−	1.95924i	−0.0740224	−	0.0621122i
$996$		0			0
$997$	19.6068	+	7.13629i	0.620954	+	0.226009i	0.633289	−	0.773915i	$-0.281704\pi$
$997$	19.6068	+	7.13629i	0.620954	+	0.226009i	−0.0123356	+	0.999924i	$0.503927\pi$
$998$		0			0
$999$	−0.908877	+	4.72149i	−0.0287556	+	0.149381i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.2.u.f.193.5		30
4.3	odd	2		216.2.q.b.193.1	yes	30
12.11	even	2		648.2.q.b.145.3		30
27.7	even	9	inner	432.2.u.f.385.5		30
108.7	odd	18		216.2.q.b.169.1	✓	30
108.47	even	18		648.2.q.b.505.3		30
108.67	odd	18		5832.2.a.k.1.9		15
108.95	even	18		5832.2.a.l.1.7		15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.q.b.169.1	✓	30	108.7	odd	18
216.2.q.b.193.1	yes	30	4.3	odd	2
432.2.u.f.193.5		30	1.1	even	1	trivial
432.2.u.f.385.5		30	27.7	even	9	inner
648.2.q.b.145.3		30	12.11	even	2
648.2.q.b.505.3		30	108.47	even	18
5832.2.a.k.1.9		15	108.67	odd	18
5832.2.a.l.1.7		15	108.95	even	18

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:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	432.u (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.72136 - 0.192108i) q^{3} +(0.0709538 - 0.402399i) q^{5} +(2.76051 - 2.31635i) q^{7} +(2.92619 - 0.661376i) q^{9} +O(q^{10})\)	\(q+(1.72136 - 0.192108i) q^{3} +(0.0709538 - 0.402399i) q^{5} +(2.76051 - 2.31635i) q^{7} +(2.92619 - 0.661376i) q^{9} +(-0.933014 - 5.29139i) q^{11} +(-6.08313 + 2.21408i) q^{13} +(0.0448332 - 0.706306i) q^{15} +(-1.42852 + 2.47428i) q^{17} +(2.71628 + 4.70473i) q^{19} +(4.30686 - 4.51759i) q^{21} +(-2.18286 - 1.83164i) q^{23} +(4.54157 + 1.65300i) q^{25} +(4.90998 - 1.70061i) q^{27} +(2.41013 + 0.877216i) q^{29} +(2.53550 + 2.12754i) q^{31} +(-2.62258 - 8.92917i) q^{33} +(-0.736226 - 1.27518i) q^{35} +(-0.462667 + 0.801362i) q^{37} +(-10.0459 + 4.97985i) q^{39} +(3.40030 - 1.23761i) q^{41} +(0.154105 + 0.873975i) q^{43} +(-0.0585128 - 1.22442i) q^{45} +(-7.89750 + 6.62679i) q^{47} +(1.03944 - 5.89495i) q^{49} +(-1.98368 + 4.53356i) q^{51} -4.56786 q^{53} -2.19545 q^{55} +(5.57952 + 7.57674i) q^{57} +(-1.06184 + 6.02201i) q^{59} +(-4.86002 + 4.07804i) q^{61} +(6.54581 - 8.60380i) q^{63} +(0.459322 + 2.60494i) q^{65} +(5.49728 - 2.00085i) q^{67} +(-4.10937 - 2.73357i) q^{69} +(5.61578 - 9.72681i) q^{71} +(3.59061 + 6.21912i) q^{73} +(8.13525 + 1.97294i) q^{75} +(-14.8323 - 12.4458i) q^{77} +(0.0666470 + 0.0242575i) q^{79} +(8.12516 - 3.87062i) q^{81} +(-15.4725 - 5.63155i) q^{83} +(0.894287 + 0.750396i) q^{85} +(4.31723 + 1.04700i) q^{87} +(3.42863 + 5.93857i) q^{89} +(-11.6640 + 20.2026i) q^{91} +(4.77323 + 3.17517i) q^{93} +(2.08591 - 0.759210i) q^{95} +(2.10988 + 11.9657i) q^{97} +(-6.22977 - 14.8665i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 3 q^{7} - 6 q^{9}+O(q^{10}) \) 30 * q - 3 * q^7 - 6 * q^9	\( 30 q - 3 q^{7} - 6 q^{9} + 3 q^{11} - 12 q^{13} - 15 q^{15} + 6 q^{17} + 9 q^{19} + 30 q^{21} + 12 q^{23} + 24 q^{25} + 15 q^{27} - 9 q^{29} - 27 q^{31} - 30 q^{33} + 18 q^{35} - 15 q^{37} + 21 q^{39} - 15 q^{41} + 30 q^{43} + 15 q^{45} + 18 q^{47} + 15 q^{49} + 6 q^{51} - 18 q^{53} - 54 q^{55} - 72 q^{57} + 12 q^{59} + 6 q^{61} + 54 q^{63} - 54 q^{65} + 45 q^{67} + 9 q^{69} - 36 q^{73} - 69 q^{75} + 12 q^{77} - 45 q^{79} - 30 q^{81} + 3 q^{83} + 57 q^{85} + 60 q^{87} + 36 q^{89} + 39 q^{91} + 30 q^{93} - 51 q^{95} - 84 q^{97} - 162 q^{99}+O(q^{100}) \) 30 * q - 3 * q^7 - 6 * q^9 + 3 * q^11 - 12 * q^13 - 15 * q^15 + 6 * q^17 + 9 * q^19 + 30 * q^21 + 12 * q^23 + 24 * q^25 + 15 * q^27 - 9 * q^29 - 27 * q^31 - 30 * q^33 + 18 * q^35 - 15 * q^37 + 21 * q^39 - 15 * q^41 + 30 * q^43 + 15 * q^45 + 18 * q^47 + 15 * q^49 + 6 * q^51 - 18 * q^53 - 54 * q^55 - 72 * q^57 + 12 * q^59 + 6 * q^61 + 54 * q^63 - 54 * q^65 + 45 * q^67 + 9 * q^69 - 36 * q^73 - 69 * q^75 + 12 * q^77 - 45 * q^79 - 30 * q^81 + 3 * q^83 + 57 * q^85 + 60 * q^87 + 36 * q^89 + 39 * q^91 + 30 * q^93 - 51 * q^95 - 84 * q^97 - 162 * q^99

Introduction

L-functions

Modular forms

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Database

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