LMFDB - Embedded newform 224.2.q.a.143.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [224,2,Mod(47,224)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(224, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 5]))

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

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

chi := DirichletCharacter("224.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 224 = 2^{5} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	224.q (of order $6$, degree $2$, 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:	$1.78864900528$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.144054149089536.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3x^{11} + x^{9} + 48x^{8} - 189x^{7} + 431x^{6} - 654x^{5} + 624x^{4} - 340x^{3} + 96x^{2} - 12x + 4 $ x^12 - 3x^11 + x^9 + 48x^8 - 189x^7 + 431x^6 - 654x^5 + 624x^4 - 340x^3 + 96x^2 - 12*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	no (minimal twist has level 56)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			143.6
Root			$0.609850 + 0.457915i$ of defining polynomial
Character	$\chi$	$=$	224.143
Dual form			224.2.q.a.47.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.27230 + 1.31191i) q^{3} +(1.03926 + 1.80005i) q^{5} +(-1.25203 - 2.33076i) q^{7} +(1.94224 + 3.36406i) q^{9} +O(q^{10})$	\(q+(2.27230 + 1.31191i) q^{3} +(1.03926 + 1.80005i) q^{5} +(-1.25203 - 2.33076i) q^{7} +(1.94224 + 3.36406i) q^{9} +(0.669938 - 1.16037i) q^{11} -2.50406 q^{13} +5.45368i q^{15} +(-2.78212 - 1.60626i) q^{17} +(-3.55442 + 2.05215i) q^{19} +(0.212768 - 6.93874i) q^{21} +(5.54952 - 3.20402i) q^{23} +(0.339877 - 0.588684i) q^{25} +2.32073i q^{27} +4.66151i q^{29} +(-2.21897 + 3.84337i) q^{31} +(3.04461 - 1.75780i) q^{33} +(2.89430 - 4.67598i) q^{35} +(5.50178 - 3.17646i) q^{37} +(-5.68997 - 3.28511i) q^{39} -5.55076i q^{41} +(-4.03699 + 6.99227i) q^{45} +(0.565988 + 0.980320i) q^{47} +(-3.86485 + 5.83634i) q^{49} +(-4.21455 - 7.29981i) q^{51} +(-7.43567 - 4.29299i) q^{53} +2.78496 q^{55} -10.7690 q^{57} +(-6.29193 - 3.63265i) q^{59} +(2.57219 + 4.45517i) q^{61} +(5.40907 - 8.73879i) q^{63} +(-2.60236 - 4.50743i) q^{65} +(-3.93243 + 6.81116i) q^{67} +16.8136 q^{69} -5.29150i q^{71} +(0.480369 + 0.277341i) q^{73} +(1.54461 - 0.891779i) q^{75} +(-3.54332 - 0.108651i) q^{77} +(-5.26862 + 3.04184i) q^{79} +(2.78212 - 4.81877i) q^{81} -0.503175i q^{83} -6.67728i q^{85} +(-6.11551 + 10.5924i) q^{87} +(1.50000 - 0.866025i) q^{89} +(3.13515 + 5.83634i) q^{91} +(-10.0844 + 5.82221i) q^{93} +(-7.38794 - 4.26543i) q^{95} +17.2234i q^{97} +5.20473 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{3}+O(q^{10}) $ 12 * q + 6 * q^3	$ 12 q + 6 q^{3} + 6 q^{11} - 6 q^{17} + 6 q^{19} - 6 q^{33} - 18 q^{35} - 12 q^{49} - 6 q^{51} - 36 q^{57} - 42 q^{59} - 12 q^{65} - 30 q^{67} + 18 q^{73} - 24 q^{75} + 6 q^{81} + 18 q^{89} + 72 q^{91} + 24 q^{99}+O(q^{100}) $ 12 * q + 6 * q^3 + 6 * q^11 - 6 * q^17 + 6 * q^19 - 6 * q^33 - 18 * q^35 - 12 * q^49 - 6 * q^51 - 36 * q^57 - 42 * q^59 - 12 * q^65 - 30 * q^67 + 18 * q^73 - 24 * q^75 + 6 * q^81 + 18 * q^89 + 72 * q^91 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/224\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$197$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	2.27230	+	1.31191i	1.31191	+	0.757434i	0.982413	−	0.186720i	$-0.0597859\pi$
$3$	2.27230	+	1.31191i	1.31191	+	0.757434i	0.329502	+	0.944155i	$0.393119\pi$
$4$		0			0
$5$	1.03926	+	1.80005i	0.464771	+	0.805007i	0.999191	−	0.0402117i	$-0.0128032\pi$
$5$	1.03926	+	1.80005i	0.464771	+	0.805007i	−0.534420	+	0.845219i	$0.679470\pi$
$6$		0			0
$7$	−1.25203	−	2.33076i	−0.473222	−	0.880943i
$7$	−1.25203	−	2.33076i	−0.473222	−	0.880943i
$8$		0			0
$9$	1.94224	+	3.36406i	0.647414	+	1.12135i
$10$		0			0
$11$	0.669938	−	1.16037i	0.201994	−	0.349864i	−0.747177	−	0.664625i	$-0.768591\pi$
$11$	0.669938	−	1.16037i	0.201994	−	0.349864i	0.949171	+	0.314761i	$0.101925\pi$
$12$		0			0
$13$	−2.50406			−0.694500			−0.347250	−	0.937773i	$-0.612884\pi$
$13$	−2.50406			−0.694500			−0.347250	+	0.937773i	$0.612884\pi$
$14$		0			0
$15$			5.45368i			1.40814i
$16$		0			0
$17$	−2.78212	−	1.60626i	−0.674763	−	0.389575i	0.123116	−	0.992392i	$-0.460711\pi$
$17$	−2.78212	−	1.60626i	−0.674763	−	0.389575i	−0.797879	+	0.602818i	$0.794045\pi$
$18$		0			0
$19$	−3.55442	+	2.05215i	−0.815440	+	0.470795i	−0.848842	−	0.528647i	$-0.822699\pi$
$19$	−3.55442	+	2.05215i	−0.815440	+	0.470795i	0.0334012	+	0.999442i	$0.489366\pi$
$20$		0			0
$21$	0.212768	−	6.93874i	0.0464297	−	1.51416i
$22$		0			0
$23$	5.54952	−	3.20402i	1.15716	−	0.668084i	0.206535	−	0.978439i	$-0.433781\pi$
$23$	5.54952	−	3.20402i	1.15716	−	0.668084i	0.950621	+	0.310355i	$0.100448\pi$
$24$		0			0
$25$	0.339877	−	0.588684i	0.0679754	−	0.117737i
$26$		0			0
$27$			2.32073i			0.446626i
$28$		0			0
$29$			4.66151i			0.865621i	0.901485	+	0.432811i	$0.142478\pi$
$29$			4.66151i			0.865621i	−0.901485	+	0.432811i	$0.857522\pi$
$30$		0			0
$31$	−2.21897	+	3.84337i	−0.398539	+	0.690290i	−0.993546	−	0.113430i	$-0.963816\pi$
$31$	−2.21897	+	3.84337i	−0.398539	+	0.690290i	0.595007	+	0.803721i	$0.297149\pi$
$32$		0			0
$33$	3.04461	−	1.75780i	0.529998	−	0.305994i
$34$		0			0
$35$	2.89430	−	4.67598i	0.489226	−	0.790384i
$36$		0			0
$37$	5.50178	−	3.17646i	0.904488	−	0.522206i	0.0258343	−	0.999666i	$-0.491776\pi$
$37$	5.50178	−	3.17646i	0.904488	−	0.522206i	0.878653	+	0.477460i	$0.158442\pi$
$38$		0			0
$39$	−5.68997	−	3.28511i	−0.911125	−	0.526038i
$40$		0			0
$41$		−	5.55076i		−	0.866882i	−0.901182	−	0.433441i	$-0.857299\pi$
$41$		−	5.55076i		−	0.866882i	0.901182	−	0.433441i	$-0.142701\pi$
$42$		0			0
$43$		0			0			−	1.00000i	$-0.5\pi$
$43$		0			0				1.00000i	$0.5\pi$
$44$		0			0
$45$	−4.03699	+	6.99227i	−0.601799	+	1.04235i
$46$		0			0
$47$	0.565988	+	0.980320i	0.0825579	+	0.142994i	0.904348	−	0.426796i	$-0.140358\pi$
$47$	0.565988	+	0.980320i	0.0825579	+	0.142994i	−0.821790	+	0.569790i	$0.807024\pi$
$48$		0			0
$49$	−3.86485	+	5.83634i	−0.552122	+	0.833763i
$50$		0			0
$51$	−4.21455	−	7.29981i	−0.590154	−	1.02218i
$52$		0			0
$53$	−7.43567	−	4.29299i	−1.02137	−	0.589687i	−0.106868	−	0.994273i	$-0.534082\pi$
$53$	−7.43567	−	4.29299i	−1.02137	−	0.589687i	−0.914500	+	0.404586i	$0.867416\pi$
$54$		0			0
$55$	2.78496			0.375524
$56$		0			0
$57$	−10.7690			−1.42638
$58$		0			0
$59$	−6.29193	−	3.63265i	−0.819140	−	0.472931i	0.0309798	−	0.999520i	$-0.490137\pi$
$59$	−6.29193	−	3.63265i	−0.819140	−	0.472931i	−0.850120	+	0.526589i	$0.823471\pi$
$60$		0			0
$61$	2.57219	+	4.45517i	0.329336	+	0.570426i	0.982380	−	0.186893i	$-0.0598419\pi$
$61$	2.57219	+	4.45517i	0.329336	+	0.570426i	−0.653045	+	0.757319i	$0.726509\pi$
$62$		0			0
$63$	5.40907	−	8.73879i	0.681479	−	1.10098i
$64$		0			0
$65$	−2.60236	−	4.50743i	−0.322784	−	0.559078i
$66$		0			0
$67$	−3.93243	+	6.81116i	−0.480422	+	0.832116i	−0.999748	−	0.0224607i	$-0.992850\pi$
$67$	−3.93243	+	6.81116i	−0.480422	+	0.832116i	0.519325	+	0.854577i	$0.326183\pi$
$68$		0			0
$69$	16.8136			2.02412
$70$		0			0
$71$		−	5.29150i		−	0.627986i	−0.949425	−	0.313993i	$-0.898333\pi$
$71$		−	5.29150i		−	0.627986i	0.949425	−	0.313993i	$-0.101667\pi$
$72$		0			0
$73$	0.480369	+	0.277341i	0.0562230	+	0.0324604i	0.527848	−	0.849339i	$-0.322999\pi$
$73$	0.480369	+	0.277341i	0.0562230	+	0.0324604i	−0.471625	+	0.881799i	$0.656332\pi$
$74$		0			0
$75$	1.54461	−	0.891779i	0.178356	−	0.102974i
$76$		0			0
$77$	−3.54332	−	0.108651i	−0.403798	−	0.0123820i
$78$		0			0
$79$	−5.26862	+	3.04184i	−0.592766	+	0.342233i	−0.766190	−	0.642614i	$-0.777850\pi$
$79$	−5.26862	+	3.04184i	−0.592766	+	0.342233i	0.173425	+	0.984847i	$0.444517\pi$
$80$		0			0
$81$	2.78212	−	4.81877i	0.309124	−	0.535419i
$82$		0			0
$83$		−	0.503175i		−	0.0552307i	−0.999619	−	0.0276153i	$-0.991209\pi$
$83$		−	0.503175i		−	0.0552307i	0.999619	−	0.0276153i	$-0.00879135\pi$
$84$		0			0
$85$		−	6.67728i		−	0.724252i
$86$		0			0
$87$	−6.11551	+	10.5924i	−0.655651	+	1.13562i
$88$		0			0
$89$	1.50000	−	0.866025i	0.159000	−	0.0917985i	−0.418389	−	0.908268i	$-0.637405\pi$
$89$	1.50000	−	0.866025i	0.159000	−	0.0917985i	0.577389	+	0.816469i	$0.304072\pi$
$90$		0			0
$91$	3.13515	+	5.83634i	0.328653	+	0.611815i
$92$		0			0
$93$	−10.0844	+	5.82221i	−1.04570	+	0.603735i
$94$		0			0
$95$	−7.38794	−	4.26543i	−0.757986	−	0.437624i
$96$		0			0
$97$			17.2234i			1.74878i	0.485228	+	0.874388i	$0.338737\pi$
$97$			17.2234i			1.74878i	−0.485228	+	0.874388i	$0.661263\pi$
$98$		0			0
$99$	5.20473			0.523095
$100$		0			0
$101$	−0.613725	+	1.06300i	−0.0610679	+	0.105773i	−0.894943	−	0.446180i	$-0.852784\pi$
$101$	−0.613725	+	1.06300i	−0.0610679	+	0.105773i	0.833875	+	0.551953i	$0.186117\pi$
$102$		0			0
$103$	7.62804	+	13.2122i	0.751613	+	1.30183i	0.947041	+	0.321114i	$0.104057\pi$
$103$	7.62804	+	13.2122i	0.751613	+	1.30183i	−0.195427	+	0.980718i	$0.562609\pi$
$104$		0			0
$105$	12.7112	−	6.82816i	1.24049	−	0.666360i
$106$		0			0
$107$	5.55442	+	9.62054i	0.536966	+	0.930053i	0.999065	+	0.0432246i	$0.0137631\pi$
$107$	5.55442	+	9.62054i	0.536966	+	0.930053i	−0.462099	+	0.886828i	$0.652904\pi$
$108$		0			0
$109$	−10.9109	−	6.29938i	−1.04507	−	0.603372i	−0.123805	−	0.992307i	$-0.539510\pi$
$109$	−10.9109	−	6.29938i	−1.04507	−	0.603372i	−0.921265	+	0.388935i	$0.872843\pi$
$110$		0			0
$111$	16.6690			1.58215
$112$		0			0
$113$	20.0629			1.88736			0.943680	−	0.330860i	$-0.107339\pi$
$113$	20.0629			1.88736			0.943680	+	0.330860i	$0.107339\pi$
$114$		0			0
$115$	11.5348	+	6.65961i	1.07562	+	0.621012i
$116$		0			0
$117$	−4.86348	−	8.42380i	−0.449629	−	0.778780i
$118$		0			0
$119$	−0.260504	+	8.49552i	−0.0238804	+	0.778783i
$120$		0			0
$121$	4.60236	+	7.97153i	0.418397	+	0.724685i
$122$		0			0
$123$	7.28212	−	12.6130i	0.656607	−	1.13728i
$124$		0			0
$125$	11.8055			1.05591
$126$		0			0
$127$		−	14.6145i		−	1.29683i	−0.761287	−	0.648415i	$-0.775432\pi$
$127$		−	14.6145i		−	1.29683i	0.761287	−	0.648415i	$-0.224568\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	5.27230	−	3.04397i	0.460643	−	0.265953i	−0.251671	−	0.967813i	$-0.580980\pi$
$131$	5.27230	−	3.04397i	0.460643	−	0.265953i	0.712315	+	0.701860i	$0.247647\pi$
$132$		0			0
$133$	9.23329	+	5.71515i	0.800628	+	0.495566i
$134$		0			0
$135$	−4.17744	+	2.41185i	−0.359537	+	0.207579i
$136$		0			0
$137$	−6.98685	+	12.1016i	−0.596927	+	1.03391i	0.396345	+	0.918102i	$0.370278\pi$
$137$	−6.98685	+	12.1016i	−0.596927	+	1.03391i	−0.993272	+	0.115806i	$0.963055\pi$
$138$		0			0
$139$			0.503175i			0.0426788i	0.999772	+	0.0213394i	$0.00679305\pi$
$139$			0.503175i			0.0426788i	−0.999772	+	0.0213394i	$0.993207\pi$
$140$		0			0
$141$			2.97011i			0.250129i
$142$		0			0
$143$	−1.67756	+	2.90562i	−0.140285	+	0.242981i
$144$		0			0
$145$	−8.39096	+	4.84452i	−0.696832	+	0.402316i
$146$		0			0
$147$	−16.4389	+	8.19159i	−1.35586	+	0.675631i
$148$		0			0
$149$	4.77077	−	2.75440i	0.390836	−	0.225649i	−0.291686	−	0.956514i	$-0.594216\pi$
$149$	4.77077	−	2.75440i	0.390836	−	0.225649i	0.682522	+	0.730865i	$0.260883\pi$
$150$		0			0
$151$	−6.09511	−	3.51901i	−0.496013	−	0.286373i	0.231053	−	0.972941i	$-0.425783\pi$
$151$	−6.09511	−	3.51901i	−0.496013	−	0.286373i	−0.727066	+	0.686568i	$0.759116\pi$
$152$		0			0
$153$		−	12.4790i		−	1.00886i
$154$		0			0
$155$	−9.22436			−0.740918
$156$		0			0
$157$	−7.15477	+	12.3924i	−0.571013	+	0.989023i	0.425450	+	0.904982i	$0.360116\pi$
$157$	−7.15477	+	12.3924i	−0.571013	+	0.989023i	−0.996462	+	0.0840409i	$0.973217\pi$
$158$		0			0
$159$	−11.2641	−	19.5099i	−0.893299	−	1.54724i
$160$		0			0
$161$	−14.4159	−	8.92306i	−1.13614	−	0.703236i
$162$		0			0
$163$	4.15679	+	7.19977i	0.325585	+	0.563929i	0.981631	−	0.190792i	$-0.0611055\pi$
$163$	4.15679	+	7.19977i	0.325585	+	0.563929i	−0.656046	+	0.754721i	$0.727772\pi$
$164$		0			0
$165$	6.32828	+	3.65363i	0.492656	+	0.284435i
$166$		0			0
$167$	2.50406			0.193770			0.0968848	−	0.995296i	$-0.469112\pi$
$167$	2.50406			0.193770			0.0968848	+	0.995296i	$0.469112\pi$
$168$		0			0
$169$	−6.72971			−0.517670
$170$		0			0
$171$	−13.8071	−	7.97153i	−1.05585	−	0.609598i
$172$		0			0
$173$	2.71682	+	4.70568i	0.206556	+	0.357766i	0.950627	−	0.310334i	$-0.100441\pi$
$173$	2.71682	+	4.70568i	0.206556	+	0.357766i	−0.744071	+	0.668100i	$0.767108\pi$
$174$		0			0
$175$	−1.79761	−	0.0551216i	−0.135887	−	0.00416680i
$176$		0			0
$177$	−9.53146	−	16.5090i	−0.716428	−	1.24089i
$178$		0			0
$179$	1.75915	−	3.04694i	0.131485	−	0.227739i	−0.792764	−	0.609529i	$-0.791359\pi$
$179$	1.75915	−	3.04694i	0.131485	−	0.227739i	0.924249	+	0.381790i	$0.124692\pi$
$180$		0			0
$181$	−22.1981			−1.64997			−0.824985	−	0.565154i	$-0.808817\pi$
$181$	−22.1981			−1.64997			−0.824985	+	0.565154i	$0.808817\pi$
$182$		0			0
$183$			13.4980i			0.997801i
$184$		0			0
$185$	11.4356	+	6.60233i	0.840760	+	0.485413i
$186$		0			0
$187$	−3.72770	+	2.15219i	−0.272596	+	0.157383i
$188$		0			0
$189$	5.40907	−	2.90562i	0.393452	−	0.211353i
$190$		0			0
$191$	1.13615	−	0.655958i	0.0822091	−	0.0474635i	−0.458332	−	0.888781i	$-0.651553\pi$
$191$	1.13615	−	0.655958i	0.0822091	−	0.0474635i	0.540541	+	0.841318i	$0.318220\pi$
$192$		0			0
$193$	5.64697	−	9.78084i	0.406478	−	0.704040i	−0.588014	−	0.808851i	$-0.700090\pi$
$193$	5.64697	−	9.78084i	0.406478	−	0.704040i	0.994492	+	0.104810i	$0.0334235\pi$
$194$		0			0
$195$		−	13.6563i		−	0.977950i
$196$		0			0
$197$		−	5.92149i		−	0.421889i	−0.977498	−	0.210944i	$-0.932346\pi$
$197$		−	5.92149i		−	0.421889i	0.977498	−	0.210944i	$-0.0676539\pi$
$198$		0			0
$199$	9.30560	−	16.1178i	0.659657	−	1.14256i	−0.321048	−	0.947063i	$-0.604035\pi$
$199$	9.30560	−	16.1178i	0.659657	−	1.14256i	0.980704	−	0.195496i	$-0.0626317\pi$
$200$		0			0
$201$	−17.8713	+	10.3180i	−1.26055	+	0.727777i
$202$		0			0
$203$	10.8649	−	5.83634i	0.762563	−	0.409631i
$204$		0			0
$205$	9.99164	−	5.76868i	0.697847	−	0.402902i
$206$		0			0
$207$	21.5570	+	12.4460i	1.49832	+	0.865054i
$208$		0			0
$209$			5.49925i			0.380391i
$210$		0			0
$211$	−5.72971			−0.394449			−0.197225	−	0.980358i	$-0.563193\pi$
$211$	−5.72971			−0.394449			−0.197225	+	0.980358i	$0.563193\pi$
$212$		0			0
$213$	6.94200	−	12.0239i	0.475658	−	0.823864i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	11.7362	+	0.359875i	0.796704	+	0.0244299i
$218$		0			0
$219$	0.727697	+	1.26041i	0.0491732	+	0.0851704i
$220$		0			0
$221$	6.96658	+	4.02216i	0.468623	+	0.270560i
$222$		0			0
$223$	−20.8668			−1.39734			−0.698672	−	0.715442i	$-0.746225\pi$
$223$	−20.8668			−1.39734			−0.698672	+	0.715442i	$0.746225\pi$
$224$		0			0
$225$	2.64049			0.176033
$226$		0			0
$227$	−14.2775	−	8.24309i	−0.947628	−	0.547113i	−0.0552847	−	0.998471i	$-0.517607\pi$
$227$	−14.2775	−	8.24309i	−0.947628	−	0.547113i	−0.892343	+	0.451357i	$0.850940\pi$
$228$		0			0
$229$	4.24976	+	7.36079i	0.280832	+	0.486415i	0.971590	−	0.236671i	$-0.0760564\pi$
$229$	4.24976	+	7.36079i	0.280832	+	0.486415i	−0.690758	+	0.723086i	$0.742723\pi$
$230$		0			0
$231$	−7.90895	−	4.89542i	−0.520371	−	0.322095i
$232$		0			0
$233$	−2.23751	−	3.87548i	−0.146584	−	0.253891i	0.783379	−	0.621545i	$-0.213495\pi$
$233$	−2.23751	−	3.87548i	−0.146584	−	0.253891i	−0.929963	+	0.367653i	$0.880161\pi$
$234$		0			0
$235$	−1.17642	+	2.03762i	−0.0767410	+	0.132919i
$236$		0			0
$237$	−15.9625			−1.03688
$238$		0			0
$239$			24.5675i			1.58914i	0.607171	+	0.794571i	$0.292304\pi$
$239$			24.5675i			1.58914i	−0.607171	+	0.794571i	$0.707696\pi$
$240$		0			0
$241$	−5.02498	−	2.90117i	−0.323687	−	0.186881i	0.329348	−	0.944209i	$-0.393171\pi$
$241$	−5.02498	−	2.90117i	−0.323687	−	0.186881i	−0.653035	+	0.757328i	$0.726505\pi$
$242$		0			0
$243$	18.6731	−	10.7809i	1.19788	−	0.691596i
$244$		0			0
$245$	−14.5223	−	0.891454i	−0.927796	−	0.0569529i
$246$		0			0
$247$	8.90047	−	5.13869i	0.566323	−	0.326967i
$248$		0			0
$249$	0.660123	−	1.14337i	0.0418336	−	0.0724579i
$250$		0			0
$251$			18.8010i			1.18671i	0.804942	+	0.593353i	$0.202196\pi$
$251$			18.8010i			1.18671i	−0.804942	+	0.593353i	$0.797804\pi$
$252$		0			0
$253$		−	8.58598i		−	0.539796i
$254$		0			0
$255$	8.76002	−	15.1728i	0.548574	−	0.950157i
$256$		0			0
$257$	10.9106	−	6.29923i	0.680584	−	0.392935i	−0.119491	−	0.992835i	$-0.538126\pi$
$257$	10.9106	−	6.29923i	0.680584	−	0.392935i	0.800075	+	0.599900i	$0.204793\pi$
$258$		0			0
$259$	−14.2919	−	8.84631i	−0.888058	−	0.549683i
$260$		0			0
$261$	−15.6816	+	9.05379i	−0.970668	+	0.560415i
$262$		0			0
$263$	4.27292	+	2.46697i	0.263479	+	0.152120i	0.625921	−	0.779887i	$-0.284723\pi$
$263$	4.27292	+	2.46697i	0.263479	+	0.152120i	−0.362441	+	0.932007i	$0.618057\pi$
$264$		0			0
$265$		−	17.8461i		−	1.09628i
$266$		0			0
$267$	4.54461			0.278125
$268$		0			0
$269$	13.1502	−	22.7769i	0.801783	−	1.38873i	−0.116658	−	0.993172i	$-0.537218\pi$
$269$	13.1502	−	22.7769i	0.801783	−	1.38873i	0.918441	−	0.395558i	$-0.129449\pi$
$270$		0			0
$271$	14.0490	+	24.3336i	0.853418	+	1.47816i	0.878105	+	0.478468i	$0.158808\pi$
$271$	14.0490	+	24.3336i	0.853418	+	1.47816i	−0.0246868	+	0.999695i	$0.507859\pi$
$272$		0			0
$273$	−0.532782	+	17.3750i	−0.0322454	+	1.05158i
$274$		0			0
$275$	−0.455393	−	0.788764i	−0.0274612	−	0.0475643i
$276$		0			0
$277$	23.3982	+	13.5090i	1.40586	+	0.811675i	0.994986	−	0.100017i	$-0.0318897\pi$
$277$	23.3982	+	13.5090i	1.40586	+	0.811675i	0.410876	+	0.911691i	$0.365223\pi$
$278$		0			0
$279$	−17.2391			−1.03208
$280$		0			0
$281$	−20.0629			−1.19685			−0.598426	−	0.801178i	$-0.704207\pi$
$281$	−20.0629			−1.19685			−0.598426	+	0.801178i	$0.704207\pi$
$282$		0			0
$283$	4.75248	+	2.74385i	0.282506	+	0.163105i	0.634557	−	0.772876i	$-0.281183\pi$
$283$	4.75248	+	2.74385i	0.282506	+	0.163105i	−0.352052	+	0.935981i	$0.614516\pi$
$284$		0			0
$285$	−11.1918	−	19.3847i	−0.662943	−	1.14825i
$286$		0			0
$287$	−12.9375	+	6.94970i	−0.763674	+	0.410228i
$288$		0			0
$289$	−3.33988	−	5.78484i	−0.196463	−	0.340284i
$290$		0			0
$291$	−22.5957	+	39.1369i	−1.32458	+	2.29425i
$292$		0			0
$293$	−13.6931			−0.799957			−0.399978	−	0.916525i	$-0.630982\pi$
$293$	−13.6931			−0.799957			−0.399978	+	0.916525i	$0.630982\pi$
$294$		0			0
$295$		−	15.1011i		−	0.879218i
$296$		0			0
$297$	2.69291	+	1.55475i	0.156258	+	0.0902157i
$298$		0			0
$299$	−13.8963	+	8.02304i	−0.803644	+	0.463984i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	−2.78914	+	1.61031i	−0.160232	+	0.0925099i
$304$		0			0
$305$	−5.34636	+	9.26016i	−0.306131	+	0.530235i
$306$		0			0
$307$		−	24.4197i		−	1.39371i	−0.717213	−	0.696854i	$-0.754583\pi$
$307$		−	24.4197i		−	1.39371i	0.717213	−	0.696854i	$-0.245417\pi$
$308$		0			0
$309$			40.0294i			2.27719i
$310$		0			0
$311$	8.61539	−	14.9223i	0.488534	−	0.846165i	−0.511379	−	0.859355i	$-0.670865\pi$
$311$	8.61539	−	14.9223i	0.488534	−	0.846165i	0.999913	+	0.0131898i	$0.00419856\pi$
$312$		0			0
$313$	15.0446	−	8.68601i	0.850371	−	0.490962i	−0.0104047	−	0.999946i	$-0.503312\pi$
$313$	15.0446	−	8.68601i	0.850371	−	0.490962i	0.860776	+	0.508984i	$0.169979\pi$
$314$		0			0
$315$	21.3517	+	0.654723i	1.20303	+	0.0368894i
$316$		0			0
$317$	16.7863	−	9.69155i	0.942810	−	0.544332i	0.0519701	−	0.998649i	$-0.483450\pi$
$317$	16.7863	−	9.69155i	0.942810	−	0.544332i	0.890840	+	0.454317i	$0.150117\pi$
$318$		0			0
$319$	5.40907	+	3.12293i	0.302850	+	0.174850i
$320$		0			0
$321$			29.1477i			1.62687i
$322$		0			0
$323$	13.1851			0.733639
$324$		0			0
$325$	−0.851071	+	1.47410i	−0.0472089	+	0.0817682i
$326$		0			0
$327$	−16.5285	−	28.6282i	−0.914029	−	1.58314i
$328$		0			0
$329$	1.57625	−	2.54657i	0.0869018	−	0.140397i
$330$		0			0
$331$	−10.4008	−	18.0147i	−0.571678	−	0.990176i	−0.996394	−	0.0848492i	$-0.972959\pi$
$331$	−10.4008	−	18.0147i	−0.571678	−	0.990176i	0.424715	−	0.905327i	$-0.360374\pi$
$332$		0			0
$333$	21.3716	+	12.3389i	1.17116	+	0.676167i
$334$		0			0
$335$	−16.3473			−0.893146
$336$		0			0
$337$	10.3332			0.562886			0.281443	−	0.959578i	$-0.409187\pi$
$337$	10.3332			0.562886			0.281443	+	0.959578i	$0.409187\pi$
$338$		0			0
$339$	45.5890	+	26.3208i	2.47606	+	1.42955i
$340$		0			0
$341$	2.97315	+	5.14965i	0.161005	+	0.278869i
$342$		0			0
$343$	18.4420	+	1.70077i	0.995774	+	0.0918328i
$344$		0			0
$345$	17.4737	+	30.2653i	0.940752	+	1.62943i
$346$		0			0
$347$	16.8169	−	29.1277i	0.902779	−	1.56366i	0.0789080	−	0.996882i	$-0.474857\pi$
$347$	16.8169	−	29.1277i	0.902779	−	1.56366i	0.823871	−	0.566777i	$-0.191810\pi$
$348$		0			0
$349$	−13.3546			−0.714858			−0.357429	−	0.933940i	$-0.616347\pi$
$349$	−13.3546			−0.714858			−0.357429	+	0.933940i	$0.616347\pi$
$350$		0			0
$351$		−	5.81125i		−	0.310182i
$352$		0			0
$353$	6.80175	+	3.92699i	0.362021	+	0.209013i	0.669967	−	0.742391i	$-0.266308\pi$
$353$	6.80175	+	3.92699i	0.362021	+	0.209013i	−0.307946	+	0.951404i	$0.599642\pi$
$354$		0			0
$355$	9.52498	−	5.49925i	0.505533	−	0.291870i
$356$		0			0
$357$	−11.7373	+	18.9626i	−0.621206	+	1.00361i
$358$		0			0
$359$	0.140453	−	0.0810905i	0.00741282	−	0.00427979i	−0.496289	−	0.868157i	$-0.665304\pi$
$359$	0.140453	−	0.0810905i	0.00741282	−	0.00427979i	0.503702	+	0.863878i	$0.331971\pi$
$360$		0			0
$361$	−1.07739	+	1.86609i	−0.0567047	+	0.0982154i
$362$		0			0
$363$			24.1516i			1.26763i
$364$		0			0
$365$			1.15292i			0.0603466i
$366$		0			0
$367$	−10.1321	+	17.5493i	−0.528891	+	0.916066i	0.470541	+	0.882378i	$0.344059\pi$
$367$	−10.1321	+	17.5493i	−0.528891	+	0.916066i	−0.999432	+	0.0336883i	$0.989275\pi$
$368$		0			0
$369$	18.6731	−	10.7809i	0.972082	−	0.561232i
$370$		0			0
$371$	−0.696241	+	22.7057i	−0.0361470	+	1.17882i
$372$		0			0
$373$	−5.78269	+	3.33864i	−0.299416	+	0.172868i	−0.642181	−	0.766553i	$-0.721970\pi$
$373$	−5.78269	+	3.33864i	−0.299416	+	0.172868i	0.342764	+	0.939421i	$0.388637\pi$
$374$		0			0
$375$	26.8256	+	15.4878i	1.38527	+	0.799786i
$376$		0			0
$377$		−	11.6727i		−	0.601174i
$378$		0			0
$379$	4.60350			0.236466			0.118233	−	0.992986i	$-0.462277\pi$
$379$	4.60350			0.236466			0.118233	+	0.992986i	$0.462277\pi$
$380$		0			0
$381$	19.1730	−	33.2086i	0.982264	−	1.70133i
$382$		0			0
$383$	−5.71038	−	9.89066i	−0.291787	−	0.505389i	0.682446	−	0.730936i	$-0.260916\pi$
$383$	−5.71038	−	9.89066i	−0.291787	−	0.505389i	−0.974232	+	0.225547i	$0.927583\pi$
$384$		0			0
$385$	−3.48685	−	6.49107i	−0.177706	−	0.330815i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−26.0307	−	15.0288i	−1.31981	−	0.761991i	−0.336109	−	0.941823i	$-0.609111\pi$
$389$	−26.0307	−	15.0288i	−1.31981	−	0.761991i	−0.983697	+	0.179832i	$0.942445\pi$
$390$		0			0
$391$	−20.5859			−1.04107
$392$		0			0
$393$	15.9737			0.805766
$394$		0			0
$395$	−10.9509	−	6.32252i	−0.551001	−	0.318120i
$396$		0			0
$397$	−2.17124	−	3.76069i	−0.108971	−	0.188744i	0.806383	−	0.591394i	$-0.201422\pi$
$397$	−2.17124	−	3.76069i	−0.108971	−	0.188744i	−0.915354	+	0.402651i	$0.868089\pi$
$398$		0			0
$399$	13.4830	+	25.0998i	0.674997	+	1.25656i
$400$		0			0
$401$	9.98685	+	17.2977i	0.498719	+	0.863807i	0.999999	−	0.00147805i	$-0.000470479\pi$
$401$	9.98685	+	17.2977i	0.498719	+	0.863807i	−0.501279	+	0.865285i	$0.667137\pi$
$402$		0			0
$403$	5.55643	−	9.62402i	0.276786	−	0.479407i
$404$		0			0
$405$	11.5654			0.574688
$406$		0			0
$407$		−	8.51212i		−	0.421930i
$408$		0			0
$409$	−26.4356	−	15.2626i	−1.30715	−	0.754686i	−0.325534	−	0.945530i	$-0.605544\pi$
$409$	−26.4356	−	15.2626i	−1.30715	−	0.754686i	−0.981620	+	0.190844i	$0.938878\pi$
$410$		0			0
$411$	−31.7525	+	18.3323i	−1.56623	+	0.904266i
$412$		0			0
$413$	−0.589147	+	19.2131i	−0.0289900	+	0.945417i
$414$		0			0
$415$	0.905741	−	0.522930i	0.0444611	−	0.0256696i
$416$		0			0
$417$	−0.660123	+	1.14337i	−0.0323264	+	0.0559909i
$418$		0			0
$419$		−	2.08070i		−	0.101649i	−0.998708	−	0.0508245i	$-0.983815\pi$
$419$		−	2.08070i		−	0.101649i	0.998708	−	0.0508245i	$-0.0161849\pi$
$420$		0			0
$421$		−	30.4039i		−	1.48180i	−0.671618	−	0.740898i	$-0.734400\pi$
$421$		−	30.4039i		−	1.48180i	0.671618	−	0.740898i	$-0.265600\pi$
$422$		0			0
$423$	−2.19857	+	3.80804i	−0.106898	+	0.185153i
$424$		0			0
$425$	−1.89116	+	1.09186i	−0.0917345	+	0.0529630i
$426$		0			0
$427$	7.16346	−	11.5732i	0.346664	−	0.560064i
$428$		0			0
$429$	−7.62386	+	4.40164i	−0.368084	+	0.212513i
$430$		0			0
$431$	−2.32280	−	1.34107i	−0.111885	−	0.0645970i	0.443013	−	0.896515i	$-0.353910\pi$
$431$	−2.32280	−	1.34107i	−0.111885	−	0.0645970i	−0.554898	+	0.831918i	$0.687243\pi$
$432$		0			0
$433$		−	29.4673i		−	1.41611i	−0.706158	−	0.708054i	$-0.749573\pi$
$433$		−	29.4673i		−	1.41611i	0.706158	−	0.708054i	$-0.250427\pi$
$434$		0			0
$435$	−25.4224			−1.21891
$436$		0			0
$437$	−13.1502	+	22.7769i	−0.629061	+	1.08957i
$438$		0			0
$439$	3.77648	+	6.54106i	0.180242	+	0.312188i	0.941963	−	0.335717i	$-0.108979\pi$
$439$	3.77648	+	6.54106i	0.180242	+	0.312188i	−0.761721	+	0.647905i	$0.775645\pi$
$440$		0			0
$441$	−27.1403	−	1.66601i	−1.29240	−	0.0793339i
$442$		0			0
$443$	−3.75915	−	6.51104i	−0.178603	−	0.309349i	0.762799	−	0.646635i	$-0.223824\pi$
$443$	−3.75915	−	6.51104i	−0.178603	−	0.309349i	−0.941402	+	0.337286i	$0.890491\pi$
$444$		0			0
$445$	3.11778	+	1.80005i	0.147797	+	0.0853306i
$446$		0			0
$447$	14.4542			0.683659
$448$		0			0
$449$	−14.3332			−0.676426			−0.338213	−	0.941070i	$-0.609822\pi$
$449$	−14.3332			−0.676426			−0.338213	+	0.941070i	$0.609822\pi$
$450$		0			0
$451$	−6.44092	−	3.71866i	−0.303291	−	0.175105i
$452$		0			0
$453$	−9.23329	−	15.9925i	−0.433818	−	0.751394i
$454$		0			0
$455$	−7.24749	+	11.7089i	−0.339767	+	0.548922i
$456$		0			0
$457$	−6.48037	−	11.2243i	−0.303139	−	0.525052i	0.673706	−	0.738999i	$-0.264701\pi$
$457$	−6.48037	−	11.2243i	−0.303139	−	0.525052i	−0.976845	+	0.213947i	$0.931368\pi$
$458$		0			0
$459$	3.72770	−	6.45656i	0.173994	−	0.301366i
$460$		0			0
$461$	33.3871			1.55499			0.777496	−	0.628888i	$-0.216490\pi$
$461$	33.3871			1.55499			0.777496	+	0.628888i	$0.216490\pi$
$462$		0			0
$463$		−	29.7739i		−	1.38371i	−0.722036	−	0.691855i	$-0.756794\pi$
$463$		−	29.7739i		−	1.38371i	0.722036	−	0.691855i	$-0.243206\pi$
$464$		0			0
$465$	−20.9605	−	12.1016i	−0.972022	−	0.561197i
$466$		0			0
$467$	−23.5399	+	13.5908i	−1.08930	+	0.628907i	−0.933390	−	0.358865i	$-0.883164\pi$
$467$	−23.5399	+	13.5908i	−1.08930	+	0.628907i	−0.155909	+	0.987771i	$0.549831\pi$
$468$		0			0
$469$	20.7987	+	0.637765i	0.960393	+	0.0294492i
$470$		0			0
$471$	−32.5156	+	18.7729i	−1.49824	+	0.865009i
$472$		0			0
$473$		0			0
$474$		0			0
$475$			2.78991i			0.128010i
$476$		0			0
$477$		−	33.3521i		−	1.52709i
$478$		0			0
$479$	17.2187	−	29.8237i	0.786744	−	1.36268i	−0.141208	−	0.989980i	$-0.545099\pi$
$479$	17.2187	−	29.8237i	0.786744	−	1.36268i	0.927952	−	0.372700i	$-0.121568\pi$
$480$		0			0
$481$	−13.7768	+	7.95402i	−0.628167	+	0.362672i
$482$		0			0
$483$	−21.0511	−	39.1884i	−0.957858	−	1.78313i
$484$		0			0
$485$	−31.0031	+	17.8996i	−1.40778	+	0.812781i
$486$		0			0
$487$	6.82613	+	3.94107i	0.309321	+	0.178587i	0.646623	−	0.762810i	$-0.276181\pi$
$487$	6.82613	+	3.94107i	0.309321	+	0.178587i	−0.337301	+	0.941397i	$0.609514\pi$
$488$		0			0
$489$			21.8134i			0.986436i
$490$		0			0
$491$	8.06291			0.363874			0.181937	−	0.983310i	$-0.441763\pi$
$491$	8.06291			0.363874			0.181937	+	0.983310i	$0.441763\pi$
$492$		0			0
$493$	7.48759	−	12.9689i	0.337224	−	0.584089i
$494$		0			0
$495$	5.40907	+	9.36878i	0.243120	+	0.421095i
$496$		0			0
$497$	−12.3332	+	6.62511i	−0.553220	+	0.297177i
$498$		0			0
$499$	−12.0216	−	20.8221i	−0.538163	−	0.932125i	−0.999003	−	0.0446419i	$-0.985785\pi$
$499$	−12.0216	−	20.8221i	−0.538163	−	0.932125i	0.460841	−	0.887483i	$-0.347548\pi$
$500$		0			0
$501$	5.68997	+	3.28511i	0.254209	+	0.146768i
$502$		0			0
$503$	40.8993			1.82361			0.911804	−	0.410626i	$-0.134690\pi$
$503$	40.8993			1.82361			0.911804	+	0.410626i	$0.134690\pi$
$504$		0			0
$505$	−2.55128			−0.113530
$506$		0			0
$507$	−15.2919	−	8.82880i	−0.679139	−	0.392101i
$508$		0			0
$509$	−2.02661	−	3.51019i	−0.0898278	−	0.155586i	0.817610	−	0.575772i	$-0.195298\pi$
$509$	−2.02661	−	3.51019i	−0.0898278	−	0.155586i	−0.907438	+	0.420186i	$0.861965\pi$
$510$		0			0
$511$	0.0449795	−	1.46686i	0.00198978	−	0.0648902i
$512$		0			0
$513$	−4.76249	−	8.24887i	−0.210269	−	0.364197i
$514$		0			0
$515$	−15.8550	+	27.4617i	−0.698656	+	1.21011i
$516$		0			0
$517$	1.51671			0.0667048
$518$		0			0
$519$			14.2570i			0.625811i
$520$		0			0
$521$	27.1927	+	15.6997i	1.19133	+	0.687817i	0.958609	−	0.284725i	$-0.0919024\pi$
$521$	27.1927	+	15.6997i	1.19133	+	0.687817i	0.232725	+	0.972543i	$0.425236\pi$
$522$		0			0
$523$	11.7132	−	6.76263i	0.512183	−	0.295709i	−0.221547	−	0.975150i	$-0.571111\pi$
$523$	11.7132	−	6.76263i	0.512183	−	0.295709i	0.733731	+	0.679440i	$0.237777\pi$
$524$		0			0
$525$	−4.01241	−	2.48357i	−0.175116	−	0.108392i
$526$		0			0
$527$	12.3469	−	7.12848i	0.537839	−	0.310522i
$528$		0			0
$529$	9.03146	−	15.6429i	0.392672	−	0.680128i
$530$		0			0
$531$		−	28.2219i		−	1.22473i
$532$		0			0
$533$			13.8994i			0.602050i
$534$		0			0
$535$	−11.5450	+	19.9965i	−0.499133	+	0.864524i
$536$		0			0
$537$	7.99465	−	4.61572i	0.344995	−	0.199183i
$538$		0			0
$539$	4.18309	+	8.39464i	0.180178	+	0.361583i
$540$		0			0
$541$	−27.1543	+	15.6775i	−1.16745	+	0.674030i	−0.953079	−	0.302722i	$-0.902105\pi$
$541$	−27.1543	+	15.6775i	−1.16745	+	0.674030i	−0.214375	+	0.976751i	$0.568771\pi$
$542$		0			0
$543$	−50.4408	−	29.1220i	−2.16462	−	1.24974i
$544$		0			0
$545$		−	26.1868i		−	1.12172i
$546$		0			0
$547$	44.7293			1.91249			0.956244	−	0.292571i	$-0.0945108\pi$
$547$	44.7293			1.91249			0.956244	+	0.292571i	$0.0945108\pi$
$548$		0			0
$549$	−9.99164	+	17.3060i	−0.426433	+	0.738604i
$550$		0			0
$551$	−9.56611	−	16.5690i	−0.407530	−	0.705863i
$552$		0			0
$553$	13.6862	+	8.47140i	0.581998	+	0.360240i
$554$		0			0
$555$	17.3234	+	30.0050i	0.735337	+	1.27364i
$556$		0			0
$557$	10.5345	+	6.08208i	0.446360	+	0.257706i	0.706292	−	0.707921i	$-0.250367\pi$
$557$	10.5345	+	6.08208i	0.446360	+	0.257706i	−0.259932	+	0.965627i	$0.583700\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	−11.2939			−0.476831
$562$		0			0
$563$	31.4311	+	18.1468i	1.32466	+	0.764794i	0.984469	−	0.175561i	$-0.0561738\pi$
$563$	31.4311	+	18.1468i	1.32466	+	0.764794i	0.340194	+	0.940355i	$0.389507\pi$
$564$		0			0
$565$	20.8506	+	36.1143i	0.877191	+	1.51934i
$566$		0			0
$567$	−14.7147	−	0.451207i	−0.617958	−	0.0189489i
$568$		0			0
$569$	−6.01830	−	10.4240i	−0.252300	−	0.436997i	0.711858	−	0.702323i	$-0.247854\pi$
$569$	−6.01830	−	10.4240i	−0.252300	−	0.436997i	−0.964159	+	0.265326i	$0.914520\pi$
$570$		0			0
$571$	4.10570	−	7.11128i	0.171818	−	0.297598i	−0.767237	−	0.641363i	$-0.778369\pi$
$571$	4.10570	−	7.11128i	0.171818	−	0.297598i	0.939056	+	0.343765i	$0.111702\pi$
$572$		0			0
$573$	3.44225			0.143802
$574$		0			0
$575$		−	4.35589i		−	0.181653i
$576$		0			0
$577$	14.5500	+	8.40042i	0.605722	+	0.349714i	0.771289	−	0.636485i	$-0.219612\pi$
$577$	14.5500	+	8.40042i	0.605722	+	0.349714i	−0.165567	+	0.986199i	$0.552945\pi$
$578$		0			0
$579$	25.6633	−	14.8167i	1.06653	−	0.615761i
$580$		0			0
$581$	−1.17278	+	0.629989i	−0.0486551	+	0.0261364i
$582$		0			0
$583$	−9.96289	+	5.75208i	−0.412621	+	0.238227i
$584$		0			0
$585$	10.1088	−	17.5090i	0.417949	−	0.723909i
$586$		0			0
$587$			25.4261i			1.04945i	0.851273	+	0.524723i	$0.175831\pi$
$587$			25.4261i			1.04945i	−0.851273	+	0.524723i	$0.824169\pi$
$588$		0			0
$589$		−	18.2146i		−	0.750521i
$590$		0			0
$591$	7.76849	−	13.4554i	0.319553	−	0.553482i
$592$		0			0
$593$	−19.0694	+	11.0097i	−0.783086	+	0.452115i	−0.837523	−	0.546402i	$-0.815997\pi$
$593$	−19.0694	+	11.0097i	−0.783086	+	0.452115i	0.0544368	+	0.998517i	$0.482664\pi$
$594$		0			0
$595$	−15.5631	+	8.36013i	−0.638025	+	0.342732i
$596$		0			0
$597$	42.2903	−	24.4163i	1.73083	−	0.999294i
$598$		0			0
$599$	0.500607	+	0.289026i	0.0204543	+	0.0118093i	0.510192	−	0.860060i	$-0.329574\pi$
$599$	0.500607	+	0.289026i	0.0204543	+	0.0118093i	−0.489738	+	0.871870i	$0.662908\pi$
$600$		0			0
$601$			27.3186i			1.11435i	0.830395	+	0.557175i	$0.188115\pi$
$601$			27.3186i			1.11435i	−0.830395	+	0.557175i	$0.811885\pi$
$602$		0			0
$603$	−30.5509			−1.24413
$604$		0			0
$605$	−9.56611	+	16.5690i	−0.388918	+	0.673625i
$606$		0			0
$607$	−5.99963	−	10.3917i	−0.243518	−	0.421785i	0.718196	−	0.695841i	$-0.244968\pi$
$607$	−5.99963	−	10.3917i	−0.243518	−	0.421785i	−0.961714	+	0.274056i	$0.911635\pi$
$608$		0			0
$609$	32.3450	+	0.991819i	1.31069	+	0.0401905i
$610$		0			0
$611$	−1.41727	−	2.45478i	−0.0573364	−	0.0993096i
$612$		0			0
$613$	−3.96050	−	2.28659i	−0.159963	−	0.0923547i	0.417882	−	0.908501i	$-0.362773\pi$
$613$	−3.96050	−	2.28659i	−0.159963	−	0.0923547i	−0.577845	+	0.816147i	$0.696106\pi$
$614$		0			0
$615$	30.2721			1.22069
$616$		0			0
$617$	5.12621			0.206373			0.103187	−	0.994662i	$-0.467096\pi$
$617$	5.12621			0.206373			0.103187	+	0.994662i	$0.467096\pi$
$618$		0			0
$619$	−39.5293	−	22.8222i	−1.58881	−	0.917303i	−0.993503	−	0.113808i	$-0.963695\pi$
$619$	−39.5293	−	22.8222i	−1.58881	−	0.917303i	−0.595312	−	0.803495i	$-0.702972\pi$
$620$		0			0
$621$	7.43567	+	12.8790i	0.298383	+	0.516815i
$622$		0			0
$623$	−3.89654	−	2.41185i	−0.156111	−	0.0966286i
$624$		0			0
$625$	10.5696	+	18.3071i	0.422783	+	0.732282i
$626$		0			0
$627$	−7.21455	+	12.4960i	−0.288121	+	0.499041i
$628$		0			0
$629$	−20.4088			−0.813753
$630$		0			0
$631$			17.1345i			0.682113i	0.940043	+	0.341057i	$0.110785\pi$
$631$			17.1345i			0.682113i	−0.940043	+	0.341057i	$0.889215\pi$
$632$		0			0
$633$	−13.0196	−	7.51689i	−0.517484	−	0.298769i
$634$		0			0
$635$	26.3069	−	15.1883i	1.04396	−	0.602729i
$636$		0			0
$637$	9.67781	−	14.6145i	0.383449	−	0.579049i
$638$		0			0
$639$	17.8009	−	10.2774i	0.704194	−	0.406567i
$640$		0			0
$641$	−4.02498	+	6.97146i	−0.158977	+	0.275356i	−0.934500	−	0.355963i	$-0.884153\pi$
$641$	−4.02498	+	6.97146i	−0.158977	+	0.275356i	0.775523	+	0.631319i	$0.217486\pi$
$642$		0			0
$643$			22.2710i			0.878283i	0.898418	+	0.439142i	$0.144717\pi$
$643$			22.2710i			0.878283i	−0.898418	+	0.439142i	$0.855283\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−18.9125	+	32.7574i	−0.743528	+	1.28783i	0.207352	+	0.978266i	$0.433516\pi$
$647$	−18.9125	+	32.7574i	−0.743528	+	1.28783i	−0.950879	+	0.309561i	$0.899818\pi$
$648$		0			0
$649$	−8.43042	+	4.86730i	−0.330923	+	0.191058i
$650$		0			0
$651$	26.1960	+	16.2146i	1.02670	+	0.635501i
$652$		0			0
$653$	25.6130	−	14.7877i	1.00231	−	0.578686i	0.0933818	−	0.995630i	$-0.470232\pi$
$653$	25.6130	−	14.7877i	1.00231	−	0.578686i	0.908932	+	0.416944i	$0.136899\pi$
$654$		0			0
$655$	10.9586	+	6.32694i	0.428188	+	0.247214i
$656$		0			0
$657$			2.15466i			0.0840611i
$658$		0			0
$659$	−18.3961			−0.716611			−0.358305	−	0.933604i	$-0.616645\pi$
$659$	−18.3961			−0.716611			−0.358305	+	0.933604i	$0.616645\pi$
$660$		0			0
$661$	5.92732	−	10.2664i	0.230546	−	0.399317i	−0.727423	−	0.686189i	$-0.759282\pi$
$661$	5.92732	−	10.2664i	0.230546	−	0.399317i	0.957969	+	0.286872i	$0.0926154\pi$
$662$		0			0
$663$	10.5535	+	18.2791i	0.409862	+	0.709902i
$664$		0			0
$665$	−0.691771	+	22.5599i	−0.0268257	+	0.874836i
$666$		0			0
$667$	14.9356	+	25.8692i	0.578308	+	1.00166i
$668$		0			0
$669$	−47.4157	−	27.3755i	−1.83320	−	1.05840i
$670$		0			0
$671$	6.89285			0.266095
$672$		0			0
$673$	10.8738			0.419154			0.209577	−	0.977792i	$-0.432791\pi$
$673$	10.8738			0.419154			0.209577	+	0.977792i	$0.432791\pi$
$674$		0			0
$675$	1.36618	+	0.788764i	0.0525843	+	0.0303595i
$676$		0			0
$677$	−22.7163	−	39.3458i	−0.873060	−	1.51218i	−0.858815	−	0.512285i	$-0.828799\pi$
$677$	−22.7163	−	39.3458i	−0.873060	−	1.51218i	−0.0142443	−	0.999899i	$-0.504534\pi$
$678$		0			0
$679$	40.1437	−	21.5642i	1.54057	−	0.827559i
$680$		0			0
$681$	−21.6285	−	37.4616i	−0.828805	−	1.43553i
$682$		0			0
$683$	12.3693	−	21.4243i	0.473299	−	0.819778i	−0.526234	−	0.850340i	$-0.676396\pi$
$683$	12.3693	−	21.4243i	0.473299	−	0.819778i	0.999533	+	0.0305620i	$0.00972970\pi$
$684$		0			0
$685$	−29.0446			−1.10974
$686$		0			0
$687$			22.3013i			0.850847i
$688$		0			0
$689$	18.6193	+	10.7499i	0.709340	+	0.409538i
$690$		0			0
$691$	4.10457	−	2.36977i	0.156145	−	0.0901504i	−0.419892	−	0.907574i	$-0.637932\pi$
$691$	4.10457	−	2.36977i	0.156145	−	0.0901504i	0.576037	+	0.817424i	$0.304599\pi$
$692$		0			0
$693$	−6.51647	−	12.1310i	−0.247540	−	0.460817i
$694$		0			0
$695$	−0.905741	+	0.522930i	−0.0343567	+	0.0198359i
$696$		0			0
$697$	−8.91594	+	15.4429i	−0.337715	+	0.584940i
$698$		0			0
$699$		−	11.7417i		−	0.444112i
$700$		0			0
$701$			39.8121i			1.50368i	0.659345	+	0.751840i	$0.270834\pi$
$701$			39.8121i			1.50368i	−0.659345	+	0.751840i	$0.729166\pi$
$702$		0			0
$703$	−13.0371	+	22.5809i	−0.491704	+	0.851656i
$704$		0			0
$705$	−5.34636	+	3.08672i	−0.201355	+	0.116253i
$706$		0			0
$707$	3.24600	+	0.0995345i	0.122078	+	0.00374338i
$708$		0			0
$709$	4.97242	−	2.87083i	0.186743	−	0.107816i	−0.403714	−	0.914885i	$-0.632281\pi$
$709$	4.97242	−	2.87083i	0.186743	−	0.107816i	0.590457	+	0.807069i	$0.298948\pi$
$710$		0			0
$711$	−20.4659	−	11.8160i	−0.767529	−	0.443133i
$712$		0			0
$713$			28.4385i			1.06503i
$714$		0			0
$715$	−6.97370			−0.260801
$716$		0			0
$717$	−32.2305	+	55.8249i	−1.20367	+	2.08482i
$718$		0			0
$719$	7.62804	+	13.2122i	0.284478	+	0.492730i	0.972482	−	0.232976i	$-0.0748464\pi$
$719$	7.62804	+	13.2122i	0.284478	+	0.492730i	−0.688005	+	0.725706i	$0.741513\pi$
$720$		0			0
$721$	21.2438	−	34.3211i	0.791160	−	1.27818i
$722$		0			0
$723$	−7.61218	−	13.1847i	−0.283100	−	0.490344i
$724$		0			0
$725$	2.74416	+	1.58434i	0.101915	+	0.0588409i
$726$		0			0
$727$	−40.8993			−1.51687			−0.758435	−	0.651749i	$-0.774036\pi$
$727$	−40.8993			−1.51687			−0.758435	+	0.651749i	$0.774036\pi$
$728$		0			0
$729$	39.8818			1.47710
$730$		0			0
$731$		0			0
$732$		0			0
$733$	12.2037	+	21.1374i	0.450753	+	0.780728i	0.998433	−	0.0559605i	$-0.0178221\pi$
$733$	12.2037	+	21.1374i	0.450753	+	0.780728i	−0.547680	+	0.836688i	$0.684489\pi$
$734$		0			0
$735$	−31.8296	−	21.0777i	−1.17405	−	0.777462i
$736$		0			0
$737$	5.26897	+	9.12612i	0.194085	+	0.336165i
$738$		0			0
$739$	−15.3996	+	26.6730i	−0.566485	+	0.981181i	0.430425	+	0.902626i	$0.358364\pi$
$739$	−15.3996	+	26.6730i	−0.566485	+	0.981181i	−0.996910	+	0.0785545i	$0.974970\pi$
$740$		0			0
$741$	26.9661			0.990624
$742$		0			0
$743$			23.9376i			0.878184i	0.898442	+	0.439092i	$0.144700\pi$
$743$			23.9376i			0.878184i	−0.898442	+	0.439092i	$0.855300\pi$
$744$		0			0
$745$	9.91613	+	5.72508i	0.363299	+	0.209751i
$746$		0			0
$747$	1.69271	−	0.977288i	0.0619331	−	0.0357571i
$748$		0			0
$749$	15.4689	−	24.9912i	0.565219	−	0.913158i
$750$		0			0
$751$	11.9543	−	6.90181i	0.436218	−	0.251851i	−0.265774	−	0.964035i	$-0.585627\pi$
$751$	11.9543	−	6.90181i	0.436218	−	0.251851i	0.701992	+	0.712185i	$0.252294\pi$
$752$		0			0
$753$	−24.6653	+	42.7215i	−0.898853	+	1.55686i
$754$		0			0
$755$		−	14.6287i		−	0.532392i
$756$		0			0
$757$		−	2.14156i		−	0.0778362i	−0.999242	−	0.0389181i	$-0.987609\pi$
$757$		−	2.14156i		−	0.0778362i	0.999242	−	0.0389181i	$-0.0123911\pi$
$758$		0			0
$759$	11.2641	−	19.5099i	0.408860	−	0.708166i
$760$		0			0
$761$	36.8321	−	21.2650i	1.33516	−	0.770856i	0.349076	−	0.937094i	$-0.386496\pi$
$761$	36.8321	−	21.2650i	1.33516	−	0.770856i	0.986086	+	0.166239i	$0.0531622\pi$
$762$		0			0
$763$	−1.02164	+	33.3175i	−0.0369859	+	1.20618i
$764$		0			0
$765$	22.4628	−	12.9689i	0.812143	−	0.468891i
$766$		0			0
$767$	15.7554	+	9.09636i	0.568893	+	0.328450i
$768$		0			0
$769$		−	15.6459i		−	0.564206i	−0.959384	−	0.282103i	$-0.908968\pi$
$769$		−	15.6459i		−	0.564206i	0.959384	−	0.282103i	$-0.0910320\pi$
$770$		0			0
$771$	33.0562			1.19049
$772$		0			0
$773$	15.2125	−	26.3489i	0.547156	−	0.947703i	−0.451311	−	0.892367i	$-0.649044\pi$
$773$	15.2125	−	26.3489i	0.547156	−	0.947703i	0.998468	−	0.0553362i	$-0.0176230\pi$
$774$		0			0
$775$	1.50836	+	2.61255i	0.0541817	+	0.0938455i
$776$		0			0
$777$	−20.8700	−	38.8513i	−0.748707	−	1.39378i
$778$		0			0
$779$	11.3910	+	19.7297i	0.408124	+	0.706891i
$780$		0			0
$781$	−6.14009	−	3.54498i	−0.219710	−	0.126849i
$782$		0			0
$783$	−10.8181			−0.386609
$784$		0			0
$785$	−29.7427			−1.06156
$786$		0			0
$787$	28.3722	+	16.3807i	1.01136	+	0.583909i	0.911590	−	0.411102i	$-0.134856\pi$
$787$	28.3722	+	16.3807i	1.01136	+	0.583909i	0.0997704	+	0.995010i	$0.468189\pi$
$788$		0			0
$789$	6.47291	+	11.2114i	0.230442	+	0.399137i
$790$		0			0
$791$	−25.1193	−	46.7618i	−0.893140	−	1.66266i
$792$		0			0
$793$	−6.44092	−	11.1560i	−0.228724	−	0.396161i
$794$		0			0
$795$	23.4126	−	40.5518i	0.830359	−	1.43822i
$796$		0			0
$797$	28.3790			1.00523			0.502617	−	0.864509i	$-0.332370\pi$
$797$	28.3790			1.00523			0.502617	+	0.864509i	$0.332370\pi$
$798$		0			0
$799$		−	3.63649i		−	0.128650i
$800$		0			0
$801$	5.82673	+	3.36406i	0.205877	+	0.118863i
$802$		0			0
$803$	0.643636	−	0.371603i	0.0227134	−	0.0131136i
$804$		0			0
$805$	1.08006	−	35.2228i	0.0380672	−	1.24144i
$806$		0			0
$807$	59.7626	−	34.5040i	2.10374	−	1.21460i
$808$		0			0
$809$	4.08387	−	7.07347i	0.143581	−	0.248690i	−0.785262	−	0.619164i	$-0.787472\pi$
$809$	4.08387	−	7.07347i	0.143581	−	0.248690i	0.928843	+	0.370474i	$0.120805\pi$
$810$		0			0
$811$		−	22.2710i		−	0.782041i	−0.920382	−	0.391021i	$-0.872122\pi$
$811$		−	22.2710i		−	0.782041i	0.920382	−	0.391021i	$-0.127878\pi$
$812$		0			0
$813$			73.7246i			2.58563i
$814$		0			0
$815$	−8.63997	+	14.9649i	−0.302645	+	0.524196i
$816$		0			0
$817$		0			0
$818$		0			0
$819$	−13.5446	+	21.8824i	−0.473287	+	0.764634i
$820$		0			0
$821$	−4.52231	+	2.61096i	−0.157830	+	0.0911230i	−0.576835	−	0.816861i	$-0.695712\pi$
$821$	−4.52231	+	2.61096i	−0.157830	+	0.0911230i	0.419005	+	0.907984i	$0.362379\pi$
$822$		0			0
$823$	−8.29368	−	4.78836i	−0.289099	−	0.166912i	0.348436	−	0.937333i	$-0.386713\pi$
$823$	−8.29368	−	4.78836i	−0.289099	−	0.166912i	−0.637536	+	0.770421i	$0.720046\pi$
$824$		0			0
$825$		−	2.38975i		−	0.0832004i
$826$		0			0
$827$	−40.6664			−1.41411			−0.707055	−	0.707159i	$-0.749977\pi$
$827$	−40.6664			−1.41411			−0.707055	+	0.707159i	$0.749977\pi$
$828$		0			0
$829$	−16.6171	+	28.7816i	−0.577134	+	0.999625i	0.418672	+	0.908137i	$0.362496\pi$
$829$	−16.6171	+	28.7816i	−0.577134	+	0.999625i	−0.995806	+	0.0914880i	$0.970838\pi$
$830$		0			0
$831$	35.4452	+	61.3929i	1.22958	+	2.12970i
$832$		0			0
$833$	20.1271	−	10.0295i	0.697364	−	0.347500i
$834$		0			0
$835$	2.60236	+	4.50743i	0.0900586	+	0.155986i
$836$		0			0
$837$	−8.91945	−	5.14965i	−0.308301	−	0.177998i
$838$		0			0
$839$	−15.0243			−0.518698			−0.259349	−	0.965784i	$-0.583508\pi$
$839$	−15.0243			−0.518698			−0.259349	+	0.965784i	$0.583508\pi$
$840$		0			0
$841$	7.27029			0.250700
$842$		0			0
$843$	−45.5890	−	26.3208i	−1.57017	−	0.906538i
$844$		0			0
$845$	−6.99392	−	12.1138i	−0.240598	−	0.416728i
$846$		0			0
$847$	12.8174	−	20.7076i	0.440411	−	0.711521i
$848$		0			0
$849$	7.19938	+	12.4697i	0.247082	+	0.427959i
$850$		0			0
$851$	20.3548	−	35.2556i	0.697755	−	1.20855i
$852$		0			0
$853$	12.5203			0.428686			0.214343	−	0.976758i	$-0.431239\pi$
$853$	12.5203			0.428686			0.214343	+	0.976758i	$0.431239\pi$
$854$		0			0
$855$		−	33.1380i		−	1.13329i
$856$		0			0
$857$	−46.8265	−	27.0353i	−1.59956	−	0.923509i	−0.991571	−	0.129566i	$-0.958641\pi$
$857$	−46.8265	−	27.0353i	−1.59956	−	0.923509i	−0.607993	−	0.793942i	$-0.708025\pi$
$858$		0			0
$859$	−17.0990	+	9.87213i	−0.583411	+	0.336833i	−0.762488	−	0.647002i	$-0.776022\pi$
$859$	−17.0990	+	9.87213i	−0.583411	+	0.336833i	0.179077	+	0.983835i	$0.442689\pi$
$860$		0			0
$861$	−38.5152	−	1.18102i	−1.31260	−	0.0402491i
$862$		0			0
$863$	−26.3755	+	15.2279i	−0.897833	+	0.518364i	−0.876497	−	0.481408i	$-0.840126\pi$
$863$	−26.3755	+	15.2279i	−0.897833	+	0.518364i	−0.0213367	+	0.999772i	$0.506792\pi$
$864$		0			0
$865$	−5.64697	+	9.78084i	−0.192003	+	0.332559i
$866$		0			0
$867$		−	17.5265i		−	0.595232i
$868$		0			0
$869$			8.15137i			0.276516i
$870$		0			0
$871$	9.84701	−	17.0555i	0.333653	−	0.577905i
$872$		0			0
$873$	−57.9407	+	33.4521i	−1.96100	+	1.13218i
$874$		0			0
$875$	−14.7808	−	27.5157i	−0.499682	−	0.930201i
$876$		0			0
$877$	−18.3275	+	10.5814i	−0.618877	+	0.357309i	−0.776432	−	0.630201i	$-0.782972\pi$
$877$	−18.3275	+	10.5814i	−0.618877	+	0.357309i	0.157555	+	0.987510i	$0.449639\pi$
$878$		0			0
$879$	−31.1148	−	17.9641i	−1.04948	−	0.605915i
$880$		0			0
$881$		−	11.5367i		−	0.388681i	−0.980934	−	0.194340i	$-0.937743\pi$
$881$		−	11.5367i		−	0.388681i	0.980934	−	0.194340i	$-0.0622566\pi$
$882$		0			0
$883$	−49.8555			−1.67777			−0.838886	−	0.544307i	$-0.816793\pi$
$883$	−49.8555			−1.67777			−0.838886	+	0.544307i	$0.816793\pi$
$884$		0			0
$885$	19.8113	−	34.3142i	0.665950	−	1.15346i
$886$		0			0
$887$	−5.56575	−	9.64015i	−0.186879	−	0.323685i	0.757329	−	0.653034i	$-0.226504\pi$
$887$	−5.56575	−	9.64015i	−0.186879	−	0.323685i	−0.944208	+	0.329349i	$0.893171\pi$
$888$		0			0
$889$	−34.0629	+	18.2978i	−1.14243	+	0.613688i
$890$		0			0
$891$	−3.72770	−	6.45656i	−0.124883	−	0.216303i
$892$		0			0
$893$	−4.02352	−	2.32298i	−0.134642	−	0.0777356i
$894$		0			0
$895$	7.31287			0.244442
$896$		0			0
$897$	−42.1022			−1.40575
$898$		0			0
$899$	−17.9159	−	10.3438i	−0.597530	−	0.344984i
$900$		0			0
$901$	13.7913	+	23.8872i	0.459454	+	0.795798i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−23.0696	−	39.9577i	−0.766859	−	1.32824i
$906$		0			0
$907$	−7.20674	+	12.4824i	−0.239296	+	0.414473i	−0.960512	−	0.278237i	$-0.910250\pi$
$907$	−7.20674	+	12.4824i	−0.239296	+	0.414473i	0.721217	+	0.692710i	$0.243583\pi$
$908$		0			0
$909$	−4.76801			−0.158145
$910$		0			0
$911$			19.1909i			0.635823i	0.948120	+	0.317911i	$0.102981\pi$
$911$			19.1909i			0.635823i	−0.948120	+	0.317911i	$0.897019\pi$
$912$		0			0
$913$	−0.583868	−	0.337096i	−0.0193232	−	0.0111563i
$914$		0			0
$915$	−24.2971	+	14.0279i	−0.803237	+	0.463749i
$916$		0			0
$917$	−13.6958	−	8.47733i	−0.452276	−	0.279946i
$918$		0			0
$919$	−22.4285	+	12.9491i	−0.739848	+	0.427151i	−0.822014	−	0.569467i	$-0.807150\pi$
$919$	−22.4285	+	12.9491i	−0.739848	+	0.427151i	0.0821662	+	0.996619i	$0.473816\pi$
$920$		0			0
$921$	32.0366	−	55.4890i	1.05564	−	1.82843i
$922$		0			0
$923$			13.2502i			0.436136i
$924$		0			0
$925$		−	4.31842i		−	0.141989i
$926$		0			0
$927$	−29.6310	+	51.3224i	−0.973210	+	1.68565i
$928$		0			0
$929$	−36.7480	+	21.2165i	−1.20566	+	0.696090i	−0.961809	−	0.273722i	$-0.911745\pi$
$929$	−36.7480	+	21.2165i	−1.20566	+	0.696090i	−0.243854	+	0.969812i	$0.578412\pi$
$930$		0			0
$931$	1.76029	−	28.6761i	0.0576910	−	0.939820i
$932$		0			0
$933$	39.1536	−	22.6053i	1.28183	−	0.740065i
$934$		0			0
$935$	−7.74809	−	4.47336i	−0.253390	−	0.146295i
$936$		0			0
$937$			46.5547i			1.52088i	0.649410	+	0.760439i	$0.275016\pi$
$937$			46.5547i			1.52088i	−0.649410	+	0.760439i	$0.724984\pi$
$938$		0			0
$939$	45.5812			1.48749
$940$		0			0
$941$	−1.48937	+	2.57967i	−0.0485522	+	0.0840949i	−0.889280	−	0.457363i	$-0.848794\pi$
$941$	−1.48937	+	2.57967i	−0.0485522	+	0.0840949i	0.840728	+	0.541458i	$0.182127\pi$
$942$		0			0
$943$	−17.7847	−	30.8040i	−0.579150	−	1.00312i
$944$		0			0
$945$	10.8517	+	6.71690i	0.353006	+	0.218501i
$946$		0			0
$947$	−13.5270	−	23.4294i	−0.439568	−	0.761354i	0.558088	−	0.829782i	$-0.311535\pi$
$947$	−13.5270	−	23.4294i	−0.439568	−	0.761354i	−0.997656	+	0.0684276i	$0.978202\pi$
$948$		0			0
$949$	−1.20287	−	0.694478i	−0.0390469	−	0.0225437i
$950$		0			0
$951$	50.8580			1.64918
$952$		0			0
$953$	28.7293			0.930634			0.465317	−	0.885144i	$-0.345940\pi$
$953$	28.7293			0.930634			0.465317	+	0.885144i	$0.345940\pi$
$954$		0			0
$955$	2.36152	+	1.36342i	0.0764169	+	0.0441193i
$956$		0			0
$957$	8.19403	+	14.1925i	0.264875	+	0.458778i
$958$		0			0
$959$	36.9536	+	1.13313i	1.19329	+	0.0365908i
$960$		0			0
$961$	5.65232	+	9.79010i	0.182333	+	0.315810i
$962$		0			0
$963$	−21.5761	+	37.3708i	−0.695279	+	1.20426i
$964$		0			0
$965$	23.4747			0.755677
$966$		0			0
$967$		−	13.3546i		−	0.429453i	−0.976674	−	0.214727i	$-0.931114\pi$
$967$		−	13.3546i		−	0.429453i	0.976674	−	0.214727i	$-0.0688861\pi$
$968$		0			0
$969$	29.9605	+	17.2977i	0.962471	+	0.555683i
$970$		0			0
$971$	1.71876	−	0.992325i	0.0551575	−	0.0318452i	−0.472168	−	0.881509i	$-0.656528\pi$
$971$	1.71876	−	0.992325i	0.0551575	−	0.0318452i	0.527325	+	0.849664i	$0.323195\pi$
$972$		0			0
$973$	1.17278	−	0.629989i	0.0375976	−	0.0201965i
$974$		0			0
$975$	−3.86778	+	2.23306i	−0.123868	+	0.0715153i
$976$		0			0
$977$	31.2242	−	54.0818i	0.998950	−	1.73023i	0.459792	−	0.888027i	$-0.347924\pi$
$977$	31.2242	−	54.0818i	0.998950	−	1.73023i	0.539158	−	0.842205i	$-0.318743\pi$
$978$		0			0
$979$		−	2.32073i		−	0.0741710i
$980$		0			0
$981$		−	48.9397i		−	1.56252i
$982$		0			0
$983$	3.64021	−	6.30503i	0.116105	−	0.201099i	−0.802116	−	0.597168i	$-0.796293\pi$
$983$	3.64021	−	6.30503i	0.116105	−	0.201099i	0.918221	+	0.396069i	$0.129626\pi$
$984$		0			0
$985$	10.6590	−	6.15397i	0.339624	−	0.196082i
$986$		0			0
$987$	6.92261	−	3.71866i	0.220349	−	0.118366i
$988$		0			0
$989$		0			0
$990$		0			0
$991$	31.3345	+	18.0910i	0.995373	+	0.574679i	0.906876	−	0.421398i	$-0.138460\pi$
$991$	31.3345	+	18.0910i	0.995373	+	0.574679i	0.0884967	+	0.996076i	$0.471794\pi$
$992$		0			0
$993$		−	54.5797i		−	1.73204i
$994$		0			0
$995$	38.6838			1.22636
$996$		0			0
$997$	−17.1218	+	29.6559i	−0.542254	+	0.939211i	0.456520	+	0.889713i	$0.349096\pi$
$997$	−17.1218	+	29.6559i	−0.542254	+	0.939211i	−0.998774	+	0.0494984i	$0.984238\pi$
$998$		0			0
$999$	7.37171	+	12.7682i	0.233231	+	0.403967i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	224.2.q.a.143.6		12
3.2	odd	2		2016.2.bs.a.1711.2		12
4.3	odd	2		56.2.m.a.3.5	yes	12
7.2	even	3		1568.2.q.g.1391.2		12
7.3	odd	6		1568.2.e.e.783.12		12
7.4	even	3		1568.2.e.e.783.1		12
7.5	odd	6	inner	224.2.q.a.47.5		12
7.6	odd	2		1568.2.q.g.815.1		12
8.3	odd	2	inner	224.2.q.a.143.5		12
8.5	even	2		56.2.m.a.3.2	✓	12
12.11	even	2		504.2.bk.a.451.2		12
21.5	even	6		2016.2.bs.a.271.5		12
24.5	odd	2		504.2.bk.a.451.5		12
24.11	even	2		2016.2.bs.a.1711.5		12
28.3	even	6		392.2.e.e.195.7		12
28.11	odd	6		392.2.e.e.195.8		12
28.19	even	6		56.2.m.a.19.1	yes	12
28.23	odd	6		392.2.m.g.19.1		12
28.27	even	2		392.2.m.g.227.5		12
56.3	even	6		1568.2.e.e.783.11		12
56.5	odd	6		56.2.m.a.19.6	yes	12
56.11	odd	6		1568.2.e.e.783.2		12
56.13	odd	2		392.2.m.g.227.2		12
56.19	even	6	inner	224.2.q.a.47.6		12
56.27	even	2		1568.2.q.g.815.2		12
56.37	even	6		392.2.m.g.19.6		12
56.45	odd	6		392.2.e.e.195.5		12
56.51	odd	6		1568.2.q.g.1391.1		12
56.53	even	6		392.2.e.e.195.6		12
84.47	odd	6		504.2.bk.a.19.6		12
168.5	even	6		504.2.bk.a.19.1		12
168.131	odd	6		2016.2.bs.a.271.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.2.m.a.3.2	✓	12	8.5	even	2
56.2.m.a.3.5	yes	12	4.3	odd	2
56.2.m.a.19.1	yes	12	28.19	even	6
56.2.m.a.19.6	yes	12	56.5	odd	6
224.2.q.a.47.5		12	7.5	odd	6	inner
224.2.q.a.47.6		12	56.19	even	6	inner
224.2.q.a.143.5		12	8.3	odd	2	inner
224.2.q.a.143.6		12	1.1	even	1	trivial
392.2.e.e.195.5		12	56.45	odd	6
392.2.e.e.195.6		12	56.53	even	6
392.2.e.e.195.7		12	28.3	even	6
392.2.e.e.195.8		12	28.11	odd	6
392.2.m.g.19.1		12	28.23	odd	6
392.2.m.g.19.6		12	56.37	even	6
392.2.m.g.227.2		12	56.13	odd	2
392.2.m.g.227.5		12	28.27	even	2
504.2.bk.a.19.1		12	168.5	even	6
504.2.bk.a.19.6		12	84.47	odd	6
504.2.bk.a.451.2		12	12.11	even	2
504.2.bk.a.451.5		12	24.5	odd	2
1568.2.e.e.783.1		12	7.4	even	3
1568.2.e.e.783.2		12	56.11	odd	6
1568.2.e.e.783.11		12	56.3	even	6
1568.2.e.e.783.12		12	7.3	odd	6
1568.2.q.g.815.1		12	7.6	odd	2
1568.2.q.g.815.2		12	56.27	even	2
1568.2.q.g.1391.1		12	56.51	odd	6
1568.2.q.g.1391.2		12	7.2	even	3
2016.2.bs.a.271.2		12	168.131	odd	6
2016.2.bs.a.271.5		12	21.5	even	6
2016.2.bs.a.1711.2		12	3.2	odd	2
2016.2.bs.a.1711.5		12	24.11	even	2

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:	\( N \)	\(=\)	\( 224 = 2^{5} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	224.q (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.27230 + 1.31191i) q^{3} +(1.03926 + 1.80005i) q^{5} +(-1.25203 - 2.33076i) q^{7} +(1.94224 + 3.36406i) q^{9} +O(q^{10})\)	\(q+(2.27230 + 1.31191i) q^{3} +(1.03926 + 1.80005i) q^{5} +(-1.25203 - 2.33076i) q^{7} +(1.94224 + 3.36406i) q^{9} +(0.669938 - 1.16037i) q^{11} -2.50406 q^{13} +5.45368i q^{15} +(-2.78212 - 1.60626i) q^{17} +(-3.55442 + 2.05215i) q^{19} +(0.212768 - 6.93874i) q^{21} +(5.54952 - 3.20402i) q^{23} +(0.339877 - 0.588684i) q^{25} +2.32073i q^{27} +4.66151i q^{29} +(-2.21897 + 3.84337i) q^{31} +(3.04461 - 1.75780i) q^{33} +(2.89430 - 4.67598i) q^{35} +(5.50178 - 3.17646i) q^{37} +(-5.68997 - 3.28511i) q^{39} -5.55076i q^{41} +(-4.03699 + 6.99227i) q^{45} +(0.565988 + 0.980320i) q^{47} +(-3.86485 + 5.83634i) q^{49} +(-4.21455 - 7.29981i) q^{51} +(-7.43567 - 4.29299i) q^{53} +2.78496 q^{55} -10.7690 q^{57} +(-6.29193 - 3.63265i) q^{59} +(2.57219 + 4.45517i) q^{61} +(5.40907 - 8.73879i) q^{63} +(-2.60236 - 4.50743i) q^{65} +(-3.93243 + 6.81116i) q^{67} +16.8136 q^{69} -5.29150i q^{71} +(0.480369 + 0.277341i) q^{73} +(1.54461 - 0.891779i) q^{75} +(-3.54332 - 0.108651i) q^{77} +(-5.26862 + 3.04184i) q^{79} +(2.78212 - 4.81877i) q^{81} -0.503175i q^{83} -6.67728i q^{85} +(-6.11551 + 10.5924i) q^{87} +(1.50000 - 0.866025i) q^{89} +(3.13515 + 5.83634i) q^{91} +(-10.0844 + 5.82221i) q^{93} +(-7.38794 - 4.26543i) q^{95} +17.2234i q^{97} +5.20473 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{3}+O(q^{10}) \) 12 * q + 6 * q^3	\( 12 q + 6 q^{3} + 6 q^{11} - 6 q^{17} + 6 q^{19} - 6 q^{33} - 18 q^{35} - 12 q^{49} - 6 q^{51} - 36 q^{57} - 42 q^{59} - 12 q^{65} - 30 q^{67} + 18 q^{73} - 24 q^{75} + 6 q^{81} + 18 q^{89} + 72 q^{91} + 24 q^{99}+O(q^{100}) \) 12 * q + 6 * q^3 + 6 * q^11 - 6 * q^17 + 6 * q^19 - 6 * q^33 - 18 * q^35 - 12 * q^49 - 6 * q^51 - 36 * q^57 - 42 * q^59 - 12 * q^65 - 30 * q^67 + 18 * q^73 - 24 * q^75 + 6 * q^81 + 18 * q^89 + 72 * q^91 + 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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