LMFDB - Embedded newform 1890.2.bi.b.719.15

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1890,2,Mod(719,1890)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1890, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5, 3, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1890.719"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1890.bi (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [48,48] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$15.0917259820$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 630)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			719.15
Character	$\chi$	$=$	1890.719
Dual form			1890.2.bi.b.899.15

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000 q^{2} +1.00000 q^{4} +(0.945479 - 2.02634i) q^{5} +(2.20085 - 1.46842i) q^{7} +1.00000 q^{8} +(0.945479 - 2.02634i) q^{10} +(0.123075 + 0.0710575i) q^{11} +(0.600465 - 1.04004i) q^{13} +(2.20085 - 1.46842i) q^{14} +1.00000 q^{16} +(-0.0902992 + 0.0521342i) q^{17} +(5.02533 + 2.90137i) q^{19} +(0.945479 - 2.02634i) q^{20} +(0.123075 + 0.0710575i) q^{22} +(-2.15286 - 3.72887i) q^{23} +(-3.21214 - 3.83173i) q^{25} +(0.600465 - 1.04004i) q^{26} +(2.20085 - 1.46842i) q^{28} +(-3.20977 + 1.85316i) q^{29} -3.59772i q^{31} +1.00000 q^{32} +(-0.0902992 + 0.0521342i) q^{34} +(-0.894657 - 5.84804i) q^{35} +(5.42899 + 3.13443i) q^{37} +(5.02533 + 2.90137i) q^{38} +(0.945479 - 2.02634i) q^{40} +(-3.96636 + 6.86994i) q^{41} +(1.49609 - 0.863766i) q^{43} +(0.123075 + 0.0710575i) q^{44} +(-2.15286 - 3.72887i) q^{46} +5.04557i q^{47} +(2.68750 - 6.46354i) q^{49} +(-3.21214 - 3.83173i) q^{50} +(0.600465 - 1.04004i) q^{52} +(1.34026 + 2.32140i) q^{53} +(0.260352 - 0.182209i) q^{55} +(2.20085 - 1.46842i) q^{56} +(-3.20977 + 1.85316i) q^{58} -9.80986 q^{59} -12.3067i q^{61} -3.59772i q^{62} +1.00000 q^{64} +(-1.53974 - 2.20008i) q^{65} -7.27754i q^{67} +(-0.0902992 + 0.0521342i) q^{68} +(-0.894657 - 5.84804i) q^{70} -12.4507i q^{71} +(4.01981 + 6.96252i) q^{73} +(5.42899 + 3.13443i) q^{74} +(5.02533 + 2.90137i) q^{76} +(0.375212 - 0.0243387i) q^{77} -8.41003 q^{79} +(0.945479 - 2.02634i) q^{80} +(-3.96636 + 6.86994i) q^{82} +(-2.03412 + 1.17440i) q^{83} +(0.0202659 + 0.232269i) q^{85} +(1.49609 - 0.863766i) q^{86} +(0.123075 + 0.0710575i) q^{88} +(0.748203 - 1.29593i) q^{89} +(-0.205672 - 3.17070i) q^{91} +(-2.15286 - 3.72887i) q^{92} +5.04557i q^{94} +(10.6305 - 7.43985i) q^{95} +(2.01118 + 3.48347i) q^{97} +(2.68750 - 6.46354i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 48 q^{2} + 48 q^{4} - 3 q^{7} + 48 q^{8} - 6 q^{11} - 3 q^{14} + 48 q^{16} - 6 q^{22} + 3 q^{23} + 18 q^{25} - 3 q^{28} + 3 q^{29} + 48 q^{32} + 18 q^{35} + 3 q^{41} - 6 q^{44} + 3 q^{46} + 3 q^{49}+ \cdots + 3 q^{98}+O(q^{100}) $ 48 * q + 48 * q^2 + 48 * q^4 - 3 * q^7 + 48 * q^8 - 6 * q^11 - 3 * q^14 + 48 * q^16 - 6 * q^22 + 3 * q^23 + 18 * q^25 - 3 * q^28 + 3 * q^29 + 48 * q^32 + 18 * q^35 + 3 * q^41 - 6 * q^44 + 3 * q^46 + 3 * q^49 + 18 * q^50 + 42 * q^55 - 3 * q^56 + 3 * q^58 + 48 * q^64 + 12 * q^65 + 18 * q^70 + 18 * q^73 - 12 * q^77 + 3 * q^82 + 9 * q^83 + 33 * q^85 - 6 * q^88 + 33 * q^89 + 3 * q^92 + 24 * q^97 + 3 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1890\mathbb{Z}\right)^\times$.

$n$	$757$	$1081$	$1541$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$		0			0
$3$		0			0
$4$	1.00000			0.500000
$5$	0.945479	−	2.02634i	0.422831	−	0.906208i
$5$	0.945479	−	2.02634i	0.422831	−	0.906208i
$6$		0			0
$7$	2.20085	−	1.46842i	0.831844	−	0.555009i
$7$	2.20085	−	1.46842i	0.831844	−	0.555009i
$8$	1.00000			0.353553
$9$		0			0
$10$	0.945479	−	2.02634i	0.298987	−	0.640786i
$11$	0.123075	+	0.0710575i	0.0371086	+	0.0214246i	0.518440	−	0.855114i	$-0.326513\pi$
$11$	0.123075	+	0.0710575i	0.0371086	+	0.0214246i	−0.481331	+	0.876539i	$0.659846\pi$
$12$		0			0
$13$	0.600465	−	1.04004i	0.166539	−	0.288454i	−0.770662	−	0.637245i	$-0.780074\pi$
$13$	0.600465	−	1.04004i	0.166539	−	0.288454i	0.937201	+	0.348790i	$0.113407\pi$
$14$	2.20085	−	1.46842i	0.588203	−	0.392451i
$15$		0			0
$16$	1.00000			0.250000
$17$	−0.0902992	+	0.0521342i	−0.0219008	+	0.0126444i	−0.510910	−	0.859634i	$-0.670692\pi$
$17$	−0.0902992	+	0.0521342i	−0.0219008	+	0.0126444i	0.489010	+	0.872278i	$0.337358\pi$
$18$		0			0
$19$	5.02533	+	2.90137i	1.15289	+	0.665621i	0.949590	−	0.313495i	$-0.101500\pi$
$19$	5.02533	+	2.90137i	1.15289	+	0.665621i	0.203300	+	0.979117i	$0.434833\pi$
$20$	0.945479	−	2.02634i	0.211416	−	0.453104i
$21$		0			0
$22$	0.123075	+	0.0710575i	0.0262397	+	0.0151495i
$23$	−2.15286	−	3.72887i	−0.448903	−	0.777523i	0.549412	−	0.835552i	$-0.314852\pi$
$23$	−2.15286	−	3.72887i	−0.448903	−	0.777523i	−0.998315	+	0.0580289i	$0.981518\pi$
$24$		0			0
$25$	−3.21214	−	3.83173i	−0.642428	−	0.766346i
$26$	0.600465	−	1.04004i	0.117761	−	0.203968i
$27$		0			0
$28$	2.20085	−	1.46842i	0.415922	−	0.277505i
$29$	−3.20977	+	1.85316i	−0.596040	+	0.344124i	−0.767482	−	0.641070i	$-0.778491\pi$
$29$	−3.20977	+	1.85316i	−0.596040	+	0.344124i	0.171442	+	0.985194i	$0.445157\pi$
$30$		0			0
$31$		−	3.59772i		−	0.646170i	−0.946370	−	0.323085i	$-0.895280\pi$
$31$		−	3.59772i		−	0.646170i	0.946370	−	0.323085i	$-0.104720\pi$
$32$	1.00000			0.176777
$33$		0			0
$34$	−0.0902992	+	0.0521342i	−0.0154862	+	0.00894095i
$35$	−0.894657	−	5.84804i	−0.151225	−	0.988499i
$36$		0			0
$37$	5.42899	+	3.13443i	0.892520	+	0.515296i	0.874766	−	0.484546i	$-0.161015\pi$
$37$	5.42899	+	3.13443i	0.892520	+	0.515296i	0.0177539	+	0.999842i	$0.494348\pi$
$38$	5.02533	+	2.90137i	0.815216	+	0.470665i
$39$		0			0
$40$	0.945479	−	2.02634i	0.149493	−	0.320393i
$41$	−3.96636	+	6.86994i	−0.619442	+	1.07290i	0.370146	+	0.928974i	$0.379308\pi$
$41$	−3.96636	+	6.86994i	−0.619442	+	1.07290i	−0.989588	+	0.143931i	$0.954026\pi$
$42$		0			0
$43$	1.49609	−	0.863766i	0.228151	−	0.131723i	−0.381568	−	0.924341i	$-0.624616\pi$
$43$	1.49609	−	0.863766i	0.228151	−	0.131723i	0.609719	+	0.792618i	$0.291282\pi$
$44$	0.123075	+	0.0710575i	0.0185543	+	0.0107123i
$45$		0			0
$46$	−2.15286	−	3.72887i	−0.317422	−	0.549792i
$47$			5.04557i			0.735973i	0.929831	+	0.367986i	$0.119953\pi$
$47$			5.04557i			0.735973i	−0.929831	+	0.367986i	$0.880047\pi$
$48$		0			0
$49$	2.68750	−	6.46354i	0.383929	−	0.923363i
$50$	−3.21214	−	3.83173i	−0.454265	−	0.541889i
$51$		0			0
$52$	0.600465	−	1.04004i	0.0832696	−	0.144227i
$53$	1.34026	+	2.32140i	0.184099	+	0.318869i	0.943273	−	0.332019i	$-0.107730\pi$
$53$	1.34026	+	2.32140i	0.184099	+	0.318869i	−0.759174	+	0.650888i	$0.774397\pi$
$54$		0			0
$55$	0.260352	−	0.182209i	0.0351059	−	0.0245691i
$56$	2.20085	−	1.46842i	0.294101	−	0.196225i
$57$		0			0
$58$	−3.20977	+	1.85316i	−0.421464	+	0.243332i
$59$	−9.80986			−1.27713			−0.638567	−	0.769566i	$-0.720473\pi$
$59$	−9.80986			−1.27713			−0.638567	+	0.769566i	$0.720473\pi$
$60$		0			0
$61$		−	12.3067i		−	1.57571i	−0.615863	−	0.787853i	$-0.711192\pi$
$61$		−	12.3067i		−	1.57571i	0.615863	−	0.787853i	$-0.288808\pi$
$62$		−	3.59772i		−	0.456911i
$63$		0			0
$64$	1.00000			0.125000
$65$	−1.53974	−	2.20008i	−0.190982	−	0.272887i
$66$		0			0
$67$		−	7.27754i		−	0.889093i	−0.895756	−	0.444547i	$-0.853365\pi$
$67$		−	7.27754i		−	0.889093i	0.895756	−	0.444547i	$-0.146635\pi$
$68$	−0.0902992	+	0.0521342i	−0.0109504	+	0.00632221i
$69$		0			0
$70$	−0.894657	−	5.84804i	−0.106932	−	0.698975i
$71$		−	12.4507i		−	1.47762i	−0.673912	−	0.738812i	$-0.735387\pi$
$71$		−	12.4507i		−	1.47762i	0.673912	−	0.738812i	$-0.264613\pi$
$72$		0			0
$73$	4.01981	+	6.96252i	0.470483	+	0.814901i	0.999430	−	0.0337541i	$-0.0107463\pi$
$73$	4.01981	+	6.96252i	0.470483	+	0.814901i	−0.528947	+	0.848655i	$0.677413\pi$
$74$	5.42899	+	3.13443i	0.631107	+	0.364370i
$75$		0			0
$76$	5.02533	+	2.90137i	0.576445	+	0.332811i
$77$	0.375212	−	0.0243387i	0.0427594	−	0.00277365i
$78$		0			0
$79$	−8.41003			−0.946202			−0.473101	−	0.881008i	$-0.656865\pi$
$79$	−8.41003			−0.946202			−0.473101	+	0.881008i	$0.656865\pi$
$80$	0.945479	−	2.02634i	0.105708	−	0.226552i
$81$		0			0
$82$	−3.96636	+	6.86994i	−0.438011	+	0.758658i
$83$	−2.03412	+	1.17440i	−0.223274	+	0.128907i	−0.607465	−	0.794346i	$-0.707814\pi$
$83$	−2.03412	+	1.17440i	−0.223274	+	0.128907i	0.384191	+	0.923253i	$0.374480\pi$
$84$		0			0
$85$	0.0202659	+	0.232269i	0.00219815	+	0.0251931i
$86$	1.49609	−	0.863766i	0.161327	−	0.0931423i
$87$		0			0
$88$	0.123075	+	0.0710575i	0.0131199	+	0.00757476i
$89$	0.748203	−	1.29593i	0.0793094	−	0.137368i	−0.823643	−	0.567109i	$-0.808062\pi$
$89$	0.748203	−	1.29593i	0.0793094	−	0.137368i	0.902952	+	0.429741i	$0.141395\pi$
$90$		0			0
$91$	−0.205672	−	3.17070i	−0.0215603	−	0.332380i
$92$	−2.15286	−	3.72887i	−0.224451	−	0.388761i
$93$		0			0
$94$			5.04557i			0.520411i
$95$	10.6305	−	7.43985i	1.09067	−	0.763313i
$96$		0			0
$97$	2.01118	+	3.48347i	0.204204	+	0.353693i	0.949879	−	0.312618i	$-0.101206\pi$
$97$	2.01118	+	3.48347i	0.204204	+	0.353693i	−0.745674	+	0.666310i	$0.767873\pi$
$98$	2.68750	−	6.46354i	0.271479	−	0.652916i
$99$		0			0
$100$	−3.21214	−	3.83173i	−0.321214	−	0.383173i
$101$	−1.68050	+	2.91071i	−0.167216	+	0.289626i	−0.937440	−	0.348147i	$-0.886811\pi$
$101$	−1.68050	+	2.91071i	−0.167216	+	0.289626i	0.770224	+	0.637773i	$0.220144\pi$
$102$		0			0
$103$	9.57498	+	16.5843i	0.943450	+	1.63410i	0.758825	+	0.651295i	$0.225774\pi$
$103$	9.57498	+	16.5843i	0.943450	+	1.63410i	0.184626	+	0.982809i	$0.440893\pi$
$104$	0.600465	−	1.04004i	0.0588805	−	0.101984i
$105$		0			0
$106$	1.34026	+	2.32140i	0.130178	+	0.225474i
$107$	−7.15043	+	12.3849i	−0.691258	+	1.19729i	0.280168	+	0.959951i	$0.409610\pi$
$107$	−7.15043	+	12.3849i	−0.691258	+	1.19729i	−0.971426	+	0.237343i	$0.923724\pi$
$108$		0			0
$109$	8.89823	+	15.4122i	0.852296	+	1.47622i	0.879131	+	0.476580i	$0.158124\pi$
$109$	8.89823	+	15.4122i	0.852296	+	1.47622i	−0.0268351	+	0.999640i	$0.508543\pi$
$110$	0.260352	−	0.182209i	0.0248236	−	0.0173730i
$111$		0			0
$112$	2.20085	−	1.46842i	0.207961	−	0.138752i
$113$	8.09024	−	14.0127i	0.761066	−	1.31820i	−0.181236	−	0.983440i	$-0.558010\pi$
$113$	8.09024	−	14.0127i	0.761066	−	1.31820i	0.942302	−	0.334765i	$-0.108657\pi$
$114$		0			0
$115$	−9.59146	+	0.836873i	−0.894408	+	0.0780388i
$116$	−3.20977	+	1.85316i	−0.298020	+	0.172062i
$117$		0			0
$118$	−9.80986			−0.903071
$119$	−0.122180	+	0.247337i	−0.0112003	+	0.0226733i
$120$		0			0
$121$	−5.48990	−	9.50879i	−0.499082	−	0.864435i
$122$		−	12.3067i		−	1.11419i
$123$		0			0
$124$		−	3.59772i		−	0.323085i
$125$	−10.8014	+	2.88607i	−0.966108	+	0.258138i
$126$		0			0
$127$			11.0556i			0.981023i	0.871435	+	0.490511i	$0.163190\pi$
$127$			11.0556i			0.981023i	−0.871435	+	0.490511i	$0.836810\pi$
$128$	1.00000			0.0883883
$129$		0			0
$130$	−1.53974	−	2.20008i	−0.135044	−	0.192960i
$131$	4.68485	+	8.11440i	0.409318	+	0.708959i	0.994813	−	0.101717i	$-0.0324335\pi$
$131$	4.68485	+	8.11440i	0.409318	+	0.708959i	−0.585496	+	0.810675i	$0.699100\pi$
$132$		0			0
$133$	15.3204	−	0.993780i	1.32845	−	0.0861717i
$134$		−	7.27754i		−	0.628684i
$135$		0			0
$136$	−0.0902992	+	0.0521342i	−0.00774309	+	0.00447047i
$137$	9.56078	−	16.5598i	0.816833	−	1.41480i	−0.0911716	−	0.995835i	$-0.529061\pi$
$137$	9.56078	−	16.5598i	0.816833	−	1.41480i	0.908004	−	0.418961i	$-0.137605\pi$
$138$		0			0
$139$	0.954315	+	0.550974i	0.0809439	+	0.0467330i	0.539926	−	0.841713i	$-0.318452\pi$
$139$	0.954315	+	0.550974i	0.0809439	+	0.0467330i	−0.458982	+	0.888446i	$0.651786\pi$
$140$	−0.894657	−	5.84804i	−0.0756123	−	0.494250i
$141$		0			0
$142$		−	12.4507i		−	1.04484i
$143$	0.147805	−	0.0853352i	0.0123601	−	0.00713608i
$144$		0			0
$145$	0.720372	+	8.25623i	0.0598236	+	0.685643i
$146$	4.01981	+	6.96252i	0.332682	+	0.576222i
$147$		0			0
$148$	5.42899	+	3.13443i	0.446260	+	0.257648i
$149$	12.1146	−	6.99438i	0.992468	−	0.573002i	0.0864572	−	0.996256i	$-0.472445\pi$
$149$	12.1146	−	6.99438i	0.992468	−	0.573002i	0.906011	+	0.423254i	$0.139112\pi$
$150$		0			0
$151$	2.45666	−	4.25506i	0.199920	−	0.346272i	−0.748582	−	0.663042i	$-0.769265\pi$
$151$	2.45666	−	4.25506i	0.199920	−	0.346272i	0.948502	+	0.316770i	$0.102598\pi$
$152$	5.02533	+	2.90137i	0.407608	+	0.235333i
$153$		0			0
$154$	0.375212	−	0.0243387i	0.0302355	−	0.00196126i
$155$	−7.29022	−	3.40157i	−0.585565	−	0.273221i
$156$		0			0
$157$	−6.40902			−0.511495			−0.255748	−	0.966744i	$-0.582322\pi$
$157$	−6.40902			−0.511495			−0.255748	+	0.966744i	$0.582322\pi$
$158$	−8.41003			−0.669066
$159$		0			0
$160$	0.945479	−	2.02634i	0.0747467	−	0.160197i
$161$	−10.2137	−	5.04539i	−0.804950	−	0.397632i
$162$		0			0
$163$	−0.970831	−	0.560510i	−0.0760414	−	0.0439025i	0.461497	−	0.887142i	$-0.347312\pi$
$163$	−0.970831	−	0.560510i	−0.0760414	−	0.0439025i	−0.537539	+	0.843239i	$0.680646\pi$
$164$	−3.96636	+	6.86994i	−0.309721	+	0.536452i
$165$		0			0
$166$	−2.03412	+	1.17440i	−0.157879	+	0.0911512i
$167$	0.739056	+	0.426694i	0.0571899	+	0.0330186i	0.528322	−	0.849044i	$-0.322821\pi$
$167$	0.739056	+	0.426694i	0.0571899	+	0.0330186i	−0.471132	+	0.882062i	$0.656155\pi$
$168$		0			0
$169$	5.77888	+	10.0093i	0.444529	+	0.769948i
$170$	0.0202659	+	0.232269i	0.00155432	+	0.0178142i
$171$		0			0
$172$	1.49609	−	0.863766i	0.114076	−	0.0658615i
$173$			25.1821i			1.91456i	0.289162	+	0.957280i	$0.406623\pi$
$173$			25.1821i			1.91456i	−0.289162	+	0.957280i	$0.593377\pi$
$174$		0			0
$175$	−12.6960	−	3.71632i	−0.959729	−	0.280927i
$176$	0.123075	+	0.0710575i	0.00927714	+	0.00535616i
$177$		0			0
$178$	0.748203	−	1.29593i	0.0560802	−	0.0971337i
$179$	14.0102	−	8.08881i	1.04717	−	0.604586i	0.125317	−	0.992117i	$-0.460005\pi$
$179$	14.0102	−	8.08881i	1.04717	−	0.604586i	0.921857	+	0.387531i	$0.126672\pi$
$180$		0			0
$181$		−	17.0243i		−	1.26540i	−0.774396	−	0.632701i	$-0.781946\pi$
$181$		−	17.0243i		−	1.26540i	0.774396	−	0.632701i	$-0.218054\pi$
$182$	−0.205672	−	3.17070i	−0.0152454	−	0.235028i
$183$		0			0
$184$	−2.15286	−	3.72887i	−0.158711	−	0.274896i
$185$	11.4844	−	8.03746i	0.844351	−	0.590925i
$186$		0			0
$187$	−0.0148181			−0.00108361
$188$			5.04557i			0.367986i
$189$		0			0
$190$	10.6305	−	7.43985i	0.771220	−	0.539744i
$191$		−	3.96791i		−	0.287108i	−0.989643	−	0.143554i	$-0.954147\pi$
$191$		−	3.96791i		−	0.287108i	0.989643	−	0.143554i	$-0.0458530\pi$
$192$		0			0
$193$		−	1.29203i		−	0.0930026i	−0.998918	−	0.0465013i	$-0.985193\pi$
$193$		−	1.29203i		−	0.0930026i	0.998918	−	0.0465013i	$-0.0148072\pi$
$194$	2.01118	+	3.48347i	0.144394	+	0.250098i
$195$		0			0
$196$	2.68750	−	6.46354i	0.191964	−	0.461681i
$197$	0.983884			0.0700988			0.0350494	−	0.999386i	$-0.488841\pi$
$197$	0.983884			0.0700988			0.0350494	+	0.999386i	$0.488841\pi$
$198$		0			0
$199$	−20.6241	+	11.9073i	−1.46200	+	0.844086i	−0.999104	−	0.0423259i	$-0.986523\pi$
$199$	−20.6241	+	11.9073i	−1.46200	+	0.844086i	−0.462897	+	0.886412i	$0.653190\pi$
$200$	−3.21214	−	3.83173i	−0.227132	−	0.270944i
$201$		0			0
$202$	−1.68050	+	2.91071i	−0.118239	+	0.204797i
$203$	−4.34302	+	8.79183i	−0.304820	+	0.617065i
$204$		0			0
$205$	10.1707	+	14.5326i	0.710356	+	1.01500i
$206$	9.57498	+	16.5843i	0.667120	+	1.15549i
$207$		0			0
$208$	0.600465	−	1.04004i	0.0416348	−	0.0721136i
$209$	0.412329	+	0.714175i	0.0285214	+	0.0494005i
$210$		0			0
$211$	−11.2221	+	19.4372i	−0.772559	+	1.33811i	0.163597	+	0.986527i	$0.447690\pi$
$211$	−11.2221	+	19.4372i	−0.772559	+	1.33811i	−0.936156	+	0.351585i	$0.885643\pi$
$212$	1.34026	+	2.32140i	0.0920495	+	0.159434i
$213$		0			0
$214$	−7.15043	+	12.3849i	−0.488793	+	0.846614i
$215$	−0.335768	−	3.84826i	−0.0228992	−	0.262449i
$216$		0			0
$217$	−5.28296	−	7.91805i	−0.358630	−	0.537513i
$218$	8.89823	+	15.4122i	0.602664	+	1.04385i
$219$		0			0
$220$	0.260352	−	0.182209i	0.0175529	−	0.0122845i
$221$			0.125219i			0.00842316i
$222$		0			0
$223$	8.99621	+	15.5819i	0.602430	+	1.04344i	0.992452	+	0.122634i	$0.0391343\pi$
$223$	8.99621	+	15.5819i	0.602430	+	1.04344i	−0.390021	+	0.920806i	$0.627532\pi$
$224$	2.20085	−	1.46842i	0.147051	−	0.0981127i
$225$		0			0
$226$	8.09024	−	14.0127i	0.538155	−	0.932111i
$227$	17.5341	+	10.1233i	1.16378	+	0.671909i	0.952207	−	0.305453i	$-0.0988080\pi$
$227$	17.5341	+	10.1233i	1.16378	+	0.671909i	0.211573	+	0.977362i	$0.432141\pi$
$228$		0			0
$229$	−0.650116	+	0.375345i	−0.0429609	+	0.0248035i	−0.521327	−	0.853357i	$-0.674563\pi$
$229$	−0.650116	+	0.375345i	−0.0429609	+	0.0248035i	0.478366	+	0.878161i	$0.341229\pi$
$230$	−9.59146	+	0.836873i	−0.632442	+	0.0551818i
$231$		0			0
$232$	−3.20977	+	1.85316i	−0.210732	+	0.121666i
$233$	−9.57787	+	16.5894i	−0.627467	+	1.08681i	0.360591	+	0.932724i	$0.382575\pi$
$233$	−9.57787	+	16.5894i	−0.627467	+	1.08681i	−0.988058	+	0.154081i	$0.950758\pi$
$234$		0			0
$235$	10.2241	+	4.77049i	0.666945	+	0.311192i
$236$	−9.80986			−0.638567
$237$		0			0
$238$	−0.122180	+	0.247337i	−0.00791977	+	0.0160325i
$239$	−1.15565	−	0.667217i	−0.0747531	−	0.0431587i	0.462158	−	0.886798i	$-0.347075\pi$
$239$	−1.15565	−	0.667217i	−0.0747531	−	0.0431587i	−0.536911	+	0.843639i	$0.680409\pi$
$240$		0			0
$241$	−17.1287	−	9.88925i	−1.10336	−	0.637023i	−0.166256	−	0.986083i	$-0.553168\pi$
$241$	−17.1287	−	9.88925i	−1.10336	−	0.637023i	−0.937100	+	0.349060i	$0.886501\pi$
$242$	−5.48990	−	9.50879i	−0.352904	−	0.611248i
$243$		0			0
$244$		−	12.3067i		−	0.787853i
$245$	−10.5564	−	11.5569i	−0.674422	−	0.738346i
$246$		0			0
$247$	6.03507	−	3.48435i	0.384002	−	0.221704i
$248$		−	3.59772i		−	0.228456i
$249$		0			0
$250$	−10.8014	+	2.88607i	−0.683142	+	0.182531i
$251$	−28.8281			−1.81961			−0.909805	−	0.415035i	$-0.863769\pi$
$251$	−28.8281			−1.81961			−0.909805	+	0.415035i	$0.863769\pi$
$252$		0			0
$253$		−	0.611908i		−	0.0384703i
$254$			11.0556i			0.693688i
$255$		0			0
$256$	1.00000			0.0625000
$257$	−15.5450	+	8.97493i	−0.969672	+	0.559841i	−0.899136	−	0.437669i	$-0.855804\pi$
$257$	−15.5450	+	8.97493i	−0.969672	+	0.559841i	−0.0705361	+	0.997509i	$0.522471\pi$
$258$		0			0
$259$	16.5510	−	1.07361i	1.02843	−	0.0667106i
$260$	−1.53974	−	2.20008i	−0.0954909	−	0.136443i
$261$		0			0
$262$	4.68485	+	8.11440i	0.289431	+	0.501310i
$263$	−7.94184	+	13.7557i	−0.489715	+	0.848211i	−0.999930	−	0.0118356i	$-0.996233\pi$
$263$	−7.94184	+	13.7557i	−0.489715	+	0.848211i	0.510215	+	0.860047i	$0.329566\pi$
$264$		0			0
$265$	5.97114	−	0.520994i	0.366804	−	0.0320044i
$266$	15.3204	−	0.993780i	0.939356	−	0.0609326i
$267$		0			0
$268$		−	7.27754i		−	0.444547i
$269$	−5.25345	−	9.09924i	−0.320308	−	0.554790i	0.660243	−	0.751052i	$-0.270453\pi$
$269$	−5.25345	−	9.09924i	−0.320308	−	0.554790i	−0.980552	+	0.196261i	$0.937120\pi$
$270$		0			0
$271$	10.9732	+	6.33540i	0.666577	+	0.384848i	0.794778	−	0.606900i	$-0.207587\pi$
$271$	10.9732	+	6.33540i	0.666577	+	0.384848i	−0.128202	+	0.991748i	$0.540920\pi$
$272$	−0.0902992	+	0.0521342i	−0.00547519	+	0.00316110i
$273$		0			0
$274$	9.56078	−	16.5598i	0.577588	−	1.00041i
$275$	−0.123061	−	0.699838i	−0.00742087	−	0.0422018i
$276$		0			0
$277$	12.8968	+	7.44600i	0.774896	+	0.447387i	0.834619	−	0.550828i	$-0.185688\pi$
$277$	12.8968	+	7.44600i	0.774896	+	0.447387i	−0.0597221	+	0.998215i	$0.519021\pi$
$278$	0.954315	+	0.550974i	0.0572360	+	0.0330452i
$279$		0			0
$280$	−0.894657	−	5.84804i	−0.0534660	−	0.349487i
$281$	−5.92114	+	3.41857i	−0.353226	+	0.203935i	−0.666105	−	0.745858i	$-0.732040\pi$
$281$	−5.92114	+	3.41857i	−0.353226	+	0.203935i	0.312879	+	0.949793i	$0.398706\pi$
$282$		0			0
$283$	11.6293			0.691292			0.345646	−	0.938365i	$-0.387660\pi$
$283$	11.6293			0.691292			0.345646	+	0.938365i	$0.387660\pi$
$284$		−	12.4507i		−	0.738812i
$285$		0			0
$286$	0.147805	−	0.0853352i	0.00873988	−	0.00504597i
$287$	1.35856	+	20.9440i	0.0801933	+	1.23629i
$288$		0			0
$289$	−8.49456	+	14.7130i	−0.499680	+	0.865472i
$290$	0.720372	+	8.25623i	0.0423017	+	0.484823i
$291$		0			0
$292$	4.01981	+	6.96252i	0.235242	+	0.407450i
$293$	−8.60234	−	4.96657i	−0.502554	−	0.290150i	0.227213	−	0.973845i	$-0.427038\pi$
$293$	−8.60234	−	4.96657i	−0.502554	−	0.290150i	−0.729768	+	0.683695i	$0.760372\pi$
$294$		0			0
$295$	−9.27502	+	19.8781i	−0.540013	+	1.15735i
$296$	5.42899	+	3.13443i	0.315553	+	0.182185i
$297$		0			0
$298$	12.1146	−	6.99438i	0.701781	−	0.405174i
$299$	−5.17088			−0.299040
$300$		0			0
$301$	2.02430	−	4.09790i	0.116679	−	0.236199i
$302$	2.45666	−	4.25506i	0.141365	−	0.244851i
$303$		0			0
$304$	5.02533	+	2.90137i	0.288222	+	0.166405i
$305$	−24.9375	−	11.6357i	−1.42792	−	0.666258i
$306$		0			0
$307$	−25.3226			−1.44524			−0.722618	−	0.691247i	$-0.757061\pi$
$307$	−25.3226			−1.44524			−0.722618	+	0.691247i	$0.757061\pi$
$308$	0.375212	−	0.0243387i	0.0213797	−	0.00138682i
$309$		0			0
$310$	−7.29022	−	3.40157i	−0.414057	−	0.193196i
$311$	−7.32275			−0.415235			−0.207618	−	0.978210i	$-0.566571\pi$
$311$	−7.32275			−0.415235			−0.207618	+	0.978210i	$0.566571\pi$
$312$		0			0
$313$	8.48704			0.479716			0.239858	−	0.970808i	$-0.422899\pi$
$313$	8.48704			0.479716			0.239858	+	0.970808i	$0.422899\pi$
$314$	−6.40902			−0.361682
$315$		0			0
$316$	−8.41003			−0.473101
$317$	2.24351			0.126008			0.0630039	−	0.998013i	$-0.479932\pi$
$317$	2.24351			0.126008			0.0630039	+	0.998013i	$0.479932\pi$
$318$		0			0
$319$	−0.526725			−0.0294909
$320$	0.945479	−	2.02634i	0.0528539	−	0.113276i
$321$		0			0
$322$	−10.2137	−	5.04539i	−0.569185	−	0.281168i
$323$	−0.605044			−0.0336655
$324$		0			0
$325$	−5.91392	+	1.03992i	−0.328045	+	0.0576843i
$326$	−0.970831	−	0.560510i	−0.0537694	−	0.0310438i
$327$		0			0
$328$	−3.96636	+	6.86994i	−0.219006	+	0.379329i
$329$	7.40901	+	11.1046i	0.408472	+	0.612214i
$330$		0			0
$331$	−5.04537			−0.277319			−0.138659	−	0.990340i	$-0.544279\pi$
$331$	−5.04537			−0.277319			−0.138659	+	0.990340i	$0.544279\pi$
$332$	−2.03412	+	1.17440i	−0.111637	+	0.0644536i
$333$		0			0
$334$	0.739056	+	0.426694i	0.0404394	+	0.0233477i
$335$	−14.7468	−	6.88077i	−0.805704	−	0.375936i
$336$		0			0
$337$	−30.0990	−	17.3777i	−1.63960	−	0.946623i	−0.980971	−	0.194155i	$-0.937804\pi$
$337$	−30.0990	−	17.3777i	−1.63960	−	0.946623i	−0.658629	−	0.752468i	$-0.728863\pi$
$338$	5.77888	+	10.0093i	0.314330	+	0.544435i
$339$		0			0
$340$	0.0202659	+	0.232269i	0.00109907	+	0.0125966i
$341$	0.255645	−	0.442790i	0.0138440	−	0.0239784i
$342$		0			0
$343$	−3.57637	−	18.1717i	−0.193106	−	0.981178i
$344$	1.49609	−	0.863766i	0.0806636	−	0.0465711i
$345$		0			0
$346$			25.1821i			1.35380i
$347$	−6.90143			−0.370488			−0.185244	−	0.982693i	$-0.559308\pi$
$347$	−6.90143			−0.370488			−0.185244	+	0.982693i	$0.559308\pi$
$348$		0			0
$349$	−0.226488	+	0.130763i	−0.0121237	+	0.00699959i	−0.506050	−	0.862504i	$-0.668895\pi$
$349$	−0.226488	+	0.130763i	−0.0121237	+	0.00699959i	0.493926	+	0.869504i	$0.335561\pi$
$350$	−12.6960	−	3.71632i	−0.678631	−	0.198646i
$351$		0			0
$352$	0.123075	+	0.0710575i	0.00655993	+	0.00378738i
$353$	24.7213	+	14.2729i	1.31578	+	0.759668i	0.983047	−	0.183351i	$-0.0586946\pi$
$353$	24.7213	+	14.2729i	1.31578	+	0.759668i	0.332737	+	0.943020i	$0.392028\pi$
$354$		0			0
$355$	−25.2294	−	11.7719i	−1.33904	−	0.624786i
$356$	0.748203	−	1.29593i	0.0396547	−	0.0686839i
$357$		0			0
$358$	14.0102	−	8.08881i	0.740464	−	0.427507i
$359$	10.5441	+	6.08767i	0.556499	+	0.321295i	0.751739	−	0.659461i	$-0.229215\pi$
$359$	10.5441	+	6.08767i	0.556499	+	0.321295i	−0.195240	+	0.980755i	$0.562549\pi$
$360$		0			0
$361$	7.33595	+	12.7062i	0.386103	+	0.668750i
$362$		−	17.0243i		−	0.894775i
$363$		0			0
$364$	−0.205672	−	3.17070i	−0.0107801	−	0.166190i
$365$	17.9091	−	1.56260i	0.937405	−	0.0817904i
$366$		0			0
$367$	−11.1198	+	19.2601i	−0.580451	+	1.00537i	0.414975	+	0.909833i	$0.363790\pi$
$367$	−11.1198	+	19.2601i	−0.580451	+	1.00537i	−0.995426	+	0.0955375i	$0.969543\pi$
$368$	−2.15286	−	3.72887i	−0.112226	−	0.194381i
$369$		0			0
$370$	11.4844	−	8.03746i	0.597046	−	0.417847i
$371$	6.35850	+	3.14100i	0.330117	+	0.163072i
$372$		0			0
$373$	3.32049	−	1.91709i	0.171929	−	0.0992631i	−0.411566	−	0.911380i	$-0.635018\pi$
$373$	3.32049	−	1.91709i	0.171929	−	0.0992631i	0.583495	+	0.812117i	$0.301685\pi$
$374$	−0.0148181			−0.000766227
$375$		0			0
$376$			5.04557i			0.260206i
$377$			4.45104i			0.229240i
$378$		0			0
$379$	−29.0957			−1.49454			−0.747272	−	0.664519i	$-0.768637\pi$
$379$	−29.0957			−1.49454			−0.747272	+	0.664519i	$0.768637\pi$
$380$	10.6305	−	7.43985i	0.545335	−	0.381656i
$381$		0			0
$382$		−	3.96791i		−	0.203016i
$383$	−12.2543	+	7.07501i	−0.626164	+	0.361516i	−0.779265	−	0.626695i	$-0.784407\pi$
$383$	−12.2543	+	7.07501i	−0.626164	+	0.361516i	0.153101	+	0.988211i	$0.451074\pi$
$384$		0			0
$385$	0.305437	−	0.783321i	0.0155665	−	0.0399217i
$386$		−	1.29203i		−	0.0657628i
$387$		0			0
$388$	2.01118	+	3.48347i	0.102102	+	0.176846i
$389$	29.9470	+	17.2899i	1.51837	+	0.876633i	0.999766	+	0.0216198i	$0.00688233\pi$
$389$	29.9470	+	17.2899i	1.51837	+	0.876633i	0.518606	+	0.855013i	$0.326451\pi$
$390$		0			0
$391$	0.388803	+	0.224476i	0.0196626	+	0.0113522i
$392$	2.68750	−	6.46354i	0.135739	−	0.326458i
$393$		0			0
$394$	0.983884			0.0495674
$395$	−7.95151	+	17.0416i	−0.400084	+	0.857456i
$396$		0			0
$397$	14.6731	−	25.4146i	0.736422	−	1.27552i	−0.217674	−	0.976022i	$-0.569847\pi$
$397$	14.6731	−	25.4146i	0.736422	−	1.27552i	0.954096	−	0.299500i	$-0.0968197\pi$
$398$	−20.6241	+	11.9073i	−1.03379	+	0.596859i
$399$		0			0
$400$	−3.21214	−	3.83173i	−0.160607	−	0.191587i
$401$	22.8472	−	13.1908i	1.14093	−	0.658719i	0.194273	−	0.980948i	$-0.437765\pi$
$401$	22.8472	−	13.1908i	1.14093	−	0.658719i	0.946662	+	0.322229i	$0.104432\pi$
$402$		0			0
$403$	−3.74176	−	2.16031i	−0.186390	−	0.107613i
$404$	−1.68050	+	2.91071i	−0.0836079	+	0.144813i
$405$		0			0
$406$	−4.34302	+	8.79183i	−0.215541	+	0.436331i
$407$	0.445449	+	0.771540i	0.0220801	+	0.0382438i
$408$		0			0
$409$			12.8464i			0.635215i	0.948222	+	0.317607i	$0.102879\pi$
$409$			12.8464i			0.635215i	−0.948222	+	0.317607i	$0.897121\pi$
$410$	10.1707	+	14.5326i	0.502297	+	0.717714i
$411$		0			0
$412$	9.57498	+	16.5843i	0.471725	+	0.817052i
$413$	−21.5901	+	14.4050i	−1.06238	+	0.708822i
$414$		0			0
$415$	0.456520	+	5.23220i	0.0224097	+	0.256839i
$416$	0.600465	−	1.04004i	0.0294402	−	0.0509920i
$417$		0			0
$418$	0.412329	+	0.714175i	0.0201677	+	0.0349314i
$419$	5.13440	−	8.89304i	0.250832	−	0.434453i	−0.712923	−	0.701242i	$-0.752629\pi$
$419$	5.13440	−	8.89304i	0.250832	−	0.434453i	0.963755	+	0.266789i	$0.0859626\pi$
$420$		0			0
$421$	3.18306	+	5.51323i	0.155133	+	0.268698i	0.933107	−	0.359598i	$-0.117086\pi$
$421$	3.18306	+	5.51323i	0.155133	+	0.268698i	−0.777974	+	0.628296i	$0.783753\pi$
$422$	−11.2221	+	19.4372i	−0.546282	+	0.946188i
$423$		0			0
$424$	1.34026	+	2.32140i	0.0650888	+	0.112737i
$425$	0.489818	+	0.178540i	0.0237597	+	0.00866045i
$426$		0			0
$427$	−18.0713	−	27.0851i	−0.874532	−	1.31074i
$428$	−7.15043	+	12.3849i	−0.345629	+	0.598647i
$429$		0			0
$430$	−0.335768	−	3.84826i	−0.0161922	−	0.185579i
$431$	3.37653	−	1.94944i	0.162642	−	0.0939012i	−0.416470	−	0.909149i	$-0.636733\pi$
$431$	3.37653	−	1.94944i	0.162642	−	0.0939012i	0.579112	+	0.815248i	$0.303400\pi$
$432$		0			0
$433$	−20.9340			−1.00603			−0.503013	−	0.864279i	$-0.667775\pi$
$433$	−20.9340			−1.00603			−0.503013	+	0.864279i	$0.667775\pi$
$434$	−5.28296	−	7.91805i	−0.253590	−	0.380079i
$435$		0			0
$436$	8.89823	+	15.4122i	0.426148	+	0.738110i
$437$		−	24.9851i		−	1.19520i
$438$		0			0
$439$			16.4017i			0.782811i	0.920218	+	0.391406i	$0.128011\pi$
$439$			16.4017i			0.782811i	−0.920218	+	0.391406i	$0.871989\pi$
$440$	0.260352	−	0.182209i	0.0124118	−	0.00868649i
$441$		0			0
$442$			0.125219i			0.00595607i
$443$	26.3852			1.25360			0.626800	−	0.779180i	$-0.284364\pi$
$443$	26.3852			1.25360			0.626800	+	0.779180i	$0.284364\pi$
$444$		0			0
$445$	−1.91858	−	2.74139i	−0.0909494	−	0.129954i
$446$	8.99621	+	15.5819i	0.425983	+	0.737824i
$447$		0			0
$448$	2.20085	−	1.46842i	0.103981	−	0.0693762i
$449$			32.5310i			1.53523i	0.640911	+	0.767615i	$0.278557\pi$
$449$			32.5310i			1.53523i	−0.640911	+	0.767615i	$0.721443\pi$
$450$		0			0
$451$	−0.976322	+	0.563680i	−0.0459732	+	0.0265426i
$452$	8.09024	−	14.0127i	0.380533	−	0.659102i
$453$		0			0
$454$	17.5341	+	10.1233i	0.822917	+	0.475111i
$455$	−6.61939	−	2.58107i	−0.310322	−	0.121002i
$456$		0			0
$457$		−	35.0085i		−	1.63763i	−0.574058	−	0.818814i	$-0.694632\pi$
$457$		−	35.0085i		−	1.63763i	0.574058	−	0.818814i	$-0.305368\pi$
$458$	−0.650116	+	0.375345i	−0.0303779	+	0.0175387i
$459$		0			0
$460$	−9.59146	+	0.836873i	−0.447204	+	0.0390194i
$461$	5.08610	+	8.80939i	0.236883	+	0.410294i	0.959818	−	0.280622i	$-0.0905407\pi$
$461$	5.08610	+	8.80939i	0.236883	+	0.410294i	−0.722935	+	0.690916i	$0.757207\pi$
$462$		0			0
$463$	27.5356	+	15.8977i	1.27969	+	0.738828i	0.976791	−	0.214195i	$-0.0687128\pi$
$463$	27.5356	+	15.8977i	1.27969	+	0.738828i	0.302897	+	0.953023i	$0.402046\pi$
$464$	−3.20977	+	1.85316i	−0.149010	+	0.0860310i
$465$		0			0
$466$	−9.57787	+	16.5894i	−0.443686	+	0.768487i
$467$	−19.5141	−	11.2665i	−0.903006	−	0.521351i	−0.0248321	−	0.999692i	$-0.507905\pi$
$467$	−19.5141	−	11.2665i	−0.903006	−	0.521351i	−0.878174	+	0.478341i	$0.841238\pi$
$468$		0			0
$469$	−10.6865	−	16.0168i	−0.493455	−	0.739587i
$470$	10.2241	+	4.77049i	0.471601	+	0.220046i
$471$		0			0
$472$	−9.80986			−0.451535
$473$	0.245508			0.0112885
$474$		0			0
$475$	−5.02476	−	28.5753i	−0.230552	−	1.31113i
$476$	−0.122180	+	0.247337i	−0.00560013	+	0.0113367i
$477$		0			0
$478$	−1.15565	−	0.667217i	−0.0528584	−	0.0305178i
$479$	−4.81018	+	8.33147i	−0.219783	+	0.380675i	−0.954741	−	0.297437i	$-0.903868\pi$
$479$	−4.81018	+	8.33147i	−0.219783	+	0.380675i	0.734959	+	0.678112i	$0.237201\pi$
$480$		0			0
$481$	6.51984	−	3.76423i	0.297279	−	0.171634i
$482$	−17.1287	−	9.88925i	−0.780191	−	0.450443i
$483$		0			0
$484$	−5.48990	−	9.50879i	−0.249541	−	0.432218i
$485$	8.96023	−	0.781797i	0.406863	−	0.0354996i
$486$		0			0
$487$	8.50444	−	4.91004i	0.385373	−	0.222495i	−0.294781	−	0.955565i	$-0.595247\pi$
$487$	8.50444	−	4.91004i	0.385373	−	0.222495i	0.680153	+	0.733070i	$0.261913\pi$
$488$		−	12.3067i		−	0.557096i
$489$		0			0
$490$	−10.5564	−	11.5569i	−0.476888	−	0.522090i
$491$	−24.7333	−	14.2798i	−1.11620	−	0.644437i	−0.175770	−	0.984431i	$-0.556242\pi$
$491$	−24.7333	−	14.2798i	−1.11620	−	0.644437i	−0.940428	+	0.339994i	$0.889575\pi$
$492$		0			0
$493$	0.193227	−	0.334678i	0.00870249	−	0.0150732i
$494$	6.03507	−	3.48435i	0.271531	−	0.156768i
$495$		0			0
$496$		−	3.59772i		−	0.161542i
$497$	−18.2828	−	27.4021i	−0.820095	−	1.22915i
$498$		0			0
$499$	−10.3032	−	17.8456i	−0.461232	−	0.798878i	0.537790	−	0.843079i	$-0.319259\pi$
$499$	−10.3032	−	17.8456i	−0.461232	−	0.798878i	−0.999023	+	0.0442006i	$0.985926\pi$
$500$	−10.8014	+	2.88607i	−0.483054	+	0.129069i
$501$		0			0
$502$	−28.8281			−1.28666
$503$			5.19287i			0.231539i	0.993276	+	0.115769i	$0.0369333\pi$
$503$			5.19287i			0.231539i	−0.993276	+	0.115769i	$0.963067\pi$
$504$		0			0
$505$	4.30922	+	6.15728i	0.191758	+	0.273995i
$506$		−	0.611908i		−	0.0272026i
$507$		0			0
$508$			11.0556i			0.490511i
$509$	17.7208	+	30.6933i	0.785461	+	1.36046i	0.928724	+	0.370773i	$0.120907\pi$
$509$	17.7208	+	30.6933i	0.785461	+	1.36046i	−0.143263	+	0.989685i	$0.545759\pi$
$510$		0			0
$511$	19.0709	+	9.42071i	0.843646	+	0.416748i
$512$	1.00000			0.0441942
$513$		0			0
$514$	−15.5450	+	8.97493i	−0.685662	+	0.395867i
$515$	42.6585	−	3.72204i	1.87976	−	0.164013i
$516$		0			0
$517$	−0.358526	+	0.620985i	−0.0157680	+	0.0273109i
$518$	16.5510	−	1.07361i	0.727211	−	0.0471715i
$519$		0			0
$520$	−1.53974	−	2.20008i	−0.0675222	−	0.0964800i
$521$	5.23647	+	9.06983i	0.229414	+	0.397356i	0.957635	−	0.287986i	$-0.0929858\pi$
$521$	5.23647	+	9.06983i	0.229414	+	0.397356i	−0.728221	+	0.685343i	$0.759652\pi$
$522$		0			0
$523$	−16.1085	+	27.9007i	−0.704375	+	1.22001i	0.262541	+	0.964921i	$0.415440\pi$
$523$	−16.1085	+	27.9007i	−0.704375	+	1.22001i	−0.966916	+	0.255093i	$0.917894\pi$
$524$	4.68485	+	8.11440i	0.204659	+	0.354479i
$525$		0			0
$526$	−7.94184	+	13.7557i	−0.346281	+	0.599776i
$527$	0.187564	+	0.324871i	0.00817044	+	0.0141516i
$528$		0			0
$529$	2.23036	−	3.86310i	0.0969723	−	0.167961i
$530$	5.97114	−	0.520994i	0.259370	−	0.0226305i
$531$		0			0
$532$	15.3204	−	0.993780i	0.664225	−	0.0430858i
$533$	4.76333	+	8.25032i	0.206323	+	0.357361i
$534$		0			0
$535$	18.3355	+	26.1989i	0.792712	+	1.13268i
$536$		−	7.27754i		−	0.314342i
$537$		0			0
$538$	−5.25345	−	9.09924i	−0.226492	−	0.392296i
$539$	0.790048	−	0.604534i	0.0340298	−	0.0260391i
$540$		0			0
$541$	12.4544	−	21.5717i	0.535457	−	0.927439i	−0.463684	−	0.886001i	$-0.653473\pi$
$541$	12.4544	−	21.5717i	0.535457	−	0.927439i	0.999141	−	0.0414381i	$-0.0131939\pi$
$542$	10.9732	+	6.33540i	0.471341	+	0.272129i
$543$		0			0
$544$	−0.0902992	+	0.0521342i	−0.00387154	+	0.00223524i
$545$	39.6435	−	3.45897i	1.69814	−	0.148166i
$546$		0			0
$547$	−23.6806	+	13.6720i	−1.01251	+	0.584574i	−0.911926	−	0.410355i	$-0.865405\pi$
$547$	−23.6806	+	13.6720i	−1.01251	+	0.584574i	−0.100585	+	0.994928i	$0.532072\pi$
$548$	9.56078	−	16.5598i	0.408416	−	0.707398i
$549$		0			0
$550$	−0.123061	−	0.699838i	−0.00524735	−	0.0298412i
$551$	−21.5069			−0.916224
$552$		0			0
$553$	−18.5092	+	12.3494i	−0.787093	+	0.525151i
$554$	12.8968	+	7.44600i	0.547935	+	0.316350i
$555$		0			0
$556$	0.954315	+	0.550974i	0.0404720	+	0.0233665i
$557$	−8.95463	−	15.5099i	−0.379420	−	0.657175i	0.611558	−	0.791200i	$-0.290543\pi$
$557$	−8.95463	−	15.5099i	−0.379420	−	0.657175i	−0.990978	+	0.134025i	$0.957210\pi$
$558$		0			0
$559$		−	2.07465i		−	0.0877482i
$560$	−0.894657	−	5.84804i	−0.0378062	−	0.247125i
$561$		0			0
$562$	−5.92114	+	3.41857i	−0.249768	+	0.144204i
$563$			30.4638i			1.28390i	0.766748	+	0.641948i	$0.221874\pi$
$563$			30.4638i			1.28390i	−0.766748	+	0.641948i	$0.778126\pi$
$564$		0			0
$565$	−20.7454	−	29.6423i	−0.872766	−	1.24706i
$566$	11.6293			0.488817
$567$		0			0
$568$		−	12.4507i		−	0.522419i
$569$		−	39.6736i		−	1.66320i	−0.555371	−	0.831602i	$-0.687424\pi$
$569$		−	39.6736i		−	1.66320i	0.555371	−	0.831602i	$-0.312576\pi$
$570$		0			0
$571$	3.24837			0.135940			0.0679699	−	0.997687i	$-0.478348\pi$
$571$	3.24837			0.135940			0.0679699	+	0.997687i	$0.478348\pi$
$572$	0.147805	−	0.0853352i	0.00618003	−	0.00356804i
$573$		0			0
$574$	1.35856	+	20.9440i	0.0567052	+	0.874186i
$575$	−7.37273	+	20.2268i	−0.307464	+	0.843517i
$576$		0			0
$577$	−0.0635247	−	0.110028i	−0.00264457	−	0.00458053i	0.864700	−	0.502289i	$-0.167508\pi$
$577$	−0.0635247	−	0.110028i	−0.00264457	−	0.00458053i	−0.867345	+	0.497708i	$0.834175\pi$
$578$	−8.49456	+	14.7130i	−0.353327	+	0.611981i
$579$		0			0
$580$	0.720372	+	8.25623i	0.0299118	+	0.342821i
$581$	−2.75229	+	5.57162i	−0.114184	+	0.231150i
$582$		0			0
$583$			0.380942i			0.0157770i
$584$	4.01981	+	6.96252i	0.166341	+	0.288111i
$585$		0			0
$586$	−8.60234	−	4.96657i	−0.355360	−	0.205167i
$587$	−2.49693	+	1.44160i	−0.103059	+	0.0595014i	−0.550644	−	0.834740i	$-0.685618\pi$
$587$	−2.49693	+	1.44160i	−0.103059	+	0.0595014i	0.447584	+	0.894242i	$0.352284\pi$
$588$		0			0
$589$	10.4383	−	18.0797i	0.430104	−	0.744962i
$590$	−9.27502	+	19.8781i	−0.381847	+	0.818370i
$591$		0			0
$592$	5.42899	+	3.13443i	0.223130	+	0.128824i
$593$	40.6636	+	23.4772i	1.66986	+	0.964092i	0.967713	+	0.252055i	$0.0811065\pi$
$593$	40.6636	+	23.4772i	1.66986	+	0.964092i	0.702143	+	0.712036i	$0.252227\pi$
$594$		0			0
$595$	0.385670	+	0.481431i	0.0158109	+	0.0197367i
$596$	12.1146	−	6.99438i	0.496234	−	0.286501i
$597$		0			0
$598$	−5.17088			−0.211453
$599$		−	5.67416i		−	0.231840i	−0.993259	−	0.115920i	$-0.963018\pi$
$599$		−	5.67416i		−	0.231840i	0.993259	−	0.115920i	$-0.0369816\pi$
$600$		0			0
$601$	−28.9131	+	16.6930i	−1.17939	+	0.680921i	−0.955873	−	0.293780i	$-0.905087\pi$
$601$	−28.9131	+	16.6930i	−1.17939	+	0.680921i	−0.223516	+	0.974700i	$0.571753\pi$
$602$	2.02430	−	4.09790i	0.0825042	−	0.167018i
$603$		0			0
$604$	2.45666	−	4.25506i	0.0999602	−	0.173136i
$605$	−24.4587	+	2.13406i	−0.994386	+	0.0867621i
$606$		0			0
$607$	22.3763	+	38.7570i	0.908228	+	1.57310i	0.816525	+	0.577310i	$0.195898\pi$
$607$	22.3763	+	38.7570i	0.908228	+	1.57310i	0.0917027	+	0.995786i	$0.470769\pi$
$608$	5.02533	+	2.90137i	0.203804	+	0.117666i
$609$		0			0
$610$	−24.9375	−	11.6357i	−1.00969	−	0.471116i
$611$	5.24758	+	3.02969i	0.212294	+	0.122568i
$612$		0			0
$613$	27.0024	−	15.5899i	1.09062	−	0.629668i	0.156877	−	0.987618i	$-0.449857\pi$
$613$	27.0024	−	15.5899i	1.09062	−	0.629668i	0.933741	+	0.357950i	$0.116524\pi$
$614$	−25.3226			−1.02194
$615$		0			0
$616$	0.375212	−	0.0243387i	0.0151177	−	0.000980632i
$617$	0.359684	−	0.622991i	0.0144803	−	0.0250807i	−0.858694	−	0.512488i	$-0.828724\pi$
$617$	0.359684	−	0.622991i	0.0144803	−	0.0250807i	0.873175	+	0.487407i	$0.162057\pi$
$618$		0			0
$619$	31.7674	+	18.3409i	1.27684	+	0.737184i	0.976266	−	0.216574i	$-0.0694884\pi$
$619$	31.7674	+	18.3409i	1.27684	+	0.737184i	0.300574	+	0.953758i	$0.402822\pi$
$620$	−7.29022	−	3.40157i	−0.292782	−	0.136610i
$621$		0			0
$622$	−7.32275			−0.293616
$623$	−0.256275	−	3.95081i	−0.0102674	−	0.158286i
$624$		0			0
$625$	−4.36434	+	24.6161i	−0.174574	+	0.984644i
$626$	8.48704			0.339210
$627$		0			0
$628$	−6.40902			−0.255748
$629$	−0.653644			−0.0260625
$630$		0			0
$631$	−15.5643			−0.619603			−0.309802	−	0.950801i	$-0.600263\pi$
$631$	−15.5643			−0.619603			−0.309802	+	0.950801i	$0.600263\pi$
$632$	−8.41003			−0.334533
$633$		0			0
$634$	2.24351			0.0891010
$635$	22.4024	+	10.4528i	0.889011	+	0.414807i
$636$		0			0
$637$	−5.10856	−	6.67623i	−0.202409	−	0.264522i
$638$	−0.526725			−0.0208532
$639$		0			0
$640$	0.945479	−	2.02634i	0.0373734	−	0.0800983i
$641$	16.3208	+	9.42280i	0.644632	+	0.372178i	0.786396	−	0.617722i	$-0.211944\pi$
$641$	16.3208	+	9.42280i	0.644632	+	0.372178i	−0.141765	+	0.989900i	$0.545278\pi$
$642$		0			0
$643$	5.39558	−	9.34542i	0.212781	−	0.368548i	−0.739803	−	0.672824i	$-0.765081\pi$
$643$	5.39558	−	9.34542i	0.212781	−	0.368548i	0.952584	+	0.304276i	$0.0984146\pi$
$644$	−10.2137	−	5.04539i	−0.402475	−	0.198816i
$645$		0			0
$646$	−0.605044			−0.0238051
$647$	43.7372	−	25.2517i	1.71949	−	0.992747i	0.799632	−	0.600491i	$-0.205028\pi$
$647$	43.7372	−	25.2517i	1.71949	−	0.992747i	0.919856	−	0.392256i	$-0.128305\pi$
$648$		0			0
$649$	−1.20735	−	0.697064i	−0.0473927	−	0.0273622i
$650$	−5.91392	+	1.03992i	−0.231963	+	0.0407889i
$651$		0			0
$652$	−0.970831	−	0.560510i	−0.0380207	−	0.0219513i
$653$	−18.0024	−	31.1811i	−0.704490	−	1.22021i	−0.966875	−	0.255249i	$-0.917842\pi$
$653$	−18.0024	−	31.1811i	−0.704490	−	1.22021i	0.262385	−	0.964963i	$-0.415491\pi$
$654$		0			0
$655$	20.8720	−	1.82112i	0.815537	−	0.0711571i
$656$	−3.96636	+	6.86994i	−0.154860	+	0.268226i
$657$		0			0
$658$	7.40901	+	11.1046i	0.288833	+	0.432901i
$659$	−4.91626	+	2.83840i	−0.191510	+	0.110568i	−0.592689	−	0.805431i	$-0.701934\pi$
$659$	−4.91626	+	2.83840i	−0.191510	+	0.110568i	0.401179	+	0.916000i	$0.368600\pi$
$660$		0			0
$661$		−	21.4910i		−	0.835902i	−0.908470	−	0.417951i	$-0.862748\pi$
$661$		−	21.4910i		−	0.835902i	0.908470	−	0.417951i	$-0.137252\pi$
$662$	−5.04537			−0.196094
$663$		0			0
$664$	−2.03412	+	1.17440i	−0.0789393	+	0.0455756i
$665$	12.4714	−	31.9841i	0.483621	−	1.24029i
$666$		0			0
$667$	13.8204	+	7.97922i	0.535128	+	0.308956i
$668$	0.739056	+	0.426694i	0.0285949	+	0.0165093i
$669$		0			0
$670$	−14.7468	−	6.88077i	−0.569719	−	0.265827i
$671$	0.874481	−	1.51465i	0.0337590	−	0.0584722i
$672$		0			0
$673$	6.60209	−	3.81172i	0.254492	−	0.146931i	−0.367327	−	0.930092i	$-0.619727\pi$
$673$	6.60209	−	3.81172i	0.254492	−	0.146931i	0.621819	+	0.783161i	$0.286394\pi$
$674$	−30.0990	−	17.3777i	−1.15937	−	0.669364i
$675$		0			0
$676$	5.77888	+	10.0093i	0.222265	+	0.384974i
$677$		−	30.8268i		−	1.18477i	−0.805654	−	0.592386i	$-0.798186\pi$
$677$		−	30.8268i		−	1.18477i	0.805654	−	0.592386i	$-0.201814\pi$
$678$		0			0
$679$	9.54150	+	4.71335i	0.366169	+	0.180882i
$680$	0.0202659	+	0.232269i	0.000777162	+	0.00890711i
$681$		0			0
$682$	0.255645	−	0.442790i	0.00978916	−	0.0169553i
$683$	−18.8176	−	32.5930i	−0.720036	−	1.24714i	−0.960985	−	0.276601i	$-0.910792\pi$
$683$	−18.8176	−	32.5930i	−0.720036	−	1.24714i	0.240949	−	0.970538i	$-0.422541\pi$
$684$		0			0
$685$	−24.5162	−	35.0303i	−0.936718	−	1.33844i
$686$	−3.57637	−	18.1717i	−0.136547	−	0.693798i
$687$		0			0
$688$	1.49609	−	0.863766i	0.0570378	−	0.0329308i
$689$	3.21912			0.122639
$690$		0			0
$691$		−	11.9246i		−	0.453633i	−0.973938	−	0.226816i	$-0.927168\pi$
$691$		−	11.9246i		−	0.453633i	0.973938	−	0.226816i	$-0.0728317\pi$
$692$			25.1821i			0.957280i
$693$		0			0
$694$	−6.90143			−0.261975
$695$	2.01875	−	1.41284i	0.0765755	−	0.0535919i
$696$		0			0
$697$		−	0.827133i		−	0.0313299i
$698$	−0.226488	+	0.130763i	−0.00857272	+	0.00494946i
$699$		0			0
$700$	−12.6960	−	3.71632i	−0.479865	−	0.140464i
$701$		−	12.4716i		−	0.471046i	−0.971869	−	0.235523i	$-0.924320\pi$
$701$		−	12.4716i		−	0.471046i	0.971869	−	0.235523i	$-0.0756803\pi$
$702$		0			0
$703$	18.1883	+	31.5030i	0.685984	+	1.18816i
$704$	0.123075	+	0.0710575i	0.00463857	+	0.00267808i
$705$		0			0
$706$	24.7213	+	14.2729i	0.930400	+	0.537167i
$707$	0.575605	+	8.87371i	0.0216479	+	0.333730i
$708$		0			0
$709$	28.2913			1.06250			0.531251	−	0.847215i	$-0.321722\pi$
$709$	28.2913			1.06250			0.531251	+	0.847215i	$0.321722\pi$
$710$	−25.2294	−	11.7719i	−0.946841	−	0.441790i
$711$		0			0
$712$	0.748203	−	1.29593i	0.0280401	−	0.0485669i
$713$	−13.4154	+	7.74540i	−0.502412	+	0.290068i
$714$		0			0
$715$	−0.0331719	−	0.380186i	−0.00124056	−	0.0142182i
$716$	14.0102	−	8.08881i	0.523587	−	0.302293i
$717$		0			0
$718$	10.5441	+	6.08767i	0.393504	+	0.227190i
$719$	−3.47046	+	6.01101i	−0.129426	+	0.224173i	−0.923454	−	0.383708i	$-0.874647\pi$
$719$	−3.47046	+	6.01101i	−0.129426	+	0.224173i	0.794028	+	0.607881i	$0.207980\pi$
$720$		0			0
$721$	45.4258	+	22.4396i	1.69175	+	0.835696i
$722$	7.33595	+	12.7062i	0.273016	+	0.472877i
$723$		0			0
$724$		−	17.0243i		−	0.632701i
$725$	17.4111	+	6.34638i	0.646631	+	0.235699i
$726$		0			0
$727$	−8.87166	−	15.3662i	−0.329032	−	0.569899i	0.653288	−	0.757109i	$-0.273389\pi$
$727$	−8.87166	−	15.3662i	−0.329032	−	0.569899i	−0.982320	+	0.187210i	$0.940056\pi$
$728$	−0.205672	−	3.17070i	−0.00762270	−	0.117514i
$729$		0			0
$730$	17.9091	−	1.56260i	0.662845	−	0.0578345i
$731$	−0.0900636	+	0.155995i	−0.00333112	+	0.00576967i
$732$		0			0
$733$	−9.39300	−	16.2692i	−0.346939	−	0.600915i	0.638765	−	0.769402i	$-0.279445\pi$
$733$	−9.39300	−	16.2692i	−0.346939	−	0.600915i	−0.985704	+	0.168486i	$0.946112\pi$
$734$	−11.1198	+	19.2601i	−0.410441	+	0.710904i
$735$		0			0
$736$	−2.15286	−	3.72887i	−0.0793556	−	0.137448i
$737$	0.517124	−	0.895685i	0.0190485	−	0.0329930i
$738$		0			0
$739$	−19.5906	−	33.9320i	−0.720653	−	1.24821i	−0.960738	−	0.277456i	$-0.910509\pi$
$739$	−19.5906	−	33.9320i	−0.720653	−	1.24821i	0.240085	−	0.970752i	$-0.422825\pi$
$740$	11.4844	−	8.03746i	0.422176	−	0.295463i
$741$		0			0
$742$	6.35850	+	3.14100i	0.233428	+	0.115310i
$743$	−3.04957	+	5.28201i	−0.111878	+	0.193778i	−0.916527	−	0.399972i	$-0.869020\pi$
$743$	−3.04957	+	5.28201i	−0.111878	+	0.193778i	0.804650	+	0.593750i	$0.202353\pi$
$744$		0			0
$745$	−2.71889	−	31.1614i	−0.0996126	−	1.14167i
$746$	3.32049	−	1.91709i	0.121572	−	0.0701896i
$747$		0			0
$748$	−0.0148181			−0.000541804
$749$	2.44917	+	37.7571i	0.0894906	+	1.37962i
$750$		0			0
$751$	−26.9458	−	46.6715i	−0.983266	−	1.70307i	−0.649404	−	0.760444i	$-0.724981\pi$
$751$	−26.9458	−	46.6715i	−0.983266	−	1.70307i	−0.333862	−	0.942622i	$-0.608352\pi$
$752$			5.04557i			0.183993i
$753$		0			0
$754$			4.45104i			0.162097i
$755$	−6.29950	−	9.00112i	−0.229262	−	0.327584i
$756$		0			0
$757$		−	18.1765i		−	0.660637i	−0.943870	−	0.330318i	$-0.892844\pi$
$757$		−	18.1765i		−	0.660637i	0.943870	−	0.330318i	$-0.107156\pi$
$758$	−29.0957			−1.05680
$759$		0			0
$760$	10.6305	−	7.43985i	0.385610	−	0.269872i
$761$	−14.9924	−	25.9677i	−0.543476	−	0.941328i	−0.998701	−	0.0509513i	$-0.983775\pi$
$761$	−14.9924	−	25.9677i	−0.543476	−	0.941328i	0.455225	−	0.890376i	$-0.349559\pi$
$762$		0			0
$763$	42.2152	+	20.8536i	1.52829	+	0.754952i
$764$		−	3.96791i		−	0.143554i
$765$		0			0
$766$	−12.2543	+	7.07501i	−0.442765	+	0.255630i
$767$	−5.89048	+	10.2026i	−0.212693	+	0.368395i
$768$		0			0
$769$	−29.1902	−	16.8530i	−1.05263	−	0.607734i	−0.129242	−	0.991613i	$-0.541255\pi$
$769$	−29.1902	−	16.8530i	−1.05263	−	0.607734i	−0.923383	+	0.383879i	$0.874588\pi$
$770$	0.305437	−	0.783321i	0.0110072	−	0.0282289i
$771$		0			0
$772$		−	1.29203i		−	0.0465013i
$773$	27.1549	−	15.6779i	0.976694	−	0.563895i	0.0754237	−	0.997152i	$-0.475969\pi$
$773$	27.1549	−	15.6779i	0.976694	−	0.563895i	0.901270	+	0.433257i	$0.142636\pi$
$774$		0			0
$775$	−13.7855	+	11.5564i	−0.495190	+	0.415117i
$776$	2.01118	+	3.48347i	0.0721972	+	0.125049i
$777$		0			0
$778$	29.9470	+	17.2899i	1.07365	+	0.619873i
$779$	−39.8645	+	23.0158i	−1.42830	+	0.824627i
$780$		0			0
$781$	0.884714	−	1.53237i	0.0316576	−	0.0548325i
$782$	0.388803	+	0.224476i	0.0139036	+	0.00802724i
$783$		0			0
$784$	2.68750	−	6.46354i	0.0959822	−	0.230841i
$785$	−6.05959	+	12.9869i	−0.216276	+	0.463521i
$786$		0			0
$787$	33.3758			1.18972			0.594859	−	0.803830i	$-0.297208\pi$
$787$	33.3758			1.18972			0.594859	+	0.803830i	$0.297208\pi$
$788$	0.983884			0.0350494
$789$		0			0
$790$	−7.95151	+	17.0416i	−0.282902	+	0.606313i
$791$	−2.77107	−	42.7197i	−0.0985280	−	1.51894i
$792$		0			0
$793$	−12.7994	−	7.38973i	−0.454519	−	0.262417i
$794$	14.6731	−	25.4146i	0.520729	−	0.901930i
$795$		0			0
$796$	−20.6241	+	11.9073i	−0.731000	+	0.422043i
$797$	4.60415	+	2.65821i	0.163087	+	0.0941585i	0.579322	−	0.815099i	$-0.303317\pi$
$797$	4.60415	+	2.65821i	0.163087	+	0.0941585i	−0.416235	+	0.909257i	$0.636651\pi$
$798$		0			0
$799$	−0.263047	−	0.455611i	−0.00930594	−	0.0161184i
$800$	−3.21214	−	3.83173i	−0.113566	−	0.135472i
$801$		0			0
$802$	22.8472	−	13.1908i	0.806762	−	0.465785i
$803$			1.14255i			0.0403197i
$804$		0			0
$805$	−19.8805	+	15.9261i	−0.700696	+	0.561321i
$806$	−3.74176	−	2.16031i	−0.131798	−	0.0760936i
$807$		0			0
$808$	−1.68050	+	2.91071i	−0.0591197	+	0.102398i
$809$	−13.1171	+	7.57314i	−0.461171	+	0.266257i	−0.712537	−	0.701635i	$-0.752454\pi$
$809$	−13.1171	+	7.57314i	−0.461171	+	0.266257i	0.251365	+	0.967892i	$0.419120\pi$
$810$		0			0
$811$			25.5538i			0.897316i	0.893704	+	0.448658i	$0.148098\pi$
$811$			25.5538i			0.897316i	−0.893704	+	0.448658i	$0.851902\pi$
$812$	−4.34302	+	8.79183i	−0.152410	+	0.308533i
$813$		0			0
$814$	0.445449	+	0.771540i	0.0156130	+	0.0270425i
$815$	−2.05369	+	1.43729i	−0.0719375	+	0.0503460i
$816$		0			0
$817$	10.0244			0.350711
$818$			12.8464i			0.449164i
$819$		0			0
$820$	10.1707	+	14.5326i	0.355178	+	0.507500i
$821$		−	30.2878i		−	1.05705i	−0.848918	−	0.528525i	$-0.822745\pi$
$821$		−	30.2878i		−	1.05705i	0.848918	−	0.528525i	$-0.177255\pi$
$822$		0			0
$823$			44.3997i			1.54768i	0.633383	+	0.773838i	$0.281666\pi$
$823$			44.3997i			1.54768i	−0.633383	+	0.773838i	$0.718334\pi$
$824$	9.57498	+	16.5843i	0.333560	+	0.577743i
$825$		0			0
$826$	−21.5901	+	14.4050i	−0.751214	+	0.501213i
$827$	8.05224			0.280004			0.140002	−	0.990151i	$-0.455289\pi$
$827$	8.05224			0.280004			0.140002	+	0.990151i	$0.455289\pi$
$828$		0			0
$829$	9.26932	−	5.35164i	0.321937	−	0.185870i	−0.330319	−	0.943869i	$-0.607156\pi$
$829$	9.26932	−	5.35164i	0.321937	−	0.185870i	0.652255	+	0.757999i	$0.273823\pi$
$830$	0.456520	+	5.23220i	0.0158460	+	0.181612i
$831$		0			0
$832$	0.600465	−	1.04004i	0.0208174	−	0.0360568i
$833$	0.0942925	+	0.723763i	0.00326704	+	0.0250769i
$834$		0			0
$835$	1.56339	−	1.09415i	0.0541034	−	0.0378647i
$836$	0.412329	+	0.714175i	0.0142607	+	0.0247002i
$837$		0			0
$838$	5.13440	−	8.89304i	0.177365	−	0.307205i
$839$	−24.9171	−	43.1577i	−0.860234	−	1.48997i	−0.871703	−	0.490034i	$-0.836984\pi$
$839$	−24.9171	−	43.1577i	−0.860234	−	1.48997i	0.0114693	−	0.999934i	$-0.496349\pi$
$840$		0			0
$841$	−7.63157	+	13.2183i	−0.263157	+	0.455802i
$842$	3.18306	+	5.51323i	0.109696	+	0.189998i
$843$		0			0
$844$	−11.2221	+	19.4372i	−0.386280	+	0.669056i
$845$	25.7461	−	2.24640i	0.885694	−	0.0772785i
$846$		0			0
$847$	−26.0453	−	12.8660i	−0.894928	−	0.442080i
$848$	1.34026	+	2.32140i	0.0460248	+	0.0797172i
$849$		0			0
$850$	0.489818	+	0.178540i	0.0168006	+	0.00612387i
$851$		−	26.9920i		−	0.925272i
$852$		0			0
$853$	−9.14863	−	15.8459i	−0.313243	−	0.542553i	0.665819	−	0.746113i	$-0.268082\pi$
$853$	−9.14863	−	15.8459i	−0.313243	−	0.542553i	−0.979062	+	0.203560i	$0.934749\pi$
$854$	−18.0713	−	27.0851i	−0.618388	−	0.926835i
$855$		0			0
$856$	−7.15043	+	12.3849i	−0.244397	+	0.423307i
$857$	−12.0422	−	6.95257i	−0.411354	−	0.237495i	0.280017	−	0.959995i	$-0.409660\pi$
$857$	−12.0422	−	6.95257i	−0.411354	−	0.237495i	−0.691371	+	0.722500i	$0.742993\pi$
$858$		0			0
$859$	33.8907	−	19.5668i	1.15634	−	0.667611i	0.205912	−	0.978570i	$-0.433984\pi$
$859$	33.8907	−	19.5668i	1.15634	−	0.667611i	0.950423	+	0.310960i	$0.100650\pi$
$860$	−0.335768	−	3.84826i	−0.0114496	−	0.131225i
$861$		0			0
$862$	3.37653	−	1.94944i	0.115005	−	0.0663982i
$863$	0.517393	−	0.896150i	0.0176122	−	0.0305053i	−0.857085	−	0.515175i	$-0.827727\pi$
$863$	0.517393	−	0.896150i	0.0176122	−	0.0305053i	0.874697	+	0.484670i	$0.161060\pi$
$864$		0			0
$865$	51.0276	+	23.8092i	1.73499	+	0.809536i
$866$	−20.9340			−0.711367
$867$		0			0
$868$	−5.28296	−	7.91805i	−0.179315	−	0.268756i
$869$	−1.03507	−	0.597596i	−0.0351122	−	0.0202720i
$870$		0			0
$871$	−7.56891	−	4.36991i	−0.256463	−	0.148069i
$872$	8.89823	+	15.4122i	0.301332	+	0.521923i
$873$		0			0
$874$		−	24.9851i		−	0.845132i
$875$	−19.5344	+	22.2128i	−0.660382	+	0.750930i
$876$		0			0
$877$	−1.34680	+	0.777575i	−0.0454782	+	0.0262568i	−0.522567	−	0.852598i	$-0.675025\pi$
$877$	−1.34680	+	0.777575i	−0.0454782	+	0.0262568i	0.477089	+	0.878855i	$0.341692\pi$
$878$			16.4017i			0.553531i
$879$		0			0
$880$	0.260352	−	0.182209i	0.00877646	−	0.00614227i
$881$	11.9598			0.402937			0.201469	−	0.979495i	$-0.435429\pi$
$881$	11.9598			0.402937			0.201469	+	0.979495i	$0.435429\pi$
$882$		0			0
$883$		−	10.7656i		−	0.362292i	−0.983456	−	0.181146i	$-0.942019\pi$
$883$		−	10.7656i		−	0.362292i	0.983456	−	0.181146i	$-0.0579806\pi$
$884$			0.125219i			0.00421158i
$885$		0			0
$886$	26.3852			0.886429
$887$	−23.0704	+	13.3197i	−0.774629	+	0.447232i	−0.834524	−	0.550972i	$-0.814257\pi$
$887$	−23.0704	+	13.3197i	−0.774629	+	0.447232i	0.0598943	+	0.998205i	$0.480924\pi$
$888$		0			0
$889$	16.2342	+	24.3317i	0.544477	+	0.816058i
$890$	−1.91858	−	2.74139i	−0.0643110	−	0.0918915i
$891$		0			0
$892$	8.99621	+	15.5819i	0.301215	+	0.521720i
$893$	−14.6391	+	25.3557i	−0.489879	+	0.848495i
$894$		0			0
$895$	−3.14433	−	36.0373i	−0.105103	−	1.20460i
$896$	2.20085	−	1.46842i	0.0735253	−	0.0490564i
$897$		0			0
$898$			32.5310i			1.08557i
$899$	6.66717	+	11.5479i	0.222362	+	0.385143i
$900$		0			0
$901$	−0.242049	−	0.139747i	−0.00806382	−	0.00465565i
$902$	−0.976322	+	0.563680i	−0.0325080	+	0.0187685i
$903$		0			0
$904$	8.09024	−	14.0127i	0.269077	−	0.466056i
$905$	−34.4970	−	16.0961i	−1.14672	−	0.535052i
$906$		0			0
$907$	6.54032	+	3.77606i	0.217168	+	0.125382i	0.604638	−	0.796500i	$-0.293318\pi$
$907$	6.54032	+	3.77606i	0.217168	+	0.125382i	−0.387470	+	0.921882i	$0.626651\pi$
$908$	17.5341	+	10.1233i	0.581890	+	0.335954i
$909$		0			0
$910$	−6.61939	−	2.58107i	−0.219431	−	0.0855617i
$911$	−21.2685	+	12.2794i	−0.704656	+	0.406834i	−0.809079	−	0.587699i	$-0.800034\pi$
$911$	−21.2685	+	12.2794i	−0.704656	+	0.406834i	0.104423	+	0.994533i	$0.466700\pi$
$912$		0			0
$913$	−0.333800			−0.0110472
$914$		−	35.0085i		−	1.15798i
$915$		0			0
$916$	−0.650116	+	0.375345i	−0.0214804	+	0.0124017i
$917$	22.2260	+	10.9793i	0.733967	+	0.362568i
$918$		0			0
$919$	−17.1584	+	29.7192i	−0.566003	+	0.980345i	0.430953	+	0.902374i	$0.358177\pi$
$919$	−17.1584	+	29.7192i	−0.566003	+	0.980345i	−0.996956	+	0.0779709i	$0.975156\pi$
$920$	−9.59146	+	0.836873i	−0.316221	+	0.0275909i
$921$		0			0
$922$	5.08610	+	8.80939i	0.167502	+	0.290122i
$923$	−12.9492	−	7.47620i	−0.426227	−	0.246082i
$924$		0			0
$925$	−5.42837	−	30.8706i	−0.178484	−	1.01502i
$926$	27.5356	+	15.8977i	0.904876	+	0.522430i
$927$		0			0
$928$	−3.20977	+	1.85316i	−0.105366	+	0.0608331i
$929$	−22.0312			−0.722821			−0.361411	−	0.932407i	$-0.617705\pi$
$929$	−22.0312			−0.722821			−0.361411	+	0.932407i	$0.617705\pi$
$930$		0			0
$931$	32.2587	−	24.6840i	1.05724	−	0.808984i
$932$	−9.57787	+	16.5894i	−0.313734	+	0.543403i
$933$		0			0
$934$	−19.5141	−	11.2665i	−0.638522	−	0.368651i
$935$	−0.0140102	+	0.0300266i	−0.000458183	+	0.000981975i
$936$		0			0
$937$	−36.9235			−1.20624			−0.603120	−	0.797651i	$-0.706076\pi$
$937$	−36.9235			−1.20624			−0.603120	+	0.797651i	$0.706076\pi$
$938$	−10.6865	−	16.0168i	−0.348926	−	0.522967i
$939$		0			0
$940$	10.2241	+	4.77049i	0.333472	+	0.155596i
$941$	−15.7517			−0.513492			−0.256746	−	0.966479i	$-0.582650\pi$
$941$	−15.7517			−0.513492			−0.256746	+	0.966479i	$0.582650\pi$
$942$		0			0
$943$	34.1561			1.11228
$944$	−9.80986			−0.319284
$945$		0			0
$946$	0.245508			0.00798216
$947$	19.2361			0.625090			0.312545	−	0.949903i	$-0.398818\pi$
$947$	19.2361			0.625090			0.312545	+	0.949903i	$0.398818\pi$
$948$		0			0
$949$	9.65503			0.313415
$950$	−5.02476	−	28.5753i	−0.163025	−	0.927106i
$951$		0			0
$952$	−0.122180	+	0.247337i	−0.00395989	+	0.00801623i
$953$	21.0241			0.681036			0.340518	−	0.940238i	$-0.389398\pi$
$953$	21.0241			0.681036			0.340518	+	0.940238i	$0.389398\pi$
$954$		0			0
$955$	−8.04034	−	3.75157i	−0.260179	−	0.121398i
$956$	−1.15565	−	0.667217i	−0.0373765	−	0.0215794i
$957$		0			0
$958$	−4.81018	+	8.33147i	−0.155410	+	0.269178i
$959$	−3.27476	−	50.4848i	−0.105748	−	1.63024i
$960$		0			0
$961$	18.0564			0.582465
$962$	6.51984	−	3.76423i	0.210208	−	0.121364i
$963$		0			0
$964$	−17.1287	−	9.88925i	−0.551678	−	0.318511i
$965$	−2.61810	−	1.22159i	−0.0842798	−	0.0393244i
$966$		0			0
$967$	31.4041	+	18.1311i	1.00989	+	0.583058i	0.911158	−	0.412056i	$-0.135189\pi$
$967$	31.4041	+	18.1311i	1.00989	+	0.583058i	0.0987282	+	0.995114i	$0.468523\pi$
$968$	−5.48990	−	9.50879i	−0.176452	−	0.305624i
$969$		0			0
$970$	8.96023	−	0.781797i	0.287696	−	0.0251020i
$971$	19.6361	−	34.0108i	0.630153	−	1.09146i	−0.357367	−	0.933964i	$-0.616325\pi$
$971$	19.6361	−	34.0108i	0.630153	−	1.09146i	0.987520	−	0.157493i	$-0.0503412\pi$
$972$		0			0
$973$	2.90937	−	0.188720i	0.0932700	−	0.00605008i
$974$	8.50444	−	4.91004i	0.272500	−	0.157328i
$975$		0			0
$976$		−	12.3067i		−	0.393927i
$977$	37.2951			1.19317			0.596587	−	0.802548i	$-0.296523\pi$
$977$	37.2951			1.19317			0.596587	+	0.802548i	$0.296523\pi$
$978$		0			0
$979$	0.184170	−	0.106331i	0.00588611	−	0.00339835i
$980$	−10.5564	−	11.5569i	−0.337211	−	0.369173i
$981$		0			0
$982$	−24.7333	−	14.2798i	−0.789271	−	0.455686i
$983$	35.5207	+	20.5079i	1.13293	+	0.654100i	0.944671	−	0.328018i	$-0.106381\pi$
$983$	35.5207	+	20.5079i	1.13293	+	0.654100i	0.188264	+	0.982119i	$0.439714\pi$
$984$		0			0
$985$	0.930242	−	1.99369i	0.0296400	−	0.0635241i
$986$	0.193227	−	0.334678i	0.00615359	−	0.0106583i
$987$		0			0
$988$	6.03507	−	3.48435i	0.192001	−	0.110852i
$989$	−6.44174	−	3.71914i	−0.204835	−	0.118262i
$990$		0			0
$991$	9.52837	+	16.5036i	0.302679	+	0.524255i	0.976742	−	0.214419i	$-0.0687858\pi$
$991$	9.52837	+	16.5036i	0.302679	+	0.524255i	−0.674063	+	0.738674i	$0.735452\pi$
$992$		−	3.59772i		−	0.114228i
$993$		0			0
$994$	−18.2828	−	27.4021i	−0.579895	−	0.869142i
$995$	4.62867	+	53.0495i	0.146739	+	1.68178i
$996$		0			0
$997$	−17.8254	+	30.8745i	−0.564536	+	0.977806i	0.432556	+	0.901607i	$0.357612\pi$
$997$	−17.8254	+	30.8745i	−0.564536	+	0.977806i	−0.997093	+	0.0761986i	$0.975722\pi$
$998$	−10.3032	−	17.8456i	−0.326141	−	0.564892i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1890.2.bi.b.719.15		48
3.2	odd	2		630.2.bi.a.509.8	yes	48
5.4	even	2		1890.2.bi.a.719.1		48
7.3	odd	6		1890.2.r.a.1529.8		48
9.2	odd	6		1890.2.r.b.89.8		48
9.7	even	3		630.2.r.a.299.9	yes	48
15.14	odd	2		630.2.bi.b.509.17	yes	48
21.17	even	6		630.2.r.b.59.16	yes	48
35.24	odd	6		1890.2.r.b.1529.8		48
45.29	odd	6		1890.2.r.a.89.8		48
45.34	even	6		630.2.r.b.299.16	yes	48
63.38	even	6		1890.2.bi.a.899.1		48
63.52	odd	6		630.2.bi.b.479.17	yes	48
105.59	even	6		630.2.r.a.59.9	✓	48
315.164	even	6	inner	1890.2.bi.b.899.15		48
315.304	odd	6		630.2.bi.a.479.8	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.r.a.59.9	✓	48	105.59	even	6
630.2.r.a.299.9	yes	48	9.7	even	3
630.2.r.b.59.16	yes	48	21.17	even	6
630.2.r.b.299.16	yes	48	45.34	even	6
630.2.bi.a.479.8	yes	48	315.304	odd	6
630.2.bi.a.509.8	yes	48	3.2	odd	2
630.2.bi.b.479.17	yes	48	63.52	odd	6
630.2.bi.b.509.17	yes	48	15.14	odd	2
1890.2.r.a.89.8		48	45.29	odd	6
1890.2.r.a.1529.8		48	7.3	odd	6
1890.2.r.b.89.8		48	9.2	odd	6
1890.2.r.b.1529.8		48	35.24	odd	6
1890.2.bi.a.719.1		48	5.4	even	2
1890.2.bi.a.899.1		48	63.38	even	6
1890.2.bi.b.719.15		48	1.1	even	1	trivial
1890.2.bi.b.899.15		48	315.164	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1890.bi (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{4} +(0.945479 - 2.02634i) q^{5} +(2.20085 - 1.46842i) q^{7} +1.00000 q^{8} +(0.945479 - 2.02634i) q^{10} +(0.123075 + 0.0710575i) q^{11} +(0.600465 - 1.04004i) q^{13} +(2.20085 - 1.46842i) q^{14} +1.00000 q^{16} +(-0.0902992 + 0.0521342i) q^{17} +(5.02533 + 2.90137i) q^{19} +(0.945479 - 2.02634i) q^{20} +(0.123075 + 0.0710575i) q^{22} +(-2.15286 - 3.72887i) q^{23} +(-3.21214 - 3.83173i) q^{25} +(0.600465 - 1.04004i) q^{26} +(2.20085 - 1.46842i) q^{28} +(-3.20977 + 1.85316i) q^{29} -3.59772i q^{31} +1.00000 q^{32} +(-0.0902992 + 0.0521342i) q^{34} +(-0.894657 - 5.84804i) q^{35} +(5.42899 + 3.13443i) q^{37} +(5.02533 + 2.90137i) q^{38} +(0.945479 - 2.02634i) q^{40} +(-3.96636 + 6.86994i) q^{41} +(1.49609 - 0.863766i) q^{43} +(0.123075 + 0.0710575i) q^{44} +(-2.15286 - 3.72887i) q^{46} +5.04557i q^{47} +(2.68750 - 6.46354i) q^{49} +(-3.21214 - 3.83173i) q^{50} +(0.600465 - 1.04004i) q^{52} +(1.34026 + 2.32140i) q^{53} +(0.260352 - 0.182209i) q^{55} +(2.20085 - 1.46842i) q^{56} +(-3.20977 + 1.85316i) q^{58} -9.80986 q^{59} -12.3067i q^{61} -3.59772i q^{62} +1.00000 q^{64} +(-1.53974 - 2.20008i) q^{65} -7.27754i q^{67} +(-0.0902992 + 0.0521342i) q^{68} +(-0.894657 - 5.84804i) q^{70} -12.4507i q^{71} +(4.01981 + 6.96252i) q^{73} +(5.42899 + 3.13443i) q^{74} +(5.02533 + 2.90137i) q^{76} +(0.375212 - 0.0243387i) q^{77} -8.41003 q^{79} +(0.945479 - 2.02634i) q^{80} +(-3.96636 + 6.86994i) q^{82} +(-2.03412 + 1.17440i) q^{83} +(0.0202659 + 0.232269i) q^{85} +(1.49609 - 0.863766i) q^{86} +(0.123075 + 0.0710575i) q^{88} +(0.748203 - 1.29593i) q^{89} +(-0.205672 - 3.17070i) q^{91} +(-2.15286 - 3.72887i) q^{92} +5.04557i q^{94} +(10.6305 - 7.43985i) q^{95} +(2.01118 + 3.48347i) q^{97} +(2.68750 - 6.46354i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 48 q^{2} + 48 q^{4} - 3 q^{7} + 48 q^{8} - 6 q^{11} - 3 q^{14} + 48 q^{16} - 6 q^{22} + 3 q^{23} + 18 q^{25} - 3 q^{28} + 3 q^{29} + 48 q^{32} + 18 q^{35} + 3 q^{41} - 6 q^{44} + 3 q^{46} + 3 q^{49}+ \cdots + 3 q^{98}+O(q^{100}) \) 48 * q + 48 * q^2 + 48 * q^4 - 3 * q^7 + 48 * q^8 - 6 * q^11 - 3 * q^14 + 48 * q^16 - 6 * q^22 + 3 * q^23 + 18 * q^25 - 3 * q^28 + 3 * q^29 + 48 * q^32 + 18 * q^35 + 3 * q^41 - 6 * q^44 + 3 * q^46 + 3 * q^49 + 18 * q^50 + 42 * q^55 - 3 * q^56 + 3 * q^58 + 48 * q^64 + 12 * q^65 + 18 * q^70 + 18 * q^73 - 12 * q^77 + 3 * q^82 + 9 * q^83 + 33 * q^85 - 6 * q^88 + 33 * q^89 + 3 * q^92 + 24 * q^97 + 3 * q^98

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