LMFDB - Embedded newform 1638.2.j.m.235.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1638,2,Mod(235,1638)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1638, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4, 0]))

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

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

chi := DirichletCharacter("1638.235");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1638.j (of order $3$, degree $2$, 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:	$13.0794958511$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 546)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			235.1
Root			$-0.707107 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	1638.235
Dual form			1638.2.j.m.1171.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.70711 - 2.95680i) q^{5} +(-2.62132 + 0.358719i) q^{7} -1.00000 q^{8} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.70711 - 2.95680i) q^{5} +(-2.62132 + 0.358719i) q^{7} -1.00000 q^{8} +(1.70711 - 2.95680i) q^{10} +(1.20711 - 2.09077i) q^{11} +1.00000 q^{13} +(-1.62132 - 2.09077i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(0.207107 - 0.358719i) q^{17} +(3.91421 + 6.77962i) q^{19} +3.41421 q^{20} +2.41421 q^{22} +(-0.707107 - 1.22474i) q^{23} +(-3.32843 + 5.76500i) q^{25} +(0.500000 + 0.866025i) q^{26} +(1.00000 - 2.44949i) q^{28} -3.82843 q^{29} +(-4.24264 + 7.34847i) q^{31} +(0.500000 - 0.866025i) q^{32} +0.414214 q^{34} +(5.53553 + 7.13834i) q^{35} +(0.707107 + 1.22474i) q^{37} +(-3.91421 + 6.77962i) q^{38} +(1.70711 + 2.95680i) q^{40} -9.89949 q^{41} -10.4853 q^{43} +(1.20711 + 2.09077i) q^{44} +(0.707107 - 1.22474i) q^{46} +(0.500000 + 0.866025i) q^{47} +(6.74264 - 1.88064i) q^{49} -6.65685 q^{50} +(-0.500000 + 0.866025i) q^{52} +(-3.74264 + 6.48244i) q^{53} -8.24264 q^{55} +(2.62132 - 0.358719i) q^{56} +(-1.91421 - 3.31552i) q^{58} +(-6.03553 + 10.4539i) q^{59} +(0.792893 + 1.37333i) q^{61} -8.48528 q^{62} +1.00000 q^{64} +(-1.70711 - 2.95680i) q^{65} +(1.91421 - 3.31552i) q^{67} +(0.207107 + 0.358719i) q^{68} +(-3.41421 + 8.36308i) q^{70} +5.00000 q^{71} +(0.707107 - 1.22474i) q^{73} +(-0.707107 + 1.22474i) q^{74} -7.82843 q^{76} +(-2.41421 + 5.91359i) q^{77} +(0.171573 + 0.297173i) q^{79} +(-1.70711 + 2.95680i) q^{80} +(-4.94975 - 8.57321i) q^{82} +3.65685 q^{83} -1.41421 q^{85} +(-5.24264 - 9.08052i) q^{86} +(-1.20711 + 2.09077i) q^{88} +(2.70711 + 4.68885i) q^{89} +(-2.62132 + 0.358719i) q^{91} +1.41421 q^{92} +(-0.500000 + 0.866025i) q^{94} +(13.3640 - 23.1471i) q^{95} -15.0711 q^{97} +(5.00000 + 4.89898i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} - 2 q^{4} - 4 q^{5} - 2 q^{7} - 4 q^{8}+O(q^{10}) $ 4 * q + 2 * q^2 - 2 * q^4 - 4 * q^5 - 2 * q^7 - 4 * q^8	$ 4 q + 2 q^{2} - 2 q^{4} - 4 q^{5} - 2 q^{7} - 4 q^{8} + 4 q^{10} + 2 q^{11} + 4 q^{13} + 2 q^{14} - 2 q^{16} - 2 q^{17} + 10 q^{19} + 8 q^{20} + 4 q^{22} - 2 q^{25} + 2 q^{26} + 4 q^{28} - 4 q^{29} + 2 q^{32} - 4 q^{34} + 8 q^{35} - 10 q^{38} + 4 q^{40} - 8 q^{43} + 2 q^{44} + 2 q^{47} + 10 q^{49} - 4 q^{50} - 2 q^{52} + 2 q^{53} - 16 q^{55} + 2 q^{56} - 2 q^{58} - 10 q^{59} + 6 q^{61} + 4 q^{64} - 4 q^{65} + 2 q^{67} - 2 q^{68} - 8 q^{70} + 20 q^{71} - 20 q^{76} - 4 q^{77} + 12 q^{79} - 4 q^{80} - 8 q^{83} - 4 q^{86} - 2 q^{88} + 8 q^{89} - 2 q^{91} - 2 q^{94} + 28 q^{95} - 32 q^{97} + 20 q^{98}+O(q^{100}) $ 4 * q + 2 * q^2 - 2 * q^4 - 4 * q^5 - 2 * q^7 - 4 * q^8 + 4 * q^10 + 2 * q^11 + 4 * q^13 + 2 * q^14 - 2 * q^16 - 2 * q^17 + 10 * q^19 + 8 * q^20 + 4 * q^22 - 2 * q^25 + 2 * q^26 + 4 * q^28 - 4 * q^29 + 2 * q^32 - 4 * q^34 + 8 * q^35 - 10 * q^38 + 4 * q^40 - 8 * q^43 + 2 * q^44 + 2 * q^47 + 10 * q^49 - 4 * q^50 - 2 * q^52 + 2 * q^53 - 16 * q^55 + 2 * q^56 - 2 * q^58 - 10 * q^59 + 6 * q^61 + 4 * q^64 - 4 * q^65 + 2 * q^67 - 2 * q^68 - 8 * q^70 + 20 * q^71 - 20 * q^76 - 4 * q^77 + 12 * q^79 - 4 * q^80 - 8 * q^83 - 4 * q^86 - 2 * q^88 + 8 * q^89 - 2 * q^91 - 2 * q^94 + 28 * q^95 - 32 * q^97 + 20 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1638\mathbb{Z}\right)^\times$.

$n$	$379$	$703$	$911$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−1.70711	−	2.95680i	−0.763441	−	1.32232i	−0.941067	−	0.338221i	$-0.890175\pi$
$5$	−1.70711	−	2.95680i	−0.763441	−	1.32232i	0.177625	−	0.984098i	$-0.443158\pi$
$6$		0			0
$7$	−2.62132	+	0.358719i	−0.990766	+	0.135583i
$7$	−2.62132	+	0.358719i	−0.990766	+	0.135583i
$8$	−1.00000			−0.353553
$9$		0			0
$10$	1.70711	−	2.95680i	0.539835	−	0.935021i
$11$	1.20711	−	2.09077i	0.363956	−	0.630391i	−0.624652	−	0.780903i	$-0.714759\pi$
$11$	1.20711	−	2.09077i	0.363956	−	0.630391i	0.988608	+	0.150513i	$0.0480924\pi$
$12$		0			0
$13$	1.00000			0.277350
$13$	1.00000			0.277350
$14$	−1.62132	−	2.09077i	−0.433316	−	0.558782i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	0.207107	−	0.358719i	0.0502308	−	0.0870023i	−0.839817	−	0.542870i	$-0.817338\pi$
$17$	0.207107	−	0.358719i	0.0502308	−	0.0870023i	0.890048	+	0.455868i	$0.150671\pi$
$18$		0			0
$19$	3.91421	+	6.77962i	0.897982	+	1.55535i	0.830070	+	0.557659i	$0.188300\pi$
$19$	3.91421	+	6.77962i	0.897982	+	1.55535i	0.0679123	+	0.997691i	$0.478366\pi$
$20$	3.41421			0.763441
$21$		0			0
$22$	2.41421			0.514712
$23$	−0.707107	−	1.22474i	−0.147442	−	0.255377i	0.782839	−	0.622224i	$-0.213771\pi$
$23$	−0.707107	−	1.22474i	−0.147442	−	0.255377i	−0.930281	+	0.366847i	$0.880437\pi$
$24$		0			0
$25$	−3.32843	+	5.76500i	−0.665685	+	1.15300i
$26$	0.500000	+	0.866025i	0.0980581	+	0.169842i
$27$		0			0
$28$	1.00000	−	2.44949i	0.188982	−	0.462910i
$29$	−3.82843			−0.710921			−0.355461	−	0.934691i	$-0.615676\pi$
$29$	−3.82843			−0.710921			−0.355461	+	0.934691i	$0.615676\pi$
$30$		0			0
$31$	−4.24264	+	7.34847i	−0.762001	+	1.31982i	0.179817	+	0.983700i	$0.442449\pi$
$31$	−4.24264	+	7.34847i	−0.762001	+	1.31982i	−0.941818	+	0.336124i	$0.890884\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$		0			0
$34$	0.414214			0.0710370
$35$	5.53553	+	7.13834i	0.935676	+	1.20660i
$36$		0			0
$37$	0.707107	+	1.22474i	0.116248	+	0.201347i	0.918278	−	0.395937i	$-0.129580\pi$
$37$	0.707107	+	1.22474i	0.116248	+	0.201347i	−0.802030	+	0.597284i	$0.796247\pi$
$38$	−3.91421	+	6.77962i	−0.634969	+	1.09980i
$39$		0			0
$40$	1.70711	+	2.95680i	0.269917	+	0.467510i
$41$	−9.89949			−1.54604			−0.773021	−	0.634381i	$-0.781255\pi$
$41$	−9.89949			−1.54604			−0.773021	+	0.634381i	$0.781255\pi$
$42$		0			0
$43$	−10.4853			−1.59899			−0.799495	−	0.600672i	$-0.794900\pi$
$43$	−10.4853			−1.59899			−0.799495	+	0.600672i	$0.794900\pi$
$44$	1.20711	+	2.09077i	0.181978	+	0.315195i
$45$		0			0
$46$	0.707107	−	1.22474i	0.104257	−	0.180579i
$47$	0.500000	+	0.866025i	0.0729325	+	0.126323i	0.900185	−	0.435507i	$-0.143431\pi$
$47$	0.500000	+	0.866025i	0.0729325	+	0.126323i	−0.827253	+	0.561830i	$0.810098\pi$
$48$		0			0
$49$	6.74264	−	1.88064i	0.963234	−	0.268662i
$50$	−6.65685			−0.941421
$51$		0			0
$52$	−0.500000	+	0.866025i	−0.0693375	+	0.120096i
$53$	−3.74264	+	6.48244i	−0.514091	+	0.890432i	0.485775	+	0.874084i	$0.338537\pi$
$53$	−3.74264	+	6.48244i	−0.514091	+	0.890432i	−0.999866	+	0.0163483i	$0.994796\pi$
$54$		0			0
$55$	−8.24264			−1.11144
$56$	2.62132	−	0.358719i	0.350289	−	0.0479359i
$57$		0			0
$58$	−1.91421	−	3.31552i	−0.251349	−	0.435348i
$59$	−6.03553	+	10.4539i	−0.785760	+	1.36098i	0.142785	+	0.989754i	$0.454394\pi$
$59$	−6.03553	+	10.4539i	−0.785760	+	1.36098i	−0.928544	+	0.371222i	$0.878939\pi$
$60$		0			0
$61$	0.792893	+	1.37333i	0.101520	+	0.175837i	0.912311	−	0.409498i	$-0.134296\pi$
$61$	0.792893	+	1.37333i	0.101520	+	0.175837i	−0.810791	+	0.585335i	$0.800963\pi$
$62$	−8.48528			−1.07763
$63$		0			0
$64$	1.00000			0.125000
$65$	−1.70711	−	2.95680i	−0.211741	−	0.366745i
$66$		0			0
$67$	1.91421	−	3.31552i	0.233858	−	0.405055i	−0.725082	−	0.688663i	$-0.758198\pi$
$67$	1.91421	−	3.31552i	0.233858	−	0.405055i	0.958940	+	0.283608i	$0.0915314\pi$
$68$	0.207107	+	0.358719i	0.0251154	+	0.0435011i
$69$		0			0
$70$	−3.41421	+	8.36308i	−0.408077	+	0.999579i
$71$	5.00000			0.593391			0.296695	−	0.954972i	$-0.404115\pi$
$71$	5.00000			0.593391			0.296695	+	0.954972i	$0.404115\pi$
$72$		0			0
$73$	0.707107	−	1.22474i	0.0827606	−	0.143346i	−0.821674	−	0.569958i	$-0.806960\pi$
$73$	0.707107	−	1.22474i	0.0827606	−	0.143346i	0.904435	+	0.426612i	$0.140293\pi$
$74$	−0.707107	+	1.22474i	−0.0821995	+	0.142374i
$75$		0			0
$76$	−7.82843			−0.897982
$77$	−2.41421	+	5.91359i	−0.275125	+	0.673916i
$78$		0			0
$79$	0.171573	+	0.297173i	0.0193035	+	0.0334346i	0.875516	−	0.483190i	$-0.160522\pi$
$79$	0.171573	+	0.297173i	0.0193035	+	0.0334346i	−0.856212	+	0.516624i	$0.827188\pi$
$80$	−1.70711	+	2.95680i	−0.190860	+	0.330580i
$81$		0			0
$82$	−4.94975	−	8.57321i	−0.546608	−	0.946753i
$83$	3.65685			0.401392			0.200696	−	0.979654i	$-0.435680\pi$
$83$	3.65685			0.401392			0.200696	+	0.979654i	$0.435680\pi$
$84$		0			0
$85$	−1.41421			−0.153393
$86$	−5.24264	−	9.08052i	−0.565328	−	0.979178i
$87$		0			0
$88$	−1.20711	+	2.09077i	−0.128678	+	0.222877i
$89$	2.70711	+	4.68885i	0.286953	+	0.497017i	0.973081	−	0.230464i	$-0.0740244\pi$
$89$	2.70711	+	4.68885i	0.286953	+	0.497017i	−0.686128	+	0.727481i	$0.740691\pi$
$90$		0			0
$91$	−2.62132	+	0.358719i	−0.274789	+	0.0376040i
$92$	1.41421			0.147442
$93$		0			0
$94$	−0.500000	+	0.866025i	−0.0515711	+	0.0893237i
$95$	13.3640	−	23.1471i	1.37111	−	2.37484i
$96$		0			0
$97$	−15.0711			−1.53024			−0.765118	−	0.643891i	$-0.777319\pi$
$97$	−15.0711			−1.53024			−0.765118	+	0.643891i	$0.777319\pi$
$98$	5.00000	+	4.89898i	0.505076	+	0.494872i
$99$		0			0
$100$	−3.32843	−	5.76500i	−0.332843	−	0.576500i
$101$	−4.58579	+	7.94282i	−0.456303	+	0.790340i	−0.998762	−	0.0497425i	$-0.984160\pi$
$101$	−4.58579	+	7.94282i	−0.456303	+	0.790340i	0.542459	+	0.840082i	$0.317493\pi$
$102$		0			0
$103$	5.58579	+	9.67487i	0.550384	+	0.953293i	0.998247	+	0.0591906i	$0.0188520\pi$
$103$	5.58579	+	9.67487i	0.550384	+	0.953293i	−0.447863	+	0.894102i	$0.647815\pi$
$104$	−1.00000			−0.0980581
$105$		0			0
$106$	−7.48528			−0.727035
$107$	1.65685	+	2.86976i	0.160174	+	0.277430i	0.934931	−	0.354830i	$-0.115461\pi$
$107$	1.65685	+	2.86976i	0.160174	+	0.277430i	−0.774757	+	0.632259i	$0.782128\pi$
$108$		0			0
$109$	−0.828427	+	1.43488i	−0.0793489	+	0.137436i	−0.902969	−	0.429705i	$-0.858617\pi$
$109$	−0.828427	+	1.43488i	−0.0793489	+	0.137436i	0.823620	+	0.567142i	$0.191951\pi$
$110$	−4.12132	−	7.13834i	−0.392952	−	0.680614i
$111$		0			0
$112$	1.62132	+	2.09077i	0.153200	+	0.197559i
$113$	14.8995			1.40163			0.700813	−	0.713345i	$-0.252821\pi$
$113$	14.8995			1.40163			0.700813	+	0.713345i	$0.252821\pi$
$114$		0			0
$115$	−2.41421	+	4.18154i	−0.225127	+	0.389931i
$116$	1.91421	−	3.31552i	0.177730	−	0.307838i
$117$		0			0
$118$	−12.0711			−1.11123
$119$	−0.414214	+	1.01461i	−0.0379709	+	0.0930093i
$120$		0			0
$121$	2.58579	+	4.47871i	0.235071	+	0.407156i
$122$	−0.792893	+	1.37333i	−0.0717852	+	0.124336i
$123$		0			0
$124$	−4.24264	−	7.34847i	−0.381000	−	0.659912i
$125$	5.65685			0.505964
$126$		0			0
$127$	11.8995			1.05591			0.527955	−	0.849273i	$-0.322959\pi$
$127$	11.8995			1.05591			0.527955	+	0.849273i	$0.322959\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$		0			0
$130$	1.70711	−	2.95680i	0.149723	−	0.259328i
$131$	10.7782	+	18.6683i	0.941693	+	1.63106i	0.762240	+	0.647295i	$0.224100\pi$
$131$	10.7782	+	18.6683i	0.941693	+	1.63106i	0.179453	+	0.983766i	$0.442567\pi$
$132$		0			0
$133$	−12.6924	−	16.3674i	−1.10057	−	1.41924i
$134$	3.82843			0.330726
$135$		0			0
$136$	−0.207107	+	0.358719i	−0.0177593	+	0.0307599i
$137$	−1.53553	+	2.65962i	−0.131190	+	0.227227i	−0.924135	−	0.382065i	$-0.875213\pi$
$137$	−1.53553	+	2.65962i	−0.131190	+	0.227227i	0.792946	+	0.609292i	$0.208546\pi$
$138$		0			0
$139$	1.07107			0.0908468			0.0454234	−	0.998968i	$-0.485536\pi$
$139$	1.07107			0.0908468			0.0454234	+	0.998968i	$0.485536\pi$
$140$	−8.94975	+	1.22474i	−0.756392	+	0.103510i
$141$		0			0
$142$	2.50000	+	4.33013i	0.209795	+	0.363376i
$143$	1.20711	−	2.09077i	0.100943	−	0.174839i
$144$		0			0
$145$	6.53553	+	11.3199i	0.542747	+	0.940065i
$146$	1.41421			0.117041
$147$		0			0
$148$	−1.41421			−0.116248
$149$	−9.53553	−	16.5160i	−0.781181	−	1.35305i	−0.931254	−	0.364371i	$-0.881284\pi$
$149$	−9.53553	−	16.5160i	−0.781181	−	1.35305i	0.150073	−	0.988675i	$-0.452049\pi$
$150$		0			0
$151$	5.03553	−	8.72180i	0.409786	−	0.709770i	−0.585080	−	0.810976i	$-0.698937\pi$
$151$	5.03553	−	8.72180i	0.409786	−	0.709770i	0.994866	+	0.101206i	$0.0322701\pi$
$152$	−3.91421	−	6.77962i	−0.317485	−	0.549900i
$153$		0			0
$154$	−6.32843	+	0.866025i	−0.509959	+	0.0697863i
$155$	28.9706			2.32697
$156$		0			0
$157$	7.86396	−	13.6208i	0.627612	−	1.08706i	−0.360417	−	0.932791i	$-0.617366\pi$
$157$	7.86396	−	13.6208i	0.627612	−	1.08706i	0.988029	−	0.154265i	$-0.0493011\pi$
$158$	−0.171573	+	0.297173i	−0.0136496	+	0.0236418i
$159$		0			0
$160$	−3.41421			−0.269917
$161$	2.29289	+	2.95680i	0.180705	+	0.233028i
$162$		0			0
$163$	3.67157	+	6.35935i	0.287580	+	0.498103i	0.973232	−	0.229827i	$-0.0738160\pi$
$163$	3.67157	+	6.35935i	0.287580	+	0.498103i	−0.685652	+	0.727930i	$0.740483\pi$
$164$	4.94975	−	8.57321i	0.386510	−	0.669456i
$165$		0			0
$166$	1.82843	+	3.16693i	0.141913	+	0.245801i
$167$	−10.6569			−0.824652			−0.412326	−	0.911036i	$-0.635284\pi$
$167$	−10.6569			−0.824652			−0.412326	+	0.911036i	$0.635284\pi$
$168$		0			0
$169$	1.00000			0.0769231
$170$	−0.707107	−	1.22474i	−0.0542326	−	0.0939336i
$171$		0			0
$172$	5.24264	−	9.08052i	0.399748	−	0.692383i
$173$	−5.74264	−	9.94655i	−0.436605	−	0.756222i	0.560820	−	0.827938i	$-0.310486\pi$
$173$	−5.74264	−	9.94655i	−0.436605	−	0.756222i	−0.997425	+	0.0717158i	$0.977153\pi$
$174$		0			0
$175$	6.65685	−	16.3059i	0.503211	−	1.23261i
$176$	−2.41421			−0.181978
$177$		0			0
$178$	−2.70711	+	4.68885i	−0.202906	+	0.351444i
$179$	4.17157	−	7.22538i	0.311798	−	0.540050i	−0.666954	−	0.745099i	$-0.732402\pi$
$179$	4.17157	−	7.22538i	0.311798	−	0.540050i	0.978752	+	0.205049i	$0.0657354\pi$
$180$		0			0
$181$	−16.8995			−1.25613			−0.628065	−	0.778161i	$-0.716153\pi$
$181$	−16.8995			−1.25613			−0.628065	+	0.778161i	$0.716153\pi$
$182$	−1.62132	−	2.09077i	−0.120180	−	0.154978i
$183$		0			0
$184$	0.707107	+	1.22474i	0.0521286	+	0.0902894i
$185$	2.41421	−	4.18154i	0.177497	−	0.307433i
$186$		0			0
$187$	−0.500000	−	0.866025i	−0.0365636	−	0.0633300i
$188$	−1.00000			−0.0729325
$189$		0			0
$190$	26.7279			1.93905
$191$	−10.8284	−	18.7554i	−0.783517	−	1.35709i	−0.929881	−	0.367861i	$-0.880090\pi$
$191$	−10.8284	−	18.7554i	−0.783517	−	1.35709i	0.146363	−	0.989231i	$-0.453243\pi$
$192$		0			0
$193$	8.53553	−	14.7840i	0.614401	−	1.06417i	−0.376088	−	0.926584i	$-0.622731\pi$
$193$	8.53553	−	14.7840i	0.614401	−	1.06417i	0.990489	−	0.137590i	$-0.0439357\pi$
$194$	−7.53553	−	13.0519i	−0.541020	−	0.937074i
$195$		0			0
$196$	−1.74264	+	6.77962i	−0.124474	+	0.484258i
$197$	−15.5563			−1.10834			−0.554172	−	0.832402i	$-0.686965\pi$
$197$	−15.5563			−1.10834			−0.554172	+	0.832402i	$0.686965\pi$
$198$		0			0
$199$	11.3640	−	19.6830i	0.805570	−	1.39529i	−0.110336	−	0.993894i	$-0.535193\pi$
$199$	11.3640	−	19.6830i	0.805570	−	1.39529i	0.915906	−	0.401394i	$-0.131474\pi$
$200$	3.32843	−	5.76500i	0.235355	−	0.407647i
$201$		0			0
$202$	−9.17157			−0.645310
$203$	10.0355	−	1.37333i	0.704356	−	0.0963890i
$204$		0			0
$205$	16.8995	+	29.2708i	1.18031	+	2.04436i
$206$	−5.58579	+	9.67487i	−0.389180	+	0.674080i
$207$		0			0
$208$	−0.500000	−	0.866025i	−0.0346688	−	0.0600481i
$209$	18.8995			1.30731
$210$		0			0
$211$	−27.0711			−1.86365			−0.931825	−	0.362909i	$-0.881784\pi$
$211$	−27.0711			−1.86365			−0.931825	+	0.362909i	$0.881784\pi$
$212$	−3.74264	−	6.48244i	−0.257046	−	0.445216i
$213$		0			0
$214$	−1.65685	+	2.86976i	−0.113260	+	0.196172i
$215$	17.8995	+	31.0028i	1.22074	+	2.11438i
$216$		0			0
$217$	8.48528	−	20.7846i	0.576018	−	1.41095i
$218$	−1.65685			−0.112216
$219$		0			0
$220$	4.12132	−	7.13834i	0.277859	−	0.481267i
$221$	0.207107	−	0.358719i	0.0139315	−	0.0241301i
$222$		0			0
$223$	−22.0711			−1.47799			−0.738994	−	0.673712i	$-0.764699\pi$
$223$	−22.0711			−1.47799			−0.738994	+	0.673712i	$0.764699\pi$
$224$	−1.00000	+	2.44949i	−0.0668153	+	0.163663i
$225$		0			0
$226$	7.44975	+	12.9033i	0.495550	+	0.858317i
$227$	−13.4142	+	23.2341i	−0.890333	+	1.54210i	−0.0508557	+	0.998706i	$0.516195\pi$
$227$	−13.4142	+	23.2341i	−0.890333	+	1.54210i	−0.839477	+	0.543395i	$0.817138\pi$
$228$		0			0
$229$	−4.75736	−	8.23999i	−0.314375	−	0.544514i	0.664929	−	0.746906i	$-0.268462\pi$
$229$	−4.75736	−	8.23999i	−0.314375	−	0.544514i	−0.979304	+	0.202393i	$0.935128\pi$
$230$	−4.82843			−0.318377
$231$		0			0
$232$	3.82843			0.251349
$233$	3.86396	+	6.69258i	0.253137	+	0.438445i	0.964388	−	0.264493i	$-0.0852045\pi$
$233$	3.86396	+	6.69258i	0.253137	+	0.438445i	−0.711251	+	0.702938i	$0.751871\pi$
$234$		0			0
$235$	1.70711	−	2.95680i	0.111359	−	0.192880i
$236$	−6.03553	−	10.4539i	−0.392880	−	0.680488i
$237$		0			0
$238$	−1.08579	+	0.148586i	−0.0703811	+	0.00963143i
$239$	−21.4853			−1.38977			−0.694884	−	0.719122i	$-0.744544\pi$
$239$	−21.4853			−1.38977			−0.694884	+	0.719122i	$0.744544\pi$
$240$		0			0
$241$	−13.0711	+	22.6398i	−0.841981	+	1.45835i	0.0462355	+	0.998931i	$0.485278\pi$
$241$	−13.0711	+	22.6398i	−0.841981	+	1.45835i	−0.888217	+	0.459424i	$0.848056\pi$
$242$	−2.58579	+	4.47871i	−0.166221	+	0.287903i
$243$		0			0
$244$	−1.58579			−0.101520
$245$	−17.0711	−	16.7262i	−1.09063	−	1.06860i
$246$		0			0
$247$	3.91421	+	6.77962i	0.249055	+	0.431377i
$248$	4.24264	−	7.34847i	0.269408	−	0.466628i
$249$		0			0
$250$	2.82843	+	4.89898i	0.178885	+	0.309839i
$251$	−19.1716			−1.21010			−0.605049	−	0.796188i	$-0.706847\pi$
$251$	−19.1716			−1.21010			−0.605049	+	0.796188i	$0.706847\pi$
$252$		0			0
$253$	−3.41421			−0.214650
$254$	5.94975	+	10.3053i	0.373320	+	0.646610i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	4.75736	+	8.23999i	0.296756	+	0.513996i	0.975392	−	0.220479i	$-0.0707619\pi$
$257$	4.75736	+	8.23999i	0.296756	+	0.513996i	−0.678636	+	0.734475i	$0.737429\pi$
$258$		0			0
$259$	−2.29289	−	2.95680i	−0.142473	−	0.183726i
$260$	3.41421			0.211741
$261$		0			0
$262$	−10.7782	+	18.6683i	−0.665878	+	1.15333i
$263$	11.7071	−	20.2773i	0.721891	−	1.25035i	−0.238350	−	0.971179i	$-0.576606\pi$
$263$	11.7071	−	20.2773i	0.721891	−	1.25035i	0.960241	−	0.279173i	$-0.0900602\pi$
$264$		0			0
$265$	25.5563			1.56991
$266$	7.82843	−	19.1757i	0.479992	−	1.17573i
$267$		0			0
$268$	1.91421	+	3.31552i	0.116929	+	0.202527i
$269$	9.57107	−	16.5776i	0.583558	−	1.01075i	−0.411495	−	0.911412i	$-0.634993\pi$
$269$	9.57107	−	16.5776i	0.583558	−	1.01075i	0.995053	−	0.0993407i	$-0.0316734\pi$
$270$		0			0
$271$	8.10660	+	14.0410i	0.492441	+	0.852933i	0.999962	−	0.00870652i	$-0.00277141\pi$
$271$	8.10660	+	14.0410i	0.492441	+	0.852933i	−0.507521	+	0.861639i	$0.669438\pi$
$272$	−0.414214			−0.0251154
$273$		0			0
$274$	−3.07107			−0.185530
$275$	8.03553	+	13.9180i	0.484561	+	0.839284i
$276$		0			0
$277$	−1.96447	+	3.40256i	−0.118033	+	0.204440i	−0.918988	−	0.394285i	$-0.870992\pi$
$277$	−1.96447	+	3.40256i	−0.118033	+	0.204440i	0.800955	+	0.598725i	$0.204326\pi$
$278$	0.535534	+	0.927572i	0.0321192	+	0.0556321i
$279$		0			0
$280$	−5.53553	−	7.13834i	−0.330811	−	0.426597i
$281$	−23.3137			−1.39078			−0.695390	−	0.718633i	$-0.744768\pi$
$281$	−23.3137			−1.39078			−0.695390	+	0.718633i	$0.744768\pi$
$282$		0			0
$283$	12.1213	−	20.9947i	0.720538	−	1.24801i	−0.240247	−	0.970712i	$-0.577228\pi$
$283$	12.1213	−	20.9947i	0.720538	−	1.24801i	0.960785	−	0.277296i	$-0.0894383\pi$
$284$	−2.50000	+	4.33013i	−0.148348	+	0.256946i
$285$		0			0
$286$	2.41421			0.142755
$287$	25.9497	−	3.55114i	1.53177	−	0.209617i
$288$		0			0
$289$	8.41421	+	14.5738i	0.494954	+	0.857285i
$290$	−6.53553	+	11.3199i	−0.383780	+	0.664726i
$291$		0			0
$292$	0.707107	+	1.22474i	0.0413803	+	0.0716728i
$293$	−9.89949			−0.578335			−0.289167	−	0.957279i	$-0.593378\pi$
$293$	−9.89949			−0.578335			−0.289167	+	0.957279i	$0.593378\pi$
$294$		0			0
$295$	41.2132			2.39953
$296$	−0.707107	−	1.22474i	−0.0410997	−	0.0711868i
$297$		0			0
$298$	9.53553	−	16.5160i	0.552379	−	0.956748i
$299$	−0.707107	−	1.22474i	−0.0408930	−	0.0708288i
$300$		0			0
$301$	27.4853	−	3.76127i	1.58423	−	0.216796i
$302$	10.0711			0.579525
$303$		0			0
$304$	3.91421	−	6.77962i	0.224496	−	0.388838i
$305$	2.70711	−	4.68885i	0.155008	−	0.268483i
$306$		0			0
$307$	34.1127			1.94691			0.973457	−	0.228869i	$-0.0735027\pi$
$307$	34.1127			1.94691			0.973457	+	0.228869i	$0.0735027\pi$
$308$	−3.91421	−	5.04757i	−0.223033	−	0.287612i
$309$		0			0
$310$	14.4853	+	25.0892i	0.822709	+	1.42497i
$311$	−13.9497	+	24.1617i	−0.791018	+	1.37008i	0.134320	+	0.990938i	$0.457115\pi$
$311$	−13.9497	+	24.1617i	−0.791018	+	1.37008i	−0.925337	+	0.379145i	$0.876218\pi$
$312$		0			0
$313$	−10.2426	−	17.7408i	−0.578948	−	1.00277i	−0.995600	−	0.0937018i	$-0.970130\pi$
$313$	−10.2426	−	17.7408i	−0.578948	−	1.00277i	0.416652	−	0.909066i	$-0.363203\pi$
$314$	15.7279			0.887578
$315$		0			0
$316$	−0.343146			−0.0193035
$317$	−4.89949	−	8.48617i	−0.275183	−	0.476631i	0.694998	−	0.719011i	$-0.255405\pi$
$317$	−4.89949	−	8.48617i	−0.275183	−	0.476631i	−0.970181	+	0.242380i	$0.922072\pi$
$318$		0			0
$319$	−4.62132	+	8.00436i	−0.258744	+	0.448158i
$320$	−1.70711	−	2.95680i	−0.0954302	−	0.165290i
$321$		0			0
$322$	−1.41421	+	3.46410i	−0.0788110	+	0.193047i
$323$	3.24264			0.180425
$324$		0			0
$325$	−3.32843	+	5.76500i	−0.184628	+	0.319785i
$326$	−3.67157	+	6.35935i	−0.203350	+	0.352212i
$327$		0			0
$328$	9.89949			0.546608
$329$	−1.62132	−	2.09077i	−0.0893863	−	0.115268i
$330$		0			0
$331$	2.75736	+	4.77589i	0.151558	+	0.262506i	0.931800	−	0.362971i	$-0.118238\pi$
$331$	2.75736	+	4.77589i	0.151558	+	0.262506i	−0.780242	+	0.625477i	$0.784904\pi$
$332$	−1.82843	+	3.16693i	−0.100348	+	0.173808i
$333$		0			0
$334$	−5.32843	−	9.22911i	−0.291559	−	0.504994i
$335$	−13.0711			−0.714149
$336$		0			0
$337$	2.31371			0.126036			0.0630179	−	0.998012i	$-0.479927\pi$
$337$	2.31371			0.126036			0.0630179	+	0.998012i	$0.479927\pi$
$338$	0.500000	+	0.866025i	0.0271964	+	0.0471056i
$339$		0			0
$340$	0.707107	−	1.22474i	0.0383482	−	0.0664211i
$341$	10.2426	+	17.7408i	0.554670	+	0.960717i
$342$		0			0
$343$	−17.0000	+	7.34847i	−0.917914	+	0.396780i
$344$	10.4853			0.565328
$345$		0			0
$346$	5.74264	−	9.94655i	0.308726	−	0.534730i
$347$	8.36396	−	14.4868i	0.449001	−	0.777692i	−0.549320	−	0.835612i	$-0.685113\pi$
$347$	8.36396	−	14.4868i	0.449001	−	0.777692i	0.998321	+	0.0579194i	$0.0184466\pi$
$348$		0			0
$349$	18.7279			1.00248			0.501241	−	0.865308i	$-0.332877\pi$
$349$	18.7279			1.00248			0.501241	+	0.865308i	$0.332877\pi$
$350$	17.4497	−	2.38794i	0.932728	−	0.127641i
$351$		0			0
$352$	−1.20711	−	2.09077i	−0.0643390	−	0.111438i
$353$	−16.3137	+	28.2562i	−0.868291	+	1.50392i	−0.00454930	+	0.999990i	$0.501448\pi$
$353$	−16.3137	+	28.2562i	−0.868291	+	1.50392i	−0.863742	+	0.503935i	$0.831885\pi$
$354$		0			0
$355$	−8.53553	−	14.7840i	−0.453019	−	0.784652i
$356$	−5.41421			−0.286953
$357$		0			0
$358$	8.34315			0.440949
$359$	2.41421	+	4.18154i	0.127417	+	0.220693i	0.922675	−	0.385578i	$-0.125998\pi$
$359$	2.41421	+	4.18154i	0.127417	+	0.220693i	−0.795258	+	0.606271i	$0.792665\pi$
$360$		0			0
$361$	−21.1421	+	36.6193i	−1.11274	+	1.92733i
$362$	−8.44975	−	14.6354i	−0.444109	−	0.769219i
$363$		0			0
$364$	1.00000	−	2.44949i	0.0524142	−	0.128388i
$365$	−4.82843			−0.252731
$366$		0			0
$367$	16.3137	−	28.2562i	0.851569	−	1.47496i	−0.0282235	−	0.999602i	$-0.508985\pi$
$367$	16.3137	−	28.2562i	0.851569	−	1.47496i	0.879792	−	0.475359i	$-0.157682\pi$
$368$	−0.707107	+	1.22474i	−0.0368605	+	0.0638442i
$369$		0			0
$370$	4.82843			0.251018
$371$	7.48528	−	18.3351i	0.388616	−	0.951912i
$372$		0			0
$373$	4.20711	+	7.28692i	0.217836	+	0.377303i	0.954146	−	0.299341i	$-0.0967670\pi$
$373$	4.20711	+	7.28692i	0.217836	+	0.377303i	−0.736310	+	0.676644i	$0.763434\pi$
$374$	0.500000	−	0.866025i	0.0258544	−	0.0447811i
$375$		0			0
$376$	−0.500000	−	0.866025i	−0.0257855	−	0.0446619i
$377$	−3.82843			−0.197174
$378$		0			0
$379$	−26.6274			−1.36776			−0.683879	−	0.729595i	$-0.739709\pi$
$379$	−26.6274			−1.36776			−0.683879	+	0.729595i	$0.739709\pi$
$380$	13.3640	+	23.1471i	0.685557	+	1.18742i
$381$		0			0
$382$	10.8284	−	18.7554i	0.554031	−	0.959609i
$383$	8.41421	+	14.5738i	0.429946	+	0.744689i	0.996868	−	0.0790829i	$-0.0251992\pi$
$383$	8.41421	+	14.5738i	0.429946	+	0.744689i	−0.566922	+	0.823772i	$0.691866\pi$
$384$		0			0
$385$	21.6066	−	2.95680i	1.10117	−	0.150692i
$386$	17.0711			0.868894
$387$		0			0
$388$	7.53553	−	13.0519i	0.382559	−	0.662611i
$389$	−10.7426	+	18.6068i	−0.544674	+	0.943402i	0.453954	+	0.891025i	$0.350013\pi$
$389$	−10.7426	+	18.6068i	−0.544674	+	0.943402i	−0.998627	+	0.0523770i	$0.983320\pi$
$390$		0			0
$391$	−0.585786			−0.0296245
$392$	−6.74264	+	1.88064i	−0.340555	+	0.0949865i
$393$		0			0
$394$	−7.77817	−	13.4722i	−0.391859	−	0.678719i
$395$	0.585786	−	1.01461i	0.0294741	−	0.0510507i
$396$		0			0
$397$	−10.7782	−	18.6683i	−0.540941	−	0.936937i	−0.998850	−	0.0479385i	$-0.984735\pi$
$397$	−10.7782	−	18.6683i	−0.540941	−	0.936937i	0.457909	−	0.888999i	$-0.348598\pi$
$398$	22.7279			1.13925
$399$		0			0
$400$	6.65685			0.332843
$401$	0.0502525	+	0.0870399i	0.00250949	+	0.00434657i	0.867277	−	0.497825i	$-0.165868\pi$
$401$	0.0502525	+	0.0870399i	0.00250949	+	0.00434657i	−0.864768	+	0.502172i	$0.832535\pi$
$402$		0			0
$403$	−4.24264	+	7.34847i	−0.211341	+	0.366053i
$404$	−4.58579	−	7.94282i	−0.228151	−	0.395170i
$405$		0			0
$406$	6.20711	+	8.00436i	0.308054	+	0.397250i
$407$	3.41421			0.169236
$408$		0			0
$409$	−17.7071	+	30.6696i	−0.875560	+	1.51651i	−0.0193952	+	0.999812i	$0.506174\pi$
$409$	−17.7071	+	30.6696i	−0.875560	+	1.51651i	−0.856165	+	0.516703i	$0.827159\pi$
$410$	−16.8995	+	29.2708i	−0.834607	+	1.44558i
$411$		0			0
$412$	−11.1716			−0.550384
$413$	12.0711	−	29.5680i	0.593978	−	1.45494i
$414$		0			0
$415$	−6.24264	−	10.8126i	−0.306439	−	0.530768i
$416$	0.500000	−	0.866025i	0.0245145	−	0.0424604i
$417$		0			0
$418$	9.44975	+	16.3674i	0.462202	+	0.800558i
$419$	23.4558			1.14589			0.572946	−	0.819593i	$-0.305800\pi$
$419$	23.4558			1.14589			0.572946	+	0.819593i	$0.305800\pi$
$420$		0			0
$421$	−13.0711			−0.637045			−0.318522	−	0.947915i	$-0.603187\pi$
$421$	−13.0711			−0.637045			−0.318522	+	0.947915i	$0.603187\pi$
$422$	−13.5355	−	23.4442i	−0.658899	−	1.14125i
$423$		0			0
$424$	3.74264	−	6.48244i	0.181759	−	0.314815i
$425$	1.37868	+	2.38794i	0.0668758	+	0.115832i
$426$		0			0
$427$	−2.57107	−	3.31552i	−0.124423	−	0.160449i
$428$	−3.31371			−0.160174
$429$		0			0
$430$	−17.8995	+	31.0028i	−0.863190	+	1.49509i
$431$	6.75736	−	11.7041i	0.325491	−	0.563766i	−0.656121	−	0.754656i	$-0.727804\pi$
$431$	6.75736	−	11.7041i	0.325491	−	0.563766i	0.981612	+	0.190890i	$0.0611372\pi$
$432$		0			0
$433$	−3.97056			−0.190813			−0.0954065	−	0.995438i	$-0.530415\pi$
$433$	−3.97056			−0.190813			−0.0954065	+	0.995438i	$0.530415\pi$
$434$	22.2426	−	3.04384i	1.06768	−	0.146109i
$435$		0			0
$436$	−0.828427	−	1.43488i	−0.0396745	−	0.0687182i
$437$	5.53553	−	9.58783i	0.264800	−	0.458648i
$438$		0			0
$439$	−9.70711	−	16.8132i	−0.463295	−	0.802450i	0.535828	−	0.844327i	$-0.320000\pi$
$439$	−9.70711	−	16.8132i	−0.463295	−	0.802450i	−0.999123	+	0.0418769i	$0.986666\pi$
$440$	8.24264			0.392952
$441$		0			0
$442$	0.414214			0.0197021
$443$	12.8492	+	22.2555i	0.610486	+	1.05739i	0.991159	+	0.132683i	$0.0423592\pi$
$443$	12.8492	+	22.2555i	0.610486	+	1.05739i	−0.380673	+	0.924710i	$0.624308\pi$
$444$		0			0
$445$	9.24264	−	16.0087i	0.438143	−	0.758886i
$446$	−11.0355	−	19.1141i	−0.522548	−	0.905079i
$447$		0			0
$448$	−2.62132	+	0.358719i	−0.123846	+	0.0169479i
$449$	8.97056			0.423347			0.211674	−	0.977340i	$-0.432109\pi$
$449$	8.97056			0.423347			0.211674	+	0.977340i	$0.432109\pi$
$450$		0			0
$451$	−11.9497	+	20.6976i	−0.562692	+	0.974610i
$452$	−7.44975	+	12.9033i	−0.350407	+	0.606922i
$453$		0			0
$454$	−26.8284			−1.25912
$455$	5.53553	+	7.13834i	0.259510	+	0.334650i
$456$		0			0
$457$	−5.53553	−	9.58783i	−0.258941	−	0.448500i	0.707017	−	0.707196i	$-0.250040\pi$
$457$	−5.53553	−	9.58783i	−0.258941	−	0.448500i	−0.965959	+	0.258697i	$0.916707\pi$
$458$	4.75736	−	8.23999i	0.222297	−	0.385029i
$459$		0			0
$460$	−2.41421	−	4.18154i	−0.112563	−	0.194965i
$461$	−12.4853			−0.581498			−0.290749	−	0.956799i	$-0.593904\pi$
$461$	−12.4853			−0.581498			−0.290749	+	0.956799i	$0.593904\pi$
$462$		0			0
$463$	12.9706			0.602793			0.301397	−	0.953499i	$-0.402547\pi$
$463$	12.9706			0.602793			0.301397	+	0.953499i	$0.402547\pi$
$464$	1.91421	+	3.31552i	0.0888651	+	0.153919i
$465$		0			0
$466$	−3.86396	+	6.69258i	−0.178995	+	0.310028i
$467$	−4.29289	−	7.43551i	−0.198651	−	0.344074i	0.749440	−	0.662072i	$-0.230323\pi$
$467$	−4.29289	−	7.43551i	−0.198651	−	0.344074i	−0.948091	+	0.317998i	$0.896989\pi$
$468$		0			0
$469$	−3.82843	+	9.37769i	−0.176780	+	0.433022i
$470$	3.41421			0.157486
$471$		0			0
$472$	6.03553	−	10.4539i	0.277808	−	0.481178i
$473$	−12.6569	+	21.9223i	−0.581963	+	1.00799i
$474$		0			0
$475$	−52.1127			−2.39109
$476$	−0.671573	−	0.866025i	−0.0307815	−	0.0396942i
$477$		0			0
$478$	−10.7426	−	18.6068i	−0.491357	−	0.851055i
$479$	15.0563	−	26.0784i	0.687942	−	1.19155i	−0.284560	−	0.958658i	$-0.591848\pi$
$479$	15.0563	−	26.0784i	0.687942	−	1.19155i	0.972502	−	0.232893i	$-0.0748191\pi$
$480$		0			0
$481$	0.707107	+	1.22474i	0.0322413	+	0.0558436i
$482$	−26.1421			−1.19074
$483$		0			0
$484$	−5.17157			−0.235071
$485$	25.7279	+	44.5621i	1.16824	+	2.02346i
$486$		0			0
$487$	13.1066	−	22.7013i	0.593917	−	1.02869i	−0.399782	−	0.916610i	$-0.630914\pi$
$487$	13.1066	−	22.7013i	0.593917	−	1.02869i	0.993699	−	0.112084i	$-0.0357525\pi$
$488$	−0.792893	−	1.37333i	−0.0358926	−	0.0621678i
$489$		0			0
$490$	5.94975	−	23.1471i	0.268782	−	1.04568i
$491$	−12.3431			−0.557038			−0.278519	−	0.960431i	$-0.589844\pi$
$491$	−12.3431			−0.557038			−0.278519	+	0.960431i	$0.589844\pi$
$492$		0			0
$493$	−0.792893	+	1.37333i	−0.0357101	+	0.0618517i
$494$	−3.91421	+	6.77962i	−0.176109	+	0.305029i
$495$		0			0
$496$	8.48528			0.381000
$497$	−13.1066	+	1.79360i	−0.587911	+	0.0804538i
$498$		0			0
$499$	3.82843	+	6.63103i	0.171384	+	0.296846i	0.938904	−	0.344179i	$-0.111843\pi$
$499$	3.82843	+	6.63103i	0.171384	+	0.296846i	−0.767520	+	0.641025i	$0.778509\pi$
$500$	−2.82843	+	4.89898i	−0.126491	+	0.219089i
$501$		0			0
$502$	−9.58579	−	16.6031i	−0.427835	−	0.741031i
$503$	2.14214			0.0955131			0.0477566	−	0.998859i	$-0.484793\pi$
$503$	2.14214			0.0955131			0.0477566	+	0.998859i	$0.484793\pi$
$504$		0			0
$505$	31.3137			1.39344
$506$	−1.70711	−	2.95680i	−0.0758902	−	0.131446i
$507$		0			0
$508$	−5.94975	+	10.3053i	−0.263977	+	0.457222i
$509$	−17.3137	−	29.9882i	−0.767417	−	1.32920i	−0.938959	−	0.344028i	$-0.888209\pi$
$509$	−17.3137	−	29.9882i	−0.767417	−	1.32920i	0.171543	−	0.985177i	$-0.445125\pi$
$510$		0			0
$511$	−1.41421	+	3.46410i	−0.0625611	+	0.153243i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	−4.75736	+	8.23999i	−0.209838	+	0.363450i
$515$	19.0711	−	33.0321i	0.840372	−	1.45557i
$516$		0			0
$517$	2.41421			0.106177
$518$	1.41421	−	3.46410i	0.0621370	−	0.152204i
$519$		0			0
$520$	1.70711	+	2.95680i	0.0748616	+	0.129664i
$521$	−2.31371	+	4.00746i	−0.101365	+	0.175570i	−0.912247	−	0.409640i	$-0.865654\pi$
$521$	−2.31371	+	4.00746i	−0.101365	+	0.175570i	0.810882	+	0.585210i	$0.198988\pi$
$522$		0			0
$523$	5.58579	+	9.67487i	0.244249	+	0.423052i	0.961920	−	0.273330i	$-0.0881251\pi$
$523$	5.58579	+	9.67487i	0.244249	+	0.423052i	−0.717671	+	0.696382i	$0.754792\pi$
$524$	−21.5563			−0.941693
$525$		0			0
$526$	23.4142			1.02091
$527$	1.75736	+	3.04384i	0.0765518	+	0.132592i
$528$		0			0
$529$	10.5000	−	18.1865i	0.456522	−	0.790719i
$530$	12.7782	+	22.1324i	0.555048	+	0.961372i
$531$		0			0
$532$	20.5208	−	2.80821i	0.889690	−	0.121751i
$533$	−9.89949			−0.428795
$534$		0			0
$535$	5.65685	−	9.79796i	0.244567	−	0.423603i
$536$	−1.91421	+	3.31552i	−0.0826814	+	0.143208i
$537$		0			0
$538$	19.1421			0.825276
$539$	4.20711	−	16.3674i	0.181213	−	0.704996i
$540$		0			0
$541$	−4.46447	−	7.73268i	−0.191942	−	0.332454i	0.753952	−	0.656930i	$-0.228145\pi$
$541$	−4.46447	−	7.73268i	−0.191942	−	0.332454i	−0.945894	+	0.324476i	$0.894812\pi$
$542$	−8.10660	+	14.0410i	−0.348208	+	0.603115i
$543$		0			0
$544$	−0.207107	−	0.358719i	−0.00887963	−	0.0153800i
$545$	5.65685			0.242313
$546$		0			0
$547$	22.8701			0.977853			0.488927	−	0.872325i	$-0.337389\pi$
$547$	22.8701			0.977853			0.488927	+	0.872325i	$0.337389\pi$
$548$	−1.53553	−	2.65962i	−0.0655948	−	0.113613i
$549$		0			0
$550$	−8.03553	+	13.9180i	−0.342636	+	0.593464i
$551$	−14.9853	−	25.9553i	−0.638394	−	1.10573i
$552$		0			0
$553$	−0.556349	−	0.717439i	−0.0236584	−	0.0305086i
$554$	−3.92893			−0.166924
$555$		0			0
$556$	−0.535534	+	0.927572i	−0.0227117	+	0.0393378i
$557$	6.31371	−	10.9357i	0.267520	−	0.463359i	−0.700700	−	0.713456i	$-0.747129\pi$
$557$	6.31371	−	10.9357i	0.267520	−	0.463359i	0.968221	+	0.250097i	$0.0804624\pi$
$558$		0			0
$559$	−10.4853			−0.443480
$560$	3.41421	−	8.36308i	0.144277	−	0.353405i
$561$		0			0
$562$	−11.6569	−	20.1903i	−0.491715	−	0.851675i
$563$	20.3848	−	35.3075i	0.859116	−	1.48803i	−0.0136575	−	0.999907i	$-0.504347\pi$
$563$	20.3848	−	35.3075i	0.859116	−	1.48803i	0.872773	−	0.488126i	$-0.162319\pi$
$564$		0			0
$565$	−25.4350	−	44.0548i	−1.07006	−	1.85340i
$566$	24.2426			1.01899
$567$		0			0
$568$	−5.00000			−0.209795
$569$	−0.863961	−	1.49642i	−0.0362191	−	0.0627334i	0.847348	−	0.531039i	$-0.178198\pi$
$569$	−0.863961	−	1.49642i	−0.0362191	−	0.0627334i	−0.883567	+	0.468305i	$0.844865\pi$
$570$		0			0
$571$	4.34315	−	7.52255i	0.181755	−	0.314809i	−0.760723	−	0.649076i	$-0.775156\pi$
$571$	4.34315	−	7.52255i	0.181755	−	0.314809i	0.942478	+	0.334267i	$0.108489\pi$
$572$	1.20711	+	2.09077i	0.0504717	+	0.0874195i
$573$		0			0
$574$	16.0503	+	20.6976i	0.669925	+	0.863900i
$575$	9.41421			0.392600
$576$		0			0
$577$	−13.8284	+	23.9515i	−0.575685	+	0.997116i	0.420282	+	0.907394i	$0.361931\pi$
$577$	−13.8284	+	23.9515i	−0.575685	+	0.997116i	−0.995967	+	0.0897220i	$0.971402\pi$
$578$	−8.41421	+	14.5738i	−0.349985	+	0.606192i
$579$		0			0
$580$	−13.0711			−0.542747
$581$	−9.58579	+	1.31178i	−0.397685	+	0.0544220i
$582$		0			0
$583$	9.03553	+	15.6500i	0.374214	+	0.648157i
$584$	−0.707107	+	1.22474i	−0.0292603	+	0.0506803i
$585$		0			0
$586$	−4.94975	−	8.57321i	−0.204472	−	0.354156i
$587$	4.41421			0.182194			0.0910970	−	0.995842i	$-0.470963\pi$
$587$	4.41421			0.182194			0.0910970	+	0.995842i	$0.470963\pi$
$588$		0			0
$589$	−66.4264			−2.73705
$590$	20.6066	+	35.6917i	0.848360	+	1.46940i
$591$		0			0
$592$	0.707107	−	1.22474i	0.0290619	−	0.0503367i
$593$	1.19239	+	2.06528i	0.0489655	+	0.0848108i	0.889469	−	0.456995i	$-0.151074\pi$
$593$	1.19239	+	2.06528i	0.0489655	+	0.0848108i	−0.840504	+	0.541806i	$0.817741\pi$
$594$		0			0
$595$	3.70711	−	0.507306i	0.151977	−	0.0207975i
$596$	19.0711			0.781181
$597$		0			0
$598$	0.707107	−	1.22474i	0.0289157	−	0.0500835i
$599$	−14.7782	+	25.5965i	−0.603820	+	1.04585i	0.388417	+	0.921484i	$0.373022\pi$
$599$	−14.7782	+	25.5965i	−0.603820	+	1.04585i	−0.992237	+	0.124363i	$0.960311\pi$
$600$		0			0
$601$	40.7990			1.66423			0.832113	−	0.554606i	$-0.187131\pi$
$601$	40.7990			1.66423			0.832113	+	0.554606i	$0.187131\pi$
$602$	17.0000	+	21.9223i	0.692868	+	0.893487i
$603$		0			0
$604$	5.03553	+	8.72180i	0.204893	+	0.354885i
$605$	8.82843	−	15.2913i	0.358927	−	0.621679i
$606$		0			0
$607$	15.2635	+	26.4371i	0.619525	+	1.07305i	0.989573	+	0.144035i	$0.0460079\pi$
$607$	15.2635	+	26.4371i	0.619525	+	1.07305i	−0.370048	+	0.929013i	$0.620659\pi$
$608$	7.82843			0.317485
$609$		0			0
$610$	5.41421			0.219215
$611$	0.500000	+	0.866025i	0.0202278	+	0.0350356i
$612$		0			0
$613$	−15.8995	+	27.5387i	−0.642175	+	1.11228i	0.342772	+	0.939419i	$0.388634\pi$
$613$	−15.8995	+	27.5387i	−0.642175	+	1.11228i	−0.984946	+	0.172860i	$0.944699\pi$
$614$	17.0563	+	29.5425i	0.688338	+	1.19224i
$615$		0			0
$616$	2.41421	−	5.91359i	0.0972714	−	0.238265i
$617$	−4.14214			−0.166756			−0.0833781	−	0.996518i	$-0.526571\pi$
$617$	−4.14214			−0.166756			−0.0833781	+	0.996518i	$0.526571\pi$
$618$		0			0
$619$	−7.58579	+	13.1390i	−0.304898	+	0.528100i	−0.977239	−	0.212143i	$-0.931956\pi$
$619$	−7.58579	+	13.1390i	−0.304898	+	0.528100i	0.672340	+	0.740242i	$0.265289\pi$
$620$	−14.4853	+	25.0892i	−0.581743	+	1.00761i
$621$		0			0
$622$	−27.8995			−1.11867
$623$	−8.77817	−	11.3199i	−0.351690	−	0.453521i
$624$		0			0
$625$	6.98528	+	12.0989i	0.279411	+	0.483954i
$626$	10.2426	−	17.7408i	0.409378	−	0.709064i
$627$		0			0
$628$	7.86396	+	13.6208i	0.313806	+	0.543528i
$629$	0.585786			0.0233568
$630$		0			0
$631$	−12.6274			−0.502690			−0.251345	−	0.967898i	$-0.580873\pi$
$631$	−12.6274			−0.502690			−0.251345	+	0.967898i	$0.580873\pi$
$632$	−0.171573	−	0.297173i	−0.00682480	−	0.0118209i
$633$		0			0
$634$	4.89949	−	8.48617i	0.194584	−	0.337029i
$635$	−20.3137	−	35.1844i	−0.806125	−	1.39625i
$636$		0			0
$637$	6.74264	−	1.88064i	0.267153	−	0.0745136i
$638$	−9.24264			−0.365920
$639$		0			0
$640$	1.70711	−	2.95680i	0.0674793	−	0.116878i
$641$	−3.89949	+	6.75412i	−0.154021	+	0.266772i	−0.932702	−	0.360648i	$-0.882556\pi$
$641$	−3.89949	+	6.75412i	−0.154021	+	0.266772i	0.778681	+	0.627420i	$0.215889\pi$
$642$		0			0
$643$	−19.4853			−0.768424			−0.384212	−	0.923245i	$-0.625527\pi$
$643$	−19.4853			−0.768424			−0.384212	+	0.923245i	$0.625527\pi$
$644$	−3.70711	+	0.507306i	−0.146080	+	0.0199907i
$645$		0			0
$646$	1.62132	+	2.80821i	0.0637900	+	0.110488i
$647$	−21.4853	+	37.2136i	−0.844674	+	1.46302i	0.0412308	+	0.999150i	$0.486872\pi$
$647$	−21.4853	+	37.2136i	−0.844674	+	1.46302i	−0.885904	+	0.463868i	$0.846461\pi$
$648$		0			0
$649$	14.5711	+	25.2378i	0.571964	+	0.990671i
$650$	−6.65685			−0.261103
$651$		0			0
$652$	−7.34315			−0.287580
$653$	−3.07107	−	5.31925i	−0.120180	−	0.208158i	0.799658	−	0.600455i	$-0.205014\pi$
$653$	−3.07107	−	5.31925i	−0.120180	−	0.208158i	−0.919839	+	0.392297i	$0.871681\pi$
$654$		0			0
$655$	36.7990	−	63.7377i	1.43786	−	2.49044i
$656$	4.94975	+	8.57321i	0.193255	+	0.334728i
$657$		0			0
$658$	1.00000	−	2.44949i	0.0389841	−	0.0954911i
$659$	−13.4142			−0.522544			−0.261272	−	0.965265i	$-0.584142\pi$
$659$	−13.4142			−0.522544			−0.261272	+	0.965265i	$0.584142\pi$
$660$		0			0
$661$	−15.8787	+	27.5027i	−0.617609	+	1.06973i	0.372312	+	0.928108i	$0.378565\pi$
$661$	−15.8787	+	27.5027i	−0.617609	+	1.06973i	−0.989921	+	0.141623i	$0.954768\pi$
$662$	−2.75736	+	4.77589i	−0.107168	+	0.185620i
$663$		0			0
$664$	−3.65685			−0.141913
$665$	−26.7279	+	65.4698i	−1.03646	+	2.53881i
$666$		0			0
$667$	2.70711	+	4.68885i	0.104820	+	0.181553i
$668$	5.32843	−	9.22911i	0.206163	−	0.357085i
$669$		0			0
$670$	−6.53553	−	11.3199i	−0.252490	−	0.437325i
$671$	3.82843			0.147795
$672$		0			0
$673$	13.8579			0.534181			0.267091	−	0.963671i	$-0.413938\pi$
$673$	13.8579			0.534181			0.267091	+	0.963671i	$0.413938\pi$
$674$	1.15685	+	2.00373i	0.0445604	+	0.0771808i
$675$		0			0
$676$	−0.500000	+	0.866025i	−0.0192308	+	0.0333087i
$677$	7.50000	+	12.9904i	0.288248	+	0.499261i	0.973392	−	0.229147i	$-0.0735938\pi$
$677$	7.50000	+	12.9904i	0.288248	+	0.499261i	−0.685143	+	0.728408i	$0.740260\pi$
$678$		0			0
$679$	39.5061	−	5.40629i	1.51610	−	0.207474i
$680$	1.41421			0.0542326
$681$		0			0
$682$	−10.2426	+	17.7408i	−0.392211	+	0.679329i
$683$	7.07107	−	12.2474i	0.270567	−	0.468636i	−0.698440	−	0.715668i	$-0.746122\pi$
$683$	7.07107	−	12.2474i	0.270567	−	0.468636i	0.969007	+	0.247033i	$0.0794555\pi$
$684$		0			0
$685$	10.4853			0.400622
$686$	−14.8640	−	11.0482i	−0.567509	−	0.421822i
$687$		0			0
$688$	5.24264	+	9.08052i	0.199874	+	0.346192i
$689$	−3.74264	+	6.48244i	−0.142583	+	0.246961i
$690$		0			0
$691$	4.67157	+	8.09140i	0.177715	+	0.307811i	0.941098	−	0.338135i	$-0.109796\pi$
$691$	4.67157	+	8.09140i	0.177715	+	0.307811i	−0.763383	+	0.645947i	$0.776463\pi$
$692$	11.4853			0.436605
$693$		0			0
$694$	16.7279			0.634983
$695$	−1.82843	−	3.16693i	−0.0693562	−	0.120128i
$696$		0			0
$697$	−2.05025	+	3.55114i	−0.0776589	+	0.134509i
$698$	9.36396	+	16.2189i	0.354431	+	0.613893i
$699$		0			0
$700$	10.7929	+	13.9180i	0.407933	+	0.526049i
$701$	34.8284			1.31545			0.657726	−	0.753257i	$-0.271519\pi$
$701$	34.8284			1.31545			0.657726	+	0.753257i	$0.271519\pi$
$702$		0			0
$703$	−5.53553	+	9.58783i	−0.208777	+	0.361612i
$704$	1.20711	−	2.09077i	0.0454945	−	0.0787989i
$705$		0			0
$706$	−32.6274			−1.22795
$707$	9.17157	−	22.4657i	0.344932	−	0.844909i
$708$		0			0
$709$	−8.43503	−	14.6099i	−0.316784	−	0.548686i	0.663031	−	0.748592i	$-0.269270\pi$
$709$	−8.43503	−	14.6099i	−0.316784	−	0.548686i	−0.979815	+	0.199906i	$0.935936\pi$
$710$	8.53553	−	14.7840i	0.320333	−	0.554833i
$711$		0			0
$712$	−2.70711	−	4.68885i	−0.101453	−	0.175722i
$713$	12.0000			0.449404
$714$		0			0
$715$	−8.24264			−0.308257
$716$	4.17157	+	7.22538i	0.155899	+	0.270025i
$717$		0			0
$718$	−2.41421	+	4.18154i	−0.0900976	+	0.156054i
$719$	−6.65685	−	11.5300i	−0.248259	−	0.429997i	0.714784	−	0.699345i	$-0.246525\pi$
$719$	−6.65685	−	11.5300i	−0.248259	−	0.429997i	−0.963043	+	0.269348i	$0.913192\pi$
$720$		0			0
$721$	−18.1127	−	23.3572i	−0.674552	−	0.869867i
$722$	−42.2843			−1.57366
$723$		0			0
$724$	8.44975	−	14.6354i	0.314032	−	0.543920i
$725$	12.7426	−	22.0709i	0.473250	−	0.819693i
$726$		0			0
$727$	34.4264			1.27680			0.638402	−	0.769703i	$-0.279596\pi$
$727$	34.4264			1.27680			0.638402	+	0.769703i	$0.279596\pi$
$728$	2.62132	−	0.358719i	0.0971526	−	0.0132950i
$729$		0			0
$730$	−2.41421	−	4.18154i	−0.0893541	−	0.154766i
$731$	−2.17157	+	3.76127i	−0.0803185	+	0.139116i
$732$		0			0
$733$	15.7071	+	27.2055i	0.580155	+	1.00486i	0.995460	+	0.0951762i	$0.0303415\pi$
$733$	15.7071	+	27.2055i	0.580155	+	1.00486i	−0.415305	+	0.909682i	$0.636325\pi$
$734$	32.6274			1.20430
$735$		0			0
$736$	−1.41421			−0.0521286
$737$	−4.62132	−	8.00436i	−0.170229	−	0.294844i
$738$		0			0
$739$	15.0000	−	25.9808i	0.551784	−	0.955718i	−0.446362	−	0.894852i	$-0.647281\pi$
$739$	15.0000	−	25.9808i	0.551784	−	0.955718i	0.998146	−	0.0608653i	$-0.0193860\pi$
$740$	2.41421	+	4.18154i	0.0887483	+	0.153716i
$741$		0			0
$742$	19.6213	−	2.68512i	0.720321	−	0.0985737i
$743$	−17.8284			−0.654062			−0.327031	−	0.945014i	$-0.606048\pi$
$743$	−17.8284			−0.654062			−0.327031	+	0.945014i	$0.606048\pi$
$744$		0			0
$745$	−32.5563	+	56.3893i	−1.19277	+	2.06594i
$746$	−4.20711	+	7.28692i	−0.154033	+	0.266793i
$747$		0			0
$748$	1.00000			0.0365636
$749$	−5.37258	−	6.92820i	−0.196310	−	0.253151i
$750$		0			0
$751$	−1.65685	−	2.86976i	−0.0604595	−	0.104719i	0.834211	−	0.551445i	$-0.185923\pi$
$751$	−1.65685	−	2.86976i	−0.0604595	−	0.104719i	−0.894671	+	0.446726i	$0.852590\pi$
$752$	0.500000	−	0.866025i	0.0182331	−	0.0315807i
$753$		0			0
$754$	−1.91421	−	3.31552i	−0.0697115	−	0.120744i
$755$	−34.3848			−1.25139
$756$		0			0
$757$	−39.2426			−1.42630			−0.713149	−	0.701012i	$-0.752732\pi$
$757$	−39.2426			−1.42630			−0.713149	+	0.701012i	$0.752732\pi$
$758$	−13.3137	−	23.0600i	−0.483576	−	0.837578i
$759$		0			0
$760$	−13.3640	+	23.1471i	−0.484762	+	0.839632i
$761$	−9.55635	−	16.5521i	−0.346417	−	0.600013i	0.639193	−	0.769046i	$-0.279269\pi$
$761$	−9.55635	−	16.5521i	−0.346417	−	0.600013i	−0.985610	+	0.169034i	$0.945935\pi$
$762$		0			0
$763$	1.65685	−	4.05845i	0.0599822	−	0.146926i
$764$	21.6569			0.783517
$765$		0			0
$766$	−8.41421	+	14.5738i	−0.304018	+	0.526574i
$767$	−6.03553	+	10.4539i	−0.217930	+	0.377467i
$768$		0			0
$769$	−9.89949			−0.356985			−0.178492	−	0.983941i	$-0.557122\pi$
$769$	−9.89949			−0.356985			−0.178492	+	0.983941i	$0.557122\pi$
$770$	13.3640	+	17.2335i	0.481604	+	0.621051i
$771$		0			0
$772$	8.53553	+	14.7840i	0.307201	+	0.532087i
$773$	−7.48528	+	12.9649i	−0.269227	+	0.466315i	−0.968662	−	0.248381i	$-0.920101\pi$
$773$	−7.48528	+	12.9649i	−0.269227	+	0.466315i	0.699436	+	0.714696i	$0.253435\pi$
$774$		0			0
$775$	−28.2426	−	48.9177i	−1.01451	−	1.75718i
$776$	15.0711			0.541020
$777$		0			0
$778$	−21.4853			−0.770285
$779$	−38.7487	−	67.1148i	−1.38832	−	2.40464i
$780$		0			0
$781$	6.03553	−	10.4539i	0.215968	−	0.374068i
$782$	−0.292893	−	0.507306i	−0.0104738	−	0.0181412i
$783$		0			0
$784$	−5.00000	−	4.89898i	−0.178571	−	0.174964i
$785$	−53.6985			−1.91658
$786$		0			0
$787$	1.84315	−	3.19242i	0.0657011	−	0.113798i	−0.831304	−	0.555818i	$-0.812405\pi$
$787$	1.84315	−	3.19242i	0.0657011	−	0.113798i	0.897005	+	0.442021i	$0.145738\pi$
$788$	7.77817	−	13.4722i	0.277086	−	0.479927i
$789$		0			0
$790$	1.17157			0.0416827
$791$	−39.0563	+	5.34474i	−1.38868	+	0.190037i
$792$		0			0
$793$	0.792893	+	1.37333i	0.0281565	+	0.0487684i
$794$	10.7782	−	18.6683i	0.382503	−	0.662515i
$795$		0			0
$796$	11.3640	+	19.6830i	0.402785	+	0.697644i
$797$	−45.6569			−1.61725			−0.808624	−	0.588325i	$-0.799787\pi$
$797$	−45.6569			−1.61725			−0.808624	+	0.588325i	$0.799787\pi$
$798$		0			0
$799$	0.414214			0.0146538
$800$	3.32843	+	5.76500i	0.117678	+	0.203824i
$801$		0			0
$802$	−0.0502525	+	0.0870399i	−0.00177448	+	0.00307349i
$803$	−1.70711	−	2.95680i	−0.0602425	−	0.104343i
$804$		0			0
$805$	4.82843	−	11.8272i	0.170180	−	0.416853i
$806$	−8.48528			−0.298881
$807$		0			0
$808$	4.58579	−	7.94282i	0.161327	−	0.279427i
$809$	−10.2071	+	17.6792i	−0.358863	+	0.621569i	−0.987771	−	0.155911i	$-0.950169\pi$
$809$	−10.2071	+	17.6792i	−0.358863	+	0.621569i	0.628908	+	0.777479i	$0.283502\pi$
$810$		0			0
$811$	4.54416			0.159567			0.0797834	−	0.996812i	$-0.474577\pi$
$811$	4.54416			0.159567			0.0797834	+	0.996812i	$0.474577\pi$
$812$	−3.82843	+	9.37769i	−0.134351	+	0.329093i
$813$		0			0
$814$	1.70711	+	2.95680i	0.0598341	+	0.103636i
$815$	12.5355	−	21.7122i	0.439101	−	0.760545i
$816$		0			0
$817$	−41.0416	−	71.0862i	−1.43586	−	2.48699i
$818$	−35.4142			−1.23823
$819$		0			0
$820$	−33.7990			−1.18031
$821$	14.0503	+	24.3358i	0.490357	+	0.849324i	0.999938	−	0.0110990i	$-0.00353299\pi$
$821$	14.0503	+	24.3358i	0.490357	+	0.849324i	−0.509581	+	0.860423i	$0.670200\pi$
$822$		0			0
$823$	−21.9203	+	37.9671i	−0.764094	+	1.32345i	0.176630	+	0.984277i	$0.443480\pi$
$823$	−21.9203	+	37.9671i	−0.764094	+	1.32345i	−0.940724	+	0.339172i	$0.889853\pi$
$824$	−5.58579	−	9.67487i	−0.194590	−	0.337040i
$825$		0			0
$826$	31.6421	−	4.33013i	1.10097	−	0.150664i
$827$	24.3553			0.846918			0.423459	−	0.905915i	$-0.360816\pi$
$827$	24.3553			0.846918			0.423459	+	0.905915i	$0.360816\pi$
$828$		0			0
$829$	−16.3492	+	28.3177i	−0.567833	+	0.983515i	0.428947	+	0.903330i	$0.358885\pi$
$829$	−16.3492	+	28.3177i	−0.567833	+	0.983515i	−0.996780	+	0.0801855i	$0.974449\pi$
$830$	6.24264	−	10.8126i	0.216685	−	0.375310i
$831$		0			0
$832$	1.00000			0.0346688
$833$	0.721825	−	2.80821i	0.0250098	−	0.0972987i
$834$		0			0
$835$	18.1924	+	31.5101i	0.629574	+	1.09045i
$836$	−9.44975	+	16.3674i	−0.326826	+	0.566080i
$837$		0			0
$838$	11.7279	+	20.3134i	0.405134	+	0.701713i
$839$	26.1716			0.903543			0.451772	−	0.892134i	$-0.350792\pi$
$839$	26.1716			0.903543			0.451772	+	0.892134i	$0.350792\pi$
$840$		0			0
$841$	−14.3431			−0.494591
$842$	−6.53553	−	11.3199i	−0.225229	−	0.390109i
$843$		0			0
$844$	13.5355	−	23.4442i	0.465912	−	0.806984i
$845$	−1.70711	−	2.95680i	−0.0587263	−	0.101717i
$846$		0			0
$847$	−8.38478	−	10.8126i	−0.288104	−	0.371524i
$848$	7.48528			0.257046
$849$		0			0
$850$	−1.37868	+	2.38794i	−0.0472883	+	0.0819058i
$851$	1.00000	−	1.73205i	0.0342796	−	0.0593739i
$852$		0			0
$853$	−18.7279			−0.641232			−0.320616	−	0.947209i	$-0.603890\pi$
$853$	−18.7279			−0.641232			−0.320616	+	0.947209i	$0.603890\pi$
$854$	1.58579	−	3.88437i	0.0542645	−	0.132920i
$855$		0			0
$856$	−1.65685	−	2.86976i	−0.0566301	−	0.0980862i
$857$	−5.27817	+	9.14207i	−0.180299	+	0.312287i	−0.941982	−	0.335662i	$-0.891040\pi$
$857$	−5.27817	+	9.14207i	−0.180299	+	0.312287i	0.761683	+	0.647949i	$0.224373\pi$
$858$		0			0
$859$	−13.8995	−	24.0746i	−0.474245	−	0.821416i	0.525320	−	0.850904i	$-0.323945\pi$
$859$	−13.8995	−	24.0746i	−0.474245	−	0.821416i	−0.999565	+	0.0294886i	$0.990612\pi$
$860$	−35.7990			−1.22074
$861$		0			0
$862$	13.5147			0.460313
$863$	8.34315	+	14.4508i	0.284004	+	0.491909i	0.972367	−	0.233457i	$-0.0750038\pi$
$863$	8.34315	+	14.4508i	0.284004	+	0.491909i	−0.688363	+	0.725366i	$0.741670\pi$
$864$		0			0
$865$	−19.6066	+	33.9596i	−0.666644	+	1.15466i
$866$	−1.98528	−	3.43861i	−0.0674626	−	0.116849i
$867$		0			0
$868$	13.7574	+	17.7408i	0.466955	+	0.602161i
$869$	0.828427			0.0281025
$870$		0			0
$871$	1.91421	−	3.31552i	0.0648607	−	0.112342i
$872$	0.828427	−	1.43488i	0.0280541	−	0.0485911i
$873$		0			0
$874$	11.0711			0.374484
$875$	−14.8284	+	2.02922i	−0.501292	+	0.0686003i
$876$		0			0
$877$	−4.02082	−	6.96426i	−0.135773	−	0.235166i	0.790119	−	0.612953i	$-0.210019\pi$
$877$	−4.02082	−	6.96426i	−0.135773	−	0.235166i	−0.925893	+	0.377787i	$0.876685\pi$
$878$	9.70711	−	16.8132i	0.327599	−	0.567418i
$879$		0			0
$880$	4.12132	+	7.13834i	0.138930	+	0.240633i
$881$	−1.51472			−0.0510322			−0.0255161	−	0.999674i	$-0.508123\pi$
$881$	−1.51472			−0.0510322			−0.0255161	+	0.999674i	$0.508123\pi$
$882$		0			0
$883$	−18.2426			−0.613914			−0.306957	−	0.951723i	$-0.599311\pi$
$883$	−18.2426			−0.613914			−0.306957	+	0.951723i	$0.599311\pi$
$884$	0.207107	+	0.358719i	0.00696575	+	0.0120650i
$885$		0			0
$886$	−12.8492	+	22.2555i	−0.431679	+	0.747690i
$887$	−26.4558	−	45.8229i	−0.888300	−	1.53858i	−0.841884	−	0.539659i	$-0.818553\pi$
$887$	−26.4558	−	45.8229i	−0.888300	−	1.53858i	−0.0464167	−	0.998922i	$-0.514780\pi$
$888$		0			0
$889$	−31.1924	+	4.26858i	−1.04616	+	0.143164i
$890$	18.4853			0.619628
$891$		0			0
$892$	11.0355	−	19.1141i	0.369497	−	0.639988i
$893$	−3.91421	+	6.77962i	−0.130984	+	0.226871i
$894$		0			0
$895$	−28.4853			−0.952158
$896$	−1.62132	−	2.09077i	−0.0541645	−	0.0698477i
$897$		0			0
$898$	4.48528	+	7.76874i	0.149676	+	0.259246i
$899$	16.2426	−	28.1331i	0.541722	−	0.938291i
$900$		0			0
$901$	1.55025	+	2.68512i	0.0516464	+	0.0894542i
$902$	−23.8995			−0.795766
$903$		0			0
$904$	−14.8995			−0.495550
$905$	28.8492	+	49.9684i	0.958981	+	1.66100i
$906$		0			0
$907$	−8.80761	+	15.2552i	−0.292452	+	0.506542i	−0.974389	−	0.224869i	$-0.927804\pi$
$907$	−8.80761	+	15.2552i	−0.292452	+	0.506542i	0.681937	+	0.731411i	$0.261138\pi$
$908$	−13.4142	−	23.2341i	−0.445166	−	0.771051i
$909$		0			0
$910$	−3.41421	+	8.36308i	−0.113180	+	0.277233i
$911$	15.6569			0.518735			0.259367	−	0.965779i	$-0.416486\pi$
$911$	15.6569			0.518735			0.259367	+	0.965779i	$0.416486\pi$
$912$		0			0
$913$	4.41421	−	7.64564i	0.146089	−	0.253034i
$914$	5.53553	−	9.58783i	0.183099	−	0.317137i
$915$		0			0
$916$	9.51472			0.314375
$917$	−34.9497	−	45.0694i	−1.15414	−	1.48832i
$918$		0			0
$919$	18.8995	+	32.7349i	0.623437	+	1.07982i	0.988841	+	0.148975i	$0.0475975\pi$
$919$	18.8995	+	32.7349i	0.623437	+	1.07982i	−0.365404	+	0.930849i	$0.619069\pi$
$920$	2.41421	−	4.18154i	0.0795943	−	0.137861i
$921$		0			0
$922$	−6.24264	−	10.8126i	−0.205590	−	0.356093i
$923$	5.00000			0.164577
$924$		0			0
$925$	−9.41421			−0.309537
$926$	6.48528	+	11.2328i	0.213120	+	0.369134i
$927$		0			0
$928$	−1.91421	+	3.31552i	−0.0628371	+	0.108837i
$929$	28.6569	+	49.6351i	0.940201	+	1.62848i	0.765086	+	0.643928i	$0.222696\pi$
$929$	28.6569	+	49.6351i	0.940201	+	1.62848i	0.175114	+	0.984548i	$0.443970\pi$
$930$		0			0
$931$	39.1421	+	38.3513i	1.28283	+	1.25691i
$932$	−7.72792			−0.253137
$933$		0			0
$934$	4.29289	−	7.43551i	0.140468	−	0.243297i
$935$	−1.70711	+	2.95680i	−0.0558284	+	0.0966976i
$936$		0			0
$937$	31.3431			1.02394			0.511968	−	0.859005i	$-0.328917\pi$
$937$	31.3431			1.02394			0.511968	+	0.859005i	$0.328917\pi$
$938$	−10.0355	+	1.37333i	−0.327672	+	0.0448409i
$939$		0			0
$940$	1.70711	+	2.95680i	0.0556797	+	0.0964400i
$941$	10.4853	−	18.1610i	0.341810	−	0.592033i	−0.642959	−	0.765901i	$-0.722293\pi$
$941$	10.4853	−	18.1610i	0.341810	−	0.592033i	0.984769	+	0.173868i	$0.0556266\pi$
$942$		0			0
$943$	7.00000	+	12.1244i	0.227951	+	0.394823i
$944$	12.0711			0.392880
$945$		0			0
$946$	−25.3137			−0.823020
$947$	2.79289	+	4.83743i	0.0907568	+	0.157195i	0.907830	−	0.419339i	$-0.137738\pi$
$947$	2.79289	+	4.83743i	0.0907568	+	0.157195i	−0.817073	+	0.576534i	$0.804405\pi$
$948$		0			0
$949$	0.707107	−	1.22474i	0.0229537	−	0.0397569i
$950$	−26.0563	−	45.1309i	−0.845380	−	1.46424i
$951$		0			0
$952$	0.414214	−	1.01461i	0.0134247	−	0.0328838i
$953$	44.4142			1.43872			0.719359	−	0.694639i	$-0.244436\pi$
$953$	44.4142			1.43872			0.719359	+	0.694639i	$0.244436\pi$
$954$		0			0
$955$	−36.9706	+	64.0349i	−1.19634	+	2.07212i
$956$	10.7426	−	18.6068i	0.347442	−	0.601787i
$957$		0			0
$958$	30.1127			0.972897
$959$	3.07107	−	7.52255i	0.0991700	−	0.242916i
$960$		0			0
$961$	−20.5000	−	35.5070i	−0.661290	−	1.14539i
$962$	−0.707107	+	1.22474i	−0.0227980	+	0.0394874i
$963$		0			0
$964$	−13.0711	−	22.6398i	−0.420991	−	0.729177i
$965$	−58.2843			−1.87624
$966$		0			0
$967$	−16.4142			−0.527846			−0.263923	−	0.964544i	$-0.585016\pi$
$967$	−16.4142			−0.527846			−0.263923	+	0.964544i	$0.585016\pi$
$968$	−2.58579	−	4.47871i	−0.0831103	−	0.143951i
$969$		0			0
$970$	−25.7279	+	44.5621i	−0.826074	+	1.43080i
$971$	16.2635	+	28.1691i	0.521919	+	0.903990i	0.999675	+	0.0254978i	$0.00811707\pi$
$971$	16.2635	+	28.1691i	0.521919	+	0.903990i	−0.477756	+	0.878493i	$0.658550\pi$
$972$		0			0
$973$	−2.80761	+	0.384213i	−0.0900079	+	0.0123173i
$974$	26.2132			0.839925
$975$		0			0
$976$	0.792893	−	1.37333i	0.0253799	−	0.0439593i
$977$	24.4142	−	42.2867i	0.781080	−	1.35287i	−0.150233	−	0.988651i	$-0.548002\pi$
$977$	24.4142	−	42.2867i	0.781080	−	1.35287i	0.931313	−	0.364219i	$-0.118664\pi$
$978$		0			0
$979$	13.0711			0.417753
$980$	23.0208	−	6.42090i	0.735373	−	0.205108i
$981$		0			0
$982$	−6.17157	−	10.6895i	−0.196943	−	0.341115i
$983$	−6.25736	+	10.8381i	−0.199579	+	0.345681i	−0.948392	−	0.317101i	$-0.897291\pi$
$983$	−6.25736	+	10.8381i	−0.199579	+	0.345681i	0.748813	+	0.662781i	$0.230624\pi$
$984$		0			0
$985$	26.5563	+	45.9969i	0.846156	+	1.46558i
$986$	−1.58579			−0.0505017
$987$		0			0
$988$	−7.82843			−0.249055
$989$	7.41421	+	12.8418i	0.235758	+	0.408345i
$990$		0			0
$991$	11.6569	−	20.1903i	0.370292	−	0.641365i	−0.619318	−	0.785140i	$-0.712591\pi$
$991$	11.6569	−	20.1903i	0.370292	−	0.641365i	0.989610	+	0.143775i	$0.0459242\pi$
$992$	4.24264	+	7.34847i	0.134704	+	0.233314i
$993$		0			0
$994$	−8.10660	−	10.4539i	−0.257126	−	0.331576i
$995$	−77.5980			−2.46002
$996$		0			0
$997$	23.2487	−	40.2680i	0.736295	−	1.27530i	−0.217858	−	0.975980i	$-0.569907\pi$
$997$	23.2487	−	40.2680i	0.736295	−	1.27530i	0.954153	−	0.299320i	$-0.0967597\pi$
$998$	−3.82843	+	6.63103i	−0.121187	+	0.209902i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1638.2.j.m.235.1		4
3.2	odd	2		546.2.i.i.235.2	yes	4
7.2	even	3	inner	1638.2.j.m.1171.1		4
21.2	odd	6		546.2.i.i.79.2	✓	4
21.11	odd	6		3822.2.a.bn.1.1		2
21.17	even	6		3822.2.a.bu.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.i.i.79.2	✓	4	21.2	odd	6
546.2.i.i.235.2	yes	4	3.2	odd	2
1638.2.j.m.235.1		4	1.1	even	1	trivial
1638.2.j.m.1171.1		4	7.2	even	3	inner
3822.2.a.bn.1.1		2	21.11	odd	6
3822.2.a.bu.1.2		2	21.17	even	6

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:	\( N \)	\(=\)	\( 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1638.j (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.70711 - 2.95680i) q^{5} +(-2.62132 + 0.358719i) q^{7} -1.00000 q^{8} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.70711 - 2.95680i) q^{5} +(-2.62132 + 0.358719i) q^{7} -1.00000 q^{8} +(1.70711 - 2.95680i) q^{10} +(1.20711 - 2.09077i) q^{11} +1.00000 q^{13} +(-1.62132 - 2.09077i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(0.207107 - 0.358719i) q^{17} +(3.91421 + 6.77962i) q^{19} +3.41421 q^{20} +2.41421 q^{22} +(-0.707107 - 1.22474i) q^{23} +(-3.32843 + 5.76500i) q^{25} +(0.500000 + 0.866025i) q^{26} +(1.00000 - 2.44949i) q^{28} -3.82843 q^{29} +(-4.24264 + 7.34847i) q^{31} +(0.500000 - 0.866025i) q^{32} +0.414214 q^{34} +(5.53553 + 7.13834i) q^{35} +(0.707107 + 1.22474i) q^{37} +(-3.91421 + 6.77962i) q^{38} +(1.70711 + 2.95680i) q^{40} -9.89949 q^{41} -10.4853 q^{43} +(1.20711 + 2.09077i) q^{44} +(0.707107 - 1.22474i) q^{46} +(0.500000 + 0.866025i) q^{47} +(6.74264 - 1.88064i) q^{49} -6.65685 q^{50} +(-0.500000 + 0.866025i) q^{52} +(-3.74264 + 6.48244i) q^{53} -8.24264 q^{55} +(2.62132 - 0.358719i) q^{56} +(-1.91421 - 3.31552i) q^{58} +(-6.03553 + 10.4539i) q^{59} +(0.792893 + 1.37333i) q^{61} -8.48528 q^{62} +1.00000 q^{64} +(-1.70711 - 2.95680i) q^{65} +(1.91421 - 3.31552i) q^{67} +(0.207107 + 0.358719i) q^{68} +(-3.41421 + 8.36308i) q^{70} +5.00000 q^{71} +(0.707107 - 1.22474i) q^{73} +(-0.707107 + 1.22474i) q^{74} -7.82843 q^{76} +(-2.41421 + 5.91359i) q^{77} +(0.171573 + 0.297173i) q^{79} +(-1.70711 + 2.95680i) q^{80} +(-4.94975 - 8.57321i) q^{82} +3.65685 q^{83} -1.41421 q^{85} +(-5.24264 - 9.08052i) q^{86} +(-1.20711 + 2.09077i) q^{88} +(2.70711 + 4.68885i) q^{89} +(-2.62132 + 0.358719i) q^{91} +1.41421 q^{92} +(-0.500000 + 0.866025i) q^{94} +(13.3640 - 23.1471i) q^{95} -15.0711 q^{97} +(5.00000 + 4.89898i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - 2 q^{4} - 4 q^{5} - 2 q^{7} - 4 q^{8}+O(q^{10}) \) 4 * q + 2 * q^2 - 2 * q^4 - 4 * q^5 - 2 * q^7 - 4 * q^8	\( 4 q + 2 q^{2} - 2 q^{4} - 4 q^{5} - 2 q^{7} - 4 q^{8} + 4 q^{10} + 2 q^{11} + 4 q^{13} + 2 q^{14} - 2 q^{16} - 2 q^{17} + 10 q^{19} + 8 q^{20} + 4 q^{22} - 2 q^{25} + 2 q^{26} + 4 q^{28} - 4 q^{29} + 2 q^{32} - 4 q^{34} + 8 q^{35} - 10 q^{38} + 4 q^{40} - 8 q^{43} + 2 q^{44} + 2 q^{47} + 10 q^{49} - 4 q^{50} - 2 q^{52} + 2 q^{53} - 16 q^{55} + 2 q^{56} - 2 q^{58} - 10 q^{59} + 6 q^{61} + 4 q^{64} - 4 q^{65} + 2 q^{67} - 2 q^{68} - 8 q^{70} + 20 q^{71} - 20 q^{76} - 4 q^{77} + 12 q^{79} - 4 q^{80} - 8 q^{83} - 4 q^{86} - 2 q^{88} + 8 q^{89} - 2 q^{91} - 2 q^{94} + 28 q^{95} - 32 q^{97} + 20 q^{98}+O(q^{100}) \) 4 * q + 2 * q^2 - 2 * q^4 - 4 * q^5 - 2 * q^7 - 4 * q^8 + 4 * q^10 + 2 * q^11 + 4 * q^13 + 2 * q^14 - 2 * q^16 - 2 * q^17 + 10 * q^19 + 8 * q^20 + 4 * q^22 - 2 * q^25 + 2 * q^26 + 4 * q^28 - 4 * q^29 + 2 * q^32 - 4 * q^34 + 8 * q^35 - 10 * q^38 + 4 * q^40 - 8 * q^43 + 2 * q^44 + 2 * q^47 + 10 * q^49 - 4 * q^50 - 2 * q^52 + 2 * q^53 - 16 * q^55 + 2 * q^56 - 2 * q^58 - 10 * q^59 + 6 * q^61 + 4 * q^64 - 4 * q^65 + 2 * q^67 - 2 * q^68 - 8 * q^70 + 20 * q^71 - 20 * q^76 - 4 * q^77 + 12 * q^79 - 4 * q^80 - 8 * q^83 - 4 * q^86 - 2 * q^88 + 8 * q^89 - 2 * q^91 - 2 * q^94 + 28 * q^95 - 32 * q^97 + 20 * q^98

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