LMFDB - Embedded newform 576.2.y.a.335.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [576,2,Mod(47,576)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(576, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 9, 2]))

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

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

chi := DirichletCharacter("576.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 576 = 2^{6} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	576.y (of order $12$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.59938315643$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$22$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 144)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			335.1
Character	$\chi$	$=$	576.335
Dual form			576.2.y.a.239.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.70352 + 0.313101i) q^{3} +(2.80938 + 0.752772i) q^{5} +(1.02581 - 1.77675i) q^{7} +(2.80394 - 1.06674i) q^{9} +O(q^{10})$	\(q+(-1.70352 + 0.313101i) q^{3} +(2.80938 + 0.752772i) q^{5} +(1.02581 - 1.77675i) q^{7} +(2.80394 - 1.06674i) q^{9} +(1.67103 - 0.447752i) q^{11} +(-4.86091 - 1.30248i) q^{13} +(-5.02153 - 0.402740i) q^{15} -2.90960i q^{17} +(3.23424 + 3.23424i) q^{19} +(-1.19118 + 3.34790i) q^{21} +(0.831633 - 0.480143i) q^{23} +(2.99585 + 1.72965i) q^{25} +(-4.44255 + 2.69513i) q^{27} +(5.55800 - 1.48926i) q^{29} +(8.00513 - 4.62177i) q^{31} +(-2.70644 + 1.28595i) q^{33} +(4.21937 - 4.21937i) q^{35} +(8.18664 + 8.18664i) q^{37} +(8.68844 + 0.696837i) q^{39} +(-4.06472 - 7.04030i) q^{41} +(-0.907834 - 3.38808i) q^{43} +(8.68035 - 0.886168i) q^{45} +(1.60711 - 2.78360i) q^{47} +(1.39544 + 2.41698i) q^{49} +(0.910997 + 4.95655i) q^{51} +(-1.65731 + 1.65731i) q^{53} +5.03163 q^{55} +(-6.52223 - 4.49694i) q^{57} +(-2.21712 + 8.27439i) q^{59} +(-0.284684 - 1.06246i) q^{61} +(0.980960 - 6.07616i) q^{63} +(-12.6757 - 7.31831i) q^{65} +(-2.50979 + 9.36667i) q^{67} +(-1.26637 + 1.07832i) q^{69} +2.40828i q^{71} +0.312935i q^{73} +(-5.64503 - 2.00849i) q^{75} +(0.918613 - 3.42831i) q^{77} +(1.15979 + 0.669606i) q^{79} +(6.72412 - 5.98216i) q^{81} +(-3.90915 - 14.5891i) q^{83} +(2.19027 - 8.17418i) q^{85} +(-9.00185 + 4.27719i) q^{87} +7.86629 q^{89} +(-7.30052 + 7.30052i) q^{91} +(-12.1898 + 10.3797i) q^{93} +(6.65158 + 11.5209i) q^{95} +(-6.48861 + 11.2386i) q^{97} +(4.20783 - 3.03803i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q + 4 q^{3} - 6 q^{5} + 4 q^{7}+O(q^{10}) $ 88 * q + 4 * q^3 - 6 * q^5 + 4 * q^7	$ 88 q + 4 q^{3} - 6 q^{5} + 4 q^{7} + 6 q^{11} - 2 q^{13} + 8 q^{19} + 2 q^{21} + 12 q^{23} + 16 q^{27} - 6 q^{29} - 8 q^{33} - 8 q^{37} + 32 q^{39} + 2 q^{43} + 6 q^{45} - 24 q^{49} + 12 q^{51} + 16 q^{55} + 42 q^{59} - 2 q^{61} - 12 q^{65} + 2 q^{67} - 10 q^{69} + 56 q^{75} - 6 q^{77} - 8 q^{81} - 54 q^{83} + 8 q^{85} - 48 q^{87} - 20 q^{91} - 34 q^{93} - 4 q^{97} - 46 q^{99}+O(q^{100}) $ 88 * q + 4 * q^3 - 6 * q^5 + 4 * q^7 + 6 * q^11 - 2 * q^13 + 8 * q^19 + 2 * q^21 + 12 * q^23 + 16 * q^27 - 6 * q^29 - 8 * q^33 - 8 * q^37 + 32 * q^39 + 2 * q^43 + 6 * q^45 - 24 * q^49 + 12 * q^51 + 16 * q^55 + 42 * q^59 - 2 * q^61 - 12 * q^65 + 2 * q^67 - 10 * q^69 + 56 * q^75 - 6 * q^77 - 8 * q^81 - 54 * q^83 + 8 * q^85 - 48 * q^87 - 20 * q^91 - 34 * q^93 - 4 * q^97 - 46 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/576\mathbb{Z}\right)^\times$.

$n$	$65$	$127$	$325$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.70352	+	0.313101i	−0.983526	+	0.180769i
$3$	−1.70352	+	0.313101i	−0.983526	+	0.180769i
$4$		0			0
$5$	2.80938	+	0.752772i	1.25639	+	0.336650i	0.824804	−	0.565419i	$-0.191286\pi$
$5$	2.80938	+	0.752772i	1.25639	+	0.336650i	0.431591	+	0.902069i	$0.357952\pi$
$6$		0			0
$7$	1.02581	−	1.77675i	0.387718	−	0.671548i	−0.604424	−	0.796663i	$-0.706597\pi$
$7$	1.02581	−	1.77675i	0.387718	−	0.671548i	0.992142	+	0.125115i	$0.0399300\pi$
$8$		0			0
$9$	2.80394	−	1.06674i	0.934645	−	0.355581i
$10$		0			0
$11$	1.67103	−	0.447752i	0.503835	−	0.135002i	0.00205598	−	0.999998i	$-0.499346\pi$
$11$	1.67103	−	0.447752i	0.503835	−	0.135002i	0.501779	+	0.864996i	$0.332679\pi$
$12$		0			0
$13$	−4.86091	−	1.30248i	−1.34817	−	0.361242i	−0.488713	−	0.872445i	$-0.662534\pi$
$13$	−4.86091	−	1.30248i	−1.34817	−	0.361242i	−0.859460	+	0.511203i	$0.829200\pi$
$14$		0			0
$15$	−5.02153	−	0.402740i	−1.29655	−	0.103987i
$16$		0			0
$17$		−	2.90960i		−	0.705681i	−0.935683	−	0.352841i	$-0.885216\pi$
$17$		−	2.90960i		−	0.705681i	0.935683	−	0.352841i	$-0.114784\pi$
$18$		0			0
$19$	3.23424	+	3.23424i	0.741986	+	0.741986i	0.972960	−	0.230974i	$-0.0741911\pi$
$19$	3.23424	+	3.23424i	0.741986	+	0.741986i	−0.230974	+	0.972960i	$0.574191\pi$
$20$		0			0
$21$	−1.19118	+	3.34790i	−0.259936	+	0.730572i
$22$		0			0
$23$	0.831633	−	0.480143i	0.173407	−	0.100117i	−0.410784	−	0.911733i	$-0.634745\pi$
$23$	0.831633	−	0.480143i	0.173407	−	0.100117i	0.584192	+	0.811616i	$0.301412\pi$
$24$		0			0
$25$	2.99585	+	1.72965i	0.599169	+	0.345931i
$26$		0			0
$27$	−4.44255	+	2.69513i	−0.854970	+	0.518678i
$28$		0			0
$29$	5.55800	−	1.48926i	1.03209	−	0.276549i	0.297261	−	0.954796i	$-0.403927\pi$
$29$	5.55800	−	1.48926i	1.03209	−	0.276549i	0.734834	+	0.678248i	$0.237260\pi$
$30$		0			0
$31$	8.00513	−	4.62177i	1.43776	−	0.830094i	0.440070	−	0.897963i	$-0.354954\pi$
$31$	8.00513	−	4.62177i	1.43776	−	0.830094i	0.997694	+	0.0678697i	$0.0216202\pi$
$32$		0			0
$33$	−2.70644	+	1.28595i	−0.471131	+	0.223856i
$34$		0			0
$35$	4.21937	−	4.21937i	0.713204	−	0.713204i
$36$		0			0
$37$	8.18664	+	8.18664i	1.34588	+	1.34588i	0.890089	+	0.455787i	$0.150642\pi$
$37$	8.18664	+	8.18664i	1.34588	+	1.34588i	0.455787	+	0.890089i	$0.349358\pi$
$38$		0			0
$39$	8.68844	+	0.696837i	1.39126	+	0.111583i
$40$		0			0
$41$	−4.06472	−	7.04030i	−0.634803	−	1.09951i	−0.986557	−	0.163418i	$-0.947748\pi$
$41$	−4.06472	−	7.04030i	−0.634803	−	1.09951i	0.351754	−	0.936092i	$-0.385585\pi$
$42$		0			0
$43$	−0.907834	−	3.38808i	−0.138443	−	0.516678i	−0.999960	−	0.00894834i	$-0.997152\pi$
$43$	−0.907834	−	3.38808i	−0.138443	−	0.516678i	0.861517	−	0.507729i	$-0.169515\pi$
$44$		0			0
$45$	8.68035	−	0.886168i	1.29399	−	0.132102i
$46$		0			0
$47$	1.60711	−	2.78360i	0.234421	−	0.406030i	−0.724683	−	0.689082i	$-0.758014\pi$
$47$	1.60711	−	2.78360i	0.234421	−	0.406030i	0.959104	+	0.283053i	$0.0913472\pi$
$48$		0			0
$49$	1.39544	+	2.41698i	0.199349	+	0.345283i
$50$		0			0
$51$	0.910997	+	4.95655i	0.127565	+	0.694056i
$52$		0			0
$53$	−1.65731	+	1.65731i	−0.227649	+	0.227649i	−0.811710	−	0.584061i	$-0.801463\pi$
$53$	−1.65731	+	1.65731i	−0.227649	+	0.227649i	0.584061	+	0.811710i	$0.301463\pi$
$54$		0			0
$55$	5.03163			0.678465
$56$		0			0
$57$	−6.52223	−	4.49694i	−0.863891	−	0.595635i
$58$		0			0
$59$	−2.21712	+	8.27439i	−0.288644	+	1.07723i	0.657491	+	0.753462i	$0.271618\pi$
$59$	−2.21712	+	8.27439i	−0.288644	+	1.07723i	−0.946135	+	0.323772i	$0.895049\pi$
$60$		0			0
$61$	−0.284684	−	1.06246i	−0.0364501	−	0.136034i	0.945303	−	0.326193i	$-0.105766\pi$
$61$	−0.284684	−	1.06246i	−0.0364501	−	0.136034i	−0.981753	+	0.190160i	$0.939099\pi$
$62$		0			0
$63$	0.980960	−	6.07616i	0.123589	−	0.765524i
$64$		0			0
$65$	−12.6757	−	7.31831i	−1.57223	−	0.907725i
$66$		0			0
$67$	−2.50979	+	9.36667i	−0.306620	+	1.14432i	0.624922	+	0.780687i	$0.285131\pi$
$67$	−2.50979	+	9.36667i	−0.306620	+	1.14432i	−0.931542	+	0.363634i	$0.881536\pi$
$68$		0			0
$69$	−1.26637	+	1.07832i	−0.152453	+	0.129814i
$70$		0			0
$71$			2.40828i			0.285810i	0.989736	+	0.142905i	$0.0456444\pi$
$71$			2.40828i			0.285810i	−0.989736	+	0.142905i	$0.954356\pi$
$72$		0			0
$73$			0.312935i			0.0366262i	0.999832	+	0.0183131i	$0.00582957\pi$
$73$			0.312935i			0.0366262i	−0.999832	+	0.0183131i	$0.994170\pi$
$74$		0			0
$75$	−5.64503	−	2.00849i	−0.651832	−	0.231921i
$76$		0			0
$77$	0.918613	−	3.42831i	0.104686	−	0.390692i
$78$		0			0
$79$	1.15979	+	0.669606i	0.130487	+	0.0753366i	0.563823	−	0.825896i	$-0.309330\pi$
$79$	1.15979	+	0.669606i	0.130487	+	0.0753366i	−0.433336	+	0.901233i	$0.642664\pi$
$80$		0			0
$81$	6.72412	−	5.98216i	0.747124	−	0.664685i
$82$		0			0
$83$	−3.90915	−	14.5891i	−0.429085	−	1.60137i	−0.754839	−	0.655911i	$-0.772285\pi$
$83$	−3.90915	−	14.5891i	−0.429085	−	1.60137i	0.325754	−	0.945455i	$-0.394382\pi$
$84$		0			0
$85$	2.19027	−	8.17418i	0.237568	−	0.886614i
$86$		0			0
$87$	−9.00185	+	4.27719i	−0.965100	+	0.458563i
$88$		0			0
$89$	7.86629			0.833826			0.416913	−	0.908947i	$-0.363112\pi$
$89$	7.86629			0.833826			0.416913	+	0.908947i	$0.363112\pi$
$90$		0			0
$91$	−7.30052	+	7.30052i	−0.765303	+	0.765303i
$92$		0			0
$93$	−12.1898	+	10.3797i	−1.26402	+	1.07632i
$94$		0			0
$95$	6.65158	+	11.5209i	0.682438	+	1.18202i
$96$		0			0
$97$	−6.48861	+	11.2386i	−0.658819	+	1.14111i	0.322103	+	0.946705i	$0.395610\pi$
$97$	−6.48861	+	11.2386i	−0.658819	+	1.14111i	−0.980922	+	0.194403i	$0.937723\pi$
$98$		0			0
$99$	4.20783	−	3.03803i	0.422903	−	0.305334i
$100$		0			0
$101$	−1.83313	−	6.84133i	−0.182403	−	0.680738i	−0.995172	−	0.0981510i	$-0.968707\pi$
$101$	−1.83313	−	6.84133i	−0.182403	−	0.680738i	0.812768	−	0.582587i	$-0.197959\pi$
$102$		0			0
$103$	2.35803	+	4.08423i	0.232344	+	0.402431i	0.958497	−	0.285101i	$-0.0920272\pi$
$103$	2.35803	+	4.08423i	0.232344	+	0.402431i	−0.726154	+	0.687533i	$0.758694\pi$
$104$		0			0
$105$	−5.86668	+	8.50885i	−0.572529	+	0.830379i
$106$		0			0
$107$	−8.28006	−	8.28006i	−0.800464	−	0.800464i	0.182704	−	0.983168i	$-0.441515\pi$
$107$	−8.28006	−	8.28006i	−0.800464	−	0.800464i	−0.983168	+	0.182704i	$0.941515\pi$
$108$		0			0
$109$	−4.14079	+	4.14079i	−0.396616	+	0.396616i	−0.877038	−	0.480422i	$-0.840484\pi$
$109$	−4.14079	+	4.14079i	−0.396616	+	0.396616i	0.480422	+	0.877038i	$0.340484\pi$
$110$		0			0
$111$	−16.5093	−	11.3828i	−1.56700	−	1.08041i
$112$		0			0
$113$	−13.3502	+	7.70777i	−1.25589	+	0.725086i	−0.972272	−	0.233853i	$-0.924866\pi$
$113$	−13.3502	+	7.70777i	−1.25589	+	0.725086i	−0.283613	+	0.958939i	$0.591533\pi$
$114$		0			0
$115$	2.69781	−	0.722877i	0.251573	−	0.0674086i
$116$		0			0
$117$	−15.0191	+	1.53328i	−1.38851	+	0.141752i
$118$		0			0
$119$	−5.16962	−	2.98468i	−0.473899	−	0.273606i
$120$		0			0
$121$	−6.93441	+	4.00358i	−0.630401	+	0.363962i
$122$		0			0
$123$	9.12864	+	10.7206i	0.823102	+	0.966644i
$124$		0			0
$125$	−3.16861	−	3.16861i	−0.283409	−	0.283409i
$126$		0			0
$127$			9.75481i			0.865599i	0.901490	+	0.432800i	$0.142474\pi$
$127$			9.75481i			0.865599i	−0.901490	+	0.432800i	$0.857526\pi$
$128$		0			0
$129$	2.60732	+	5.48741i	0.229562	+	0.483140i
$130$		0			0
$131$	−11.1267	−	2.98138i	−0.972142	−	0.260485i	−0.262410	−	0.964956i	$-0.584517\pi$
$131$	−11.1267	−	2.98138i	−0.972142	−	0.260485i	−0.709732	+	0.704472i	$0.751184\pi$
$132$		0			0
$133$	9.06414	−	2.42873i	0.785961	−	0.210598i
$134$		0			0
$135$	−14.5097	+	4.22742i	−1.24879	+	0.363839i
$136$		0			0
$137$	4.19840	−	7.27184i	0.358694	−	0.621276i	−0.629049	−	0.777365i	$-0.716556\pi$
$137$	4.19840	−	7.27184i	0.358694	−	0.621276i	0.987743	+	0.156090i	$0.0498890\pi$
$138$		0			0
$139$	−9.78090	−	2.62078i	−0.829605	−	0.222292i	−0.181064	−	0.983471i	$-0.557954\pi$
$139$	−9.78090	−	2.62078i	−0.829605	−	0.222292i	−0.648541	+	0.761179i	$0.724621\pi$
$140$		0			0
$141$	−1.86619	+	5.24509i	−0.157162	+	0.441716i
$142$		0			0
$143$	−8.70593			−0.728026
$144$		0			0
$145$	16.7356			1.38982
$146$		0			0
$147$	−3.13392	−	3.68045i	−0.258481	−	0.303558i
$148$		0			0
$149$	13.2792	+	3.55815i	1.08787	+	0.291495i	0.757818	−	0.652466i	$-0.226266\pi$
$149$	13.2792	+	3.55815i	1.08787	+	0.291495i	0.330056	+	0.943961i	$0.392932\pi$
$150$		0			0
$151$	1.77992	−	3.08290i	0.144848	−	0.250883i	−0.784469	−	0.620169i	$-0.787064\pi$
$151$	1.77992	−	3.08290i	0.144848	−	0.250883i	0.929316	+	0.369285i	$0.120398\pi$
$152$		0			0
$153$	−3.10380	−	8.15833i	−0.250927	−	0.659562i
$154$		0			0
$155$	25.9686	−	6.95827i	2.08585	−	0.558902i
$156$		0			0
$157$	5.63069	+	1.50874i	0.449378	+	0.120411i	0.476408	−	0.879224i	$-0.341938\pi$
$157$	5.63069	+	1.50874i	0.449378	+	0.120411i	−0.0270302	+	0.999635i	$0.508605\pi$
$158$		0			0
$159$	2.30435	−	3.34215i	0.182747	−	0.265050i
$160$		0			0
$161$		−	1.97014i		−	0.155268i
$162$		0			0
$163$	−11.8727	−	11.8727i	−0.929944	−	0.929944i	0.0677576	−	0.997702i	$-0.478416\pi$
$163$	−11.8727	−	11.8727i	−0.929944	−	0.929944i	−0.997702	+	0.0677576i	$0.978416\pi$
$164$		0			0
$165$	−8.57146	+	1.57541i	−0.667288	+	0.122645i
$166$		0			0
$167$	4.69768	−	2.71220i	0.363517	−	0.209877i	−0.307105	−	0.951676i	$-0.599360\pi$
$167$	4.69768	−	2.71220i	0.363517	−	0.209877i	0.670622	+	0.741799i	$0.266027\pi$
$168$		0			0
$169$	10.6737	+	6.16244i	0.821050	+	0.474034i
$170$		0			0
$171$	12.5187	+	5.61850i	0.957331	+	0.429658i
$172$		0			0
$173$	15.4112	−	4.12941i	1.17169	−	0.313953i	0.380064	−	0.924960i	$-0.375902\pi$
$173$	15.4112	−	4.12941i	1.17169	−	0.313953i	0.791625	+	0.611007i	$0.209235\pi$
$174$		0			0
$175$	6.14632	−	3.54858i	0.464618	−	0.268247i
$176$		0			0
$177$	1.18618	−	14.7897i	0.0891586	−	1.11167i
$178$		0			0
$179$	−9.89241	+	9.89241i	−0.739394	+	0.739394i	−0.972461	−	0.233067i	$-0.925124\pi$
$179$	−9.89241	+	9.89241i	−0.739394	+	0.739394i	0.233067	+	0.972461i	$0.425124\pi$
$180$		0			0
$181$	−12.4781	−	12.4781i	−0.927486	−	0.927486i	0.0700567	−	0.997543i	$-0.477682\pi$
$181$	−12.4781	−	12.4781i	−0.927486	−	0.927486i	−0.997543	+	0.0700567i	$0.977682\pi$
$182$		0			0
$183$	0.817620	+	1.72078i	0.0604402	+	0.127203i
$184$		0			0
$185$	16.8368	+	29.1621i	1.23786	+	2.14404i
$186$		0			0
$187$	−1.30278	−	4.86204i	−0.0952686	−	0.355547i
$188$		0			0
$189$	0.231368	+	10.6580i	0.0168295	+	0.775254i
$190$		0			0
$191$	−2.68392	+	4.64869i	−0.194202	+	0.336367i	−0.946639	−	0.322297i	$-0.895545\pi$
$191$	−2.68392	+	4.64869i	−0.194202	+	0.336367i	0.752437	+	0.658664i	$0.228878\pi$
$192$		0			0
$193$	−2.67918	−	4.64047i	−0.192852	−	0.334029i	0.753343	−	0.657628i	$-0.228440\pi$
$193$	−2.67918	−	4.64047i	−0.192852	−	0.334029i	−0.946194	+	0.323600i	$0.895107\pi$
$194$		0			0
$195$	23.8846	+	8.49810i	1.71041	+	0.608562i
$196$		0			0
$197$	−8.66946	+	8.66946i	−0.617673	+	0.617673i	−0.944934	−	0.327261i	$-0.893874\pi$
$197$	−8.66946	+	8.66946i	−0.617673	+	0.617673i	0.327261	+	0.944934i	$0.393874\pi$
$198$		0			0
$199$	−10.3440			−0.733266			−0.366633	−	0.930366i	$-0.619490\pi$
$199$	−10.3440			−0.733266			−0.366633	+	0.930366i	$0.619490\pi$
$200$		0			0
$201$	1.34276	−	16.7421i	0.0947111	−	1.18090i
$202$		0			0
$203$	3.05539	−	11.4029i	0.214446	−	0.800324i
$204$		0			0
$205$	−6.11962	−	22.8387i	−0.427413	−	1.59513i
$206$		0			0
$207$	1.81966	−	2.23343i	0.126475	−	0.155234i
$208$		0			0
$209$	6.85267	+	3.95639i	0.474009	+	0.273669i
$210$		0			0
$211$	−6.15510	+	22.9712i	−0.423735	+	1.58140i	0.342936	+	0.939359i	$0.388579\pi$
$211$	−6.15510	+	22.9712i	−0.423735	+	1.58140i	−0.766671	+	0.642041i	$0.778088\pi$
$212$		0			0
$213$	−0.754033	−	4.10254i	−0.0516655	−	0.281102i
$214$		0			0
$215$		−	10.2018i		−	0.695758i
$216$		0			0
$217$		−	18.9641i		−	1.28737i
$218$		0			0
$219$	−0.0979800	−	0.533089i	−0.00662088	−	0.0360228i
$220$		0			0
$221$	−3.78968	+	14.1433i	−0.254922	+	0.951381i
$222$		0			0
$223$	10.1818	+	5.87844i	0.681821	+	0.393650i	0.800541	−	0.599278i	$-0.204546\pi$
$223$	10.1818	+	5.87844i	0.681821	+	0.393650i	−0.118720	+	0.992928i	$0.537879\pi$
$224$		0			0
$225$	10.2453	+	1.65404i	0.683017	+	0.110269i
$226$		0			0
$227$	−0.495968	−	1.85098i	−0.0329185	−	0.122854i	0.947511	−	0.319722i	$-0.103590\pi$
$227$	−0.495968	−	1.85098i	−0.0329185	−	0.122854i	−0.980430	+	0.196868i	$0.936923\pi$
$228$		0			0
$229$	0.784708	−	2.92857i	0.0518550	−	0.193525i	−0.935139	−	0.354280i	$-0.884726\pi$
$229$	0.784708	−	2.92857i	0.0518550	−	0.193525i	0.986994	+	0.160754i	$0.0513927\pi$
$230$		0			0
$231$	−0.491467	+	6.12780i	−0.0323361	+	0.403180i
$232$		0			0
$233$	−22.3128			−1.46176			−0.730881	−	0.682505i	$-0.760891\pi$
$233$	−22.3128			−1.46176			−0.730881	+	0.682505i	$0.760891\pi$
$234$		0			0
$235$	6.61041	−	6.61041i	0.431216	−	0.431216i
$236$		0			0
$237$	−2.18538	−	0.777554i	−0.141956	−	0.0505076i
$238$		0			0
$239$	2.20682	+	3.82232i	0.142747	+	0.247246i	0.928530	−	0.371257i	$-0.121073\pi$
$239$	2.20682	+	3.82232i	0.142747	+	0.247246i	−0.785783	+	0.618502i	$0.787740\pi$
$240$		0			0
$241$	−6.92239	+	11.9899i	−0.445911	+	0.772340i	−0.998115	−	0.0613689i	$-0.980453\pi$
$241$	−6.92239	+	11.9899i	−0.445911	+	0.772340i	0.552205	+	0.833709i	$0.313787\pi$
$242$		0			0
$243$	−9.58162	+	12.2960i	−0.614661	+	0.788791i
$244$		0			0
$245$	2.10090	+	7.84068i	0.134222	+	0.500922i
$246$		0			0
$247$	−11.5088	−	19.9339i	−0.732290	−	1.26836i
$248$		0			0
$249$	11.2272	+	23.6289i	0.711492	+	1.49742i
$250$		0			0
$251$	5.46337	+	5.46337i	0.344845	+	0.344845i	0.858185	−	0.513340i	$-0.171592\pi$
$251$	5.46337	+	5.46337i	0.344845	+	0.344845i	−0.513340	+	0.858185i	$0.671592\pi$
$252$		0			0
$253$	1.17470	−	1.17470i	0.0738528	−	0.0738528i
$254$		0			0
$255$	−1.17181	+	14.6106i	−0.0733817	+	0.914953i
$256$		0			0
$257$	3.48944	−	2.01463i	0.217665	−	0.125669i	−0.387203	−	0.921994i	$-0.626559\pi$
$257$	3.48944	−	2.01463i	0.217665	−	0.125669i	0.604869	+	0.796325i	$0.293226\pi$
$258$		0			0
$259$	22.9435	−	6.14770i	1.42564	−	0.381999i
$260$		0			0
$261$	13.9956	−	10.1048i	0.866307	−	0.625468i
$262$		0			0
$263$	1.38048	+	0.797018i	0.0851238	+	0.0491463i	0.541958	−	0.840406i	$-0.317683\pi$
$263$	1.38048	+	0.797018i	0.0851238	+	0.0491463i	−0.456834	+	0.889552i	$0.651017\pi$
$264$		0			0
$265$	−5.90359	+	3.40844i	−0.362655	+	0.209379i
$266$		0			0
$267$	−13.4004	+	2.46294i	−0.820089	+	0.150730i
$268$		0			0
$269$	−7.39664	−	7.39664i	−0.450981	−	0.450981i	0.444699	−	0.895680i	$-0.353311\pi$
$269$	−7.39664	−	7.39664i	−0.450981	−	0.450981i	−0.895680	+	0.444699i	$0.853311\pi$
$270$		0			0
$271$			9.52293i			0.578477i	0.957257	+	0.289238i	$0.0934020\pi$
$271$			9.52293i			0.578477i	−0.957257	+	0.289238i	$0.906598\pi$
$272$		0			0
$273$	10.1508	−	14.7224i	0.614352	−	0.891038i
$274$		0			0
$275$	5.78061	+	1.54891i	0.348584	+	0.0934029i
$276$		0			0
$277$	−12.4837	+	3.34499i	−0.750071	+	0.200981i	−0.613549	−	0.789656i	$-0.710259\pi$
$277$	−12.4837	+	3.34499i	−0.750071	+	0.200981i	−0.136521	+	0.990637i	$0.543592\pi$
$278$		0			0
$279$	17.5156	−	21.4986i	1.04863	−	1.28709i
$280$		0			0
$281$	−3.22268	+	5.58184i	−0.192249	+	0.332985i	−0.945995	−	0.324181i	$-0.894911\pi$
$281$	−3.22268	+	5.58184i	−0.192249	+	0.332985i	0.753746	+	0.657165i	$0.228245\pi$
$282$		0			0
$283$	16.8566	+	4.51670i	1.00202	+	0.268490i	0.722291	−	0.691589i	$-0.243089\pi$
$283$	16.8566	+	4.51670i	1.00202	+	0.268490i	0.279727	+	0.960079i	$0.409756\pi$
$284$		0			0
$285$	−14.9383	−	17.5434i	−0.884867	−	1.03918i
$286$		0			0
$287$	−16.6785			−0.984498
$288$		0			0
$289$	8.53424			0.502014
$290$		0			0
$291$	7.53464	−	21.1767i	0.441689	−	1.24140i
$292$		0			0
$293$	−6.53579	−	1.75126i	−0.381825	−	0.102310i	0.0628008	−	0.998026i	$-0.479997\pi$
$293$	−6.53579	−	1.75126i	−0.381825	−	0.102310i	−0.444626	+	0.895716i	$0.646663\pi$
$294$		0			0
$295$	−12.4575	+	21.5770i	−0.725302	+	1.25626i
$296$		0			0
$297$	−6.21690	+	6.49281i	−0.360741	+	0.376751i
$298$		0			0
$299$	−4.66787	+	1.25075i	−0.269950	+	0.0723328i
$300$		0			0
$301$	−6.95103	−	1.86252i	−0.400651	−	0.107354i
$302$		0			0
$303$	5.26479	+	11.0804i	0.302454	+	0.636550i
$304$		0			0
$305$		−	3.19915i		−	0.183183i
$306$		0			0
$307$	−4.83046	−	4.83046i	−0.275689	−	0.275689i	0.555696	−	0.831385i	$-0.312452\pi$
$307$	−4.83046	−	4.83046i	−0.275689	−	0.275689i	−0.831385	+	0.555696i	$0.812452\pi$
$308$		0			0
$309$	−5.29572	−	6.21926i	−0.301263	−	0.353801i
$310$		0			0
$311$	0.0401112	−	0.0231582i	0.00227450	−	0.00131318i	−0.498862	−	0.866681i	$-0.666249\pi$
$311$	0.0401112	−	0.0231582i	0.00227450	−	0.00131318i	0.501137	+	0.865368i	$0.332915\pi$
$312$		0			0
$313$	−0.548529	−	0.316693i	−0.0310047	−	0.0179006i	0.484418	−	0.874837i	$-0.339032\pi$
$313$	−0.548529	−	0.316693i	−0.0310047	−	0.0179006i	−0.515422	+	0.856936i	$0.672365\pi$
$314$		0			0
$315$	7.32986	−	16.3318i	0.412991	−	0.920194i
$316$		0			0
$317$	10.9578	−	2.93614i	0.615453	−	0.164910i	0.0623932	−	0.998052i	$-0.480127\pi$
$317$	10.9578	−	2.93614i	0.615453	−	0.164910i	0.553060	+	0.833141i	$0.313460\pi$
$318$		0			0
$319$	8.62078	−	4.97721i	0.482671	−	0.278670i
$320$		0			0
$321$	16.6977	+	11.5127i	0.931975	+	0.642578i
$322$		0			0
$323$	9.41035	−	9.41035i	0.523606	−	0.523606i
$324$		0			0
$325$	−12.3097	−	12.3097i	−0.682820	−	0.682820i
$326$		0			0
$327$	5.75742	−	8.35039i	0.318386	−	0.461778i
$328$		0			0
$329$	−3.29717	−	5.71086i	−0.181779	−	0.314850i
$330$		0			0
$331$	−4.84419	−	18.0788i	−0.266261	−	0.993699i	−0.961474	−	0.274896i	$-0.911357\pi$
$331$	−4.84419	−	18.0788i	−0.266261	−	0.993699i	0.695213	−	0.718804i	$-0.255310\pi$
$332$		0			0
$333$	31.6879	+	14.2218i	1.73649	+	0.779349i
$334$		0			0
$335$	−14.1019	+	24.4253i	−0.770471	+	1.33449i
$336$		0			0
$337$	14.8168	+	25.6634i	0.807120	+	1.39797i	0.914850	+	0.403793i	$0.132309\pi$
$337$	14.8168	+	25.6634i	0.807120	+	1.39797i	−0.107730	+	0.994180i	$0.534358\pi$
$338$		0			0
$339$	20.3290	−	17.3103i	1.10412	−	0.940165i
$340$		0			0
$341$	11.3074	−	11.3074i	0.612332	−	0.612332i
$342$		0			0
$343$	20.0871			1.08460
$344$		0			0
$345$	−4.36944	+	2.07612i	−0.235243	+	0.111775i
$346$		0			0
$347$	3.30055	−	12.3178i	0.177183	−	0.661254i	−0.818987	−	0.573812i	$-0.805464\pi$
$347$	3.30055	−	12.3178i	0.177183	−	0.661254i	0.996170	−	0.0874424i	$-0.0278694\pi$
$348$		0			0
$349$	0.986864	+	3.68302i	0.0528256	+	0.197148i	0.987296	−	0.158894i	$-0.0507928\pi$
$349$	0.986864	+	3.68302i	0.0528256	+	0.197148i	−0.934470	+	0.356042i	$0.884126\pi$
$350$		0			0
$351$	25.1052	−	7.31445i	1.34002	−	0.390417i
$352$		0			0
$353$	5.12202	+	2.95720i	0.272618	+	0.157396i	0.630077	−	0.776533i	$-0.283023\pi$
$353$	5.12202	+	2.95720i	0.272618	+	0.157396i	−0.357459	+	0.933929i	$0.616357\pi$
$354$		0			0
$355$	−1.81289	+	6.76578i	−0.0962180	+	0.359090i
$356$		0			0
$357$	9.74105	+	3.46585i	0.515551	+	0.183432i
$358$		0			0
$359$			30.3546i			1.60206i	0.598626	+	0.801028i	$0.295713\pi$
$359$			30.3546i			1.60206i	−0.598626	+	0.801028i	$0.704287\pi$
$360$		0			0
$361$			1.92066i			0.101088i
$362$		0			0
$363$	10.5594	−	8.99134i	0.554222	−	0.471923i
$364$		0			0
$365$	−0.235569	+	0.879154i	−0.0123302	+	0.0460170i
$366$		0			0
$367$	−24.4676	−	14.1264i	−1.27720	−	0.737392i	−0.300868	−	0.953666i	$-0.597276\pi$
$367$	−24.4676	−	14.1264i	−1.27720	−	0.737392i	−0.976333	+	0.216274i	$0.930610\pi$
$368$		0			0
$369$	−18.9074	−	15.4045i	−0.984281	−	0.801928i
$370$		0			0
$371$	1.24454	+	4.64469i	0.0646134	+	0.241141i
$372$		0			0
$373$	−0.380211	+	1.41897i	−0.0196866	+	0.0734714i	−0.975070	−	0.221896i	$-0.928775\pi$
$373$	−0.380211	+	1.41897i	−0.0196866	+	0.0734714i	0.955384	+	0.295367i	$0.0954421\pi$
$374$		0			0
$375$	6.38987	+	4.40569i	0.329972	+	0.227509i
$376$		0			0
$377$	−28.9566			−1.49134
$378$		0			0
$379$	−1.06529	+	1.06529i	−0.0547204	+	0.0547204i	−0.733937	−	0.679217i	$-0.762320\pi$
$379$	−1.06529	+	1.06529i	−0.0547204	+	0.0547204i	0.679217	+	0.733937i	$0.262320\pi$
$380$		0			0
$381$	−3.05424	−	16.6175i	−0.156473	−	0.851339i
$382$		0			0
$383$	9.90139	+	17.1497i	0.505937	+	0.876309i	0.999976	+	0.00686957i	$0.00218667\pi$
$383$	9.90139	+	17.1497i	0.505937	+	0.876309i	−0.494039	+	0.869440i	$0.664480\pi$
$384$		0			0
$385$	5.16148	−	8.93994i	0.263053	−	0.455621i
$386$		0			0
$387$	−6.15972	−	8.53154i	−0.313116	−	0.433683i
$388$		0			0
$389$	−0.661123	−	2.46734i	−0.0335203	−	0.125099i	0.947138	−	0.320825i	$-0.103960\pi$
$389$	−0.661123	−	2.46734i	−0.0335203	−	0.125099i	−0.980659	+	0.195726i	$0.937294\pi$
$390$		0			0
$391$	−1.39702	−	2.41972i	−0.0706506	−	0.122370i
$392$		0			0
$393$	19.8880	+	1.59507i	1.00321	+	0.0804606i
$394$		0			0
$395$	2.75424	+	2.75424i	0.138581	+	0.138581i
$396$		0			0
$397$	−21.2472	+	21.2472i	−1.06637	+	1.06637i	−0.0687299	+	0.997635i	$0.521895\pi$
$397$	−21.2472	+	21.2472i	−1.06637	+	1.06637i	−0.997635	+	0.0687299i	$0.978105\pi$
$398$		0			0
$399$	−14.6805	+	6.97537i	−0.734943	+	0.349205i
$400$		0			0
$401$	17.0300	−	9.83227i	0.850437	−	0.491000i	−0.0103610	−	0.999946i	$-0.503298\pi$
$401$	17.0300	−	9.83227i	0.850437	−	0.491000i	0.860798	+	0.508946i	$0.169965\pi$
$402$		0			0
$403$	−44.9320	+	12.0395i	−2.23822	+	0.599729i
$404$		0			0
$405$	23.3938	−	11.7445i	1.16245	−	0.583587i
$406$		0			0
$407$	17.3457	+	10.0146i	0.859796	+	0.496404i
$408$		0			0
$409$	0.370476	−	0.213894i	0.0183189	−	0.0105764i	−0.490813	−	0.871265i	$-0.663300\pi$
$409$	0.370476	−	0.213894i	0.0183189	−	0.0105764i	0.509131	+	0.860689i	$0.329967\pi$
$410$		0			0
$411$	−4.87523	+	13.7022i	−0.240477	+	0.675881i
$412$		0			0
$413$	12.4272	+	12.4272i	0.611502	+	0.611502i
$414$		0			0
$415$		−	43.9292i		−	2.15640i
$416$		0			0
$417$	17.4825	+	1.40214i	0.856121	+	0.0686633i
$418$		0			0
$419$	33.0490	+	8.85545i	1.61455	+	0.432617i	0.949394	−	0.314088i	$-0.101699\pi$
$419$	33.0490	+	8.85545i	1.61455	+	0.432617i	0.665155	+	0.746705i	$0.268365\pi$
$420$		0			0
$421$	15.5390	−	4.16367i	0.757326	−	0.202925i	0.140561	−	0.990072i	$-0.455109\pi$
$421$	15.5390	−	4.16367i	0.757326	−	0.202925i	0.616765	+	0.787147i	$0.288443\pi$
$422$		0			0
$423$	1.53685	−	9.51941i	0.0747243	−	0.462849i
$424$		0			0
$425$	5.03260	−	8.71671i	0.244117	−	0.422823i
$426$		0			0
$427$	−2.17975	−	0.584062i	−0.105485	−	0.0282647i
$428$		0			0
$429$	14.8307	−	2.72583i	0.716032	−	0.131604i
$430$		0			0
$431$	6.69108			0.322298			0.161149	−	0.986930i	$-0.448480\pi$
$431$	6.69108			0.322298			0.161149	+	0.986930i	$0.448480\pi$
$432$		0			0
$433$	−16.7354			−0.804254			−0.402127	−	0.915584i	$-0.631729\pi$
$433$	−16.7354			−0.804254			−0.402127	+	0.915584i	$0.631729\pi$
$434$		0			0
$435$	−28.5094	+	5.23993i	−1.36692	+	0.251236i
$436$		0			0
$437$	4.24260	+	1.13680i	0.202951	+	0.0543806i
$438$		0			0
$439$	−5.71817	+	9.90416i	−0.272913	+	0.472700i	−0.969607	−	0.244669i	$-0.921321\pi$
$439$	−5.71817	+	9.90416i	−0.272913	+	0.472700i	0.696693	+	0.717369i	$0.254654\pi$
$440$		0			0
$441$	6.49103	+	5.28848i	0.309097	+	0.251832i
$442$		0			0
$443$	−32.6782	+	8.75609i	−1.55259	+	0.416014i	−0.930307	−	0.366781i	$-0.880460\pi$
$443$	−32.6782	+	8.75609i	−1.55259	+	0.416014i	−0.622280	+	0.782795i	$0.713793\pi$
$444$		0			0
$445$	22.0994	+	5.92153i	1.04761	+	0.280707i
$446$		0			0
$447$	−23.7354	−	1.90364i	−1.12265	−	0.0900392i
$448$		0			0
$449$			10.7735i			0.508432i	0.967147	+	0.254216i	$0.0818174\pi$
$449$			10.7735i			0.508432i	−0.967147	+	0.254216i	$0.918183\pi$
$450$		0			0
$451$	−9.94459	−	9.94459i	−0.468273	−	0.468273i
$452$		0			0
$453$	−2.06686	+	5.80907i	−0.0971094	+	0.272934i
$454$		0			0
$455$	−26.0056	+	15.0143i	−1.21916	+	0.703883i
$456$		0			0
$457$	6.74050	+	3.89163i	0.315307	+	0.182043i	0.649299	−	0.760533i	$-0.275062\pi$
$457$	6.74050	+	3.89163i	0.315307	+	0.182043i	−0.333992	+	0.942576i	$0.608396\pi$
$458$		0			0
$459$	7.84174	+	12.9260i	0.366021	+	0.603336i
$460$		0			0
$461$	−24.2137	+	6.48803i	−1.12774	+	0.302178i	−0.774013	−	0.633170i	$-0.781753\pi$
$461$	−24.2137	+	6.48803i	−1.12774	+	0.302178i	−0.353730	+	0.935348i	$0.615087\pi$
$462$		0			0
$463$	1.11241	−	0.642249i	0.0516980	−	0.0298479i	−0.473928	−	0.880563i	$-0.657164\pi$
$463$	1.11241	−	0.642249i	0.0516980	−	0.0298479i	0.525626	+	0.850716i	$0.323831\pi$
$464$		0			0
$465$	−42.0594	+	19.9843i	−1.95046	+	0.926751i
$466$		0			0
$467$	−21.0842	+	21.0842i	−0.975659	+	0.975659i	−0.999711	−	0.0240512i	$-0.992344\pi$
$467$	−21.0842	+	21.0842i	−0.975659	+	0.975659i	0.0240512	+	0.999711i	$0.492344\pi$
$468$		0			0
$469$	14.0677	+	14.0677i	0.649584	+	0.649584i
$470$		0			0
$471$	−10.0644	−	0.807190i	−0.463741	−	0.0371933i
$472$		0			0
$473$	−3.03404	−	5.25511i	−0.139505	−	0.241630i
$474$		0			0
$475$	4.09518	+	15.2834i	0.187900	+	0.701251i
$476$		0			0
$477$	−2.87906	+	6.41491i	−0.131823	+	0.293718i
$478$		0			0
$479$	20.5401	−	35.5766i	0.938503	−	1.62553i	0.170238	−	0.985403i	$-0.445546\pi$
$479$	20.5401	−	35.5766i	0.938503	−	1.62553i	0.768265	−	0.640132i	$-0.221120\pi$
$480$		0			0
$481$	−29.1316	−	50.4574i	−1.32829	−	2.30066i
$482$		0			0
$483$	0.616851	+	3.35616i	0.0280677	+	0.152711i
$484$		0			0
$485$	−26.6891	+	26.6891i	−1.21189	+	1.21189i
$486$		0			0
$487$	4.02337			0.182316			0.0911581	−	0.995836i	$-0.470943\pi$
$487$	4.02337			0.182316			0.0911581	+	0.995836i	$0.470943\pi$
$488$		0			0
$489$	23.9428	+	16.5080i	1.08273	+	0.746519i
$490$		0			0
$491$	−7.76101	+	28.9645i	−0.350250	+	1.30715i	0.536108	+	0.844149i	$0.319894\pi$
$491$	−7.76101	+	28.9645i	−0.350250	+	1.30715i	−0.886358	+	0.463000i	$0.846773\pi$
$492$		0			0
$493$	−4.33315	−	16.1715i	−0.195155	−	0.728330i
$494$		0			0
$495$	14.1084	−	5.36746i	0.634124	−	0.241249i
$496$		0			0
$497$	4.27890	+	2.47043i	0.191935	+	0.110814i
$498$		0			0
$499$	8.31074	−	31.0161i	0.372040	−	1.38847i	−0.485583	−	0.874191i	$-0.661392\pi$
$499$	8.31074	−	31.0161i	0.372040	−	1.38847i	0.857622	−	0.514280i	$-0.171941\pi$
$500$		0			0
$501$	−7.15337	+	6.09113i	−0.319589	+	0.272132i
$502$		0			0
$503$		−	31.7936i		−	1.41761i	−0.705406	−	0.708803i	$-0.749235\pi$
$503$		−	31.7936i		−	1.41761i	0.705406	−	0.708803i	$-0.250765\pi$
$504$		0			0
$505$		−	20.5999i		−	0.916682i
$506$		0			0
$507$	−20.1122	−	7.15589i	−0.893215	−	0.317804i
$508$		0			0
$509$	9.11633	−	34.0226i	0.404074	−	1.50803i	−0.401683	−	0.915779i	$-0.631575\pi$
$509$	9.11633	−	34.0226i	0.404074	−	1.50803i	0.805757	−	0.592246i	$-0.201759\pi$
$510$		0			0
$511$	0.556006	+	0.321010i	0.0245963	+	0.0142007i
$512$		0			0
$513$	−23.0850	−	5.65159i	−1.01923	−	0.249524i
$514$		0			0
$515$	3.55012	+	13.2492i	0.156437	+	0.583831i
$516$		0			0
$517$	1.43917	−	5.37107i	0.0632948	−	0.236219i
$518$		0			0
$519$	−24.9603	+	11.8598i	−1.09563	+	0.520586i
$520$		0			0
$521$	11.5494			0.505989			0.252994	−	0.967468i	$-0.418585\pi$
$521$	11.5494			0.505989			0.252994	+	0.967468i	$0.418585\pi$
$522$		0			0
$523$	−2.36739	+	2.36739i	−0.103519	+	0.103519i	−0.756969	−	0.653451i	$-0.773321\pi$
$523$	−2.36739	+	2.36739i	−0.103519	+	0.103519i	0.653451	+	0.756969i	$0.273321\pi$
$524$		0			0
$525$	−9.35929	+	7.96947i	−0.408473	+	0.347816i
$526$		0			0
$527$	−13.4475	−	23.2917i	−0.585782	−	1.01460i
$528$		0			0
$529$	−11.0389	+	19.1200i	−0.479953	+	0.831303i
$530$		0			0
$531$	2.61000	+	25.5660i	0.113264	+	1.10947i
$532$		0			0
$533$	10.5884	+	39.5165i	0.458635	+	1.71165i
$534$		0			0
$535$	−17.0289	−	29.4949i	−0.736222	−	1.27517i
$536$		0			0
$537$	13.7546	−	19.9492i	0.593553	−	0.860872i
$538$		0			0
$539$	3.41404	+	3.41404i	0.147053	+	0.147053i
$540$		0			0
$541$	−20.9332	+	20.9332i	−0.899989	+	0.899989i	−0.995435	−	0.0954454i	$-0.969572\pi$
$541$	−20.9332	+	20.9332i	−0.899989	+	0.899989i	0.0954454	+	0.995435i	$0.469572\pi$
$542$		0			0
$543$	25.1635	+	17.3497i	1.07987	+	0.744546i
$544$		0			0
$545$	−14.7501	+	8.51600i	−0.631827	+	0.364785i
$546$		0			0
$547$	34.2985	−	9.19026i	1.46650	−	0.392947i	0.564770	−	0.825248i	$-0.308965\pi$
$547$	34.2985	−	9.19026i	1.46650	−	0.392947i	0.901729	+	0.432301i	$0.142298\pi$
$548$		0			0
$549$	−1.93160	−	2.67537i	−0.0824389	−	0.114182i
$550$		0			0
$551$	22.7926	+	13.1593i	0.970995	+	0.560604i
$552$		0			0
$553$	2.37944	−	1.37377i	0.101184	−	0.0584188i
$554$		0			0
$555$	−37.8124	−	44.4065i	−1.60504	−	1.88495i
$556$		0			0
$557$	−11.1853	−	11.1853i	−0.473937	−	0.473937i	0.429249	−	0.903186i	$-0.358778\pi$
$557$	−11.1853	−	11.1853i	−0.473937	−	0.473937i	−0.903186	+	0.429249i	$0.858778\pi$
$558$		0			0
$559$			17.6516i			0.746583i
$560$		0			0
$561$	3.74161	+	7.87466i	0.157971	+	0.332468i
$562$		0			0
$563$	−4.63936	−	1.24311i	−0.195526	−	0.0523910i	0.159727	−	0.987161i	$-0.448939\pi$
$563$	−4.63936	−	1.24311i	−0.195526	−	0.0523910i	−0.355253	+	0.934770i	$0.615605\pi$
$564$		0			0
$565$	−43.3082	+	11.6044i	−1.82199	+	0.488200i
$566$		0			0
$567$	−3.73116	−	18.0836i	−0.156694	−	0.759440i
$568$		0			0
$569$	5.74273	−	9.94671i	0.240748	−	0.416988i	−0.720180	−	0.693788i	$-0.755941\pi$
$569$	5.74273	−	9.94671i	0.240748	−	0.416988i	0.960928	+	0.276800i	$0.0892740\pi$
$570$		0			0
$571$	4.99227	+	1.33767i	0.208920	+	0.0559799i	0.361761	−	0.932271i	$-0.382176\pi$
$571$	4.99227	+	1.33767i	0.208920	+	0.0559799i	−0.152841	+	0.988251i	$0.548842\pi$
$572$		0			0
$573$	3.11660	−	8.75945i	0.130198	−	0.365931i
$574$		0			0
$575$	3.32193			0.138534
$576$		0			0
$577$	−25.5971			−1.06562			−0.532810	−	0.846235i	$-0.678864\pi$
$577$	−25.5971			−1.06562			−0.532810	+	0.846235i	$0.678864\pi$
$578$		0			0
$579$	6.01696	+	7.06627i	0.250056	+	0.293664i
$580$		0			0
$581$	−29.9312	−	8.02005i	−1.24176	−	0.332728i
$582$		0			0
$583$	−2.02735	+	3.51148i	−0.0839644	+	0.145431i
$584$		0			0
$585$	−43.3486	−	6.99837i	−1.79224	−	0.289347i
$586$		0			0
$587$	2.68525	−	0.719512i	0.110832	−	0.0296974i	−0.202977	−	0.979184i	$-0.565062\pi$
$587$	2.68525	−	0.719512i	0.110832	−	0.0296974i	0.313809	+	0.949486i	$0.398395\pi$
$588$		0			0
$589$	40.8385	+	10.9426i	1.68272	+	0.450883i
$590$		0			0
$591$	12.0541	−	17.4830i	0.495841	−	0.719153i
$592$		0			0
$593$			0.335583i			0.0137807i	0.999976	+	0.00689036i	$0.00219329\pi$
$593$			0.335583i			0.0137807i	−0.999976	+	0.00689036i	$0.997807\pi$
$594$		0			0
$595$	−12.2767	−	12.2767i	−0.503295	−	0.503295i
$596$		0			0
$597$	17.6212	−	3.23871i	0.721186	−	0.132552i
$598$		0			0
$599$	3.98883	−	2.30295i	0.162979	−	0.0940961i	−0.416292	−	0.909231i	$-0.636671\pi$
$599$	3.98883	−	2.30295i	0.162979	−	0.0940961i	0.579271	+	0.815135i	$0.303337\pi$
$600$		0			0
$601$	−29.9967	−	17.3186i	−1.22359	−	0.706440i	−0.257909	−	0.966169i	$-0.583034\pi$
$601$	−29.9967	−	17.3186i	−1.22359	−	0.706440i	−0.965682	+	0.259729i	$0.916367\pi$
$602$		0			0
$603$	2.95454	+	28.9408i	0.120318	+	1.17856i
$604$		0			0
$605$	−22.4952	+	6.02757i	−0.914560	+	0.245056i
$606$		0			0
$607$	−18.3567	+	10.5982i	−0.745074	+	0.430169i	−0.823911	−	0.566719i	$-0.808213\pi$
$607$	−18.3567	+	10.5982i	−0.745074	+	0.430169i	0.0788371	+	0.996888i	$0.474879\pi$
$608$		0			0
$609$	−1.63466	+	20.3816i	−0.0662398	+	0.825904i
$610$		0			0
$611$	−11.4376	+	11.4376i	−0.462715	+	0.462715i
$612$		0			0
$613$	15.1548	+	15.1548i	0.612098	+	0.612098i	0.943492	−	0.331394i	$-0.107519\pi$
$613$	15.1548	+	15.1548i	0.612098	+	0.612098i	−0.331394	+	0.943492i	$0.607519\pi$
$614$		0			0
$615$	17.5757	+	36.9901i	0.708720	+	1.49158i
$616$		0			0
$617$	2.56785	+	4.44764i	0.103378	+	0.179055i	0.913074	−	0.407793i	$-0.133702\pi$
$617$	2.56785	+	4.44764i	0.103378	+	0.179055i	−0.809697	+	0.586849i	$0.800368\pi$
$618$		0			0
$619$	9.73767	+	36.3415i	0.391390	+	1.46069i	0.827842	+	0.560961i	$0.189568\pi$
$619$	9.73767	+	36.3415i	0.391390	+	1.46069i	−0.436452	+	0.899727i	$0.643765\pi$
$620$		0			0
$621$	−2.40052	+	4.37442i	−0.0963297	+	0.175539i
$622$		0			0
$623$	8.06929	−	13.9764i	0.323289	−	0.559954i
$624$		0			0
$625$	−15.1649	−	26.2663i	−0.606595	−	1.05065i
$626$		0			0
$627$	−12.9124	−	4.59420i	−0.515671	−	0.183475i
$628$		0			0
$629$	23.8198	−	23.8198i	0.949760	−	0.949760i
$630$		0			0
$631$	30.8454			1.22794			0.613969	−	0.789330i	$-0.289572\pi$
$631$	30.8454			1.22794			0.613969	+	0.789330i	$0.289572\pi$
$632$		0			0
$633$	3.29304	−	41.0589i	0.130886	−	1.63194i
$634$		0			0
$635$	−7.34315	+	27.4050i	−0.291404	+	1.08753i
$636$		0			0
$637$	−3.63507	−	13.5662i	−0.144027	−	0.537514i
$638$		0			0
$639$	2.56902	+	6.75266i	0.101629	+	0.267131i
$640$		0			0
$641$	3.40556	+	1.96620i	0.134512	+	0.0776603i	0.565746	−	0.824580i	$-0.308588\pi$
$641$	3.40556	+	1.96620i	0.134512	+	0.0776603i	−0.431234	+	0.902240i	$0.641922\pi$
$642$		0			0
$643$	1.64315	−	6.13231i	0.0647994	−	0.241835i	−0.925928	−	0.377700i	$-0.876715\pi$
$643$	1.64315	−	6.13231i	0.0647994	−	0.241835i	0.990727	+	0.135866i	$0.0433816\pi$
$644$		0			0
$645$	3.19419	+	17.3790i	0.125771	+	0.684296i
$646$		0			0
$647$		−	29.0686i		−	1.14280i	−0.820670	−	0.571402i	$-0.806400\pi$
$647$		−	29.0686i		−	1.14280i	0.820670	−	0.571402i	$-0.193600\pi$
$648$		0			0
$649$			14.8195i			0.581717i
$650$		0			0
$651$	5.93768	+	32.3057i	0.232716	+	1.26616i
$652$		0			0
$653$	−12.6939	+	47.3742i	−0.496750	+	1.85390i	0.0232472	+	0.999730i	$0.492600\pi$
$653$	−12.6939	+	47.3742i	−0.496750	+	1.85390i	−0.519998	+	0.854168i	$0.674067\pi$
$654$		0			0
$655$	−29.0148	−	16.7517i	−1.13370	−	0.654543i
$656$		0			0
$657$	0.333821	+	0.877449i	0.0130236	+	0.0342325i
$658$		0			0
$659$	−0.429334	−	1.60230i	−0.0167245	−	0.0624166i	0.957059	−	0.289892i	$-0.0936195\pi$
$659$	−0.429334	−	1.60230i	−0.0167245	−	0.0624166i	−0.973784	+	0.227476i	$0.926953\pi$
$660$		0			0
$661$	−10.4327	+	38.9352i	−0.405783	+	1.51440i	0.396824	+	0.917895i	$0.370112\pi$
$661$	−10.4327	+	38.9352i	−0.405783	+	1.51440i	−0.802607	+	0.596508i	$0.796554\pi$
$662$		0			0
$663$	2.02752	−	25.2799i	0.0787422	−	0.981789i
$664$		0			0
$665$	27.2929			1.05837
$666$		0			0
$667$	3.90715	−	3.90715i	0.151286	−	0.151286i
$668$		0			0
$669$	−19.1853	−	6.82611i	−0.741748	−	0.263913i
$670$		0			0
$671$	−0.951434	−	1.64793i	−0.0367297	−	0.0636177i
$672$		0			0
$673$	16.4569	−	28.5042i	0.634366	−	1.09875i	−0.352283	−	0.935894i	$-0.614595\pi$
$673$	16.4569	−	28.5042i	0.634366	−	1.09875i	0.986649	−	0.162861i	$-0.0520722\pi$
$674$		0			0
$675$	−17.9708	+	0.390119i	−0.691698	+	0.0150157i
$676$		0			0
$677$	−11.8480	−	44.2173i	−0.455355	−	1.69941i	−0.687042	−	0.726617i	$-0.741091\pi$
$677$	−11.8480	−	44.2173i	−0.455355	−	1.69941i	0.231687	−	0.972790i	$-0.425575\pi$
$678$		0			0
$679$	13.3121	+	23.0573i	0.510872	+	0.884856i
$680$		0			0
$681$	1.42443	+	2.99788i	0.0545843	+	0.114879i
$682$		0			0
$683$	−13.5540	−	13.5540i	−0.518630	−	0.518630i	0.398527	−	0.917157i	$-0.369522\pi$
$683$	−13.5540	−	13.5540i	−0.518630	−	0.518630i	−0.917157	+	0.398527i	$0.869522\pi$
$684$		0			0
$685$	17.2690	−	17.2690i	0.659813	−	0.659813i
$686$		0			0
$687$	−0.419826	+	5.23456i	−0.0160174	+	0.199711i
$688$		0			0
$689$	10.2146	−	5.89742i	0.389146	−	0.224674i
$690$		0			0
$691$	48.4658	−	12.9864i	1.84373	−	0.494025i	0.844583	−	0.535425i	$-0.179849\pi$
$691$	48.4658	−	12.9864i	1.84373	−	0.494025i	0.999143	+	0.0414008i	$0.0131820\pi$
$692$		0			0
$693$	−1.08140	−	10.5927i	−0.0410789	−	0.402383i
$694$		0			0
$695$	−25.5055	−	14.7256i	−0.967477	−	0.558573i
$696$		0			0
$697$	−20.4845	+	11.8267i	−0.775904	+	0.447968i
$698$		0			0
$699$	38.0103	−	6.98616i	1.43768	−	0.264241i
$700$		0			0
$701$	−3.21893	−	3.21893i	−0.121577	−	0.121577i	0.643700	−	0.765278i	$-0.277398\pi$
$701$	−3.21893	−	3.21893i	−0.121577	−	0.121577i	−0.765278	+	0.643700i	$0.777398\pi$
$702$		0			0
$703$			52.9552i			1.99724i
$704$		0			0
$705$	−9.19122	+	13.3307i	−0.346161	+	0.502062i
$706$		0			0
$707$	−14.0358	−	3.76087i	−0.527869	−	0.141442i
$708$		0			0
$709$	−0.389561	+	0.104383i	−0.0146303	+	0.00392017i	−0.266127	−	0.963938i	$-0.585744\pi$
$709$	−0.389561	+	0.104383i	−0.0146303	+	0.00392017i	0.251496	+	0.967858i	$0.419077\pi$
$710$		0			0
$711$	3.96628	+	0.640333i	0.148747	+	0.0240143i
$712$		0			0
$713$	4.43822	−	7.68722i	0.166213	−	0.287889i
$714$		0			0
$715$	−24.4583	−	6.55358i	−0.914688	−	0.245090i
$716$		0			0
$717$	−4.95612	−	5.82043i	−0.185090	−	0.217368i
$718$		0			0
$719$	4.42409			0.164991			0.0824953	−	0.996591i	$-0.473711\pi$
$719$	4.42409			0.164991			0.0824953	+	0.996591i	$0.473711\pi$
$720$		0			0
$721$	9.67554			0.360336
$722$		0			0
$723$	8.03836	−	22.5925i	0.298950	−	0.840223i
$724$		0			0
$725$	19.2268	+	5.15181i	0.714066	+	0.191333i
$726$		0			0
$727$	−24.1060	+	41.7529i	−0.894044	+	1.54853i	−0.0590597	+	0.998254i	$0.518810\pi$
$727$	−24.1060	+	41.7529i	−0.894044	+	1.54853i	−0.834984	+	0.550274i	$0.814523\pi$
$728$		0			0
$729$	12.4726	−	23.9465i	0.461947	−	0.886908i
$730$		0			0
$731$	−9.85796	+	2.64143i	−0.364610	+	0.0976969i
$732$		0			0
$733$	42.2183	+	11.3124i	1.55937	+	0.417831i	0.932463	−	0.361265i	$-0.117655\pi$
$733$	42.2183	+	11.3124i	1.55937	+	0.417831i	0.626904	+	0.779096i	$0.284322\pi$
$734$		0			0
$735$	−6.03384	−	12.6989i	−0.222562	−	0.468407i
$736$		0			0
$737$			16.7758i			0.617944i
$738$		0			0
$739$	4.26794	+	4.26794i	0.156999	+	0.156999i	0.781235	−	0.624237i	$-0.214590\pi$
$739$	4.26794	+	4.26794i	0.156999	+	0.156999i	−0.624237	+	0.781235i	$0.714590\pi$
$740$		0			0
$741$	25.8468	+	30.3543i	0.949506	+	1.11509i
$742$		0			0
$743$	10.5668	−	6.10073i	0.387657	−	0.223814i	−0.293487	−	0.955963i	$-0.594816\pi$
$743$	10.5668	−	6.10073i	0.387657	−	0.223814i	0.681145	+	0.732149i	$0.261482\pi$
$744$		0			0
$745$	34.6279	+	19.9924i	1.26867	+	0.732466i
$746$		0			0
$747$	−26.5239	−	36.7369i	−0.970457	−	1.34413i
$748$		0			0
$749$	−23.2053	+	6.21785i	−0.847904	+	0.227195i
$750$		0			0
$751$	12.1070	−	6.99000i	0.441792	−	0.255069i	−0.262566	−	0.964914i	$-0.584569\pi$
$751$	12.1070	−	6.99000i	0.441792	−	0.255069i	0.704357	+	0.709846i	$0.251235\pi$
$752$		0			0
$753$	−11.0175	−	7.59635i	−0.401501	−	0.276826i
$754$		0			0
$755$	7.32119	−	7.32119i	0.266445	−	0.266445i
$756$		0			0
$757$	−0.365397	−	0.365397i	−0.0132806	−	0.0132806i	0.700435	−	0.713716i	$-0.252989\pi$
$757$	−0.365397	−	0.365397i	−0.0132806	−	0.0132806i	−0.713716	+	0.700435i	$0.752989\pi$
$758$		0			0
$759$	−1.63332	+	2.36892i	−0.0592859	+	0.0859864i
$760$		0			0
$761$	2.63786	+	4.56890i	0.0956222	+	0.165623i	0.909868	−	0.414898i	$-0.136183\pi$
$761$	2.63786	+	4.56890i	0.0956222	+	0.165623i	−0.814246	+	0.580520i	$0.802849\pi$
$762$		0			0
$763$	3.10949	+	11.6048i	0.112571	+	0.420122i
$764$		0			0
$765$	−2.57839	−	25.2563i	−0.0932220	−	0.913145i
$766$		0			0
$767$	21.5544	−	37.3333i	0.778285	−	1.34803i
$768$		0			0
$769$	18.6972	+	32.3845i	0.674238	+	1.16781i	0.976691	+	0.214650i	$0.0688610\pi$
$769$	18.6972	+	32.3845i	0.674238	+	1.16781i	−0.302453	+	0.953164i	$0.597806\pi$
$770$		0			0
$771$	−5.31354	+	4.52450i	−0.191363	+	0.162946i
$772$		0			0
$773$	26.3255	−	26.3255i	0.946864	−	0.946864i	−0.0517940	−	0.998658i	$-0.516494\pi$
$773$	26.3255	−	26.3255i	0.946864	−	0.946864i	0.998658	+	0.0517940i	$0.0164939\pi$
$774$		0			0
$775$	31.9762			1.14862
$776$		0			0
$777$	−37.1598	+	17.6563i	−1.33310	+	0.633417i
$778$		0			0
$779$	9.62376	−	35.9163i	0.344807	−	1.28684i
$780$		0			0
$781$	1.07831	+	4.02431i	0.0385850	+	0.144001i
$782$		0			0
$783$	−20.6780	+	21.5956i	−0.738970	+	0.771765i
$784$		0			0
$785$	14.6830	+	8.47726i	0.524060	+	0.302566i
$786$		0			0
$787$	−6.42145	+	23.9652i	−0.228900	+	0.854267i	0.751904	+	0.659272i	$0.229136\pi$
$787$	−6.42145	+	23.9652i	−0.228900	+	0.854267i	−0.980804	+	0.194995i	$0.937531\pi$
$788$		0			0
$789$	−2.60121	−	0.925506i	−0.0926056	−	0.0329489i
$790$		0			0
$791$			31.6267i			1.12452i
$792$		0			0
$793$			5.53530i			0.196564i
$794$		0			0
$795$	8.98968	−	7.65475i	0.318831	−	0.271486i
$796$		0			0
$797$	8.82476	−	32.9345i	0.312589	−	1.16660i	−0.613624	−	0.789598i	$-0.710289\pi$
$797$	8.82476	−	32.9345i	0.312589	−	1.16660i	0.926213	−	0.377000i	$-0.123044\pi$
$798$		0			0
$799$	−8.09915	−	4.67605i	−0.286527	−	0.165427i
$800$		0			0
$801$	22.0566	−	8.39132i	0.779331	−	0.296493i
$802$		0			0
$803$	0.140117	+	0.522924i	0.00494463	+	0.0184536i
$804$		0			0
$805$	1.48306	−	5.53487i	0.0522711	−	0.195079i
$806$		0			0
$807$	14.9162	+	10.2844i	0.525075	+	0.362028i
$808$		0			0
$809$	17.0673			0.600054			0.300027	−	0.953931i	$-0.403004\pi$
$809$	17.0673			0.600054			0.300027	+	0.953931i	$0.403004\pi$
$810$		0			0
$811$	14.4248	−	14.4248i	0.506523	−	0.506523i	−0.406934	−	0.913458i	$-0.633402\pi$
$811$	14.4248	−	14.4248i	0.506523	−	0.506523i	0.913458	+	0.406934i	$0.133402\pi$
$812$		0			0
$813$	−2.98163	−	16.2225i	−0.104570	−	0.568947i
$814$		0			0
$815$	−24.4176	−	42.2925i	−0.855311	−	1.48144i
$816$		0			0
$817$	8.02173	−	13.8940i	0.280645	−	0.486091i
$818$		0			0
$819$	−12.6824	+	28.2580i	−0.443159	+	0.987414i
$820$		0			0
$821$	−4.87342	−	18.1878i	−0.170083	−	0.634760i	−0.997337	−	0.0729313i	$-0.976765\pi$
$821$	−4.87342	−	18.1878i	−0.170083	−	0.634760i	0.827253	−	0.561829i	$-0.189902\pi$
$822$		0			0
$823$	5.61636	+	9.72781i	0.195774	+	0.339090i	0.947154	−	0.320779i	$-0.103945\pi$
$823$	5.61636	+	9.72781i	0.195774	+	0.339090i	−0.751380	+	0.659870i	$0.770611\pi$
$824$		0			0
$825$	−10.3323	−	0.828682i	−0.359726	−	0.0288510i
$826$		0			0
$827$	3.22006	+	3.22006i	0.111972	+	0.111972i	0.760873	−	0.648901i	$-0.224771\pi$
$827$	3.22006	+	3.22006i	0.111972	+	0.111972i	−0.648901	+	0.760873i	$0.724771\pi$
$828$		0			0
$829$	15.2226	−	15.2226i	0.528704	−	0.528704i	−0.391482	−	0.920186i	$-0.628037\pi$
$829$	15.2226	−	15.2226i	0.528704	−	0.528704i	0.920186	+	0.391482i	$0.128037\pi$
$830$		0			0
$831$	20.2188	−	9.60688i	0.701383	−	0.333259i
$832$		0			0
$833$	7.03244	−	4.06018i	0.243660	−	0.140677i
$834$		0			0
$835$	15.2392	−	4.08334i	0.527376	−	0.141310i
$836$		0			0
$837$	−23.1070	+	42.1073i	−0.798694	+	1.45544i
$838$		0			0
$839$	−27.5530	−	15.9078i	−0.951236	−	0.549197i	−0.0577716	−	0.998330i	$-0.518400\pi$
$839$	−27.5530	−	15.9078i	−0.951236	−	0.549197i	−0.893465	+	0.449133i	$0.851733\pi$
$840$		0			0
$841$	3.55870	−	2.05462i	0.122714	−	0.0708489i
$842$		0			0
$843$	3.74221	−	10.5178i	0.128888	−	0.362252i
$844$		0			0
$845$	25.3475	+	25.3475i	0.871980	+	0.871980i
$846$		0			0
$847$			16.4276i			0.564459i
$848$		0			0
$849$	−30.1296	−	2.41648i	−1.03405	−	0.0829333i
$850$		0			0
$851$	10.7390	+	2.87752i	0.368130	+	0.0986401i
$852$		0			0
$853$	43.6946	−	11.7079i	1.49608	−	0.400872i	0.584292	−	0.811543i	$-0.301372\pi$
$853$	43.6946	−	11.7079i	1.49608	−	0.400872i	0.911784	+	0.410671i	$0.134705\pi$
$854$		0			0
$855$	30.9404	+	25.2083i	1.05814	+	0.862105i
$856$		0			0
$857$	−15.6306	+	27.0731i	−0.533933	+	0.924799i	0.465281	+	0.885163i	$0.345953\pi$
$857$	−15.6306	+	27.0731i	−0.533933	+	0.924799i	−0.999214	+	0.0396358i	$0.987380\pi$
$858$		0			0
$859$	−9.61547	−	2.57646i	−0.328076	−	0.0879076i	0.0910217	−	0.995849i	$-0.470987\pi$
$859$	−9.61547	−	2.57646i	−0.328076	−	0.0879076i	−0.419097	+	0.907941i	$0.637653\pi$
$860$		0			0
$861$	28.4120	−	5.22203i	0.968279	−	0.177966i
$862$		0			0
$863$	41.5499			1.41438			0.707188	−	0.707025i	$-0.249963\pi$
$863$	41.5499			1.41438			0.707188	+	0.707025i	$0.249963\pi$
$864$		0			0
$865$	46.4044			1.57780
$866$		0			0
$867$	−14.5382	+	2.67207i	−0.493744	+	0.0907484i
$868$		0			0
$869$	2.23787	+	0.599635i	0.0759145	+	0.0203412i
$870$		0			0
$871$	24.3997	−	42.2616i	0.826753	−	1.43198i
$872$		0			0
$873$	−6.20494	+	38.4340i	−0.210005	+	1.30079i
$874$		0			0
$875$	−8.88020	+	2.37944i	−0.300206	+	0.0804398i
$876$		0			0
$877$	−3.63096	−	0.972912i	−0.122609	−	0.0328529i	0.196993	−	0.980405i	$-0.436882\pi$
$877$	−3.63096	−	0.972912i	−0.122609	−	0.0328529i	−0.319602	+	0.947552i	$0.603549\pi$
$878$		0			0
$879$	11.6822	+	0.936941i	0.394029	+	0.0316022i
$880$		0			0
$881$		−	1.07656i		−	0.0362701i	−0.999836	−	0.0181350i	$-0.994227\pi$
$881$		−	1.07656i		−	0.0362701i	0.999836	−	0.0181350i	$-0.00577288\pi$
$882$		0			0
$883$	11.9386	+	11.9386i	0.401765	+	0.401765i	0.878855	−	0.477090i	$-0.158308\pi$
$883$	11.9386	+	11.9386i	0.401765	+	0.401765i	−0.477090	+	0.878855i	$0.658308\pi$
$884$		0			0
$885$	14.4657	−	40.6572i	0.486261	−	1.36668i
$886$		0			0
$887$	29.4527	−	17.0045i	0.988925	−	0.570956i	0.0839719	−	0.996468i	$-0.473239\pi$
$887$	29.4527	−	17.0045i	0.988925	−	0.570956i	0.904953	+	0.425512i	$0.139906\pi$
$888$		0			0
$889$	17.3318	+	10.0065i	0.581291	+	0.335609i
$890$		0			0
$891$	8.55770	−	13.0071i	0.286694	−	0.435755i
$892$		0			0
$893$	14.2006	−	3.80505i	0.475206	−	0.127331i
$894$		0			0
$895$	−35.2383	+	20.3449i	−1.17789	+	0.680054i
$896$		0			0
$897$	7.56018	−	3.59219i	0.252427	−	0.119940i
$898$		0			0
$899$	37.6095	−	37.6095i	1.25435	−	1.25435i
$900$		0			0
$901$	4.82210	+	4.82210i	0.160647	+	0.160647i
$902$		0			0
$903$	12.4244	+	0.996468i	0.413457	+	0.0331604i
$904$		0			0
$905$	−25.6625	−	44.4488i	−0.853051	−	1.47753i
$906$		0			0
$907$	0.815443	+	3.04327i	0.0270763	+	0.101050i	0.978142	−	0.207940i	$-0.0666758\pi$
$907$	0.815443	+	3.04327i	0.0270763	+	0.101050i	−0.951065	+	0.308990i	$0.900009\pi$
$908$		0			0
$909$	−12.4379	−	17.2272i	−0.412540	−	0.571389i
$910$		0			0
$911$	−1.83892	+	3.18510i	−0.0609261	+	0.105527i	−0.894880	−	0.446308i	$-0.852739\pi$
$911$	−1.83892	+	3.18510i	−0.0609261	+	0.105527i	0.833954	+	0.551835i	$0.186072\pi$
$912$		0			0
$913$	−13.0646	−	22.6286i	−0.432376	−	0.748897i
$914$		0			0
$915$	1.00166	+	5.44980i	0.0331137	+	0.180165i
$916$		0			0
$917$	−16.7110	+	16.7110i	−0.551845	+	0.551845i
$918$		0			0
$919$	−30.6795			−1.01202			−0.506012	−	0.862526i	$-0.668881\pi$
$919$	−30.6795			−1.01202			−0.506012	+	0.862526i	$0.668881\pi$
$920$		0			0
$921$	9.74118	+	6.71634i	0.320983	+	0.221311i
$922$		0			0
$923$	3.13673	−	11.7064i	0.103247	−	0.385322i
$924$		0			0
$925$	10.3659	+	38.6860i	0.340828	+	1.27199i
$926$		0			0
$927$	10.9686	+	8.93651i	0.360256	+	0.293513i
$928$		0			0
$929$	−27.1179	−	15.6565i	−0.889711	−	0.513675i	−0.0158629	−	0.999874i	$-0.505050\pi$
$929$	−27.1179	−	15.6565i	−0.889711	−	0.513675i	−0.873848	+	0.486199i	$0.838383\pi$
$930$		0			0
$931$	−3.30390	+	12.3303i	−0.108281	+	0.404109i
$932$		0			0
$933$	−0.0610792	+	0.0520092i	−0.00199964	+	0.00170270i
$934$		0			0
$935$		−	14.6400i		−	0.478780i
$936$		0			0
$937$		−	27.3142i		−	0.892317i	−0.894954	−	0.446158i	$-0.852792\pi$
$937$		−	27.3142i		−	0.892317i	0.894954	−	0.446158i	$-0.147208\pi$
$938$		0			0
$939$	1.03358	+	0.367747i	0.0337297	+	0.0120010i
$940$		0			0
$941$	−14.7882	+	55.1903i	−0.482081	+	1.79915i	0.110777	+	0.993845i	$0.464666\pi$
$941$	−14.7882	+	55.1903i	−0.482081	+	1.79915i	−0.592859	+	0.805306i	$0.702001\pi$
$942$		0			0
$943$	−6.76071	−	3.90330i	−0.220159	−	0.127109i
$944$		0			0
$945$	−7.37303	+	30.1165i	−0.239845	+	0.979691i
$946$		0			0
$947$	12.9097	+	48.1796i	0.419508	+	1.56563i	0.775631	+	0.631187i	$0.217432\pi$
$947$	12.9097	+	48.1796i	0.419508	+	1.56563i	−0.356123	+	0.934439i	$0.615902\pi$
$948$		0			0
$949$	0.407590	−	1.52115i	0.0132309	−	0.0493785i
$950$		0			0
$951$	−17.7475	+	8.43267i	−0.575503	+	0.273448i
$952$		0			0
$953$	7.53287			0.244013			0.122007	−	0.992529i	$-0.461067\pi$
$953$	7.53287			0.244013			0.122007	+	0.992529i	$0.461067\pi$
$954$		0			0
$955$	−11.0396	+	11.0396i	−0.357232	+	0.357232i
$956$		0			0
$957$	−13.1273	+	11.1779i	−0.424344	+	0.361331i
$958$		0			0
$959$	−8.61349	−	14.9190i	−0.278144	−	0.481760i
$960$		0			0
$961$	27.2214	−	47.1489i	0.878111	−	1.52093i
$962$		0			0
$963$	−32.0495	−	14.3841i	−1.03278	−	0.463520i
$964$		0			0
$965$	−4.03362	−	15.0537i	−0.129847	−	0.484595i
$966$		0			0
$967$	−9.30387	−	16.1148i	−0.299192	−	0.518216i	0.676759	−	0.736205i	$-0.263384\pi$
$967$	−9.30387	−	16.1148i	−0.299192	−	0.518216i	−0.975951	+	0.217988i	$0.930051\pi$
$968$		0			0
$969$	−13.0843	+	18.9771i	−0.420328	+	0.609631i
$970$		0			0
$971$	−11.9201	−	11.9201i	−0.382535	−	0.382535i	0.489480	−	0.872015i	$-0.337187\pi$
$971$	−11.9201	−	11.9201i	−0.382535	−	0.382535i	−0.872015	+	0.489480i	$0.837187\pi$
$972$		0			0
$973$	−14.6898	+	14.6898i	−0.470933	+	0.470933i
$974$		0			0
$975$	24.8240	+	17.1156i	0.795003	+	0.548138i
$976$		0			0
$977$	50.0976	−	28.9239i	1.60276	−	0.925356i	0.611833	−	0.790987i	$-0.290433\pi$
$977$	50.0976	−	28.9239i	1.60276	−	0.925356i	0.990931	−	0.134369i	$-0.0429008\pi$
$978$		0			0
$979$	13.1448	−	3.52215i	0.420111	−	0.112568i
$980$		0			0
$981$	−7.19335	+	16.0277i	−0.229666	+	0.511724i
$982$		0			0
$983$	−4.97282	−	2.87106i	−0.158608	−	0.0915725i	0.418595	−	0.908173i	$-0.362523\pi$
$983$	−4.97282	−	2.87106i	−0.158608	−	0.0915725i	−0.577203	+	0.816600i	$0.695856\pi$
$984$		0			0
$985$	−30.8820	+	17.8297i	−0.983981	+	0.568102i
$986$		0			0
$987$	7.40486	+	8.69621i	0.235699	+	0.276803i
$988$		0			0
$989$	−2.38175	−	2.38175i	−0.0757353	−	0.0757353i
$990$		0			0
$991$			5.44789i			0.173058i	0.996249	+	0.0865289i	$0.0275775\pi$
$991$			5.44789i			0.173058i	−0.996249	+	0.0865289i	$0.972422\pi$
$992$		0			0
$993$	13.9126	+	29.2808i	0.441504	+	0.929197i
$994$		0			0
$995$	−29.0603	−	7.78667i	−0.921272	−	0.246854i
$996$		0			0
$997$	1.30892	−	0.350724i	0.0414539	−	0.0111075i	−0.238032	−	0.971257i	$-0.576502\pi$
$997$	1.30892	−	0.350724i	0.0414539	−	0.0111075i	0.279486	+	0.960150i	$0.409836\pi$
$998$		0			0
$999$	−58.4337	−	14.3055i	−1.84876	−	0.452607i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	576.2.y.a.335.1		88
3.2	odd	2		1728.2.z.a.143.3		88
4.3	odd	2		144.2.u.a.11.8	✓	88
9.4	even	3		1728.2.z.a.719.3		88
9.5	odd	6	inner	576.2.y.a.527.12		88
12.11	even	2		432.2.v.a.251.15		88
16.3	odd	4	inner	576.2.y.a.47.12		88
16.13	even	4		144.2.u.a.83.1	yes	88
36.23	even	6		144.2.u.a.59.1	yes	88
36.31	odd	6		432.2.v.a.395.22		88
48.29	odd	4		432.2.v.a.35.22		88
48.35	even	4		1728.2.z.a.1007.3		88
144.13	even	12		432.2.v.a.179.15		88
144.67	odd	12		1728.2.z.a.1583.3		88
144.77	odd	12		144.2.u.a.131.8	yes	88
144.131	even	12	inner	576.2.y.a.239.1		88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.2.u.a.11.8	✓	88	4.3	odd	2
144.2.u.a.59.1	yes	88	36.23	even	6
144.2.u.a.83.1	yes	88	16.13	even	4
144.2.u.a.131.8	yes	88	144.77	odd	12
432.2.v.a.35.22		88	48.29	odd	4
432.2.v.a.179.15		88	144.13	even	12
432.2.v.a.251.15		88	12.11	even	2
432.2.v.a.395.22		88	36.31	odd	6
576.2.y.a.47.12		88	16.3	odd	4	inner
576.2.y.a.239.1		88	144.131	even	12	inner
576.2.y.a.335.1		88	1.1	even	1	trivial
576.2.y.a.527.12		88	9.5	odd	6	inner
1728.2.z.a.143.3		88	3.2	odd	2
1728.2.z.a.719.3		88	9.4	even	3
1728.2.z.a.1007.3		88	48.35	even	4
1728.2.z.a.1583.3		88	144.67	odd	12

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:	\( N \)	\(=\)	\( 576 = 2^{6} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	576.y (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.70352 + 0.313101i) q^{3} +(2.80938 + 0.752772i) q^{5} +(1.02581 - 1.77675i) q^{7} +(2.80394 - 1.06674i) q^{9} +O(q^{10})\)	\(q+(-1.70352 + 0.313101i) q^{3} +(2.80938 + 0.752772i) q^{5} +(1.02581 - 1.77675i) q^{7} +(2.80394 - 1.06674i) q^{9} +(1.67103 - 0.447752i) q^{11} +(-4.86091 - 1.30248i) q^{13} +(-5.02153 - 0.402740i) q^{15} -2.90960i q^{17} +(3.23424 + 3.23424i) q^{19} +(-1.19118 + 3.34790i) q^{21} +(0.831633 - 0.480143i) q^{23} +(2.99585 + 1.72965i) q^{25} +(-4.44255 + 2.69513i) q^{27} +(5.55800 - 1.48926i) q^{29} +(8.00513 - 4.62177i) q^{31} +(-2.70644 + 1.28595i) q^{33} +(4.21937 - 4.21937i) q^{35} +(8.18664 + 8.18664i) q^{37} +(8.68844 + 0.696837i) q^{39} +(-4.06472 - 7.04030i) q^{41} +(-0.907834 - 3.38808i) q^{43} +(8.68035 - 0.886168i) q^{45} +(1.60711 - 2.78360i) q^{47} +(1.39544 + 2.41698i) q^{49} +(0.910997 + 4.95655i) q^{51} +(-1.65731 + 1.65731i) q^{53} +5.03163 q^{55} +(-6.52223 - 4.49694i) q^{57} +(-2.21712 + 8.27439i) q^{59} +(-0.284684 - 1.06246i) q^{61} +(0.980960 - 6.07616i) q^{63} +(-12.6757 - 7.31831i) q^{65} +(-2.50979 + 9.36667i) q^{67} +(-1.26637 + 1.07832i) q^{69} +2.40828i q^{71} +0.312935i q^{73} +(-5.64503 - 2.00849i) q^{75} +(0.918613 - 3.42831i) q^{77} +(1.15979 + 0.669606i) q^{79} +(6.72412 - 5.98216i) q^{81} +(-3.90915 - 14.5891i) q^{83} +(2.19027 - 8.17418i) q^{85} +(-9.00185 + 4.27719i) q^{87} +7.86629 q^{89} +(-7.30052 + 7.30052i) q^{91} +(-12.1898 + 10.3797i) q^{93} +(6.65158 + 11.5209i) q^{95} +(-6.48861 + 11.2386i) q^{97} +(4.20783 - 3.03803i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q + 4 q^{3} - 6 q^{5} + 4 q^{7}+O(q^{10}) \) 88 * q + 4 * q^3 - 6 * q^5 + 4 * q^7	\( 88 q + 4 q^{3} - 6 q^{5} + 4 q^{7} + 6 q^{11} - 2 q^{13} + 8 q^{19} + 2 q^{21} + 12 q^{23} + 16 q^{27} - 6 q^{29} - 8 q^{33} - 8 q^{37} + 32 q^{39} + 2 q^{43} + 6 q^{45} - 24 q^{49} + 12 q^{51} + 16 q^{55} + 42 q^{59} - 2 q^{61} - 12 q^{65} + 2 q^{67} - 10 q^{69} + 56 q^{75} - 6 q^{77} - 8 q^{81} - 54 q^{83} + 8 q^{85} - 48 q^{87} - 20 q^{91} - 34 q^{93} - 4 q^{97} - 46 q^{99}+O(q^{100}) \) 88 * q + 4 * q^3 - 6 * q^5 + 4 * q^7 + 6 * q^11 - 2 * q^13 + 8 * q^19 + 2 * q^21 + 12 * q^23 + 16 * q^27 - 6 * q^29 - 8 * q^33 - 8 * q^37 + 32 * q^39 + 2 * q^43 + 6 * q^45 - 24 * q^49 + 12 * q^51 + 16 * q^55 + 42 * q^59 - 2 * q^61 - 12 * q^65 + 2 * q^67 - 10 * q^69 + 56 * q^75 - 6 * q^77 - 8 * q^81 - 54 * q^83 + 8 * q^85 - 48 * q^87 - 20 * q^91 - 34 * q^93 - 4 * q^97 - 46 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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