LMFDB - Embedded newform 704.2.u.c.127.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [704,2,Mod(63,704)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(704, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 0, 3]))

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

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

chi := DirichletCharacter("704.63");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 704 = 2^{6} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	704.u (of order $10$, 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:	$5.62146830230$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 5 x^{15} + 13 x^{14} - 25 x^{13} + 35 x^{12} - 30 x^{11} - 2 x^{10} + 60 x^{9} - 116 x^{8} + \cdots + 256 $ x^16 - 5x^15 + 13x^14 - 25x^13 + 35x^12 - 30x^11 - 2x^10 + 60x^9 - 116x^8 + 120x^7 - 8x^6 - 240x^5 + 560x^4 - 800x^3 + 832x^2 - 640*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 44)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			127.1
Root			$1.06665 + 0.928579i$ of defining polynomial
Character	$\chi$	$=$	704.127
Dual form			704.2.u.c.255.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.59814 + 2.19965i) q^{3} +(0.720859 - 2.21858i) q^{5} +(-1.04462 + 0.758960i) q^{7} +(-1.35736 - 4.17752i) q^{9} +O(q^{10})$	\(q+(-1.59814 + 2.19965i) q^{3} +(0.720859 - 2.21858i) q^{5} +(-1.04462 + 0.758960i) q^{7} +(-1.35736 - 4.17752i) q^{9} +(3.29387 - 0.387833i) q^{11} +(0.279141 - 0.0906984i) q^{13} +(3.72806 + 5.13123i) q^{15} +(2.82281 + 0.917186i) q^{17} +(1.38671 + 1.00751i) q^{19} -3.51072i q^{21} +0.525735i q^{23} +(-0.357358 - 0.259635i) q^{25} +(3.60079 + 1.16997i) q^{27} +(4.84416 + 6.66742i) q^{29} +(4.22806 - 1.37378i) q^{31} +(-4.41097 + 7.86517i) q^{33} +(0.930788 + 2.86467i) q^{35} +(-4.22613 + 3.07046i) q^{37} +(-0.246601 + 0.758960i) q^{39} +(3.28821 - 4.52583i) q^{41} -3.49429 q^{43} -10.2466 q^{45} +(-4.50223 + 6.19679i) q^{47} +(-1.64791 + 5.07175i) q^{49} +(-6.52872 + 4.74340i) q^{51} +(-0.484791 - 1.49203i) q^{53} +(1.51398 - 7.58728i) q^{55} +(-4.43232 + 1.44015i) q^{57} +(8.27247 + 11.3861i) q^{59} +(8.98451 + 2.91924i) q^{61} +(4.58849 + 3.33373i) q^{63} -0.684676i q^{65} -10.4249i q^{67} +(-1.15643 - 0.840198i) q^{69} +(3.41904 + 1.11091i) q^{71} +(2.51668 + 3.46391i) q^{73} +(1.14221 - 0.371128i) q^{75} +(-3.14649 + 2.90506i) q^{77} +(3.04387 + 9.36807i) q^{79} +(2.33275 - 1.69484i) q^{81} +(1.16185 - 3.57581i) q^{83} +(4.06969 - 5.60145i) q^{85} -22.4076 q^{87} +0.598152 q^{89} +(-0.222760 + 0.306602i) q^{91} +(-3.73519 + 11.4957i) q^{93} +(3.23485 - 2.35026i) q^{95} +(-2.57295 - 7.91872i) q^{97} +(-6.09114 - 13.2338i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 6 q^{5} - 10 q^{9}+O(q^{10}) $ 16 * q + 6 * q^5 - 10 * q^9	$ 16 q + 6 q^{5} - 10 q^{9} + 10 q^{13} - 10 q^{17} + 6 q^{25} + 10 q^{29} - 12 q^{33} - 18 q^{37} + 10 q^{41} - 40 q^{45} + 6 q^{49} - 38 q^{53} + 10 q^{61} + 16 q^{69} - 30 q^{73} - 2 q^{77} - 4 q^{81} + 50 q^{85} - 36 q^{89} + 38 q^{93} - 68 q^{97}+O(q^{100}) $ 16 * q + 6 * q^5 - 10 * q^9 + 10 * q^13 - 10 * q^17 + 6 * q^25 + 10 * q^29 - 12 * q^33 - 18 * q^37 + 10 * q^41 - 40 * q^45 + 6 * q^49 - 38 * q^53 + 10 * q^61 + 16 * q^69 - 30 * q^73 - 2 * q^77 - 4 * q^81 + 50 * q^85 - 36 * q^89 + 38 * q^93 - 68 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/704\mathbb{Z}\right)^\times$.

$n$	$133$	$321$	$639$
$\chi(n)$	$1$	$e\left(\frac{9}{10}\right)$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.59814	+	2.19965i	−0.922686	+	1.26997i	0.0399594	+	0.999201i	$0.487277\pi$
$3$	−1.59814	+	2.19965i	−0.922686	+	1.26997i	−0.962645	+	0.270767i	$0.912723\pi$
$4$		0			0
$5$	0.720859	−	2.21858i	0.322378	−	0.992177i	−0.650232	−	0.759735i	$-0.725328\pi$
$5$	0.720859	−	2.21858i	0.322378	−	0.992177i	0.972610	−	0.232442i	$-0.0746716\pi$
$6$		0			0
$7$	−1.04462	+	0.758960i	−0.394829	+	0.286860i	−0.767431	−	0.641131i	$-0.778466\pi$
$7$	−1.04462	+	0.758960i	−0.394829	+	0.286860i	0.372602	+	0.927991i	$0.378466\pi$
$8$		0			0
$9$	−1.35736	−	4.17752i	−0.452453	−	1.39251i
$10$		0			0
$11$	3.29387	−	0.387833i	0.993139	−	0.116936i
$11$	3.29387	−	0.387833i	0.993139	−	0.116936i
$12$		0			0
$13$	0.279141	−	0.0906984i	0.0774198	−	0.0251552i	−0.270051	−	0.962846i	$-0.587041\pi$
$13$	0.279141	−	0.0906984i	0.0774198	−	0.0251552i	0.347471	+	0.937691i	$0.387041\pi$
$14$		0			0
$15$	3.72806	+	5.13123i	0.962580	+	1.32488i
$16$		0			0
$17$	2.82281	+	0.917186i	0.684631	+	0.222450i	0.630622	−	0.776090i	$-0.282800\pi$
$17$	2.82281	+	0.917186i	0.684631	+	0.222450i	0.0540095	+	0.998540i	$0.482800\pi$
$18$		0			0
$19$	1.38671	+	1.00751i	0.318134	+	0.231138i	0.735379	−	0.677656i	$-0.237004\pi$
$19$	1.38671	+	1.00751i	0.318134	+	0.231138i	−0.417245	+	0.908794i	$0.637004\pi$
$20$		0			0
$21$		−	3.51072i		−	0.766102i
$22$		0			0
$23$			0.525735i			0.109623i	0.998497	+	0.0548117i	$0.0174559\pi$
$23$			0.525735i			0.109623i	−0.998497	+	0.0548117i	$0.982544\pi$
$24$		0			0
$25$	−0.357358	−	0.259635i	−0.0714715	−	0.0519271i
$26$		0			0
$27$	3.60079	+	1.16997i	0.692972	+	0.225160i
$28$		0			0
$29$	4.84416	+	6.66742i	0.899538	+	1.23811i	0.970615	+	0.240637i	$0.0773564\pi$
$29$	4.84416	+	6.66742i	0.899538	+	1.23811i	−0.0710771	+	0.997471i	$0.522644\pi$
$30$		0			0
$31$	4.22806	−	1.37378i	0.759382	−	0.246738i	0.0963686	−	0.995346i	$-0.469277\pi$
$31$	4.22806	−	1.37378i	0.759382	−	0.246738i	0.663013	+	0.748608i	$0.269277\pi$
$32$		0			0
$33$	−4.41097	+	7.86517i	−0.767851	+	1.36915i
$34$		0			0
$35$	0.930788	+	2.86467i	0.157332	+	0.484218i
$36$		0			0
$37$	−4.22613	+	3.07046i	−0.694771	+	0.504781i	−0.878225	−	0.478248i	$-0.841272\pi$
$37$	−4.22613	+	3.07046i	−0.694771	+	0.504781i	0.183454	+	0.983028i	$0.441272\pi$
$38$		0			0
$39$	−0.246601	+	0.758960i	−0.0394878	+	0.121531i
$40$		0			0
$41$	3.28821	−	4.52583i	0.513531	−	0.706815i	−0.470978	−	0.882145i	$-0.656099\pi$
$41$	3.28821	−	4.52583i	0.513531	−	0.706815i	0.984510	+	0.175329i	$0.0560990\pi$
$42$		0			0
$43$	−3.49429			−0.532874			−0.266437	−	0.963852i	$-0.585846\pi$
$43$	−3.49429			−0.532874			−0.266437	+	0.963852i	$0.585846\pi$
$44$		0			0
$45$	−10.2466			−1.52747
$46$		0			0
$47$	−4.50223	+	6.19679i	−0.656718	+	0.903895i	−0.999367	−	0.0355685i	$-0.988676\pi$
$47$	−4.50223	+	6.19679i	−0.656718	+	0.903895i	0.342649	+	0.939463i	$0.388676\pi$
$48$		0			0
$49$	−1.64791	+	5.07175i	−0.235416	+	0.724535i
$50$		0			0
$51$	−6.52872	+	4.74340i	−0.914204	+	0.664208i
$52$		0			0
$53$	−0.484791	−	1.49203i	−0.0665912	−	0.204947i	0.912224	−	0.409691i	$-0.134364\pi$
$53$	−0.484791	−	1.49203i	−0.0665912	−	0.204947i	−0.978815	+	0.204745i	$0.934364\pi$
$54$		0			0
$55$	1.51398	−	7.58728i	0.204145	−	1.02307i
$56$		0			0
$57$	−4.43232	+	1.44015i	−0.587075	+	0.190752i
$58$		0			0
$59$	8.27247	+	11.3861i	1.07698	+	1.48234i	0.862799	+	0.505548i	$0.168710\pi$
$59$	8.27247	+	11.3861i	1.07698	+	1.48234i	0.214185	+	0.976793i	$0.431290\pi$
$60$		0			0
$61$	8.98451	+	2.91924i	1.15035	+	0.373771i	0.821274	−	0.570533i	$-0.193263\pi$
$61$	8.98451	+	2.91924i	1.15035	+	0.373771i	0.329074	+	0.944304i	$0.393263\pi$
$62$		0			0
$63$	4.58849	+	3.33373i	0.578096	+	0.420011i
$64$		0			0
$65$		−	0.684676i		−	0.0849236i
$66$		0			0
$67$		−	10.4249i		−	1.27361i	−0.771026	−	0.636803i	$-0.780256\pi$
$67$		−	10.4249i		−	1.27361i	0.771026	−	0.636803i	$-0.219744\pi$
$68$		0			0
$69$	−1.15643	−	0.840198i	−0.139218	−	0.101148i
$70$		0			0
$71$	3.41904	+	1.11091i	0.405765	+	0.131841i	0.504786	−	0.863244i	$-0.331571\pi$
$71$	3.41904	+	1.11091i	0.405765	+	0.131841i	−0.0990215	+	0.995085i	$0.531571\pi$
$72$		0			0
$73$	2.51668	+	3.46391i	0.294555	+	0.405420i	0.930487	−	0.366325i	$-0.119384\pi$
$73$	2.51668	+	3.46391i	0.294555	+	0.405420i	−0.635932	+	0.771745i	$0.719384\pi$
$74$		0			0
$75$	1.14221	−	0.371128i	0.131891	−	0.0428541i
$76$		0			0
$77$	−3.14649	+	2.90506i	−0.358576	+	0.331062i
$78$		0			0
$79$	3.04387	+	9.36807i	0.342462	+	1.05399i	0.962929	+	0.269757i	$0.0869433\pi$
$79$	3.04387	+	9.36807i	0.342462	+	1.05399i	−0.620467	+	0.784233i	$0.713057\pi$
$80$		0			0
$81$	2.33275	−	1.69484i	0.259194	−	0.188316i
$82$		0			0
$83$	1.16185	−	3.57581i	0.127530	−	0.392496i	−0.866824	−	0.498615i	$-0.833842\pi$
$83$	1.16185	−	3.57581i	0.127530	−	0.392496i	0.994354	+	0.106118i	$0.0338423\pi$
$84$		0			0
$85$	4.06969	−	5.60145i	0.441420	−	0.607563i
$86$		0			0
$87$	−22.4076			−2.40235
$88$		0			0
$89$	0.598152			0.0634039			0.0317020	−	0.999497i	$-0.489907\pi$
$89$	0.598152			0.0634039			0.0317020	+	0.999497i	$0.489907\pi$
$90$		0			0
$91$	−0.222760	+	0.306602i	−0.0233515	+	0.0321406i
$92$		0			0
$93$	−3.73519	+	11.4957i	−0.387321	+	1.19205i
$94$		0			0
$95$	3.23485	−	2.35026i	0.331889	−	0.241131i
$96$		0			0
$97$	−2.57295	−	7.91872i	−0.261243	−	0.804024i	−0.992535	−	0.121960i	$-0.961082\pi$
$97$	−2.57295	−	7.91872i	−0.261243	−	0.804024i	0.731292	−	0.682065i	$-0.238918\pi$
$98$		0			0
$99$	−6.09114	−	13.2338i	−0.612182	−	1.33004i
$100$		0			0
$101$	7.30672	−	2.37410i	0.727046	−	0.236232i	0.0779707	−	0.996956i	$-0.475156\pi$
$101$	7.30672	−	2.37410i	0.727046	−	0.236232i	0.649075	+	0.760724i	$0.275156\pi$
$102$		0			0
$103$	0.242398	+	0.333632i	0.0238841	+	0.0328737i	0.820792	−	0.571227i	$-0.193532\pi$
$103$	0.242398	+	0.333632i	0.0238841	+	0.0328737i	−0.796908	+	0.604101i	$0.793532\pi$
$104$		0			0
$105$	−7.78880	−	2.53073i	−0.760109	−	0.246974i
$106$		0			0
$107$	−4.18738	−	3.04231i	−0.404809	−	0.294111i	0.366688	−	0.930344i	$-0.380492\pi$
$107$	−4.18738	−	3.04231i	−0.404809	−	0.294111i	−0.771497	+	0.636233i	$0.780492\pi$
$108$		0			0
$109$		−	12.5948i		−	1.20636i	−0.797604	−	0.603181i	$-0.793899\pi$
$109$		−	12.5948i		−	1.20636i	0.797604	−	0.603181i	$-0.206101\pi$
$110$		0			0
$111$		−	14.2030i		−	1.34809i
$112$		0			0
$113$	2.15258	+	1.56394i	0.202498	+	0.147123i	0.684413	−	0.729095i	$-0.260059\pi$
$113$	2.15258	+	1.56394i	0.202498	+	0.147123i	−0.481915	+	0.876218i	$0.660059\pi$
$114$		0			0
$115$	1.16638	+	0.378981i	0.108766	+	0.0353402i
$116$		0			0
$117$	−0.757788	−	1.04301i	−0.0700575	−	0.0964259i
$118$		0			0
$119$	−3.64487	+	1.18429i	−0.334124	+	0.108564i
$120$		0			0
$121$	10.6992	−	2.55494i	0.972652	−	0.232267i
$122$		0			0
$123$	4.70022	+	14.4658i	0.423805	+	1.30434i
$124$		0			0
$125$	8.60254	−	6.25011i	0.769435	−	0.559027i
$126$		0			0
$127$	6.16979	−	18.9887i	0.547481	−	1.68497i	−0.167537	−	0.985866i	$-0.553581\pi$
$127$	6.16979	−	18.9887i	0.547481	−	1.68497i	0.715018	−	0.699107i	$-0.246419\pi$
$128$		0			0
$129$	5.58436	−	7.68621i	0.491676	−	0.676733i
$130$		0			0
$131$	−20.5136			−1.79228			−0.896139	−	0.443773i	$-0.853640\pi$
$131$	−20.5136			−1.79228			−0.896139	+	0.443773i	$0.853640\pi$
$132$		0			0
$133$	−2.21324			−0.191913
$134$		0			0
$135$	5.19132	−	7.14524i	0.446798	−	0.614965i
$136$		0			0
$137$	−1.93612	+	5.95875i	−0.165414	+	0.509091i	−0.999067	−	0.0431981i	$-0.986245\pi$
$137$	−1.93612	+	5.95875i	−0.165414	+	0.509091i	0.833653	+	0.552289i	$0.186245\pi$
$138$		0			0
$139$	10.9058	−	7.92352i	0.925017	−	0.672064i	−0.0197506	−	0.999805i	$-0.506287\pi$
$139$	10.9058	−	7.92352i	0.925017	−	0.672064i	0.944768	+	0.327741i	$0.106287\pi$
$140$		0			0
$141$	−6.43557	−	19.8067i	−0.541973	−	1.66802i
$142$		0			0
$143$	0.884278	−	0.407009i	0.0739471	−	0.0340358i
$144$		0			0
$145$	18.2841	−	5.94087i	1.51841	−	0.493363i
$146$		0			0
$147$	−8.52247	−	11.7302i	−0.702922	−	0.967489i
$148$		0			0
$149$	−16.5960	−	5.39238i	−1.35960	−	0.441761i	−0.463690	−	0.885997i	$-0.653475\pi$
$149$	−16.5960	−	5.39238i	−1.35960	−	0.441761i	−0.895910	+	0.444237i	$0.853475\pi$
$150$		0			0
$151$	−7.94818	−	5.77469i	−0.646814	−	0.469938i	0.215370	−	0.976532i	$-0.430904\pi$
$151$	−7.94818	−	5.77469i	−0.646814	−	0.469938i	−0.862184	+	0.506595i	$0.830904\pi$
$152$		0			0
$153$		−	13.0373i		−	1.05400i
$154$		0			0
$155$		−	10.3706i		−	0.832985i
$156$		0			0
$157$	12.4622	+	9.05431i	0.994591	+	0.722613i	0.960922	−	0.276820i	$-0.0892806\pi$
$157$	12.4622	+	9.05431i	0.994591	+	0.722613i	0.0336696	+	0.999433i	$0.489281\pi$
$158$		0			0
$159$	4.05671	+	1.31811i	0.321718	+	0.104533i
$160$		0			0
$161$	−0.399012	−	0.549193i	−0.0314466	−	0.0432825i
$162$		0			0
$163$	10.2403	−	3.32727i	0.802080	−	0.260612i	0.120840	−	0.992672i	$-0.461441\pi$
$163$	10.2403	−	3.32727i	0.802080	−	0.260612i	0.681240	+	0.732060i	$0.261441\pi$
$164$		0			0
$165$	14.2698	+	15.4557i	1.11090	+	1.20323i
$166$		0			0
$167$	−1.98451	−	6.10771i	−0.153566	−	0.472629i	0.844446	−	0.535640i	$-0.179930\pi$
$167$	−1.98451	−	6.10771i	−0.153566	−	0.472629i	−0.998013	+	0.0630114i	$0.979930\pi$
$168$		0			0
$169$	−10.4475	+	7.59057i	−0.803656	+	0.583890i
$170$		0			0
$171$	2.32661	−	7.16056i	0.177920	−	0.547582i
$172$		0			0
$173$	2.12650	−	2.92688i	0.161675	−	0.222527i	−0.720492	−	0.693463i	$-0.756084\pi$
$173$	2.12650	−	2.92688i	0.161675	−	0.222527i	0.882167	+	0.470937i	$0.156084\pi$
$174$		0			0
$175$	0.570356			0.0431148
$176$		0			0
$177$	−38.2659			−2.87624
$178$		0			0
$179$	−2.94347	+	4.05134i	−0.220006	+	0.302812i	−0.904726	−	0.425994i	$-0.859924\pi$
$179$	−2.94347	+	4.05134i	−0.220006	+	0.302812i	0.684720	+	0.728806i	$0.259924\pi$
$180$		0			0
$181$	−3.02897	+	9.32220i	−0.225141	+	0.692914i	0.773136	+	0.634240i	$0.218687\pi$
$181$	−3.02897	+	9.32220i	−0.225141	+	0.692914i	−0.998277	+	0.0586734i	$0.981313\pi$
$182$		0			0
$183$	−20.7798	+	15.0974i	−1.53609	+	1.11603i
$184$		0			0
$185$	3.76561	+	11.5894i	0.276853	+	0.852066i
$186$		0			0
$187$	9.65368	+	1.92631i	0.705947	+	0.140866i
$188$		0			0
$189$	−4.64941	+	1.51069i	−0.338195	+	0.109886i
$190$		0			0
$191$	6.87102	+	9.45715i	0.497170	+	0.684295i	0.981690	−	0.190485i	$-0.0610059\pi$
$191$	6.87102	+	9.45715i	0.497170	+	0.684295i	−0.484521	+	0.874780i	$0.661006\pi$
$192$		0			0
$193$	−1.09807	−	0.356784i	−0.0790406	−	0.0256818i	0.269230	−	0.963076i	$-0.413231\pi$
$193$	−1.09807	−	0.356784i	−0.0790406	−	0.0256818i	−0.348270	+	0.937394i	$0.613231\pi$
$194$		0			0
$195$	1.50605	+	1.09421i	0.107850	+	0.0783578i
$196$		0			0
$197$			15.6248i			1.11322i	0.830774	+	0.556610i	$0.187898\pi$
$197$			15.6248i			1.11322i	−0.830774	+	0.556610i	$0.812102\pi$
$198$		0			0
$199$		−	10.9684i		−	0.777526i	−0.921338	−	0.388763i	$-0.872902\pi$
$199$		−	10.9684i		−	0.777526i	0.921338	−	0.388763i	$-0.127098\pi$
$200$		0			0
$201$	22.9312	+	16.6605i	1.61744	+	1.17514i
$202$		0			0
$203$	−10.1206	−	3.28839i	−0.710328	−	0.230799i
$204$		0			0
$205$	−7.67056	−	10.5576i	−0.535735	−	0.737376i
$206$		0			0
$207$	2.19627	−	0.713611i	0.152651	−	0.0495994i
$208$		0			0
$209$	4.95840	+	2.78078i	0.342980	+	0.192351i
$210$		0			0
$211$	−5.96517	−	18.3589i	−0.410659	−	1.26388i	−0.916076	−	0.401004i	$-0.868661\pi$
$211$	−5.96517	−	18.3589i	−0.410659	−	1.26388i	0.505417	−	0.862875i	$-0.331339\pi$
$212$		0			0
$213$	−7.90771	+	5.74529i	−0.541827	+	0.393661i
$214$		0			0
$215$	−2.51889	+	7.75235i	−0.171787	+	0.528706i
$216$		0			0
$217$	−3.37407	+	4.64401i	−0.229047	+	0.315256i
$218$		0			0
$219$	−11.6414			−0.786652
$220$		0			0
$221$	0.871148			0.0585998
$222$		0			0
$223$	−6.37102	+	8.76895i	−0.426635	+	0.587212i	−0.967177	−	0.254105i	$-0.918219\pi$
$223$	−6.37102	+	8.76895i	−0.426635	+	0.587212i	0.540542	+	0.841317i	$0.318219\pi$
$224$		0			0
$225$	−0.599570	+	1.84529i	−0.0399713	+	0.123019i
$226$		0			0
$227$	−19.4139	+	14.1050i	−1.28854	+	0.936181i	−0.999775	−	0.0212179i	$-0.993246\pi$
$227$	−19.4139	+	14.1050i	−1.28854	+	0.936181i	−0.288768	+	0.957399i	$0.593246\pi$
$228$		0			0
$229$	7.59603	+	23.3782i	0.501960	+	1.54487i	0.805822	+	0.592158i	$0.201724\pi$
$229$	7.59603	+	23.3782i	0.501960	+	1.54487i	−0.303862	+	0.952716i	$0.598276\pi$
$230$		0			0
$231$	−1.36157	−	11.5639i	−0.0895849	−	0.760846i
$232$		0			0
$233$	−13.6046	+	4.42039i	−0.891264	+	0.289589i	−0.718627	−	0.695396i	$-0.755229\pi$
$233$	−13.6046	+	4.42039i	−0.891264	+	0.289589i	−0.172637	+	0.984985i	$0.555229\pi$
$234$		0			0
$235$	10.5026	+	14.4556i	0.685113	+	0.942977i
$236$		0			0
$237$	−25.4710	−	8.27602i	−1.65452	−	0.537585i
$238$		0			0
$239$	−15.9893	−	11.6169i	−1.03426	−	0.751436i	−0.0651055	−	0.997878i	$-0.520738\pi$
$239$	−15.9893	−	11.6169i	−1.03426	−	0.751436i	−0.969157	+	0.246442i	$0.920738\pi$
$240$		0			0
$241$		−	6.53055i		−	0.420669i	−0.977629	−	0.210335i	$-0.932545\pi$
$241$		−	6.53055i		−	0.420669i	0.977629	−	0.210335i	$-0.0674554\pi$
$242$		0			0
$243$			19.1981i			1.23156i
$244$		0			0
$245$	10.0641	+	7.31203i	0.642975	+	0.467148i
$246$		0			0
$247$	0.478467	+	0.155464i	0.0304442	+	0.00989191i
$248$		0			0
$249$	6.00873	+	8.27031i	0.380788	+	0.524109i
$250$		0			0
$251$	4.53708	−	1.47419i	0.286378	−	0.0930498i	−0.162306	−	0.986741i	$-0.551893\pi$
$251$	4.53708	−	1.47419i	0.286378	−	0.0930498i	0.448684	+	0.893691i	$0.351893\pi$
$252$		0			0
$253$	0.203897	+	1.73170i	0.0128189	+	0.108871i
$254$		0			0
$255$	5.81729	+	17.9038i	0.364293	+	1.12118i
$256$		0			0
$257$	2.45693	−	1.78506i	0.153259	−	0.111349i	−0.508513	−	0.861054i	$-0.669805\pi$
$257$	2.45693	−	1.78506i	0.153259	−	0.111349i	0.661772	+	0.749705i	$0.269805\pi$
$258$		0			0
$259$	2.08434	−	6.41493i	0.129514	−	0.398604i
$260$		0			0
$261$	21.2780	−	29.2866i	1.31707	−	1.81280i
$262$		0			0
$263$	14.1671			0.873580			0.436790	−	0.899564i	$-0.356115\pi$
$263$	14.1671			0.873580			0.436790	+	0.899564i	$0.356115\pi$
$264$		0			0
$265$	−3.65966			−0.224811
$266$		0			0
$267$	−0.955929	+	1.31572i	−0.0585019	+	0.0805210i
$268$		0			0
$269$	−0.309559	+	0.952724i	−0.0188741	+	0.0580886i	−0.960050	−	0.279829i	$-0.909722\pi$
$269$	−0.309559	+	0.952724i	−0.0188741	+	0.0580886i	0.941176	+	0.337917i	$0.109722\pi$
$270$		0			0
$271$	14.3933	−	10.4573i	0.874330	−	0.635238i	−0.0574157	−	0.998350i	$-0.518286\pi$
$271$	14.3933	−	10.4573i	0.874330	−	0.635238i	0.931745	+	0.363113i	$0.118286\pi$
$272$		0			0
$273$	−0.318417	−	0.979986i	−0.0192714	−	0.0593114i
$274$		0			0
$275$	−1.27778	−	0.716611i	−0.0770533	−	0.0432133i
$276$		0			0
$277$	−18.4378	+	5.99082i	−1.10782	+	0.359953i	−0.805108	−	0.593128i	$-0.797893\pi$
$277$	−18.4378	+	5.99082i	−1.10782	+	0.359953i	−0.302714	+	0.953081i	$0.597893\pi$
$278$		0			0
$279$	−11.4780	−	15.7981i	−0.687169	−	0.945806i
$280$		0			0
$281$	−13.9771	−	4.54142i	−0.833802	−	0.270919i	−0.139156	−	0.990270i	$-0.544439\pi$
$281$	−13.9771	−	4.54142i	−0.833802	−	0.270919i	−0.694646	+	0.719352i	$0.744439\pi$
$282$		0			0
$283$	−2.02002	−	1.46763i	−0.120078	−	0.0872415i	0.526126	−	0.850407i	$-0.323644\pi$
$283$	−2.02002	−	1.46763i	−0.120078	−	0.0872415i	−0.646203	+	0.763165i	$0.723644\pi$
$284$		0			0
$285$			10.8716i			0.643977i
$286$		0			0
$287$			7.22339i			0.426383i
$288$		0			0
$289$	−6.62627	−	4.81427i	−0.389781	−	0.283192i
$290$		0			0
$291$	21.5303	+	6.99563i	1.26213	+	0.410091i
$292$		0			0
$293$	−4.41949	−	6.08290i	−0.258189	−	0.355367i	0.660169	−	0.751117i	$-0.270485\pi$
$293$	−4.41949	−	6.08290i	−0.258189	−	0.355367i	−0.918358	+	0.395750i	$0.870485\pi$
$294$		0			0
$295$	31.2242	−	10.1453i	1.81794	−	0.590685i
$296$		0			0
$297$	12.3143	+	2.45722i	0.714547	+	0.142582i
$298$		0			0
$299$	0.0476833	+	0.146754i	0.00275760	+	0.00848702i
$300$		0			0
$301$	3.65020	−	2.65203i	0.210394	−	0.152860i
$302$		0			0
$303$	−6.45497	+	19.8664i	−0.370828	+	1.14129i
$304$		0			0
$305$	12.9531	−	17.8285i	0.741694	−	1.02085i
$306$		0			0
$307$	25.7991			1.47243			0.736216	−	0.676747i	$-0.236611\pi$
$307$	25.7991			1.47243			0.736216	+	0.676747i	$0.236611\pi$
$308$		0			0
$309$	−1.12126			−0.0637861
$310$		0			0
$311$	−1.74241	+	2.39822i	−0.0988030	+	0.135991i	−0.855556	−	0.517710i	$-0.826785\pi$
$311$	−1.74241	+	2.39822i	−0.0988030	+	0.135991i	0.756753	+	0.653701i	$0.226785\pi$
$312$		0			0
$313$	0.186644	−	0.574432i	0.0105498	−	0.0324688i	−0.945643	−	0.325206i	$-0.894566\pi$
$313$	0.186644	−	0.574432i	0.0105498	−	0.0324688i	0.956193	+	0.292738i	$0.0945662\pi$
$314$		0			0
$315$	10.7038	−	7.77677i	0.603091	−	0.438171i
$316$		0			0
$317$	−7.09054	−	21.8224i	−0.398244	−	1.22567i	−0.926406	−	0.376526i	$-0.877119\pi$
$317$	−7.09054	−	21.8224i	−0.398244	−	1.22567i	0.528162	−	0.849144i	$-0.322881\pi$
$318$		0			0
$319$	18.5419	+	20.0829i	1.03815	+	1.12443i
$320$		0			0
$321$	13.3840	−	4.34874i	0.747024	−	0.242723i
$322$		0			0
$323$	2.99035	+	4.11587i	0.166388	+	0.229013i
$324$		0			0
$325$	−0.123302	−	0.0400631i	−0.00683954	−	0.00222230i
$326$		0			0
$327$	27.7041	+	20.1282i	1.53204	+	1.11309i
$328$		0			0
$329$		−	9.89031i		−	0.545270i
$330$		0			0
$331$			4.43442i			0.243738i	0.992546	+	0.121869i	$0.0388887\pi$
$331$			4.43442i			0.243738i	−0.992546	+	0.121869i	$0.961111\pi$
$332$		0			0
$333$	18.5633	+	13.4870i	1.01726	+	0.739083i
$334$		0			0
$335$	−23.1285	−	7.51490i	−1.26364	−	0.410583i
$336$		0			0
$337$	10.4401	+	14.3696i	0.568711	+	0.782763i	0.992401	−	0.123044i	$-0.0392656\pi$
$337$	10.4401	+	14.3696i	0.568711	+	0.782763i	−0.423691	+	0.905807i	$0.639266\pi$
$338$		0			0
$339$	−6.88025	+	2.23553i	−0.373684	+	0.121417i
$340$		0			0
$341$	13.3939	−	6.16483i	0.725320	−	0.333844i
$342$		0			0
$343$	−4.92088	−	15.1449i	−0.265703	−	0.817748i
$344$		0			0
$345$	−2.69767	+	1.95997i	−0.145238	+	0.105521i
$346$		0			0
$347$	1.19913	−	3.69054i	0.0643726	−	0.198119i	−0.913697	−	0.406396i	$-0.866786\pi$
$347$	1.19913	−	3.69054i	0.0643726	−	0.198119i	0.978070	+	0.208277i	$0.0667855\pi$
$348$		0			0
$349$	11.5900	−	15.9522i	0.620396	−	0.853903i	−0.376985	−	0.926219i	$-0.623039\pi$
$349$	11.5900	−	15.9522i	0.620396	−	0.853903i	0.997382	+	0.0723168i	$0.0230392\pi$
$350$		0			0
$351$	1.11124			0.0593137
$352$		0			0
$353$	−1.59623			−0.0849587			−0.0424794	−	0.999097i	$-0.513526\pi$
$353$	−1.59623			−0.0849587			−0.0424794	+	0.999097i	$0.513526\pi$
$354$		0			0
$355$	4.92929	−	6.78458i	0.261619	−	0.360088i
$356$		0			0
$357$	3.21998	−	9.91009i	0.170420	−	0.524497i
$358$		0			0
$359$	−12.4772	+	9.06523i	−0.658522	+	0.478445i	−0.866164	−	0.499760i	$-0.833421\pi$
$359$	−12.4772	+	9.06523i	−0.658522	+	0.478445i	0.207641	+	0.978205i	$0.433421\pi$
$360$		0			0
$361$	−4.96342	−	15.2758i	−0.261233	−	0.803991i
$362$		0			0
$363$	−11.4788	+	27.6176i	−0.602480	+	1.44955i
$364$		0			0
$365$	9.49912	−	3.08645i	0.497207	−	0.161552i
$366$		0			0
$367$	6.20229	+	8.53673i	0.323757	+	0.445613i	0.939610	−	0.342248i	$-0.111188\pi$
$367$	6.20229	+	8.53673i	0.323757	+	0.445613i	−0.615853	+	0.787861i	$0.711188\pi$
$368$		0			0
$369$	−23.3700	−	7.59337i	−1.21659	−	0.395295i
$370$		0			0
$371$	1.63882	+	1.19067i	0.0850831	+	0.0618165i
$372$		0			0
$373$		−	37.4953i		−	1.94143i	−0.240225	−	0.970717i	$-0.577221\pi$
$373$		−	37.4953i		−	1.94143i	0.240225	−	0.970717i	$-0.422779\pi$
$374$		0			0
$375$			28.9111i			1.49296i
$376$		0			0
$377$	1.95693	+	1.42179i	0.100787	+	0.0732259i
$378$		0			0
$379$	−20.2850	−	6.59100i	−1.04197	−	0.338557i	−0.262459	−	0.964943i	$-0.584533\pi$
$379$	−20.2850	−	6.59100i	−1.04197	−	0.338557i	−0.779513	+	0.626386i	$0.784533\pi$
$380$		0			0
$381$	31.9082	+	43.9179i	1.63471	+	2.24998i
$382$		0			0
$383$	−27.4201	+	8.90933i	−1.40110	+	0.455245i	−0.909547	−	0.415602i	$-0.863571\pi$
$383$	−27.4201	+	8.90933i	−1.40110	+	0.455245i	−0.491554	+	0.870847i	$0.663571\pi$
$384$		0			0
$385$	4.17691	+	9.07487i	0.212875	+	0.462498i
$386$		0			0
$387$	4.74300	+	14.5975i	0.241100	+	0.742031i
$388$		0			0
$389$	−28.2179	+	20.5015i	−1.43070	+	1.03947i	−0.440817	+	0.897597i	$0.645311\pi$
$389$	−28.2179	+	20.5015i	−1.43070	+	1.03947i	−0.989885	+	0.141869i	$0.954689\pi$
$390$		0			0
$391$	−0.482197	+	1.48405i	−0.0243858	+	0.0750516i
$392$		0			0
$393$	32.7835	−	45.1226i	1.65371	−	2.27614i
$394$		0			0
$395$	22.9780			1.15615
$396$		0			0
$397$	−16.9102			−0.848698			−0.424349	−	0.905499i	$-0.639497\pi$
$397$	−16.9102			−0.848698			−0.424349	+	0.905499i	$0.639497\pi$
$398$		0			0
$399$	3.53707	−	4.86836i	0.177075	−	0.243723i
$400$		0			0
$401$	4.90100	−	15.0837i	0.244744	−	0.753246i	−0.750934	−	0.660377i	$-0.770396\pi$
$401$	4.90100	−	15.0837i	0.244744	−	0.753246i	0.995678	−	0.0928687i	$-0.0296037\pi$
$402$		0			0
$403$	1.05562	−	0.766956i	0.0525844	−	0.0382048i
$404$		0			0
$405$	−2.07855	−	6.39712i	−0.103284	−	0.317876i
$406$		0			0
$407$	−12.7295	+	11.7527i	−0.630977	+	0.582561i
$408$		0			0
$409$	−26.3195	+	8.55173i	−1.30142	+	0.422856i	−0.876074	−	0.482176i	$-0.839846\pi$
$409$	−26.3195	+	8.55173i	−1.30142	+	0.422856i	−0.425343	+	0.905032i	$0.639846\pi$
$410$		0			0
$411$	−10.0130	−	13.7817i	−0.493904	−	0.679800i
$412$		0			0
$413$	−17.2832	−	5.61564i	−0.850449	−	0.276328i
$414$		0			0
$415$	−7.09568	−	5.15531i	−0.348313	−	0.253064i
$416$		0			0
$417$			36.6518i			1.79485i
$418$		0			0
$419$			22.9710i			1.12221i	0.827746	+	0.561103i	$0.189623\pi$
$419$			22.9710i			1.12221i	−0.827746	+	0.561103i	$0.810377\pi$
$420$		0			0
$421$	−24.3592	−	17.6980i	−1.18719	−	0.862546i	−0.194229	−	0.980956i	$-0.562220\pi$
$421$	−24.3592	−	17.6980i	−1.18719	−	0.862546i	−0.992965	+	0.118410i	$0.962220\pi$
$422$		0			0
$423$	31.9983	+	10.3969i	1.55581	+	0.505514i
$424$		0			0
$425$	−0.770618	−	1.06066i	−0.0373804	−	0.0514498i
$426$		0			0
$427$	−11.6010	+	3.76939i	−0.561411	+	0.182413i
$428$		0			0
$429$	−0.517923	+	2.59556i	−0.0250055	+	0.125315i
$430$		0			0
$431$	−3.14369	−	9.67528i	−0.151426	−	0.466042i	0.846355	−	0.532619i	$-0.178792\pi$
$431$	−3.14369	−	9.67528i	−0.151426	−	0.466042i	−0.997781	+	0.0665771i	$0.978792\pi$
$432$		0			0
$433$	−22.2763	+	16.1847i	−1.07053	+	0.777785i	−0.976007	−	0.217737i	$-0.930132\pi$
$433$	−22.2763	+	16.1847i	−1.07053	+	0.777785i	−0.0945224	+	0.995523i	$0.530132\pi$
$434$		0			0
$435$	−16.1527	+	49.7130i	−0.774464	+	2.38356i
$436$		0			0
$437$	−0.529682	+	0.729044i	−0.0253381	+	0.0348749i
$438$		0			0
$439$	11.5438			0.550957			0.275479	−	0.961307i	$-0.411164\pi$
$439$	11.5438			0.550957			0.275479	+	0.961307i	$0.411164\pi$
$440$		0			0
$441$	23.4241			1.11543
$442$		0			0
$443$	−9.98691	+	13.7458i	−0.474492	+	0.653083i	−0.977435	−	0.211237i	$-0.932251\pi$
$443$	−9.98691	+	13.7458i	−0.474492	+	0.653083i	0.502942	+	0.864320i	$0.332251\pi$
$444$		0			0
$445$	0.431183	−	1.32704i	0.0204400	−	0.0629080i
$446$		0			0
$447$	38.3841	−	27.8877i	1.81551	−	1.31904i
$448$		0			0
$449$	1.89015	+	5.81730i	0.0892019	+	0.274535i	0.985699	−	0.168514i	$-0.0538968\pi$
$449$	1.89015	+	5.81730i	0.0892019	+	0.274535i	−0.896497	+	0.443049i	$0.853897\pi$
$450$		0			0
$451$	9.07566	−	16.1828i	0.427356	−	0.762017i
$452$		0			0
$453$	25.4046	−	8.25445i	1.19361	−	0.387828i
$454$		0			0
$455$	0.519642	+	0.715226i	0.0243612	+	0.0335303i
$456$		0			0
$457$	−6.20446	−	2.01595i	−0.290232	−	0.0943022i	0.160282	−	0.987071i	$-0.448760\pi$
$457$	−6.20446	−	2.01595i	−0.290232	−	0.0943022i	−0.450515	+	0.892769i	$0.648760\pi$
$458$		0			0
$459$	9.09126	+	6.60518i	0.424344	+	0.308304i
$460$		0			0
$461$			19.0882i			0.889026i	0.895773	+	0.444513i	$0.146623\pi$
$461$			19.0882i			0.889026i	−0.895773	+	0.444513i	$0.853377\pi$
$462$		0			0
$463$			13.0359i			0.605829i	0.953018	+	0.302915i	$0.0979597\pi$
$463$			13.0359i			0.605829i	−0.953018	+	0.302915i	$0.902040\pi$
$464$		0			0
$465$	22.8116	+	16.5736i	1.05786	+	0.768583i
$466$		0			0
$467$	14.4349	+	4.69019i	0.667969	+	0.217036i	0.623320	−	0.781967i	$-0.285783\pi$
$467$	14.4349	+	4.69019i	0.667969	+	0.217036i	0.0446484	+	0.999003i	$0.485783\pi$
$468$		0			0
$469$	7.91210	+	10.8901i	0.365347	+	0.502857i
$470$		0			0
$471$	−39.8326	+	12.9424i	−1.83539	+	0.596355i
$472$		0			0
$473$	−11.5097	+	1.35520i	−0.529219	+	0.0623122i
$474$		0			0
$475$	−0.233968	−	0.720080i	−0.0107352	−	0.0330395i
$476$		0			0
$477$	−5.57496	+	4.05045i	−0.255260	+	0.185457i
$478$		0			0
$479$	8.09752	−	24.9216i	0.369985	−	1.13870i	−0.576815	−	0.816875i	$-0.695705\pi$
$479$	8.09752	−	24.9216i	0.369985	−	1.13870i	0.946800	−	0.321822i	$-0.104295\pi$
$480$		0			0
$481$	−0.901199	+	1.24039i	−0.0410911	+	0.0565571i
$482$		0			0
$483$	1.84571			0.0839827
$484$		0			0
$485$	−19.4230			−0.881954
$486$		0			0
$487$	16.0181	−	22.0471i	0.725851	−	0.999048i	−0.273458	−	0.961884i	$-0.588168\pi$
$487$	16.0181	−	22.0471i	0.725851	−	0.999048i	0.999309	−	0.0371640i	$-0.0118324\pi$
$488$		0			0
$489$	−9.04656	+	27.8424i	−0.409099	+	1.25908i
$490$		0			0
$491$	17.3230	−	12.5859i	0.781778	−	0.567995i	−0.123734	−	0.992315i	$-0.539487\pi$
$491$	17.3230	−	12.5859i	0.781778	−	0.567995i	0.905512	+	0.424320i	$0.139487\pi$
$492$		0			0
$493$	7.55888	+	23.2638i	0.340435	+	1.04775i
$494$		0			0
$495$	−33.7510	+	3.97397i	−1.51699	+	0.178617i
$496$		0			0
$497$	−4.41473	+	1.43443i	−0.198028	+	0.0643431i
$498$		0			0
$499$	−18.1317	−	24.9561i	−0.811685	−	1.11719i	−0.991061	−	0.133408i	$-0.957408\pi$
$499$	−18.1317	−	24.9561i	−0.811685	−	1.11719i	0.179376	−	0.983781i	$-0.442592\pi$
$500$		0			0
$501$	16.6063	+	5.39573i	0.741917	+	0.241063i
$502$		0			0
$503$	25.6773	+	18.6557i	1.14489	+	0.831815i	0.987794	−	0.155768i	$-0.0497852\pi$
$503$	25.6773	+	18.6557i	1.14489	+	0.831815i	0.157101	+	0.987583i	$0.449785\pi$
$504$		0			0
$505$		−	17.9219i		−	0.797515i
$506$		0			0
$507$		−	35.1117i		−	1.55936i
$508$		0			0
$509$	5.41179	+	3.93190i	0.239873	+	0.174278i	0.701227	−	0.712938i	$-0.252636\pi$
$509$	5.41179	+	3.93190i	0.239873	+	0.174278i	−0.461354	+	0.887216i	$0.652636\pi$
$510$		0			0
$511$	−5.25794	−	1.70841i	−0.232598	−	0.0755756i
$512$		0			0
$513$	3.81451	+	5.25022i	0.168415	+	0.231803i
$514$		0			0
$515$	0.914922	−	0.297276i	0.0403163	−	0.0130995i
$516$		0			0
$517$	−12.4265	+	22.1575i	−0.546515	+	0.974488i
$518$		0			0
$519$	3.03967	+	9.35513i	0.133426	+	0.410645i
$520$		0			0
$521$	−10.0067	+	7.27028i	−0.438401	+	0.318517i	−0.784999	−	0.619497i	$-0.787337\pi$
$521$	−10.0067	+	7.27028i	−0.438401	+	0.318517i	0.346598	+	0.938014i	$0.387337\pi$
$522$		0			0
$523$	−1.92840	+	5.93501i	−0.0843231	+	0.259520i	−0.984324	−	0.176367i	$-0.943565\pi$
$523$	−1.92840	+	5.93501i	−0.0843231	+	0.259520i	0.900001	+	0.435887i	$0.143565\pi$
$524$		0			0
$525$	−0.911507	+	1.25458i	−0.0397814	+	0.0547545i
$526$		0			0
$527$	13.1950			0.574784
$528$		0			0
$529$	22.7236			0.987983
$530$		0			0
$531$	36.3368	−	50.0134i	1.57688	−	2.17039i
$532$		0			0
$533$	0.507388	−	1.56158i	0.0219774	−	0.0676395i
$534$		0			0
$535$	−9.76811	+	7.09695i	−0.422312	+	0.306828i
$536$		0			0
$537$	−4.20746	−	12.9492i	−0.181565	−	0.558800i
$538$		0			0
$539$	−3.46101	+	17.3448i	−0.149076	+	0.747093i
$540$		0			0
$541$	−24.6331	+	8.00377i	−1.05906	+	0.344109i	−0.786217	−	0.617950i	$-0.787963\pi$
$541$	−24.6331	+	8.00377i	−1.05906	+	0.344109i	−0.272841	+	0.962059i	$0.587963\pi$
$542$		0			0
$543$	−15.6649	−	21.5608i	−0.672244	−	0.925264i
$544$		0			0
$545$	−27.9425	−	9.07907i	−1.19693	−	0.388905i
$546$		0			0
$547$	13.5035	+	9.81087i	0.577368	+	0.419482i	0.837774	−	0.546017i	$-0.183857\pi$
$547$	13.5035	+	9.81087i	0.577368	+	0.419482i	−0.260406	+	0.965499i	$0.583857\pi$
$548$		0			0
$549$		−	41.4954i		−	1.77098i
$550$		0			0
$551$			14.1263i			0.601801i
$552$		0			0
$553$	−10.2897	−	7.47589i	−0.437562	−	0.317907i
$554$		0			0
$555$	−31.5105	−	10.2384i	−1.33755	−	0.434595i
$556$		0			0
$557$	10.9144	+	15.0224i	0.462460	+	0.636522i	0.975017	−	0.222132i	$-0.0713015\pi$
$557$	10.9144	+	15.0224i	0.462460	+	0.636522i	−0.512557	+	0.858653i	$0.671302\pi$
$558$		0			0
$559$	−0.975400	+	0.316927i	−0.0412550	+	0.0134046i
$560$		0			0
$561$	−19.6651	+	18.1562i	−0.830262	+	0.766555i
$562$		0			0
$563$	−7.00832	−	21.5694i	−0.295366	−	0.909042i	−0.983098	−	0.183078i	$-0.941394\pi$
$563$	−7.00832	−	21.5694i	−0.295366	−	0.909042i	0.687733	−	0.725964i	$-0.258606\pi$
$564$		0			0
$565$	5.02144	−	3.64829i	0.211253	−	0.153485i
$566$		0			0
$567$	−1.15052	+	3.54093i	−0.0483172	+	0.148705i
$568$		0			0
$569$	0.0874036	−	0.120301i	0.00366415	−	0.00504327i	−0.807181	−	0.590304i	$-0.799008\pi$
$569$	0.0874036	−	0.120301i	0.00366415	−	0.00504327i	0.810845	+	0.585261i	$0.199008\pi$
$570$		0			0
$571$	22.0331			0.922057			0.461028	−	0.887385i	$-0.347481\pi$
$571$	22.0331			0.922057			0.461028	+	0.887385i	$0.347481\pi$
$572$		0			0
$573$	−31.7832			−1.32776
$574$		0			0
$575$	0.136500	−	0.187876i	0.00569242	−	0.00783495i
$576$		0			0
$577$	1.21706	−	3.74573i	0.0506669	−	0.155937i	−0.922522	−	0.385945i	$-0.873875\pi$
$577$	1.21706	−	3.74573i	0.0506669	−	0.155937i	0.973189	+	0.230008i	$0.0738754\pi$
$578$		0			0
$579$	2.53966	−	1.84517i	0.105545	−	0.0766827i
$580$		0			0
$581$	1.50021	+	4.61716i	0.0622391	+	0.191552i
$582$		0			0
$583$	−2.17550	−	4.72655i	−0.0901000	−	0.195754i
$584$		0			0
$585$	−2.86025	+	0.929350i	−0.118257	+	0.0384239i
$586$		0			0
$587$	−11.1451	−	15.3399i	−0.460006	−	0.633144i	0.514504	−	0.857488i	$-0.327976\pi$
$587$	−11.1451	−	15.3399i	−0.460006	−	0.633144i	−0.974510	+	0.224344i	$0.927976\pi$
$588$		0			0
$589$	7.24720	+	2.35476i	0.298616	+	0.0970261i
$590$		0			0
$591$	−34.3690	−	24.9706i	−1.41375	−	1.02715i
$592$		0			0
$593$			31.9983i			1.31401i	0.753885	+	0.657007i	$0.228178\pi$
$593$			31.9983i			1.31401i	−0.753885	+	0.657007i	$0.771822\pi$
$594$		0			0
$595$			8.94012i			0.366509i
$596$		0			0
$597$	24.1265	+	17.5290i	0.987433	+	0.717412i
$598$		0			0
$599$	−8.23336	−	2.67518i	−0.336406	−	0.109305i	0.135943	−	0.990717i	$-0.456594\pi$
$599$	−8.23336	−	2.67518i	−0.336406	−	0.109305i	−0.472349	+	0.881412i	$0.656594\pi$
$600$		0			0
$601$	−12.9491	−	17.8228i	−0.528203	−	0.727009i	0.458652	−	0.888616i	$-0.348332\pi$
$601$	−12.9491	−	17.8228i	−0.528203	−	0.727009i	−0.986855	+	0.161607i	$0.948332\pi$
$602$		0			0
$603$	−43.5503	+	14.1503i	−1.77350	+	0.576246i
$604$		0			0
$605$	2.04426	−	25.5787i	0.0831110	−	1.03992i
$606$		0			0
$607$	−13.2005	−	40.6268i	−0.535790	−	1.64899i	−0.741936	−	0.670471i	$-0.766092\pi$
$607$	−13.2005	−	40.6268i	−0.535790	−	1.64899i	0.206146	−	0.978521i	$-0.433908\pi$
$608$		0			0
$609$	23.4074	−	17.0065i	0.948517	−	0.689138i
$610$		0			0
$611$	−0.694718	+	2.13812i	−0.0281053	+	0.0864992i
$612$		0			0
$613$	5.74748	−	7.91073i	0.232139	−	0.319511i	−0.677018	−	0.735967i	$-0.736728\pi$
$613$	5.74748	−	7.91073i	0.232139	−	0.319511i	0.909156	+	0.416456i	$0.136728\pi$
$614$		0			0
$615$	35.4817			1.43076
$616$		0			0
$617$	−22.4213			−0.902649			−0.451324	−	0.892360i	$-0.649048\pi$
$617$	−22.4213			−0.902649			−0.451324	+	0.892360i	$0.649048\pi$
$618$		0			0
$619$	−11.3322	+	15.5975i	−0.455481	+	0.626916i	−0.973564	−	0.228414i	$-0.926646\pi$
$619$	−11.3322	+	15.5975i	−0.455481	+	0.626916i	0.518083	+	0.855331i	$0.326646\pi$
$620$		0			0
$621$	−0.615093	+	1.89306i	−0.0246828	+	0.0759660i
$622$		0			0
$623$	−0.624841	+	0.453973i	−0.0250337	+	0.0181881i
$624$		0			0
$625$	−8.34762	−	25.6913i	−0.333905	−	1.02765i
$626$		0			0
$627$	−14.0409	+	6.46266i	−0.560741	+	0.258094i
$628$		0			0
$629$	−14.7457	+	4.79118i	−0.587951	+	0.191037i
$630$		0			0
$631$	−22.5021	−	30.9715i	−0.895794	−	1.23296i	−0.971790	−	0.235847i	$-0.924214\pi$
$631$	−22.5021	−	30.9715i	−0.895794	−	1.23296i	0.0759958	−	0.997108i	$-0.475786\pi$
$632$		0			0
$633$	49.9163	+	16.2188i	1.98400	+	0.644639i
$634$		0			0
$635$	−37.6803	−	27.3763i	−1.49530	−	1.08640i
$636$		0			0
$637$			1.56519i			0.0620153i
$638$		0			0
$639$		−	15.7910i		−	0.624682i
$640$		0			0
$641$	25.5946	+	18.5955i	1.01092	+	0.734480i	0.964403	−	0.264438i	$-0.0851864\pi$
$641$	25.5946	+	18.5955i	1.01092	+	0.734480i	0.0465216	+	0.998917i	$0.485186\pi$
$642$		0			0
$643$	14.1716	+	4.60464i	0.558874	+	0.181589i	0.574814	−	0.818284i	$-0.305074\pi$
$643$	14.1716	+	4.60464i	0.558874	+	0.181589i	−0.0159405	+	0.999873i	$0.505074\pi$
$644$		0			0
$645$	−13.0269	−	17.9300i	−0.512934	−	0.705993i
$646$		0			0
$647$	39.0933	−	12.7022i	1.53692	−	0.499374i	0.586393	−	0.810027i	$-0.300548\pi$
$647$	39.0933	−	12.7022i	1.53692	−	0.499374i	0.950523	+	0.310653i	$0.100548\pi$
$648$		0			0
$649$	31.6643	+	34.2959i	1.24293	+	1.34623i
$650$		0			0
$651$	−4.82296	−	14.8435i	−0.189027	−	0.581764i
$652$		0			0
$653$	3.70761	−	2.69374i	0.145090	−	0.105414i	−0.512872	−	0.858465i	$-0.671419\pi$
$653$	3.70761	−	2.69374i	0.145090	−	0.105414i	0.657962	+	0.753051i	$0.271419\pi$
$654$		0			0
$655$	−14.7874	+	45.5109i	−0.577791	+	1.77826i
$656$		0			0
$657$	11.0545	−	15.2152i	0.431278	−	0.593603i
$658$		0			0
$659$	38.0732			1.48312			0.741560	−	0.670886i	$-0.234086\pi$
$659$	38.0732			1.48312			0.741560	+	0.670886i	$0.234086\pi$
$660$		0			0
$661$	9.34038			0.363299			0.181649	−	0.983363i	$-0.441856\pi$
$661$	9.34038			0.363299			0.181649	+	0.983363i	$0.441856\pi$
$662$		0			0
$663$	−1.39222	+	1.91622i	−0.0540692	+	0.0744198i
$664$		0			0
$665$	−1.59544	+	4.91025i	−0.0618684	+	0.190411i
$666$		0			0
$667$	−3.50530	+	2.54675i	−0.135726	+	0.0986104i
$668$		0			0
$669$	−9.10685	−	28.0280i	−0.352091	−	1.08363i
$670$		0			0
$671$	30.7260	+	6.13113i	1.18616	+	0.236689i
$672$		0			0
$673$	13.4864	−	4.38199i	0.519862	−	0.168913i	−0.0373208	−	0.999303i	$-0.511882\pi$
$673$	13.4864	−	4.38199i	0.519862	−	0.168913i	0.557183	+	0.830390i	$0.311882\pi$
$674$		0			0
$675$	−0.983004	−	1.35299i	−0.0378358	−	0.0520766i
$676$		0			0
$677$	4.48196	+	1.45628i	0.172256	+	0.0559692i	0.393875	−	0.919164i	$-0.371134\pi$
$677$	4.48196	+	1.45628i	0.172256	+	0.0559692i	−0.221619	+	0.975133i	$0.571134\pi$
$678$		0			0
$679$	8.69775	+	6.31929i	0.333789	+	0.242512i
$680$		0			0
$681$		−	65.2454i		−	2.50021i
$682$		0			0
$683$			18.0462i			0.690519i	0.938507	+	0.345260i	$0.112209\pi$
$683$			18.0462i			0.690519i	−0.938507	+	0.345260i	$0.887791\pi$
$684$		0			0
$685$	11.8243	+	8.59084i	0.451782	+	0.328239i
$686$		0			0
$687$	−63.5633	−	20.6530i	−2.42509	−	0.787960i
$688$		0			0
$689$	−0.270650	−	0.372518i	−0.0103109	−	0.0141918i
$690$		0			0
$691$	−1.27888	+	0.415533i	−0.0486509	+	0.0158076i	−0.333241	−	0.942842i	$-0.608142\pi$
$691$	−1.27888	+	0.415533i	−0.0486509	+	0.0158076i	0.284590	+	0.958649i	$0.408142\pi$
$692$		0			0
$693$	16.4068	+	9.20132i	0.623244	+	0.349529i
$694$		0			0
$695$	−9.71740	−	29.9071i	−0.368602	−	1.13444i
$696$		0			0
$697$	13.4330	−	9.75964i	0.508811	−	0.369673i
$698$		0			0
$699$	12.0187	−	36.9896i	0.454587	−	1.39908i
$700$		0			0
$701$	9.79382	−	13.4800i	0.369907	−	0.509134i	−0.582968	−	0.812495i	$-0.698109\pi$
$701$	9.79382	−	13.4800i	0.369907	−	0.509134i	0.952876	+	0.303361i	$0.0981088\pi$
$702$		0			0
$703$	−8.95393			−0.337704
$704$		0			0
$705$	−48.5817			−1.82969
$706$		0			0
$707$	−5.83090	+	8.02554i	−0.219293	+	0.301832i
$708$		0			0
$709$	−7.43557	+	22.8843i	−0.279249	+	0.859440i	0.708815	+	0.705394i	$0.249230\pi$
$709$	−7.43557	+	22.8843i	−0.279249	+	0.859440i	−0.988064	+	0.154045i	$0.950770\pi$
$710$		0			0
$711$	35.0036	−	25.4316i	1.31274	−	0.953761i
$712$		0			0
$713$	0.722245	+	2.22284i	0.0270483	+	0.0832460i
$714$		0			0
$715$	−0.265540	−	2.25523i	−0.00993063	−	0.0843410i
$716$		0			0
$717$	51.1063	−	16.6054i	1.90860	−	0.620141i
$718$		0			0
$719$	6.65923	+	9.16564i	0.248347	+	0.341821i	0.914932	−	0.403609i	$-0.132244\pi$
$719$	6.65923	+	9.16564i	0.248347	+	0.341821i	−0.666584	+	0.745430i	$0.732244\pi$
$720$		0			0
$721$	−0.506426	−	0.164548i	−0.0188603	−	0.00612808i
$722$		0			0
$723$	14.3649	+	10.4367i	0.534237	+	0.388146i
$724$		0			0
$725$		−	3.64037i		−	0.135200i
$726$		0			0
$727$			0.700673i			0.0259865i	0.999916	+	0.0129933i	$0.00413600\pi$
$727$			0.700673i			0.0259865i	−0.999916	+	0.0129933i	$0.995864\pi$
$728$		0			0
$729$	−35.2308	−	25.5967i	−1.30485	−	0.948026i
$730$		0			0
$731$	−9.86371	−	3.20491i	−0.364823	−	0.118538i
$732$		0			0
$733$	−17.6206	−	24.2526i	−0.650830	−	0.895790i	0.348305	−	0.937381i	$-0.386757\pi$
$733$	−17.6206	−	24.2526i	−0.650830	−	0.895790i	−0.999135	+	0.0415908i	$0.986757\pi$
$734$		0			0
$735$	−32.1678	+	10.4519i	−1.18653	+	0.385526i
$736$		0			0
$737$	−4.04313	−	34.3383i	−0.148930	−	1.26487i
$738$		0			0
$739$	−13.4812	−	41.4910i	−0.495915	−	1.52627i	−0.815526	−	0.578721i	$-0.803552\pi$
$739$	−13.4812	−	41.4910i	−0.495915	−	1.52627i	0.319611	−	0.947549i	$-0.396448\pi$
$740$		0			0
$741$	−1.10662	+	0.804008i	−0.0406528	+	0.0295360i
$742$		0			0
$743$	−10.5703	+	32.5321i	−0.387788	+	1.19349i	0.546650	+	0.837361i	$0.315903\pi$
$743$	−10.5703	+	32.5321i	−0.387788	+	1.19349i	−0.934438	+	0.356127i	$0.884097\pi$
$744$		0			0
$745$	−23.9268	+	32.9324i	−0.876610	+	1.20655i
$746$		0			0
$747$	−16.5151			−0.604255
$748$		0			0
$749$	6.68321			0.244199
$750$		0			0
$751$	−0.851372	+	1.17181i	−0.0310670	+	0.0427600i	−0.824268	−	0.566200i	$-0.808413\pi$
$751$	−0.851372	+	1.17181i	−0.0310670	+	0.0427600i	0.793201	+	0.608960i	$0.208413\pi$
$752$		0			0
$753$	−4.00819	+	12.3359i	−0.146067	+	0.449546i
$754$		0			0
$755$	−18.5411	+	13.4709i	−0.674780	+	0.490257i
$756$		0			0
$757$	−9.41100	−	28.9641i	−0.342049	−	1.05272i	−0.963145	−	0.268983i	$-0.913312\pi$
$757$	−9.41100	−	28.9641i	−0.342049	−	1.05272i	0.621096	−	0.783734i	$-0.286688\pi$
$758$		0			0
$759$	−4.13500	−	2.31900i	−0.150091	−	0.0841744i
$760$		0			0
$761$	22.8716	−	7.43142i	0.829094	−	0.269389i	0.136430	−	0.990650i	$-0.456437\pi$
$761$	22.8716	−	7.43142i	0.829094	−	0.269389i	0.692664	+	0.721261i	$0.256437\pi$
$762$		0			0
$763$	9.55895	+	13.1568i	0.346057	+	0.476307i
$764$		0			0
$765$	−28.9242	−	9.39804i	−1.04576	−	0.339787i
$766$		0			0
$767$	3.34188	+	2.42802i	0.120668	+	0.0876707i
$768$		0			0
$769$		−	14.6461i		−	0.528151i	−0.964502	−	0.264076i	$-0.914933\pi$
$769$		−	14.6461i		−	0.528151i	0.964502	−	0.264076i	$-0.0850669\pi$
$770$		0			0
$771$			8.25715i			0.297374i
$772$		0			0
$773$	−21.4727	−	15.6009i	−0.772320	−	0.561124i	0.130344	−	0.991469i	$-0.458392\pi$
$773$	−21.4727	−	15.6009i	−0.772320	−	0.561124i	−0.902664	+	0.430345i	$0.858392\pi$
$774$		0			0
$775$	−1.86761	−	0.606824i	−0.0670866	−	0.0217977i
$776$		0			0
$777$	10.7795	+	14.8367i	0.386713	+	0.532265i
$778$		0			0
$779$	9.11960	−	2.96314i	0.326743	−	0.106165i
$780$		0			0
$781$	11.6927	+	2.33319i	0.418398	+	0.0834880i
$782$		0			0
$783$	9.64214	+	29.6755i	0.344582	+	1.06051i
$784$		0			0
$785$	29.0712	−	21.1214i	1.03759	−	0.753857i
$786$		0			0
$787$	6.33834	−	19.5074i	0.225937	−	0.695364i	−0.772258	−	0.635309i	$-0.780873\pi$
$787$	6.33834	−	19.5074i	0.225937	−	0.695364i	0.998195	−	0.0600544i	$-0.0191274\pi$
$788$		0			0
$789$	−22.6410	+	31.1626i	−0.806040	+	1.10942i
$790$		0			0
$791$	−3.43560			−0.122156
$792$		0			0
$793$	2.77271			0.0984620
$794$		0			0
$795$	5.84864	−	8.04996i	0.207430	−	0.285503i
$796$		0			0
$797$	10.1514	−	31.2427i	0.359580	−	1.10667i	−0.593726	−	0.804667i	$-0.702344\pi$
$797$	10.1514	−	31.2427i	0.359580	−	1.10667i	0.953306	−	0.302006i	$-0.0976564\pi$
$798$		0			0
$799$	−18.3925	+	13.3630i	−0.650682	+	0.472748i
$800$		0			0
$801$	−0.811905	−	2.49879i	−0.0286873	−	0.0882903i
$802$		0			0
$803$	9.63304	+	10.4336i	0.339942	+	0.368195i
$804$		0			0
$805$	−1.50606	+	0.489348i	−0.0530816	+	0.0172473i
$806$		0			0
$807$	−1.60094	−	2.20350i	−0.0563557	−	0.0775670i
$808$		0			0
$809$	17.7783	+	5.77654i	0.625053	+	0.203092i	0.604383	−	0.796694i	$-0.293420\pi$
$809$	17.7783	+	5.77654i	0.625053	+	0.203092i	0.0206708	+	0.999786i	$0.493420\pi$
$810$		0			0
$811$	−22.1490	−	16.0922i	−0.777758	−	0.565074i	0.126547	−	0.991961i	$-0.459610\pi$
$811$	−22.1490	−	16.0922i	−0.777758	−	0.565074i	−0.904305	+	0.426886i	$0.859610\pi$
$812$		0			0
$813$			48.3724i			1.69650i
$814$		0			0
$815$		−	25.1173i		−	0.879821i
$816$		0			0
$817$	−4.84558	−	3.52052i	−0.169525	−	0.123167i
$818$		0			0
$819$	1.58320	+	0.514413i	0.0553215	+	0.0179750i
$820$		0			0
$821$	−5.06427	−	6.97036i	−0.176744	−	0.243267i	0.711449	−	0.702738i	$-0.248039\pi$
$821$	−5.06427	−	6.97036i	−0.176744	−	0.243267i	−0.888193	+	0.459470i	$0.848039\pi$
$822$		0			0
$823$	3.63990	−	1.18267i	0.126879	−	0.0412254i	−0.244889	−	0.969551i	$-0.578752\pi$
$823$	3.63990	−	1.18267i	0.126879	−	0.0412254i	0.371768	+	0.928326i	$0.378752\pi$
$824$		0			0
$825$	3.61837	−	1.66543i	0.125975	−	0.0579830i
$826$		0			0
$827$	−8.45284	−	26.0152i	−0.293934	−	0.904636i	−0.983577	−	0.180487i	$-0.942233\pi$
$827$	−8.45284	−	26.0152i	−0.293934	−	0.904636i	0.689643	−	0.724149i	$-0.257767\pi$
$828$		0			0
$829$	14.2443	−	10.3491i	0.494723	−	0.359438i	−0.312274	−	0.949992i	$-0.601091\pi$
$829$	14.2443	−	10.3491i	0.494723	−	0.359438i	0.806998	+	0.590554i	$0.201091\pi$
$830$		0			0
$831$	16.2885	−	50.1309i	0.565043	−	1.73902i
$832$		0			0
$833$	−9.30347	+	12.8051i	−0.322346	+	0.443671i
$834$		0			0
$835$	−14.9810			−0.518438
$836$		0			0
$837$	16.8316			0.581786
$838$		0			0
$839$	0.148971	−	0.205041i	0.00514306	−	0.00707881i	−0.806438	−	0.591319i	$-0.798607\pi$
$839$	0.148971	−	0.205041i	0.00514306	−	0.00707881i	0.811581	+	0.584240i	$0.198607\pi$
$840$		0			0
$841$	−12.0270	+	37.0154i	−0.414726	+	1.27639i
$842$		0			0
$843$	32.3268	−	23.4868i	1.11340	−	0.808929i
$844$		0			0
$845$	9.30907	+	28.6504i	0.320242	+	0.985603i
$846$		0			0
$847$	−9.23746	+	10.7892i	−0.317403	+	0.370721i
$848$		0			0
$849$	6.45654	−	2.09786i	0.221588	−	0.0719983i
$850$		0			0
$851$	−1.61425	−	2.22182i	−0.0553358	−	0.0761632i
$852$		0			0
$853$	35.2985	+	11.4692i	1.20860	+	0.392697i	0.842917	−	0.538044i	$-0.180837\pi$
$853$	35.2985	+	11.4692i	1.20860	+	0.392697i	0.365680	+	0.930741i	$0.380837\pi$
$854$		0			0
$855$	−14.2091	−	10.3235i	−0.485941	−	0.353057i
$856$		0			0
$857$			20.9360i			0.715161i	0.933882	+	0.357580i	$0.116398\pi$
$857$			20.9360i			0.715161i	−0.933882	+	0.357580i	$0.883602\pi$
$858$		0			0
$859$			20.6926i			0.706022i	0.935619	+	0.353011i	$0.114842\pi$
$859$			20.6926i			0.706022i	−0.935619	+	0.353011i	$0.885158\pi$
$860$		0			0
$861$	−15.8889	−	11.5440i	−0.541493	−	0.393417i
$862$		0			0
$863$	35.9307	+	11.6746i	1.22309	+	0.397408i	0.848208	−	0.529663i	$-0.177682\pi$
$863$	35.9307	+	11.6746i	1.22309	+	0.397408i	0.374887	+	0.927071i	$0.377682\pi$
$864$		0			0
$865$	−4.96060	−	6.82768i	−0.168666	−	0.232148i
$866$		0			0
$867$	21.1794	−	6.88161i	0.719290	−	0.233712i
$868$		0			0
$869$	13.6594	+	29.6767i	0.463362	+	1.00671i
$870$		0			0
$871$	−0.945523	−	2.91002i	−0.0320378	−	0.0986023i
$872$		0			0
$873$	−29.5882	+	21.4971i	−1.00141	+	0.727566i
$874$		0			0
$875$	−4.24279	+	13.0580i	−0.143433	+	0.441440i
$876$		0			0
$877$	−6.81007	+	9.37325i	−0.229960	+	0.316512i	−0.908367	−	0.418173i	$-0.862670\pi$
$877$	−6.81007	+	9.37325i	−0.229960	+	0.316512i	0.678408	+	0.734686i	$0.262670\pi$
$878$		0			0
$879$	20.4432			0.689532
$880$		0			0
$881$	−24.6157			−0.829325			−0.414662	−	0.909975i	$-0.636100\pi$
$881$	−24.6157			−0.829325			−0.414662	+	0.909975i	$0.636100\pi$
$882$		0			0
$883$	−23.0095	+	31.6699i	−0.774333	+	1.06578i	0.221552	+	0.975149i	$0.428888\pi$
$883$	−23.0095	+	31.6699i	−0.774333	+	1.06578i	−0.995885	+	0.0906289i	$0.971112\pi$
$884$		0			0
$885$	−27.5843	+	84.8959i	−0.927237	+	2.85374i
$886$		0			0
$887$	−38.4919	+	27.9660i	−1.29243	+	0.939006i	−0.999851	−	0.0172350i	$-0.994514\pi$
$887$	−38.4919	+	27.9660i	−1.29243	+	0.939006i	−0.292580	+	0.956241i	$0.594514\pi$
$888$		0			0
$889$	7.96657	+	24.5186i	0.267190	+	0.822326i
$890$		0			0
$891$	7.02646	−	6.48731i	0.235395	−	0.217333i
$892$		0			0
$893$	−12.4866	+	4.05715i	−0.417848	+	0.135767i
$894$		0			0
$895$	6.86639	+	9.45077i	0.229518	+	0.315904i
$896$		0			0
$897$	−0.399012	−	0.129647i	−0.0133226	−	0.00432879i
$898$		0			0
$899$	29.6410	+	21.5354i	0.988581	+	0.718246i
$900$		0			0
$901$		−	4.65637i		−	0.155126i
$902$		0			0
$903$			12.2675i			0.408236i
$904$		0			0
$905$	18.4986	+	13.4400i	0.614913	+	0.446760i
$906$		0			0
$907$	−3.43208	−	1.11515i	−0.113960	−	0.0370279i	0.251482	−	0.967862i	$-0.419082\pi$
$907$	−3.43208	−	1.11515i	−0.113960	−	0.0370279i	−0.365442	+	0.930834i	$0.619082\pi$
$908$		0			0
$909$	−19.8357	−	27.3015i	−0.657908	−	0.905532i
$910$		0			0
$911$	29.8894	−	9.71164i	0.990278	−	0.321761i	0.231304	−	0.972881i	$-0.425701\pi$
$911$	29.8894	−	9.71164i	0.990278	−	0.321761i	0.758974	+	0.651121i	$0.225701\pi$
$912$		0			0
$913$	2.44017	−	12.2289i	0.0807579	−	0.404716i
$914$		0			0
$915$	18.5154	+	56.9847i	0.612102	+	1.88386i
$916$		0			0
$917$	21.4289	−	15.5690i	0.707643	−	0.514133i
$918$		0			0
$919$	8.08812	−	24.8927i	0.266802	−	0.821133i	−0.724470	−	0.689306i	$-0.757916\pi$
$919$	8.08812	−	24.8927i	0.266802	−	0.821133i	0.991273	−	0.131827i	$-0.0420845\pi$
$920$		0			0
$921$	−41.2305	+	56.7489i	−1.35859	+	1.86994i
$922$		0			0
$923$	1.05515			0.0347307
$924$		0			0
$925$	2.30744			0.0758681
$926$		0			0
$927$	1.06473	−	1.46548i	0.0349704	−	0.0481326i
$928$		0			0
$929$	8.71671	−	26.8273i	0.285986	−	0.880175i	−0.700115	−	0.714030i	$-0.746868\pi$
$929$	8.71671	−	26.8273i	0.285986	−	0.880175i	0.986101	−	0.166145i	$-0.0531320\pi$
$930$		0			0
$931$	−7.39499	+	5.37278i	−0.242361	+	0.176086i
$932$		0			0
$933$	−2.49063	−	7.66538i	−0.0815397	−	0.250953i
$934$		0			0
$935$	11.2326	−	20.0288i	0.367346	−	0.655013i
$936$		0			0
$937$	20.4298	−	6.63805i	0.667413	−	0.216856i	0.0443365	−	0.999017i	$-0.485883\pi$
$937$	20.4298	−	6.63805i	0.667413	−	0.216856i	0.623076	+	0.782161i	$0.285883\pi$
$938$		0			0
$939$	0.965265	+	1.32857i	0.0315002	+	0.0433563i
$940$		0			0
$941$	−27.2146	−	8.84257i	−0.887172	−	0.288260i	−0.170240	−	0.985403i	$-0.554454\pi$
$941$	−27.2146	−	8.84257i	−0.887172	−	0.288260i	−0.716932	+	0.697143i	$0.754454\pi$
$942$		0			0
$943$	2.37939	+	1.72873i	0.0774835	+	0.0562951i
$944$		0			0
$945$			11.4041i			0.370974i
$946$		0			0
$947$			0.894236i			0.0290588i	0.999894	+	0.0145294i	$0.00462501\pi$
$947$			0.894236i			0.0290588i	−0.999894	+	0.0145294i	$0.995375\pi$
$948$		0			0
$949$	1.01668	+	0.738661i	0.0330028	+	0.0239779i
$950$		0			0
$951$	59.3333	+	19.2786i	1.92402	+	0.625150i
$952$		0			0
$953$	−5.07423	−	6.98407i	−0.164370	−	0.226236i	0.718885	−	0.695129i	$-0.244653\pi$
$953$	−5.07423	−	6.98407i	−0.164370	−	0.226236i	−0.883255	+	0.468893i	$0.844653\pi$
$954$		0			0
$955$	25.9344	−	8.42661i	0.839219	−	0.272679i
$956$		0			0
$957$	−73.8078	+	8.69041i	−2.38587	+	0.280921i
$958$		0			0
$959$	−2.49995	−	7.69406i	−0.0807277	−	0.248454i
$960$		0			0
$961$	−9.09031	+	6.60449i	−0.293236	+	0.213048i
$962$		0			0
$963$	−7.02553	+	21.6224i	−0.226395	+	0.696771i
$964$		0			0
$965$	−1.58310	+	2.17895i	−0.0509619	+	0.0701430i
$966$		0			0
$967$	23.2776			0.748557			0.374278	−	0.927316i	$-0.377890\pi$
$967$	23.2776			0.748557			0.374278	+	0.927316i	$0.377890\pi$
$968$		0			0
$969$	−13.8325			−0.444363
$970$		0			0
$971$	18.9657	−	26.1040i	0.608638	−	0.837718i	−0.387827	−	0.921732i	$-0.626774\pi$
$971$	18.9657	−	26.1040i	0.608638	−	0.837718i	0.996465	+	0.0840143i	$0.0267742\pi$
$972$		0			0
$973$	−5.37876	+	16.5541i	−0.172435	+	0.530701i
$974$		0			0
$975$	0.285178	−	0.207194i	0.00913300	−	0.00663551i
$976$		0			0
$977$	2.86676	+	8.82297i	0.0917157	+	0.282272i	0.986384	−	0.164459i	$-0.0525880\pi$
$977$	2.86676	+	8.82297i	0.0917157	+	0.282272i	−0.894668	+	0.446731i	$0.852588\pi$
$978$		0			0
$979$	1.97023	−	0.231983i	0.0629689	−	0.00741420i
$980$		0			0
$981$	−52.6150	+	17.0956i	−1.67987	+	0.545822i
$982$		0			0
$983$	13.6886	+	18.8408i	0.436599	+	0.600927i	0.969452	−	0.245281i	$-0.0788801\pi$
$983$	13.6886	+	18.8408i	0.436599	+	0.600927i	−0.532853	+	0.846208i	$0.678880\pi$
$984$		0			0
$985$	34.6648	+	11.2633i	1.10451	+	0.358877i
$986$		0			0
$987$	21.7552	+	15.8061i	0.692476	+	0.503113i
$988$		0			0
$989$		−	1.83707i		−	0.0584155i
$990$		0			0
$991$			42.4003i			1.34689i	0.739237	+	0.673446i	$0.235186\pi$
$991$			42.4003i			1.34689i	−0.739237	+	0.673446i	$0.764814\pi$
$992$		0			0
$993$	−9.75417	−	7.08682i	−0.309539	−	0.224893i
$994$		0			0
$995$	−24.3341	−	7.90664i	−0.771444	−	0.250657i
$996$		0			0
$997$	2.61173	+	3.59473i	0.0827142	+	0.113846i	0.848369	−	0.529405i	$-0.177585\pi$
$997$	2.61173	+	3.59473i	0.0827142	+	0.113846i	−0.765655	+	0.643252i	$0.777585\pi$
$998$		0			0
$999$	−18.8097	+	6.11165i	−0.595113	+	0.193364i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	704.2.u.c.127.1		16
4.3	odd	2	inner	704.2.u.c.127.4		16
8.3	odd	2		44.2.g.a.39.1	yes	16
8.5	even	2		44.2.g.a.39.2	yes	16
11.2	odd	10	inner	704.2.u.c.255.4		16
24.5	odd	2		396.2.r.a.127.3		16
24.11	even	2		396.2.r.a.127.4		16
44.35	even	10	inner	704.2.u.c.255.1		16
88.3	odd	10		484.2.c.d.483.8		16
88.5	even	10		484.2.g.j.403.2		16
88.13	odd	10		44.2.g.a.35.1	✓	16
88.19	even	10		484.2.c.d.483.9		16
88.21	odd	2		484.2.g.i.215.3		16
88.27	odd	10		484.2.g.j.403.3		16
88.29	odd	10		484.2.g.j.239.3		16
88.35	even	10		44.2.g.a.35.2	yes	16
88.37	even	10		484.2.g.f.239.2		16
88.43	even	2		484.2.g.i.215.4		16
88.51	even	10		484.2.g.j.239.2		16
88.53	even	10		484.2.g.i.475.4		16
88.59	odd	10		484.2.g.f.239.3		16
88.61	odd	10		484.2.g.f.403.3		16
88.69	even	10		484.2.c.d.483.10		16
88.75	odd	10		484.2.g.i.475.3		16
88.83	even	10		484.2.g.f.403.2		16
88.85	odd	10		484.2.c.d.483.7		16
264.35	odd	10		396.2.r.a.343.3		16
264.101	even	10		396.2.r.a.343.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
44.2.g.a.35.1	✓	16	88.13	odd	10
44.2.g.a.35.2	yes	16	88.35	even	10
44.2.g.a.39.1	yes	16	8.3	odd	2
44.2.g.a.39.2	yes	16	8.5	even	2
396.2.r.a.127.3		16	24.5	odd	2
396.2.r.a.127.4		16	24.11	even	2
396.2.r.a.343.3		16	264.35	odd	10
396.2.r.a.343.4		16	264.101	even	10
484.2.c.d.483.7		16	88.85	odd	10
484.2.c.d.483.8		16	88.3	odd	10
484.2.c.d.483.9		16	88.19	even	10
484.2.c.d.483.10		16	88.69	even	10
484.2.g.f.239.2		16	88.37	even	10
484.2.g.f.239.3		16	88.59	odd	10
484.2.g.f.403.2		16	88.83	even	10
484.2.g.f.403.3		16	88.61	odd	10
484.2.g.i.215.3		16	88.21	odd	2
484.2.g.i.215.4		16	88.43	even	2
484.2.g.i.475.3		16	88.75	odd	10
484.2.g.i.475.4		16	88.53	even	10
484.2.g.j.239.2		16	88.51	even	10
484.2.g.j.239.3		16	88.29	odd	10
484.2.g.j.403.2		16	88.5	even	10
484.2.g.j.403.3		16	88.27	odd	10
704.2.u.c.127.1		16	1.1	even	1	trivial
704.2.u.c.127.4		16	4.3	odd	2	inner
704.2.u.c.255.1		16	44.35	even	10	inner
704.2.u.c.255.4		16	11.2	odd	10	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 704 = 2^{6} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	704.u (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.59814 + 2.19965i) q^{3} +(0.720859 - 2.21858i) q^{5} +(-1.04462 + 0.758960i) q^{7} +(-1.35736 - 4.17752i) q^{9} +O(q^{10})\)	\(q+(-1.59814 + 2.19965i) q^{3} +(0.720859 - 2.21858i) q^{5} +(-1.04462 + 0.758960i) q^{7} +(-1.35736 - 4.17752i) q^{9} +(3.29387 - 0.387833i) q^{11} +(0.279141 - 0.0906984i) q^{13} +(3.72806 + 5.13123i) q^{15} +(2.82281 + 0.917186i) q^{17} +(1.38671 + 1.00751i) q^{19} -3.51072i q^{21} +0.525735i q^{23} +(-0.357358 - 0.259635i) q^{25} +(3.60079 + 1.16997i) q^{27} +(4.84416 + 6.66742i) q^{29} +(4.22806 - 1.37378i) q^{31} +(-4.41097 + 7.86517i) q^{33} +(0.930788 + 2.86467i) q^{35} +(-4.22613 + 3.07046i) q^{37} +(-0.246601 + 0.758960i) q^{39} +(3.28821 - 4.52583i) q^{41} -3.49429 q^{43} -10.2466 q^{45} +(-4.50223 + 6.19679i) q^{47} +(-1.64791 + 5.07175i) q^{49} +(-6.52872 + 4.74340i) q^{51} +(-0.484791 - 1.49203i) q^{53} +(1.51398 - 7.58728i) q^{55} +(-4.43232 + 1.44015i) q^{57} +(8.27247 + 11.3861i) q^{59} +(8.98451 + 2.91924i) q^{61} +(4.58849 + 3.33373i) q^{63} -0.684676i q^{65} -10.4249i q^{67} +(-1.15643 - 0.840198i) q^{69} +(3.41904 + 1.11091i) q^{71} +(2.51668 + 3.46391i) q^{73} +(1.14221 - 0.371128i) q^{75} +(-3.14649 + 2.90506i) q^{77} +(3.04387 + 9.36807i) q^{79} +(2.33275 - 1.69484i) q^{81} +(1.16185 - 3.57581i) q^{83} +(4.06969 - 5.60145i) q^{85} -22.4076 q^{87} +0.598152 q^{89} +(-0.222760 + 0.306602i) q^{91} +(-3.73519 + 11.4957i) q^{93} +(3.23485 - 2.35026i) q^{95} +(-2.57295 - 7.91872i) q^{97} +(-6.09114 - 13.2338i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 6 q^{5} - 10 q^{9}+O(q^{10}) \) 16 * q + 6 * q^5 - 10 * q^9	\( 16 q + 6 q^{5} - 10 q^{9} + 10 q^{13} - 10 q^{17} + 6 q^{25} + 10 q^{29} - 12 q^{33} - 18 q^{37} + 10 q^{41} - 40 q^{45} + 6 q^{49} - 38 q^{53} + 10 q^{61} + 16 q^{69} - 30 q^{73} - 2 q^{77} - 4 q^{81} + 50 q^{85} - 36 q^{89} + 38 q^{93} - 68 q^{97}+O(q^{100}) \) 16 * q + 6 * q^5 - 10 * q^9 + 10 * q^13 - 10 * q^17 + 6 * q^25 + 10 * q^29 - 12 * q^33 - 18 * q^37 + 10 * q^41 - 40 * q^45 + 6 * q^49 - 38 * q^53 + 10 * q^61 + 16 * q^69 - 30 * q^73 - 2 * q^77 - 4 * q^81 + 50 * q^85 - 36 * q^89 + 38 * q^93 - 68 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more