LMFDB - Embedded newform 1521.2.i.d.746.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1521,2,Mod(746,1521)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1521, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3]))

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

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

chi := DirichletCharacter("1521.746");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1521 = 3^{2} \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1521.i (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$12.1452461474$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 117)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			746.1
Root			$-0.965926 - 0.258819i$ of defining polynomial
Character	$\chi$	$=$	1521.746
Dual form			1521.2.i.d.944.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.41421 - 1.41421i) q^{2} +2.00000i q^{4} +(-0.517638 - 0.517638i) q^{5} +(-1.36603 - 1.36603i) q^{7} +1.46410i q^{10} +(-4.38134 + 4.38134i) q^{11} +3.86370i q^{14} +4.00000 q^{16} -1.79315 q^{17} +(-2.46410 + 2.46410i) q^{19} +(1.03528 - 1.03528i) q^{20} +12.3923 q^{22} +2.44949 q^{23} -4.46410i q^{25} +(2.73205 - 2.73205i) q^{28} +1.41421i q^{29} +(6.36603 - 6.36603i) q^{31} +(-5.65685 - 5.65685i) q^{32} +(2.53590 + 2.53590i) q^{34} +1.41421i q^{35} +(5.73205 + 5.73205i) q^{37} +6.96953 q^{38} +(-3.86370 - 3.86370i) q^{41} +4.26795i q^{43} +(-8.76268 - 8.76268i) q^{44} +(-3.46410 - 3.46410i) q^{46} +(4.76028 - 4.76028i) q^{47} -3.26795i q^{49} +(-6.31319 + 6.31319i) q^{50} +8.76268i q^{53} +4.53590 q^{55} +(2.00000 - 2.00000i) q^{58} +(7.20977 - 7.20977i) q^{59} +2.80385 q^{61} -18.0058 q^{62} +8.00000i q^{64} +(-6.56218 + 6.56218i) q^{67} -3.58630i q^{68} +(2.00000 - 2.00000i) q^{70} +(-1.17398 - 1.17398i) q^{71} +(8.09808 + 8.09808i) q^{73} -16.2127i q^{74} +(-4.92820 - 4.92820i) q^{76} +11.9700 q^{77} -3.19615 q^{79} +(-2.07055 - 2.07055i) q^{80} +10.9282i q^{82} +(0.378937 + 0.378937i) q^{83} +(0.928203 + 0.928203i) q^{85} +(6.03579 - 6.03579i) q^{86} +(8.10634 - 8.10634i) q^{89} +4.89898i q^{92} -13.4641 q^{94} +2.55103 q^{95} +(8.56218 - 8.56218i) q^{97} +(-4.62158 + 4.62158i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{7} + 32 q^{16} + 8 q^{19} + 16 q^{22} + 8 q^{28} + 44 q^{31} + 48 q^{34} + 32 q^{37} + 64 q^{55} + 16 q^{58} + 64 q^{61} - 4 q^{67} + 16 q^{70} + 44 q^{73} + 16 q^{76} + 16 q^{79} - 48 q^{85}+ \cdots + 20 q^{97}+O(q^{100}) $ 8 * q - 4 * q^7 + 32 * q^16 + 8 * q^19 + 16 * q^22 + 8 * q^28 + 44 * q^31 + 48 * q^34 + 32 * q^37 + 64 * q^55 + 16 * q^58 + 64 * q^61 - 4 * q^67 + 16 * q^70 + 44 * q^73 + 16 * q^76 + 16 * q^79 - 48 * q^85 - 80 * q^94 + 20 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1521\mathbb{Z}\right)^\times$.

$n$	$677$	$847$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−1.41421	−	1.41421i	−1.00000	−	1.00000i		−	1.00000i	$-0.5\pi$
$2$	−1.41421	−	1.41421i	−1.00000	−	1.00000i	−1.00000			$\pi$
$3$		0			0
$3$		0			0
$4$			2.00000i			1.00000i
$5$	−0.517638	−	0.517638i	−0.231495	−	0.231495i	0.581822	−	0.813316i	$-0.302340\pi$
$5$	−0.517638	−	0.517638i	−0.231495	−	0.231495i	−0.813316	+	0.581822i	$0.802340\pi$
$6$		0			0
$7$	−1.36603	−	1.36603i	−0.516309	−	0.516309i	0.400143	−	0.916453i	$-0.368960\pi$
$7$	−1.36603	−	1.36603i	−0.516309	−	0.516309i	−0.916453	+	0.400143i	$0.868960\pi$
$8$		0			0
$9$		0			0
$10$			1.46410i			0.462990i
$11$	−4.38134	+	4.38134i	−1.32102	+	1.32102i	−0.408076	+	0.912948i	$0.633800\pi$
$11$	−4.38134	+	4.38134i	−1.32102	+	1.32102i	−0.912948	+	0.408076i	$0.866200\pi$
$12$		0			0
$13$		0			0
$13$		0			0
$14$			3.86370i			1.03262i
$15$		0			0
$16$	4.00000			1.00000
$17$	−1.79315			−0.434903			−0.217451	−	0.976071i	$-0.569774\pi$
$17$	−1.79315			−0.434903			−0.217451	+	0.976071i	$0.569774\pi$
$18$		0			0
$19$	−2.46410	+	2.46410i	−0.565304	+	0.565304i	−0.930809	−	0.365505i	$-0.880896\pi$
$19$	−2.46410	+	2.46410i	−0.565304	+	0.565304i	0.365505	+	0.930809i	$0.380896\pi$
$20$	1.03528	−	1.03528i	0.231495	−	0.231495i
$21$		0			0
$22$	12.3923			2.64205
$23$	2.44949			0.510754			0.255377	−	0.966842i	$-0.417800\pi$
$23$	2.44949			0.510754			0.255377	+	0.966842i	$0.417800\pi$
$24$		0			0
$25$		−	4.46410i		−	0.892820i
$26$		0			0
$27$		0			0
$28$	2.73205	−	2.73205i	0.516309	−	0.516309i
$29$			1.41421i			0.262613i	0.991342	+	0.131306i	$0.0419172\pi$
$29$			1.41421i			0.262613i	−0.991342	+	0.131306i	$0.958083\pi$
$30$		0			0
$31$	6.36603	−	6.36603i	1.14337	−	1.14337i	0.155543	−	0.987829i	$-0.450287\pi$
$31$	6.36603	−	6.36603i	1.14337	−	1.14337i	0.987829	−	0.155543i	$-0.0497126\pi$
$32$	−5.65685	−	5.65685i	−1.00000	−	1.00000i
$33$		0			0
$34$	2.53590	+	2.53590i	0.434903	+	0.434903i
$35$			1.41421i			0.239046i
$36$		0			0
$37$	5.73205	+	5.73205i	0.942343	+	0.942343i	0.998426	−	0.0560828i	$-0.0178611\pi$
$37$	5.73205	+	5.73205i	0.942343	+	0.942343i	−0.0560828	+	0.998426i	$0.517861\pi$
$38$	6.96953			1.13061
$39$		0			0
$40$		0			0
$41$	−3.86370	−	3.86370i	−0.603409	−	0.603409i	0.337807	−	0.941216i	$-0.390315\pi$
$41$	−3.86370	−	3.86370i	−0.603409	−	0.603409i	−0.941216	+	0.337807i	$0.890315\pi$
$42$		0			0
$43$			4.26795i			0.650856i	0.945567	+	0.325428i	$0.105508\pi$
$43$			4.26795i			0.650856i	−0.945567	+	0.325428i	$0.894492\pi$
$44$	−8.76268	−	8.76268i	−1.32102	−	1.32102i
$45$		0			0
$46$	−3.46410	−	3.46410i	−0.510754	−	0.510754i
$47$	4.76028	−	4.76028i	0.694358	−	0.694358i	−0.268830	−	0.963188i	$-0.586637\pi$
$47$	4.76028	−	4.76028i	0.694358	−	0.694358i	0.963188	+	0.268830i	$0.0866369\pi$
$48$		0			0
$49$		−	3.26795i		−	0.466850i
$50$	−6.31319	+	6.31319i	−0.892820	+	0.892820i
$51$		0			0
$52$		0			0
$53$			8.76268i			1.20365i	0.798629	+	0.601824i	$0.205559\pi$
$53$			8.76268i			1.20365i	−0.798629	+	0.601824i	$0.794441\pi$
$54$		0			0
$55$	4.53590			0.611620
$56$		0			0
$57$		0			0
$58$	2.00000	−	2.00000i	0.262613	−	0.262613i
$59$	7.20977	−	7.20977i	0.938632	−	0.938632i	−0.0595910	−	0.998223i	$-0.518980\pi$
$59$	7.20977	−	7.20977i	0.938632	−	0.938632i	0.998223	+	0.0595910i	$0.0189796\pi$
$60$		0			0
$61$	2.80385			0.358996			0.179498	−	0.983758i	$-0.442553\pi$
$61$	2.80385			0.358996			0.179498	+	0.983758i	$0.442553\pi$
$62$	−18.0058			−2.28674
$63$		0			0
$64$			8.00000i			1.00000i
$65$		0			0
$66$		0			0
$67$	−6.56218	+	6.56218i	−0.801698	+	0.801698i	−0.983361	−	0.181663i	$-0.941852\pi$
$67$	−6.56218	+	6.56218i	−0.801698	+	0.801698i	0.181663	+	0.983361i	$0.441852\pi$
$68$		−	3.58630i		−	0.434903i
$69$		0			0
$70$	2.00000	−	2.00000i	0.239046	−	0.239046i
$71$	−1.17398	−	1.17398i	−0.139325	−	0.139325i	0.634004	−	0.773330i	$-0.281410\pi$
$71$	−1.17398	−	1.17398i	−0.139325	−	0.139325i	−0.773330	+	0.634004i	$0.781410\pi$
$72$		0			0
$73$	8.09808	+	8.09808i	0.947808	+	0.947808i	0.998704	−	0.0508958i	$-0.0162077\pi$
$73$	8.09808	+	8.09808i	0.947808	+	0.947808i	−0.0508958	+	0.998704i	$0.516208\pi$
$74$		−	16.2127i		−	1.88469i
$75$		0			0
$76$	−4.92820	−	4.92820i	−0.565304	−	0.565304i
$77$	11.9700			1.36411
$78$		0			0
$79$	−3.19615			−0.359595			−0.179798	−	0.983704i	$-0.557544\pi$
$79$	−3.19615			−0.359595			−0.179798	+	0.983704i	$0.557544\pi$
$80$	−2.07055	−	2.07055i	−0.231495	−	0.231495i
$81$		0			0
$82$			10.9282i			1.20682i
$83$	0.378937	+	0.378937i	0.0415938	+	0.0415938i	0.727598	−	0.686004i	$-0.240637\pi$
$83$	0.378937	+	0.378937i	0.0415938	+	0.0415938i	−0.686004	+	0.727598i	$0.740637\pi$
$84$		0			0
$85$	0.928203	+	0.928203i	0.100678	+	0.100678i
$86$	6.03579	−	6.03579i	0.650856	−	0.650856i
$87$		0			0
$88$		0			0
$89$	8.10634	−	8.10634i	0.859271	−	0.859271i	−0.131981	−	0.991252i	$-0.542134\pi$
$89$	8.10634	−	8.10634i	0.859271	−	0.859271i	0.991252	+	0.131981i	$0.0421339\pi$
$90$		0			0
$91$		0			0
$92$			4.89898i			0.510754i
$93$		0			0
$94$	−13.4641			−1.38872
$95$	2.55103			0.261730
$96$		0			0
$97$	8.56218	−	8.56218i	0.869357	−	0.869357i	−0.123044	−	0.992401i	$-0.539266\pi$
$97$	8.56218	−	8.56218i	0.869357	−	0.869357i	0.992401	+	0.123044i	$0.0392656\pi$
$98$	−4.62158	+	4.62158i	−0.466850	+	0.466850i
$99$		0			0
$100$	8.92820			0.892820
$101$	15.8338			1.57552			0.787759	−	0.615984i	$-0.211241\pi$
$101$	15.8338			1.57552			0.787759	+	0.615984i	$0.211241\pi$
$102$		0			0
$103$			8.66025i			0.853320i	0.904412	+	0.426660i	$0.140310\pi$
$103$			8.66025i			0.853320i	−0.904412	+	0.426660i	$0.859690\pi$
$104$		0			0
$105$		0			0
$106$	12.3923	−	12.3923i	1.20365	−	1.20365i
$107$			13.0053i			1.25727i	0.777700	+	0.628636i	$0.216386\pi$
$107$			13.0053i			1.25727i	−0.777700	+	0.628636i	$0.783614\pi$
$108$		0			0
$109$	4.29423	−	4.29423i	0.411313	−	0.411313i	−0.470883	−	0.882196i	$-0.656065\pi$
$109$	4.29423	−	4.29423i	0.411313	−	0.411313i	0.882196	+	0.470883i	$0.156065\pi$
$110$	−6.41473	−	6.41473i	−0.611620	−	0.611620i
$111$		0			0
$112$	−5.46410	−	5.46410i	−0.516309	−	0.516309i
$113$		−	10.1769i		−	0.957362i	−0.877989	−	0.478681i	$-0.841115\pi$
$113$		−	10.1769i		−	0.957362i	0.877989	−	0.478681i	$-0.158885\pi$
$114$		0			0
$115$	−1.26795	−	1.26795i	−0.118237	−	0.118237i
$116$	−2.82843			−0.262613
$117$		0			0
$118$	−20.3923			−1.87726
$119$	2.44949	+	2.44949i	0.224544	+	0.224544i
$120$		0			0
$121$		−	27.3923i		−	2.49021i
$122$	−3.96524	−	3.96524i	−0.358996	−	0.358996i
$123$		0			0
$124$	12.7321	+	12.7321i	1.14337	+	1.14337i
$125$	−4.89898	+	4.89898i	−0.438178	+	0.438178i
$126$		0			0
$127$		−	3.92820i		−	0.348572i	−0.984695	−	0.174286i	$-0.944238\pi$
$127$		−	3.92820i		−	0.348572i	0.984695	−	0.174286i	$-0.0557617\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$		−	7.07107i		−	0.617802i	−0.951094	−	0.308901i	$-0.900039\pi$
$131$		−	7.07107i		−	0.617802i	0.951094	−	0.308901i	$-0.0999612\pi$
$132$		0			0
$133$	6.73205			0.583743
$134$	18.5606			1.60340
$135$		0			0
$136$		0			0
$137$	0.757875	−	0.757875i	0.0647496	−	0.0647496i	−0.673990	−	0.738740i	$-0.735421\pi$
$137$	0.757875	−	0.757875i	0.0647496	−	0.0647496i	0.738740	+	0.673990i	$0.235421\pi$
$138$		0			0
$139$	−17.3923			−1.47520			−0.737598	−	0.675240i	$-0.764040\pi$
$139$	−17.3923			−1.47520			−0.737598	+	0.675240i	$0.764040\pi$
$140$	−2.82843			−0.239046
$141$		0			0
$142$			3.32051i			0.278651i
$143$		0			0
$144$		0			0
$145$	0.732051	−	0.732051i	0.0607935	−	0.0607935i
$146$		−	22.9048i		−	1.89562i
$147$		0			0
$148$	−11.4641	+	11.4641i	−0.942343	+	0.942343i
$149$	10.1769	+	10.1769i	0.833724	+	0.833724i	0.988024	−	0.154300i	$-0.0493123\pi$
$149$	10.1769	+	10.1769i	0.833724	+	0.833724i	−0.154300	+	0.988024i	$0.549312\pi$
$150$		0			0
$151$	−1.53590	−	1.53590i	−0.124990	−	0.124990i	0.641845	−	0.766835i	$-0.278169\pi$
$151$	−1.53590	−	1.53590i	−0.124990	−	0.124990i	−0.766835	+	0.641845i	$0.778169\pi$
$152$		0			0
$153$		0			0
$154$	−16.9282	−	16.9282i	−1.36411	−	1.36411i
$155$	−6.59059			−0.529369
$156$		0			0
$157$	9.39230			0.749588			0.374794	−	0.927108i	$-0.377714\pi$
$157$	9.39230			0.749588			0.374794	+	0.927108i	$0.377714\pi$
$158$	4.52004	+	4.52004i	0.359595	+	0.359595i
$159$		0			0
$160$			5.85641i			0.462990i
$161$	−3.34607	−	3.34607i	−0.263707	−	0.263707i
$162$		0			0
$163$	10.7583	+	10.7583i	0.842657	+	0.842657i	0.989204	−	0.146546i	$-0.0468157\pi$
$163$	10.7583	+	10.7583i	0.842657	+	0.842657i	−0.146546	+	0.989204i	$0.546816\pi$
$164$	7.72741	−	7.72741i	0.603409	−	0.603409i
$165$		0			0
$166$		−	1.07180i		−	0.0831876i
$167$	−1.03528	+	1.03528i	−0.0801121	+	0.0801121i	−0.746027	−	0.665915i	$-0.768041\pi$
$167$	−1.03528	+	1.03528i	−0.0801121	+	0.0801121i	0.665915	+	0.746027i	$0.268041\pi$
$168$		0			0
$169$		0			0
$170$		−	2.62536i		−	0.201356i
$171$		0			0
$172$	−8.53590			−0.650856
$173$	−5.55532			−0.422363			−0.211182	−	0.977447i	$-0.567731\pi$
$173$	−5.55532			−0.422363			−0.211182	+	0.977447i	$0.567731\pi$
$174$		0			0
$175$	−6.09808	+	6.09808i	−0.460971	+	0.460971i
$176$	−17.5254	+	17.5254i	−1.32102	+	1.32102i
$177$		0			0
$178$	−22.9282			−1.71854
$179$	8.00481			0.598307			0.299154	−	0.954205i	$-0.403296\pi$
$179$	8.00481			0.598307			0.299154	+	0.954205i	$0.403296\pi$
$180$		0			0
$181$		−	6.00000i		−	0.445976i	−0.974821	−	0.222988i	$-0.928419\pi$
$181$		−	6.00000i		−	0.445976i	0.974821	−	0.222988i	$-0.0715812\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$		−	5.93426i		−	0.436295i
$186$		0			0
$187$	7.85641	−	7.85641i	0.574517	−	0.574517i
$188$	9.52056	+	9.52056i	0.694358	+	0.694358i
$189$		0			0
$190$	−3.60770	−	3.60770i	−0.261730	−	0.261730i
$191$		−	1.69161i		−	0.122401i	−0.998125	−	0.0612005i	$-0.980507\pi$
$191$		−	1.69161i		−	0.122401i	0.998125	−	0.0612005i	$-0.0194929\pi$
$192$		0			0
$193$	−7.83013	−	7.83013i	−0.563625	−	0.563625i	0.366710	−	0.930335i	$-0.380484\pi$
$193$	−7.83013	−	7.83013i	−0.563625	−	0.563625i	−0.930335	+	0.366710i	$0.880484\pi$
$194$	−24.2175			−1.73871
$195$		0			0
$196$	6.53590			0.466850
$197$	−14.7985	−	14.7985i	−1.05435	−	1.05435i	−0.998436	−	0.0559119i	$-0.982193\pi$
$197$	−14.7985	−	14.7985i	−1.05435	−	1.05435i	−0.0559119	−	0.998436i	$-0.517807\pi$
$198$		0			0
$199$		−	6.46410i		−	0.458228i	−0.973400	−	0.229114i	$-0.926417\pi$
$199$		−	6.46410i		−	0.458228i	0.973400	−	0.229114i	$-0.0735829\pi$
$200$		0			0
$201$		0			0
$202$	−22.3923	−	22.3923i	−1.57552	−	1.57552i
$203$	1.93185	−	1.93185i	0.135589	−	0.135589i
$204$		0			0
$205$			4.00000i			0.279372i
$206$	12.2474	−	12.2474i	0.853320	−	0.853320i
$207$		0			0
$208$		0			0
$209$		−	21.5921i		−	1.49356i
$210$		0			0
$211$	−4.80385			−0.330711			−0.165355	−	0.986234i	$-0.552877\pi$
$211$	−4.80385			−0.330711			−0.165355	+	0.986234i	$0.552877\pi$
$212$	−17.5254			−1.20365
$213$		0			0
$214$	18.3923	−	18.3923i	1.25727	−	1.25727i
$215$	2.20925	−	2.20925i	0.150670	−	0.150670i
$216$		0			0
$217$	−17.3923			−1.18067
$218$	−12.1459			−0.822625
$219$		0			0
$220$			9.07180i			0.611620i
$221$		0			0
$222$		0			0
$223$	−3.39230	+	3.39230i	−0.227166	+	0.227166i	−0.811508	−	0.584342i	$-0.801353\pi$
$223$	−3.39230	+	3.39230i	−0.227166	+	0.227166i	0.584342	+	0.811508i	$0.301353\pi$
$224$			15.4548i			1.03262i
$225$		0			0
$226$	−14.3923	+	14.3923i	−0.957362	+	0.957362i
$227$	9.52056	+	9.52056i	0.631902	+	0.631902i	0.948545	−	0.316643i	$-0.102556\pi$
$227$	9.52056	+	9.52056i	0.631902	+	0.631902i	−0.316643	+	0.948545i	$0.602556\pi$
$228$		0			0
$229$	−0.267949	−	0.267949i	−0.0177066	−	0.0177066i	0.698198	−	0.715905i	$-0.253985\pi$
$229$	−0.267949	−	0.267949i	−0.0177066	−	0.0177066i	−0.715905	+	0.698198i	$0.753985\pi$
$230$			3.58630i			0.236474i
$231$		0			0
$232$		0			0
$233$	−10.4543			−0.684884			−0.342442	−	0.939539i	$-0.611254\pi$
$233$	−10.4543			−0.684884			−0.342442	+	0.939539i	$0.611254\pi$
$234$		0			0
$235$	−4.92820			−0.321481
$236$	14.4195	+	14.4195i	0.938632	+	0.938632i
$237$		0			0
$238$		−	6.92820i		−	0.449089i
$239$	9.52056	+	9.52056i	0.615834	+	0.615834i	0.944460	−	0.328626i	$-0.106586\pi$
$239$	9.52056	+	9.52056i	0.615834	+	0.615834i	−0.328626	+	0.944460i	$0.606586\pi$
$240$		0			0
$241$	11.7321	+	11.7321i	0.755728	+	0.755728i	0.975542	−	0.219814i	$-0.0705450\pi$
$241$	11.7321	+	11.7321i	0.755728	+	0.755728i	−0.219814	+	0.975542i	$0.570545\pi$
$242$	−38.7386	+	38.7386i	−2.49021	+	2.49021i
$243$		0			0
$244$			5.60770i			0.358996i
$245$	−1.69161	+	1.69161i	−0.108073	+	0.108073i
$246$		0			0
$247$		0			0
$248$		0			0
$249$		0			0
$250$	13.8564			0.876356
$251$	12.9038			0.814480			0.407240	−	0.913321i	$-0.366491\pi$
$251$	12.9038			0.814480			0.407240	+	0.913321i	$0.366491\pi$
$252$		0			0
$253$	−10.7321	+	10.7321i	−0.674718	+	0.674718i
$254$	−5.55532	+	5.55532i	−0.348572	+	0.348572i
$255$		0			0
$256$	16.0000			1.00000
$257$	18.2832			1.14048			0.570239	−	0.821479i	$-0.306851\pi$
$257$	18.2832			1.14048			0.570239	+	0.821479i	$0.306851\pi$
$258$		0			0
$259$		−	15.6603i		−	0.973081i
$260$		0			0
$261$		0			0
$262$	−10.0000	+	10.0000i	−0.617802	+	0.617802i
$263$		−	20.6312i		−	1.27217i	−0.771617	−	0.636087i	$-0.780552\pi$
$263$		−	20.6312i		−	1.27217i	0.771617	−	0.636087i	$-0.219448\pi$
$264$		0			0
$265$	4.53590	−	4.53590i	0.278638	−	0.278638i
$266$	−9.52056	−	9.52056i	−0.583743	−	0.583743i
$267$		0			0
$268$	−13.1244	−	13.1244i	−0.801698	−	0.801698i
$269$			23.4596i			1.43036i	0.698941	+	0.715179i	$0.253655\pi$
$269$			23.4596i			1.43036i	−0.698941	+	0.715179i	$0.746345\pi$
$270$		0			0
$271$	15.8301	+	15.8301i	0.961612	+	0.961612i	0.999290	−	0.0376782i	$-0.0119962\pi$
$271$	15.8301	+	15.8301i	0.961612	+	0.961612i	−0.0376782	+	0.999290i	$0.511996\pi$
$272$	−7.17260			−0.434903
$273$		0			0
$274$	−2.14359			−0.129499
$275$	19.5588	+	19.5588i	1.17944	+	1.17944i
$276$		0			0
$277$			7.85641i			0.472046i	0.971748	+	0.236023i	$0.0758440\pi$
$277$			7.85641i			0.472046i	−0.971748	+	0.236023i	$0.924156\pi$
$278$	24.5964	+	24.5964i	1.47520	+	1.47520i
$279$		0			0
$280$		0			0
$281$	15.2146	−	15.2146i	0.907626	−	0.907626i	−0.0884547	−	0.996080i	$-0.528193\pi$
$281$	15.2146	−	15.2146i	0.907626	−	0.907626i	0.996080	+	0.0884547i	$0.0281928\pi$
$282$		0			0
$283$		−	4.85641i		−	0.288683i	−0.989528	−	0.144342i	$-0.953894\pi$
$283$		−	4.85641i		−	0.288683i	0.989528	−	0.144342i	$-0.0461064\pi$
$284$	2.34795	−	2.34795i	0.139325	−	0.139325i
$285$		0			0
$286$		0			0
$287$			10.5558i			0.623091i
$288$		0			0
$289$	−13.7846			−0.810859
$290$	−2.07055			−0.121587
$291$		0			0
$292$	−16.1962	+	16.1962i	−0.947808	+	0.947808i
$293$	15.6950	−	15.6950i	0.916915	−	0.916915i	−0.0798891	−	0.996804i	$-0.525457\pi$
$293$	15.6950	−	15.6950i	0.916915	−	0.916915i	0.996804	+	0.0798891i	$0.0254566\pi$
$294$		0			0
$295$	−7.46410			−0.434577
$296$		0			0
$297$		0			0
$298$		−	28.7846i		−	1.66745i
$299$		0			0
$300$		0			0
$301$	5.83013	−	5.83013i	0.336043	−	0.336043i
$302$			4.34418i			0.249979i
$303$		0			0
$304$	−9.85641	+	9.85641i	−0.565304	+	0.565304i
$305$	−1.45138	−	1.45138i	−0.0831057	−	0.0831057i
$306$		0			0
$307$	3.70577	+	3.70577i	0.211500	+	0.211500i	0.804904	−	0.593405i	$-0.202217\pi$
$307$	3.70577	+	3.70577i	0.211500	+	0.211500i	−0.593405	+	0.804904i	$0.702217\pi$
$308$			23.9401i			1.36411i
$309$		0			0
$310$	9.32051	+	9.32051i	0.529369	+	0.529369i
$311$	28.0812			1.59234			0.796169	−	0.605074i	$-0.206856\pi$
$311$	28.0812			1.59234			0.796169	+	0.605074i	$0.206856\pi$
$312$		0			0
$313$	7.19615			0.406751			0.203375	−	0.979101i	$-0.434809\pi$
$313$	7.19615			0.406751			0.203375	+	0.979101i	$0.434809\pi$
$314$	−13.2827	−	13.2827i	−0.749588	−	0.749588i
$315$		0			0
$316$		−	6.39230i		−	0.359595i
$317$	−0.757875	−	0.757875i	−0.0425665	−	0.0425665i	0.685503	−	0.728070i	$-0.259582\pi$
$317$	−0.757875	−	0.757875i	−0.0425665	−	0.0425665i	−0.728070	+	0.685503i	$0.759582\pi$
$318$		0			0
$319$	−6.19615	−	6.19615i	−0.346918	−	0.346918i
$320$	4.14110	−	4.14110i	0.231495	−	0.231495i
$321$		0			0
$322$			9.46410i			0.527414i
$323$	4.41851	−	4.41851i	0.245852	−	0.245852i
$324$		0			0
$325$		0			0
$326$		−	30.4292i		−	1.68531i
$327$		0			0
$328$		0			0
$329$	−13.0053			−0.717007
$330$		0			0
$331$	−4.83013	+	4.83013i	−0.265488	+	0.265488i	−0.827279	−	0.561791i	$-0.810112\pi$
$331$	−4.83013	+	4.83013i	−0.265488	+	0.265488i	0.561791	+	0.827279i	$0.310112\pi$
$332$	−0.757875	+	0.757875i	−0.0415938	+	0.0415938i
$333$		0			0
$334$	2.92820			0.160224
$335$	6.79367			0.371178
$336$		0			0
$337$			14.0718i			0.766540i	0.923636	+	0.383270i	$0.125202\pi$
$337$			14.0718i			0.766540i	−0.923636	+	0.383270i	$0.874798\pi$
$338$		0			0
$339$		0			0
$340$	−1.85641	+	1.85641i	−0.100678	+	0.100678i
$341$			55.7835i			3.02084i
$342$		0			0
$343$	−14.0263	+	14.0263i	−0.757348	+	0.757348i
$344$		0			0
$345$		0			0
$346$	7.85641	+	7.85641i	0.422363	+	0.422363i
$347$			14.9743i			0.803865i	0.915669	+	0.401932i	$0.131661\pi$
$347$			14.9743i			0.803865i	−0.915669	+	0.401932i	$0.868339\pi$
$348$		0			0
$349$	24.4904	+	24.4904i	1.31094	+	1.31094i	0.920723	+	0.390217i	$0.127600\pi$
$349$	24.4904	+	24.4904i	1.31094	+	1.31094i	0.390217	+	0.920723i	$0.372400\pi$
$350$	17.2480			0.921942
$351$		0			0
$352$	49.5692			2.64205
$353$	8.62398	+	8.62398i	0.459008	+	0.459008i	0.898330	−	0.439322i	$-0.144781\pi$
$353$	8.62398	+	8.62398i	0.459008	+	0.459008i	−0.439322	+	0.898330i	$0.644781\pi$
$354$		0			0
$355$			1.21539i			0.0645062i
$356$	16.2127	+	16.2127i	0.859271	+	0.859271i
$357$		0			0
$358$	−11.3205	−	11.3205i	−0.598307	−	0.598307i
$359$	−7.07107	+	7.07107i	−0.373197	+	0.373197i	−0.868640	−	0.495443i	$-0.835006\pi$
$359$	−7.07107	+	7.07107i	−0.373197	+	0.373197i	0.495443	+	0.868640i	$0.335006\pi$
$360$		0			0
$361$			6.85641i			0.360863i
$362$	−8.48528	+	8.48528i	−0.445976	+	0.445976i
$363$		0			0
$364$		0			0
$365$		−	8.38375i		−	0.438825i
$366$		0			0
$367$	15.3923			0.803472			0.401736	−	0.915756i	$-0.368407\pi$
$367$	15.3923			0.803472			0.401736	+	0.915756i	$0.368407\pi$
$368$	9.79796			0.510754
$369$		0			0
$370$	−8.39230	+	8.39230i	−0.436295	+	0.436295i
$371$	11.9700	−	11.9700i	0.621454	−	0.621454i
$372$		0			0
$373$	23.5885			1.22136			0.610682	−	0.791876i	$-0.290895\pi$
$373$	23.5885			1.22136			0.610682	+	0.791876i	$0.290895\pi$
$374$	−22.2213			−1.14903
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	−14.6340	+	14.6340i	−0.751697	+	0.751697i	−0.974796	−	0.223099i	$-0.928383\pi$
$379$	−14.6340	+	14.6340i	−0.751697	+	0.751697i	0.223099	+	0.974796i	$0.428383\pi$
$380$			5.10205i			0.261730i
$381$		0			0
$382$	−2.39230	+	2.39230i	−0.122401	+	0.122401i
$383$	7.07107	+	7.07107i	0.361315	+	0.361315i	0.864297	−	0.502982i	$-0.167764\pi$
$383$	7.07107	+	7.07107i	0.361315	+	0.361315i	−0.502982	+	0.864297i	$0.667764\pi$
$384$		0			0
$385$	−6.19615	−	6.19615i	−0.315785	−	0.315785i
$386$			22.1469i			1.12725i
$387$		0			0
$388$	17.1244	+	17.1244i	0.869357	+	0.869357i
$389$	−1.79315			−0.0909164			−0.0454582	−	0.998966i	$-0.514475\pi$
$389$	−1.79315			−0.0909164			−0.0454582	+	0.998966i	$0.514475\pi$
$390$		0			0
$391$	−4.39230			−0.222128
$392$		0			0
$393$		0			0
$394$			41.8564i			2.10870i
$395$	1.65445	+	1.65445i	0.0832444	+	0.0832444i
$396$		0			0
$397$	−18.2224	−	18.2224i	−0.914558	−	0.914558i	0.0820690	−	0.996627i	$-0.473847\pi$
$397$	−18.2224	−	18.2224i	−0.914558	−	0.914558i	−0.996627	+	0.0820690i	$0.973847\pi$
$398$	−9.14162	+	9.14162i	−0.458228	+	0.458228i
$399$		0			0
$400$		−	17.8564i		−	0.892820i
$401$	8.58682	−	8.58682i	0.428805	−	0.428805i	−0.459416	−	0.888221i	$-0.651941\pi$
$401$	8.58682	−	8.58682i	0.428805	−	0.428805i	0.888221	+	0.459416i	$0.151941\pi$
$402$		0			0
$403$		0			0
$404$			31.6675i			1.57552i
$405$		0			0
$406$	−5.46410			−0.271179
$407$	−50.2281			−2.48972
$408$		0			0
$409$	−6.90192	+	6.90192i	−0.341278	+	0.341278i	−0.856848	−	0.515570i	$-0.827580\pi$
$409$	−6.90192	+	6.90192i	−0.341278	+	0.341278i	0.515570	+	0.856848i	$0.327580\pi$
$410$	5.65685	−	5.65685i	0.279372	−	0.279372i
$411$		0			0
$412$	−17.3205			−0.853320
$413$	−19.6975			−0.969248
$414$		0			0
$415$		−	0.392305i		−	0.0192575i
$416$		0			0
$417$		0			0
$418$	−30.5359	+	30.5359i	−1.49356	+	1.49356i
$419$		−	26.0106i		−	1.27070i	−0.772223	−	0.635352i	$-0.780855\pi$
$419$		−	26.0106i		−	1.27070i	0.772223	−	0.635352i	$-0.219145\pi$
$420$		0			0
$421$	13.6340	−	13.6340i	0.664479	−	0.664479i	−0.291953	−	0.956433i	$-0.594305\pi$
$421$	13.6340	−	13.6340i	0.664479	−	0.664479i	0.956433	+	0.291953i	$0.0943052\pi$
$422$	6.79367	+	6.79367i	0.330711	+	0.330711i
$423$		0			0
$424$		0			0
$425$			8.00481i			0.388290i
$426$		0			0
$427$	−3.83013	−	3.83013i	−0.185353	−	0.185353i
$428$	−26.0106			−1.25727
$429$		0			0
$430$	−6.24871			−0.301340
$431$	8.38375	+	8.38375i	0.403831	+	0.403831i	0.879581	−	0.475750i	$-0.157823\pi$
$431$	8.38375	+	8.38375i	0.403831	+	0.403831i	−0.475750	+	0.879581i	$0.657823\pi$
$432$		0			0
$433$			11.5359i			0.554380i	0.960815	+	0.277190i	$0.0894031\pi$
$433$			11.5359i			0.554380i	−0.960815	+	0.277190i	$0.910597\pi$
$434$	24.5964	+	24.5964i	1.18067	+	1.18067i
$435$		0			0
$436$	8.58846	+	8.58846i	0.411313	+	0.411313i
$437$	−6.03579	+	6.03579i	−0.288731	+	0.288731i
$438$		0			0
$439$			21.5885i			1.03036i	0.857082	+	0.515180i	$0.172275\pi$
$439$			21.5885i			1.03036i	−0.857082	+	0.515180i	$0.827725\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$			35.0507i			1.66531i	0.553792	+	0.832655i	$0.313180\pi$
$443$			35.0507i			1.66531i	−0.553792	+	0.832655i	$0.686820\pi$
$444$		0			0
$445$	−8.39230			−0.397833
$446$	9.59489			0.454331
$447$		0			0
$448$	10.9282	−	10.9282i	0.516309	−	0.516309i
$449$	−3.72500	+	3.72500i	−0.175794	+	0.175794i	−0.789519	−	0.613726i	$-0.789670\pi$
$449$	−3.72500	+	3.72500i	−0.175794	+	0.175794i	0.613726	+	0.789519i	$0.289670\pi$
$450$		0			0
$451$	33.8564			1.59424
$452$	20.3538			0.957362
$453$		0			0
$454$		−	26.9282i		−	1.26380i
$455$		0			0
$456$		0			0
$457$	2.90192	−	2.90192i	0.135746	−	0.135746i	−0.635969	−	0.771715i	$-0.719399\pi$
$457$	2.90192	−	2.90192i	0.135746	−	0.135746i	0.771715	+	0.635969i	$0.219399\pi$
$458$			0.757875i			0.0354132i
$459$		0			0
$460$	2.53590	−	2.53590i	0.118237	−	0.118237i
$461$	−26.3896	−	26.3896i	−1.22909	−	1.22909i	−0.964310	−	0.264775i	$-0.914702\pi$
$461$	−26.3896	−	26.3896i	−1.22909	−	1.22909i	−0.264775	−	0.964310i	$-0.585298\pi$
$462$		0			0
$463$	3.83013	+	3.83013i	0.178001	+	0.178001i	0.790484	−	0.612483i	$-0.209829\pi$
$463$	3.83013	+	3.83013i	0.178001	+	0.178001i	−0.612483	+	0.790484i	$0.709829\pi$
$464$			5.65685i			0.262613i
$465$		0			0
$466$	14.7846	+	14.7846i	0.684884	+	0.684884i
$467$	−22.0454			−1.02014			−0.510070	−	0.860133i	$-0.670380\pi$
$467$	−22.0454			−1.02014			−0.510070	+	0.860133i	$0.670380\pi$
$468$		0			0
$469$	17.9282			0.827848
$470$	6.96953	+	6.96953i	0.321481	+	0.321481i
$471$		0			0
$472$		0			0
$473$	−18.6993	−	18.6993i	−0.859797	−	0.859797i
$474$		0			0
$475$	11.0000	+	11.0000i	0.504715	+	0.504715i
$476$	−4.89898	+	4.89898i	−0.224544	+	0.224544i
$477$		0			0
$478$		−	26.9282i		−	1.23167i
$479$	−2.82843	+	2.82843i	−0.129234	+	0.129234i	−0.768765	−	0.639531i	$-0.779129\pi$
$479$	−2.82843	+	2.82843i	−0.129234	+	0.129234i	0.639531	+	0.768765i	$0.279129\pi$
$480$		0			0
$481$		0			0
$482$		−	33.1833i		−	1.51146i
$483$		0			0
$484$	54.7846			2.49021
$485$	−8.86422			−0.402503
$486$		0			0
$487$	10.1244	−	10.1244i	0.458778	−	0.458778i	−0.439476	−	0.898254i	$-0.644836\pi$
$487$	10.1244	−	10.1244i	0.458778	−	0.458778i	0.898254	+	0.439476i	$0.144836\pi$
$488$		0			0
$489$		0			0
$490$	4.78461			0.216147
$491$	16.3142			0.736251			0.368125	−	0.929776i	$-0.380000\pi$
$491$	16.3142			0.736251			0.368125	+	0.929776i	$0.380000\pi$
$492$		0			0
$493$		−	2.53590i		−	0.114211i
$494$		0			0
$495$		0			0
$496$	25.4641	−	25.4641i	1.14337	−	1.14337i
$497$			3.20736i			0.143870i
$498$		0			0
$499$	−27.7321	+	27.7321i	−1.24146	+	1.24146i	−0.282060	+	0.959397i	$0.591018\pi$
$499$	−27.7321	+	27.7321i	−1.24146	+	1.24146i	−0.959397	+	0.282060i	$0.908982\pi$
$500$	−9.79796	−	9.79796i	−0.438178	−	0.438178i
$501$		0			0
$502$	−18.2487	−	18.2487i	−0.814480	−	0.814480i
$503$			26.8701i			1.19808i	0.800720	+	0.599038i	$0.204450\pi$
$503$			26.8701i			1.19808i	−0.800720	+	0.599038i	$0.795550\pi$
$504$		0			0
$505$	−8.19615	−	8.19615i	−0.364724	−	0.364724i
$506$	30.3548			1.34944
$507$		0			0
$508$	7.85641			0.348572
$509$	−18.1445	−	18.1445i	−0.804243	−	0.804243i	0.179513	−	0.983756i	$-0.442548\pi$
$509$	−18.1445	−	18.1445i	−0.804243	−	0.804243i	−0.983756	+	0.179513i	$0.942548\pi$
$510$		0			0
$511$		−	22.1244i		−	0.978724i
$512$	−22.6274	−	22.6274i	−1.00000	−	1.00000i
$513$		0			0
$514$	−25.8564	−	25.8564i	−1.14048	−	1.14048i
$515$	4.48288	−	4.48288i	0.197539	−	0.197539i
$516$		0			0
$517$			41.7128i			1.83453i
$518$	−22.1469	+	22.1469i	−0.973081	+	0.973081i
$519$		0			0
$520$		0			0
$521$		−	32.2223i		−	1.41168i	−0.708369	−	0.705842i	$-0.750569\pi$
$521$		−	32.2223i		−	1.41168i	0.708369	−	0.705842i	$-0.249431\pi$
$522$		0			0
$523$	−1.21539			−0.0531453			−0.0265727	−	0.999647i	$-0.508459\pi$
$523$	−1.21539			−0.0531453			−0.0265727	+	0.999647i	$0.508459\pi$
$524$	14.1421			0.617802
$525$		0			0
$526$	−29.1769	+	29.1769i	−1.27217	+	1.27217i
$527$	−11.4152	+	11.4152i	−0.497256	+	0.497256i
$528$		0			0
$529$	−17.0000			−0.739130
$530$	−12.8295			−0.557276
$531$		0			0
$532$			13.4641i			0.583743i
$533$		0			0
$534$		0			0
$535$	6.73205	−	6.73205i	0.291052	−	0.291052i
$536$		0			0
$537$		0			0
$538$	33.1769	−	33.1769i	1.43036	−	1.43036i
$539$	14.3180	+	14.3180i	0.616720	+	0.616720i
$540$		0			0
$541$	5.68653	+	5.68653i	0.244483	+	0.244483i	0.818702	−	0.574219i	$-0.194694\pi$
$541$	5.68653	+	5.68653i	0.244483	+	0.244483i	−0.574219	+	0.818702i	$0.694694\pi$
$542$		−	44.7744i		−	1.92322i
$543$		0			0
$544$	10.1436	+	10.1436i	0.434903	+	0.434903i
$545$	−4.44571			−0.190433
$546$		0			0
$547$	3.39230			0.145044			0.0725222	−	0.997367i	$-0.476895\pi$
$547$	3.39230			0.145044			0.0725222	+	0.997367i	$0.476895\pi$
$548$	1.51575	+	1.51575i	0.0647496	+	0.0647496i
$549$		0			0
$550$		−	55.3205i		−	2.35887i
$551$	−3.48477	−	3.48477i	−0.148456	−	0.148456i
$552$		0			0
$553$	4.36603	+	4.36603i	0.185662	+	0.185662i
$554$	11.1106	−	11.1106i	0.472046	−	0.472046i
$555$		0			0
$556$		−	34.7846i		−	1.47520i
$557$	8.10634	−	8.10634i	0.343477	−	0.343477i	−0.514196	−	0.857673i	$-0.671910\pi$
$557$	8.10634	−	8.10634i	0.343477	−	0.343477i	0.857673	+	0.514196i	$0.171910\pi$
$558$		0			0
$559$		0			0
$560$			5.65685i			0.239046i
$561$		0			0
$562$	−43.0333			−1.81525
$563$	29.6985			1.25164			0.625821	−	0.779967i	$-0.284764\pi$
$563$	29.6985			1.25164			0.625821	+	0.779967i	$0.284764\pi$
$564$		0			0
$565$	−5.26795	+	5.26795i	−0.221624	+	0.221624i
$566$	−6.86800	+	6.86800i	−0.288683	+	0.288683i
$567$		0			0
$568$		0			0
$569$	7.34847			0.308064			0.154032	−	0.988066i	$-0.450774\pi$
$569$	7.34847			0.308064			0.154032	+	0.988066i	$0.450774\pi$
$570$		0			0
$571$		−	33.7128i		−	1.41084i	−0.708791	−	0.705419i	$-0.750759\pi$
$571$		−	33.7128i		−	1.41084i	0.708791	−	0.705419i	$-0.249241\pi$
$572$		0			0
$573$		0			0
$574$	14.9282	−	14.9282i	0.623091	−	0.623091i
$575$		−	10.9348i		−	0.456011i
$576$		0			0
$577$	−1.19615	+	1.19615i	−0.0497965	+	0.0497965i	−0.731567	−	0.681770i	$-0.761210\pi$
$577$	−1.19615	+	1.19615i	−0.0497965	+	0.0497965i	0.681770	+	0.731567i	$0.261210\pi$
$578$	19.4944	+	19.4944i	0.810859	+	0.810859i
$579$		0			0
$580$	1.46410	+	1.46410i	0.0607935	+	0.0607935i
$581$		−	1.03528i		−	0.0429505i
$582$		0			0
$583$	−38.3923	−	38.3923i	−1.59005	−	1.59005i
$584$		0			0
$585$		0			0
$586$	−44.3923			−1.83383
$587$	−5.24075	−	5.24075i	−0.216309	−	0.216309i	0.590632	−	0.806941i	$-0.298878\pi$
$587$	−5.24075	−	5.24075i	−0.216309	−	0.216309i	−0.806941	+	0.590632i	$0.798878\pi$
$588$		0			0
$589$			31.3731i			1.29270i
$590$	10.5558	+	10.5558i	0.434577	+	0.434577i
$591$		0			0
$592$	22.9282	+	22.9282i	0.942343	+	0.942343i
$593$	11.4524	−	11.4524i	0.470294	−	0.470294i	−0.431716	−	0.902010i	$-0.642092\pi$
$593$	11.4524	−	11.4524i	0.470294	−	0.470294i	0.902010	+	0.431716i	$0.142092\pi$
$594$		0			0
$595$		−	2.53590i		−	0.103962i
$596$	−20.3538	+	20.3538i	−0.833724	+	0.833724i
$597$		0			0
$598$		0			0
$599$			29.9759i			1.22478i	0.790555	+	0.612391i	$0.209792\pi$
$599$			29.9759i			1.22478i	−0.790555	+	0.612391i	$0.790208\pi$
$600$		0			0
$601$	4.78461			0.195168			0.0975842	−	0.995227i	$-0.468888\pi$
$601$	4.78461			0.195168			0.0975842	+	0.995227i	$0.468888\pi$
$602$	−16.4901			−0.672086
$603$		0			0
$604$	3.07180	−	3.07180i	0.124990	−	0.124990i
$605$	−14.1793	+	14.1793i	−0.576471	+	0.576471i
$606$		0			0
$607$	−17.6077			−0.714674			−0.357337	−	0.933975i	$-0.616315\pi$
$607$	−17.6077			−0.714674			−0.357337	+	0.933975i	$0.616315\pi$
$608$	27.8781			1.13061
$609$		0			0
$610$			4.10512i			0.166211i
$611$		0			0
$612$		0			0
$613$	6.36603	−	6.36603i	0.257121	−	0.257121i	−0.566761	−	0.823882i	$-0.691804\pi$
$613$	6.36603	−	6.36603i	0.257121	−	0.257121i	0.823882	+	0.566761i	$0.191804\pi$
$614$		−	10.4815i		−	0.422999i
$615$		0			0
$616$		0			0
$617$	14.8356	+	14.8356i	0.597260	+	0.597260i	0.939583	−	0.342322i	$-0.111213\pi$
$617$	14.8356	+	14.8356i	0.597260	+	0.597260i	−0.342322	+	0.939583i	$0.611213\pi$
$618$		0			0
$619$	4.16987	+	4.16987i	0.167601	+	0.167601i	0.785924	−	0.618323i	$-0.212188\pi$
$619$	4.16987	+	4.16987i	0.167601	+	0.167601i	−0.618323	+	0.785924i	$0.712188\pi$
$620$		−	13.1812i		−	0.529369i
$621$		0			0
$622$	−39.7128	−	39.7128i	−1.59234	−	1.59234i
$623$	−22.1469			−0.887299
$624$		0			0
$625$	−17.2487			−0.689948
$626$	−10.1769	−	10.1769i	−0.406751	−	0.406751i
$627$		0			0
$628$			18.7846i			0.749588i
$629$	−10.2784	−	10.2784i	−0.409828	−	0.409828i
$630$		0			0
$631$	15.1506	+	15.1506i	0.603137	+	0.603137i	0.941144	−	0.338007i	$-0.109753\pi$
$631$	15.1506	+	15.1506i	0.603137	+	0.603137i	−0.338007	+	0.941144i	$0.609753\pi$
$632$		0			0
$633$		0			0
$634$			2.14359i			0.0851330i
$635$	−2.03339	+	2.03339i	−0.0806925	+	0.0806925i
$636$		0			0
$637$		0			0
$638$			17.5254i			0.693836i
$639$		0			0
$640$		0			0
$641$	26.9444			1.06424			0.532120	−	0.846669i	$-0.321396\pi$
$641$	26.9444			1.06424			0.532120	+	0.846669i	$0.321396\pi$
$642$		0			0
$643$	0.705771	−	0.705771i	0.0278329	−	0.0278329i	−0.693053	−	0.720886i	$-0.743735\pi$
$643$	0.705771	−	0.705771i	0.0278329	−	0.0278329i	0.720886	+	0.693053i	$0.243735\pi$
$644$	6.69213	−	6.69213i	0.263707	−	0.263707i
$645$		0			0
$646$	−12.4974			−0.491705
$647$	−47.9817			−1.88636			−0.943178	−	0.332288i	$-0.892180\pi$
$647$	−47.9817			−1.88636			−0.943178	+	0.332288i	$0.892180\pi$
$648$		0			0
$649$			63.1769i			2.47991i
$650$		0			0
$651$		0			0
$652$	−21.5167	+	21.5167i	−0.842657	+	0.842657i
$653$		−	11.3137i		−	0.442740i	−0.975190	−	0.221370i	$-0.928947\pi$
$653$		−	11.3137i		−	0.442740i	0.975190	−	0.221370i	$-0.0710528\pi$
$654$		0			0
$655$	−3.66025	+	3.66025i	−0.143018	+	0.143018i
$656$	−15.4548	−	15.4548i	−0.603409	−	0.603409i
$657$		0			0
$658$	18.3923	+	18.3923i	0.717007	+	0.717007i
$659$		−	26.8429i		−	1.04565i	−0.852440	−	0.522825i	$-0.824878\pi$
$659$		−	26.8429i		−	1.04565i	0.852440	−	0.522825i	$-0.175122\pi$
$660$		0			0
$661$	−3.22243	−	3.22243i	−0.125338	−	0.125338i	0.641655	−	0.766993i	$-0.278248\pi$
$661$	−3.22243	−	3.22243i	−0.125338	−	0.125338i	−0.766993	+	0.641655i	$0.778248\pi$
$662$	13.6617			0.530976
$663$		0			0
$664$		0			0
$665$	−3.48477	−	3.48477i	−0.135133	−	0.135133i
$666$		0			0
$667$			3.46410i			0.134131i
$668$	−2.07055	−	2.07055i	−0.0801121	−	0.0801121i
$669$		0			0
$670$	−9.60770	−	9.60770i	−0.371178	−	0.371178i
$671$	−12.2846	+	12.2846i	−0.474242	+	0.474242i
$672$		0			0
$673$			39.5885i			1.52602i	0.646385	+	0.763011i	$0.276280\pi$
$673$			39.5885i			1.52602i	−0.646385	+	0.763011i	$0.723720\pi$
$674$	19.9005	−	19.9005i	0.766540	−	0.766540i
$675$		0			0
$676$		0			0
$677$		−	42.9812i		−	1.65190i	−0.563742	−	0.825951i	$-0.690639\pi$
$677$		−	42.9812i		−	1.65190i	0.563742	−	0.825951i	$-0.309361\pi$
$678$		0			0
$679$	−23.3923			−0.897714
$680$		0			0
$681$		0			0
$682$	78.8897	−	78.8897i	3.02084	−	3.02084i
$683$	19.4572	−	19.4572i	0.744510	−	0.744510i	−0.228933	−	0.973442i	$-0.573524\pi$
$683$	19.4572	−	19.4572i	0.744510	−	0.744510i	0.973442	+	0.228933i	$0.0735235\pi$
$684$		0			0
$685$	−0.784610			−0.0299784
$686$	39.6723			1.51470
$687$		0			0
$688$			17.0718i			0.650856i
$689$		0			0
$690$		0			0
$691$	28.8827	−	28.8827i	1.09875	−	1.09875i	0.104192	−	0.994557i	$-0.466774\pi$
$691$	28.8827	−	28.8827i	1.09875	−	1.09875i	0.994557	−	0.104192i	$-0.0332256\pi$
$692$		−	11.1106i		−	0.422363i
$693$		0			0
$694$	21.1769	−	21.1769i	0.803865	−	0.803865i
$695$	9.00292	+	9.00292i	0.341500	+	0.341500i
$696$		0			0
$697$	6.92820	+	6.92820i	0.262424	+	0.262424i
$698$		−	69.2693i		−	2.62188i
$699$		0			0
$700$	−12.1962	−	12.1962i	−0.460971	−	0.460971i
$701$	−6.21166			−0.234611			−0.117306	−	0.993096i	$-0.537426\pi$
$701$	−6.21166			−0.234611			−0.117306	+	0.993096i	$0.537426\pi$
$702$		0			0
$703$	−28.2487			−1.06542
$704$	−35.0507	−	35.0507i	−1.32102	−	1.32102i
$705$		0			0
$706$		−	24.3923i		−	0.918017i
$707$	−21.6293	−	21.6293i	−0.813454	−	0.813454i
$708$		0			0
$709$	−3.56218	−	3.56218i	−0.133780	−	0.133780i	0.637046	−	0.770826i	$-0.280156\pi$
$709$	−3.56218	−	3.56218i	−0.133780	−	0.133780i	−0.770826	+	0.637046i	$0.780156\pi$
$710$	1.71882	−	1.71882i	0.0645062	−	0.0645062i
$711$		0			0
$712$		0			0
$713$	15.5935	−	15.5935i	0.583982	−	0.583982i
$714$		0			0
$715$		0			0
$716$			16.0096i			0.598307i
$717$		0			0
$718$	20.0000			0.746393
$719$	−9.97382			−0.371961			−0.185980	−	0.982553i	$-0.559546\pi$
$719$	−9.97382			−0.371961			−0.185980	+	0.982553i	$0.559546\pi$
$720$		0			0
$721$	11.8301	−	11.8301i	0.440577	−	0.440577i
$722$	9.69642	−	9.69642i	0.360863	−	0.360863i
$723$		0			0
$724$	12.0000			0.445976
$725$	6.31319			0.234466
$726$		0			0
$727$			41.1051i			1.52450i	0.647280	+	0.762252i	$0.275906\pi$
$727$			41.1051i			1.52450i	−0.647280	+	0.762252i	$0.724094\pi$
$728$		0			0
$729$		0			0
$730$	−11.8564	+	11.8564i	−0.438825	+	0.438825i
$731$		−	7.65308i		−	0.283059i
$732$		0			0
$733$	−10.2417	+	10.2417i	−0.378285	+	0.378285i	−0.870483	−	0.492198i	$-0.836193\pi$
$733$	−10.2417	+	10.2417i	−0.378285	+	0.378285i	0.492198	+	0.870483i	$0.336193\pi$
$734$	−21.7680	−	21.7680i	−0.803472	−	0.803472i
$735$		0			0
$736$	−13.8564	−	13.8564i	−0.510754	−	0.510754i
$737$		−	57.5023i		−	2.11812i
$738$		0			0
$739$	−8.46410	−	8.46410i	−0.311357	−	0.311357i	0.534078	−	0.845435i	$-0.320659\pi$
$739$	−8.46410	−	8.46410i	−0.311357	−	0.311357i	−0.845435	+	0.534078i	$0.820659\pi$
$740$	11.8685			0.436295
$741$		0			0
$742$	−33.8564			−1.24291
$743$	22.0082	+	22.0082i	0.807404	+	0.807404i	0.984240	−	0.176836i	$-0.0565863\pi$
$743$	22.0082	+	22.0082i	0.807404	+	0.807404i	−0.176836	+	0.984240i	$0.556586\pi$
$744$		0			0
$745$		−	10.5359i		−	0.386005i
$746$	−33.3591	−	33.3591i	−1.22136	−	1.22136i
$747$		0			0
$748$	15.7128	+	15.7128i	0.574517	+	0.574517i
$749$	17.7656	−	17.7656i	0.649141	−	0.649141i
$750$		0			0
$751$		−	37.8564i		−	1.38140i	−0.723141	−	0.690700i	$-0.757303\pi$
$751$		−	37.8564i		−	1.38140i	0.723141	−	0.690700i	$-0.242697\pi$
$752$	19.0411	−	19.0411i	0.694358	−	0.694358i
$753$		0			0
$754$		0			0
$755$			1.59008i			0.0578689i
$756$		0			0
$757$	−50.3923			−1.83154			−0.915770	−	0.401704i	$-0.868418\pi$
$757$	−50.3923			−1.83154			−0.915770	+	0.401704i	$0.868418\pi$
$758$	41.3911			1.50339
$759$		0			0
$760$		0			0
$761$	−30.2533	+	30.2533i	−1.09668	+	1.09668i	−0.101885	+	0.994796i	$0.532487\pi$
$761$	−30.2533	+	30.2533i	−1.09668	+	1.09668i	−0.994796	+	0.101885i	$0.967513\pi$
$762$		0			0
$763$	−11.7321			−0.424729
$764$	3.38323			0.122401
$765$		0			0
$766$		−	20.0000i		−	0.722629i
$767$		0			0
$768$		0			0
$769$	20.5167	−	20.5167i	0.739850	−	0.739850i	−0.232699	−	0.972549i	$-0.574756\pi$
$769$	20.5167	−	20.5167i	0.739850	−	0.739850i	0.972549	+	0.232699i	$0.0747557\pi$
$770$			17.5254i			0.631570i
$771$		0			0
$772$	15.6603	−	15.6603i	0.563625	−	0.563625i
$773$	−29.7356	−	29.7356i	−1.06952	−	1.06952i	−0.997396	−	0.0721211i	$-0.977023\pi$
$773$	−29.7356	−	29.7356i	−1.06952	−	1.06952i	−0.0721211	−	0.997396i	$-0.522977\pi$
$774$		0			0
$775$	−28.4186	−	28.4186i	−1.02083	−	1.02083i
$776$		0			0
$777$		0			0
$778$	2.53590	+	2.53590i	0.0909164	+	0.0909164i
$779$	19.0411			0.682219
$780$		0			0
$781$	10.2872			0.368104
$782$	6.21166	+	6.21166i	0.222128	+	0.222128i
$783$		0			0
$784$		−	13.0718i		−	0.466850i
$785$	−4.86181	−	4.86181i	−0.173526	−	0.173526i
$786$		0			0
$787$	14.0981	+	14.0981i	0.502542	+	0.502542i	0.912227	−	0.409685i	$-0.134361\pi$
$787$	14.0981	+	14.0981i	0.502542	+	0.502542i	−0.409685	+	0.912227i	$0.634361\pi$
$788$	29.5969	−	29.5969i	1.05435	−	1.05435i
$789$		0			0
$790$		−	4.67949i		−	0.166489i
$791$	−13.9019	+	13.9019i	−0.494295	+	0.494295i
$792$		0			0
$793$		0			0
$794$			51.5408i			1.82912i
$795$		0			0
$796$	12.9282			0.458228
$797$	−13.8647			−0.491114			−0.245557	−	0.969382i	$-0.578971\pi$
$797$	−13.8647			−0.491114			−0.245557	+	0.969382i	$0.578971\pi$
$798$		0			0
$799$	−8.53590	+	8.53590i	−0.301978	+	0.301978i
$800$	−25.2528	+	25.2528i	−0.892820	+	0.892820i
$801$		0			0
$802$	−24.2872			−0.857610
$803$	−70.9609			−2.50415
$804$		0			0
$805$			3.46410i			0.122094i
$806$		0			0
$807$		0			0
$808$		0			0
$809$		−	33.6637i		−	1.18355i	−0.806102	−	0.591777i	$-0.798427\pi$
$809$		−	33.6637i		−	1.18355i	0.806102	−	0.591777i	$-0.201573\pi$
$810$		0			0
$811$	2.90192	−	2.90192i	0.101900	−	0.101900i	−0.654319	−	0.756219i	$-0.727044\pi$
$811$	2.90192	−	2.90192i	0.101900	−	0.101900i	0.756219	+	0.654319i	$0.227044\pi$
$812$	3.86370	+	3.86370i	0.135589	+	0.135589i
$813$		0			0
$814$	71.0333	+	71.0333i	2.48972	+	2.48972i
$815$		−	11.1378i		−	0.390142i
$816$		0			0
$817$	−10.5167	−	10.5167i	−0.367931	−	0.367931i
$818$	19.5216			0.682556
$819$		0			0
$820$	−8.00000			−0.279372
$821$	15.1402	+	15.1402i	0.528398	+	0.528398i	0.920095	−	0.391696i	$-0.128112\pi$
$821$	15.1402	+	15.1402i	0.528398	+	0.528398i	−0.391696	+	0.920095i	$0.628112\pi$
$822$		0			0
$823$			16.3923i			0.571400i	0.958319	+	0.285700i	$0.0922261\pi$
$823$			16.3923i			0.571400i	−0.958319	+	0.285700i	$0.907774\pi$
$824$		0			0
$825$		0			0
$826$	27.8564	+	27.8564i	0.969248	+	0.969248i
$827$	11.8685	−	11.8685i	0.412709	−	0.412709i	−0.469972	−	0.882681i	$-0.655736\pi$
$827$	11.8685	−	11.8685i	0.412709	−	0.412709i	0.882681	+	0.469972i	$0.155736\pi$
$828$		0			0
$829$		−	36.7128i		−	1.27509i	−0.770414	−	0.637544i	$-0.779950\pi$
$829$		−	36.7128i		−	1.27509i	0.770414	−	0.637544i	$-0.220050\pi$
$830$	−0.554803	+	0.554803i	−0.0192575	+	0.0192575i
$831$		0			0
$832$		0			0
$833$			5.85993i			0.203034i
$834$		0			0
$835$	1.07180			0.0370911
$836$	43.1843			1.49356
$837$		0			0
$838$	−36.7846	+	36.7846i	−1.27070	+	1.27070i
$839$	22.3872	−	22.3872i	0.772891	−	0.772891i	−0.205720	−	0.978611i	$-0.565954\pi$
$839$	22.3872	−	22.3872i	0.772891	−	0.772891i	0.978611	+	0.205720i	$0.0659535\pi$
$840$		0			0
$841$	27.0000			0.931034
$842$	−38.5627			−1.32896
$843$		0			0
$844$		−	9.60770i		−	0.330711i
$845$		0			0
$846$		0			0
$847$	−37.4186	+	37.4186i	−1.28572	+	1.28572i
$848$			35.0507i			1.20365i
$849$		0			0
$850$	11.3205	−	11.3205i	0.388290	−	0.388290i
$851$	14.0406	+	14.0406i	0.481306	+	0.481306i
$852$		0			0
$853$	−18.2224	−	18.2224i	−0.623924	−	0.623924i	0.322608	−	0.946533i	$-0.395440\pi$
$853$	−18.2224	−	18.2224i	−0.623924	−	0.623924i	−0.946533	+	0.322608i	$0.895440\pi$
$854$			10.8332i			0.370706i
$855$		0			0
$856$		0			0
$857$	45.7081			1.56136			0.780679	−	0.624932i	$-0.214873\pi$
$857$	45.7081			1.56136			0.780679	+	0.624932i	$0.214873\pi$
$858$		0			0
$859$	−40.8038			−1.39221			−0.696105	−	0.717940i	$-0.745085\pi$
$859$	−40.8038			−1.39221			−0.696105	+	0.717940i	$0.745085\pi$
$860$	4.41851	+	4.41851i	0.150670	+	0.150670i
$861$		0			0
$862$		−	23.7128i		−	0.807662i
$863$	11.7298	+	11.7298i	0.399287	+	0.399287i	0.877982	−	0.478694i	$-0.158890\pi$
$863$	11.7298	+	11.7298i	0.399287	+	0.399287i	−0.478694	+	0.877982i	$0.658890\pi$
$864$		0			0
$865$	2.87564	+	2.87564i	0.0977748	+	0.0977748i
$866$	16.3142	−	16.3142i	0.554380	−	0.554380i
$867$		0			0
$868$		−	34.7846i		−	1.18067i
$869$	14.0034	−	14.0034i	0.475034	−	0.475034i
$870$		0			0
$871$		0			0
$872$		0			0
$873$		0			0
$874$	17.0718			0.577462
$875$	13.3843			0.452471
$876$		0			0
$877$	27.1962	−	27.1962i	0.918349	−	0.918349i	−0.0785605	−	0.996909i	$-0.525032\pi$
$877$	27.1962	−	27.1962i	0.918349	−	0.918349i	0.996909	+	0.0785605i	$0.0250324\pi$
$878$	30.5307	−	30.5307i	1.03036	−	1.03036i
$879$		0			0
$880$	18.1436			0.611620
$881$	24.9754			0.841442			0.420721	−	0.907190i	$-0.361777\pi$
$881$	24.9754			0.841442			0.420721	+	0.907190i	$0.361777\pi$
$882$		0			0
$883$			17.7846i			0.598500i	0.954175	+	0.299250i	$0.0967364\pi$
$883$			17.7846i			0.598500i	−0.954175	+	0.299250i	$0.903264\pi$
$884$		0			0
$885$		0			0
$886$	49.5692	−	49.5692i	1.66531	−	1.66531i
$887$			0.582009i			0.0195420i	0.999952	+	0.00977098i	$0.00311025\pi$
$887$			0.582009i			0.0195420i	−0.999952	+	0.00977098i	$0.996890\pi$
$888$		0			0
$889$	−5.36603	+	5.36603i	−0.179971	+	0.179971i
$890$	11.8685	+	11.8685i	0.397833	+	0.397833i
$891$		0			0
$892$	−6.78461	−	6.78461i	−0.227166	−	0.227166i
$893$			23.4596i			0.785046i
$894$		0			0
$895$	−4.14359	−	4.14359i	−0.138505	−	0.138505i
$896$		0			0
$897$		0			0
$898$	10.5359			0.351587
$899$	9.00292	+	9.00292i	0.300264	+	0.300264i
$900$		0			0
$901$		−	15.7128i		−	0.523470i
$902$	−47.8802	−	47.8802i	−1.59424	−	1.59424i
$903$		0			0
$904$		0			0
$905$	−3.10583	+	3.10583i	−0.103241	+	0.103241i
$906$		0			0
$907$		−	18.0000i		−	0.597680i	−0.954303	−	0.298840i	$-0.903400\pi$
$907$		−	18.0000i		−	0.597680i	0.954303	−	0.298840i	$-0.0965997\pi$
$908$	−19.0411	+	19.0411i	−0.631902	+	0.631902i
$909$		0			0
$910$		0			0
$911$		−	6.76646i		−	0.224183i	−0.993698	−	0.112091i	$-0.964245\pi$
$911$		−	6.76646i		−	0.224183i	0.993698	−	0.112091i	$-0.0357549\pi$
$912$		0			0
$913$	−3.32051			−0.109893
$914$	−8.20788			−0.271493
$915$		0			0
$916$	0.535898	−	0.535898i	0.0177066	−	0.0177066i
$917$	−9.65926	+	9.65926i	−0.318977	+	0.318977i
$918$		0			0
$919$	33.1769			1.09441			0.547203	−	0.837000i	$-0.315693\pi$
$919$	33.1769			1.09441			0.547203	+	0.837000i	$0.315693\pi$
$920$		0			0
$921$		0			0
$922$			74.6410i			2.45817i
$923$		0			0
$924$		0			0
$925$	25.5885	−	25.5885i	0.841343	−	0.841343i
$926$		−	10.8332i		−	0.356002i
$927$		0			0
$928$	8.00000	−	8.00000i	0.262613	−	0.262613i
$929$	−30.6322	−	30.6322i	−1.00501	−	1.00501i	−0.999987	−	0.00502332i	$-0.998401\pi$
$929$	−30.6322	−	30.6322i	−1.00501	−	1.00501i	−0.00502332	−	0.999987i	$-0.501599\pi$
$930$		0			0
$931$	8.05256	+	8.05256i	0.263912	+	0.263912i
$932$		−	20.9086i		−	0.684884i
$933$		0			0
$934$	31.1769	+	31.1769i	1.02014	+	1.02014i
$935$	−8.13355			−0.265996
$936$		0			0
$937$	31.5692			1.03132			0.515661	−	0.856793i	$-0.327547\pi$
$937$	31.5692			1.03132			0.515661	+	0.856793i	$0.327547\pi$
$938$	−25.3543	−	25.3543i	−0.827848	−	0.827848i
$939$		0			0
$940$		−	9.85641i		−	0.321481i
$941$	−9.00292	−	9.00292i	−0.293487	−	0.293487i	0.544969	−	0.838456i	$-0.316541\pi$
$941$	−9.00292	−	9.00292i	−0.293487	−	0.293487i	−0.838456	+	0.544969i	$0.816541\pi$
$942$		0			0
$943$	−9.46410	−	9.46410i	−0.308194	−	0.308194i
$944$	28.8391	−	28.8391i	0.938632	−	0.938632i
$945$		0			0
$946$			52.8897i			1.71959i
$947$	−2.82843	+	2.82843i	−0.0919115	+	0.0919115i	−0.751568	−	0.659656i	$-0.770702\pi$
$947$	−2.82843	+	2.82843i	−0.0919115	+	0.0919115i	0.659656	+	0.751568i	$0.270702\pi$
$948$		0			0
$949$		0			0
$950$		−	31.1127i		−	1.00943i
$951$		0			0
$952$		0			0
$953$	−25.2800			−0.818899			−0.409449	−	0.912333i	$-0.634279\pi$
$953$	−25.2800			−0.818899			−0.409449	+	0.912333i	$0.634279\pi$
$954$		0			0
$955$	−0.875644	+	0.875644i	−0.0283352	+	0.0283352i
$956$	−19.0411	+	19.0411i	−0.615834	+	0.615834i
$957$		0			0
$958$	8.00000			0.258468
$959$	−2.07055			−0.0668616
$960$		0			0
$961$		−	50.0526i		−	1.61460i
$962$		0			0
$963$		0			0
$964$	−23.4641	+	23.4641i	−0.755728	+	0.755728i
$965$			8.10634i			0.260952i
$966$		0			0
$967$	2.26795	−	2.26795i	0.0729323	−	0.0729323i	−0.669700	−	0.742632i	$-0.733577\pi$
$967$	2.26795	−	2.26795i	0.0729323	−	0.0729323i	0.742632	+	0.669700i	$0.233577\pi$
$968$		0			0
$969$		0			0
$970$	12.5359	+	12.5359i	0.402503	+	0.402503i
$971$		−	6.76646i		−	0.217146i	−0.994088	−	0.108573i	$-0.965372\pi$
$971$		−	6.76646i		−	0.217146i	0.994088	−	0.108573i	$-0.0346281\pi$
$972$		0			0
$973$	23.7583	+	23.7583i	0.761657	+	0.761657i
$974$	−28.6360			−0.917557
$975$		0			0
$976$	11.2154			0.358996
$977$	−27.0459	−	27.0459i	−0.865276	−	0.865276i	0.126669	−	0.991945i	$-0.459571\pi$
$977$	−27.0459	−	27.0459i	−0.865276	−	0.865276i	−0.991945	+	0.126669i	$0.959571\pi$
$978$		0			0
$979$			71.0333i			2.27023i
$980$	−3.38323	−	3.38323i	−0.108073	−	0.108073i
$981$		0			0
$982$	−23.0718	−	23.0718i	−0.736251	−	0.736251i
$983$	−22.6646	+	22.6646i	−0.722888	+	0.722888i	−0.969192	−	0.246305i	$-0.920784\pi$
$983$	−22.6646	+	22.6646i	−0.722888	+	0.722888i	0.246305	+	0.969192i	$0.420784\pi$
$984$		0			0
$985$			15.3205i			0.488152i
$986$	−3.58630	+	3.58630i	−0.114211	+	0.114211i
$987$		0			0
$988$		0			0
$989$			10.4543i			0.332427i
$990$		0			0
$991$	30.3923			0.965443			0.482722	−	0.875774i	$-0.339648\pi$
$991$	30.3923			0.965443			0.482722	+	0.875774i	$0.339648\pi$
$992$	−72.0234			−2.28674
$993$		0			0
$994$	4.53590	−	4.53590i	0.143870	−	0.143870i
$995$	−3.34607	+	3.34607i	−0.106077	+	0.106077i
$996$		0			0
$997$	1.78461			0.0565192			0.0282596	−	0.999601i	$-0.491003\pi$
$997$	1.78461			0.0565192			0.0282596	+	0.999601i	$0.491003\pi$
$998$	78.4381			2.48291
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1521.2.i.d.746.1		8
3.2	odd	2	inner	1521.2.i.d.746.4		8
13.3	even	3		117.2.ba.a.71.2	yes	8
13.5	odd	4		1521.2.i.e.944.1		8
13.7	odd	12		117.2.ba.a.89.1	yes	8
13.8	odd	4	inner	1521.2.i.d.944.4		8
13.12	even	2		1521.2.i.e.746.4		8
39.5	even	4		1521.2.i.e.944.4		8
39.8	even	4	inner	1521.2.i.d.944.1		8
39.20	even	12		117.2.ba.a.89.2	yes	8
39.29	odd	6		117.2.ba.a.71.1	✓	8
39.38	odd	2		1521.2.i.e.746.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.2.ba.a.71.1	✓	8	39.29	odd	6
117.2.ba.a.71.2	yes	8	13.3	even	3
117.2.ba.a.89.1	yes	8	13.7	odd	12
117.2.ba.a.89.2	yes	8	39.20	even	12
1521.2.i.d.746.1		8	1.1	even	1	trivial
1521.2.i.d.746.4		8	3.2	odd	2	inner
1521.2.i.d.944.1		8	39.8	even	4	inner
1521.2.i.d.944.4		8	13.8	odd	4	inner
1521.2.i.e.746.1		8	39.38	odd	2
1521.2.i.e.746.4		8	13.12	even	2
1521.2.i.e.944.1		8	13.5	odd	4
1521.2.i.e.944.4		8	39.5	even	4

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:	\( N \)	\(=\)	\( 1521 = 3^{2} \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1521.i (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.41421 - 1.41421i) q^{2} +2.00000i q^{4} +(-0.517638 - 0.517638i) q^{5} +(-1.36603 - 1.36603i) q^{7} +1.46410i q^{10} +(-4.38134 + 4.38134i) q^{11} +3.86370i q^{14} +4.00000 q^{16} -1.79315 q^{17} +(-2.46410 + 2.46410i) q^{19} +(1.03528 - 1.03528i) q^{20} +12.3923 q^{22} +2.44949 q^{23} -4.46410i q^{25} +(2.73205 - 2.73205i) q^{28} +1.41421i q^{29} +(6.36603 - 6.36603i) q^{31} +(-5.65685 - 5.65685i) q^{32} +(2.53590 + 2.53590i) q^{34} +1.41421i q^{35} +(5.73205 + 5.73205i) q^{37} +6.96953 q^{38} +(-3.86370 - 3.86370i) q^{41} +4.26795i q^{43} +(-8.76268 - 8.76268i) q^{44} +(-3.46410 - 3.46410i) q^{46} +(4.76028 - 4.76028i) q^{47} -3.26795i q^{49} +(-6.31319 + 6.31319i) q^{50} +8.76268i q^{53} +4.53590 q^{55} +(2.00000 - 2.00000i) q^{58} +(7.20977 - 7.20977i) q^{59} +2.80385 q^{61} -18.0058 q^{62} +8.00000i q^{64} +(-6.56218 + 6.56218i) q^{67} -3.58630i q^{68} +(2.00000 - 2.00000i) q^{70} +(-1.17398 - 1.17398i) q^{71} +(8.09808 + 8.09808i) q^{73} -16.2127i q^{74} +(-4.92820 - 4.92820i) q^{76} +11.9700 q^{77} -3.19615 q^{79} +(-2.07055 - 2.07055i) q^{80} +10.9282i q^{82} +(0.378937 + 0.378937i) q^{83} +(0.928203 + 0.928203i) q^{85} +(6.03579 - 6.03579i) q^{86} +(8.10634 - 8.10634i) q^{89} +4.89898i q^{92} -13.4641 q^{94} +2.55103 q^{95} +(8.56218 - 8.56218i) q^{97} +(-4.62158 + 4.62158i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{7} + 32 q^{16} + 8 q^{19} + 16 q^{22} + 8 q^{28} + 44 q^{31} + 48 q^{34} + 32 q^{37} + 64 q^{55} + 16 q^{58} + 64 q^{61} - 4 q^{67} + 16 q^{70} + 44 q^{73} + 16 q^{76} + 16 q^{79} - 48 q^{85}+ \cdots + 20 q^{97}+O(q^{100}) \) 8 * q - 4 * q^7 + 32 * q^16 + 8 * q^19 + 16 * q^22 + 8 * q^28 + 44 * q^31 + 48 * q^34 + 32 * q^37 + 64 * q^55 + 16 * q^58 + 64 * q^61 - 4 * q^67 + 16 * q^70 + 44 * q^73 + 16 * q^76 + 16 * q^79 - 48 * q^85 - 80 * q^94 + 20 * q^97

Introduction

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