LMFDB - Embedded newform 847.2.b.f.846.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [847,2,Mod(846,847)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(847, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1]))

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

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

chi := DirichletCharacter("847.846");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 847 = 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	847.b (of order $2$, degree $1$, 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:	$6.76332905120$
Analytic rank:	$0$
Dimension:	$16$
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} + 20x^{14} + 260x^{12} + 2030x^{10} + 11605x^{8} + 42100x^{6} + 106925x^{4} + 113575x^{2} + 87025 $ x^16 + 20x^14 + 260x^12 + 2030x^10 + 11605x^8 + 42100x^6 + 106925x^4 + 113575*x^2 + 87025
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	no (minimal twist has level 77)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			846.7
Root			$1.17141 + 2.02895i$ of defining polynomial
Character	$\chi$	$=$	847.846
Dual form			847.2.b.f.846.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.502754i q^{2} -2.88003i q^{3} +1.74724 q^{4} +0.602090i q^{5} -1.44795 q^{6} +(-2.34283 - 1.22930i) q^{7} -1.88394i q^{8} -5.29456 q^{9} +O(q^{10})$	\(q-0.502754i q^{2} -2.88003i q^{3} +1.74724 q^{4} +0.602090i q^{5} -1.44795 q^{6} +(-2.34283 - 1.22930i) q^{7} -1.88394i q^{8} -5.29456 q^{9} +0.302703 q^{10} -5.03209i q^{12} -2.34283 q^{13} +(-0.618034 + 1.17787i) q^{14} +1.73403 q^{15} +2.54732 q^{16} -1.14524 q^{17} +2.66186i q^{18} -5.07304 q^{19} +1.05199i q^{20} +(-3.54041 + 6.74740i) q^{21} -3.85410 q^{23} -5.42580 q^{24} +4.63749 q^{25} +1.17787i q^{26} +6.60838i q^{27} +(-4.09347 - 2.14787i) q^{28} -2.15911i q^{29} -0.871793i q^{30} -6.23627i q^{31} -5.04855i q^{32} +0.575775i q^{34} +(0.740147 - 1.41059i) q^{35} -9.25085 q^{36} -7.41056 q^{37} +2.55049i q^{38} +6.74740i q^{39} +1.13430 q^{40} +11.7597 q^{41} +(3.39228 + 1.77995i) q^{42} -1.73205i q^{43} -3.18780i q^{45} +1.93767i q^{46} -9.92205i q^{47} -7.33635i q^{48} +(3.97766 + 5.76005i) q^{49} -2.33152i q^{50} +3.29833i q^{51} -4.09347 q^{52} +6.12165 q^{53} +3.32239 q^{54} +(-2.31592 + 4.41374i) q^{56} +14.6105i q^{57} -1.08550 q^{58} +4.70256i q^{59} +3.02977 q^{60} +8.70908 q^{61} -3.13531 q^{62} +(12.4042 + 6.50858i) q^{63} +2.55645 q^{64} -1.41059i q^{65} -6.46905 q^{67} -2.00101 q^{68} +11.0999i q^{69} +(-0.709180 - 0.372112i) q^{70} +5.32603 q^{71} +9.97462i q^{72} +2.49756 q^{73} +3.72569i q^{74} -13.3561i q^{75} -8.86381 q^{76} +3.39228 q^{78} +1.19060i q^{79} +1.53371i q^{80} +3.14866 q^{81} -5.91224i q^{82} -7.90565 q^{83} +(-6.18594 + 11.7893i) q^{84} -0.689539i q^{85} -0.870796 q^{86} -6.21828 q^{87} -11.9963i q^{89} -1.60268 q^{90} +(5.48883 + 2.88003i) q^{91} -6.73403 q^{92} -17.9606 q^{93} -4.98835 q^{94} -3.05443i q^{95} -14.5400 q^{96} +5.82158i q^{97} +(2.89589 - 1.99978i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 32 q^{9}+O(q^{10}) $ 16 * q - 32 * q^9	$ 16 q - 32 q^{9} + 8 q^{14} - 20 q^{15} + 16 q^{16} - 8 q^{23} - 40 q^{25} - 60 q^{36} - 36 q^{37} - 20 q^{42} + 48 q^{49} + 20 q^{53} - 4 q^{56} + 28 q^{58} - 140 q^{60} + 12 q^{64} - 4 q^{67} + 100 q^{70} + 44 q^{71} - 20 q^{78} - 56 q^{81} - 24 q^{86} + 80 q^{91} - 60 q^{92} - 20 q^{93}+O(q^{100}) $ 16 * q - 32 * q^9 + 8 * q^14 - 20 * q^15 + 16 * q^16 - 8 * q^23 - 40 * q^25 - 60 * q^36 - 36 * q^37 - 20 * q^42 + 48 * q^49 + 20 * q^53 - 4 * q^56 + 28 * q^58 - 140 * q^60 + 12 * q^64 - 4 * q^67 + 100 * q^70 + 44 * q^71 - 20 * q^78 - 56 * q^81 - 24 * q^86 + 80 * q^91 - 60 * q^92 - 20 * q^93

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/847\mathbb{Z}\right)^\times$.

$n$	$122$	$365$
$\chi(n)$	$-1$	$-1$

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 $

$2$		−	0.502754i		−	0.355501i	−0.984076	−	0.177750i	$-0.943118\pi$
$2$		−	0.502754i		−	0.355501i	0.984076	−	0.177750i	$-0.0568820\pi$
$3$		−	2.88003i		−	1.66278i	−0.555686	−	0.831392i	$-0.687544\pi$
$3$		−	2.88003i		−	1.66278i	0.555686	−	0.831392i	$-0.312456\pi$
$4$	1.74724			0.873619
$5$			0.602090i			0.269263i	0.990896	+	0.134631i	$0.0429850\pi$
$5$			0.602090i			0.269263i	−0.990896	+	0.134631i	$0.957015\pi$
$6$	−1.44795			−0.591121
$7$	−2.34283	−	1.22930i	−0.885505	−	0.464630i
$7$	−2.34283	−	1.22930i	−0.885505	−	0.464630i
$8$		−	1.88394i		−	0.666073i
$9$	−5.29456			−1.76485
$10$	0.302703			0.0957231
$11$		0			0
$11$		0			0
$12$		−	5.03209i		−	1.45264i
$13$	−2.34283			−0.649783			−0.324891	−	0.945751i	$-0.605328\pi$
$13$	−2.34283			−0.649783			−0.324891	+	0.945751i	$0.605328\pi$
$14$	−0.618034	+	1.17787i	−0.165177	+	0.314798i
$15$	1.73403			0.447726
$16$	2.54732			0.636830
$17$	−1.14524			−0.277762			−0.138881	−	0.990309i	$-0.544351\pi$
$17$	−1.14524			−0.277762			−0.138881	+	0.990309i	$0.544351\pi$
$18$			2.66186i			0.627406i
$19$	−5.07304			−1.16384			−0.581918	−	0.813248i	$-0.697697\pi$
$19$	−5.07304			−1.16384			−0.581918	+	0.813248i	$0.697697\pi$
$20$			1.05199i			0.235233i
$21$	−3.54041	+	6.74740i	−0.772580	+	1.47240i
$22$		0			0
$23$	−3.85410			−0.803636			−0.401818	−	0.915720i	$-0.631622\pi$
$23$	−3.85410			−0.803636			−0.401818	+	0.915720i	$0.631622\pi$
$24$	−5.42580			−1.10754
$25$	4.63749			0.927498
$26$			1.17787i			0.230998i
$27$			6.60838i			1.27178i
$28$	−4.09347	−	2.14787i	−0.773594	−	0.405910i
$29$		−	2.15911i		−	0.400936i	−0.979700	−	0.200468i	$-0.935754\pi$
$29$		−	2.15911i		−	0.400936i	0.979700	−	0.200468i	$-0.0642463\pi$
$30$		−	0.871793i		−	0.159167i
$31$		−	6.23627i		−	1.12007i	−0.828470	−	0.560034i	$-0.810788\pi$
$31$		−	6.23627i		−	1.12007i	0.828470	−	0.560034i	$-0.189212\pi$
$32$		−	5.04855i		−	0.892467i
$33$		0			0
$34$			0.575775i			0.0987447i
$35$	0.740147	−	1.41059i	0.125108	−	0.238433i
$36$	−9.25085			−1.54181
$37$	−7.41056			−1.21829			−0.609144	−	0.793060i	$-0.708487\pi$
$37$	−7.41056			−1.21829			−0.609144	+	0.793060i	$0.708487\pi$
$38$			2.55049i			0.413745i
$39$			6.74740i			1.08045i
$40$	1.13430			0.179349
$41$	11.7597			1.83656			0.918279	−	0.395935i	$-0.129579\pi$
$41$	11.7597			1.83656			0.918279	+	0.395935i	$0.129579\pi$
$42$	3.39228	+	1.77995i	0.523441	+	0.274653i
$43$		−	1.73205i		−	0.264135i	−0.991241	−	0.132068i	$-0.957838\pi$
$43$		−	1.73205i		−	0.264135i	0.991241	−	0.132068i	$-0.0421616\pi$
$44$		0			0
$45$		−	3.18780i		−	0.475209i
$46$			1.93767i			0.285693i
$47$		−	9.92205i		−	1.44728i	−0.690178	−	0.723640i	$-0.742468\pi$
$47$		−	9.92205i		−	1.44728i	0.690178	−	0.723640i	$-0.257532\pi$
$48$		−	7.33635i		−	1.05891i
$49$	3.97766	+	5.76005i	0.568237	+	0.822865i
$50$		−	2.33152i		−	0.329726i
$51$			3.29833i			0.461859i
$52$	−4.09347			−0.567663
$53$	6.12165			0.840873			0.420436	−	0.907322i	$-0.361877\pi$
$53$	6.12165			0.840873			0.420436	+	0.907322i	$0.361877\pi$
$54$	3.32239			0.452120
$55$		0			0
$56$	−2.31592	+	4.41374i	−0.309478	+	0.589811i
$57$			14.6105i			1.93521i
$58$	−1.08550			−0.142533
$59$			4.70256i			0.612221i	0.951996	+	0.306111i	$0.0990277\pi$
$59$			4.70256i			0.612221i	−0.951996	+	0.306111i	$0.900972\pi$
$60$	3.02977			0.391142
$61$	8.70908			1.11508			0.557542	−	0.830149i	$-0.311745\pi$
$61$	8.70908			1.11508			0.557542	+	0.830149i	$0.311745\pi$
$62$	−3.13531			−0.398185
$63$	12.4042	+	6.50858i	1.56278	+	0.820004i
$64$	2.55645			0.319557
$65$		−	1.41059i		−	0.174962i
$66$		0			0
$67$	−6.46905			−0.790320			−0.395160	−	0.918612i	$-0.629311\pi$
$67$	−6.46905			−0.790320			−0.395160	+	0.918612i	$0.629311\pi$
$68$	−2.00101			−0.242658
$69$			11.0999i			1.33627i
$70$	−0.709180	−	0.372112i	−0.0847633	−	0.0444759i
$71$	5.32603			0.632084			0.316042	−	0.948745i	$-0.397646\pi$
$71$	5.32603			0.632084			0.316042	+	0.948745i	$0.397646\pi$
$72$			9.97462i			1.17552i
$73$	2.49756			0.292317			0.146159	−	0.989261i	$-0.453309\pi$
$73$	2.49756			0.292317			0.146159	+	0.989261i	$0.453309\pi$
$74$			3.72569i			0.433102i
$75$		−	13.3561i		−	1.54223i
$76$	−8.86381			−1.01675
$77$		0			0
$78$	3.39228			0.384100
$79$			1.19060i			0.133953i	0.997755	+	0.0669766i	$0.0213353\pi$
$79$			1.19060i			0.133953i	−0.997755	+	0.0669766i	$0.978665\pi$
$80$			1.53371i			0.171474i
$81$	3.14866			0.349851
$82$		−	5.91224i		−	0.652898i
$83$	−7.90565			−0.867758			−0.433879	−	0.900971i	$-0.642855\pi$
$83$	−7.90565			−0.867758			−0.433879	+	0.900971i	$0.642855\pi$
$84$	−6.18594	+	11.7893i	−0.674941	+	1.28632i
$85$		−	0.689539i		−	0.0747910i
$86$	−0.870796			−0.0939003
$87$	−6.21828			−0.666670
$88$		0			0
$89$		−	11.9963i		−	1.27161i	−0.771850	−	0.635804i	$-0.780669\pi$
$89$		−	11.9963i		−	1.27161i	0.771850	−	0.635804i	$-0.219331\pi$
$90$	−1.60268			−0.168937
$91$	5.48883	+	2.88003i	0.575386	+	0.301909i
$92$	−6.73403			−0.702072
$93$	−17.9606			−1.86243
$94$	−4.98835			−0.514509
$95$		−	3.05443i		−	0.313377i
$96$	−14.5400			−1.48398
$97$			5.82158i			0.591092i	0.955328	+	0.295546i	$0.0955016\pi$
$97$			5.82158i			0.591092i	−0.955328	+	0.295546i	$0.904498\pi$
$98$	2.89589	−	1.99978i	0.292529	−	0.202009i
$99$		0			0
$100$	8.10280			0.810280
$101$	14.4443			1.43727			0.718633	−	0.695390i	$-0.244768\pi$
$101$	14.4443			1.43727			0.718633	+	0.695390i	$0.244768\pi$
$102$	1.65825			0.164191
$103$			5.61792i			0.553550i	0.960935	+	0.276775i	$0.0892657\pi$
$103$			5.61792i			0.553550i	−0.960935	+	0.276775i	$0.910734\pi$
$104$			4.41374i			0.432803i
$105$	−4.06254	−	2.13164i	−0.396463	−	0.208027i
$106$		−	3.07768i		−	0.298931i
$107$		−	8.02953i		−	0.776244i	−0.921608	−	0.388122i	$-0.873124\pi$
$107$		−	8.02953i		−	0.776244i	0.921608	−	0.388122i	$-0.126876\pi$
$108$			11.5464i			1.11106i
$109$			13.2943i			1.27336i	0.771128	+	0.636680i	$0.219693\pi$
$109$			13.2943i			1.27336i	−0.771128	+	0.636680i	$0.780307\pi$
$110$		0			0
$111$			21.3426i			2.02575i
$112$	−5.96792	−	3.13141i	−0.563916	−	0.295890i
$113$	−1.00658			−0.0946911			−0.0473456	−	0.998879i	$-0.515076\pi$
$113$	−1.00658			−0.0946911			−0.0473456	+	0.998879i	$0.515076\pi$
$114$	7.34549			0.687968
$115$		−	2.32051i		−	0.216389i
$116$		−	3.77247i		−	0.350265i
$117$	12.4042			1.14677
$118$	2.36423			0.217645
$119$	2.68310	+	1.40784i	0.245960	+	0.129057i
$120$		−	3.26682i		−	0.298218i
$121$		0			0
$122$		−	4.37853i		−	0.396413i
$123$		−	33.8683i		−	3.05380i
$124$		−	10.8963i		−	0.978513i
$125$			5.80263i			0.519003i
$126$	3.27222	−	6.23627i	0.291512	−	0.555571i
$127$		−	9.46758i		−	0.840112i	−0.907498	−	0.420056i	$-0.862010\pi$
$127$		−	9.46758i		−	0.840112i	0.907498	−	0.420056i	$-0.137990\pi$
$128$		−	11.3824i		−	1.00607i
$129$	−4.98835			−0.439200
$130$	−0.709180			−0.0621992
$131$	11.5794			1.01170			0.505848	−	0.862623i	$-0.331180\pi$
$131$	11.5794			1.01170			0.505848	+	0.862623i	$0.331180\pi$
$132$		0			0
$133$	11.8852	+	6.23627i	1.03058	+	0.540753i
$134$			3.25234i			0.280959i
$135$	−3.97884			−0.342444
$136$			2.15757i			0.185010i
$137$	9.87920			0.844037			0.422019	−	0.906587i	$-0.361322\pi$
$137$	9.87920			0.844037			0.422019	+	0.906587i	$0.361322\pi$
$138$	5.58053			0.475046
$139$	−10.2161			−0.866521			−0.433260	−	0.901269i	$-0.642637\pi$
$139$	−10.2161			−0.866521			−0.433260	+	0.901269i	$0.642637\pi$
$140$	1.29321	−	2.46464i	0.109296	−	0.208300i
$141$	−28.5758			−2.40652
$142$		−	2.67769i		−	0.224706i
$143$		0			0
$144$	−13.4869			−1.12391
$145$	1.29998			0.107957
$146$		−	1.25566i		−	0.103919i
$147$	16.5891	−	11.4558i	1.36825	−	0.944856i
$148$	−12.9480			−1.06432
$149$		−	4.58975i		−	0.376007i	−0.982168	−	0.188003i	$-0.939798\pi$
$149$		−	4.58975i		−	0.376007i	0.982168	−	0.188003i	$-0.0602016\pi$
$150$	−6.71483			−0.548264
$151$		−	13.1434i		−	1.06960i	−0.844979	−	0.534799i	$-0.820387\pi$
$151$		−	13.1434i		−	1.06960i	0.844979	−	0.534799i	$-0.179613\pi$
$152$			9.55730i			0.775200i
$153$	6.06355			0.490209
$154$		0			0
$155$	3.75480			0.301592
$156$			11.7893i			0.943901i
$157$			3.09105i			0.246693i	0.992364	+	0.123346i	$0.0393626\pi$
$157$			3.09105i			0.246693i	−0.992364	+	0.123346i	$0.960637\pi$
$158$	0.598580			0.0476205
$159$		−	17.6305i		−	1.39819i
$160$	3.03968			0.240308
$161$	9.02949	+	4.73783i	0.711623	+	0.373394i
$162$		−	1.58300i		−	0.124372i
$163$	−2.04431			−0.160123			−0.0800613	−	0.996790i	$-0.525512\pi$
$163$	−2.04431			−0.160123			−0.0800613	+	0.996790i	$0.525512\pi$
$164$	20.5470			1.60445
$165$		0			0
$166$			3.97460i			0.308489i
$167$	7.30977			0.565647			0.282824	−	0.959172i	$-0.408729\pi$
$167$	7.30977			0.565647			0.282824	+	0.959172i	$0.408729\pi$
$168$	12.7117	+	6.66991i	0.980728	+	0.514595i
$169$	−7.51117			−0.577782
$170$	−0.346668			−0.0265883
$171$	26.8595			2.05400
$172$		−	3.02631i		−	0.230754i
$173$	−8.17601			−0.621610			−0.310805	−	0.950474i	$-0.600599\pi$
$173$	−8.17601			−0.621610			−0.310805	+	0.950474i	$0.600599\pi$
$174$			3.12627i			0.237002i
$175$	−10.8648	−	5.70085i	−0.821303	−	0.430944i
$176$		0			0
$177$	13.5435			1.01799
$178$	−6.03120			−0.452058
$179$	6.22884			0.465565			0.232783	−	0.972529i	$-0.425217\pi$
$179$	6.22884			0.465565			0.232783	+	0.972529i	$0.425217\pi$
$180$		−	5.56984i		−	0.415151i
$181$		−	19.7608i		−	1.46881i	−0.678712	−	0.734405i	$-0.737461\pi$
$181$		−	19.7608i		−	1.46881i	0.678712	−	0.734405i	$-0.262539\pi$
$182$	1.44795	−	2.75953i	0.107329	−	0.204550i
$183$		−	25.0824i		−	1.85414i
$184$			7.26090i			0.535280i
$185$		−	4.46182i		−	0.328039i
$186$			9.02978i			0.662096i
$187$		0			0
$188$		−	17.3362i		−	1.26437i
$189$	8.12367	−	15.4823i	0.590910	−	1.12617i
$190$	−1.53563			−0.111406
$191$	0.619944			0.0448576			0.0224288	−	0.999748i	$-0.492860\pi$
$191$	0.619944			0.0448576			0.0224288	+	0.999748i	$0.492860\pi$
$192$		−	7.36266i		−	0.531354i
$193$		−	12.4324i		−	0.894905i	−0.894308	−	0.447453i	$-0.852331\pi$
$193$		−	12.4324i		−	0.894905i	0.894308	−	0.447453i	$-0.147669\pi$
$194$	2.92683			0.210134
$195$	−4.06254			−0.290925
$196$	6.94992	+	10.0642i	0.496423	+	0.718871i
$197$		−	12.4251i		−	0.885254i	−0.896706	−	0.442627i	$-0.854047\pi$
$197$		−	12.4251i		−	0.885254i	0.896706	−	0.442627i	$-0.145953\pi$
$198$		0			0
$199$			8.51876i			0.603879i	0.953327	+	0.301939i	$0.0976340\pi$
$199$			8.51876i			0.603879i	−0.953327	+	0.301939i	$0.902366\pi$
$200$		−	8.73675i		−	0.617781i
$201$			18.6310i			1.31413i
$202$		−	7.26195i		−	0.510949i
$203$	−2.65418	+	5.05841i	−0.186287	+	0.355031i
$204$			5.76297i			0.403488i
$205$			7.08040i			0.494516i
$206$	2.82443			0.196788
$207$	20.4058			1.41830
$208$	−5.96792			−0.413801
$209$		0			0
$210$	−1.07169	+	2.04246i	−0.0739538	+	0.140943i
$211$			17.7450i			1.22162i	0.791777	+	0.610810i	$0.209156\pi$
$211$			17.7450i			1.22162i	−0.791777	+	0.610810i	$0.790844\pi$
$212$	10.6960			0.734603
$213$		−	15.3391i		−	1.05102i
$214$	−4.03688			−0.275955
$215$	1.04285			0.0711218
$216$	12.4498			0.847101
$217$	−7.66623	+	14.6105i	−0.520418	+	0.991825i
$218$	6.68375			0.452681
$219$		−	7.19303i		−	0.486060i
$220$		0			0
$221$	2.68310			0.180485
$222$	10.7301			0.720156
$223$			1.48564i			0.0994855i	0.998762	+	0.0497428i	$0.0158401\pi$
$223$			1.48564i			0.0994855i	−0.998762	+	0.0497428i	$0.984160\pi$
$224$	−6.20617	+	11.8279i	−0.414667	+	0.790283i
$225$	−24.5534			−1.63690
$226$			0.506063i			0.0336628i
$227$	23.9850			1.59194			0.795971	−	0.605335i	$-0.206961\pi$
$227$	23.9850			1.59194			0.795971	+	0.605335i	$0.206961\pi$
$228$			25.5280i			1.69063i
$229$			0.364750i			0.0241033i	0.999927	+	0.0120517i	$0.00383626\pi$
$229$			0.364750i			0.0241033i	−0.999927	+	0.0120517i	$0.996164\pi$
$230$	−1.16665			−0.0769265
$231$		0			0
$232$	−4.06763			−0.267053
$233$			2.64448i			0.173246i	0.996241	+	0.0866229i	$0.0276075\pi$
$233$			2.64448i			0.173246i	−0.996241	+	0.0866229i	$0.972392\pi$
$234$		−	6.23627i		−	0.407678i
$235$	5.97397			0.389699
$236$			8.21649i			0.534848i
$237$	3.42897			0.222735
$238$	0.707799	−	1.34894i	0.0458798	−	0.0874389i
$239$		−	17.6050i		−	1.13878i	−0.822069	−	0.569388i	$-0.807180\pi$
$239$		−	17.6050i		−	1.13878i	0.822069	−	0.569388i	$-0.192820\pi$
$240$	4.41714			0.285125
$241$	−8.56111			−0.551470			−0.275735	−	0.961234i	$-0.588921\pi$
$241$	−8.56111			−0.551470			−0.275735	+	0.961234i	$0.588921\pi$
$242$		0			0
$243$			10.7569i			0.690058i
$244$	15.2168			0.974158
$245$	−3.46807	+	2.39491i	−0.221567	+	0.153005i
$246$	−17.0274			−1.08563
$247$	11.8852			0.756240
$248$	−11.7488			−0.746047
$249$			22.7685i			1.44289i
$250$	2.91730			0.184506
$251$		−	3.09714i		−	0.195490i	−0.995211	−	0.0977449i	$-0.968837\pi$
$251$		−	3.09714i		−	0.195490i	0.995211	−	0.0977449i	$-0.0311629\pi$
$252$	21.6731	+	11.3720i	1.36528	+	0.716371i
$253$		0			0
$254$	−4.75987			−0.298660
$255$	−1.98589			−0.124361
$256$	−0.609627			−0.0381017
$257$			13.6504i			0.851489i	0.904843	+	0.425745i	$0.139988\pi$
$257$			13.6504i			0.851489i	−0.904843	+	0.425745i	$0.860012\pi$
$258$			2.50792i			0.156136i
$259$	17.3616	+	9.10977i	1.07880	+	0.566054i
$260$		−	2.46464i		−	0.152850i
$261$			11.4315i			0.707593i
$262$		−	5.82158i		−	0.359659i
$263$		−	21.1997i		−	1.30723i	−0.756827	−	0.653615i	$-0.773251\pi$
$263$		−	21.1997i		−	1.30723i	0.756827	−	0.653615i	$-0.226749\pi$
$264$		0			0
$265$			3.68578i			0.226416i
$266$	3.13531	−	5.97536i	0.192238	−	0.366373i
$267$	−34.5497			−2.11441
$268$	−11.3030			−0.690438
$269$		−	14.1104i		−	0.860324i	−0.902752	−	0.430162i	$-0.858456\pi$
$269$		−	14.1104i		−	0.860324i	0.902752	−	0.430162i	$-0.141544\pi$
$270$			2.00038i			0.121739i
$271$	−15.7466			−0.956538			−0.478269	−	0.878213i	$-0.658736\pi$
$271$	−15.7466			−0.956538			−0.478269	+	0.878213i	$0.658736\pi$
$272$	−2.91730			−0.176887
$273$	8.29456	−	15.8080i	0.502009	−	0.956742i
$274$		−	4.96681i		−	0.300056i
$275$		0			0
$276$			19.3942i			1.16739i
$277$			6.68430i			0.401621i	0.979630	+	0.200810i	$0.0643575\pi$
$277$			6.68430i			0.401621i	−0.979630	+	0.200810i	$0.935643\pi$
$278$			5.13620i			0.308049i
$279$			33.0183i			1.97675i
$280$	−2.65747	−	1.39439i	−0.158814	−	0.0833308i
$281$			22.1229i			1.31974i	0.751379	+	0.659871i	$0.229389\pi$
$281$			22.1229i			1.31974i	−0.751379	+	0.659871i	$0.770611\pi$
$282$			14.3666i			0.855518i
$283$	13.8766			0.824880			0.412440	−	0.910985i	$-0.364677\pi$
$283$	13.8766			0.824880			0.412440	+	0.910985i	$0.364677\pi$
$284$	9.30585			0.552201
$285$	−8.79683			−0.521079
$286$		0			0
$287$	−27.5509	−	14.4562i	−1.62628	−	0.853320i
$288$			26.7299i			1.57507i
$289$	−15.6884			−0.922848
$290$		−	0.653568i		−	0.0383788i
$291$	16.7663			0.982859
$292$	4.36383			0.255374
$293$	7.11175			0.415473			0.207736	−	0.978185i	$-0.433390\pi$
$293$	7.11175			0.415473			0.207736	+	0.978185i	$0.433390\pi$
$294$	−5.75943	−	8.34025i	−0.335897	−	0.486413i
$295$	−2.83136			−0.164848
$296$			13.9610i			0.811469i
$297$		0			0
$298$	−2.30751			−0.133671
$299$	9.02949			0.522189
$300$		−	23.3363i		−	1.34732i
$301$	−2.12920	+	4.05789i	−0.122725	+	0.233893i
$302$	−6.60792			−0.380243
$303$		−	41.6001i		−	2.38986i
$304$	−12.9227			−0.741165
$305$			5.24365i			0.300250i
$306$		−	3.04848i		−	0.174270i
$307$	18.7705			1.07129			0.535644	−	0.844444i	$-0.320069\pi$
$307$	18.7705			1.07129			0.535644	+	0.844444i	$0.320069\pi$
$308$		0			0
$309$	16.1798			0.920435
$310$		−	1.88774i		−	0.107216i
$311$			3.58717i			0.203410i	0.994815	+	0.101705i	$0.0324298\pi$
$311$			3.58717i			0.203410i	−0.994815	+	0.101705i	$0.967570\pi$
$312$	12.7117			0.719658
$313$			26.3802i			1.49110i	0.666451	+	0.745549i	$0.267812\pi$
$313$			26.3802i			1.49110i	−0.666451	+	0.745549i	$0.732188\pi$
$314$	1.55404			0.0876995
$315$	−3.91875	+	7.46845i	−0.220796	+	0.420800i
$316$			2.08026i			0.117024i
$317$	−6.36467			−0.357475			−0.178738	−	0.983897i	$-0.557201\pi$
$317$	−6.36467			−0.357475			−0.178738	+	0.983897i	$0.557201\pi$
$318$	−8.86381			−0.497058
$319$		0			0
$320$			1.53921i			0.0860447i
$321$	−23.1253			−1.29073
$322$	2.38197	−	4.53961i	0.132742	−	0.252983i
$323$	5.80986			0.323269
$324$	5.50146			0.305636
$325$	−10.8648			−0.602672
$326$			1.02778i			0.0569237i
$327$	38.2879			2.11732
$328$		−	22.1546i		−	1.22328i
$329$	−12.1971	+	23.2456i	−0.672450	+	1.28157i
$330$		0			0
$331$	−9.41523			−0.517508			−0.258754	−	0.965943i	$-0.583312\pi$
$331$	−9.41523			−0.517508			−0.258754	+	0.965943i	$0.583312\pi$
$332$	−13.8131			−0.758090
$333$	39.2356			2.15010
$334$		−	3.67502i		−	0.201088i
$335$		−	3.89495i		−	0.212804i
$336$	−9.01854	+	17.1878i	−0.492002	+	0.937670i
$337$		−	5.51775i		−	0.300571i	−0.988643	−	0.150285i	$-0.951981\pi$
$337$		−	5.51775i		−	0.300571i	0.988643	−	0.150285i	$-0.0480193\pi$
$338$			3.77627i			0.205402i
$339$			2.89898i			0.157451i
$340$		−	1.20479i		−	0.0653388i
$341$		0			0
$342$		−	13.5037i		−	0.730198i
$343$	−2.23814	−	18.3845i	−0.120848	−	0.992671i
$344$	−3.26308			−0.175933
$345$	−6.68315			−0.359808
$346$			4.11052i			0.220983i
$347$			32.9752i			1.77020i	0.465399	+	0.885101i	$0.345911\pi$
$347$			32.9752i			1.77020i	−0.465399	+	0.885101i	$0.654089\pi$
$348$	−10.8648			−0.582416
$349$	−26.6401			−1.42601			−0.713005	−	0.701159i	$-0.752666\pi$
$349$	−26.6401			−1.42601			−0.713005	+	0.701159i	$0.752666\pi$
$350$	−2.86613	+	5.46234i	−0.153201	+	0.291974i
$351$		−	15.4823i		−	0.826384i
$352$		0			0
$353$		−	31.7997i		−	1.69253i	−0.532764	−	0.846264i	$-0.678847\pi$
$353$		−	31.7997i		−	1.69253i	0.532764	−	0.846264i	$-0.321153\pi$
$354$		−	6.80905i		−	0.361897i
$355$			3.20675i			0.170197i
$356$		−	20.9604i		−	1.11090i
$357$	4.05463	−	7.72741i	0.214594	−	0.408978i
$358$		−	3.13158i		−	0.165509i
$359$		−	31.6580i		−	1.67085i	−0.549607	−	0.835423i	$-0.685223\pi$
$359$		−	31.6580i		−	1.67085i	0.549607	−	0.835423i	$-0.314777\pi$
$360$	−6.00562			−0.316524
$361$	6.73575			0.354513
$362$	−9.93483			−0.522163
$363$		0			0
$364$	9.59029	+	5.03209i	0.502668	+	0.263753i
$365$			1.50375i			0.0787101i
$366$	−12.6103			−0.659150
$367$		−	10.8963i		−	0.568780i	−0.958709	−	0.284390i	$-0.908209\pi$
$367$		−	10.8963i		−	0.568780i	0.958709	−	0.284390i	$-0.0917910\pi$
$368$	−9.81762			−0.511779
$369$	−62.2624			−3.24125
$370$	−2.24320			−0.116618
$371$	−14.3419	−	7.52532i	−0.744597	−	0.390695i
$372$	−31.3815			−1.62706
$373$			5.45840i			0.282625i	0.989965	+	0.141313i	$0.0451322\pi$
$373$			5.45840i			0.282625i	−0.989965	+	0.141313i	$0.954868\pi$
$374$		0			0
$375$	16.7117			0.862990
$376$	−18.6925			−0.963995
$377$			5.05841i			0.260521i
$378$	−7.78379	−	4.08421i	−0.400355	−	0.210069i
$379$	5.95918			0.306103			0.153051	−	0.988218i	$-0.451090\pi$
$379$	5.95918			0.306103			0.153051	+	0.988218i	$0.451090\pi$
$380$		−	5.33681i		−	0.273773i
$381$	−27.2669			−1.39692
$382$		−	0.311679i		−	0.0159469i
$383$			31.0218i			1.58514i	0.609780	+	0.792570i	$0.291258\pi$
$383$			31.0218i			1.58514i	−0.609780	+	0.792570i	$0.708742\pi$
$384$	−32.7816			−1.67288
$385$		0			0
$386$	−6.25045			−0.318140
$387$			9.17044i			0.466160i
$388$			10.1717i			0.516390i
$389$	23.4135			1.18711			0.593556	−	0.804792i	$-0.297723\pi$
$389$	23.4135			1.18711			0.593556	+	0.804792i	$0.297723\pi$
$390$			2.04246i			0.103424i
$391$	4.41388			0.223220
$392$	10.8516	−	7.49367i	0.548088	−	0.378487i
$393$		−	33.3489i		−	1.68223i
$394$	−6.24678			−0.314708
$395$	−0.716849			−0.0360686
$396$		0			0
$397$			29.8394i			1.49760i	0.662798	+	0.748798i	$0.269369\pi$
$397$			29.8394i			1.49760i	−0.662798	+	0.748798i	$0.730631\pi$
$398$	4.28284			0.214679
$399$	17.9606	−	34.2298i	0.899156	−	1.71364i
$400$	11.8132			0.590658
$401$	20.5447			1.02595			0.512976	−	0.858403i	$-0.328543\pi$
$401$	20.5447			1.02595			0.512976	+	0.858403i	$0.328543\pi$
$402$	9.36683			0.467175
$403$			14.6105i			0.727801i
$404$	25.2377			1.25562
$405$			1.89577i			0.0942018i
$406$	2.54314	+	1.33440i	0.126214	+	0.0662252i
$407$		0			0
$408$	6.21385			0.307632
$409$	12.4456			0.615396			0.307698	−	0.951484i	$-0.400441\pi$
$409$	12.4456			0.615396			0.307698	+	0.951484i	$0.400441\pi$
$410$	3.55970			0.175801
$411$		−	28.4524i		−	1.40345i
$412$			9.81585i			0.483592i
$413$	5.78084	−	11.0173i	0.284457	−	0.542125i
$414$		−	10.2591i		−	0.504206i
$415$		−	4.75991i		−	0.233655i
$416$			11.8279i			0.579909i
$417$			29.4227i			1.44084i
$418$		0			0
$419$		−	15.0711i		−	0.736272i	−0.929772	−	0.368136i	$-0.879996\pi$
$419$		−	15.0711i		−	0.736272i	0.929772	−	0.368136i	$-0.120004\pi$
$420$	−7.09822	−	3.72449i	−0.346358	−	0.181736i
$421$	−6.04842			−0.294782			−0.147391	−	0.989078i	$-0.547088\pi$
$421$	−6.04842			−0.294782			−0.147391	+	0.989078i	$0.547088\pi$
$422$	8.92140			0.434287
$423$			52.5329i			2.55424i
$424$		−	11.5328i		−	0.560083i
$425$	−5.31105			−0.257624
$426$	−7.71181			−0.373638
$427$	−20.4039	−	10.7060i	−0.987412	−	0.518102i
$428$		−	14.0295i		−	0.678141i
$429$		0			0
$430$		−	0.524297i		−	0.0252838i
$431$			7.24556i			0.349006i	0.984657	+	0.174503i	$0.0558319\pi$
$431$			7.24556i			0.349006i	−0.984657	+	0.174503i	$0.944168\pi$
$432$			16.8337i			0.809910i
$433$		−	10.1694i		−	0.488712i	−0.969686	−	0.244356i	$-0.921423\pi$
$433$		−	10.1694i		−	0.488712i	0.969686	−	0.244356i	$-0.0785766\pi$
$434$	7.34549	+	3.85423i	0.352595	+	0.185009i
$435$		−	3.74396i		−	0.179509i
$436$			23.2283i			1.11243i
$437$	19.5520			0.935300
$438$	−3.61633			−0.172795
$439$	−8.57434			−0.409231			−0.204615	−	0.978842i	$-0.565594\pi$
$439$	−8.57434			−0.409231			−0.204615	+	0.978842i	$0.565594\pi$
$440$		0			0
$441$	−21.0599	−	30.4969i	−1.00285	−	1.45223i
$442$		−	1.34894i		−	0.0641626i
$443$	−9.81527			−0.466338			−0.233169	−	0.972436i	$-0.574909\pi$
$443$	−9.81527			−0.466338			−0.233169	+	0.972436i	$0.574909\pi$
$444$			37.2906i			1.76973i
$445$	7.22286			0.342397
$446$	0.746909			0.0353672
$447$	−13.2186			−0.625218
$448$	−5.98933	−	3.14264i	−0.282969	−	0.148476i
$449$	−15.5194			−0.732405			−0.366202	−	0.930535i	$-0.619342\pi$
$449$	−15.5194			−0.732405			−0.366202	+	0.930535i	$0.619342\pi$
$450$			12.3443i			0.581918i
$451$		0			0
$452$	−1.75874			−0.0827240
$453$	−37.8535			−1.77851
$454$		−	12.0586i		−	0.565937i
$455$	−1.73403	+	3.30477i	−0.0812928	+	0.154930i
$456$	27.5253			1.28899
$457$			27.2910i			1.27662i	0.769779	+	0.638310i	$0.220366\pi$
$457$			27.2910i			1.27662i	−0.769779	+	0.638310i	$0.779634\pi$
$458$	0.183379			0.00856876
$459$		−	7.56820i		−	0.353253i
$460$		−	4.05449i		−	0.189042i
$461$	34.0355			1.58519			0.792595	−	0.609748i	$-0.208730\pi$
$461$	34.0355			1.58519			0.792595	+	0.609748i	$0.208730\pi$
$462$		0			0
$463$	19.2899			0.896477			0.448239	−	0.893914i	$-0.352052\pi$
$463$	19.2899			0.896477			0.448239	+	0.893914i	$0.352052\pi$
$464$		−	5.49993i		−	0.255328i
$465$		−	10.8139i		−	0.501483i
$466$	1.32952			0.0615890
$467$			24.1293i			1.11657i	0.829649	+	0.558285i	$0.188540\pi$
$467$			24.1293i			1.11657i	−0.829649	+	0.558285i	$0.811460\pi$
$468$	21.6731			1.00184
$469$	15.1558	+	7.95238i	0.699832	+	0.367207i
$470$		−	3.00344i		−	0.138538i
$471$	8.90232			0.410197
$472$	8.85934			0.407784
$473$		0			0
$474$		−	1.72393i		−	0.0791826i
$475$	−23.5262			−1.07945
$476$	4.68802	+	2.45984i	0.214875	+	0.112746i
$477$	−32.4114			−1.48402
$478$	−8.85101			−0.404836
$479$	−38.9852			−1.78128			−0.890639	−	0.454710i	$-0.849743\pi$
$479$	−38.9852			−1.78128			−0.890639	+	0.454710i	$0.849743\pi$
$480$		−	8.75437i		−	0.399580i
$481$	17.3616			0.791623
$482$			4.30413i			0.196048i
$483$	13.6451	−	26.0052i	0.620873	−	1.18328i
$484$		0			0
$485$	−3.50512			−0.159159
$486$	5.40809			0.245316
$487$	−0.834071			−0.0377954			−0.0188977	−	0.999821i	$-0.506016\pi$
$487$	−0.834071			−0.0377954			−0.0188977	+	0.999821i	$0.506016\pi$
$488$		−	16.4074i		−	0.742727i
$489$			5.88766i			0.266249i
$490$	1.20405	+	1.74359i	0.0543934	+	0.0787672i
$491$			27.3903i			1.23611i	0.786136	+	0.618053i	$0.212078\pi$
$491$			27.3903i			1.23611i	−0.786136	+	0.618053i	$0.787922\pi$
$492$		−	59.1759i		−	2.66786i
$493$			2.47270i			0.111365i
$494$		−	5.97536i		−	0.268844i
$495$		0			0
$496$		−	15.8858i		−	0.713292i
$497$	−12.4780	−	6.54728i	−0.559713	−	0.293685i
$498$	11.4470			0.512950
$499$	19.9086			0.891233			0.445617	−	0.895224i	$-0.352984\pi$
$499$	19.9086			0.891233			0.445617	+	0.895224i	$0.352984\pi$
$500$			10.1386i			0.453411i
$501$		−	21.0523i		−	0.940549i
$502$	−1.55710			−0.0694968
$503$	−1.70877			−0.0761904			−0.0380952	−	0.999274i	$-0.512129\pi$
$503$	−1.70877			−0.0761904			−0.0380952	+	0.999274i	$0.512129\pi$
$504$	12.2618	−	23.3688i	0.546183	−	1.04093i
$505$			8.69679i			0.387002i
$506$		0			0
$507$			21.6324i			0.960727i
$508$		−	16.5421i		−	0.733938i
$509$			12.5195i			0.554916i	0.960738	+	0.277458i	$0.0894919\pi$
$509$			12.5195i			0.554916i	−0.960738	+	0.277458i	$0.910508\pi$
$510$			0.998414i			0.0442105i
$511$	−5.85134	−	3.07024i	−0.258848	−	0.135819i
$512$		−	22.4583i		−	0.992524i
$513$		−	33.5246i		−	1.48015i
$514$	6.86280			0.302705
$515$	−3.38249			−0.149050
$516$	−8.71584			−0.383694
$517$		0			0
$518$	4.57998	−	8.72864i	0.201233	−	0.383514i
$519$			23.5471i			1.03360i
$520$	−2.65747			−0.116538
$521$		−	12.8670i		−	0.563714i	−0.959456	−	0.281857i	$-0.909050\pi$
$521$		−	12.8670i		−	0.563714i	0.959456	−	0.281857i	$-0.0909504\pi$
$522$	5.74724			0.251550
$523$	22.9599			1.00397			0.501983	−	0.864878i	$-0.332604\pi$
$523$	22.9599			1.00397			0.501983	+	0.864878i	$0.332604\pi$
$524$	20.2319			0.883837
$525$	−16.4186	+	31.2910i	−0.716566	+	1.36565i
$526$	−10.6582			−0.464722
$527$			7.14204i			0.311112i
$528$		0			0
$529$	−8.14590			−0.354169
$530$	1.85304			0.0804910
$531$		−	24.8980i		−	1.08048i
$532$	20.7664	+	10.8963i	0.900336	+	0.472413i
$533$	−27.5509			−1.19336
$534$			17.3700i			0.751675i
$535$	4.83449			0.209013
$536$			12.1873i			0.526411i
$537$		−	17.9392i		−	0.774135i
$538$	−7.09405			−0.305846
$539$		0			0
$540$	−6.95198			−0.299166
$541$			23.2351i			0.998953i	0.866327	+	0.499477i	$0.166474\pi$
$541$			23.2351i			0.998953i	−0.866327	+	0.499477i	$0.833526\pi$
$542$			7.91667i			0.340050i
$543$	−56.9117			−2.44231
$544$			5.78182i			0.247893i
$545$	−8.00434			−0.342868
$546$	−7.94753	−	4.17012i	−0.340123	−	0.178465i
$547$			32.3259i			1.38216i	0.722780	+	0.691078i	$0.242864\pi$
$547$			32.3259i			1.38216i	−0.722780	+	0.691078i	$0.757136\pi$
$548$	17.2613			0.737367
$549$	−46.1107			−1.96796
$550$		0			0
$551$			10.9532i			0.466623i
$552$	20.9116			0.890056
$553$	1.46360	−	2.78937i	0.0622387	−	0.118616i
$554$	3.36056			0.142776
$555$	−12.8502			−0.545459
$556$	−17.8500			−0.757009
$557$			12.4366i			0.526957i	0.964665	+	0.263478i	$0.0848698\pi$
$557$			12.4366i			0.526957i	−0.964665	+	0.263478i	$0.915130\pi$
$558$	16.6001			0.702738
$559$			4.05789i			0.171631i
$560$	1.88539	−	3.59322i	0.0796722	−	0.151841i
$561$		0			0
$562$	11.1224			0.469169
$563$	2.20132			0.0927747			0.0463873	−	0.998924i	$-0.485229\pi$
$563$	2.20132			0.0927747			0.0463873	+	0.998924i	$0.485229\pi$
$564$	−49.9287			−2.10238
$565$		−	0.606052i		−	0.0254968i
$566$		−	6.97653i		−	0.293246i
$567$	−7.37676	−	3.87064i	−0.309795	−	0.162551i
$568$		−	10.0339i		−	0.421014i
$569$			45.9285i			1.92542i	0.270532	+	0.962711i	$0.412800\pi$
$569$			45.9285i			1.92542i	−0.270532	+	0.962711i	$0.587200\pi$
$570$			4.42264i			0.185244i
$571$			42.4864i			1.77800i	0.457905	+	0.889001i	$0.348600\pi$
$571$			42.4864i			1.77800i	−0.457905	+	0.889001i	$0.651400\pi$
$572$		0			0
$573$		−	1.78546i		−	0.0745885i
$574$	−7.26790	+	13.8513i	−0.303356	+	0.578144i
$575$	−17.8734			−0.745370
$576$	−13.5353			−0.563971
$577$		−	30.7067i		−	1.27834i	−0.769067	−	0.639168i	$-0.779279\pi$
$577$		−	30.7067i		−	1.27834i	0.769067	−	0.639168i	$-0.220721\pi$
$578$			7.88742i			0.328073i
$579$	−35.8057			−1.48803
$580$	2.27137			0.0943134
$581$	18.5216	+	9.71839i	0.768404	+	0.403187i
$582$		−	8.42934i		−	0.349407i
$583$		0			0
$584$		−	4.70525i		−	0.194705i
$585$			7.46845i			0.308782i
$586$		−	3.57546i		−	0.147701i
$587$			17.4323i			0.719510i	0.933047	+	0.359755i	$0.117140\pi$
$587$			17.4323i			0.719510i	−0.933047	+	0.359755i	$0.882860\pi$
$588$	28.9851	−	20.0160i	1.19533	−	0.825444i
$589$			31.6369i			1.30357i
$590$			1.42348i			0.0586037i
$591$	−35.7847			−1.47199
$592$	−18.8770			−0.775842
$593$	−5.06886			−0.208153			−0.104077	−	0.994569i	$-0.533189\pi$
$593$	−5.06886			−0.208153			−0.104077	+	0.994569i	$0.533189\pi$
$594$		0			0
$595$	−0.847648	+	1.61547i	−0.0347502	+	0.0662278i
$596$		−	8.01938i		−	0.328487i
$597$	24.5343			1.00412
$598$		−	4.53961i		−	0.185639i
$599$	−0.951499			−0.0388772			−0.0194386	−	0.999811i	$-0.506188\pi$
$599$	−0.951499			−0.0388772			−0.0194386	+	0.999811i	$0.506188\pi$
$600$	−25.1621			−1.02724
$601$	19.2998			0.787257			0.393629	−	0.919270i	$-0.371220\pi$
$601$	19.2998			0.787257			0.393629	+	0.919270i	$0.371220\pi$
$602$	2.04012	+	1.07047i	0.0831492	+	0.0436289i
$603$	34.2507			1.39480
$604$		−	22.9647i		−	0.934422i
$605$		0			0
$606$	−20.9146			−0.849598
$607$	19.2580			0.781657			0.390828	−	0.920464i	$-0.372189\pi$
$607$	19.2580			0.781657			0.390828	+	0.920464i	$0.372189\pi$
$608$			25.6115i			1.03868i
$609$	14.5684	+	7.64412i	0.590339	+	0.309755i
$610$	2.63626			0.106739
$611$			23.2456i			0.940418i
$612$	10.5945			0.428256
$613$		−	4.95657i		−	0.200194i	−0.994978	−	0.100097i	$-0.968085\pi$
$613$		−	4.95657i		−	0.200194i	0.994978	−	0.100097i	$-0.0319153\pi$
$614$		−	9.43693i		−	0.380844i
$615$	20.3917			0.822274
$616$		0			0
$617$	−41.6246			−1.67574			−0.837871	−	0.545869i	$-0.816200\pi$
$617$	−41.6246			−1.67574			−0.837871	+	0.545869i	$0.816200\pi$
$618$		−	8.13444i		−	0.327215i
$619$		−	6.13121i		−	0.246434i	−0.992380	−	0.123217i	$-0.960679\pi$
$619$		−	6.13121i		−	0.246434i	0.992380	−	0.123217i	$-0.0393212\pi$
$620$	6.56052			0.263477
$621$		−	25.4694i		−	1.02205i
$622$	1.80347			0.0723124
$623$	−14.7470	+	28.1053i	−0.590828	+	1.12601i
$624$			17.1878i			0.688062i
$625$	19.6937			0.787749
$626$	13.2628			0.530086
$627$		0			0
$628$			5.40081i			0.215516i
$629$	8.48688			0.338394
$630$	3.75480	+	1.97017i	0.149595	+	0.0784933i
$631$	−7.86270			−0.313009			−0.156505	−	0.987677i	$-0.550023\pi$
$631$	−7.86270			−0.313009			−0.156505	+	0.987677i	$0.550023\pi$
$632$	2.24302			0.0892226
$633$	51.1062			2.03129
$634$			3.19986i			0.127083i
$635$	5.70033			0.226211
$636$		−	30.8047i		−	1.22149i
$637$	−9.31896	−	13.4948i	−0.369231	−	0.534683i
$638$		0			0
$639$	−28.1990			−1.11553
$640$	6.85321			0.270897
$641$	12.8203			0.506370			0.253185	−	0.967418i	$-0.418522\pi$
$641$	12.8203			0.506370			0.253185	+	0.967418i	$0.418522\pi$
$642$			11.6263i			0.458854i
$643$			3.76638i			0.148532i	0.997238	+	0.0742659i	$0.0236613\pi$
$643$			3.76638i			0.148532i	−0.997238	+	0.0742659i	$0.976339\pi$
$644$	15.7767	+	8.27813i	0.621688	+	0.326204i
$645$		−	3.00344i		−	0.118260i
$646$		−	2.92093i		−	0.114923i
$647$		−	32.2695i		−	1.26865i	−0.773068	−	0.634323i	$-0.781279\pi$
$647$		−	32.2695i		−	1.26865i	0.773068	−	0.634323i	$-0.218721\pi$
$648$		−	5.93188i		−	0.233026i
$649$		0			0
$650$			5.46234i			0.214250i
$651$	42.0786	+	22.0789i	1.64919	+	0.865342i
$652$	−3.57189			−0.139886
$653$	18.6427			0.729547			0.364773	−	0.931096i	$-0.381146\pi$
$653$	18.6427			0.729547			0.364773	+	0.931096i	$0.381146\pi$
$654$		−	19.2494i		−	0.752710i
$655$			6.97183i			0.272412i
$656$	29.9557			1.16957
$657$	−13.2235			−0.515896
$658$	11.6868	+	6.13217i	0.455600	+	0.239057i
$659$			29.3896i			1.14486i	0.819954	+	0.572429i	$0.193999\pi$
$659$			29.3896i			1.14486i	−0.819954	+	0.572429i	$0.806001\pi$
$660$		0			0
$661$		−	10.6779i		−	0.415321i	−0.978201	−	0.207660i	$-0.933415\pi$
$661$		−	10.6779i		−	0.415321i	0.978201	−	0.207660i	$-0.0665849\pi$
$662$			4.73354i			0.183974i
$663$		−	7.72741i		−	0.300108i
$664$			14.8938i			0.577990i
$665$	−3.75480	+	7.15599i	−0.145605	+	0.277497i
$666$		−	19.7259i		−	0.764362i
$667$			8.32141i			0.322206i
$668$	12.7719			0.494160
$669$	4.27867			0.165423
$670$	−1.95820			−0.0756519
$671$		0			0
$672$	34.0646	+	17.8739i	1.31407	+	0.689502i
$673$		−	3.94666i		−	0.152133i	−0.997103	−	0.0760663i	$-0.975764\pi$
$673$		−	3.94666i		−	0.152133i	0.997103	−	0.0760663i	$-0.0242361\pi$
$674$	−2.77407			−0.106853
$675$			30.6463i			1.17958i
$676$	−13.1238			−0.504762
$677$	22.7416			0.874029			0.437015	−	0.899454i	$-0.356036\pi$
$677$	22.7416			0.874029			0.437015	+	0.899454i	$0.356036\pi$
$678$	1.45747			0.0559739
$679$	7.15645	−	13.6390i	0.274639	−	0.523415i
$680$	−1.29905			−0.0498163
$681$		−	69.0775i		−	2.64706i
$682$		0			0
$683$	24.2074			0.926271			0.463136	−	0.886287i	$-0.346724\pi$
$683$	24.2074			0.926271			0.463136	+	0.886287i	$0.346724\pi$
$684$	46.9300			1.79441
$685$			5.94817i			0.227268i
$686$	−9.24290	+	1.12524i	−0.352895	+	0.0429617i
$687$	1.05049			0.0400787
$688$		−	4.41208i		−	0.168209i
$689$	−14.3419			−0.546385
$690$			3.35998i			0.127912i
$691$			42.7569i			1.62655i	0.581880	+	0.813275i	$0.302317\pi$
$691$			42.7569i			1.62655i	−0.581880	+	0.813275i	$0.697683\pi$
$692$	−14.2854			−0.543051
$693$		0			0
$694$	16.5784			0.629308
$695$		−	6.15102i		−	0.233322i
$696$			11.7149i			0.444051i
$697$	−13.4677			−0.510126
$698$			13.3934i			0.506948i
$699$	7.61618			0.288070
$700$	−18.9834	−	9.96074i	−0.717506	−	0.376481i
$701$			0.417984i			0.0157870i	0.999969	+	0.00789352i	$0.00251261\pi$
$701$			0.417984i			0.0157870i	−0.999969	+	0.00789352i	$0.997487\pi$
$702$	−7.78379			−0.293780
$703$	37.5941			1.41789
$704$		0			0
$705$		−	17.2052i		−	0.647985i
$706$	−15.9874			−0.601695
$707$	−33.8406	−	17.7564i	−1.27271	−	0.667797i
$708$	23.6637			0.889337
$709$	−38.7298			−1.45453			−0.727264	−	0.686357i	$-0.759209\pi$
$709$	−38.7298			−1.45453			−0.727264	+	0.686357i	$0.759209\pi$
$710$	1.61221			0.0605050
$711$		−	6.30371i		−	0.236407i
$712$	−22.6004			−0.846984
$713$			24.0352i			0.900127i
$714$	−3.88499	−	2.03848i	−0.145392	−	0.0762882i
$715$		0			0
$716$	10.8833			0.406727
$717$	−50.7030			−1.89354
$718$	−15.9162			−0.593987
$719$			27.7446i			1.03470i	0.855774	+	0.517350i	$0.173082\pi$
$719$			27.7446i			1.03470i	−0.855774	+	0.517350i	$0.826918\pi$
$720$		−	8.12033i		−	0.302627i
$721$	6.90609	−	13.1618i	0.257196	−	0.490171i
$722$		−	3.38643i		−	0.126030i
$723$			24.6562i			0.916975i
$724$		−	34.5268i		−	1.28318i
$725$		−	10.0128i		−	0.371867i
$726$		0			0
$727$			0.575775i			0.0213543i	0.999943	+	0.0106772i	$0.00339871\pi$
$727$			0.575775i			0.0213543i	−0.999943	+	0.0106772i	$0.996601\pi$
$728$	5.42580	−	10.3406i	0.201093	−	0.383249i
$729$	40.4262			1.49727
$730$	0.756018			0.0279815
$731$			1.98362i			0.0733668i
$732$		−	43.8249i		−	1.61982i
$733$	20.4997			0.757174			0.378587	−	0.925566i	$-0.376410\pi$
$733$	20.4997			0.757174			0.378587	+	0.925566i	$0.376410\pi$
$734$	−5.47814			−0.202202
$735$	6.89740	+	9.98813i	0.254414	+	0.368418i
$736$			19.4576i			0.717218i
$737$		0			0
$738$			31.3027i			1.15227i
$739$		−	30.6943i		−	1.12911i	−0.825396	−	0.564554i	$-0.809048\pi$
$739$		−	30.6943i		−	1.12911i	0.825396	−	0.564554i	$-0.190952\pi$
$740$		−	7.79586i		−	0.286582i
$741$		−	34.2298i		−	1.25746i
$742$	−3.78339	+	7.21047i	−0.138892	+	0.264705i
$743$		−	23.7676i		−	0.871950i	−0.899959	−	0.435975i	$-0.856404\pi$
$743$		−	23.7676i		−	0.871950i	0.899959	−	0.435975i	$-0.143596\pi$
$744$			33.8368i			1.24052i
$745$	2.76344			0.101245
$746$	2.74423			0.100473
$747$	41.8569			1.53146
$748$		0			0
$749$	−9.87067	+	18.8118i	−0.360666	+	0.687367i
$750$		−	8.40189i		−	0.306794i
$751$	12.7514			0.465304			0.232652	−	0.972560i	$-0.425260\pi$
$751$	12.7514			0.465304			0.232652	+	0.972560i	$0.425260\pi$
$752$		−	25.2746i		−	0.921671i
$753$	−8.91985			−0.325057
$754$	2.54314			0.0926155
$755$	7.91353			0.288003
$756$	14.1940	−	27.0512i	0.516230	−	0.983844i
$757$	25.0044			0.908800			0.454400	−	0.890798i	$-0.349854\pi$
$757$	25.0044			0.908800			0.454400	+	0.890798i	$0.349854\pi$
$758$		−	2.99600i		−	0.108820i
$759$		0			0
$760$	−5.75435			−0.208732
$761$	−3.28328			−0.119019			−0.0595094	−	0.998228i	$-0.518954\pi$
$761$	−3.28328			−0.119019			−0.0595094	+	0.998228i	$0.518954\pi$
$762$			13.7085i			0.496608i
$763$	16.3426	−	31.1461i	0.591642	−	1.12757i
$764$	1.08319			0.0391884
$765$			3.65080i			0.131995i
$766$	15.5963			0.563519
$767$		−	11.0173i		−	0.397811i
$768$			1.75574i			0.0633549i
$769$	−16.9051			−0.609613			−0.304806	−	0.952414i	$-0.598592\pi$
$769$	−16.9051			−0.609613			−0.304806	+	0.952414i	$0.598592\pi$
$770$		0			0
$771$	39.3136			1.41584
$772$		−	21.7224i		−	0.781806i
$773$		−	2.95877i		−	0.106420i	−0.998583	−	0.0532098i	$-0.983055\pi$
$773$		−	2.95877i		−	0.106420i	0.998583	−	0.0532098i	$-0.0169452\pi$
$774$	4.61048			0.165720
$775$		−	28.9206i		−	1.03886i
$776$	10.9675			0.393711
$777$	26.2364	−	50.0020i	0.941225	−	1.79381i
$778$		−	11.7712i		−	0.422020i
$779$	−59.6575			−2.13745
$780$	−7.09822			−0.254157
$781$		0			0
$782$		−	2.21910i		−	0.0793548i
$783$	14.2682			0.509904
$784$	10.1324	+	14.6727i	0.361870	+	0.524025i
$785$	−1.86109			−0.0664252
$786$	−16.7663			−0.598035
$787$	−17.2483			−0.614836			−0.307418	−	0.951575i	$-0.599465\pi$
$787$	−17.2483			−0.614836			−0.307418	+	0.951575i	$0.599465\pi$
$788$		−	21.7097i		−	0.773375i
$789$	−61.0558			−2.17364
$790$			0.360399i			0.0128224i
$791$	2.35824	+	1.23739i	0.0838494	+	0.0439964i
$792$		0			0
$793$	−20.4039			−0.724562
$794$	15.0019			0.532397
$795$	10.6151			0.376480
$796$			14.8843i			0.527560i
$797$		−	22.2363i		−	0.787651i	−0.919185	−	0.393826i	$-0.871151\pi$
$797$		−	22.2363i		−	0.787651i	0.919185	−	0.393826i	$-0.128849\pi$
$798$	−17.2092	−	9.02978i	−0.609199	−	0.319651i
$799$			11.3632i			0.402000i
$800$		−	23.4126i		−	0.827761i
$801$			63.5152i			2.24420i
$802$		−	10.3289i		−	0.364727i
$803$		0			0
$804$			32.5528i			1.14805i
$805$	−2.85260	+	5.43656i	−0.100541	+	0.191614i
$806$	7.34549			0.258734
$807$	−40.6382			−1.43053
$808$		−	27.2123i		−	0.957324i
$809$			9.44132i			0.331939i	0.986131	+	0.165970i	$0.0530753\pi$
$809$			9.44132i			0.331939i	−0.986131	+	0.165970i	$0.946925\pi$
$810$	0.953109			0.0334888
$811$	29.6025			1.03948			0.519742	−	0.854323i	$-0.326028\pi$
$811$	29.6025			1.03948			0.519742	+	0.854323i	$0.326028\pi$
$812$	−4.63749	+	8.83824i	−0.162744	+	0.310162i
$813$			45.3506i			1.59052i
$814$		0			0
$815$		−	1.23086i		−	0.0431150i
$816$			8.40189i			0.294125i
$817$			8.78677i			0.307410i
$818$		−	6.25709i		−	0.218774i
$819$	−29.0609	−	15.2485i	−1.01547	−	0.532825i
$820$			12.3711i			0.432019i
$821$		−	40.3174i		−	1.40709i	−0.710653	−	0.703543i	$-0.751600\pi$
$821$		−	40.3174i		−	1.40709i	0.710653	−	0.703543i	$-0.248400\pi$
$822$	−14.3045			−0.498928
$823$	−41.4204			−1.44382			−0.721912	−	0.691984i	$-0.756737\pi$
$823$	−41.4204			−1.44382			−0.721912	+	0.691984i	$0.756737\pi$
$824$	10.5838			0.368705
$825$		0			0
$826$	−5.53898	−	2.90634i	−0.192726	−	0.101125i
$827$		−	30.7178i		−	1.06816i	−0.845433	−	0.534081i	$-0.820658\pi$
$827$		−	30.7178i		−	1.06816i	0.845433	−	0.534081i	$-0.179342\pi$
$828$	35.6537			1.23905
$829$		−	44.6514i		−	1.55081i	−0.631466	−	0.775404i	$-0.717546\pi$
$829$		−	44.6514i		−	1.55081i	0.631466	−	0.775404i	$-0.282454\pi$
$830$	−2.39306			−0.0830645
$831$	19.2510			0.667809
$832$	−5.98933			−0.207643
$833$	−4.55538	−	6.59666i	−0.157835	−	0.228561i
$834$	14.7924			0.512219
$835$			4.40114i			0.152308i
$836$		0			0
$837$	41.2117			1.42448
$838$	−7.57707			−0.261745
$839$		−	1.76555i		−	0.0609536i	−0.999535	−	0.0304768i	$-0.990297\pi$
$839$		−	1.76555i		−	0.0609536i	0.999535	−	0.0304768i	$-0.00970258\pi$
$840$	−4.01589	+	7.65358i	−0.138561	+	0.264074i
$841$	24.3383			0.839250
$842$			3.04087i			0.104795i
$843$	63.7145			2.19445
$844$			31.0048i			1.06723i
$845$		−	4.52240i		−	0.155575i
$846$	26.4111			0.908033
$847$		0			0
$848$	15.5938			0.535493
$849$		−	39.9651i		−	1.37160i
$850$			2.67015i			0.0915854i
$851$	28.5610			0.979060
$852$		−	26.8011i		−	0.918191i
$853$	−32.1461			−1.10066			−0.550331	−	0.834947i	$-0.685498\pi$
$853$	−32.1461			−1.10066			−0.550331	+	0.834947i	$0.685498\pi$
$854$	−5.38251	+	10.2581i	−0.184186	+	0.351026i
$855$			16.1718i			0.553065i
$856$	−15.1271			−0.517035
$857$	16.6829			0.569876			0.284938	−	0.958546i	$-0.408027\pi$
$857$	16.6829			0.569876			0.284938	+	0.958546i	$0.408027\pi$
$858$		0			0
$859$		−	33.8229i		−	1.15402i	−0.816736	−	0.577011i	$-0.804219\pi$
$859$		−	33.8229i		−	1.15402i	0.816736	−	0.577011i	$-0.195781\pi$
$860$	1.82211			0.0621333
$861$	−41.6341	+	79.3474i	−1.41889	+	2.70415i
$862$	3.64274			0.124072
$863$	45.3184			1.54266			0.771329	−	0.636437i	$-0.219593\pi$
$863$	45.3184			1.54266			0.771329	+	0.636437i	$0.219593\pi$
$864$	33.3628			1.13503
$865$		−	4.92269i		−	0.167376i
$866$	−5.11273			−0.173738
$867$			45.1831i			1.53450i
$868$	−13.3947	+	25.5280i	−0.454647	+	0.866477i
$869$		0			0
$870$	−1.88229			−0.0638157
$871$	15.1558			0.513536
$872$	25.0456			0.848151
$873$		−	30.8227i		−	1.04319i
$874$		−	9.82986i		−	0.332500i
$875$	7.13316	−	13.5946i	0.241145	−	0.459580i
$876$		−	12.5679i		−	0.424632i
$877$		−	42.6831i		−	1.44130i	−0.693297	−	0.720652i	$-0.743842\pi$
$877$		−	42.6831i		−	1.44130i	0.693297	−	0.720652i	$-0.256158\pi$
$878$			4.31078i			0.145482i
$879$		−	20.4820i		−	0.690842i
$880$		0			0
$881$			21.4936i			0.724139i	0.932151	+	0.362070i	$0.117930\pi$
$881$			21.4936i			0.724139i	−0.932151	+	0.362070i	$0.882070\pi$
$882$	−15.3325	+	10.5880i	−0.516271	+	0.356516i
$883$	14.8074			0.498310			0.249155	−	0.968464i	$-0.419847\pi$
$883$	14.8074			0.498310			0.249155	+	0.968464i	$0.419847\pi$
$884$	4.68802			0.157675
$885$			8.15440i			0.274107i
$886$			4.93467i			0.165783i
$887$	−9.23398			−0.310047			−0.155023	−	0.987911i	$-0.549545\pi$
$887$	−9.23398			−0.310047			−0.155023	+	0.987911i	$0.549545\pi$
$888$	40.2082			1.34930
$889$	−11.6385	+	22.1809i	−0.390342	+	0.743923i
$890$		−	3.63132i		−	0.121722i
$891$		0			0
$892$			2.59576i			0.0869124i
$893$			50.3350i			1.68440i
$894$			6.64570i			0.222266i
$895$			3.75032i			0.125359i
$896$	−13.9923	+	26.6669i	−0.467450	+	0.890879i
$897$		−	26.0052i		−	0.868287i
$898$			7.80243i			0.260370i
$899$	−13.4648			−0.449075
$900$	−42.9007			−1.43002
$901$	−7.01077			−0.233563
$902$		0			0
$903$	11.6868	+	6.13217i	0.388914	+	0.204066i
$904$			1.89634i			0.0630712i
$905$	11.8978			0.395496
$906$			19.0310i			0.632262i
$907$	1.00834			0.0334813			0.0167407	−	0.999860i	$-0.494671\pi$
$907$	1.00834			0.0334813			0.0167407	+	0.999860i	$0.494671\pi$
$908$	41.9075			1.39075
$909$	−76.4764			−2.53656
$910$	1.66149	+	0.871793i	0.0550777	+	0.0288997i
$911$	26.1008			0.864759			0.432379	−	0.901692i	$-0.357674\pi$
$911$	26.1008			0.864759			0.432379	+	0.901692i	$0.357674\pi$
$912$			37.2176i			1.23240i
$913$		0			0
$914$	13.7207			0.453840
$915$	15.1018			0.499252
$916$			0.637305i			0.0210571i
$917$	−27.1285	−	14.2345i	−0.895861	−	0.470065i
$918$	−3.80495			−0.125582
$919$		−	47.3762i		−	1.56280i	−0.624034	−	0.781398i	$-0.714507\pi$
$919$		−	47.3762i		−	1.56280i	0.624034	−	0.781398i	$-0.285493\pi$
$920$	−4.37171			−0.144131
$921$		−	54.0595i		−	1.78132i
$922$		−	17.1115i		−	0.563536i
$923$	−12.4780			−0.410717
$924$		0			0
$925$	−34.3664			−1.12996
$926$		−	9.69807i		−	0.318698i
$927$		−	29.7444i		−	0.976934i
$928$	−10.9004			−0.357822
$929$		−	21.8535i		−	0.716988i	−0.933532	−	0.358494i	$-0.883290\pi$
$929$		−	21.8535i		−	0.716988i	0.933532	−	0.358494i	$-0.116710\pi$
$930$	−5.43674			−0.178278
$931$	−20.1788	−	29.2210i	−0.661334	−	0.957679i
$932$			4.62054i			0.151351i
$933$	10.3312			0.338227
$934$	12.1311			0.396942
$935$		0			0
$936$		−	23.3688i		−	0.763833i
$937$	21.2841			0.695321			0.347660	−	0.937621i	$-0.386976\pi$
$937$	21.2841			0.695321			0.347660	+	0.937621i	$0.386976\pi$
$938$	3.99809	−	7.61966i	0.130542	−	0.248791i
$939$	75.9757			2.47937
$940$	10.4379			0.340448
$941$	2.43028			0.0792248			0.0396124	−	0.999215i	$-0.487388\pi$
$941$	2.43028			0.0792248			0.0396124	+	0.999215i	$0.487388\pi$
$942$		−	4.47568i		−	0.145825i
$943$	−45.3231			−1.47592
$944$			11.9789i			0.389880i
$945$	9.32173	+	4.89117i	0.303236	+	0.159110i
$946$		0			0
$947$	2.50040			0.0812520			0.0406260	−	0.999174i	$-0.487065\pi$
$947$	2.50040			0.0812520			0.0406260	+	0.999174i	$0.487065\pi$
$948$	5.99122			0.194586
$949$	−5.85134			−0.189943
$950$			11.8279i			0.383747i
$951$			18.3304i			0.594405i
$952$	2.65229	−	5.05480i	0.0859612	−	0.163827i
$953$			23.0007i			0.745065i	0.928019	+	0.372532i	$0.121510\pi$
$953$			23.0007i			0.745065i	−0.928019	+	0.372532i	$0.878490\pi$
$954$			16.2950i			0.527569i
$955$			0.373262i			0.0120785i
$956$		−	30.7602i		−	0.994856i
$957$		0			0
$958$			19.6000i			0.633246i
$959$	−23.1452	−	12.1445i	−0.747399	−	0.392165i
$960$	4.43298			0.143074
$961$	−7.89110			−0.254552
$962$		−	8.72864i		−	0.281423i
$963$			42.5128i			1.36996i
$964$	−14.9583			−0.481774
$965$	7.48543			0.240965
$966$	−13.0742	−	6.86013i	−0.420656	−	0.220721i
$967$		−	38.6426i		−	1.24266i	−0.783548	−	0.621331i	$-0.786592\pi$
$967$		−	38.6426i		−	1.24266i	0.783548	−	0.621331i	$-0.213408\pi$
$968$		0			0
$969$		−	16.7326i		−	0.537527i
$970$			1.76221i			0.0565812i
$971$		−	55.2628i		−	1.77347i	−0.462280	−	0.886734i	$-0.652968\pi$
$971$		−	55.2628i		−	1.77347i	0.462280	−	0.886734i	$-0.347032\pi$
$972$			18.7949i			0.602847i
$973$	23.9346	+	12.5587i	0.767308	+	0.402612i
$974$			0.419333i			0.0134363i
$975$			31.2910i			1.00211i
$976$	22.1848			0.710118
$977$	53.9445			1.72584			0.862919	−	0.505343i	$-0.168634\pi$
$977$	53.9445			1.72584			0.862919	+	0.505343i	$0.168634\pi$
$978$	2.96005			0.0946519
$979$		0			0
$980$	−6.05954	+	4.18447i	−0.193565	+	0.133668i
$981$		−	70.3873i		−	2.24729i
$982$	13.7706			0.439437
$983$			31.9443i			1.01887i	0.860510	+	0.509433i	$0.170145\pi$
$983$			31.9443i			1.01887i	−0.860510	+	0.509433i	$0.829855\pi$
$984$	−63.8058			−2.03405
$985$	7.48104			0.238366
$986$	1.24316			0.0395903
$987$	66.9481	+	35.1281i	2.13098	+	1.11814i
$988$	20.7664			0.660666
$989$			6.67550i			0.212269i
$990$		0			0
$991$	46.5004			1.47713			0.738567	−	0.674180i	$-0.235503\pi$
$991$	46.5004			1.47713			0.738567	+	0.674180i	$0.235503\pi$
$992$	−31.4842			−0.999623
$993$			27.1161i			0.860504i
$994$	−3.29167	+	6.27335i	−0.104405	+	0.198979i
$995$	−5.12906			−0.162602
$996$			39.7820i			1.26054i
$997$	−54.9489			−1.74025			−0.870125	−	0.492831i	$-0.835962\pi$
$997$	−54.9489			−1.74025			−0.870125	+	0.492831i	$0.835962\pi$
$998$		−	10.0092i		−	0.316834i
$999$		−	48.9718i		−	1.54940i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	847.2.b.f.846.7		16
7.6	odd	2	inner	847.2.b.f.846.8		16
11.2	odd	10		847.2.l.j.524.3		16
11.3	even	5		847.2.l.i.475.2		16
11.4	even	5		77.2.l.b.6.3	✓	16
11.5	even	5		847.2.l.j.118.4		16
11.6	odd	10		847.2.l.e.118.2		16
11.7	odd	10		847.2.l.i.699.1		16
11.8	odd	10		77.2.l.b.13.4	yes	16
11.9	even	5		847.2.l.e.524.1		16
11.10	odd	2	inner	847.2.b.f.846.9		16
33.8	even	10		693.2.bu.d.244.2		16
33.26	odd	10		693.2.bu.d.622.1		16
77.4	even	15		539.2.s.b.215.2		16
77.6	even	10		847.2.l.e.118.1		16
77.13	even	10		847.2.l.j.524.4		16
77.19	even	30		539.2.s.b.178.2		16
77.20	odd	10		847.2.l.e.524.2		16
77.26	odd	30		539.2.s.c.325.2		16
77.27	odd	10		847.2.l.j.118.3		16
77.30	odd	30		539.2.s.b.178.1		16
77.37	even	15		539.2.s.c.325.1		16
77.41	even	10		77.2.l.b.13.3	yes	16
77.48	odd	10		77.2.l.b.6.4	yes	16
77.52	even	30		539.2.s.c.68.1		16
77.59	odd	30		539.2.s.b.215.1		16
77.62	even	10		847.2.l.i.699.2		16
77.69	odd	10		847.2.l.i.475.1		16
77.74	odd	30		539.2.s.c.68.2		16
77.76	even	2	inner	847.2.b.f.846.10		16
231.41	odd	10		693.2.bu.d.244.1		16
231.125	even	10		693.2.bu.d.622.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.l.b.6.3	✓	16	11.4	even	5
77.2.l.b.6.4	yes	16	77.48	odd	10
77.2.l.b.13.3	yes	16	77.41	even	10
77.2.l.b.13.4	yes	16	11.8	odd	10
539.2.s.b.178.1		16	77.30	odd	30
539.2.s.b.178.2		16	77.19	even	30
539.2.s.b.215.1		16	77.59	odd	30
539.2.s.b.215.2		16	77.4	even	15
539.2.s.c.68.1		16	77.52	even	30
539.2.s.c.68.2		16	77.74	odd	30
539.2.s.c.325.1		16	77.37	even	15
539.2.s.c.325.2		16	77.26	odd	30
693.2.bu.d.244.1		16	231.41	odd	10
693.2.bu.d.244.2		16	33.8	even	10
693.2.bu.d.622.1		16	33.26	odd	10
693.2.bu.d.622.2		16	231.125	even	10
847.2.b.f.846.7		16	1.1	even	1	trivial
847.2.b.f.846.8		16	7.6	odd	2	inner
847.2.b.f.846.9		16	11.10	odd	2	inner
847.2.b.f.846.10		16	77.76	even	2	inner
847.2.l.e.118.1		16	77.6	even	10
847.2.l.e.118.2		16	11.6	odd	10
847.2.l.e.524.1		16	11.9	even	5
847.2.l.e.524.2		16	77.20	odd	10
847.2.l.i.475.1		16	77.69	odd	10
847.2.l.i.475.2		16	11.3	even	5
847.2.l.i.699.1		16	11.7	odd	10
847.2.l.i.699.2		16	77.62	even	10
847.2.l.j.118.3		16	77.27	odd	10
847.2.l.j.118.4		16	11.5	even	5
847.2.l.j.524.3		16	11.2	odd	10
847.2.l.j.524.4		16	77.13	even	10

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:	\( N \)	\(=\)	\( 847 = 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	847.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-0.502754i q^{2} -2.88003i q^{3} +1.74724 q^{4} +0.602090i q^{5} -1.44795 q^{6} +(-2.34283 - 1.22930i) q^{7} -1.88394i q^{8} -5.29456 q^{9} +O(q^{10})\)	\(q-0.502754i q^{2} -2.88003i q^{3} +1.74724 q^{4} +0.602090i q^{5} -1.44795 q^{6} +(-2.34283 - 1.22930i) q^{7} -1.88394i q^{8} -5.29456 q^{9} +0.302703 q^{10} -5.03209i q^{12} -2.34283 q^{13} +(-0.618034 + 1.17787i) q^{14} +1.73403 q^{15} +2.54732 q^{16} -1.14524 q^{17} +2.66186i q^{18} -5.07304 q^{19} +1.05199i q^{20} +(-3.54041 + 6.74740i) q^{21} -3.85410 q^{23} -5.42580 q^{24} +4.63749 q^{25} +1.17787i q^{26} +6.60838i q^{27} +(-4.09347 - 2.14787i) q^{28} -2.15911i q^{29} -0.871793i q^{30} -6.23627i q^{31} -5.04855i q^{32} +0.575775i q^{34} +(0.740147 - 1.41059i) q^{35} -9.25085 q^{36} -7.41056 q^{37} +2.55049i q^{38} +6.74740i q^{39} +1.13430 q^{40} +11.7597 q^{41} +(3.39228 + 1.77995i) q^{42} -1.73205i q^{43} -3.18780i q^{45} +1.93767i q^{46} -9.92205i q^{47} -7.33635i q^{48} +(3.97766 + 5.76005i) q^{49} -2.33152i q^{50} +3.29833i q^{51} -4.09347 q^{52} +6.12165 q^{53} +3.32239 q^{54} +(-2.31592 + 4.41374i) q^{56} +14.6105i q^{57} -1.08550 q^{58} +4.70256i q^{59} +3.02977 q^{60} +8.70908 q^{61} -3.13531 q^{62} +(12.4042 + 6.50858i) q^{63} +2.55645 q^{64} -1.41059i q^{65} -6.46905 q^{67} -2.00101 q^{68} +11.0999i q^{69} +(-0.709180 - 0.372112i) q^{70} +5.32603 q^{71} +9.97462i q^{72} +2.49756 q^{73} +3.72569i q^{74} -13.3561i q^{75} -8.86381 q^{76} +3.39228 q^{78} +1.19060i q^{79} +1.53371i q^{80} +3.14866 q^{81} -5.91224i q^{82} -7.90565 q^{83} +(-6.18594 + 11.7893i) q^{84} -0.689539i q^{85} -0.870796 q^{86} -6.21828 q^{87} -11.9963i q^{89} -1.60268 q^{90} +(5.48883 + 2.88003i) q^{91} -6.73403 q^{92} -17.9606 q^{93} -4.98835 q^{94} -3.05443i q^{95} -14.5400 q^{96} +5.82158i q^{97} +(2.89589 - 1.99978i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 32 q^{9}+O(q^{10}) \) 16 * q - 32 * q^9	\( 16 q - 32 q^{9} + 8 q^{14} - 20 q^{15} + 16 q^{16} - 8 q^{23} - 40 q^{25} - 60 q^{36} - 36 q^{37} - 20 q^{42} + 48 q^{49} + 20 q^{53} - 4 q^{56} + 28 q^{58} - 140 q^{60} + 12 q^{64} - 4 q^{67} + 100 q^{70} + 44 q^{71} - 20 q^{78} - 56 q^{81} - 24 q^{86} + 80 q^{91} - 60 q^{92} - 20 q^{93}+O(q^{100}) \) 16 * q - 32 * q^9 + 8 * q^14 - 20 * q^15 + 16 * q^16 - 8 * q^23 - 40 * q^25 - 60 * q^36 - 36 * q^37 - 20 * q^42 + 48 * q^49 + 20 * q^53 - 4 * q^56 + 28 * q^58 - 140 * q^60 + 12 * q^64 - 4 * q^67 + 100 * q^70 + 44 * q^71 - 20 * q^78 - 56 * q^81 - 24 * q^86 + 80 * q^91 - 60 * q^92 - 20 * q^93

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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