LMFDB - Embedded newform 168.2.i.e.125.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [168,2,Mod(125,168)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(168, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 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("168.125");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 168 = 2^{3} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	168.i (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:	$1.34148675396$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.3317760000.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 8x^{6} + 13x^{4} + 12x^{2} + 36 $ x^8 - 8x^6 + 13x^4 + 12*x^2 + 36
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			125.8
Root			$2.15988 - 0.258819i$ of defining polynomial
Character	$\chi$	$=$	168.125
Dual form			168.2.i.e.125.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 1.11803i) q^{2} +(1.58114 + 0.707107i) q^{3} +(-0.500000 + 1.93649i) q^{4} -1.41421i q^{5} +(0.578737 + 2.38014i) q^{6} +(1.00000 - 2.44949i) q^{7} +(-2.59808 + 1.11803i) q^{8} +(2.00000 + 2.23607i) q^{9} +O(q^{10})$	\(q+(0.866025 + 1.11803i) q^{2} +(1.58114 + 0.707107i) q^{3} +(-0.500000 + 1.93649i) q^{4} -1.41421i q^{5} +(0.578737 + 2.38014i) q^{6} +(1.00000 - 2.44949i) q^{7} +(-2.59808 + 1.11803i) q^{8} +(2.00000 + 2.23607i) q^{9} +(1.58114 - 1.22474i) q^{10} -3.46410 q^{11} +(-2.15988 + 2.70831i) q^{12} -3.16228 q^{13} +(3.60464 - 1.00329i) q^{14} +(1.00000 - 2.23607i) q^{15} +(-3.50000 - 1.93649i) q^{16} +(-0.767949 + 4.17256i) q^{18} -3.16228 q^{19} +(2.73861 + 0.707107i) q^{20} +(3.31319 - 3.16588i) q^{21} +(-3.00000 - 3.87298i) q^{22} -4.47214i q^{23} +(-4.89849 - 0.0693504i) q^{24} +3.00000 q^{25} +(-2.73861 - 3.53553i) q^{26} +(1.58114 + 4.94975i) q^{27} +(4.24342 + 3.16124i) q^{28} +6.92820 q^{29} +(3.36603 - 0.818458i) q^{30} +4.89898i q^{31} +(-0.866025 - 5.59017i) q^{32} +(-5.47723 - 2.44949i) q^{33} +(-3.46410 - 1.41421i) q^{35} +(-5.33013 + 2.75495i) q^{36} +(-2.73861 - 3.53553i) q^{38} +(-5.00000 - 2.23607i) q^{39} +(1.58114 + 3.67423i) q^{40} +10.9545 q^{41} +(6.40886 + 0.962529i) q^{42} +7.74597i q^{43} +(1.73205 - 6.70820i) q^{44} +(3.16228 - 2.82843i) q^{45} +(5.00000 - 3.87298i) q^{46} -10.9545 q^{47} +(-4.16468 - 5.53674i) q^{48} +(-5.00000 - 4.89898i) q^{49} +(2.59808 + 3.35410i) q^{50} +(1.58114 - 6.12372i) q^{52} +(-4.16468 + 6.05437i) q^{54} +4.89898i q^{55} +(0.140537 + 7.48200i) q^{56} +(-5.00000 - 2.23607i) q^{57} +(6.00000 + 7.74597i) q^{58} -9.89949i q^{59} +(3.83013 + 3.05453i) q^{60} -3.16228 q^{61} +(-5.47723 + 4.24264i) q^{62} +(7.47723 - 2.66291i) q^{63} +(5.50000 - 5.80948i) q^{64} +4.47214i q^{65} +(-2.00480 - 8.24504i) q^{66} -7.74597i q^{67} +(3.16228 - 7.07107i) q^{69} +(-1.41886 - 5.09773i) q^{70} +8.94427i q^{71} +(-7.69615 - 3.57341i) q^{72} +14.6969i q^{73} +(4.74342 + 2.12132i) q^{75} +(1.58114 - 6.12372i) q^{76} +(-3.46410 + 8.48528i) q^{77} +(-1.83013 - 7.52666i) q^{78} -10.0000 q^{79} +(-2.73861 + 4.94975i) q^{80} +(-1.00000 + 8.94427i) q^{81} +(9.48683 + 12.2474i) q^{82} +7.07107i q^{83} +(4.47410 + 7.99890i) q^{84} +(-8.66025 + 6.70820i) q^{86} +(10.9545 + 4.89898i) q^{87} +(9.00000 - 3.87298i) q^{88} +(5.90089 + 1.08604i) q^{90} +(-3.16228 + 7.74597i) q^{91} +(8.66025 + 2.23607i) q^{92} +(-3.46410 + 7.74597i) q^{93} +(-9.48683 - 12.2474i) q^{94} +4.47214i q^{95} +(2.58354 - 9.45121i) q^{96} -4.89898i q^{97} +(1.14710 - 9.83281i) q^{98} +(-6.92820 - 7.74597i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{4} + 8 q^{7} + 16 q^{9}+O(q^{10}) $ 8 * q - 4 * q^4 + 8 * q^7 + 16 * q^9	$ 8 q - 4 q^{4} + 8 q^{7} + 16 q^{9} + 8 q^{15} - 28 q^{16} - 20 q^{18} - 24 q^{22} + 24 q^{25} - 4 q^{28} + 20 q^{30} - 8 q^{36} - 40 q^{39} + 12 q^{42} + 40 q^{46} - 40 q^{49} - 40 q^{57} + 48 q^{58} - 4 q^{60} + 16 q^{63} + 44 q^{64} - 24 q^{70} - 20 q^{72} + 20 q^{78} - 80 q^{79} - 8 q^{81} + 60 q^{84} + 72 q^{88}+O(q^{100}) $ 8 * q - 4 * q^4 + 8 * q^7 + 16 * q^9 + 8 * q^15 - 28 * q^16 - 20 * q^18 - 24 * q^22 + 24 * q^25 - 4 * q^28 + 20 * q^30 - 8 * q^36 - 40 * q^39 + 12 * q^42 + 40 * q^46 - 40 * q^49 - 40 * q^57 + 48 * q^58 - 4 * q^60 + 16 * q^63 + 44 * q^64 - 24 * q^70 - 20 * q^72 + 20 * q^78 - 80 * q^79 - 8 * q^81 + 60 * q^84 + 72 * q^88

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/168\mathbb{Z}\right)^\times$.

$n$	$73$	$85$	$113$	$127$
$\chi(n)$	$-1$	$-1$	$-1$	$1$

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 $

$2$	0.866025	+	1.11803i	0.612372	+	0.790569i
$2$	0.866025	+	1.11803i	0.612372	+	0.790569i
$3$	1.58114	+	0.707107i	0.912871	+	0.408248i
$3$	1.58114	+	0.707107i	0.912871	+	0.408248i
$4$	−0.500000	+	1.93649i	−0.250000	+	0.968246i
$5$		−	1.41421i		−	0.632456i	−0.948683	−	0.316228i	$-0.897584\pi$
$5$		−	1.41421i		−	0.632456i	0.948683	−	0.316228i	$-0.102416\pi$
$6$	0.578737	+	2.38014i	0.236268	+	0.971688i
$7$	1.00000	−	2.44949i	0.377964	−	0.925820i
$7$	1.00000	−	2.44949i	0.377964	−	0.925820i
$8$	−2.59808	+	1.11803i	−0.918559	+	0.395285i
$9$	2.00000	+	2.23607i	0.666667	+	0.745356i
$10$	1.58114	−	1.22474i	0.500000	−	0.387298i
$11$	−3.46410			−1.04447			−0.522233	−	0.852803i	$-0.674901\pi$
$11$	−3.46410			−1.04447			−0.522233	+	0.852803i	$0.674901\pi$
$12$	−2.15988	+	2.70831i	−0.623502	+	0.781821i
$13$	−3.16228			−0.877058			−0.438529	−	0.898717i	$-0.644500\pi$
$13$	−3.16228			−0.877058			−0.438529	+	0.898717i	$0.644500\pi$
$14$	3.60464	−	1.00329i	0.963380	−	0.268140i
$15$	1.00000	−	2.23607i	0.258199	−	0.577350i
$16$	−3.50000	−	1.93649i	−0.875000	−	0.484123i
$17$		0			0			−	1.00000i	$-0.5\pi$
$17$		0			0				1.00000i	$0.5\pi$
$18$	−0.767949	+	4.17256i	−0.181007	+	0.983482i
$19$	−3.16228			−0.725476			−0.362738	−	0.931891i	$-0.618158\pi$
$19$	−3.16228			−0.725476			−0.362738	+	0.931891i	$0.618158\pi$
$20$	2.73861	+	0.707107i	0.612372	+	0.158114i
$21$	3.31319	−	3.16588i	0.722997	−	0.690851i
$22$	−3.00000	−	3.87298i	−0.639602	−	0.825723i
$23$		−	4.47214i		−	0.932505i	−0.884652	−	0.466252i	$-0.845604\pi$
$23$		−	4.47214i		−	0.932505i	0.884652	−	0.466252i	$-0.154396\pi$
$24$	−4.89849	−	0.0693504i	−0.999900	−	0.0141561i
$25$	3.00000			0.600000
$26$	−2.73861	−	3.53553i	−0.537086	−	0.693375i
$27$	1.58114	+	4.94975i	0.304290	+	0.952579i
$28$	4.24342	+	3.16124i	0.801930	+	0.597418i
$29$	6.92820			1.28654			0.643268	−	0.765641i	$-0.277578\pi$
$29$	6.92820			1.28654			0.643268	+	0.765641i	$0.277578\pi$
$30$	3.36603	−	0.818458i	0.614549	−	0.149429i
$31$			4.89898i			0.879883i	0.898027	+	0.439941i	$0.145001\pi$
$31$			4.89898i			0.879883i	−0.898027	+	0.439941i	$0.854999\pi$
$32$	−0.866025	−	5.59017i	−0.153093	−	0.988212i
$33$	−5.47723	−	2.44949i	−0.953463	−	0.426401i
$34$		0			0
$35$	−3.46410	−	1.41421i	−0.585540	−	0.239046i
$36$	−5.33013	+	2.75495i	−0.888355	+	0.459158i
$37$		0			0		1.00000			$0$
$37$		0			0		−1.00000			$\pi$
$38$	−2.73861	−	3.53553i	−0.444262	−	0.573539i
$39$	−5.00000	−	2.23607i	−0.800641	−	0.358057i
$40$	1.58114	+	3.67423i	0.250000	+	0.580948i
$41$	10.9545			1.71080			0.855399	−	0.517970i	$-0.173312\pi$
$41$	10.9545			1.71080			0.855399	+	0.517970i	$0.173312\pi$
$42$	6.40886	+	0.962529i	0.988909	+	0.148521i
$43$			7.74597i			1.18125i	0.806947	+	0.590624i	$0.201119\pi$
$43$			7.74597i			1.18125i	−0.806947	+	0.590624i	$0.798881\pi$
$44$	1.73205	−	6.70820i	0.261116	−	1.01130i
$45$	3.16228	−	2.82843i	0.471405	−	0.421637i
$46$	5.00000	−	3.87298i	0.737210	−	0.571040i
$47$	−10.9545			−1.59787			−0.798935	−	0.601417i	$-0.794603\pi$
$47$	−10.9545			−1.59787			−0.798935	+	0.601417i	$0.794603\pi$
$48$	−4.16468	−	5.53674i	−0.601120	−	0.799159i
$49$	−5.00000	−	4.89898i	−0.714286	−	0.699854i
$50$	2.59808	+	3.35410i	0.367423	+	0.474342i
$51$		0			0
$52$	1.58114	−	6.12372i	0.219265	−	0.849208i
$53$		0			0			−	1.00000i	$-0.5\pi$
$53$		0			0				1.00000i	$0.5\pi$
$54$	−4.16468	+	6.05437i	−0.566741	+	0.823896i
$55$			4.89898i			0.660578i
$56$	0.140537	+	7.48200i	0.0187800	+	0.999824i
$57$	−5.00000	−	2.23607i	−0.662266	−	0.296174i
$58$	6.00000	+	7.74597i	0.787839	+	1.01710i
$59$		−	9.89949i		−	1.28880i	−0.764687	−	0.644402i	$-0.777106\pi$
$59$		−	9.89949i		−	1.28880i	0.764687	−	0.644402i	$-0.222894\pi$
$60$	3.83013	+	3.05453i	0.494467	+	0.394338i
$61$	−3.16228			−0.404888			−0.202444	−	0.979294i	$-0.564888\pi$
$61$	−3.16228			−0.404888			−0.202444	+	0.979294i	$0.564888\pi$
$62$	−5.47723	+	4.24264i	−0.695608	+	0.538816i
$63$	7.47723	−	2.66291i	0.942042	−	0.335495i
$64$	5.50000	−	5.80948i	0.687500	−	0.726184i
$65$			4.47214i			0.554700i
$66$	−2.00480	−	8.24504i	−0.246774	−	1.01489i
$67$		−	7.74597i		−	0.946320i	−0.880976	−	0.473160i	$-0.843113\pi$
$67$		−	7.74597i		−	0.946320i	0.880976	−	0.473160i	$-0.156887\pi$
$68$		0			0
$69$	3.16228	−	7.07107i	0.380693	−	0.851257i
$70$	−1.41886	−	5.09773i	−0.169586	−	0.609295i
$71$			8.94427i			1.06149i	0.847532	+	0.530745i	$0.178088\pi$
$71$			8.94427i			1.06149i	−0.847532	+	0.530745i	$0.821912\pi$
$72$	−7.69615	−	3.57341i	−0.907000	−	0.421130i
$73$			14.6969i			1.72015i	0.510171	+	0.860073i	$0.329582\pi$
$73$			14.6969i			1.72015i	−0.510171	+	0.860073i	$0.670418\pi$
$74$		0			0
$75$	4.74342	+	2.12132i	0.547723	+	0.244949i
$76$	1.58114	−	6.12372i	0.181369	−	0.702439i
$77$	−3.46410	+	8.48528i	−0.394771	+	0.966988i
$78$	−1.83013	−	7.52666i	−0.207221	−	0.852227i
$79$	−10.0000			−1.12509			−0.562544	−	0.826767i	$-0.690177\pi$
$79$	−10.0000			−1.12509			−0.562544	+	0.826767i	$0.690177\pi$
$80$	−2.73861	+	4.94975i	−0.306186	+	0.553399i
$81$	−1.00000	+	8.94427i	−0.111111	+	0.993808i
$82$	9.48683	+	12.2474i	1.04765	+	1.35250i
$83$			7.07107i			0.776151i	0.921628	+	0.388075i	$0.126860\pi$
$83$			7.07107i			0.776151i	−0.921628	+	0.388075i	$0.873140\pi$
$84$	4.47410	+	7.99890i	0.488164	+	0.872752i
$85$		0			0
$86$	−8.66025	+	6.70820i	−0.933859	+	0.723364i
$87$	10.9545	+	4.89898i	1.17444	+	0.525226i
$88$	9.00000	−	3.87298i	0.959403	−	0.412861i
$89$		0			0			−	1.00000i	$-0.5\pi$
$89$		0			0				1.00000i	$0.5\pi$
$90$	5.90089	+	1.08604i	0.622008	+	0.114479i
$91$	−3.16228	+	7.74597i	−0.331497	+	0.811998i
$92$	8.66025	+	2.23607i	0.902894	+	0.233126i
$93$	−3.46410	+	7.74597i	−0.359211	+	0.803219i
$94$	−9.48683	−	12.2474i	−0.978492	−	1.26323i
$95$			4.47214i			0.458831i
$96$	2.58354	−	9.45121i	0.263682	−	0.964610i
$97$		−	4.89898i		−	0.497416i	−0.968579	−	0.248708i	$-0.919994\pi$
$97$		−	4.89898i		−	0.497416i	0.968579	−	0.248708i	$-0.0800060\pi$
$98$	1.14710	−	9.83281i	0.115874	−	0.993264i
$99$	−6.92820	−	7.74597i	−0.696311	−	0.778499i
$100$	−1.50000	+	5.80948i	−0.150000	+	0.580948i
$101$			15.5563i			1.54791i	0.633238	+	0.773957i	$0.281726\pi$
$101$			15.5563i			1.54791i	−0.633238	+	0.773957i	$0.718274\pi$
$102$		0			0
$103$		−	9.79796i		−	0.965422i	−0.875780	−	0.482711i	$-0.839652\pi$
$103$		−	9.79796i		−	0.965422i	0.875780	−	0.482711i	$-0.160348\pi$
$104$	8.21584	−	3.53553i	0.805629	−	0.346688i
$105$	−4.47723	−	4.68556i	−0.436932	−	0.457264i
$106$		0			0
$107$	10.3923			1.00466			0.502331	−	0.864675i	$-0.332476\pi$
$107$	10.3923			1.00466			0.502331	+	0.864675i	$0.332476\pi$
$108$	−10.3757	+	0.586988i	−0.998404	+	0.0564830i
$109$		0			0		1.00000			$0$
$109$		0			0		−1.00000			$\pi$
$110$	−5.47723	+	4.24264i	−0.522233	+	0.404520i
$111$		0			0
$112$	−8.24342	+	6.63672i	−0.778930	+	0.627111i
$113$		−	4.47214i		−	0.420703i	−0.977626	−	0.210352i	$-0.932539\pi$
$113$		−	4.47214i		−	0.420703i	0.977626	−	0.210352i	$-0.0674609\pi$
$114$	−1.83013	−	7.52666i	−0.171407	−	0.704936i
$115$	−6.32456			−0.589768
$116$	−3.46410	+	13.4164i	−0.321634	+	1.24568i
$117$	−6.32456	−	7.07107i	−0.584705	−	0.653720i
$118$	11.0680	−	8.57321i	1.01889	−	0.789228i
$119$		0			0
$120$	−0.0980762	+	6.92751i	−0.00895309	+	0.632392i
$121$	1.00000			0.0909091
$122$	−2.73861	−	3.53553i	−0.247942	−	0.320092i
$123$	17.3205	+	7.74597i	1.56174	+	0.698430i
$124$	−9.48683	−	2.44949i	−0.851943	−	0.219971i
$125$		−	11.3137i		−	1.01193i
$126$	9.45269	+	6.05364i	0.842113	+	0.539301i
$127$	8.00000			0.709885			0.354943	−	0.934888i	$-0.384500\pi$
$127$	8.00000			0.709885			0.354943	+	0.934888i	$0.384500\pi$
$128$	11.2583	+	1.11803i	0.995105	+	0.0988212i
$129$	−5.47723	+	12.2474i	−0.482243	+	1.07833i
$130$	−5.00000	+	3.87298i	−0.438529	+	0.339683i
$131$		−	1.41421i		−	0.123560i	−0.998090	−	0.0617802i	$-0.980322\pi$
$131$		−	1.41421i		−	0.123560i	0.998090	−	0.0617802i	$-0.0196778\pi$
$132$	7.48203	−	9.38186i	0.651227	−	0.816586i
$133$	−3.16228	+	7.74597i	−0.274204	+	0.671660i
$134$	8.66025	−	6.70820i	0.748132	−	0.579501i
$135$	7.00000	−	2.23607i	0.602464	−	0.192450i
$136$		0			0
$137$		−	17.8885i		−	1.52832i	−0.645026	−	0.764161i	$-0.723153\pi$
$137$		−	17.8885i		−	1.52832i	0.645026	−	0.764161i	$-0.276847\pi$
$138$	10.6443	−	2.58819i	0.906104	−	0.220321i
$139$	15.8114			1.34110			0.670552	−	0.741862i	$-0.266057\pi$
$139$	15.8114			1.34110			0.670552	+	0.741862i	$0.266057\pi$
$140$	4.47066	−	6.00110i	0.377840	−	0.507185i
$141$	−17.3205	−	7.74597i	−1.45865	−	0.652328i
$142$	−10.0000	+	7.74597i	−0.839181	+	0.650027i
$143$	10.9545			0.916057
$144$	−2.66987	−	11.6992i	−0.222489	−	0.974935i
$145$		−	9.79796i		−	0.813676i
$146$	−16.4317	+	12.7279i	−1.35990	+	1.05337i
$147$	−4.44159	−	11.2815i	−0.366336	−	0.930482i
$148$		0			0
$149$	−6.92820			−0.567581			−0.283790	−	0.958886i	$-0.591592\pi$
$149$	−6.92820			−0.567581			−0.283790	+	0.958886i	$0.591592\pi$
$150$	1.73621	+	7.14042i	0.141761	+	0.583013i
$151$	8.00000			0.651031			0.325515	−	0.945537i	$-0.394462\pi$
$151$	8.00000			0.651031			0.325515	+	0.945537i	$0.394462\pi$
$152$	8.21584	−	3.53553i	0.666392	−	0.286770i
$153$		0			0
$154$	−12.4868	+	3.47549i	−1.00622	+	0.280063i
$155$	6.92820			0.556487
$156$	6.83013	−	8.56442i	0.546848	−	0.685703i
$157$	15.8114			1.26189			0.630943	−	0.775829i	$-0.282668\pi$
$157$	15.8114			1.26189			0.630943	+	0.775829i	$0.282668\pi$
$158$	−8.66025	−	11.1803i	−0.688973	−	0.889460i
$159$		0			0
$160$	−7.90569	+	1.22474i	−0.625000	+	0.0968246i
$161$	−10.9545	−	4.47214i	−0.863332	−	0.352454i
$162$	−10.8660	+	6.62793i	−0.853716	+	0.520740i
$163$		−	23.2379i		−	1.82013i	−0.414462	−	0.910066i	$-0.636030\pi$
$163$		−	23.2379i		−	1.82013i	0.414462	−	0.910066i	$-0.363970\pi$
$164$	−5.47723	+	21.2132i	−0.427699	+	1.65647i
$165$	−3.46410	+	7.74597i	−0.269680	+	0.603023i
$166$	−7.90569	+	6.12372i	−0.613601	+	0.475293i
$167$	−21.9089			−1.69536			−0.847681	−	0.530506i	$-0.822002\pi$
$167$	−21.9089			−1.69536			−0.847681	+	0.530506i	$0.822002\pi$
$168$	−5.06836	+	11.9294i	−0.391033	+	0.920377i
$169$	−3.00000			−0.230769
$170$		0			0
$171$	−6.32456	−	7.07107i	−0.483651	−	0.540738i
$172$	−15.0000	−	3.87298i	−1.14374	−	0.295312i
$173$			7.07107i			0.537603i	0.963196	+	0.268802i	$0.0866276\pi$
$173$			7.07107i			0.537603i	−0.963196	+	0.268802i	$0.913372\pi$
$174$	4.00961	+	16.4901i	0.303968	+	1.25011i
$175$	3.00000	−	7.34847i	0.226779	−	0.555492i
$176$	12.1244	+	6.70820i	0.913908	+	0.505650i
$177$	7.00000	−	15.6525i	0.526152	−	1.17651i
$178$		0			0
$179$	−10.3923			−0.776757			−0.388379	−	0.921500i	$-0.626965\pi$
$179$	−10.3923			−0.776757			−0.388379	+	0.921500i	$0.626965\pi$
$180$	3.89609	+	7.53794i	0.290397	+	0.561845i
$181$	−3.16228			−0.235050			−0.117525	−	0.993070i	$-0.537496\pi$
$181$	−3.16228			−0.235050			−0.117525	+	0.993070i	$0.537496\pi$
$182$	−11.3989	+	3.17267i	−0.844940	+	0.235174i
$183$	−5.00000	−	2.23607i	−0.369611	−	0.165295i
$184$	5.00000	+	11.6190i	0.368605	+	0.856560i
$185$		0			0
$186$	−11.6603	+	2.83522i	−0.854971	+	0.207888i
$187$		0			0
$188$	5.47723	−	21.2132i	0.399468	−	1.54713i
$189$	13.7055	+	1.07676i	0.996928	+	0.0783231i
$190$	−5.00000	+	3.87298i	−0.362738	+	0.280976i
$191$			8.94427i			0.647185i	0.946197	+	0.323592i	$0.104891\pi$
$191$			8.94427i			0.647185i	−0.946197	+	0.323592i	$0.895109\pi$
$192$	12.8042	−	5.29650i	0.924062	−	0.382242i
$193$	−4.00000			−0.287926			−0.143963	−	0.989583i	$-0.545985\pi$
$193$	−4.00000			−0.287926			−0.143963	+	0.989583i	$0.545985\pi$
$194$	5.47723	−	4.24264i	0.393242	−	0.304604i
$195$	−3.16228	+	7.07107i	−0.226455	+	0.506370i
$196$	11.9868	−	7.23297i	0.856202	−	0.516641i
$197$		0			0			−	1.00000i	$-0.5\pi$
$197$		0			0				1.00000i	$0.5\pi$
$198$	2.66025	−	14.4542i	0.189056	−	1.02721i
$199$		0			0		1.00000			$0$
$199$		0			0		−1.00000			$\pi$
$200$	−7.79423	+	3.35410i	−0.551135	+	0.237171i
$201$	5.47723	−	12.2474i	0.386334	−	0.863868i
$202$	−17.3925	+	13.4722i	−1.22373	+	0.947900i
$203$	6.92820	−	16.9706i	0.486265	−	1.19110i
$204$		0			0
$205$		−	15.4919i		−	1.08200i
$206$	10.9545	−	8.48528i	0.763233	−	0.591198i
$207$	10.0000	−	8.94427i	0.695048	−	0.621670i
$208$	11.0680	+	6.12372i	0.767426	+	0.424604i
$209$	10.9545			0.757735
$210$	1.36122	−	9.06350i	0.0939332	−	0.625441i
$211$		−	7.74597i		−	0.533254i	−0.963800	−	0.266627i	$-0.914091\pi$
$211$		−	7.74597i		−	0.533254i	0.963800	−	0.266627i	$-0.0859092\pi$
$212$		0			0
$213$	−6.32456	+	14.1421i	−0.433351	+	0.969003i
$214$	9.00000	+	11.6190i	0.615227	+	0.794255i
$215$	10.9545			0.747087
$216$	−9.64191	−	11.0921i	−0.656049	−	0.754719i
$217$	12.0000	+	4.89898i	0.814613	+	0.332564i
$218$		0			0
$219$	−10.3923	+	23.2379i	−0.702247	+	1.57027i
$220$	−9.48683	−	2.44949i	−0.639602	−	0.165145i
$221$		0			0
$222$		0			0
$223$			9.79796i			0.656120i	0.944657	+	0.328060i	$0.106395\pi$
$223$			9.79796i			0.656120i	−0.944657	+	0.328060i	$0.893605\pi$
$224$	−14.5591	−	3.46885i	−0.972770	−	0.231772i
$225$	6.00000	+	6.70820i	0.400000	+	0.447214i
$226$	5.00000	−	3.87298i	0.332595	−	0.257627i
$227$		−	9.89949i		−	0.657053i	−0.944495	−	0.328526i	$-0.893448\pi$
$227$		−	9.89949i		−	0.657053i	0.944495	−	0.328526i	$-0.106552\pi$
$228$	6.83013	−	8.56442i	0.452336	−	0.567193i
$229$	15.8114			1.04485			0.522423	−	0.852686i	$-0.325028\pi$
$229$	15.8114			1.04485			0.522423	+	0.852686i	$0.325028\pi$
$230$	−5.47723	−	7.07107i	−0.361158	−	0.466252i
$231$	−11.4772	+	10.9669i	−0.755146	+	0.721570i
$232$	−18.0000	+	7.74597i	−1.18176	+	0.508548i
$233$			8.94427i			0.585959i	0.956119	+	0.292979i	$0.0946467\pi$
$233$			8.94427i			0.585959i	−0.956119	+	0.292979i	$0.905353\pi$
$234$	2.42847	−	13.1948i	0.158754	−	0.862571i
$235$			15.4919i			1.01058i
$236$	19.1703	+	4.94975i	1.24788	+	0.322201i
$237$	−15.8114	−	7.07107i	−1.02706	−	0.459315i
$238$		0			0
$239$		−	4.47214i		−	0.289278i	−0.989484	−	0.144639i	$-0.953798\pi$
$239$		−	4.47214i		−	0.289278i	0.989484	−	0.144639i	$-0.0462022\pi$
$240$	−7.83013	+	5.88975i	−0.505433	+	0.380181i
$241$		−	4.89898i		−	0.315571i	−0.987473	−	0.157786i	$-0.949565\pi$
$241$		−	4.89898i		−	0.315571i	0.987473	−	0.157786i	$-0.0504355\pi$
$242$	0.866025	+	1.11803i	0.0556702	+	0.0718699i
$243$	−7.90569	+	13.4350i	−0.507151	+	0.861858i
$244$	1.58114	−	6.12372i	0.101222	−	0.392031i
$245$	−6.92820	+	7.07107i	−0.442627	+	0.451754i
$246$	6.33975	+	26.0731i	0.404207	+	1.66236i
$247$	10.0000			0.636285
$248$	−5.47723	−	12.7279i	−0.347804	−	0.808224i
$249$	−5.00000	+	11.1803i	−0.316862	+	0.708525i
$250$	12.6491	−	9.79796i	0.800000	−	0.619677i
$251$			15.5563i			0.981908i	0.871185	+	0.490954i	$0.163352\pi$
$251$			15.5563i			0.981908i	−0.871185	+	0.490954i	$0.836648\pi$
$252$	1.41809	+	15.8110i	0.0893315	+	0.996002i
$253$			15.4919i			0.973970i
$254$	6.92820	+	8.94427i	0.434714	+	0.561214i
$255$		0			0
$256$	8.50000	+	13.5554i	0.531250	+	0.847215i
$257$	10.9545			0.683320			0.341660	−	0.939824i	$-0.389011\pi$
$257$	10.9545			0.683320			0.341660	+	0.939824i	$0.389011\pi$
$258$	−18.4365	+	4.48288i	−1.14781	+	0.279092i
$259$		0			0
$260$	−8.66025	−	2.23607i	−0.537086	−	0.138675i
$261$	13.8564	+	15.4919i	0.857690	+	0.958927i
$262$	1.58114	−	1.22474i	0.0976831	−	0.0756650i
$263$			8.94427i			0.551527i	0.961225	+	0.275764i	$0.0889307\pi$
$263$			8.94427i			0.551527i	−0.961225	+	0.275764i	$0.911069\pi$
$264$	16.9689	+	0.240237i	1.04436	+	0.0147855i
$265$		0			0
$266$	−11.3989	+	3.17267i	−0.698909	+	0.194529i
$267$		0			0
$268$	15.0000	+	3.87298i	0.916271	+	0.236580i
$269$		−	9.89949i		−	0.603583i	−0.953374	−	0.301791i	$-0.902415\pi$
$269$		−	9.89949i		−	0.603583i	0.953374	−	0.301791i	$-0.0975846\pi$
$270$	8.56218	+	5.88975i	0.521078	+	0.358439i
$271$		0			0		1.00000			$0$
$271$		0			0		−1.00000			$\pi$
$272$		0			0
$273$	−10.4772	+	10.0114i	−0.634111	+	0.605916i
$274$	20.0000	−	15.4919i	1.20824	−	0.935902i
$275$	−10.3923			−0.626680
$276$	12.1119	+	9.65926i	0.729052	+	0.581419i
$277$		−	15.4919i		−	0.930820i	−0.885095	−	0.465410i	$-0.845907\pi$
$277$		−	15.4919i		−	0.930820i	0.885095	−	0.465410i	$-0.154093\pi$
$278$	13.6931	+	17.6777i	0.821255	+	1.06024i
$279$	−10.9545	+	9.79796i	−0.655826	+	0.586588i
$280$	10.5811	−	0.198749i	0.632344	−	0.0118775i
$281$			8.94427i			0.533571i	0.963756	+	0.266785i	$0.0859614\pi$
$281$			8.94427i			0.533571i	−0.963756	+	0.266785i	$0.914039\pi$
$282$	−6.33975	−	26.0731i	−0.377526	−	1.55263i
$283$	15.8114			0.939889			0.469945	−	0.882696i	$-0.344274\pi$
$283$	15.8114			0.939889			0.469945	+	0.882696i	$0.344274\pi$
$284$	−17.3205	−	4.47214i	−1.02778	−	0.265372i
$285$	−3.16228	+	7.07107i	−0.187317	+	0.418854i
$286$	9.48683	+	12.2474i	0.560968	+	0.724207i
$287$	10.9545	−	26.8328i	0.646621	−	1.58389i
$288$	10.7679	−	13.1168i	0.634507	−	0.772917i
$289$	−17.0000			−1.00000
$290$	10.9545	−	8.48528i	0.643268	−	0.498273i
$291$	3.46410	−	7.74597i	0.203069	−	0.454077i
$292$	−28.4605	−	7.34847i	−1.66552	−	0.430037i
$293$		−	26.8701i		−	1.56977i	−0.619644	−	0.784883i	$-0.712723\pi$
$293$		−	26.8701i		−	1.56977i	0.619644	−	0.784883i	$-0.287277\pi$
$294$	8.76657	−	14.7359i	0.511277	−	0.859416i
$295$	−14.0000			−0.815112
$296$		0			0
$297$	−5.47723	−	17.1464i	−0.317821	−	0.994937i
$298$	−6.00000	−	7.74597i	−0.347571	−	0.448712i
$299$			14.1421i			0.817861i
$300$	−6.47963	+	8.12493i	−0.374101	+	0.469093i
$301$	18.9737	+	7.74597i	1.09362	+	0.446470i
$302$	6.92820	+	8.94427i	0.398673	+	0.514685i
$303$	−11.0000	+	24.5967i	−0.631933	+	1.41305i
$304$	11.0680	+	6.12372i	0.634792	+	0.351220i
$305$			4.47214i			0.256074i
$306$		0			0
$307$	−3.16228			−0.180481			−0.0902404	−	0.995920i	$-0.528764\pi$
$307$	−3.16228			−0.180481			−0.0902404	+	0.995920i	$0.528764\pi$
$308$	−14.6996	−	10.9508i	−0.837589	−	0.623982i
$309$	6.92820	−	15.4919i	0.394132	−	0.881305i
$310$	6.00000	+	7.74597i	0.340777	+	0.439941i
$311$	10.9545			0.621170			0.310585	−	0.950546i	$-0.399475\pi$
$311$	10.9545			0.621170			0.310585	+	0.950546i	$0.399475\pi$
$312$	15.4904	+	0.219305i	0.876970	+	0.0124157i
$313$			9.79796i			0.553813i	0.960897	+	0.276907i	$0.0893093\pi$
$313$			9.79796i			0.553813i	−0.960897	+	0.276907i	$0.910691\pi$
$314$	13.6931	+	17.6777i	0.772744	+	0.997609i
$315$	−3.76593	−	10.5744i	−0.212186	−	0.595800i
$316$	5.00000	−	19.3649i	0.281272	−	1.08936i
$317$	6.92820			0.389127			0.194563	−	0.980890i	$-0.437671\pi$
$317$	6.92820			0.389127			0.194563	+	0.980890i	$0.437671\pi$
$318$		0			0
$319$	−24.0000			−1.34374
$320$	−8.21584	−	7.77817i	−0.459279	−	0.434813i
$321$	16.4317	+	7.34847i	0.917127	+	0.410152i
$322$	−4.48683	−	16.1204i	−0.250041	−	0.898357i
$323$		0			0
$324$	−16.8205	−	6.40863i	−0.934473	−	0.356035i
$325$	−9.48683			−0.526235
$326$	25.9808	−	20.1246i	1.43894	−	1.11460i
$327$		0			0
$328$	−28.4605	+	12.2474i	−1.57147	+	0.676252i
$329$	−10.9545	+	26.8328i	−0.603938	+	1.47934i
$330$	−11.6603	+	2.83522i	−0.641876	+	0.156074i
$331$			7.74597i			0.425757i	0.977079	+	0.212878i	$0.0682838\pi$
$331$			7.74597i			0.425757i	−0.977079	+	0.212878i	$0.931716\pi$
$332$	−13.6931	−	3.53553i	−0.751505	−	0.194038i
$333$		0			0
$334$	−18.9737	−	24.4949i	−1.03819	−	1.34030i
$335$	−10.9545			−0.598506
$336$	−17.7269	+	4.66460i	−0.967079	+	0.254475i
$337$	8.00000			0.435788			0.217894	−	0.975972i	$-0.430081\pi$
$337$	8.00000			0.435788			0.217894	+	0.975972i	$0.430081\pi$
$338$	−2.59808	−	3.35410i	−0.141317	−	0.182439i
$339$	3.16228	−	7.07107i	0.171751	−	0.384048i
$340$		0			0
$341$		−	16.9706i		−	0.919007i
$342$	2.42847	−	13.1948i	0.131317	−	0.713493i
$343$	−17.0000	+	7.34847i	−0.917914	+	0.396780i
$344$	−8.66025	−	20.1246i	−0.466930	−	1.08505i
$345$	−10.0000	−	4.47214i	−0.538382	−	0.240772i
$346$	−7.90569	+	6.12372i	−0.425013	+	0.329213i
$347$	−17.3205			−0.929814			−0.464907	−	0.885360i	$-0.653912\pi$
$347$	−17.3205			−0.929814			−0.464907	+	0.885360i	$0.653912\pi$
$348$	−14.9641	+	18.7637i	−0.802158	+	1.00584i
$349$	−22.1359			−1.18491			−0.592455	−	0.805604i	$-0.701841\pi$
$349$	−22.1359			−1.18491			−0.592455	+	0.805604i	$0.701841\pi$
$350$	10.8139	−	3.00986i	0.578028	−	0.160884i
$351$	−5.00000	−	15.6525i	−0.266880	−	0.835467i
$352$	3.00000	+	19.3649i	0.159901	+	1.03215i
$353$	−10.9545			−0.583047			−0.291523	−	0.956564i	$-0.594162\pi$
$353$	−10.9545			−0.583047			−0.291523	+	0.956564i	$0.594162\pi$
$354$	23.5622	−	5.72920i	1.25232	−	0.304504i
$355$	12.6491			0.671345
$356$		0			0
$357$		0			0
$358$	−9.00000	−	11.6190i	−0.475665	−	0.614081i
$359$		−	31.3050i		−	1.65221i	−0.563515	−	0.826106i	$-0.690551\pi$
$359$		−	31.3050i		−	1.65221i	0.563515	−	0.826106i	$-0.309449\pi$
$360$	−5.05356	+	10.8840i	−0.266346	+	0.573637i
$361$	−9.00000			−0.473684
$362$	−2.73861	−	3.53553i	−0.143938	−	0.185824i
$363$	1.58114	+	0.707107i	0.0829883	+	0.0371135i
$364$	−13.4189	−	9.99671i	−0.703339	−	0.523970i
$365$	20.7846			1.08792
$366$	−1.83013	−	7.52666i	−0.0956623	−	0.393425i
$367$		−	19.5959i		−	1.02290i	−0.859313	−	0.511449i	$-0.829109\pi$
$367$		−	19.5959i		−	1.02290i	0.859313	−	0.511449i	$-0.170891\pi$
$368$	−8.66025	+	15.6525i	−0.451447	+	0.815942i
$369$	21.9089	+	24.4949i	1.14053	+	1.27515i
$370$		0			0
$371$		0			0
$372$	−13.2679	−	10.5812i	−0.687911	−	0.548609i
$373$		−	30.9839i		−	1.60428i	−0.597133	−	0.802142i	$-0.703694\pi$
$373$		−	30.9839i		−	1.60428i	0.597133	−	0.802142i	$-0.296306\pi$
$374$		0			0
$375$	8.00000	−	17.8885i	0.413118	−	0.923760i
$376$	28.4605	−	12.2474i	1.46774	−	0.631614i
$377$	−21.9089			−1.12837
$378$	10.6654	+	16.2557i	0.548571	+	0.836104i
$379$			23.2379i			1.19365i	0.802371	+	0.596825i	$0.203571\pi$
$379$			23.2379i			1.19365i	−0.802371	+	0.596825i	$0.796429\pi$
$380$	−8.66025	−	2.23607i	−0.444262	−	0.114708i
$381$	12.6491	+	5.65685i	0.648034	+	0.289809i
$382$	−10.0000	+	7.74597i	−0.511645	+	0.396318i
$383$	10.9545			0.559746			0.279873	−	0.960037i	$-0.409708\pi$
$383$	10.9545			0.559746			0.279873	+	0.960037i	$0.409708\pi$
$384$	17.0104	+	9.72861i	0.868059	+	0.496461i
$385$	12.0000	+	4.89898i	0.611577	+	0.249675i
$386$	−3.46410	−	4.47214i	−0.176318	−	0.227626i
$387$	−17.3205	+	15.4919i	−0.880451	+	0.787499i
$388$	9.48683	+	2.44949i	0.481621	+	0.124354i
$389$	27.7128			1.40510			0.702548	−	0.711637i	$-0.252046\pi$
$389$	27.7128			1.40510			0.702548	+	0.711637i	$0.252046\pi$
$390$	−10.6443	+	2.58819i	−0.538995	+	0.131058i
$391$		0			0
$392$	18.4676	+	7.13775i	0.932755	+	0.360511i
$393$	1.00000	−	2.23607i	0.0504433	−	0.112795i
$394$		0			0
$395$			14.1421i			0.711568i
$396$	18.4641	−	9.54342i	0.927856	−	0.479575i
$397$	−22.1359			−1.11097			−0.555486	−	0.831526i	$-0.687468\pi$
$397$	−22.1359			−1.11097			−0.555486	+	0.831526i	$0.687468\pi$
$398$		0			0
$399$	−10.4772	+	10.0114i	−0.524517	+	0.501196i
$400$	−10.5000	−	5.80948i	−0.525000	−	0.290474i
$401$		−	4.47214i		−	0.223328i	−0.993746	−	0.111664i	$-0.964382\pi$
$401$		−	4.47214i		−	0.223328i	0.993746	−	0.111664i	$-0.0356180\pi$
$402$	18.4365	−	4.48288i	0.919528	−	0.223586i
$403$		−	15.4919i		−	0.771708i
$404$	−30.1247	−	7.77817i	−1.49876	−	0.386979i
$405$	12.6491	+	1.41421i	0.628539	+	0.0702728i
$406$	24.9737	−	6.95097i	1.23942	−	0.344971i
$407$		0			0
$408$		0			0
$409$		−	9.79796i		−	0.484478i	−0.970217	−	0.242239i	$-0.922118\pi$
$409$		−	9.79796i		−	0.484478i	0.970217	−	0.242239i	$-0.0778818\pi$
$410$	17.3205	−	13.4164i	0.855399	−	0.662589i
$411$	12.6491	−	28.2843i	0.623935	−	1.39516i
$412$	18.9737	+	4.89898i	0.934765	+	0.241355i
$413$	−24.2487	−	9.89949i	−1.19320	−	0.487122i
$414$	18.6603	+	3.43437i	0.917101	+	0.168790i
$415$	10.0000			0.490881
$416$	2.73861	+	17.6777i	0.134272	+	0.866719i
$417$	25.0000	+	11.1803i	1.22426	+	0.547504i
$418$	9.48683	+	12.2474i	0.464016	+	0.599042i
$419$			24.0416i			1.17451i	0.809402	+	0.587255i	$0.199792\pi$
$419$			24.0416i			1.17451i	−0.809402	+	0.587255i	$0.800208\pi$
$420$	11.3122	−	6.32733i	0.551977	−	0.308742i
$421$			30.9839i			1.51006i	0.655690	+	0.755031i	$0.272378\pi$
$421$			30.9839i			1.51006i	−0.655690	+	0.755031i	$0.727622\pi$
$422$	8.66025	−	6.70820i	0.421575	−	0.326550i
$423$	−21.9089	−	24.4949i	−1.06525	−	1.19098i
$424$		0			0
$425$		0			0
$426$	−21.2886	+	5.17638i	−1.03144	+	0.250796i
$427$	−3.16228	+	7.74597i	−0.153033	+	0.374854i
$428$	−5.19615	+	20.1246i	−0.251166	+	0.972760i
$429$	17.3205	+	7.74597i	0.836242	+	0.373979i
$430$	9.48683	+	12.2474i	0.457496	+	0.590624i
$431$			22.3607i			1.07708i	0.842601	+	0.538538i	$0.181023\pi$
$431$			22.3607i			1.07708i	−0.842601	+	0.538538i	$0.818977\pi$
$432$	4.05116	−	20.3860i	0.194911	−	0.980821i
$433$		−	14.6969i		−	0.706290i	−0.935569	−	0.353145i	$-0.885112\pi$
$433$		−	14.6969i		−	0.706290i	0.935569	−	0.353145i	$-0.114888\pi$
$434$	4.91508	+	17.6590i	0.235931	+	0.847661i
$435$	6.92820	−	15.4919i	0.332182	−	0.742781i
$436$		0			0
$437$			14.1421i			0.676510i
$438$	−34.9808	+	8.50566i	−1.67145	+	0.406416i
$439$			24.4949i			1.16908i	0.811366	+	0.584539i	$0.198725\pi$
$439$			24.4949i			1.16908i	−0.811366	+	0.584539i	$0.801275\pi$
$440$	−5.47723	−	12.7279i	−0.261116	−	0.606780i
$441$	0.954451	−	20.9783i	0.0454501	−	0.998967i
$442$		0			0
$443$	17.3205			0.822922			0.411461	−	0.911427i	$-0.365019\pi$
$443$	17.3205			0.822922			0.411461	+	0.911427i	$0.365019\pi$
$444$		0			0
$445$		0			0
$446$	−10.9545	+	8.48528i	−0.518708	+	0.401790i
$447$	−10.9545	−	4.89898i	−0.518128	−	0.231714i
$448$	−8.73025	−	19.2817i	−0.412466	−	0.910973i
$449$			8.94427i			0.422106i	0.977475	+	0.211053i	$0.0676893\pi$
$449$			8.94427i			0.422106i	−0.977475	+	0.211053i	$0.932311\pi$
$450$	−2.30385	+	12.5177i	−0.108604	+	0.590089i
$451$	−37.9473			−1.78687
$452$	8.66025	+	2.23607i	0.407344	+	0.105176i
$453$	12.6491	+	5.65685i	0.594307	+	0.265782i
$454$	11.0680	−	8.57321i	0.519446	−	0.402361i
$455$	10.9545	+	4.47214i	0.513553	+	0.209657i
$456$	15.4904	+	0.219305i	0.725404	+	0.0102699i
$457$	8.00000			0.374224			0.187112	−	0.982339i	$-0.440087\pi$
$457$	8.00000			0.374224			0.187112	+	0.982339i	$0.440087\pi$
$458$	13.6931	+	17.6777i	0.639835	+	0.826023i
$459$		0			0
$460$	3.16228	−	12.2474i	0.147442	−	0.571040i
$461$			15.5563i			0.724531i	0.932075	+	0.362266i	$0.117997\pi$
$461$			15.5563i			0.724531i	−0.932075	+	0.362266i	$0.882003\pi$
$462$	−22.2010	−	3.33430i	−1.03288	−	0.155126i
$463$	14.0000			0.650635			0.325318	−	0.945605i	$-0.394529\pi$
$463$	14.0000			0.650635			0.325318	+	0.945605i	$0.394529\pi$
$464$	−24.2487	−	13.4164i	−1.12572	−	0.622841i
$465$	10.9545	+	4.89898i	0.508001	+	0.227185i
$466$	−10.0000	+	7.74597i	−0.463241	+	0.358825i
$467$			7.07107i			0.327210i	0.986526	+	0.163605i	$0.0523123\pi$
$467$			7.07107i			0.327210i	−0.986526	+	0.163605i	$0.947688\pi$
$468$	16.8553	−	8.71191i	0.779138	−	0.402708i
$469$	−18.9737	−	7.74597i	−0.876122	−	0.357676i
$470$	−17.3205	+	13.4164i	−0.798935	+	0.618853i
$471$	25.0000	+	11.1803i	1.15194	+	0.515163i
$472$	11.0680	+	25.7196i	0.509445	+	1.18384i
$473$		−	26.8328i		−	1.23377i
$474$	−5.78737	−	23.8014i	−0.265823	−	1.09323i
$475$	−9.48683			−0.435286
$476$		0			0
$477$		0			0
$478$	5.00000	−	3.87298i	0.228695	−	0.177146i
$479$	−10.9545			−0.500522			−0.250261	−	0.968178i	$-0.580516\pi$
$479$	−10.9545			−0.500522			−0.250261	+	0.968178i	$0.580516\pi$
$480$	−13.3660	−	3.65368i	−0.610073	−	0.166767i
$481$		0			0
$482$	5.47723	−	4.24264i	0.249481	−	0.193247i
$483$	−14.1582	−	14.8170i	−0.644222	−	0.674198i
$484$	−0.500000	+	1.93649i	−0.0227273	+	0.0880223i
$485$	−6.92820			−0.314594
$486$	−21.8674	+	2.79624i	−0.991923	+	0.126840i
$487$	8.00000			0.362515			0.181257	−	0.983436i	$-0.441983\pi$
$487$	8.00000			0.362515			0.181257	+	0.983436i	$0.441983\pi$
$488$	8.21584	−	3.53553i	0.371914	−	0.160046i
$489$	16.4317	−	36.7423i	0.743066	−	1.66155i
$490$	−13.9057	−	1.62224i	−0.628195	−	0.0732854i
$491$	3.46410			0.156333			0.0781664	−	0.996940i	$-0.475093\pi$
$491$	3.46410			0.156333			0.0781664	+	0.996940i	$0.475093\pi$
$492$	−23.6603	+	29.6680i	−1.06669	+	1.33754i
$493$		0			0
$494$	8.66025	+	11.1803i	0.389643	+	0.503027i
$495$	−10.9545	+	9.79796i	−0.492366	+	0.440386i
$496$	9.48683	−	17.1464i	0.425971	−	0.769897i
$497$	21.9089	+	8.94427i	0.982749	+	0.401205i
$498$	−16.8301	+	4.09229i	−0.754176	+	0.183380i
$499$		−	7.74597i		−	0.346757i	−0.984855	−	0.173379i	$-0.944532\pi$
$499$		−	7.74597i		−	0.346757i	0.984855	−	0.173379i	$-0.0554684\pi$
$500$	21.9089	+	5.65685i	0.979796	+	0.252982i
$501$	−34.6410	−	15.4919i	−1.54765	−	0.692129i
$502$	−17.3925	+	13.4722i	−0.776266	+	0.601293i
$503$	32.8634			1.46530			0.732652	−	0.680603i	$-0.238282\pi$
$503$	32.8634			1.46530			0.732652	+	0.680603i	$0.238282\pi$
$504$	−16.4492	+	15.2782i	−0.732705	+	0.680547i
$505$	22.0000			0.978987
$506$	−17.3205	+	13.4164i	−0.769991	+	0.596432i
$507$	−4.74342	−	2.12132i	−0.210663	−	0.0942111i
$508$	−4.00000	+	15.4919i	−0.177471	+	0.687343i
$509$		−	9.89949i		−	0.438787i	−0.975636	−	0.219394i	$-0.929592\pi$
$509$		−	9.89949i		−	0.438787i	0.975636	−	0.219394i	$-0.0704079\pi$
$510$		0			0
$511$	36.0000	+	14.6969i	1.59255	+	0.650154i
$512$	−7.79423	+	21.2426i	−0.344459	+	0.938801i
$513$	−5.00000	−	15.6525i	−0.220755	−	0.691074i
$514$	9.48683	+	12.2474i	0.418446	+	0.540212i
$515$	−13.8564			−0.610586
$516$	−20.9785	−	16.7303i	−0.923526	−	0.736512i
$517$	37.9473			1.66892
$518$		0			0
$519$	−5.00000	+	11.1803i	−0.219476	+	0.490762i
$520$	−5.00000	−	11.6190i	−0.219265	−	0.509525i
$521$	−32.8634			−1.43977			−0.719885	−	0.694094i	$-0.755805\pi$
$521$	−32.8634			−1.43977			−0.719885	+	0.694094i	$0.755805\pi$
$522$	−5.32051	+	28.9083i	−0.232872	+	1.26528i
$523$	−3.16228			−0.138277			−0.0691384	−	0.997607i	$-0.522025\pi$
$523$	−3.16228			−0.138277			−0.0691384	+	0.997607i	$0.522025\pi$
$524$	2.73861	+	0.707107i	0.119637	+	0.0308901i
$525$	9.93957	−	9.49763i	0.433798	−	0.414511i
$526$	−10.0000	+	7.74597i	−0.436021	+	0.337740i
$527$		0			0
$528$	14.4269	+	19.1798i	0.627849	+	0.834694i
$529$	3.00000			0.130435
$530$		0			0
$531$	22.1359	−	19.7990i	0.960618	−	0.859203i
$532$	−13.4189	−	9.99671i	−0.581781	−	0.433412i
$533$	−34.6410			−1.50047
$534$		0			0
$535$		−	14.6969i		−	0.635404i
$536$	8.66025	+	20.1246i	0.374066	+	0.869251i
$537$	−16.4317	−	7.34847i	−0.709079	−	0.317110i
$538$	11.0680	−	8.57321i	0.477174	−	0.369618i
$539$	17.3205	+	16.9706i	0.746047	+	0.730974i
$540$	0.830127	+	14.6735i	0.0357230	+	0.631446i
$541$		0			0		1.00000			$0$
$541$		0			0		−1.00000			$\pi$
$542$		0			0
$543$	−5.00000	−	2.23607i	−0.214571	−	0.0959589i
$544$		0			0
$545$		0			0
$546$	−20.2666	−	3.04378i	−0.867331	−	0.130262i
$547$			7.74597i			0.331194i	0.986194	+	0.165597i	$0.0529550\pi$
$547$			7.74597i			0.331194i	−0.986194	+	0.165597i	$0.947045\pi$
$548$	34.6410	+	8.94427i	1.47979	+	0.382080i
$549$	−6.32456	−	7.07107i	−0.269925	−	0.301786i
$550$	−9.00000	−	11.6190i	−0.383761	−	0.495434i
$551$	−21.9089			−0.933351
$552$	−0.310144	+	21.9067i	−0.0132006	+	0.932411i
$553$	−10.0000	+	24.4949i	−0.425243	+	1.04163i
$554$	17.3205	−	13.4164i	0.735878	−	0.570009i
$555$		0			0
$556$	−7.90569	+	30.6186i	−0.335276	+	1.29852i
$557$		0			0			−	1.00000i	$-0.5\pi$
$557$		0			0				1.00000i	$0.5\pi$
$558$	−20.4413	−	3.76217i	−0.865349	−	0.159265i
$559$		−	24.4949i		−	1.03602i
$560$	9.38574	+	11.6580i	0.396620	+	0.492638i
$561$		0			0
$562$	−10.0000	+	7.74597i	−0.421825	+	0.326744i
$563$		−	1.41421i		−	0.0596020i	−0.999556	−	0.0298010i	$-0.990513\pi$
$563$		−	1.41421i		−	0.0596020i	0.999556	−	0.0298010i	$-0.00948736\pi$
$564$	23.6603	−	29.6680i	0.996276	−	1.24925i
$565$	−6.32456			−0.266076
$566$	13.6931	+	17.6777i	0.575562	+	0.743048i
$567$	20.9089	+	11.3938i	0.878091	+	0.478493i
$568$	−10.0000	−	23.2379i	−0.419591	−	0.975041i
$569$			22.3607i			0.937408i	0.883355	+	0.468704i	$0.155279\pi$
$569$			22.3607i			0.937408i	−0.883355	+	0.468704i	$0.844721\pi$
$570$	−10.6443	+	2.58819i	−0.445841	+	0.108407i
$571$		−	7.74597i		−	0.324159i	−0.986778	−	0.162079i	$-0.948180\pi$
$571$		−	7.74597i		−	0.324159i	0.986778	−	0.162079i	$-0.0518200\pi$
$572$	−5.47723	+	21.2132i	−0.229014	+	0.886969i
$573$	−6.32456	+	14.1421i	−0.264212	+	0.590796i
$574$	39.4868	−	10.9905i	1.64815	−	0.458733i
$575$		−	13.4164i		−	0.559503i
$576$	23.9904	+	0.679424i	0.999599	+	0.0283093i
$577$		−	29.3939i		−	1.22368i	−0.790980	−	0.611842i	$-0.790429\pi$
$577$		−	29.3939i		−	1.22368i	0.790980	−	0.611842i	$-0.209571\pi$
$578$	−14.7224	−	19.0066i	−0.612372	−	0.790569i
$579$	−6.32456	−	2.82843i	−0.262840	−	0.117545i
$580$	18.9737	+	4.89898i	0.787839	+	0.203419i
$581$	17.3205	+	7.07107i	0.718576	+	0.293357i
$582$	11.6603	−	2.83522i	0.483333	−	0.117524i
$583$		0			0
$584$	−16.4317	−	38.1838i	−0.679948	−	1.58006i
$585$	−10.0000	+	8.94427i	−0.413449	+	0.369800i
$586$	30.0416	−	23.2702i	1.24101	−	0.961281i
$587$		−	35.3553i		−	1.45927i	−0.683836	−	0.729636i	$-0.739690\pi$
$587$		−	35.3553i		−	1.45927i	0.683836	−	0.729636i	$-0.260310\pi$
$588$	24.0673	−	2.96036i	0.992520	−	0.122083i
$589$		−	15.4919i		−	0.638334i
$590$	−12.1244	−	15.6525i	−0.499152	−	0.644402i
$591$		0			0
$592$		0			0
$593$	−32.8634			−1.34954			−0.674768	−	0.738030i	$-0.735756\pi$
$593$	−32.8634			−1.34954			−0.674768	+	0.738030i	$0.735756\pi$
$594$	14.4269	−	20.9730i	0.591942	−	0.860531i
$595$		0			0
$596$	3.46410	−	13.4164i	0.141895	−	0.549557i
$597$		0			0
$598$	−15.8114	+	12.2474i	−0.646576	+	0.500835i
$599$			8.94427i			0.365453i	0.983164	+	0.182727i	$0.0584923\pi$
$599$			8.94427i			0.365453i	−0.983164	+	0.182727i	$0.941508\pi$
$600$	−14.6955	−	0.208051i	−0.599940	−	0.00849365i
$601$			24.4949i			0.999168i	0.866266	+	0.499584i	$0.166514\pi$
$601$			24.4949i			0.999168i	−0.866266	+	0.499584i	$0.833486\pi$
$602$	7.77142	+	27.9214i	0.316740	+	1.13799i
$603$	17.3205	−	15.4919i	0.705346	−	0.630880i
$604$	−4.00000	+	15.4919i	−0.162758	+	0.630358i
$605$		−	1.41421i		−	0.0574960i
$606$	−37.0263	+	9.00303i	−1.50409	+	0.365723i
$607$			19.5959i			0.795374i	0.917521	+	0.397687i	$0.130187\pi$
$607$			19.5959i			0.795374i	−0.917521	+	0.397687i	$0.869813\pi$
$608$	2.73861	+	17.6777i	0.111065	+	0.716924i
$609$	22.9545	−	21.9338i	0.930161	−	0.888804i
$610$	−5.00000	+	3.87298i	−0.202444	+	0.156813i
$611$	34.6410			1.40143
$612$		0			0
$613$			46.4758i			1.87714i	0.345089	+	0.938570i	$0.387849\pi$
$613$			46.4758i			1.87714i	−0.345089	+	0.938570i	$0.612151\pi$
$614$	−2.73861	−	3.53553i	−0.110521	−	0.142683i
$615$	10.9545	−	24.4949i	0.441726	−	0.987730i
$616$	−0.486833	−	25.9184i	−0.0196151	−	1.04428i
$617$		−	31.3050i		−	1.26029i	−0.776478	−	0.630145i	$-0.782995\pi$
$617$		−	31.3050i		−	1.26029i	0.776478	−	0.630145i	$-0.217005\pi$
$618$	23.3205	−	5.67044i	0.938088	−	0.228099i
$619$	−3.16228			−0.127103			−0.0635513	−	0.997979i	$-0.520243\pi$
$619$	−3.16228			−0.127103			−0.0635513	+	0.997979i	$0.520243\pi$
$620$	−3.46410	+	13.4164i	−0.139122	+	0.538816i
$621$	22.1359	−	7.07107i	0.888285	−	0.283752i
$622$	9.48683	+	12.2474i	0.380387	+	0.491078i
$623$		0			0
$624$	13.1699	+	17.5087i	0.527217	+	0.700909i
$625$	−1.00000			−0.0400000
$626$	−10.9545	+	8.48528i	−0.437828	+	0.339140i
$627$	17.3205	+	7.74597i	0.691714	+	0.309344i
$628$	−7.90569	+	30.6186i	−0.315472	+	1.22182i
$629$		0			0
$630$	8.56114	−	13.3681i	0.341084	−	0.532599i
$631$	−10.0000			−0.398094			−0.199047	−	0.979990i	$-0.563785\pi$
$631$	−10.0000			−0.398094			−0.199047	+	0.979990i	$0.563785\pi$
$632$	25.9808	−	11.1803i	1.03346	−	0.444730i
$633$	5.47723	−	12.2474i	0.217700	−	0.486792i
$634$	6.00000	+	7.74597i	0.238290	+	0.307632i
$635$		−	11.3137i		−	0.448971i
$636$		0			0
$637$	15.8114	+	15.4919i	0.626470	+	0.613813i
$638$	−20.7846	−	26.8328i	−0.822871	−	1.06232i
$639$	−20.0000	+	17.8885i	−0.791188	+	0.707660i
$640$	1.58114	−	15.9217i	0.0625000	−	0.629360i
$641$		−	31.3050i		−	1.23647i	−0.785993	−	0.618236i	$-0.787848\pi$
$641$		−	31.3050i		−	1.23647i	0.785993	−	0.618236i	$-0.212152\pi$
$642$	6.01441	+	24.7351i	0.237370	+	0.976218i
$643$	−3.16228			−0.124708			−0.0623540	−	0.998054i	$-0.519861\pi$
$643$	−3.16228			−0.124708			−0.0623540	+	0.998054i	$0.519861\pi$
$644$	14.1375	−	18.9771i	0.557095	−	0.747804i
$645$	17.3205	+	7.74597i	0.681994	+	0.304997i
$646$		0			0
$647$		0			0			−	1.00000i	$-0.5\pi$
$647$		0			0				1.00000i	$0.5\pi$
$648$	−7.40192	−	24.3559i	−0.290775	−	0.956791i
$649$			34.2929i			1.34611i
$650$	−8.21584	−	10.6066i	−0.322252	−	0.416025i
$651$	15.5096	+	16.2312i	0.607868	+	0.636153i
$652$	45.0000	+	11.6190i	1.76234	+	0.455033i
$653$	−48.4974			−1.89785			−0.948925	−	0.315501i	$-0.897828\pi$
$653$	−48.4974			−1.89785			−0.948925	+	0.315501i	$0.897828\pi$
$654$		0			0
$655$	−2.00000			−0.0781465
$656$	−38.3406	−	21.2132i	−1.49695	−	0.828236i
$657$	−32.8634	+	29.3939i	−1.28212	+	1.14676i
$658$	−39.4868	+	10.9905i	−1.53936	+	0.428452i
$659$	−24.2487			−0.944596			−0.472298	−	0.881439i	$-0.656575\pi$
$659$	−24.2487			−0.944596			−0.472298	+	0.881439i	$0.656575\pi$
$660$	−13.2679	−	10.5812i	−0.516454	−	0.411872i
$661$	−41.1096			−1.59898			−0.799489	−	0.600680i	$-0.794896\pi$
$661$	−41.1096			−1.59898			−0.799489	+	0.600680i	$0.794896\pi$
$662$	−8.66025	+	6.70820i	−0.336590	+	0.260722i
$663$		0			0
$664$	−7.90569	−	18.3712i	−0.306800	−	0.712940i
$665$	10.9545	+	4.47214i	0.424795	+	0.173422i
$666$		0			0
$667$		−	30.9839i		−	1.19970i
$668$	10.9545	−	42.4264i	0.423840	−	1.64153i
$669$	−6.92820	+	15.4919i	−0.267860	+	0.598953i
$670$	−9.48683	−	12.2474i	−0.366508	−	0.473160i
$671$	10.9545			0.422892
$672$	−20.5671	−	15.7796i	−0.793393	−	0.608710i
$673$	−46.0000			−1.77317			−0.886585	−	0.462566i	$-0.846929\pi$
$673$	−46.0000			−1.77317			−0.886585	+	0.462566i	$0.846929\pi$
$674$	6.92820	+	8.94427i	0.266864	+	0.344520i
$675$	4.74342	+	14.8492i	0.182574	+	0.571548i
$676$	1.50000	−	5.80948i	0.0576923	−	0.223441i
$677$			7.07107i			0.271763i	0.990725	+	0.135882i	$0.0433867\pi$
$677$			7.07107i			0.271763i	−0.990725	+	0.135882i	$0.956613\pi$
$678$	10.6443	−	2.58819i	0.408792	−	0.0993989i
$679$	−12.0000	−	4.89898i	−0.460518	−	0.188006i
$680$		0			0
$681$	7.00000	−	15.6525i	0.268241	−	0.599804i
$682$	18.9737	−	14.6969i	0.726539	−	0.562775i
$683$	31.1769			1.19295			0.596476	−	0.802631i	$-0.296567\pi$
$683$	31.1769			1.19295			0.596476	+	0.802631i	$0.296567\pi$
$684$	16.8553	−	8.71191i	0.644480	−	0.333108i
$685$	−25.2982			−0.966595
$686$	−22.9383	−	12.6426i	−0.875787	−	0.482697i
$687$	25.0000	+	11.1803i	0.953809	+	0.426557i
$688$	15.0000	−	27.1109i	0.571870	−	1.03359i
$689$		0			0
$690$	−3.66025	−	15.0533i	−0.139343	−	0.573070i
$691$	−3.16228			−0.120299			−0.0601494	−	0.998189i	$-0.519158\pi$
$691$	−3.16228			−0.120299			−0.0601494	+	0.998189i	$0.519158\pi$
$692$	−13.6931	−	3.53553i	−0.520532	−	0.134401i
$693$	−25.9019	+	9.22460i	−0.983931	+	0.350413i
$694$	−15.0000	−	19.3649i	−0.569392	−	0.735082i
$695$		−	22.3607i		−	0.848189i
$696$	−33.9377	−	0.480473i	−1.28641	−	0.0182123i
$697$		0			0
$698$	−19.1703	−	24.7487i	−0.725606	−	0.936754i
$699$	−6.32456	+	14.1421i	−0.239217	+	0.534905i
$700$	12.7302	+	9.48371i	0.481158	+	0.358451i
$701$	−20.7846			−0.785024			−0.392512	−	0.919747i	$-0.628394\pi$
$701$	−20.7846			−0.785024			−0.392512	+	0.919747i	$0.628394\pi$
$702$	13.1699	−	19.1456i	0.497065	−	0.722605i
$703$		0			0
$704$	−19.0526	+	20.1246i	−0.718070	+	0.758475i
$705$	−10.9545	+	24.4949i	−0.412568	+	0.922531i
$706$	−9.48683	−	12.2474i	−0.357042	−	0.460939i
$707$	38.1051	+	15.5563i	1.43309	+	0.585057i
$708$	26.8109	+	21.3817i	1.00761	+	0.803573i
$709$			30.9839i			1.16362i	0.813323	+	0.581812i	$0.197656\pi$
$709$			30.9839i			1.16362i	−0.813323	+	0.581812i	$0.802344\pi$
$710$	10.9545	+	14.1421i	0.411113	+	0.530745i
$711$	−20.0000	−	22.3607i	−0.750059	−	0.838591i
$712$		0			0
$713$	21.9089			0.820495
$714$		0			0
$715$		−	15.4919i		−	0.579365i
$716$	5.19615	−	20.1246i	0.194189	−	0.752092i
$717$	3.16228	−	7.07107i	0.118097	−	0.264074i
$718$	35.0000	−	27.1109i	1.30619	−	1.01177i
$719$	32.8634			1.22560			0.612798	−	0.790239i	$-0.290044\pi$
$719$	32.8634			1.22560			0.612798	+	0.790239i	$0.290044\pi$
$720$	−16.5452	+	3.77577i	−0.616603	+	0.140715i
$721$	−24.0000	−	9.79796i	−0.893807	−	0.364895i
$722$	−7.79423	−	10.0623i	−0.290071	−	0.374480i
$723$	3.46410	−	7.74597i	0.128831	−	0.288076i
$724$	1.58114	−	6.12372i	0.0587626	−	0.227586i
$725$	20.7846			0.771921
$726$	0.578737	+	2.38014i	0.0214789	+	0.0883353i
$727$		−	19.5959i		−	0.726772i	−0.931639	−	0.363386i	$-0.881621\pi$
$727$		−	19.5959i		−	0.726772i	0.931639	−	0.363386i	$-0.118379\pi$
$728$	−0.444416	−	23.6601i	−0.0164711	−	0.876903i
$729$	−22.0000	+	15.6525i	−0.814815	+	0.579721i
$730$	18.0000	+	23.2379i	0.666210	+	0.860073i
$731$		0			0
$732$	6.83013	−	8.56442i	0.252449	−	0.316550i
$733$	15.8114			0.584007			0.292003	−	0.956417i	$-0.405678\pi$
$733$	15.8114			0.584007			0.292003	+	0.956417i	$0.405678\pi$
$734$	21.9089	−	16.9706i	0.808672	−	0.626395i
$735$	−15.9545	+	6.28136i	−0.588489	+	0.231691i
$736$	−25.0000	+	3.87298i	−0.921512	+	0.142760i
$737$			26.8328i			0.988399i
$738$	−8.41246	+	45.7081i	−0.309667	+	1.68254i
$739$			23.2379i			0.854820i	0.904058	+	0.427410i	$0.140574\pi$
$739$			23.2379i			0.854820i	−0.904058	+	0.427410i	$0.859426\pi$
$740$		0			0
$741$	15.8114	+	7.07107i	0.580846	+	0.259762i
$742$		0			0
$743$			49.1935i			1.80473i	0.430968	+	0.902367i	$0.358172\pi$
$743$			49.1935i			1.80473i	−0.430968	+	0.902367i	$0.641828\pi$
$744$	0.339746	−	23.9976i	0.0124557	−	0.879795i
$745$			9.79796i			0.358969i
$746$	34.6410	−	26.8328i	1.26830	−	0.982419i
$747$	−15.8114	+	14.1421i	−0.578508	+	0.517434i
$748$		0			0
$749$	10.3923	−	25.4558i	0.379727	−	0.930136i
$750$	26.9282	−	6.54766i	0.983279	−	0.239087i
$751$	−40.0000			−1.45962			−0.729810	−	0.683650i	$-0.760392\pi$
$751$	−40.0000			−1.45962			−0.729810	+	0.683650i	$0.760392\pi$
$752$	38.3406	+	21.2132i	1.39814	+	0.773566i
$753$	−11.0000	+	24.5967i	−0.400862	+	0.896355i
$754$	−18.9737	−	24.4949i	−0.690980	−	0.892052i
$755$		−	11.3137i		−	0.411748i
$756$	−8.93789	+	26.0022i	−0.325068	+	0.945691i
$757$		−	46.4758i		−	1.68919i	−0.535404	−	0.844596i	$-0.679841\pi$
$757$		−	46.4758i		−	1.68919i	0.535404	−	0.844596i	$-0.320159\pi$
$758$	−25.9808	+	20.1246i	−0.943664	+	0.730959i
$759$	−10.9545	+	24.4949i	−0.397621	+	0.889108i
$760$	−5.00000	−	11.6190i	−0.181369	−	0.421464i
$761$	10.9545			0.397099			0.198549	−	0.980091i	$-0.436377\pi$
$761$	10.9545			0.397099			0.198549	+	0.980091i	$0.436377\pi$
$762$	4.62990	+	19.0411i	0.167723	+	0.689787i
$763$		0			0
$764$	−17.3205	−	4.47214i	−0.626634	−	0.161796i
$765$		0			0
$766$	9.48683	+	12.2474i	0.342773	+	0.442518i
$767$			31.3050i			1.13036i
$768$	3.85454	+	27.4434i	0.139089	+	0.990280i
$769$		−	24.4949i		−	0.883309i	−0.897185	−	0.441654i	$-0.854392\pi$
$769$		−	24.4949i		−	0.883309i	0.897185	−	0.441654i	$-0.145608\pi$
$770$	4.91508	+	17.6590i	0.177127	+	0.636388i
$771$	17.3205	+	7.74597i	0.623783	+	0.278964i
$772$	2.00000	−	7.74597i	0.0719816	−	0.278783i
$773$		−	35.3553i		−	1.27164i	−0.771836	−	0.635822i	$-0.780661\pi$
$773$		−	35.3553i		−	1.27164i	0.771836	−	0.635822i	$-0.219339\pi$
$774$	−32.3205	−	5.94851i	−1.16174	−	0.213815i
$775$			14.6969i			0.527930i
$776$	5.47723	+	12.7279i	0.196621	+	0.456906i
$777$		0			0
$778$	24.0000	+	30.9839i	0.860442	+	1.11083i
$779$	−34.6410			−1.24114
$780$	−12.1119	−	9.65926i	−0.433676	−	0.345857i
$781$		−	30.9839i		−	1.10869i
$782$		0			0
$783$	10.9545	+	34.2929i	0.391480	+	1.22553i
$784$	8.01317	+	26.8289i	0.286185	+	0.958175i
$785$		−	22.3607i		−	0.798087i
$786$	3.36603	−	0.818458i	0.120062	−	0.0291934i
$787$	53.7587			1.91629			0.958146	−	0.286281i	$-0.0924191\pi$
$787$	53.7587			1.91629			0.958146	+	0.286281i	$0.0924191\pi$
$788$		0			0
$789$	−6.32456	+	14.1421i	−0.225160	+	0.503473i
$790$	−15.8114	+	12.2474i	−0.562544	+	0.435745i
$791$	−10.9545	−	4.47214i	−0.389495	−	0.159011i
$792$	26.6603	+	12.3786i	0.947331	+	0.439856i
$793$	10.0000			0.355110
$794$	−19.1703	−	24.7487i	−0.680328	−	0.878300i
$795$		0			0
$796$		0			0
$797$			49.4975i			1.75329i	0.481137	+	0.876645i	$0.340224\pi$
$797$			49.4975i			1.75329i	−0.481137	+	0.876645i	$0.659776\pi$
$798$	−20.2666	−	3.04378i	−0.717430	−	0.107749i
$799$		0			0
$800$	−2.59808	−	16.7705i	−0.0918559	−	0.592927i
$801$		0			0
$802$	5.00000	−	3.87298i	0.176556	−	0.136760i
$803$		−	50.9117i		−	1.79663i
$804$	20.9785	+	16.7303i	0.739854	+	0.590033i
$805$	−6.32456	+	15.4919i	−0.222911	+	0.546019i
$806$	17.3205	−	13.4164i	0.610089	−	0.472573i
$807$	7.00000	−	15.6525i	0.246412	−	0.550993i
$808$	−17.3925	−	40.4166i	−0.611867	−	1.42185i
$809$			22.3607i			0.786160i	0.919504	+	0.393080i	$0.128590\pi$
$809$			22.3607i			0.786160i	−0.919504	+	0.393080i	$0.871410\pi$
$810$	9.37331	+	15.3669i	0.329345	+	0.539937i
$811$	−22.1359			−0.777298			−0.388649	−	0.921386i	$-0.627058\pi$
$811$	−22.1359			−0.777298			−0.388649	+	0.921386i	$0.627058\pi$
$812$	29.3993	+	21.9017i	1.03171	+	0.768599i
$813$		0			0
$814$		0			0
$815$	−32.8634			−1.15115
$816$		0			0
$817$		−	24.4949i		−	0.856968i
$818$	10.9545	−	8.48528i	0.383013	−	0.296681i
$819$	−23.6451	+	8.42087i	−0.826225	+	0.294249i
$820$	30.0000	+	7.74597i	1.04765	+	0.270501i
$821$	−13.8564			−0.483592			−0.241796	−	0.970327i	$-0.577736\pi$
$821$	−13.8564			−0.483592			−0.241796	+	0.970327i	$0.577736\pi$
$822$	42.5772	−	10.3528i	1.48505	−	0.361094i
$823$	26.0000			0.906303			0.453152	−	0.891434i	$-0.350300\pi$
$823$	26.0000			0.906303			0.453152	+	0.891434i	$0.350300\pi$
$824$	10.9545	+	25.4558i	0.381616	+	0.886796i
$825$	−16.4317	−	7.34847i	−0.572078	−	0.255841i
$826$	−9.93203	−	35.6841i	−0.345579	−	1.24161i
$827$	−51.9615			−1.80688			−0.903440	−	0.428715i	$-0.858966\pi$
$827$	−51.9615			−1.80688			−0.903440	+	0.428715i	$0.858966\pi$
$828$	12.3205	+	23.8371i	0.428167	+	0.828395i
$829$	34.7851			1.20813			0.604067	−	0.796933i	$-0.293546\pi$
$829$	34.7851			1.20813			0.604067	+	0.796933i	$0.293546\pi$
$830$	8.66025	+	11.1803i	0.300602	+	0.388075i
$831$	10.9545	−	24.4949i	0.380006	−	0.849719i
$832$	−17.3925	+	18.3712i	−0.602977	+	0.636906i
$833$		0			0
$834$	9.15064	+	37.6333i	0.316861	+	1.30313i
$835$			30.9839i			1.07224i
$836$	−5.47723	+	21.2132i	−0.189434	+	0.733674i
$837$	−24.2487	+	7.74597i	−0.838158	+	0.267740i
$838$	−26.8794	+	20.8207i	−0.928532	+	0.719238i
$839$	21.9089			0.756379			0.378190	−	0.925728i	$-0.376547\pi$
$839$	21.9089			0.756379			0.378190	+	0.925728i	$0.376547\pi$
$840$	16.8708	+	7.16775i	0.582097	+	0.247311i
$841$	19.0000			0.655172
$842$	−34.6410	+	26.8328i	−1.19381	+	0.924720i
$843$	−6.32456	+	14.1421i	−0.217829	+	0.487081i
$844$	15.0000	+	3.87298i	0.516321	+	0.133314i
$845$			4.24264i			0.145951i
$846$	8.41246	−	45.7081i	0.289226	−	1.57148i
$847$	1.00000	−	2.44949i	0.0343604	−	0.0841655i
$848$		0			0
$849$	25.0000	+	11.1803i	0.857998	+	0.383708i
$850$		0			0
$851$		0			0
$852$	−24.2239	−	19.3185i	−0.829895	−	0.661841i
$853$	53.7587			1.84066			0.920332	−	0.391139i	$-0.127919\pi$
$853$	53.7587			1.84066			0.920332	+	0.391139i	$0.127919\pi$
$854$	−11.3989	+	3.17267i	−0.390061	+	0.108567i
$855$	−10.0000	+	8.94427i	−0.341993	+	0.305888i
$856$	−27.0000	+	11.6190i	−0.922841	+	0.397128i
$857$	54.7723			1.87098			0.935492	−	0.353347i	$-0.114957\pi$
$857$	54.7723			1.87098			0.935492	+	0.353347i	$0.114957\pi$
$858$	6.33975	+	26.0731i	0.216435	+	0.890122i
$859$	−3.16228			−0.107896			−0.0539478	−	0.998544i	$-0.517180\pi$
$859$	−3.16228			−0.107896			−0.0539478	+	0.998544i	$0.517180\pi$
$860$	−5.47723	+	21.2132i	−0.186772	+	0.723364i
$861$	36.2942	−	34.6804i	1.23690	−	1.18191i
$862$	−25.0000	+	19.3649i	−0.851503	+	0.659572i
$863$			8.94427i			0.304467i	0.988345	+	0.152233i	$0.0486465\pi$
$863$			8.94427i			0.304467i	−0.988345	+	0.152233i	$0.951353\pi$
$864$	26.3006	−	13.1254i	0.894765	−	0.446537i
$865$	10.0000			0.340010
$866$	16.4317	−	12.7279i	0.558371	−	0.432512i
$867$	−26.8794	−	12.0208i	−0.912871	−	0.408248i
$868$	−15.4868	+	20.7884i	−0.525657	+	0.705605i
$869$	34.6410			1.17512
$870$	23.3205	−	5.67044i	0.790639	−	0.192246i
$871$			24.4949i			0.829978i
$872$		0			0
$873$	10.9545	−	9.79796i	0.370752	−	0.331611i
$874$	−15.8114	+	12.2474i	−0.534828	+	0.414276i
$875$	−27.7128	−	11.3137i	−0.936864	−	0.382473i
$876$	−39.8038	−	31.7436i	−1.34485	−	1.07252i
$877$			15.4919i			0.523125i	0.965186	+	0.261563i	$0.0842378\pi$
$877$			15.4919i			0.523125i	−0.965186	+	0.261563i	$0.915762\pi$
$878$	−27.3861	+	21.2132i	−0.924237	+	0.715911i
$879$	19.0000	−	42.4853i	0.640854	−	1.43299i
$880$	9.48683	−	17.1464i	0.319801	−	0.578006i
$881$	−32.8634			−1.10719			−0.553597	−	0.832785i	$-0.686745\pi$
$881$	−32.8634			−1.10719			−0.553597	+	0.832785i	$0.686745\pi$
$882$	24.2810	−	17.1006i	0.817585	−	0.575808i
$883$			23.2379i			0.782018i	0.920387	+	0.391009i	$0.127874\pi$
$883$			23.2379i			0.782018i	−0.920387	+	0.391009i	$0.872126\pi$
$884$		0			0
$885$	−22.1359	−	9.89949i	−0.744092	−	0.332768i
$886$	15.0000	+	19.3649i	0.503935	+	0.650577i
$887$	−21.9089			−0.735629			−0.367814	−	0.929899i	$-0.619894\pi$
$887$	−21.9089			−0.735629			−0.367814	+	0.929899i	$0.619894\pi$
$888$		0			0
$889$	8.00000	−	19.5959i	0.268311	−	0.657226i
$890$		0			0
$891$	3.46410	−	30.9839i	0.116052	−	1.03800i
$892$	−18.9737	−	4.89898i	−0.635285	−	0.164030i
$893$	34.6410			1.15922
$894$	−4.00961	−	16.4901i	−0.134101	−	0.551511i
$895$			14.6969i			0.491264i
$896$	13.9969	−	26.4591i	0.467605	−	0.883938i
$897$	−10.0000	+	22.3607i	−0.333890	+	0.746601i
$898$	−10.0000	+	7.74597i	−0.333704	+	0.258486i
$899$			33.9411i			1.13200i
$900$	−15.9904	+	8.26485i	−0.533013	+	0.275495i
$901$		0			0
$902$	−32.8634	−	42.4264i	−1.09423	−	1.41264i
$903$	24.5228	+	25.6639i	0.816067	+	0.854040i
$904$	5.00000	+	11.6190i	0.166298	+	0.386441i
$905$			4.47214i			0.148659i
$906$	4.62990	+	19.0411i	0.153818	+	0.632599i
$907$		−	38.7298i		−	1.28600i	−0.765865	−	0.643002i	$-0.777689\pi$
$907$		−	38.7298i		−	1.28600i	0.765865	−	0.643002i	$-0.222311\pi$
$908$	19.1703	+	4.94975i	0.636188	+	0.164263i
$909$	−34.7851	+	31.1127i	−1.15375	+	1.03194i
$910$	4.48683	+	16.1204i	0.148737	+	0.534387i
$911$		−	31.3050i		−	1.03718i	−0.855023	−	0.518590i	$-0.826457\pi$
$911$		−	31.3050i		−	1.03718i	0.855023	−	0.518590i	$-0.173543\pi$
$912$	13.1699	+	17.5087i	0.436098	+	0.579771i
$913$		−	24.4949i		−	0.810663i
$914$	6.92820	+	8.94427i	0.229165	+	0.295850i
$915$	−3.16228	+	7.07107i	−0.104542	+	0.233762i
$916$	−7.90569	+	30.6186i	−0.261211	+	1.01167i
$917$	−3.46410	−	1.41421i	−0.114395	−	0.0467014i
$918$		0			0
$919$	−10.0000			−0.329870			−0.164935	−	0.986304i	$-0.552741\pi$
$919$	−10.0000			−0.329870			−0.164935	+	0.986304i	$0.552741\pi$
$920$	16.4317	−	7.07107i	0.541736	−	0.233126i
$921$	−5.00000	−	2.23607i	−0.164756	−	0.0736809i
$922$	−17.3925	+	13.4722i	−0.572792	+	0.443683i
$923$		−	28.2843i		−	0.930988i
$924$	−15.4987	−	27.7090i	−0.509871	−	0.911560i
$925$		0			0
$926$	12.1244	+	15.6525i	0.398431	+	0.514372i
$927$	21.9089	−	19.5959i	0.719583	−	0.643614i
$928$	−6.00000	−	38.7298i	−0.196960	−	1.27137i
$929$	21.9089			0.718808			0.359404	−	0.933182i	$-0.382980\pi$
$929$	21.9089			0.718808			0.359404	+	0.933182i	$0.382980\pi$
$930$	4.00961	+	16.4901i	0.131480	+	0.540731i
$931$	15.8114	+	15.4919i	0.518197	+	0.507728i
$932$	−17.3205	−	4.47214i	−0.567352	−	0.146490i
$933$	17.3205	+	7.74597i	0.567048	+	0.253592i
$934$	−7.90569	+	6.12372i	−0.258682	+	0.200374i
$935$		0			0
$936$	24.3374	+	11.3001i	0.795492	+	0.369355i
$937$			44.0908i			1.44038i	0.693775	+	0.720192i	$0.255946\pi$
$937$			44.0908i			1.44038i	−0.693775	+	0.720192i	$0.744054\pi$
$938$	−7.77142	−	27.9214i	−0.253746	−	0.911666i
$939$	−6.92820	+	15.4919i	−0.226093	+	0.505560i
$940$	−30.0000	−	7.74597i	−0.978492	−	0.252646i
$941$		−	1.41421i		−	0.0461020i	−0.999734	−	0.0230510i	$-0.992662\pi$
$941$		−	1.41421i		−	0.0461020i	0.999734	−	0.0230510i	$-0.00733802\pi$
$942$	9.15064	+	37.6333i	0.298144	+	1.22616i
$943$		−	48.9898i		−	1.59533i
$944$	−19.1703	+	34.6482i	−0.623940	+	1.12770i
$945$	1.52277	−	19.3825i	0.0495359	−	0.630513i
$946$	30.0000	−	23.2379i	0.975384	−	0.755529i
$947$	17.3205			0.562841			0.281420	−	0.959585i	$-0.409194\pi$
$947$	17.3205			0.562841			0.281420	+	0.959585i	$0.409194\pi$
$948$	21.5988	−	27.0831i	0.701495	−	0.879618i
$949$		−	46.4758i		−	1.50867i
$950$	−8.21584	−	10.6066i	−0.266557	−	0.344124i
$951$	10.9545	+	4.89898i	0.355222	+	0.158860i
$952$		0			0
$953$		−	17.8885i		−	0.579467i	−0.957107	−	0.289733i	$-0.906433\pi$
$953$		−	17.8885i		−	0.579467i	0.957107	−	0.289733i	$-0.0935666\pi$
$954$		0			0
$955$	12.6491			0.409316
$956$	8.66025	+	2.23607i	0.280093	+	0.0723196i
$957$	−37.9473	−	16.9706i	−1.22666	−	0.548580i
$958$	−9.48683	−	12.2474i	−0.306506	−	0.395697i
$959$	−43.8178	−	17.8885i	−1.41495	−	0.577651i
$960$	−7.49038	−	18.1078i	−0.241751	−	0.584428i
$961$	7.00000			0.225806
$962$		0			0
$963$	20.7846	+	23.2379i	0.669775	+	0.748831i
$964$	9.48683	+	2.44949i	0.305550	+	0.0788928i
$965$			5.65685i			0.182101i
$966$	4.30456	−	28.6613i	0.138497	−	0.922163i
$967$	32.0000			1.02905			0.514525	−	0.857475i	$-0.327968\pi$
$967$	32.0000			1.02905			0.514525	+	0.857475i	$0.327968\pi$
$968$	−2.59808	+	1.11803i	−0.0835053	+	0.0359350i
$969$		0			0
$970$	−6.00000	−	7.74597i	−0.192648	−	0.248708i
$971$			41.0122i			1.31614i	0.752955	+	0.658072i	$0.228628\pi$
$971$			41.0122i			1.31614i	−0.752955	+	0.658072i	$0.771372\pi$
$972$	−22.0640	−	22.0268i	−0.707702	−	0.706511i
$973$	15.8114	−	38.7298i	0.506890	−	1.24162i
$974$	6.92820	+	8.94427i	0.221994	+	0.286593i
$975$	−15.0000	−	6.70820i	−0.480384	−	0.214834i
$976$	11.0680	+	6.12372i	0.354277	+	0.196016i
$977$			8.94427i			0.286153i	0.989712	+	0.143076i	$0.0456994\pi$
$977$			8.94427i			0.286153i	−0.989712	+	0.143076i	$0.954301\pi$
$978$	55.3094	−	13.4486i	1.76860	−	0.430040i
$979$		0			0
$980$	−10.2290	−	16.9519i	−0.326752	−	0.541510i
$981$		0			0
$982$	3.00000	+	3.87298i	0.0957338	+	0.123592i
$983$	−43.8178			−1.39757			−0.698785	−	0.715331i	$-0.746276\pi$
$983$	−43.8178			−1.39757			−0.698785	+	0.715331i	$0.746276\pi$
$984$	−53.6603	−	0.759695i	−1.71063	−	0.0242182i
$985$		0			0
$986$		0			0
$987$	−36.2942	+	34.6804i	−1.15526	+	1.10389i
$988$	−5.00000	+	19.3649i	−0.159071	+	0.616080i
$989$	34.6410			1.10152
$990$	−20.4413	−	3.76217i	−0.649667	−	0.119570i
$991$	2.00000			0.0635321			0.0317660	−	0.999495i	$-0.489887\pi$
$991$	2.00000			0.0635321			0.0317660	+	0.999495i	$0.489887\pi$
$992$	27.3861	−	4.24264i	0.869510	−	0.134704i
$993$	−5.47723	+	12.2474i	−0.173814	+	0.388661i
$994$	8.97367	+	32.2409i	0.284627	+	1.02262i
$995$		0			0
$996$	−19.1506	−	15.2726i	−0.606811	−	0.483932i
$997$	−3.16228			−0.100150			−0.0500752	−	0.998745i	$-0.515946\pi$
$997$	−3.16228			−0.100150			−0.0500752	+	0.998745i	$0.515946\pi$
$998$	8.66025	−	6.70820i	0.274136	−	0.212344i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	168.2.i.e.125.8	yes	8
3.2	odd	2	inner	168.2.i.e.125.2	yes	8
4.3	odd	2		672.2.i.d.209.2		8
7.6	odd	2	inner	168.2.i.e.125.7	yes	8
8.3	odd	2		672.2.i.d.209.8		8
8.5	even	2	inner	168.2.i.e.125.3	yes	8
12.11	even	2		672.2.i.d.209.4		8
21.20	even	2	inner	168.2.i.e.125.1	✓	8
24.5	odd	2	inner	168.2.i.e.125.5	yes	8
24.11	even	2		672.2.i.d.209.6		8
28.27	even	2		672.2.i.d.209.7		8
56.13	odd	2	inner	168.2.i.e.125.4	yes	8
56.27	even	2		672.2.i.d.209.1		8
84.83	odd	2		672.2.i.d.209.5		8
168.83	odd	2		672.2.i.d.209.3		8
168.125	even	2	inner	168.2.i.e.125.6	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.2.i.e.125.1	✓	8	21.20	even	2	inner
168.2.i.e.125.2	yes	8	3.2	odd	2	inner
168.2.i.e.125.3	yes	8	8.5	even	2	inner
168.2.i.e.125.4	yes	8	56.13	odd	2	inner
168.2.i.e.125.5	yes	8	24.5	odd	2	inner
168.2.i.e.125.6	yes	8	168.125	even	2	inner
168.2.i.e.125.7	yes	8	7.6	odd	2	inner
168.2.i.e.125.8	yes	8	1.1	even	1	trivial
672.2.i.d.209.1		8	56.27	even	2
672.2.i.d.209.2		8	4.3	odd	2
672.2.i.d.209.3		8	168.83	odd	2
672.2.i.d.209.4		8	12.11	even	2
672.2.i.d.209.5		8	84.83	odd	2
672.2.i.d.209.6		8	24.11	even	2
672.2.i.d.209.7		8	28.27	even	2
672.2.i.d.209.8		8	8.3	odd	2

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:	\( N \)	\(=\)	\( 168 = 2^{3} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	168.i (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 1.11803i) q^{2} +(1.58114 + 0.707107i) q^{3} +(-0.500000 + 1.93649i) q^{4} -1.41421i q^{5} +(0.578737 + 2.38014i) q^{6} +(1.00000 - 2.44949i) q^{7} +(-2.59808 + 1.11803i) q^{8} +(2.00000 + 2.23607i) q^{9} +O(q^{10})\)	\(q+(0.866025 + 1.11803i) q^{2} +(1.58114 + 0.707107i) q^{3} +(-0.500000 + 1.93649i) q^{4} -1.41421i q^{5} +(0.578737 + 2.38014i) q^{6} +(1.00000 - 2.44949i) q^{7} +(-2.59808 + 1.11803i) q^{8} +(2.00000 + 2.23607i) q^{9} +(1.58114 - 1.22474i) q^{10} -3.46410 q^{11} +(-2.15988 + 2.70831i) q^{12} -3.16228 q^{13} +(3.60464 - 1.00329i) q^{14} +(1.00000 - 2.23607i) q^{15} +(-3.50000 - 1.93649i) q^{16} +(-0.767949 + 4.17256i) q^{18} -3.16228 q^{19} +(2.73861 + 0.707107i) q^{20} +(3.31319 - 3.16588i) q^{21} +(-3.00000 - 3.87298i) q^{22} -4.47214i q^{23} +(-4.89849 - 0.0693504i) q^{24} +3.00000 q^{25} +(-2.73861 - 3.53553i) q^{26} +(1.58114 + 4.94975i) q^{27} +(4.24342 + 3.16124i) q^{28} +6.92820 q^{29} +(3.36603 - 0.818458i) q^{30} +4.89898i q^{31} +(-0.866025 - 5.59017i) q^{32} +(-5.47723 - 2.44949i) q^{33} +(-3.46410 - 1.41421i) q^{35} +(-5.33013 + 2.75495i) q^{36} +(-2.73861 - 3.53553i) q^{38} +(-5.00000 - 2.23607i) q^{39} +(1.58114 + 3.67423i) q^{40} +10.9545 q^{41} +(6.40886 + 0.962529i) q^{42} +7.74597i q^{43} +(1.73205 - 6.70820i) q^{44} +(3.16228 - 2.82843i) q^{45} +(5.00000 - 3.87298i) q^{46} -10.9545 q^{47} +(-4.16468 - 5.53674i) q^{48} +(-5.00000 - 4.89898i) q^{49} +(2.59808 + 3.35410i) q^{50} +(1.58114 - 6.12372i) q^{52} +(-4.16468 + 6.05437i) q^{54} +4.89898i q^{55} +(0.140537 + 7.48200i) q^{56} +(-5.00000 - 2.23607i) q^{57} +(6.00000 + 7.74597i) q^{58} -9.89949i q^{59} +(3.83013 + 3.05453i) q^{60} -3.16228 q^{61} +(-5.47723 + 4.24264i) q^{62} +(7.47723 - 2.66291i) q^{63} +(5.50000 - 5.80948i) q^{64} +4.47214i q^{65} +(-2.00480 - 8.24504i) q^{66} -7.74597i q^{67} +(3.16228 - 7.07107i) q^{69} +(-1.41886 - 5.09773i) q^{70} +8.94427i q^{71} +(-7.69615 - 3.57341i) q^{72} +14.6969i q^{73} +(4.74342 + 2.12132i) q^{75} +(1.58114 - 6.12372i) q^{76} +(-3.46410 + 8.48528i) q^{77} +(-1.83013 - 7.52666i) q^{78} -10.0000 q^{79} +(-2.73861 + 4.94975i) q^{80} +(-1.00000 + 8.94427i) q^{81} +(9.48683 + 12.2474i) q^{82} +7.07107i q^{83} +(4.47410 + 7.99890i) q^{84} +(-8.66025 + 6.70820i) q^{86} +(10.9545 + 4.89898i) q^{87} +(9.00000 - 3.87298i) q^{88} +(5.90089 + 1.08604i) q^{90} +(-3.16228 + 7.74597i) q^{91} +(8.66025 + 2.23607i) q^{92} +(-3.46410 + 7.74597i) q^{93} +(-9.48683 - 12.2474i) q^{94} +4.47214i q^{95} +(2.58354 - 9.45121i) q^{96} -4.89898i q^{97} +(1.14710 - 9.83281i) q^{98} +(-6.92820 - 7.74597i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{4} + 8 q^{7} + 16 q^{9}+O(q^{10}) \) 8 * q - 4 * q^4 + 8 * q^7 + 16 * q^9	\( 8 q - 4 q^{4} + 8 q^{7} + 16 q^{9} + 8 q^{15} - 28 q^{16} - 20 q^{18} - 24 q^{22} + 24 q^{25} - 4 q^{28} + 20 q^{30} - 8 q^{36} - 40 q^{39} + 12 q^{42} + 40 q^{46} - 40 q^{49} - 40 q^{57} + 48 q^{58} - 4 q^{60} + 16 q^{63} + 44 q^{64} - 24 q^{70} - 20 q^{72} + 20 q^{78} - 80 q^{79} - 8 q^{81} + 60 q^{84} + 72 q^{88}+O(q^{100}) \) 8 * q - 4 * q^4 + 8 * q^7 + 16 * q^9 + 8 * q^15 - 28 * q^16 - 20 * q^18 - 24 * q^22 + 24 * q^25 - 4 * q^28 + 20 * q^30 - 8 * q^36 - 40 * q^39 + 12 * q^42 + 40 * q^46 - 40 * q^49 - 40 * q^57 + 48 * q^58 - 4 * q^60 + 16 * q^63 + 44 * q^64 - 24 * q^70 - 20 * q^72 + 20 * q^78 - 80 * q^79 - 8 * q^81 + 60 * q^84 + 72 * q^88

Introduction

L-functions

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