LMFDB - Embedded newform 168.2.i.e.125.4

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			125.4
Root			$-0.578737 + 0.965926i$ of defining polynomial
Character	$\chi$	$=$	168.125
Dual form			168.2.i.e.125.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 1.11803i) q^{2} +(1.58114 + 0.707107i) q^{3} +(-0.500000 - 1.93649i) q^{4} -1.41421i q^{5} +(-2.15988 + 1.15539i) q^{6} +(1.00000 + 2.44949i) q^{7} +(2.59808 + 1.11803i) q^{8} +(2.00000 + 2.23607i) q^{9} +O(q^{10})$	\(q+(-0.866025 + 1.11803i) q^{2} +(1.58114 + 0.707107i) q^{3} +(-0.500000 - 1.93649i) q^{4} -1.41421i q^{5} +(-2.15988 + 1.15539i) 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} +(0.578737 - 3.41542i) q^{12} -3.16228 q^{13} +(-3.60464 - 1.00329i) q^{14} +(1.00000 - 2.23607i) q^{15} +(-3.50000 + 1.93649i) q^{16} +(-4.23205 + 0.299576i) q^{18} -3.16228 q^{19} +(-2.73861 + 0.707107i) q^{20} +(-0.150912 + 4.58009i) q^{21} +(-3.00000 + 3.87298i) q^{22} -4.47214i q^{23} +(3.31735 + 3.60488i) 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} +(1.63397 + 3.05453i) q^{30} -4.89898i q^{31} +(0.866025 - 5.59017i) q^{32} +(5.47723 + 2.44949i) q^{33} +(3.46410 - 1.41421i) q^{35} +(3.33013 - 4.99102i) q^{36} +(2.73861 - 3.53553i) q^{38} +(-5.00000 - 2.23607i) q^{39} +(1.58114 - 3.67423i) q^{40} -10.9545 q^{41} +(-4.99000 - 4.13520i) 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} +(-6.90329 + 0.586988i) q^{48} +(-5.00000 + 4.89898i) q^{49} +(-2.59808 + 3.35410i) q^{50} +(1.58114 + 6.12372i) q^{52} +(-6.90329 - 2.51884i) 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} +(-4.83013 - 0.818458i) q^{60} -3.16228 q^{61} +(5.47723 + 4.24264i) q^{62} +(-3.47723 + 7.13505i) q^{63} +(5.50000 + 5.80948i) q^{64} +4.47214i q^{65} +(-7.48203 + 4.00240i) q^{66} +7.74597i q^{67} +(3.16228 - 7.07107i) q^{69} +(-1.41886 + 5.09773i) q^{70} +8.94427i q^{71} +(2.69615 + 8.04554i) q^{72} -14.6969i q^{73} +(4.74342 + 2.12132i) q^{75} +(1.58114 + 6.12372i) q^{76} +(3.46410 + 8.48528i) q^{77} +(6.83013 - 3.65368i) 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} +(8.94476 - 1.99781i) q^{84} +(8.66025 + 6.70820i) q^{86} +(-10.9545 - 4.89898i) q^{87} +(9.00000 + 3.87298i) q^{88} +(0.423665 + 5.98502i) 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} +(5.32215 - 8.22646i) 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	$-0.102416\pi$
$6$	−2.15988	+	1.15539i	−0.881766	+	0.471688i
$7$	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	$-0.325099\pi$
$11$	3.46410			1.04447			0.522233	+	0.852803i	$0.325099\pi$
$12$	0.578737	−	3.41542i	0.167067	−	0.985946i
$13$	−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	$0.5\pi$
$18$	−4.23205	+	0.299576i	−0.997504	+	0.0706108i
$19$	−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
$21$	−0.150912	+	4.58009i	−0.0329317	+	0.999458i
$22$	−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	$-0.154396\pi$
$24$	3.31735	+	3.60488i	0.677151	+	0.735844i
$25$	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	$-0.722422\pi$
$29$	−6.92820			−1.28654			−0.643268	+	0.765641i	$0.722422\pi$
$30$	1.63397	+	3.05453i	0.298322	+	0.557678i
$31$		−	4.89898i		−	0.879883i	−0.898027	−	0.439941i	$-0.854999\pi$
$31$		−	4.89898i		−	0.879883i	0.898027	−	0.439941i	$-0.145001\pi$
$32$	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
$36$	3.33013	−	4.99102i	0.555021	−	0.831836i
$37$		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	$-0.826688\pi$
$41$	−10.9545			−1.71080			−0.855399	+	0.517970i	$0.826688\pi$
$42$	−4.99000	−	4.13520i	−0.769974	−	0.638075i
$43$		−	7.74597i		−	1.18125i	−0.806947	−	0.590624i	$-0.798881\pi$
$43$		−	7.74597i		−	1.18125i	0.806947	−	0.590624i	$-0.201119\pi$
$44$	−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	$-0.205397\pi$
$47$	10.9545			1.59787			0.798935	+	0.601417i	$0.205397\pi$
$48$	−6.90329	+	0.586988i	−0.996404	+	0.0847245i
$49$	−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	$0.5\pi$
$54$	−6.90329	−	2.51884i	−0.939419	−	0.342771i
$55$		−	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	$-0.222894\pi$
$60$	−4.83013	−	0.818458i	−0.623567	−	0.105662i
$61$	−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
$63$	−3.47723	+	7.13505i	−0.438089	+	0.898931i
$64$	5.50000	+	5.80948i	0.687500	+	0.726184i
$65$			4.47214i			0.554700i
$66$	−7.48203	+	4.00240i	−0.920974	+	0.492662i
$67$			7.74597i			0.946320i	0.880976	+	0.473160i	$0.156887\pi$
$67$			7.74597i			0.946320i	−0.880976	+	0.473160i	$0.843113\pi$
$68$		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	$0.821912\pi$
$72$	2.69615	+	8.04554i	0.317745	+	0.948176i
$73$		−	14.6969i		−	1.72015i	−0.510171	−	0.860073i	$-0.670418\pi$
$73$		−	14.6969i		−	1.72015i	0.510171	−	0.860073i	$-0.329582\pi$
$74$		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
$78$	6.83013	−	3.65368i	0.773360	−	0.413698i
$79$	−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	$0.873140\pi$
$84$	8.94476	−	1.99781i	0.975954	−	0.217978i
$85$		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	$0.5\pi$
$90$	0.423665	+	5.98502i	0.0446582	+	0.630877i
$91$	−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
$96$	5.32215	−	8.22646i	0.543190	−	0.839610i
$97$			4.89898i			0.497416i	0.968579	+	0.248708i	$0.0800060\pi$
$97$			4.89898i			0.497416i	−0.968579	+	0.248708i	$0.919994\pi$
$98$	−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	$0.160348\pi$
$103$			9.79796i			0.965422i	−0.875780	+	0.482711i	$0.839652\pi$
$104$	−8.21584	−	3.53553i	−0.805629	−	0.346688i
$105$	6.47723	+	0.213422i	0.632112	+	0.0208278i
$106$		0			0
$107$	−10.3923			−1.00466			−0.502331	−	0.864675i	$-0.667524\pi$
$107$	−10.3923			−1.00466			−0.502331	+	0.864675i	$0.667524\pi$
$108$	8.79458	−	5.53674i	0.846258	−	0.532773i
$109$		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	$-0.0674609\pi$
$114$	6.83013	−	3.65368i	0.639700	−	0.342198i
$115$	−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
$120$	5.09808	−	4.69144i	0.465389	−	0.428268i
$121$	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
$126$	−4.96586	−	10.0668i	−0.442394	−	0.896821i
$127$	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	$-0.0196778\pi$
$132$	2.00480	−	11.8313i	0.174496	−	1.02979i
$133$	−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	$-0.276847\pi$
$138$	5.16708	+	9.65926i	0.439851	+	0.822251i
$139$	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
$144$	−11.3301	−	3.95325i	−0.944177	−	0.329438i
$145$			9.79796i			0.813676i
$146$	16.4317	+	12.7279i	1.35990	+	1.05337i
$147$	−11.3698	+	4.21043i	−0.937765	+	0.347271i
$148$		0			0
$149$	6.92820			0.567581			0.283790	−	0.958886i	$-0.408408\pi$
$149$	6.92820			0.567581			0.283790	+	0.958886i	$0.408408\pi$
$150$	−6.47963	+	3.46618i	−0.529059	+	0.283013i
$151$	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
$156$	−1.83013	+	10.8005i	−0.146527	+	0.864731i
$157$	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
$162$	−9.13397	−	8.86400i	−0.717633	−	0.696422i
$163$			23.2379i			1.82013i	0.414462	+	0.910066i	$0.363970\pi$
$163$			23.2379i			1.82013i	−0.414462	+	0.910066i	$0.636030\pi$
$164$	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	$-0.177998\pi$
$167$	21.9089			1.69536			0.847681	+	0.530506i	$0.177998\pi$
$168$	−5.51278	+	11.7307i	−0.425320	+	0.905043i
$169$	−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	$0.913372\pi$
$174$	14.9641	−	8.00481i	1.13442	−	0.606843i
$175$	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	$-0.373035\pi$
$179$	10.3923			0.776757			0.388379	+	0.921500i	$0.373035\pi$
$180$	−7.05836	−	4.70951i	−0.526099	−	0.351026i
$181$	−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
$186$	5.66025	+	10.5812i	0.415030	+	0.775850i
$187$		0			0
$188$	−5.47723	−	21.2132i	−0.399468	−	1.54713i
$189$	−10.5432	+	8.82273i	−0.766906	+	0.641759i
$190$	−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	$0.895109\pi$
$192$	4.58834	+	13.0747i	0.331135	+	0.943583i
$193$	−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	$0.5\pi$
$198$	−14.6603	+	1.03776i	−1.04186	+	0.0737506i
$199$		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
$210$	−5.84805	+	7.05693i	−0.403554	+	0.486974i
$211$			7.74597i			0.533254i	0.963800	+	0.266627i	$0.0859092\pi$
$211$			7.74597i			0.533254i	−0.963800	+	0.266627i	$0.914091\pi$
$212$		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
$216$	−1.42607	+	14.6276i	−0.0970316	+	0.995281i
$217$	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	$-0.893605\pi$
$223$		−	9.79796i		−	0.656120i	0.944657	−	0.328060i	$-0.106395\pi$
$224$	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	$-0.106552\pi$
$228$	−1.83013	+	10.8005i	−0.121203	+	0.715280i
$229$	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
$231$	−0.522774	+	15.8659i	−0.0343960	+	1.04390i
$232$	−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	$0.905353\pi$
$234$	13.3829	−	0.947343i	0.874869	−	0.0619298i
$235$		−	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	$-0.0462022\pi$
$240$	0.830127	+	9.76273i	0.0535845	+	0.630181i
$241$			4.89898i			0.315571i	0.987473	+	0.157786i	$0.0504355\pi$
$241$			4.89898i			0.315571i	−0.987473	+	0.157786i	$0.949565\pi$
$242$	−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
$246$	23.6603	−	12.6567i	1.50852	−	0.806963i
$247$	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	$0.836648\pi$
$252$	15.5556	+	3.16609i	0.979909	+	0.199445i
$253$		−	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	$-0.610989\pi$
$257$	−10.9545			−0.683320			−0.341660	+	0.939824i	$0.610989\pi$
$258$	8.94965	+	16.7303i	0.557181	+	1.04158i
$259$		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	$0.911069\pi$
$264$	11.4916	+	12.4877i	0.707261	+	0.768564i
$265$		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	$-0.0975846\pi$
$270$	−3.56218	+	9.76273i	−0.216787	+	0.594141i
$271$		0			0		1.00000			$0$
$271$		0			0		−1.00000			$\pi$
$272$		0			0
$273$	0.477226	−	14.4835i	0.0288830	−	0.876582i
$274$	20.0000	+	15.4919i	1.20824	+	0.935902i
$275$	10.3923			0.626680
$276$	−15.2742	−	2.58819i	−0.919399	−	0.155791i
$277$			15.4919i			0.930820i	0.885095	+	0.465410i	$0.154093\pi$
$277$			15.4919i			0.930820i	−0.885095	+	0.465410i	$0.845907\pi$
$278$	−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	$0.914039\pi$
$282$	−23.6603	+	12.6567i	−1.40895	+	0.753696i
$283$	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
$288$	14.2321	−	9.24385i	0.838632	−	0.544699i
$289$	−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	$-0.287277\pi$
$294$	5.13913	−	16.3582i	0.299720	−	0.954027i
$295$	−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
$300$	1.73621	−	10.2462i	0.100240	−	0.591567i
$301$	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	$-0.600525\pi$
$311$	−10.9545			−0.621170			−0.310585	+	0.950546i	$0.600525\pi$
$312$	−10.4904	−	11.3996i	−0.593901	−	0.645378i
$313$		−	9.79796i		−	0.553813i	−0.960897	−	0.276907i	$-0.910691\pi$
$313$		−	9.79796i		−	0.553813i	0.960897	−	0.276907i	$-0.0893093\pi$
$314$	−13.6931	+	17.6777i	−0.772744	+	0.997609i
$315$	10.0905	+	4.91754i	0.568534	+	0.277072i
$316$	5.00000	+	19.3649i	0.281272	+	1.08936i
$317$	−6.92820			−0.389127			−0.194563	−	0.980890i	$-0.562329\pi$
$317$	−6.92820			−0.389127			−0.194563	+	0.980890i	$0.562329\pi$
$318$		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
$324$	17.8205	−	2.53564i	0.990028	−	0.140869i
$325$	−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
$330$	5.66025	+	10.5812i	0.311587	+	0.582475i
$331$		−	7.74597i		−	0.425757i	−0.977079	−	0.212878i	$-0.931716\pi$
$331$		−	7.74597i		−	0.425757i	0.977079	−	0.212878i	$-0.0682838\pi$
$332$	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
$336$	−8.34111	−	16.3226i	−0.455045	−	0.890468i
$337$	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
$342$	13.3829	−	0.947343i	0.723665	−	0.0512265i
$343$	−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	$-0.346088\pi$
$347$	17.3205			0.929814			0.464907	+	0.885360i	$0.346088\pi$
$348$	−4.00961	+	23.6627i	−0.214938	+	1.26845i
$349$	−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	$-0.405838\pi$
$353$	10.9545			0.583047			0.291523	+	0.956564i	$0.405838\pi$
$354$	11.4378	+	21.3817i	0.607913	+	1.13642i
$355$	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	$-0.309449\pi$
$360$	11.3781	−	3.81294i	0.599679	−	0.200959i
$361$	−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
$366$	6.83013	−	3.65368i	0.357016	−	0.190981i
$367$			19.5959i			1.02290i	0.859313	+	0.511449i	$0.170891\pi$
$367$			19.5959i			1.02290i	−0.859313	+	0.511449i	$0.829109\pi$
$368$	8.66025	+	15.6525i	0.451447	+	0.815942i
$369$	−21.9089	−	24.4949i	−1.14053	−	1.27515i
$370$		0			0
$371$		0			0
$372$	−16.7321	−	2.83522i	−0.867516	−	0.146999i
$373$			30.9839i			1.60428i	0.597133	+	0.802142i	$0.296306\pi$
$373$			30.9839i			1.60428i	−0.597133	+	0.802142i	$0.703694\pi$
$374$		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
$378$	−0.733419	−	19.4284i	−0.0377230	−	0.999288i
$379$		−	23.2379i		−	1.19365i	−0.802371	−	0.596825i	$-0.796429\pi$
$379$		−	23.2379i		−	1.19365i	0.802371	−	0.596825i	$-0.203571\pi$
$380$	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	$-0.590292\pi$
$383$	−10.9545			−0.559746			−0.279873	+	0.960037i	$0.590292\pi$
$384$	−18.5916	−	6.19307i	−0.948746	−	0.316039i
$385$	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	$-0.747954\pi$
$389$	−27.7128			−1.40510			−0.702548	+	0.711637i	$0.747954\pi$
$390$	−5.16708	−	9.65926i	−0.261645	−	0.489116i
$391$		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
$396$	11.5359	−	17.2894i	0.579701	−	0.868825i
$397$	−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
$399$	0.477226	−	14.4835i	0.0238912	−	0.725083i
$400$	−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	$-0.0356180\pi$
$402$	−8.94965	−	16.7303i	−0.446368	−	0.834433i
$403$			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	$0.0778818\pi$
$409$			9.79796i			0.484478i	−0.970217	+	0.242239i	$0.922118\pi$
$410$	−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
$414$	1.33975	+	18.9263i	0.0658449	+	0.930177i
$415$	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	$0.800208\pi$
$420$	−2.82532	−	12.6498i	−0.137862	−	0.617247i
$421$		−	30.9839i		−	1.51006i	−0.655690	−	0.755031i	$-0.727622\pi$
$421$		−	30.9839i		−	1.51006i	0.655690	−	0.755031i	$-0.272378\pi$
$422$	−8.66025	−	6.70820i	−0.421575	−	0.326550i
$423$	21.9089	+	24.4949i	1.06525	+	1.19098i
$424$		0			0
$425$		0			0
$426$	−10.3342	−	19.3185i	−0.500692	−	0.935985i
$427$	−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	$0.818977\pi$
$432$	−15.1191	−	14.2623i	−0.727420	−	0.686193i
$433$			14.6969i			0.706290i	0.935569	+	0.353145i	$0.114888\pi$
$433$			14.6969i			0.706290i	−0.935569	+	0.353145i	$0.885112\pi$
$434$	−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
$438$	16.9808	+	31.7436i	0.811372	+	1.51677i
$439$		−	24.4949i		−	1.16908i	−0.811366	−	0.584539i	$-0.801275\pi$
$439$		−	24.4949i		−	1.16908i	0.811366	−	0.584539i	$-0.198725\pi$
$440$	5.47723	−	12.7279i	0.261116	−	0.606780i
$441$	−20.9545	−	1.38238i	−0.997831	−	0.0658277i
$442$		0			0
$443$	−17.3205			−0.822922			−0.411461	−	0.911427i	$-0.634981\pi$
$443$	−17.3205			−0.822922			−0.411461	+	0.911427i	$0.634981\pi$
$444$		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	$0.932311\pi$
$450$	−12.6962	+	0.898729i	−0.598502	+	0.0423665i
$451$	−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
$456$	−10.4904	−	11.3996i	−0.491257	−	0.533837i
$457$	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	$0.882003\pi$
$462$	−17.2859	−	14.3247i	−0.804212	−	0.666448i
$463$	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	$0.947688\pi$
$468$	−10.5308	+	15.7830i	−0.486786	+	0.729569i
$469$	−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
$474$	21.5988	−	11.5539i	0.992064	−	0.530690i
$475$	−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	$-0.419484\pi$
$479$	10.9545			0.500522			0.250261	+	0.968178i	$0.419484\pi$
$480$	−11.6340	−	7.52666i	−0.531016	−	0.343544i
$481$		0			0
$482$	−5.47723	−	4.24264i	−0.249481	−	0.193247i
$483$	20.4828	+	0.674899i	0.931999	+	0.0307090i
$484$	−0.500000	−	1.93649i	−0.0227273	−	0.0880223i
$485$	6.92820			0.314594
$486$	−8.17429	−	20.4739i	−0.370793	−	0.928715i
$487$	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	$-0.524907\pi$
$491$	−3.46410			−0.156333			−0.0781664	+	0.996940i	$0.524907\pi$
$492$	−6.33975	+	37.4140i	−0.285818	+	1.68675i
$493$		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
$498$	−8.16987	−	15.2726i	−0.366101	−	0.684383i
$499$			7.74597i			0.346757i	0.984855	+	0.173379i	$0.0554684\pi$
$499$			7.74597i			0.346757i	−0.984855	+	0.173379i	$0.944532\pi$
$500$	−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	$-0.761718\pi$
$503$	−32.8634			−1.46530			−0.732652	+	0.680603i	$0.761718\pi$
$504$	−17.0113	+	14.6497i	−0.757745	+	0.652551i
$505$	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
$516$	−26.4557	−	4.48288i	−1.16465	−	0.197348i
$517$	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	$-0.244195\pi$
$521$	32.8634			1.43977			0.719885	+	0.694094i	$0.244195\pi$
$522$	29.3205	−	2.07553i	1.28332	−	0.0908433i
$523$	−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
$525$	−0.452736	+	13.7403i	−0.0197590	+	0.599675i
$526$	−10.0000	−	7.74597i	−0.436021	−	0.337740i
$527$		0			0
$528$	−23.9137	+	2.03339i	−1.04071	+	0.0884918i
$529$	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
$540$	−7.83013	−	12.4374i	−0.336955	−	0.535221i
$541$		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
$546$	15.7798	+	13.0766i	0.675312	+	0.559629i
$547$		−	7.74597i		−	0.331194i	−0.986194	−	0.165597i	$-0.947045\pi$
$547$		−	7.74597i		−	0.331194i	0.986194	−	0.165597i	$-0.0529550\pi$
$548$	−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
$552$	16.1215	−	14.8356i	0.686178	−	0.631447i
$553$	−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	$0.5\pi$
$558$	1.46762	+	20.7327i	0.0621292	+	0.877686i
$559$			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	$-0.00948736\pi$
$564$	6.33975	−	37.4140i	0.266951	−	1.57541i
$565$	−6.32456			−0.266076
$566$	−13.6931	+	17.6777i	−0.575562	+	0.743048i
$567$	−22.9089	+	6.49478i	−0.962083	+	0.272755i
$568$	−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	$0.844721\pi$
$570$	−5.16708	−	9.65926i	−0.216425	−	0.404582i
$571$			7.74597i			0.324159i	0.986778	+	0.162079i	$0.0518200\pi$
$571$			7.74597i			0.324159i	−0.986778	+	0.162079i	$0.948180\pi$
$572$	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
$576$	−1.99038	+	23.9173i	−0.0829325	+	0.996555i
$577$			29.3939i			1.22368i	0.790980	+	0.611842i	$0.209571\pi$
$577$			29.3939i			1.22368i	−0.790980	+	0.611842i	$0.790429\pi$
$578$	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
$582$	−5.66025	−	10.5812i	−0.234625	−	0.438604i
$583$		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	$-0.260310\pi$
$588$	13.8384	+	19.9123i	0.570685	+	0.821169i
$589$			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	$-0.264244\pi$
$593$	32.8634			1.34954			0.674768	+	0.738030i	$0.264244\pi$
$594$	−23.9137	−	8.72552i	−0.981191	−	0.358012i
$595$		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	$0.941508\pi$
$600$	9.95205	+	10.8147i	0.406291	+	0.441506i
$601$		−	24.4949i		−	0.999168i	−0.866266	−	0.499584i	$-0.833486\pi$
$601$		−	24.4949i		−	0.999168i	0.866266	−	0.499584i	$-0.166514\pi$
$602$	−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
$606$	−17.9737	−	33.5998i	−0.730132	−	1.36490i
$607$		−	19.5959i		−	0.795374i	−0.917521	−	0.397687i	$-0.869813\pi$
$607$		−	19.5959i		−	0.795374i	0.917521	−	0.397687i	$-0.130187\pi$
$608$	−2.73861	+	17.6777i	−0.111065	+	0.716924i
$609$	1.04555	−	31.7318i	0.0423678	−	1.28584i
$610$	−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	$-0.612151\pi$
$613$		−	46.4758i		−	1.87714i	0.345089	−	0.938570i	$-0.387849\pi$
$614$	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	$-0.217005\pi$
$618$	−11.3205	−	21.1624i	−0.455378	−	0.851276i
$619$	−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
$624$	21.8301	−	1.85622i	0.873904	−	0.0743083i
$625$	−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
$630$	−14.2366	+	7.02279i	−0.567199	+	0.279795i
$631$	−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	$-0.212152\pi$
$642$	22.4461	−	12.0072i	0.885876	−	0.473887i
$643$	−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	$0.5\pi$
$648$	−12.5981	+	22.1199i	−0.494899	+	0.868950i
$649$		−	34.2929i		−	1.34611i
$650$	8.21584	−	10.6066i	0.322252	−	0.416025i
$651$	22.4378	+	0.739315i	0.879405	+	0.0289760i
$652$	45.0000	−	11.6190i	1.76234	−	0.455033i
$653$	48.4974			1.89785			0.948925	−	0.315501i	$-0.102172\pi$
$653$	48.4974			1.89785			0.948925	+	0.315501i	$0.102172\pi$
$654$		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	$-0.343425\pi$
$659$	24.2487			0.944596			0.472298	+	0.881439i	$0.343425\pi$
$660$	−16.7321	−	2.83522i	−0.651294	−	0.110361i
$661$	−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
$672$	25.4728	+	4.81010i	0.982634	+	0.185554i
$673$	−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	$0.956613\pi$
$678$	5.16708	+	9.65926i	0.198441	+	0.370962i
$679$	−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	$-0.703433\pi$
$683$	−31.1769			−1.19295			−0.596476	+	0.802631i	$0.703433\pi$
$684$	−10.5308	+	15.7830i	−0.402655	+	0.603477i
$685$	−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
$690$	13.6603	−	7.30736i	0.520037	−	0.278186i
$691$	−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
$693$	−12.0455	+	24.7165i	−0.457569	+	0.938903i
$694$	−15.0000	+	19.3649i	−0.569392	+	0.735082i
$695$		−	22.3607i		−	0.848189i
$696$	−22.9833	−	24.9754i	−0.871179	−	0.946689i
$697$		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	$-0.371606\pi$
$701$	20.7846			0.785024			0.392512	+	0.919747i	$0.371606\pi$
$702$	21.8301	+	7.96527i	0.823925	+	0.300630i
$703$		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
$708$	−33.8109	−	5.72920i	−1.27069	−	0.215317i
$709$		−	30.9839i		−	1.16362i	−0.813323	−	0.581812i	$-0.802344\pi$
$709$		−	30.9839i		−	1.16362i	0.813323	−	0.581812i	$-0.197656\pi$
$710$	−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	$-0.709956\pi$
$719$	−32.8634			−1.22560			−0.612798	+	0.790239i	$0.709956\pi$
$720$	−5.59075	+	16.0232i	−0.208355	+	0.597150i
$721$	−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
$726$	−2.15988	+	1.15539i	−0.0801605	+	0.0428807i
$727$			19.5959i			0.726772i	0.931639	+	0.363386i	$0.118379\pi$
$727$			19.5959i			0.726772i	−0.931639	+	0.363386i	$0.881621\pi$
$728$	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
$732$	−1.83013	+	10.8005i	−0.0676434	+	0.399198i
$733$	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
$735$	5.95445	+	16.0793i	0.219633	+	0.593095i
$736$	−25.0000	−	3.87298i	−0.921512	−	0.142760i
$737$			26.8328i			0.988399i
$738$	46.3598	−	3.28169i	1.70653	−	0.120801i
$739$		−	23.2379i		−	0.854820i	−0.904058	−	0.427410i	$-0.859426\pi$
$739$		−	23.2379i		−	0.854820i	0.904058	−	0.427410i	$-0.140574\pi$
$740$		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	$0.641828\pi$
$744$	17.6603	−	16.2516i	0.647456	−	0.595814i
$745$		−	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
$750$	13.0718	+	24.4362i	0.477315	+	0.892284i
$751$	−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
$756$	22.3568	+	16.0055i	0.813107	+	0.582114i
$757$			46.4758i			1.68919i	0.535404	+	0.844596i	$0.320159\pi$
$757$			46.4758i			1.68919i	−0.535404	+	0.844596i	$0.679841\pi$
$758$	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	$-0.563623\pi$
$761$	−10.9545			−0.397099			−0.198549	+	0.980091i	$0.563623\pi$
$762$	−17.2790	+	9.24316i	−0.625952	+	0.334844i
$763$		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
$768$	23.0248	−	15.4226i	0.830837	−	0.556516i
$769$			24.4949i			0.883309i	0.897185	+	0.441654i	$0.145608\pi$
$769$			24.4949i			0.883309i	−0.897185	+	0.441654i	$0.854392\pi$
$770$	−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	$-0.219339\pi$
$774$	2.32051	+	32.7813i	0.0834089	+	1.17830i
$775$		−	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
$780$	15.2742	+	2.58819i	0.546904	+	0.0926721i
$781$			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
$786$	1.63397	+	3.05453i	0.0582819	+	0.108951i
$787$	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
$792$	9.33975	+	27.8706i	0.331873	+	0.990338i
$793$	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	$0.659776\pi$
$798$	15.7798	+	13.0766i	0.558598	+	0.462908i
$799$		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
$804$	26.4557	+	4.48288i	0.933020	+	0.158099i
$805$	−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	$0.871410\pi$
$810$	−12.5356	+	12.9174i	−0.440456	+	0.453871i
$811$	−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
$819$	10.9960	−	22.5630i	0.384230	−	0.788415i
$820$	30.0000	−	7.74597i	1.04765	−	0.270501i
$821$	13.8564			0.483592			0.241796	−	0.970327i	$-0.422264\pi$
$821$	13.8564			0.483592			0.241796	+	0.970327i	$0.422264\pi$
$822$	20.6683	+	38.6370i	0.720891	+	1.34762i
$823$	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	$-0.141034\pi$
$827$	51.9615			1.80688			0.903440	+	0.428715i	$0.141034\pi$
$828$	−22.3205	−	14.8928i	−0.775691	−	0.517560i
$829$	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
$834$	−34.1506	+	18.2684i	−1.18254	+	0.632583i
$835$		−	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	$-0.623453\pi$
$839$	−21.9089			−0.756379			−0.378190	+	0.925728i	$0.623453\pi$
$840$	16.5897	+	7.79624i	0.572399	+	0.268996i
$841$	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
$846$	−46.3598	+	3.28169i	−1.59388	+	0.112827i
$847$	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
$852$	30.5484	+	5.17638i	1.04657	+	0.177340i
$853$	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	$-0.885043\pi$
$857$	−54.7723			−1.87098			−0.935492	+	0.353347i	$0.885043\pi$
$858$	23.6603	−	12.6567i	0.807748	−	0.432093i
$859$	−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
$861$	1.65316	−	50.1724i	0.0563395	−	1.70987i
$862$	−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	$0.951353\pi$
$864$	29.0392	−	4.55223i	0.987935	−	0.154870i
$865$	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
$870$	−11.3205	−	21.1624i	−0.383801	−	0.717472i
$871$		−	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
$876$	−50.1962	−	8.50566i	−1.69597	−	0.287380i
$877$		−	15.4919i		−	0.523125i	−0.965186	−	0.261563i	$-0.915762\pi$
$877$		−	15.4919i		−	0.523125i	0.965186	−	0.261563i	$-0.0842378\pi$
$878$	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	$-0.313255\pi$
$881$	32.8634			1.10719			0.553597	+	0.832785i	$0.313255\pi$
$882$	19.6926	−	22.2306i	0.663086	−	0.748544i
$883$		−	23.2379i		−	0.782018i	−0.920387	−	0.391009i	$-0.872126\pi$
$883$		−	23.2379i		−	0.782018i	0.920387	−	0.391009i	$-0.127874\pi$
$884$		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	$-0.380106\pi$
$887$	21.9089			0.735629			0.367814	+	0.929899i	$0.380106\pi$
$888$		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
$894$	−14.9641	+	8.00481i	−0.500473	+	0.267721i
$895$		−	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
$900$	9.99038	−	14.9731i	0.333013	−	0.499102i
$901$		0			0
$902$	32.8634	−	42.4264i	1.09423	−	1.41264i
$903$	35.4772	+	1.16896i	1.18061	+	0.0389005i
$904$	5.00000	−	11.6190i	0.166298	−	0.386441i
$905$			4.47214i			0.148659i
$906$	−17.2790	+	9.24316i	−0.574057	+	0.307083i
$907$			38.7298i			1.28600i	0.765865	+	0.643002i	$0.222311\pi$
$907$			38.7298i			1.28600i	−0.765865	+	0.643002i	$0.777689\pi$
$908$	−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	$-0.173543\pi$
$912$	21.8301	−	1.85622i	0.722868	−	0.0614656i
$913$			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
$924$	30.9856	−	6.92060i	1.01935	−	0.227671i
$925$		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	$-0.617020\pi$
$929$	−21.9089			−0.718808			−0.359404	+	0.933182i	$0.617020\pi$
$930$	14.9641	−	8.00481i	0.490691	−	0.262488i
$931$	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
$936$	−8.52598	−	25.4422i	−0.278680	−	0.831606i
$937$		−	44.0908i		−	1.44038i	−0.693775	−	0.720192i	$-0.744054\pi$
$937$		−	44.0908i		−	1.44038i	0.693775	−	0.720192i	$-0.255946\pi$
$938$	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	$-0.00733802\pi$
$942$	−34.1506	+	18.2684i	−1.11269	+	0.595216i
$943$			48.9898i			1.59533i
$944$	19.1703	+	34.6482i	0.623940	+	1.12770i
$945$	12.4772	+	14.9104i	0.405884	+	0.485034i
$946$	30.0000	+	23.2379i	0.975384	+	0.755529i
$947$	−17.3205			−0.562841			−0.281420	−	0.959585i	$-0.590806\pi$
$947$	−17.3205			−0.562841			−0.281420	+	0.959585i	$0.590806\pi$
$948$	−5.78737	+	34.1542i	−0.187965	+	1.10928i
$949$			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
$960$	18.4904	−	6.48890i	0.596774	−	0.209428i
$961$	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
$966$	−18.4932	+	22.3160i	−0.595008	+	0.718005i
$967$	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	$0.771372\pi$
$972$	29.9697	+	8.59180i	0.961278	+	0.275582i
$973$	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	$0.954301\pi$
$978$	−26.8489	−	50.1910i	−0.858535	−	1.60493i
$979$		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	$-0.253724\pi$
$983$	43.8178			1.39757			0.698785	+	0.715331i	$0.253724\pi$
$984$	−36.3397	−	39.4895i	−1.15847	−	1.25888i
$985$		0			0
$986$		0			0
$987$	−1.65316	+	50.1724i	−0.0526206	+	1.59700i
$988$	−5.00000	−	19.3649i	−0.159071	−	0.616080i
$989$	−34.6410			−1.10152
$990$	1.46762	+	20.7327i	0.0466440	+	0.658929i
$991$	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
$996$	24.1506	+	4.09229i	0.765242	+	0.129669i
$997$	−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.125.4	yes	8
3.2	odd	2	inner	168.2.i.e.125.6	yes	8
4.3	odd	2		672.2.i.d.209.1		8
7.6	odd	2	inner	168.2.i.e.125.3	yes	8
8.3	odd	2		672.2.i.d.209.7		8
8.5	even	2	inner	168.2.i.e.125.7	yes	8
12.11	even	2		672.2.i.d.209.3		8
21.20	even	2	inner	168.2.i.e.125.5	yes	8
24.5	odd	2	inner	168.2.i.e.125.1	✓	8
24.11	even	2		672.2.i.d.209.5		8
28.27	even	2		672.2.i.d.209.8		8
56.13	odd	2	inner	168.2.i.e.125.8	yes	8
56.27	even	2		672.2.i.d.209.2		8
84.83	odd	2		672.2.i.d.209.6		8
168.83	odd	2		672.2.i.d.209.4		8
168.125	even	2	inner	168.2.i.e.125.2	yes	8

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

\(f(q)\)	\(=\)	\(q+(-0.866025 + 1.11803i) q^{2} +(1.58114 + 0.707107i) q^{3} +(-0.500000 - 1.93649i) q^{4} -1.41421i q^{5} +(-2.15988 + 1.15539i) q^{6} +(1.00000 + 2.44949i) q^{7} +(2.59808 + 1.11803i) q^{8} +(2.00000 + 2.23607i) q^{9} +O(q^{10})\)	\(q+(-0.866025 + 1.11803i) q^{2} +(1.58114 + 0.707107i) q^{3} +(-0.500000 - 1.93649i) q^{4} -1.41421i q^{5} +(-2.15988 + 1.15539i) 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} +(0.578737 - 3.41542i) q^{12} -3.16228 q^{13} +(-3.60464 - 1.00329i) q^{14} +(1.00000 - 2.23607i) q^{15} +(-3.50000 + 1.93649i) q^{16} +(-4.23205 + 0.299576i) q^{18} -3.16228 q^{19} +(-2.73861 + 0.707107i) q^{20} +(-0.150912 + 4.58009i) q^{21} +(-3.00000 + 3.87298i) q^{22} -4.47214i q^{23} +(3.31735 + 3.60488i) 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} +(1.63397 + 3.05453i) q^{30} -4.89898i q^{31} +(0.866025 - 5.59017i) q^{32} +(5.47723 + 2.44949i) q^{33} +(3.46410 - 1.41421i) q^{35} +(3.33013 - 4.99102i) q^{36} +(2.73861 - 3.53553i) q^{38} +(-5.00000 - 2.23607i) q^{39} +(1.58114 - 3.67423i) q^{40} -10.9545 q^{41} +(-4.99000 - 4.13520i) 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} +(-6.90329 + 0.586988i) q^{48} +(-5.00000 + 4.89898i) q^{49} +(-2.59808 + 3.35410i) q^{50} +(1.58114 + 6.12372i) q^{52} +(-6.90329 - 2.51884i) 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} +(-4.83013 - 0.818458i) q^{60} -3.16228 q^{61} +(5.47723 + 4.24264i) q^{62} +(-3.47723 + 7.13505i) q^{63} +(5.50000 + 5.80948i) q^{64} +4.47214i q^{65} +(-7.48203 + 4.00240i) q^{66} +7.74597i q^{67} +(3.16228 - 7.07107i) q^{69} +(-1.41886 + 5.09773i) q^{70} +8.94427i q^{71} +(2.69615 + 8.04554i) q^{72} -14.6969i q^{73} +(4.74342 + 2.12132i) q^{75} +(1.58114 + 6.12372i) q^{76} +(3.46410 + 8.48528i) q^{77} +(6.83013 - 3.65368i) 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} +(8.94476 - 1.99781i) q^{84} +(8.66025 + 6.70820i) q^{86} +(-10.9545 - 4.89898i) q^{87} +(9.00000 + 3.87298i) q^{88} +(0.423665 + 5.98502i) 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} +(5.32215 - 8.22646i) 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

Modular forms

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