LMFDB - Embedded newform 975.2.bl.b.193.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [975,2,Mod(193,975)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(975, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 9, 7]))

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

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

chi := DirichletCharacter("975.193");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 975 = 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	975.bl (of order $12$, degree $4$, 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:	$7.78541419707$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{12})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			193.1
Root			$0.965926 - 0.258819i$ of defining polynomial
Character	$\chi$	$=$	975.193
Dual form			975.2.bl.b.682.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.965926 - 1.67303i) q^{2} +(0.258819 - 0.965926i) q^{3} +(-0.866025 + 1.50000i) q^{4} +(-1.86603 + 0.500000i) q^{6} -0.517638 q^{8} +(-0.866025 - 0.500000i) q^{9} +O(q^{10})$	\(q+(-0.965926 - 1.67303i) q^{2} +(0.258819 - 0.965926i) q^{3} +(-0.866025 + 1.50000i) q^{4} +(-1.86603 + 0.500000i) q^{6} -0.517638 q^{8} +(-0.866025 - 0.500000i) q^{9} +(5.96410 + 1.59808i) q^{11} +(1.22474 + 1.22474i) q^{12} +(3.60488 + 0.0693504i) q^{13} +(2.23205 + 3.86603i) q^{16} +(5.98502 - 1.60368i) q^{17} +1.93185i q^{18} +(1.90192 + 7.09808i) q^{19} +(-3.08725 - 11.5218i) q^{22} +(0.258819 + 0.0693504i) q^{23} +(-0.133975 + 0.500000i) q^{24} +(-3.36603 - 6.09808i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(-4.56218 + 2.63397i) q^{29} +(3.00000 + 3.00000i) q^{31} +(3.79435 - 6.57201i) q^{32} +(3.08725 - 5.34727i) q^{33} +(-8.46410 - 8.46410i) q^{34} +(1.50000 - 0.866025i) q^{36} +(-5.91567 + 3.41542i) q^{37} +(10.0382 - 10.0382i) q^{38} +(1.00000 - 3.46410i) q^{39} +(2.46410 - 9.19615i) q^{41} +(0.0507680 + 0.189469i) q^{43} +(-7.56218 + 7.56218i) q^{44} +(-0.133975 - 0.500000i) q^{46} +1.41421i q^{47} +(4.31199 - 1.15539i) q^{48} +(-3.50000 - 6.06218i) q^{49} -6.19615i q^{51} +(-3.22595 + 5.34727i) q^{52} +(0.378937 + 0.378937i) q^{53} +(1.86603 + 0.500000i) q^{54} +7.34847 q^{57} +(8.81345 + 5.08845i) q^{58} +(0.633975 - 0.169873i) q^{59} +(-4.59808 + 7.96410i) q^{61} +(2.12132 - 7.91688i) q^{62} -5.73205 q^{64} -11.9282 q^{66} +(1.22474 + 2.12132i) q^{67} +(-2.77766 + 10.3664i) q^{68} +(0.133975 - 0.232051i) q^{69} +(11.3301 - 3.03590i) q^{71} +(0.448288 + 0.258819i) q^{72} -3.34607 q^{73} +(11.4282 + 6.59808i) q^{74} +(-12.2942 - 3.29423i) q^{76} +(-6.76148 + 1.67303i) q^{78} -5.26795i q^{79} +(0.500000 + 0.866025i) q^{81} +(-17.7656 + 4.76028i) q^{82} -17.1093i q^{83} +(0.267949 - 0.267949i) q^{86} +(1.36345 + 5.08845i) q^{87} +(-3.08725 - 0.827225i) q^{88} +(2.16987 - 8.09808i) q^{89} +(-0.328169 + 0.328169i) q^{92} +(3.67423 - 2.12132i) q^{93} +(2.36603 - 1.36603i) q^{94} +(-5.36603 - 5.36603i) q^{96} +(-4.31199 + 7.46859i) q^{97} +(-6.76148 + 11.7112i) q^{98} +(-4.36603 - 4.36603i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{6}+O(q^{10}) $ 8 * q - 8 * q^6	$ 8 q - 8 q^{6} + 20 q^{11} + 4 q^{16} + 36 q^{19} - 8 q^{24} - 20 q^{26} + 12 q^{29} + 24 q^{31} - 40 q^{34} + 12 q^{36} + 8 q^{39} - 8 q^{41} - 12 q^{44} - 8 q^{46} - 28 q^{49} + 8 q^{54} + 12 q^{59} - 16 q^{61} - 32 q^{64} - 40 q^{66} + 8 q^{69} + 56 q^{71} + 36 q^{74} - 36 q^{76} + 4 q^{81} + 16 q^{86} + 52 q^{89} + 12 q^{94} - 36 q^{96} - 28 q^{99}+O(q^{100}) $ 8 * q - 8 * q^6 + 20 * q^11 + 4 * q^16 + 36 * q^19 - 8 * q^24 - 20 * q^26 + 12 * q^29 + 24 * q^31 - 40 * q^34 + 12 * q^36 + 8 * q^39 - 8 * q^41 - 12 * q^44 - 8 * q^46 - 28 * q^49 + 8 * q^54 + 12 * q^59 - 16 * q^61 - 32 * q^64 - 40 * q^66 + 8 * q^69 + 56 * q^71 + 36 * q^74 - 36 * q^76 + 4 * q^81 + 16 * q^86 + 52 * q^89 + 12 * q^94 - 36 * q^96 - 28 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/975\mathbb{Z}\right)^\times$.

$n$	$301$	$326$	$352$
$\chi(n)$	$e\left(\frac{7}{12}\right)$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−0.965926	−	1.67303i	−0.683013	−	1.18301i	−0.974057	−	0.226303i	$-0.927336\pi$
$2$	−0.965926	−	1.67303i	−0.683013	−	1.18301i	0.291044	−	0.956710i	$-0.405997\pi$
$3$	0.258819	−	0.965926i	0.149429	−	0.557678i
$3$	0.258819	−	0.965926i	0.149429	−	0.557678i
$4$	−0.866025	+	1.50000i	−0.433013	+	0.750000i
$5$		0			0
$5$		0			0
$6$	−1.86603	+	0.500000i	−0.761802	+	0.204124i
$7$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$7$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$8$	−0.517638			−0.183013
$9$	−0.866025	−	0.500000i	−0.288675	−	0.166667i
$10$		0			0
$11$	5.96410	+	1.59808i	1.79824	+	0.481838i	0.993702	−	0.112057i	$-0.0357439\pi$
$11$	5.96410	+	1.59808i	1.79824	+	0.481838i	0.804543	+	0.593895i	$0.202411\pi$
$12$	1.22474	+	1.22474i	0.353553	+	0.353553i
$13$	3.60488	+	0.0693504i	0.999815	+	0.0192343i
$13$	3.60488	+	0.0693504i	0.999815	+	0.0192343i
$14$		0			0
$15$		0			0
$16$	2.23205	+	3.86603i	0.558013	+	0.966506i
$17$	5.98502	−	1.60368i	1.45158	−	0.388950i	0.555008	−	0.831845i	$-0.312715\pi$
$17$	5.98502	−	1.60368i	1.45158	−	0.388950i	0.896574	+	0.442895i	$0.146049\pi$
$18$			1.93185i			0.455342i
$19$	1.90192	+	7.09808i	0.436331	+	1.62841i	0.737860	+	0.674953i	$0.235836\pi$
$19$	1.90192	+	7.09808i	0.436331	+	1.62841i	−0.301529	+	0.953457i	$0.597497\pi$
$20$		0			0
$21$		0			0
$22$	−3.08725	−	11.5218i	−0.658203	−	2.45645i
$23$	0.258819	+	0.0693504i	0.0539675	+	0.0144605i	0.285702	−	0.958319i	$-0.407773\pi$
$23$	0.258819	+	0.0693504i	0.0539675	+	0.0144605i	−0.231734	+	0.972779i	$0.574440\pi$
$24$	−0.133975	+	0.500000i	−0.0273474	+	0.102062i
$25$		0			0
$26$	−3.36603	−	6.09808i	−0.660132	−	1.19593i
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$		0			0
$29$	−4.56218	+	2.63397i	−0.847175	+	0.489117i	−0.859697	−	0.510805i	$-0.829347\pi$
$29$	−4.56218	+	2.63397i	−0.847175	+	0.489117i	0.0125216	+	0.999922i	$0.496014\pi$
$30$		0			0
$31$	3.00000	+	3.00000i	0.538816	+	0.538816i	0.923181	−	0.384365i	$-0.125580\pi$
$31$	3.00000	+	3.00000i	0.538816	+	0.538816i	−0.384365	+	0.923181i	$0.625580\pi$
$32$	3.79435	−	6.57201i	0.670753	−	1.16178i
$33$	3.08725	−	5.34727i	0.537421	−	0.930840i
$34$	−8.46410	−	8.46410i	−1.45158	−	1.45158i
$35$		0			0
$36$	1.50000	−	0.866025i	0.250000	−	0.144338i
$37$	−5.91567	+	3.41542i	−0.972531	+	0.561491i	−0.900007	−	0.435876i	$-0.856439\pi$
$37$	−5.91567	+	3.41542i	−0.972531	+	0.561491i	−0.0725239	+	0.997367i	$0.523105\pi$
$38$	10.0382	−	10.0382i	1.62841	−	1.62841i
$39$	1.00000	−	3.46410i	0.160128	−	0.554700i
$40$		0			0
$41$	2.46410	−	9.19615i	0.384828	−	1.43620i	−0.453610	−	0.891200i	$-0.649864\pi$
$41$	2.46410	−	9.19615i	0.384828	−	1.43620i	0.838438	−	0.544997i	$-0.183469\pi$
$42$		0			0
$43$	0.0507680	+	0.189469i	0.00774204	+	0.0288937i	0.969689	−	0.244343i	$-0.0785724\pi$
$43$	0.0507680	+	0.189469i	0.00774204	+	0.0288937i	−0.961947	+	0.273237i	$0.911906\pi$
$44$	−7.56218	+	7.56218i	−1.14004	+	1.14004i
$45$		0			0
$46$	−0.133975	−	0.500000i	−0.0197535	−	0.0737210i
$47$			1.41421i			0.206284i	0.994667	+	0.103142i	$0.0328896\pi$
$47$			1.41421i			0.206284i	−0.994667	+	0.103142i	$0.967110\pi$
$48$	4.31199	−	1.15539i	0.622382	−	0.166767i
$49$	−3.50000	−	6.06218i	−0.500000	−	0.866025i
$50$		0			0
$51$		−	6.19615i		−	0.867635i
$52$	−3.22595	+	5.34727i	−0.447358	+	0.741533i
$53$	0.378937	+	0.378937i	0.0520511	+	0.0520511i	0.732653	−	0.680602i	$-0.238282\pi$
$53$	0.378937	+	0.378937i	0.0520511	+	0.0520511i	−0.680602	+	0.732653i	$0.738282\pi$
$54$	1.86603	+	0.500000i	0.253934	+	0.0680414i
$55$		0			0
$56$		0			0
$57$	7.34847			0.973329
$58$	8.81345	+	5.08845i	1.15726	+	0.668146i
$59$	0.633975	−	0.169873i	0.0825365	−	0.0221156i	−0.217314	−	0.976102i	$-0.569730\pi$
$59$	0.633975	−	0.169873i	0.0825365	−	0.0221156i	0.299851	+	0.953986i	$0.403063\pi$
$60$		0			0
$61$	−4.59808	+	7.96410i	−0.588723	+	1.01970i	0.405677	+	0.914017i	$0.367036\pi$
$61$	−4.59808	+	7.96410i	−0.588723	+	1.01970i	−0.994400	+	0.105682i	$0.966297\pi$
$62$	2.12132	−	7.91688i	0.269408	−	1.00544i
$63$		0			0
$64$	−5.73205			−0.716506
$65$		0			0
$66$	−11.9282			−1.46826
$67$	1.22474	+	2.12132i	0.149626	+	0.259161i	0.931089	−	0.364791i	$-0.118860\pi$
$67$	1.22474	+	2.12132i	0.149626	+	0.259161i	−0.781463	+	0.623952i	$0.785526\pi$
$68$	−2.77766	+	10.3664i	−0.336841	+	1.25711i
$69$	0.133975	−	0.232051i	0.0161286	−	0.0279356i
$70$		0			0
$71$	11.3301	−	3.03590i	1.34464	−	0.360295i	0.486486	−	0.873689i	$-0.338279\pi$
$71$	11.3301	−	3.03590i	1.34464	−	0.360295i	0.858153	+	0.513394i	$0.171612\pi$
$72$	0.448288	+	0.258819i	0.0528312	+	0.0305021i
$73$	−3.34607			−0.391627			−0.195814	−	0.980641i	$-0.562735\pi$
$73$	−3.34607			−0.391627			−0.195814	+	0.980641i	$0.562735\pi$
$74$	11.4282	+	6.59808i	1.32850	+	0.767011i
$75$		0			0
$76$	−12.2942	−	3.29423i	−1.41024	−	0.377874i
$77$		0			0
$78$	−6.76148	+	1.67303i	−0.765587	+	0.189434i
$79$		−	5.26795i		−	0.592691i	−0.955081	−	0.296345i	$-0.904232\pi$
$79$		−	5.26795i		−	0.592691i	0.955081	−	0.296345i	$-0.0957679\pi$
$80$		0			0
$81$	0.500000	+	0.866025i	0.0555556	+	0.0962250i
$82$	−17.7656	+	4.76028i	−1.96188	+	0.525685i
$83$		−	17.1093i		−	1.87799i	−0.343937	−	0.938993i	$-0.611761\pi$
$83$		−	17.1093i		−	1.87799i	0.343937	−	0.938993i	$-0.388239\pi$
$84$		0			0
$85$		0			0
$86$	0.267949	−	0.267949i	0.0288937	−	0.0288937i
$87$	1.36345	+	5.08845i	0.146177	+	0.545539i
$88$	−3.08725	−	0.827225i	−0.329102	−	0.0881825i
$89$	2.16987	−	8.09808i	0.230006	−	0.858394i	−0.750331	−	0.661063i	$-0.770106\pi$
$89$	2.16987	−	8.09808i	0.230006	−	0.858394i	0.980337	−	0.197332i	$-0.0632276\pi$
$90$		0			0
$91$		0			0
$92$	−0.328169	+	0.328169i	−0.0342140	+	0.0342140i
$93$	3.67423	−	2.12132i	0.381000	−	0.219971i
$94$	2.36603	−	1.36603i	0.244037	−	0.140895i
$95$		0			0
$96$	−5.36603	−	5.36603i	−0.547668	−	0.547668i
$97$	−4.31199	+	7.46859i	−0.437816	+	0.758320i	−0.997521	−	0.0703721i	$-0.977581\pi$
$97$	−4.31199	+	7.46859i	−0.437816	+	0.758320i	0.559704	+	0.828692i	$0.310915\pi$
$98$	−6.76148	+	11.7112i	−0.683013	+	1.18301i
$99$	−4.36603	−	4.36603i	−0.438802	−	0.438802i
$100$		0			0
$101$	−13.0981	+	7.56218i	−1.30331	+	0.752465i	−0.980970	−	0.194160i	$-0.937802\pi$
$101$	−13.0981	+	7.56218i	−1.30331	+	0.752465i	−0.322337	+	0.946625i	$0.604469\pi$
$102$	−10.3664	+	5.98502i	−1.02642	+	0.592606i
$103$	−9.00292	+	9.00292i	−0.887084	+	0.887084i	−0.994242	−	0.107158i	$-0.965825\pi$
$103$	−9.00292	+	9.00292i	−0.887084	+	0.887084i	0.107158	+	0.994242i	$0.465825\pi$
$104$	−1.86603	−	0.0358984i	−0.182979	−	0.00352013i
$105$		0			0
$106$	0.267949	−	1.00000i	0.0260255	−	0.0971286i
$107$	−6.69213	−	1.79315i	−0.646953	−	0.173350i	−0.0796020	−	0.996827i	$-0.525365\pi$
$107$	−6.69213	−	1.79315i	−0.646953	−	0.173350i	−0.567351	+	0.823476i	$0.692032\pi$
$108$	−0.448288	−	1.67303i	−0.0431365	−	0.160988i
$109$	8.29423	−	8.29423i	0.794443	−	0.794443i	−0.187770	−	0.982213i	$-0.560126\pi$
$109$	8.29423	−	8.29423i	0.794443	−	0.794443i	0.982213	+	0.187770i	$0.0601260\pi$
$110$		0			0
$111$	1.76795	+	6.59808i	0.167806	+	0.626262i
$112$		0			0
$113$	7.53794	−	2.01978i	0.709110	−	0.190005i	0.113802	−	0.993503i	$-0.463697\pi$
$113$	7.53794	−	2.01978i	0.709110	−	0.190005i	0.595307	+	0.803498i	$0.297030\pi$
$114$	−7.09808	−	12.2942i	−0.664796	−	1.15146i
$115$		0			0
$116$		−	9.12436i		−	0.847175i
$117$	−3.08725	−	1.86250i	−0.285416	−	0.172188i
$118$	−0.896575	−	0.896575i	−0.0825365	−	0.0825365i
$119$		0			0
$120$		0			0
$121$	23.4904	+	13.5622i	2.13549	+	1.23293i
$122$	17.7656			1.60842
$123$	−8.24504	−	4.76028i	−0.743431	−	0.429220i
$124$	−7.09808	+	1.90192i	−0.637426	+	0.170798i
$125$		0			0
$126$		0			0
$127$	0.656339	−	2.44949i	0.0582407	−	0.217357i	−0.930672	−	0.365854i	$-0.880777\pi$
$127$	0.656339	−	2.44949i	0.0582407	−	0.217357i	0.988913	+	0.148497i	$0.0474436\pi$
$128$	−2.05197	−	3.55412i	−0.181370	−	0.314142i
$129$	0.196152			0.0172703
$130$		0			0
$131$	−12.0000			−1.04844			−0.524222	−	0.851581i	$-0.675644\pi$
$131$	−12.0000			−1.04844			−0.524222	+	0.851581i	$0.675644\pi$
$132$	5.34727	+	9.26174i	0.465420	+	0.806131i
$133$		0			0
$134$	2.36603	−	4.09808i	0.204393	−	0.354020i
$135$		0			0
$136$	−3.09808	+	0.830127i	−0.265658	+	0.0711828i
$137$	1.13681	+	0.656339i	0.0971244	+	0.0560748i	0.547775	−	0.836625i	$-0.315475\pi$
$137$	1.13681	+	0.656339i	0.0971244	+	0.0560748i	−0.450651	+	0.892700i	$0.648808\pi$
$138$	−0.517638			−0.0440643
$139$	−3.63397	−	2.09808i	−0.308230	−	0.177957i	0.337904	−	0.941180i	$-0.390282\pi$
$139$	−3.63397	−	2.09808i	−0.308230	−	0.177957i	−0.646134	+	0.763224i	$0.723615\pi$
$140$		0			0
$141$	1.36603	+	0.366025i	0.115040	+	0.0308249i
$142$	−16.0232	−	16.0232i	−1.34464	−	1.34464i
$143$	21.3891	+	6.17449i	1.78864	+	0.516337i
$144$		−	4.46410i		−	0.372008i
$145$		0			0
$146$	3.23205	+	5.59808i	0.267486	+	0.463300i
$147$	−6.76148	+	1.81173i	−0.557678	+	0.149429i
$148$		−	11.8313i		−	0.972531i
$149$	3.90192	+	14.5622i	0.319658	+	1.19298i	0.919574	+	0.392917i	$0.128534\pi$
$149$	3.90192	+	14.5622i	0.319658	+	1.19298i	−0.599916	+	0.800063i	$0.704799\pi$
$150$		0			0
$151$	6.53590	−	6.53590i	0.531884	−	0.531884i	−0.389249	−	0.921133i	$-0.627265\pi$
$151$	6.53590	−	6.53590i	0.531884	−	0.531884i	0.921133	+	0.389249i	$0.127265\pi$
$152$	−0.984508	−	3.67423i	−0.0798542	−	0.298020i
$153$	−5.98502	−	1.60368i	−0.483860	−	0.129650i
$154$		0			0
$155$		0			0
$156$	4.33013	+	4.50000i	0.346688	+	0.360288i
$157$	−8.05558	+	8.05558i	−0.642905	+	0.642905i	−0.951269	−	0.308364i	$-0.900219\pi$
$157$	−8.05558	+	8.05558i	−0.642905	+	0.642905i	0.308364	+	0.951269i	$0.400219\pi$
$158$	−8.81345	+	5.08845i	−0.701160	+	0.404815i
$159$	0.464102	−	0.267949i	0.0368057	−	0.0212498i
$160$		0			0
$161$		0			0
$162$	0.965926	−	1.67303i	0.0758903	−	0.131446i
$163$	−3.34607	+	5.79555i	−0.262084	+	0.453943i	−0.966796	−	0.255551i	$-0.917743\pi$
$163$	−3.34607	+	5.79555i	−0.262084	+	0.453943i	0.704712	+	0.709494i	$0.251076\pi$
$164$	11.6603	+	11.6603i	0.910513	+	0.910513i
$165$		0			0
$166$	−28.6244	+	16.5263i	−2.22168	+	1.28269i
$167$	−6.90018	+	3.98382i	−0.533952	+	0.308277i	−0.742624	−	0.669708i	$-0.766419\pi$
$167$	−6.90018	+	3.98382i	−0.533952	+	0.308277i	0.208672	+	0.977986i	$0.433086\pi$
$168$		0			0
$169$	12.9904	+	0.500000i	0.999260	+	0.0384615i
$170$		0			0
$171$	1.90192	−	7.09808i	0.145444	−	0.542803i
$172$	−0.328169	−	0.0879327i	−0.0250227	−	0.00670481i
$173$	1.69161	+	6.31319i	0.128611	+	0.479983i	0.999943	−	0.0107116i	$-0.00340968\pi$
$173$	1.69161	+	6.31319i	0.128611	+	0.479983i	−0.871332	+	0.490695i	$0.836743\pi$
$174$	7.19615	−	7.19615i	0.545539	−	0.545539i
$175$		0			0
$176$	7.13397	+	26.6244i	0.537744	+	2.00689i
$177$		−	0.656339i		−	0.0493334i
$178$	−15.6443	+	4.19187i	−1.17259	+	0.314194i
$179$	−4.33013	−	7.50000i	−0.323649	−	0.560576i	0.657589	−	0.753377i	$-0.271576\pi$
$179$	−4.33013	−	7.50000i	−0.323649	−	0.560576i	−0.981238	+	0.192800i	$0.938243\pi$
$180$		0			0
$181$		−	23.3923i		−	1.73874i	−0.494165	−	0.869368i	$-0.664526\pi$
$181$		−	23.3923i		−	1.73874i	0.494165	−	0.869368i	$-0.335474\pi$
$182$		0			0
$183$	6.50266	+	6.50266i	0.480691	+	0.480691i
$184$	−0.133975	−	0.0358984i	−0.00987674	−	0.00264646i
$185$		0			0
$186$	−7.09808	−	4.09808i	−0.520456	−	0.300486i
$187$	38.2581			2.79771
$188$	−2.12132	−	1.22474i	−0.154713	−	0.0893237i
$189$		0			0
$190$		0			0
$191$	2.33013	−	4.03590i	0.168602	−	0.292027i	−0.769327	−	0.638856i	$-0.779408\pi$
$191$	2.33013	−	4.03590i	0.168602	−	0.292027i	0.937929	+	0.346828i	$0.112741\pi$
$192$	−1.48356	+	5.53674i	−0.107067	+	0.399579i
$193$	−10.3478	−	17.9229i	−0.744850	−	1.29012i	−0.950265	−	0.311443i	$-0.899188\pi$
$193$	−10.3478	−	17.9229i	−0.744850	−	1.29012i	0.205415	−	0.978675i	$-0.434146\pi$
$194$	16.6603			1.19614
$195$		0			0
$196$	12.1244			0.866025
$197$	12.2474	+	21.2132i	0.872595	+	1.51138i	0.859303	+	0.511466i	$0.170898\pi$
$197$	12.2474	+	21.2132i	0.872595	+	1.51138i	0.0132914	+	0.999912i	$0.495769\pi$
$198$	−3.08725	+	11.5218i	−0.219401	+	0.818816i
$199$	7.36603	−	12.7583i	0.522164	−	0.904414i	−0.477504	−	0.878630i	$-0.658458\pi$
$199$	7.36603	−	12.7583i	0.522164	−	0.904414i	0.999668	−	0.0257844i	$-0.00820833\pi$
$200$		0			0
$201$	2.36603	−	0.633975i	0.166887	−	0.0447171i
$202$	25.3035	+	14.6090i	1.78035	+	1.02789i
$203$		0			0
$204$	9.29423	+	5.36603i	0.650726	+	0.375697i
$205$		0			0
$206$	23.7583	+	6.36603i	1.65532	+	0.443542i
$207$	−0.189469	−	0.189469i	−0.0131690	−	0.0131690i
$208$	7.77817	+	14.0914i	0.539319	+	0.977061i
$209$			45.3731i			3.13852i
$210$		0			0
$211$	0.928203	+	1.60770i	0.0639001	+	0.110678i	0.896206	−	0.443639i	$-0.146313\pi$
$211$	0.928203	+	1.60770i	0.0639001	+	0.110678i	−0.832305	+	0.554317i	$0.812979\pi$
$212$	−0.896575	+	0.240237i	−0.0615771	+	0.0164995i
$213$		−	11.7298i		−	0.803713i
$214$	3.46410	+	12.9282i	0.236801	+	0.883754i
$215$		0			0
$216$	0.366025	−	0.366025i	0.0249049	−	0.0249049i
$217$		0			0
$218$	−21.8881	−	5.86491i	−1.48245	−	0.397222i
$219$	−0.866025	+	3.23205i	−0.0585206	+	0.218402i
$220$		0			0
$221$	21.6865	−	5.36603i	1.45879	−	0.360958i
$222$	9.33109	−	9.33109i	0.626262	−	0.626262i
$223$	0.328169	−	0.189469i	0.0219758	−	0.0126878i	−0.488972	−	0.872300i	$-0.662628\pi$
$223$	0.328169	−	0.189469i	0.0219758	−	0.0126878i	0.510948	+	0.859612i	$0.329295\pi$
$224$		0			0
$225$		0			0
$226$	−10.6603	−	10.6603i	−0.709110	−	0.709110i
$227$	4.50146	−	7.79676i	0.298772	−	0.517489i	−0.677083	−	0.735907i	$-0.736756\pi$
$227$	4.50146	−	7.79676i	0.298772	−	0.517489i	0.975855	+	0.218418i	$0.0700895\pi$
$228$	−6.36396	+	11.0227i	−0.421464	+	0.729996i
$229$	19.4904	+	19.4904i	1.28796	+	1.28796i	0.936024	+	0.351937i	$0.114477\pi$
$229$	19.4904	+	19.4904i	1.28796	+	1.28796i	0.351937	+	0.936024i	$0.385523\pi$
$230$		0			0
$231$		0			0
$232$	2.36156	−	1.36345i	0.155044	−	0.0895146i
$233$	−5.79555	+	5.79555i	−0.379679	+	0.379679i	−0.870986	−	0.491307i	$-0.836519\pi$
$233$	−5.79555	+	5.79555i	−0.379679	+	0.379679i	0.491307	+	0.870986i	$0.336519\pi$
$234$	−0.133975	+	6.96410i	−0.00875819	+	0.455258i
$235$		0			0
$236$	−0.294229	+	1.09808i	−0.0191527	+	0.0714787i
$237$	−5.08845	−	1.36345i	−0.330530	−	0.0885653i
$238$		0			0
$239$	5.29423	−	5.29423i	0.342455	−	0.342455i	−0.514834	−	0.857290i	$-0.672147\pi$
$239$	5.29423	−	5.29423i	0.342455	−	0.342455i	0.857290	+	0.514834i	$0.172147\pi$
$240$		0			0
$241$	−2.83013	−	10.5622i	−0.182305	−	0.680370i	−0.995192	−	0.0979483i	$-0.968772\pi$
$241$	−2.83013	−	10.5622i	−0.182305	−	0.680370i	0.812887	−	0.582421i	$-0.197895\pi$
$242$		−	52.4002i		−	3.36841i
$243$	0.965926	−	0.258819i	0.0619642	−	0.0166032i
$244$	−7.96410	−	13.7942i	−0.509849	−	0.883085i
$245$		0			0
$246$			18.3923i			1.17265i
$247$	6.36396	+	25.7196i	0.404929	+	1.63650i
$248$	−1.55291	−	1.55291i	−0.0986102	−	0.0986102i
$249$	−16.5263	−	4.42820i	−1.04731	−	0.280626i
$250$		0			0
$251$	−22.4545	−	12.9641i	−1.41731	−	0.818287i	−0.421252	−	0.906944i	$-0.638409\pi$
$251$	−22.4545	−	12.9641i	−1.41731	−	0.818287i	−0.996062	+	0.0886567i	$0.971743\pi$
$252$		0			0
$253$	1.43280	+	0.827225i	0.0900791	+	0.0520072i
$254$	−4.73205	+	1.26795i	−0.296915	+	0.0795582i
$255$		0			0
$256$	−9.69615	+	16.7942i	−0.606010	+	1.04964i
$257$	2.36156	−	8.81345i	0.147310	−	0.549768i	−0.852332	−	0.523001i	$-0.824812\pi$
$257$	2.36156	−	8.81345i	0.147310	−	0.549768i	0.999642	−	0.0267666i	$-0.00852108\pi$
$258$	−0.189469	−	0.328169i	−0.0117958	−	0.0204309i
$259$		0			0
$260$		0			0
$261$	5.26795			0.326078
$262$	11.5911	+	20.0764i	0.716101	+	1.24032i
$263$	−2.62038	+	9.77938i	−0.161579	+	0.603022i	0.836872	+	0.547398i	$0.184382\pi$
$263$	−2.62038	+	9.77938i	−0.161579	+	0.603022i	−0.998452	+	0.0556243i	$0.982285\pi$
$264$	−1.59808	+	2.76795i	−0.0983548	+	0.170355i
$265$		0			0
$266$		0			0
$267$	−7.26054	−	4.19187i	−0.444338	−	0.256538i
$268$	−4.24264			−0.259161
$269$	6.75833	+	3.90192i	0.412063	+	0.237904i	0.691676	−	0.722208i	$-0.256873\pi$
$269$	6.75833	+	3.90192i	0.412063	+	0.237904i	−0.279613	+	0.960113i	$0.590206\pi$
$270$		0			0
$271$	14.7583	+	3.95448i	0.896505	+	0.240218i	0.677515	−	0.735509i	$-0.263057\pi$
$271$	14.7583	+	3.95448i	0.896505	+	0.240218i	0.218990	+	0.975727i	$0.429724\pi$
$272$	19.5588	+	19.5588i	1.18592	+	1.18592i
$273$		0			0
$274$		−	2.53590i		−	0.153199i
$275$		0			0
$276$	0.232051	+	0.401924i	0.0139678	+	0.0241930i
$277$	−15.2468	+	4.08536i	−0.916089	+	0.245465i	−0.685913	−	0.727684i	$-0.740597\pi$
$277$	−15.2468	+	4.08536i	−0.916089	+	0.245465i	−0.230176	+	0.973149i	$0.573930\pi$
$278$			8.10634i			0.486186i
$279$	−1.09808	−	4.09808i	−0.0657401	−	0.245345i
$280$		0			0
$281$	−5.00000	+	5.00000i	−0.298275	+	0.298275i	−0.840338	−	0.542063i	$-0.817643\pi$
$281$	−5.00000	+	5.00000i	−0.298275	+	0.298275i	0.542063	+	0.840338i	$0.317643\pi$
$282$	−0.707107	−	2.63896i	−0.0421076	−	0.157148i
$283$	0.517638	+	0.138701i	0.0307704	+	0.00824490i	0.274171	−	0.961681i	$-0.411596\pi$
$283$	0.517638	+	0.138701i	0.0307704	+	0.00824490i	−0.243401	+	0.969926i	$0.578263\pi$
$284$	−5.25833	+	19.6244i	−0.312024	+	1.16449i
$285$		0			0
$286$	−10.3301	−	41.7487i	−0.610833	−	2.46865i
$287$		0			0
$288$	−6.57201	+	3.79435i	−0.387260	+	0.223584i
$289$	18.5263	−	10.6962i	1.08978	−	0.629185i
$290$		0			0
$291$	6.09808	+	6.09808i	0.357476	+	0.357476i
$292$	2.89778	−	5.01910i	0.169580	−	0.293720i
$293$	5.98502	−	10.3664i	0.349649	−	0.605610i	−0.636538	−	0.771245i	$-0.719634\pi$
$293$	5.98502	−	10.3664i	0.349649	−	0.605610i	0.986187	+	0.165636i	$0.0529676\pi$
$294$	9.56218	+	9.56218i	0.557678	+	0.557678i
$295$		0			0
$296$	3.06218	−	1.76795i	0.177985	−	0.102760i
$297$	−5.34727	+	3.08725i	−0.310280	+	0.179140i
$298$	20.5940	−	20.5940i	1.19298	−	1.19298i
$299$	0.928203	+	0.267949i	0.0536794	+	0.0154959i
$300$		0			0
$301$		0			0
$302$	−17.2480	−	4.62158i	−0.992509	−	0.265942i
$303$	3.91447	+	14.6090i	0.224880	+	0.839265i
$304$	−23.1962	+	23.1962i	−1.33039	+	1.33039i
$305$		0			0
$306$	3.09808	+	11.5622i	0.177105	+	0.660966i
$307$		−	27.7023i		−	1.58105i	−0.612429	−	0.790526i	$-0.709807\pi$
$307$		−	27.7023i		−	1.58105i	0.612429	−	0.790526i	$-0.290193\pi$
$308$		0			0
$309$	6.36603	+	11.0263i	0.362151	+	0.627263i
$310$		0			0
$311$		−	22.8564i		−	1.29607i	−0.761611	−	0.648034i	$-0.775591\pi$
$311$		−	22.8564i		−	1.29607i	0.761611	−	0.648034i	$-0.224409\pi$
$312$	−0.517638	+	1.79315i	−0.0293055	+	0.101517i
$313$	−1.50215	−	1.50215i	−0.0849063	−	0.0849063i	0.663378	−	0.748284i	$-0.269122\pi$
$313$	−1.50215	−	1.50215i	−0.0849063	−	0.0849063i	−0.748284	+	0.663378i	$0.769122\pi$
$314$	21.2583	+	5.69615i	1.19968	+	0.321452i
$315$		0			0
$316$	7.90192	+	4.56218i	0.444518	+	0.256643i
$317$	−9.52056			−0.534728			−0.267364	−	0.963596i	$-0.586153\pi$
$317$	−9.52056			−0.534728			−0.267364	+	0.963596i	$0.586153\pi$
$318$	−0.896575	−	0.517638i	−0.0502775	−	0.0290277i
$319$	−31.4186	+	8.41858i	−1.75910	+	0.471350i
$320$		0			0
$321$	−3.46410	+	6.00000i	−0.193347	+	0.334887i
$322$		0			0
$323$	22.7661	+	39.4321i	1.26674	+	2.19406i
$324$	−1.73205			−0.0962250
$325$		0			0
$326$	12.9282			0.716027
$327$	−5.86491	−	10.1583i	−0.324330	−	0.561756i
$328$	−1.27551	+	4.76028i	−0.0704284	+	0.262842i
$329$		0			0
$330$		0			0
$331$	−7.92820	+	2.12436i	−0.435773	+	0.116765i	−0.470035	−	0.882648i	$-0.655759\pi$
$331$	−7.92820	+	2.12436i	−0.435773	+	0.116765i	0.0342616	+	0.999413i	$0.489092\pi$
$332$	25.6639	+	14.8171i	1.40849	+	0.813192i
$333$	6.83083			0.374327
$334$	13.3301	+	7.69615i	0.729392	+	0.421115i
$335$		0			0
$336$		0			0
$337$	22.4243	+	22.4243i	1.22153	+	1.22153i	0.967087	+	0.254445i	$0.0818926\pi$
$337$	22.4243	+	22.4243i	1.22153	+	1.22153i	0.254445	+	0.967087i	$0.418107\pi$
$338$	−11.7112	−	22.2163i	−0.637007	−	1.20841i
$339$		−	7.80385i		−	0.423847i
$340$		0			0
$341$	13.0981	+	22.6865i	0.709301	+	1.22854i
$342$	−13.7124	+	3.67423i	−0.741483	+	0.198680i
$343$		0			0
$344$	−0.0262794	−	0.0980762i	−0.00141689	−	0.00528791i
$345$		0			0
$346$	8.92820	−	8.92820i	0.479983	−	0.479983i
$347$	−6.91378	−	25.8026i	−0.371151	−	1.38516i	−0.858887	−	0.512165i	$-0.828844\pi$
$347$	−6.91378	−	25.8026i	−0.371151	−	1.38516i	0.487736	−	0.872991i	$-0.337823\pi$
$348$	−8.81345	−	2.36156i	−0.472451	−	0.126593i
$349$	1.33013	−	4.96410i	0.0712001	−	0.265722i	−0.921145	−	0.389220i	$-0.872745\pi$
$349$	1.33013	−	4.96410i	0.0712001	−	0.265722i	0.992345	+	0.123498i	$0.0394112\pi$
$350$		0			0
$351$	−2.59808	+	2.50000i	−0.138675	+	0.133440i
$352$	33.1325	−	33.1325i	1.76597	−	1.76597i
$353$	−26.7685	+	15.4548i	−1.42474	+	0.822577i	−0.996699	−	0.0811806i	$-0.974131\pi$
$353$	−26.7685	+	15.4548i	−1.42474	+	0.822577i	−0.428045	+	0.903757i	$0.640798\pi$
$354$	−1.09808	+	0.633975i	−0.0583621	+	0.0336954i
$355$		0			0
$356$	10.2679	+	10.2679i	0.544200	+	0.544200i
$357$		0			0
$358$	−8.36516	+	14.4889i	−0.442113	+	0.765761i
$359$	−17.5885	−	17.5885i	−0.928283	−	0.928283i	0.0693118	−	0.997595i	$-0.477920\pi$
$359$	−17.5885	−	17.5885i	−0.928283	−	0.928283i	−0.997595	+	0.0693118i	$0.977920\pi$
$360$		0			0
$361$	−30.3109	+	17.5000i	−1.59531	+	0.921053i
$362$	−39.1361	+	22.5952i	−2.05695	+	1.18758i
$363$	19.1798	−	19.1798i	1.00668	−	1.00668i
$364$		0			0
$365$		0			0
$366$	4.59808	−	17.1603i	0.240345	−	0.896981i
$367$	3.15660	+	0.845807i	0.164773	+	0.0441508i	0.340262	−	0.940331i	$-0.389484\pi$
$367$	3.15660	+	0.845807i	0.164773	+	0.0441508i	−0.175489	+	0.984481i	$0.556151\pi$
$368$	0.309587	+	1.15539i	0.0161383	+	0.0602291i
$369$	−6.73205	+	6.73205i	−0.350457	+	0.350457i
$370$		0			0
$371$		0			0
$372$			7.34847i			0.381000i
$373$	−15.4362	+	4.13613i	−0.799258	+	0.214160i	−0.635258	−	0.772300i	$-0.719106\pi$
$373$	−15.4362	+	4.13613i	−0.799258	+	0.214160i	−0.164000	+	0.986460i	$0.552440\pi$
$374$	−36.9545	−	64.0070i	−1.91087	−	3.30973i
$375$		0			0
$376$		−	0.732051i		−	0.0377526i
$377$	−16.6288	+	9.17878i	−0.856426	+	0.472731i
$378$		0			0
$379$	16.5622	+	4.43782i	0.850742	+	0.227956i	0.657742	−	0.753243i	$-0.271512\pi$
$379$	16.5622	+	4.43782i	0.850742	+	0.227956i	0.193000	+	0.981199i	$0.438178\pi$
$380$		0			0
$381$	−2.19615	−	1.26795i	−0.112512	−	0.0649590i
$382$	−9.00292			−0.460629
$383$	25.0076	+	14.4381i	1.27783	+	0.737753i	0.976448	−	0.215751i	$-0.0692200\pi$
$383$	25.0076	+	14.4381i	1.27783	+	0.737753i	0.301378	+	0.953505i	$0.402553\pi$
$384$	−3.96410	+	1.06218i	−0.202292	+	0.0542040i
$385$		0			0
$386$	−19.9904	+	34.6244i	−1.01748	+	1.76233i
$387$	0.0507680	−	0.189469i	0.00258068	−	0.00963123i
$388$	−7.46859	−	12.9360i	−0.379160	−	0.656725i
$389$	−21.0718			−1.06838			−0.534191	−	0.845364i	$-0.679384\pi$
$389$	−21.0718			−1.06838			−0.534191	+	0.845364i	$0.679384\pi$
$390$		0			0
$391$	1.66025			0.0839627
$392$	1.81173	+	3.13801i	0.0915064	+	0.158494i
$393$	−3.10583	+	11.5911i	−0.156668	+	0.584694i
$394$	23.6603	−	40.9808i	1.19199	−	2.06458i
$395$		0			0
$396$	10.3301	−	2.76795i	0.519108	−	0.139095i
$397$	−9.46979	−	5.46739i	−0.475275	−	0.274400i	0.243170	−	0.969984i	$-0.421813\pi$
$397$	−9.46979	−	5.46739i	−0.475275	−	0.274400i	−0.718445	+	0.695583i	$0.755146\pi$
$398$	−28.4601			−1.42658
$399$		0			0
$400$		0			0
$401$	−24.0263	−	6.43782i	−1.19982	−	0.321489i	−0.397057	−	0.917794i	$-0.629968\pi$
$401$	−24.0263	−	6.43782i	−1.19982	−	0.321489i	−0.802758	+	0.596305i	$0.796635\pi$
$402$	−3.34607	−	3.34607i	−0.166887	−	0.166887i
$403$	10.6066	+	11.0227i	0.528352	+	0.549080i
$404$		−	26.1962i		−	1.30331i
$405$		0			0
$406$		0			0
$407$	−40.7398	+	10.9162i	−2.01940	+	0.541095i
$408$			3.20736i			0.158788i
$409$	5.50962	+	20.5622i	0.272433	+	1.01673i	0.957542	+	0.288294i	$0.0930879\pi$
$409$	5.50962	+	20.5622i	0.272433	+	1.01673i	−0.685109	+	0.728441i	$0.740245\pi$
$410$		0			0
$411$	0.928203	−	0.928203i	0.0457849	−	0.0457849i
$412$	−5.70762	−	21.3011i	−0.281194	−	1.04943i
$413$		0			0
$414$	−0.133975	+	0.500000i	−0.00658449	+	0.0245737i
$415$		0			0
$416$	14.1340	−	23.4282i	0.692975	−	1.14866i
$417$	−2.96713	+	2.96713i	−0.145301	+	0.145301i
$418$	75.9106	−	43.8270i	3.71291	−	2.14365i
$419$	−12.0622	+	6.96410i	−0.589276	+	0.340219i	−0.764811	−	0.644255i	$-0.777168\pi$
$419$	−12.0622	+	6.96410i	−0.589276	+	0.340219i	0.175535	+	0.984473i	$0.443834\pi$
$420$		0			0
$421$	−25.8301	−	25.8301i	−1.25888	−	1.25888i	−0.951627	−	0.307257i	$-0.900589\pi$
$421$	−25.8301	−	25.8301i	−1.25888	−	1.25888i	−0.307257	−	0.951627i	$-0.599411\pi$
$422$	1.79315	−	3.10583i	0.0872892	−	0.151189i
$423$	0.707107	−	1.22474i	0.0343807	−	0.0595491i
$424$	−0.196152	−	0.196152i	−0.00952600	−	0.00952600i
$425$		0			0
$426$	−19.6244	+	11.3301i	−0.950803	+	0.548946i
$427$		0			0
$428$	8.48528	−	8.48528i	0.410152	−	0.410152i
$429$	11.5000	−	19.0622i	0.555225	−	0.920331i
$430$		0			0
$431$	1.72243	−	6.42820i	0.0829666	−	0.309636i	−0.911955	−	0.410291i	$-0.865427\pi$
$431$	1.72243	−	6.42820i	0.0829666	−	0.309636i	0.994921	+	0.100655i	$0.0320939\pi$
$432$	−4.31199	−	1.15539i	−0.207461	−	0.0555889i
$433$	−7.51936	−	28.0626i	−0.361357	−	1.34860i	−0.872293	−	0.488984i	$-0.837368\pi$
$433$	−7.51936	−	28.0626i	−0.361357	−	1.34860i	0.510935	−	0.859619i	$-0.329299\pi$
$434$		0			0
$435$		0			0
$436$	5.25833	+	19.6244i	0.251828	+	0.939836i
$437$			1.96902i			0.0941908i
$438$	6.24384	−	1.67303i	0.298342	−	0.0799406i
$439$	0.803848	+	1.39230i	0.0383656	+	0.0664511i	0.884571	−	0.466406i	$-0.154452\pi$
$439$	0.803848	+	1.39230i	0.0383656	+	0.0664511i	−0.846205	+	0.532857i	$0.821118\pi$
$440$		0			0
$441$			7.00000i			0.333333i
$442$	−29.9251	−	31.0991i	−1.42339	−	1.47923i
$443$	−19.5080	−	19.5080i	−0.926852	−	0.926852i	0.0706489	−	0.997501i	$-0.477493\pi$
$443$	−19.5080	−	19.5080i	−0.926852	−	0.926852i	−0.997501	+	0.0706489i	$0.977493\pi$
$444$	−11.4282	−	3.06218i	−0.542359	−	0.145325i
$445$		0			0
$446$	−0.633975	−	0.366025i	−0.0300196	−	0.0173318i
$447$	15.0759			0.713064
$448$		0			0
$449$	−10.0000	+	2.67949i	−0.471929	+	0.126453i	−0.486942	−	0.873434i	$-0.661888\pi$
$449$	−10.0000	+	2.67949i	−0.471929	+	0.126453i	0.0150129	+	0.999887i	$0.495221\pi$
$450$		0			0
$451$	29.3923	−	50.9090i	1.38403	−	2.39721i
$452$	−3.49837	+	13.0561i	−0.164549	+	0.614107i
$453$	−4.62158	−	8.00481i	−0.217141	−	0.376099i
$454$	−17.3923			−0.816261
$455$		0			0
$456$	−3.80385			−0.178131
$457$	8.22646	+	14.2487i	0.384818	+	0.666524i	0.991744	−	0.128234i	$-0.0409310\pi$
$457$	8.22646	+	14.2487i	0.384818	+	0.666524i	−0.606926	+	0.794758i	$0.707598\pi$
$458$	13.7818	−	51.4343i	0.643980	−	2.40337i
$459$	−3.09808	+	5.36603i	−0.144606	+	0.250465i
$460$		0			0
$461$	−10.8301	+	2.90192i	−0.504409	+	0.135156i	−0.502046	−	0.864841i	$-0.667419\pi$
$461$	−10.8301	+	2.90192i	−0.504409	+	0.135156i	−0.00236369	+	0.999997i	$0.500752\pi$
$462$		0			0
$463$	34.2185			1.59027			0.795135	−	0.606433i	$-0.207400\pi$
$463$	34.2185			1.59027			0.795135	+	0.606433i	$0.207400\pi$
$464$	−20.3660	−	11.7583i	−0.945469	−	0.545867i
$465$		0			0
$466$	15.2942	+	4.09808i	0.708491	+	0.189840i
$467$	0.0879327	+	0.0879327i	0.00406904	+	0.00406904i	0.709138	−	0.705069i	$-0.249084\pi$
$467$	0.0879327	+	0.0879327i	0.00406904	+	0.00406904i	−0.705069	+	0.709138i	$0.749084\pi$
$468$	5.46739	−	3.01790i	0.252730	−	0.139502i
$469$		0			0
$470$		0			0
$471$	5.69615	+	9.86603i	0.262465	+	0.454602i
$472$	−0.328169	+	0.0879327i	−0.0151052	+	0.00404743i
$473$			1.21114i			0.0556884i
$474$	2.63397	+	9.83013i	0.120982	+	0.451513i
$475$		0			0
$476$		0			0
$477$	−0.138701	−	0.517638i	−0.00635067	−	0.0237010i
$478$	−13.9712	−	3.74358i	−0.639030	−	0.171228i
$479$	−0.222432	+	0.830127i	−0.0101632	+	0.0379295i	−0.970821	−	0.239804i	$-0.922917\pi$
$479$	−0.222432	+	0.830127i	−0.0101632	+	0.0379295i	0.960658	+	0.277734i	$0.0895833\pi$
$480$		0			0
$481$	−21.5622	+	11.9019i	−0.983151	+	0.542681i
$482$	−14.9372	+	14.9372i	−0.680370	+	0.680370i
$483$		0			0
$484$	−40.6865	+	23.4904i	−1.84939	+	1.06774i
$485$		0			0
$486$	−1.36603	−	1.36603i	−0.0619642	−	0.0619642i
$487$	−6.78006	+	11.7434i	−0.307234	+	0.532145i	−0.977756	−	0.209745i	$-0.932737\pi$
$487$	−6.78006	+	11.7434i	−0.307234	+	0.532145i	0.670522	+	0.741889i	$0.266070\pi$
$488$	2.38014	−	4.12252i	0.107744	−	0.186618i
$489$	4.73205	+	4.73205i	0.213991	+	0.213991i
$490$		0			0
$491$	−7.79423	+	4.50000i	−0.351749	+	0.203082i	−0.665455	−	0.746438i	$-0.731763\pi$
$491$	−7.79423	+	4.50000i	−0.351749	+	0.203082i	0.313707	+	0.949520i	$0.398429\pi$
$492$	14.2808	−	8.24504i	0.643830	−	0.371715i
$493$	−23.0807	+	23.0807i	−1.03950	+	1.03950i
$494$	36.8827	−	35.4904i	1.65943	−	1.59679i
$495$		0			0
$496$	−4.90192	+	18.2942i	−0.220103	+	0.821435i
$497$		0			0
$498$	8.55463	+	31.9263i	0.383342	+	1.43065i
$499$	25.3205	−	25.3205i	1.13350	−	1.13350i	0.143911	−	0.989591i	$-0.454032\pi$
$499$	25.3205	−	25.3205i	1.13350	−	1.13350i	0.989591	−	0.143911i	$-0.0459679\pi$
$500$		0			0
$501$	2.06218	+	7.69615i	0.0921313	+	0.343839i
$502$			50.0894i			2.23560i
$503$	6.81225	−	1.82534i	0.303743	−	0.0813877i	−0.103728	−	0.994606i	$-0.533077\pi$
$503$	6.81225	−	1.82534i	0.303743	−	0.0813877i	0.407471	+	0.913218i	$0.366411\pi$
$504$		0			0
$505$		0			0
$506$		−	3.19615i		−	0.142086i
$507$	3.84512	−	12.4183i	0.170768	−	0.551518i
$508$	3.10583	+	3.10583i	0.137799	+	0.137799i
$509$	−2.36603	−	0.633975i	−0.104872	−	0.0281004i	0.206001	−	0.978552i	$-0.433955\pi$
$509$	−2.36603	−	0.633975i	−0.104872	−	0.0281004i	−0.310874	+	0.950451i	$0.600622\pi$
$510$		0			0
$511$		0			0
$512$	29.2552			1.29291
$513$	−6.36396	−	3.67423i	−0.280976	−	0.162221i
$514$	−17.0263	+	4.56218i	−0.750997	+	0.201229i
$515$		0			0
$516$	−0.169873	+	0.294229i	−0.00747824	+	0.0129527i
$517$	−2.26002	+	8.43451i	−0.0993956	+	0.370949i
$518$		0			0
$519$	6.53590			0.286894
$520$		0			0
$521$	−3.60770			−0.158056			−0.0790280	−	0.996872i	$-0.525182\pi$
$521$	−3.60770			−0.158056			−0.0790280	+	0.996872i	$0.525182\pi$
$522$	−5.08845	−	8.81345i	−0.222715	−	0.385754i
$523$	−6.16089	+	22.9928i	−0.269397	+	1.00540i	0.690107	+	0.723707i	$0.257563\pi$
$523$	−6.16089	+	22.9928i	−0.269397	+	1.00540i	−0.959504	+	0.281695i	$0.909103\pi$
$524$	10.3923	−	18.0000i	0.453990	−	0.786334i
$525$		0			0
$526$	18.8923	−	5.06218i	0.823744	−	0.220721i
$527$	22.7661	+	13.1440i	0.991708	+	0.572563i
$528$	27.5636			1.19955
$529$	−19.8564	−	11.4641i	−0.863322	−	0.498439i
$530$		0			0
$531$	−0.633975	−	0.169873i	−0.0275122	−	0.00737186i
$532$		0			0
$533$	9.52056	−	32.9802i	0.412381	−	1.42853i
$534$			16.1962i			0.700876i
$535$		0			0
$536$	−0.633975	−	1.09808i	−0.0273835	−	0.0474297i
$537$	−8.36516	+	2.24144i	−0.360983	+	0.0967252i
$538$		−	15.0759i		−	0.649967i
$539$	−11.1865	−	41.7487i	−0.481838	−	1.79824i
$540$		0			0
$541$	4.56218	−	4.56218i	0.196143	−	0.196143i	−0.602201	−	0.798344i	$-0.705709\pi$
$541$	4.56218	−	4.56218i	0.196143	−	0.196143i	0.798344	+	0.602201i	$0.205709\pi$
$542$	−7.63947	−	28.5109i	−0.328144	−	1.22465i
$543$	−22.5952	−	6.05437i	−0.969654	−	0.259818i
$544$	12.1699	−	45.4186i	0.521779	−	1.94731i
$545$		0			0
$546$		0			0
$547$	11.3137	−	11.3137i	0.483739	−	0.483739i	−0.422584	−	0.906324i	$-0.638877\pi$
$547$	11.3137	−	11.3137i	0.483739	−	0.483739i	0.906324	+	0.422584i	$0.138877\pi$
$548$	−1.96902	+	1.13681i	−0.0841122	+	0.0485622i
$549$	7.96410	−	4.59808i	0.339900	−	0.196241i
$550$		0			0
$551$	−27.3731	−	27.3731i	−1.16613	−	1.16613i
$552$	−0.0693504	+	0.120118i	−0.00295175	+	0.00511258i
$553$		0			0
$554$	21.5622	+	21.5622i	0.916089	+	0.916089i
$555$		0			0
$556$	6.29423	−	3.63397i	0.266935	−	0.154115i
$557$	−8.15711	+	4.70951i	−0.345628	+	0.199548i	−0.662758	−	0.748834i	$-0.730614\pi$
$557$	−8.15711	+	4.70951i	−0.345628	+	0.199548i	0.317130	+	0.948382i	$0.397281\pi$
$558$	−5.79555	+	5.79555i	−0.245345	+	0.245345i
$559$	0.169873	+	0.686533i	0.00718486	+	0.0290373i
$560$		0			0
$561$	9.90192	−	36.9545i	0.418060	−	1.56022i
$562$	13.1948	+	3.53553i	0.556589	+	0.149137i
$563$	3.40181	+	12.6957i	0.143369	+	0.535061i	0.999823	+	0.0188369i	$0.00599634\pi$
$563$	3.40181	+	12.6957i	0.143369	+	0.535061i	−0.856453	+	0.516225i	$0.827337\pi$
$564$	−1.73205	+	1.73205i	−0.0729325	+	0.0729325i
$565$		0			0
$566$	−0.267949	−	1.00000i	−0.0112627	−	0.0420331i
$567$		0			0
$568$	−5.86491	+	1.57150i	−0.246086	+	0.0659385i
$569$	1.75833	+	3.04552i	0.0737130	+	0.127675i	0.900526	−	0.434802i	$-0.143182\pi$
$569$	1.75833	+	3.04552i	0.0737130	+	0.127675i	−0.826813	+	0.562477i	$0.809848\pi$
$570$		0			0
$571$			24.5359i			1.02680i	0.858151	+	0.513398i	$0.171613\pi$
$571$			24.5359i			1.02680i	−0.858151	+	0.513398i	$0.828387\pi$
$572$	−27.7852	+	26.7363i	−1.16176	+	1.11790i
$573$	−3.29530	−	3.29530i	−0.137663	−	0.137663i
$574$		0			0
$575$		0			0
$576$	4.96410	+	2.86603i	0.206838	+	0.119418i
$577$	18.0430			0.751140			0.375570	−	0.926794i	$-0.377447\pi$
$577$	18.0430			0.751140			0.375570	+	0.926794i	$0.377447\pi$
$578$	−35.7900	−	20.6634i	−1.48867	−	0.859483i
$579$	−19.9904	+	5.35641i	−0.830772	+	0.222605i
$580$		0			0
$581$		0			0
$582$	4.31199	−	16.0926i	0.178738	−	0.667058i
$583$	1.65445	+	2.86559i	0.0685203	+	0.118681i
$584$	1.73205			0.0716728
$585$		0			0
$586$	−23.1244			−0.955258
$587$	−5.31010	−	9.19737i	−0.219171	−	0.379616i	0.735383	−	0.677651i	$-0.237002\pi$
$587$	−5.31010	−	9.19737i	−0.219171	−	0.379616i	−0.954555	+	0.298035i	$0.903669\pi$
$588$	3.13801	−	11.7112i	0.129410	−	0.482963i
$589$	−15.5885	+	27.0000i	−0.642311	+	1.11252i
$590$		0			0
$591$	23.6603	−	6.33975i	0.973253	−	0.260782i
$592$	−26.4082	−	15.2468i	−1.08537	−	0.626638i
$593$	27.0459			1.11064			0.555321	−	0.831636i	$-0.312595\pi$
$593$	27.0459			1.11064			0.555321	+	0.831636i	$0.312595\pi$
$594$	10.3301	+	5.96410i	0.423850	+	0.244710i
$595$		0			0
$596$	−25.2224	−	6.75833i	−1.03315	−	0.276832i
$597$	−10.4171	−	10.4171i	−0.426345	−	0.426345i
$598$	−0.448288	−	1.81173i	−0.0183318	−	0.0740873i
$599$		−	1.39230i		−	0.0568880i	−0.999595	−	0.0284440i	$-0.990945\pi$
$599$		−	1.39230i		−	0.0568880i	0.999595	−	0.0284440i	$-0.00905523\pi$
$600$		0			0
$601$	15.2679	+	26.4449i	0.622793	+	1.07871i	0.988963	+	0.148161i	$0.0473353\pi$
$601$	15.2679	+	26.4449i	0.622793	+	1.07871i	−0.366171	+	0.930548i	$0.619331\pi$
$602$		0			0
$603$		−	2.44949i		−	0.0997509i
$604$	4.14359	+	15.4641i	0.168600	+	0.629225i
$605$		0			0
$606$	20.6603	−	20.6603i	0.839265	−	0.839265i
$607$	−7.77817	−	29.0285i	−0.315706	−	1.17823i	−0.923330	−	0.384007i	$-0.874544\pi$
$607$	−7.77817	−	29.0285i	−0.315706	−	1.17823i	0.607624	−	0.794225i	$-0.292123\pi$
$608$	53.8652	+	14.4331i	2.18452	+	0.585341i
$609$		0			0
$610$		0			0
$611$	−0.0980762	+	5.09808i	−0.00396774	+	0.206246i
$612$	7.58871	−	7.58871i	0.306755	−	0.306755i
$613$	18.4355	−	10.6438i	0.744605	−	0.429898i	−0.0791365	−	0.996864i	$-0.525216\pi$
$613$	18.4355	−	10.6438i	0.744605	−	0.429898i	0.823741	+	0.566966i	$0.191883\pi$
$614$	−46.3468	+	26.7583i	−1.87040	+	1.07988i
$615$		0			0
$616$		0			0
$617$	9.76079	−	16.9062i	0.392955	−	0.680618i	−0.599883	−	0.800088i	$-0.704786\pi$
$617$	9.76079	−	16.9062i	0.392955	−	0.680618i	0.992838	+	0.119470i	$0.0381196\pi$
$618$	12.2982	−	21.3011i	0.494707	−	0.856857i
$619$	−21.4641	−	21.4641i	−0.862715	−	0.862715i	0.128938	−	0.991653i	$-0.458843\pi$
$619$	−21.4641	−	21.4641i	−0.862715	−	0.862715i	−0.991653	+	0.128938i	$0.958843\pi$
$620$		0			0
$621$	−0.232051	+	0.133975i	−0.00931188	+	0.00537622i
$622$	−38.2395	+	22.0776i	−1.53326	+	0.885231i
$623$		0			0
$624$	15.6244	−	3.86603i	0.625475	−	0.154765i
$625$		0			0
$626$	−1.06218	+	3.96410i	−0.0424532	+	0.158437i
$627$	43.8270	+	11.7434i	1.75028	+	0.468987i
$628$	−5.10703	−	19.0597i	−0.203793	−	0.760565i
$629$	−29.9282	+	29.9282i	−1.19332	+	1.19332i
$630$		0			0
$631$	6.29423	+	23.4904i	0.250569	+	0.935137i	0.970502	+	0.241093i	$0.0775060\pi$
$631$	6.29423	+	23.4904i	0.250569	+	0.935137i	−0.719933	+	0.694044i	$0.755827\pi$
$632$			2.72689i			0.108470i
$633$	1.79315	−	0.480473i	0.0712714	−	0.0190971i
$634$	9.19615	+	15.9282i	0.365226	+	0.632590i
$635$		0			0
$636$			0.928203i			0.0368057i
$637$	−12.1967	−	22.0962i	−0.483250	−	0.875482i
$638$	44.4326	+	44.4326i	1.75910	+	1.75910i
$639$	−11.3301	−	3.03590i	−0.448213	−	0.120098i
$640$		0			0
$641$	−30.9282	−	17.8564i	−1.22159	−	0.705286i	−0.256334	−	0.966588i	$-0.582515\pi$
$641$	−30.9282	−	17.8564i	−1.22159	−	0.705286i	−0.965257	+	0.261303i	$0.915848\pi$
$642$	13.3843			0.528235
$643$	26.0478	+	15.0387i	1.02723	+	0.593069i	0.916189	−	0.400747i	$-0.131250\pi$
$643$	26.0478	+	15.0387i	1.02723	+	0.593069i	0.111037	+	0.993816i	$0.464583\pi$
$644$		0			0
$645$		0			0
$646$	43.9808	−	76.1769i	1.73040	−	2.99714i
$647$	0.0557471	−	0.208051i	0.00219165	−	0.00817933i	−0.964821	−	0.262906i	$-0.915319\pi$
$647$	0.0557471	−	0.208051i	0.00219165	−	0.00817933i	0.967013	+	0.254727i	$0.0819856\pi$
$648$	−0.258819	−	0.448288i	−0.0101674	−	0.0176104i
$649$	4.05256			0.159077
$650$		0			0
$651$		0			0
$652$	−5.79555	−	10.0382i	−0.226971	−	0.393126i
$653$	−6.59059	+	24.5964i	−0.257910	+	0.962533i	0.708539	+	0.705672i	$0.249355\pi$
$653$	−6.59059	+	24.5964i	−0.257910	+	0.962533i	−0.966448	+	0.256861i	$0.917312\pi$
$654$	−11.3301	+	19.6244i	−0.443043	+	0.767373i
$655$		0			0
$656$	41.0526	−	11.0000i	1.60283	−	0.429478i
$657$	2.89778	+	1.67303i	0.113053	+	0.0652712i
$658$		0			0
$659$	26.0885	+	15.0622i	1.01626	+	0.586739i	0.913019	−	0.407917i	$-0.133745\pi$
$659$	26.0885	+	15.0622i	1.01626	+	0.586739i	0.103243	+	0.994656i	$0.467078\pi$
$660$		0			0
$661$	−6.36603	−	1.70577i	−0.247610	−	0.0663468i	0.132879	−	0.991132i	$-0.457578\pi$
$661$	−6.36603	−	1.70577i	−0.247610	−	0.0663468i	−0.380489	+	0.924785i	$0.624244\pi$
$662$	11.2122	+	11.2122i	0.435773	+	0.435773i
$663$	0.429705	−	22.3364i	0.0166884	−	0.867474i
$664$			8.85641i			0.343695i
$665$		0			0
$666$	−6.59808	−	11.4282i	−0.255670	−	0.442834i
$667$	−1.36345	+	0.365334i	−0.0527928	+	0.0141458i
$668$		−	13.8004i		−	0.533952i
$669$	−0.0980762	−	0.366025i	−0.00379185	−	0.0141514i
$670$		0			0
$671$	−40.1506	+	40.1506i	−1.55000	+	1.55000i
$672$		0			0
$673$	−6.05437	−	1.62226i	−0.233379	−	0.0625337i	0.140234	−	0.990118i	$-0.455215\pi$
$673$	−6.05437	−	1.62226i	−0.233379	−	0.0625337i	−0.373613	+	0.927585i	$0.621881\pi$
$674$	15.8564	−	59.1769i	0.610766	−	2.27941i
$675$		0			0
$676$	−12.0000	+	19.0526i	−0.461538	+	0.732791i
$677$	−19.5959	+	19.5959i	−0.753132	+	0.753132i	−0.975063	−	0.221930i	$-0.928764\pi$
$677$	−19.5959	+	19.5959i	−0.753132	+	0.753132i	0.221930	+	0.975063i	$0.428764\pi$
$678$	−13.0561	+	7.53794i	−0.501416	+	0.289493i
$679$		0			0
$680$		0			0
$681$	−6.36603	−	6.36603i	−0.243947	−	0.243947i
$682$	25.3035	−	43.8270i	0.968923	−	1.67822i
$683$	2.24144	−	3.88229i	0.0857663	−	0.148552i	−0.819951	−	0.572433i	$-0.806000\pi$
$683$	2.24144	−	3.88229i	0.0857663	−	0.148552i	0.905717	+	0.423882i	$0.139333\pi$
$684$	9.00000	+	9.00000i	0.344124	+	0.344124i
$685$		0			0
$686$		0			0
$687$	23.8707	−	13.7818i	0.910726	−	0.525808i
$688$	−0.619174	+	0.619174i	−0.0236058	+	0.0236058i
$689$	1.33975	+	1.39230i	0.0510403	+	0.0530426i
$690$		0			0
$691$	−10.3468	+	38.6147i	−0.393610	+	1.46897i	0.430524	+	0.902579i	$0.358329\pi$
$691$	−10.3468	+	38.6147i	−0.393610	+	1.46897i	−0.824134	+	0.566395i	$0.808338\pi$
$692$	−10.9348	−	2.92996i	−0.415678	−	0.111380i
$693$		0			0
$694$	−36.4904	+	36.4904i	−1.38516	+	1.38516i
$695$		0			0
$696$	−0.705771	−	2.63397i	−0.0267522	−	0.0998405i
$697$		−	58.9908i		−	2.23444i
$698$	−9.58991	+	2.56961i	−0.362983	+	0.0972611i
$699$	4.09808	+	7.09808i	0.155003	+	0.268474i
$700$		0			0
$701$			42.9282i			1.62138i	0.585479	+	0.810688i	$0.300907\pi$
$701$			42.9282i			1.62138i	−0.585479	+	0.810688i	$0.699093\pi$
$702$	6.69213	+	1.93185i	0.252578	+	0.0729130i
$703$	−35.4940	−	35.4940i	−1.33868	−	1.33868i
$704$	−34.1865	−	9.16025i	−1.28845	−	0.345240i
$705$		0			0
$706$	51.7128	+	29.8564i	1.94624	+	1.12366i
$707$		0			0
$708$	0.984508	+	0.568406i	0.0370001	+	0.0213620i
$709$	−44.7487	+	11.9904i	−1.68057	+	0.450308i	−0.967930	−	0.251219i	$-0.919169\pi$
$709$	−44.7487	+	11.9904i	−1.68057	+	0.450308i	−0.712643	+	0.701527i	$0.752502\pi$
$710$		0			0
$711$	−2.63397	+	4.56218i	−0.0987818	+	0.171095i
$712$	−1.12321	+	4.19187i	−0.0420940	+	0.157097i
$713$	0.568406	+	0.984508i	0.0212870	+	0.0368701i
$714$		0			0
$715$		0			0
$716$	15.0000			0.560576
$717$	−3.74358	−	6.48408i	−0.139807	−	0.242152i
$718$	−12.4369	+	46.4152i	−0.464142	+	1.73220i
$719$	−0.428203	+	0.741670i	−0.0159693	+	0.0276596i	−0.873900	−	0.486106i	$-0.838417\pi$
$719$	−0.428203	+	0.741670i	−0.0159693	+	0.0276596i	0.857930	+	0.513766i	$0.171750\pi$
$720$		0			0
$721$		0			0
$722$	58.5561	+	33.8074i	2.17923	+	1.25818i
$723$	−10.9348			−0.406669
$724$	35.0885	+	20.2583i	1.30405	+	0.752895i
$725$		0			0
$726$	−50.6147	−	13.5622i	−1.87849	−	0.503340i
$727$	−34.3944	−	34.3944i	−1.27562	−	1.27562i	−0.943096	−	0.332522i	$-0.892100\pi$
$727$	−34.3944	−	34.3944i	−1.27562	−	1.27562i	−0.332522	−	0.943096i	$-0.607900\pi$
$728$		0			0
$729$		−	1.00000i		−	0.0370370i
$730$		0			0
$731$	0.607695	+	1.05256i	0.0224764	+	0.0389303i
$732$	−15.3855	+	4.12252i	−0.568663	+	0.152373i
$733$			49.8120i			1.83985i	0.392095	+	0.919925i	$0.371751\pi$
$733$			49.8120i			1.83985i	−0.392095	+	0.919925i	$0.628249\pi$
$734$	−1.63397	−	6.09808i	−0.0603111	−	0.225084i
$735$		0			0
$736$	1.43782	−	1.43782i	0.0529988	−	0.0529988i
$737$	3.91447	+	14.6090i	0.144191	+	0.538130i
$738$	17.7656	+	4.76028i	0.653961	+	0.175228i
$739$	−12.1244	+	45.2487i	−0.446002	+	1.66450i	0.267277	+	0.963620i	$0.413876\pi$
$739$	−12.1244	+	45.2487i	−0.446002	+	1.66450i	−0.713278	+	0.700881i	$0.752790\pi$
$740$		0			0
$741$	26.4904	+	0.509619i	0.973148	+	0.0187213i
$742$		0			0
$743$	−30.4428	+	17.5761i	−1.11684	+	0.644806i	−0.940591	−	0.339541i	$-0.889728\pi$
$743$	−30.4428	+	17.5761i	−1.11684	+	0.644806i	−0.176245	+	0.984346i	$0.556395\pi$
$744$	−1.90192	+	1.09808i	−0.0697279	+	0.0402574i
$745$		0			0
$746$	21.8301	+	21.8301i	0.799258	+	0.799258i
$747$	−8.55463	+	14.8171i	−0.312998	+	0.542128i
$748$	−33.1325	+	57.3871i	−1.21144	+	2.09828i
$749$		0			0
$750$		0			0
$751$	−25.0070	+	14.4378i	−0.912520	+	0.526844i	−0.881241	−	0.472667i	$-0.843291\pi$
$751$	−25.0070	+	14.4378i	−0.912520	+	0.526844i	−0.0312788	+	0.999511i	$0.509958\pi$
$752$	−5.46739	+	3.15660i	−0.199375	+	0.115109i
$753$	−18.3340	+	18.3340i	−0.668128	+	0.668128i
$754$	31.4186	+	18.9545i	1.14420	+	0.690282i
$755$		0			0
$756$		0			0
$757$	−15.0759	−	4.03957i	−0.547942	−	0.146821i	−0.0257811	−	0.999668i	$-0.508207\pi$
$757$	−15.0759	−	4.03957i	−0.547942	−	0.146821i	−0.522161	+	0.852847i	$0.674874\pi$
$758$	−8.57321	−	31.9957i	−0.311393	−	1.16214i
$759$	1.16987	−	1.16987i	0.0424637	−	0.0424637i
$760$		0			0
$761$	−7.58846	−	28.3205i	−0.275081	−	1.02662i	−0.955787	−	0.294060i	$-0.904993\pi$
$761$	−7.58846	−	28.3205i	−0.275081	−	1.02662i	0.680705	−	0.732557i	$-0.261673\pi$
$762$			4.89898i			0.177471i
$763$		0			0
$764$	4.03590	+	6.99038i	0.146014	+	0.252903i
$765$		0			0
$766$		−	55.7846i		−	2.01558i
$767$	2.29719	−	0.568406i	0.0829466	−	0.0205240i
$768$	13.7124	+	13.7124i	0.494805	+	0.494805i
$769$	38.4904	+	10.3135i	1.38800	+	0.371913i	0.874020	−	0.485890i	$-0.161504\pi$
$769$	38.4904	+	10.3135i	1.38800	+	0.371913i	0.513979	+	0.857803i	$0.328171\pi$
$770$		0			0
$771$	−7.90192	−	4.56218i	−0.284581	−	0.164303i
$772$	35.8458			1.29012
$773$	−3.73861	−	2.15849i	−0.134468	−	0.0776353i	0.431257	−	0.902229i	$-0.358070\pi$
$773$	−3.73861	−	2.15849i	−0.134468	−	0.0776353i	−0.565725	+	0.824594i	$0.691404\pi$
$774$	−0.366025	+	0.0980762i	−0.0131565	+	0.00352528i
$775$		0			0
$776$	2.23205	−	3.86603i	0.0801260	−	0.138782i
$777$		0			0
$778$	20.3538	+	35.2538i	0.729719	+	1.26391i
$779$	69.9615			2.50663
$780$		0			0
$781$	72.4256			2.59159
$782$	−1.60368	−	2.77766i	−0.0573476	−	0.0993289i
$783$	1.36345	−	5.08845i	0.0487256	−	0.181846i
$784$	15.6244	−	27.0622i	0.558013	−	0.966506i
$785$		0			0
$786$	22.3923	−	6.00000i	0.798707	−	0.214013i
$787$	7.02030	+	4.05317i	0.250247	+	0.144480i	0.619877	−	0.784699i	$-0.287182\pi$
$787$	7.02030	+	4.05317i	0.250247	+	0.144480i	−0.369631	+	0.929179i	$0.620516\pi$
$788$	−42.4264			−1.51138
$789$	8.76795	+	5.06218i	0.312147	+	0.180218i
$790$		0			0
$791$		0			0
$792$	2.26002	+	2.26002i	0.0803064	+	0.0803064i
$793$	−17.1278	+	28.3908i	−0.608228	+	1.00819i
$794$			21.1244i			0.749675i
$795$		0			0
$796$	12.7583	+	22.0981i	0.452207	+	0.783246i
$797$	47.0715	−	12.6128i	1.66736	−	0.446768i	0.702963	−	0.711227i	$-0.251860\pi$
$797$	47.0715	−	12.6128i	1.66736	−	0.446768i	0.964397	+	0.264459i	$0.0851934\pi$
$798$		0			0
$799$	2.26795	+	8.46410i	0.0802343	+	0.299438i
$800$		0			0
$801$	−5.92820	+	5.92820i	−0.209463	+	0.209463i
$802$	12.4369	+	46.4152i	0.439163	+	1.63898i
$803$	−19.9563	−	5.34727i	−0.704242	−	0.188701i
$804$	−1.09808	+	4.09808i	−0.0387262	+	0.144528i
$805$		0			0
$806$	8.19615	−	28.3923i	0.288697	−	1.00008i
$807$	5.51815	−	5.51815i	0.194248	−	0.194248i
$808$	6.78006	−	3.91447i	0.238522	−	0.137711i
$809$	11.3205	−	6.53590i	0.398008	−	0.229790i	−0.287616	−	0.957746i	$-0.592863\pi$
$809$	11.3205	−	6.53590i	0.398008	−	0.229790i	0.685624	+	0.727956i	$0.259529\pi$
$810$		0			0
$811$	23.7846	+	23.7846i	0.835191	+	0.835191i	0.988221	−	0.153031i	$-0.0489034\pi$
$811$	23.7846	+	23.7846i	0.835191	+	0.835191i	−0.153031	+	0.988221i	$0.548903\pi$
$812$		0			0
$813$	7.63947	−	13.2320i	0.267928	−	0.464065i
$814$	57.6147	+	57.6147i	2.01940	+	2.01940i
$815$		0			0
$816$	23.9545	−	13.8301i	0.838575	−	0.484151i
$817$	−1.24831	+	0.720710i	−0.0436727	+	0.0252145i
$818$	29.0793	−	29.0793i	1.01673	−	1.01673i
$819$		0			0
$820$		0			0
$821$	−1.04552	+	3.90192i	−0.0364888	+	0.136178i	−0.981767	−	0.190086i	$-0.939123\pi$
$821$	−1.04552	+	3.90192i	−0.0364888	+	0.136178i	0.945279	+	0.326264i	$0.105790\pi$
$822$	−2.44949	−	0.656339i	−0.0854358	−	0.0228924i
$823$	−9.24316	−	34.4959i	−0.322196	−	1.20245i	−0.917101	−	0.398656i	$-0.869477\pi$
$823$	−9.24316	−	34.4959i	−0.322196	−	1.20245i	0.594904	−	0.803796i	$-0.297190\pi$
$824$	4.66025	−	4.66025i	0.162348	−	0.162348i
$825$		0			0
$826$		0			0
$827$		−	36.7052i		−	1.27636i	−0.769885	−	0.638182i	$-0.779687\pi$
$827$		−	36.7052i		−	1.27636i	0.769885	−	0.638182i	$-0.220313\pi$
$828$	0.448288	−	0.120118i	0.0155791	−	0.00417440i
$829$	−1.00000	−	1.73205i	−0.0347314	−	0.0601566i	0.848137	−	0.529777i	$-0.177724\pi$
$829$	−1.00000	−	1.73205i	−0.0347314	−	0.0601566i	−0.882869	+	0.469620i	$0.844391\pi$
$830$		0			0
$831$			15.7846i			0.547562i
$832$	−20.6634	−	0.397520i	−0.716374	−	0.0137815i
$833$	−30.6694	−	30.6694i	−1.06263	−	1.06263i
$834$	7.83013	+	2.09808i	0.271135	+	0.0726504i
$835$		0			0
$836$	−68.0596	−	39.2942i	−2.35389	−	1.35902i
$837$	−4.24264			−0.146647
$838$	23.3023	+	13.4536i	0.804966	+	0.464747i
$839$	−13.5263	+	3.62436i	−0.466979	+	0.125127i	−0.484633	−	0.874718i	$-0.661047\pi$
$839$	−13.5263	+	3.62436i	−0.466979	+	0.125127i	0.0176541	+	0.999844i	$0.494380\pi$
$840$		0			0
$841$	−0.624356	+	1.08142i	−0.0215295	+	0.0372902i
$842$	−18.2647	+	68.1646i	−0.629442	+	2.34911i
$843$	3.53553	+	6.12372i	0.121770	+	0.210912i
$844$	−3.21539			−0.110678
$845$		0			0
$846$	−2.73205			−0.0939298
$847$		0			0
$848$	−0.619174	+	2.31079i	−0.0212625	+	0.0793528i
$849$	0.267949	−	0.464102i	0.00919599	−	0.0159279i
$850$		0			0
$851$	−1.76795	+	0.473721i	−0.0606045	+	0.0162389i
$852$	17.5947	+	10.1583i	0.602785	+	0.348018i
$853$	−43.9149			−1.50362			−0.751810	−	0.659380i	$-0.770819\pi$
$853$	−43.9149			−1.50362			−0.751810	+	0.659380i	$0.770819\pi$
$854$		0			0
$855$		0			0
$856$	3.46410	+	0.928203i	0.118401	+	0.0317253i
$857$	23.4225	+	23.4225i	0.800096	+	0.800096i	0.983110	−	0.183014i	$-0.0585855\pi$
$857$	23.4225	+	23.4225i	0.800096	+	0.800096i	−0.183014	+	0.983110i	$0.558585\pi$
$858$	−42.9998	−	0.827225i	−1.46799	−	0.0282410i
$859$		−	37.4641i		−	1.27826i	−0.769099	−	0.639129i	$-0.779295\pi$
$859$		−	37.4641i		−	1.27826i	0.769099	−	0.639129i	$-0.220705\pi$
$860$		0			0
$861$		0			0
$862$	−12.4183	+	3.32748i	−0.422970	+	0.113335i
$863$			34.0526i			1.15916i	0.814914	+	0.579582i	$0.196784\pi$
$863$			34.0526i			1.15916i	−0.814914	+	0.579582i	$0.803216\pi$
$864$	1.96410	+	7.33013i	0.0668201	+	0.249376i
$865$		0			0
$866$	−39.6865	+	39.6865i	−1.34860	+	1.34860i
$867$	−5.53674	−	20.6634i	−0.188037	−	0.701765i
$868$		0			0
$869$	8.41858	−	31.4186i	0.285581	−	1.06580i
$870$		0			0
$871$	4.26795	+	7.73205i	0.144614	+	0.261991i
$872$	−4.29341	+	4.29341i	−0.145393	+	0.145393i
$873$	7.46859	−	4.31199i	0.252773	−	0.145939i
$874$	3.29423	−	1.90192i	0.111429	−	0.0643335i
$875$		0			0
$876$	−4.09808	−	4.09808i	−0.138461	−	0.138461i
$877$	4.93117	−	8.54103i	0.166514	−	0.288410i	−0.770678	−	0.637225i	$-0.780082\pi$
$877$	4.93117	−	8.54103i	0.166514	−	0.288410i	0.937192	+	0.348815i	$0.113416\pi$
$878$	1.55291	−	2.68973i	0.0524083	−	0.0907739i
$879$	−8.46410	−	8.46410i	−0.285487	−	0.285487i
$880$		0			0
$881$	−9.80385	+	5.66025i	−0.330300	+	0.190699i	−0.655974	−	0.754783i	$-0.727742\pi$
$881$	−9.80385	+	5.66025i	−0.330300	+	0.190699i	0.325674	+	0.945482i	$0.394409\pi$
$882$	11.7112	−	6.76148i	0.394338	−	0.227671i
$883$	−8.34658	+	8.34658i	−0.280885	+	0.280885i	−0.833462	−	0.552577i	$-0.813645\pi$
$883$	−8.34658	+	8.34658i	−0.280885	+	0.280885i	0.552577	+	0.833462i	$0.313645\pi$
$884$	−10.7321	+	37.1769i	−0.360958	+	1.25039i
$885$		0			0
$886$	−13.7942	+	51.4808i	−0.463426	+	1.72953i
$887$	49.7105	+	13.3199i	1.66912	+	0.447238i	0.964872	−	0.262720i	$-0.0846197\pi$
$887$	49.7105	+	13.3199i	1.66912	+	0.447238i	0.704243	+	0.709959i	$0.251286\pi$
$888$	−0.915158	−	3.41542i	−0.0307107	−	0.114614i
$889$		0			0
$890$		0			0
$891$	1.59808	+	5.96410i	0.0535376	+	0.199805i
$892$			0.656339i			0.0219758i
$893$	−10.0382	+	2.68973i	−0.335915	+	0.0900083i
$894$	−14.5622	−	25.2224i	−0.487032	−	0.843564i
$895$		0			0
$896$		0			0
$897$	0.499056	−	0.827225i	0.0166630	−	0.0276202i
$898$	14.1421	+	14.1421i	0.471929	+	0.471929i
$899$	−21.5885	−	5.78461i	−0.720015	−	0.192928i
$900$		0			0
$901$	2.87564	+	1.66025i	0.0958016	+	0.0553111i
$902$	−113.563			−3.78124
$903$		0			0
$904$	−3.90192	+	1.04552i	−0.129776	+	0.0347734i
$905$		0			0
$906$	−8.92820	+	15.4641i	−0.296620	+	0.513760i
$907$	−9.93666	+	37.0841i	−0.329941	+	1.23136i	0.579309	+	0.815108i	$0.303323\pi$
$907$	−9.93666	+	37.0841i	−0.329941	+	1.23136i	−0.909250	+	0.416250i	$0.863344\pi$
$908$	7.79676	+	13.5044i	0.258744	+	0.448159i
$909$	15.1244			0.501643
$910$		0			0
$911$	22.9090			0.759008			0.379504	−	0.925190i	$-0.376095\pi$
$911$	22.9090			0.759008			0.379504	+	0.925190i	$0.376095\pi$
$912$	16.4022	+	28.4094i	0.543130	+	0.940728i
$913$	27.3419	−	102.041i	0.904885	−	3.37708i
$914$	15.8923	−	27.5263i	0.525671	−	0.910488i
$915$		0			0
$916$	−46.1147	+	12.3564i	−1.52367	+	0.408267i
$917$		0			0
$918$	11.9700			0.395070
$919$	−46.5167	−	26.8564i	−1.53444	−	0.885911i	−0.999149	−	0.0412453i	$-0.986867\pi$
$919$	−46.5167	−	26.8564i	−1.53444	−	0.885911i	−0.535294	−	0.844666i	$-0.679799\pi$
$920$		0			0
$921$	−26.7583	−	7.16987i	−0.881717	−	0.236255i
$922$	15.3161	+	15.3161i	0.504409	+	0.504409i
$923$	41.0543	−	10.1583i	1.35132	−	0.334365i
$924$		0			0
$925$		0			0
$926$	−33.0526	−	57.2487i	−1.08617	−	1.88131i
$927$	12.2982	−	3.29530i	0.403926	−	0.108232i
$928$			39.9769i			1.31231i
$929$	11.2750	+	42.0788i	0.369920	+	1.38056i	0.860626	+	0.509237i	$0.170072\pi$
$929$	11.2750	+	42.0788i	0.369920	+	1.38056i	−0.490706	+	0.871325i	$0.663261\pi$
$930$		0			0
$931$	36.3731	−	36.3731i	1.19208	−	1.19208i
$932$	−3.67423	−	13.7124i	−0.120354	−	0.449166i
$933$	−22.0776	−	5.91567i	−0.722788	−	0.193670i
$934$	0.0621778	−	0.232051i	0.00203452	−	0.00759293i
$935$		0			0
$936$	1.59808	+	0.964102i	0.0522348	+	0.0315126i
$937$	5.43022	−	5.43022i	0.177398	−	0.177398i	−0.612823	−	0.790220i	$-0.709966\pi$
$937$	5.43022	−	5.43022i	0.177398	−	0.177398i	0.790220	+	0.612823i	$0.209966\pi$
$938$		0			0
$939$	−1.83975	+	1.06218i	−0.0600378	+	0.0346629i
$940$		0			0
$941$	23.0000	+	23.0000i	0.749779	+	0.749779i	0.974437	−	0.224659i	$-0.0721268\pi$
$941$	23.0000	+	23.0000i	0.749779	+	0.749779i	−0.224659	+	0.974437i	$0.572127\pi$
$942$	11.0041	−	19.0597i	0.358534	−	0.620999i
$943$	1.27551	−	2.20925i	0.0415364	−	0.0719432i
$944$	2.07180	+	2.07180i	0.0674312	+	0.0674312i
$945$		0			0
$946$	2.02628	−	1.16987i	0.0658800	−	0.0380359i
$947$	16.5223	−	9.53914i	0.536902	−	0.309980i	−0.206921	−	0.978358i	$-0.566344\pi$
$947$	16.5223	−	9.53914i	0.536902	−	0.309980i	0.743822	+	0.668377i	$0.233011\pi$
$948$	6.45189	−	6.45189i	0.209548	−	0.209548i
$949$	−12.0622	−	0.232051i	−0.391555	−	0.00753269i
$950$		0			0
$951$	−2.46410	+	9.19615i	−0.0799040	+	0.298206i
$952$		0			0
$953$	7.31130	+	27.2862i	0.236836	+	0.883885i	0.977312	+	0.211803i	$0.0679334\pi$
$953$	7.31130	+	27.2862i	0.236836	+	0.883885i	−0.740476	+	0.672083i	$0.765400\pi$
$954$	−0.732051	+	0.732051i	−0.0237010	+	0.0237010i
$955$		0			0
$956$	3.35641	+	12.5263i	0.108554	+	0.405129i
$957$			32.5269i			1.05145i
$958$	1.60368	−	0.429705i	0.0518126	−	0.0138832i
$959$		0			0
$960$		0			0
$961$		−	13.0000i		−	0.419355i
$962$	40.7398	+	24.5779i	1.31350	+	0.792422i
$963$	4.89898	+	4.89898i	0.157867	+	0.157867i
$964$	18.2942	+	4.90192i	0.589217	+	0.157880i
$965$		0			0
$966$		0			0
$967$	−25.3543			−0.815340			−0.407670	−	0.913129i	$-0.633659\pi$
$967$	−25.3543			−0.815340			−0.407670	+	0.913129i	$0.633659\pi$
$968$	−12.1595	−	7.02030i	−0.390822	−	0.225641i
$969$	43.9808	−	11.7846i	1.41287	−	0.378576i
$970$		0			0
$971$	4.53590	−	7.85641i	0.145564	−	0.252124i	−0.784019	−	0.620736i	$-0.786834\pi$
$971$	4.53590	−	7.85641i	0.145564	−	0.252124i	0.929583	+	0.368612i	$0.120167\pi$
$972$	−0.448288	+	1.67303i	−0.0143788	+	0.0536625i
$973$		0			0
$974$	26.1962			0.839379
$975$		0			0
$976$	−41.0526			−1.31406
$977$	−28.4601	−	49.2944i	−0.910520	−	1.57707i	−0.813331	−	0.581802i	$-0.802348\pi$
$977$	−28.4601	−	49.2944i	−0.910520	−	1.57707i	−0.0971898	−	0.995266i	$-0.530985\pi$
$978$	3.34607	−	12.4877i	0.106995	−	0.399312i
$979$	25.8827	−	44.8301i	0.827214	−	1.43278i
$980$		0			0
$981$	−11.3301	+	3.03590i	−0.361743	+	0.0969288i
$982$	15.0573	+	8.69333i	0.480498	+	0.277415i
$983$	−12.7279			−0.405958			−0.202979	−	0.979183i	$-0.565062\pi$
$983$	−12.7279			−0.405958			−0.202979	+	0.979183i	$0.565062\pi$
$984$	4.26795	+	2.46410i	0.136057	+	0.0785527i
$985$		0			0
$986$	60.9090	+	16.3205i	1.93974	+	0.519751i
$987$		0			0
$988$	−44.0908	−	12.7279i	−1.40272	−	0.404929i
$989$			0.0525589i			0.00167128i
$990$		0			0
$991$	2.39230	+	4.14359i	0.0759941	+	0.131626i	0.901518	−	0.432741i	$-0.142454\pi$
$991$	2.39230	+	4.14359i	0.0759941	+	0.131626i	−0.825524	+	0.564367i	$0.809120\pi$
$992$	31.0991	−	8.33298i	0.987397	−	0.264572i
$993$			8.20788i			0.260469i
$994$		0			0
$995$		0			0
$996$	20.9545	−	20.9545i	0.663968	−	0.663968i
$997$	9.17878	+	34.2557i	0.290695	+	1.08489i	0.944576	+	0.328292i	$0.106473\pi$
$997$	9.17878	+	34.2557i	0.290695	+	1.08489i	−0.653881	+	0.756597i	$0.726860\pi$
$998$	−66.8198	−	17.9043i	−2.11514	−	0.566751i
$999$	1.76795	−	6.59808i	0.0559354	−	0.208754i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	975.2.bl.b.193.1	✓	8
5.2	odd	4		975.2.bu.a.232.2	yes	8
5.3	odd	4		975.2.bu.a.232.1	yes	8
5.4	even	2	inner	975.2.bl.b.193.2	yes	8
13.6	odd	12		975.2.bu.a.643.2	yes	8
65.19	odd	12		975.2.bu.a.643.1	yes	8
65.32	even	12	inner	975.2.bl.b.682.1	yes	8
65.58	even	12	inner	975.2.bl.b.682.2	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
975.2.bl.b.193.1	✓	8	1.1	even	1	trivial
975.2.bl.b.193.2	yes	8	5.4	even	2	inner
975.2.bl.b.682.1	yes	8	65.32	even	12	inner
975.2.bl.b.682.2	yes	8	65.58	even	12	inner
975.2.bu.a.232.1	yes	8	5.3	odd	4
975.2.bu.a.232.2	yes	8	5.2	odd	4
975.2.bu.a.643.1	yes	8	65.19	odd	12
975.2.bu.a.643.2	yes	8	13.6	odd	12

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:	\( N \)	\(=\)	\( 975 = 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	975.bl (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.965926 - 1.67303i) q^{2} +(0.258819 - 0.965926i) q^{3} +(-0.866025 + 1.50000i) q^{4} +(-1.86603 + 0.500000i) q^{6} -0.517638 q^{8} +(-0.866025 - 0.500000i) q^{9} +O(q^{10})\)	\(q+(-0.965926 - 1.67303i) q^{2} +(0.258819 - 0.965926i) q^{3} +(-0.866025 + 1.50000i) q^{4} +(-1.86603 + 0.500000i) q^{6} -0.517638 q^{8} +(-0.866025 - 0.500000i) q^{9} +(5.96410 + 1.59808i) q^{11} +(1.22474 + 1.22474i) q^{12} +(3.60488 + 0.0693504i) q^{13} +(2.23205 + 3.86603i) q^{16} +(5.98502 - 1.60368i) q^{17} +1.93185i q^{18} +(1.90192 + 7.09808i) q^{19} +(-3.08725 - 11.5218i) q^{22} +(0.258819 + 0.0693504i) q^{23} +(-0.133975 + 0.500000i) q^{24} +(-3.36603 - 6.09808i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(-4.56218 + 2.63397i) q^{29} +(3.00000 + 3.00000i) q^{31} +(3.79435 - 6.57201i) q^{32} +(3.08725 - 5.34727i) q^{33} +(-8.46410 - 8.46410i) q^{34} +(1.50000 - 0.866025i) q^{36} +(-5.91567 + 3.41542i) q^{37} +(10.0382 - 10.0382i) q^{38} +(1.00000 - 3.46410i) q^{39} +(2.46410 - 9.19615i) q^{41} +(0.0507680 + 0.189469i) q^{43} +(-7.56218 + 7.56218i) q^{44} +(-0.133975 - 0.500000i) q^{46} +1.41421i q^{47} +(4.31199 - 1.15539i) q^{48} +(-3.50000 - 6.06218i) q^{49} -6.19615i q^{51} +(-3.22595 + 5.34727i) q^{52} +(0.378937 + 0.378937i) q^{53} +(1.86603 + 0.500000i) q^{54} +7.34847 q^{57} +(8.81345 + 5.08845i) q^{58} +(0.633975 - 0.169873i) q^{59} +(-4.59808 + 7.96410i) q^{61} +(2.12132 - 7.91688i) q^{62} -5.73205 q^{64} -11.9282 q^{66} +(1.22474 + 2.12132i) q^{67} +(-2.77766 + 10.3664i) q^{68} +(0.133975 - 0.232051i) q^{69} +(11.3301 - 3.03590i) q^{71} +(0.448288 + 0.258819i) q^{72} -3.34607 q^{73} +(11.4282 + 6.59808i) q^{74} +(-12.2942 - 3.29423i) q^{76} +(-6.76148 + 1.67303i) q^{78} -5.26795i q^{79} +(0.500000 + 0.866025i) q^{81} +(-17.7656 + 4.76028i) q^{82} -17.1093i q^{83} +(0.267949 - 0.267949i) q^{86} +(1.36345 + 5.08845i) q^{87} +(-3.08725 - 0.827225i) q^{88} +(2.16987 - 8.09808i) q^{89} +(-0.328169 + 0.328169i) q^{92} +(3.67423 - 2.12132i) q^{93} +(2.36603 - 1.36603i) q^{94} +(-5.36603 - 5.36603i) q^{96} +(-4.31199 + 7.46859i) q^{97} +(-6.76148 + 11.7112i) q^{98} +(-4.36603 - 4.36603i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{6}+O(q^{10}) \) 8 * q - 8 * q^6	\( 8 q - 8 q^{6} + 20 q^{11} + 4 q^{16} + 36 q^{19} - 8 q^{24} - 20 q^{26} + 12 q^{29} + 24 q^{31} - 40 q^{34} + 12 q^{36} + 8 q^{39} - 8 q^{41} - 12 q^{44} - 8 q^{46} - 28 q^{49} + 8 q^{54} + 12 q^{59} - 16 q^{61} - 32 q^{64} - 40 q^{66} + 8 q^{69} + 56 q^{71} + 36 q^{74} - 36 q^{76} + 4 q^{81} + 16 q^{86} + 52 q^{89} + 12 q^{94} - 36 q^{96} - 28 q^{99}+O(q^{100}) \) 8 * q - 8 * q^6 + 20 * q^11 + 4 * q^16 + 36 * q^19 - 8 * q^24 - 20 * q^26 + 12 * q^29 + 24 * q^31 - 40 * q^34 + 12 * q^36 + 8 * q^39 - 8 * q^41 - 12 * q^44 - 8 * q^46 - 28 * q^49 + 8 * q^54 + 12 * q^59 - 16 * q^61 - 32 * q^64 - 40 * q^66 + 8 * q^69 + 56 * q^71 + 36 * q^74 - 36 * q^76 + 4 * q^81 + 16 * q^86 + 52 * q^89 + 12 * q^94 - 36 * q^96 - 28 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more