LMFDB - Embedded newform 504.2.bm.a.179.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(107,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("504.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.bm (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			179.4
Root			$-0.258819 - 0.965926i$ of defining polynomial
Character	$\chi$	$=$	504.179
Dual form			504.2.bm.a.107.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.366025 - 1.36603i) q^{2} +(-1.73205 - 1.00000i) q^{4} +(1.91421 + 3.31552i) q^{5} +(-2.09077 + 1.62132i) q^{7} +(-2.00000 + 2.00000i) q^{8} +O(q^{10})$	\(q+(0.366025 - 1.36603i) q^{2} +(-1.73205 - 1.00000i) q^{4} +(1.91421 + 3.31552i) q^{5} +(-2.09077 + 1.62132i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(5.22973 - 1.40130i) q^{10} +(-3.82282 - 2.20711i) q^{11} +5.41421i q^{13} +(1.44949 + 3.44949i) q^{14} +(2.00000 + 3.46410i) q^{16} +(1.94218 + 1.12132i) q^{17} +(2.70711 + 4.68885i) q^{19} -7.65685i q^{20} +(-4.41421 + 4.41421i) q^{22} +(-1.70711 - 2.95680i) q^{23} +(-4.82843 + 8.36308i) q^{25} +(7.39595 + 1.98174i) q^{26} +(5.24264 - 0.717439i) q^{28} -3.00000 q^{29} +(-1.37333 - 0.792893i) q^{31} +(5.46410 - 1.46410i) q^{32} +(2.24264 - 2.24264i) q^{34} +(-9.37769 - 3.82843i) q^{35} +(4.39167 - 2.53553i) q^{37} +(7.39595 - 1.98174i) q^{38} +(-10.4595 - 2.80260i) q^{40} -3.17157i q^{41} +8.58579 q^{43} +(4.41421 + 7.64564i) q^{44} +(-4.66390 + 1.24969i) q^{46} +(2.70711 + 4.68885i) q^{47} +(1.74264 - 6.77962i) q^{49} +(9.65685 + 9.65685i) q^{50} +(5.41421 - 9.37769i) q^{52} +(5.91421 - 10.2437i) q^{53} -16.8995i q^{55} +(0.938900 - 7.42418i) q^{56} +(-1.09808 + 4.09808i) q^{58} +(5.25770 + 3.03553i) q^{59} +(-1.94218 + 1.12132i) q^{61} +(-1.58579 + 1.58579i) q^{62} -8.00000i q^{64} +(-17.9509 + 10.3640i) q^{65} +(-1.82843 + 3.16693i) q^{67} +(-2.24264 - 3.88437i) q^{68} +(-8.66220 + 11.4089i) q^{70} -5.89949 q^{71} +(-7.65685 + 13.2621i) q^{73} +(-1.85614 - 6.92721i) q^{74} -10.8284i q^{76} +(11.5711 - 1.58346i) q^{77} +(-5.25770 + 3.03553i) q^{79} +(-7.65685 + 13.2621i) q^{80} +(-4.33245 - 1.16088i) q^{82} -6.07107i q^{83} +8.58579i q^{85} +(3.14262 - 11.7284i) q^{86} +(12.0599 - 3.23143i) q^{88} +(-8.77817 - 11.3199i) q^{91} +6.82843i q^{92} +(7.39595 - 1.98174i) q^{94} +(-10.3640 + 17.9509i) q^{95} -10.1716 q^{97} +(-8.62328 - 4.86200i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{2} + 4 q^{5} - 16 q^{8}+O(q^{10}) $ 8 * q - 4 * q^2 + 4 * q^5 - 16 * q^8	$ 8 q - 4 q^{2} + 4 q^{5} - 16 q^{8} + 4 q^{10} - 8 q^{14} + 16 q^{16} + 16 q^{19} - 24 q^{22} - 8 q^{23} - 16 q^{25} + 16 q^{26} + 8 q^{28} - 24 q^{29} + 16 q^{32} - 16 q^{34} + 16 q^{38} - 8 q^{40} + 80 q^{43} + 24 q^{44} - 8 q^{46} + 16 q^{47} - 20 q^{49} + 32 q^{50} + 32 q^{52} + 36 q^{53} + 8 q^{56} + 12 q^{58} - 24 q^{62} + 8 q^{67} + 16 q^{68} - 52 q^{70} + 32 q^{71} - 16 q^{73} - 8 q^{74} + 36 q^{77} - 16 q^{80} - 24 q^{82} - 40 q^{86} + 24 q^{88} - 8 q^{91} + 16 q^{94} - 32 q^{95} - 104 q^{97} - 20 q^{98}+O(q^{100}) $ 8 * q - 4 * q^2 + 4 * q^5 - 16 * q^8 + 4 * q^10 - 8 * q^14 + 16 * q^16 + 16 * q^19 - 24 * q^22 - 8 * q^23 - 16 * q^25 + 16 * q^26 + 8 * q^28 - 24 * q^29 + 16 * q^32 - 16 * q^34 + 16 * q^38 - 8 * q^40 + 80 * q^43 + 24 * q^44 - 8 * q^46 + 16 * q^47 - 20 * q^49 + 32 * q^50 + 32 * q^52 + 36 * q^53 + 8 * q^56 + 12 * q^58 - 24 * q^62 + 8 * q^67 + 16 * q^68 - 52 * q^70 + 32 * q^71 - 16 * q^73 - 8 * q^74 + 36 * q^77 - 16 * q^80 - 24 * q^82 - 40 * q^86 + 24 * q^88 - 8 * q^91 + 16 * q^94 - 32 * q^95 - 104 * q^97 - 20 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$	$-1$	$-1$

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 $

$2$	0.366025	−	1.36603i	0.258819	−	0.965926i
$2$	0.366025	−	1.36603i	0.258819	−	0.965926i
$3$		0			0
$3$		0			0
$4$	−1.73205	−	1.00000i	−0.866025	−	0.500000i
$5$	1.91421	+	3.31552i	0.856062	+	1.48274i	0.875656	+	0.482935i	$0.160429\pi$
$5$	1.91421	+	3.31552i	0.856062	+	1.48274i	−0.0195936	+	0.999808i	$0.506237\pi$
$6$		0			0
$7$	−2.09077	+	1.62132i	−0.790237	+	0.612801i
$7$	−2.09077	+	1.62132i	−0.790237	+	0.612801i
$8$	−2.00000	+	2.00000i	−0.707107	+	0.707107i
$9$		0			0
$10$	5.22973	−	1.40130i	1.65379	−	0.443130i
$11$	−3.82282	−	2.20711i	−1.15262	−	0.665468i	−0.203099	−	0.979158i	$-0.565101\pi$
$11$	−3.82282	−	2.20711i	−1.15262	−	0.665468i	−0.949525	+	0.313691i	$0.898435\pi$
$12$		0			0
$13$			5.41421i			1.50163i	0.660511	+	0.750816i	$0.270340\pi$
$13$			5.41421i			1.50163i	−0.660511	+	0.750816i	$0.729660\pi$
$14$	1.44949	+	3.44949i	0.387392	+	0.921915i
$15$		0			0
$16$	2.00000	+	3.46410i	0.500000	+	0.866025i
$17$	1.94218	+	1.12132i	0.471049	+	0.271960i	0.716679	−	0.697404i	$-0.245661\pi$
$17$	1.94218	+	1.12132i	0.471049	+	0.271960i	−0.245630	+	0.969364i	$0.578995\pi$
$18$		0			0
$19$	2.70711	+	4.68885i	0.621053	+	1.07570i	0.989290	+	0.145963i	$0.0466281\pi$
$19$	2.70711	+	4.68885i	0.621053	+	1.07570i	−0.368237	+	0.929732i	$0.620039\pi$
$20$		−	7.65685i		−	1.71212i
$21$		0			0
$22$	−4.41421	+	4.41421i	−0.941113	+	0.941113i
$23$	−1.70711	−	2.95680i	−0.355956	−	0.616535i	0.631325	−	0.775519i	$-0.282511\pi$
$23$	−1.70711	−	2.95680i	−0.355956	−	0.616535i	−0.987281	+	0.158984i	$0.949178\pi$
$24$		0			0
$25$	−4.82843	+	8.36308i	−0.965685	+	1.67262i
$26$	7.39595	+	1.98174i	1.45047	+	0.388651i
$27$		0			0
$28$	5.24264	−	0.717439i	0.990766	−	0.135583i
$29$	−3.00000			−0.557086			−0.278543	−	0.960424i	$-0.589851\pi$
$29$	−3.00000			−0.557086			−0.278543	+	0.960424i	$0.589851\pi$
$30$		0			0
$31$	−1.37333	−	0.792893i	−0.246658	−	0.142408i	0.371575	−	0.928403i	$-0.378818\pi$
$31$	−1.37333	−	0.792893i	−0.246658	−	0.142408i	−0.618233	+	0.785995i	$0.712151\pi$
$32$	5.46410	−	1.46410i	0.965926	−	0.258819i
$33$		0			0
$34$	2.24264	−	2.24264i	0.384610	−	0.384610i
$35$	−9.37769	−	3.82843i	−1.58512	−	0.647122i
$36$		0			0
$37$	4.39167	−	2.53553i	0.721987	−	0.416839i	−0.0934968	−	0.995620i	$-0.529804\pi$
$37$	4.39167	−	2.53553i	0.721987	−	0.416839i	0.815483	+	0.578780i	$0.196471\pi$
$38$	7.39595	−	1.98174i	1.19978	−	0.321481i
$39$		0			0
$40$	−10.4595	−	2.80260i	−1.65379	−	0.443130i
$41$		−	3.17157i		−	0.495316i	−0.968847	−	0.247658i	$-0.920339\pi$
$41$		−	3.17157i		−	0.495316i	0.968847	−	0.247658i	$-0.0796610\pi$
$42$		0			0
$43$	8.58579			1.30932			0.654660	−	0.755923i	$-0.272812\pi$
$43$	8.58579			1.30932			0.654660	+	0.755923i	$0.272812\pi$
$44$	4.41421	+	7.64564i	0.665468	+	1.15262i
$45$		0			0
$46$	−4.66390	+	1.24969i	−0.687655	+	0.184257i
$47$	2.70711	+	4.68885i	0.394872	+	0.683939i	0.993085	−	0.117399i	$-0.0374556\pi$
$47$	2.70711	+	4.68885i	0.394872	+	0.683939i	−0.598213	+	0.801337i	$0.704122\pi$
$48$		0			0
$49$	1.74264	−	6.77962i	0.248949	−	0.968517i
$50$	9.65685	+	9.65685i	1.36569	+	1.36569i
$51$		0			0
$52$	5.41421	−	9.37769i	0.750816	−	1.30045i
$53$	5.91421	−	10.2437i	0.812380	−	1.40708i	−0.0988145	−	0.995106i	$-0.531505\pi$
$53$	5.91421	−	10.2437i	0.812380	−	1.40708i	0.911194	−	0.411977i	$-0.135162\pi$
$54$		0			0
$55$		−	16.8995i		−	2.27873i
$56$	0.938900	−	7.42418i	0.125466	−	0.992098i
$57$		0			0
$58$	−1.09808	+	4.09808i	−0.144184	+	0.538104i
$59$	5.25770	+	3.03553i	0.684494	+	0.395193i	0.801546	−	0.597933i	$-0.204011\pi$
$59$	5.25770	+	3.03553i	0.684494	+	0.395193i	−0.117052	+	0.993126i	$0.537344\pi$
$60$		0			0
$61$	−1.94218	+	1.12132i	−0.248671	+	0.143570i	−0.619156	−	0.785268i	$-0.712525\pi$
$61$	−1.94218	+	1.12132i	−0.248671	+	0.143570i	0.370484	+	0.928839i	$0.379192\pi$
$62$	−1.58579	+	1.58579i	−0.201395	+	0.201395i
$63$		0			0
$64$		−	8.00000i		−	1.00000i
$65$	−17.9509	+	10.3640i	−2.22654	+	1.28549i
$66$		0			0
$67$	−1.82843	+	3.16693i	−0.223378	+	0.386902i	−0.955832	−	0.293915i	$-0.905042\pi$
$67$	−1.82843	+	3.16693i	−0.223378	+	0.386902i	0.732454	+	0.680817i	$0.238375\pi$
$68$	−2.24264	−	3.88437i	−0.271960	−	0.471049i
$69$		0			0
$70$	−8.66220	+	11.4089i	−1.03533	+	1.36362i
$71$	−5.89949			−0.700141			−0.350071	−	0.936723i	$-0.613842\pi$
$71$	−5.89949			−0.700141			−0.350071	+	0.936723i	$0.613842\pi$
$72$		0			0
$73$	−7.65685	+	13.2621i	−0.896167	+	1.55221i	−0.0638134	+	0.997962i	$0.520326\pi$
$73$	−7.65685	+	13.2621i	−0.896167	+	1.55221i	−0.832354	+	0.554245i	$0.813007\pi$
$74$	−1.85614	−	6.92721i	−0.215772	−	0.805272i
$75$		0			0
$76$		−	10.8284i		−	1.24211i
$77$	11.5711	−	1.58346i	1.31865	−	0.180453i
$78$		0			0
$79$	−5.25770	+	3.03553i	−0.591537	+	0.341524i	−0.765705	−	0.643192i	$-0.777610\pi$
$79$	−5.25770	+	3.03553i	−0.591537	+	0.341524i	0.174168	+	0.984716i	$0.444276\pi$
$80$	−7.65685	+	13.2621i	−0.856062	+	1.48274i
$81$		0			0
$82$	−4.33245	−	1.16088i	−0.478439	−	0.128197i
$83$		−	6.07107i		−	0.666386i	−0.942859	−	0.333193i	$-0.891874\pi$
$83$		−	6.07107i		−	0.666386i	0.942859	−	0.333193i	$-0.108126\pi$
$84$		0			0
$85$			8.58579i			0.931259i
$86$	3.14262	−	11.7284i	0.338877	−	1.26471i
$87$		0			0
$88$	12.0599	−	3.23143i	1.28558	−	0.344471i
$89$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$89$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$90$		0			0
$91$	−8.77817	−	11.3199i	−0.920203	−	1.18665i
$92$			6.82843i			0.711913i
$93$		0			0
$94$	7.39595	−	1.98174i	0.762834	−	0.204401i
$95$	−10.3640	+	17.9509i	−1.06332	+	1.84172i
$96$		0			0
$97$	−10.1716			−1.03277			−0.516383	−	0.856358i	$-0.672722\pi$
$97$	−10.1716			−1.03277			−0.516383	+	0.856358i	$0.672722\pi$
$98$	−8.62328	−	4.86200i	−0.871083	−	0.491137i
$99$		0			0
$100$	16.7262	−	9.65685i	1.67262	−	0.965685i
$101$	2.24264	−	3.88437i	0.223151	−	0.386509i	−0.732612	−	0.680646i	$-0.761699\pi$
$101$	2.24264	−	3.88437i	0.223151	−	0.386509i	0.955763	+	0.294137i	$0.0950323\pi$
$102$		0			0
$103$	5.49333	−	3.17157i	0.541273	−	0.312504i	−0.204321	−	0.978904i	$-0.565499\pi$
$103$	5.49333	−	3.17157i	0.541273	−	0.312504i	0.745595	+	0.666399i	$0.232165\pi$
$104$	−10.8284	−	10.8284i	−1.06181	−	1.06181i
$105$		0			0
$106$	−11.8284	−	11.8284i	−1.14888	−	1.14888i
$107$	5.85204	−	3.37868i	0.565739	−	0.326629i	−0.189707	−	0.981841i	$-0.560754\pi$
$107$	5.85204	−	3.37868i	0.565739	−	0.326629i	0.755446	+	0.655211i	$0.227420\pi$
$108$		0			0
$109$	12.5446	+	7.24264i	1.20156	+	0.693719i	0.960901	−	0.276891i	$-0.0893042\pi$
$109$	12.5446	+	7.24264i	1.20156	+	0.693719i	0.240656	+	0.970611i	$0.422638\pi$
$110$	−23.0851	−	6.18564i	−2.20108	−	0.589778i
$111$		0			0
$112$	−9.79796	−	4.00000i	−0.925820	−	0.377964i
$113$			0.828427i			0.0779319i	0.999241	+	0.0389659i	$0.0124064\pi$
$113$			0.828427i			0.0779319i	−0.999241	+	0.0389659i	$0.987594\pi$
$114$		0			0
$115$	6.53553	−	11.3199i	0.609442	−	1.05558i
$116$	5.19615	+	3.00000i	0.482451	+	0.278543i
$117$		0			0
$118$	6.07107	−	6.07107i	0.558887	−	0.558887i
$119$	−5.87868	+	0.804479i	−0.538898	+	0.0737465i
$120$		0			0
$121$	4.24264	+	7.34847i	0.385695	+	0.668043i
$122$	0.820863	+	3.06350i	0.0743175	+	0.277357i
$123$		0			0
$124$	1.58579	+	2.74666i	0.142408	+	0.246658i
$125$	−17.8284			−1.59462
$126$		0			0
$127$			6.07107i			0.538720i	0.963040	+	0.269360i	$0.0868122\pi$
$127$			6.07107i			0.538720i	−0.963040	+	0.269360i	$0.913188\pi$
$128$	−10.9282	−	2.92820i	−0.965926	−	0.258819i
$129$		0			0
$130$	7.58695	+	28.3149i	0.665419	+	2.48338i
$131$	−10.7510	+	6.20711i	−0.939321	+	0.542317i	−0.889748	−	0.456453i	$-0.849120\pi$
$131$	−10.7510	+	6.20711i	−0.939321	+	0.542317i	−0.0495738	+	0.998770i	$0.515786\pi$
$132$		0			0
$133$	−13.2621	−	5.41421i	−1.14997	−	0.469472i
$134$	3.65685	+	3.65685i	0.315904	+	0.315904i
$135$		0			0
$136$	−6.12701	+	1.64173i	−0.525387	+	0.140777i
$137$	14.5738	+	8.41421i	1.24513	+	0.718875i	0.970134	−	0.242571i	$-0.0779908\pi$
$137$	14.5738	+	8.41421i	1.24513	+	0.718875i	0.274994	+	0.961446i	$0.411324\pi$
$138$		0			0
$139$	15.3137			1.29889			0.649446	−	0.760408i	$-0.275001\pi$
$139$	15.3137			1.29889			0.649446	+	0.760408i	$0.275001\pi$
$140$	12.4142	+	16.0087i	1.04919	+	1.35298i
$141$		0			0
$142$	−2.15937	+	8.05886i	−0.181210	+	0.676285i
$143$	11.9497	−	20.6976i	0.999288	−	1.73082i
$144$		0			0
$145$	−5.74264	−	9.94655i	−0.476900	−	0.826016i
$146$	15.3137	+	15.3137i	1.26737	+	1.26737i
$147$		0			0
$148$	−10.1421			−0.833678
$149$	1.00000	+	1.73205i	0.0819232	+	0.141895i	0.904076	−	0.427372i	$-0.140560\pi$
$149$	1.00000	+	1.73205i	0.0819232	+	0.141895i	−0.822153	+	0.569267i	$0.807227\pi$
$150$		0			0
$151$	8.72180	+	5.03553i	0.709770	+	0.409786i	0.810976	−	0.585080i	$-0.198937\pi$
$151$	8.72180	+	5.03553i	0.709770	+	0.409786i	−0.101206	+	0.994866i	$0.532270\pi$
$152$	−14.7919	−	3.96348i	−1.19978	−	0.321481i
$153$		0			0
$154$	2.07225	−	16.3860i	0.166987	−	1.32042i
$155$		−	6.07107i		−	0.487640i
$156$		0			0
$157$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$157$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$158$	2.22217	+	8.29323i	0.176786	+	0.659774i
$159$		0			0
$160$	15.3137	+	15.3137i	1.21065	+	1.21065i
$161$	8.36308	+	3.41421i	0.659103	+	0.269078i
$162$		0			0
$163$	0.292893	+	0.507306i	0.0229412	+	0.0397353i	0.877268	−	0.480001i	$-0.159364\pi$
$163$	0.292893	+	0.507306i	0.0229412	+	0.0397353i	−0.854327	+	0.519736i	$0.826030\pi$
$164$	−3.17157	+	5.49333i	−0.247658	+	0.428957i
$165$		0			0
$166$	−8.29323	−	2.22217i	−0.643680	−	0.172473i
$167$	−7.65685			−0.592505			−0.296253	−	0.955110i	$-0.595737\pi$
$167$	−7.65685			−0.592505			−0.296253	+	0.955110i	$0.595737\pi$
$168$		0			0
$169$	−16.3137			−1.25490
$170$	11.7284	+	3.14262i	0.899527	+	0.241028i
$171$		0			0
$172$	−14.8710	−	8.58579i	−1.13390	−	0.654660i
$173$	4.48528	+	7.76874i	0.341010	+	0.590646i	0.984620	−	0.174707i	$-0.0558978\pi$
$173$	4.48528	+	7.76874i	0.341010	+	0.590646i	−0.643611	+	0.765353i	$0.722564\pi$
$174$		0			0
$175$	−3.46410	−	25.3137i	−0.261861	−	1.91354i
$176$		−	17.6569i		−	1.33094i
$177$		0			0
$178$		0			0
$179$	7.94282	+	4.58579i	0.593674	+	0.342758i	0.766549	−	0.642186i	$-0.221972\pi$
$179$	7.94282	+	4.58579i	0.593674	+	0.342758i	−0.172875	+	0.984944i	$0.555306\pi$
$180$		0			0
$181$			3.17157i			0.235741i	0.993029	+	0.117871i	$0.0376068\pi$
$181$			3.17157i			0.235741i	−0.993029	+	0.117871i	$0.962393\pi$
$182$	−18.6763	+	7.84785i	−1.38438	+	0.581721i
$183$		0			0
$184$	9.32780	+	2.49938i	0.687655	+	0.184257i
$185$	16.8132	+	9.70711i	1.23613	+	0.713681i
$186$		0			0
$187$	−4.94975	−	8.57321i	−0.361961	−	0.626936i
$188$		−	10.8284i		−	0.789744i
$189$		0			0
$190$	20.7279	+	20.7279i	1.50376	+	1.50376i
$191$	−10.4853	−	18.1610i	−0.758688	−	1.31409i	−0.943520	−	0.331316i	$-0.892507\pi$
$191$	−10.4853	−	18.1610i	−0.758688	−	1.31409i	0.184831	−	0.982770i	$-0.440826\pi$
$192$		0			0
$193$	13.3995	−	23.2086i	0.964517	−	1.67059i	0.253609	−	0.967307i	$-0.418382\pi$
$193$	13.3995	−	23.2086i	0.964517	−	1.67059i	0.710908	−	0.703285i	$-0.248284\pi$
$194$	−3.72305	+	13.8946i	−0.267300	+	0.997576i
$195$		0			0
$196$	−9.79796	+	10.0000i	−0.699854	+	0.714286i
$197$	−2.14214			−0.152621			−0.0763104	−	0.997084i	$-0.524314\pi$
$197$	−2.14214			−0.152621			−0.0763104	+	0.997084i	$0.524314\pi$
$198$		0			0
$199$	−5.49333	−	3.17157i	−0.389412	−	0.224827i	0.292494	−	0.956267i	$-0.405515\pi$
$199$	−5.49333	−	3.17157i	−0.389412	−	0.224827i	−0.681905	+	0.731441i	$0.738848\pi$
$200$	−7.06931	−	26.3830i	−0.499876	−	1.86556i
$201$		0			0
$202$	−4.48528	−	4.48528i	−0.315583	−	0.315583i
$203$	6.27231	−	4.86396i	0.440230	−	0.341383i
$204$		0			0
$205$	10.5154	−	6.07107i	0.734427	−	0.424022i
$206$	−2.32175	−	8.66490i	−0.161764	−	0.603712i
$207$		0			0
$208$	−18.7554	+	10.8284i	−1.30045	+	0.750816i
$209$		−	23.8995i		−	1.65316i
$210$		0			0
$211$	3.55635			0.244829			0.122415	−	0.992479i	$-0.460936\pi$
$211$	3.55635			0.244829			0.122415	+	0.992479i	$0.460936\pi$
$212$	−20.4874	+	11.8284i	−1.40708	+	0.812380i
$213$		0			0
$214$	−2.47337	−	9.23072i	−0.169076	−	0.630999i
$215$	16.4350	+	28.4663i	1.12086	+	1.94139i
$216$		0			0
$217$	4.15685	−	0.568852i	0.282186	−	0.0386162i
$218$	14.4853	−	14.4853i	0.981067	−	0.981067i
$219$		0			0
$220$	−16.8995	+	29.2708i	−1.13936	+	1.97344i
$221$	−6.07107	+	10.5154i	−0.408384	+	0.707342i
$222$		0			0
$223$			0.272078i			0.0182197i	0.999959	+	0.00910984i	$0.00289979\pi$
$223$			0.272078i			0.0182197i	−0.999959	+	0.00910984i	$0.997100\pi$
$224$	−9.05040	+	11.9202i	−0.604706	+	0.796449i
$225$		0			0
$226$	1.13165	+	0.303225i	0.0752764	+	0.0201703i
$227$	−11.8887	−	6.86396i	−0.789083	−	0.455577i	0.0505568	−	0.998721i	$-0.483900\pi$
$227$	−11.8887	−	6.86396i	−0.789083	−	0.455577i	−0.839640	+	0.543144i	$0.817234\pi$
$228$		0			0
$229$	16.0087	−	9.24264i	1.05789	−	0.610771i	0.133039	−	0.991111i	$-0.457526\pi$
$229$	16.0087	−	9.24264i	1.05789	−	0.610771i	0.924847	+	0.380340i	$0.124193\pi$
$230$	−13.0711	−	13.0711i	−0.861881	−	0.861881i
$231$		0			0
$232$	6.00000	−	6.00000i	0.393919	−	0.393919i
$233$	20.1032	−	11.6066i	1.31701	−	0.760374i	0.333760	−	0.942658i	$-0.391682\pi$
$233$	20.1032	−	11.6066i	1.31701	−	0.760374i	0.983246	+	0.182284i	$0.0583491\pi$
$234$		0			0
$235$	−10.3640	+	17.9509i	−0.676070	+	1.17099i
$236$	−6.07107	−	10.5154i	−0.395193	−	0.684494i
$237$		0			0
$238$	−1.05281	+	8.32489i	−0.0682434	+	0.539622i
$239$	1.75736			0.113674			0.0568371	−	0.998383i	$-0.481898\pi$
$239$	1.75736			0.113674			0.0568371	+	0.998383i	$0.481898\pi$
$240$		0			0
$241$	−0.328427	+	0.568852i	−0.0211559	+	0.0366430i	−0.876410	−	0.481567i	$-0.840068\pi$
$241$	−0.328427	+	0.568852i	−0.0211559	+	0.0366430i	0.855254	+	0.518210i	$0.173401\pi$
$242$	11.5911	−	3.10583i	0.745105	−	0.199650i
$243$		0			0
$244$	4.48528			0.287141
$245$	25.8137	−	7.19988i	1.64918	−	0.459984i
$246$		0			0
$247$	−25.3864	+	14.6569i	−1.61530	+	0.932593i
$248$	4.33245	−	1.16088i	0.275111	−	0.0737157i
$249$		0			0
$250$	−6.52566	+	24.3541i	−0.412719	+	1.54029i
$251$			27.7279i			1.75017i	0.483968	+	0.875085i	$0.339195\pi$
$251$			27.7279i			1.75017i	−0.483968	+	0.875085i	$0.660805\pi$
$252$		0			0
$253$			15.0711i			0.947510i
$254$	8.29323	+	2.22217i	0.520364	+	0.139431i
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.500000	+	0.866025i
$257$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$257$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$258$		0			0
$259$	−5.07107	+	12.4215i	−0.315101	+	0.771836i
$260$	41.4558			2.57098
$261$		0			0
$262$	4.54392	+	16.9581i	0.280724	+	1.04768i
$263$	13.3640	−	23.1471i	0.824057	−	1.42731i	−0.0785806	−	0.996908i	$-0.525039\pi$
$263$	13.3640	−	23.1471i	0.824057	−	1.42731i	0.902638	−	0.430401i	$-0.141628\pi$
$264$		0			0
$265$	45.2843			2.78179
$266$	−12.2502	+	16.1346i	−0.751108	+	0.989274i
$267$		0			0
$268$	6.33386	−	3.65685i	0.386902	−	0.223378i
$269$	−6.67157	+	11.5555i	−0.406773	+	0.704551i	−0.994526	−	0.104489i	$-0.966679\pi$
$269$	−6.67157	+	11.5555i	−0.406773	+	0.704551i	0.587753	+	0.809040i	$0.300013\pi$
$270$		0			0
$271$	−5.25770	+	3.03553i	−0.319382	+	0.184396i	−0.651117	−	0.758977i	$-0.725699\pi$
$271$	−5.25770	+	3.03553i	−0.319382	+	0.184396i	0.331735	+	0.943373i	$0.392366\pi$
$272$			8.97056i			0.543920i
$273$		0			0
$274$	16.8284	−	16.8284i	1.01664	−	1.01664i
$275$	36.9164	−	21.3137i	2.22614	−	1.28526i
$276$		0			0
$277$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$277$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$278$	5.60521	−	20.9189i	0.336178	−	1.25463i
$279$		0			0
$280$	26.4122	−	11.0985i	1.57843	−	0.663264i
$281$			20.8284i			1.24252i	0.783605	+	0.621260i	$0.213379\pi$
$281$			20.8284i			1.24252i	−0.783605	+	0.621260i	$0.786621\pi$
$282$		0			0
$283$	11.0208	−	19.0886i	0.655119	−	1.13470i	−0.326744	−	0.945113i	$-0.605952\pi$
$283$	11.0208	−	19.0886i	0.655119	−	1.13470i	0.981864	−	0.189587i	$-0.0607151\pi$
$284$	10.2182	+	5.89949i	0.606340	+	0.350071i
$285$		0			0
$286$	−23.8995	−	23.8995i	−1.41321	−	1.41321i
$287$	5.14214	+	6.63103i	0.303531	+	0.391417i
$288$		0			0
$289$	−5.98528	−	10.3668i	−0.352075	−	0.609812i
$290$	−15.6892	+	4.20390i	−0.921301	+	0.246862i
$291$		0			0
$292$	26.5241	−	15.3137i	1.55221	−	0.896167i
$293$	21.0000			1.22683			0.613417	−	0.789760i	$-0.289795\pi$
$293$	21.0000			1.22683			0.613417	+	0.789760i	$0.289795\pi$
$294$		0			0
$295$			23.2426i			1.35324i
$296$	−3.71228	+	13.8544i	−0.215772	+	0.805272i
$297$		0			0
$298$	2.73205	−	0.732051i	0.158263	−	0.0424066i
$299$	16.0087	−	9.24264i	0.925808	−	0.534516i
$300$		0			0
$301$	−17.9509	+	13.9203i	−1.03467	+	0.802353i
$302$	10.0711	−	10.0711i	0.579525	−	0.579525i
$303$		0			0
$304$	−10.8284	+	18.7554i	−0.621053	+	1.07570i
$305$	−7.43551	−	4.29289i	−0.425756	−	0.245810i
$306$		0			0
$307$	−6.72792			−0.383983			−0.191991	−	0.981397i	$-0.561495\pi$
$307$	−6.72792			−0.383983			−0.191991	+	0.981397i	$0.561495\pi$
$308$	−21.6251	−	8.82843i	−1.23221	−	0.503046i
$309$		0			0
$310$	−8.29323	−	2.22217i	−0.471024	−	0.126210i
$311$	3.82843	−	6.63103i	0.217090	−	0.376011i	−0.736827	−	0.676081i	$-0.763677\pi$
$311$	3.82843	−	6.63103i	0.217090	−	0.376011i	0.953917	+	0.300070i	$0.0970101\pi$
$312$		0			0
$313$	−4.15685	−	7.19988i	−0.234959	−	0.406961i	0.724302	−	0.689483i	$-0.242162\pi$
$313$	−4.15685	−	7.19988i	−0.234959	−	0.406961i	−0.959261	+	0.282522i	$0.908829\pi$
$314$		0			0
$315$		0			0
$316$	12.1421			0.683048
$317$	−9.91421	−	17.1719i	−0.556838	−	0.964471i	−0.997758	−	0.0669249i	$-0.978681\pi$
$317$	−9.91421	−	17.1719i	−0.556838	−	0.964471i	0.440920	−	0.897546i	$-0.354652\pi$
$318$		0			0
$319$	11.4685	+	6.62132i	0.642111	+	0.370723i
$320$	26.5241	−	15.3137i	1.48274	−	0.856062i
$321$		0			0
$322$	7.72500	−	10.1745i	0.430498	−	0.567002i
$323$			12.1421i			0.675606i
$324$		0			0
$325$	−45.2795	−	26.1421i	−2.51166	−	1.45010i
$326$	0.800199	−	0.214413i	0.0443189	−	0.0118752i
$327$		0			0
$328$	6.34315	+	6.34315i	0.350242	+	0.350242i
$329$	−13.2621	−	5.41421i	−0.731161	−	0.298495i
$330$		0			0
$331$	12.1421	+	21.0308i	0.667392	+	1.15596i	0.978631	+	0.205625i	$0.0659228\pi$
$331$	12.1421	+	21.0308i	0.667392	+	1.15596i	−0.311239	+	0.950332i	$0.600744\pi$
$332$	−6.07107	+	10.5154i	−0.333193	+	0.577107i
$333$		0			0
$334$	−2.80260	+	10.4595i	−0.153352	+	0.572316i
$335$	−14.0000			−0.764902
$336$		0			0
$337$	−14.6569			−0.798410			−0.399205	−	0.916862i	$-0.630714\pi$
$337$	−14.6569			−0.798410			−0.399205	+	0.916862i	$0.630714\pi$
$338$	−5.97123	+	22.2849i	−0.324792	+	1.21214i
$339$		0			0
$340$	8.58579	−	14.8710i	0.465630	−	0.806494i
$341$	3.50000	+	6.06218i	0.189536	+	0.328285i
$342$		0			0
$343$	7.34847	+	17.0000i	0.396780	+	0.917914i
$344$	−17.1716	+	17.1716i	−0.925829	+	0.925829i
$345$		0			0
$346$	12.2540	−	3.28345i	0.658780	−	0.176520i
$347$	−2.44949	−	1.41421i	−0.131495	−	0.0759190i	0.432809	−	0.901486i	$-0.357522\pi$
$347$	−2.44949	−	1.41421i	−0.131495	−	0.0759190i	−0.564305	+	0.825567i	$0.690856\pi$
$348$		0			0
$349$			5.79899i			0.310413i	0.987882	+	0.155206i	$0.0496043\pi$
$349$			5.79899i			0.310413i	−0.987882	+	0.155206i	$0.950396\pi$
$350$	−35.8471	−	4.53341i	−1.91611	−	0.242321i
$351$		0			0
$352$	−24.1197	−	6.46286i	−1.28558	−	0.344471i
$353$	−21.0308	−	12.1421i	−1.11936	−	0.646261i	−0.178120	−	0.984009i	$-0.557001\pi$
$353$	−21.0308	−	12.1421i	−1.11936	−	0.646261i	−0.941237	+	0.337748i	$0.890335\pi$
$354$		0			0
$355$	−11.2929	−	19.5599i	−0.599365	−	1.03813i
$356$		0			0
$357$		0			0
$358$	9.17157	−	9.17157i	0.484733	−	0.484733i
$359$	17.4853	+	30.2854i	0.922838	+	1.59840i	0.795002	+	0.606607i	$0.207470\pi$
$359$	17.4853	+	30.2854i	0.922838	+	1.59840i	0.127836	+	0.991795i	$0.459197\pi$
$360$		0			0
$361$	−5.15685	+	8.93193i	−0.271413	+	0.470102i
$362$	4.33245	+	1.16088i	0.227708	+	0.0610143i
$363$		0			0
$364$	3.88437	+	28.3848i	0.203596	+	1.48777i
$365$	−58.6274			−3.06870
$366$		0			0
$367$	25.1508	+	14.5208i	1.31286	+	0.757980i	0.982569	−	0.185899i	$-0.0595196\pi$
$367$	25.1508	+	14.5208i	1.31286	+	0.757980i	0.330292	+	0.943879i	$0.392853\pi$
$368$	6.82843	−	11.8272i	0.355956	−	0.616535i
$369$		0			0
$370$	19.4142	−	19.4142i	1.00930	−	1.00930i
$371$	4.24309	+	31.0061i	0.220290	+	1.60976i
$372$		0			0
$373$	10.5154	−	6.07107i	0.544467	−	0.314348i	−0.202421	−	0.979299i	$-0.564881\pi$
$373$	10.5154	−	6.07107i	0.544467	−	0.314348i	0.746887	+	0.664951i	$0.231547\pi$
$374$	−13.5230	+	3.62347i	−0.699256	+	0.187365i
$375$		0			0
$376$	−14.7919	−	3.96348i	−0.762834	−	0.204401i
$377$		−	16.2426i		−	0.836539i
$378$		0			0
$379$	−29.3137			−1.50574			−0.752872	−	0.658167i	$-0.771332\pi$
$379$	−29.3137			−1.50574			−0.752872	+	0.658167i	$0.771332\pi$
$380$	35.9018	−	20.7279i	1.84172	−	1.06332i
$381$		0			0
$382$	−28.6463	+	7.67576i	−1.46567	+	0.392726i
$383$	7.65685	+	13.2621i	0.391247	+	0.677660i	0.992614	−	0.121313i	$-0.0387105\pi$
$383$	7.65685	+	13.2621i	0.391247	+	0.677660i	−0.601367	+	0.798973i	$0.705377\pi$
$384$		0			0
$385$	27.3995	+	35.3330i	1.39641	+	1.80073i
$386$	−26.7990	−	26.7990i	−1.36403	−	1.36403i
$387$		0			0
$388$	17.6177	+	10.1716i	0.894402	+	0.516383i
$389$	−3.65685	+	6.33386i	−0.185410	+	0.321139i	−0.943715	−	0.330761i	$-0.892695\pi$
$389$	−3.65685	+	6.33386i	−0.185410	+	0.321139i	0.758305	+	0.651900i	$0.226028\pi$
$390$		0			0
$391$		−	7.65685i		−	0.387224i
$392$	10.0740	+	17.0445i	0.508811	+	0.860878i
$393$		0			0
$394$	−0.784076	+	2.92621i	−0.0395012	+	0.147420i
$395$	−20.1287	−	11.6213i	−1.01279	−	0.584732i
$396$		0			0
$397$	10.9867	−	6.34315i	0.551404	−	0.318353i	−0.198284	−	0.980145i	$-0.563537\pi$
$397$	10.9867	−	6.34315i	0.551404	−	0.318353i	0.749688	+	0.661791i	$0.230203\pi$
$398$	−6.34315	+	6.34315i	−0.317953	+	0.317953i
$399$		0			0
$400$	−38.6274			−1.93137
$401$	−0.594346	+	0.343146i	−0.0296802	+	0.0171359i	−0.514767	−	0.857330i	$-0.672121\pi$
$401$	−0.594346	+	0.343146i	−0.0296802	+	0.0171359i	0.485086	+	0.874466i	$0.338788\pi$
$402$		0			0
$403$	4.29289	−	7.43551i	0.213844	−	0.370389i
$404$	−7.76874	+	4.48528i	−0.386509	+	0.223151i
$405$		0			0
$406$	−4.34847	−	10.3485i	−0.215811	−	0.513586i
$407$	−22.3848			−1.10957
$408$		0			0
$409$	1.25736	−	2.17781i	0.0621724	−	0.107686i	−0.833264	−	0.552876i	$-0.813530\pi$
$409$	1.25736	−	2.17781i	0.0621724	−	0.107686i	0.895436	+	0.445190i	$0.146864\pi$
$410$	−4.44433	−	16.5865i	−0.219490	−	0.819147i
$411$		0			0
$412$	−12.6863			−0.625009
$413$	−15.9142	+	2.17781i	−0.783087	+	0.107163i
$414$		0			0
$415$	20.1287	−	11.6213i	0.988080	−	0.570468i
$416$	7.92696	+	29.5838i	0.388651	+	1.45047i
$417$		0			0
$418$	−32.6473	−	8.74782i	−1.59683	−	0.427870i
$419$			8.97056i			0.438241i	0.975698	+	0.219120i	$0.0703187\pi$
$419$			8.97056i			0.438241i	−0.975698	+	0.219120i	$0.929681\pi$
$420$		0			0
$421$		−	32.8701i		−	1.60199i	−0.598672	−	0.800994i	$-0.704305\pi$
$421$		−	32.8701i		−	1.60199i	0.598672	−	0.800994i	$-0.295695\pi$
$422$	1.30171	−	4.85806i	0.0633665	−	0.236487i
$423$		0			0
$424$	8.65901	+	32.3159i	0.420519	+	1.56940i
$425$	−18.7554	+	10.8284i	−0.909770	+	0.525256i
$426$		0			0
$427$	2.24264	−	5.49333i	0.108529	−	0.265841i
$428$	−13.5147			−0.653259
$429$		0			0
$430$	44.9013	−	12.0313i	2.16533	−	0.580200i
$431$	−12.3137	+	21.3280i	−0.593130	+	1.02733i	0.400677	+	0.916219i	$0.368775\pi$
$431$	−12.3137	+	21.3280i	−0.593130	+	1.02733i	−0.993808	+	0.111113i	$0.964558\pi$
$432$		0			0
$433$	1.85786			0.0892833			0.0446416	−	0.999003i	$-0.485785\pi$
$433$	1.85786			0.0892833			0.0446416	+	0.999003i	$0.485785\pi$
$434$	0.744447	−	5.88658i	0.0357346	−	0.282565i
$435$		0			0
$436$	−14.4853	−	25.0892i	−0.693719	−	1.20156i
$437$	9.24264	−	16.0087i	0.442135	−	0.765801i
$438$		0			0
$439$	33.3908	−	19.2782i	1.59365	−	0.920097i	0.600982	−	0.799262i	$-0.294776\pi$
$439$	33.3908	−	19.2782i	1.59365	−	0.920097i	0.992673	−	0.120835i	$-0.0385571\pi$
$440$	33.7990	+	33.7990i	1.61130	+	1.61130i
$441$		0			0
$442$	12.1421	+	12.1421i	0.577542	+	0.577542i
$443$	−28.9121	+	16.6924i	−1.37365	+	0.793079i	−0.991386	−	0.130972i	$-0.958190\pi$
$443$	−28.9121	+	16.6924i	−1.37365	+	0.793079i	−0.382268	+	0.924052i	$0.624857\pi$
$444$		0			0
$445$		0			0
$446$	0.371665	+	0.0995874i	0.0175989	+	0.00471560i
$447$		0			0
$448$	12.9706	+	16.7262i	0.612801	+	0.790237i
$449$		−	7.55635i		−	0.356606i	−0.983976	−	0.178303i	$-0.942939\pi$
$449$		−	7.55635i		−	0.356606i	0.983976	−	0.178303i	$-0.0570607\pi$
$450$		0			0
$451$	−7.00000	+	12.1244i	−0.329617	+	0.570914i
$452$	0.828427	−	1.43488i	0.0389659	−	0.0674910i
$453$		0			0
$454$	−13.7279	+	13.7279i	−0.644283	+	0.644283i
$455$	20.7279	−	50.7728i	0.971740	−	2.38027i
$456$		0			0
$457$	−19.4706	−	33.7240i	−0.910795	−	1.57754i	−0.812944	−	0.582341i	$-0.802137\pi$
$457$	−19.4706	−	33.7240i	−0.910795	−	1.57754i	−0.0978500	−	0.995201i	$-0.531197\pi$
$458$	−6.76608	−	25.2514i	−0.316158	−	1.17992i
$459$		0			0
$460$	−22.6398	+	13.0711i	−1.05558	+	0.609442i
$461$	6.34315			0.295430			0.147715	−	0.989030i	$-0.452808\pi$
$461$	6.34315			0.295430			0.147715	+	0.989030i	$0.452808\pi$
$462$		0			0
$463$			17.1716i			0.798031i	0.916944	+	0.399015i	$0.130648\pi$
$463$			17.1716i			0.798031i	−0.916944	+	0.399015i	$0.869352\pi$
$464$	−6.00000	−	10.3923i	−0.278543	−	0.482451i
$465$		0			0
$466$	−8.49662	−	31.7098i	−0.393598	−	1.46893i
$467$	4.35562	−	2.51472i	0.201554	−	0.116367i	−0.395826	−	0.918325i	$-0.629542\pi$
$467$	4.35562	−	2.51472i	0.201554	−	0.116367i	0.597380	+	0.801958i	$0.296208\pi$
$468$		0			0
$469$	−1.31178	−	9.58579i	−0.0605726	−	0.442630i
$470$	20.7279	+	20.7279i	0.956108	+	0.956108i
$471$		0			0
$472$	−16.5865	+	4.44433i	−0.763454	+	0.204567i
$473$	−32.8219	−	18.9497i	−1.50915	−	0.871310i
$474$		0			0
$475$	−52.2843			−2.39897
$476$	10.9867	+	4.48528i	0.503572	+	0.205583i
$477$		0			0
$478$	0.643238	−	2.40060i	0.0294210	−	0.109801i
$479$	16.4350	−	28.4663i	0.750936	−	1.30066i	−0.196434	−	0.980517i	$-0.562936\pi$
$479$	16.4350	−	28.4663i	0.750936	−	1.30066i	0.947370	−	0.320142i	$-0.103731\pi$
$480$		0			0
$481$	13.7279	+	23.7775i	0.625939	+	1.08416i
$482$	0.656854	+	0.656854i	0.0299189	+	0.0299189i
$483$		0			0
$484$		−	16.9706i		−	0.771389i
$485$	−19.4706	−	33.7240i	−0.884113	−	1.53133i
$486$		0			0
$487$	−20.3749	−	11.7635i	−0.923275	−	0.533053i	−0.0385966	−	0.999255i	$-0.512289\pi$
$487$	−20.3749	−	11.7635i	−0.923275	−	0.533053i	−0.884678	+	0.466202i	$0.845622\pi$
$488$	1.64173	−	6.12701i	0.0743175	−	0.277357i
$489$		0			0
$490$	−0.386750	−	37.8975i	−0.0174716	−	1.71204i
$491$		−	1.10051i		−	0.0496651i	−0.999692	−	0.0248325i	$-0.992095\pi$
$491$		−	1.10051i		−	0.0496651i	0.999692	−	0.0248325i	$-0.00790526\pi$
$492$		0			0
$493$	−5.82655	−	3.36396i	−0.262415	−	0.151505i
$494$	10.7296	+	40.0433i	0.482746	+	1.80163i
$495$		0			0
$496$		−	6.34315i		−	0.284816i
$497$	12.3345	−	9.56497i	0.553277	−	0.429048i
$498$		0			0
$499$	12.1421	+	21.0308i	0.543557	+	0.941468i	0.998696	+	0.0510476i	$0.0162560\pi$
$499$	12.1421	+	21.0308i	0.543557	+	0.941468i	−0.455140	+	0.890420i	$0.650411\pi$
$500$	30.8797	+	17.8284i	1.38098	+	0.797311i
$501$		0			0
$502$	37.8770	+	10.1491i	1.69054	+	0.452978i
$503$	−11.7574			−0.524235			−0.262117	−	0.965036i	$-0.584421\pi$
$503$	−11.7574			−0.524235			−0.262117	+	0.965036i	$0.584421\pi$
$504$		0			0
$505$	17.1716			0.764125
$506$	20.5875	+	5.51639i	0.915224	+	0.245234i
$507$		0			0
$508$	6.07107	−	10.5154i	0.269360	−	0.466545i
$509$	17.2279	+	29.8396i	0.763614	+	1.32262i	0.940976	+	0.338473i	$0.109910\pi$
$509$	17.2279	+	29.8396i	0.763614	+	1.32262i	−0.177362	+	0.984146i	$0.556756\pi$
$510$		0			0
$511$	−5.49333	−	40.1421i	−0.243010	−	1.77578i
$512$	16.0000	+	16.0000i	0.707107	+	0.707107i
$513$		0			0
$514$		0			0
$515$	21.0308	+	12.1421i	0.926728	+	0.535046i
$516$		0			0
$517$		−	23.8995i		−	1.05110i
$518$	15.1120	+	11.4738i	0.663982	+	0.504130i
$519$		0			0
$520$	15.1739	−	56.6297i	0.665419	−	2.48338i
$521$	−10.1822	−	5.87868i	−0.446089	−	0.257550i	0.260088	−	0.965585i	$-0.416248\pi$
$521$	−10.1822	−	5.87868i	−0.446089	−	0.257550i	−0.706177	+	0.708035i	$0.749582\pi$
$522$		0			0
$523$	21.8492	+	37.8440i	0.955401	+	1.65480i	0.733449	+	0.679745i	$0.237910\pi$
$523$	21.8492	+	37.8440i	0.955401	+	1.65480i	0.221952	+	0.975058i	$0.428757\pi$
$524$	24.8284			1.08463
$525$		0			0
$526$	−26.7279	−	26.7279i	−1.16539	−	1.16539i
$527$	−1.77817	−	3.07989i	−0.0774585	−	0.134162i
$528$		0			0
$529$	5.67157	−	9.82345i	0.246590	−	0.427107i
$530$	16.5752	−	61.8595i	0.719980	−	2.68700i
$531$		0			0
$532$	17.5563	+	22.6398i	0.761164	+	0.981558i
$533$	17.1716			0.743783
$534$		0			0
$535$	22.4041	+	12.9350i	0.968615	+	0.559230i
$536$	−2.67700	−	9.99071i	−0.115629	−	0.431533i
$537$		0			0
$538$	13.3431	+	13.3431i	0.575264	+	0.575264i
$539$	−21.6251	+	22.0711i	−0.931461	+	0.950668i
$540$		0			0
$541$	−3.07989	+	1.77817i	−0.132415	+	0.0764497i	−0.564744	−	0.825266i	$-0.691025\pi$
$541$	−3.07989	+	1.77817i	−0.132415	+	0.0764497i	0.432329	+	0.901716i	$0.357692\pi$
$542$	2.22217	+	8.29323i	0.0954502	+	0.356225i
$543$		0			0
$544$	12.2540	+	3.28345i	0.525387	+	0.140777i
$545$			55.4558i			2.37547i
$546$		0			0
$547$	−15.0711			−0.644392			−0.322196	−	0.946673i	$-0.604421\pi$
$547$	−15.0711			−0.644392			−0.322196	+	0.946673i	$0.604421\pi$
$548$	−16.8284	−	29.1477i	−0.718875	−	1.24513i
$549$		0			0
$550$	−15.6027	−	58.2301i	−0.665302	−	2.48294i
$551$	−8.12132	−	14.0665i	−0.345980	−	0.599255i
$552$		0			0
$553$	6.07107	−	14.8710i	0.258168	−	0.632380i
$554$		0			0
$555$		0			0
$556$	−26.5241	−	15.3137i	−1.12487	−	0.649446i
$557$	−12.9142	+	22.3681i	−0.547193	+	0.947766i	0.451273	+	0.892386i	$0.350970\pi$
$557$	−12.9142	+	22.3681i	−0.547193	+	0.947766i	−0.998465	+	0.0553796i	$0.982363\pi$
$558$		0			0
$559$			46.4853i			1.96612i
$560$	−5.49333	−	40.1421i	−0.232135	−	1.69631i
$561$		0			0
$562$	28.4522	+	7.62373i	1.20018	+	0.321588i
$563$	−26.7597	−	15.4497i	−1.12779	−	0.651129i	−0.184411	−	0.982849i	$-0.559038\pi$
$563$	−26.7597	−	15.4497i	−1.12779	−	0.651129i	−0.943378	+	0.331720i	$0.892371\pi$
$564$		0			0
$565$	−2.74666	+	1.58579i	−0.115553	+	0.0667145i
$566$	−22.0416	−	22.0416i	−0.926479	−	0.926479i
$567$		0			0
$568$	11.7990	−	11.7990i	0.495075	−	0.495075i
$569$	−29.4809	+	17.0208i	−1.23590	+	0.713550i	−0.968254	−	0.249967i	$-0.919580\pi$
$569$	−29.4809	+	17.0208i	−1.23590	+	0.713550i	−0.267650	+	0.963516i	$0.586247\pi$
$570$		0			0
$571$	−4.70711	+	8.15295i	−0.196986	+	0.341190i	−0.947550	−	0.319608i	$-0.896449\pi$
$571$	−4.70711	+	8.15295i	−0.196986	+	0.341190i	0.750564	+	0.660798i	$0.229782\pi$
$572$	−41.3951	+	23.8995i	−1.73082	+	0.999288i
$573$		0			0
$574$	10.9403	−	4.59716i	0.456640	−	0.191882i
$575$	32.9706			1.37497
$576$		0			0
$577$	−18.8137	+	32.5863i	−0.783225	+	1.35659i	0.146829	+	0.989162i	$0.453093\pi$
$577$	−18.8137	+	32.5863i	−0.783225	+	1.35659i	−0.930054	+	0.367423i	$0.880240\pi$
$578$	−16.3521	+	4.38153i	−0.680157	+	0.182248i
$579$		0			0
$580$			22.9706i			0.953801i
$581$	9.84315	+	12.6932i	0.408362	+	0.526603i
$582$		0			0
$583$	−45.2180	+	26.1066i	−1.87274	+	1.08122i
$584$	−11.2104	−	41.8378i	−0.463890	−	1.73126i
$585$		0			0
$586$	7.68653	−	28.6865i	0.317528	−	1.18503i
$587$		−	36.6985i		−	1.51471i	−0.653004	−	0.757354i	$-0.726492\pi$
$587$		−	36.6985i		−	1.51471i	0.653004	−	0.757354i	$-0.273508\pi$
$588$		0			0
$589$		−	8.58579i		−	0.353771i
$590$	31.7500	+	8.50740i	1.30713	+	0.350244i
$591$		0			0
$592$	17.5667	+	10.1421i	0.721987	+	0.416839i
$593$	21.8353	−	12.6066i	0.896667	−	0.517691i	0.0205498	−	0.999789i	$-0.493458\pi$
$593$	21.8353	−	12.6066i	0.896667	−	0.517691i	0.876117	+	0.482098i	$0.160125\pi$
$594$		0			0
$595$	−13.9203	−	17.9509i	−0.570677	−	0.735915i
$596$		−	4.00000i		−	0.163846i
$597$		0			0
$598$	−6.76608	−	25.2514i	−0.276686	−	1.03261i
$599$	−1.68629	+	2.92074i	−0.0689000	+	0.119338i	−0.898417	−	0.439143i	$-0.855282\pi$
$599$	−1.68629	+	2.92074i	−0.0689000	+	0.119338i	0.829517	+	0.558481i	$0.188616\pi$
$600$		0			0
$601$	8.31371			0.339123			0.169562	−	0.985520i	$-0.445765\pi$
$601$	8.31371			0.339123			0.169562	+	0.985520i	$0.445765\pi$
$602$	12.4450	+	29.6166i	0.507221	+	1.20708i
$603$		0			0
$604$	−10.0711	−	17.4436i	−0.409786	−	0.709770i
$605$	−16.2426	+	28.1331i	−0.660357	+	1.14377i
$606$		0			0
$607$	−33.3908	+	19.2782i	−1.35529	+	0.782477i	−0.988985	−	0.148018i	$-0.952711\pi$
$607$	−33.3908	+	19.2782i	−1.35529	+	0.782477i	−0.366305	+	0.930495i	$0.619377\pi$
$608$	21.6569	+	21.6569i	0.878301	+	0.878301i
$609$		0			0
$610$	−8.58579	+	8.58579i	−0.347628	+	0.347628i
$611$	−25.3864	+	14.6569i	−1.02702	+	0.592953i
$612$		0			0
$613$	17.9509	+	10.3640i	0.725030	+	0.418596i	0.816601	−	0.577202i	$-0.195856\pi$
$613$	17.9509	+	10.3640i	0.725030	+	0.418596i	−0.0915710	+	0.995799i	$0.529189\pi$
$614$	−2.46259	+	9.19051i	−0.0993821	+	0.370899i
$615$		0			0
$616$	−19.9752	+	26.3091i	−0.804824	+	1.06002i
$617$		−	26.2426i		−	1.05649i	−0.849092	−	0.528244i	$-0.822850\pi$
$617$		−	26.2426i		−	1.05649i	0.849092	−	0.528244i	$-0.177150\pi$
$618$		0			0
$619$	−8.12132	+	14.0665i	−0.326423	+	0.565382i	−0.981799	−	0.189921i	$-0.939177\pi$
$619$	−8.12132	+	14.0665i	−0.326423	+	0.565382i	0.655376	+	0.755303i	$0.272510\pi$
$620$	−6.07107	+	10.5154i	−0.243820	+	0.422309i
$621$		0			0
$622$	−7.65685	−	7.65685i	−0.307012	−	0.307012i
$623$		0			0
$624$		0			0
$625$	−9.98528	−	17.2950i	−0.399411	−	0.691801i
$626$	−11.3567	+	3.04303i	−0.453907	+	0.121624i
$627$		0			0
$628$		0			0
$629$	11.3726			0.453455
$630$		0			0
$631$			18.2132i			0.725056i	0.931973	+	0.362528i	$0.118086\pi$
$631$			18.2132i			0.725056i	−0.931973	+	0.362528i	$0.881914\pi$
$632$	4.44433	−	16.5865i	0.176786	−	0.659774i
$633$		0			0
$634$	−27.0861	+	7.25771i	−1.07573	+	0.288240i
$635$	−20.1287	+	11.6213i	−0.798784	+	0.461178i
$636$		0			0
$637$	36.7063	+	9.43503i	1.45436	+	0.373829i
$638$	13.2426	−	13.2426i	0.524281	−	0.524281i
$639$		0			0
$640$	−11.2104	−	41.8378i	−0.443130	−	1.65379i
$641$	−4.98602	−	2.87868i	−0.196936	−	0.113701i	0.398290	−	0.917260i	$-0.369604\pi$
$641$	−4.98602	−	2.87868i	−0.196936	−	0.113701i	−0.595225	+	0.803559i	$0.702937\pi$
$642$		0			0
$643$	−16.6274			−0.655721			−0.327861	−	0.944726i	$-0.606328\pi$
$643$	−16.6274			−0.655721			−0.327861	+	0.944726i	$0.606328\pi$
$644$	−11.0711	−	14.2767i	−0.436261	−	0.562580i
$645$		0			0
$646$	16.5865	+	4.44433i	0.652586	+	0.174860i
$647$	1.39340	−	2.41344i	0.0547801	−	0.0948820i	−0.837335	−	0.546690i	$-0.815888\pi$
$647$	1.39340	−	2.41344i	0.0547801	−	0.0948820i	0.892115	+	0.451808i	$0.149221\pi$
$648$		0			0
$649$	−13.3995	−	23.2086i	−0.525976	−	0.911017i
$650$	−52.2843	+	52.2843i	−2.05076	+	2.05076i
$651$		0			0
$652$		−	1.17157i		−	0.0458823i
$653$	−7.01472	−	12.1498i	−0.274507	−	0.475460i	0.695504	−	0.718523i	$-0.255181\pi$
$653$	−7.01472	−	12.1498i	−0.274507	−	0.475460i	−0.970011	+	0.243062i	$0.921848\pi$
$654$		0			0
$655$	−41.1595	−	23.7635i	−1.60824	−	0.928515i
$656$	10.9867	−	6.34315i	0.428957	−	0.247658i
$657$		0			0
$658$	−12.2502	+	16.1346i	−0.477563	+	0.628991i
$659$		−	43.7990i		−	1.70617i	−0.521775	−	0.853083i	$-0.674730\pi$
$659$		−	43.7990i		−	1.70617i	0.521775	−	0.853083i	$-0.325270\pi$
$660$		0			0
$661$	−25.7196	−	14.8492i	−1.00038	−	0.577569i	−0.0920180	−	0.995757i	$-0.529332\pi$
$661$	−25.7196	−	14.8492i	−1.00038	−	0.577569i	−0.908360	+	0.418189i	$0.862665\pi$
$662$	33.1729	−	8.88866i	1.28930	−	0.345468i
$663$		0			0
$664$	12.1421	+	12.1421i	0.471206	+	0.471206i
$665$	−7.43551	−	54.3345i	−0.288337	−	2.10700i
$666$		0			0
$667$	5.12132	+	8.87039i	0.198298	+	0.343463i
$668$	13.2621	+	7.65685i	0.513125	+	0.296253i
$669$		0			0
$670$	−5.12436	+	19.1244i	−0.197971	+	0.738838i
$671$	9.89949			0.382166
$672$		0			0
$673$	31.8284			1.22690			0.613448	−	0.789735i	$-0.289782\pi$
$673$	31.8284			1.22690			0.613448	+	0.789735i	$0.289782\pi$
$674$	−5.36478	+	20.0216i	−0.206644	+	0.771205i
$675$		0			0
$676$	28.2562	+	16.3137i	1.08678	+	0.627450i
$677$	0.328427	+	0.568852i	0.0126225	+	0.0218628i	0.872268	−	0.489029i	$-0.162649\pi$
$677$	0.328427	+	0.568852i	0.0126225	+	0.0218628i	−0.859645	+	0.510892i	$0.829315\pi$
$678$		0			0
$679$	21.2664	−	16.4914i	0.816130	−	0.632881i
$680$	−17.1716	−	17.1716i	−0.658500	−	0.658500i
$681$		0			0
$682$	9.56218	−	2.56218i	0.366155	−	0.0981109i
$683$	13.7949	+	7.96447i	0.527846	+	0.304752i	0.740139	−	0.672454i	$-0.234760\pi$
$683$	13.7949	+	7.96447i	0.527846	+	0.304752i	−0.212293	+	0.977206i	$0.568093\pi$
$684$		0			0
$685$			64.4264i			2.46161i
$686$	25.9122	−	3.81576i	0.989331	−	0.145687i
$687$		0			0
$688$	17.1716	+	29.7420i	0.654660	+	1.13390i
$689$	55.4617	+	32.0208i	2.11292	+	1.21990i
$690$		0			0
$691$	22.3137	+	38.6485i	0.848853	+	1.47026i	0.882232	+	0.470815i	$0.156040\pi$
$691$	22.3137	+	38.6485i	0.848853	+	1.47026i	−0.0333787	+	0.999443i	$0.510627\pi$
$692$		−	17.9411i		−	0.682019i
$693$		0			0
$694$	−2.82843	+	2.82843i	−0.107366	+	0.107366i
$695$	29.3137	+	50.7728i	1.11193	+	1.92592i
$696$		0			0
$697$	3.55635	−	6.15978i	0.134706	−	0.233318i
$698$	7.92157	+	2.12258i	0.299836	+	0.0803407i
$699$		0			0
$700$	−19.3137	+	47.3087i	−0.729990	+	1.78810i
$701$	−3.34315			−0.126269			−0.0631344	−	0.998005i	$-0.520110\pi$
$701$	−3.34315			−0.126269			−0.0631344	+	0.998005i	$0.520110\pi$
$702$		0			0
$703$	23.7775	+	13.7279i	0.896784	+	0.517758i
$704$	−17.6569	+	30.5826i	−0.665468	+	1.15262i
$705$		0			0
$706$	−24.2843	+	24.2843i	−0.913951	+	0.913951i
$707$	1.60896	+	11.7574i	0.0605111	+	0.442181i
$708$		0			0
$709$	−36.0759	+	20.8284i	−1.35486	+	0.782228i	−0.988925	−	0.148413i	$-0.952583\pi$
$709$	−36.0759	+	20.8284i	−1.35486	+	0.782228i	−0.365933	+	0.930641i	$0.619250\pi$
$710$	−30.8528	+	8.26697i	−1.15788	+	0.310254i
$711$		0			0
$712$		0			0
$713$			5.41421i			0.202764i
$714$		0			0
$715$	91.4975			3.42181
$716$	−9.17157	−	15.8856i	−0.342758	−	0.593674i
$717$		0			0
$718$	47.7707	−	12.8001i	1.78279	−	0.477696i
$719$	−17.1716	−	29.7420i	−0.640392	−	1.10919i	−0.985345	−	0.170571i	$-0.945439\pi$
$719$	−17.1716	−	29.7420i	−0.640392	−	1.10919i	0.344954	−	0.938620i	$-0.387895\pi$
$720$		0			0
$721$	−6.34315	+	15.5375i	−0.236231	+	0.578646i
$722$	10.3137	+	10.3137i	0.383836	+	0.383836i
$723$		0			0
$724$	3.17157	−	5.49333i	0.117871	−	0.204158i
$725$	14.4853	−	25.0892i	0.537970	−	0.931791i
$726$		0			0
$727$		−	51.2426i		−	1.90048i	−0.311512	−	0.950242i	$-0.600835\pi$
$727$		−	51.2426i		−	1.90048i	0.311512	−	0.950242i	$-0.399165\pi$
$728$	40.1961	+	5.08340i	1.48977	+	0.188404i
$729$		0			0
$730$	−21.4591	+	80.0865i	−0.794238	+	2.96414i
$731$	16.6752	+	9.62742i	0.616754	+	0.356083i
$732$		0			0
$733$	25.7196	−	14.8492i	0.949977	−	0.548469i	0.0569030	−	0.998380i	$-0.481877\pi$
$733$	25.7196	−	14.8492i	0.949977	−	0.548469i	0.893074	+	0.449910i	$0.148544\pi$
$734$	29.0416	−	29.0416i	1.07195	−	1.07195i
$735$		0			0
$736$	−13.6569	−	13.6569i	−0.503398	−	0.503398i
$737$	13.9795	−	8.07107i	0.514941	−	0.297302i
$738$		0			0
$739$	14.1421	−	24.4949i	0.520227	−	0.901059i	−0.479497	−	0.877544i	$-0.659181\pi$
$739$	14.1421	−	24.4949i	0.520227	−	0.901059i	0.999723	−	0.0235156i	$-0.00748595\pi$
$740$	−19.4142	−	33.6264i	−0.713681	−	1.23613i
$741$		0			0
$742$	43.9082	+	5.55285i	1.61192	+	0.203852i
$743$	−25.3137			−0.928670			−0.464335	−	0.885660i	$-0.653707\pi$
$743$	−25.3137			−0.928670			−0.464335	+	0.885660i	$0.653707\pi$
$744$		0			0
$745$	−3.82843	+	6.63103i	−0.140263	+	0.242942i
$746$	−4.44433	−	16.5865i	−0.162718	−	0.607274i
$747$		0			0
$748$			19.7990i			0.723923i
$749$	−6.75736	+	16.5521i	−0.246909	+	0.604800i
$750$		0			0
$751$	27.0569	−	15.6213i	0.987321	−	0.570030i	0.0828486	−	0.996562i	$-0.473598\pi$
$751$	27.0569	−	15.6213i	0.987321	−	0.570030i	0.904472	+	0.426532i	$0.140265\pi$
$752$	−10.8284	+	18.7554i	−0.394872	+	0.683939i
$753$		0			0
$754$	−22.1879	−	5.94522i	−0.808034	−	0.216512i
$755$			38.5563i			1.40321i
$756$		0			0
$757$		−	36.1838i		−	1.31512i	−0.753402	−	0.657561i	$-0.771588\pi$
$757$		−	36.1838i		−	1.31512i	0.753402	−	0.657561i	$-0.228412\pi$
$758$	−10.7296	+	40.0433i	−0.389715	+	1.45444i
$759$		0			0
$760$	−15.1739	−	56.6297i	−0.550415	−	2.05418i
$761$	−27.3286	+	15.7782i	−0.990661	+	0.571958i	−0.905472	−	0.424406i	$-0.860483\pi$
$761$	−27.3286	+	15.7782i	−0.990661	+	0.571958i	−0.0851892	+	0.996365i	$0.527149\pi$
$762$		0			0
$763$	−37.9706	+	5.19615i	−1.37463	+	0.188113i
$764$			41.9411i			1.51738i
$765$		0			0
$766$	20.9189	−	5.60521i	0.755831	−	0.202524i
$767$	−16.4350	+	28.4663i	−0.593434	+	1.02786i
$768$		0			0
$769$	8.31371			0.299800			0.149900	−	0.988701i	$-0.452105\pi$
$769$	8.31371			0.299800			0.149900	+	0.988701i	$0.452105\pi$
$770$	58.2946	−	24.4956i	2.10079	−	0.882762i
$771$		0			0
$772$	−46.4172	+	26.7990i	−1.67059	+	0.964517i
$773$	8.31371	−	14.3998i	0.299023	−	0.517924i	−0.676889	−	0.736085i	$-0.736672\pi$
$773$	8.31371	−	14.3998i	0.299023	−	0.517924i	0.975913	+	0.218161i	$0.0700058\pi$
$774$		0			0
$775$	13.2621	−	7.65685i	0.476387	−	0.275042i
$776$	20.3431	−	20.3431i	0.730276	−	0.730276i
$777$		0			0
$778$	7.31371	+	7.31371i	0.262209	+	0.262209i
$779$	14.8710	−	8.58579i	0.532810	−	0.307618i
$780$		0			0
$781$	22.5527	+	13.0208i	0.807000	+	0.465921i
$782$	−10.4595	−	2.80260i	−0.374029	−	0.100221i
$783$		0			0
$784$	26.9706	−	7.52255i	0.963234	−	0.268662i
$785$		0			0
$786$		0			0
$787$	14.8492	−	25.7196i	0.529318	−	0.916806i	−0.470097	−	0.882615i	$-0.655781\pi$
$787$	14.8492	−	25.7196i	0.529318	−	0.916806i	0.999415	−	0.0341915i	$-0.0108856\pi$
$788$	3.71029	+	2.14214i	0.132174	+	0.0763104i
$789$		0			0
$790$	−23.2426	+	23.2426i	−0.826936	+	0.826936i
$791$	−1.34315	−	1.73205i	−0.0477568	−	0.0615846i
$792$		0			0
$793$	−6.07107	−	10.5154i	−0.215590	−	0.373413i
$794$	−4.64350	−	17.3298i	−0.164792	−	0.615011i
$795$		0			0
$796$	6.34315	+	10.9867i	0.224827	+	0.389412i
$797$	−1.20101			−0.0425420			−0.0212710	−	0.999774i	$-0.506771\pi$
$797$	−1.20101			−0.0425420			−0.0212710	+	0.999774i	$0.506771\pi$
$798$		0			0
$799$			12.1421i			0.429558i
$800$	−14.1386	+	52.7660i	−0.499876	+	1.86556i
$801$		0			0
$802$	0.251200	+	0.937492i	0.00887018	+	0.0331040i
$803$	58.5416	−	33.7990i	2.06589	−	1.19274i
$804$		0			0
$805$	4.68885	+	34.2635i	0.165260	+	1.20763i
$806$	−8.58579	−	8.58579i	−0.302421	−	0.302421i
$807$		0			0
$808$	3.28345	+	12.2540i	0.115512	+	0.431095i
$809$	−11.8272	−	6.82843i	−0.415822	−	0.240075i	0.277466	−	0.960735i	$-0.410505\pi$
$809$	−11.8272	−	6.82843i	−0.415822	−	0.240075i	−0.693288	+	0.720661i	$0.743839\pi$
$810$		0			0
$811$	−38.2843			−1.34434			−0.672171	−	0.740396i	$-0.734638\pi$
$811$	−38.2843			−1.34434			−0.672171	+	0.740396i	$0.734638\pi$
$812$	−15.7279	+	2.15232i	−0.551942	+	0.0755315i
$813$		0			0
$814$	−8.19340	+	30.5782i	−0.287178	+	1.07176i
$815$	−1.12132	+	1.94218i	−0.0392781	+	0.0680317i
$816$		0			0
$817$	23.2426	+	40.2574i	0.813157	+	1.40843i
$818$	−2.51472	−	2.51472i	−0.0879251	−	0.0879251i
$819$		0			0
$820$	−24.2843			−0.848044
$821$	8.57107	+	14.8455i	0.299132	+	0.518112i	0.975938	−	0.218050i	$-0.0699695\pi$
$821$	8.57107	+	14.8455i	0.299132	+	0.518112i	−0.676805	+	0.736162i	$0.736636\pi$
$822$		0			0
$823$	35.9018	+	20.7279i	1.25146	+	0.722530i	0.971399	−	0.237453i	$-0.0763125\pi$
$823$	35.9018	+	20.7279i	1.25146	+	0.722530i	0.280059	+	0.959983i	$0.409646\pi$
$824$	−4.64350	+	17.3298i	−0.161764	+	0.603712i
$825$		0			0
$826$	−2.85006	+	22.5364i	−0.0991664	+	0.784140i
$827$			0.757359i			0.0263360i	0.999913	+	0.0131680i	$0.00419162\pi$
$827$			0.757359i			0.0263360i	−0.999913	+	0.0131680i	$0.995808\pi$
$828$		0			0
$829$	−39.4530	−	22.7782i	−1.37026	−	0.791119i	−0.379298	−	0.925275i	$-0.623834\pi$
$829$	−39.4530	−	22.7782i	−1.37026	−	0.791119i	−0.990960	+	0.134156i	$0.957168\pi$
$830$	−8.50740	−	31.7500i	−0.295296	−	1.10206i
$831$		0			0
$832$	43.3137			1.50163
$833$	10.9867	−	11.2132i	0.380665	−	0.388514i
$834$		0			0
$835$	−14.6569	−	25.3864i	−0.507221	−	0.878533i
$836$	−23.8995	+	41.3951i	−0.826581	+	1.43168i
$837$		0			0
$838$	12.2540	+	3.28345i	0.423308	+	0.113425i
$839$	−40.5269			−1.39914			−0.699572	−	0.714562i	$-0.746626\pi$
$839$	−40.5269			−1.39914			−0.699572	+	0.714562i	$0.746626\pi$
$840$		0			0
$841$	−20.0000			−0.689655
$842$	−44.9013	−	12.0313i	−1.54740	−	0.414625i
$843$		0			0
$844$	−6.15978	−	3.55635i	−0.212028	−	0.122415i
$845$	−31.2279	−	54.0883i	−1.07427	−	1.86070i
$846$		0			0
$847$	−20.7846	−	8.48528i	−0.714168	−	0.291558i
$848$	47.3137			1.62476
$849$		0			0
$850$	7.92696	+	29.5838i	0.271892	+	1.01472i
$851$	−14.9941	−	8.65685i	−0.513992	−	0.296753i
$852$		0			0
$853$			18.4853i			0.632924i	0.948605	+	0.316462i	$0.102495\pi$
$853$			18.4853i			0.632924i	−0.948605	+	0.316462i	$0.897505\pi$
$854$	−6.68316	−	5.07420i	−0.228693	−	0.173636i
$855$		0			0
$856$	−4.94673	+	18.4614i	−0.169076	+	0.630999i
$857$	48.8306	+	28.1924i	1.66802	+	0.963034i	0.968702	+	0.248226i	$0.0798475\pi$
$857$	48.8306	+	28.1924i	1.66802	+	0.963034i	0.699321	+	0.714808i	$0.253486\pi$
$858$		0			0
$859$	−16.4350	−	28.4663i	−0.560756	−	0.971258i	−0.997431	−	0.0716383i	$-0.977177\pi$
$859$	−16.4350	−	28.4663i	−0.560756	−	0.971258i	0.436675	−	0.899619i	$-0.356156\pi$
$860$		−	65.7401i		−	2.24172i
$861$		0			0
$862$	24.6274	+	24.6274i	0.838813	+	0.838813i
$863$	9.17157	+	15.8856i	0.312204	+	0.540753i	0.978839	−	0.204631i	$-0.0655994\pi$
$863$	9.17157	+	15.8856i	0.312204	+	0.540753i	−0.666635	+	0.745384i	$0.732266\pi$
$864$		0			0
$865$	−17.1716	+	29.7420i	−0.583851	+	1.01126i
$866$	0.680026	−	2.53789i	0.0231082	−	0.0862410i
$867$		0			0
$868$	−7.76874	−	3.17157i	−0.263688	−	0.107650i
$869$	26.7990			0.909093
$870$		0			0
$871$	−17.1464	−	9.89949i	−0.580985	−	0.335432i
$872$	−39.5745	+	10.6040i	−1.34016	+	0.359095i
$873$		0			0
$874$	−18.4853	−	18.4853i	−0.625274	−	0.625274i
$875$	37.2751	−	28.9056i	1.26013	−	0.977187i
$876$		0			0
$877$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$877$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$878$	−14.1126	−	52.6690i	−0.476277	−	1.77749i
$879$		0			0
$880$	58.5416	−	33.7990i	1.97344	−	1.13936i
$881$			9.51472i			0.320559i	0.987072	+	0.160280i	$0.0512396\pi$
$881$			9.51472i			0.320559i	−0.987072	+	0.160280i	$0.948760\pi$
$882$		0			0
$883$	29.3137			0.986485			0.493242	−	0.869892i	$-0.335812\pi$
$883$	29.3137			0.986485			0.493242	+	0.869892i	$0.335812\pi$
$884$	21.0308	−	12.1421i	0.707342	−	0.408384i
$885$		0			0
$886$	12.2197	+	45.6045i	0.410528	+	1.53211i
$887$	2.97918	+	5.16010i	0.100031	+	0.173259i	0.911697	−	0.410863i	$-0.134772\pi$
$887$	2.97918	+	5.16010i	0.100031	+	0.173259i	−0.811666	+	0.584122i	$0.801439\pi$
$888$		0			0
$889$	−9.84315	−	12.6932i	−0.330129	−	0.425717i
$890$		0			0
$891$		0			0
$892$	0.272078	−	0.471253i	0.00910984	−	0.0157787i
$893$	−14.6569	+	25.3864i	−0.490473	+	0.849524i
$894$		0			0
$895$			35.1127i			1.17369i
$896$	27.5959	−	11.5959i	0.921915	−	0.387392i
$897$		0			0
$898$	−10.3222	−	2.76582i	−0.344455	−	0.0922965i
$899$	4.11999	+	2.37868i	0.137409	+	0.0793334i
$900$		0			0
$901$	22.9730	−	13.2635i	0.765341	−	0.441870i
$902$	14.0000	+	14.0000i	0.466149	+	0.466149i
$903$		0			0
$904$	−1.65685	−	1.65685i	−0.0551062	−	0.0551062i
$905$	−10.5154	+	6.07107i	−0.349544	+	0.201809i
$906$		0			0
$907$	25.0208	−	43.3373i	0.830803	−	1.43899i	−0.0666001	−	0.997780i	$-0.521215\pi$
$907$	25.0208	−	43.3373i	0.830803	−	1.43899i	0.897403	−	0.441212i	$-0.145451\pi$
$908$	13.7279	+	23.7775i	0.455577	+	0.789083i
$909$		0			0
$910$	−61.7700	−	46.8990i	−2.04766	−	1.55469i
$911$	−3.07107			−0.101749			−0.0508745	−	0.998705i	$-0.516201\pi$
$911$	−3.07107			−0.101749			−0.0508745	+	0.998705i	$0.516201\pi$
$912$		0			0
$913$	−13.3995	+	23.2086i	−0.443459	+	0.768093i
$914$	−53.1946	+	14.2534i	−1.75952	+	0.471462i
$915$		0			0
$916$	−36.9706			−1.22154
$917$	12.4142	−	30.4085i	0.409953	−	1.00418i
$918$		0			0
$919$	−9.20361	+	5.31371i	−0.303599	+	0.175283i	−0.644059	−	0.764976i	$-0.722751\pi$
$919$	−9.20361	+	5.31371i	−0.303599	+	0.175283i	0.340459	+	0.940259i	$0.389417\pi$
$920$	9.56869	+	35.7108i	0.315470	+	1.17735i
$921$		0			0
$922$	2.32175	−	8.66490i	0.0764628	−	0.285363i
$923$		−	31.9411i		−	1.05135i
$924$		0			0
$925$			48.9706i			1.61014i
$926$	23.4568	+	6.28523i	0.770838	+	0.206546i
$927$		0			0
$928$	−16.3923	+	4.39230i	−0.538104	+	0.144184i
$929$	15.6755	−	9.05025i	0.514296	−	0.296929i	−0.220302	−	0.975432i	$-0.570704\pi$
$929$	15.6755	−	9.05025i	0.514296	−	0.296929i	0.734598	+	0.678503i	$0.237371\pi$
$930$		0			0
$931$	36.5061	−	10.1822i	1.19644	−	0.333707i
$932$	−46.4264			−1.52075
$933$		0			0
$934$	−1.84090	−	6.87034i	−0.0602361	−	0.224804i
$935$	18.9497	−	32.8219i	0.619723	−	1.07339i
$936$		0			0
$937$	−16.5147			−0.539512			−0.269756	−	0.962929i	$-0.586943\pi$
$937$	−16.5147			−0.539512			−0.269756	+	0.962929i	$0.586943\pi$
$938$	−13.5746	−	1.71671i	−0.443226	−	0.0560526i
$939$		0			0
$940$	35.9018	−	20.7279i	1.17099	−	0.676070i
$941$	−7.32843	+	12.6932i	−0.238900	+	0.413787i	−0.960399	−	0.278629i	$-0.910120\pi$
$941$	−7.32843	+	12.6932i	−0.238900	+	0.413787i	0.721499	+	0.692415i	$0.243453\pi$
$942$		0			0
$943$	−9.37769	+	5.41421i	−0.305380	+	0.176311i
$944$			24.2843i			0.790386i
$945$		0			0
$946$	−37.8995	+	37.8995i	−1.23222	+	1.23222i
$947$	4.89898	−	2.82843i	0.159195	−	0.0919115i	−0.418286	−	0.908315i	$-0.637369\pi$
$947$	4.89898	−	2.82843i	0.159195	−	0.0919115i	0.577481	+	0.816404i	$0.304036\pi$
$948$		0			0
$949$	−71.8036	−	41.4558i	−2.33084	−	1.34571i
$950$	−19.1374	+	71.4216i	−0.620898	+	2.31722i
$951$		0			0
$952$	10.1484	−	13.3663i	0.328912	−	0.433205i
$953$			35.5563i			1.15178i	0.817526	+	0.575892i	$0.195345\pi$
$953$			35.5563i			1.15178i	−0.817526	+	0.575892i	$0.804655\pi$
$954$		0			0
$955$	40.1421	−	69.5282i	1.29897	−	2.24988i
$956$	−3.04384	−	1.75736i	−0.0984447	−	0.0568371i
$957$		0			0
$958$	−32.8701	−	32.8701i	−1.06198	−	1.06198i
$959$	−44.1127	+	6.03668i	−1.42447	+	0.194935i
$960$		0			0
$961$	−14.2426	−	24.6690i	−0.459440	−	0.795773i
$962$	37.5054	−	10.0495i	1.20922	−	0.324010i
$963$		0			0
$964$	1.13770	−	0.656854i	0.0366430	−	0.0211559i
$965$	102.598			3.30275
$966$		0			0
$967$		−	52.5563i		−	1.69010i	−0.534689	−	0.845049i	$-0.679571\pi$
$967$		−	52.5563i		−	1.69010i	0.534689	−	0.845049i	$-0.320429\pi$
$968$	−23.1822	−	6.21166i	−0.745105	−	0.199650i
$969$		0			0
$970$	−53.1946	+	14.2534i	−1.70797	+	0.457650i
$971$	−19.6575	+	11.3492i	−0.630838	+	0.364215i	−0.781077	−	0.624435i	$-0.785329\pi$
$971$	−19.6575	+	11.3492i	−0.630838	+	0.364215i	0.150239	+	0.988650i	$0.451996\pi$
$972$		0			0
$973$	−32.0174	+	24.8284i	−1.02643	+	0.795963i
$974$	−23.5269	+	23.5269i	−0.753851	+	0.753851i
$975$		0			0
$976$	−7.76874	−	4.48528i	−0.248671	−	0.143570i
$977$	−24.2848	−	14.0208i	−0.776938	−	0.448566i	0.0584057	−	0.998293i	$-0.481398\pi$
$977$	−24.2848	−	14.0208i	−0.776938	−	0.448566i	−0.835344	+	0.549727i	$0.814732\pi$
$978$		0			0
$979$		0			0
$980$	−51.9105	−	13.3431i	−1.65822	−	0.426231i
$981$		0			0
$982$	−1.50332	−	0.402813i	−0.0479728	−	0.0128543i
$983$	−22.3137	+	38.6485i	−0.711697	+	1.23269i	0.252523	+	0.967591i	$0.418740\pi$
$983$	−22.3137	+	38.6485i	−0.711697	+	1.23269i	−0.964220	+	0.265104i	$0.914594\pi$
$984$		0			0
$985$	−4.10051	−	7.10228i	−0.130653	−	0.226298i
$986$	−6.72792	+	6.72792i	−0.214261	+	0.214261i
$987$		0			0
$988$	58.6274			1.86519
$989$	−14.6569	−	25.3864i	−0.466061	−	0.807241i
$990$		0			0
$991$	−43.4859	−	25.1066i	−1.38138	−	0.797537i	−0.389053	−	0.921215i	$-0.627198\pi$
$991$	−43.4859	−	25.1066i	−1.38138	−	0.797537i	−0.992322	+	0.123678i	$0.960531\pi$
$992$	−8.66490	−	2.32175i	−0.275111	−	0.0737157i
$993$		0			0
$994$	−8.55126	−	20.3502i	−0.271229	−	0.645471i
$995$		−	24.2843i		−	0.769863i
$996$		0			0
$997$	32.4887	+	18.7574i	1.02893	+	0.594052i	0.916677	−	0.399628i	$-0.130861\pi$
$997$	32.4887	+	18.7574i	1.02893	+	0.594052i	0.112250	+	0.993680i	$0.464194\pi$
$998$	33.1729	−	8.88866i	1.05007	−	0.281366i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.bm.a.179.4	yes	8
3.2	odd	2		504.2.bm.b.179.1	yes	8
4.3	odd	2		2016.2.bu.b.431.4		8
7.2	even	3	inner	504.2.bm.a.107.2	✓	8
8.3	odd	2		504.2.bm.b.179.3	yes	8
8.5	even	2		2016.2.bu.a.431.1		8
12.11	even	2		2016.2.bu.a.431.2		8
21.2	odd	6		504.2.bm.b.107.3	yes	8
24.5	odd	2		2016.2.bu.b.431.3		8
24.11	even	2	inner	504.2.bm.a.179.2	yes	8
28.23	odd	6		2016.2.bu.b.1871.3		8
56.37	even	6		2016.2.bu.a.1871.2		8
56.51	odd	6		504.2.bm.b.107.1	yes	8
84.23	even	6		2016.2.bu.a.1871.1		8
168.107	even	6	inner	504.2.bm.a.107.4	yes	8
168.149	odd	6		2016.2.bu.b.1871.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.bm.a.107.2	✓	8	7.2	even	3	inner
504.2.bm.a.107.4	yes	8	168.107	even	6	inner
504.2.bm.a.179.2	yes	8	24.11	even	2	inner
504.2.bm.a.179.4	yes	8	1.1	even	1	trivial
504.2.bm.b.107.1	yes	8	56.51	odd	6
504.2.bm.b.107.3	yes	8	21.2	odd	6
504.2.bm.b.179.1	yes	8	3.2	odd	2
504.2.bm.b.179.3	yes	8	8.3	odd	2
2016.2.bu.a.431.1		8	8.5	even	2
2016.2.bu.a.431.2		8	12.11	even	2
2016.2.bu.a.1871.1		8	84.23	even	6
2016.2.bu.a.1871.2		8	56.37	even	6
2016.2.bu.b.431.3		8	24.5	odd	2
2016.2.bu.b.431.4		8	4.3	odd	2
2016.2.bu.b.1871.3		8	28.23	odd	6
2016.2.bu.b.1871.4		8	168.149	odd	6

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:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.bm (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.366025 - 1.36603i) q^{2} +(-1.73205 - 1.00000i) q^{4} +(1.91421 + 3.31552i) q^{5} +(-2.09077 + 1.62132i) q^{7} +(-2.00000 + 2.00000i) q^{8} +O(q^{10})\)	\(q+(0.366025 - 1.36603i) q^{2} +(-1.73205 - 1.00000i) q^{4} +(1.91421 + 3.31552i) q^{5} +(-2.09077 + 1.62132i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(5.22973 - 1.40130i) q^{10} +(-3.82282 - 2.20711i) q^{11} +5.41421i q^{13} +(1.44949 + 3.44949i) q^{14} +(2.00000 + 3.46410i) q^{16} +(1.94218 + 1.12132i) q^{17} +(2.70711 + 4.68885i) q^{19} -7.65685i q^{20} +(-4.41421 + 4.41421i) q^{22} +(-1.70711 - 2.95680i) q^{23} +(-4.82843 + 8.36308i) q^{25} +(7.39595 + 1.98174i) q^{26} +(5.24264 - 0.717439i) q^{28} -3.00000 q^{29} +(-1.37333 - 0.792893i) q^{31} +(5.46410 - 1.46410i) q^{32} +(2.24264 - 2.24264i) q^{34} +(-9.37769 - 3.82843i) q^{35} +(4.39167 - 2.53553i) q^{37} +(7.39595 - 1.98174i) q^{38} +(-10.4595 - 2.80260i) q^{40} -3.17157i q^{41} +8.58579 q^{43} +(4.41421 + 7.64564i) q^{44} +(-4.66390 + 1.24969i) q^{46} +(2.70711 + 4.68885i) q^{47} +(1.74264 - 6.77962i) q^{49} +(9.65685 + 9.65685i) q^{50} +(5.41421 - 9.37769i) q^{52} +(5.91421 - 10.2437i) q^{53} -16.8995i q^{55} +(0.938900 - 7.42418i) q^{56} +(-1.09808 + 4.09808i) q^{58} +(5.25770 + 3.03553i) q^{59} +(-1.94218 + 1.12132i) q^{61} +(-1.58579 + 1.58579i) q^{62} -8.00000i q^{64} +(-17.9509 + 10.3640i) q^{65} +(-1.82843 + 3.16693i) q^{67} +(-2.24264 - 3.88437i) q^{68} +(-8.66220 + 11.4089i) q^{70} -5.89949 q^{71} +(-7.65685 + 13.2621i) q^{73} +(-1.85614 - 6.92721i) q^{74} -10.8284i q^{76} +(11.5711 - 1.58346i) q^{77} +(-5.25770 + 3.03553i) q^{79} +(-7.65685 + 13.2621i) q^{80} +(-4.33245 - 1.16088i) q^{82} -6.07107i q^{83} +8.58579i q^{85} +(3.14262 - 11.7284i) q^{86} +(12.0599 - 3.23143i) q^{88} +(-8.77817 - 11.3199i) q^{91} +6.82843i q^{92} +(7.39595 - 1.98174i) q^{94} +(-10.3640 + 17.9509i) q^{95} -10.1716 q^{97} +(-8.62328 - 4.86200i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{2} + 4 q^{5} - 16 q^{8}+O(q^{10}) \) 8 * q - 4 * q^2 + 4 * q^5 - 16 * q^8	\( 8 q - 4 q^{2} + 4 q^{5} - 16 q^{8} + 4 q^{10} - 8 q^{14} + 16 q^{16} + 16 q^{19} - 24 q^{22} - 8 q^{23} - 16 q^{25} + 16 q^{26} + 8 q^{28} - 24 q^{29} + 16 q^{32} - 16 q^{34} + 16 q^{38} - 8 q^{40} + 80 q^{43} + 24 q^{44} - 8 q^{46} + 16 q^{47} - 20 q^{49} + 32 q^{50} + 32 q^{52} + 36 q^{53} + 8 q^{56} + 12 q^{58} - 24 q^{62} + 8 q^{67} + 16 q^{68} - 52 q^{70} + 32 q^{71} - 16 q^{73} - 8 q^{74} + 36 q^{77} - 16 q^{80} - 24 q^{82} - 40 q^{86} + 24 q^{88} - 8 q^{91} + 16 q^{94} - 32 q^{95} - 104 q^{97} - 20 q^{98}+O(q^{100}) \) 8 * q - 4 * q^2 + 4 * q^5 - 16 * q^8 + 4 * q^10 - 8 * q^14 + 16 * q^16 + 16 * q^19 - 24 * q^22 - 8 * q^23 - 16 * q^25 + 16 * q^26 + 8 * q^28 - 24 * q^29 + 16 * q^32 - 16 * q^34 + 16 * q^38 - 8 * q^40 + 80 * q^43 + 24 * q^44 - 8 * q^46 + 16 * q^47 - 20 * q^49 + 32 * q^50 + 32 * q^52 + 36 * q^53 + 8 * q^56 + 12 * q^58 - 24 * q^62 + 8 * q^67 + 16 * q^68 - 52 * q^70 + 32 * q^71 - 16 * q^73 - 8 * q^74 + 36 * q^77 - 16 * q^80 - 24 * q^82 - 40 * q^86 + 24 * q^88 - 8 * q^91 + 16 * q^94 - 32 * q^95 - 104 * q^97 - 20 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more