LMFDB - Embedded newform 315.2.p.d.118.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(118,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 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("315.118");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.p (of order $4$, 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:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.40960000.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 7x^{4} + 1 $ x^8 + 7*x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			118.1
Root			$-0.437016 + 0.437016i$ of defining polynomial
Character	$\chi$	$=$	315.118
Dual form			315.2.p.d.307.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +1.00000i q^{4} -2.23607i q^{5} +(-2.58114 - 0.581139i) q^{7} +(-2.12132 - 2.12132i) q^{8} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +1.00000i q^{4} -2.23607i q^{5} +(-2.58114 - 0.581139i) q^{7} +(-2.12132 - 2.12132i) q^{8} +(1.58114 + 1.58114i) q^{10} -4.24264 q^{11} +(-3.16228 + 3.16228i) q^{13} +(2.23607 - 1.41421i) q^{14} +1.00000 q^{16} +(-2.23607 - 2.23607i) q^{17} +3.16228 q^{19} +2.23607 q^{20} +(3.00000 - 3.00000i) q^{22} +(-1.41421 - 1.41421i) q^{23} -5.00000 q^{25} -4.47214i q^{26} +(0.581139 - 2.58114i) q^{28} +5.65685i q^{29} -9.48683i q^{31} +(3.53553 - 3.53553i) q^{32} +3.16228 q^{34} +(-1.29947 + 5.77160i) q^{35} +(1.00000 - 1.00000i) q^{37} +(-2.23607 + 2.23607i) q^{38} +(-4.74342 + 4.74342i) q^{40} +8.94427i q^{41} +(-2.00000 - 2.00000i) q^{43} -4.24264i q^{44} +2.00000 q^{46} +(-8.94427 - 8.94427i) q^{47} +(6.32456 + 3.00000i) q^{49} +(3.53553 - 3.53553i) q^{50} +(-3.16228 - 3.16228i) q^{52} +(7.07107 + 7.07107i) q^{53} +9.48683i q^{55} +(4.24264 + 6.70820i) q^{56} +(-4.00000 - 4.00000i) q^{58} +(6.70820 + 6.70820i) q^{62} +7.00000i q^{64} +(7.07107 + 7.07107i) q^{65} +(4.00000 - 4.00000i) q^{67} +(2.23607 - 2.23607i) q^{68} +(-3.16228 - 5.00000i) q^{70} +4.24264 q^{71} +(-3.16228 + 3.16228i) q^{73} +1.41421i q^{74} +3.16228i q^{76} +(10.9508 + 2.46556i) q^{77} +12.0000i q^{79} -2.23607i q^{80} +(-6.32456 - 6.32456i) q^{82} +(-4.47214 + 4.47214i) q^{83} +(-5.00000 + 5.00000i) q^{85} +2.82843 q^{86} +(9.00000 + 9.00000i) q^{88} -13.4164 q^{89} +(10.0000 - 6.32456i) q^{91} +(1.41421 - 1.41421i) q^{92} +12.6491 q^{94} -7.07107i q^{95} +(-3.16228 - 3.16228i) q^{97} +(-6.59346 + 2.35082i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{7}+O(q^{10}) $ 8 * q - 8 * q^7	$ 8 q - 8 q^{7} + 8 q^{16} + 24 q^{22} - 40 q^{25} - 8 q^{28} + 8 q^{37} - 16 q^{43} + 16 q^{46} - 32 q^{58} + 32 q^{67} - 40 q^{85} + 72 q^{88} + 80 q^{91}+O(q^{100}) $ 8 * q - 8 * q^7 + 8 * q^16 + 24 * q^22 - 40 * q^25 - 8 * q^28 + 8 * q^37 - 16 * q^43 + 16 * q^46 - 32 * q^58 + 32 * q^67 - 40 * q^85 + 72 * q^88 + 80 * q^91

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$1$

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 $

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i	−0.911438	−	0.411438i	$-0.865027\pi$
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i	0.411438	+	0.911438i	$0.365027\pi$
$3$		0			0
$3$		0			0
$4$			1.00000i			0.500000i
$5$		−	2.23607i		−	1.00000i
$5$		−	2.23607i		−	1.00000i
$6$		0			0
$7$	−2.58114	−	0.581139i	−0.975579	−	0.219650i
$7$	−2.58114	−	0.581139i	−0.975579	−	0.219650i
$8$	−2.12132	−	2.12132i	−0.750000	−	0.750000i
$9$		0			0
$10$	1.58114	+	1.58114i	0.500000	+	0.500000i
$11$	−4.24264			−1.27920			−0.639602	−	0.768706i	$-0.720901\pi$
$11$	−4.24264			−1.27920			−0.639602	+	0.768706i	$0.720901\pi$
$12$		0			0
$13$	−3.16228	+	3.16228i	−0.877058	+	0.877058i	−0.993229	−	0.116171i	$-0.962938\pi$
$13$	−3.16228	+	3.16228i	−0.877058	+	0.877058i	0.116171	+	0.993229i	$0.462938\pi$
$14$	2.23607	−	1.41421i	0.597614	−	0.377964i
$15$		0			0
$16$	1.00000			0.250000
$17$	−2.23607	−	2.23607i	−0.542326	−	0.542326i	0.381884	−	0.924210i	$-0.375275\pi$
$17$	−2.23607	−	2.23607i	−0.542326	−	0.542326i	−0.924210	+	0.381884i	$0.875275\pi$
$18$		0			0
$19$	3.16228			0.725476			0.362738	−	0.931891i	$-0.381842\pi$
$19$	3.16228			0.725476			0.362738	+	0.931891i	$0.381842\pi$
$20$	2.23607			0.500000
$21$		0			0
$22$	3.00000	−	3.00000i	0.639602	−	0.639602i
$23$	−1.41421	−	1.41421i	−0.294884	−	0.294884i	0.544122	−	0.839006i	$-0.316863\pi$
$23$	−1.41421	−	1.41421i	−0.294884	−	0.294884i	−0.839006	+	0.544122i	$0.816863\pi$
$24$		0			0
$25$	−5.00000			−1.00000
$26$		−	4.47214i		−	0.877058i
$27$		0			0
$28$	0.581139	−	2.58114i	0.109825	−	0.487789i
$29$			5.65685i			1.05045i	0.850963	+	0.525226i	$0.176019\pi$
$29$			5.65685i			1.05045i	−0.850963	+	0.525226i	$0.823981\pi$
$30$		0			0
$31$		−	9.48683i		−	1.70389i	−0.523635	−	0.851943i	$-0.675424\pi$
$31$		−	9.48683i		−	1.70389i	0.523635	−	0.851943i	$-0.324576\pi$
$32$	3.53553	−	3.53553i	0.625000	−	0.625000i
$33$		0			0
$34$	3.16228			0.542326
$35$	−1.29947	+	5.77160i	−0.219650	+	0.975579i
$36$		0			0
$37$	1.00000	−	1.00000i	0.164399	−	0.164399i	−0.620113	−	0.784512i	$-0.712913\pi$
$37$	1.00000	−	1.00000i	0.164399	−	0.164399i	0.784512	+	0.620113i	$0.212913\pi$
$38$	−2.23607	+	2.23607i	−0.362738	+	0.362738i
$39$		0			0
$40$	−4.74342	+	4.74342i	−0.750000	+	0.750000i
$41$			8.94427i			1.39686i	0.715678	+	0.698430i	$0.246118\pi$
$41$			8.94427i			1.39686i	−0.715678	+	0.698430i	$0.753882\pi$
$42$		0			0
$43$	−2.00000	−	2.00000i	−0.304997	−	0.304997i	0.537968	−	0.842965i	$-0.319192\pi$
$43$	−2.00000	−	2.00000i	−0.304997	−	0.304997i	−0.842965	+	0.537968i	$0.819192\pi$
$44$		−	4.24264i		−	0.639602i
$45$		0			0
$46$	2.00000			0.294884
$47$	−8.94427	−	8.94427i	−1.30466	−	1.30466i	−0.925216	−	0.379440i	$-0.876117\pi$
$47$	−8.94427	−	8.94427i	−1.30466	−	1.30466i	−0.379440	−	0.925216i	$-0.623883\pi$
$48$		0			0
$49$	6.32456	+	3.00000i	0.903508	+	0.428571i
$50$	3.53553	−	3.53553i	0.500000	−	0.500000i
$51$		0			0
$52$	−3.16228	−	3.16228i	−0.438529	−	0.438529i
$53$	7.07107	+	7.07107i	0.971286	+	0.971286i	0.999599	−	0.0283132i	$-0.00901359\pi$
$53$	7.07107	+	7.07107i	0.971286	+	0.971286i	−0.0283132	+	0.999599i	$0.509014\pi$
$54$		0			0
$55$			9.48683i			1.27920i
$56$	4.24264	+	6.70820i	0.566947	+	0.896421i
$57$		0			0
$58$	−4.00000	−	4.00000i	−0.525226	−	0.525226i
$59$		0			0			−	1.00000i	$-0.5\pi$
$59$		0			0				1.00000i	$0.5\pi$
$60$		0			0
$61$		0			0		1.00000			$0$
$61$		0			0		−1.00000			$\pi$
$62$	6.70820	+	6.70820i	0.851943	+	0.851943i
$63$		0			0
$64$			7.00000i			0.875000i
$65$	7.07107	+	7.07107i	0.877058	+	0.877058i
$66$		0			0
$67$	4.00000	−	4.00000i	0.488678	−	0.488678i	−0.419211	−	0.907889i	$-0.637693\pi$
$67$	4.00000	−	4.00000i	0.488678	−	0.488678i	0.907889	+	0.419211i	$0.137693\pi$
$68$	2.23607	−	2.23607i	0.271163	−	0.271163i
$69$		0			0
$70$	−3.16228	−	5.00000i	−0.377964	−	0.597614i
$71$	4.24264			0.503509			0.251754	−	0.967791i	$-0.418992\pi$
$71$	4.24264			0.503509			0.251754	+	0.967791i	$0.418992\pi$
$72$		0			0
$73$	−3.16228	+	3.16228i	−0.370117	+	0.370117i	−0.867520	−	0.497403i	$-0.834287\pi$
$73$	−3.16228	+	3.16228i	−0.370117	+	0.370117i	0.497403	+	0.867520i	$0.334287\pi$
$74$			1.41421i			0.164399i
$75$		0			0
$76$			3.16228i			0.362738i
$77$	10.9508	+	2.46556i	1.24796	+	0.280977i
$78$		0			0
$79$			12.0000i			1.35011i	0.737769	+	0.675053i	$0.235879\pi$
$79$			12.0000i			1.35011i	−0.737769	+	0.675053i	$0.764121\pi$
$80$		−	2.23607i		−	0.250000i
$81$		0			0
$82$	−6.32456	−	6.32456i	−0.698430	−	0.698430i
$83$	−4.47214	+	4.47214i	−0.490881	+	0.490881i	−0.908584	−	0.417703i	$-0.862835\pi$
$83$	−4.47214	+	4.47214i	−0.490881	+	0.490881i	0.417703	+	0.908584i	$0.362835\pi$
$84$		0			0
$85$	−5.00000	+	5.00000i	−0.542326	+	0.542326i
$86$	2.82843			0.304997
$87$		0			0
$88$	9.00000	+	9.00000i	0.959403	+	0.959403i
$89$	−13.4164			−1.42214			−0.711068	−	0.703123i	$-0.751788\pi$
$89$	−13.4164			−1.42214			−0.711068	+	0.703123i	$0.751788\pi$
$90$		0			0
$91$	10.0000	−	6.32456i	1.04828	−	0.662994i
$92$	1.41421	−	1.41421i	0.147442	−	0.147442i
$93$		0			0
$94$	12.6491			1.30466
$95$		−	7.07107i		−	0.725476i
$96$		0			0
$97$	−3.16228	−	3.16228i	−0.321081	−	0.321081i	0.528101	−	0.849182i	$-0.322904\pi$
$97$	−3.16228	−	3.16228i	−0.321081	−	0.321081i	−0.849182	+	0.528101i	$0.822904\pi$
$98$	−6.59346	+	2.35082i	−0.666040	+	0.237468i
$99$		0			0
$100$		−	5.00000i		−	0.500000i
$101$		−	4.47214i		−	0.444994i	−0.974933	−	0.222497i	$-0.928579\pi$
$101$		−	4.47214i		−	0.444994i	0.974933	−	0.222497i	$-0.0714208\pi$
$102$		0			0
$103$	−3.16228	+	3.16228i	−0.311588	+	0.311588i	−0.845525	−	0.533936i	$-0.820712\pi$
$103$	−3.16228	+	3.16228i	−0.311588	+	0.311588i	0.533936	+	0.845525i	$0.320712\pi$
$104$	13.4164			1.31559
$105$		0			0
$106$	−10.0000			−0.971286
$107$	−7.07107	+	7.07107i	−0.683586	+	0.683586i	−0.960806	−	0.277220i	$-0.910587\pi$
$107$	−7.07107	+	7.07107i	−0.683586	+	0.683586i	0.277220	+	0.960806i	$0.410587\pi$
$108$		0			0
$109$		−	12.0000i		−	1.14939i	−0.818367	−	0.574696i	$-0.805120\pi$
$109$		−	12.0000i		−	1.14939i	0.818367	−	0.574696i	$-0.194880\pi$
$110$	−6.70820	−	6.70820i	−0.639602	−	0.639602i
$111$		0			0
$112$	−2.58114	−	0.581139i	−0.243895	−	0.0549125i
$113$	−1.41421	−	1.41421i	−0.133038	−	0.133038i	0.637452	−	0.770490i	$-0.279988\pi$
$113$	−1.41421	−	1.41421i	−0.133038	−	0.133038i	−0.770490	+	0.637452i	$0.779988\pi$
$114$		0			0
$115$	−3.16228	+	3.16228i	−0.294884	+	0.294884i
$116$	−5.65685			−0.525226
$117$		0			0
$118$		0			0
$119$	4.47214	+	7.07107i	0.409960	+	0.648204i
$120$		0			0
$121$	7.00000			0.636364
$122$		0			0
$123$		0			0
$124$	9.48683			0.851943
$125$			11.1803i			1.00000i
$126$		0			0
$127$	4.00000	−	4.00000i	0.354943	−	0.354943i	−0.507002	−	0.861945i	$-0.669246\pi$
$127$	4.00000	−	4.00000i	0.354943	−	0.354943i	0.861945	+	0.507002i	$0.169246\pi$
$128$	2.12132	+	2.12132i	0.187500	+	0.187500i
$129$		0			0
$130$	−10.0000			−0.877058
$131$		−	17.8885i		−	1.56293i	−0.623949	−	0.781465i	$-0.714473\pi$
$131$		−	17.8885i		−	1.56293i	0.623949	−	0.781465i	$-0.285527\pi$
$132$		0			0
$133$	−8.16228	−	1.83772i	−0.707759	−	0.159351i
$134$			5.65685i			0.488678i
$135$		0			0
$136$			9.48683i			0.813489i
$137$	−7.07107	+	7.07107i	−0.604122	+	0.604122i	−0.941404	−	0.337282i	$-0.890493\pi$
$137$	−7.07107	+	7.07107i	−0.604122	+	0.604122i	0.337282	+	0.941404i	$0.390493\pi$
$138$		0			0
$139$	3.16228			0.268221			0.134110	−	0.990966i	$-0.457182\pi$
$139$	3.16228			0.268221			0.134110	+	0.990966i	$0.457182\pi$
$140$	−5.77160	−	1.29947i	−0.487789	−	0.109825i
$141$		0			0
$142$	−3.00000	+	3.00000i	−0.251754	+	0.251754i
$143$	13.4164	−	13.4164i	1.12194	−	1.12194i
$144$		0			0
$145$	12.6491			1.05045
$146$		−	4.47214i		−	0.370117i
$147$		0			0
$148$	1.00000	+	1.00000i	0.0821995	+	0.0821995i
$149$		−	19.7990i		−	1.62200i	−0.585049	−	0.810998i	$-0.698925\pi$
$149$		−	19.7990i		−	1.62200i	0.585049	−	0.810998i	$-0.301075\pi$
$150$		0			0
$151$	−4.00000			−0.325515			−0.162758	−	0.986666i	$-0.552039\pi$
$151$	−4.00000			−0.325515			−0.162758	+	0.986666i	$0.552039\pi$
$152$	−6.70820	−	6.70820i	−0.544107	−	0.544107i
$153$		0			0
$154$	−9.48683	+	6.00000i	−0.764471	+	0.483494i
$155$	−21.2132			−1.70389
$156$		0			0
$157$	−3.16228	−	3.16228i	−0.252377	−	0.252377i	0.569567	−	0.821945i	$-0.307111\pi$
$157$	−3.16228	−	3.16228i	−0.252377	−	0.252377i	−0.821945	+	0.569567i	$0.807111\pi$
$158$	−8.48528	−	8.48528i	−0.675053	−	0.675053i
$159$		0			0
$160$	−7.90569	−	7.90569i	−0.625000	−	0.625000i
$161$	2.82843	+	4.47214i	0.222911	+	0.352454i
$162$		0			0
$163$	−14.0000	−	14.0000i	−1.09656	−	1.09656i	−0.994809	−	0.101755i	$-0.967554\pi$
$163$	−14.0000	−	14.0000i	−1.09656	−	1.09656i	−0.101755	−	0.994809i	$-0.532446\pi$
$164$	−8.94427			−0.698430
$165$		0			0
$166$		−	6.32456i		−	0.490881i
$167$	4.47214	+	4.47214i	0.346064	+	0.346064i	0.858641	−	0.512577i	$-0.171309\pi$
$167$	4.47214	+	4.47214i	0.346064	+	0.346064i	−0.512577	+	0.858641i	$0.671309\pi$
$168$		0			0
$169$		−	7.00000i		−	0.538462i
$170$		−	7.07107i		−	0.542326i
$171$		0			0
$172$	2.00000	−	2.00000i	0.152499	−	0.152499i
$173$	2.23607	−	2.23607i	0.170005	−	0.170005i	−0.616976	−	0.786982i	$-0.711643\pi$
$173$	2.23607	−	2.23607i	0.170005	−	0.170005i	0.786982	+	0.616976i	$0.211643\pi$
$174$		0			0
$175$	12.9057	+	2.90569i	0.975579	+	0.219650i
$176$	−4.24264			−0.319801
$177$		0			0
$178$	9.48683	−	9.48683i	0.711068	−	0.711068i
$179$		−	7.07107i		−	0.528516i	−0.964452	−	0.264258i	$-0.914873\pi$
$179$		−	7.07107i		−	0.528516i	0.964452	−	0.264258i	$-0.0851271\pi$
$180$		0			0
$181$		−	18.9737i		−	1.41030i	−0.709057	−	0.705151i	$-0.750879\pi$
$181$		−	18.9737i		−	1.41030i	0.709057	−	0.705151i	$-0.249121\pi$
$182$	−2.59893	+	11.5432i	−0.192646	+	0.855639i
$183$		0			0
$184$			6.00000i			0.442326i
$185$	−2.23607	−	2.23607i	−0.164399	−	0.164399i
$186$		0			0
$187$	9.48683	+	9.48683i	0.693746	+	0.693746i
$188$	8.94427	−	8.94427i	0.652328	−	0.652328i
$189$		0			0
$190$	5.00000	+	5.00000i	0.362738	+	0.362738i
$191$	−21.2132			−1.53493			−0.767467	−	0.641089i	$-0.778483\pi$
$191$	−21.2132			−1.53493			−0.767467	+	0.641089i	$0.778483\pi$
$192$		0			0
$193$	13.0000	+	13.0000i	0.935760	+	0.935760i	0.998058	−	0.0622972i	$-0.0198427\pi$
$193$	13.0000	+	13.0000i	0.935760	+	0.935760i	−0.0622972	+	0.998058i	$0.519843\pi$
$194$	4.47214			0.321081
$195$		0			0
$196$	−3.00000	+	6.32456i	−0.214286	+	0.451754i
$197$	9.89949	−	9.89949i	0.705310	−	0.705310i	−0.260235	−	0.965545i	$-0.583800\pi$
$197$	9.89949	−	9.89949i	0.705310	−	0.705310i	0.965545	+	0.260235i	$0.0838002\pi$
$198$		0			0
$199$	−15.8114			−1.12084			−0.560420	−	0.828209i	$-0.689360\pi$
$199$	−15.8114			−1.12084			−0.560420	+	0.828209i	$0.689360\pi$
$200$	10.6066	+	10.6066i	0.750000	+	0.750000i
$201$		0			0
$202$	3.16228	+	3.16228i	0.222497	+	0.222497i
$203$	3.28742	−	14.6011i	0.230731	−	1.02480i
$204$		0			0
$205$	20.0000			1.39686
$206$		−	4.47214i		−	0.311588i
$207$		0			0
$208$	−3.16228	+	3.16228i	−0.219265	+	0.219265i
$209$	−13.4164			−0.928032
$210$		0			0
$211$	8.00000			0.550743			0.275371	−	0.961338i	$-0.411199\pi$
$211$	8.00000			0.550743			0.275371	+	0.961338i	$0.411199\pi$
$212$	−7.07107	+	7.07107i	−0.485643	+	0.485643i
$213$		0			0
$214$		−	10.0000i		−	0.683586i
$215$	−4.47214	+	4.47214i	−0.304997	+	0.304997i
$216$		0			0
$217$	−5.51317	+	24.4868i	−0.374258	+	1.66227i
$218$	8.48528	+	8.48528i	0.574696	+	0.574696i
$219$		0			0
$220$	−9.48683			−0.639602
$221$	14.1421			0.951303
$222$		0			0
$223$	6.32456	−	6.32456i	0.423524	−	0.423524i	−0.462891	−	0.886415i	$-0.653188\pi$
$223$	6.32456	−	6.32456i	0.423524	−	0.423524i	0.886415	+	0.462891i	$0.153188\pi$
$224$	−11.1803	+	7.07107i	−0.747018	+	0.472456i
$225$		0			0
$226$	2.00000			0.133038
$227$	4.47214	+	4.47214i	0.296826	+	0.296826i	0.839769	−	0.542943i	$-0.182690\pi$
$227$	4.47214	+	4.47214i	0.296826	+	0.296826i	−0.542943	+	0.839769i	$0.682690\pi$
$228$		0			0
$229$	−25.2982			−1.67175			−0.835877	−	0.548917i	$-0.815040\pi$
$229$	−25.2982			−1.67175			−0.835877	+	0.548917i	$0.815040\pi$
$230$		−	4.47214i		−	0.294884i
$231$		0			0
$232$	12.0000	−	12.0000i	0.787839	−	0.787839i
$233$	15.5563	+	15.5563i	1.01913	+	1.01913i	0.999813	+	0.0193169i	$0.00614915\pi$
$233$	15.5563	+	15.5563i	1.01913	+	1.01913i	0.0193169	+	0.999813i	$0.493851\pi$
$234$		0			0
$235$	−20.0000	+	20.0000i	−1.30466	+	1.30466i
$236$		0			0
$237$		0			0
$238$	−8.16228	−	1.83772i	−0.529082	−	0.119122i
$239$		−	7.07107i		−	0.457389i	−0.973498	−	0.228695i	$-0.926554\pi$
$239$		−	7.07107i		−	0.457389i	0.973498	−	0.228695i	$-0.0734457\pi$
$240$		0			0
$241$			18.9737i			1.22220i	0.791553	+	0.611101i	$0.209273\pi$
$241$			18.9737i			1.22220i	−0.791553	+	0.611101i	$0.790727\pi$
$242$	−4.94975	+	4.94975i	−0.318182	+	0.318182i
$243$		0			0
$244$		0			0
$245$	6.70820	−	14.1421i	0.428571	−	0.903508i
$246$		0			0
$247$	−10.0000	+	10.0000i	−0.636285	+	0.636285i
$248$	−20.1246	+	20.1246i	−1.27791	+	1.27791i
$249$		0			0
$250$	−7.90569	−	7.90569i	−0.500000	−	0.500000i
$251$			8.94427i			0.564557i	0.959332	+	0.282279i	$0.0910903\pi$
$251$			8.94427i			0.564557i	−0.959332	+	0.282279i	$0.908910\pi$
$252$		0			0
$253$	6.00000	+	6.00000i	0.377217	+	0.377217i
$254$			5.65685i			0.354943i
$255$		0			0
$256$	−17.0000			−1.06250
$257$	11.1803	+	11.1803i	0.697410	+	0.697410i	0.963851	−	0.266441i	$-0.0858477\pi$
$257$	11.1803	+	11.1803i	0.697410	+	0.697410i	−0.266441	+	0.963851i	$0.585848\pi$
$258$		0			0
$259$	−3.16228	+	2.00000i	−0.196494	+	0.124274i
$260$	−7.07107	+	7.07107i	−0.438529	+	0.438529i
$261$		0			0
$262$	12.6491	+	12.6491i	0.781465	+	0.781465i
$263$	−5.65685	−	5.65685i	−0.348817	−	0.348817i	0.510852	−	0.859669i	$-0.329330\pi$
$263$	−5.65685	−	5.65685i	−0.348817	−	0.348817i	−0.859669	+	0.510852i	$0.829330\pi$
$264$		0			0
$265$	15.8114	−	15.8114i	0.971286	−	0.971286i
$266$	7.07107	−	4.47214i	0.433555	−	0.274204i
$267$		0			0
$268$	4.00000	+	4.00000i	0.244339	+	0.244339i
$269$	13.4164			0.818013			0.409006	−	0.912532i	$-0.365875\pi$
$269$	13.4164			0.818013			0.409006	+	0.912532i	$0.365875\pi$
$270$		0			0
$271$		−	9.48683i		−	0.576284i	−0.957588	−	0.288142i	$-0.906962\pi$
$271$		−	9.48683i		−	0.576284i	0.957588	−	0.288142i	$-0.0930375\pi$
$272$	−2.23607	−	2.23607i	−0.135582	−	0.135582i
$273$		0			0
$274$		−	10.0000i		−	0.604122i
$275$	21.2132			1.27920
$276$		0			0
$277$	7.00000	−	7.00000i	0.420589	−	0.420589i	−0.464817	−	0.885407i	$-0.653880\pi$
$277$	7.00000	−	7.00000i	0.420589	−	0.420589i	0.885407	+	0.464817i	$0.153880\pi$
$278$	−2.23607	+	2.23607i	−0.134110	+	0.134110i
$279$		0			0
$280$	15.0000	−	9.48683i	0.896421	−	0.566947i
$281$	25.4558			1.51857			0.759284	−	0.650759i	$-0.225549\pi$
$281$	25.4558			1.51857			0.759284	+	0.650759i	$0.225549\pi$
$282$		0			0
$283$	−12.6491	+	12.6491i	−0.751912	+	0.751912i	−0.974836	−	0.222924i	$-0.928440\pi$
$283$	−12.6491	+	12.6491i	−0.751912	+	0.751912i	0.222924	+	0.974836i	$0.428440\pi$
$284$			4.24264i			0.251754i
$285$		0			0
$286$			18.9737i			1.12194i
$287$	5.19786	−	23.0864i	0.306820	−	1.36275i
$288$		0			0
$289$		−	7.00000i		−	0.411765i
$290$	−8.94427	+	8.94427i	−0.525226	+	0.525226i
$291$		0			0
$292$	−3.16228	−	3.16228i	−0.185058	−	0.185058i
$293$	−11.1803	+	11.1803i	−0.653162	+	0.653162i	−0.953753	−	0.300591i	$-0.902816\pi$
$293$	−11.1803	+	11.1803i	−0.653162	+	0.653162i	0.300591	+	0.953753i	$0.402816\pi$
$294$		0			0
$295$		0			0
$296$	−4.24264			−0.246598
$297$		0			0
$298$	14.0000	+	14.0000i	0.810998	+	0.810998i
$299$	8.94427			0.517261
$300$		0			0
$301$	4.00000	+	6.32456i	0.230556	+	0.364541i
$302$	2.82843	−	2.82843i	0.162758	−	0.162758i
$303$		0			0
$304$	3.16228			0.181369
$305$		0			0
$306$		0			0
$307$	−3.16228	−	3.16228i	−0.180481	−	0.180481i	0.611085	−	0.791565i	$-0.290734\pi$
$307$	−3.16228	−	3.16228i	−0.180481	−	0.180481i	−0.791565	+	0.611085i	$0.790734\pi$
$308$	−2.46556	+	10.9508i	−0.140489	+	0.623982i
$309$		0			0
$310$	15.0000	−	15.0000i	0.851943	−	0.851943i
$311$			8.94427i			0.507183i	0.967311	+	0.253592i	$0.0816119\pi$
$311$			8.94427i			0.507183i	−0.967311	+	0.253592i	$0.918388\pi$
$312$		0			0
$313$	15.8114	−	15.8114i	0.893713	−	0.893713i	−0.101158	−	0.994870i	$-0.532255\pi$
$313$	15.8114	−	15.8114i	0.893713	−	0.893713i	0.994870	+	0.101158i	$0.0322547\pi$
$314$	4.47214			0.252377
$315$		0			0
$316$	−12.0000			−0.675053
$317$	9.89949	−	9.89949i	0.556011	−	0.556011i	−0.372158	−	0.928169i	$-0.621382\pi$
$317$	9.89949	−	9.89949i	0.556011	−	0.556011i	0.928169	+	0.372158i	$0.121382\pi$
$318$		0			0
$319$		−	24.0000i		−	1.34374i
$320$	15.6525			0.875000
$321$		0			0
$322$	−5.16228	−	1.16228i	−0.287682	−	0.0647712i
$323$	−7.07107	−	7.07107i	−0.393445	−	0.393445i
$324$		0			0
$325$	15.8114	−	15.8114i	0.877058	−	0.877058i
$326$	19.7990			1.09656
$327$		0			0
$328$	18.9737	−	18.9737i	1.04765	−	1.04765i
$329$	17.8885	+	28.2843i	0.986227	+	1.55936i
$330$		0			0
$331$	−4.00000			−0.219860			−0.109930	−	0.993939i	$-0.535063\pi$
$331$	−4.00000			−0.219860			−0.109930	+	0.993939i	$0.535063\pi$
$332$	−4.47214	−	4.47214i	−0.245440	−	0.245440i
$333$		0			0
$334$	−6.32456			−0.346064
$335$	−8.94427	−	8.94427i	−0.488678	−	0.488678i
$336$		0			0
$337$	−17.0000	+	17.0000i	−0.926049	+	0.926049i	−0.997448	−	0.0713988i	$-0.977254\pi$
$337$	−17.0000	+	17.0000i	−0.926049	+	0.926049i	0.0713988	+	0.997448i	$0.477254\pi$
$338$	4.94975	+	4.94975i	0.269231	+	0.269231i
$339$		0			0
$340$	−5.00000	−	5.00000i	−0.271163	−	0.271163i
$341$			40.2492i			2.17962i
$342$		0			0
$343$	−14.5811	−	11.4189i	−0.787307	−	0.616561i
$344$			8.48528i			0.457496i
$345$		0			0
$346$			3.16228i			0.170005i
$347$	−2.82843	+	2.82843i	−0.151838	+	0.151838i	−0.778938	−	0.627100i	$-0.784242\pi$
$347$	−2.82843	+	2.82843i	−0.151838	+	0.151838i	0.627100	+	0.778938i	$0.284242\pi$
$348$		0			0
$349$	−25.2982			−1.35418			−0.677091	−	0.735899i	$-0.736760\pi$
$349$	−25.2982			−1.35418			−0.677091	+	0.735899i	$0.736760\pi$
$350$	−11.1803	+	7.07107i	−0.597614	+	0.377964i
$351$		0			0
$352$	−15.0000	+	15.0000i	−0.799503	+	0.799503i
$353$	2.23607	−	2.23607i	0.119014	−	0.119014i	−0.645091	−	0.764105i	$-0.723181\pi$
$353$	2.23607	−	2.23607i	0.119014	−	0.119014i	0.764105	+	0.645091i	$0.223181\pi$
$354$		0			0
$355$		−	9.48683i		−	0.503509i
$356$		−	13.4164i		−	0.711068i
$357$		0			0
$358$	5.00000	+	5.00000i	0.264258	+	0.264258i
$359$		−	15.5563i		−	0.821033i	−0.911853	−	0.410516i	$-0.865348\pi$
$359$		−	15.5563i		−	0.821033i	0.911853	−	0.410516i	$-0.134652\pi$
$360$		0			0
$361$	−9.00000			−0.473684
$362$	13.4164	+	13.4164i	0.705151	+	0.705151i
$363$		0			0
$364$	6.32456	+	10.0000i	0.331497	+	0.524142i
$365$	7.07107	+	7.07107i	0.370117	+	0.370117i
$366$		0			0
$367$	6.32456	+	6.32456i	0.330139	+	0.330139i	0.852639	−	0.522500i	$-0.175001\pi$
$367$	6.32456	+	6.32456i	0.330139	+	0.330139i	−0.522500	+	0.852639i	$0.675001\pi$
$368$	−1.41421	−	1.41421i	−0.0737210	−	0.0737210i
$369$		0			0
$370$	3.16228			0.164399
$371$	−14.1421	−	22.3607i	−0.734223	−	1.16091i
$372$		0			0
$373$	−23.0000	−	23.0000i	−1.19089	−	1.19089i	−0.976816	−	0.214078i	$-0.931325\pi$
$373$	−23.0000	−	23.0000i	−1.19089	−	1.19089i	−0.214078	−	0.976816i	$-0.568675\pi$
$374$	−13.4164			−0.693746
$375$		0			0
$376$			37.9473i			1.95698i
$377$	−17.8885	−	17.8885i	−0.921307	−	0.921307i
$378$		0			0
$379$		−	12.0000i		−	0.616399i	−0.951322	−	0.308199i	$-0.900274\pi$
$379$		−	12.0000i		−	0.616399i	0.951322	−	0.308199i	$-0.0997264\pi$
$380$	7.07107			0.362738
$381$		0			0
$382$	15.0000	−	15.0000i	0.767467	−	0.767467i
$383$	−4.47214	+	4.47214i	−0.228515	+	0.228515i	−0.812072	−	0.583557i	$-0.801661\pi$
$383$	−4.47214	+	4.47214i	−0.228515	+	0.228515i	0.583557	+	0.812072i	$0.301661\pi$
$384$		0			0
$385$	5.51317	−	24.4868i	0.280977	−	1.24796i
$386$	−18.3848			−0.935760
$387$		0			0
$388$	3.16228	−	3.16228i	0.160540	−	0.160540i
$389$		−	19.7990i		−	1.00385i	−0.864912	−	0.501924i	$-0.832626\pi$
$389$		−	19.7990i		−	1.00385i	0.864912	−	0.501924i	$-0.167374\pi$
$390$		0			0
$391$			6.32456i			0.319847i
$392$	−7.05245	−	19.7804i	−0.356202	−	0.999059i
$393$		0			0
$394$			14.0000i			0.705310i
$395$	26.8328			1.35011
$396$		0			0
$397$	15.8114	+	15.8114i	0.793551	+	0.793551i	0.982070	−	0.188519i	$-0.0603686\pi$
$397$	15.8114	+	15.8114i	0.793551	+	0.793551i	−0.188519	+	0.982070i	$0.560369\pi$
$398$	11.1803	−	11.1803i	0.560420	−	0.560420i
$399$		0			0
$400$	−5.00000			−0.250000
$401$	−16.9706			−0.847469			−0.423735	−	0.905786i	$-0.639281\pi$
$401$	−16.9706			−0.847469			−0.423735	+	0.905786i	$0.639281\pi$
$402$		0			0
$403$	30.0000	+	30.0000i	1.49441	+	1.49441i
$404$	4.47214			0.222497
$405$		0			0
$406$	8.00000	+	12.6491i	0.397033	+	0.627765i
$407$	−4.24264	+	4.24264i	−0.210300	+	0.210300i
$408$		0			0
$409$	−25.2982			−1.25092			−0.625458	−	0.780258i	$-0.715088\pi$
$409$	−25.2982			−1.25092			−0.625458	+	0.780258i	$0.715088\pi$
$410$	−14.1421	+	14.1421i	−0.698430	+	0.698430i
$411$		0			0
$412$	−3.16228	−	3.16228i	−0.155794	−	0.155794i
$413$		0			0
$414$		0			0
$415$	10.0000	+	10.0000i	0.490881	+	0.490881i
$416$			22.3607i			1.09632i
$417$		0			0
$418$	9.48683	−	9.48683i	0.464016	−	0.464016i
$419$	−26.8328			−1.31087			−0.655434	−	0.755252i	$-0.727514\pi$
$419$	−26.8328			−1.31087			−0.655434	+	0.755252i	$0.727514\pi$
$420$		0			0
$421$	−16.0000			−0.779792			−0.389896	−	0.920859i	$-0.627489\pi$
$421$	−16.0000			−0.779792			−0.389896	+	0.920859i	$0.627489\pi$
$422$	−5.65685	+	5.65685i	−0.275371	+	0.275371i
$423$		0			0
$424$		−	30.0000i		−	1.45693i
$425$	11.1803	+	11.1803i	0.542326	+	0.542326i
$426$		0			0
$427$		0			0
$428$	−7.07107	−	7.07107i	−0.341793	−	0.341793i
$429$		0			0
$430$		−	6.32456i		−	0.304997i
$431$	−21.2132			−1.02180			−0.510902	−	0.859639i	$-0.670689\pi$
$431$	−21.2132			−1.02180			−0.510902	+	0.859639i	$0.670689\pi$
$432$		0			0
$433$	−22.1359	+	22.1359i	−1.06379	+	1.06379i	−0.0659635	+	0.997822i	$0.521012\pi$
$433$	−22.1359	+	22.1359i	−1.06379	+	1.06379i	−0.997822	+	0.0659635i	$0.978988\pi$
$434$	−13.4164	−	21.2132i	−0.644008	−	1.01827i
$435$		0			0
$436$	12.0000			0.574696
$437$	−4.47214	−	4.47214i	−0.213931	−	0.213931i
$438$		0			0
$439$	22.1359			1.05649			0.528245	−	0.849092i	$-0.322850\pi$
$439$	22.1359			1.05649			0.528245	+	0.849092i	$0.322850\pi$
$440$	20.1246	−	20.1246i	0.959403	−	0.959403i
$441$		0			0
$442$	−10.0000	+	10.0000i	−0.475651	+	0.475651i
$443$	−14.1421	−	14.1421i	−0.671913	−	0.671913i	0.286244	−	0.958157i	$-0.407593\pi$
$443$	−14.1421	−	14.1421i	−0.671913	−	0.671913i	−0.958157	+	0.286244i	$0.907593\pi$
$444$		0			0
$445$			30.0000i			1.42214i
$446$			8.94427i			0.423524i
$447$		0			0
$448$	4.06797	−	18.0680i	0.192194	−	0.853631i
$449$			22.6274i			1.06785i	0.845531	+	0.533927i	$0.179284\pi$
$449$			22.6274i			1.06785i	−0.845531	+	0.533927i	$0.820716\pi$
$450$		0			0
$451$		−	37.9473i		−	1.78687i
$452$	1.41421	−	1.41421i	0.0665190	−	0.0665190i
$453$		0			0
$454$	−6.32456			−0.296826
$455$	−14.1421	−	22.3607i	−0.662994	−	1.04828i
$456$		0			0
$457$	1.00000	−	1.00000i	0.0467780	−	0.0467780i	−0.683331	−	0.730109i	$-0.739469\pi$
$457$	1.00000	−	1.00000i	0.0467780	−	0.0467780i	0.730109	+	0.683331i	$0.239469\pi$
$458$	17.8885	−	17.8885i	0.835877	−	0.835877i
$459$		0			0
$460$	−3.16228	−	3.16228i	−0.147442	−	0.147442i
$461$		−	17.8885i		−	0.833153i	−0.909101	−	0.416576i	$-0.863230\pi$
$461$		−	17.8885i		−	0.833153i	0.909101	−	0.416576i	$-0.136770\pi$
$462$		0			0
$463$	16.0000	+	16.0000i	0.743583	+	0.743583i	0.973266	−	0.229683i	$-0.0737688\pi$
$463$	16.0000	+	16.0000i	0.743583	+	0.743583i	−0.229683	+	0.973266i	$0.573769\pi$
$464$			5.65685i			0.262613i
$465$		0			0
$466$	−22.0000			−1.01913
$467$	4.47214	+	4.47214i	0.206946	+	0.206946i	0.802968	−	0.596022i	$-0.203253\pi$
$467$	4.47214	+	4.47214i	0.206946	+	0.206946i	−0.596022	+	0.802968i	$0.703253\pi$
$468$		0			0
$469$	−12.6491	+	8.00000i	−0.584082	+	0.369406i
$470$		−	28.2843i		−	1.30466i
$471$		0			0
$472$		0			0
$473$	8.48528	+	8.48528i	0.390154	+	0.390154i
$474$		0			0
$475$	−15.8114			−0.725476
$476$	−7.07107	+	4.47214i	−0.324102	+	0.204980i
$477$		0			0
$478$	5.00000	+	5.00000i	0.228695	+	0.228695i
$479$	26.8328			1.22602			0.613011	−	0.790074i	$-0.289958\pi$
$479$	26.8328			1.22602			0.613011	+	0.790074i	$0.289958\pi$
$480$		0			0
$481$			6.32456i			0.288375i
$482$	−13.4164	−	13.4164i	−0.611101	−	0.611101i
$483$		0			0
$484$			7.00000i			0.318182i
$485$	−7.07107	+	7.07107i	−0.321081	+	0.321081i
$486$		0			0
$487$	16.0000	−	16.0000i	0.725029	−	0.725029i	−0.244596	−	0.969625i	$-0.578655\pi$
$487$	16.0000	−	16.0000i	0.725029	−	0.725029i	0.969625	+	0.244596i	$0.0786553\pi$
$488$		0			0
$489$		0			0
$490$	5.25658	+	14.7434i	0.237468	+	0.666040i
$491$	4.24264			0.191468			0.0957338	−	0.995407i	$-0.469480\pi$
$491$	4.24264			0.191468			0.0957338	+	0.995407i	$0.469480\pi$
$492$		0			0
$493$	12.6491	−	12.6491i	0.569687	−	0.569687i
$494$		−	14.1421i		−	0.636285i
$495$		0			0
$496$		−	9.48683i		−	0.425971i
$497$	−10.9508	−	2.46556i	−0.491213	−	0.110596i
$498$		0			0
$499$			24.0000i			1.07439i	0.843459	+	0.537194i	$0.180516\pi$
$499$			24.0000i			1.07439i	−0.843459	+	0.537194i	$0.819484\pi$
$500$	−11.1803			−0.500000
$501$		0			0
$502$	−6.32456	−	6.32456i	−0.282279	−	0.282279i
$503$	−4.47214	+	4.47214i	−0.199403	+	0.199403i	−0.799744	−	0.600341i	$-0.795031\pi$
$503$	−4.47214	+	4.47214i	−0.199403	+	0.199403i	0.600341	+	0.799744i	$0.295031\pi$
$504$		0			0
$505$	−10.0000			−0.444994
$506$	−8.48528			−0.377217
$507$		0			0
$508$	4.00000	+	4.00000i	0.177471	+	0.177471i
$509$	26.8328			1.18934			0.594672	−	0.803969i	$-0.297282\pi$
$509$	26.8328			1.18934			0.594672	+	0.803969i	$0.297282\pi$
$510$		0			0
$511$	10.0000	−	6.32456i	0.442374	−	0.279782i
$512$	7.77817	−	7.77817i	0.343750	−	0.343750i
$513$		0			0
$514$	−15.8114			−0.697410
$515$	7.07107	+	7.07107i	0.311588	+	0.311588i
$516$		0			0
$517$	37.9473	+	37.9473i	1.66892	+	1.66892i
$518$	0.821854	−	3.65028i	0.0361102	−	0.160384i
$519$		0			0
$520$		−	30.0000i		−	1.31559i
$521$		−	31.3050i		−	1.37149i	−0.727840	−	0.685747i	$-0.759475\pi$
$521$		−	31.3050i		−	1.37149i	0.727840	−	0.685747i	$-0.240525\pi$
$522$		0			0
$523$	−22.1359	+	22.1359i	−0.967937	+	0.967937i	−0.999502	−	0.0315645i	$-0.989951\pi$
$523$	−22.1359	+	22.1359i	−0.967937	+	0.967937i	0.0315645	+	0.999502i	$0.489951\pi$
$524$	17.8885			0.781465
$525$		0			0
$526$	8.00000			0.348817
$527$	−21.2132	+	21.2132i	−0.924062	+	0.924062i
$528$		0			0
$529$		−	19.0000i		−	0.826087i
$530$			22.3607i			0.971286i
$531$		0			0
$532$	1.83772	−	8.16228i	0.0796754	−	0.353880i
$533$	−28.2843	−	28.2843i	−1.22513	−	1.22513i
$534$		0			0
$535$	15.8114	+	15.8114i	0.683586	+	0.683586i
$536$	−16.9706			−0.733017
$537$		0			0
$538$	−9.48683	+	9.48683i	−0.409006	+	0.409006i
$539$	−26.8328	−	12.7279i	−1.15577	−	0.548230i
$540$		0			0
$541$	14.0000			0.601907			0.300954	−	0.953639i	$-0.402695\pi$
$541$	14.0000			0.601907			0.300954	+	0.953639i	$0.402695\pi$
$542$	6.70820	+	6.70820i	0.288142	+	0.288142i
$543$		0			0
$544$	−15.8114			−0.677908
$545$	−26.8328			−1.14939
$546$		0			0
$547$	4.00000	−	4.00000i	0.171028	−	0.171028i	−0.616403	−	0.787431i	$-0.711411\pi$
$547$	4.00000	−	4.00000i	0.171028	−	0.171028i	0.787431	+	0.616403i	$0.211411\pi$
$548$	−7.07107	−	7.07107i	−0.302061	−	0.302061i
$549$		0			0
$550$	−15.0000	+	15.0000i	−0.639602	+	0.639602i
$551$			17.8885i			0.762078i
$552$		0			0
$553$	6.97367	−	30.9737i	0.296550	−	1.31713i
$554$			9.89949i			0.420589i
$555$		0			0
$556$			3.16228i			0.134110i
$557$	18.3848	−	18.3848i	0.778988	−	0.778988i	−0.200671	−	0.979659i	$-0.564312\pi$
$557$	18.3848	−	18.3848i	0.778988	−	0.778988i	0.979659	+	0.200671i	$0.0643121\pi$
$558$		0			0
$559$	12.6491			0.535000
$560$	−1.29947	+	5.77160i	−0.0549125	+	0.243895i
$561$		0			0
$562$	−18.0000	+	18.0000i	−0.759284	+	0.759284i
$563$	−17.8885	+	17.8885i	−0.753912	+	0.753912i	−0.975207	−	0.221295i	$-0.928972\pi$
$563$	−17.8885	+	17.8885i	−0.753912	+	0.753912i	0.221295	+	0.975207i	$0.428972\pi$
$564$		0			0
$565$	−3.16228	+	3.16228i	−0.133038	+	0.133038i
$566$		−	17.8885i		−	0.751912i
$567$		0			0
$568$	−9.00000	−	9.00000i	−0.377632	−	0.377632i
$569$			5.65685i			0.237148i	0.992945	+	0.118574i	$0.0378322\pi$
$569$			5.65685i			0.237148i	−0.992945	+	0.118574i	$0.962168\pi$
$570$		0			0
$571$	−16.0000			−0.669579			−0.334790	−	0.942293i	$-0.608665\pi$
$571$	−16.0000			−0.669579			−0.334790	+	0.942293i	$0.608665\pi$
$572$	13.4164	+	13.4164i	0.560968	+	0.560968i
$573$		0			0
$574$	12.6491	+	20.0000i	0.527964	+	0.834784i
$575$	7.07107	+	7.07107i	0.294884	+	0.294884i
$576$		0			0
$577$	−3.16228	−	3.16228i	−0.131647	−	0.131647i	0.638213	−	0.769860i	$-0.279674\pi$
$577$	−3.16228	−	3.16228i	−0.131647	−	0.131647i	−0.769860	+	0.638213i	$0.779674\pi$
$578$	4.94975	+	4.94975i	0.205882	+	0.205882i
$579$		0			0
$580$			12.6491i			0.525226i
$581$	14.1421	−	8.94427i	0.586715	−	0.371071i
$582$		0			0
$583$	−30.0000	−	30.0000i	−1.24247	−	1.24247i
$584$	13.4164			0.555175
$585$		0			0
$586$		−	15.8114i		−	0.653162i
$587$	−8.94427	−	8.94427i	−0.369170	−	0.369170i	0.498005	−	0.867174i	$-0.334066\pi$
$587$	−8.94427	−	8.94427i	−0.369170	−	0.369170i	−0.867174	+	0.498005i	$0.834066\pi$
$588$		0			0
$589$		−	30.0000i		−	1.23613i
$590$		0			0
$591$		0			0
$592$	1.00000	−	1.00000i	0.0410997	−	0.0410997i
$593$	−24.5967	+	24.5967i	−1.01007	+	1.01007i	−0.0101186	+	0.999949i	$0.503221\pi$
$593$	−24.5967	+	24.5967i	−1.01007	+	1.01007i	−0.999949	+	0.0101186i	$0.996779\pi$
$594$		0			0
$595$	15.8114	−	10.0000i	0.648204	−	0.409960i
$596$	19.7990			0.810998
$597$		0			0
$598$	−6.32456	+	6.32456i	−0.258630	+	0.258630i
$599$			43.8406i			1.79128i	0.444781	+	0.895640i	$0.353282\pi$
$599$			43.8406i			1.79128i	−0.444781	+	0.895640i	$0.646718\pi$
$600$		0			0
$601$			18.9737i			0.773952i	0.922090	+	0.386976i	$0.126480\pi$
$601$			18.9737i			0.773952i	−0.922090	+	0.386976i	$0.873520\pi$
$602$	−7.30056	−	1.64371i	−0.297549	−	0.0669926i
$603$		0			0
$604$		−	4.00000i		−	0.162758i
$605$		−	15.6525i		−	0.636364i
$606$		0			0
$607$	−31.6228	−	31.6228i	−1.28353	−	1.28353i	−0.938646	−	0.344883i	$-0.887918\pi$
$607$	−31.6228	−	31.6228i	−1.28353	−	1.28353i	−0.344883	−	0.938646i	$-0.612082\pi$
$608$	11.1803	−	11.1803i	0.453423	−	0.453423i
$609$		0			0
$610$		0			0
$611$	56.5685			2.28852
$612$		0			0
$613$	7.00000	+	7.00000i	0.282727	+	0.282727i	0.834196	−	0.551468i	$-0.185932\pi$
$613$	7.00000	+	7.00000i	0.282727	+	0.282727i	−0.551468	+	0.834196i	$0.685932\pi$
$614$	4.47214			0.180481
$615$		0			0
$616$	−18.0000	−	28.4605i	−0.725241	−	1.14671i
$617$	−24.0416	+	24.0416i	−0.967880	+	0.967880i	−0.999500	−	0.0316203i	$-0.989933\pi$
$617$	−24.0416	+	24.0416i	−0.967880	+	0.967880i	0.0316203	+	0.999500i	$0.489933\pi$
$618$		0			0
$619$	41.1096			1.65233			0.826167	−	0.563425i	$-0.190517\pi$
$619$	41.1096			1.65233			0.826167	+	0.563425i	$0.190517\pi$
$620$		−	21.2132i		−	0.851943i
$621$		0			0
$622$	−6.32456	−	6.32456i	−0.253592	−	0.253592i
$623$	34.6296	+	7.79680i	1.38741	+	0.312372i
$624$		0			0
$625$	25.0000			1.00000
$626$			22.3607i			0.893713i
$627$		0			0
$628$	3.16228	−	3.16228i	0.126189	−	0.126189i
$629$	−4.47214			−0.178316
$630$		0			0
$631$	44.0000			1.75161			0.875806	−	0.482663i	$-0.160330\pi$
$631$	44.0000			1.75161			0.875806	+	0.482663i	$0.160330\pi$
$632$	25.4558	−	25.4558i	1.01258	−	1.01258i
$633$		0			0
$634$			14.0000i			0.556011i
$635$	−8.94427	−	8.94427i	−0.354943	−	0.354943i
$636$		0			0
$637$	−29.4868	+	10.5132i	−1.16831	+	0.416547i
$638$	16.9706	+	16.9706i	0.671871	+	0.671871i
$639$		0			0
$640$	4.74342	−	4.74342i	0.187500	−	0.187500i
$641$	−25.4558			−1.00545			−0.502723	−	0.864448i	$-0.667668\pi$
$641$	−25.4558			−1.00545			−0.502723	+	0.864448i	$0.667668\pi$
$642$		0			0
$643$	−3.16228	+	3.16228i	−0.124708	+	0.124708i	−0.766706	−	0.641998i	$-0.778106\pi$
$643$	−3.16228	+	3.16228i	−0.124708	+	0.124708i	0.641998	+	0.766706i	$0.278106\pi$
$644$	−4.47214	+	2.82843i	−0.176227	+	0.111456i
$645$		0			0
$646$	10.0000			0.393445
$647$	31.3050	+	31.3050i	1.23072	+	1.23072i	0.963686	+	0.267039i	$0.0860452\pi$
$647$	31.3050	+	31.3050i	1.23072	+	1.23072i	0.267039	+	0.963686i	$0.413955\pi$
$648$		0			0
$649$		0			0
$650$			22.3607i			0.877058i
$651$		0			0
$652$	14.0000	−	14.0000i	0.548282	−	0.548282i
$653$	7.07107	+	7.07107i	0.276712	+	0.276712i	0.831795	−	0.555083i	$-0.187313\pi$
$653$	7.07107	+	7.07107i	0.276712	+	0.276712i	−0.555083	+	0.831795i	$0.687313\pi$
$654$		0			0
$655$	−40.0000			−1.56293
$656$			8.94427i			0.349215i
$657$		0			0
$658$	−32.6491	−	7.35089i	−1.27279	−	0.286568i
$659$		−	7.07107i		−	0.275450i	−0.990471	−	0.137725i	$-0.956021\pi$
$659$		−	7.07107i		−	0.275450i	0.990471	−	0.137725i	$-0.0439790\pi$
$660$		0			0
$661$		0			0		1.00000			$0$
$661$		0			0		−1.00000			$\pi$
$662$	2.82843	−	2.82843i	0.109930	−	0.109930i
$663$		0			0
$664$	18.9737			0.736321
$665$	−4.10927	+	18.2514i	−0.159351	+	0.707759i
$666$		0			0
$667$	8.00000	−	8.00000i	0.309761	−	0.309761i
$668$	−4.47214	+	4.47214i	−0.173032	+	0.173032i
$669$		0			0
$670$	12.6491			0.488678
$671$		0			0
$672$		0			0
$673$	19.0000	+	19.0000i	0.732396	+	0.732396i	0.971094	−	0.238698i	$-0.0767205\pi$
$673$	19.0000	+	19.0000i	0.732396	+	0.732396i	−0.238698	+	0.971094i	$0.576721\pi$
$674$		−	24.0416i		−	0.926049i
$675$		0			0
$676$	7.00000			0.269231
$677$	24.5967	+	24.5967i	0.945330	+	0.945330i	0.998581	−	0.0532513i	$-0.0169584\pi$
$677$	24.5967	+	24.5967i	0.945330	+	0.945330i	−0.0532513	+	0.998581i	$0.516958\pi$
$678$		0			0
$679$	6.32456	+	10.0000i	0.242714	+	0.383765i
$680$	21.2132			0.813489
$681$		0			0
$682$	−28.4605	−	28.4605i	−1.08981	−	1.08981i
$683$	19.7990	+	19.7990i	0.757587	+	0.757587i	0.975883	−	0.218295i	$-0.0700496\pi$
$683$	19.7990	+	19.7990i	0.757587	+	0.757587i	−0.218295	+	0.975883i	$0.570050\pi$
$684$		0			0
$685$	15.8114	+	15.8114i	0.604122	+	0.604122i
$686$	18.3848	−	2.23607i	0.701934	−	0.0853735i
$687$		0			0
$688$	−2.00000	−	2.00000i	−0.0762493	−	0.0762493i
$689$	−44.7214			−1.70375
$690$		0			0
$691$		−	9.48683i		−	0.360896i	−0.983585	−	0.180448i	$-0.942245\pi$
$691$		−	9.48683i		−	0.360896i	0.983585	−	0.180448i	$-0.0577548\pi$
$692$	2.23607	+	2.23607i	0.0850026	+	0.0850026i
$693$		0			0
$694$		−	4.00000i		−	0.151838i
$695$		−	7.07107i		−	0.268221i
$696$		0			0
$697$	20.0000	−	20.0000i	0.757554	−	0.757554i
$698$	17.8885	−	17.8885i	0.677091	−	0.677091i
$699$		0			0
$700$	−2.90569	+	12.9057i	−0.109825	+	0.487789i
$701$		0			0			−	1.00000i	$-0.5\pi$
$701$		0			0				1.00000i	$0.5\pi$
$702$		0			0
$703$	3.16228	−	3.16228i	0.119268	−	0.119268i
$704$		−	29.6985i		−	1.11930i
$705$		0			0
$706$			3.16228i			0.119014i
$707$	−2.59893	+	11.5432i	−0.0977429	+	0.434127i
$708$		0			0
$709$			24.0000i			0.901339i	0.892691	+	0.450669i	$0.148815\pi$
$709$			24.0000i			0.901339i	−0.892691	+	0.450669i	$0.851185\pi$
$710$	6.70820	+	6.70820i	0.251754	+	0.251754i
$711$		0			0
$712$	28.4605	+	28.4605i	1.06660	+	1.06660i
$713$	−13.4164	+	13.4164i	−0.502448	+	0.502448i
$714$		0			0
$715$	−30.0000	−	30.0000i	−1.12194	−	1.12194i
$716$	7.07107			0.264258
$717$		0			0
$718$	11.0000	+	11.0000i	0.410516	+	0.410516i
$719$	−26.8328			−1.00070			−0.500348	−	0.865825i	$-0.666794\pi$
$719$	−26.8328			−1.00070			−0.500348	+	0.865825i	$0.666794\pi$
$720$		0			0
$721$	10.0000	−	6.32456i	0.372419	−	0.235539i
$722$	6.36396	−	6.36396i	0.236842	−	0.236842i
$723$		0			0
$724$	18.9737			0.705151
$725$		−	28.2843i		−	1.05045i
$726$		0			0
$727$	−31.6228	−	31.6228i	−1.17282	−	1.17282i	−0.981533	−	0.191290i	$-0.938733\pi$
$727$	−31.6228	−	31.6228i	−1.17282	−	1.17282i	−0.191290	−	0.981533i	$-0.561267\pi$
$728$	−34.6296	−	7.79680i	−1.28346	−	0.288968i
$729$		0			0
$730$	−10.0000			−0.370117
$731$			8.94427i			0.330816i
$732$		0			0
$733$	−22.1359	+	22.1359i	−0.817610	+	0.817610i	−0.985761	−	0.168151i	$-0.946220\pi$
$733$	−22.1359	+	22.1359i	−0.817610	+	0.817610i	0.168151	+	0.985761i	$0.446220\pi$
$734$	−8.94427			−0.330139
$735$		0			0
$736$	−10.0000			−0.368605
$737$	−16.9706	+	16.9706i	−0.625119	+	0.625119i
$738$		0			0
$739$			12.0000i			0.441427i	0.975339	+	0.220714i	$0.0708386\pi$
$739$			12.0000i			0.441427i	−0.975339	+	0.220714i	$0.929161\pi$
$740$	2.23607	−	2.23607i	0.0821995	−	0.0821995i
$741$		0			0
$742$	25.8114	+	5.81139i	0.947566	+	0.213343i
$743$	28.2843	+	28.2843i	1.03765	+	1.03765i	0.999263	+	0.0383863i	$0.0122217\pi$
$743$	28.2843	+	28.2843i	1.03765	+	1.03765i	0.0383863	+	0.999263i	$0.487778\pi$
$744$		0			0
$745$	−44.2719			−1.62200
$746$	32.5269			1.19089
$747$		0			0
$748$	−9.48683	+	9.48683i	−0.346873	+	0.346873i
$749$	22.3607	−	14.1421i	0.817041	−	0.516742i
$750$		0			0
$751$	8.00000			0.291924			0.145962	−	0.989290i	$-0.453372\pi$
$751$	8.00000			0.291924			0.145962	+	0.989290i	$0.453372\pi$
$752$	−8.94427	−	8.94427i	−0.326164	−	0.326164i
$753$		0			0
$754$	25.2982			0.921307
$755$			8.94427i			0.325515i
$756$		0			0
$757$	1.00000	−	1.00000i	0.0363456	−	0.0363456i	−0.688700	−	0.725046i	$-0.741818\pi$
$757$	1.00000	−	1.00000i	0.0363456	−	0.0363456i	0.725046	+	0.688700i	$0.241818\pi$
$758$	8.48528	+	8.48528i	0.308199	+	0.308199i
$759$		0			0
$760$	−15.0000	+	15.0000i	−0.544107	+	0.544107i
$761$		−	17.8885i		−	0.648459i	−0.945978	−	0.324230i	$-0.894895\pi$
$761$		−	17.8885i		−	0.648459i	0.945978	−	0.324230i	$-0.105105\pi$
$762$		0			0
$763$	−6.97367	+	30.9737i	−0.252464	+	1.12132i
$764$		−	21.2132i		−	0.767467i
$765$		0			0
$766$		−	6.32456i		−	0.228515i
$767$		0			0
$768$		0			0
$769$	−6.32456			−0.228069			−0.114035	−	0.993477i	$-0.536377\pi$
$769$	−6.32456			−0.228069			−0.114035	+	0.993477i	$0.536377\pi$
$770$	13.4164	+	21.2132i	0.483494	+	0.764471i
$771$		0			0
$772$	−13.0000	+	13.0000i	−0.467880	+	0.467880i
$773$	29.0689	−	29.0689i	1.04554	−	1.04554i	0.0466225	−	0.998913i	$-0.485154\pi$
$773$	29.0689	−	29.0689i	1.04554	−	1.04554i	0.998913	−	0.0466225i	$-0.0148458\pi$
$774$		0			0
$775$			47.4342i			1.70389i
$776$			13.4164i			0.481621i
$777$		0			0
$778$	14.0000	+	14.0000i	0.501924	+	0.501924i
$779$			28.2843i			1.01339i
$780$		0			0
$781$	−18.0000			−0.644091
$782$	−4.47214	−	4.47214i	−0.159923	−	0.159923i
$783$		0			0
$784$	6.32456	+	3.00000i	0.225877	+	0.107143i
$785$	−7.07107	+	7.07107i	−0.252377	+	0.252377i
$786$		0			0
$787$	−3.16228	−	3.16228i	−0.112723	−	0.112723i	0.648495	−	0.761219i	$-0.275399\pi$
$787$	−3.16228	−	3.16228i	−0.112723	−	0.112723i	−0.761219	+	0.648495i	$0.775399\pi$
$788$	9.89949	+	9.89949i	0.352655	+	0.352655i
$789$		0			0
$790$	−18.9737	+	18.9737i	−0.675053	+	0.675053i
$791$	2.82843	+	4.47214i	0.100567	+	0.159011i
$792$		0			0
$793$		0			0
$794$	−22.3607			−0.793551
$795$		0			0
$796$		−	15.8114i		−	0.560420i
$797$	11.1803	+	11.1803i	0.396028	+	0.396028i	0.876829	−	0.480802i	$-0.159654\pi$
$797$	11.1803	+	11.1803i	0.396028	+	0.396028i	−0.480802	+	0.876829i	$0.659654\pi$
$798$		0			0
$799$			40.0000i			1.41510i
$800$	−17.6777	+	17.6777i	−0.625000	+	0.625000i
$801$		0			0
$802$	12.0000	−	12.0000i	0.423735	−	0.423735i
$803$	13.4164	−	13.4164i	0.473455	−	0.473455i
$804$		0			0
$805$	10.0000	−	6.32456i	0.352454	−	0.222911i
$806$	−42.4264			−1.49441
$807$		0			0
$808$	−9.48683	+	9.48683i	−0.333746	+	0.333746i
$809$			48.0833i			1.69052i	0.534357	+	0.845259i	$0.320554\pi$
$809$			48.0833i			1.69052i	−0.534357	+	0.845259i	$0.679446\pi$
$810$		0			0
$811$		−	9.48683i		−	0.333128i	−0.986031	−	0.166564i	$-0.946733\pi$
$811$		−	9.48683i		−	0.333128i	0.986031	−	0.166564i	$-0.0532672\pi$
$812$	14.6011	+	3.28742i	0.512399	+	0.115366i
$813$		0			0
$814$		−	6.00000i		−	0.210300i
$815$	−31.3050	+	31.3050i	−1.09656	+	1.09656i
$816$		0			0
$817$	−6.32456	−	6.32456i	−0.221268	−	0.221268i
$818$	17.8885	−	17.8885i	0.625458	−	0.625458i
$819$		0			0
$820$			20.0000i			0.698430i
$821$		0			0			−	1.00000i	$-0.5\pi$
$821$		0			0				1.00000i	$0.5\pi$
$822$		0			0
$823$	−8.00000	−	8.00000i	−0.278862	−	0.278862i	0.553792	−	0.832655i	$-0.313180\pi$
$823$	−8.00000	−	8.00000i	−0.278862	−	0.278862i	−0.832655	+	0.553792i	$0.813180\pi$
$824$	13.4164			0.467383
$825$		0			0
$826$		0			0
$827$	9.89949	−	9.89949i	0.344239	−	0.344239i	−0.513719	−	0.857958i	$-0.671733\pi$
$827$	9.89949	−	9.89949i	0.344239	−	0.344239i	0.857958	+	0.513719i	$0.171733\pi$
$828$		0			0
$829$	31.6228			1.09830			0.549152	−	0.835722i	$-0.314951\pi$
$829$	31.6228			1.09830			0.549152	+	0.835722i	$0.314951\pi$
$830$	−14.1421			−0.490881
$831$		0			0
$832$	−22.1359	−	22.1359i	−0.767426	−	0.767426i
$833$	−7.43393	−	20.8503i	−0.257570	−	0.722421i
$834$		0			0
$835$	10.0000	−	10.0000i	0.346064	−	0.346064i
$836$		−	13.4164i		−	0.464016i
$837$		0			0
$838$	18.9737	−	18.9737i	0.655434	−	0.655434i
$839$		0			0			−	1.00000i	$-0.5\pi$
$839$		0			0				1.00000i	$0.5\pi$
$840$		0			0
$841$	−3.00000			−0.103448
$842$	11.3137	−	11.3137i	0.389896	−	0.389896i
$843$		0			0
$844$			8.00000i			0.275371i
$845$	−15.6525			−0.538462
$846$		0			0
$847$	−18.0680	−	4.06797i	−0.620823	−	0.139777i
$848$	7.07107	+	7.07107i	0.242821	+	0.242821i
$849$		0			0
$850$	−15.8114			−0.542326
$851$	−2.82843			−0.0969572
$852$		0			0
$853$	34.7851	−	34.7851i	1.19102	−	1.19102i	0.214236	−	0.976782i	$-0.431274\pi$
$853$	34.7851	−	34.7851i	1.19102	−	1.19102i	0.976782	−	0.214236i	$-0.0687260\pi$
$854$		0			0
$855$		0			0
$856$	30.0000			1.02538
$857$	−29.0689	−	29.0689i	−0.992974	−	0.992974i	0.00700134	−	0.999975i	$-0.497771\pi$
$857$	−29.0689	−	29.0689i	−0.992974	−	0.992974i	−0.999975	+	0.00700134i	$0.997771\pi$
$858$		0			0
$859$	22.1359			0.755269			0.377634	−	0.925955i	$-0.376738\pi$
$859$	22.1359			0.755269			0.377634	+	0.925955i	$0.376738\pi$
$860$	−4.47214	−	4.47214i	−0.152499	−	0.152499i
$861$		0			0
$862$	15.0000	−	15.0000i	0.510902	−	0.510902i
$863$	−26.8701	−	26.8701i	−0.914667	−	0.914667i	0.0819676	−	0.996635i	$-0.473880\pi$
$863$	−26.8701	−	26.8701i	−0.914667	−	0.914667i	−0.996635	+	0.0819676i	$0.973880\pi$
$864$		0			0
$865$	−5.00000	−	5.00000i	−0.170005	−	0.170005i
$866$		−	31.3050i		−	1.06379i
$867$		0			0
$868$	−24.4868	−	5.51317i	−0.831137	−	0.187129i
$869$		−	50.9117i		−	1.72706i
$870$		0			0
$871$			25.2982i			0.857198i
$872$	−25.4558	+	25.4558i	−0.862044	+	0.862044i
$873$		0			0
$874$	6.32456			0.213931
$875$	6.49733	−	28.8580i	0.219650	−	0.975579i
$876$		0			0
$877$	7.00000	−	7.00000i	0.236373	−	0.236373i	−0.578973	−	0.815347i	$-0.696546\pi$
$877$	7.00000	−	7.00000i	0.236373	−	0.236373i	0.815347	+	0.578973i	$0.196546\pi$
$878$	−15.6525	+	15.6525i	−0.528245	+	0.528245i
$879$		0			0
$880$			9.48683i			0.319801i
$881$		−	4.47214i		−	0.150670i	−0.997158	−	0.0753350i	$-0.975997\pi$
$881$		−	4.47214i		−	0.150670i	0.997158	−	0.0753350i	$-0.0240026\pi$
$882$		0			0
$883$	−32.0000	−	32.0000i	−1.07689	−	1.07689i	−0.996787	−	0.0800988i	$-0.974476\pi$
$883$	−32.0000	−	32.0000i	−1.07689	−	1.07689i	−0.0800988	−	0.996787i	$-0.525524\pi$
$884$			14.1421i			0.475651i
$885$		0			0
$886$	20.0000			0.671913
$887$	−35.7771	−	35.7771i	−1.20128	−	1.20128i	−0.973778	−	0.227499i	$-0.926945\pi$
$887$	−35.7771	−	35.7771i	−1.20128	−	1.20128i	−0.227499	−	0.973778i	$-0.573055\pi$
$888$		0			0
$889$	−12.6491	+	8.00000i	−0.424238	+	0.268311i
$890$	−21.2132	−	21.2132i	−0.711068	−	0.711068i
$891$		0			0
$892$	6.32456	+	6.32456i	0.211762	+	0.211762i
$893$	−28.2843	−	28.2843i	−0.946497	−	0.946497i
$894$		0			0
$895$	−15.8114			−0.528516
$896$	−4.24264	−	6.70820i	−0.141737	−	0.224105i
$897$		0			0
$898$	−16.0000	−	16.0000i	−0.533927	−	0.533927i
$899$	53.6656			1.78985
$900$		0			0
$901$		−	31.6228i		−	1.05351i
$902$	26.8328	+	26.8328i	0.893435	+	0.893435i
$903$		0			0
$904$			6.00000i			0.199557i
$905$	−42.4264			−1.41030
$906$		0			0
$907$	28.0000	−	28.0000i	0.929725	−	0.929725i	−0.0679631	−	0.997688i	$-0.521650\pi$
$907$	28.0000	−	28.0000i	0.929725	−	0.929725i	0.997688	+	0.0679631i	$0.0216500\pi$
$908$	−4.47214	+	4.47214i	−0.148413	+	0.148413i
$909$		0			0
$910$	25.8114	+	5.81139i	0.855639	+	0.192646i
$911$	−4.24264			−0.140565			−0.0702825	−	0.997527i	$-0.522390\pi$
$911$	−4.24264			−0.140565			−0.0702825	+	0.997527i	$0.522390\pi$
$912$		0			0
$913$	18.9737	−	18.9737i	0.627937	−	0.627937i
$914$			1.41421i			0.0467780i
$915$		0			0
$916$		−	25.2982i		−	0.835877i
$917$	−10.3957	+	46.1728i	−0.343297	+	1.52476i
$918$		0			0
$919$			48.0000i			1.58337i	0.610927	+	0.791687i	$0.290797\pi$
$919$			48.0000i			1.58337i	−0.610927	+	0.791687i	$0.709203\pi$
$920$	13.4164			0.442326
$921$		0			0
$922$	12.6491	+	12.6491i	0.416576	+	0.416576i
$923$	−13.4164	+	13.4164i	−0.441606	+	0.441606i
$924$		0			0
$925$	−5.00000	+	5.00000i	−0.164399	+	0.164399i
$926$	−22.6274			−0.743583
$927$		0			0
$928$	20.0000	+	20.0000i	0.656532	+	0.656532i
$929$		0			0			−	1.00000i	$-0.5\pi$
$929$		0			0				1.00000i	$0.5\pi$
$930$		0			0
$931$	20.0000	+	9.48683i	0.655474	+	0.310918i
$932$	−15.5563	+	15.5563i	−0.509565	+	0.509565i
$933$		0			0
$934$	−6.32456			−0.206946
$935$	21.2132	−	21.2132i	0.693746	−	0.693746i
$936$		0			0
$937$	−3.16228	−	3.16228i	−0.103307	−	0.103307i	0.653564	−	0.756871i	$-0.273273\pi$
$937$	−3.16228	−	3.16228i	−0.103307	−	0.103307i	−0.756871	+	0.653564i	$0.773273\pi$
$938$	3.28742	−	14.6011i	0.107338	−	0.476744i
$939$		0			0
$940$	−20.0000	−	20.0000i	−0.652328	−	0.652328i
$941$		−	17.8885i		−	0.583150i	−0.956548	−	0.291575i	$-0.905821\pi$
$941$		−	17.8885i		−	0.583150i	0.956548	−	0.291575i	$-0.0941793\pi$
$942$		0			0
$943$	12.6491	−	12.6491i	0.411912	−	0.411912i
$944$		0			0
$945$		0			0
$946$	−12.0000			−0.390154
$947$	14.1421	−	14.1421i	0.459558	−	0.459558i	−0.438953	−	0.898510i	$-0.644650\pi$
$947$	14.1421	−	14.1421i	0.459558	−	0.459558i	0.898510	+	0.438953i	$0.144650\pi$
$948$		0			0
$949$		−	20.0000i		−	0.649227i
$950$	11.1803	−	11.1803i	0.362738	−	0.362738i
$951$		0			0
$952$	5.51317	−	24.4868i	0.178683	−	0.793623i
$953$	−1.41421	−	1.41421i	−0.0458109	−	0.0458109i	0.683830	−	0.729641i	$-0.260313\pi$
$953$	−1.41421	−	1.41421i	−0.0458109	−	0.0458109i	−0.729641	+	0.683830i	$0.760313\pi$
$954$		0			0
$955$			47.4342i			1.53493i
$956$	7.07107			0.228695
$957$		0			0
$958$	−18.9737	+	18.9737i	−0.613011	+	0.613011i
$959$	22.3607	−	14.1421i	0.722064	−	0.456673i
$960$		0			0
$961$	−59.0000			−1.90323
$962$	−4.47214	−	4.47214i	−0.144187	−	0.144187i
$963$		0			0
$964$	−18.9737			−0.611101
$965$	29.0689	−	29.0689i	0.935760	−	0.935760i
$966$		0			0
$967$	−38.0000	+	38.0000i	−1.22200	+	1.22200i	−0.255077	+	0.966921i	$0.582101\pi$
$967$	−38.0000	+	38.0000i	−1.22200	+	1.22200i	−0.966921	+	0.255077i	$0.917899\pi$
$968$	−14.8492	−	14.8492i	−0.477273	−	0.477273i
$969$		0			0
$970$		−	10.0000i		−	0.321081i
$971$		−	44.7214i		−	1.43518i	−0.696467	−	0.717588i	$-0.745246\pi$
$971$		−	44.7214i		−	1.43518i	0.696467	−	0.717588i	$-0.254754\pi$
$972$		0			0
$973$	−8.16228	−	1.83772i	−0.261671	−	0.0589147i
$974$			22.6274i			0.725029i
$975$		0			0
$976$		0			0
$977$	9.89949	−	9.89949i	0.316713	−	0.316713i	−0.530790	−	0.847503i	$-0.678105\pi$
$977$	9.89949	−	9.89949i	0.316713	−	0.316713i	0.847503	+	0.530790i	$0.178105\pi$
$978$		0			0
$979$	56.9210			1.81920
$980$	14.1421	+	6.70820i	0.451754	+	0.214286i
$981$		0			0
$982$	−3.00000	+	3.00000i	−0.0957338	+	0.0957338i
$983$	−17.8885	+	17.8885i	−0.570556	+	0.570556i	−0.932284	−	0.361728i	$-0.882187\pi$
$983$	−17.8885	+	17.8885i	−0.570556	+	0.570556i	0.361728	+	0.932284i	$0.382187\pi$
$984$		0			0
$985$	−22.1359	−	22.1359i	−0.705310	−	0.705310i
$986$			17.8885i			0.569687i
$987$		0			0
$988$	−10.0000	−	10.0000i	−0.318142	−	0.318142i
$989$			5.65685i			0.179878i
$990$		0			0
$991$	−4.00000			−0.127064			−0.0635321	−	0.997980i	$-0.520237\pi$
$991$	−4.00000			−0.127064			−0.0635321	+	0.997980i	$0.520237\pi$
$992$	−33.5410	−	33.5410i	−1.06493	−	1.06493i
$993$		0			0
$994$	9.48683	−	6.00000i	0.300904	−	0.190308i
$995$			35.3553i			1.12084i
$996$		0			0
$997$	15.8114	+	15.8114i	0.500752	+	0.500752i	0.911671	−	0.410920i	$-0.134792\pi$
$997$	15.8114	+	15.8114i	0.500752	+	0.500752i	−0.410920	+	0.911671i	$0.634792\pi$
$998$	−16.9706	−	16.9706i	−0.537194	−	0.537194i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.p.d.118.1	✓	8
3.2	odd	2	inner	315.2.p.d.118.4	yes	8
5.2	odd	4	inner	315.2.p.d.307.1	yes	8
7.6	odd	2	inner	315.2.p.d.118.2	yes	8
15.2	even	4	inner	315.2.p.d.307.4	yes	8
21.20	even	2	inner	315.2.p.d.118.3	yes	8
35.27	even	4	inner	315.2.p.d.307.2	yes	8
105.62	odd	4	inner	315.2.p.d.307.3	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.p.d.118.1	✓	8	1.1	even	1	trivial
315.2.p.d.118.2	yes	8	7.6	odd	2	inner
315.2.p.d.118.3	yes	8	21.20	even	2	inner
315.2.p.d.118.4	yes	8	3.2	odd	2	inner
315.2.p.d.307.1	yes	8	5.2	odd	4	inner
315.2.p.d.307.2	yes	8	35.27	even	4	inner
315.2.p.d.307.3	yes	8	105.62	odd	4	inner
315.2.p.d.307.4	yes	8	15.2	even	4	inner

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:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.p (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +1.00000i q^{4} -2.23607i q^{5} +(-2.58114 - 0.581139i) q^{7} +(-2.12132 - 2.12132i) q^{8} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +1.00000i q^{4} -2.23607i q^{5} +(-2.58114 - 0.581139i) q^{7} +(-2.12132 - 2.12132i) q^{8} +(1.58114 + 1.58114i) q^{10} -4.24264 q^{11} +(-3.16228 + 3.16228i) q^{13} +(2.23607 - 1.41421i) q^{14} +1.00000 q^{16} +(-2.23607 - 2.23607i) q^{17} +3.16228 q^{19} +2.23607 q^{20} +(3.00000 - 3.00000i) q^{22} +(-1.41421 - 1.41421i) q^{23} -5.00000 q^{25} -4.47214i q^{26} +(0.581139 - 2.58114i) q^{28} +5.65685i q^{29} -9.48683i q^{31} +(3.53553 - 3.53553i) q^{32} +3.16228 q^{34} +(-1.29947 + 5.77160i) q^{35} +(1.00000 - 1.00000i) q^{37} +(-2.23607 + 2.23607i) q^{38} +(-4.74342 + 4.74342i) q^{40} +8.94427i q^{41} +(-2.00000 - 2.00000i) q^{43} -4.24264i q^{44} +2.00000 q^{46} +(-8.94427 - 8.94427i) q^{47} +(6.32456 + 3.00000i) q^{49} +(3.53553 - 3.53553i) q^{50} +(-3.16228 - 3.16228i) q^{52} +(7.07107 + 7.07107i) q^{53} +9.48683i q^{55} +(4.24264 + 6.70820i) q^{56} +(-4.00000 - 4.00000i) q^{58} +(6.70820 + 6.70820i) q^{62} +7.00000i q^{64} +(7.07107 + 7.07107i) q^{65} +(4.00000 - 4.00000i) q^{67} +(2.23607 - 2.23607i) q^{68} +(-3.16228 - 5.00000i) q^{70} +4.24264 q^{71} +(-3.16228 + 3.16228i) q^{73} +1.41421i q^{74} +3.16228i q^{76} +(10.9508 + 2.46556i) q^{77} +12.0000i q^{79} -2.23607i q^{80} +(-6.32456 - 6.32456i) q^{82} +(-4.47214 + 4.47214i) q^{83} +(-5.00000 + 5.00000i) q^{85} +2.82843 q^{86} +(9.00000 + 9.00000i) q^{88} -13.4164 q^{89} +(10.0000 - 6.32456i) q^{91} +(1.41421 - 1.41421i) q^{92} +12.6491 q^{94} -7.07107i q^{95} +(-3.16228 - 3.16228i) q^{97} +(-6.59346 + 2.35082i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{7}+O(q^{10}) \) 8 * q - 8 * q^7	\( 8 q - 8 q^{7} + 8 q^{16} + 24 q^{22} - 40 q^{25} - 8 q^{28} + 8 q^{37} - 16 q^{43} + 16 q^{46} - 32 q^{58} + 32 q^{67} - 40 q^{85} + 72 q^{88} + 80 q^{91}+O(q^{100}) \) 8 * q - 8 * q^7 + 8 * q^16 + 24 * q^22 - 40 * q^25 - 8 * q^28 + 8 * q^37 - 16 * q^43 + 16 * q^46 - 32 * q^58 + 32 * q^67 - 40 * q^85 + 72 * q^88 + 80 * q^91

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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