LMFDB - Embedded newform 315.2.m.a.197.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(8,315)]

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([2, 3, 0]))

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

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

chi := DirichletCharacter("315.8");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.m (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:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 18x^{10} + 107x^{8} + 240x^{6} + 151x^{4} + 30x^{2} + 1 $ x^12 + 18x^10 + 107x^8 + 240x^6 + 151x^4 + 30*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			197.2
Root			$-0.699479i$ of defining polynomial
Character	$\chi$	$=$	315.197
Dual form			315.2.m.a.8.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.62044 + 1.62044i) q^{2} -3.25168i q^{4} +(-1.83294 + 1.28075i) q^{5} +(-0.707107 - 0.707107i) q^{7} +(2.02827 + 2.02827i) q^{8} +O(q^{10})$	\(q+(-1.62044 + 1.62044i) q^{2} -3.25168i q^{4} +(-1.83294 + 1.28075i) q^{5} +(-0.707107 - 0.707107i) q^{7} +(2.02827 + 2.02827i) q^{8} +(0.894803 - 5.04556i) q^{10} -3.03260i q^{11} +(-2.54141 + 2.54141i) q^{13} +2.29165 q^{14} -0.0700407 q^{16} +(2.70395 - 2.70395i) q^{17} -6.63081i q^{19} +(4.16458 + 5.96014i) q^{20} +(4.91416 + 4.91416i) q^{22} +(-2.99113 - 2.99113i) q^{23} +(1.71937 - 4.69508i) q^{25} -8.23642i q^{26} +(-2.29928 + 2.29928i) q^{28} +5.10191 q^{29} -3.28427 q^{31} +(-3.94304 + 3.94304i) q^{32} +8.76319i q^{34} +(2.20171 + 0.390462i) q^{35} +(6.68770 + 6.68770i) q^{37} +(10.7449 + 10.7449i) q^{38} +(-6.31541 - 1.12000i) q^{40} -7.36835i q^{41} +(1.74832 - 1.74832i) q^{43} -9.86103 q^{44} +9.69392 q^{46} +(0.173326 - 0.173326i) q^{47} +1.00000i q^{49} +(4.82197 + 10.3943i) q^{50} +(8.26384 + 8.26384i) q^{52} +(-8.45145 - 8.45145i) q^{53} +(3.88399 + 5.55858i) q^{55} -2.86841i q^{56} +(-8.26736 + 8.26736i) q^{58} -4.60104 q^{59} -10.5309 q^{61} +(5.32198 - 5.32198i) q^{62} -12.9190i q^{64} +(1.40336 - 7.91316i) q^{65} +(-8.00655 - 8.00655i) q^{67} +(-8.79236 - 8.79236i) q^{68} +(-4.20047 + 2.93503i) q^{70} +5.47459i q^{71} +(-5.58444 + 5.58444i) q^{73} -21.6741 q^{74} -21.5612 q^{76} +(-2.14437 + 2.14437i) q^{77} -16.1081i q^{79} +(0.128381 - 0.0897044i) q^{80} +(11.9400 + 11.9400i) q^{82} +(0.998247 + 0.998247i) q^{83} +(-1.49311 + 8.41926i) q^{85} +5.66612i q^{86} +(6.15093 - 6.15093i) q^{88} -3.00035 q^{89} +3.59409 q^{91} +(-9.72619 + 9.72619i) q^{92} +0.561731i q^{94} +(8.49240 + 12.1539i) q^{95} +(-8.52367 - 8.52367i) q^{97} +(-1.62044 - 1.62044i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 4 q^{5} + 24 q^{8}+O(q^{10}) $ 12 * q - 4 * q^5 + 24 * q^8	$ 12 q - 4 q^{5} + 24 q^{8} + 16 q^{10} - 4 q^{13} - 4 q^{14} - 20 q^{16} + 8 q^{17} - 12 q^{20} - 8 q^{22} + 8 q^{23} - 8 q^{25} - 32 q^{29} + 48 q^{32} + 8 q^{35} + 4 q^{37} + 24 q^{38} - 28 q^{40} + 40 q^{43} - 64 q^{44} + 16 q^{46} + 24 q^{47} - 16 q^{50} + 36 q^{52} - 40 q^{53} - 16 q^{55} - 28 q^{58} - 80 q^{59} - 32 q^{61} + 16 q^{62} + 48 q^{65} - 48 q^{67} + 32 q^{68} + 8 q^{70} - 20 q^{73} - 64 q^{74} + 16 q^{76} + 36 q^{80} + 20 q^{82} + 24 q^{83} - 56 q^{89} + 8 q^{92} + 56 q^{95} + 12 q^{97}+O(q^{100}) $ 12 * q - 4 * q^5 + 24 * q^8 + 16 * q^10 - 4 * q^13 - 4 * q^14 - 20 * q^16 + 8 * q^17 - 12 * q^20 - 8 * q^22 + 8 * q^23 - 8 * q^25 - 32 * q^29 + 48 * q^32 + 8 * q^35 + 4 * q^37 + 24 * q^38 - 28 * q^40 + 40 * q^43 - 64 * q^44 + 16 * q^46 + 24 * q^47 - 16 * q^50 + 36 * q^52 - 40 * q^53 - 16 * q^55 - 28 * q^58 - 80 * q^59 - 32 * q^61 + 16 * q^62 + 48 * q^65 - 48 * q^67 + 32 * q^68 + 8 * q^70 - 20 * q^73 - 64 * q^74 + 16 * q^76 + 36 * q^80 + 20 * q^82 + 24 * q^83 - 56 * q^89 + 8 * q^92 + 56 * q^95 + 12 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−1.62044	+	1.62044i	−1.14583	+	1.14583i	−0.158462	+	0.987365i	$0.550653\pi$
$2$	−1.62044	+	1.62044i	−1.14583	+	1.14583i	−0.987365	+	0.158462i	$0.949347\pi$
$3$		0			0
$3$		0			0
$4$		−	3.25168i		−	1.62584i
$5$	−1.83294	+	1.28075i	−0.819718	+	0.572768i
$5$	−1.83294	+	1.28075i	−0.819718	+	0.572768i
$6$		0			0
$7$	−0.707107	−	0.707107i	−0.267261	−	0.267261i
$7$	−0.707107	−	0.707107i	−0.267261	−	0.267261i
$8$	2.02827	+	2.02827i	0.717101	+	0.717101i
$9$		0			0
$10$	0.894803	−	5.04556i	0.282962	−	1.59555i
$11$		−	3.03260i		−	0.914363i	−0.889373	−	0.457181i	$-0.848859\pi$
$11$		−	3.03260i		−	0.914363i	0.889373	−	0.457181i	$-0.151141\pi$
$12$		0			0
$13$	−2.54141	+	2.54141i	−0.704860	+	0.704860i	−0.965450	−	0.260590i	$-0.916083\pi$
$13$	−2.54141	+	2.54141i	−0.704860	+	0.704860i	0.260590	+	0.965450i	$0.416083\pi$
$14$	2.29165			0.612470
$15$		0			0
$16$	−0.0700407			−0.0175102
$17$	2.70395	−	2.70395i	0.655803	−	0.655803i	−0.298581	−	0.954384i	$-0.596513\pi$
$17$	2.70395	−	2.70395i	0.655803	−	0.655803i	0.954384	+	0.298581i	$0.0965133\pi$
$18$		0			0
$19$		−	6.63081i		−	1.52121i	−0.649214	−	0.760606i	$-0.724902\pi$
$19$		−	6.63081i		−	1.52121i	0.649214	−	0.760606i	$-0.275098\pi$
$20$	4.16458	+	5.96014i	0.931227	+	1.33273i
$21$		0			0
$22$	4.91416	+	4.91416i	1.04770	+	1.04770i
$23$	−2.99113	−	2.99113i	−0.623694	−	0.623694i	0.322780	−	0.946474i	$-0.395383\pi$
$23$	−2.99113	−	2.99113i	−0.623694	−	0.623694i	−0.946474	+	0.322780i	$0.895383\pi$
$24$		0			0
$25$	1.71937	−	4.69508i	0.343874	−	0.939016i
$26$		−	8.23642i		−	1.61529i
$27$		0			0
$28$	−2.29928	+	2.29928i	−0.434523	+	0.434523i
$29$	5.10191			0.947401			0.473701	−	0.880686i	$-0.342918\pi$
$29$	5.10191			0.947401			0.473701	+	0.880686i	$0.342918\pi$
$30$		0			0
$31$	−3.28427			−0.589873			−0.294937	−	0.955517i	$-0.595298\pi$
$31$	−3.28427			−0.589873			−0.294937	+	0.955517i	$0.595298\pi$
$32$	−3.94304	+	3.94304i	−0.697038	+	0.697038i
$33$		0			0
$34$			8.76319i			1.50287i
$35$	2.20171	+	0.390462i	0.372157	+	0.0660001i
$36$		0			0
$37$	6.68770	+	6.68770i	1.09945	+	1.09945i	0.994475	+	0.104976i	$0.0334767\pi$
$37$	6.68770	+	6.68770i	1.09945	+	1.09945i	0.104976	+	0.994475i	$0.466523\pi$
$38$	10.7449	+	10.7449i	1.74305	+	1.74305i
$39$		0			0
$40$	−6.31541	−	1.12000i	−0.998553	−	0.177088i
$41$		−	7.36835i		−	1.15074i	−0.817892	−	0.575371i	$-0.804858\pi$
$41$		−	7.36835i		−	1.15074i	0.817892	−	0.575371i	$-0.195142\pi$
$42$		0			0
$43$	1.74832	−	1.74832i	0.266617	−	0.266617i	−0.561118	−	0.827736i	$-0.689629\pi$
$43$	1.74832	−	1.74832i	0.266617	−	0.266617i	0.827736	+	0.561118i	$0.189629\pi$
$44$	−9.86103			−1.48661
$45$		0			0
$46$	9.69392			1.42929
$47$	0.173326	−	0.173326i	0.0252822	−	0.0252822i	−0.694353	−	0.719635i	$-0.744309\pi$
$47$	0.173326	−	0.173326i	0.0252822	−	0.0252822i	0.719635	+	0.694353i	$0.244309\pi$
$48$		0			0
$49$			1.00000i			0.142857i
$50$	4.82197	+	10.3943i	0.681929	+	1.46997i
$51$		0			0
$52$	8.26384	+	8.26384i	1.14599	+	1.14599i
$53$	−8.45145	−	8.45145i	−1.16090	−	1.16090i	−0.984280	−	0.176616i	$-0.943485\pi$
$53$	−8.45145	−	8.45145i	−1.16090	−	1.16090i	−0.176616	−	0.984280i	$-0.556515\pi$
$54$		0			0
$55$	3.88399	+	5.55858i	0.523718	+	0.749519i
$56$		−	2.86841i		−	0.383307i
$57$		0			0
$58$	−8.26736	+	8.26736i	−1.08556	+	1.08556i
$59$	−4.60104			−0.599005			−0.299502	−	0.954096i	$-0.596821\pi$
$59$	−4.60104			−0.599005			−0.299502	+	0.954096i	$0.596821\pi$
$60$		0			0
$61$	−10.5309			−1.34834			−0.674171	−	0.738575i	$-0.735499\pi$
$61$	−10.5309			−1.34834			−0.674171	+	0.738575i	$0.735499\pi$
$62$	5.32198	−	5.32198i	0.675892	−	0.675892i
$63$		0			0
$64$		−	12.9190i		−	1.61488i
$65$	1.40336	−	7.91316i	0.174065	−	0.981507i
$66$		0			0
$67$	−8.00655	−	8.00655i	−0.978156	−	0.978156i	0.0216101	−	0.999766i	$-0.493121\pi$
$67$	−8.00655	−	8.00655i	−0.978156	−	0.978156i	−0.999766	+	0.0216101i	$0.993121\pi$
$68$	−8.79236	−	8.79236i	−1.06623	−	1.06623i
$69$		0			0
$70$	−4.20047	+	2.93503i	−0.502053	+	0.350803i
$71$			5.47459i			0.649714i	0.945763	+	0.324857i	$0.105316\pi$
$71$			5.47459i			0.649714i	−0.945763	+	0.324857i	$0.894684\pi$
$72$		0			0
$73$	−5.58444	+	5.58444i	−0.653610	+	0.653610i	−0.953860	−	0.300251i	$-0.902930\pi$
$73$	−5.58444	+	5.58444i	−0.653610	+	0.653610i	0.300251	+	0.953860i	$0.402930\pi$
$74$	−21.6741			−2.51956
$75$		0			0
$76$	−21.5612			−2.47324
$77$	−2.14437	+	2.14437i	−0.244374	+	0.244374i
$78$		0			0
$79$		−	16.1081i		−	1.81230i	−0.422951	−	0.906152i	$-0.639006\pi$
$79$		−	16.1081i		−	1.81230i	0.422951	−	0.906152i	$-0.360994\pi$
$80$	0.128381	−	0.0897044i	0.0143534	−	0.0100293i
$81$		0			0
$82$	11.9400	+	11.9400i	1.31855	+	1.31855i
$83$	0.998247	+	0.998247i	0.109572	+	0.109572i	0.759767	−	0.650195i	$-0.225313\pi$
$83$	0.998247	+	0.998247i	0.109572	+	0.109572i	−0.650195	+	0.759767i	$0.725313\pi$
$84$		0			0
$85$	−1.49311	+	8.41926i	−0.161951	+	0.913197i
$86$			5.66612i			0.610994i
$87$		0			0
$88$	6.15093	−	6.15093i	0.655691	−	0.655691i
$89$	−3.00035			−0.318037			−0.159018	−	0.987276i	$-0.550833\pi$
$89$	−3.00035			−0.318037			−0.159018	+	0.987276i	$0.550833\pi$
$90$		0			0
$91$	3.59409			0.376763
$92$	−9.72619	+	9.72619i	−1.01403	+	1.01403i
$93$		0			0
$94$			0.561731i			0.0579381i
$95$	8.49240	+	12.1539i	0.871301	+	1.24696i
$96$		0			0
$97$	−8.52367	−	8.52367i	−0.865448	−	0.865448i	0.126517	−	0.991964i	$-0.459620\pi$
$97$	−8.52367	−	8.52367i	−0.865448	−	0.865448i	−0.991964	+	0.126517i	$0.959620\pi$
$98$	−1.62044	−	1.62044i	−0.163690	−	0.163690i
$99$		0			0
$100$	−15.2669	−	5.59083i	−1.52669	−	0.559083i
$101$			16.8630i			1.67793i	0.544183	+	0.838966i	$0.316840\pi$
$101$			16.8630i			1.67793i	−0.544183	+	0.838966i	$0.683160\pi$
$102$		0			0
$103$	−1.24992	+	1.24992i	−0.123158	+	0.123158i	−0.766000	−	0.642841i	$-0.777756\pi$
$103$	−1.24992	+	1.24992i	−0.123158	+	0.123158i	0.642841	+	0.766000i	$0.277756\pi$
$104$	−10.3093			−1.01091
$105$		0			0
$106$	27.3902			2.66037
$107$	14.1755	−	14.1755i	1.37040	−	1.37040i	0.510544	−	0.859852i	$-0.329444\pi$
$107$	14.1755	−	14.1755i	1.37040	−	1.37040i	0.859852	−	0.510544i	$-0.170556\pi$
$108$		0			0
$109$			0.574370i			0.0550146i	0.999622	+	0.0275073i	$0.00875696\pi$
$109$			0.574370i			0.0550146i	−0.999622	+	0.0275073i	$0.991243\pi$
$110$	−15.3012	−	2.71358i	−1.45891	−	0.258730i
$111$		0			0
$112$	0.0495262	+	0.0495262i	0.00467979	+	0.00467979i
$113$	−6.98481	−	6.98481i	−0.657076	−	0.657076i	0.297611	−	0.954687i	$-0.403810\pi$
$113$	−6.98481	−	6.98481i	−0.657076	−	0.657076i	−0.954687	+	0.297611i	$0.903810\pi$
$114$		0			0
$115$	9.31346	+	1.65169i	0.868485	+	0.154021i
$116$		−	16.5898i		−	1.54032i
$117$		0			0
$118$	7.45573	−	7.45573i	0.686356	−	0.686356i
$119$	−3.82396			−0.350542
$120$		0			0
$121$	1.80334			0.163940
$122$	17.0647	−	17.0647i	1.54497	−	1.54497i
$123$		0			0
$124$			10.6794i			0.959038i
$125$	2.86170	+	10.8079i	0.255959	+	0.966688i
$126$		0			0
$127$	−3.96367	−	3.96367i	−0.351718	−	0.351718i	0.509030	−	0.860749i	$-0.330004\pi$
$127$	−3.96367	−	3.96367i	−0.351718	−	0.351718i	−0.860749	+	0.509030i	$0.830004\pi$
$128$	13.0485	+	13.0485i	1.15333	+	1.15333i
$129$		0			0
$130$	10.5488	+	15.0969i	0.925189	+	1.32409i
$131$			19.0779i			1.66684i	0.552640	+	0.833420i	$0.313620\pi$
$131$			19.0779i			1.66684i	−0.552640	+	0.833420i	$0.686380\pi$
$132$		0			0
$133$	−4.68869	+	4.68869i	−0.406561	+	0.406561i
$134$	25.9483			2.24160
$135$		0			0
$136$	10.9687			0.940555
$137$	0.370993	−	0.370993i	0.0316961	−	0.0316961i	−0.691081	−	0.722777i	$-0.742865\pi$
$137$	0.370993	−	0.370993i	0.0316961	−	0.0316961i	0.722777	+	0.691081i	$0.242865\pi$
$138$		0			0
$139$			16.3127i			1.38363i	0.722076	+	0.691814i	$0.243188\pi$
$139$			16.3127i			1.38363i	−0.722076	+	0.691814i	$0.756812\pi$
$140$	1.26966	−	7.15925i	0.107305	−	0.605067i
$141$		0			0
$142$	−8.87127	−	8.87127i	−0.744460	−	0.744460i
$143$	7.70707	+	7.70707i	0.644498	+	0.644498i
$144$		0			0
$145$	−9.35152	+	6.53426i	−0.776602	+	0.542641i
$146$		−	18.0986i		−	1.49785i
$147$		0			0
$148$	21.7462	−	21.7462i	1.78753	−	1.78753i
$149$	11.9577			0.979611			0.489806	−	0.871832i	$-0.337068\pi$
$149$	11.9577			0.979611			0.489806	+	0.871832i	$0.337068\pi$
$150$		0			0
$151$	−1.85059			−0.150599			−0.0752994	−	0.997161i	$-0.523991\pi$
$151$	−1.85059			−0.150599			−0.0752994	+	0.997161i	$0.523991\pi$
$152$	13.4491	−	13.4491i	1.09086	−	1.09086i
$153$		0			0
$154$		−	6.94967i		−	0.560020i
$155$	6.01989	−	4.20633i	0.483529	−	0.337860i
$156$		0			0
$157$	2.71202	+	2.71202i	0.216443	+	0.216443i	0.806998	−	0.590555i	$-0.201091\pi$
$157$	2.71202	+	2.71202i	0.216443	+	0.216443i	−0.590555	+	0.806998i	$0.701091\pi$
$158$	26.1023	+	26.1023i	2.07659	+	2.07659i
$159$		0			0
$160$	2.17733	−	12.2774i	0.172133	−	0.970615i
$161$			4.23010i			0.333379i
$162$		0			0
$163$	−5.24571	+	5.24571i	−0.410876	+	0.410876i	−0.882043	−	0.471168i	$-0.843833\pi$
$163$	−5.24571	+	5.24571i	−0.410876	+	0.410876i	0.471168	+	0.882043i	$0.343833\pi$
$164$	−23.9595			−1.87092
$165$		0			0
$166$	−3.23520			−0.251101
$167$	8.01311	−	8.01311i	0.620073	−	0.620073i	−0.325477	−	0.945550i	$-0.605525\pi$
$167$	8.01311	−	8.01311i	0.620073	−	0.620073i	0.945550	+	0.325477i	$0.105525\pi$
$168$		0			0
$169$			0.0824845i			0.00634496i
$170$	−11.2234	−	16.0624i	−0.860798	−	1.23193i
$171$		0			0
$172$	−5.68498	−	5.68498i	−0.433476	−	0.433476i
$173$	0.181459	+	0.181459i	0.0137961	+	0.0137961i	0.713971	−	0.700175i	$-0.246895\pi$
$173$	0.181459	+	0.181459i	0.0137961	+	0.0137961i	−0.700175	+	0.713971i	$0.746895\pi$
$174$		0			0
$175$	−4.53570	+	2.10414i	−0.342867	+	0.159058i
$176$			0.212405i			0.0160106i
$177$		0			0
$178$	4.86190	−	4.86190i	0.364415	−	0.364415i
$179$	12.4629			0.931523			0.465762	−	0.884910i	$-0.345780\pi$
$179$	12.4629			0.931523			0.465762	+	0.884910i	$0.345780\pi$
$180$		0			0
$181$	14.2000			1.05548			0.527738	−	0.849407i	$-0.323040\pi$
$181$	14.2000			1.05548			0.527738	+	0.849407i	$0.323040\pi$
$182$	−5.82403	+	5.82403i	−0.431706	+	0.431706i
$183$		0			0
$184$		−	12.1336i		−	0.894504i
$185$	−20.8234	−	3.69292i	−1.53097	−	0.271509i
$186$		0			0
$187$	−8.19999	−	8.19999i	−0.599642	−	0.599642i
$188$	−0.563601	−	0.563601i	−0.0411048	−	0.0411048i
$189$		0			0
$190$	−33.4562	−	5.93327i	−2.42717	−	0.430445i
$191$		−	10.3158i		−	0.746425i	−0.927746	−	0.373212i	$-0.878256\pi$
$191$		−	10.3158i		−	0.746425i	0.927746	−	0.373212i	$-0.121744\pi$
$192$		0			0
$193$	0.266580	−	0.266580i	0.0191888	−	0.0191888i	−0.697447	−	0.716636i	$-0.745681\pi$
$193$	0.266580	−	0.266580i	0.0191888	−	0.0191888i	0.716636	+	0.697447i	$0.245681\pi$
$194$	27.6243			1.98331
$195$		0			0
$196$	3.25168			0.232263
$197$	−6.98481	+	6.98481i	−0.497647	+	0.497647i	−0.910705	−	0.413058i	$-0.864461\pi$
$197$	−6.98481	+	6.98481i	−0.497647	+	0.497647i	0.413058	+	0.910705i	$0.364461\pi$
$198$		0			0
$199$		−	16.7701i		−	1.18880i	−0.804168	−	0.594402i	$-0.797389\pi$
$199$		−	16.7701i		−	1.18880i	0.804168	−	0.594402i	$-0.202611\pi$
$200$	13.0102	−	6.03554i	0.919962	−	0.426777i
$201$		0			0
$202$	−27.3256	−	27.3256i	−1.92262	−	1.92262i
$203$	−3.60760	−	3.60760i	−0.253204	−	0.253204i
$204$		0			0
$205$	9.43700	+	13.5058i	0.659108	+	0.943284i
$206$		−	4.05086i		−	0.282236i
$207$		0			0
$208$	0.178002	−	0.178002i	0.0123422	−	0.0123422i
$209$	−20.1086			−1.39094
$210$		0			0
$211$	16.9651			1.16793			0.583963	−	0.811780i	$-0.301501\pi$
$211$	16.9651			1.16793			0.583963	+	0.811780i	$0.301501\pi$
$212$	−27.4814	+	27.4814i	−1.88743	+	1.88743i
$213$		0			0
$214$			45.9411i			3.14047i
$215$	−0.965419	+	5.44375i	−0.0658410	+	0.371260i
$216$		0			0
$217$	2.32233	+	2.32233i	0.157650	+	0.157650i
$218$	−0.930734	−	0.930734i	−0.0630372	−	0.0630372i
$219$		0			0
$220$	18.0747	−	12.6295i	1.21860	−	0.851480i
$221$			13.7437i			0.924499i
$222$		0			0
$223$	13.3495	−	13.3495i	0.893947	−	0.893947i	−0.100945	−	0.994892i	$-0.532187\pi$
$223$	13.3495	−	13.3495i	0.893947	−	0.893947i	0.994892	+	0.100945i	$0.0321867\pi$
$224$	5.57630			0.372582
$225$		0			0
$226$	22.6370			1.50579
$227$	−11.9255	+	11.9255i	−0.791525	+	0.791525i	−0.981742	−	0.190217i	$-0.939081\pi$
$227$	−11.9255	+	11.9255i	−0.791525	+	0.791525i	0.190217	+	0.981742i	$0.439081\pi$
$228$		0			0
$229$		−	8.42386i		−	0.556665i	−0.960485	−	0.278332i	$-0.910218\pi$
$229$		−	8.42386i		−	0.556665i	0.960485	−	0.278332i	$-0.0897816\pi$
$230$	−17.7684	+	12.4155i	−1.17161	+	0.818652i
$231$		0			0
$232$	10.3481	+	10.3481i	0.679383	+	0.679383i
$233$	−0.822128	−	0.822128i	−0.0538594	−	0.0538594i	0.679664	−	0.733524i	$-0.262126\pi$
$233$	−0.822128	−	0.822128i	−0.0538594	−	0.0538594i	−0.733524	+	0.679664i	$0.762126\pi$
$234$		0			0
$235$	−0.0957102	+	0.539685i	−0.00624344	+	0.0352052i
$236$			14.9611i			0.973884i
$237$		0			0
$238$	6.19651	−	6.19651i	0.401660	−	0.401660i
$239$	−11.4492			−0.740586			−0.370293	−	0.928915i	$-0.620743\pi$
$239$	−11.4492			−0.740586			−0.370293	+	0.928915i	$0.620743\pi$
$240$		0			0
$241$	−22.9679			−1.47949			−0.739747	−	0.672885i	$-0.765055\pi$
$241$	−22.9679			−1.47949			−0.739747	+	0.672885i	$0.765055\pi$
$242$	−2.92222	+	2.92222i	−0.187847	+	0.187847i
$243$		0			0
$244$			34.2430i			2.19218i
$245$	−1.28075	−	1.83294i	−0.0818240	−	0.117103i
$246$		0			0
$247$	16.8516	+	16.8516i	1.07224	+	1.07224i
$248$	−6.66139	−	6.66139i	−0.422999	−	0.422999i
$249$		0			0
$250$	−22.1508	−	12.8764i	−1.40094	−	0.814372i
$251$		−	3.83285i		−	0.241928i	−0.992657	−	0.120964i	$-0.961402\pi$
$251$		−	3.83285i		−	0.241928i	0.992657	−	0.120964i	$-0.0385985\pi$
$252$		0			0
$253$	−9.07090	+	9.07090i	−0.570283	+	0.570283i
$254$	12.8458			0.806017
$255$		0			0
$256$	−16.4506			−1.02816
$257$	14.4687	−	14.4687i	0.902532	−	0.902532i	−0.0931230	−	0.995655i	$-0.529685\pi$
$257$	14.4687	−	14.4687i	0.902532	−	0.902532i	0.995655	+	0.0931230i	$0.0296850\pi$
$258$		0			0
$259$		−	9.45784i		−	0.587681i
$260$	−25.7310	−	4.56326i	−1.59577	−	0.283001i
$261$		0			0
$262$	−30.9146	−	30.9146i	−1.90991	−	1.90991i
$263$	14.4785	+	14.4785i	0.892783	+	0.892783i	0.994784	−	0.102002i	$-0.0325247\pi$
$263$	14.4785	+	14.4785i	0.892783	+	0.892783i	−0.102002	+	0.994784i	$0.532525\pi$
$264$		0			0
$265$	26.3152	+	4.66686i	1.61653	+	0.286683i
$266$		−	15.1955i		−	0.931697i
$267$		0			0
$268$	−26.0347	+	26.0347i	−1.59032	+	1.59032i
$269$	−6.60739			−0.402860			−0.201430	−	0.979503i	$-0.564559\pi$
$269$	−6.60739			−0.402860			−0.201430	+	0.979503i	$0.564559\pi$
$270$		0			0
$271$	22.9409			1.39356			0.696780	−	0.717285i	$-0.254615\pi$
$271$	22.9409			1.39356			0.696780	+	0.717285i	$0.254615\pi$
$272$	−0.189386	+	0.189386i	−0.0114832	+	0.0114832i
$273$		0			0
$274$			1.20235i			0.0726365i
$275$	−14.2383	−	5.21416i	−0.858601	−	0.314426i
$276$		0			0
$277$	−13.9239	−	13.9239i	−0.836605	−	0.836605i	0.151806	−	0.988410i	$-0.451491\pi$
$277$	−13.9239	−	13.9239i	−0.836605	−	0.836605i	−0.988410	+	0.151806i	$0.951491\pi$
$278$	−26.4339	−	26.4339i	−1.58540	−	1.58540i
$279$		0			0
$280$	3.67370	+	5.25763i	0.219546	+	0.314203i
$281$			14.7206i			0.878156i	0.898449	+	0.439078i	$0.144695\pi$
$281$			14.7206i			0.878156i	−0.898449	+	0.439078i	$0.855305\pi$
$282$		0			0
$283$	8.42004	−	8.42004i	0.500520	−	0.500520i	−0.411080	−	0.911599i	$-0.634848\pi$
$283$	8.42004	−	8.42004i	0.500520	−	0.500520i	0.911599	+	0.411080i	$0.134848\pi$
$284$	17.8016			1.05633
$285$		0			0
$286$	−24.9778			−1.47697
$287$	−5.21021	+	5.21021i	−0.307549	+	0.307549i
$288$		0			0
$289$			2.37734i			0.139844i
$290$	4.56521	−	25.7420i	0.268078	−	1.51162i
$291$		0			0
$292$	18.1588	+	18.1588i	1.06266	+	1.06266i
$293$	−21.6859	−	21.6859i	−1.26690	−	1.26690i	−0.947680	−	0.319221i	$-0.896579\pi$
$293$	−21.6859	−	21.6859i	−1.26690	−	1.26690i	−0.319221	−	0.947680i	$-0.603421\pi$
$294$		0			0
$295$	8.43346	−	5.89278i	0.491015	−	0.343091i
$296$			27.1289i			1.57684i
$297$		0			0
$298$	−19.3767	+	19.3767i	−1.12246	+	1.12246i
$299$	15.2034			0.879234
$300$		0			0
$301$	−2.47250			−0.142513
$302$	2.99878	−	2.99878i	0.172560	−	0.172560i
$303$		0			0
$304$			0.464426i			0.0266367i
$305$	19.3025	−	13.4874i	1.10526	−	0.772287i
$306$		0			0
$307$	8.85014	+	8.85014i	0.505104	+	0.505104i	0.913020	−	0.407915i	$-0.133744\pi$
$307$	8.85014	+	8.85014i	0.505104	+	0.505104i	−0.407915	+	0.913020i	$0.633744\pi$
$308$	6.97280	+	6.97280i	0.397312	+	0.397312i
$309$		0			0
$310$	−2.93878	+	16.5710i	−0.166911	+	0.941170i
$311$		−	12.8964i		−	0.731286i	−0.930755	−	0.365643i	$-0.880849\pi$
$311$		−	12.8964i		−	0.731286i	0.930755	−	0.365643i	$-0.119151\pi$
$312$		0			0
$313$	−1.54078	+	1.54078i	−0.0870900	+	0.0870900i	−0.749310	−	0.662220i	$-0.769615\pi$
$313$	−1.54078	+	1.54078i	−0.0870900	+	0.0870900i	0.662220	+	0.749310i	$0.269615\pi$
$314$	−8.78935			−0.496012
$315$		0			0
$316$	−52.3784			−2.94651
$317$	−1.84855	+	1.84855i	−0.103825	+	0.103825i	−0.757111	−	0.653286i	$-0.773390\pi$
$317$	−1.84855	+	1.84855i	−0.103825	+	0.103825i	0.653286	+	0.757111i	$0.273390\pi$
$318$		0			0
$319$		−	15.4721i		−	0.866269i
$320$	16.5460	+	23.6799i	0.924951	+	1.32374i
$321$		0			0
$322$	−6.85464	−	6.85464i	−0.381994	−	0.381994i
$323$	−17.9294	−	17.9294i	−0.997616	−	0.997616i
$324$		0			0
$325$	7.56249	+	16.3017i	0.419492	+	0.904258i
$326$		−	17.0007i		−	0.941584i
$327$		0			0
$328$	14.9450	−	14.9450i	0.825199	−	0.825199i
$329$	−0.245120			−0.0135139
$330$		0			0
$331$	−9.39910			−0.516621			−0.258310	−	0.966062i	$-0.583166\pi$
$331$	−9.39910			−0.516621			−0.258310	+	0.966062i	$0.583166\pi$
$332$	3.24597	−	3.24597i	0.178146	−	0.178146i
$333$		0			0
$334$			25.9696i			1.42099i
$335$	24.9299	+	4.42119i	1.36207	+	0.241555i
$336$		0			0
$337$	18.1546	+	18.1546i	0.988942	+	0.988942i	0.999940	−	0.0109971i	$-0.00350056\pi$
$337$	18.1546	+	18.1546i	0.988942	+	0.988942i	−0.0109971	+	0.999940i	$0.503501\pi$
$338$	−0.133661	−	0.133661i	−0.00727022	−	0.00727022i
$339$		0			0
$340$	27.3767	+	4.85511i	1.48471	+	0.263305i
$341$			9.95988i			0.539358i
$342$		0			0
$343$	0.707107	−	0.707107i	0.0381802	−	0.0381802i
$344$	7.09215			0.382383
$345$		0			0
$346$	−0.588089			−0.0316158
$347$	6.52324	−	6.52324i	0.350186	−	0.350186i	−0.509993	−	0.860179i	$-0.670352\pi$
$347$	6.52324	−	6.52324i	0.350186	−	0.350186i	0.860179	+	0.509993i	$0.170352\pi$
$348$		0			0
$349$			28.6246i			1.53224i	0.642697	+	0.766121i	$0.277816\pi$
$349$			28.6246i			1.53224i	−0.642697	+	0.766121i	$0.722184\pi$
$350$	3.94020	−	10.7595i	0.210613	−	0.575119i
$351$		0			0
$352$	11.9577	+	11.9577i	0.637345	+	0.637345i
$353$	−7.79446	−	7.79446i	−0.414857	−	0.414857i	0.468570	−	0.883427i	$-0.344770\pi$
$353$	−7.79446	−	7.79446i	−0.414857	−	0.414857i	−0.883427	+	0.468570i	$0.844770\pi$
$354$		0			0
$355$	−7.01157	−	10.0346i	−0.372136	−	0.532582i
$356$			9.75617i			0.517076i
$357$		0			0
$358$	−20.1955	+	20.1955i	−1.06736	+	1.06736i
$359$	−0.715285			−0.0377513			−0.0188756	−	0.999822i	$-0.506009\pi$
$359$	−0.715285			−0.0377513			−0.0188756	+	0.999822i	$0.506009\pi$
$360$		0			0
$361$	−24.9676			−1.31409
$362$	−23.0103	+	23.0103i	−1.20939	+	1.20939i
$363$		0			0
$364$		−	11.6868i		−	0.612556i
$365$	3.08371	−	17.3882i	0.161409	−	0.910142i
$366$		0			0
$367$	13.6098	+	13.6098i	0.710427	+	0.710427i	0.966624	−	0.256198i	$-0.0824698\pi$
$367$	13.6098	+	13.6098i	0.710427	+	0.710427i	−0.256198	+	0.966624i	$0.582470\pi$
$368$	0.209501	+	0.209501i	0.0109210	+	0.0109210i
$369$		0			0
$370$	39.7274	−	27.7590i	2.06533	−	1.44312i
$371$			11.9522i			0.620525i
$372$		0			0
$373$	22.2558	−	22.2558i	1.15236	−	1.15236i	0.166284	−	0.986078i	$-0.446823\pi$
$373$	22.2558	−	22.2558i	1.15236	−	1.15236i	0.986078	−	0.166284i	$-0.0531767\pi$
$374$	26.5752			1.37417
$375$		0			0
$376$	0.703105			0.0362599
$377$	−12.9660	+	12.9660i	−0.667785	+	0.667785i
$378$		0			0
$379$			0.695620i			0.0357316i	0.999840	+	0.0178658i	$0.00568717\pi$
$379$			0.695620i			0.0357316i	−0.999840	+	0.0178658i	$0.994313\pi$
$380$	39.5206	−	27.6145i	2.02736	−	1.41659i
$381$		0			0
$382$	16.7162	+	16.7162i	0.855273	+	0.855273i
$383$	−7.23025	−	7.23025i	−0.369448	−	0.369448i	0.497828	−	0.867276i	$-0.334131\pi$
$383$	−7.23025	−	7.23025i	−0.369448	−	0.369448i	−0.867276	+	0.497828i	$0.834131\pi$
$384$		0			0
$385$	1.18411	−	6.67691i	0.0603480	−	0.340287i
$386$			0.863955i			0.0439741i
$387$		0			0
$388$	−27.7162	+	27.7162i	−1.40708	+	1.40708i
$389$	−20.5075			−1.03977			−0.519885	−	0.854236i	$-0.674025\pi$
$389$	−20.5075			−1.03977			−0.519885	+	0.854236i	$0.674025\pi$
$390$		0			0
$391$	−16.1757			−0.818042
$392$	−2.02827	+	2.02827i	−0.102443	+	0.102443i
$393$		0			0
$394$		−	22.6370i		−	1.14044i
$395$	20.6304	+	29.5253i	1.03803	+	1.48558i
$396$		0			0
$397$	8.69971	+	8.69971i	0.436626	+	0.436626i	0.890875	−	0.454249i	$-0.150092\pi$
$397$	8.69971	+	8.69971i	0.436626	+	0.436626i	−0.454249	+	0.890875i	$0.650092\pi$
$398$	27.1751	+	27.1751i	1.36216	+	1.36216i
$399$		0			0
$400$	−0.120426	+	0.328846i	−0.00602129	+	0.0164423i
$401$		−	1.07299i		−	0.0535826i	−0.999641	−	0.0267913i	$-0.991471\pi$
$401$		−	1.07299i		−	0.0535826i	0.999641	−	0.0267913i	$-0.00852896\pi$
$402$		0			0
$403$	8.34668	−	8.34668i	0.415778	−	0.415778i
$404$	54.8330			2.72805
$405$		0			0
$406$	11.6918			0.580255
$407$	20.2811	−	20.2811i	1.00530	−	1.00530i
$408$		0			0
$409$			17.9019i			0.885193i	0.896721	+	0.442596i	$0.145943\pi$
$409$			17.9019i			0.885193i	−0.896721	+	0.442596i	$0.854057\pi$
$410$	−37.1775	−	6.59322i	−1.83606	−	0.325616i
$411$		0			0
$412$	4.06434	+	4.06434i	0.200236	+	0.200236i
$413$	3.25343	+	3.25343i	0.160091	+	0.160091i
$414$		0			0
$415$	−3.10823	−	0.551228i	−0.152577	−	0.0270587i
$416$		−	20.0418i		−	0.982628i
$417$		0			0
$418$	32.5848	−	32.5848i	1.59378	−	1.59378i
$419$	−14.8415			−0.725057			−0.362528	−	0.931973i	$-0.618086\pi$
$419$	−14.8415			−0.725057			−0.362528	+	0.931973i	$0.618086\pi$
$420$		0			0
$421$	17.4595			0.850925			0.425463	−	0.904976i	$-0.360111\pi$
$421$	17.4595			0.850925			0.425463	+	0.904976i	$0.360111\pi$
$422$	−27.4910	+	27.4910i	−1.33824	+	1.33824i
$423$		0			0
$424$		−	34.2836i		−	1.66496i
$425$	−8.04616	−	17.3443i	−0.390296	−	0.841324i
$426$		0			0
$427$	7.44646	+	7.44646i	0.360359	+	0.360359i
$428$	−46.0941	−	46.0941i	−2.22804	−	2.22804i
$429$		0			0
$430$	−7.25688	−	10.3857i	−0.349958	−	0.500842i
$431$		−	2.29829i		−	0.110705i	−0.998467	−	0.0553524i	$-0.982372\pi$
$431$		−	2.29829i		−	0.110705i	0.998467	−	0.0553524i	$-0.0176282\pi$
$432$		0			0
$433$	2.80323	−	2.80323i	0.134715	−	0.134715i	−0.636534	−	0.771249i	$-0.719633\pi$
$433$	2.80323	−	2.80323i	0.134715	−	0.134715i	0.771249	+	0.636534i	$0.219633\pi$
$434$	−7.52642			−0.361280
$435$		0			0
$436$	1.86766			0.0894449
$437$	−19.8336	+	19.8336i	−0.948771	+	0.948771i
$438$		0			0
$439$		−	15.5162i		−	0.740548i	−0.928923	−	0.370274i	$-0.879264\pi$
$439$		−	15.5162i		−	0.740548i	0.928923	−	0.370274i	$-0.120736\pi$
$440$	−3.39652	+	19.1521i	−0.161923	+	0.913040i
$441$		0			0
$442$	−22.2708	−	22.2708i	−1.05932	−	1.05932i
$443$	6.66424	+	6.66424i	0.316628	+	0.316628i	0.847470	−	0.530843i	$-0.178124\pi$
$443$	6.66424	+	6.66424i	0.316628	+	0.316628i	−0.530843	+	0.847470i	$0.678124\pi$
$444$		0			0
$445$	5.49948	−	3.84269i	0.260700	−	0.182161i
$446$			43.2641i			2.04862i
$447$		0			0
$448$	−9.13514	+	9.13514i	−0.431595	+	0.431595i
$449$	16.4469			0.776178			0.388089	−	0.921622i	$-0.373135\pi$
$449$	16.4469			0.776178			0.388089	+	0.921622i	$0.373135\pi$
$450$		0			0
$451$	−22.3452			−1.05220
$452$	−22.7123	+	22.7123i	−1.06830	+	1.06830i
$453$		0			0
$454$		−	38.6493i		−	1.81390i
$455$	−6.58778	+	4.60313i	−0.308840	+	0.215798i
$456$		0			0
$457$	−12.2198	−	12.2198i	−0.571619	−	0.571619i	0.360961	−	0.932581i	$-0.382449\pi$
$457$	−12.2198	−	12.2198i	−0.571619	−	0.571619i	−0.932581	+	0.360961i	$0.882449\pi$
$458$	13.6504	+	13.6504i	0.637841	+	0.637841i
$459$		0			0
$460$	5.37077	−	30.2844i	0.250413	−	1.41202i
$461$			10.3252i			0.480891i	0.970663	+	0.240446i	$0.0772936\pi$
$461$			10.3252i			0.480891i	−0.970663	+	0.240446i	$0.922706\pi$
$462$		0			0
$463$	−13.2678	+	13.2678i	−0.616605	+	0.616605i	−0.944659	−	0.328054i	$-0.893607\pi$
$463$	−13.2678	+	13.2678i	−0.616605	+	0.616605i	0.328054	+	0.944659i	$0.393607\pi$
$464$	−0.357341			−0.0165892
$465$		0			0
$466$	2.66443			0.123427
$467$	−9.71989	+	9.71989i	−0.449783	+	0.449783i	−0.895282	−	0.445499i	$-0.853026\pi$
$467$	−9.71989	+	9.71989i	−0.449783	+	0.449783i	0.445499	+	0.895282i	$0.353026\pi$
$468$		0			0
$469$			11.3230i			0.522847i
$470$	−0.719436	−	1.02962i	−0.0331851	−	0.0474929i
$471$		0			0
$472$	−9.33215	−	9.33215i	−0.429547	−	0.429547i
$473$	−5.30197	−	5.30197i	−0.243785	−	0.243785i
$474$		0			0
$475$	−31.1322	−	11.4008i	−1.42844	−	0.523105i
$476$			12.4343i			0.569924i
$477$		0			0
$478$	18.5527	−	18.5527i	0.848583	−	0.848583i
$479$	1.57498			0.0719627			0.0359814	−	0.999352i	$-0.488544\pi$
$479$	1.57498			0.0719627			0.0359814	+	0.999352i	$0.488544\pi$
$480$		0			0
$481$	−33.9924			−1.54992
$482$	37.2182	−	37.2182i	1.69524	−	1.69524i
$483$		0			0
$484$		−	5.86389i		−	0.266540i
$485$	26.5401	+	4.70674i	1.20512	+	0.213722i
$486$		0			0
$487$	−14.0684	−	14.0684i	−0.637502	−	0.637502i	0.312437	−	0.949939i	$-0.398855\pi$
$487$	−14.0684	−	14.0684i	−0.637502	−	0.637502i	−0.949939	+	0.312437i	$0.898855\pi$
$488$	−21.3595	−	21.3595i	−0.966898	−	0.966898i
$489$		0			0
$490$	5.04556	+	0.894803i	0.227935	+	0.0404231i
$491$			22.6169i			1.02069i	0.859971	+	0.510344i	$0.170482\pi$
$491$			22.6169i			1.02069i	−0.859971	+	0.510344i	$0.829518\pi$
$492$		0			0
$493$	13.7953	−	13.7953i	0.621309	−	0.621309i
$494$	−54.6141			−2.45721
$495$		0			0
$496$	0.230033			0.0103288
$497$	3.87112	−	3.87112i	0.173643	−	0.173643i
$498$		0			0
$499$		−	35.1641i		−	1.57416i	−0.616851	−	0.787080i	$-0.711592\pi$
$499$		−	35.1641i		−	1.57416i	0.616851	−	0.787080i	$-0.288408\pi$
$500$	35.1438	−	9.30533i	1.57168	−	0.416147i
$501$		0			0
$502$	6.21092	+	6.21092i	0.277207	+	0.277207i
$503$	−3.09215	−	3.09215i	−0.137872	−	0.137872i	0.634802	−	0.772674i	$-0.281081\pi$
$503$	−3.09215	−	3.09215i	−0.137872	−	0.137872i	−0.772674	+	0.634802i	$0.781081\pi$
$504$		0			0
$505$	−21.5973	−	30.9090i	−0.961066	−	1.37543i
$506$		−	29.3978i		−	1.30689i
$507$		0			0
$508$	−12.8886	+	12.8886i	−0.571837	+	0.571837i
$509$	−7.39653			−0.327845			−0.163923	−	0.986473i	$-0.552415\pi$
$509$	−7.39653			−0.327845			−0.163923	+	0.986473i	$0.552415\pi$
$510$		0			0
$511$	7.89760			0.349369
$512$	0.560296	−	0.560296i	0.0247618	−	0.0247618i
$513$		0			0
$514$			46.8914i			2.06829i
$515$	0.690202	−	3.89187i	0.0304139	−	0.171496i
$516$		0			0
$517$	−0.525629	−	0.525629i	−0.0231171	−	0.0231171i
$518$	15.3259	+	15.3259i	0.673381	+	0.673381i
$519$		0			0
$520$	18.8964	−	13.2036i	0.828662	−	0.579018i
$521$		−	40.5578i		−	1.77687i	−0.459002	−	0.888435i	$-0.651793\pi$
$521$		−	40.5578i		−	1.77687i	0.459002	−	0.888435i	$-0.348207\pi$
$522$		0			0
$523$	21.0323	−	21.0323i	0.919680	−	0.919680i	−0.0773260	−	0.997006i	$-0.524638\pi$
$523$	21.0323	−	21.0323i	0.919680	−	0.919680i	0.997006	+	0.0773260i	$0.0246382\pi$
$524$	62.0350			2.71001
$525$		0			0
$526$	−46.9232			−2.04595
$527$	−8.88050	+	8.88050i	−0.386841	+	0.386841i
$528$		0			0
$529$		−	5.10626i		−	0.222011i
$530$	−50.2047	+	35.0799i	−2.18075	+	1.52377i
$531$		0			0
$532$	15.2461	+	15.2461i	0.661002	+	0.661002i
$533$	18.7260	+	18.7260i	0.811112	+	0.811112i
$534$		0			0
$535$	−7.82765	+	44.1381i	−0.338419	+	1.90826i
$536$		−	32.4789i		−	1.40287i
$537$		0			0
$538$	10.7069	−	10.7069i	0.461607	−	0.461607i
$539$	3.03260			0.130623
$540$		0			0
$541$	12.2534			0.526813			0.263406	−	0.964685i	$-0.415154\pi$
$541$	12.2534			0.526813			0.263406	+	0.964685i	$0.415154\pi$
$542$	−37.1744	+	37.1744i	−1.59678	+	1.59678i
$543$		0			0
$544$			21.3235i			0.914240i
$545$	−0.735623	−	1.05279i	−0.0315106	−	0.0450965i
$546$		0			0
$547$	9.49738	+	9.49738i	0.406079	+	0.406079i	0.880369	−	0.474290i	$-0.157295\pi$
$547$	9.49738	+	9.49738i	0.406079	+	0.406079i	−0.474290	+	0.880369i	$0.657295\pi$
$548$	−1.20635	−	1.20635i	−0.0515327	−	0.0515327i
$549$		0			0
$550$	31.5216	−	14.6231i	1.34409	−	0.623531i
$551$		−	33.8298i		−	1.44120i
$552$		0			0
$553$	−11.3902	+	11.3902i	−0.484359	+	0.484359i
$554$	45.1257			1.91721
$555$		0			0
$556$	53.0437			2.24955
$557$	5.20644	−	5.20644i	0.220604	−	0.220604i	−0.588149	−	0.808753i	$-0.700143\pi$
$557$	5.20644	−	5.20644i	0.220604	−	0.220604i	0.808753	+	0.588149i	$0.200143\pi$
$558$		0			0
$559$			8.88642i			0.375855i
$560$	−0.154209	−	0.0273482i	−0.00651654	−	0.00115567i
$561$		0			0
$562$	−23.8539	−	23.8539i	−1.00621	−	1.00621i
$563$	11.2865	+	11.2865i	0.475670	+	0.475670i	0.903744	−	0.428074i	$-0.140808\pi$
$563$	11.2865	+	11.2865i	0.475670	+	0.475670i	−0.428074	+	0.903744i	$0.640808\pi$
$564$		0			0
$565$	21.7486	+	3.85699i	0.914969	+	0.162265i
$566$			27.2884i			1.14702i
$567$		0			0
$568$	−11.1039	+	11.1039i	−0.465911	+	0.465911i
$569$	16.7669			0.702903			0.351452	−	0.936206i	$-0.385688\pi$
$569$	16.7669			0.702903			0.351452	+	0.936206i	$0.385688\pi$
$570$		0			0
$571$	35.3888			1.48097			0.740487	−	0.672070i	$-0.234595\pi$
$571$	35.3888			1.48097			0.740487	+	0.672070i	$0.234595\pi$
$572$	25.0609	−	25.0609i	1.04785	−	1.04785i
$573$		0			0
$574$		−	16.8857i		−	0.704795i
$575$	−19.1865	+	8.90074i	−0.800131	+	0.371186i
$576$		0			0
$577$	−11.4351	−	11.4351i	−0.476048	−	0.476048i	0.427817	−	0.903865i	$-0.359283\pi$
$577$	−11.4351	−	11.4351i	−0.476048	−	0.476048i	−0.903865	+	0.427817i	$0.859283\pi$
$578$	−3.85235	−	3.85235i	−0.160236	−	0.160236i
$579$		0			0
$580$	21.2473	+	30.4081i	0.882246	+	1.26263i
$581$		−	1.41173i		−	0.0585686i
$582$		0			0
$583$	−25.6298	+	25.6298i	−1.06148	+	1.06148i
$584$	−22.6535			−0.937409
$585$		0			0
$586$	70.2814			2.90330
$587$	13.2944	−	13.2944i	0.548721	−	0.548721i	−0.377350	−	0.926071i	$-0.623165\pi$
$587$	13.2944	−	13.2944i	0.548721	−	0.548721i	0.926071	+	0.377350i	$0.123165\pi$
$588$		0			0
$589$			21.7774i			0.897322i
$590$	−4.11703	+	23.2148i	−0.169495	+	0.955740i
$591$		0			0
$592$	−0.468411	−	0.468411i	−0.0192516	−	0.0192516i
$593$	15.2944	+	15.2944i	0.628066	+	0.628066i	0.947581	−	0.319515i	$-0.103520\pi$
$593$	15.2944	+	15.2944i	0.628066	+	0.628066i	−0.319515	+	0.947581i	$0.603520\pi$
$594$		0			0
$595$	7.00910	−	4.89753i	0.287345	−	0.200779i
$596$		−	38.8825i		−	1.59269i
$597$		0			0
$598$	−24.6362	+	24.6362i	−1.00745	+	1.00745i
$599$	−27.3235			−1.11641			−0.558203	−	0.829704i	$-0.688509\pi$
$599$	−27.3235			−1.11641			−0.558203	+	0.829704i	$0.688509\pi$
$600$		0			0
$601$	1.42918			0.0582974			0.0291487	−	0.999575i	$-0.490720\pi$
$601$	1.42918			0.0582974			0.0291487	+	0.999575i	$0.490720\pi$
$602$	4.00655	−	4.00655i	0.163295	−	0.163295i
$603$		0			0
$604$			6.01752i			0.244849i
$605$	−3.30543	+	2.30963i	−0.134385	+	0.0938998i
$606$		0			0
$607$	8.27456	+	8.27456i	0.335854	+	0.335854i	0.854804	−	0.518950i	$-0.173677\pi$
$607$	8.27456	+	8.27456i	0.335854	+	0.335854i	−0.518950	+	0.854804i	$0.673677\pi$
$608$	26.1456	+	26.1456i	1.06034	+	1.06034i
$609$		0			0
$610$	−9.42307	+	53.1342i	−0.381529	+	2.15134i
$611$			0.880986i			0.0356409i
$612$		0			0
$613$	−15.7991	+	15.7991i	−0.638122	+	0.638122i	−0.950092	−	0.311970i	$-0.899011\pi$
$613$	−15.7991	+	15.7991i	−0.638122	+	0.638122i	0.311970	+	0.950092i	$0.399011\pi$
$614$	−28.6823			−1.15752
$615$		0			0
$616$	−8.69872			−0.350482
$617$	8.74842	−	8.74842i	0.352198	−	0.352198i	−0.508729	−	0.860927i	$-0.669884\pi$
$617$	8.74842	−	8.74842i	0.352198	−	0.352198i	0.860927	+	0.508729i	$0.169884\pi$
$618$		0			0
$619$			15.7537i			0.633195i	0.948560	+	0.316597i	$0.102540\pi$
$619$			15.7537i			0.633195i	−0.948560	+	0.316597i	$0.897460\pi$
$620$	−13.6776	−	19.5747i	−0.549306	−	0.786140i
$621$		0			0
$622$	20.8978	+	20.8978i	0.837927	+	0.837927i
$623$	2.12157	+	2.12157i	0.0849989	+	0.0849989i
$624$		0			0
$625$	−19.0875	−	16.1452i	−0.763501	−	0.645806i
$626$		−	4.99349i		−	0.199580i
$627$		0			0
$628$	8.81861	−	8.81861i	0.351901	−	0.351901i
$629$	36.1664			1.44205
$630$		0			0
$631$	−31.6048			−1.25817			−0.629083	−	0.777338i	$-0.716569\pi$
$631$	−31.6048			−1.25817			−0.629083	+	0.777338i	$0.716569\pi$
$632$	32.6716	−	32.6716i	1.29961	−	1.29961i
$633$		0			0
$634$		−	5.99093i		−	0.237930i
$635$	12.3416	+	2.18872i	0.489763	+	0.0868568i
$636$		0			0
$637$	−2.54141	−	2.54141i	−0.100694	−	0.100694i
$638$	25.0716	+	25.0716i	0.992594	+	0.992594i
$639$		0			0
$640$	−40.6290	−	7.20533i	−1.60600	−	0.284815i
$641$			2.19982i			0.0868877i	0.999056	+	0.0434439i	$0.0138330\pi$
$641$			2.19982i			0.0868877i	−0.999056	+	0.0434439i	$0.986167\pi$
$642$		0			0
$643$	−31.0585	+	31.0585i	−1.22483	+	1.22483i	−0.258934	+	0.965895i	$0.583371\pi$
$643$	−31.0585	+	31.0585i	−1.22483	+	1.22483i	−0.965895	+	0.258934i	$0.916629\pi$
$644$	13.7549			0.542019
$645$		0			0
$646$	58.1070			2.28619
$647$	−4.31046	+	4.31046i	−0.169462	+	0.169462i	−0.786743	−	0.617281i	$-0.788234\pi$
$647$	−4.31046	+	4.31046i	−0.169462	+	0.169462i	0.617281	+	0.786743i	$0.288234\pi$
$648$		0			0
$649$			13.9531i			0.547708i
$650$	−38.6706	−	14.1614i	−1.51679	−	0.555458i
$651$		0			0
$652$	17.0573	+	17.0573i	0.668017	+	0.668017i
$653$	13.3336	+	13.3336i	0.521784	+	0.521784i	0.918110	−	0.396326i	$-0.129715\pi$
$653$	13.3336	+	13.3336i	0.521784	+	0.521784i	−0.396326	+	0.918110i	$0.629715\pi$
$654$		0			0
$655$	−24.4339	−	34.9687i	−0.954712	−	1.36634i
$656$			0.516084i			0.0201497i
$657$		0			0
$658$	0.397204	−	0.397204i	0.0154846	−	0.0154846i
$659$	−42.9189			−1.67188			−0.835941	−	0.548819i	$-0.815077\pi$
$659$	−42.9189			−1.67188			−0.835941	+	0.548819i	$0.815077\pi$
$660$		0			0
$661$	−14.5564			−0.566180			−0.283090	−	0.959093i	$-0.591359\pi$
$661$	−14.5564			−0.566180			−0.283090	+	0.959093i	$0.591359\pi$
$662$	15.2307	−	15.2307i	0.591958	−	0.591958i
$663$		0			0
$664$			4.04942i			0.157148i
$665$	2.58908	−	14.5991i	0.100400	−	0.566130i
$666$		0			0
$667$	−15.2605	−	15.2605i	−0.590889	−	0.590889i
$668$	−26.0560	−	26.0560i	−1.00814	−	1.00814i
$669$		0			0
$670$	−47.5619	+	33.2333i	−1.83748	+	1.28391i
$671$			31.9360i			1.23287i
$672$		0			0
$673$	−0.0675877	+	0.0675877i	−0.00260531	+	0.00260531i	−0.708408	−	0.705803i	$-0.750586\pi$
$673$	−0.0675877	+	0.0675877i	−0.00260531	+	0.00260531i	0.705803	+	0.708408i	$0.250586\pi$
$674$	−58.8369			−2.26631
$675$		0			0
$676$	0.268213			0.0103159
$677$	−6.34254	+	6.34254i	−0.243763	+	0.243763i	−0.818405	−	0.574642i	$-0.805141\pi$
$677$	−6.34254	+	6.34254i	−0.243763	+	0.243763i	0.574642	+	0.818405i	$0.305141\pi$
$678$		0			0
$679$			12.0543i			0.462601i
$680$	−20.1049	+	14.0481i	−0.770990	+	0.538720i
$681$		0			0
$682$	−16.1394	−	16.1394i	−0.618011	−	0.618011i
$683$	−1.00502	−	1.00502i	−0.0384559	−	0.0384559i	0.687617	−	0.726073i	$-0.258657\pi$
$683$	−1.00502	−	1.00502i	−0.0384559	−	0.0384559i	−0.726073	+	0.687617i	$0.758657\pi$
$684$		0			0
$685$	−0.204861	+	1.15516i	−0.00782734	+	0.0441364i
$686$			2.29165i			0.0874957i
$687$		0			0
$688$	−0.122454	+	0.122454i	−0.00466851	+	0.00466851i
$689$	42.9572			1.63654
$690$		0			0
$691$	−22.1726			−0.843487			−0.421744	−	0.906715i	$-0.638582\pi$
$691$	−22.1726			−0.843487			−0.421744	+	0.906715i	$0.638582\pi$
$692$	0.590046	−	0.590046i	0.0224302	−	0.0224302i
$693$		0			0
$694$			21.1411i			0.802505i
$695$	−20.8925	−	29.9003i	−0.792497	−	1.13418i
$696$		0			0
$697$	−19.9236	−	19.9236i	−0.754661	−	0.754661i
$698$	−46.3846	−	46.3846i	−1.75568	−	1.75568i
$699$		0			0
$700$	6.84199	+	14.7486i	0.258603	+	0.557446i
$701$			5.69755i			0.215194i	0.994195	+	0.107597i	$0.0343155\pi$
$701$			5.69755i			0.215194i	−0.994195	+	0.107597i	$0.965684\pi$
$702$		0			0
$703$	44.3449	−	44.3449i	1.67250	−	1.67250i
$704$	−39.1782			−1.47659
$705$		0			0
$706$	25.2610			0.950709
$707$	11.9240	−	11.9240i	0.448446	−	0.448446i
$708$		0			0
$709$			14.5892i			0.547908i	0.961743	+	0.273954i	$0.0883317\pi$
$709$			14.5892i			0.547908i	−0.961743	+	0.273954i	$0.911668\pi$
$710$	27.6224	+	4.89868i	1.03665	+	0.183844i
$711$		0			0
$712$	−6.08552	−	6.08552i	−0.228065	−	0.228065i
$713$	9.82370	+	9.82370i	0.367900	+	0.367900i
$714$		0			0
$715$	−23.9975	−	4.25582i	−0.897454	−	0.159159i
$716$		−	40.5254i		−	1.51451i
$717$		0			0
$718$	1.15908	−	1.15908i	0.0432564	−	0.0432564i
$719$	7.14831			0.266587			0.133293	−	0.991077i	$-0.457445\pi$
$719$	7.14831			0.266587			0.133293	+	0.991077i	$0.457445\pi$
$720$		0			0
$721$	1.76766			0.0658310
$722$	40.4587	−	40.4587i	1.50572	−	1.50572i
$723$		0			0
$724$		−	46.1737i		−	1.71603i
$725$	8.77208	−	23.9539i	0.325787	−	0.889625i
$726$		0			0
$727$	8.29940	+	8.29940i	0.307808	+	0.307808i	0.844059	−	0.536251i	$-0.180160\pi$
$727$	8.29940	+	8.29940i	0.307808	+	0.307808i	−0.536251	+	0.844059i	$0.680160\pi$
$728$	7.28979	+	7.28979i	0.270178	+	0.270178i
$729$		0			0
$730$	23.1797	+	33.1736i	0.857919	+	1.22781i
$731$		−	9.45476i		−	0.349697i
$732$		0			0
$733$	22.8769	−	22.8769i	0.844978	−	0.844978i	−0.144523	−	0.989501i	$-0.546165\pi$
$733$	22.8769	−	22.8769i	0.844978	−	0.844978i	0.989501	+	0.144523i	$0.0461649\pi$
$734$	−44.1079			−1.62805
$735$		0			0
$736$	23.5883			0.869477
$737$	−24.2807	+	24.2807i	−0.894390	+	0.894390i
$738$		0			0
$739$			21.9271i			0.806601i	0.915068	+	0.403301i	$0.132137\pi$
$739$			21.9271i			0.806601i	−0.915068	+	0.403301i	$0.867863\pi$
$740$	−12.0082	+	67.7111i	−0.441430	+	2.48911i
$741$		0			0
$742$	−19.3678	−	19.3678i	−0.711014	−	0.711014i
$743$	14.6434	+	14.6434i	0.537213	+	0.537213i	0.922709	−	0.385496i	$-0.125970\pi$
$743$	14.6434	+	14.6434i	0.537213	+	0.537213i	−0.385496	+	0.922709i	$0.625970\pi$
$744$		0			0
$745$	−21.9178	+	15.3148i	−0.803005	+	0.561090i
$746$			72.1285i			2.64081i
$747$		0			0
$748$	−26.6637	+	26.6637i	−0.974921	+	0.974921i
$749$	−20.0472			−0.732507
$750$		0			0
$751$	−46.6877			−1.70366			−0.851829	−	0.523820i	$-0.824506\pi$
$751$	−46.6877			−1.70366			−0.851829	+	0.523820i	$0.824506\pi$
$752$	−0.0121399	+	0.0121399i	−0.000442696	+	0.000442696i
$753$		0			0
$754$		−	42.0215i		−	1.53033i
$755$	3.39203	−	2.37014i	0.123449	−	0.0862582i
$756$		0			0
$757$	4.34878	+	4.34878i	0.158059	+	0.158059i	0.781706	−	0.623647i	$-0.214350\pi$
$757$	4.34878	+	4.34878i	0.158059	+	0.158059i	−0.623647	+	0.781706i	$0.714350\pi$
$758$	−1.12721	−	1.12721i	−0.0409422	−	0.0409422i
$759$		0			0
$760$	−7.42653	+	41.8763i	−0.269388	+	1.51901i
$761$		−	20.3466i		−	0.737562i	−0.929516	−	0.368781i	$-0.879775\pi$
$761$		−	20.3466i		−	0.737562i	0.929516	−	0.368781i	$-0.120225\pi$
$762$		0			0
$763$	0.406141	−	0.406141i	0.0147033	−	0.0147033i
$764$	−33.5436			−1.21357
$765$		0			0
$766$	23.4324			0.846647
$767$	11.6931	−	11.6931i	0.422214	−	0.422214i
$768$		0			0
$769$		−	10.6781i		−	0.385063i	−0.981291	−	0.192532i	$-0.938330\pi$
$769$		−	10.6781i		−	0.385063i	0.981291	−	0.192532i	$-0.0616698\pi$
$770$	8.90077	+	12.7383i	0.320761	+	0.459058i
$771$		0			0
$772$	−0.866831	−	0.866831i	−0.0311979	−	0.0311979i
$773$	−16.1983	−	16.1983i	−0.582611	−	0.582611i	0.353009	−	0.935620i	$-0.385159\pi$
$773$	−16.1983	−	16.1983i	−0.582611	−	0.582611i	−0.935620	+	0.353009i	$0.885159\pi$
$774$		0			0
$775$	−5.64688	+	15.4199i	−0.202842	+	0.553900i
$776$		−	34.5766i		−	1.24123i
$777$		0			0
$778$	33.2312	−	33.2312i	1.19140	−	1.19140i
$779$	−48.8581			−1.75052
$780$		0			0
$781$	16.6022			0.594075
$782$	26.2119	−	26.2119i	0.937334	−	0.937334i
$783$		0			0
$784$		−	0.0700407i		−	0.00250145i
$785$	−8.44440	−	1.49757i	−0.301393	−	0.0534505i
$786$		0			0
$787$	3.85920	+	3.85920i	0.137566	+	0.137566i	0.772536	−	0.634971i	$-0.218988\pi$
$787$	3.85920	+	3.85920i	0.137566	+	0.137566i	−0.634971	+	0.772536i	$0.718988\pi$
$788$	22.7123	+	22.7123i	0.809094	+	0.809094i
$789$		0			0
$790$	−81.2745	−	14.4136i	−2.89162	−	0.512813i
$791$			9.87802i			0.351222i
$792$		0			0
$793$	26.7633	−	26.7633i	0.950392	−	0.950392i
$794$	−28.1948			−1.00060
$795$		0			0
$796$	−54.5311			−1.93280
$797$	−31.4439	+	31.4439i	−1.11380	+	1.11380i	−0.121168	+	0.992632i	$0.538664\pi$
$797$	−31.4439	+	31.4439i	−1.11380	+	1.11380i	−0.992632	+	0.121168i	$0.961336\pi$
$798$		0			0
$799$		−	0.937330i		−	0.0331604i
$800$	11.7333	+	25.2924i	0.414836	+	0.894223i
$801$		0			0
$802$	1.73872	+	1.73872i	0.0613964	+	0.0613964i
$803$	16.9354	+	16.9354i	0.597636	+	0.597636i
$804$		0			0
$805$	−5.41769	−	7.75354i	−0.190949	−	0.273276i
$806$			27.0507i			0.952819i
$807$		0			0
$808$	−34.2027	+	34.2027i	−1.20325	+	1.20325i
$809$	29.8706			1.05019			0.525097	−	0.851043i	$-0.324029\pi$
$809$	29.8706			1.05019			0.525097	+	0.851043i	$0.324029\pi$
$810$		0			0
$811$	41.5858			1.46028			0.730138	−	0.683300i	$-0.239456\pi$
$811$	41.5858			1.46028			0.730138	+	0.683300i	$0.239456\pi$
$812$	−11.7307	+	11.7307i	−0.411668	+	0.411668i
$813$		0			0
$814$			65.7288i			2.30379i
$815$	2.89666	−	16.3335i	0.101466	−	0.572138i
$816$		0			0
$817$	−11.5928	−	11.5928i	−0.405581	−	0.405581i
$818$	−29.0090	−	29.0090i	−1.01428	−	1.01428i
$819$		0			0
$820$	43.9164	−	30.6860i	1.53363	−	1.07160i
$821$			49.6249i			1.73192i	0.500114	+	0.865960i	$0.333292\pi$
$821$			49.6249i			1.73192i	−0.500114	+	0.865960i	$0.666708\pi$
$822$		0			0
$823$	11.9691	−	11.9691i	0.417216	−	0.417216i	−0.467027	−	0.884243i	$-0.654675\pi$
$823$	11.9691	−	11.9691i	0.417216	−	0.417216i	0.884243	+	0.467027i	$0.154675\pi$
$824$	−5.07035			−0.176634
$825$		0			0
$826$	−10.5440			−0.366873
$827$	24.1358	−	24.1358i	0.839285	−	0.839285i	−0.149480	−	0.988765i	$-0.547760\pi$
$827$	24.1358	−	24.1358i	0.839285	−	0.839285i	0.988765	+	0.149480i	$0.0477598\pi$
$828$		0			0
$829$		−	24.8211i		−	0.862071i	−0.902335	−	0.431035i	$-0.858148\pi$
$829$		−	24.8211i		−	0.862071i	0.902335	−	0.431035i	$-0.141852\pi$
$830$	5.92995	−	4.14348i	0.205832	−	0.143822i
$831$		0			0
$832$	32.8325	+	32.8325i	1.13826	+	1.13826i
$833$	2.70395	+	2.70395i	0.0936862	+	0.0936862i
$834$		0			0
$835$	−4.42481	+	24.9504i	−0.153127	+	0.863443i
$836$			65.3866i			2.26144i
$837$		0			0
$838$	24.0499	−	24.0499i	0.830789	−	0.830789i
$839$	−31.3907			−1.08373			−0.541863	−	0.840467i	$-0.682281\pi$
$839$	−31.3907			−1.08373			−0.541863	+	0.840467i	$0.682281\pi$
$840$		0			0
$841$	−2.97048			−0.102430
$842$	−28.2922	+	28.2922i	−0.975013	+	0.975013i
$843$		0			0
$844$		−	55.1650i		−	1.89886i
$845$	−0.105642	−	0.151189i	−0.00363419	−	0.00520108i
$846$		0			0
$847$	−1.27516	−	1.27516i	−0.0438149	−	0.0438149i
$848$	0.591945	+	0.591945i	0.0203275	+	0.0203275i
$849$		0			0
$850$	41.1439	+	15.0672i	1.41122	+	0.516799i
$851$		−	40.0076i		−	1.37144i
$852$		0			0
$853$	38.4133	−	38.4133i	1.31525	−	1.31525i	0.397755	−	0.917491i	$-0.369789\pi$
$853$	38.4133	−	38.4133i	1.31525	−	1.31525i	0.917491	−	0.397755i	$-0.130211\pi$
$854$	−24.1331			−0.825819
$855$		0			0
$856$	57.5034			1.96542
$857$	16.0449	−	16.0449i	0.548084	−	0.548084i	−0.377802	−	0.925886i	$-0.623320\pi$
$857$	16.0449	−	16.0449i	0.548084	−	0.548084i	0.925886	+	0.377802i	$0.123320\pi$
$858$		0			0
$859$		−	27.9426i		−	0.953389i	−0.879069	−	0.476695i	$-0.841835\pi$
$859$		−	27.9426i		−	0.953389i	0.879069	−	0.476695i	$-0.158165\pi$
$860$	17.7013	+	3.13923i	0.603609	+	0.107047i
$861$		0			0
$862$	3.72425	+	3.72425i	0.126849	+	0.126849i
$863$	6.65308	+	6.65308i	0.226474	+	0.226474i	0.811218	−	0.584744i	$-0.198805\pi$
$863$	6.65308	+	6.65308i	0.226474	+	0.226474i	−0.584744	+	0.811218i	$0.698805\pi$
$864$		0			0
$865$	−0.565008	−	0.100201i	−0.0192108	−	0.00340694i
$866$			9.08495i			0.308719i
$867$		0			0
$868$	7.55147	−	7.55147i	0.256314	−	0.256314i
$869$	−48.8495			−1.65710
$870$		0			0
$871$	40.6959			1.37893
$872$	−1.16498	+	1.16498i	−0.0394511	+	0.0394511i
$873$		0			0
$874$		−	64.2786i		−	2.17425i
$875$	5.61881	−	9.66587i	0.189950	−	0.326766i
$876$		0			0
$877$	17.2572	+	17.2572i	0.582734	+	0.582734i	0.935654	−	0.352920i	$-0.114811\pi$
$877$	17.2572	+	17.2572i	0.582734	+	0.582734i	−0.352920	+	0.935654i	$0.614811\pi$
$878$	25.1431	+	25.1431i	0.848540	+	0.848540i
$879$		0			0
$880$	−0.272038	−	0.389327i	−0.00917038	−	0.0131242i
$881$		−	10.6210i		−	0.357830i	−0.983865	−	0.178915i	$-0.942741\pi$
$881$		−	10.6210i		−	0.357830i	0.983865	−	0.178915i	$-0.0572587\pi$
$882$		0			0
$883$	−11.4145	+	11.4145i	−0.384130	+	0.384130i	−0.872588	−	0.488458i	$-0.837560\pi$
$883$	−11.4145	+	11.4145i	−0.384130	+	0.384130i	0.488458	+	0.872588i	$0.337560\pi$
$884$	44.6899			1.50309
$885$		0			0
$886$	−21.5981			−0.725601
$887$	18.4290	−	18.4290i	0.618786	−	0.618786i	−0.326434	−	0.945220i	$-0.605847\pi$
$887$	18.4290	−	18.4290i	0.618786	−	0.618786i	0.945220	+	0.326434i	$0.105847\pi$
$888$		0			0
$889$			5.60547i			0.188001i
$890$	−2.68472	+	15.1385i	−0.0899922	+	0.507442i
$891$		0			0
$892$	−43.4081	−	43.4081i	−1.45341	−	1.45341i
$893$	−1.14929	−	1.14929i	−0.0384597	−	0.0384597i
$894$		0			0
$895$	−22.8439	+	15.9619i	−0.763586	+	0.533547i
$896$		−	18.4533i		−	0.616483i
$897$		0			0
$898$	−26.6513	+	26.6513i	−0.889366	+	0.889366i
$899$	−16.7561			−0.558847
$900$		0			0
$901$	−45.7045			−1.52264
$902$	36.2092	−	36.2092i	1.20563	−	1.20563i
$903$		0			0
$904$		−	28.3342i		−	0.942380i
$905$	−26.0278	+	18.1866i	−0.865193	+	0.604543i
$906$		0			0
$907$	39.8245	+	39.8245i	1.32235	+	1.32235i	0.911868	+	0.410483i	$0.134640\pi$
$907$	39.8245	+	39.8245i	1.32235	+	1.32235i	0.410483	+	0.911868i	$0.365360\pi$
$908$	38.7779	+	38.7779i	1.28689	+	1.28689i
$909$		0			0
$910$	3.21601	−	18.1342i	0.106610	−	0.601144i
$911$			1.26894i			0.0420419i	0.999779	+	0.0210210i	$0.00669167\pi$
$911$			1.26894i			0.0420419i	−0.999779	+	0.0210210i	$0.993308\pi$
$912$		0			0
$913$	3.02728	−	3.02728i	0.100188	−	0.100188i
$914$	39.6031			1.30995
$915$		0			0
$916$	−27.3917			−0.905046
$917$	13.4901	−	13.4901i	0.445482	−	0.445482i
$918$		0			0
$919$			41.5356i			1.37013i	0.728481	+	0.685066i	$0.240227\pi$
$919$			41.5356i			1.37013i	−0.728481	+	0.685066i	$0.759773\pi$
$920$	15.5401	+	22.2403i	0.512343	+	0.733241i
$921$		0			0
$922$	−16.7314	−	16.7314i	−0.551018	−	0.551018i
$923$	−13.9132	−	13.9132i	−0.457958	−	0.457958i
$924$		0			0
$925$	42.8979	−	19.9006i	1.41047	−	0.654329i
$926$		−	42.9993i		−	1.41304i
$927$		0			0
$928$	−20.1171	+	20.1171i	−0.660375	+	0.660375i
$929$	41.6802			1.36748			0.683741	−	0.729725i	$-0.260352\pi$
$929$	41.6802			1.36748			0.683741	+	0.729725i	$0.260352\pi$
$930$		0			0
$931$	6.63081			0.217316
$932$	−2.67329	+	2.67329i	−0.0875667	+	0.0875667i
$933$		0			0
$934$		−	31.5011i		−	1.03075i
$935$	25.5322	+	4.52800i	0.834993	+	0.148082i
$936$		0			0
$937$	−41.7653	−	41.7653i	−1.36441	−	1.36441i	−0.868203	−	0.496210i	$-0.834725\pi$
$937$	−41.7653	−	41.7653i	−1.36441	−	1.36441i	−0.496210	−	0.868203i	$-0.665275\pi$
$938$	−18.3482	−	18.3482i	−0.599092	−	0.599092i
$939$		0			0
$940$	1.75488	+	0.311218i	0.0572379	+	0.0101508i
$941$		−	51.7350i		−	1.68651i	−0.537511	−	0.843257i	$-0.680635\pi$
$941$		−	51.7350i		−	1.68651i	0.537511	−	0.843257i	$-0.319365\pi$
$942$		0			0
$943$	−22.0397	+	22.0397i	−0.717711	+	0.717711i
$944$	0.322260			0.0104887
$945$		0			0
$946$	17.1831			0.558670
$947$	25.5564	−	25.5564i	0.830472	−	0.830472i	−0.157109	−	0.987581i	$-0.550217\pi$
$947$	25.5564	−	25.5564i	0.830472	−	0.830472i	0.987581	+	0.157109i	$0.0502175\pi$
$948$		0			0
$949$		−	28.3847i		−	0.921407i
$950$	68.9223	−	31.9736i	2.23614	−	1.03736i
$951$		0			0
$952$	−7.75602	−	7.75602i	−0.251374	−	0.251374i
$953$	−11.2847	−	11.2847i	−0.365546	−	0.365546i	0.500304	−	0.865850i	$-0.333222\pi$
$953$	−11.2847	−	11.2847i	−0.365546	−	0.365546i	−0.865850	+	0.500304i	$0.833222\pi$
$954$		0			0
$955$	13.2119	+	18.9083i	0.427528	+	0.611857i
$956$			37.2290i			1.20407i
$957$		0			0
$958$	−2.55217	+	2.55217i	−0.0824568	+	0.0824568i
$959$	−0.524664			−0.0169423
$960$		0			0
$961$	−20.2135			−0.652050
$962$	55.0827	−	55.0827i	1.77594	−	1.77594i
$963$		0			0
$964$			74.6842i			2.40542i
$965$	−0.147204	+	0.830047i	−0.00473868	+	0.0267202i
$966$		0			0
$967$	−11.3331	−	11.3331i	−0.364447	−	0.364447i	0.501000	−	0.865447i	$-0.332966\pi$
$967$	−11.3331	−	11.3331i	−0.364447	−	0.364447i	−0.865447	+	0.501000i	$0.832966\pi$
$968$	3.65767	+	3.65767i	0.117562	+	0.117562i
$969$		0			0
$970$	−50.6337	+	35.3797i	−1.62575	+	1.13597i
$971$		−	30.7436i		−	0.986609i	−0.869857	−	0.493304i	$-0.835789\pi$
$971$		−	30.7436i		−	0.986609i	0.869857	−	0.493304i	$-0.164211\pi$
$972$		0			0
$973$	11.5348	−	11.5348i	0.369790	−	0.369790i
$974$	45.5942			1.46093
$975$		0			0
$976$	0.737590			0.0236097
$977$	6.76461	−	6.76461i	0.216419	−	0.216419i	−0.590568	−	0.806988i	$-0.701096\pi$
$977$	6.76461	−	6.76461i	0.216419	−	0.216419i	0.806988	+	0.590568i	$0.201096\pi$
$978$		0			0
$979$			9.09886i			0.290801i
$980$	−5.96014	+	4.16458i	−0.190390	+	0.133032i
$981$		0			0
$982$	−36.6494	−	36.6494i	−1.16953	−	1.16953i
$983$	15.0257	+	15.0257i	0.479247	+	0.479247i	0.904891	−	0.425644i	$-0.139952\pi$
$983$	15.0257	+	15.0257i	0.479247	+	0.479247i	−0.425644	+	0.904891i	$0.639952\pi$
$984$		0			0
$985$	3.85699	−	21.7486i	0.122894	−	0.692967i
$986$			44.7090i			1.42383i
$987$		0			0
$988$	54.7959	−	54.7959i	1.74329	−	1.74329i
$989$	−10.4589			−0.332575
$990$		0			0
$991$	37.5534			1.19292			0.596461	−	0.802642i	$-0.296573\pi$
$991$	37.5534			1.19292			0.596461	+	0.802642i	$0.296573\pi$
$992$	12.9500	−	12.9500i	0.411164	−	0.411164i
$993$		0			0
$994$			12.5459i			0.397931i
$995$	21.4783	+	30.7387i	0.680909	+	0.974483i
$996$		0			0
$997$	36.6256	+	36.6256i	1.15995	+	1.15995i	0.984487	+	0.175459i	$0.0561408\pi$
$997$	36.6256	+	36.6256i	1.15995	+	1.15995i	0.175459	+	0.984487i	$0.443859\pi$
$998$	56.9814	+	56.9814i	1.80371	+	1.80371i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.m.a.197.2	yes	12
3.2	odd	2		315.2.m.b.197.5	yes	12
5.2	odd	4		1575.2.m.d.1268.2		12
5.3	odd	4		315.2.m.b.8.5	yes	12
5.4	even	2		1575.2.m.c.1457.5		12
15.2	even	4		1575.2.m.c.1268.5		12
15.8	even	4	inner	315.2.m.a.8.2	✓	12
15.14	odd	2		1575.2.m.d.1457.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.m.a.8.2	✓	12	15.8	even	4	inner
315.2.m.a.197.2	yes	12	1.1	even	1	trivial
315.2.m.b.8.5	yes	12	5.3	odd	4
315.2.m.b.197.5	yes	12	3.2	odd	2
1575.2.m.c.1268.5		12	15.2	even	4
1575.2.m.c.1457.5		12	5.4	even	2
1575.2.m.d.1268.2		12	5.2	odd	4
1575.2.m.d.1457.2		12	15.14	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-1.62044 + 1.62044i) q^{2} -3.25168i q^{4} +(-1.83294 + 1.28075i) q^{5} +(-0.707107 - 0.707107i) q^{7} +(2.02827 + 2.02827i) q^{8} +O(q^{10})\)	\(q+(-1.62044 + 1.62044i) q^{2} -3.25168i q^{4} +(-1.83294 + 1.28075i) q^{5} +(-0.707107 - 0.707107i) q^{7} +(2.02827 + 2.02827i) q^{8} +(0.894803 - 5.04556i) q^{10} -3.03260i q^{11} +(-2.54141 + 2.54141i) q^{13} +2.29165 q^{14} -0.0700407 q^{16} +(2.70395 - 2.70395i) q^{17} -6.63081i q^{19} +(4.16458 + 5.96014i) q^{20} +(4.91416 + 4.91416i) q^{22} +(-2.99113 - 2.99113i) q^{23} +(1.71937 - 4.69508i) q^{25} -8.23642i q^{26} +(-2.29928 + 2.29928i) q^{28} +5.10191 q^{29} -3.28427 q^{31} +(-3.94304 + 3.94304i) q^{32} +8.76319i q^{34} +(2.20171 + 0.390462i) q^{35} +(6.68770 + 6.68770i) q^{37} +(10.7449 + 10.7449i) q^{38} +(-6.31541 - 1.12000i) q^{40} -7.36835i q^{41} +(1.74832 - 1.74832i) q^{43} -9.86103 q^{44} +9.69392 q^{46} +(0.173326 - 0.173326i) q^{47} +1.00000i q^{49} +(4.82197 + 10.3943i) q^{50} +(8.26384 + 8.26384i) q^{52} +(-8.45145 - 8.45145i) q^{53} +(3.88399 + 5.55858i) q^{55} -2.86841i q^{56} +(-8.26736 + 8.26736i) q^{58} -4.60104 q^{59} -10.5309 q^{61} +(5.32198 - 5.32198i) q^{62} -12.9190i q^{64} +(1.40336 - 7.91316i) q^{65} +(-8.00655 - 8.00655i) q^{67} +(-8.79236 - 8.79236i) q^{68} +(-4.20047 + 2.93503i) q^{70} +5.47459i q^{71} +(-5.58444 + 5.58444i) q^{73} -21.6741 q^{74} -21.5612 q^{76} +(-2.14437 + 2.14437i) q^{77} -16.1081i q^{79} +(0.128381 - 0.0897044i) q^{80} +(11.9400 + 11.9400i) q^{82} +(0.998247 + 0.998247i) q^{83} +(-1.49311 + 8.41926i) q^{85} +5.66612i q^{86} +(6.15093 - 6.15093i) q^{88} -3.00035 q^{89} +3.59409 q^{91} +(-9.72619 + 9.72619i) q^{92} +0.561731i q^{94} +(8.49240 + 12.1539i) q^{95} +(-8.52367 - 8.52367i) q^{97} +(-1.62044 - 1.62044i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 4 q^{5} + 24 q^{8}+O(q^{10}) \) 12 * q - 4 * q^5 + 24 * q^8	\( 12 q - 4 q^{5} + 24 q^{8} + 16 q^{10} - 4 q^{13} - 4 q^{14} - 20 q^{16} + 8 q^{17} - 12 q^{20} - 8 q^{22} + 8 q^{23} - 8 q^{25} - 32 q^{29} + 48 q^{32} + 8 q^{35} + 4 q^{37} + 24 q^{38} - 28 q^{40} + 40 q^{43} - 64 q^{44} + 16 q^{46} + 24 q^{47} - 16 q^{50} + 36 q^{52} - 40 q^{53} - 16 q^{55} - 28 q^{58} - 80 q^{59} - 32 q^{61} + 16 q^{62} + 48 q^{65} - 48 q^{67} + 32 q^{68} + 8 q^{70} - 20 q^{73} - 64 q^{74} + 16 q^{76} + 36 q^{80} + 20 q^{82} + 24 q^{83} - 56 q^{89} + 8 q^{92} + 56 q^{95} + 12 q^{97}+O(q^{100}) \) 12 * q - 4 * q^5 + 24 * q^8 + 16 * q^10 - 4 * q^13 - 4 * q^14 - 20 * q^16 + 8 * q^17 - 12 * q^20 - 8 * q^22 + 8 * q^23 - 8 * q^25 - 32 * q^29 + 48 * q^32 + 8 * q^35 + 4 * q^37 + 24 * q^38 - 28 * q^40 + 40 * q^43 - 64 * q^44 + 16 * q^46 + 24 * q^47 - 16 * q^50 + 36 * q^52 - 40 * q^53 - 16 * q^55 - 28 * q^58 - 80 * q^59 - 32 * q^61 + 16 * q^62 + 48 * q^65 - 48 * q^67 + 32 * q^68 + 8 * q^70 - 20 * q^73 - 64 * q^74 + 16 * q^76 + 36 * q^80 + 20 * q^82 + 24 * q^83 - 56 * q^89 + 8 * q^92 + 56 * q^95 + 12 * q^97

Introduction

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