LMFDB - Embedded newform 315.2.m.b.8.1

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			8.1
Root			$2.91021i$ of defining polynomial
Character	$\chi$	$=$	315.8
Dual form			315.2.m.b.197.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.45137 - 1.45137i) q^{2} +2.21293i q^{4} +(1.31357 - 1.80957i) q^{5} +(-0.707107 + 0.707107i) q^{7} +(0.309035 - 0.309035i) q^{8} +O(q^{10})$	\(q+(-1.45137 - 1.45137i) q^{2} +2.21293i q^{4} +(1.31357 - 1.80957i) q^{5} +(-0.707107 + 0.707107i) q^{7} +(0.309035 - 0.309035i) q^{8} +(-4.53282 + 0.719873i) q^{10} -5.62971i q^{11} +(-0.00747830 - 0.00747830i) q^{13} +2.05254 q^{14} +3.52881 q^{16} +(-1.20876 - 1.20876i) q^{17} -5.69344i q^{19} +(4.00444 + 2.90683i) q^{20} +(-8.17077 + 8.17077i) q^{22} +(-4.96275 + 4.96275i) q^{23} +(-1.54907 - 4.75399i) q^{25} +0.0217075i q^{26} +(-1.56478 - 1.56478i) q^{28} -1.55541 q^{29} -4.84264 q^{31} +(-5.73966 - 5.73966i) q^{32} +3.50872i q^{34} +(0.350723 + 2.20839i) q^{35} +(3.14119 - 3.14119i) q^{37} +(-8.26326 + 8.26326i) q^{38} +(-0.153280 - 0.965159i) q^{40} +9.02203i q^{41} +(2.78707 + 2.78707i) q^{43} +12.4581 q^{44} +14.4055 q^{46} +(-6.31695 - 6.31695i) q^{47} -1.00000i q^{49} +(-4.65151 + 9.14804i) q^{50} +(0.0165489 - 0.0165489i) q^{52} +(4.17043 - 4.17043i) q^{53} +(-10.1873 - 7.39502i) q^{55} +0.437041i q^{56} +(2.25746 + 2.25746i) q^{58} +11.8204 q^{59} +4.82074 q^{61} +(7.02844 + 7.02844i) q^{62} +9.60309i q^{64} +(-0.0233558 + 0.00370921i) q^{65} +(1.72058 - 1.72058i) q^{67} +(2.67491 - 2.67491i) q^{68} +(2.69616 - 3.71421i) q^{70} -4.89804i q^{71} +(2.69985 + 2.69985i) q^{73} -9.11804 q^{74} +12.5992 q^{76} +(3.98081 + 3.98081i) q^{77} -10.6179i q^{79} +(4.63534 - 6.38562i) q^{80} +(13.0943 - 13.0943i) q^{82} +(5.14537 - 5.14537i) q^{83} +(-3.77514 + 0.599544i) q^{85} -8.09013i q^{86} +(-1.73978 - 1.73978i) q^{88} +16.4527 q^{89} +0.0105759 q^{91} +(-10.9822 - 10.9822i) q^{92} +18.3364i q^{94} +(-10.3027 - 7.47873i) q^{95} +(9.91803 - 9.91803i) q^{97} +(-1.45137 + 1.45137i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

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

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 $

$2$	−1.45137	−	1.45137i	−1.02627	−	1.02627i	−0.999645	−	0.0266253i	$-0.991524\pi$
$2$	−1.45137	−	1.45137i	−1.02627	−	1.02627i	−0.0266253	−	0.999645i	$-0.508476\pi$
$3$		0			0
$3$		0			0
$4$			2.21293i			1.10646i
$5$	1.31357	−	1.80957i	0.587446	−	0.809263i
$5$	1.31357	−	1.80957i	0.587446	−	0.809263i
$6$		0			0
$7$	−0.707107	+	0.707107i	−0.267261	+	0.267261i
$7$	−0.707107	+	0.707107i	−0.267261	+	0.267261i
$8$	0.309035	−	0.309035i	0.109260	−	0.109260i
$9$		0			0
$10$	−4.53282	+	0.719873i	−1.43340	+	0.227644i
$11$		−	5.62971i		−	1.69742i	−0.528857	−	0.848711i	$-0.677379\pi$
$11$		−	5.62971i		−	1.69742i	0.528857	−	0.848711i	$-0.322621\pi$
$12$		0			0
$13$	−0.00747830	−	0.00747830i	−0.00207411	−	0.00207411i	0.706069	−	0.708143i	$-0.250467\pi$
$13$	−0.00747830	−	0.00747830i	−0.00207411	−	0.00207411i	−0.708143	+	0.706069i	$0.750467\pi$
$14$	2.05254			0.548565
$15$		0			0
$16$	3.52881			0.882202
$17$	−1.20876	−	1.20876i	−0.293169	−	0.293169i	0.545162	−	0.838331i	$-0.316468\pi$
$17$	−1.20876	−	1.20876i	−0.293169	−	0.293169i	−0.838331	+	0.545162i	$0.816468\pi$
$18$		0			0
$19$		−	5.69344i		−	1.30616i	−0.757287	−	0.653082i	$-0.773476\pi$
$19$		−	5.69344i		−	1.30616i	0.757287	−	0.653082i	$-0.226524\pi$
$20$	4.00444	+	2.90683i	0.895420	+	0.649988i
$21$		0			0
$22$	−8.17077	+	8.17077i	−1.74201	+	1.74201i
$23$	−4.96275	+	4.96275i	−1.03481	+	1.03481i	−0.0354333	+	0.999372i	$0.511281\pi$
$23$	−4.96275	+	4.96275i	−1.03481	+	1.03481i	−0.999372	+	0.0354333i	$0.988719\pi$
$24$		0			0
$25$	−1.54907	−	4.75399i	−0.309813	−	0.950797i
$26$			0.0217075i			0.00425719i
$27$		0			0
$28$	−1.56478	−	1.56478i	−0.295715	−	0.295715i
$29$	−1.55541			−0.288831			−0.144416	−	0.989517i	$-0.546130\pi$
$29$	−1.55541			−0.288831			−0.144416	+	0.989517i	$0.546130\pi$
$30$		0			0
$31$	−4.84264			−0.869763			−0.434882	−	0.900488i	$-0.643210\pi$
$31$	−4.84264			−0.869763			−0.434882	+	0.900488i	$0.643210\pi$
$32$	−5.73966	−	5.73966i	−1.01464	−	1.01464i
$33$		0			0
$34$			3.50872i			0.601741i
$35$	0.350723	+	2.20839i	0.0592830	+	0.373286i
$36$		0			0
$37$	3.14119	−	3.14119i	0.516409	−	0.516409i	−0.400074	−	0.916483i	$-0.631016\pi$
$37$	3.14119	−	3.14119i	0.516409	−	0.516409i	0.916483	+	0.400074i	$0.131016\pi$
$38$	−8.26326	+	8.26326i	−1.34048	+	1.34048i
$39$		0			0
$40$	−0.153280	−	0.965159i	−0.0242358	−	0.152605i
$41$			9.02203i			1.40900i	0.709702	+	0.704502i	$0.248830\pi$
$41$			9.02203i			1.40900i	−0.709702	+	0.704502i	$0.751170\pi$
$42$		0			0
$43$	2.78707	+	2.78707i	0.425025	+	0.425025i	0.886929	−	0.461905i	$-0.152834\pi$
$43$	2.78707	+	2.78707i	0.425025	+	0.425025i	−0.461905	+	0.886929i	$0.652834\pi$
$44$	12.4581			1.87813
$45$		0			0
$46$	14.4055			2.12398
$47$	−6.31695	−	6.31695i	−0.921421	−	0.921421i	0.0757087	−	0.997130i	$-0.475878\pi$
$47$	−6.31695	−	6.31695i	−0.921421	−	0.921421i	−0.997130	+	0.0757087i	$0.975878\pi$
$48$		0			0
$49$		−	1.00000i		−	0.142857i
$50$	−4.65151	+	9.14804i	−0.657823	+	1.29373i
$51$		0			0
$52$	0.0165489	−	0.0165489i	0.00229492	−	0.00229492i
$53$	4.17043	−	4.17043i	0.572853	−	0.572853i	−0.360072	−	0.932925i	$-0.617248\pi$
$53$	4.17043	−	4.17043i	0.572853	−	0.572853i	0.932925	+	0.360072i	$0.117248\pi$
$54$		0			0
$55$	−10.1873	−	7.39502i	−1.37366	−	0.997144i
$56$			0.437041i			0.0584021i
$57$		0			0
$58$	2.25746	+	2.25746i	0.296419	+	0.296419i
$59$	11.8204			1.53889			0.769444	−	0.638714i	$-0.220533\pi$
$59$	11.8204			1.53889			0.769444	+	0.638714i	$0.220533\pi$
$60$		0			0
$61$	4.82074			0.617232			0.308616	−	0.951187i	$-0.400134\pi$
$61$	4.82074			0.617232			0.308616	+	0.951187i	$0.400134\pi$
$62$	7.02844	+	7.02844i	0.892613	+	0.892613i
$63$		0			0
$64$			9.60309i			1.20039i
$65$	−0.0233558	+	0.00370921i	−0.00289693	+	0.000460071i
$66$		0			0
$67$	1.72058	−	1.72058i	0.210203	−	0.210203i	−0.594151	−	0.804354i	$-0.702512\pi$
$67$	1.72058	−	1.72058i	0.210203	−	0.210203i	0.804354	+	0.594151i	$0.202512\pi$
$68$	2.67491	−	2.67491i	0.324380	−	0.324380i
$69$		0			0
$70$	2.69616	−	3.71421i	0.322252	−	0.443933i
$71$		−	4.89804i		−	0.581291i	−0.956831	−	0.290645i	$-0.906130\pi$
$71$		−	4.89804i		−	0.581291i	0.956831	−	0.290645i	$-0.0938700\pi$
$72$		0			0
$73$	2.69985	+	2.69985i	0.315994	+	0.315994i	0.847226	−	0.531232i	$-0.178271\pi$
$73$	2.69985	+	2.69985i	0.315994	+	0.315994i	−0.531232	+	0.847226i	$0.678271\pi$
$74$	−9.11804			−1.05995
$75$		0			0
$76$	12.5992			1.44522
$77$	3.98081	+	3.98081i	0.453655	+	0.453655i
$78$		0			0
$79$		−	10.6179i		−	1.19460i	−0.802016	−	0.597302i	$-0.796239\pi$
$79$		−	10.6179i		−	1.19460i	0.802016	−	0.597302i	$-0.203761\pi$
$80$	4.63534	−	6.38562i	0.518246	−	0.713934i
$81$		0			0
$82$	13.0943	−	13.0943i	1.44602	−	1.44602i
$83$	5.14537	−	5.14537i	0.564778	−	0.564778i	−0.365883	−	0.930661i	$-0.619233\pi$
$83$	5.14537	−	5.14537i	0.564778	−	0.564778i	0.930661	+	0.365883i	$0.119233\pi$
$84$		0			0
$85$	−3.77514	+	0.599544i	−0.409471	+	0.0650296i
$86$		−	8.09013i		−	0.872381i
$87$		0			0
$88$	−1.73978	−	1.73978i	−0.185461	−	0.185461i
$89$	16.4527			1.74398			0.871991	−	0.489521i	$-0.162828\pi$
$89$	16.4527			1.74398			0.871991	+	0.489521i	$0.162828\pi$
$90$		0			0
$91$	0.0105759			0.00110866
$92$	−10.9822	−	10.9822i	−1.14497	−	1.14497i
$93$		0			0
$94$			18.3364i			1.89126i
$95$	−10.3027	−	7.47873i	−1.05703	−	0.767302i
$96$		0			0
$97$	9.91803	−	9.91803i	1.00702	−	1.00702i	0.00704778	−	0.999975i	$-0.497757\pi$
$97$	9.91803	−	9.91803i	1.00702	−	1.00702i	0.999975	−	0.00704778i	$-0.00224340\pi$
$98$	−1.45137	+	1.45137i	−0.146610	+	0.146610i
$99$		0			0
$100$	10.5202	−	3.42797i	1.05202	−	0.342797i
$101$			12.8862i			1.28223i	0.767445	+	0.641115i	$0.221528\pi$
$101$			12.8862i			1.28223i	−0.767445	+	0.641115i	$0.778472\pi$
$102$		0			0
$103$	5.93245	+	5.93245i	0.584541	+	0.584541i	0.936148	−	0.351607i	$-0.114365\pi$
$103$	5.93245	+	5.93245i	0.584541	+	0.584541i	−0.351607	+	0.936148i	$0.614365\pi$
$104$	−0.00462211			−0.000453236
$105$		0			0
$106$	−12.1057			−1.17580
$107$	−4.75259	−	4.75259i	−0.459450	−	0.459450i	0.439025	−	0.898475i	$-0.355324\pi$
$107$	−4.75259	−	4.75259i	−0.459450	−	0.459450i	−0.898475	+	0.439025i	$0.855324\pi$
$108$		0			0
$109$			12.3430i			1.18225i	0.806581	+	0.591124i	$0.201316\pi$
$109$			12.3430i			1.18225i	−0.806581	+	0.591124i	$0.798684\pi$
$110$	4.05268	+	25.5184i	0.386408	+	2.43309i
$111$		0			0
$112$	−2.49524	+	2.49524i	−0.235778	+	0.235778i
$113$	−3.95944	+	3.95944i	−0.372472	+	0.372472i	−0.868377	−	0.495905i	$-0.834837\pi$
$113$	−3.95944	+	3.95944i	−0.372472	+	0.372472i	0.495905	+	0.868377i	$0.334837\pi$
$114$		0			0
$115$	2.46151	+	15.4994i	0.229537	+	1.44532i
$116$		−	3.44200i		−	0.319581i
$117$		0			0
$118$	−17.1558	−	17.1558i	−1.57932	−	1.57932i
$119$	1.70945			0.156705
$120$		0			0
$121$	−20.6936			−1.88124
$122$	−6.99666	−	6.99666i	−0.633448	−	0.633448i
$123$		0			0
$124$		−	10.7164i		−	0.962361i
$125$	−10.6375	−	3.44156i	−0.951444	−	0.307822i
$126$		0			0
$127$	−5.55904	+	5.55904i	−0.493285	+	0.493285i	−0.909340	−	0.416055i	$-0.863412\pi$
$127$	−5.55904	+	5.55904i	−0.493285	+	0.493285i	0.416055	+	0.909340i	$0.363412\pi$
$128$	2.45827	−	2.45827i	0.217282	−	0.217282i
$129$		0			0
$130$	0.0392812	+	0.0285143i	0.00344519	+	0.00250087i
$131$		−	3.36678i		−	0.294157i	−0.989125	−	0.147079i	$-0.953013\pi$
$131$		−	3.36678i		−	0.294157i	0.989125	−	0.147079i	$-0.0469870\pi$
$132$		0			0
$133$	4.02587	+	4.02587i	0.349087	+	0.349087i
$134$	−4.99439			−0.431450
$135$		0			0
$136$	−0.747101			−0.0640634
$137$	16.3236	+	16.3236i	1.39462	+	1.39462i	0.814605	+	0.580016i	$0.196954\pi$
$137$	16.3236	+	16.3236i	1.39462	+	1.39462i	0.580016	+	0.814605i	$0.303046\pi$
$138$		0			0
$139$			12.6535i			1.07325i	0.843820	+	0.536626i	$0.180301\pi$
$139$			12.6535i			1.07325i	−0.843820	+	0.536626i	$0.819699\pi$
$140$	−4.88701	+	0.776124i	−0.413028	+	0.0655944i
$141$		0			0
$142$	−7.10885	+	7.10885i	−0.596562	+	0.596562i
$143$	−0.0421007	+	0.0421007i	−0.00352064	+	0.00352064i
$144$		0			0
$145$	−2.04313	+	2.81461i	−0.169673	+	0.233741i
$146$		−	7.83695i		−	0.648591i
$147$		0			0
$148$	6.95123	+	6.95123i	0.571387	+	0.571387i
$149$	7.42258			0.608081			0.304041	−	0.952659i	$-0.401664\pi$
$149$	7.42258			0.608081			0.304041	+	0.952659i	$0.401664\pi$
$150$		0			0
$151$	−12.7952			−1.04126			−0.520628	−	0.853783i	$-0.674302\pi$
$151$	−12.7952			−1.04126			−0.520628	+	0.853783i	$0.674302\pi$
$152$	−1.75947	−	1.75947i	−0.142712	−	0.142712i
$153$		0			0
$154$		−	11.5552i		−	0.931146i
$155$	−6.36114	+	8.76308i	−0.510939	+	0.703867i
$156$		0			0
$157$	10.3508	−	10.3508i	0.826085	−	0.826085i	−0.160887	−	0.986973i	$-0.551436\pi$
$157$	10.3508	−	10.3508i	0.826085	−	0.826085i	0.986973	+	0.160887i	$0.0514356\pi$
$158$	−15.4104	+	15.4104i	−1.22599	+	1.22599i
$159$		0			0
$160$	−17.9258	+	2.84685i	−1.41716	+	0.225064i
$161$		−	7.01839i		−	0.553127i
$162$		0			0
$163$	−14.6689	−	14.6689i	−1.14896	−	1.14896i	−0.986757	−	0.162203i	$-0.948140\pi$
$163$	−14.6689	−	14.6689i	−1.14896	−	1.14896i	−0.162203	−	0.986757i	$-0.551860\pi$
$164$	−19.9651			−1.55901
$165$		0			0
$166$	−14.9356			−1.15923
$167$	11.4412	+	11.4412i	0.885344	+	0.885344i	0.994072	−	0.108728i	$-0.0346776\pi$
$167$	11.4412	+	11.4412i	0.885344	+	0.885344i	−0.108728	+	0.994072i	$0.534678\pi$
$168$		0			0
$169$		−	12.9999i		−	0.999991i
$170$	6.34927	+	4.60895i	0.486966	+	0.353490i
$171$		0			0
$172$	−6.16759	+	6.16759i	−0.470274	+	0.470274i
$173$	7.83527	−	7.83527i	0.595704	−	0.595704i	−0.343462	−	0.939166i	$-0.611600\pi$
$173$	7.83527	−	7.83527i	0.595704	−	0.595704i	0.939166	+	0.343462i	$0.111600\pi$
$174$		0			0
$175$	4.45693	+	2.26622i	0.336912	+	0.171310i
$176$		−	19.8662i		−	1.49747i
$177$		0			0
$178$	−23.8789	−	23.8789i	−1.78980	−	1.78980i
$179$	11.1315			0.832007			0.416003	−	0.909363i	$-0.363430\pi$
$179$	11.1315			0.832007			0.416003	+	0.909363i	$0.363430\pi$
$180$		0			0
$181$	12.8050			0.951788			0.475894	−	0.879503i	$-0.342125\pi$
$181$	12.8050			0.951788			0.475894	+	0.879503i	$0.342125\pi$
$182$	−0.0153495	−	0.0153495i	−0.00113778	−	0.00113778i
$183$		0			0
$184$			3.06733i			0.226126i
$185$	−1.55802	−	9.81037i	−0.114548	−	0.721273i
$186$		0			0
$187$	−6.80500	+	6.80500i	−0.497631	+	0.497631i
$188$	13.9789	−	13.9789i	1.01952	−	1.01952i
$189$		0			0
$190$	4.09855	+	25.8073i	0.297340	+	1.87226i
$191$			1.52585i			0.110407i	0.998475	+	0.0552033i	$0.0175807\pi$
$191$			1.52585i			0.110407i	−0.998475	+	0.0552033i	$0.982419\pi$
$192$		0			0
$193$	−7.00514	−	7.00514i	−0.504241	−	0.504241i	0.408512	−	0.912753i	$-0.366048\pi$
$193$	−7.00514	−	7.00514i	−0.504241	−	0.504241i	−0.912753	+	0.408512i	$0.866048\pi$
$194$	−28.7894			−2.06696
$195$		0			0
$196$	2.21293			0.158066
$197$	−3.95944	−	3.95944i	−0.282098	−	0.282098i	0.551847	−	0.833945i	$-0.313923\pi$
$197$	−3.95944	−	3.95944i	−0.282098	−	0.282098i	−0.833945	+	0.551847i	$0.813923\pi$
$198$		0			0
$199$			19.0634i			1.35137i	0.737193	+	0.675683i	$0.236151\pi$
$199$			19.0634i			1.35137i	−0.737193	+	0.675683i	$0.763849\pi$
$200$	−1.94786	−	0.990432i	−0.137735	−	0.0700342i
$201$		0			0
$202$	18.7027	−	18.7027i	1.31591	−	1.31591i
$203$	1.09984	−	1.09984i	0.0771935	−	0.0771935i
$204$		0			0
$205$	16.3260	+	11.8511i	1.14025	+	0.827714i
$206$		−	17.2203i		−	1.19980i
$207$		0			0
$208$	−0.0263895	−	0.0263895i	−0.00182978	−	0.00182978i
$209$	−32.0524			−2.21711
$210$		0			0
$211$	−14.1156			−0.971756			−0.485878	−	0.874027i	$-0.661500\pi$
$211$	−14.1156			−0.971756			−0.485878	+	0.874027i	$0.661500\pi$
$212$	9.22886	+	9.22886i	0.633841	+	0.633841i
$213$		0			0
$214$			13.7955i			0.943040i
$215$	8.70441	−	1.38238i	0.593636	−	0.0942775i
$216$		0			0
$217$	3.42426	−	3.42426i	0.232454	−	0.232454i
$218$	17.9143	−	17.9143i	1.21331	−	1.21331i
$219$		0			0
$220$	16.3646	−	22.5438i	1.10330	−	1.51991i
$221$			0.0180790i			0.00121613i
$222$		0			0
$223$	20.1021	+	20.1021i	1.34613	+	1.34613i	0.889818	+	0.456315i	$0.150831\pi$
$223$	20.1021	+	20.1021i	1.34613	+	1.34613i	0.456315	+	0.889818i	$0.349169\pi$
$224$	8.11711			0.542347
$225$		0			0
$226$	11.4932			0.764515
$227$	−7.18784	−	7.18784i	−0.477074	−	0.477074i	0.427121	−	0.904195i	$-0.359528\pi$
$227$	−7.18784	−	7.18784i	−0.477074	−	0.477074i	−0.904195	+	0.427121i	$0.859528\pi$
$228$		0			0
$229$		−	12.4777i		−	0.824552i	−0.911059	−	0.412276i	$-0.864734\pi$
$229$		−	12.4777i		−	0.824552i	0.911059	−	0.412276i	$-0.135266\pi$
$230$	18.9227	−	26.0678i	1.24773	−	1.71886i
$231$		0			0
$232$	−0.480675	+	0.480675i	−0.0315578	+	0.0315578i
$233$	−16.7330	+	16.7330i	−1.09622	+	1.09622i	−0.101367	+	0.994849i	$0.532322\pi$
$233$	−16.7330	+	16.7330i	−1.09622	+	1.09622i	−0.994849	+	0.101367i	$0.967678\pi$
$234$		0			0
$235$	−19.7287	+	3.13319i	−1.28696	+	0.204386i
$236$			26.1577i			1.70272i
$237$		0			0
$238$	−2.48104	−	2.48104i	−0.160822	−	0.160822i
$239$	−3.43517			−0.222203			−0.111101	−	0.993809i	$-0.535438\pi$
$239$	−3.43517			−0.222203			−0.111101	+	0.993809i	$0.535438\pi$
$240$		0			0
$241$	22.7302			1.46418			0.732091	−	0.681206i	$-0.238544\pi$
$241$	22.7302			1.46418			0.732091	+	0.681206i	$0.238544\pi$
$242$	30.0340	+	30.0340i	1.93066	+	1.93066i
$243$		0			0
$244$			10.6679i			0.682945i
$245$	−1.80957	−	1.31357i	−0.115609	−	0.0839209i
$246$		0			0
$247$	−0.0425773	+	0.0425773i	−0.00270913	+	0.00270913i
$248$	−1.49654	+	1.49654i	−0.0950306	+	0.0950306i
$249$		0			0
$250$	10.4439	+	20.4338i	0.660530	+	1.29235i
$251$			1.13033i			0.0713455i	0.999364	+	0.0356727i	$0.0113574\pi$
$251$			1.13033i			0.0713455i	−0.999364	+	0.0356727i	$0.988643\pi$
$252$		0			0
$253$	27.9389	+	27.9389i	1.75650	+	1.75650i
$254$	16.1364			1.01249
$255$		0			0
$256$	12.0705			0.754405
$257$	1.03499	+	1.03499i	0.0645611	+	0.0645611i	0.738650	−	0.674089i	$-0.235464\pi$
$257$	1.03499	+	1.03499i	0.0645611	+	0.0645611i	−0.674089	+	0.738650i	$0.735464\pi$
$258$		0			0
$259$			4.44232i			0.276032i
$260$	−0.00820822	−	0.0516846i	−0.000509052	−	0.00320534i
$261$		0			0
$262$	−4.88643	+	4.88643i	−0.301885	+	0.301885i
$263$	5.31703	−	5.31703i	0.327862	−	0.327862i	−0.523911	−	0.851773i	$-0.675528\pi$
$263$	5.31703	−	5.31703i	0.327862	−	0.327862i	0.851773	+	0.523911i	$0.175528\pi$
$264$		0			0
$265$	−2.06852	−	13.0248i	−0.127068	−	0.800109i
$266$		−	11.6860i		−	0.716516i
$267$		0			0
$268$	3.80753	+	3.80753i	0.232582	+	0.232582i
$269$	−3.78057			−0.230506			−0.115253	−	0.993336i	$-0.536768\pi$
$269$	−3.78057			−0.230506			−0.115253	+	0.993336i	$0.536768\pi$
$270$		0			0
$271$	−27.8404			−1.69119			−0.845593	−	0.533828i	$-0.820753\pi$
$271$	−27.8404			−1.69119			−0.845593	+	0.533828i	$0.820753\pi$
$272$	−4.26550	−	4.26550i	−0.258634	−	0.258634i
$273$		0			0
$274$		−	47.3831i		−	2.86252i
$275$	−26.7636	+	8.72079i	−1.61390	+	0.525884i
$276$		0			0
$277$	−1.81486	+	1.81486i	−0.109044	+	0.109044i	−0.759524	−	0.650480i	$-0.774568\pi$
$277$	−1.81486	+	1.81486i	−0.109044	+	0.109044i	0.650480	+	0.759524i	$0.274568\pi$
$278$	18.3648	−	18.3648i	1.10145	−	1.10145i
$279$		0			0
$280$	0.790856	+	0.574085i	0.0472627	+	0.0343081i
$281$			8.13136i			0.485076i	0.970142	+	0.242538i	$0.0779800\pi$
$281$			8.13136i			0.485076i	−0.970142	+	0.242538i	$0.922020\pi$
$282$		0			0
$283$	−3.85187	−	3.85187i	−0.228970	−	0.228970i	0.583292	−	0.812262i	$-0.301764\pi$
$283$	−3.85187	−	3.85187i	−0.228970	−	0.228970i	−0.812262	+	0.583292i	$0.801764\pi$
$284$	10.8390			0.643177
$285$		0			0
$286$	0.122207			0.00722625
$287$	−6.37954	−	6.37954i	−0.376572	−	0.376572i
$288$		0			0
$289$		−	14.0778i		−	0.828104i
$290$	7.05036	−	1.11969i	0.414012	−	0.0657507i
$291$		0			0
$292$	−5.97458	+	5.97458i	−0.349636	+	0.349636i
$293$	−9.16944	+	9.16944i	−0.535684	+	0.535684i	−0.922258	−	0.386574i	$-0.873658\pi$
$293$	−9.16944	+	9.16944i	−0.535684	+	0.535684i	0.386574	+	0.922258i	$0.373658\pi$
$294$		0			0
$295$	15.5270	−	21.3898i	0.904014	−	1.24536i
$296$		−	1.94148i		−	0.112846i
$297$		0			0
$298$	−10.7729	−	10.7729i	−0.624056	−	0.624056i
$299$	0.0742259			0.00429260
$300$		0			0
$301$	−3.94152			−0.227185
$302$	18.5705	+	18.5705i	1.06861	+	1.06861i
$303$		0			0
$304$		−	20.0911i		−	1.15230i
$305$	6.33238	−	8.72345i	0.362591	−	0.499503i
$306$		0			0
$307$	11.6101	−	11.6101i	0.662626	−	0.662626i	−0.293372	−	0.955998i	$-0.594778\pi$
$307$	11.6101	−	11.6101i	0.662626	−	0.662626i	0.955998	+	0.293372i	$0.0947776\pi$
$308$	−8.80923	+	8.80923i	−0.501953	+	0.501953i
$309$		0			0
$310$	21.9508	−	3.48608i	1.24672	−	0.197996i
$311$			6.53623i			0.370635i	0.982679	+	0.185318i	$0.0593314\pi$
$311$			6.53623i			0.370635i	−0.982679	+	0.185318i	$0.940669\pi$
$312$		0			0
$313$	8.80568	+	8.80568i	0.497727	+	0.497727i	0.910730	−	0.413003i	$-0.135520\pi$
$313$	8.80568	+	8.80568i	0.497727	+	0.497727i	−0.413003	+	0.910730i	$0.635520\pi$
$314$	−30.0457			−1.69557
$315$		0			0
$316$	23.4966			1.32179
$317$	−14.2899	−	14.2899i	−0.802602	−	0.802602i	0.180899	−	0.983502i	$-0.442099\pi$
$317$	−14.2899	−	14.2899i	−0.802602	−	0.802602i	−0.983502	+	0.180899i	$0.942099\pi$
$318$		0			0
$319$			8.75648i			0.490269i
$320$	17.3774	+	12.6143i	0.971428	+	0.705162i
$321$		0			0
$322$	−10.1863	+	10.1863i	−0.567658	+	0.567658i
$323$	−6.88203	+	6.88203i	−0.382926	+	0.382926i
$324$		0			0
$325$	−0.0239674	+	0.0471361i	−0.00132947	+	0.00261464i
$326$			42.5800i			2.35829i
$327$		0			0
$328$	2.78812	+	2.78812i	0.153948	+	0.153948i
$329$	8.93351			0.492520
$330$		0			0
$331$	5.27002			0.289667			0.144833	−	0.989456i	$-0.453735\pi$
$331$	5.27002			0.289667			0.144833	+	0.989456i	$0.453735\pi$
$332$	11.3863	+	11.3863i	0.624906	+	0.624906i
$333$		0			0
$334$		−	33.2106i		−	1.81721i
$335$	−0.853404	−	5.37362i	−0.0466264	−	0.293592i
$336$		0			0
$337$	8.55379	−	8.55379i	0.465955	−	0.465955i	−0.434646	−	0.900601i	$-0.643127\pi$
$337$	8.55379	−	8.55379i	0.465955	−	0.465955i	0.900601	+	0.434646i	$0.143127\pi$
$338$	−18.8676	+	18.8676i	−1.02626	+	1.02626i
$339$		0			0
$340$	−1.32675	−	8.35411i	−0.0719529	−	0.453065i
$341$			27.2626i			1.47635i
$342$		0			0
$343$	0.707107	+	0.707107i	0.0381802	+	0.0381802i
$344$	1.72261			0.0928767
$345$		0			0
$346$	−22.7437			−1.22271
$347$	−4.78700	−	4.78700i	−0.256980	−	0.256980i	0.566845	−	0.823824i	$-0.308164\pi$
$347$	−4.78700	−	4.78700i	−0.256980	−	0.256980i	−0.823824	+	0.566845i	$0.808164\pi$
$348$		0			0
$349$			9.62377i			0.515149i	0.966258	+	0.257574i	$0.0829232\pi$
$349$			9.62377i			0.515149i	−0.966258	+	0.257574i	$0.917077\pi$
$350$	−3.17952	−	9.75776i	−0.169953	−	0.521574i
$351$		0			0
$352$	−32.3126	+	32.3126i	−1.72227	+	1.72227i
$353$	17.5108	−	17.5108i	0.932003	−	0.932003i	−0.0658276	−	0.997831i	$-0.520969\pi$
$353$	17.5108	−	17.5108i	0.932003	−	0.932003i	0.997831	+	0.0658276i	$0.0209687\pi$
$354$		0			0
$355$	−8.86334	−	6.43392i	−0.470417	−	0.341477i
$356$			36.4086i			1.92965i
$357$		0			0
$358$	−16.1559	−	16.1559i	−0.853864	−	0.853864i
$359$	3.99422			0.210807			0.105403	−	0.994430i	$-0.466387\pi$
$359$	3.99422			0.210807			0.105403	+	0.994430i	$0.466387\pi$
$360$		0			0
$361$	−13.4153			−0.706066
$362$	−18.5847	−	18.5847i	−0.976792	−	0.976792i
$363$		0			0
$364$			0.0234037i			0.00122669i
$365$	8.43201	−	1.33912i	0.441352	−	0.0700927i
$366$		0			0
$367$	−8.18932	+	8.18932i	−0.427479	+	0.427479i	−0.887769	−	0.460290i	$-0.847746\pi$
$367$	−8.18932	+	8.18932i	−0.427479	+	0.427479i	0.460290	+	0.887769i	$0.347746\pi$
$368$	−17.5126	+	17.5126i	−0.912907	+	0.912907i
$369$		0			0
$370$	−11.9772	+	16.4997i	−0.622664	+	0.857779i
$371$			5.89788i			0.306203i
$372$		0			0
$373$	13.6414	+	13.6414i	0.706326	+	0.706326i	0.965761	−	0.259434i	$-0.0835361\pi$
$373$	13.6414	+	13.6414i	0.706326	+	0.706326i	−0.259434	+	0.965761i	$0.583536\pi$
$374$	19.7531			1.02141
$375$		0			0
$376$	−3.90431			−0.201350
$377$	0.0116318	+	0.0116318i	0.000599068	+	0.000599068i
$378$		0			0
$379$			3.05127i			0.156733i	0.996925	+	0.0783666i	$0.0249705\pi$
$379$			3.05127i			0.156733i	−0.996925	+	0.0783666i	$0.975030\pi$
$380$	16.5499	−	22.7990i	0.848991	−	1.16957i
$381$		0			0
$382$	2.21457	−	2.21457i	0.113307	−	0.113307i
$383$	1.55390	−	1.55390i	0.0794006	−	0.0794006i	−0.666291	−	0.745692i	$-0.732119\pi$
$383$	1.55390	−	1.55390i	0.0794006	−	0.0794006i	0.745692	+	0.666291i	$0.232119\pi$
$384$		0			0
$385$	12.4326	−	1.97447i	0.633624	−	0.100628i
$386$			20.3340i			1.03498i
$387$		0			0
$388$	21.9479	+	21.9479i	1.11423	+	1.11423i
$389$	−20.5833			−1.04361			−0.521807	−	0.853064i	$-0.674742\pi$
$389$	−20.5833			−1.04361			−0.521807	+	0.853064i	$0.674742\pi$
$390$		0			0
$391$	11.9976			0.606745
$392$	−0.309035	−	0.309035i	−0.0156086	−	0.0156086i
$393$		0			0
$394$			11.4932i			0.579018i
$395$	−19.2138	−	13.9473i	−0.966749	−	0.701766i
$396$		0			0
$397$	−7.62748	+	7.62748i	−0.382812	+	0.382812i	−0.872114	−	0.489302i	$-0.837252\pi$
$397$	−7.62748	+	7.62748i	−0.382812	+	0.382812i	0.489302	+	0.872114i	$0.337252\pi$
$398$	27.6679	−	27.6679i	1.38687	−	1.38687i
$399$		0			0
$400$	−5.46636	−	16.7759i	−0.273318	−	0.838795i
$401$			19.2725i			0.962421i	0.876605	+	0.481211i	$0.159803\pi$
$401$			19.2725i			0.962421i	−0.876605	+	0.481211i	$0.840197\pi$
$402$		0			0
$403$	0.0362147	+	0.0362147i	0.00180398	+	0.00180398i
$404$	−28.5163			−1.41874
$405$		0			0
$406$	−3.19253			−0.158443
$407$	−17.6840	−	17.6840i	−0.876563	−	0.876563i
$408$		0			0
$409$		−	16.5809i		−	0.819875i	−0.912114	−	0.409938i	$-0.865551\pi$
$409$		−	16.5809i		−	0.819875i	0.912114	−	0.409938i	$-0.134449\pi$
$410$	−6.49471	−	40.8952i	−0.320751	−	2.01967i
$411$		0			0
$412$	−13.1281	+	13.1281i	−0.646774	+	0.646774i
$413$	−8.35830	+	8.35830i	−0.411285	+	0.411285i
$414$		0			0
$415$	−2.55209	−	16.0697i	−0.125277	−	0.788831i
$416$			0.0858459i			0.00420894i
$417$		0			0
$418$	46.5198	+	46.5198i	2.27536	+	2.27536i
$419$	−4.61274			−0.225347			−0.112674	−	0.993632i	$-0.535941\pi$
$419$	−4.61274			−0.225347			−0.112674	+	0.993632i	$0.535941\pi$
$420$		0			0
$421$	−19.9277			−0.971215			−0.485608	−	0.874177i	$-0.661402\pi$
$421$	−19.9277			−0.971215			−0.485608	+	0.874177i	$0.661402\pi$
$422$	20.4869	+	20.4869i	0.997285	+	0.997285i
$423$		0			0
$424$		−	2.57762i		−	0.125180i
$425$	−3.87400	+	7.61891i	−0.187916	+	0.369571i
$426$		0			0
$427$	−3.40878	+	3.40878i	−0.164962	+	0.164962i
$428$	10.5171	−	10.5171i	0.508364	−	0.508364i
$429$		0			0
$430$	−14.6396	−	10.6269i	−0.705986	−	0.512477i
$431$		−	26.8886i		−	1.29518i	−0.761990	−	0.647589i	$-0.775778\pi$
$431$		−	26.8886i		−	1.29518i	0.761990	−	0.647589i	$-0.224222\pi$
$432$		0			0
$433$	−20.2612	−	20.2612i	−0.973692	−	0.973692i	0.0259707	−	0.999663i	$-0.491732\pi$
$433$	−20.2612	−	20.2612i	−0.973692	−	0.973692i	−0.999663	+	0.0259707i	$0.991732\pi$
$434$	−9.93971			−0.477122
$435$		0			0
$436$	−27.3142			−1.30811
$437$	28.2551	+	28.2551i	1.35163	+	1.35163i
$438$		0			0
$439$			31.0619i			1.48250i	0.671228	+	0.741251i	$0.265767\pi$
$439$			31.0619i			1.48250i	−0.671228	+	0.741251i	$0.734233\pi$
$440$	−5.43356	+	0.862924i	−0.259035	+	0.0411383i
$441$		0			0
$442$	0.0262393	−	0.0262393i	0.00124808	−	0.00124808i
$443$	25.6712	−	25.6712i	1.21968	−	1.21968i	0.251933	−	0.967745i	$-0.418934\pi$
$443$	25.6712	−	25.6712i	1.21968	−	1.21968i	0.967745	−	0.251933i	$-0.0810663\pi$
$444$		0			0
$445$	21.6118	−	29.7723i	1.02450	−	1.41134i
$446$		−	58.3509i		−	2.76299i
$447$		0			0
$448$	−6.79041	−	6.79041i	−0.320817	−	0.320817i
$449$	23.6055			1.11401			0.557007	−	0.830508i	$-0.311950\pi$
$449$	23.6055			1.11401			0.557007	+	0.830508i	$0.311950\pi$
$450$		0			0
$451$	50.7914			2.39167
$452$	−8.76194	−	8.76194i	−0.412127	−	0.412127i
$453$		0			0
$454$			20.8644i			0.979214i
$455$	0.0138922	−	0.0191378i	0.000651277	−	0.000897195i
$456$		0			0
$457$	−17.8226	+	17.8226i	−0.833708	+	0.833708i	−0.988022	−	0.154314i	$-0.950683\pi$
$457$	−17.8226	+	17.8226i	−0.833708	+	0.833708i	0.154314	+	0.988022i	$0.450683\pi$
$458$	−18.1098	+	18.1098i	−0.846214	+	0.846214i
$459$		0			0
$460$	−34.2989	+	5.44714i	−1.59920	+	0.253974i
$461$			7.13491i			0.332306i	0.986100	+	0.166153i	$0.0531345\pi$
$461$			7.13491i			0.332306i	−0.986100	+	0.166153i	$0.946865\pi$
$462$		0			0
$463$	−7.46573	−	7.46573i	−0.346962	−	0.346962i	0.512015	−	0.858977i	$-0.328899\pi$
$463$	−7.46573	−	7.46573i	−0.346962	−	0.346962i	−0.858977	+	0.512015i	$0.828899\pi$
$464$	−5.48873			−0.254808
$465$		0			0
$466$	48.5715			2.25003
$467$	−28.5436	−	28.5436i	−1.32084	−	1.32084i	−0.913094	−	0.407748i	$-0.866314\pi$
$467$	−28.5436	−	28.5436i	−1.32084	−	1.32084i	−0.407748	−	0.913094i	$-0.633686\pi$
$468$		0			0
$469$			2.43327i			0.112358i
$470$	33.1809	+	24.0862i	1.53052	+	1.11101i
$471$		0			0
$472$	3.65292	−	3.65292i	0.168139	−	0.168139i
$473$	15.6904	−	15.6904i	0.721446	−	0.721446i
$474$		0			0
$475$	−27.0665	+	8.81952i	−1.24190	+	0.404667i
$476$			3.78289i			0.173389i
$477$		0			0
$478$	4.98570	+	4.98570i	0.228040	+	0.228040i
$479$	6.46156			0.295236			0.147618	−	0.989044i	$-0.452839\pi$
$479$	6.46156			0.295236			0.147618	+	0.989044i	$0.452839\pi$
$480$		0			0
$481$	−0.0469816			−0.00214217
$482$	−32.9899	−	32.9899i	−1.50265	−	1.50265i
$483$		0			0
$484$		−	45.7935i		−	2.08152i
$485$	−4.91931	−	30.9754i	−0.223374	−	1.40652i
$486$		0			0
$487$	0.192093	−	0.192093i	0.00870456	−	0.00870456i	−0.702741	−	0.711446i	$-0.748041\pi$
$487$	0.192093	−	0.192093i	0.00870456	−	0.00870456i	0.711446	+	0.702741i	$0.248041\pi$
$488$	1.48978	−	1.48978i	0.0674390	−	0.0674390i
$489$		0			0
$490$	0.719873	+	4.53282i	0.0325205	+	0.204772i
$491$			20.9550i			0.945688i	0.881146	+	0.472844i	$0.156773\pi$
$491$			20.9550i			0.945688i	−0.881146	+	0.472844i	$0.843227\pi$
$492$		0			0
$493$	1.88012	+	1.88012i	0.0846763	+	0.0846763i
$494$	0.123590			0.00556059
$495$		0			0
$496$	−17.0887			−0.767307
$497$	3.46344	+	3.46344i	0.155356	+	0.155356i
$498$		0			0
$499$		−	6.23105i		−	0.278940i	−0.990226	−	0.139470i	$-0.955460\pi$
$499$		−	6.23105i		−	0.278940i	0.990226	−	0.139470i	$-0.0445399\pi$
$500$	7.61591	−	23.5399i	0.340594	−	1.05274i
$501$		0			0
$502$	1.64052	−	1.64052i	0.0732198	−	0.0732198i
$503$	−5.72261	+	5.72261i	−0.255158	+	0.255158i	−0.823082	−	0.567923i	$-0.807747\pi$
$503$	−5.72261	+	5.72261i	−0.255158	+	0.255158i	0.567923	+	0.823082i	$0.307747\pi$
$504$		0			0
$505$	23.3185	+	16.9270i	1.03766	+	0.753241i
$506$		−	81.0990i		−	3.60529i
$507$		0			0
$508$	−12.3017	−	12.3017i	−0.545802	−	0.545802i
$509$	−5.37263			−0.238138			−0.119069	−	0.992886i	$-0.537991\pi$
$509$	−5.37263			−0.238138			−0.119069	+	0.992886i	$0.537991\pi$
$510$		0			0
$511$	−3.81817			−0.168906
$512$	−22.4352	−	22.4352i	−0.991506	−	0.991506i
$513$		0			0
$514$		−	3.00431i		−	0.132514i
$515$	18.5278	−	2.94247i	0.816434	−	0.129661i
$516$		0			0
$517$	−35.5626	+	35.5626i	−1.56404	+	1.56404i
$518$	6.44743	−	6.44743i	0.283284	−	0.283284i
$519$		0			0
$520$	−0.00607147	+	0.00836402i	−0.000266252	+	0.000366787i
$521$			12.7159i			0.557095i	0.960422	+	0.278548i	$0.0898530\pi$
$521$			12.7159i			0.557095i	−0.960422	+	0.278548i	$0.910147\pi$
$522$		0			0
$523$	−8.11255	−	8.11255i	−0.354737	−	0.354737i	0.507132	−	0.861869i	$-0.330706\pi$
$523$	−8.11255	−	8.11255i	−0.354737	−	0.354737i	−0.861869	+	0.507132i	$0.830706\pi$
$524$	7.45044			0.325474
$525$		0			0
$526$	−15.4339			−0.672951
$527$	5.85361	+	5.85361i	0.254987	+	0.254987i
$528$		0			0
$529$		−	26.2578i		−	1.14164i
$530$	−15.9016	+	21.9060i	−0.690722	+	0.951535i
$531$		0			0
$532$	−8.90896	+	8.90896i	−0.386252	+	0.386252i
$533$	0.0674694	−	0.0674694i	0.00292243	−	0.00292243i
$534$		0			0
$535$	−14.8430	+	2.35727i	−0.641718	+	0.101914i
$536$		−	1.06344i		−	0.0459336i
$537$		0			0
$538$	5.48699	+	5.48699i	0.236561	+	0.236561i
$539$	−5.62971			−0.242489
$540$		0			0
$541$	−1.73394			−0.0745479			−0.0372740	−	0.999305i	$-0.511867\pi$
$541$	−1.73394			−0.0745479			−0.0372740	+	0.999305i	$0.511867\pi$
$542$	40.4067	+	40.4067i	1.73562	+	1.73562i
$543$		0			0
$544$			13.8758i			0.594920i
$545$	22.3355	+	16.2134i	0.956750	+	0.694508i
$546$		0			0
$547$	17.8819	−	17.8819i	0.764574	−	0.764574i	−0.212572	−	0.977145i	$-0.568184\pi$
$547$	17.8819	−	17.8819i	0.764574	−	0.764574i	0.977145	+	0.212572i	$0.0681840\pi$
$548$	−36.1230	+	36.1230i	−1.54310	+	1.54310i
$549$		0			0
$550$	51.5008	+	26.1867i	2.19600	+	1.11660i
$551$			8.85560i			0.377261i
$552$		0			0
$553$	7.50797	+	7.50797i	0.319272	+	0.319272i
$554$	5.26805			0.223818
$555$		0			0
$556$	−28.0012			−1.18751
$557$	−18.4069	−	18.4069i	−0.779925	−	0.779925i	0.199893	−	0.979818i	$-0.435941\pi$
$557$	−18.4069	−	18.4069i	−0.779925	−	0.779925i	−0.979818	+	0.199893i	$0.935941\pi$
$558$		0			0
$559$		−	0.0416852i		−	0.00176309i
$560$	1.23763	+	7.79299i	0.0522996	+	0.329314i
$561$		0			0
$562$	11.8016	−	11.8016i	0.497820	−	0.497820i
$563$	−6.57537	+	6.57537i	−0.277119	+	0.277119i	−0.831958	−	0.554839i	$-0.812780\pi$
$563$	−6.57537	+	6.57537i	−0.277119	+	0.277119i	0.554839	+	0.831958i	$0.312780\pi$
$564$		0			0
$565$	1.96387	+	12.3659i	0.0826205	+	0.520236i
$566$			11.1809i			0.469970i
$567$		0			0
$568$	−1.51367	−	1.51367i	−0.0635120	−	0.0635120i
$569$	2.00559			0.0840787			0.0420393	−	0.999116i	$-0.486615\pi$
$569$	2.00559			0.0840787			0.0420393	+	0.999116i	$0.486615\pi$
$570$		0			0
$571$	−6.05799			−0.253519			−0.126759	−	0.991933i	$-0.540458\pi$
$571$	−6.05799			−0.253519			−0.126759	+	0.991933i	$0.540458\pi$
$572$	−0.0931657	−	0.0931657i	−0.00389545	−	0.00389545i
$573$		0			0
$574$			18.5181i			0.772930i
$575$	31.2805	+	15.9052i	1.30449	+	0.663294i
$576$		0			0
$577$	−21.1731	+	21.1731i	−0.881446	+	0.881446i	−0.993682	−	0.112236i	$-0.964199\pi$
$577$	−21.1731	+	21.1731i	−0.881446	+	0.881446i	0.112236	+	0.993682i	$0.464199\pi$
$578$	−20.4320	+	20.4320i	−0.849859	+	0.849859i
$579$		0			0
$580$	−6.22853	−	4.52131i	−0.258625	−	0.187737i
$581$			7.27666i			0.301887i
$582$		0			0
$583$	−23.4783	−	23.4783i	−0.972373	−	0.972373i
$584$	1.66870			0.0690512
$585$		0			0
$586$	26.6164			1.09951
$587$	25.2367	+	25.2367i	1.04163	+	1.04163i	0.999095	+	0.0425335i	$0.0135429\pi$
$587$	25.2367	+	25.2367i	1.04163	+	1.04163i	0.0425335	+	0.999095i	$0.486457\pi$
$588$		0			0
$589$			27.5713i			1.13605i
$590$	−53.5798	+	8.50920i	−2.20584	+	0.350318i
$591$		0			0
$592$	11.0847	−	11.0847i	0.455577	−	0.455577i
$593$	28.2414	−	28.2414i	1.15973	−	1.15973i	0.175202	−	0.984533i	$-0.443942\pi$
$593$	28.2414	−	28.2414i	1.15973	−	1.15973i	0.984533	−	0.175202i	$-0.0560577\pi$
$594$		0			0
$595$	2.24548	−	3.09337i	0.0920559	−	0.126816i
$596$			16.4256i			0.672820i
$597$		0			0
$598$	−0.107729	−	0.107729i	−0.00440537	−	0.00440537i
$599$	15.8076			0.645881			0.322940	−	0.946419i	$-0.395329\pi$
$599$	15.8076			0.645881			0.322940	+	0.946419i	$0.395329\pi$
$600$		0			0
$601$	−2.49573			−0.101803			−0.0509016	−	0.998704i	$-0.516209\pi$
$601$	−2.49573			−0.101803			−0.0509016	+	0.998704i	$0.516209\pi$
$602$	5.72058	+	5.72058i	0.233154	+	0.233154i
$603$		0			0
$604$		−	28.3148i		−	1.15211i
$605$	−27.1825	+	37.4465i	−1.10513	+	1.52242i
$606$		0			0
$607$	15.4046	−	15.4046i	0.625253	−	0.625253i	−0.321617	−	0.946870i	$-0.604226\pi$
$607$	15.4046	−	15.4046i	0.625253	−	0.625253i	0.946870	+	0.321617i	$0.104226\pi$
$608$	−32.6784	+	32.6784i	−1.32528	+	1.32528i
$609$		0			0
$610$	−21.8515	+	3.47032i	−0.884742	+	0.140509i
$611$			0.0944801i			0.00382225i
$612$		0			0
$613$	−12.8394	−	12.8394i	−0.518580	−	0.518580i	0.398561	−	0.917142i	$-0.369510\pi$
$613$	−12.8394	−	12.8394i	−0.518580	−	0.518580i	−0.917142	+	0.398561i	$0.869510\pi$
$614$	−33.7011			−1.36007
$615$		0			0
$616$	2.46042			0.0991330
$617$	14.5354	+	14.5354i	0.585173	+	0.585173i	0.936320	−	0.351147i	$-0.114208\pi$
$617$	14.5354	+	14.5354i	0.585173	+	0.585173i	−0.351147	+	0.936320i	$0.614208\pi$
$618$		0			0
$619$		−	10.1884i		−	0.409506i	−0.978814	−	0.204753i	$-0.934361\pi$
$619$		−	10.1884i		−	0.409506i	0.978814	−	0.204753i	$-0.0656391\pi$
$620$	−19.3920	−	14.0767i	−0.778803	−	0.565336i
$621$		0			0
$622$	9.48646	−	9.48646i	0.380372	−	0.380372i
$623$	−11.6338	+	11.6338i	−0.466099	+	0.466099i
$624$		0			0
$625$	−20.2008	+	14.7285i	−0.808031	+	0.589139i
$626$		−	25.5605i		−	1.02160i
$627$		0			0
$628$	22.9056	+	22.9056i	0.914033	+	0.914033i
$629$	−7.59392			−0.302790
$630$		0			0
$631$	−6.95627			−0.276925			−0.138462	−	0.990368i	$-0.544216\pi$
$631$	−6.95627			−0.276925			−0.138462	+	0.990368i	$0.544216\pi$
$632$	−3.28130	−	3.28130i	−0.130523	−	0.130523i
$633$		0			0
$634$			41.4798i			1.64737i
$635$	2.75727	+	17.3616i	0.109419	+	0.688976i
$636$		0			0
$637$	−0.00747830	+	0.00747830i	−0.000296301	+	0.000296301i
$638$	12.7089	−	12.7089i	0.503149	−	0.503149i
$639$		0			0
$640$	−1.21929	−	7.67751i	−0.0481968	−	0.303480i
$641$		−	36.2049i		−	1.43001i	−0.699120	−	0.715004i	$-0.746425\pi$
$641$		−	36.2049i		−	1.43001i	0.699120	−	0.715004i	$-0.253575\pi$
$642$		0			0
$643$	4.93368	+	4.93368i	0.194565	+	0.194565i	0.797665	−	0.603100i	$-0.206068\pi$
$643$	4.93368	+	4.93368i	0.194565	+	0.194565i	−0.603100	+	0.797665i	$0.706068\pi$
$644$	15.5312			0.612015
$645$		0			0
$646$	19.9767			0.785972
$647$	10.7433	+	10.7433i	0.422364	+	0.422364i	0.886017	−	0.463653i	$-0.153462\pi$
$647$	10.7433	+	10.7433i	0.422364	+	0.422364i	−0.463653	+	0.886017i	$0.653462\pi$
$648$		0			0
$649$		−	66.5455i		−	2.61214i
$650$	0.103197	−	0.0336264i	0.00404773	−	0.00131893i
$651$		0			0
$652$	32.4613	−	32.4613i	1.27128	−	1.27128i
$653$	14.0006	−	14.0006i	0.547884	−	0.547884i	−0.377944	−	0.925828i	$-0.623369\pi$
$653$	14.0006	−	14.0006i	0.547884	−	0.547884i	0.925828	+	0.377944i	$0.123369\pi$
$654$		0			0
$655$	−6.09242	−	4.42251i	−0.238051	−	0.172802i
$656$			31.8370i			1.24303i
$657$		0			0
$658$	−12.9658	−	12.9658i	−0.505459	−	0.505459i
$659$	6.35539			0.247571			0.123785	−	0.992309i	$-0.460497\pi$
$659$	6.35539			0.247571			0.123785	+	0.992309i	$0.460497\pi$
$660$		0			0
$661$	3.73321			0.145205			0.0726025	−	0.997361i	$-0.476870\pi$
$661$	3.73321			0.145205			0.0726025	+	0.997361i	$0.476870\pi$
$662$	−7.64873	−	7.64873i	−0.297276	−	0.297276i
$663$		0			0
$664$		−	3.18020i		−	0.123416i
$665$	12.5733	−	1.99682i	0.487573	−	0.0774333i
$666$		0			0
$667$	7.71909	−	7.71909i	0.298884	−	0.298884i
$668$	−25.3185	+	25.3185i	−0.979601	+	0.979601i
$669$		0			0
$670$	−6.56049	+	9.03769i	−0.253454	+	0.349156i
$671$		−	27.1394i		−	1.04770i
$672$		0			0
$673$	−32.2398	−	32.2398i	−1.24275	−	1.24275i	−0.958854	−	0.283901i	$-0.908371\pi$
$673$	−32.2398	−	32.2398i	−1.24275	−	1.24275i	−0.283901	−	0.958854i	$-0.591629\pi$
$674$	−24.8294			−0.956392
$675$		0			0
$676$	28.7678			1.10645
$677$	4.36523	+	4.36523i	0.167769	+	0.167769i	0.785998	−	0.618229i	$-0.212149\pi$
$677$	4.36523	+	4.36523i	0.167769	+	0.167769i	−0.618229	+	0.785998i	$0.712149\pi$
$678$		0			0
$679$			14.0262i			0.538276i
$680$	−0.981370	+	1.35193i	−0.0376338	+	0.0518441i
$681$		0			0
$682$	39.5681	−	39.5681i	1.51514	−	1.51514i
$683$	−13.0185	+	13.0185i	−0.498138	+	0.498138i	−0.910858	−	0.412720i	$-0.864579\pi$
$683$	−13.0185	+	13.0185i	−0.498138	+	0.498138i	0.412720	+	0.910858i	$0.364579\pi$
$684$		0			0
$685$	50.9809	−	8.09647i	1.94788	−	0.309350i
$686$		−	2.05254i		−	0.0783664i
$687$		0			0
$688$	9.83505	+	9.83505i	0.374958	+	0.374958i
$689$	−0.0623755			−0.00237632
$690$		0			0
$691$	−0.404163			−0.0153751			−0.00768755	−	0.999970i	$-0.502447\pi$
$691$	−0.404163			−0.0153751			−0.00768755	+	0.999970i	$0.502447\pi$
$692$	17.3389	+	17.3389i	0.659125	+	0.659125i
$693$		0			0
$694$			13.8954i			0.527461i
$695$	22.8973	+	16.6212i	0.868543	+	0.630478i
$696$		0			0
$697$	10.9055	−	10.9055i	0.413076	−	0.413076i
$698$	13.9676	−	13.9676i	0.528682	−	0.528682i
$699$		0			0
$700$	−5.01498	+	9.86286i	−0.189548	+	0.372781i
$701$			21.5747i			0.814864i	0.913236	+	0.407432i	$0.133576\pi$
$701$			21.5747i			0.814864i	−0.913236	+	0.407432i	$0.866424\pi$
$702$		0			0
$703$	−17.8842	−	17.8842i	−0.674515	−	0.674515i
$704$	54.0626			2.03756
$705$		0			0
$706$	−50.8290			−1.91298
$707$	−9.11195	−	9.11195i	−0.342690	−	0.342690i
$708$		0			0
$709$			51.3287i			1.92769i	0.266461	+	0.963846i	$0.414146\pi$
$709$			51.3287i			1.92769i	−0.266461	+	0.963846i	$0.585854\pi$
$710$	3.52597	+	22.2019i	0.132327	+	0.833223i
$711$		0			0
$712$	5.08446	−	5.08446i	0.190548	−	0.190548i
$713$	24.0328	−	24.0328i	0.900036	−	0.900036i
$714$		0			0
$715$	0.0208818	+	0.131486i	0.000780935	+	0.00491731i
$716$			24.6332i			0.920585i
$717$		0			0
$718$	−5.79708	−	5.79708i	−0.216345	−	0.216345i
$719$	−18.4190			−0.686911			−0.343456	−	0.939169i	$-0.611598\pi$
$719$	−18.4190			−0.686911			−0.343456	+	0.939169i	$0.611598\pi$
$720$		0			0
$721$	−8.38975			−0.312450
$722$	19.4704	+	19.4704i	0.724615	+	0.724615i
$723$		0			0
$724$			28.3365i			1.05312i
$725$	2.40943	+	7.39438i	0.0894838	+	0.274620i
$726$		0			0
$727$	28.2891	−	28.2891i	1.04918	−	1.04918i	0.0504586	−	0.998726i	$-0.483932\pi$
$727$	28.2891	−	28.2891i	1.04918	−	1.04918i	0.998726	−	0.0504586i	$-0.0160683\pi$
$728$	0.00326833	−	0.00326833i	0.000121132	−	0.000121132i
$729$		0			0
$730$	−14.1815	−	10.2944i	−0.524880	−	0.381012i
$731$		−	6.73783i		−	0.249208i
$732$		0			0
$733$	−13.6024	−	13.6024i	−0.502416	−	0.502416i	0.409772	−	0.912188i	$-0.365608\pi$
$733$	−13.6024	−	13.6024i	−0.502416	−	0.502416i	−0.912188	+	0.409772i	$0.865608\pi$
$734$	23.7714			0.877419
$735$		0			0
$736$	56.9690			2.09991
$737$	−9.68639	−	9.68639i	−0.356803	−	0.356803i
$738$		0			0
$739$			27.2219i			1.00137i	0.865629	+	0.500686i	$0.166919\pi$
$739$			27.2219i			1.00137i	−0.865629	+	0.500686i	$0.833081\pi$
$740$	21.7096	−	3.44779i	0.798062	−	0.126743i
$741$		0			0
$742$	8.55999	−	8.55999i	0.314247	−	0.314247i
$743$	0.997164	−	0.997164i	0.0365824	−	0.0365824i	−0.688579	−	0.725161i	$-0.741765\pi$
$743$	0.997164	−	0.997164i	0.0365824	−	0.0365824i	0.725161	+	0.688579i	$0.241765\pi$
$744$		0			0
$745$	9.75008	−	13.4316i	0.357215	−	0.492098i
$746$		−	39.5974i		−	1.44976i
$747$		0			0
$748$	−15.0590	−	15.0590i	−0.550610	−	0.550610i
$749$	6.72117			0.245586
$750$		0			0
$751$	53.3536			1.94690			0.973451	−	0.228895i	$-0.0735113\pi$
$751$	53.3536			1.94690			0.973451	+	0.228895i	$0.0735113\pi$
$752$	−22.2913	−	22.2913i	−0.812880	−	0.812880i
$753$		0			0
$754$		−	0.0337640i		−	0.00122961i
$755$	−16.8074	+	23.1537i	−0.611683	+	0.842651i
$756$		0			0
$757$	11.8721	−	11.8721i	0.431497	−	0.431497i	−0.457640	−	0.889138i	$-0.651305\pi$
$757$	11.8721	−	11.8721i	0.431497	−	0.431497i	0.889138	+	0.457640i	$0.151305\pi$
$758$	4.42851	−	4.42851i	0.160851	−	0.160851i
$759$		0			0
$760$	−5.49507	+	0.872692i	−0.199327	+	0.0316559i
$761$		−	37.9016i		−	1.37393i	−0.726690	−	0.686965i	$-0.758942\pi$
$761$		−	37.9016i		−	1.37393i	0.726690	−	0.686965i	$-0.241058\pi$
$762$		0			0
$763$	−8.72784	−	8.72784i	−0.315969	−	0.315969i
$764$	−3.37660			−0.122161
$765$		0			0
$766$	−4.51056			−0.162973
$767$	−0.0883967	−	0.0883967i	−0.00319182	−	0.00319182i
$768$		0			0
$769$			50.8876i			1.83505i	0.397673	+	0.917527i	$0.369818\pi$
$769$			50.8876i			1.83505i	−0.397673	+	0.917527i	$0.630182\pi$
$770$	−20.9099	−	15.1786i	−0.753542	−	0.546998i
$771$		0			0
$772$	15.5019	−	15.5019i	0.557924	−	0.557924i
$773$	17.4266	−	17.4266i	0.626790	−	0.626790i	−0.320469	−	0.947259i	$-0.603841\pi$
$773$	17.4266	−	17.4266i	0.626790	−	0.626790i	0.947259	+	0.320469i	$0.103841\pi$
$774$		0			0
$775$	7.50157	+	23.0218i	0.269464	+	0.826969i
$776$		−	6.13003i		−	0.220055i
$777$		0			0
$778$	29.8739	+	29.8739i	1.07103	+	1.07103i
$779$	51.3664			1.84039
$780$		0			0
$781$	−27.5746			−0.986695
$782$	−17.4129	−	17.4129i	−0.622684	−	0.622684i
$783$		0			0
$784$		−	3.52881i		−	0.126029i
$785$	−5.13398	−	32.3270i	−0.183239	−	1.15380i
$786$		0			0
$787$	−18.7795	+	18.7795i	−0.669416	+	0.669416i	−0.957581	−	0.288165i	$-0.906955\pi$
$787$	−18.7795	+	18.7795i	−0.669416	+	0.669416i	0.288165	+	0.957581i	$0.406955\pi$
$788$	8.76194	−	8.76194i	0.312131	−	0.312131i
$789$		0			0
$790$	7.64352	+	48.1289i	0.271944	+	1.71235i
$791$		−	5.59949i		−	0.199095i
$792$		0			0
$793$	−0.0360509	−	0.0360509i	−0.00128021	−	0.00128021i
$794$	22.1405			0.785738
$795$		0			0
$796$	−42.1858			−1.49524
$797$	−5.50268	−	5.50268i	−0.194915	−	0.194915i	0.602901	−	0.797816i	$-0.294011\pi$
$797$	−5.50268	−	5.50268i	−0.194915	−	0.194915i	−0.797816	+	0.602901i	$0.794011\pi$
$798$		0			0
$799$			15.2714i			0.540263i
$800$	−18.3952	+	36.1774i	−0.650367	+	1.27906i
$801$		0			0
$802$	27.9714	−	27.9714i	0.987705	−	0.987705i
$803$	15.1994	−	15.1994i	0.536375	−	0.536375i
$804$		0			0
$805$	−12.7003	−	9.21915i	−0.447625	−	0.324932i
$806$		−	0.105122i		−	0.00370275i
$807$		0			0
$808$	3.98230	+	3.98230i	0.140097	+	0.140097i
$809$	−13.0716			−0.459574			−0.229787	−	0.973241i	$-0.573803\pi$
$809$	−13.0716			−0.459574			−0.229787	+	0.973241i	$0.573803\pi$
$810$		0			0
$811$	0.00662423			0.000232608			0.000116304	−	1.00000i	$-0.499963\pi$
$811$	0.00662423			0.000232608			0.000116304		1.00000i	$0.499963\pi$
$812$	2.43386	+	2.43386i	0.0854117	+	0.0854117i
$813$		0			0
$814$			51.3319i			1.79918i
$815$	−45.8131	+	7.27575i	−1.60476	+	0.254858i
$816$		0			0
$817$	15.8680	−	15.8680i	0.555152	−	0.555152i
$818$	−24.0650	+	24.0650i	−0.841414	+	0.841414i
$819$		0			0
$820$	−26.2255	+	36.1282i	−0.915836	+	1.26165i
$821$		−	14.3629i		−	0.501270i	−0.968082	−	0.250635i	$-0.919361\pi$
$821$		−	14.3629i		−	0.501270i	0.968082	−	0.250635i	$-0.0806394\pi$
$822$		0			0
$823$	5.50624	+	5.50624i	0.191936	+	0.191936i	0.796532	−	0.604596i	$-0.206666\pi$
$823$	5.50624	+	5.50624i	0.191936	+	0.191936i	−0.604596	+	0.796532i	$0.706666\pi$
$824$	3.66667			0.127734
$825$		0			0
$826$	24.2619			0.844180
$827$	−6.58070	−	6.58070i	−0.228833	−	0.228833i	0.583372	−	0.812205i	$-0.301733\pi$
$827$	−6.58070	−	6.58070i	−0.228833	−	0.228833i	−0.812205	+	0.583372i	$0.801733\pi$
$828$		0			0
$829$		−	37.1189i		−	1.28919i	−0.764522	−	0.644597i	$-0.777025\pi$
$829$		−	37.1189i		−	1.28919i	0.764522	−	0.644597i	$-0.222975\pi$
$830$	−19.6190	+	27.0270i	−0.680986	+	0.938122i
$831$		0			0
$832$	0.0718148	−	0.0718148i	0.00248973	−	0.00248973i
$833$	−1.20876	+	1.20876i	−0.0418812	+	0.0418812i
$834$		0			0
$835$	35.7323	−	5.67478i	1.23657	−	0.196384i
$836$		−	70.9296i		−	2.45315i
$837$		0			0
$838$	6.69477	+	6.69477i	0.231267	+	0.231267i
$839$	36.8376			1.27178			0.635888	−	0.771782i	$-0.280634\pi$
$839$	36.8376			1.27178			0.635888	+	0.771782i	$0.280634\pi$
$840$		0			0
$841$	−26.5807			−0.916576
$842$	28.9223	+	28.9223i	0.996730	+	0.996730i
$843$		0			0
$844$		−	31.2367i		−	1.07521i
$845$	−23.5242	−	17.0763i	−0.809256	−	0.587441i
$846$		0			0
$847$	14.6326	−	14.6326i	0.502782	−	0.502782i
$848$	14.7167	−	14.7167i	0.505372	−	0.505372i
$849$		0			0
$850$	16.6804	−	5.43524i	0.572133	−	0.186427i
$851$			31.1779i			1.06876i
$852$		0			0
$853$	36.7552	+	36.7552i	1.25848	+	1.25848i	0.951821	+	0.306655i	$0.0992097\pi$
$853$	36.7552	+	36.7552i	1.25848	+	1.25848i	0.306655	+	0.951821i	$0.400790\pi$
$854$	9.89477			0.338592
$855$		0			0
$856$	−2.93743			−0.100399
$857$	−12.2360	−	12.2360i	−0.417974	−	0.417974i	0.466531	−	0.884505i	$-0.345504\pi$
$857$	−12.2360	−	12.2360i	−0.417974	−	0.417974i	−0.884505	+	0.466531i	$0.845504\pi$
$858$		0			0
$859$			35.9638i			1.22707i	0.789668	+	0.613535i	$0.210253\pi$
$859$			35.9638i			1.22707i	−0.789668	+	0.613535i	$0.789747\pi$
$860$	3.05910	+	19.2622i	0.104315	+	0.656837i
$861$		0			0
$862$	−39.0252	+	39.0252i	−1.32920	+	1.32920i
$863$	−8.62624	+	8.62624i	−0.293641	+	0.293641i	−0.838517	−	0.544876i	$-0.816577\pi$
$863$	−8.62624	+	8.62624i	−0.293641	+	0.293641i	0.544876	+	0.838517i	$0.316577\pi$
$864$		0			0
$865$	−3.88627	−	24.4706i	−0.132137	−	0.832026i
$866$			58.8129i			1.99854i
$867$		0			0
$868$	7.57764	+	7.57764i	0.257202	+	0.257202i
$869$	−59.7756			−2.02775
$870$		0			0
$871$	−0.0257341			−0.000871966
$872$	3.81443	+	3.81443i	0.129173	+	0.129173i
$873$		0			0
$874$		−	82.0171i		−	2.77427i
$875$	9.95537	−	5.08828i	0.336553	−	0.172015i
$876$		0			0
$877$	−2.42813	+	2.42813i	−0.0819920	+	0.0819920i	−0.746913	−	0.664921i	$-0.768465\pi$
$877$	−2.42813	+	2.42813i	−0.0819920	+	0.0819920i	0.664921	+	0.746913i	$0.268465\pi$
$878$	45.0821	−	45.0821i	1.52145	−	1.52145i
$879$		0			0
$880$	−35.9492	−	26.0956i	−1.21185	−	0.879683i
$881$		−	6.54850i		−	0.220625i	−0.993897	−	0.110312i	$-0.964815\pi$
$881$		−	6.54850i		−	0.220625i	0.993897	−	0.110312i	$-0.0351851\pi$
$882$		0			0
$883$	11.8913	+	11.8913i	0.400175	+	0.400175i	0.878295	−	0.478120i	$-0.158682\pi$
$883$	11.8913	+	11.8913i	0.400175	+	0.400175i	−0.478120	+	0.878295i	$0.658682\pi$
$884$	−0.0400076			−0.00134560
$885$		0			0
$886$	−74.5168			−2.50344
$887$	10.2116	+	10.2116i	0.342872	+	0.342872i	0.857446	−	0.514574i	$-0.172050\pi$
$887$	10.2116	+	10.2116i	0.342872	+	0.342872i	−0.514574	+	0.857446i	$0.672050\pi$
$888$		0			0
$889$		−	7.86167i		−	0.263672i
$890$	−74.5771	+	11.8439i	−2.49983	+	0.397007i
$891$		0			0
$892$	−44.4844	+	44.4844i	−1.48945	+	1.48945i
$893$	−35.9651	+	35.9651i	−1.20353	+	1.20353i
$894$		0			0
$895$	14.6220	−	20.1432i	0.488759	−	0.673312i
$896$			3.47652i			0.116142i
$897$		0			0
$898$	−34.2603	−	34.2603i	−1.14328	−	1.14328i
$899$	7.53226			0.251215
$900$		0			0
$901$	−10.0821			−0.335885
$902$	−73.7169	−	73.7169i	−2.45450	−	2.45450i
$903$		0			0
$904$			2.44721i			0.0813929i
$905$	16.8203	−	23.1715i	0.559124	−	0.770247i
$906$		0			0
$907$	−25.9887	+	25.9887i	−0.862942	+	0.862942i	−0.991679	−	0.128737i	$-0.958908\pi$
$907$	−25.9887	+	25.9887i	−0.862942	+	0.862942i	0.128737	+	0.991679i	$0.458908\pi$
$908$	15.9062	−	15.9062i	0.527865	−	0.527865i
$909$		0			0
$910$	−0.0479387	+	0.00761332i	−0.00158915	+	0.000252379i
$911$		−	51.9902i		−	1.72251i	−0.508172	−	0.861256i	$-0.669678\pi$
$911$		−	51.9902i		−	1.72251i	0.508172	−	0.861256i	$-0.330322\pi$
$912$		0			0
$913$	−28.9670	−	28.9670i	−0.958666	−	0.958666i
$914$	51.7343			1.71122
$915$		0			0
$916$	27.6123			0.912337
$917$	2.38067	+	2.38067i	0.0786168	+	0.0786168i
$918$		0			0
$919$			6.77384i			0.223448i	0.993739	+	0.111724i	$0.0356373\pi$
$919$			6.77384i			0.223448i	−0.993739	+	0.111724i	$0.964363\pi$
$920$	5.55053	+	4.02915i	0.182996	+	0.132837i
$921$		0			0
$922$	10.3554	−	10.3554i	0.341036	−	0.341036i
$923$	−0.0366290	+	0.0366290i	−0.00120566	+	0.00120566i
$924$		0			0
$925$	−19.7991	−	10.0673i	−0.650990	−	0.331010i
$926$			21.6710i			0.712154i
$927$		0			0
$928$	8.92750	+	8.92750i	0.293060	+	0.293060i
$929$	−22.6568			−0.743347			−0.371673	−	0.928364i	$-0.621216\pi$
$929$	−22.6568			−0.743347			−0.371673	+	0.928364i	$0.621216\pi$
$930$		0			0
$931$	−5.69344			−0.186595
$932$	−37.0289	−	37.0289i	−1.21292	−	1.21292i
$933$		0			0
$934$			82.8546i			2.71108i
$935$	3.37526	+	21.2529i	0.110383	+	0.695045i
$936$		0			0
$937$	−18.1664	+	18.1664i	−0.593470	+	0.593470i	−0.938567	−	0.345097i	$-0.887846\pi$
$937$	−18.1664	+	18.1664i	−0.593470	+	0.593470i	0.345097	+	0.938567i	$0.387846\pi$
$938$	3.53157	−	3.53157i	0.115310	−	0.115310i
$939$		0			0
$940$	−6.93351	−	43.6581i	−0.226146	−	1.42397i
$941$			12.6080i			0.411010i	0.978656	+	0.205505i	$0.0658837\pi$
$941$			12.6080i			0.411010i	−0.978656	+	0.205505i	$0.934116\pi$
$942$		0			0
$943$	−44.7741	−	44.7741i	−1.45804	−	1.45804i
$944$	41.7120			1.35761
$945$		0			0
$946$	−45.5451			−1.48080
$947$	6.67439	+	6.67439i	0.216889	+	0.216889i	0.807186	−	0.590297i	$-0.200989\pi$
$947$	6.67439	+	6.67439i	0.216889	+	0.216889i	−0.590297	+	0.807186i	$0.700989\pi$
$948$		0			0
$949$		−	0.0403806i		−	0.00131081i
$950$	52.0838	+	26.4831i	1.68982	+	0.859225i
$951$		0			0
$952$	0.528280	−	0.528280i	0.0171217	−	0.0171217i
$953$	−12.6293	+	12.6293i	−0.409104	+	0.409104i	−0.881426	−	0.472322i	$-0.843416\pi$
$953$	−12.6293	+	12.6293i	−0.409104	+	0.409104i	0.472322	+	0.881426i	$0.343416\pi$
$954$		0			0
$955$	2.76113	+	2.00431i	0.0893480	+	0.0648580i
$956$		−	7.60179i		−	0.245859i
$957$		0			0
$958$	−9.37809	−	9.37809i	−0.302992	−	0.302992i
$959$	−23.0851			−0.745456
$960$		0			0
$961$	−7.54887			−0.243512
$962$	0.0681874	+	0.0681874i	0.00219845	+	0.00219845i
$963$		0			0
$964$			50.3003i			1.62006i
$965$	−21.8780	+	3.47453i	−0.704278	+	0.111849i
$966$		0			0
$967$	28.9926	−	28.9926i	0.932340	−	0.932340i	−0.0655119	−	0.997852i	$-0.520868\pi$
$967$	28.9926	−	28.9926i	0.932340	−	0.932340i	0.997852	+	0.0655119i	$0.0208680\pi$
$968$	−6.39506	+	6.39506i	−0.205545	+	0.205545i
$969$		0			0
$970$	−37.8169	+	52.0963i	−1.21423	+	1.67271i
$971$		−	2.51860i		−	0.0808259i	−0.999183	−	0.0404129i	$-0.987133\pi$
$971$		−	2.51860i		−	0.0808259i	0.999183	−	0.0404129i	$-0.0128673\pi$
$972$		0			0
$973$	−8.94734	−	8.94734i	−0.286839	−	0.286839i
$974$	−0.557594			−0.0178665
$975$		0			0
$976$	17.0115			0.544524
$977$	27.3808	+	27.3808i	0.875990	+	0.875990i	0.993117	−	0.117127i	$-0.0373686\pi$
$977$	27.3808	+	27.3808i	0.875990	+	0.875990i	−0.117127	+	0.993117i	$0.537369\pi$
$978$		0			0
$979$		−	92.6239i		−	2.96027i
$980$	2.90683	−	4.00444i	0.0928554	−	0.127917i
$981$		0			0
$982$	30.4134	−	30.4134i	0.970532	−	0.970532i
$983$	−24.7375	+	24.7375i	−0.789005	+	0.789005i	−0.981331	−	0.192326i	$-0.938397\pi$
$983$	−24.7375	+	24.7375i	−0.789005	+	0.789005i	0.192326	+	0.981331i	$0.438397\pi$
$984$		0			0
$985$	−12.3659	+	1.96387i	−0.394009	+	0.0625740i
$986$		−	5.45748i		−	0.173802i
$987$		0			0
$988$	−0.0942204	−	0.0942204i	−0.00299755	−	0.00299755i
$989$	−27.6631			−0.879636
$990$		0			0
$991$	−8.57525			−0.272402			−0.136201	−	0.990681i	$-0.543489\pi$
$991$	−8.57525			−0.272402			−0.136201	+	0.990681i	$0.543489\pi$
$992$	27.7951	+	27.7951i	0.882495	+	0.882495i
$993$		0			0
$994$		−	10.0534i		−	0.318876i
$995$	34.4964	+	25.0411i	1.09361	+	0.793855i
$996$		0			0
$997$	−10.7299	+	10.7299i	−0.339820	+	0.339820i	−0.856299	−	0.516480i	$-0.827242\pi$
$997$	−10.7299	+	10.7299i	−0.339820	+	0.339820i	0.516480	+	0.856299i	$0.327242\pi$
$998$	−9.04353	+	9.04353i	−0.286268	+	0.286268i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.m.b.8.1	yes	12
3.2	odd	2		315.2.m.a.8.6	✓	12
5.2	odd	4		315.2.m.a.197.6	yes	12
5.3	odd	4		1575.2.m.c.1457.1		12
5.4	even	2		1575.2.m.d.1268.6		12
15.2	even	4	inner	315.2.m.b.197.1	yes	12
15.8	even	4		1575.2.m.d.1457.6		12
15.14	odd	2		1575.2.m.c.1268.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.m.a.8.6	✓	12	3.2	odd	2
315.2.m.a.197.6	yes	12	5.2	odd	4
315.2.m.b.8.1	yes	12	1.1	even	1	trivial
315.2.m.b.197.1	yes	12	15.2	even	4	inner
1575.2.m.c.1268.1		12	15.14	odd	2
1575.2.m.c.1457.1		12	5.3	odd	4
1575.2.m.d.1268.6		12	5.4	even	2
1575.2.m.d.1457.6		12	15.8	even	4

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)

\(f(q)\)	\(=\)	\(q+(-1.45137 - 1.45137i) q^{2} +2.21293i q^{4} +(1.31357 - 1.80957i) q^{5} +(-0.707107 + 0.707107i) q^{7} +(0.309035 - 0.309035i) q^{8} +O(q^{10})\)	\(q+(-1.45137 - 1.45137i) q^{2} +2.21293i q^{4} +(1.31357 - 1.80957i) q^{5} +(-0.707107 + 0.707107i) q^{7} +(0.309035 - 0.309035i) q^{8} +(-4.53282 + 0.719873i) q^{10} -5.62971i q^{11} +(-0.00747830 - 0.00747830i) q^{13} +2.05254 q^{14} +3.52881 q^{16} +(-1.20876 - 1.20876i) q^{17} -5.69344i q^{19} +(4.00444 + 2.90683i) q^{20} +(-8.17077 + 8.17077i) q^{22} +(-4.96275 + 4.96275i) q^{23} +(-1.54907 - 4.75399i) q^{25} +0.0217075i q^{26} +(-1.56478 - 1.56478i) q^{28} -1.55541 q^{29} -4.84264 q^{31} +(-5.73966 - 5.73966i) q^{32} +3.50872i q^{34} +(0.350723 + 2.20839i) q^{35} +(3.14119 - 3.14119i) q^{37} +(-8.26326 + 8.26326i) q^{38} +(-0.153280 - 0.965159i) q^{40} +9.02203i q^{41} +(2.78707 + 2.78707i) q^{43} +12.4581 q^{44} +14.4055 q^{46} +(-6.31695 - 6.31695i) q^{47} -1.00000i q^{49} +(-4.65151 + 9.14804i) q^{50} +(0.0165489 - 0.0165489i) q^{52} +(4.17043 - 4.17043i) q^{53} +(-10.1873 - 7.39502i) q^{55} +0.437041i q^{56} +(2.25746 + 2.25746i) q^{58} +11.8204 q^{59} +4.82074 q^{61} +(7.02844 + 7.02844i) q^{62} +9.60309i q^{64} +(-0.0233558 + 0.00370921i) q^{65} +(1.72058 - 1.72058i) q^{67} +(2.67491 - 2.67491i) q^{68} +(2.69616 - 3.71421i) q^{70} -4.89804i q^{71} +(2.69985 + 2.69985i) q^{73} -9.11804 q^{74} +12.5992 q^{76} +(3.98081 + 3.98081i) q^{77} -10.6179i q^{79} +(4.63534 - 6.38562i) q^{80} +(13.0943 - 13.0943i) q^{82} +(5.14537 - 5.14537i) q^{83} +(-3.77514 + 0.599544i) q^{85} -8.09013i q^{86} +(-1.73978 - 1.73978i) q^{88} +16.4527 q^{89} +0.0105759 q^{91} +(-10.9822 - 10.9822i) q^{92} +18.3364i q^{94} +(-10.3027 - 7.47873i) q^{95} +(9.91803 - 9.91803i) q^{97} +(-1.45137 + 1.45137i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{5} - 24 q^{8}+O(q^{10}) \) 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

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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