LMFDB - Embedded newform 315.2.m.a.197.6

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			197.6
Root			$2.91021i$ of defining polynomial
Character	$\chi$	$=$	315.197
Dual form			315.2.m.a.8.6

$q$-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 $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

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

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 $

$2$	1.45137	−	1.45137i	1.02627	−	1.02627i	0.0266253	−	0.999645i	$-0.491524\pi$
$2$	1.45137	−	1.45137i	1.02627	−	1.02627i	0.999645	−	0.0266253i	$-0.00847610\pi$
$3$		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	−0.708143	−	0.706069i	$-0.750467\pi$
$13$	−0.00747830	+	0.00747830i	−0.00207411	+	0.00207411i	0.706069	+	0.708143i	$0.250467\pi$
$14$	−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	$-0.683532\pi$
$17$	1.20876	−	1.20876i	0.293169	−	0.293169i	0.838331	+	0.545162i	$0.183532\pi$
$18$		0			0
$19$			5.69344i			1.30616i	0.757287	+	0.653082i	$0.226524\pi$
$19$			5.69344i			1.30616i	−0.757287	+	0.653082i	$0.773476\pi$
$20$	−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	0.999372	+	0.0354333i	$0.0112811\pi$
$23$	4.96275	+	4.96275i	1.03481	+	1.03481i	0.0354333	+	0.999372i	$0.488719\pi$
$24$		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	$-0.453870\pi$
$29$	1.55541			0.288831			0.144416	+	0.989517i	$0.453870\pi$
$30$		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	0.916483	−	0.400074i	$-0.131016\pi$
$37$	3.14119	+	3.14119i	0.516409	+	0.516409i	−0.400074	+	0.916483i	$0.631016\pi$
$38$	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	−0.461905	−	0.886929i	$-0.652834\pi$
$43$	2.78707	−	2.78707i	0.425025	−	0.425025i	0.886929	+	0.461905i	$0.152834\pi$
$44$	−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	$-0.524122\pi$
$47$	6.31695	−	6.31695i	0.921421	−	0.921421i	0.997130	+	0.0757087i	$0.0241219\pi$
$48$		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	$-0.382752\pi$
$53$	−4.17043	−	4.17043i	−0.572853	−	0.572853i	−0.932925	+	0.360072i	$0.882752\pi$
$54$		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	$-0.779467\pi$
$59$	−11.8204			−1.53889			−0.769444	+	0.638714i	$0.779467\pi$
$60$		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	0.804354	−	0.594151i	$-0.202512\pi$
$67$	1.72058	+	1.72058i	0.210203	+	0.210203i	−0.594151	+	0.804354i	$0.702512\pi$
$68$	−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	−0.531232	−	0.847226i	$-0.678271\pi$
$73$	2.69985	−	2.69985i	0.315994	−	0.315994i	0.847226	+	0.531232i	$0.178271\pi$
$74$	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	$0.203761\pi$
$79$			10.6179i			1.19460i	−0.802016	+	0.597302i	$0.796239\pi$
$80$	−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	$-0.380767\pi$
$83$	−5.14537	−	5.14537i	−0.564778	−	0.564778i	−0.930661	+	0.365883i	$0.880767\pi$
$84$		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	$-0.837172\pi$
$89$	−16.4527			−1.74398			−0.871991	+	0.489521i	$0.837172\pi$
$90$		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	0.999975	+	0.00704778i	$0.00224340\pi$
$97$	9.91803	+	9.91803i	1.00702	+	1.00702i	0.00704778	+	0.999975i	$0.497757\pi$
$98$	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	−0.351607	−	0.936148i	$-0.614365\pi$
$103$	5.93245	−	5.93245i	0.584541	−	0.584541i	0.936148	+	0.351607i	$0.114365\pi$
$104$	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	$-0.644676\pi$
$107$	4.75259	−	4.75259i	0.459450	−	0.459450i	0.898475	+	0.439025i	$0.144676\pi$
$108$		0			0
$109$		−	12.3430i		−	1.18225i	−0.806581	−	0.591124i	$-0.798684\pi$
$109$		−	12.3430i		−	1.18225i	0.806581	−	0.591124i	$-0.201316\pi$
$110$	−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	$-0.165163\pi$
$113$	3.95944	+	3.95944i	0.372472	+	0.372472i	−0.495905	+	0.868377i	$0.665163\pi$
$114$		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	0.416055	−	0.909340i	$-0.363412\pi$
$127$	−5.55904	−	5.55904i	−0.493285	−	0.493285i	−0.909340	+	0.416055i	$0.863412\pi$
$128$	−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	−0.580016	+	0.814605i	$0.696954\pi$
$137$	−16.3236	+	16.3236i	−1.39462	+	1.39462i	−0.814605	+	0.580016i	$0.803046\pi$
$138$		0			0
$139$		−	12.6535i		−	1.07325i	−0.843820	−	0.536626i	$-0.819699\pi$
$139$		−	12.6535i		−	1.07325i	0.843820	−	0.536626i	$-0.180301\pi$
$140$	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	$-0.598336\pi$
$149$	−7.42258			−0.608081			−0.304041	+	0.952659i	$0.598336\pi$
$150$		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	0.986973	−	0.160887i	$-0.0514356\pi$
$157$	10.3508	+	10.3508i	0.826085	+	0.826085i	−0.160887	+	0.986973i	$0.551436\pi$
$158$	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	−0.162203	+	0.986757i	$0.551860\pi$
$163$	−14.6689	+	14.6689i	−1.14896	+	1.14896i	−0.986757	+	0.162203i	$0.948140\pi$
$164$	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	$-0.965322\pi$
$167$	−11.4412	+	11.4412i	−0.885344	+	0.885344i	0.108728	+	0.994072i	$0.465322\pi$
$168$		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	$-0.388400\pi$
$173$	−7.83527	−	7.83527i	−0.595704	−	0.595704i	−0.939166	+	0.343462i	$0.888400\pi$
$174$		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	$-0.636570\pi$
$179$	−11.1315			−0.832007			−0.416003	+	0.909363i	$0.636570\pi$
$180$		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	−0.912753	−	0.408512i	$-0.866048\pi$
$193$	−7.00514	+	7.00514i	−0.504241	+	0.504241i	0.408512	+	0.912753i	$0.366048\pi$
$194$	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	$-0.686077\pi$
$197$	3.95944	−	3.95944i	0.282098	−	0.282098i	0.833945	+	0.551847i	$0.186077\pi$
$198$		0			0
$199$		−	19.0634i		−	1.35137i	−0.737193	−	0.675683i	$-0.763849\pi$
$199$		−	19.0634i		−	1.35137i	0.737193	−	0.675683i	$-0.236151\pi$
$200$	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	0.456315	−	0.889818i	$-0.349169\pi$
$223$	20.1021	−	20.1021i	1.34613	−	1.34613i	0.889818	−	0.456315i	$-0.150831\pi$
$224$	−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	$-0.640472\pi$
$227$	7.18784	−	7.18784i	0.477074	−	0.477074i	0.904195	+	0.427121i	$0.140472\pi$
$228$		0			0
$229$			12.4777i			0.824552i	0.911059	+	0.412276i	$0.135266\pi$
$229$			12.4777i			0.824552i	−0.911059	+	0.412276i	$0.864734\pi$
$230$	−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	0.994849	+	0.101367i	$0.0323217\pi$
$233$	16.7330	+	16.7330i	1.09622	+	1.09622i	0.101367	+	0.994849i	$0.467678\pi$
$234$		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	$-0.464562\pi$
$239$	3.43517			0.222203			0.111101	+	0.993809i	$0.464562\pi$
$240$		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	$-0.764536\pi$
$257$	−1.03499	+	1.03499i	−0.0645611	+	0.0645611i	0.674089	+	0.738650i	$0.264536\pi$
$258$		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	$-0.324472\pi$
$263$	−5.31703	−	5.31703i	−0.327862	−	0.327862i	−0.851773	+	0.523911i	$0.824472\pi$
$264$		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	$-0.463232\pi$
$269$	3.78057			0.230506			0.115253	+	0.993336i	$0.463232\pi$
$270$		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	0.650480	−	0.759524i	$-0.274568\pi$
$277$	−1.81486	−	1.81486i	−0.109044	−	0.109044i	−0.759524	+	0.650480i	$0.774568\pi$
$278$	−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	−0.812262	−	0.583292i	$-0.801764\pi$
$283$	−3.85187	+	3.85187i	−0.228970	+	0.228970i	0.583292	+	0.812262i	$0.301764\pi$
$284$	−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	$-0.126342\pi$
$293$	9.16944	+	9.16944i	0.535684	+	0.535684i	−0.386574	+	0.922258i	$0.626342\pi$
$294$		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	0.955998	−	0.293372i	$-0.0947776\pi$
$307$	11.6101	+	11.6101i	0.662626	+	0.662626i	−0.293372	+	0.955998i	$0.594778\pi$
$308$	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	−0.413003	−	0.910730i	$-0.635520\pi$
$313$	8.80568	−	8.80568i	0.497727	−	0.497727i	0.910730	+	0.413003i	$0.135520\pi$
$314$	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	$-0.557901\pi$
$317$	14.2899	−	14.2899i	0.802602	−	0.802602i	0.983502	+	0.180899i	$0.0579009\pi$
$318$		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	0.900601	−	0.434646i	$-0.143127\pi$
$337$	8.55379	+	8.55379i	0.465955	+	0.465955i	−0.434646	+	0.900601i	$0.643127\pi$
$338$	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	$-0.691836\pi$
$347$	4.78700	−	4.78700i	0.256980	−	0.256980i	0.823824	+	0.566845i	$0.191836\pi$
$348$		0			0
$349$		−	9.62377i		−	0.515149i	−0.966258	−	0.257574i	$-0.917077\pi$
$349$		−	9.62377i		−	0.515149i	0.966258	−	0.257574i	$-0.0829232\pi$
$350$	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	$-0.479031\pi$
$353$	−17.5108	−	17.5108i	−0.932003	−	0.932003i	−0.997831	+	0.0658276i	$0.979031\pi$
$354$		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	$-0.533613\pi$
$359$	−3.99422			−0.210807			−0.105403	+	0.994430i	$0.533613\pi$
$360$		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	0.460290	−	0.887769i	$-0.347746\pi$
$367$	−8.18932	−	8.18932i	−0.427479	−	0.427479i	−0.887769	+	0.460290i	$0.847746\pi$
$368$	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	−0.259434	−	0.965761i	$-0.583536\pi$
$373$	13.6414	−	13.6414i	0.706326	−	0.706326i	0.965761	+	0.259434i	$0.0835361\pi$
$374$	−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	$-0.975030\pi$
$379$		−	3.05127i		−	0.156733i	0.996925	−	0.0783666i	$-0.0249705\pi$
$380$	−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	$-0.267881\pi$
$383$	−1.55390	−	1.55390i	−0.0794006	−	0.0794006i	−0.745692	+	0.666291i	$0.767881\pi$
$384$		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	$-0.325258\pi$
$389$	20.5833			1.04361			0.521807	+	0.853064i	$0.325258\pi$
$390$		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	0.489302	−	0.872114i	$-0.337252\pi$
$397$	−7.62748	−	7.62748i	−0.382812	−	0.382812i	−0.872114	+	0.489302i	$0.837252\pi$
$398$	−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	$0.134449\pi$
$409$			16.5809i			0.819875i	−0.912114	+	0.409938i	$0.865551\pi$
$410$	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	$-0.464059\pi$
$419$	4.61274			0.225347			0.112674	+	0.993632i	$0.464059\pi$
$420$		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	−0.999663	−	0.0259707i	$-0.991732\pi$
$433$	−20.2612	+	20.2612i	−0.973692	+	0.973692i	0.0259707	+	0.999663i	$0.491732\pi$
$434$	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	$-0.734233\pi$
$439$		−	31.0619i		−	1.48250i	0.671228	−	0.741251i	$-0.265767\pi$
$440$	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	−0.967745	−	0.251933i	$-0.918934\pi$
$443$	−25.6712	−	25.6712i	−1.21968	−	1.21968i	−0.251933	−	0.967745i	$-0.581066\pi$
$444$		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	$-0.688050\pi$
$449$	−23.6055			−1.11401			−0.557007	+	0.830508i	$0.688050\pi$
$450$		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	0.154314	−	0.988022i	$-0.450683\pi$
$457$	−17.8226	−	17.8226i	−0.833708	−	0.833708i	−0.988022	+	0.154314i	$0.950683\pi$
$458$	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	−0.858977	−	0.512015i	$-0.828899\pi$
$463$	−7.46573	+	7.46573i	−0.346962	+	0.346962i	0.512015	+	0.858977i	$0.328899\pi$
$464$	5.48873			0.254808
$465$		0			0
$466$	48.5715			2.25003
$467$	28.5436	−	28.5436i	1.32084	−	1.32084i	0.407748	−	0.913094i	$-0.366314\pi$
$467$	28.5436	−	28.5436i	1.32084	−	1.32084i	0.913094	−	0.407748i	$-0.133686\pi$
$468$		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	$-0.547161\pi$
$479$	−6.46156			−0.295236			−0.147618	+	0.989044i	$0.547161\pi$
$480$		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	0.711446	−	0.702741i	$-0.248041\pi$
$487$	0.192093	+	0.192093i	0.00870456	+	0.00870456i	−0.702741	+	0.711446i	$0.748041\pi$
$488$	−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	$0.0445399\pi$
$499$			6.23105i			0.278940i	−0.990226	+	0.139470i	$0.955460\pi$
$500$	−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	$-0.192253\pi$
$503$	5.72261	+	5.72261i	0.255158	+	0.255158i	−0.567923	+	0.823082i	$0.692253\pi$
$504$		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	$-0.462009\pi$
$509$	5.37263			0.238138			0.119069	+	0.992886i	$0.462009\pi$
$510$		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	−0.861869	−	0.507132i	$-0.830706\pi$
$523$	−8.11255	+	8.11255i	−0.354737	+	0.354737i	0.507132	+	0.861869i	$0.330706\pi$
$524$	−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	0.977145	−	0.212572i	$-0.0681840\pi$
$547$	17.8819	+	17.8819i	0.764574	+	0.764574i	−0.212572	+	0.977145i	$0.568184\pi$
$548$	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	$-0.564059\pi$
$557$	18.4069	−	18.4069i	0.779925	−	0.779925i	0.979818	+	0.199893i	$0.0640594\pi$
$558$		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	$-0.187220\pi$
$563$	6.57537	+	6.57537i	0.277119	+	0.277119i	−0.554839	+	0.831958i	$0.687220\pi$
$564$		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	$-0.513385\pi$
$569$	−2.00559			−0.0840787			−0.0420393	+	0.999116i	$0.513385\pi$
$570$		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	0.112236	−	0.993682i	$-0.464199\pi$
$577$	−21.1731	−	21.1731i	−0.881446	−	0.881446i	−0.993682	+	0.112236i	$0.964199\pi$
$578$	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	−0.0425335	+	0.999095i	$0.513543\pi$
$587$	−25.2367	+	25.2367i	−1.04163	+	1.04163i	−0.999095	+	0.0425335i	$0.986457\pi$
$588$		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	−0.984533	−	0.175202i	$-0.943942\pi$
$593$	−28.2414	−	28.2414i	−1.15973	−	1.15973i	−0.175202	−	0.984533i	$-0.556058\pi$
$594$		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	$-0.604671\pi$
$599$	−15.8076			−0.645881			−0.322940	+	0.946419i	$0.604671\pi$
$600$		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	0.946870	−	0.321617i	$-0.104226\pi$
$607$	15.4046	+	15.4046i	0.625253	+	0.625253i	−0.321617	+	0.946870i	$0.604226\pi$
$608$	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	−0.917142	−	0.398561i	$-0.869510\pi$
$613$	−12.8394	+	12.8394i	−0.518580	+	0.518580i	0.398561	+	0.917142i	$0.369510\pi$
$614$	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	$-0.885792\pi$
$617$	−14.5354	+	14.5354i	−0.585173	+	0.585173i	0.351147	+	0.936320i	$0.385792\pi$
$618$		0			0
$619$			10.1884i			0.409506i	0.978814	+	0.204753i	$0.0656391\pi$
$619$			10.1884i			0.409506i	−0.978814	+	0.204753i	$0.934361\pi$
$620$	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	−0.603100	−	0.797665i	$-0.706068\pi$
$643$	4.93368	−	4.93368i	0.194565	−	0.194565i	0.797665	+	0.603100i	$0.206068\pi$
$644$	−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	$-0.846538\pi$
$647$	−10.7433	+	10.7433i	−0.422364	+	0.422364i	0.463653	+	0.886017i	$0.346538\pi$
$648$		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	$-0.376631\pi$
$653$	−14.0006	−	14.0006i	−0.547884	−	0.547884i	−0.925828	+	0.377944i	$0.876631\pi$
$654$		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	$-0.539503\pi$
$659$	−6.35539			−0.247571			−0.123785	+	0.992309i	$0.539503\pi$
$660$		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	−0.283901	+	0.958854i	$0.591629\pi$
$673$	−32.2398	+	32.2398i	−1.24275	+	1.24275i	−0.958854	+	0.283901i	$0.908371\pi$
$674$	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	$-0.787851\pi$
$677$	−4.36523	+	4.36523i	−0.167769	+	0.167769i	0.618229	+	0.785998i	$0.287851\pi$
$678$		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	$-0.135421\pi$
$683$	13.0185	+	13.0185i	0.498138	+	0.498138i	−0.412720	+	0.910858i	$0.635421\pi$
$684$		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	$-0.585854\pi$
$709$		−	51.3287i		−	1.92769i	0.266461	−	0.963846i	$-0.414146\pi$
$710$	−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	$-0.388402\pi$
$719$	18.4190			0.686911			0.343456	+	0.939169i	$0.388402\pi$
$720$		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	0.998726	+	0.0504586i	$0.0160683\pi$
$727$	28.2891	+	28.2891i	1.04918	+	1.04918i	0.0504586	+	0.998726i	$0.483932\pi$
$728$	−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	−0.912188	−	0.409772i	$-0.865608\pi$
$733$	−13.6024	+	13.6024i	−0.502416	+	0.502416i	0.409772	+	0.912188i	$0.365608\pi$
$734$	−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	$-0.833081\pi$
$739$		−	27.2219i		−	1.00137i	0.865629	−	0.500686i	$-0.166919\pi$
$740$	−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	$-0.258235\pi$
$743$	−0.997164	−	0.997164i	−0.0365824	−	0.0365824i	−0.725161	+	0.688579i	$0.758235\pi$
$744$		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	0.889138	−	0.457640i	$-0.151305\pi$
$757$	11.8721	+	11.8721i	0.431497	+	0.431497i	−0.457640	+	0.889138i	$0.651305\pi$
$758$	−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	$-0.630182\pi$
$769$		−	50.8876i		−	1.83505i	0.397673	−	0.917527i	$-0.369818\pi$
$770$	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	$-0.396159\pi$
$773$	−17.4266	−	17.4266i	−0.626790	−	0.626790i	−0.947259	+	0.320469i	$0.896159\pi$
$774$		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	0.288165	−	0.957581i	$-0.406955\pi$
$787$	−18.7795	−	18.7795i	−0.669416	−	0.669416i	−0.957581	+	0.288165i	$0.906955\pi$
$788$	−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	$-0.705989\pi$
$797$	5.50268	−	5.50268i	0.194915	−	0.194915i	0.797816	+	0.602901i	$0.205989\pi$
$798$		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	$-0.426197\pi$
$809$	13.0716			0.459574			0.229787	+	0.973241i	$0.426197\pi$
$810$		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	−0.604596	−	0.796532i	$-0.706666\pi$
$823$	5.50624	−	5.50624i	0.191936	−	0.191936i	0.796532	+	0.604596i	$0.206666\pi$
$824$	−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	$-0.698267\pi$
$827$	6.58070	−	6.58070i	0.228833	−	0.228833i	0.812205	+	0.583372i	$0.198267\pi$
$828$		0			0
$829$			37.1189i			1.28919i	0.764522	+	0.644597i	$0.222975\pi$
$829$			37.1189i			1.28919i	−0.764522	+	0.644597i	$0.777025\pi$
$830$	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	$-0.719366\pi$
$839$	−36.8376			−1.27178			−0.635888	+	0.771782i	$0.719366\pi$
$840$		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	0.306655	−	0.951821i	$-0.400790\pi$
$853$	36.7552	−	36.7552i	1.25848	−	1.25848i	0.951821	−	0.306655i	$-0.0992097\pi$
$854$	−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	$-0.654496\pi$
$857$	12.2360	−	12.2360i	0.417974	−	0.417974i	0.884505	+	0.466531i	$0.154496\pi$
$858$		0			0
$859$		−	35.9638i		−	1.22707i	−0.789668	−	0.613535i	$-0.789747\pi$
$859$		−	35.9638i		−	1.22707i	0.789668	−	0.613535i	$-0.210253\pi$
$860$	−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	$-0.183423\pi$
$863$	8.62624	+	8.62624i	0.293641	+	0.293641i	−0.544876	+	0.838517i	$0.683423\pi$
$864$		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	0.664921	−	0.746913i	$-0.268465\pi$
$877$	−2.42813	−	2.42813i	−0.0819920	−	0.0819920i	−0.746913	+	0.664921i	$0.768465\pi$
$878$	−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	−0.478120	−	0.878295i	$-0.658682\pi$
$883$	11.8913	−	11.8913i	0.400175	−	0.400175i	0.878295	+	0.478120i	$0.158682\pi$
$884$	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	$-0.827950\pi$
$887$	−10.2116	+	10.2116i	−0.342872	+	0.342872i	0.514574	+	0.857446i	$0.327950\pi$
$888$		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	0.128737	−	0.991679i	$-0.458908\pi$
$907$	−25.9887	−	25.9887i	−0.862942	−	0.862942i	−0.991679	+	0.128737i	$0.958908\pi$
$908$	−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	$-0.964363\pi$
$919$		−	6.77384i		−	0.223448i	0.993739	−	0.111724i	$-0.0356373\pi$
$920$	−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	$-0.378784\pi$
$929$	22.6568			0.743347			0.371673	+	0.928364i	$0.378784\pi$
$930$		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	0.345097	−	0.938567i	$-0.387846\pi$
$937$	−18.1664	−	18.1664i	−0.593470	−	0.593470i	−0.938567	+	0.345097i	$0.887846\pi$
$938$	−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	$-0.799011\pi$
$947$	−6.67439	+	6.67439i	−0.216889	+	0.216889i	0.590297	+	0.807186i	$0.299011\pi$
$948$		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	$-0.156584\pi$
$953$	12.6293	+	12.6293i	0.409104	+	0.409104i	−0.472322	+	0.881426i	$0.656584\pi$
$954$		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	0.997852	−	0.0655119i	$-0.0208680\pi$
$967$	28.9926	+	28.9926i	0.932340	+	0.932340i	−0.0655119	+	0.997852i	$0.520868\pi$
$968$	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	$-0.962631\pi$
$977$	−27.3808	+	27.3808i	−0.875990	+	0.875990i	0.117127	+	0.993117i	$0.462631\pi$
$978$		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	$-0.0616031\pi$
$983$	24.7375	+	24.7375i	0.789005	+	0.789005i	−0.192326	+	0.981331i	$0.561603\pi$
$984$		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	0.516480	−	0.856299i	$-0.327242\pi$
$997$	−10.7299	−	10.7299i	−0.339820	−	0.339820i	−0.856299	+	0.516480i	$0.827242\pi$
$998$	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.a.197.6	yes	12
3.2	odd	2		315.2.m.b.197.1	yes	12
5.2	odd	4		1575.2.m.d.1268.6		12
5.3	odd	4		315.2.m.b.8.1	yes	12
5.4	even	2		1575.2.m.c.1457.1		12
15.2	even	4		1575.2.m.c.1268.1		12
15.8	even	4	inner	315.2.m.a.8.6	✓	12
15.14	odd	2		1575.2.m.d.1457.6		12

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

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

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