LMFDB - Embedded newform 315.2.p.e.307.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([0, 3, 2]))

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

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

chi := DirichletCharacter("315.118");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4x^{14} + 6x^{12} - 12x^{10} + 33x^{8} - 48x^{6} + 96x^{4} - 256x^{2} + 256 $ x^16 - 4x^14 + 6x^12 - 12x^10 + 33x^8 - 48x^6 + 96x^4 - 256*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			307.8
Root			$-0.517174 + 1.31626i$ of defining polynomial
Character	$\chi$	$=$	315.307
Dual form			315.2.p.e.118.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.86147 + 1.86147i) q^{2} +4.93012i q^{4} +(1.50619 - 1.65269i) q^{5} +(-2.20563 + 1.46123i) q^{7} +(-5.45433 + 5.45433i) q^{8} +O(q^{10})$	\(q+(1.86147 + 1.86147i) q^{2} +4.93012i q^{4} +(1.50619 - 1.65269i) q^{5} +(-2.20563 + 1.46123i) q^{7} +(-5.45433 + 5.45433i) q^{8} +(5.88016 - 0.272713i) q^{10} +1.46279 q^{11} +(0.887844 + 0.887844i) q^{13} +(-6.82574 - 1.38567i) q^{14} -10.4459 q^{16} +(2.10614 - 2.10614i) q^{17} -3.95987 q^{19} +(8.14798 + 7.42570i) q^{20} +(2.72294 + 2.72294i) q^{22} +(4.13007 - 4.13007i) q^{23} +(-0.462789 - 4.97854i) q^{25} +3.30539i q^{26} +(-7.20405 - 10.8740i) q^{28} -5.18572i q^{29} -6.10346i q^{31} +(-8.53599 - 8.53599i) q^{32} +7.84104 q^{34} +(-0.907129 + 5.84612i) q^{35} +(2.25560 + 2.25560i) q^{37} +(-7.37117 - 7.37117i) q^{38} +(0.799082 + 17.2296i) q^{40} -0.769968i q^{41} +(-5.18572 + 5.18572i) q^{43} +7.21173i q^{44} +15.3760 q^{46} +(-8.57041 + 8.57041i) q^{47} +(2.72961 - 6.44587i) q^{49} +(8.40592 - 10.1289i) q^{50} +(-4.37718 + 4.37718i) q^{52} +(0.544449 - 0.544449i) q^{53} +(2.20324 - 2.41754i) q^{55} +(4.06020 - 20.0003i) q^{56} +(9.65306 - 9.65306i) q^{58} +3.19633 q^{59} +1.42064i q^{61} +(11.3614 - 11.3614i) q^{62} -10.8872i q^{64} +(2.80460 - 0.130073i) q^{65} +(-5.93012 - 5.93012i) q^{67} +(10.3835 + 10.3835i) q^{68} +(-12.5710 + 9.19377i) q^{70} -7.62611 q^{71} +(6.81378 + 6.81378i) q^{73} +8.39746i q^{74} -19.5226i q^{76} +(-3.22637 + 2.13747i) q^{77} +4.52029i q^{79} +(-15.7335 + 17.2638i) q^{80} +(1.43327 - 1.43327i) q^{82} +(6.75794 + 6.75794i) q^{83} +(-0.308559 - 6.65306i) q^{85} -19.3061 q^{86} +(-7.97854 + 7.97854i) q^{88} -1.19991 q^{89} +(-3.25560 - 0.660910i) q^{91} +(20.3618 + 20.3618i) q^{92} -31.9071 q^{94} +(-5.96431 + 6.54445i) q^{95} +(-8.68829 + 8.68829i) q^{97} +(17.0799 - 6.91770i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{7} - 24 q^{8}+O(q^{10}) $ 16 * q - 8 * q^7 - 24 * q^8	$ 16 q - 8 q^{7} - 24 q^{8} + 16 q^{11} - 48 q^{16} - 16 q^{22} + 40 q^{23} + 24 q^{28} - 48 q^{32} + 8 q^{35} + 32 q^{37} - 16 q^{43} + 64 q^{46} + 72 q^{50} - 24 q^{53} - 24 q^{56} + 32 q^{58} - 40 q^{65} - 32 q^{67} - 40 q^{70} - 64 q^{71} + 24 q^{77} + 48 q^{85} - 64 q^{86} - 64 q^{88} - 48 q^{91} + 40 q^{92} + 72 q^{95} + 96 q^{98}+O(q^{100}) $ 16 * q - 8 * q^7 - 24 * q^8 + 16 * q^11 - 48 * q^16 - 16 * q^22 + 40 * q^23 + 24 * q^28 - 48 * q^32 + 8 * q^35 + 32 * q^37 - 16 * q^43 + 64 * q^46 + 72 * q^50 - 24 * q^53 - 24 * q^56 + 32 * q^58 - 40 * q^65 - 32 * q^67 - 40 * q^70 - 64 * q^71 + 24 * q^77 + 48 * q^85 - 64 * q^86 - 64 * q^88 - 48 * q^91 + 40 * q^92 + 72 * q^95 + 96 * q^98

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 $

$2$	1.86147	+	1.86147i	1.31626	+	1.31626i	0.916715	+	0.399541i	$0.130831\pi$
$2$	1.86147	+	1.86147i	1.31626	+	1.31626i	0.399541	+	0.916715i	$0.369169\pi$
$3$		0			0
$3$		0			0
$4$			4.93012i			2.46506i
$5$	1.50619	−	1.65269i	0.673588	−	0.739107i
$5$	1.50619	−	1.65269i	0.673588	−	0.739107i
$6$		0			0
$7$	−2.20563	+	1.46123i	−0.833650	+	0.552293i
$7$	−2.20563	+	1.46123i	−0.833650	+	0.552293i
$8$	−5.45433	+	5.45433i	−1.92840	+	1.92840i
$9$		0			0
$10$	5.88016	−	0.272713i	1.85947	−	0.0862394i
$11$	1.46279			0.441048			0.220524	−	0.975382i	$-0.429223\pi$
$11$	1.46279			0.441048			0.220524	+	0.975382i	$0.429223\pi$
$12$		0			0
$13$	0.887844	+	0.887844i	0.246244	+	0.246244i	0.819427	−	0.573183i	$-0.194292\pi$
$13$	0.887844	+	0.887844i	0.246244	+	0.246244i	−0.573183	+	0.819427i	$0.694292\pi$
$14$	−6.82574	−	1.38567i	−1.82426	−	0.370337i
$15$		0			0
$16$	−10.4459			−2.61147
$17$	2.10614	−	2.10614i	0.510815	−	0.510815i	−0.403961	−	0.914776i	$-0.632367\pi$
$17$	2.10614	−	2.10614i	0.510815	−	0.510815i	0.914776	+	0.403961i	$0.132367\pi$
$18$		0			0
$19$	−3.95987			−0.908456			−0.454228	−	0.890885i	$-0.650085\pi$
$19$	−3.95987			−0.908456			−0.454228	+	0.890885i	$0.650085\pi$
$20$	8.14798	+	7.42570i	1.82194	+	1.66044i
$21$		0			0
$22$	2.72294	+	2.72294i	0.580532	+	0.580532i
$23$	4.13007	−	4.13007i	0.861180	−	0.861180i	−0.130295	−	0.991475i	$-0.541593\pi$
$23$	4.13007	−	4.13007i	0.861180	−	0.861180i	0.991475	+	0.130295i	$0.0415926\pi$
$24$		0			0
$25$	−0.462789	−	4.97854i	−0.0925579	−	0.995707i
$26$			3.30539i			0.648240i
$27$		0			0
$28$	−7.20405	−	10.8740i	−1.36144	−	2.05500i
$29$		−	5.18572i		−	0.962965i	−0.876456	−	0.481482i	$-0.840099\pi$
$29$		−	5.18572i		−	0.962965i	0.876456	−	0.481482i	$-0.159901\pi$
$30$		0			0
$31$		−	6.10346i		−	1.09621i	−0.836408	−	0.548107i	$-0.815349\pi$
$31$		−	6.10346i		−	1.09621i	0.836408	−	0.548107i	$-0.184651\pi$
$32$	−8.53599	−	8.53599i	−1.50896	−	1.50896i
$33$		0			0
$34$	7.84104			1.34473
$35$	−0.907129	+	5.84612i	−0.153333	+	0.988175i
$36$		0			0
$37$	2.25560	+	2.25560i	0.370819	+	0.370819i	0.867775	−	0.496957i	$-0.165549\pi$
$37$	2.25560	+	2.25560i	0.370819	+	0.370819i	−0.496957	+	0.867775i	$0.665549\pi$
$38$	−7.37117	−	7.37117i	−1.19576	−	1.19576i
$39$		0			0
$40$	0.799082	+	17.2296i	0.126346	+	2.72424i
$41$		−	0.769968i		−	0.120249i	−0.998191	−	0.0601244i	$-0.980850\pi$
$41$		−	0.769968i		−	0.120249i	0.998191	−	0.0601244i	$-0.0191497\pi$
$42$		0			0
$43$	−5.18572	+	5.18572i	−0.790816	+	0.790816i	−0.981627	−	0.190811i	$-0.938888\pi$
$43$	−5.18572	+	5.18572i	−0.790816	+	0.790816i	0.190811	+	0.981627i	$0.438888\pi$
$44$			7.21173i			1.08721i
$45$		0			0
$46$	15.3760			2.26707
$47$	−8.57041	+	8.57041i	−1.25012	+	1.25012i	−0.294459	+	0.955664i	$0.595139\pi$
$47$	−8.57041	+	8.57041i	−1.25012	+	1.25012i	−0.955664	+	0.294459i	$0.904861\pi$
$48$		0			0
$49$	2.72961	−	6.44587i	0.389944	−	0.920839i
$50$	8.40592	−	10.1289i	1.18878	−	1.43244i
$51$		0			0
$52$	−4.37718	+	4.37718i	−0.607006	+	0.607006i
$53$	0.544449	−	0.544449i	0.0747859	−	0.0747859i	−0.668724	−	0.743510i	$-0.733159\pi$
$53$	0.544449	−	0.544449i	0.0747859	−	0.0747859i	0.743510	+	0.668724i	$0.233159\pi$
$54$		0			0
$55$	2.20324	−	2.41754i	0.297084	−	0.325981i
$56$	4.06020	−	20.0003i	0.542567	−	2.67265i
$57$		0			0
$58$	9.65306	−	9.65306i	1.26751	−	1.26751i
$59$	3.19633			0.416127			0.208063	−	0.978115i	$-0.433284\pi$
$59$	3.19633			0.416127			0.208063	+	0.978115i	$0.433284\pi$
$60$		0			0
$61$			1.42064i			0.181894i	0.995856	+	0.0909472i	$0.0289894\pi$
$61$			1.42064i			0.181894i	−0.995856	+	0.0909472i	$0.971011\pi$
$62$	11.3614	−	11.3614i	1.44290	−	1.44290i
$63$		0			0
$64$		−	10.8872i		−	1.36090i
$65$	2.80460	−	0.130073i	0.347867	−	0.0161336i
$66$		0			0
$67$	−5.93012	−	5.93012i	−0.724480	−	0.724480i	0.245034	−	0.969514i	$-0.421201\pi$
$67$	−5.93012	−	5.93012i	−0.724480	−	0.724480i	−0.969514	+	0.245034i	$0.921201\pi$
$68$	10.3835	+	10.3835i	1.25919	+	1.25919i
$69$		0			0
$70$	−12.5710	+	9.19377i	−1.50252	+	1.09887i
$71$	−7.62611			−0.905053			−0.452526	−	0.891751i	$-0.649477\pi$
$71$	−7.62611			−0.905053			−0.452526	+	0.891751i	$0.649477\pi$
$72$		0			0
$73$	6.81378	+	6.81378i	0.797493	+	0.797493i	0.982700	−	0.185207i	$-0.0592955\pi$
$73$	6.81378	+	6.81378i	0.797493	+	0.797493i	−0.185207	+	0.982700i	$0.559296\pi$
$74$			8.39746i			0.976185i
$75$		0			0
$76$		−	19.5226i		−	2.23940i
$77$	−3.22637	+	2.13747i	−0.367679	+	0.243588i
$78$		0			0
$79$			4.52029i			0.508573i	0.967129	+	0.254286i	$0.0818405\pi$
$79$			4.52029i			0.508573i	−0.967129	+	0.254286i	$0.918159\pi$
$80$	−15.7335	+	17.2638i	−1.75905	+	1.93015i
$81$		0			0
$82$	1.43327	−	1.43327i	0.158278	−	0.158278i
$83$	6.75794	+	6.75794i	0.741781	+	0.741781i	0.972921	−	0.231140i	$-0.0742455\pi$
$83$	6.75794	+	6.75794i	0.741781	+	0.741781i	−0.231140	+	0.972921i	$0.574246\pi$
$84$		0			0
$85$	−0.308559	−	6.65306i	−0.0334679	−	0.721626i
$86$	−19.3061			−2.08183
$87$		0			0
$88$	−7.97854	+	7.97854i	−0.850515	+	0.850515i
$89$	−1.19991			−0.127190			−0.0635950	−	0.997976i	$-0.520257\pi$
$89$	−1.19991			−0.127190			−0.0635950	+	0.997976i	$0.520257\pi$
$90$		0			0
$91$	−3.25560	−	0.660910i	−0.341280	−	0.0692822i
$92$	20.3618	+	20.3618i	2.12286	+	2.12286i
$93$		0			0
$94$	−31.9071			−3.29096
$95$	−5.96431	+	6.54445i	−0.611925	+	0.671446i
$96$		0			0
$97$	−8.68829	+	8.68829i	−0.882162	+	0.882162i	−0.993754	−	0.111592i	$-0.964405\pi$
$97$	−8.68829	+	8.68829i	−0.882162	+	0.882162i	0.111592	+	0.993754i	$0.464405\pi$
$98$	17.0799	−	6.91770i	1.72533	−	0.698794i
$99$		0			0
$100$	24.5448	−	2.28161i	2.45448	−	0.228161i
$101$		−	15.3420i		−	1.52659i	−0.646050	−	0.763295i	$-0.723580\pi$
$101$		−	15.3420i		−	1.52659i	0.646050	−	0.763295i	$-0.276420\pi$
$102$		0			0
$103$	8.30776	+	8.30776i	0.818588	+	0.818588i	0.985903	−	0.167316i	$-0.0535099\pi$
$103$	8.30776	+	8.30776i	0.818588	+	0.818588i	−0.167316	+	0.985903i	$0.553510\pi$
$104$	−9.68519			−0.949711
$105$		0			0
$106$	2.02695			0.196875
$107$	−4.39022	−	4.39022i	−0.424418	−	0.424418i	0.462303	−	0.886722i	$-0.347023\pi$
$107$	−4.39022	−	4.39022i	−0.424418	−	0.424418i	−0.886722	+	0.462303i	$0.847023\pi$
$108$		0			0
$109$			7.44587i			0.713185i	0.934260	+	0.356593i	$0.116062\pi$
$109$			7.44587i			0.713185i	−0.934260	+	0.356593i	$0.883938\pi$
$110$	8.60143	−	0.398921i	0.820114	−	0.0380357i
$111$		0			0
$112$	23.0397	−	15.2638i	2.17705	−	1.44230i
$113$	−2.54445	+	2.54445i	−0.239362	+	0.239362i	−0.816586	−	0.577224i	$-0.804136\pi$
$113$	−2.54445	+	2.54445i	−0.239362	+	0.239362i	0.577224	+	0.816586i	$0.304136\pi$
$114$		0			0
$115$	−0.605073	−	13.0464i	−0.0564233	−	1.21658i
$116$	25.5663			2.37377
$117$		0			0
$118$	5.94986	+	5.94986i	0.547729	+	0.547729i
$119$	−1.56781	+	7.72294i	−0.143721	+	0.707960i
$120$		0			0
$121$	−8.86025			−0.805477
$122$	−2.64448	+	2.64448i	−0.239420	+	0.239420i
$123$		0			0
$124$	30.0908			2.70223
$125$	−8.92504	−	6.73377i	−0.798280	−	0.602287i
$126$		0			0
$127$	7.86025	+	7.86025i	0.697484	+	0.697484i	0.963867	−	0.266383i	$-0.0858286\pi$
$127$	7.86025	+	7.86025i	0.697484	+	0.697484i	−0.266383	+	0.963867i	$0.585829\pi$
$128$	3.19418	−	3.19418i	0.282329	−	0.282329i
$129$		0			0
$130$	5.46279	+	4.97854i	0.479118	+	0.436647i
$131$		−	6.18216i		−	0.540138i	−0.962841	−	0.270069i	$-0.912953\pi$
$131$		−	6.18216i		−	0.540138i	0.962841	−	0.270069i	$-0.0870465\pi$
$132$		0			0
$133$	8.73401	−	5.78628i	0.757334	−	0.501735i
$134$		−	22.0775i		−	1.90720i
$135$		0			0
$136$			22.9752i			1.97011i
$137$	−9.05565	−	9.05565i	−0.773677	−	0.773677i	0.205071	−	0.978747i	$-0.434258\pi$
$137$	−9.05565	−	9.05565i	−0.773677	−	0.773677i	−0.978747	+	0.205071i	$0.934258\pi$
$138$		0			0
$139$	−11.9913			−1.01709			−0.508544	−	0.861036i	$-0.669816\pi$
$139$	−11.9913			−1.01709			−0.508544	+	0.861036i	$0.669816\pi$
$140$	−28.8221	−	4.47226i	−2.43591	−	0.377975i
$141$		0			0
$142$	−14.1958	−	14.1958i	−1.19128	−	1.19128i
$143$	1.29873	+	1.29873i	0.108605	+	0.108605i
$144$		0			0
$145$	−8.57041	−	7.81068i	−0.711734	−	0.648642i
$146$			25.3673i			2.09941i
$147$		0			0
$148$	−11.1204	+	11.1204i	−0.914091	+	0.914091i
$149$			0.0968261i			0.00793230i	0.999992	+	0.00396615i	$0.00126247\pi$
$149$			0.0968261i			0.00793230i	−0.999992	+	0.00396615i	$0.998738\pi$
$150$		0			0
$151$	−13.4550			−1.09495			−0.547475	−	0.836822i	$-0.684411\pi$
$151$	−13.4550			−1.09495			−0.547475	+	0.836822i	$0.684411\pi$
$152$	21.5984	−	21.5984i	1.75186	−	1.75186i
$153$		0			0
$154$	−9.98463	−	2.02695i	−0.804584	−	0.163336i
$155$	−10.0871	−	9.19296i	−0.810219	−	0.738397i
$156$		0			0
$157$	1.64757	−	1.64757i	0.131491	−	0.131491i	−0.638298	−	0.769789i	$-0.720361\pi$
$157$	1.64757	−	1.64757i	0.131491	−	0.131491i	0.769789	+	0.638298i	$0.220361\pi$
$158$	−8.41438	+	8.41438i	−0.669412	+	0.669412i
$159$		0			0
$160$	−26.9642	+	1.25056i	−2.13171	+	0.0988653i
$161$	−3.07442	+	15.1444i	−0.242298	+	1.19355i
$162$		0			0
$163$	−10.2746	+	10.2746i	−0.804771	+	0.804771i	−0.983837	−	0.179066i	$-0.942692\pi$
$163$	−10.2746	+	10.2746i	−0.804771	+	0.804771i	0.179066	+	0.983837i	$0.442692\pi$
$164$	3.79604			0.296421
$165$		0			0
$166$			25.1594i			1.95275i
$167$	−0.293008	+	0.293008i	−0.0226737	+	0.0226737i	−0.718353	−	0.695679i	$-0.755104\pi$
$167$	−0.293008	+	0.293008i	−0.0226737	+	0.0226737i	0.695679	+	0.718353i	$0.255104\pi$
$168$		0			0
$169$		−	11.4235i		−	0.878728i
$170$	11.8101	−	12.9588i	0.905792	−	0.993897i
$171$		0			0
$172$	−25.5663	−	25.5663i	−1.94941	−	1.94941i
$173$	3.45189	+	3.45189i	0.262442	+	0.262442i	0.826046	−	0.563603i	$-0.190585\pi$
$173$	3.45189	+	3.45189i	0.262442	+	0.262442i	−0.563603	+	0.826046i	$0.690585\pi$
$174$		0			0
$175$	8.29554	+	10.3046i	0.627084	+	0.778952i
$176$	−15.2801			−1.15178
$177$		0			0
$178$	−2.23359	−	2.23359i	−0.167415	−	0.167415i
$179$			1.99756i			0.149305i	0.997210	+	0.0746523i	$0.0237847\pi$
$179$			1.99756i			0.149305i	−0.997210	+	0.0746523i	$0.976215\pi$
$180$		0			0
$181$		−	8.48528i		−	0.630706i	−0.948974	−	0.315353i	$-0.897877\pi$
$181$		−	8.48528i		−	0.630706i	0.948974	−	0.315353i	$-0.102123\pi$
$182$	−4.82993	−	7.29046i	−0.358019	−	0.540405i
$183$		0			0
$184$			45.0536i			3.32139i
$185$	7.12518	−	0.330455i	0.523854	−	0.0242955i
$186$		0			0
$187$	3.08084	−	3.08084i	0.225294	−	0.225294i
$188$	−42.2532	−	42.2532i	−3.08163	−	3.08163i
$189$		0			0
$190$	−23.2847	+	1.07991i	−1.68925	+	0.0783447i
$191$	7.83424			0.566866			0.283433	−	0.958992i	$-0.408527\pi$
$191$	7.83424			0.566866			0.283433	+	0.958992i	$0.408527\pi$
$192$		0			0
$193$	13.5617	−	13.5617i	0.976194	−	0.976194i	−0.0235293	−	0.999723i	$-0.507490\pi$
$193$	13.5617	−	13.5617i	0.976194	−	0.976194i	0.999723	+	0.0235293i	$0.00749029\pi$
$194$	−32.3459			−2.32230
$195$		0			0
$196$	31.7789	+	13.4573i	2.26992	+	0.961236i
$197$	11.4791	+	11.4791i	0.817853	+	0.817853i	0.985797	−	0.167943i	$-0.0537126\pi$
$197$	11.4791	+	11.4791i	0.817853	+	0.817853i	−0.167943	+	0.985797i	$0.553713\pi$
$198$		0			0
$199$	20.1468			1.42817			0.714084	−	0.700061i	$-0.246844\pi$
$199$	20.1468			1.42817			0.714084	+	0.700061i	$0.246844\pi$
$200$	29.6788	+	24.6304i	2.09861	+	1.74163i
$201$		0			0
$202$	28.5587	−	28.5587i	2.00938	−	2.00938i
$203$	7.57754	+	11.4378i	0.531839	+	0.802775i
$204$		0			0
$205$	−1.27252	−	1.15972i	−0.0888767	−	0.0809981i
$206$			30.9292i			2.15494i
$207$		0			0
$208$	−9.27431	−	9.27431i	−0.643057	−	0.643057i
$209$	−5.79246			−0.400673
$210$		0			0
$211$	11.9662			0.823785			0.411892	−	0.911233i	$-0.364868\pi$
$211$	11.9662			0.823785			0.411892	+	0.911233i	$0.364868\pi$
$212$	2.68420	+	2.68420i	0.184352	+	0.184352i
$213$		0			0
$214$		−	16.3445i		−	1.11729i
$215$	0.759730	+	16.3811i	0.0518132	+	1.11718i
$216$		0			0
$217$	8.91857	+	13.4620i	0.605432	+	0.913858i
$218$	−13.8602	+	13.8602i	−0.938734	+	0.938734i
$219$		0			0
$220$	11.9188	+	10.8622i	0.803564	+	0.732332i
$221$	3.73985			0.251570
$222$		0			0
$223$	−0.660910	−	0.660910i	−0.0442578	−	0.0442578i	0.684632	−	0.728889i	$-0.259963\pi$
$223$	−0.660910	−	0.660910i	−0.0442578	−	0.0442578i	−0.728889	+	0.684632i	$0.759963\pi$
$224$	31.3003	+	6.35418i	2.09134	+	0.424557i
$225$		0			0
$226$	−9.47282			−0.630123
$227$	17.3487	−	17.3487i	1.15147	−	1.15147i	0.165216	−	0.986257i	$-0.447168\pi$
$227$	17.3487	−	17.3487i	1.15147	−	1.15147i	0.986257	−	0.165216i	$-0.0528323\pi$
$228$		0			0
$229$	−25.0782			−1.65721			−0.828607	−	0.559831i	$-0.810866\pi$
$229$	−25.0782			−1.65721			−0.828607	+	0.559831i	$0.810866\pi$
$230$	23.1592	−	25.4118i	1.52707	−	1.67560i
$231$		0			0
$232$	28.2847	+	28.2847i	1.85698	+	1.85698i
$233$	−2.24138	+	2.24138i	−0.146837	+	0.146837i	−0.776704	−	0.629866i	$-0.783110\pi$
$233$	−2.24138	+	2.24138i	−0.146837	+	0.146837i	0.629866	+	0.776704i	$0.283110\pi$
$234$		0			0
$235$	1.25560	+	27.0729i	0.0819064	+	1.76604i
$236$			15.7583i			1.02578i
$237$		0			0
$238$	−17.2944	+	11.4576i	−1.12103	+	0.742684i
$239$			21.3769i			1.38276i	0.722492	+	0.691380i	$0.242997\pi$
$239$			21.3769i			1.38276i	−0.722492	+	0.691380i	$0.757003\pi$
$240$		0			0
$241$		−	0.624129i		−	0.0402037i	−0.999798	−	0.0201018i	$-0.993601\pi$
$241$		−	0.624129i		−	0.0402037i	0.999798	−	0.0201018i	$-0.00639905\pi$
$242$	−16.4931	−	16.4931i	−1.06021	−	1.06021i
$243$		0			0
$244$	−7.00393			−0.448381
$245$	−6.54174	−	14.2199i	−0.417937	−	0.908476i
$246$		0			0
$247$	−3.51575	−	3.51575i	−0.223702	−	0.223702i
$248$	33.2903	+	33.2903i	2.11394	+	2.11394i
$249$		0			0
$250$	−4.07899	−	29.1484i	−0.257978	−	1.84350i
$251$		−	16.3443i		−	1.03164i	−0.856696	−	0.515822i	$-0.827487\pi$
$251$		−	16.3443i		−	1.03164i	0.856696	−	0.515822i	$-0.172513\pi$
$252$		0			0
$253$	6.04143	−	6.04143i	0.379821	−	0.379821i
$254$			29.2632i			1.83614i
$255$		0			0
$256$	−9.88265			−0.617666
$257$	−21.3054	+	21.3054i	−1.32900	+	1.32900i	−0.422749	+	0.906247i	$0.638935\pi$
$257$	−21.3054	+	21.3054i	−1.32900	+	1.32900i	−0.906247	+	0.422749i	$0.861065\pi$
$258$		0			0
$259$	−8.27098	−	1.67907i	−0.513933	−	0.104332i
$260$	0.641275	+	13.8270i	0.0397702	+	0.857514i
$261$		0			0
$262$	11.5079	−	11.5079i	0.710960	−	0.710960i
$263$	16.3449	−	16.3449i	1.00787	−	1.00787i	0.00789784	−	0.999969i	$-0.497486\pi$
$263$	16.3449	−	16.3449i	1.00787	−	1.00787i	0.999969	−	0.00789784i	$-0.00251399\pi$
$264$		0			0
$265$	−0.0797641	−	1.71985i	−0.00489987	−	0.105650i
$266$	27.0291	+	5.48709i	1.65726	+	0.336435i
$267$		0			0
$268$	29.2362	−	29.2362i	1.78589	−	1.78589i
$269$	16.5903			1.01153			0.505764	−	0.862672i	$-0.331211\pi$
$269$	16.5903			1.01153			0.505764	+	0.862672i	$0.331211\pi$
$270$		0			0
$271$			7.78033i			0.472621i	0.971678	+	0.236311i	$0.0759383\pi$
$271$			7.78033i			0.472621i	−0.971678	+	0.236311i	$0.924062\pi$
$272$	−22.0005	+	22.0005i	−1.33398	+	1.33398i
$273$		0			0
$274$		−	33.7136i		−	2.03671i
$275$	−0.676964	−	7.28255i	−0.0408224	−	0.439154i
$276$		0			0
$277$	21.3107	+	21.3107i	1.28043	+	1.28043i	0.940421	+	0.340013i	$0.110431\pi$
$277$	21.3107	+	21.3107i	1.28043	+	1.28043i	0.340013	+	0.940421i	$0.389569\pi$
$278$	−22.3214	−	22.3214i	−1.33875	−	1.33875i
$279$		0			0
$280$	−26.9389	−	36.8344i	−1.60991	−	2.20128i
$281$	21.1519			1.26182			0.630908	−	0.775858i	$-0.282683\pi$
$281$	21.1519			1.26182			0.630908	+	0.775858i	$0.282683\pi$
$282$		0			0
$283$	2.65471	+	2.65471i	0.157806	+	0.157806i	0.781594	−	0.623788i	$-0.214407\pi$
$283$	2.65471	+	2.65471i	0.157806	+	0.157806i	−0.623788	+	0.781594i	$0.714407\pi$
$284$		−	37.5977i		−	2.23101i
$285$		0			0
$286$			4.83508i			0.285905i
$287$	1.12510	+	1.69826i	0.0664126	+	0.100245i
$288$		0			0
$289$			8.12832i			0.478136i
$290$	−1.41421	−	30.4929i	−0.0830455	−	1.79060i
$291$		0			0
$292$	−33.5928	+	33.5928i	−1.96587	+	1.96587i
$293$	1.56714	+	1.56714i	0.0915536	+	0.0915536i	0.751400	−	0.659847i	$-0.229379\pi$
$293$	1.56714	+	1.56714i	0.0915536	+	0.0915536i	−0.659847	+	0.751400i	$0.729379\pi$
$294$		0			0
$295$	4.81428	−	5.28255i	0.280298	−	0.307562i
$296$	−24.6056			−1.43017
$297$		0			0
$298$	−0.180239	+	0.180239i	−0.0104409	+	0.0104409i
$299$	7.33372			0.424120
$300$		0			0
$301$	3.86025	−	19.0153i	0.222501	−	1.09603i
$302$	−25.0460	−	25.0460i	−1.44123	−	1.44123i
$303$		0			0
$304$	41.3643			2.37240
$305$	2.34788	+	2.13975i	0.134439	+	0.122522i
$306$		0			0
$307$	−17.3551	+	17.3551i	−0.990510	+	0.990510i	−0.999955	−	0.00944588i	$-0.996993\pi$
$307$	−17.3551	+	17.3551i	−0.990510	+	0.990510i	0.00944588	+	0.999955i	$0.496993\pi$
$308$	−10.5380	−	15.9064i	−0.600459	−	0.906352i
$309$		0			0
$310$	−1.66449	−	35.8893i	−0.0945368	−	2.03838i
$311$		−	31.0648i		−	1.76153i	−0.473558	−	0.880763i	$-0.657030\pi$
$311$		−	31.0648i		−	1.76153i	0.473558	−	0.880763i	$-0.342970\pi$
$312$		0			0
$313$	5.72426	+	5.72426i	0.323554	+	0.323554i	0.850129	−	0.526575i	$-0.176524\pi$
$313$	5.72426	+	5.72426i	0.323554	+	0.323554i	−0.526575	+	0.850129i	$0.676524\pi$
$314$	6.13381			0.346151
$315$		0			0
$316$	−22.2856			−1.25366
$317$	−0.752579	−	0.752579i	−0.0422691	−	0.0422691i	0.685656	−	0.727925i	$-0.259515\pi$
$317$	−0.752579	−	0.752579i	−0.0422691	−	0.0422691i	−0.727925	+	0.685656i	$0.759515\pi$
$318$		0			0
$319$		−	7.58562i		−	0.424713i
$320$	−17.9932	−	16.3982i	−1.00585	−	0.916686i
$321$		0			0
$322$	−33.9138	+	22.4679i	−1.88994	+	1.25209i
$323$	−8.34005	+	8.34005i	−0.464053	+	0.464053i
$324$		0			0
$325$	4.00928	−	4.83105i	0.222395	−	0.267978i
$326$	−38.2518			−2.11857
$327$		0			0
$328$	4.19966	+	4.19966i	0.231887	+	0.231887i
$329$	6.37980	−	31.4265i	0.351730	−	1.73260i
$330$		0			0
$331$	15.8082			0.868899			0.434449	−	0.900696i	$-0.356943\pi$
$331$	15.8082			0.868899			0.434449	+	0.900696i	$0.356943\pi$
$332$	−33.3175	+	33.3175i	−1.82853	+	1.82853i
$333$		0			0
$334$	−1.09085			−0.0596887
$335$	−18.7326	+	0.868788i	−1.02347	+	0.0474670i
$336$		0			0
$337$	−20.0460	−	20.0460i	−1.09197	−	1.09197i	−0.995318	−	0.0966558i	$-0.969185\pi$
$337$	−20.0460	−	20.0460i	−1.09197	−	1.09197i	−0.0966558	−	0.995318i	$-0.530815\pi$
$338$	21.2644	−	21.2644i	1.15663	−	1.15663i
$339$		0			0
$340$	32.8004	−	1.52123i	1.77885	−	0.0825005i
$341$		−	8.92808i		−	0.483482i
$342$		0			0
$343$	3.39840	+	18.2058i	0.183497	+	0.983020i
$344$		−	56.5693i		−	3.05001i
$345$		0			0
$346$			12.8512i			0.690883i
$347$	20.0847	+	20.0847i	1.07820	+	1.07820i	0.996671	+	0.0815328i	$0.0259815\pi$
$347$	20.0847	+	20.0847i	1.07820	+	1.07820i	0.0815328	+	0.996671i	$0.474018\pi$
$348$		0			0
$349$	14.7663			0.790420			0.395210	−	0.918591i	$-0.370672\pi$
$349$	14.7663			0.790420			0.395210	+	0.918591i	$0.370672\pi$
$350$	−3.73975	+	34.6235i	−0.199898	+	1.85070i
$351$		0			0
$352$	−12.4864	−	12.4864i	−0.665525	−	0.665525i
$353$	12.4890	+	12.4890i	0.664724	+	0.664724i	0.956490	−	0.291766i	$-0.0942429\pi$
$353$	12.4890	+	12.4890i	0.664724	+	0.664724i	−0.291766	+	0.956490i	$0.594243\pi$
$354$		0			0
$355$	−11.4864	+	12.6036i	−0.609633	+	0.668931i
$356$		−	5.91570i		−	0.313531i
$357$		0			0
$358$	−3.71839	+	3.71839i	−0.196523	+	0.196523i
$359$			10.5372i			0.556133i	0.960562	+	0.278066i	$0.0896935\pi$
$359$			10.5372i			0.556133i	−0.960562	+	0.278066i	$0.910306\pi$
$360$		0			0
$361$	−3.31943			−0.174707
$362$	15.7951	−	15.7951i	0.830171	−	0.830171i
$363$		0			0
$364$	3.25837	−	16.0505i	0.170785	−	0.841276i
$365$	21.5239	−	0.998247i	1.12661	−	0.0522507i
$366$		0			0
$367$	11.1910	−	11.1910i	0.584163	−	0.584163i	−0.351881	−	0.936045i	$-0.614458\pi$
$367$	11.1910	−	11.1910i	0.584163	−	0.584163i	0.936045	+	0.351881i	$0.114458\pi$
$368$	−43.1422	+	43.1422i	−2.24894	+	2.24894i
$369$		0			0
$370$	13.8784	+	12.6482i	0.721505	+	0.657546i
$371$	−0.405287	+	1.99642i	−0.0210415	+	0.103649i
$372$		0			0
$373$	17.2746	−	17.2746i	0.894446	−	0.894446i	−0.100492	−	0.994938i	$-0.532042\pi$
$373$	17.2746	−	17.2746i	0.894446	−	0.894446i	0.994938	+	0.100492i	$0.0320416\pi$
$374$	11.4698			0.593088
$375$		0			0
$376$		−	93.4917i		−	4.82147i
$377$	4.60412	−	4.60412i	0.237124	−	0.237124i
$378$		0			0
$379$			17.6237i			0.905267i	0.891697	+	0.452634i	$0.149515\pi$
$379$			17.6237i			0.905267i	−0.891697	+	0.452634i	$0.850485\pi$
$380$	−32.2649	−	29.4048i	−1.65516	−	1.50843i
$381$		0			0
$382$	14.5832	+	14.5832i	0.746141	+	0.746141i
$383$	−16.1249	−	16.1249i	−0.823942	−	0.823942i	0.162729	−	0.986671i	$-0.447970\pi$
$383$	−16.1249	−	16.1249i	−0.823942	−	0.823942i	−0.986671	+	0.162729i	$0.947970\pi$
$384$		0			0
$385$	−1.32694	+	8.55164i	−0.0676270	+	0.435832i
$386$	50.4894			2.56984
$387$		0			0
$388$	−42.8343	−	42.8343i	−2.17458	−	2.17458i
$389$		−	15.4011i		−	0.780865i	−0.920632	−	0.390432i	$-0.872326\pi$
$389$		−	15.4011i		−	0.780865i	0.920632	−	0.390432i	$-0.127674\pi$
$390$		0			0
$391$		−	17.3971i		−	0.879807i
$392$	20.2697	+	50.0461i	1.02378	+	2.52771i
$393$		0			0
$394$			42.7360i			2.15301i
$395$	7.47066	+	6.80841i	0.375889	+	0.342568i
$396$		0			0
$397$	16.1781	−	16.1781i	0.811955	−	0.811955i	−0.172972	−	0.984927i	$-0.555337\pi$
$397$	16.1781	−	16.1781i	0.811955	−	0.811955i	0.984927	+	0.172972i	$0.0553370\pi$
$398$	37.5026	+	37.5026i	1.87983	+	1.87983i
$399$		0			0
$400$	4.83424	+	52.0051i	0.241712	+	2.60026i
$401$	0.977595			0.0488188			0.0244094	−	0.999702i	$-0.492229\pi$
$401$	0.977595			0.0488188			0.0244094	+	0.999702i	$0.492229\pi$
$402$		0			0
$403$	5.41892	−	5.41892i	0.269936	−	0.269936i
$404$	75.6382			3.76314
$405$		0			0
$406$	−7.18572	+	35.3964i	−0.356622	+	1.75670i
$407$	3.29947	+	3.29947i	0.163549	+	0.163549i
$408$		0			0
$409$	24.3171			1.20241			0.601203	−	0.799097i	$-0.294688\pi$
$409$	24.3171			1.20241			0.601203	+	0.799097i	$0.294688\pi$
$410$	−0.209980	−	4.52753i	−0.0103702	−	0.223599i
$411$		0			0
$412$	−40.9583	+	40.9583i	−2.01787	+	2.01787i
$413$	−7.04992	+	4.67058i	−0.346904	+	0.229824i
$414$		0			0
$415$	21.3475	−	0.990067i	1.04791	−	0.0486005i
$416$		−	15.1573i		−	0.743146i
$417$		0			0
$418$	−10.7825	−	10.7825i	−0.527388	−	0.527388i
$419$	−15.9893			−0.781127			−0.390563	−	0.920576i	$-0.627720\pi$
$419$	−15.9893			−0.781127			−0.390563	+	0.920576i	$0.627720\pi$
$420$		0			0
$421$	14.7000			0.716433			0.358216	−	0.933639i	$-0.383385\pi$
$421$	14.7000			0.716433			0.358216	+	0.933639i	$0.383385\pi$
$422$	22.2746	+	22.2746i	1.08431	+	1.08431i
$423$		0			0
$424$			5.93921i			0.288434i
$425$	−11.4602	−	9.51081i	−0.555902	−	0.461342i
$426$		0			0
$427$	−2.07588	−	3.13341i	−0.100459	−	0.151636i
$428$	21.6443	−	21.6443i	1.04622	−	1.04622i
$429$		0			0
$430$	−29.0787	+	31.9071i	−1.40230	+	1.53870i
$431$	−22.2722			−1.07281			−0.536407	−	0.843960i	$-0.680219\pi$
$431$	−22.2722			−1.07281			−0.536407	+	0.843960i	$0.680219\pi$
$432$		0			0
$433$	−28.0171	−	28.0171i	−1.34642	−	1.34642i	−0.889520	−	0.456896i	$-0.848961\pi$
$433$	−28.0171	−	28.0171i	−1.34642	−	1.34642i	−0.456896	−	0.889520i	$-0.651039\pi$
$434$	−8.45741	+	41.6606i	−0.405968	+	1.99978i
$435$		0			0
$436$	−36.7091			−1.75805
$437$	−16.3545	+	16.3545i	−0.782344	+	0.782344i
$438$		0			0
$439$	−2.35656			−0.112473			−0.0562363	−	0.998417i	$-0.517910\pi$
$439$	−2.35656			−0.112473			−0.0562363	+	0.998417i	$0.517910\pi$
$440$	1.16889	+	25.2033i	0.0557246	+	1.20152i
$441$		0			0
$442$	6.96162	+	6.96162i	0.331130	+	0.331130i
$443$	5.47247	−	5.47247i	0.260005	−	0.260005i	−0.565051	−	0.825056i	$-0.691144\pi$
$443$	5.47247	−	5.47247i	0.260005	−	0.260005i	0.825056	+	0.565051i	$0.191144\pi$
$444$		0			0
$445$	−1.80729	+	1.98308i	−0.0856737	+	0.0940071i
$446$		−	2.46053i		−	0.116509i
$447$		0			0
$448$	15.9087	+	24.0131i	0.751616	+	1.13451i
$449$			1.20020i			0.0566410i	0.999599	+	0.0283205i	$0.00901591\pi$
$449$			1.20020i			0.0566410i	−0.999599	+	0.0283205i	$0.990984\pi$
$450$		0			0
$451$		−	1.12630i		−	0.0530354i
$452$	−12.5444	−	12.5444i	−0.590041	−	0.590041i
$453$		0			0
$454$	64.5881			3.03127
$455$	−5.99583	+	4.38505i	−0.281089	+	0.205575i
$456$		0			0
$457$	−21.0775	−	21.0775i	−0.985962	−	0.985962i	0.0139406	−	0.999903i	$-0.495562\pi$
$457$	−21.0775	−	21.0775i	−0.985962	−	0.985962i	−0.999903	+	0.0139406i	$0.995562\pi$
$458$	−46.6823	−	46.6823i	−2.18132	−	2.18132i
$459$		0			0
$460$	64.3204	−	2.98308i	2.99896	−	0.139087i
$461$			21.9670i			1.02311i	0.859252	+	0.511553i	$0.170929\pi$
$461$			21.9670i			1.02311i	−0.859252	+	0.511553i	$0.829071\pi$
$462$		0			0
$463$	−21.6776	+	21.6776i	−1.00744	+	1.00744i	−0.00746987	+	0.999972i	$0.502378\pi$
$463$	−21.6776	+	21.6776i	−1.00744	+	1.00744i	−0.999972	+	0.00746987i	$0.997622\pi$
$464$			54.1694i			2.51475i
$465$		0			0
$466$	−8.34450			−0.386551
$467$	−7.11299	+	7.11299i	−0.329150	+	0.329150i	−0.852263	−	0.523113i	$-0.824770\pi$
$467$	−7.11299	+	7.11299i	−0.329150	+	0.329150i	0.523113	+	0.852263i	$0.324770\pi$
$468$		0			0
$469$	21.7449	+	4.41438i	1.00409	+	0.203837i
$470$	−48.0581	+	52.7326i	−2.21676	+	2.43237i
$471$		0			0
$472$	−17.4338	+	17.4338i	−0.802457	+	0.802457i
$473$	−7.58562	+	7.58562i	−0.348787	+	0.348787i
$474$		0			0
$475$	1.83259	+	19.7144i	0.0840848	+	0.904557i
$476$	−38.0750	−	7.72950i	−1.74517	−	0.354281i
$477$		0			0
$478$	−39.7925	+	39.7925i	−1.82007	+	1.82007i
$479$	−31.7749			−1.45183			−0.725917	−	0.687782i	$-0.758584\pi$
$479$	−31.7749			−1.45183			−0.725917	+	0.687782i	$0.758584\pi$
$480$		0			0
$481$			4.00524i			0.182623i
$482$	1.16180	−	1.16180i	0.0529184	−	0.0529184i
$483$		0			0
$484$		−	43.6821i		−	1.98555i
$485$	1.27287	+	27.4453i	0.0577981	+	1.24623i
$486$		0			0
$487$	−4.81428	−	4.81428i	−0.218156	−	0.218156i	0.589565	−	0.807721i	$-0.299299\pi$
$487$	−4.81428	−	4.81428i	−0.218156	−	0.218156i	−0.807721	+	0.589565i	$0.799299\pi$
$488$	−7.74864	−	7.74864i	−0.350765	−	0.350765i
$489$		0			0
$490$	14.2926	−	38.6471i	0.645676	−	1.74590i
$491$	−28.3401			−1.27897			−0.639484	−	0.768804i	$-0.720852\pi$
$491$	−28.3401			−1.27897			−0.639484	+	0.768804i	$0.720852\pi$
$492$		0			0
$493$	−10.9219	−	10.9219i	−0.491897	−	0.491897i
$494$		−	13.0889i		−	0.588897i
$495$		0			0
$496$			63.7559i			2.86273i
$497$	16.8204	−	11.1435i	0.754497	−	0.499855i
$498$		0			0
$499$			3.39197i			0.151845i	0.997114	+	0.0759227i	$0.0241902\pi$
$499$			3.39197i			0.151845i	−0.997114	+	0.0759227i	$0.975810\pi$
$500$	33.1983	−	44.0016i	1.48467	−	1.96781i
$501$		0			0
$502$	30.4244	−	30.4244i	1.35791	−	1.35791i
$503$	8.32921	+	8.32921i	0.371381	+	0.371381i	0.867980	−	0.496599i	$-0.165418\pi$
$503$	8.32921	+	8.32921i	0.371381	+	0.371381i	−0.496599	+	0.867980i	$0.665418\pi$
$504$		0			0
$505$	−25.3557	−	23.1080i	−1.12831	−	1.02829i
$506$	22.4918			0.999884
$507$		0			0
$508$	−38.7520	+	38.7520i	−1.71934	+	1.71934i
$509$	38.9452			1.72622			0.863108	−	0.505020i	$-0.168515\pi$
$509$	38.9452			1.72622			0.863108	+	0.505020i	$0.168515\pi$
$510$		0			0
$511$	−24.9852	−	5.07217i	−1.10528	−	0.224380i
$512$	−24.7846	−	24.7846i	−1.09534	−	1.09534i
$513$		0			0
$514$	−79.3187			−3.49860
$515$	26.2432	−	1.21712i	1.15641	−	0.0536328i
$516$		0			0
$517$	−12.5367	+	12.5367i	−0.551364	+	0.551364i
$518$	−12.2706	−	18.5217i	−0.539140	−	0.813796i
$519$		0			0
$520$	−14.5877	+	16.0066i	−0.639714	+	0.701938i
$521$			7.06726i			0.309622i	0.987944	+	0.154811i	$0.0494769\pi$
$521$			7.06726i			0.309622i	−0.987944	+	0.154811i	$0.950523\pi$
$522$		0			0
$523$	14.5887	+	14.5887i	0.637921	+	0.637921i	0.950042	−	0.312121i	$-0.101040\pi$
$523$	14.5887	+	14.5887i	0.637921	+	0.637921i	−0.312121	+	0.950042i	$0.601040\pi$
$524$	30.4788			1.33147
$525$		0			0
$526$	60.8508			2.65322
$527$	−12.8548	−	12.8548i	−0.559962	−	0.559962i
$528$		0			0
$529$		−	11.1150i		−	0.483261i
$530$	3.05297	−	3.34993i	0.132613	−	0.145511i
$531$		0			0
$532$	28.5271	+	43.0597i	1.23681	+	1.86688i
$533$	0.683611	−	0.683611i	0.0296105	−	0.0296105i
$534$		0			0
$535$	−13.8682	+	0.643185i	−0.599574	+	0.0278073i
$536$	64.6897			2.79417
$537$		0			0
$538$	30.8823	+	30.8823i	1.33143	+	1.33143i
$539$	3.99284	−	9.42895i	0.171984	−	0.406134i
$540$		0			0
$541$	18.6013			0.799731			0.399865	−	0.916574i	$-0.369057\pi$
$541$	18.6013			0.799731			0.399865	+	0.916574i	$0.369057\pi$
$542$	−14.4828	+	14.4828i	−0.622091	+	0.622091i
$543$		0			0
$544$	−35.9560			−1.54160
$545$	12.3057	+	11.2149i	0.527120	+	0.480393i
$546$		0			0
$547$	−7.22715	−	7.22715i	−0.309011	−	0.309011i	0.535515	−	0.844526i	$-0.320118\pi$
$547$	−7.22715	−	7.22715i	−0.309011	−	0.309011i	−0.844526	+	0.535515i	$0.820118\pi$
$548$	44.6455	−	44.6455i	1.90716	−	1.90716i
$549$		0			0
$550$	12.2961	−	14.8164i	0.524307	−	0.631772i
$551$			20.5348i			0.874812i
$552$		0			0
$553$	−6.60519	−	9.97009i	−0.280881	−	0.423971i
$554$			79.3382i			3.37076i
$555$		0			0
$556$		−	59.1185i		−	2.50718i
$557$	0.558927	+	0.558927i	0.0236825	+	0.0236825i	0.718849	−	0.695166i	$-0.244669\pi$
$557$	0.558927	+	0.558927i	0.0236825	+	0.0236825i	−0.695166	+	0.718849i	$0.744669\pi$
$558$		0			0
$559$	−9.20823			−0.389467
$560$	9.47575	−	61.0678i	0.400423	−	2.58059i
$561$		0			0
$562$	39.3736	+	39.3736i	1.66087	+	1.66087i
$563$	−0.702475	−	0.702475i	−0.0296058	−	0.0296058i	0.692149	−	0.721755i	$-0.256664\pi$
$563$	−0.702475	−	0.702475i	−0.0296058	−	0.0296058i	−0.721755	+	0.692149i	$0.756664\pi$
$564$		0			0
$565$	0.372772	+	8.03762i	0.0156827	+	0.338145i
$566$			9.88333i			0.415427i
$567$		0			0
$568$	41.5953	−	41.5953i	1.74530	−	1.74530i
$569$		−	9.72049i		−	0.407504i	−0.979023	−	0.203752i	$-0.934686\pi$
$569$		−	9.72049i		−	0.407504i	0.979023	−	0.203752i	$-0.0653137\pi$
$570$		0			0
$571$	−0.986684			−0.0412914			−0.0206457	−	0.999787i	$-0.506572\pi$
$571$	−0.986684			−0.0412914			−0.0206457	+	0.999787i	$0.506572\pi$
$572$	−6.40289	+	6.40289i	−0.267718	+	0.267718i
$573$		0			0
$574$	−1.06692	+	5.25560i	−0.0445326	+	0.219365i
$575$	−22.4731	−	18.6504i	−0.937192	−	0.777774i
$576$		0			0
$577$	−10.3510	+	10.3510i	−0.430917	+	0.430917i	−0.888940	−	0.458024i	$-0.848558\pi$
$577$	−10.3510	+	10.3510i	−0.430917	+	0.430917i	0.458024	+	0.888940i	$0.348558\pi$
$578$	−15.1306	+	15.1306i	−0.629350	+	0.629350i
$579$		0			0
$580$	38.5076	−	42.2532i	1.59894	−	1.75447i
$581$	−24.7804	−	5.03060i	−1.02807	−	0.208705i
$582$		0			0
$583$	0.796415	−	0.796415i	0.0329841	−	0.0329841i
$584$	−74.3292			−3.07576
$585$		0			0
$586$			5.83438i			0.241016i
$587$	21.1413	−	21.1413i	0.872594	−	0.872594i	−0.120160	−	0.992755i	$-0.538341\pi$
$587$	21.1413	−	21.1413i	0.872594	−	0.872594i	0.992755	+	0.120160i	$0.0383409\pi$
$588$		0			0
$589$			24.1689i			0.995862i
$590$	18.7949	−	0.871680i	0.773774	−	0.0358865i
$591$		0			0
$592$	−23.5617	−	23.5617i	−0.968381	−	0.968381i
$593$	−7.07816	−	7.07816i	−0.290665	−	0.290665i	0.546678	−	0.837343i	$-0.315892\pi$
$593$	−7.07816	−	7.07816i	−0.290665	−	0.290665i	−0.837343	+	0.546678i	$0.815892\pi$
$594$		0			0
$595$	10.4022	+	14.2233i	0.426450	+	0.583099i
$596$	−0.477365			−0.0195536
$597$		0			0
$598$	13.6515	+	13.6515i	0.558251	+	0.558251i
$599$			7.13847i			0.291670i	0.989309	+	0.145835i	$0.0465869\pi$
$599$			7.13847i			0.291670i	−0.989309	+	0.145835i	$0.953413\pi$
$600$		0			0
$601$			35.0829i			1.43106i	0.698580	+	0.715532i	$0.253815\pi$
$601$			35.0829i			1.43106i	−0.698580	+	0.715532i	$0.746185\pi$
$602$	42.5822	−	28.2107i	1.73552	−	1.14978i
$603$		0			0
$604$		−	66.3346i		−	2.69912i
$605$	−13.3452	+	14.6433i	−0.542560	+	0.595334i
$606$		0			0
$607$	−5.36385	+	5.36385i	−0.217712	+	0.217712i	−0.807533	−	0.589822i	$-0.799198\pi$
$607$	−5.36385	+	5.36385i	−0.217712	+	0.217712i	0.589822	+	0.807533i	$0.299198\pi$
$608$	33.8014	+	33.8014i	1.37083	+	1.37083i
$609$		0			0
$610$	0.387427	+	8.35359i	0.0156865	+	0.338227i
$611$	−15.2184			−0.615670
$612$		0			0
$613$	−10.4888	+	10.4888i	−0.423639	+	0.423639i	−0.886454	−	0.462816i	$-0.846839\pi$
$613$	−10.4888	+	10.4888i	−0.423639	+	0.423639i	0.462816	+	0.886454i	$0.346839\pi$
$614$	−64.6120			−2.60753
$615$		0			0
$616$	5.93921	−	29.2562i	0.239298	−	1.17877i
$617$	−19.7986	−	19.7986i	−0.797060	−	0.797060i	0.185571	−	0.982631i	$-0.440586\pi$
$617$	−19.7986	−	19.7986i	−0.797060	−	0.797060i	−0.982631	+	0.185571i	$0.940586\pi$
$618$		0			0
$619$	−12.0675			−0.485034			−0.242517	−	0.970147i	$-0.577973\pi$
$619$	−12.0675			−0.485034			−0.242517	+	0.970147i	$0.577973\pi$
$620$	45.3224	−	49.7309i	1.82019	−	1.99724i
$621$		0			0
$622$	57.8262	−	57.8262i	2.31862	−	2.31862i
$623$	2.64655	−	1.75334i	0.106032	−	0.0702462i
$624$		0			0
$625$	−24.5717	+	4.60803i	−0.982866	+	0.184321i
$626$			21.3110i			0.851761i
$627$		0			0
$628$	8.12275	+	8.12275i	0.324133	+	0.324133i
$629$	9.50124			0.378839
$630$		0			0
$631$	30.4435			1.21194			0.605969	−	0.795488i	$-0.292786\pi$
$631$	30.4435			1.21194			0.605969	+	0.795488i	$0.292786\pi$
$632$	−24.6552	−	24.6552i	−0.980730	−	0.980730i
$633$		0			0
$634$		−	2.80180i		−	0.111274i
$635$	24.8296	−	1.15156i	0.985332	−	0.0456982i
$636$		0			0
$637$	8.14639	−	3.29946i	0.322772	−	0.130729i
$638$	14.1204	−	14.1204i	0.559032	−	0.559032i
$639$		0			0
$640$	−0.467961	−	10.0901i	−0.0184978	−	0.398844i
$641$	−36.5929			−1.44533			−0.722666	−	0.691198i	$-0.757083\pi$
$641$	−36.5929			−1.44533			−0.722666	+	0.691198i	$0.757083\pi$
$642$		0			0
$643$	−12.1140	−	12.1140i	−0.477731	−	0.477731i	0.426675	−	0.904405i	$-0.359685\pi$
$643$	−12.1140	−	12.1140i	−0.477731	−	0.477731i	−0.904405	+	0.426675i	$0.859685\pi$
$644$	−74.6638	−	15.1573i	−2.94217	−	0.597280i
$645$		0			0
$646$	−31.0495			−1.22163
$647$	19.0978	−	19.0978i	0.750814	−	0.750814i	−0.223817	−	0.974631i	$-0.571852\pi$
$647$	19.0978	−	19.0978i	0.750814	−	0.750814i	0.974631	+	0.223817i	$0.0718519\pi$
$648$		0			0
$649$	4.67556			0.183532
$650$	16.4560	−	1.52970i	0.645457	−	0.0599997i
$651$		0			0
$652$	−50.6552	−	50.6552i	−1.98381	−	1.98381i
$653$	−20.3709	+	20.3709i	−0.797173	+	0.797173i	−0.982649	−	0.185476i	$-0.940617\pi$
$653$	−20.3709	+	20.3709i	−0.797173	+	0.797173i	0.185476	+	0.982649i	$0.440617\pi$
$654$		0			0
$655$	−10.2172	−	9.31151i	−0.399220	−	0.363831i
$656$			8.04298i			0.314026i
$657$		0			0
$658$	70.3752	−	46.6236i	2.74351	−	1.81758i
$659$		−	31.4882i		−	1.22661i	−0.789847	−	0.613304i	$-0.789840\pi$
$659$		−	31.4882i		−	1.22661i	0.789847	−	0.613304i	$-0.210160\pi$
$660$		0			0
$661$			48.1880i			1.87430i	0.348931	+	0.937149i	$0.386545\pi$
$661$			48.1880i			1.87430i	−0.348931	+	0.937149i	$0.613455\pi$
$662$	29.4265	+	29.4265i	1.14369	+	1.14369i
$663$		0			0
$664$	−73.7201			−2.86089
$665$	3.59211	−	23.1499i	0.139296	−	0.897714i
$666$		0			0
$667$	−21.4174	−	21.4174i	−0.829286	−	0.829286i
$668$	−1.44457	−	1.44457i	−0.0558920	−	0.0558920i
$669$		0			0
$670$	−36.4873	−	33.2528i	−1.40963	−	1.28467i
$671$			2.07810i			0.0802241i
$672$		0			0
$673$	−30.6900	+	30.6900i	−1.18301	+	1.18301i	−0.204055	+	0.978960i	$0.565412\pi$
$673$	−30.6900	+	30.6900i	−1.18301	+	1.18301i	−0.978960	+	0.204055i	$0.934588\pi$
$674$		−	74.6299i		−	2.87463i
$675$		0			0
$676$	56.3191			2.16612
$677$	1.54060	−	1.54060i	0.0592101	−	0.0592101i	−0.676882	−	0.736092i	$-0.736669\pi$
$677$	1.54060	−	1.54060i	0.0592101	−	0.0592101i	0.736092	+	0.676882i	$0.236669\pi$
$678$		0			0
$679$	6.46755	−	31.8587i	0.248202	−	1.22263i
$680$	37.9710	+	34.6050i	1.45612	+	1.32704i
$681$		0			0
$682$	16.6193	−	16.6193i	0.636387	−	0.636387i
$683$	−14.2154	+	14.2154i	−0.543936	+	0.543936i	−0.924680	−	0.380744i	$-0.875668\pi$
$683$	−14.2154	+	14.2154i	−0.543936	+	0.543936i	0.380744	+	0.924680i	$0.375668\pi$
$684$		0			0
$685$	−28.6057	+	1.32669i	−1.09297	+	0.0506903i
$686$	−27.5635	+	40.2155i	−1.05238	+	1.53544i
$687$		0			0
$688$	54.1694	−	54.1694i	2.06519	−	2.06519i
$689$	0.966772			0.0368311
$690$		0			0
$691$		−	10.2887i		−	0.391401i	−0.980664	−	0.195700i	$-0.937302\pi$
$691$		−	10.2887i		−	0.391401i	0.980664	−	0.195700i	$-0.0626980\pi$
$692$	−17.0182	+	17.0182i	−0.646937	+	0.646937i
$693$		0			0
$694$			74.7741i			2.83838i
$695$	−18.0611	+	19.8179i	−0.685098	+	0.751736i
$696$		0			0
$697$	−1.62166	−	1.62166i	−0.0614248	−	0.0614248i
$698$	27.4869	+	27.4869i	1.04040	+	1.04040i
$699$		0			0
$700$	−50.8028	+	40.8980i	−1.92016	+	1.54580i
$701$	44.3183			1.67388			0.836939	−	0.547297i	$-0.184343\pi$
$701$	44.3183			1.67388			0.836939	+	0.547297i	$0.184343\pi$
$702$		0			0
$703$	−8.93189	−	8.93189i	−0.336872	−	0.336872i
$704$		−	15.9257i		−	0.600222i
$705$		0			0
$706$			46.4958i			1.74989i
$707$	22.4183	+	33.8389i	0.843126	+	1.27264i
$708$		0			0
$709$		−	0.817976i		−	0.0307197i	−0.999882	−	0.0153599i	$-0.995111\pi$
$709$		−	0.817976i		−	0.0307197i	0.999882	−	0.0153599i	$-0.00488939\pi$
$710$	−44.8427	+	2.07974i	−1.68292	+	0.0780512i
$711$		0			0
$712$	6.54470	−	6.54470i	0.245273	−	0.245273i
$713$	−25.2077	−	25.2077i	−0.944037	−	0.944037i
$714$		0			0
$715$	4.10253	−	0.190269i	0.153426	−	0.00711567i
$716$	−9.84821			−0.368045
$717$		0			0
$718$	−19.6147	+	19.6147i	−0.732013	+	0.732013i
$719$	−0.00762056			−0.000284199			−0.000142099	−	1.00000i	$-0.500045\pi$
$719$	−0.00762056			−0.000284199			−0.000142099		1.00000i	$0.500045\pi$
$720$		0			0
$721$	−30.4634	−	6.18428i	−1.13452	−	0.230315i
$722$	−6.17902	−	6.17902i	−0.229959	−	0.229959i
$723$		0			0
$724$	41.8335			1.55473
$725$	−25.8173	+	2.39990i	−0.958831	+	0.0891300i
$726$		0			0
$727$	28.5738	−	28.5738i	1.05974	−	1.05974i	0.0616465	−	0.998098i	$-0.480365\pi$
$727$	28.5738	−	28.5738i	1.05974	−	1.05974i	0.998098	−	0.0616465i	$-0.0196352\pi$
$728$	21.3619	−	14.1523i	0.791726	−	0.524519i
$729$		0			0
$730$	41.9243	+	38.2079i	1.55169	+	1.41414i
$731$			21.8438i			0.807921i
$732$		0			0
$733$	−24.1522	−	24.1522i	−0.892083	−	0.892083i	0.102636	−	0.994719i	$-0.467272\pi$
$733$	−24.1522	−	24.1522i	−0.892083	−	0.892083i	−0.994719	+	0.102636i	$0.967272\pi$
$734$	41.6632			1.53782
$735$		0			0
$736$	−70.5085			−2.59898
$737$	−8.67452	−	8.67452i	−0.319530	−	0.319530i
$738$		0			0
$739$		−	37.9522i		−	1.39609i	−0.716052	−	0.698047i	$-0.754053\pi$
$739$		−	37.9522i		−	1.39609i	0.716052	−	0.698047i	$-0.245947\pi$
$740$	1.62918	+	35.1280i	0.0598900	+	1.29133i
$741$		0			0
$742$	−4.47070	+	2.96184i	−0.164125	+	0.108733i
$743$	18.8022	−	18.8022i	0.689784	−	0.689784i	−0.272400	−	0.962184i	$-0.587817\pi$
$743$	18.8022	−	18.8022i	0.689784	−	0.689784i	0.962184	+	0.272400i	$0.0878174\pi$
$744$		0			0
$745$	0.160024	+	0.145838i	0.00586282	+	0.00534311i
$746$	64.3123			2.35464
$747$		0			0
$748$	15.1889	+	15.1889i	0.555363	+	0.555363i
$749$	16.0983	+	3.26807i	0.588220	+	0.119413i
$750$		0			0
$751$	0.105915			0.00386490			0.00193245	−	0.999998i	$-0.499385\pi$
$751$	0.105915			0.00386490			0.00193245	+	0.999998i	$0.499385\pi$
$752$	89.5254	−	89.5254i	3.26466	−	3.26466i
$753$		0			0
$754$	17.1408			0.624232
$755$	−20.2657	+	22.2369i	−0.737545	+	0.809284i
$756$		0			0
$757$	3.14514	+	3.14514i	0.114312	+	0.114312i	0.761949	−	0.647637i	$-0.224243\pi$
$757$	3.14514	+	3.14514i	0.114312	+	0.114312i	−0.647637	+	0.761949i	$0.724243\pi$
$758$	−32.8059	+	32.8059i	−1.19156	+	1.19156i
$759$		0			0
$760$	−3.16426	−	68.2269i	−0.114780	−	2.47485i
$761$		−	35.1123i		−	1.27282i	−0.771351	−	0.636410i	$-0.780419\pi$
$761$		−	35.1123i		−	1.27282i	0.771351	−	0.636410i	$-0.219581\pi$
$762$		0			0
$763$	−10.8801	−	16.4228i	−0.393887	−	0.594547i
$764$			38.6238i			1.39736i
$765$		0			0
$766$		−	60.0318i		−	2.16904i
$767$	2.83784	+	2.83784i	0.102469	+	0.102469i
$768$		0			0
$769$	8.16835			0.294558			0.147279	−	0.989095i	$-0.452948\pi$
$769$	8.16835			0.294558			0.147279	+	0.989095i	$0.452948\pi$
$770$	−18.3887	+	13.4486i	−0.662681	+	0.484652i
$771$		0			0
$772$	66.8609	+	66.8609i	2.40638	+	2.40638i
$773$	2.51166	+	2.51166i	0.0903382	+	0.0903382i	0.750832	−	0.660494i	$-0.229653\pi$
$773$	2.51166	+	2.51166i	0.0903382	+	0.0903382i	−0.660494	+	0.750832i	$0.729653\pi$
$774$		0			0
$775$	−30.3863	+	2.82462i	−1.09151	+	0.101463i
$776$		−	94.7776i		−	3.40232i
$777$		0			0
$778$	28.6686	−	28.6686i	1.02782	−	1.02782i
$779$			3.04897i			0.109241i
$780$		0			0
$781$	−11.1554			−0.399171
$782$	32.3840	−	32.3840i	1.15805	−	1.15805i
$783$		0			0
$784$	−28.5131	+	67.3327i	−1.01833	+	2.40474i
$785$	−0.241377	−	5.20449i	−0.00861510	−	0.185756i
$786$		0			0
$787$	12.7347	−	12.7347i	0.453943	−	0.453943i	−0.442718	−	0.896661i	$-0.645986\pi$
$787$	12.7347	−	12.7347i	0.453943	−	0.453943i	0.896661	+	0.442718i	$0.145986\pi$
$788$	−56.5935	+	56.5935i	−2.01606	+	2.01606i
$789$		0			0
$790$	1.23274	+	26.5800i	0.0438590	+	0.945675i
$791$	1.89408	−	9.33014i	0.0673459	−	0.331742i
$792$		0			0
$793$	−1.26131	+	1.26131i	−0.0447903	+	0.0447903i
$794$	60.2300			2.13748
$795$		0			0
$796$			99.3261i			3.52052i
$797$	−23.3462	+	23.3462i	−0.826967	+	0.826967i	−0.987096	−	0.160129i	$-0.948809\pi$
$797$	−23.3462	+	23.3462i	−0.826967	+	0.826967i	0.160129	+	0.987096i	$0.448809\pi$
$798$		0			0
$799$			36.1010i			1.27716i
$800$	−38.5464	+	46.4471i	−1.36282	+	1.64215i
$801$		0			0
$802$	1.81976	+	1.81976i	0.0642580	+	0.0642580i
$803$	9.96713	+	9.96713i	0.351732	+	0.351732i
$804$		0			0
$805$	20.3984	+	27.8914i	0.718949	+	0.983043i
$806$	20.1743			0.710609
$807$		0			0
$808$	83.6806	+	83.6806i	2.94387	+	2.94387i
$809$			27.8210i			0.978135i	0.872246	+	0.489067i	$0.162663\pi$
$809$			27.8210i			0.978135i	−0.872246	+	0.489067i	$0.837337\pi$
$810$		0			0
$811$		−	5.12216i		−	0.179863i	−0.995948	−	0.0899317i	$-0.971335\pi$
$811$		−	5.12216i		−	0.179863i	0.995948	−	0.0899317i	$-0.0286649\pi$
$812$	−56.3897	+	37.3582i	−1.97889	+	1.31102i
$813$		0			0
$814$			12.2837i			0.430544i
$815$	1.50528	+	32.4563i	0.0527275	+	1.13690i
$816$		0			0
$817$	20.5348	−	20.5348i	0.718421	−	0.718421i
$818$	45.2656	+	45.2656i	1.58267	+	1.58267i
$819$		0			0
$820$	5.71755	−	6.27368i	0.199665	−	0.219086i
$821$	26.1405			0.912308			0.456154	−	0.889901i	$-0.349227\pi$
$821$	26.1405			0.912308			0.456154	+	0.889901i	$0.349227\pi$
$822$		0			0
$823$	13.7296	−	13.7296i	0.478583	−	0.478583i	−0.426095	−	0.904678i	$-0.640111\pi$
$823$	13.7296	−	13.7296i	0.478583	−	0.478583i	0.904678	+	0.426095i	$0.140111\pi$
$824$	−90.6265			−3.15712
$825$		0			0
$826$	−21.8173	−	4.42907i	−0.759122	−	0.154107i
$827$	−15.7484	−	15.7484i	−0.547624	−	0.547624i	0.378129	−	0.925753i	$-0.376568\pi$
$827$	−15.7484	−	15.7484i	−0.547624	−	0.547624i	−0.925753	+	0.378129i	$0.876568\pi$
$828$		0			0
$829$	47.2996			1.64278			0.821392	−	0.570365i	$-0.193198\pi$
$829$	47.2996			1.64278			0.821392	+	0.570365i	$0.193198\pi$
$830$	41.5807	+	37.8948i	1.44329	+	1.31535i
$831$		0			0
$832$	9.66613	−	9.66613i	0.335113	−	0.335113i
$833$	−7.82698	−	19.3249i	−0.271189	−	0.669567i
$834$		0			0
$835$	0.0429270	+	0.925579i	0.00148555	+	0.0320310i
$836$		−	28.5575i		−	0.987683i
$837$		0			0
$838$	−29.7635	−	29.7635i	−1.02816	−	1.02816i
$839$	−10.8244			−0.373699			−0.186850	−	0.982389i	$-0.559828\pi$
$839$	−10.8244			−0.373699			−0.186850	+	0.982389i	$0.559828\pi$
$840$		0			0
$841$	2.10826			0.0726986
$842$	27.3635	+	27.3635i	0.943009	+	0.943009i
$843$		0			0
$844$			58.9947i			2.03068i
$845$	−18.8795	−	17.2059i	−0.649474	−	0.591901i
$846$		0			0
$847$	19.5424	−	12.9469i	0.671486	−	0.444860i
$848$	−5.68725	+	5.68725i	−0.195301	+	0.195301i
$849$		0			0
$850$	−3.62875	−	39.0369i	−0.124465	−	1.33895i
$851$	18.6316			0.638683
$852$		0			0
$853$	33.5751	+	33.5751i	1.14959	+	1.14959i	0.986633	+	0.162958i	$0.0521034\pi$
$853$	33.5751	+	33.5751i	1.14959	+	1.14959i	0.162958	+	0.986633i	$0.447897\pi$
$854$	1.96854	−	9.69693i	0.0673622	−	0.331822i
$855$		0			0
$856$	47.8914			1.63689
$857$	−8.92479	+	8.92479i	−0.304865	+	0.304865i	−0.842914	−	0.538049i	$-0.819162\pi$
$857$	−8.92479	+	8.92479i	−0.304865	+	0.304865i	0.538049	+	0.842914i	$0.319162\pi$
$858$		0			0
$859$	20.3701			0.695020			0.347510	−	0.937676i	$-0.387027\pi$
$859$	20.3701			0.695020			0.347510	+	0.937676i	$0.387027\pi$
$860$	−80.7608	+	3.74556i	−2.75392	+	0.127723i
$861$		0			0
$862$	−41.4589	−	41.4589i	−1.41210	−	1.41210i
$863$	14.9014	−	14.9014i	0.507250	−	0.507250i	−0.406431	−	0.913681i	$-0.633227\pi$
$863$	14.9014	−	14.9014i	0.507250	−	0.507250i	0.913681	+	0.406431i	$0.133227\pi$
$864$		0			0
$865$	10.9041	−	0.505716i	0.370751	−	0.0171949i
$866$		−	104.306i		−	3.54446i
$867$		0			0
$868$	−66.3692	+	43.9696i	−2.25272	+	1.49243i
$869$			6.61223i			0.224305i
$870$		0			0
$871$		−	10.5301i		−	0.356797i
$872$	−40.6122	−	40.6122i	−1.37530	−	1.37530i
$873$		0			0
$874$	−60.8869			−2.05953
$875$	29.5249	+	1.81065i	0.998125	+	0.0612112i
$876$		0			0
$877$	23.4634	+	23.4634i	0.792302	+	0.792302i	0.981868	−	0.189566i	$-0.0607080\pi$
$877$	23.4634	+	23.4634i	0.792302	+	0.792302i	−0.189566	+	0.981868i	$0.560708\pi$
$878$	−4.38667	−	4.38667i	−0.148043	−	0.148043i
$879$		0			0
$880$	−23.0147	+	25.2533i	−0.775826	+	0.851290i
$881$			34.9639i			1.17796i	0.808147	+	0.588981i	$0.200471\pi$
$881$			34.9639i			1.17796i	−0.808147	+	0.588981i	$0.799529\pi$
$882$		0			0
$883$	19.3814	−	19.3814i	0.652235	−	0.652235i	−0.301295	−	0.953531i	$-0.597419\pi$
$883$	19.3814	−	19.3814i	0.652235	−	0.652235i	0.953531	+	0.301295i	$0.0974190\pi$
$884$			18.4379i			0.620135i
$885$		0			0
$886$	20.3737			0.684466
$887$	19.2450	−	19.2450i	0.646184	−	0.646184i	−0.305884	−	0.952069i	$-0.598952\pi$
$887$	19.2450	−	19.2450i	0.646184	−	0.646184i	0.952069	+	0.305884i	$0.0989521\pi$
$888$		0			0
$889$	−28.8224	−	5.85116i	−0.966673	−	0.196242i
$890$	−7.05565	+	0.327230i	−0.236506	+	0.0109688i
$891$		0			0
$892$	3.25837	−	3.25837i	0.109098	−	0.109098i
$893$	33.9377	−	33.9377i	1.13568	−	1.13568i
$894$		0			0
$895$	3.30135	+	3.00870i	0.110352	+	0.100570i
$896$	−2.37775	+	11.7126i	−0.0794349	+	0.391292i
$897$		0			0
$898$	−2.23414	+	2.23414i	−0.0745541	+	0.0745541i
$899$	−31.6509			−1.05562
$900$		0			0
$901$		−	2.29338i		−	0.0764035i
$902$	2.09657	−	2.09657i	0.0698082	−	0.0698082i
$903$		0			0
$904$		−	27.7565i		−	0.923169i
$905$	−14.0236	−	12.7804i	−0.466159	−	0.424836i
$906$		0			0
$907$	−14.8842	−	14.8842i	−0.494220	−	0.494220i	0.415413	−	0.909633i	$-0.363637\pi$
$907$	−14.8842	−	14.8842i	−0.494220	−	0.494220i	−0.909633	+	0.415413i	$0.863637\pi$
$908$	85.5312	+	85.5312i	2.83845	+	2.83845i
$909$		0			0
$910$	−19.3237	−	2.99841i	−0.640574	−	0.0993963i
$911$	23.7484			0.786819			0.393410	−	0.919363i	$-0.371295\pi$
$911$	23.7484			0.786819			0.393410	+	0.919363i	$0.371295\pi$
$912$		0			0
$913$	9.88545	+	9.88545i	0.327161	+	0.327161i
$914$		−	78.4700i		−	2.59556i
$915$		0			0
$916$		−	123.639i		−	4.08514i
$917$	9.03357	+	13.6356i	0.298315	+	0.450286i
$918$		0			0
$919$		−	35.7695i		−	1.17993i	−0.807430	−	0.589964i	$-0.799142\pi$
$919$		−	35.7695i		−	1.17993i	0.807430	−	0.589964i	$-0.200858\pi$
$920$	74.4597	+	67.8592i	2.45486	+	2.23725i
$921$		0			0
$922$	−40.8909	+	40.8909i	−1.34667	+	1.34667i
$923$	−6.77080	−	6.77080i	−0.222863	−	0.222863i
$924$		0			0
$925$	10.1857	−	12.2735i	0.334905	−	0.403549i
$926$	−80.7042			−2.65210
$927$		0			0
$928$	−44.2653	+	44.2653i	−1.45308	+	1.45308i
$929$	5.58936			0.183381			0.0916905	−	0.995788i	$-0.470773\pi$
$929$	5.58936			0.183381			0.0916905	+	0.995788i	$0.470773\pi$
$930$		0			0
$931$	−10.8089	+	25.5248i	−0.354247	+	0.836542i
$932$	−11.0503	−	11.0503i	−0.361963	−	0.361963i
$933$		0			0
$934$	−26.4812			−0.866491
$935$	−0.451357	−	9.73202i	−0.0147609	−	0.318271i
$936$		0			0
$937$	−20.4143	+	20.4143i	−0.666906	+	0.666906i	−0.956999	−	0.290092i	$-0.906314\pi$
$937$	−20.4143	+	20.4143i	−0.666906	+	0.666906i	0.290092	+	0.956999i	$0.406314\pi$
$938$	32.2603	+	48.6947i	1.05334	+	1.58994i
$939$		0			0
$940$	−133.473	+	6.19027i	−4.35340	+	0.201904i
$941$			17.1143i			0.557910i	0.960304	+	0.278955i	$0.0899880\pi$
$941$			17.1143i			0.557910i	−0.960304	+	0.278955i	$0.910012\pi$
$942$		0			0
$943$	−3.18002	−	3.18002i	−0.103556	−	0.103556i
$944$	−33.3884			−1.08670
$945$		0			0
$946$	−28.2408			−0.918187
$947$	−6.82151	−	6.82151i	−0.221669	−	0.221669i	0.587532	−	0.809201i	$-0.300100\pi$
$947$	−6.82151	−	6.82151i	−0.221669	−	0.221669i	−0.809201	+	0.587532i	$0.800100\pi$
$948$		0			0
$949$			12.0991i			0.392755i
$950$	−33.2863	+	40.1089i	−1.07995	+	1.30131i
$951$		0			0
$952$	−33.5721	−	50.6748i	−1.08808	−	1.64238i
$953$	−30.7169	+	30.7169i	−0.995017	+	0.995017i	−0.999988	−	0.00497101i	$-0.998418\pi$
$953$	−30.7169	+	30.7169i	−0.995017	+	0.995017i	0.00497101	+	0.999988i	$0.498418\pi$
$954$		0			0
$955$	11.7998	−	12.9476i	0.381834	−	0.418974i
$956$	−105.391			−3.40859
$957$		0			0
$958$	−59.1480	−	59.1480i	−1.91099	−	1.91099i
$959$	33.2058	+	6.74102i	1.07227	+	0.217679i
$960$		0			0
$961$	−6.25222			−0.201684
$962$	−7.45563	+	7.45563i	−0.240379	+	0.240379i
$963$		0			0
$964$	3.07703			0.0991046
$965$	−1.98685	−	42.8399i	−0.0639589	−	1.37906i
$966$		0			0
$967$	24.6730	+	24.6730i	0.793431	+	0.793431i	0.982050	−	0.188619i	$-0.0604012\pi$
$967$	24.6730	+	24.6730i	0.793431	+	0.793431i	−0.188619	+	0.982050i	$0.560401\pi$
$968$	48.3267	−	48.3267i	1.55328	−	1.55328i
$969$		0			0
$970$	−48.7191	+	53.4579i	−1.56428	+	1.71643i
$971$			21.2020i			0.680404i	0.940352	+	0.340202i	$0.110496\pi$
$971$			21.2020i			0.680404i	−0.940352	+	0.340202i	$0.889504\pi$
$972$		0			0
$973$	26.4483	−	17.5220i	0.847895	−	0.561731i
$974$		−	17.9232i		−	0.574297i
$975$		0			0
$976$		−	14.8398i		−	0.475011i
$977$	−8.19657	−	8.19657i	−0.262231	−	0.262231i	0.563729	−	0.825960i	$-0.309366\pi$
$977$	−8.19657	−	8.19657i	−0.262231	−	0.262231i	−0.825960	+	0.563729i	$0.809366\pi$
$978$		0			0
$979$	−1.75521			−0.0560969
$980$	70.1059	−	32.2516i	2.23945	−	1.03024i
$981$		0			0
$982$	−52.7541	−	52.7541i	−1.68345	−	1.68345i
$983$	1.74914	+	1.74914i	0.0557891	+	0.0557891i	0.734451	−	0.678662i	$-0.237440\pi$
$983$	1.74914	+	1.74914i	0.0557891	+	0.0557891i	−0.678662	+	0.734451i	$0.737440\pi$
$984$		0			0
$985$	36.2612	−	1.68174i	1.15538	−	0.0535847i
$986$		−	40.6615i		−	1.29492i
$987$		0			0
$988$	17.3331	−	17.3331i	0.551438	−	0.551438i
$989$			42.8348i			1.36207i
$990$		0			0
$991$	−37.1253			−1.17932			−0.589662	−	0.807650i	$-0.700739\pi$
$991$	−37.1253			−1.17932			−0.589662	+	0.807650i	$0.700739\pi$
$992$	−52.0991	+	52.0991i	−1.65415	+	1.65415i
$993$		0			0
$994$	52.0539	+	10.5673i	1.65105	+	0.335174i
$995$	30.3449	−	33.2964i	0.961996	−	1.05557i
$996$		0			0
$997$	−40.5538	+	40.5538i	−1.28435	+	1.28435i	−0.346186	+	0.938166i	$0.612524\pi$
$997$	−40.5538	+	40.5538i	−1.28435	+	1.28435i	−0.938166	+	0.346186i	$0.887476\pi$
$998$	−6.31404	+	6.31404i	−0.199868	+	0.199868i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.p.e.307.8		16
3.2	odd	2		105.2.m.a.97.1	yes	16
5.3	odd	4	inner	315.2.p.e.118.7		16
7.6	odd	2	inner	315.2.p.e.307.7		16
12.11	even	2		1680.2.cz.d.97.6		16
15.2	even	4		525.2.m.b.118.7		16
15.8	even	4		105.2.m.a.13.2	yes	16
15.14	odd	2		525.2.m.b.307.8		16
21.2	odd	6		735.2.v.a.472.2		32
21.5	even	6		735.2.v.a.472.1		32
21.11	odd	6		735.2.v.a.607.7		32
21.17	even	6		735.2.v.a.607.8		32
21.20	even	2		105.2.m.a.97.2	yes	16
35.13	even	4	inner	315.2.p.e.118.8		16
60.23	odd	4		1680.2.cz.d.433.3		16
84.83	odd	2		1680.2.cz.d.97.3		16
105.23	even	12		735.2.v.a.178.8		32
105.38	odd	12		735.2.v.a.313.2		32
105.53	even	12		735.2.v.a.313.1		32
105.62	odd	4		525.2.m.b.118.8		16
105.68	odd	12		735.2.v.a.178.7		32
105.83	odd	4		105.2.m.a.13.1	✓	16
105.104	even	2		525.2.m.b.307.7		16
420.83	even	4		1680.2.cz.d.433.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.m.a.13.1	✓	16	105.83	odd	4
105.2.m.a.13.2	yes	16	15.8	even	4
105.2.m.a.97.1	yes	16	3.2	odd	2
105.2.m.a.97.2	yes	16	21.20	even	2
315.2.p.e.118.7		16	5.3	odd	4	inner
315.2.p.e.118.8		16	35.13	even	4	inner
315.2.p.e.307.7		16	7.6	odd	2	inner
315.2.p.e.307.8		16	1.1	even	1	trivial
525.2.m.b.118.7		16	15.2	even	4
525.2.m.b.118.8		16	105.62	odd	4
525.2.m.b.307.7		16	105.104	even	2
525.2.m.b.307.8		16	15.14	odd	2
735.2.v.a.178.7		32	105.68	odd	12
735.2.v.a.178.8		32	105.23	even	12
735.2.v.a.313.1		32	105.53	even	12
735.2.v.a.313.2		32	105.38	odd	12
735.2.v.a.472.1		32	21.5	even	6
735.2.v.a.472.2		32	21.2	odd	6
735.2.v.a.607.7		32	21.11	odd	6
735.2.v.a.607.8		32	21.17	even	6
1680.2.cz.d.97.3		16	84.83	odd	2
1680.2.cz.d.97.6		16	12.11	even	2
1680.2.cz.d.433.3		16	60.23	odd	4
1680.2.cz.d.433.6		16	420.83	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.p (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.86147 + 1.86147i) q^{2} +4.93012i q^{4} +(1.50619 - 1.65269i) q^{5} +(-2.20563 + 1.46123i) q^{7} +(-5.45433 + 5.45433i) q^{8} +O(q^{10})\)	\(q+(1.86147 + 1.86147i) q^{2} +4.93012i q^{4} +(1.50619 - 1.65269i) q^{5} +(-2.20563 + 1.46123i) q^{7} +(-5.45433 + 5.45433i) q^{8} +(5.88016 - 0.272713i) q^{10} +1.46279 q^{11} +(0.887844 + 0.887844i) q^{13} +(-6.82574 - 1.38567i) q^{14} -10.4459 q^{16} +(2.10614 - 2.10614i) q^{17} -3.95987 q^{19} +(8.14798 + 7.42570i) q^{20} +(2.72294 + 2.72294i) q^{22} +(4.13007 - 4.13007i) q^{23} +(-0.462789 - 4.97854i) q^{25} +3.30539i q^{26} +(-7.20405 - 10.8740i) q^{28} -5.18572i q^{29} -6.10346i q^{31} +(-8.53599 - 8.53599i) q^{32} +7.84104 q^{34} +(-0.907129 + 5.84612i) q^{35} +(2.25560 + 2.25560i) q^{37} +(-7.37117 - 7.37117i) q^{38} +(0.799082 + 17.2296i) q^{40} -0.769968i q^{41} +(-5.18572 + 5.18572i) q^{43} +7.21173i q^{44} +15.3760 q^{46} +(-8.57041 + 8.57041i) q^{47} +(2.72961 - 6.44587i) q^{49} +(8.40592 - 10.1289i) q^{50} +(-4.37718 + 4.37718i) q^{52} +(0.544449 - 0.544449i) q^{53} +(2.20324 - 2.41754i) q^{55} +(4.06020 - 20.0003i) q^{56} +(9.65306 - 9.65306i) q^{58} +3.19633 q^{59} +1.42064i q^{61} +(11.3614 - 11.3614i) q^{62} -10.8872i q^{64} +(2.80460 - 0.130073i) q^{65} +(-5.93012 - 5.93012i) q^{67} +(10.3835 + 10.3835i) q^{68} +(-12.5710 + 9.19377i) q^{70} -7.62611 q^{71} +(6.81378 + 6.81378i) q^{73} +8.39746i q^{74} -19.5226i q^{76} +(-3.22637 + 2.13747i) q^{77} +4.52029i q^{79} +(-15.7335 + 17.2638i) q^{80} +(1.43327 - 1.43327i) q^{82} +(6.75794 + 6.75794i) q^{83} +(-0.308559 - 6.65306i) q^{85} -19.3061 q^{86} +(-7.97854 + 7.97854i) q^{88} -1.19991 q^{89} +(-3.25560 - 0.660910i) q^{91} +(20.3618 + 20.3618i) q^{92} -31.9071 q^{94} +(-5.96431 + 6.54445i) q^{95} +(-8.68829 + 8.68829i) q^{97} +(17.0799 - 6.91770i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{7} - 24 q^{8}+O(q^{10}) \) 16 * q - 8 * q^7 - 24 * q^8	\( 16 q - 8 q^{7} - 24 q^{8} + 16 q^{11} - 48 q^{16} - 16 q^{22} + 40 q^{23} + 24 q^{28} - 48 q^{32} + 8 q^{35} + 32 q^{37} - 16 q^{43} + 64 q^{46} + 72 q^{50} - 24 q^{53} - 24 q^{56} + 32 q^{58} - 40 q^{65} - 32 q^{67} - 40 q^{70} - 64 q^{71} + 24 q^{77} + 48 q^{85} - 64 q^{86} - 64 q^{88} - 48 q^{91} + 40 q^{92} + 72 q^{95} + 96 q^{98}+O(q^{100}) \) 16 * q - 8 * q^7 - 24 * q^8 + 16 * q^11 - 48 * q^16 - 16 * q^22 + 40 * q^23 + 24 * q^28 - 48 * q^32 + 8 * q^35 + 32 * q^37 - 16 * q^43 + 64 * q^46 + 72 * q^50 - 24 * q^53 - 24 * q^56 + 32 * q^58 - 40 * q^65 - 32 * q^67 - 40 * q^70 - 64 * q^71 + 24 * q^77 + 48 * q^85 - 64 * q^86 - 64 * q^88 - 48 * q^91 + 40 * q^92 + 72 * q^95 + 96 * q^98

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