LMFDB - Embedded newform 315.2.p.e.118.8

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			118.8
Root			$-0.517174 - 1.31626i$ of defining polynomial
Character	$\chi$	$=$	315.118
Dual form			315.2.p.e.307.8

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.86147	−	1.86147i	1.31626	−	1.31626i	0.399541	−	0.916715i	$-0.369169\pi$
$2$	1.86147	−	1.86147i	1.31626	−	1.31626i	0.916715	−	0.399541i	$-0.130831\pi$
$3$		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	−0.573183	−	0.819427i	$-0.694292\pi$
$13$	0.887844	−	0.887844i	0.246244	−	0.246244i	0.819427	+	0.573183i	$0.194292\pi$
$14$	−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	0.914776	−	0.403961i	$-0.132367\pi$
$17$	2.10614	+	2.10614i	0.510815	+	0.510815i	−0.403961	+	0.914776i	$0.632367\pi$
$18$		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	0.991475	−	0.130295i	$-0.0415926\pi$
$23$	4.13007	+	4.13007i	0.861180	+	0.861180i	−0.130295	+	0.991475i	$0.541593\pi$
$24$		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	$0.159901\pi$
$29$			5.18572i			0.962965i	−0.876456	+	0.481482i	$0.840099\pi$
$30$		0			0
$31$			6.10346i			1.09621i	0.836408	+	0.548107i	$0.184651\pi$
$31$			6.10346i			1.09621i	−0.836408	+	0.548107i	$0.815349\pi$
$32$	−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	−0.496957	−	0.867775i	$-0.665549\pi$
$37$	2.25560	−	2.25560i	0.370819	−	0.370819i	0.867775	+	0.496957i	$0.165549\pi$
$38$	−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	$0.0191497\pi$
$41$			0.769968i			0.120249i	−0.998191	+	0.0601244i	$0.980850\pi$
$42$		0			0
$43$	−5.18572	−	5.18572i	−0.790816	−	0.790816i	0.190811	−	0.981627i	$-0.438888\pi$
$43$	−5.18572	−	5.18572i	−0.790816	−	0.790816i	−0.981627	+	0.190811i	$0.938888\pi$
$44$		−	7.21173i		−	1.08721i
$45$		0			0
$46$	15.3760			2.26707
$47$	−8.57041	−	8.57041i	−1.25012	−	1.25012i	−0.955664	−	0.294459i	$-0.904861\pi$
$47$	−8.57041	−	8.57041i	−1.25012	−	1.25012i	−0.294459	−	0.955664i	$-0.595139\pi$
$48$		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	0.743510	−	0.668724i	$-0.233159\pi$
$53$	0.544449	+	0.544449i	0.0747859	+	0.0747859i	−0.668724	+	0.743510i	$0.733159\pi$
$54$		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	$-0.971011\pi$
$61$		−	1.42064i		−	0.181894i	0.995856	−	0.0909472i	$-0.0289894\pi$
$62$	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	−0.969514	−	0.245034i	$-0.921201\pi$
$67$	−5.93012	+	5.93012i	−0.724480	+	0.724480i	0.245034	+	0.969514i	$0.421201\pi$
$68$	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	−0.185207	−	0.982700i	$-0.559296\pi$
$73$	6.81378	−	6.81378i	0.797493	−	0.797493i	0.982700	+	0.185207i	$0.0592955\pi$
$74$		−	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	$-0.918159\pi$
$79$		−	4.52029i		−	0.508573i	0.967129	−	0.254286i	$-0.0818405\pi$
$80$	−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	−0.231140	−	0.972921i	$-0.574246\pi$
$83$	6.75794	−	6.75794i	0.741781	−	0.741781i	0.972921	+	0.231140i	$0.0742455\pi$
$84$		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	0.111592	−	0.993754i	$-0.464405\pi$
$97$	−8.68829	−	8.68829i	−0.882162	−	0.882162i	−0.993754	+	0.111592i	$0.964405\pi$
$98$	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	$0.276420\pi$
$101$			15.3420i			1.52659i	−0.646050	+	0.763295i	$0.723580\pi$
$102$		0			0
$103$	8.30776	−	8.30776i	0.818588	−	0.818588i	−0.167316	−	0.985903i	$-0.553510\pi$
$103$	8.30776	−	8.30776i	0.818588	−	0.818588i	0.985903	+	0.167316i	$0.0535099\pi$
$104$	−9.68519			−0.949711
$105$		0			0
$106$	2.02695			0.196875
$107$	−4.39022	+	4.39022i	−0.424418	+	0.424418i	−0.886722	−	0.462303i	$-0.847023\pi$
$107$	−4.39022	+	4.39022i	−0.424418	+	0.424418i	0.462303	+	0.886722i	$0.347023\pi$
$108$		0			0
$109$		−	7.44587i		−	0.713185i	−0.934260	−	0.356593i	$-0.883938\pi$
$109$		−	7.44587i		−	0.713185i	0.934260	−	0.356593i	$-0.116062\pi$
$110$	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	0.577224	−	0.816586i	$-0.304136\pi$
$113$	−2.54445	−	2.54445i	−0.239362	−	0.239362i	−0.816586	+	0.577224i	$0.804136\pi$
$114$		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	−0.266383	−	0.963867i	$-0.585829\pi$
$127$	7.86025	−	7.86025i	0.697484	−	0.697484i	0.963867	+	0.266383i	$0.0858286\pi$
$128$	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	$0.0870465\pi$
$131$			6.18216i			0.540138i	−0.962841	+	0.270069i	$0.912953\pi$
$132$		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	−0.978747	−	0.205071i	$-0.934258\pi$
$137$	−9.05565	+	9.05565i	−0.773677	+	0.773677i	0.205071	+	0.978747i	$0.434258\pi$
$138$		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	$-0.998738\pi$
$149$		−	0.0968261i		−	0.00793230i	0.999992	−	0.00396615i	$-0.00126247\pi$
$150$		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	0.769789	−	0.638298i	$-0.220361\pi$
$157$	1.64757	+	1.64757i	0.131491	+	0.131491i	−0.638298	+	0.769789i	$0.720361\pi$
$158$	−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	0.179066	−	0.983837i	$-0.442692\pi$
$163$	−10.2746	−	10.2746i	−0.804771	−	0.804771i	−0.983837	+	0.179066i	$0.942692\pi$
$164$	3.79604			0.296421
$165$		0			0
$166$		−	25.1594i		−	1.95275i
$167$	−0.293008	−	0.293008i	−0.0226737	−	0.0226737i	0.695679	−	0.718353i	$-0.255104\pi$
$167$	−0.293008	−	0.293008i	−0.0226737	−	0.0226737i	−0.718353	+	0.695679i	$0.755104\pi$
$168$		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	−0.563603	−	0.826046i	$-0.690585\pi$
$173$	3.45189	−	3.45189i	0.262442	−	0.262442i	0.826046	+	0.563603i	$0.190585\pi$
$174$		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	$-0.976215\pi$
$179$		−	1.99756i		−	0.149305i	0.997210	−	0.0746523i	$-0.0237847\pi$
$180$		0			0
$181$			8.48528i			0.630706i	0.948974	+	0.315353i	$0.102123\pi$
$181$			8.48528i			0.630706i	−0.948974	+	0.315353i	$0.897877\pi$
$182$	−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	0.999723	−	0.0235293i	$-0.00749029\pi$
$193$	13.5617	+	13.5617i	0.976194	+	0.976194i	−0.0235293	+	0.999723i	$0.507490\pi$
$194$	−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	−0.167943	−	0.985797i	$-0.553713\pi$
$197$	11.4791	−	11.4791i	0.817853	−	0.817853i	0.985797	+	0.167943i	$0.0537126\pi$
$198$		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	−0.728889	−	0.684632i	$-0.759963\pi$
$223$	−0.660910	+	0.660910i	−0.0442578	+	0.0442578i	0.684632	+	0.728889i	$0.259963\pi$
$224$	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	0.986257	+	0.165216i	$0.0528323\pi$
$227$	17.3487	+	17.3487i	1.15147	+	1.15147i	0.165216	+	0.986257i	$0.447168\pi$
$228$		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	0.629866	−	0.776704i	$-0.283110\pi$
$233$	−2.24138	−	2.24138i	−0.146837	−	0.146837i	−0.776704	+	0.629866i	$0.783110\pi$
$234$		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	$-0.757003\pi$
$239$		−	21.3769i		−	1.38276i	0.722492	−	0.691380i	$-0.242997\pi$
$240$		0			0
$241$			0.624129i			0.0402037i	0.999798	+	0.0201018i	$0.00639905\pi$
$241$			0.624129i			0.0402037i	−0.999798	+	0.0201018i	$0.993601\pi$
$242$	−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	$0.172513\pi$
$251$			16.3443i			1.03164i	−0.856696	+	0.515822i	$0.827487\pi$
$252$		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	−0.906247	−	0.422749i	$-0.861065\pi$
$257$	−21.3054	−	21.3054i	−1.32900	−	1.32900i	−0.422749	−	0.906247i	$-0.638935\pi$
$258$		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	0.999969	+	0.00789784i	$0.00251399\pi$
$263$	16.3449	+	16.3449i	1.00787	+	1.00787i	0.00789784	+	0.999969i	$0.497486\pi$
$264$		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	$-0.924062\pi$
$271$		−	7.78033i		−	0.472621i	0.971678	−	0.236311i	$-0.0759383\pi$
$272$	−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	0.340013	−	0.940421i	$-0.389569\pi$
$277$	21.3107	−	21.3107i	1.28043	−	1.28043i	0.940421	−	0.340013i	$-0.110431\pi$
$278$	−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	−0.623788	−	0.781594i	$-0.714407\pi$
$283$	2.65471	−	2.65471i	0.157806	−	0.157806i	0.781594	+	0.623788i	$0.214407\pi$
$284$			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	−0.659847	−	0.751400i	$-0.729379\pi$
$293$	1.56714	−	1.56714i	0.0915536	−	0.0915536i	0.751400	+	0.659847i	$0.229379\pi$
$294$		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	0.00944588	−	0.999955i	$-0.496993\pi$
$307$	−17.3551	−	17.3551i	−0.990510	−	0.990510i	−0.999955	+	0.00944588i	$0.996993\pi$
$308$	−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	$0.342970\pi$
$311$			31.0648i			1.76153i	−0.473558	+	0.880763i	$0.657030\pi$
$312$		0			0
$313$	5.72426	−	5.72426i	0.323554	−	0.323554i	−0.526575	−	0.850129i	$-0.676524\pi$
$313$	5.72426	−	5.72426i	0.323554	−	0.323554i	0.850129	+	0.526575i	$0.176524\pi$
$314$	6.13381			0.346151
$315$		0			0
$316$	−22.2856			−1.25366
$317$	−0.752579	+	0.752579i	−0.0422691	+	0.0422691i	−0.727925	−	0.685656i	$-0.759515\pi$
$317$	−0.752579	+	0.752579i	−0.0422691	+	0.0422691i	0.685656	+	0.727925i	$0.259515\pi$
$318$		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	−0.0966558	+	0.995318i	$0.530815\pi$
$337$	−20.0460	+	20.0460i	−1.09197	+	1.09197i	−0.995318	+	0.0966558i	$0.969185\pi$
$338$	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	0.0815328	−	0.996671i	$-0.474018\pi$
$347$	20.0847	−	20.0847i	1.07820	−	1.07820i	0.996671	−	0.0815328i	$-0.0259815\pi$
$348$		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	−0.291766	−	0.956490i	$-0.594243\pi$
$353$	12.4890	−	12.4890i	0.664724	−	0.664724i	0.956490	+	0.291766i	$0.0942429\pi$
$354$		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	$-0.910306\pi$
$359$		−	10.5372i		−	0.556133i	0.960562	−	0.278066i	$-0.0896935\pi$
$360$		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	0.936045	−	0.351881i	$-0.114458\pi$
$367$	11.1910	+	11.1910i	0.584163	+	0.584163i	−0.351881	+	0.936045i	$0.614458\pi$
$368$	−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	0.994938	−	0.100492i	$-0.0320416\pi$
$373$	17.2746	+	17.2746i	0.894446	+	0.894446i	−0.100492	+	0.994938i	$0.532042\pi$
$374$	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	$-0.850485\pi$
$379$		−	17.6237i		−	0.905267i	0.891697	−	0.452634i	$-0.149515\pi$
$380$	−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	−0.986671	−	0.162729i	$-0.947970\pi$
$383$	−16.1249	+	16.1249i	−0.823942	+	0.823942i	0.162729	+	0.986671i	$0.447970\pi$
$384$		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	$0.127674\pi$
$389$			15.4011i			0.780865i	−0.920632	+	0.390432i	$0.872326\pi$
$390$		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	0.984927	−	0.172972i	$-0.0553370\pi$
$397$	16.1781	+	16.1781i	0.811955	+	0.811955i	−0.172972	+	0.984927i	$0.555337\pi$
$398$	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	−0.456896	+	0.889520i	$0.651039\pi$
$433$	−28.0171	+	28.0171i	−1.34642	+	1.34642i	−0.889520	+	0.456896i	$0.848961\pi$
$434$	−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	0.825056	−	0.565051i	$-0.191144\pi$
$443$	5.47247	+	5.47247i	0.260005	+	0.260005i	−0.565051	+	0.825056i	$0.691144\pi$
$444$		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	$-0.990984\pi$
$449$		−	1.20020i		−	0.0566410i	0.999599	−	0.0283205i	$-0.00901591\pi$
$450$		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	−0.999903	−	0.0139406i	$-0.995562\pi$
$457$	−21.0775	+	21.0775i	−0.985962	+	0.985962i	0.0139406	+	0.999903i	$0.495562\pi$
$458$	−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	$-0.829071\pi$
$461$		−	21.9670i		−	1.02311i	0.859252	−	0.511553i	$-0.170929\pi$
$462$		0			0
$463$	−21.6776	−	21.6776i	−1.00744	−	1.00744i	−0.999972	−	0.00746987i	$-0.997622\pi$
$463$	−21.6776	−	21.6776i	−1.00744	−	1.00744i	−0.00746987	−	0.999972i	$-0.502378\pi$
$464$		−	54.1694i		−	2.51475i
$465$		0			0
$466$	−8.34450			−0.386551
$467$	−7.11299	−	7.11299i	−0.329150	−	0.329150i	0.523113	−	0.852263i	$-0.324770\pi$
$467$	−7.11299	−	7.11299i	−0.329150	−	0.329150i	−0.852263	+	0.523113i	$0.824770\pi$
$468$		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	−0.807721	−	0.589565i	$-0.799299\pi$
$487$	−4.81428	+	4.81428i	−0.218156	+	0.218156i	0.589565	+	0.807721i	$0.299299\pi$
$488$	−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	$-0.975810\pi$
$499$		−	3.39197i		−	0.151845i	0.997114	−	0.0759227i	$-0.0241902\pi$
$500$	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	−0.496599	−	0.867980i	$-0.665418\pi$
$503$	8.32921	−	8.32921i	0.371381	−	0.371381i	0.867980	+	0.496599i	$0.165418\pi$
$504$		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	$-0.950523\pi$
$521$		−	7.06726i		−	0.309622i	0.987944	−	0.154811i	$-0.0494769\pi$
$522$		0			0
$523$	14.5887	−	14.5887i	0.637921	−	0.637921i	−0.312121	−	0.950042i	$-0.601040\pi$
$523$	14.5887	−	14.5887i	0.637921	−	0.637921i	0.950042	+	0.312121i	$0.101040\pi$
$524$	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	−0.844526	−	0.535515i	$-0.820118\pi$
$547$	−7.22715	+	7.22715i	−0.309011	+	0.309011i	0.535515	+	0.844526i	$0.320118\pi$
$548$	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	−0.695166	−	0.718849i	$-0.744669\pi$
$557$	0.558927	−	0.558927i	0.0236825	−	0.0236825i	0.718849	+	0.695166i	$0.244669\pi$
$558$		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	−0.721755	−	0.692149i	$-0.756664\pi$
$563$	−0.702475	+	0.702475i	−0.0296058	+	0.0296058i	0.692149	+	0.721755i	$0.256664\pi$
$564$		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	$0.0653137\pi$
$569$			9.72049i			0.407504i	−0.979023	+	0.203752i	$0.934686\pi$
$570$		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	0.458024	−	0.888940i	$-0.348558\pi$
$577$	−10.3510	−	10.3510i	−0.430917	−	0.430917i	−0.888940	+	0.458024i	$0.848558\pi$
$578$	−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	0.992755	−	0.120160i	$-0.0383409\pi$
$587$	21.1413	+	21.1413i	0.872594	+	0.872594i	−0.120160	+	0.992755i	$0.538341\pi$
$588$		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	−0.837343	−	0.546678i	$-0.815892\pi$
$593$	−7.07816	+	7.07816i	−0.290665	+	0.290665i	0.546678	+	0.837343i	$0.315892\pi$
$594$		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	$-0.953413\pi$
$599$		−	7.13847i		−	0.291670i	0.989309	−	0.145835i	$-0.0465869\pi$
$600$		0			0
$601$		−	35.0829i		−	1.43106i	−0.698580	−	0.715532i	$-0.746185\pi$
$601$		−	35.0829i		−	1.43106i	0.698580	−	0.715532i	$-0.253815\pi$
$602$	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	0.589822	−	0.807533i	$-0.299198\pi$
$607$	−5.36385	−	5.36385i	−0.217712	−	0.217712i	−0.807533	+	0.589822i	$0.799198\pi$
$608$	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	0.462816	−	0.886454i	$-0.346839\pi$
$613$	−10.4888	−	10.4888i	−0.423639	−	0.423639i	−0.886454	+	0.462816i	$0.846839\pi$
$614$	−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	−0.982631	−	0.185571i	$-0.940586\pi$
$617$	−19.7986	+	19.7986i	−0.797060	+	0.797060i	0.185571	+	0.982631i	$0.440586\pi$
$618$		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	−0.904405	−	0.426675i	$-0.859685\pi$
$643$	−12.1140	+	12.1140i	−0.477731	+	0.477731i	0.426675	+	0.904405i	$0.359685\pi$
$644$	−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	0.974631	−	0.223817i	$-0.0718519\pi$
$647$	19.0978	+	19.0978i	0.750814	+	0.750814i	−0.223817	+	0.974631i	$0.571852\pi$
$648$		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	0.185476	−	0.982649i	$-0.440617\pi$
$653$	−20.3709	−	20.3709i	−0.797173	−	0.797173i	−0.982649	+	0.185476i	$0.940617\pi$
$654$		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	$0.210160\pi$
$659$			31.4882i			1.22661i	−0.789847	+	0.613304i	$0.789840\pi$
$660$		0			0
$661$		−	48.1880i		−	1.87430i	−0.348931	−	0.937149i	$-0.613455\pi$
$661$		−	48.1880i		−	1.87430i	0.348931	−	0.937149i	$-0.386545\pi$
$662$	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	−0.978960	−	0.204055i	$-0.934588\pi$
$673$	−30.6900	−	30.6900i	−1.18301	−	1.18301i	−0.204055	−	0.978960i	$-0.565412\pi$
$674$			74.6299i			2.87463i
$675$		0			0
$676$	56.3191			2.16612
$677$	1.54060	+	1.54060i	0.0592101	+	0.0592101i	0.736092	−	0.676882i	$-0.236669\pi$
$677$	1.54060	+	1.54060i	0.0592101	+	0.0592101i	−0.676882	+	0.736092i	$0.736669\pi$
$678$		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	0.380744	−	0.924680i	$-0.375668\pi$
$683$	−14.2154	−	14.2154i	−0.543936	−	0.543936i	−0.924680	+	0.380744i	$0.875668\pi$
$684$		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	$0.0626980\pi$
$691$			10.2887i			0.391401i	−0.980664	+	0.195700i	$0.937302\pi$
$692$	−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	$0.00488939\pi$
$709$			0.817976i			0.0307197i	−0.999882	+	0.0153599i	$0.995111\pi$
$710$	−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	0.998098	+	0.0616465i	$0.0196352\pi$
$727$	28.5738	+	28.5738i	1.05974	+	1.05974i	0.0616465	+	0.998098i	$0.480365\pi$
$728$	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	−0.994719	−	0.102636i	$-0.967272\pi$
$733$	−24.1522	+	24.1522i	−0.892083	+	0.892083i	0.102636	+	0.994719i	$0.467272\pi$
$734$	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	$0.245947\pi$
$739$			37.9522i			1.39609i	−0.716052	+	0.698047i	$0.754053\pi$
$740$	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	0.962184	−	0.272400i	$-0.0878174\pi$
$743$	18.8022	+	18.8022i	0.689784	+	0.689784i	−0.272400	+	0.962184i	$0.587817\pi$
$744$		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	−0.647637	−	0.761949i	$-0.724243\pi$
$757$	3.14514	−	3.14514i	0.114312	−	0.114312i	0.761949	+	0.647637i	$0.224243\pi$
$758$	−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	$0.219581\pi$
$761$			35.1123i			1.27282i	−0.771351	+	0.636410i	$0.780419\pi$
$762$		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	−0.660494	−	0.750832i	$-0.729653\pi$
$773$	2.51166	−	2.51166i	0.0903382	−	0.0903382i	0.750832	+	0.660494i	$0.229653\pi$
$774$		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	0.896661	−	0.442718i	$-0.145986\pi$
$787$	12.7347	+	12.7347i	0.453943	+	0.453943i	−0.442718	+	0.896661i	$0.645986\pi$
$788$	−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	0.160129	−	0.987096i	$-0.448809\pi$
$797$	−23.3462	−	23.3462i	−0.826967	−	0.826967i	−0.987096	+	0.160129i	$0.948809\pi$
$798$		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	$-0.837337\pi$
$809$		−	27.8210i		−	0.978135i	0.872246	−	0.489067i	$-0.162663\pi$
$810$		0			0
$811$			5.12216i			0.179863i	0.995948	+	0.0899317i	$0.0286649\pi$
$811$			5.12216i			0.179863i	−0.995948	+	0.0899317i	$0.971335\pi$
$812$	−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	0.904678	−	0.426095i	$-0.140111\pi$
$823$	13.7296	+	13.7296i	0.478583	+	0.478583i	−0.426095	+	0.904678i	$0.640111\pi$
$824$	−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	−0.925753	−	0.378129i	$-0.876568\pi$
$827$	−15.7484	+	15.7484i	−0.547624	+	0.547624i	0.378129	+	0.925753i	$0.376568\pi$
$828$		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	0.162958	−	0.986633i	$-0.447897\pi$
$853$	33.5751	−	33.5751i	1.14959	−	1.14959i	0.986633	−	0.162958i	$-0.0521034\pi$
$854$	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	0.538049	−	0.842914i	$-0.319162\pi$
$857$	−8.92479	−	8.92479i	−0.304865	−	0.304865i	−0.842914	+	0.538049i	$0.819162\pi$
$858$		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	0.913681	−	0.406431i	$-0.133227\pi$
$863$	14.9014	+	14.9014i	0.507250	+	0.507250i	−0.406431	+	0.913681i	$0.633227\pi$
$864$		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	−0.189566	−	0.981868i	$-0.560708\pi$
$877$	23.4634	−	23.4634i	0.792302	−	0.792302i	0.981868	+	0.189566i	$0.0607080\pi$
$878$	−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	$-0.799529\pi$
$881$		−	34.9639i		−	1.17796i	0.808147	−	0.588981i	$-0.200471\pi$
$882$		0			0
$883$	19.3814	+	19.3814i	0.652235	+	0.652235i	0.953531	−	0.301295i	$-0.0974190\pi$
$883$	19.3814	+	19.3814i	0.652235	+	0.652235i	−0.301295	+	0.953531i	$0.597419\pi$
$884$		−	18.4379i		−	0.620135i
$885$		0			0
$886$	20.3737			0.684466
$887$	19.2450	+	19.2450i	0.646184	+	0.646184i	0.952069	−	0.305884i	$-0.0989521\pi$
$887$	19.2450	+	19.2450i	0.646184	+	0.646184i	−0.305884	+	0.952069i	$0.598952\pi$
$888$		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	−0.909633	−	0.415413i	$-0.863637\pi$
$907$	−14.8842	+	14.8842i	−0.494220	+	0.494220i	0.415413	+	0.909633i	$0.363637\pi$
$908$	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	$0.200858\pi$
$919$			35.7695i			1.17993i	−0.807430	+	0.589964i	$0.799142\pi$
$920$	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	0.290092	−	0.956999i	$-0.406314\pi$
$937$	−20.4143	−	20.4143i	−0.666906	−	0.666906i	−0.956999	+	0.290092i	$0.906314\pi$
$938$	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	$-0.910012\pi$
$941$		−	17.1143i		−	0.557910i	0.960304	−	0.278955i	$-0.0899880\pi$
$942$		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	−0.809201	−	0.587532i	$-0.800100\pi$
$947$	−6.82151	+	6.82151i	−0.221669	+	0.221669i	0.587532	+	0.809201i	$0.300100\pi$
$948$		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	0.00497101	−	0.999988i	$-0.498418\pi$
$953$	−30.7169	−	30.7169i	−0.995017	−	0.995017i	−0.999988	+	0.00497101i	$0.998418\pi$
$954$		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	−0.188619	−	0.982050i	$-0.560401\pi$
$967$	24.6730	−	24.6730i	0.793431	−	0.793431i	0.982050	+	0.188619i	$0.0604012\pi$
$968$	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	$-0.889504\pi$
$971$		−	21.2020i		−	0.680404i	0.940352	−	0.340202i	$-0.110496\pi$
$972$		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	−0.825960	−	0.563729i	$-0.809366\pi$
$977$	−8.19657	+	8.19657i	−0.262231	+	0.262231i	0.563729	+	0.825960i	$0.309366\pi$
$978$		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	−0.678662	−	0.734451i	$-0.737440\pi$
$983$	1.74914	−	1.74914i	0.0557891	−	0.0557891i	0.734451	+	0.678662i	$0.237440\pi$
$984$		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	−0.938166	−	0.346186i	$-0.887476\pi$
$997$	−40.5538	−	40.5538i	−1.28435	−	1.28435i	−0.346186	−	0.938166i	$-0.612524\pi$
$998$	−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.118.8		16
3.2	odd	2		105.2.m.a.13.1	✓	16
5.2	odd	4	inner	315.2.p.e.307.7		16
7.6	odd	2	inner	315.2.p.e.118.7		16
12.11	even	2		1680.2.cz.d.433.6		16
15.2	even	4		105.2.m.a.97.2	yes	16
15.8	even	4		525.2.m.b.307.7		16
15.14	odd	2		525.2.m.b.118.8		16
21.2	odd	6		735.2.v.a.178.7		32
21.5	even	6		735.2.v.a.178.8		32
21.11	odd	6		735.2.v.a.313.2		32
21.17	even	6		735.2.v.a.313.1		32
21.20	even	2		105.2.m.a.13.2	yes	16
35.27	even	4	inner	315.2.p.e.307.8		16
60.47	odd	4		1680.2.cz.d.97.3		16
84.83	odd	2		1680.2.cz.d.433.3		16
105.2	even	12		735.2.v.a.472.1		32
105.17	odd	12		735.2.v.a.607.7		32
105.32	even	12		735.2.v.a.607.8		32
105.47	odd	12		735.2.v.a.472.2		32
105.62	odd	4		105.2.m.a.97.1	yes	16
105.83	odd	4		525.2.m.b.307.8		16
105.104	even	2		525.2.m.b.118.7		16
420.167	even	4		1680.2.cz.d.97.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.m.a.13.1	✓	16	3.2	odd	2
105.2.m.a.13.2	yes	16	21.20	even	2
105.2.m.a.97.1	yes	16	105.62	odd	4
105.2.m.a.97.2	yes	16	15.2	even	4
315.2.p.e.118.7		16	7.6	odd	2	inner
315.2.p.e.118.8		16	1.1	even	1	trivial
315.2.p.e.307.7		16	5.2	odd	4	inner
315.2.p.e.307.8		16	35.27	even	4	inner
525.2.m.b.118.7		16	105.104	even	2
525.2.m.b.118.8		16	15.14	odd	2
525.2.m.b.307.7		16	15.8	even	4
525.2.m.b.307.8		16	105.83	odd	4
735.2.v.a.178.7		32	21.2	odd	6
735.2.v.a.178.8		32	21.5	even	6
735.2.v.a.313.1		32	21.17	even	6
735.2.v.a.313.2		32	21.11	odd	6
735.2.v.a.472.1		32	105.2	even	12
735.2.v.a.472.2		32	105.47	odd	12
735.2.v.a.607.7		32	105.17	odd	12
735.2.v.a.607.8		32	105.32	even	12
1680.2.cz.d.97.3		16	60.47	odd	4
1680.2.cz.d.97.6		16	420.167	even	4
1680.2.cz.d.433.3		16	84.83	odd	2
1680.2.cz.d.433.6		16	12.11	even	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.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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