LMFDB - Embedded newform 315.2.p.e.118.7

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			118.7
Root			$0.517174 + 1.31626i$ of defining polynomial
Character	$\chi$	$=$	315.118
Dual form			315.2.p.e.307.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.86147 - 1.86147i) q^{2} -4.93012i q^{4} +(-1.50619 - 1.65269i) q^{5} +(1.46123 + 2.20563i) q^{7} +(-5.45433 - 5.45433i) q^{8} +O(q^{10})$	\(q+(1.86147 - 1.86147i) q^{2} -4.93012i q^{4} +(-1.50619 - 1.65269i) q^{5} +(1.46123 + 2.20563i) q^{7} +(-5.45433 - 5.45433i) q^{8} +(-5.88016 - 0.272713i) q^{10} +1.46279 q^{11} +(-0.887844 + 0.887844i) q^{13} +(6.82574 + 1.38567i) q^{14} -10.4459 q^{16} +(-2.10614 - 2.10614i) q^{17} +3.95987 q^{19} +(-8.14798 + 7.42570i) q^{20} +(2.72294 - 2.72294i) q^{22} +(4.13007 + 4.13007i) q^{23} +(-0.462789 + 4.97854i) q^{25} +3.30539i q^{26} +(10.8740 - 7.20405i) q^{28} +5.18572i q^{29} -6.10346i q^{31} +(-8.53599 + 8.53599i) q^{32} -7.84104 q^{34} +(1.44434 - 5.73706i) q^{35} +(2.25560 - 2.25560i) q^{37} +(7.37117 - 7.37117i) q^{38} +(-0.799082 + 17.2296i) q^{40} -0.769968i q^{41} +(-5.18572 - 5.18572i) q^{43} -7.21173i q^{44} +15.3760 q^{46} +(8.57041 + 8.57041i) q^{47} +(-2.72961 + 6.44587i) q^{49} +(8.40592 + 10.1289i) q^{50} +(4.37718 + 4.37718i) q^{52} +(0.544449 + 0.544449i) q^{53} +(-2.20324 - 2.41754i) q^{55} +(4.06020 - 20.0003i) q^{56} +(9.65306 + 9.65306i) q^{58} -3.19633 q^{59} +1.42064i q^{61} +(-11.3614 - 11.3614i) q^{62} +10.8872i q^{64} +(2.80460 + 0.130073i) q^{65} +(-5.93012 + 5.93012i) q^{67} +(-10.3835 + 10.3835i) q^{68} +(-7.99077 - 13.3679i) q^{70} -7.62611 q^{71} +(-6.81378 + 6.81378i) q^{73} -8.39746i q^{74} -19.5226i q^{76} +(2.13747 + 3.22637i) q^{77} -4.52029i q^{79} +(15.7335 + 17.2638i) q^{80} +(-1.43327 - 1.43327i) q^{82} +(-6.75794 + 6.75794i) q^{83} +(-0.308559 + 6.65306i) q^{85} -19.3061 q^{86} +(-7.97854 - 7.97854i) q^{88} +1.19991 q^{89} +(-3.25560 - 0.660910i) q^{91} +(20.3618 - 20.3618i) q^{92} +31.9071 q^{94} +(-5.96431 - 6.54445i) q^{95} +(8.68829 + 8.68829i) q^{97} +(6.91770 + 17.0799i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$7$	1.46123	+	2.20563i	0.552293	+	0.833650i
$7$	1.46123	+	2.20563i	0.552293	+	0.833650i
$8$	−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	$-0.805708\pi$
$13$	−0.887844	+	0.887844i	−0.246244	+	0.246244i	0.573183	+	0.819427i	$0.305708\pi$
$14$	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	$-0.367633\pi$
$17$	−2.10614	−	2.10614i	−0.510815	−	0.510815i	−0.914776	+	0.403961i	$0.867633\pi$
$18$		0			0
$19$	3.95987			0.908456			0.454228	−	0.890885i	$-0.349915\pi$
$19$	3.95987			0.908456			0.454228	+	0.890885i	$0.349915\pi$
$20$	−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
$28$	10.8740	−	7.20405i	2.05500	−	1.36144i
$29$			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	$-0.815349\pi$
$31$		−	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
$35$	1.44434	−	5.73706i	0.244138	−	0.969741i
$36$		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	$-0.980850\pi$
$41$		−	0.769968i		−	0.120249i	0.998191	−	0.0601244i	$-0.0191497\pi$
$42$		0			0
$43$	−5.18572	−	5.18572i	−0.790816	−	0.790816i	0.190811	−	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	$0.0951394\pi$
$47$	8.57041	+	8.57041i	1.25012	+	1.25012i	0.294459	+	0.955664i	$0.404861\pi$
$48$		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	$-0.566716\pi$
$59$	−3.19633			−0.416127			−0.208063	+	0.978115i	$0.566716\pi$
$60$		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	−0.969514	−	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
$70$	−7.99077	−	13.3679i	−0.955079	−	1.59778i
$71$	−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	$-0.940704\pi$
$73$	−6.81378	+	6.81378i	−0.797493	+	0.797493i	0.185207	+	0.982700i	$0.440704\pi$
$74$		−	8.39746i		−	0.976185i
$75$		0			0
$76$		−	19.5226i		−	2.23940i
$77$	2.13747	+	3.22637i	0.243588	+	0.367679i
$78$		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	−0.972921	−	0.231140i	$-0.925754\pi$
$83$	−6.75794	+	6.75794i	−0.741781	+	0.741781i	0.231140	+	0.972921i	$0.425754\pi$
$84$		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	$-0.479743\pi$
$89$	1.19991			0.127190			0.0635950	+	0.997976i	$0.479743\pi$
$90$		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	$-0.0355950\pi$
$97$	8.68829	+	8.68829i	0.882162	+	0.882162i	−0.111592	+	0.993754i	$0.535595\pi$
$98$	6.91770	+	17.0799i	0.698794	+	1.72533i
$99$		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	$-0.946490\pi$
$103$	−8.30776	+	8.30776i	−0.818588	+	0.818588i	0.167316	+	0.985903i	$0.446490\pi$
$104$	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
$112$	−15.2638	−	23.0397i	−1.44230	−	2.17705i
$113$	−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	$-0.912953\pi$
$131$		−	6.18216i		−	0.540138i	0.962841	−	0.270069i	$-0.0870465\pi$
$132$		0			0
$133$	5.78628	+	8.73401i	0.501735	+	0.757334i
$134$			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	$-0.330184\pi$
$139$	11.9913			1.01709			0.508544	+	0.861036i	$0.330184\pi$
$140$	−28.2844	−	7.12077i	−2.39047	−	0.601815i
$141$		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	0.638298	−	0.769789i	$-0.279639\pi$
$157$	−1.64757	−	1.64757i	−0.131491	−	0.131491i	−0.769789	+	0.638298i	$0.779639\pi$
$158$	−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	0.718353	−	0.695679i	$-0.244896\pi$
$167$	0.293008	+	0.293008i	0.0226737	+	0.0226737i	−0.695679	+	0.718353i	$0.744896\pi$
$168$		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	$-0.809415\pi$
$173$	−3.45189	+	3.45189i	−0.262442	+	0.262442i	0.563603	+	0.826046i	$0.309415\pi$
$174$		0			0
$175$	−11.6571	+	6.25405i	−0.881190	+	0.472762i
$176$	−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	$-0.897877\pi$
$181$		−	8.48528i		−	0.630706i	0.948974	−	0.315353i	$-0.102123\pi$
$182$	−7.29046	+	4.82993i	−0.540405	+	0.358019i
$183$		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	$-0.753156\pi$
$199$	−20.1468			−1.42817			−0.714084	+	0.700061i	$0.753156\pi$
$200$	29.6788	−	24.6304i	2.09861	−	1.74163i
$201$		0			0
$202$	−28.5587	−	28.5587i	−2.00938	−	2.00938i
$203$	−11.4378	+	7.57754i	−0.802775	+	0.531839i
$204$		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
$217$	13.4620	−	8.91857i	0.913858	−	0.605432i
$218$	−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	$-0.740037\pi$
$223$	0.660910	−	0.660910i	0.0442578	−	0.0442578i	0.728889	+	0.684632i	$0.240037\pi$
$224$	−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	$-0.947168\pi$
$227$	−17.3487	−	17.3487i	−1.15147	−	1.15147i	−0.165216	−	0.986257i	$-0.552832\pi$
$228$		0			0
$229$	25.0782			1.65721			0.828607	−	0.559831i	$-0.189134\pi$
$229$	25.0782			1.65721			0.828607	+	0.559831i	$0.189134\pi$
$230$	−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
$238$	−11.4576	−	17.2944i	−0.742684	−	1.12103i
$239$		−	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	$-0.993601\pi$
$241$		−	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
$245$	14.7643	−	5.19750i	0.943260	−	0.332056i
$246$		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	0.906247	+	0.422749i	$0.138935\pi$
$257$	21.3054	+	21.3054i	1.32900	+	1.32900i	0.422749	+	0.906247i	$0.361065\pi$
$258$		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	$-0.668789\pi$
$269$	−16.5903			−1.01153			−0.505764	+	0.862672i	$0.668789\pi$
$270$		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	0.340013	−	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
$280$	−39.1697	+	23.4139i	−2.34084	+	1.39925i
$281$	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	$-0.785593\pi$
$283$	−2.65471	+	2.65471i	−0.157806	+	0.157806i	0.623788	+	0.781594i	$0.285593\pi$
$284$			37.5977i			2.23101i
$285$		0			0
$286$			4.83508i			0.285905i
$287$	1.69826	−	1.12510i	0.100245	−	0.0664126i
$288$		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	$-0.770621\pi$
$293$	−1.56714	+	1.56714i	−0.0915536	+	0.0915536i	0.659847	+	0.751400i	$0.270621\pi$
$294$		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	$-0.00300676\pi$
$307$	17.3551	+	17.3551i	0.990510	+	0.990510i	−0.00944588	+	0.999955i	$0.503007\pi$
$308$	15.9064	−	10.5380i	0.906352	−	0.600459i
$309$		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	$-0.823476\pi$
$313$	−5.72426	+	5.72426i	−0.323554	+	0.323554i	0.526575	+	0.850129i	$0.323476\pi$
$314$	−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
$322$	22.4679	+	33.9138i	1.25209	+	1.88994i
$323$	−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
$343$	−18.2058	+	3.39840i	−0.983020	+	0.183497i
$344$			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	$-0.629328\pi$
$349$	−14.7663			−0.790420			−0.395210	+	0.918591i	$0.629328\pi$
$350$	−10.0575	+	33.3409i	−0.537597	+	1.78215i
$351$		0			0
$352$	−12.4864	+	12.4864i	−0.665525	+	0.665525i
$353$	−12.4890	+	12.4890i	−0.664724	+	0.664724i	−0.956490	−	0.291766i	$-0.905757\pi$
$353$	−12.4890	+	12.4890i	−0.664724	+	0.664724i	0.291766	+	0.956490i	$0.405757\pi$
$354$		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	0.351881	−	0.936045i	$-0.385542\pi$
$367$	−11.1910	−	11.1910i	−0.584163	−	0.584163i	−0.936045	+	0.351881i	$0.885542\pi$
$368$	−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	−0.162729	−	0.986671i	$-0.552030\pi$
$383$	16.1249	−	16.1249i	0.823942	−	0.823942i	0.986671	+	0.162729i	$0.0520295\pi$
$384$		0			0
$385$	2.11276	−	8.39211i	0.107676	−	0.427702i
$386$	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
$392$	50.0461	−	20.2697i	2.52771	−	1.02378i
$393$		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	$-0.444663\pi$
$397$	−16.1781	−	16.1781i	−0.811955	−	0.811955i	−0.984927	+	0.172972i	$0.944663\pi$
$398$	−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	$-0.705312\pi$
$409$	−24.3171			−1.20241			−0.601203	+	0.799097i	$0.705312\pi$
$410$	−0.209980	+	4.52753i	−0.0103702	+	0.223599i
$411$		0			0
$412$	40.9583	+	40.9583i	2.01787	+	2.01787i
$413$	−4.67058	−	7.04992i	−0.229824	−	0.346904i
$414$		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	$-0.372280\pi$
$419$	15.9893			0.781127			0.390563	+	0.920576i	$0.372280\pi$
$420$		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
$427$	−3.13341	+	2.07588i	−0.151636	+	0.100459i
$428$	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	$-0.348961\pi$
$433$	28.0171	−	28.0171i	1.34642	−	1.34642i	0.889520	−	0.456896i	$-0.151039\pi$
$434$	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	$-0.482090\pi$
$439$	2.35656			0.112473			0.0562363	+	0.998417i	$0.482090\pi$
$440$	−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
$448$	−24.0131	+	15.9087i	−1.13451	+	0.751616i
$449$		−	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
$455$	3.81127	+	6.37597i	0.178675	+	0.298910i
$456$		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	$0.170929\pi$
$461$			21.9670i			1.02311i	−0.859252	+	0.511553i	$0.829071\pi$
$462$		0			0
$463$	−21.6776	−	21.6776i	−1.00744	−	1.00744i	−0.999972	−	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	0.852263	−	0.523113i	$-0.175230\pi$
$467$	7.11299	+	7.11299i	0.329150	+	0.329150i	−0.523113	+	0.852263i	$0.675230\pi$
$468$		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	$-0.241416\pi$
$479$	31.7749			1.45183			0.725917	+	0.687782i	$0.241416\pi$
$480$		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
$490$	17.8084	−	37.1583i	0.804501	−	1.67864i
$491$	−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
$497$	−11.1435	−	16.8204i	−0.499855	−	0.754497i
$498$		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	−0.867980	−	0.496599i	$-0.834582\pi$
$503$	−8.32921	+	8.32921i	−0.371381	+	0.371381i	0.496599	+	0.867980i	$0.334582\pi$
$504$		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	$-0.831485\pi$
$509$	−38.9452			−1.72622			−0.863108	+	0.505020i	$0.831485\pi$
$510$		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
$518$	18.5217	−	12.2706i	0.813796	−	0.539140i
$519$		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	$-0.898960\pi$
$523$	−14.5887	+	14.5887i	−0.637921	+	0.637921i	0.312121	+	0.950042i	$0.398960\pi$
$524$	−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
$532$	43.0597	−	28.5271i	1.86688	−	1.23681i
$533$	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
$553$	9.97009	−	6.60519i	0.423971	−	0.280881i
$554$		−	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
$560$	−15.0874	+	59.9286i	−0.637558	+	2.53245i
$561$		0			0
$562$	39.3736	−	39.3736i	1.66087	−	1.66087i
$563$	0.702475	−	0.702475i	0.0296058	−	0.0296058i	−0.692149	−	0.721755i	$-0.743336\pi$
$563$	0.702475	−	0.702475i	0.0296058	−	0.0296058i	0.721755	+	0.692149i	$0.243336\pi$
$564$		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	0.888940	−	0.458024i	$-0.151442\pi$
$577$	10.3510	+	10.3510i	0.430917	+	0.430917i	−0.458024	+	0.888940i	$0.651442\pi$
$578$	−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	$-0.461659\pi$
$587$	−21.1413	−	21.1413i	−0.872594	−	0.872594i	−0.992755	+	0.120160i	$0.961659\pi$
$588$		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	$-0.684108\pi$
$593$	7.07816	−	7.07816i	0.290665	−	0.290665i	0.837343	+	0.546678i	$0.184108\pi$
$594$		0			0
$595$	−15.1251	+	9.04109i	−0.620067	+	0.370649i
$596$	−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	$0.253815\pi$
$601$			35.0829i			1.43106i	−0.698580	+	0.715532i	$0.746185\pi$
$602$	−28.2107	−	42.5822i	−1.14978	−	1.73552i
$603$		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	$-0.200802\pi$
$607$	5.36385	+	5.36385i	0.217712	+	0.217712i	−0.589822	+	0.807533i	$0.700802\pi$
$608$	−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	$-0.422027\pi$
$619$	12.0675			0.485034			0.242517	+	0.970147i	$0.422027\pi$
$620$	45.3224	+	49.7309i	1.82019	+	1.99724i
$621$		0			0
$622$	−57.8262	−	57.8262i	−2.31862	−	2.31862i
$623$	1.75334	+	2.64655i	0.0702462	+	0.106032i
$624$		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
$637$	−3.29946	−	8.14639i	−0.130729	−	0.322772i
$638$	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	$-0.640315\pi$
$643$	12.1140	−	12.1140i	0.477731	−	0.477731i	0.904405	+	0.426675i	$0.140315\pi$
$644$	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	$-0.428148\pi$
$647$	−19.0978	−	19.0978i	−0.750814	−	0.750814i	−0.974631	+	0.223817i	$0.928148\pi$
$648$		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
$658$	46.6236	+	70.3752i	1.81758	+	2.74351i
$659$			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	$0.386545\pi$
$661$			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
$665$	5.71939	−	22.7180i	0.221789	−	0.880967i
$666$		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	0.676882	−	0.736092i	$-0.263331\pi$
$677$	−1.54060	−	1.54060i	−0.0592101	−	0.0592101i	−0.736092	+	0.676882i	$0.763331\pi$
$678$		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	$-0.937302\pi$
$691$		−	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
$700$	30.8332	+	57.4707i	1.16539	+	2.17219i
$701$	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
$707$	33.8389	−	22.4183i	1.27264	−	0.843126i
$708$		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	$-0.499955\pi$
$719$	0.00762056			0.000284199			0.000142099		1.00000i	$0.499955\pi$
$720$		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	$-0.980365\pi$
$727$	−28.5738	−	28.5738i	−1.05974	−	1.05974i	−0.0616465	−	0.998098i	$-0.519635\pi$
$728$	14.1523	+	21.3619i	0.524519	+	0.791726i
$729$		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	$-0.532728\pi$
$733$	24.1522	−	24.1522i	0.892083	−	0.892083i	0.994719	+	0.102636i	$0.0327275\pi$
$734$	−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
$742$	2.96184	+	4.47070i	0.108733	+	0.164125i
$743$	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	$-0.780419\pi$
$761$		−	35.1123i		−	1.27282i	0.771351	−	0.636410i	$-0.219581\pi$
$762$		0			0
$763$	16.4228	−	10.8801i	0.594547	−	0.393887i
$764$		−	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	$-0.547052\pi$
$769$	−8.16835			−0.294558			−0.147279	+	0.989095i	$0.547052\pi$
$770$	−11.6888	−	19.5545i	−0.421235	−	0.704695i
$771$		0			0
$772$	66.8609	−	66.8609i	2.40638	−	2.40638i
$773$	−2.51166	+	2.51166i	−0.0903382	+	0.0903382i	−0.750832	−	0.660494i	$-0.770347\pi$
$773$	−2.51166	+	2.51166i	−0.0903382	+	0.0903382i	0.660494	+	0.750832i	$0.270347\pi$
$774$		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	$-0.354014\pi$
$787$	−12.7347	−	12.7347i	−0.453943	−	0.453943i	−0.896661	+	0.442718i	$0.854014\pi$
$788$	−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	$-0.0511912\pi$
$797$	23.3462	+	23.3462i	0.826967	+	0.826967i	−0.160129	+	0.987096i	$0.551191\pi$
$798$		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
$805$	29.6597	−	17.7293i	1.04537	−	0.624874i
$806$	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	$-0.971335\pi$
$811$		−	5.12216i		−	0.179863i	0.995948	−	0.0899317i	$-0.0286649\pi$
$812$	37.3582	+	56.3897i	1.31102	+	1.97889i
$813$		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	$-0.806802\pi$
$829$	−47.2996			−1.64278			−0.821392	+	0.570365i	$0.806802\pi$
$830$	41.5807	−	37.8948i	1.44329	−	1.31535i
$831$		0			0
$832$	−9.66613	−	9.66613i	−0.335113	−	0.335113i
$833$	19.3249	−	7.82698i	0.669567	−	0.271189i
$834$		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	$-0.440172\pi$
$839$	10.8244			0.373699			0.186850	+	0.982389i	$0.440172\pi$
$840$		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
$847$	−12.9469	−	19.5424i	−0.444860	−	0.671486i
$848$	−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	$0.552103\pi$
$853$	−33.5751	+	33.5751i	−1.14959	+	1.14959i	−0.986633	+	0.162958i	$0.947897\pi$
$854$	−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	$-0.180838\pi$
$857$	8.92479	+	8.92479i	0.304865	+	0.304865i	−0.538049	+	0.842914i	$0.680838\pi$
$858$		0			0
$859$	−20.3701			−0.695020			−0.347510	−	0.937676i	$-0.612973\pi$
$859$	−20.3701			−0.695020			−0.347510	+	0.937676i	$0.612973\pi$
$860$	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
$868$	−43.9696	−	66.3692i	−1.49243	−	2.25272i
$869$		−	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
$875$	27.8937	+	9.84575i	0.942981	+	0.332847i
$876$		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	$0.200471\pi$
$881$			34.9639i			1.17796i	−0.808147	+	0.588981i	$0.799529\pi$
$882$		0			0
$883$	19.3814	+	19.3814i	0.652235	+	0.652235i	0.953531	−	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	0.305884	−	0.952069i	$-0.401048\pi$
$887$	−19.2450	−	19.2450i	−0.646184	−	0.646184i	−0.952069	+	0.305884i	$0.901048\pi$
$888$		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
$910$	18.9632	+	4.77410i	0.628624	+	0.158260i
$911$	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
$917$	13.6356	−	9.03357i	0.450286	−	0.298315i
$918$		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	$-0.529227\pi$
$929$	−5.58936			−0.183381			−0.0916905	+	0.995788i	$0.529227\pi$
$930$		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	$-0.0936861\pi$
$937$	20.4143	+	20.4143i	0.666906	+	0.666906i	−0.290092	+	0.956999i	$0.593686\pi$
$938$	−48.6947	+	32.2603i	−1.58994	+	1.05334i
$939$		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	−0.809201	−	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
$952$	−50.6748	+	33.5721i	−1.64238	+	1.08808i
$953$	−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	$0.110496\pi$
$971$			21.2020i			0.680404i	−0.940352	+	0.340202i	$0.889504\pi$
$972$		0			0
$973$	17.5220	+	26.4483i	0.561731	+	0.847895i
$974$			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
$980$	−25.6243	−	72.7901i	−0.818538	−	2.32519i
$981$		0			0
$982$	−52.7541	+	52.7541i	−1.68345	+	1.68345i
$983$	−1.74914	+	1.74914i	−0.0557891	+	0.0557891i	−0.734451	−	0.678662i	$-0.762560\pi$
$983$	−1.74914	+	1.74914i	−0.0557891	+	0.0557891i	0.678662	+	0.734451i	$0.262560\pi$
$984$		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	$0.112524\pi$
$997$	40.5538	+	40.5538i	1.28435	+	1.28435i	0.346186	+	0.938166i	$0.387476\pi$
$998$	−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.118.7		16
3.2	odd	2		105.2.m.a.13.2	yes	16
5.2	odd	4	inner	315.2.p.e.307.8		16
7.6	odd	2	inner	315.2.p.e.118.8		16
12.11	even	2		1680.2.cz.d.433.3		16
15.2	even	4		105.2.m.a.97.1	yes	16
15.8	even	4		525.2.m.b.307.8		16
15.14	odd	2		525.2.m.b.118.7		16
21.2	odd	6		735.2.v.a.178.8		32
21.5	even	6		735.2.v.a.178.7		32
21.11	odd	6		735.2.v.a.313.1		32
21.17	even	6		735.2.v.a.313.2		32
21.20	even	2		105.2.m.a.13.1	✓	16
35.27	even	4	inner	315.2.p.e.307.7		16
60.47	odd	4		1680.2.cz.d.97.6		16
84.83	odd	2		1680.2.cz.d.433.6		16
105.2	even	12		735.2.v.a.472.2		32
105.17	odd	12		735.2.v.a.607.8		32
105.32	even	12		735.2.v.a.607.7		32
105.47	odd	12		735.2.v.a.472.1		32
105.62	odd	4		105.2.m.a.97.2	yes	16
105.83	odd	4		525.2.m.b.307.7		16
105.104	even	2		525.2.m.b.118.8		16
420.167	even	4		1680.2.cz.d.97.3		16

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(1.86147 - 1.86147i) q^{2} -4.93012i q^{4} +(-1.50619 - 1.65269i) q^{5} +(1.46123 + 2.20563i) q^{7} +(-5.45433 - 5.45433i) q^{8} +O(q^{10})\)	\(q+(1.86147 - 1.86147i) q^{2} -4.93012i q^{4} +(-1.50619 - 1.65269i) q^{5} +(1.46123 + 2.20563i) q^{7} +(-5.45433 - 5.45433i) q^{8} +(-5.88016 - 0.272713i) q^{10} +1.46279 q^{11} +(-0.887844 + 0.887844i) q^{13} +(6.82574 + 1.38567i) q^{14} -10.4459 q^{16} +(-2.10614 - 2.10614i) q^{17} +3.95987 q^{19} +(-8.14798 + 7.42570i) q^{20} +(2.72294 - 2.72294i) q^{22} +(4.13007 + 4.13007i) q^{23} +(-0.462789 + 4.97854i) q^{25} +3.30539i q^{26} +(10.8740 - 7.20405i) q^{28} +5.18572i q^{29} -6.10346i q^{31} +(-8.53599 + 8.53599i) q^{32} -7.84104 q^{34} +(1.44434 - 5.73706i) q^{35} +(2.25560 - 2.25560i) q^{37} +(7.37117 - 7.37117i) q^{38} +(-0.799082 + 17.2296i) q^{40} -0.769968i q^{41} +(-5.18572 - 5.18572i) q^{43} -7.21173i q^{44} +15.3760 q^{46} +(8.57041 + 8.57041i) q^{47} +(-2.72961 + 6.44587i) q^{49} +(8.40592 + 10.1289i) q^{50} +(4.37718 + 4.37718i) q^{52} +(0.544449 + 0.544449i) q^{53} +(-2.20324 - 2.41754i) q^{55} +(4.06020 - 20.0003i) q^{56} +(9.65306 + 9.65306i) q^{58} -3.19633 q^{59} +1.42064i q^{61} +(-11.3614 - 11.3614i) q^{62} +10.8872i q^{64} +(2.80460 + 0.130073i) q^{65} +(-5.93012 + 5.93012i) q^{67} +(-10.3835 + 10.3835i) q^{68} +(-7.99077 - 13.3679i) q^{70} -7.62611 q^{71} +(-6.81378 + 6.81378i) q^{73} -8.39746i q^{74} -19.5226i q^{76} +(2.13747 + 3.22637i) q^{77} -4.52029i q^{79} +(15.7335 + 17.2638i) q^{80} +(-1.43327 - 1.43327i) q^{82} +(-6.75794 + 6.75794i) q^{83} +(-0.308559 + 6.65306i) q^{85} -19.3061 q^{86} +(-7.97854 - 7.97854i) q^{88} +1.19991 q^{89} +(-3.25560 - 0.660910i) q^{91} +(20.3618 - 20.3618i) q^{92} +31.9071 q^{94} +(-5.96431 - 6.54445i) q^{95} +(8.68829 + 8.68829i) q^{97} +(6.91770 + 17.0799i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{7} - 24 q^{8}+O(q^{10}) \) 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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