LMFDB - Embedded newform 525.2.m.b.307.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(118,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, 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("525.118");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.m (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4x^{14} + 6x^{12} - 12x^{10} + 33x^{8} - 48x^{6} + 96x^{4} - 256x^{2} + 256 $ x^16 - 4x^14 + 6x^12 - 12x^10 + 33x^8 - 48x^6 + 96x^4 - 256*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			307.8
Root			$0.517174 + 1.31626i$ of defining polynomial
Character	$\chi$	$=$	525.307
Dual form			525.2.m.b.118.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.86147 + 1.86147i) q^{2} +(0.707107 + 0.707107i) q^{3} +4.93012i q^{4} +2.63251i q^{6} +(2.20563 - 1.46123i) q^{7} +(-5.45433 + 5.45433i) q^{8} +1.00000i q^{9} +O(q^{10})$	\(q+(1.86147 + 1.86147i) q^{2} +(0.707107 + 0.707107i) q^{3} +4.93012i q^{4} +2.63251i q^{6} +(2.20563 - 1.46123i) q^{7} +(-5.45433 + 5.45433i) q^{8} +1.00000i q^{9} -1.46279 q^{11} +(-3.48612 + 3.48612i) q^{12} +(-0.887844 - 0.887844i) q^{13} +(6.82574 + 1.38567i) q^{14} -10.4459 q^{16} +(2.10614 - 2.10614i) q^{17} +(-1.86147 + 1.86147i) q^{18} -3.95987 q^{19} +(2.59286 + 0.526369i) q^{21} +(-2.72294 - 2.72294i) q^{22} +(4.13007 - 4.13007i) q^{23} -7.71359 q^{24} -3.30539i q^{26} +(-0.707107 + 0.707107i) q^{27} +(7.20405 + 10.8740i) q^{28} +5.18572i q^{29} -6.10346i q^{31} +(-8.53599 - 8.53599i) q^{32} +(-1.03435 - 1.03435i) q^{33} +7.84104 q^{34} -4.93012 q^{36} +(-2.25560 - 2.25560i) q^{37} +(-7.37117 - 7.37117i) q^{38} -1.25560i q^{39} +0.769968i q^{41} +(3.84671 + 5.80635i) q^{42} +(5.18572 - 5.18572i) q^{43} -7.21173i q^{44} +15.3760 q^{46} +(-8.57041 + 8.57041i) q^{47} +(-7.38635 - 7.38635i) q^{48} +(2.72961 - 6.44587i) q^{49} +2.97854 q^{51} +(4.37718 - 4.37718i) q^{52} +(0.544449 - 0.544449i) q^{53} -2.63251 q^{54} +(-4.06020 + 20.0003i) q^{56} +(-2.80005 - 2.80005i) q^{57} +(-9.65306 + 9.65306i) q^{58} -3.19633 q^{59} +1.42064i q^{61} +(11.3614 - 11.3614i) q^{62} +(1.46123 + 2.20563i) q^{63} -10.8872i q^{64} -3.85081i q^{66} +(5.93012 + 5.93012i) q^{67} +(10.3835 + 10.3835i) q^{68} +5.84081 q^{69} +7.62611 q^{71} +(-5.45433 - 5.45433i) q^{72} +(-6.81378 - 6.81378i) q^{73} -8.39746i q^{74} -19.5226i q^{76} +(-3.22637 + 2.13747i) q^{77} +(2.33726 - 2.33726i) q^{78} +4.52029i q^{79} -1.00000 q^{81} +(-1.43327 + 1.43327i) q^{82} +(6.75794 + 6.75794i) q^{83} +(-2.59507 + 12.7831i) q^{84} +19.3061 q^{86} +(-3.66686 + 3.66686i) q^{87} +(7.97854 - 7.97854i) q^{88} +1.19991 q^{89} +(-3.25560 - 0.660910i) q^{91} +(20.3618 + 20.3618i) q^{92} +(4.31580 - 4.31580i) q^{93} -31.9071 q^{94} -12.0717i q^{96} +(8.68829 - 8.68829i) q^{97} +(17.0799 - 6.91770i) q^{98} -1.46279i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} + 8 q^{21} + 16 q^{22} + 40 q^{23} - 24 q^{28} - 48 q^{32} - 16 q^{36} - 32 q^{37} + 16 q^{42} + 16 q^{43} + 64 q^{46} - 16 q^{51} - 24 q^{53} + 24 q^{56} - 8 q^{57} - 32 q^{58} - 8 q^{63} + 32 q^{67} + 64 q^{71} - 24 q^{72} + 24 q^{77} + 8 q^{78} - 16 q^{81} + 64 q^{86} + 64 q^{88} - 48 q^{91} + 40 q^{92} - 24 q^{93} + 96 q^{98}+O(q^{100}) $ 16 * q + 8 * q^7 - 24 * q^8 - 16 * q^11 - 48 * q^16 + 8 * q^21 + 16 * q^22 + 40 * q^23 - 24 * q^28 - 48 * q^32 - 16 * q^36 - 32 * q^37 + 16 * q^42 + 16 * q^43 + 64 * q^46 - 16 * q^51 - 24 * q^53 + 24 * q^56 - 8 * q^57 - 32 * q^58 - 8 * q^63 + 32 * q^67 + 64 * q^71 - 24 * q^72 + 24 * q^77 + 8 * q^78 - 16 * q^81 + 64 * q^86 + 64 * q^88 - 48 * q^91 + 40 * q^92 - 24 * q^93 + 96 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$	1.86147	+	1.86147i	1.31626	+	1.31626i	0.916715	+	0.399541i	$0.130831\pi$
$2$	1.86147	+	1.86147i	1.31626	+	1.31626i	0.399541	+	0.916715i	$0.369169\pi$
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$4$			4.93012i			2.46506i
$5$		0			0
$5$		0			0
$6$			2.63251i			1.07472i
$7$	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
$9$			1.00000i			0.333333i
$10$		0			0
$11$	−1.46279			−0.441048			−0.220524	−	0.975382i	$-0.570777\pi$
$11$	−1.46279			−0.441048			−0.220524	+	0.975382i	$0.570777\pi$
$12$	−3.48612	+	3.48612i	−1.00636	+	1.00636i
$13$	−0.887844	−	0.887844i	−0.246244	−	0.246244i	0.573183	−	0.819427i	$-0.305708\pi$
$13$	−0.887844	−	0.887844i	−0.246244	−	0.246244i	−0.819427	+	0.573183i	$0.805708\pi$
$14$	6.82574	+	1.38567i	1.82426	+	0.370337i
$15$		0			0
$16$	−10.4459			−2.61147
$17$	2.10614	−	2.10614i	0.510815	−	0.510815i	−0.403961	−	0.914776i	$-0.632367\pi$
$17$	2.10614	−	2.10614i	0.510815	−	0.510815i	0.914776	+	0.403961i	$0.132367\pi$
$18$	−1.86147	+	1.86147i	−0.438752	+	0.438752i
$19$	−3.95987			−0.908456			−0.454228	−	0.890885i	$-0.650085\pi$
$19$	−3.95987			−0.908456			−0.454228	+	0.890885i	$0.650085\pi$
$20$		0			0
$21$	2.59286	+	0.526369i	0.565809	+	0.114863i
$22$	−2.72294	−	2.72294i	−0.580532	−	0.580532i
$23$	4.13007	−	4.13007i	0.861180	−	0.861180i	−0.130295	−	0.991475i	$-0.541593\pi$
$23$	4.13007	−	4.13007i	0.861180	−	0.861180i	0.991475	+	0.130295i	$0.0415926\pi$
$24$	−7.71359			−1.57453
$25$		0			0
$26$		−	3.30539i		−	0.648240i
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$	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	$-0.815349\pi$
$31$		−	6.10346i		−	1.09621i	0.836408	−	0.548107i	$-0.184651\pi$
$32$	−8.53599	−	8.53599i	−1.50896	−	1.50896i
$33$	−1.03435	−	1.03435i	−0.180057	−	0.180057i
$34$	7.84104			1.34473
$35$		0			0
$36$	−4.93012			−0.821687
$37$	−2.25560	−	2.25560i	−0.370819	−	0.370819i	0.496957	−	0.867775i	$-0.334451\pi$
$37$	−2.25560	−	2.25560i	−0.370819	−	0.370819i	−0.867775	+	0.496957i	$0.834451\pi$
$38$	−7.37117	−	7.37117i	−1.19576	−	1.19576i
$39$		−	1.25560i		−	0.201057i
$40$		0			0
$41$			0.769968i			0.120249i	0.998191	+	0.0601244i	$0.0191497\pi$
$41$			0.769968i			0.120249i	−0.998191	+	0.0601244i	$0.980850\pi$
$42$	3.84671	+	5.80635i	0.593560	+	0.895939i
$43$	5.18572	−	5.18572i	0.790816	−	0.790816i	−0.190811	−	0.981627i	$-0.561112\pi$
$43$	5.18572	−	5.18572i	0.790816	−	0.790816i	0.981627	+	0.190811i	$0.0611118\pi$
$44$		−	7.21173i		−	1.08721i
$45$		0			0
$46$	15.3760			2.26707
$47$	−8.57041	+	8.57041i	−1.25012	+	1.25012i	−0.294459	+	0.955664i	$0.595139\pi$
$47$	−8.57041	+	8.57041i	−1.25012	+	1.25012i	−0.955664	+	0.294459i	$0.904861\pi$
$48$	−7.38635	−	7.38635i	−1.06613	−	1.06613i
$49$	2.72961	−	6.44587i	0.389944	−	0.920839i
$50$		0			0
$51$	2.97854			0.417079
$52$	4.37718	−	4.37718i	0.607006	−	0.607006i
$53$	0.544449	−	0.544449i	0.0747859	−	0.0747859i	−0.668724	−	0.743510i	$-0.733159\pi$
$53$	0.544449	−	0.544449i	0.0747859	−	0.0747859i	0.743510	+	0.668724i	$0.233159\pi$
$54$	−2.63251			−0.358240
$55$		0			0
$56$	−4.06020	+	20.0003i	−0.542567	+	2.67265i
$57$	−2.80005	−	2.80005i	−0.370876	−	0.370876i
$58$	−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
$63$	1.46123	+	2.20563i	0.184098	+	0.277883i
$64$		−	10.8872i		−	1.36090i
$65$		0			0
$66$		−	3.85081i		−	0.474002i
$67$	5.93012	+	5.93012i	0.724480	+	0.724480i	0.969514	−	0.245034i	$-0.0787993\pi$
$67$	5.93012	+	5.93012i	0.724480	+	0.724480i	−0.245034	+	0.969514i	$0.578799\pi$
$68$	10.3835	+	10.3835i	1.25919	+	1.25919i
$69$	5.84081			0.703150
$70$		0			0
$71$	7.62611			0.905053			0.452526	−	0.891751i	$-0.350523\pi$
$71$	7.62611			0.905053			0.452526	+	0.891751i	$0.350523\pi$
$72$	−5.45433	−	5.45433i	−0.642799	−	0.642799i
$73$	−6.81378	−	6.81378i	−0.797493	−	0.797493i	0.185207	−	0.982700i	$-0.440704\pi$
$73$	−6.81378	−	6.81378i	−0.797493	−	0.797493i	−0.982700	+	0.185207i	$0.940704\pi$
$74$		−	8.39746i		−	0.976185i
$75$		0			0
$76$		−	19.5226i		−	2.23940i
$77$	−3.22637	+	2.13747i	−0.367679	+	0.243588i
$78$	2.33726	−	2.33726i	0.264643	−	0.264643i
$79$			4.52029i			0.508573i	0.967129	+	0.254286i	$0.0818405\pi$
$79$			4.52029i			0.508573i	−0.967129	+	0.254286i	$0.918159\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$	−1.43327	+	1.43327i	−0.158278	+	0.158278i
$83$	6.75794	+	6.75794i	0.741781	+	0.741781i	0.972921	−	0.231140i	$-0.0742455\pi$
$83$	6.75794	+	6.75794i	0.741781	+	0.741781i	−0.231140	+	0.972921i	$0.574246\pi$
$84$	−2.59507	+	12.7831i	−0.283145	+	1.39475i
$85$		0			0
$86$	19.3061			2.08183
$87$	−3.66686	+	3.66686i	−0.393129	+	0.393129i
$88$	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
$93$	4.31580	−	4.31580i	0.447527	−	0.447527i
$94$	−31.9071			−3.29096
$95$		0			0
$96$		−	12.0717i		−	1.23206i
$97$	8.68829	−	8.68829i	0.882162	−	0.882162i	−0.111592	−	0.993754i	$-0.535595\pi$
$97$	8.68829	−	8.68829i	0.882162	−	0.882162i	0.993754	+	0.111592i	$0.0355950\pi$
$98$	17.0799	−	6.91770i	1.72533	−	0.698794i
$99$		−	1.46279i		−	0.147016i
$100$		0			0
$101$			15.3420i			1.52659i	0.646050	+	0.763295i	$0.276420\pi$
$101$			15.3420i			1.52659i	−0.646050	+	0.763295i	$0.723580\pi$
$102$	5.54445	+	5.54445i	0.548982	+	0.548982i
$103$	−8.30776	−	8.30776i	−0.818588	−	0.818588i	0.167316	−	0.985903i	$-0.446490\pi$
$103$	−8.30776	−	8.30776i	−0.818588	−	0.818588i	−0.985903	+	0.167316i	$0.946490\pi$
$104$	9.68519			0.949711
$105$		0			0
$106$	2.02695			0.196875
$107$	−4.39022	−	4.39022i	−0.424418	−	0.424418i	0.462303	−	0.886722i	$-0.347023\pi$
$107$	−4.39022	−	4.39022i	−0.424418	−	0.424418i	−0.886722	+	0.462303i	$0.847023\pi$
$108$	−3.48612	−	3.48612i	−0.335452	−	0.335452i
$109$			7.44587i			0.713185i	0.934260	+	0.356593i	$0.116062\pi$
$109$			7.44587i			0.713185i	−0.934260	+	0.356593i	$0.883938\pi$
$110$		0			0
$111$		−	3.18990i		−	0.302772i
$112$	−23.0397	+	15.2638i	−2.17705	+	1.44230i
$113$	−2.54445	+	2.54445i	−0.239362	+	0.239362i	−0.816586	−	0.577224i	$-0.804136\pi$
$113$	−2.54445	+	2.54445i	−0.239362	+	0.239362i	0.577224	+	0.816586i	$0.304136\pi$
$114$		−	10.4244i		−	0.976335i
$115$		0			0
$116$	−25.5663			−2.37377
$117$	0.887844	−	0.887844i	0.0820812	−	0.0820812i
$118$	−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
$123$	−0.544449	+	0.544449i	−0.0490913	+	0.0490913i
$124$	30.0908			2.70223
$125$		0			0
$126$	−1.38567	+	6.82574i	−0.123446	+	0.608086i
$127$	−7.86025	−	7.86025i	−0.697484	−	0.697484i	0.266383	−	0.963867i	$-0.414171\pi$
$127$	−7.86025	−	7.86025i	−0.697484	−	0.697484i	−0.963867	+	0.266383i	$0.914171\pi$
$128$	3.19418	−	3.19418i	0.282329	−	0.282329i
$129$	7.33372			0.645698
$130$		0			0
$131$			6.18216i			0.540138i	0.962841	+	0.270069i	$0.0870465\pi$
$131$			6.18216i			0.540138i	−0.962841	+	0.270069i	$0.912953\pi$
$132$	5.09947	−	5.09947i	0.443851	−	0.443851i
$133$	−8.73401	+	5.78628i	−0.757334	+	0.501735i
$134$			22.0775i			1.90720i
$135$		0			0
$136$			22.9752i			1.97011i
$137$	−9.05565	−	9.05565i	−0.773677	−	0.773677i	0.205071	−	0.978747i	$-0.434258\pi$
$137$	−9.05565	−	9.05565i	−0.773677	−	0.773677i	−0.978747	+	0.205071i	$0.934258\pi$
$138$	10.8725	+	10.8725i	0.925526	+	0.925526i
$139$	−11.9913			−1.01709			−0.508544	−	0.861036i	$-0.669816\pi$
$139$	−11.9913			−1.01709			−0.508544	+	0.861036i	$0.669816\pi$
$140$		0			0
$141$	−12.1204			−1.02072
$142$	14.1958	+	14.1958i	1.19128	+	1.19128i
$143$	1.29873	+	1.29873i	0.108605	+	0.108605i
$144$		−	10.4459i		−	0.870489i
$145$		0			0
$146$		−	25.3673i		−	2.09941i
$147$	6.48804	−	2.62780i	0.535125	−	0.216737i
$148$	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
$153$	2.10614	+	2.10614i	0.170272	+	0.170272i
$154$	−9.98463	−	2.02695i	−0.804584	−	0.163336i
$155$		0			0
$156$	6.19027			0.495618
$157$	−1.64757	+	1.64757i	−0.131491	+	0.131491i	−0.769789	−	0.638298i	$-0.779639\pi$
$157$	−1.64757	+	1.64757i	−0.131491	+	0.131491i	0.638298	+	0.769789i	$0.279639\pi$
$158$	−8.41438	+	8.41438i	−0.669412	+	0.669412i
$159$	0.769968			0.0610624
$160$		0			0
$161$	3.07442	−	15.1444i	0.242298	−	1.19355i
$162$	−1.86147	−	1.86147i	−0.146251	−	0.146251i
$163$	10.2746	−	10.2746i	0.804771	−	0.804771i	−0.179066	−	0.983837i	$-0.557308\pi$
$163$	10.2746	−	10.2746i	0.804771	−	0.804771i	0.983837	+	0.179066i	$0.0573077\pi$
$164$	−3.79604			−0.296421
$165$		0			0
$166$			25.1594i			1.95275i
$167$	−0.293008	+	0.293008i	−0.0226737	+	0.0226737i	−0.718353	−	0.695679i	$-0.755104\pi$
$167$	−0.293008	+	0.293008i	−0.0226737	+	0.0226737i	0.695679	+	0.718353i	$0.255104\pi$
$168$	−17.0133	+	11.2713i	−1.31261	+	0.869602i
$169$		−	11.4235i		−	0.878728i
$170$		0			0
$171$		−	3.95987i		−	0.302819i
$172$	25.5663	+	25.5663i	1.94941	+	1.94941i
$173$	3.45189	+	3.45189i	0.262442	+	0.262442i	0.826046	−	0.563603i	$-0.190585\pi$
$173$	3.45189	+	3.45189i	0.262442	+	0.262442i	−0.563603	+	0.826046i	$0.690585\pi$
$174$	−13.6515			−1.03492
$175$		0			0
$176$	15.2801			1.15178
$177$	−2.26015	−	2.26015i	−0.169883	−	0.169883i
$178$	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	$-0.102123\pi$
$182$	−4.82993	−	7.29046i	−0.358019	−	0.540405i
$183$	−1.00454	+	1.00454i	−0.0742581	+	0.0742581i
$184$			45.0536i			3.32139i
$185$		0			0
$186$	16.0674			1.17812
$187$	−3.08084	+	3.08084i	−0.225294	+	0.225294i
$188$	−42.2532	−	42.2532i	−3.08163	−	3.08163i
$189$	−0.526369	+	2.59286i	−0.0382877	+	0.188603i
$190$		0			0
$191$	−7.83424			−0.566866			−0.283433	−	0.958992i	$-0.591473\pi$
$191$	−7.83424			−0.566866			−0.283433	+	0.958992i	$0.591473\pi$
$192$	7.69841	−	7.69841i	0.555585	−	0.555585i
$193$	−13.5617	+	13.5617i	−0.976194	+	0.976194i	−0.999723	−	0.0235293i	$-0.992510\pi$
$193$	−13.5617	+	13.5617i	−0.976194	+	0.976194i	0.0235293	+	0.999723i	$0.492510\pi$
$194$	32.3459			2.32230
$195$		0			0
$196$	31.7789	+	13.4573i	2.26992	+	0.961236i
$197$	11.4791	+	11.4791i	0.817853	+	0.817853i	0.985797	−	0.167943i	$-0.0537126\pi$
$197$	11.4791	+	11.4791i	0.817853	+	0.817853i	−0.167943	+	0.985797i	$0.553713\pi$
$198$	2.72294	−	2.72294i	0.193511	−	0.193511i
$199$	20.1468			1.42817			0.714084	−	0.700061i	$-0.246844\pi$
$199$	20.1468			1.42817			0.714084	+	0.700061i	$0.246844\pi$
$200$		0			0
$201$			8.38646i			0.591535i
$202$	−28.5587	+	28.5587i	−2.00938	+	2.00938i
$203$	7.57754	+	11.4378i	0.531839	+	0.802775i
$204$			14.6846i			1.02812i
$205$		0			0
$206$		−	30.9292i		−	2.15494i
$207$	4.13007	+	4.13007i	0.287060	+	0.287060i
$208$	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
$213$	5.39247	+	5.39247i	0.369486	+	0.369486i
$214$		−	16.3445i		−	1.11729i
$215$		0			0
$216$		−	7.71359i		−	0.524843i
$217$	−8.91857	−	13.4620i	−0.605432	−	0.913858i
$218$	−13.8602	+	13.8602i	−0.938734	+	0.938734i
$219$		−	9.63614i		−	0.651150i
$220$		0			0
$221$	−3.73985			−0.251570
$222$	5.93790	−	5.93790i	0.398526	−	0.398526i
$223$	0.660910	+	0.660910i	0.0442578	+	0.0442578i	0.728889	−	0.684632i	$-0.240037\pi$
$223$	0.660910	+	0.660910i	0.0442578	+	0.0442578i	−0.684632	+	0.728889i	$0.740037\pi$
$224$	−31.3003	−	6.35418i	−2.09134	−	0.424557i
$225$		0			0
$226$	−9.47282			−0.630123
$227$	17.3487	−	17.3487i	1.15147	−	1.15147i	0.165216	−	0.986257i	$-0.447168\pi$
$227$	17.3487	−	17.3487i	1.15147	−	1.15147i	0.986257	−	0.165216i	$-0.0528323\pi$
$228$	13.8046	−	13.8046i	0.914232	−	0.914232i
$229$	−25.0782			−1.65721			−0.828607	−	0.559831i	$-0.810866\pi$
$229$	−25.0782			−1.65721			−0.828607	+	0.559831i	$0.810866\pi$
$230$		0			0
$231$	−3.79281	−	0.769968i	−0.249549	−	0.0506601i
$232$	−28.2847	−	28.2847i	−1.85698	−	1.85698i
$233$	−2.24138	+	2.24138i	−0.146837	+	0.146837i	−0.776704	−	0.629866i	$-0.783110\pi$
$233$	−2.24138	+	2.24138i	−0.146837	+	0.146837i	0.629866	+	0.776704i	$0.283110\pi$
$234$	3.30539			0.216080
$235$		0			0
$236$		−	15.7583i		−	1.02578i
$237$	−3.19633	+	3.19633i	−0.207624	+	0.207624i
$238$	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	$-0.993601\pi$
$241$		−	0.624129i		−	0.0402037i	0.999798	−	0.0201018i	$-0.00639905\pi$
$242$	−16.4931	−	16.4931i	−1.06021	−	1.06021i
$243$	−0.707107	−	0.707107i	−0.0453609	−	0.0453609i
$244$	−7.00393			−0.448381
$245$		0			0
$246$	−2.02695			−0.129234
$247$	3.51575	+	3.51575i	0.223702	+	0.223702i
$248$	33.2903	+	33.2903i	2.11394	+	2.11394i
$249$			9.55717i			0.605661i
$250$		0			0
$251$			16.3443i			1.03164i	0.856696	+	0.515822i	$0.172513\pi$
$251$			16.3443i			1.03164i	−0.856696	+	0.515822i	$0.827487\pi$
$252$	−10.8740	+	7.20405i	−0.684999	+	0.453813i
$253$	−6.04143	+	6.04143i	−0.379821	+	0.379821i
$254$		−	29.2632i		−	1.83614i
$255$		0			0
$256$	−9.88265			−0.617666
$257$	−21.3054	+	21.3054i	−1.32900	+	1.32900i	−0.422749	+	0.906247i	$0.638935\pi$
$257$	−21.3054	+	21.3054i	−1.32900	+	1.32900i	−0.906247	+	0.422749i	$0.861065\pi$
$258$	13.6515	+	13.6515i	0.849904	+	0.849904i
$259$	−8.27098	−	1.67907i	−0.513933	−	0.104332i
$260$		0			0
$261$	−5.18572			−0.320988
$262$	−11.5079	+	11.5079i	−0.710960	+	0.710960i
$263$	16.3449	−	16.3449i	1.00787	−	1.00787i	0.00789784	−	0.999969i	$-0.497486\pi$
$263$	16.3449	−	16.3449i	1.00787	−	1.00787i	0.999969	−	0.00789784i	$-0.00251399\pi$
$264$	11.2834			0.694442
$265$		0			0
$266$	−27.0291	−	5.48709i	−1.65726	−	0.336435i
$267$	0.848464	+	0.848464i	0.0519251	+	0.0519251i
$268$	−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
$273$	−1.83472	−	2.76939i	−0.111043	−	0.167611i
$274$		−	33.7136i		−	2.03671i
$275$		0			0
$276$			28.7959i			1.73331i
$277$	−21.3107	−	21.3107i	−1.28043	−	1.28043i	−0.940421	−	0.340013i	$-0.889569\pi$
$277$	−21.3107	−	21.3107i	−1.28043	−	1.28043i	−0.340013	−	0.940421i	$-0.610431\pi$
$278$	−22.3214	−	22.3214i	−1.33875	−	1.33875i
$279$	6.10346			0.365405
$280$		0			0
$281$	−21.1519			−1.26182			−0.630908	−	0.775858i	$-0.717317\pi$
$281$	−21.1519			−1.26182			−0.630908	+	0.775858i	$0.717317\pi$
$282$	−22.5617	−	22.5617i	−1.34353	−	1.34353i
$283$	−2.65471	−	2.65471i	−0.157806	−	0.157806i	0.623788	−	0.781594i	$-0.285593\pi$
$283$	−2.65471	−	2.65471i	−0.157806	−	0.157806i	−0.781594	+	0.623788i	$0.785593\pi$
$284$			37.5977i			2.23101i
$285$		0			0
$286$			4.83508i			0.285905i
$287$	1.12510	+	1.69826i	0.0664126	+	0.100245i
$288$	8.53599	−	8.53599i	0.502988	−	0.502988i
$289$			8.12832i			0.478136i
$290$		0			0
$291$	12.2871			0.720282
$292$	33.5928	−	33.5928i	1.96587	−	1.96587i
$293$	1.56714	+	1.56714i	0.0915536	+	0.0915536i	0.751400	−	0.659847i	$-0.229379\pi$
$293$	1.56714	+	1.56714i	0.0915536	+	0.0915536i	−0.659847	+	0.751400i	$0.729379\pi$
$294$	16.9688	+	7.18572i	0.989643	+	0.419080i
$295$		0			0
$296$	24.6056			1.43017
$297$	1.03435	−	1.03435i	0.0600190	−	0.0600190i
$298$	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
$303$	−10.8485	+	10.8485i	−0.623228	+	0.623228i
$304$	41.3643			2.37240
$305$		0			0
$306$			7.84104i			0.448242i
$307$	17.3551	−	17.3551i	0.990510	−	0.990510i	−0.00944588	−	0.999955i	$-0.503007\pi$
$307$	17.3551	−	17.3551i	0.990510	−	0.990510i	0.999955	+	0.00944588i	$0.00300676\pi$
$308$	−10.5380	−	15.9064i	−0.600459	−	0.906352i
$309$		−	11.7489i		−	0.668374i
$310$		0			0
$311$			31.0648i			1.76153i	0.473558	+	0.880763i	$0.342970\pi$
$311$			31.0648i			1.76153i	−0.473558	+	0.880763i	$0.657030\pi$
$312$	6.84846	+	6.84846i	0.387718	+	0.387718i
$313$	−5.72426	−	5.72426i	−0.323554	−	0.323554i	0.526575	−	0.850129i	$-0.323476\pi$
$313$	−5.72426	−	5.72426i	−0.323554	−	0.323554i	−0.850129	+	0.526575i	$0.823476\pi$
$314$	−6.13381			−0.346151
$315$		0			0
$316$	−22.2856			−1.25366
$317$	−0.752579	−	0.752579i	−0.0422691	−	0.0422691i	0.685656	−	0.727925i	$-0.259515\pi$
$317$	−0.752579	−	0.752579i	−0.0422691	−	0.0422691i	−0.727925	+	0.685656i	$0.759515\pi$
$318$	1.43327	+	1.43327i	0.0803738	+	0.0803738i
$319$		−	7.58562i		−	0.424713i
$320$		0			0
$321$		−	6.20871i		−	0.346536i
$322$	33.9138	−	22.4679i	1.88994	−	1.25209i
$323$	−8.34005	+	8.34005i	−0.464053	+	0.464053i
$324$		−	4.93012i		−	0.273896i
$325$		0			0
$326$	38.2518			2.11857
$327$	−5.26503	+	5.26503i	−0.291157	+	0.291157i
$328$	−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
$333$	2.25560	−	2.25560i	0.123606	−	0.123606i
$334$	−1.09085			−0.0596887
$335$		0			0
$336$	−27.0847	−	5.49839i	−1.47759	−	0.299962i
$337$	20.0460	+	20.0460i	1.09197	+	1.09197i	0.995318	+	0.0966558i	$0.0308146\pi$
$337$	20.0460	+	20.0460i	1.09197	+	1.09197i	0.0966558	+	0.995318i	$0.469185\pi$
$338$	21.2644	−	21.2644i	1.15663	−	1.15663i
$339$	−3.59839			−0.195438
$340$		0			0
$341$			8.92808i			0.483482i
$342$	7.37117	−	7.37117i	0.398587	−	0.398587i
$343$	−3.39840	−	18.2058i	−0.183497	−	0.983020i
$344$			56.5693i			3.05001i
$345$		0			0
$346$			12.8512i			0.690883i
$347$	20.0847	+	20.0847i	1.07820	+	1.07820i	0.996671	+	0.0815328i	$0.0259815\pi$
$347$	20.0847	+	20.0847i	1.07820	+	1.07820i	0.0815328	+	0.996671i	$0.474018\pi$
$348$	−18.0781	−	18.0781i	−0.969087	−	0.969087i
$349$	14.7663			0.790420			0.395210	−	0.918591i	$-0.370672\pi$
$349$	14.7663			0.790420			0.395210	+	0.918591i	$0.370672\pi$
$350$		0			0
$351$	1.25560			0.0670190
$352$	12.4864	+	12.4864i	0.665525	+	0.665525i
$353$	12.4890	+	12.4890i	0.664724	+	0.664724i	0.956490	−	0.291766i	$-0.0942429\pi$
$353$	12.4890	+	12.4890i	0.664724	+	0.664724i	−0.291766	+	0.956490i	$0.594243\pi$
$354$		−	8.41438i		−	0.447219i
$355$		0			0
$356$			5.91570i			0.313531i
$357$	6.56955	−	4.35233i	0.347697	−	0.230350i
$358$	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
$363$	−6.26514	−	6.26514i	−0.328835	−	0.328835i
$364$	3.25837	−	16.0505i	0.170785	−	0.841276i
$365$		0			0
$366$	−3.73985			−0.195485
$367$	−11.1910	+	11.1910i	−0.584163	+	0.584163i	−0.936045	−	0.351881i	$-0.885542\pi$
$367$	−11.1910	+	11.1910i	−0.584163	+	0.584163i	0.351881	+	0.936045i	$0.385542\pi$
$368$	−43.1422	+	43.1422i	−2.24894	+	2.24894i
$369$	−0.769968			−0.0400829
$370$		0			0
$371$	0.405287	−	1.99642i	0.0210415	−	0.103649i
$372$	21.2774	+	21.2774i	1.10318	+	1.10318i
$373$	−17.2746	+	17.2746i	−0.894446	+	0.894446i	−0.994938	−	0.100492i	$-0.967958\pi$
$373$	−17.2746	+	17.2746i	−0.894446	+	0.894446i	0.100492	+	0.994938i	$0.467958\pi$
$374$	−11.4698			−0.593088
$375$		0			0
$376$		−	93.4917i		−	4.82147i
$377$	4.60412	−	4.60412i	0.237124	−	0.237124i
$378$	−5.80635	+	3.84671i	−0.298646	+	0.197853i
$379$			17.6237i			0.905267i	0.891697	+	0.452634i	$0.149515\pi$
$379$			17.6237i			0.905267i	−0.891697	+	0.452634i	$0.850485\pi$
$380$		0			0
$381$		−	11.1161i		−	0.569493i
$382$	−14.5832	−	14.5832i	−0.746141	−	0.746141i
$383$	−16.1249	−	16.1249i	−0.823942	−	0.823942i	0.162729	−	0.986671i	$-0.447970\pi$
$383$	−16.1249	−	16.1249i	−0.823942	−	0.823942i	−0.986671	+	0.162729i	$0.947970\pi$
$384$	4.51726			0.230520
$385$		0			0
$386$	−50.4894			−2.56984
$387$	5.18572	+	5.18572i	0.263605	+	0.263605i
$388$	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
$393$	−4.37145	+	4.37145i	−0.220510	+	0.220510i
$394$			42.7360i			2.15301i
$395$		0			0
$396$	7.21173			0.362403
$397$	−16.1781	+	16.1781i	−0.811955	+	0.811955i	−0.984927	−	0.172972i	$-0.944663\pi$
$397$	−16.1781	+	16.1781i	−0.811955	+	0.811955i	0.172972	+	0.984927i	$0.444663\pi$
$398$	37.5026	+	37.5026i	1.87983	+	1.87983i
$399$	−10.2674	−	2.08435i	−0.514013	−	0.104348i
$400$		0			0
$401$	−0.977595			−0.0488188			−0.0244094	−	0.999702i	$-0.507771\pi$
$401$	−0.977595			−0.0488188			−0.0244094	+	0.999702i	$0.507771\pi$
$402$	−15.6111	+	15.6111i	−0.778612	+	0.778612i
$403$	−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
$408$	−16.2459	+	16.2459i	−0.804293	+	0.804293i
$409$	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			0
$411$		−	12.8066i		−	0.631704i
$412$	40.9583	−	40.9583i	2.01787	−	2.01787i
$413$	−7.04992	+	4.67058i	−0.346904	+	0.229824i
$414$			15.3760i			0.755689i
$415$		0			0
$416$			15.1573i			0.743146i
$417$	−8.47912	−	8.47912i	−0.415224	−	0.415224i
$418$	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
$423$	−8.57041	−	8.57041i	−0.416708	−	0.416708i
$424$			5.93921i			0.288434i
$425$		0			0
$426$			20.0758i			0.972677i
$427$	2.07588	+	3.13341i	0.100459	+	0.151636i
$428$	21.6443	−	21.6443i	1.04622	−	1.04622i
$429$			1.83668i			0.0886758i
$430$		0			0
$431$	22.2722			1.07281			0.536407	−	0.843960i	$-0.319781\pi$
$431$	22.2722			1.07281			0.536407	+	0.843960i	$0.319781\pi$
$432$	7.38635	−	7.38635i	0.355376	−	0.355376i
$433$	28.0171	+	28.0171i	1.34642	+	1.34642i	0.889520	+	0.456896i	$0.151039\pi$
$433$	28.0171	+	28.0171i	1.34642	+	1.34642i	0.456896	+	0.889520i	$0.348961\pi$
$434$	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
$438$	17.9374	−	17.9374i	0.857080	−	0.857080i
$439$	−2.35656			−0.112473			−0.0562363	−	0.998417i	$-0.517910\pi$
$439$	−2.35656			−0.112473			−0.0562363	+	0.998417i	$0.517910\pi$
$440$		0			0
$441$	6.44587	+	2.72961i	0.306946	+	0.129981i
$442$	−6.96162	−	6.96162i	−0.331130	−	0.331130i
$443$	5.47247	−	5.47247i	0.260005	−	0.260005i	−0.565051	−	0.825056i	$-0.691144\pi$
$443$	5.47247	−	5.47247i	0.260005	−	0.260005i	0.825056	+	0.565051i	$0.191144\pi$
$444$	15.7266			0.746352
$445$		0			0
$446$			2.46053i			0.116509i
$447$	0.0684664	−	0.0684664i	0.00323835	−	0.00323835i
$448$	−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
$453$	−9.51409	−	9.51409i	−0.447011	−	0.447011i
$454$	64.5881			3.03127
$455$		0			0
$456$	30.5448			1.43039
$457$	21.0775	+	21.0775i	0.985962	+	0.985962i	0.999903	−	0.0139406i	$-0.00443756\pi$
$457$	21.0775	+	21.0775i	0.985962	+	0.985962i	−0.0139406	+	0.999903i	$0.504438\pi$
$458$	−46.6823	−	46.6823i	−2.18132	−	2.18132i
$459$			2.97854i			0.139026i
$460$		0			0
$461$		−	21.9670i		−	1.02311i	−0.859252	−	0.511553i	$-0.829071\pi$
$461$		−	21.9670i		−	1.02311i	0.859252	−	0.511553i	$-0.170929\pi$
$462$	−5.62693	−	8.49347i	−0.261788	−	0.395152i
$463$	21.6776	−	21.6776i	1.00744	−	1.00744i	0.00746987	−	0.999972i	$-0.497622\pi$
$463$	21.6776	−	21.6776i	1.00744	−	1.00744i	0.999972	−	0.00746987i	$-0.00237776\pi$
$464$		−	54.1694i		−	2.51475i
$465$		0			0
$466$	−8.34450			−0.386551
$467$	−7.11299	+	7.11299i	−0.329150	+	0.329150i	−0.852263	−	0.523113i	$-0.824770\pi$
$467$	−7.11299	+	7.11299i	−0.329150	+	0.329150i	0.523113	+	0.852263i	$0.324770\pi$
$468$	4.37718	+	4.37718i	0.202335	+	0.202335i
$469$	21.7449	+	4.41438i	1.00409	+	0.203837i
$470$		0			0
$471$	−2.33002			−0.107362
$472$	17.4338	−	17.4338i	0.802457	−	0.802457i
$473$	−7.58562	+	7.58562i	−0.348787	+	0.348787i
$474$	−11.8997			−0.546572
$475$		0			0
$476$	38.0750	+	7.72950i	1.74517	+	0.354281i
$477$	0.544449	+	0.544449i	0.0249286	+	0.0249286i
$478$	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
$483$	12.8827	−	8.53477i	0.586181	−	0.388345i
$484$		−	43.6821i		−	1.98555i
$485$		0			0
$486$		−	2.63251i		−	0.119413i
$487$	4.81428	+	4.81428i	0.218156	+	0.218156i	0.807721	−	0.589565i	$-0.200701\pi$
$487$	4.81428	+	4.81428i	0.218156	+	0.218156i	−0.589565	+	0.807721i	$0.700701\pi$
$488$	−7.74864	−	7.74864i	−0.350765	−	0.350765i
$489$	14.5305			0.657092
$490$		0			0
$491$	28.3401			1.27897			0.639484	−	0.768804i	$-0.279148\pi$
$491$	28.3401			1.27897			0.639484	+	0.768804i	$0.279148\pi$
$492$	−2.68420	−	2.68420i	−0.121013	−	0.121013i
$493$	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
$498$	−17.7904	+	17.7904i	−0.797206	+	0.797206i
$499$			3.39197i			0.151845i	0.997114	+	0.0759227i	$0.0241902\pi$
$499$			3.39197i			0.151845i	−0.997114	+	0.0759227i	$0.975810\pi$
$500$		0			0
$501$	−0.414376			−0.0185130
$502$	−30.4244	+	30.4244i	−1.35791	+	1.35791i
$503$	8.32921	+	8.32921i	0.371381	+	0.371381i	0.867980	−	0.496599i	$-0.165418\pi$
$503$	8.32921	+	8.32921i	0.371381	+	0.371381i	−0.496599	+	0.867980i	$0.665418\pi$
$504$	−20.0003	−	4.06020i	−0.890883	−	0.180856i
$505$		0			0
$506$	−22.4918			−0.999884
$507$	8.07761	−	8.07761i	0.358739	−	0.358739i
$508$	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
$513$	2.80005	−	2.80005i	0.123625	−	0.123625i
$514$	−79.3187			−3.49860
$515$		0			0
$516$			36.1562i			1.59169i
$517$	12.5367	−	12.5367i	0.551364	−	0.551364i
$518$	−12.2706	−	18.5217i	−0.539140	−	0.813796i
$519$			4.88171i			0.214283i
$520$		0			0
$521$		−	7.06726i		−	0.309622i	−0.987944	−	0.154811i	$-0.950523\pi$
$521$		−	7.06726i		−	0.309622i	0.987944	−	0.154811i	$-0.0494769\pi$
$522$	−9.65306	−	9.65306i	−0.422503	−	0.422503i
$523$	−14.5887	−	14.5887i	−0.637921	−	0.637921i	0.312121	−	0.950042i	$-0.398960\pi$
$523$	−14.5887	−	14.5887i	−0.637921	−	0.637921i	−0.950042	+	0.312121i	$0.898960\pi$
$524$	−30.4788			−1.33147
$525$		0			0
$526$	60.8508			2.65322
$527$	−12.8548	−	12.8548i	−0.559962	−	0.559962i
$528$	10.8047	+	10.8047i	0.470213	+	0.470213i
$529$		−	11.1150i		−	0.483261i
$530$		0			0
$531$		−	3.19633i		−	0.138709i
$532$	−28.5271	−	43.0597i	−1.23681	−	1.86688i
$533$	0.683611	−	0.683611i	0.0296105	−	0.0296105i
$534$			3.15878i			0.136694i
$535$		0			0
$536$	−64.6897			−2.79417
$537$	1.41249	−	1.41249i	0.0609533	−	0.0609533i
$538$	−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
$543$	6.00000	−	6.00000i	0.257485	−	0.257485i
$544$	−35.9560			−1.54160
$545$		0			0
$546$	1.73985	−	8.57041i	0.0744589	−	0.366780i
$547$	7.22715	+	7.22715i	0.309011	+	0.309011i	0.844526	−	0.535515i	$-0.179882\pi$
$547$	7.22715	+	7.22715i	0.309011	+	0.309011i	−0.535515	+	0.844526i	$0.679882\pi$
$548$	44.6455	−	44.6455i	1.90716	−	1.90716i
$549$	−1.42064			−0.0606315
$550$		0			0
$551$		−	20.5348i		−	0.874812i
$552$	−31.8577	+	31.8577i	−1.35595	+	1.35595i
$553$	6.60519	+	9.97009i	0.280881	+	0.423971i
$554$		−	79.3382i		−	3.37076i
$555$		0			0
$556$		−	59.1185i		−	2.50718i
$557$	0.558927	+	0.558927i	0.0236825	+	0.0236825i	0.718849	−	0.695166i	$-0.244669\pi$
$557$	0.558927	+	0.558927i	0.0236825	+	0.0236825i	−0.695166	+	0.718849i	$0.744669\pi$
$558$	11.3614	+	11.3614i	0.480966	+	0.480966i
$559$	−9.20823			−0.389467
$560$		0			0
$561$	−4.35697			−0.183951
$562$	−39.3736	−	39.3736i	−1.66087	−	1.66087i
$563$	−0.702475	−	0.702475i	−0.0296058	−	0.0296058i	0.692149	−	0.721755i	$-0.256664\pi$
$563$	−0.702475	−	0.702475i	−0.0296058	−	0.0296058i	−0.721755	+	0.692149i	$0.756664\pi$
$564$		−	59.7550i		−	2.51614i
$565$		0			0
$566$		−	9.88333i		−	0.415427i
$567$	−2.20563	+	1.46123i	−0.0926278	+	0.0613659i
$568$	−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
$573$	−5.53964	−	5.53964i	−0.231422	−	0.231422i
$574$	−1.06692	+	5.25560i	−0.0445326	+	0.219365i
$575$		0			0
$576$	10.8872			0.453633
$577$	10.3510	−	10.3510i	0.430917	−	0.430917i	−0.458024	−	0.888940i	$-0.651442\pi$
$577$	10.3510	−	10.3510i	0.430917	−	0.430917i	0.888940	+	0.458024i	$0.151442\pi$
$578$	−15.1306	+	15.1306i	−0.629350	+	0.629350i
$579$	−19.1792			−0.797059
$580$		0			0
$581$	24.7804	+	5.03060i	1.02807	+	0.208705i
$582$	22.8720	+	22.8720i	0.948076	+	0.948076i
$583$	−0.796415	+	0.796415i	−0.0329841	+	0.0329841i
$584$	74.3292			3.07576
$585$		0			0
$586$			5.83438i			0.241016i
$587$	21.1413	−	21.1413i	0.872594	−	0.872594i	−0.120160	−	0.992755i	$-0.538341\pi$
$587$	21.1413	−	21.1413i	0.872594	−	0.872594i	0.992755	+	0.120160i	$0.0383409\pi$
$588$	12.9554	+	31.9868i	0.534270	+	1.31912i
$589$			24.1689i			0.995862i
$590$		0			0
$591$			16.2339i			0.667774i
$592$	23.5617	+	23.5617i	0.968381	+	0.968381i
$593$	−7.07816	−	7.07816i	−0.290665	−	0.290665i	0.546678	−	0.837343i	$-0.315892\pi$
$593$	−7.07816	−	7.07816i	−0.290665	−	0.290665i	−0.837343	+	0.546678i	$0.815892\pi$
$594$	3.85081			0.158001
$595$		0			0
$596$	0.477365			0.0195536
$597$	14.2459	+	14.2459i	0.583047	+	0.583047i
$598$	−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	$0.746185\pi$
$602$	42.5822	−	28.2107i	1.73552	−	1.14978i
$603$	−5.93012	+	5.93012i	−0.241493	+	0.241493i
$604$		−	66.3346i		−	2.69912i
$605$		0			0
$606$	−40.3881			−1.64066
$607$	5.36385	−	5.36385i	0.217712	−	0.217712i	−0.589822	−	0.807533i	$-0.700802\pi$
$607$	5.36385	−	5.36385i	0.217712	−	0.217712i	0.807533	+	0.589822i	$0.200802\pi$
$608$	33.8014	+	33.8014i	1.37083	+	1.37083i
$609$	−2.72961	+	13.4459i	−0.110609	+	0.544854i
$610$		0			0
$611$	15.2184			0.615670
$612$	−10.3835	+	10.3835i	−0.419730	+	0.419730i
$613$	10.4888	−	10.4888i	0.423639	−	0.423639i	−0.462816	−	0.886454i	$-0.653161\pi$
$613$	10.4888	−	10.4888i	0.423639	−	0.423639i	0.886454	+	0.462816i	$0.153161\pi$
$614$	64.6120			2.60753
$615$		0			0
$616$	5.93921	−	29.2562i	0.239298	−	1.17877i
$617$	−19.7986	−	19.7986i	−0.797060	−	0.797060i	0.185571	−	0.982631i	$-0.440586\pi$
$617$	−19.7986	−	19.7986i	−0.797060	−	0.797060i	−0.982631	+	0.185571i	$0.940586\pi$
$618$	21.8703	−	21.8703i	0.879752	−	0.879752i
$619$	−12.0675			−0.485034			−0.242517	−	0.970147i	$-0.577973\pi$
$619$	−12.0675			−0.485034			−0.242517	+	0.970147i	$0.577973\pi$
$620$		0			0
$621$			5.84081i			0.234383i
$622$	−57.8262	+	57.8262i	−2.31862	+	2.31862i
$623$	2.64655	−	1.75334i	0.106032	−	0.0702462i
$624$			13.1158i			0.525054i
$625$		0			0
$626$		−	21.3110i		−	0.851761i
$627$	4.09588	+	4.09588i	0.163574	+	0.163574i
$628$	−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
$633$	8.46135	+	8.46135i	0.336309	+	0.336309i
$634$		−	2.80180i		−	0.111274i
$635$		0			0
$636$			3.79604i			0.150523i
$637$	−8.14639	+	3.29946i	−0.322772	+	0.130729i
$638$	14.1204	−	14.1204i	0.559032	−	0.559032i
$639$			7.62611i			0.301684i
$640$		0			0
$641$	36.5929			1.44533			0.722666	−	0.691198i	$-0.242917\pi$
$641$	36.5929			1.44533			0.722666	+	0.691198i	$0.242917\pi$
$642$	11.5573	−	11.5573i	0.456131	−	0.456131i
$643$	12.1140	+	12.1140i	0.477731	+	0.477731i	0.904405	−	0.426675i	$-0.140315\pi$
$643$	12.1140	+	12.1140i	0.477731	+	0.477731i	−0.426675	+	0.904405i	$0.640315\pi$
$644$	74.6638	+	15.1573i	2.94217	+	0.597280i
$645$		0			0
$646$	−31.0495			−1.22163
$647$	19.0978	−	19.0978i	0.750814	−	0.750814i	−0.223817	−	0.974631i	$-0.571852\pi$
$647$	19.0978	−	19.0978i	0.750814	−	0.750814i	0.974631	+	0.223817i	$0.0718519\pi$
$648$	5.45433	−	5.45433i	0.214266	−	0.214266i
$649$	4.67556			0.183532
$650$		0			0
$651$	3.21267	−	15.8254i	0.125915	−	0.620248i
$652$	50.6552	+	50.6552i	1.98381	+	1.98381i
$653$	−20.3709	+	20.3709i	−0.797173	+	0.797173i	−0.982649	−	0.185476i	$-0.940617\pi$
$653$	−20.3709	+	20.3709i	−0.797173	+	0.797173i	0.185476	+	0.982649i	$0.440617\pi$
$654$	−19.6013			−0.766473
$655$		0			0
$656$		−	8.04298i		−	0.314026i
$657$	6.81378	−	6.81378i	0.265831	−	0.265831i
$658$	−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	$0.386545\pi$
$661$			48.1880i			1.87430i	−0.348931	+	0.937149i	$0.613455\pi$
$662$	29.4265	+	29.4265i	1.14369	+	1.14369i
$663$	−2.64448	−	2.64448i	−0.102703	−	0.102703i
$664$	−73.7201			−2.86089
$665$		0			0
$666$	8.39746			0.325395
$667$	21.4174	+	21.4174i	0.829286	+	0.829286i
$668$	−1.44457	−	1.44457i	−0.0558920	−	0.0558920i
$669$			0.934668i			0.0361364i
$670$		0			0
$671$		−	2.07810i		−	0.0802241i
$672$	−17.6396	−	26.6257i	−0.680461	−	1.02711i
$673$	30.6900	−	30.6900i	1.18301	−	1.18301i	0.204055	−	0.978960i	$-0.434588\pi$
$673$	30.6900	−	30.6900i	1.18301	−	1.18301i	0.978960	−	0.204055i	$-0.0654120\pi$
$674$			74.6299i			2.87463i
$675$		0			0
$676$	56.3191			2.16612
$677$	1.54060	−	1.54060i	0.0592101	−	0.0592101i	−0.676882	−	0.736092i	$-0.736669\pi$
$677$	1.54060	−	1.54060i	0.0592101	−	0.0592101i	0.736092	+	0.676882i	$0.236669\pi$
$678$	−6.69830	−	6.69830i	−0.257246	−	0.257246i
$679$	6.46755	−	31.8587i	0.248202	−	1.22263i
$680$		0			0
$681$	24.5348			0.940174
$682$	−16.6193	+	16.6193i	−0.636387	+	0.636387i
$683$	−14.2154	+	14.2154i	−0.543936	+	0.543936i	−0.924680	−	0.380744i	$-0.875668\pi$
$683$	−14.2154	+	14.2154i	−0.543936	+	0.543936i	0.380744	+	0.924680i	$0.375668\pi$
$684$	19.5226			0.746467
$685$		0			0
$686$	27.5635	−	40.2155i	1.05238	−	1.53544i
$687$	−17.7330	−	17.7330i	−0.676555	−	0.676555i
$688$	−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
$693$	−2.13747	−	3.22637i	−0.0811959	−	0.122560i
$694$			74.7741i			2.83838i
$695$		0			0
$696$		−	40.0005i		−	1.51622i
$697$	1.62166	+	1.62166i	0.0614248	+	0.0614248i
$698$	27.4869	+	27.4869i	1.04040	+	1.04040i
$699$	−3.16979			−0.119892
$700$		0			0
$701$	−44.3183			−1.67388			−0.836939	−	0.547297i	$-0.815657\pi$
$701$	−44.3183			−1.67388			−0.836939	+	0.547297i	$0.815657\pi$
$702$	2.33726	+	2.33726i	0.0882142	+	0.0882142i
$703$	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
$708$	11.1428	−	11.1428i	0.418772	−	0.418772i
$709$		−	0.817976i		−	0.0307197i	−0.999882	−	0.0153599i	$-0.995111\pi$
$709$		−	0.817976i		−	0.0307197i	0.999882	−	0.0153599i	$-0.00488939\pi$
$710$		0			0
$711$	−4.52029			−0.169524
$712$	−6.54470	+	6.54470i	−0.245273	+	0.245273i
$713$	−25.2077	−	25.2077i	−0.944037	−	0.944037i
$714$	20.3307	+	4.12728i	0.760858	+	0.154460i
$715$		0			0
$716$	9.84821			0.368045
$717$	15.1158	−	15.1158i	0.564509	−	0.564509i
$718$	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
$723$	0.441326	−	0.441326i	0.0164131	−	0.0164131i
$724$	41.8335			1.55473
$725$		0			0
$726$		−	23.3247i		−	0.865661i
$727$	−28.5738	+	28.5738i	−1.05974	+	1.05974i	−0.0616465	+	0.998098i	$0.519635\pi$
$727$	−28.5738	+	28.5738i	−1.05974	+	1.05974i	−0.998098	+	0.0616465i	$0.980365\pi$
$728$	21.3619	−	14.1523i	0.791726	−	0.524519i
$729$		−	1.00000i		−	0.0370370i
$730$		0			0
$731$		−	21.8438i		−	0.807921i
$732$	−4.95253	−	4.95253i	−0.183051	−	0.183051i
$733$	24.1522	+	24.1522i	0.892083	+	0.892083i	0.994719	−	0.102636i	$-0.0327275\pi$
$733$	24.1522	+	24.1522i	0.892083	+	0.892083i	−0.102636	+	0.994719i	$0.532728\pi$
$734$	−41.6632			−1.53782
$735$		0			0
$736$	−70.5085			−2.59898
$737$	−8.67452	−	8.67452i	−0.319530	−	0.319530i
$738$	−1.43327	−	1.43327i	−0.0527594	−	0.0527594i
$739$		−	37.9522i		−	1.39609i	−0.716052	−	0.698047i	$-0.754053\pi$
$739$		−	37.9522i		−	1.39609i	0.716052	−	0.698047i	$-0.245947\pi$
$740$		0			0
$741$			4.97202i			0.182652i
$742$	4.47070	−	2.96184i	0.164125	−	0.108733i
$743$	18.8022	−	18.8022i	0.689784	−	0.689784i	−0.272400	−	0.962184i	$-0.587817\pi$
$743$	18.8022	−	18.8022i	0.689784	−	0.689784i	0.962184	+	0.272400i	$0.0878174\pi$
$744$			47.0796i			1.72602i
$745$		0			0
$746$	−64.3123			−2.35464
$747$	−6.75794	+	6.75794i	−0.247260	+	0.247260i
$748$	−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
$753$	−11.5572	+	11.5572i	−0.421167	+	0.421167i
$754$	17.1408			0.624232
$755$		0			0
$756$	−12.7831	−	2.59507i	−0.464918	−	0.0943816i
$757$	−3.14514	−	3.14514i	−0.114312	−	0.114312i	0.647637	−	0.761949i	$-0.275757\pi$
$757$	−3.14514	−	3.14514i	−0.114312	−	0.114312i	−0.761949	+	0.647637i	$0.775757\pi$
$758$	−32.8059	+	32.8059i	−1.19156	+	1.19156i
$759$	−8.54387			−0.310123
$760$		0			0
$761$			35.1123i			1.27282i	0.771351	+	0.636410i	$0.219581\pi$
$761$			35.1123i			1.27282i	−0.771351	+	0.636410i	$0.780419\pi$
$762$	20.6922	−	20.6922i	0.749599	−	0.749599i
$763$	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
$768$	−6.98809	−	6.98809i	−0.252161	−	0.252161i
$769$	8.16835			0.294558			0.147279	−	0.989095i	$-0.452948\pi$
$769$	8.16835			0.294558			0.147279	+	0.989095i	$0.452948\pi$
$770$		0			0
$771$	−30.1304			−1.08512
$772$	−66.8609	−	66.8609i	−2.40638	−	2.40638i
$773$	2.51166	+	2.51166i	0.0903382	+	0.0903382i	0.750832	−	0.660494i	$-0.229653\pi$
$773$	2.51166	+	2.51166i	0.0903382	+	0.0903382i	−0.660494	+	0.750832i	$0.729653\pi$
$774$			19.3061i			0.693944i
$775$		0			0
$776$			94.7776i			3.40232i
$777$	−4.66118	−	7.03574i	−0.167219	−	0.252406i
$778$	−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
$783$	−3.66686	−	3.66686i	−0.131043	−	0.131043i
$784$	−28.5131	+	67.3327i	−1.01833	+	2.40474i
$785$		0			0
$786$	−16.2746			−0.580497
$787$	−12.7347	+	12.7347i	−0.453943	+	0.453943i	−0.896661	−	0.442718i	$-0.854014\pi$
$787$	−12.7347	+	12.7347i	−0.453943	+	0.453943i	0.442718	+	0.896661i	$0.354014\pi$
$788$	−56.5935	+	56.5935i	−2.01606	+	2.01606i
$789$	23.1151			0.822920
$790$		0			0
$791$	−1.89408	+	9.33014i	−0.0673459	+	0.331742i
$792$	7.97854	+	7.97854i	0.283505	+	0.283505i
$793$	1.26131	−	1.26131i	0.0447903	−	0.0447903i
$794$	−60.2300			−2.13748
$795$		0			0
$796$			99.3261i			3.52052i
$797$	−23.3462	+	23.3462i	−0.826967	+	0.826967i	−0.987096	−	0.160129i	$-0.948809\pi$
$797$	−23.3462	+	23.3462i	−0.826967	+	0.826967i	0.160129	+	0.987096i	$0.448809\pi$
$798$	−15.2325	−	22.9924i	−0.539224	−	0.813922i
$799$			36.1010i			1.27716i
$800$		0			0
$801$			1.19991i			0.0423967i
$802$	−1.81976	−	1.81976i	−0.0642580	−	0.0642580i
$803$	9.96713	+	9.96713i	0.351732	+	0.351732i
$804$	−41.3463			−1.45817
$805$		0			0
$806$	−20.1743			−0.710609
$807$	−11.7311	−	11.7311i	−0.412955	−	0.412955i
$808$	−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	$-0.0286649\pi$
$812$	−56.3897	+	37.3582i	−1.97889	+	1.31102i
$813$	−5.50152	+	5.50152i	−0.192947	+	0.192947i
$814$			12.2837i			0.430544i
$815$		0			0
$816$	−31.1134			−1.08919
$817$	−20.5348	+	20.5348i	−0.718421	+	0.718421i
$818$	45.2656	+	45.2656i	1.58267	+	1.58267i
$819$	0.660910	−	3.25560i	0.0230941	−	0.113760i
$820$		0			0
$821$	−26.1405			−0.912308			−0.456154	−	0.889901i	$-0.650773\pi$
$821$	−26.1405			−0.912308			−0.456154	+	0.889901i	$0.650773\pi$
$822$	23.8391	−	23.8391i	0.831485	−	0.831485i
$823$	−13.7296	+	13.7296i	−0.478583	+	0.478583i	−0.904678	−	0.426095i	$-0.859889\pi$
$823$	−13.7296	+	13.7296i	−0.478583	+	0.478583i	0.426095	+	0.904678i	$0.359889\pi$
$824$	90.6265			3.15712
$825$		0			0
$826$	−21.8173	−	4.42907i	−0.759122	−	0.154107i
$827$	−15.7484	−	15.7484i	−0.547624	−	0.547624i	0.378129	−	0.925753i	$-0.376568\pi$
$827$	−15.7484	−	15.7484i	−0.547624	−	0.547624i	−0.925753	+	0.378129i	$0.876568\pi$
$828$	−20.3618	+	20.3618i	−0.707620	+	0.707620i
$829$	47.2996			1.64278			0.821392	−	0.570365i	$-0.193198\pi$
$829$	47.2996			1.64278			0.821392	+	0.570365i	$0.193198\pi$
$830$		0			0
$831$		−	30.1378i		−	1.04547i
$832$	−9.66613	+	9.66613i	−0.335113	+	0.335113i
$833$	−7.82698	−	19.3249i	−0.271189	−	0.669567i
$834$		−	31.5672i		−	1.09308i
$835$		0			0
$836$			28.5575i			0.987683i
$837$	4.31580	+	4.31580i	0.149176	+	0.149176i
$838$	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
$843$	−14.9566	−	14.9566i	−0.515134	−	0.515134i
$844$			58.9947i			2.03068i
$845$		0			0
$846$		−	31.9071i		−	1.09699i
$847$	−19.5424	+	12.9469i	−0.671486	+	0.444860i
$848$	−5.68725	+	5.68725i	−0.195301	+	0.195301i
$849$		−	3.75433i		−	0.128848i
$850$		0			0
$851$	−18.6316			−0.638683
$852$	−26.5856	+	26.5856i	−0.910806	+	0.910806i
$853$	−33.5751	−	33.5751i	−1.14959	−	1.14959i	−0.986633	−	0.162958i	$-0.947897\pi$
$853$	−33.5751	−	33.5751i	−1.14959	−	1.14959i	−0.162958	−	0.986633i	$-0.552103\pi$
$854$	−1.96854	+	9.69693i	−0.0673622	+	0.331822i
$855$		0			0
$856$	47.8914			1.63689
$857$	−8.92479	+	8.92479i	−0.304865	+	0.304865i	−0.842914	−	0.538049i	$-0.819162\pi$
$857$	−8.92479	+	8.92479i	−0.304865	+	0.304865i	0.538049	+	0.842914i	$0.319162\pi$
$858$	−3.41892	+	3.41892i	−0.116720	+	0.116720i
$859$	20.3701			0.695020			0.347510	−	0.937676i	$-0.387027\pi$
$859$	20.3701			0.695020			0.347510	+	0.937676i	$0.387027\pi$
$860$		0			0
$861$	−0.405287	+	1.99642i	−0.0138122	+	0.0680378i
$862$	41.4589	+	41.4589i	1.41210	+	1.41210i
$863$	14.9014	−	14.9014i	0.507250	−	0.507250i	−0.406431	−	0.913681i	$-0.633227\pi$
$863$	14.9014	−	14.9014i	0.507250	−	0.507250i	0.913681	+	0.406431i	$0.133227\pi$
$864$	12.0717			0.410688
$865$		0			0
$866$			104.306i			3.54446i
$867$	−5.74759	+	5.74759i	−0.195198	+	0.195198i
$868$	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
$873$	8.68829	+	8.68829i	0.294054	+	0.294054i
$874$	−60.8869			−2.05953
$875$		0			0
$876$	47.5074			1.60512
$877$	−23.4634	−	23.4634i	−0.792302	−	0.792302i	0.189566	−	0.981868i	$-0.439292\pi$
$877$	−23.4634	−	23.4634i	−0.792302	−	0.792302i	−0.981868	+	0.189566i	$0.939292\pi$
$878$	−4.38667	−	4.38667i	−0.148043	−	0.148043i
$879$			2.21628i			0.0747532i
$880$		0			0
$881$		−	34.9639i		−	1.17796i	−0.808147	−	0.588981i	$-0.799529\pi$
$881$		−	34.9639i		−	1.17796i	0.808147	−	0.588981i	$-0.200471\pi$
$882$	6.91770	+	17.0799i	0.232931	+	0.575109i
$883$	−19.3814	+	19.3814i	−0.652235	+	0.652235i	−0.953531	−	0.301295i	$-0.902581\pi$
$883$	−19.3814	+	19.3814i	−0.652235	+	0.652235i	0.301295	+	0.953531i	$0.402581\pi$
$884$		−	18.4379i		−	0.620135i
$885$		0			0
$886$	20.3737			0.684466
$887$	19.2450	−	19.2450i	0.646184	−	0.646184i	−0.305884	−	0.952069i	$-0.598952\pi$
$887$	19.2450	−	19.2450i	0.646184	−	0.646184i	0.952069	+	0.305884i	$0.0989521\pi$
$888$	17.3988	+	17.3988i	0.583865	+	0.583865i
$889$	−28.8224	−	5.85116i	−0.966673	−	0.196242i
$890$		0			0
$891$	1.46279			0.0490053
$892$	−3.25837	+	3.25837i	−0.109098	+	0.109098i
$893$	33.9377	−	33.9377i	1.13568	−	1.13568i
$894$	0.254896			0.00852500
$895$		0			0
$896$	2.37775	−	11.7126i	0.0794349	−	0.391292i
$897$	−5.18572	−	5.18572i	−0.173146	−	0.173146i
$898$	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
$903$	16.1755	−	10.7163i	0.538286	−	0.356615i
$904$		−	27.7565i		−	0.923169i
$905$		0			0
$906$		−	35.4204i		−	1.17676i
$907$	14.8842	+	14.8842i	0.494220	+	0.494220i	0.909633	−	0.415413i	$-0.136363\pi$
$907$	14.8842	+	14.8842i	0.494220	+	0.494220i	−0.415413	+	0.909633i	$0.636363\pi$
$908$	85.5312	+	85.5312i	2.83845	+	2.83845i
$909$	−15.3420			−0.508863
$910$		0			0
$911$	−23.7484			−0.786819			−0.393410	−	0.919363i	$-0.628705\pi$
$911$	−23.7484			−0.786819			−0.393410	+	0.919363i	$0.628705\pi$
$912$	29.2490	+	29.2490i	0.968530	+	0.968530i
$913$	−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
$918$	−5.54445	+	5.54445i	−0.182994	+	0.182994i
$919$		−	35.7695i		−	1.17993i	−0.807430	−	0.589964i	$-0.799142\pi$
$919$		−	35.7695i		−	1.17993i	0.807430	−	0.589964i	$-0.200858\pi$
$920$		0			0
$921$	24.5439			0.808748
$922$	40.8909	−	40.8909i	1.34667	−	1.34667i
$923$	−6.77080	−	6.77080i	−0.222863	−	0.222863i
$924$	3.79604	−	18.6990i	0.124880	−	0.615153i
$925$		0			0
$926$	80.7042			2.65210
$927$	8.30776	−	8.30776i	0.272863	−	0.272863i
$928$	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
$933$	−21.9662	+	21.9662i	−0.719140	+	0.719140i
$934$	−26.4812			−0.866491
$935$		0			0
$936$			9.68519i			0.316570i
$937$	20.4143	−	20.4143i	0.666906	−	0.666906i	−0.290092	−	0.956999i	$-0.593686\pi$
$937$	20.4143	−	20.4143i	0.666906	−	0.666906i	0.956999	+	0.290092i	$0.0936861\pi$
$938$	32.2603	+	48.6947i	1.05334	+	1.58994i
$939$		−	8.09533i		−	0.264181i
$940$		0			0
$941$		−	17.1143i		−	0.557910i	−0.960304	−	0.278955i	$-0.910012\pi$
$941$		−	17.1143i		−	0.557910i	0.960304	−	0.278955i	$-0.0899880\pi$
$942$	−4.33726	−	4.33726i	−0.141316	−	0.141316i
$943$	3.18002	+	3.18002i	0.103556	+	0.103556i
$944$	33.3884			1.08670
$945$		0			0
$946$	−28.2408			−0.918187
$947$	−6.82151	−	6.82151i	−0.221669	−	0.221669i	0.587532	−	0.809201i	$-0.300100\pi$
$947$	−6.82151	−	6.82151i	−0.221669	−	0.221669i	−0.809201	+	0.587532i	$0.800100\pi$
$948$	−15.7583	−	15.7583i	−0.511806	−	0.511806i
$949$			12.0991i			0.392755i
$950$		0			0
$951$		−	1.06431i		−	0.0345125i
$952$	33.5721	+	50.6748i	1.08808	+	1.64238i
$953$	−30.7169	+	30.7169i	−0.995017	+	0.995017i	−0.999988	−	0.00497101i	$-0.998418\pi$
$953$	−30.7169	+	30.7169i	−0.995017	+	0.995017i	0.00497101	+	0.999988i	$0.498418\pi$
$954$			2.02695i			0.0656249i
$955$		0			0
$956$	105.391			3.40859
$957$	5.36385	−	5.36385i	0.173389	−	0.173389i
$958$	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
$963$	4.39022	−	4.39022i	0.141473	−	0.141473i
$964$	3.07703			0.0991046
$965$		0			0
$966$	39.8678	+	8.09345i	1.28273	+	0.260403i
$967$	−24.6730	−	24.6730i	−0.793431	−	0.793431i	0.188619	−	0.982050i	$-0.439599\pi$
$967$	−24.6730	−	24.6730i	−0.793431	−	0.793431i	−0.982050	+	0.188619i	$0.939599\pi$
$968$	48.3267	−	48.3267i	1.55328	−	1.55328i
$969$	−11.7946			−0.378898
$970$		0			0
$971$		−	21.2020i		−	0.680404i	−0.940352	−	0.340202i	$-0.889504\pi$
$971$		−	21.2020i		−	0.680404i	0.940352	−	0.340202i	$-0.110496\pi$
$972$	3.48612	−	3.48612i	0.111817	−	0.111817i
$973$	−26.4483	+	17.5220i	−0.847895	+	0.561731i
$974$			17.9232i			0.574297i
$975$		0			0
$976$		−	14.8398i		−	0.475011i
$977$	−8.19657	−	8.19657i	−0.262231	−	0.262231i	0.563729	−	0.825960i	$-0.309366\pi$
$977$	−8.19657	−	8.19657i	−0.262231	−	0.262231i	−0.825960	+	0.563729i	$0.809366\pi$
$978$	27.0481	+	27.0481i	0.864902	+	0.864902i
$979$	−1.75521			−0.0560969
$980$		0			0
$981$	−7.44587			−0.237728
$982$	52.7541	+	52.7541i	1.68345	+	1.68345i
$983$	1.74914	+	1.74914i	0.0557891	+	0.0557891i	0.734451	−	0.678662i	$-0.237440\pi$
$983$	1.74914	+	1.74914i	0.0557891	+	0.0557891i	−0.678662	+	0.734451i	$0.737440\pi$
$984$		−	5.93921i		−	0.189335i
$985$		0			0
$986$			40.6615i			1.29492i
$987$	−26.7331	+	17.7107i	−0.850924	+	0.563738i
$988$	−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
$993$	11.1781	+	11.1781i	0.354727	+	0.354727i
$994$	52.0539	+	10.5673i	1.65105	+	0.335174i
$995$		0			0
$996$	−47.1180			−1.49299
$997$	40.5538	−	40.5538i	1.28435	−	1.28435i	0.346186	−	0.938166i	$-0.387476\pi$
$997$	40.5538	−	40.5538i	1.28435	−	1.28435i	0.938166	−	0.346186i	$-0.112524\pi$
$998$	−6.31404	+	6.31404i	−0.199868	+	0.199868i
$999$	3.18990			0.100924

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.m.b.307.8		16
5.2	odd	4		105.2.m.a.13.2	yes	16
5.3	odd	4	inner	525.2.m.b.118.7		16
5.4	even	2		105.2.m.a.97.1	yes	16
7.6	odd	2	inner	525.2.m.b.307.7		16
15.2	even	4		315.2.p.e.118.7		16
15.14	odd	2		315.2.p.e.307.8		16
20.7	even	4		1680.2.cz.d.433.3		16
20.19	odd	2		1680.2.cz.d.97.6		16
35.2	odd	12		735.2.v.a.178.8		32
35.4	even	6		735.2.v.a.607.7		32
35.9	even	6		735.2.v.a.472.2		32
35.12	even	12		735.2.v.a.178.7		32
35.13	even	4	inner	525.2.m.b.118.8		16
35.17	even	12		735.2.v.a.313.2		32
35.19	odd	6		735.2.v.a.472.1		32
35.24	odd	6		735.2.v.a.607.8		32
35.27	even	4		105.2.m.a.13.1	✓	16
35.32	odd	12		735.2.v.a.313.1		32
35.34	odd	2		105.2.m.a.97.2	yes	16
105.62	odd	4		315.2.p.e.118.8		16
105.104	even	2		315.2.p.e.307.7		16
140.27	odd	4		1680.2.cz.d.433.6		16
140.139	even	2		1680.2.cz.d.97.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.m.a.13.1	✓	16	35.27	even	4
105.2.m.a.13.2	yes	16	5.2	odd	4
105.2.m.a.97.1	yes	16	5.4	even	2
105.2.m.a.97.2	yes	16	35.34	odd	2
315.2.p.e.118.7		16	15.2	even	4
315.2.p.e.118.8		16	105.62	odd	4
315.2.p.e.307.7		16	105.104	even	2
315.2.p.e.307.8		16	15.14	odd	2
525.2.m.b.118.7		16	5.3	odd	4	inner
525.2.m.b.118.8		16	35.13	even	4	inner
525.2.m.b.307.7		16	7.6	odd	2	inner
525.2.m.b.307.8		16	1.1	even	1	trivial
735.2.v.a.178.7		32	35.12	even	12
735.2.v.a.178.8		32	35.2	odd	12
735.2.v.a.313.1		32	35.32	odd	12
735.2.v.a.313.2		32	35.17	even	12
735.2.v.a.472.1		32	35.19	odd	6
735.2.v.a.472.2		32	35.9	even	6
735.2.v.a.607.7		32	35.4	even	6
735.2.v.a.607.8		32	35.24	odd	6
1680.2.cz.d.97.3		16	140.139	even	2
1680.2.cz.d.97.6		16	20.19	odd	2
1680.2.cz.d.433.3		16	20.7	even	4
1680.2.cz.d.433.6		16	140.27	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.86147 + 1.86147i) q^{2} +(0.707107 + 0.707107i) q^{3} +4.93012i q^{4} +2.63251i q^{6} +(2.20563 - 1.46123i) q^{7} +(-5.45433 + 5.45433i) q^{8} +1.00000i q^{9} +O(q^{10})\)	\(q+(1.86147 + 1.86147i) q^{2} +(0.707107 + 0.707107i) q^{3} +4.93012i q^{4} +2.63251i q^{6} +(2.20563 - 1.46123i) q^{7} +(-5.45433 + 5.45433i) q^{8} +1.00000i q^{9} -1.46279 q^{11} +(-3.48612 + 3.48612i) q^{12} +(-0.887844 - 0.887844i) q^{13} +(6.82574 + 1.38567i) q^{14} -10.4459 q^{16} +(2.10614 - 2.10614i) q^{17} +(-1.86147 + 1.86147i) q^{18} -3.95987 q^{19} +(2.59286 + 0.526369i) q^{21} +(-2.72294 - 2.72294i) q^{22} +(4.13007 - 4.13007i) q^{23} -7.71359 q^{24} -3.30539i q^{26} +(-0.707107 + 0.707107i) q^{27} +(7.20405 + 10.8740i) q^{28} +5.18572i q^{29} -6.10346i q^{31} +(-8.53599 - 8.53599i) q^{32} +(-1.03435 - 1.03435i) q^{33} +7.84104 q^{34} -4.93012 q^{36} +(-2.25560 - 2.25560i) q^{37} +(-7.37117 - 7.37117i) q^{38} -1.25560i q^{39} +0.769968i q^{41} +(3.84671 + 5.80635i) q^{42} +(5.18572 - 5.18572i) q^{43} -7.21173i q^{44} +15.3760 q^{46} +(-8.57041 + 8.57041i) q^{47} +(-7.38635 - 7.38635i) q^{48} +(2.72961 - 6.44587i) q^{49} +2.97854 q^{51} +(4.37718 - 4.37718i) q^{52} +(0.544449 - 0.544449i) q^{53} -2.63251 q^{54} +(-4.06020 + 20.0003i) q^{56} +(-2.80005 - 2.80005i) q^{57} +(-9.65306 + 9.65306i) q^{58} -3.19633 q^{59} +1.42064i q^{61} +(11.3614 - 11.3614i) q^{62} +(1.46123 + 2.20563i) q^{63} -10.8872i q^{64} -3.85081i q^{66} +(5.93012 + 5.93012i) q^{67} +(10.3835 + 10.3835i) q^{68} +5.84081 q^{69} +7.62611 q^{71} +(-5.45433 - 5.45433i) q^{72} +(-6.81378 - 6.81378i) q^{73} -8.39746i q^{74} -19.5226i q^{76} +(-3.22637 + 2.13747i) q^{77} +(2.33726 - 2.33726i) q^{78} +4.52029i q^{79} -1.00000 q^{81} +(-1.43327 + 1.43327i) q^{82} +(6.75794 + 6.75794i) q^{83} +(-2.59507 + 12.7831i) q^{84} +19.3061 q^{86} +(-3.66686 + 3.66686i) q^{87} +(7.97854 - 7.97854i) q^{88} +1.19991 q^{89} +(-3.25560 - 0.660910i) q^{91} +(20.3618 + 20.3618i) q^{92} +(4.31580 - 4.31580i) q^{93} -31.9071 q^{94} -12.0717i q^{96} +(8.68829 - 8.68829i) q^{97} +(17.0799 - 6.91770i) q^{98} -1.46279i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{7} - 24 q^{8}+O(q^{10}) \) 16 * q + 8 * q^7 - 24 * q^8	\( 16 q + 8 q^{7} - 24 q^{8} - 16 q^{11} - 48 q^{16} + 8 q^{21} + 16 q^{22} + 40 q^{23} - 24 q^{28} - 48 q^{32} - 16 q^{36} - 32 q^{37} + 16 q^{42} + 16 q^{43} + 64 q^{46} - 16 q^{51} - 24 q^{53} + 24 q^{56} - 8 q^{57} - 32 q^{58} - 8 q^{63} + 32 q^{67} + 64 q^{71} - 24 q^{72} + 24 q^{77} + 8 q^{78} - 16 q^{81} + 64 q^{86} + 64 q^{88} - 48 q^{91} + 40 q^{92} - 24 q^{93} + 96 q^{98}+O(q^{100}) \) 16 * q + 8 * q^7 - 24 * q^8 - 16 * q^11 - 48 * q^16 + 8 * q^21 + 16 * q^22 + 40 * q^23 - 24 * q^28 - 48 * q^32 - 16 * q^36 - 32 * q^37 + 16 * q^42 + 16 * q^43 + 64 * q^46 - 16 * q^51 - 24 * q^53 + 24 * q^56 - 8 * q^57 - 32 * q^58 - 8 * q^63 + 32 * q^67 + 64 * q^71 - 24 * q^72 + 24 * q^77 + 8 * q^78 - 16 * q^81 + 64 * q^86 + 64 * q^88 - 48 * q^91 + 40 * q^92 - 24 * q^93 + 96 * q^98

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