LMFDB - Embedded newform 525.2.m.b.307.7

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			307.7
Root			$-0.517174 - 1.31626i$ of defining polynomial
Character	$\chi$	$=$	525.307
Dual form			525.2.m.b.118.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.86147 + 1.86147i) q^{2} +(-0.707107 - 0.707107i) q^{3} +4.93012i q^{4} -2.63251i q^{6} +(-1.46123 + 2.20563i) q^{7} +(-5.45433 + 5.45433i) q^{8} +1.00000i q^{9} +O(q^{10})$	\(q+(1.86147 + 1.86147i) q^{2} +(-0.707107 - 0.707107i) q^{3} +4.93012i q^{4} -2.63251i q^{6} +(-1.46123 + 2.20563i) q^{7} +(-5.45433 + 5.45433i) q^{8} +1.00000i q^{9} -1.46279 q^{11} +(3.48612 - 3.48612i) q^{12} +(0.887844 + 0.887844i) q^{13} +(-6.82574 + 1.38567i) q^{14} -10.4459 q^{16} +(-2.10614 + 2.10614i) q^{17} +(-1.86147 + 1.86147i) q^{18} +3.95987 q^{19} +(2.59286 - 0.526369i) q^{21} +(-2.72294 - 2.72294i) q^{22} +(4.13007 - 4.13007i) q^{23} +7.71359 q^{24} +3.30539i q^{26} +(0.707107 - 0.707107i) q^{27} +(-10.8740 - 7.20405i) q^{28} +5.18572i q^{29} +6.10346i q^{31} +(-8.53599 - 8.53599i) q^{32} +(1.03435 + 1.03435i) q^{33} -7.84104 q^{34} -4.93012 q^{36} +(-2.25560 - 2.25560i) q^{37} +(7.37117 + 7.37117i) q^{38} -1.25560i q^{39} -0.769968i q^{41} +(5.80635 + 3.84671i) q^{42} +(5.18572 - 5.18572i) q^{43} -7.21173i q^{44} +15.3760 q^{46} +(8.57041 - 8.57041i) q^{47} +(7.38635 + 7.38635i) q^{48} +(-2.72961 - 6.44587i) q^{49} +2.97854 q^{51} +(-4.37718 + 4.37718i) q^{52} +(0.544449 - 0.544449i) q^{53} +2.63251 q^{54} +(-4.06020 - 20.0003i) q^{56} +(-2.80005 - 2.80005i) q^{57} +(-9.65306 + 9.65306i) q^{58} +3.19633 q^{59} -1.42064i q^{61} +(-11.3614 + 11.3614i) q^{62} +(-2.20563 - 1.46123i) q^{63} -10.8872i q^{64} +3.85081i q^{66} +(5.93012 + 5.93012i) q^{67} +(-10.3835 - 10.3835i) q^{68} -5.84081 q^{69} +7.62611 q^{71} +(-5.45433 - 5.45433i) q^{72} +(6.81378 + 6.81378i) q^{73} -8.39746i q^{74} +19.5226i q^{76} +(2.13747 - 3.22637i) q^{77} +(2.33726 - 2.33726i) q^{78} +4.52029i q^{79} -1.00000 q^{81} +(1.43327 - 1.43327i) q^{82} +(-6.75794 - 6.75794i) q^{83} +(2.59507 + 12.7831i) q^{84} +19.3061 q^{86} +(3.66686 - 3.66686i) q^{87} +(7.97854 - 7.97854i) q^{88} -1.19991 q^{89} +(-3.25560 + 0.660910i) q^{91} +(20.3618 + 20.3618i) q^{92} +(4.31580 - 4.31580i) q^{93} +31.9071 q^{94} +12.0717i q^{96} +(-8.68829 + 8.68829i) q^{97} +(6.91770 - 17.0799i) q^{98} -1.46279i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$7$	−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
$9$			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	0.819427	−	0.573183i	$-0.194292\pi$
$13$	0.887844	+	0.887844i	0.246244	+	0.246244i	−0.573183	+	0.819427i	$0.694292\pi$
$14$	−6.82574	+	1.38567i	−1.82426	+	0.370337i
$15$		0			0
$16$	−10.4459			−2.61147
$17$	−2.10614	+	2.10614i	−0.510815	+	0.510815i	−0.914776	−	0.403961i	$-0.867633\pi$
$17$	−2.10614	+	2.10614i	−0.510815	+	0.510815i	0.403961	+	0.914776i	$0.367633\pi$
$18$	−1.86147	+	1.86147i	−0.438752	+	0.438752i
$19$	3.95987			0.908456			0.454228	−	0.890885i	$-0.349915\pi$
$19$	3.95987			0.908456			0.454228	+	0.890885i	$0.349915\pi$
$20$		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
$28$	−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	$0.184651\pi$
$31$			6.10346i			1.09621i	−0.836408	+	0.548107i	$0.815349\pi$
$32$	−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	$-0.980850\pi$
$41$		−	0.769968i		−	0.120249i	0.998191	−	0.0601244i	$-0.0191497\pi$
$42$	5.80635	+	3.84671i	0.895939	+	0.593560i
$43$	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	$-0.404861\pi$
$47$	8.57041	−	8.57041i	1.25012	−	1.25012i	0.955664	−	0.294459i	$-0.0951394\pi$
$48$	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	$-0.433284\pi$
$59$	3.19633			0.416127			0.208063	+	0.978115i	$0.433284\pi$
$60$		0			0
$61$		−	1.42064i		−	0.181894i	−0.995856	−	0.0909472i	$-0.971011\pi$
$61$		−	1.42064i		−	0.181894i	0.995856	−	0.0909472i	$-0.0289894\pi$
$62$	−11.3614	+	11.3614i	−1.44290	+	1.44290i
$63$	−2.20563	−	1.46123i	−0.277883	−	0.184098i
$64$		−	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	0.982700	−	0.185207i	$-0.0592955\pi$
$73$	6.81378	+	6.81378i	0.797493	+	0.797493i	−0.185207	+	0.982700i	$0.559296\pi$
$74$		−	8.39746i		−	0.976185i
$75$		0			0
$76$			19.5226i			2.23940i
$77$	2.13747	−	3.22637i	0.243588	−	0.367679i
$78$	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	0.231140	−	0.972921i	$-0.425754\pi$
$83$	−6.75794	−	6.75794i	−0.741781	−	0.741781i	−0.972921	+	0.231140i	$0.925754\pi$
$84$	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	$-0.520257\pi$
$89$	−1.19991			−0.127190			−0.0635950	+	0.997976i	$0.520257\pi$
$90$		0			0
$91$	−3.25560	+	0.660910i	−0.341280	+	0.0692822i
$92$	20.3618	+	20.3618i	2.12286	+	2.12286i
$93$	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	−0.993754	−	0.111592i	$-0.964405\pi$
$97$	−8.68829	+	8.68829i	−0.882162	+	0.882162i	0.111592	+	0.993754i	$0.464405\pi$
$98$	6.91770	−	17.0799i	0.698794	−	1.72533i
$99$		−	1.46279i		−	0.147016i
$100$		0			0
$101$		−	15.3420i		−	1.52659i	−0.646050	−	0.763295i	$-0.723580\pi$
$101$		−	15.3420i		−	1.52659i	0.646050	−	0.763295i	$-0.276420\pi$
$102$	5.54445	+	5.54445i	0.548982	+	0.548982i
$103$	8.30776	+	8.30776i	0.818588	+	0.818588i	0.985903	−	0.167316i	$-0.0535099\pi$
$103$	8.30776	+	8.30776i	0.818588	+	0.818588i	−0.167316	+	0.985903i	$0.553510\pi$
$104$	−9.68519			−0.949711
$105$		0			0
$106$	2.02695			0.196875
$107$	−4.39022	−	4.39022i	−0.424418	−	0.424418i	0.462303	−	0.886722i	$-0.347023\pi$
$107$	−4.39022	−	4.39022i	−0.424418	−	0.424418i	−0.886722	+	0.462303i	$0.847023\pi$
$108$	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
$112$	15.2638	−	23.0397i	1.44230	−	2.17705i
$113$	−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	$-0.912953\pi$
$131$		−	6.18216i		−	0.540138i	0.962841	−	0.270069i	$-0.0870465\pi$
$132$	−5.09947	+	5.09947i	−0.443851	+	0.443851i
$133$	−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	0.205071	−	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	$-0.330184\pi$
$139$	11.9913			1.01709			0.508544	+	0.861036i	$0.330184\pi$
$140$		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
$147$	−2.62780	+	6.48804i	−0.216737	+	0.535125i
$148$	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	−0.638298	−	0.769789i	$-0.720361\pi$
$157$	1.64757	−	1.64757i	0.131491	−	0.131491i	0.769789	+	0.638298i	$0.220361\pi$
$158$	−8.41438	+	8.41438i	−0.669412	+	0.669412i
$159$	−0.769968			−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	−0.695679	−	0.718353i	$-0.744896\pi$
$167$	0.293008	−	0.293008i	0.0226737	−	0.0226737i	0.718353	+	0.695679i	$0.244896\pi$
$168$	−11.2713	+	17.0133i	−0.869602	+	1.31261i
$169$		−	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	0.563603	−	0.826046i	$-0.309415\pi$
$173$	−3.45189	−	3.45189i	−0.262442	−	0.262442i	−0.826046	+	0.563603i	$0.809415\pi$
$174$	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	$0.102123\pi$
$181$			8.48528i			0.630706i	−0.948974	+	0.315353i	$0.897877\pi$
$182$	−7.29046	−	4.82993i	−0.540405	−	0.358019i
$183$	−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	$-0.753156\pi$
$199$	−20.1468			−1.42817			−0.714084	+	0.700061i	$0.753156\pi$
$200$		0			0
$201$		−	8.38646i		−	0.591535i
$202$	28.5587	−	28.5587i	2.00938	−	2.00938i
$203$	−11.4378	−	7.57754i	−0.802775	−	0.531839i
$204$			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
$217$	−13.4620	−	8.91857i	−0.913858	−	0.605432i
$218$	−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	0.684632	−	0.728889i	$-0.259963\pi$
$223$	−0.660910	−	0.660910i	−0.0442578	−	0.0442578i	−0.728889	+	0.684632i	$0.759963\pi$
$224$	31.3003	−	6.35418i	2.09134	−	0.424557i
$225$		0			0
$226$	−9.47282			−0.630123
$227$	−17.3487	+	17.3487i	−1.15147	+	1.15147i	−0.165216	+	0.986257i	$0.552832\pi$
$227$	−17.3487	+	17.3487i	−1.15147	+	1.15147i	−0.986257	+	0.165216i	$0.947168\pi$
$228$	13.8046	−	13.8046i	0.914232	−	0.914232i
$229$	25.0782			1.65721			0.828607	−	0.559831i	$-0.189134\pi$
$229$	25.0782			1.65721			0.828607	+	0.559831i	$0.189134\pi$
$230$		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
$238$	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	$0.00639905\pi$
$241$			0.624129i			0.0402037i	−0.999798	+	0.0201018i	$0.993601\pi$
$242$	−16.4931	−	16.4931i	−1.06021	−	1.06021i
$243$	0.707107	+	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	$-0.827487\pi$
$251$		−	16.3443i		−	1.03164i	0.856696	−	0.515822i	$-0.172513\pi$
$252$	7.20405	−	10.8740i	0.453813	−	0.684999i
$253$	−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	$-0.361065\pi$
$257$	21.3054	−	21.3054i	1.32900	−	1.32900i	0.906247	−	0.422749i	$-0.138935\pi$
$258$	−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	$-0.331211\pi$
$269$	16.5903			1.01153			0.505764	+	0.862672i	$0.331211\pi$
$270$		0			0
$271$		−	7.78033i		−	0.472621i	−0.971678	−	0.236311i	$-0.924062\pi$
$271$		−	7.78033i		−	0.472621i	0.971678	−	0.236311i	$-0.0759383\pi$
$272$	22.0005	−	22.0005i	1.33398	−	1.33398i
$273$	2.76939	+	1.83472i	0.167611	+	0.111043i
$274$		−	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	0.781594	−	0.623788i	$-0.214407\pi$
$283$	2.65471	+	2.65471i	0.157806	+	0.157806i	−0.623788	+	0.781594i	$0.714407\pi$
$284$			37.5977i			2.23101i
$285$		0			0
$286$		−	4.83508i		−	0.285905i
$287$	1.69826	+	1.12510i	0.100245	+	0.0664126i
$288$	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	0.659847	−	0.751400i	$-0.270621\pi$
$293$	−1.56714	−	1.56714i	−0.0915536	−	0.0915536i	−0.751400	+	0.659847i	$0.770621\pi$
$294$	−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	−0.999955	−	0.00944588i	$-0.996993\pi$
$307$	−17.3551	+	17.3551i	−0.990510	+	0.990510i	0.00944588	+	0.999955i	$0.496993\pi$
$308$	15.9064	+	10.5380i	0.906352	+	0.600459i
$309$		−	11.7489i		−	0.668374i
$310$		0			0
$311$		−	31.0648i		−	1.76153i	−0.473558	−	0.880763i	$-0.657030\pi$
$311$		−	31.0648i		−	1.76153i	0.473558	−	0.880763i	$-0.342970\pi$
$312$	6.84846	+	6.84846i	0.387718	+	0.387718i
$313$	5.72426	+	5.72426i	0.323554	+	0.323554i	0.850129	−	0.526575i	$-0.176524\pi$
$313$	5.72426	+	5.72426i	0.323554	+	0.323554i	−0.526575	+	0.850129i	$0.676524\pi$
$314$	6.13381			0.346151
$315$		0			0
$316$	−22.2856			−1.25366
$317$	−0.752579	−	0.752579i	−0.0422691	−	0.0422691i	0.685656	−	0.727925i	$-0.259515\pi$
$317$	−0.752579	−	0.752579i	−0.0422691	−	0.0422691i	−0.727925	+	0.685656i	$0.759515\pi$
$318$	−1.43327	−	1.43327i	−0.0803738	−	0.0803738i
$319$		−	7.58562i		−	0.424713i
$320$		0			0
$321$			6.20871i			0.346536i
$322$	−22.4679	+	33.9138i	−1.25209	+	1.88994i
$323$	−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
$343$	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	0.996671	+	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	$-0.629328\pi$
$349$	−14.7663			−0.790420			−0.395210	+	0.918591i	$0.629328\pi$
$350$		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	0.291766	−	0.956490i	$-0.405757\pi$
$353$	−12.4890	−	12.4890i	−0.664724	−	0.664724i	−0.956490	+	0.291766i	$0.905757\pi$
$354$		−	8.41438i		−	0.447219i
$355$		0			0
$356$		−	5.91570i		−	0.313531i
$357$	−4.35233	+	6.56955i	−0.230350	+	0.347697i
$358$	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	−0.351881	−	0.936045i	$-0.614458\pi$
$367$	11.1910	−	11.1910i	0.584163	−	0.584163i	0.936045	+	0.351881i	$0.114458\pi$
$368$	−43.1422	+	43.1422i	−2.24894	+	2.24894i
$369$	0.769968			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
$378$	−3.84671	+	5.80635i	−0.197853	+	0.298646i
$379$			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	0.986671	−	0.162729i	$-0.0520295\pi$
$383$	16.1249	+	16.1249i	0.823942	+	0.823942i	−0.162729	+	0.986671i	$0.552030\pi$
$384$	−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
$392$	50.0461	+	20.2697i	2.52771	+	1.02378i
$393$	−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	−0.172972	−	0.984927i	$-0.555337\pi$
$397$	16.1781	−	16.1781i	0.811955	−	0.811955i	0.984927	+	0.172972i	$0.0553370\pi$
$398$	−37.5026	−	37.5026i	−1.87983	−	1.87983i
$399$	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	$-0.705312\pi$
$409$	−24.3171			−1.20241			−0.601203	+	0.799097i	$0.705312\pi$
$410$		0			0
$411$			12.8066i			0.631704i
$412$	−40.9583	+	40.9583i	−2.01787	+	2.01787i
$413$	−4.67058	+	7.04992i	−0.229824	+	0.346904i
$414$			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	$-0.627720\pi$
$419$	−15.9893			−0.781127			−0.390563	+	0.920576i	$0.627720\pi$
$420$		0			0
$421$	14.7000			0.716433			0.358216	−	0.933639i	$-0.383385\pi$
$421$	14.7000			0.716433			0.358216	+	0.933639i	$0.383385\pi$
$422$	22.2746	+	22.2746i	1.08431	+	1.08431i
$423$	8.57041	+	8.57041i	0.416708	+	0.416708i
$424$			5.93921i			0.288434i
$425$		0			0
$426$		−	20.0758i		−	0.972677i
$427$	3.13341	+	2.07588i	0.151636	+	0.100459i
$428$	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	$-0.848961\pi$
$433$	−28.0171	−	28.0171i	−1.34642	−	1.34642i	−0.456896	−	0.889520i	$-0.651039\pi$
$434$	−8.45741	−	41.6606i	−0.405968	−	1.99978i
$435$		0			0
$436$	−36.7091			−1.75805
$437$	16.3545	−	16.3545i	0.782344	−	0.782344i
$438$	17.9374	−	17.9374i	0.857080	−	0.857080i
$439$	2.35656			0.112473			0.0562363	−	0.998417i	$-0.482090\pi$
$439$	2.35656			0.112473			0.0562363	+	0.998417i	$0.482090\pi$
$440$		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
$448$	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
$453$	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	$0.170929\pi$
$461$			21.9670i			1.02311i	−0.859252	+	0.511553i	$0.829071\pi$
$462$	−8.49347	−	5.62693i	−0.395152	−	0.261788i
$463$	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	−0.523113	−	0.852263i	$-0.675230\pi$
$467$	7.11299	−	7.11299i	0.329150	−	0.329150i	0.852263	+	0.523113i	$0.175230\pi$
$468$	−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	$-0.758584\pi$
$479$	−31.7749			−1.45183			−0.725917	+	0.687782i	$0.758584\pi$
$480$		0			0
$481$		−	4.00524i		−	0.182623i
$482$	−1.16180	+	1.16180i	−0.0529184	+	0.0529184i
$483$	8.53477	−	12.8827i	0.388345	−	0.586181i
$484$		−	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
$497$	−11.1435	+	16.8204i	−0.499855	+	0.754497i
$498$	−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	0.496599	−	0.867980i	$-0.334582\pi$
$503$	−8.32921	−	8.32921i	−0.371381	−	0.371381i	−0.867980	+	0.496599i	$0.834582\pi$
$504$	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	$-0.168515\pi$
$509$	38.9452			1.72622			0.863108	+	0.505020i	$0.168515\pi$
$510$		0			0
$511$	−24.9852	+	5.07217i	−1.10528	+	0.224380i
$512$	−24.7846	−	24.7846i	−1.09534	−	1.09534i
$513$	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
$518$	18.5217	+	12.2706i	0.813796	+	0.539140i
$519$			4.88171i			0.214283i
$520$		0			0
$521$			7.06726i			0.309622i	0.987944	+	0.154811i	$0.0494769\pi$
$521$			7.06726i			0.309622i	−0.987944	+	0.154811i	$0.950523\pi$
$522$	−9.65306	−	9.65306i	−0.422503	−	0.422503i
$523$	14.5887	+	14.5887i	0.637921	+	0.637921i	0.950042	−	0.312121i	$-0.101040\pi$
$523$	14.5887	+	14.5887i	0.637921	+	0.637921i	−0.312121	+	0.950042i	$0.601040\pi$
$524$	30.4788			1.33147
$525$		0			0
$526$	60.8508			2.65322
$527$	−12.8548	−	12.8548i	−0.559962	−	0.559962i
$528$	−10.8047	−	10.8047i	−0.470213	−	0.470213i
$529$		−	11.1150i		−	0.483261i
$530$		0			0
$531$			3.19633i			0.138709i
$532$	−43.0597	−	28.5271i	−1.86688	−	1.23681i
$533$	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
$553$	−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	0.718849	−	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	0.721755	−	0.692149i	$-0.243336\pi$
$563$	0.702475	+	0.702475i	0.0296058	+	0.0296058i	−0.692149	+	0.721755i	$0.743336\pi$
$564$		−	59.7550i		−	2.51614i
$565$		0			0
$566$			9.88333i			0.415427i
$567$	1.46123	−	2.20563i	0.0613659	−	0.0926278i
$568$	−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	−0.888940	−	0.458024i	$-0.848558\pi$
$577$	−10.3510	+	10.3510i	−0.430917	+	0.430917i	0.458024	+	0.888940i	$0.348558\pi$
$578$	−15.1306	+	15.1306i	−0.629350	+	0.629350i
$579$	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	−0.992755	−	0.120160i	$-0.961659\pi$
$587$	−21.1413	+	21.1413i	−0.872594	+	0.872594i	0.120160	+	0.992755i	$0.461659\pi$
$588$	−31.9868	−	12.9554i	−1.31912	−	0.534270i
$589$			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	0.837343	−	0.546678i	$-0.184108\pi$
$593$	7.07816	+	7.07816i	0.290665	+	0.290665i	−0.546678	+	0.837343i	$0.684108\pi$
$594$	−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	$-0.746185\pi$
$601$		−	35.0829i		−	1.43106i	0.698580	−	0.715532i	$-0.253815\pi$
$602$	−28.2107	+	42.5822i	−1.14978	+	1.73552i
$603$	−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	−0.807533	−	0.589822i	$-0.799198\pi$
$607$	−5.36385	+	5.36385i	−0.217712	+	0.217712i	0.589822	+	0.807533i	$0.299198\pi$
$608$	−33.8014	−	33.8014i	−1.37083	−	1.37083i
$609$	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	$-0.422027\pi$
$619$	12.0675			0.485034			0.242517	+	0.970147i	$0.422027\pi$
$620$		0			0
$621$		−	5.84081i		−	0.234383i
$622$	57.8262	−	57.8262i	2.31862	−	2.31862i
$623$	1.75334	−	2.64655i	0.0702462	−	0.106032i
$624$			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
$637$	3.29946	−	8.14639i	0.130729	−	0.322772i
$638$	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	0.426675	−	0.904405i	$-0.359685\pi$
$643$	−12.1140	−	12.1140i	−0.477731	−	0.477731i	−0.904405	+	0.426675i	$0.859685\pi$
$644$	−74.6638	+	15.1573i	−2.94217	+	0.597280i
$645$		0			0
$646$	−31.0495			−1.22163
$647$	−19.0978	+	19.0978i	−0.750814	+	0.750814i	−0.974631	−	0.223817i	$-0.928148\pi$
$647$	−19.0978	+	19.0978i	−0.750814	+	0.750814i	0.223817	+	0.974631i	$0.428148\pi$
$648$	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
$658$	−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	$-0.613455\pi$
$661$		−	48.1880i		−	1.87430i	0.348931	−	0.937149i	$-0.386545\pi$
$662$	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
$672$	−26.6257	−	17.6396i	−1.02711	−	0.680461i
$673$	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	−0.736092	−	0.676882i	$-0.763331\pi$
$677$	−1.54060	+	1.54060i	−0.0592101	+	0.0592101i	0.676882	+	0.736092i	$0.263331\pi$
$678$	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	$0.0626980\pi$
$691$			10.2887i			0.391401i	−0.980664	+	0.195700i	$0.937302\pi$
$692$	17.0182	−	17.0182i	0.646937	−	0.646937i
$693$	3.22637	+	2.13747i	0.122560	+	0.0811959i
$694$			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
$707$	33.8389	+	22.4183i	1.27264	+	0.843126i
$708$	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	$-0.500045\pi$
$719$	−0.00762056			−0.000284199			−0.000142099		1.00000i	$0.500045\pi$
$720$		0			0
$721$	−30.4634	+	6.18428i	−1.13452	+	0.230315i
$722$	−6.17902	−	6.17902i	−0.229959	−	0.229959i
$723$	0.441326	−	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	$-0.480365\pi$
$727$	28.5738	−	28.5738i	1.05974	−	1.05974i	0.998098	−	0.0616465i	$-0.0196352\pi$
$728$	14.1523	−	21.3619i	0.524519	−	0.791726i
$729$		−	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	0.102636	−	0.994719i	$-0.467272\pi$
$733$	−24.1522	−	24.1522i	−0.892083	−	0.892083i	−0.994719	+	0.102636i	$0.967272\pi$
$734$	41.6632			1.53782
$735$		0			0
$736$	−70.5085			−2.59898
$737$	−8.67452	−	8.67452i	−0.319530	−	0.319530i
$738$	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
$742$	−2.96184	+	4.47070i	−0.108733	+	0.164125i
$743$	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	$-0.780419\pi$
$761$		−	35.1123i		−	1.27282i	0.771351	−	0.636410i	$-0.219581\pi$
$762$	−20.6922	+	20.6922i	−0.749599	+	0.749599i
$763$	−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
$768$	6.98809	+	6.98809i	0.252161	+	0.252161i
$769$	−8.16835			−0.294558			−0.147279	−	0.989095i	$-0.547052\pi$
$769$	−8.16835			−0.294558			−0.147279	+	0.989095i	$0.547052\pi$
$770$		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	0.660494	−	0.750832i	$-0.270347\pi$
$773$	−2.51166	−	2.51166i	−0.0903382	−	0.0903382i	−0.750832	+	0.660494i	$0.770347\pi$
$774$			19.3061i			0.693944i
$775$		0			0
$776$		−	94.7776i		−	3.40232i
$777$	−7.03574	−	4.66118i	−0.252406	−	0.167219i
$778$	−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	−0.442718	−	0.896661i	$-0.645986\pi$
$787$	12.7347	−	12.7347i	0.453943	−	0.453943i	0.896661	+	0.442718i	$0.145986\pi$
$788$	−56.5935	+	56.5935i	−2.01606	+	2.01606i
$789$	−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	−0.160129	−	0.987096i	$-0.551191\pi$
$797$	23.3462	−	23.3462i	0.826967	−	0.826967i	0.987096	+	0.160129i	$0.0511912\pi$
$798$	22.9924	+	15.2325i	0.813922	+	0.539224i
$799$			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	$0.0286649\pi$
$811$			5.12216i			0.179863i	−0.995948	+	0.0899317i	$0.971335\pi$
$812$	37.3582	−	56.3897i	1.31102	−	1.97889i
$813$	−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	$-0.806802\pi$
$829$	−47.2996			−1.64278			−0.821392	+	0.570365i	$0.806802\pi$
$830$		0			0
$831$			30.1378i			1.04547i
$832$	9.66613	−	9.66613i	0.335113	−	0.335113i
$833$	19.3249	+	7.82698i	0.669567	+	0.271189i
$834$		−	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	$-0.559828\pi$
$839$	−10.8244			−0.373699			−0.186850	+	0.982389i	$0.559828\pi$
$840$		0			0
$841$	2.10826			0.0726986
$842$	27.3635	+	27.3635i	0.943009	+	0.943009i
$843$	14.9566	+	14.9566i	0.515134	+	0.515134i
$844$			58.9947i			2.03068i
$845$		0			0
$846$			31.9071i			1.09699i
$847$	12.9469	−	19.5424i	0.444860	−	0.671486i
$848$	−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	$0.0521034\pi$
$853$	33.5751	+	33.5751i	1.14959	+	1.14959i	0.162958	+	0.986633i	$0.447897\pi$
$854$	1.96854	+	9.69693i	0.0673622	+	0.331822i
$855$		0			0
$856$	47.8914			1.63689
$857$	8.92479	−	8.92479i	0.304865	−	0.304865i	−0.538049	−	0.842914i	$-0.680838\pi$
$857$	8.92479	−	8.92479i	0.304865	−	0.304865i	0.842914	+	0.538049i	$0.180838\pi$
$858$	−3.41892	+	3.41892i	−0.116720	+	0.116720i
$859$	−20.3701			−0.695020			−0.347510	−	0.937676i	$-0.612973\pi$
$859$	−20.3701			−0.695020			−0.347510	+	0.937676i	$0.612973\pi$
$860$		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
$868$	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
$873$	−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	$0.200471\pi$
$881$			34.9639i			1.17796i	−0.808147	+	0.588981i	$0.799529\pi$
$882$	17.0799	+	6.91770i	0.575109	+	0.232931i
$883$	−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	−0.952069	−	0.305884i	$-0.901048\pi$
$887$	−19.2450	+	19.2450i	−0.646184	+	0.646184i	0.305884	+	0.952069i	$0.401048\pi$
$888$	−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
$903$	10.7163	−	16.1755i	0.356615	−	0.538286i
$904$		−	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
$917$	13.6356	+	9.03357i	0.450286	+	0.298315i
$918$	−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	$-0.470773\pi$
$929$	5.58936			0.183381			0.0916905	+	0.995788i	$0.470773\pi$
$930$		0			0
$931$	−10.8089	−	25.5248i	−0.354247	−	0.836542i
$932$	−11.0503	−	11.0503i	−0.361963	−	0.361963i
$933$	−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	−0.956999	−	0.290092i	$-0.906314\pi$
$937$	−20.4143	+	20.4143i	−0.666906	+	0.666906i	0.290092	+	0.956999i	$0.406314\pi$
$938$	−48.6947	−	32.2603i	−1.58994	−	1.05334i
$939$		−	8.09533i		−	0.264181i
$940$		0			0
$941$			17.1143i			0.557910i	0.960304	+	0.278955i	$0.0899880\pi$
$941$			17.1143i			0.557910i	−0.960304	+	0.278955i	$0.910012\pi$
$942$	−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
$952$	50.6748	+	33.5721i	1.64238	+	1.08808i
$953$	−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	$0.110496\pi$
$971$			21.2020i			0.680404i	−0.940352	+	0.340202i	$0.889504\pi$
$972$	−3.48612	+	3.48612i	−0.111817	+	0.111817i
$973$	−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	0.563729	−	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	0.678662	−	0.734451i	$-0.262560\pi$
$983$	−1.74914	−	1.74914i	−0.0557891	−	0.0557891i	−0.734451	+	0.678662i	$0.762560\pi$
$984$		−	5.93921i		−	0.189335i
$985$		0			0
$986$		−	40.6615i		−	1.29492i
$987$	17.7107	−	26.7331i	0.563738	−	0.850924i
$988$	−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	$0.612524\pi$
$997$	−40.5538	+	40.5538i	−1.28435	+	1.28435i	−0.938166	+	0.346186i	$0.887476\pi$
$998$	−6.31404	+	6.31404i	−0.199868	+	0.199868i
$999$	−3.18990			−0.100924

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

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