LMFDB - Embedded newform 864.2.w.b.107.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [864,2,Mod(107,864)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(864, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 5, 4]))

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

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

chi := DirichletCharacter("864.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 864 = 2^{5} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	864.w (of order $8$, degree $4$, 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:	$6.89907473464$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$32$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			107.4
Character	$\chi$	$=$	864.107
Dual form			864.2.w.b.323.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.31895 + 0.510265i) q^{2} +(1.47926 - 1.34603i) q^{4} +(1.03442 + 0.428472i) q^{5} +(-0.461188 + 0.461188i) q^{7} +(-1.26424 + 2.53016i) q^{8} +O(q^{10})$	\(q+(-1.31895 + 0.510265i) q^{2} +(1.47926 - 1.34603i) q^{4} +(1.03442 + 0.428472i) q^{5} +(-0.461188 + 0.461188i) q^{7} +(-1.26424 + 2.53016i) q^{8} +(-1.58299 - 0.0373037i) q^{10} +(-1.50832 - 0.624765i) q^{11} +(-2.43213 - 5.87169i) q^{13} +(0.372956 - 0.843612i) q^{14} +(0.376419 - 3.98225i) q^{16} -4.84737 q^{17} +(4.84058 - 2.00503i) q^{19} +(2.10692 - 0.758541i) q^{20} +(2.30819 + 0.0543934i) q^{22} +(0.883120 - 0.883120i) q^{23} +(-2.64909 - 2.64909i) q^{25} +(6.20398 + 6.50343i) q^{26} +(-0.0614450 + 1.30299i) q^{28} +(1.12421 + 2.71408i) q^{29} -6.23807i q^{31} +(1.53552 + 5.44446i) q^{32} +(6.39344 - 2.47344i) q^{34} +(-0.674670 + 0.279457i) q^{35} +(-3.38363 + 8.16881i) q^{37} +(-5.36138 + 5.11451i) q^{38} +(-2.39186 + 2.07556i) q^{40} +(-4.37343 - 4.37343i) q^{41} +(1.83532 - 4.43085i) q^{43} +(-3.07214 + 1.10605i) q^{44} +(-0.714166 + 1.61542i) q^{46} -12.2416i q^{47} +6.57461i q^{49} +(4.84576 + 2.14228i) q^{50} +(-11.5012 - 5.41203i) q^{52} +(0.564607 - 1.36308i) q^{53} +(-1.29254 - 1.29254i) q^{55} +(-0.583827 - 1.74993i) q^{56} +(-2.86768 - 3.00609i) q^{58} +(0.0955207 - 0.230607i) q^{59} +(1.86867 - 0.774030i) q^{61} +(3.18307 + 8.22770i) q^{62} +(-4.80340 - 6.39745i) q^{64} -7.11591i q^{65} +(-1.93426 - 4.66971i) q^{67} +(-7.17052 + 6.52469i) q^{68} +(0.747259 - 0.712851i) q^{70} +(2.81874 + 2.81874i) q^{71} +(-3.20918 + 3.20918i) q^{73} +(0.294586 - 12.5008i) q^{74} +(4.46164 - 9.48151i) q^{76} +(0.983752 - 0.407483i) q^{77} +9.43849 q^{79} +(2.09566 - 3.95805i) q^{80} +(7.99994 + 3.53673i) q^{82} +(-3.11411 - 7.51813i) q^{83} +(-5.01423 - 2.07696i) q^{85} +(-0.159787 + 6.78057i) q^{86} +(3.48763 - 3.02643i) q^{88} +(11.9031 - 11.9031i) q^{89} +(3.82963 + 1.58628i) q^{91} +(0.117660 - 2.49507i) q^{92} +(6.24645 + 16.1460i) q^{94} +5.86630 q^{95} +3.84945 q^{97} +(-3.35479 - 8.67158i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q+O(q^{10}) $ 128 * q	$ 128 q + 8 q^{10} + 32 q^{16} - 32 q^{22} + 64 q^{40} + 64 q^{46} + 40 q^{52} + 64 q^{55} + 64 q^{58} + 32 q^{61} + 96 q^{64} - 64 q^{67} - 48 q^{70} - 32 q^{76} - 32 q^{79} + 40 q^{82} + 40 q^{88} - 48 q^{91} + 72 q^{94}+O(q^{100}) $ 128 * q + 8 * q^10 + 32 * q^16 - 32 * q^22 + 64 * q^40 + 64 * q^46 + 40 * q^52 + 64 * q^55 + 64 * q^58 + 32 * q^61 + 96 * q^64 - 64 * q^67 - 48 * q^70 - 32 * q^76 - 32 * q^79 + 40 * q^82 + 40 * q^88 - 48 * q^91 + 72 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/864\mathbb{Z}\right)^\times$.

$n$	$325$	$353$	$703$
$\chi(n)$	$e\left(\frac{5}{8}\right)$	$-1$	$-1$

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 $

$2$	−1.31895	+	0.510265i	−0.932639	+	0.360812i
$2$	−1.31895	+	0.510265i	−0.932639	+	0.360812i
$3$		0			0
$3$		0			0
$4$	1.47926	−	1.34603i	0.739630	−	0.673014i
$5$	1.03442	+	0.428472i	0.462608	+	0.191619i	0.601800	−	0.798647i	$-0.294450\pi$
$5$	1.03442	+	0.428472i	0.462608	+	0.191619i	−0.139192	+	0.990265i	$0.544450\pi$
$6$		0			0
$7$	−0.461188	+	0.461188i	−0.174313	+	0.174313i	−0.788871	−	0.614558i	$-0.789334\pi$
$7$	−0.461188	+	0.461188i	−0.174313	+	0.174313i	0.614558	+	0.788871i	$0.289334\pi$
$8$	−1.26424	+	2.53016i	−0.446976	+	0.894546i
$9$		0			0
$10$	−1.58299	−	0.0373037i	−0.500584	−	0.0117965i
$11$	−1.50832	−	0.624765i	−0.454774	−	0.188374i	0.143524	−	0.989647i	$-0.454156\pi$
$11$	−1.50832	−	0.624765i	−0.454774	−	0.188374i	−0.598299	+	0.801273i	$0.704156\pi$
$12$		0			0
$13$	−2.43213	−	5.87169i	−0.674552	−	1.62851i	−0.773784	−	0.633449i	$-0.781639\pi$
$13$	−2.43213	−	5.87169i	−0.674552	−	1.62851i	0.0992318	−	0.995064i	$-0.468361\pi$
$14$	0.372956	−	0.843612i	0.0996767	−	0.225465i
$15$		0			0
$16$	0.376419	−	3.98225i	0.0941046	−	0.995562i
$17$	−4.84737			−1.17566			−0.587830	−	0.808985i	$-0.700018\pi$
$17$	−4.84737			−1.17566			−0.587830	+	0.808985i	$0.700018\pi$
$18$		0			0
$19$	4.84058	−	2.00503i	1.11050	−	0.459986i	0.249393	−	0.968402i	$-0.419769\pi$
$19$	4.84058	−	2.00503i	1.11050	−	0.459986i	0.861111	+	0.508416i	$0.169769\pi$
$20$	2.10692	−	0.758541i	0.471121	−	0.169615i
$21$		0			0
$22$	2.30819	+	0.0543934i	0.492108	+	0.0115967i
$23$	0.883120	−	0.883120i	0.184143	−	0.184143i	−0.609015	−	0.793159i	$-0.708435\pi$
$23$	0.883120	−	0.883120i	0.184143	−	0.184143i	0.793159	+	0.609015i	$0.208435\pi$
$24$		0			0
$25$	−2.64909	−	2.64909i	−0.529818	−	0.529818i
$26$	6.20398	+	6.50343i	1.21670	+	1.27543i
$27$		0			0
$28$	−0.0614450	+	1.30299i	−0.0116120	+	0.246242i
$29$	1.12421	+	2.71408i	0.208760	+	0.503992i	0.993229	−	0.116177i	$-0.0370640\pi$
$29$	1.12421	+	2.71408i	0.208760	+	0.503992i	−0.784468	+	0.620169i	$0.787064\pi$
$30$		0			0
$31$		−	6.23807i		−	1.12039i	−0.828361	−	0.560195i	$-0.810726\pi$
$31$		−	6.23807i		−	1.12039i	0.828361	−	0.560195i	$-0.189274\pi$
$32$	1.53552	+	5.44446i	0.271445	+	0.962454i
$33$		0			0
$34$	6.39344	−	2.47344i	1.09647	−	0.424192i
$35$	−0.674670	+	0.279457i	−0.114040	+	0.0472369i
$36$		0			0
$37$	−3.38363	+	8.16881i	−0.556266	+	1.34294i	0.356437	+	0.934320i	$0.383992\pi$
$37$	−3.38363	+	8.16881i	−0.556266	+	1.34294i	−0.912702	+	0.408625i	$0.866008\pi$
$38$	−5.36138	+	5.11451i	−0.869731	+	0.829684i
$39$		0			0
$40$	−2.39186	+	2.07556i	−0.378186	+	0.328175i
$41$	−4.37343	−	4.37343i	−0.683015	−	0.683015i	0.277663	−	0.960678i	$-0.410440\pi$
$41$	−4.37343	−	4.37343i	−0.683015	−	0.683015i	−0.960678	+	0.277663i	$0.910440\pi$
$42$		0			0
$43$	1.83532	−	4.43085i	0.279883	−	0.675698i	−0.719949	−	0.694027i	$-0.755835\pi$
$43$	1.83532	−	4.43085i	0.279883	−	0.675698i	0.999832	+	0.0183291i	$0.00583466\pi$
$44$	−3.07214	+	1.10605i	−0.463143	+	0.166743i
$45$		0			0
$46$	−0.714166	+	1.61542i	−0.105298	+	0.238180i
$47$		−	12.2416i		−	1.78562i	−0.450435	−	0.892809i	$-0.648731\pi$
$47$		−	12.2416i		−	1.78562i	0.450435	−	0.892809i	$-0.351269\pi$
$48$		0			0
$49$			6.57461i			0.939230i
$50$	4.84576	+	2.14228i	0.685294	+	0.302964i
$51$		0			0
$52$	−11.5012	−	5.41203i	−1.59493	−	0.750514i
$53$	0.564607	−	1.36308i	0.0775548	−	0.187234i	−0.880347	−	0.474331i	$-0.842690\pi$
$53$	0.564607	−	1.36308i	0.0775548	−	0.187234i	0.957902	+	0.287097i	$0.0926901\pi$
$54$		0			0
$55$	−1.29254	−	1.29254i	−0.174286	−	0.174286i
$56$	−0.583827	−	1.74993i	−0.0780171	−	0.233844i
$57$		0			0
$58$	−2.86768	−	3.00609i	−0.376544	−	0.394719i
$59$	0.0955207	−	0.230607i	0.0124357	−	0.0300225i	−0.917540	−	0.397644i	$-0.869828\pi$
$59$	0.0955207	−	0.230607i	0.0124357	−	0.0300225i	0.929975	+	0.367622i	$0.119828\pi$
$60$		0			0
$61$	1.86867	−	0.774030i	0.239259	−	0.0991043i	−0.259832	−	0.965654i	$-0.583667\pi$
$61$	1.86867	−	0.774030i	0.239259	−	0.0991043i	0.499091	+	0.866549i	$0.333667\pi$
$62$	3.18307	+	8.22770i	0.404250	+	1.04492i
$63$		0			0
$64$	−4.80340	−	6.39745i	−0.600425	−	0.799681i
$65$		−	7.11591i		−	0.882620i
$66$		0			0
$67$	−1.93426	−	4.66971i	−0.236307	−	0.570495i	0.760588	−	0.649234i	$-0.224911\pi$
$67$	−1.93426	−	4.66971i	−0.236307	−	0.570495i	−0.996895	+	0.0787391i	$0.974911\pi$
$68$	−7.17052	+	6.52469i	−0.869553	+	0.791235i
$69$		0			0
$70$	0.747259	−	0.712851i	0.0893145	−	0.0852020i
$71$	2.81874	+	2.81874i	0.334523	+	0.334523i	0.854301	−	0.519778i	$-0.173985\pi$
$71$	2.81874	+	2.81874i	0.334523	+	0.334523i	−0.519778	+	0.854301i	$0.673985\pi$
$72$		0			0
$73$	−3.20918	+	3.20918i	−0.375606	+	0.375606i	−0.869514	−	0.493908i	$-0.835568\pi$
$73$	−3.20918	+	3.20918i	−0.375606	+	0.375606i	0.493908	+	0.869514i	$0.335568\pi$
$74$	0.294586	−	12.5008i	0.0342450	−	1.45319i
$75$		0			0
$76$	4.46164	−	9.48151i	0.511785	−	1.08760i
$77$	0.983752	−	0.407483i	0.112109	−	0.0464370i
$78$		0			0
$79$	9.43849			1.06191			0.530957	−	0.847399i	$-0.321833\pi$
$79$	9.43849			1.06191			0.530957	+	0.847399i	$0.321833\pi$
$80$	2.09566	−	3.95805i	0.234302	−	0.442523i
$81$		0			0
$82$	7.99994	+	3.53673i	0.883446	+	0.390566i
$83$	−3.11411	−	7.51813i	−0.341818	−	0.825222i	−0.997532	−	0.0702125i	$-0.977632\pi$
$83$	−3.11411	−	7.51813i	−0.341818	−	0.825222i	0.655714	−	0.755009i	$-0.272368\pi$
$84$		0			0
$85$	−5.01423	−	2.07696i	−0.543870	−	0.225278i
$86$	−0.159787	+	6.78057i	−0.0172302	+	0.731168i
$87$		0			0
$88$	3.48763	−	3.02643i	0.371782	−	0.322618i
$89$	11.9031	−	11.9031i	1.26172	−	1.26172i	0.311462	−	0.950258i	$-0.399181\pi$
$89$	11.9031	−	11.9031i	1.26172	−	1.26172i	0.950258	−	0.311462i	$-0.100819\pi$
$90$		0			0
$91$	3.82963	+	1.58628i	0.401454	+	0.166288i
$92$	0.117660	−	2.49507i	0.0122669	−	0.260129i
$93$		0			0
$94$	6.24645	+	16.1460i	0.644272	+	1.66534i
$95$	5.86630			0.601870
$96$		0			0
$97$	3.84945			0.390852			0.195426	−	0.980718i	$-0.437391\pi$
$97$	3.84945			0.390852			0.195426	+	0.980718i	$0.437391\pi$
$98$	−3.35479	−	8.67158i	−0.338885	−	0.875962i
$99$		0			0
$100$	−7.48444	−	0.352944i	−0.748444	−	0.0352944i
$101$	−7.75862	−	3.21372i	−0.772011	−	0.319778i	−0.0383245	−	0.999265i	$-0.512202\pi$
$101$	−7.75862	−	3.21372i	−0.772011	−	0.319778i	−0.733687	+	0.679488i	$0.762202\pi$
$102$		0			0
$103$	4.64942	−	4.64942i	0.458121	−	0.458121i	−0.439917	−	0.898038i	$-0.644992\pi$
$103$	4.64942	−	4.64942i	0.458121	−	0.458121i	0.898038	+	0.439917i	$0.144992\pi$
$104$	17.9311	+	1.26954i	1.75829	+	0.124489i
$105$		0			0
$106$	−0.0491559	+	2.08594i	−0.00477444	+	0.202604i
$107$	−14.5357	−	6.02090i	−1.40522	−	0.582062i	−0.454121	−	0.890940i	$-0.650046\pi$
$107$	−14.5357	−	6.02090i	−1.40522	−	0.582062i	−0.951102	+	0.308878i	$0.900046\pi$
$108$		0			0
$109$	1.97695	+	4.77277i	0.189357	+	0.457149i	0.989836	−	0.142212i	$-0.0454215\pi$
$109$	1.97695	+	4.77277i	0.189357	+	0.457149i	−0.800479	+	0.599361i	$0.795421\pi$
$110$	2.36434	+	1.04526i	0.225431	+	0.0996617i
$111$		0			0
$112$	1.66297	+	2.01017i	0.157136	+	0.189943i
$113$	9.19168			0.864681			0.432340	−	0.901710i	$-0.357688\pi$
$113$	9.19168			0.864681			0.432340	+	0.901710i	$0.357688\pi$
$114$		0			0
$115$	1.29191	−	0.535127i	0.120471	−	0.0499009i
$116$	5.31623	+	2.50161i	0.493599	+	0.232269i
$117$		0			0
$118$	−0.00831623	+	0.352900i	−0.000765571	+	0.0324871i
$119$	2.23555	−	2.23555i	0.204932	−	0.204932i
$120$		0			0
$121$	−5.89349	−	5.89349i	−0.535772	−	0.535772i
$122$	−2.06973	+	1.97442i	−0.187384	+	0.178756i
$123$		0			0
$124$	−8.39661	−	9.22772i	−0.754038	−	0.828674i
$125$	−3.74758	−	9.04746i	−0.335194	−	0.809229i
$126$		0			0
$127$			11.2701i			1.00006i	0.866008	+	0.500029i	$0.166677\pi$
$127$			11.2701i			1.00006i	−0.866008	+	0.500029i	$0.833323\pi$
$128$	9.59984	+	5.98692i	0.848514	+	0.529174i
$129$		0			0
$130$	3.63100	+	9.38553i	0.318460	+	0.823166i
$131$	−5.93001	+	2.45629i	−0.518108	+	0.214607i	−0.626385	−	0.779513i	$-0.715466\pi$
$131$	−5.93001	+	2.45629i	−0.518108	+	0.214607i	0.108278	+	0.994121i	$0.465466\pi$
$132$		0			0
$133$	−1.30772	+	3.15711i	−0.113394	+	0.273756i
$134$	4.93397	+	5.17213i	0.426230	+	0.446804i
$135$		0			0
$136$	6.12823	−	12.2646i	0.525492	−	1.05168i
$137$	−9.89966	−	9.89966i	−0.845785	−	0.845785i	0.143819	−	0.989604i	$-0.454062\pi$
$137$	−9.89966	−	9.89966i	−0.845785	−	0.845785i	−0.989604	+	0.143819i	$0.954062\pi$
$138$		0			0
$139$	4.48614	−	10.8305i	0.380509	−	0.918631i	−0.611358	−	0.791354i	$-0.709376\pi$
$139$	4.48614	−	10.8305i	0.380509	−	0.918631i	0.991867	−	0.127277i	$-0.0406236\pi$
$140$	−0.621855	+	1.32151i	−0.0525563	+	0.111688i
$141$		0			0
$142$	−5.15608	−	2.27948i	−0.432689	−	0.191289i
$143$			10.3759i			0.867674i
$144$		0			0
$145$			3.28920i			0.273153i
$146$	2.59522	−	5.87028i	0.214782	−	0.485828i
$147$		0			0
$148$	5.99018	+	16.6383i	0.492389	+	1.36766i
$149$	−6.54755	+	15.8072i	−0.536396	+	1.29497i	0.390827	+	0.920464i	$0.372189\pi$
$149$	−6.54755	+	15.8072i	−0.536396	+	1.29497i	−0.927223	+	0.374510i	$0.877811\pi$
$150$		0			0
$151$	−1.79108	−	1.79108i	−0.145756	−	0.145756i	0.630463	−	0.776219i	$-0.282865\pi$
$151$	−1.79108	−	1.79108i	−0.145756	−	0.145756i	−0.776219	+	0.630463i	$0.782865\pi$
$152$	−1.04660	+	14.7823i	−0.0848904	+	1.19900i
$153$		0			0
$154$	−1.08960	+	1.03942i	−0.0878021	+	0.0837592i
$155$	2.67284	−	6.45280i	0.214687	−	0.518301i
$156$		0			0
$157$	−13.6745	+	5.66416i	−1.09134	+	0.452050i	−0.854475	−	0.519492i	$-0.826121\pi$
$157$	−13.6745	+	5.66416i	−1.09134	+	0.452050i	−0.236869	+	0.971542i	$0.576121\pi$
$158$	−12.4489	+	4.81613i	−0.990381	+	0.383151i
$159$		0			0
$160$	−0.744418	+	6.28981i	−0.0588514	+	0.497253i
$161$			0.814569i			0.0641970i
$162$		0			0
$163$	4.62848	+	11.1741i	0.362530	+	0.875226i	0.994929	+	0.100582i	$0.0320706\pi$
$163$	4.62848	+	11.1741i	0.362530	+	0.875226i	−0.632398	+	0.774643i	$0.717929\pi$
$164$	−12.3562	−	0.582681i	−0.964857	−	0.0454997i
$165$		0			0
$166$	7.94359	+	8.32702i	0.616543	+	0.646302i
$167$	−3.77738	−	3.77738i	−0.292303	−	0.292303i	0.545687	−	0.837989i	$-0.316269\pi$
$167$	−3.77738	−	3.77738i	−0.292303	−	0.292303i	−0.837989	+	0.545687i	$0.816269\pi$
$168$		0			0
$169$	−19.3691	+	19.3691i	−1.48993	+	1.48993i
$170$	7.67332	+	0.180825i	0.588517	+	0.0138686i
$171$		0			0
$172$	−3.24913	−	9.02477i	−0.247744	−	0.688132i
$173$	2.16608	−	0.897221i	0.164684	−	0.0682145i	−0.298818	−	0.954310i	$-0.596592\pi$
$173$	2.16608	−	0.897221i	0.164684	−	0.0682145i	0.463503	+	0.886096i	$0.346592\pi$
$174$		0			0
$175$	2.44346			0.184708
$176$	−3.05573	+	5.77132i	−0.230334	+	0.435029i
$177$		0			0
$178$	−9.62582	+	21.7732i	−0.721486	+	1.63197i
$179$	3.99680	+	9.64912i	0.298735	+	0.721209i	0.999966	+	0.00827525i	$0.00263412\pi$
$179$	3.99680	+	9.64912i	0.298735	+	0.721209i	−0.701231	+	0.712934i	$0.747366\pi$
$180$		0			0
$181$	1.73413	+	0.718300i	0.128897	+	0.0533908i	0.446200	−	0.894933i	$-0.352777\pi$
$181$	1.73413	+	0.718300i	0.128897	+	0.0533908i	−0.317303	+	0.948324i	$0.602777\pi$
$182$	−5.86051	−	0.138105i	−0.434410	−	0.0102370i
$183$		0			0
$184$	1.11796	+	3.35091i	0.0824169	+	0.247032i
$185$	−7.00022	+	7.00022i	−0.514666	+	0.514666i
$186$		0			0
$187$	7.31136	+	3.02847i	0.534660	+	0.221463i
$188$	−16.4775	−	18.1085i	−1.20175	−	1.32070i
$189$		0			0
$190$	−7.73736	+	2.99337i	−0.561327	+	0.217162i
$191$	19.8110			1.43348			0.716739	−	0.697342i	$-0.245634\pi$
$191$	19.8110			1.43348			0.716739	+	0.697342i	$0.245634\pi$
$192$		0			0
$193$	−4.34597			−0.312830			−0.156415	−	0.987691i	$-0.549994\pi$
$193$	−4.34597			−0.312830			−0.156415	+	0.987691i	$0.549994\pi$
$194$	−5.07723	+	1.96424i	−0.364524	+	0.141024i
$195$		0			0
$196$	8.84961	+	9.72556i	0.632115	+	0.694683i
$197$	21.9793	+	9.10413i	1.56596	+	0.648642i	0.986112	−	0.166081i	$-0.0531114\pi$
$197$	21.9793	+	9.10413i	1.56596	+	0.648642i	0.579849	+	0.814724i	$0.303111\pi$
$198$		0			0
$199$	14.8155	−	14.8155i	1.05024	−	1.05024i	0.0515701	−	0.998669i	$-0.483577\pi$
$199$	14.8155	−	14.8155i	1.05024	−	1.05024i	0.998669	−	0.0515701i	$-0.0164226\pi$
$200$	10.0517	−	3.35353i	0.710763	−	0.237131i
$201$		0			0
$202$	11.8731	+	0.279794i	0.835387	+	0.0196862i
$203$	−1.77017	−	0.733230i	−0.124242	−	0.0514627i
$204$		0			0
$205$	−2.65008	−	6.39787i	−0.185090	−	0.446847i
$206$	−3.75992	+	8.50479i	−0.261966	+	0.592557i
$207$		0			0
$208$	−24.2980	+	7.47515i	−1.68477	+	0.518308i
$209$	−8.55379			−0.591678
$210$		0			0
$211$	−12.0361	+	4.98552i	−0.828599	+	0.343217i	−0.756348	−	0.654169i	$-0.773018\pi$
$211$	−12.0361	+	4.98552i	−0.828599	+	0.343217i	−0.0722513	+	0.997386i	$0.523018\pi$
$212$	−0.999546	−	2.77633i	−0.0686491	−	0.190679i
$213$		0			0
$214$	22.2442	+	0.524192i	1.52058	+	0.0358330i
$215$	3.79699	−	3.79699i	0.258953	−	0.258953i
$216$		0			0
$217$	2.87692	+	2.87692i	0.195298	+	0.195298i
$218$	−5.04287	−	5.28629i	−0.341547	−	0.358032i
$219$		0			0
$220$	−3.65180	−	0.172208i	−0.246205	−	0.0116103i
$221$	11.7894	+	28.4622i	0.793044	+	1.91458i
$222$		0			0
$223$			24.3513i			1.63069i	0.578978	+	0.815343i	$0.303452\pi$
$223$			24.3513i			1.63069i	−0.578978	+	0.815343i	$0.696548\pi$
$224$	−3.21909	−	1.80276i	−0.215084	−	0.120452i
$225$		0			0
$226$	−12.1234	+	4.69019i	−0.806435	+	0.311987i
$227$	−14.9214	+	6.18065i	−0.990368	+	0.410224i	−0.818256	−	0.574853i	$-0.805059\pi$
$227$	−14.9214	+	6.18065i	−0.990368	+	0.410224i	−0.172112	+	0.985077i	$0.555059\pi$
$228$		0			0
$229$	−6.33851	+	15.3025i	−0.418861	+	1.01122i	0.563817	+	0.825899i	$0.309332\pi$
$229$	−6.33851	+	15.3025i	−0.418861	+	1.01122i	−0.982678	+	0.185320i	$0.940668\pi$
$230$	−1.43091	+	1.36502i	−0.0943515	+	0.0900070i
$231$		0			0
$232$	−8.28832	−	0.586822i	−0.544155	−	0.0385267i
$233$	−8.15060	−	8.15060i	−0.533964	−	0.533964i	0.387786	−	0.921750i	$-0.373240\pi$
$233$	−8.15060	−	8.15060i	−0.533964	−	0.533964i	−0.921750	+	0.387786i	$0.873240\pi$
$234$		0			0
$235$	5.24518	−	12.6630i	0.342158	−	0.826042i
$236$	−0.169104	−	0.469702i	−0.0110077	−	0.0305750i
$237$		0			0
$238$	−1.80786	+	4.08930i	−0.117186	+	0.265070i
$239$		−	4.90872i		−	0.317519i	−0.987317	−	0.158759i	$-0.949251\pi$
$239$		−	4.90872i		−	0.317519i	0.987317	−	0.158759i	$-0.0507494\pi$
$240$		0			0
$241$			15.5129i			0.999273i	0.866235	+	0.499637i	$0.166533\pi$
$241$			15.5129i			0.999273i	−0.866235	+	0.499637i	$0.833467\pi$
$242$	10.7805	+	4.76598i	0.692994	+	0.306369i
$243$		0			0
$244$	1.72239	−	3.66028i	0.110265	−	0.234325i
$245$	−2.81704	+	6.80093i	−0.179974	+	0.434495i
$246$		0			0
$247$	−23.5459	−	23.5459i	−1.49819	−	1.49819i
$248$	15.7833	+	7.88641i	1.00224	+	0.500787i
$249$		0			0
$250$	9.55947	+	10.0209i	0.604594	+	0.633777i
$251$	−11.5266	+	27.8276i	−0.727551	+	1.75646i	−0.0769625	+	0.997034i	$0.524522\pi$
$251$	−11.5266	+	27.8276i	−0.727551	+	1.75646i	−0.650589	+	0.759430i	$0.725478\pi$
$252$		0			0
$253$	−1.88377	+	0.780282i	−0.118431	+	0.0490559i
$254$	−5.75073	−	14.8647i	−0.360833	−	0.932693i
$255$		0			0
$256$	−15.7166	−	2.99799i	−0.982289	−	0.187374i
$257$		−	28.1601i		−	1.75658i	−0.478131	−	0.878289i	$-0.658686\pi$
$257$		−	28.1601i		−	1.75658i	0.478131	−	0.878289i	$-0.341314\pi$
$258$		0			0
$259$	−2.20687	−	5.32785i	−0.137128	−	0.331057i
$260$	−9.57821	−	10.5263i	−0.594016	−	0.652812i
$261$		0			0
$262$	6.56803	−	6.26560i	0.405774	−	0.387090i
$263$	6.19449	+	6.19449i	0.381969	+	0.381969i	0.871811	−	0.489842i	$-0.162946\pi$
$263$	6.19449	+	6.19449i	0.381969	+	0.381969i	−0.489842	+	0.871811i	$0.662946\pi$
$264$		0			0
$265$	1.16809	−	1.16809i	0.0717549	−	0.0717549i
$266$	0.113853	−	4.83136i	0.00698076	−	0.296230i
$267$		0			0
$268$	−9.14682	−	4.30415i	−0.558731	−	0.262918i
$269$	5.53745	−	2.29369i	0.337625	−	0.139849i	−0.207429	−	0.978250i	$-0.566509\pi$
$269$	5.53745	−	2.29369i	0.337625	−	0.139849i	0.545053	+	0.838401i	$0.316509\pi$
$270$		0			0
$271$	16.9375			1.02888			0.514440	−	0.857526i	$-0.328000\pi$
$271$	16.9375			1.02888			0.514440	+	0.857526i	$0.328000\pi$
$272$	−1.82464	+	19.3034i	−0.110635	+	1.17044i
$273$		0			0
$274$	18.1086	+	8.00571i	1.09398	+	0.483643i
$275$	2.34061	+	5.65073i	0.141144	+	0.340752i
$276$		0			0
$277$	14.2826	+	5.91604i	0.858157	+	0.355460i	0.767987	−	0.640466i	$-0.221259\pi$
$277$	14.2826	+	5.91604i	0.858157	+	0.355460i	0.0901707	+	0.995926i	$0.471259\pi$
$278$	−0.390573	+	16.5740i	−0.0234250	+	0.994043i
$279$		0			0
$280$	0.145873	−	2.06032i	0.00871758	−	0.123128i
$281$	−3.21316	+	3.21316i	−0.191681	+	0.191681i	−0.796422	−	0.604741i	$-0.793277\pi$
$281$	−3.21316	+	3.21316i	−0.191681	+	0.191681i	0.604741	+	0.796422i	$0.293277\pi$
$282$		0			0
$283$	20.8888	+	8.65244i	1.24171	+	0.514334i	0.904249	−	0.427005i	$-0.140431\pi$
$283$	20.8888	+	8.65244i	1.24171	+	0.514334i	0.337463	+	0.941339i	$0.390431\pi$
$284$	7.96375	+	0.375546i	0.472562	+	0.0222846i
$285$		0			0
$286$	−5.29444	−	13.6853i	−0.313067	−	0.809227i
$287$	4.03395			0.238116
$288$		0			0
$289$	6.49698			0.382175
$290$	−1.67836	−	4.33829i	−0.0985569	−	0.254753i
$291$		0			0
$292$	−0.427565	+	9.06685i	−0.0250214	+	0.530598i
$293$	−15.2023	−	6.29702i	−0.888130	−	0.367876i	−0.108486	−	0.994098i	$-0.534600\pi$
$293$	−15.2023	−	6.29702i	−0.888130	−	0.367876i	−0.779644	+	0.626222i	$0.784600\pi$
$294$		0			0
$295$	0.197618	−	0.197618i	0.0115057	−	0.0115057i
$296$	−16.3907	−	18.8885i	−0.952688	−	1.09787i
$297$		0			0
$298$	0.570043	−	24.1899i	0.0330217	−	1.40128i
$299$	−7.33327	−	3.03754i	−0.424094	−	0.175666i
$300$		0			0
$301$	1.19703	+	2.88988i	0.0689956	+	0.166570i
$302$	3.27628	+	1.44842i	0.188528	+	0.0833473i
$303$		0			0
$304$	−6.16246	−	20.0311i	−0.353441	−	1.14886i
$305$	2.26465			0.129673
$306$		0			0
$307$	−20.3690	+	8.43712i	−1.16252	+	0.481532i	−0.878714	−	0.477349i	$-0.841598\pi$
$307$	−20.3690	+	8.43712i	−1.16252	+	0.481532i	−0.283807	+	0.958881i	$0.591598\pi$
$308$	0.906741	−	1.92693i	0.0516663	−	0.109797i
$309$		0			0
$310$	−0.232703	+	9.87478i	−0.0132166	+	0.560850i
$311$	15.6176	−	15.6176i	0.885593	−	0.885593i	−0.108503	−	0.994096i	$-0.534606\pi$
$311$	15.6176	−	15.6176i	0.885593	−	0.885593i	0.994096	+	0.108503i	$0.0346056\pi$
$312$		0			0
$313$	−2.82959	−	2.82959i	−0.159938	−	0.159938i	0.622601	−	0.782539i	$-0.286076\pi$
$313$	−2.82959	−	2.82959i	−0.159938	−	0.159938i	−0.782539	+	0.622601i	$0.786076\pi$
$314$	15.1458	−	14.4484i	0.854725	−	0.815369i
$315$		0			0
$316$	13.9620	−	12.7045i	0.785423	−	0.714682i
$317$	10.0517	+	24.2669i	0.564558	+	1.36296i	0.906087	+	0.423092i	$0.139055\pi$
$317$	10.0517	+	24.2669i	0.564558	+	1.36296i	−0.341529	+	0.939871i	$0.610945\pi$
$318$		0			0
$319$		−	4.79606i		−	0.268528i
$320$	−2.22762	−	8.67579i	−0.124528	−	0.484991i
$321$		0			0
$322$	−0.415646	−	1.07438i	−0.0231630	−	0.0598726i
$323$	−23.4641	+	9.71913i	−1.30557	+	0.540787i
$324$		0			0
$325$	−9.11170	+	21.9976i	−0.505426	+	1.22021i
$326$	−11.8065	−	12.3764i	−0.653902	−	0.685464i
$327$		0			0
$328$	16.5945	−	5.53640i	0.916280	−	0.305697i
$329$	5.64567	+	5.64567i	0.311256	+	0.311256i
$330$		0			0
$331$	8.25917	−	19.9394i	0.453965	−	1.09597i	−0.516837	−	0.856084i	$-0.672891\pi$
$331$	8.25917	−	19.9394i	0.453965	−	1.09597i	0.970802	−	0.239884i	$-0.0771094\pi$
$332$	−14.7262	−	6.92959i	−0.808205	−	0.380310i
$333$		0			0
$334$	6.90964	+	3.05471i	0.378079	+	0.167146i
$335$		−	5.65923i		−	0.309197i
$336$		0			0
$337$		−	33.8500i		−	1.84393i	−0.387278	−	0.921963i	$-0.626585\pi$
$337$		−	33.8500i		−	1.84393i	0.387278	−	0.921963i	$-0.373415\pi$
$338$	15.6635	−	35.4302i	0.851982	−	1.92715i
$339$		0			0
$340$	−10.2130	+	3.67693i	−0.553877	+	0.199409i
$341$	−3.89733	+	9.40898i	−0.211052	+	0.509525i
$342$		0			0
$343$	−6.26045	−	6.26045i	−0.338033	−	0.338033i
$344$	8.89047	+	10.2453i	0.479342	+	0.552390i
$345$		0			0
$346$	−2.39914	+	2.28867i	−0.128978	+	0.123039i
$347$	−7.48342	+	18.0666i	−0.401731	+	0.969864i	0.585515	+	0.810661i	$0.300892\pi$
$347$	−7.48342	+	18.0666i	−0.401731	+	0.969864i	−0.987246	+	0.159203i	$0.949108\pi$
$348$		0			0
$349$	15.7807	−	6.53658i	0.844721	−	0.349895i	0.0820080	−	0.996632i	$-0.473867\pi$
$349$	15.7807	−	6.53658i	0.844721	−	0.349895i	0.762713	+	0.646737i	$0.223867\pi$
$350$	−3.22280	+	1.24681i	−0.172266	+	0.0666449i
$351$		0			0
$352$	1.08545	−	9.17131i	0.0578549	−	0.488833i
$353$			28.0339i			1.49209i	0.665894	+	0.746047i	$0.268050\pi$
$353$			28.0339i			1.49209i	−0.665894	+	0.746047i	$0.731950\pi$
$354$		0			0
$355$	1.70802	+	4.12352i	0.0906522	+	0.218854i
$356$	1.58587	−	33.6295i	0.0840508	−	1.78236i
$357$		0			0
$358$	−10.1952	−	10.6873i	−0.538832	−	0.564841i
$359$	14.6000	+	14.6000i	0.770559	+	0.770559i	0.978204	−	0.207645i	$-0.0665799\pi$
$359$	14.6000	+	14.6000i	0.770559	+	0.770559i	−0.207645	+	0.978204i	$0.566580\pi$
$360$		0			0
$361$	5.97599	−	5.97599i	0.314526	−	0.314526i
$362$	−2.65375	−	0.0625367i	−0.139478	−	0.00328686i
$363$		0			0
$364$	7.80019	−	2.80826i	0.408841	−	0.147193i
$365$	−4.69469	+	1.94461i	−0.245731	+	0.101785i
$366$		0			0
$367$	33.9941			1.77448			0.887238	−	0.461311i	$-0.152621\pi$
$367$	33.9941			1.77448			0.887238	+	0.461311i	$0.152621\pi$
$368$	−3.18438	−	3.84923i	−0.165997	−	0.200655i
$369$		0			0
$370$	5.66097	−	12.8049i	0.294300	−	0.665695i
$371$	0.368247	+	0.889028i	0.0191185	+	0.0461560i
$372$		0			0
$373$	−8.96494	−	3.71340i	−0.464187	−	0.192273i	0.138318	−	0.990388i	$-0.455831\pi$
$373$	−8.96494	−	3.71340i	−0.464187	−	0.192273i	−0.602505	+	0.798115i	$0.705831\pi$
$374$	−11.1886	−	0.263665i	−0.578551	−	0.0136338i
$375$		0			0
$376$	30.9731	+	15.4763i	1.59732	+	0.798129i
$377$	13.2020	−	13.2020i	0.679938	−	0.679938i
$378$		0			0
$379$	11.8198	+	4.89591i	0.607141	+	0.251486i	0.665006	−	0.746838i	$-0.268429\pi$
$379$	11.8198	+	4.89591i	0.607141	+	0.251486i	−0.0578644	+	0.998324i	$0.518429\pi$
$380$	8.67779	−	7.89621i	0.445161	−	0.405067i
$381$		0			0
$382$	−26.1298	+	10.1089i	−1.33692	+	0.517215i
$383$	12.3736			0.632262			0.316131	−	0.948716i	$-0.397616\pi$
$383$	12.3736			0.632262			0.316131	+	0.948716i	$0.397616\pi$
$384$		0			0
$385$	1.19221			0.0607607
$386$	5.73212	−	2.21760i	0.291757	−	0.112873i
$387$		0			0
$388$	5.69433	−	5.18146i	0.289086	−	0.263049i
$389$	26.9580	+	11.1664i	1.36683	+	0.566158i	0.940926	−	0.338613i	$-0.109958\pi$
$389$	26.9580	+	11.1664i	1.36683	+	0.566158i	0.425899	+	0.904771i	$0.359958\pi$
$390$		0			0
$391$	−4.28081	+	4.28081i	−0.216490	+	0.216490i
$392$	−16.6348	−	8.31188i	−0.840184	−	0.419813i
$393$		0			0
$394$	−33.6351	−	0.792625i	−1.69451	−	0.0399319i
$395$	9.76339	+	4.04413i	0.491250	+	0.203482i
$396$		0			0
$397$	−12.0775	−	29.1576i	−0.606151	−	1.46338i	−0.867154	−	0.498040i	$-0.834053\pi$
$397$	−12.0775	−	29.1576i	−0.606151	−	1.46338i	0.261003	−	0.965338i	$-0.415947\pi$
$398$	−11.9810	+	27.1006i	−0.600555	+	1.35843i
$399$		0			0
$400$	−11.5465	+	9.55217i	−0.577325	+	0.477609i
$401$	−10.3275			−0.515733			−0.257867	−	0.966181i	$-0.583019\pi$
$401$	−10.3275			−0.515733			−0.257867	+	0.966181i	$0.583019\pi$
$402$		0			0
$403$	−36.6280	+	15.1718i	−1.82457	+	0.755762i
$404$	−15.8028	+	5.68938i	−0.786217	+	0.283057i
$405$		0			0
$406$	2.70891	+	0.0638366i	0.134441	+	0.00316816i
$407$	10.2072	−	10.2072i	0.505951	−	0.505951i
$408$		0			0
$409$	−26.2307	−	26.2307i	−1.29702	−	1.29702i	−0.930349	−	0.366675i	$-0.880496\pi$
$409$	−26.2307	−	26.2307i	−1.29702	−	1.29702i	−0.366675	−	0.930349i	$-0.619504\pi$
$410$	6.75994	+	7.08623i	0.333849	+	0.349964i
$411$		0			0
$412$	0.619451	−	13.1359i	0.0305182	−	0.647162i
$413$	0.0623004	+	0.150406i	0.00306560	+	0.00740101i
$414$		0			0
$415$		−	9.11124i		−	0.447253i
$416$	28.2336	−	22.2578i	1.38427	−	1.09128i
$417$		0			0
$418$	11.2820	−	4.36470i	0.551822	−	0.213484i
$419$	35.1598	−	14.5637i	1.71767	−	0.711481i	0.717784	−	0.696266i	$-0.245157\pi$
$419$	35.1598	−	14.5637i	1.71767	−	0.711481i	0.999884	−	0.0152155i	$-0.00484343\pi$
$420$		0			0
$421$	1.30869	−	3.15946i	0.0637818	−	0.153983i	−0.888775	−	0.458344i	$-0.848443\pi$
$421$	1.30869	−	3.15946i	0.0637818	−	0.153983i	0.952557	+	0.304361i	$0.0984429\pi$
$422$	13.3311	−	12.7172i	0.648947	−	0.619066i
$423$		0			0
$424$	2.73502	+	3.15181i	0.132824	+	0.153065i
$425$	12.8411	+	12.8411i	0.622886	+	0.622886i
$426$		0			0
$427$	−0.504836	+	1.21878i	−0.0244307	+	0.0589810i
$428$	−29.6064	+	10.6590i	−1.43108	+	0.515224i
$429$		0			0
$430$	−3.07057	+	6.94551i	−0.148076	+	0.334942i
$431$			1.19790i			0.0577007i	0.999584	+	0.0288503i	$0.00918462\pi$
$431$			1.19790i			0.0577007i	−0.999584	+	0.0288503i	$0.990815\pi$
$432$		0			0
$433$			1.60818i			0.0772842i	0.999253	+	0.0386421i	$0.0123032\pi$
$433$			1.60818i			0.0772842i	−0.999253	+	0.0386421i	$0.987697\pi$
$434$	−5.26251	−	2.32653i	−0.252609	−	0.111677i
$435$		0			0
$436$	9.34871	+	4.39915i	0.447722	+	0.210681i
$437$	2.50413	−	6.04549i	0.119789	−	0.289195i
$438$		0			0
$439$	8.07633	+	8.07633i	0.385462	+	0.385462i	0.873065	−	0.487603i	$-0.162129\pi$
$439$	8.07633	+	8.07633i	0.385462	+	0.385462i	−0.487603	+	0.873065i	$0.662129\pi$
$440$	4.90442	−	1.63625i	0.233809	−	0.0780053i
$441$		0			0
$442$	−30.0730	−	31.5245i	−1.43043	−	1.49947i
$443$	4.94217	−	11.9315i	0.234810	−	0.566881i	−0.761921	−	0.647669i	$-0.775744\pi$
$443$	4.94217	−	11.9315i	0.234810	−	0.566881i	0.996731	+	0.0807884i	$0.0257438\pi$
$444$		0			0
$445$	17.4129	−	7.21267i	0.825451	−	0.341913i
$446$	−12.4256	−	32.1182i	−0.588371	−	1.52084i
$447$		0			0
$448$	5.16570	+	0.735159i	0.244056	+	0.0347330i
$449$		−	37.2223i		−	1.75663i	−0.478082	−	0.878315i	$-0.658668\pi$
$449$		−	37.2223i		−	1.75663i	0.478082	−	0.878315i	$-0.341332\pi$
$450$		0			0
$451$	3.86415	+	9.32888i	0.181956	+	0.439280i
$452$	13.5969	−	12.3723i	0.639544	−	0.581942i
$453$		0			0
$454$	16.5268	−	15.7658i	0.775642	−	0.739927i
$455$	3.28177	+	3.28177i	0.153852	+	0.153852i
$456$		0			0
$457$	−8.59103	+	8.59103i	−0.401871	+	0.401871i	−0.878892	−	0.477021i	$-0.841717\pi$
$457$	−8.59103	+	8.59103i	−0.401871	+	0.401871i	0.477021	+	0.878892i	$0.341717\pi$
$458$	0.551845	−	23.4176i	0.0257860	−	1.09423i
$459$		0			0
$460$	1.19078	−	2.53054i	0.0555203	−	0.117987i
$461$	−33.1723	+	13.7404i	−1.54499	+	0.639956i	−0.982402	−	0.186781i	$-0.940195\pi$
$461$	−33.1723	+	13.7404i	−1.54499	+	0.639956i	−0.562589	+	0.826737i	$0.690195\pi$
$462$		0			0
$463$	−20.7862			−0.966016			−0.483008	−	0.875616i	$-0.660456\pi$
$463$	−20.7862			−0.966016			−0.483008	+	0.875616i	$0.660456\pi$
$464$	11.2313	−	3.45525i	0.521401	−	0.160406i
$465$		0			0
$466$	14.9092	+	6.59127i	0.690656	+	0.305335i
$467$	−2.85128	−	6.88360i	−0.131942	−	0.318535i	0.844077	−	0.536222i	$-0.180149\pi$
$467$	−2.85128	−	6.88360i	−0.131942	−	0.318535i	−0.976019	+	0.217687i	$0.930149\pi$
$468$		0			0
$469$	3.04567	+	1.26156i	0.140636	+	0.0582533i
$470$	−0.456656	+	19.3783i	−0.0210640	+	0.893853i
$471$		0			0
$472$	0.462712	+	0.533225i	0.0212980	+	0.0245437i
$473$	−5.53648	+	5.53648i	−0.254568	+	0.254568i
$474$		0			0
$475$	−18.1346	−	7.51161i	−0.832074	−	0.344656i
$476$	0.297847	−	6.31607i	0.0136518	−	0.289497i
$477$		0			0
$478$	2.50475	+	6.47436i	0.114564	+	0.296130i
$479$	−0.904497			−0.0413275			−0.0206638	−	0.999786i	$-0.506578\pi$
$479$	−0.904497			−0.0413275			−0.0206638	+	0.999786i	$0.506578\pi$
$480$		0			0
$481$	56.1942			2.56223
$482$	−7.91568	−	20.4607i	−0.360549	−	0.931961i
$483$		0			0
$484$	−16.6508	−	0.785201i	−0.756854	−	0.0356910i
$485$	3.98196	+	1.64938i	0.180811	+	0.0748945i
$486$		0			0
$487$	−8.95124	+	8.95124i	−0.405619	+	0.405619i	−0.880208	−	0.474588i	$-0.842597\pi$
$487$	−8.95124	+	8.95124i	−0.405619	+	0.405619i	0.474588	+	0.880208i	$0.342597\pi$
$488$	−0.404033	+	5.70660i	−0.0182897	+	0.258325i
$489$		0			0
$490$	0.245257	−	10.4075i	0.0110796	−	0.470164i
$491$	−31.4738	−	13.0369i	−1.42039	−	0.588347i	−0.465435	−	0.885082i	$-0.654102\pi$
$491$	−31.4738	−	13.0369i	−1.42039	−	0.588347i	−0.954960	+	0.296736i	$0.904102\pi$
$492$		0			0
$493$	−5.44946	−	13.1562i	−0.245431	−	0.592523i
$494$	43.0704	+	19.0412i	1.93783	+	0.856704i
$495$		0			0
$496$	−24.8415	−	2.34812i	−1.11542	−	0.105434i
$497$	−2.59994			−0.116623
$498$		0			0
$499$	13.6146	−	5.63937i	0.609475	−	0.252453i	−0.0565290	−	0.998401i	$-0.518003\pi$
$499$	13.6146	−	5.63937i	0.609475	−	0.252453i	0.666004	+	0.745948i	$0.268003\pi$
$500$	−17.7218	−	8.33919i	−0.792542	−	0.372940i
$501$		0			0
$502$	1.00353	−	42.5849i	0.0447897	−	1.90066i
$503$	−25.8767	+	25.8767i	−1.15379	+	1.15379i	−0.167999	+	0.985787i	$0.553731\pi$
$503$	−25.8767	+	25.8767i	−1.15379	+	1.15379i	−0.985787	+	0.167999i	$0.946269\pi$
$504$		0			0
$505$	−6.64870	−	6.64870i	−0.295863	−	0.295863i
$506$	2.08644	−	1.99037i	0.0927538	−	0.0884829i
$507$		0			0
$508$	15.1699	+	16.6714i	0.673053	+	0.739673i
$509$	3.99432	+	9.64315i	0.177045	+	0.427425i	0.987344	−	0.158592i	$-0.0506953\pi$
$509$	3.99432	+	9.64315i	0.177045	+	0.427425i	−0.810299	+	0.586017i	$0.800695\pi$
$510$		0			0
$511$		−	2.96007i		−	0.130946i
$512$	22.2592	−	4.06544i	0.983727	−	0.179669i
$513$		0			0
$514$	14.3691	+	37.1417i	0.633794	+	1.63825i
$515$	6.80161	−	2.81732i	0.299715	−	0.124146i
$516$		0			0
$517$	−7.64811	+	18.4642i	−0.336364	+	0.812054i
$518$	5.62936	+	5.90108i	0.247340	+	0.259279i
$519$		0			0
$520$	18.0044	+	8.99622i	0.789544	+	0.394510i
$521$	−11.3274	−	11.3274i	−0.496260	−	0.496260i	0.414011	−	0.910272i	$-0.364127\pi$
$521$	−11.3274	−	11.3274i	−0.496260	−	0.496260i	−0.910272	+	0.414011i	$0.864127\pi$
$522$		0			0
$523$	−0.302800	+	0.731024i	−0.0132405	+	0.0319654i	−0.930362	−	0.366643i	$-0.880507\pi$
$523$	−0.302800	+	0.731024i	−0.0132405	+	0.0319654i	0.917121	+	0.398609i	$0.130507\pi$
$524$	−5.46579	+	11.6155i	−0.238774	+	0.507424i
$525$		0			0
$526$	−11.3311	−	5.00939i	−0.494057	−	0.218420i
$527$			30.2382i			1.31720i
$528$		0			0
$529$			21.4402i			0.932183i
$530$	−0.944614	+	2.13668i	−0.0410314	+	0.0928114i
$531$		0			0
$532$	2.31511	+	6.43042i	0.100373	+	0.278794i
$533$	−15.0427	+	36.3162i	−0.651570	+	1.57303i
$534$		0			0
$535$	−12.4563	−	12.4563i	−0.538533	−	0.538533i
$536$	14.2605	+	1.00965i	0.615958	+	0.0436104i
$537$		0			0
$538$	−6.13324	+	5.85083i	−0.264423	+	0.252247i
$539$	4.10759	−	9.91659i	0.176926	−	0.427138i
$540$		0			0
$541$	33.9761	−	14.0734i	1.46075	−	0.605062i	0.496021	−	0.868311i	$-0.334794\pi$
$541$	33.9761	−	14.0734i	1.46075	−	0.605062i	0.964728	+	0.263249i	$0.0847940\pi$
$542$	−22.3397	+	8.64261i	−0.959574	+	0.371232i
$543$		0			0
$544$	−7.44325	−	26.3913i	−0.319127	−	1.13152i
$545$			5.78413i			0.247765i
$546$		0			0
$547$	−13.8793	−	33.5076i	−0.593437	−	1.43268i	−0.880163	−	0.474671i	$-0.842567\pi$
$547$	−13.8793	−	33.5076i	−0.593437	−	1.43268i	0.286726	−	0.958013i	$-0.407433\pi$
$548$	−27.9694	−	1.31895i	−1.19479	−	0.0563428i
$549$		0			0
$550$	−5.97051	−	6.25870i	−0.254584	−	0.266872i
$551$	10.8836	+	10.8836i	0.463659	+	0.463659i
$552$		0			0
$553$	−4.35292	+	4.35292i	−0.185105	+	0.185105i
$554$	−21.8568	−	0.515063i	−0.928605	−	0.0218829i
$555$		0			0
$556$	−7.94199	−	22.0596i	−0.336815	−	0.935535i
$557$	13.2218	−	5.47665i	0.560226	−	0.232053i	−0.0845575	−	0.996419i	$-0.526948\pi$
$557$	13.2218	−	5.47665i	0.560226	−	0.232053i	0.644783	+	0.764366i	$0.276948\pi$
$558$		0			0
$559$	−30.4803			−1.28918
$560$	0.858911	+	2.79190i	0.0362956	+	0.117979i
$561$		0			0
$562$	2.59843	−	5.87755i	0.109608	−	0.247930i
$563$	−10.9271	−	26.3804i	−0.460522	−	1.11180i	−0.968183	−	0.250242i	$-0.919490\pi$
$563$	−10.9271	−	26.3804i	−0.460522	−	1.11180i	0.507661	−	0.861557i	$-0.330510\pi$
$564$		0			0
$565$	9.50809	+	3.93838i	0.400008	+	0.165689i
$566$	−31.9664	−	0.753300i	−1.34365	−	0.0316636i
$567$		0			0
$568$	−10.6954	+	3.56830i	−0.448770	+	0.149722i
$569$	9.04486	−	9.04486i	0.379180	−	0.379180i	−0.491626	−	0.870806i	$-0.663597\pi$
$569$	9.04486	−	9.04486i	0.379180	−	0.379180i	0.870806	+	0.491626i	$0.163597\pi$
$570$		0			0
$571$	−10.3574	−	4.29017i	−0.433443	−	0.179538i	0.155284	−	0.987870i	$-0.450371\pi$
$571$	−10.3574	−	4.29017i	−0.433443	−	0.179538i	−0.588727	+	0.808332i	$0.700371\pi$
$572$	13.9662	+	15.3486i	0.583957	+	0.641758i
$573$		0			0
$574$	−5.32058	+	2.05838i	−0.222077	+	0.0859152i
$575$	−4.67893			−0.195125
$576$		0			0
$577$	33.8164			1.40779			0.703897	−	0.710302i	$-0.251441\pi$
$577$	33.8164			1.40779			0.703897	+	0.710302i	$0.251441\pi$
$578$	−8.56919	+	3.31518i	−0.356431	+	0.137893i
$579$		0			0
$580$	4.42735	+	4.86558i	0.183836	+	0.202032i
$581$	4.90346	+	2.03108i	0.203430	+	0.0842635i
$582$		0			0
$583$	−1.70321	+	1.70321i	−0.0705399	+	0.0705399i
$584$	−4.06256	−	12.1769i	−0.168110	−	0.503884i
$585$		0			0
$586$	23.2643	+	0.548232i	0.961038	+	0.0226472i
$587$	18.8155	+	7.79362i	0.776598	+	0.321677i	0.735542	−	0.677480i	$-0.236928\pi$
$587$	18.8155	+	7.79362i	0.776598	+	0.321677i	0.0410561	+	0.999157i	$0.486928\pi$
$588$		0			0
$589$	−12.5075	−	30.1958i	−0.515363	−	1.24420i
$590$	−0.159810	+	0.361485i	−0.00657929	+	0.0148821i
$591$		0			0
$592$	31.2566	+	16.5494i	1.28464	+	0.680175i
$593$	13.8350			0.568137			0.284069	−	0.958804i	$-0.408316\pi$
$593$	13.8350			0.568137			0.284069	+	0.958804i	$0.408316\pi$
$594$		0			0
$595$	3.27037	−	1.35463i	0.134072	−	0.0555345i
$596$	11.5914	+	32.1961i	0.474801	+	1.31880i
$597$		0			0
$598$	11.2222	+	0.264455i	0.458909	+	0.0108144i
$599$	13.9987	−	13.9987i	0.571973	−	0.571973i	−0.360706	−	0.932679i	$-0.617464\pi$
$599$	13.9987	−	13.9987i	0.571973	−	0.571973i	0.932679	+	0.360706i	$0.117464\pi$
$600$		0			0
$601$	−27.1784	−	27.1784i	−1.10863	−	1.10863i	−0.993331	−	0.115299i	$-0.963217\pi$
$601$	−27.1784	−	27.1784i	−1.10863	−	1.10863i	−0.115299	−	0.993331i	$-0.536783\pi$
$602$	−3.05343	−	3.20081i	−0.124448	−	0.130455i
$603$		0			0
$604$	−5.06032	−	0.238629i	−0.205902	−	0.00970969i
$605$	−3.57116	−	8.62155i	−0.145188	−	0.350516i
$606$		0			0
$607$			25.7503i			1.04517i	0.852587	+	0.522585i	$0.175032\pi$
$607$			25.7503i			1.04517i	−0.852587	+	0.522585i	$0.824968\pi$
$608$	18.3491	+	23.2756i	0.744156	+	0.943948i
$609$		0			0
$610$	−2.98696	+	1.15557i	−0.120938	+	0.0467877i
$611$	−71.8788	+	29.7732i	−2.90790	+	1.20449i
$612$		0			0
$613$	−7.60344	+	18.3563i	−0.307100	+	0.741405i	0.692696	+	0.721229i	$0.256423\pi$
$613$	−7.60344	+	18.3563i	−0.307100	+	0.741405i	−0.999796	+	0.0201758i	$0.993577\pi$
$614$	22.5605	−	21.5217i	0.910470	−	0.868546i
$615$		0			0
$616$	−0.212701	+	3.00420i	−0.00856996	+	0.121043i
$617$	−0.576308	−	0.576308i	−0.0232013	−	0.0232013i	0.695411	−	0.718612i	$-0.255222\pi$
$617$	−0.576308	−	0.576308i	−0.0232013	−	0.0232013i	−0.718612	+	0.695411i	$0.755222\pi$
$618$		0			0
$619$	4.65177	−	11.2304i	0.186971	−	0.451387i	−0.802403	−	0.596783i	$-0.796445\pi$
$619$	4.65177	−	11.2304i	0.186971	−	0.451387i	0.989374	+	0.145396i	$0.0464455\pi$
$620$	−4.73183	−	13.1431i	−0.190035	−	0.527839i
$621$		0			0
$622$	−12.6297	+	28.5680i	−0.506406	+	1.14547i
$623$			10.9791i			0.439868i
$624$		0			0
$625$			7.76727i			0.310691i
$626$	5.17593	+	2.28825i	0.206872	+	0.0914569i
$627$		0			0
$628$	−12.6040	+	26.7850i	−0.502955	+	1.06884i
$629$	16.4017	−	39.5972i	0.653979	−	1.57885i
$630$		0			0
$631$	−14.0469	−	14.0469i	−0.559197	−	0.559197i	0.369882	−	0.929079i	$-0.379398\pi$
$631$	−14.0469	−	14.0469i	−0.559197	−	0.559197i	−0.929079	+	0.369882i	$0.879398\pi$
$632$	−11.9325	+	23.8809i	−0.474650	+	0.949930i
$633$		0			0
$634$	−25.6402	−	26.8778i	−1.01830	−	1.06745i
$635$	−4.82892	+	11.6580i	−0.191630	+	0.462635i
$636$		0			0
$637$	38.6041	−	15.9903i	1.52955	−	0.633560i
$638$	2.44726	+	6.32576i	0.0968880	+	0.250439i
$639$		0			0
$640$	7.36507	+	10.3063i	0.291130	+	0.407391i
$641$		−	5.96286i		−	0.235519i	−0.993042	−	0.117759i	$-0.962429\pi$
$641$		−	5.96286i		−	0.235519i	0.993042	−	0.117759i	$-0.0375712\pi$
$642$		0			0
$643$	12.8196	+	30.9492i	0.505556	+	1.22052i	0.946418	+	0.322944i	$0.104673\pi$
$643$	12.8196	+	30.9492i	0.505556	+	1.22052i	−0.440862	+	0.897575i	$0.645327\pi$
$644$	1.09643	+	1.20496i	0.0432055	+	0.0474820i
$645$		0			0
$646$	25.9886	−	24.7919i	1.02251	−	0.975425i
$647$	6.79378	+	6.79378i	0.267091	+	0.267091i	0.827927	−	0.560836i	$-0.189520\pi$
$647$	6.79378	+	6.79378i	0.267091	+	0.267091i	−0.560836	+	0.827927i	$0.689520\pi$
$648$		0			0
$649$	−0.288151	+	0.288151i	−0.0113109	+	0.0113109i
$650$	0.793284	−	33.6631i	0.0311152	−	1.32038i
$651$		0			0
$652$	21.8874	+	10.2994i	0.857177	+	0.403355i
$653$	−0.997069	+	0.412999i	−0.0390183	+	0.0161619i	−0.402107	−	0.915593i	$-0.631722\pi$
$653$	−0.997069	+	0.412999i	−0.0390183	+	0.0161619i	0.363089	+	0.931754i	$0.381722\pi$
$654$		0			0
$655$	−7.18659			−0.280803
$656$	−19.0623	+	15.7698i	−0.744259	+	0.615709i
$657$		0			0
$658$	−10.3272	−	4.56558i	−0.402594	−	0.177985i
$659$	7.53319	+	18.1867i	0.293452	+	0.708455i	1.00000		0.000789765i	$0.000251390\pi$
$659$	7.53319	+	18.1867i	0.293452	+	0.708455i	−0.706548	+	0.707665i	$0.749749\pi$
$660$		0			0
$661$	−9.26135	−	3.83618i	−0.360225	−	0.149210i	0.195228	−	0.980758i	$-0.437455\pi$
$661$	−9.26135	−	3.83618i	−0.360225	−	0.149210i	−0.555453	+	0.831548i	$0.687455\pi$
$662$	−0.719061	+	30.5134i	−0.0279471	+	1.18594i
$663$		0			0
$664$	22.9590	+	1.62552i	0.890983	+	0.0630825i
$665$	−2.70547	+	2.70547i	−0.104914	+	0.104914i
$666$		0			0
$667$	3.38967	+	1.40405i	0.131249	+	0.0543649i
$668$	−10.6722	−	0.503268i	−0.412919	−	0.0194720i
$669$		0			0
$670$	2.88770	+	7.46424i	0.111562	+	0.288369i
$671$	−3.30214			−0.127478
$672$		0			0
$673$	11.7766			0.453956			0.226978	−	0.973900i	$-0.427115\pi$
$673$	11.7766			0.453956			0.226978	+	0.973900i	$0.427115\pi$
$674$	17.2725	+	44.6464i	0.665310	+	1.71972i
$675$		0			0
$676$	−2.58058	+	54.7232i	−0.0992531	+	2.10474i
$677$	12.3539	+	5.11715i	0.474798	+	0.196668i	0.607233	−	0.794524i	$-0.292279\pi$
$677$	12.3539	+	5.11715i	0.474798	+	0.196668i	−0.132435	+	0.991192i	$0.542279\pi$
$678$		0			0
$679$	−1.77532	+	1.77532i	−0.0681305	+	0.0681305i
$680$	11.5942	−	10.0610i	0.444618	−	0.385822i
$681$		0			0
$682$	0.339309	−	14.3986i	0.0129928	−	0.551352i
$683$	42.8039	+	17.7299i	1.63784	+	0.678418i	0.996078	−	0.0884821i	$-0.0282016\pi$
$683$	42.8039	+	17.7299i	1.63784	+	0.678418i	0.641767	+	0.766900i	$0.278202\pi$
$684$		0			0
$685$	−5.99871	−	14.4822i	−0.229199	−	0.553335i
$686$	11.4517	+	5.06274i	0.437228	+	0.193296i
$687$		0			0
$688$	−16.9539	−	8.97655i	−0.646361	−	0.342228i
$689$	−9.37680			−0.357228
$690$		0			0
$691$	−3.13069	+	1.29677i	−0.119097	+	0.0493316i	−0.441436	−	0.897293i	$-0.645531\pi$
$691$	−3.13069	+	1.29677i	−0.119097	+	0.0493316i	0.322339	+	0.946624i	$0.395531\pi$
$692$	1.99652	−	4.24283i	0.0758961	−	0.161288i
$693$		0			0
$694$	0.651522	−	27.6474i	0.0247314	−	1.04948i
$695$	9.28113	−	9.28113i	0.352053	−	0.352053i
$696$		0			0
$697$	21.1996	+	21.1996i	0.802993	+	0.802993i
$698$	−17.4786	+	16.6738i	−0.661574	+	0.631111i
$699$		0			0
$700$	3.61451	−	3.28896i	0.136616	−	0.124311i
$701$	−2.91889	−	7.04682i	−0.110245	−	0.266155i	0.859122	−	0.511770i	$-0.171010\pi$
$701$	−2.91889	−	7.04682i	−0.110245	−	0.266155i	−0.969367	+	0.245615i	$0.921010\pi$
$702$		0			0
$703$			46.3260i			1.74722i
$704$	3.24814	+	12.6504i	0.122419	+	0.476779i
$705$		0			0
$706$	−14.3047	−	36.9753i	−0.538365	−	1.39158i
$707$	5.06031	−	2.09605i	0.190313	−	0.0788301i
$708$		0			0
$709$	5.50561	−	13.2917i	0.206768	−	0.499181i	−0.786143	−	0.618045i	$-0.787925\pi$
$709$	5.50561	−	13.2917i	0.206768	−	0.499181i	0.992911	+	0.118863i	$0.0379250\pi$
$710$	−4.35688	−	4.56718i	−0.163511	−	0.171403i
$711$		0			0
$712$	15.0683	+	45.1649i	0.564708	+	1.69263i
$713$	−5.50896	−	5.50896i	−0.206312	−	0.206312i
$714$		0			0
$715$	−4.44577	+	10.7330i	−0.166262	+	0.401393i
$716$	18.9003	+	8.89376i	0.706337	+	0.332375i
$717$		0			0
$718$	−26.7066	−	11.8068i	−0.996680	−	0.440627i
$719$		−	44.7109i		−	1.66744i	−0.552190	−	0.833718i	$-0.686208\pi$
$719$		−	44.7109i		−	1.66744i	0.552190	−	0.833718i	$-0.313792\pi$
$720$		0			0
$721$			4.28851i			0.159713i
$722$	−4.83270	+	10.9314i	−0.179854	+	0.406824i
$723$		0			0
$724$	3.53208	−	1.27163i	0.131269	−	0.0472599i
$725$	4.21172	−	10.1680i	0.156419	−	0.377629i
$726$		0			0
$727$	8.14552	+	8.14552i	0.302101	+	0.302101i	0.841835	−	0.539735i	$-0.181475\pi$
$727$	8.14552	+	8.14552i	0.302101	+	0.302101i	−0.539735	+	0.841835i	$0.681475\pi$
$728$	−8.85511	+	7.68411i	−0.328192	+	0.284792i
$729$		0			0
$730$	5.19980	−	4.96037i	0.192453	−	0.183592i
$731$	−8.89646	+	21.4780i	−0.329048	+	0.794391i
$732$		0			0
$733$	−5.53190	+	2.29139i	−0.204326	+	0.0846344i	−0.482499	−	0.875896i	$-0.660271\pi$
$733$	−5.53190	+	2.29139i	−0.204326	+	0.0846344i	0.278174	+	0.960531i	$0.410271\pi$
$734$	−44.8365	+	17.3460i	−1.65495	+	0.640252i
$735$		0			0
$736$	6.16417	+	3.45206i	0.227214	+	0.127245i
$737$			8.25185i			0.303961i
$738$		0			0
$739$	17.2710	+	41.6959i	0.635324	+	1.53381i	0.832843	+	0.553509i	$0.186712\pi$
$739$	17.2710	+	41.6959i	0.635324	+	1.53381i	−0.197519	+	0.980299i	$0.563288\pi$
$740$	−0.932652	+	19.7776i	−0.0342850	+	0.727040i
$741$		0			0
$742$	−0.939340	−	0.984680i	−0.0344842	−	0.0361487i
$743$	−37.1387	−	37.1387i	−1.36249	−	1.36249i	−0.870734	−	0.491753i	$-0.836356\pi$
$743$	−37.1387	−	37.1387i	−1.36249	−	1.36249i	−0.491753	−	0.870734i	$-0.663644\pi$
$744$		0			0
$745$	−13.5459	+	13.5459i	−0.496282	+	0.496282i
$746$	13.7191	+	0.323296i	0.502293	+	0.0118367i
$747$		0			0
$748$	14.8918	−	5.36141i	0.544498	−	0.196033i
$749$	9.48047	−	3.92694i	0.346409	−	0.143487i
$750$		0			0
$751$	36.3191			1.32530			0.662652	−	0.748927i	$-0.269431\pi$
$751$	36.3191			1.32530			0.662652	+	0.748927i	$0.269431\pi$
$752$	−48.7490	−	4.60796i	−1.77769	−	0.168035i
$753$		0			0
$754$	−10.6763	+	24.1493i	−0.388807	+	0.879467i
$755$	−1.08531	−	2.62017i	−0.0394984	−	0.0953576i
$756$		0			0
$757$	12.1064	+	5.01461i	0.440013	+	0.182259i	0.591681	−	0.806172i	$-0.298465\pi$
$757$	12.1064	+	5.01461i	0.440013	+	0.182259i	−0.151668	+	0.988431i	$0.548465\pi$
$758$	−18.0879	−	0.426249i	−0.656983	−	0.0154820i
$759$		0			0
$760$	−7.41641	+	14.8427i	−0.269022	+	0.538400i
$761$	−14.9253	+	14.9253i	−0.541042	+	0.541042i	−0.923834	−	0.382792i	$-0.874963\pi$
$761$	−14.9253	+	14.9253i	−0.541042	+	0.541042i	0.382792	+	0.923834i	$0.374963\pi$
$762$		0			0
$763$	−3.11289	−	1.28940i	−0.112694	−	0.0466795i
$764$	29.3057	−	26.6662i	1.06024	−	0.964750i
$765$		0			0
$766$	−16.3202	+	6.31382i	−0.589672	+	0.228127i
$767$	−1.58637			−0.0572806
$768$		0			0
$769$	34.0952			1.22951			0.614753	−	0.788720i	$-0.289256\pi$
$769$	34.0952			1.22951			0.614753	+	0.788720i	$0.289256\pi$
$770$	−1.57247	+	0.608343i	−0.0566678	+	0.0219232i
$771$		0			0
$772$	−6.42882	+	5.84980i	−0.231378	+	0.210539i
$773$	−8.70561	−	3.60598i	−0.313119	−	0.129698i	0.220589	−	0.975367i	$-0.429202\pi$
$773$	−8.70561	−	3.60598i	−0.313119	−	0.129698i	−0.533708	+	0.845669i	$0.679202\pi$
$774$		0			0
$775$	−16.5252	+	16.5252i	−0.593603	+	0.593603i
$776$	−4.86662	+	9.73971i	−0.174702	+	0.349635i
$777$		0			0
$778$	−41.2541	−	0.972168i	−1.47903	−	0.0348539i
$779$	−29.9388	−	12.4011i	−1.07267	−	0.444314i
$780$		0			0
$781$	−2.49050	−	6.01260i	−0.0891172	−	0.215148i
$782$	3.46183	−	7.83052i	0.123795	−	0.280019i
$783$		0			0
$784$	26.1817	+	2.47481i	0.935062	+	0.0883859i
$785$	−16.5722			−0.591486
$786$		0			0
$787$	−48.6829	+	20.1651i	−1.73536	+	0.718808i	−0.736243	+	0.676718i	$0.763402\pi$
$787$	−48.6829	+	20.1651i	−1.73536	+	0.718808i	−0.999114	+	0.0420904i	$0.986598\pi$
$788$	44.7675	−	16.1174i	1.59478	−	0.574158i
$789$		0			0
$790$	−14.9410	−	0.352091i	−0.531577	−	0.0125268i
$791$	−4.23910	+	4.23910i	−0.150725	+	0.150725i
$792$		0			0
$793$	−9.08972	−	9.08972i	−0.322786	−	0.322786i
$794$	30.8077	+	32.2947i	1.09332	+	1.14610i
$795$		0			0
$796$	1.97389	−	41.8579i	0.0699627	−	1.48361i
$797$	−3.00671	−	7.25885i	−0.106503	−	0.257122i	0.861639	−	0.507521i	$-0.169438\pi$
$797$	−3.00671	−	7.25885i	−0.106503	−	0.257122i	−0.968143	+	0.250399i	$0.919438\pi$
$798$		0			0
$799$			59.3395i			2.09928i
$800$	10.3551	−	18.4906i	0.366109	−	0.653742i
$801$		0			0
$802$	13.6215	−	5.26978i	0.480993	−	0.186083i
$803$	6.84544	−	2.83547i	0.241570	−	0.100062i
$804$		0			0
$805$	−0.349020	+	0.842609i	−0.0123013	+	0.0296981i
$806$	40.5689	−	38.7008i	1.42898	−	1.36318i
$807$		0			0
$808$	17.9400	−	15.5676i	0.631126	−	0.547667i
$809$	−6.03676	−	6.03676i	−0.212241	−	0.212241i	0.592978	−	0.805219i	$-0.297952\pi$
$809$	−6.03676	−	6.03676i	−0.212241	−	0.212241i	−0.805219	+	0.592978i	$0.797952\pi$
$810$		0			0
$811$	5.74431	−	13.8680i	0.201710	−	0.486971i	−0.790362	−	0.612640i	$-0.790108\pi$
$811$	5.74431	−	13.8680i	0.201710	−	0.486971i	0.992072	+	0.125669i	$0.0401077\pi$
$812$	−3.60550	+	1.29807i	−0.126528	+	0.0455532i
$813$		0			0
$814$	−8.25440	+	18.6711i	−0.289316	+	0.654423i
$815$			13.5420i			0.474354i
$816$		0			0
$817$		−	25.1277i		−	0.879108i
$818$	47.9816	+	21.2124i	1.67764	+	0.741673i
$819$		0			0
$820$	−12.5319	−	5.89702i	−0.437632	−	0.205933i
$821$	−5.81709	+	14.0437i	−0.203018	+	0.490128i	−0.992293	−	0.123911i	$-0.960456\pi$
$821$	−5.81709	+	14.0437i	−0.203018	+	0.490128i	0.789276	+	0.614039i	$0.210456\pi$
$822$		0			0
$823$	−27.6935	−	27.6935i	−0.965334	−	0.965334i	0.0340853	−	0.999419i	$-0.489148\pi$
$823$	−27.6935	−	27.6935i	−0.965334	−	0.965334i	−0.999419	+	0.0340853i	$0.989148\pi$
$824$	5.88578	+	17.6417i	0.205041	+	0.614579i
$825$		0			0
$826$	−0.158918	−	0.166589i	−0.00552947	−	0.00579637i
$827$	15.0430	−	36.3171i	0.523097	−	1.26287i	−0.412873	−	0.910789i	$-0.635475\pi$
$827$	15.0430	−	36.3171i	0.523097	−	1.26287i	0.935970	−	0.352080i	$-0.114525\pi$
$828$		0			0
$829$	−41.4825	+	17.1826i	−1.44075	+	0.596776i	−0.959979	−	0.280072i	$-0.909642\pi$
$829$	−41.4825	+	17.1826i	−1.44075	+	0.596776i	−0.480767	+	0.876849i	$0.659642\pi$
$830$	4.64914	+	12.0173i	0.161374	+	0.417125i
$831$		0			0
$832$	−25.8813	+	43.7635i	−0.897274	+	1.51723i
$833$		−	31.8696i		−	1.10421i
$834$		0			0
$835$	−2.28891	−	5.52591i	−0.0792109	−	0.191232i
$836$	−12.6533	+	11.5136i	−0.437623	+	0.398208i
$837$		0			0
$838$	−38.9427	+	37.1495i	−1.34525	+	1.28331i
$839$	−24.7167	−	24.7167i	−0.853315	−	0.853315i	0.137225	−	0.990540i	$-0.456182\pi$
$839$	−24.7167	−	24.7167i	−0.853315	−	0.853315i	−0.990540	+	0.137225i	$0.956182\pi$
$840$		0			0
$841$	14.4037	−	14.4037i	0.496680	−	0.496680i
$842$	−0.113938	+	4.83496i	−0.00392655	+	0.166624i
$843$		0			0
$844$	−11.0939	+	23.5758i	−0.381867	+	0.811513i
$845$	−28.3349	+	11.7367i	−0.974751	+	0.403755i
$846$		0			0
$847$	5.43601			0.186784
$848$	−5.21561	−	2.76150i	−0.179105	−	0.0948302i
$849$		0			0
$850$	−23.4892	−	10.3844i	−0.805672	−	0.356183i
$851$	4.22589	+	10.2022i	0.144862	+	0.349727i
$852$		0			0
$853$	13.1295	+	5.43842i	0.449545	+	0.186208i	0.595958	−	0.803016i	$-0.296773\pi$
$853$	13.1295	+	5.43842i	0.449545	+	0.186208i	−0.146412	+	0.989224i	$0.546773\pi$
$854$	0.0439521	−	1.86511i	0.00150401	−	0.0638229i
$855$		0			0
$856$	33.6105	−	29.1658i	1.14878	−	0.996868i
$857$	7.13158	−	7.13158i	0.243610	−	0.243610i	−0.574732	−	0.818342i	$-0.694894\pi$
$857$	7.13158	−	7.13158i	0.243610	−	0.243610i	0.818342	+	0.574732i	$0.194894\pi$
$858$		0			0
$859$	25.5834	+	10.5970i	0.872896	+	0.361565i	0.773738	−	0.633506i	$-0.218385\pi$
$859$	25.5834	+	10.5970i	0.872896	+	0.361565i	0.0991585	+	0.995072i	$0.468385\pi$
$860$	0.505880	−	10.7276i	0.0172504	−	0.365808i
$861$		0			0
$862$	−0.611245	−	1.57997i	−0.0208191	−	0.0538139i
$863$	−12.7695			−0.434678			−0.217339	−	0.976096i	$-0.569738\pi$
$863$	−12.7695			−0.434678			−0.217339	+	0.976096i	$0.569738\pi$
$864$		0			0
$865$	2.62508			0.0892554
$866$	−0.820598	−	2.12111i	−0.0278851	−	0.0720783i
$867$		0			0
$868$	8.12813	+	0.383298i	0.275887	+	0.0130100i
$869$	−14.2362	−	5.89684i	−0.482931	−	0.200037i
$870$		0			0
$871$	−22.7147	+	22.7147i	−0.769658	+	0.769658i
$872$	−14.5752	−	1.03194i	−0.493579	−	0.0349459i
$873$		0			0
$874$	−0.218014	+	9.25147i	−0.00737445	+	0.312936i
$875$	5.90092	+	2.44424i	0.199488	+	0.0826304i
$876$		0			0
$877$	9.24212	+	22.3124i	0.312084	+	0.753438i	0.999627	+	0.0272943i	$0.00868911\pi$
$877$	9.24212	+	22.3124i	0.312084	+	0.753438i	−0.687543	+	0.726143i	$0.741311\pi$
$878$	−14.7733	−	6.53121i	−0.498576	−	0.220418i
$879$		0			0
$880$	−5.63376	+	4.66069i	−0.189914	+	0.157112i
$881$	−4.00859			−0.135053			−0.0675264	−	0.997717i	$-0.521511\pi$
$881$	−4.00859			−0.135053			−0.0675264	+	0.997717i	$0.521511\pi$
$882$		0			0
$883$	−53.7634	+	22.2695i	−1.80928	+	0.749429i	−0.826953	+	0.562271i	$0.809928\pi$
$883$	−53.7634	+	22.2695i	−1.80928	+	0.749429i	−0.982330	+	0.187158i	$0.940072\pi$
$884$	55.7506	+	26.2341i	1.87510	+	0.882349i
$885$		0			0
$886$	−0.430276	+	18.2588i	−0.0144554	+	0.613417i
$887$	26.8595	−	26.8595i	0.901855	−	0.901855i	−0.0937413	−	0.995597i	$-0.529883\pi$
$887$	26.8595	−	26.8595i	0.901855	−	0.901855i	0.995597	+	0.0937413i	$0.0298826\pi$
$888$		0			0
$889$	−5.19763	−	5.19763i	−0.174323	−	0.174323i
$890$	−19.2864	+	18.3983i	−0.646482	+	0.616714i
$891$		0			0
$892$	32.7776	+	36.0220i	1.09747	+	1.20610i
$893$	−24.5448	−	59.2563i	−0.821359	−	1.98294i
$894$		0			0
$895$			11.6938i			0.390880i
$896$	−7.18843	+	1.66624i	−0.240148	+	0.0556651i
$897$		0			0
$898$	18.9932	+	49.0944i	0.633813	+	1.63830i
$899$	16.9306	−	7.01289i	0.564668	−	0.233893i
$900$		0			0
$901$	−2.73686	+	6.60736i	−0.0911780	+	0.220123i
$902$	−9.85682	−	10.3326i	−0.328196	−	0.344038i
$903$		0			0
$904$	−11.6205	+	23.2564i	−0.386492	+	0.773497i
$905$	1.48605	+	1.48605i	0.0493980	+	0.0493980i
$906$		0			0
$907$	2.30425	−	5.56296i	0.0765114	−	0.184715i	−0.880996	−	0.473124i	$-0.843126\pi$
$907$	2.30425	−	5.56296i	0.0765114	−	0.184715i	0.957507	+	0.288409i	$0.0931263\pi$
$908$	−13.7533	+	29.2274i	−0.456420	+	0.969945i
$909$		0			0
$910$	−6.00307	−	2.65392i	−0.199000	−	0.0879767i
$911$		−	23.5189i		−	0.779217i	−0.920981	−	0.389609i	$-0.872610\pi$
$911$		−	23.5189i		−	0.779217i	0.920981	−	0.389609i	$-0.127390\pi$
$912$		0			0
$913$			13.2853i			0.439679i
$914$	6.94744	−	15.7148i	0.229801	−	0.519801i
$915$		0			0
$916$	11.2213	+	31.1682i	0.370763	+	1.02983i
$917$	1.60204	−	3.86766i	0.0529040	−	0.127722i
$918$		0			0
$919$	−34.5792	−	34.5792i	−1.14066	−	1.14066i	−0.988329	−	0.152334i	$-0.951321\pi$
$919$	−34.5792	−	34.5792i	−1.14066	−	1.14066i	−0.152334	−	0.988329i	$-0.548679\pi$
$920$	−0.279329	+	3.94527i	−0.00920921	+	0.130072i
$921$		0			0
$922$	36.7414	−	35.0496i	1.21001	−	1.15430i
$923$	9.69522	−	23.4063i	0.319122	−	0.770429i
$924$		0			0
$925$	30.6035	−	12.6764i	1.00624	−	0.416797i
$926$	27.4159	−	10.6065i	0.900944	−	0.348550i
$927$		0			0
$928$	−13.0505	+	10.2883i	−0.428402	+	0.337728i
$929$			12.7627i			0.418730i	0.977838	+	0.209365i	$0.0671397\pi$
$929$			12.7627i			0.418730i	−0.977838	+	0.209365i	$0.932860\pi$
$930$		0			0
$931$	13.1823	+	31.8249i	0.432033	+	1.04302i
$932$	−23.0278	−	1.08592i	−0.754300	−	0.0355705i
$933$		0			0
$934$	7.27316	+	7.62422i	0.237985	+	0.249472i
$935$	6.26543	+	6.26543i	0.204901	+	0.204901i
$936$		0			0
$937$	7.21974	−	7.21974i	0.235859	−	0.235859i	−0.579274	−	0.815133i	$-0.696664\pi$
$937$	7.21974	−	7.21974i	0.235859	−	0.235859i	0.815133	+	0.579274i	$0.196664\pi$
$938$	−4.66081	−	0.109834i	−0.152181	−	0.00358620i
$939$		0			0
$940$	−9.28574	−	25.7920i	−0.302867	−	0.841242i
$941$	51.1130	−	21.1717i	1.66624	−	0.690178i	0.667709	−	0.744422i	$-0.267275\pi$
$941$	51.1130	−	21.1717i	1.66624	−	0.690178i	0.998528	+	0.0542444i	$0.0172750\pi$
$942$		0			0
$943$	−7.72453			−0.251545
$944$	−0.882380	−	0.467192i	−0.0287190	−	0.0152058i
$945$		0			0
$946$	4.47727	−	10.1274i	0.145569	−	0.329271i
$947$	−12.8340	−	30.9840i	−0.417048	−	1.00684i	−0.983198	−	0.182541i	$-0.941568\pi$
$947$	−12.8340	−	30.9840i	−0.417048	−	1.00684i	0.566150	−	0.824302i	$-0.308432\pi$
$948$		0			0
$949$	26.6485	+	11.0382i	0.865046	+	0.358314i
$950$	27.7516	+	0.653977i	0.900381	+	0.0212178i
$951$		0			0
$952$	2.83002	+	8.48256i	0.0917216	+	0.274921i
$953$	29.1685	−	29.1685i	0.944862	−	0.944862i	−0.0536956	−	0.998557i	$-0.517100\pi$
$953$	29.1685	−	29.1685i	0.944862	−	0.944862i	0.998557	+	0.0536956i	$0.0171001\pi$
$954$		0			0
$955$	20.4930	+	8.48848i	0.663138	+	0.274681i
$956$	−6.60727	−	7.26127i	−0.213694	−	0.234846i
$957$		0			0
$958$	1.19299	−	0.461533i	0.0385437	−	0.0149115i
$959$	9.13121			0.294862
$960$		0			0
$961$	−7.91347			−0.255273
$962$	−74.1173	+	28.6739i	−2.38964	+	0.924484i
$963$		0			0
$964$	20.8808	+	22.9476i	0.672525	+	0.739092i
$965$	−4.49558	−	1.86213i	−0.144718	−	0.0599440i
$966$		0			0
$967$	16.5294	−	16.5294i	0.531550	−	0.531550i	−0.389484	−	0.921033i	$-0.627346\pi$
$967$	16.5294	−	16.5294i	0.531550	−	0.531550i	0.921033	+	0.389484i	$0.127346\pi$
$968$	22.3622	−	7.46067i	0.718749	−	0.239795i
$969$		0			0
$970$	−6.09362	−	0.143599i	−0.195654	−	0.00461067i
$971$	5.25996	+	2.17875i	0.168800	+	0.0699193i	0.465483	−	0.885057i	$-0.345881\pi$
$971$	5.25996	+	2.17875i	0.168800	+	0.0699193i	−0.296683	+	0.954976i	$0.595881\pi$
$972$		0			0
$973$	2.92594	+	7.06385i	0.0938015	+	0.226457i
$974$	7.23874	−	16.3737i	0.231944	−	0.524649i
$975$		0			0
$976$	−2.37898	−	7.73288i	−0.0761492	−	0.247523i
$977$	52.4983			1.67957			0.839785	−	0.542919i	$-0.182681\pi$
$977$	52.4983			1.67957			0.839785	+	0.542919i	$0.182681\pi$
$978$		0			0
$979$	−25.3902	+	10.5170i	−0.811474	+	0.336123i
$980$	4.98711	+	13.8521i	0.159307	+	0.442491i
$981$		0			0
$982$	48.1647	+	1.13502i	1.53700	+	0.0362199i
$983$	1.00832	−	1.00832i	0.0321603	−	0.0321603i	−0.690844	−	0.723004i	$-0.742761\pi$
$983$	1.00832	−	1.00832i	0.0321603	−	0.0321603i	0.723004	+	0.690844i	$0.242761\pi$
$984$		0			0
$985$	18.8350	+	18.8350i	0.600134	+	0.600134i
$986$	13.9007	+	14.5716i	0.442688	+	0.464056i
$987$		0			0
$988$	−66.5238	−	3.13706i	−2.11640	−	0.0998032i
$989$	−2.29217	−	5.53378i	−0.0728866	−	0.175964i
$990$		0			0
$991$		−	35.1146i		−	1.11545i	−0.830026	−	0.557725i	$-0.811674\pi$
$991$		−	35.1146i		−	1.11545i	0.830026	−	0.557725i	$-0.188326\pi$
$992$	33.9629	−	9.57870i	1.07832	−	0.304124i
$993$		0			0
$994$	3.42919	−	1.32666i	0.108767	−	0.0420790i
$995$	21.6735	−	8.97744i	0.687095	−	0.284604i
$996$		0			0
$997$	9.28822	−	22.4237i	0.294161	−	0.710167i	−0.705838	−	0.708374i	$-0.749429\pi$
$997$	9.28822	−	22.4237i	0.294161	−	0.710167i	0.999998	−	0.00179328i	$-0.000570821\pi$
$998$	−15.0795	+	14.3851i	−0.477332	+	0.455353i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.w.b.107.4	✓	128
3.2	odd	2	inner	864.2.w.b.107.29	yes	128
32.3	odd	8	inner	864.2.w.b.323.29	yes	128
96.35	even	8	inner	864.2.w.b.323.4	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
864.2.w.b.107.4	✓	128	1.1	even	1	trivial
864.2.w.b.107.29	yes	128	3.2	odd	2	inner
864.2.w.b.323.4	yes	128	96.35	even	8	inner
864.2.w.b.323.29	yes	128	32.3	odd	8	inner

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:	\( N \)	\(=\)	\( 864 = 2^{5} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	864.w (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.31895 + 0.510265i) q^{2} +(1.47926 - 1.34603i) q^{4} +(1.03442 + 0.428472i) q^{5} +(-0.461188 + 0.461188i) q^{7} +(-1.26424 + 2.53016i) q^{8} +O(q^{10})\)	\(q+(-1.31895 + 0.510265i) q^{2} +(1.47926 - 1.34603i) q^{4} +(1.03442 + 0.428472i) q^{5} +(-0.461188 + 0.461188i) q^{7} +(-1.26424 + 2.53016i) q^{8} +(-1.58299 - 0.0373037i) q^{10} +(-1.50832 - 0.624765i) q^{11} +(-2.43213 - 5.87169i) q^{13} +(0.372956 - 0.843612i) q^{14} +(0.376419 - 3.98225i) q^{16} -4.84737 q^{17} +(4.84058 - 2.00503i) q^{19} +(2.10692 - 0.758541i) q^{20} +(2.30819 + 0.0543934i) q^{22} +(0.883120 - 0.883120i) q^{23} +(-2.64909 - 2.64909i) q^{25} +(6.20398 + 6.50343i) q^{26} +(-0.0614450 + 1.30299i) q^{28} +(1.12421 + 2.71408i) q^{29} -6.23807i q^{31} +(1.53552 + 5.44446i) q^{32} +(6.39344 - 2.47344i) q^{34} +(-0.674670 + 0.279457i) q^{35} +(-3.38363 + 8.16881i) q^{37} +(-5.36138 + 5.11451i) q^{38} +(-2.39186 + 2.07556i) q^{40} +(-4.37343 - 4.37343i) q^{41} +(1.83532 - 4.43085i) q^{43} +(-3.07214 + 1.10605i) q^{44} +(-0.714166 + 1.61542i) q^{46} -12.2416i q^{47} +6.57461i q^{49} +(4.84576 + 2.14228i) q^{50} +(-11.5012 - 5.41203i) q^{52} +(0.564607 - 1.36308i) q^{53} +(-1.29254 - 1.29254i) q^{55} +(-0.583827 - 1.74993i) q^{56} +(-2.86768 - 3.00609i) q^{58} +(0.0955207 - 0.230607i) q^{59} +(1.86867 - 0.774030i) q^{61} +(3.18307 + 8.22770i) q^{62} +(-4.80340 - 6.39745i) q^{64} -7.11591i q^{65} +(-1.93426 - 4.66971i) q^{67} +(-7.17052 + 6.52469i) q^{68} +(0.747259 - 0.712851i) q^{70} +(2.81874 + 2.81874i) q^{71} +(-3.20918 + 3.20918i) q^{73} +(0.294586 - 12.5008i) q^{74} +(4.46164 - 9.48151i) q^{76} +(0.983752 - 0.407483i) q^{77} +9.43849 q^{79} +(2.09566 - 3.95805i) q^{80} +(7.99994 + 3.53673i) q^{82} +(-3.11411 - 7.51813i) q^{83} +(-5.01423 - 2.07696i) q^{85} +(-0.159787 + 6.78057i) q^{86} +(3.48763 - 3.02643i) q^{88} +(11.9031 - 11.9031i) q^{89} +(3.82963 + 1.58628i) q^{91} +(0.117660 - 2.49507i) q^{92} +(6.24645 + 16.1460i) q^{94} +5.86630 q^{95} +3.84945 q^{97} +(-3.35479 - 8.67158i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q+O(q^{10}) \) 128 * q	\( 128 q + 8 q^{10} + 32 q^{16} - 32 q^{22} + 64 q^{40} + 64 q^{46} + 40 q^{52} + 64 q^{55} + 64 q^{58} + 32 q^{61} + 96 q^{64} - 64 q^{67} - 48 q^{70} - 32 q^{76} - 32 q^{79} + 40 q^{82} + 40 q^{88} - 48 q^{91} + 72 q^{94}+O(q^{100}) \) 128 * q + 8 * q^10 + 32 * q^16 - 32 * q^22 + 64 * q^40 + 64 * q^46 + 40 * q^52 + 64 * q^55 + 64 * q^58 + 32 * q^61 + 96 * q^64 - 64 * q^67 - 48 * q^70 - 32 * q^76 - 32 * q^79 + 40 * q^82 + 40 * q^88 - 48 * q^91 + 72 * q^94

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