LMFDB - Embedded newform 425.2.m.b.26.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [425,2,Mod(26,425)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(425, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("425.26");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 425 = 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	425.m (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:	$3.39364208590$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{8})$
Twist minimal:	no (minimal twist has level 85)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			26.5
Character	$\chi$	$=$	425.26
Dual form			425.2.m.b.376.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.27691 - 1.27691i) q^{2} +(-0.635552 - 0.263254i) q^{3} -1.26102i q^{4} +(-1.14770 + 0.475393i) q^{6} +(-1.66158 - 4.01142i) q^{7} +(0.943613 + 0.943613i) q^{8} +(-1.78670 - 1.78670i) q^{9} +(0.0485041 - 0.0200910i) q^{11} +(-0.331970 + 0.801445i) q^{12} -3.02508i q^{13} +(-7.24394 - 3.00054i) q^{14} +4.93187 q^{16} +(-3.12202 + 2.69314i) q^{17} -4.56292 q^{18} +(5.52988 - 5.52988i) q^{19} +2.98689i q^{21} +(0.0362810 - 0.0875901i) q^{22} +(-0.962654 + 0.398744i) q^{23} +(-0.351305 - 0.848125i) q^{24} +(-3.86277 - 3.86277i) q^{26} +(1.45495 + 3.51255i) q^{27} +(-5.05848 + 2.09529i) q^{28} +(-0.161016 + 0.388726i) q^{29} +(-1.27892 - 0.529745i) q^{31} +(4.41035 - 4.41035i) q^{32} -0.0361159 q^{33} +(-0.547638 + 7.42546i) q^{34} +(-2.25306 + 2.25306i) q^{36} +(-0.311301 - 0.128945i) q^{37} -14.1224i q^{38} +(-0.796365 + 1.92260i) q^{39} +(2.52291 + 6.09084i) q^{41} +(3.81400 + 3.81400i) q^{42} +(7.06729 + 7.06729i) q^{43} +(-0.0253352 - 0.0611647i) q^{44} +(-0.720064 + 1.73839i) q^{46} +6.13168i q^{47} +(-3.13446 - 1.29834i) q^{48} +(-8.38087 + 8.38087i) q^{49} +(2.69319 - 0.889748i) q^{51} -3.81469 q^{52} +(8.52974 - 8.52974i) q^{53} +(6.34307 + 2.62739i) q^{54} +(2.21733 - 5.35312i) q^{56} +(-4.97030 + 2.05876i) q^{57} +(0.290767 + 0.701974i) q^{58} +(3.60468 + 3.60468i) q^{59} +(-2.28486 - 5.51614i) q^{61} +(-2.30951 + 0.956630i) q^{62} +(-4.19844 + 10.1359i) q^{63} -1.39954i q^{64} +(-0.0461170 + 0.0461170i) q^{66} -0.916040 q^{67} +(3.39611 + 3.93693i) q^{68} +0.716788 q^{69} +(3.86169 + 1.59956i) q^{71} -3.37190i q^{72} +(-2.06289 + 4.98025i) q^{73} +(-0.562156 + 0.232853i) q^{74} +(-6.97330 - 6.97330i) q^{76} +(-0.161187 - 0.161187i) q^{77} +(1.43810 + 3.47188i) q^{78} +(9.22305 - 3.82031i) q^{79} +4.96488i q^{81} +(10.9990 + 4.55595i) q^{82} +(4.61746 - 4.61746i) q^{83} +3.76653 q^{84} +18.0487 q^{86} +(0.204668 - 0.204668i) q^{87} +(0.0647272 + 0.0268109i) q^{88} -10.2159i q^{89} +(-12.1349 + 5.02642i) q^{91} +(0.502825 + 1.21393i) q^{92} +(0.673362 + 0.673362i) q^{93} +(7.82963 + 7.82963i) q^{94} +(-3.96405 + 1.64196i) q^{96} +(7.35663 - 17.7605i) q^{97} +21.4033i q^{98} +(-0.122559 - 0.0507655i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 8 q^{6} - 24 q^{9} - 8 q^{11} - 24 q^{12} - 24 q^{16} + 8 q^{17} - 8 q^{18} - 8 q^{19} + 32 q^{22} + 16 q^{23} - 8 q^{24} + 16 q^{26} - 24 q^{27} - 48 q^{28} - 8 q^{29} + 16 q^{34} - 24 q^{36} - 24 q^{37}+ \cdots - 8 q^{99}+O(q^{100}) $ 24 * q - 8 * q^6 - 24 * q^9 - 8 * q^11 - 24 * q^12 - 24 * q^16 + 8 * q^17 - 8 * q^18 - 8 * q^19 + 32 * q^22 + 16 * q^23 - 8 * q^24 + 16 * q^26 - 24 * q^27 - 48 * q^28 - 8 * q^29 + 16 * q^34 - 24 * q^36 - 24 * q^37 + 8 * q^39 + 16 * q^41 + 24 * q^42 - 8 * q^43 + 16 * q^44 + 8 * q^46 - 80 * q^48 - 56 * q^51 + 48 * q^52 - 24 * q^53 - 32 * q^54 + 64 * q^56 - 32 * q^57 + 64 * q^58 + 32 * q^59 + 32 * q^61 + 32 * q^62 + 56 * q^63 + 96 * q^66 - 16 * q^67 + 40 * q^68 + 96 * q^69 - 24 * q^71 - 64 * q^74 - 8 * q^76 - 24 * q^77 + 112 * q^78 + 80 * q^82 + 96 * q^83 - 64 * q^84 - 16 * q^86 + 48 * q^87 + 8 * q^88 - 24 * q^91 - 80 * q^92 - 64 * q^93 + 56 * q^94 - 168 * q^96 + 40 * q^97 - 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/425\mathbb{Z}\right)^\times$.

$n$	$52$	$326$
$\chi(n)$	$1$	$e\left(\frac{1}{8}\right)$

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 $

$2$	1.27691	−	1.27691i	0.902915	−	0.902915i	−0.0927724	−	0.995687i	$-0.529573\pi$
$2$	1.27691	−	1.27691i	0.902915	−	0.902915i	0.995687	+	0.0927724i	$0.0295729\pi$
$3$	−0.635552	−	0.263254i	−0.366936	−	0.151990i	0.191594	−	0.981474i	$-0.438634\pi$
$3$	−0.635552	−	0.263254i	−0.366936	−	0.151990i	−0.558530	+	0.829484i	$0.688634\pi$
$4$		−	1.26102i		−	0.630511i
$5$		0			0
$5$		0			0
$6$	−1.14770	+	0.475393i	−0.468546	+	0.194078i
$7$	−1.66158	−	4.01142i	−0.628020	−	1.51617i	−0.842080	−	0.539353i	$-0.818669\pi$
$7$	−1.66158	−	4.01142i	−0.628020	−	1.51617i	0.214060	−	0.976821i	$-0.431331\pi$
$8$	0.943613	+	0.943613i	0.333617	+	0.333617i
$9$	−1.78670	−	1.78670i	−0.595565	−	0.595565i
$10$		0			0
$11$	0.0485041	−	0.0200910i	0.0146245	−	0.00605768i	−0.375359	−	0.926879i	$-0.622481\pi$
$11$	0.0485041	−	0.0200910i	0.0146245	−	0.00605768i	0.389984	+	0.920822i	$0.372481\pi$
$12$	−0.331970	+	0.801445i	−0.0958313	+	0.231357i
$13$		−	3.02508i		−	0.839006i	−0.907754	−	0.419503i	$-0.862204\pi$
$13$		−	3.02508i		−	0.839006i	0.907754	−	0.419503i	$-0.137796\pi$
$14$	−7.24394	−	3.00054i	−1.93602	−	0.801928i
$15$		0			0
$16$	4.93187			1.23297
$17$	−3.12202	+	2.69314i	−0.757200	+	0.653183i
$17$	−3.12202	+	2.69314i	−0.757200	+	0.653183i
$18$	−4.56292			−1.07549
$19$	5.52988	−	5.52988i	1.26864	−	1.26864i	0.321851	−	0.946790i	$-0.395695\pi$
$19$	5.52988	−	5.52988i	1.26864	−	1.26864i	0.946790	−	0.321851i	$-0.104305\pi$
$20$		0			0
$21$			2.98689i			0.651792i
$22$	0.0362810	−	0.0875901i	0.00773514	−	0.0186743i
$23$	−0.962654	+	0.398744i	−0.200727	+	0.0831439i	−0.480782	−	0.876840i	$-0.659647\pi$
$23$	−0.962654	+	0.398744i	−0.200727	+	0.0831439i	0.280055	+	0.959984i	$0.409647\pi$
$24$	−0.351305	−	0.848125i	−0.0717098	−	0.173123i
$25$		0			0
$26$	−3.86277	−	3.86277i	−0.757551	−	0.757551i
$27$	1.45495	+	3.51255i	0.280005	+	0.675991i
$28$	−5.05848	+	2.09529i	−0.955964	+	0.395973i
$29$	−0.161016	+	0.388726i	−0.0298999	+	0.0721847i	−0.938124	−	0.346299i	$-0.887438\pi$
$29$	−0.161016	+	0.388726i	−0.0298999	+	0.0721847i	0.908224	+	0.418484i	$0.137438\pi$
$30$		0			0
$31$	−1.27892	−	0.529745i	−0.229701	−	0.0951451i	0.264865	−	0.964286i	$-0.414673\pi$
$31$	−1.27892	−	0.529745i	−0.229701	−	0.0951451i	−0.494565	+	0.869141i	$0.664673\pi$
$32$	4.41035	−	4.41035i	0.779647	−	0.779647i
$33$	−0.0361159			−0.00628698
$34$	−0.547638	+	7.42546i	−0.0939192	+	1.27346i
$35$		0			0
$36$	−2.25306	+	2.25306i	−0.375510	+	0.375510i
$37$	−0.311301	−	0.128945i	−0.0511775	−	0.0211984i	0.356948	−	0.934124i	$-0.383817\pi$
$37$	−0.311301	−	0.128945i	−0.0511775	−	0.0211984i	−0.408125	+	0.912926i	$0.633817\pi$
$38$		−	14.1224i		−	2.29095i
$39$	−0.796365	+	1.92260i	−0.127520	+	0.307862i
$40$		0			0
$41$	2.52291	+	6.09084i	0.394012	+	0.951230i	0.989057	+	0.147537i	$0.0471345\pi$
$41$	2.52291	+	6.09084i	0.394012	+	0.951230i	−0.595044	+	0.803693i	$0.702865\pi$
$42$	3.81400	+	3.81400i	0.588513	+	0.588513i
$43$	7.06729	+	7.06729i	1.07775	+	1.07775i	0.996711	+	0.0810414i	$0.0258246\pi$
$43$	7.06729	+	7.06729i	1.07775	+	1.07775i	0.0810414	+	0.996711i	$0.474175\pi$
$44$	−0.0253352	−	0.0611647i	−0.00381943	−	0.00922092i
$45$		0			0
$46$	−0.720064	+	1.73839i	−0.106168	+	0.256311i
$47$			6.13168i			0.894398i	0.894435	+	0.447199i	$0.147578\pi$
$47$			6.13168i			0.894398i	−0.894435	+	0.447199i	$0.852422\pi$
$48$	−3.13446	−	1.29834i	−0.452420	−	0.187399i
$49$	−8.38087	+	8.38087i	−1.19727	+	1.19727i
$50$		0			0
$51$	2.69319	−	0.889748i	0.377122	−	0.124590i
$52$	−3.81469			−0.529002
$53$	8.52974	−	8.52974i	1.17165	−	1.17165i	0.189834	−	0.981816i	$-0.439205\pi$
$53$	8.52974	−	8.52974i	1.17165	−	1.17165i	0.981816	−	0.189834i	$-0.0607949\pi$
$54$	6.34307	+	2.62739i	0.863183	+	0.357542i
$55$		0			0
$56$	2.21733	−	5.35312i	0.296304	−	0.715340i
$57$	−4.97030	+	2.05876i	−0.658332	+	0.272690i
$58$	0.290767	+	0.701974i	0.0381796	+	0.0921737i
$59$	3.60468	+	3.60468i	0.469290	+	0.469290i	0.901684	−	0.432395i	$-0.142331\pi$
$59$	3.60468	+	3.60468i	0.469290	+	0.469290i	−0.432395	+	0.901684i	$0.642331\pi$
$60$		0			0
$61$	−2.28486	−	5.51614i	−0.292547	−	0.706270i	0.707453	−	0.706760i	$-0.249844\pi$
$61$	−2.28486	−	5.51614i	−0.292547	−	0.706270i	−1.00000		0.000490243i	$0.999844\pi$
$62$	−2.30951	+	0.956630i	−0.293308	+	0.121492i
$63$	−4.19844	+	10.1359i	−0.528954	+	1.27701i
$64$		−	1.39954i		−	0.174943i
$65$		0			0
$66$	−0.0461170	+	0.0461170i	−0.00567661	+	0.00567661i
$67$	−0.916040			−0.111912			−0.0559561	−	0.998433i	$-0.517821\pi$
$67$	−0.916040			−0.111912			−0.0559561	+	0.998433i	$0.517821\pi$
$68$	3.39611	+	3.93693i	0.411839	+	0.477423i
$69$	0.716788			0.0862912
$70$		0			0
$71$	3.86169	+	1.59956i	0.458298	+	0.189833i	0.599875	−	0.800094i	$-0.295217\pi$
$71$	3.86169	+	1.59956i	0.458298	+	0.189833i	−0.141577	+	0.989927i	$0.545217\pi$
$72$		−	3.37190i		−	0.397382i
$73$	−2.06289	+	4.98025i	−0.241443	+	0.582895i	−0.997427	−	0.0716959i	$-0.977159\pi$
$73$	−2.06289	+	4.98025i	−0.241443	+	0.582895i	0.755984	+	0.654590i	$0.227159\pi$
$74$	−0.562156	+	0.232853i	−0.0653493	+	0.0270686i
$75$		0			0
$76$	−6.97330	−	6.97330i	−0.799892	−	0.799892i
$77$	−0.161187	−	0.161187i	−0.0183690	−	0.0183690i
$78$	1.43810	+	3.47188i	0.162833	+	0.393113i
$79$	9.22305	−	3.82031i	1.03767	−	0.429819i	0.202198	−	0.979345i	$-0.435192\pi$
$79$	9.22305	−	3.82031i	1.03767	−	0.429819i	0.835477	+	0.549526i	$0.185192\pi$
$80$		0			0
$81$			4.96488i			0.551653i
$82$	10.9990	+	4.55595i	1.21464	+	0.503120i
$83$	4.61746	−	4.61746i	0.506833	−	0.506833i	−0.406720	−	0.913553i	$-0.633328\pi$
$83$	4.61746	−	4.61746i	0.506833	−	0.506833i	0.913553	+	0.406720i	$0.133328\pi$
$84$	3.76653			0.410962
$85$		0			0
$86$	18.0487			1.94624
$87$	0.204668	−	0.204668i	0.0219427	−	0.0219427i
$88$	0.0647272	+	0.0268109i	0.00689994	+	0.00285805i
$89$		−	10.2159i		−	1.08289i	−0.840738	−	0.541443i	$-0.817878\pi$
$89$		−	10.2159i		−	1.08289i	0.840738	−	0.541443i	$-0.182122\pi$
$90$		0			0
$91$	−12.1349	+	5.02642i	−1.27208	+	0.526912i
$92$	0.502825	+	1.21393i	0.0524231	+	0.126561i
$93$	0.673362	+	0.673362i	0.0698244	+	0.0698244i
$94$	7.82963	+	7.82963i	0.807565	+	0.807565i
$95$		0			0
$96$	−3.96405	+	1.64196i	−0.404579	+	0.167582i
$97$	7.35663	−	17.7605i	0.746952	−	1.80330i	0.172036	−	0.985091i	$-0.444965\pi$
$97$	7.35663	−	17.7605i	0.746952	−	1.80330i	0.574916	−	0.818212i	$-0.305035\pi$
$98$			21.4033i			2.16206i
$99$	−0.122559	−	0.0507655i	−0.0123176	−	0.00510212i
$100$		0			0
$101$	−13.2926			−1.32266			−0.661331	−	0.750094i	$-0.730008\pi$
$101$	−13.2926			−1.32266			−0.661331	+	0.750094i	$0.730008\pi$
$102$	2.30284	−	4.57510i	0.228015	−	0.453003i
$103$	6.91299			0.681157			0.340579	−	0.940216i	$-0.389377\pi$
$103$	6.91299			0.681157			0.340579	+	0.940216i	$0.389377\pi$
$104$	2.85450	−	2.85450i	0.279907	−	0.279907i
$105$		0			0
$106$		−	21.7835i		−	2.11580i
$107$	−5.64104	+	13.6187i	−0.545339	+	1.31657i	0.375572	+	0.926793i	$0.377446\pi$
$107$	−5.64104	+	13.6187i	−0.545339	+	1.31657i	−0.920911	+	0.389773i	$0.872554\pi$
$108$	4.42940	−	1.83472i	0.426220	−	0.176546i
$109$	−1.81709	−	4.38684i	−0.174046	−	0.420183i	0.812652	−	0.582749i	$-0.198023\pi$
$109$	−1.81709	−	4.38684i	−0.174046	−	0.420183i	−0.986698	+	0.162566i	$0.948023\pi$
$110$		0			0
$111$	0.163903	+	0.163903i	0.0155569	+	0.0155569i
$112$	−8.19471	−	19.7838i	−0.774328	−	1.86939i
$113$	−2.78393	+	1.15314i	−0.261890	+	0.108478i	−0.509765	−	0.860314i	$-0.670268\pi$
$113$	−2.78393	+	1.15314i	−0.261890	+	0.108478i	0.247875	+	0.968792i	$0.420268\pi$
$114$	−3.71778	+	8.97551i	−0.348202	+	0.840633i
$115$		0			0
$116$	0.490192	+	0.203044i	0.0455132	+	0.0188522i
$117$	−5.40490	+	5.40490i	−0.499683	+	0.499683i
$118$	9.20574			0.847457
$119$	15.9908	+	8.04884i	1.46588	+	0.737836i
$120$		0			0
$121$	−7.77623	+	7.77623i	−0.706930	+	0.706930i
$122$	−9.96122	−	4.12607i	−0.901846	−	0.373557i
$123$		−	4.53522i		−	0.408927i
$124$	−0.668020	+	1.61274i	−0.0599900	+	0.144829i
$125$		0			0
$126$	7.58167	+	18.3038i	0.675429	+	1.63063i
$127$	−0.00585984	−	0.00585984i	−0.000519977	−	0.000519977i	0.706847	−	0.707367i	$-0.250117\pi$
$127$	−0.00585984	−	0.00585984i	−0.000519977	−	0.000519977i	−0.707367	+	0.706847i	$0.750117\pi$
$128$	7.03360	+	7.03360i	0.621689	+	0.621689i
$129$	−2.63114	−	6.35213i	−0.231659	−	0.559274i
$130$		0			0
$131$	3.13210	−	7.56157i	0.273653	−	0.660657i	−0.725981	−	0.687715i	$-0.758614\pi$
$131$	3.13210	−	7.56157i	0.273653	−	0.660657i	0.999634	+	0.0270577i	$0.00861380\pi$
$132$			0.0455430i			0.00396401i
$133$	−31.3710	−	12.9943i	−2.72021	−	1.12675i
$134$	−1.16971	+	1.16971i	−0.101047	+	0.101047i
$135$		0			0
$136$	−5.48726	−	0.404693i	−0.470528	−	0.0347021i
$137$	2.23387			0.190852			0.0954260	−	0.995437i	$-0.469579\pi$
$137$	2.23387			0.190852			0.0954260	+	0.995437i	$0.469579\pi$
$138$	0.915277	−	0.915277i	0.0779136	−	0.0779136i
$139$	−18.2335	−	7.55257i	−1.54655	−	0.640601i	−0.563859	−	0.825871i	$-0.690684\pi$
$139$	−18.2335	−	7.55257i	−1.54655	−	0.640601i	−0.982688	+	0.185270i	$0.940684\pi$
$140$		0			0
$141$	1.61419	−	3.89701i	0.135940	−	0.328187i
$142$	6.97355	−	2.88854i	0.585207	−	0.242401i
$143$	−0.0607770	−	0.146729i	−0.00508243	−	0.0122701i
$144$	−8.81175	−	8.81175i	−0.734313	−	0.734313i
$145$		0			0
$146$	3.72523	+	8.99349i	0.308302	+	0.744306i
$147$	7.53279	−	3.12018i	0.621294	−	0.257348i
$148$	−0.162602	+	0.392557i	−0.0133658	+	0.0322680i
$149$			10.1835i			0.834263i	0.908846	+	0.417132i	$0.136965\pi$
$149$			10.1835i			0.834263i	−0.908846	+	0.417132i	$0.863035\pi$
$150$		0			0
$151$	10.8529	−	10.8529i	0.883200	−	0.883200i	−0.110659	−	0.993858i	$-0.535296\pi$
$151$	10.8529	−	10.8529i	0.883200	−	0.883200i	0.993858	+	0.110659i	$0.0352961\pi$
$152$	10.4361			0.846482
$153$	10.3899	+	0.766271i	0.839975	+	0.0619494i
$154$	−0.411645			−0.0331713
$155$		0			0
$156$	2.42443	+	1.00423i	0.194110	+	0.0804030i
$157$			9.41222i			0.751177i	0.926787	+	0.375588i	$0.122559\pi$
$157$			9.41222i			0.751177i	−0.926787	+	0.375588i	$0.877441\pi$
$158$	6.89884	−	16.6553i	0.548842	−	1.32502i
$159$	−7.66659	+	3.17561i	−0.608000	+	0.251842i
$160$		0			0
$161$	3.19906	+	3.19906i	0.252121	+	0.252121i
$162$	6.33972	+	6.33972i	0.498096	+	0.498096i
$163$	4.76262	+	11.4980i	0.373037	+	0.900592i	0.993232	+	0.116144i	$0.0370534\pi$
$163$	4.76262	+	11.4980i	0.373037	+	0.900592i	−0.620195	+	0.784448i	$0.712947\pi$
$164$	7.68068	−	3.18144i	0.599761	−	0.248429i
$165$		0			0
$166$		−	11.7922i		−	0.915253i
$167$	−11.6432	−	4.82277i	−0.900977	−	0.373197i	−0.116382	−	0.993205i	$-0.537130\pi$
$167$	−11.6432	−	4.82277i	−0.900977	−	0.373197i	−0.784596	+	0.620008i	$0.787130\pi$
$168$	−2.81846	+	2.81846i	−0.217449	+	0.217449i
$169$	3.84890			0.296069
$170$		0			0
$171$	−19.7604			−1.51112
$172$	8.91201	−	8.91201i	0.679534	−	0.679534i
$173$	−11.2681	−	4.66741i	−0.856699	−	0.354856i	−0.0892832	−	0.996006i	$-0.528458\pi$
$173$	−11.2681	−	4.66741i	−0.856699	−	0.354856i	−0.767416	+	0.641150i	$0.778458\pi$
$174$		−	0.522687i		−	0.0396248i
$175$		0			0
$176$	0.239216	−	0.0990864i	0.0180316	−	0.00746892i
$177$	−1.34202	−	3.23991i	−0.100872	−	0.243527i
$178$	−13.0449	−	13.0449i	−0.977754	−	0.977754i
$179$	9.80106	+	9.80106i	0.732566	+	0.732566i	0.971127	−	0.238562i	$-0.0766759\pi$
$179$	9.80106	+	9.80106i	0.732566	+	0.732566i	−0.238562	+	0.971127i	$0.576676\pi$
$180$		0			0
$181$	1.88863	−	0.782297i	0.140381	−	0.0581476i	−0.311387	−	0.950283i	$-0.600794\pi$
$181$	1.88863	−	0.782297i	0.140381	−	0.0581476i	0.451768	+	0.892136i	$0.350794\pi$
$182$	−9.07686	+	21.9135i	−0.672822	+	1.62434i
$183$			4.10730i			0.303620i
$184$	−1.28463	−	0.532112i	−0.0947043	−	0.0392278i
$185$		0			0
$186$	1.71965			0.126091
$187$	−0.0973225	+	0.193353i	−0.00711693	+	0.0141394i
$188$	7.73218			0.563927
$189$	11.6728	−	11.6728i	0.849071	−	0.849071i
$190$		0			0
$191$			3.08056i			0.222902i	0.993770	+	0.111451i	$0.0355498\pi$
$191$			3.08056i			0.222902i	−0.993770	+	0.111451i	$0.964450\pi$
$192$	−0.368435	+	0.889482i	−0.0265895	+	0.0641928i
$193$	−19.0706	+	7.89931i	−1.37273	+	0.568605i	−0.942528	−	0.334126i	$-0.891559\pi$
$193$	−19.0706	+	7.89931i	−1.37273	+	0.568605i	−0.430205	+	0.902731i	$0.641559\pi$
$194$	−13.2848	−	32.0724i	−0.953794	−	2.30266i
$195$		0			0
$196$	10.5685	+	10.5685i	0.754890	+	0.754890i
$197$	6.97881	+	16.8483i	0.497219	+	1.20039i	0.950975	+	0.309268i	$0.100084\pi$
$197$	6.97881	+	16.8483i	0.497219	+	1.20039i	−0.453756	+	0.891126i	$0.649916\pi$
$198$	−0.221320	+	0.0916738i	−0.0157285	+	0.00651497i
$199$	−10.2053	+	24.6377i	−0.723432	+	1.74652i	−0.0601040	+	0.998192i	$0.519143\pi$
$199$	−10.2053	+	24.6377i	−0.723432	+	1.74652i	−0.663328	+	0.748328i	$0.730857\pi$
$200$		0			0
$201$	0.582192	+	0.241152i	0.0410646	+	0.0170095i
$202$	−16.9735	+	16.9735i	−1.19425	+	1.19425i
$203$	1.82689			0.128222
$204$	−1.12199	−	3.39617i	−0.0785551	−	0.237779i
$205$		0			0
$206$	8.82730	−	8.82730i	0.615027	−	0.615027i
$207$	2.43240	+	1.00754i	0.169064	+	0.0700285i
$208$		−	14.9193i		−	1.03447i
$209$	0.157121	−	0.379323i	0.0108683	−	0.0262383i
$210$		0			0
$211$	2.98710	+	7.21149i	0.205640	+	0.496460i	0.992728	−	0.120382i	$-0.0384119\pi$
$211$	2.98710	+	7.21149i	0.205640	+	0.496460i	−0.787087	+	0.616842i	$0.788412\pi$
$212$	−10.7562	−	10.7562i	−0.738738	−	0.738738i
$213$	−2.03321	−	2.03321i	−0.139313	−	0.139313i
$214$	10.1868	+	24.5930i	0.696352	+	1.68114i
$215$		0			0
$216$	−1.94158	+	4.68739i	−0.132108	+	0.318937i
$217$			6.01049i			0.408019i
$218$	−7.92189	−	3.28135i	−0.536538	−	0.222241i
$219$	2.62215	−	2.62215i	0.177188	−	0.177188i
$220$		0			0
$221$	8.14696	+	9.44435i	0.548024	+	0.635295i
$222$	0.418579			0.0280932
$223$	−3.37213	+	3.37213i	−0.225815	+	0.225815i	−0.810942	−	0.585127i	$-0.801045\pi$
$223$	−3.37213	+	3.37213i	−0.225815	+	0.225815i	0.585127	+	0.810942i	$0.301045\pi$
$224$	−25.0199	−	10.3636i	−1.67171	−	0.692447i
$225$		0			0
$226$	−2.08238	+	5.02731i	−0.138518	+	0.334411i
$227$	10.3577	−	4.29029i	0.687464	−	0.284757i	−0.0114793	−	0.999934i	$-0.503654\pi$
$227$	10.3577	−	4.29029i	0.687464	−	0.284757i	0.698943	+	0.715177i	$0.253654\pi$
$228$	2.59614	+	6.26765i	0.171934	+	0.415085i
$229$	−14.6007	−	14.6007i	−0.964838	−	0.964838i	0.0345640	−	0.999402i	$-0.488996\pi$
$229$	−14.6007	−	14.6007i	−0.964838	−	0.964838i	−0.999402	+	0.0345640i	$0.988996\pi$
$230$		0			0
$231$	0.0600097	+	0.144876i	0.00394835	+	0.00953215i
$232$	−0.518744	+	0.214871i	−0.0340572	+	0.0141069i
$233$	1.17044	−	2.82569i	0.0766781	−	0.185117i	−0.880892	−	0.473317i	$-0.843057\pi$
$233$	1.17044	−	2.82569i	0.0766781	−	0.185117i	0.957570	+	0.288199i	$0.0930566\pi$
$234$			13.8032i			0.902342i
$235$		0			0
$236$	4.54558	−	4.54558i	0.295892	−	0.295892i
$237$	−6.86745			−0.446089
$238$	30.6966	−	10.1412i	1.98976	−	0.657358i
$239$	4.94072			0.319588			0.159794	−	0.987150i	$-0.448917\pi$
$239$	4.94072			0.319588			0.159794	+	0.987150i	$0.448917\pi$
$240$		0			0
$241$	1.53527	+	0.635928i	0.0988952	+	0.0409637i	0.431583	−	0.902073i	$-0.357955\pi$
$241$	1.53527	+	0.635928i	0.0988952	+	0.0409637i	−0.332687	+	0.943037i	$0.607955\pi$
$242$			19.8592i			1.27659i
$243$	5.67187	−	13.6931i	0.363850	−	0.878413i
$244$	−6.95597	+	2.88126i	−0.445311	+	0.184454i
$245$		0			0
$246$	−5.79109	−	5.79109i	−0.369226	−	0.369226i
$247$	−16.7283	−	16.7283i	−1.06440	−	1.06440i
$248$	−0.706929	−	1.70668i	−0.0448900	−	0.108374i
$249$	−4.15021	+	1.71907i	−0.263009	+	0.108942i
$250$		0			0
$251$			9.14240i			0.577063i	0.957470	+	0.288531i	$0.0931670\pi$
$251$			9.14240i			0.577063i	−0.957470	+	0.288531i	$0.906833\pi$
$252$	12.7816	+	5.29432i	0.805167	+	0.333511i
$253$	−0.0386814	+	0.0386814i	−0.00243188	+	0.00243188i
$254$	−0.0149650			−0.000938989
$255$		0			0
$256$	20.7617			1.29761
$257$	11.7749	−	11.7749i	0.734498	−	0.734498i	−0.237009	−	0.971507i	$-0.576167\pi$
$257$	11.7749	−	11.7749i	0.734498	−	0.734498i	0.971507	+	0.237009i	$0.0761671\pi$
$258$	−11.4709	−	4.75139i	−0.714145	−	0.295809i
$259$			1.46301i			0.0909070i
$260$		0			0
$261$	0.982222	−	0.406850i	0.0607980	−	0.0251834i
$262$	−5.65605	−	13.6549i	−0.349432	−	0.843603i
$263$	−15.3640	−	15.3640i	−0.947387	−	0.947387i	0.0512969	−	0.998683i	$-0.483665\pi$
$263$	−15.3640	−	15.3640i	−0.947387	−	0.947387i	−0.998683	+	0.0512969i	$0.983665\pi$
$264$	−0.0340795	−	0.0340795i	−0.00209745	−	0.00209745i
$265$		0			0
$266$	−56.6507	+	23.4655i	−3.47348	+	1.43876i
$267$	−2.68939	+	6.49276i	−0.164588	+	0.397350i
$268$			1.15515i			0.0705618i
$269$	−21.4082	−	8.86758i	−1.30528	−	0.540666i	−0.381779	−	0.924254i	$-0.624688\pi$
$269$	−21.4082	−	8.86758i	−1.30528	−	0.540666i	−0.923504	+	0.383588i	$0.874688\pi$
$270$		0			0
$271$	−3.95595			−0.240307			−0.120153	−	0.992755i	$-0.538339\pi$
$271$	−3.95595			−0.240307			−0.120153	+	0.992755i	$0.538339\pi$
$272$	−15.3974	+	13.2822i	−0.933603	+	0.805353i
$273$	9.03556			0.546857
$274$	2.85246	−	2.85246i	0.172323	−	0.172323i
$275$		0			0
$276$		−	0.903885i		−	0.0544075i
$277$	6.47115	−	15.6227i	0.388814	−	0.938679i	−0.601378	−	0.798964i	$-0.705382\pi$
$277$	6.47115	−	15.6227i	0.388814	−	0.938679i	0.990192	−	0.139714i	$-0.0446185\pi$
$278$	−32.9266	+	13.6387i	−1.97481	+	0.817992i
$279$	1.33854	+	3.23153i	0.0801366	+	0.193467i
$280$		0			0
$281$	3.30210	+	3.30210i	0.196987	+	0.196987i	0.798707	−	0.601720i	$-0.205518\pi$
$281$	3.30210	+	3.30210i	0.196987	+	0.196987i	−0.601720	+	0.798707i	$0.705518\pi$
$282$	−2.91496	−	7.03733i	−0.173583	−	0.419067i
$283$	8.03809	−	3.32949i	0.477815	−	0.197917i	−0.130760	−	0.991414i	$-0.541742\pi$
$283$	8.03809	−	3.32949i	0.477815	−	0.197917i	0.608575	+	0.793497i	$0.291742\pi$
$284$	2.01708	−	4.86967i	0.119692	−	0.288962i
$285$		0			0
$286$	−0.264967	−	0.109753i	−0.0156678	−	0.00648982i
$287$	20.2409	−	20.2409i	1.19478	−	1.19478i
$288$	−15.7599			−0.928661
$289$	2.49398	−	16.8161i	0.146705	−	0.989180i
$290$		0			0
$291$	−9.35105	+	9.35105i	−0.548168	+	0.548168i
$292$	6.28021	+	2.60135i	0.367521	+	0.152232i
$293$			0.739100i			0.0431787i	0.999767	+	0.0215893i	$0.00687263\pi$
$293$			0.739100i			0.0431787i	−0.999767	+	0.0215893i	$0.993127\pi$
$294$	5.63452	−	13.6029i	0.328612	−	0.793339i
$295$		0			0
$296$	−0.172073	−	0.415421i	−0.0100015	−	0.0241459i
$297$	0.141142	+	0.141142i	0.00818987	+	0.00818987i
$298$	13.0034	+	13.0034i	0.753269	+	0.753269i
$299$	1.20623	+	2.91210i	0.0697582	+	0.168411i
$300$		0			0
$301$	16.6070	−	40.0928i	0.957210	−	2.31091i
$302$		−	27.7165i		−	1.59491i
$303$	8.44813	+	3.49933i	0.485333	+	0.201031i
$304$	27.2726	−	27.2726i	1.56419	−	1.56419i
$305$		0			0
$306$	14.2455	−	12.2886i	0.814361	−	0.702491i
$307$	2.86108			0.163290			0.0816451	−	0.996661i	$-0.473983\pi$
$307$	2.86108			0.163290			0.0816451	+	0.996661i	$0.473983\pi$
$308$	−0.203261	+	0.203261i	−0.0115818	+	0.0115818i
$309$	−4.39357	−	1.81988i	−0.249941	−	0.103529i
$310$		0			0
$311$	7.84424	−	18.9377i	0.444806	−	1.07386i	−0.529435	−	0.848350i	$-0.677596\pi$
$311$	7.84424	−	18.9377i	0.444806	−	1.07386i	0.974242	−	0.225507i	$-0.0724038\pi$
$312$	−2.56565	+	1.06273i	−0.145251	+	0.0601650i
$313$	−3.23958	−	7.82103i	−0.183112	−	0.442071i	0.805493	−	0.592605i	$-0.201901\pi$
$313$	−3.23958	−	7.82103i	−0.183112	−	0.442071i	−0.988605	+	0.150534i	$0.951901\pi$
$314$	12.0186	+	12.0186i	0.678249	+	0.678249i
$315$		0			0
$316$	−4.81750	−	11.6305i	−0.271005	−	0.654265i
$317$	19.4863	−	8.07149i	1.09446	−	0.453340i	0.238900	−	0.971044i	$-0.423213\pi$
$317$	19.4863	−	8.07149i	1.09446	−	0.453340i	0.855560	+	0.517704i	$0.173213\pi$
$318$	−5.73460	+	13.8446i	−0.321581	+	0.776364i
$319$			0.0220898i			0.00123679i
$320$		0			0
$321$	7.17035	−	7.17035i	0.400210	−	0.400210i
$322$	8.16985			0.455288
$323$	−2.37163	+	32.1571i	−0.131961	+	1.78927i
$324$	6.26082			0.347823
$325$		0			0
$326$	20.7634	+	8.60048i	1.14998	+	0.476337i
$327$			3.26643i			0.180634i
$328$	−3.36675	+	8.12805i	−0.185897	+	0.448796i
$329$	24.5967	−	10.1883i	1.35606	−	0.561699i
$330$		0			0
$331$	10.7665	+	10.7665i	0.591780	+	0.591780i	0.938112	−	0.346332i	$-0.112573\pi$
$331$	10.7665	+	10.7665i	0.591780	+	0.591780i	−0.346332	+	0.938112i	$0.612573\pi$
$332$	−5.82272	−	5.82272i	−0.319563	−	0.319563i
$333$	0.325814	+	0.786585i	0.0178545	+	0.0431046i
$334$	−21.0256	+	8.70910i	−1.15047	+	0.476541i
$335$		0			0
$336$			14.7309i			0.803638i
$337$	−10.6003	−	4.39079i	−0.577435	−	0.239182i	0.0747994	−	0.997199i	$-0.476168\pi$
$337$	−10.6003	−	4.39079i	−0.577435	−	0.239182i	−0.652235	+	0.758017i	$0.726168\pi$
$338$	4.91472	−	4.91472i	0.267326	−	0.267326i
$339$	2.07290			0.112585
$340$		0			0
$341$	−0.0726759			−0.00393562
$342$	−25.2324	+	25.2324i	−1.36441	+	1.36441i
$343$	19.4648	+	8.06258i	1.05100	+	0.435338i
$344$			13.3376i			0.719114i
$345$		0			0
$346$	−20.3483	+	8.42854i	−1.09393	+	0.453121i
$347$	5.73424	+	13.8437i	0.307830	+	0.743168i	0.999775	+	0.0212172i	$0.00675416\pi$
$347$	5.73424	+	13.8437i	0.307830	+	0.743168i	−0.691945	+	0.721950i	$0.743246\pi$
$348$	−0.258091	−	0.258091i	−0.0138351	−	0.0138351i
$349$	−3.20791	−	3.20791i	−0.171715	−	0.171715i	0.616017	−	0.787733i	$-0.288745\pi$
$349$	−3.20791	−	3.20791i	−0.171715	−	0.171715i	−0.787733	+	0.616017i	$0.788745\pi$
$350$		0			0
$351$	10.6257	−	4.40133i	0.567160	−	0.234925i
$352$	0.125311	−	0.302528i	0.00667912	−	0.0161248i
$353$			7.71469i			0.410612i	0.978698	+	0.205306i	$0.0658189\pi$
$353$			7.71469i			0.410612i	−0.978698	+	0.205306i	$0.934181\pi$
$354$	−5.85073	−	2.42345i	−0.310963	−	0.128805i
$355$		0			0
$356$	−12.8825			−0.682771
$357$	−8.04411	−	9.32511i	−0.425739	−	0.493537i
$358$	25.0302			1.32289
$359$	−7.79826	+	7.79826i	−0.411577	+	0.411577i	−0.882287	−	0.470711i	$-0.843997\pi$
$359$	−7.79826	+	7.79826i	−0.411577	+	0.411577i	0.470711	+	0.882287i	$0.343997\pi$
$360$		0			0
$361$		−	42.1592i		−	2.21890i
$362$	1.41269	−	3.41055i	0.0742496	−	0.179254i
$363$	6.98933	−	2.89507i	0.366844	−	0.151952i
$364$	6.33843	+	15.3023i	0.332224	+	0.802059i
$365$		0			0
$366$	5.24467	+	5.24467i	0.274143	+	0.274143i
$367$	6.13386	+	14.8084i	0.320185	+	0.772995i	0.999243	+	0.0389098i	$0.0123885\pi$
$367$	6.13386	+	14.8084i	0.320185	+	0.772995i	−0.679058	+	0.734085i	$0.737611\pi$
$368$	−4.74768	+	1.96655i	−0.247490	+	0.102514i
$369$	6.37481	−	15.3902i	0.331860	−	0.801180i
$370$		0			0
$371$	−48.3892	−	20.0435i	−2.51224	−	1.04061i
$372$	0.849124	−	0.849124i	0.0440250	−	0.0440250i
$373$	10.2501			0.530732			0.265366	−	0.964148i	$-0.414507\pi$
$373$	10.2501			0.530732			0.265366	+	0.964148i	$0.414507\pi$
$374$	0.122623	+	0.371168i	0.00634066	+	0.0191926i
$375$		0			0
$376$	−5.78593	+	5.78593i	−0.298387	+	0.298387i
$377$	1.17593	+	0.487085i	0.0605634	+	0.0250862i
$378$		−	29.8103i		−	1.53328i
$379$	−5.33919	+	12.8899i	−0.274256	+	0.662112i	−0.999656	−	0.0262152i	$-0.991654\pi$
$379$	−5.33919	+	12.8899i	−0.274256	+	0.662112i	0.725401	+	0.688327i	$0.241654\pi$
$380$		0			0
$381$	0.00218161	+	0.00526686i	0.000111767	+	0.000269830i
$382$	3.93362	+	3.93362i	0.201261	+	0.201261i
$383$	3.97525	+	3.97525i	0.203126	+	0.203126i	0.801338	−	0.598212i	$-0.204122\pi$
$383$	3.97525	+	3.97525i	0.203126	+	0.203126i	−0.598212	+	0.801338i	$0.704122\pi$
$384$	−2.61860	−	6.32185i	−0.133630	−	0.322611i
$385$		0			0
$386$	−14.2648	+	34.4383i	−0.726060	+	1.75286i
$387$		−	25.2542i		−	1.28374i
$388$	−22.3963	−	9.27687i	−1.13700	−	0.470962i
$389$	−25.3255	+	25.3255i	−1.28406	+	1.28406i	−0.345717	+	0.938339i	$0.612364\pi$
$389$	−25.3255	+	25.3255i	−1.28406	+	1.28406i	−0.938339	+	0.345717i	$0.887636\pi$
$390$		0			0
$391$	1.93155	−	3.83745i	0.0976825	−	0.194068i
$392$	−15.8166			−0.798858
$393$	−3.98123	+	3.98123i	−0.200827	+	0.200827i
$394$	30.4252	+	12.6025i	1.53280	+	0.634907i
$395$		0			0
$396$	−0.0640163	+	0.154549i	−0.00321694	+	0.00776638i
$397$	−3.59405	+	1.48870i	−0.180380	+	0.0747159i	−0.471046	−	0.882109i	$-0.656123\pi$
$397$	−3.59405	+	1.48870i	−0.180380	+	0.0747159i	0.290665	+	0.956825i	$0.406123\pi$
$398$	18.4290	+	44.4915i	0.923761	+	2.23016i
$399$	16.5171	+	16.5171i	0.826891	+	0.826891i
$400$		0			0
$401$	14.0592	+	33.9420i	0.702085	+	1.69498i	0.718890	+	0.695124i	$0.244650\pi$
$401$	14.0592	+	33.9420i	0.702085	+	1.69498i	−0.0168056	+	0.999859i	$0.505350\pi$
$402$	1.05134	−	0.435479i	0.0524360	−	0.0217197i
$403$	−1.60252	+	3.86883i	−0.0798273	+	0.192720i
$404$			16.7622i			0.833952i
$405$		0			0
$406$	2.33278	−	2.33278i	0.115774	−	0.115774i
$407$	−0.0176900			−0.000876860
$408$	3.38090	+	1.70175i	0.167380	+	0.0842491i
$409$	−22.3529			−1.10528			−0.552641	−	0.833419i	$-0.686380\pi$
$409$	−22.3529			−1.10528			−0.552641	+	0.833419i	$0.686380\pi$
$410$		0			0
$411$	−1.41974	−	0.588075i	−0.0700306	−	0.0290076i
$412$		−	8.71743i		−	0.429477i
$413$	8.47041	−	20.4494i	0.416802	−	1.00625i
$414$	4.39251	−	1.81944i	0.215880	−	0.0894204i
$415$		0			0
$416$	−13.3416	−	13.3416i	−0.654128	−	0.654128i
$417$	9.60011	+	9.60011i	0.470119	+	0.470119i
$418$	−0.283733	−	0.684993i	−0.0138778	−	0.0335041i
$419$	20.2014	−	8.36768i	0.986901	−	0.408788i	0.169924	−	0.985457i	$-0.445648\pi$
$419$	20.2014	−	8.36768i	0.986901	−	0.408788i	0.816978	+	0.576669i	$0.195648\pi$
$420$		0			0
$421$			20.6111i			1.00453i	0.864715	+	0.502263i	$0.167499\pi$
$421$			20.6111i			1.00453i	−0.864715	+	0.502263i	$0.832501\pi$
$422$	13.0227	+	5.39419i	0.633937	+	0.262585i
$423$	10.9555	−	10.9555i	0.532672	−	0.532672i
$424$	16.0975			0.781766
$425$		0			0
$426$	−5.19248			−0.251576
$427$	−18.3311	+	18.3311i	−0.887103	+	0.887103i
$428$	17.1734	+	7.11347i	0.830109	+	0.343842i
$429$			0.109254i			0.00527481i
$430$		0			0
$431$	20.6074	−	8.53585i	0.992621	−	0.411157i	0.173535	−	0.984828i	$-0.444481\pi$
$431$	20.6074	−	8.53585i	0.992621	−	0.411157i	0.819086	+	0.573670i	$0.194481\pi$
$432$	7.17561	+	17.3234i	0.345236	+	0.833475i
$433$	6.31536	+	6.31536i	0.303497	+	0.303497i	0.842380	−	0.538883i	$-0.181154\pi$
$433$	6.31536	+	6.31536i	0.303497	+	0.303497i	−0.538883	+	0.842380i	$0.681154\pi$
$434$	7.67489	+	7.67489i	0.368406	+	0.368406i
$435$		0			0
$436$	−5.53190	+	2.29139i	−0.264930	+	0.109738i
$437$	−3.11835	+	7.52837i	−0.149171	+	0.360131i
$438$		−	6.69652i		−	0.319972i
$439$	20.5695	+	8.52016i	0.981728	+	0.406645i	0.815066	−	0.579369i	$-0.196701\pi$
$439$	20.5695	+	8.52016i	0.981728	+	0.406645i	0.166663	+	0.986014i	$0.446701\pi$
$440$		0			0
$441$	29.9481			1.42610
$442$	22.4626	+	1.65665i	1.06844	+	0.0787987i
$443$	6.17421			0.293346			0.146673	−	0.989185i	$-0.453144\pi$
$443$	6.17421			0.293346			0.146673	+	0.989185i	$0.453144\pi$
$444$	0.206685	−	0.206685i	0.00980882	−	0.00980882i
$445$		0			0
$446$			8.61184i			0.407783i
$447$	2.68085	−	6.47214i	0.126800	−	0.306122i
$448$	−5.61414	+	2.32545i	−0.265243	+	0.109867i
$449$	11.5947	+	27.9922i	0.547189	+	1.32103i	0.919561	+	0.392948i	$0.128545\pi$
$449$	11.5947	+	27.9922i	0.547189	+	1.32103i	−0.372371	+	0.928084i	$0.621455\pi$
$450$		0			0
$451$	0.244743	+	0.244743i	0.0115245	+	0.0115245i
$452$	1.45414	+	3.51060i	0.0683968	+	0.165125i
$453$	−9.75470	+	4.04053i	−0.458316	+	0.189841i
$454$	7.74754	−	18.7042i	0.363610	−	0.877833i
$455$		0			0
$456$	−6.63271	−	2.74736i	−0.310605	−	0.128657i
$457$	−18.0847	+	18.0847i	−0.845965	+	0.845965i	−0.989627	−	0.143662i	$-0.954112\pi$
$457$	−18.0847	+	18.0847i	−0.845965	+	0.845965i	0.143662	+	0.989627i	$0.454112\pi$
$458$	−37.2876			−1.74233
$459$	−14.0022	−	7.04787i	−0.653565	−	0.328966i
$460$		0			0
$461$	−9.93945	+	9.93945i	−0.462926	+	0.462926i	−0.899613	−	0.436687i	$-0.856152\pi$
$461$	−9.93945	+	9.93945i	−0.462926	+	0.462926i	0.436687	+	0.899613i	$0.356152\pi$
$462$	0.261622	+	0.108367i	0.0121717	+	0.00504170i
$463$		−	25.1233i		−	1.16758i	−0.811905	−	0.583789i	$-0.801569\pi$
$463$		−	25.1233i		−	1.16758i	0.811905	−	0.583789i	$-0.198431\pi$
$464$	−0.794108	+	1.91715i	−0.0368656	+	0.0890013i
$465$		0			0
$466$	−2.11362	−	5.10272i	−0.0979114	−	0.236379i
$467$	15.7614	+	15.7614i	0.729352	+	0.729352i	0.970491	−	0.241139i	$-0.0775209\pi$
$467$	15.7614	+	15.7614i	0.729352	+	0.729352i	−0.241139	+	0.970491i	$0.577521\pi$
$468$	6.81569	+	6.81569i	0.315055	+	0.315055i
$469$	1.52208	+	3.67462i	0.0702830	+	0.169678i
$470$		0			0
$471$	2.47781	−	5.98196i	0.114171	−	0.275634i
$472$			6.80285i			0.313126i
$473$	0.484782	+	0.200803i	0.0222903	+	0.00923294i
$474$	−8.76915	+	8.76915i	−0.402780	+	0.402780i
$475$		0			0
$476$	10.1498	−	20.1648i	0.465213	−	0.924250i
$477$	−30.4801			−1.39559
$478$	6.30887	−	6.30887i	0.288561	−	0.288561i
$479$	24.7134	+	10.2366i	1.12919	+	0.467724i	0.867504	−	0.497430i	$-0.165723\pi$
$479$	24.7134	+	10.2366i	1.12919	+	0.467724i	0.261681	+	0.965154i	$0.415723\pi$
$480$		0			0
$481$	−0.390068	+	0.941709i	−0.0177856	+	0.0429382i
$482$	2.77243	−	1.14838i	0.126281	−	0.0523072i
$483$	−1.19100	−	2.87534i	−0.0541926	−	0.130832i
$484$	9.80599	+	9.80599i	0.445727	+	0.445727i
$485$		0			0
$486$	−10.2424	−	24.7274i	−0.464606	−	1.12166i
$487$	21.3841	−	8.85760i	0.969008	−	0.401376i	0.158665	−	0.987332i	$-0.449281\pi$
$487$	21.3841	−	8.85760i	0.969008	−	0.401376i	0.810343	+	0.585956i	$0.199281\pi$
$488$	3.04908	−	7.36113i	0.138025	−	0.333223i
$489$		−	8.56135i		−	0.387158i
$490$		0			0
$491$	−5.50823	+	5.50823i	−0.248583	+	0.248583i	−0.820389	−	0.571806i	$-0.806243\pi$
$491$	−5.50823	+	5.50823i	−0.248583	+	0.248583i	0.571806	+	0.820389i	$0.306243\pi$
$492$	−5.71901			−0.257833
$493$	−0.544201	−	1.64725i	−0.0245096	−	0.0741883i
$494$	−42.7213			−1.92212
$495$		0			0
$496$	−6.30746	−	2.61263i	−0.283213	−	0.117311i
$497$		−	18.1487i		−	0.814079i
$498$	−3.10435	+	7.49457i	−0.139109	+	0.335840i
$499$	−8.12796	+	3.36671i	−0.363858	+	0.150715i	−0.557119	−	0.830432i	$-0.688093\pi$
$499$	−8.12796	+	3.36671i	−0.363858	+	0.150715i	0.193262	+	0.981147i	$0.438093\pi$
$500$		0			0
$501$	6.13025	+	6.13025i	0.273879	+	0.273879i
$502$	11.6741	+	11.6741i	0.521039	+	0.521039i
$503$	3.00003	+	7.24271i	0.133765	+	0.322937i	0.976542	−	0.215325i	$-0.0690812\pi$
$503$	3.00003	+	7.24271i	0.133765	+	0.322937i	−0.842778	+	0.538262i	$0.819081\pi$
$504$	−13.5261	+	5.60269i	−0.602500	+	0.249564i
$505$		0			0
$506$			0.0987858i			0.00439156i
$507$	−2.44618	−	1.01324i	−0.108639	−	0.0449996i
$508$	−0.00738938	+	0.00738938i	−0.000327851	+	0.000327851i
$509$	2.52868			0.112082			0.0560409	−	0.998428i	$-0.482152\pi$
$509$	2.52868			0.112082			0.0560409	+	0.998428i	$0.482152\pi$
$510$		0			0
$511$	23.4055			1.03540
$512$	12.4437	−	12.4437i	0.549940	−	0.549940i
$513$	27.4697	+	11.3783i	1.21282	+	0.502365i
$514$		−	30.0711i		−	1.32638i
$515$		0			0
$516$	−8.01017	+	3.31792i	−0.352628	+	0.146063i
$517$	0.123192	+	0.297412i	0.00541797	+	0.0130801i
$518$	1.86814	+	1.86814i	0.0820813	+	0.0820813i
$519$	5.93276	+	5.93276i	0.260419	+	0.260419i
$520$		0			0
$521$	9.33885	−	3.86828i	0.409142	−	0.169472i	−0.168613	−	0.985682i	$-0.553929\pi$
$521$	9.33885	−	3.86828i	0.409142	−	0.169472i	0.577755	+	0.816210i	$0.303929\pi$
$522$	0.734701	−	1.77373i	0.0321570	−	0.0776339i
$523$			5.80494i			0.253833i	0.991913	+	0.126916i	$0.0405079\pi$
$523$			5.80494i			0.253833i	−0.991913	+	0.126916i	$0.959492\pi$
$524$	−9.53530	−	3.94965i	−0.416552	−	0.172541i
$525$		0			0
$526$	−39.2371			−1.71082
$527$	5.41948	−	1.79043i	0.236076	−	0.0779925i
$528$	−0.178119			−0.00775164
$529$	−15.4958	+	15.4958i	−0.673728	+	0.673728i
$530$		0			0
$531$		−	12.8809i		−	0.558985i
$532$	−16.3861	+	39.5595i	−0.710427	+	1.71512i
$533$	18.4253	−	7.63200i	0.798087	−	0.330579i
$534$	4.85658	+	11.7248i	0.210165	+	0.507382i
$535$		0			0
$536$	−0.864387	−	0.864387i	−0.0373358	−	0.0373358i
$537$	−3.64892	−	8.80926i	−0.157462	−	0.380148i
$538$	−38.6596	+	16.0133i	−1.66674	+	0.690384i
$539$	−0.238126	+	0.574887i	−0.0102568	+	0.0247621i
$540$		0			0
$541$	39.1174	+	16.2030i	1.68179	+	0.696620i	0.999409	−	0.0343783i	$-0.0109451\pi$
$541$	39.1174	+	16.2030i	1.68179	+	0.696620i	0.682380	+	0.730998i	$0.260945\pi$
$542$	−5.05141	+	5.05141i	−0.216976	+	0.216976i
$543$	−1.40627			−0.0603487
$544$	−1.89149	+	25.6469i	−0.0810971	+	1.09960i
$545$		0			0
$546$	11.5376	−	11.5376i	0.493766	−	0.493766i
$547$	−18.4832	−	7.65599i	−0.790285	−	0.327347i	−0.0492266	−	0.998788i	$-0.515676\pi$
$547$	−18.4832	−	7.65599i	−0.790285	−	0.327347i	−0.741058	+	0.671441i	$0.765676\pi$
$548$		−	2.81695i		−	0.120334i
$549$	−5.77332	+	13.9380i	−0.246399	+	0.594860i
$550$		0			0
$551$	1.25921	+	3.04001i	0.0536443	+	0.129509i
$552$	0.676370	+	0.676370i	0.0287882	+	0.0287882i
$553$	−30.6498	−	30.6498i	−1.30336	−	1.30336i
$554$	−11.6858	−	28.2120i	−0.496482	−	1.19861i
$555$		0			0
$556$	−9.52395	+	22.9929i	−0.403906	+	0.975114i
$557$			25.8965i			1.09727i	0.836062	+	0.548636i	$0.184853\pi$
$557$			25.8965i			1.09727i	−0.836062	+	0.548636i	$0.815147\pi$
$558$	5.83560	+	2.41718i	0.247041	+	0.102328i
$559$	21.3791	−	21.3791i	0.904240	−	0.904240i
$560$		0			0
$561$	0.112755	−	0.0972653i	0.00476050	−	0.00410655i
$562$	8.43299			0.355724
$563$	−19.8208	+	19.8208i	−0.835349	+	0.835349i	−0.988243	−	0.152894i	$-0.951141\pi$
$563$	−19.8208	+	19.8208i	−0.835349	+	0.835349i	0.152894	+	0.988243i	$0.451141\pi$
$564$	−4.91421	−	2.03553i	−0.206925	−	0.0857113i
$565$		0			0
$566$	6.01248	−	14.5154i	0.252724	−	0.610129i
$567$	19.9162	−	8.24956i	0.836402	−	0.346449i
$568$	2.13457	+	5.15331i	0.0895645	+	0.216228i
$569$	−27.7130	−	27.7130i	−1.16179	−	1.16179i	−0.984084	−	0.177706i	$-0.943132\pi$
$569$	−27.7130	−	27.7130i	−1.16179	−	1.16179i	−0.177706	−	0.984084i	$-0.556868\pi$
$570$		0			0
$571$	1.48008	+	3.57322i	0.0619392	+	0.149535i	0.951819	−	0.306661i	$-0.0992118\pi$
$571$	1.48008	+	3.57322i	0.0619392	+	0.149535i	−0.889880	+	0.456196i	$0.849212\pi$
$572$	−0.185028	+	0.0766411i	−0.00773641	+	0.00320452i
$573$	0.810972	−	1.95786i	0.0338788	−	0.0817908i
$574$		−	51.6918i		−	2.15757i
$575$		0			0
$576$	−2.50055	+	2.50055i	−0.104190	+	0.104190i
$577$	−14.4808			−0.602845			−0.301423	−	0.953491i	$-0.597461\pi$
$577$	−14.4808			−0.602845			−0.301423	+	0.953491i	$0.597461\pi$
$578$	−18.2881	−	24.6573i	−0.760684	−	1.02561i
$579$	14.1999			0.590128
$580$		0			0
$581$	−26.1949	−	10.8503i	−1.08675	−	0.450145i
$582$			23.8810i			0.989898i
$583$	0.242356	−	0.585099i	0.0100374	−	0.0242323i
$584$	−6.64600	+	2.75286i	−0.275013	+	0.113914i
$585$		0			0
$586$	0.943767	+	0.943767i	0.0389867	+	0.0389867i
$587$	−22.0937	−	22.0937i	−0.911905	−	0.911905i	0.0845171	−	0.996422i	$-0.473065\pi$
$587$	−22.0937	−	22.0937i	−0.911905	−	0.911905i	−0.996422	+	0.0845171i	$0.973065\pi$
$588$	−3.93462	−	9.49900i	−0.162261	−	0.391732i
$589$	−10.0017	+	4.14284i	−0.412113	+	0.170703i
$590$		0			0
$591$		−	12.5452i		−	0.516041i
$592$	−1.53529	−	0.635939i	−0.0631002	−	0.0261369i
$593$	−1.41805	+	1.41805i	−0.0582323	+	0.0582323i	−0.735623	−	0.677391i	$-0.763111\pi$
$593$	−1.41805	+	1.41805i	−0.0582323	+	0.0582323i	0.677391	+	0.735623i	$0.263111\pi$
$594$	0.360452			0.0147895
$595$		0			0
$596$	12.8416			0.526012
$597$	12.9720	−	12.9720i	0.530907	−	0.530907i
$598$	5.25876	+	2.17825i	0.215047	+	0.0890753i
$599$		−	36.0451i		−	1.47276i	−0.676567	−	0.736381i	$-0.736533\pi$
$599$		−	36.0451i		−	1.47276i	0.676567	−	0.736381i	$-0.263467\pi$
$600$		0			0
$601$	−35.8417	+	14.8461i	−1.46201	+	0.605586i	−0.965022	−	0.262168i	$-0.915562\pi$
$601$	−35.8417	+	14.8461i	−1.46201	+	0.605586i	−0.496993	+	0.867755i	$0.665562\pi$
$602$	−29.9894	−	72.4007i	−1.22228	−	2.95083i
$603$	1.63669	+	1.63669i	0.0666510	+	0.0666510i
$604$	−13.6858	−	13.6858i	−0.556867	−	0.556867i
$605$		0			0
$606$	15.2559	−	6.31920i	0.619728	−	0.256700i
$607$	11.0800	−	26.7496i	0.449725	−	1.08573i	−0.522701	−	0.852516i	$-0.675075\pi$
$607$	11.0800	−	26.7496i	0.449725	−	1.08573i	0.972425	−	0.233215i	$-0.0749246\pi$
$608$		−	48.7774i		−	1.97818i
$609$	−1.16108	−	0.480936i	−0.0470494	−	0.0194885i
$610$		0			0
$611$	18.5488			0.750405
$612$	0.966284	−	13.1019i	0.0390597	−	0.529613i
$613$	−9.10707			−0.367831			−0.183915	−	0.982942i	$-0.558877\pi$
$613$	−9.10707			−0.367831			−0.183915	+	0.982942i	$0.558877\pi$
$614$	3.65335	−	3.65335i	0.147437	−	0.147437i
$615$		0			0
$616$		−	0.304197i		−	0.0122564i
$617$	1.93466	−	4.67068i	0.0778864	−	0.188035i	−0.880140	−	0.474714i	$-0.842551\pi$
$617$	1.93466	−	4.67068i	0.0778864	−	0.188035i	0.958027	+	0.286680i	$0.0925515\pi$
$618$	−7.93404	+	3.28639i	−0.319154	+	0.132198i
$619$	6.45177	+	15.5760i	0.259319	+	0.626051i	0.998894	−	0.0470233i	$-0.0149735\pi$
$619$	6.45177	+	15.5760i	0.259319	+	0.626051i	−0.739575	+	0.673074i	$0.764974\pi$
$620$		0			0
$621$	−2.80122	−	2.80122i	−0.112409	−	0.112409i
$622$	−14.1654	−	34.1982i	−0.567979	−	1.37122i
$623$	−40.9803	+	16.9746i	−1.64184	+	0.680074i
$624$	−3.92757	+	9.48199i	−0.157229	+	0.379583i
$625$		0			0
$626$	−14.1235	−	5.85013i	−0.564487	−	0.233818i
$627$	−0.199717	+	0.199717i	−0.00797592	+	0.00797592i
$628$	11.8690			0.473625
$629$	1.31915	−	0.435808i	0.0525981	−	0.0173768i
$630$		0			0
$631$	1.91845	−	1.91845i	0.0763722	−	0.0763722i	−0.667889	−	0.744261i	$-0.732802\pi$
$631$	1.91845	−	1.91845i	0.0763722	−	0.0763722i	0.744261	+	0.667889i	$0.232802\pi$
$632$	12.3079	+	5.09809i	0.489581	+	0.202791i
$633$		−	5.36965i		−	0.213424i
$634$	14.5757	−	35.1889i	0.578876	−	1.39753i
$635$		0			0
$636$	4.00451	+	9.66773i	0.158789	+	0.383351i
$637$	25.3528	+	25.3528i	1.00451	+	1.00451i
$638$	0.0282068	+	0.0282068i	0.00111672	+	0.00111672i
$639$	−4.04173	−	9.75760i	−0.159888	−	0.386005i
$640$		0			0
$641$	−8.72988	+	21.0758i	−0.344809	+	0.832443i	0.652406	+	0.757870i	$0.273760\pi$
$641$	−8.72988	+	21.0758i	−0.344809	+	0.832443i	−0.997215	+	0.0745739i	$0.976240\pi$
$642$		−	18.3118i		−	0.722711i
$643$	17.8097	+	7.37702i	0.702346	+	0.290921i	0.705133	−	0.709075i	$-0.250887\pi$
$643$	17.8097	+	7.37702i	0.702346	+	0.290921i	−0.00278691	+	0.999996i	$0.500887\pi$
$644$	4.03408	−	4.03408i	0.158965	−	0.158965i
$645$		0			0
$646$	38.0335	+	44.0903i	1.49641	+	1.73471i
$647$	−12.8098			−0.503606			−0.251803	−	0.967778i	$-0.581024\pi$
$647$	−12.8098			−0.503606			−0.251803	+	0.967778i	$0.581024\pi$
$648$	−4.68492	+	4.68492i	−0.184041	+	0.184041i
$649$	0.247264	+	0.102420i	0.00970595	+	0.00402033i
$650$		0			0
$651$	1.58229	−	3.81998i	0.0620148	−	0.149717i
$652$	14.4992	−	6.00577i	0.567833	−	0.235204i
$653$	15.9656	+	38.5442i	0.624780	+	1.50835i	0.846030	+	0.533136i	$0.178987\pi$
$653$	15.9656	+	38.5442i	0.624780	+	1.50835i	−0.221249	+	0.975217i	$0.571013\pi$
$654$	4.17095	+	4.17095i	0.163097	+	0.163097i
$655$		0			0
$656$	12.4427	+	30.0392i	0.485804	+	1.17284i
$657$	12.5840	−	5.21244i	0.490947	−	0.203357i
$658$	18.3983	−	44.4175i	0.717242	−	1.73158i
$659$		−	34.3290i		−	1.33727i	−0.743592	−	0.668633i	$-0.766880\pi$
$659$		−	34.3290i		−	1.33727i	0.743592	−	0.668633i	$-0.233120\pi$
$660$		0			0
$661$	−19.5875	+	19.5875i	−0.761865	+	0.761865i	−0.976659	−	0.214794i	$-0.931092\pi$
$661$	−19.5875	+	19.5875i	−0.761865	+	0.761865i	0.214794	+	0.976659i	$0.431092\pi$
$662$	27.4958			1.06865
$663$	−2.69156	−	8.14710i	−0.104531	−	0.316407i
$664$	8.71419			0.338176
$665$		0			0
$666$	1.42044	+	0.588365i	0.0550409	+	0.0227987i
$667$		−	0.438413i		−	0.0169754i
$668$	−6.08161	+	14.6823i	−0.235305	+	0.568076i
$669$	3.03089	−	1.25544i	0.117181	−	0.0485380i
$670$		0			0
$671$	−0.221650	−	0.221650i	−0.00855671	−	0.00855671i
$672$	13.1732	+	13.1732i	0.508168	+	0.508168i
$673$	−13.8561	−	33.4517i	−0.534115	−	1.28947i	−0.928777	−	0.370640i	$-0.879138\pi$
$673$	−13.8561	−	33.4517i	−0.534115	−	1.28947i	0.394662	−	0.918826i	$-0.370862\pi$
$674$	−19.1423	+	7.92902i	−0.737336	+	0.305414i
$675$		0			0
$676$		−	4.85355i		−	0.186675i
$677$	−15.8129	−	6.54992i	−0.607739	−	0.251734i	0.0575224	−	0.998344i	$-0.481680\pi$
$677$	−15.8129	−	6.54992i	−0.607739	−	0.251734i	−0.665262	+	0.746610i	$0.731680\pi$
$678$	2.64692	−	2.64692i	0.101654	−	0.101654i
$679$	−83.4684			−3.20322
$680$		0			0
$681$	−7.71229			−0.295536
$682$	−0.0928009	+	0.0928009i	−0.00355353	+	0.00355353i
$683$	−8.17654	−	3.38683i	−0.312866	−	0.129594i	0.220725	−	0.975336i	$-0.429158\pi$
$683$	−8.17654	−	3.38683i	−0.312866	−	0.129594i	−0.533591	+	0.845743i	$0.679158\pi$
$684$			24.9183i			0.952776i
$685$		0			0
$686$	35.1501	−	14.5596i	1.34204	−	0.555890i
$687$	5.43580	+	13.1232i	0.207389	+	0.500680i
$688$	34.8550	+	34.8550i	1.32883	+	1.32883i
$689$	−25.8031	−	25.8031i	−0.983021	−	0.983021i
$690$		0			0
$691$	1.29190	−	0.535121i	0.0491461	−	0.0203570i	−0.357975	−	0.933731i	$-0.616533\pi$
$691$	1.29190	−	0.535121i	0.0491461	−	0.0203570i	0.407121	+	0.913374i	$0.366533\pi$
$692$	−5.88570	+	14.2093i	−0.223741	+	0.540158i
$693$			0.575985i			0.0218799i
$694$	24.9993	+	10.3551i	0.948962	+	0.393073i
$695$		0			0
$696$	0.386254			0.0146409
$697$	−24.2801	−	12.2212i	−0.919673	−	0.462910i
$698$	−8.19245			−0.310089
$699$	−1.48775	+	1.48775i	−0.0562720	+	0.0562720i
$700$		0			0
$701$		−	2.36331i		−	0.0892608i	−0.999004	−	0.0446304i	$-0.985789\pi$
$701$		−	2.36331i		−	0.0892608i	0.999004	−	0.0446304i	$-0.0142110\pi$
$702$	7.94805	−	19.1883i	0.299980	−	0.724215i
$703$	−2.43451	+	1.00841i	−0.0918191	+	0.0380327i
$704$	−0.0281182	−	0.0678834i	−0.00105975	−	0.00255845i
$705$		0			0
$706$	9.85100	+	9.85100i	0.370747	+	0.370747i
$707$	22.0867	+	53.3221i	0.830657	+	2.00538i
$708$	−4.08560	+	1.69231i	−0.153546	+	0.0636009i
$709$	12.4474	−	30.0507i	0.467472	−	1.12858i	−0.497791	−	0.867297i	$-0.665855\pi$
$709$	12.4474	−	30.0507i	0.467472	−	1.12858i	0.965263	−	0.261280i	$-0.0841447\pi$
$710$		0			0
$711$	−23.3045	−	9.65306i	−0.873988	−	0.362018i
$712$	9.63987	−	9.63987i	0.361270	−	0.361270i
$713$	1.44239			0.0540179
$714$	−22.1790	−	1.63573i	−0.830028	−	0.0612158i
$715$		0			0
$716$	12.3594	−	12.3594i	0.461891	−	0.461891i
$717$	−3.14009	−	1.30067i	−0.117269	−	0.0485743i
$718$			19.9154i			0.743237i
$719$	−6.28758	+	15.1796i	−0.234487	+	0.566102i	−0.996695	−	0.0812299i	$-0.974115\pi$
$719$	−6.28758	+	15.1796i	−0.234487	+	0.566102i	0.762208	+	0.647332i	$0.224115\pi$
$720$		0			0
$721$	−11.4865	−	27.7309i	−0.427780	−	1.03275i
$722$	−53.8336	−	53.8336i	−2.00348	−	2.00348i
$723$	−0.808332	−	0.808332i	−0.0300622	−	0.0300622i
$724$	−0.986493	−	2.38160i	−0.0366627	−	0.0885116i
$725$		0			0
$726$	5.22801	−	12.6215i	0.194030	−	0.468429i
$727$			32.4709i			1.20428i	0.798391	+	0.602139i	$0.205685\pi$
$727$			32.4709i			1.20428i	−0.798391	+	0.602139i	$0.794315\pi$
$728$	−16.1936	−	6.70761i	−0.600175	−	0.248600i
$729$	3.32256	−	3.32256i	0.123058	−	0.123058i
$730$		0			0
$731$	−41.0974	−	3.03099i	−1.52004	−	0.112105i
$732$	5.17939			0.191436
$733$	6.10533	−	6.10533i	0.225506	−	0.225506i	−0.585307	−	0.810812i	$-0.699026\pi$
$733$	6.10533	−	6.10533i	0.225506	−	0.225506i	0.810812	+	0.585307i	$0.199026\pi$
$734$	26.7415	+	11.0767i	0.987048	+	0.408849i
$735$		0			0
$736$	−2.48704	+	6.00424i	−0.0916734	+	0.221319i
$737$	−0.0444317	+	0.0184042i	−0.00163666	+	0.000677928i
$738$	−11.5118	−	27.7920i	−0.423756	−	1.02304i
$739$	−7.49715	−	7.49715i	−0.275787	−	0.275787i	0.555637	−	0.831425i	$-0.312474\pi$
$739$	−7.49715	−	7.49715i	−0.275787	−	0.275787i	−0.831425	+	0.555637i	$0.812474\pi$
$740$		0			0
$741$	6.22792	+	15.0355i	0.228788	+	0.552344i
$742$	−87.3827	+	36.1951i	−3.20792	+	1.32876i
$743$	8.55008	−	20.6417i	0.313672	−	0.757272i	−0.685891	−	0.727705i	$-0.740587\pi$
$743$	8.55008	−	20.6417i	0.313672	−	0.757272i	0.999563	−	0.0295670i	$-0.00941283\pi$
$744$			1.27079i			0.0465893i
$745$		0			0
$746$	13.0886	−	13.0886i	0.479206	−	0.479206i
$747$	−16.5000			−0.603704
$748$	0.243822	+	0.122726i	0.00891502	+	0.00448730i
$749$	64.0032			2.33863
$750$		0			0
$751$	6.59640	+	2.73232i	0.240706	+	0.0997037i	0.499775	−	0.866155i	$-0.333416\pi$
$751$	6.59640	+	2.73232i	0.240706	+	0.0997037i	−0.259069	+	0.965859i	$0.583416\pi$
$752$			30.2406i			1.10276i
$753$	2.40678	−	5.81047i	0.0877078	−	0.211745i
$754$	2.12353	−	0.879593i	0.0773342	−	0.0320329i
$755$		0			0
$756$	−14.7197	−	14.7197i	−0.535349	−	0.535349i
$757$	−12.7467	−	12.7467i	−0.463287	−	0.463287i	0.436444	−	0.899731i	$-0.356238\pi$
$757$	−12.7467	−	12.7467i	−0.463287	−	0.463287i	−0.899731	+	0.436444i	$0.856238\pi$
$758$	9.64166	+	23.2770i	0.350201	+	0.845460i
$759$	0.0347671	−	0.0144010i	0.00126197	−	0.000522724i
$760$		0			0
$761$		−	49.9437i		−	1.81046i	−0.424923	−	0.905230i	$-0.639699\pi$
$761$		−	49.9437i		−	1.81046i	0.424923	−	0.905230i	$-0.360301\pi$
$762$	0.00951106	+	0.00393961i	0.000344549	+	0.000142717i
$763$	−14.5782	+	14.5782i	−0.527767	+	0.527767i
$764$	3.88466			0.140542
$765$		0			0
$766$	10.1521			0.366811
$767$	10.9044	−	10.9044i	0.393737	−	0.393737i
$768$	−13.1952	−	5.46561i	−0.476139	−	0.197223i
$769$			43.9115i			1.58349i	0.610852	+	0.791745i	$0.290827\pi$
$769$			43.9115i			1.58349i	−0.610852	+	0.791745i	$0.709173\pi$
$770$		0			0
$771$	−10.5834	+	4.38377i	−0.381151	+	0.157878i
$772$	9.96120	+	24.0485i	0.358511	+	0.865523i
$773$	−6.84309	−	6.84309i	−0.246129	−	0.246129i	0.573251	−	0.819380i	$-0.305682\pi$
$773$	−6.84309	−	6.84309i	−0.246129	−	0.246129i	−0.819380	+	0.573251i	$0.805682\pi$
$774$	−32.2475	−	32.2475i	−1.15911	−	1.15911i
$775$		0			0
$776$	23.7008	−	9.81720i	0.850810	−	0.352417i
$777$	0.385144	−	0.929820i	0.0138170	−	0.0333571i
$778$			64.6771i			2.31879i
$779$	47.6330	+	19.7302i	1.70663	+	0.706909i
$780$		0			0
$781$	0.219445			0.00785234
$782$	−2.43367	−	7.36651i	−0.0870280	−	0.263426i
$783$	−1.59969			−0.0571683
$784$	−41.3334	+	41.3334i	−1.47619	+	1.47619i
$785$		0			0
$786$			10.1674i			0.362659i
$787$	−7.59181	+	18.3283i	−0.270619	+	0.653332i	−0.999510	−	0.0312976i	$-0.990036\pi$
$787$	−7.59181	+	18.3283i	−0.270619	+	0.653332i	0.728891	+	0.684630i	$0.240036\pi$
$788$	21.2461	−	8.80043i	0.756861	−	0.313502i
$789$	5.72000	+	13.8093i	0.203637	+	0.491624i
$790$		0			0
$791$	9.25147	+	9.25147i	0.328944	+	0.328944i
$792$	−0.0677450	−	0.163551i	−0.00240721	−	0.00581152i
$793$	−16.6868	+	6.91188i	−0.592564	+	0.245448i
$794$	−2.68835	+	6.49024i	−0.0954059	+	0.230330i
$795$		0			0
$796$	31.0687	+	12.8691i	1.10120	+	0.456132i
$797$	3.93230	−	3.93230i	0.139289	−	0.139289i	−0.634024	−	0.773313i	$-0.718598\pi$
$797$	3.93230	−	3.93230i	0.139289	−	0.139289i	0.773313	+	0.634024i	$0.218598\pi$
$798$	42.1819			1.49322
$799$	−16.5135	−	19.1432i	−0.584205	−	0.677238i
$800$		0			0
$801$	−18.2528	+	18.2528i	−0.644929	+	0.644929i
$802$	61.2935	+	25.3886i	2.16435	+	0.896502i
$803$			0.283008i			0.00998714i
$804$	0.304097	−	0.734156i	0.0107247	−	0.0258917i
$805$		0			0
$806$	2.89388	+	6.98644i	0.101933	+	0.246087i
$807$	11.2716	+	11.2716i	0.396780	+	0.396780i
$808$	−12.5430	−	12.5430i	−0.441263	−	0.441263i
$809$	11.8801	+	28.6811i	0.417683	+	1.00838i	0.983017	+	0.183513i	$0.0587471\pi$
$809$	11.8801	+	28.6811i	0.417683	+	1.00838i	−0.565335	+	0.824862i	$0.691253\pi$
$810$		0			0
$811$	−17.9749	+	43.3953i	−0.631185	+	1.52382i	0.206949	+	0.978352i	$0.433647\pi$
$811$	−17.9749	+	43.3953i	−0.631185	+	1.52382i	−0.838134	+	0.545464i	$0.816353\pi$
$812$		−	2.30374i		−	0.0808455i
$813$	2.51421	+	1.04142i	0.0881773	+	0.0365242i
$814$	−0.0225886	+	0.0225886i	−0.000791730	+	0.000791730i
$815$		0			0
$816$	13.2824	−	4.38812i	0.464979	−	0.153615i
$817$	78.1626			2.73456
$818$	−28.5428	+	28.5428i	−0.997976	+	0.997976i
$819$	30.6620	+	12.7006i	1.07142	+	0.443795i
$820$		0			0
$821$	6.40739	−	15.4688i	0.223619	−	0.539865i	−0.771757	−	0.635918i	$-0.780622\pi$
$821$	6.40739	−	15.4688i	0.223619	−	0.539865i	0.995376	+	0.0960527i	$0.0306217\pi$
$822$	−2.56381	+	1.06196i	−0.0894231	+	0.0370402i
$823$	10.1792	+	24.5749i	0.354826	+	0.856626i	0.996010	+	0.0892387i	$0.0284434\pi$
$823$	10.1792	+	24.5749i	0.354826	+	0.856626i	−0.641184	+	0.767387i	$0.721557\pi$
$824$	6.52318	+	6.52318i	0.227246	+	0.227246i
$825$		0			0
$826$	−15.2961	−	36.9281i	−0.532220	−	1.28489i
$827$	−31.8605	+	13.1970i	−1.10790	+	0.458906i	−0.860213	−	0.509934i	$-0.829670\pi$
$827$	−31.8605	+	13.1970i	−1.10790	+	0.458906i	−0.247684	+	0.968841i	$0.579670\pi$
$828$	1.27052	−	3.06731i	0.0441537	−	0.106597i
$829$		−	7.29346i		−	0.253312i	−0.991947	−	0.126656i	$-0.959576\pi$
$829$		−	7.29346i		−	0.253312i	0.991947	−	0.126656i	$-0.0404245\pi$
$830$		0			0
$831$	−8.22551	+	8.22551i	−0.285340	+	0.285340i
$832$	−4.23372			−0.146778
$833$	3.59436	−	48.7361i	0.124537	−	1.68861i
$834$	24.5170			0.848956
$835$		0			0
$836$	−0.478334	−	0.198133i	−0.0165435	−	0.00685256i
$837$		−	5.26302i		−	0.181917i
$838$	15.1106	−	36.4802i	0.521987	−	1.26019i
$839$	−32.8053	+	13.5884i	−1.13257	+	0.469124i	−0.868652	−	0.495422i	$-0.835013\pi$
$839$	−32.8053	+	13.5884i	−1.13257	+	0.469124i	−0.263913	+	0.964546i	$0.585013\pi$
$840$		0			0
$841$	20.3809	+	20.3809i	0.702790	+	0.702790i
$842$	26.3187	+	26.3187i	0.907001	+	0.907001i
$843$	−1.22936	−	2.96795i	−0.0423415	−	0.102222i
$844$	9.09385	−	3.76680i	0.313023	−	0.129658i
$845$		0			0
$846$		−	27.9784i		−	0.961916i
$847$	44.1146	+	18.2728i	1.51579	+	0.627862i
$848$	42.0676	−	42.0676i	1.44461	−	1.44461i
$849$	−5.98513			−0.205409
$850$		0			0
$851$	0.351091			0.0120352
$852$	−2.56393	+	2.56393i	−0.0878386	+	0.0878386i
$853$	−0.220643	−	0.0913933i	−0.00755467	−	0.00312925i	0.378903	−	0.925436i	$-0.376301\pi$
$853$	−0.220643	−	0.0913933i	−0.00755467	−	0.00312925i	−0.386458	+	0.922307i	$0.626301\pi$
$854$			46.8144i			1.60196i
$855$		0			0
$856$	−18.1737	+	7.52779i	−0.621164	+	0.257295i
$857$	6.96291	+	16.8099i	0.237848	+	0.574217i	0.997060	−	0.0766273i	$-0.0244152\pi$
$857$	6.96291	+	16.8099i	0.237848	+	0.574217i	−0.759211	+	0.650844i	$0.774415\pi$
$858$	0.139507	+	0.139507i	0.00476271	+	0.00476271i
$859$	−14.2525	−	14.2525i	−0.486288	−	0.486288i	0.420845	−	0.907133i	$-0.361734\pi$
$859$	−14.2525	−	14.2525i	−0.486288	−	0.486288i	−0.907133	+	0.420845i	$0.861734\pi$
$860$		0			0
$861$	−18.1927	+	7.53565i	−0.620004	+	0.256814i
$862$	15.4143	−	37.2134i	0.525013	−	1.26749i
$863$		−	14.7597i		−	0.502424i	−0.967932	−	0.251212i	$-0.919171\pi$
$863$		−	14.7597i		−	0.502424i	0.967932	−	0.251212i	$-0.0808292\pi$
$864$	21.9084	+	9.07476i	0.745339	+	0.308730i
$865$		0			0
$866$	16.1284			0.548064
$867$	−6.01196	+	10.0309i	−0.204177	+	0.340669i
$868$	7.57936			0.257260
$869$	0.370602	−	0.370602i	0.0125718	−	0.0125718i
$870$		0			0
$871$			2.77109i			0.0938949i
$872$	2.42485	−	5.85411i	0.0821158	−	0.198245i
$873$	−44.8766	+	18.5885i	−1.51884	+	0.629126i
$874$	5.63121	+	13.5950i	0.190479	+	0.459856i
$875$		0			0
$876$	−3.30658	−	3.30658i	−0.111719	−	0.111719i
$877$	−16.3627	−	39.5030i	−0.552528	−	1.33392i	−0.915574	−	0.402149i	$-0.868263\pi$
$877$	−16.3627	−	39.5030i	−0.552528	−	1.33392i	0.363046	−	0.931771i	$-0.381737\pi$
$878$	37.1450	−	15.3860i	1.25358	−	0.519251i
$879$	0.194571	−	0.469737i	0.00656273	−	0.0158438i
$880$		0			0
$881$	−40.3580	−	16.7168i	−1.35970	−	0.563205i	−0.420721	−	0.907190i	$-0.638223\pi$
$881$	−40.3580	−	16.7168i	−1.35970	−	0.563205i	−0.938975	+	0.343985i	$0.888223\pi$
$882$	38.2412	−	38.2412i	1.28765	−	1.28765i
$883$	−41.4824			−1.39599			−0.697997	−	0.716101i	$-0.745925\pi$
$883$	−41.4824			−1.39599			−0.697997	+	0.716101i	$0.745925\pi$
$884$	11.9095	−	10.2735i	0.400561	−	0.345535i
$885$		0			0
$886$	7.88394	−	7.88394i	0.264866	−	0.264866i
$887$	−30.3770	−	12.5826i	−1.01996	−	0.422481i	−0.190881	−	0.981613i	$-0.561134\pi$
$887$	−30.3770	−	12.5826i	−1.01996	−	0.422481i	−0.829078	+	0.559132i	$0.811134\pi$
$888$			0.309321i			0.0103801i
$889$	−0.0137697	+	0.0332429i	−0.000461819	+	0.00111493i
$890$		0			0
$891$	0.0997496	+	0.240817i	0.00334174	+	0.00806767i
$892$	4.25233	+	4.25233i	0.142378	+	0.142378i
$893$	33.9075	+	33.9075i	1.13467	+	1.13467i
$894$	−4.84115	−	11.6876i	−0.161912	−	0.390891i
$895$		0			0
$896$	16.5278	−	39.9017i	0.552155	−	1.33302i
$897$		−	2.16834i		−	0.0723988i
$898$	50.5491	+	20.9381i	1.68685	+	0.698714i
$899$	0.411852	−	0.411852i	0.0137360	−	0.0137360i
$900$		0			0
$901$	−3.65820	+	49.6018i	−0.121872	+	1.65248i
$902$	0.625031			0.0208113
$903$	−21.1092	+	21.1092i	−0.702470	+	0.702470i
$904$	−3.71507	−	1.53883i	−0.123561	−	0.0511808i
$905$		0			0
$906$	−7.29650	+	17.6153i	−0.242410	+	0.585230i
$907$	−33.6731	+	13.9479i	−1.11810	+	0.463131i	−0.863719	−	0.503973i	$-0.831871\pi$
$907$	−33.6731	+	13.9479i	−1.11810	+	0.463131i	−0.254379	+	0.967105i	$0.581871\pi$
$908$	−5.41015	−	13.0613i	−0.179542	−	0.433453i
$909$	23.7498	+	23.7498i	0.787731	+	0.787731i
$910$		0			0
$911$	−11.4322	−	27.5999i	−0.378767	−	0.914425i	−0.992197	−	0.124676i	$-0.960211\pi$
$911$	−11.4322	−	27.5999i	−0.378767	−	0.914425i	0.613430	−	0.789749i	$-0.289789\pi$
$912$	−24.5128	+	10.1535i	−0.811701	+	0.336218i
$913$	0.131196	−	0.316736i	0.00434196	−	0.0104824i
$914$			46.1852i			1.52767i
$915$		0			0
$916$	−18.4117	+	18.4117i	−0.608341	+	0.608341i
$917$	−35.5369			−1.17353
$918$	−26.8791	+	8.88004i	−0.887143	+	0.293085i
$919$	11.6218			0.383368			0.191684	−	0.981457i	$-0.438605\pi$
$919$	11.6218			0.383368			0.191684	+	0.981457i	$0.438605\pi$
$920$		0			0
$921$	−1.81836	−	0.753191i	−0.0599171	−	0.0248185i
$922$			25.3837i			0.835966i
$923$	4.83880	−	11.6819i	0.159271	−	0.384515i
$924$	0.182692	−	0.0756735i	0.00601012	−	0.00248947i
$925$		0			0
$926$	−32.0803	−	32.0803i	−1.05422	−	1.05422i
$927$	−12.3514	−	12.3514i	−0.405674	−	0.405674i
$928$	1.00428	+	2.42455i	0.0329672	+	0.0795899i
$929$	−4.65849	+	1.92961i	−0.152840	+	0.0633085i	−0.457792	−	0.889059i	$-0.651360\pi$
$929$	−4.65849	+	1.92961i	−0.152840	+	0.0633085i	0.304952	+	0.952368i	$0.401360\pi$
$930$		0			0
$931$			92.6904i			3.03781i
$932$	−3.56326	−	1.47595i	−0.116718	−	0.0483464i
$933$	−9.97085	+	9.97085i	−0.326431	+	0.326431i
$934$	40.2520			1.31709
$935$		0			0
$936$	−10.2003			−0.333406
$937$	−24.6863	+	24.6863i	−0.806465	+	0.806465i	−0.984097	−	0.177632i	$-0.943156\pi$
$937$	−24.6863	+	24.6863i	−0.806465	+	0.806465i	0.177632	+	0.984097i	$0.443156\pi$
$938$	6.63574	+	2.74861i	0.216665	+	0.0897454i
$939$			5.82351i			0.190043i
$940$		0			0
$941$	10.2169	−	4.23196i	0.333060	−	0.137958i	−0.209885	−	0.977726i	$-0.567309\pi$
$941$	10.2169	−	4.23196i	0.333060	−	0.137958i	0.542945	+	0.839768i	$0.317309\pi$
$942$	−4.47450	−	10.8024i	−0.145787	−	0.351961i
$943$	−4.85738	−	4.85738i	−0.158178	−	0.158178i
$944$	17.7778	+	17.7778i	0.578619	+	0.578619i
$945$		0			0
$946$	0.875434	−	0.362616i	0.0284628	−	0.0117897i
$947$	−4.39774	+	10.6171i	−0.142907	+	0.345008i	−0.979086	−	0.203449i	$-0.934785\pi$
$947$	−4.39774	+	10.6171i	−0.142907	+	0.345008i	0.836178	+	0.548458i	$0.184785\pi$
$948$			8.66000i			0.281264i
$949$	15.0657	+	6.24040i	0.489052	+	0.202572i
$950$		0			0
$951$	−14.5094			−0.470500
$952$	7.49414	+	22.6841i	0.242887	+	0.735196i
$953$	0.704896			0.0228338			0.0114169	−	0.999935i	$-0.496366\pi$
$953$	0.704896			0.0228338			0.0114169	+	0.999935i	$0.496366\pi$
$954$	−38.9205	+	38.9205i	−1.26010	+	1.26010i
$955$		0			0
$956$		−	6.23035i		−	0.201504i
$957$	0.00581524	−	0.0140392i	0.000187980	−	0.000453824i
$958$	44.6282	−	18.4856i	1.44187	−	0.597243i
$959$	−3.71176	−	8.96097i	−0.119859	−	0.289365i
$960$		0			0
$961$	−20.5653	−	20.5653i	−0.663397	−	0.663397i
$962$	0.704397	+	1.70057i	0.0227107	+	0.0548284i
$963$	34.4112	−	14.2536i	1.10889	−	0.459316i
$964$	0.801919	−	1.93600i	0.0258281	−	0.0623545i
$965$		0			0
$966$	−5.19237	−	2.15075i	−0.167062	−	0.0691993i
$967$	−28.2521	+	28.2521i	−0.908527	+	0.908527i	−0.996153	−	0.0876267i	$-0.972072\pi$
$967$	−28.2521	+	28.2521i	−0.908527	+	0.908527i	0.0876267	+	0.996153i	$0.472072\pi$
$968$	−14.6755			−0.471688
$969$	9.97281	−	19.8132i	0.320373	−	0.636492i
$970$		0			0
$971$	30.5851	−	30.5851i	0.981521	−	0.981521i	−0.0183111	−	0.999832i	$-0.505829\pi$
$971$	30.5851	−	30.5851i	0.981521	−	0.981521i	0.999832	+	0.0183111i	$0.00582892\pi$
$972$	−17.2673	−	7.15235i	−0.553849	−	0.229412i
$973$			85.6915i			2.74714i
$974$	15.9953	−	38.6161i	0.512523	−	1.23734i
$975$		0			0
$976$	−11.2686	−	27.2049i	−0.360700	−	0.870807i
$977$	34.5543	+	34.5543i	1.10549	+	1.10549i	0.993736	+	0.111753i	$0.0356467\pi$
$977$	34.5543	+	34.5543i	1.10549	+	1.10549i	0.111753	+	0.993736i	$0.464353\pi$
$978$	−10.9321	−	10.9321i	−0.349571	−	0.349571i
$979$	−0.205249	−	0.495514i	−0.00655977	−	0.0158367i
$980$		0			0
$981$	−4.59137	+	11.0845i	−0.146591	+	0.353902i
$982$			14.0671i			0.448898i
$983$	45.1621	+	18.7068i	1.44045	+	0.596653i	0.959907	−	0.280318i	$-0.0904401\pi$
$983$	45.1621	+	18.7068i	1.44045	+	0.596653i	0.480542	+	0.876972i	$0.340440\pi$
$984$	4.27949	−	4.27949i	0.136425	−	0.136425i
$985$		0			0
$986$	−2.79829	−	1.40850i	−0.0891158	−	0.0448557i
$987$	−18.3146			−0.582961
$988$	−21.0948	+	21.0948i	−0.671114	+	0.671114i
$989$	−9.62140	−	3.98531i	−0.305943	−	0.126726i
$990$		0			0
$991$	5.56191	−	13.4276i	0.176680	−	0.426543i	−0.810586	−	0.585619i	$-0.800851\pi$
$991$	5.56191	−	13.4276i	0.176680	−	0.426543i	0.987266	+	0.159076i	$0.0508515\pi$
$992$	−7.97684	+	3.30411i	−0.253265	+	0.104906i
$993$	−4.00834	−	9.67699i	−0.127201	−	0.307090i
$994$	−23.1743	−	23.1743i	−0.735044	−	0.735044i
$995$		0			0
$996$	2.16779	+	5.23350i	0.0686890	+	0.165830i
$997$	40.8392	−	16.9161i	1.29339	−	0.535740i	0.373396	−	0.927672i	$-0.378193\pi$
$997$	40.8392	−	16.9161i	1.29339	−	0.535740i	0.919994	+	0.391933i	$0.128193\pi$
$998$	−6.07971	+	14.6777i	−0.192450	+	0.464615i
$999$		−	1.28107i		−	0.0405312i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	425.2.m.b.26.5		24
5.2	odd	4		425.2.n.c.349.5		24
5.3	odd	4		425.2.n.f.349.2		24
5.4	even	2		85.2.l.a.26.2	✓	24
15.14	odd	2		765.2.be.b.451.5		24
17.2	even	8	inner	425.2.m.b.376.5		24
17.6	odd	16		7225.2.a.bs.1.10		12
17.11	odd	16		7225.2.a.bq.1.10		12
85.2	odd	8		425.2.n.f.274.2		24
85.19	even	8		85.2.l.a.36.2	yes	24
85.24	odd	16		1445.2.d.j.866.20		24
85.44	odd	16		1445.2.d.j.866.19		24
85.53	odd	8		425.2.n.c.274.5		24
85.74	odd	16		1445.2.a.p.1.3		12
85.79	odd	16		1445.2.a.q.1.3		12
255.104	odd	8		765.2.be.b.631.5		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
85.2.l.a.26.2	✓	24	5.4	even	2
85.2.l.a.36.2	yes	24	85.19	even	8
425.2.m.b.26.5		24	1.1	even	1	trivial
425.2.m.b.376.5		24	17.2	even	8	inner
425.2.n.c.274.5		24	85.53	odd	8
425.2.n.c.349.5		24	5.2	odd	4
425.2.n.f.274.2		24	85.2	odd	8
425.2.n.f.349.2		24	5.3	odd	4
765.2.be.b.451.5		24	15.14	odd	2
765.2.be.b.631.5		24	255.104	odd	8
1445.2.a.p.1.3		12	85.74	odd	16
1445.2.a.q.1.3		12	85.79	odd	16
1445.2.d.j.866.19		24	85.44	odd	16
1445.2.d.j.866.20		24	85.24	odd	16
7225.2.a.bq.1.10		12	17.11	odd	16
7225.2.a.bs.1.10		12	17.6	odd	16

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:	\( N \)	\(=\)	\( 425 = 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	425.m (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.27691 - 1.27691i) q^{2} +(-0.635552 - 0.263254i) q^{3} -1.26102i q^{4} +(-1.14770 + 0.475393i) q^{6} +(-1.66158 - 4.01142i) q^{7} +(0.943613 + 0.943613i) q^{8} +(-1.78670 - 1.78670i) q^{9} +(0.0485041 - 0.0200910i) q^{11} +(-0.331970 + 0.801445i) q^{12} -3.02508i q^{13} +(-7.24394 - 3.00054i) q^{14} +4.93187 q^{16} +(-3.12202 + 2.69314i) q^{17} -4.56292 q^{18} +(5.52988 - 5.52988i) q^{19} +2.98689i q^{21} +(0.0362810 - 0.0875901i) q^{22} +(-0.962654 + 0.398744i) q^{23} +(-0.351305 - 0.848125i) q^{24} +(-3.86277 - 3.86277i) q^{26} +(1.45495 + 3.51255i) q^{27} +(-5.05848 + 2.09529i) q^{28} +(-0.161016 + 0.388726i) q^{29} +(-1.27892 - 0.529745i) q^{31} +(4.41035 - 4.41035i) q^{32} -0.0361159 q^{33} +(-0.547638 + 7.42546i) q^{34} +(-2.25306 + 2.25306i) q^{36} +(-0.311301 - 0.128945i) q^{37} -14.1224i q^{38} +(-0.796365 + 1.92260i) q^{39} +(2.52291 + 6.09084i) q^{41} +(3.81400 + 3.81400i) q^{42} +(7.06729 + 7.06729i) q^{43} +(-0.0253352 - 0.0611647i) q^{44} +(-0.720064 + 1.73839i) q^{46} +6.13168i q^{47} +(-3.13446 - 1.29834i) q^{48} +(-8.38087 + 8.38087i) q^{49} +(2.69319 - 0.889748i) q^{51} -3.81469 q^{52} +(8.52974 - 8.52974i) q^{53} +(6.34307 + 2.62739i) q^{54} +(2.21733 - 5.35312i) q^{56} +(-4.97030 + 2.05876i) q^{57} +(0.290767 + 0.701974i) q^{58} +(3.60468 + 3.60468i) q^{59} +(-2.28486 - 5.51614i) q^{61} +(-2.30951 + 0.956630i) q^{62} +(-4.19844 + 10.1359i) q^{63} -1.39954i q^{64} +(-0.0461170 + 0.0461170i) q^{66} -0.916040 q^{67} +(3.39611 + 3.93693i) q^{68} +0.716788 q^{69} +(3.86169 + 1.59956i) q^{71} -3.37190i q^{72} +(-2.06289 + 4.98025i) q^{73} +(-0.562156 + 0.232853i) q^{74} +(-6.97330 - 6.97330i) q^{76} +(-0.161187 - 0.161187i) q^{77} +(1.43810 + 3.47188i) q^{78} +(9.22305 - 3.82031i) q^{79} +4.96488i q^{81} +(10.9990 + 4.55595i) q^{82} +(4.61746 - 4.61746i) q^{83} +3.76653 q^{84} +18.0487 q^{86} +(0.204668 - 0.204668i) q^{87} +(0.0647272 + 0.0268109i) q^{88} -10.2159i q^{89} +(-12.1349 + 5.02642i) q^{91} +(0.502825 + 1.21393i) q^{92} +(0.673362 + 0.673362i) q^{93} +(7.82963 + 7.82963i) q^{94} +(-3.96405 + 1.64196i) q^{96} +(7.35663 - 17.7605i) q^{97} +21.4033i q^{98} +(-0.122559 - 0.0507655i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 8 q^{6} - 24 q^{9} - 8 q^{11} - 24 q^{12} - 24 q^{16} + 8 q^{17} - 8 q^{18} - 8 q^{19} + 32 q^{22} + 16 q^{23} - 8 q^{24} + 16 q^{26} - 24 q^{27} - 48 q^{28} - 8 q^{29} + 16 q^{34} - 24 q^{36} - 24 q^{37}+ \cdots - 8 q^{99}+O(q^{100}) \) 24 * q - 8 * q^6 - 24 * q^9 - 8 * q^11 - 24 * q^12 - 24 * q^16 + 8 * q^17 - 8 * q^18 - 8 * q^19 + 32 * q^22 + 16 * q^23 - 8 * q^24 + 16 * q^26 - 24 * q^27 - 48 * q^28 - 8 * q^29 + 16 * q^34 - 24 * q^36 - 24 * q^37 + 8 * q^39 + 16 * q^41 + 24 * q^42 - 8 * q^43 + 16 * q^44 + 8 * q^46 - 80 * q^48 - 56 * q^51 + 48 * q^52 - 24 * q^53 - 32 * q^54 + 64 * q^56 - 32 * q^57 + 64 * q^58 + 32 * q^59 + 32 * q^61 + 32 * q^62 + 56 * q^63 + 96 * q^66 - 16 * q^67 + 40 * q^68 + 96 * q^69 - 24 * q^71 - 64 * q^74 - 8 * q^76 - 24 * q^77 + 112 * q^78 + 80 * q^82 + 96 * q^83 - 64 * q^84 - 16 * q^86 + 48 * q^87 + 8 * q^88 - 24 * q^91 - 80 * q^92 - 64 * q^93 + 56 * q^94 - 168 * q^96 + 40 * q^97 - 8 * q^99

Introduction

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