LMFDB - Embedded newform 425.2.n.c.274.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [425,2,Mod(49,425)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("425.49"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(425, base_ring=CyclotomicField(8)) chi = DirichletCharacter(H, H._module([4, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 425 = 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	425.n (of order $8$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [24,0,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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			274.5
Character	$\chi$	$=$	425.274
Dual form			425.2.n.c.349.5

$q$-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} +(-0.263254 - 0.635552i) q^{3} -1.26102i q^{4} +(-1.14770 - 0.475393i) q^{6} +(4.01142 + 1.66158i) q^{7} +(0.943613 + 0.943613i) q^{8} +(1.78670 - 1.78670i) q^{9} +(0.0485041 + 0.0200910i) q^{11} +(-0.801445 + 0.331970i) q^{12} -3.02508 q^{13} +(7.24394 - 3.00054i) q^{14} +4.93187 q^{16} +(-2.69314 + 3.12202i) q^{17} -4.56292i q^{18} +(-5.52988 - 5.52988i) q^{19} -2.98689i q^{21} +(0.0875901 - 0.0362810i) q^{22} +(0.398744 - 0.962654i) q^{23} +(0.351305 - 0.848125i) q^{24} +(-3.86277 + 3.86277i) q^{26} +(-3.51255 - 1.45495i) q^{27} +(2.09529 - 5.05848i) q^{28} +(0.161016 + 0.388726i) q^{29} +(-1.27892 + 0.529745i) q^{31} +(4.41035 - 4.41035i) q^{32} -0.0361159i q^{33} +(0.547638 + 7.42546i) q^{34} +(-2.25306 - 2.25306i) q^{36} +(0.128945 + 0.311301i) q^{37} -14.1224 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} -6.13168 q^{47} +(-1.29834 - 3.13446i) q^{48} +(8.38087 + 8.38087i) q^{49} +(2.69319 + 0.889748i) q^{51} +3.81469i q^{52} +(-8.52974 + 8.52974i) q^{53} +(-6.34307 + 2.62739i) q^{54} +(2.21733 + 5.35312i) q^{56} +(-2.05876 + 4.97030i) q^{57} +(0.701974 + 0.290767i) q^{58} +(-3.60468 + 3.60468i) q^{59} +(-2.28486 + 5.51614i) q^{61} +(-0.956630 + 2.30951i) q^{62} +(10.1359 - 4.19844i) q^{63} -1.39954i q^{64} +(-0.0461170 - 0.0461170i) q^{66} +0.916040i q^{67} +(3.93693 + 3.39611i) q^{68} -0.716788 q^{69} +(3.86169 - 1.59956i) q^{71} +3.37190 q^{72} +(4.98025 - 2.06289i) q^{73} +(0.562156 + 0.232853i) q^{74} +(-6.97330 + 6.97330i) q^{76} +(0.161187 + 0.161187i) q^{77} +(3.47188 + 1.43810i) q^{78} +(-9.22305 - 3.82031i) q^{79} -4.96488i q^{81} +(-4.55595 - 10.9990i) q^{82} +(-4.61746 + 4.61746i) q^{83} -3.76653 q^{84} +18.0487 q^{86} +(0.204668 - 0.204668i) q^{87} +(0.0268109 + 0.0647272i) q^{88} -10.2159i q^{89} +(-12.1349 - 5.02642i) q^{91} +(-1.21393 - 0.502825i) q^{92} +(0.673362 + 0.673362i) q^{93} +(-7.82963 + 7.82963i) q^{94} +(-3.96405 - 1.64196i) q^{96} +(17.7605 - 7.35663i) q^{97} +21.4033 q^{98} +(0.122559 - 0.0507655i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 8 q^{3} - 8 q^{6} + 24 q^{9} - 8 q^{11} + 40 q^{12} + 16 q^{13} - 24 q^{16} + 8 q^{19} - 24 q^{22} + 8 q^{23} + 8 q^{24} + 16 q^{26} + 16 q^{27} - 40 q^{28} + 8 q^{29} - 16 q^{34} - 24 q^{36} - 16 q^{37}+ \cdots + 8 q^{99}+O(q^{100}) $ 24 * q - 8 * q^3 - 8 * q^6 + 24 * q^9 - 8 * q^11 + 40 * q^12 + 16 * q^13 - 24 * q^16 + 8 * q^19 - 24 * q^22 + 8 * q^23 + 8 * q^24 + 16 * q^26 + 16 * q^27 - 40 * q^28 + 8 * q^29 - 16 * q^34 - 24 * q^36 - 16 * q^37 - 48 * q^38 - 8 * q^39 + 16 * q^41 - 24 * q^42 - 8 * q^43 - 16 * q^44 + 8 * q^46 - 64 * q^47 - 8 * q^48 - 56 * q^51 + 24 * q^53 + 32 * q^54 + 64 * q^56 + 16 * q^57 + 56 * q^58 - 32 * q^59 + 32 * q^61 - 32 * q^62 + 80 * q^63 + 96 * q^66 + 24 * q^68 - 96 * q^69 - 24 * q^71 - 24 * q^72 - 64 * q^73 + 64 * q^74 - 8 * q^76 + 24 * q^77 + 8 * q^78 - 16 * q^82 - 96 * q^83 + 64 * q^84 - 16 * q^86 + 48 * q^87 + 8 * q^88 - 24 * q^91 + 112 * q^92 - 64 * q^93 - 56 * q^94 - 168 * q^96 + 48 * q^97 + 120 * q^98 + 8 * q^99

Character values

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

$n$	$52$	$326$
$\chi(n)$	$-1$	$e\left(\frac{7}{8}\right)$

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	$0.0295729\pi$
$3$	−0.263254	−	0.635552i	−0.151990	−	0.366936i	0.829484	−	0.558530i	$-0.188634\pi$
$3$	−0.263254	−	0.635552i	−0.151990	−	0.366936i	−0.981474	+	0.191594i	$0.938634\pi$
$4$		−	1.26102i		−	0.630511i
$5$		0			0
$5$		0			0
$6$	−1.14770	−	0.475393i	−0.468546	−	0.194078i
$7$	4.01142	+	1.66158i	1.51617	+	0.628020i	0.976821	−	0.214060i	$-0.0686688\pi$
$7$	4.01142	+	1.66158i	1.51617	+	0.628020i	0.539353	+	0.842080i	$0.318669\pi$
$8$	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	0.389984	−	0.920822i	$-0.372481\pi$
$11$	0.0485041	+	0.0200910i	0.0146245	+	0.00605768i	−0.375359	+	0.926879i	$0.622481\pi$
$12$	−0.801445	+	0.331970i	−0.231357	+	0.0958313i
$13$	−3.02508			−0.839006			−0.419503	−	0.907754i	$-0.637796\pi$
$13$	−3.02508			−0.839006			−0.419503	+	0.907754i	$0.637796\pi$
$14$	7.24394	−	3.00054i	1.93602	−	0.801928i
$15$		0			0
$16$	4.93187			1.23297
$17$	−2.69314	+	3.12202i	−0.653183	+	0.757200i
$17$	−2.69314	+	3.12202i	−0.653183	+	0.757200i
$18$		−	4.56292i		−	1.07549i
$19$	−5.52988	−	5.52988i	−1.26864	−	1.26864i	−0.946790	−	0.321851i	$-0.895695\pi$
$19$	−5.52988	−	5.52988i	−1.26864	−	1.26864i	−0.321851	−	0.946790i	$-0.604305\pi$
$20$		0			0
$21$		−	2.98689i		−	0.651792i
$22$	0.0875901	−	0.0362810i	0.0186743	−	0.00773514i
$23$	0.398744	−	0.962654i	0.0831439	−	0.200727i	−0.876840	−	0.480782i	$-0.840353\pi$
$23$	0.398744	−	0.962654i	0.0831439	−	0.200727i	0.959984	+	0.280055i	$0.0903527\pi$
$24$	0.351305	−	0.848125i	0.0717098	−	0.173123i
$25$		0			0
$26$	−3.86277	+	3.86277i	−0.757551	+	0.757551i
$27$	−3.51255	−	1.45495i	−0.675991	−	0.280005i
$28$	2.09529	−	5.05848i	0.395973	−	0.955964i
$29$	0.161016	+	0.388726i	0.0298999	+	0.0721847i	0.938124	−	0.346299i	$-0.112562\pi$
$29$	0.161016	+	0.388726i	0.0298999	+	0.0721847i	−0.908224	+	0.418484i	$0.862562\pi$
$30$		0			0
$31$	−1.27892	+	0.529745i	−0.229701	+	0.0951451i	−0.494565	−	0.869141i	$-0.664673\pi$
$31$	−1.27892	+	0.529745i	−0.229701	+	0.0951451i	0.264865	+	0.964286i	$0.414673\pi$
$32$	4.41035	−	4.41035i	0.779647	−	0.779647i
$33$		−	0.0361159i		−	0.00628698i
$34$	0.547638	+	7.42546i	0.0939192	+	1.27346i
$35$		0			0
$36$	−2.25306	−	2.25306i	−0.375510	−	0.375510i
$37$	0.128945	+	0.311301i	0.0211984	+	0.0511775i	0.934124	−	0.356948i	$-0.116183\pi$
$37$	0.128945	+	0.311301i	0.0211984	+	0.0511775i	−0.912926	+	0.408125i	$0.866183\pi$
$38$	−14.1224			−2.29095
$39$	0.796365	+	1.92260i	0.127520	+	0.307862i
$40$		0			0
$41$	2.52291	−	6.09084i	0.394012	−	0.951230i	−0.595044	−	0.803693i	$-0.702865\pi$
$41$	2.52291	−	6.09084i	0.394012	−	0.951230i	0.989057	−	0.147537i	$-0.0471345\pi$
$42$	−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
$47$	−6.13168			−0.894398			−0.447199	−	0.894435i	$-0.647578\pi$
$47$	−6.13168			−0.894398			−0.447199	+	0.894435i	$0.647578\pi$
$48$	−1.29834	−	3.13446i	−0.187399	−	0.452420i
$49$	8.38087	+	8.38087i	1.19727	+	1.19727i
$50$		0			0
$51$	2.69319	+	0.889748i	0.377122	+	0.124590i
$52$			3.81469i			0.529002i
$53$	−8.52974	+	8.52974i	−1.17165	+	1.17165i	−0.189834	+	0.981816i	$0.560795\pi$
$53$	−8.52974	+	8.52974i	−1.17165	+	1.17165i	−0.981816	+	0.189834i	$0.939205\pi$
$54$	−6.34307	+	2.62739i	−0.863183	+	0.357542i
$55$		0			0
$56$	2.21733	+	5.35312i	0.296304	+	0.715340i
$57$	−2.05876	+	4.97030i	−0.272690	+	0.658332i
$58$	0.701974	+	0.290767i	0.0921737	+	0.0381796i
$59$	−3.60468	+	3.60468i	−0.469290	+	0.469290i	−0.901684	−	0.432395i	$-0.857669\pi$
$59$	−3.60468	+	3.60468i	−0.469290	+	0.469290i	0.432395	+	0.901684i	$0.357669\pi$
$60$		0			0
$61$	−2.28486	+	5.51614i	−0.292547	+	0.706270i	−1.00000		0.000490243i	$-0.999844\pi$
$61$	−2.28486	+	5.51614i	−0.292547	+	0.706270i	0.707453	+	0.706760i	$0.249844\pi$
$62$	−0.956630	+	2.30951i	−0.121492	+	0.293308i
$63$	10.1359	−	4.19844i	1.27701	−	0.528954i
$64$		−	1.39954i		−	0.174943i
$65$		0			0
$66$	−0.0461170	−	0.0461170i	−0.00567661	−	0.00567661i
$67$			0.916040i			0.111912i	0.998433	+	0.0559561i	$0.0178207\pi$
$67$			0.916040i			0.111912i	−0.998433	+	0.0559561i	$0.982179\pi$
$68$	3.93693	+	3.39611i	0.477423	+	0.411839i
$69$	−0.716788			−0.0862912
$70$		0			0
$71$	3.86169	−	1.59956i	0.458298	−	0.189833i	−0.141577	−	0.989927i	$-0.545217\pi$
$71$	3.86169	−	1.59956i	0.458298	−	0.189833i	0.599875	+	0.800094i	$0.295217\pi$
$72$	3.37190			0.397382
$73$	4.98025	−	2.06289i	0.582895	−	0.241443i	−0.0716959	−	0.997427i	$-0.522841\pi$
$73$	4.98025	−	2.06289i	0.582895	−	0.241443i	0.654590	+	0.755984i	$0.272841\pi$
$74$	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
$78$	3.47188	+	1.43810i	0.393113	+	0.162833i
$79$	−9.22305	−	3.82031i	−1.03767	−	0.429819i	−0.202198	−	0.979345i	$-0.564808\pi$
$79$	−9.22305	−	3.82031i	−1.03767	−	0.429819i	−0.835477	+	0.549526i	$0.814808\pi$
$80$		0			0
$81$		−	4.96488i		−	0.551653i
$82$	−4.55595	−	10.9990i	−0.503120	−	1.21464i
$83$	−4.61746	+	4.61746i	−0.506833	+	0.506833i	−0.913553	−	0.406720i	$-0.866672\pi$
$83$	−4.61746	+	4.61746i	−0.506833	+	0.506833i	0.406720	+	0.913553i	$0.366672\pi$
$84$	−3.76653			−0.410962
$85$		0			0
$86$	18.0487			1.94624
$87$	0.204668	−	0.204668i	0.0219427	−	0.0219427i
$88$	0.0268109	+	0.0647272i	0.00285805	+	0.00689994i
$89$		−	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
$92$	−1.21393	−	0.502825i	−0.126561	−	0.0524231i
$93$	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
$97$	17.7605	−	7.35663i	1.80330	−	0.746952i	0.818212	−	0.574916i	$-0.194965\pi$
$97$	17.7605	−	7.35663i	1.80330	−	0.746952i	0.985091	−	0.172036i	$-0.0550346\pi$
$98$	21.4033			2.16206
$99$	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	$0.730008\pi$
$102$	4.57510	−	2.30284i	0.453003	−	0.228015i
$103$			6.91299i			0.681157i	0.940216	+	0.340579i	$0.110623\pi$
$103$			6.91299i			0.681157i	−0.940216	+	0.340579i	$0.889377\pi$
$104$	−2.85450	−	2.85450i	−0.279907	−	0.279907i
$105$		0			0
$106$			21.7835i			2.11580i
$107$	−13.6187	+	5.64104i	−1.31657	+	0.545339i	−0.926793	−	0.375572i	$-0.877446\pi$
$107$	−13.6187	+	5.64104i	−1.31657	+	0.545339i	−0.389773	+	0.920911i	$0.627446\pi$
$108$	−1.83472	+	4.42940i	−0.176546	+	0.426220i
$109$	1.81709	−	4.38684i	0.174046	−	0.420183i	−0.812652	−	0.582749i	$-0.801977\pi$
$109$	1.81709	−	4.38684i	0.174046	−	0.420183i	0.986698	+	0.162566i	$0.0519770\pi$
$110$		0			0
$111$	0.163903	−	0.163903i	0.0155569	−	0.0155569i
$112$	19.7838	+	8.19471i	1.86939	+	0.774328i
$113$	1.15314	−	2.78393i	0.108478	−	0.261890i	−0.860314	−	0.509765i	$-0.829732\pi$
$113$	1.15314	−	2.78393i	0.108478	−	0.261890i	0.968792	+	0.247875i	$0.0797322\pi$
$114$	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
$118$			9.20574i			0.847457i
$119$	−15.9908	+	8.04884i	−1.46588	+	0.737836i
$120$		0			0
$121$	−7.77623	−	7.77623i	−0.706930	−	0.706930i
$122$	4.12607	+	9.96122i	0.373557	+	0.901846i
$123$	−4.53522			−0.408927
$124$	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	0.707367	−	0.706847i	$-0.249883\pi$
$127$	0.00585984	+	0.00585984i	0.000519977	+	0.000519977i	−0.706847	+	0.707367i	$0.749883\pi$
$128$	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	0.999634	−	0.0270577i	$-0.00861380\pi$
$131$	3.13210	+	7.56157i	0.273653	+	0.660657i	−0.725981	+	0.687715i	$0.758614\pi$
$132$	−0.0455430			−0.00396401
$133$	−12.9943	−	31.3710i	−1.12675	−	2.72021i
$134$	1.16971	+	1.16971i	0.101047	+	0.101047i
$135$		0			0
$136$	−5.48726	+	0.404693i	−0.470528	+	0.0347021i
$137$		−	2.23387i		−	0.190852i	−0.995437	−	0.0954260i	$-0.969579\pi$
$137$		−	2.23387i		−	0.190852i	0.995437	−	0.0954260i	$-0.0304213\pi$
$138$	−0.915277	+	0.915277i	−0.0779136	+	0.0779136i
$139$	18.2335	−	7.55257i	1.54655	−	0.640601i	0.563859	−	0.825871i	$-0.309316\pi$
$139$	18.2335	−	7.55257i	1.54655	−	0.640601i	0.982688	+	0.185270i	$0.0593160\pi$
$140$		0			0
$141$	1.61419	+	3.89701i	0.135940	+	0.328187i
$142$	2.88854	−	6.97355i	0.242401	−	0.585207i
$143$	−0.146729	−	0.0607770i	−0.0122701	−	0.00508243i
$144$	8.81175	−	8.81175i	0.734313	−	0.734313i
$145$		0			0
$146$	3.72523	−	8.99349i	0.308302	−	0.744306i
$147$	3.12018	−	7.53279i	0.257348	−	0.621294i
$148$	0.392557	−	0.162602i	0.0322680	−	0.0133658i
$149$			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	0.993858	−	0.110659i	$-0.0352961\pi$
$151$	10.8529	+	10.8529i	0.883200	+	0.883200i	−0.110659	+	0.993858i	$0.535296\pi$
$152$		−	10.4361i		−	0.846482i
$153$	0.766271	+	10.3899i	0.0619494	+	0.839975i
$154$	0.411645			0.0331713
$155$		0			0
$156$	2.42443	−	1.00423i	0.194110	−	0.0804030i
$157$	−9.41222			−0.751177			−0.375588	−	0.926787i	$-0.622559\pi$
$157$	−9.41222			−0.751177			−0.375588	+	0.926787i	$0.622559\pi$
$158$	−16.6553	+	6.89884i	−1.32502	+	0.548842i
$159$	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
$163$	11.4980	+	4.76262i	0.900592	+	0.373037i	0.784448	−	0.620195i	$-0.212947\pi$
$163$	11.4980	+	4.76262i	0.900592	+	0.373037i	0.116144	+	0.993232i	$0.462947\pi$
$164$	−7.68068	−	3.18144i	−0.599761	−	0.248429i
$165$		0			0
$166$			11.7922i			0.915253i
$167$	4.82277	+	11.6432i	0.373197	+	0.900977i	0.993205	+	0.116382i	$0.0371295\pi$
$167$	4.82277	+	11.6432i	0.373197	+	0.900977i	−0.620008	+	0.784596i	$0.712870\pi$
$168$	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
$173$	−4.66741	−	11.2681i	−0.354856	−	0.856699i	−0.996006	−	0.0892832i	$-0.971542\pi$
$173$	−4.66741	−	11.2681i	−0.354856	−	0.856699i	0.641150	−	0.767416i	$-0.278458\pi$
$174$		−	0.522687i		−	0.0396248i
$175$		0			0
$176$	0.239216	+	0.0990864i	0.0180316	+	0.00746892i
$177$	3.23991	+	1.34202i	0.243527	+	0.100872i
$178$	−13.0449	−	13.0449i	−0.977754	−	0.977754i
$179$	−9.80106	+	9.80106i	−0.732566	+	0.732566i	−0.971127	−	0.238562i	$-0.923324\pi$
$179$	−9.80106	+	9.80106i	−0.732566	+	0.732566i	0.238562	+	0.971127i	$0.423324\pi$
$180$		0			0
$181$	1.88863	+	0.782297i	0.140381	+	0.0581476i	0.451768	−	0.892136i	$-0.350794\pi$
$181$	1.88863	+	0.782297i	0.140381	+	0.0581476i	−0.311387	+	0.950283i	$0.600794\pi$
$182$	−21.9135	+	9.07686i	−1.62434	+	0.672822i
$183$	4.10730			0.303620
$184$	1.28463	−	0.532112i	0.0947043	−	0.0392278i
$185$		0			0
$186$	1.71965			0.126091
$187$	−0.193353	+	0.0973225i	−0.0141394	+	0.00711693i
$188$			7.73218i			0.563927i
$189$	−11.6728	−	11.6728i	−0.849071	−	0.849071i
$190$		0			0
$191$		−	3.08056i		−	0.222902i	−0.993770	−	0.111451i	$-0.964450\pi$
$191$		−	3.08056i		−	0.222902i	0.993770	−	0.111451i	$-0.0355498\pi$
$192$	−0.889482	+	0.368435i	−0.0641928	+	0.0265895i
$193$	7.89931	−	19.0706i	0.568605	−	1.37273i	−0.334126	−	0.942528i	$-0.608441\pi$
$193$	7.89931	−	19.0706i	0.568605	−	1.37273i	0.902731	−	0.430205i	$-0.141559\pi$
$194$	13.2848	−	32.0724i	0.953794	−	2.30266i
$195$		0			0
$196$	10.5685	−	10.5685i	0.754890	−	0.754890i
$197$	−16.8483	−	6.97881i	−1.20039	−	0.497219i	−0.309268	−	0.950975i	$-0.600084\pi$
$197$	−16.8483	−	6.97881i	−1.20039	−	0.497219i	−0.891126	+	0.453756i	$0.850084\pi$
$198$	0.0916738	−	0.221320i	0.00651497	−	0.0157285i
$199$	10.2053	+	24.6377i	0.723432	+	1.74652i	0.663328	+	0.748328i	$0.269143\pi$
$199$	10.2053	+	24.6377i	0.723432	+	1.74652i	0.0601040	+	0.998192i	$0.480857\pi$
$200$		0			0
$201$	0.582192	−	0.241152i	0.0410646	−	0.0170095i
$202$	−16.9735	+	16.9735i	−1.19425	+	1.19425i
$203$			1.82689i			0.128222i
$204$	1.12199	−	3.39617i	0.0785551	−	0.237779i
$205$		0			0
$206$	8.82730	+	8.82730i	0.615027	+	0.615027i
$207$	−1.00754	−	2.43240i	−0.0700285	−	0.169064i
$208$	−14.9193			−1.03447
$209$	−0.157121	−	0.379323i	−0.0108683	−	0.0262383i
$210$		0			0
$211$	2.98710	−	7.21149i	0.205640	−	0.496460i	−0.787087	−	0.616842i	$-0.788412\pi$
$211$	2.98710	−	7.21149i	0.205640	−	0.496460i	0.992728	+	0.120382i	$0.0384119\pi$
$212$	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
$217$	−6.01049			−0.408019
$218$	−3.28135	−	7.92189i	−0.222241	−	0.536538i
$219$	−2.62215	−	2.62215i	−0.177188	−	0.177188i
$220$		0			0
$221$	8.14696	−	9.44435i	0.548024	−	0.635295i
$222$		−	0.418579i		−	0.0280932i
$223$	3.37213	−	3.37213i	0.225815	−	0.225815i	−0.585127	−	0.810942i	$-0.698955\pi$
$223$	3.37213	−	3.37213i	0.225815	−	0.225815i	0.810942	+	0.585127i	$0.198955\pi$
$224$	25.0199	−	10.3636i	1.67171	−	0.692447i
$225$		0			0
$226$	−2.08238	−	5.02731i	−0.138518	−	0.334411i
$227$	4.29029	−	10.3577i	0.284757	−	0.687464i	−0.715177	−	0.698943i	$-0.753654\pi$
$227$	4.29029	−	10.3577i	0.284757	−	0.687464i	0.999934	+	0.0114793i	$0.00365405\pi$
$228$	6.26765	+	2.59614i	0.415085	+	0.171934i
$229$	14.6007	−	14.6007i	0.964838	−	0.964838i	−0.0345640	−	0.999402i	$-0.511004\pi$
$229$	14.6007	−	14.6007i	0.964838	−	0.964838i	0.999402	+	0.0345640i	$0.0110043\pi$
$230$		0			0
$231$	0.0600097	−	0.144876i	0.00394835	−	0.00953215i
$232$	−0.214871	+	0.518744i	−0.0141069	+	0.0340572i
$233$	−2.82569	+	1.17044i	−0.185117	+	0.0766781i	−0.473317	−	0.880892i	$-0.656943\pi$
$233$	−2.82569	+	1.17044i	−0.185117	+	0.0766781i	0.288199	+	0.957570i	$0.406943\pi$
$234$			13.8032i			0.902342i
$235$		0			0
$236$	4.54558	+	4.54558i	0.295892	+	0.295892i
$237$			6.86745i			0.446089i
$238$	−10.1412	+	30.6966i	−0.657358	+	1.98976i
$239$	−4.94072			−0.319588			−0.159794	−	0.987150i	$-0.551083\pi$
$239$	−4.94072			−0.319588			−0.159794	+	0.987150i	$0.551083\pi$
$240$		0			0
$241$	1.53527	−	0.635928i	0.0988952	−	0.0409637i	−0.332687	−	0.943037i	$-0.607955\pi$
$241$	1.53527	−	0.635928i	0.0988952	−	0.0409637i	0.431583	+	0.902073i	$0.357955\pi$
$242$	−19.8592			−1.27659
$243$	−13.6931	+	5.67187i	−0.878413	+	0.363850i
$244$	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
$248$	−1.70668	−	0.706929i	−0.108374	−	0.0448900i
$249$	4.15021	+	1.71907i	0.263009	+	0.108942i
$250$		0			0
$251$		−	9.14240i		−	0.577063i	−0.957470	−	0.288531i	$-0.906833\pi$
$251$		−	9.14240i		−	0.577063i	0.957470	−	0.288531i	$-0.0931670\pi$
$252$	−5.29432	−	12.7816i	−0.333511	−	0.805167i
$253$	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	$0.0761671\pi$
$258$	−4.75139	−	11.4709i	−0.295809	−	0.714145i
$259$			1.46301i			0.0909070i
$260$		0			0
$261$	0.982222	+	0.406850i	0.0607980	+	0.0251834i
$262$	13.6549	+	5.65605i	0.843603	+	0.349432i
$263$	−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
$267$	−6.49276	+	2.68939i	−0.397350	+	0.164588i
$268$	1.15515			0.0705618
$269$	21.4082	−	8.86758i	1.30528	−	0.540666i	0.381779	−	0.924254i	$-0.375312\pi$
$269$	21.4082	−	8.86758i	1.30528	−	0.540666i	0.923504	+	0.383588i	$0.125312\pi$
$270$		0			0
$271$	−3.95595			−0.240307			−0.120153	−	0.992755i	$-0.538339\pi$
$271$	−3.95595			−0.240307			−0.120153	+	0.992755i	$0.538339\pi$
$272$	−13.2822	+	15.3974i	−0.805353	+	0.933603i
$273$			9.03556i			0.546857i
$274$	−2.85246	−	2.85246i	−0.172323	−	0.172323i
$275$		0			0
$276$			0.903885i			0.0544075i
$277$	15.6227	−	6.47115i	0.938679	−	0.388814i	0.139714	−	0.990192i	$-0.455382\pi$
$277$	15.6227	−	6.47115i	0.938679	−	0.388814i	0.798964	+	0.601378i	$0.205382\pi$
$278$	13.6387	−	32.9266i	0.817992	−	1.97481i
$279$	−1.33854	+	3.23153i	−0.0801366	+	0.193467i
$280$		0			0
$281$	3.30210	−	3.30210i	0.196987	−	0.196987i	−0.601720	−	0.798707i	$-0.705518\pi$
$281$	3.30210	−	3.30210i	0.196987	−	0.196987i	0.798707	+	0.601720i	$0.205518\pi$
$282$	7.03733	+	2.91496i	0.419067	+	0.173583i
$283$	−3.32949	+	8.03809i	−0.197917	+	0.477815i	−0.991414	−	0.130760i	$-0.958258\pi$
$283$	−3.32949	+	8.03809i	−0.197917	+	0.477815i	0.793497	+	0.608575i	$0.208258\pi$
$284$	−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
$288$		−	15.7599i		−	0.928661i
$289$	−2.49398	−	16.8161i	−0.146705	−	0.989180i
$290$		0			0
$291$	−9.35105	−	9.35105i	−0.548168	−	0.548168i
$292$	−2.60135	−	6.28021i	−0.152232	−	0.367521i
$293$	0.739100			0.0431787			0.0215893	−	0.999767i	$-0.493127\pi$
$293$	0.739100			0.0431787			0.0215893	+	0.999767i	$0.493127\pi$
$294$	−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
$302$	27.7165			1.59491
$303$	3.49933	+	8.44813i	0.201031	+	0.485333i
$304$	−27.2726	−	27.2726i	−1.56419	−	1.56419i
$305$		0			0
$306$	14.2455	+	12.2886i	0.814361	+	0.702491i
$307$		−	2.86108i		−	0.163290i	−0.996661	−	0.0816451i	$-0.973983\pi$
$307$		−	2.86108i		−	0.163290i	0.996661	−	0.0816451i	$-0.0260174\pi$
$308$	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	0.974242	+	0.225507i	$0.0724038\pi$
$311$	7.84424	+	18.9377i	0.444806	+	1.07386i	−0.529435	+	0.848350i	$0.677596\pi$
$312$	−1.06273	+	2.56565i	−0.0601650	+	0.145251i
$313$	−7.82103	−	3.23958i	−0.442071	−	0.183112i	0.150534	−	0.988605i	$-0.451901\pi$
$313$	−7.82103	−	3.23958i	−0.442071	−	0.183112i	−0.592605	+	0.805493i	$0.701901\pi$
$314$	−12.0186	+	12.0186i	−0.678249	+	0.678249i
$315$		0			0
$316$	−4.81750	+	11.6305i	−0.271005	+	0.654265i
$317$	8.07149	−	19.4863i	0.453340	−	1.09446i	−0.517704	−	0.855560i	$-0.673213\pi$
$317$	8.07149	−	19.4863i	0.453340	−	1.09446i	0.971044	−	0.238900i	$-0.0767867\pi$
$318$	13.8446	−	5.73460i	0.776364	−	0.321581i
$319$			0.0220898i			0.00123679i
$320$		0			0
$321$	7.17035	+	7.17035i	0.400210	+	0.400210i
$322$		−	8.16985i		−	0.455288i
$323$	32.1571	−	2.37163i	1.78927	−	0.131961i
$324$	−6.26082			−0.347823
$325$		0			0
$326$	20.7634	−	8.60048i	1.14998	−	0.476337i
$327$	−3.26643			−0.180634
$328$	8.12805	−	3.36675i	0.448796	−	0.185897i
$329$	−24.5967	−	10.1883i	−1.35606	−	0.561699i
$330$		0			0
$331$	10.7665	−	10.7665i	0.591780	−	0.591780i	−0.346332	−	0.938112i	$-0.612573\pi$
$331$	10.7665	−	10.7665i	0.591780	−	0.591780i	0.938112	+	0.346332i	$0.112573\pi$
$332$	5.82272	+	5.82272i	0.319563	+	0.319563i
$333$	0.786585	+	0.325814i	0.0431046	+	0.0178545i
$334$	21.0256	+	8.70910i	1.15047	+	0.476541i
$335$		0			0
$336$		−	14.7309i		−	0.803638i
$337$	4.39079	+	10.6003i	0.239182	+	0.577435i	0.997199	−	0.0747994i	$-0.0238316\pi$
$337$	4.39079	+	10.6003i	0.239182	+	0.577435i	−0.758017	+	0.652235i	$0.773832\pi$
$338$	−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
$343$	8.06258	+	19.4648i	0.435338	+	1.05100i
$344$			13.3376i			0.719114i
$345$		0			0
$346$	−20.3483	−	8.42854i	−1.09393	−	0.453121i
$347$	−13.8437	−	5.73424i	−0.743168	−	0.307830i	−0.0212172	−	0.999775i	$-0.506754\pi$
$347$	−13.8437	−	5.73424i	−0.743168	−	0.307830i	−0.721950	+	0.691945i	$0.756754\pi$
$348$	−0.258091	−	0.258091i	−0.0138351	−	0.0138351i
$349$	3.20791	−	3.20791i	0.171715	−	0.171715i	−0.616017	−	0.787733i	$-0.711255\pi$
$349$	3.20791	−	3.20791i	0.171715	−	0.171715i	0.787733	+	0.616017i	$0.211255\pi$
$350$		0			0
$351$	10.6257	+	4.40133i	0.567160	+	0.234925i
$352$	0.302528	−	0.125311i	0.0161248	−	0.00667912i
$353$	7.71469			0.410612			0.205306	−	0.978698i	$-0.434181\pi$
$353$	7.71469			0.410612			0.205306	+	0.978698i	$0.434181\pi$
$354$	5.85073	−	2.42345i	0.310963	−	0.128805i
$355$		0			0
$356$	−12.8825			−0.682771
$357$	9.32511	+	8.04411i	0.493537	+	0.425739i
$358$			25.0302i			1.32289i
$359$	7.79826	+	7.79826i	0.411577	+	0.411577i	0.882287	−	0.470711i	$-0.156003\pi$
$359$	7.79826	+	7.79826i	0.411577	+	0.411577i	−0.470711	+	0.882287i	$0.656003\pi$
$360$		0			0
$361$			42.1592i			2.21890i
$362$	3.41055	−	1.41269i	0.179254	−	0.0742496i
$363$	−2.89507	+	6.98933i	−0.151952	+	0.366844i
$364$	−6.33843	+	15.3023i	−0.332224	+	0.802059i
$365$		0			0
$366$	5.24467	−	5.24467i	0.274143	−	0.274143i
$367$	−14.8084	−	6.13386i	−0.772995	−	0.320185i	−0.0389098	−	0.999243i	$-0.512389\pi$
$367$	−14.8084	−	6.13386i	−0.772995	−	0.320185i	−0.734085	+	0.679058i	$0.762389\pi$
$368$	1.96655	−	4.74768i	0.102514	−	0.247490i
$369$	−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
$373$			10.2501i			0.530732i	0.964148	+	0.265366i	$0.0854928\pi$
$373$			10.2501i			0.530732i	−0.964148	+	0.265366i	$0.914507\pi$
$374$	−0.122623	+	0.371168i	−0.00634066	+	0.0191926i
$375$		0			0
$376$	−5.78593	−	5.78593i	−0.298387	−	0.298387i
$377$	−0.487085	−	1.17593i	−0.0250862	−	0.0605634i
$378$	−29.8103			−1.53328
$379$	5.33919	+	12.8899i	0.274256	+	0.662112i	0.999656	−	0.0262152i	$-0.00834551\pi$
$379$	5.33919	+	12.8899i	0.274256	+	0.662112i	−0.725401	+	0.688327i	$0.758346\pi$
$380$		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
$387$	25.2542			1.28374
$388$	−9.27687	−	22.3963i	−0.470962	−	1.13700i
$389$	25.3255	+	25.3255i	1.28406	+	1.28406i	0.938339	+	0.345717i	$0.112364\pi$
$389$	25.3255	+	25.3255i	1.28406	+	1.28406i	0.345717	+	0.938339i	$0.387636\pi$
$390$		0			0
$391$	1.93155	+	3.83745i	0.0976825	+	0.194068i
$392$			15.8166i			0.798858i
$393$	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
$397$	−1.48870	+	3.59405i	−0.0747159	+	0.180380i	−0.956825	−	0.290665i	$-0.906123\pi$
$397$	−1.48870	+	3.59405i	−0.0747159	+	0.180380i	0.882109	+	0.471046i	$0.156123\pi$
$398$	44.4915	+	18.4290i	2.23016	+	0.923761i
$399$	−16.5171	+	16.5171i	−0.826891	+	0.826891i
$400$		0			0
$401$	14.0592	−	33.9420i	0.702085	−	1.69498i	−0.0168056	−	0.999859i	$-0.505350\pi$
$401$	14.0592	−	33.9420i	0.702085	−	1.69498i	0.718890	−	0.695124i	$-0.244650\pi$
$402$	0.435479	−	1.05134i	0.0217197	−	0.0524360i
$403$	3.86883	−	1.60252i	0.192720	−	0.0798273i
$404$			16.7622i			0.833952i
$405$		0			0
$406$	2.33278	+	2.33278i	0.115774	+	0.115774i
$407$			0.0176900i			0.000876860i
$408$	1.70175	+	3.38090i	0.0842491	+	0.167380i
$409$	22.3529			1.10528			0.552641	−	0.833419i	$-0.313620\pi$
$409$	22.3529			1.10528			0.552641	+	0.833419i	$0.313620\pi$
$410$		0			0
$411$	−1.41974	+	0.588075i	−0.0700306	+	0.0290076i
$412$	8.71743			0.429477
$413$	−20.4494	+	8.47041i	−1.00625	+	0.416802i
$414$	−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
$418$	−0.684993	−	0.283733i	−0.0335041	−	0.0138778i
$419$	−20.2014	−	8.36768i	−0.986901	−	0.408788i	−0.169924	−	0.985457i	$-0.554352\pi$
$419$	−20.2014	−	8.36768i	−0.986901	−	0.408788i	−0.816978	+	0.576669i	$0.804352\pi$
$420$		0			0
$421$		−	20.6111i		−	1.00453i	−0.864715	−	0.502263i	$-0.832501\pi$
$421$		−	20.6111i		−	1.00453i	0.864715	−	0.502263i	$-0.167499\pi$
$422$	−5.39419	−	13.0227i	−0.262585	−	0.633937i
$423$	−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
$428$	7.11347	+	17.1734i	0.343842	+	0.830109i
$429$			0.109254i			0.00527481i
$430$		0			0
$431$	20.6074	+	8.53585i	0.992621	+	0.411157i	0.819086	−	0.573670i	$-0.194481\pi$
$431$	20.6074	+	8.53585i	0.992621	+	0.411157i	0.173535	+	0.984828i	$0.444481\pi$
$432$	−17.3234	−	7.17561i	−0.833475	−	0.345236i
$433$	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
$437$	−7.52837	+	3.11835i	−0.360131	+	0.149171i
$438$	−6.69652			−0.319972
$439$	−20.5695	+	8.52016i	−0.981728	+	0.406645i	−0.815066	−	0.579369i	$-0.803299\pi$
$439$	−20.5695	+	8.52016i	−0.981728	+	0.406645i	−0.166663	+	0.986014i	$0.553299\pi$
$440$		0			0
$441$	29.9481			1.42610
$442$	−1.65665	−	22.4626i	−0.0787987	−	1.06844i
$443$			6.17421i			0.293346i	0.989185	+	0.146673i	$0.0468564\pi$
$443$			6.17421i			0.293346i	−0.989185	+	0.146673i	$0.953144\pi$
$444$	−0.206685	−	0.206685i	−0.00980882	−	0.00980882i
$445$		0			0
$446$		−	8.61184i		−	0.407783i
$447$	6.47214	−	2.68085i	0.306122	−	0.126800i
$448$	2.32545	−	5.61414i	0.109867	−	0.265243i
$449$	−11.5947	+	27.9922i	−0.547189	+	1.32103i	0.372371	+	0.928084i	$0.378545\pi$
$449$	−11.5947	+	27.9922i	−0.547189	+	1.32103i	−0.919561	+	0.392948i	$0.871455\pi$
$450$		0			0
$451$	0.244743	−	0.244743i	0.0115245	−	0.0115245i
$452$	−3.51060	−	1.45414i	−0.165125	−	0.0683968i
$453$	4.04053	−	9.75470i	0.189841	−	0.458316i
$454$	−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	$0.454112\pi$
$458$		−	37.2876i		−	1.74233i
$459$	14.0022	−	7.04787i	0.653565	−	0.328966i
$460$		0			0
$461$	−9.93945	−	9.93945i	−0.462926	−	0.462926i	0.436687	−	0.899613i	$-0.356152\pi$
$461$	−9.93945	−	9.93945i	−0.462926	−	0.462926i	−0.899613	+	0.436687i	$0.856152\pi$
$462$	−0.108367	−	0.261622i	−0.00504170	−	0.0121717i
$463$	−25.1233			−1.16758			−0.583789	−	0.811905i	$-0.698431\pi$
$463$	−25.1233			−1.16758			−0.583789	+	0.811905i	$0.698431\pi$
$464$	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	0.241139	−	0.970491i	$-0.422479\pi$
$467$	−15.7614	−	15.7614i	−0.729352	−	0.729352i	−0.970491	+	0.241139i	$0.922479\pi$
$468$	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
$472$	−6.80285			−0.313126
$473$	0.200803	+	0.484782i	0.00923294	+	0.0222903i
$474$	8.76915	+	8.76915i	0.402780	+	0.402780i
$475$		0			0
$476$	10.1498	+	20.1648i	0.465213	+	0.924250i
$477$			30.4801i			1.39559i
$478$	−6.30887	+	6.30887i	−0.288561	+	0.288561i
$479$	−24.7134	+	10.2366i	−1.12919	+	0.467724i	−0.867504	−	0.497430i	$-0.834277\pi$
$479$	−24.7134	+	10.2366i	−1.12919	+	0.467724i	−0.261681	+	0.965154i	$0.584277\pi$
$480$		0			0
$481$	−0.390068	−	0.941709i	−0.0177856	−	0.0429382i
$482$	1.14838	−	2.77243i	0.0523072	−	0.126281i
$483$	−2.87534	−	1.19100i	−0.130832	−	0.0541926i
$484$	−9.80599	+	9.80599i	−0.445727	+	0.445727i
$485$		0			0
$486$	−10.2424	+	24.7274i	−0.464606	+	1.12166i
$487$	8.85760	−	21.3841i	0.401376	−	0.969008i	−0.585956	−	0.810343i	$-0.699281\pi$
$487$	8.85760	−	21.3841i	0.401376	−	0.969008i	0.987332	−	0.158665i	$-0.0507190\pi$
$488$	−7.36113	+	3.04908i	−0.333223	+	0.138025i
$489$		−	8.56135i		−	0.387158i
$490$		0			0
$491$	−5.50823	−	5.50823i	−0.248583	−	0.248583i	0.571806	−	0.820389i	$-0.306243\pi$
$491$	−5.50823	−	5.50823i	−0.248583	−	0.248583i	−0.820389	+	0.571806i	$0.806243\pi$
$492$			5.71901i			0.257833i
$493$	−1.64725	−	0.544201i	−0.0741883	−	0.0245096i
$494$	42.7213			1.92212
$495$		0			0
$496$	−6.30746	+	2.61263i	−0.283213	+	0.117311i
$497$	18.1487			0.814079
$498$	7.49457	−	3.10435i	0.335840	−	0.139109i
$499$	8.12796	+	3.36671i	0.363858	+	0.150715i	0.557119	−	0.830432i	$-0.311907\pi$
$499$	8.12796	+	3.36671i	0.363858	+	0.150715i	−0.193262	+	0.981147i	$0.561907\pi$
$500$		0			0
$501$	6.13025	−	6.13025i	0.273879	−	0.273879i
$502$	−11.6741	−	11.6741i	−0.521039	−	0.521039i
$503$	7.24271	+	3.00003i	0.322937	+	0.133765i	0.538262	−	0.842778i	$-0.319081\pi$
$503$	7.24271	+	3.00003i	0.322937	+	0.133765i	−0.215325	+	0.976542i	$0.569081\pi$
$504$	13.5261	+	5.60269i	0.602500	+	0.249564i
$505$		0			0
$506$		−	0.0987858i		−	0.00439156i
$507$	1.01324	+	2.44618i	0.0449996	+	0.108639i
$508$	0.00738938	−	0.00738938i	0.000327851	−	0.000327851i
$509$	−2.52868			−0.112082			−0.0560409	−	0.998428i	$-0.517848\pi$
$509$	−2.52868			−0.112082			−0.0560409	+	0.998428i	$0.517848\pi$
$510$		0			0
$511$	23.4055			1.03540
$512$	12.4437	−	12.4437i	0.549940	−	0.549940i
$513$	11.3783	+	27.4697i	0.502365	+	1.21282i
$514$		−	30.0711i		−	1.32638i
$515$		0			0
$516$	−8.01017	−	3.31792i	−0.352628	−	0.146063i
$517$	−0.297412	−	0.123192i	−0.0130801	−	0.00541797i
$518$	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	0.577755	−	0.816210i	$-0.303929\pi$
$521$	9.33885	+	3.86828i	0.409142	+	0.169472i	−0.168613	+	0.985682i	$0.553929\pi$
$522$	1.77373	−	0.734701i	0.0776339	−	0.0321570i
$523$	5.80494			0.253833			0.126916	−	0.991913i	$-0.459492\pi$
$523$	5.80494			0.253833			0.126916	+	0.991913i	$0.459492\pi$
$524$	9.53530	−	3.94965i	0.416552	−	0.172541i
$525$		0			0
$526$	−39.2371			−1.71082
$527$	1.79043	−	5.41948i	0.0779925	−	0.236076i
$528$		−	0.178119i		−	0.00775164i
$529$	15.4958	+	15.4958i	0.673728	+	0.673728i
$530$		0			0
$531$			12.8809i			0.558985i
$532$	−39.5595	+	16.3861i	−1.71512	+	0.710427i
$533$	−7.63200	+	18.4253i	−0.330579	+	0.798087i
$534$	−4.85658	+	11.7248i	−0.210165	+	0.507382i
$535$		0			0
$536$	−0.864387	+	0.864387i	−0.0373358	+	0.0373358i
$537$	8.80926	+	3.64892i	0.380148	+	0.157462i
$538$	16.0133	−	38.6596i	0.690384	−	1.66674i
$539$	0.238126	+	0.574887i	0.0102568	+	0.0247621i
$540$		0			0
$541$	39.1174	−	16.2030i	1.68179	−	0.696620i	0.682380	−	0.730998i	$-0.260945\pi$
$541$	39.1174	−	16.2030i	1.68179	−	0.696620i	0.999409	+	0.0343783i	$0.0109451\pi$
$542$	−5.05141	+	5.05141i	−0.216976	+	0.216976i
$543$		−	1.40627i		−	0.0603487i
$544$	1.89149	+	25.6469i	0.0810971	+	1.09960i
$545$		0			0
$546$	11.5376	+	11.5376i	0.493766	+	0.493766i
$547$	7.65599	+	18.4832i	0.327347	+	0.790285i	0.998788	+	0.0492266i	$0.0156757\pi$
$547$	7.65599	+	18.4832i	0.327347	+	0.790285i	−0.671441	+	0.741058i	$0.734324\pi$
$548$	−2.81695			−0.120334
$549$	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
$557$	−25.8965			−1.09727			−0.548636	−	0.836062i	$-0.684853\pi$
$557$	−25.8965			−1.09727			−0.548636	+	0.836062i	$0.684853\pi$
$558$	2.41718	+	5.83560i	0.102328	+	0.247041i
$559$	−21.3791	−	21.3791i	−0.904240	−	0.904240i
$560$		0			0
$561$	0.112755	+	0.0972653i	0.00476050	+	0.00410655i
$562$		−	8.43299i		−	0.355724i
$563$	19.8208	−	19.8208i	0.835349	−	0.835349i	−0.152894	−	0.988243i	$-0.548859\pi$
$563$	19.8208	−	19.8208i	0.835349	−	0.835349i	0.988243	+	0.152894i	$0.0488593\pi$
$564$	4.91421	−	2.03553i	0.206925	−	0.0857113i
$565$		0			0
$566$	6.01248	+	14.5154i	0.252724	+	0.610129i
$567$	8.24956	−	19.9162i	0.346449	−	0.836402i
$568$	5.15331	+	2.13457i	0.216228	+	0.0895645i
$569$	27.7130	−	27.7130i	1.16179	−	1.16179i	0.177706	−	0.984084i	$-0.443132\pi$
$569$	27.7130	−	27.7130i	1.16179	−	1.16179i	0.984084	−	0.177706i	$-0.0568675\pi$
$570$		0			0
$571$	1.48008	−	3.57322i	0.0619392	−	0.149535i	−0.889880	−	0.456196i	$-0.849212\pi$
$571$	1.48008	−	3.57322i	0.0619392	−	0.149535i	0.951819	+	0.306661i	$0.0992118\pi$
$572$	−0.0766411	+	0.185028i	−0.00320452	+	0.00773641i
$573$	−1.95786	+	0.810972i	−0.0817908	+	0.0338788i
$574$		−	51.6918i		−	2.15757i
$575$		0			0
$576$	−2.50055	−	2.50055i	−0.104190	−	0.104190i
$577$			14.4808i			0.602845i	0.953491	+	0.301423i	$0.0974615\pi$
$577$			14.4808i			0.602845i	−0.953491	+	0.301423i	$0.902539\pi$
$578$	−24.6573	−	18.2881i	−1.02561	−	0.760684i
$579$	−14.1999			−0.590128
$580$		0			0
$581$	−26.1949	+	10.8503i	−1.08675	+	0.450145i
$582$	−23.8810			−0.989898
$583$	−0.585099	+	0.242356i	−0.0242323	+	0.0100374i
$584$	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	0.996422	−	0.0845171i	$-0.0269347\pi$
$587$	22.0937	+	22.0937i	0.911905	+	0.911905i	−0.0845171	+	0.996422i	$0.526935\pi$
$588$	−9.49900	−	3.93462i	−0.391732	−	0.162261i
$589$	10.0017	+	4.14284i	0.412113	+	0.170703i
$590$		0			0
$591$			12.5452i			0.516041i
$592$	0.635939	+	1.53529i	0.0261369	+	0.0631002i
$593$	1.41805	−	1.41805i	0.0582323	−	0.0582323i	−0.677391	−	0.735623i	$-0.736889\pi$
$593$	1.41805	−	1.41805i	0.0582323	−	0.0582323i	0.735623	+	0.677391i	$0.236889\pi$
$594$	−0.360452			−0.0147895
$595$		0			0
$596$	12.8416			0.526012
$597$	12.9720	−	12.9720i	0.530907	−	0.530907i
$598$	2.17825	+	5.25876i	0.0890753	+	0.215047i
$599$		−	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	−0.496993	−	0.867755i	$-0.665562\pi$
$601$	−35.8417	−	14.8461i	−1.46201	−	0.605586i	−0.965022	+	0.262168i	$0.915562\pi$
$602$	72.4007	+	29.9894i	2.95083	+	1.22228i
$603$	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
$607$	26.7496	−	11.0800i	1.08573	−	0.449725i	0.233215	−	0.972425i	$-0.425075\pi$
$607$	26.7496	−	11.0800i	1.08573	−	0.449725i	0.852516	+	0.522701i	$0.175075\pi$
$608$	−48.7774			−1.97818
$609$	1.16108	−	0.480936i	0.0470494	−	0.0194885i
$610$		0			0
$611$	18.5488			0.750405
$612$	13.1019	−	0.966284i	0.529613	−	0.0390597i
$613$		−	9.10707i		−	0.367831i	−0.982942	−	0.183915i	$-0.941123\pi$
$613$		−	9.10707i		−	0.367831i	0.982942	−	0.183915i	$-0.0588773\pi$
$614$	−3.65335	−	3.65335i	−0.147437	−	0.147437i
$615$		0			0
$616$			0.304197i			0.0122564i
$617$	4.67068	−	1.93466i	0.188035	−	0.0778864i	−0.286680	−	0.958027i	$-0.592551\pi$
$617$	4.67068	−	1.93466i	0.188035	−	0.0778864i	0.474714	+	0.880140i	$0.342551\pi$
$618$	3.28639	−	7.93404i	0.132198	−	0.319154i
$619$	−6.45177	+	15.5760i	−0.259319	+	0.626051i	−0.998894	−	0.0470233i	$-0.985026\pi$
$619$	−6.45177	+	15.5760i	−0.259319	+	0.626051i	0.739575	+	0.673074i	$0.235026\pi$
$620$		0			0
$621$	−2.80122	+	2.80122i	−0.112409	+	0.112409i
$622$	34.1982	+	14.1654i	1.37122	+	0.567979i
$623$	16.9746	−	40.9803i	0.680074	−	1.64184i
$624$	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
$628$			11.8690i			0.473625i
$629$	−1.31915	−	0.435808i	−0.0525981	−	0.0173768i
$630$		0			0
$631$	1.91845	+	1.91845i	0.0763722	+	0.0763722i	0.744261	−	0.667889i	$-0.232802\pi$
$631$	1.91845	+	1.91845i	0.0763722	+	0.0763722i	−0.667889	+	0.744261i	$0.732802\pi$
$632$	−5.09809	−	12.3079i	−0.202791	−	0.489581i
$633$	−5.36965			−0.213424
$634$	−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	−0.997215	−	0.0745739i	$-0.976240\pi$
$641$	−8.72988	−	21.0758i	−0.344809	−	0.832443i	0.652406	−	0.757870i	$-0.273760\pi$
$642$	18.3118			0.722711
$643$	7.37702	+	17.8097i	0.290921	+	0.702346i	0.999996	−	0.00278691i	$-0.000887101\pi$
$643$	7.37702	+	17.8097i	0.290921	+	0.702346i	−0.709075	+	0.705133i	$0.750887\pi$
$644$	−4.03408	−	4.03408i	−0.158965	−	0.158965i
$645$		0			0
$646$	38.0335	−	44.0903i	1.49641	−	1.73471i
$647$			12.8098i			0.503606i	0.967778	+	0.251803i	$0.0810235\pi$
$647$			12.8098i			0.503606i	−0.967778	+	0.251803i	$0.918976\pi$
$648$	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
$652$	6.00577	−	14.4992i	0.235204	−	0.567833i
$653$	38.5442	+	15.9656i	1.50835	+	0.624780i	0.975217	−	0.221249i	$-0.0710135\pi$
$653$	38.5442	+	15.9656i	1.50835	+	0.624780i	0.533136	+	0.846030i	$0.321013\pi$
$654$	−4.17095	+	4.17095i	−0.163097	+	0.163097i
$655$		0			0
$656$	12.4427	−	30.0392i	0.485804	−	1.17284i
$657$	5.21244	−	12.5840i	0.203357	−	0.490947i
$658$	−44.4175	+	18.3983i	−1.73158	+	0.717242i
$659$		−	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	0.214794	−	0.976659i	$-0.431092\pi$
$661$	−19.5875	−	19.5875i	−0.761865	−	0.761865i	−0.976659	+	0.214794i	$0.931092\pi$
$662$		−	27.4958i		−	1.06865i
$663$	−8.14710	−	2.69156i	−0.316407	−	0.104531i
$664$	−8.71419			−0.338176
$665$		0			0
$666$	1.42044	−	0.588365i	0.0550409	−	0.0227987i
$667$	0.438413			0.0169754
$668$	14.6823	−	6.08161i	0.568076	−	0.235305i
$669$	−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
$673$	−33.4517	−	13.8561i	−1.28947	−	0.534115i	−0.370640	−	0.928777i	$-0.620862\pi$
$673$	−33.4517	−	13.8561i	−1.28947	−	0.534115i	−0.918826	+	0.394662i	$0.870862\pi$
$674$	19.1423	+	7.92902i	0.737336	+	0.305414i
$675$		0			0
$676$			4.85355i			0.186675i
$677$	6.54992	+	15.8129i	0.251734	+	0.607739i	0.998344	−	0.0575224i	$-0.0183201\pi$
$677$	6.54992	+	15.8129i	0.251734	+	0.607739i	−0.746610	+	0.665262i	$0.768320\pi$
$678$	−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
$683$	−3.38683	−	8.17654i	−0.129594	−	0.312866i	0.845743	−	0.533591i	$-0.179158\pi$
$683$	−3.38683	−	8.17654i	−0.129594	−	0.312866i	−0.975336	+	0.220725i	$0.929158\pi$
$684$			24.9183i			0.952776i
$685$		0			0
$686$	35.1501	+	14.5596i	1.34204	+	0.555890i
$687$	−13.1232	−	5.43580i	−0.500680	−	0.207389i
$688$	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	0.407121	−	0.913374i	$-0.366533\pi$
$691$	1.29190	+	0.535121i	0.0491461	+	0.0203570i	−0.357975	+	0.933731i	$0.616533\pi$
$692$	−14.2093	+	5.88570i	−0.540158	+	0.223741i
$693$	0.575985			0.0218799
$694$	−24.9993	+	10.3551i	−0.948962	+	0.393073i
$695$		0			0
$696$	0.386254			0.0146409
$697$	12.2212	+	24.2801i	0.462910	+	0.919673i
$698$		−	8.19245i		−	0.310089i
$699$	1.48775	+	1.48775i	0.0562720	+	0.0562720i
$700$		0			0
$701$			2.36331i			0.0892608i	0.999004	+	0.0446304i	$0.0142110\pi$
$701$			2.36331i			0.0892608i	−0.999004	+	0.0446304i	$0.985789\pi$
$702$	19.1883	−	7.94805i	0.724215	−	0.299980i
$703$	1.00841	−	2.43451i	0.0380327	−	0.0918191i
$704$	0.0281182	−	0.0678834i	0.00105975	−	0.00255845i
$705$		0			0
$706$	9.85100	−	9.85100i	0.370747	−	0.370747i
$707$	−53.3221	−	22.0867i	−2.00538	−	0.830657i
$708$	1.69231	−	4.08560i	0.0636009	−	0.153546i
$709$	−12.4474	−	30.0507i	−0.467472	−	1.12858i	−0.965263	−	0.261280i	$-0.915855\pi$
$709$	−12.4474	−	30.0507i	−0.467472	−	1.12858i	0.497791	−	0.867297i	$-0.334145\pi$
$710$		0			0
$711$	−23.3045	+	9.65306i	−0.873988	+	0.362018i
$712$	9.63987	−	9.63987i	0.361270	−	0.361270i
$713$			1.44239i			0.0540179i
$714$	22.1790	−	1.63573i	0.830028	−	0.0612158i
$715$		0			0
$716$	12.3594	+	12.3594i	0.461891	+	0.461891i
$717$	1.30067	+	3.14009i	0.0485743	+	0.117269i
$718$	19.9154			0.743237
$719$	6.28758	+	15.1796i	0.234487	+	0.566102i	0.996695	−	0.0812299i	$-0.0258848\pi$
$719$	6.28758	+	15.1796i	0.234487	+	0.566102i	−0.762208	+	0.647332i	$0.775885\pi$
$720$		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
$727$	−32.4709			−1.20428			−0.602139	−	0.798391i	$-0.705685\pi$
$727$	−32.4709			−1.20428			−0.602139	+	0.798391i	$0.705685\pi$
$728$	−6.70761	−	16.1936i	−0.248600	−	0.600175i
$729$	−3.32256	−	3.32256i	−0.123058	−	0.123058i
$730$		0			0
$731$	−41.0974	+	3.03099i	−1.52004	+	0.112105i
$732$		−	5.17939i		−	0.191436i
$733$	−6.10533	+	6.10533i	−0.225506	+	0.225506i	−0.810812	−	0.585307i	$-0.800974\pi$
$733$	−6.10533	+	6.10533i	−0.225506	+	0.225506i	0.585307	+	0.810812i	$0.300974\pi$
$734$	−26.7415	+	11.0767i	−0.987048	+	0.408849i
$735$		0			0
$736$	−2.48704	−	6.00424i	−0.0916734	−	0.221319i
$737$	−0.0184042	+	0.0444317i	−0.000677928	+	0.00163666i
$738$	−27.7920	−	11.5118i	−1.02304	−	0.423756i
$739$	7.49715	−	7.49715i	0.275787	−	0.275787i	−0.555637	−	0.831425i	$-0.687526\pi$
$739$	7.49715	−	7.49715i	0.275787	−	0.275787i	0.831425	+	0.555637i	$0.187526\pi$
$740$		0			0
$741$	6.22792	−	15.0355i	0.228788	−	0.552344i
$742$	−36.1951	+	87.3827i	−1.32876	+	3.20792i
$743$	−20.6417	+	8.55008i	−0.757272	+	0.313672i	−0.727705	−	0.685891i	$-0.759413\pi$
$743$	−20.6417	+	8.55008i	−0.757272	+	0.313672i	−0.0295670	+	0.999563i	$0.509413\pi$
$744$			1.27079i			0.0465893i
$745$		0			0
$746$	13.0886	+	13.0886i	0.479206	+	0.479206i
$747$			16.5000i			0.603704i
$748$	0.122726	+	0.243822i	0.00448730	+	0.00891502i
$749$	−64.0032			−2.33863
$750$		0			0
$751$	6.59640	−	2.73232i	0.240706	−	0.0997037i	−0.259069	−	0.965859i	$-0.583416\pi$
$751$	6.59640	−	2.73232i	0.240706	−	0.0997037i	0.499775	+	0.866155i	$0.333416\pi$
$752$	−30.2406			−1.10276
$753$	−5.81047	+	2.40678i	−0.211745	+	0.0877078i
$754$	−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	0.899731	−	0.436444i	$-0.143762\pi$
$757$	12.7467	+	12.7467i	0.463287	+	0.463287i	−0.436444	+	0.899731i	$0.643762\pi$
$758$	23.2770	+	9.64166i	0.845460	+	0.350201i
$759$	−0.0347671	−	0.0144010i	−0.00126197	−	0.000522724i
$760$		0			0
$761$			49.9437i			1.81046i	0.424923	+	0.905230i	$0.360301\pi$
$761$			49.9437i			1.81046i	−0.424923	+	0.905230i	$0.639699\pi$
$762$	−0.00393961	−	0.00951106i	−0.000142717	−	0.000344549i
$763$	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
$768$	−5.46561	−	13.1952i	−0.197223	−	0.476139i
$769$			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
$772$	−24.0485	−	9.96120i	−0.865523	−	0.358511i
$773$	−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
$777$	0.929820	−	0.385144i	0.0333571	−	0.0138170i
$778$	64.6771			2.31879
$779$	−47.6330	+	19.7302i	−1.70663	+	0.706909i
$780$		0			0
$781$	0.219445			0.00785234
$782$	7.36651	+	2.43367i	0.263426	+	0.0870280i
$783$		−	1.59969i		−	0.0571683i
$784$	41.3334	+	41.3334i	1.47619	+	1.47619i
$785$		0			0
$786$		−	10.1674i		−	0.362659i
$787$	−18.3283	+	7.59181i	−0.653332	+	0.270619i	−0.684630	−	0.728891i	$-0.740036\pi$
$787$	−18.3283	+	7.59181i	−0.653332	+	0.270619i	0.0312976	+	0.999510i	$0.490036\pi$
$788$	−8.80043	+	21.2461i	−0.313502	+	0.756861i
$789$	−5.72000	+	13.8093i	−0.203637	+	0.491624i
$790$		0			0
$791$	9.25147	−	9.25147i	0.328944	−	0.328944i
$792$	0.163551	+	0.0677450i	0.00581152	+	0.00240721i
$793$	6.91188	−	16.6868i	0.245448	−	0.592564i
$794$	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	$0.218598\pi$
$798$			42.1819i			1.49322i
$799$	16.5135	−	19.1432i	0.584205	−	0.677238i
$800$		0			0
$801$	−18.2528	−	18.2528i	−0.644929	−	0.644929i
$802$	−25.3886	−	61.2935i	−0.896502	−	2.16435i
$803$	0.283008			0.00998714
$804$	−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	0.565335	+	0.824862i	$0.308747\pi$
$809$	−11.8801	+	28.6811i	−0.417683	+	1.00838i	−0.983017	+	0.183513i	$0.941253\pi$
$810$		0			0
$811$	−17.9749	−	43.3953i	−0.631185	−	1.52382i	−0.838134	−	0.545464i	$-0.816353\pi$
$811$	−17.9749	−	43.3953i	−0.631185	−	1.52382i	0.206949	−	0.978352i	$-0.433647\pi$
$812$	2.30374			0.0808455
$813$	1.04142	+	2.51421i	0.0365242	+	0.0881773i
$814$	0.0225886	+	0.0225886i	0.000791730	+	0.000791730i
$815$		0			0
$816$	13.2824	+	4.38812i	0.464979	+	0.153615i
$817$		−	78.1626i		−	2.73456i
$818$	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	0.995376	−	0.0960527i	$-0.0306217\pi$
$821$	6.40739	+	15.4688i	0.223619	+	0.539865i	−0.771757	+	0.635918i	$0.780622\pi$
$822$	−1.06196	+	2.56381i	−0.0370402	+	0.0894231i
$823$	24.5749	+	10.1792i	0.856626	+	0.354826i	0.767387	−	0.641184i	$-0.221557\pi$
$823$	24.5749	+	10.1792i	0.856626	+	0.354826i	0.0892387	+	0.996010i	$0.471557\pi$
$824$	−6.52318	+	6.52318i	−0.227246	+	0.227246i
$825$		0			0
$826$	−15.2961	+	36.9281i	−0.532220	+	1.28489i
$827$	−13.1970	+	31.8605i	−0.458906	+	1.10790i	0.509934	+	0.860213i	$0.329670\pi$
$827$	−13.1970	+	31.8605i	−0.458906	+	1.10790i	−0.968841	+	0.247684i	$0.920330\pi$
$828$	−3.06731	+	1.27052i	−0.106597	+	0.0441537i
$829$		−	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
$832$			4.23372i			0.146778i
$833$	−48.7361	+	3.59436i	−1.68861	+	0.124537i
$834$	−24.5170			−0.848956
$835$		0			0
$836$	−0.478334	+	0.198133i	−0.0165435	+	0.00685256i
$837$	5.26302			0.181917
$838$	−36.4802	+	15.1106i	−1.26019	+	0.521987i
$839$	32.8053	+	13.5884i	1.13257	+	0.469124i	0.868652	−	0.495422i	$-0.164987\pi$
$839$	32.8053	+	13.5884i	1.13257	+	0.469124i	0.263913	+	0.964546i	$0.414987\pi$
$840$		0			0
$841$	20.3809	−	20.3809i	0.702790	−	0.702790i
$842$	−26.3187	−	26.3187i	−0.907001	−	0.907001i
$843$	−2.96795	−	1.22936i	−0.102222	−	0.0423415i
$844$	−9.09385	−	3.76680i	−0.313023	−	0.129658i
$845$		0			0
$846$			27.9784i			0.961916i
$847$	−18.2728	−	44.1146i	−0.627862	−	1.51579i
$848$	−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
$853$	−0.0913933	−	0.220643i	−0.00312925	−	0.00755467i	0.922307	−	0.386458i	$-0.126301\pi$
$853$	−0.0913933	−	0.220643i	−0.00312925	−	0.00755467i	−0.925436	+	0.378903i	$0.876301\pi$
$854$			46.8144i			1.60196i
$855$		0			0
$856$	−18.1737	−	7.52779i	−0.621164	−	0.257295i
$857$	−16.8099	−	6.96291i	−0.574217	−	0.237848i	0.0766273	−	0.997060i	$-0.475585\pi$
$857$	−16.8099	−	6.96291i	−0.574217	−	0.237848i	−0.650844	+	0.759211i	$0.725585\pi$
$858$	0.139507	+	0.139507i	0.00476271	+	0.00476271i
$859$	14.2525	−	14.2525i	0.486288	−	0.486288i	−0.420845	−	0.907133i	$-0.638266\pi$
$859$	14.2525	−	14.2525i	0.486288	−	0.486288i	0.907133	+	0.420845i	$0.138266\pi$
$860$		0			0
$861$	−18.1927	−	7.53565i	−0.620004	−	0.256814i
$862$	37.2134	−	15.4143i	1.26749	−	0.525013i
$863$	−14.7597			−0.502424			−0.251212	−	0.967932i	$-0.580829\pi$
$863$	−14.7597			−0.502424			−0.251212	+	0.967932i	$0.580829\pi$
$864$	−21.9084	+	9.07476i	−0.745339	+	0.308730i
$865$		0			0
$866$	16.1284			0.548064
$867$	−10.0309	+	6.01196i	−0.340669	+	0.204177i
$868$			7.57936i			0.257260i
$869$	−0.370602	−	0.370602i	−0.0125718	−	0.0125718i
$870$		0			0
$871$		−	2.77109i		−	0.0938949i
$872$	5.85411	−	2.42485i	0.198245	−	0.0821158i
$873$	18.5885	−	44.8766i	0.629126	−	1.51884i
$874$	−5.63121	+	13.5950i	−0.190479	+	0.459856i
$875$		0			0
$876$	−3.30658	+	3.30658i	−0.111719	+	0.111719i
$877$	39.5030	+	16.3627i	1.33392	+	0.552528i	0.931771	−	0.363046i	$-0.118263\pi$
$877$	39.5030	+	16.3627i	1.33392	+	0.552528i	0.402149	+	0.915574i	$0.368263\pi$
$878$	−15.3860	+	37.1450i	−0.519251	+	1.25358i
$879$	−0.194571	−	0.469737i	−0.00656273	−	0.0158438i
$880$		0			0
$881$	−40.3580	+	16.7168i	−1.35970	+	0.563205i	−0.938975	−	0.343985i	$-0.888223\pi$
$881$	−40.3580	+	16.7168i	−1.35970	+	0.563205i	−0.420721	+	0.907190i	$0.638223\pi$
$882$	38.2412	−	38.2412i	1.28765	−	1.28765i
$883$		−	41.4824i		−	1.39599i	−0.716101	−	0.697997i	$-0.754075\pi$
$883$		−	41.4824i		−	1.39599i	0.716101	−	0.697997i	$-0.245925\pi$
$884$	−11.9095	−	10.2735i	−0.400561	−	0.345535i
$885$		0			0
$886$	7.88394	+	7.88394i	0.264866	+	0.264866i
$887$	12.5826	+	30.3770i	0.422481	+	1.01996i	0.981613	+	0.190881i	$0.0611344\pi$
$887$	12.5826	+	30.3770i	0.422481	+	1.01996i	−0.559132	+	0.829078i	$0.688866\pi$
$888$	0.309321			0.0103801
$889$	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
$897$	2.16834			0.0723988
$898$	20.9381	+	50.5491i	0.698714	+	1.68685i
$899$	−0.411852	−	0.411852i	−0.0137360	−	0.0137360i
$900$		0			0
$901$	−3.65820	−	49.6018i	−0.121872	−	1.65248i
$902$		−	0.625031i		−	0.0208113i
$903$	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
$907$	−13.9479	+	33.6731i	−0.463131	+	1.11810i	0.503973	+	0.863719i	$0.331871\pi$
$907$	−13.9479	+	33.6731i	−0.463131	+	1.11810i	−0.967105	+	0.254379i	$0.918129\pi$
$908$	−13.0613	−	5.41015i	−0.433453	−	0.179542i
$909$	−23.7498	+	23.7498i	−0.787731	+	0.787731i
$910$		0			0
$911$	−11.4322	+	27.5999i	−0.378767	+	0.914425i	0.613430	+	0.789749i	$0.289789\pi$
$911$	−11.4322	+	27.5999i	−0.378767	+	0.914425i	−0.992197	+	0.124676i	$0.960211\pi$
$912$	−10.1535	+	24.5128i	−0.336218	+	0.811701i
$913$	−0.316736	+	0.131196i	−0.0104824	+	0.00434196i
$914$			46.1852i			1.52767i
$915$		0			0
$916$	−18.4117	−	18.4117i	−0.608341	−	0.608341i
$917$			35.5369i			1.17353i
$918$	8.88004	−	26.8791i	0.293085	−	0.887143i
$919$	−11.6218			−0.383368			−0.191684	−	0.981457i	$-0.561395\pi$
$919$	−11.6218			−0.383368			−0.191684	+	0.981457i	$0.561395\pi$
$920$		0			0
$921$	−1.81836	+	0.753191i	−0.0599171	+	0.0248185i
$922$	−25.3837			−0.835966
$923$	−11.6819	+	4.83880i	−0.384515	+	0.159271i
$924$	−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
$928$	2.42455	+	1.00428i	0.0795899	+	0.0329672i
$929$	4.65849	+	1.92961i	0.152840	+	0.0633085i	0.457792	−	0.889059i	$-0.348640\pi$
$929$	4.65849	+	1.92961i	0.152840	+	0.0633085i	−0.304952	+	0.952368i	$0.598640\pi$
$930$		0			0
$931$		−	92.6904i		−	3.03781i
$932$	1.47595	+	3.56326i	0.0483464	+	0.116718i
$933$	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	$0.443156\pi$
$938$	2.74861	+	6.63574i	0.0897454	+	0.216665i
$939$			5.82351i			0.190043i
$940$		0			0
$941$	10.2169	+	4.23196i	0.333060	+	0.137958i	0.542945	−	0.839768i	$-0.317309\pi$
$941$	10.2169	+	4.23196i	0.333060	+	0.137958i	−0.209885	+	0.977726i	$0.567309\pi$
$942$	10.8024	+	4.47450i	0.351961	+	0.145787i
$943$	−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
$947$	−10.6171	+	4.39774i	−0.345008	+	0.142907i	−0.548458	−	0.836178i	$-0.684785\pi$
$947$	−10.6171	+	4.39774i	−0.345008	+	0.142907i	0.203449	+	0.979086i	$0.434785\pi$
$948$	8.66000			0.281264
$949$	−15.0657	+	6.24040i	−0.489052	+	0.202572i
$950$		0			0
$951$	−14.5094			−0.470500
$952$	−22.6841	−	7.49414i	−0.735196	−	0.242887i
$953$			0.704896i			0.0228338i	0.999935	+	0.0114169i	$0.00363419\pi$
$953$			0.704896i			0.0228338i	−0.999935	+	0.0114169i	$0.996366\pi$
$954$	38.9205	+	38.9205i	1.26010	+	1.26010i
$955$		0			0
$956$			6.23035i			0.201504i
$957$	0.0140392	−	0.00581524i	0.000453824	−	0.000187980i
$958$	−18.4856	+	44.6282i	−0.597243	+	1.44187i
$959$	3.71176	−	8.96097i	0.119859	−	0.289365i
$960$		0			0
$961$	−20.5653	+	20.5653i	−0.663397	+	0.663397i
$962$	−1.70057	−	0.704397i	−0.0548284	−	0.0227107i
$963$	−14.2536	+	34.4112i	−0.459316	+	1.10889i
$964$	−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	$0.472072\pi$
$968$		−	14.6755i		−	0.471688i
$969$	−9.97281	−	19.8132i	−0.320373	−	0.636492i
$970$		0			0
$971$	30.5851	+	30.5851i	0.981521	+	0.981521i	0.999832	−	0.0183111i	$-0.00582892\pi$
$971$	30.5851	+	30.5851i	0.981521	+	0.981521i	−0.0183111	+	0.999832i	$0.505829\pi$
$972$	7.15235	+	17.2673i	0.229412	+	0.553849i
$973$	85.6915			2.74714
$974$	−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	$-0.964353\pi$
$977$	−34.5543	−	34.5543i	−1.10549	−	1.10549i	−0.111753	−	0.993736i	$-0.535647\pi$
$978$	−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
$982$	−14.0671			−0.448898
$983$	18.7068	+	45.1621i	0.596653	+	1.44045i	0.876972	+	0.480542i	$0.159560\pi$
$983$	18.7068	+	45.1621i	0.596653	+	1.44045i	−0.280318	+	0.959907i	$0.590440\pi$
$984$	−4.27949	−	4.27949i	−0.136425	−	0.136425i
$985$		0			0
$986$	−2.79829	+	1.40850i	−0.0891158	+	0.0448557i
$987$			18.3146i			0.582961i
$988$	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	0.987266	−	0.159076i	$-0.0508515\pi$
$991$	5.56191	+	13.4276i	0.176680	+	0.426543i	−0.810586	+	0.585619i	$0.800851\pi$
$992$	−3.30411	+	7.97684i	−0.104906	+	0.253265i
$993$	−9.67699	−	4.00834i	−0.307090	−	0.127201i
$994$	23.1743	−	23.1743i	0.735044	−	0.735044i
$995$		0			0
$996$	2.16779	−	5.23350i	0.0686890	−	0.165830i
$997$	16.9161	−	40.8392i	0.535740	−	1.29339i	−0.391933	−	0.919994i	$-0.628193\pi$
$997$	16.9161	−	40.8392i	0.535740	−	1.29339i	0.927672	−	0.373396i	$-0.121807\pi$
$998$	14.6777	−	6.07971i	0.464615	−	0.192450i
$999$		−	1.28107i		−	0.0405312i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	425.2.n.c.274.5		24
5.2	odd	4		425.2.m.b.376.5		24
5.3	odd	4		85.2.l.a.36.2	yes	24
5.4	even	2		425.2.n.f.274.2		24
15.8	even	4		765.2.be.b.631.5		24
17.9	even	8		425.2.n.f.349.2		24
85.3	even	16		1445.2.a.p.1.3		12
85.9	even	8	inner	425.2.n.c.349.5		24
85.37	even	16		7225.2.a.bs.1.10		12
85.43	odd	8		85.2.l.a.26.2	✓	24
85.48	even	16		1445.2.a.q.1.3		12
85.63	even	16		1445.2.d.j.866.20		24
85.73	even	16		1445.2.d.j.866.19		24
85.77	odd	8		425.2.m.b.26.5		24
85.82	even	16		7225.2.a.bq.1.10		12
255.128	even	8		765.2.be.b.451.5		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
85.2.l.a.26.2	✓	24	85.43	odd	8
85.2.l.a.36.2	yes	24	5.3	odd	4
425.2.m.b.26.5		24	85.77	odd	8
425.2.m.b.376.5		24	5.2	odd	4
425.2.n.c.274.5		24	1.1	even	1	trivial
425.2.n.c.349.5		24	85.9	even	8	inner
425.2.n.f.274.2		24	5.4	even	2
425.2.n.f.349.2		24	17.9	even	8
765.2.be.b.451.5		24	255.128	even	8
765.2.be.b.631.5		24	15.8	even	4
1445.2.a.p.1.3		12	85.3	even	16
1445.2.a.q.1.3		12	85.48	even	16
1445.2.d.j.866.19		24	85.73	even	16
1445.2.d.j.866.20		24	85.63	even	16
7225.2.a.bq.1.10		12	85.82	even	16
7225.2.a.bs.1.10		12	85.37	even	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 425 = 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	425.n (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.27691 - 1.27691i) q^{2} +(-0.263254 - 0.635552i) q^{3} -1.26102i q^{4} +(-1.14770 - 0.475393i) q^{6} +(4.01142 + 1.66158i) q^{7} +(0.943613 + 0.943613i) q^{8} +(1.78670 - 1.78670i) q^{9} +(0.0485041 + 0.0200910i) q^{11} +(-0.801445 + 0.331970i) q^{12} -3.02508 q^{13} +(7.24394 - 3.00054i) q^{14} +4.93187 q^{16} +(-2.69314 + 3.12202i) q^{17} -4.56292i q^{18} +(-5.52988 - 5.52988i) q^{19} -2.98689i q^{21} +(0.0875901 - 0.0362810i) q^{22} +(0.398744 - 0.962654i) q^{23} +(0.351305 - 0.848125i) q^{24} +(-3.86277 + 3.86277i) q^{26} +(-3.51255 - 1.45495i) q^{27} +(2.09529 - 5.05848i) q^{28} +(0.161016 + 0.388726i) q^{29} +(-1.27892 + 0.529745i) q^{31} +(4.41035 - 4.41035i) q^{32} -0.0361159i q^{33} +(0.547638 + 7.42546i) q^{34} +(-2.25306 - 2.25306i) q^{36} +(0.128945 + 0.311301i) q^{37} -14.1224 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} -6.13168 q^{47} +(-1.29834 - 3.13446i) q^{48} +(8.38087 + 8.38087i) q^{49} +(2.69319 + 0.889748i) q^{51} +3.81469i q^{52} +(-8.52974 + 8.52974i) q^{53} +(-6.34307 + 2.62739i) q^{54} +(2.21733 + 5.35312i) q^{56} +(-2.05876 + 4.97030i) q^{57} +(0.701974 + 0.290767i) q^{58} +(-3.60468 + 3.60468i) q^{59} +(-2.28486 + 5.51614i) q^{61} +(-0.956630 + 2.30951i) q^{62} +(10.1359 - 4.19844i) q^{63} -1.39954i q^{64} +(-0.0461170 - 0.0461170i) q^{66} +0.916040i q^{67} +(3.93693 + 3.39611i) q^{68} -0.716788 q^{69} +(3.86169 - 1.59956i) q^{71} +3.37190 q^{72} +(4.98025 - 2.06289i) q^{73} +(0.562156 + 0.232853i) q^{74} +(-6.97330 + 6.97330i) q^{76} +(0.161187 + 0.161187i) q^{77} +(3.47188 + 1.43810i) q^{78} +(-9.22305 - 3.82031i) q^{79} -4.96488i q^{81} +(-4.55595 - 10.9990i) q^{82} +(-4.61746 + 4.61746i) q^{83} -3.76653 q^{84} +18.0487 q^{86} +(0.204668 - 0.204668i) q^{87} +(0.0268109 + 0.0647272i) q^{88} -10.2159i q^{89} +(-12.1349 - 5.02642i) q^{91} +(-1.21393 - 0.502825i) q^{92} +(0.673362 + 0.673362i) q^{93} +(-7.82963 + 7.82963i) q^{94} +(-3.96405 - 1.64196i) q^{96} +(17.7605 - 7.35663i) q^{97} +21.4033 q^{98} +(0.122559 - 0.0507655i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 8 q^{3} - 8 q^{6} + 24 q^{9} - 8 q^{11} + 40 q^{12} + 16 q^{13} - 24 q^{16} + 8 q^{19} - 24 q^{22} + 8 q^{23} + 8 q^{24} + 16 q^{26} + 16 q^{27} - 40 q^{28} + 8 q^{29} - 16 q^{34} - 24 q^{36} - 16 q^{37}+ \cdots + 8 q^{99}+O(q^{100}) \) 24 * q - 8 * q^3 - 8 * q^6 + 24 * q^9 - 8 * q^11 + 40 * q^12 + 16 * q^13 - 24 * q^16 + 8 * q^19 - 24 * q^22 + 8 * q^23 + 8 * q^24 + 16 * q^26 + 16 * q^27 - 40 * q^28 + 8 * q^29 - 16 * q^34 - 24 * q^36 - 16 * q^37 - 48 * q^38 - 8 * q^39 + 16 * q^41 - 24 * q^42 - 8 * q^43 - 16 * q^44 + 8 * q^46 - 64 * q^47 - 8 * q^48 - 56 * q^51 + 24 * q^53 + 32 * q^54 + 64 * q^56 + 16 * q^57 + 56 * q^58 - 32 * q^59 + 32 * q^61 - 32 * q^62 + 80 * q^63 + 96 * q^66 + 24 * q^68 - 96 * q^69 - 24 * q^71 - 24 * q^72 - 64 * q^73 + 64 * q^74 - 8 * q^76 + 24 * q^77 + 8 * q^78 - 16 * q^82 - 96 * q^83 + 64 * q^84 - 16 * q^86 + 48 * q^87 + 8 * q^88 - 24 * q^91 + 112 * q^92 - 64 * q^93 - 56 * q^94 - 168 * q^96 + 48 * q^97 + 120 * q^98 + 8 * q^99

Introduction

L-functions

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