LMFDB - Embedded newform 425.2.n.c.349.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [425,2,Mod(49,425)]

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([4, 3]))

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

//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);

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: 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			349.5
Character	$\chi$	$=$	425.349
Dual form			425.2.n.c.274.5

$q$-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 $\left(\mathbb{Z}/425\mathbb{Z}\right)^\times$.

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

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	0.995687	−	0.0927724i	$-0.0295729\pi$
$2$	1.27691	+	1.27691i	0.902915	+	0.902915i	−0.0927724	+	0.995687i	$0.529573\pi$
$3$	−0.263254	+	0.635552i	−0.151990	+	0.366936i	−0.981474	−	0.191594i	$-0.938634\pi$
$3$	−0.263254	+	0.635552i	−0.151990	+	0.366936i	0.829484	+	0.558530i	$0.188634\pi$
$4$			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	0.539353	−	0.842080i	$-0.318669\pi$
$7$	4.01142	−	1.66158i	1.51617	−	0.628020i	0.976821	+	0.214060i	$0.0686688\pi$
$8$	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	$0.372481\pi$
$12$	−0.801445	−	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	−0.321851	+	0.946790i	$0.604305\pi$
$19$	−5.52988	+	5.52988i	−1.26864	+	1.26864i	−0.946790	+	0.321851i	$0.895695\pi$
$20$		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	0.959984	−	0.280055i	$-0.0903527\pi$
$23$	0.398744	+	0.962654i	0.0831439	+	0.200727i	−0.876840	+	0.480782i	$0.840353\pi$
$24$	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	−0.908224	−	0.418484i	$-0.862562\pi$
$29$	0.161016	−	0.388726i	0.0298999	−	0.0721847i	0.938124	+	0.346299i	$0.112562\pi$
$30$		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
$33$			0.0361159i			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	−0.912926	−	0.408125i	$-0.866183\pi$
$37$	0.128945	−	0.311301i	0.0211984	−	0.0511775i	0.934124	+	0.356948i	$0.116183\pi$
$38$	−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	0.989057	+	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	0.0810414	−	0.996711i	$-0.474175\pi$
$43$	7.06729	−	7.06729i	1.07775	−	1.07775i	0.996711	−	0.0810414i	$-0.0258246\pi$
$44$	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	−0.981816	−	0.189834i	$-0.939205\pi$
$53$	−8.52974	−	8.52974i	−1.17165	−	1.17165i	−0.189834	−	0.981816i	$-0.560795\pi$
$54$	−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	0.432395	−	0.901684i	$-0.357669\pi$
$59$	−3.60468	−	3.60468i	−0.469290	−	0.469290i	−0.901684	+	0.432395i	$0.857669\pi$
$60$		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	$0.999844\pi$
$62$	−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	$-0.982179\pi$
$67$		−	0.916040i		−	0.111912i	0.998433	−	0.0559561i	$-0.0178207\pi$
$68$	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	0.599875	−	0.800094i	$-0.295217\pi$
$71$	3.86169	+	1.59956i	0.458298	+	0.189833i	−0.141577	+	0.989927i	$0.545217\pi$
$72$	3.37190			0.397382
$73$	4.98025	+	2.06289i	0.582895	+	0.241443i	0.654590	−	0.755984i	$-0.272841\pi$
$73$	4.98025	+	2.06289i	0.582895	+	0.241443i	−0.0716959	+	0.997427i	$0.522841\pi$
$74$	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	−0.835477	−	0.549526i	$-0.814808\pi$
$79$	−9.22305	+	3.82031i	−1.03767	+	0.429819i	−0.202198	+	0.979345i	$0.564808\pi$
$80$		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	0.406720	−	0.913553i	$-0.366672\pi$
$83$	−4.61746	−	4.61746i	−0.506833	−	0.506833i	−0.913553	+	0.406720i	$0.866672\pi$
$84$	−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	$0.182122\pi$
$89$			10.2159i			1.08289i	−0.840738	+	0.541443i	$0.817878\pi$
$90$		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	0.985091	+	0.172036i	$0.0550346\pi$
$97$	17.7605	+	7.35663i	1.80330	+	0.746952i	0.818212	+	0.574916i	$0.194965\pi$
$98$	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	$-0.889377\pi$
$103$		−	6.91299i		−	0.681157i	0.940216	−	0.340579i	$-0.110623\pi$
$104$	−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	−0.389773	−	0.920911i	$-0.627446\pi$
$107$	−13.6187	−	5.64104i	−1.31657	−	0.545339i	−0.926793	+	0.375572i	$0.877446\pi$
$108$	−1.83472	−	4.42940i	−0.176546	−	0.426220i
$109$	1.81709	+	4.38684i	0.174046	+	0.420183i	0.986698	−	0.162566i	$-0.0519770\pi$
$109$	1.81709	+	4.38684i	0.174046	+	0.420183i	−0.812652	+	0.582749i	$0.801977\pi$
$110$		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	0.968792	−	0.247875i	$-0.0797322\pi$
$113$	1.15314	+	2.78393i	0.108478	+	0.261890i	−0.860314	+	0.509765i	$0.829732\pi$
$114$	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	−0.706847	−	0.707367i	$-0.749883\pi$
$127$	0.00585984	−	0.00585984i	0.000519977	−	0.000519977i	0.707367	+	0.706847i	$0.249883\pi$
$128$	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	$0.00861380\pi$
$132$	−0.0455430			−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	$0.0304213\pi$
$137$			2.23387i			0.190852i	−0.995437	+	0.0954260i	$0.969579\pi$
$138$	−0.915277	−	0.915277i	−0.0779136	−	0.0779136i
$139$	18.2335	+	7.55257i	1.54655	+	0.640601i	0.982688	−	0.185270i	$-0.0593160\pi$
$139$	18.2335	+	7.55257i	1.54655	+	0.640601i	0.563859	+	0.825871i	$0.309316\pi$
$140$		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	$-0.863035\pi$
$149$		−	10.1835i		−	0.834263i	0.908846	−	0.417132i	$-0.136965\pi$
$150$		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	$0.0352961\pi$
$152$			10.4361i			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	0.116144	−	0.993232i	$-0.462947\pi$
$163$	11.4980	−	4.76262i	0.900592	−	0.373037i	0.784448	+	0.620195i	$0.212947\pi$
$164$	−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	−0.620008	−	0.784596i	$-0.712870\pi$
$167$	4.82277	−	11.6432i	0.373197	−	0.900977i	0.993205	−	0.116382i	$-0.0371295\pi$
$168$	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	0.641150	+	0.767416i	$0.278458\pi$
$173$	−4.66741	+	11.2681i	−0.354856	+	0.856699i	−0.996006	+	0.0892832i	$0.971542\pi$
$174$			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	0.238562	−	0.971127i	$-0.423324\pi$
$179$	−9.80106	−	9.80106i	−0.732566	−	0.732566i	−0.971127	+	0.238562i	$0.923324\pi$
$180$		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	$0.350794\pi$
$182$	−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	$0.0355498\pi$
$191$			3.08056i			0.222902i	−0.993770	+	0.111451i	$0.964450\pi$
$192$	−0.889482	−	0.368435i	−0.0641928	−	0.0265895i
$193$	7.89931	+	19.0706i	0.568605	+	1.37273i	0.902731	+	0.430205i	$0.141559\pi$
$193$	7.89931	+	19.0706i	0.568605	+	1.37273i	−0.334126	+	0.942528i	$0.608441\pi$
$194$	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	−0.891126	−	0.453756i	$-0.850084\pi$
$197$	−16.8483	+	6.97881i	−1.20039	+	0.497219i	−0.309268	+	0.950975i	$0.600084\pi$
$198$	0.0916738	+	0.221320i	0.00651497	+	0.0157285i
$199$	10.2053	−	24.6377i	0.723432	−	1.74652i	0.0601040	−	0.998192i	$-0.480857\pi$
$199$	10.2053	−	24.6377i	0.723432	−	1.74652i	0.663328	−	0.748328i	$-0.269143\pi$
$200$		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	0.992728	−	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
$217$	−6.01049			−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	0.810942	−	0.585127i	$-0.198955\pi$
$223$	3.37213	+	3.37213i	0.225815	+	0.225815i	−0.585127	+	0.810942i	$0.698955\pi$
$224$	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	0.999934	−	0.0114793i	$-0.00365405\pi$
$227$	4.29029	+	10.3577i	0.284757	+	0.687464i	−0.715177	+	0.698943i	$0.753654\pi$
$228$	6.26765	−	2.59614i	0.415085	−	0.171934i
$229$	14.6007	+	14.6007i	0.964838	+	0.964838i	0.999402	−	0.0345640i	$-0.0110043\pi$
$229$	14.6007	+	14.6007i	0.964838	+	0.964838i	−0.0345640	+	0.999402i	$0.511004\pi$
$230$		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	0.288199	−	0.957570i	$-0.406943\pi$
$233$	−2.82569	−	1.17044i	−0.185117	−	0.0766781i	−0.473317	+	0.880892i	$0.656943\pi$
$234$		−	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	0.431583	−	0.902073i	$-0.357955\pi$
$241$	1.53527	+	0.635928i	0.0988952	+	0.0409637i	−0.332687	+	0.943037i	$0.607955\pi$
$242$	−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	$0.0931670\pi$
$251$			9.14240i			0.577063i	−0.957470	+	0.288531i	$0.906833\pi$
$252$	−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	0.971507	−	0.237009i	$-0.0761671\pi$
$257$	11.7749	+	11.7749i	0.734498	+	0.734498i	−0.237009	+	0.971507i	$0.576167\pi$
$258$	−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	−0.998683	−	0.0512969i	$-0.983665\pi$
$263$	−15.3640	+	15.3640i	−0.947387	+	0.947387i	0.0512969	+	0.998683i	$0.483665\pi$
$264$	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	0.923504	−	0.383588i	$-0.125312\pi$
$269$	21.4082	+	8.86758i	1.30528	+	0.540666i	0.381779	+	0.924254i	$0.375312\pi$
$270$		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	0.798964	−	0.601378i	$-0.205382\pi$
$277$	15.6227	+	6.47115i	0.938679	+	0.388814i	0.139714	+	0.990192i	$0.455382\pi$
$278$	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	0.798707	−	0.601720i	$-0.205518\pi$
$281$	3.30210	+	3.30210i	0.196987	+	0.196987i	−0.601720	+	0.798707i	$0.705518\pi$
$282$	7.03733	−	2.91496i	0.419067	−	0.173583i
$283$	−3.32949	−	8.03809i	−0.197917	−	0.477815i	0.793497	−	0.608575i	$-0.208258\pi$
$283$	−3.32949	−	8.03809i	−0.197917	−	0.477815i	−0.991414	+	0.130760i	$0.958258\pi$
$284$	−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	$0.0260174\pi$
$307$			2.86108i			0.163290i	−0.996661	+	0.0816451i	$0.973983\pi$
$308$	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	$-0.0724038\pi$
$312$	−1.06273	−	2.56565i	−0.0601650	−	0.145251i
$313$	−7.82103	+	3.23958i	−0.442071	+	0.183112i	−0.592605	−	0.805493i	$-0.701901\pi$
$313$	−7.82103	+	3.23958i	−0.442071	+	0.183112i	0.150534	+	0.988605i	$0.451901\pi$
$314$	−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	0.971044	+	0.238900i	$0.0767867\pi$
$317$	8.07149	+	19.4863i	0.453340	+	1.09446i	−0.517704	+	0.855560i	$0.673213\pi$
$318$	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	0.938112	−	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
$333$	0.786585	−	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	−0.758017	−	0.652235i	$-0.773832\pi$
$337$	4.39079	−	10.6003i	0.239182	−	0.577435i	0.997199	+	0.0747994i	$0.0238316\pi$
$338$	−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	−0.721950	−	0.691945i	$-0.756754\pi$
$347$	−13.8437	+	5.73424i	−0.743168	+	0.307830i	−0.0212172	+	0.999775i	$0.506754\pi$
$348$	−0.258091	+	0.258091i	−0.0138351	+	0.0138351i
$349$	3.20791	+	3.20791i	0.171715	+	0.171715i	0.787733	−	0.616017i	$-0.211255\pi$
$349$	3.20791	+	3.20791i	0.171715	+	0.171715i	−0.616017	+	0.787733i	$0.711255\pi$
$350$		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	−0.470711	−	0.882287i	$-0.656003\pi$
$359$	7.79826	−	7.79826i	0.411577	−	0.411577i	0.882287	+	0.470711i	$0.156003\pi$
$360$		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	−0.734085	−	0.679058i	$-0.762389\pi$
$367$	−14.8084	+	6.13386i	−0.772995	+	0.320185i	−0.0389098	+	0.999243i	$0.512389\pi$
$368$	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	$-0.914507\pi$
$373$		−	10.2501i		−	0.530732i	0.964148	−	0.265366i	$-0.0854928\pi$
$374$	−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	−0.725401	−	0.688327i	$-0.758346\pi$
$379$	5.33919	−	12.8899i	0.274256	−	0.662112i	0.999656	+	0.0262152i	$0.00834551\pi$
$380$		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	−0.598212	−	0.801338i	$-0.704122\pi$
$383$	3.97525	−	3.97525i	0.203126	−	0.203126i	0.801338	+	0.598212i	$0.204122\pi$
$384$	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	0.345717	−	0.938339i	$-0.387636\pi$
$389$	25.3255	−	25.3255i	1.28406	−	1.28406i	0.938339	−	0.345717i	$-0.112364\pi$
$390$		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	0.882109	−	0.471046i	$-0.156123\pi$
$397$	−1.48870	−	3.59405i	−0.0747159	−	0.180380i	−0.956825	+	0.290665i	$0.906123\pi$
$398$	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	0.718890	+	0.695124i	$0.244650\pi$
$401$	14.0592	+	33.9420i	0.702085	+	1.69498i	−0.0168056	+	0.999859i	$0.505350\pi$
$402$	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	−0.816978	−	0.576669i	$-0.804352\pi$
$419$	−20.2014	+	8.36768i	−0.986901	+	0.408788i	−0.169924	+	0.985457i	$0.554352\pi$
$420$		0			0
$421$			20.6111i			1.00453i	0.864715	+	0.502263i	$0.167499\pi$
$421$			20.6111i			1.00453i	−0.864715	+	0.502263i	$0.832501\pi$
$422$	−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	0.173535	−	0.984828i	$-0.444481\pi$
$431$	20.6074	−	8.53585i	0.992621	−	0.411157i	0.819086	+	0.573670i	$0.194481\pi$
$432$	−17.3234	+	7.17561i	−0.833475	+	0.345236i
$433$	6.31536	−	6.31536i	0.303497	−	0.303497i	−0.538883	−	0.842380i	$-0.681154\pi$
$433$	6.31536	−	6.31536i	0.303497	−	0.303497i	0.842380	+	0.538883i	$0.181154\pi$
$434$	−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	−0.166663	−	0.986014i	$-0.553299\pi$
$439$	−20.5695	−	8.52016i	−0.981728	−	0.406645i	−0.815066	+	0.579369i	$0.803299\pi$
$440$		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	$-0.953144\pi$
$443$		−	6.17421i		−	0.293346i	0.989185	−	0.146673i	$-0.0468564\pi$
$444$	−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	−0.919561	−	0.392948i	$-0.871455\pi$
$449$	−11.5947	−	27.9922i	−0.547189	−	1.32103i	0.372371	−	0.928084i	$-0.378545\pi$
$450$		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	0.143662	−	0.989627i	$-0.454112\pi$
$457$	−18.0847	−	18.0847i	−0.845965	−	0.845965i	−0.989627	+	0.143662i	$0.954112\pi$
$458$			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	−0.899613	−	0.436687i	$-0.856152\pi$
$461$	−9.93945	+	9.93945i	−0.462926	+	0.462926i	0.436687	+	0.899613i	$0.356152\pi$
$462$	−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	−0.970491	−	0.241139i	$-0.922479\pi$
$467$	−15.7614	+	15.7614i	−0.729352	+	0.729352i	0.241139	+	0.970491i	$0.422479\pi$
$468$	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	−0.261681	−	0.965154i	$-0.584277\pi$
$479$	−24.7134	−	10.2366i	−1.12919	−	0.467724i	−0.867504	+	0.497430i	$0.834277\pi$
$480$		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	0.987332	+	0.158665i	$0.0507190\pi$
$487$	8.85760	+	21.3841i	0.401376	+	0.969008i	−0.585956	+	0.810343i	$0.699281\pi$
$488$	−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	−0.820389	−	0.571806i	$-0.806243\pi$
$491$	−5.50823	+	5.50823i	−0.248583	+	0.248583i	0.571806	+	0.820389i	$0.306243\pi$
$492$		−	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	−0.193262	−	0.981147i	$-0.561907\pi$
$499$	8.12796	−	3.36671i	0.363858	−	0.150715i	0.557119	+	0.830432i	$0.311907\pi$
$500$		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	−0.215325	−	0.976542i	$-0.569081\pi$
$503$	7.24271	−	3.00003i	0.322937	−	0.133765i	0.538262	+	0.842778i	$0.319081\pi$
$504$	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	−0.168613	−	0.985682i	$-0.553929\pi$
$521$	9.33885	−	3.86828i	0.409142	−	0.169472i	0.577755	+	0.816210i	$0.303929\pi$
$522$	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	0.999409	−	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
$543$			1.40627i			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	−0.671441	−	0.741058i	$-0.734324\pi$
$547$	7.65599	−	18.4832i	0.327347	−	0.790285i	0.998788	−	0.0492266i	$-0.0156757\pi$
$548$	−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	0.988243	−	0.152894i	$-0.0488593\pi$
$563$	19.8208	+	19.8208i	0.835349	+	0.835349i	−0.152894	+	0.988243i	$0.548859\pi$
$564$	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	0.984084	+	0.177706i	$0.0568675\pi$
$569$	27.7130	+	27.7130i	1.16179	+	1.16179i	0.177706	+	0.984084i	$0.443132\pi$
$570$		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	$0.849212\pi$
$572$	−0.0766411	−	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	$-0.902539\pi$
$577$		−	14.4808i		−	0.602845i	0.953491	−	0.301423i	$-0.0974615\pi$
$578$	−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	−0.0845171	−	0.996422i	$-0.526935\pi$
$587$	22.0937	−	22.0937i	0.911905	−	0.911905i	0.996422	+	0.0845171i	$0.0269347\pi$
$588$	−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	0.735623	−	0.677391i	$-0.236889\pi$
$593$	1.41805	+	1.41805i	0.0582323	+	0.0582323i	−0.677391	+	0.735623i	$0.736889\pi$
$594$	−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	$0.263467\pi$
$599$			36.0451i			1.47276i	−0.676567	+	0.736381i	$0.736533\pi$
$600$		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	$0.665562\pi$
$602$	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	0.852516	−	0.522701i	$-0.175075\pi$
$607$	26.7496	+	11.0800i	1.08573	+	0.449725i	0.233215	+	0.972425i	$0.425075\pi$
$608$	−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	$0.0588773\pi$
$613$			9.10707i			0.367831i	−0.982942	+	0.183915i	$0.941123\pi$
$614$	−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	0.474714	−	0.880140i	$-0.342551\pi$
$617$	4.67068	+	1.93466i	0.188035	+	0.0778864i	−0.286680	+	0.958027i	$0.592551\pi$
$618$	3.28639	+	7.93404i	0.132198	+	0.319154i
$619$	−6.45177	−	15.5760i	−0.259319	−	0.626051i	0.739575	−	0.673074i	$-0.235026\pi$
$619$	−6.45177	−	15.5760i	−0.259319	−	0.626051i	−0.998894	+	0.0470233i	$0.985026\pi$
$620$		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	−0.667889	−	0.744261i	$-0.732802\pi$
$631$	1.91845	−	1.91845i	0.0763722	−	0.0763722i	0.744261	+	0.667889i	$0.232802\pi$
$632$	−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	0.652406	+	0.757870i	$0.273760\pi$
$641$	−8.72988	+	21.0758i	−0.344809	+	0.832443i	−0.997215	+	0.0745739i	$0.976240\pi$
$642$	18.3118			0.722711
$643$	7.37702	−	17.8097i	0.290921	−	0.702346i	−0.709075	−	0.705133i	$-0.750887\pi$
$643$	7.37702	−	17.8097i	0.290921	−	0.702346i	0.999996	+	0.00278691i	$0.000887101\pi$
$644$	−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	$-0.918976\pi$
$647$		−	12.8098i		−	0.503606i	0.967778	−	0.251803i	$-0.0810235\pi$
$648$	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	0.533136	−	0.846030i	$-0.321013\pi$
$653$	38.5442	−	15.9656i	1.50835	−	0.624780i	0.975217	+	0.221249i	$0.0710135\pi$
$654$	−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	$0.233120\pi$
$659$			34.3290i			1.33727i	−0.743592	+	0.668633i	$0.766880\pi$
$660$		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	$0.431092\pi$
$662$			27.4958i			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	−0.918826	−	0.394662i	$-0.870862\pi$
$673$	−33.4517	+	13.8561i	−1.28947	+	0.534115i	−0.370640	+	0.928777i	$0.620862\pi$
$674$	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	−0.746610	−	0.665262i	$-0.768320\pi$
$677$	6.54992	−	15.8129i	0.251734	−	0.607739i	0.998344	+	0.0575224i	$0.0183201\pi$
$678$	−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	−0.975336	−	0.220725i	$-0.929158\pi$
$683$	−3.38683	+	8.17654i	−0.129594	+	0.312866i	0.845743	+	0.533591i	$0.179158\pi$
$684$		−	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	−0.357975	−	0.933731i	$-0.616533\pi$
$691$	1.29190	−	0.535121i	0.0491461	−	0.0203570i	0.407121	+	0.913374i	$0.366533\pi$
$692$	−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	$-0.985789\pi$
$701$		−	2.36331i		−	0.0892608i	0.999004	−	0.0446304i	$-0.0142110\pi$
$702$	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	0.497791	+	0.867297i	$0.334145\pi$
$709$	−12.4474	+	30.0507i	−0.467472	+	1.12858i	−0.965263	+	0.261280i	$0.915855\pi$
$710$		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	−0.762208	−	0.647332i	$-0.775885\pi$
$719$	6.28758	−	15.1796i	0.234487	−	0.566102i	0.996695	+	0.0812299i	$0.0258848\pi$
$720$		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	0.585307	−	0.810812i	$-0.300974\pi$
$733$	−6.10533	−	6.10533i	−0.225506	−	0.225506i	−0.810812	+	0.585307i	$0.800974\pi$
$734$	−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	0.831425	−	0.555637i	$-0.187526\pi$
$739$	7.49715	+	7.49715i	0.275787	+	0.275787i	−0.555637	+	0.831425i	$0.687526\pi$
$740$		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	−0.0295670	−	0.999563i	$-0.509413\pi$
$743$	−20.6417	−	8.55008i	−0.757272	−	0.313672i	−0.727705	+	0.685891i	$0.759413\pi$
$744$		−	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	0.499775	−	0.866155i	$-0.333416\pi$
$751$	6.59640	+	2.73232i	0.240706	+	0.0997037i	−0.259069	+	0.965859i	$0.583416\pi$
$752$	−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	−0.436444	−	0.899731i	$-0.643762\pi$
$757$	12.7467	−	12.7467i	0.463287	−	0.463287i	0.899731	+	0.436444i	$0.143762\pi$
$758$	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	$-0.639699\pi$
$761$		−	49.9437i		−	1.81046i	0.424923	−	0.905230i	$-0.360301\pi$
$762$	−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	$-0.709173\pi$
$769$		−	43.9115i		−	1.58349i	0.610852	−	0.791745i	$-0.290827\pi$
$770$		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	−0.819380	−	0.573251i	$-0.805682\pi$
$773$	−6.84309	+	6.84309i	−0.246129	+	0.246129i	0.573251	+	0.819380i	$0.305682\pi$
$774$	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	0.0312976	−	0.999510i	$-0.490036\pi$
$787$	−18.3283	−	7.59181i	−0.653332	−	0.270619i	−0.684630	+	0.728891i	$0.740036\pi$
$788$	−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	0.773313	−	0.634024i	$-0.218598\pi$
$797$	3.93230	+	3.93230i	0.139289	+	0.139289i	−0.634024	+	0.773313i	$0.718598\pi$
$798$		−	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	−0.983017	−	0.183513i	$-0.941253\pi$
$809$	−11.8801	−	28.6811i	−0.417683	−	1.00838i	0.565335	−	0.824862i	$-0.308747\pi$
$810$		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	$0.816353\pi$
$812$	2.30374			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	−0.771757	−	0.635918i	$-0.780622\pi$
$821$	6.40739	−	15.4688i	0.223619	−	0.539865i	0.995376	+	0.0960527i	$0.0306217\pi$
$822$	−1.06196	−	2.56381i	−0.0370402	−	0.0894231i
$823$	24.5749	−	10.1792i	0.856626	−	0.354826i	0.0892387	−	0.996010i	$-0.471557\pi$
$823$	24.5749	−	10.1792i	0.856626	−	0.354826i	0.767387	+	0.641184i	$0.221557\pi$
$824$	−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	−0.968841	−	0.247684i	$-0.920330\pi$
$827$	−13.1970	−	31.8605i	−0.458906	−	1.10790i	0.509934	−	0.860213i	$-0.329670\pi$
$828$	−3.06731	−	1.27052i	−0.106597	−	0.0441537i
$829$			7.29346i			0.253312i	0.991947	+	0.126656i	$0.0404245\pi$
$829$			7.29346i			0.253312i	−0.991947	+	0.126656i	$0.959576\pi$
$830$		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	0.263913	−	0.964546i	$-0.414987\pi$
$839$	32.8053	−	13.5884i	1.13257	−	0.469124i	0.868652	+	0.495422i	$0.164987\pi$
$840$		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	−0.925436	−	0.378903i	$-0.876301\pi$
$853$	−0.0913933	+	0.220643i	−0.00312925	+	0.00755467i	0.922307	+	0.386458i	$0.126301\pi$
$854$		−	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	−0.650844	−	0.759211i	$-0.725585\pi$
$857$	−16.8099	+	6.96291i	−0.574217	+	0.237848i	0.0766273	+	0.997060i	$0.475585\pi$
$858$	0.139507	−	0.139507i	0.00476271	−	0.00476271i
$859$	14.2525	+	14.2525i	0.486288	+	0.486288i	0.907133	−	0.420845i	$-0.138266\pi$
$859$	14.2525	+	14.2525i	0.486288	+	0.486288i	−0.420845	+	0.907133i	$0.638266\pi$
$860$		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	0.402149	−	0.915574i	$-0.368263\pi$
$877$	39.5030	−	16.3627i	1.33392	−	0.552528i	0.931771	+	0.363046i	$0.118263\pi$
$878$	−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	−0.420721	−	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
$883$			41.4824i			1.39599i	0.716101	+	0.697997i	$0.245925\pi$
$883$			41.4824i			1.39599i	−0.716101	+	0.697997i	$0.754075\pi$
$884$	−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	−0.559132	−	0.829078i	$-0.688866\pi$
$887$	12.5826	−	30.3770i	0.422481	−	1.01996i	0.981613	−	0.190881i	$-0.0611344\pi$
$888$	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	−0.967105	−	0.254379i	$-0.918129\pi$
$907$	−13.9479	−	33.6731i	−0.463131	−	1.11810i	0.503973	−	0.863719i	$-0.331871\pi$
$908$	−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	−0.992197	−	0.124676i	$-0.960211\pi$
$911$	−11.4322	−	27.5999i	−0.378767	−	0.914425i	0.613430	−	0.789749i	$-0.289789\pi$
$912$	−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	−0.304952	−	0.952368i	$-0.598640\pi$
$929$	4.65849	−	1.92961i	0.152840	−	0.0633085i	0.457792	+	0.889059i	$0.348640\pi$
$930$		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	0.177632	−	0.984097i	$-0.443156\pi$
$937$	−24.6863	−	24.6863i	−0.806465	−	0.806465i	−0.984097	+	0.177632i	$0.943156\pi$
$938$	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	−0.209885	−	0.977726i	$-0.567309\pi$
$941$	10.2169	−	4.23196i	0.333060	−	0.137958i	0.542945	+	0.839768i	$0.317309\pi$
$942$	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	0.203449	−	0.979086i	$-0.434785\pi$
$947$	−10.6171	−	4.39774i	−0.345008	−	0.142907i	−0.548458	+	0.836178i	$0.684785\pi$
$948$	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	$-0.996366\pi$
$953$		−	0.704896i		−	0.0228338i	0.999935	−	0.0114169i	$-0.00363419\pi$
$954$	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	0.0876267	−	0.996153i	$-0.472072\pi$
$967$	−28.2521	−	28.2521i	−0.908527	−	0.908527i	−0.996153	+	0.0876267i	$0.972072\pi$
$968$			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	−0.0183111	−	0.999832i	$-0.505829\pi$
$971$	30.5851	−	30.5851i	0.981521	−	0.981521i	0.999832	+	0.0183111i	$0.00582892\pi$
$972$	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	−0.111753	+	0.993736i	$0.535647\pi$
$977$	−34.5543	+	34.5543i	−1.10549	+	1.10549i	−0.993736	+	0.111753i	$0.964353\pi$
$978$	−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	−0.280318	−	0.959907i	$-0.590440\pi$
$983$	18.7068	−	45.1621i	0.596653	−	1.44045i	0.876972	−	0.480542i	$-0.159560\pi$
$984$	−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	−0.810586	−	0.585619i	$-0.800851\pi$
$991$	5.56191	−	13.4276i	0.176680	−	0.426543i	0.987266	+	0.159076i	$0.0508515\pi$
$992$	−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	0.927672	+	0.373396i	$0.121807\pi$
$997$	16.9161	+	40.8392i	0.535740	+	1.29339i	−0.391933	+	0.919994i	$0.628193\pi$
$998$	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.349.5		24
5.2	odd	4		85.2.l.a.26.2	✓	24
5.3	odd	4		425.2.m.b.26.5		24
5.4	even	2		425.2.n.f.349.2		24
15.2	even	4		765.2.be.b.451.5		24
17.2	even	8		425.2.n.f.274.2		24
85.2	odd	8		85.2.l.a.36.2	yes	24
85.7	even	16		1445.2.d.j.866.20		24
85.19	even	8	inner	425.2.n.c.274.5		24
85.23	even	16		7225.2.a.bs.1.10		12
85.27	even	16		1445.2.d.j.866.19		24
85.28	even	16		7225.2.a.bq.1.10		12
85.53	odd	8		425.2.m.b.376.5		24
85.57	even	16		1445.2.a.p.1.3		12
85.62	even	16		1445.2.a.q.1.3		12
255.2	even	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	5.2	odd	4
85.2.l.a.36.2	yes	24	85.2	odd	8
425.2.m.b.26.5		24	5.3	odd	4
425.2.m.b.376.5		24	85.53	odd	8
425.2.n.c.274.5		24	85.19	even	8	inner
425.2.n.c.349.5		24	1.1	even	1	trivial
425.2.n.f.274.2		24	17.2	even	8
425.2.n.f.349.2		24	5.4	even	2
765.2.be.b.451.5		24	15.2	even	4
765.2.be.b.631.5		24	255.2	even	8
1445.2.a.p.1.3		12	85.57	even	16
1445.2.a.q.1.3		12	85.62	even	16
1445.2.d.j.866.19		24	85.27	even	16
1445.2.d.j.866.20		24	85.7	even	16
7225.2.a.bq.1.10		12	85.28	even	16
7225.2.a.bs.1.10		12	85.23	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 $\F_{q}$

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

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