LMFDB - Embedded newform 625.2.d.o.376.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [625,2,Mod(126,625)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(625, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("625.126");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 625 = 5^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	625.d (of order $5$, 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:	$4.99065012633$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + x^{14} - 4x^{12} - 49x^{10} + 11x^{8} + 395x^{6} + 900x^{4} + 1125x^{2} + 625 $ x^16 + x^14 - 4x^12 - 49x^10 + 11x^8 + 395x^6 + 900x^4 + 1125x^2 + 625
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 5^{2} $
Twist minimal:	no (minimal twist has level 25)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			376.4
Root			$0.0566033 + 1.17421i$ of defining polynomial
Character	$\chi$	$=$	625.376
Dual form			625.2.d.o.251.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.68703 + 1.22570i) q^{2} +(-0.679371 - 2.09089i) q^{3} +(0.725700 + 2.23347i) q^{4} +(1.41668 - 4.36010i) q^{6} +0.992398 q^{7} +(-0.224514 + 0.690983i) q^{8} +(-1.48322 + 1.07763i) q^{9} +(-1.61803 - 1.17557i) q^{11} +(4.17693 - 3.03472i) q^{12} +(2.72967 - 1.98322i) q^{13} +(1.67421 + 1.21638i) q^{14} +(2.57411 - 1.87020i) q^{16} +(0.894453 - 2.75284i) q^{17} -3.82309 q^{18} +(-0.798649 + 2.45799i) q^{19} +(-0.674207 - 2.07500i) q^{21} +(-1.28878 - 3.96645i) q^{22} +(3.68073 + 2.67421i) q^{23} +1.59730 q^{24} +7.03588 q^{26} +(-2.07500 - 1.50757i) q^{27} +(0.720183 + 2.21650i) q^{28} +(-1.66384 - 5.12077i) q^{29} +(0.0421925 - 0.129855i) q^{31} +8.08800 q^{32} +(-1.35874 + 4.18178i) q^{33} +(4.88313 - 3.54780i) q^{34} +(-3.48322 - 2.53071i) q^{36} +(1.73866 - 1.26321i) q^{37} +(-4.36010 + 3.16780i) q^{38} +(-6.00116 - 4.36010i) q^{39} +(-6.98439 + 5.07446i) q^{41} +(1.40591 - 4.32696i) q^{42} +4.64398 q^{43} +(1.45140 - 4.46695i) q^{44} +(2.93173 + 9.02294i) q^{46} +(3.06739 + 9.44047i) q^{47} +(-5.65917 - 4.11163i) q^{48} -6.01515 q^{49} -6.36356 q^{51} +(6.41040 + 4.65743i) q^{52} +(2.33778 + 7.19494i) q^{53} +(-1.65275 - 5.08664i) q^{54} +(-0.222807 + 0.685730i) q^{56} +5.68196 q^{57} +(3.46958 - 10.6783i) q^{58} +(-3.97854 + 2.89058i) q^{59} +(2.24075 + 1.62800i) q^{61} +(0.230343 - 0.167354i) q^{62} +(-1.47195 + 1.06943i) q^{63} +(8.49648 + 6.17306i) q^{64} +(-7.41785 + 5.38938i) q^{66} +(0.675441 - 2.07879i) q^{67} +6.79751 q^{68} +(3.09089 - 9.51278i) q^{69} +(2.97971 + 9.17060i) q^{71} +(-0.411616 - 1.26682i) q^{72} +(-0.627740 - 0.456080i) q^{73} +4.48150 q^{74} -6.06943 q^{76} +(-1.60573 - 1.16663i) q^{77} +(-4.77998 - 14.7113i) q^{78} +(4.89818 + 15.0750i) q^{79} +(-3.44210 + 10.5937i) q^{81} -18.0026 q^{82} +(-0.547301 + 1.68442i) q^{83} +(4.14518 - 3.01165i) q^{84} +(7.83453 + 5.69212i) q^{86} +(-9.57660 + 6.95781i) q^{87} +(1.17557 - 0.854102i) q^{88} +(-11.7372 - 8.52760i) q^{89} +(2.70892 - 1.96815i) q^{91} +(-3.30167 + 10.1615i) q^{92} -0.300177 q^{93} +(-6.39639 + 19.6861i) q^{94} +(-5.49476 - 16.9111i) q^{96} +(-5.26228 - 16.1956i) q^{97} +(-10.1477 - 7.37276i) q^{98} +3.66673 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{4} + 12 q^{6} - 2 q^{9} - 8 q^{11} + 14 q^{14} - 4 q^{16} - 20 q^{19} + 2 q^{21} + 40 q^{24} + 12 q^{26} - 30 q^{29} + 2 q^{31} + 24 q^{34} - 34 q^{36} - 24 q^{39} - 18 q^{41} - 16 q^{44} + 32 q^{46}+ \cdots + 16 q^{99}+O(q^{100}) $ 16 * q - 8 * q^4 + 12 * q^6 - 2 * q^9 - 8 * q^11 + 14 * q^14 - 4 * q^16 - 20 * q^19 + 2 * q^21 + 40 * q^24 + 12 * q^26 - 30 * q^29 + 2 * q^31 + 24 * q^34 - 34 * q^36 - 24 * q^39 - 18 * q^41 - 16 * q^44 + 32 * q^46 - 28 * q^49 - 8 * q^51 + 20 * q^54 - 30 * q^56 - 30 * q^59 + 12 * q^61 + 52 * q^64 - 36 * q^66 + 26 * q^69 - 58 * q^71 + 24 * q^74 - 40 * q^76 + 20 * q^79 - 24 * q^81 + 54 * q^84 + 32 * q^86 - 80 * q^89 + 2 * q^91 + 14 * q^94 + 22 * q^96 + 16 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/625\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{5}\right)$

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 $

$2$	1.68703	+	1.22570i	1.19291	+	0.866701i	0.993569	−	0.113229i	$-0.0361195\pi$
$2$	1.68703	+	1.22570i	1.19291	+	0.866701i	0.199342	+	0.979930i	$0.436119\pi$
$3$	−0.679371	−	2.09089i	−0.392235	−	1.20718i	−0.931094	−	0.364780i	$-0.881144\pi$
$3$	−0.679371	−	2.09089i	−0.392235	−	1.20718i	0.538859	−	0.842396i	$-0.318856\pi$
$4$	0.725700	+	2.23347i	0.362850	+	1.11674i
$5$		0			0
$5$		0			0
$6$	1.41668	−	4.36010i	0.578358	−	1.78000i
$7$	0.992398			0.375091			0.187546	−	0.982256i	$-0.439947\pi$
$7$	0.992398			0.375091			0.187546	+	0.982256i	$0.439947\pi$
$8$	−0.224514	+	0.690983i	−0.0793777	+	0.244299i
$9$	−1.48322	+	1.07763i	−0.494408	+	0.359208i
$10$		0			0
$11$	−1.61803	−	1.17557i	−0.487856	−	0.354448i	0.316503	−	0.948591i	$-0.397491\pi$
$11$	−1.61803	−	1.17557i	−0.487856	−	0.354448i	−0.804359	+	0.594144i	$0.797491\pi$
$12$	4.17693	−	3.03472i	1.20578	−	0.876047i
$13$	2.72967	−	1.98322i	0.757075	−	0.550047i	−0.140937	−	0.990019i	$-0.545011\pi$
$13$	2.72967	−	1.98322i	0.757075	−	0.550047i	0.898012	+	0.439971i	$0.145011\pi$
$14$	1.67421	+	1.21638i	0.447451	+	0.325092i
$15$		0			0
$16$	2.57411	−	1.87020i	0.643528	−	0.467551i
$17$	0.894453	−	2.75284i	0.216937	−	0.667663i	−0.782074	−	0.623186i	$-0.785838\pi$
$17$	0.894453	−	2.75284i	0.216937	−	0.667663i	0.999010	−	0.0444767i	$-0.0141621\pi$
$18$	−3.82309			−0.901111
$19$	−0.798649	+	2.45799i	−0.183223	+	0.563901i	−0.999913	−	0.0131746i	$-0.995806\pi$
$19$	−0.798649	+	2.45799i	−0.183223	+	0.563901i	0.816691	+	0.577076i	$0.195806\pi$
$20$		0			0
$21$	−0.674207	−	2.07500i	−0.147124	−	0.452801i
$22$	−1.28878	−	3.96645i	−0.274768	−	0.845650i
$23$	3.68073	+	2.67421i	0.767485	+	0.557611i	0.901197	−	0.433410i	$-0.142690\pi$
$23$	3.68073	+	2.67421i	0.767485	+	0.557611i	−0.133712	+	0.991020i	$0.542690\pi$
$24$	1.59730			0.326047
$25$		0			0
$26$	7.03588			1.37985
$27$	−2.07500	−	1.50757i	−0.399333	−	0.290132i
$28$	0.720183	+	2.21650i	0.136102	+	0.418878i
$29$	−1.66384	−	5.12077i	−0.308967	−	0.950903i	−0.978167	−	0.207821i	$-0.933363\pi$
$29$	−1.66384	−	5.12077i	−0.308967	−	0.950903i	0.669200	−	0.743082i	$-0.266637\pi$
$30$		0			0
$31$	0.0421925	−	0.129855i	0.00757799	−	0.0233227i	−0.947196	−	0.320655i	$-0.896097\pi$
$31$	0.0421925	−	0.129855i	0.00757799	−	0.0233227i	0.954774	+	0.297332i	$0.0960970\pi$
$32$	8.08800			1.42977
$33$	−1.35874	+	4.18178i	−0.236527	+	0.727954i
$34$	4.88313	−	3.54780i	0.837450	−	0.608443i
$35$		0			0
$36$	−3.48322	−	2.53071i	−0.580537	−	0.421785i
$37$	1.73866	−	1.26321i	0.285834	−	0.207671i	−0.435624	−	0.900129i	$-0.643472\pi$
$37$	1.73866	−	1.26321i	0.285834	−	0.207671i	0.721458	+	0.692458i	$0.243472\pi$
$38$	−4.36010	+	3.16780i	−0.707302	+	0.513885i
$39$	−6.00116	−	4.36010i	−0.960955	−	0.698175i
$40$		0			0
$41$	−6.98439	+	5.07446i	−1.09078	+	0.792497i	−0.979530	−	0.201296i	$-0.935485\pi$
$41$	−6.98439	+	5.07446i	−1.09078	+	0.792497i	−0.111248	+	0.993793i	$0.535485\pi$
$42$	1.40591	−	4.32696i	0.216937	−	0.667664i
$43$	4.64398			0.708200			0.354100	−	0.935208i	$-0.384787\pi$
$43$	4.64398			0.708200			0.354100	+	0.935208i	$0.384787\pi$
$44$	1.45140	−	4.46695i	0.218807	−	0.673418i
$45$		0			0
$46$	2.93173	+	9.02294i	0.432260	+	1.33036i
$47$	3.06739	+	9.44047i	0.447425	+	1.37703i	0.879802	+	0.475341i	$0.157675\pi$
$47$	3.06739	+	9.44047i	0.447425	+	1.37703i	−0.432376	+	0.901693i	$0.642325\pi$
$48$	−5.65917	−	4.11163i	−0.816831	−	0.593462i
$49$	−6.01515			−0.859306
$50$		0			0
$51$	−6.36356			−0.891077
$52$	6.41040	+	4.65743i	0.888963	+	0.645869i
$53$	2.33778	+	7.19494i	0.321119	+	0.988301i	0.973162	+	0.230120i	$0.0739119\pi$
$53$	2.33778	+	7.19494i	0.321119	+	0.988301i	−0.652044	+	0.758181i	$0.726088\pi$
$54$	−1.65275	−	5.08664i	−0.224911	−	0.692205i
$55$		0			0
$56$	−0.222807	+	0.685730i	−0.0297739	+	0.0916346i
$57$	5.68196			0.752594
$58$	3.46958	−	10.6783i	0.455578	−	1.40212i
$59$	−3.97854	+	2.89058i	−0.517962	+	0.376322i	−0.815836	−	0.578284i	$-0.803723\pi$
$59$	−3.97854	+	2.89058i	−0.517962	+	0.376322i	0.297873	+	0.954605i	$0.403723\pi$
$60$		0			0
$61$	2.24075	+	1.62800i	0.286898	+	0.208444i	0.721921	−	0.691976i	$-0.243260\pi$
$61$	2.24075	+	1.62800i	0.286898	+	0.208444i	−0.435022	+	0.900420i	$0.643260\pi$
$62$	0.230343	−	0.167354i	0.0292536	−	0.0212540i
$63$	−1.47195	+	1.06943i	−0.185448	+	0.134736i
$64$	8.49648	+	6.17306i	1.06206	+	0.771632i
$65$		0			0
$66$	−7.41785	+	5.38938i	−0.913074	+	0.663387i
$67$	0.675441	−	2.07879i	0.0825183	−	0.253965i	−0.901282	−	0.433233i	$-0.857373\pi$
$67$	0.675441	−	2.07879i	0.0825183	−	0.253965i	0.983800	+	0.179268i	$0.0573728\pi$
$68$	6.79751			0.824319
$69$	3.09089	−	9.51278i	0.372099	−	1.14520i
$70$		0			0
$71$	2.97971	+	9.17060i	0.353626	+	1.08835i	0.956802	+	0.290741i	$0.0939019\pi$
$71$	2.97971	+	9.17060i	0.353626	+	1.08835i	−0.603175	+	0.797609i	$0.706098\pi$
$72$	−0.411616	−	1.26682i	−0.0485094	−	0.149297i
$73$	−0.627740	−	0.456080i	−0.0734714	−	0.0533801i	0.550443	−	0.834873i	$-0.314459\pi$
$73$	−0.627740	−	0.456080i	−0.0734714	−	0.0533801i	−0.623915	+	0.781492i	$0.714459\pi$
$74$	4.48150			0.520963
$75$		0			0
$76$	−6.06943			−0.696212
$77$	−1.60573	−	1.16663i	−0.182990	−	0.132950i
$78$	−4.77998	−	14.7113i	−0.541226	−	1.66572i
$79$	4.89818	+	15.0750i	0.551088	+	1.69608i	0.706056	+	0.708156i	$0.250473\pi$
$79$	4.89818	+	15.0750i	0.551088	+	1.69608i	−0.154968	+	0.987919i	$0.549527\pi$
$80$		0			0
$81$	−3.44210	+	10.5937i	−0.382455	+	1.17708i
$82$	−18.0026			−1.98806
$83$	−0.547301	+	1.68442i	−0.0600740	+	0.184889i	−0.976590	−	0.215109i	$-0.930989\pi$
$83$	−0.547301	+	1.68442i	−0.0600740	+	0.184889i	0.916516	+	0.399998i	$0.130989\pi$
$84$	4.14518	−	3.01165i	0.452276	−	0.328598i
$85$		0			0
$86$	7.83453	+	5.69212i	0.844819	+	0.613797i
$87$	−9.57660	+	6.95781i	−1.02672	+	0.745955i
$88$	1.17557	−	0.854102i	0.125316	−	0.0910476i
$89$	−11.7372	−	8.52760i	−1.24414	−	0.903924i	−0.246277	−	0.969200i	$-0.579207\pi$
$89$	−11.7372	−	8.52760i	−1.24414	−	0.903924i	−0.997867	+	0.0652758i	$0.979207\pi$
$90$		0			0
$91$	2.70892	−	1.96815i	0.283972	−	0.206318i
$92$	−3.30167	+	10.1615i	−0.344223	+	1.05941i
$93$	−0.300177			−0.0311269
$94$	−6.39639	+	19.6861i	−0.659737	+	2.03046i
$95$		0			0
$96$	−5.49476	−	16.9111i	−0.560806	−	1.72598i
$97$	−5.26228	−	16.1956i	−0.534304	−	1.64442i	−0.745148	−	0.666899i	$-0.767621\pi$
$97$	−5.26228	−	16.1956i	−0.534304	−	1.64442i	0.210844	−	0.977520i	$-0.432379\pi$
$98$	−10.1477	−	7.37276i	−1.02508	−	0.744761i
$99$	3.66673			0.368520
$100$		0			0
$101$	−2.54716			−0.253452			−0.126726	−	0.991938i	$-0.540447\pi$
$101$	−2.54716			−0.253452			−0.126726	+	0.991938i	$0.540447\pi$
$102$	−10.7355	−	7.79981i	−1.06298	−	0.772297i
$103$	3.14129	+	9.66790i	0.309520	+	0.952606i	0.977952	+	0.208832i	$0.0669662\pi$
$103$	3.14129	+	9.66790i	0.309520	+	0.952606i	−0.668431	+	0.743774i	$0.733034\pi$
$104$	0.757524	+	2.33142i	0.0742814	+	0.228615i
$105$		0			0
$106$	−4.87494	+	15.0035i	−0.473496	+	1.45727i
$107$	−4.81720			−0.465697			−0.232848	−	0.972513i	$-0.574805\pi$
$107$	−4.81720			−0.465697			−0.232848	+	0.972513i	$0.574805\pi$
$108$	1.86130	−	5.72850i	0.179104	−	0.551225i
$109$	−13.1662	+	9.56578i	−1.26109	+	0.916236i	−0.998811	−	0.0487563i	$-0.984474\pi$
$109$	−13.1662	+	9.56578i	−1.26109	+	0.916236i	−0.262280	+	0.964992i	$0.584474\pi$
$110$		0			0
$111$	−3.82243	−	2.77716i	−0.362809	−	0.263596i
$112$	2.55455	−	1.85599i	0.241382	−	0.175374i
$113$	−5.46656	+	3.97169i	−0.514251	+	0.373625i	−0.814434	−	0.580256i	$-0.802952\pi$
$113$	−5.46656	+	3.97169i	−0.514251	+	0.373625i	0.300183	+	0.953882i	$0.402952\pi$
$114$	9.58565	+	6.96438i	0.897778	+	0.652274i
$115$		0			0
$116$	10.2297	−	7.43228i	0.949800	−	0.690070i
$117$	−1.91155	+	5.88313i	−0.176722	+	0.543896i
$118$	−10.2549			−0.944041
$119$	0.887654	−	2.73192i	0.0813711	−	0.250435i
$120$		0			0
$121$	−2.16312	−	6.65740i	−0.196647	−	0.605218i
$122$	1.78477	+	5.49297i	0.161586	+	0.497310i
$123$	15.3551	+	11.1561i	1.38452	+	1.00592i
$124$	0.320647			0.0287950
$125$		0			0
$126$	−3.79403			−0.337999
$127$	1.20609	+	0.876278i	0.107023	+	0.0777571i	0.640010	−	0.768367i	$-0.278930\pi$
$127$	1.20609	+	0.876278i	0.107023	+	0.0777571i	−0.532986	+	0.846124i	$0.678930\pi$
$128$	1.76886	+	5.44398i	0.156346	+	0.481185i
$129$	−3.15498	−	9.71004i	−0.277781	−	0.854921i
$130$		0			0
$131$	4.36167	−	13.4239i	0.381081	−	1.17285i	−0.558202	−	0.829705i	$-0.688509\pi$
$131$	4.36167	−	13.4239i	0.381081	−	1.17285i	0.939283	−	0.343143i	$-0.111491\pi$
$132$	−10.3259			−0.898757
$133$	−0.792578	+	2.43930i	−0.0687252	+	0.211514i
$134$	3.68747	−	2.67910i	0.318549	−	0.231439i
$135$		0			0
$136$	1.70135	+	1.23610i	0.145890	+	0.105995i
$137$	0.557775	−	0.405247i	0.0476539	−	0.0346226i	−0.563703	−	0.825977i	$-0.690624\pi$
$137$	0.557775	−	0.405247i	0.0476539	−	0.0346226i	0.611357	+	0.791355i	$0.290624\pi$
$138$	16.8742	−	12.2599i	1.43643	−	1.04363i
$139$	13.4069	+	9.74070i	1.13716	+	0.826195i	0.986721	−	0.162424i	$-0.0519313\pi$
$139$	13.4069	+	9.74070i	1.13716	+	0.826195i	0.150439	+	0.988619i	$0.451931\pi$
$140$		0			0
$141$	17.6551	−	12.8272i	1.48683	−	1.08024i
$142$	−6.21354	+	19.1233i	−0.521429	+	1.60479i
$143$	−6.74812			−0.564307
$144$	−1.80261	+	5.54786i	−0.150217	+	0.462322i
$145$		0			0
$146$	−0.500000	−	1.53884i	−0.0413803	−	0.127355i
$147$	4.08652	+	12.5770i	0.337050	+	1.03733i
$148$	4.08310	+	2.96655i	0.335629	+	0.243849i
$149$	3.21156			0.263101			0.131551	−	0.991309i	$-0.458004\pi$
$149$	3.21156			0.263101			0.131551	+	0.991309i	$0.458004\pi$
$150$		0			0
$151$	17.6863			1.43929			0.719647	−	0.694340i	$-0.244304\pi$
$151$	17.6863			1.43929			0.719647	+	0.694340i	$0.244304\pi$
$152$	−1.51912	−	1.10371i	−0.123217	−	0.0895223i
$153$	1.63986	+	5.04697i	0.132575	+	0.408023i
$154$	−1.27898	−	3.93630i	−0.103063	−	0.317196i
$155$		0			0
$156$	5.38313	−	16.5676i	0.430995	−	1.32647i
$157$	1.65512			0.132093			0.0660465	−	0.997817i	$-0.478961\pi$
$157$	1.65512			0.132093			0.0660465	+	0.997817i	$0.478961\pi$
$158$	−10.2141	+	31.4358i	−0.812590	+	2.50090i
$159$	13.4556	−	9.77608i	1.06710	−	0.775293i
$160$		0			0
$161$	3.65275	+	2.65388i	0.287877	+	0.209155i
$162$	−18.7916	+	13.6529i	−1.47641	+	1.07267i
$163$	−0.722399	+	0.524854i	−0.0565827	+	0.0411097i	−0.615717	−	0.787967i	$-0.711134\pi$
$163$	−0.722399	+	0.524854i	−0.0565827	+	0.0411097i	0.559134	+	0.829077i	$0.311134\pi$
$164$	−16.4022	−	11.9169i	−1.28080	−	0.930555i
$165$		0			0
$166$	−2.98790	+	2.17084i	−0.231906	+	0.168490i
$167$	1.60552	−	4.94129i	0.124239	−	0.382368i	−0.869523	−	0.493893i	$-0.835573\pi$
$167$	1.60552	−	4.94129i	0.124239	−	0.382368i	0.993762	+	0.111525i	$0.0355735\pi$
$168$	1.58516			0.122297
$169$	−0.499280	+	1.53663i	−0.0384062	+	0.118202i
$170$		0			0
$171$	−1.46422	−	4.50639i	−0.111971	−	0.344612i
$172$	3.37013	+	10.3722i	0.256970	+	0.790873i
$173$	4.66370	+	3.38837i	0.354574	+	0.257613i	0.750785	−	0.660546i	$-0.229675\pi$
$173$	4.66370	+	3.38837i	0.354574	+	0.257613i	−0.396211	+	0.918159i	$0.629675\pi$
$174$	−24.6842			−1.87130
$175$		0			0
$176$	−6.36356			−0.479671
$177$	8.74680	+	6.35492i	0.657449	+	0.477665i
$178$	−9.34880	−	28.7726i	−0.700722	−	2.15660i
$179$	2.67883	+	8.24458i	0.200225	+	0.616229i	0.999876	+	0.0157637i	$0.00501795\pi$
$179$	2.67883	+	8.24458i	0.200225	+	0.616229i	−0.799651	+	0.600465i	$0.794982\pi$
$180$		0			0
$181$	4.41612	−	13.5914i	0.328248	−	1.01024i	−0.641706	−	0.766951i	$-0.721773\pi$
$181$	4.41612	−	13.5914i	0.328248	−	1.01024i	0.969953	−	0.243291i	$-0.0782271\pi$
$182$	6.98240			0.517570
$183$	1.88167	−	5.79117i	0.139097	−	0.428096i
$184$	−2.67421	+	1.94293i	−0.197145	+	0.143234i
$185$		0			0
$186$	−0.506408	−	0.367927i	−0.0371316	−	0.0269777i
$187$	−4.68342	+	3.40270i	−0.342485	+	0.248830i
$188$	−18.8590	+	13.7019i	−1.37544	+	0.999313i
$189$	−2.05922	−	1.49611i	−0.149786	−	0.108826i
$190$		0			0
$191$	1.02451	−	0.744347i	0.0741306	−	0.0538591i	−0.550103	−	0.835097i	$-0.685411\pi$
$191$	1.02451	−	0.744347i	0.0741306	−	0.0538591i	0.624233	+	0.781238i	$0.285411\pi$
$192$	7.13492	−	21.9590i	0.514918	−	1.58476i
$193$	21.1730			1.52406			0.762031	−	0.647540i	$-0.224202\pi$
$193$	21.1730			1.52406			0.762031	+	0.647540i	$0.224202\pi$
$194$	10.9734	−	33.7725i	0.787841	−	2.42473i
$195$		0			0
$196$	−4.36519	−	13.4347i	−0.311799	−	0.959620i
$197$	−3.77042	−	11.6042i	−0.268631	−	0.826761i	−0.990835	−	0.135081i	$-0.956871\pi$
$197$	−3.77042	−	11.6042i	−0.268631	−	0.826761i	0.722203	−	0.691681i	$-0.243129\pi$
$198$	6.18589	+	4.49431i	0.439612	+	0.319397i
$199$	10.4065			0.737695			0.368848	−	0.929490i	$-0.379752\pi$
$199$	10.4065			0.737695			0.368848	+	0.929490i	$0.379752\pi$
$200$		0			0
$201$	−4.80540			−0.338947
$202$	−4.29714	−	3.12205i	−0.302346	−	0.219667i
$203$	−1.65119	−	5.08184i	−0.115891	−	0.356675i
$204$	−4.61803	−	14.2128i	−0.323327	−	0.995098i
$205$		0			0
$206$	−6.55049	+	20.1603i	−0.456394	+	1.40464i
$207$	−8.34114			−0.579749
$208$	3.31746	−	10.2101i	0.230024	−	0.707942i
$209$	4.18178	−	3.03824i	0.289260	−	0.210160i
$210$		0			0
$211$	7.00421	+	5.08886i	0.482190	+	0.350332i	0.802173	−	0.597092i	$-0.203677\pi$
$211$	7.00421	+	5.08886i	0.482190	+	0.350332i	−0.319983	+	0.947423i	$0.603677\pi$
$212$	−14.3732	+	10.4427i	−0.987155	+	0.717210i
$213$	17.1504	−	12.4605i	1.17513	−	0.853778i
$214$	−8.12677	−	5.90445i	−0.555535	−	0.403620i
$215$		0			0
$216$	1.50757	−	1.09532i	0.102577	−	0.0745268i
$217$	0.0418717	−	0.128868i	0.00284244	−	0.00874813i
$218$	−33.9365			−2.29847
$219$	−0.527144	+	1.62238i	−0.0356211	+	0.109630i
$220$		0			0
$221$	−3.01794	−	9.28827i	−0.203009	−	0.624796i
$222$	−3.04460	−	9.37032i	−0.204340	−	0.628894i
$223$	−22.9303	−	16.6598i	−1.53552	−	1.11562i	−0.953065	−	0.302764i	$-0.902091\pi$
$223$	−22.9303	−	16.6598i	−1.53552	−	1.11562i	−0.582459	−	0.812860i	$-0.697909\pi$
$224$	8.02652			0.536295
$225$		0			0
$226$	−14.0904			−0.937277
$227$	−17.9937	−	13.0732i	−1.19429	−	0.867699i	−0.200575	−	0.979678i	$-0.564281\pi$
$227$	−17.9937	−	13.0732i	−1.19429	−	0.867699i	−0.993711	+	0.111979i	$0.964281\pi$
$228$	4.12340	+	12.6905i	0.273079	+	0.840450i
$229$	0.765000	+	2.35443i	0.0505526	+	0.155585i	0.973146	−	0.230189i	$-0.0739345\pi$
$229$	0.765000	+	2.35443i	0.0505526	+	0.155585i	−0.922593	+	0.385774i	$0.873934\pi$
$230$		0			0
$231$	−1.34841	+	4.14999i	−0.0887191	+	0.273049i
$232$	3.91192			0.256830
$233$	1.84052	−	5.66454i	0.120576	−	0.371096i	−0.872493	−	0.488627i	$-0.837498\pi$
$233$	1.84052	−	5.66454i	0.120576	−	0.371096i	0.993069	+	0.117531i	$0.0374979\pi$
$234$	−10.4358	+	7.58204i	−0.682209	+	0.495654i
$235$		0			0
$236$	−9.34327	−	6.78828i	−0.608195	−	0.441879i
$237$	28.1926	−	20.4831i	1.83130	−	1.33052i
$238$	4.84601	−	3.52083i	0.314120	−	0.228222i
$239$	5.68935	+	4.13356i	0.368014	+	0.267378i	0.756387	−	0.654125i	$-0.226963\pi$
$239$	5.68935	+	4.13356i	0.368014	+	0.267378i	−0.388373	+	0.921502i	$0.626963\pi$
$240$		0			0
$241$	−0.954449	+	0.693448i	−0.0614815	+	0.0446689i	−0.618102	−	0.786098i	$-0.712098\pi$
$241$	−0.954449	+	0.693448i	−0.0614815	+	0.0446689i	0.556620	+	0.830767i	$0.312098\pi$
$242$	4.51072	−	13.8826i	0.289960	−	0.892405i
$243$	16.7942			1.07735
$244$	−2.00998	+	6.18609i	−0.128676	+	0.396024i
$245$		0			0
$246$	12.2305	+	37.6415i	0.779787	+	2.39994i
$247$	2.69469	+	8.29341i	0.171459	+	0.527697i
$248$	0.0802548	+	0.0583086i	0.00509619	+	0.00370260i
$249$	3.89375			0.246757
$250$		0			0
$251$	4.60867			0.290897			0.145448	−	0.989366i	$-0.453538\pi$
$251$	4.60867			0.290897			0.145448	+	0.989366i	$0.453538\pi$
$252$	−3.45675	−	2.51147i	−0.217755	−	0.158208i
$253$	−2.81183	−	8.65392i	−0.176778	−	0.544067i
$254$	0.960663	+	2.95662i	0.0602774	+	0.185515i
$255$		0			0
$256$	2.80216	−	8.62417i	0.175135	−	0.539011i
$257$	−9.75542			−0.608526			−0.304263	−	0.952588i	$-0.598410\pi$
$257$	−9.75542			−0.608526			−0.304263	+	0.952588i	$0.598410\pi$
$258$	6.57904	−	20.2482i	0.409593	−	1.26060i
$259$	1.72545	−	1.25361i	0.107214	−	0.0778955i
$260$		0			0
$261$	7.98612	+	5.80225i	0.494328	+	0.359150i
$262$	23.8119	−	17.3004i	1.47110	−	1.06882i
$263$	−0.805641	+	0.585333i	−0.0496780	+	0.0360932i	−0.612347	−	0.790589i	$-0.709775\pi$
$263$	−0.805641	+	0.585333i	−0.0496780	+	0.0360932i	0.562669	+	0.826682i	$0.309775\pi$
$264$	−2.58448	−	1.87774i	−0.159064	−	0.115567i
$265$		0			0
$266$	−4.32696	+	3.14372i	−0.265303	+	0.192754i
$267$	−9.85633	+	30.3347i	−0.603198	+	1.85645i
$268$	5.13310			0.313554
$269$	−1.01621	+	3.12758i	−0.0619596	+	0.190692i	−0.977245	−	0.212114i	$-0.931965\pi$
$269$	−1.01621	+	3.12758i	−0.0619596	+	0.190692i	0.915285	+	0.402806i	$0.131965\pi$
$270$		0			0
$271$	3.75457	+	11.5554i	0.228074	+	0.701940i	0.997965	+	0.0637642i	$0.0203105\pi$
$271$	3.75457	+	11.5554i	0.228074	+	0.701940i	−0.769891	+	0.638175i	$0.779689\pi$
$272$	−2.84595	−	8.75894i	−0.172561	−	0.531089i
$273$	−5.95555	−	4.32696i	−0.360446	−	0.261879i
$274$	1.43769			0.0868543
$275$		0			0
$276$	23.4896			1.41391
$277$	9.60025	+	6.97499i	0.576823	+	0.419087i	0.837577	−	0.546319i	$-0.183971\pi$
$277$	9.60025	+	6.97499i	0.576823	+	0.419087i	−0.260754	+	0.965405i	$0.583971\pi$
$278$	10.6787	+	32.8657i	0.640467	+	1.97115i
$279$	0.0773542	+	0.238072i	0.00463108	+	0.0142530i
$280$		0			0
$281$	−7.61468	+	23.4356i	−0.454253	+	1.39805i	0.417756	+	0.908559i	$0.362817\pi$
$281$	−7.61468	+	23.4356i	−0.454253	+	1.39805i	−0.872009	+	0.489489i	$0.837183\pi$
$282$	45.5069			2.70990
$283$	−1.03936	+	3.19881i	−0.0617833	+	0.190150i	−0.977184	−	0.212394i	$-0.931874\pi$
$283$	−1.03936	+	3.19881i	−0.0617833	+	0.190150i	0.915401	+	0.402544i	$0.131874\pi$
$284$	−18.3199	+	13.3102i	−1.08709	+	0.789815i
$285$		0			0
$286$	−11.3843	−	8.27117i	−0.673168	−	0.489085i
$287$	−6.93130	+	5.03588i	−0.409141	+	0.297259i
$288$	−11.9963	+	8.71584i	−0.706890	+	0.513586i
$289$	6.97519	+	5.06777i	0.410305	+	0.298104i
$290$		0			0
$291$	−30.2883	+	22.0057i	−1.77553	+	1.29000i
$292$	0.563092	−	1.73302i	0.0329525	−	0.101417i
$293$	−8.96340			−0.523647			−0.261824	−	0.965116i	$-0.584324\pi$
$293$	−8.96340			−0.523647			−0.261824	+	0.965116i	$0.584324\pi$
$294$	−8.52155	+	26.2266i	−0.496987	+	1.52957i
$295$		0			0
$296$	0.482504	+	1.48499i	0.0280450	+	0.0863136i
$297$	1.58516	+	4.87861i	0.0919801	+	0.283086i
$298$	5.41801	+	3.93641i	0.313857	+	0.228030i
$299$	15.3507			0.887756
$300$		0			0
$301$	4.60867			0.265640
$302$	29.8374	+	21.6781i	1.71695	+	1.24744i
$303$	1.73047	+	5.32583i	0.0994128	+	0.305961i
$304$	2.54112	+	7.82078i	0.145743	+	0.448552i
$305$		0			0
$306$	−3.41958	+	10.5244i	−0.195484	+	0.601638i
$307$	9.48133			0.541128			0.270564	−	0.962702i	$-0.412790\pi$
$307$	9.48133			0.541128			0.270564	+	0.962702i	$0.412790\pi$
$308$	1.44037	−	4.43299i	0.0820725	−	0.252593i
$309$	18.0804	−	13.1362i	1.02856	−	0.747291i
$310$		0			0
$311$	−23.7301	−	17.2409i	−1.34561	−	0.977643i	−0.999217	−	0.0395541i	$-0.987406\pi$
$311$	−23.7301	−	17.2409i	−1.34561	−	0.977643i	−0.346393	−	0.938089i	$-0.612594\pi$
$312$	4.36010	−	3.16780i	0.246842	−	0.179341i
$313$	−15.2824	+	11.1033i	−0.863811	+	0.627596i	−0.928919	−	0.370283i	$-0.879261\pi$
$313$	−15.2824	+	11.1033i	−0.863811	+	0.627596i	0.0651079	+	0.997878i	$0.479261\pi$
$314$	2.79224	+	2.02868i	0.157575	+	0.114485i
$315$		0			0
$316$	−30.1151	+	21.8799i	−1.69411	+	1.23084i
$317$	7.04229	−	21.6739i	0.395534	−	1.21733i	−0.533010	−	0.846109i	$-0.678939\pi$
$317$	7.04229	−	21.6739i	0.395534	−	1.21733i	0.928545	−	0.371221i	$-0.121061\pi$
$318$	34.6826			1.94490
$319$	−3.32768	+	10.2415i	−0.186314	+	0.573416i
$320$		0			0
$321$	3.27267	+	10.0722i	0.182663	+	0.562178i
$322$	2.90945	+	8.95435i	0.162137	+	0.499007i
$323$	6.05210	+	4.39711i	0.336748	+	0.244662i
$324$	−26.1587			−1.45326
$325$		0			0
$326$	−1.86202			−0.103128
$327$	28.9457	+	21.0303i	1.60070	+	1.16298i
$328$	−1.93827	−	5.96538i	−0.107023	−	0.329383i
$329$	3.04408	+	9.36871i	0.167825	+	0.516513i
$330$		0			0
$331$	0.915615	−	2.81797i	0.0503268	−	0.154890i	−0.922735	−	0.385436i	$-0.874051\pi$
$331$	0.915615	−	2.81797i	0.0503268	−	0.154890i	0.973061	+	0.230546i	$0.0740512\pi$
$332$	−4.15928			−0.228270
$333$	−1.21756	+	3.74725i	−0.0667217	+	0.205348i
$334$	8.76510	−	6.36822i	0.479605	−	0.348453i
$335$		0			0
$336$	−5.61615	−	4.08037i	−0.306386	−	0.222603i
$337$	15.2195	−	11.0576i	0.829057	−	0.602345i	−0.0902353	−	0.995920i	$-0.528762\pi$
$337$	15.2195	−	11.0576i	0.829057	−	0.602345i	0.919292	+	0.393575i	$0.128762\pi$
$338$	−2.72574	+	1.98037i	−0.148261	+	0.107718i
$339$	12.0182	+	8.73173i	0.652739	+	0.474242i
$340$		0			0
$341$	−0.220923	+	0.160510i	−0.0119636	+	0.00869209i
$342$	3.05331	−	9.39711i	0.165104	−	0.508138i
$343$	−12.9162			−0.697410
$344$	−1.04264	+	3.20891i	−0.0562152	+	0.173013i
$345$		0			0
$346$	3.71467	+	11.4326i	0.199702	+	0.614620i
$347$	−7.02649	−	21.6253i	−0.377201	−	1.16091i	−0.941981	−	0.335665i	$-0.891039\pi$
$347$	−7.02649	−	21.6253i	−0.377201	−	1.16091i	0.564780	−	0.825242i	$-0.308961\pi$
$348$	−22.4898	−	16.3398i	−1.20558	−	0.875906i
$349$	1.93849			0.103765			0.0518824	−	0.998653i	$-0.483478\pi$
$349$	1.93849			0.103765			0.0518824	+	0.998653i	$0.483478\pi$
$350$		0			0
$351$	−8.65392			−0.461912
$352$	−13.0867	−	9.50802i	−0.697522	−	0.506779i
$353$	1.62217	+	4.99252i	0.0863394	+	0.265725i	0.984900	−	0.173124i	$-0.0553862\pi$
$353$	1.62217	+	4.99252i	0.0863394	+	0.265725i	−0.898561	+	0.438849i	$0.855386\pi$
$354$	6.96689	+	21.4419i	0.370286	+	1.13962i
$355$		0			0
$356$	10.5285	−	32.4033i	0.558008	−	1.71737i
$357$	−6.31519			−0.334235
$358$	−5.58612	+	17.1923i	−0.295236	+	0.908642i
$359$	−18.2787	+	13.2803i	−0.964713	+	0.700905i	−0.954241	−	0.299040i	$-0.903334\pi$
$359$	−18.2787	+	13.2803i	−0.964713	+	0.700905i	−0.0104726	+	0.999945i	$0.503334\pi$
$360$		0			0
$361$	9.96746	+	7.24178i	0.524603	+	0.381146i
$362$	24.1091	−	17.5163i	1.26715	−	0.920637i
$363$	−12.4503	+	9.04569i	−0.653472	+	0.474775i
$364$	6.36167	+	4.62203i	0.333442	+	0.242260i
$365$		0			0
$366$	10.2727	−	7.46353i	0.536961	−	0.390125i
$367$	−2.25543	+	6.94150i	−0.117732	+	0.362343i	−0.992507	−	0.122187i	$-0.961009\pi$
$367$	−2.25543	+	6.94150i	−0.117732	+	0.362343i	0.874775	+	0.484530i	$0.161009\pi$
$368$	14.4759			0.754610
$369$	4.89105	−	15.0531i	0.254618	−	0.783634i
$370$		0			0
$371$	2.32001	+	7.14025i	0.120449	+	0.370703i
$372$	−0.217838	−	0.670438i	−0.0112944	−	0.0347606i
$373$	18.0470	+	13.1119i	0.934440	+	0.678911i	0.947076	−	0.321010i	$-0.104022\pi$
$373$	18.0470	+	13.1119i	0.934440	+	0.678911i	−0.0126358	+	0.999920i	$0.504022\pi$
$374$	−12.0718			−0.624216
$375$		0			0
$376$	−7.21188			−0.371924
$377$	−14.6974	−	10.6783i	−0.756953	−	0.549959i
$378$	−1.64019	−	5.04798i	−0.0843621	−	0.259640i
$379$	−10.1811	−	31.3341i	−0.522966	−	1.60952i	−0.768303	−	0.640086i	$-0.778899\pi$
$379$	−10.1811	−	31.3341i	−0.522966	−	1.60952i	0.245337	−	0.969438i	$-0.421101\pi$
$380$		0			0
$381$	1.01282	−	3.11713i	0.0518881	−	0.159695i
$382$	2.64072			0.135111
$383$	−6.39671	+	19.6871i	−0.326857	+	1.00596i	0.643739	+	0.765245i	$0.277382\pi$
$383$	−6.39671	+	19.6871i	−0.326857	+	1.00596i	−0.970595	+	0.240716i	$0.922618\pi$
$384$	10.1811	−	7.39697i	0.519550	−	0.377475i
$385$		0			0
$386$	35.7194	+	25.9517i	1.81807	+	1.32091i
$387$	−6.88806	+	5.00447i	−0.350140	+	0.254391i
$388$	32.3537	−	23.5063i	1.64251	−	1.19335i
$389$	0.925886	+	0.672696i	0.0469443	+	0.0341070i	0.611010	−	0.791623i	$-0.290764\pi$
$389$	0.925886	+	0.672696i	0.0469443	+	0.0341070i	−0.564066	+	0.825730i	$0.690764\pi$
$390$		0			0
$391$	10.6539	−	7.74052i	0.538792	−	0.391455i
$392$	1.35048	−	4.15636i	0.0682098	−	0.209928i
$393$	−31.0310			−1.56531
$394$	7.86239	−	24.1980i	0.396102	−	1.21908i
$395$		0			0
$396$	2.66095	+	8.18955i	0.133718	+	0.411540i
$397$	−1.44779	−	4.45583i	−0.0726623	−	0.223631i	0.908129	−	0.418690i	$-0.137510\pi$
$397$	−1.44779	−	4.45583i	−0.0726623	−	0.223631i	−0.980792	+	0.195058i	$0.937510\pi$
$398$	17.5560	+	12.7552i	0.880005	+	0.639361i
$399$	5.63877			0.282292
$400$		0			0
$401$	−24.0851			−1.20275			−0.601376	−	0.798966i	$-0.705381\pi$
$401$	−24.0851			−1.20275			−0.601376	+	0.798966i	$0.705381\pi$
$402$	−8.10687	−	5.88998i	−0.404334	−	0.293766i
$403$	−0.142360	−	0.438139i	−0.00709146	−	0.0218253i
$404$	−1.84847	−	5.68902i	−0.0919650	−	0.283039i
$405$		0			0
$406$	3.44320	−	10.5971i	0.170883	−	0.525925i
$407$	−4.29821			−0.213054
$408$	1.42871	−	4.39711i	0.0707316	−	0.217689i
$409$	1.53660	−	1.11641i	0.0759801	−	0.0552027i	−0.549147	−	0.835726i	$-0.685047\pi$
$409$	1.53660	−	1.11641i	0.0759801	−	0.0552027i	0.625127	+	0.780523i	$0.285047\pi$
$410$		0			0
$411$	−1.22626	−	0.890932i	−0.0604871	−	0.0439464i
$412$	−19.3134	+	14.0320i	−0.951501	+	0.691306i
$413$	−3.94830	+	2.86861i	−0.194283	+	0.141155i
$414$	−14.0718	−	10.2237i	−0.691589	−	0.502469i
$415$		0			0
$416$	22.0776	−	16.0403i	1.08244	−	0.786441i
$417$	11.2584	−	34.6499i	0.551328	−	1.69681i
$418$	10.7788			0.527207
$419$	−0.719410	+	2.21412i	−0.0351455	+	0.108167i	−0.967090	−	0.254434i	$-0.918111\pi$
$419$	−0.719410	+	2.21412i	−0.0351455	+	0.108167i	0.931945	+	0.362600i	$0.118111\pi$
$420$		0			0
$421$	−7.40097	−	22.7779i	−0.360701	−	1.11012i	−0.952629	−	0.304134i	$-0.901633\pi$
$421$	−7.40097	−	22.7779i	−0.360701	−	1.11012i	0.591928	−	0.805991i	$-0.298367\pi$
$422$	5.57891	+	17.1701i	0.271577	+	0.835829i
$423$	−14.7229	−	10.6968i	−0.715853	−	0.520098i
$424$	−5.49645			−0.266931
$425$		0			0
$426$	44.2060			2.14179
$427$	2.22371	+	1.61562i	0.107613	+	0.0781855i
$428$	−3.49584	−	10.7591i	−0.168978	−	0.520061i
$429$	4.58448	+	14.1096i	0.221341	+	0.681217i
$430$		0			0
$431$	0.368430	−	1.13391i	0.0177467	−	0.0546186i	−0.941791	−	0.336199i	$-0.890859\pi$
$431$	0.368430	−	1.13391i	0.0177467	−	0.0546186i	0.959538	+	0.281580i	$0.0908586\pi$
$432$	−8.16074			−0.392634
$433$	7.91511	−	24.3602i	0.380376	−	1.17068i	−0.559404	−	0.828895i	$-0.688970\pi$
$433$	7.91511	−	24.3602i	0.380376	−	1.17068i	0.939780	−	0.341781i	$-0.111030\pi$
$434$	0.228592	−	0.166082i	0.0109728	−	0.00797219i
$435$		0			0
$436$	−30.9196	−	22.4644i	−1.48078	−	1.07585i
$437$	−9.51278	+	6.91144i	−0.455058	+	0.330619i
$438$	−2.87786	+	2.09089i	−0.137510	+	0.0999066i
$439$	−15.6740	−	11.3878i	−0.748079	−	0.543511i	0.147152	−	0.989114i	$-0.452989\pi$
$439$	−15.6740	−	11.3878i	−0.748079	−	0.543511i	−0.895231	+	0.445603i	$0.852989\pi$
$440$		0			0
$441$	8.92181	−	6.48207i	0.424848	−	0.308670i
$442$	6.29327	−	19.3687i	0.299340	−	0.921274i
$443$	−2.46263			−0.117003			−0.0585016	−	0.998287i	$-0.518632\pi$
$443$	−2.46263			−0.117003			−0.0585016	+	0.998287i	$0.518632\pi$
$444$	3.42878	−	10.5527i	0.162723	−	0.500809i
$445$		0			0
$446$	−18.2641	−	56.2113i	−0.864833	−	2.66168i
$447$	−2.18184	−	6.71502i	−0.103198	−	0.317610i
$448$	8.43190	+	6.12613i	0.398370	+	0.289433i
$449$	−14.3585			−0.677618			−0.338809	−	0.940855i	$-0.610024\pi$
$449$	−14.3585			−0.677618			−0.338809	+	0.940855i	$0.610024\pi$
$450$		0			0
$451$	17.2664			0.813041
$452$	−12.8378	−	9.32717i	−0.603837	−	0.438713i
$453$	−12.0156	−	36.9802i	−0.564542	−	1.73748i
$454$	−14.3321	−	44.1098i	−0.672641	−	2.07018i
$455$		0			0
$456$	−1.27568	+	3.92614i	−0.0597392	+	0.183858i
$457$	25.1964			1.17864			0.589319	−	0.807901i	$-0.299396\pi$
$457$	25.1964			1.17864			0.589319	+	0.807901i	$0.299396\pi$
$458$	−1.59524	+	4.90965i	−0.0745408	+	0.229413i
$459$	−6.00610	+	4.36369i	−0.280341	+	0.203679i
$460$		0			0
$461$	−23.3203	−	16.9432i	−1.08614	−	0.789124i	−0.107394	−	0.994217i	$-0.534251\pi$
$461$	−23.3203	−	16.9432i	−1.08614	−	0.789124i	−0.978743	+	0.205092i	$0.934251\pi$
$462$	−7.36146	+	5.34841i	−0.342486	+	0.248831i
$463$	25.7911	−	18.7384i	1.19862	−	0.870846i	0.204468	−	0.978873i	$-0.434453\pi$
$463$	25.7911	−	18.7384i	1.19862	−	0.870846i	0.994148	+	0.108028i	$0.0344535\pi$
$464$	−13.8598	−	10.0697i	−0.643425	−	0.467475i
$465$		0			0
$466$	10.0480	−	7.30033i	0.465466	−	0.338181i
$467$	−13.3185	+	40.9902i	−0.616307	+	1.89680i	−0.237106	+	0.971484i	$0.576199\pi$
$467$	−13.3185	+	40.9902i	−0.616307	+	1.89680i	−0.379201	+	0.925314i	$0.623801\pi$
$468$	−14.5270			−0.671512
$469$	0.670307	−	2.06299i	0.0309519	−	0.0952601i
$470$		0			0
$471$	−1.12444	−	3.46068i	−0.0518115	−	0.159460i
$472$	−1.10410	−	3.39808i	−0.0508205	−	0.156409i
$473$	−7.51411	−	5.45932i	−0.345499	−	0.251020i
$474$	72.6679			3.33775
$475$		0			0
$476$	6.74584			0.309195
$477$	−11.2209	−	8.15246i	−0.513770	−	0.373276i
$478$	4.53161	+	13.9469i	0.207271	+	0.637915i
$479$	6.49749	+	19.9972i	0.296878	+	0.913697i	0.982584	+	0.185818i	$0.0594935\pi$
$479$	6.49749	+	19.9972i	0.296878	+	0.913697i	−0.685706	+	0.727878i	$0.740506\pi$
$480$		0			0
$481$	2.24075	−	6.89631i	0.102169	−	0.314445i
$482$	−2.46014			−0.112057
$483$	3.06739	−	9.44047i	0.139571	−	0.429556i
$484$	13.2993	−	9.66254i	0.604516	−	0.439206i
$485$		0			0
$486$	28.3323	+	20.5846i	1.28518	+	0.933739i
$487$	−22.5869	+	16.4104i	−1.02351	+	0.743625i	−0.967000	−	0.254777i	$-0.917998\pi$
$487$	−22.5869	+	16.4104i	−1.02351	+	0.743625i	−0.0565121	+	0.998402i	$0.517998\pi$
$488$	−1.62800	+	1.18281i	−0.0736960	+	0.0535433i
$489$	1.58819	+	1.15389i	0.0718204	+	0.0521805i
$490$		0			0
$491$	−12.1037	+	8.79389i	−0.546234	+	0.396862i	−0.826395	−	0.563091i	$-0.809612\pi$
$491$	−12.1037	+	8.79389i	−0.546234	+	0.396862i	0.280161	+	0.959953i	$0.409612\pi$
$492$	−13.7738	+	42.3913i	−0.620969	+	1.91115i
$493$	−15.5849			−0.701909
$494$	−5.61920	+	17.2941i	−0.252820	+	0.778099i
$495$		0			0
$496$	−0.134247	−	0.413170i	−0.00602787	−	0.0185519i
$497$	2.95706	+	9.10089i	0.132642	+	0.408231i
$498$	6.56888	+	4.77257i	0.294359	+	0.213864i
$499$	−44.3253			−1.98427			−0.992137	−	0.125160i	$-0.960056\pi$
$499$	−44.3253			−1.98427			−0.992137	+	0.125160i	$0.960056\pi$
$500$		0			0
$501$	−11.4224			−0.510316
$502$	7.77498	+	5.64885i	0.347014	+	0.252121i
$503$	−7.29936	−	22.4651i	−0.325462	−	1.00167i	−0.971232	−	0.238137i	$-0.923463\pi$
$503$	−7.29936	−	22.4651i	−0.325462	−	1.00167i	0.645769	−	0.763532i	$-0.276537\pi$
$504$	−0.408487	−	1.25719i	−0.0181955	−	0.0559999i
$505$		0			0
$506$	5.86346	−	18.0459i	0.260663	−	0.802237i
$507$	3.55211			0.157755
$508$	−1.08188	+	3.32969i	−0.0480008	+	0.147731i
$509$	21.6132	−	15.7029i	0.957990	−	0.696020i	0.00530682	−	0.999986i	$-0.498311\pi$
$509$	21.6132	−	15.7029i	0.957990	−	0.696020i	0.952683	+	0.303966i	$0.0983108\pi$
$510$		0			0
$511$	−0.622968	−	0.452613i	−0.0275585	−	0.0200224i
$512$	24.5598	−	17.8438i	1.08540	−	0.788591i
$513$	5.36279	−	3.89629i	0.236773	−	0.172026i
$514$	−16.4577	−	11.9572i	−0.725918	−	0.527410i
$515$		0			0
$516$	19.3976	−	14.0931i	0.853930	−	0.620416i
$517$	6.13479	−	18.8809i	0.269808	−	0.830383i
$518$	4.44743			0.195409
$519$	3.91633	−	12.0532i	0.171908	−	0.529078i
$520$		0			0
$521$	10.1071	+	31.1065i	0.442800	+	1.36280i	0.884878	+	0.465822i	$0.154241\pi$
$521$	10.1071	+	31.1065i	0.442800	+	1.36280i	−0.442078	+	0.896977i	$0.645759\pi$
$522$	6.36101	+	19.5772i	0.278414	+	0.856869i
$523$	−0.190901	−	0.138697i	−0.00834750	−	0.00606481i	0.583604	−	0.812039i	$-0.301642\pi$
$523$	−0.190901	−	0.138697i	−0.00834750	−	0.00606481i	−0.591951	+	0.805974i	$0.701642\pi$
$524$	33.1471			1.44804
$525$		0			0
$526$	−2.07658			−0.0905434
$527$	−0.319732	−	0.232299i	−0.0139277	−	0.0101191i
$528$	4.32322	+	13.3055i	0.188144	+	0.579048i
$529$	−0.710999	−	2.18823i	−0.0309130	−	0.0951405i
$530$		0			0
$531$	2.78611	−	8.57476i	0.120907	−	0.372113i
$532$	−6.02330			−0.261143
$533$	−9.00132	+	27.7032i	−0.389890	+	1.19996i
$534$	−53.8091	+	39.0946i	−2.32855	+	1.69179i
$535$		0			0
$536$	1.28477	+	0.933437i	0.0554934	+	0.0403183i
$537$	15.4186	−	11.2023i	0.665361	−	0.483413i
$538$	−5.54786	+	4.03076i	−0.239185	+	0.173778i
$539$	9.73271	+	7.07123i	0.419217	+	0.304579i
$540$		0			0
$541$	27.1484	−	19.7244i	1.16720	−	0.848020i	0.176528	−	0.984296i	$-0.443513\pi$
$541$	27.1484	−	19.7244i	1.16720	−	0.848020i	0.990671	+	0.136276i	$0.0435133\pi$
$542$	−7.82935	+	24.0963i	−0.336299	+	1.03502i
$543$	−31.4183			−1.34829
$544$	7.23434	−	22.2650i	0.310170	−	0.954604i
$545$		0			0
$546$	−4.74364	−	14.5994i	−0.203009	−	0.624798i
$547$	11.9010	+	36.6276i	0.508851	+	1.56608i	0.794199	+	0.607658i	$0.207891\pi$
$547$	11.9010	+	36.6276i	0.508851	+	1.56608i	−0.285348	+	0.958424i	$0.592109\pi$
$548$	1.30989	+	0.951688i	0.0559555	+	0.0406541i
$549$	−5.07790			−0.216720
$550$		0			0
$551$	13.9156			0.592825
$552$	5.87922	+	4.27150i	0.250236	+	0.181807i
$553$	4.86095	+	14.9605i	0.206708	+	0.636183i
$554$	7.64668	+	23.5341i	0.324876	+	0.999866i
$555$		0			0
$556$	−12.0262	+	37.0128i	−0.510024	+	1.56969i
$557$	4.33445			0.183657			0.0918283	−	0.995775i	$-0.470729\pi$
$557$	4.33445			0.183657			0.0918283	+	0.995775i	$0.470729\pi$
$558$	−0.161306	+	0.496448i	−0.00682861	+	0.0210163i
$559$	12.6765	−	9.21004i	0.536160	−	0.389543i
$560$		0			0
$561$	10.2965	+	7.48081i	0.434717	+	0.315840i
$562$	−41.5712	+	30.2032i	−1.75357	+	1.27405i
$563$	28.2362	−	20.5148i	1.19001	−	0.864595i	0.196747	−	0.980454i	$-0.436962\pi$
$563$	28.2362	−	20.5148i	1.19001	−	0.864595i	0.993266	+	0.115860i	$0.0369623\pi$
$564$	41.4614	+	30.1235i	1.74584	+	1.26843i
$565$		0			0
$566$	−5.67421	+	4.12255i	−0.238505	+	0.173284i
$567$	−3.41593	+	10.5132i	−0.143456	+	0.441511i
$568$	−7.00572			−0.293953
$569$	−12.9678	+	39.9107i	−0.543637	+	1.67314i	0.180571	+	0.983562i	$0.442205\pi$
$569$	−12.9678	+	39.9107i	−0.543637	+	1.67314i	−0.724208	+	0.689581i	$0.757795\pi$
$570$		0			0
$571$	−4.27469	−	13.1561i	−0.178890	−	0.550567i	0.820900	−	0.571072i	$-0.193472\pi$
$571$	−4.27469	−	13.1561i	−0.178890	−	0.550567i	−0.999790	+	0.0205055i	$0.993472\pi$
$572$	−4.89711	−	15.0718i	−0.204759	−	0.630182i
$573$	−2.25237	−	1.63644i	−0.0940940	−	0.0683633i
$574$	−17.8658			−0.745704
$575$		0			0
$576$	−19.2544			−0.802268
$577$	−10.3387	−	7.51147i	−0.430404	−	0.312707i	0.351407	−	0.936223i	$-0.385704\pi$
$577$	−10.3387	−	7.51147i	−0.430404	−	0.312707i	−0.781810	+	0.623516i	$0.785704\pi$
$578$	5.55579	+	17.0990i	0.231090	+	0.711223i
$579$	−14.3843	−	44.2703i	−0.597791	−	1.83981i
$580$		0			0
$581$	−0.543140	+	1.67161i	−0.0225333	+	0.0693502i
$582$	−78.0696			−3.23609
$583$	4.67556	−	14.3899i	0.193642	−	0.595968i
$584$	0.456080	−	0.331361i	0.0188727	−	0.0137118i
$585$		0			0
$586$	−15.1215	−	10.9864i	−0.624665	−	0.453845i
$587$	−9.85945	+	7.16331i	−0.406943	+	0.295661i	−0.772363	−	0.635181i	$-0.780925\pi$
$587$	−9.85945	+	7.16331i	−0.406943	+	0.295661i	0.365420	+	0.930843i	$0.380925\pi$
$588$	−25.1248	+	18.2543i	−1.03613	+	0.752793i
$589$	0.285485	+	0.207417i	0.0117632	+	0.00854648i
$590$		0			0
$591$	−21.7015	+	15.7671i	−0.892680	+	0.648570i
$592$	2.11305	−	6.50330i	0.0868459	−	0.267284i
$593$	31.2580			1.28361			0.641807	−	0.766866i	$-0.278185\pi$
$593$	31.2580			1.28361			0.641807	+	0.766866i	$0.278185\pi$
$594$	−3.30550	+	10.1733i	−0.135626	+	0.417415i
$595$		0			0
$596$	2.33063	+	7.17294i	0.0954663	+	0.293815i
$597$	−7.06986	−	21.7588i	−0.289350	−	0.890528i
$598$	25.8972	+	18.8154i	1.05901	+	0.769419i
$599$	−33.3707			−1.36349			−0.681746	−	0.731589i	$-0.738779\pi$
$599$	−33.3707			−1.36349			−0.681746	+	0.731589i	$0.738779\pi$
$600$		0			0
$601$	−46.8052			−1.90922			−0.954611	−	0.297854i	$-0.903729\pi$
$601$	−46.8052			−1.90922			−0.954611	+	0.297854i	$0.903729\pi$
$602$	7.77498	+	5.64885i	0.316884	+	0.230230i
$603$	1.23833	+	3.81119i	0.0504287	+	0.155204i
$604$	12.8350	+	39.5020i	0.522248	+	1.60731i
$605$		0			0
$606$	−3.60852	+	11.1059i	−0.146586	+	0.451145i
$607$	−30.7401			−1.24770			−0.623851	−	0.781543i	$-0.714433\pi$
$607$	−30.7401			−1.24770			−0.623851	+	0.781543i	$0.714433\pi$
$608$	−6.45947	+	19.8802i	−0.261966	+	0.806249i
$609$	−9.50380	+	6.90492i	−0.385114	+	0.279801i
$610$		0			0
$611$	27.0955	+	19.6861i	1.09617	+	0.796413i
$612$	−10.0822	+	7.32517i	−0.407550	+	0.296102i
$613$	−30.9768	+	22.5060i	−1.25114	+	0.909008i	−0.998288	−	0.0584964i	$-0.981369\pi$
$613$	−30.9768	+	22.5060i	−1.25114	+	0.909008i	−0.252854	+	0.967504i	$0.581369\pi$
$614$	15.9953	+	11.6213i	0.645518	+	0.468996i
$615$		0			0
$616$	1.16663	−	0.847609i	0.0470050	−	0.0341512i
$617$	−0.131427	+	0.404490i	−0.00529104	+	0.0162842i	−0.953667	−	0.300864i	$-0.902725\pi$
$617$	−0.131427	+	0.404490i	−0.00529104	+	0.0162842i	0.948376	+	0.317148i	$0.102725\pi$
$618$	46.6032			1.87466
$619$	2.32117	−	7.14384i	0.0932958	−	0.287135i	−0.893510	−	0.449043i	$-0.851765\pi$
$619$	2.32117	−	7.14384i	0.0932958	−	0.287135i	0.986806	+	0.161908i	$0.0517649\pi$
$620$		0			0
$621$	−3.60594	−	11.0979i	−0.144701	−	0.445345i
$622$	−18.9012	−	58.1720i	−0.757870	−	2.33248i
$623$	−11.6480	−	8.46278i	−0.466668	−	0.339054i
$624$	−23.6020			−0.944834
$625$		0			0
$626$	−39.3912			−1.57439
$627$	−9.19361	−	6.67955i	−0.367157	−	0.266755i
$628$	1.20112	+	3.69667i	0.0479300	+	0.147513i
$629$	−1.92227	−	5.91615i	−0.0766461	−	0.235892i
$630$		0			0
$631$	−3.48311	+	10.7199i	−0.138660	+	0.426752i	−0.996141	−	0.0877630i	$-0.972028\pi$
$631$	−3.48311	+	10.7199i	−0.138660	+	0.426752i	0.857481	+	0.514515i	$0.172028\pi$
$632$	−11.5163			−0.458094
$633$	5.88178	−	18.1023i	0.233780	−	0.719500i
$634$	38.4463	−	27.9329i	1.52690	−	1.10936i
$635$		0			0
$636$	31.5994	+	22.9583i	1.25300	+	0.910355i
$637$	−16.4194	+	11.9294i	−0.650560	+	0.472659i
$638$	−18.1669	+	13.1991i	−0.719236	+	0.522556i
$639$	−14.3020	−	10.3910i	−0.565780	−	0.411063i
$640$		0			0
$641$	−21.1012	+	15.3309i	−0.833447	+	0.605535i	−0.920533	−	0.390666i	$-0.872245\pi$
$641$	−21.1012	+	15.3309i	−0.833447	+	0.605535i	0.0870851	+	0.996201i	$0.472245\pi$
$642$	−6.82445	+	21.0035i	−0.269340	+	0.828942i
$643$	31.9492			1.25995			0.629977	−	0.776614i	$-0.283064\pi$
$643$	31.9492			1.25995			0.629977	+	0.776614i	$0.283064\pi$
$644$	−3.27657	+	10.0842i	−0.129115	+	0.397375i
$645$		0			0
$646$	4.82055	+	14.8361i	0.189662	+	0.583720i
$647$	2.28497	+	7.03243i	0.0898316	+	0.276473i	0.985872	−	0.167499i	$-0.0535690\pi$
$647$	2.28497	+	7.03243i	0.0898316	+	0.276473i	−0.896041	+	0.443972i	$0.853569\pi$
$648$	−6.54726	−	4.75686i	−0.257201	−	0.186867i
$649$	9.83550			0.386077
$650$		0			0
$651$	−0.297895			−0.0116754
$652$	−1.69649	−	1.23257i	−0.0664398	−	0.0482713i
$653$	−5.77407	−	17.7708i	−0.225957	−	0.695424i	−0.998193	−	0.0600882i	$-0.980862\pi$
$653$	−5.77407	−	17.7708i	−0.225957	−	0.695424i	0.772236	−	0.635336i	$-0.219138\pi$
$654$	23.0555	+	70.9575i	0.901541	+	2.77466i
$655$		0			0
$656$	−8.48835	+	26.1245i	−0.331414	+	1.01999i
$657$	1.42256			0.0554994
$658$	−6.34777	+	19.5364i	−0.247462	+	0.761609i
$659$	−7.92963	+	5.76122i	−0.308895	+	0.224425i	−0.731422	−	0.681925i	$-0.761143\pi$
$659$	−7.92963	+	5.76122i	−0.308895	+	0.224425i	0.422527	+	0.906350i	$0.361143\pi$
$660$		0			0
$661$	22.7807	+	16.5511i	0.886066	+	0.643765i	0.934849	−	0.355045i	$-0.115534\pi$
$661$	22.7807	+	16.5511i	0.886066	+	0.643765i	−0.0487833	+	0.998809i	$0.515534\pi$
$662$	4.99866	−	3.63174i	0.194278	−	0.141152i
$663$	−17.3704	+	12.6204i	−0.674612	+	0.490134i
$664$	−1.04103	−	0.756351i	−0.0403997	−	0.0293521i
$665$		0			0
$666$	−6.64706	+	4.82937i	−0.257568	+	0.187134i
$667$	7.56986	−	23.2976i	0.293106	−	0.902087i
$668$	12.2014			0.472085
$669$	−19.2557	+	59.2629i	−0.744468	+	2.29124i
$670$		0			0
$671$	−1.71178	−	5.26831i	−0.0660825	−	0.203381i
$672$	−5.45299	−	16.7826i	−0.210354	−	0.647402i
$673$	−31.5721	−	22.9385i	−1.21702	−	0.884214i	−0.221168	−	0.975236i	$-0.570987\pi$
$673$	−31.5721	−	22.9385i	−1.21702	−	0.884214i	−0.995849	+	0.0910215i	$0.970987\pi$
$674$	39.2290			1.51104
$675$		0			0
$676$	−3.79434			−0.145936
$677$	4.07367	+	2.95969i	0.156564	+	0.113750i	0.663309	−	0.748346i	$-0.269152\pi$
$677$	4.07367	+	2.95969i	0.156564	+	0.113750i	−0.506745	+	0.862096i	$0.669152\pi$
$678$	9.57259	+	29.4614i	0.367633	+	1.13146i
$679$	−5.22228	−	16.0725i	−0.200413	−	0.616807i
$680$		0			0
$681$	−15.1102	+	46.5044i	−0.579025	+	1.78205i
$682$	−0.569440			−0.0218050
$683$	9.37285	−	28.8467i	0.358642	−	1.10379i	−0.595225	−	0.803559i	$-0.702937\pi$
$683$	9.37285	−	28.8467i	0.358642	−	1.10379i	0.953867	−	0.300228i	$-0.0970628\pi$
$684$	9.00233	−	6.54058i	0.344213	−	0.250085i
$685$		0			0
$686$	−21.7900	−	15.8314i	−0.831948	−	0.604446i
$687$	4.40313	−	3.19906i	0.167990	−	0.122052i
$688$	11.9541	−	8.68518i	0.455747	−	0.331119i
$689$	20.6506	+	15.0035i	0.786724	+	0.571588i
$690$		0			0
$691$	17.1778	−	12.4804i	0.653474	−	0.474777i	−0.210979	−	0.977491i	$-0.567665\pi$
$691$	17.1778	−	12.4804i	0.653474	−	0.474777i	0.864453	+	0.502714i	$0.167665\pi$
$692$	−4.18340	+	12.8752i	−0.159029	+	0.489441i
$693$	3.63886			0.138229
$694$	14.6522	−	45.0949i	0.556191	−	1.71178i
$695$		0			0
$696$	−2.65765	−	8.17939i	−0.100738	−	0.310039i
$697$	7.72198	+	23.7658i	0.292491	+	0.900194i
$698$	3.27029	+	2.37600i	0.123782	+	0.0899330i
$699$	−13.0943			−0.495273
$700$		0			0
$701$	32.7698			1.23770			0.618849	−	0.785510i	$-0.287599\pi$
$701$	32.7698			1.23770			0.618849	+	0.785510i	$0.287599\pi$
$702$	−14.5994	−	10.6071i	−0.551020	−	0.400339i
$703$	1.71638	+	5.28247i	0.0647345	+	0.199232i
$704$	−6.49074	−	19.9764i	−0.244629	−	0.752890i
$705$		0			0
$706$	−3.38269	+	10.4108i	−0.127309	+	0.391817i
$707$	−2.52780			−0.0950676
$708$	−7.84600	+	24.1475i	−0.294871	+	0.907519i
$709$	−16.0557	+	11.6652i	−0.602985	+	0.438094i	−0.846937	−	0.531693i	$-0.821556\pi$
$709$	−16.0557	+	11.6652i	−0.602985	+	0.438094i	0.243952	+	0.969787i	$0.421556\pi$
$710$		0			0
$711$	−23.5103	−	17.0813i	−0.881707	−	0.640598i
$712$	8.52760	−	6.19566i	0.319585	−	0.232192i
$713$	0.502558	−	0.365130i	0.0188210	−	0.0136742i
$714$	−10.6539	−	7.74052i	−0.398713	−	0.289682i
$715$		0			0
$716$	−16.4700	+	11.9662i	−0.615514	+	0.447197i
$717$	4.77763	−	14.7040i	0.178424	−	0.549132i
$718$	−47.1144			−1.75829
$719$	7.48443	−	23.0347i	0.279122	−	0.859049i	−0.708977	−	0.705231i	$-0.750843\pi$
$719$	7.48443	−	23.0347i	0.279122	−	0.859049i	0.988099	−	0.153818i	$-0.0491569\pi$
$720$		0			0
$721$	3.11741	+	9.59440i	0.116098	+	0.357314i
$722$	7.93916	+	24.4342i	0.295465	+	0.909347i
$723$	2.09835	+	1.52454i	0.0780384	+	0.0566982i
$724$	33.5609			1.24728
$725$		0			0
$726$	−32.0914			−1.19102
$727$	−4.74496	−	3.44742i	−0.175981	−	0.127858i	0.496308	−	0.868147i	$-0.334689\pi$
$727$	−4.74496	−	3.44742i	−0.175981	−	0.127858i	−0.672289	+	0.740289i	$0.734689\pi$
$728$	0.751766	+	2.31370i	0.0278623	+	0.0857513i
$729$	−1.08320	−	3.33374i	−0.0401185	−	0.123472i
$730$		0			0
$731$	4.15382	−	12.7841i	0.153635	−	0.472838i
$732$	14.3000			0.528542
$733$	10.6615	−	32.8129i	0.393793	−	1.21197i	−0.536104	−	0.844152i	$-0.680105\pi$
$733$	10.6615	−	32.8129i	0.393793	−	1.21197i	0.929897	−	0.367819i	$-0.119895\pi$
$734$	−12.3132	+	8.94604i	−0.454487	+	0.330204i
$735$		0			0
$736$	29.7698	+	21.6290i	1.09733	+	0.797255i
$737$	−3.53666	+	2.56953i	−0.130274	+	0.0946499i
$738$	26.7019	−	19.4001i	0.982912	−	0.714128i
$739$	−32.0138	−	23.2594i	−1.17765	−	0.855611i	−0.185743	−	0.982598i	$-0.559469\pi$
$739$	−32.0138	−	23.2594i	−1.17765	−	0.855611i	−0.991904	+	0.126988i	$0.959469\pi$
$740$		0			0
$741$	15.5099	−	11.2686i	0.569770	−	0.413962i
$742$	−4.83788	+	14.8895i	−0.177604	+	0.546609i
$743$	−29.7058			−1.08980			−0.544900	−	0.838501i	$-0.683433\pi$
$743$	−29.7058			−1.08980			−0.544900	+	0.838501i	$0.683433\pi$
$744$	0.0673939	−	0.207417i	0.00247078	−	0.00760428i
$745$		0			0
$746$	14.3746	+	44.2405i	0.526292	+	1.61976i
$747$	−1.00340	−	3.08815i	−0.0367126	−	0.112990i
$748$	−10.9986	−	7.99095i	−0.402149	−	0.292178i
$749$	−4.78058			−0.174679
$750$		0			0
$751$	26.8870			0.981122			0.490561	−	0.871407i	$-0.336792\pi$
$751$	26.8870			0.981122			0.490561	+	0.871407i	$0.336792\pi$
$752$	25.5514	+	18.5642i	0.931764	+	0.676966i
$753$	−3.13100	−	9.63623i	−0.114100	−	0.351164i
$754$	−11.7066	−	36.0291i	−0.426328	−	1.31210i
$755$		0			0
$756$	1.84715	−	5.68495i	0.0671803	−	0.206760i
$757$	44.6792			1.62389			0.811947	−	0.583731i	$-0.198408\pi$
$757$	44.6792			1.62389			0.811947	+	0.583731i	$0.198408\pi$
$758$	21.2304	−	65.3405i	0.771123	−	2.37327i
$759$	−16.1841	+	11.7584i	−0.587446	+	0.426804i
$760$		0			0
$761$	−16.4295	−	11.9367i	−0.595568	−	0.432706i	0.248735	−	0.968572i	$-0.419985\pi$
$761$	−16.4295	−	11.9367i	−0.595568	−	0.432706i	−0.844303	+	0.535866i	$0.819985\pi$
$762$	5.52931	−	4.01728i	0.200306	−	0.145531i
$763$	−13.0661	+	9.49307i	−0.473024	+	0.343672i
$764$	2.40596	+	1.74803i	0.0870447	+	0.0632417i
$765$		0			0
$766$	−34.9219	+	25.3722i	−1.26178	+	0.916736i
$767$	−5.12746	+	15.7807i	−0.185142	+	0.569808i
$768$	−19.9359			−0.719375
$769$	8.05227	−	24.7823i	0.290372	−	0.893674i	−0.694364	−	0.719624i	$-0.744314\pi$
$769$	8.05227	−	24.7823i	0.290372	−	0.893674i	0.984737	−	0.174051i	$-0.0556856\pi$
$770$		0			0
$771$	6.62755	+	20.3975i	0.238685	+	0.734598i
$772$	15.3652	+	47.2892i	0.553006	+	1.70198i
$773$	−11.1082	−	8.07058i	−0.399534	−	0.290278i	0.369817	−	0.929105i	$-0.379420\pi$
$773$	−11.1082	−	8.07058i	−0.399534	−	0.290278i	−0.769351	+	0.638826i	$0.779420\pi$
$774$	−17.7543			−0.638166
$775$		0			0
$776$	12.3724			0.444142
$777$	−3.79338	−	2.75605i	−0.136087	−	0.0988728i
$778$	0.737476	+	2.26972i	0.0264398	+	0.0813733i
$779$	−6.89488	−	21.2203i	−0.247035	−	0.760295i
$780$		0			0
$781$	5.95942	−	18.3412i	0.213245	−	0.656300i
$782$	27.4610			0.982005
$783$	−4.26747	+	13.1339i	−0.152507	+	0.469368i
$784$	−15.4837	+	11.2495i	−0.552988	+	0.401769i
$785$		0			0
$786$	−52.3503	−	38.0347i	−1.86727	−	1.35665i
$787$	15.9101	−	11.5594i	0.567136	−	0.412048i	−0.266928	−	0.963716i	$-0.586009\pi$
$787$	15.9101	−	11.5594i	0.567136	−	0.412048i	0.834064	+	0.551668i	$0.186009\pi$
$788$	23.1814	−	16.8423i	0.825803	−	0.599981i
$789$	1.77120	+	1.28685i	0.0630562	+	0.0458130i
$790$		0			0
$791$	−5.42501	+	3.94150i	−0.192891	+	0.140144i
$792$	−0.823232	+	2.53365i	−0.0292523	+	0.0900293i
$793$	9.34520			0.331858
$794$	3.01905	−	9.29167i	0.107142	−	0.329749i
$795$		0			0
$796$	7.55197	+	23.2426i	0.267673	+	0.823812i
$797$	3.38191	+	10.4085i	0.119793	+	0.368686i	0.992917	−	0.118813i	$-0.0379090\pi$
$797$	3.38191	+	10.4085i	0.119793	+	0.368686i	−0.873123	+	0.487500i	$0.837909\pi$
$798$	9.51278	+	6.91144i	0.336749	+	0.244662i
$799$	28.7318			1.01646
$800$		0			0
$801$	26.5985			0.939812
$802$	−40.6323	−	29.5211i	−1.43478	−	1.04243i
$803$	0.479551	+	1.47591i	0.0169230	+	0.0520836i
$804$	−3.48728	−	10.7327i	−0.122987	−	0.378515i
$805$		0			0
$806$	0.296861	−	0.913645i	0.0104565	−	0.0321818i
$807$	7.22982			0.254502
$808$	0.571873	−	1.76004i	0.0201184	−	0.0619182i
$809$	−13.3025	+	9.66480i	−0.467689	+	0.339796i	−0.796540	−	0.604586i	$-0.793339\pi$
$809$	−13.3025	+	9.66480i	−0.467689	+	0.339796i	0.328851	+	0.944382i	$0.393339\pi$
$810$		0			0
$811$	−18.3220	−	13.3117i	−0.643373	−	0.467438i	0.217634	−	0.976030i	$-0.430166\pi$
$811$	−18.3220	−	13.3117i	−0.643373	−	0.467438i	−0.861007	+	0.508592i	$0.830166\pi$
$812$	10.1519	−	7.37579i	0.356262	−	0.258839i
$813$	21.6103	−	15.7008i	0.757906	−	0.550651i
$814$	−7.25121	−	5.26831i	−0.254155	−	0.184654i
$815$		0			0
$816$	−16.3805	+	11.9011i	−0.573433	+	0.416624i
$817$	−3.70891	+	11.4148i	−0.129758	+	0.399355i
$818$	3.96067			0.138482
$819$	−1.89701	+	5.83841i	−0.0662870	+	0.204011i
$820$		0			0
$821$	−12.2924	−	37.8322i	−0.429009	−	1.32035i	−0.899103	−	0.437737i	$-0.855780\pi$
$821$	−12.2924	−	37.8322i	−0.429009	−	1.32035i	0.470094	−	0.882616i	$-0.344220\pi$
$822$	−0.976728	−	3.00606i	−0.0340673	−	0.104848i
$823$	−13.3975	−	9.73384i	−0.467007	−	0.339300i	0.329267	−	0.944237i	$-0.393198\pi$
$823$	−13.3975	−	9.73384i	−0.467007	−	0.339300i	−0.796274	+	0.604937i	$0.793198\pi$
$824$	−7.38562			−0.257290
$825$		0			0
$826$	−10.1770			−0.354102
$827$	21.0637	+	15.3037i	0.732456	+	0.532160i	0.890339	−	0.455297i	$-0.150467\pi$
$827$	21.0637	+	15.3037i	0.732456	+	0.532160i	−0.157884	+	0.987458i	$0.550467\pi$
$828$	−6.05316	−	18.6297i	−0.210362	−	0.647428i
$829$	1.58945	+	4.89182i	0.0552039	+	0.169900i	0.974857	−	0.222832i	$-0.0715301\pi$
$829$	1.58945	+	4.89182i	0.0552039	+	0.169900i	−0.919653	+	0.392732i	$0.871530\pi$
$830$		0			0
$831$	8.06180	−	24.8117i	0.279661	−	0.860708i
$832$	35.4352			1.22849
$833$	−5.38027	+	16.5588i	−0.186415	+	0.573727i
$834$	61.4638	−	44.6560i	2.12832	−	1.54631i
$835$		0			0
$836$	9.82055	+	7.13505i	0.339651	+	0.246771i
$837$	−0.283315	+	0.205840i	−0.00979280	+	0.00711489i
$838$	−3.92751	+	2.85350i	−0.135674	+	0.0985726i
$839$	−31.2009	−	22.6688i	−1.07717	−	0.782612i	−0.0999856	−	0.994989i	$-0.531880\pi$
$839$	−31.2009	−	22.6688i	−1.07717	−	0.782612i	−0.977188	+	0.212377i	$0.931880\pi$
$840$		0			0
$841$	0.00757268	−	0.00550188i	0.000261127	−	0.000189720i
$842$	15.4331	−	47.4983i	0.531861	−	1.63690i
$843$	54.1744			1.86586
$844$	−6.28288	+	19.3367i	−0.216266	+	0.665597i
$845$		0			0
$846$	−11.7269	−	36.0918i	−0.403180	−	1.24086i
$847$	−2.14668	−	6.60679i	−0.0737607	−	0.227012i
$848$	19.4737	+	14.1485i	0.668730	+	0.485861i
$849$	7.39447			0.253777
$850$		0			0
$851$	9.77764			0.335173
$852$	40.2762	+	29.2624i	1.37984	+	1.00251i
$853$	2.82677	+	8.69991i	0.0967868	+	0.297879i	0.987715	−	0.156265i	$-0.0499452\pi$
$853$	2.82677	+	8.69991i	0.0967868	+	0.297879i	−0.890928	+	0.454144i	$0.849945\pi$
$854$	1.77121	+	5.45121i	0.0606094	+	0.186537i
$855$		0			0
$856$	1.08153	−	3.32861i	0.0369659	−	0.113769i
$857$	−13.6712			−0.466998			−0.233499	−	0.972357i	$-0.575018\pi$
$857$	−13.6712			−0.466998			−0.233499	+	0.972357i	$0.575018\pi$
$858$	−9.55995	+	29.4225i	−0.326371	+	1.00447i
$859$	28.8460	−	20.9579i	0.984213	−	0.715073i	0.0255669	−	0.999673i	$-0.491861\pi$
$859$	28.8460	−	20.9579i	0.984213	−	0.715073i	0.958646	+	0.284600i	$0.0918609\pi$
$860$		0			0
$861$	15.2384	+	11.0713i	0.519323	+	0.377310i
$862$	2.01139	−	1.46136i	0.0685082	−	0.0497741i
$863$	−27.4526	+	19.9455i	−0.934498	+	0.678953i	−0.947090	−	0.320968i	$-0.895992\pi$
$863$	−27.4526	+	19.9455i	−0.934498	+	0.678953i	0.0125918	+	0.999921i	$0.495992\pi$
$864$	−16.7826	−	12.1933i	−0.570955	−	0.414823i
$865$		0			0
$866$	43.2113	−	31.3949i	1.46838	−	1.06684i
$867$	5.85741	−	18.0272i	0.198928	−	0.612237i
$868$	0.318210			0.0108007
$869$	9.79636	−	30.1501i	0.332319	−	1.02277i
$870$		0			0
$871$	−2.27898	−	7.01398i	−0.0772203	−	0.237660i
$872$	−3.65380	−	11.2453i	−0.123733	−	0.380812i
$873$	25.2580	+	18.3510i	0.854853	+	0.621087i
$874$	−24.5197			−0.829391
$875$		0			0
$876$	−4.00610			−0.135354
$877$	−23.2181	−	16.8689i	−0.784018	−	0.569622i	0.122164	−	0.992510i	$-0.461017\pi$
$877$	−23.2181	−	16.8689i	−0.784018	−	0.569622i	−0.906182	+	0.422888i	$0.861017\pi$
$878$	−12.4845	−	38.4232i	−0.421330	−	1.29672i
$879$	6.08947	+	18.7415i	0.205393	+	0.632134i
$880$		0			0
$881$	2.57423	−	7.92267i	0.0867281	−	0.266922i	−0.898282	−	0.439420i	$-0.855184\pi$
$881$	2.57423	−	7.92267i	0.0867281	−	0.266922i	0.985010	+	0.172498i	$0.0551840\pi$
$882$	22.9964			0.774331
$883$	−15.5487	+	47.8539i	−0.523254	+	1.61041i	0.244488	+	0.969652i	$0.421380\pi$
$883$	−15.5487	+	47.8539i	−0.523254	+	1.61041i	−0.767742	+	0.640759i	$0.778620\pi$
$884$	18.5550	−	13.4810i	0.624072	−	0.453415i
$885$		0			0
$886$	−4.15454	−	3.01845i	−0.139574	−	0.101407i
$887$	−9.80417	+	7.12315i	−0.329192	+	0.239172i	−0.740088	−	0.672510i	$-0.765216\pi$
$887$	−9.80417	+	7.12315i	−0.329192	+	0.239172i	0.410896	+	0.911682i	$0.365216\pi$
$888$	2.77716	−	2.01773i	0.0931954	−	0.0677104i
$889$	1.19693	+	0.869617i	0.0401436	+	0.0291660i
$890$		0			0
$891$	18.0231	−	13.0945i	0.603795	−	0.438683i
$892$	20.5688	−	63.3042i	0.688694	−	2.11958i
$893$	−25.6543			−0.858490
$894$	4.54977	−	14.0027i	0.152167	−	0.468322i
$895$		0			0
$896$	1.75541	+	5.40260i	0.0586442	+	0.180488i
$897$	−10.4289	−	32.0967i	−0.348209	−	1.07168i
$898$	−24.2232	−	17.5992i	−0.808338	−	0.587292i
$899$	−0.735159			−0.0245189
$900$		0			0
$901$	21.8976			0.729514
$902$	29.1289	+	21.1634i	0.969886	+	0.704663i
$903$	−3.13100	−	9.63623i	−0.104193	−	0.320674i
$904$	−1.51705	−	4.66900i	−0.0504564	−	0.155289i
$905$		0			0
$906$	25.0559	−	77.1142i	0.832428	−	2.56195i
$907$	−31.9105			−1.05957			−0.529786	−	0.848132i	$-0.677728\pi$
$907$	−31.9105			−1.05957			−0.529786	+	0.848132i	$0.677728\pi$
$908$	16.1406	−	49.6757i	0.535645	−	1.64855i
$909$	3.77801	−	2.74488i	0.125309	−	0.0910421i
$910$		0			0
$911$	19.9730	+	14.5112i	0.661735	+	0.480778i	0.867248	−	0.497876i	$-0.165886\pi$
$911$	19.9730	+	14.5112i	0.661735	+	0.480778i	−0.205514	+	0.978654i	$0.565886\pi$
$912$	14.6260	−	10.6264i	0.484316	−	0.351876i
$913$	2.86570	−	2.08206i	0.0948409	−	0.0689060i
$914$	42.5071	+	30.8832i	1.40601	+	1.02153i
$915$		0			0
$916$	−4.70339	+	3.41721i	−0.155404	+	0.112908i
$917$	4.32852	−	13.3218i	0.142940	−	0.439925i
$918$	−15.4810			−0.510951
$919$	−6.02121	+	18.5314i	−0.198621	+	0.611293i	0.801294	+	0.598271i	$0.204145\pi$
$919$	−6.02121	+	18.5314i	−0.198621	+	0.611293i	−0.999915	+	0.0130225i	$0.995855\pi$
$920$		0			0
$921$	−6.44134	−	19.8244i	−0.212249	−	0.653237i
$922$	−18.5748	−	57.1675i	−0.611730	−	1.88271i
$923$	26.3210	+	19.1233i	0.866366	+	0.629452i
$924$	−10.2474			−0.337116
$925$		0			0
$926$	66.4781			2.18461
$927$	−15.0776	−	10.9545i	−0.495214	−	0.359794i
$928$	−13.4571	−	41.4168i	−0.441752	−	1.35957i
$929$	3.63535	+	11.1885i	0.119272	+	0.367082i	0.992814	−	0.119667i	$-0.0381827\pi$
$929$	3.63535	+	11.1885i	0.119272	+	0.367082i	−0.873542	+	0.486749i	$0.838183\pi$
$930$		0			0
$931$	4.80399	−	14.7852i	0.157444	−	0.484564i
$932$	13.9873			0.458168
$933$	−19.9273	+	61.3300i	−0.652392	+	2.00786i
$934$	−72.7104	+	52.8272i	−2.37916	+	1.72856i
$935$		0			0
$936$	−3.63597	−	2.64169i	−0.118846	−	0.0863463i
$937$	17.0446	−	12.3836i	0.556823	−	0.404556i	−0.273472	−	0.961880i	$-0.588172\pi$
$937$	17.0446	−	12.3836i	0.556823	−	0.404556i	0.830295	+	0.557324i	$0.188172\pi$
$938$	3.65944	−	2.65874i	0.119485	−	0.0868108i
$939$	33.5982	+	24.4105i	1.09644	+	0.796607i
$940$		0			0
$941$	1.81791	−	1.32079i	0.0592622	−	0.0430565i	−0.557760	−	0.830002i	$-0.688339\pi$
$941$	1.81791	−	1.32079i	0.0592622	−	0.0430565i	0.617022	+	0.786946i	$0.288339\pi$
$942$	2.34478	−	7.21650i	0.0763971	−	0.235126i
$943$	−39.2778			−1.27906
$944$	−4.83525	+	14.8814i	−0.157374	+	0.484347i
$945$		0			0
$946$	−5.98505	−	18.4201i	−0.194591	−	0.598889i
$947$	−2.08780	−	6.42557i	−0.0678442	−	0.208803i	0.911387	−	0.411551i	$-0.135013\pi$
$947$	−2.08780	−	6.42557i	−0.0678442	−	0.208803i	−0.979231	+	0.202748i	$0.935013\pi$
$948$	66.2078	+	48.1028i	2.15033	+	1.56231i
$949$	−2.61803			−0.0849850
$950$		0			0
$951$	−50.1021			−1.62467
$952$	1.68842	+	1.22671i	0.0547219	+	0.0397578i
$953$	18.5266	+	57.0190i	0.600136	+	1.84703i	0.527292	+	0.849684i	$0.323207\pi$
$953$	18.5266	+	57.0190i	0.600136	+	1.84703i	0.0728437	+	0.997343i	$0.476793\pi$
$954$	−8.93754	−	27.5069i	−0.289364	−	0.890569i
$955$		0			0
$956$	−5.10343	+	15.7067i	−0.165057	+	0.507992i
$957$	23.6747			0.765293
$958$	−13.5491	+	41.6999i	−0.437752	+	1.34726i
$959$	0.553535	−	0.402166i	0.0178746	−	0.0129866i
$960$		0			0
$961$	25.0644	+	18.2104i	0.808530	+	0.587432i
$962$	12.2330	−	8.88781i	0.394408	−	0.286555i
$963$	7.14499	−	5.19114i	0.230244	−	0.167282i
$964$	−2.24144	−	1.62850i	−0.0721920	−	0.0524505i
$965$		0			0
$966$	16.7460	−	12.1667i	0.538793	−	0.391456i
$967$	−2.79845	+	8.61276i	−0.0899922	+	0.276968i	−0.985916	−	0.167240i	$-0.946515\pi$
$967$	−2.79845	+	8.61276i	−0.0899922	+	0.276968i	0.895924	+	0.444207i	$0.146515\pi$
$968$	5.08580			0.163464
$969$	5.08225	−	15.6416i	0.163265	−	0.502479i
$970$		0			0
$971$	14.6322	+	45.0333i	0.469570	+	1.44519i	0.853143	+	0.521677i	$0.174693\pi$
$971$	14.6322	+	45.0333i	0.469570	+	1.44519i	−0.383573	+	0.923511i	$0.625307\pi$
$972$	12.1875	+	37.5094i	0.390916	+	1.20312i
$973$	13.3050	+	9.66665i	0.426539	+	0.309899i
$974$	−58.2191			−1.86546
$975$		0			0
$976$	8.81263			0.282085
$977$	3.83852	+	2.78885i	0.122805	+	0.0892231i	0.647492	−	0.762072i	$-0.275818\pi$
$977$	3.83852	+	2.78885i	0.122805	+	0.0892231i	−0.524687	+	0.851295i	$0.675818\pi$
$978$	1.26500	+	3.89328i	0.0404504	+	0.124493i
$979$	8.96645	+	27.5959i	0.286569	+	0.881968i
$980$		0			0
$981$	9.22005	−	28.3764i	0.294374	−	0.905988i
$982$	−31.1981			−0.995570
$983$	5.73708	−	17.6569i	0.182984	−	0.563168i	−0.816924	−	0.576746i	$-0.804322\pi$
$983$	5.73708	−	17.6569i	0.182984	−	0.563168i	0.999908	+	0.0135783i	$0.00432224\pi$
$984$	−11.1561	+	8.10542i	−0.355645	+	0.258391i
$985$		0			0
$986$	−26.2922	−	19.1024i	−0.837315	−	0.608345i
$987$	17.5209	−	12.7297i	0.557696	−	0.405190i
$988$	−16.5676	+	12.0370i	−0.527085	+	0.382949i
$989$	17.0932	+	12.4190i	0.543533	+	0.394900i
$990$		0			0
$991$	32.1340	−	23.3467i	1.02077	−	0.741634i	0.0543304	−	0.998523i	$-0.482698\pi$
$991$	32.1340	−	23.3467i	1.02077	−	0.741634i	0.966441	+	0.256889i	$0.0826976\pi$
$992$	0.341253	−	1.05027i	0.0108348	−	0.0333460i
$993$	−6.51411			−0.206719
$994$	−6.16631	+	18.9779i	−0.195583	+	0.601944i
$995$		0			0
$996$	2.82570	+	8.69660i	0.0895356	+	0.275562i
$997$	9.36056	+	28.8088i	0.296452	+	0.912385i	0.982730	+	0.185046i	$0.0592433\pi$
$997$	9.36056	+	28.8088i	0.296452	+	0.912385i	−0.686278	+	0.727339i	$0.740757\pi$
$998$	−74.7782	−	54.3295i	−2.36706	−	1.71977i
$999$	−5.51210			−0.174395

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	625.2.d.o.376.4		16
5.2	odd	4		625.2.e.a.249.1		8
5.3	odd	4		625.2.e.i.249.2		8
5.4	even	2	inner	625.2.d.o.376.1		16
25.2	odd	20		625.2.e.i.374.2		8
25.3	odd	20		25.2.e.a.19.1	yes	8
25.4	even	10		125.2.d.b.26.4		16
25.6	even	5		625.2.a.f.1.2		8
25.8	odd	20		625.2.b.c.624.7		8
25.9	even	10		125.2.d.b.101.4		16
25.11	even	5	inner	625.2.d.o.251.4		16
25.12	odd	20		25.2.e.a.4.1	✓	8
25.13	odd	20		125.2.e.b.24.2		8
25.14	even	10	inner	625.2.d.o.251.1		16
25.16	even	5		125.2.d.b.101.1		16
25.17	odd	20		625.2.b.c.624.2		8
25.19	even	10		625.2.a.f.1.7		8
25.21	even	5		125.2.d.b.26.1		16
25.22	odd	20		125.2.e.b.99.2		8
25.23	odd	20		625.2.e.a.374.1		8
75.44	odd	10		5625.2.a.x.1.2		8
75.53	even	20		225.2.m.a.19.2		8
75.56	odd	10		5625.2.a.x.1.7		8
75.62	even	20		225.2.m.a.154.2		8
100.3	even	20		400.2.y.c.369.1		8
100.19	odd	10		10000.2.a.bj.1.2		8
100.31	odd	10		10000.2.a.bj.1.7		8
100.87	even	20		400.2.y.c.129.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.2.e.a.4.1	✓	8	25.12	odd	20
25.2.e.a.19.1	yes	8	25.3	odd	20
125.2.d.b.26.1		16	25.21	even	5
125.2.d.b.26.4		16	25.4	even	10
125.2.d.b.101.1		16	25.16	even	5
125.2.d.b.101.4		16	25.9	even	10
125.2.e.b.24.2		8	25.13	odd	20
125.2.e.b.99.2		8	25.22	odd	20
225.2.m.a.19.2		8	75.53	even	20
225.2.m.a.154.2		8	75.62	even	20
400.2.y.c.129.1		8	100.87	even	20
400.2.y.c.369.1		8	100.3	even	20
625.2.a.f.1.2		8	25.6	even	5
625.2.a.f.1.7		8	25.19	even	10
625.2.b.c.624.2		8	25.17	odd	20
625.2.b.c.624.7		8	25.8	odd	20
625.2.d.o.251.1		16	25.14	even	10	inner
625.2.d.o.251.4		16	25.11	even	5	inner
625.2.d.o.376.1		16	5.4	even	2	inner
625.2.d.o.376.4		16	1.1	even	1	trivial
625.2.e.a.249.1		8	5.2	odd	4
625.2.e.a.374.1		8	25.23	odd	20
625.2.e.i.249.2		8	5.3	odd	4
625.2.e.i.374.2		8	25.2	odd	20
5625.2.a.x.1.2		8	75.44	odd	10
5625.2.a.x.1.7		8	75.56	odd	10
10000.2.a.bj.1.2		8	100.19	odd	10
10000.2.a.bj.1.7		8	100.31	odd	10

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:	\( N \)	\(=\)	\( 625 = 5^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	625.d (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.68703 + 1.22570i) q^{2} +(-0.679371 - 2.09089i) q^{3} +(0.725700 + 2.23347i) q^{4} +(1.41668 - 4.36010i) q^{6} +0.992398 q^{7} +(-0.224514 + 0.690983i) q^{8} +(-1.48322 + 1.07763i) q^{9} +(-1.61803 - 1.17557i) q^{11} +(4.17693 - 3.03472i) q^{12} +(2.72967 - 1.98322i) q^{13} +(1.67421 + 1.21638i) q^{14} +(2.57411 - 1.87020i) q^{16} +(0.894453 - 2.75284i) q^{17} -3.82309 q^{18} +(-0.798649 + 2.45799i) q^{19} +(-0.674207 - 2.07500i) q^{21} +(-1.28878 - 3.96645i) q^{22} +(3.68073 + 2.67421i) q^{23} +1.59730 q^{24} +7.03588 q^{26} +(-2.07500 - 1.50757i) q^{27} +(0.720183 + 2.21650i) q^{28} +(-1.66384 - 5.12077i) q^{29} +(0.0421925 - 0.129855i) q^{31} +8.08800 q^{32} +(-1.35874 + 4.18178i) q^{33} +(4.88313 - 3.54780i) q^{34} +(-3.48322 - 2.53071i) q^{36} +(1.73866 - 1.26321i) q^{37} +(-4.36010 + 3.16780i) q^{38} +(-6.00116 - 4.36010i) q^{39} +(-6.98439 + 5.07446i) q^{41} +(1.40591 - 4.32696i) q^{42} +4.64398 q^{43} +(1.45140 - 4.46695i) q^{44} +(2.93173 + 9.02294i) q^{46} +(3.06739 + 9.44047i) q^{47} +(-5.65917 - 4.11163i) q^{48} -6.01515 q^{49} -6.36356 q^{51} +(6.41040 + 4.65743i) q^{52} +(2.33778 + 7.19494i) q^{53} +(-1.65275 - 5.08664i) q^{54} +(-0.222807 + 0.685730i) q^{56} +5.68196 q^{57} +(3.46958 - 10.6783i) q^{58} +(-3.97854 + 2.89058i) q^{59} +(2.24075 + 1.62800i) q^{61} +(0.230343 - 0.167354i) q^{62} +(-1.47195 + 1.06943i) q^{63} +(8.49648 + 6.17306i) q^{64} +(-7.41785 + 5.38938i) q^{66} +(0.675441 - 2.07879i) q^{67} +6.79751 q^{68} +(3.09089 - 9.51278i) q^{69} +(2.97971 + 9.17060i) q^{71} +(-0.411616 - 1.26682i) q^{72} +(-0.627740 - 0.456080i) q^{73} +4.48150 q^{74} -6.06943 q^{76} +(-1.60573 - 1.16663i) q^{77} +(-4.77998 - 14.7113i) q^{78} +(4.89818 + 15.0750i) q^{79} +(-3.44210 + 10.5937i) q^{81} -18.0026 q^{82} +(-0.547301 + 1.68442i) q^{83} +(4.14518 - 3.01165i) q^{84} +(7.83453 + 5.69212i) q^{86} +(-9.57660 + 6.95781i) q^{87} +(1.17557 - 0.854102i) q^{88} +(-11.7372 - 8.52760i) q^{89} +(2.70892 - 1.96815i) q^{91} +(-3.30167 + 10.1615i) q^{92} -0.300177 q^{93} +(-6.39639 + 19.6861i) q^{94} +(-5.49476 - 16.9111i) q^{96} +(-5.26228 - 16.1956i) q^{97} +(-10.1477 - 7.37276i) q^{98} +3.66673 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{4} + 12 q^{6} - 2 q^{9} - 8 q^{11} + 14 q^{14} - 4 q^{16} - 20 q^{19} + 2 q^{21} + 40 q^{24} + 12 q^{26} - 30 q^{29} + 2 q^{31} + 24 q^{34} - 34 q^{36} - 24 q^{39} - 18 q^{41} - 16 q^{44} + 32 q^{46}+ \cdots + 16 q^{99}+O(q^{100}) \) 16 * q - 8 * q^4 + 12 * q^6 - 2 * q^9 - 8 * q^11 + 14 * q^14 - 4 * q^16 - 20 * q^19 + 2 * q^21 + 40 * q^24 + 12 * q^26 - 30 * q^29 + 2 * q^31 + 24 * q^34 - 34 * q^36 - 24 * q^39 - 18 * q^41 - 16 * q^44 + 32 * q^46 - 28 * q^49 - 8 * q^51 + 20 * q^54 - 30 * q^56 - 30 * q^59 + 12 * q^61 + 52 * q^64 - 36 * q^66 + 26 * q^69 - 58 * q^71 + 24 * q^74 - 40 * q^76 + 20 * q^79 - 24 * q^81 + 54 * q^84 + 32 * q^86 - 80 * q^89 + 2 * q^91 + 14 * q^94 + 22 * q^96 + 16 * q^99

Introduction

L-functions

Modular forms

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