LMFDB - Embedded newform 625.2.e.i.374.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [625,2,Mod(124,625)]

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([1]))

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

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

chi := DirichletCharacter("625.124");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$625 = 5^{4}$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	625.e (of order $10$ , 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:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{10})$
Coefficient field:	8.0.58140625.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$x^{8} - 3x^{7} + 4x^{6} - 7x^{5} + 11x^{4} + 5x^{3} - 10x^{2} - 25x + 25$ x^8 - 3x^7 + 4x^6 - 7x^5 + 11x^4 + 5x^3 - 10x^2 - 25*x + 25
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 25)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			374.2
Root			$-0.983224 + 0.644389i$ of defining polynomial
Character	$\chi$	$=$	625.374
Dual form			625.2.e.i.249.2

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.22570 + 1.68703i) q^{2} +(2.09089 + 0.679371i) q^{3} +(-0.725700 + 2.23347i) q^{4} +(1.41668 + 4.36010i) q^{6} +0.992398i q^{7} +(-0.690983 + 0.224514i) q^{8} +(1.48322 + 1.07763i) q^{9} +(-1.61803 + 1.17557i) q^{11} +(-3.03472 + 4.17693i) q^{12} +(1.98322 - 2.72967i) q^{13} +(-1.67421 + 1.21638i) q^{14} +(2.57411 + 1.87020i) q^{16} +(-2.75284 + 0.894453i) q^{17} +3.82309i q^{18} +(0.798649 + 2.45799i) q^{19} +(-0.674207 + 2.07500i) q^{21} +(-3.96645 - 1.28878i) q^{22} +(-2.67421 - 3.68073i) q^{23} -1.59730 q^{24} +7.03588 q^{26} +(-1.50757 - 2.07500i) q^{27} +(-2.21650 - 0.720183i) q^{28} +(1.66384 - 5.12077i) q^{29} +(0.0421925 + 0.129855i) q^{31} +8.08800i q^{32} +(-4.18178 + 1.35874i) q^{33} +(-4.88313 - 3.54780i) q^{34} +(-3.48322 + 2.53071i) q^{36} +(-1.26321 + 1.73866i) q^{37} +(-3.16780 + 4.36010i) q^{38} +(6.00116 - 4.36010i) q^{39} +(-6.98439 - 5.07446i) q^{41} +(-4.32696 + 1.40591i) q^{42} -4.64398i q^{43} +(-1.45140 - 4.46695i) q^{44} +(2.93173 - 9.02294i) q^{46} +(9.44047 + 3.06739i) q^{47} +(4.11163 + 5.65917i) q^{48} +6.01515 q^{49} -6.36356 q^{51} +(4.65743 + 6.41040i) q^{52} +(-7.19494 - 2.33778i) q^{53} +(1.65275 - 5.08664i) q^{54} +(-0.222807 - 0.685730i) q^{56} +5.68196i q^{57} +(10.6783 - 3.46958i) q^{58} +(3.97854 + 2.89058i) q^{59} +(2.24075 - 1.62800i) q^{61} +(-0.167354 + 0.230343i) q^{62} +(-1.06943 + 1.47195i) q^{63} +(-8.49648 + 6.17306i) q^{64} +(-7.41785 - 5.38938i) q^{66} +(-2.07879 + 0.675441i) q^{67} -6.79751i q^{68} +(-3.09089 - 9.51278i) q^{69} +(2.97971 - 9.17060i) q^{71} +(-1.26682 - 0.411616i) q^{72} +(0.456080 + 0.627740i) q^{73} -4.48150 q^{74} -6.06943 q^{76} +(-1.16663 - 1.60573i) q^{77} +(14.7113 + 4.77998i) q^{78} +(-4.89818 + 15.0750i) q^{79} +(-3.44210 - 10.5937i) q^{81} -18.0026i q^{82} +(-1.68442 + 0.547301i) q^{83} +(-4.14518 - 3.01165i) q^{84} +(7.83453 - 5.69212i) q^{86} +(6.95781 - 9.57660i) q^{87} +(0.854102 - 1.17557i) q^{88} +(11.7372 - 8.52760i) q^{89} +(2.70892 + 1.96815i) q^{91} +(10.1615 - 3.30167i) q^{92} +0.300177i q^{93} +(6.39639 + 19.6861i) q^{94} +(-5.49476 + 16.9111i) q^{96} +(-16.1956 - 5.26228i) q^{97} +(7.37276 + 10.1477i) q^{98} -3.66673 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$8 q + 5 q^{3} + 4 q^{4} + 6 q^{6} - 10 q^{8} + q^{9} - 4 q^{11} - 10 q^{12} + 5 q^{13} - 7 q^{14} - 2 q^{16} - 15 q^{17} + 10 q^{19} + q^{21} - 10 q^{22} - 15 q^{23} - 20 q^{24} + 6 q^{26} + 5 q^{27}+ \cdots - 8 q^{99}+O(q^{100})$ 8 * q + 5 * q^3 + 4 * q^4 + 6 * q^6 - 10 * q^8 + q^9 - 4 * q^11 - 10 * q^12 + 5 * q^13 - 7 * q^14 - 2 * q^16 - 15 * q^17 + 10 * q^19 + q^21 - 10 * q^22 - 15 * q^23 - 20 * q^24 + 6 * q^26 + 5 * q^27 + 20 * q^28 + 15 * q^29 + q^31 - 10 * q^33 - 12 * q^34 - 17 * q^36 + 5 * q^37 + 12 * q^39 - 9 * q^41 - 5 * q^42 + 8 * q^44 + 16 * q^46 + 15 * q^47 + 5 * q^48 + 14 * q^49 - 4 * q^51 + 20 * q^52 - 35 * q^53 - 10 * q^54 - 15 * q^56 + 20 * q^58 + 15 * q^59 + 6 * q^61 - 45 * q^62 + 20 * q^63 - 26 * q^64 - 18 * q^66 - 13 * q^69 - 29 * q^71 - 5 * q^72 - 10 * q^73 - 12 * q^74 - 20 * q^76 - 20 * q^77 + 25 * q^78 - 10 * q^79 - 12 * q^81 - 15 * q^83 - 27 * q^84 + 16 * q^86 + 55 * q^87 - 20 * q^88 + 40 * q^89 + q^91 + 5 * q^92 - 7 * q^94 + 11 * q^96 + 10 * q^97 + 40 * q^98 - 8 * q^99

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{3}{10}\right)$

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

)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$\alpha_n$			$\theta_n$
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$\alpha_p$			$\theta_p$

$2$	1.22570	+	1.68703i	0.866701	+	1.19291i	0.979930	+	0.199342i	$0.0638805\pi$
$2$	1.22570	+	1.68703i	0.866701	+	1.19291i	−0.113229	+	0.993569i	$0.536119\pi$
$3$	2.09089	+	0.679371i	1.20718	+	0.392235i	0.842396	−	0.538859i	$-0.181144\pi$
$3$	2.09089	+	0.679371i	1.20718	+	0.392235i	0.364780	+	0.931094i	$0.381144\pi$
$4$	−0.725700	+	2.23347i	−0.362850	+	1.11674i
$5$		0			0
$5$		0			0
$6$	1.41668	+	4.36010i	0.578358	+	1.78000i
$7$			0.992398i			0.375091i	0.982256	+	0.187546i	$0.0600533\pi$
$7$			0.992398i			0.375091i	−0.982256	+	0.187546i	$0.939947\pi$
$8$	−0.690983	+	0.224514i	−0.244299	+	0.0793777i
$9$	1.48322	+	1.07763i	0.494408	+	0.359208i
$10$		0			0
$11$	−1.61803	+	1.17557i	−0.487856	+	0.354448i	−0.804359	−	0.594144i	$-0.797491\pi$
$11$	−1.61803	+	1.17557i	−0.487856	+	0.354448i	0.316503	+	0.948591i	$0.397491\pi$
$12$	−3.03472	+	4.17693i	−0.876047	+	1.20578i
$13$	1.98322	−	2.72967i	0.550047	−	0.757075i	−0.439971	−	0.898012i	$-0.645011\pi$
$13$	1.98322	−	2.72967i	0.550047	−	0.757075i	0.990019	+	0.140937i	$0.0450114\pi$
$14$	−1.67421	+	1.21638i	−0.447451	+	0.325092i
$15$		0			0
$16$	2.57411	+	1.87020i	0.643528	+	0.467551i
$17$	−2.75284	+	0.894453i	−0.667663	+	0.216937i	−0.623186	−	0.782074i	$-0.714162\pi$
$17$	−2.75284	+	0.894453i	−0.667663	+	0.216937i	−0.0444767	+	0.999010i	$0.514162\pi$
$18$			3.82309i			0.901111i
$19$	0.798649	+	2.45799i	0.183223	+	0.563901i	0.999913	−	0.0131746i	$-0.00419372\pi$
$19$	0.798649	+	2.45799i	0.183223	+	0.563901i	−0.816691	+	0.577076i	$0.804194\pi$
$20$		0			0
$21$	−0.674207	+	2.07500i	−0.147124	+	0.452801i
$22$	−3.96645	−	1.28878i	−0.845650	−	0.274768i
$23$	−2.67421	−	3.68073i	−0.557611	−	0.767485i	0.433410	−	0.901197i	$-0.357310\pi$
$23$	−2.67421	−	3.68073i	−0.557611	−	0.767485i	−0.991020	+	0.133712i	$0.957310\pi$
$24$	−1.59730			−0.326047
$25$		0			0
$26$	7.03588			1.37985
$27$	−1.50757	−	2.07500i	−0.290132	−	0.399333i
$28$	−2.21650	−	0.720183i	−0.418878	−	0.136102i
$29$	1.66384	−	5.12077i	0.308967	−	0.950903i	−0.669200	−	0.743082i	$-0.733363\pi$
$29$	1.66384	−	5.12077i	0.308967	−	0.950903i	0.978167	−	0.207821i	$-0.0666370\pi$
$30$		0			0
$31$	0.0421925	+	0.129855i	0.00757799	+	0.0233227i	0.954774	−	0.297332i	$-0.0960970\pi$
$31$	0.0421925	+	0.129855i	0.00757799	+	0.0233227i	−0.947196	+	0.320655i	$0.896097\pi$
$32$			8.08800i			1.42977i
$33$	−4.18178	+	1.35874i	−0.727954	+	0.236527i
$34$	−4.88313	−	3.54780i	−0.837450	−	0.608443i
$35$		0			0
$36$	−3.48322	+	2.53071i	−0.580537	+	0.421785i
$37$	−1.26321	+	1.73866i	−0.207671	+	0.285834i	−0.900129	−	0.435624i	$-0.856528\pi$
$37$	−1.26321	+	1.73866i	−0.207671	+	0.285834i	0.692458	+	0.721458i	$0.256528\pi$
$38$	−3.16780	+	4.36010i	−0.513885	+	0.707302i
$39$	6.00116	−	4.36010i	0.960955	−	0.698175i
$40$		0			0
$41$	−6.98439	−	5.07446i	−1.09078	−	0.792497i	−0.111248	−	0.993793i	$-0.535485\pi$
$41$	−6.98439	−	5.07446i	−1.09078	−	0.792497i	−0.979530	+	0.201296i	$0.935485\pi$
$42$	−4.32696	+	1.40591i	−0.667664	+	0.216937i
$43$		−	4.64398i		−	0.708200i	−0.935208	−	0.354100i	$-0.884787\pi$
$43$		−	4.64398i		−	0.708200i	0.935208	−	0.354100i	$-0.115213\pi$
$44$	−1.45140	−	4.46695i	−0.218807	−	0.673418i
$45$		0			0
$46$	2.93173	−	9.02294i	0.432260	−	1.33036i
$47$	9.44047	+	3.06739i	1.37703	+	0.447425i	0.901693	−	0.432376i	$-0.142325\pi$
$47$	9.44047	+	3.06739i	1.37703	+	0.447425i	0.475341	+	0.879802i	$0.342325\pi$
$48$	4.11163	+	5.65917i	0.593462	+	0.816831i
$49$	6.01515			0.859306
$50$		0			0
$51$	−6.36356			−0.891077
$52$	4.65743	+	6.41040i	0.645869	+	0.888963i
$53$	−7.19494	−	2.33778i	−0.988301	−	0.321119i	−0.230120	−	0.973162i	$-0.573912\pi$
$53$	−7.19494	−	2.33778i	−0.988301	−	0.321119i	−0.758181	+	0.652044i	$0.773912\pi$
$54$	1.65275	−	5.08664i	0.224911	−	0.692205i
$55$		0			0
$56$	−0.222807	−	0.685730i	−0.0297739	−	0.0916346i
$57$			5.68196i			0.752594i
$58$	10.6783	−	3.46958i	1.40212	−	0.455578i
$59$	3.97854	+	2.89058i	0.517962	+	0.376322i	0.815836	−	0.578284i	$-0.196277\pi$
$59$	3.97854	+	2.89058i	0.517962	+	0.376322i	−0.297873	+	0.954605i	$0.596277\pi$
$60$		0			0
$61$	2.24075	−	1.62800i	0.286898	−	0.208444i	−0.435022	−	0.900420i	$-0.643260\pi$
$61$	2.24075	−	1.62800i	0.286898	−	0.208444i	0.721921	+	0.691976i	$0.243260\pi$
$62$	−0.167354	+	0.230343i	−0.0212540	+	0.0292536i
$63$	−1.06943	+	1.47195i	−0.134736	+	0.185448i
$64$	−8.49648	+	6.17306i	−1.06206	+	0.771632i
$65$		0			0
$66$	−7.41785	−	5.38938i	−0.913074	−	0.663387i
$67$	−2.07879	+	0.675441i	−0.253965	+	0.0825183i	−0.433233	−	0.901282i	$-0.642627\pi$
$67$	−2.07879	+	0.675441i	−0.253965	+	0.0825183i	0.179268	+	0.983800i	$0.442627\pi$
$68$		−	6.79751i		−	0.824319i
$69$	−3.09089	−	9.51278i	−0.372099	−	1.14520i
$70$		0			0
$71$	2.97971	−	9.17060i	0.353626	−	1.08835i	−0.603175	−	0.797609i	$-0.706098\pi$
$71$	2.97971	−	9.17060i	0.353626	−	1.08835i	0.956802	−	0.290741i	$-0.0939019\pi$
$72$	−1.26682	−	0.411616i	−0.149297	−	0.0485094i
$73$	0.456080	+	0.627740i	0.0533801	+	0.0734714i	0.834873	−	0.550443i	$-0.185541\pi$
$73$	0.456080	+	0.627740i	0.0533801	+	0.0734714i	−0.781492	+	0.623915i	$0.785541\pi$
$74$	−4.48150			−0.520963
$75$		0			0
$76$	−6.06943			−0.696212
$77$	−1.16663	−	1.60573i	−0.132950	−	0.182990i
$78$	14.7113	+	4.77998i	1.66572	+	0.541226i
$79$	−4.89818	+	15.0750i	−0.551088	+	1.69608i	0.154968	+	0.987919i	$0.450473\pi$
$79$	−4.89818	+	15.0750i	−0.551088	+	1.69608i	−0.706056	+	0.708156i	$0.749527\pi$
$80$		0			0
$81$	−3.44210	−	10.5937i	−0.382455	−	1.17708i
$82$		−	18.0026i		−	1.98806i
$83$	−1.68442	+	0.547301i	−0.184889	+	0.0600740i	−0.399998	−	0.916516i	$-0.630989\pi$
$83$	−1.68442	+	0.547301i	−0.184889	+	0.0600740i	0.215109	+	0.976590i	$0.430989\pi$
$84$	−4.14518	−	3.01165i	−0.452276	−	0.328598i
$85$		0			0
$86$	7.83453	−	5.69212i	0.844819	−	0.613797i
$87$	6.95781	−	9.57660i	0.745955	−	1.02672i
$88$	0.854102	−	1.17557i	0.0910476	−	0.125316i
$89$	11.7372	−	8.52760i	1.24414	−	0.903924i	0.246277	−	0.969200i	$-0.420793\pi$
$89$	11.7372	−	8.52760i	1.24414	−	0.903924i	0.997867	+	0.0652758i	$0.0207927\pi$
$90$		0			0
$91$	2.70892	+	1.96815i	0.283972	+	0.206318i
$92$	10.1615	−	3.30167i	1.05941	−	0.344223i
$93$			0.300177i			0.0311269i
$94$	6.39639	+	19.6861i	0.659737	+	2.03046i
$95$		0			0
$96$	−5.49476	+	16.9111i	−0.560806	+	1.72598i
$97$	−16.1956	−	5.26228i	−1.64442	−	0.534304i	−0.666899	−	0.745148i	$-0.732379\pi$
$97$	−16.1956	−	5.26228i	−1.64442	−	0.534304i	−0.977520	+	0.210844i	$0.932379\pi$
$98$	7.37276	+	10.1477i	0.744761	+	1.02508i
$99$	−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	$0.540447\pi$
$102$	−7.79981	−	10.7355i	−0.772297	−	1.06298i
$103$	−9.66790	−	3.14129i	−0.952606	−	0.309520i	−0.208832	−	0.977952i	$-0.566966\pi$
$103$	−9.66790	−	3.14129i	−0.952606	−	0.309520i	−0.743774	+	0.668431i	$0.766966\pi$
$104$	−0.757524	+	2.33142i	−0.0742814	+	0.228615i
$105$		0			0
$106$	−4.87494	−	15.0035i	−0.473496	−	1.45727i
$107$		−	4.81720i		−	0.465697i	−0.972513	−	0.232848i	$-0.925195\pi$
$107$		−	4.81720i		−	0.465697i	0.972513	−	0.232848i	$-0.0748046\pi$
$108$	5.72850	−	1.86130i	0.551225	−	0.179104i
$109$	13.1662	+	9.56578i	1.26109	+	0.916236i	0.998811	−	0.0487563i	$-0.0155258\pi$
$109$	13.1662	+	9.56578i	1.26109	+	0.916236i	0.262280	+	0.964992i	$0.415526\pi$
$110$		0			0
$111$	−3.82243	+	2.77716i	−0.362809	+	0.263596i
$112$	−1.85599	+	2.55455i	−0.175374	+	0.241382i
$113$	−3.97169	+	5.46656i	−0.373625	+	0.514251i	−0.953882	−	0.300183i	$-0.902952\pi$
$113$	−3.97169	+	5.46656i	−0.373625	+	0.514251i	0.580256	+	0.814434i	$0.302952\pi$
$114$	−9.58565	+	6.96438i	−0.897778	+	0.652274i
$115$		0			0
$116$	10.2297	+	7.43228i	0.949800	+	0.690070i
$117$	5.88313	−	1.91155i	0.543896	−	0.176722i
$118$			10.2549i			0.944041i
$119$	−0.887654	−	2.73192i	−0.0813711	−	0.250435i
$120$		0			0
$121$	−2.16312	+	6.65740i	−0.196647	+	0.605218i
$122$	5.49297	+	1.78477i	0.497310	+	0.161586i
$123$	−11.1561	−	15.3551i	−1.00592	−	1.38452i
$124$	−0.320647			−0.0287950
$125$		0			0
$126$	−3.79403			−0.337999
$127$	0.876278	+	1.20609i	0.0777571	+	0.107023i	0.846124	−	0.532986i	$-0.178930\pi$
$127$	0.876278	+	1.20609i	0.0777571	+	0.107023i	−0.768367	+	0.640010i	$0.778930\pi$
$128$	−5.44398	−	1.76886i	−0.481185	−	0.156346i
$129$	3.15498	−	9.71004i	0.277781	−	0.854921i
$130$		0			0
$131$	4.36167	+	13.4239i	0.381081	+	1.17285i	0.939283	+	0.343143i	$0.111491\pi$
$131$	4.36167	+	13.4239i	0.381081	+	1.17285i	−0.558202	+	0.829705i	$0.688509\pi$
$132$		−	10.3259i		−	0.898757i
$133$	−2.43930	+	0.792578i	−0.211514	+	0.0687252i
$134$	−3.68747	−	2.67910i	−0.318549	−	0.231439i
$135$		0			0
$136$	1.70135	−	1.23610i	0.145890	−	0.105995i
$137$	−0.405247	+	0.557775i	−0.0346226	+	0.0476539i	−0.825977	−	0.563703i	$-0.809376\pi$
$137$	−0.405247	+	0.557775i	−0.0346226	+	0.0476539i	0.791355	+	0.611357i	$0.209376\pi$
$138$	12.2599	−	16.8742i	1.04363	−	1.43643i
$139$	−13.4069	+	9.74070i	−1.13716	+	0.826195i	−0.986721	−	0.162424i	$-0.948069\pi$
$139$	−13.4069	+	9.74070i	−1.13716	+	0.826195i	−0.150439	+	0.988619i	$0.548069\pi$
$140$		0			0
$141$	17.6551	+	12.8272i	1.48683	+	1.08024i
$142$	19.1233	−	6.21354i	1.60479	−	0.521429i
$143$			6.74812i			0.564307i
$144$	1.80261	+	5.54786i	0.150217	+	0.462322i
$145$		0			0
$146$	−0.500000	+	1.53884i	−0.0413803	+	0.127355i
$147$	12.5770	+	4.08652i	1.03733	+	0.337050i
$148$	−2.96655	−	4.08310i	−0.243849	−	0.335629i
$149$	−3.21156			−0.263101			−0.131551	−	0.991309i	$-0.541996\pi$
$149$	−3.21156			−0.263101			−0.131551	+	0.991309i	$0.541996\pi$
$150$		0			0
$151$	17.6863			1.43929			0.719647	−	0.694340i	$-0.244304\pi$
$151$	17.6863			1.43929			0.719647	+	0.694340i	$0.244304\pi$
$152$	−1.10371	−	1.51912i	−0.0895223	−	0.123217i
$153$	−5.04697	−	1.63986i	−0.408023	−	0.132575i
$154$	1.27898	−	3.93630i	0.103063	−	0.317196i
$155$		0			0
$156$	5.38313	+	16.5676i	0.430995	+	1.32647i
$157$			1.65512i			0.132093i	0.997817	+	0.0660465i	$0.0210386\pi$
$157$			1.65512i			0.132093i	−0.997817	+	0.0660465i	$0.978961\pi$
$158$	−31.4358	+	10.2141i	−2.50090	+	0.812590i
$159$	−13.4556	−	9.77608i	−1.06710	−	0.775293i
$160$		0			0
$161$	3.65275	−	2.65388i	0.287877	−	0.209155i
$162$	13.6529	−	18.7916i	1.07267	−	1.47641i
$163$	−0.524854	+	0.722399i	−0.0411097	+	0.0565827i	−0.829077	−	0.559134i	$-0.811134\pi$
$163$	−0.524854	+	0.722399i	−0.0411097	+	0.0565827i	0.787967	+	0.615717i	$0.211134\pi$
$164$	16.4022	−	11.9169i	1.28080	−	0.930555i
$165$		0			0
$166$	−2.98790	−	2.17084i	−0.231906	−	0.168490i
$167$	−4.94129	+	1.60552i	−0.382368	+	0.124239i	−0.493893	−	0.869523i	$-0.664427\pi$
$167$	−4.94129	+	1.60552i	−0.382368	+	0.124239i	0.111525	+	0.993762i	$0.464427\pi$
$168$		−	1.58516i		−	0.122297i
$169$	0.499280	+	1.53663i	0.0384062	+	0.118202i
$170$		0			0
$171$	−1.46422	+	4.50639i	−0.111971	+	0.344612i
$172$	10.3722	+	3.37013i	0.790873	+	0.256970i
$173$	−3.38837	−	4.66370i	−0.257613	−	0.354574i	0.660546	−	0.750785i	$-0.270325\pi$
$173$	−3.38837	−	4.66370i	−0.257613	−	0.354574i	−0.918159	+	0.396211i	$0.870325\pi$
$174$	24.6842			1.87130
$175$		0			0
$176$	−6.36356			−0.479671
$177$	6.35492	+	8.74680i	0.477665	+	0.657449i
$178$	28.7726	+	9.34880i	2.15660	+	0.700722i
$179$	−2.67883	+	8.24458i	−0.200225	+	0.616229i	0.799651	+	0.600465i	$0.205018\pi$
$179$	−2.67883	+	8.24458i	−0.200225	+	0.616229i	−0.999876	+	0.0157637i	$0.994982\pi$
$180$		0			0
$181$	4.41612	+	13.5914i	0.328248	+	1.01024i	0.969953	+	0.243291i	$0.0782271\pi$
$181$	4.41612	+	13.5914i	0.328248	+	1.01024i	−0.641706	+	0.766951i	$0.721773\pi$
$182$			6.98240i			0.517570i
$183$	5.79117	−	1.88167i	0.428096	−	0.139097i
$184$	2.67421	+	1.94293i	0.197145	+	0.143234i
$185$		0			0
$186$	−0.506408	+	0.367927i	−0.0371316	+	0.0269777i
$187$	3.40270	−	4.68342i	0.248830	−	0.342485i
$188$	−13.7019	+	18.8590i	−0.999313	+	1.37544i
$189$	2.05922	−	1.49611i	0.149786	−	0.108826i
$190$		0			0
$191$	1.02451	+	0.744347i	0.0741306	+	0.0538591i	0.624233	−	0.781238i	$-0.285411\pi$
$191$	1.02451	+	0.744347i	0.0741306	+	0.0538591i	−0.550103	+	0.835097i	$0.685411\pi$
$192$	−21.9590	+	7.13492i	−1.58476	+	0.514918i
$193$		−	21.1730i		−	1.52406i	−0.647540	−	0.762031i	$-0.724202\pi$
$193$		−	21.1730i		−	1.52406i	0.647540	−	0.762031i	$-0.275798\pi$
$194$	−10.9734	−	33.7725i	−0.787841	−	2.42473i
$195$		0			0
$196$	−4.36519	+	13.4347i	−0.311799	+	0.959620i
$197$	−11.6042	−	3.77042i	−0.826761	−	0.268631i	−0.135081	−	0.990835i	$-0.543129\pi$
$197$	−11.6042	−	3.77042i	−0.826761	−	0.268631i	−0.691681	+	0.722203i	$0.743129\pi$
$198$	−4.49431	−	6.18589i	−0.319397	−	0.439612i
$199$	−10.4065			−0.737695			−0.368848	−	0.929490i	$-0.620248\pi$
$199$	−10.4065			−0.737695			−0.368848	+	0.929490i	$0.620248\pi$
$200$		0			0
$201$	−4.80540			−0.338947
$202$	−3.12205	−	4.29714i	−0.219667	−	0.302346i
$203$	5.08184	+	1.65119i	0.356675	+	0.115891i
$204$	4.61803	−	14.2128i	0.323327	−	0.995098i
$205$		0			0
$206$	−6.55049	−	20.1603i	−0.456394	−	1.40464i
$207$		−	8.34114i		−	0.579749i
$208$	10.2101	−	3.31746i	0.707942	−	0.230024i
$209$	−4.18178	−	3.03824i	−0.289260	−	0.210160i
$210$		0			0
$211$	7.00421	−	5.08886i	0.482190	−	0.350332i	−0.319983	−	0.947423i	$-0.603677\pi$
$211$	7.00421	−	5.08886i	0.482190	−	0.350332i	0.802173	+	0.597092i	$0.203677\pi$
$212$	10.4427	−	14.3732i	0.717210	−	0.987155i
$213$	12.4605	−	17.1504i	0.853778	−	1.17513i
$214$	8.12677	−	5.90445i	0.555535	−	0.403620i
$215$		0			0
$216$	1.50757	+	1.09532i	0.102577	+	0.0745268i
$217$	−0.128868	+	0.0418717i	−0.00874813	+	0.00284244i
$218$			33.9365i			2.29847i
$219$	0.527144	+	1.62238i	0.0356211	+	0.109630i
$220$		0			0
$221$	−3.01794	+	9.28827i	−0.203009	+	0.624796i
$222$	−9.37032	−	3.04460i	−0.628894	−	0.204340i
$223$	16.6598	+	22.9303i	1.11562	+	1.53552i	0.812860	+	0.582459i	$0.197909\pi$
$223$	16.6598	+	22.9303i	1.11562	+	1.53552i	0.302764	+	0.953065i	$0.402091\pi$
$224$	−8.02652			−0.536295
$225$		0			0
$226$	−14.0904			−0.937277
$227$	−13.0732	−	17.9937i	−0.867699	−	1.19429i	−0.979678	−	0.200575i	$-0.935719\pi$
$227$	−13.0732	−	17.9937i	−0.867699	−	1.19429i	0.111979	−	0.993711i	$-0.464281\pi$
$228$	−12.6905	−	4.12340i	−0.840450	−	0.273079i
$229$	−0.765000	+	2.35443i	−0.0505526	+	0.155585i	−0.973146	−	0.230189i	$-0.926066\pi$
$229$	−0.765000	+	2.35443i	−0.0505526	+	0.155585i	0.922593	+	0.385774i	$0.126066\pi$
$230$		0			0
$231$	−1.34841	−	4.14999i	−0.0887191	−	0.273049i
$232$			3.91192i			0.256830i
$233$	5.66454	−	1.84052i	0.371096	−	0.120576i	−0.117531	−	0.993069i	$-0.537498\pi$
$233$	5.66454	−	1.84052i	0.371096	−	0.120576i	0.488627	+	0.872493i	$0.337498\pi$
$234$	10.4358	+	7.58204i	0.682209	+	0.495654i
$235$		0			0
$236$	−9.34327	+	6.78828i	−0.608195	+	0.441879i
$237$	−20.4831	+	28.1926i	−1.33052	+	1.83130i
$238$	3.52083	−	4.84601i	0.228222	−	0.314120i
$239$	−5.68935	+	4.13356i	−0.368014	+	0.267378i	−0.756387	−	0.654125i	$-0.773037\pi$
$239$	−5.68935	+	4.13356i	−0.368014	+	0.267378i	0.388373	+	0.921502i	$0.373037\pi$
$240$		0			0
$241$	−0.954449	−	0.693448i	−0.0614815	−	0.0446689i	0.556620	−	0.830767i	$-0.312098\pi$
$241$	−0.954449	−	0.693448i	−0.0614815	−	0.0446689i	−0.618102	+	0.786098i	$0.712098\pi$
$242$	−13.8826	+	4.51072i	−0.892405	+	0.289960i
$243$		−	16.7942i		−	1.07735i
$244$	2.00998	+	6.18609i	0.128676	+	0.396024i
$245$		0			0
$246$	12.2305	−	37.6415i	0.779787	−	2.39994i
$247$	8.29341	+	2.69469i	0.527697	+	0.171459i
$248$	−0.0583086	−	0.0802548i	−0.00370260	−	0.00509619i
$249$	−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	$0.453538\pi$
$252$	−2.51147	−	3.45675i	−0.158208	−	0.217755i
$253$	8.65392	+	2.81183i	0.544067	+	0.176778i
$254$	−0.960663	+	2.95662i	−0.0602774	+	0.185515i
$255$		0			0
$256$	2.80216	+	8.62417i	0.175135	+	0.539011i
$257$		−	9.75542i		−	0.608526i	−0.952588	−	0.304263i	$-0.901590\pi$
$257$		−	9.75542i		−	0.608526i	0.952588	−	0.304263i	$-0.0984102\pi$
$258$	20.2482	−	6.57904i	1.26060	−	0.409593i
$259$	−1.72545	−	1.25361i	−0.107214	−	0.0778955i
$260$		0			0
$261$	7.98612	−	5.80225i	0.494328	−	0.359150i
$262$	−17.3004	+	23.8119i	−1.06882	+	1.47110i
$263$	−0.585333	+	0.805641i	−0.0360932	+	0.0496780i	−0.826682	−	0.562669i	$-0.809775\pi$
$263$	−0.585333	+	0.805641i	−0.0360932	+	0.0496780i	0.790589	+	0.612347i	$0.209775\pi$
$264$	2.58448	−	1.87774i	0.159064	−	0.115567i
$265$		0			0
$266$	−4.32696	−	3.14372i	−0.265303	−	0.192754i
$267$	30.3347	−	9.85633i	1.85645	−	0.603198i
$268$		−	5.13310i		−	0.313554i
$269$	1.01621	+	3.12758i	0.0619596	+	0.190692i	0.977245	−	0.212114i	$-0.0680349\pi$
$269$	1.01621	+	3.12758i	0.0619596	+	0.190692i	−0.915285	+	0.402806i	$0.868035\pi$
$270$		0			0
$271$	3.75457	−	11.5554i	0.228074	−	0.701940i	−0.769891	−	0.638175i	$-0.779689\pi$
$271$	3.75457	−	11.5554i	0.228074	−	0.701940i	0.997965	−	0.0637642i	$-0.0203105\pi$
$272$	−8.75894	−	2.84595i	−0.531089	−	0.172561i
$273$	4.32696	+	5.95555i	0.261879	+	0.360446i
$274$	−1.43769			−0.0868543
$275$		0			0
$276$	23.4896			1.41391
$277$	6.97499	+	9.60025i	0.419087	+	0.576823i	0.965405	−	0.260754i	$-0.0839712\pi$
$277$	6.97499	+	9.60025i	0.419087	+	0.576823i	−0.546319	+	0.837577i	$0.683971\pi$
$278$	−32.8657	−	10.6787i	−1.97115	−	0.640467i
$279$	−0.0773542	+	0.238072i	−0.00463108	+	0.0142530i
$280$		0			0
$281$	−7.61468	−	23.4356i	−0.454253	−	1.39805i	−0.872009	−	0.489489i	$-0.837183\pi$
$281$	−7.61468	−	23.4356i	−0.454253	−	1.39805i	0.417756	−	0.908559i	$-0.362817\pi$
$282$			45.5069i			2.70990i
$283$	−3.19881	+	1.03936i	−0.190150	+	0.0617833i	−0.402544	−	0.915401i	$-0.631874\pi$
$283$	−3.19881	+	1.03936i	−0.190150	+	0.0617833i	0.212394	+	0.977184i	$0.431874\pi$
$284$	18.3199	+	13.3102i	1.08709	+	0.789815i
$285$		0			0
$286$	−11.3843	+	8.27117i	−0.673168	+	0.489085i
$287$	5.03588	−	6.93130i	0.297259	−	0.409141i
$288$	−8.71584	+	11.9963i	−0.513586	+	0.706890i
$289$	−6.97519	+	5.06777i	−0.410305	+	0.298104i
$290$		0			0
$291$	−30.2883	−	22.0057i	−1.77553	−	1.29000i
$292$	−1.73302	+	0.563092i	−0.101417	+	0.0329525i
$293$			8.96340i			0.523647i	0.965116	+	0.261824i	$0.0843239\pi$
$293$			8.96340i			0.523647i	−0.965116	+	0.261824i	$0.915676\pi$
$294$	8.52155	+	26.2266i	0.496987	+	1.52957i
$295$		0			0
$296$	0.482504	−	1.48499i	0.0280450	−	0.0863136i
$297$	4.87861	+	1.58516i	0.283086	+	0.0919801i
$298$	−3.93641	−	5.41801i	−0.228030	−	0.313857i
$299$	−15.3507			−0.887756
$300$		0			0
$301$	4.60867			0.265640
$302$	21.6781	+	29.8374i	1.24744	+	1.71695i
$303$	−5.32583	−	1.73047i	−0.305961	−	0.0994128i
$304$	−2.54112	+	7.82078i	−0.145743	+	0.448552i
$305$		0			0
$306$	−3.41958	−	10.5244i	−0.195484	−	0.601638i
$307$			9.48133i			0.541128i	0.962702	+	0.270564i	$0.0872102\pi$
$307$			9.48133i			0.541128i	−0.962702	+	0.270564i	$0.912790\pi$
$308$	4.43299	−	1.44037i	0.252593	−	0.0820725i
$309$	−18.0804	−	13.1362i	−1.02856	−	0.747291i
$310$		0			0
$311$	−23.7301	+	17.2409i	−1.34561	+	0.977643i	−0.346393	+	0.938089i	$0.612594\pi$
$311$	−23.7301	+	17.2409i	−1.34561	+	0.977643i	−0.999217	+	0.0395541i	$0.987406\pi$
$312$	−3.16780	+	4.36010i	−0.179341	+	0.246842i
$313$	−11.1033	+	15.2824i	−0.627596	+	0.863811i	−0.997878	−	0.0651079i	$-0.979261\pi$
$313$	−11.1033	+	15.2824i	−0.627596	+	0.863811i	0.370283	+	0.928919i	$0.379261\pi$
$314$	−2.79224	+	2.02868i	−0.157575	+	0.114485i
$315$		0			0
$316$	−30.1151	−	21.8799i	−1.69411	−	1.23084i
$317$	−21.6739	+	7.04229i	−1.21733	+	0.395534i	−0.846109	−	0.533010i	$-0.821061\pi$
$317$	−21.6739	+	7.04229i	−1.21733	+	0.395534i	−0.371221	+	0.928545i	$0.621061\pi$
$318$		−	34.6826i		−	1.94490i
$319$	3.32768	+	10.2415i	0.186314	+	0.573416i
$320$		0			0
$321$	3.27267	−	10.0722i	0.182663	−	0.562178i
$322$	8.95435	+	2.90945i	0.499007	+	0.162137i
$323$	−4.39711	−	6.05210i	−0.244662	−	0.336748i
$324$	26.1587			1.45326
$325$		0			0
$326$	−1.86202			−0.103128
$327$	21.0303	+	28.9457i	1.16298	+	1.60070i
$328$	5.96538	+	1.93827i	0.329383	+	0.107023i
$329$	−3.04408	+	9.36871i	−0.167825	+	0.516513i
$330$		0			0
$331$	0.915615	+	2.81797i	0.0503268	+	0.154890i	0.973061	−	0.230546i	$-0.0740512\pi$
$331$	0.915615	+	2.81797i	0.0503268	+	0.154890i	−0.922735	+	0.385436i	$0.874051\pi$
$332$		−	4.15928i		−	0.228270i
$333$	−3.74725	+	1.21756i	−0.205348	+	0.0667217i
$334$	−8.76510	−	6.36822i	−0.479605	−	0.348453i
$335$		0			0
$336$	−5.61615	+	4.08037i	−0.306386	+	0.222603i
$337$	−11.0576	+	15.2195i	−0.602345	+	0.829057i	−0.995920	−	0.0902353i	$-0.971238\pi$
$337$	−11.0576	+	15.2195i	−0.602345	+	0.829057i	0.393575	+	0.919292i	$0.371238\pi$
$338$	−1.98037	+	2.72574i	−0.107718	+	0.148261i
$339$	−12.0182	+	8.73173i	−0.652739	+	0.474242i
$340$		0			0
$341$	−0.220923	−	0.160510i	−0.0119636	−	0.00869209i
$342$	−9.39711	+	3.05331i	−0.508138	+	0.165104i
$343$			12.9162i			0.697410i
$344$	1.04264	+	3.20891i	0.0562152	+	0.173013i
$345$		0			0
$346$	3.71467	−	11.4326i	0.199702	−	0.614620i
$347$	−21.6253	−	7.02649i	−1.16091	−	0.377201i	−0.335665	−	0.941981i	$-0.608961\pi$
$347$	−21.6253	−	7.02649i	−1.16091	−	0.377201i	−0.825242	+	0.564780i	$0.808961\pi$
$348$	16.3398	+	22.4898i	0.875906	+	1.20558i
$349$	−1.93849			−0.103765			−0.0518824	−	0.998653i	$-0.516522\pi$
$349$	−1.93849			−0.103765			−0.0518824	+	0.998653i	$0.516522\pi$
$350$		0			0
$351$	−8.65392			−0.461912
$352$	−9.50802	−	13.0867i	−0.506779	−	0.697522i
$353$	−4.99252	−	1.62217i	−0.265725	−	0.0863394i	0.173124	−	0.984900i	$-0.444614\pi$
$353$	−4.99252	−	1.62217i	−0.265725	−	0.0863394i	−0.438849	+	0.898561i	$0.644614\pi$
$354$	−6.96689	+	21.4419i	−0.370286	+	1.13962i
$355$		0			0
$356$	10.5285	+	32.4033i	0.558008	+	1.71737i
$357$		−	6.31519i		−	0.334235i
$358$	−17.1923	+	5.58612i	−0.908642	+	0.295236i
$359$	18.2787	+	13.2803i	0.964713	+	0.700905i	0.954241	−	0.299040i	$-0.0966664\pi$
$359$	18.2787	+	13.2803i	0.964713	+	0.700905i	0.0104726	+	0.999945i	$0.496666\pi$
$360$		0			0
$361$	9.96746	−	7.24178i	0.524603	−	0.381146i
$362$	−17.5163	+	24.1091i	−0.920637	+	1.26715i
$363$	−9.04569	+	12.4503i	−0.474775	+	0.653472i
$364$	−6.36167	+	4.62203i	−0.333442	+	0.242260i
$365$		0			0
$366$	10.2727	+	7.46353i	0.536961	+	0.390125i
$367$	6.94150	−	2.25543i	0.362343	−	0.117732i	−0.122187	−	0.992507i	$-0.538991\pi$
$367$	6.94150	−	2.25543i	0.362343	−	0.117732i	0.484530	+	0.874775i	$0.338991\pi$
$368$		−	14.4759i		−	0.754610i
$369$	−4.89105	−	15.0531i	−0.254618	−	0.783634i
$370$		0			0
$371$	2.32001	−	7.14025i	0.120449	−	0.370703i
$372$	−0.670438	−	0.217838i	−0.0347606	−	0.0112944i
$373$	−13.1119	−	18.0470i	−0.678911	−	0.934440i	0.321010	−	0.947076i	$-0.395978\pi$
$373$	−13.1119	−	18.0470i	−0.678911	−	0.934440i	−0.999920	+	0.0126358i	$0.995978\pi$
$374$	12.0718			0.624216
$375$		0			0
$376$	−7.21188			−0.371924
$377$	−10.6783	−	14.6974i	−0.549959	−	0.756953i
$378$	5.04798	+	1.64019i	0.259640	+	0.0843621i
$379$	10.1811	−	31.3341i	0.522966	−	1.60952i	−0.245337	−	0.969438i	$-0.578899\pi$
$379$	10.1811	−	31.3341i	0.522966	−	1.60952i	0.768303	−	0.640086i	$-0.221101\pi$
$380$		0			0
$381$	1.01282	+	3.11713i	0.0518881	+	0.159695i
$382$			2.64072i			0.135111i
$383$	−19.6871	+	6.39671i	−1.00596	+	0.326857i	−0.765245	−	0.643739i	$-0.777382\pi$
$383$	−19.6871	+	6.39671i	−1.00596	+	0.326857i	−0.240716	+	0.970595i	$0.577382\pi$
$384$	−10.1811	−	7.39697i	−0.519550	−	0.377475i
$385$		0			0
$386$	35.7194	−	25.9517i	1.81807	−	1.32091i
$387$	5.00447	−	6.88806i	0.254391	−	0.350140i
$388$	23.5063	−	32.3537i	1.19335	−	1.64251i
$389$	−0.925886	+	0.672696i	−0.0469443	+	0.0341070i	−0.611010	−	0.791623i	$-0.709236\pi$
$389$	−0.925886	+	0.672696i	−0.0469443	+	0.0341070i	0.564066	+	0.825730i	$0.309236\pi$
$390$		0			0
$391$	10.6539	+	7.74052i	0.538792	+	0.391455i
$392$	−4.15636	+	1.35048i	−0.209928	+	0.0682098i
$393$			31.0310i			1.56531i
$394$	−7.86239	−	24.1980i	−0.396102	−	1.21908i
$395$		0			0
$396$	2.66095	−	8.18955i	0.133718	−	0.411540i
$397$	−4.45583	−	1.44779i	−0.223631	−	0.0726623i	0.195058	−	0.980792i	$-0.437510\pi$
$397$	−4.45583	−	1.44779i	−0.223631	−	0.0726623i	−0.418690	+	0.908129i	$0.637510\pi$
$398$	−12.7552	−	17.5560i	−0.639361	−	0.880005i
$399$	−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	$0.705381\pi$
$402$	−5.88998	−	8.10687i	−0.293766	−	0.404334i
$403$	0.438139	+	0.142360i	0.0218253	+	0.00709146i
$404$	1.84847	−	5.68902i	0.0919650	−	0.283039i
$405$		0			0
$406$	3.44320	+	10.5971i	0.170883	+	0.525925i
$407$		−	4.29821i		−	0.213054i
$408$	4.39711	−	1.42871i	0.217689	−	0.0707316i
$409$	−1.53660	−	1.11641i	−0.0759801	−	0.0552027i	0.549147	−	0.835726i	$-0.314953\pi$
$409$	−1.53660	−	1.11641i	−0.0759801	−	0.0552027i	−0.625127	+	0.780523i	$0.714953\pi$
$410$		0			0
$411$	−1.22626	+	0.890932i	−0.0604871	+	0.0439464i
$412$	14.0320	−	19.3134i	0.691306	−	0.951501i
$413$	−2.86861	+	3.94830i	−0.141155	+	0.194283i
$414$	14.0718	−	10.2237i	0.691589	−	0.502469i
$415$		0			0
$416$	22.0776	+	16.0403i	1.08244	+	0.786441i
$417$	−34.6499	+	11.2584i	−1.69681	+	0.551328i
$418$		−	10.7788i		−	0.527207i
$419$	0.719410	+	2.21412i	0.0351455	+	0.108167i	0.967090	−	0.254434i	$-0.0818890\pi$
$419$	0.719410	+	2.21412i	0.0351455	+	0.108167i	−0.931945	+	0.362600i	$0.881889\pi$
$420$		0			0
$421$	−7.40097	+	22.7779i	−0.360701	+	1.11012i	0.591928	+	0.805991i	$0.298367\pi$
$421$	−7.40097	+	22.7779i	−0.360701	+	1.11012i	−0.952629	+	0.304134i	$0.901633\pi$
$422$	17.1701	+	5.57891i	0.835829	+	0.271577i
$423$	10.6968	+	14.7229i	0.520098	+	0.715853i
$424$	5.49645			0.266931
$425$		0			0
$426$	44.2060			2.14179
$427$	1.61562	+	2.22371i	0.0781855	+	0.107613i
$428$	10.7591	+	3.49584i	0.520061	+	0.168978i
$429$	−4.58448	+	14.1096i	−0.221341	+	0.681217i
$430$		0			0
$431$	0.368430	+	1.13391i	0.0177467	+	0.0546186i	0.959538	−	0.281580i	$-0.0908586\pi$
$431$	0.368430	+	1.13391i	0.0177467	+	0.0546186i	−0.941791	+	0.336199i	$0.890859\pi$
$432$		−	8.16074i		−	0.392634i
$433$	24.3602	−	7.91511i	1.17068	−	0.380376i	0.341781	−	0.939780i	$-0.388970\pi$
$433$	24.3602	−	7.91511i	1.17068	−	0.380376i	0.828895	+	0.559404i	$0.188970\pi$
$434$	−0.228592	−	0.166082i	−0.0109728	−	0.00797219i
$435$		0			0
$436$	−30.9196	+	22.4644i	−1.48078	+	1.07585i
$437$	6.91144	−	9.51278i	0.330619	−	0.455058i
$438$	−2.09089	+	2.87786i	−0.0999066	+	0.137510i
$439$	15.6740	−	11.3878i	0.748079	−	0.543511i	−0.147152	−	0.989114i	$-0.547011\pi$
$439$	15.6740	−	11.3878i	0.748079	−	0.543511i	0.895231	+	0.445603i	$0.147011\pi$
$440$		0			0
$441$	8.92181	+	6.48207i	0.424848	+	0.308670i
$442$	−19.3687	+	6.29327i	−0.921274	+	0.299340i
$443$			2.46263i			0.117003i	0.998287	+	0.0585016i	$0.0186323\pi$
$443$			2.46263i			0.117003i	−0.998287	+	0.0585016i	$0.981368\pi$
$444$	−3.42878	−	10.5527i	−0.162723	−	0.500809i
$445$		0			0
$446$	−18.2641	+	56.2113i	−0.864833	+	2.66168i
$447$	−6.71502	−	2.18184i	−0.317610	−	0.103198i
$448$	−6.12613	−	8.43190i	−0.289433	−	0.398370i
$449$	14.3585			0.677618			0.338809	−	0.940855i	$-0.389976\pi$
$449$	14.3585			0.677618			0.338809	+	0.940855i	$0.389976\pi$
$450$		0			0
$451$	17.2664			0.813041
$452$	−9.32717	−	12.8378i	−0.438713	−	0.603837i
$453$	36.9802	+	12.0156i	1.73748	+	0.564542i
$454$	14.3321	−	44.1098i	0.672641	−	2.07018i
$455$		0			0
$456$	−1.27568	−	3.92614i	−0.0597392	−	0.183858i
$457$			25.1964i			1.17864i	0.807901	+	0.589319i	$0.200604\pi$
$457$			25.1964i			1.17864i	−0.807901	+	0.589319i	$0.799396\pi$
$458$	−4.90965	+	1.59524i	−0.229413	+	0.0745408i
$459$	6.00610	+	4.36369i	0.280341	+	0.203679i
$460$		0			0
$461$	−23.3203	+	16.9432i	−1.08614	+	0.789124i	−0.978743	−	0.205092i	$-0.934251\pi$
$461$	−23.3203	+	16.9432i	−1.08614	+	0.789124i	−0.107394	+	0.994217i	$0.534251\pi$
$462$	5.34841	−	7.36146i	0.248831	−	0.342486i
$463$	18.7384	−	25.7911i	0.870846	−	1.19862i	−0.108028	−	0.994148i	$-0.534453\pi$
$463$	18.7384	−	25.7911i	0.870846	−	1.19862i	0.978873	−	0.204468i	$-0.0655465\pi$
$464$	13.8598	−	10.0697i	0.643425	−	0.467475i
$465$		0			0
$466$	10.0480	+	7.30033i	0.465466	+	0.338181i
$467$	40.9902	−	13.3185i	1.89680	−	0.616307i	0.925314	−	0.379201i	$-0.123801\pi$
$467$	40.9902	−	13.3185i	1.89680	−	0.616307i	0.971484	−	0.237106i	$-0.0761988\pi$
$468$			14.5270i			0.671512i
$469$	−0.670307	−	2.06299i	−0.0309519	−	0.0952601i
$470$		0			0
$471$	−1.12444	+	3.46068i	−0.0518115	+	0.159460i
$472$	−3.39808	−	1.10410i	−0.156409	−	0.0508205i
$473$	5.45932	+	7.51411i	0.251020	+	0.345499i
$474$	−72.6679			−3.33775
$475$		0			0
$476$	6.74584			0.309195
$477$	−8.15246	−	11.2209i	−0.373276	−	0.513770i
$478$	−13.9469	−	4.53161i	−0.637915	−	0.207271i
$479$	−6.49749	+	19.9972i	−0.296878	+	0.913697i	0.685706	+	0.727878i	$0.259494\pi$
$479$	−6.49749	+	19.9972i	−0.296878	+	0.913697i	−0.982584	+	0.185818i	$0.940506\pi$
$480$		0			0
$481$	2.24075	+	6.89631i	0.102169	+	0.314445i
$482$		−	2.46014i		−	0.112057i
$483$	9.44047	−	3.06739i	0.429556	−	0.139571i
$484$	−13.2993	−	9.66254i	−0.604516	−	0.439206i
$485$		0			0
$486$	28.3323	−	20.5846i	1.28518	−	0.933739i
$487$	16.4104	−	22.5869i	0.743625	−	1.02351i	−0.254777	−	0.967000i	$-0.582002\pi$
$487$	16.4104	−	22.5869i	0.743625	−	1.02351i	0.998402	−	0.0565121i	$-0.0179979\pi$
$488$	−1.18281	+	1.62800i	−0.0535433	+	0.0736960i
$489$	−1.58819	+	1.15389i	−0.0718204	+	0.0521805i
$490$		0			0
$491$	−12.1037	−	8.79389i	−0.546234	−	0.396862i	0.280161	−	0.959953i	$-0.409612\pi$
$491$	−12.1037	−	8.79389i	−0.546234	−	0.396862i	−0.826395	+	0.563091i	$0.809612\pi$
$492$	42.3913	−	13.7738i	1.91115	−	0.620969i
$493$			15.5849i			0.701909i
$494$	5.61920	+	17.2941i	0.252820	+	0.778099i
$495$		0			0
$496$	−0.134247	+	0.413170i	−0.00602787	+	0.0185519i
$497$	9.10089	+	2.95706i	0.408231	+	0.132642i
$498$	−4.77257	−	6.56888i	−0.213864	−	0.294359i
$499$	44.3253			1.98427			0.992137	−	0.125160i	$-0.0399443\pi$
$499$	44.3253			1.98427			0.992137	+	0.125160i	$0.0399443\pi$
$500$		0			0
$501$	−11.4224			−0.510316
$502$	5.64885	+	7.77498i	0.252121	+	0.347014i
$503$	22.4651	+	7.29936i	1.00167	+	0.325462i	0.763532	−	0.645769i	$-0.223463\pi$
$503$	22.4651	+	7.29936i	1.00167	+	0.325462i	0.238137	+	0.971232i	$0.423463\pi$
$504$	0.408487	−	1.25719i	0.0181955	−	0.0559999i
$505$		0			0
$506$	5.86346	+	18.0459i	0.260663	+	0.802237i
$507$			3.55211i			0.157755i
$508$	−3.32969	+	1.08188i	−0.147731	+	0.0480008i
$509$	−21.6132	−	15.7029i	−0.957990	−	0.696020i	−0.00530682	−	0.999986i	$-0.501689\pi$
$509$	−21.6132	−	15.7029i	−0.957990	−	0.696020i	−0.952683	+	0.303966i	$0.901689\pi$
$510$		0			0
$511$	−0.622968	+	0.452613i	−0.0275585	+	0.0200224i
$512$	−17.8438	+	24.5598i	−0.788591	+	1.08540i
$513$	3.89629	−	5.36279i	0.172026	−	0.236773i
$514$	16.4577	−	11.9572i	0.725918	−	0.527410i
$515$		0			0
$516$	19.3976	+	14.0931i	0.853930	+	0.620416i
$517$	−18.8809	+	6.13479i	−0.830383	+	0.269808i
$518$		−	4.44743i		−	0.195409i
$519$	−3.91633	−	12.0532i	−0.171908	−	0.529078i
$520$		0			0
$521$	10.1071	−	31.1065i	0.442800	−	1.36280i	−0.442078	−	0.896977i	$-0.645759\pi$
$521$	10.1071	−	31.1065i	0.442800	−	1.36280i	0.884878	−	0.465822i	$-0.154241\pi$
$522$	19.5772	+	6.36101i	0.856869	+	0.278414i
$523$	0.138697	+	0.190901i	0.00606481	+	0.00834750i	0.812039	−	0.583604i	$-0.198358\pi$
$523$	0.138697	+	0.190901i	0.00606481	+	0.00834750i	−0.805974	+	0.591951i	$0.798358\pi$
$524$	−33.1471			−1.44804
$525$		0			0
$526$	−2.07658			−0.0905434
$527$	−0.232299	−	0.319732i	−0.0101191	−	0.0139277i
$528$	−13.3055	−	4.32322i	−0.579048	−	0.188144i
$529$	0.710999	−	2.18823i	0.0309130	−	0.0951405i
$530$		0			0
$531$	2.78611	+	8.57476i	0.120907	+	0.372113i
$532$		−	6.02330i		−	0.261143i
$533$	−27.7032	+	9.00132i	−1.19996	+	0.389890i
$534$	53.8091	+	39.0946i	2.32855	+	1.69179i
$535$		0			0
$536$	1.28477	−	0.933437i	0.0554934	−	0.0403183i
$537$	−11.2023	+	15.4186i	−0.483413	+	0.665361i
$538$	−4.03076	+	5.54786i	−0.173778	+	0.239185i
$539$	−9.73271	+	7.07123i	−0.419217	+	0.304579i
$540$		0			0
$541$	27.1484	+	19.7244i	1.16720	+	0.848020i	0.990671	−	0.136276i	$-0.0435133\pi$
$541$	27.1484	+	19.7244i	1.16720	+	0.848020i	0.176528	+	0.984296i	$0.443513\pi$
$542$	24.0963	−	7.82935i	1.03502	−	0.336299i
$543$			31.4183i			1.34829i
$544$	−7.23434	−	22.2650i	−0.310170	−	0.954604i
$545$		0			0
$546$	−4.74364	+	14.5994i	−0.203009	+	0.624798i
$547$	36.6276	+	11.9010i	1.56608	+	0.508851i	0.958424	−	0.285348i	$-0.0921093\pi$
$547$	36.6276	+	11.9010i	1.56608	+	0.508851i	0.607658	+	0.794199i	$0.292109\pi$
$548$	−0.951688	−	1.30989i	−0.0406541	−	0.0559555i
$549$	5.07790			0.216720
$550$		0			0
$551$	13.9156			0.592825
$552$	4.27150	+	5.87922i	0.181807	+	0.250236i
$553$	−14.9605	−	4.86095i	−0.636183	−	0.206708i
$554$	−7.64668	+	23.5341i	−0.324876	+	0.999866i
$555$		0			0
$556$	−12.0262	−	37.0128i	−0.510024	−	1.56969i
$557$			4.33445i			0.183657i	0.995775	+	0.0918283i	$0.0292711\pi$
$557$			4.33445i			0.183657i	−0.995775	+	0.0918283i	$0.970729\pi$
$558$	−0.496448	+	0.161306i	−0.0210163	+	0.00682861i
$559$	−12.6765	−	9.21004i	−0.536160	−	0.389543i
$560$		0			0
$561$	10.2965	−	7.48081i	0.434717	−	0.315840i
$562$	30.2032	−	41.5712i	1.27405	−	1.75357i
$563$	20.5148	−	28.2362i	0.864595	−	1.19001i	−0.115860	−	0.993266i	$-0.536962\pi$
$563$	20.5148	−	28.2362i	0.864595	−	1.19001i	0.980454	−	0.196747i	$-0.0630377\pi$
$564$	−41.4614	+	30.1235i	−1.74584	+	1.26843i
$565$		0			0
$566$	−5.67421	−	4.12255i	−0.238505	−	0.173284i
$567$	10.5132	−	3.41593i	0.441511	−	0.143456i
$568$			7.00572i			0.293953i
$569$	12.9678	+	39.9107i	0.543637	+	1.67314i	0.724208	+	0.689581i	$0.242205\pi$
$569$	12.9678	+	39.9107i	0.543637	+	1.67314i	−0.180571	+	0.983562i	$0.557795\pi$
$570$		0			0
$571$	−4.27469	+	13.1561i	−0.178890	+	0.550567i	−0.999790	−	0.0205055i	$-0.993472\pi$
$571$	−4.27469	+	13.1561i	−0.178890	+	0.550567i	0.820900	+	0.571072i	$0.193472\pi$
$572$	−15.0718	−	4.89711i	−0.630182	−	0.204759i
$573$	1.63644	+	2.25237i	0.0683633	+	0.0940940i
$574$	17.8658			0.745704
$575$		0			0
$576$	−19.2544			−0.802268
$577$	−7.51147	−	10.3387i	−0.312707	−	0.430404i	0.623516	−	0.781810i	$-0.285704\pi$
$577$	−7.51147	−	10.3387i	−0.312707	−	0.430404i	−0.936223	+	0.351407i	$0.885704\pi$
$578$	−17.0990	−	5.55579i	−0.711223	−	0.231090i
$579$	14.3843	−	44.2703i	0.597791	−	1.83981i
$580$		0			0
$581$	−0.543140	−	1.67161i	−0.0225333	−	0.0693502i
$582$		−	78.0696i		−	3.23609i
$583$	14.3899	−	4.67556i	0.595968	−	0.193642i
$584$	−0.456080	−	0.331361i	−0.0188727	−	0.0137118i
$585$		0			0
$586$	−15.1215	+	10.9864i	−0.624665	+	0.453845i
$587$	7.16331	−	9.85945i	0.295661	−	0.406943i	−0.635181	−	0.772363i	$-0.719075\pi$
$587$	7.16331	−	9.85945i	0.295661	−	0.406943i	0.930843	+	0.365420i	$0.119075\pi$
$588$	−18.2543	+	25.1248i	−0.752793	+	1.03613i
$589$	−0.285485	+	0.207417i	−0.0117632	+	0.00854648i
$590$		0			0
$591$	−21.7015	−	15.7671i	−0.892680	−	0.648570i
$592$	−6.50330	+	2.11305i	−0.267284	+	0.0868459i
$593$		−	31.2580i		−	1.28361i	−0.766866	−	0.641807i	$-0.778185\pi$
$593$		−	31.2580i		−	1.28361i	0.766866	−	0.641807i	$-0.221815\pi$
$594$	3.30550	+	10.1733i	0.135626	+	0.417415i
$595$		0			0
$596$	2.33063	−	7.17294i	0.0954663	−	0.293815i
$597$	−21.7588	−	7.06986i	−0.890528	−	0.289350i
$598$	−18.8154	−	25.8972i	−0.769419	−	1.05901i
$599$	33.3707			1.36349			0.681746	−	0.731589i	$-0.261221\pi$
$599$	33.3707			1.36349			0.681746	+	0.731589i	$0.261221\pi$
$600$		0			0
$601$	−46.8052			−1.90922			−0.954611	−	0.297854i	$-0.903729\pi$
$601$	−46.8052			−1.90922			−0.954611	+	0.297854i	$0.903729\pi$
$602$	5.64885	+	7.77498i	0.230230	+	0.316884i
$603$	−3.81119	−	1.23833i	−0.155204	−	0.0504287i
$604$	−12.8350	+	39.5020i	−0.522248	+	1.60731i
$605$		0			0
$606$	−3.60852	−	11.1059i	−0.146586	−	0.451145i
$607$		−	30.7401i		−	1.24770i	−0.781543	−	0.623851i	$-0.785567\pi$
$607$		−	30.7401i		−	1.24770i	0.781543	−	0.623851i	$-0.214433\pi$
$608$	−19.8802	+	6.45947i	−0.806249	+	0.261966i
$609$	9.50380	+	6.90492i	0.385114	+	0.279801i
$610$		0			0
$611$	27.0955	−	19.6861i	1.09617	−	0.796413i
$612$	7.32517	−	10.0822i	0.296102	−	0.407550i
$613$	−22.5060	+	30.9768i	−0.909008	+	1.25114i	0.0584964	+	0.998288i	$0.481369\pi$
$613$	−22.5060	+	30.9768i	−0.909008	+	1.25114i	−0.967504	+	0.252854i	$0.918631\pi$
$614$	−15.9953	+	11.6213i	−0.645518	+	0.468996i
$615$		0			0
$616$	1.16663	+	0.847609i	0.0470050	+	0.0341512i
$617$	0.404490	−	0.131427i	0.0162842	−	0.00529104i	−0.300864	−	0.953667i	$-0.597275\pi$
$617$	0.404490	−	0.131427i	0.0162842	−	0.00529104i	0.317148	+	0.948376i	$0.397275\pi$
$618$		−	46.6032i		−	1.87466i
$619$	−2.32117	−	7.14384i	−0.0932958	−	0.287135i	0.893510	−	0.449043i	$-0.148235\pi$
$619$	−2.32117	−	7.14384i	−0.0932958	−	0.287135i	−0.986806	+	0.161908i	$0.948235\pi$
$620$		0			0
$621$	−3.60594	+	11.0979i	−0.144701	+	0.445345i
$622$	−58.1720	−	18.9012i	−2.33248	−	0.757870i
$623$	8.46278	+	11.6480i	0.339054	+	0.466668i
$624$	23.6020			0.944834
$625$		0			0
$626$	−39.3912			−1.57439
$627$	−6.67955	−	9.19361i	−0.266755	−	0.367157i
$628$	−3.69667	−	1.20112i	−0.147513	−	0.0479300i
$629$	1.92227	−	5.91615i	0.0766461	−	0.235892i
$630$		0			0
$631$	−3.48311	−	10.7199i	−0.138660	−	0.426752i	0.857481	−	0.514515i	$-0.172028\pi$
$631$	−3.48311	−	10.7199i	−0.138660	−	0.426752i	−0.996141	+	0.0877630i	$0.972028\pi$
$632$		−	11.5163i		−	0.458094i
$633$	18.1023	−	5.88178i	0.719500	−	0.233780i
$634$	−38.4463	−	27.9329i	−1.52690	−	1.10936i
$635$		0			0
$636$	31.5994	−	22.9583i	1.25300	−	0.910355i
$637$	11.9294	−	16.4194i	0.472659	−	0.650560i
$638$	−13.1991	+	18.1669i	−0.522556	+	0.719236i
$639$	14.3020	−	10.3910i	0.565780	−	0.411063i
$640$		0			0
$641$	−21.1012	−	15.3309i	−0.833447	−	0.605535i	0.0870851	−	0.996201i	$-0.472245\pi$
$641$	−21.1012	−	15.3309i	−0.833447	−	0.605535i	−0.920533	+	0.390666i	$0.872245\pi$
$642$	21.0035	−	6.82445i	0.828942	−	0.269340i
$643$		−	31.9492i		−	1.25995i	−0.776614	−	0.629977i	$-0.783064\pi$
$643$		−	31.9492i		−	1.25995i	0.776614	−	0.629977i	$-0.216936\pi$
$644$	3.27657	+	10.0842i	0.129115	+	0.397375i
$645$		0			0
$646$	4.82055	−	14.8361i	0.189662	−	0.583720i
$647$	7.03243	+	2.28497i	0.276473	+	0.0898316i	0.443972	−	0.896041i	$-0.353569\pi$
$647$	7.03243	+	2.28497i	0.276473	+	0.0898316i	−0.167499	+	0.985872i	$0.553569\pi$
$648$	4.75686	+	6.54726i	0.186867	+	0.257201i
$649$	−9.83550			−0.386077
$650$		0			0
$651$	−0.297895			−0.0116754
$652$	−1.23257	−	1.69649i	−0.0482713	−	0.0664398i
$653$	17.7708	+	5.77407i	0.695424	+	0.225957i	0.635336	−	0.772236i	$-0.280862\pi$
$653$	17.7708	+	5.77407i	0.695424	+	0.225957i	0.0600882	+	0.998193i	$0.480862\pi$
$654$	−23.0555	+	70.9575i	−0.901541	+	2.77466i
$655$		0			0
$656$	−8.48835	−	26.1245i	−0.331414	−	1.01999i
$657$			1.42256i			0.0554994i
$658$	−19.5364	+	6.34777i	−0.761609	+	0.247462i
$659$	7.92963	+	5.76122i	0.308895	+	0.224425i	0.731422	−	0.681925i	$-0.238857\pi$
$659$	7.92963	+	5.76122i	0.308895	+	0.224425i	−0.422527	+	0.906350i	$0.638857\pi$
$660$		0			0
$661$	22.7807	−	16.5511i	0.886066	−	0.643765i	−0.0487833	−	0.998809i	$-0.515534\pi$
$661$	22.7807	−	16.5511i	0.886066	−	0.643765i	0.934849	+	0.355045i	$0.115534\pi$
$662$	−3.63174	+	4.99866i	−0.141152	+	0.194278i
$663$	−12.6204	+	17.3704i	−0.490134	+	0.674612i
$664$	1.04103	−	0.756351i	0.0403997	−	0.0293521i
$665$		0			0
$666$	−6.64706	−	4.82937i	−0.257568	−	0.187134i
$667$	−23.2976	+	7.56986i	−0.902087	+	0.293106i
$668$		−	12.2014i		−	0.472085i
$669$	19.2557	+	59.2629i	0.744468	+	2.29124i
$670$		0			0
$671$	−1.71178	+	5.26831i	−0.0660825	+	0.203381i
$672$	−16.7826	−	5.45299i	−0.647402	−	0.210354i
$673$	22.9385	+	31.5721i	0.884214	+	1.21702i	0.975236	+	0.221168i	$0.0709868\pi$
$673$	22.9385	+	31.5721i	0.884214	+	1.21702i	−0.0910215	+	0.995849i	$0.529013\pi$
$674$	−39.2290			−1.51104
$675$		0			0
$676$	−3.79434			−0.145936
$677$	2.95969	+	4.07367i	0.113750	+	0.156564i	0.862096	−	0.506745i	$-0.169152\pi$
$677$	2.95969	+	4.07367i	0.113750	+	0.156564i	−0.748346	+	0.663309i	$0.769152\pi$
$678$	−29.4614	−	9.57259i	−1.13146	−	0.367633i
$679$	5.22228	−	16.0725i	0.200413	−	0.616807i
$680$		0			0
$681$	−15.1102	−	46.5044i	−0.579025	−	1.78205i
$682$		−	0.569440i		−	0.0218050i
$683$	28.8467	−	9.37285i	1.10379	−	0.358642i	0.300228	−	0.953867i	$-0.402937\pi$
$683$	28.8467	−	9.37285i	1.10379	−	0.358642i	0.803559	+	0.595225i	$0.202937\pi$
$684$	−9.00233	−	6.54058i	−0.344213	−	0.250085i
$685$		0			0
$686$	−21.7900	+	15.8314i	−0.831948	+	0.604446i
$687$	−3.19906	+	4.40313i	−0.122052	+	0.167990i
$688$	8.68518	−	11.9541i	0.331119	−	0.455747i
$689$	−20.6506	+	15.0035i	−0.786724	+	0.571588i
$690$		0			0
$691$	17.1778	+	12.4804i	0.653474	+	0.474777i	0.864453	−	0.502714i	$-0.167665\pi$
$691$	17.1778	+	12.4804i	0.653474	+	0.474777i	−0.210979	+	0.977491i	$0.567665\pi$
$692$	12.8752	−	4.18340i	0.489441	−	0.159029i
$693$		−	3.63886i		−	0.138229i
$694$	−14.6522	−	45.0949i	−0.556191	−	1.71178i
$695$		0			0
$696$	−2.65765	+	8.17939i	−0.100738	+	0.310039i
$697$	23.7658	+	7.72198i	0.900194	+	0.292491i
$698$	−2.37600	−	3.27029i	−0.0899330	−	0.123782i
$699$	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	$0.287599\pi$
$702$	−10.6071	−	14.5994i	−0.400339	−	0.551020i
$703$	−5.28247	−	1.71638i	−0.199232	−	0.0647345i
$704$	6.49074	−	19.9764i	0.244629	−	0.752890i
$705$		0			0
$706$	−3.38269	−	10.4108i	−0.127309	−	0.391817i
$707$		−	2.52780i		−	0.0950676i
$708$	−24.1475	+	7.84600i	−0.907519	+	0.294871i
$709$	16.0557	+	11.6652i	0.602985	+	0.438094i	0.846937	−	0.531693i	$-0.178444\pi$
$709$	16.0557	+	11.6652i	0.602985	+	0.438094i	−0.243952	+	0.969787i	$0.578444\pi$
$710$		0			0
$711$	−23.5103	+	17.0813i	−0.881707	+	0.640598i
$712$	−6.19566	+	8.52760i	−0.232192	+	0.319585i
$713$	0.365130	−	0.502558i	0.0136742	−	0.0188210i
$714$	10.6539	−	7.74052i	0.398713	−	0.289682i
$715$		0			0
$716$	−16.4700	−	11.9662i	−0.615514	−	0.447197i
$717$	−14.7040	+	4.77763i	−0.549132	+	0.178424i
$718$			47.1144i			1.75829i
$719$	−7.48443	−	23.0347i	−0.279122	−	0.859049i	−0.988099	−	0.153818i	$-0.950843\pi$
$719$	−7.48443	−	23.0347i	−0.279122	−	0.859049i	0.708977	−	0.705231i	$-0.249157\pi$
$720$		0			0
$721$	3.11741	−	9.59440i	0.116098	−	0.357314i
$722$	24.4342	+	7.93916i	0.909347	+	0.295465i
$723$	−1.52454	−	2.09835i	−0.0566982	−	0.0780384i
$724$	−33.5609			−1.24728
$725$		0			0
$726$	−32.0914			−1.19102
$727$	−3.44742	−	4.74496i	−0.127858	−	0.175981i	0.740289	−	0.672289i	$-0.234689\pi$
$727$	−3.44742	−	4.74496i	−0.127858	−	0.175981i	−0.868147	+	0.496308i	$0.834689\pi$
$728$	−2.31370	−	0.751766i	−0.0857513	−	0.0278623i
$729$	1.08320	−	3.33374i	0.0401185	−	0.123472i
$730$		0			0
$731$	4.15382	+	12.7841i	0.153635	+	0.472838i
$732$			14.3000i			0.528542i
$733$	32.8129	−	10.6615i	1.21197	−	0.393793i	0.367819	−	0.929897i	$-0.380105\pi$
$733$	32.8129	−	10.6615i	1.21197	−	0.393793i	0.844152	+	0.536104i	$0.180105\pi$
$734$	12.3132	+	8.94604i	0.454487	+	0.330204i
$735$		0			0
$736$	29.7698	−	21.6290i	1.09733	−	0.797255i
$737$	2.56953	−	3.53666i	0.0946499	−	0.130274i
$738$	19.4001	−	26.7019i	0.714128	−	0.982912i
$739$	32.0138	−	23.2594i	1.17765	−	0.855611i	0.185743	−	0.982598i	$-0.440531\pi$
$739$	32.0138	−	23.2594i	1.17765	−	0.855611i	0.991904	+	0.126988i	$0.0405309\pi$
$740$		0			0
$741$	15.5099	+	11.2686i	0.569770	+	0.413962i
$742$	14.8895	−	4.83788i	0.546609	−	0.177604i
$743$			29.7058i			1.08980i	0.838501	+	0.544900i	$0.183433\pi$
$743$			29.7058i			1.08980i	−0.838501	+	0.544900i	$0.816567\pi$
$744$	−0.0673939	−	0.207417i	−0.00247078	−	0.00760428i
$745$		0			0
$746$	14.3746	−	44.2405i	0.526292	−	1.61976i
$747$	−3.08815	−	1.00340i	−0.112990	−	0.0367126i
$748$	7.99095	+	10.9986i	0.292178	+	0.402149i
$749$	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	$0.336792\pi$
$752$	18.5642	+	25.5514i	0.676966	+	0.931764i
$753$	9.63623	+	3.13100i	0.351164	+	0.114100i
$754$	11.7066	−	36.0291i	0.426328	−	1.31210i
$755$		0			0
$756$	1.84715	+	5.68495i	0.0671803	+	0.206760i
$757$			44.6792i			1.62389i	0.583731	+	0.811947i	$0.301592\pi$
$757$			44.6792i			1.62389i	−0.583731	+	0.811947i	$0.698408\pi$
$758$	65.3405	−	21.2304i	2.37327	−	0.771123i
$759$	16.1841	+	11.7584i	0.587446	+	0.426804i
$760$		0			0
$761$	−16.4295	+	11.9367i	−0.595568	+	0.432706i	−0.844303	−	0.535866i	$-0.819985\pi$
$761$	−16.4295	+	11.9367i	−0.595568	+	0.432706i	0.248735	+	0.968572i	$0.419985\pi$
$762$	−4.01728	+	5.52931i	−0.145531	+	0.200306i
$763$	−9.49307	+	13.0661i	−0.343672	+	0.473024i
$764$	−2.40596	+	1.74803i	−0.0870447	+	0.0632417i
$765$		0			0
$766$	−34.9219	−	25.3722i	−1.26178	−	0.916736i
$767$	15.7807	−	5.12746i	0.569808	−	0.185142i
$768$			19.9359i			0.719375i
$769$	−8.05227	−	24.7823i	−0.290372	−	0.893674i	−0.984737	−	0.174051i	$-0.944314\pi$
$769$	−8.05227	−	24.7823i	−0.290372	−	0.893674i	0.694364	−	0.719624i	$-0.255686\pi$
$770$		0			0
$771$	6.62755	−	20.3975i	0.238685	−	0.734598i
$772$	47.2892	+	15.3652i	1.70198	+	0.553006i
$773$	8.07058	+	11.1082i	0.290278	+	0.399534i	0.929105	−	0.369817i	$-0.120580\pi$
$773$	8.07058	+	11.1082i	0.290278	+	0.399534i	−0.638826	+	0.769351i	$0.720580\pi$
$774$	17.7543			0.638166
$775$		0			0
$776$	12.3724			0.444142
$777$	−2.75605	−	3.79338i	−0.0988728	−	0.136087i
$778$	−2.26972	−	0.737476i	−0.0813733	−	0.0264398i
$779$	6.89488	−	21.2203i	0.247035	−	0.760295i
$780$		0			0
$781$	5.95942	+	18.3412i	0.213245	+	0.656300i
$782$			27.4610i			0.982005i
$783$	−13.1339	+	4.26747i	−0.469368	+	0.152507i
$784$	15.4837	+	11.2495i	0.552988	+	0.401769i
$785$		0			0
$786$	−52.3503	+	38.0347i	−1.86727	+	1.35665i
$787$	−11.5594	+	15.9101i	−0.412048	+	0.567136i	−0.963716	−	0.266928i	$-0.913991\pi$
$787$	−11.5594	+	15.9101i	−0.412048	+	0.567136i	0.551668	+	0.834064i	$0.313991\pi$
$788$	16.8423	−	23.1814i	0.599981	−	0.825803i
$789$	−1.77120	+	1.28685i	−0.0630562	+	0.0458130i
$790$		0			0
$791$	−5.42501	−	3.94150i	−0.192891	−	0.140144i
$792$	2.53365	−	0.823232i	0.0900293	−	0.0292523i
$793$		−	9.34520i		−	0.331858i
$794$	−3.01905	−	9.29167i	−0.107142	−	0.329749i
$795$		0			0
$796$	7.55197	−	23.2426i	0.267673	−	0.823812i
$797$	10.4085	+	3.38191i	0.368686	+	0.119793i	0.487500	−	0.873123i	$-0.337909\pi$
$797$	10.4085	+	3.38191i	0.368686	+	0.119793i	−0.118813	+	0.992917i	$0.537909\pi$
$798$	−6.91144	−	9.51278i	−0.244662	−	0.336749i
$799$	−28.7318			−1.01646
$800$		0			0
$801$	26.5985			0.939812
$802$	−29.5211	−	40.6323i	−1.04243	−	1.43478i
$803$	−1.47591	−	0.479551i	−0.0520836	−	0.0169230i
$804$	3.48728	−	10.7327i	0.122987	−	0.378515i
$805$		0			0
$806$	0.296861	+	0.913645i	0.0104565	+	0.0321818i
$807$			7.22982i			0.254502i
$808$	1.76004	−	0.571873i	0.0619182	−	0.0201184i
$809$	13.3025	+	9.66480i	0.467689	+	0.339796i	0.796540	−	0.604586i	$-0.206661\pi$
$809$	13.3025	+	9.66480i	0.467689	+	0.339796i	−0.328851	+	0.944382i	$0.606661\pi$
$810$		0			0
$811$	−18.3220	+	13.3117i	−0.643373	+	0.467438i	−0.861007	−	0.508592i	$-0.830166\pi$
$811$	−18.3220	+	13.3117i	−0.643373	+	0.467438i	0.217634	+	0.976030i	$0.430166\pi$
$812$	−7.37579	+	10.1519i	−0.258839	+	0.356262i
$813$	15.7008	−	21.6103i	0.550651	−	0.757906i
$814$	7.25121	−	5.26831i	0.254155	−	0.184654i
$815$		0			0
$816$	−16.3805	−	11.9011i	−0.573433	−	0.416624i
$817$	11.4148	−	3.70891i	0.399355	−	0.129758i
$818$		−	3.96067i		−	0.138482i
$819$	1.89701	+	5.83841i	0.0662870	+	0.204011i
$820$		0			0
$821$	−12.2924	+	37.8322i	−0.429009	+	1.32035i	0.470094	+	0.882616i	$0.344220\pi$
$821$	−12.2924	+	37.8322i	−0.429009	+	1.32035i	−0.899103	+	0.437737i	$0.855780\pi$
$822$	−3.00606	−	0.976728i	−0.104848	−	0.0340673i
$823$	9.73384	+	13.3975i	0.339300	+	0.467007i	0.944237	−	0.329267i	$-0.106802\pi$
$823$	9.73384	+	13.3975i	0.339300	+	0.467007i	−0.604937	+	0.796274i	$0.706802\pi$
$824$	7.38562			0.257290
$825$		0			0
$826$	−10.1770			−0.354102
$827$	15.3037	+	21.0637i	0.532160	+	0.732456i	0.987458	−	0.157884i	$-0.0504671\pi$
$827$	15.3037	+	21.0637i	0.532160	+	0.732456i	−0.455297	+	0.890339i	$0.650467\pi$
$828$	18.6297	+	6.05316i	0.647428	+	0.210362i
$829$	−1.58945	+	4.89182i	−0.0552039	+	0.169900i	−0.974857	−	0.222832i	$-0.928470\pi$
$829$	−1.58945	+	4.89182i	−0.0552039	+	0.169900i	0.919653	+	0.392732i	$0.128470\pi$
$830$		0			0
$831$	8.06180	+	24.8117i	0.279661	+	0.860708i
$832$			35.4352i			1.22849i
$833$	−16.5588	+	5.38027i	−0.573727	+	0.186415i
$834$	−61.4638	−	44.6560i	−2.12832	−	1.54631i
$835$		0			0
$836$	9.82055	−	7.13505i	0.339651	−	0.246771i
$837$	0.205840	−	0.283315i	0.00711489	−	0.00979280i
$838$	−2.85350	+	3.92751i	−0.0985726	+	0.135674i
$839$	31.2009	−	22.6688i	1.07717	−	0.782612i	0.0999856	−	0.994989i	$-0.468120\pi$
$839$	31.2009	−	22.6688i	1.07717	−	0.782612i	0.977188	+	0.212377i	$0.0681203\pi$
$840$		0			0
$841$	0.00757268	+	0.00550188i	0.000261127	+	0.000189720i
$842$	−47.4983	+	15.4331i	−1.63690	+	0.531861i
$843$		−	54.1744i		−	1.86586i
$844$	6.28288	+	19.3367i	0.216266	+	0.665597i
$845$		0			0
$846$	−11.7269	+	36.0918i	−0.403180	+	1.24086i
$847$	−6.60679	−	2.14668i	−0.227012	−	0.0737607i
$848$	−14.1485	−	19.4737i	−0.485861	−	0.668730i
$849$	−7.39447			−0.253777
$850$		0			0
$851$	9.77764			0.335173
$852$	29.2624	+	40.2762i	1.00251	+	1.37984i
$853$	−8.69991	−	2.82677i	−0.297879	−	0.0967868i	0.156265	−	0.987715i	$-0.450055\pi$
$853$	−8.69991	−	2.82677i	−0.297879	−	0.0967868i	−0.454144	+	0.890928i	$0.650055\pi$
$854$	−1.77121	+	5.45121i	−0.0606094	+	0.186537i
$855$		0			0
$856$	1.08153	+	3.32861i	0.0369659	+	0.113769i
$857$		−	13.6712i		−	0.466998i	−0.972357	−	0.233499i	$-0.924982\pi$
$857$		−	13.6712i		−	0.466998i	0.972357	−	0.233499i	$-0.0750176\pi$
$858$	−29.4225	+	9.55995i	−1.00447	+	0.326371i
$859$	−28.8460	−	20.9579i	−0.984213	−	0.715073i	−0.0255669	−	0.999673i	$-0.508139\pi$
$859$	−28.8460	−	20.9579i	−0.984213	−	0.715073i	−0.958646	+	0.284600i	$0.908139\pi$
$860$		0			0
$861$	15.2384	−	11.0713i	0.519323	−	0.377310i
$862$	−1.46136	+	2.01139i	−0.0497741	+	0.0685082i
$863$	−19.9455	+	27.4526i	−0.678953	+	0.934498i	−0.999921	−	0.0125918i	$-0.995992\pi$
$863$	−19.9455	+	27.4526i	−0.678953	+	0.934498i	0.320968	+	0.947090i	$0.395992\pi$
$864$	16.7826	−	12.1933i	0.570955	−	0.414823i
$865$		0			0
$866$	43.2113	+	31.3949i	1.46838	+	1.06684i
$867$	−18.0272	+	5.85741i	−0.612237	+	0.198928i
$868$		−	0.318210i		−	0.0108007i
$869$	−9.79636	−	30.1501i	−0.332319	−	1.02277i
$870$		0			0
$871$	−2.27898	+	7.01398i	−0.0772203	+	0.237660i
$872$	−11.2453	−	3.65380i	−0.380812	−	0.123733i
$873$	−18.3510	−	25.2580i	−0.621087	−	0.854853i
$874$	24.5197			0.829391
$875$		0			0
$876$	−4.00610			−0.135354
$877$	−16.8689	−	23.2181i	−0.569622	−	0.784018i	0.422888	−	0.906182i	$-0.361017\pi$
$877$	−16.8689	−	23.2181i	−0.569622	−	0.784018i	−0.992510	+	0.122164i	$0.961017\pi$
$878$	38.4232	+	12.4845i	1.29672	+	0.421330i
$879$	−6.08947	+	18.7415i	−0.205393	+	0.632134i
$880$		0			0
$881$	2.57423	+	7.92267i	0.0867281	+	0.266922i	0.985010	−	0.172498i	$-0.0551840\pi$
$881$	2.57423	+	7.92267i	0.0867281	+	0.266922i	−0.898282	+	0.439420i	$0.855184\pi$
$882$			22.9964i			0.774331i
$883$	−47.8539	+	15.5487i	−1.61041	+	0.523254i	−0.969652	−	0.244488i	$-0.921380\pi$
$883$	−47.8539	+	15.5487i	−1.61041	+	0.523254i	−0.640759	+	0.767742i	$0.721380\pi$
$884$	−18.5550	−	13.4810i	−0.624072	−	0.453415i
$885$		0			0
$886$	−4.15454	+	3.01845i	−0.139574	+	0.101407i
$887$	7.12315	−	9.80417i	0.239172	−	0.329192i	−0.672510	−	0.740088i	$-0.734784\pi$
$887$	7.12315	−	9.80417i	0.239172	−	0.329192i	0.911682	+	0.410896i	$0.134784\pi$
$888$	2.01773	−	2.77716i	0.0677104	−	0.0931954i
$889$	−1.19693	+	0.869617i	−0.0401436	+	0.0291660i
$890$		0			0
$891$	18.0231	+	13.0945i	0.603795	+	0.438683i
$892$	−63.3042	+	20.5688i	−2.11958	+	0.688694i
$893$			25.6543i			0.858490i
$894$	−4.54977	−	14.0027i	−0.152167	−	0.468322i
$895$		0			0
$896$	1.75541	−	5.40260i	0.0586442	−	0.180488i
$897$	−32.0967	−	10.4289i	−1.07168	−	0.348209i
$898$	17.5992	+	24.2232i	0.587292	+	0.808338i
$899$	0.735159			0.0245189
$900$		0			0
$901$	21.8976			0.729514
$902$	21.1634	+	29.1289i	0.704663	+	0.969886i
$903$	9.63623	+	3.13100i	0.320674	+	0.104193i
$904$	1.51705	−	4.66900i	0.0504564	−	0.155289i
$905$		0			0
$906$	25.0559	+	77.1142i	0.832428	+	2.56195i
$907$		−	31.9105i		−	1.05957i	−0.848132	−	0.529786i	$-0.822272\pi$
$907$		−	31.9105i		−	1.05957i	0.848132	−	0.529786i	$-0.177728\pi$
$908$	49.6757	−	16.1406i	1.64855	−	0.535645i
$909$	−3.77801	−	2.74488i	−0.125309	−	0.0910421i
$910$		0			0
$911$	19.9730	−	14.5112i	0.661735	−	0.480778i	−0.205514	−	0.978654i	$-0.565886\pi$
$911$	19.9730	−	14.5112i	0.661735	−	0.480778i	0.867248	+	0.497876i	$0.165886\pi$
$912$	−10.6264	+	14.6260i	−0.351876	+	0.484316i
$913$	2.08206	−	2.86570i	0.0689060	−	0.0948409i
$914$	−42.5071	+	30.8832i	−1.40601	+	1.02153i
$915$		0			0
$916$	−4.70339	−	3.41721i	−0.155404	−	0.112908i
$917$	−13.3218	+	4.32852i	−0.439925	+	0.142940i
$918$			15.4810i			0.510951i
$919$	6.02121	+	18.5314i	0.198621	+	0.611293i	0.999915	+	0.0130225i	$0.00414530\pi$
$919$	6.02121	+	18.5314i	0.198621	+	0.611293i	−0.801294	+	0.598271i	$0.795855\pi$
$920$		0			0
$921$	−6.44134	+	19.8244i	−0.212249	+	0.653237i
$922$	−57.1675	−	18.5748i	−1.88271	−	0.611730i
$923$	−19.1233	−	26.3210i	−0.629452	−	0.866366i
$924$	10.2474			0.337116
$925$		0			0
$926$	66.4781			2.18461
$927$	−10.9545	−	15.0776i	−0.359794	−	0.495214i
$928$	41.4168	+	13.4571i	1.35957	+	0.441752i
$929$	−3.63535	+	11.1885i	−0.119272	+	0.367082i	−0.992814	−	0.119667i	$-0.961817\pi$
$929$	−3.63535	+	11.1885i	−0.119272	+	0.367082i	0.873542	+	0.486749i	$0.161817\pi$
$930$		0			0
$931$	4.80399	+	14.7852i	0.157444	+	0.484564i
$932$			13.9873i			0.458168i
$933$	−61.3300	+	19.9273i	−2.00786	+	0.652392i
$934$	72.7104	+	52.8272i	2.37916	+	1.72856i
$935$		0			0
$936$	−3.63597	+	2.64169i	−0.118846	+	0.0863463i
$937$	−12.3836	+	17.0446i	−0.404556	+	0.556823i	−0.961880	−	0.273472i	$-0.911828\pi$
$937$	−12.3836	+	17.0446i	−0.404556	+	0.556823i	0.557324	+	0.830295i	$0.311828\pi$
$938$	2.65874	−	3.65944i	0.0868108	−	0.119485i
$939$	−33.5982	+	24.4105i	−1.09644	+	0.796607i
$940$		0			0
$941$	1.81791	+	1.32079i	0.0592622	+	0.0430565i	0.617022	−	0.786946i	$-0.288339\pi$
$941$	1.81791	+	1.32079i	0.0592622	+	0.0430565i	−0.557760	+	0.830002i	$0.688339\pi$
$942$	−7.21650	+	2.34478i	−0.235126	+	0.0763971i
$943$			39.2778i			1.27906i
$944$	4.83525	+	14.8814i	0.157374	+	0.484347i
$945$		0			0
$946$	−5.98505	+	18.4201i	−0.194591	+	0.598889i
$947$	−6.42557	−	2.08780i	−0.208803	−	0.0678442i	0.202748	−	0.979231i	$-0.435013\pi$
$947$	−6.42557	−	2.08780i	−0.208803	−	0.0678442i	−0.411551	+	0.911387i	$0.635013\pi$
$948$	−48.1028	−	66.2078i	−1.56231	−	2.15033i
$949$	2.61803			0.0849850
$950$		0			0
$951$	−50.1021			−1.62467
$952$	1.22671	+	1.68842i	0.0397578	+	0.0547219i
$953$	−57.0190	−	18.5266i	−1.84703	−	0.600136i	−0.997343	−	0.0728437i	$-0.976793\pi$
$953$	−57.0190	−	18.5266i	−1.84703	−	0.600136i	−0.849684	−	0.527292i	$-0.823207\pi$
$954$	8.93754	−	27.5069i	0.289364	−	0.890569i
$955$		0			0
$956$	−5.10343	−	15.7067i	−0.165057	−	0.507992i
$957$			23.6747i			0.765293i
$958$	−41.6999	+	13.5491i	−1.34726	+	0.437752i
$959$	−0.553535	−	0.402166i	−0.0178746	−	0.0129866i
$960$		0			0
$961$	25.0644	−	18.2104i	0.808530	−	0.587432i
$962$	−8.88781	+	12.2330i	−0.286555	+	0.394408i
$963$	5.19114	−	7.14499i	0.167282	−	0.230244i
$964$	2.24144	−	1.62850i	0.0721920	−	0.0524505i
$965$		0			0
$966$	16.7460	+	12.1667i	0.538793	+	0.391456i
$967$	8.61276	−	2.79845i	0.276968	−	0.0899922i	−0.167240	−	0.985916i	$-0.553485\pi$
$967$	8.61276	−	2.79845i	0.276968	−	0.0899922i	0.444207	+	0.895924i	$0.353485\pi$
$968$		−	5.08580i		−	0.163464i
$969$	−5.08225	−	15.6416i	−0.163265	−	0.502479i
$970$		0			0
$971$	14.6322	−	45.0333i	0.469570	−	1.44519i	−0.383573	−	0.923511i	$-0.625307\pi$
$971$	14.6322	−	45.0333i	0.469570	−	1.44519i	0.853143	−	0.521677i	$-0.174693\pi$
$972$	37.5094	+	12.1875i	1.20312	+	0.390916i
$973$	−9.66665	−	13.3050i	−0.309899	−	0.426539i
$974$	58.2191			1.86546
$975$		0			0
$976$	8.81263			0.282085
$977$	2.78885	+	3.83852i	0.0892231	+	0.122805i	0.851295	−	0.524687i	$-0.175818\pi$
$977$	2.78885	+	3.83852i	0.0892231	+	0.122805i	−0.762072	+	0.647492i	$0.775818\pi$
$978$	−3.89328	−	1.26500i	−0.124493	−	0.0404504i
$979$	−8.96645	+	27.5959i	−0.286569	+	0.881968i
$980$		0			0
$981$	9.22005	+	28.3764i	0.294374	+	0.905988i
$982$		−	31.1981i		−	0.995570i
$983$	17.6569	−	5.73708i	0.563168	−	0.182984i	−0.0135783	−	0.999908i	$-0.504322\pi$
$983$	17.6569	−	5.73708i	0.563168	−	0.182984i	0.576746	+	0.816924i	$0.304322\pi$
$984$	11.1561	+	8.10542i	0.355645	+	0.258391i
$985$		0			0
$986$	−26.2922	+	19.1024i	−0.837315	+	0.608345i
$987$	−12.7297	+	17.5209i	−0.405190	+	0.557696i
$988$	−12.0370	+	16.5676i	−0.382949	+	0.527085i
$989$	−17.0932	+	12.4190i	−0.543533	+	0.394900i
$990$		0			0
$991$	32.1340	+	23.3467i	1.02077	+	0.741634i	0.966441	−	0.256889i	$-0.0826976\pi$
$991$	32.1340	+	23.3467i	1.02077	+	0.741634i	0.0543304	+	0.998523i	$0.482698\pi$
$992$	−1.05027	+	0.341253i	−0.0333460	+	0.0108348i
$993$			6.51411i			0.206719i
$994$	6.16631	+	18.9779i	0.195583	+	0.601944i
$995$		0			0
$996$	2.82570	−	8.69660i	0.0895356	−	0.275562i
$997$	28.8088	+	9.36056i	0.912385	+	0.296452i	0.727339	−	0.686278i	$-0.240757\pi$
$997$	28.8088	+	9.36056i	0.912385	+	0.296452i	0.185046	+	0.982730i	$0.440757\pi$
$998$	54.3295	+	74.7782i	1.71977	+	2.36706i
$999$	5.51210			0.174395

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

)

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.2.e.a.4.1	✓	8	25.6	even	5
25.2.e.a.19.1	yes	8	25.14	even	10
125.2.d.b.26.1		16	25.23	odd	20
125.2.d.b.26.4		16	25.2	odd	20
125.2.d.b.101.1		16	25.8	odd	20
125.2.d.b.101.4		16	25.17	odd	20
125.2.e.b.24.2		8	25.19	even	10
125.2.e.b.99.2		8	25.11	even	5
225.2.m.a.19.2		8	75.14	odd	10
225.2.m.a.154.2		8	75.56	odd	10
400.2.y.c.129.1		8	100.31	odd	10
400.2.y.c.369.1		8	100.39	odd	10
625.2.a.f.1.2		8	25.3	odd	20
625.2.a.f.1.7		8	25.22	odd	20
625.2.b.c.624.2		8	25.21	even	5
625.2.b.c.624.7		8	25.4	even	10
625.2.d.o.251.1		16	5.2	odd	4
625.2.d.o.251.4		16	5.3	odd	4
625.2.d.o.376.1		16	25.12	odd	20
625.2.d.o.376.4		16	25.13	odd	20
625.2.e.a.249.1		8	25.16	even	5
625.2.e.a.374.1		8	5.4	even	2
625.2.e.i.249.2		8	25.9	even	10	inner
625.2.e.i.374.2		8	1.1	even	1	trivial
5625.2.a.x.1.2		8	75.47	even	20
5625.2.a.x.1.7		8	75.53	even	20
10000.2.a.bj.1.2		8	100.47	even	20
10000.2.a.bj.1.7		8	100.3	even	20

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 $\F_{q}$

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	625.2.e.i.374.2

Level	$625$
Weight	$2$
Character	625.374
Analytic conductor	$4.991$
Analytic rank	$0$
Dimension	$8$
Inner twists	$2$