LMFDB - Embedded newform 325.2.s.b.293.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [325,2,Mod(32,325)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("325.32"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(325, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([3, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 325 = 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	325.s (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [20] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.59513806569$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 26 x^{18} + 279 x^{16} + 1604 x^{14} + 5353 x^{12} + 10466 x^{10} + 11441 x^{8} + 6176 x^{6} + \cdots + 1 $ x^20 + 26x^18 + 279x^16 + 1604x^14 + 5353x^12 + 10466x^10 + 11441x^8 + 6176x^6 + 1263x^4 + 78*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			293.4
Root			$-1.83163i$ of defining polynomial
Character	$\chi$	$=$	325.293
Dual form			325.2.s.b.132.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.915816 - 1.58624i) q^{2} +(-1.91432 + 0.512942i) q^{3} +(-0.677439 - 1.17336i) q^{4} +(-0.939520 + 3.50634i) q^{6} +(3.06478 - 1.76945i) q^{7} +1.18163 q^{8} +(0.803451 - 0.463873i) q^{9} +(-1.00269 - 3.74209i) q^{11} +(1.89870 + 1.89870i) q^{12} +(-0.573112 - 3.55971i) q^{13} -6.48197i q^{14} +(2.43703 - 4.22106i) q^{16} +(-0.524334 + 1.95684i) q^{17} -1.69929i q^{18} +(-0.518968 - 0.139057i) q^{19} +(-4.95936 + 4.95936i) q^{21} +(-6.85414 - 1.83656i) q^{22} +(-0.0788026 - 0.294095i) q^{23} +(-2.26202 + 0.606106i) q^{24} +(-6.17142 - 2.35095i) q^{26} +(2.90402 - 2.90402i) q^{27} +(-4.15240 - 2.39739i) q^{28} +(1.71273 + 0.988843i) q^{29} +(4.13563 + 4.13563i) q^{31} +(-3.28212 - 5.68479i) q^{32} +(3.83895 + 6.64926i) q^{33} +(2.62382 + 2.62382i) q^{34} +(-1.08858 - 0.628491i) q^{36} +(-4.69189 - 2.70887i) q^{37} +(-0.695857 + 0.695857i) q^{38} +(2.92305 + 6.52047i) q^{39} +(0.649884 - 0.174136i) q^{41} +(3.32487 + 12.4086i) q^{42} +(8.51164 + 2.28069i) q^{43} +(-3.71155 + 3.71155i) q^{44} +(-0.538675 - 0.144337i) q^{46} +9.75201i q^{47} +(-2.50011 + 9.33053i) q^{48} +(2.76192 - 4.78379i) q^{49} -4.01498i q^{51} +(-3.78857 + 3.08395i) q^{52} +(-3.16254 - 3.16254i) q^{53} +(-1.94693 - 7.26602i) q^{54} +(3.62143 - 2.09083i) q^{56} +1.06480 q^{57} +(3.13709 - 1.81120i) q^{58} +(-3.14703 + 11.7449i) q^{59} +(1.44316 + 2.49963i) q^{61} +(10.3476 - 2.77263i) q^{62} +(1.64160 - 2.84334i) q^{63} -2.27514 q^{64} +14.0631 q^{66} +(1.14494 - 1.98310i) q^{67} +(2.65128 - 0.710408i) q^{68} +(0.301707 + 0.522573i) q^{69} +(-1.19607 + 4.46378i) q^{71} +(0.949380 - 0.548125i) q^{72} -14.7546 q^{73} +(-8.59382 + 4.96165i) q^{74} +(0.188405 + 0.703137i) q^{76} +(-9.69449 - 9.69449i) q^{77} +(13.0200 + 1.33490i) q^{78} -1.59718i q^{79} +(-5.46126 + 9.45918i) q^{81} +(0.318953 - 1.19035i) q^{82} +7.57341i q^{83} +(9.17877 + 2.45944i) q^{84} +(11.4128 - 11.4128i) q^{86} +(-3.78593 - 1.01444i) q^{87} +(-1.18481 - 4.42176i) q^{88} +(-4.54423 + 1.21762i) q^{89} +(-8.05520 - 9.89564i) q^{91} +(-0.291695 + 0.291695i) q^{92} +(-10.0383 - 5.79560i) q^{93} +(15.4690 + 8.93105i) q^{94} +(9.19900 + 9.19900i) q^{96} +(8.91268 + 15.4372i) q^{97} +(-5.05883 - 8.76215i) q^{98} +(-2.54147 - 2.54147i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 4 q^{2} + 2 q^{3} - 6 q^{4} - 8 q^{6} + 6 q^{7} - 12 q^{8} - 12 q^{9} - 16 q^{11} - 24 q^{12} - 2 q^{13} - 2 q^{16} + 10 q^{17} + 20 q^{19} + 4 q^{21} - 16 q^{22} + 2 q^{23} - 32 q^{24} - 24 q^{26}+ \cdots - 60 q^{99}+O(q^{100}) $ 20 * q + 4 * q^2 + 2 * q^3 - 6 * q^4 - 8 * q^6 + 6 * q^7 - 12 * q^8 - 12 * q^9 - 16 * q^11 - 24 * q^12 - 2 * q^13 - 2 * q^16 + 10 * q^17 + 20 * q^19 + 4 * q^21 - 16 * q^22 + 2 * q^23 - 32 * q^24 - 24 * q^26 - 4 * q^27 - 6 * q^28 + 6 * q^32 + 18 * q^33 - 2 * q^34 + 36 * q^36 - 42 * q^37 - 8 * q^38 - 4 * q^39 + 10 * q^41 + 56 * q^42 + 22 * q^43 + 36 * q^44 + 4 * q^46 - 28 * q^48 - 18 * q^49 - 46 * q^52 + 10 * q^53 + 48 * q^54 + 12 * q^57 + 90 * q^58 + 16 * q^59 - 16 * q^61 + 40 * q^62 + 32 * q^63 - 20 * q^64 - 32 * q^66 + 58 * q^67 - 28 * q^68 + 16 * q^69 - 16 * q^71 + 66 * q^72 - 72 * q^73 - 18 * q^74 - 64 * q^76 - 28 * q^77 - 32 * q^78 - 14 * q^81 - 22 * q^82 + 40 * q^84 + 60 * q^86 - 62 * q^87 - 50 * q^88 + 6 * q^89 + 8 * q^91 + 8 * q^92 - 48 * q^93 + 48 * q^94 + 56 * q^96 + 22 * q^97 - 4 * q^98 - 60 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/325\mathbb{Z}\right)^\times$.

$n$	$27$	$301$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{11}{12}\right)$

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 $

$2$	0.915816	−	1.58624i	0.647580	−	1.12164i	−0.336119	−	0.941819i	$-0.609115\pi$
$2$	0.915816	−	1.58624i	0.647580	−	1.12164i	0.983699	−	0.179822i	$-0.0575521\pi$
$3$	−1.91432	+	0.512942i	−1.10524	+	0.296147i	−0.764895	−	0.644155i	$-0.777209\pi$
$3$	−1.91432	+	0.512942i	−1.10524	+	0.296147i	−0.340341	+	0.940302i	$0.610542\pi$
$4$	−0.677439	−	1.17336i	−0.338719	−	0.586679i
$5$		0			0
$5$		0			0
$6$	−0.939520	+	3.50634i	−0.383558	+	1.43146i
$7$	3.06478	−	1.76945i	1.15838	−	0.668790i	0.207464	−	0.978243i	$-0.433479\pi$
$7$	3.06478	−	1.76945i	1.15838	−	0.668790i	0.950915	+	0.309453i	$0.100146\pi$
$8$	1.18163			0.417769
$9$	0.803451	−	0.463873i	0.267817	−	0.154624i
$10$		0			0
$11$	−1.00269	−	3.74209i	−0.302323	−	1.12828i	−0.935226	−	0.354053i	$-0.884803\pi$
$11$	−1.00269	−	3.74209i	−0.302323	−	1.12828i	0.632903	−	0.774231i	$-0.281863\pi$
$12$	1.89870	+	1.89870i	0.548108	+	0.548108i
$13$	−0.573112	−	3.55971i	−0.158953	−	0.987286i
$13$	−0.573112	−	3.55971i	−0.158953	−	0.987286i
$14$		−	6.48197i		−	1.73238i
$15$		0			0
$16$	2.43703	−	4.22106i	0.609258	−	1.05527i
$17$	−0.524334	+	1.95684i	−0.127170	+	0.474603i	−0.999908	−	0.0135853i	$-0.995676\pi$
$17$	−0.524334	+	1.95684i	−0.127170	+	0.474603i	0.872738	+	0.488189i	$0.162342\pi$
$18$		−	1.69929i		−	0.400526i
$19$	−0.518968	−	0.139057i	−0.119059	−	0.0319019i	0.198797	−	0.980041i	$-0.436296\pi$
$19$	−0.518968	−	0.139057i	−0.119059	−	0.0319019i	−0.317857	+	0.948139i	$0.602963\pi$
$20$		0			0
$21$	−4.95936	+	4.95936i	−1.08222	+	1.08222i
$22$	−6.85414	−	1.83656i	−1.46131	−	0.391556i
$23$	−0.0788026	−	0.294095i	−0.0164315	−	0.0613231i	0.957223	−	0.289350i	$-0.0934392\pi$
$23$	−0.0788026	−	0.294095i	−0.0164315	−	0.0613231i	−0.973655	+	0.228027i	$0.926773\pi$
$24$	−2.26202	+	0.606106i	−0.461733	+	0.123721i
$25$		0			0
$26$	−6.17142	−	2.35095i	−1.21032	−	0.461059i
$27$	2.90402	−	2.90402i	0.558879	−	0.558879i
$28$	−4.15240	−	2.39739i	−0.784730	−	0.453064i
$29$	1.71273	+	0.988843i	0.318045	+	0.183624i	0.650521	−	0.759488i	$-0.274551\pi$
$29$	1.71273	+	0.988843i	0.318045	+	0.183624i	−0.332476	+	0.943112i	$0.607884\pi$
$30$		0			0
$31$	4.13563	+	4.13563i	0.742781	+	0.742781i	0.973112	−	0.230331i	$-0.0739810\pi$
$31$	4.13563	+	4.13563i	0.742781	+	0.742781i	−0.230331	+	0.973112i	$0.573981\pi$
$32$	−3.28212	−	5.68479i	−0.580202	−	1.00494i
$33$	3.83895	+	6.64926i	0.668276	+	1.15749i
$34$	2.62382	+	2.62382i	0.449982	+	0.449982i
$35$		0			0
$36$	−1.08858	−	0.628491i	−0.181430	−	0.104748i
$37$	−4.69189	−	2.70887i	−0.771342	−	0.445335i	0.0620109	−	0.998075i	$-0.480249\pi$
$37$	−4.69189	−	2.70887i	−0.771342	−	0.445335i	−0.833353	+	0.552741i	$0.813582\pi$
$38$	−0.695857	+	0.695857i	−0.112883	+	0.112883i
$39$	2.92305	+	6.52047i	0.468062	+	1.04411i
$40$		0			0
$41$	0.649884	−	0.174136i	0.101495	−	0.0271955i	−0.207714	−	0.978190i	$-0.566602\pi$
$41$	0.649884	−	0.174136i	0.101495	−	0.0271955i	0.309209	+	0.950994i	$0.399936\pi$
$42$	3.32487	+	12.4086i	0.513039	+	1.91469i
$43$	8.51164	+	2.28069i	1.29801	+	0.347802i	0.840698	−	0.541504i	$-0.182145\pi$
$43$	8.51164	+	2.28069i	1.29801	+	0.347802i	0.457314	+	0.889305i	$0.348811\pi$
$44$	−3.71155	+	3.71155i	−0.559538	+	0.559538i
$45$		0			0
$46$	−0.538675	−	0.144337i	−0.0794232	−	0.0212814i
$47$			9.75201i			1.42248i	0.702951	+	0.711238i	$0.251865\pi$
$47$			9.75201i			1.42248i	−0.702951	+	0.711238i	$0.748135\pi$
$48$	−2.50011	+	9.33053i	−0.360860	+	1.34675i
$49$	2.76192	−	4.78379i	0.394561	−	0.683399i
$50$		0			0
$51$		−	4.01498i		−	0.562209i
$52$	−3.78857	+	3.08395i	−0.525380	+	0.427667i
$53$	−3.16254	−	3.16254i	−0.434409	−	0.434409i	0.455716	−	0.890125i	$-0.349383\pi$
$53$	−3.16254	−	3.16254i	−0.434409	−	0.434409i	−0.890125	+	0.455716i	$0.849383\pi$
$54$	−1.94693	−	7.26602i	−0.264943	−	0.988781i
$55$		0			0
$56$	3.62143	−	2.09083i	0.483934	−	0.279399i
$57$	1.06480			0.141036
$58$	3.13709	−	1.81120i	0.411919	−	0.237822i
$59$	−3.14703	+	11.7449i	−0.409708	+	1.52905i	0.385495	+	0.922710i	$0.374031\pi$
$59$	−3.14703	+	11.7449i	−0.409708	+	1.52905i	−0.795203	+	0.606343i	$0.792636\pi$
$60$		0			0
$61$	1.44316	+	2.49963i	0.184778	+	0.320044i	0.943502	−	0.331368i	$-0.107510\pi$
$61$	1.44316	+	2.49963i	0.184778	+	0.320044i	−0.758724	+	0.651412i	$0.774177\pi$
$62$	10.3476	−	2.77263i	1.31414	−	0.352124i
$63$	1.64160	−	2.84334i	0.206822	−	0.358227i
$64$	−2.27514			−0.284392
$65$		0			0
$66$	14.0631			1.73105
$67$	1.14494	−	1.98310i	0.139877	−	0.242274i	−0.787573	−	0.616222i	$-0.788663\pi$
$67$	1.14494	−	1.98310i	0.139877	−	0.242274i	0.927450	+	0.373947i	$0.121996\pi$
$68$	2.65128	−	0.710408i	0.321515	−	0.0861496i
$69$	0.301707	+	0.522573i	0.0363213	+	0.0629104i
$70$		0			0
$71$	−1.19607	+	4.46378i	−0.141947	+	0.529753i	0.857925	+	0.513774i	$0.171753\pi$
$71$	−1.19607	+	4.46378i	−0.141947	+	0.529753i	−0.999872	+	0.0159789i	$0.994914\pi$
$72$	0.949380	−	0.548125i	0.111886	−	0.0645972i
$73$	−14.7546			−1.72690			−0.863449	−	0.504436i	$-0.831701\pi$
$73$	−14.7546			−1.72690			−0.863449	+	0.504436i	$0.831701\pi$
$74$	−8.59382	+	4.96165i	−0.999011	+	0.576780i
$75$		0			0
$76$	0.188405	+	0.703137i	0.0216115	+	0.0806554i
$77$	−9.69449	−	9.69449i	−1.10479	−	1.10479i
$78$	13.0200	+	1.33490i	1.47422	+	0.151147i
$79$		−	1.59718i		−	0.179696i	−0.995955	−	0.0898482i	$-0.971362\pi$
$79$		−	1.59718i		−	0.179696i	0.995955	−	0.0898482i	$-0.0286382\pi$
$80$		0			0
$81$	−5.46126	+	9.45918i	−0.606807	+	1.05102i
$82$	0.318953	−	1.19035i	0.0352225	−	0.131452i
$83$			7.57341i			0.831290i	0.909527	+	0.415645i	$0.136444\pi$
$83$			7.57341i			0.831290i	−0.909527	+	0.415645i	$0.863556\pi$
$84$	9.17877	+	2.45944i	1.00149	+	0.268347i
$85$		0			0
$86$	11.4128	−	11.4128i	1.23068	−	1.23068i
$87$	−3.78593	−	1.01444i	−0.405895	−	0.108759i
$88$	−1.18481	−	4.42176i	−0.126301	−	0.471361i
$89$	−4.54423	+	1.21762i	−0.481687	+	0.129068i	−0.491488	−	0.870884i	$-0.663547\pi$
$89$	−4.54423	+	1.21762i	−0.481687	+	0.129068i	0.00980081	+	0.999952i	$0.496880\pi$
$90$		0			0
$91$	−8.05520	−	9.89564i	−0.844415	−	1.03735i
$92$	−0.291695	+	0.291695i	−0.0304113	+	0.0304113i
$93$	−10.0383	−	5.79560i	−1.04092	−	0.600976i
$94$	15.4690	+	8.93105i	1.59551	+	0.921167i
$95$		0			0
$96$	9.19900	+	9.19900i	0.938869	+	0.938869i
$97$	8.91268	+	15.4372i	0.904945	+	1.56741i	0.820991	+	0.570942i	$0.193422\pi$
$97$	8.91268	+	15.4372i	0.904945	+	1.56741i	0.0839547	+	0.996470i	$0.473245\pi$
$98$	−5.05883	−	8.76215i	−0.511019	−	0.885111i
$99$	−2.54147	−	2.54147i	−0.255427	−	0.255427i
$100$		0			0
$101$	−3.94379	−	2.27695i	−0.392421	−	0.226565i	0.290787	−	0.956788i	$-0.406083\pi$
$101$	−3.94379	−	2.27695i	−0.392421	−	0.226565i	−0.683209	+	0.730223i	$0.739416\pi$
$102$	−6.36872	−	3.67698i	−0.630597	−	0.364075i
$103$	9.79285	−	9.79285i	0.964918	−	0.964918i	−0.0344872	−	0.999405i	$-0.510980\pi$
$103$	9.79285	−	9.79285i	0.964918	−	0.964918i	0.999405	+	0.0344872i	$0.0109798\pi$
$104$	−0.677205	−	4.20625i	−0.0664055	−	0.412457i
$105$		0			0
$106$	−7.91286	+	2.12024i	−0.768565	+	0.205936i
$107$	1.82991	+	6.82933i	0.176904	+	0.660216i	0.996219	+	0.0868725i	$0.0276873\pi$
$107$	1.82991	+	6.82933i	0.176904	+	0.660216i	−0.819315	+	0.573344i	$0.805646\pi$
$108$	−5.37475	−	1.44016i	−0.517186	−	0.138580i
$109$	9.89281	−	9.89281i	0.947560	−	0.947560i	−0.0511324	−	0.998692i	$-0.516283\pi$
$109$	9.89281	−	9.89281i	0.947560	−	0.947560i	0.998692	+	0.0511324i	$0.0162830\pi$
$110$		0			0
$111$	10.3713	+	2.77898i	0.984399	+	0.263769i
$112$		−	17.2488i		−	1.62986i
$113$	−0.593341	+	2.21438i	−0.0558168	+	0.208311i	−0.988202	−	0.153154i	$-0.951057\pi$
$113$	−0.593341	+	2.21438i	−0.0558168	+	0.208311i	0.932385	+	0.361466i	$0.117723\pi$
$114$	0.975161	−	1.68903i	0.0913322	−	0.158192i
$115$		0			0
$116$		−	2.67952i		−	0.248787i
$117$	−2.11172	−	2.59420i	−0.195229	−	0.239834i
$118$	15.7481	+	15.7481i	1.44973	+	1.44973i
$119$	1.85557	+	6.92507i	0.170099	+	0.634820i
$120$		0			0
$121$	−3.47160	+	2.00433i	−0.315600	+	0.182212i
$122$	5.28668			0.478633
$123$	−1.15477	+	0.666705i	−0.104122	+	0.0601148i
$124$	2.05094	−	7.65421i	0.184180	−	0.687368i
$125$		0			0
$126$	−3.00681	−	5.20795i	−0.267868	−	0.463961i
$127$	1.24225	−	0.332860i	0.110232	−	0.0295366i	−0.203281	−	0.979120i	$-0.565161\pi$
$127$	1.24225	−	0.332860i	0.110232	−	0.0295366i	0.313513	+	0.949584i	$0.398494\pi$
$128$	4.48062	−	7.76067i	0.396035	−	0.685953i
$129$	−17.4639			−1.53761
$130$		0			0
$131$	−5.59439			−0.488785			−0.244392	−	0.969676i	$-0.578588\pi$
$131$	−5.59439			−0.488785			−0.244392	+	0.969676i	$0.578588\pi$
$132$	5.20131	−	9.00893i	0.452716	−	0.784127i
$133$	−1.83658	+	0.492109i	−0.159251	+	0.0426713i
$134$	−2.09712	−	3.63231i	−0.181163	−	0.313784i
$135$		0			0
$136$	−0.619567	+	2.31226i	−0.0531274	+	0.198274i
$137$	−12.3757	+	7.14509i	−1.05732	+	0.610446i	−0.924691	−	0.380719i	$-0.875676\pi$
$137$	−12.3757	+	7.14509i	−1.05732	+	0.610446i	−0.132633	+	0.991165i	$0.542343\pi$
$138$	1.10523			0.0940838
$139$	15.0832	−	8.70830i	1.27934	−	0.738629i	0.302615	−	0.953113i	$-0.402140\pi$
$139$	15.0832	−	8.70830i	1.27934	−	0.738629i	0.976727	+	0.214484i	$0.0688071\pi$
$140$		0			0
$141$	−5.00221	−	18.6685i	−0.421262	−	1.57217i
$142$	5.98525	+	5.98525i	0.502271	+	0.502271i
$143$	−12.7461	+	5.71393i	−1.06588	+	0.477823i
$144$		−	4.52189i		−	0.376824i
$145$		0			0
$146$	−13.5125	+	23.4044i	−1.11830	+	1.93696i
$147$	−2.83341	+	10.5744i	−0.233696	+	0.872165i
$148$			7.34036i			0.603374i
$149$	−12.6828	−	3.39833i	−1.03901	−	0.278402i	−0.301308	−	0.953527i	$-0.597423\pi$
$149$	−12.6828	−	3.39833i	−1.03901	−	0.278402i	−0.737704	+	0.675124i	$0.764090\pi$
$150$		0			0
$151$	0.765191	−	0.765191i	0.0622704	−	0.0622704i	−0.675286	−	0.737556i	$-0.735980\pi$
$151$	0.765191	−	0.765191i	0.0622704	−	0.0622704i	0.737556	+	0.675286i	$0.235980\pi$
$152$	−0.613227	−	0.164314i	−0.0497392	−	0.0133276i
$153$	0.486448	+	1.81545i	0.0393270	+	0.146770i
$154$	−24.2562	+	6.49942i	−1.95462	+	0.523738i
$155$		0			0
$156$	5.67066	−	7.84700i	0.454016	−	0.628263i
$157$	−3.03481	+	3.03481i	−0.242204	+	0.242204i	−0.817762	−	0.575557i	$-0.804785\pi$
$157$	−3.03481	+	3.03481i	−0.242204	+	0.242204i	0.575557	+	0.817762i	$0.304785\pi$
$158$	−2.53350	−	1.46272i	−0.201555	−	0.116368i
$159$	7.67633	+	4.43193i	0.608773	+	0.351475i
$160$		0			0
$161$	−0.761901	−	0.761901i	−0.0600462	−	0.0600462i
$162$	10.0030	+	17.3257i	0.785912	+	1.36124i
$163$	1.13179	+	1.96032i	0.0886486	+	0.153544i	0.906940	−	0.421260i	$-0.138412\pi$
$163$	1.13179	+	1.96032i	0.0886486	+	0.153544i	−0.818292	+	0.574803i	$0.805079\pi$
$164$	−0.644580	−	0.644580i	−0.0503333	−	0.0503333i
$165$		0			0
$166$	12.0133	+	6.93585i	0.932409	+	0.538327i
$167$	0.536563	+	0.309785i	0.0415205	+	0.0239719i	0.520617	−	0.853791i	$-0.325702\pi$
$167$	0.536563	+	0.309785i	0.0415205	+	0.0239719i	−0.479096	+	0.877762i	$0.659035\pi$
$168$	−5.86012	+	5.86012i	−0.452118	+	0.452118i
$169$	−12.3431	+	4.08023i	−0.949468	+	0.313864i
$170$		0			0
$171$	−0.481470	+	0.129009i	−0.0368189	+	0.00986560i
$172$	−3.09005	−	11.5322i	−0.235614	−	0.879324i
$173$	6.39606	+	1.71382i	0.486283	+	0.130299i	0.493627	−	0.869674i	$-0.335671\pi$
$173$	6.39606	+	1.71382i	0.486283	+	0.130299i	−0.00734343	+	0.999973i	$0.502338\pi$
$174$	−5.07636	+	5.07636i	−0.384838	+	0.384838i
$175$		0			0
$176$	−18.2392	−	4.88718i	−1.37483	−	0.368385i
$177$		−	24.0977i		−	1.81130i
$178$	−2.23024	+	8.32336i	−0.167163	+	0.623862i
$179$	1.09512	−	1.89680i	0.0818528	−	0.141773i	−0.822193	−	0.569209i	$-0.807250\pi$
$179$	1.09512	−	1.89680i	0.0818528	−	0.141773i	0.904046	+	0.427436i	$0.140583\pi$
$180$		0			0
$181$			9.59255i			0.713009i	0.934294	+	0.356504i	$0.116031\pi$
$181$			9.59255i			0.713009i	−0.934294	+	0.356504i	$0.883969\pi$
$182$	−23.0739	+	3.71490i	−1.71035	+	0.275367i
$183$	−4.04484	−	4.04484i	−0.299003	−	0.299003i
$184$	−0.0931154	−	0.347511i	−0.00686456	−	0.0256189i
$185$		0			0
$186$	−18.3864	+	10.6154i	−1.34816	+	0.778359i
$187$	7.84842			0.573933
$188$	11.4426	−	6.60639i	0.834537	−	0.481820i
$189$	3.76166	−	14.0387i	0.273621	−	1.02117i
$190$		0			0
$191$	−1.86557	−	3.23126i	−0.134988	−	0.233806i	0.790605	−	0.612326i	$-0.209766\pi$
$191$	−1.86557	−	3.23126i	−0.134988	−	0.233806i	−0.925593	+	0.378521i	$0.876433\pi$
$192$	4.35536	−	1.16701i	0.314321	−	0.0842220i
$193$	0.142043	−	0.246025i	0.0102245	−	0.0177093i	−0.860868	−	0.508829i	$-0.830079\pi$
$193$	0.142043	−	0.246025i	0.0102245	−	0.0177093i	0.871092	+	0.491119i	$0.163412\pi$
$194$	32.6495			2.34410
$195$		0			0
$196$	−7.48414			−0.534581
$197$	12.9246	−	22.3860i	0.920838	−	1.59494i	0.122716	−	0.992442i	$-0.460840\pi$
$197$	12.9246	−	22.3860i	0.920838	−	1.59494i	0.798122	−	0.602496i	$-0.205827\pi$
$198$	−6.35890	+	1.70386i	−0.451907	+	0.121088i
$199$	2.87625	+	4.98181i	0.203892	+	0.353151i	0.949779	−	0.312921i	$-0.101308\pi$
$199$	2.87625	+	4.98181i	0.203892	+	0.353151i	−0.745887	+	0.666072i	$0.767974\pi$
$200$		0			0
$201$	−1.17458	+	4.38359i	−0.0828484	+	0.309194i
$202$	−7.22357	+	4.17053i	−0.508248	+	0.293437i
$203$	6.99884			0.491223
$204$	−4.71101	+	2.71990i	−0.329836	+	0.190431i
$205$		0			0
$206$	−6.56536	−	24.5023i	−0.457430	−	1.70715i
$207$	−0.199737	−	0.199737i	−0.0138827	−	0.0138827i
$208$	−16.4225	−	6.25598i	−1.13869	−	0.433774i
$209$			2.08146i			0.143977i
$210$		0			0
$211$	1.61372	−	2.79504i	0.111093	−	0.192418i	−0.805118	−	0.593114i	$-0.797898\pi$
$211$	1.61372	−	2.79504i	0.111093	−	0.192418i	0.916211	+	0.400696i	$0.131232\pi$
$212$	−1.56837	+	5.85322i	−0.107716	+	0.402001i
$213$		−	9.15863i		−	0.627539i
$214$	12.5088	+	3.35173i	0.855085	+	0.229119i
$215$		0			0
$216$	3.43147	−	3.43147i	0.233482	−	0.233482i
$217$	19.9926	+	5.35700i	1.35719	+	0.363657i
$218$	−6.63238	−	24.7524i	−0.449201	−	1.67644i
$219$	28.2451	−	7.56826i	1.90863	−	0.511416i
$220$		0			0
$221$	7.26628	+	0.744987i	0.488783	+	0.0501133i
$222$	13.9063	−	13.9063i	0.933331	−	0.933331i
$223$	−6.42178	−	3.70762i	−0.430034	−	0.248280i	0.269327	−	0.963049i	$-0.413199\pi$
$223$	−6.42178	−	3.70762i	−0.430034	−	0.248280i	−0.699361	+	0.714768i	$0.746532\pi$
$224$	−20.1179	−	11.6151i	−1.34419	−	0.776067i
$225$		0			0
$226$	2.96914	+	2.96914i	0.197504	+	0.197504i
$227$	−1.95115	−	3.37949i	−0.129502	−	0.224305i	0.793981	−	0.607942i	$-0.208005\pi$
$227$	−1.95115	−	3.37949i	−0.129502	−	0.224305i	−0.923484	+	0.383637i	$0.874671\pi$
$228$	−0.721337	−	1.24939i	−0.0477717	−	0.0827430i
$229$	−12.3946	−	12.3946i	−0.819060	−	0.819060i	0.166912	−	0.985972i	$-0.446621\pi$
$229$	−12.3946	−	12.3946i	−0.819060	−	0.819060i	−0.985972	+	0.166912i	$0.946621\pi$
$230$		0			0
$231$	23.5311	+	13.5857i	1.54823	+	0.893872i
$232$	2.02381	+	1.16844i	0.132869	+	0.0767121i
$233$	2.88962	−	2.88962i	0.189305	−	0.189305i	−0.606090	−	0.795396i	$-0.707263\pi$
$233$	2.88962	−	2.88962i	0.189305	−	0.189305i	0.795396	+	0.606090i	$0.207263\pi$
$234$	−6.04898	+	0.973883i	−0.395434	+	0.0636647i
$235$		0			0
$236$	15.9129	−	4.26384i	1.03584	−	0.277552i
$237$	0.819258	+	3.05751i	0.0532165	+	0.198607i
$238$	12.6842	+	3.39872i	0.822193	+	0.220306i
$239$	8.97299	−	8.97299i	0.580415	−	0.580415i	−0.354602	−	0.935017i	$-0.615384\pi$
$239$	8.97299	−	8.97299i	0.580415	−	0.580415i	0.935017	+	0.354602i	$0.115384\pi$
$240$		0			0
$241$	16.9497	+	4.54165i	1.09183	+	0.292554i	0.759432	−	0.650587i	$-0.225477\pi$
$241$	16.9497	+	4.54165i	1.09183	+	0.292554i	0.332394	+	0.943141i	$0.392144\pi$
$242$			7.34239i			0.471986i
$243$	2.41378	−	9.00835i	0.154844	−	0.577886i
$244$	1.95530	−	3.38669i	0.125176	−	0.216810i
$245$		0			0
$246$			2.44232i			0.155716i
$247$	−0.197576	+	1.92707i	−0.0125715	+	0.122617i
$248$	4.88677	+	4.88677i	0.310311	+	0.310311i
$249$	−3.88472	−	14.4980i	−0.246184	−	0.918771i
$250$		0			0
$251$	18.8524	−	10.8845i	1.18996	−	0.687021i	0.231659	−	0.972797i	$-0.425585\pi$
$251$	18.8524	−	10.8845i	1.18996	−	0.687021i	0.958296	+	0.285776i	$0.0922513\pi$
$252$	−4.44834			−0.280219
$253$	−1.02152	+	0.589774i	−0.0642223	+	0.0370787i
$254$	0.609678	−	2.27535i	0.0382546	−	0.142768i
$255$		0			0
$256$	−10.4820	−	18.1554i	−0.655125	−	1.13471i
$257$	−12.3766	+	3.31629i	−0.772029	+	0.206864i	−0.623268	−	0.782009i	$-0.714195\pi$
$257$	−12.3766	+	3.31629i	−0.772029	+	0.206864i	−0.148761	+	0.988873i	$0.547529\pi$
$258$	−15.9937	+	27.7019i	−0.995725	+	1.72465i
$259$	−19.1728			−1.19134
$260$		0			0
$261$	1.83479			0.113571
$262$	−5.12344	+	8.87405i	−0.316527	+	0.548241i
$263$	15.9426	−	4.27179i	0.983060	−	0.263410i	0.268727	−	0.963216i	$-0.413397\pi$
$263$	15.9426	−	4.27179i	0.983060	−	0.263410i	0.714333	+	0.699806i	$0.246730\pi$
$264$	4.53621	+	7.85695i	0.279185	+	0.483562i
$265$		0			0
$266$	−0.901363	+	3.36393i	−0.0552661	+	0.206256i
$267$	8.07456	−	4.66185i	0.494155	−	0.285301i
$268$	−3.10252			−0.189516
$269$	−27.9787	+	16.1535i	−1.70589	+	0.984895i	−0.766370	+	0.642400i	$0.777939\pi$
$269$	−27.9787	+	16.1535i	−1.70589	+	0.984895i	−0.939519	+	0.342495i	$0.888728\pi$
$270$		0			0
$271$	4.52218	+	16.8770i	0.274703	+	1.02521i	0.956040	+	0.293236i	$0.0947321\pi$
$271$	4.52218	+	16.8770i	0.274703	+	1.02521i	−0.681337	+	0.731970i	$0.738601\pi$
$272$	6.98212	+	6.98212i	0.423353	+	0.423353i
$273$	20.4962	+	14.8116i	1.24048	+	0.896440i
$274$			26.1743i			1.58125i
$275$		0			0
$276$	0.408777	−	0.708022i	0.0246055	−	0.0426179i
$277$	0.795705	−	2.96961i	0.0478093	−	0.178427i	−0.937892	−	0.346926i	$-0.887225\pi$
$277$	0.795705	−	2.96961i	0.0478093	−	0.178427i	0.985702	+	0.168499i	$0.0538921\pi$
$278$		−	31.9008i		−	1.91328i
$279$	5.24118	+	1.40437i	0.313781	+	0.0840775i
$280$		0			0
$281$	−18.6757	+	18.6757i	−1.11410	+	1.11410i	−0.121508	+	0.992590i	$0.538773\pi$
$281$	−18.6757	+	18.6757i	−1.11410	+	1.11410i	−0.992590	+	0.121508i	$0.961227\pi$
$282$	−34.1938	−	9.16221i	−2.03621	−	0.545602i
$283$	3.97005	+	14.8164i	0.235995	+	0.880745i	0.977698	+	0.210016i	$0.0673517\pi$
$283$	3.97005	+	14.8164i	0.235995	+	0.880745i	−0.741703	+	0.670728i	$0.765982\pi$
$284$	6.04787	−	1.62052i	0.358875	−	0.0961603i
$285$		0			0
$286$	−2.60944	+	25.4513i	−0.154299	+	1.50497i
$287$	1.68363	−	1.68363i	0.0993814	−	0.0993814i
$288$	−5.27404	−	3.04497i	−0.310776	−	0.179427i
$289$	11.1681	+	6.44793i	0.656949	+	0.379290i
$290$		0			0
$291$	−24.9801	−	24.9801i	−1.46436	−	1.46436i
$292$	9.99535	+	17.3125i	0.584934	+	1.01314i
$293$	−5.18835	−	8.98649i	−0.303107	−	0.524996i	0.673731	−	0.738976i	$-0.264691\pi$
$293$	−5.18835	−	8.98649i	−0.303107	−	0.524996i	−0.976838	+	0.213980i	$0.931357\pi$
$294$	14.1787	+	14.1787i	0.826919	+	0.826919i
$295$		0			0
$296$	−5.54407	−	3.20087i	−0.322243	−	0.186047i
$297$	−13.7790	−	7.95528i	−0.799536	−	0.461612i
$298$	−17.0057	+	17.0057i	−0.985111	+	0.985111i
$299$	−1.00173	+	0.449064i	−0.0579316	+	0.0259701i
$300$		0			0
$301$	30.1219	−	8.07113i	1.73620	−	0.465212i
$302$	−0.513002	−	1.91455i	−0.0295200	−	0.110170i
$303$	8.71763	+	2.33588i	0.500814	+	0.134193i
$304$	−1.85171	+	1.85171i	−0.106203	+	0.106203i
$305$		0			0
$306$	3.32524	+	0.890994i	0.190091	+	0.0509347i
$307$			2.13935i			0.122099i	0.998135	+	0.0610496i	$0.0194448\pi$
$307$			2.13935i			0.122099i	−0.998135	+	0.0610496i	$0.980555\pi$
$308$	−4.80768	+	17.9425i	−0.273943	+	1.02237i
$309$	−13.7235	+	23.7698i	−0.780704	+	1.35222i
$310$		0			0
$311$		−	3.82084i		−	0.216660i	−0.994115	−	0.108330i	$-0.965450\pi$
$311$		−	3.82084i		−	0.216660i	0.994115	−	0.108330i	$-0.0345503\pi$
$312$	3.45395	+	7.70477i	0.195542	+	0.436196i
$313$	−3.04531	−	3.04531i	−0.172131	−	0.172131i	0.615784	−	0.787915i	$-0.288839\pi$
$313$	−3.04531	−	3.04531i	−0.172131	−	0.172131i	−0.787915	+	0.615784i	$0.788839\pi$
$314$	2.03461	+	7.59327i	0.114820	+	0.428513i
$315$		0			0
$316$	−1.87406	+	1.08199i	−0.105424	+	0.0608666i
$317$	23.1127			1.29814			0.649068	−	0.760730i	$-0.275159\pi$
$317$	23.1127			1.29814			0.649068	+	0.760730i	$0.275159\pi$
$318$	14.0602	−	8.11767i	0.788458	−	0.455216i
$319$	1.98301	−	7.40069i	0.111027	−	0.414359i
$320$		0			0
$321$	−7.00609	−	12.1349i	−0.391042	−	0.677305i
$322$	−1.90632	+	0.510796i	−0.106235	+	0.0284656i
$323$	0.544224	−	0.942624i	0.0302814	−	0.0524490i
$324$	14.7987			0.822149
$325$		0			0
$326$	4.14604			0.229628
$327$	−13.8636	+	24.0125i	−0.766660	+	1.32789i
$328$	0.767921	−	0.205764i	0.0424013	−	0.0113614i
$329$	17.2557	+	29.8878i	0.951338	+	1.64777i
$330$		0			0
$331$	0.516858	−	1.92894i	0.0284091	−	0.106024i	−0.950265	−	0.311441i	$-0.899188\pi$
$331$	0.516858	−	1.92894i	0.0284091	−	0.106024i	0.978675	+	0.205417i	$0.0658550\pi$
$332$	8.88632	−	5.13052i	0.487700	−	0.281574i
$333$	−5.02628			−0.275438
$334$	0.982786	−	0.567412i	0.0537756	−	0.0310474i
$335$		0			0
$336$	8.84765	+	33.0199i	0.482679	+	1.80138i
$337$	6.12727	+	6.12727i	0.333773	+	0.333773i	0.854018	−	0.520244i	$-0.174159\pi$
$337$	6.12727	+	6.12727i	0.333773	+	0.333773i	−0.520244	+	0.854018i	$0.674159\pi$
$338$	−4.83178	+	23.3158i	−0.262814	+	1.26821i
$339$		−	4.54338i		−	0.246763i
$340$		0			0
$341$	11.3292	−	19.6227i	0.613508	−	1.06263i
$342$	−0.236298	+	0.881876i	−0.0127775	+	0.0476864i
$343$			5.22396i			0.282067i
$344$	10.0576	+	2.69492i	0.542269	+	0.145301i
$345$		0			0
$346$	8.57614	−	8.57614i	0.461056	−	0.461056i
$347$	−31.4009	−	8.41384i	−1.68569	−	0.451679i	−0.716417	−	0.697673i	$-0.754219\pi$
$347$	−31.4009	−	8.41384i	−1.68569	−	0.451679i	−0.969271	+	0.245994i	$0.920886\pi$
$348$	1.37444	+	5.12947i	0.0736776	+	0.274969i
$349$	−6.57321	+	1.76129i	−0.351856	+	0.0942795i	−0.430418	−	0.902630i	$-0.641634\pi$
$349$	−6.57321	+	1.76129i	−0.351856	+	0.0942795i	0.0785620	+	0.996909i	$0.474967\pi$
$350$		0			0
$351$	−12.0018	−	8.67315i	−0.640609	−	0.462938i
$352$	−17.9821	+	17.9821i	−0.958448	+	0.958448i
$353$	23.6652	+	13.6631i	1.25957	+	0.727213i	0.972991	−	0.230843i	$-0.0741485\pi$
$353$	23.6652	+	13.6631i	1.25957	+	0.727213i	0.286579	+	0.958057i	$0.407482\pi$
$354$	−38.2248	−	22.0691i	−2.03163	−	1.17296i
$355$		0			0
$356$	4.50714	+	4.50714i	0.238878	+	0.238878i
$357$	−7.10431	−	12.3050i	−0.376000	−	0.651251i
$358$	−2.00585	−	3.47423i	−0.106012	−	0.183619i
$359$	−3.89871	−	3.89871i	−0.205766	−	0.205766i	0.596699	−	0.802465i	$-0.296479\pi$
$359$	−3.89871	−	3.89871i	−0.205766	−	0.205766i	−0.802465	+	0.596699i	$0.796479\pi$
$360$		0			0
$361$	−16.2045	−	9.35567i	−0.852868	−	0.492404i
$362$	15.2161	+	8.78501i	0.799740	+	0.461730i
$363$	5.61766	−	5.61766i	0.294851	−	0.294851i
$364$	−6.15423	+	16.1553i	−0.322569	+	0.846769i
$365$		0			0
$366$	−10.1204	+	2.71176i	−0.529003	+	0.141746i
$367$	−4.67826	−	17.4595i	−0.244203	−	0.911378i	−0.973782	−	0.227482i	$-0.926951\pi$
$367$	−4.67826	−	17.4595i	−0.244203	−	0.911378i	0.729579	−	0.683896i	$-0.239716\pi$
$368$	−1.43344	−	0.384089i	−0.0747232	−	0.0200220i
$369$	0.441373	−	0.441373i	0.0229770	−	0.0229770i
$370$		0			0
$371$	−15.2885	−	4.09653i	−0.793738	−	0.212681i
$372$			15.7046i			0.814248i
$373$	−4.01536	+	14.9855i	−0.207907	+	0.775921i	0.780636	+	0.624986i	$0.214895\pi$
$373$	−4.01536	+	14.9855i	−0.207907	+	0.775921i	−0.988544	+	0.150936i	$0.951771\pi$
$374$	7.18771	−	12.4495i	0.371668	−	0.643747i
$375$		0			0
$376$			11.5232i			0.594266i
$377$	2.53841	−	6.66353i	0.130735	−	0.343189i
$378$	−18.8238	−	18.8238i	−0.968191	−	0.968191i
$379$	5.53029	+	20.6393i	0.284072	+	1.06017i	0.949515	+	0.313722i	$0.101576\pi$
$379$	5.53029	+	20.6393i	0.284072	+	1.06017i	−0.665443	+	0.746449i	$0.731757\pi$
$380$		0			0
$381$	−2.20733	+	1.27440i	−0.113085	+	0.0652897i
$382$	−6.83407			−0.349661
$383$	−16.8072	+	9.70362i	−0.858806	+	0.495832i	−0.863612	−	0.504157i	$-0.831803\pi$
$383$	−16.8072	+	9.70362i	−0.858806	+	0.495832i	0.00480620	+	0.999988i	$0.498470\pi$
$384$	−4.59660	+	17.1547i	−0.234569	+	0.875424i
$385$		0			0
$386$	−0.260170	−	0.450628i	−0.0132423	−	0.0229364i
$387$	7.89664	−	2.11590i	0.401409	−	0.107557i
$388$	12.0756	−	20.9155i	0.613045	−	1.06182i
$389$	14.8591			0.753387			0.376693	−	0.926338i	$-0.377061\pi$
$389$	14.8591			0.753387			0.376693	+	0.926338i	$0.377061\pi$
$390$		0			0
$391$	0.616816			0.0311937
$392$	3.26357	−	5.65266i	0.164835	−	0.285503i
$393$	10.7095	−	2.86960i	0.540222	−	0.144752i
$394$	−23.6731	−	41.0030i	−1.19263	−	2.06570i
$395$		0			0
$396$	−1.26036	+	4.70374i	−0.0633357	+	0.236372i
$397$	4.57070	−	2.63889i	0.229397	−	0.132442i	−0.380897	−	0.924617i	$-0.624385\pi$
$397$	4.57070	−	2.63889i	0.229397	−	0.132442i	0.610294	+	0.792175i	$0.291051\pi$
$398$	10.5365			0.528145
$399$	3.26338	−	1.88411i	0.163373	−	0.0943236i
$400$		0			0
$401$	7.21557	+	26.9289i	0.360328	+	1.34476i	0.873645	+	0.486564i	$0.161750\pi$
$401$	7.21557	+	26.9289i	0.360328	+	1.34476i	−0.513317	+	0.858199i	$0.671583\pi$
$402$	5.87772	+	5.87772i	0.293154	+	0.293154i
$403$	12.3515	−	17.0918i	0.615270	−	0.851404i
$404$			6.16996i			0.306967i
$405$		0			0
$406$	6.40965	−	11.1018i	0.318106	−	0.550975i
$407$	−5.43231	+	20.2737i	−0.269270	+	1.00493i
$408$		−	4.74421i		−	0.234873i
$409$	−2.54532	−	0.682016i	−0.125858	−	0.0337235i	0.195340	−	0.980736i	$-0.437419\pi$
$409$	−2.54532	−	0.682016i	−0.125858	−	0.0337235i	−0.321198	+	0.947012i	$0.604086\pi$
$410$		0			0
$411$	20.0260	−	20.0260i	0.987810	−	0.987810i
$412$	−18.1246	−	4.85646i	−0.892933	−	0.239261i
$413$	11.1370	+	41.5640i	0.548018	+	2.04523i
$414$	−0.499753	+	0.133908i	−0.0245615	+	0.00658124i
$415$		0			0
$416$	−18.3552	+	14.9414i	−0.899938	+	0.732563i
$417$	−24.4073	+	24.4073i	−1.19523	+	1.19523i
$418$	3.30169	+	1.90623i	0.161491	+	0.0932368i
$419$	−17.0348	−	9.83506i	−0.832205	−	0.480474i	0.0224018	−	0.999749i	$-0.492869\pi$
$419$	−17.0348	−	9.83506i	−0.832205	−	0.480474i	−0.854607	+	0.519275i	$0.826202\pi$
$420$		0			0
$421$	10.4427	+	10.4427i	0.508948	+	0.508948i	0.914203	−	0.405256i	$-0.132817\pi$
$421$	10.4427	+	10.4427i	0.508948	+	0.508948i	−0.405256	+	0.914203i	$0.632817\pi$
$422$	−2.95573	−	5.11948i	−0.143883	−	0.249212i
$423$	4.52369	+	7.83526i	0.219949	+	0.380964i
$424$	−3.73695	−	3.73695i	−0.181482	−	0.181482i
$425$		0			0
$426$	−14.5278	−	8.38762i	−0.703874	−	0.406382i
$427$	8.84594	+	5.10721i	0.428085	+	0.247155i
$428$	6.77359	−	6.77359i	0.327414	−	0.327414i
$429$	21.4693	−	17.4763i	1.03655	−	0.843765i
$430$		0			0
$431$	16.5486	−	4.43419i	0.797119	−	0.213587i	0.162800	−	0.986659i	$-0.447947\pi$
$431$	16.5486	−	4.43419i	0.797119	−	0.213587i	0.634319	+	0.773072i	$0.281281\pi$
$432$	−5.18086	−	19.3352i	−0.249264	−	0.930267i
$433$	−10.8538	−	2.90826i	−0.521599	−	0.139762i	−0.0115927	−	0.999933i	$-0.503690\pi$
$433$	−10.8538	−	2.90826i	−0.521599	−	0.139762i	−0.510006	+	0.860171i	$0.670357\pi$
$434$	26.8070	−	26.8070i	1.28678	−	1.28678i
$435$		0			0
$436$	−18.3096	−	4.90604i	−0.876870	−	0.234957i
$437$			0.163584i			0.00782528i
$438$	13.8623	−	51.7347i	0.662365	−	2.47198i
$439$	−2.12218	+	3.67572i	−0.101286	+	0.175432i	−0.912215	−	0.409712i	$-0.865629\pi$
$439$	−2.12218	+	3.67572i	−0.101286	+	0.175432i	0.810929	+	0.585145i	$0.198962\pi$
$440$		0			0
$441$		−	5.12473i		−	0.244035i
$442$	7.83631	−	10.8438i	0.372735	−	0.515787i
$443$	−15.1569	−	15.1569i	−0.720126	−	0.720126i	0.248505	−	0.968631i	$-0.420061\pi$
$443$	−15.1569	−	15.1569i	−0.720126	−	0.720126i	−0.968631	+	0.248505i	$0.920061\pi$
$444$	−3.76518	−	14.0518i	−0.178687	−	0.666870i
$445$		0			0
$446$	−11.7623	+	6.79099i	−0.556963	+	0.321563i
$447$	26.0221			1.23080
$448$	−6.97281	+	4.02575i	−0.329434	+	0.190199i
$449$	3.76524	−	14.0521i	0.177693	−	0.663158i	−0.818385	−	0.574671i	$-0.805130\pi$
$449$	3.76524	−	14.0521i	0.177693	−	0.663158i	0.996077	−	0.0884873i	$-0.0282033\pi$
$450$		0			0
$451$	−1.30327	−	2.25732i	−0.0613684	−	0.106293i
$452$	3.00021	−	0.803904i	0.141118	−	0.0378124i
$453$	−1.07233	+	1.85732i	−0.0503822	+	0.0872646i
$454$	−7.14758			−0.335453
$455$		0			0
$456$	1.25820			0.0589205
$457$	15.1476	−	26.2365i	0.708576	−	1.22729i	−0.256809	−	0.966462i	$-0.582671\pi$
$457$	15.1476	−	26.2365i	0.708576	−	1.22729i	0.965385	−	0.260828i	$-0.0839956\pi$
$458$	−31.0121	+	8.30966i	−1.44910	+	0.388285i
$459$	4.16003	+	7.20538i	0.194173	+	0.336318i
$460$		0			0
$461$	1.79565	−	6.70146i	0.0836318	−	0.312118i	−0.911420	−	0.411478i	$-0.865013\pi$
$461$	1.79565	−	6.70146i	0.0836318	−	0.312118i	0.995052	+	0.0993596i	$0.0316794\pi$
$462$	43.1003	−	24.8840i	2.00521	−	1.15771i
$463$	−31.4463			−1.46143			−0.730717	−	0.682680i	$-0.760814\pi$
$463$	−31.4463			−1.46143			−0.730717	+	0.682680i	$0.760814\pi$
$464$	8.34794	−	4.81968i	0.387543	−	0.223748i
$465$		0			0
$466$	−1.93727	−	7.22999i	−0.0897423	−	0.334923i
$467$	−3.69622	−	3.69622i	−0.171041	−	0.171041i	0.616396	−	0.787436i	$-0.288592\pi$
$467$	−3.69622	−	3.69622i	−0.171041	−	0.171041i	−0.787436	+	0.616396i	$0.788592\pi$
$468$	−1.61337	+	4.23522i	−0.0745780	+	0.195773i
$469$		−	8.10369i		−	0.374194i
$470$		0			0
$471$	4.25293	−	7.36630i	0.195965	−	0.339421i
$472$	−3.71862	+	13.8781i	−0.171163	+	0.638790i
$473$		−	34.1382i		−	1.56968i
$474$	5.60024	+	1.50058i	0.257227	+	0.0689239i
$475$		0			0
$476$	6.86855	−	6.86855i	0.314820	−	0.314820i
$477$	−4.00797	−	1.07393i	−0.183512	−	0.0491720i
$478$	−6.01571	−	22.4509i	−0.275152	−	1.02688i
$479$	18.6940	−	5.00904i	0.854150	−	0.228869i	0.194928	−	0.980818i	$-0.437553\pi$
$479$	18.6940	−	5.00904i	0.854150	−	0.228869i	0.659222	+	0.751949i	$0.270886\pi$
$480$		0			0
$481$	−6.95380	+	18.2543i	−0.317066	+	0.832323i
$482$	22.7270	−	22.7270i	1.03518	−	1.03518i
$483$	1.84934	+	1.06771i	0.0841477	+	0.0485827i
$484$	4.70359	+	2.71562i	0.213800	+	0.123437i
$485$		0			0
$486$	−12.0788	−	12.0788i	−0.547907	−	0.547907i
$487$	−11.6813	−	20.2327i	−0.529332	−	0.916830i	−0.999415	−	0.0342077i	$-0.989109\pi$
$487$	−11.6813	−	20.2327i	−0.529332	−	0.916830i	0.470083	−	0.882622i	$-0.344224\pi$
$488$	1.70528	+	2.95363i	0.0771943	+	0.133704i
$489$	−3.17214	−	3.17214i	−0.143449	−	0.143449i
$490$		0			0
$491$	18.4624	+	10.6593i	0.833198	+	0.481047i	0.854946	−	0.518716i	$-0.173590\pi$
$491$	18.4624	+	10.6593i	0.833198	+	0.481047i	−0.0217482	+	0.999763i	$0.506923\pi$
$492$	1.56457	+	0.903303i	0.0705362	+	0.0407241i
$493$	−2.83305	+	2.83305i	−0.127594	+	0.127594i
$494$	2.87585	+	2.07824i	0.129391	+	0.0935046i
$495$		0			0
$496$	27.5354	−	7.37809i	1.23638	−	0.331286i
$497$	4.23276	+	15.7969i	0.189865	+	0.708587i
$498$	−26.5549	−	7.11538i	−1.18996	−	0.318848i
$499$	−23.0389	+	23.0389i	−1.03136	+	1.03136i	−0.0318687	+	0.999492i	$0.510146\pi$
$499$	−23.0389	+	23.0389i	−1.03136	+	1.03136i	−0.999492	+	0.0318687i	$0.989854\pi$
$500$		0			0
$501$	−1.18606	−	0.317803i	−0.0529891	−	0.0141984i
$502$		−	39.8727i		−	1.77960i
$503$	−0.169996	+	0.634433i	−0.00757973	+	0.0282879i	−0.969612	−	0.244647i	$-0.921328\pi$
$503$	−0.169996	+	0.634433i	−0.00757973	+	0.0282879i	0.962032	+	0.272935i	$0.0879945\pi$
$504$	1.93976	−	3.35977i	0.0864039	−	0.149656i
$505$		0			0
$506$			2.16050i			0.0960458i
$507$	21.5357	−	14.1422i	0.956436	−	0.628075i
$508$	−1.23211	−	1.23211i	−0.0546662	−	0.0546662i
$509$	−8.29035	−	30.9400i	−0.367463	−	1.37139i	−0.864050	−	0.503405i	$-0.832080\pi$
$509$	−8.29035	−	30.9400i	−0.367463	−	1.37139i	0.496587	−	0.867987i	$-0.334586\pi$
$510$		0			0
$511$	−45.2197	+	26.1076i	−2.00040	+	1.15493i
$512$	−20.4758			−0.904912
$513$	−1.91092	+	1.10327i	−0.0843690	+	0.0487105i
$514$	−6.07422	+	22.6693i	−0.267923	+	0.999901i
$515$		0			0
$516$	11.8307	+	20.4914i	0.520818	+	0.902084i
$517$	36.4929	−	9.77825i	1.60496	−	0.430047i
$518$	−17.5588	+	30.4127i	−0.771489	+	1.33626i
$519$	−13.1232			−0.576046
$520$		0			0
$521$	−23.4746			−1.02844			−0.514220	−	0.857658i	$-0.671919\pi$
$521$	−23.4746			−1.02844			−0.514220	+	0.857658i	$0.671919\pi$
$522$	1.68033	−	2.91042i	0.0735461	−	0.127386i
$523$	23.9001	−	6.40400i	1.04508	−	0.280027i	0.304861	−	0.952397i	$-0.401390\pi$
$523$	23.9001	−	6.40400i	1.04508	−	0.280027i	0.740216	+	0.672370i	$0.234723\pi$
$524$	3.78986	+	6.56423i	0.165561	+	0.286760i
$525$		0			0
$526$	7.82436	−	29.2009i	0.341158	−	1.27322i
$527$	−10.2612	+	5.92431i	−0.446985	+	0.258067i
$528$	37.4226			1.62861
$529$	19.8383	−	11.4536i	0.862535	−	0.497985i
$530$		0			0
$531$	2.91964	+	10.8963i	0.126702	+	0.472857i
$532$	1.82159	+	1.82159i	0.0789759	+	0.0789759i
$533$	−0.992330	−	2.21360i	−0.0429826	−	0.0958817i
$534$		−	17.0776i		−	0.739019i
$535$		0			0
$536$	1.35290	−	2.34329i	0.0584363	−	0.101215i
$537$	−1.12346	+	4.19281i	−0.0484809	+	0.180933i
$538$			59.1745i			2.55119i
$539$	−20.6708	−	5.53871i	−0.890353	−	0.238569i
$540$		0			0
$541$	−27.6908	+	27.6908i	−1.19052	+	1.19052i	−0.213597	+	0.976922i	$0.568518\pi$
$541$	−27.6908	+	27.6908i	−1.19052	+	1.19052i	−0.976922	+	0.213597i	$0.931482\pi$
$542$	30.9125	+	8.28297i	1.32780	+	0.355784i
$543$	−4.92042	−	18.3632i	−0.211155	−	0.788042i
$544$	12.8452	−	3.44185i	0.550731	−	0.147568i
$545$		0			0
$546$	42.2655	−	18.9471i	1.80880	−	0.810861i
$547$	−6.53914	+	6.53914i	−0.279593	+	0.279593i	−0.832947	−	0.553353i	$-0.813348\pi$
$547$	−6.53914	+	6.53914i	−0.279593	+	0.279593i	0.553353	+	0.832947i	$0.313348\pi$
$548$	16.7675	+	9.68071i	0.716272	+	0.413540i
$549$	2.31902	+	1.33889i	0.0989733	+	0.0571422i
$550$		0			0
$551$	−0.751344	−	0.751344i	−0.0320083	−	0.0320083i
$552$	0.356506	+	0.617486i	0.0151739	+	0.0262820i
$553$	−2.82613	−	4.89500i	−0.120179	−	0.208156i
$554$	−3.98180	−	3.98180i	−0.169170	−	0.169170i
$555$		0			0
$556$	−20.4359	−	11.7987i	−0.866676	−	0.500375i
$557$	−14.0717	−	8.12429i	−0.596237	−	0.344237i	0.171323	−	0.985215i	$-0.445196\pi$
$557$	−14.0717	−	8.12429i	−0.596237	−	0.344237i	−0.767560	+	0.640978i	$0.778529\pi$
$558$	7.02763	−	7.02763i	0.297503	−	0.297503i
$559$	3.24046	−	31.6061i	0.137057	−	1.33679i
$560$		0			0
$561$	−15.0244	+	4.02578i	−0.634332	+	0.169969i
$562$	12.5206	+	46.7277i	0.528151	+	1.97109i
$563$	−31.4174	−	8.41827i	−1.32409	−	0.354788i	−0.473579	−	0.880751i	$-0.657038\pi$
$563$	−31.4174	−	8.41827i	−1.32409	−	0.354788i	−0.850507	+	0.525964i	$0.823705\pi$
$564$	−18.5161	+	18.5161i	−0.779670	+	0.779670i
$565$		0			0
$566$	27.1382	+	7.27167i	1.14071	+	0.305651i
$567$			38.6538i			1.62331i
$568$	−1.41331	+	5.27453i	−0.0593010	+	0.221314i
$569$	−16.4164	+	28.4341i	−0.688212	+	1.19202i	0.284203	+	0.958764i	$0.408271\pi$
$569$	−16.4164	+	28.4341i	−0.688212	+	1.19202i	−0.972416	+	0.233255i	$0.925062\pi$
$570$		0			0
$571$		−	31.7967i		−	1.33065i	−0.746554	−	0.665325i	$-0.768293\pi$
$571$		−	31.7967i		−	1.33065i	0.746554	−	0.665325i	$-0.231707\pi$
$572$	15.3392	+	11.0849i	0.641364	+	0.463484i
$573$	5.22875	+	5.22875i	0.218434	+	0.218434i
$574$	−1.12874	−	4.21253i	−0.0471129	−	0.175828i
$575$		0			0
$576$	−1.82796	+	1.05538i	−0.0761652	+	0.0439740i
$577$	−39.9389			−1.66268			−0.831338	−	0.555767i	$-0.812425\pi$
$577$	−39.9389			−1.66268			−0.831338	+	0.555767i	$0.812425\pi$
$578$	20.4559	−	11.8102i	0.850854	−	0.491241i
$579$	−0.145719	+	0.543832i	−0.00605589	+	0.0226009i
$580$		0			0
$581$	13.4008	+	23.2109i	0.555959	+	0.962949i
$582$	−62.5017	+	16.7473i	−2.59078	+	0.694197i
$583$	−8.66348	+	15.0056i	−0.358805	+	0.621468i
$584$	−17.4345			−0.721444
$585$		0			0
$586$	−19.0063			−0.785143
$587$	−9.32773	+	16.1561i	−0.384997	+	0.666834i	−0.991769	−	0.128042i	$-0.959131\pi$
$587$	−9.32773	+	16.1561i	−0.384997	+	0.666834i	0.606772	+	0.794876i	$0.292464\pi$
$588$	14.3271	−	3.83892i	0.590838	−	0.158315i
$589$	−1.57117	−	2.72135i	−0.0647389	−	0.112131i
$590$		0			0
$591$	−13.2591	+	49.4837i	−0.545407	+	2.03549i
$592$	−22.8686	+	13.2032i	−0.939893	+	0.542647i
$593$	−8.65172			−0.355284			−0.177642	−	0.984095i	$-0.556847\pi$
$593$	−8.65172			−0.355284			−0.177642	+	0.984095i	$0.556847\pi$
$594$	−25.2380	+	14.5712i	−1.03553	+	0.597862i
$595$		0			0
$596$	4.60433	+	17.1836i	0.188601	+	0.703867i
$597$	−8.06145	−	8.06145i	−0.329933	−	0.329933i
$598$	−0.205079	+	2.00025i	−0.00838628	+	0.0817962i
$599$			35.1779i			1.43733i	0.695356	+	0.718666i	$0.255247\pi$
$599$			35.1779i			1.43733i	−0.695356	+	0.718666i	$0.744753\pi$
$600$		0			0
$601$	20.0384	−	34.7076i	0.817385	−	1.41575i	−0.0902170	−	0.995922i	$-0.528756\pi$
$601$	20.0384	−	34.7076i	0.817385	−	1.41575i	0.907602	−	0.419831i	$-0.137911\pi$
$602$	14.7834	−	55.1722i	0.602524	−	2.24865i
$603$		−	2.12443i		−	0.0865136i
$604$	−1.41621	−	0.379473i	−0.0576249	−	0.0154405i
$605$		0			0
$606$	11.6890	−	11.6890i	0.474834	−	0.474834i
$607$	41.5934	+	11.1449i	1.68822	+	0.452358i	0.969930	−	0.243384i	$-0.0782575\pi$
$607$	41.5934	+	11.1449i	1.68822	+	0.452358i	0.718292	+	0.695742i	$0.244924\pi$
$608$	0.912802	+	3.40662i	0.0370190	+	0.138157i
$609$	−13.3981	+	3.59000i	−0.542917	+	0.145474i
$610$		0			0
$611$	34.7143	−	5.58899i	1.40439	−	0.226106i
$612$	1.80063	−	1.80063i	0.0727863	−	0.0727863i
$613$	−17.5625	−	10.1397i	−0.709344	−	0.409540i	0.101474	−	0.994838i	$-0.467644\pi$
$613$	−17.5625	−	10.1397i	−0.709344	−	0.409540i	−0.810818	+	0.585298i	$0.800978\pi$
$614$	3.39352	+	1.95925i	0.136952	+	0.0790690i
$615$		0			0
$616$	−11.4553	−	11.4553i	−0.461546	−	0.461546i
$617$	4.33527	+	7.50891i	0.174531	+	0.302297i	0.939999	−	0.341177i	$-0.110826\pi$
$617$	4.33527	+	7.50891i	0.174531	+	0.302297i	−0.765468	+	0.643474i	$0.777492\pi$
$618$	25.1365	+	43.5376i	1.01114	+	1.75134i
$619$	−21.3034	−	21.3034i	−0.856257	−	0.856257i	0.134638	−	0.990895i	$-0.457013\pi$
$619$	−21.3034	−	21.3034i	−0.856257	−	0.856257i	−0.990895	+	0.134638i	$0.957013\pi$
$620$		0			0
$621$	−1.08290	−	0.625215i	−0.0434554	−	0.0250890i
$622$	−6.06077	−	3.49919i	−0.243015	−	0.140305i
$623$	−11.7725	+	11.7725i	−0.471657	+	0.471657i
$624$	34.6468	+	3.55222i	1.38698	+	0.142203i
$625$		0			0
$626$	−7.61954	+	2.04165i	−0.304538	+	0.0816007i
$627$	−1.06767	−	3.98458i	−0.0426385	−	0.159129i
$628$	5.61682	+	1.50502i	0.224136	+	0.0600569i
$629$	7.76093	−	7.76093i	0.309449	−	0.309449i
$630$		0			0
$631$	−27.4324	−	7.35050i	−1.09207	−	0.292619i	−0.332537	−	0.943090i	$-0.607905\pi$
$631$	−27.4324	−	7.35050i	−1.09207	−	0.292619i	−0.759531	+	0.650472i	$0.774571\pi$
$632$		−	1.88727i		−	0.0750715i
$633$	−1.65548	+	6.17835i	−0.0657996	+	0.245567i
$634$	21.1670	−	36.6622i	0.840647	−	1.45604i
$635$		0			0
$636$		−	12.0094i		−	0.476206i
$637$	−18.6118	−	7.09000i	−0.737427	−	0.280916i
$638$	−9.92320	−	9.92320i	−0.392863	−	0.392863i
$639$	1.10965	+	4.14125i	0.0438969	+	0.163825i
$640$		0			0
$641$	14.1756	−	8.18429i	0.559903	−	0.323260i	−0.193204	−	0.981159i	$-0.561888\pi$
$641$	14.1756	−	8.18429i	0.559903	−	0.323260i	0.753107	+	0.657899i	$0.228554\pi$
$642$	−25.6652			−1.01292
$643$	35.5518	−	20.5258i	1.40203	−	0.809460i	0.407425	−	0.913239i	$-0.366427\pi$
$643$	35.5518	−	20.5258i	1.40203	−	0.809460i	0.994600	+	0.103779i	$0.0330933\pi$
$644$	−0.377841	+	1.41012i	−0.0148890	+	0.0555666i
$645$		0			0
$646$	−0.996819	−	1.72654i	−0.0392193	−	0.0679298i
$647$	−2.73861	+	0.733807i	−0.107666	+	0.0288489i	−0.312250	−	0.950000i	$-0.601083\pi$
$647$	−2.73861	+	0.733807i	−0.107666	+	0.0288489i	0.204584	+	0.978849i	$0.434416\pi$
$648$	−6.45318	+	11.1772i	−0.253505	+	0.439083i
$649$	47.1059			1.84907
$650$		0			0
$651$	−41.0201			−1.60771
$652$	1.53344	−	2.65599i	0.0600540	−	0.104017i
$653$	1.21283	−	0.324978i	0.0474619	−	0.0127174i	−0.235010	−	0.971993i	$-0.575512\pi$
$653$	1.21283	−	0.324978i	0.0474619	−	0.0127174i	0.282472	+	0.959276i	$0.408846\pi$
$654$	25.3930	+	43.9820i	0.992947	+	1.71983i
$655$		0			0
$656$	0.848749	−	3.16758i	0.0331381	−	0.123673i
$657$	−11.8546	+	6.84427i	−0.462493	+	0.267020i
$658$	63.2122			2.46427
$659$	8.09916	−	4.67605i	0.315498	−	0.182153i	−0.333886	−	0.942613i	$-0.608360\pi$
$659$	8.09916	−	4.67605i	0.315498	−	0.182153i	0.649384	+	0.760460i	$0.275027\pi$
$660$		0			0
$661$	−6.64415	−	24.7963i	−0.258427	−	0.964464i	−0.966152	−	0.257975i	$-0.916945\pi$
$661$	−6.64415	−	24.7963i	−0.258427	−	0.964464i	0.707724	−	0.706489i	$-0.249722\pi$
$662$	−2.58641	−	2.58641i	−0.100524	−	0.100524i
$663$	−14.2922	+	2.30103i	−0.555061	+	0.0893647i
$664$			8.94896i			0.347287i
$665$		0			0
$666$	−4.60315	+	7.97288i	−0.178368	+	0.308943i
$667$	0.155847	−	0.581628i	0.00603441	−	0.0225207i
$668$		−	0.839440i		−	0.0324789i
$669$	14.1952	+	3.80358i	0.548817	+	0.147055i
$670$		0			0
$671$	7.90679	−	7.90679i	0.305238	−	0.305238i
$672$	44.4701	+	11.9157i	1.71547	+	0.459660i
$673$	−10.6983	−	39.9267i	−0.412390	−	1.53906i	−0.790007	−	0.613098i	$-0.789923\pi$
$673$	−10.6983	−	39.9267i	−0.412390	−	1.53906i	0.377617	−	0.925962i	$-0.376744\pi$
$674$	15.3308	−	4.10787i	0.590519	−	0.158229i
$675$		0			0
$676$	13.1493	+	11.7188i	0.505740	+	0.450721i
$677$	−15.5322	+	15.5322i	−0.596950	+	0.596950i	−0.939500	−	0.342549i	$-0.888710\pi$
$677$	−15.5322	+	15.5322i	−0.596950	+	0.596950i	0.342549	+	0.939500i	$0.388710\pi$
$678$	−7.20690	−	4.16090i	−0.276779	−	0.159799i
$679$	54.6308	+	31.5411i	2.09654	+	1.21044i
$680$		0			0
$681$	5.46862	+	5.46862i	0.209558	+	0.209558i
$682$	−20.7508	−	35.9415i	−0.794591	−	1.37627i
$683$	−3.32652	−	5.76170i	−0.127286	−	0.220465i	0.795338	−	0.606166i	$-0.207293\pi$
$683$	−3.32652	−	5.76170i	−0.127286	−	0.220465i	−0.922624	+	0.385700i	$0.873960\pi$
$684$	0.477541	+	0.477541i	0.0182592	+	0.0182592i
$685$		0			0
$686$	8.28646	+	4.78419i	0.316378	+	0.182661i
$687$	30.0851	+	17.3696i	1.14782	+	0.662692i
$688$	30.3701	−	30.3701i	1.15785	−	1.15785i
$689$	−9.44525	+	13.0702i	−0.359835	+	0.497936i
$690$		0			0
$691$	−36.3445	+	9.73848i	−1.38261	+	0.370469i	−0.872069	−	0.489384i	$-0.837222\pi$
$691$	−36.3445	+	9.73848i	−1.38261	+	0.370469i	−0.510542	+	0.859853i	$0.670555\pi$
$692$	−2.32201	−	8.66588i	−0.0882698	−	0.329427i
$693$	−12.2861	−	3.29204i	−0.466709	−	0.125054i
$694$	−42.1038	+	42.1038i	−1.59824	+	1.59824i
$695$		0			0
$696$	−4.47356	−	1.19869i	−0.169570	−	0.0454361i
$697$			1.36302i			0.0516282i
$698$	−3.22603	+	12.0397i	−0.122107	+	0.455710i
$699$	−4.04946	+	7.01387i	−0.153165	+	0.265289i
$700$		0			0
$701$			40.3398i			1.52361i	0.647804	+	0.761807i	$0.275688\pi$
$701$			40.3398i			1.52361i	−0.647804	+	0.761807i	$0.724312\pi$
$702$	−24.7491	+	11.0947i	−0.934096	+	0.418744i
$703$	2.05825	+	2.05825i	0.0776285	+	0.0776285i
$704$	2.28126	+	8.51379i	0.0859783	+	0.320875i
$705$		0			0
$706$	43.3459	−	25.0258i	1.63134	−	0.941857i
$707$	−16.1158			−0.606097
$708$	−28.2753	+	16.3247i	−1.06265	+	0.613521i
$709$	−11.5415	+	43.0733i	−0.433449	+	1.61765i	0.311304	+	0.950311i	$0.399234\pi$
$709$	−11.5415	+	43.0733i	−0.433449	+	1.61765i	−0.744752	+	0.667341i	$0.767432\pi$
$710$		0			0
$711$	−0.740887	−	1.28325i	−0.0277854	−	0.0481258i
$712$	−5.36959	+	1.43878i	−0.201234	+	0.0539204i
$713$	0.890371	−	1.54217i	0.0333447	−	0.0577546i
$714$	−26.0250			−0.973960
$715$		0			0
$716$	−2.96749			−0.110900
$717$	−12.5746	+	21.7798i	−0.469607	+	0.813383i
$718$	−9.75479	+	2.61379i	−0.364045	+	0.0975457i
$719$	−13.7825	−	23.8720i	−0.514001	−	0.890276i	−0.999868	−	0.0162430i	$-0.994829\pi$
$719$	−13.7825	−	23.8720i	−0.514001	−	0.890276i	0.485867	−	0.874033i	$-0.338504\pi$
$720$		0			0
$721$	12.6850	−	47.3409i	0.472413	−	1.76307i
$722$	−29.6807	+	17.1361i	−1.10460	+	0.637741i
$723$	−34.7768			−1.29336
$724$	11.2555	−	6.49836i	0.418307	−	0.241510i
$725$		0			0
$726$	−3.76622	−	14.0557i	−0.139777	−	0.521656i
$727$	−29.4624	−	29.4624i	−1.09270	−	1.09270i	−0.995240	−	0.0974593i	$-0.968928\pi$
$727$	−29.4624	−	29.4624i	−1.09270	−	1.09270i	−0.0974593	−	0.995240i	$-0.531072\pi$
$728$	−9.51825	−	11.6930i	−0.352770	−	0.433370i
$729$		−	14.2845i		−	0.529057i
$730$		0			0
$731$	−8.92588	+	15.4601i	−0.330135	+	0.571811i
$732$	−2.00591	+	7.48617i	−0.0741407	+	0.276697i
$733$			23.3958i			0.864144i	0.901839	+	0.432072i	$0.142217\pi$
$733$			23.3958i			0.864144i	−0.901839	+	0.432072i	$0.857783\pi$
$734$	−31.9794	−	8.56885i	−1.18038	−	0.316282i
$735$		0			0
$736$	−1.41323	+	1.41323i	−0.0520924	+	0.0520924i
$737$	−8.56897	−	2.29605i	−0.315642	−	0.0845761i
$738$	−0.295907	−	1.10434i	−0.0108925	−	0.0406513i
$739$	−15.5120	+	4.15644i	−0.570620	+	0.152897i	−0.532581	−	0.846379i	$-0.678778\pi$
$739$	−15.5120	+	4.15644i	−0.570620	+	0.152897i	−0.0380389	+	0.999276i	$0.512111\pi$
$740$		0			0
$741$	−0.610250	−	3.79038i	−0.0224181	−	0.139243i
$742$	−20.4995	+	20.4995i	−0.752561	+	0.752561i
$743$	45.2759	+	26.1400i	1.66101	+	0.958985i	0.972234	+	0.234011i	$0.0751853\pi$
$743$	45.2759	+	26.1400i	1.66101	+	0.958985i	0.688777	+	0.724973i	$0.258148\pi$
$744$	−11.8615	−	6.84824i	−0.434864	−	0.251069i
$745$		0			0
$746$	20.0933	+	20.0933i	0.735669	+	0.735669i
$747$	3.51310	+	6.08487i	0.128538	+	0.222634i
$748$	−5.31682	−	9.20901i	−0.194402	−	0.336715i
$749$	17.6925	+	17.6925i	0.646468	+	0.646468i
$750$		0			0
$751$	23.7599	+	13.7178i	0.867010	+	0.500569i	0.866354	−	0.499431i	$-0.166458\pi$
$751$	23.7599	+	13.7178i	0.867010	+	0.500569i	0.000656703		1.00000i	$0.499791\pi$
$752$	41.1638	+	23.7659i	1.50109	+	0.866655i
$753$	−30.5066	+	30.5066i	−1.11172	+	1.11172i
$754$	−8.24524	−	10.1291i	−0.300274	−	0.368880i
$755$		0			0
$756$	−19.0207	+	5.09659i	−0.691777	+	0.185361i
$757$	−0.622824	−	2.32441i	−0.0226369	−	0.0844821i	0.953683	−	0.300813i	$-0.0972578\pi$
$757$	−0.622824	−	2.32441i	−0.0226369	−	0.0844821i	−0.976320	+	0.216330i	$0.930591\pi$
$758$	37.8037	+	10.1295i	1.37309	+	0.367919i
$759$	1.65300	−	1.65300i	0.0600000	−	0.0600000i
$760$		0			0
$761$	2.35997	+	0.632352i	0.0855488	+	0.0229227i	0.301340	−	0.953517i	$-0.402566\pi$
$761$	2.35997	+	0.632352i	0.0855488	+	0.0229227i	−0.215791	+	0.976440i	$0.569233\pi$
$762$			4.66848i			0.169121i
$763$	12.8144	−	47.8242i	0.463914	−	1.73135i
$764$	−2.52761	+	4.37796i	−0.0914459	+	0.158389i
$765$		0			0
$766$			35.5469i			1.28436i
$767$	43.6120	+	4.47139i	1.57474	+	0.161452i
$768$	29.3786	+	29.3786i	1.06011	+	1.06011i
$769$	−3.50862	−	13.0944i	−0.126524	−	0.472195i	0.873365	−	0.487066i	$-0.161933\pi$
$769$	−3.50862	−	13.0944i	−0.126524	−	0.472195i	−0.999889	+	0.0148712i	$0.995266\pi$
$770$		0			0
$771$	21.9917	−	12.6969i	0.792011	−	0.457268i
$772$	−0.384901			−0.0138529
$773$	−19.4375	+	11.2222i	−0.699118	+	0.403636i	−0.807019	−	0.590525i	$-0.798921\pi$
$773$	−19.4375	+	11.2222i	−0.699118	+	0.403636i	0.107901	+	0.994162i	$0.465587\pi$
$774$	3.87555	−	14.4637i	0.139304	−	0.519888i
$775$		0			0
$776$	10.5315	+	18.2410i	0.378058	+	0.654815i
$777$	36.7030	−	9.83454i	1.31671	−	0.352812i
$778$	13.6082	−	23.5701i	0.487878	−	0.845030i
$779$	−0.361484			−0.0129515
$780$		0			0
$781$	17.9032			0.640626
$782$	0.564890	−	0.978419i	0.0202004	−	0.0349882i
$783$	7.84541	−	2.10217i	0.280372	−	0.0751255i
$784$	−13.4618	−	23.3165i	−0.480778	−	0.832732i
$785$		0			0
$786$	5.25605	−	19.6158i	0.187477	−	0.699674i
$787$	−11.6877	+	6.74791i	−0.416622	+	0.240537i	−0.693631	−	0.720330i	$-0.743990\pi$
$787$	−11.6877	+	6.74791i	−0.416622	+	0.240537i	0.277009	+	0.960867i	$0.410657\pi$
$788$	−35.0224			−1.24762
$789$	−28.3280	+	16.3552i	−1.00850	+	0.582260i
$790$		0			0
$791$	2.09978	+	7.83647i	0.0746594	+	0.278633i
$792$	−3.00307	−	3.00307i	−0.106709	−	0.106709i
$793$	8.07086	−	6.56980i	0.286605	−	0.233300i
$794$		−	9.66696i		−	0.343068i
$795$		0			0
$796$	3.89696	−	6.74974i	0.138124	−	0.239238i
$797$	1.62398	−	6.06076i	0.0575242	−	0.214683i	−0.931181	−	0.364558i	$-0.881220\pi$
$797$	1.62398	−	6.06076i	0.0575242	−	0.214683i	0.988705	+	0.149874i	$0.0478869\pi$
$798$		−	6.90201i		−	0.244328i
$799$	−19.0831	−	5.11330i	−0.675112	−	0.180896i
$800$		0			0
$801$	−3.08625	+	3.08625i	−0.109047	+	0.109047i
$802$	49.3238	+	13.2163i	1.74168	+	0.466683i
$803$	14.7943	+	55.2132i	0.522081	+	1.94843i
$804$	5.93922	−	1.59141i	0.209460	−	0.0561247i
$805$		0			0
$806$	−15.8001	−	35.2454i	−0.556534	−	1.24146i
$807$	45.2744	−	45.2744i	1.59374	−	1.59374i
$808$	−4.66009	−	2.69050i	−0.163941	−	0.0946516i
$809$	18.6872	+	10.7890i	0.657006	+	0.379322i	0.791135	−	0.611641i	$-0.209490\pi$
$809$	18.6872	+	10.7890i	0.657006	+	0.379322i	−0.134130	+	0.990964i	$0.542824\pi$
$810$		0			0
$811$	22.5473	+	22.5473i	0.791743	+	0.791743i	0.981777	−	0.190035i	$-0.0608601\pi$
$811$	22.5473	+	22.5473i	0.791743	+	0.791743i	−0.190035	+	0.981777i	$0.560860\pi$
$812$	−4.74129	−	8.21215i	−0.166387	−	0.288190i
$813$	−17.3138	−	29.9885i	−0.607223	−	1.05174i
$814$	27.1839	+	27.1839i	0.952795	+	0.952795i
$815$		0			0
$816$	−16.9475	−	9.78462i	−0.593280	−	0.342530i
$817$	−4.10012	−	2.36721i	−0.143445	−	0.0828180i
$818$	−3.41289	+	3.41289i	−0.119329	+	0.119329i
$819$	−11.0623	−	4.21408i	−0.386547	−	0.147252i
$820$		0			0
$821$	−17.3216	+	4.64130i	−0.604526	+	0.161982i	−0.548084	−	0.836423i	$-0.684642\pi$
$821$	−17.3216	+	4.64130i	−0.604526	+	0.161982i	−0.0564427	+	0.998406i	$0.517976\pi$
$822$	−13.4259	−	50.1062i	−0.468282	−	1.74765i
$823$	−1.11284	−	0.298185i	−0.0387913	−	0.0103941i	0.239371	−	0.970928i	$-0.423059\pi$
$823$	−1.11284	−	0.298185i	−0.0387913	−	0.0103941i	−0.278162	+	0.960534i	$0.589725\pi$
$824$	11.5715	−	11.5715i	0.403112	−	0.403112i
$825$		0			0
$826$	76.1300	+	20.3990i	2.64890	+	0.709771i
$827$		−	4.45029i		−	0.154752i	−0.997002	−	0.0773759i	$-0.975346\pi$
$827$		−	4.45029i		−	0.154752i	0.997002	−	0.0773759i	$-0.0246542\pi$
$828$	−0.0990534	+	0.369672i	−0.00344234	+	0.0128470i
$829$	14.5637	−	25.2251i	0.505819	−	0.876103i	−0.494159	−	0.869372i	$-0.664524\pi$
$829$	14.5637	−	25.2251i	0.505819	−	0.876103i	0.999977	−	0.00673181i	$-0.00214282\pi$
$830$		0			0
$831$			6.09295i			0.211362i
$832$	1.30391	+	8.09884i	0.0452050	+	0.280777i
$833$	7.91294	+	7.91294i	0.274167	+	0.274167i
$834$	16.3633	+	61.0685i	0.566613	+	2.11463i
$835$		0			0
$836$	2.44229	−	1.41006i	0.0844685	−	0.0487679i
$837$	24.0199			0.830249
$838$	−31.2015	+	18.0142i	−1.07784	+	0.622291i
$839$	8.36719	−	31.2268i	0.288867	−	1.07807i	−0.657099	−	0.753804i	$-0.728217\pi$
$839$	8.36719	−	31.2268i	0.288867	−	1.07807i	0.945967	−	0.324264i	$-0.105117\pi$
$840$		0			0
$841$	−12.5444	−	21.7275i	−0.432565	−	0.749224i
$842$	26.1283	−	7.00106i	0.900441	−	0.241273i
$843$	26.1718	−	45.3309i	0.901405	−	1.56128i
$844$	−4.37277			−0.150517
$845$		0			0
$846$	16.5715			0.569739
$847$	−7.09313	+	12.2857i	−0.243723	+	0.422140i
$848$	−21.0565	+	5.64207i	−0.723083	+	0.193750i
$849$	−15.1999	−	26.3270i	−0.521660	−	0.903541i
$850$		0			0
$851$	−0.426931	+	1.59333i	−0.0146350	+	0.0546186i
$852$	−10.7464	+	6.20441i	−0.368164	+	0.212560i
$853$	−9.24230			−0.316450			−0.158225	−	0.987403i	$-0.550577\pi$
$853$	−9.24230			−0.316450			−0.158225	+	0.987403i	$0.550577\pi$
$854$	16.2025	−	9.35453i	0.554439	−	0.320105i
$855$		0			0
$856$	2.16228	+	8.06972i	0.0739051	+	0.275817i
$857$	37.7913	+	37.7913i	1.29093	+	1.29093i	0.934214	+	0.356713i	$0.116103\pi$
$857$	37.7913	+	37.7913i	1.29093	+	1.29093i	0.356713	+	0.934214i	$0.383897\pi$
$858$	−8.05973	−	50.0606i	−0.275155	−	1.70904i
$859$		−	6.16263i		−	0.210266i	−0.994458	−	0.105133i	$-0.966473\pi$
$859$		−	6.16263i		−	0.210266i	0.994458	−	0.105133i	$-0.0335269\pi$
$860$		0			0
$861$	−2.35941	+	4.08661i	−0.0804083	+	0.139271i
$862$	8.12181	−	30.3110i	0.276630	−	1.03240i
$863$			33.7740i			1.14968i	0.818266	+	0.574840i	$0.194936\pi$
$863$			33.7740i			1.14968i	−0.818266	+	0.574840i	$0.805064\pi$
$864$	−26.0401	−	6.97742i	−0.885902	−	0.237377i
$865$		0			0
$866$	−14.5532	+	14.5532i	−0.494539	+	0.494539i
$867$	−24.6868	−	6.61482i	−0.838409	−	0.224651i
$868$	−7.25808	−	27.0875i	−0.246355	−	0.919410i
$869$	−5.97678	+	1.60147i	−0.202748	+	0.0543263i
$870$		0			0
$871$	−7.71545	−	2.93913i	−0.261428	−	0.0995886i
$872$	11.6896	−	11.6896i	0.395861	−	0.395861i
$873$	14.3218	+	8.26870i	0.484720	+	0.279853i
$874$	0.259484	+	0.149813i	0.00877716	+	0.00506750i
$875$		0			0
$876$	−28.0146	−	28.0146i	−0.946527	−	0.946527i
$877$	11.3486	+	19.6563i	0.383214	+	0.663747i	0.991520	−	0.129956i	$-0.0414837\pi$
$877$	11.3486	+	19.6563i	0.383214	+	0.663747i	−0.608305	+	0.793703i	$0.708150\pi$
$878$	3.88705	+	6.73256i	0.131181	+	0.227213i
$879$	14.5417	+	14.5417i	0.490480	+	0.490480i
$880$		0			0
$881$	−6.78312	−	3.91623i	−0.228529	−	0.131941i	0.381364	−	0.924425i	$-0.375454\pi$
$881$	−6.78312	−	3.91623i	−0.228529	−	0.131941i	−0.609893	+	0.792484i	$0.708788\pi$
$882$	−8.12905	−	4.69331i	−0.273719	−	0.158032i
$883$	−18.9296	+	18.9296i	−0.637032	+	0.637032i	−0.949822	−	0.312790i	$-0.898736\pi$
$883$	−18.9296	+	18.9296i	−0.637032	+	0.637032i	0.312790	+	0.949822i	$0.398736\pi$
$884$	−4.04832	−	9.03064i	−0.136160	−	0.303733i
$885$		0			0
$886$	−37.9234	+	10.1615i	−1.27406	+	0.341384i
$887$	−9.19729	−	34.3248i	−0.308815	−	1.15251i	−0.929612	−	0.368541i	$-0.879857\pi$
$887$	−9.19729	−	34.3248i	−0.308815	−	1.15251i	0.620797	−	0.783972i	$-0.286809\pi$
$888$	12.2550	+	3.28372i	0.411251	+	0.110194i
$889$	3.21825	−	3.21825i	0.107937	−	0.107937i
$890$		0			0
$891$	40.8731	+	10.9519i	1.36930	+	0.366903i
$892$			10.0467i			0.336389i
$893$	1.35608	−	5.06098i	0.0453796	−	0.169359i
$894$	23.8314	−	41.2772i	0.797042	−	1.38052i
$895$		0			0
$896$		−	31.7130i		−	1.05946i
$897$	1.68730	−	1.37348i	0.0563372	−	0.0458593i
$898$	−18.8417	−	18.8417i	−0.628755	−	0.628755i
$899$	2.99371	+	11.1727i	0.0998459	+	0.372630i
$900$		0			0
$901$	7.84682	−	4.53036i	0.261415	−	0.150928i
$902$	−4.77421			−0.158964
$903$	−53.5230	+	30.9015i	−1.78113	+	1.02834i
$904$	−0.701108	+	2.61657i	−0.0233185	+	0.0870258i
$905$		0			0
$906$	1.96411	+	3.40193i	0.0652530	+	0.113022i
$907$	−44.9172	+	12.0355i	−1.49145	+	0.399633i	−0.910227	−	0.414109i	$-0.864093\pi$
$907$	−44.9172	+	12.0355i	−1.49145	+	0.399633i	−0.581225	+	0.813743i	$0.697426\pi$
$908$	−2.64357	+	4.57880i	−0.0877300	+	0.151953i
$909$	−4.22485			−0.140130
$910$		0			0
$911$	17.7325			0.587504			0.293752	−	0.955882i	$-0.405096\pi$
$911$	17.7325			0.587504			0.293752	+	0.955882i	$0.405096\pi$
$912$	2.59495	−	4.49459i	0.0859274	−	0.148831i
$913$	28.3404	−	7.59379i	0.937931	−	0.251318i
$914$	−27.7449	−	48.0556i	−0.917720	−	1.58954i
$915$		0			0
$916$	−6.14674	+	22.9399i	−0.203094	+	0.757957i
$917$	−17.1456	+	9.89902i	−0.566198	+	0.326894i
$918$	15.2393			0.502971
$919$	42.2580	−	24.3977i	1.39396	−	0.804806i	0.400213	−	0.916422i	$-0.368936\pi$
$919$	42.2580	−	24.3977i	1.39396	−	0.804806i	0.993751	+	0.111617i	$0.0356029\pi$
$920$		0			0
$921$	−1.09736	−	4.09541i	−0.0361593	−	0.134948i
$922$	−8.98564	−	8.98564i	−0.295926	−	0.295926i
$923$	16.5752	+	1.69940i	0.545581	+	0.0559365i
$924$		−	36.8139i		−	1.21109i
$925$		0			0
$926$	−28.7990	+	49.8814i	−0.946395	+	1.63920i
$927$	3.32544	−	12.4107i	0.109222	−	0.407621i
$928$		−	12.9820i		−	0.426155i
$929$	10.0330	+	2.68833i	0.329171	+	0.0882012i	0.419620	−	0.907700i	$-0.362163\pi$
$929$	10.0330	+	2.68833i	0.329171	+	0.0882012i	−0.0904485	+	0.995901i	$0.528830\pi$
$930$		0			0
$931$	−2.09857	+	2.09857i	−0.0687778	+	0.0687778i
$932$	−5.34810	−	1.43302i	−0.175183	−	0.0469401i
$933$	1.95987	+	7.31433i	0.0641632	+	0.239460i
$934$	−9.24814	+	2.47803i	−0.302608	+	0.0810837i
$935$		0			0
$936$	−2.49527	−	3.06538i	−0.0815604	−	0.100195i
$937$	−5.31856	+	5.31856i	−0.173750	+	0.173750i	−0.788625	−	0.614875i	$-0.789206\pi$
$937$	−5.31856	+	5.31856i	−0.173750	+	0.173750i	0.614875	+	0.788625i	$0.289206\pi$
$938$	−12.8544	−	7.42149i	−0.419711	−	0.242320i
$939$	7.39178	+	4.26764i	0.241221	+	0.139269i
$940$		0			0
$941$	−38.9093	−	38.9093i	−1.26841	−	1.26841i	−0.946911	−	0.321497i	$-0.895814\pi$
$941$	−38.9093	−	38.9093i	−1.26841	−	1.26841i	−0.321497	−	0.946911i	$-0.604186\pi$
$942$	−7.78981	−	13.4923i	−0.253806	−	0.439604i
$943$	−0.102425	−	0.177406i	−0.00333542	−	0.00577712i
$944$	41.9064	+	41.9064i	1.36394	+	1.36394i
$945$		0			0
$946$	−54.1514	−	31.2643i	−1.76061	−	1.01649i
$947$	−29.2298	−	16.8759i	−0.949842	−	0.548392i	−0.0568101	−	0.998385i	$-0.518093\pi$
$947$	−29.2298	−	16.8759i	−0.949842	−	0.548392i	−0.893032	+	0.449993i	$0.851426\pi$
$948$	3.03256	−	3.03256i	0.0984930	−	0.0984930i
$949$	8.45606	+	52.5222i	0.274495	+	1.70494i
$950$		0			0
$951$	−44.2451	+	11.8554i	−1.43475	+	0.384439i
$952$	2.19259	+	8.18285i	0.0710622	+	0.265208i
$953$	−4.26581	−	1.14302i	−0.138183	−	0.0370260i	0.189065	−	0.981965i	$-0.439454\pi$
$953$	−4.26581	−	1.14302i	−0.138183	−	0.0370260i	−0.327248	+	0.944939i	$0.606121\pi$
$954$	−5.37407	+	5.37407i	−0.173992	+	0.173992i
$955$		0			0
$956$	−16.6072	−	4.44988i	−0.537115	−	0.143919i
$957$			15.1845i			0.490845i
$958$	9.17471	−	34.2405i	0.296422	−	1.10626i
$959$	−25.2858	+	43.7963i	−0.816520	+	1.41425i
$960$		0			0
$961$			3.20686i			0.103447i
$962$	22.5872	+	27.7479i	0.728242	+	0.894630i
$963$	4.63819	+	4.63819i	0.149463	+	0.149463i
$964$	−6.15338	−	22.9647i	−0.198187	−	0.739645i
$965$		0			0
$966$	3.38730	−	1.95566i	0.108985	−	0.0629223i
$967$	−16.2803			−0.523540			−0.261770	−	0.965130i	$-0.584306\pi$
$967$	−16.2803			−0.523540			−0.261770	+	0.965130i	$0.584306\pi$
$968$	−4.10214	+	2.36837i	−0.131848	+	0.0761223i
$969$	−0.558310	+	2.08364i	−0.0179355	+	0.0669363i
$970$		0			0
$971$	−6.40146	−	11.0877i	−0.205433	−	0.355820i	0.744838	−	0.667245i	$-0.232527\pi$
$971$	−6.40146	−	11.0877i	−0.205433	−	0.355820i	−0.950270	+	0.311426i	$0.899193\pi$
$972$	−12.2052	+	3.27038i	−0.391482	+	0.104897i
$973$	30.8179	−	53.3781i	0.987975	−	1.71122i
$974$	−42.7918			−1.37114
$975$		0			0
$976$	14.0681			0.450309
$977$	−8.02436	+	13.8986i	−0.256722	+	0.444655i	−0.965362	−	0.260915i	$-0.915976\pi$
$977$	−8.02436	+	13.8986i	−0.256722	+	0.444655i	0.708640	+	0.705570i	$0.249309\pi$
$978$	−7.93687	+	2.12668i	−0.253793	+	0.0680037i
$979$	9.11292	+	15.7840i	0.291250	+	0.504460i
$980$		0			0
$981$	3.35939	−	12.5374i	0.107257	−	0.400288i
$982$	33.8164	−	19.5239i	1.07912	−	0.623033i
$983$	34.3036			1.09411			0.547057	−	0.837096i	$-0.315748\pi$
$983$	34.3036			1.09411			0.547057	+	0.837096i	$0.315748\pi$
$984$	−1.36450	+	0.787797i	−0.0434988	+	0.0251141i
$985$		0			0
$986$	1.89934	+	7.08844i	0.0604874	+	0.225742i
$987$	−48.3637	−	48.3637i	−1.53943	−	1.53943i
$988$	2.39499	−	1.07364i	0.0761947	−	0.0341572i
$989$		−	2.68296i		−	0.0853131i
$990$		0			0
$991$	−11.1772	+	19.3596i	−0.355057	+	0.614977i	−0.987128	−	0.159934i	$-0.948872\pi$
$991$	−11.1772	+	19.3596i	−0.355057	+	0.614977i	0.632071	+	0.774911i	$0.282205\pi$
$992$	9.93658	−	37.0838i	0.315487	−	1.17741i
$993$			3.95773i			0.125595i
$994$	28.9341	+	7.75287i	0.917734	+	0.245906i
$995$		0			0
$996$	−14.3796	+	14.3796i	−0.455637	+	0.455637i
$997$	11.4991	+	3.08118i	0.364181	+	0.0975820i	0.436269	−	0.899816i	$-0.356300\pi$
$997$	11.4991	+	3.08118i	0.364181	+	0.0975820i	−0.0720881	+	0.997398i	$0.522966\pi$
$998$	15.4458	+	57.6445i	0.488928	+	1.82471i
$999$	−21.4920	+	5.75875i	−0.679975	+	0.182199i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	325.2.s.b.293.4		20
5.2	odd	4		325.2.x.b.7.4		20
5.3	odd	4		65.2.t.a.7.2	yes	20
5.4	even	2		65.2.o.a.33.2	yes	20
13.2	odd	12		325.2.x.b.93.4		20
15.8	even	4		585.2.dp.a.397.4		20
15.14	odd	2		585.2.cf.a.163.4		20
65.2	even	12	inner	325.2.s.b.132.4		20
65.3	odd	12		845.2.t.f.427.4		20
65.4	even	6		845.2.k.d.268.3		20
65.8	even	4		845.2.o.f.357.4		20
65.9	even	6		845.2.k.e.268.8		20
65.18	even	4		845.2.o.e.357.2		20
65.19	odd	12		845.2.f.e.408.3		20
65.23	odd	12		845.2.t.e.427.2		20
65.24	odd	12		845.2.t.g.418.4		20
65.28	even	12		65.2.o.a.2.2	✓	20
65.29	even	6		845.2.o.e.258.2		20
65.33	even	12		845.2.k.d.577.3		20
65.34	odd	4		845.2.t.e.188.2		20
65.38	odd	4		845.2.t.g.657.4		20
65.43	odd	12		845.2.f.d.437.3		20
65.44	odd	4		845.2.t.f.188.4		20
65.48	odd	12		845.2.f.e.437.8		20
65.49	even	6		845.2.o.f.258.4		20
65.54	odd	12		65.2.t.a.28.2	yes	20
65.58	even	12		845.2.k.e.577.8		20
65.59	odd	12		845.2.f.d.408.8		20
65.63	even	12		845.2.o.g.587.4		20
65.64	even	2		845.2.o.g.488.4		20
195.119	even	12		585.2.dp.a.28.4		20
195.158	odd	12		585.2.cf.a.262.4		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.o.a.2.2	✓	20	65.28	even	12
65.2.o.a.33.2	yes	20	5.4	even	2
65.2.t.a.7.2	yes	20	5.3	odd	4
65.2.t.a.28.2	yes	20	65.54	odd	12
325.2.s.b.132.4		20	65.2	even	12	inner
325.2.s.b.293.4		20	1.1	even	1	trivial
325.2.x.b.7.4		20	5.2	odd	4
325.2.x.b.93.4		20	13.2	odd	12
585.2.cf.a.163.4		20	15.14	odd	2
585.2.cf.a.262.4		20	195.158	odd	12
585.2.dp.a.28.4		20	195.119	even	12
585.2.dp.a.397.4		20	15.8	even	4
845.2.f.d.408.8		20	65.59	odd	12
845.2.f.d.437.3		20	65.43	odd	12
845.2.f.e.408.3		20	65.19	odd	12
845.2.f.e.437.8		20	65.48	odd	12
845.2.k.d.268.3		20	65.4	even	6
845.2.k.d.577.3		20	65.33	even	12
845.2.k.e.268.8		20	65.9	even	6
845.2.k.e.577.8		20	65.58	even	12
845.2.o.e.258.2		20	65.29	even	6
845.2.o.e.357.2		20	65.18	even	4
845.2.o.f.258.4		20	65.49	even	6
845.2.o.f.357.4		20	65.8	even	4
845.2.o.g.488.4		20	65.64	even	2
845.2.o.g.587.4		20	65.63	even	12
845.2.t.e.188.2		20	65.34	odd	4
845.2.t.e.427.2		20	65.23	odd	12
845.2.t.f.188.4		20	65.44	odd	4
845.2.t.f.427.4		20	65.3	odd	12
845.2.t.g.418.4		20	65.24	odd	12
845.2.t.g.657.4		20	65.38	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 325 = 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	325.s (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.915816 - 1.58624i) q^{2} +(-1.91432 + 0.512942i) q^{3} +(-0.677439 - 1.17336i) q^{4} +(-0.939520 + 3.50634i) q^{6} +(3.06478 - 1.76945i) q^{7} +1.18163 q^{8} +(0.803451 - 0.463873i) q^{9} +(-1.00269 - 3.74209i) q^{11} +(1.89870 + 1.89870i) q^{12} +(-0.573112 - 3.55971i) q^{13} -6.48197i q^{14} +(2.43703 - 4.22106i) q^{16} +(-0.524334 + 1.95684i) q^{17} -1.69929i q^{18} +(-0.518968 - 0.139057i) q^{19} +(-4.95936 + 4.95936i) q^{21} +(-6.85414 - 1.83656i) q^{22} +(-0.0788026 - 0.294095i) q^{23} +(-2.26202 + 0.606106i) q^{24} +(-6.17142 - 2.35095i) q^{26} +(2.90402 - 2.90402i) q^{27} +(-4.15240 - 2.39739i) q^{28} +(1.71273 + 0.988843i) q^{29} +(4.13563 + 4.13563i) q^{31} +(-3.28212 - 5.68479i) q^{32} +(3.83895 + 6.64926i) q^{33} +(2.62382 + 2.62382i) q^{34} +(-1.08858 - 0.628491i) q^{36} +(-4.69189 - 2.70887i) q^{37} +(-0.695857 + 0.695857i) q^{38} +(2.92305 + 6.52047i) q^{39} +(0.649884 - 0.174136i) q^{41} +(3.32487 + 12.4086i) q^{42} +(8.51164 + 2.28069i) q^{43} +(-3.71155 + 3.71155i) q^{44} +(-0.538675 - 0.144337i) q^{46} +9.75201i q^{47} +(-2.50011 + 9.33053i) q^{48} +(2.76192 - 4.78379i) q^{49} -4.01498i q^{51} +(-3.78857 + 3.08395i) q^{52} +(-3.16254 - 3.16254i) q^{53} +(-1.94693 - 7.26602i) q^{54} +(3.62143 - 2.09083i) q^{56} +1.06480 q^{57} +(3.13709 - 1.81120i) q^{58} +(-3.14703 + 11.7449i) q^{59} +(1.44316 + 2.49963i) q^{61} +(10.3476 - 2.77263i) q^{62} +(1.64160 - 2.84334i) q^{63} -2.27514 q^{64} +14.0631 q^{66} +(1.14494 - 1.98310i) q^{67} +(2.65128 - 0.710408i) q^{68} +(0.301707 + 0.522573i) q^{69} +(-1.19607 + 4.46378i) q^{71} +(0.949380 - 0.548125i) q^{72} -14.7546 q^{73} +(-8.59382 + 4.96165i) q^{74} +(0.188405 + 0.703137i) q^{76} +(-9.69449 - 9.69449i) q^{77} +(13.0200 + 1.33490i) q^{78} -1.59718i q^{79} +(-5.46126 + 9.45918i) q^{81} +(0.318953 - 1.19035i) q^{82} +7.57341i q^{83} +(9.17877 + 2.45944i) q^{84} +(11.4128 - 11.4128i) q^{86} +(-3.78593 - 1.01444i) q^{87} +(-1.18481 - 4.42176i) q^{88} +(-4.54423 + 1.21762i) q^{89} +(-8.05520 - 9.89564i) q^{91} +(-0.291695 + 0.291695i) q^{92} +(-10.0383 - 5.79560i) q^{93} +(15.4690 + 8.93105i) q^{94} +(9.19900 + 9.19900i) q^{96} +(8.91268 + 15.4372i) q^{97} +(-5.05883 - 8.76215i) q^{98} +(-2.54147 - 2.54147i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 4 q^{2} + 2 q^{3} - 6 q^{4} - 8 q^{6} + 6 q^{7} - 12 q^{8} - 12 q^{9} - 16 q^{11} - 24 q^{12} - 2 q^{13} - 2 q^{16} + 10 q^{17} + 20 q^{19} + 4 q^{21} - 16 q^{22} + 2 q^{23} - 32 q^{24} - 24 q^{26}+ \cdots - 60 q^{99}+O(q^{100}) \) 20 * q + 4 * q^2 + 2 * q^3 - 6 * q^4 - 8 * q^6 + 6 * q^7 - 12 * q^8 - 12 * q^9 - 16 * q^11 - 24 * q^12 - 2 * q^13 - 2 * q^16 + 10 * q^17 + 20 * q^19 + 4 * q^21 - 16 * q^22 + 2 * q^23 - 32 * q^24 - 24 * q^26 - 4 * q^27 - 6 * q^28 + 6 * q^32 + 18 * q^33 - 2 * q^34 + 36 * q^36 - 42 * q^37 - 8 * q^38 - 4 * q^39 + 10 * q^41 + 56 * q^42 + 22 * q^43 + 36 * q^44 + 4 * q^46 - 28 * q^48 - 18 * q^49 - 46 * q^52 + 10 * q^53 + 48 * q^54 + 12 * q^57 + 90 * q^58 + 16 * q^59 - 16 * q^61 + 40 * q^62 + 32 * q^63 - 20 * q^64 - 32 * q^66 + 58 * q^67 - 28 * q^68 + 16 * q^69 - 16 * q^71 + 66 * q^72 - 72 * q^73 - 18 * q^74 - 64 * q^76 - 28 * q^77 - 32 * q^78 - 14 * q^81 - 22 * q^82 + 40 * q^84 + 60 * q^86 - 62 * q^87 - 50 * q^88 + 6 * q^89 + 8 * q^91 + 8 * q^92 - 48 * q^93 + 48 * q^94 + 56 * q^96 + 22 * q^97 - 4 * q^98 - 60 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more