LMFDB - Embedded newform 275.2.z.b.124.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [275,2,Mod(49,275)] 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("275.49"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(275, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([5, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 275 = 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	275.z (of order $10$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,0,12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

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

Self dual:	no
Analytic conductor:	$2.19588605559$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 11x^{14} + 56x^{12} - 141x^{10} + 551x^{8} - 1245x^{6} + 1400x^{4} + 125x^{2} + 625 $ x^16 - 11x^14 + 56x^12 - 141x^10 + 551x^8 - 1245x^6 + 1400x^4 + 125*x^2 + 625
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 55)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			124.4
Root			$2.34600 - 0.762262i$ of defining polynomial
Character	$\chi$	$=$	275.124
Dual form			275.2.z.b.224.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.48388 + 2.04238i) q^{2} +(2.34600 - 0.762262i) q^{3} +(-1.35140 + 4.15918i) q^{4} +(5.03801 + 3.66033i) q^{6} +(-1.99105 - 0.646930i) q^{7} +(-5.69802 + 1.85140i) q^{8} +(2.49563 - 1.81318i) q^{9} +(-1.64693 - 2.87882i) q^{11} +10.7876i q^{12} +(-0.757336 - 1.04238i) q^{13} +(-1.63319 - 5.02644i) q^{14} +(-5.16042 - 3.74926i) q^{16} +(1.75822 - 2.41998i) q^{17} +(7.40641 + 2.40649i) q^{18} +(-0.664789 - 2.04601i) q^{19} -5.16413 q^{21} +(3.43582 - 7.63548i) q^{22} +8.77882i q^{23} +(-11.9563 + 8.68677i) q^{24} +(1.00515 - 3.09354i) q^{26} +(0.122903 - 0.169161i) q^{27} +(5.38140 - 7.40686i) q^{28} +(0.189313 - 0.582646i) q^{29} +(2.94887 - 2.14248i) q^{31} -4.12048i q^{32} +(-6.05812 - 5.49833i) q^{33} +7.55150 q^{34} +(4.16875 + 12.8301i) q^{36} +(1.77921 + 0.578100i) q^{37} +(3.19227 - 4.39378i) q^{38} +(-2.57128 - 1.86814i) q^{39} +(-1.57810 - 4.85689i) q^{41} +(-7.66294 - 10.5471i) q^{42} +5.17287i q^{43} +(14.1992 - 2.95944i) q^{44} +(-17.9297 + 13.0267i) q^{46} +(-6.94907 + 2.25789i) q^{47} +(-14.9643 - 4.86218i) q^{48} +(-2.11737 - 1.53836i) q^{49} +(2.28012 - 7.01749i) q^{51} +(5.35892 - 1.74122i) q^{52} +(1.72939 + 2.38030i) q^{53} +0.527864 q^{54} +12.5428 q^{56} +(-3.11919 - 4.29320i) q^{57} +(1.47090 - 0.477925i) q^{58} +(2.00682 - 6.17636i) q^{59} +(0.406490 + 0.295332i) q^{61} +(8.75154 + 2.84355i) q^{62} +(-6.14191 + 1.99563i) q^{63} +(-1.90523 + 1.38423i) q^{64} +(2.24019 - 20.5318i) q^{66} +7.80964i q^{67} +(7.68907 + 10.5831i) q^{68} +(6.69176 + 20.5951i) q^{69} +(9.14526 + 6.64442i) q^{71} +(-10.8632 + 14.9519i) q^{72} +(-10.5730 - 3.43539i) q^{73} +(1.45943 + 4.49166i) q^{74} +9.40812 q^{76} +(1.41672 + 6.79732i) q^{77} -8.02363i q^{78} +(4.33558 - 3.14998i) q^{79} +(-2.70035 + 8.31082i) q^{81} +(7.57793 - 10.4301i) q^{82} +(6.37474 - 8.77408i) q^{83} +(6.97880 - 21.4785i) q^{84} +(-10.5650 + 7.67591i) q^{86} -1.51119i q^{87} +(14.7141 + 13.3545i) q^{88} +4.32336 q^{89} +(0.833541 + 2.56538i) q^{91} +(-36.5127 - 11.8637i) q^{92} +(5.28493 - 7.27408i) q^{93} +(-14.9230 - 10.8422i) q^{94} +(-3.14089 - 9.66666i) q^{96} +(-0.206696 - 0.284493i) q^{97} -6.60723i q^{98} +(-9.32995 - 4.19829i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 12 q^{4} + 26 q^{6} + 10 q^{9} - 10 q^{11} - 32 q^{14} - 40 q^{16} + 2 q^{19} - 24 q^{21} - 50 q^{24} - 28 q^{26} - 38 q^{29} + 12 q^{31} + 40 q^{34} + 42 q^{36} - 18 q^{39} - 8 q^{41} + 56 q^{44}+ \cdots - 8 q^{99}+O(q^{100}) $ 16 * q + 12 * q^4 + 26 * q^6 + 10 * q^9 - 10 * q^11 - 32 * q^14 - 40 * q^16 + 2 * q^19 - 24 * q^21 - 50 * q^24 - 28 * q^26 - 38 * q^29 + 12 * q^31 + 40 * q^34 + 42 * q^36 - 18 * q^39 - 8 * q^41 + 56 * q^44 - 82 * q^46 + 30 * q^49 + 26 * q^51 + 80 * q^54 + 60 * q^56 + 38 * q^59 - 4 * q^61 - 12 * q^64 + 26 * q^66 + 42 * q^69 + 80 * q^71 - 96 * q^74 + 32 * q^76 - 34 * q^79 + 8 * q^84 - 62 * q^86 - 24 * q^91 - 66 * q^94 + 46 * q^96 - 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/275\mathbb{Z}\right)^\times$.

$n$	$101$	$177$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$-1$

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 $

$2$	1.48388	+	2.04238i	1.04926	+	1.44418i	0.889449	+	0.457035i	$0.151089\pi$
$2$	1.48388	+	2.04238i	1.04926	+	1.44418i	0.159812	+	0.987148i	$0.448911\pi$
$3$	2.34600	−	0.762262i	1.35446	−	0.440092i	0.460273	−	0.887777i	$-0.347751\pi$
$3$	2.34600	−	0.762262i	1.35446	−	0.440092i	0.894191	+	0.447685i	$0.147751\pi$
$4$	−1.35140	+	4.15918i	−0.675700	+	2.07959i
$5$		0			0
$5$		0			0
$6$	5.03801	+	3.66033i	2.05676	+	1.49432i
$7$	−1.99105	−	0.646930i	−0.752545	−	0.244517i	−0.0924689	−	0.995716i	$-0.529476\pi$
$7$	−1.99105	−	0.646930i	−0.752545	−	0.244517i	−0.660076	+	0.751199i	$0.729476\pi$
$8$	−5.69802	+	1.85140i	−2.01456	+	0.654569i
$9$	2.49563	−	1.81318i	0.831876	−	0.604393i
$10$		0			0
$11$	−1.64693	−	2.87882i	−0.496568	−	0.867998i
$11$	−1.64693	−	2.87882i	−0.496568	−	0.867998i
$12$			10.7876i			3.11410i
$13$	−0.757336	−	1.04238i	−0.210047	−	0.289105i	0.690975	−	0.722879i	$-0.257182\pi$
$13$	−0.757336	−	1.04238i	−0.210047	−	0.289105i	−0.901022	+	0.433774i	$0.857182\pi$
$14$	−1.63319	−	5.02644i	−0.436489	−	1.34337i
$15$		0			0
$16$	−5.16042	−	3.74926i	−1.29010	−	0.937316i
$17$	1.75822	−	2.41998i	0.426430	−	0.586931i	−0.540699	−	0.841216i	$-0.681840\pi$
$17$	1.75822	−	2.41998i	0.426430	−	0.586931i	0.967129	+	0.254285i	$0.0818403\pi$
$18$	7.40641	+	2.40649i	1.74571	+	0.567215i
$19$	−0.664789	−	2.04601i	−0.152513	−	0.469387i	0.845387	−	0.534154i	$-0.179370\pi$
$19$	−0.664789	−	2.04601i	−0.152513	−	0.469387i	−0.997900	+	0.0647668i	$0.979370\pi$
$20$		0			0
$21$	−5.16413			−1.12690
$22$	3.43582	−	7.63548i	0.732518	−	1.62789i
$23$			8.77882i			1.83051i	0.402874	+	0.915255i	$0.368011\pi$
$23$			8.77882i			1.83051i	−0.402874	+	0.915255i	$0.631989\pi$
$24$	−11.9563	+	8.68677i	−2.44057	+	1.77318i
$25$		0			0
$26$	1.00515	−	3.09354i	0.197126	−	0.606693i
$27$	0.122903	−	0.169161i	0.0236526	−	0.0325550i
$28$	5.38140	−	7.40686i	1.01699	−	1.39977i
$29$	0.189313	−	0.582646i	0.0351545	−	0.108195i	−0.931939	−	0.362614i	$-0.881884\pi$
$29$	0.189313	−	0.582646i	0.0351545	−	0.108195i	0.967094	+	0.254419i	$0.0818844\pi$
$30$		0			0
$31$	2.94887	−	2.14248i	0.529633	−	0.384801i	−0.290587	−	0.956848i	$-0.593851\pi$
$31$	2.94887	−	2.14248i	0.529633	−	0.384801i	0.820221	+	0.572047i	$0.193851\pi$
$32$		−	4.12048i		−	0.728405i
$33$	−6.05812	−	5.49833i	−1.05458	−	0.957136i
$34$	7.55150			1.29507
$35$		0			0
$36$	4.16875	+	12.8301i	0.694792	+	2.13835i
$37$	1.77921	+	0.578100i	0.292500	+	0.0950391i	0.451592	−	0.892225i	$-0.350856\pi$
$37$	1.77921	+	0.578100i	0.292500	+	0.0950391i	−0.159091	+	0.987264i	$0.550856\pi$
$38$	3.19227	−	4.39378i	0.517855	−	0.712766i
$39$	−2.57128	−	1.86814i	−0.411734	−	0.299142i
$40$		0			0
$41$	−1.57810	−	4.85689i	−0.246458	−	0.758519i	−0.995393	−	0.0958763i	$-0.969435\pi$
$41$	−1.57810	−	4.85689i	−0.246458	−	0.758519i	0.748935	−	0.662643i	$-0.230565\pi$
$42$	−7.66294	−	10.5471i	−1.18242	−	1.62746i
$43$			5.17287i			0.788856i	0.918927	+	0.394428i	$0.129057\pi$
$43$			5.17287i			0.788856i	−0.918927	+	0.394428i	$0.870943\pi$
$44$	14.1992	−	2.95944i	2.14061	−	0.446152i
$45$		0			0
$46$	−17.9297	+	13.0267i	−2.64359	+	1.92068i
$47$	−6.94907	+	2.25789i	−1.01363	+	0.329347i	−0.768298	−	0.640093i	$-0.778896\pi$
$47$	−6.94907	+	2.25789i	−1.01363	+	0.329347i	−0.245329	+	0.969440i	$0.578896\pi$
$48$	−14.9643	−	4.86218i	−2.15991	−	0.701796i
$49$	−2.11737	−	1.53836i	−0.302482	−	0.219766i
$50$		0			0
$51$	2.28012	−	7.01749i	0.319281	−	0.982645i
$52$	5.35892	−	1.74122i	0.743149	−	0.241464i
$53$	1.72939	+	2.38030i	0.237549	+	0.326959i	0.911102	−	0.412180i	$-0.135233\pi$
$53$	1.72939	+	2.38030i	0.237549	+	0.326959i	−0.673553	+	0.739139i	$0.735233\pi$
$54$	0.527864			0.0718332
$55$		0			0
$56$	12.5428			1.67610
$57$	−3.11919	−	4.29320i	−0.413147	−	0.568648i
$58$	1.47090	−	0.477925i	0.193139	−	0.0627547i
$59$	2.00682	−	6.17636i	0.261266	−	0.804094i	−0.731264	−	0.682094i	$-0.761069\pi$
$59$	2.00682	−	6.17636i	0.261266	−	0.804094i	0.992530	−	0.121999i	$-0.0389306\pi$
$60$		0			0
$61$	0.406490	+	0.295332i	0.0520457	+	0.0378134i	0.613504	−	0.789692i	$-0.289759\pi$
$61$	0.406490	+	0.295332i	0.0520457	+	0.0378134i	−0.561458	+	0.827505i	$0.689759\pi$
$62$	8.75154	+	2.84355i	1.11145	+	0.361131i
$63$	−6.14191	+	1.99563i	−0.773808	+	0.251425i
$64$	−1.90523	+	1.38423i	−0.238154	+	0.173029i
$65$		0			0
$66$	2.24019	−	20.5318i	0.275748	−	2.52730i
$67$			7.80964i			0.954099i	0.878876	+	0.477050i	$0.158294\pi$
$67$			7.80964i			0.954099i	−0.878876	+	0.477050i	$0.841706\pi$
$68$	7.68907	+	10.5831i	0.932437	+	1.28339i
$69$	6.69176	+	20.5951i	0.805594	+	2.47936i
$70$		0			0
$71$	9.14526	+	6.64442i	1.08534	+	0.788548i	0.978607	−	0.205740i	$-0.0659600\pi$
$71$	9.14526	+	6.64442i	1.08534	+	0.788548i	0.106736	+	0.994287i	$0.465960\pi$
$72$	−10.8632	+	14.9519i	−1.28024	+	1.76210i
$73$	−10.5730	−	3.43539i	−1.23748	−	0.402082i	−0.384061	−	0.923308i	$-0.625475\pi$
$73$	−10.5730	−	3.43539i	−1.23748	−	0.402082i	−0.853419	+	0.521226i	$0.825475\pi$
$74$	1.45943	+	4.49166i	0.169655	+	0.522145i
$75$		0			0
$76$	9.40812			1.07919
$77$	1.41672	+	6.79732i	0.161450	+	0.774626i
$78$		−	8.02363i		−	0.908498i
$79$	4.33558	−	3.14998i	0.487791	−	0.354401i	−0.316543	−	0.948578i	$-0.602522\pi$
$79$	4.33558	−	3.14998i	0.487791	−	0.354401i	0.804334	+	0.594177i	$0.202522\pi$
$80$		0			0
$81$	−2.70035	+	8.31082i	−0.300039	+	0.923425i
$82$	7.57793	−	10.4301i	0.836842	−	1.15181i
$83$	6.37474	−	8.77408i	0.699719	−	0.963080i	−0.300239	−	0.953864i	$-0.597066\pi$
$83$	6.37474	−	8.77408i	0.699719	−	0.963080i	0.999958	−	0.00921619i	$-0.00293364\pi$
$84$	6.97880	−	21.4785i	0.761450	−	2.34350i
$85$		0			0
$86$	−10.5650	+	7.67591i	−1.13925	+	0.827715i
$87$		−	1.51119i		−	0.162017i
$88$	14.7141	+	13.3545i	1.56853	+	1.42359i
$89$	4.32336			0.458275			0.229137	−	0.973394i	$-0.426409\pi$
$89$	4.32336			0.458275			0.229137	+	0.973394i	$0.426409\pi$
$90$		0			0
$91$	0.833541	+	2.56538i	0.0873788	+	0.268924i
$92$	−36.5127	−	11.8637i	−3.80671	−	1.23688i
$93$	5.28493	−	7.27408i	0.548021	−	0.754287i
$94$	−14.9230	−	10.8422i	−1.53920	−	1.11829i
$95$		0			0
$96$	−3.14089	−	9.66666i	−0.320566	−	0.986599i
$97$	−0.206696	−	0.284493i	−0.0209868	−	0.0288859i	0.798395	−	0.602135i	$-0.205683\pi$
$97$	−0.206696	−	0.284493i	−0.0209868	−	0.0288859i	−0.819381	+	0.573249i	$0.805683\pi$
$98$		−	6.60723i		−	0.667431i
$99$	−9.32995	−	4.19829i	−0.937695	−	0.421944i
$100$		0			0
$101$	12.7011	−	9.22791i	1.26381	−	0.918211i	0.264872	−	0.964284i	$-0.414670\pi$
$101$	12.7011	−	9.22791i	1.26381	−	0.918211i	0.998938	+	0.0460722i	$0.0146704\pi$
$102$	17.7158	−	5.75622i	1.75413	−	0.569951i
$103$	6.35297	+	2.06420i	0.625977	+	0.203392i	0.604792	−	0.796383i	$-0.293256\pi$
$103$	6.35297	+	2.06420i	0.625977	+	0.203392i	0.0211846	+	0.999776i	$0.493256\pi$
$104$	6.24518	+	4.53739i	0.612391	+	0.444928i
$105$		0			0
$106$	−2.29528	+	7.06414i	−0.222937	+	0.686130i
$107$	14.8441	−	4.82313i	1.43503	−	0.466269i	0.514685	−	0.857379i	$-0.327909\pi$
$107$	14.8441	−	4.82313i	1.43503	−	0.466269i	0.920344	+	0.391110i	$0.127909\pi$
$108$	0.537481	+	0.739779i	0.0517191	+	0.0711852i
$109$	−11.5070			−1.10217			−0.551087	−	0.834448i	$-0.685787\pi$
$109$	−11.5070			−1.10217			−0.551087	+	0.834448i	$0.685787\pi$
$110$		0			0
$111$	4.61469			0.438007
$112$	7.84912	+	10.8034i	0.741672	+	1.02082i
$113$	−8.60538	+	2.79606i	−0.809526	+	0.263031i	−0.684397	−	0.729110i	$-0.739934\pi$
$113$	−8.60538	+	2.79606i	−0.809526	+	0.263031i	−0.125129	+	0.992140i	$0.539934\pi$
$114$	4.13986	−	12.7412i	0.387733	−	1.19332i
$115$		0			0
$116$	2.16749	+	1.57477i	0.201246	+	0.146214i
$117$	−3.78006	−	1.22821i	−0.349466	−	0.113548i
$118$	15.5924	−	5.06627i	1.43539	−	0.466388i
$119$	−5.06625	+	3.68084i	−0.464422	+	0.337422i
$120$		0			0
$121$	−5.57524	+	9.48244i	−0.506840	+	0.862040i
$122$			1.26845i			0.114840i
$123$	−7.40445	−	10.1914i	−0.667637	−	0.918923i
$124$	4.92586	+	15.1602i	0.442356	+	1.36143i
$125$		0			0
$126$	−13.1897	−	9.58287i	−1.17503	−	0.853710i
$127$	−11.0704	+	15.2371i	−0.982339	+	1.35207i	−0.0467796	+	0.998905i	$0.514896\pi$
$127$	−11.0704	+	15.2371i	−0.982339	+	1.35207i	−0.935560	+	0.353169i	$0.885104\pi$
$128$	−13.4919	−	4.38378i	−1.19252	−	0.387475i
$129$	3.94308	+	12.1356i	0.347169	+	1.06848i
$130$		0			0
$131$	−20.0997			−1.75612			−0.878058	−	0.478555i	$-0.841161\pi$
$131$	−20.0997			−1.75612			−0.878058	+	0.478555i	$0.841161\pi$
$132$	31.0555	−	17.7664i	2.70303	−	1.54636i
$133$			4.50377i			0.390527i
$134$	−15.9503	+	11.5886i	−1.37789	+	1.00110i
$135$		0			0
$136$	−5.53801	+	17.0442i	−0.474881	+	1.46153i
$137$	10.5632	−	14.5390i	0.902478	−	1.24215i	−0.0671930	−	0.997740i	$-0.521404\pi$
$137$	10.5632	−	14.5390i	0.902478	−	1.24215i	0.969671	−	0.244414i	$-0.0785957\pi$
$138$	−32.1334	+	44.2278i	−2.73537	+	3.76492i
$139$	−5.21098	+	16.0377i	−0.441989	+	1.36030i	0.443762	+	0.896145i	$0.353643\pi$
$139$	−5.21098	+	16.0377i	−0.441989	+	1.36030i	−0.885752	+	0.464159i	$0.846357\pi$
$140$		0			0
$141$	−14.5814	+	10.5940i	−1.22798	+	0.892178i
$142$			28.5376i			2.39482i
$143$	−1.75356	+	3.89697i	−0.146640	+	0.325881i
$144$	−19.6766			−1.63971
$145$		0			0
$146$	−8.67272	−	26.6919i	−0.717759	−	2.20904i
$147$	−6.13999	−	1.99500i	−0.506418	−	0.164545i
$148$	−4.80885	+	6.61881i	−0.395285	+	0.544063i
$149$	1.88797	+	1.37169i	0.154669	+	0.112373i	0.662428	−	0.749126i	$-0.269526\pi$
$149$	1.88797	+	1.37169i	0.154669	+	0.112373i	−0.507759	+	0.861499i	$0.669526\pi$
$150$		0			0
$151$	−1.21718	−	3.74609i	−0.0990525	−	0.304852i	0.889236	−	0.457448i	$-0.151237\pi$
$151$	−1.21718	−	3.74609i	−0.0990525	−	0.304852i	−0.988289	+	0.152596i	$0.951237\pi$
$152$	7.57597	+	10.4274i	0.614492	+	0.845776i
$153$		−	9.22732i		−	0.745985i
$154$	−11.7805	+	12.9799i	−0.949299	+	1.04595i
$155$		0			0
$156$	11.2448	−	8.16981i	0.900302	−	0.654108i
$157$	−4.64218	+	1.50834i	−0.370486	+	0.120378i	−0.488342	−	0.872652i	$-0.662398\pi$
$157$	−4.64218	+	1.50834i	−0.370486	+	0.120378i	0.117856	+	0.993031i	$0.462398\pi$
$158$	12.8669	+	4.18073i	1.02364	+	0.332601i
$159$	5.87155	+	4.26593i	0.465644	+	0.338310i
$160$		0			0
$161$	5.67928	−	17.4790i	0.447590	−	1.37754i
$162$	−20.9809	+	6.81710i	−1.64841	+	0.535602i
$163$	4.13549	+	5.69202i	0.323917	+	0.445833i	0.939658	−	0.342115i	$-0.111143\pi$
$163$	4.13549	+	5.69202i	0.323917	+	0.445833i	−0.615741	+	0.787948i	$0.711143\pi$
$164$	22.3333			1.74394
$165$		0			0
$166$	27.3794			2.12505
$167$	6.30075	+	8.67223i	0.487566	+	0.671078i	0.979937	−	0.199308i	$-0.0638695\pi$
$167$	6.30075	+	8.67223i	0.487566	+	0.671078i	−0.492370	+	0.870386i	$0.663869\pi$
$168$	29.4253	−	9.56086i	2.27021	−	0.737637i
$169$	3.50422	−	10.7849i	0.269555	−	0.829605i
$170$		0			0
$171$	−5.36885	−	3.90070i	−0.410566	−	0.298294i
$172$	−21.5149	−	6.99062i	−1.64050	−	0.533030i
$173$	−8.00012	+	2.59940i	−0.608238	+	0.197628i	−0.596911	−	0.802307i	$-0.703605\pi$
$173$	−8.00012	+	2.59940i	−0.608238	+	0.197628i	−0.0113267	+	0.999936i	$0.503605\pi$
$174$	3.08644	−	2.24243i	0.233982	−	0.169998i
$175$		0			0
$176$	−2.29462	+	21.0307i	−0.172963	+	1.58525i
$177$		−	16.0195i		−	1.20410i
$178$	6.41533	+	8.82995i	0.480850	+	0.661833i
$179$	−6.50062	−	20.0069i	−0.485879	−	1.49538i	−0.830703	−	0.556716i	$-0.812061\pi$
$179$	−6.50062	−	20.0069i	−0.485879	−	1.49538i	0.344824	−	0.938667i	$-0.387939\pi$
$180$		0			0
$181$	1.41020	+	1.02457i	0.104819	+	0.0761557i	0.638960	−	0.769240i	$-0.279365\pi$
$181$	1.41020	+	1.02457i	0.104819	+	0.0761557i	−0.534141	+	0.845395i	$0.679365\pi$
$182$	−4.00261	+	5.50911i	−0.296693	+	0.408363i
$183$	1.17875	+	0.382998i	0.0871355	+	0.0283120i
$184$	−16.2531	−	50.0219i	−1.19820	−	3.68767i
$185$		0			0
$186$	22.6986			1.66435
$187$	−9.86234	−	1.07606i	−0.721206	−	0.0786893i
$188$		−	31.9538i		−	2.33047i
$189$	−0.354140	+	0.257298i	−0.0257599	+	0.0187157i
$190$		0			0
$191$	0.00771200	−	0.0237351i	0.000558021	−	0.00171741i	−0.950777	−	0.309876i	$-0.899713\pi$
$191$	0.00771200	−	0.0237351i	0.000558021	−	0.00171741i	0.951335	+	0.308158i	$0.0997126\pi$
$192$	−3.41452	+	4.69969i	−0.246422	+	0.339171i
$193$	0.856548	−	1.17894i	0.0616557	−	0.0848618i	−0.777076	−	0.629407i	$-0.783298\pi$
$193$	0.856548	−	1.17894i	0.0616557	−	0.0848618i	0.838731	+	0.544545i	$0.183298\pi$
$194$	0.274331	−	0.844306i	0.0196959	−	0.0606176i
$195$		0			0
$196$	9.25974	−	6.72759i	0.661410	−	0.480542i
$197$		−	22.7027i		−	1.61750i	−0.588151	−	0.808751i	$-0.700144\pi$
$197$		−	22.7027i		−	1.61750i	0.588151	−	0.808751i	$-0.299856\pi$
$198$	−5.26999	−	25.2851i	−0.374522	−	1.79693i
$199$	6.62834			0.469870			0.234935	−	0.972011i	$-0.424512\pi$
$199$	6.62834			0.469870			0.234935	+	0.972011i	$0.424512\pi$
$200$		0			0
$201$	5.95299	+	18.3214i	0.419892	+	1.29229i
$202$	37.6939	+	12.2475i	2.65213	+	0.861729i
$203$	−0.753862	+	1.03760i	−0.0529107	+	0.0728254i
$204$	26.1057	+	18.9669i	1.82776	+	1.32795i
$205$		0			0
$206$	5.21114	+	16.0382i	0.363077	+	1.11744i
$207$	15.9176	+	21.9087i	1.10635	+	1.52276i
$208$			8.21858i			0.569856i
$209$	−4.79524	+	5.28345i	−0.331694	+	0.365464i
$210$		0			0
$211$	−4.57709	+	3.32545i	−0.315100	+	0.228934i	−0.734082	−	0.679061i	$-0.762387\pi$
$211$	−4.57709	+	3.32545i	−0.315100	+	0.228934i	0.418982	+	0.907995i	$0.362387\pi$
$212$	−12.2372	+	3.97610i	−0.840453	+	0.273080i
$213$	26.5196	+	8.61673i	1.81709	+	0.590409i
$214$	31.8774	+	23.1603i	2.17910	+	1.58321i
$215$		0			0
$216$	−0.387117	+	1.19143i	−0.0263400	+	0.0810662i
$217$	−7.25738	+	2.35807i	−0.492663	+	0.160076i
$218$	−17.0750	−	23.5018i	−1.15647	−	1.59174i
$219$	−27.4230			−1.85308
$220$		0			0
$221$	−3.85410			−0.259255
$222$	6.84764	+	9.42497i	0.459584	+	0.632563i
$223$	−7.49852	+	2.43642i	−0.502138	+	0.163155i	−0.549124	−	0.835741i	$-0.685039\pi$
$223$	−7.49852	+	2.43642i	−0.502138	+	0.163155i	0.0469856	+	0.998896i	$0.485039\pi$
$224$	−2.66566	+	8.20407i	−0.178107	+	0.548158i
$225$		0			0
$226$	−18.4800	−	13.4265i	−1.22927	−	0.893116i
$227$	10.6627	+	3.46451i	0.707706	+	0.229948i	0.640685	−	0.767804i	$-0.278650\pi$
$227$	10.6627	+	3.46451i	0.707706	+	0.229948i	0.0670213	+	0.997752i	$0.478650\pi$
$228$	22.0715	−	7.17145i	1.46172	−	0.474941i
$229$	21.8360	−	15.8647i	1.44296	−	1.04837i	0.455547	−	0.890212i	$-0.349444\pi$
$229$	21.8360	−	15.8647i	1.44296	−	1.04837i	0.987413	−	0.158160i	$-0.0505563\pi$
$230$		0			0
$231$	8.50496	+	14.8666i	0.559585	+	0.978151i
$232$			3.67042i			0.240975i
$233$	6.37792	+	8.77845i	0.417831	+	0.575095i	0.965107	−	0.261857i	$-0.0843349\pi$
$233$	6.37792	+	8.77845i	0.417831	+	0.575095i	−0.547275	+	0.836953i	$0.684335\pi$
$234$	−3.10066	−	9.54284i	−0.202696	−	0.623835i
$235$		0			0
$236$	22.9766	+	16.6935i	1.49565	+	1.08665i
$237$	7.77017	−	10.6947i	0.504727	−	0.694697i
$238$	−15.0354	−	4.88529i	−0.974599	−	0.316666i
$239$	3.54327	+	10.9051i	0.229195	+	0.705391i	0.997839	+	0.0657129i	$0.0209322\pi$
$239$	3.54327	+	10.9051i	0.229195	+	0.705391i	−0.768643	+	0.639678i	$0.779068\pi$
$240$		0			0
$241$	12.7542			0.821572			0.410786	−	0.911732i	$-0.365254\pi$
$241$	12.7542			0.821572			0.410786	+	0.911732i	$0.365254\pi$
$242$	−27.6398	+	2.68401i	−1.77675	+	0.172534i
$243$			22.1829i			1.42303i
$244$	−1.77767	+	1.29155i	−0.113804	+	0.0826833i
$245$		0			0
$246$	9.82734	−	30.2455i	0.626568	−	1.92838i
$247$	−1.62926	+	2.24248i	−0.103667	+	0.142686i
$248$	−12.8362	+	17.6675i	−0.815097	+	1.12188i
$249$	8.26700	−	25.4432i	0.523900	−	1.61240i
$250$		0			0
$251$	9.87130	−	7.17192i	0.623071	−	0.452687i	−0.230922	−	0.972972i	$-0.574174\pi$
$251$	9.87130	−	7.17192i	0.623071	−	0.452687i	0.853993	+	0.520285i	$0.174174\pi$
$252$		−	28.2422i		−	1.77909i
$253$	25.2727	−	14.4581i	1.58888	−	0.908973i
$254$	−47.5471			−2.98337
$255$		0			0
$256$	−9.61149	−	29.5811i	−0.600718	−	1.84882i
$257$	5.60747	+	1.82198i	0.349784	+	0.113652i	0.478639	−	0.878012i	$-0.341130\pi$
$257$	5.60747	+	1.82198i	0.349784	+	0.113652i	−0.128855	+	0.991663i	$0.541130\pi$
$258$	−18.9344	+	26.0610i	−1.17881	+	1.62249i
$259$	−3.16850	−	2.30205i	−0.196881	−	0.143042i
$260$		0			0
$261$	−0.583986	−	1.79733i	−0.0361478	−	0.111252i
$262$	−29.8254	−	41.0512i	−1.84262	−	2.53615i
$263$		−	21.7305i		−	1.33996i	−0.742379	−	0.669980i	$-0.766302\pi$
$263$		−	21.7305i		−	1.33996i	0.742379	−	0.669980i	$-0.233698\pi$
$264$	44.6989	+	20.1136i	2.75103	+	1.23791i
$265$		0			0
$266$	−9.19843	+	6.68305i	−0.563992	+	0.409764i
$267$	10.1426	−	3.29553i	0.620717	−	0.201683i
$268$	−32.4817	−	10.5539i	−1.98414	−	0.644685i
$269$	−3.66042	−	2.65945i	−0.223180	−	0.162149i	0.470577	−	0.882359i	$-0.344046\pi$
$269$	−3.66042	−	2.65945i	−0.223180	−	0.162149i	−0.693757	+	0.720209i	$0.744046\pi$
$270$		0			0
$271$	−6.72447	+	20.6958i	−0.408482	+	1.25718i	0.509470	+	0.860488i	$0.329841\pi$
$271$	−6.72447	+	20.6958i	−0.408482	+	1.25718i	−0.917952	+	0.396691i	$0.870159\pi$
$272$	−18.1463	+	5.89608i	−1.10028	+	0.357502i
$273$	3.91098	+	5.38300i	0.236703	+	0.325794i
$274$	45.3688			2.74083
$275$		0			0
$276$	−94.7021			−5.70040
$277$	−7.66154	−	10.5452i	−0.460337	−	0.633600i	0.514241	−	0.857645i	$-0.328074\pi$
$277$	−7.66154	−	10.5452i	−0.460337	−	0.633600i	−0.974579	+	0.224046i	$0.928074\pi$
$278$	−40.4877	+	13.1552i	−2.42829	+	0.788999i
$279$	3.47459	−	10.6937i	0.208018	−	0.640214i
$280$		0			0
$281$	−7.59310	−	5.51671i	−0.452966	−	0.329099i	0.337799	−	0.941218i	$-0.390317\pi$
$281$	−7.59310	−	5.51671i	−0.452966	−	0.329099i	−0.790766	+	0.612119i	$0.790317\pi$
$282$	−43.2741	−	14.0606i	−2.57694	−	0.837297i
$283$	−13.2574	+	4.30760i	−0.788072	+	0.256060i	−0.675283	−	0.737559i	$-0.735979\pi$
$283$	−13.2574	+	4.30760i	−0.788072	+	0.256060i	−0.112789	+	0.993619i	$0.535979\pi$
$284$	−39.9943	+	29.0575i	−2.37322	+	1.72425i
$285$		0			0
$286$	−10.5612	+	2.20119i	−0.624495	+	0.130159i
$287$			10.6912i			0.631083i
$288$	−7.47118	−	10.2832i	−0.440243	−	0.605943i
$289$	2.48832	+	7.65828i	0.146372	+	0.450487i
$290$		0			0
$291$	−0.701768	−	0.509864i	−0.0411383	−	0.0298888i
$292$	28.5768	−	39.3326i	1.67233	−	2.30176i
$293$	28.9787	+	9.41576i	1.69296	+	0.550075i	0.987354	−	0.158534i	$-0.0506766\pi$
$293$	28.9787	+	9.41576i	1.69296	+	0.550075i	0.705602	+	0.708608i	$0.250677\pi$
$294$	−5.03644	−	15.5006i	−0.293731	−	0.904011i
$295$		0			0
$296$	−11.2083			−0.651468
$297$	−0.689397	−	0.0752186i	−0.0400028	−	0.00436463i
$298$			5.89138i			0.341278i
$299$	9.15089	−	6.64851i	0.529210	−	0.384493i
$300$		0			0
$301$	3.34649	−	10.2994i	0.192888	−	0.593649i
$302$	5.84480	−	8.04468i	0.336330	−	0.462919i
$303$	22.7628	−	31.3303i	1.30769	−	1.79988i
$304$	−4.24044	+	13.0507i	−0.243206	+	0.748511i
$305$		0			0
$306$	18.8457	−	13.6922i	1.07734	−	0.782732i
$307$		−	5.08609i		−	0.290278i	−0.989411	−	0.145139i	$-0.953637\pi$
$307$		−	5.08609i		−	0.290278i	0.989411	−	0.145139i	$-0.0463630\pi$
$308$	−30.1858	−	3.29351i	−1.72000	−	0.187665i
$309$	16.4775			0.937375
$310$		0			0
$311$	4.25249	+	13.0878i	0.241136	+	0.742141i	0.996248	+	0.0865451i	$0.0275827\pi$
$311$	4.25249	+	13.0878i	0.241136	+	0.742141i	−0.755112	+	0.655596i	$0.772417\pi$
$312$	18.1099	+	5.88426i	1.02527	+	0.333131i
$313$	9.37676	−	12.9060i	0.530006	−	0.729491i	−0.457125	−	0.889402i	$-0.651121\pi$
$313$	9.37676	−	12.9060i	0.530006	−	0.729491i	0.987131	+	0.159912i	$0.0511209\pi$
$314$	−9.96903	−	7.24292i	−0.562585	−	0.408742i
$315$		0			0
$316$	7.24225	+	22.2894i	0.407408	+	1.25387i
$317$	6.29364	+	8.66246i	0.353486	+	0.486532i	0.948320	−	0.317317i	$-0.102782\pi$
$317$	6.29364	+	8.66246i	0.353486	+	0.486532i	−0.594833	+	0.803849i	$0.702782\pi$
$318$			18.3221i			1.02745i
$319$	−1.98912	+	0.414578i	−0.111369	+	0.0232119i
$320$		0			0
$321$	31.1477	−	22.6301i	1.73849	−	1.26309i
$322$	44.1263	−	14.3375i	2.45906	−	0.798997i
$323$	−6.12014	−	1.98855i	−0.340534	−	0.110646i
$324$	−30.9170	−	22.4625i	−1.71761	−	1.24792i
$325$		0			0
$326$	−5.48871	+	16.8925i	−0.303992	+	0.935590i
$327$	−26.9955	+	8.77138i	−1.49286	+	0.485058i
$328$	17.9841	+	24.7530i	0.993006	+	1.36676i
$329$	15.2966			0.843330
$330$		0			0
$331$	−8.84618			−0.486230			−0.243115	−	0.969997i	$-0.578169\pi$
$331$	−8.84618			−0.486230			−0.243115	+	0.969997i	$0.578169\pi$
$332$	27.8782	+	38.3710i	1.53001	+	2.10588i
$333$	5.48845	−	1.78330i	0.300765	−	0.0977245i
$334$	−8.36248	+	25.7371i	−0.457575	+	1.40827i
$335$		0			0
$336$	26.6491	+	19.3617i	1.45382	+	1.05627i
$337$	11.0225	+	3.58143i	0.600434	+	0.195093i	0.593434	−	0.804883i	$-0.297772\pi$
$337$	11.0225	+	3.58143i	0.600434	+	0.195093i	0.00699978	+	0.999976i	$0.497772\pi$
$338$	27.2267	−	8.84648i	1.48093	−	0.481185i
$339$	−18.0569	+	13.1191i	−0.980716	+	0.712532i
$340$		0			0
$341$	−11.0244	−	4.96077i	−0.597005	−	0.268641i
$342$		−	16.7534i		−	0.905920i
$343$	11.8343	+	16.2885i	0.638993	+	0.879498i
$344$	−9.57705	−	29.4751i	−0.516360	−	1.58919i
$345$		0			0
$346$	−17.1802	−	12.4821i	−0.923611	−	0.671043i
$347$	2.87368	−	3.95529i	0.154267	−	0.212331i	−0.724887	−	0.688868i	$-0.758108\pi$
$347$	2.87368	−	3.95529i	0.154267	−	0.212331i	0.879155	+	0.476537i	$0.158108\pi$
$348$	6.28533	+	2.04223i	0.336929	+	0.109475i
$349$	−0.294654	−	0.906853i	−0.0157725	−	0.0485427i	0.942861	−	0.333188i	$-0.108124\pi$
$349$	−0.294654	−	0.906853i	−0.0157725	−	0.0485427i	−0.958633	+	0.284645i	$0.908124\pi$
$350$		0			0
$351$	−0.269409			−0.0143800
$352$	−11.8621	+	6.78615i	−0.632254	+	0.361703i
$353$		−	15.5166i		−	0.825865i	−0.910762	−	0.412933i	$-0.864505\pi$
$353$		−	15.5166i		−	0.825865i	0.910762	−	0.412933i	$-0.135495\pi$
$354$	32.7179	−	23.7709i	1.73894	−	1.26341i
$355$		0			0
$356$	−5.84258	+	17.9816i	−0.309656	+	0.953024i
$357$	−9.07965	+	12.4971i	−0.480546	+	0.661415i
$358$	31.2155	−	42.9645i	1.64979	−	2.27074i
$359$	−6.25915	+	19.2637i	−0.330345	+	1.01670i	0.638624	+	0.769519i	$0.279504\pi$
$359$	−6.25915	+	19.2637i	−0.330345	+	1.01670i	−0.968970	+	0.247180i	$0.920496\pi$
$360$		0			0
$361$	11.6271	−	8.44759i	0.611953	−	0.444610i
$362$			4.40051i			0.231286i
$363$	−5.85142	+	26.4956i	−0.307120	+	1.39066i
$364$	−11.7963			−0.618295
$365$		0			0
$366$	0.966888	+	2.97578i	0.0505400	+	0.155546i
$367$	−33.9099	−	11.0180i	−1.77008	−	0.575135i	−0.771920	−	0.635719i	$-0.780704\pi$
$367$	−33.9099	−	11.0180i	−1.77008	−	0.575135i	−0.998163	+	0.0605844i	$0.980704\pi$
$368$	32.9141	−	45.3024i	1.71577	−	2.36155i
$369$	−12.7448	−	9.25962i	−0.663466	−	0.482037i
$370$		0			0
$371$	−1.90340	−	5.85807i	−0.0988198	−	0.304136i
$372$	23.1122	+	31.8112i	1.19831	+	1.64933i
$373$			12.1358i			0.628370i	0.949362	+	0.314185i	$0.101731\pi$
$373$			12.1358i			0.628370i	−0.949362	+	0.314185i	$0.898269\pi$
$374$	−12.4368	−	21.7394i	−0.643091	−	1.12412i
$375$		0			0
$376$	35.4157	−	25.7310i	1.82643	−	1.32698i
$377$	−0.750713	+	0.243922i	−0.0386637	+	0.0125626i
$378$	−1.05100	−	0.341491i	−0.0540577	−	0.0175644i
$379$	5.77971	+	4.19921i	0.296884	+	0.215699i	0.726248	−	0.687433i	$-0.241262\pi$
$379$	5.77971	+	4.19921i	0.296884	+	0.215699i	−0.429364	+	0.903131i	$0.641262\pi$
$380$		0			0
$381$	−14.3565	+	44.1848i	−0.735506	+	2.26366i
$382$	0.0599198	−	0.0194691i	0.00306576	−	0.000996127i
$383$	−9.38279	−	12.9143i	−0.479438	−	0.659890i	0.498959	−	0.866626i	$-0.333716\pi$
$383$	−9.38279	−	12.9143i	−0.479438	−	0.659890i	−0.978397	+	0.206736i	$0.933716\pi$
$384$	−34.9936			−1.78576
$385$		0			0
$386$	3.67885			0.187249
$387$	9.37935	+	12.9096i	0.476779	+	0.656230i
$388$	1.46259	−	0.475223i	0.0742516	−	0.0241258i
$389$	7.75336	−	23.8624i	0.393111	−	1.20987i	−0.537312	−	0.843384i	$-0.680560\pi$
$389$	7.75336	−	23.8624i	0.393111	−	1.20987i	0.930423	−	0.366488i	$-0.119440\pi$
$390$		0			0
$391$	21.2445	+	15.4351i	1.07438	+	0.780585i
$392$	14.9130	+	4.84551i	0.753218	+	0.244735i
$393$	−47.1538	+	15.3212i	−2.37860	+	0.772853i
$394$	46.3677	−	33.6881i	2.33597	−	1.69718i
$395$		0			0
$396$	30.0699	−	33.1314i	1.51107	−	1.66491i
$397$		−	3.57490i		−	0.179419i	−0.995968	−	0.0897094i	$-0.971406\pi$
$397$		−	3.57490i		−	0.179419i	0.995968	−	0.0897094i	$-0.0285938\pi$
$398$	9.83564	+	13.5376i	0.493016	+	0.678579i
$399$	3.43305	+	10.5659i	0.171868	+	0.528954i
$400$		0			0
$401$	−23.3675	−	16.9775i	−1.16692	−	0.847815i	−0.176281	−	0.984340i	$-0.556407\pi$
$401$	−23.3675	−	16.9775i	−1.16692	−	0.847815i	−0.990637	+	0.136524i	$0.956407\pi$
$402$	−28.5859	+	39.3451i	−1.42573	+	1.96235i
$403$	−4.46657	−	1.45128i	−0.222496	−	0.0722933i
$404$	21.2162	+	65.2969i	1.05555	+	3.24864i
$405$		0			0
$406$	−3.23782			−0.160690
$407$	−1.26599	−	6.07412i	−0.0627526	−	0.301083i
$408$			44.2072i			2.18858i
$409$	7.78197	−	5.65393i	0.384794	−	0.279569i	−0.378525	−	0.925591i	$-0.623569\pi$
$409$	7.78197	−	5.65393i	0.384794	−	0.279569i	0.763319	+	0.646022i	$0.223569\pi$
$410$		0			0
$411$	13.6988	−	42.1606i	0.675712	−	2.07963i
$412$	−17.1708	+	23.6336i	−0.845945	+	1.16434i
$413$	−7.99135	+	10.9991i	−0.393229	+	0.541233i
$414$	−21.1261	+	65.0196i	−1.03829	+	3.19554i
$415$		0			0
$416$	−4.29512	+	3.12059i	−0.210586	+	0.152999i
$417$			41.5967i			2.03700i
$418$	−17.9064	−	1.95373i	−0.875829	−	0.0955599i
$419$	30.6537			1.49753			0.748765	−	0.662836i	$-0.230647\pi$
$419$	30.6537			1.49753			0.748765	+	0.662836i	$0.230647\pi$
$420$		0			0
$421$	−2.14755	−	6.60949i	−0.104665	−	0.322127i	0.884986	−	0.465617i	$-0.154168\pi$
$421$	−2.14755	−	6.60949i	−0.104665	−	0.322127i	−0.989652	+	0.143490i	$0.954168\pi$
$422$	−13.5837	−	4.41361i	−0.661244	−	0.214851i
$423$	−13.2483	+	18.2348i	−0.644156	+	0.886605i
$424$	−14.2610	−	10.3612i	−0.692574	−	0.503184i
$425$		0			0
$426$	21.7532	+	66.9493i	1.05394	+	3.24371i
$427$	−0.618281	−	0.850991i	−0.0299207	−	0.0411823i
$428$			68.2571i			3.29933i
$429$	−1.14334	+	10.4790i	−0.0552009	+	0.505929i
$430$		0			0
$431$	2.61636	−	1.90090i	0.126026	−	0.0915631i	−0.522987	−	0.852341i	$-0.675182\pi$
$431$	2.61636	−	1.90090i	0.126026	−	0.0915631i	0.649013	+	0.760778i	$0.275182\pi$
$432$	−1.26846	+	0.412147i	−0.0610287	+	0.0198294i
$433$	−28.9044	−	9.39161i	−1.38906	−	0.451332i	−0.483421	−	0.875388i	$-0.660606\pi$
$433$	−28.9044	−	9.39161i	−1.38906	−	0.451332i	−0.905636	+	0.424056i	$0.860606\pi$
$434$	−15.5851	−	11.3233i	−0.748110	−	0.543534i
$435$		0			0
$436$	15.5506	−	47.8598i	0.744739	−	2.29207i
$437$	17.9616	−	5.83606i	0.859218	−	0.279177i
$438$	−40.6924	−	56.0083i	−1.94436	−	2.67618i
$439$	−36.5311			−1.74353			−0.871767	−	0.489921i	$-0.837026\pi$
$439$	−36.5311			−1.74353			−0.871767	+	0.489921i	$0.837026\pi$
$440$		0			0
$441$	−8.07350			−0.384452
$442$	−5.71902	−	7.87155i	−0.272026	−	0.374412i
$443$	2.05574	−	0.667949i	0.0976710	−	0.0317352i	−0.259774	−	0.965669i	$-0.583648\pi$
$443$	2.05574	−	0.667949i	0.0976710	−	0.0317352i	0.357445	+	0.933934i	$0.383648\pi$
$444$	−6.23630	+	19.1933i	−0.295962	+	0.910876i
$445$		0			0
$446$	−16.1030	−	11.6995i	−0.762499	−	0.553988i
$447$	5.47477	+	1.77886i	0.258948	+	0.0841372i
$448$	4.68890	−	1.52352i	0.221530	−	0.0719793i
$449$	−9.32124	+	6.77228i	−0.439897	+	0.319604i	−0.785594	−	0.618742i	$-0.787642\pi$
$449$	−9.32124	+	6.77228i	−0.439897	+	0.319604i	0.345697	+	0.938346i	$0.387642\pi$
$450$		0			0
$451$	−11.3831	+	12.5420i	−0.536010	+	0.590581i
$452$		−	39.5699i		−	1.86121i
$453$	−5.71100	−	7.86051i	−0.268326	−	0.369319i
$454$	8.74624	+	26.9182i	0.410482	+	1.26333i
$455$		0			0
$456$	25.7217	+	18.6879i	1.20453	+	0.875140i
$457$	9.36427	−	12.8888i	0.438042	−	0.602913i	−0.531734	−	0.846912i	$-0.678459\pi$
$457$	9.36427	−	12.8888i	0.438042	−	0.602913i	0.969776	+	0.243999i	$0.0784592\pi$
$458$	64.8038	+	21.0560i	3.02808	+	0.983883i
$459$	−0.193276	−	0.594843i	−0.00902136	−	0.0277649i
$460$		0			0
$461$	1.52527			0.0710387			0.0355193	−	0.999369i	$-0.488691\pi$
$461$	1.52527			0.0710387			0.0355193	+	0.999369i	$0.488691\pi$
$462$	−17.7430	+	39.4306i	−0.825478	+	1.83448i
$463$			14.2073i			0.660268i	0.943934	+	0.330134i	$0.107094\pi$
$463$			14.2073i			0.660268i	−0.943934	+	0.330134i	$0.892906\pi$
$464$	−3.16143	+	2.29691i	−0.146765	+	0.106631i
$465$		0			0
$466$	−8.46491	+	26.0523i	−0.392129	+	1.20685i
$467$	3.56020	−	4.90020i	0.164746	−	0.226754i	−0.718660	−	0.695362i	$-0.755244\pi$
$467$	3.56020	−	4.90020i	0.164746	−	0.226754i	0.883406	+	0.468608i	$0.155244\pi$
$468$	10.2167	−	14.0621i	0.472269	−	0.650022i
$469$	5.05229	−	15.5494i	0.233293	−	0.718002i
$470$		0			0
$471$	−9.74081	+	7.07711i	−0.448833	+	0.326096i
$472$			38.9085i			1.79091i
$473$	14.8918	−	8.51936i	0.684725	−	0.391720i
$474$	33.3727			1.53286
$475$		0			0
$476$	−8.46277	−	26.0457i	−0.387890	−	1.19380i
$477$	8.63181	+	2.80464i	0.395223	+	0.128416i
$478$	−17.0146	+	23.4185i	−0.778227	+	1.07114i
$479$	−14.2455	−	10.3500i	−0.650894	−	0.472902i	0.212681	−	0.977122i	$-0.431780\pi$
$479$	−14.2455	−	10.3500i	−0.650894	−	0.472902i	−0.863576	+	0.504219i	$0.831780\pi$
$480$		0			0
$481$	−0.744857	−	2.29243i	−0.0339626	−	0.104526i
$482$	18.9257	+	26.0490i	0.862043	+	1.18650i
$483$		−	45.3350i		−	2.06281i
$484$	−31.9048	−	36.0030i	−1.45022	−	1.63650i
$485$		0			0
$486$	−45.3059	+	32.9167i	−2.05512	+	1.49313i
$487$	6.45140	−	2.09619i	0.292341	−	0.0949874i	−0.159175	−	0.987250i	$-0.550883\pi$
$487$	6.45140	−	2.09619i	0.292341	−	0.0949874i	0.451516	+	0.892263i	$0.350883\pi$
$488$	−2.86297	−	0.930235i	−0.129600	−	0.0421097i
$489$	14.0407	+	10.2011i	0.634941	+	0.461312i
$490$		0			0
$491$	0.160261	−	0.493232i	0.00723247	−	0.0222592i	−0.947375	−	0.320125i	$-0.896275\pi$
$491$	0.160261	−	0.493232i	0.00723247	−	0.0222592i	0.954608	+	0.297866i	$0.0962749\pi$
$492$	52.3941	−	17.0239i	2.36211	−	0.767495i
$493$	−1.07714	−	1.48255i	−0.0485117	−	0.0667707i
$494$	−6.99762			−0.314838
$495$		0			0
$496$	−23.2501			−1.04396
$497$	−13.9102	−	19.1457i	−0.623956	−	0.858802i
$498$	64.2320	−	20.8703i	2.87831	−	0.935218i
$499$	−6.75534	+	20.7908i	−0.302411	+	0.930725i	0.678220	+	0.734859i	$0.262752\pi$
$499$	−6.75534	+	20.7908i	−0.302411	+	0.930725i	−0.980631	+	0.195866i	$0.937248\pi$
$500$		0			0
$501$	21.3921	+	15.5423i	0.955727	+	0.694377i
$502$	29.2956	+	9.51872i	1.30753	+	0.424841i
$503$	−2.86902	+	0.932202i	−0.127923	+	0.0415649i	−0.372279	−	0.928121i	$-0.621424\pi$
$503$	−2.86902	+	0.932202i	−0.127923	+	0.0415649i	0.244356	+	0.969686i	$0.421424\pi$
$504$	31.3020	−	22.7423i	1.39430	−	1.01302i
$505$		0			0
$506$	67.0306	+	30.1624i	2.97987	+	1.34088i
$507$		−	27.9724i		−	1.24230i
$508$	−48.4133	−	66.6352i	−2.14799	−	2.95646i
$509$	7.94418	+	24.4497i	0.352119	+	1.08371i	0.957661	+	0.287898i	$0.0929565\pi$
$509$	7.94418	+	24.4497i	0.352119	+	1.08371i	−0.605542	+	0.795814i	$0.707043\pi$
$510$		0			0
$511$	18.8289	+	13.6800i	0.832943	+	0.605169i
$512$	29.4768	−	40.5713i	1.30270	−	1.79302i
$513$	−0.427809	−	0.139004i	−0.0188882	−	0.00613716i
$514$	4.59962	+	14.1562i	0.202881	+	0.624403i
$515$		0			0
$516$	−55.8027			−2.45658
$517$	17.9447	+	16.2866i	0.789207	+	0.716282i
$518$		−	9.88725i		−	0.434421i
$519$	−16.7869	+	12.1964i	−0.736862	+	0.535361i
$520$		0			0
$521$	3.44017	−	10.5877i	0.150716	−	0.463858i	−0.846985	−	0.531616i	$-0.821585\pi$
$521$	3.44017	−	10.5877i	0.150716	−	0.463858i	0.997702	+	0.0677588i	$0.0215848\pi$
$522$	2.80426	−	3.85974i	0.122739	−	0.168936i
$523$	−3.84318	+	5.28968i	−0.168050	+	0.231302i	−0.884733	−	0.466098i	$-0.845660\pi$
$523$	−3.84318	+	5.28968i	−0.168050	+	0.231302i	0.716683	+	0.697399i	$0.245660\pi$
$524$	27.1627	−	83.5981i	1.18661	−	3.65200i
$525$		0			0
$526$	44.3820	−	32.2454i	1.93515	−	1.40597i
$527$		−	10.9032i		−	0.474949i
$528$	10.6477	+	51.0871i	0.463383	+	2.22328i
$529$	−54.0677			−2.35077
$530$		0			0
$531$	−6.19057	−	19.0526i	−0.268648	−	0.826814i
$532$	−18.7320	−	6.08640i	−0.812135	−	0.263879i
$533$	−3.86759	+	5.32328i	−0.167524	+	0.230577i
$534$	21.7811	+	15.8249i	0.942561	+	0.684811i
$535$		0			0
$536$	−14.4588	−	44.4995i	−0.624524	−	1.92209i
$537$	−30.5009	−	41.9809i	−1.31621	−	1.81161i
$538$		−	11.4223i		−	0.492449i
$539$	−0.941505	+	8.62911i	−0.0405535	+	0.371682i
$540$		0			0
$541$	−33.7684	+	24.5342i	−1.45182	+	1.05481i	−0.466413	+	0.884567i	$0.654454\pi$
$541$	−33.7684	+	24.5342i	−1.45182	+	1.05481i	−0.985403	+	0.170239i	$0.945546\pi$
$542$	−52.2470	+	16.9761i	−2.24420	+	0.729185i
$543$	4.08932	+	1.32870i	0.175490	+	0.0570201i
$544$	−9.97147	−	7.24470i	−0.427523	−	0.310614i
$545$		0			0
$546$	−5.19073	+	15.9754i	−0.222143	+	0.683685i
$547$	−4.23806	+	1.37703i	−0.181206	+	0.0588775i	−0.398215	−	0.917292i	$-0.630370\pi$
$547$	−4.23806	+	1.37703i	−0.181206	+	0.0588775i	0.217008	+	0.976170i	$0.430370\pi$
$548$	46.1954	+	63.5825i	1.97337	+	2.71611i
$549$	1.54994			0.0661498
$550$		0			0
$551$	−1.31795			−0.0561466
$552$	−76.2596	−	104.962i	−3.24583	−	4.46750i
$553$	−10.6702	+	3.46695i	−0.453742	+	0.147430i
$554$	10.1686	−	31.2956i	0.432020	−	1.32962i
$555$		0			0
$556$	−59.6618	−	43.3468i	−2.53022	−	1.83831i
$557$	−18.4233	−	5.98608i	−0.780619	−	0.253638i	−0.108514	−	0.994095i	$-0.534609\pi$
$557$	−18.4233	−	5.98608i	−0.780619	−	0.253638i	−0.672104	+	0.740456i	$0.734609\pi$
$558$	26.9964	−	8.77167i	1.14285	−	0.371335i
$559$	5.39211	−	3.91760i	0.228062	−	0.165697i
$560$		0			0
$561$	−23.9573	+	4.99325i	−1.01148	+	0.210815i
$562$		−	23.6941i		−	0.999477i
$563$	−12.1925	−	16.7816i	−0.513853	−	0.707259i	0.470710	−	0.882288i	$-0.343998\pi$
$563$	−12.1925	−	16.7816i	−0.513853	−	0.707259i	−0.984563	+	0.175030i	$0.943998\pi$
$564$	−24.3571	−	74.9636i	−1.02562	−	3.15654i
$565$		0			0
$566$	−28.4702	−	20.6848i	−1.19669	−	0.869447i
$567$	10.7530	−	14.8003i	0.451585	−	0.621554i
$568$	−64.4114	−	20.9285i	−2.70264	−	0.878141i
$569$	13.0945	+	40.3007i	0.548950	+	1.68949i	0.711408	+	0.702779i	$0.248058\pi$
$569$	13.0945	+	40.3007i	0.548950	+	1.68949i	−0.162458	+	0.986716i	$0.551942\pi$
$570$		0			0
$571$	−5.03980			−0.210909			−0.105455	−	0.994424i	$-0.533630\pi$
$571$	−5.03980			−0.210909			−0.105455	+	0.994424i	$0.533630\pi$
$572$	−13.8384	−	12.5597i	−0.578614	−	0.525148i
$573$		−	0.0615611i		−	0.00257175i
$574$	−21.8356	+	15.8645i	−0.911399	+	0.662170i
$575$		0			0
$576$	−2.24488	+	6.90905i	−0.0935369	+	0.287877i
$577$	−20.4796	+	28.1877i	−0.852576	+	1.17347i	0.130713	+	0.991420i	$0.458273\pi$
$577$	−20.4796	+	28.1877i	−0.852576	+	1.17347i	−0.983289	+	0.182050i	$0.941727\pi$
$578$	−11.9488	+	16.4461i	−0.497003	+	0.684066i
$579$	1.11080	−	3.41870i	0.0461634	−	0.142076i
$580$		0			0
$581$	−18.3686	+	13.3456i	−0.762059	+	0.553668i
$582$		−	2.18985i		−	0.0907724i
$583$	4.00427	−	8.89878i	0.165840	−	0.368550i
$584$	66.6057			2.75616
$585$		0			0
$586$	23.7703	+	73.1575i	0.981943	+	3.02211i
$587$	13.1039	+	4.25772i	0.540857	+	0.175735i	0.566690	−	0.823931i	$-0.308224\pi$
$587$	13.1039	+	4.25772i	0.540857	+	0.175735i	−0.0258331	+	0.999666i	$0.508224\pi$
$588$	16.5952	−	22.8413i	0.684373	−	0.941959i
$589$	−6.34392	−	4.60913i	−0.261397	−	0.189916i
$590$		0			0
$591$	−17.3054	−	53.2606i	−0.711850	−	2.19085i
$592$	−7.01402	−	9.65397i	−0.288274	−	0.396776i
$593$		−	25.1595i		−	1.03318i	−0.856234	−	0.516588i	$-0.827202\pi$
$593$		−	25.1595i		−	1.03318i	0.856234	−	0.516588i	$-0.172798\pi$
$594$	−0.869355	−	1.51963i	−0.0356701	−	0.0623511i
$595$		0			0
$596$	−8.25651	+	5.99871i	−0.338200	+	0.245717i
$597$	15.5501	−	5.05253i	0.636423	−	0.206786i
$598$	27.1576	+	8.82405i	1.11056	+	0.360842i
$599$	−13.3539	−	9.70216i	−0.545624	−	0.396419i	0.280545	−	0.959841i	$-0.409485\pi$
$599$	−13.3539	−	9.70216i	−0.545624	−	0.396419i	−0.826170	+	0.563421i	$0.809485\pi$
$600$		0			0
$601$	12.2509	−	37.7045i	0.499726	−	1.53800i	−0.309734	−	0.950823i	$-0.600240\pi$
$601$	12.2509	−	37.7045i	0.499726	−	1.53800i	0.809460	−	0.587175i	$-0.199760\pi$
$602$	26.0011	−	8.44829i	1.05973	−	0.344326i
$603$	14.1603	+	19.4900i	0.576651	+	0.793692i
$604$	17.2255			0.700897
$605$		0			0
$606$	97.7656			3.97146
$607$	8.34036	+	11.4795i	0.338525	+	0.465939i	0.944010	−	0.329917i	$-0.107021\pi$
$607$	8.34036	+	11.4795i	0.338525	+	0.465939i	−0.605485	+	0.795857i	$0.707021\pi$
$608$	−8.43055	+	2.73925i	−0.341904	+	0.111091i
$609$	−0.977637	+	3.00886i	−0.0396158	+	0.121925i
$610$		0			0
$611$	7.61636	+	5.53361i	0.308125	+	0.223866i
$612$	38.3781	+	12.4698i	1.55134	+	0.504062i
$613$	−28.6785	+	9.31820i	−1.15831	+	0.376359i	−0.824269	−	0.566199i	$-0.808414\pi$
$613$	−28.6785	+	9.31820i	−1.15831	+	0.376359i	−0.334044	+	0.942557i	$0.608414\pi$
$614$	10.3877	−	7.54714i	0.419215	−	0.304578i
$615$		0			0
$616$	−20.6570	−	36.1084i	−0.832296	−	1.45485i
$617$			31.3844i			1.26349i	0.775177	+	0.631744i	$0.217661\pi$
$617$			31.3844i			1.26349i	−0.775177	+	0.631744i	$0.782339\pi$
$618$	24.4507	+	33.6534i	0.983550	+	1.35374i
$619$	−10.8876	−	33.5087i	−0.437611	−	1.34683i	−0.890387	−	0.455205i	$-0.849566\pi$
$619$	−10.8876	−	33.5087i	−0.437611	−	1.34683i	0.452775	−	0.891625i	$-0.350434\pi$
$620$		0			0
$621$	1.48503	+	1.07894i	0.0595924	+	0.0432964i
$622$	−20.4201	+	28.1059i	−0.818773	+	1.12694i
$623$	−8.60800	−	2.79691i	−0.344872	−	0.112056i
$624$	6.26471	+	19.2808i	0.250789	+	0.771850i
$625$		0			0
$626$	40.2730			1.60963
$627$	−7.22227	+	16.0502i	−0.288430	+	0.640983i
$628$		−	21.3460i		−	0.851799i
$629$	4.52723	−	3.28922i	0.180512	−	0.131150i
$630$		0			0
$631$	1.77213	−	5.45404i	0.0705472	−	0.217122i	−0.909567	−	0.415558i	$-0.863586\pi$
$631$	1.77213	−	5.45404i	0.0705472	−	0.217122i	0.980114	+	0.198436i	$0.0635863\pi$
$632$	−18.8724	+	25.9756i	−0.750702	+	1.03325i
$633$	−8.20300	+	11.2905i	−0.326040	+	0.448755i
$634$	−8.35306	+	25.7081i	−0.331742	+	1.02100i
$635$		0			0
$636$	−25.6776	+	18.6559i	−1.01818	+	0.739753i
$637$			3.37217i			0.133610i
$638$	−3.79834	−	3.44736i	−0.150378	−	0.136482i
$639$	34.8707			1.37946
$640$		0			0
$641$	−2.20167	−	6.77605i	−0.0869608	−	0.267638i	0.898115	−	0.439762i	$-0.144937\pi$
$641$	−2.20167	−	6.77605i	−0.0869608	−	0.267638i	−0.985075	+	0.172124i	$0.944937\pi$
$642$	92.4388	+	30.0352i	3.64827	+	1.18539i
$643$	−12.4549	+	17.1427i	−0.491173	+	0.676042i	−0.980604	−	0.196000i	$-0.937205\pi$
$643$	−12.4549	+	17.1427i	−0.491173	+	0.676042i	0.489431	+	0.872042i	$0.337205\pi$
$644$	65.0235	+	47.2423i	2.56229	+	1.86161i
$645$		0			0
$646$	−5.02015	−	15.4504i	−0.197515	−	0.607889i
$647$	−3.32083	−	4.57074i	−0.130555	−	0.179694i	0.738735	−	0.673996i	$-0.235424\pi$
$647$	−3.32083	−	4.57074i	−0.130555	−	0.179694i	−0.869290	+	0.494302i	$0.835424\pi$
$648$		−	52.3547i		−	2.05669i
$649$	−21.0857	+	4.39475i	−0.827688	+	0.172509i
$650$		0			0
$651$	−15.2284	+	11.0640i	−0.596846	+	0.433634i
$652$	−29.2628	+	9.50807i	−1.14602	+	0.372365i
$653$	−14.9441	−	4.85563i	−0.584808	−	0.190016i	0.00164558	−	0.999999i	$-0.499476\pi$
$653$	−14.9441	−	4.85563i	−0.584808	−	0.190016i	−0.586453	+	0.809983i	$0.699476\pi$
$654$	−57.9726	−	42.1195i	−2.26691	−	1.64700i
$655$		0			0
$656$	−10.0661	+	30.9803i	−0.393016	+	1.20958i
$657$	−32.6153	+	10.5974i	−1.27245	+	0.413442i
$658$	22.6983	+	31.2416i	0.884872	+	1.21792i
$659$	41.7884			1.62784			0.813922	−	0.580975i	$-0.197329\pi$
$659$	41.7884			1.62784			0.813922	+	0.580975i	$0.197329\pi$
$660$		0			0
$661$	15.8742			0.617435			0.308717	−	0.951154i	$-0.400100\pi$
$661$	15.8742			0.617435			0.308717	+	0.951154i	$0.400100\pi$
$662$	−13.1266	−	18.0673i	−0.510182	−	0.702205i
$663$	−9.04173	+	2.93784i	−0.351152	+	0.114096i
$664$	−20.0791	+	61.7971i	−0.779220	+	2.39819i
$665$		0			0
$666$	11.7864	+	8.56330i	0.456713	+	0.331821i
$667$	5.11494	+	1.66195i	0.198051	+	0.0643508i
$668$	−44.5842	+	14.4863i	−1.72502	+	0.560491i
$669$	−15.7344	+	11.4317i	−0.608325	+	0.441974i
$670$		0			0
$671$	0.180749	−	1.65660i	0.00697773	−	0.0639525i
$672$			21.2787i			0.820844i
$673$	−18.9529	−	26.0864i	−0.730580	−	1.00556i	−0.999106	−	0.0422850i	$-0.986536\pi$
$673$	−18.9529	−	26.0864i	−0.730580	−	1.00556i	0.268525	−	0.963273i	$-0.413464\pi$
$674$	9.04140	+	27.8266i	0.348262	+	1.07184i
$675$		0			0
$676$	40.1206	+	29.1493i	1.54310	+	1.12113i
$677$	−10.3230	+	14.2084i	−0.396745	+	0.546073i	−0.959923	−	0.280263i	$-0.909578\pi$
$677$	−10.3230	+	14.2084i	−0.396745	+	0.546073i	0.563178	+	0.826336i	$0.309578\pi$
$678$	−53.5885	−	17.4120i	−2.05805	−	0.668702i
$679$	0.227495	+	0.700157i	0.00873044	+	0.0268695i
$680$		0			0
$681$	27.6555			1.05976
$682$	−6.22710	−	29.8772i	−0.238448	−	1.14406i
$683$		−	5.93856i		−	0.227233i	−0.993525	−	0.113616i	$-0.963757\pi$
$683$		−	5.93856i		−	0.227233i	0.993525	−	0.113616i	$-0.0362434\pi$
$684$	23.4792	−	17.0586i	0.897749	−	0.652253i
$685$		0			0
$686$	−15.7067	+	48.3404i	−0.599686	+	1.84565i
$687$	39.1341	−	53.8634i	1.49306	−	2.05502i
$688$	19.3945	−	26.6942i	0.739407	−	1.01771i
$689$	1.17145	−	3.60537i	0.0446289	−	0.137353i
$690$		0			0
$691$	−17.7463	+	12.8934i	−0.675100	+	0.490489i	−0.871728	−	0.489989i	$-0.837001\pi$
$691$	−17.7463	+	12.8934i	−0.675100	+	0.490489i	0.196629	+	0.980478i	$0.437001\pi$
$692$		−	36.7868i		−	1.39842i
$693$	15.8604	+	14.3948i	0.602485	+	0.546814i
$694$	12.3424			0.468511
$695$		0			0
$696$	2.79782	+	8.61082i	0.106051	+	0.326392i
$697$	−14.5282	−	4.72050i	−0.550295	−	0.178802i
$698$	1.41491	−	1.94746i	0.0535551	−	0.0737123i
$699$	21.6541	+	15.7326i	0.819033	+	0.595062i
$700$		0			0
$701$	10.0186	+	30.8341i	0.378397	+	1.16459i	0.941158	+	0.337967i	$0.109739\pi$
$701$	10.0186	+	30.8341i	0.378397	+	1.16459i	−0.562761	+	0.826620i	$0.690261\pi$
$702$	−0.399770	−	0.550236i	−0.0150884	−	0.0207673i
$703$		−	4.02460i		−	0.151791i
$704$	7.12273	+	3.20509i	0.268448	+	0.120796i
$705$		0			0
$706$	31.6908	−	23.0247i	1.19270	−	0.866547i
$707$	−31.2584	+	10.1565i	−1.17559	+	0.381973i
$708$	66.6279	+	21.6487i	2.50403	+	0.813609i
$709$	−13.0256	−	9.46362i	−0.489185	−	0.355414i	0.315686	−	0.948864i	$-0.397765\pi$
$709$	−13.0256	−	9.46362i	−0.489185	−	0.355414i	−0.804871	+	0.593450i	$0.797765\pi$
$710$		0			0
$711$	5.10851	−	15.7224i	0.191584	−	0.589635i
$712$	−24.6346	+	8.00426i	−0.923220	+	0.299972i
$713$	18.8085	+	25.8876i	0.704383	+	0.969499i
$714$	−38.9969			−1.45942
$715$		0			0
$716$	91.9971			3.43809
$717$	16.6250	+	22.8824i	0.620874	+	0.854559i
$718$	−48.6316	+	15.8014i	−1.81492	+	0.589702i
$719$	2.41409	−	7.42981i	0.0900304	−	0.277085i	−0.895896	−	0.444263i	$-0.853466\pi$
$719$	2.41409	−	7.42981i	0.0900304	−	0.277085i	0.985927	+	0.167178i	$0.0534655\pi$
$720$		0			0
$721$	−11.3137	−	8.21985i	−0.421343	−	0.306123i
$722$	34.5064	+	11.2118i	1.28420	+	0.417261i
$723$	29.9214	−	9.72206i	1.11279	−	0.361567i
$724$	−6.16712	+	4.48068i	−0.229199	+	0.166523i
$725$		0			0
$726$	−62.7970	+	27.3654i	−2.33061	+	1.01563i
$727$			49.1218i			1.82183i	0.412597	+	0.910914i	$0.364622\pi$
$727$			49.1218i			1.82183i	−0.412597	+	0.910914i	$0.635378\pi$
$728$	−9.49907	−	13.0744i	−0.352059	−	0.484568i
$729$	8.80810	+	27.1086i	0.326226	+	1.00402i
$730$		0			0
$731$	12.5182	+	9.09503i	0.463003	+	0.336392i
$732$	−3.18592	+	4.38504i	−0.117755	+	0.162076i
$733$	−0.635255	−	0.206407i	−0.0234637	−	0.00762382i	0.297262	−	0.954796i	$-0.403927\pi$
$733$	−0.635255	−	0.206407i	−0.0234637	−	0.00762382i	−0.320725	+	0.947172i	$0.603927\pi$
$734$	−27.8152	−	85.6064i	−1.02668	−	3.15979i
$735$		0			0
$736$	36.1730			1.33335
$737$	22.4826	−	12.8619i	0.828156	−	0.473775i
$738$		−	39.7699i		−	1.46395i
$739$	30.8186	−	22.3911i	1.13368	−	0.823668i	0.147456	−	0.989069i	$-0.452892\pi$
$739$	30.8186	−	22.3911i	1.13368	−	0.823668i	0.986227	+	0.165400i	$0.0528916\pi$
$740$		0			0
$741$	−2.11288	+	6.50278i	−0.0776187	+	0.238886i
$742$	9.14001	−	12.5801i	0.335540	−	0.461832i
$743$	−18.4186	+	25.3511i	−0.675714	+	0.930041i	−0.999873	−	0.0159622i	$-0.994919\pi$
$743$	−18.4186	+	25.3511i	−0.675714	+	0.930041i	0.324159	+	0.946003i	$0.394919\pi$
$744$	−16.6464	+	51.2324i	−0.610287	+	1.87827i
$745$		0			0
$746$	−24.7860	+	18.0081i	−0.907480	+	0.659323i
$747$		−	33.4554i		−	1.22407i
$748$	17.8035	−	39.5651i	0.650960	−	1.44664i
$749$	−32.6754			−1.19393
$750$		0			0
$751$	−11.4915	−	35.3673i	−0.419332	−	1.29057i	−0.908318	−	0.418280i	$-0.862633\pi$
$751$	−11.4915	−	35.3673i	−0.419332	−	1.29057i	0.488986	−	0.872292i	$-0.337367\pi$
$752$	44.3255	+	14.4022i	1.61639	+	0.525196i
$753$	17.6912	−	24.3498i	0.644703	−	0.887358i
$754$	−1.61215	−	1.17129i	−0.0587110	−	0.0426560i
$755$		0			0
$756$	−0.591564	−	1.82065i	−0.0215150	−	0.0662162i
$757$	3.92680	+	5.40478i	0.142722	+	0.196440i	0.874394	−	0.485217i	$-0.161259\pi$
$757$	3.92680	+	5.40478i	0.142722	+	0.196440i	−0.731672	+	0.681657i	$0.761259\pi$
$758$			18.0355i			0.655079i
$759$	48.2689	−	53.1831i	1.75205	−	1.93043i
$760$		0			0
$761$	18.5213	−	13.4565i	0.671398	−	0.487799i	−0.199095	−	0.979980i	$-0.563800\pi$
$761$	18.5213	−	13.4565i	0.671398	−	0.487799i	0.870493	+	0.492181i	$0.163800\pi$
$762$	−111.546	+	36.2434i	−4.04087	+	1.31296i
$763$	22.9110	+	7.44425i	0.829435	+	0.269500i
$764$	0.0882966	+	0.0641512i	0.00319446	+	0.00232091i
$765$		0			0
$766$	12.4530	−	38.3265i	0.449947	−	1.38479i
$767$	−7.95797	+	2.58570i	−0.287346	+	0.0933643i
$768$	−45.0971	−	62.0709i	−1.62730	−	2.23979i
$769$	13.1946			0.475808			0.237904	−	0.971289i	$-0.423540\pi$
$769$	13.1946			0.475808			0.237904	+	0.971289i	$0.423540\pi$
$770$		0			0
$771$	14.5440			0.523788
$772$	3.74587	+	5.15575i	0.134817	+	0.185560i
$773$	11.8130	−	3.83827i	0.424883	−	0.138053i	−0.0887673	−	0.996052i	$-0.528293\pi$
$773$	11.8130	−	3.83827i	0.424883	−	0.138053i	0.513651	+	0.857999i	$0.328293\pi$
$774$	−12.4485	+	38.3124i	−0.447451	+	1.37711i
$775$		0			0
$776$	1.70447	+	1.23837i	0.0611869	+	0.0444549i
$777$	−9.18807	−	2.98538i	−0.329620	−	0.107100i
$778$	60.2412	−	19.5735i	2.15975	−	0.701746i
$779$	−8.88815	+	6.45762i	−0.318451	+	0.231368i
$780$		0			0
$781$	4.06650	−	37.2705i	0.145511	−	1.33364i
$782$			66.2932i			2.37064i
$783$	−0.0752938	−	0.103633i	−0.00269078	−	0.00370354i
$784$	5.15881	+	15.8772i	0.184243	+	0.567042i
$785$		0			0
$786$	−101.262	−	73.5714i	−3.61191	−	2.62420i
$787$	−12.6286	+	17.3818i	−0.450162	+	0.619595i	−0.972432	−	0.233185i	$-0.925085\pi$
$787$	−12.6286	+	17.3818i	−0.450162	+	0.619595i	0.522270	+	0.852780i	$0.325085\pi$
$788$	94.4247	+	30.6805i	3.36374	+	1.09295i
$789$	−16.5643	−	50.9798i	−0.589706	−	1.81493i
$790$		0			0
$791$	18.9426			0.673520
$792$	60.9350	+	6.64849i	2.16523	+	0.236244i
$793$		−	0.647384i		−	0.0229893i
$794$	7.30130	−	5.30471i	0.259114	−	0.188257i
$795$		0			0
$796$	−8.95753	+	27.5685i	−0.317491	+	0.977138i
$797$	−1.25157	+	1.72264i	−0.0443330	+	0.0610191i	−0.830608	−	0.556858i	$-0.812007\pi$
$797$	−1.25157	+	1.72264i	−0.0443330	+	0.0610191i	0.786275	+	0.617877i	$0.212007\pi$
$798$	−16.4853	+	22.6901i	−0.583573	+	0.803219i
$799$	−6.75393	+	20.7864i	−0.238937	+	0.735372i
$800$		0			0
$801$	10.7895	−	7.83902i	0.381228	−	0.276978i
$802$		−	72.9179i		−	2.57482i
$803$	7.52318	+	36.0957i	0.265487	+	1.27379i
$804$	−84.2470			−2.97116
$805$		0			0
$806$	−3.66378	−	11.2760i	−0.129051	−	0.397179i
$807$	−10.6145	−	3.44887i	−0.373649	−	0.121406i
$808$	−55.2868	+	76.0957i	−1.94498	+	2.67704i
$809$	−4.33820	−	3.15189i	−0.152523	−	0.110815i	0.508906	−	0.860822i	$-0.330050\pi$
$809$	−4.33820	−	3.15189i	−0.152523	−	0.110815i	−0.661430	+	0.750007i	$0.730050\pi$
$810$		0			0
$811$	6.05047	+	18.6214i	0.212461	+	0.653887i	0.999324	+	0.0367600i	$0.0117037\pi$
$811$	6.05047	+	18.6214i	0.212461	+	0.653887i	−0.786863	+	0.617127i	$0.788296\pi$
$812$	−3.29681	−	4.53766i	−0.115695	−	0.159241i
$813$			53.6781i			1.88257i
$814$	10.5271	−	11.5989i	0.368975	−	0.406541i
$815$		0			0
$816$	−38.0768	+	27.6644i	−1.33295	+	0.968448i
$817$	10.5837	−	3.43887i	0.370278	−	0.120311i
$818$	23.0950	+	7.50402i	0.807497	+	0.262372i
$819$	6.73170	+	4.89086i	0.235224	+	0.170901i
$820$		0			0
$821$	−5.14095	+	15.8222i	−0.179420	+	0.552199i	−0.999808	−	0.0196092i	$-0.993758\pi$
$821$	−5.14095	+	15.8222i	−0.179420	+	0.552199i	0.820387	+	0.571808i	$0.193758\pi$
$822$	106.435	−	34.5829i	3.71236	−	1.20622i
$823$	10.7523	+	14.7993i	0.374801	+	0.515870i	0.954198	−	0.299176i	$-0.0967117\pi$
$823$	10.7523	+	14.7993i	0.374801	+	0.515870i	−0.579397	+	0.815046i	$0.696712\pi$
$824$	−40.0210			−1.39420
$825$		0			0
$826$	−34.3227			−1.19424
$827$	−22.3466	−	30.7575i	−0.777069	−	1.06954i	−0.995599	−	0.0937136i	$-0.970126\pi$
$827$	−22.3466	−	30.7575i	−0.777069	−	1.06954i	0.218530	−	0.975830i	$-0.429874\pi$
$828$	−112.633	+	36.5967i	−3.91427	+	1.27182i
$829$	−15.9762	+	49.1698i	−0.554877	+	1.70774i	0.141389	+	0.989954i	$0.454843\pi$
$829$	−15.9762	+	49.1698i	−0.554877	+	1.70774i	−0.696267	+	0.717783i	$0.745157\pi$
$830$		0			0
$831$	−26.0122	−	18.8990i	−0.902353	−	0.655598i
$832$	2.88580	+	0.937652i	0.100047	+	0.0325072i
$833$	−7.44560	+	2.41922i	−0.257975	+	0.0838210i
$834$	−84.9564	+	61.7244i	−2.94180	+	2.13734i
$835$		0			0
$836$	−15.4945	−	27.0843i	−0.535889	−	0.936731i
$837$		−	0.762151i		−	0.0263438i
$838$	45.4863	+	62.6065i	1.57130	+	2.16271i
$839$	−11.9288	−	36.7132i	−0.411829	−	1.26748i	−0.915056	−	0.403326i	$-0.867854\pi$
$839$	−11.9288	−	36.7132i	−0.411829	−	1.26748i	0.503227	−	0.864154i	$-0.332146\pi$
$840$		0			0
$841$	23.1579	+	16.8252i	0.798547	+	0.580178i
$842$	10.3124	−	14.1938i	0.355389	−	0.489151i
$843$	−22.0186	−	7.15428i	−0.758361	−	0.246406i
$844$	−7.64568	−	23.5310i	−0.263175	−	0.809969i
$845$		0			0
$846$	−56.9013			−1.95631
$847$	17.2350	−	15.2732i	0.592203	−	0.524793i
$848$		−	18.7672i		−	0.644470i
$849$	−27.8184	+	20.2113i	−0.954726	+	0.693649i
$850$		0			0
$851$	−5.07504	+	15.6194i	−0.173970	+	0.535425i
$852$	−71.6771	+	98.6551i	−2.45562	+	3.37987i
$853$	19.9293	−	27.4303i	0.682366	−	0.939197i	−0.317593	−	0.948227i	$-0.602874\pi$
$853$	19.9293	−	27.4303i	0.682366	−	0.939197i	0.999959	+	0.00903033i	$0.00287448\pi$
$854$	0.820596	−	2.52553i	0.0280802	−	0.0864220i
$855$		0			0
$856$	−75.6523	+	54.9646i	−2.58574	+	1.87865i
$857$			56.7117i			1.93723i	0.248558	+	0.968617i	$0.420043\pi$
$857$			56.7117i			1.93723i	−0.248558	+	0.968617i	$0.579957\pi$
$858$	−23.0986	+	13.2144i	−0.788574	+	0.451131i
$859$	25.7505			0.878597			0.439298	−	0.898341i	$-0.355227\pi$
$859$	25.7505			0.878597			0.439298	+	0.898341i	$0.355227\pi$
$860$		0			0
$861$	8.14951	+	25.0816i	0.277735	+	0.854779i
$862$	7.76473	+	2.52291i	0.264468	+	0.0859308i
$863$	21.0222	−	28.9345i	0.715603	−	0.984942i	−0.284056	−	0.958808i	$-0.591680\pi$
$863$	21.0222	−	28.9345i	0.715603	−	0.984942i	0.999658	−	0.0261347i	$-0.00831990\pi$
$864$	−0.697025	−	0.506418i	−0.0237133	−	0.0172287i
$865$		0			0
$866$	−23.7093	−	72.9698i	−0.805676	−	2.47962i
$867$	11.6752	+	16.0696i	0.396511	+	0.545751i
$868$		−	33.3714i		−	1.13270i
$869$	−16.2086	−	7.29357i	−0.549841	−	0.247417i
$870$		0			0
$871$	8.14064	−	5.91452i	0.275835	−	0.200406i
$872$	65.5674	−	21.3041i	2.22039	−	0.721449i
$873$	−1.03167	−	0.335211i	−0.0349169	−	0.0113452i
$874$	38.5722	+	28.0244i	1.30473	+	0.947938i
$875$		0			0
$876$	37.0595	−	114.057i	1.25212	−	3.85364i
$877$	16.4629	−	5.34913i	0.555913	−	0.180627i	−0.0175682	−	0.999846i	$-0.505592\pi$
$877$	16.4629	−	5.34913i	0.555913	−	0.180627i	0.573482	+	0.819218i	$0.305592\pi$
$878$	−54.2077	−	74.6105i	−1.82942	−	2.51798i
$879$	75.1614			2.53513
$880$		0			0
$881$	−4.15822			−0.140094			−0.0700470	−	0.997544i	$-0.522315\pi$
$881$	−4.15822			−0.140094			−0.0700470	+	0.997544i	$0.522315\pi$
$882$	−11.9801	−	16.4892i	−0.403391	−	0.555219i
$883$	39.2505	−	12.7533i	1.32088	−	0.429182i	0.438086	−	0.898933i	$-0.355656\pi$
$883$	39.2505	−	12.7533i	1.32088	−	0.429182i	0.882799	+	0.469751i	$0.155656\pi$
$884$	5.20843	−	16.0299i	0.175179	−	0.539144i
$885$		0			0
$886$	4.41467	+	3.20744i	0.148314	+	0.107756i
$887$	−28.9873	−	9.41854i	−0.973297	−	0.316243i	−0.221151	−	0.975240i	$-0.570981\pi$
$887$	−28.9873	−	9.41854i	−0.973297	−	0.316243i	−0.752146	+	0.658996i	$0.770981\pi$
$888$	−26.2946	+	8.54364i	−0.882390	+	0.286706i
$889$	31.8990	−	23.1760i	1.06986	−	0.777298i
$890$		0			0
$891$	28.3727	−	5.91352i	0.950520	−	0.198110i
$892$		−	34.4803i		−	1.15449i
$893$	9.23933	+	12.7168i	0.309182	+	0.425553i
$894$	4.49077	+	13.8212i	0.150194	+	0.462249i
$895$		0			0
$896$	24.0270	+	17.4566i	0.802684	+	0.583184i
$897$	16.4001	−	22.5728i	0.547583	−	0.753684i
$898$	−27.6632	−	8.98831i	−0.923132	−	0.299944i
$899$	−0.690047	−	2.12375i	−0.0230144	−	0.0708309i
$900$		0			0
$901$	8.80090			0.293200
$902$	−42.5068	−	4.63783i	−1.41532	−	0.154423i
$903$		−	26.7134i		−	0.888965i
$904$	43.8570	−	31.8640i	1.45866	−	1.05978i
$905$		0			0
$906$	7.57976	−	23.3281i	0.251821	−	0.775024i
$907$	−6.63578	+	9.13337i	−0.220338	+	0.303269i	−0.904848	−	0.425734i	$-0.860016\pi$
$907$	−6.63578	+	9.13337i	−0.220338	+	0.303269i	0.684511	+	0.729003i	$0.260016\pi$
$908$	−28.8191	+	39.6660i	−0.956394	+	1.31636i
$909$	14.9654	−	46.0589i	0.496372	−	1.52768i
$910$		0			0
$911$	−40.9417	+	29.7459i	−1.35646	+	0.985525i	−0.357797	+	0.933799i	$0.616472\pi$
$911$	−40.9417	+	29.7459i	−1.35646	+	0.985525i	−0.998661	+	0.0517251i	$0.983528\pi$
$912$			33.8494i			1.12086i
$913$	−35.7578	−	3.90146i	−1.18341	−	0.129119i
$914$	40.2193			1.33034
$915$		0			0
$916$	36.4753	+	112.259i	1.20518	+	3.70915i
$917$	40.0193	+	13.0031i	1.32156	+	0.429399i
$918$	0.928099	−	1.27742i	0.0306318	−	0.0421611i
$919$	−22.0198	−	15.9983i	−0.726366	−	0.527736i	0.162046	−	0.986783i	$-0.448191\pi$
$919$	−22.0198	−	15.9983i	−0.726366	−	0.527736i	−0.888412	+	0.459048i	$0.848191\pi$
$920$		0			0
$921$	−3.87693	−	11.9320i	−0.127749	−	0.393172i
$922$	2.26331	+	3.11518i	0.0745381	+	0.102593i
$923$		−	14.5649i		−	0.479410i
$924$	−73.3265	+	15.2829i	−2.41227	+	0.502771i
$925$		0			0
$926$	−29.0167	+	21.0819i	−0.953547	+	0.692793i
$927$	19.5974	−	6.36759i	0.643664	−	0.209139i
$928$	−2.40078	−	0.780061i	−0.0788095	−	0.0256068i
$929$	−18.7776	−	13.6427i	−0.616073	−	0.447603i	0.235475	−	0.971880i	$-0.424336\pi$
$929$	−18.7776	−	13.6427i	−0.616073	−	0.447603i	−0.851548	+	0.524277i	$0.824336\pi$
$930$		0			0
$931$	−1.73990	+	5.35485i	−0.0570228	+	0.175498i
$932$	−45.1303	+	14.6637i	−1.47829	+	0.480326i
$933$	19.9527	+	27.4625i	0.653221	+	0.899082i
$934$	15.2910			0.500336
$935$		0			0
$936$	23.8128			0.778344
$937$	−24.8114	−	34.1500i	−0.810554	−	1.11563i	−0.991238	−	0.132090i	$-0.957831\pi$
$937$	−24.8114	−	34.1500i	−0.810554	−	1.11563i	0.180684	−	0.983541i	$-0.442169\pi$
$938$	39.2547	−	12.7546i	1.28171	−	0.416453i
$939$	12.1601	−	37.4251i	0.396831	−	1.22132i
$940$		0			0
$941$	23.6336	+	17.1708i	0.770435	+	0.559754i	0.902093	−	0.431542i	$-0.142030\pi$
$941$	23.6336	+	17.1708i	0.770435	+	0.559754i	−0.131658	+	0.991295i	$0.542030\pi$
$942$	−28.9083	−	9.39289i	−0.941885	−	0.306037i
$943$	42.6378	−	13.8539i	1.38848	−	0.451144i
$944$	−33.5128	+	24.3485i	−1.09075	+	0.792476i
$945$		0			0
$946$	39.4974	+	17.7730i	1.28417	+	0.577851i
$947$		−	9.63809i		−	0.313196i	−0.987662	−	0.156598i	$-0.949947\pi$
$947$		−	9.63809i		−	0.313196i	0.987662	−	0.156598i	$-0.0500527\pi$
$948$	33.9807	+	46.7704i	1.10364	+	1.51903i
$949$	4.42634	+	13.6229i	0.143685	+	0.442218i
$950$		0			0
$951$	21.3680	+	15.5247i	0.692904	+	0.503424i
$952$	22.0529	−	30.3532i	0.714738	−	0.983752i
$953$	4.96593	+	1.61353i	0.160862	+	0.0522673i	0.388341	−	0.921516i	$-0.373048\pi$
$953$	4.96593	+	1.61353i	0.160862	+	0.0522673i	−0.227479	+	0.973783i	$0.573048\pi$
$954$	7.08039	+	21.7912i	0.229236	+	0.705517i
$955$		0			0
$956$	−50.1446			−1.62179
$957$	−4.35046	+	2.48883i	−0.140630	+	0.0804525i
$958$		−	44.4529i		−	1.43621i
$959$	−30.4376	+	22.1142i	−0.982882	+	0.714106i
$960$		0			0
$961$	−5.47390	+	16.8469i	−0.176577	+	0.543450i
$962$	3.57675	−	4.92298i	0.115319	−	0.158723i
$963$	28.3001	−	38.9517i	0.911956	−	1.25520i
$964$	−17.2361	+	53.0471i	−0.555136	+	1.70853i
$965$		0			0
$966$	92.5913	−	67.2715i	2.97908	−	2.16443i
$967$		−	38.4583i		−	1.23674i	−0.785889	−	0.618368i	$-0.787794\pi$
$967$		−	38.4583i		−	1.23674i	0.785889	−	0.618368i	$-0.212206\pi$
$968$	14.2121	−	64.3532i	0.456793	−	2.06839i
$969$	−15.8737			−0.509935
$970$		0			0
$971$	13.4928	+	41.5267i	0.433006	+	1.33265i	0.895116	+	0.445832i	$0.147092\pi$
$971$	13.4928	+	41.5267i	0.433006	+	1.33265i	−0.462111	+	0.886822i	$0.652908\pi$
$972$	−92.2625	−	29.9779i	−2.95932	−	0.961542i
$973$	20.7506	−	28.5608i	0.665234	−	0.915616i
$974$	13.8543	+	10.0658i	0.443921	+	0.322527i
$975$		0			0
$976$	−0.990380	−	3.04808i	−0.0317013	−	0.0975665i
$977$	−6.90455	−	9.50330i	−0.220896	−	0.304038i	0.684158	−	0.729334i	$-0.260170\pi$
$977$	−6.90455	−	9.50330i	−0.220896	−	0.304038i	−0.905054	+	0.425296i	$0.860170\pi$
$978$			43.8137i			1.40101i
$979$	−7.12027	−	12.4462i	−0.227565	−	0.397782i
$980$		0			0
$981$	−28.7173	+	20.8643i	−0.916872	+	0.666147i
$982$	1.24518	−	0.404582i	0.0397351	−	0.0129107i
$983$	8.89417	+	2.88989i	0.283680	+	0.0921733i	0.447401	−	0.894333i	$-0.352350\pi$
$983$	8.89417	+	2.88989i	0.283680	+	0.0921733i	−0.163721	+	0.986507i	$0.552350\pi$
$984$	61.0590	+	44.3620i	1.94649	+	1.41421i
$985$		0			0
$986$	1.42960	−	4.39985i	0.0455276	−	0.140120i
$987$	35.8859	−	11.6600i	1.14226	−	0.371143i
$988$	−7.12510	−	9.80687i	−0.226680	−	0.311998i
$989$	−45.4117			−1.44401
$990$		0			0
$991$	−32.3450			−1.02747			−0.513737	−	0.857948i	$-0.671739\pi$
$991$	−32.3450			−1.02747			−0.513737	+	0.857948i	$0.671739\pi$
$992$	−8.82806	−	12.1508i	−0.280291	−	0.385788i
$993$	−20.7531	+	6.74310i	−0.658581	+	0.213986i
$994$	18.4619	−	56.8197i	0.585574	−	1.80221i
$995$		0			0
$996$	94.6510	+	68.7679i	2.99913	+	2.17900i
$997$	27.6923	+	8.99777i	0.877023	+	0.284962i	0.712721	−	0.701448i	$-0.247463\pi$
$997$	27.6923	+	8.99777i	0.877023	+	0.284962i	0.164302	+	0.986410i	$0.447463\pi$
$998$	−52.4869	+	17.0540i	−1.66144	+	0.539836i
$999$	0.316462	−	0.229923i	0.0100124	−	0.00727444i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	275.2.z.b.124.4		16
5.2	odd	4		55.2.g.a.36.1	yes	8
5.3	odd	4		275.2.h.b.201.2		8
5.4	even	2	inner	275.2.z.b.124.1		16
11.4	even	5	inner	275.2.z.b.224.1		16
15.2	even	4		495.2.n.f.91.2		8
20.7	even	4		880.2.bo.e.641.2		8
55.2	even	20		605.2.a.i.1.1		4
55.4	even	10	inner	275.2.z.b.224.4		16
55.7	even	20		605.2.g.n.81.2		8
55.13	even	20		3025.2.a.be.1.4		4
55.17	even	20		605.2.g.g.251.1		8
55.27	odd	20		605.2.g.j.251.2		8
55.32	even	4		605.2.g.n.366.2		8
55.37	odd	20		55.2.g.a.26.1	✓	8
55.42	odd	20		605.2.a.l.1.4		4
55.47	odd	20		605.2.g.j.511.2		8
55.48	odd	20		275.2.h.b.26.2		8
55.52	even	20		605.2.g.g.511.1		8
55.53	odd	20		3025.2.a.v.1.1		4
165.2	odd	20		5445.2.a.bu.1.4		4
165.92	even	20		495.2.n.f.136.2		8
165.152	even	20		5445.2.a.bg.1.1		4
220.147	even	20		880.2.bo.e.81.2		8
220.167	odd	20		9680.2.a.cv.1.4		4
220.207	even	20		9680.2.a.cs.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.g.a.26.1	✓	8	55.37	odd	20
55.2.g.a.36.1	yes	8	5.2	odd	4
275.2.h.b.26.2		8	55.48	odd	20
275.2.h.b.201.2		8	5.3	odd	4
275.2.z.b.124.1		16	5.4	even	2	inner
275.2.z.b.124.4		16	1.1	even	1	trivial
275.2.z.b.224.1		16	11.4	even	5	inner
275.2.z.b.224.4		16	55.4	even	10	inner
495.2.n.f.91.2		8	15.2	even	4
495.2.n.f.136.2		8	165.92	even	20
605.2.a.i.1.1		4	55.2	even	20
605.2.a.l.1.4		4	55.42	odd	20
605.2.g.g.251.1		8	55.17	even	20
605.2.g.g.511.1		8	55.52	even	20
605.2.g.j.251.2		8	55.27	odd	20
605.2.g.j.511.2		8	55.47	odd	20
605.2.g.n.81.2		8	55.7	even	20
605.2.g.n.366.2		8	55.32	even	4
880.2.bo.e.81.2		8	220.147	even	20
880.2.bo.e.641.2		8	20.7	even	4
3025.2.a.v.1.1		4	55.53	odd	20
3025.2.a.be.1.4		4	55.13	even	20
5445.2.a.bg.1.1		4	165.152	even	20
5445.2.a.bu.1.4		4	165.2	odd	20
9680.2.a.cs.1.4		4	220.207	even	20
9680.2.a.cv.1.4		4	220.167	odd	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 275 = 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	275.z (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.48388 + 2.04238i) q^{2} +(2.34600 - 0.762262i) q^{3} +(-1.35140 + 4.15918i) q^{4} +(5.03801 + 3.66033i) q^{6} +(-1.99105 - 0.646930i) q^{7} +(-5.69802 + 1.85140i) q^{8} +(2.49563 - 1.81318i) q^{9} +(-1.64693 - 2.87882i) q^{11} +10.7876i q^{12} +(-0.757336 - 1.04238i) q^{13} +(-1.63319 - 5.02644i) q^{14} +(-5.16042 - 3.74926i) q^{16} +(1.75822 - 2.41998i) q^{17} +(7.40641 + 2.40649i) q^{18} +(-0.664789 - 2.04601i) q^{19} -5.16413 q^{21} +(3.43582 - 7.63548i) q^{22} +8.77882i q^{23} +(-11.9563 + 8.68677i) q^{24} +(1.00515 - 3.09354i) q^{26} +(0.122903 - 0.169161i) q^{27} +(5.38140 - 7.40686i) q^{28} +(0.189313 - 0.582646i) q^{29} +(2.94887 - 2.14248i) q^{31} -4.12048i q^{32} +(-6.05812 - 5.49833i) q^{33} +7.55150 q^{34} +(4.16875 + 12.8301i) q^{36} +(1.77921 + 0.578100i) q^{37} +(3.19227 - 4.39378i) q^{38} +(-2.57128 - 1.86814i) q^{39} +(-1.57810 - 4.85689i) q^{41} +(-7.66294 - 10.5471i) q^{42} +5.17287i q^{43} +(14.1992 - 2.95944i) q^{44} +(-17.9297 + 13.0267i) q^{46} +(-6.94907 + 2.25789i) q^{47} +(-14.9643 - 4.86218i) q^{48} +(-2.11737 - 1.53836i) q^{49} +(2.28012 - 7.01749i) q^{51} +(5.35892 - 1.74122i) q^{52} +(1.72939 + 2.38030i) q^{53} +0.527864 q^{54} +12.5428 q^{56} +(-3.11919 - 4.29320i) q^{57} +(1.47090 - 0.477925i) q^{58} +(2.00682 - 6.17636i) q^{59} +(0.406490 + 0.295332i) q^{61} +(8.75154 + 2.84355i) q^{62} +(-6.14191 + 1.99563i) q^{63} +(-1.90523 + 1.38423i) q^{64} +(2.24019 - 20.5318i) q^{66} +7.80964i q^{67} +(7.68907 + 10.5831i) q^{68} +(6.69176 + 20.5951i) q^{69} +(9.14526 + 6.64442i) q^{71} +(-10.8632 + 14.9519i) q^{72} +(-10.5730 - 3.43539i) q^{73} +(1.45943 + 4.49166i) q^{74} +9.40812 q^{76} +(1.41672 + 6.79732i) q^{77} -8.02363i q^{78} +(4.33558 - 3.14998i) q^{79} +(-2.70035 + 8.31082i) q^{81} +(7.57793 - 10.4301i) q^{82} +(6.37474 - 8.77408i) q^{83} +(6.97880 - 21.4785i) q^{84} +(-10.5650 + 7.67591i) q^{86} -1.51119i q^{87} +(14.7141 + 13.3545i) q^{88} +4.32336 q^{89} +(0.833541 + 2.56538i) q^{91} +(-36.5127 - 11.8637i) q^{92} +(5.28493 - 7.27408i) q^{93} +(-14.9230 - 10.8422i) q^{94} +(-3.14089 - 9.66666i) q^{96} +(-0.206696 - 0.284493i) q^{97} -6.60723i q^{98} +(-9.32995 - 4.19829i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 12 q^{4} + 26 q^{6} + 10 q^{9} - 10 q^{11} - 32 q^{14} - 40 q^{16} + 2 q^{19} - 24 q^{21} - 50 q^{24} - 28 q^{26} - 38 q^{29} + 12 q^{31} + 40 q^{34} + 42 q^{36} - 18 q^{39} - 8 q^{41} + 56 q^{44}+ \cdots - 8 q^{99}+O(q^{100}) \) 16 * q + 12 * q^4 + 26 * q^6 + 10 * q^9 - 10 * q^11 - 32 * q^14 - 40 * q^16 + 2 * q^19 - 24 * q^21 - 50 * q^24 - 28 * q^26 - 38 * q^29 + 12 * q^31 + 40 * q^34 + 42 * q^36 - 18 * q^39 - 8 * q^41 + 56 * q^44 - 82 * q^46 + 30 * q^49 + 26 * q^51 + 80 * q^54 + 60 * q^56 + 38 * q^59 - 4 * q^61 - 12 * q^64 + 26 * q^66 + 42 * q^69 + 80 * q^71 - 96 * q^74 + 32 * q^76 - 34 * q^79 + 8 * q^84 - 62 * q^86 - 24 * q^91 - 66 * q^94 + 46 * q^96 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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