LMFDB - Embedded newform 275.2.z.b.224.1

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)

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")

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);

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			224.1
Root			$-2.34600 - 0.762262i$ of defining polynomial
Character	$\chi$	$=$	275.224
Dual form			275.2.z.b.124.1

$q$-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 $\left(\mathbb{Z}/275\mathbb{Z}\right)^\times$.

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

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	−0.159812	+	0.987148i	$0.551089\pi$
$2$	−1.48388	+	2.04238i	−1.04926	+	1.44418i	−0.889449	+	0.457035i	$0.848911\pi$
$3$	−2.34600	−	0.762262i	−1.35446	−	0.440092i	−0.460273	−	0.887777i	$-0.652249\pi$
$3$	−2.34600	−	0.762262i	−1.35446	−	0.440092i	−0.894191	+	0.447685i	$0.852249\pi$
$4$	−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	$-0.470524\pi$
$7$	1.99105	−	0.646930i	0.752545	−	0.244517i	0.660076	+	0.751199i	$0.270524\pi$
$8$	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	$-0.742818\pi$
$13$	0.757336	−	1.04238i	0.210047	−	0.289105i	0.901022	+	0.433774i	$0.142818\pi$
$14$	−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	$-0.318160\pi$
$17$	−1.75822	−	2.41998i	−0.426430	−	0.586931i	−0.967129	+	0.254285i	$0.918160\pi$
$18$	−7.40641	+	2.40649i	−1.74571	+	0.567215i
$19$	−0.664789	+	2.04601i	−0.152513	+	0.469387i	−0.997900	−	0.0647668i	$-0.979370\pi$
$19$	−0.664789	+	2.04601i	−0.152513	+	0.469387i	0.845387	+	0.534154i	$0.179370\pi$
$20$		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	0.967094	−	0.254419i	$-0.0818844\pi$
$29$	0.189313	+	0.582646i	0.0351545	+	0.108195i	−0.931939	+	0.362614i	$0.881884\pi$
$30$		0			0
$31$	2.94887	+	2.14248i	0.529633	+	0.384801i	0.820221	−	0.572047i	$-0.193851\pi$
$31$	2.94887	+	2.14248i	0.529633	+	0.384801i	−0.290587	+	0.956848i	$0.593851\pi$
$32$		−	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	$-0.649144\pi$
$37$	−1.77921	+	0.578100i	−0.292500	+	0.0950391i	0.159091	+	0.987264i	$0.449144\pi$
$38$	−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	0.748935	+	0.662643i	$0.230565\pi$
$41$	−1.57810	+	4.85689i	−0.246458	+	0.758519i	−0.995393	+	0.0958763i	$0.969435\pi$
$42$	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	$-0.221104\pi$
$47$	6.94907	+	2.25789i	1.01363	+	0.329347i	0.245329	+	0.969440i	$0.421104\pi$
$48$	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	$-0.864767\pi$
$53$	−1.72939	+	2.38030i	−0.237549	+	0.326959i	0.673553	+	0.739139i	$0.264767\pi$
$54$	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	0.992530	+	0.121999i	$0.0389306\pi$
$59$	2.00682	+	6.17636i	0.261266	+	0.804094i	−0.731264	+	0.682094i	$0.761069\pi$
$60$		0			0
$61$	0.406490	−	0.295332i	0.0520457	−	0.0378134i	−0.561458	−	0.827505i	$-0.689759\pi$
$61$	0.406490	−	0.295332i	0.0520457	−	0.0378134i	0.613504	+	0.789692i	$0.289759\pi$
$62$	−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	0.106736	−	0.994287i	$-0.465960\pi$
$71$	9.14526	−	6.64442i	1.08534	−	0.788548i	0.978607	+	0.205740i	$0.0659600\pi$
$72$	10.8632	+	14.9519i	1.28024	+	1.76210i
$73$	10.5730	−	3.43539i	1.23748	−	0.402082i	0.384061	−	0.923308i	$-0.374525\pi$
$73$	10.5730	−	3.43539i	1.23748	−	0.402082i	0.853419	+	0.521226i	$0.174525\pi$
$74$	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	0.804334	−	0.594177i	$-0.202522\pi$
$79$	4.33558	+	3.14998i	0.487791	+	0.354401i	−0.316543	+	0.948578i	$0.602522\pi$
$80$		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	−0.999958	−	0.00921619i	$-0.997066\pi$
$83$	−6.37474	−	8.77408i	−0.699719	−	0.963080i	0.300239	−	0.953864i	$-0.402934\pi$
$84$	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	$-0.794317\pi$
$97$	0.206696	−	0.284493i	0.0209868	−	0.0288859i	0.819381	+	0.573249i	$0.194317\pi$
$98$		−	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	0.998938	−	0.0460722i	$-0.0146704\pi$
$101$	12.7011	+	9.22791i	1.26381	+	0.918211i	0.264872	+	0.964284i	$0.414670\pi$
$102$	−17.7158	−	5.75622i	−1.75413	−	0.569951i
$103$	−6.35297	+	2.06420i	−0.625977	+	0.203392i	−0.604792	−	0.796383i	$-0.706744\pi$
$103$	−6.35297	+	2.06420i	−0.625977	+	0.203392i	−0.0211846	+	0.999776i	$0.506744\pi$
$104$	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	$-0.672091\pi$
$107$	−14.8441	−	4.82313i	−1.43503	−	0.466269i	−0.920344	+	0.391110i	$0.872091\pi$
$108$	−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	$-0.260066\pi$
$113$	8.60538	+	2.79606i	0.809526	+	0.263031i	0.125129	+	0.992140i	$0.460066\pi$
$114$	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	0.935560	+	0.353169i	$0.114896\pi$
$127$	11.0704	+	15.2371i	0.982339	+	1.35207i	0.0467796	+	0.998905i	$0.485104\pi$
$128$	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	−0.969671	−	0.244414i	$-0.921404\pi$
$137$	−10.5632	−	14.5390i	−0.902478	−	1.24215i	0.0671930	−	0.997740i	$-0.478596\pi$
$138$	32.1334	+	44.2278i	2.73537	+	3.76492i
$139$	−5.21098	−	16.0377i	−0.441989	−	1.36030i	−0.885752	−	0.464159i	$-0.846357\pi$
$139$	−5.21098	−	16.0377i	−0.441989	−	1.36030i	0.443762	−	0.896145i	$-0.353643\pi$
$140$		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	−0.507759	−	0.861499i	$-0.669526\pi$
$149$	1.88797	−	1.37169i	0.154669	−	0.112373i	0.662428	+	0.749126i	$0.269526\pi$
$150$		0			0
$151$	−1.21718	+	3.74609i	−0.0990525	+	0.304852i	−0.988289	−	0.152596i	$-0.951237\pi$
$151$	−1.21718	+	3.74609i	−0.0990525	+	0.304852i	0.889236	+	0.457448i	$0.151237\pi$
$152$	−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	$-0.337602\pi$
$157$	4.64218	+	1.50834i	0.370486	+	0.120378i	−0.117856	+	0.993031i	$0.537602\pi$
$158$	−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	$-0.888857\pi$
$163$	−4.13549	+	5.69202i	−0.323917	+	0.445833i	0.615741	+	0.787948i	$0.288857\pi$
$164$	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	$-0.936131\pi$
$167$	−6.30075	+	8.67223i	−0.487566	+	0.671078i	0.492370	+	0.870386i	$0.336131\pi$
$168$	−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	$-0.296395\pi$
$173$	8.00012	+	2.59940i	0.608238	+	0.197628i	0.0113267	+	0.999936i	$0.496395\pi$
$174$	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	0.344824	+	0.938667i	$0.387939\pi$
$179$	−6.50062	+	20.0069i	−0.485879	+	1.49538i	−0.830703	+	0.556716i	$0.812061\pi$
$180$		0			0
$181$	1.41020	−	1.02457i	0.104819	−	0.0761557i	−0.534141	−	0.845395i	$-0.679365\pi$
$181$	1.41020	−	1.02457i	0.104819	−	0.0761557i	0.638960	+	0.769240i	$0.279365\pi$
$182$	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	0.951335	−	0.308158i	$-0.0997126\pi$
$191$	0.00771200	+	0.0237351i	0.000558021	+	0.00171741i	−0.950777	+	0.309876i	$0.899713\pi$
$192$	3.41452	+	4.69969i	0.246422	+	0.339171i
$193$	−0.856548	−	1.17894i	−0.0616557	−	0.0848618i	0.777076	−	0.629407i	$-0.216702\pi$
$193$	−0.856548	−	1.17894i	−0.0616557	−	0.0848618i	−0.838731	+	0.544545i	$0.816702\pi$
$194$	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	0.418982	−	0.907995i	$-0.362387\pi$
$211$	−4.57709	−	3.32545i	−0.315100	−	0.228934i	−0.734082	+	0.679061i	$0.762387\pi$
$212$	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	$-0.314961\pi$
$223$	7.49852	+	2.43642i	0.502138	+	0.163155i	−0.0469856	+	0.998896i	$0.514961\pi$
$224$	−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	$-0.721350\pi$
$227$	−10.6627	+	3.46451i	−0.707706	+	0.229948i	−0.0670213	+	0.997752i	$0.521350\pi$
$228$	−22.0715	−	7.17145i	−1.46172	−	0.474941i
$229$	21.8360	+	15.8647i	1.44296	+	1.04837i	0.987413	+	0.158160i	$0.0505563\pi$
$229$	21.8360	+	15.8647i	1.44296	+	1.04837i	0.455547	+	0.890212i	$0.349444\pi$
$230$		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	$-0.915665\pi$
$233$	−6.37792	+	8.77845i	−0.417831	+	0.575095i	0.547275	+	0.836953i	$0.315665\pi$
$234$	−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	−0.768643	−	0.639678i	$-0.779068\pi$
$239$	3.54327	−	10.9051i	0.229195	−	0.705391i	0.997839	−	0.0657129i	$-0.0209322\pi$
$240$		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	0.853993	−	0.520285i	$-0.174174\pi$
$251$	9.87130	+	7.17192i	0.623071	+	0.452687i	−0.230922	+	0.972972i	$0.574174\pi$
$252$		−	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	$-0.658870\pi$
$257$	−5.60747	+	1.82198i	−0.349784	+	0.113652i	0.128855	+	0.991663i	$0.458870\pi$
$258$	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	−0.693757	−	0.720209i	$-0.744046\pi$
$269$	−3.66042	+	2.65945i	−0.223180	+	0.162149i	0.470577	+	0.882359i	$0.344046\pi$
$270$		0			0
$271$	−6.72447	−	20.6958i	−0.408482	−	1.25718i	−0.917952	−	0.396691i	$-0.870159\pi$
$271$	−6.72447	−	20.6958i	−0.408482	−	1.25718i	0.509470	−	0.860488i	$-0.329841\pi$
$272$	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	$-0.671926\pi$
$277$	7.66154	−	10.5452i	0.460337	−	0.633600i	0.974579	+	0.224046i	$0.0719265\pi$
$278$	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	−0.790766	−	0.612119i	$-0.790317\pi$
$281$	−7.59310	+	5.51671i	−0.452966	+	0.329099i	0.337799	+	0.941218i	$0.390317\pi$
$282$	43.2741	−	14.0606i	2.57694	−	0.837297i
$283$	13.2574	+	4.30760i	0.788072	+	0.256060i	0.675283	−	0.737559i	$-0.264021\pi$
$283$	13.2574	+	4.30760i	0.788072	+	0.256060i	0.112789	+	0.993619i	$0.464021\pi$
$284$	−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	$-0.949323\pi$
$293$	−28.9787	+	9.41576i	−1.69296	+	0.550075i	−0.705602	+	0.708608i	$0.749323\pi$
$294$	−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	−0.755112	−	0.655596i	$-0.772417\pi$
$311$	4.25249	−	13.0878i	0.241136	−	0.742141i	0.996248	−	0.0865451i	$-0.0275827\pi$
$312$	−18.1099	+	5.88426i	−1.02527	+	0.333131i
$313$	−9.37676	−	12.9060i	−0.530006	−	0.729491i	0.457125	−	0.889402i	$-0.348879\pi$
$313$	−9.37676	−	12.9060i	−0.530006	−	0.729491i	−0.987131	+	0.159912i	$0.948879\pi$
$314$	−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	$-0.897218\pi$
$317$	−6.29364	+	8.66246i	−0.353486	+	0.486532i	0.594833	+	0.803849i	$0.297218\pi$
$318$			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	$-0.702228\pi$
$337$	−11.0225	+	3.58143i	−0.600434	+	0.195093i	−0.00699978	+	0.999976i	$0.502228\pi$
$338$	−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	$-0.241892\pi$
$347$	−2.87368	−	3.95529i	−0.154267	−	0.212331i	−0.879155	+	0.476537i	$0.841892\pi$
$348$	−6.28533	+	2.04223i	−0.336929	+	0.109475i
$349$	−0.294654	+	0.906853i	−0.0157725	+	0.0485427i	−0.958633	−	0.284645i	$-0.908124\pi$
$349$	−0.294654	+	0.906853i	−0.0157725	+	0.0485427i	0.942861	+	0.333188i	$0.108124\pi$
$350$		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	−0.968970	−	0.247180i	$-0.920496\pi$
$359$	−6.25915	−	19.2637i	−0.330345	−	1.01670i	0.638624	−	0.769519i	$-0.279504\pi$
$360$		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	$-0.219296\pi$
$367$	33.9099	−	11.0180i	1.77008	−	0.575135i	0.998163	+	0.0605844i	$0.0192964\pi$
$368$	−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	−0.429364	−	0.903131i	$-0.641262\pi$
$379$	5.77971	−	4.19921i	0.296884	−	0.215699i	0.726248	+	0.687433i	$0.241262\pi$
$380$		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	$-0.666284\pi$
$383$	9.38279	−	12.9143i	0.479438	−	0.659890i	0.978397	+	0.206736i	$0.0662840\pi$
$384$	−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	0.930423	+	0.366488i	$0.119440\pi$
$389$	7.75336	+	23.8624i	0.393111	+	1.20987i	−0.537312	+	0.843384i	$0.680560\pi$
$390$		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	−0.990637	−	0.136524i	$-0.956407\pi$
$401$	−23.3675	+	16.9775i	−1.16692	+	0.847815i	−0.176281	+	0.984340i	$0.556407\pi$
$402$	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	0.763319	−	0.646022i	$-0.223569\pi$
$409$	7.78197	+	5.65393i	0.384794	+	0.279569i	−0.378525	+	0.925591i	$0.623569\pi$
$410$		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	−0.989652	−	0.143490i	$-0.954168\pi$
$421$	−2.14755	+	6.60949i	−0.104665	+	0.322127i	0.884986	+	0.465617i	$0.154168\pi$
$422$	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	0.649013	−	0.760778i	$-0.275182\pi$
$431$	2.61636	+	1.90090i	0.126026	+	0.0915631i	−0.522987	+	0.852341i	$0.675182\pi$
$432$	1.26846	+	0.412147i	0.0610287	+	0.0198294i
$433$	28.9044	−	9.39161i	1.38906	−	0.451332i	0.483421	−	0.875388i	$-0.339394\pi$
$433$	28.9044	−	9.39161i	1.38906	−	0.451332i	0.905636	+	0.424056i	$0.139394\pi$
$434$	−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	$-0.416352\pi$
$443$	−2.05574	−	0.667949i	−0.0976710	−	0.0317352i	−0.357445	+	0.933934i	$0.616352\pi$
$444$	−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	0.345697	−	0.938346i	$-0.387642\pi$
$449$	−9.32124	−	6.77228i	−0.439897	−	0.319604i	−0.785594	+	0.618742i	$0.787642\pi$
$450$		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	$-0.321541\pi$
$457$	−9.36427	−	12.8888i	−0.438042	−	0.602913i	−0.969776	+	0.243999i	$0.921541\pi$
$458$	−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	$-0.244756\pi$
$467$	−3.56020	−	4.90020i	−0.164746	−	0.226754i	−0.883406	+	0.468608i	$0.844756\pi$
$468$	−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	−0.863576	−	0.504219i	$-0.831780\pi$
$479$	−14.2455	+	10.3500i	−0.650894	+	0.472902i	0.212681	+	0.977122i	$0.431780\pi$
$480$		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	$-0.449117\pi$
$487$	−6.45140	−	2.09619i	−0.292341	−	0.0949874i	−0.451516	+	0.892263i	$0.649117\pi$
$488$	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	0.954608	−	0.297866i	$-0.0962749\pi$
$491$	0.160261	+	0.493232i	0.00723247	+	0.0222592i	−0.947375	+	0.320125i	$0.896275\pi$
$492$	−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	−0.980631	−	0.195866i	$-0.937248\pi$
$499$	−6.75534	−	20.7908i	−0.302411	−	0.930725i	0.678220	−	0.734859i	$-0.262752\pi$
$500$		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	$-0.378576\pi$
$503$	2.86902	+	0.932202i	0.127923	+	0.0415649i	−0.244356	+	0.969686i	$0.578576\pi$
$504$	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	−0.605542	−	0.795814i	$-0.707043\pi$
$509$	7.94418	−	24.4497i	0.352119	−	1.08371i	0.957661	−	0.287898i	$-0.0929565\pi$
$510$		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	0.997702	−	0.0677588i	$-0.0215848\pi$
$521$	3.44017	+	10.5877i	0.150716	+	0.463858i	−0.846985	+	0.531616i	$0.821585\pi$
$522$	−2.80426	−	3.85974i	−0.122739	−	0.168936i
$523$	3.84318	+	5.28968i	0.168050	+	0.231302i	0.884733	−	0.466098i	$-0.154340\pi$
$523$	3.84318	+	5.28968i	0.168050	+	0.231302i	−0.716683	+	0.697399i	$0.754340\pi$
$524$	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	−0.985403	−	0.170239i	$-0.945546\pi$
$541$	−33.7684	−	24.5342i	−1.45182	−	1.05481i	−0.466413	−	0.884567i	$-0.654454\pi$
$542$	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	$-0.369630\pi$
$547$	4.23806	+	1.37703i	0.181206	+	0.0588775i	−0.217008	+	0.976170i	$0.569630\pi$
$548$	−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	$-0.465391\pi$
$557$	18.4233	−	5.98608i	0.780619	−	0.253638i	0.672104	+	0.740456i	$0.265391\pi$
$558$	−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	$-0.656002\pi$
$563$	12.1925	−	16.7816i	0.513853	−	0.707259i	0.984563	+	0.175030i	$0.0560021\pi$
$564$	−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	−0.162458	−	0.986716i	$-0.551942\pi$
$569$	13.0945	−	40.3007i	0.548950	−	1.68949i	0.711408	−	0.702779i	$-0.248058\pi$
$570$		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	0.983289	+	0.182050i	$0.0582733\pi$
$577$	20.4796	+	28.1877i	0.852576	+	1.17347i	−0.130713	+	0.991420i	$0.541727\pi$
$578$	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	$-0.691776\pi$
$587$	−13.1039	+	4.25772i	−0.540857	+	0.175735i	0.0258331	+	0.999666i	$0.491776\pi$
$588$	−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	−0.826170	−	0.563421i	$-0.809485\pi$
$599$	−13.3539	+	9.70216i	−0.545624	+	0.396419i	0.280545	+	0.959841i	$0.409485\pi$
$600$		0			0
$601$	12.2509	+	37.7045i	0.499726	+	1.53800i	0.809460	+	0.587175i	$0.199760\pi$
$601$	12.2509	+	37.7045i	0.499726	+	1.53800i	−0.309734	+	0.950823i	$0.600240\pi$
$602$	−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	$-0.892979\pi$
$607$	−8.34036	+	11.4795i	−0.338525	+	0.465939i	0.605485	+	0.795857i	$0.292979\pi$
$608$	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	$-0.191586\pi$
$613$	28.6785	+	9.31820i	1.15831	+	0.376359i	0.334044	+	0.942557i	$0.391586\pi$
$614$	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	0.452775	+	0.891625i	$0.350434\pi$
$619$	−10.8876	+	33.5087i	−0.437611	+	1.34683i	−0.890387	+	0.455205i	$0.849566\pi$
$620$		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	0.980114	−	0.198436i	$-0.0635863\pi$
$631$	1.77213	+	5.45404i	0.0705472	+	0.217122i	−0.909567	+	0.415558i	$0.863586\pi$
$632$	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	−0.985075	−	0.172124i	$-0.944937\pi$
$641$	−2.20167	+	6.77605i	−0.0869608	+	0.267638i	0.898115	+	0.439762i	$0.144937\pi$
$642$	−92.4388	+	30.0352i	−3.64827	+	1.18539i
$643$	12.4549	+	17.1427i	0.491173	+	0.676042i	0.980604	−	0.196000i	$-0.0627953\pi$
$643$	12.4549	+	17.1427i	0.491173	+	0.676042i	−0.489431	+	0.872042i	$0.662795\pi$
$644$	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	$-0.764576\pi$
$647$	3.32083	−	4.57074i	0.130555	−	0.179694i	0.869290	+	0.494302i	$0.164576\pi$
$648$		−	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	$-0.500524\pi$
$653$	14.9441	−	4.85563i	0.584808	−	0.190016i	0.586453	+	0.809983i	$0.300524\pi$
$654$	−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	−0.268525	−	0.963273i	$-0.586536\pi$
$673$	18.9529	−	26.0864i	0.730580	−	1.00556i	0.999106	−	0.0422850i	$-0.0134637\pi$
$674$	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	$-0.0904215\pi$
$677$	10.3230	+	14.2084i	0.396745	+	0.546073i	−0.563178	+	0.826336i	$0.690422\pi$
$678$	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	0.196629	−	0.980478i	$-0.437001\pi$
$691$	−17.7463	−	12.8934i	−0.675100	−	0.490489i	−0.871728	+	0.489989i	$0.837001\pi$
$692$		−	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	−0.562761	−	0.826620i	$-0.690261\pi$
$701$	10.0186	−	30.8341i	0.378397	−	1.16459i	0.941158	−	0.337967i	$-0.109739\pi$
$702$	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	−0.804871	−	0.593450i	$-0.797765\pi$
$709$	−13.0256	+	9.46362i	−0.489185	+	0.355414i	0.315686	+	0.948864i	$0.397765\pi$
$710$		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	0.985927	−	0.167178i	$-0.0534655\pi$
$719$	2.41409	+	7.42981i	0.0900304	+	0.277085i	−0.895896	+	0.444263i	$0.853466\pi$
$720$		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	$-0.596073\pi$
$733$	0.635255	−	0.206407i	0.0234637	−	0.00762382i	0.320725	+	0.947172i	$0.396073\pi$
$734$	−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	0.986227	−	0.165400i	$-0.0528916\pi$
$739$	30.8186	+	22.3911i	1.13368	+	0.823668i	0.147456	+	0.989069i	$0.452892\pi$
$740$		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	$-0.00508114\pi$
$743$	18.4186	+	25.3511i	0.675714	+	0.930041i	−0.324159	+	0.946003i	$0.605081\pi$
$744$	−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	0.488986	+	0.872292i	$0.337367\pi$
$751$	−11.4915	+	35.3673i	−0.419332	+	1.29057i	−0.908318	+	0.418280i	$0.862633\pi$
$752$	−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	$-0.838741\pi$
$757$	−3.92680	+	5.40478i	−0.142722	+	0.196440i	0.731672	+	0.681657i	$0.238741\pi$
$758$			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	0.870493	−	0.492181i	$-0.163800\pi$
$761$	18.5213	+	13.4565i	0.671398	+	0.487799i	−0.199095	+	0.979980i	$0.563800\pi$
$762$	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	$-0.471707\pi$
$773$	−11.8130	−	3.83827i	−0.424883	−	0.138053i	−0.513651	+	0.857999i	$0.671707\pi$
$774$	−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	$-0.0749148\pi$
$787$	12.6286	+	17.3818i	0.450162	+	0.619595i	−0.522270	+	0.852780i	$0.674915\pi$
$788$	−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	$-0.187993\pi$
$797$	1.25157	+	1.72264i	0.0443330	+	0.0610191i	−0.786275	+	0.617877i	$0.787993\pi$
$798$	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	−0.661430	−	0.750007i	$-0.730050\pi$
$809$	−4.33820	+	3.15189i	−0.152523	+	0.110815i	0.508906	+	0.860822i	$0.330050\pi$
$810$		0			0
$811$	6.05047	−	18.6214i	0.212461	−	0.653887i	−0.786863	−	0.617127i	$-0.788296\pi$
$811$	6.05047	−	18.6214i	0.212461	−	0.653887i	0.999324	−	0.0367600i	$-0.0117037\pi$
$812$	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	0.820387	−	0.571808i	$-0.193758\pi$
$821$	−5.14095	−	15.8222i	−0.179420	−	0.552199i	−0.999808	+	0.0196092i	$0.993758\pi$
$822$	−106.435	−	34.5829i	−3.71236	−	1.20622i
$823$	−10.7523	+	14.7993i	−0.374801	+	0.515870i	−0.954198	−	0.299176i	$-0.903288\pi$
$823$	−10.7523	+	14.7993i	−0.374801	+	0.515870i	0.579397	+	0.815046i	$0.303288\pi$
$824$	−40.0210			−1.39420
$825$		0			0
$826$	−34.3227			−1.19424
$827$	22.3466	−	30.7575i	0.777069	−	1.06954i	−0.218530	−	0.975830i	$-0.570126\pi$
$827$	22.3466	−	30.7575i	0.777069	−	1.06954i	0.995599	−	0.0937136i	$-0.0298738\pi$
$828$	112.633	+	36.5967i	3.91427	+	1.27182i
$829$	−15.9762	−	49.1698i	−0.554877	−	1.70774i	−0.696267	−	0.717783i	$-0.745157\pi$
$829$	−15.9762	−	49.1698i	−0.554877	−	1.70774i	0.141389	−	0.989954i	$-0.454843\pi$
$830$		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	0.503227	+	0.864154i	$0.332146\pi$
$839$	−11.9288	+	36.7132i	−0.411829	+	1.26748i	−0.915056	+	0.403326i	$0.867854\pi$
$840$		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	$-0.397126\pi$
$853$	−19.9293	−	27.4303i	−0.682366	−	0.939197i	−0.999959	+	0.00903033i	$0.997126\pi$
$854$	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	−0.999658	−	0.0261347i	$-0.991680\pi$
$863$	−21.0222	−	28.9345i	−0.715603	−	0.984942i	0.284056	−	0.958808i	$-0.408320\pi$
$864$	−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	$-0.494408\pi$
$877$	−16.4629	−	5.34913i	−0.555913	−	0.180627i	−0.573482	+	0.819218i	$0.694408\pi$
$878$	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	$-0.644344\pi$
$883$	−39.2505	−	12.7533i	−1.32088	−	0.429182i	−0.882799	+	0.469751i	$0.844344\pi$
$884$	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	$-0.429019\pi$
$887$	28.9873	−	9.41854i	0.973297	−	0.316243i	0.752146	+	0.658996i	$0.229019\pi$
$888$	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	$-0.139984\pi$
$907$	6.63578	+	9.13337i	0.220338	+	0.303269i	−0.684511	+	0.729003i	$0.739984\pi$
$908$	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	−0.998661	−	0.0517251i	$-0.983528\pi$
$911$	−40.9417	−	29.7459i	−1.35646	−	0.985525i	−0.357797	−	0.933799i	$-0.616472\pi$
$912$			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	−0.888412	−	0.459048i	$-0.848191\pi$
$919$	−22.0198	+	15.9983i	−0.726366	+	0.527736i	0.162046	+	0.986783i	$0.448191\pi$
$920$		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	−0.851548	−	0.524277i	$-0.824336\pi$
$929$	−18.7776	+	13.6427i	−0.616073	+	0.447603i	0.235475	+	0.971880i	$0.424336\pi$
$930$		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	−0.180684	−	0.983541i	$-0.557831\pi$
$937$	24.8114	−	34.1500i	0.810554	−	1.11563i	0.991238	−	0.132090i	$-0.0421689\pi$
$938$	−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	−0.131658	−	0.991295i	$-0.542030\pi$
$941$	23.6336	−	17.1708i	0.770435	−	0.559754i	0.902093	+	0.431542i	$0.142030\pi$
$942$	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	$-0.626952\pi$
$953$	−4.96593	+	1.61353i	−0.160862	+	0.0522673i	0.227479	+	0.973783i	$0.426952\pi$
$954$	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	−0.462111	−	0.886822i	$-0.652908\pi$
$971$	13.4928	−	41.5267i	0.433006	−	1.33265i	0.895116	−	0.445832i	$-0.147092\pi$
$972$	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	$-0.739830\pi$
$977$	6.90455	−	9.50330i	0.220896	−	0.304038i	0.905054	+	0.425296i	$0.139830\pi$
$978$			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	$-0.647650\pi$
$983$	−8.89417	+	2.88989i	−0.283680	+	0.0921733i	0.163721	+	0.986507i	$0.447650\pi$
$984$	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	$-0.752537\pi$
$997$	−27.6923	+	8.99777i	−0.877023	+	0.284962i	−0.164302	+	0.986410i	$0.552537\pi$
$998$	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.224.1		16
5.2	odd	4		55.2.g.a.26.1	✓	8
5.3	odd	4		275.2.h.b.26.2		8
5.4	even	2	inner	275.2.z.b.224.4		16
11.3	even	5	inner	275.2.z.b.124.4		16
15.2	even	4		495.2.n.f.136.2		8
20.7	even	4		880.2.bo.e.81.2		8
55.2	even	20		605.2.g.g.511.1		8
55.3	odd	20		275.2.h.b.201.2		8
55.7	even	20		605.2.g.g.251.1		8
55.14	even	10	inner	275.2.z.b.124.1		16
55.17	even	20		605.2.a.i.1.1		4
55.27	odd	20		605.2.a.l.1.4		4
55.28	even	20		3025.2.a.be.1.4		4
55.32	even	4		605.2.g.n.81.2		8
55.37	odd	20		605.2.g.j.251.2		8
55.38	odd	20		3025.2.a.v.1.1		4
55.42	odd	20		605.2.g.j.511.2		8
55.47	odd	20		55.2.g.a.36.1	yes	8
55.52	even	20		605.2.g.n.366.2		8
165.17	odd	20		5445.2.a.bu.1.4		4
165.47	even	20		495.2.n.f.91.2		8
165.137	even	20		5445.2.a.bg.1.1		4
220.27	even	20		9680.2.a.cs.1.4		4
220.47	even	20		880.2.bo.e.641.2		8
220.127	odd	20		9680.2.a.cv.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.g.a.26.1	✓	8	5.2	odd	4
55.2.g.a.36.1	yes	8	55.47	odd	20
275.2.h.b.26.2		8	5.3	odd	4
275.2.h.b.201.2		8	55.3	odd	20
275.2.z.b.124.1		16	55.14	even	10	inner
275.2.z.b.124.4		16	11.3	even	5	inner
275.2.z.b.224.1		16	1.1	even	1	trivial
275.2.z.b.224.4		16	5.4	even	2	inner
495.2.n.f.91.2		8	165.47	even	20
495.2.n.f.136.2		8	15.2	even	4
605.2.a.i.1.1		4	55.17	even	20
605.2.a.l.1.4		4	55.27	odd	20
605.2.g.g.251.1		8	55.7	even	20
605.2.g.g.511.1		8	55.2	even	20
605.2.g.j.251.2		8	55.37	odd	20
605.2.g.j.511.2		8	55.42	odd	20
605.2.g.n.81.2		8	55.32	even	4
605.2.g.n.366.2		8	55.52	even	20
880.2.bo.e.81.2		8	20.7	even	4
880.2.bo.e.641.2		8	220.47	even	20
3025.2.a.v.1.1		4	55.38	odd	20
3025.2.a.be.1.4		4	55.28	even	20
5445.2.a.bg.1.1		4	165.137	even	20
5445.2.a.bu.1.4		4	165.17	odd	20
9680.2.a.cs.1.4		4	220.27	even	20
9680.2.a.cv.1.4		4	220.127	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

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Representations

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Database

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