LMFDB - Embedded newform 275.2.h.b.201.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [275,2,Mod(26,275)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(275, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("275.26");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 275 = 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	275.h (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$2.19588605559$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.159390625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 6x^{6} - 11x^{5} + 21x^{4} - 5x^{3} + 10x^{2} + 25x + 25 $ x^8 - x^7 + 6x^6 - 11x^5 + 21x^4 - 5x^3 + 10x^2 + 25x + 25
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 55)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			201.2
Root			$-0.762262 - 2.34600i$ of defining polynomial
Character	$\chi$	$=$	275.201
Dual form			275.2.h.b.26.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.04238 - 1.48388i) q^{2} +(0.762262 + 2.34600i) q^{3} +(1.35140 - 4.15918i) q^{4} +(5.03801 + 3.66033i) q^{6} +(-0.646930 + 1.99105i) q^{7} +(-1.85140 - 5.69802i) q^{8} +(-2.49563 + 1.81318i) q^{9} +O(q^{10})$	\(q+(2.04238 - 1.48388i) q^{2} +(0.762262 + 2.34600i) q^{3} +(1.35140 - 4.15918i) q^{4} +(5.03801 + 3.66033i) q^{6} +(-0.646930 + 1.99105i) q^{7} +(-1.85140 - 5.69802i) q^{8} +(-2.49563 + 1.81318i) q^{9} +(-1.64693 - 2.87882i) q^{11} +10.7876 q^{12} +(1.04238 - 0.757336i) q^{13} +(1.63319 + 5.02644i) q^{14} +(-5.16042 - 3.74926i) q^{16} +(-2.41998 - 1.75822i) q^{17} +(-2.40649 + 7.40641i) q^{18} +(0.664789 + 2.04601i) q^{19} -5.16413 q^{21} +(-7.63548 - 3.43582i) q^{22} -8.77882 q^{23} +(11.9563 - 8.68677i) q^{24} +(1.00515 - 3.09354i) q^{26} +(-0.169161 - 0.122903i) q^{27} +(7.40686 + 5.38140i) q^{28} +(-0.189313 + 0.582646i) q^{29} +(2.94887 - 2.14248i) q^{31} -4.12048 q^{32} +(5.49833 - 6.05812i) q^{33} -7.55150 q^{34} +(4.16875 + 12.8301i) q^{36} +(0.578100 - 1.77921i) q^{37} +(4.39378 + 3.19227i) q^{38} +(2.57128 + 1.86814i) q^{39} +(-1.57810 - 4.85689i) q^{41} +(-10.5471 + 7.66294i) q^{42} -5.17287 q^{43} +(-14.1992 + 2.95944i) q^{44} +(-17.9297 + 13.0267i) q^{46} +(2.25789 + 6.94907i) q^{47} +(4.86218 - 14.9643i) q^{48} +(2.11737 + 1.53836i) q^{49} +(2.28012 - 7.01749i) q^{51} +(-1.74122 - 5.35892i) q^{52} +(-2.38030 + 1.72939i) q^{53} -0.527864 q^{54} +12.5428 q^{56} +(-4.29320 + 3.11919i) q^{57} +(0.477925 + 1.47090i) q^{58} +(-2.00682 + 6.17636i) q^{59} +(0.406490 + 0.295332i) q^{61} +(2.84355 - 8.75154i) q^{62} +(-1.99563 - 6.14191i) q^{63} +(1.90523 - 1.38423i) q^{64} +(2.24019 - 20.5318i) q^{66} +7.80964 q^{67} +(-10.5831 + 7.68907i) q^{68} +(-6.69176 - 20.5951i) q^{69} +(9.14526 + 6.64442i) q^{71} +(14.9519 + 10.8632i) q^{72} +(3.43539 - 10.5730i) q^{73} +(-1.45943 - 4.49166i) q^{74} +9.40812 q^{76} +(6.79732 - 1.41672i) q^{77} +8.02363 q^{78} +(-4.33558 + 3.14998i) q^{79} +(-2.70035 + 8.31082i) q^{81} +(-10.4301 - 7.57793i) q^{82} +(8.77408 + 6.37474i) q^{83} +(-6.97880 + 21.4785i) q^{84} +(-10.5650 + 7.67591i) q^{86} -1.51119 q^{87} +(-13.3545 + 14.7141i) q^{88} -4.32336 q^{89} +(0.833541 + 2.56538i) q^{91} +(-11.8637 + 36.5127i) q^{92} +(7.27408 + 5.28493i) q^{93} +(14.9230 + 10.8422i) q^{94} +(-3.14089 - 9.66666i) q^{96} +(-0.284493 + 0.206696i) q^{97} +6.60723 q^{98} +(9.32995 + 4.19829i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{2} - q^{3} - 6 q^{4} + 13 q^{6} + 3 q^{7} + 2 q^{8} - 5 q^{9}+O(q^{10}) $ 8 * q + 4 * q^2 - q^3 - 6 * q^4 + 13 * q^6 + 3 * q^7 + 2 * q^8 - 5 * q^9	$ 8 q + 4 q^{2} - q^{3} - 6 q^{4} + 13 q^{6} + 3 q^{7} + 2 q^{8} - 5 q^{9} - 5 q^{11} + 28 q^{12} - 4 q^{13} + 16 q^{14} - 20 q^{16} - q^{17} - 14 q^{18} - q^{19} - 12 q^{21} - 33 q^{22} + 18 q^{23} + 25 q^{24} - 14 q^{26} - 10 q^{27} - 4 q^{28} + 19 q^{29} + 6 q^{31} - 12 q^{32} + 19 q^{33} - 20 q^{34} + 21 q^{36} - 4 q^{37} + 6 q^{38} + 9 q^{39} - 4 q^{41} - 29 q^{42} - 42 q^{43} - 28 q^{44} - 41 q^{46} - 4 q^{47} + 19 q^{48} - 15 q^{49} + 13 q^{51} + 26 q^{52} - 3 q^{53} - 40 q^{54} + 30 q^{56} + 5 q^{57} + 6 q^{58} - 19 q^{59} - 2 q^{61} + 38 q^{62} - q^{63} + 6 q^{64} + 13 q^{66} + 2 q^{67} - 35 q^{68} - 21 q^{69} + 40 q^{71} + 34 q^{72} + 23 q^{73} + 48 q^{74} + 16 q^{76} + 28 q^{77} - 12 q^{78} + 17 q^{79} - 2 q^{82} + 25 q^{83} - 4 q^{84} - 31 q^{86} - 30 q^{87} - 22 q^{88} - 12 q^{91} - 81 q^{92} + 13 q^{93} + 33 q^{94} + 23 q^{96} - 12 q^{97} + 84 q^{98} + 4 q^{99}+O(q^{100}) $ 8 * q + 4 * q^2 - q^3 - 6 * q^4 + 13 * q^6 + 3 * q^7 + 2 * q^8 - 5 * q^9 - 5 * q^11 + 28 * q^12 - 4 * q^13 + 16 * q^14 - 20 * q^16 - q^17 - 14 * q^18 - q^19 - 12 * q^21 - 33 * q^22 + 18 * q^23 + 25 * q^24 - 14 * q^26 - 10 * q^27 - 4 * q^28 + 19 * q^29 + 6 * q^31 - 12 * q^32 + 19 * q^33 - 20 * q^34 + 21 * q^36 - 4 * q^37 + 6 * q^38 + 9 * q^39 - 4 * q^41 - 29 * q^42 - 42 * q^43 - 28 * q^44 - 41 * q^46 - 4 * q^47 + 19 * q^48 - 15 * q^49 + 13 * q^51 + 26 * q^52 - 3 * q^53 - 40 * q^54 + 30 * q^56 + 5 * q^57 + 6 * q^58 - 19 * q^59 - 2 * q^61 + 38 * q^62 - q^63 + 6 * q^64 + 13 * q^66 + 2 * q^67 - 35 * q^68 - 21 * q^69 + 40 * q^71 + 34 * q^72 + 23 * q^73 + 48 * q^74 + 16 * q^76 + 28 * q^77 - 12 * q^78 + 17 * q^79 - 2 * q^82 + 25 * q^83 - 4 * q^84 - 31 * q^86 - 30 * q^87 - 22 * q^88 - 12 * q^91 - 81 * q^92 + 13 * q^93 + 33 * q^94 + 23 * q^96 - 12 * q^97 + 84 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	2.04238	−	1.48388i	1.44418	−	1.04926i	0.457035	−	0.889449i	$-0.348911\pi$
$2$	2.04238	−	1.48388i	1.44418	−	1.04926i	0.987148	−	0.159812i	$-0.0510887\pi$
$3$	0.762262	+	2.34600i	0.440092	+	1.35446i	0.887777	+	0.460273i	$0.152249\pi$
$3$	0.762262	+	2.34600i	0.440092	+	1.35446i	−0.447685	+	0.894191i	$0.647751\pi$
$4$	1.35140	−	4.15918i	0.675700	−	2.07959i
$5$		0			0
$5$		0			0
$6$	5.03801	+	3.66033i	2.05676	+	1.49432i
$7$	−0.646930	+	1.99105i	−0.244517	+	0.752545i	0.751199	+	0.660076i	$0.229476\pi$
$7$	−0.646930	+	1.99105i	−0.244517	+	0.752545i	−0.995716	+	0.0924689i	$0.970524\pi$
$8$	−1.85140	−	5.69802i	−0.654569	−	2.01456i
$9$	−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
$12$	10.7876			3.11410
$13$	1.04238	−	0.757336i	0.289105	−	0.210047i	−0.433774	−	0.901022i	$-0.642818\pi$
$13$	1.04238	−	0.757336i	0.289105	−	0.210047i	0.722879	+	0.690975i	$0.242818\pi$
$14$	1.63319	+	5.02644i	0.436489	+	1.34337i
$15$		0			0
$16$	−5.16042	−	3.74926i	−1.29010	−	0.937316i
$17$	−2.41998	−	1.75822i	−0.586931	−	0.426430i	0.254285	−	0.967129i	$-0.418160\pi$
$17$	−2.41998	−	1.75822i	−0.586931	−	0.426430i	−0.841216	+	0.540699i	$0.818160\pi$
$18$	−2.40649	+	7.40641i	−0.567215	+	1.74571i
$19$	0.664789	+	2.04601i	0.152513	+	0.469387i	0.997900	−	0.0647668i	$-0.0206304\pi$
$19$	0.664789	+	2.04601i	0.152513	+	0.469387i	−0.845387	+	0.534154i	$0.820630\pi$
$20$		0			0
$21$	−5.16413			−1.12690
$22$	−7.63548	−	3.43582i	−1.62789	−	0.732518i
$23$	−8.77882			−1.83051			−0.915255	−	0.402874i	$-0.868011\pi$
$23$	−8.77882			−1.83051			−0.915255	+	0.402874i	$0.868011\pi$
$24$	11.9563	−	8.68677i	2.44057	−	1.77318i
$25$		0			0
$26$	1.00515	−	3.09354i	0.197126	−	0.606693i
$27$	−0.169161	−	0.122903i	−0.0325550	−	0.0236526i
$28$	7.40686	+	5.38140i	1.39977	+	1.01699i
$29$	−0.189313	+	0.582646i	−0.0351545	+	0.108195i	−0.967094	−	0.254419i	$-0.918116\pi$
$29$	−0.189313	+	0.582646i	−0.0351545	+	0.108195i	0.931939	+	0.362614i	$0.118116\pi$
$30$		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	$0.193851\pi$
$32$	−4.12048			−0.728405
$33$	5.49833	−	6.05812i	0.957136	−	1.05458i
$34$	−7.55150			−1.29507
$35$		0			0
$36$	4.16875	+	12.8301i	0.694792	+	2.13835i
$37$	0.578100	−	1.77921i	0.0950391	−	0.292500i	−0.892225	−	0.451592i	$-0.850856\pi$
$37$	0.578100	−	1.77921i	0.0950391	−	0.292500i	0.987264	+	0.159091i	$0.0508564\pi$
$38$	4.39378	+	3.19227i	0.712766	+	0.517855i
$39$	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	$-0.230565\pi$
$42$	−10.5471	+	7.66294i	−1.62746	+	1.18242i
$43$	−5.17287			−0.788856			−0.394428	−	0.918927i	$-0.629057\pi$
$43$	−5.17287			−0.788856			−0.394428	+	0.918927i	$0.629057\pi$
$44$	−14.1992	+	2.95944i	−2.14061	+	0.446152i
$45$		0			0
$46$	−17.9297	+	13.0267i	−2.64359	+	1.92068i
$47$	2.25789	+	6.94907i	0.329347	+	1.01363i	0.969440	+	0.245329i	$0.0788959\pi$
$47$	2.25789	+	6.94907i	0.329347	+	1.01363i	−0.640093	+	0.768298i	$0.721104\pi$
$48$	4.86218	−	14.9643i	0.701796	−	2.15991i
$49$	2.11737	+	1.53836i	0.302482	+	0.219766i
$50$		0			0
$51$	2.28012	−	7.01749i	0.319281	−	0.982645i
$52$	−1.74122	−	5.35892i	−0.241464	−	0.743149i
$53$	−2.38030	+	1.72939i	−0.326959	+	0.237549i	−0.739139	−	0.673553i	$-0.764767\pi$
$53$	−2.38030	+	1.72939i	−0.326959	+	0.237549i	0.412180	+	0.911102i	$0.364767\pi$
$54$	−0.527864			−0.0718332
$55$		0			0
$56$	12.5428			1.67610
$57$	−4.29320	+	3.11919i	−0.568648	+	0.413147i
$58$	0.477925	+	1.47090i	0.0627547	+	0.193139i
$59$	−2.00682	+	6.17636i	−0.261266	+	0.804094i	0.731264	+	0.682094i	$0.238931\pi$
$59$	−2.00682	+	6.17636i	−0.261266	+	0.804094i	−0.992530	+	0.121999i	$0.961069\pi$
$60$		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	$0.689759\pi$
$62$	2.84355	−	8.75154i	0.361131	−	1.11145i
$63$	−1.99563	−	6.14191i	−0.251425	−	0.773808i
$64$	1.90523	−	1.38423i	0.238154	−	0.173029i
$65$		0			0
$66$	2.24019	−	20.5318i	0.275748	−	2.52730i
$67$	7.80964			0.954099			0.477050	−	0.878876i	$-0.341706\pi$
$67$	7.80964			0.954099			0.477050	+	0.878876i	$0.341706\pi$
$68$	−10.5831	+	7.68907i	−1.28339	+	0.932437i
$69$	−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	$0.465960\pi$
$72$	14.9519	+	10.8632i	1.76210	+	1.28024i
$73$	3.43539	−	10.5730i	0.402082	−	1.23748i	−0.521226	−	0.853419i	$-0.674525\pi$
$73$	3.43539	−	10.5730i	0.402082	−	1.23748i	0.923308	−	0.384061i	$-0.125475\pi$
$74$	−1.45943	−	4.49166i	−0.169655	−	0.522145i
$75$		0			0
$76$	9.40812			1.07919
$77$	6.79732	−	1.41672i	0.774626	−	0.161450i
$78$	8.02363			0.908498
$79$	−4.33558	+	3.14998i	−0.487791	+	0.354401i	−0.804334	−	0.594177i	$-0.797478\pi$
$79$	−4.33558	+	3.14998i	−0.487791	+	0.354401i	0.316543	+	0.948578i	$0.397478\pi$
$80$		0			0
$81$	−2.70035	+	8.31082i	−0.300039	+	0.923425i
$82$	−10.4301	−	7.57793i	−1.15181	−	0.836842i
$83$	8.77408	+	6.37474i	0.963080	+	0.699719i	0.953864	−	0.300239i	$-0.0970664\pi$
$83$	8.77408	+	6.37474i	0.963080	+	0.699719i	0.00921619	+	0.999958i	$0.497066\pi$
$84$	−6.97880	+	21.4785i	−0.761450	+	2.34350i
$85$		0			0
$86$	−10.5650	+	7.67591i	−1.13925	+	0.827715i
$87$	−1.51119			−0.162017
$88$	−13.3545	+	14.7141i	−1.42359	+	1.56853i
$89$	−4.32336			−0.458275			−0.229137	−	0.973394i	$-0.573591\pi$
$89$	−4.32336			−0.458275			−0.229137	+	0.973394i	$0.573591\pi$
$90$		0			0
$91$	0.833541	+	2.56538i	0.0873788	+	0.268924i
$92$	−11.8637	+	36.5127i	−1.23688	+	3.80671i
$93$	7.27408	+	5.28493i	0.754287	+	0.548021i
$94$	14.9230	+	10.8422i	1.53920	+	1.11829i
$95$		0			0
$96$	−3.14089	−	9.66666i	−0.320566	−	0.986599i
$97$	−0.284493	+	0.206696i	−0.0288859	+	0.0209868i	−0.602135	−	0.798395i	$-0.705683\pi$
$97$	−0.284493	+	0.206696i	−0.0288859	+	0.0209868i	0.573249	+	0.819381i	$0.305683\pi$
$98$	6.60723			0.667431
$99$	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	$0.0146704\pi$
$102$	−5.75622	−	17.7158i	−0.569951	−	1.75413i
$103$	−2.06420	+	6.35297i	−0.203392	+	0.625977i	0.796383	+	0.604792i	$0.206744\pi$
$103$	−2.06420	+	6.35297i	−0.203392	+	0.625977i	−0.999776	+	0.0211846i	$0.993256\pi$
$104$	−6.24518	−	4.53739i	−0.612391	−	0.444928i
$105$		0			0
$106$	−2.29528	+	7.06414i	−0.222937	+	0.686130i
$107$	−4.82313	−	14.8441i	−0.466269	−	1.43503i	−0.857379	−	0.514685i	$-0.827909\pi$
$107$	−4.82313	−	14.8441i	−0.466269	−	1.43503i	0.391110	−	0.920344i	$-0.372091\pi$
$108$	−0.739779	+	0.537481i	−0.0711852	+	0.0517191i
$109$	11.5070			1.10217			0.551087	−	0.834448i	$-0.314213\pi$
$109$	11.5070			1.10217			0.551087	+	0.834448i	$0.314213\pi$
$110$		0			0
$111$	4.61469			0.438007
$112$	10.8034	−	7.84912i	1.02082	−	0.741672i
$113$	−2.79606	−	8.60538i	−0.263031	−	0.809526i	−0.992140	−	0.125129i	$-0.960066\pi$
$113$	−2.79606	−	8.60538i	−0.263031	−	0.809526i	0.729110	−	0.684397i	$-0.239934\pi$
$114$	−4.13986	+	12.7412i	−0.387733	+	1.19332i
$115$		0			0
$116$	2.16749	+	1.57477i	0.201246	+	0.146214i
$117$	−1.22821	+	3.78006i	−0.113548	+	0.349466i
$118$	5.06627	+	15.5924i	0.466388	+	1.43539i
$119$	5.06625	−	3.68084i	0.464422	−	0.337422i
$120$		0			0
$121$	−5.57524	+	9.48244i	−0.506840	+	0.862040i
$122$	1.26845			0.114840
$123$	10.1914	−	7.40445i	0.918923	−	0.667637i
$124$	−4.92586	−	15.1602i	−0.442356	−	1.36143i
$125$		0			0
$126$	−13.1897	−	9.58287i	−1.17503	−	0.853710i
$127$	15.2371	+	11.0704i	1.35207	+	0.982339i	0.998905	+	0.0467796i	$0.0148959\pi$
$127$	15.2371	+	11.0704i	1.35207	+	0.982339i	0.353169	+	0.935560i	$0.385104\pi$
$128$	4.38378	−	13.4919i	0.387475	−	1.19252i
$129$	−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	$0.841161\pi$
$132$	−17.7664	−	31.0555i	−1.54636	−	2.70303i
$133$	−4.50377			−0.390527
$134$	15.9503	−	11.5886i	1.37789	−	1.00110i
$135$		0			0
$136$	−5.53801	+	17.0442i	−0.474881	+	1.46153i
$137$	−14.5390	−	10.5632i	−1.24215	−	0.902478i	−0.244414	−	0.969671i	$-0.578596\pi$
$137$	−14.5390	−	10.5632i	−1.24215	−	0.902478i	−0.997740	+	0.0671930i	$0.978596\pi$
$138$	−44.2278	−	32.1334i	−3.76492	−	2.73537i
$139$	5.21098	−	16.0377i	0.441989	−	1.36030i	−0.443762	−	0.896145i	$-0.646357\pi$
$139$	5.21098	−	16.0377i	0.441989	−	1.36030i	0.885752	−	0.464159i	$-0.153643\pi$
$140$		0			0
$141$	−14.5814	+	10.5940i	−1.22798	+	0.892178i
$142$	28.5376			2.39482
$143$	−3.89697	−	1.75356i	−0.325881	−	0.146640i
$144$	19.6766			1.63971
$145$		0			0
$146$	−8.67272	−	26.6919i	−0.717759	−	2.20904i
$147$	−1.99500	+	6.13999i	−0.164545	+	0.506418i
$148$	−6.61881	−	4.80885i	−0.544063	−	0.395285i
$149$	−1.88797	−	1.37169i	−0.154669	−	0.112373i	0.507759	−	0.861499i	$-0.330474\pi$
$149$	−1.88797	−	1.37169i	−0.154669	−	0.112373i	−0.662428	+	0.749126i	$0.730474\pi$
$150$		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	$0.951237\pi$
$152$	10.4274	−	7.57597i	0.845776	−	0.614492i
$153$	9.22732			0.745985
$154$	11.7805	−	12.9799i	0.949299	−	1.04595i
$155$		0			0
$156$	11.2448	−	8.16981i	0.900302	−	0.654108i
$157$	1.50834	+	4.64218i	0.120378	+	0.370486i	0.993031	−	0.117856i	$-0.0376020\pi$
$157$	1.50834	+	4.64218i	0.120378	+	0.370486i	−0.872652	+	0.488342i	$0.837602\pi$
$158$	−4.18073	+	12.8669i	−0.332601	+	1.02364i
$159$	−5.87155	−	4.26593i	−0.465644	−	0.338310i
$160$		0			0
$161$	5.67928	−	17.4790i	0.447590	−	1.37754i
$162$	6.81710	+	20.9809i	0.535602	+	1.64841i
$163$	−5.69202	+	4.13549i	−0.445833	+	0.323917i	−0.787948	−	0.615741i	$-0.788857\pi$
$163$	−5.69202	+	4.13549i	−0.445833	+	0.323917i	0.342115	+	0.939658i	$0.388857\pi$
$164$	−22.3333			−1.74394
$165$		0			0
$166$	27.3794			2.12505
$167$	8.67223	−	6.30075i	0.671078	−	0.487566i	−0.199308	−	0.979937i	$-0.563869\pi$
$167$	8.67223	−	6.30075i	0.671078	−	0.487566i	0.870386	+	0.492370i	$0.163869\pi$
$168$	9.56086	+	29.4253i	0.737637	+	2.27021i
$169$	−3.50422	+	10.7849i	−0.269555	+	0.829605i
$170$		0			0
$171$	−5.36885	−	3.90070i	−0.410566	−	0.298294i
$172$	−6.99062	+	21.5149i	−0.533030	+	1.64050i
$173$	−2.59940	−	8.00012i	−0.197628	−	0.608238i	−0.999936	−	0.0113267i	$-0.996395\pi$
$173$	−2.59940	−	8.00012i	−0.197628	−	0.608238i	0.802307	−	0.596911i	$-0.203605\pi$
$174$	−3.08644	+	2.24243i	−0.233982	+	0.169998i
$175$		0			0
$176$	−2.29462	+	21.0307i	−0.172963	+	1.58525i
$177$	−16.0195			−1.20410
$178$	−8.82995	+	6.41533i	−0.661833	+	0.480850i
$179$	6.50062	+	20.0069i	0.485879	+	1.49538i	0.830703	+	0.556716i	$0.187939\pi$
$179$	6.50062	+	20.0069i	0.485879	+	1.49538i	−0.344824	+	0.938667i	$0.612061\pi$
$180$		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	$0.679365\pi$
$182$	5.50911	+	4.00261i	0.408363	+	0.296693i
$183$	−0.382998	+	1.17875i	−0.0283120	+	0.0871355i
$184$	16.2531	+	50.0219i	1.19820	+	3.68767i
$185$		0			0
$186$	22.6986			1.66435
$187$	−1.07606	+	9.86234i	−0.0786893	+	0.721206i
$188$	31.9538			2.33047
$189$	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	$0.0997126\pi$
$192$	4.69969	+	3.41452i	0.339171	+	0.246422i
$193$	1.17894	+	0.856548i	0.0848618	+	0.0616557i	0.629407	−	0.777076i	$-0.283298\pi$
$193$	1.17894	+	0.856548i	0.0848618	+	0.0616557i	−0.544545	+	0.838731i	$0.683298\pi$
$194$	−0.274331	+	0.844306i	−0.0196959	+	0.0606176i
$195$		0			0
$196$	9.25974	−	6.72759i	0.661410	−	0.480542i
$197$	−22.7027			−1.61750			−0.808751	−	0.588151i	$-0.799856\pi$
$197$	−22.7027			−1.61750			−0.808751	+	0.588151i	$0.799856\pi$
$198$	25.2851	−	5.26999i	1.79693	−	0.374522i
$199$	−6.62834			−0.469870			−0.234935	−	0.972011i	$-0.575488\pi$
$199$	−6.62834			−0.469870			−0.234935	+	0.972011i	$0.575488\pi$
$200$		0			0
$201$	5.95299	+	18.3214i	0.419892	+	1.29229i
$202$	12.2475	−	37.6939i	0.861729	−	2.65213i
$203$	−1.03760	−	0.753862i	−0.0728254	−	0.0529107i
$204$	−26.1057	−	18.9669i	−1.82776	−	1.32795i
$205$		0			0
$206$	5.21114	+	16.0382i	0.363077	+	1.11744i
$207$	21.9087	−	15.9176i	1.52276	−	1.10635i
$208$	−8.21858			−0.569856
$209$	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	$0.362387\pi$
$212$	3.97610	+	12.2372i	0.273080	+	0.840453i
$213$	−8.61673	+	26.5196i	−0.590409	+	1.81709i
$214$	−31.8774	−	23.1603i	−2.17910	−	1.58321i
$215$		0			0
$216$	−0.387117	+	1.19143i	−0.0263400	+	0.0810662i
$217$	2.35807	+	7.25738i	0.160076	+	0.492663i
$218$	23.5018	−	17.0750i	1.59174	−	1.15647i
$219$	27.4230			1.85308
$220$		0			0
$221$	−3.85410			−0.259255
$222$	9.42497	−	6.84764i	0.632563	−	0.459584i
$223$	−2.43642	−	7.49852i	−0.163155	−	0.502138i	0.835741	−	0.549124i	$-0.185039\pi$
$223$	−2.43642	−	7.49852i	−0.163155	−	0.502138i	−0.998896	+	0.0469856i	$0.985039\pi$
$224$	2.66566	−	8.20407i	0.178107	−	0.548158i
$225$		0			0
$226$	−18.4800	−	13.4265i	−1.22927	−	0.893116i
$227$	3.46451	−	10.6627i	0.229948	−	0.707706i	−0.767804	−	0.640685i	$-0.778650\pi$
$227$	3.46451	−	10.6627i	0.229948	−	0.707706i	0.997752	−	0.0670213i	$-0.0213495\pi$
$228$	7.17145	+	22.0715i	0.474941	+	1.46172i
$229$	−21.8360	+	15.8647i	−1.44296	+	1.04837i	−0.455547	+	0.890212i	$0.650556\pi$
$229$	−21.8360	+	15.8647i	−1.44296	+	1.04837i	−0.987413	+	0.158160i	$0.949444\pi$
$230$		0			0
$231$	8.50496	+	14.8666i	0.559585	+	0.978151i
$232$	3.67042			0.240975
$233$	−8.77845	+	6.37792i	−0.575095	+	0.417831i	−0.836953	−	0.547275i	$-0.815665\pi$
$233$	−8.77845	+	6.37792i	−0.575095	+	0.417831i	0.261857	+	0.965107i	$0.415665\pi$
$234$	3.10066	+	9.54284i	0.202696	+	0.623835i
$235$		0			0
$236$	22.9766	+	16.6935i	1.49565	+	1.08665i
$237$	−10.6947	−	7.77017i	−0.694697	−	0.504727i
$238$	4.88529	−	15.0354i	0.316666	−	0.974599i
$239$	−3.54327	−	10.9051i	−0.229195	−	0.705391i	−0.997839	−	0.0657129i	$-0.979068\pi$
$239$	−3.54327	−	10.9051i	−0.229195	−	0.705391i	0.768643	−	0.639678i	$-0.220932\pi$
$240$		0			0
$241$	12.7542			0.821572			0.410786	−	0.911732i	$-0.365254\pi$
$241$	12.7542			0.821572			0.410786	+	0.911732i	$0.365254\pi$
$242$	2.68401	+	27.6398i	0.172534	+	1.77675i
$243$	−22.1829			−1.42303
$244$	1.77767	−	1.29155i	0.113804	−	0.0826833i
$245$		0			0
$246$	9.82734	−	30.2455i	0.626568	−	1.92838i
$247$	2.24248	+	1.62926i	0.142686	+	0.103667i
$248$	−17.6675	−	12.8362i	−1.12188	−	0.815097i
$249$	−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	$0.174174\pi$
$252$	−28.2422			−1.77909
$253$	14.4581	+	25.2727i	0.908973	+	1.58888i
$254$	47.5471			2.98337
$255$		0			0
$256$	−9.61149	−	29.5811i	−0.600718	−	1.84882i
$257$	1.82198	−	5.60747i	0.113652	−	0.349784i	−0.878012	−	0.478639i	$-0.841130\pi$
$257$	1.82198	−	5.60747i	0.113652	−	0.349784i	0.991663	+	0.128855i	$0.0411302\pi$
$258$	−26.0610	−	18.9344i	−1.62249	−	1.17881i
$259$	3.16850	+	2.30205i	0.196881	+	0.143042i
$260$		0			0
$261$	−0.583986	−	1.79733i	−0.0361478	−	0.111252i
$262$	−41.0512	+	29.8254i	−2.53615	+	1.84262i
$263$	21.7305			1.33996			0.669980	−	0.742379i	$-0.266302\pi$
$263$	21.7305			1.33996			0.669980	+	0.742379i	$0.266302\pi$
$264$	−44.6989	−	20.1136i	−2.75103	−	1.23791i
$265$		0			0
$266$	−9.19843	+	6.68305i	−0.563992	+	0.409764i
$267$	−3.29553	−	10.1426i	−0.201683	−	0.620717i
$268$	10.5539	−	32.4817i	0.644685	−	1.98414i
$269$	3.66042	+	2.65945i	0.223180	+	0.162149i	0.693757	−	0.720209i	$-0.255954\pi$
$269$	3.66042	+	2.65945i	0.223180	+	0.162149i	−0.470577	+	0.882359i	$0.655954\pi$
$270$		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	$0.870159\pi$
$272$	5.89608	+	18.1463i	0.357502	+	1.10028i
$273$	−5.38300	+	3.91098i	−0.325794	+	0.236703i
$274$	−45.3688			−2.74083
$275$		0			0
$276$	−94.7021			−5.70040
$277$	−10.5452	+	7.66154i	−0.633600	+	0.460337i	−0.857645	−	0.514241i	$-0.828074\pi$
$277$	−10.5452	+	7.66154i	−0.633600	+	0.460337i	0.224046	+	0.974579i	$0.428074\pi$
$278$	−13.1552	−	40.4877i	−0.788999	−	2.42829i
$279$	−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	$0.790317\pi$
$282$	−14.0606	+	43.2741i	−0.837297	+	2.57694i
$283$	−4.30760	−	13.2574i	−0.256060	−	0.788072i	−0.993619	−	0.112789i	$-0.964021\pi$
$283$	−4.30760	−	13.2574i	−0.256060	−	0.788072i	0.737559	−	0.675283i	$-0.235979\pi$
$284$	39.9943	−	29.0575i	2.37322	−	1.72425i
$285$		0			0
$286$	−10.5612	+	2.20119i	−0.624495	+	0.130159i
$287$	10.6912			0.631083
$288$	10.2832	−	7.47118i	0.605943	−	0.440243i
$289$	−2.48832	−	7.65828i	−0.146372	−	0.450487i
$290$		0			0
$291$	−0.701768	−	0.509864i	−0.0411383	−	0.0298888i
$292$	−39.3326	−	28.5768i	−2.30176	−	1.67233i
$293$	−9.41576	+	28.9787i	−0.550075	+	1.69296i	0.158534	+	0.987354i	$0.449323\pi$
$293$	−9.41576	+	28.9787i	−0.550075	+	1.69296i	−0.708608	+	0.705602i	$0.750677\pi$
$294$	5.03644	+	15.5006i	0.293731	+	0.904011i
$295$		0			0
$296$	−11.2083			−0.651468
$297$	−0.0752186	+	0.689397i	−0.00436463	+	0.0400028i
$298$	−5.89138			−0.341278
$299$	−9.15089	+	6.64851i	−0.529210	+	0.384493i
$300$		0			0
$301$	3.34649	−	10.2994i	0.192888	−	0.593649i
$302$	−8.04468	−	5.84480i	−0.462919	−	0.336330i
$303$	31.3303	+	22.7628i	1.79988	+	1.30769i
$304$	4.24044	−	13.0507i	0.243206	−	0.748511i
$305$		0			0
$306$	18.8457	−	13.6922i	1.07734	−	0.782732i
$307$	−5.08609			−0.290278			−0.145139	−	0.989411i	$-0.546363\pi$
$307$	−5.08609			−0.290278			−0.145139	+	0.989411i	$0.546363\pi$
$308$	3.29351	−	30.1858i	0.187665	−	1.72000i
$309$	−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	$0.772417\pi$
$312$	5.88426	−	18.1099i	0.333131	−	1.02527i
$313$	12.9060	+	9.37676i	0.729491	+	0.530006i	0.889402	−	0.457125i	$-0.151121\pi$
$313$	12.9060	+	9.37676i	0.729491	+	0.530006i	−0.159912	+	0.987131i	$0.551121\pi$
$314$	9.96903	+	7.24292i	0.562585	+	0.408742i
$315$		0			0
$316$	7.24225	+	22.2894i	0.407408	+	1.25387i
$317$	8.66246	−	6.29364i	0.486532	−	0.353486i	−0.317317	−	0.948320i	$-0.602782\pi$
$317$	8.66246	−	6.29364i	0.486532	−	0.353486i	0.803849	+	0.594833i	$0.202782\pi$
$318$	−18.3221			−1.02745
$319$	1.98912	−	0.414578i	0.111369	−	0.0232119i
$320$		0			0
$321$	31.1477	−	22.6301i	1.73849	−	1.26309i
$322$	−14.3375	−	44.1263i	−0.798997	−	2.45906i
$323$	1.98855	−	6.12014i	0.110646	−	0.340534i
$324$	30.9170	+	22.4625i	1.71761	+	1.24792i
$325$		0			0
$326$	−5.48871	+	16.8925i	−0.303992	+	0.935590i
$327$	8.77138	+	26.9955i	0.485058	+	1.49286i
$328$	−24.7530	+	17.9841i	−1.36676	+	0.993006i
$329$	−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	$0.578169\pi$
$332$	38.3710	−	27.8782i	2.10588	−	1.53001i
$333$	1.78330	+	5.48845i	0.0977245	+	0.300765i
$334$	8.36248	−	25.7371i	0.457575	−	1.40827i
$335$		0			0
$336$	26.6491	+	19.3617i	1.45382	+	1.05627i
$337$	3.58143	−	11.0225i	0.195093	−	0.600434i	−0.804883	−	0.593434i	$-0.797772\pi$
$337$	3.58143	−	11.0225i	0.195093	−	0.600434i	0.999976	−	0.00699978i	$-0.00222812\pi$
$338$	8.84648	+	27.2267i	0.481185	+	1.48093i
$339$	18.0569	−	13.1191i	0.980716	−	0.712532i
$340$		0			0
$341$	−11.0244	−	4.96077i	−0.597005	−	0.268641i
$342$	−16.7534			−0.905920
$343$	−16.2885	+	11.8343i	−0.879498	+	0.638993i
$344$	9.57705	+	29.4751i	0.516360	+	1.58919i
$345$		0			0
$346$	−17.1802	−	12.4821i	−0.923611	−	0.671043i
$347$	−3.95529	−	2.87368i	−0.212331	−	0.154267i	0.476537	−	0.879155i	$-0.341892\pi$
$347$	−3.95529	−	2.87368i	−0.212331	−	0.154267i	−0.688868	+	0.724887i	$0.741892\pi$
$348$	−2.04223	+	6.28533i	−0.109475	+	0.336929i
$349$	0.294654	+	0.906853i	0.0157725	+	0.0485427i	0.958633	−	0.284645i	$-0.0918757\pi$
$349$	0.294654	+	0.906853i	0.0157725	+	0.0485427i	−0.942861	+	0.333188i	$0.891876\pi$
$350$		0			0
$351$	−0.269409			−0.0143800
$352$	6.78615	+	11.8621i	0.361703	+	0.632254i
$353$	15.5166			0.825865			0.412933	−	0.910762i	$-0.364505\pi$
$353$	15.5166			0.825865			0.412933	+	0.910762i	$0.364505\pi$
$354$	−32.7179	+	23.7709i	−1.73894	+	1.26341i
$355$		0			0
$356$	−5.84258	+	17.9816i	−0.309656	+	0.953024i
$357$	12.4971	+	9.07965i	0.661415	+	0.480546i
$358$	42.9645	+	31.2155i	2.27074	+	1.64979i
$359$	6.25915	−	19.2637i	0.330345	−	1.01670i	−0.638624	−	0.769519i	$-0.720496\pi$
$359$	6.25915	−	19.2637i	0.330345	−	1.01670i	0.968970	−	0.247180i	$-0.0795038\pi$
$360$		0			0
$361$	11.6271	−	8.44759i	0.611953	−	0.444610i
$362$	4.40051			0.231286
$363$	−26.4956	−	5.85142i	−1.39066	−	0.307120i
$364$	11.7963			0.618295
$365$		0			0
$366$	0.966888	+	2.97578i	0.0505400	+	0.155546i
$367$	−11.0180	+	33.9099i	−0.575135	+	1.77008i	0.0605844	+	0.998163i	$0.480704\pi$
$367$	−11.0180	+	33.9099i	−0.575135	+	1.77008i	−0.635719	+	0.771920i	$0.719296\pi$
$368$	45.3024	+	32.9141i	2.36155	+	1.71577i
$369$	12.7448	+	9.25962i	0.663466	+	0.482037i
$370$		0			0
$371$	−1.90340	−	5.85807i	−0.0988198	−	0.304136i
$372$	31.8112	−	23.1122i	1.64933	−	1.19831i
$373$	−12.1358			−0.628370			−0.314185	−	0.949362i	$-0.601731\pi$
$373$	−12.1358			−0.628370			−0.314185	+	0.949362i	$0.601731\pi$
$374$	12.4368	+	21.7394i	0.643091	+	1.12412i
$375$		0			0
$376$	35.4157	−	25.7310i	1.82643	−	1.32698i
$377$	0.243922	+	0.750713i	0.0125626	+	0.0386637i
$378$	0.341491	−	1.05100i	0.0175644	−	0.0540577i
$379$	−5.77971	−	4.19921i	−0.296884	−	0.215699i	0.429364	−	0.903131i	$-0.358738\pi$
$379$	−5.77971	−	4.19921i	−0.296884	−	0.215699i	−0.726248	+	0.687433i	$0.758738\pi$
$380$		0			0
$381$	−14.3565	+	44.1848i	−0.735506	+	2.26366i
$382$	−0.0194691	−	0.0599198i	−0.000996127	−	0.00306576i
$383$	12.9143	−	9.38279i	0.659890	−	0.479438i	−0.206736	−	0.978397i	$-0.566284\pi$
$383$	12.9143	−	9.38279i	0.659890	−	0.479438i	0.866626	+	0.498959i	$0.166284\pi$
$384$	34.9936			1.78576
$385$		0			0
$386$	3.67885			0.187249
$387$	12.9096	−	9.37935i	0.656230	−	0.476779i
$388$	0.475223	+	1.46259i	0.0241258	+	0.0742516i
$389$	−7.75336	+	23.8624i	−0.393111	+	1.20987i	0.537312	+	0.843384i	$0.319440\pi$
$389$	−7.75336	+	23.8624i	−0.393111	+	1.20987i	−0.930423	+	0.366488i	$0.880560\pi$
$390$		0			0
$391$	21.2445	+	15.4351i	1.07438	+	0.780585i
$392$	4.84551	−	14.9130i	0.244735	−	0.753218i
$393$	−15.3212	−	47.1538i	−0.772853	−	2.37860i
$394$	−46.3677	+	33.6881i	−2.33597	+	1.69718i
$395$		0			0
$396$	30.0699	−	33.1314i	1.51107	−	1.66491i
$397$	−3.57490			−0.179419			−0.0897094	−	0.995968i	$-0.528594\pi$
$397$	−3.57490			−0.179419			−0.0897094	+	0.995968i	$0.528594\pi$
$398$	−13.5376	+	9.83564i	−0.678579	+	0.493016i
$399$	−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	$0.956407\pi$
$402$	39.3451	+	28.5859i	1.96235	+	1.42573i
$403$	1.45128	−	4.46657i	0.0722933	−	0.222496i
$404$	−21.2162	−	65.2969i	−1.05555	−	3.24864i
$405$		0			0
$406$	−3.23782			−0.160690
$407$	−6.07412	+	1.26599i	−0.301083	+	0.0627526i
$408$	−44.2072			−2.18858
$409$	−7.78197	+	5.65393i	−0.384794	+	0.279569i	−0.763319	−	0.646022i	$-0.776431\pi$
$409$	−7.78197	+	5.65393i	−0.384794	+	0.279569i	0.378525	+	0.925591i	$0.376431\pi$
$410$		0			0
$411$	13.6988	−	42.1606i	0.675712	−	2.07963i
$412$	23.6336	+	17.1708i	1.16434	+	0.845945i
$413$	−10.9991	−	7.99135i	−0.541233	−	0.393229i
$414$	21.1261	−	65.0196i	1.03829	−	3.19554i
$415$		0			0
$416$	−4.29512	+	3.12059i	−0.210586	+	0.152999i
$417$	41.5967			2.03700
$418$	1.95373	−	17.9064i	0.0955599	−	0.875829i
$419$	−30.6537			−1.49753			−0.748765	−	0.662836i	$-0.769353\pi$
$419$	−30.6537			−1.49753			−0.748765	+	0.662836i	$0.769353\pi$
$420$		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	$0.954168\pi$
$422$	−4.41361	+	13.5837i	−0.214851	+	0.661244i
$423$	−18.2348	−	13.2483i	−0.886605	−	0.644156i
$424$	14.2610	+	10.3612i	0.692574	+	0.503184i
$425$		0			0
$426$	21.7532	+	66.9493i	1.05394	+	3.24371i
$427$	−0.850991	+	0.618281i	−0.0411823	+	0.0299207i
$428$	−68.2571			−3.29933
$429$	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	$0.275182\pi$
$432$	0.412147	+	1.26846i	0.0198294	+	0.0610287i
$433$	9.39161	−	28.9044i	0.451332	−	1.38906i	−0.424056	−	0.905636i	$-0.639394\pi$
$433$	9.39161	−	28.9044i	0.451332	−	1.38906i	0.875388	−	0.483421i	$-0.160606\pi$
$434$	15.5851	+	11.3233i	0.748110	+	0.543534i
$435$		0			0
$436$	15.5506	−	47.8598i	0.744739	−	2.29207i
$437$	−5.83606	−	17.9616i	−0.279177	−	0.859218i
$438$	56.0083	−	40.6924i	2.67618	−	1.94436i
$439$	36.5311			1.74353			0.871767	−	0.489921i	$-0.162974\pi$
$439$	36.5311			1.74353			0.871767	+	0.489921i	$0.162974\pi$
$440$		0			0
$441$	−8.07350			−0.384452
$442$	−7.87155	+	5.71902i	−0.374412	+	0.272026i
$443$	0.667949	+	2.05574i	0.0317352	+	0.0976710i	0.965669	−	0.259774i	$-0.0836480\pi$
$443$	0.667949	+	2.05574i	0.0317352	+	0.0976710i	−0.933934	+	0.357445i	$0.883648\pi$
$444$	6.23630	−	19.1933i	0.295962	−	0.910876i
$445$		0			0
$446$	−16.1030	−	11.6995i	−0.762499	−	0.553988i
$447$	1.77886	−	5.47477i	0.0841372	−	0.258948i
$448$	1.52352	+	4.68890i	0.0719793	+	0.221530i
$449$	9.32124	−	6.77228i	0.439897	−	0.319604i	−0.345697	−	0.938346i	$-0.612358\pi$
$449$	9.32124	−	6.77228i	0.439897	−	0.319604i	0.785594	+	0.618742i	$0.212358\pi$
$450$		0			0
$451$	−11.3831	+	12.5420i	−0.536010	+	0.590581i
$452$	−39.5699			−1.86121
$453$	7.86051	−	5.71100i	0.369319	−	0.268326i
$454$	−8.74624	−	26.9182i	−0.410482	−	1.26333i
$455$		0			0
$456$	25.7217	+	18.6879i	1.20453	+	0.875140i
$457$	−12.8888	−	9.36427i	−0.602913	−	0.438042i	0.243999	−	0.969776i	$-0.421541\pi$
$457$	−12.8888	−	9.36427i	−0.602913	−	0.438042i	−0.846912	+	0.531734i	$0.821541\pi$
$458$	−21.0560	+	64.8038i	−0.983883	+	3.02808i
$459$	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	$0.488691\pi$
$462$	39.4306	+	17.7430i	1.83448	+	0.825478i
$463$	−14.2073			−0.660268			−0.330134	−	0.943934i	$-0.607094\pi$
$463$	−14.2073			−0.660268			−0.330134	+	0.943934i	$0.607094\pi$
$464$	3.16143	−	2.29691i	0.146765	−	0.106631i
$465$		0			0
$466$	−8.46491	+	26.0523i	−0.392129	+	1.20685i
$467$	−4.90020	−	3.56020i	−0.226754	−	0.164746i	0.468608	−	0.883406i	$-0.344756\pi$
$467$	−4.90020	−	3.56020i	−0.226754	−	0.164746i	−0.695362	+	0.718660i	$0.744756\pi$
$468$	14.0621	+	10.2167i	0.650022	+	0.472269i
$469$	−5.05229	+	15.5494i	−0.233293	+	0.718002i
$470$		0			0
$471$	−9.74081	+	7.07711i	−0.448833	+	0.326096i
$472$	38.9085			1.79091
$473$	8.51936	+	14.8918i	0.391720	+	0.684725i
$474$	−33.3727			−1.53286
$475$		0			0
$476$	−8.46277	−	26.0457i	−0.387890	−	1.19380i
$477$	2.80464	−	8.63181i	0.128416	−	0.395223i
$478$	−23.4185	−	17.0146i	−1.07114	−	0.778227i
$479$	14.2455	+	10.3500i	0.650894	+	0.472902i	0.863576	−	0.504219i	$-0.168220\pi$
$479$	14.2455	+	10.3500i	0.650894	+	0.472902i	−0.212681	+	0.977122i	$0.568220\pi$
$480$		0			0
$481$	−0.744857	−	2.29243i	−0.0339626	−	0.104526i
$482$	26.0490	−	18.9257i	1.18650	−	0.862043i
$483$	45.3350			2.06281
$484$	31.9048	+	36.0030i	1.45022	+	1.63650i
$485$		0			0
$486$	−45.3059	+	32.9167i	−2.05512	+	1.49313i
$487$	−2.09619	−	6.45140i	−0.0949874	−	0.292341i	0.892263	−	0.451516i	$-0.149117\pi$
$487$	−2.09619	−	6.45140i	−0.0949874	−	0.292341i	−0.987250	+	0.159175i	$0.949117\pi$
$488$	0.930235	−	2.86297i	0.0421097	−	0.129600i
$489$	−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	$0.0962749\pi$
$492$	−17.0239	−	52.3941i	−0.767495	−	2.36211i
$493$	1.48255	−	1.07714i	0.0667707	−	0.0485117i
$494$	6.99762			0.314838
$495$		0			0
$496$	−23.2501			−1.04396
$497$	−19.1457	+	13.9102i	−0.858802	+	0.623956i
$498$	20.8703	+	64.2320i	0.935218	+	2.87831i
$499$	6.75534	−	20.7908i	0.302411	−	0.930725i	−0.678220	−	0.734859i	$-0.737248\pi$
$499$	6.75534	−	20.7908i	0.302411	−	0.930725i	0.980631	−	0.195866i	$-0.0627516\pi$
$500$		0			0
$501$	21.3921	+	15.5423i	0.955727	+	0.694377i
$502$	9.51872	−	29.2956i	0.424841	−	1.30753i
$503$	−0.932202	−	2.86902i	−0.0415649	−	0.127923i	0.928121	−	0.372279i	$-0.121424\pi$
$503$	−0.932202	−	2.86902i	−0.0415649	−	0.127923i	−0.969686	+	0.244356i	$0.921424\pi$
$504$	−31.3020	+	22.7423i	−1.39430	+	1.01302i
$505$		0			0
$506$	67.0306	+	30.1624i	2.97987	+	1.34088i
$507$	−27.9724			−1.24230
$508$	66.6352	−	48.4133i	2.95646	−	2.14799i
$509$	−7.94418	−	24.4497i	−0.352119	−	1.08371i	−0.957661	−	0.287898i	$-0.907043\pi$
$509$	−7.94418	−	24.4497i	−0.352119	−	1.08371i	0.605542	−	0.795814i	$-0.292957\pi$
$510$		0			0
$511$	18.8289	+	13.6800i	0.832943	+	0.605169i
$512$	−40.5713	−	29.4768i	−1.79302	−	1.30270i
$513$	0.139004	−	0.427809i	0.00613716	−	0.0188882i
$514$	−4.59962	−	14.1562i	−0.202881	−	0.624403i
$515$		0			0
$516$	−55.8027			−2.45658
$517$	16.2866	−	17.9447i	0.716282	−	0.789207i
$518$	9.88725			0.434421
$519$	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	$0.0215848\pi$
$522$	−3.85974	−	2.80426i	−0.168936	−	0.122739i
$523$	−5.28968	−	3.84318i	−0.231302	−	0.168050i	0.466098	−	0.884733i	$-0.345660\pi$
$523$	−5.28968	−	3.84318i	−0.231302	−	0.168050i	−0.697399	+	0.716683i	$0.745660\pi$
$524$	−27.1627	+	83.5981i	−1.18661	+	3.65200i
$525$		0			0
$526$	44.3820	−	32.2454i	1.93515	−	1.40597i
$527$	−10.9032			−0.474949
$528$	−51.0871	+	10.6477i	−2.22328	+	0.463383i
$529$	54.0677			2.35077
$530$		0			0
$531$	−6.19057	−	19.0526i	−0.268648	−	0.826814i
$532$	−6.08640	+	18.7320i	−0.263879	+	0.812135i
$533$	−5.32328	−	3.86759i	−0.230577	−	0.167524i
$534$	−21.7811	−	15.8249i	−0.942561	−	0.684811i
$535$		0			0
$536$	−14.4588	−	44.4995i	−0.624524	−	1.92209i
$537$	−41.9809	+	30.5009i	−1.81161	+	1.31621i
$538$	11.4223			0.492449
$539$	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	$0.945546\pi$
$542$	16.9761	+	52.2470i	0.729185	+	2.24420i
$543$	−1.32870	+	4.08932i	−0.0570201	+	0.175490i
$544$	9.97147	+	7.24470i	0.427523	+	0.310614i
$545$		0			0
$546$	−5.19073	+	15.9754i	−0.222143	+	0.683685i
$547$	1.37703	+	4.23806i	0.0588775	+	0.181206i	0.976170	−	0.217008i	$-0.0696299\pi$
$547$	1.37703	+	4.23806i	0.0588775	+	0.181206i	−0.917292	+	0.398215i	$0.869630\pi$
$548$	−63.5825	+	46.1954i	−2.71611	+	1.97337i
$549$	−1.54994			−0.0661498
$550$		0			0
$551$	−1.31795			−0.0561466
$552$	−104.962	+	76.2596i	−4.46750	+	3.24583i
$553$	−3.46695	−	10.6702i	−0.147430	−	0.453742i
$554$	−10.1686	+	31.2956i	−0.432020	+	1.32962i
$555$		0			0
$556$	−59.6618	−	43.3468i	−2.53022	−	1.83831i
$557$	−5.98608	+	18.4233i	−0.253638	+	0.780619i	0.740456	+	0.672104i	$0.234609\pi$
$557$	−5.98608	+	18.4233i	−0.253638	+	0.780619i	−0.994095	+	0.108514i	$0.965391\pi$
$558$	8.77167	+	26.9964i	0.371335	+	1.14285i
$559$	−5.39211	+	3.91760i	−0.228062	+	0.165697i
$560$		0			0
$561$	−23.9573	+	4.99325i	−1.01148	+	0.210815i
$562$	−23.6941			−0.999477
$563$	16.7816	−	12.1925i	0.707259	−	0.513853i	−0.175030	−	0.984563i	$-0.556002\pi$
$563$	16.7816	−	12.1925i	0.707259	−	0.513853i	0.882288	+	0.470710i	$0.156002\pi$
$564$	24.3571	+	74.9636i	1.02562	+	3.15654i
$565$		0			0
$566$	−28.4702	−	20.6848i	−1.19669	−	0.869447i
$567$	−14.8003	−	10.7530i	−0.621554	−	0.451585i
$568$	20.9285	−	64.4114i	0.878141	−	2.70264i
$569$	−13.0945	−	40.3007i	−0.548950	−	1.68949i	−0.711408	−	0.702779i	$-0.751942\pi$
$569$	−13.0945	−	40.3007i	−0.548950	−	1.68949i	0.162458	−	0.986716i	$-0.448058\pi$
$570$		0			0
$571$	−5.03980			−0.210909			−0.105455	−	0.994424i	$-0.533630\pi$
$571$	−5.03980			−0.210909			−0.105455	+	0.994424i	$0.533630\pi$
$572$	−12.5597	+	13.8384i	−0.525148	+	0.578614i
$573$	0.0615611			0.00257175
$574$	21.8356	−	15.8645i	0.911399	−	0.662170i
$575$		0			0
$576$	−2.24488	+	6.90905i	−0.0935369	+	0.287877i
$577$	28.1877	+	20.4796i	1.17347	+	0.852576i	0.991420	−	0.130713i	$-0.0417267\pi$
$577$	28.1877	+	20.4796i	1.17347	+	0.852576i	0.182050	+	0.983289i	$0.441727\pi$
$578$	−16.4461	−	11.9488i	−0.684066	−	0.497003i
$579$	−1.11080	+	3.41870i	−0.0461634	+	0.142076i
$580$		0			0
$581$	−18.3686	+	13.3456i	−0.762059	+	0.553668i
$582$	−2.18985			−0.0907724
$583$	8.89878	+	4.00427i	0.368550	+	0.165840i
$584$	−66.6057			−2.75616
$585$		0			0
$586$	23.7703	+	73.1575i	0.981943	+	3.02211i
$587$	4.25772	−	13.1039i	0.175735	−	0.540857i	−0.823931	−	0.566690i	$-0.808224\pi$
$587$	4.25772	−	13.1039i	0.175735	−	0.540857i	0.999666	+	0.0258331i	$0.00822386\pi$
$588$	22.8413	+	16.5952i	0.941959	+	0.684373i
$589$	6.34392	+	4.60913i	0.261397	+	0.189916i
$590$		0			0
$591$	−17.3054	−	53.2606i	−0.711850	−	2.19085i
$592$	−9.65397	+	7.01402i	−0.396776	+	0.288274i
$593$	25.1595			1.03318			0.516588	−	0.856234i	$-0.327202\pi$
$593$	25.1595			1.03318			0.516588	+	0.856234i	$0.327202\pi$
$594$	0.869355	+	1.51963i	0.0356701	+	0.0623511i
$595$		0			0
$596$	−8.25651	+	5.99871i	−0.338200	+	0.245717i
$597$	−5.05253	−	15.5501i	−0.206786	−	0.636423i
$598$	−8.82405	+	27.1576i	−0.360842	+	1.11056i
$599$	13.3539	+	9.70216i	0.545624	+	0.396419i	0.826170	−	0.563421i	$-0.190515\pi$
$599$	13.3539	+	9.70216i	0.545624	+	0.396419i	−0.280545	+	0.959841i	$0.590515\pi$
$600$		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	$-0.199760\pi$
$602$	−8.44829	−	26.0011i	−0.344326	−	1.05973i
$603$	−19.4900	+	14.1603i	−0.793692	+	0.576651i
$604$	−17.2255			−0.700897
$605$		0			0
$606$	97.7656			3.97146
$607$	11.4795	−	8.34036i	0.465939	−	0.338525i	−0.329917	−	0.944010i	$-0.607021\pi$
$607$	11.4795	−	8.34036i	0.465939	−	0.338525i	0.795857	+	0.605485i	$0.207021\pi$
$608$	−2.73925	−	8.43055i	−0.111091	−	0.341904i
$609$	0.977637	−	3.00886i	0.0396158	−	0.121925i
$610$		0			0
$611$	7.61636	+	5.53361i	0.308125	+	0.223866i
$612$	12.4698	−	38.3781i	0.504062	−	1.55134i
$613$	−9.31820	−	28.6785i	−0.376359	−	1.15831i	−0.942557	−	0.334044i	$-0.891586\pi$
$613$	−9.31820	−	28.6785i	−0.376359	−	1.15831i	0.566199	−	0.824269i	$-0.308414\pi$
$614$	−10.3877	+	7.54714i	−0.419215	+	0.304578i
$615$		0			0
$616$	−20.6570	−	36.1084i	−0.832296	−	1.45485i
$617$	31.3844			1.26349			0.631744	−	0.775177i	$-0.282339\pi$
$617$	31.3844			1.26349			0.631744	+	0.775177i	$0.282339\pi$
$618$	−33.6534	+	24.4507i	−1.35374	+	0.983550i
$619$	10.8876	+	33.5087i	0.437611	+	1.34683i	0.890387	+	0.455205i	$0.150434\pi$
$619$	10.8876	+	33.5087i	0.437611	+	1.34683i	−0.452775	+	0.891625i	$0.649566\pi$
$620$		0			0
$621$	1.48503	+	1.07894i	0.0595924	+	0.0432964i
$622$	28.1059	+	20.4201i	1.12694	+	0.818773i
$623$	2.79691	−	8.60800i	0.112056	−	0.344872i
$624$	−6.26471	−	19.2808i	−0.250789	−	0.771850i
$625$		0			0
$626$	40.2730			1.60963
$627$	16.0502	+	7.22227i	0.640983	+	0.288430i
$628$	21.3460			0.851799
$629$	−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	$0.0635863\pi$
$632$	25.9756	+	18.8724i	1.03325	+	0.750702i
$633$	−11.2905	−	8.20300i	−0.448755	−	0.326040i
$634$	8.35306	−	25.7081i	0.331742	−	1.02100i
$635$		0			0
$636$	−25.6776	+	18.6559i	−1.01818	+	0.739753i
$637$	3.37217			0.133610
$638$	3.44736	−	3.79834i	0.136482	−	0.150378i
$639$	−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	$0.944937\pi$
$642$	30.0352	−	92.4388i	1.18539	−	3.64827i
$643$	−17.1427	−	12.4549i	−0.676042	−	0.491173i	0.196000	−	0.980604i	$-0.437205\pi$
$643$	−17.1427	−	12.4549i	−0.676042	−	0.491173i	−0.872042	+	0.489431i	$0.837205\pi$
$644$	−65.0235	−	47.2423i	−2.56229	−	1.86161i
$645$		0			0
$646$	−5.02015	−	15.4504i	−0.197515	−	0.607889i
$647$	−4.57074	+	3.32083i	−0.179694	+	0.130555i	−0.673996	−	0.738735i	$-0.735424\pi$
$647$	−4.57074	+	3.32083i	−0.179694	+	0.130555i	0.494302	+	0.869290i	$0.335424\pi$
$648$	52.3547			2.05669
$649$	21.0857	−	4.39475i	0.827688	−	0.172509i
$650$		0			0
$651$	−15.2284	+	11.0640i	−0.596846	+	0.433634i
$652$	9.50807	+	29.2628i	0.372365	+	1.14602i
$653$	4.85563	−	14.9441i	0.190016	−	0.584808i	−0.809983	−	0.586453i	$-0.800524\pi$
$653$	4.85563	−	14.9441i	0.190016	−	0.584808i	0.999999	+	0.00164558i	$0.000523804\pi$
$654$	57.9726	+	42.1195i	2.26691	+	1.64700i
$655$		0			0
$656$	−10.0661	+	30.9803i	−0.393016	+	1.20958i
$657$	10.5974	+	32.6153i	0.413442	+	1.27245i
$658$	−31.2416	+	22.6983i	−1.21792	+	0.884872i
$659$	−41.7884			−1.62784			−0.813922	−	0.580975i	$-0.802671\pi$
$659$	−41.7884			−1.62784			−0.813922	+	0.580975i	$0.802671\pi$
$660$		0			0
$661$	15.8742			0.617435			0.308717	−	0.951154i	$-0.400100\pi$
$661$	15.8742			0.617435			0.308717	+	0.951154i	$0.400100\pi$
$662$	−18.0673	+	13.1266i	−0.702205	+	0.510182i
$663$	−2.93784	−	9.04173i	−0.114096	−	0.351152i
$664$	20.0791	−	61.7971i	0.779220	−	2.39819i
$665$		0			0
$666$	11.7864	+	8.56330i	0.456713	+	0.331821i
$667$	1.66195	−	5.11494i	0.0643508	−	0.198051i
$668$	−14.4863	−	44.5842i	−0.560491	−	1.72502i
$669$	15.7344	−	11.4317i	0.608325	−	0.441974i
$670$		0			0
$671$	0.180749	−	1.65660i	0.00697773	−	0.0639525i
$672$	21.2787			0.820844
$673$	26.0864	−	18.9529i	1.00556	−	0.730580i	0.0422850	−	0.999106i	$-0.486536\pi$
$673$	26.0864	−	18.9529i	1.00556	−	0.730580i	0.963273	+	0.268525i	$0.0865363\pi$
$674$	−9.04140	−	27.8266i	−0.348262	−	1.07184i
$675$		0			0
$676$	40.1206	+	29.1493i	1.54310	+	1.12113i
$677$	14.2084	+	10.3230i	0.546073	+	0.396745i	0.826336	−	0.563178i	$-0.190422\pi$
$677$	14.2084	+	10.3230i	0.546073	+	0.396745i	−0.280263	+	0.959923i	$0.590422\pi$
$678$	17.4120	−	53.5885i	0.668702	−	2.05805i
$679$	−0.227495	−	0.700157i	−0.00873044	−	0.0268695i
$680$		0			0
$681$	27.6555			1.05976
$682$	−29.8772	+	6.22710i	−1.14406	+	0.238448i
$683$	5.93856			0.227233			0.113616	−	0.993525i	$-0.463757\pi$
$683$	5.93856			0.227233			0.113616	+	0.993525i	$0.463757\pi$
$684$	−23.4792	+	17.0586i	−0.897749	+	0.652253i
$685$		0			0
$686$	−15.7067	+	48.3404i	−0.599686	+	1.84565i
$687$	−53.8634	−	39.1341i	−2.05502	−	1.49306i
$688$	26.6942	+	19.3945i	1.01771	+	0.739407i
$689$	−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	$0.437001\pi$
$692$	−36.7868			−1.39842
$693$	−14.3948	+	15.8604i	−0.546814	+	0.602485i
$694$	−12.3424			−0.468511
$695$		0			0
$696$	2.79782	+	8.61082i	0.106051	+	0.326392i
$697$	−4.72050	+	14.5282i	−0.178802	+	0.550295i
$698$	1.94746	+	1.41491i	0.0737123	+	0.0535551i
$699$	−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	$0.690261\pi$
$702$	−0.550236	+	0.399770i	−0.0207673	+	0.0150884i
$703$	4.02460			0.151791
$704$	−7.12273	−	3.20509i	−0.268448	−	0.120796i
$705$		0			0
$706$	31.6908	−	23.0247i	1.19270	−	0.866547i
$707$	10.1565	+	31.2584i	0.381973	+	1.17559i
$708$	−21.6487	+	66.6279i	−0.813609	+	2.50403i
$709$	13.0256	+	9.46362i	0.489185	+	0.355414i	0.804871	−	0.593450i	$-0.202235\pi$
$709$	13.0256	+	9.46362i	0.489185	+	0.355414i	−0.315686	+	0.948864i	$0.602235\pi$
$710$		0			0
$711$	5.10851	−	15.7224i	0.191584	−	0.589635i
$712$	8.00426	+	24.6346i	0.299972	+	0.923220i
$713$	−25.8876	+	18.8085i	−0.969499	+	0.704383i
$714$	38.9969			1.45942
$715$		0			0
$716$	91.9971			3.43809
$717$	22.8824	−	16.6250i	0.854559	−	0.620874i
$718$	−15.8014	−	48.6316i	−0.589702	−	1.81492i
$719$	−2.41409	+	7.42981i	−0.0900304	+	0.277085i	−0.985927	−	0.167178i	$-0.946534\pi$
$719$	−2.41409	+	7.42981i	−0.0900304	+	0.277085i	0.895896	+	0.444263i	$0.146534\pi$
$720$		0			0
$721$	−11.3137	−	8.21985i	−0.421343	−	0.306123i
$722$	11.2118	−	34.5064i	0.417261	−	1.28420i
$723$	9.72206	+	29.9214i	0.361567	+	1.11279i
$724$	6.16712	−	4.48068i	0.229199	−	0.166523i
$725$		0			0
$726$	−62.7970	+	27.3654i	−2.33061	+	1.01563i
$727$	49.1218			1.82183			0.910914	−	0.412597i	$-0.135378\pi$
$727$	49.1218			1.82183			0.910914	+	0.412597i	$0.135378\pi$
$728$	13.0744	−	9.49907i	0.484568	−	0.352059i
$729$	−8.80810	−	27.1086i	−0.326226	−	1.00402i
$730$		0			0
$731$	12.5182	+	9.09503i	0.463003	+	0.336392i
$732$	4.38504	+	3.18592i	0.162076	+	0.117755i
$733$	0.206407	−	0.635255i	0.00762382	−	0.0234637i	−0.947172	−	0.320725i	$-0.896073\pi$
$733$	0.206407	−	0.635255i	0.00762382	−	0.0234637i	0.954796	+	0.297262i	$0.0960734\pi$
$734$	27.8152	+	85.6064i	1.02668	+	3.15979i
$735$		0			0
$736$	36.1730			1.33335
$737$	−12.8619	−	22.4826i	−0.473775	−	0.828156i
$738$	39.7699			1.46395
$739$	−30.8186	+	22.3911i	−1.13368	+	0.823668i	−0.986227	−	0.165400i	$-0.947108\pi$
$739$	−30.8186	+	22.3911i	−1.13368	+	0.823668i	−0.147456	+	0.989069i	$0.547108\pi$
$740$		0			0
$741$	−2.11288	+	6.50278i	−0.0776187	+	0.238886i
$742$	−12.5801	−	9.14001i	−0.461832	−	0.335540i
$743$	−25.3511	−	18.4186i	−0.930041	−	0.675714i	0.0159622	−	0.999873i	$-0.494919\pi$
$743$	−25.3511	−	18.4186i	−0.930041	−	0.675714i	−0.946003	+	0.324159i	$0.894919\pi$
$744$	16.6464	−	51.2324i	0.610287	−	1.87827i
$745$		0			0
$746$	−24.7860	+	18.0081i	−0.907480	+	0.659323i
$747$	−33.4554			−1.22407
$748$	39.5651	+	17.8035i	1.44664	+	0.650960i
$749$	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	$-0.337367\pi$
$752$	14.4022	−	44.3255i	0.525196	−	1.61639i
$753$	24.3498	+	17.6912i	0.887358	+	0.644703i
$754$	1.61215	+	1.17129i	0.0587110	+	0.0426560i
$755$		0			0
$756$	−0.591564	−	1.82065i	−0.0215150	−	0.0662162i
$757$	5.40478	−	3.92680i	0.196440	−	0.142722i	−0.485217	−	0.874394i	$-0.661259\pi$
$757$	5.40478	−	3.92680i	0.196440	−	0.142722i	0.681657	+	0.731672i	$0.261259\pi$
$758$	−18.0355			−0.655079
$759$	−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	$0.163800\pi$
$762$	36.2434	+	111.546i	1.31296	+	4.04087i
$763$	−7.44425	+	22.9110i	−0.269500	+	0.829435i
$764$	−0.0882966	−	0.0641512i	−0.00319446	−	0.00232091i
$765$		0			0
$766$	12.4530	−	38.3265i	0.449947	−	1.38479i
$767$	2.58570	+	7.95797i	0.0933643	+	0.287346i
$768$	62.0709	−	45.0971i	2.23979	−	1.62730i
$769$	−13.1946			−0.475808			−0.237904	−	0.971289i	$-0.576460\pi$
$769$	−13.1946			−0.475808			−0.237904	+	0.971289i	$0.576460\pi$
$770$		0			0
$771$	14.5440			0.523788
$772$	5.15575	−	3.74587i	0.185560	−	0.134817i
$773$	3.83827	+	11.8130i	0.138053	+	0.424883i	0.996052	−	0.0887673i	$-0.0282928\pi$
$773$	3.83827	+	11.8130i	0.138053	+	0.424883i	−0.857999	+	0.513651i	$0.828293\pi$
$774$	12.4485	−	38.3124i	0.447451	−	1.37711i
$775$		0			0
$776$	1.70447	+	1.23837i	0.0611869	+	0.0444549i
$777$	−2.98538	+	9.18807i	−0.107100	+	0.329620i
$778$	19.5735	+	60.2412i	0.701746	+	2.15975i
$779$	8.88815	−	6.45762i	0.318451	−	0.231368i
$780$		0			0
$781$	4.06650	−	37.2705i	0.145511	−	1.33364i
$782$	66.2932			2.37064
$783$	0.103633	−	0.0752938i	0.00370354	−	0.00269078i
$784$	−5.15881	−	15.8772i	−0.184243	−	0.567042i
$785$		0			0
$786$	−101.262	−	73.5714i	−3.61191	−	2.62420i
$787$	17.3818	+	12.6286i	0.619595	+	0.450162i	0.852780	−	0.522270i	$-0.174915\pi$
$787$	17.3818	+	12.6286i	0.619595	+	0.450162i	−0.233185	+	0.972432i	$0.574915\pi$
$788$	−30.6805	+	94.4247i	−1.09295	+	3.36374i
$789$	16.5643	+	50.9798i	0.589706	+	1.81493i
$790$		0			0
$791$	18.9426			0.673520
$792$	6.64849	−	60.9350i	0.236244	−	2.16523i
$793$	0.647384			0.0229893
$794$	−7.30130	+	5.30471i	−0.259114	+	0.188257i
$795$		0			0
$796$	−8.95753	+	27.5685i	−0.317491	+	0.977138i
$797$	1.72264	+	1.25157i	0.0610191	+	0.0443330i	0.617877	−	0.786275i	$-0.287993\pi$
$797$	1.72264	+	1.25157i	0.0610191	+	0.0443330i	−0.556858	+	0.830608i	$0.687993\pi$
$798$	−22.6901	−	16.4853i	−0.803219	−	0.583573i
$799$	6.75393	−	20.7864i	0.238937	−	0.735372i
$800$		0			0
$801$	10.7895	−	7.83902i	0.381228	−	0.276978i
$802$	−72.9179			−2.57482
$803$	−36.0957	+	7.52318i	−1.27379	+	0.265487i
$804$	84.2470			2.97116
$805$		0			0
$806$	−3.66378	−	11.2760i	−0.129051	−	0.397179i
$807$	−3.44887	+	10.6145i	−0.121406	+	0.373649i
$808$	−76.0957	−	55.2868i	−2.67704	−	1.94498i
$809$	4.33820	+	3.15189i	0.152523	+	0.110815i	0.661430	−	0.750007i	$-0.269950\pi$
$809$	4.33820	+	3.15189i	0.152523	+	0.110815i	−0.508906	+	0.860822i	$0.669950\pi$
$810$		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	$0.788296\pi$
$812$	−4.53766	+	3.29681i	−0.159241	+	0.115695i
$813$	−53.6781			−1.88257
$814$	−10.5271	+	11.5989i	−0.368975	+	0.406541i
$815$		0			0
$816$	−38.0768	+	27.6644i	−1.33295	+	0.968448i
$817$	−3.43887	−	10.5837i	−0.120311	−	0.370278i
$818$	−7.50402	+	23.0950i	−0.262372	+	0.807497i
$819$	−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	$0.193758\pi$
$822$	−34.5829	−	106.435i	−1.20622	−	3.71236i
$823$	−14.7993	+	10.7523i	−0.515870	+	0.374801i	−0.815046	−	0.579397i	$-0.803288\pi$
$823$	−14.7993	+	10.7523i	−0.515870	+	0.374801i	0.299176	+	0.954198i	$0.403288\pi$
$824$	40.0210			1.39420
$825$		0			0
$826$	−34.3227			−1.19424
$827$	−30.7575	+	22.3466i	−1.06954	+	0.777069i	−0.975830	−	0.218530i	$-0.929874\pi$
$827$	−30.7575	+	22.3466i	−1.06954	+	0.777069i	−0.0937136	+	0.995599i	$0.529874\pi$
$828$	−36.5967	−	112.633i	−1.27182	−	3.91427i
$829$	15.9762	−	49.1698i	0.554877	−	1.70774i	−0.141389	−	0.989954i	$-0.545157\pi$
$829$	15.9762	−	49.1698i	0.554877	−	1.70774i	0.696267	−	0.717783i	$-0.254843\pi$
$830$		0			0
$831$	−26.0122	−	18.8990i	−0.902353	−	0.655598i
$832$	0.937652	−	2.88580i	0.0325072	−	0.100047i
$833$	−2.41922	−	7.44560i	−0.0838210	−	0.257975i
$834$	84.9564	−	61.7244i	2.94180	−	2.13734i
$835$		0			0
$836$	−15.4945	−	27.0843i	−0.535889	−	0.936731i
$837$	−0.762151			−0.0263438
$838$	−62.6065	+	45.4863i	−2.16271	+	1.57130i
$839$	11.9288	+	36.7132i	0.411829	+	1.26748i	0.915056	+	0.403326i	$0.132146\pi$
$839$	11.9288	+	36.7132i	0.411829	+	1.26748i	−0.503227	+	0.864154i	$0.667854\pi$
$840$		0			0
$841$	23.1579	+	16.8252i	0.798547	+	0.580178i
$842$	−14.1938	−	10.3124i	−0.489151	−	0.355389i
$843$	7.15428	−	22.0186i	0.246406	−	0.758361i
$844$	7.64568	+	23.5310i	0.263175	+	0.809969i
$845$		0			0
$846$	−56.9013			−1.95631
$847$	−15.2732	−	17.2350i	−0.524793	−	0.592203i
$848$	18.7672			0.644470
$849$	27.8184	−	20.2113i	0.954726	−	0.693649i
$850$		0			0
$851$	−5.07504	+	15.6194i	−0.173970	+	0.535425i
$852$	98.6551	+	71.6771i	3.37987	+	2.45562i
$853$	27.4303	+	19.9293i	0.939197	+	0.682366i	0.948227	−	0.317593i	$-0.102874\pi$
$853$	27.4303	+	19.9293i	0.939197	+	0.682366i	−0.00903033	+	0.999959i	$0.502874\pi$
$854$	−0.820596	+	2.52553i	−0.0280802	+	0.0864220i
$855$		0			0
$856$	−75.6523	+	54.9646i	−2.58574	+	1.87865i
$857$	56.7117			1.93723			0.968617	−	0.248558i	$-0.0799568\pi$
$857$	56.7117			1.93723			0.968617	+	0.248558i	$0.0799568\pi$
$858$	−13.2144	−	23.0986i	−0.451131	−	0.788574i
$859$	−25.7505			−0.878597			−0.439298	−	0.898341i	$-0.644773\pi$
$859$	−25.7505			−0.878597			−0.439298	+	0.898341i	$0.644773\pi$
$860$		0			0
$861$	8.14951	+	25.0816i	0.277735	+	0.854779i
$862$	2.52291	−	7.76473i	0.0859308	−	0.264468i
$863$	28.9345	+	21.0222i	0.984942	+	0.715603i	0.958808	−	0.284056i	$-0.0916801\pi$
$863$	28.9345	+	21.0222i	0.984942	+	0.715603i	0.0261347	+	0.999658i	$0.491680\pi$
$864$	0.697025	+	0.506418i	0.0237133	+	0.0172287i
$865$		0			0
$866$	−23.7093	−	72.9698i	−0.805676	−	2.47962i
$867$	16.0696	−	11.6752i	0.545751	−	0.396511i
$868$	33.3714			1.13270
$869$	16.2086	+	7.29357i	0.549841	+	0.247417i
$870$		0			0
$871$	8.14064	−	5.91452i	0.275835	−	0.200406i
$872$	−21.3041	−	65.5674i	−0.721449	−	2.22039i
$873$	0.335211	−	1.03167i	0.0113452	−	0.0349169i
$874$	−38.5722	−	28.0244i	−1.30473	−	0.947938i
$875$		0			0
$876$	37.0595	−	114.057i	1.25212	−	3.85364i
$877$	−5.34913	−	16.4629i	−0.180627	−	0.555913i	0.819218	−	0.573482i	$-0.194408\pi$
$877$	−5.34913	−	16.4629i	−0.180627	−	0.555913i	−0.999846	+	0.0175682i	$0.994408\pi$
$878$	74.6105	−	54.2077i	2.51798	−	1.82942i
$879$	−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	$0.522315\pi$
$882$	−16.4892	+	11.9801i	−0.555219	+	0.403391i
$883$	12.7533	+	39.2505i	0.429182	+	1.32088i	0.898933	+	0.438086i	$0.144344\pi$
$883$	12.7533	+	39.2505i	0.429182	+	1.32088i	−0.469751	+	0.882799i	$0.655656\pi$
$884$	−5.20843	+	16.0299i	−0.175179	+	0.539144i
$885$		0			0
$886$	4.41467	+	3.20744i	0.148314	+	0.107756i
$887$	−9.41854	+	28.9873i	−0.316243	+	0.973297i	0.658996	+	0.752146i	$0.270981\pi$
$887$	−9.41854	+	28.9873i	−0.316243	+	0.973297i	−0.975240	+	0.221151i	$0.929019\pi$
$888$	−8.54364	−	26.2946i	−0.286706	−	0.882390i
$889$	−31.8990	+	23.1760i	−1.06986	+	0.777298i
$890$		0			0
$891$	28.3727	−	5.91352i	0.950520	−	0.198110i
$892$	−34.4803			−1.15449
$893$	−12.7168	+	9.23933i	−0.425553	+	0.309182i
$894$	−4.49077	−	13.8212i	−0.150194	−	0.462249i
$895$		0			0
$896$	24.0270	+	17.4566i	0.802684	+	0.583184i
$897$	−22.5728	−	16.4001i	−0.753684	−	0.547583i
$898$	8.98831	−	27.6632i	0.299944	−	0.923132i
$899$	0.690047	+	2.12375i	0.0230144	+	0.0708309i
$900$		0			0
$901$	8.80090			0.293200
$902$	−4.63783	+	42.5068i	−0.154423	+	1.41532i
$903$	26.7134			0.888965
$904$	−43.8570	+	31.8640i	−1.45866	+	1.05978i
$905$		0			0
$906$	7.57976	−	23.3281i	0.251821	−	0.775024i
$907$	9.13337	+	6.63578i	0.303269	+	0.220338i	0.729003	−	0.684511i	$-0.239984\pi$
$907$	9.13337	+	6.63578i	0.303269	+	0.220338i	−0.425734	+	0.904848i	$0.639984\pi$
$908$	−39.6660	−	28.8191i	−1.31636	−	0.956394i
$909$	−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	$0.983528\pi$
$912$	33.8494			1.12086
$913$	3.90146	−	35.7578i	0.129119	−	1.18341i
$914$	−40.2193			−1.33034
$915$		0			0
$916$	36.4753	+	112.259i	1.20518	+	3.70915i
$917$	13.0031	−	40.0193i	0.429399	−	1.32156i
$918$	1.27742	+	0.928099i	0.0421611	+	0.0306318i
$919$	22.0198	+	15.9983i	0.726366	+	0.527736i	0.888412	−	0.459048i	$-0.151809\pi$
$919$	22.0198	+	15.9983i	0.726366	+	0.527736i	−0.162046	+	0.986783i	$0.551809\pi$
$920$		0			0
$921$	−3.87693	−	11.9320i	−0.127749	−	0.393172i
$922$	3.11518	−	2.26331i	0.102593	−	0.0745381i
$923$	14.5649			0.479410
$924$	73.3265	−	15.2829i	2.41227	−	0.502771i
$925$		0			0
$926$	−29.0167	+	21.0819i	−0.953547	+	0.692793i
$927$	−6.36759	−	19.5974i	−0.209139	−	0.643664i
$928$	0.780061	−	2.40078i	0.0256068	−	0.0788095i
$929$	18.7776	+	13.6427i	0.616073	+	0.447603i	0.851548	−	0.524277i	$-0.175664\pi$
$929$	18.7776	+	13.6427i	0.616073	+	0.447603i	−0.235475	+	0.971880i	$0.575664\pi$
$930$		0			0
$931$	−1.73990	+	5.35485i	−0.0570228	+	0.175498i
$932$	14.6637	+	45.1303i	0.480326	+	1.47829i
$933$	−27.4625	+	19.9527i	−0.899082	+	0.653221i
$934$	−15.2910			−0.500336
$935$		0			0
$936$	23.8128			0.778344
$937$	−34.1500	+	24.8114i	−1.11563	+	0.810554i	−0.983541	−	0.180684i	$-0.942169\pi$
$937$	−34.1500	+	24.8114i	−1.11563	+	0.810554i	−0.132090	+	0.991238i	$0.542169\pi$
$938$	12.7546	+	39.2547i	0.416453	+	1.28171i
$939$	−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	$0.542030\pi$
$942$	−9.39289	+	28.9083i	−0.306037	+	0.941885i
$943$	13.8539	+	42.6378i	0.451144	+	1.38848i
$944$	33.5128	−	24.3485i	1.09075	−	0.792476i
$945$		0			0
$946$	39.4974	+	17.7730i	1.28417	+	0.577851i
$947$	−9.63809			−0.313196			−0.156598	−	0.987662i	$-0.550053\pi$
$947$	−9.63809			−0.313196			−0.156598	+	0.987662i	$0.550053\pi$
$948$	−46.7704	+	33.9807i	−1.51903	+	1.10364i
$949$	−4.42634	−	13.6229i	−0.143685	−	0.442218i
$950$		0			0
$951$	21.3680	+	15.5247i	0.692904	+	0.503424i
$952$	−30.3532	−	22.0529i	−0.983752	−	0.714738i
$953$	−1.61353	+	4.96593i	−0.0522673	+	0.160862i	−0.973783	−	0.227479i	$-0.926952\pi$
$953$	−1.61353	+	4.96593i	−0.0522673	+	0.160862i	0.921516	+	0.388341i	$0.126952\pi$
$954$	−7.08039	−	21.7912i	−0.229236	−	0.705517i
$955$		0			0
$956$	−50.1446			−1.62179
$957$	2.48883	+	4.35046i	0.0804525	+	0.140630i
$958$	44.4529			1.43621
$959$	30.4376	−	22.1142i	0.982882	−	0.714106i
$960$		0			0
$961$	−5.47390	+	16.8469i	−0.176577	+	0.543450i
$962$	−4.92298	−	3.57675i	−0.158723	−	0.115319i
$963$	38.9517	+	28.3001i	1.25520	+	0.911956i
$964$	17.2361	−	53.0471i	0.555136	−	1.70853i
$965$		0			0
$966$	92.5913	−	67.2715i	2.97908	−	2.16443i
$967$	−38.4583			−1.23674			−0.618368	−	0.785889i	$-0.712206\pi$
$967$	−38.4583			−1.23674			−0.618368	+	0.785889i	$0.712206\pi$
$968$	64.3532	+	14.2121i	2.06839	+	0.456793i
$969$	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	$0.652908\pi$
$972$	−29.9779	+	92.2625i	−0.961542	+	2.95932i
$973$	28.5608	+	20.7506i	0.915616	+	0.665234i
$974$	−13.8543	−	10.0658i	−0.443921	−	0.322527i
$975$		0			0
$976$	−0.990380	−	3.04808i	−0.0317013	−	0.0975665i
$977$	−9.50330	+	6.90455i	−0.304038	+	0.220896i	−0.729334	−	0.684158i	$-0.760170\pi$
$977$	−9.50330	+	6.90455i	−0.304038	+	0.220896i	0.425296	+	0.905054i	$0.360170\pi$
$978$	−43.8137			−1.40101
$979$	7.12027	+	12.4462i	0.227565	+	0.397782i
$980$		0			0
$981$	−28.7173	+	20.8643i	−0.916872	+	0.666147i
$982$	−0.404582	−	1.24518i	−0.0129107	−	0.0397351i
$983$	−2.88989	+	8.89417i	−0.0921733	+	0.283680i	−0.986507	−	0.163721i	$-0.947650\pi$
$983$	−2.88989	+	8.89417i	−0.0921733	+	0.283680i	0.894333	+	0.447401i	$0.147650\pi$
$984$	−61.0590	−	44.3620i	−1.94649	−	1.41421i
$985$		0			0
$986$	1.42960	−	4.39985i	0.0455276	−	0.140120i
$987$	−11.6600	−	35.8859i	−0.371143	−	1.14226i
$988$	9.80687	−	7.12510i	0.311998	−	0.226680i
$989$	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	$0.671739\pi$
$992$	−12.1508	+	8.82806i	−0.385788	+	0.280291i
$993$	−6.74310	−	20.7531i	−0.213986	−	0.658581i
$994$	−18.4619	+	56.8197i	−0.585574	+	1.80221i
$995$		0			0
$996$	94.6510	+	68.7679i	2.99913	+	2.17900i
$997$	8.99777	−	27.6923i	0.284962	−	0.877023i	−0.701448	−	0.712721i	$-0.747463\pi$
$997$	8.99777	−	27.6923i	0.284962	−	0.877023i	0.986410	−	0.164302i	$-0.0525373\pi$
$998$	−17.0540	−	52.4869i	−0.539836	−	1.66144i
$999$	−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.h.b.201.2		8
5.2	odd	4		275.2.z.b.124.4		16
5.3	odd	4		275.2.z.b.124.1		16
5.4	even	2		55.2.g.a.36.1	yes	8
11.2	odd	10		3025.2.a.be.1.4		4
11.4	even	5	inner	275.2.h.b.26.2		8
11.9	even	5		3025.2.a.v.1.1		4
15.14	odd	2		495.2.n.f.91.2		8
20.19	odd	2		880.2.bo.e.641.2		8
55.4	even	10		55.2.g.a.26.1	✓	8
55.9	even	10		605.2.a.l.1.4		4
55.14	even	10		605.2.g.j.511.2		8
55.19	odd	10		605.2.g.g.511.1		8
55.24	odd	10		605.2.a.i.1.1		4
55.29	odd	10		605.2.g.n.81.2		8
55.37	odd	20		275.2.z.b.224.1		16
55.39	odd	10		605.2.g.g.251.1		8
55.48	odd	20		275.2.z.b.224.4		16
55.49	even	10		605.2.g.j.251.2		8
55.54	odd	2		605.2.g.n.366.2		8
165.59	odd	10		495.2.n.f.136.2		8
165.119	odd	10		5445.2.a.bg.1.1		4
165.134	even	10		5445.2.a.bu.1.4		4
220.59	odd	10		880.2.bo.e.81.2		8
220.79	even	10		9680.2.a.cv.1.4		4
220.119	odd	10		9680.2.a.cs.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.g.a.26.1	✓	8	55.4	even	10
55.2.g.a.36.1	yes	8	5.4	even	2
275.2.h.b.26.2		8	11.4	even	5	inner
275.2.h.b.201.2		8	1.1	even	1	trivial
275.2.z.b.124.1		16	5.3	odd	4
275.2.z.b.124.4		16	5.2	odd	4
275.2.z.b.224.1		16	55.37	odd	20
275.2.z.b.224.4		16	55.48	odd	20
495.2.n.f.91.2		8	15.14	odd	2
495.2.n.f.136.2		8	165.59	odd	10
605.2.a.i.1.1		4	55.24	odd	10
605.2.a.l.1.4		4	55.9	even	10
605.2.g.g.251.1		8	55.39	odd	10
605.2.g.g.511.1		8	55.19	odd	10
605.2.g.j.251.2		8	55.49	even	10
605.2.g.j.511.2		8	55.14	even	10
605.2.g.n.81.2		8	55.29	odd	10
605.2.g.n.366.2		8	55.54	odd	2
880.2.bo.e.81.2		8	220.59	odd	10
880.2.bo.e.641.2		8	20.19	odd	2
3025.2.a.v.1.1		4	11.9	even	5
3025.2.a.be.1.4		4	11.2	odd	10
5445.2.a.bg.1.1		4	165.119	odd	10
5445.2.a.bu.1.4		4	165.134	even	10
9680.2.a.cs.1.4		4	220.119	odd	10
9680.2.a.cv.1.4		4	220.79	even	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 275 = 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	275.h (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(2.04238 - 1.48388i) q^{2} +(0.762262 + 2.34600i) q^{3} +(1.35140 - 4.15918i) q^{4} +(5.03801 + 3.66033i) q^{6} +(-0.646930 + 1.99105i) q^{7} +(-1.85140 - 5.69802i) q^{8} +(-2.49563 + 1.81318i) q^{9} +O(q^{10})\)	\(q+(2.04238 - 1.48388i) q^{2} +(0.762262 + 2.34600i) q^{3} +(1.35140 - 4.15918i) q^{4} +(5.03801 + 3.66033i) q^{6} +(-0.646930 + 1.99105i) q^{7} +(-1.85140 - 5.69802i) q^{8} +(-2.49563 + 1.81318i) q^{9} +(-1.64693 - 2.87882i) q^{11} +10.7876 q^{12} +(1.04238 - 0.757336i) q^{13} +(1.63319 + 5.02644i) q^{14} +(-5.16042 - 3.74926i) q^{16} +(-2.41998 - 1.75822i) q^{17} +(-2.40649 + 7.40641i) q^{18} +(0.664789 + 2.04601i) q^{19} -5.16413 q^{21} +(-7.63548 - 3.43582i) q^{22} -8.77882 q^{23} +(11.9563 - 8.68677i) q^{24} +(1.00515 - 3.09354i) q^{26} +(-0.169161 - 0.122903i) q^{27} +(7.40686 + 5.38140i) q^{28} +(-0.189313 + 0.582646i) q^{29} +(2.94887 - 2.14248i) q^{31} -4.12048 q^{32} +(5.49833 - 6.05812i) q^{33} -7.55150 q^{34} +(4.16875 + 12.8301i) q^{36} +(0.578100 - 1.77921i) q^{37} +(4.39378 + 3.19227i) q^{38} +(2.57128 + 1.86814i) q^{39} +(-1.57810 - 4.85689i) q^{41} +(-10.5471 + 7.66294i) q^{42} -5.17287 q^{43} +(-14.1992 + 2.95944i) q^{44} +(-17.9297 + 13.0267i) q^{46} +(2.25789 + 6.94907i) q^{47} +(4.86218 - 14.9643i) q^{48} +(2.11737 + 1.53836i) q^{49} +(2.28012 - 7.01749i) q^{51} +(-1.74122 - 5.35892i) q^{52} +(-2.38030 + 1.72939i) q^{53} -0.527864 q^{54} +12.5428 q^{56} +(-4.29320 + 3.11919i) q^{57} +(0.477925 + 1.47090i) q^{58} +(-2.00682 + 6.17636i) q^{59} +(0.406490 + 0.295332i) q^{61} +(2.84355 - 8.75154i) q^{62} +(-1.99563 - 6.14191i) q^{63} +(1.90523 - 1.38423i) q^{64} +(2.24019 - 20.5318i) q^{66} +7.80964 q^{67} +(-10.5831 + 7.68907i) q^{68} +(-6.69176 - 20.5951i) q^{69} +(9.14526 + 6.64442i) q^{71} +(14.9519 + 10.8632i) q^{72} +(3.43539 - 10.5730i) q^{73} +(-1.45943 - 4.49166i) q^{74} +9.40812 q^{76} +(6.79732 - 1.41672i) q^{77} +8.02363 q^{78} +(-4.33558 + 3.14998i) q^{79} +(-2.70035 + 8.31082i) q^{81} +(-10.4301 - 7.57793i) q^{82} +(8.77408 + 6.37474i) q^{83} +(-6.97880 + 21.4785i) q^{84} +(-10.5650 + 7.67591i) q^{86} -1.51119 q^{87} +(-13.3545 + 14.7141i) q^{88} -4.32336 q^{89} +(0.833541 + 2.56538i) q^{91} +(-11.8637 + 36.5127i) q^{92} +(7.27408 + 5.28493i) q^{93} +(14.9230 + 10.8422i) q^{94} +(-3.14089 - 9.66666i) q^{96} +(-0.284493 + 0.206696i) q^{97} +6.60723 q^{98} +(9.32995 + 4.19829i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{2} - q^{3} - 6 q^{4} + 13 q^{6} + 3 q^{7} + 2 q^{8} - 5 q^{9}+O(q^{10}) \) 8 * q + 4 * q^2 - q^3 - 6 * q^4 + 13 * q^6 + 3 * q^7 + 2 * q^8 - 5 * q^9	\( 8 q + 4 q^{2} - q^{3} - 6 q^{4} + 13 q^{6} + 3 q^{7} + 2 q^{8} - 5 q^{9} - 5 q^{11} + 28 q^{12} - 4 q^{13} + 16 q^{14} - 20 q^{16} - q^{17} - 14 q^{18} - q^{19} - 12 q^{21} - 33 q^{22} + 18 q^{23} + 25 q^{24} - 14 q^{26} - 10 q^{27} - 4 q^{28} + 19 q^{29} + 6 q^{31} - 12 q^{32} + 19 q^{33} - 20 q^{34} + 21 q^{36} - 4 q^{37} + 6 q^{38} + 9 q^{39} - 4 q^{41} - 29 q^{42} - 42 q^{43} - 28 q^{44} - 41 q^{46} - 4 q^{47} + 19 q^{48} - 15 q^{49} + 13 q^{51} + 26 q^{52} - 3 q^{53} - 40 q^{54} + 30 q^{56} + 5 q^{57} + 6 q^{58} - 19 q^{59} - 2 q^{61} + 38 q^{62} - q^{63} + 6 q^{64} + 13 q^{66} + 2 q^{67} - 35 q^{68} - 21 q^{69} + 40 q^{71} + 34 q^{72} + 23 q^{73} + 48 q^{74} + 16 q^{76} + 28 q^{77} - 12 q^{78} + 17 q^{79} - 2 q^{82} + 25 q^{83} - 4 q^{84} - 31 q^{86} - 30 q^{87} - 22 q^{88} - 12 q^{91} - 81 q^{92} + 13 q^{93} + 33 q^{94} + 23 q^{96} - 12 q^{97} + 84 q^{98} + 4 q^{99}+O(q^{100}) \) 8 * q + 4 * q^2 - q^3 - 6 * q^4 + 13 * q^6 + 3 * q^7 + 2 * q^8 - 5 * q^9 - 5 * q^11 + 28 * q^12 - 4 * q^13 + 16 * q^14 - 20 * q^16 - q^17 - 14 * q^18 - q^19 - 12 * q^21 - 33 * q^22 + 18 * q^23 + 25 * q^24 - 14 * q^26 - 10 * q^27 - 4 * q^28 + 19 * q^29 + 6 * q^31 - 12 * q^32 + 19 * q^33 - 20 * q^34 + 21 * q^36 - 4 * q^37 + 6 * q^38 + 9 * q^39 - 4 * q^41 - 29 * q^42 - 42 * q^43 - 28 * q^44 - 41 * q^46 - 4 * q^47 + 19 * q^48 - 15 * q^49 + 13 * q^51 + 26 * q^52 - 3 * q^53 - 40 * q^54 + 30 * q^56 + 5 * q^57 + 6 * q^58 - 19 * q^59 - 2 * q^61 + 38 * q^62 - q^63 + 6 * q^64 + 13 * q^66 + 2 * q^67 - 35 * q^68 - 21 * q^69 + 40 * q^71 + 34 * q^72 + 23 * q^73 + 48 * q^74 + 16 * q^76 + 28 * q^77 - 12 * q^78 + 17 * q^79 - 2 * q^82 + 25 * q^83 - 4 * q^84 - 31 * q^86 - 30 * q^87 - 22 * q^88 - 12 * q^91 - 81 * q^92 + 13 * q^93 + 33 * q^94 + 23 * q^96 - 12 * q^97 + 84 * q^98 + 4 * q^99

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