LMFDB - Embedded newform 1155.2.c.e.694.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1155,2,Mod(694,1155)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1155, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))

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

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

chi := DirichletCharacter("1155.694");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1155 = 3 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1155.c (of order $2$, degree $1$, 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:	$9.22272143346$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 33 x^{18} + 456 x^{16} + 3426 x^{14} + 15194 x^{12} + 40320 x^{10} + 61593 x^{8} + 48545 x^{6} + \cdots + 100 $ x^20 + 33x^18 + 456x^16 + 3426x^14 + 15194x^12 + 40320x^10 + 61593x^8 + 48545x^6 + 15624x^4 + 2116*x^2 + 100
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			694.13
Root			$0.445112i$ of defining polynomial
Character	$\chi$	$=$	1155.694
Dual form			1155.2.c.e.694.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.445112i q^{2} -1.00000i q^{3} +1.80187 q^{4} +(-2.13786 + 0.655413i) q^{5} +0.445112 q^{6} +1.00000i q^{7} +1.69226i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+0.445112i q^{2} -1.00000i q^{3} +1.80187 q^{4} +(-2.13786 + 0.655413i) q^{5} +0.445112 q^{6} +1.00000i q^{7} +1.69226i q^{8} -1.00000 q^{9} +(-0.291732 - 0.951587i) q^{10} -1.00000 q^{11} -1.80187i q^{12} -5.70387i q^{13} -0.445112 q^{14} +(0.655413 + 2.13786i) q^{15} +2.85050 q^{16} +5.56222i q^{17} -0.445112i q^{18} +7.31377 q^{19} +(-3.85215 + 1.18097i) q^{20} +1.00000 q^{21} -0.445112i q^{22} -1.80010i q^{23} +1.69226 q^{24} +(4.14087 - 2.80236i) q^{25} +2.53886 q^{26} +1.00000i q^{27} +1.80187i q^{28} +9.46717 q^{29} +(-0.951587 + 0.291732i) q^{30} +2.72181 q^{31} +4.65332i q^{32} +1.00000i q^{33} -2.47581 q^{34} +(-0.655413 - 2.13786i) q^{35} -1.80187 q^{36} +7.51711i q^{37} +3.25545i q^{38} -5.70387 q^{39} +(-1.10913 - 3.61781i) q^{40} +5.87423 q^{41} +0.445112i q^{42} +3.62051i q^{43} -1.80187 q^{44} +(2.13786 - 0.655413i) q^{45} +0.801249 q^{46} -0.419467i q^{47} -2.85050i q^{48} -1.00000 q^{49} +(1.24736 + 1.84315i) q^{50} +5.56222 q^{51} -10.2777i q^{52} +2.52806i q^{53} -0.445112 q^{54} +(2.13786 - 0.655413i) q^{55} -1.69226 q^{56} -7.31377i q^{57} +4.21396i q^{58} -1.23421 q^{59} +(1.18097 + 3.85215i) q^{60} -13.7500 q^{61} +1.21151i q^{62} -1.00000i q^{63} +3.62976 q^{64} +(3.73839 + 12.1941i) q^{65} -0.445112 q^{66} +7.15848i q^{67} +10.0224i q^{68} -1.80010 q^{69} +(0.951587 - 0.291732i) q^{70} +12.4319 q^{71} -1.69226i q^{72} -7.61626i q^{73} -3.34596 q^{74} +(-2.80236 - 4.14087i) q^{75} +13.1785 q^{76} -1.00000i q^{77} -2.53886i q^{78} +2.94103 q^{79} +(-6.09397 + 1.86826i) q^{80} +1.00000 q^{81} +2.61469i q^{82} -16.3358i q^{83} +1.80187 q^{84} +(-3.64555 - 11.8912i) q^{85} -1.61153 q^{86} -9.46717i q^{87} -1.69226i q^{88} +1.12458 q^{89} +(0.291732 + 0.951587i) q^{90} +5.70387 q^{91} -3.24356i q^{92} -2.72181i q^{93} +0.186710 q^{94} +(-15.6358 + 4.79354i) q^{95} +4.65332 q^{96} -9.90641i q^{97} -0.445112i q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 26 q^{4} - 2 q^{5} + 6 q^{6} - 20 q^{9}+O(q^{10}) $ 20 * q - 26 * q^4 - 2 * q^5 + 6 * q^6 - 20 * q^9	$ 20 q - 26 q^{4} - 2 q^{5} + 6 q^{6} - 20 q^{9} - 2 q^{10} - 20 q^{11} - 6 q^{14} + 2 q^{15} + 38 q^{16} + 2 q^{19} + 4 q^{20} + 20 q^{21} - 18 q^{24} + 12 q^{25} + 20 q^{26} - 38 q^{29} + 6 q^{30} + 20 q^{31} - 32 q^{34} - 2 q^{35} + 26 q^{36} + 2 q^{40} + 12 q^{41} + 26 q^{44} + 2 q^{45} + 8 q^{46} - 20 q^{49} - 6 q^{50} + 26 q^{51} - 6 q^{54} + 2 q^{55} + 18 q^{56} - 22 q^{59} + 16 q^{60} + 34 q^{61} - 26 q^{64} - 28 q^{65} - 6 q^{66} - 26 q^{69} - 6 q^{70} + 72 q^{71} - 72 q^{74} - 8 q^{75} + 44 q^{76} + 4 q^{79} - 8 q^{80} + 20 q^{81} - 26 q^{84} - 16 q^{85} + 52 q^{86} + 6 q^{89} + 2 q^{90} + 16 q^{94} + 14 q^{95} + 62 q^{96} + 20 q^{99}+O(q^{100}) $ 20 * q - 26 * q^4 - 2 * q^5 + 6 * q^6 - 20 * q^9 - 2 * q^10 - 20 * q^11 - 6 * q^14 + 2 * q^15 + 38 * q^16 + 2 * q^19 + 4 * q^20 + 20 * q^21 - 18 * q^24 + 12 * q^25 + 20 * q^26 - 38 * q^29 + 6 * q^30 + 20 * q^31 - 32 * q^34 - 2 * q^35 + 26 * q^36 + 2 * q^40 + 12 * q^41 + 26 * q^44 + 2 * q^45 + 8 * q^46 - 20 * q^49 - 6 * q^50 + 26 * q^51 - 6 * q^54 + 2 * q^55 + 18 * q^56 - 22 * q^59 + 16 * q^60 + 34 * q^61 - 26 * q^64 - 28 * q^65 - 6 * q^66 - 26 * q^69 - 6 * q^70 + 72 * q^71 - 72 * q^74 - 8 * q^75 + 44 * q^76 + 4 * q^79 - 8 * q^80 + 20 * q^81 - 26 * q^84 - 16 * q^85 + 52 * q^86 + 6 * q^89 + 2 * q^90 + 16 * q^94 + 14 * q^95 + 62 * q^96 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1155\mathbb{Z}\right)^\times$.

$n$	$211$	$232$	$386$	$661$
$\chi(n)$	$1$	$-1$	$1$	$1$

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 $

$2$			0.445112i			0.314742i	0.987540	+	0.157371i	$0.0503018\pi$
$2$			0.445112i			0.314742i	−0.987540	+	0.157371i	$0.949698\pi$
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	1.80187			0.900937
$5$	−2.13786	+	0.655413i	−0.956079	+	0.293110i
$5$	−2.13786	+	0.655413i	−0.956079	+	0.293110i
$6$	0.445112			0.181716
$7$			1.00000i			0.377964i
$7$			1.00000i			0.377964i
$8$			1.69226i			0.598305i
$9$	−1.00000			−0.333333
$10$	−0.291732	−	0.951587i	−0.0922539	−	0.300918i
$11$	−1.00000			−0.301511
$11$	−1.00000			−0.301511
$12$		−	1.80187i		−	0.520156i
$13$		−	5.70387i		−	1.58197i	−0.611837	−	0.790984i	$-0.709569\pi$
$13$		−	5.70387i		−	1.58197i	0.611837	−	0.790984i	$-0.290431\pi$
$14$	−0.445112			−0.118961
$15$	0.655413	+	2.13786i	0.169227	+	0.551992i
$16$	2.85050			0.712626
$17$			5.56222i			1.34904i	0.738258	+	0.674518i	$0.235649\pi$
$17$			5.56222i			1.34904i	−0.738258	+	0.674518i	$0.764351\pi$
$18$		−	0.445112i		−	0.104914i
$19$	7.31377			1.67790			0.838948	−	0.544212i	$-0.183171\pi$
$19$	7.31377			1.67790			0.838948	+	0.544212i	$0.183171\pi$
$20$	−3.85215	+	1.18097i	−0.861367	+	0.264073i
$21$	1.00000			0.218218
$22$		−	0.445112i		−	0.0948983i
$23$		−	1.80010i		−	0.375348i	−0.982231	−	0.187674i	$-0.939905\pi$
$23$		−	1.80010i		−	0.375348i	0.982231	−	0.187674i	$-0.0600948\pi$
$24$	1.69226			0.345431
$25$	4.14087	−	2.80236i	0.828174	−	0.560472i
$26$	2.53886			0.497912
$27$			1.00000i			0.192450i
$28$			1.80187i			0.340522i
$29$	9.46717			1.75801			0.879005	−	0.476813i	$-0.158208\pi$
$29$	9.46717			1.75801			0.879005	+	0.476813i	$0.158208\pi$
$30$	−0.951587	+	0.291732i	−0.173735	+	0.0532628i
$31$	2.72181			0.488851			0.244425	−	0.969668i	$-0.421401\pi$
$31$	2.72181			0.488851			0.244425	+	0.969668i	$0.421401\pi$
$32$			4.65332i			0.822598i
$33$			1.00000i			0.174078i
$34$	−2.47581			−0.424598
$35$	−0.655413	−	2.13786i	−0.110785	−	0.361364i
$36$	−1.80187			−0.300312
$37$			7.51711i			1.23581i	0.786254	+	0.617903i	$0.212018\pi$
$37$			7.51711i			1.23581i	−0.786254	+	0.617903i	$0.787982\pi$
$38$			3.25545i			0.528104i
$39$	−5.70387			−0.913349
$40$	−1.10913	−	3.61781i	−0.175369	−	0.572027i
$41$	5.87423			0.917400			0.458700	−	0.888591i	$-0.348315\pi$
$41$	5.87423			0.917400			0.458700	+	0.888591i	$0.348315\pi$
$42$			0.445112i			0.0686823i
$43$			3.62051i			0.552122i	0.961140	+	0.276061i	$0.0890292\pi$
$43$			3.62051i			0.552122i	−0.961140	+	0.276061i	$0.910971\pi$
$44$	−1.80187			−0.271643
$45$	2.13786	−	0.655413i	0.318693	−	0.0977032i
$46$	0.801249			0.118138
$47$		−	0.419467i		−	0.0611856i	−0.999532	−	0.0305928i	$-0.990260\pi$
$47$		−	0.419467i		−	0.0611856i	0.999532	−	0.0305928i	$-0.00973951\pi$
$48$		−	2.85050i		−	0.411435i
$49$	−1.00000			−0.142857
$50$	1.24736	+	1.84315i	0.176404	+	0.260661i
$51$	5.56222			0.778866
$52$		−	10.2777i		−	1.42525i
$53$			2.52806i			0.347256i	0.984811	+	0.173628i	$0.0555490\pi$
$53$			2.52806i			0.347256i	−0.984811	+	0.173628i	$0.944451\pi$
$54$	−0.445112			−0.0605721
$55$	2.13786	−	0.655413i	0.288269	−	0.0883758i
$56$	−1.69226			−0.226138
$57$		−	7.31377i		−	0.968733i
$58$			4.21396i			0.553320i
$59$	−1.23421			−0.160681			−0.0803404	−	0.996767i	$-0.525601\pi$
$59$	−1.23421			−0.160681			−0.0803404	+	0.996767i	$0.525601\pi$
$60$	1.18097	+	3.85215i	0.152463	+	0.497311i
$61$	−13.7500			−1.76051			−0.880256	−	0.474499i	$-0.842629\pi$
$61$	−13.7500			−1.76051			−0.880256	+	0.474499i	$0.842629\pi$
$62$			1.21151i			0.153862i
$63$		−	1.00000i		−	0.125988i
$64$	3.62976			0.453720
$65$	3.73839	+	12.1941i	0.463690	+	1.51249i
$66$	−0.445112			−0.0547896
$67$			7.15848i			0.874548i	0.899328	+	0.437274i	$0.144056\pi$
$67$			7.15848i			0.874548i	−0.899328	+	0.437274i	$0.855944\pi$
$68$			10.0224i			1.21540i
$69$	−1.80010			−0.216707
$70$	0.951587	−	0.291732i	0.113736	−	0.0348687i
$71$	12.4319			1.47539			0.737695	−	0.675134i	$-0.235914\pi$
$71$	12.4319			1.47539			0.737695	+	0.675134i	$0.235914\pi$
$72$		−	1.69226i		−	0.199435i
$73$		−	7.61626i		−	0.891416i	−0.895178	−	0.445708i	$-0.852952\pi$
$73$		−	7.61626i		−	0.891416i	0.895178	−	0.445708i	$-0.147048\pi$
$74$	−3.34596			−0.388960
$75$	−2.80236	−	4.14087i	−0.323588	−	0.478146i
$76$	13.1785			1.51168
$77$		−	1.00000i		−	0.113961i
$78$		−	2.53886i		−	0.287469i
$79$	2.94103			0.330892			0.165446	−	0.986219i	$-0.447094\pi$
$79$	2.94103			0.330892			0.165446	+	0.986219i	$0.447094\pi$
$80$	−6.09397	+	1.86826i	−0.681326	+	0.208877i
$81$	1.00000			0.111111
$82$			2.61469i			0.288744i
$83$		−	16.3358i		−	1.79308i	−0.442958	−	0.896542i	$-0.646071\pi$
$83$		−	16.3358i		−	1.79308i	0.442958	−	0.896542i	$-0.353929\pi$
$84$	1.80187			0.196601
$85$	−3.64555	−	11.8912i	−0.395415	−	1.28979i
$86$	−1.61153			−0.173776
$87$		−	9.46717i		−	1.01499i
$88$		−	1.69226i		−	0.180396i
$89$	1.12458			0.119205			0.0596024	−	0.998222i	$-0.481017\pi$
$89$	1.12458			0.119205			0.0596024	+	0.998222i	$0.481017\pi$
$90$	0.291732	+	0.951587i	0.0307513	+	0.100306i
$91$	5.70387			0.597928
$92$		−	3.24356i		−	0.338165i
$93$		−	2.72181i		−	0.282238i
$94$	0.186710			0.0192577
$95$	−15.6358	+	4.79354i	−1.60420	+	0.491807i
$96$	4.65332			0.474927
$97$		−	9.90641i		−	1.00584i	−0.864332	−	0.502922i	$-0.832258\pi$
$97$		−	9.90641i		−	1.00584i	0.864332	−	0.502922i	$-0.167742\pi$
$98$		−	0.445112i		−	0.0449631i
$99$	1.00000			0.100504
$100$	7.46133	−	5.04950i	0.746133	−	0.504950i
$101$	−12.4126			−1.23510			−0.617548	−	0.786533i	$-0.711874\pi$
$101$	−12.4126			−1.23510			−0.617548	+	0.786533i	$0.711874\pi$
$102$			2.47581i			0.245142i
$103$		−	9.22426i		−	0.908893i	−0.890774	−	0.454446i	$-0.849837\pi$
$103$		−	9.22426i		−	0.908893i	0.890774	−	0.454446i	$-0.150163\pi$
$104$	9.65243			0.946499
$105$	−2.13786	+	0.655413i	−0.208634	+	0.0639617i
$106$	−1.12527			−0.109296
$107$			15.9093i			1.53801i	0.639240	+	0.769007i	$0.279249\pi$
$107$			15.9093i			1.53801i	−0.639240	+	0.769007i	$0.720751\pi$
$108$			1.80187i			0.173385i
$109$	4.68458			0.448702			0.224351	−	0.974508i	$-0.427974\pi$
$109$	4.68458			0.448702			0.224351	+	0.974508i	$0.427974\pi$
$110$	0.291732	+	0.951587i	0.0278156	+	0.0907302i
$111$	7.51711			0.713493
$112$			2.85050i			0.269347i
$113$		−	2.13098i		−	0.200466i	−0.994964	−	0.100233i	$-0.968041\pi$
$113$		−	2.13098i		−	0.200466i	0.994964	−	0.100233i	$-0.0319588\pi$
$114$	3.25545			0.304901
$115$	1.17981	+	3.84837i	0.110018	+	0.358862i
$116$	17.0587			1.58386
$117$			5.70387i			0.527323i
$118$		−	0.549363i		−	0.0505730i
$119$	−5.56222			−0.509888
$120$	−3.61781	+	1.10913i	−0.330260	+	0.101249i
$121$	1.00000			0.0909091
$122$		−	6.12031i		−	0.554107i
$123$		−	5.87423i		−	0.529661i
$124$	4.90435			0.440424
$125$	−7.01588	+	8.70502i	−0.627520	+	0.778601i
$126$	0.445112			0.0396538
$127$			4.62338i			0.410258i	0.978735	+	0.205129i	$0.0657614\pi$
$127$			4.62338i			0.410258i	−0.978735	+	0.205129i	$0.934239\pi$
$128$			10.9223i			0.965403i
$129$	3.62051			0.318768
$130$	−5.42772	+	1.66400i	−0.476043	+	0.145943i
$131$	−3.81707			−0.333499			−0.166750	−	0.985999i	$-0.553327\pi$
$131$	−3.81707			−0.333499			−0.166750	+	0.985999i	$0.553327\pi$
$132$			1.80187i			0.156833i
$133$			7.31377i			0.634185i
$134$	−3.18633			−0.275257
$135$	−0.655413	−	2.13786i	−0.0564090	−	0.183997i
$136$	−9.41273			−0.807135
$137$		−	5.74767i		−	0.491057i	−0.969389	−	0.245528i	$-0.921039\pi$
$137$		−	5.74767i		−	0.491057i	0.969389	−	0.245528i	$-0.0789615\pi$
$138$		−	0.801249i		−	0.0682068i
$139$	12.1762			1.03277			0.516387	−	0.856355i	$-0.327277\pi$
$139$	12.1762			1.03277			0.516387	+	0.856355i	$0.327277\pi$
$140$	−1.18097	−	3.85215i	−0.0998103	−	0.325566i
$141$	−0.419467			−0.0353255
$142$			5.53357i			0.464367i
$143$			5.70387i			0.476981i
$144$	−2.85050			−0.237542
$145$	−20.2395	+	6.20491i	−1.68080	+	0.515289i
$146$	3.39009			0.280566
$147$			1.00000i			0.0824786i
$148$			13.5449i			1.11338i
$149$	−19.4284			−1.59163			−0.795817	−	0.605537i	$-0.792958\pi$
$149$	−19.4284			−1.59163			−0.795817	+	0.605537i	$0.792958\pi$
$150$	1.84315	−	1.24736i	0.150493	−	0.101847i
$151$	−9.25312			−0.753008			−0.376504	−	0.926415i	$-0.622874\pi$
$151$	−9.25312			−0.753008			−0.376504	+	0.926415i	$0.622874\pi$
$152$			12.3768i			1.00389i
$153$		−	5.56222i		−	0.449679i
$154$	0.445112			0.0358682
$155$	−5.81883	+	1.78391i	−0.467380	+	0.143287i
$156$	−10.2777			−0.822871
$157$			24.4819i			1.95387i	0.213541	+	0.976934i	$0.431500\pi$
$157$			24.4819i			1.95387i	−0.213541	+	0.976934i	$0.568500\pi$
$158$			1.30909i			0.104146i
$159$	2.52806			0.200488
$160$	−3.04984	−	9.94813i	−0.241111	−	0.786469i
$161$	1.80010			0.141868
$162$			0.445112i			0.0349713i
$163$			7.49524i			0.587072i	0.955948	+	0.293536i	$0.0948321\pi$
$163$			7.49524i			0.587072i	−0.955948	+	0.293536i	$0.905168\pi$
$164$	10.5846			0.826520
$165$	−0.655413	−	2.13786i	−0.0510238	−	0.166432i
$166$	7.27126			0.564359
$167$		−	17.3771i		−	1.34468i	−0.740242	−	0.672341i	$-0.765289\pi$
$167$		−	17.3771i		−	1.34468i	0.740242	−	0.672341i	$-0.234711\pi$
$168$			1.69226i			0.130561i
$169$	−19.5341			−1.50262
$170$	5.29293	−	1.62268i	0.405950	−	0.124454i
$171$	−7.31377			−0.559298
$172$			6.52370i			0.497427i
$173$		−	18.9081i		−	1.43755i	−0.695240	−	0.718777i	$-0.744702\pi$
$173$		−	18.9081i		−	1.43755i	0.695240	−	0.718777i	$-0.255298\pi$
$174$	4.21396			0.319459
$175$	2.80236	+	4.14087i	0.211838	+	0.313020i
$176$	−2.85050			−0.214865
$177$			1.23421i			0.0927691i
$178$			0.500563i			0.0375187i
$179$	−13.7469			−1.02749			−0.513744	−	0.857944i	$-0.671742\pi$
$179$	−13.7469			−1.02749			−0.513744	+	0.857944i	$0.671742\pi$
$180$	3.85215	−	1.18097i	0.287122	−	0.0880244i
$181$	25.9480			1.92870			0.964350	−	0.264630i	$-0.0852498\pi$
$181$	25.9480			1.92870			0.964350	+	0.264630i	$0.0852498\pi$
$182$			2.53886i			0.188193i
$183$			13.7500i			1.01643i
$184$	3.04625			0.224572
$185$	−4.92681	−	16.0705i	−0.362226	−	1.18153i
$186$	1.21151			0.0888322
$187$		−	5.56222i		−	0.406750i
$188$		−	0.755828i		−	0.0551244i
$189$	−1.00000			−0.0727393
$190$	−2.13366	−	6.95969i	−0.154792	−	0.504909i
$191$	8.50940			0.615718			0.307859	−	0.951432i	$-0.400387\pi$
$191$	8.50940			0.615718			0.307859	+	0.951432i	$0.400387\pi$
$192$		−	3.62976i		−	0.261955i
$193$		−	20.2227i		−	1.45566i	−0.685755	−	0.727832i	$-0.740528\pi$
$193$		−	20.2227i		−	1.45566i	0.685755	−	0.727832i	$-0.259472\pi$
$194$	4.40947			0.316581
$195$	12.1941	−	3.73839i	0.873234	−	0.267711i
$196$	−1.80187			−0.128705
$197$			2.93596i			0.209178i	0.994516	+	0.104589i	$0.0333528\pi$
$197$			2.93596i			0.209178i	−0.994516	+	0.104589i	$0.966647\pi$
$198$			0.445112i			0.0316328i
$199$	−18.7390			−1.32837			−0.664185	−	0.747569i	$-0.731221\pi$
$199$	−18.7390			−1.32837			−0.664185	+	0.747569i	$0.731221\pi$
$200$	4.74232	+	7.00743i	0.335333	+	0.495500i
$201$	7.15848			0.504920
$202$		−	5.52499i		−	0.388737i
$203$			9.46717i			0.664465i
$204$	10.0224			0.701710
$205$	−12.5583	+	3.85004i	−0.877107	+	0.268899i
$206$	4.10583			0.286067
$207$			1.80010i			0.125116i
$208$		−	16.2589i		−	1.12735i
$209$	−7.31377			−0.505904
$210$	−0.291732	−	0.951587i	−0.0201314	−	0.0656657i
$211$	−4.33673			−0.298553			−0.149276	−	0.988796i	$-0.547694\pi$
$211$	−4.33673			−0.298553			−0.149276	+	0.988796i	$0.547694\pi$
$212$			4.55525i			0.312856i
$213$		−	12.4319i		−	0.851817i
$214$	−7.08145			−0.484078
$215$	−2.37293	−	7.74013i	−0.161832	−	0.527872i
$216$	−1.69226			−0.115144
$217$			2.72181i			0.184768i
$218$			2.08517i			0.141225i
$219$	−7.61626			−0.514659
$220$	3.85215	−	1.18097i	0.259712	−	0.0796211i
$221$	31.7261			2.13413
$222$			3.34596i			0.224566i
$223$			14.5857i			0.976731i	0.872639	+	0.488366i	$0.162407\pi$
$223$			14.5857i			0.976731i	−0.872639	+	0.488366i	$0.837593\pi$
$224$	−4.65332			−0.310913
$225$	−4.14087	+	2.80236i	−0.276058	+	0.186824i
$226$	0.948526			0.0630950
$227$			7.44903i			0.494409i	0.968963	+	0.247205i	$0.0795120\pi$
$227$			7.44903i			0.494409i	−0.968963	+	0.247205i	$0.920488\pi$
$228$		−	13.1785i		−	0.872768i
$229$	1.19391			0.0788960			0.0394480	−	0.999222i	$-0.487440\pi$
$229$	1.19391			0.0788960			0.0394480	+	0.999222i	$0.487440\pi$
$230$	−1.71296	+	0.525149i	−0.112949	+	0.0346273i
$231$	−1.00000			−0.0657952
$232$			16.0209i			1.05183i
$233$		−	11.2844i		−	0.739263i	−0.929178	−	0.369631i	$-0.879484\pi$
$233$		−	11.2844i		−	0.739263i	0.929178	−	0.369631i	$-0.120516\pi$
$234$	−2.53886			−0.165971
$235$	0.274924	+	0.896761i	0.0179341	+	0.0584983i
$236$	−2.22390			−0.144763
$237$		−	2.94103i		−	0.191041i
$238$		−	2.47581i		−	0.160483i
$239$	−18.3680			−1.18813			−0.594064	−	0.804417i	$-0.702478\pi$
$239$	−18.3680			−1.18813			−0.594064	+	0.804417i	$0.702478\pi$
$240$	1.86826	+	6.09397i	0.120595	+	0.393364i
$241$	24.9436			1.60676			0.803380	−	0.595467i	$-0.203033\pi$
$241$	24.9436			1.60676			0.803380	+	0.595467i	$0.203033\pi$
$242$			0.445112i			0.0286129i
$243$		−	1.00000i		−	0.0641500i
$244$	−24.7759			−1.58611
$245$	2.13786	−	0.655413i	0.136583	−	0.0418728i
$246$	2.61469			0.166707
$247$		−	41.7168i		−	2.65438i
$248$			4.60601i			0.292482i
$249$	−16.3358			−1.03524
$250$	−3.87471	−	3.12286i	−0.245058	−	0.197507i
$251$	−30.6912			−1.93721			−0.968606	−	0.248600i	$-0.920030\pi$
$251$	−30.6912			−1.93721			−0.968606	+	0.248600i	$0.920030\pi$
$252$		−	1.80187i		−	0.113507i
$253$			1.80010i			0.113172i
$254$	−2.05792			−0.129125
$255$	−11.8912	+	3.64555i	−0.744658	+	0.228293i
$256$	2.39787			0.149867
$257$			19.5868i			1.22179i	0.791712	+	0.610894i	$0.209190\pi$
$257$			19.5868i			1.22179i	−0.791712	+	0.610894i	$0.790810\pi$
$258$			1.61153i			0.100330i
$259$	−7.51711			−0.467091
$260$	6.73610	+	21.9722i	0.417755	+	1.36266i
$261$	−9.46717			−0.586003
$262$		−	1.69903i		−	0.104966i
$263$		−	18.2865i		−	1.12759i	−0.825913	−	0.563797i	$-0.809340\pi$
$263$		−	18.2865i		−	1.12759i	0.825913	−	0.563797i	$-0.190660\pi$
$264$	−1.69226			−0.104152
$265$	−1.65692	−	5.40463i	−0.101784	−	0.332004i
$266$	−3.25545			−0.199605
$267$		−	1.12458i		−	0.0688229i
$268$			12.8987i			0.787913i
$269$	−3.30061			−0.201242			−0.100621	−	0.994925i	$-0.532083\pi$
$269$	−3.30061			−0.201242			−0.100621	+	0.994925i	$0.532083\pi$
$270$	0.951587	−	0.291732i	0.0579117	−	0.0177543i
$271$	−16.0986			−0.977921			−0.488961	−	0.872306i	$-0.662624\pi$
$271$	−16.0986			−0.977921			−0.488961	+	0.872306i	$0.662624\pi$
$272$			15.8551i			0.961358i
$273$		−	5.70387i		−	0.345214i
$274$	2.55836			0.154556
$275$	−4.14087	+	2.80236i	−0.249704	+	0.168989i
$276$	−3.24356			−0.195240
$277$		−	7.40878i		−	0.445150i	−0.974916	−	0.222575i	$-0.928554\pi$
$277$		−	7.40878i		−	0.445150i	0.974916	−	0.222575i	$-0.0714463\pi$
$278$			5.41979i			0.325057i
$279$	−2.72181			−0.162950
$280$	3.61781	−	1.10913i	0.216206	−	0.0662832i
$281$	8.42016			0.502304			0.251152	−	0.967948i	$-0.419191\pi$
$281$	8.42016			0.502304			0.251152	+	0.967948i	$0.419191\pi$
$282$		−	0.186710i		−	0.0111184i
$283$			4.53405i			0.269522i	0.990878	+	0.134761i	$0.0430266\pi$
$283$			4.53405i			0.269522i	−0.990878	+	0.134761i	$0.956973\pi$
$284$	22.4007			1.32923
$285$	4.79354	+	15.6358i	0.283945	+	0.926185i
$286$	−2.53886			−0.150126
$287$			5.87423i			0.346745i
$288$		−	4.65332i		−	0.274199i
$289$	−13.9383			−0.819899
$290$	−2.76188	−	9.00884i	−0.162183	−	0.529017i
$291$	−9.90641			−0.580724
$292$		−	13.7236i		−	0.803110i
$293$			2.40041i			0.140233i	0.997539	+	0.0701166i	$0.0223371\pi$
$293$			2.40041i			0.140233i	−0.997539	+	0.0701166i	$0.977663\pi$
$294$	−0.445112			−0.0259595
$295$	2.63857	−	0.808919i	0.153623	−	0.0470971i
$296$	−12.7209			−0.739389
$297$		−	1.00000i		−	0.0580259i
$298$		−	8.64781i		−	0.500954i
$299$	−10.2676			−0.593788
$300$	−5.04950	−	7.46133i	−0.291533	−	0.430780i
$301$	−3.62051			−0.208683
$302$		−	4.11868i		−	0.237003i
$303$			12.4126i			0.713083i
$304$	20.8479			1.19571
$305$	29.3956	−	9.01195i	1.68319	−	0.516023i
$306$	2.47581			0.141533
$307$		−	25.8860i		−	1.47739i	−0.674040	−	0.738695i	$-0.735443\pi$
$307$		−	25.8860i		−	1.47739i	0.674040	−	0.738695i	$-0.264557\pi$
$308$		−	1.80187i		−	0.102671i
$309$	−9.22426			−0.524750
$310$	−0.794039	−	2.59003i	−0.0450984	−	0.147104i
$311$	−20.5726			−1.16656			−0.583282	−	0.812269i	$-0.698232\pi$
$311$	−20.5726			−1.16656			−0.583282	+	0.812269i	$0.698232\pi$
$312$		−	9.65243i		−	0.546461i
$313$			28.3283i			1.60121i	0.599194	+	0.800604i	$0.295488\pi$
$313$			28.3283i			1.60121i	−0.599194	+	0.800604i	$0.704512\pi$
$314$	−10.8972			−0.614964
$315$	0.655413	+	2.13786i	0.0369283	+	0.120455i
$316$	5.29937			0.298113
$317$		−	10.0969i		−	0.567098i	−0.958958	−	0.283549i	$-0.908488\pi$
$317$		−	10.0969i		−	0.567098i	0.958958	−	0.283549i	$-0.0915118\pi$
$318$			1.12527i			0.0631020i
$319$	−9.46717			−0.530060
$320$	−7.75990	+	2.37899i	−0.433792	+	0.132990i
$321$	15.9093			0.887973
$322$			0.801249i			0.0446518i
$323$			40.6808i			2.26354i
$324$	1.80187			0.100104
$325$	−15.9843	−	23.6190i	−0.886648	−	1.31014i
$326$	−3.33622			−0.184776
$327$		−	4.68458i		−	0.259058i
$328$			9.94073i			0.548885i
$329$	0.419467			0.0231260
$330$	0.951587	−	0.291732i	0.0523831	−	0.0160593i
$331$	17.9293			0.985486			0.492743	−	0.870175i	$-0.335994\pi$
$331$	17.9293			0.985486			0.492743	+	0.870175i	$0.335994\pi$
$332$		−	29.4350i		−	1.61546i
$333$		−	7.51711i		−	0.411935i
$334$	7.73477			0.423228
$335$	−4.69176	−	15.3038i	−0.256338	−	0.836137i
$336$	2.85050			0.155508
$337$		−	18.6882i		−	1.01801i	−0.860763	−	0.509006i	$-0.830013\pi$
$337$		−	18.6882i		−	1.01801i	0.860763	−	0.509006i	$-0.169987\pi$
$338$		−	8.69486i		−	0.472938i
$339$	−2.13098			−0.115739
$340$	−6.56882	−	21.4265i	−0.356245	−	1.16202i
$341$	−2.72181			−0.147394
$342$		−	3.25545i		−	0.176035i
$343$		−	1.00000i		−	0.0539949i
$344$	−6.12684			−0.330337
$345$	3.84837	−	1.17981i	0.207189	−	0.0635189i
$346$	8.41622			0.452459
$347$			16.5031i			0.885933i	0.896538	+	0.442967i	$0.146074\pi$
$347$			16.5031i			0.885933i	−0.896538	+	0.442967i	$0.853926\pi$
$348$		−	17.0587i		−	0.914440i
$349$	−27.1175			−1.45157			−0.725783	−	0.687924i	$-0.758522\pi$
$349$	−27.1175			−1.45157			−0.725783	+	0.687924i	$0.758522\pi$
$350$	−1.84315	+	1.24736i	−0.0985206	+	0.0666744i
$351$	5.70387			0.304450
$352$		−	4.65332i		−	0.248023i
$353$		−	3.64538i		−	0.194024i	−0.995283	−	0.0970119i	$-0.969072\pi$
$353$		−	3.64538i		−	0.194024i	0.995283	−	0.0970119i	$-0.0309285\pi$
$354$	−0.549363			−0.0291983
$355$	−26.5775	+	8.14800i	−1.41059	+	0.432451i
$356$	2.02634			0.107396
$357$			5.56222i			0.294384i
$358$		−	6.11889i		−	0.323394i
$359$	−17.9100			−0.945252			−0.472626	−	0.881263i	$-0.656694\pi$
$359$	−17.9100			−0.945252			−0.472626	+	0.881263i	$0.656694\pi$
$360$	1.10913	+	3.61781i	0.0584563	+	0.190676i
$361$	34.4913			1.81533
$362$			11.5498i			0.607043i
$363$		−	1.00000i		−	0.0524864i
$364$	10.2777			0.538695
$365$	4.99180	+	16.2825i	0.261283	+	0.852264i
$366$	−6.12031			−0.319914
$367$			23.3575i			1.21925i	0.792690	+	0.609625i	$0.208680\pi$
$367$			23.3575i			1.21925i	−0.792690	+	0.609625i	$0.791320\pi$
$368$		−	5.13120i		−	0.267482i
$369$	−5.87423			−0.305800
$370$	7.15319	−	2.19299i	0.371876	−	0.114008i
$371$	−2.52806			−0.131250
$372$		−	4.90435i		−	0.254279i
$373$			7.80753i			0.404259i	0.979359	+	0.202129i	$0.0647861\pi$
$373$			7.80753i			0.404259i	−0.979359	+	0.202129i	$0.935214\pi$
$374$	2.47581			0.128021
$375$	8.70502	+	7.01588i	0.449525	+	0.362299i
$376$	0.709849			0.0366076
$377$		−	53.9995i		−	2.78111i
$378$		−	0.445112i		−	0.0228941i
$379$	−5.80682			−0.298276			−0.149138	−	0.988816i	$-0.547650\pi$
$379$	−5.80682			−0.298276			−0.149138	+	0.988816i	$0.547650\pi$
$380$	−28.1738	+	8.63736i	−1.44528	+	0.443087i
$381$	4.62338			0.236863
$382$			3.78764i			0.193792i
$383$		−	6.42918i		−	0.328516i	−0.986417	−	0.164258i	$-0.947477\pi$
$383$		−	6.42918i		−	0.328516i	0.986417	−	0.164258i	$-0.0525229\pi$
$384$	10.9223			0.557376
$385$	0.655413	+	2.13786i	0.0334029	+	0.108955i
$386$	9.00139			0.458159
$387$		−	3.62051i		−	0.184041i
$388$		−	17.8501i		−	0.906202i
$389$	14.2737			0.723706			0.361853	−	0.932235i	$-0.382144\pi$
$389$	14.2737			0.723706			0.361853	+	0.932235i	$0.382144\pi$
$390$	1.66400	+	5.42772i	0.0842600	+	0.274843i
$391$	10.0126			0.506358
$392$		−	1.69226i		−	0.0854721i
$393$			3.81707i			0.192546i
$394$	−1.30683			−0.0658372
$395$	−6.28751	+	1.92759i	−0.316359	+	0.0969876i
$396$	1.80187			0.0905476
$397$			19.5336i			0.980362i	0.871621	+	0.490181i	$0.163069\pi$
$397$			19.5336i			0.980362i	−0.871621	+	0.490181i	$0.836931\pi$
$398$		−	8.34094i		−	0.418094i
$399$	7.31377			0.366147
$400$	11.8036	−	7.98813i	0.590178	−	0.399407i
$401$	25.7520			1.28599			0.642997	−	0.765868i	$-0.277691\pi$
$401$	25.7520			1.28599			0.642997	+	0.765868i	$0.277691\pi$
$402$			3.18633i			0.158920i
$403$		−	15.5248i		−	0.773346i
$404$	−22.3659			−1.11274
$405$	−2.13786	+	0.655413i	−0.106231	+	0.0325677i
$406$	−4.21396			−0.209135
$407$		−	7.51711i		−	0.372609i
$408$			9.41273i			0.466000i
$409$	−25.7032			−1.27094			−0.635471	−	0.772124i	$-0.719194\pi$
$409$	−25.7032			−1.27094			−0.635471	+	0.772124i	$0.719194\pi$
$410$	−1.71370	−	5.58984i	−0.0846337	−	0.276062i
$411$	−5.74767			−0.283512
$412$		−	16.6210i		−	0.818856i
$413$		−	1.23421i		−	0.0607316i
$414$	−0.801249			−0.0393792
$415$	10.7067	+	34.9236i	0.525570	+	1.71433i
$416$	26.5419			1.30132
$417$		−	12.1762i		−	0.596272i
$418$		−	3.25545i		−	0.159229i
$419$	27.5132			1.34411			0.672055	−	0.740501i	$-0.265412\pi$
$419$	27.5132			1.34411			0.672055	+	0.740501i	$0.265412\pi$
$420$	−3.85215	+	1.18097i	−0.187966	+	0.0576255i
$421$	−33.1580			−1.61602			−0.808011	−	0.589167i	$-0.799456\pi$
$421$	−33.1580			−1.61602			−0.808011	+	0.589167i	$0.799456\pi$
$422$		−	1.93033i		−	0.0939670i
$423$			0.419467i			0.0203952i
$424$	−4.27814			−0.207765
$425$	15.5873	+	23.0324i	0.756097	+	1.11724i
$426$	5.53357			0.268103
$427$		−	13.7500i		−	0.665411i
$428$			28.6666i			1.38565i
$429$	5.70387			0.275385
$430$	3.44523	−	1.05622i	0.166144	−	0.0509354i
$431$	−5.15869			−0.248485			−0.124243	−	0.992252i	$-0.539650\pi$
$431$	−5.15869			−0.248485			−0.124243	+	0.992252i	$0.539650\pi$
$432$			2.85050i			0.137145i
$433$			3.51191i			0.168772i	0.996433	+	0.0843858i	$0.0268928\pi$
$433$			3.51191i			0.168772i	−0.996433	+	0.0843858i	$0.973107\pi$
$434$	−1.21151			−0.0581543
$435$	6.20491	+	20.2395i	0.297502	+	0.970408i
$436$	8.44104			0.404252
$437$		−	13.1656i		−	0.629794i
$438$		−	3.39009i		−	0.161985i
$439$	1.92771			0.0920046			0.0460023	−	0.998941i	$-0.485352\pi$
$439$	1.92771			0.0920046			0.0460023	+	0.998941i	$0.485352\pi$
$440$	1.10913	+	3.61781i	0.0528757	+	0.172473i
$441$	1.00000			0.0476190
$442$			14.1217i			0.671701i
$443$			5.12312i			0.243407i	0.992567	+	0.121703i	$0.0388357\pi$
$443$			5.12312i			0.243407i	−0.992567	+	0.121703i	$0.961164\pi$
$444$	13.5449			0.642812
$445$	−2.40418	+	0.737061i	−0.113969	+	0.0349400i
$446$	−6.49228			−0.307418
$447$			19.4284i			0.918931i
$448$			3.62976i			0.171490i
$449$	1.97336			0.0931286			0.0465643	−	0.998915i	$-0.485173\pi$
$449$	1.97336			0.0931286			0.0465643	+	0.998915i	$0.485173\pi$
$450$	−1.24736	−	1.84315i	−0.0588013	−	0.0868870i
$451$	−5.87423			−0.276607
$452$		−	3.83976i		−	0.180607i
$453$			9.25312i			0.434749i
$454$	−3.31565			−0.155611
$455$	−12.1941	+	3.73839i	−0.571666	+	0.175258i
$456$	12.3768			0.579598
$457$		−	1.45296i		−	0.0679666i	−0.999422	−	0.0339833i	$-0.989181\pi$
$457$		−	1.45296i		−	0.0679666i	0.999422	−	0.0339833i	$-0.0108193\pi$
$458$			0.531426i			0.0248319i
$459$	−5.56222			−0.259622
$460$	2.12587	+	6.93427i	0.0991193	+	0.323312i
$461$	−12.6461			−0.588986			−0.294493	−	0.955654i	$-0.595151\pi$
$461$	−12.6461			−0.588986			−0.294493	+	0.955654i	$0.595151\pi$
$462$		−	0.445112i		−	0.0207085i
$463$		−	15.8414i		−	0.736214i	−0.929783	−	0.368107i	$-0.880006\pi$
$463$		−	15.8414i		−	0.736214i	0.929783	−	0.368107i	$-0.119994\pi$
$464$	26.9862			1.25280
$465$	1.78391	+	5.81883i	0.0827267	+	0.269842i
$466$	5.02281			0.232677
$467$			7.97075i			0.368842i	0.982847	+	0.184421i	$0.0590410\pi$
$467$			7.97075i			0.368842i	−0.982847	+	0.184421i	$0.940959\pi$
$468$			10.2777i			0.475085i
$469$	−7.15848			−0.330548
$470$	−0.399160	+	0.122372i	−0.0184119	+	0.00564461i
$471$	24.4819			1.12807
$472$		−	2.08861i		−	0.0961361i
$473$		−	3.62051i		−	0.166471i
$474$	1.30909			0.0601285
$475$	30.2854	−	20.4958i	1.38959	−	0.940413i
$476$	−10.0224			−0.459377
$477$		−	2.52806i		−	0.115752i
$478$		−	8.17584i		−	0.373954i
$479$	26.6026			1.21550			0.607751	−	0.794127i	$-0.292072\pi$
$479$	26.6026			1.21550			0.607751	+	0.794127i	$0.292072\pi$
$480$	−9.94813	+	3.04984i	−0.454068	+	0.139206i
$481$	42.8766			1.95500
$482$			11.1027i			0.505715i
$483$		−	1.80010i		−	0.0819076i
$484$	1.80187			0.0819034
$485$	6.49279	+	21.1785i	0.294822	+	0.961666i
$486$	0.445112			0.0201907
$487$		−	18.8576i		−	0.854517i	−0.904129	−	0.427259i	$-0.859479\pi$
$487$		−	18.8576i		−	0.854517i	0.904129	−	0.427259i	$-0.140521\pi$
$488$		−	23.2687i		−	1.05332i
$489$	7.49524			0.338946
$490$	0.291732	+	0.951587i	0.0131791	+	0.0429883i
$491$	−17.4349			−0.786824			−0.393412	−	0.919362i	$-0.628705\pi$
$491$	−17.4349			−0.786824			−0.393412	+	0.919362i	$0.628705\pi$
$492$		−	10.5846i		−	0.477192i
$493$			52.6585i			2.37162i
$494$	18.5687			0.835444
$495$	−2.13786	+	0.655413i	−0.0960895	+	0.0294586i
$496$	7.75851			0.348368
$497$			12.4319i			0.557645i
$498$		−	7.27126i		−	0.325833i
$499$	6.85161			0.306720			0.153360	−	0.988170i	$-0.450991\pi$
$499$	6.85161			0.306720			0.153360	+	0.988170i	$0.450991\pi$
$500$	−12.6417	+	15.6854i	−0.565356	+	0.701471i
$501$	−17.3771			−0.776352
$502$		−	13.6610i		−	0.609722i
$503$			1.88679i			0.0841279i	0.999115	+	0.0420640i	$0.0133933\pi$
$503$			1.88679i			0.0841279i	−0.999115	+	0.0420640i	$0.986607\pi$
$504$	1.69226			0.0753793
$505$	26.5363	−	8.13535i	1.18085	−	0.362018i
$506$	−0.801249			−0.0356198
$507$			19.5341i			0.867539i
$508$			8.33074i			0.369617i
$509$	19.4075			0.860224			0.430112	−	0.902775i	$-0.358474\pi$
$509$	19.4075			0.860224			0.430112	+	0.902775i	$0.358474\pi$
$510$	−1.62268	−	5.29293i	−0.0718534	−	0.234375i
$511$	7.61626			0.336924
$512$			22.9119i			1.01257i
$513$			7.31377i			0.322911i
$514$	−8.71831			−0.384548
$515$	6.04570	+	19.7201i	0.266405	+	0.868973i
$516$	6.52370			0.287190
$517$			0.419467i			0.0184482i
$518$		−	3.34596i		−	0.147013i
$519$	−18.9081			−0.829973
$520$	−20.6355	+	6.32633i	−0.904928	+	0.277428i
$521$	−0.268337			−0.0117561			−0.00587803	−	0.999983i	$-0.501871\pi$
$521$	−0.268337			−0.0117561			−0.00587803	+	0.999983i	$0.501871\pi$
$522$		−	4.21396i		−	0.184440i
$523$			25.6552i			1.12182i	0.827875	+	0.560912i	$0.189549\pi$
$523$			25.6552i			1.12182i	−0.827875	+	0.560912i	$0.810451\pi$
$524$	−6.87789			−0.300462
$525$	4.14087	−	2.80236i	0.180722	−	0.122305i
$526$	8.13955			0.354901
$527$			15.1393i			0.659477i
$528$			2.85050i			0.124052i
$529$	19.7596			0.859114
$530$	2.40567	−	0.737517i	0.104496	−	0.0320357i
$531$	1.23421			0.0535603
$532$			13.1785i			0.571361i
$533$		−	33.5058i		−	1.45130i
$534$	0.500563			0.0216615
$535$	−10.4272	−	34.0119i	−0.450807	−	1.47046i
$536$	−12.1140			−0.523246
$537$			13.7469i			0.593220i
$538$		−	1.46914i		−	0.0633392i
$539$	1.00000			0.0430730
$540$	−1.18097	−	3.85215i	−0.0508209	−	0.165770i
$541$	4.76180			0.204726			0.102363	−	0.994747i	$-0.467360\pi$
$541$	4.76180			0.204726			0.102363	+	0.994747i	$0.467360\pi$
$542$		−	7.16569i		−	0.307793i
$543$		−	25.9480i		−	1.11354i
$544$	−25.8828			−1.10971
$545$	−10.0150	+	3.07034i	−0.428994	+	0.131519i
$546$	2.53886			0.108653
$547$			21.2289i			0.907681i	0.891083	+	0.453840i	$0.149946\pi$
$547$			21.2289i			0.907681i	−0.891083	+	0.453840i	$0.850054\pi$
$548$		−	10.3566i		−	0.442412i
$549$	13.7500			0.586838
$550$	−1.24736	−	1.84315i	−0.0531878	−	0.0785923i
$551$	69.2408			2.94976
$552$		−	3.04625i		−	0.129657i
$553$			2.94103i			0.125065i
$554$	3.29774			0.140107
$555$	−16.0705	+	4.92681i	−0.682155	+	0.209132i
$556$	21.9400			0.930464
$557$		−	38.5100i		−	1.63172i	−0.578250	−	0.815860i	$-0.696264\pi$
$557$		−	38.5100i		−	1.63172i	0.578250	−	0.815860i	$-0.303736\pi$
$558$		−	1.21151i		−	0.0512873i
$559$	20.6509			0.873439
$560$	−1.86826	−	6.09397i	−0.0789482	−	0.257517i
$561$	−5.56222			−0.234837
$562$			3.74792i			0.158096i
$563$		−	11.3651i		−	0.478981i	−0.970899	−	0.239490i	$-0.923020\pi$
$563$		−	11.3651i		−	0.478981i	0.970899	−	0.239490i	$-0.0769804\pi$
$564$	−0.755828			−0.0318261
$565$	1.39667	+	4.55573i	0.0587584	+	0.191661i
$566$	−2.01816			−0.0848298
$567$			1.00000i			0.0419961i
$568$			21.0380i			0.882733i
$569$	5.28873			0.221715			0.110858	−	0.993836i	$-0.464640\pi$
$569$	5.28873			0.221715			0.110858	+	0.993836i	$0.464640\pi$
$570$	−6.95969	+	2.13366i	−0.291509	+	0.0893694i
$571$	−28.4484			−1.19053			−0.595264	−	0.803530i	$-0.702953\pi$
$571$	−28.4484			−1.19053			−0.595264	+	0.803530i	$0.702953\pi$
$572$			10.2777i			0.429730i
$573$		−	8.50940i		−	0.355485i
$574$	−2.61469			−0.109135
$575$	−5.04454	−	7.45399i	−0.210372	−	0.310853i
$576$	−3.62976			−0.151240
$577$			21.5497i			0.897125i	0.893751	+	0.448562i	$0.148064\pi$
$577$			21.5497i			0.897125i	−0.893751	+	0.448562i	$0.851936\pi$
$578$		−	6.20410i		−	0.258057i
$579$	−20.2227			−0.840428
$580$	−36.4690	+	11.1805i	−1.51429	+	0.464244i
$581$	16.3358			0.677722
$582$		−	4.40947i		−	0.182778i
$583$		−	2.52806i		−	0.104702i
$584$	12.8887			0.533339
$585$	−3.73839	−	12.1941i	−0.154563	−	0.504162i
$586$	−1.06845			−0.0441373
$587$		−	22.1348i		−	0.913601i	−0.889569	−	0.456800i	$-0.848995\pi$
$587$		−	22.1348i		−	0.913601i	0.889569	−	0.456800i	$-0.151005\pi$
$588$			1.80187i			0.0743081i
$589$	19.9067			0.820240
$590$	0.360060	+	1.17446i	0.0148234	+	0.0483518i
$591$	2.93596			0.120769
$592$			21.4276i			0.880667i
$593$			30.9209i			1.26977i	0.772608	+	0.634884i	$0.218952\pi$
$593$			30.9209i			1.26977i	−0.772608	+	0.634884i	$0.781048\pi$
$594$	0.445112			0.0182632
$595$	11.8912	−	3.64555i	0.487493	−	0.149453i
$596$	−35.0075			−1.43396
$597$			18.7390i			0.766934i
$598$		−	4.57021i		−	0.186890i
$599$	27.1492			1.10929			0.554643	−	0.832088i	$-0.312855\pi$
$599$	27.1492			1.10929			0.554643	+	0.832088i	$0.312855\pi$
$600$	7.00743	−	4.74232i	0.286077	−	0.193605i
$601$	14.0299			0.572291			0.286146	−	0.958186i	$-0.407626\pi$
$601$	14.0299			0.572291			0.286146	+	0.958186i	$0.407626\pi$
$602$		−	1.61153i		−	0.0656812i
$603$		−	7.15848i		−	0.291516i
$604$	−16.6730			−0.678413
$605$	−2.13786	+	0.655413i	−0.0869163	+	0.0266463i
$606$	−5.52499			−0.224437
$607$			7.12214i			0.289079i	0.989499	+	0.144539i	$0.0461700\pi$
$607$			7.12214i			0.289079i	−0.989499	+	0.144539i	$0.953830\pi$
$608$			34.0333i			1.38023i
$609$	9.46717			0.383629
$610$	4.01133	+	13.0844i	0.162414	+	0.529770i
$611$	−2.39259			−0.0967936
$612$		−	10.0224i		−	0.405132i
$613$			25.6702i			1.03681i	0.855136	+	0.518404i	$0.173474\pi$
$613$			25.6702i			1.03681i	−0.855136	+	0.518404i	$0.826526\pi$
$614$	11.5222			0.464996
$615$	3.85004	+	12.5583i	0.155249	+	0.506398i
$616$	1.69226			0.0681832
$617$			5.17504i			0.208339i	0.994560	+	0.104170i	$0.0332185\pi$
$617$			5.17504i			0.208339i	−0.994560	+	0.104170i	$0.966782\pi$
$618$		−	4.10583i		−	0.165161i
$619$	1.85678			0.0746302			0.0373151	−	0.999304i	$-0.488119\pi$
$619$	1.85678			0.0746302			0.0373151	+	0.999304i	$0.488119\pi$
$620$	−10.4848	+	3.21438i	−0.421080	+	0.129092i
$621$	1.80010			0.0722357
$622$		−	9.15712i		−	0.367167i
$623$			1.12458i			0.0450552i
$624$	−16.2589			−0.650876
$625$	9.29358	−	23.2084i	0.371743	−	0.928336i
$626$	−12.6093			−0.503968
$627$			7.31377i			0.292084i
$628$			44.1133i			1.76031i
$629$	−41.8118			−1.66715
$630$	−0.951587	+	0.291732i	−0.0379121	+	0.0116229i
$631$	−39.2745			−1.56349			−0.781746	−	0.623597i	$-0.785670\pi$
$631$	−39.2745			−1.56349			−0.781746	+	0.623597i	$0.785670\pi$
$632$			4.97700i			0.197974i
$633$			4.33673i			0.172369i
$634$	4.49425			0.178490
$635$	−3.03022	−	9.88412i	−0.120251	−	0.392239i
$636$	4.55525			0.180627
$637$			5.70387i			0.225995i
$638$		−	4.21396i		−	0.166832i
$639$	−12.4319			−0.491797
$640$	−7.15861	−	23.3503i	−0.282969	−	0.923001i
$641$	26.4634			1.04524			0.522621	−	0.852565i	$-0.324954\pi$
$641$	26.4634			1.04524			0.522621	+	0.852565i	$0.324954\pi$
$642$			7.08145i			0.279482i
$643$			28.8122i			1.13624i	0.822944	+	0.568122i	$0.192330\pi$
$643$			28.8122i			1.13624i	−0.822944	+	0.568122i	$0.807670\pi$
$644$	3.24356			0.127814
$645$	−7.74013	+	2.37293i	−0.304767	+	0.0934339i
$646$	−18.1075			−0.712431
$647$			26.5546i			1.04397i	0.852956	+	0.521984i	$0.174808\pi$
$647$			26.5546i			1.04397i	−0.852956	+	0.521984i	$0.825192\pi$
$648$			1.69226i			0.0664783i
$649$	1.23421			0.0484471
$650$	10.5131	−	7.11480i	0.412357	−	0.279065i
$651$	2.72181			0.106676
$652$			13.5055i			0.528915i
$653$		−	30.6424i		−	1.19913i	−0.800326	−	0.599564i	$-0.795341\pi$
$653$		−	30.6424i		−	1.19913i	0.800326	−	0.599564i	$-0.204659\pi$
$654$	2.08517			0.0815365
$655$	8.16036	−	2.50176i	0.318852	−	0.0977518i
$656$	16.7445			0.653763
$657$			7.61626i			0.297139i
$658$			0.186710i			0.00727872i
$659$	−10.1550			−0.395583			−0.197792	−	0.980244i	$-0.563377\pi$
$659$	−10.1550			−0.395583			−0.197792	+	0.980244i	$0.563377\pi$
$660$	−1.18097	−	3.85215i	−0.0459693	−	0.149945i
$661$	−4.39400			−0.170907			−0.0854534	−	0.996342i	$-0.527234\pi$
$661$	−4.39400			−0.170907			−0.0854534	+	0.996342i	$0.527234\pi$
$662$			7.98057i			0.310174i
$663$		−	31.7261i		−	1.23214i
$664$	27.6444			1.07281
$665$	−4.79354	−	15.6358i	−0.185886	−	0.606331i
$666$	3.34596			0.129653
$667$		−	17.0419i		−	0.659865i
$668$		−	31.3114i		−	1.21147i
$669$	14.5857			0.563916
$670$	6.81192	−	2.08836i	0.263167	−	0.0806804i
$671$	13.7500			0.530815
$672$			4.65332i			0.179506i
$673$			28.9610i			1.11637i	0.829718	+	0.558183i	$0.188501\pi$
$673$			28.9610i			1.11637i	−0.829718	+	0.558183i	$0.811499\pi$
$674$	8.31836			0.320411
$675$	2.80236	+	4.14087i	0.107863	+	0.159382i
$676$	−35.1980			−1.35377
$677$		−	24.5078i		−	0.941909i	−0.882157	−	0.470955i	$-0.843910\pi$
$677$		−	24.5078i		−	0.941909i	0.882157	−	0.470955i	$-0.156090\pi$
$678$		−	0.948526i		−	0.0364279i
$679$	9.90641			0.380173
$680$	20.1231	−	6.16922i	0.771685	−	0.236579i
$681$	7.44903			0.285447
$682$		−	1.21151i		−	0.0463911i
$683$		−	0.188272i		−	0.00720402i	−0.999994	−	0.00360201i	$-0.998853\pi$
$683$		−	0.188272i		−	0.00720402i	0.999994	−	0.00360201i	$-0.00114656\pi$
$684$	−13.1785			−0.503893
$685$	3.76710	+	12.2877i	0.143933	+	0.469489i
$686$	0.445112			0.0169945
$687$		−	1.19391i		−	0.0455506i
$688$			10.3203i			0.393456i
$689$	14.4197			0.549347
$690$	0.525149	+	1.71296i	0.0199921	+	0.0652111i
$691$	−29.0067			−1.10347			−0.551733	−	0.834021i	$-0.686033\pi$
$691$	−29.0067			−1.10347			−0.551733	+	0.834021i	$0.686033\pi$
$692$		−	34.0700i		−	1.29515i
$693$			1.00000i			0.0379869i
$694$	−7.34574			−0.278840
$695$	−26.0310	+	7.98045i	−0.987413	+	0.302716i
$696$	16.0209			0.607272
$697$			32.6737i			1.23761i
$698$		−	12.0703i		−	0.456869i
$699$	−11.2844			−0.426814
$700$	5.04950	+	7.46133i	0.190853	+	0.282012i
$701$	6.79334			0.256581			0.128291	−	0.991737i	$-0.459051\pi$
$701$	6.79334			0.256581			0.128291	+	0.991737i	$0.459051\pi$
$702$			2.53886i			0.0958231i
$703$			54.9785i			2.07355i
$704$	−3.62976			−0.136802
$705$	0.896761	−	0.274924i	0.0337740	−	0.0103542i
$706$	1.62260			0.0610674
$707$		−	12.4126i		−	0.466823i
$708$			2.22390i			0.0835791i
$709$	−5.98674			−0.224837			−0.112418	−	0.993661i	$-0.535860\pi$
$709$	−5.98674			−0.224837			−0.112418	+	0.993661i	$0.535860\pi$
$710$	−3.62678	−	11.8300i	−0.136110	−	0.443972i
$711$	−2.94103			−0.110297
$712$			1.90308i			0.0713208i
$713$		−	4.89953i		−	0.183489i
$714$	−2.47581			−0.0926550
$715$	−3.73839	−	12.1941i	−0.139808	−	0.456032i
$716$	−24.7701			−0.925702
$717$			18.3680i			0.685967i
$718$		−	7.97195i		−	0.297510i
$719$	−0.717546			−0.0267599			−0.0133800	−	0.999910i	$-0.504259\pi$
$719$	−0.717546			−0.0267599			−0.0133800	+	0.999910i	$0.504259\pi$
$720$	6.09397	−	1.86826i	0.227109	−	0.0696258i
$721$	9.22426			0.343529
$722$			15.3525i			0.571361i
$723$		−	24.9436i		−	0.927663i
$724$	46.7551			1.73764
$725$	39.2023	−	26.5304i	1.45594	−	0.985315i
$726$	0.445112			0.0165197
$727$		−	38.5712i		−	1.43053i	−0.698856	−	0.715263i	$-0.746307\pi$
$727$		−	38.5712i		−	1.43053i	0.698856	−	0.715263i	$-0.253693\pi$
$728$			9.65243i			0.357743i
$729$	−1.00000			−0.0370370
$730$	−7.24754	+	2.22191i	−0.268243	+	0.0822366i
$731$	−20.1380			−0.744833
$732$			24.7759i			0.915742i
$733$		−	11.0884i		−	0.409561i	−0.978808	−	0.204781i	$-0.934352\pi$
$733$		−	11.0884i		−	0.409561i	0.978808	−	0.204781i	$-0.0656481\pi$
$734$	−10.3967			−0.383749
$735$	−0.655413	−	2.13786i	−0.0241753	−	0.0788561i
$736$	8.37646			0.308760
$737$		−	7.15848i		−	0.263686i
$738$		−	2.61469i		−	0.0962481i
$739$	−38.8139			−1.42779			−0.713896	−	0.700252i	$-0.753071\pi$
$739$	−38.8139			−1.42779			−0.713896	+	0.700252i	$0.753071\pi$
$740$	−8.87750	−	28.9571i	−0.326343	−	1.06448i
$741$	−41.7168			−1.53250
$742$		−	1.12527i		−	0.0413100i
$743$		−	46.8650i		−	1.71931i	−0.510874	−	0.859656i	$-0.670678\pi$
$743$		−	46.8650i		−	1.71931i	0.510874	−	0.859656i	$-0.329322\pi$
$744$	4.60601			0.168864
$745$	41.5351	−	12.7336i	1.52173	−	0.466523i
$746$	−3.47523			−0.127237
$747$			16.3358i			0.597695i
$748$		−	10.0224i		−	0.366456i
$749$	−15.9093			−0.581315
$750$	−3.12286	+	3.87471i	−0.114031	+	0.141484i
$751$	−40.6134			−1.48201			−0.741003	−	0.671502i	$-0.765649\pi$
$751$	−40.6134			−1.48201			−0.741003	+	0.671502i	$0.765649\pi$
$752$		−	1.19569i		−	0.0436024i
$753$			30.6912i			1.11845i
$754$	24.0358			0.875334
$755$	19.7818	−	6.06461i	0.719935	−	0.220714i
$756$	−1.80187			−0.0655336
$757$		−	9.97953i		−	0.362712i	−0.983418	−	0.181356i	$-0.941951\pi$
$757$		−	9.97953i		−	0.362712i	0.983418	−	0.181356i	$-0.0580486\pi$
$758$		−	2.58469i		−	0.0938801i
$759$	1.80010			0.0653396
$760$	−8.11193	−	26.4599i	−0.294251	−	0.959801i
$761$	13.4428			0.487303			0.243651	−	0.969863i	$-0.421655\pi$
$761$	13.4428			0.487303			0.243651	+	0.969863i	$0.421655\pi$
$762$			2.05792i			0.0745506i
$763$			4.68458i			0.169593i
$764$	15.3329			0.554724
$765$	3.64555	+	11.8912i	0.131805	+	0.429928i
$766$	2.86171			0.103398
$767$			7.03978i			0.254192i
$768$		−	2.39787i		−	0.0865256i
$769$	27.6322			0.996442			0.498221	−	0.867050i	$-0.333987\pi$
$769$	27.6322			0.996442			0.498221	+	0.867050i	$0.333987\pi$
$770$	−0.951587	+	0.291732i	−0.0342928	+	0.0105133i
$771$	19.5868			0.705400
$772$		−	36.4388i		−	1.31146i
$773$		−	33.6953i		−	1.21194i	−0.795489	−	0.605968i	$-0.792786\pi$
$773$		−	33.6953i		−	1.21194i	0.795489	−	0.605968i	$-0.207214\pi$
$774$	1.61153			0.0579253
$775$	11.2706	−	7.62747i	0.404853	−	0.273987i
$776$	16.7642			0.601801
$777$			7.51711i			0.269675i
$778$			6.35341i			0.227781i
$779$	42.9628			1.53930
$780$	21.9722	−	6.73610i	0.786729	−	0.241191i
$781$	−12.4319			−0.444847
$782$			4.45672i			0.159372i
$783$			9.46717i			0.338329i
$784$	−2.85050			−0.101804
$785$	−16.0457	−	52.3388i	−0.572697	−	1.86805i
$786$	−1.69903			−0.0606023
$787$		−	54.9533i		−	1.95888i	−0.201747	−	0.979438i	$-0.564662\pi$
$787$		−	54.9533i		−	1.95888i	0.201747	−	0.979438i	$-0.435338\pi$
$788$			5.29023i			0.188457i
$789$	−18.2865			−0.651017
$790$	−0.857994	−	2.79865i	−0.0305261	−	0.0995714i
$791$	2.13098			0.0757690
$792$			1.69226i			0.0601319i
$793$			78.4284i			2.78507i
$794$	−8.69464			−0.308561
$795$	−5.40463	+	1.65692i	−0.191682	+	0.0587650i
$796$	−33.7653			−1.19678
$797$		−	12.6766i		−	0.449029i	−0.974471	−	0.224514i	$-0.927920\pi$
$797$		−	12.6766i		−	0.449029i	0.974471	−	0.224514i	$-0.0720796\pi$
$798$			3.25545i			0.115242i
$799$	2.33317			0.0825416
$800$	13.0403	+	19.2688i	0.461043	+	0.681254i
$801$	−1.12458			−0.0397349
$802$			11.4625i			0.404757i
$803$			7.61626i			0.268772i
$804$	12.8987			0.454902
$805$	−3.84837	+	1.17981i	−0.135637	+	0.0415829i
$806$	6.91029			0.243404
$807$			3.30061i			0.116187i
$808$		−	21.0053i		−	0.738964i
$809$	11.3378			0.398614			0.199307	−	0.979937i	$-0.436131\pi$
$809$	11.3378			0.398614			0.199307	+	0.979937i	$0.436131\pi$
$810$	−0.291732	−	0.951587i	−0.0102504	−	0.0334354i
$811$	−35.0803			−1.23183			−0.615917	−	0.787811i	$-0.711214\pi$
$811$	−35.0803			−1.23183			−0.615917	+	0.787811i	$0.711214\pi$
$812$			17.0587i			0.598642i
$813$			16.0986i			0.564603i
$814$	3.34596			0.117276
$815$	−4.91247	−	16.0237i	−0.172076	−	0.561287i
$816$	15.8551			0.555040
$817$			26.4796i			0.926403i
$818$		−	11.4408i		−	0.400019i
$819$	−5.70387			−0.199309
$820$	−22.6284	+	6.93730i	−0.790219	+	0.242261i
$821$	22.2421			0.776253			0.388127	−	0.921606i	$-0.373122\pi$
$821$	22.2421			0.776253			0.388127	+	0.921606i	$0.373122\pi$
$822$		−	2.55836i		−	0.0892331i
$823$		−	37.2368i		−	1.29799i	−0.760792	−	0.648996i	$-0.775189\pi$
$823$		−	37.2368i		−	1.29799i	0.760792	−	0.648996i	$-0.224811\pi$
$824$	15.6099			0.543795
$825$	2.80236	+	4.14087i	0.0975656	+	0.144167i
$826$	0.549363			0.0191148
$827$		−	6.89613i		−	0.239802i	−0.992786	−	0.119901i	$-0.961742\pi$
$827$		−	6.89613i		−	0.239802i	0.992786	−	0.119901i	$-0.0382577\pi$
$828$			3.24356i			0.112722i
$829$	52.6502			1.82862			0.914309	−	0.405018i	$-0.132735\pi$
$829$	52.6502			1.82862			0.914309	+	0.405018i	$0.132735\pi$
$830$	−15.5449	+	4.76568i	−0.539572	+	0.165419i
$831$	−7.40878			−0.257008
$832$		−	20.7036i		−	0.717770i
$833$		−	5.56222i		−	0.192719i
$834$	5.41979			0.187672
$835$	11.3892	+	37.1498i	0.394139	+	1.28562i
$836$	−13.1785			−0.455788
$837$			2.72181i			0.0940794i
$838$			12.2465i			0.423048i
$839$	−48.9070			−1.68846			−0.844228	−	0.535985i	$-0.819941\pi$
$839$	−48.9070			−1.68846			−0.844228	+	0.535985i	$0.819941\pi$
$840$	−1.10913	−	3.61781i	−0.0382686	−	0.124826i
$841$	60.6274			2.09060
$842$		−	14.7590i		−	0.508630i
$843$		−	8.42016i		−	0.290006i
$844$	−7.81424			−0.268977
$845$	41.7611	−	12.8029i	1.43662	−	0.440433i
$846$	−0.186710			−0.00641923
$847$			1.00000i			0.0343604i
$848$			7.20624i			0.247463i
$849$	4.53405			0.155608
$850$	−10.2520	+	6.93811i	−0.351641	+	0.237975i
$851$	13.5316			0.463857
$852$		−	22.4007i		−	0.767434i
$853$		−	37.0057i		−	1.26705i	−0.773722	−	0.633525i	$-0.781607\pi$
$853$		−	37.0057i		−	1.26705i	0.773722	−	0.633525i	$-0.218393\pi$
$854$	6.12031			0.209433
$855$	15.6358	−	4.79354i	0.534733	−	0.163936i
$856$	−26.9228			−0.920201
$857$			36.4312i			1.24447i	0.782832	+	0.622233i	$0.213774\pi$
$857$			36.4312i			1.24447i	−0.782832	+	0.622233i	$0.786226\pi$
$858$			2.53886i			0.0866753i
$859$	−15.3146			−0.522526			−0.261263	−	0.965268i	$-0.584139\pi$
$859$	−15.3146			−0.522526			−0.261263	+	0.965268i	$0.584139\pi$
$860$	−4.27572	−	13.9467i	−0.145801	−	0.475580i
$861$	5.87423			0.200193
$862$		−	2.29620i		−	0.0782088i
$863$		−	11.6000i		−	0.394868i	−0.980316	−	0.197434i	$-0.936739\pi$
$863$		−	11.6000i		−	0.394868i	0.980316	−	0.197434i	$-0.0632608\pi$
$864$	−4.65332			−0.158309
$865$	12.3926	+	40.4228i	0.421361	+	1.37442i
$866$	−1.56319			−0.0531195
$867$			13.9383i			0.473369i
$868$			4.90435i			0.166465i
$869$	−2.94103			−0.0997677
$870$	−9.00884	+	2.76188i	−0.305428	+	0.0936365i
$871$	40.8310			1.38351
$872$			7.92754i			0.268461i
$873$			9.90641i			0.335281i
$874$	5.86015			0.198223
$875$	−8.70502	−	7.01588i	−0.294283	−	0.237180i
$876$	−13.7236			−0.463676
$877$		−	35.1776i		−	1.18786i	−0.804516	−	0.593931i	$-0.797575\pi$
$877$		−	35.1776i		−	1.18786i	0.804516	−	0.593931i	$-0.202425\pi$
$878$			0.858048i			0.0289577i
$879$	2.40041			0.0809637
$880$	6.09397	−	1.86826i	0.205428	−	0.0629789i
$881$	4.67172			0.157394			0.0786971	−	0.996899i	$-0.474924\pi$
$881$	4.67172			0.157394			0.0786971	+	0.996899i	$0.474924\pi$
$882$			0.445112i			0.0149877i
$883$			40.9683i			1.37869i	0.724431	+	0.689347i	$0.242102\pi$
$883$			40.9683i			1.37869i	−0.724431	+	0.689347i	$0.757898\pi$
$884$	57.1666			1.92272
$885$	−0.808919	−	2.63857i	−0.0271915	−	0.0886946i
$886$	−2.28036			−0.0766103
$887$			14.7699i			0.495926i	0.968769	+	0.247963i	$0.0797612\pi$
$887$			14.7699i			0.495926i	−0.968769	+	0.247963i	$0.920239\pi$
$888$			12.7209i			0.426886i
$889$	−4.62338			−0.155063
$890$	−0.328075	−	1.07013i	−0.0109971	−	0.0358709i
$891$	−1.00000			−0.0335013
$892$			26.2816i			0.879974i
$893$		−	3.06789i		−	0.102663i
$894$	−8.64781			−0.289226
$895$	29.3888	−	9.00986i	0.982359	−	0.301166i
$896$	−10.9223			−0.364888
$897$			10.2676i			0.342824i
$898$			0.878367i			0.0293115i
$899$	25.7678			0.859404
$900$	−7.46133	+	5.04950i	−0.248711	+	0.168317i
$901$	−14.0616			−0.468460
$902$		−	2.61469i		−	0.0870597i
$903$			3.62051i			0.120483i
$904$	3.60618			0.119940
$905$	−55.4731	+	17.0067i	−1.84399	+	0.565320i
$906$	−4.11868			−0.136834
$907$		−	7.44269i		−	0.247131i	−0.992336	−	0.123565i	$-0.960567\pi$
$907$		−	7.44269i		−	0.247131i	0.992336	−	0.123565i	$-0.0394328\pi$
$908$			13.4222i			0.445432i
$909$	12.4126			0.411699
$910$	−1.66400	−	5.42772i	−0.0551611	−	0.179927i
$911$	−35.8707			−1.18845			−0.594224	−	0.804299i	$-0.702541\pi$
$911$	−35.8707			−1.18845			−0.594224	+	0.804299i	$0.702541\pi$
$912$		−	20.8479i		−	0.690344i
$913$			16.3358i			0.540635i
$914$	0.646731			0.0213919
$915$	−9.01195	−	29.3956i	−0.297926	−	0.971790i
$916$	2.15128			0.0710804
$917$		−	3.81707i		−	0.126051i
$918$		−	2.47581i		−	0.0817140i
$919$	4.20344			0.138659			0.0693293	−	0.997594i	$-0.477914\pi$
$919$	4.20344			0.138659			0.0693293	+	0.997594i	$0.477914\pi$
$920$	−6.51244	+	1.99655i	−0.214709	+	0.0658243i
$921$	−25.8860			−0.852971
$922$		−	5.62892i		−	0.185378i
$923$		−	70.9097i		−	2.33402i
$924$	−1.80187			−0.0592773
$925$	21.0656	+	31.1274i	0.692634	+	1.02346i
$926$	7.05122			0.231718
$927$			9.22426i			0.302964i
$928$			44.0538i			1.44614i
$929$	−12.7510			−0.418346			−0.209173	−	0.977879i	$-0.567077\pi$
$929$	−12.7510			−0.418346			−0.209173	+	0.977879i	$0.567077\pi$
$930$	−2.59003	+	0.794039i	−0.0849306	+	0.0260376i
$931$	−7.31377			−0.239699
$932$		−	20.3330i		−	0.666030i
$933$			20.5726i			0.673516i
$934$	−3.54788			−0.116090
$935$	3.64555	+	11.8912i	0.119222	+	0.388885i
$936$	−9.65243			−0.315500
$937$			24.2073i			0.790819i	0.918505	+	0.395410i	$0.129397\pi$
$937$			24.2073i			0.790819i	−0.918505	+	0.395410i	$0.870603\pi$
$938$		−	3.18633i		−	0.104037i
$939$	28.3283			0.924458
$940$	0.495379	+	1.61585i	0.0161575	+	0.0527033i
$941$	−9.86465			−0.321579			−0.160789	−	0.986989i	$-0.551404\pi$
$941$	−9.86465			−0.321579			−0.160789	+	0.986989i	$0.551404\pi$
$942$			10.8972i			0.355050i
$943$		−	10.5742i		−	0.344344i
$944$	−3.51813			−0.114505
$945$	2.13786	−	0.655413i	0.0695445	−	0.0213206i
$946$	1.61153			0.0523954
$947$			15.9168i			0.517226i	0.965981	+	0.258613i	$0.0832654\pi$
$947$			15.9168i			0.517226i	−0.965981	+	0.258613i	$0.916735\pi$
$948$		−	5.29937i		−	0.172116i
$949$	−43.4421			−1.41019
$950$	9.12294	+	13.4804i	0.295987	+	0.437362i
$951$	−10.0969			−0.327414
$952$		−	9.41273i		−	0.305068i
$953$		−	38.3732i		−	1.24303i	−0.783402	−	0.621515i	$-0.786517\pi$
$953$		−	38.3732i		−	1.24303i	0.783402	−	0.621515i	$-0.213483\pi$
$954$	1.12527			0.0364320
$955$	−18.1919	+	5.57717i	−0.588675	+	0.180473i
$956$	−33.0969			−1.07043
$957$			9.46717i			0.306030i
$958$			11.8411i			0.382570i
$959$	5.74767			0.185602
$960$	2.37899	+	7.75990i	0.0767815	+	0.250450i
$961$	−23.5918			−0.761025
$962$			19.0849i			0.615322i
$963$		−	15.9093i		−	0.512671i
$964$	44.9453			1.44759
$965$	13.2542	+	43.2333i	0.426669	+	1.39173i
$966$	0.801249			0.0257798
$967$		−	56.0564i		−	1.80265i	−0.433141	−	0.901326i	$-0.642595\pi$
$967$		−	56.0564i		−	1.80265i	0.433141	−	0.901326i	$-0.357405\pi$
$968$			1.69226i			0.0543914i
$969$	40.6808			1.30686
$970$	−9.42681	+	2.89002i	−0.302677	+	0.0927930i
$971$	−32.7157			−1.04990			−0.524948	−	0.851134i	$-0.675915\pi$
$971$	−32.7157			−1.04990			−0.524948	+	0.851134i	$0.675915\pi$
$972$		−	1.80187i		−	0.0577952i
$973$			12.1762i			0.390352i
$974$	8.39373			0.268952
$975$	−23.6190	+	15.9843i	−0.756412	+	0.511906i
$976$	−39.1945			−1.25459
$977$			42.6145i			1.36336i	0.731651	+	0.681680i	$0.238750\pi$
$977$			42.6145i			1.36336i	−0.731651	+	0.681680i	$0.761250\pi$
$978$			3.33622i			0.106681i
$979$	−1.12458			−0.0359416
$980$	3.85215	−	1.18097i	0.123052	−	0.0377248i
$981$	−4.68458			−0.149567
$982$		−	7.76047i		−	0.247647i
$983$		−	20.7636i		−	0.662257i	−0.943586	−	0.331128i	$-0.892571\pi$
$983$		−	20.7636i		−	0.662257i	0.943586	−	0.331128i	$-0.107429\pi$
$984$	9.94073			0.316899
$985$	−1.92426	−	6.27666i	−0.0613121	−	0.199991i
$986$	−23.4389			−0.746448
$987$		−	0.419467i		−	0.0133518i
$988$		−	75.1684i		−	2.39143i
$989$	6.51729			0.207238
$990$	−0.291732	−	0.951587i	−0.00927186	−	0.0302434i
$991$	−3.19859			−0.101607			−0.0508033	−	0.998709i	$-0.516178\pi$
$991$	−3.19859			−0.101607			−0.0508033	+	0.998709i	$0.516178\pi$
$992$			12.6654i			0.402128i
$993$		−	17.9293i		−	0.568970i
$994$	−5.53357			−0.175514
$995$	40.0612	−	12.2817i	1.27003	−	0.389358i
$996$	−29.4350			−0.932685
$997$		−	41.8947i		−	1.32682i	−0.748257	−	0.663409i	$-0.769109\pi$
$997$		−	41.8947i		−	1.32682i	0.748257	−	0.663409i	$-0.230891\pi$
$998$			3.04974i			0.0965377i
$999$	−7.51711			−0.237831

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1155.2.c.e.694.13	yes	20
5.2	odd	4		5775.2.a.cm.1.5		10
5.3	odd	4		5775.2.a.cp.1.6		10
5.4	even	2	inner	1155.2.c.e.694.8	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1155.2.c.e.694.8	✓	20	5.4	even	2	inner
1155.2.c.e.694.13	yes	20	1.1	even	1	trivial
5775.2.a.cm.1.5		10	5.2	odd	4
5775.2.a.cp.1.6		10	5.3	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1155.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+0.445112i q^{2} -1.00000i q^{3} +1.80187 q^{4} +(-2.13786 + 0.655413i) q^{5} +0.445112 q^{6} +1.00000i q^{7} +1.69226i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+0.445112i q^{2} -1.00000i q^{3} +1.80187 q^{4} +(-2.13786 + 0.655413i) q^{5} +0.445112 q^{6} +1.00000i q^{7} +1.69226i q^{8} -1.00000 q^{9} +(-0.291732 - 0.951587i) q^{10} -1.00000 q^{11} -1.80187i q^{12} -5.70387i q^{13} -0.445112 q^{14} +(0.655413 + 2.13786i) q^{15} +2.85050 q^{16} +5.56222i q^{17} -0.445112i q^{18} +7.31377 q^{19} +(-3.85215 + 1.18097i) q^{20} +1.00000 q^{21} -0.445112i q^{22} -1.80010i q^{23} +1.69226 q^{24} +(4.14087 - 2.80236i) q^{25} +2.53886 q^{26} +1.00000i q^{27} +1.80187i q^{28} +9.46717 q^{29} +(-0.951587 + 0.291732i) q^{30} +2.72181 q^{31} +4.65332i q^{32} +1.00000i q^{33} -2.47581 q^{34} +(-0.655413 - 2.13786i) q^{35} -1.80187 q^{36} +7.51711i q^{37} +3.25545i q^{38} -5.70387 q^{39} +(-1.10913 - 3.61781i) q^{40} +5.87423 q^{41} +0.445112i q^{42} +3.62051i q^{43} -1.80187 q^{44} +(2.13786 - 0.655413i) q^{45} +0.801249 q^{46} -0.419467i q^{47} -2.85050i q^{48} -1.00000 q^{49} +(1.24736 + 1.84315i) q^{50} +5.56222 q^{51} -10.2777i q^{52} +2.52806i q^{53} -0.445112 q^{54} +(2.13786 - 0.655413i) q^{55} -1.69226 q^{56} -7.31377i q^{57} +4.21396i q^{58} -1.23421 q^{59} +(1.18097 + 3.85215i) q^{60} -13.7500 q^{61} +1.21151i q^{62} -1.00000i q^{63} +3.62976 q^{64} +(3.73839 + 12.1941i) q^{65} -0.445112 q^{66} +7.15848i q^{67} +10.0224i q^{68} -1.80010 q^{69} +(0.951587 - 0.291732i) q^{70} +12.4319 q^{71} -1.69226i q^{72} -7.61626i q^{73} -3.34596 q^{74} +(-2.80236 - 4.14087i) q^{75} +13.1785 q^{76} -1.00000i q^{77} -2.53886i q^{78} +2.94103 q^{79} +(-6.09397 + 1.86826i) q^{80} +1.00000 q^{81} +2.61469i q^{82} -16.3358i q^{83} +1.80187 q^{84} +(-3.64555 - 11.8912i) q^{85} -1.61153 q^{86} -9.46717i q^{87} -1.69226i q^{88} +1.12458 q^{89} +(0.291732 + 0.951587i) q^{90} +5.70387 q^{91} -3.24356i q^{92} -2.72181i q^{93} +0.186710 q^{94} +(-15.6358 + 4.79354i) q^{95} +4.65332 q^{96} -9.90641i q^{97} -0.445112i q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 26 q^{4} - 2 q^{5} + 6 q^{6} - 20 q^{9}+O(q^{10}) \) 20 * q - 26 * q^4 - 2 * q^5 + 6 * q^6 - 20 * q^9	\( 20 q - 26 q^{4} - 2 q^{5} + 6 q^{6} - 20 q^{9} - 2 q^{10} - 20 q^{11} - 6 q^{14} + 2 q^{15} + 38 q^{16} + 2 q^{19} + 4 q^{20} + 20 q^{21} - 18 q^{24} + 12 q^{25} + 20 q^{26} - 38 q^{29} + 6 q^{30} + 20 q^{31} - 32 q^{34} - 2 q^{35} + 26 q^{36} + 2 q^{40} + 12 q^{41} + 26 q^{44} + 2 q^{45} + 8 q^{46} - 20 q^{49} - 6 q^{50} + 26 q^{51} - 6 q^{54} + 2 q^{55} + 18 q^{56} - 22 q^{59} + 16 q^{60} + 34 q^{61} - 26 q^{64} - 28 q^{65} - 6 q^{66} - 26 q^{69} - 6 q^{70} + 72 q^{71} - 72 q^{74} - 8 q^{75} + 44 q^{76} + 4 q^{79} - 8 q^{80} + 20 q^{81} - 26 q^{84} - 16 q^{85} + 52 q^{86} + 6 q^{89} + 2 q^{90} + 16 q^{94} + 14 q^{95} + 62 q^{96} + 20 q^{99}+O(q^{100}) \) 20 * q - 26 * q^4 - 2 * q^5 + 6 * q^6 - 20 * q^9 - 2 * q^10 - 20 * q^11 - 6 * q^14 + 2 * q^15 + 38 * q^16 + 2 * q^19 + 4 * q^20 + 20 * q^21 - 18 * q^24 + 12 * q^25 + 20 * q^26 - 38 * q^29 + 6 * q^30 + 20 * q^31 - 32 * q^34 - 2 * q^35 + 26 * q^36 + 2 * q^40 + 12 * q^41 + 26 * q^44 + 2 * q^45 + 8 * q^46 - 20 * q^49 - 6 * q^50 + 26 * q^51 - 6 * q^54 + 2 * q^55 + 18 * q^56 - 22 * q^59 + 16 * q^60 + 34 * q^61 - 26 * q^64 - 28 * q^65 - 6 * q^66 - 26 * q^69 - 6 * q^70 + 72 * q^71 - 72 * q^74 - 8 * q^75 + 44 * q^76 + 4 * q^79 - 8 * q^80 + 20 * q^81 - 26 * q^84 - 16 * q^85 + 52 * q^86 + 6 * q^89 + 2 * q^90 + 16 * q^94 + 14 * q^95 + 62 * q^96 + 20 * q^99

Introduction

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Modular forms

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