LMFDB - Embedded newform 693.2.m.j.190.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [693,2,Mod(64,693)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(693, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 6]))

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

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

chi := DirichletCharacter("693.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 693 = 3^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	693.m (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:	$5.53363286007$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{5})$
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} + 12 x^{18} - 3 x^{17} + 94 x^{16} - 10 x^{15} + 662 x^{14} - 153 x^{13} + 4638 x^{12} + \cdots + 121 $ x^20 + 12x^18 - 3x^17 + 94x^16 - 10x^15 + 662x^14 - 153x^13 + 4638x^12 - 1174x^11 + 15808x^10 - 3393x^9 + 26062x^8 - 15494x^7 + 11660x^6 - 33295x^5 + 67756x^4 - 43696x^3 + 13084x^2 - 1155x + 121
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 231)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			190.3
Root			$0.383242 + 0.278442i$ of defining polynomial
Character	$\chi$	$=$	693.190
Dual form			693.2.m.j.631.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.383242 - 0.278442i) q^{2} +(-0.548689 + 1.68869i) q^{4} +(3.04094 + 2.20937i) q^{5} +(-0.309017 + 0.951057i) q^{7} +(0.552692 + 1.70101i) q^{8} +1.78060 q^{10} +(2.47012 - 2.21326i) q^{11} +(-2.19061 + 1.59157i) q^{13} +(0.146385 + 0.450528i) q^{14} +(-2.18753 - 1.58933i) q^{16} +(2.00865 + 1.45937i) q^{17} +(-0.539130 - 1.65927i) q^{19} +(-5.39949 + 3.92296i) q^{20} +(0.330389 - 1.53600i) q^{22} -3.79843 q^{23} +(2.82092 + 8.68189i) q^{25} +(-0.396374 + 1.21991i) q^{26} +(-1.43649 - 1.04367i) q^{28} +(1.79248 - 5.51669i) q^{29} +(-1.81837 + 1.32112i) q^{31} -4.85799 q^{32} +1.17615 q^{34} +(-3.04094 + 2.20937i) q^{35} +(-2.36494 + 7.27854i) q^{37} +(-0.668627 - 0.485786i) q^{38} +(-2.07747 + 6.39378i) q^{40} +(1.29324 + 3.98017i) q^{41} +7.75162 q^{43} +(2.38219 + 5.38566i) q^{44} +(-1.45572 + 1.05764i) q^{46} +(-3.83399 - 11.7998i) q^{47} +(-0.809017 - 0.587785i) q^{49} +(3.49849 + 2.54180i) q^{50} +(-1.48571 - 4.57254i) q^{52} +(7.15135 - 5.19576i) q^{53} +(12.4014 - 1.27298i) q^{55} -1.78855 q^{56} +(-0.849122 - 2.61333i) q^{58} +(-1.40345 + 4.31938i) q^{59} +(9.28955 + 6.74925i) q^{61} +(-0.329020 + 1.01262i) q^{62} +(2.51327 - 1.82600i) q^{64} -10.1779 q^{65} -12.2041 q^{67} +(-3.56655 + 2.59125i) q^{68} +(-0.550235 + 1.69345i) q^{70} +(6.27787 + 4.56114i) q^{71} +(4.84526 - 14.9122i) q^{73} +(1.12030 + 3.44794i) q^{74} +3.09781 q^{76} +(1.34163 + 3.03316i) q^{77} +(5.70664 - 4.14612i) q^{79} +(-3.14072 - 9.66614i) q^{80} +(1.60387 + 1.16528i) q^{82} +(9.62766 + 6.99490i) q^{83} +(2.88389 + 8.87571i) q^{85} +(2.97075 - 2.15837i) q^{86} +(5.12999 + 2.97845i) q^{88} +1.69179 q^{89} +(-0.836738 - 2.57522i) q^{91} +(2.08416 - 6.41439i) q^{92} +(-4.75491 - 3.45464i) q^{94} +(2.02649 - 6.23689i) q^{95} +(-5.66019 + 4.11237i) q^{97} -0.473713 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 14 q^{4} + 5 q^{5} + 5 q^{7} + 9 q^{8} + 12 q^{10} + q^{11} + 13 q^{13} - 24 q^{16} + q^{17} + 10 q^{19} + 46 q^{20} + 26 q^{22} - 8 q^{25} + 53 q^{26} + 4 q^{28} - 3 q^{29} - 13 q^{31} - 82 q^{32}+ \cdots - 27 q^{97}+O(q^{100}) $ 20 * q - 14 * q^4 + 5 * q^5 + 5 * q^7 + 9 * q^8 + 12 * q^10 + q^11 + 13 * q^13 - 24 * q^16 + q^17 + 10 * q^19 + 46 * q^20 + 26 * q^22 - 8 * q^25 + 53 * q^26 + 4 * q^28 - 3 * q^29 - 13 * q^31 - 82 * q^32 + 42 * q^34 - 5 * q^35 - 32 * q^37 - 16 * q^38 + 20 * q^40 + 3 * q^41 + 12 * q^43 - 25 * q^44 - 13 * q^46 - 20 * q^47 - 5 * q^49 + 83 * q^50 - 80 * q^52 - 3 * q^53 - 28 * q^55 + 6 * q^56 + 2 * q^58 + 9 * q^59 - 15 * q^61 + 37 * q^62 - 49 * q^64 - 58 * q^65 + 76 * q^67 - 51 * q^68 + 3 * q^70 - 37 * q^71 + 27 * q^73 + 32 * q^74 + 4 * q^76 - 6 * q^77 + 5 * q^79 - 137 * q^80 - 55 * q^82 + 42 * q^83 - 48 * q^85 - 3 * q^86 + 151 * q^88 + 18 * q^89 + 7 * q^91 - 39 * q^92 - 35 * q^94 + 96 * q^95 - 27 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/693\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$442$
$\chi(n)$	$1$	$1$	$e\left(\frac{4}{5}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.383242	−	0.278442i	0.270993	−	0.196888i	−0.443986	−	0.896034i	$-0.646436\pi$
$2$	0.383242	−	0.278442i	0.270993	−	0.196888i	0.714979	+	0.699146i	$0.246436\pi$
$3$		0			0
$3$		0			0
$4$	−0.548689	+	1.68869i	−0.274345	+	0.844346i
$5$	3.04094	+	2.20937i	1.35995	+	0.988062i	0.998448	+	0.0556917i	$0.0177364\pi$
$5$	3.04094	+	2.20937i	1.35995	+	0.988062i	0.361503	+	0.932371i	$0.382264\pi$
$6$		0			0
$7$	−0.309017	+	0.951057i	−0.116797	+	0.359466i
$7$	−0.309017	+	0.951057i	−0.116797	+	0.359466i
$8$	0.552692	+	1.70101i	0.195406	+	0.601398i
$9$		0			0
$10$	1.78060			0.563075
$11$	2.47012	−	2.21326i	0.744768	−	0.667323i
$11$	2.47012	−	2.21326i	0.744768	−	0.667323i
$12$		0			0
$13$	−2.19061	+	1.59157i	−0.607566	+	0.441422i	−0.848556	−	0.529105i	$-0.822528\pi$
$13$	−2.19061	+	1.59157i	−0.607566	+	0.441422i	0.240991	+	0.970527i	$0.422528\pi$
$14$	0.146385	+	0.450528i	0.0391231	+	0.120409i
$15$		0			0
$16$	−2.18753	−	1.58933i	−0.546882	−	0.397333i
$17$	2.00865	+	1.45937i	0.487169	+	0.353949i	0.804094	−	0.594502i	$-0.202651\pi$
$17$	2.00865	+	1.45937i	0.487169	+	0.353949i	−0.316926	+	0.948450i	$0.602651\pi$
$18$		0			0
$19$	−0.539130	−	1.65927i	−0.123685	−	0.380663i	0.869974	−	0.493097i	$-0.164135\pi$
$19$	−0.539130	−	1.65927i	−0.123685	−	0.380663i	−0.993659	+	0.112434i	$0.964135\pi$
$20$	−5.39949	+	3.92296i	−1.20736	+	0.877200i
$21$		0			0
$22$	0.330389	−	1.53600i	0.0704391	−	0.327476i
$23$	−3.79843			−0.792028			−0.396014	−	0.918244i	$-0.629607\pi$
$23$	−3.79843			−0.792028			−0.396014	+	0.918244i	$0.629607\pi$
$24$		0			0
$25$	2.82092	+	8.68189i	0.564183	+	1.73638i
$26$	−0.396374	+	1.21991i	−0.0777353	+	0.239245i
$27$		0			0
$28$	−1.43649	−	1.04367i	−0.271471	−	0.197235i
$29$	1.79248	−	5.51669i	0.332856	−	1.02442i	−0.634913	−	0.772584i	$-0.718964\pi$
$29$	1.79248	−	5.51669i	0.332856	−	1.02442i	0.967769	−	0.251841i	$-0.0810359\pi$
$30$		0			0
$31$	−1.81837	+	1.32112i	−0.326589	+	0.237281i	−0.738982	−	0.673725i	$-0.764693\pi$
$31$	−1.81837	+	1.32112i	−0.326589	+	0.237281i	0.412393	+	0.911006i	$0.364693\pi$
$32$	−4.85799			−0.858779
$33$		0			0
$34$	1.17615			0.201707
$35$	−3.04094	+	2.20937i	−0.514013	+	0.373453i
$36$		0			0
$37$	−2.36494	+	7.27854i	−0.388794	+	1.19658i	0.544897	+	0.838503i	$0.316569\pi$
$37$	−2.36494	+	7.27854i	−0.388794	+	1.19658i	−0.933690	+	0.358081i	$0.883431\pi$
$38$	−0.668627	−	0.485786i	−0.108466	−	0.0788049i
$39$		0			0
$40$	−2.07747	+	6.39378i	−0.328476	+	1.01095i
$41$	1.29324	+	3.98017i	0.201969	+	0.621598i	0.999824	+	0.0187483i	$0.00596811\pi$
$41$	1.29324	+	3.98017i	0.201969	+	0.621598i	−0.797855	+	0.602850i	$0.794032\pi$
$42$		0			0
$43$	7.75162			1.18211			0.591056	−	0.806631i	$-0.298711\pi$
$43$	7.75162			1.18211			0.591056	+	0.806631i	$0.298711\pi$
$44$	2.38219	+	5.38566i	0.359128	+	0.811919i
$45$		0			0
$46$	−1.45572	+	1.05764i	−0.214634	+	0.155941i
$47$	−3.83399	−	11.7998i	−0.559246	−	1.72118i	−0.684459	−	0.729051i	$-0.739962\pi$
$47$	−3.83399	−	11.7998i	−0.559246	−	1.72118i	0.125214	−	0.992130i	$-0.460038\pi$
$48$		0			0
$49$	−0.809017	−	0.587785i	−0.115574	−	0.0839693i
$50$	3.49849	+	2.54180i	0.494761	+	0.359465i
$51$		0			0
$52$	−1.48571	−	4.57254i	−0.206031	−	0.634098i
$53$	7.15135	−	5.19576i	0.982314	−	0.713693i	0.0240892	−	0.999710i	$-0.492331\pi$
$53$	7.15135	−	5.19576i	0.982314	−	0.713693i	0.958225	+	0.286017i	$0.0923314\pi$
$54$		0			0
$55$	12.4014	−	1.27298i	1.67221	−	0.171649i
$56$	−1.78855			−0.239005
$57$		0			0
$58$	−0.849122	−	2.61333i	−0.111495	−	0.343147i
$59$	−1.40345	+	4.31938i	−0.182714	+	0.562335i	−0.999901	−	0.0140367i	$-0.995532\pi$
$59$	−1.40345	+	4.31938i	−0.182714	+	0.562335i	0.817188	+	0.576371i	$0.195532\pi$
$60$		0			0
$61$	9.28955	+	6.74925i	1.18940	+	0.864153i	0.993201	−	0.116410i	$-0.0371386\pi$
$61$	9.28955	+	6.74925i	1.18940	+	0.864153i	0.196204	+	0.980563i	$0.437139\pi$
$62$	−0.329020	+	1.01262i	−0.0417856	+	0.128603i
$63$		0			0
$64$	2.51327	−	1.82600i	0.314159	−	0.228250i
$65$	−10.1779			−1.26241
$66$		0			0
$67$	−12.2041			−1.49096			−0.745481	−	0.666527i	$-0.767780\pi$
$67$	−12.2041			−1.49096			−0.745481	+	0.666527i	$0.767780\pi$
$68$	−3.56655	+	2.59125i	−0.432507	+	0.314235i
$69$		0			0
$70$	−0.550235	+	1.69345i	−0.0657657	+	0.202406i
$71$	6.27787	+	4.56114i	0.745047	+	0.541308i	0.894288	−	0.447493i	$-0.147683\pi$
$71$	6.27787	+	4.56114i	0.745047	+	0.541308i	−0.149241	+	0.988801i	$0.547683\pi$
$72$		0			0
$73$	4.84526	−	14.9122i	0.567095	−	1.74534i	−0.0945471	−	0.995520i	$-0.530140\pi$
$73$	4.84526	−	14.9122i	0.567095	−	1.74534i	0.661642	−	0.749820i	$-0.269860\pi$
$74$	1.12030	+	3.44794i	0.130233	+	0.400815i
$75$		0			0
$76$	3.09781			0.355344
$77$	1.34163	+	3.03316i	0.152893	+	0.345660i
$78$		0			0
$79$	5.70664	−	4.14612i	0.642048	−	0.466475i	−0.218505	−	0.975836i	$-0.570118\pi$
$79$	5.70664	−	4.14612i	0.642048	−	0.466475i	0.860553	+	0.509361i	$0.170118\pi$
$80$	−3.14072	−	9.66614i	−0.351143	−	1.08071i
$81$		0			0
$82$	1.60387	+	1.16528i	0.177117	+	0.128683i
$83$	9.62766	+	6.99490i	1.05677	+	0.767790i	0.973489	−	0.228735i	$-0.0734591\pi$
$83$	9.62766	+	6.99490i	1.05677	+	0.767790i	0.0832842	+	0.996526i	$0.473459\pi$
$84$		0			0
$85$	2.88389	+	8.87571i	0.312802	+	0.962706i
$86$	2.97075	−	2.15837i	0.320344	−	0.232743i
$87$		0			0
$88$	5.12999	+	2.97845i	0.546859	+	0.317503i
$89$	1.69179			0.179329			0.0896647	−	0.995972i	$-0.471420\pi$
$89$	1.69179			0.179329			0.0896647	+	0.995972i	$0.471420\pi$
$90$		0			0
$91$	−0.836738	−	2.57522i	−0.0877140	−	0.269956i
$92$	2.08416	−	6.41439i	0.217289	−	0.668746i
$93$		0			0
$94$	−4.75491	−	3.45464i	−0.490431	−	0.356319i
$95$	2.02649	−	6.23689i	0.207913	−	0.639892i
$96$		0			0
$97$	−5.66019	+	4.11237i	−0.574706	+	0.417548i	−0.836812	−	0.547491i	$-0.815583\pi$
$97$	−5.66019	+	4.11237i	−0.574706	+	0.417548i	0.262106	+	0.965039i	$0.415583\pi$
$98$	−0.473713			−0.0478522
$99$		0			0
$100$	−16.2088			−1.62088
$101$	2.19796	−	1.59691i	0.218705	−	0.158899i	−0.473038	−	0.881042i	$-0.656843\pi$
$101$	2.19796	−	1.59691i	0.218705	−	0.158899i	0.691744	+	0.722143i	$0.256843\pi$
$102$		0			0
$103$	−0.0790429	+	0.243269i	−0.00778833	+	0.0239700i	−0.954875	−	0.297007i	$-0.904011\pi$
$103$	−0.0790429	+	0.243269i	−0.00778833	+	0.0239700i	0.947087	+	0.320977i	$0.104011\pi$
$104$	−3.91801	−	2.84660i	−0.384193	−	0.279132i
$105$		0			0
$106$	1.29398	−	3.98247i	0.125683	−	0.386811i
$107$	−3.66517	−	11.2802i	−0.354326	−	1.09050i	−0.956399	−	0.292062i	$-0.905659\pi$
$107$	−3.66517	−	11.2802i	−0.354326	−	1.09050i	0.602074	−	0.798441i	$-0.294341\pi$
$108$		0			0
$109$	−15.8720			−1.52026			−0.760129	−	0.649772i	$-0.774864\pi$
$109$	−15.8720			−1.52026			−0.760129	+	0.649772i	$0.774864\pi$
$110$	4.39829	−	3.94093i	0.419360	−	0.375753i
$111$		0			0
$112$	2.18753	−	1.58933i	0.206702	−	0.150178i
$113$	1.58109	+	4.86608i	0.148736	+	0.457763i	0.997473	−	0.0710535i	$-0.0226361\pi$
$113$	1.58109	+	4.86608i	0.148736	+	0.457763i	−0.848736	+	0.528816i	$0.822636\pi$
$114$		0			0
$115$	−11.5508	−	8.39217i	−1.07712	−	0.782573i
$116$	8.33248	+	6.05390i	0.773652	+	0.562091i
$117$		0			0
$118$	0.664833	+	2.04614i	0.0612028	+	0.188363i
$119$	−2.00865	+	1.45937i	−0.184132	+	0.133780i
$120$		0			0
$121$	1.20296	−	10.9340i	0.109360	−	0.994002i
$122$	5.43942			0.492462
$123$		0			0
$124$	−1.23325	−	3.79556i	−0.110749	−	0.340851i
$125$	−4.79561	+	14.7594i	−0.428932	+	1.32012i
$126$		0			0
$127$	−0.164504	−	0.119519i	−0.0145974	−	0.0106056i	0.580463	−	0.814287i	$-0.302872\pi$
$127$	−0.164504	−	0.119519i	−0.0145974	−	0.0106056i	−0.595060	+	0.803681i	$0.702872\pi$
$128$	3.45716	−	10.6400i	0.305572	−	0.940455i
$129$		0			0
$130$	−3.90060	+	2.83395i	−0.342105	+	0.248554i
$131$	10.2788			0.898067			0.449034	−	0.893515i	$-0.351768\pi$
$131$	10.2788			0.898067			0.449034	+	0.893515i	$0.351768\pi$
$132$		0			0
$133$	1.74466			0.151281
$134$	−4.67710	+	3.39812i	−0.404040	+	0.293552i
$135$		0			0
$136$	−1.37224	+	4.22331i	−0.117668	+	0.362146i
$137$	−13.8420	−	10.0568i	−1.18260	−	0.859209i	−0.190137	−	0.981758i	$-0.560893\pi$
$137$	−13.8420	−	10.0568i	−1.18260	−	0.859209i	−0.992463	+	0.122549i	$0.960893\pi$
$138$		0			0
$139$	6.02612	−	18.5465i	0.511129	−	1.57309i	−0.279089	−	0.960265i	$-0.590032\pi$
$139$	6.02612	−	18.5465i	0.511129	−	1.57309i	0.790217	−	0.612827i	$-0.209968\pi$
$140$	−2.06242	−	6.34748i	−0.174306	−	0.536460i
$141$		0			0
$142$	3.67596			0.308479
$143$	−1.88850	+	8.77976i	−0.157924	+	0.734200i
$144$		0			0
$145$	17.6393	−	12.8157i	1.46486	−	1.06429i
$146$	−2.29526	−	7.06410i	−0.189957	−	0.584629i
$147$		0			0
$148$	−10.9936	−	7.98731i	−0.903668	−	0.656553i
$149$	−8.00148	−	5.81342i	−0.655507	−	0.476254i	0.209636	−	0.977780i	$-0.432772\pi$
$149$	−8.00148	−	5.81342i	−0.655507	−	0.476254i	−0.865143	+	0.501526i	$0.832772\pi$
$150$		0			0
$151$	−4.79018	−	14.7427i	−0.389819	−	1.19974i	−0.932923	−	0.360075i	$-0.882751\pi$
$151$	−4.79018	−	14.7427i	−0.389819	−	1.19974i	0.543104	−	0.839666i	$-0.317249\pi$
$152$	2.52447	−	1.83413i	0.204761	−	0.148768i
$153$		0			0
$154$	1.35872	+	0.788868i	0.109489	+	0.0635688i
$155$	−8.44843			−0.678594
$156$		0			0
$157$	5.23896	+	16.1238i	0.418114	+	1.28682i	0.909436	+	0.415845i	$0.136514\pi$
$157$	5.23896	+	16.1238i	0.418114	+	1.28682i	−0.491321	+	0.870978i	$0.663486\pi$
$158$	1.03257	−	3.17793i	0.0821471	−	0.252823i
$159$		0			0
$160$	−14.7729	−	10.7331i	−1.16790	−	0.848527i
$161$	1.17378	−	3.61253i	0.0925069	−	0.284707i
$162$		0			0
$163$	−16.1592	+	11.7403i	−1.26569	+	0.919574i	−0.999022	−	0.0442152i	$-0.985921\pi$
$163$	−16.1592	+	11.7403i	−1.26569	+	0.919574i	−0.266664	+	0.963790i	$0.585921\pi$
$164$	−7.43086			−0.580253
$165$		0			0
$166$	5.63739			0.437547
$167$	14.1186	−	10.2578i	1.09253	−	0.793771i	0.112706	−	0.993628i	$-0.464048\pi$
$167$	14.1186	−	10.2578i	1.09253	−	0.793771i	0.979825	+	0.199858i	$0.0640480\pi$
$168$		0			0
$169$	−1.75155	+	5.39071i	−0.134735	+	0.414670i
$170$	3.57660	+	2.59855i	0.274312	+	0.199300i
$171$		0			0
$172$	−4.25323	+	13.0901i	−0.324306	+	0.998111i
$173$	2.89223	+	8.90136i	0.219892	+	0.676758i	0.998770	+	0.0495825i	$0.0157891\pi$
$173$	2.89223	+	8.90136i	0.219892	+	0.676758i	−0.778878	+	0.627175i	$0.784211\pi$
$174$		0			0
$175$	−9.12868			−0.690063
$176$	−8.92106	+	0.915732i	−0.672450	+	0.0690259i
$177$		0			0
$178$	0.648365	−	0.471064i	0.0485970	−	0.0353078i
$179$	−1.69758	−	5.22460i	−0.126883	−	0.390505i	0.867357	−	0.497687i	$-0.165817\pi$
$179$	−1.69758	−	5.22460i	−0.126883	−	0.390505i	−0.994239	+	0.107182i	$0.965817\pi$
$180$		0			0
$181$	9.04839	+	6.57404i	0.672562	+	0.488645i	0.870882	−	0.491493i	$-0.163549\pi$
$181$	9.04839	+	6.57404i	0.672562	+	0.488645i	−0.198320	+	0.980137i	$0.563549\pi$
$182$	−1.03772	−	0.753948i	−0.0769209	−	0.0558863i
$183$		0			0
$184$	−2.09936	−	6.46118i	−0.154767	−	0.476324i
$185$	−23.2727	+	16.9086i	−1.71104	+	1.24314i
$186$		0			0
$187$	8.19156	−	0.840850i	0.599026	−	0.0614891i
$188$	22.0299			1.60670
$189$		0			0
$190$	−0.959974	−	2.95450i	−0.0696438	−	0.214342i
$191$	1.77939	−	5.47639i	0.128752	−	0.396258i	−0.865814	−	0.500366i	$-0.833199\pi$
$191$	1.77939	−	5.47639i	0.128752	−	0.396258i	0.994566	+	0.104108i	$0.0331988\pi$
$192$		0			0
$193$	12.0419	+	8.74893i	0.866793	+	0.629762i	0.929725	−	0.368256i	$-0.120045\pi$
$193$	12.0419	+	8.74893i	0.866793	+	0.629762i	−0.0629313	+	0.998018i	$0.520045\pi$
$194$	−1.02417	+	3.15207i	−0.0735310	+	0.226305i
$195$		0			0
$196$	1.43649	−	1.04367i	0.102606	−	0.0745478i
$197$	−12.5476			−0.893978			−0.446989	−	0.894540i	$-0.647504\pi$
$197$	−12.5476			−0.893978			−0.446989	+	0.894540i	$0.647504\pi$
$198$		0			0
$199$	0.834418			0.0591503			0.0295752	−	0.999563i	$-0.490585\pi$
$199$	0.834418			0.0591503			0.0295752	+	0.999563i	$0.490585\pi$
$200$	−13.2089	+	9.59682i	−0.934009	+	0.678598i
$201$		0			0
$202$	0.397704	−	1.22401i	0.0279824	−	0.0861209i
$203$	4.69278	+	3.40950i	0.329369	+	0.239300i
$204$		0			0
$205$	−4.86103	+	14.9607i	−0.339509	+	1.04490i
$206$	0.0374437	+	0.115240i	0.00260882	+	0.00802913i
$207$		0			0
$208$	7.32155			0.507658
$209$	−5.00411	−	2.90536i	−0.346142	−	0.200968i
$210$		0			0
$211$	21.7385	−	15.7940i	1.49654	−	1.08730i	0.524809	−	0.851220i	$-0.324137\pi$
$211$	21.7385	−	15.7940i	1.49654	−	1.08730i	0.971733	−	0.236082i	$-0.0758633\pi$
$212$	4.85017	+	14.9273i	0.333111	+	1.02521i
$213$		0			0
$214$	−4.54554	−	3.30253i	−0.310727	−	0.225756i
$215$	23.5722	+	17.1262i	1.60761	+	1.16800i
$216$		0			0
$217$	−0.694556	−	2.13762i	−0.0471495	−	0.145111i
$218$	−6.08280	+	4.41941i	−0.411979	+	0.299320i
$219$		0			0
$220$	−4.65484	+	21.6406i	−0.313829	+	1.45901i
$221$	−6.72285			−0.452228
$222$		0			0
$223$	1.24199	+	3.82247i	0.0831701	+	0.255971i	0.983991	−	0.178221i	$-0.0570340\pi$
$223$	1.24199	+	3.82247i	0.0831701	+	0.255971i	−0.900820	+	0.434192i	$0.857034\pi$
$224$	1.50120	−	4.62022i	0.100303	−	0.308701i
$225$		0			0
$226$	1.96086	+	1.42465i	0.130434	+	0.0947661i
$227$	3.61612	−	11.1293i	0.240010	−	0.738676i	−0.756407	−	0.654102i	$-0.773047\pi$
$227$	3.61612	−	11.1293i	0.240010	−	0.738676i	0.996417	−	0.0845746i	$-0.0269531\pi$
$228$		0			0
$229$	5.29505	−	3.84708i	0.349906	−	0.254222i	−0.398923	−	0.916984i	$-0.630616\pi$
$229$	5.29505	−	3.84708i	0.349906	−	0.254222i	0.748830	+	0.662762i	$0.230616\pi$
$230$	−6.76349			−0.445971
$231$		0			0
$232$	10.3746			0.681129
$233$	0.139610	−	0.101432i	0.00914614	−	0.00664506i	−0.583203	−	0.812327i	$-0.698201\pi$
$233$	0.139610	−	0.101432i	0.00914614	−	0.00664506i	0.592349	+	0.805682i	$0.298201\pi$
$234$		0			0
$235$	14.4113	−	44.3533i	0.940088	−	2.89329i
$236$	−6.52404	−	4.73999i	−0.424679	−	0.308547i
$237$		0			0
$238$	−0.363449	+	1.11858i	−0.0235589	+	0.0725069i
$239$	3.22936	+	9.93895i	0.208890	+	0.642897i	0.999531	+	0.0306176i	$0.00974741\pi$
$239$	3.22936	+	9.93895i	0.208890	+	0.642897i	−0.790641	+	0.612280i	$0.790253\pi$
$240$		0			0
$241$	−3.41821			−0.220186			−0.110093	−	0.993921i	$-0.535115\pi$
$241$	−3.41821			−0.220186			−0.110093	+	0.993921i	$0.535115\pi$
$242$	−2.58346	−	4.52533i	−0.166071	−	0.290899i
$243$		0			0
$244$	−16.4945	+	11.9839i	−1.05595	+	0.767194i
$245$	−1.16154	−	3.57484i	−0.0742079	−	0.228388i
$246$		0			0
$247$	3.82187	+	2.77675i	0.243180	+	0.176681i
$248$	−3.25225	−	2.36290i	−0.206518	−	0.150044i
$249$		0			0
$250$	2.27174	+	6.99171i	0.143678	+	0.442194i
$251$	10.2544	−	7.45026i	0.647252	−	0.470256i	−0.215082	−	0.976596i	$-0.569002\pi$
$251$	10.2544	−	7.45026i	0.647252	−	0.470256i	0.862334	+	0.506340i	$0.169002\pi$
$252$		0			0
$253$	−9.38258	+	8.40692i	−0.589878	+	0.528539i
$254$	−0.0963238			−0.00604389
$255$		0			0
$256$	0.282269	+	0.868734i	0.0176418	+	0.0542959i
$257$	5.61954	−	17.2952i	0.350538	−	1.07884i	−0.608014	−	0.793926i	$-0.708034\pi$
$257$	5.61954	−	17.2952i	0.350538	−	1.07884i	0.958552	−	0.284918i	$-0.0919663\pi$
$258$		0			0
$259$	−6.19149	−	4.49838i	−0.384721	−	0.279516i
$260$	5.58450	−	17.1873i	0.346336	−	1.06591i
$261$		0			0
$262$	3.93929	−	2.86206i	0.243370	−	0.176819i
$263$	−15.7837			−0.973264			−0.486632	−	0.873607i	$-0.661775\pi$
$263$	−15.7837			−0.973264			−0.486632	+	0.873607i	$0.661775\pi$
$264$		0			0
$265$	33.2262			2.04107
$266$	0.668627	−	0.485786i	0.0409962	−	0.0297855i
$267$		0			0
$268$	6.69623	−	20.6089i	0.409038	−	1.25889i
$269$	18.5990	+	13.5130i	1.13400	+	0.823900i	0.986272	−	0.165128i	$-0.0528039\pi$
$269$	18.5990	+	13.5130i	1.13400	+	0.823900i	0.147728	+	0.989028i	$0.452804\pi$
$270$		0			0
$271$	2.88628	−	8.88306i	0.175329	−	0.539608i	−0.824319	−	0.566125i	$-0.808442\pi$
$271$	2.88628	−	8.88306i	0.175329	−	0.539608i	0.999648	+	0.0265176i	$0.00844182\pi$
$272$	−2.07455	−	6.38482i	−0.125788	−	0.387136i
$273$		0			0
$274$	−8.10505			−0.489644
$275$	26.1833	+	15.2019i	1.57891	+	0.916706i
$276$		0			0
$277$	−15.7246	+	11.4246i	−0.944799	+	0.686437i	−0.949571	−	0.313552i	$-0.898481\pi$
$277$	−15.7246	+	11.4246i	−0.944799	+	0.686437i	0.00477176	+	0.999989i	$0.498481\pi$
$278$	−2.85465	−	8.78571i	−0.171211	−	0.526932i
$279$		0			0
$280$	−5.43888	−	3.95157i	−0.325035	−	0.236152i
$281$	−3.59493	−	2.61187i	−0.214456	−	0.155811i	0.475372	−	0.879785i	$-0.342314\pi$
$281$	−3.59493	−	2.61187i	−0.214456	−	0.155811i	−0.689827	+	0.723974i	$0.742314\pi$
$282$		0			0
$283$	4.27947	+	13.1708i	0.254388	+	0.782925i	0.993950	+	0.109837i	$0.0350328\pi$
$283$	4.27947	+	13.1708i	0.254388	+	0.782925i	−0.739562	+	0.673089i	$0.764967\pi$
$284$	−11.1470	+	8.09875i	−0.661451	+	0.480572i
$285$		0			0
$286$	1.72090	+	3.89061i	0.101759	+	0.230056i
$287$	−4.18500			−0.247033
$288$		0			0
$289$	−3.34838	−	10.3052i	−0.196963	−	0.606191i
$290$	3.19169	−	9.82302i	0.187423	−	0.576828i
$291$		0			0
$292$	22.5236	+	16.3643i	1.31809	+	0.957649i
$293$	5.94422	−	18.2944i	0.347265	−	1.06877i	−0.613095	−	0.790009i	$-0.710076\pi$
$293$	5.94422	−	18.2944i	0.347265	−	1.06877i	0.960360	−	0.278763i	$-0.0899243\pi$
$294$		0			0
$295$	−13.8109	+	10.0342i	−0.804104	+	0.584215i
$296$	−13.6880			−0.795596
$297$		0			0
$298$	−4.68520			−0.271406
$299$	8.32089	−	6.04548i	0.481209	−	0.349619i
$300$		0			0
$301$	−2.39538	+	7.37223i	−0.138068	+	0.424928i
$302$	−5.94077	−	4.31622i	−0.341853	−	0.248371i
$303$		0			0
$304$	−1.45777	+	4.48656i	−0.0836089	+	0.257322i
$305$	13.3374	+	41.0482i	0.763695	+	2.35041i
$306$		0			0
$307$	2.24474			0.128114			0.0640571	−	0.997946i	$-0.479596\pi$
$307$	2.24474			0.128114			0.0640571	+	0.997946i	$0.479596\pi$
$308$	−5.85820	+	0.601335i	−0.333802	+	0.0342643i
$309$		0			0
$310$	−3.23779	+	2.35239i	−0.183894	+	0.133607i
$311$	−3.90260	−	12.0110i	−0.221296	−	0.681080i	−0.998646	−	0.0520116i	$-0.983437\pi$
$311$	−3.90260	−	12.0110i	−0.221296	−	0.681080i	0.777350	−	0.629068i	$-0.216563\pi$
$312$		0			0
$313$	−0.862781	−	0.626847i	−0.0487673	−	0.0354315i	0.563135	−	0.826365i	$-0.309595\pi$
$313$	−0.862781	−	0.626847i	−0.0487673	−	0.0354315i	−0.611902	+	0.790934i	$0.709595\pi$
$314$	6.49734	+	4.72059i	0.366666	+	0.266398i
$315$		0			0
$316$	3.87035	+	11.9117i	0.217724	+	0.670085i
$317$	−20.3638	+	14.7951i	−1.14374	+	0.830978i	−0.987636	−	0.156763i	$-0.949894\pi$
$317$	−20.3638	+	14.7951i	−1.14374	+	0.830978i	−0.156106	+	0.987740i	$0.549894\pi$
$318$		0			0
$319$	−7.78224	−	17.5941i	−0.435722	−	0.985081i
$320$	11.6770			0.652766
$321$		0			0
$322$	−0.556035	−	1.71130i	−0.0309866	−	0.0953670i
$323$	1.33857	−	4.11968i	0.0744798	−	0.229225i
$324$		0			0
$325$	−19.9974	−	14.5289i	−1.10925	−	0.805920i
$326$	−2.92388	+	8.99878i	−0.161939	+	0.498396i
$327$		0			0
$328$	−6.05555	+	4.39961i	−0.334362	+	0.242928i
$329$	12.4071			0.684024
$330$		0			0
$331$	−8.53640			−0.469203			−0.234601	−	0.972092i	$-0.575378\pi$
$331$	−8.53640			−0.469203			−0.234601	+	0.972092i	$0.575378\pi$
$332$	−17.0948	+	12.4201i	−0.938201	+	0.681643i
$333$		0			0
$334$	2.55465	−	7.86242i	0.139784	−	0.430212i
$335$	−37.1118	−	26.9633i	−2.02764	−	1.47316i
$336$		0			0
$337$	−5.33254	+	16.4119i	−0.290482	+	0.894012i	0.694219	+	0.719763i	$0.255750\pi$
$337$	−5.33254	+	16.4119i	−0.290482	+	0.894012i	−0.984702	+	0.174249i	$0.944250\pi$
$338$	0.829732	+	2.55365i	0.0451315	+	0.138900i
$339$		0			0
$340$	−16.5707			−0.898673
$341$	−1.56760	+	7.28786i	−0.0848903	+	0.394660i
$342$		0			0
$343$	0.809017	−	0.587785i	0.0436828	−	0.0317374i
$344$	4.28426	+	13.1856i	0.230992	+	0.710920i
$345$		0			0
$346$	3.58693	+	2.60606i	0.192835	+	0.140103i
$347$	3.36307	+	2.44341i	0.180539	+	0.131169i	0.674384	−	0.738380i	$-0.264409\pi$
$347$	3.36307	+	2.44341i	0.180539	+	0.131169i	−0.493845	+	0.869550i	$0.664409\pi$
$348$		0			0
$349$	2.38186	+	7.33060i	0.127498	+	0.392398i	0.994348	−	0.106171i	$-0.0338590\pi$
$349$	2.38186	+	7.33060i	0.127498	+	0.392398i	−0.866850	+	0.498569i	$0.833859\pi$
$350$	−3.49849	+	2.54180i	−0.187002	+	0.135865i
$351$		0			0
$352$	−11.9998	+	10.7520i	−0.639591	+	0.573083i
$353$	4.84242			0.257736			0.128868	−	0.991662i	$-0.458866\pi$
$353$	4.84242			0.257736			0.128868	+	0.991662i	$0.458866\pi$
$354$		0			0
$355$	9.01339	+	27.7404i	0.478381	+	1.47231i
$356$	−0.928267	+	2.85691i	−0.0491980	+	0.151416i
$357$		0			0
$358$	−2.10533	−	1.52961i	−0.111270	−	0.0808425i
$359$	−1.36534	+	4.20209i	−0.0720600	+	0.221778i	−0.980600	−	0.196020i	$-0.937198\pi$
$359$	−1.36534	+	4.20209i	−0.0720600	+	0.221778i	0.908540	+	0.417798i	$0.137198\pi$
$360$		0			0
$361$	12.9088	−	9.37879i	0.679411	−	0.493621i
$362$	5.29821			0.278468
$363$		0			0
$364$	4.80786			0.252000
$365$	47.6808	−	34.6421i	2.49573	−	1.81325i
$366$		0			0
$367$	−9.12574	+	28.0861i	−0.476360	+	1.46608i	0.367756	+	0.929922i	$0.380126\pi$
$367$	−9.12574	+	28.0861i	−0.476360	+	1.46608i	−0.844115	+	0.536161i	$0.819874\pi$
$368$	8.30918	+	6.03697i	0.433146	+	0.314699i
$369$		0			0
$370$	−4.21101	+	12.9602i	−0.218920	+	0.673766i
$371$	2.73157	+	8.40692i	0.141816	+	0.436465i
$372$		0			0
$373$	7.64965			0.396084			0.198042	−	0.980194i	$-0.436542\pi$
$373$	7.64965			0.396084			0.198042	+	0.980194i	$0.436542\pi$
$374$	2.90522	−	2.60312i	0.150225	−	0.134604i
$375$		0			0
$376$	17.9526	−	13.0433i	0.925835	−	0.672659i
$377$	4.85358	+	14.9378i	0.249972	+	0.769335i
$378$		0			0
$379$	9.06860	+	6.58872i	0.465823	+	0.338440i	0.795811	−	0.605545i	$-0.207045\pi$
$379$	9.06860	+	6.58872i	0.465823	+	0.338440i	−0.329988	+	0.943985i	$0.607045\pi$
$380$	9.42028	+	6.84423i	0.483250	+	0.351102i
$381$		0			0
$382$	−0.842919	−	2.59424i	−0.0431275	−	0.132733i
$383$	−20.0189	+	14.5446i	−1.02292	+	0.743194i	−0.966879	−	0.255235i	$-0.917847\pi$
$383$	−20.0189	+	14.5446i	−1.02292	+	0.743194i	−0.0560396	+	0.998429i	$0.517847\pi$
$384$		0			0
$385$	−2.62157	+	12.1878i	−0.133607	+	0.621149i
$386$	7.05102			0.358887
$387$		0			0
$388$	−3.83884	−	11.8147i	−0.194888	−	0.599802i
$389$	8.97223	−	27.6137i	0.454910	−	1.40007i	−0.416331	−	0.909213i	$-0.636684\pi$
$389$	8.97223	−	27.6137i	0.454910	−	1.40007i	0.871241	−	0.490856i	$-0.163316\pi$
$390$		0			0
$391$	−7.62972	−	5.54331i	−0.385851	−	0.280337i
$392$	0.552692	−	1.70101i	0.0279152	−	0.0859140i
$393$		0			0
$394$	−4.80876	+	3.49377i	−0.242262	+	0.176013i
$395$	26.5139			1.33406
$396$		0			0
$397$	−8.27461			−0.415291			−0.207645	−	0.978204i	$-0.566580\pi$
$397$	−8.27461			−0.415291			−0.207645	+	0.978204i	$0.566580\pi$
$398$	0.319784	−	0.232337i	0.0160293	−	0.0116460i
$399$		0			0
$400$	7.62757	−	23.4752i	0.381378	−	1.17376i
$401$	−21.6323	−	15.7168i	−1.08027	−	0.784860i	−0.102538	−	0.994729i	$-0.532696\pi$
$401$	−21.6323	−	15.7168i	−1.08027	−	0.784860i	−0.977729	+	0.209869i	$0.932696\pi$
$402$		0			0
$403$	1.88068	−	5.78814i	0.0936833	−	0.288328i
$404$	1.49070	+	4.58789i	0.0741649	+	0.228256i
$405$		0			0
$406$	2.74782			0.136372
$407$	10.2676	+	23.2131i	0.508947	+	1.15063i
$408$		0			0
$409$	−28.0590	+	20.3861i	−1.38743	+	1.00803i	−0.391288	+	0.920268i	$0.627970\pi$
$409$	−28.0590	+	20.3861i	−1.38743	+	1.00803i	−0.996142	+	0.0877586i	$0.972030\pi$
$410$	2.30273	+	7.08708i	0.113724	+	0.350006i
$411$		0			0
$412$	−0.367437	−	0.266958i	−0.0181023	−	0.0131521i
$413$	−3.67428	−	2.66952i	−0.180800	−	0.131359i
$414$		0			0
$415$	13.8228	+	42.5422i	0.678535	+	2.08832i
$416$	10.6419	−	7.73183i	0.521764	−	0.379084i
$417$		0			0
$418$	−2.72676	+	0.279897i	−0.133370	+	0.0136902i
$419$	4.34546			0.212290			0.106145	−	0.994351i	$-0.466149\pi$
$419$	4.34546			0.212290			0.106145	+	0.994351i	$0.466149\pi$
$420$		0			0
$421$	−1.46425	−	4.50649i	−0.0713631	−	0.219633i	0.909014	−	0.416767i	$-0.136837\pi$
$421$	−1.46425	−	4.50649i	−0.0713631	−	0.219633i	−0.980377	+	0.197133i	$0.936837\pi$
$422$	3.93342	−	12.1058i	0.191476	−	0.589302i
$423$		0			0
$424$	12.7905	+	9.29287i	0.621164	+	0.451302i
$425$	−7.00384	+	21.5556i	−0.339736	+	1.04560i
$426$		0			0
$427$	−9.28955	+	6.74925i	−0.449553	+	0.326619i
$428$	21.0599			1.01797
$429$		0			0
$430$	13.8025			0.665617
$431$	−24.1590	+	17.5526i	−1.16370	+	0.845478i	−0.990241	−	0.139363i	$-0.955494\pi$
$431$	−24.1590	+	17.5526i	−1.16370	+	0.845478i	−0.173459	+	0.984841i	$0.555494\pi$
$432$		0			0
$433$	−6.71306	+	20.6607i	−0.322609	+	0.992889i	0.649899	+	0.760020i	$0.274811\pi$
$433$	−6.71306	+	20.6607i	−0.322609	+	0.992889i	−0.972508	+	0.232868i	$0.925189\pi$
$434$	−0.861386	−	0.625834i	−0.0413479	−	0.0300410i
$435$		0			0
$436$	8.70878	−	26.8029i	0.417075	−	1.28362i
$437$	2.04785	+	6.30263i	0.0979620	+	0.301496i
$438$		0			0
$439$	−40.3447			−1.92555			−0.962773	−	0.270313i	$-0.912873\pi$
$439$	−40.3447			−1.92555			−0.962773	+	0.270313i	$0.912873\pi$
$440$	9.01952	+	20.3914i	0.429989	+	0.972120i
$441$		0			0
$442$	−2.57648	+	1.87192i	−0.122551	+	0.0890382i
$443$	4.28883	+	13.1996i	0.203768	+	0.627134i	0.999762	+	0.0218290i	$0.00694893\pi$
$443$	4.28883	+	13.1996i	0.203768	+	0.627134i	−0.795993	+	0.605305i	$0.793051\pi$
$444$		0			0
$445$	5.14464	+	3.73780i	0.243879	+	0.177189i
$446$	1.54032	+	1.11911i	0.0729361	+	0.0529912i
$447$		0			0
$448$	0.959985	+	2.95453i	0.0453550	+	0.139588i
$449$	−11.5708	+	8.40666i	−0.546059	+	0.396735i	−0.826330	−	0.563186i	$-0.809575\pi$
$449$	−11.5708	+	8.40666i	−0.546059	+	0.396735i	0.280272	+	0.959921i	$0.409575\pi$
$450$		0			0
$451$	12.0036	+	6.96922i	0.565227	+	0.328168i
$452$	−9.08484			−0.427315
$453$		0			0
$454$	−1.71300	−	5.27208i	−0.0803953	−	0.247431i
$455$	3.14514	−	9.67975i	0.147447	−	0.453794i
$456$		0			0
$457$	11.4296	+	8.30410i	0.534655	+	0.388449i	0.822096	−	0.569349i	$-0.192805\pi$
$457$	11.4296	+	8.30410i	0.534655	+	0.388449i	−0.287441	+	0.957798i	$0.592805\pi$
$458$	0.958097	−	2.94872i	0.0447690	−	0.137785i
$459$		0			0
$460$	20.5096	−	14.9011i	0.956265	−	0.694767i
$461$	0.966736			0.0450254			0.0225127	−	0.999747i	$-0.492833\pi$
$461$	0.966736			0.0450254			0.0225127	+	0.999747i	$0.492833\pi$
$462$		0			0
$463$	31.8119			1.47842			0.739212	−	0.673473i	$-0.235198\pi$
$463$	31.8119			1.47842			0.739212	+	0.673473i	$0.235198\pi$
$464$	−12.6890	+	9.21907i	−0.589070	+	0.427985i
$465$		0			0
$466$	0.0252613	−	0.0777463i	0.00117021	−	0.00360153i
$467$	−23.9576	−	17.4062i	−1.10863	−	0.805465i	−0.126180	−	0.992007i	$-0.540272\pi$
$467$	−23.9576	−	17.4062i	−1.10863	−	0.805465i	−0.982447	+	0.186543i	$0.940272\pi$
$468$		0			0
$469$	3.77126	−	11.6067i	0.174141	−	0.535950i
$470$	−6.82681	−	21.0107i	−0.314897	−	0.969153i
$471$		0			0
$472$	−8.12298			−0.373891
$473$	19.1474	−	17.1564i	0.880399	−	0.788850i
$474$		0			0
$475$	12.8848	−	9.36133i	0.591194	−	0.429527i
$476$	−1.36230	−	4.19273i	−0.0624409	−	0.192173i
$477$		0			0
$478$	4.00504	+	2.90983i	0.183186	+	0.133093i
$479$	−21.5079	−	15.6264i	−0.982723	−	0.713990i	−0.0244075	−	0.999702i	$-0.507770\pi$
$479$	−21.5079	−	15.6264i	−0.982723	−	0.713990i	−0.958316	+	0.285712i	$0.907770\pi$
$480$		0			0
$481$	−6.40365	−	19.7084i	−0.291981	−	0.898626i
$482$	−1.31000	+	0.951771i	−0.0596689	+	0.0433520i
$483$		0			0
$484$	17.8042	+	8.03081i	0.809280	+	0.365037i
$485$	−26.2981			−1.19414
$486$		0			0
$487$	4.36774	+	13.4425i	0.197921	+	0.609138i	0.999930	+	0.0118263i	$0.00376451\pi$
$487$	4.36774	+	13.4425i	0.197921	+	0.609138i	−0.802009	+	0.597312i	$0.796235\pi$
$488$	−6.34629	+	19.5319i	−0.287283	+	0.884167i
$489$		0			0
$490$	−1.44053	−	1.04661i	−0.0650767	−	0.0472810i
$491$	−4.76461	+	14.6639i	−0.215024	+	0.661775i	0.784128	+	0.620599i	$0.213110\pi$
$491$	−4.76461	+	14.6639i	−0.215024	+	0.661775i	−0.999152	+	0.0411759i	$0.986890\pi$
$492$		0			0
$493$	11.6514	−	8.46520i	0.524751	−	0.381254i
$494$	2.23786			0.100686
$495$		0			0
$496$	6.07744			0.272885
$497$	−6.27787	+	4.56114i	−0.281601	+	0.204595i
$498$		0			0
$499$	9.48757	−	29.1997i	0.424722	−	1.30716i	−0.478538	−	0.878067i	$-0.658833\pi$
$499$	9.48757	−	29.1997i	0.424722	−	1.30716i	0.903260	−	0.429093i	$-0.141167\pi$
$500$	−22.2927	−	16.1966i	−0.996961	−	0.724335i
$501$		0			0
$502$	1.85545	−	5.71050i	0.0828130	−	0.254872i
$503$	5.62070	+	17.2987i	0.250614	+	0.771312i	0.994662	+	0.103185i	$0.0329035\pi$
$503$	5.62070	+	17.2987i	0.250614	+	0.771312i	−0.744048	+	0.668127i	$0.767096\pi$
$504$		0			0
$505$	10.2121			0.454431
$506$	−1.25496	+	5.83438i	−0.0557898	+	0.259370i
$507$		0			0
$508$	0.292092	−	0.212217i	0.0129595	−	0.00941563i
$509$	9.94245	+	30.5997i	0.440691	+	1.35631i	0.887140	+	0.461499i	$0.152688\pi$
$509$	9.94245	+	30.5997i	0.440691	+	1.35631i	−0.446449	+	0.894809i	$0.647312\pi$
$510$		0			0
$511$	12.6851	+	9.21624i	0.561154	+	0.407702i
$512$	18.4520	+	13.4061i	0.815470	+	0.592474i
$513$		0			0
$514$	−2.66205	−	8.19295i	−0.117418	−	0.361376i
$515$	−0.777838	+	0.565132i	−0.0342756	+	0.0249027i
$516$		0			0
$517$	−35.5865	−	20.6613i	−1.56509	−	0.908684i
$518$	−3.62538			−0.159290
$519$		0			0
$520$	−5.62524	−	17.3127i	−0.246683	−	0.759213i
$521$	8.59801	−	26.4620i	0.376686	−	1.15932i	−0.565648	−	0.824646i	$-0.691374\pi$
$521$	8.59801	−	26.4620i	0.376686	−	1.15932i	0.942334	−	0.334673i	$-0.108626\pi$
$522$		0			0
$523$	15.4751	+	11.2433i	0.676677	+	0.491635i	0.872254	−	0.489054i	$-0.162658\pi$
$523$	15.4751	+	11.2433i	0.676677	+	0.491635i	−0.195577	+	0.980688i	$0.562658\pi$
$524$	−5.63990	+	17.3578i	−0.246380	+	0.758280i
$525$		0			0
$526$	−6.04897	+	4.39483i	−0.263748	+	0.191624i
$527$	−5.58048			−0.243089
$528$		0			0
$529$	−8.57190			−0.372691
$530$	12.7337	−	9.25156i	0.553116	−	0.401862i
$531$		0			0
$532$	−0.957277	+	2.94620i	−0.0415032	+	0.127734i
$533$	−9.16769	−	6.66072i	−0.397097	−	0.288508i
$534$		0			0
$535$	13.7767	−	42.4003i	0.595619	−	1.83313i
$536$	−6.74508	−	20.7592i	−0.291343	−	0.896662i
$537$		0			0
$538$	10.8905			0.469522
$539$	−3.29929	+	0.338667i	−0.142110	+	0.0145874i
$540$		0			0
$541$	−34.5304	+	25.0878i	−1.48458	+	1.07861i	−0.508534	+	0.861042i	$0.669813\pi$
$541$	−34.5304	+	25.0878i	−1.48458	+	1.07861i	−0.976045	+	0.217569i	$0.930187\pi$
$542$	−1.36727	−	4.20802i	−0.0587293	−	0.180750i
$543$		0			0
$544$	−9.75798	−	7.08959i	−0.418370	−	0.303964i
$545$	−48.2657	−	35.0671i	−2.06748	−	1.50211i
$546$		0			0
$547$	−7.76134	−	23.8869i	−0.331851	−	1.02133i	−0.968253	−	0.249974i	$-0.919578\pi$
$547$	−7.76134	−	23.8869i	−0.331851	−	1.02133i	0.636402	−	0.771358i	$-0.280422\pi$
$548$	24.5778	−	17.8568i	1.04991	−	0.762804i
$549$		0			0
$550$	14.2674	−	1.46452i	0.608362	−	0.0624474i
$551$	−10.1201			−0.431130
$552$		0			0
$553$	2.17974	+	6.70856i	0.0926922	+	0.285277i
$554$	−2.84524	+	8.75676i	−0.120883	+	0.372039i
$555$		0			0
$556$	28.0128	+	20.3525i	1.18801	+	0.863139i
$557$	1.31555	−	4.04884i	0.0557415	−	0.171555i	−0.919310	−	0.393535i	$-0.871252\pi$
$557$	1.31555	−	4.04884i	0.0557415	−	0.171555i	0.975051	+	0.221980i	$0.0712520\pi$
$558$		0			0
$559$	−16.9808	+	12.3373i	−0.718210	+	0.521810i
$560$	10.1636			0.429490
$561$		0			0
$562$	−2.10498			−0.0887933
$563$	−6.01677	+	4.37144i	−0.253577	+	0.184234i	−0.707310	−	0.706903i	$-0.750092\pi$
$563$	−6.01677	+	4.37144i	−0.253577	+	0.184234i	0.453734	+	0.891137i	$0.350092\pi$
$564$		0			0
$565$	−5.94301	+	18.2907i	−0.250024	+	0.769496i
$566$	5.30738	+	3.85604i	0.223086	+	0.162081i
$567$		0			0
$568$	−4.28882	+	13.1996i	−0.179955	+	0.553845i
$569$	−13.4822	−	41.4939i	−0.565203	−	1.73952i	−0.667348	−	0.744746i	$-0.732570\pi$
$569$	−13.4822	−	41.4939i	−0.565203	−	1.73952i	0.102145	−	0.994770i	$-0.467430\pi$
$570$		0			0
$571$	−34.1074			−1.42735			−0.713676	−	0.700476i	$-0.752971\pi$
$571$	−34.1074			−1.42735			−0.713676	+	0.700476i	$0.752971\pi$
$572$	−13.7901	−	8.00646i	−0.576593	−	0.334767i
$573$		0			0
$574$	−1.60387	+	1.16528i	−0.0669441	+	0.0486377i
$575$	−10.7151	−	32.9776i	−0.446849	−	1.37526i
$576$		0			0
$577$	−22.7175	−	16.5052i	−0.945743	−	0.687122i	0.00405352	−	0.999992i	$-0.498710\pi$
$577$	−22.7175	−	16.5052i	−0.945743	−	0.687122i	−0.949796	+	0.312870i	$0.898710\pi$
$578$	−4.15265	−	3.01707i	−0.172727	−	0.125494i
$579$		0			0
$580$	11.9633	+	36.8192i	0.496748	+	1.52883i
$581$	−9.62766	+	6.99490i	−0.399423	+	0.290198i
$582$		0			0
$583$	6.16511	−	28.6619i	0.255333	−	1.18706i
$584$	28.0437			1.16046
$585$		0			0
$586$	−2.81585	−	8.66631i	−0.116322	−	0.358002i
$587$	2.07887	−	6.39809i	0.0858040	−	0.264078i	−0.898944	−	0.438063i	$-0.855665\pi$
$587$	2.07887	−	6.39809i	0.0858040	−	0.264078i	0.984748	+	0.173986i	$0.0556646\pi$
$588$		0			0
$589$	3.17244	+	2.30491i	0.130718	+	0.0949724i
$590$	−2.49898	+	7.69107i	−0.102881	+	0.316636i
$591$		0			0
$592$	16.7414	−	12.1633i	0.688067	−	0.499910i
$593$	−20.8442			−0.855969			−0.427984	−	0.903786i	$-0.640776\pi$
$593$	−20.8442			−0.855969			−0.427984	+	0.903786i	$0.640776\pi$
$594$		0			0
$595$	−9.33248			−0.382594
$596$	14.2074	−	10.3223i	0.581958	−	0.422817i
$597$		0			0
$598$	1.50560	−	4.63376i	0.0615686	−	0.189489i
$599$	0.146169	+	0.106198i	0.00597231	+	0.00433913i	0.590767	−	0.806842i	$-0.298825\pi$
$599$	0.146169	+	0.106198i	0.00597231	+	0.00433913i	−0.584795	+	0.811181i	$0.698825\pi$
$600$		0			0
$601$	8.53019	−	26.2532i	0.347954	−	1.07089i	−0.612030	−	0.790835i	$-0.709647\pi$
$601$	8.53019	−	26.2532i	0.347954	−	1.07089i	0.959984	−	0.280056i	$-0.0903532\pi$
$602$	1.13472	+	3.49232i	0.0462479	+	0.142336i
$603$		0			0
$604$	27.5241			1.11994
$605$	27.8155	−	30.5920i	1.13086	−	1.24374i
$606$		0			0
$607$	−18.8727	+	13.7118i	−0.766021	+	0.556547i	−0.900751	−	0.434336i	$-0.856983\pi$
$607$	−18.8727	+	13.7118i	−0.766021	+	0.556547i	0.134730	+	0.990882i	$0.456983\pi$
$608$	2.61909	+	8.06072i	0.106218	+	0.326905i
$609$		0			0
$610$	16.5410	+	12.0177i	0.669724	+	0.486583i
$611$	27.1790	+	19.7467i	1.09955	+	0.798867i
$612$		0			0
$613$	−6.02591	−	18.5459i	−0.243384	−	0.749060i	−0.995898	−	0.0904833i	$-0.971159\pi$
$613$	−6.02591	−	18.5459i	−0.243384	−	0.749060i	0.752514	−	0.658577i	$-0.228841\pi$
$614$	0.860279	−	0.625029i	0.0347180	−	0.0252241i
$615$		0			0
$616$	−4.41793	+	3.95852i	−0.178003	+	0.159493i
$617$	23.2566			0.936276			0.468138	−	0.883655i	$-0.344925\pi$
$617$	23.2566			0.936276			0.468138	+	0.883655i	$0.344925\pi$
$618$		0			0
$619$	−8.82217	−	27.1518i	−0.354593	−	1.09132i	−0.956245	−	0.292566i	$-0.905491\pi$
$619$	−8.82217	−	27.1518i	−0.354593	−	1.09132i	0.601652	−	0.798758i	$-0.294509\pi$
$620$	4.63556	−	14.2668i	0.186169	−	0.572968i
$621$		0			0
$622$	−4.83999	−	3.51646i	−0.194066	−	0.140997i
$623$	−0.522792	+	1.60899i	−0.0209452	+	0.0644627i
$624$		0			0
$625$	−10.2659	+	7.45861i	−0.410636	+	0.298344i
$626$	−0.505194			−0.0201916
$627$		0			0
$628$	−30.1028			−1.20123
$629$	−15.3724	+	11.1687i	−0.612938	+	0.445325i
$630$		0			0
$631$	1.63814	−	5.04166i	0.0652131	−	0.200705i	−0.913141	−	0.407645i	$-0.866350\pi$
$631$	1.63814	−	5.04166i	0.0652131	−	0.200705i	0.978354	+	0.206939i	$0.0663502\pi$
$632$	10.2066	+	7.41554i	0.405997	+	0.294974i
$633$		0			0
$634$	−3.68466	+	11.3402i	−0.146337	+	0.450378i
$635$	−0.236185	−	0.726901i	−0.00937270	−	0.0288462i
$636$		0			0
$637$	2.70774			0.107285
$638$	−7.88141	−	4.57590i	−0.312028	−	0.181162i
$639$		0			0
$640$	34.0209	−	24.7176i	1.34479	−	0.977049i
$641$	9.23593	+	28.4253i	0.364797	+	1.12273i	0.950108	+	0.311922i	$0.100973\pi$
$641$	9.23593	+	28.4253i	0.364797	+	1.12273i	−0.585310	+	0.810809i	$0.699027\pi$
$642$		0			0
$643$	−31.0989	−	22.5946i	−1.22642	−	0.891046i	−0.229803	−	0.973237i	$-0.573808\pi$
$643$	−31.0989	−	22.5946i	−1.22642	−	0.891046i	−0.996617	+	0.0821916i	$0.973808\pi$
$644$	5.45640	+	3.96431i	0.215012	+	0.156216i
$645$		0			0
$646$	−0.634096	−	1.95155i	−0.0249482	−	0.0767826i
$647$	−26.1799	+	19.0208i	−1.02924	+	0.747786i	−0.968156	−	0.250347i	$-0.919455\pi$
$647$	−26.1799	+	19.0208i	−1.02924	+	0.747786i	−0.0610828	+	0.998133i	$0.519455\pi$
$648$		0			0
$649$	6.09322	+	13.7756i	0.239180	+	0.540738i
$650$	−11.7093			−0.459276
$651$		0			0
$652$	−10.9594	−	33.7297i	−0.429205	−	1.32096i
$653$	−7.38692	+	22.7346i	−0.289073	+	0.889674i	0.696076	+	0.717969i	$0.254928\pi$
$653$	−7.38692	+	22.7346i	−0.289073	+	0.889674i	−0.985148	+	0.171706i	$0.945072\pi$
$654$		0			0
$655$	31.2574	+	22.7098i	1.22133	+	0.887347i
$656$	3.49682	−	10.7621i	0.136528	−	0.420190i
$657$		0			0
$658$	4.75491	−	3.45464i	0.185366	−	0.134676i
$659$	−34.5124			−1.34441			−0.672205	−	0.740365i	$-0.734653\pi$
$659$	−34.5124			−1.34441			−0.672205	+	0.740365i	$0.734653\pi$
$660$		0			0
$661$	−2.56237			−0.0996647			−0.0498324	−	0.998758i	$-0.515869\pi$
$661$	−2.56237			−0.0996647			−0.0498324	+	0.998758i	$0.515869\pi$
$662$	−3.27150	+	2.37689i	−0.127151	+	0.0923803i
$663$		0			0
$664$	−6.57728	+	20.2428i	−0.255248	+	0.785572i
$665$	5.30542	+	3.85461i	0.205735	+	0.149475i
$666$		0			0
$667$	−6.80863	+	20.9548i	−0.263631	+	0.811373i
$668$	9.57549	+	29.4703i	0.370487	+	1.14024i
$669$		0			0
$670$	−21.7305			−0.839523
$671$	37.8841	−	3.88875i	1.46250	−	0.150123i
$672$		0			0
$673$	−29.6642	+	21.5523i	−1.14347	+	0.830781i	−0.987599	−	0.156996i	$-0.949819\pi$
$673$	−29.6642	+	21.5523i	−1.14347	+	0.830781i	−0.155872	+	0.987777i	$0.549819\pi$
$674$	2.52610	+	7.77452i	0.0973016	+	0.299463i
$675$		0			0
$676$	−8.14220	−	5.91566i	−0.313162	−	0.227525i
$677$	25.8733	+	18.7981i	0.994392	+	0.722468i	0.960879	−	0.276970i	$-0.0893302\pi$
$677$	25.8733	+	18.7981i	0.994392	+	0.722468i	0.0335138	+	0.999438i	$0.489330\pi$
$678$		0			0
$679$	−2.16200	−	6.65396i	−0.0829700	−	0.255355i
$680$	−13.5038	+	9.81107i	−0.517846	+	0.376237i
$681$		0			0
$682$	1.42847	+	3.22950i	0.0546991	+	0.123664i
$683$	−6.96871			−0.266650			−0.133325	−	0.991072i	$-0.542565\pi$
$683$	−6.96871			−0.266650			−0.133325	+	0.991072i	$0.542565\pi$
$684$		0			0
$685$	−19.8735	−	61.1642i	−0.759326	−	2.33696i
$686$	0.146385	−	0.450528i	0.00558902	−	0.0172012i
$687$		0			0
$688$	−16.9569	−	12.3199i	−0.646475	−	0.469692i
$689$	−7.39640	+	22.7638i	−0.281780	+	0.867230i
$690$		0			0
$691$	4.10336	−	2.98127i	0.156099	−	0.113413i	−0.506994	−	0.861950i	$-0.669243\pi$
$691$	4.10336	−	2.98127i	0.156099	−	0.113413i	0.663093	+	0.748537i	$0.269243\pi$
$692$	−16.6186			−0.631744
$693$		0			0
$694$	1.96922			0.0747505
$695$	59.3012	−	43.0848i	2.24942	−	1.63430i
$696$		0			0
$697$	−3.21088	+	9.88206i	−0.121621	+	0.374310i
$698$	2.95397	+	2.14619i	0.111809	+	0.0812344i
$699$		0			0
$700$	5.00881	−	15.4155i	0.189315	−	0.582652i
$701$	−0.129238	−	0.397753i	−0.00488125	−	0.0150229i	0.948586	−	0.316519i	$-0.102514\pi$
$701$	−0.129238	−	0.397753i	−0.00488125	−	0.0150229i	−0.953467	+	0.301496i	$0.902514\pi$
$702$		0			0
$703$	13.3521			0.503583
$704$	2.16667	−	10.0730i	0.0816593	−	0.379639i
$705$		0			0
$706$	1.85582	−	1.34833i	0.0698447	−	0.0507451i
$707$	0.839547	+	2.58386i	0.0315744	+	0.0971760i
$708$		0			0
$709$	2.91783	+	2.11993i	0.109582	+	0.0796157i	0.641226	−	0.767352i	$-0.278426\pi$
$709$	2.91783	+	2.11993i	0.109582	+	0.0796157i	−0.531645	+	0.846967i	$0.678426\pi$
$710$	11.1784	+	8.12156i	0.419517	+	0.304797i
$711$		0			0
$712$	0.935039	+	2.87775i	0.0350420	+	0.107848i
$713$	6.90697	−	5.01820i	0.258668	−	0.187933i
$714$		0			0
$715$	−25.1406	+	22.5263i	−0.940205	+	0.842437i
$716$	9.75419			0.364531
$717$		0			0
$718$	0.646781	+	1.99059i	0.0241376	+	0.0742880i
$719$	5.55293	−	17.0902i	0.207089	−	0.637356i	−0.792532	−	0.609831i	$-0.791237\pi$
$719$	5.55293	−	17.0902i	0.207089	−	0.637356i	0.999621	−	0.0275250i	$-0.00876258\pi$
$720$		0			0
$721$	−0.206937	−	0.150349i	−0.00770674	−	0.00559928i
$722$	2.33575	−	7.18869i	0.0869275	−	0.267535i
$723$		0			0
$724$	−16.0663	+	11.6728i	−0.597099	+	0.433818i
$725$	52.9518			1.96658
$726$		0			0
$727$	10.0774			0.373752			0.186876	−	0.982384i	$-0.440164\pi$
$727$	10.0774			0.373752			0.186876	+	0.982384i	$0.440164\pi$
$728$	3.91801	−	2.84660i	0.145211	−	0.105502i
$729$		0			0
$730$	8.62747	−	26.5526i	0.319317	−	0.982757i
$731$	15.5703	+	11.3125i	0.575888	+	0.418407i
$732$		0			0
$733$	−3.77849	+	11.6290i	−0.139562	+	0.429527i	−0.996272	−	0.0862717i	$-0.972505\pi$
$733$	−3.77849	+	11.6290i	−0.139562	+	0.429527i	0.856710	+	0.515799i	$0.172505\pi$
$734$	4.32298	+	13.3048i	0.159564	+	0.491088i
$735$		0			0
$736$	18.4527			0.680177
$737$	−30.1454	+	27.0107i	−1.11042	+	0.994954i
$738$		0			0
$739$	−2.83011	+	2.05620i	−0.104107	+	0.0756385i	−0.638621	−	0.769521i	$-0.720495\pi$
$739$	−2.83011	+	2.05620i	−0.104107	+	0.0756385i	0.534514	+	0.845160i	$0.320495\pi$
$740$	−15.7839	−	48.5779i	−0.580229	−	1.78576i
$741$		0			0
$742$	3.38769	+	2.46130i	0.124366	+	0.0903571i
$743$	2.21381	+	1.60843i	0.0812167	+	0.0590074i	0.627653	−	0.778493i	$-0.284016\pi$
$743$	2.21381	+	1.60843i	0.0812167	+	0.0590074i	−0.546436	+	0.837501i	$0.684016\pi$
$744$		0			0
$745$	−11.4880	−	35.3565i	−0.420889	−	1.29536i
$746$	2.93166	−	2.12998i	0.107336	−	0.0779841i
$747$		0			0
$748$	−3.07468	+	14.2944i	−0.112422	+	0.522654i
$749$	11.8608			0.433382
$750$		0			0
$751$	−3.10499	−	9.55617i	−0.113303	−	0.348710i	0.878287	−	0.478135i	$-0.158687\pi$
$751$	−3.10499	−	9.55617i	−0.113303	−	0.348710i	−0.991589	+	0.129425i	$0.958687\pi$
$752$	−10.3669	+	31.9059i	−0.378041	+	1.16349i
$753$		0			0
$754$	6.01940	+	4.37335i	0.219213	+	0.159268i
$755$	18.0054	−	55.4149i	0.655283	−	2.01676i
$756$		0			0
$757$	−12.2558	+	8.90436i	−0.445445	+	0.323634i	−0.787795	−	0.615938i	$-0.788777\pi$
$757$	−12.2558	+	8.90436i	−0.445445	+	0.323634i	0.342350	+	0.939573i	$0.388777\pi$
$758$	5.31004			0.192869
$759$		0			0
$760$	11.7290			0.425457
$761$	28.6726	−	20.8319i	1.03938	−	0.755154i	0.0692162	−	0.997602i	$-0.477950\pi$
$761$	28.6726	−	20.8319i	1.03938	−	0.755154i	0.970165	+	0.242447i	$0.0779502\pi$
$762$		0			0
$763$	4.90471	−	15.0951i	0.177562	−	0.546481i
$764$	8.27161	+	6.00967i	0.299256	+	0.217422i
$765$		0			0
$766$	−3.62227	+	11.1482i	−0.130878	+	0.402801i
$767$	−3.80018	−	11.6958i	−0.137217	−	0.422309i
$768$		0			0
$769$	38.7592			1.39769			0.698845	−	0.715273i	$-0.253698\pi$
$769$	38.7592			1.39769			0.698845	+	0.715273i	$0.253698\pi$
$770$	2.38890	+	5.40083i	0.0860900	+	0.194633i
$771$		0			0
$772$	−21.3815	+	15.5346i	−0.769537	+	0.559102i
$773$	−8.20190	−	25.2428i	−0.295002	−	0.907922i	−0.983221	−	0.182419i	$-0.941607\pi$
$773$	−8.20190	−	25.2428i	−0.295002	−	0.907922i	0.688219	−	0.725503i	$-0.258393\pi$
$774$		0			0
$775$	−16.5993	−	12.0601i	−0.596265	−	0.433212i
$776$	−10.1235	−	7.35518i	−0.363414	−	0.264035i
$777$		0			0
$778$	−4.25026	−	13.0810i	−0.152379	−	0.468975i
$779$	5.90696	−	4.29166i	0.211639	−	0.153765i
$780$		0			0
$781$	25.6021	−	2.62801i	0.916114	−	0.0940377i
$782$	−4.46752			−0.159758
$783$		0			0
$784$	0.835561	+	2.57159i	0.0298415	+	0.0918426i
$785$	−19.6923	+	60.6065i	−0.702847	+	2.16314i
$786$		0			0
$787$	−15.9216	−	11.5677i	−0.567545	−	0.412345i	0.266668	−	0.963788i	$-0.414077\pi$
$787$	−15.9216	−	11.5677i	−0.567545	−	0.412345i	−0.834212	+	0.551443i	$0.814077\pi$
$788$	6.88472	−	21.1890i	0.245258	−	0.754827i
$789$		0			0
$790$	10.1612	−	7.38258i	0.361521	−	0.262660i
$791$	−5.11650			−0.181922
$792$		0			0
$793$	−31.0917			−1.10410
$794$	−3.17118	+	2.30400i	−0.112541	+	0.0817658i
$795$		0			0
$796$	−0.457836	+	1.40907i	−0.0162276	+	0.0499433i
$797$	−20.4517	−	14.8590i	−0.724435	−	0.526333i	0.163363	−	0.986566i	$-0.447766\pi$
$797$	−20.4517	−	14.8590i	−0.724435	−	0.526333i	−0.887798	+	0.460233i	$0.847766\pi$
$798$		0			0
$799$	9.51914	−	29.2969i	0.336763	−	1.03645i
$800$	−13.7040	−	42.1765i	−0.484509	−	1.49116i
$801$		0			0
$802$	−12.6666			−0.447274
$803$	−21.0362	−	47.5587i	−0.742351	−	1.67831i
$804$		0			0
$805$	11.5508	−	8.39217i	0.407113	−	0.295785i
$806$	−0.890902	−	2.74191i	−0.0313807	−	0.0965798i
$807$		0			0
$808$	3.93116	+	2.85616i	0.138298	+	0.100479i
$809$	−28.9540	−	21.0363i	−1.01797	−	0.739597i	−0.0521021	−	0.998642i	$-0.516592\pi$
$809$	−28.9540	−	21.0363i	−1.01797	−	0.739597i	−0.965865	+	0.259045i	$0.916592\pi$
$810$		0			0
$811$	6.47127	+	19.9165i	0.227237	+	0.699364i	0.998057	+	0.0623105i	$0.0198469\pi$
$811$	6.47127	+	19.9165i	0.227237	+	0.699364i	−0.770820	+	0.637053i	$0.780153\pi$
$812$	−8.33248	+	6.05390i	−0.292413	+	0.212450i
$813$		0			0
$814$	10.3985	+	6.03729i	0.364466	+	0.211607i
$815$	−75.0780			−2.62987
$816$		0			0
$817$	−4.17913	−	12.8620i	−0.146209	−	0.449986i
$818$	−5.07706	+	15.6256i	−0.177515	+	0.546336i
$819$		0			0
$820$	−22.5968	−	16.4176i	−0.789116	−	0.573326i
$821$	2.49273	−	7.67182i	0.0869967	−	0.267748i	−0.898089	−	0.439814i	$-0.855044\pi$
$821$	2.49273	−	7.67182i	0.0869967	−	0.267748i	0.985085	+	0.172066i	$0.0550442\pi$
$822$		0			0
$823$	16.2903	−	11.8356i	0.567845	−	0.412564i	−0.266477	−	0.963841i	$-0.585860\pi$
$823$	16.2903	−	11.8356i	0.567845	−	0.412564i	0.834322	+	0.551278i	$0.185860\pi$
$824$	−0.457490			−0.0159374
$825$		0			0
$826$	−2.15144			−0.0748583
$827$	−17.3276	+	12.5892i	−0.602540	+	0.437771i	−0.846779	−	0.531944i	$-0.821462\pi$
$827$	−17.3276	+	12.5892i	−0.602540	+	0.437771i	0.244240	+	0.969715i	$0.421462\pi$
$828$		0			0
$829$	−8.46584	+	26.0552i	−0.294031	+	0.904934i	0.689514	+	0.724272i	$0.257824\pi$
$829$	−8.46584	+	26.0552i	−0.294031	+	0.904934i	−0.983545	+	0.180662i	$0.942176\pi$
$830$	17.1430	+	12.4551i	0.595042	+	0.432323i
$831$		0			0
$832$	−2.59939	+	8.00010i	−0.0901177	+	0.277354i
$833$	−0.767235	−	2.36131i	−0.0265831	−	0.0818144i
$834$		0			0
$835$	65.5972			2.27008
$836$	7.65196	−	6.85627i	0.264649	−	0.237129i
$837$		0			0
$838$	1.66536	−	1.20996i	0.0575290	−	0.0417972i
$839$	6.29643	+	19.3784i	0.217377	+	0.669017i	0.998976	+	0.0452363i	$0.0144041\pi$
$839$	6.29643	+	19.3784i	0.217377	+	0.669017i	−0.781600	+	0.623781i	$0.785596\pi$
$840$		0			0
$841$	−3.75943	−	2.73139i	−0.129636	−	0.0941858i
$842$	−1.81596	−	1.31937i	−0.0625820	−	0.0454685i
$843$		0			0
$844$	14.7435	+	45.3757i	0.507490	+	1.56190i
$845$	−17.2365	+	12.5230i	−0.592953	+	0.430805i
$846$		0			0
$847$	10.0271	+	4.52288i	0.344537	+	0.155408i
$848$	−23.9016			−0.820783
$849$		0			0
$850$	3.31781	+	10.2112i	0.113800	+	0.350240i
$851$	8.98307	−	27.6471i	0.307936	−	0.947729i
$852$		0			0
$853$	6.70421	+	4.87090i	0.229548	+	0.166776i	0.696614	−	0.717446i	$-0.254689\pi$
$853$	6.70421	+	4.87090i	0.229548	+	0.166776i	−0.467066	+	0.884222i	$0.654689\pi$
$854$	−1.68087	+	5.17319i	−0.0575183	+	0.177023i
$855$		0			0
$856$	17.1621	−	12.4690i	0.586589	−	0.426182i
$857$	31.0459			1.06051			0.530254	−	0.847839i	$-0.322097\pi$
$857$	31.0459			1.06051			0.530254	+	0.847839i	$0.322097\pi$
$858$		0			0
$859$	−1.63124			−0.0556573			−0.0278287	−	0.999613i	$-0.508859\pi$
$859$	−1.63124			−0.0556573			−0.0278287	+	0.999613i	$0.508859\pi$
$860$	−41.8548	+	30.4093i	−1.42724	+	1.03695i
$861$		0			0
$862$	−4.37139	+	13.4538i	−0.148890	+	0.458237i
$863$	4.31095	+	3.13209i	0.146746	+	0.106617i	0.658736	−	0.752374i	$-0.271091\pi$
$863$	4.31095	+	3.13209i	0.146746	+	0.106617i	−0.511990	+	0.858992i	$0.671091\pi$
$864$		0			0
$865$	−10.8713	+	33.4586i	−0.369637	+	1.13762i
$866$	3.18006	+	9.78723i	0.108063	+	0.332584i
$867$		0			0
$868$	3.99088			0.135459
$869$	4.91964	−	22.8717i	0.166887	−	0.775869i
$870$		0			0
$871$	26.7343	−	19.4236i	0.905858	−	0.658144i
$872$	−8.77231	−	26.9984i	−0.297068	−	0.914281i
$873$		0			0
$874$	2.53974	+	1.84523i	0.0859079	+	0.0624157i
$875$	−12.5551	−	9.12179i	−0.424439	−	0.308373i
$876$		0			0
$877$	−4.98344	−	15.3374i	−0.168279	−	0.517909i	0.830984	−	0.556296i	$-0.187778\pi$
$877$	−4.98344	−	15.3374i	−0.168279	−	0.517909i	−0.999263	+	0.0383874i	$0.987778\pi$
$878$	−15.4618	+	11.2336i	−0.521809	+	0.379117i
$879$		0			0
$880$	−29.1516	−	16.9253i	−0.982701	−	0.570551i
$881$	35.1173			1.18313			0.591565	−	0.806257i	$-0.298510\pi$
$881$	35.1173			1.18313			0.591565	+	0.806257i	$0.298510\pi$
$882$		0			0
$883$	0.148400	+	0.456727i	0.00499405	+	0.0153701i	0.953522	−	0.301322i	$-0.0974279\pi$
$883$	0.148400	+	0.456727i	0.00499405	+	0.0153701i	−0.948528	+	0.316692i	$0.897428\pi$
$884$	3.68876	−	11.3528i	0.124066	−	0.381837i
$885$		0			0
$886$	5.31899	+	3.86447i	0.178695	+	0.129829i
$887$	−11.3483	+	34.9264i	−0.381038	+	1.17271i	0.558276	+	0.829655i	$0.311463\pi$
$887$	−11.3483	+	34.9264i	−0.381038	+	1.17271i	−0.939314	+	0.343059i	$0.888537\pi$
$888$		0			0
$889$	0.164504	−	0.119519i	0.00551728	−	0.00400854i
$890$	3.01240			0.100976
$891$		0			0
$892$	−7.13644			−0.238946
$893$	−17.5121	+	12.7233i	−0.586020	+	0.425768i
$894$		0			0
$895$	6.38087	−	19.6383i	0.213289	−	0.656436i
$896$	9.05096	+	6.57590i	0.302371	+	0.219686i
$897$		0			0
$898$	−2.09364	+	6.44357i	−0.0698657	+	0.215025i
$899$	4.02884	+	12.3995i	0.134369	+	0.413546i
$900$		0			0
$901$	21.9471			0.731163
$902$	6.54080	−	0.671402i	0.217785	−	0.0223553i
$903$		0			0
$904$	−7.40341	+	5.37889i	−0.246234	+	0.178899i
$905$	12.9911	+	39.9826i	0.431840	+	1.32907i
$906$		0			0
$907$	−9.86328	−	7.16609i	−0.327505	−	0.237946i	0.411866	−	0.911244i	$-0.364877\pi$
$907$	−9.86328	−	7.16609i	−0.327505	−	0.237946i	−0.739371	+	0.673298i	$0.764877\pi$
$908$	16.8098	+	12.2130i	0.557853	+	0.405304i
$909$		0			0
$910$	−1.48990	−	4.58543i	−0.0493895	−	0.152005i
$911$	−6.56799	+	4.77193i	−0.217607	+	0.158101i	−0.691249	−	0.722617i	$-0.742939\pi$
$911$	−6.56799	+	4.77193i	−0.217607	+	0.158101i	0.473642	+	0.880718i	$0.342939\pi$
$912$		0			0
$913$	39.2630	−	4.03028i	1.29942	−	0.133383i
$914$	6.69251			0.221369
$915$		0			0
$916$	3.59119	+	11.0526i	0.118656	+	0.365187i
$917$	−3.17634	+	9.77577i	−0.104892	+	0.322824i
$918$		0			0
$919$	40.1708	+	29.1858i	1.32511	+	0.962751i	0.999853	+	0.0171266i	$0.00545185\pi$
$919$	40.1708	+	29.1858i	1.32511	+	0.962751i	0.325260	+	0.945625i	$0.394548\pi$
$920$	7.89112	−	24.2864i	0.260162	−	0.800698i
$921$		0			0
$922$	0.370494	−	0.269179i	0.0122016	−	0.00886495i
$923$	−21.0118			−0.691610
$924$		0			0
$925$	−69.8627			−2.29707
$926$	12.1917	−	8.85775i	0.400643	−	0.291084i
$927$		0			0
$928$	−8.70786	+	26.8000i	−0.285849	+	0.879754i
$929$	−0.302391	−	0.219700i	−0.00992114	−	0.00720813i	0.582814	−	0.812606i	$-0.301952\pi$
$929$	−0.302391	−	0.219700i	−0.00992114	−	0.00720813i	−0.592735	+	0.805398i	$0.701952\pi$
$930$		0			0
$931$	−0.539130	+	1.65927i	−0.0176693	+	0.0543804i
$932$	0.0946857	+	0.291413i	0.00310153	+	0.00954554i
$933$		0			0
$934$	−14.0282			−0.459016
$935$	26.7678	+	15.5412i	0.875401	+	0.508253i
$936$		0			0
$937$	37.2687	−	27.0773i	1.21752	−	0.884578i	0.221625	−	0.975132i	$-0.428864\pi$
$937$	37.2687	−	27.0773i	1.21752	−	0.884578i	0.995892	+	0.0905544i	$0.0288639\pi$
$938$	−1.78649	−	5.49827i	−0.0583311	−	0.179525i
$939$		0			0
$940$	66.9918	+	48.6724i	2.18503	+	1.58752i
$941$	−15.6443	−	11.3662i	−0.509988	−	0.370528i	0.302831	−	0.953044i	$-0.402068\pi$
$941$	−15.6443	−	11.3662i	−0.509988	−	0.370528i	−0.812819	+	0.582516i	$0.802068\pi$
$942$		0			0
$943$	−4.91227	−	15.1184i	−0.159965	−	0.492323i
$944$	9.93501	−	7.21821i	0.323357	−	0.234933i
$945$		0			0
$946$	2.56105	−	11.9065i	0.0832669	−	0.387113i
$947$	8.06969			0.262230			0.131115	−	0.991367i	$-0.458144\pi$
$947$	8.06969			0.262230			0.131115	+	0.991367i	$0.458144\pi$
$948$		0			0
$949$	13.1197	+	40.3784i	0.425884	+	1.31074i
$950$	2.33140	−	7.17531i	0.0756406	−	0.232798i
$951$		0			0
$952$	−3.59256	−	2.61015i	−0.116436	−	0.0845955i
$953$	−10.7030	+	32.9406i	−0.346706	+	1.06705i	0.613959	+	0.789338i	$0.289576\pi$
$953$	−10.7030	+	32.9406i	−0.346706	+	1.06705i	−0.960664	+	0.277712i	$0.910424\pi$
$954$		0			0
$955$	17.5104	−	12.7221i	0.566624	−	0.411676i
$956$	−18.5557			−0.600136
$957$		0			0
$958$	−12.5938			−0.406887
$959$	13.8420	−	10.0568i	0.446981	−	0.324750i
$960$		0			0
$961$	−8.01842	+	24.6782i	−0.258659	+	0.796070i
$962$	−7.94178	−	5.77004i	−0.256053	−	0.186034i
$963$		0			0
$964$	1.87553	−	5.77230i	0.0604069	−	0.185913i
$965$	17.2890	+	53.2100i	0.556552	+	1.71289i
$966$		0			0
$967$	8.15074			0.262110			0.131055	−	0.991375i	$-0.458164\pi$
$967$	8.15074			0.262110			0.131055	+	0.991375i	$0.458164\pi$
$968$	19.2638	−	3.99690i	0.619161	−	0.128465i
$969$		0			0
$970$	−10.0785	+	7.32248i	−0.323602	+	0.235111i
$971$	−10.3314	−	31.7967i	−0.331549	−	1.02040i	−0.968397	−	0.249414i	$-0.919762\pi$
$971$	−10.3314	−	31.7967i	−0.331549	−	1.02040i	0.636848	−	0.770990i	$-0.280238\pi$
$972$		0			0
$973$	15.7766	+	11.4624i	0.505774	+	0.367466i
$974$	5.41685	+	3.93557i	0.173567	+	0.126104i
$975$		0			0
$976$	−9.59435	−	29.5284i	−0.307108	−	0.945180i
$977$	−4.43987	+	3.22575i	−0.142044	+	0.103201i	−0.656538	−	0.754293i	$-0.727980\pi$
$977$	−4.43987	+	3.22575i	−0.142044	+	0.103201i	0.514494	+	0.857494i	$0.327980\pi$
$978$		0			0
$979$	4.17892	−	3.74437i	0.133559	−	0.119671i
$980$	6.67413			0.213197
$981$		0			0
$982$	2.25706	+	6.94650i	0.0720255	+	0.221672i
$983$	−4.49323	+	13.8288i	−0.143312	+	0.441069i	−0.996790	−	0.0800600i	$-0.974489\pi$
$983$	−4.49323	+	13.8288i	−0.143312	+	0.441069i	0.853478	+	0.521129i	$0.174489\pi$
$984$		0			0
$985$	−38.1565	−	27.7223i	−1.21577	−	0.883306i
$986$	2.10822	−	6.48844i	0.0671395	−	0.206634i
$987$		0			0
$988$	−6.78610	+	4.93039i	−0.215895	+	0.156857i
$989$	−29.4440			−0.936266
$990$		0			0
$991$	−9.68326			−0.307599			−0.153799	−	0.988102i	$-0.549151\pi$
$991$	−9.68326			−0.307599			−0.153799	+	0.988102i	$0.549151\pi$
$992$	8.83362	−	6.41800i	0.280468	−	0.203772i
$993$		0			0
$994$	−1.13593	+	3.49604i	−0.0360296	+	0.110888i
$995$	2.53742	+	1.84354i	0.0804415	+	0.0584442i
$996$		0			0
$997$	−7.79389	+	23.9871i	−0.246835	+	0.759680i	0.748494	+	0.663141i	$0.230777\pi$
$997$	−7.79389	+	23.9871i	−0.246835	+	0.759680i	−0.995329	+	0.0965389i	$0.969223\pi$
$998$	−4.49438	−	13.8323i	−0.142267	−	0.437854i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	693.2.m.j.190.3		20
3.2	odd	2		231.2.j.g.190.3	yes	20
11.2	odd	10		7623.2.a.cy.1.6		10
11.4	even	5	inner	693.2.m.j.631.3		20
11.9	even	5		7623.2.a.cx.1.5		10
33.2	even	10		2541.2.a.br.1.5		10
33.20	odd	10		2541.2.a.bq.1.6		10
33.26	odd	10		231.2.j.g.169.3	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.j.g.169.3	✓	20	33.26	odd	10
231.2.j.g.190.3	yes	20	3.2	odd	2
693.2.m.j.190.3		20	1.1	even	1	trivial
693.2.m.j.631.3		20	11.4	even	5	inner
2541.2.a.bq.1.6		10	33.20	odd	10
2541.2.a.br.1.5		10	33.2	even	10
7623.2.a.cx.1.5		10	11.9	even	5
7623.2.a.cy.1.6		10	11.2	odd	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:	\( N \)	\(=\)	\( 693 = 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	693.m (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.383242 - 0.278442i) q^{2} +(-0.548689 + 1.68869i) q^{4} +(3.04094 + 2.20937i) q^{5} +(-0.309017 + 0.951057i) q^{7} +(0.552692 + 1.70101i) q^{8} +1.78060 q^{10} +(2.47012 - 2.21326i) q^{11} +(-2.19061 + 1.59157i) q^{13} +(0.146385 + 0.450528i) q^{14} +(-2.18753 - 1.58933i) q^{16} +(2.00865 + 1.45937i) q^{17} +(-0.539130 - 1.65927i) q^{19} +(-5.39949 + 3.92296i) q^{20} +(0.330389 - 1.53600i) q^{22} -3.79843 q^{23} +(2.82092 + 8.68189i) q^{25} +(-0.396374 + 1.21991i) q^{26} +(-1.43649 - 1.04367i) q^{28} +(1.79248 - 5.51669i) q^{29} +(-1.81837 + 1.32112i) q^{31} -4.85799 q^{32} +1.17615 q^{34} +(-3.04094 + 2.20937i) q^{35} +(-2.36494 + 7.27854i) q^{37} +(-0.668627 - 0.485786i) q^{38} +(-2.07747 + 6.39378i) q^{40} +(1.29324 + 3.98017i) q^{41} +7.75162 q^{43} +(2.38219 + 5.38566i) q^{44} +(-1.45572 + 1.05764i) q^{46} +(-3.83399 - 11.7998i) q^{47} +(-0.809017 - 0.587785i) q^{49} +(3.49849 + 2.54180i) q^{50} +(-1.48571 - 4.57254i) q^{52} +(7.15135 - 5.19576i) q^{53} +(12.4014 - 1.27298i) q^{55} -1.78855 q^{56} +(-0.849122 - 2.61333i) q^{58} +(-1.40345 + 4.31938i) q^{59} +(9.28955 + 6.74925i) q^{61} +(-0.329020 + 1.01262i) q^{62} +(2.51327 - 1.82600i) q^{64} -10.1779 q^{65} -12.2041 q^{67} +(-3.56655 + 2.59125i) q^{68} +(-0.550235 + 1.69345i) q^{70} +(6.27787 + 4.56114i) q^{71} +(4.84526 - 14.9122i) q^{73} +(1.12030 + 3.44794i) q^{74} +3.09781 q^{76} +(1.34163 + 3.03316i) q^{77} +(5.70664 - 4.14612i) q^{79} +(-3.14072 - 9.66614i) q^{80} +(1.60387 + 1.16528i) q^{82} +(9.62766 + 6.99490i) q^{83} +(2.88389 + 8.87571i) q^{85} +(2.97075 - 2.15837i) q^{86} +(5.12999 + 2.97845i) q^{88} +1.69179 q^{89} +(-0.836738 - 2.57522i) q^{91} +(2.08416 - 6.41439i) q^{92} +(-4.75491 - 3.45464i) q^{94} +(2.02649 - 6.23689i) q^{95} +(-5.66019 + 4.11237i) q^{97} -0.473713 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 14 q^{4} + 5 q^{5} + 5 q^{7} + 9 q^{8} + 12 q^{10} + q^{11} + 13 q^{13} - 24 q^{16} + q^{17} + 10 q^{19} + 46 q^{20} + 26 q^{22} - 8 q^{25} + 53 q^{26} + 4 q^{28} - 3 q^{29} - 13 q^{31} - 82 q^{32}+ \cdots - 27 q^{97}+O(q^{100}) \) 20 * q - 14 * q^4 + 5 * q^5 + 5 * q^7 + 9 * q^8 + 12 * q^10 + q^11 + 13 * q^13 - 24 * q^16 + q^17 + 10 * q^19 + 46 * q^20 + 26 * q^22 - 8 * q^25 + 53 * q^26 + 4 * q^28 - 3 * q^29 - 13 * q^31 - 82 * q^32 + 42 * q^34 - 5 * q^35 - 32 * q^37 - 16 * q^38 + 20 * q^40 + 3 * q^41 + 12 * q^43 - 25 * q^44 - 13 * q^46 - 20 * q^47 - 5 * q^49 + 83 * q^50 - 80 * q^52 - 3 * q^53 - 28 * q^55 + 6 * q^56 + 2 * q^58 + 9 * q^59 - 15 * q^61 + 37 * q^62 - 49 * q^64 - 58 * q^65 + 76 * q^67 - 51 * q^68 + 3 * q^70 - 37 * q^71 + 27 * q^73 + 32 * q^74 + 4 * q^76 - 6 * q^77 + 5 * q^79 - 137 * q^80 - 55 * q^82 + 42 * q^83 - 48 * q^85 - 3 * q^86 + 151 * q^88 + 18 * q^89 + 7 * q^91 - 39 * q^92 - 35 * q^94 + 96 * q^95 - 27 * q^97

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