LMFDB - Embedded newform 252.2.b.e.55.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,2,Mod(55,252)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(252, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("252.55");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	252.b (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:	$2.01223013094$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.0.2312.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 2x + 4 $ x^4 - x^3 - 2*x + 4
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 84)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			55.1
Root			$-0.780776 - 1.17915i$ of defining polynomial
Character	$\chi$	$=$	252.55
Dual form			252.2.b.e.55.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.780776 - 1.17915i) q^{2} +(-0.780776 + 1.84130i) q^{4} -1.69614i q^{5} +(2.56155 - 0.662153i) q^{7} +(2.78078 - 0.516994i) q^{8} +O(q^{10})$	\(q+(-0.780776 - 1.17915i) q^{2} +(-0.780776 + 1.84130i) q^{4} -1.69614i q^{5} +(2.56155 - 0.662153i) q^{7} +(2.78078 - 0.516994i) q^{8} +(-2.00000 + 1.32431i) q^{10} +3.02045i q^{11} -6.04090i q^{13} +(-2.78078 - 2.50345i) q^{14} +(-2.78078 - 2.87529i) q^{16} -4.34475i q^{17} -1.12311 q^{19} +(3.12311 + 1.32431i) q^{20} +(3.56155 - 2.35829i) q^{22} -3.02045i q^{23} +2.12311 q^{25} +(-7.12311 + 4.71659i) q^{26} +(-0.780776 + 5.23358i) q^{28} +2.00000 q^{29} +(-1.21922 + 5.52390i) q^{32} +(-5.12311 + 3.39228i) q^{34} +(-1.12311 - 4.34475i) q^{35} -7.12311 q^{37} +(0.876894 + 1.32431i) q^{38} +(-0.876894 - 4.71659i) q^{40} +7.73704i q^{41} +8.10887i q^{43} +(-5.56155 - 2.35829i) q^{44} +(-3.56155 + 2.35829i) q^{46} +10.2462 q^{47} +(6.12311 - 3.39228i) q^{49} +(-1.65767 - 2.50345i) q^{50} +(11.1231 + 4.71659i) q^{52} +4.24621 q^{53} +5.12311 q^{55} +(6.78078 - 3.16561i) q^{56} +(-1.56155 - 2.35829i) q^{58} -4.00000 q^{59} +9.43318i q^{61} +(7.46543 - 2.87529i) q^{64} -10.2462 q^{65} -2.06798i q^{67} +(8.00000 + 3.39228i) q^{68} +(-4.24621 + 4.71659i) q^{70} +12.4536i q^{71} +3.39228i q^{73} +(5.56155 + 8.39919i) q^{74} +(0.876894 - 2.06798i) q^{76} +(2.00000 + 7.73704i) q^{77} -4.71659i q^{79} +(-4.87689 + 4.71659i) q^{80} +(9.12311 - 6.04090i) q^{82} -6.24621 q^{83} -7.36932 q^{85} +(9.56155 - 6.33122i) q^{86} +(1.56155 + 8.39919i) q^{88} -7.73704i q^{89} +(-4.00000 - 15.4741i) q^{91} +(5.56155 + 2.35829i) q^{92} +(-8.00000 - 12.0818i) q^{94} +1.90495i q^{95} +8.68951i q^{97} +(-8.78078 - 4.57143i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{2} + q^{4} + 2 q^{7} + 7 q^{8}+O(q^{10}) $ 4 * q + q^2 + q^4 + 2 * q^7 + 7 * q^8	$ 4 q + q^{2} + q^{4} + 2 q^{7} + 7 q^{8} - 8 q^{10} - 7 q^{14} - 7 q^{16} + 12 q^{19} - 4 q^{20} + 6 q^{22} - 8 q^{25} - 12 q^{26} + q^{28} + 8 q^{29} - 9 q^{32} - 4 q^{34} + 12 q^{35} - 12 q^{37} + 20 q^{38} - 20 q^{40} - 14 q^{44} - 6 q^{46} + 8 q^{47} + 8 q^{49} - 19 q^{50} + 28 q^{52} - 16 q^{53} + 4 q^{55} + 23 q^{56} + 2 q^{58} - 16 q^{59} + q^{64} - 8 q^{65} + 32 q^{68} + 16 q^{70} + 14 q^{74} + 20 q^{76} + 8 q^{77} - 36 q^{80} + 20 q^{82} + 8 q^{83} + 20 q^{85} + 30 q^{86} - 2 q^{88} - 16 q^{91} + 14 q^{92} - 32 q^{94} - 31 q^{98}+O(q^{100}) $ 4 * q + q^2 + q^4 + 2 * q^7 + 7 * q^8 - 8 * q^10 - 7 * q^14 - 7 * q^16 + 12 * q^19 - 4 * q^20 + 6 * q^22 - 8 * q^25 - 12 * q^26 + q^28 + 8 * q^29 - 9 * q^32 - 4 * q^34 + 12 * q^35 - 12 * q^37 + 20 * q^38 - 20 * q^40 - 14 * q^44 - 6 * q^46 + 8 * q^47 + 8 * q^49 - 19 * q^50 + 28 * q^52 - 16 * q^53 + 4 * q^55 + 23 * q^56 + 2 * q^58 - 16 * q^59 + q^64 - 8 * q^65 + 32 * q^68 + 16 * q^70 + 14 * q^74 + 20 * q^76 + 8 * q^77 - 36 * q^80 + 20 * q^82 + 8 * q^83 + 20 * q^85 + 30 * q^86 - 2 * q^88 - 16 * q^91 + 14 * q^92 - 32 * q^94 - 31 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$1$	$-1$	$-1$

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 $

$2$	−0.780776	−	1.17915i	−0.552092	−	0.833783i
$2$	−0.780776	−	1.17915i	−0.552092	−	0.833783i
$3$		0			0
$3$		0			0
$4$	−0.780776	+	1.84130i	−0.390388	+	0.920650i
$5$		−	1.69614i		−	0.758537i	−0.925287	−	0.379269i	$-0.876176\pi$
$5$		−	1.69614i		−	0.758537i	0.925287	−	0.379269i	$-0.123824\pi$
$6$		0			0
$7$	2.56155	−	0.662153i	0.968176	−	0.250270i
$7$	2.56155	−	0.662153i	0.968176	−	0.250270i
$8$	2.78078	−	0.516994i	0.983153	−	0.182785i
$9$		0			0
$10$	−2.00000	+	1.32431i	−0.632456	+	0.418783i
$11$			3.02045i			0.910699i	0.890313	+	0.455350i	$0.150486\pi$
$11$			3.02045i			0.910699i	−0.890313	+	0.455350i	$0.849514\pi$
$12$		0			0
$13$		−	6.04090i		−	1.67544i	−0.546098	−	0.837722i	$-0.683887\pi$
$13$		−	6.04090i		−	1.67544i	0.546098	−	0.837722i	$-0.316113\pi$
$14$	−2.78078	−	2.50345i	−0.743194	−	0.669076i
$15$		0			0
$16$	−2.78078	−	2.87529i	−0.695194	−	0.718822i
$17$		−	4.34475i		−	1.05376i	−0.849940	−	0.526879i	$-0.823362\pi$
$17$		−	4.34475i		−	1.05376i	0.849940	−	0.526879i	$-0.176638\pi$
$18$		0			0
$19$	−1.12311			−0.257658			−0.128829	−	0.991667i	$-0.541122\pi$
$19$	−1.12311			−0.257658			−0.128829	+	0.991667i	$0.541122\pi$
$20$	3.12311	+	1.32431i	0.698348	+	0.296124i
$21$		0			0
$22$	3.56155	−	2.35829i	0.759326	−	0.502790i
$23$		−	3.02045i		−	0.629807i	−0.949124	−	0.314903i	$-0.898028\pi$
$23$		−	3.02045i		−	0.629807i	0.949124	−	0.314903i	$-0.101972\pi$
$24$		0			0
$25$	2.12311			0.424621
$26$	−7.12311	+	4.71659i	−1.39696	+	0.924999i
$27$		0			0
$28$	−0.780776	+	5.23358i	−0.147553	+	0.989054i
$29$	2.00000			0.371391			0.185695	−	0.982607i	$-0.440546\pi$
$29$	2.00000			0.371391			0.185695	+	0.982607i	$0.440546\pi$
$30$		0			0
$31$		0			0			−	1.00000i	$-0.5\pi$
$31$		0			0				1.00000i	$0.5\pi$
$32$	−1.21922	+	5.52390i	−0.215530	+	0.976497i
$33$		0			0
$34$	−5.12311	+	3.39228i	−0.878605	+	0.581772i
$35$	−1.12311	−	4.34475i	−0.189839	−	0.734398i
$36$		0			0
$37$	−7.12311			−1.17103			−0.585516	−	0.810661i	$-0.699108\pi$
$37$	−7.12311			−1.17103			−0.585516	+	0.810661i	$0.699108\pi$
$38$	0.876894	+	1.32431i	0.142251	+	0.214831i
$39$		0			0
$40$	−0.876894	−	4.71659i	−0.138649	−	0.745758i
$41$			7.73704i			1.20832i	0.796862	+	0.604161i	$0.206492\pi$
$41$			7.73704i			1.20832i	−0.796862	+	0.604161i	$0.793508\pi$
$42$		0			0
$43$			8.10887i			1.23659i	0.785946	+	0.618296i	$0.212177\pi$
$43$			8.10887i			1.23659i	−0.785946	+	0.618296i	$0.787823\pi$
$44$	−5.56155	−	2.35829i	−0.838436	−	0.355526i
$45$		0			0
$46$	−3.56155	+	2.35829i	−0.525122	+	0.347712i
$47$	10.2462			1.49456			0.747282	−	0.664507i	$-0.231359\pi$
$47$	10.2462			1.49456			0.747282	+	0.664507i	$0.231359\pi$
$48$		0			0
$49$	6.12311	−	3.39228i	0.874729	−	0.484612i
$50$	−1.65767	−	2.50345i	−0.234430	−	0.354042i
$51$		0			0
$52$	11.1231	+	4.71659i	1.54250	+	0.654073i
$53$	4.24621			0.583262			0.291631	−	0.956531i	$-0.405802\pi$
$53$	4.24621			0.583262			0.291631	+	0.956531i	$0.405802\pi$
$54$		0			0
$55$	5.12311			0.690799
$56$	6.78078	−	3.16561i	0.906119	−	0.423022i
$57$		0			0
$58$	−1.56155	−	2.35829i	−0.205042	−	0.309659i
$59$	−4.00000			−0.520756			−0.260378	−	0.965507i	$-0.583847\pi$
$59$	−4.00000			−0.520756			−0.260378	+	0.965507i	$0.583847\pi$
$60$		0			0
$61$			9.43318i			1.20779i	0.797062	+	0.603897i	$0.206386\pi$
$61$			9.43318i			1.20779i	−0.797062	+	0.603897i	$0.793614\pi$
$62$		0			0
$63$		0			0
$64$	7.46543	−	2.87529i	0.933179	−	0.359411i
$65$	−10.2462			−1.27089
$66$		0			0
$67$		−	2.06798i		−	0.252643i	−0.991989	−	0.126322i	$-0.959683\pi$
$67$		−	2.06798i		−	0.252643i	0.991989	−	0.126322i	$-0.0403172\pi$
$68$	8.00000	+	3.39228i	0.970143	+	0.411375i
$69$		0			0
$70$	−4.24621	+	4.71659i	−0.507519	+	0.563740i
$71$			12.4536i			1.47797i	0.673720	+	0.738987i	$0.264695\pi$
$71$			12.4536i			1.47797i	−0.673720	+	0.738987i	$0.735305\pi$
$72$		0			0
$73$			3.39228i			0.397037i	0.980097	+	0.198518i	$0.0636129\pi$
$73$			3.39228i			0.397037i	−0.980097	+	0.198518i	$0.936387\pi$
$74$	5.56155	+	8.39919i	0.646517	+	0.976386i
$75$		0			0
$76$	0.876894	−	2.06798i	0.100587	−	0.237213i
$77$	2.00000	+	7.73704i	0.227921	+	0.881717i
$78$		0			0
$79$		−	4.71659i		−	0.530658i	−0.964158	−	0.265329i	$-0.914519\pi$
$79$		−	4.71659i		−	0.530658i	0.964158	−	0.265329i	$-0.0854805\pi$
$80$	−4.87689	+	4.71659i	−0.545253	+	0.527331i
$81$		0			0
$82$	9.12311	−	6.04090i	1.00748	−	0.667105i
$83$	−6.24621			−0.685611			−0.342805	−	0.939406i	$-0.611377\pi$
$83$	−6.24621			−0.685611			−0.342805	+	0.939406i	$0.611377\pi$
$84$		0			0
$85$	−7.36932			−0.799315
$86$	9.56155	−	6.33122i	1.03105	−	0.682712i
$87$		0			0
$88$	1.56155	+	8.39919i	0.166462	+	0.895357i
$89$		−	7.73704i		−	0.820124i	−0.912058	−	0.410062i	$-0.865507\pi$
$89$		−	7.73704i		−	0.820124i	0.912058	−	0.410062i	$-0.134493\pi$
$90$		0			0
$91$	−4.00000	−	15.4741i	−0.419314	−	1.62212i
$92$	5.56155	+	2.35829i	0.579832	+	0.245869i
$93$		0			0
$94$	−8.00000	−	12.0818i	−0.825137	−	1.24614i
$95$			1.90495i			0.195443i
$96$		0			0
$97$			8.68951i			0.882286i	0.897437	+	0.441143i	$0.145427\pi$
$97$			8.68951i			0.882286i	−0.897437	+	0.441143i	$0.854573\pi$
$98$	−8.78078	−	4.57143i	−0.886992	−	0.461784i
$99$		0			0
$100$	−1.65767	+	3.90928i	−0.165767	+	0.390928i
$101$			6.99337i			0.695866i	0.937519	+	0.347933i	$0.113116\pi$
$101$			6.99337i			0.695866i	−0.937519	+	0.347933i	$0.886884\pi$
$102$		0			0
$103$	−8.00000			−0.788263			−0.394132	−	0.919054i	$-0.628955\pi$
$103$	−8.00000			−0.788263			−0.394132	+	0.919054i	$0.628955\pi$
$104$	−3.12311	−	16.7984i	−0.306246	−	1.64722i
$105$		0			0
$106$	−3.31534	−	5.00691i	−0.322014	−	0.486314i
$107$		−	5.66906i		−	0.548049i	−0.961723	−	0.274024i	$-0.911645\pi$
$107$		−	5.66906i		−	0.548049i	0.961723	−	0.274024i	$-0.0883549\pi$
$108$		0			0
$109$	8.24621			0.789844			0.394922	−	0.918715i	$-0.370772\pi$
$109$	8.24621			0.789844			0.394922	+	0.918715i	$0.370772\pi$
$110$	−4.00000	−	6.04090i	−0.381385	−	0.575977i
$111$		0			0
$112$	−9.02699	−	5.52390i	−0.852970	−	0.521960i
$113$	−12.2462			−1.15203			−0.576013	−	0.817440i	$-0.695392\pi$
$113$	−12.2462			−1.15203			−0.576013	+	0.817440i	$0.695392\pi$
$114$		0			0
$115$	−5.12311			−0.477732
$116$	−1.56155	+	3.68260i	−0.144987	+	0.341921i
$117$		0			0
$118$	3.12311	+	4.71659i	0.287505	+	0.434197i
$119$	−2.87689	−	11.1293i	−0.263724	−	1.02022i
$120$		0			0
$121$	1.87689			0.170627
$122$	11.1231	−	7.36520i	1.00704	−	0.666814i
$123$		0			0
$124$		0			0
$125$		−	12.0818i		−	1.08063i
$126$		0			0
$127$			19.4470i			1.72564i	0.505510	+	0.862821i	$0.331304\pi$
$127$			19.4470i			1.72564i	−0.505510	+	0.862821i	$0.668696\pi$
$128$	−9.21922	−	6.55789i	−0.814872	−	0.579641i
$129$		0			0
$130$	8.00000	+	12.0818i	0.701646	+	1.05964i
$131$	−22.2462			−1.94366			−0.971830	−	0.235682i	$-0.924268\pi$
$131$	−22.2462			−1.94366			−0.971830	+	0.235682i	$0.924268\pi$
$132$		0			0
$133$	−2.87689	+	0.743668i	−0.249458	+	0.0644842i
$134$	−2.43845	+	1.61463i	−0.210650	+	0.139482i
$135$		0			0
$136$	−2.24621	−	12.0818i	−0.192611	−	1.03601i
$137$	16.2462			1.38801			0.694004	−	0.719971i	$-0.255845\pi$
$137$	16.2462			1.38801			0.694004	+	0.719971i	$0.255845\pi$
$138$		0			0
$139$	−12.0000			−1.01783			−0.508913	−	0.860818i	$-0.669953\pi$
$139$	−12.0000			−1.01783			−0.508913	+	0.860818i	$0.669953\pi$
$140$	8.87689	+	1.32431i	0.750235	+	0.111924i
$141$		0			0
$142$	14.6847	−	9.72350i	1.23231	−	0.815978i
$143$	18.2462			1.52582
$144$		0			0
$145$		−	3.39228i		−	0.281714i
$146$	4.00000	−	2.64861i	0.331042	−	0.219201i
$147$		0			0
$148$	5.56155	−	13.1158i	0.457157	−	1.07811i
$149$	10.0000			0.819232			0.409616	−	0.912258i	$-0.365663\pi$
$149$	10.0000			0.819232			0.409616	+	0.912258i	$0.365663\pi$
$150$		0			0
$151$		−	8.10887i		−	0.659891i	−0.944000	−	0.329945i	$-0.892970\pi$
$151$		−	8.10887i		−	0.659891i	0.944000	−	0.329945i	$-0.107030\pi$
$152$	−3.12311	+	0.580639i	−0.253317	+	0.0470960i
$153$		0			0
$154$	7.56155	−	8.39919i	0.609327	−	0.676826i
$155$		0			0
$156$		0			0
$157$		−	4.13595i		−	0.330085i	−0.986286	−	0.165042i	$-0.947224\pi$
$157$		−	4.13595i		−	0.330085i	0.986286	−	0.165042i	$-0.0527761\pi$
$158$	−5.56155	+	3.68260i	−0.442453	+	0.292972i
$159$		0			0
$160$	9.36932	+	2.06798i	0.740710	+	0.163488i
$161$	−2.00000	−	7.73704i	−0.157622	−	0.609764i
$162$		0			0
$163$			11.5012i			0.900840i	0.892817	+	0.450420i	$0.148726\pi$
$163$			11.5012i			0.900840i	−0.892817	+	0.450420i	$0.851274\pi$
$164$	−14.2462	−	6.04090i	−1.11244	−	0.471715i
$165$		0			0
$166$	4.87689	+	7.36520i	0.378520	+	0.571651i
$167$	2.24621			0.173817			0.0869085	−	0.996216i	$-0.472301\pi$
$167$	2.24621			0.173817			0.0869085	+	0.996216i	$0.472301\pi$
$168$		0			0
$169$	−23.4924			−1.80711
$170$	5.75379	+	8.68951i	0.441295	+	0.666455i
$171$		0			0
$172$	−14.9309	−	6.33122i	−1.13847	−	0.482751i
$173$			8.48071i			0.644776i	0.946608	+	0.322388i	$0.104486\pi$
$173$			8.48071i			0.644776i	−0.946608	+	0.322388i	$0.895514\pi$
$174$		0			0
$175$	5.43845	−	1.40582i	0.411108	−	0.106270i
$176$	8.68466	−	8.39919i	0.654631	−	0.633113i
$177$		0			0
$178$	−9.12311	+	6.04090i	−0.683806	+	0.452784i
$179$		−	2.27678i		−	0.170175i	−0.996374	−	0.0850873i	$-0.972883\pi$
$179$		−	2.27678i		−	0.170175i	0.996374	−	0.0850873i	$-0.0271169\pi$
$180$		0			0
$181$			6.04090i			0.449016i	0.974472	+	0.224508i	$0.0720775\pi$
$181$			6.04090i			0.449016i	−0.974472	+	0.224508i	$0.927922\pi$
$182$	−15.1231	+	16.7984i	−1.12100	+	1.24518i
$183$		0			0
$184$	−1.56155	−	8.39919i	−0.115119	−	0.619197i
$185$			12.0818i			0.888271i
$186$		0			0
$187$	13.1231			0.959657
$188$	−8.00000	+	18.8664i	−0.583460	+	1.37597i
$189$		0			0
$190$	2.24621	−	1.48734i	0.162957	−	0.107903i
$191$			9.06134i			0.655656i	0.944737	+	0.327828i	$0.106317\pi$
$191$			9.06134i			0.655656i	−0.944737	+	0.327828i	$0.893683\pi$
$192$		0			0
$193$	9.36932			0.674418			0.337209	−	0.941430i	$-0.390517\pi$
$193$	9.36932			0.674418			0.337209	+	0.941430i	$0.390517\pi$
$194$	10.2462	−	6.78456i	0.735635	−	0.487103i
$195$		0			0
$196$	1.46543	+	13.9231i	0.104674	+	0.994507i
$197$	−0.246211			−0.0175418			−0.00877091	−	0.999962i	$-0.502792\pi$
$197$	−0.246211			−0.0175418			−0.00877091	+	0.999962i	$0.502792\pi$
$198$		0			0
$199$	5.12311			0.363167			0.181584	−	0.983375i	$-0.441878\pi$
$199$	5.12311			0.363167			0.181584	+	0.983375i	$0.441878\pi$
$200$	5.90388	−	1.09763i	0.417468	−	0.0776143i
$201$		0			0
$202$	8.24621	−	5.46026i	0.580201	−	0.384182i
$203$	5.12311	−	1.32431i	0.359572	−	0.0929481i
$204$		0			0
$205$	13.1231			0.916557
$206$	6.24621	+	9.43318i	0.435194	+	0.657241i
$207$		0			0
$208$	−17.3693	+	16.7984i	−1.20435	+	1.16476i
$209$		−	3.39228i		−	0.234649i
$210$		0			0
$211$		−	3.97292i		−	0.273507i	−0.990605	−	0.136754i	$-0.956333\pi$
$211$		−	3.97292i		−	0.273507i	0.990605	−	0.136754i	$-0.0436668\pi$
$212$	−3.31534	+	7.81855i	−0.227699	+	0.536980i
$213$		0			0
$214$	−6.68466	+	4.42627i	−0.456954	+	0.302574i
$215$	13.7538			0.938001
$216$		0			0
$217$		0			0
$218$	−6.43845	−	9.72350i	−0.436067	−	0.658558i
$219$		0			0
$220$	−4.00000	+	9.43318i	−0.269680	+	0.635985i
$221$	−26.2462			−1.76551
$222$		0			0
$223$	18.8769			1.26409			0.632045	−	0.774932i	$-0.282216\pi$
$223$	18.8769			1.26409			0.632045	+	0.774932i	$0.282216\pi$
$224$	0.534565	+	14.9571i	0.0357171	+	0.999362i
$225$		0			0
$226$	9.56155	+	14.4401i	0.636025	+	0.960540i
$227$	−16.4924			−1.09464			−0.547320	−	0.836923i	$-0.684352\pi$
$227$	−16.4924			−1.09464			−0.547320	+	0.836923i	$0.684352\pi$
$228$		0			0
$229$		−	18.1227i		−	1.19758i	−0.800906	−	0.598790i	$-0.795648\pi$
$229$		−	18.1227i		−	1.19758i	0.800906	−	0.598790i	$-0.204352\pi$
$230$	4.00000	+	6.04090i	0.263752	+	0.398325i
$231$		0			0
$232$	5.56155	−	1.03399i	0.365134	−	0.0678846i
$233$	10.4924			0.687381			0.343691	−	0.939083i	$-0.388323\pi$
$233$	10.4924			0.687381			0.343691	+	0.939083i	$0.388323\pi$
$234$		0			0
$235$		−	17.3790i		−	1.13368i
$236$	3.12311	−	7.36520i	0.203297	−	0.479434i
$237$		0			0
$238$	−10.8769	+	12.0818i	−0.705044	+	0.783146i
$239$			2.27678i			0.147273i	0.997285	+	0.0736363i	$0.0234604\pi$
$239$			2.27678i			0.147273i	−0.997285	+	0.0736363i	$0.976540\pi$
$240$		0			0
$241$		−	1.90495i		−	0.122708i	−0.998116	−	0.0613542i	$-0.980458\pi$
$241$		−	1.90495i		−	0.122708i	0.998116	−	0.0613542i	$-0.0195419\pi$
$242$	−1.46543	−	2.21313i	−0.0942017	−	0.142266i
$243$		0			0
$244$	−17.3693	−	7.36520i	−1.11196	−	0.471509i
$245$	−5.75379	−	10.3857i	−0.367596	−	0.663515i
$246$		0			0
$247$			6.78456i			0.431691i
$248$		0			0
$249$		0			0
$250$	−14.2462	+	9.43318i	−0.901010	+	0.596607i
$251$	22.2462			1.40417			0.702084	−	0.712094i	$-0.252253\pi$
$251$	22.2462			1.40417			0.702084	+	0.712094i	$0.252253\pi$
$252$		0			0
$253$	9.12311			0.573565
$254$	22.9309	−	15.1838i	1.43881	−	0.952713i
$255$		0			0
$256$	−0.534565	+	15.9911i	−0.0334103	+	0.999442i
$257$			19.8188i			1.23626i	0.786074	+	0.618132i	$0.212110\pi$
$257$			19.8188i			1.23626i	−0.786074	+	0.618132i	$0.787890\pi$
$258$		0			0
$259$	−18.2462	+	4.71659i	−1.13376	+	0.293075i
$260$	8.00000	−	18.8664i	0.496139	−	1.17004i
$261$		0			0
$262$	17.3693	+	26.2316i	1.07308	+	1.62059i
$263$		−	4.92539i		−	0.303713i	−0.988403	−	0.151856i	$-0.951475\pi$
$263$		−	4.92539i		−	0.303713i	0.988403	−	0.151856i	$-0.0485251\pi$
$264$		0			0
$265$		−	7.20217i		−	0.442426i
$266$	3.12311	+	2.81164i	0.191490	+	0.172393i
$267$		0			0
$268$	3.80776	+	1.61463i	0.232596	+	0.0986290i
$269$		−	22.4674i		−	1.36986i	−0.728607	−	0.684932i	$-0.759832\pi$
$269$		−	22.4674i		−	1.36986i	0.728607	−	0.684932i	$-0.240168\pi$
$270$		0			0
$271$	4.49242			0.272895			0.136448	−	0.990647i	$-0.456431\pi$
$271$	4.49242			0.272895			0.136448	+	0.990647i	$0.456431\pi$
$272$	−12.4924	+	12.0818i	−0.757464	+	0.732566i
$273$		0			0
$274$	−12.6847	−	19.1567i	−0.766308	−	1.15730i
$275$			6.41273i			0.386702i
$276$		0			0
$277$	3.12311			0.187649			0.0938246	−	0.995589i	$-0.470091\pi$
$277$	3.12311			0.187649			0.0938246	+	0.995589i	$0.470091\pi$
$278$	9.36932	+	14.1498i	0.561934	+	0.848647i
$279$		0			0
$280$	−5.36932	−	11.5012i	−0.320878	−	0.687325i
$281$	0.246211			0.0146877			0.00734387	−	0.999973i	$-0.497662\pi$
$281$	0.246211			0.0146877			0.00734387	+	0.999973i	$0.497662\pi$
$282$		0			0
$283$	17.1231			1.01786			0.508931	−	0.860807i	$-0.330041\pi$
$283$	17.1231			1.01786			0.508931	+	0.860807i	$0.330041\pi$
$284$	−22.9309	−	9.72350i	−1.36070	−	0.576983i
$285$		0			0
$286$	−14.2462	−	21.5150i	−0.842396	−	1.27221i
$287$	5.12311	+	19.8188i	0.302407	+	1.16987i
$288$		0			0
$289$	−1.87689			−0.110406
$290$	−4.00000	+	2.64861i	−0.234888	+	0.155532i
$291$		0			0
$292$	−6.24621	−	2.64861i	−0.365532	−	0.154998i
$293$			6.99337i			0.408557i	0.978913	+	0.204278i	$0.0654848\pi$
$293$			6.99337i			0.408557i	−0.978913	+	0.204278i	$0.934515\pi$
$294$		0			0
$295$			6.78456i			0.395013i
$296$	−19.8078	+	3.68260i	−1.15130	+	0.214047i
$297$		0			0
$298$	−7.80776	−	11.7915i	−0.452292	−	0.683062i
$299$	−18.2462			−1.05521
$300$		0			0
$301$	5.36932	+	20.7713i	0.309482	+	1.19724i
$302$	−9.56155	+	6.33122i	−0.550206	+	0.364320i
$303$		0			0
$304$	3.12311	+	3.22925i	0.179122	+	0.185210i
$305$	16.0000			0.916157
$306$		0			0
$307$	−21.6155			−1.23366			−0.616832	−	0.787095i	$-0.711584\pi$
$307$	−21.6155			−1.23366			−0.616832	+	0.787095i	$0.711584\pi$
$308$	−15.8078	−	2.35829i	−0.900731	−	0.134376i
$309$		0			0
$310$		0			0
$311$	−8.00000			−0.453638			−0.226819	−	0.973937i	$-0.572833\pi$
$311$	−8.00000			−0.453638			−0.226819	+	0.973937i	$0.572833\pi$
$312$		0			0
$313$		−	25.6509i		−	1.44988i	−0.688814	−	0.724938i	$-0.741868\pi$
$313$		−	25.6509i		−	1.44988i	0.688814	−	0.724938i	$-0.258132\pi$
$314$	−4.87689	+	3.22925i	−0.275219	+	0.182237i
$315$		0			0
$316$	8.68466	+	3.68260i	0.488550	+	0.207163i
$317$	−18.4924			−1.03864			−0.519319	−	0.854580i	$-0.673814\pi$
$317$	−18.4924			−1.03864			−0.519319	+	0.854580i	$0.673814\pi$
$318$		0			0
$319$			6.04090i			0.338225i
$320$	−4.87689	−	12.6624i	−0.272627	−	0.707851i
$321$		0			0
$322$	−7.56155	+	8.39919i	−0.421389	+	0.468069i
$323$			4.87962i			0.271509i
$324$		0			0
$325$		−	12.8255i		−	0.711429i
$326$	13.5616	−	8.97983i	0.751105	−	0.497347i
$327$		0			0
$328$	4.00000	+	21.5150i	0.220863	+	1.18797i
$329$	26.2462	−	6.78456i	1.44700	−	0.374045i
$330$		0			0
$331$		−	5.46026i		−	0.300123i	−0.988677	−	0.150061i	$-0.952053\pi$
$331$		−	5.46026i		−	0.300123i	0.988677	−	0.150061i	$-0.0479472\pi$
$332$	4.87689	−	11.5012i	0.267654	−	0.631208i
$333$		0			0
$334$	−1.75379	−	2.64861i	−0.0959631	−	0.144926i
$335$	−3.50758			−0.191639
$336$		0			0
$337$	−8.24621			−0.449200			−0.224600	−	0.974451i	$-0.572108\pi$
$337$	−8.24621			−0.449200			−0.224600	+	0.974451i	$0.572108\pi$
$338$	18.3423	+	27.7010i	0.997691	+	1.50674i
$339$		0			0
$340$	5.75379	−	13.5691i	0.312043	−	0.735889i
$341$		0			0
$342$		0			0
$343$	13.4384	−	12.7439i	0.725608	−	0.688108i
$344$	4.19224	+	22.5490i	0.226030	+	1.21576i
$345$		0			0
$346$	10.0000	−	6.62153i	0.537603	−	0.355976i
$347$		−	34.7123i		−	1.86345i	−0.363162	−	0.931726i	$-0.618303\pi$
$347$		−	34.7123i		−	1.86345i	0.363162	−	0.931726i	$-0.381697\pi$
$348$		0			0
$349$		−	4.13595i		−	0.221392i	−0.993854	−	0.110696i	$-0.964692\pi$
$349$		−	4.13595i		−	0.221392i	0.993854	−	0.110696i	$-0.0353080\pi$
$350$	−5.90388	−	5.31510i	−0.315576	−	0.284104i
$351$		0			0
$352$	−16.6847	−	3.68260i	−0.889295	−	0.196283i
$353$		−	6.24970i		−	0.332638i	−0.986072	−	0.166319i	$-0.946812\pi$
$353$		−	6.24970i		−	0.332638i	0.986072	−	0.166319i	$-0.0531881\pi$
$354$		0			0
$355$	21.1231			1.12110
$356$	14.2462	+	6.04090i	0.755048	+	0.320167i
$357$		0			0
$358$	−2.68466	+	1.77766i	−0.141889	+	0.0939520i
$359$		−	1.11550i		−	0.0588740i	−0.999567	−	0.0294370i	$-0.990629\pi$
$359$		−	1.11550i		−	0.0588740i	0.999567	−	0.0294370i	$-0.00937144\pi$
$360$		0			0
$361$	−17.7386			−0.933612
$362$	7.12311	−	4.71659i	0.374382	−	0.247898i
$363$		0			0
$364$	31.6155	+	4.71659i	1.65710	+	0.247216i
$365$	5.75379			0.301167
$366$		0			0
$367$	−8.63068			−0.450518			−0.225259	−	0.974299i	$-0.572323\pi$
$367$	−8.63068			−0.450518			−0.225259	+	0.974299i	$0.572323\pi$
$368$	−8.68466	+	8.39919i	−0.452719	+	0.437838i
$369$		0			0
$370$	14.2462	−	9.43318i	0.740625	−	0.490408i
$371$	10.8769	−	2.81164i	0.564700	−	0.145973i
$372$		0			0
$373$	−10.0000			−0.517780			−0.258890	−	0.965907i	$-0.583357\pi$
$373$	−10.0000			−0.517780			−0.258890	+	0.965907i	$0.583357\pi$
$374$	−10.2462	−	15.4741i	−0.529819	−	0.800145i
$375$		0			0
$376$	28.4924	−	5.29723i	1.46938	−	0.273184i
$377$		−	12.0818i		−	0.622244i
$378$		0			0
$379$			18.7033i			0.960725i	0.877070	+	0.480363i	$0.159495\pi$
$379$			18.7033i			0.960725i	−0.877070	+	0.480363i	$0.840505\pi$
$380$	−3.50758	−	1.48734i	−0.179935	−	0.0762988i
$381$		0			0
$382$	10.6847	−	7.07488i	0.546675	−	0.361983i
$383$	26.2462			1.34112			0.670559	−	0.741856i	$-0.266054\pi$
$383$	26.2462			1.34112			0.670559	+	0.741856i	$0.266054\pi$
$384$		0			0
$385$	13.1231	−	3.39228i	0.668815	−	0.172887i
$386$	−7.31534	−	11.0478i	−0.372341	−	0.562318i
$387$		0			0
$388$	−16.0000	−	6.78456i	−0.812277	−	0.344434i
$389$	−0.246211			−0.0124834			−0.00624170	−	0.999981i	$-0.501987\pi$
$389$	−0.246211			−0.0124834			−0.00624170	+	0.999981i	$0.501987\pi$
$390$		0			0
$391$	−13.1231			−0.663664
$392$	15.2732	−	12.5988i	0.771413	−	0.636335i
$393$		0			0
$394$	0.192236	+	0.290319i	0.00968471	+	0.0146261i
$395$	−8.00000			−0.402524
$396$		0			0
$397$			16.2177i			0.813945i	0.913440	+	0.406973i	$0.133416\pi$
$397$			16.2177i			0.813945i	−0.913440	+	0.406973i	$0.866584\pi$
$398$	−4.00000	−	6.04090i	−0.200502	−	0.302803i
$399$		0			0
$400$	−5.90388	−	6.10454i	−0.295194	−	0.305227i
$401$	8.24621			0.411796			0.205898	−	0.978573i	$-0.433988\pi$
$401$	8.24621			0.411796			0.205898	+	0.978573i	$0.433988\pi$
$402$		0			0
$403$		0			0
$404$	−12.8769	−	5.46026i	−0.640649	−	0.271658i
$405$		0			0
$406$	−5.56155	−	5.00691i	−0.276015	−	0.248489i
$407$		−	21.5150i		−	1.06646i
$408$		0			0
$409$			27.5559i			1.36255i	0.732028	+	0.681275i	$0.238574\pi$
$409$			27.5559i			1.36255i	−0.732028	+	0.681275i	$0.761426\pi$
$410$	−10.2462	−	15.4741i	−0.506024	−	0.764210i
$411$		0			0
$412$	6.24621	−	14.7304i	0.307729	−	0.725715i
$413$	−10.2462	+	2.64861i	−0.504183	+	0.130330i
$414$		0			0
$415$			10.5945i			0.520061i
$416$	33.3693	+	7.36520i	1.63607	+	0.361109i
$417$		0			0
$418$	−4.00000	+	2.64861i	−0.195646	+	0.129548i
$419$	−16.4924			−0.805708			−0.402854	−	0.915264i	$-0.631982\pi$
$419$	−16.4924			−0.805708			−0.402854	+	0.915264i	$0.631982\pi$
$420$		0			0
$421$	19.1231			0.932003			0.466002	−	0.884784i	$-0.345694\pi$
$421$	19.1231			0.932003			0.466002	+	0.884784i	$0.345694\pi$
$422$	−4.68466	+	3.10196i	−0.228046	+	0.151001i
$423$		0			0
$424$	11.8078	−	2.19526i	0.573436	−	0.106611i
$425$		−	9.22437i		−	0.447448i
$426$		0			0
$427$	6.24621	+	24.1636i	0.302275	+	1.16936i
$428$	10.4384	+	4.42627i	0.504561	+	0.213952i
$429$		0			0
$430$	−10.7386	−	16.2177i	−0.517863	−	0.782089i
$431$		−	15.1022i		−	0.727449i	−0.931507	−	0.363725i	$-0.881505\pi$
$431$		−	15.1022i		−	0.727449i	0.931507	−	0.363725i	$-0.118495\pi$
$432$		0			0
$433$		−	6.78456i		−	0.326045i	−0.986622	−	0.163023i	$-0.947876\pi$
$433$		−	6.78456i		−	0.326045i	0.986622	−	0.163023i	$-0.0521244\pi$
$434$		0			0
$435$		0			0
$436$	−6.43845	+	15.1838i	−0.308346	+	0.727170i
$437$			3.39228i			0.162275i
$438$		0			0
$439$	−31.3693			−1.49718			−0.748588	−	0.663036i	$-0.769268\pi$
$439$	−31.3693			−1.49718			−0.748588	+	0.663036i	$0.769268\pi$
$440$	14.2462	−	2.64861i	0.679161	−	0.126268i
$441$		0			0
$442$	20.4924	+	30.9481i	0.974725	+	1.47205i
$443$			35.8735i			1.70440i	0.523213	+	0.852202i	$0.324733\pi$
$443$			35.8735i			1.70440i	−0.523213	+	0.852202i	$0.675267\pi$
$444$		0			0
$445$	−13.1231			−0.622095
$446$	−14.7386	−	22.2586i	−0.697895	−	1.05398i
$447$		0			0
$448$	17.2192	−	12.3085i	0.813532	−	0.581520i
$449$	−28.2462			−1.33302			−0.666511	−	0.745496i	$-0.732213\pi$
$449$	−28.2462			−1.33302			−0.666511	+	0.745496i	$0.732213\pi$
$450$		0			0
$451$	−23.3693			−1.10042
$452$	9.56155	−	22.5490i	0.449738	−	1.06061i
$453$		0			0
$454$	12.8769	+	19.4470i	0.604343	+	0.912693i
$455$	−26.2462	+	6.78456i	−1.23044	+	0.318065i
$456$		0			0
$457$	−16.2462			−0.759966			−0.379983	−	0.924994i	$-0.624070\pi$
$457$	−16.2462			−0.759966			−0.379983	+	0.924994i	$0.624070\pi$
$458$	−21.3693	+	14.1498i	−0.998523	+	0.661175i
$459$		0			0
$460$	4.00000	−	9.43318i	0.186501	−	0.439824i
$461$			17.1702i			0.799697i	0.916581	+	0.399848i	$0.130937\pi$
$461$			17.1702i			0.799697i	−0.916581	+	0.399848i	$0.869063\pi$
$462$		0			0
$463$		−	39.4746i		−	1.83454i	−0.398264	−	0.917271i	$-0.630387\pi$
$463$		−	39.4746i		−	1.83454i	0.398264	−	0.917271i	$-0.369613\pi$
$464$	−5.56155	−	5.75058i	−0.258189	−	0.266964i
$465$		0			0
$466$	−8.19224	−	12.3721i	−0.379498	−	0.573127i
$467$	−17.7538			−0.821547			−0.410774	−	0.911737i	$-0.634741\pi$
$467$	−17.7538			−0.821547			−0.410774	+	0.911737i	$0.634741\pi$
$468$		0			0
$469$	−1.36932	−	5.29723i	−0.0632292	−	0.244603i
$470$	−20.4924	+	13.5691i	−0.945245	+	0.625897i
$471$		0			0
$472$	−11.1231	+	2.06798i	−0.511982	+	0.0951863i
$473$	−24.4924			−1.12616
$474$		0			0
$475$	−2.38447			−0.109407
$476$	22.7386	+	3.39228i	1.04222	+	0.155485i
$477$		0			0
$478$	2.68466	−	1.77766i	0.122793	−	0.0813081i
$479$	20.4924			0.936323			0.468161	−	0.883643i	$-0.344917\pi$
$479$	20.4924			0.936323			0.468161	+	0.883643i	$0.344917\pi$
$480$		0			0
$481$			43.0299i			1.96200i
$482$	−2.24621	+	1.48734i	−0.102312	+	0.0677463i
$483$		0			0
$484$	−1.46543	+	3.45593i	−0.0666107	+	0.157088i
$485$	14.7386			0.669247
$486$		0			0
$487$		−	32.2725i		−	1.46240i	−0.682161	−	0.731202i	$-0.738960\pi$
$487$		−	32.2725i		−	1.46240i	0.682161	−	0.731202i	$-0.261040\pi$
$488$	4.87689	+	26.2316i	0.220767	+	1.18745i
$489$		0			0
$490$	−7.75379	+	14.8934i	−0.350280	+	0.672817i
$491$			11.7100i			0.528463i	0.964459	+	0.264231i	$0.0851183\pi$
$491$			11.7100i			0.528463i	−0.964459	+	0.264231i	$0.914882\pi$
$492$		0			0
$493$		−	8.68951i		−	0.391356i
$494$	8.00000	−	5.29723i	0.359937	−	0.238334i
$495$		0			0
$496$		0			0
$497$	8.24621	+	31.9006i	0.369893	+	1.43094i
$498$		0			0
$499$		−	17.5420i		−	0.785290i	−0.919690	−	0.392645i	$-0.871560\pi$
$499$		−	17.5420i		−	0.785290i	0.919690	−	0.392645i	$-0.128440\pi$
$500$	22.2462	+	9.43318i	0.994881	+	0.421865i
$501$		0			0
$502$	−17.3693	−	26.2316i	−0.775231	−	1.17077i
$503$	−22.7386			−1.01387			−0.506933	−	0.861986i	$-0.669221\pi$
$503$	−22.7386			−1.01387			−0.506933	+	0.861986i	$0.669221\pi$
$504$		0			0
$505$	11.8617			0.527840
$506$	−7.12311	−	10.7575i	−0.316661	−	0.478229i
$507$		0			0
$508$	−35.8078	−	15.1838i	−1.58871	−	0.673670i
$509$			1.69614i			0.0751801i	0.999293	+	0.0375901i	$0.0119681\pi$
$509$			1.69614i			0.0751801i	−0.999293	+	0.0375901i	$0.988032\pi$
$510$		0			0
$511$	2.24621	+	8.68951i	0.0993665	+	0.384401i
$512$	19.2732	−	11.8551i	0.851763	−	0.523927i
$513$		0			0
$514$	23.3693	−	15.4741i	1.03078	−	0.682532i
$515$			13.5691i			0.597927i
$516$		0			0
$517$			30.9481i			1.36110i
$518$	19.8078	+	17.8324i	0.870303	+	0.783509i
$519$		0			0
$520$	−28.4924	+	5.29723i	−1.24948	+	0.232299i
$521$			33.8056i			1.48105i	0.672030	+	0.740524i	$0.265423\pi$
$521$			33.8056i			1.48105i	−0.672030	+	0.740524i	$0.734577\pi$
$522$		0			0
$523$	−0.492423			−0.0215321			−0.0107661	−	0.999942i	$-0.503427\pi$
$523$	−0.492423			−0.0215321			−0.0107661	+	0.999942i	$0.503427\pi$
$524$	17.3693	−	40.9620i	0.758782	−	1.78943i
$525$		0			0
$526$	−5.80776	+	3.84563i	−0.253231	+	0.167677i
$527$		0			0
$528$		0			0
$529$	13.8769			0.603343
$530$	−8.49242	+	5.62329i	−0.368887	+	0.244260i
$531$		0			0
$532$	0.876894	−	5.87787i	0.0380182	−	0.254838i
$533$	46.7386			2.02447
$534$		0			0
$535$	−9.61553			−0.415716
$536$	−1.06913	−	5.75058i	−0.0461794	−	0.248387i
$537$		0			0
$538$	−26.4924	+	17.5420i	−1.14217	+	0.756291i
$539$	10.2462	+	18.4945i	0.441336	+	0.796615i
$540$		0			0
$541$	11.1231			0.478220			0.239110	−	0.970993i	$-0.423144\pi$
$541$	11.1231			0.478220			0.239110	+	0.970993i	$0.423144\pi$
$542$	−3.50758	−	5.29723i	−0.150663	−	0.227535i
$543$		0			0
$544$	24.0000	+	5.29723i	1.02899	+	0.227117i
$545$		−	13.9867i		−	0.599126i
$546$		0			0
$547$		−	33.0161i		−	1.41167i	−0.708378	−	0.705834i	$-0.750573\pi$
$547$		−	33.0161i		−	1.41167i	0.708378	−	0.705834i	$-0.249427\pi$
$548$	−12.6847	+	29.9142i	−0.541862	+	1.27787i
$549$		0			0
$550$	7.56155	−	5.00691i	0.322426	−	0.213495i
$551$	−2.24621			−0.0956918
$552$		0			0
$553$	−3.12311	−	12.0818i	−0.132808	−	0.513770i
$554$	−2.43845	−	3.68260i	−0.103600	−	0.156459i
$555$		0			0
$556$	9.36932	−	22.0956i	0.397348	−	0.937063i
$557$	−14.0000			−0.593199			−0.296600	−	0.955002i	$-0.595853\pi$
$557$	−14.0000			−0.593199			−0.296600	+	0.955002i	$0.595853\pi$
$558$		0			0
$559$	48.9848			2.07184
$560$	−9.36932	+	15.3110i	−0.395926	+	0.647010i
$561$		0			0
$562$	−0.192236	−	0.290319i	−0.00810898	−	0.0122464i
$563$	14.2462			0.600406			0.300203	−	0.953875i	$-0.402946\pi$
$563$	14.2462			0.600406			0.300203	+	0.953875i	$0.402946\pi$
$564$		0			0
$565$			20.7713i			0.873855i
$566$	−13.3693	−	20.1907i	−0.561954	−	0.848677i
$567$		0			0
$568$	6.43845	+	34.6307i	0.270151	+	1.45307i
$569$	−34.9848			−1.46664			−0.733320	−	0.679883i	$-0.762031\pi$
$569$	−34.9848			−1.46664			−0.733320	+	0.679883i	$0.762031\pi$
$570$		0			0
$571$			40.9620i			1.71420i	0.515146	+	0.857102i	$0.327738\pi$
$571$			40.9620i			1.71420i	−0.515146	+	0.857102i	$0.672262\pi$
$572$	−14.2462	+	33.5968i	−0.595664	+	1.40475i
$573$		0			0
$574$	19.3693	−	21.5150i	0.808460	−	0.898017i
$575$		−	6.41273i		−	0.267429i
$576$		0			0
$577$		0			0		1.00000			$0$
$577$		0			0		−1.00000			$\pi$
$578$	1.46543	+	2.21313i	0.0609541	+	0.0920543i
$579$		0			0
$580$	6.24621	+	2.64861i	0.259360	+	0.109978i
$581$	−16.0000	+	4.13595i	−0.663792	+	0.171588i
$582$		0			0
$583$			12.8255i			0.531176i
$584$	1.75379	+	9.43318i	0.0725723	+	0.390348i
$585$		0			0
$586$	8.24621	−	5.46026i	0.340648	−	0.225561i
$587$	38.2462			1.57859			0.789295	−	0.614014i	$-0.210446\pi$
$587$	38.2462			1.57859			0.789295	+	0.614014i	$0.210446\pi$
$588$		0			0
$589$		0			0
$590$	8.00000	−	5.29723i	0.329355	−	0.218083i
$591$		0			0
$592$	19.8078	+	20.4810i	0.814094	+	0.841763i
$593$		−	21.7238i		−	0.892088i	−0.895011	−	0.446044i	$-0.852832\pi$
$593$		−	21.7238i		−	0.892088i	0.895011	−	0.446044i	$-0.147168\pi$
$594$		0			0
$595$	−18.8769	+	4.87962i	−0.773877	+	0.200045i
$596$	−7.80776	+	18.4130i	−0.319818	+	0.754226i
$597$		0			0
$598$	14.2462	+	21.5150i	0.582571	+	0.879813i
$599$			19.2382i			0.786051i	0.919528	+	0.393026i	$0.128572\pi$
$599$			19.2382i			0.786051i	−0.919528	+	0.393026i	$0.871428\pi$
$600$		0			0
$601$			5.29723i			0.216078i	0.994147	+	0.108039i	$0.0344572\pi$
$601$			5.29723i			0.216078i	−0.994147	+	0.108039i	$0.965543\pi$
$602$	20.3002	−	22.5490i	0.827374	−	0.919027i
$603$		0			0
$604$	14.9309	+	6.33122i	0.607528	+	0.257613i
$605$		−	3.18348i		−	0.129427i
$606$		0			0
$607$	−33.6155			−1.36441			−0.682206	−	0.731160i	$-0.738979\pi$
$607$	−33.6155			−1.36441			−0.682206	+	0.731160i	$0.738979\pi$
$608$	1.36932	−	6.20393i	0.0555331	−	0.251602i
$609$		0			0
$610$	−12.4924	−	18.8664i	−0.505803	−	0.763876i
$611$		−	61.8963i		−	2.50406i
$612$		0			0
$613$	−40.7386			−1.64542			−0.822709	−	0.568463i	$-0.807538\pi$
$613$	−40.7386			−1.64542			−0.822709	+	0.568463i	$0.807538\pi$
$614$	16.8769	+	25.4879i	0.681096	+	1.02861i
$615$		0			0
$616$	9.56155	+	20.4810i	0.385246	+	0.825202i
$617$	−15.7538			−0.634224			−0.317112	−	0.948388i	$-0.602713\pi$
$617$	−15.7538			−0.634224			−0.317112	+	0.948388i	$0.602713\pi$
$618$		0			0
$619$	20.0000			0.803868			0.401934	−	0.915669i	$-0.368338\pi$
$619$	20.0000			0.803868			0.401934	+	0.915669i	$0.368338\pi$
$620$		0			0
$621$		0			0
$622$	6.24621	+	9.43318i	0.250450	+	0.378236i
$623$	−5.12311	−	19.8188i	−0.205253	−	0.794025i
$624$		0			0
$625$	−9.87689			−0.395076
$626$	−30.2462	+	20.0276i	−1.20888	+	0.800465i
$627$		0			0
$628$	7.61553	+	3.22925i	0.303893	+	0.128861i
$629$			30.9481i			1.23398i
$630$		0			0
$631$			17.9597i			0.714963i	0.933920	+	0.357481i	$0.116364\pi$
$631$			17.9597i			0.714963i	−0.933920	+	0.357481i	$0.883636\pi$
$632$	−2.43845	−	13.1158i	−0.0969962	−	0.521718i
$633$		0			0
$634$	14.4384	+	21.8053i	0.573424	+	0.865999i
$635$	32.9848			1.30896
$636$		0			0
$637$	−20.4924	−	36.9890i	−0.811939	−	1.46556i
$638$	7.12311	−	4.71659i	0.282006	−	0.186732i
$639$		0			0
$640$	−11.1231	+	15.6371i	−0.439679	+	0.618111i
$641$	9.50758			0.375527			0.187763	−	0.982214i	$-0.439876\pi$
$641$	9.50758			0.375527			0.187763	+	0.982214i	$0.439876\pi$
$642$		0			0
$643$	29.6155			1.16792			0.583961	−	0.811782i	$-0.301502\pi$
$643$	29.6155			1.16792			0.583961	+	0.811782i	$0.301502\pi$
$644$	15.8078	+	2.35829i	0.622913	+	0.0929298i
$645$		0			0
$646$	5.75379	−	3.80989i	0.226380	−	0.149898i
$647$	−32.9848			−1.29677			−0.648384	−	0.761313i	$-0.724555\pi$
$647$	−32.9848			−1.29677			−0.648384	+	0.761313i	$0.724555\pi$
$648$		0			0
$649$		−	12.0818i		−	0.474252i
$650$	−15.1231	+	10.0138i	−0.593177	+	0.392774i
$651$		0			0
$652$	−21.1771	−	8.97983i	−0.829358	−	0.351677i
$653$	32.7386			1.28116			0.640581	−	0.767891i	$-0.278694\pi$
$653$	32.7386			1.28116			0.640581	+	0.767891i	$0.278694\pi$
$654$		0			0
$655$			37.7327i			1.47434i
$656$	22.2462	−	21.5150i	0.868569	−	0.840018i
$657$		0			0
$658$	−28.4924	−	25.6509i	−1.11075	−	0.999977i
$659$		−	38.1045i		−	1.48434i	−0.670210	−	0.742171i	$-0.733796\pi$
$659$		−	38.1045i		−	1.48434i	0.670210	−	0.742171i	$-0.266204\pi$
$660$		0			0
$661$		−	2.64861i		−	0.103019i	−0.998673	−	0.0515096i	$-0.983597\pi$
$661$		−	2.64861i		−	0.103019i	0.998673	−	0.0515096i	$-0.0164033\pi$
$662$	−6.43845	+	4.26324i	−0.250237	+	0.165696i
$663$		0			0
$664$	−17.3693	+	3.22925i	−0.674060	+	0.125319i
$665$	1.26137	+	4.87962i	0.0489137	+	0.189223i
$666$		0			0
$667$		−	6.04090i		−	0.233904i
$668$	−1.75379	+	4.13595i	−0.0678561	+	0.160025i
$669$		0			0
$670$	2.73863	+	4.13595i	0.105803	+	0.159786i
$671$	−28.4924			−1.09994
$672$		0			0
$673$	29.8617			1.15109			0.575543	−	0.817772i	$-0.304791\pi$
$673$	29.8617			1.15109			0.575543	+	0.817772i	$0.304791\pi$
$674$	6.43845	+	9.72350i	0.248000	+	0.374535i
$675$		0			0
$676$	18.3423	−	43.2566i	0.705474	−	1.66372i
$677$		−	32.6443i		−	1.25462i	−0.778769	−	0.627311i	$-0.784156\pi$
$677$		−	32.6443i		−	1.25462i	0.778769	−	0.627311i	$-0.215844\pi$
$678$		0			0
$679$	5.75379	+	22.2586i	0.220810	+	0.854208i
$680$	−20.4924	+	3.80989i	−0.785849	+	0.146103i
$681$		0			0
$682$		0			0
$683$			29.0890i			1.11306i	0.830828	+	0.556529i	$0.187867\pi$
$683$			29.0890i			1.11306i	−0.830828	+	0.556529i	$0.812133\pi$
$684$		0			0
$685$		−	27.5559i		−	1.05286i
$686$	−25.5194	−	5.89574i	−0.974336	−	0.225100i
$687$		0			0
$688$	23.3153	−	22.5490i	0.888889	−	0.859671i
$689$		−	25.6509i		−	0.977222i
$690$		0			0
$691$	12.0000			0.456502			0.228251	−	0.973602i	$-0.426699\pi$
$691$	12.0000			0.456502			0.228251	+	0.973602i	$0.426699\pi$
$692$	−15.6155	−	6.62153i	−0.593613	−	0.251713i
$693$		0			0
$694$	−40.9309	+	27.1025i	−1.55371	+	1.02880i
$695$			20.3537i			0.772060i
$696$		0			0
$697$	33.6155			1.27328
$698$	−4.87689	+	3.22925i	−0.184593	+	0.122229i
$699$		0			0
$700$	−1.65767	+	11.1114i	−0.0626541	+	0.419973i
$701$	34.0000			1.28416			0.642081	−	0.766637i	$-0.278071\pi$
$701$	34.0000			1.28416			0.642081	+	0.766637i	$0.278071\pi$
$702$		0			0
$703$	8.00000			0.301726
$704$	8.68466	+	22.5490i	0.327315	+	0.849846i
$705$		0			0
$706$	−7.36932	+	4.87962i	−0.277348	+	0.183647i
$707$	4.63068	+	17.9139i	0.174155	+	0.673721i
$708$		0			0
$709$	6.00000			0.225335			0.112667	−	0.993633i	$-0.464061\pi$
$709$	6.00000			0.225335			0.112667	+	0.993633i	$0.464061\pi$
$710$	−16.4924	−	24.9073i	−0.618950	−	0.934752i
$711$		0			0
$712$	−4.00000	−	21.5150i	−0.149906	−	0.806308i
$713$		0			0
$714$		0			0
$715$		−	30.9481i		−	1.15740i
$716$	4.19224	+	1.77766i	0.156671	+	0.0664341i
$717$		0			0
$718$	−1.31534	+	0.870958i	−0.0490881	+	0.0325039i
$719$	4.49242			0.167539			0.0837695	−	0.996485i	$-0.473304\pi$
$719$	4.49242			0.167539			0.0837695	+	0.996485i	$0.473304\pi$
$720$		0			0
$721$	−20.4924	+	5.29723i	−0.763178	+	0.197279i
$722$	13.8499	+	20.9165i	0.515440	+	0.778430i
$723$		0			0
$724$	−11.1231	−	4.71659i	−0.413387	−	0.175291i
$725$	4.24621			0.157700
$726$		0			0
$727$	−32.9848			−1.22334			−0.611670	−	0.791113i	$-0.709502\pi$
$727$	−32.9848			−1.22334			−0.611670	+	0.791113i	$0.709502\pi$
$728$	−19.1231	−	40.9620i	−0.708749	−	1.51815i
$729$		0			0
$730$	−4.49242	−	6.78456i	−0.166272	−	0.251108i
$731$	35.2311			1.30307
$732$		0			0
$733$		−	16.6354i		−	0.614441i	−0.951638	−	0.307220i	$-0.900601\pi$
$733$		−	16.6354i		−	0.614441i	0.951638	−	0.307220i	$-0.0993989\pi$
$734$	6.73863	+	10.1768i	0.248728	+	0.375634i
$735$		0			0
$736$	16.6847	+	3.68260i	0.615005	+	0.135742i
$737$	6.24621			0.230082
$738$		0			0
$739$		−	5.87787i		−	0.216221i	−0.994139	−	0.108110i	$-0.965520\pi$
$739$		−	5.87787i		−	0.216221i	0.994139	−	0.108110i	$-0.0344800\pi$
$740$	−22.2462	−	9.43318i	−0.817787	−	0.346771i
$741$		0			0
$742$	−11.8078	−	10.6302i	−0.433477	−	0.390247i
$743$		−	13.6149i		−	0.499482i	−0.968313	−	0.249741i	$-0.919654\pi$
$743$		−	13.6149i		−	0.499482i	0.968313	−	0.249741i	$-0.0803455\pi$
$744$		0			0
$745$		−	16.9614i		−	0.621418i
$746$	7.80776	+	11.7915i	0.285863	+	0.431716i
$747$		0			0
$748$	−10.2462	+	24.1636i	−0.374639	+	0.883508i
$749$	−3.75379	−	14.5216i	−0.137160	−	0.530608i
$750$		0			0
$751$		−	30.7851i		−	1.12336i	−0.827353	−	0.561682i	$-0.810154\pi$
$751$		−	30.7851i		−	1.12336i	0.827353	−	0.561682i	$-0.189846\pi$
$752$	−28.4924	−	29.4608i	−1.03901	−	1.07433i
$753$		0			0
$754$	−14.2462	+	9.43318i	−0.518816	+	0.343536i
$755$	−13.7538			−0.500552
$756$		0			0
$757$	30.9848			1.12616			0.563082	−	0.826401i	$-0.309616\pi$
$757$	30.9848			1.12616			0.563082	+	0.826401i	$0.309616\pi$
$758$	22.0540	−	14.6031i	0.801036	−	0.530409i
$759$		0			0
$760$	0.984845	+	5.29723i	0.0357241	+	0.192151i
$761$		−	33.8056i		−	1.22545i	−0.790296	−	0.612725i	$-0.790073\pi$
$761$		−	33.8056i		−	1.22545i	0.790296	−	0.612725i	$-0.209927\pi$
$762$		0			0
$763$	21.1231	−	5.46026i	0.764708	−	0.197675i
$764$	−16.6847	−	7.07488i	−0.603630	−	0.255960i
$765$		0			0
$766$	−20.4924	−	30.9481i	−0.740421	−	1.11820i
$767$			24.1636i			0.872496i
$768$		0			0
$769$		−	44.5173i		−	1.60533i	−0.596427	−	0.802667i	$-0.703414\pi$
$769$		−	44.5173i		−	1.60533i	0.596427	−	0.802667i	$-0.296586\pi$
$770$	−14.2462	−	12.8255i	−0.513398	−	0.462197i
$771$		0			0
$772$	−7.31534	+	17.2517i	−0.263285	+	0.620903i
$773$		−	1.69614i		−	0.0610060i	−0.999535	−	0.0305030i	$-0.990289\pi$
$773$		−	1.69614i		−	0.0610060i	0.999535	−	0.0305030i	$-0.00971091\pi$
$774$		0			0
$775$		0			0
$776$	4.49242	+	24.1636i	0.161269	+	0.867422i
$777$		0			0
$778$	0.192236	+	0.290319i	0.00689199	+	0.0104085i
$779$		−	8.68951i		−	0.311334i
$780$		0			0
$781$	−37.6155			−1.34599
$782$	10.2462	+	15.4741i	0.366404	+	0.553352i
$783$		0			0
$784$	−26.7808	−	8.17252i	−0.956456	−	0.291876i
$785$	−7.01515			−0.250382
$786$		0			0
$787$	20.9848			0.748029			0.374014	−	0.927423i	$-0.377981\pi$
$787$	20.9848			0.748029			0.374014	+	0.927423i	$0.377981\pi$
$788$	0.192236	−	0.453349i	0.00684812	−	0.0161499i
$789$		0			0
$790$	6.24621	+	9.43318i	0.222230	+	0.335617i
$791$	−31.3693	+	8.10887i	−1.11536	+	0.288318i
$792$		0			0
$793$	56.9848			2.02359
$794$	19.1231	−	12.6624i	0.678654	−	0.449373i
$795$		0			0
$796$	−4.00000	+	9.43318i	−0.141776	+	0.334350i
$797$		−	34.1316i		−	1.20900i	−0.796604	−	0.604502i	$-0.793372\pi$
$797$		−	34.1316i		−	1.20900i	0.796604	−	0.604502i	$-0.206628\pi$
$798$		0			0
$799$		−	44.5173i		−	1.57491i
$800$	−2.58854	+	11.7278i	−0.0915187	+	0.414641i
$801$		0			0
$802$	−6.43845	−	9.72350i	−0.227349	−	0.343349i
$803$	−10.2462			−0.361581
$804$		0			0
$805$	−13.1231	+	3.39228i	−0.462529	+	0.119562i
$806$		0			0
$807$		0			0
$808$	3.61553	+	19.4470i	0.127194	+	0.684143i
$809$	10.4924			0.368894			0.184447	−	0.982842i	$-0.440951\pi$
$809$	10.4924			0.368894			0.184447	+	0.982842i	$0.440951\pi$
$810$		0			0
$811$	−32.4924			−1.14096			−0.570482	−	0.821310i	$-0.693243\pi$
$811$	−32.4924			−1.14096			−0.570482	+	0.821310i	$0.693243\pi$
$812$	−1.56155	+	10.4672i	−0.0547998	+	0.367325i
$813$		0			0
$814$	−25.3693	+	16.7984i	−0.889194	+	0.588783i
$815$	19.5076			0.683321
$816$		0			0
$817$		−	9.10712i		−	0.318618i
$818$	32.4924	−	21.5150i	1.13607	−	0.752253i
$819$		0			0
$820$	−10.2462	+	24.1636i	−0.357813	+	0.843829i
$821$	−25.2311			−0.880570			−0.440285	−	0.897858i	$-0.645123\pi$
$821$	−25.2311			−0.880570			−0.440285	+	0.897858i	$0.645123\pi$
$822$		0			0
$823$			45.0979i			1.57201i	0.618217	+	0.786007i	$0.287855\pi$
$823$			45.0979i			1.57201i	−0.618217	+	0.786007i	$0.712145\pi$
$824$	−22.2462	+	4.13595i	−0.774983	+	0.144083i
$825$		0			0
$826$	11.1231	+	10.0138i	0.387022	+	0.348425i
$827$			30.9939i			1.07776i	0.842381	+	0.538882i	$0.181153\pi$
$827$			30.9939i			1.07776i	−0.842381	+	0.538882i	$0.818847\pi$
$828$		0			0
$829$			31.6918i			1.10070i	0.834933	+	0.550351i	$0.185506\pi$
$829$			31.6918i			1.10070i	−0.834933	+	0.550351i	$0.814494\pi$
$830$	12.4924	−	8.27190i	0.433618	−	0.287122i
$831$		0			0
$832$	−17.3693	−	45.0979i	−0.602173	−	1.56349i
$833$	−14.7386	−	26.6034i	−0.510663	−	0.921753i
$834$		0			0
$835$		−	3.80989i		−	0.131847i
$836$	6.24621	+	2.64861i	0.216030	+	0.0916042i
$837$		0			0
$838$	12.8769	+	19.4470i	0.444825	+	0.671785i
$839$	−6.73863			−0.232643			−0.116322	−	0.993212i	$-0.537110\pi$
$839$	−6.73863			−0.232643			−0.116322	+	0.993212i	$0.537110\pi$
$840$		0			0
$841$	−25.0000			−0.862069
$842$	−14.9309	−	22.5490i	−0.514552	−	0.777088i
$843$		0			0
$844$	7.31534	+	3.10196i	0.251804	+	0.106774i
$845$			39.8465i			1.37076i
$846$		0			0
$847$	4.80776	−	1.24279i	0.165197	−	0.0427028i
$848$	−11.8078	−	12.2091i	−0.405480	−	0.419262i
$849$		0			0
$850$	−10.8769	+	7.20217i	−0.373074	+	0.247032i
$851$			21.5150i			0.737524i
$852$		0			0
$853$		−	37.4067i		−	1.28078i	−0.768050	−	0.640390i	$-0.778773\pi$
$853$		−	37.4067i		−	1.28078i	0.768050	−	0.640390i	$-0.221227\pi$
$854$	23.6155	−	26.2316i	0.808107	−	0.897625i
$855$		0			0
$856$	−2.93087	−	15.7644i	−0.100175	−	0.538816i
$857$		−	20.2364i		−	0.691264i	−0.938370	−	0.345632i	$-0.887665\pi$
$857$		−	20.2364i		−	0.691264i	0.938370	−	0.345632i	$-0.112335\pi$
$858$		0			0
$859$	31.8617			1.08711			0.543554	−	0.839374i	$-0.317078\pi$
$859$	31.8617			1.08711			0.543554	+	0.839374i	$0.317078\pi$
$860$	−10.7386	+	25.3249i	−0.366184	+	0.863571i
$861$		0			0
$862$	−17.8078	+	11.7915i	−0.606535	+	0.401619i
$863$		−	21.8868i		−	0.745035i	−0.928025	−	0.372518i	$-0.878495\pi$
$863$		−	21.8868i		−	0.745035i	0.928025	−	0.372518i	$-0.121505\pi$
$864$		0			0
$865$	14.3845			0.489087
$866$	−8.00000	+	5.29723i	−0.271851	+	0.180007i
$867$		0			0
$868$		0			0
$869$	14.2462			0.483270
$870$		0			0
$871$	−12.4924			−0.423290
$872$	22.9309	−	4.26324i	0.776537	−	0.144372i
$873$		0			0
$874$	4.00000	−	2.64861i	0.135302	−	0.0895907i
$875$	−8.00000	−	30.9481i	−0.270449	−	1.04624i
$876$		0			0
$877$	19.7538			0.667038			0.333519	−	0.942743i	$-0.391764\pi$
$877$	19.7538			0.667038			0.333519	+	0.942743i	$0.391764\pi$
$878$	24.4924	+	36.9890i	0.826579	+	1.24832i
$879$		0			0
$880$	−14.2462	−	14.7304i	−0.480240	−	0.496562i
$881$			39.1028i			1.31741i	0.752403	+	0.658703i	$0.228895\pi$
$881$			39.1028i			1.31741i	−0.752403	+	0.658703i	$0.771105\pi$
$882$		0			0
$883$			26.9752i			0.907789i	0.891056	+	0.453894i	$0.149966\pi$
$883$			26.9752i			0.907789i	−0.891056	+	0.453894i	$0.850034\pi$
$884$	20.4924	−	48.3272i	0.689235	−	1.62542i
$885$		0			0
$886$	42.3002	−	28.0092i	1.42110	−	0.940988i
$887$	−22.7386			−0.763489			−0.381744	−	0.924268i	$-0.624677\pi$
$887$	−22.7386			−0.763489			−0.381744	+	0.924268i	$0.624677\pi$
$888$		0			0
$889$	12.8769	+	49.8145i	0.431877	+	1.67072i
$890$	10.2462	+	15.4741i	0.343454	+	0.518692i
$891$		0			0
$892$	−14.7386	+	34.7580i	−0.493486	+	1.16379i
$893$	−11.5076			−0.385086
$894$		0			0
$895$	−3.86174			−0.129084
$896$	−27.9579	−	10.6938i	−0.934006	−	0.357256i
$897$		0			0
$898$	22.0540	+	33.3064i	0.735951	+	1.11145i
$899$		0			0
$900$		0			0
$901$		−	18.4487i		−	0.614617i
$902$	18.2462	+	27.5559i	0.607532	+	0.917510i
$903$		0			0
$904$	−34.0540	+	6.33122i	−1.13262	+	0.210573i
$905$	10.2462			0.340596
$906$		0			0
$907$			11.9188i			0.395756i	0.980227	+	0.197878i	$0.0634050\pi$
$907$			11.9188i			0.395756i	−0.980227	+	0.197878i	$0.936595\pi$
$908$	12.8769	−	30.3675i	0.427335	−	1.00778i
$909$		0			0
$910$	28.4924	+	25.6509i	0.944515	+	0.850320i
$911$		−	6.41273i		−	0.212463i	−0.994341	−	0.106232i	$-0.966122\pi$
$911$		−	6.41273i		−	0.212463i	0.994341	−	0.106232i	$-0.0338785\pi$
$912$		0			0
$913$		−	18.8664i		−	0.624385i
$914$	12.6847	+	19.1567i	0.419571	+	0.633646i
$915$		0			0
$916$	33.3693	+	14.1498i	1.10255	+	0.467521i
$917$	−56.9848	+	14.7304i	−1.88181	+	0.486441i
$918$		0			0
$919$		−	8.10887i		−	0.267487i	−0.991016	−	0.133743i	$-0.957300\pi$
$919$		−	8.10887i		−	0.267487i	0.991016	−	0.133743i	$-0.0426998\pi$
$920$	−14.2462	+	2.64861i	−0.469684	+	0.0873222i
$921$		0			0
$922$	20.2462	−	13.4061i	0.666773	−	0.441506i
$923$	75.2311			2.47626
$924$		0			0
$925$	−15.1231			−0.497245
$926$	−46.5464	+	30.8209i	−1.52961	+	1.01284i
$927$		0			0
$928$	−2.43845	+	11.0478i	−0.0800460	+	0.362662i
$929$			50.7670i			1.66561i	0.553566	+	0.832805i	$0.313267\pi$
$929$			50.7670i			1.66561i	−0.553566	+	0.832805i	$0.686733\pi$
$930$		0			0
$931$	−6.87689	+	3.80989i	−0.225381	+	0.124864i
$932$	−8.19224	+	19.3197i	−0.268346	+	0.632838i
$933$		0			0
$934$	13.8617	+	20.9343i	0.453570	+	0.684992i
$935$		−	22.2586i		−	0.727935i
$936$		0			0
$937$			56.5991i			1.84901i	0.381169	+	0.924505i	$0.375522\pi$
$937$			56.5991i			1.84901i	−0.381169	+	0.924505i	$0.624478\pi$
$938$	−5.17708	+	5.75058i	−0.169038	+	0.187763i
$939$		0			0
$940$	32.0000	+	13.5691i	1.04372	+	0.442576i
$941$			13.3603i			0.435534i	0.976001	+	0.217767i	$0.0698773\pi$
$941$			13.3603i			0.435534i	−0.976001	+	0.217767i	$0.930123\pi$
$942$		0			0
$943$	23.3693			0.761010
$944$	11.1231	+	11.5012i	0.362026	+	0.374331i
$945$		0			0
$946$	19.1231	+	28.8802i	0.621746	+	0.938975i
$947$			42.2405i			1.37263i	0.727304	+	0.686316i	$0.240773\pi$
$947$			42.2405i			1.37263i	−0.727304	+	0.686316i	$0.759227\pi$
$948$		0			0
$949$	20.4924			0.665212
$950$	1.86174	+	2.81164i	0.0604028	+	0.0912218i
$951$		0			0
$952$	−13.7538	−	29.4608i	−0.445763	−	0.954830i
$953$	−61.2311			−1.98347			−0.991734	−	0.128309i	$-0.959045\pi$
$953$	−61.2311			−1.98347			−0.991734	+	0.128309i	$0.959045\pi$
$954$		0			0
$955$	15.3693			0.497339
$956$	−4.19224	−	1.77766i	−0.135587	−	0.0574935i
$957$		0			0
$958$	−16.0000	−	24.1636i	−0.516937	−	0.780690i
$959$	41.6155	−	10.7575i	1.34384	−	0.347377i
$960$		0			0
$961$	−31.0000			−1.00000
$962$	50.7386	−	33.5968i	1.63588	−	1.08320i
$963$		0			0
$964$	3.50758	+	1.48734i	0.112971	+	0.0479039i
$965$		−	15.8917i		−	0.511571i
$966$		0			0
$967$		−	40.9620i		−	1.31725i	−0.752472	−	0.658624i	$-0.771139\pi$
$967$		−	40.9620i		−	1.31725i	0.752472	−	0.658624i	$-0.228861\pi$
$968$	5.21922	−	0.970343i	0.167752	−	0.0311880i
$969$		0			0
$970$	−11.5076	−	17.3790i	−0.369486	−	0.558007i
$971$	12.0000			0.385098			0.192549	−	0.981287i	$-0.438325\pi$
$971$	12.0000			0.385098			0.192549	+	0.981287i	$0.438325\pi$
$972$		0			0
$973$	−30.7386	+	7.94584i	−0.985435	+	0.254732i
$974$	−38.0540	+	25.1976i	−1.21933	+	0.807382i
$975$		0			0
$976$	27.1231	−	26.2316i	0.868189	−	0.839652i
$977$	60.7386			1.94320			0.971601	−	0.236627i	$-0.0760420\pi$
$977$	60.7386			1.94320			0.971601	+	0.236627i	$0.0760420\pi$
$978$		0			0
$979$	23.3693			0.746887
$980$	23.6155	−	2.48558i	0.754370	−	0.0793991i
$981$		0			0
$982$	13.8078	−	9.14286i	0.440623	−	0.291760i
$983$	−54.7386			−1.74589			−0.872946	−	0.487818i	$-0.837793\pi$
$983$	−54.7386			−1.74589			−0.872946	+	0.487818i	$0.837793\pi$
$984$		0			0
$985$			0.417609i			0.0133061i
$986$	−10.2462	+	6.78456i	−0.326306	+	0.216065i
$987$		0			0
$988$	−12.4924	−	5.29723i	−0.397437	−	0.168527i
$989$	24.4924			0.778814
$990$		0			0
$991$			10.7575i			0.341723i	0.985295	+	0.170861i	$0.0546550\pi$
$991$			10.7575i			0.341723i	−0.985295	+	0.170861i	$0.945345\pi$
$992$		0			0
$993$		0			0
$994$	31.1771	−	34.6307i	0.988877	−	1.09842i
$995$		−	8.68951i		−	0.275476i
$996$		0			0
$997$			38.8940i			1.23178i	0.787830	+	0.615892i	$0.211204\pi$
$997$			38.8940i			1.23178i	−0.787830	+	0.615892i	$0.788796\pi$
$998$	−20.6847	+	13.6964i	−0.654761	+	0.433553i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.2.b.e.55.1		4
3.2	odd	2		84.2.b.a.55.4	yes	4
4.3	odd	2		252.2.b.d.55.2		4
7.6	odd	2		252.2.b.d.55.1		4
8.3	odd	2		4032.2.b.j.3583.3		4
8.5	even	2		4032.2.b.n.3583.3		4
12.11	even	2		84.2.b.b.55.3	yes	4
21.2	odd	6		588.2.o.c.31.3		8
21.5	even	6		588.2.o.a.31.3		8
21.11	odd	6		588.2.o.c.19.1		8
21.17	even	6		588.2.o.a.19.1		8
21.20	even	2		84.2.b.b.55.4	yes	4
24.5	odd	2		1344.2.b.f.895.2		4
24.11	even	2		1344.2.b.e.895.2		4
28.27	even	2	inner	252.2.b.e.55.2		4
56.13	odd	2		4032.2.b.j.3583.2		4
56.27	even	2		4032.2.b.n.3583.2		4
84.11	even	6		588.2.o.a.19.3		8
84.23	even	6		588.2.o.a.31.1		8
84.47	odd	6		588.2.o.c.31.1		8
84.59	odd	6		588.2.o.c.19.3		8
84.83	odd	2		84.2.b.a.55.3	✓	4
168.83	odd	2		1344.2.b.f.895.3		4
168.125	even	2		1344.2.b.e.895.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.2.b.a.55.3	✓	4	84.83	odd	2
84.2.b.a.55.4	yes	4	3.2	odd	2
84.2.b.b.55.3	yes	4	12.11	even	2
84.2.b.b.55.4	yes	4	21.20	even	2
252.2.b.d.55.1		4	7.6	odd	2
252.2.b.d.55.2		4	4.3	odd	2
252.2.b.e.55.1		4	1.1	even	1	trivial
252.2.b.e.55.2		4	28.27	even	2	inner
588.2.o.a.19.1		8	21.17	even	6
588.2.o.a.19.3		8	84.11	even	6
588.2.o.a.31.1		8	84.23	even	6
588.2.o.a.31.3		8	21.5	even	6
588.2.o.c.19.1		8	21.11	odd	6
588.2.o.c.19.3		8	84.59	odd	6
588.2.o.c.31.1		8	84.47	odd	6
588.2.o.c.31.3		8	21.2	odd	6
1344.2.b.e.895.2		4	24.11	even	2
1344.2.b.e.895.3		4	168.125	even	2
1344.2.b.f.895.2		4	24.5	odd	2
1344.2.b.f.895.3		4	168.83	odd	2
4032.2.b.j.3583.2		4	56.13	odd	2
4032.2.b.j.3583.3		4	8.3	odd	2
4032.2.b.n.3583.2		4	56.27	even	2
4032.2.b.n.3583.3		4	8.5	even	2

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:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	252.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.780776 - 1.17915i) q^{2} +(-0.780776 + 1.84130i) q^{4} -1.69614i q^{5} +(2.56155 - 0.662153i) q^{7} +(2.78078 - 0.516994i) q^{8} +O(q^{10})\)	\(q+(-0.780776 - 1.17915i) q^{2} +(-0.780776 + 1.84130i) q^{4} -1.69614i q^{5} +(2.56155 - 0.662153i) q^{7} +(2.78078 - 0.516994i) q^{8} +(-2.00000 + 1.32431i) q^{10} +3.02045i q^{11} -6.04090i q^{13} +(-2.78078 - 2.50345i) q^{14} +(-2.78078 - 2.87529i) q^{16} -4.34475i q^{17} -1.12311 q^{19} +(3.12311 + 1.32431i) q^{20} +(3.56155 - 2.35829i) q^{22} -3.02045i q^{23} +2.12311 q^{25} +(-7.12311 + 4.71659i) q^{26} +(-0.780776 + 5.23358i) q^{28} +2.00000 q^{29} +(-1.21922 + 5.52390i) q^{32} +(-5.12311 + 3.39228i) q^{34} +(-1.12311 - 4.34475i) q^{35} -7.12311 q^{37} +(0.876894 + 1.32431i) q^{38} +(-0.876894 - 4.71659i) q^{40} +7.73704i q^{41} +8.10887i q^{43} +(-5.56155 - 2.35829i) q^{44} +(-3.56155 + 2.35829i) q^{46} +10.2462 q^{47} +(6.12311 - 3.39228i) q^{49} +(-1.65767 - 2.50345i) q^{50} +(11.1231 + 4.71659i) q^{52} +4.24621 q^{53} +5.12311 q^{55} +(6.78078 - 3.16561i) q^{56} +(-1.56155 - 2.35829i) q^{58} -4.00000 q^{59} +9.43318i q^{61} +(7.46543 - 2.87529i) q^{64} -10.2462 q^{65} -2.06798i q^{67} +(8.00000 + 3.39228i) q^{68} +(-4.24621 + 4.71659i) q^{70} +12.4536i q^{71} +3.39228i q^{73} +(5.56155 + 8.39919i) q^{74} +(0.876894 - 2.06798i) q^{76} +(2.00000 + 7.73704i) q^{77} -4.71659i q^{79} +(-4.87689 + 4.71659i) q^{80} +(9.12311 - 6.04090i) q^{82} -6.24621 q^{83} -7.36932 q^{85} +(9.56155 - 6.33122i) q^{86} +(1.56155 + 8.39919i) q^{88} -7.73704i q^{89} +(-4.00000 - 15.4741i) q^{91} +(5.56155 + 2.35829i) q^{92} +(-8.00000 - 12.0818i) q^{94} +1.90495i q^{95} +8.68951i q^{97} +(-8.78078 - 4.57143i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{2} + q^{4} + 2 q^{7} + 7 q^{8}+O(q^{10}) \) 4 * q + q^2 + q^4 + 2 * q^7 + 7 * q^8	\( 4 q + q^{2} + q^{4} + 2 q^{7} + 7 q^{8} - 8 q^{10} - 7 q^{14} - 7 q^{16} + 12 q^{19} - 4 q^{20} + 6 q^{22} - 8 q^{25} - 12 q^{26} + q^{28} + 8 q^{29} - 9 q^{32} - 4 q^{34} + 12 q^{35} - 12 q^{37} + 20 q^{38} - 20 q^{40} - 14 q^{44} - 6 q^{46} + 8 q^{47} + 8 q^{49} - 19 q^{50} + 28 q^{52} - 16 q^{53} + 4 q^{55} + 23 q^{56} + 2 q^{58} - 16 q^{59} + q^{64} - 8 q^{65} + 32 q^{68} + 16 q^{70} + 14 q^{74} + 20 q^{76} + 8 q^{77} - 36 q^{80} + 20 q^{82} + 8 q^{83} + 20 q^{85} + 30 q^{86} - 2 q^{88} - 16 q^{91} + 14 q^{92} - 32 q^{94} - 31 q^{98}+O(q^{100}) \) 4 * q + q^2 + q^4 + 2 * q^7 + 7 * q^8 - 8 * q^10 - 7 * q^14 - 7 * q^16 + 12 * q^19 - 4 * q^20 + 6 * q^22 - 8 * q^25 - 12 * q^26 + q^28 + 8 * q^29 - 9 * q^32 - 4 * q^34 + 12 * q^35 - 12 * q^37 + 20 * q^38 - 20 * q^40 - 14 * q^44 - 6 * q^46 + 8 * q^47 + 8 * q^49 - 19 * q^50 + 28 * q^52 - 16 * q^53 + 4 * q^55 + 23 * q^56 + 2 * q^58 - 16 * q^59 + q^64 - 8 * q^65 + 32 * q^68 + 16 * q^70 + 14 * q^74 + 20 * q^76 + 8 * q^77 - 36 * q^80 + 20 * q^82 + 8 * q^83 + 20 * q^85 + 30 * q^86 - 2 * q^88 - 16 * q^91 + 14 * q^92 - 32 * q^94 - 31 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more