LMFDB - Embedded newform 1620.2.e.b.971.40

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1620,2,Mod(971,1620)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1620, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1620.971");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1620 = 2^{2} \cdot 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1620.e (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:	$12.9357651274$
Analytic rank:	$0$
Dimension:	$48$
Twist minimal:	no (minimal twist has level 180)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			971.40
Character	$\chi$	$=$	1620.971
Dual form			1620.2.e.b.971.39

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.14547 + 0.829399i) q^{2} +(0.624193 + 1.90010i) q^{4} +1.00000i q^{5} -2.90505i q^{7} +(-0.860949 + 2.69421i) q^{8} +O(q^{10})$	\(q+(1.14547 + 0.829399i) q^{2} +(0.624193 + 1.90010i) q^{4} +1.00000i q^{5} -2.90505i q^{7} +(-0.860949 + 2.69421i) q^{8} +(-0.829399 + 1.14547i) q^{10} +2.72840 q^{11} -1.84768 q^{13} +(2.40945 - 3.32764i) q^{14} +(-3.22076 + 2.37206i) q^{16} +6.64799i q^{17} +4.90413i q^{19} +(-1.90010 + 0.624193i) q^{20} +(3.12529 + 2.26293i) q^{22} +6.63496 q^{23} -1.00000 q^{25} +(-2.11646 - 1.53247i) q^{26} +(5.51989 - 1.81331i) q^{28} -5.65558i q^{29} +5.22792i q^{31} +(-5.65667 + 0.0458194i) q^{32} +(-5.51384 + 7.61506i) q^{34} +2.90505 q^{35} -0.280524 q^{37} +(-4.06748 + 5.61753i) q^{38} +(-2.69421 - 0.860949i) q^{40} +8.44462i q^{41} +7.15600i q^{43} +(1.70305 + 5.18423i) q^{44} +(7.60014 + 5.50304i) q^{46} -1.48605 q^{47} -1.43932 q^{49} +(-1.14547 - 0.829399i) q^{50} +(-1.15331 - 3.51079i) q^{52} -4.62498i q^{53} +2.72840i q^{55} +(7.82682 + 2.50110i) q^{56} +(4.69073 - 6.47828i) q^{58} +5.12297 q^{59} +11.2317 q^{61} +(-4.33603 + 5.98842i) q^{62} +(-6.51754 - 4.63915i) q^{64} -1.84768i q^{65} +1.71296i q^{67} +(-12.6318 + 4.14963i) q^{68} +(3.32764 + 2.40945i) q^{70} +5.25318 q^{71} -9.36719 q^{73} +(-0.321331 - 0.232666i) q^{74} +(-9.31835 + 3.06113i) q^{76} -7.92613i q^{77} -8.18558i q^{79} +(-2.37206 - 3.22076i) q^{80} +(-7.00396 + 9.67304i) q^{82} -9.15508 q^{83} -6.64799 q^{85} +(-5.93518 + 8.19697i) q^{86} +(-2.34901 + 7.35088i) q^{88} -14.8298i q^{89} +5.36761i q^{91} +(4.14150 + 12.6071i) q^{92} +(-1.70223 - 1.23253i) q^{94} -4.90413 q^{95} -11.8860 q^{97} +(-1.64869 - 1.19377i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q+O(q^{10}) $ 48 * q	$ 48 q - 48 q^{25} + 12 q^{34} + 12 q^{40} - 12 q^{46} - 48 q^{49} + 36 q^{52} + 36 q^{58} - 48 q^{64} - 24 q^{73} - 12 q^{76} - 36 q^{82} - 36 q^{94} + 24 q^{97}+O(q^{100}) $ 48 * q - 48 * q^25 + 12 * q^34 + 12 * q^40 - 12 * q^46 - 48 * q^49 + 36 * q^52 + 36 * q^58 - 48 * q^64 - 24 * q^73 - 12 * q^76 - 36 * q^82 - 36 * q^94 + 24 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1620\mathbb{Z}\right)^\times$.

$n$	$811$	$1297$	$1541$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$	1.14547	+	0.829399i	0.809968	+	0.586474i
$2$	1.14547	+	0.829399i	0.809968	+	0.586474i
$3$		0			0
$3$		0			0
$4$	0.624193	+	1.90010i	0.312097	+	0.950050i
$5$			1.00000i			0.447214i
$5$			1.00000i			0.447214i
$6$		0			0
$7$		−	2.90505i		−	1.09801i	−0.835820	−	0.549003i	$-0.815008\pi$
$7$		−	2.90505i		−	1.09801i	0.835820	−	0.549003i	$-0.184992\pi$
$8$	−0.860949	+	2.69421i	−0.304391	+	0.952547i
$9$		0			0
$10$	−0.829399	+	1.14547i	−0.262279	+	0.362229i
$11$	2.72840			0.822643			0.411322	−	0.911490i	$-0.365067\pi$
$11$	2.72840			0.822643			0.411322	+	0.911490i	$0.365067\pi$
$12$		0			0
$13$	−1.84768			−0.512455			−0.256228	−	0.966616i	$-0.582480\pi$
$13$	−1.84768			−0.512455			−0.256228	+	0.966616i	$0.582480\pi$
$14$	2.40945	−	3.32764i	0.643952	−	0.889350i
$15$		0			0
$16$	−3.22076	+	2.37206i	−0.805191	+	0.593015i
$17$			6.64799i			1.61237i	0.591661	+	0.806187i	$0.298472\pi$
$17$			6.64799i			1.61237i	−0.591661	+	0.806187i	$0.701528\pi$
$18$		0			0
$19$			4.90413i			1.12509i	0.826768	+	0.562543i	$0.190177\pi$
$19$			4.90413i			1.12509i	−0.826768	+	0.562543i	$0.809823\pi$
$20$	−1.90010	+	0.624193i	−0.424875	+	0.139574i
$21$		0			0
$22$	3.12529	+	2.26293i	0.666315	+	0.482459i
$23$	6.63496			1.38349			0.691743	−	0.722144i	$-0.256843\pi$
$23$	6.63496			1.38349			0.691743	+	0.722144i	$0.256843\pi$
$24$		0			0
$25$	−1.00000			−0.200000
$26$	−2.11646	−	1.53247i	−0.415072	−	0.300542i
$27$		0			0
$28$	5.51989	−	1.81331i	1.04316	−	0.342684i
$29$		−	5.65558i		−	1.05021i	−0.851036	−	0.525107i	$-0.824025\pi$
$29$		−	5.65558i		−	1.05021i	0.851036	−	0.525107i	$-0.175975\pi$
$30$		0			0
$31$			5.22792i			0.938962i	0.882942	+	0.469481i	$0.155559\pi$
$31$			5.22792i			0.938962i	−0.882942	+	0.469481i	$0.844441\pi$
$32$	−5.65667	+	0.0458194i	−0.999967	+	0.00809980i
$33$		0			0
$34$	−5.51384	+	7.61506i	−0.945615	+	1.30597i
$35$	2.90505			0.491043
$36$		0			0
$37$	−0.280524			−0.0461178			−0.0230589	−	0.999734i	$-0.507341\pi$
$37$	−0.280524			−0.0461178			−0.0230589	+	0.999734i	$0.507341\pi$
$38$	−4.06748	+	5.61753i	−0.659833	+	0.911283i
$39$		0			0
$40$	−2.69421	−	0.860949i	−0.425992	−	0.136128i
$41$			8.44462i			1.31883i	0.751780	+	0.659414i	$0.229196\pi$
$41$			8.44462i			1.31883i	−0.751780	+	0.659414i	$0.770804\pi$
$42$		0			0
$43$			7.15600i			1.09128i	0.838020	+	0.545640i	$0.183713\pi$
$43$			7.15600i			1.09128i	−0.838020	+	0.545640i	$0.816287\pi$
$44$	1.70305	+	5.18423i	0.256744	+	0.781552i
$45$		0			0
$46$	7.60014	+	5.50304i	1.12058	+	0.811378i
$47$	−1.48605			−0.216763			−0.108381	−	0.994109i	$-0.534567\pi$
$47$	−1.48605			−0.216763			−0.108381	+	0.994109i	$0.534567\pi$
$48$		0			0
$49$	−1.43932			−0.205617
$50$	−1.14547	−	0.829399i	−0.161994	−	0.117295i
$51$		0			0
$52$	−1.15331	−	3.51079i	−0.159936	−	0.486858i
$53$		−	4.62498i		−	0.635290i	−0.948210	−	0.317645i	$-0.897108\pi$
$53$		−	4.62498i		−	0.635290i	0.948210	−	0.317645i	$-0.102892\pi$
$54$		0			0
$55$			2.72840i			0.367897i
$56$	7.82682	+	2.50110i	1.04590	+	0.334223i
$57$		0			0
$58$	4.69073	−	6.47828i	0.615923	−	0.850640i
$59$	5.12297			0.666953			0.333477	−	0.942758i	$-0.391778\pi$
$59$	5.12297			0.666953			0.333477	+	0.942758i	$0.391778\pi$
$60$		0			0
$61$	11.2317			1.43807			0.719034	−	0.694975i	$-0.244585\pi$
$61$	11.2317			1.43807			0.719034	+	0.694975i	$0.244585\pi$
$62$	−4.33603	+	5.98842i	−0.550677	+	0.760530i
$63$		0			0
$64$	−6.51754	−	4.63915i	−0.814692	−	0.579894i
$65$		−	1.84768i		−	0.229177i
$66$		0			0
$67$			1.71296i			0.209272i	0.994511	+	0.104636i	$0.0333677\pi$
$67$			1.71296i			0.209272i	−0.994511	+	0.104636i	$0.966632\pi$
$68$	−12.6318	+	4.14963i	−1.53184	+	0.503217i
$69$		0			0
$70$	3.32764	+	2.40945i	0.397729	+	0.287984i
$71$	5.25318			0.623438			0.311719	−	0.950174i	$-0.399095\pi$
$71$	5.25318			0.623438			0.311719	+	0.950174i	$0.399095\pi$
$72$		0			0
$73$	−9.36719			−1.09635			−0.548173	−	0.836365i	$-0.684677\pi$
$73$	−9.36719			−1.09635			−0.548173	+	0.836365i	$0.684677\pi$
$74$	−0.321331	−	0.232666i	−0.0373540	−	0.0270469i
$75$		0			0
$76$	−9.31835	+	3.06113i	−1.06889	+	0.351135i
$77$		−	7.92613i		−	0.903267i
$78$		0			0
$79$		−	8.18558i		−	0.920950i	−0.887673	−	0.460475i	$-0.847679\pi$
$79$		−	8.18558i		−	0.920950i	0.887673	−	0.460475i	$-0.152321\pi$
$80$	−2.37206	−	3.22076i	−0.265204	−	0.360092i
$81$		0			0
$82$	−7.00396	+	9.67304i	−0.773458	+	1.06821i
$83$	−9.15508			−1.00490			−0.502451	−	0.864606i	$-0.667568\pi$
$83$	−9.15508			−1.00490			−0.502451	+	0.864606i	$0.667568\pi$
$84$		0			0
$85$	−6.64799			−0.721075
$86$	−5.93518	+	8.19697i	−0.640007	+	0.883902i
$87$		0			0
$88$	−2.34901	+	7.35088i	−0.250405	+	0.783606i
$89$		−	14.8298i		−	1.57195i	−0.618255	−	0.785977i	$-0.712160\pi$
$89$		−	14.8298i		−	1.57195i	0.618255	−	0.785977i	$-0.287840\pi$
$90$		0			0
$91$			5.36761i			0.562679i
$92$	4.14150	+	12.6071i	0.431781	+	1.31438i
$93$		0			0
$94$	−1.70223	−	1.23253i	−0.175571	−	0.127126i
$95$	−4.90413			−0.503153
$96$		0			0
$97$	−11.8860			−1.20684			−0.603418	−	0.797425i	$-0.706195\pi$
$97$	−11.8860			−1.20684			−0.603418	+	0.797425i	$0.706195\pi$
$98$	−1.64869	−	1.19377i	−0.166543	−	0.120589i
$99$		0			0
$100$	−0.624193	−	1.90010i	−0.0624193	−	0.190010i
$101$			0.612468i			0.0609428i	0.999536	+	0.0304714i	$0.00970085\pi$
$101$			0.612468i			0.0609428i	−0.999536	+	0.0304714i	$0.990299\pi$
$102$		0			0
$103$			3.06840i			0.302338i	0.988508	+	0.151169i	$0.0483038\pi$
$103$			3.06840i			0.302338i	−0.988508	+	0.151169i	$0.951696\pi$
$104$	1.59076	−	4.97805i	0.155987	−	0.488138i
$105$		0			0
$106$	3.83596	−	5.29777i	0.372581	−	0.514565i
$107$	7.58586			0.733352			0.366676	−	0.930349i	$-0.380496\pi$
$107$	7.58586			0.733352			0.366676	+	0.930349i	$0.380496\pi$
$108$		0			0
$109$	−14.2287			−1.36286			−0.681430	−	0.731883i	$-0.738642\pi$
$109$	−14.2287			−1.36286			−0.681430	+	0.731883i	$0.738642\pi$
$110$	−2.26293	+	3.12529i	−0.215762	+	0.297985i
$111$		0			0
$112$	6.89096	+	9.35648i	0.651134	+	0.884105i
$113$		−	9.94258i		−	0.935319i	−0.883909	−	0.467660i	$-0.845097\pi$
$113$		−	9.94258i		−	0.935319i	0.883909	−	0.467660i	$-0.154903\pi$
$114$		0			0
$115$			6.63496i			0.618714i
$116$	10.7462	−	3.53017i	0.997756	−	0.327768i
$117$		0			0
$118$	5.86819	+	4.24898i	0.540211	+	0.391151i
$119$	19.3127			1.77040
$120$		0			0
$121$	−3.55584			−0.323258
$122$	12.8655	+	9.31554i	1.16479	+	0.843389i
$123$		0			0
$124$	−9.93358	+	3.26323i	−0.892062	+	0.293047i
$125$		−	1.00000i		−	0.0894427i
$126$		0			0
$127$		−	15.7476i		−	1.39738i	−0.715426	−	0.698688i	$-0.753767\pi$
$127$		−	15.7476i		−	1.39738i	0.715426	−	0.698688i	$-0.246233\pi$
$128$	−3.61792	−	10.7196i	−0.319782	−	0.947491i
$129$		0			0
$130$	1.53247	−	2.11646i	0.134406	−	0.185626i
$131$	13.6141			1.18947			0.594733	−	0.803923i	$-0.297258\pi$
$131$	13.6141			1.18947			0.594733	+	0.803923i	$0.297258\pi$
$132$		0			0
$133$	14.2468			1.23535
$134$	−1.42073	+	1.96214i	−0.122732	+	0.169503i
$135$		0			0
$136$	−17.9111	−	5.72357i	−1.53586	−	0.490792i
$137$		−	10.7793i		−	0.920939i	−0.887676	−	0.460469i	$-0.847681\pi$
$137$		−	10.7793i		−	0.920939i	0.887676	−	0.460469i	$-0.152319\pi$
$138$		0			0
$139$			5.96003i			0.505523i	0.967529	+	0.252762i	$0.0813389\pi$
$139$			5.96003i			0.505523i	−0.967529	+	0.252762i	$0.918661\pi$
$140$	1.81331	+	5.51989i	0.153253	+	0.466516i
$141$		0			0
$142$	6.01735	+	4.35699i	0.504965	+	0.365630i
$143$	−5.04122			−0.421568
$144$		0			0
$145$	5.65558			0.469670
$146$	−10.7298	−	7.76914i	−0.888006	−	0.642979i
$147$		0			0
$148$	−0.175101	−	0.533024i	−0.0143932	−	0.0438143i
$149$		−	1.29486i		−	0.106079i	−0.998592	−	0.0530396i	$-0.983109\pi$
$149$		−	1.29486i		−	0.106079i	0.998592	−	0.0530396i	$-0.0168910\pi$
$150$		0			0
$151$			7.15572i			0.582324i	0.956674	+	0.291162i	$0.0940419\pi$
$151$			7.15572i			0.582324i	−0.956674	+	0.291162i	$0.905958\pi$
$152$	−13.2128	−	4.22221i	−1.07170	−	0.342466i
$153$		0			0
$154$	6.57393	−	9.07913i	0.529742	−	0.731617i
$155$	−5.22792			−0.419917
$156$		0			0
$157$	15.7059			1.25346			0.626732	−	0.779235i	$-0.284392\pi$
$157$	15.7059			1.25346			0.626732	+	0.779235i	$0.284392\pi$
$158$	6.78912	−	9.37632i	0.540113	−	0.745940i
$159$		0			0
$160$	−0.0458194	−	5.65667i	−0.00362234	−	0.447199i
$161$		−	19.2749i		−	1.51908i
$162$		0			0
$163$			5.63727i			0.441545i	0.975325	+	0.220772i	$0.0708578\pi$
$163$			5.63727i			0.441545i	−0.975325	+	0.220772i	$0.929142\pi$
$164$	−16.0456	+	5.27108i	−1.25295	+	0.411602i
$165$		0			0
$166$	−10.4869	−	7.59322i	−0.813938	−	0.589348i
$167$	1.77257			0.137165			0.0685826	−	0.997645i	$-0.478152\pi$
$167$	1.77257			0.137165			0.0685826	+	0.997645i	$0.478152\pi$
$168$		0			0
$169$	−9.58606			−0.737390
$170$	−7.61506	−	5.51384i	−0.584048	−	0.422892i
$171$		0			0
$172$	−13.5971	+	4.46673i	−1.03677	+	0.340585i
$173$		−	3.87865i		−	0.294888i	−0.989070	−	0.147444i	$-0.952895\pi$
$173$		−	3.87865i		−	0.294888i	0.989070	−	0.147444i	$-0.0471046\pi$
$174$		0			0
$175$			2.90505i			0.219601i
$176$	−8.78753	+	6.47193i	−0.662385	+	0.487840i
$177$		0			0
$178$	12.2998	−	16.9871i	0.921910	−	1.27323i
$179$	1.59068			0.118893			0.0594466	−	0.998231i	$-0.481066\pi$
$179$	1.59068			0.118893			0.0594466	+	0.998231i	$0.481066\pi$
$180$		0			0
$181$	21.6836			1.61173			0.805866	−	0.592098i	$-0.201700\pi$
$181$	21.6836			1.61173			0.805866	+	0.592098i	$0.201700\pi$
$182$	−4.45190	+	6.14843i	−0.329996	+	0.455752i
$183$		0			0
$184$	−5.71236	+	17.8760i	−0.421121	+	1.31784i
$185$		−	0.280524i		−	0.0206245i
$186$		0			0
$187$			18.1384i			1.32641i
$188$	−0.927584	−	2.82365i	−0.0676510	−	0.205936i
$189$		0			0
$190$	−5.61753	−	4.06748i	−0.407538	−	0.295086i
$191$	18.5944			1.34544			0.672722	−	0.739895i	$-0.265125\pi$
$191$	18.5944			1.34544			0.672722	+	0.739895i	$0.265125\pi$
$192$		0			0
$193$	12.4117			0.893411			0.446705	−	0.894681i	$-0.352597\pi$
$193$	12.4117			0.893411			0.446705	+	0.894681i	$0.352597\pi$
$194$	−13.6150	−	9.85820i	−0.977499	−	0.707778i
$195$		0			0
$196$	−0.898413	−	2.73485i	−0.0641724	−	0.195346i
$197$			19.1297i			1.36293i	0.731849	+	0.681467i	$0.238658\pi$
$197$			19.1297i			1.36293i	−0.731849	+	0.681467i	$0.761342\pi$
$198$		0			0
$199$			11.9817i			0.849361i	0.905343	+	0.424681i	$0.139614\pi$
$199$			11.9817i			0.849361i	−0.905343	+	0.424681i	$0.860386\pi$
$200$	0.860949	−	2.69421i	0.0608783	−	0.190509i
$201$		0			0
$202$	−0.507980	+	0.701562i	−0.0357414	+	0.0493617i
$203$	−16.4297			−1.15314
$204$		0			0
$205$	−8.44462			−0.589798
$206$	−2.54493	+	3.51475i	−0.177313	+	0.244884i
$207$		0			0
$208$	5.95096	−	4.38282i	0.412624	−	0.303894i
$209$			13.3804i			0.925544i
$210$		0			0
$211$		−	19.9960i		−	1.37658i	−0.725436	−	0.688290i	$-0.758362\pi$
$211$		−	19.9960i		−	1.37658i	0.725436	−	0.688290i	$-0.241638\pi$
$212$	8.78793	−	2.88688i	0.603558	−	0.198272i
$213$		0			0
$214$	8.68935	+	6.29170i	0.593992	+	0.430092i
$215$	−7.15600			−0.488035
$216$		0			0
$217$	15.1874			1.03099
$218$	−16.2985	−	11.8013i	−1.10387	−	0.799282i
$219$		0			0
$220$	−5.18423	+	1.70305i	−0.349521	+	0.114820i
$221$		−	12.2834i		−	0.826269i
$222$		0			0
$223$		−	22.7466i		−	1.52322i	−0.648034	−	0.761611i	$-0.724409\pi$
$223$		−	22.7466i		−	1.52322i	0.648034	−	0.761611i	$-0.275591\pi$
$224$	0.133108	+	16.4329i	0.00889363	+	1.09797i
$225$		0			0
$226$	8.24637	−	11.3889i	0.548540	−	0.757579i
$227$	7.31961			0.485820			0.242910	−	0.970049i	$-0.421898\pi$
$227$	7.31961			0.485820			0.242910	+	0.970049i	$0.421898\pi$
$228$		0			0
$229$	−12.3938			−0.819008			−0.409504	−	0.912308i	$-0.634298\pi$
$229$	−12.3938			−0.819008			−0.409504	+	0.912308i	$0.634298\pi$
$230$	−5.50304	+	7.60014i	−0.362859	+	0.501138i
$231$		0			0
$232$	15.2373	+	4.86916i	1.00038	+	0.319676i
$233$		−	10.9146i		−	0.715040i	−0.933905	−	0.357520i	$-0.883622\pi$
$233$		−	10.9146i		−	0.715040i	0.933905	−	0.357520i	$-0.116378\pi$
$234$		0			0
$235$		−	1.48605i		−	0.0969394i
$236$	3.19772	+	9.73415i	0.208154	+	0.633639i
$237$		0			0
$238$	22.1221	+	16.0180i	1.43396	+	1.03829i
$239$	−0.324550			−0.0209934			−0.0104967	−	0.999945i	$-0.503341\pi$
$239$	−0.324550			−0.0209934			−0.0104967	+	0.999945i	$0.503341\pi$
$240$		0			0
$241$	9.39624			0.605265			0.302633	−	0.953107i	$-0.402134\pi$
$241$	9.39624			0.605265			0.302633	+	0.953107i	$0.402134\pi$
$242$	−4.07310	−	2.94921i	−0.261829	−	0.189583i
$243$		0			0
$244$	7.01074	+	21.3413i	0.448816	+	1.36624i
$245$		−	1.43932i		−	0.0919547i
$246$		0			0
$247$		−	9.06129i		−	0.576556i
$248$	−14.0851	−	4.50097i	−0.894406	−	0.285812i
$249$		0			0
$250$	0.829399	−	1.14547i	0.0524558	−	0.0724458i
$251$	25.1401			1.58683			0.793415	−	0.608681i	$-0.208301\pi$
$251$	25.1401			1.58683			0.793415	+	0.608681i	$0.208301\pi$
$252$		0			0
$253$	18.1028			1.13811
$254$	13.0611	−	18.0384i	0.819525	−	1.13183i
$255$		0			0
$256$	4.74665	−	15.2797i	0.296666	−	0.954981i
$257$		−	24.7081i		−	1.54125i	−0.637290	−	0.770624i	$-0.719945\pi$
$257$		−	24.7081i		−	1.54125i	0.637290	−	0.770624i	$-0.280055\pi$
$258$		0			0
$259$			0.814936i			0.0506377i
$260$	3.51079	−	1.15331i	0.217730	−	0.0715254i
$261$		0			0
$262$	15.5945	+	11.2915i	0.963430	+	0.697591i
$263$	18.6421			1.14952			0.574761	−	0.818321i	$-0.305095\pi$
$263$	18.6421			1.14952			0.574761	+	0.818321i	$0.305095\pi$
$264$		0			0
$265$	4.62498			0.284110
$266$	16.3192	+	11.8162i	1.00059	+	0.724501i
$267$		0			0
$268$	−3.25480	+	1.06922i	−0.198819	+	0.0653130i
$269$			5.91652i			0.360736i	0.983599	+	0.180368i	$0.0577289\pi$
$269$			5.91652i			0.360736i	−0.983599	+	0.180368i	$0.942271\pi$
$270$		0			0
$271$			1.37246i			0.0833710i	0.999131	+	0.0416855i	$0.0132728\pi$
$271$			1.37246i			0.0833710i	−0.999131	+	0.0416855i	$0.986727\pi$
$272$	−15.7694	−	21.4116i	−0.956162	−	1.29827i
$273$		0			0
$274$	8.94035	−	12.3474i	0.540106	−	0.745931i
$275$	−2.72840			−0.164529
$276$		0			0
$277$	−31.7192			−1.90583			−0.952913	−	0.303245i	$-0.901930\pi$
$277$	−31.7192			−1.90583			−0.952913	+	0.303245i	$0.901930\pi$
$278$	−4.94325	+	6.82703i	−0.296476	+	0.409458i
$279$		0			0
$280$	−2.50110	+	7.82682i	−0.149469	+	0.467742i
$281$		−	1.59785i		−	0.0953200i	−0.998864	−	0.0476600i	$-0.984824\pi$
$281$		−	1.59785i		−	0.0953200i	0.998864	−	0.0476600i	$-0.0151764\pi$
$282$		0			0
$283$		−	7.64193i		−	0.454266i	−0.973864	−	0.227133i	$-0.927065\pi$
$283$		−	7.64193i		−	0.454266i	0.973864	−	0.227133i	$-0.0729352\pi$
$284$	3.27900	+	9.98157i	0.194573	+	0.592297i
$285$		0			0
$286$	−5.77455	−	4.18118i	−0.341456	−	0.247238i
$287$	24.5320			1.44808
$288$		0			0
$289$	−27.1957			−1.59975
$290$	6.47828	+	4.69073i	0.380418	+	0.275449i
$291$		0			0
$292$	−5.84694	−	17.7986i	−0.342166	−	1.04158i
$293$			4.59933i			0.268696i	0.990934	+	0.134348i	$0.0428940\pi$
$293$			4.59933i			0.268696i	−0.990934	+	0.134348i	$0.957106\pi$
$294$		0			0
$295$			5.12297i			0.298271i
$296$	0.241517	−	0.755790i	0.0140379	−	0.0439294i
$297$		0			0
$298$	1.07396	−	1.48322i	0.0622127	−	0.0859208i
$299$	−12.2593			−0.708975
$300$		0			0
$301$	20.7885			1.19823
$302$	−5.93495	+	8.19665i	−0.341518	+	0.471664i
$303$		0			0
$304$	−11.6329	−	15.7951i	−0.667193	−	0.905909i
$305$			11.2317i			0.643124i
$306$		0			0
$307$		−	25.6885i		−	1.46612i	−0.680165	−	0.733059i	$-0.738092\pi$
$307$		−	25.6885i		−	1.46612i	0.680165	−	0.733059i	$-0.261908\pi$
$308$	15.0605	−	4.94744i	0.858149	−	0.281907i
$309$		0			0
$310$	−5.98842	−	4.33603i	−0.340119	−	0.246270i
$311$	4.95904			0.281201			0.140601	−	0.990066i	$-0.455097\pi$
$311$	4.95904			0.281201			0.140601	+	0.990066i	$0.455097\pi$
$312$		0			0
$313$	−23.7596			−1.34297			−0.671487	−	0.741017i	$-0.734344\pi$
$313$	−23.7596			−1.34297			−0.671487	+	0.741017i	$0.734344\pi$
$314$	17.9906	+	13.0264i	1.01527	+	0.735124i
$315$		0			0
$316$	15.5534	−	5.10939i	0.874949	−	0.287425i
$317$			7.54836i			0.423958i	0.977274	+	0.211979i	$0.0679909\pi$
$317$			7.54836i			0.423958i	−0.977274	+	0.211979i	$0.932009\pi$
$318$		0			0
$319$		−	15.4307i		−	0.863951i
$320$	4.63915	−	6.51754i	0.259337	−	0.364341i
$321$		0			0
$322$	15.9866	−	22.0788i	0.890898	−	1.23040i
$323$	−32.6026			−1.81406
$324$		0			0
$325$	1.84768			0.102491
$326$	−4.67555	+	6.45731i	−0.258955	+	0.357637i
$327$		0			0
$328$	−22.7516	−	7.27038i	−1.25625	−	0.401440i
$329$			4.31706i			0.238007i
$330$		0			0
$331$			4.13001i			0.227006i	0.993538	+	0.113503i	$0.0362072\pi$
$331$			4.13001i			0.227006i	−0.993538	+	0.113503i	$0.963793\pi$
$332$	−5.71454	−	17.3956i	−0.313626	−	0.954707i
$333$		0			0
$334$	2.03042	+	1.47016i	0.111099	+	0.0804438i
$335$	−1.71296			−0.0935891
$336$		0			0
$337$	−33.9830			−1.85117			−0.925585	−	0.378539i	$-0.876427\pi$
$337$	−33.9830			−1.85117			−0.925585	+	0.378539i	$0.876427\pi$
$338$	−10.9805	−	7.95068i	−0.597262	−	0.432460i
$339$		0			0
$340$	−4.14963	−	12.6318i	−0.225045	−	0.685058i
$341$			14.2639i			0.772431i
$342$		0			0
$343$		−	16.1541i		−	0.872237i
$344$	−19.2798	−	6.16095i	−1.03950	−	0.332176i
$345$		0			0
$346$	3.21695	−	4.44286i	0.172944	−	0.238850i
$347$	16.7947			0.901586			0.450793	−	0.892629i	$-0.351141\pi$
$347$	16.7947			0.901586			0.450793	+	0.892629i	$0.351141\pi$
$348$		0			0
$349$	17.8945			0.957872			0.478936	−	0.877850i	$-0.341023\pi$
$349$	17.8945			0.957872			0.478936	+	0.877850i	$0.341023\pi$
$350$	−2.40945	+	3.32764i	−0.128790	+	0.177870i
$351$		0			0
$352$	−15.4336	+	0.125014i	−0.822616	+	0.00666325i
$353$		−	0.534587i		−	0.0284532i	−0.999899	−	0.0142266i	$-0.995471\pi$
$353$		−	0.534587i		−	0.0284532i	0.999899	−	0.0142266i	$-0.00452862\pi$
$354$		0			0
$355$			5.25318i			0.278810i
$356$	28.1781	−	9.25666i	1.49344	−	0.490602i
$357$		0			0
$358$	1.82207	+	1.31931i	0.0962996	+	0.0697277i
$359$	−21.8779			−1.15467			−0.577336	−	0.816507i	$-0.695908\pi$
$359$	−21.8779			−1.15467			−0.577336	+	0.816507i	$0.695908\pi$
$360$		0			0
$361$	−5.05052			−0.265817
$362$	24.8379	+	17.9844i	1.30545	+	0.945239i
$363$		0			0
$364$	−10.1990	+	3.35043i	−0.534573	+	0.175610i
$365$		−	9.36719i		−	0.490301i
$366$		0			0
$367$		−	23.3231i		−	1.21746i	−0.793379	−	0.608728i	$-0.791680\pi$
$367$		−	23.3231i		−	1.21746i	0.793379	−	0.608728i	$-0.208320\pi$
$368$	−21.3697	+	15.7385i	−1.11397	+	0.820428i
$369$		0			0
$370$	0.232666	−	0.321331i	0.0120957	−	0.0167052i
$371$	−13.4358			−0.697552
$372$		0			0
$373$	2.00065			0.103590			0.0517950	−	0.998658i	$-0.483506\pi$
$373$	2.00065			0.103590			0.0517950	+	0.998658i	$0.483506\pi$
$374$	−15.0439	+	20.7769i	−0.777904	+	1.07435i
$375$		0			0
$376$	1.27941	−	4.00374i	0.0659808	−	0.206477i
$377$			10.4497i			0.538188i
$378$		0			0
$379$		−	28.6355i		−	1.47091i	−0.677576	−	0.735453i	$-0.736969\pi$
$379$		−	28.6355i		−	1.47091i	0.677576	−	0.735453i	$-0.263031\pi$
$380$	−3.06113	−	9.31835i	−0.157033	−	0.478021i
$381$		0			0
$382$	21.2993	+	15.4222i	1.08977	+	0.789068i
$383$	−20.3957			−1.04217			−0.521086	−	0.853504i	$-0.674473\pi$
$383$	−20.3957			−1.04217			−0.521086	+	0.853504i	$0.674473\pi$
$384$		0			0
$385$	7.92613			0.403953
$386$	14.2172	+	10.2942i	0.723634	+	0.523962i
$387$		0			0
$388$	−7.41914	−	22.5845i	−0.376650	−	1.14655i
$389$			20.7725i			1.05321i	0.850111	+	0.526604i	$0.176535\pi$
$389$			20.7725i			1.05321i	−0.850111	+	0.526604i	$0.823465\pi$
$390$		0			0
$391$			44.1092i			2.23070i
$392$	1.23918	−	3.87783i	0.0625880	−	0.195860i
$393$		0			0
$394$	−15.8661	+	21.9124i	−0.799325	+	1.10393i
$395$	8.18558			0.411861
$396$		0			0
$397$	3.48794			0.175054			0.0875272	−	0.996162i	$-0.472104\pi$
$397$	3.48794			0.175054			0.0875272	+	0.996162i	$0.472104\pi$
$398$	−9.93762	+	13.7247i	−0.498128	+	0.687955i
$399$		0			0
$400$	3.22076	−	2.37206i	0.161038	−	0.118603i
$401$			9.10978i			0.454921i	0.973787	+	0.227460i	$0.0730423\pi$
$401$			9.10978i			0.454921i	−0.973787	+	0.227460i	$0.926958\pi$
$402$		0			0
$403$		−	9.65955i		−	0.481176i
$404$	−1.16375	+	0.382298i	−0.0578987	+	0.0190201i
$405$		0			0
$406$	−18.8197	−	13.6268i	−0.934008	−	0.676287i
$407$	−0.765381			−0.0379385
$408$		0			0
$409$	11.4864			0.567964			0.283982	−	0.958830i	$-0.408344\pi$
$409$	11.4864			0.567964			0.283982	+	0.958830i	$0.408344\pi$
$410$	−9.67304	−	7.00396i	−0.477717	−	0.345901i
$411$		0			0
$412$	−5.83026	+	1.91527i	−0.287237	+	0.0943588i
$413$		−	14.8825i		−	0.732319i
$414$		0			0
$415$		−	9.15508i		−	0.449405i
$416$	10.4517	−	0.0846598i	0.512438	−	0.00415079i
$417$		0			0
$418$	−11.0977	+	15.3269i	−0.542807	+	0.749661i
$419$	33.1520			1.61958			0.809790	−	0.586720i	$-0.199581\pi$
$419$	33.1520			1.61958			0.809790	+	0.586720i	$0.199581\pi$
$420$		0			0
$421$	2.64491			0.128905			0.0644525	−	0.997921i	$-0.479470\pi$
$421$	2.64491			0.128905			0.0644525	+	0.997921i	$0.479470\pi$
$422$	16.5846	−	22.9047i	0.807328	−	1.11499i
$423$		0			0
$424$	12.4607	+	3.98187i	0.605144	+	0.193377i
$425$		−	6.64799i		−	0.322475i
$426$		0			0
$427$		−	32.6286i		−	1.57901i
$428$	4.73504	+	14.4139i	0.228877	+	0.696722i
$429$		0			0
$430$	−8.19697	−	5.93518i	−0.395293	−	0.286220i
$431$	−21.3143			−1.02668			−0.513338	−	0.858187i	$-0.671591\pi$
$431$	−21.3143			−1.02668			−0.513338	+	0.858187i	$0.671591\pi$
$432$		0			0
$433$	−8.37576			−0.402513			−0.201257	−	0.979539i	$-0.564503\pi$
$433$	−8.37576			−0.402513			−0.201257	+	0.979539i	$0.564503\pi$
$434$	17.3967	+	12.5964i	0.835066	+	0.604647i
$435$		0			0
$436$	−8.88145	−	27.0359i	−0.425344	−	1.29479i
$437$			32.5387i			1.55654i
$438$		0			0
$439$		−	23.5522i		−	1.12409i	−0.827108	−	0.562043i	$-0.810016\pi$
$439$		−	23.5522i		−	1.12409i	0.827108	−	0.562043i	$-0.189984\pi$
$440$	−7.35088	−	2.34901i	−0.350439	−	0.111985i
$441$		0			0
$442$	10.1878	−	14.0702i	0.484585	−	0.669252i
$443$	−17.3378			−0.823741			−0.411871	−	0.911242i	$-0.635124\pi$
$443$	−17.3378			−0.823741			−0.411871	+	0.911242i	$0.635124\pi$
$444$		0			0
$445$	14.8298			0.703000
$446$	18.8660	−	26.0555i	0.893330	−	1.23376i
$447$		0			0
$448$	−13.4770	+	18.9338i	−0.636727	+	0.894536i
$449$		−	9.70770i		−	0.458135i	−0.973411	−	0.229067i	$-0.926432\pi$
$449$		−	9.70770i		−	0.458135i	0.973411	−	0.229067i	$-0.0735676\pi$
$450$		0			0
$451$			23.0403i			1.08492i
$452$	18.8919	−	6.20609i	0.888600	−	0.291910i
$453$		0			0
$454$	8.38438	+	6.07088i	0.393499	+	0.284921i
$455$	−5.36761			−0.251638
$456$		0			0
$457$	21.1727			0.990417			0.495208	−	0.868774i	$-0.335092\pi$
$457$	21.1727			0.990417			0.495208	+	0.868774i	$0.335092\pi$
$458$	−14.1968	−	10.2794i	−0.663371	−	0.480327i
$459$		0			0
$460$	−12.6071	+	4.14150i	−0.587809	+	0.193099i
$461$			10.1985i			0.474992i	0.971389	+	0.237496i	$0.0763266\pi$
$461$			10.1985i			0.474992i	−0.971389	+	0.237496i	$0.923673\pi$
$462$		0			0
$463$		−	6.28574i		−	0.292123i	−0.989275	−	0.146062i	$-0.953340\pi$
$463$		−	6.28574i		−	0.292123i	0.989275	−	0.146062i	$-0.0466598\pi$
$464$	13.4154	+	18.2153i	0.622793	+	0.845623i
$465$		0			0
$466$	9.05257	−	12.5023i	0.419352	−	0.579160i
$467$	20.7682			0.961037			0.480519	−	0.876984i	$-0.340448\pi$
$467$	20.7682			0.961037			0.480519	+	0.876984i	$0.340448\pi$
$468$		0			0
$469$	4.97624			0.229782
$470$	1.23253	−	1.70223i	0.0568524	−	0.0785178i
$471$		0			0
$472$	−4.41061	+	13.8023i	−0.203015	+	0.635304i
$473$			19.5244i			0.897734i
$474$		0			0
$475$		−	4.90413i		−	0.225017i
$476$	12.0549	+	36.6961i	0.552535	+	1.68196i
$477$		0			0
$478$	−0.371762	−	0.269182i	−0.0170040	−	0.0123121i
$479$	−23.4887			−1.07323			−0.536614	−	0.843828i	$-0.680297\pi$
$479$	−23.4887			−1.07323			−0.536614	+	0.843828i	$0.680297\pi$
$480$		0			0
$481$	0.518319			0.0236333
$482$	10.7631	+	7.79324i	0.490246	+	0.354972i
$483$		0			0
$484$	−2.21953	−	6.75646i	−0.100888	−	0.307112i
$485$		−	11.8860i		−	0.539713i
$486$		0			0
$487$			23.1434i			1.04873i	0.851495	+	0.524363i	$0.175696\pi$
$487$			23.1434i			1.04873i	−0.851495	+	0.524363i	$0.824304\pi$
$488$	−9.66989	+	30.2605i	−0.437735	+	1.36983i
$489$		0			0
$490$	1.19377	−	1.64869i	0.0539290	−	0.0744804i
$491$	−13.0388			−0.588434			−0.294217	−	0.955739i	$-0.595059\pi$
$491$	−13.0388			−0.588434			−0.294217	+	0.955739i	$0.595059\pi$
$492$		0			0
$493$	37.5982			1.69334
$494$	7.51542	−	10.3794i	0.338135	−	0.466992i
$495$		0			0
$496$	−12.4009	−	16.8379i	−0.556819	−	0.756044i
$497$		−	15.2608i		−	0.684539i
$498$		0			0
$499$		−	21.6538i		−	0.969359i	−0.874692	−	0.484679i	$-0.838936\pi$
$499$		−	21.6538i		−	0.969359i	0.874692	−	0.484679i	$-0.161064\pi$
$500$	1.90010	−	0.624193i	0.0849751	−	0.0279148i
$501$		0			0
$502$	28.7972	+	20.8512i	1.28528	+	0.930634i
$503$	7.47335			0.333220			0.166610	−	0.986023i	$-0.446718\pi$
$503$	7.47335			0.333220			0.166610	+	0.986023i	$0.446718\pi$
$504$		0			0
$505$	−0.612468			−0.0272544
$506$	20.7362	+	15.0145i	0.921837	+	0.667475i
$507$		0			0
$508$	29.9221	−	9.82957i	1.32758	−	0.436117i
$509$			20.7405i			0.919308i	0.888098	+	0.459654i	$0.152027\pi$
$509$			20.7405i			0.919308i	−0.888098	+	0.459654i	$0.847973\pi$
$510$		0			0
$511$			27.2122i			1.20380i
$512$	18.1101	−	13.5655i	0.800362	−	0.599518i
$513$		0			0
$514$	20.4929	−	28.3023i	0.903902	−	1.24836i
$515$	−3.06840			−0.135210
$516$		0			0
$517$	−4.05454			−0.178319
$518$	−0.675907	+	0.933483i	−0.0296977	+	0.0410149i
$519$		0			0
$520$	4.97805	+	1.59076i	0.218302	+	0.0697595i
$521$			25.8070i			1.13063i	0.824877	+	0.565313i	$0.191245\pi$
$521$			25.8070i			1.13063i	−0.824877	+	0.565313i	$0.808755\pi$
$522$		0			0
$523$			23.3489i			1.02098i	0.859885	+	0.510488i	$0.170535\pi$
$523$			23.3489i			1.02098i	−0.859885	+	0.510488i	$0.829465\pi$
$524$	8.49781	+	25.8681i	0.371229	+	1.13005i
$525$		0			0
$526$	21.3540	+	15.4618i	0.931077	+	0.674165i
$527$	−34.7552			−1.51396
$528$		0			0
$529$	21.0228			0.914033
$530$	5.29777	+	3.83596i	0.230120	+	0.166623i
$531$		0			0
$532$	8.89273	+	27.0703i	0.385549	+	1.17364i
$533$		−	15.6030i		−	0.675840i
$534$		0			0
$535$			7.58586i			0.327965i
$536$	−4.61508	−	1.47477i	−0.199341	−	0.0637005i
$537$		0			0
$538$	−4.90715	+	6.77718i	−0.211562	+	0.292185i
$539$	−3.92703			−0.169149
$540$		0			0
$541$	−19.1224			−0.822135			−0.411068	−	0.911605i	$-0.634844\pi$
$541$	−19.1224			−0.822135			−0.411068	+	0.911605i	$0.634844\pi$
$542$	−1.13832	+	1.57211i	−0.0488949	+	0.0675279i
$543$		0			0
$544$	−0.304607	−	37.6055i	−0.0130599	−	1.61232i
$545$		−	14.2287i		−	0.609489i
$546$		0			0
$547$		−	12.6517i		−	0.540950i	−0.962727	−	0.270475i	$-0.912819\pi$
$547$		−	12.6517i		−	0.540950i	0.962727	−	0.270475i	$-0.0871807\pi$
$548$	20.4818	−	6.72838i	0.874938	−	0.287422i
$549$		0			0
$550$	−3.12529	−	2.26293i	−0.133263	−	0.0964917i
$551$	27.7357			1.18158
$552$		0			0
$553$	−23.7795			−1.01121
$554$	−36.3334	−	26.3079i	−1.54366	−	1.11772i
$555$		0			0
$556$	−11.3247	+	3.72021i	−0.480273	+	0.157772i
$557$		−	35.4783i		−	1.50327i	−0.659582	−	0.751633i	$-0.729267\pi$
$557$		−	35.4783i		−	1.50327i	0.659582	−	0.751633i	$-0.270733\pi$
$558$		0			0
$559$		−	13.2220i		−	0.559232i
$560$	−9.35648	+	6.89096i	−0.395384	+	0.291196i
$561$		0			0
$562$	1.32526	−	1.83029i	0.0559027	−	0.0772062i
$563$	0.616901			0.0259993			0.0129996	−	0.999916i	$-0.495862\pi$
$563$	0.616901			0.0259993			0.0129996	+	0.999916i	$0.495862\pi$
$564$		0			0
$565$	9.94258			0.418287
$566$	6.33821	−	8.75359i	0.266415	−	0.367941i
$567$		0			0
$568$	−4.52272	+	14.1532i	−0.189769	+	0.593854i
$569$		−	12.8151i		−	0.537236i	−0.963247	−	0.268618i	$-0.913433\pi$
$569$		−	12.8151i		−	0.537236i	0.963247	−	0.268618i	$-0.0865669\pi$
$570$		0			0
$571$			20.5078i			0.858224i	0.903251	+	0.429112i	$0.141173\pi$
$571$			20.5078i			0.858224i	−0.903251	+	0.429112i	$0.858827\pi$
$572$	−3.14669	−	9.57882i	−0.131570	−	0.400511i
$573$		0			0
$574$	28.1007	+	20.3469i	1.17290	+	0.849262i
$575$	−6.63496			−0.276697
$576$		0			0
$577$	−20.2930			−0.844811			−0.422405	−	0.906407i	$-0.638814\pi$
$577$	−20.2930			−0.844811			−0.422405	+	0.906407i	$0.638814\pi$
$578$	−31.1518	−	22.5561i	−1.29575	−	0.938211i
$579$		0			0
$580$	3.53017	+	10.7462i	0.146583	+	0.446210i
$581$			26.5960i			1.10339i
$582$		0			0
$583$		−	12.6188i		−	0.522617i
$584$	8.06467	−	25.2372i	0.333718	−	1.04432i
$585$		0			0
$586$	−3.81468	+	5.26839i	−0.157583	+	0.217635i
$587$	−3.16188			−0.130505			−0.0652524	−	0.997869i	$-0.520785\pi$
$587$	−3.16188			−0.130505			−0.0652524	+	0.997869i	$0.520785\pi$
$588$		0			0
$589$	−25.6384			−1.05641
$590$	−4.24898	+	5.86819i	−0.174928	+	0.241590i
$591$		0			0
$592$	0.903501	−	0.665420i	0.0371337	−	0.0273486i
$593$			25.3926i			1.04275i	0.853328	+	0.521374i	$0.174581\pi$
$593$			25.3926i			1.04275i	−0.853328	+	0.521374i	$0.825419\pi$
$594$		0			0
$595$			19.3127i			0.791745i
$596$	2.46037	−	0.808245i	0.100781	−	0.0331070i
$597$		0			0
$598$	−14.0427	−	10.1679i	−0.574247	−	0.415795i
$599$	−21.0250			−0.859057			−0.429529	−	0.903053i	$-0.641320\pi$
$599$	−21.0250			−0.859057			−0.429529	+	0.903053i	$0.641320\pi$
$600$		0			0
$601$	−20.8073			−0.848749			−0.424374	−	0.905487i	$-0.639506\pi$
$601$	−20.8073			−0.848749			−0.424374	+	0.905487i	$0.639506\pi$
$602$	23.8126	+	17.2420i	0.970530	+	0.702732i
$603$		0			0
$604$	−13.5966	+	4.46656i	−0.553238	+	0.181742i
$605$		−	3.55584i		−	0.144566i
$606$		0			0
$607$			5.77892i			0.234559i	0.993099	+	0.117280i	$0.0374174\pi$
$607$			5.77892i			0.234559i	−0.993099	+	0.117280i	$0.962583\pi$
$608$	−0.224704	−	27.7411i	−0.00911297	−	1.12505i
$609$		0			0
$610$	−9.31554	+	12.8655i	−0.377175	+	0.520910i
$611$	2.74575			0.111081
$612$		0			0
$613$	3.50597			0.141605			0.0708025	−	0.997490i	$-0.477444\pi$
$613$	3.50597			0.141605			0.0708025	+	0.997490i	$0.477444\pi$
$614$	21.3060	−	29.4253i	0.859840	−	1.18751i
$615$		0			0
$616$	21.3547	+	6.82399i	0.860404	+	0.274947i
$617$			25.7684i			1.03740i	0.854957	+	0.518698i	$0.173583\pi$
$617$			25.7684i			1.03740i	−0.854957	+	0.518698i	$0.826417\pi$
$618$		0			0
$619$			24.1674i			0.971369i	0.874134	+	0.485685i	$0.161430\pi$
$619$			24.1674i			0.971369i	−0.874134	+	0.485685i	$0.838570\pi$
$620$	−3.26323	−	9.93358i	−0.131055	−	0.398942i
$621$		0			0
$622$	5.68042	+	4.11302i	0.227764	+	0.164917i
$623$	−43.0813			−1.72602
$624$		0			0
$625$	1.00000			0.0400000
$626$	−27.2159	−	19.7062i	−1.08777	−	0.787619i
$627$		0			0
$628$	9.80350	+	29.8427i	0.391202	+	1.19085i
$629$		−	1.86492i		−	0.0743592i
$630$		0			0
$631$			31.4403i			1.25162i	0.779976	+	0.625809i	$0.215231\pi$
$631$			31.4403i			1.25162i	−0.779976	+	0.625809i	$0.784769\pi$
$632$	22.0537	+	7.04737i	0.877248	+	0.280329i
$633$		0			0
$634$	−6.26061	+	8.64641i	−0.248641	+	0.343393i
$635$	15.7476			0.624926
$636$		0			0
$637$	2.65941			0.105369
$638$	12.7982	−	17.6753i	0.506685	−	0.699773i
$639$		0			0
$640$	10.7196	−	3.61792i	0.423731	−	0.143011i
$641$			8.61783i			0.340384i	0.985411	+	0.170192i	$0.0544388\pi$
$641$			8.61783i			0.340384i	−0.985411	+	0.170192i	$0.945561\pi$
$642$		0			0
$643$		−	6.27152i		−	0.247325i	−0.992324	−	0.123662i	$-0.960536\pi$
$643$		−	6.27152i		−	0.247325i	0.992324	−	0.123662i	$-0.0394640\pi$
$644$	36.6243	−	12.0313i	1.44320	−	0.474099i
$645$		0			0
$646$	−37.3452	−	27.0406i	−1.46933	−	1.06390i
$647$	−29.1559			−1.14624			−0.573119	−	0.819472i	$-0.694267\pi$
$647$	−29.1559			−1.14624			−0.573119	+	0.819472i	$0.694267\pi$
$648$		0			0
$649$	13.9775			0.548665
$650$	2.11646	+	1.53247i	0.0830145	+	0.0601083i
$651$		0			0
$652$	−10.7114	+	3.51875i	−0.419490	+	0.137805i
$653$			1.11680i			0.0437037i	0.999761	+	0.0218518i	$0.00695621\pi$
$653$			1.11680i			0.0437037i	−0.999761	+	0.0218518i	$0.993044\pi$
$654$		0			0
$655$			13.6141i			0.531946i
$656$	−20.0312	−	27.1981i	−0.782085	−	1.06191i
$657$		0			0
$658$	−3.58056	+	4.94505i	−0.139585	+	0.192778i
$659$	29.1898			1.13707			0.568536	−	0.822658i	$-0.307510\pi$
$659$	29.1898			1.13707			0.568536	+	0.822658i	$0.307510\pi$
$660$		0			0
$661$	43.2186			1.68101			0.840504	−	0.541805i	$-0.182259\pi$
$661$	43.2186			1.68101			0.840504	+	0.541805i	$0.182259\pi$
$662$	−3.42543	+	4.73080i	−0.133133	+	0.183868i
$663$		0			0
$664$	7.88206	−	24.6657i	0.305883	−	0.957216i
$665$			14.2468i			0.552465i
$666$		0			0
$667$		−	37.5246i		−	1.45296i
$668$	1.10642	+	3.36805i	0.0428088	+	0.130314i
$669$		0			0
$670$	−1.96214	−	1.42073i	−0.0758042	−	0.0548876i
$671$	30.6445			1.18302
$672$		0			0
$673$	4.90840			0.189205			0.0946025	−	0.995515i	$-0.469842\pi$
$673$	4.90840			0.189205			0.0946025	+	0.995515i	$0.469842\pi$
$674$	−38.9264	−	28.1855i	−1.49939	−	1.08566i
$675$		0			0
$676$	−5.98356	−	18.2145i	−0.230137	−	0.700557i
$677$			14.4018i			0.553505i	0.960941	+	0.276753i	$0.0892582\pi$
$677$			14.4018i			0.553505i	−0.960941	+	0.276753i	$0.910742\pi$
$678$		0			0
$679$			34.5293i			1.32511i
$680$	5.72357	−	17.9111i	0.219489	−	0.686858i
$681$		0			0
$682$	−11.8304	+	16.3388i	−0.453011	+	0.625644i
$683$	4.73033			0.181001			0.0905006	−	0.995896i	$-0.471153\pi$
$683$	4.73033			0.181001			0.0905006	+	0.995896i	$0.471153\pi$
$684$		0			0
$685$	10.7793			0.411856
$686$	13.3982	−	18.5040i	0.511544	−	0.706484i
$687$		0			0
$688$	−16.9745	−	23.0478i	−0.647146	−	0.878689i
$689$			8.54550i			0.325558i
$690$		0			0
$691$		−	1.43953i		−	0.0547624i	−0.999625	−	0.0273812i	$-0.991283\pi$
$691$		−	1.43953i		−	0.0547624i	0.999625	−	0.0273812i	$-0.00871680\pi$
$692$	7.36982	−	2.42103i	0.280158	−	0.0920336i
$693$		0			0
$694$	19.2378	+	13.9295i	0.730256	+	0.528757i
$695$	−5.96003			−0.226077
$696$		0			0
$697$	−56.1397			−2.12644
$698$	20.4976	+	14.8417i	0.775845	+	0.561767i
$699$		0			0
$700$	−5.51989	+	1.81331i	−0.208632	+	0.0685368i
$701$			22.0819i			0.834023i	0.908901	+	0.417012i	$0.136923\pi$
$701$			22.0819i			0.834023i	−0.908901	+	0.417012i	$0.863077\pi$
$702$		0			0
$703$		−	1.37573i		−	0.0518865i
$704$	−17.7824	−	12.6575i	−0.670201	−	0.477046i
$705$		0			0
$706$	0.443386	−	0.612352i	0.0166871	−	0.0230462i
$707$	1.77925			0.0669156
$708$		0			0
$709$	−15.0289			−0.564421			−0.282211	−	0.959352i	$-0.591068\pi$
$709$	−15.0289			−0.564421			−0.282211	+	0.959352i	$0.591068\pi$
$710$	−4.35699	+	6.01735i	−0.163515	+	0.225827i
$711$		0			0
$712$	39.9546	+	12.7677i	1.49736	+	0.478489i
$713$			34.6871i			1.29904i
$714$		0			0
$715$		−	5.04122i		−	0.188531i
$716$	0.992893	+	3.02245i	0.0371062	+	0.112954i
$717$		0			0
$718$	−25.0604	−	18.1455i	−0.935247	−	0.677185i
$719$	9.57708			0.357165			0.178582	−	0.983925i	$-0.442849\pi$
$719$	9.57708			0.357165			0.178582	+	0.983925i	$0.442849\pi$
$720$		0			0
$721$	8.91385			0.331969
$722$	−5.78521	−	4.18890i	−0.215303	−	0.155895i
$723$		0			0
$724$	13.5348	+	41.2011i	0.503016	+	1.53123i
$725$			5.65558i			0.210043i
$726$		0			0
$727$		−	19.7760i		−	0.733451i	−0.930329	−	0.366726i	$-0.880479\pi$
$727$		−	19.7760i		−	0.733451i	0.930329	−	0.366726i	$-0.119521\pi$
$728$	−14.4615	−	4.62124i	−0.535978	−	0.171275i
$729$		0			0
$730$	7.76914	−	10.7298i	0.287549	−	0.397128i
$731$	−47.5730			−1.75955
$732$		0			0
$733$	17.5678			0.648883			0.324441	−	0.945906i	$-0.394824\pi$
$733$	17.5678			0.648883			0.324441	+	0.945906i	$0.394824\pi$
$734$	19.3442	−	26.7159i	0.714006	−	0.986100i
$735$		0			0
$736$	−37.5318	+	0.304010i	−1.38344	+	0.0112060i
$737$			4.67364i			0.172156i
$738$		0			0
$739$			22.3060i			0.820538i	0.911965	+	0.410269i	$0.134565\pi$
$739$			22.3060i			0.820538i	−0.911965	+	0.410269i	$0.865435\pi$
$740$	0.533024	−	0.175101i	0.0195943	−	0.00643685i
$741$		0			0
$742$	−15.3903	−	11.1436i	−0.564995	−	0.409096i
$743$	−1.45450			−0.0533605			−0.0266803	−	0.999644i	$-0.508494\pi$
$743$	−1.45450			−0.0533605			−0.0266803	+	0.999644i	$0.508494\pi$
$744$		0			0
$745$	1.29486			0.0474401
$746$	2.29168	+	1.65934i	0.0839045	+	0.0607528i
$747$		0			0
$748$	−34.4647	+	11.3218i	−1.26015	+	0.413968i
$749$		−	22.0373i		−	0.805225i
$750$		0			0
$751$			32.8402i			1.19836i	0.800616	+	0.599178i	$0.204506\pi$
$751$			32.8402i			1.19836i	−0.800616	+	0.599178i	$0.795494\pi$
$752$	4.78622	−	3.52501i	0.174536	−	0.128544i
$753$		0			0
$754$	−8.66699	+	11.9698i	−0.315633	+	0.435915i
$755$	−7.15572			−0.260423
$756$		0			0
$757$	−19.4550			−0.707105			−0.353552	−	0.935415i	$-0.615026\pi$
$757$	−19.4550			−0.707105			−0.353552	+	0.935415i	$0.615026\pi$
$758$	23.7503	−	32.8010i	0.862648	−	1.19139i
$759$		0			0
$760$	4.22221	−	13.2128i	0.153156	−	0.479277i
$761$		−	50.7910i		−	1.84117i	−0.390538	−	0.920587i	$-0.627711\pi$
$761$		−	50.7910i		−	1.84117i	0.390538	−	0.920587i	$-0.372289\pi$
$762$		0			0
$763$			41.3350i			1.49643i
$764$	11.6065	+	35.3313i	0.419909	+	1.27824i
$765$		0			0
$766$	−23.3626	−	16.9162i	−0.844127	−	0.611207i
$767$	−9.46562			−0.341784
$768$		0			0
$769$	7.41941			0.267551			0.133775	−	0.991012i	$-0.457290\pi$
$769$	7.41941			0.267551			0.133775	+	0.991012i	$0.457290\pi$
$770$	9.07913	+	6.57393i	0.327189	+	0.236908i
$771$		0			0
$772$	7.74728	+	23.5834i	0.278831	+	0.848785i
$773$			8.44881i			0.303882i	0.988390	+	0.151941i	$0.0485525\pi$
$773$			8.44881i			0.303882i	−0.988390	+	0.151941i	$0.951448\pi$
$774$		0			0
$775$		−	5.22792i		−	0.187792i
$776$	10.2332	−	32.0233i	0.367350	−	1.14957i
$777$		0			0
$778$	−17.2287	+	23.7942i	−0.617679	+	0.853064i
$779$	−41.4135			−1.48379
$780$		0			0
$781$	14.3328			0.512867
$782$	−36.5841	+	50.5256i	−1.30824	+	1.80679i
$783$		0			0
$784$	4.63571	−	3.41415i	0.165561	−	0.121934i
$785$			15.7059i			0.560567i
$786$		0			0
$787$			22.7419i			0.810661i	0.914170	+	0.405331i	$0.132844\pi$
$787$			22.7419i			0.810661i	−0.914170	+	0.405331i	$0.867156\pi$
$788$	−36.3483	+	11.9406i	−1.29486	+	0.425367i
$789$		0			0
$790$	9.37632	+	6.78912i	0.333595	+	0.241546i
$791$	−28.8837			−1.02699
$792$		0			0
$793$	−20.7526			−0.736946
$794$	3.99532	+	2.89289i	0.141789	+	0.102665i
$795$		0			0
$796$	−22.7665	+	7.47891i	−0.806936	+	0.265083i
$797$		−	19.5651i		−	0.693031i	−0.938044	−	0.346515i	$-0.887365\pi$
$797$		−	19.5651i		−	0.693031i	0.938044	−	0.346515i	$-0.112635\pi$
$798$		0			0
$799$		−	9.87925i		−	0.349503i
$800$	5.65667	−	0.0458194i	0.199993	−	0.00161996i
$801$		0			0
$802$	−7.55565	+	10.4350i	−0.266799	+	0.368471i
$803$	−25.5574			−0.901902
$804$		0			0
$805$	19.2749			0.679351
$806$	8.01162	−	11.0647i	0.282197	−	0.389737i
$807$		0			0
$808$	−1.65012	−	0.527303i	−0.0580509	−	0.0185505i
$809$			6.76733i			0.237927i	0.992899	+	0.118963i	$0.0379571\pi$
$809$			6.76733i			0.237927i	−0.992899	+	0.118963i	$0.962043\pi$
$810$		0			0
$811$			17.7744i			0.624144i	0.950059	+	0.312072i	$0.101023\pi$
$811$			17.7744i			0.624144i	−0.950059	+	0.312072i	$0.898977\pi$
$812$	−10.2553	−	31.2182i	−0.359892	−	1.09554i
$813$		0			0
$814$	−0.876719	−	0.634806i	−0.0307290	−	0.0222500i
$815$	−5.63727			−0.197465
$816$		0			0
$817$	−35.0940			−1.22778
$818$	13.1573	+	9.52678i	0.460033	+	0.333096i
$819$		0			0
$820$	−5.27108	−	16.0456i	−0.184074	−	0.560338i
$821$		−	11.6752i		−	0.407466i	−0.979026	−	0.203733i	$-0.934692\pi$
$821$		−	11.6752i		−	0.407466i	0.979026	−	0.203733i	$-0.0653075\pi$
$822$		0			0
$823$		−	9.29678i		−	0.324065i	−0.986785	−	0.162033i	$-0.948195\pi$
$823$		−	9.29678i		−	0.324065i	0.986785	−	0.162033i	$-0.0518050\pi$
$824$	−8.26691	−	2.64173i	−0.287991	−	0.0920291i
$825$		0			0
$826$	12.3435	−	17.0474i	0.429486	−	0.593155i
$827$	−52.8269			−1.83697			−0.918485	−	0.395456i	$-0.870587\pi$
$827$	−52.8269			−1.83697			−0.918485	+	0.395456i	$0.870587\pi$
$828$		0			0
$829$	29.7034			1.03164			0.515821	−	0.856696i	$-0.327487\pi$
$829$	29.7034			1.03164			0.515821	+	0.856696i	$0.327487\pi$
$830$	7.59322	−	10.4869i	0.263565	−	0.364004i
$831$		0			0
$832$	12.0423	+	8.57169i	0.417493	+	0.297170i
$833$		−	9.56857i		−	0.331531i
$834$		0			0
$835$			1.77257i			0.0613421i
$836$	−25.4242	+	8.35198i	−0.879313	+	0.288859i
$837$		0			0
$838$	37.9745	+	27.4962i	1.31181	+	0.949841i
$839$	−23.9258			−0.826009			−0.413005	−	0.910729i	$-0.635521\pi$
$839$	−23.9258			−0.826009			−0.413005	+	0.910729i	$0.635521\pi$
$840$		0			0
$841$	−2.98555			−0.102950
$842$	3.02966	+	2.19369i	0.104409	+	0.0755994i
$843$		0			0
$844$	37.9944	−	12.4814i	1.30782	−	0.429626i
$845$		−	9.58606i		−	0.329771i
$846$		0			0
$847$			10.3299i			0.354940i
$848$	10.9707	+	14.8960i	0.376737	+	0.511530i
$849$		0			0
$850$	5.51384	−	7.61506i	0.189123	−	0.261194i
$851$	−1.86127			−0.0638034
$852$		0			0
$853$	−41.2614			−1.41276			−0.706382	−	0.707831i	$-0.749674\pi$
$853$	−41.2614			−1.41276			−0.706382	+	0.707831i	$0.749674\pi$
$854$	27.0621	−	37.3750i	0.926047	−	1.27895i
$855$		0			0
$856$	−6.53103	+	20.4379i	−0.223226	+	0.698553i
$857$		−	24.5979i		−	0.840248i	−0.907467	−	0.420124i	$-0.861987\pi$
$857$		−	24.5979i		−	0.840248i	0.907467	−	0.420124i	$-0.138013\pi$
$858$		0			0
$859$		−	9.40262i		−	0.320813i	−0.987051	−	0.160407i	$-0.948719\pi$
$859$		−	9.40262i		−	0.320813i	0.987051	−	0.160407i	$-0.0512806\pi$
$860$	−4.46673	−	13.5971i	−0.152314	−	0.463658i
$861$		0			0
$862$	−24.4149	−	17.6781i	−0.831575	−	0.602119i
$863$	−14.4801			−0.492909			−0.246455	−	0.969154i	$-0.579266\pi$
$863$	−14.4801			−0.492909			−0.246455	+	0.969154i	$0.579266\pi$
$864$		0			0
$865$	3.87865			0.131878
$866$	−9.59416	−	6.94685i	−0.326023	−	0.236064i
$867$		0			0
$868$	9.47986	+	28.8575i	0.321767	+	0.979489i
$869$		−	22.3335i		−	0.757613i
$870$		0			0
$871$		−	3.16501i		−	0.107242i
$872$	12.2502	−	38.3350i	0.414843	−	1.29819i
$873$		0			0
$874$	−26.9876	+	37.2721i	−0.912870	+	1.26075i
$875$	−2.90505			−0.0982086
$876$		0			0
$877$	27.2297			0.919480			0.459740	−	0.888053i	$-0.347943\pi$
$877$	27.2297			0.919480			0.459740	+	0.888053i	$0.347943\pi$
$878$	19.5342	−	26.9783i	0.659247	−	0.910474i
$879$		0			0
$880$	−6.47193	−	8.78753i	−0.218169	−	0.296228i
$881$			24.9990i			0.842236i	0.907006	+	0.421118i	$0.138362\pi$
$881$			24.9990i			0.842236i	−0.907006	+	0.421118i	$0.861638\pi$
$882$		0			0
$883$		−	50.7029i		−	1.70629i	−0.521676	−	0.853143i	$-0.674693\pi$
$883$		−	50.7029i		−	1.70629i	0.521676	−	0.853143i	$-0.325307\pi$
$884$	23.3397	−	7.66720i	0.784997	−	0.257876i
$885$		0			0
$886$	−19.8598	−	14.3799i	−0.667204	−	0.483103i
$887$	26.8363			0.901074			0.450537	−	0.892758i	$-0.351233\pi$
$887$	26.8363			0.901074			0.450537	+	0.892758i	$0.351233\pi$
$888$		0			0
$889$	−45.7477			−1.53433
$890$	16.9871	+	12.2998i	0.569407	+	0.412291i
$891$		0			0
$892$	43.2208	−	14.1983i	1.44714	−	0.475393i
$893$		−	7.28780i		−	0.243877i
$894$		0			0
$895$			1.59068i			0.0531706i
$896$	−31.1411	+	10.5102i	−1.04035	+	0.351122i
$897$		0			0
$898$	8.05156	−	11.1199i	0.268684	−	0.371075i
$899$	29.5669			0.986112
$900$		0			0
$901$	30.7468			1.02432
$902$	−19.1096	+	26.3919i	−0.636280	+	0.878754i
$903$		0			0
$904$	26.7874	+	8.56005i	0.890936	+	0.284703i
$905$			21.6836i			0.720789i
$906$		0			0
$907$		−	2.89120i		−	0.0960009i	−0.998847	−	0.0480004i	$-0.984715\pi$
$907$		−	2.89120i		−	0.0960009i	0.998847	−	0.0480004i	$-0.0152849\pi$
$908$	4.56885	+	13.9080i	0.151623	+	0.461553i
$909$		0			0
$910$	−6.14843	−	4.45190i	−0.203818	−	0.147579i
$911$	59.2509			1.96307			0.981534	−	0.191287i	$-0.0612662\pi$
$911$	59.2509			1.96307			0.981534	+	0.191287i	$0.0612662\pi$
$912$		0			0
$913$	−24.9787			−0.826675
$914$	24.2526	+	17.5606i	0.802206	+	0.580854i
$915$		0			0
$916$	−7.73616	−	23.5496i	−0.255610	−	0.778099i
$917$		−	39.5496i		−	1.30604i
$918$		0			0
$919$			21.5957i			0.712378i	0.934414	+	0.356189i	$0.115924\pi$
$919$			21.5957i			0.712378i	−0.934414	+	0.356189i	$0.884076\pi$
$920$	−17.8760	−	5.71236i	−0.589354	−	0.188331i
$921$		0			0
$922$	−8.45863	+	11.6821i	−0.278570	+	0.384728i
$923$	−9.70622			−0.319484
$924$		0			0
$925$	0.280524			0.00922357
$926$	5.21339	−	7.20012i	0.171323	−	0.236611i
$927$		0			0
$928$	0.259135	+	31.9917i	0.00850653	+	1.05018i
$929$			16.1178i			0.528808i	0.964412	+	0.264404i	$0.0851752\pi$
$929$			16.1178i			0.528808i	−0.964412	+	0.264404i	$0.914825\pi$
$930$		0			0
$931$		−	7.05861i		−	0.231337i
$932$	20.7389	−	6.81283i	0.679324	−	0.223162i
$933$		0			0
$934$	23.7893	+	17.2251i	0.778410	+	0.563623i
$935$	−18.1384			−0.593188
$936$		0			0
$937$	−49.1241			−1.60481			−0.802407	−	0.596778i	$-0.796447\pi$
$937$	−49.1241			−1.60481			−0.802407	+	0.596778i	$0.796447\pi$
$938$	5.70013	+	4.12729i	0.186116	+	0.134761i
$939$		0			0
$940$	2.82365	−	0.927584i	0.0920973	−	0.0302545i
$941$		−	13.9023i		−	0.453201i	−0.973988	−	0.226601i	$-0.927239\pi$
$941$		−	13.9023i		−	0.453201i	0.973988	−	0.226601i	$-0.0727612\pi$
$942$		0			0
$943$			56.0298i			1.82458i
$944$	−16.4999	+	12.1520i	−0.537025	+	0.395514i
$945$		0			0
$946$	−16.1935	+	22.3646i	−0.526498	+	0.727136i
$947$	16.5462			0.537679			0.268840	−	0.963185i	$-0.413360\pi$
$947$	16.5462			0.537679			0.268840	+	0.963185i	$0.413360\pi$
$948$		0			0
$949$	17.3076			0.561829
$950$	4.06748	−	5.61753i	0.131967	−	0.182257i
$951$		0			0
$952$	−16.6273	+	52.0326i	−0.538893	+	1.68639i
$953$		−	4.44099i		−	0.143858i	−0.997410	−	0.0719288i	$-0.977085\pi$
$953$		−	4.44099i		−	0.143858i	0.997410	−	0.0719288i	$-0.0229155\pi$
$954$		0			0
$955$			18.5944i			0.601701i
$956$	−0.202582	−	0.616678i	−0.00655197	−	0.0199448i
$957$		0			0
$958$	−26.9056	−	19.4815i	−0.869281	−	0.629420i
$959$	−31.3144			−1.01120
$960$		0			0
$961$	3.66884			0.118350
$962$	0.593718	+	0.429894i	0.0191422	+	0.0138603i
$963$		0			0
$964$	5.86507	+	17.8538i	0.188901	+	0.575032i
$965$			12.4117i			0.399545i
$966$		0			0
$967$		−	56.4877i		−	1.81652i	−0.418402	−	0.908262i	$-0.637410\pi$
$967$		−	56.4877i		−	1.81652i	0.418402	−	0.908262i	$-0.362590\pi$
$968$	3.06140	−	9.58019i	0.0983971	−	0.307919i
$969$		0			0
$970$	9.85820	−	13.6150i	0.316528	−	0.437151i
$971$	23.7664			0.762699			0.381350	−	0.924431i	$-0.375459\pi$
$971$	23.7664			0.762699			0.381350	+	0.924431i	$0.375459\pi$
$972$		0			0
$973$	17.3142			0.555068
$974$	−19.1951	+	26.5100i	−0.615050	+	0.849435i
$975$		0			0
$976$	−36.1746	+	26.6422i	−1.15792	+	0.852796i
$977$			26.0224i			0.832532i	0.909243	+	0.416266i	$0.136661\pi$
$977$			26.0224i			0.832532i	−0.909243	+	0.416266i	$0.863339\pi$
$978$		0			0
$979$		−	40.4616i		−	1.29316i
$980$	2.73485	−	0.898413i	0.0873616	−	0.0286988i
$981$		0			0
$982$	−14.9356	−	10.8144i	−0.476613	−	0.345101i
$983$	36.7952			1.17359			0.586793	−	0.809737i	$-0.300390\pi$
$983$	36.7952			1.17359			0.586793	+	0.809737i	$0.300390\pi$
$984$		0			0
$985$	−19.1297			−0.609522
$986$	43.0675	+	31.1839i	1.37155	+	0.993098i
$987$		0			0
$988$	17.2174	−	5.65600i	0.547757	−	0.179941i
$989$			47.4798i			1.50977i
$990$		0			0
$991$		−	52.7208i		−	1.67473i	−0.546644	−	0.837365i	$-0.684095\pi$
$991$		−	52.7208i		−	1.67473i	0.546644	−	0.837365i	$-0.315905\pi$
$992$	−0.239540	−	29.5726i	−0.00760541	−	0.938932i
$993$		0			0
$994$	12.6573	−	17.4807i	0.401464	−	0.554454i
$995$	−11.9817			−0.379846
$996$		0			0
$997$	31.5789			1.00011			0.500057	−	0.865993i	$-0.333312\pi$
$997$	31.5789			1.00011			0.500057	+	0.865993i	$0.333312\pi$
$998$	17.9597	−	24.8038i	0.568504	−	0.785150i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1620.2.e.b.971.40		48
3.2	odd	2	inner	1620.2.e.b.971.9		48
4.3	odd	2	inner	1620.2.e.b.971.10		48
9.2	odd	6		180.2.q.a.131.12	yes	48
9.4	even	3		180.2.q.a.11.4	✓	48
9.5	odd	6		540.2.q.a.251.21		48
9.7	even	3		540.2.q.a.71.13		48
12.11	even	2	inner	1620.2.e.b.971.39		48
36.7	odd	6		540.2.q.a.71.21		48
36.11	even	6		180.2.q.a.131.4	yes	48
36.23	even	6		540.2.q.a.251.13		48
36.31	odd	6		180.2.q.a.11.12	yes	48
45.2	even	12		900.2.o.c.599.2		48
45.4	even	6		900.2.r.f.551.21		48
45.13	odd	12		900.2.o.c.299.16		48
45.22	odd	12		900.2.o.b.299.9		48
45.29	odd	6		900.2.r.f.851.13		48
45.38	even	12		900.2.o.b.599.23		48
180.47	odd	12		900.2.o.c.599.16		48
180.67	even	12		900.2.o.b.299.23		48
180.83	odd	12		900.2.o.b.599.9		48
180.103	even	12		900.2.o.c.299.2		48
180.119	even	6		900.2.r.f.851.21		48
180.139	odd	6		900.2.r.f.551.13		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
180.2.q.a.11.4	✓	48	9.4	even	3
180.2.q.a.11.12	yes	48	36.31	odd	6
180.2.q.a.131.4	yes	48	36.11	even	6
180.2.q.a.131.12	yes	48	9.2	odd	6
540.2.q.a.71.13		48	9.7	even	3
540.2.q.a.71.21		48	36.7	odd	6
540.2.q.a.251.13		48	36.23	even	6
540.2.q.a.251.21		48	9.5	odd	6
900.2.o.b.299.9		48	45.22	odd	12
900.2.o.b.299.23		48	180.67	even	12
900.2.o.b.599.9		48	180.83	odd	12
900.2.o.b.599.23		48	45.38	even	12
900.2.o.c.299.2		48	180.103	even	12
900.2.o.c.299.16		48	45.13	odd	12
900.2.o.c.599.2		48	45.2	even	12
900.2.o.c.599.16		48	180.47	odd	12
900.2.r.f.551.13		48	180.139	odd	6
900.2.r.f.551.21		48	45.4	even	6
900.2.r.f.851.13		48	45.29	odd	6
900.2.r.f.851.21		48	180.119	even	6
1620.2.e.b.971.9		48	3.2	odd	2	inner
1620.2.e.b.971.10		48	4.3	odd	2	inner
1620.2.e.b.971.39		48	12.11	even	2	inner
1620.2.e.b.971.40		48	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1620 = 2^{2} \cdot 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1620.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.14547 + 0.829399i) q^{2} +(0.624193 + 1.90010i) q^{4} +1.00000i q^{5} -2.90505i q^{7} +(-0.860949 + 2.69421i) q^{8} +O(q^{10})\)	\(q+(1.14547 + 0.829399i) q^{2} +(0.624193 + 1.90010i) q^{4} +1.00000i q^{5} -2.90505i q^{7} +(-0.860949 + 2.69421i) q^{8} +(-0.829399 + 1.14547i) q^{10} +2.72840 q^{11} -1.84768 q^{13} +(2.40945 - 3.32764i) q^{14} +(-3.22076 + 2.37206i) q^{16} +6.64799i q^{17} +4.90413i q^{19} +(-1.90010 + 0.624193i) q^{20} +(3.12529 + 2.26293i) q^{22} +6.63496 q^{23} -1.00000 q^{25} +(-2.11646 - 1.53247i) q^{26} +(5.51989 - 1.81331i) q^{28} -5.65558i q^{29} +5.22792i q^{31} +(-5.65667 + 0.0458194i) q^{32} +(-5.51384 + 7.61506i) q^{34} +2.90505 q^{35} -0.280524 q^{37} +(-4.06748 + 5.61753i) q^{38} +(-2.69421 - 0.860949i) q^{40} +8.44462i q^{41} +7.15600i q^{43} +(1.70305 + 5.18423i) q^{44} +(7.60014 + 5.50304i) q^{46} -1.48605 q^{47} -1.43932 q^{49} +(-1.14547 - 0.829399i) q^{50} +(-1.15331 - 3.51079i) q^{52} -4.62498i q^{53} +2.72840i q^{55} +(7.82682 + 2.50110i) q^{56} +(4.69073 - 6.47828i) q^{58} +5.12297 q^{59} +11.2317 q^{61} +(-4.33603 + 5.98842i) q^{62} +(-6.51754 - 4.63915i) q^{64} -1.84768i q^{65} +1.71296i q^{67} +(-12.6318 + 4.14963i) q^{68} +(3.32764 + 2.40945i) q^{70} +5.25318 q^{71} -9.36719 q^{73} +(-0.321331 - 0.232666i) q^{74} +(-9.31835 + 3.06113i) q^{76} -7.92613i q^{77} -8.18558i q^{79} +(-2.37206 - 3.22076i) q^{80} +(-7.00396 + 9.67304i) q^{82} -9.15508 q^{83} -6.64799 q^{85} +(-5.93518 + 8.19697i) q^{86} +(-2.34901 + 7.35088i) q^{88} -14.8298i q^{89} +5.36761i q^{91} +(4.14150 + 12.6071i) q^{92} +(-1.70223 - 1.23253i) q^{94} -4.90413 q^{95} -11.8860 q^{97} +(-1.64869 - 1.19377i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q+O(q^{10}) \) 48 * q	\( 48 q - 48 q^{25} + 12 q^{34} + 12 q^{40} - 12 q^{46} - 48 q^{49} + 36 q^{52} + 36 q^{58} - 48 q^{64} - 24 q^{73} - 12 q^{76} - 36 q^{82} - 36 q^{94} + 24 q^{97}+O(q^{100}) \) 48 * q - 48 * q^25 + 12 * q^34 + 12 * q^40 - 12 * q^46 - 48 * q^49 + 36 * q^52 + 36 * q^58 - 48 * q^64 - 24 * q^73 - 12 * q^76 - 36 * q^82 - 36 * q^94 + 24 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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