LMFDB - Embedded newform 552.2.q.c.169.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [552,2,Mod(25,552)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(552, base_ring=CyclotomicField(22))

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

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

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

chi := DirichletCharacter("552.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 552 = 2^{3} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	552.q (of order $11$, degree $10$, 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:	$4.40774219157$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$3$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			169.3
Character	$\chi$	$=$	552.169
Dual form			552.2.q.c.49.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.415415 - 0.909632i) q^{3} +(2.51217 + 2.89920i) q^{5} +(2.61719 + 1.68197i) q^{7} +(-0.654861 + 0.755750i) q^{9} +O(q^{10})$	\(q+(-0.415415 - 0.909632i) q^{3} +(2.51217 + 2.89920i) q^{5} +(2.61719 + 1.68197i) q^{7} +(-0.654861 + 0.755750i) q^{9} +(0.0478738 + 0.332970i) q^{11} +(-4.73267 + 3.04150i) q^{13} +(1.59361 - 3.48952i) q^{15} +(-5.48646 + 1.61097i) q^{17} +(4.28467 + 1.25809i) q^{19} +(0.442750 - 3.07940i) q^{21} +(-4.68923 - 1.00555i) q^{23} +(-1.38279 + 9.61748i) q^{25} +(0.959493 + 0.281733i) q^{27} +(1.37053 - 0.402425i) q^{29} +(3.93521 - 8.61691i) q^{31} +(0.282993 - 0.181868i) q^{33} +(1.69848 + 11.8132i) q^{35} +(5.66392 - 6.53651i) q^{37} +(4.73267 + 3.04150i) q^{39} +(4.86668 + 5.61645i) q^{41} +(0.385078 + 0.843203i) q^{43} -3.83619 q^{45} +1.77722 q^{47} +(1.11277 + 2.43664i) q^{49} +(3.74455 + 4.32144i) q^{51} +(5.74810 + 3.69408i) q^{53} +(-0.845080 + 0.975274i) q^{55} +(-0.635515 - 4.42010i) q^{57} +(6.13224 - 3.94095i) q^{59} +(3.51576 - 7.69845i) q^{61} +(-2.98504 + 0.876487i) q^{63} +(-20.7072 - 6.08019i) q^{65} +(1.46100 - 10.1615i) q^{67} +(1.03330 + 4.68319i) q^{69} +(-0.180304 + 1.25404i) q^{71} +(6.23776 + 1.83157i) q^{73} +(9.32280 - 2.73742i) q^{75} +(-0.434749 + 0.951968i) q^{77} +(-5.06474 + 3.25491i) q^{79} +(-0.142315 - 0.989821i) q^{81} +(-6.39485 + 7.38005i) q^{83} +(-18.4535 - 11.8593i) q^{85} +(-0.935399 - 1.07951i) q^{87} +(-5.09455 - 11.1555i) q^{89} -17.5020 q^{91} -9.47297 q^{93} +(7.11637 + 15.5827i) q^{95} +(5.23566 + 6.04227i) q^{97} +(-0.282993 - 0.181868i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 3 q^{3} - 2 q^{5} - 2 q^{7} - 3 q^{9}+O(q^{10}) $ 30 * q + 3 * q^3 - 2 * q^5 - 2 * q^7 - 3 * q^9	$ 30 q + 3 q^{3} - 2 q^{5} - 2 q^{7} - 3 q^{9} + 13 q^{11} - 13 q^{13} + 2 q^{15} - 11 q^{17} + 11 q^{19} - 9 q^{21} - 12 q^{23} + 17 q^{25} + 3 q^{27} + 9 q^{29} + 33 q^{31} + 9 q^{33} + 62 q^{35} + 11 q^{37} + 13 q^{39} + 2 q^{41} - 40 q^{43} - 2 q^{45} - 38 q^{47} - 13 q^{49} + 11 q^{51} - 25 q^{53} + 62 q^{55} + 22 q^{57} + 73 q^{59} + 4 q^{61} - 2 q^{63} - 12 q^{65} - 29 q^{67} - 21 q^{69} - 19 q^{71} - 38 q^{73} + 27 q^{75} + 4 q^{77} - 12 q^{79} - 3 q^{81} - 65 q^{83} + 8 q^{85} + 2 q^{87} - 61 q^{89} - 150 q^{91} - 22 q^{93} - 9 q^{95} - 9 q^{97} - 9 q^{99}+O(q^{100}) $ 30 * q + 3 * q^3 - 2 * q^5 - 2 * q^7 - 3 * q^9 + 13 * q^11 - 13 * q^13 + 2 * q^15 - 11 * q^17 + 11 * q^19 - 9 * q^21 - 12 * q^23 + 17 * q^25 + 3 * q^27 + 9 * q^29 + 33 * q^31 + 9 * q^33 + 62 * q^35 + 11 * q^37 + 13 * q^39 + 2 * q^41 - 40 * q^43 - 2 * q^45 - 38 * q^47 - 13 * q^49 + 11 * q^51 - 25 * q^53 + 62 * q^55 + 22 * q^57 + 73 * q^59 + 4 * q^61 - 2 * q^63 - 12 * q^65 - 29 * q^67 - 21 * q^69 - 19 * q^71 - 38 * q^73 + 27 * q^75 + 4 * q^77 - 12 * q^79 - 3 * q^81 - 65 * q^83 + 8 * q^85 + 2 * q^87 - 61 * q^89 - 150 * q^91 - 22 * q^93 - 9 * q^95 - 9 * q^97 - 9 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/552\mathbb{Z}\right)^\times$.

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$e\left(\frac{3}{11}\right)$	$1$	$1$	$1$

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			0
$2$		0			0
$3$	−0.415415	−	0.909632i	−0.239840	−	0.525176i
$3$	−0.415415	−	0.909632i	−0.239840	−	0.525176i
$4$		0			0
$5$	2.51217	+	2.89920i	1.12348	+	1.29656i	0.950183	+	0.311692i	$0.100896\pi$
$5$	2.51217	+	2.89920i	1.12348	+	1.29656i	0.173295	+	0.984870i	$0.444559\pi$
$6$		0			0
$7$	2.61719	+	1.68197i	0.989206	+	0.635724i	0.931931	−	0.362635i	$-0.118123\pi$
$7$	2.61719	+	1.68197i	0.989206	+	0.635724i	0.0572742	+	0.998358i	$0.481759\pi$
$8$		0			0
$9$	−0.654861	+	0.755750i	−0.218287	+	0.251917i
$10$		0			0
$11$	0.0478738	+	0.332970i	0.0144345	+	0.100394i	0.995765	−	0.0919346i	$-0.0293051\pi$
$11$	0.0478738	+	0.332970i	0.0144345	+	0.100394i	−0.981331	+	0.192329i	$0.938396\pi$
$12$		0			0
$13$	−4.73267	+	3.04150i	−1.31261	+	0.843561i	−0.994525	−	0.104502i	$-0.966675\pi$
$13$	−4.73267	+	3.04150i	−1.31261	+	0.843561i	−0.318082	+	0.948063i	$0.603039\pi$
$14$		0			0
$15$	1.59361	−	3.48952i	0.411469	−	0.900991i
$16$		0			0
$17$	−5.48646	+	1.61097i	−1.33066	+	0.390718i	−0.868329	−	0.495989i	$-0.834806\pi$
$17$	−5.48646	+	1.61097i	−1.33066	+	0.390718i	−0.462333	+	0.886706i	$0.652987\pi$
$18$		0			0
$19$	4.28467	+	1.25809i	0.982971	+	0.288626i	0.733450	−	0.679743i	$-0.237909\pi$
$19$	4.28467	+	1.25809i	0.982971	+	0.288626i	0.249520	+	0.968370i	$0.419727\pi$
$20$		0			0
$21$	0.442750	−	3.07940i	0.0966160	−	0.671979i
$22$		0			0
$23$	−4.68923	−	1.00555i	−0.977772	−	0.209672i
$23$	−4.68923	−	1.00555i	−0.977772	−	0.209672i
$24$		0			0
$25$	−1.38279	+	9.61748i	−0.276557	+	1.92350i
$26$		0			0
$27$	0.959493	+	0.281733i	0.184655	+	0.0542195i
$28$		0			0
$29$	1.37053	−	0.402425i	0.254502	−	0.0747284i	−0.151993	−	0.988382i	$-0.548569\pi$
$29$	1.37053	−	0.402425i	0.254502	−	0.0747284i	0.406495	+	0.913653i	$0.366751\pi$
$30$		0			0
$31$	3.93521	−	8.61691i	0.706785	−	1.54764i	−0.124761	−	0.992187i	$-0.539816\pi$
$31$	3.93521	−	8.61691i	0.706785	−	1.54764i	0.831546	−	0.555456i	$-0.187456\pi$
$32$		0			0
$33$	0.282993	−	0.181868i	0.0492627	−	0.0316592i
$34$		0			0
$35$	1.69848	+	11.8132i	0.287095	+	1.99679i
$36$		0			0
$37$	5.66392	−	6.53651i	0.931143	−	1.07460i	−0.0659057	−	0.997826i	$-0.520994\pi$
$37$	5.66392	−	6.53651i	0.931143	−	1.07460i	0.997049	−	0.0767706i	$-0.0244609\pi$
$38$		0			0
$39$	4.73267	+	3.04150i	0.757834	+	0.487030i
$40$		0			0
$41$	4.86668	+	5.61645i	0.760048	+	0.877142i	0.995502	−	0.0947431i	$-0.0302030\pi$
$41$	4.86668	+	5.61645i	0.760048	+	0.877142i	−0.235453	+	0.971886i	$0.575658\pi$
$42$		0			0
$43$	0.385078	+	0.843203i	0.0587239	+	0.128587i	0.936719	−	0.350082i	$-0.113846\pi$
$43$	0.385078	+	0.843203i	0.0587239	+	0.128587i	−0.877995	+	0.478670i	$0.841119\pi$
$44$		0			0
$45$	−3.83619			−0.571866
$46$		0			0
$47$	1.77722			0.259234			0.129617	−	0.991564i	$-0.458625\pi$
$47$	1.77722			0.259234			0.129617	+	0.991564i	$0.458625\pi$
$48$		0			0
$49$	1.11277	+	2.43664i	0.158968	+	0.348091i
$50$		0			0
$51$	3.74455	+	4.32144i	0.524341	+	0.605122i
$52$		0			0
$53$	5.74810	+	3.69408i	0.789563	+	0.507421i	0.872195	−	0.489159i	$-0.162696\pi$
$53$	5.74810	+	3.69408i	0.789563	+	0.507421i	−0.0826320	+	0.996580i	$0.526333\pi$
$54$		0			0
$55$	−0.845080	+	0.975274i	−0.113951	+	0.131506i
$56$		0			0
$57$	−0.635515	−	4.42010i	−0.0841760	−	0.585457i
$58$		0			0
$59$	6.13224	−	3.94095i	0.798350	−	0.513068i	−0.0767272	−	0.997052i	$-0.524447\pi$
$59$	6.13224	−	3.94095i	0.798350	−	0.513068i	0.875077	+	0.483984i	$0.160811\pi$
$60$		0			0
$61$	3.51576	−	7.69845i	0.450147	−	0.985685i	−0.539476	−	0.842001i	$-0.681378\pi$
$61$	3.51576	−	7.69845i	0.450147	−	0.985685i	0.989624	−	0.143684i	$-0.0458950\pi$
$62$		0			0
$63$	−2.98504	+	0.876487i	−0.376080	+	0.110427i
$64$		0			0
$65$	−20.7072	−	6.08019i	−2.56841	−	0.754154i
$66$		0			0
$67$	1.46100	−	10.1615i	0.178490	−	1.24142i	−0.681770	−	0.731567i	$-0.738789\pi$
$67$	1.46100	−	10.1615i	0.178490	−	1.24142i	0.860259	−	0.509857i	$-0.170302\pi$
$68$		0			0
$69$	1.03330	+	4.68319i	0.124394	+	0.563790i
$70$		0			0
$71$	−0.180304	+	1.25404i	−0.0213981	+	0.148827i	−0.997719	−	0.0674984i	$-0.978498\pi$
$71$	−0.180304	+	1.25404i	−0.0213981	+	0.148827i	0.976321	+	0.216326i	$0.0694073\pi$
$72$		0			0
$73$	6.23776	+	1.83157i	0.730075	+	0.214369i	0.625584	−	0.780157i	$-0.284861\pi$
$73$	6.23776	+	1.83157i	0.730075	+	0.214369i	0.104491	+	0.994526i	$0.466679\pi$
$74$		0			0
$75$	9.32280	−	2.73742i	1.07650	−	0.316090i
$76$		0			0
$77$	−0.434749	+	0.951968i	−0.0495443	+	0.108487i
$78$		0			0
$79$	−5.06474	+	3.25491i	−0.569828	+	0.366206i	−0.793604	−	0.608434i	$-0.791798\pi$
$79$	−5.06474	+	3.25491i	−0.569828	+	0.366206i	0.223776	+	0.974641i	$0.428162\pi$
$80$		0			0
$81$	−0.142315	−	0.989821i	−0.0158128	−	0.109980i
$82$		0			0
$83$	−6.39485	+	7.38005i	−0.701926	+	0.810066i	−0.989011	−	0.147839i	$-0.952768\pi$
$83$	−6.39485	+	7.38005i	−0.701926	+	0.810066i	0.287085	+	0.957905i	$0.407314\pi$
$84$		0			0
$85$	−18.4535	−	11.8593i	−2.00156	−	1.28632i
$86$		0			0
$87$	−0.935399	−	1.07951i	−0.100285	−	0.115735i
$88$		0			0
$89$	−5.09455	−	11.1555i	−0.540022	−	1.18248i	−0.961288	−	0.275546i	$-0.911141\pi$
$89$	−5.09455	−	11.1555i	−0.540022	−	1.18248i	0.421266	−	0.906937i	$-0.361586\pi$
$90$		0			0
$91$	−17.5020			−1.83471
$92$		0			0
$93$	−9.47297			−0.982301
$94$		0			0
$95$	7.11637	+	15.5827i	0.730124	+	1.59875i
$96$		0			0
$97$	5.23566	+	6.04227i	0.531601	+	0.613500i	0.956497	−	0.291742i	$-0.0942349\pi$
$97$	5.23566	+	6.04227i	0.531601	+	0.613500i	−0.424896	+	0.905242i	$0.639689\pi$
$98$		0			0
$99$	−0.282993	−	0.181868i	−0.0284418	−	0.0182784i
$100$		0			0
$101$	−3.63583	+	4.19598i	−0.361779	+	0.417515i	−0.907235	−	0.420624i	$-0.861811\pi$
$101$	−3.63583	+	4.19598i	−0.361779	+	0.417515i	0.545456	+	0.838140i	$0.316357\pi$
$102$		0			0
$103$	−2.78560	−	19.3742i	−0.274473	−	1.90900i	−0.399297	−	0.916822i	$-0.630746\pi$
$103$	−2.78560	−	19.3742i	−0.274473	−	1.90900i	0.124824	−	0.992179i	$-0.460163\pi$
$104$		0			0
$105$	10.0401	−	6.45235i	0.979809	−	0.629685i
$106$		0			0
$107$	3.96937	−	8.69171i	0.383734	−	0.840260i	−0.614930	−	0.788582i	$-0.710816\pi$
$107$	3.96937	−	8.69171i	0.383734	−	0.840260i	0.998664	−	0.0516781i	$-0.0164570\pi$
$108$		0			0
$109$	−1.05464	+	0.309669i	−0.101016	+	0.0296609i	−0.331850	−	0.943332i	$-0.607673\pi$
$109$	−1.05464	+	0.309669i	−0.101016	+	0.0296609i	0.230834	+	0.972993i	$0.425855\pi$
$110$		0			0
$111$	−8.29870	−	2.43672i	−0.787678	−	0.231283i
$112$		0			0
$113$	−2.28157	+	15.8686i	−0.214632	+	1.49280i	0.542789	+	0.839869i	$0.317368\pi$
$113$	−2.28157	+	15.8686i	−0.214632	+	1.49280i	−0.757421	+	0.652927i	$0.773541\pi$
$114$		0			0
$115$	−8.86486	−	16.1211i	−0.826653	−	1.50330i
$116$		0			0
$117$	0.800626	−	5.56847i	0.0740179	−	0.514806i
$118$		0			0
$119$	−17.0687	−	5.01183i	−1.56469	−	0.459433i
$120$		0			0
$121$	10.4458	−	3.06718i	0.949622	−	0.278834i
$122$		0			0
$123$	3.08721	−	6.76005i	0.278364	−	0.609533i
$124$		0			0
$125$	−15.2208	+	9.78179i	−1.36139	+	0.874910i
$126$		0			0
$127$	−0.365156	−	2.53972i	−0.0324024	−	0.225364i	0.967185	−	0.254071i	$-0.0817698\pi$
$127$	−0.365156	−	2.53972i	−0.0324024	−	0.225364i	−0.999588	+	0.0287078i	$0.990861\pi$
$128$		0			0
$129$	0.607038	−	0.700559i	0.0534467	−	0.0616808i
$130$		0			0
$131$	4.54663	+	2.92194i	0.397241	+	0.255291i	0.723977	−	0.689824i	$-0.242312\pi$
$131$	4.54663	+	2.92194i	0.397241	+	0.255291i	−0.326736	+	0.945116i	$0.605949\pi$
$132$		0			0
$133$	9.09773	+	10.4993i	0.788873	+	0.910408i
$134$		0			0
$135$	1.59361	+	3.48952i	0.137156	+	0.300330i
$136$		0			0
$137$	−16.5279			−1.41207			−0.706035	−	0.708177i	$-0.749518\pi$
$137$	−16.5279			−1.41207			−0.706035	+	0.708177i	$0.749518\pi$
$138$		0			0
$139$	20.2896			1.72094			0.860472	−	0.509498i	$-0.170169\pi$
$139$	20.2896			1.72094			0.860472	+	0.509498i	$0.170169\pi$
$140$		0			0
$141$	−0.738284	−	1.61662i	−0.0621748	−	0.136144i
$142$		0			0
$143$	−1.23930	−	1.43023i	−0.103635	−	0.119602i
$144$		0			0
$145$	4.60973	+	2.96249i	0.382817	+	0.246022i
$146$		0			0
$147$	1.75418	−	2.02443i	0.144682	−	0.166972i
$148$		0			0
$149$	−1.77776	−	12.3646i	−0.145640	−	1.01295i	−0.923250	−	0.384200i	$-0.874477\pi$
$149$	−1.77776	−	12.3646i	−0.145640	−	1.01295i	0.777610	−	0.628747i	$-0.216432\pi$
$150$		0			0
$151$	−11.8699	+	7.62835i	−0.965963	+	0.620787i	−0.925642	−	0.378400i	$-0.876474\pi$
$151$	−11.8699	+	7.62835i	−0.965963	+	0.620787i	−0.0403207	+	0.999187i	$0.512838\pi$
$152$		0			0
$153$	2.37538	−	5.20135i	0.192038	−	0.420504i
$154$		0			0
$155$	34.8681	−	10.2382i	2.80067	−	0.822352i
$156$		0			0
$157$	17.9142	+	5.26008i	1.42971	+	0.419800i	0.902778	−	0.430108i	$-0.141524\pi$
$157$	17.9142	+	5.26008i	1.42971	+	0.419800i	0.526931	+	0.849908i	$0.323343\pi$
$158$		0			0
$159$	0.972406	−	6.76323i	0.0771168	−	0.536359i
$160$		0			0
$161$	−10.5813	−	10.5188i	−0.833924	−	0.829001i
$162$		0			0
$163$	−0.264003	+	1.83618i	−0.0206783	+	0.143821i	−0.997545	−	0.0700284i	$-0.977691\pi$
$163$	−0.264003	+	1.83618i	−0.0206783	+	0.143821i	0.976867	+	0.213849i	$0.0686001\pi$
$164$		0			0
$165$	1.23820	+	0.363568i	0.0963937	+	0.0283037i
$166$		0			0
$167$	−0.552670	+	0.162279i	−0.0427669	+	0.0125575i	−0.303046	−	0.952976i	$-0.598004\pi$
$167$	−0.552670	+	0.162279i	−0.0427669	+	0.0125575i	0.260279	+	0.965533i	$0.416185\pi$
$168$		0			0
$169$	7.74703	−	16.9636i	0.595925	−	1.30489i
$170$		0			0
$171$	−3.75666	+	2.41426i	−0.287279	+	0.184623i
$172$		0			0
$173$	0.770174	+	5.35668i	0.0585552	+	0.407261i	0.997927	+	0.0643596i	$0.0205005\pi$
$173$	0.770174	+	5.35668i	0.0585552	+	0.407261i	−0.939372	+	0.342901i	$0.888590\pi$
$174$		0			0
$175$	−19.7953	+	22.8450i	−1.49638	+	1.72692i
$176$		0			0
$177$	−6.13224	−	3.94095i	−0.460927	−	0.296220i
$178$		0			0
$179$	−4.45432	−	5.14056i	−0.332931	−	0.384223i	0.564459	−	0.825461i	$-0.309085\pi$
$179$	−4.45432	−	5.14056i	−0.332931	−	0.384223i	−0.897390	+	0.441238i	$0.854539\pi$
$180$		0			0
$181$	−2.64320	−	5.78779i	−0.196467	−	0.430203i	0.785600	−	0.618735i	$-0.212354\pi$
$181$	−2.64320	−	5.78779i	−0.196467	−	0.430203i	−0.982067	+	0.188532i	$0.939627\pi$
$182$		0			0
$183$	−8.46325			−0.625622
$184$		0			0
$185$	33.1794			2.43940
$186$		0			0
$187$	−0.799062	−	1.74970i	−0.0584332	−	0.127951i
$188$		0			0
$189$	2.03731	+	2.35118i	0.148193	+	0.171023i
$190$		0			0
$191$	−13.2765	−	8.53230i	−0.960655	−	0.617375i	−0.0364756	−	0.999335i	$-0.511613\pi$
$191$	−13.2765	−	8.53230i	−0.960655	−	0.617375i	−0.924179	+	0.381959i	$0.875249\pi$
$192$		0			0
$193$	−10.4796	+	12.0941i	−0.754336	+	0.870551i	−0.994981	−	0.100063i	$-0.968096\pi$
$193$	−10.4796	+	12.0941i	−0.754336	+	0.870551i	0.240645	+	0.970613i	$0.422641\pi$
$194$		0			0
$195$	3.07135	+	21.3617i	0.219944	+	1.52975i
$196$		0			0
$197$	18.7131	−	12.0262i	1.33325	−	0.856829i	0.336848	−	0.941559i	$-0.390639\pi$
$197$	18.7131	−	12.0262i	1.33325	−	0.856829i	0.996404	+	0.0847299i	$0.0270027\pi$
$198$		0			0
$199$	−4.81213	+	10.5371i	−0.341123	+	0.746954i	−0.999986	−	0.00530834i	$-0.998310\pi$
$199$	−4.81213	+	10.5371i	−0.341123	+	0.746954i	0.658863	+	0.752263i	$0.271038\pi$
$200$		0			0
$201$	−9.85014	+	2.89226i	−0.694775	+	0.204004i
$202$		0			0
$203$	4.26381	+	1.25197i	0.299261	+	0.0878710i
$204$		0			0
$205$	−4.05728	+	28.2190i	−0.283373	+	1.97090i
$206$		0			0
$207$	3.83074	−	2.88539i	0.266255	−	0.200548i
$208$		0			0
$209$	−0.213783	+	1.48690i	−0.0147877	+	0.102851i
$210$		0			0
$211$	−2.22050	−	0.651997i	−0.152865	−	0.0448853i	0.204405	−	0.978887i	$-0.434474\pi$
$211$	−2.22050	−	0.651997i	−0.152865	−	0.0448853i	−0.357270	+	0.934001i	$0.616292\pi$
$212$		0			0
$213$	1.21562	−	0.356937i	0.0832927	−	0.0244569i
$214$		0			0
$215$	−1.47723	+	3.23469i	−0.100747	+	0.220604i
$216$		0			0
$217$	24.7926	−	15.9332i	1.68303	−	1.08162i
$218$		0			0
$219$	−0.925203	−	6.43493i	−0.0625195	−	0.434832i
$220$		0			0
$221$	21.0658	−	24.3113i	1.41704	−	1.63535i
$222$		0			0
$223$	4.10859	+	2.64043i	0.275131	+	0.176816i	0.670929	−	0.741522i	$-0.265896\pi$
$223$	4.10859	+	2.64043i	0.275131	+	0.176816i	−0.395798	+	0.918338i	$0.629532\pi$
$224$		0			0
$225$	−6.36288	−	7.34315i	−0.424192	−	0.489543i
$226$		0			0
$227$	−3.84149	−	8.41169i	−0.254969	−	0.558304i	0.738255	−	0.674522i	$-0.235650\pi$
$227$	−3.84149	−	8.41169i	−0.254969	−	0.558304i	−0.993224	+	0.116218i	$0.962923\pi$
$228$		0			0
$229$	−5.19522			−0.343310			−0.171655	−	0.985157i	$-0.554911\pi$
$229$	−5.19522			−0.343310			−0.171655	+	0.985157i	$0.554911\pi$
$230$		0			0
$231$	1.04654			0.0688574
$232$		0			0
$233$	−4.52248	−	9.90285i	−0.296277	−	0.648757i	0.701690	−	0.712482i	$-0.252429\pi$
$233$	−4.52248	−	9.90285i	−0.296277	−	0.648757i	−0.997967	+	0.0637252i	$0.979702\pi$
$234$		0			0
$235$	4.46469	+	5.15252i	0.291244	+	0.336114i
$236$		0			0
$237$	5.06474	+	3.25491i	0.328990	+	0.211429i
$238$		0			0
$239$	−13.4515	+	15.5239i	−0.870108	+	1.00416i	0.129813	+	0.991539i	$0.458562\pi$
$239$	−13.4515	+	15.5239i	−0.870108	+	1.00416i	−0.999920	+	0.0126192i	$0.995983\pi$
$240$		0			0
$241$	1.11236	+	7.73663i	0.0716534	+	0.498360i	0.993770	+	0.111449i	$0.0355491\pi$
$241$	1.11236	+	7.73663i	0.0716534	+	0.498360i	−0.922117	+	0.386912i	$0.873542\pi$
$242$		0			0
$243$	−0.841254	+	0.540641i	−0.0539664	+	0.0346821i
$244$		0			0
$245$	−4.26882	+	9.34741i	−0.272725	+	0.597184i
$246$		0			0
$247$	−24.1044	+	7.07769i	−1.53373	+	0.450343i
$248$		0			0
$249$	9.36965	+	2.75118i	0.593777	+	0.174349i
$250$		0			0
$251$	−2.47906	+	17.2423i	−0.156477	+	1.08832i	0.748584	+	0.663040i	$0.230734\pi$
$251$	−2.47906	+	17.2423i	−0.156477	+	1.08832i	−0.905061	+	0.425282i	$0.860175\pi$
$252$		0			0
$253$	0.110326	−	1.60951i	0.00693616	−	0.101189i
$254$		0			0
$255$	−3.12177	+	21.7124i	−0.195493	+	1.35968i
$256$		0			0
$257$	−24.0194	−	7.05273i	−1.49829	−	0.439937i	−0.573112	−	0.819477i	$-0.694264\pi$
$257$	−24.0194	−	7.05273i	−1.49829	−	0.439937i	−0.925175	+	0.379540i	$0.876082\pi$
$258$		0			0
$259$	25.8178	−	7.58078i	1.60424	−	0.471047i
$260$		0			0
$261$	−0.593376	+	1.29931i	−0.0367291	+	0.0804254i
$262$		0			0
$263$	−15.8086	+	10.1596i	−0.974800	+	0.626466i	−0.928056	−	0.372441i	$-0.878521\pi$
$263$	−15.8086	+	10.1596i	−0.974800	+	0.626466i	−0.0467439	+	0.998907i	$0.514884\pi$
$264$		0			0
$265$	3.73034	+	25.9451i	0.229153	+	1.59379i
$266$		0			0
$267$	−8.03106	+	9.26834i	−0.491493	+	0.567213i
$268$		0			0
$269$	2.51208	+	1.61442i	0.153164	+	0.0984328i	0.614978	−	0.788544i	$-0.289165\pi$
$269$	2.51208	+	1.61442i	0.153164	+	0.0984328i	−0.461814	+	0.886977i	$0.652801\pi$
$270$		0			0
$271$	−14.7833	−	17.0608i	−0.898022	−	1.03637i	−0.999139	−	0.0414981i	$-0.986787\pi$
$271$	−14.7833	−	17.0608i	−0.898022	−	1.03637i	0.101117	−	0.994875i	$-0.467759\pi$
$272$		0			0
$273$	7.27060	+	15.9204i	0.440037	+	0.963546i
$274$		0			0
$275$	−3.26853			−0.197100
$276$		0			0
$277$	−22.5158			−1.35284			−0.676422	−	0.736514i	$-0.736470\pi$
$277$	−22.5158			−1.35284			−0.676422	+	0.736514i	$0.736470\pi$
$278$		0			0
$279$	3.93521	+	8.61691i	0.235595	+	0.515881i
$280$		0			0
$281$	6.28907	+	7.25797i	0.375174	+	0.432974i	0.911666	−	0.410931i	$-0.134796\pi$
$281$	6.28907	+	7.25797i	0.375174	+	0.432974i	−0.536492	+	0.843905i	$0.680251\pi$
$282$		0			0
$283$	−8.48892	−	5.45550i	−0.504614	−	0.324296i	0.263445	−	0.964674i	$-0.415141\pi$
$283$	−8.48892	−	5.45550i	−0.504614	−	0.324296i	−0.768059	+	0.640379i	$0.778777\pi$
$284$		0			0
$285$	11.2182	−	12.9465i	0.664512	−	0.766887i
$286$		0			0
$287$	3.29036	+	22.8849i	0.194224	+	1.35086i
$288$		0			0
$289$	13.2047	−	8.48615i	0.776747	−	0.499185i
$290$		0			0
$291$	3.32127	−	7.27257i	0.194696	−	0.426326i
$292$		0			0
$293$	10.1193	−	2.97131i	0.591179	−	0.173586i	0.0275591	−	0.999620i	$-0.491227\pi$
$293$	10.1193	−	2.97131i	0.591179	−	0.173586i	0.563620	+	0.826034i	$0.309408\pi$
$294$		0			0
$295$	26.8309	+	7.87825i	1.56215	+	0.458690i
$296$		0			0
$297$	−0.0478738	+	0.332970i	−0.00277792	+	0.0193209i
$298$		0			0
$299$	25.2510	−	9.50337i	1.46030	−	0.549594i
$300$		0			0
$301$	−0.410417	+	2.85451i	−0.0236561	+	0.164531i
$302$		0			0
$303$	5.32718	+	1.56420i	0.306038	+	0.0898609i
$304$		0			0
$305$	31.1516	−	9.14692i	1.78373	−	0.523751i
$306$		0			0
$307$	1.20894	−	2.64722i	0.0689980	−	0.151085i	−0.871991	−	0.489522i	$-0.837171\pi$
$307$	1.20894	−	2.64722i	0.0689980	−	0.151085i	0.940989	+	0.338438i	$0.109898\pi$
$308$		0			0
$309$	−16.4663	+	10.5822i	−0.936732	+	0.602001i
$310$		0			0
$311$	−0.343036	−	2.38587i	−0.0194518	−	0.135290i	0.977781	−	0.209627i	$-0.0672251\pi$
$311$	−0.343036	−	2.38587i	−0.0194518	−	0.135290i	−0.997233	+	0.0743369i	$0.976316\pi$
$312$		0			0
$313$	−4.74106	+	5.47147i	−0.267980	+	0.309266i	−0.873751	−	0.486373i	$-0.838319\pi$
$313$	−4.74106	+	5.47147i	−0.267980	+	0.309266i	0.605771	+	0.795639i	$0.292865\pi$
$314$		0			0
$315$	−10.0401	−	6.45235i	−0.565693	−	0.363549i
$316$		0			0
$317$	12.9976	+	15.0001i	0.730021	+	0.842489i	0.992474	−	0.122456i	$-0.0390770\pi$
$317$	12.9976	+	15.0001i	0.730021	+	0.842489i	−0.262453	+	0.964945i	$0.584532\pi$
$318$		0			0
$319$	0.199608	+	0.437081i	0.0111759	+	0.0244718i
$320$		0			0
$321$	−9.55520			−0.533319
$322$		0			0
$323$	−25.5344			−1.42077
$324$		0			0
$325$	−22.7073	−	49.7221i	−1.25958	−	2.75809i
$326$		0			0
$327$	0.719796	+	0.830689i	0.0398048	+	0.0459372i
$328$		0			0
$329$	4.65133	+	2.98923i	0.256436	+	0.164801i
$330$		0			0
$331$	−0.838492	+	0.967671i	−0.0460877	+	0.0531880i	−0.778325	−	0.627861i	$-0.783931\pi$
$331$	−0.838492	+	0.967671i	−0.0460877	+	0.0531880i	0.732238	+	0.681049i	$0.238476\pi$
$332$		0			0
$333$	1.23089	+	8.56101i	0.0674522	+	0.469141i
$334$		0			0
$335$	33.1305	−	21.2917i	1.81011	−	1.16329i
$336$		0			0
$337$	−7.36457	+	16.1262i	−0.401174	+	0.878448i	0.595976	+	0.803002i	$0.296765\pi$
$337$	−7.36457	+	16.1262i	−0.401174	+	0.878448i	−0.997150	+	0.0754460i	$0.975962\pi$
$338$		0			0
$339$	15.3824	−	4.51669i	0.835458	−	0.245313i
$340$		0			0
$341$	3.05757	+	0.897782i	0.165576	+	0.0486176i
$342$		0			0
$343$	1.91325	−	13.3070i	0.103306	−	0.718509i
$344$		0			0
$345$	−10.9817	+	14.7607i	−0.591235	+	0.794691i
$346$		0			0
$347$	−0.200439	+	1.39408i	−0.0107601	+	0.0748382i	−0.994494	−	0.104794i	$-0.966582\pi$
$347$	−0.200439	+	1.39408i	−0.0107601	+	0.0748382i	0.983734	+	0.179632i	$0.0574908\pi$
$348$		0			0
$349$	34.8731	+	10.2397i	1.86672	+	0.548117i	0.998666	+	0.0516393i	$0.0164446\pi$
$349$	34.8731	+	10.2397i	1.86672	+	0.548117i	0.868049	+	0.496478i	$0.165374\pi$
$350$		0			0
$351$	−5.39785	+	1.58495i	−0.288116	+	0.0845985i
$352$		0			0
$353$	−0.263503	+	0.576991i	−0.0140249	+	0.0307102i	−0.916515	−	0.400001i	$-0.869010\pi$
$353$	−0.263503	+	0.576991i	−0.0140249	+	0.0307102i	0.902490	+	0.430711i	$0.141737\pi$
$354$		0			0
$355$	−4.08867	+	2.62763i	−0.217004	+	0.139460i
$356$		0			0
$357$	2.53168	+	17.6082i	0.133991	+	0.931927i
$358$		0			0
$359$	24.3209	−	28.0679i	1.28361	−	1.48136i	0.491648	−	0.870794i	$-0.336395\pi$
$359$	24.3209	−	28.0679i	1.28361	−	1.48136i	0.791962	−	0.610571i	$-0.209060\pi$
$360$		0			0
$361$	0.791777	+	0.508844i	0.0416725	+	0.0267813i
$362$		0			0
$363$	−7.12936	−	8.22772i	−0.374195	−	0.431844i
$364$		0			0
$365$	10.3602	+	22.6858i	0.542280	+	1.18743i
$366$		0			0
$367$	−17.0645			−0.890760			−0.445380	−	0.895342i	$-0.646931\pi$
$367$	−17.0645			−0.890760			−0.445380	+	0.895342i	$0.646931\pi$
$368$		0			0
$369$	−7.43163			−0.386875
$370$		0			0
$371$	8.83056	+	19.3362i	0.458460	+	1.00389i
$372$		0			0
$373$	9.16700	+	10.5793i	0.474649	+	0.547774i	0.941699	−	0.336457i	$-0.109229\pi$
$373$	9.16700	+	10.5793i	0.474649	+	0.547774i	−0.467050	+	0.884231i	$0.654683\pi$
$374$		0			0
$375$	15.2208	+	9.78179i	0.785997	+	0.505130i
$376$		0			0
$377$	−5.26230	+	6.07302i	−0.271022	+	0.312777i
$378$		0			0
$379$	1.78669	+	12.4267i	0.0917760	+	0.638316i	0.982843	+	0.184444i	$0.0590485\pi$
$379$	1.78669	+	12.4267i	0.0917760	+	0.638316i	−0.891067	+	0.453872i	$0.850042\pi$
$380$		0			0
$381$	−2.15852	+	1.38720i	−0.110584	+	0.0710682i
$382$		0			0
$383$	−2.12032	+	4.64285i	−0.108343	+	0.237238i	−0.956036	−	0.293249i	$-0.905264\pi$
$383$	−2.12032	+	4.64285i	−0.108343	+	0.237238i	0.847693	+	0.530487i	$0.177991\pi$
$384$		0			0
$385$	−3.85211	+	1.13108i	−0.196322	+	0.0576453i
$386$		0			0
$387$	−0.889423	−	0.261158i	−0.0452119	−	0.0132754i
$388$		0			0
$389$	−0.300376	+	2.08916i	−0.0152296	+	0.105925i	−0.996018	−	0.0891487i	$-0.971585\pi$
$389$	−0.300376	+	2.08916i	−0.0152296	+	0.105925i	0.980789	+	0.195073i	$0.0624945\pi$
$390$		0			0
$391$	27.3472	−	2.03730i	1.38301	−	0.103031i
$392$		0			0
$393$	0.769154	−	5.34958i	0.0387987	−	0.269851i
$394$		0			0
$395$	−22.1602	−	6.50681i	−1.11500	−	0.327393i
$396$		0			0
$397$	−37.1154	+	10.8981i	−1.86277	+	0.546958i	−0.863691	+	0.504021i	$0.831853\pi$
$397$	−37.1154	+	10.8981i	−1.86277	+	0.546958i	−0.999078	+	0.0429368i	$0.986329\pi$
$398$		0			0
$399$	5.77120	−	12.6372i	0.288922	−	0.632650i
$400$		0			0
$401$	25.0743	−	16.1143i	1.25215	−	0.804710i	0.264963	−	0.964259i	$-0.414640\pi$
$401$	25.0743	−	16.1143i	1.25215	−	0.804710i	0.987190	+	0.159548i	$0.0510038\pi$
$402$		0			0
$403$	7.58430	+	52.7500i	0.377801	+	2.62766i
$404$		0			0
$405$	2.51217	−	2.89920i	0.124831	−	0.144062i
$406$		0			0
$407$	2.44762	+	1.57299i	0.121324	+	0.0779701i
$408$		0			0
$409$	−3.16411	−	3.65158i	−0.156455	−	0.180559i	0.672110	−	0.740451i	$-0.265388\pi$
$409$	−3.16411	−	3.65158i	−0.156455	−	0.180559i	−0.828566	+	0.559892i	$0.810843\pi$
$410$		0			0
$411$	6.86592	+	15.0343i	0.338671	+	0.741586i
$412$		0			0
$413$	22.6778			1.11590
$414$		0			0
$415$	−37.4612			−1.83890
$416$		0			0
$417$	−8.42862	−	18.4561i	−0.412751	−	0.903799i
$418$		0			0
$419$	−16.0545	−	18.5279i	−0.784315	−	0.905148i	0.213098	−	0.977031i	$-0.431645\pi$
$419$	−16.0545	−	18.5279i	−0.784315	−	0.905148i	−0.997413	+	0.0718826i	$0.977099\pi$
$420$		0			0
$421$	−8.55550	−	5.49829i	−0.416970	−	0.267970i	0.315290	−	0.948995i	$-0.397898\pi$
$421$	−8.55550	−	5.49829i	−0.416970	−	0.267970i	−0.732260	+	0.681025i	$0.761534\pi$
$422$		0			0
$423$	−1.16383	+	1.34313i	−0.0565875	+	0.0653054i
$424$		0			0
$425$	−7.90688	−	54.9936i	−0.383540	−	2.66758i
$426$		0			0
$427$	22.1500	−	14.2349i	1.07191	−	0.688876i
$428$		0			0
$429$	−0.786157	+	1.72144i	−0.0379560	+	0.0831121i
$430$		0			0
$431$	12.8585	−	3.77561i	0.619374	−	0.181865i	0.0430329	−	0.999074i	$-0.486298\pi$
$431$	12.8585	−	3.77561i	0.619374	−	0.181865i	0.576342	+	0.817209i	$0.304480\pi$
$432$		0			0
$433$	−17.3004	−	5.07987i	−0.831406	−	0.244123i	−0.161785	−	0.986826i	$-0.551725\pi$
$433$	−17.3004	−	5.07987i	−0.831406	−	0.244123i	−0.669621	+	0.742703i	$0.733543\pi$
$434$		0			0
$435$	0.779827	−	5.42382i	0.0373899	−	0.260052i
$436$		0			0
$437$	−18.8267	−	10.2079i	−0.900604	−	0.488312i
$438$		0			0
$439$	0.269232	−	1.87255i	0.0128497	−	0.0893718i	−0.982387	−	0.186856i	$-0.940170\pi$
$439$	0.269232	−	1.87255i	0.0128497	−	0.0893718i	0.995237	+	0.0974838i	$0.0310794\pi$
$440$		0			0
$441$	−2.57020	−	0.754679i	−0.122390	−	0.0359371i
$442$		0			0
$443$	−29.6037	+	8.69243i	−1.40651	+	0.412990i	−0.894916	−	0.446235i	$-0.852764\pi$
$443$	−29.6037	+	8.69243i	−1.40651	+	0.412990i	−0.511598	+	0.859225i	$0.670946\pi$
$444$		0			0
$445$	19.5437	−	42.7947i	0.926460	−	2.02866i
$446$		0			0
$447$	−10.5087	+	6.75355i	−0.497046	+	0.319432i
$448$		0			0
$449$	−0.945319	−	6.57484i	−0.0446124	−	0.310286i	−0.999894	−	0.0145871i	$-0.995357\pi$
$449$	−0.945319	−	6.57484i	−0.0446124	−	0.310286i	0.955281	−	0.295699i	$-0.0955525\pi$
$450$		0			0
$451$	−1.63712	+	1.88934i	−0.0770891	+	0.0889656i
$452$		0			0
$453$	11.8699	+	7.62835i	0.557699	+	0.358411i
$454$		0			0
$455$	−43.9681	−	50.7419i	−2.06126	−	2.37882i
$456$		0			0
$457$	3.58297	+	7.84562i	0.167604	+	0.367002i	0.974733	−	0.223373i	$-0.0717069\pi$
$457$	3.58297	+	7.84562i	0.167604	+	0.367002i	−0.807129	+	0.590376i	$0.798980\pi$
$458$		0			0
$459$	−5.71808			−0.266897
$460$		0			0
$461$	−31.7241			−1.47754			−0.738770	−	0.673958i	$-0.764593\pi$
$461$	−31.7241			−1.47754			−0.738770	+	0.673958i	$0.764593\pi$
$462$		0			0
$463$	−13.4340	−	29.4164i	−0.624333	−	1.36710i	−0.912326	−	0.409466i	$-0.865715\pi$
$463$	−13.4340	−	29.4164i	−0.624333	−	1.36710i	0.287993	−	0.957633i	$-0.407012\pi$
$464$		0			0
$465$	−23.7977	−	27.4640i	−1.10359	−	1.27361i
$466$		0			0
$467$	16.7388	+	10.7573i	0.774577	+	0.497791i	0.867230	−	0.497908i	$-0.165898\pi$
$467$	16.7388	+	10.7573i	0.774577	+	0.497791i	−0.0926526	+	0.995698i	$0.529535\pi$
$468$		0			0
$469$	20.9150	−	24.1372i	0.965766	−	1.11455i
$470$		0			0
$471$	−2.65709	−	18.4804i	−0.122432	−	0.851534i
$472$		0			0
$473$	−0.262326	+	0.168587i	−0.0120618	+	0.00775163i
$474$		0			0
$475$	−18.0245	+	39.4681i	−0.827019	+	1.81092i
$476$		0			0
$477$	−6.55601	+	1.92502i	−0.300179	+	0.0881405i
$478$		0			0
$479$	20.1260	+	5.90954i	0.919582	+	0.270014i	0.707069	−	0.707145i	$-0.250017\pi$
$479$	20.1260	+	5.90954i	0.919582	+	0.270014i	0.212513	+	0.977158i	$0.431835\pi$
$480$		0			0
$481$	−6.92465	+	48.1620i	−0.315737	+	2.19600i
$482$		0			0
$483$	−5.17264	+	13.9948i	−0.235363	+	0.636785i
$484$		0			0
$485$	−4.36489	+	30.3585i	−0.198199	+	1.37851i
$486$		0			0
$487$	0.0948803	+	0.0278594i	0.00429943	+	0.00126243i	0.283882	−	0.958859i	$-0.408378\pi$
$487$	0.0948803	+	0.0278594i	0.00429943	+	0.00126243i	−0.279582	+	0.960122i	$0.590196\pi$
$488$		0			0
$489$	1.77992	−	0.522631i	0.0804907	−	0.0236342i
$490$		0			0
$491$	3.87552	−	8.48621i	0.174900	−	0.382977i	−0.801798	−	0.597595i	$-0.796123\pi$
$491$	3.87552	−	8.48621i	0.174900	−	0.382977i	0.976698	+	0.214617i	$0.0688504\pi$
$492$		0			0
$493$	−6.87108	+	4.41578i	−0.309458	+	0.198877i
$494$		0			0
$495$	−0.183653	−	1.27734i	−0.00825460	−	0.0574120i
$496$		0			0
$497$	−2.58115	+	2.97880i	−0.115780	+	0.133618i
$498$		0			0
$499$	−0.744967	−	0.478761i	−0.0333493	−	0.0214323i	0.523860	−	0.851804i	$-0.324492\pi$
$499$	−0.744967	−	0.478761i	−0.0333493	−	0.0214323i	−0.557209	+	0.830372i	$0.688128\pi$
$500$		0			0
$501$	0.377201	+	0.435313i	0.0168521	+	0.0194484i
$502$		0			0
$503$	−2.34389	−	5.13241i	−0.104509	−	0.228843i	0.850152	−	0.526537i	$-0.176510\pi$
$503$	−2.34389	−	5.13241i	−0.104509	−	0.228843i	−0.954661	+	0.297694i	$0.903783\pi$
$504$		0			0
$505$	−21.2988			−0.947785
$506$		0			0
$507$	−18.6489			−0.828226
$508$		0			0
$509$	−16.1153	−	35.2876i	−0.714298	−	1.56410i	−0.821726	−	0.569882i	$-0.806989\pi$
$509$	−16.1153	−	35.2876i	−0.714298	−	1.56410i	0.107428	−	0.994213i	$-0.465738\pi$
$510$		0			0
$511$	13.2448	+	15.2853i	0.585914	+	0.676181i
$512$		0			0
$513$	3.75666	+	2.41426i	0.165861	+	0.106592i
$514$		0			0
$515$	49.1719	−	56.7474i	2.16677	−	2.50059i
$516$		0			0
$517$	0.0850824	+	0.591761i	0.00374192	+	0.0260256i
$518$		0			0
$519$	4.55266	−	2.92582i	0.199840	−	0.128429i
$520$		0			0
$521$	−1.97080	+	4.31545i	−0.0863423	+	0.189063i	−0.947878	−	0.318634i	$-0.896776\pi$
$521$	−1.97080	+	4.31545i	−0.0863423	+	0.189063i	0.861535	+	0.507697i	$0.169503\pi$
$522$		0			0
$523$	15.0334	−	4.41419i	0.657363	−	0.193019i	0.0639946	−	0.997950i	$-0.479616\pi$
$523$	15.0334	−	4.41419i	0.657363	−	0.193019i	0.593368	+	0.804931i	$0.297798\pi$
$524$		0			0
$525$	29.0038	+	8.51629i	1.26583	+	0.371681i
$526$		0			0
$527$	−7.70880	+	53.6158i	−0.335800	+	2.33554i
$528$		0			0
$529$	20.9777	+	9.43050i	0.912076	+	0.410022i
$530$		0			0
$531$	−1.03739	+	7.21521i	−0.0450189	+	0.313114i
$532$		0			0
$533$	−40.1149	−	11.7788i	−1.73757	−	0.510196i
$534$		0			0
$535$	35.1708	−	10.3271i	1.52057	−	0.446478i
$536$		0			0
$537$	−2.82563	+	6.18726i	−0.121935	+	0.267000i
$538$		0			0
$539$	−0.758054	+	0.487172i	−0.0326517	+	0.0209840i
$540$		0			0
$541$	−3.26901	−	22.7364i	−0.140546	−	0.977516i	−0.931006	−	0.365003i	$-0.881068\pi$
$541$	−3.26901	−	22.7364i	−0.140546	−	0.977516i	0.790461	−	0.612513i	$-0.209841\pi$
$542$		0			0
$543$	−4.16674	+	4.80867i	−0.178812	+	0.206360i
$544$		0			0
$545$	−3.54722	−	2.27966i	−0.151946	−	0.0976499i
$546$		0			0
$547$	20.9239	+	24.1474i	0.894640	+	1.03247i	0.999279	+	0.0379589i	$0.0120856\pi$
$547$	20.9239	+	24.1474i	0.894640	+	1.03247i	−0.104640	+	0.994510i	$0.533369\pi$
$548$		0			0
$549$	3.51576	+	7.69845i	0.150049	+	0.328562i
$550$		0			0
$551$	6.37857			0.271736
$552$		0			0
$553$	−18.7301			−0.796483
$554$		0			0
$555$	−13.7832	−	30.1811i	−0.585066	−	1.28111i
$556$		0			0
$557$	−11.7546	−	13.5655i	−0.498059	−	0.574791i	0.449942	−	0.893058i	$-0.351445\pi$
$557$	−11.7546	−	13.5655i	−0.498059	−	0.574791i	−0.948001	+	0.318267i	$0.896899\pi$
$558$		0			0
$559$	−4.38705	−	2.81939i	−0.185553	−	0.119247i
$560$		0			0
$561$	−1.25964	+	1.45371i	−0.0531822	+	0.0613755i
$562$		0			0
$563$	−2.60187	−	18.0964i	−0.109656	−	0.762673i	−0.968244	−	0.250007i	$-0.919567\pi$
$563$	−2.60187	−	18.0964i	−0.109656	−	0.762673i	0.858588	−	0.512666i	$-0.171342\pi$
$564$		0			0
$565$	−51.7381	+	33.2500i	−2.17664	+	1.39884i
$566$		0			0
$567$	1.29238	−	2.82992i	0.0542749	−	0.118846i
$568$		0			0
$569$	23.7557	−	6.97530i	0.995891	−	0.292420i	0.257122	−	0.966379i	$-0.417226\pi$
$569$	23.7557	−	6.97530i	0.995891	−	0.292420i	0.738769	+	0.673959i	$0.235408\pi$
$570$		0			0
$571$	−1.32137	−	0.387988i	−0.0552975	−	0.0162368i	0.253967	−	0.967213i	$-0.418265\pi$
$571$	−1.32137	−	0.387988i	−0.0552975	−	0.0162368i	−0.309264	+	0.950976i	$0.600083\pi$
$572$		0			0
$573$	−2.24599	+	15.6212i	−0.0938275	+	0.652584i
$574$		0			0
$575$	16.1551	−	43.7081i	0.673712	−	1.82275i
$576$		0			0
$577$	0.566280	−	3.93857i	0.0235746	−	0.163965i	−0.974633	−	0.223808i	$-0.928151\pi$
$577$	0.566280	−	3.93857i	0.0235746	−	0.163965i	0.998208	+	0.0598435i	$0.0190602\pi$
$578$		0			0
$579$	15.3545	+	4.50850i	0.638112	+	0.187367i
$580$		0			0
$581$	−29.1496	+	8.55908i	−1.20933	+	0.355091i
$582$		0			0
$583$	−0.954834	+	2.09079i	−0.0395452	+	0.0865919i
$584$		0			0
$585$	18.1554	−	11.6678i	0.750635	−	0.482404i
$586$		0			0
$587$	4.10437	+	28.5465i	0.169406	+	1.17824i	0.880117	+	0.474757i	$0.157464\pi$
$587$	4.10437	+	28.5465i	0.169406	+	1.17824i	−0.710711	+	0.703484i	$0.751627\pi$
$588$		0			0
$589$	27.7020	−	31.9698i	1.14144	−	1.31729i
$590$		0			0
$591$	−18.7131	−	12.0262i	−0.769753	−	0.494691i
$592$		0			0
$593$	−22.0896	−	25.4927i	−0.907110	−	1.04686i	−0.998695	−	0.0510637i	$-0.983739\pi$
$593$	−22.0896	−	25.4927i	−0.907110	−	1.04686i	0.0915852	−	0.995797i	$-0.470807\pi$
$594$		0			0
$595$	−28.3493	−	62.0762i	−1.16221	−	2.54488i
$596$		0			0
$597$	11.5839			0.474098
$598$		0			0
$599$	−2.39192			−0.0977313			−0.0488657	−	0.998805i	$-0.515561\pi$
$599$	−2.39192			−0.0977313			−0.0488657	+	0.998805i	$0.515561\pi$
$600$		0			0
$601$	17.2586	+	37.7911i	0.703994	+	1.54153i	0.835061	+	0.550157i	$0.185432\pi$
$601$	17.2586	+	37.7911i	0.703994	+	1.54153i	−0.131068	+	0.991373i	$0.541840\pi$
$602$		0			0
$603$	6.72279	+	7.75851i	0.273773	+	0.315951i
$604$		0			0
$605$	35.1341	+	22.5793i	1.42841	+	0.917981i
$606$		0			0
$607$	25.0290	−	28.8850i	1.01590	−	1.17241i	0.0309534	−	0.999521i	$-0.490146\pi$
$607$	25.0290	−	28.8850i	1.01590	−	1.17241i	0.984942	−	0.172885i	$-0.0553089\pi$
$608$		0			0
$609$	−0.632422	−	4.39859i	−0.0256270	−	0.178240i
$610$		0			0
$611$	−8.41100	+	5.40542i	−0.340273	+	0.218680i
$612$		0			0
$613$	−15.0598	+	32.9764i	−0.608260	+	1.33190i	0.315497	+	0.948927i	$0.397829\pi$
$613$	−15.0598	+	32.9764i	−0.608260	+	1.33190i	−0.923757	+	0.382978i	$0.874898\pi$
$614$		0			0
$615$	27.3544	−	8.03196i	1.10303	−	0.323880i
$616$		0			0
$617$	44.9213	+	13.1901i	1.80847	+	0.531013i	0.998463	−	0.0554141i	$-0.0176479\pi$
$617$	44.9213	+	13.1901i	1.80847	+	0.531013i	0.810002	+	0.586427i	$0.199466\pi$
$618$		0			0
$619$	4.05561	−	28.2074i	0.163009	−	1.13375i	−0.729913	−	0.683540i	$-0.760440\pi$
$619$	4.05561	−	28.2074i	0.163009	−	1.13375i	0.892922	−	0.450211i	$-0.148651\pi$
$620$		0			0
$621$	−4.21599	−	2.28593i	−0.169182	−	0.0917311i
$622$		0			0
$623$	5.42979	−	37.7650i	0.217540	−	1.51302i
$624$		0			0
$625$	−19.9826	−	5.86741i	−0.799303	−	0.234697i
$626$		0			0
$627$	1.44134	−	0.423215i	0.0575614	−	0.0169016i
$628$		0			0
$629$	−20.5448	+	44.9867i	−0.819173	+	1.79374i
$630$		0			0
$631$	−24.9177	+	16.0136i	−0.991957	+	0.637492i	−0.932663	−	0.360749i	$-0.882521\pi$
$631$	−24.9177	+	16.0136i	−0.991957	+	0.637492i	−0.0592938	+	0.998241i	$0.518885\pi$
$632$		0			0
$633$	0.329351	+	2.29069i	0.0130905	+	0.0910466i
$634$		0			0
$635$	6.44582	−	7.43888i	0.255795	−	0.295203i
$636$		0			0
$637$	−12.6774	−	8.14729i	−0.502298	−	0.322807i
$638$		0			0
$639$	−0.829667	−	0.957487i	−0.0328211	−	0.0378776i
$640$		0			0
$641$	1.58207	+	3.46425i	0.0624879	+	0.136830i	0.938300	−	0.345824i	$-0.112400\pi$
$641$	1.58207	+	3.46425i	0.0624879	+	0.136830i	−0.875812	+	0.482653i	$0.839673\pi$
$642$		0			0
$643$	−6.64827			−0.262182			−0.131091	−	0.991370i	$-0.541848\pi$
$643$	−6.64827			−0.262182			−0.131091	+	0.991370i	$0.541848\pi$
$644$		0			0
$645$	3.55604			0.140019
$646$		0			0
$647$	−4.06444	−	8.89988i	−0.159790	−	0.349890i	0.812756	−	0.582605i	$-0.197966\pi$
$647$	−4.06444	−	8.89988i	−0.159790	−	0.349890i	−0.972545	+	0.232715i	$0.925239\pi$
$648$		0			0
$649$	1.60579	+	1.85318i	0.0630329	+	0.0727438i
$650$		0			0
$651$	−24.7926	−	15.9332i	−0.971697	−	0.624472i
$652$		0			0
$653$	−27.5360	+	31.7782i	−1.07757	+	1.24358i	−0.109205	+	0.994019i	$0.534830\pi$
$653$	−27.5360	+	31.7782i	−1.07757	+	1.24358i	−0.968360	+	0.249557i	$0.919715\pi$
$654$		0			0
$655$	2.95062	+	20.5220i	0.115290	+	0.801862i
$656$		0			0
$657$	−5.46908	+	3.51476i	−0.213369	+	0.137124i
$658$		0			0
$659$	−12.3130	+	26.9618i	−0.479647	+	1.05028i	0.502913	+	0.864337i	$0.332262\pi$
$659$	−12.3130	+	26.9618i	−0.479647	+	1.05028i	−0.982560	+	0.185944i	$0.940466\pi$
$660$		0			0
$661$	11.1871	−	3.28484i	0.435129	−	0.127765i	−0.0568297	−	0.998384i	$-0.518099\pi$
$661$	11.1871	−	3.28484i	0.435129	−	0.127765i	0.491959	+	0.870618i	$0.336281\pi$
$662$		0			0
$663$	−30.8654	−	9.06289i	−1.19871	−	0.351973i
$664$		0			0
$665$	−7.58464	+	52.7523i	−0.294120	+	2.04565i
$666$		0			0
$667$	−6.83140	+	0.508923i	−0.264513	+	0.0197056i
$668$		0			0
$669$	0.695050	−	4.83418i	0.0268722	−	0.186900i
$670$		0			0
$671$	2.73166	+	0.802089i	0.105455	+	0.0309643i
$672$		0			0
$673$	1.22241	−	0.358933i	0.0471206	−	0.0138358i	−0.258087	−	0.966122i	$-0.583092\pi$
$673$	1.22241	−	0.358933i	0.0471206	−	0.0138358i	0.305208	+	0.952286i	$0.401274\pi$
$674$		0			0
$675$	−4.03633	+	8.83833i	−0.155358	+	0.340188i
$676$		0			0
$677$	12.9819	−	8.34293i	0.498933	−	0.320645i	−0.266856	−	0.963736i	$-0.585985\pi$
$677$	12.9819	−	8.34293i	0.498933	−	0.320645i	0.765789	+	0.643092i	$0.222349\pi$
$678$		0			0
$679$	3.53982	+	24.6200i	0.135846	+	0.944829i
$680$		0			0
$681$	−6.05573	+	6.98869i	−0.232056	+	0.267807i
$682$		0			0
$683$	4.15008	+	2.66710i	0.158799	+	0.102054i	0.617627	−	0.786471i	$-0.288094\pi$
$683$	4.15008	+	2.66710i	0.158799	+	0.102054i	−0.458828	+	0.888525i	$0.651731\pi$
$684$		0			0
$685$	−41.5208	−	47.9176i	−1.58643	−	1.83084i
$686$		0			0
$687$	2.15817	+	4.72574i	0.0823395	+	0.180298i
$688$		0			0
$689$	−38.4394			−1.46443
$690$		0			0
$691$	14.6012			0.555456			0.277728	−	0.960660i	$-0.410419\pi$
$691$	14.6012			0.555456			0.277728	+	0.960660i	$0.410419\pi$
$692$		0			0
$693$	−0.434749	−	0.951968i	−0.0165148	−	0.0361623i
$694$		0			0
$695$	50.9711	+	58.8237i	1.93344	+	2.23131i
$696$		0			0
$697$	−35.7488	−	22.9744i	−1.35408	−	0.870216i
$698$		0			0
$699$	−7.12924	+	8.22758i	−0.269653	+	0.311196i
$700$		0			0
$701$	1.02528	+	7.13097i	0.0387242	+	0.269333i	0.999980	−	0.00632506i	$-0.00201334\pi$
$701$	1.02528	+	7.13097i	0.0387242	+	0.269333i	−0.961256	+	0.275658i	$0.911104\pi$
$702$		0			0
$703$	32.4916	−	20.8811i	1.22544	−	0.787544i
$704$		0			0
$705$	2.83220	−	6.20166i	0.106667	−	0.233568i
$706$		0			0
$707$	−16.5732	+	4.86632i	−0.623298	+	0.183017i
$708$		0			0
$709$	−9.51170	−	2.79289i	−0.357219	−	0.104889i	0.0981985	−	0.995167i	$-0.468692\pi$
$709$	−9.51170	−	2.79289i	−0.357219	−	0.104889i	−0.455418	+	0.890278i	$0.650510\pi$
$710$		0			0
$711$	0.856802	−	5.95919i	0.0321326	−	0.223487i
$712$		0			0
$713$	−27.1178	+	36.4496i	−1.01557	+	1.36505i
$714$		0			0
$715$	1.03318	−	7.18596i	0.0386389	−	0.268740i
$716$		0			0
$717$	19.7090	+	5.78709i	0.736046	+	0.216123i
$718$		0			0
$719$	36.2951	−	10.6572i	1.35358	−	0.397446i	0.477083	−	0.878858i	$-0.341694\pi$
$719$	36.2951	−	10.6572i	1.35358	−	0.397446i	0.876495	+	0.481412i	$0.159876\pi$
$720$		0			0
$721$	25.2964	−	55.3914i	0.942087	−	2.06288i
$722$		0			0
$723$	6.57540	−	4.22575i	0.244542	−	0.157157i
$724$		0			0
$725$	1.97516	+	13.7375i	0.0733557	+	0.510200i
$726$		0			0
$727$	33.6680	−	38.8550i	1.24868	−	1.44105i	0.396304	−	0.918119i	$-0.370293\pi$
$727$	33.6680	−	38.8550i	1.24868	−	1.44105i	0.852374	−	0.522932i	$-0.175162\pi$
$728$		0			0
$729$	0.841254	+	0.540641i	0.0311575	+	0.0200237i
$730$		0			0
$731$	−3.47109	−	4.00585i	−0.128383	−	0.148162i
$732$		0			0
$733$	−9.66503	−	21.1635i	−0.356986	−	0.781690i	−0.999876	−	0.0157321i	$-0.994992\pi$
$733$	−9.66503	−	21.1635i	−0.356986	−	0.781690i	0.642890	−	0.765958i	$-0.277735\pi$
$734$		0			0
$735$	10.2760			0.379037
$736$		0			0
$737$	3.45341			0.127208
$738$		0			0
$739$	−5.08027	−	11.1242i	−0.186881	−	0.409212i	0.792882	−	0.609376i	$-0.208580\pi$
$739$	−5.08027	−	11.1242i	−0.186881	−	0.409212i	−0.979762	+	0.200164i	$0.935853\pi$
$740$		0			0
$741$	16.4514	+	18.9860i	0.604358	+	0.697467i
$742$		0			0
$743$	−31.3764	−	20.1644i	−1.15109	−	0.739760i	−0.181234	−	0.983440i	$-0.558009\pi$
$743$	−31.3764	−	20.1644i	−1.15109	−	0.739760i	−0.969856	+	0.243680i	$0.921645\pi$
$744$		0			0
$745$	31.3814	−	36.2161i	1.14973	−	1.32686i
$746$		0			0
$747$	−1.38973	−	9.66581i	−0.0508477	−	0.353654i
$748$		0			0
$749$	25.0078	−	16.0715i	0.913765	−	0.587241i
$750$		0			0
$751$	−17.2908	+	37.8615i	−0.630949	+	1.38159i	0.276332	+	0.961062i	$0.410881\pi$
$751$	−17.2908	+	37.8615i	−0.630949	+	1.38159i	−0.907281	+	0.420524i	$0.861846\pi$
$752$		0			0
$753$	16.7140	−	4.90766i	0.609091	−	0.178845i
$754$		0			0
$755$	−51.9355	−	15.2496i	−1.89013	−	0.554991i
$756$		0			0
$757$	−0.833113	+	5.79443i	−0.0302800	+	0.210602i	−0.999344	−	0.0362062i	$-0.988473\pi$
$757$	−0.833113	+	5.79443i	−0.0302800	+	0.210602i	0.969064	+	0.246808i	$0.0793818\pi$
$758$		0			0
$759$	−1.50989	+	0.568259i	−0.0548057	+	0.0206265i
$760$		0			0
$761$	−1.60295	+	11.1488i	−0.0581070	+	0.404143i	0.939922	+	0.341389i	$0.110897\pi$
$761$	−1.60295	+	11.1488i	−0.0581070	+	0.404143i	−0.998029	+	0.0627539i	$0.980012\pi$
$762$		0			0
$763$	−3.28104	−	0.963399i	−0.118781	−	0.0348774i
$764$		0			0
$765$	21.0471	−	6.17999i	0.760960	−	0.223438i
$766$		0			0
$767$	−17.0355	+	37.3024i	−0.615115	+	1.34691i
$768$		0			0
$769$	2.92936	−	1.88258i	0.105635	−	0.0678877i	−0.486757	−	0.873538i	$-0.661820\pi$
$769$	2.92936	−	1.88258i	0.105635	−	0.0678877i	0.592392	+	0.805650i	$0.298184\pi$
$770$		0			0
$771$	3.56262	+	24.7786i	0.128305	+	0.892380i
$772$		0			0
$773$	7.25126	−	8.36841i	0.260810	−	0.300991i	−0.610209	−	0.792241i	$-0.708914\pi$
$773$	7.25126	−	8.36841i	0.260810	−	0.300991i	0.871019	+	0.491250i	$0.163460\pi$
$774$		0			0
$775$	77.4315	+	49.7622i	2.78142	+	1.78751i
$776$		0			0
$777$	−17.6208	−	20.3355i	−0.632143	−	0.729532i
$778$		0			0
$779$	13.7861	+	30.1874i	0.493939	+	1.08158i
$780$		0			0
$781$	−0.426190			−0.0152503
$782$		0			0
$783$	1.42839			0.0510466
$784$		0			0
$785$	29.7535	+	65.1511i	1.06195	+	2.32534i
$786$		0			0
$787$	11.9400	+	13.7795i	0.425615	+	0.491186i	0.927539	−	0.373725i	$-0.121920\pi$
$787$	11.9400	+	13.7795i	0.425615	+	0.491186i	−0.501924	+	0.864912i	$0.667374\pi$
$788$		0			0
$789$	15.8086	+	10.1596i	0.562801	+	0.361690i
$790$		0			0
$791$	−32.6618	+	37.6938i	−1.16132	+	1.34024i
$792$		0			0
$793$	6.77590	+	47.1274i	0.240619	+	1.67354i
$794$		0			0
$795$	22.0508	−	14.1712i	0.782063	−	0.502601i
$796$		0			0
$797$	−0.186792	+	0.409018i	−0.00661652	+	0.0144882i	−0.912911	−	0.408158i	$-0.866171\pi$
$797$	−0.186792	+	0.409018i	−0.00661652	+	0.0144882i	0.906295	+	0.422646i	$0.138899\pi$
$798$		0			0
$799$	−9.75065	+	2.86305i	−0.344953	+	0.101287i
$800$		0			0
$801$	11.7670	+	3.45510i	0.415767	+	0.122080i
$802$		0			0
$803$	−0.311233	+	2.16467i	−0.0109832	+	0.0763896i
$804$		0			0
$805$	3.91417	−	57.1025i	0.137957	−	2.01260i
$806$		0			0
$807$	0.424969	−	2.95572i	0.0149596	−	0.104046i
$808$		0			0
$809$	32.0126	+	9.39975i	1.12550	+	0.330478i	0.790939	−	0.611895i	$-0.209592\pi$
$809$	32.0126	+	9.39975i	1.12550	+	0.330478i	0.334565	+	0.942373i	$0.391411\pi$
$810$		0			0
$811$	6.93529	−	2.03638i	0.243531	−	0.0715071i	−0.157689	−	0.987489i	$-0.550404\pi$
$811$	6.93529	−	2.03638i	0.243531	−	0.0715071i	0.401220	+	0.915982i	$0.368586\pi$
$812$		0			0
$813$	−9.37788	+	20.5347i	−0.328897	+	0.720183i
$814$		0			0
$815$	−5.98668	+	3.84740i	−0.209704	+	0.134769i
$816$		0			0
$817$	0.589105	+	4.09731i	0.0206102	+	0.143347i
$818$		0			0
$819$	11.4614	−	13.2271i	0.400493	−	0.462194i
$820$		0			0
$821$	−14.0924	−	9.05665i	−0.491829	−	0.316079i	0.271112	−	0.962548i	$-0.412609\pi$
$821$	−14.0924	−	9.05665i	−0.491829	−	0.316079i	−0.762941	+	0.646469i	$0.776245\pi$
$822$		0			0
$823$	23.3007	+	26.8904i	0.812210	+	0.937341i	0.998984	−	0.0450623i	$-0.0143486\pi$
$823$	23.3007	+	26.8904i	0.812210	+	0.937341i	−0.186774	+	0.982403i	$0.559803\pi$
$824$		0			0
$825$	1.35780	+	2.97316i	0.0472724	+	0.103512i
$826$		0			0
$827$	28.6561			0.996471			0.498236	−	0.867042i	$-0.333981\pi$
$827$	28.6561			0.996471			0.498236	+	0.867042i	$0.333981\pi$
$828$		0			0
$829$	46.7748			1.62456			0.812278	−	0.583271i	$-0.198227\pi$
$829$	46.7748			1.62456			0.812278	+	0.583271i	$0.198227\pi$
$830$		0			0
$831$	9.35341	+	20.4811i	0.324466	+	0.710482i
$832$		0			0
$833$	−10.0305	−	11.5759i	−0.347538	−	0.401080i
$834$		0			0
$835$	−1.85888	−	1.19463i	−0.0643292	−	0.0413419i
$836$		0			0
$837$	6.20347	−	7.15919i	0.214423	−	0.247458i
$838$		0			0
$839$	2.76080	+	19.2018i	0.0953135	+	0.662920i	0.980331	+	0.197362i	$0.0632373\pi$
$839$	2.76080	+	19.2018i	0.0953135	+	0.662920i	−0.885017	+	0.465558i	$0.845854\pi$
$840$		0			0
$841$	−22.6799	+	14.5755i	−0.782067	+	0.502604i
$842$		0			0
$843$	3.98951	−	8.73581i	0.137406	−	0.300877i
$844$		0			0
$845$	68.6429	−	20.1554i	2.36139	−	0.693366i
$846$		0			0
$847$	32.4977	+	9.54218i	1.11663	+	0.327873i
$848$		0			0
$849$	−1.43607	+	9.98809i	−0.0492858	+	0.342790i
$850$		0			0
$851$	−33.1322	+	24.9559i	−1.13576	+	0.855476i
$852$		0			0
$853$	−0.363797	+	2.53026i	−0.0124562	+	0.0866345i	−0.995101	−	0.0988612i	$-0.968480\pi$
$853$	−0.363797	+	2.53026i	−0.0124562	+	0.0866345i	0.982645	+	0.185496i	$0.0593891\pi$
$854$		0			0
$855$	−16.4368	−	4.82629i	−0.562127	−	0.165056i
$856$		0			0
$857$	43.9875	−	12.9159i	1.50258	−	0.441198i	0.576051	−	0.817414i	$-0.304593\pi$
$857$	43.9875	−	12.9159i	1.50258	−	0.441198i	0.926532	+	0.376215i	$0.122775\pi$
$858$		0			0
$859$	−15.8304	+	34.6637i	−0.540125	+	1.18271i	0.421118	+	0.907006i	$0.361638\pi$
$859$	−15.8304	+	34.6637i	−0.540125	+	1.18271i	−0.961243	+	0.275703i	$0.911089\pi$
$860$		0			0
$861$	19.4500	−	12.4998i	0.662854	−	0.425991i
$862$		0			0
$863$	3.12204	+	21.7143i	0.106276	+	0.739163i	0.971373	+	0.237559i	$0.0763473\pi$
$863$	3.12204	+	21.7143i	0.106276	+	0.739163i	−0.865098	+	0.501604i	$0.832744\pi$
$864$		0			0
$865$	−13.5953	+	15.6898i	−0.462253	+	0.533469i
$866$		0			0
$867$	−13.2047	−	8.48615i	−0.448455	−	0.288205i
$868$		0			0
$869$	−1.32626	−	1.53058i	−0.0449902	−	0.0519214i
$870$		0			0
$871$	23.9918	+	52.5346i	0.812930	+	1.78007i
$872$		0			0
$873$	−7.99507			−0.270592
$874$		0			0
$875$	−56.2883			−1.90289
$876$		0			0
$877$	−5.11857	−	11.2081i	−0.172842	−	0.378471i	0.803310	−	0.595562i	$-0.203070\pi$
$877$	−5.11857	−	11.2081i	−0.172842	−	0.378471i	−0.976151	+	0.217091i	$0.930343\pi$
$878$		0			0
$879$	−6.90653	−	7.97056i	−0.232951	−	0.268840i
$880$		0			0
$881$	−24.9375	−	16.0263i	−0.840164	−	0.539941i	0.0483286	−	0.998831i	$-0.484611\pi$
$881$	−24.9375	−	16.0263i	−0.840164	−	0.539941i	−0.888493	+	0.458891i	$0.848247\pi$
$882$		0			0
$883$	−0.240928	+	0.278046i	−0.00810787	+	0.00935698i	−0.759789	−	0.650170i	$-0.774698\pi$
$883$	−0.240928	+	0.278046i	−0.00810787	+	0.00935698i	0.751681	+	0.659527i	$0.229243\pi$
$884$		0			0
$885$	−3.97963	−	27.6790i	−0.133774	−	0.930418i
$886$		0			0
$887$	16.7760	−	10.7813i	0.563283	−	0.362000i	−0.227801	−	0.973708i	$-0.573153\pi$
$887$	16.7760	−	10.7813i	0.563283	−	0.362000i	0.791084	+	0.611708i	$0.209517\pi$
$888$		0			0
$889$	3.31604	−	7.26111i	0.111216	−	0.243530i
$890$		0			0
$891$	0.322768	−	0.0947731i	0.0108131	−	0.00317502i
$892$		0			0
$893$	7.61480	+	2.23591i	0.254820	+	0.0748218i
$894$		0			0
$895$	3.71350	−	25.8279i	0.124129	−	0.863333i
$896$		0			0
$897$	−19.1342	−	19.0212i	−0.638872	−	0.635100i
$898$		0			0
$899$	1.92568	−	13.3934i	0.0642250	−	0.446695i
$900$		0			0
$901$	−37.4878	−	11.0074i	−1.24890	−	0.366710i
$902$		0			0
$903$	2.76705	−	0.812479i	0.0920817	−	0.0270376i
$904$		0			0
$905$	10.1398	−	22.2031i	0.337059	−	0.738056i
$906$		0			0
$907$	−44.8428	+	28.8187i	−1.48898	+	0.956910i	−0.492750	+	0.870171i	$0.664008\pi$
$907$	−44.8428	+	28.8187i	−1.48898	+	0.956910i	−0.996231	+	0.0867394i	$0.972355\pi$
$908$		0			0
$909$	−0.790142	−	5.49556i	−0.0262074	−	0.182276i
$910$		0			0
$911$	−16.9777	+	19.5933i	−0.562496	+	0.649155i	−0.963748	−	0.266812i	$-0.914030\pi$
$911$	−16.9777	+	19.5933i	−0.562496	+	0.649155i	0.401252	+	0.915968i	$0.368575\pi$
$912$		0			0
$913$	−2.76348	−	1.77598i	−0.0914579	−	0.0587764i
$914$		0			0
$915$	−21.2612	−	24.5367i	−0.702872	−	0.811158i
$916$		0			0
$917$	6.98480	+	15.2946i	0.230658	+	0.505071i
$918$		0			0
$919$	−46.8782			−1.54637			−0.773185	−	0.634180i	$-0.781338\pi$
$919$	−46.8782			−1.54637			−0.773185	+	0.634180i	$0.781338\pi$
$920$		0			0
$921$	−2.91021			−0.0958945
$922$		0			0
$923$	−2.96085	−	6.48336i	−0.0974576	−	0.213402i
$924$		0			0
$925$	55.0328	+	63.5113i	1.80947	+	2.08824i
$926$		0			0
$927$	16.4663	+	10.5822i	0.540823	+	0.347566i
$928$		0			0
$929$	−0.749128	+	0.864540i	−0.0245781	+	0.0283646i	−0.767906	−	0.640563i	$-0.778701\pi$
$929$	−0.749128	+	0.864540i	−0.0245781	+	0.0283646i	0.743327	+	0.668928i	$0.233246\pi$
$930$		0			0
$931$	1.70236	+	11.8402i	0.0557925	+	0.388046i
$932$		0			0
$933$	−2.02776	+	1.30316i	−0.0663860	+	0.0426637i
$934$		0			0
$935$	3.06536	−	6.71220i	0.100248	−	0.219512i
$936$		0			0
$937$	4.92657	−	1.44657i	0.160944	−	0.0472574i	−0.200268	−	0.979741i	$-0.564181\pi$
$937$	4.92657	−	1.44657i	0.160944	−	0.0472574i	0.361212	+	0.932484i	$0.382363\pi$
$938$		0			0
$939$	6.94653	+	2.03969i	0.226692	+	0.0665627i
$940$		0			0
$941$	4.52284	−	31.4570i	0.147440	−	1.02547i	−0.772949	−	0.634468i	$-0.781219\pi$
$941$	4.52284	−	31.4570i	0.147440	−	1.02547i	0.920390	−	0.391002i	$-0.127872\pi$
$942$		0			0
$943$	−17.1734	−	31.2305i	−0.559242	−	1.01701i
$944$		0			0
$945$	−1.69848	+	11.8132i	−0.0552514	+	0.384282i
$946$		0			0
$947$	42.7105	+	12.5409i	1.38791	+	0.407526i	0.888514	−	0.458850i	$-0.151739\pi$
$947$	42.7105	+	12.5409i	1.38791	+	0.407526i	0.499392	+	0.866376i	$0.333557\pi$
$948$		0			0
$949$	−35.0920	+	10.3039i	−1.13913	+	0.334480i
$950$		0			0
$951$	8.24514	−	18.0543i	0.267367	−	0.585452i
$952$		0			0
$953$	−29.2246	+	18.7815i	−0.946678	+	0.608393i	−0.920281	−	0.391259i	$-0.872040\pi$
$953$	−29.2246	+	18.7815i	−0.946678	+	0.608393i	−0.0263970	+	0.999652i	$0.508403\pi$
$954$		0			0
$955$	−8.61604	−	59.9259i	−0.278809	−	1.93916i
$956$		0			0
$957$	0.314662	−	0.363140i	0.0101716	−	0.0117386i
$958$		0			0
$959$	−43.2566	−	27.7993i	−1.39683	−	0.897687i
$960$		0			0
$961$	−38.4646	−	44.3905i	−1.24079	−	1.43195i
$962$		0			0
$963$	3.96937	+	8.69171i	0.127911	+	0.280087i
$964$		0			0
$965$	−61.3897			−1.97620
$966$		0			0
$967$	−48.9574			−1.57436			−0.787182	−	0.616720i	$-0.788461\pi$
$967$	−48.9574			−1.57436			−0.787182	+	0.616720i	$0.788461\pi$
$968$		0			0
$969$	10.6074	+	23.2269i	0.340758	+	0.746156i
$970$		0			0
$971$	12.5110	+	14.4385i	0.401499	+	0.463354i	0.920112	−	0.391655i	$-0.128097\pi$
$971$	12.5110	+	14.4385i	0.401499	+	0.463354i	−0.518614	+	0.855009i	$0.673552\pi$
$972$		0			0
$973$	53.1019	+	34.1265i	1.70237	+	1.09405i
$974$		0			0
$975$	−35.7959	+	41.3106i	−1.14639	+	1.32300i
$976$		0			0
$977$	−4.07290	−	28.3276i	−0.130303	−	0.906281i	−0.945158	−	0.326615i	$-0.894092\pi$
$977$	−4.07290	−	28.3276i	−0.130303	−	0.906281i	0.814854	−	0.579666i	$-0.196817\pi$
$978$		0			0
$979$	3.47056	−	2.23039i	0.110919	−	0.0712836i
$980$		0			0
$981$	0.456607	−	0.999830i	0.0145783	−	0.0319221i
$982$		0			0
$983$	−12.1327	+	3.56247i	−0.386972	+	0.113625i	−0.469431	−	0.882969i	$-0.655541\pi$
$983$	−12.1327	+	3.56247i	−0.386972	+	0.113625i	0.0824590	+	0.996594i	$0.473723\pi$
$984$		0			0
$985$	81.8768	+	24.0412i	2.60881	+	0.766016i
$986$		0			0
$987$	0.786865	−	5.47277i	0.0250462	−	0.174200i
$988$		0			0
$989$	−0.957837	−	4.34119i	−0.0304574	−	0.138042i
$990$		0			0
$991$	7.78085	−	54.1170i	0.247167	−	1.71908i	−0.367268	−	0.930115i	$-0.619707\pi$
$991$	7.78085	−	54.1170i	0.247167	−	1.71908i	0.614435	−	0.788968i	$-0.289384\pi$
$992$		0			0
$993$	1.22855	+	0.360734i	0.0389868	+	0.0114475i
$994$		0			0
$995$	−42.6380	+	12.5197i	−1.35172	+	0.396900i
$996$		0			0
$997$	−9.53482	+	20.8783i	−0.301971	+	0.661224i	−0.998409	−	0.0563934i	$-0.982040\pi$
$997$	−9.53482	+	20.8783i	−0.301971	+	0.661224i	0.696438	+	0.717617i	$0.254767\pi$
$998$		0			0
$999$	7.27604	−	4.67603i	0.230204	−	0.147943i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.q.c.169.3	yes	30
23.3	even	11	inner	552.2.q.c.49.3	✓	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.q.c.49.3	✓	30	23.3	even	11	inner
552.2.q.c.169.3	yes	30	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:	\( N \)	\(=\)	\( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	552.q (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.415415 - 0.909632i) q^{3} +(2.51217 + 2.89920i) q^{5} +(2.61719 + 1.68197i) q^{7} +(-0.654861 + 0.755750i) q^{9} +O(q^{10})\)	\(q+(-0.415415 - 0.909632i) q^{3} +(2.51217 + 2.89920i) q^{5} +(2.61719 + 1.68197i) q^{7} +(-0.654861 + 0.755750i) q^{9} +(0.0478738 + 0.332970i) q^{11} +(-4.73267 + 3.04150i) q^{13} +(1.59361 - 3.48952i) q^{15} +(-5.48646 + 1.61097i) q^{17} +(4.28467 + 1.25809i) q^{19} +(0.442750 - 3.07940i) q^{21} +(-4.68923 - 1.00555i) q^{23} +(-1.38279 + 9.61748i) q^{25} +(0.959493 + 0.281733i) q^{27} +(1.37053 - 0.402425i) q^{29} +(3.93521 - 8.61691i) q^{31} +(0.282993 - 0.181868i) q^{33} +(1.69848 + 11.8132i) q^{35} +(5.66392 - 6.53651i) q^{37} +(4.73267 + 3.04150i) q^{39} +(4.86668 + 5.61645i) q^{41} +(0.385078 + 0.843203i) q^{43} -3.83619 q^{45} +1.77722 q^{47} +(1.11277 + 2.43664i) q^{49} +(3.74455 + 4.32144i) q^{51} +(5.74810 + 3.69408i) q^{53} +(-0.845080 + 0.975274i) q^{55} +(-0.635515 - 4.42010i) q^{57} +(6.13224 - 3.94095i) q^{59} +(3.51576 - 7.69845i) q^{61} +(-2.98504 + 0.876487i) q^{63} +(-20.7072 - 6.08019i) q^{65} +(1.46100 - 10.1615i) q^{67} +(1.03330 + 4.68319i) q^{69} +(-0.180304 + 1.25404i) q^{71} +(6.23776 + 1.83157i) q^{73} +(9.32280 - 2.73742i) q^{75} +(-0.434749 + 0.951968i) q^{77} +(-5.06474 + 3.25491i) q^{79} +(-0.142315 - 0.989821i) q^{81} +(-6.39485 + 7.38005i) q^{83} +(-18.4535 - 11.8593i) q^{85} +(-0.935399 - 1.07951i) q^{87} +(-5.09455 - 11.1555i) q^{89} -17.5020 q^{91} -9.47297 q^{93} +(7.11637 + 15.5827i) q^{95} +(5.23566 + 6.04227i) q^{97} +(-0.282993 - 0.181868i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 3 q^{3} - 2 q^{5} - 2 q^{7} - 3 q^{9}+O(q^{10}) \) 30 * q + 3 * q^3 - 2 * q^5 - 2 * q^7 - 3 * q^9	\( 30 q + 3 q^{3} - 2 q^{5} - 2 q^{7} - 3 q^{9} + 13 q^{11} - 13 q^{13} + 2 q^{15} - 11 q^{17} + 11 q^{19} - 9 q^{21} - 12 q^{23} + 17 q^{25} + 3 q^{27} + 9 q^{29} + 33 q^{31} + 9 q^{33} + 62 q^{35} + 11 q^{37} + 13 q^{39} + 2 q^{41} - 40 q^{43} - 2 q^{45} - 38 q^{47} - 13 q^{49} + 11 q^{51} - 25 q^{53} + 62 q^{55} + 22 q^{57} + 73 q^{59} + 4 q^{61} - 2 q^{63} - 12 q^{65} - 29 q^{67} - 21 q^{69} - 19 q^{71} - 38 q^{73} + 27 q^{75} + 4 q^{77} - 12 q^{79} - 3 q^{81} - 65 q^{83} + 8 q^{85} + 2 q^{87} - 61 q^{89} - 150 q^{91} - 22 q^{93} - 9 q^{95} - 9 q^{97} - 9 q^{99}+O(q^{100}) \) 30 * q + 3 * q^3 - 2 * q^5 - 2 * q^7 - 3 * q^9 + 13 * q^11 - 13 * q^13 + 2 * q^15 - 11 * q^17 + 11 * q^19 - 9 * q^21 - 12 * q^23 + 17 * q^25 + 3 * q^27 + 9 * q^29 + 33 * q^31 + 9 * q^33 + 62 * q^35 + 11 * q^37 + 13 * q^39 + 2 * q^41 - 40 * q^43 - 2 * q^45 - 38 * q^47 - 13 * q^49 + 11 * q^51 - 25 * q^53 + 62 * q^55 + 22 * q^57 + 73 * q^59 + 4 * q^61 - 2 * q^63 - 12 * q^65 - 29 * q^67 - 21 * q^69 - 19 * q^71 - 38 * q^73 + 27 * q^75 + 4 * q^77 - 12 * q^79 - 3 * q^81 - 65 * q^83 + 8 * q^85 + 2 * q^87 - 61 * q^89 - 150 * q^91 - 22 * q^93 - 9 * q^95 - 9 * q^97 - 9 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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