LMFDB - Embedded newform 552.2.n.a.91.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [552,2,Mod(91,552)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(552, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("552.91");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 552 = 2^{3} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	552.n (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:	$4.40774219157$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			91.8
Character	$\chi$	$=$	552.91
Dual form			552.2.n.a.91.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.21506 + 0.723626i) q^{2} +1.00000 q^{3} +(0.952732 - 1.75849i) q^{4} +4.31142 q^{5} +(-1.21506 + 0.723626i) q^{6} -1.64666 q^{7} +(0.114868 + 2.82609i) q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(-1.21506 + 0.723626i) q^{2} +1.00000 q^{3} +(0.952732 - 1.75849i) q^{4} +4.31142 q^{5} +(-1.21506 + 0.723626i) q^{6} -1.64666 q^{7} +(0.114868 + 2.82609i) q^{8} +1.00000 q^{9} +(-5.23862 + 3.11985i) q^{10} +2.66476i q^{11} +(0.952732 - 1.75849i) q^{12} +4.33558i q^{13} +(2.00079 - 1.19157i) q^{14} +4.31142 q^{15} +(-2.18460 - 3.35075i) q^{16} +0.417408i q^{17} +(-1.21506 + 0.723626i) q^{18} +7.23941i q^{19} +(4.10762 - 7.58161i) q^{20} -1.64666 q^{21} +(-1.92829 - 3.23784i) q^{22} +(-3.61238 - 3.15447i) q^{23} +(0.114868 + 2.82609i) q^{24} +13.5883 q^{25} +(-3.13734 - 5.26798i) q^{26} +1.00000 q^{27} +(-1.56882 + 2.89564i) q^{28} -9.62409i q^{29} +(-5.23862 + 3.11985i) q^{30} -6.72959i q^{31} +(5.07911 + 2.49051i) q^{32} +2.66476i q^{33} +(-0.302047 - 0.507175i) q^{34} -7.09944 q^{35} +(0.952732 - 1.75849i) q^{36} +5.50965 q^{37} +(-5.23862 - 8.79630i) q^{38} +4.33558i q^{39} +(0.495243 + 12.1845i) q^{40} +1.83509 q^{41} +(2.00079 - 1.19157i) q^{42} -1.68409i q^{43} +(4.68596 + 2.53880i) q^{44} +4.31142 q^{45} +(6.67191 + 1.21885i) q^{46} -1.93026i q^{47} +(-2.18460 - 3.35075i) q^{48} -4.28851 q^{49} +(-16.5106 + 9.83287i) q^{50} +0.417408i q^{51} +(7.62409 + 4.13064i) q^{52} -5.44690 q^{53} +(-1.21506 + 0.723626i) q^{54} +11.4889i q^{55} +(-0.189148 - 4.65361i) q^{56} +7.23941i q^{57} +(6.96424 + 11.6938i) q^{58} +9.10371 q^{59} +(4.10762 - 7.58161i) q^{60} +0.402762 q^{61} +(4.86970 + 8.17684i) q^{62} -1.64666 q^{63} +(-7.97361 + 0.649254i) q^{64} +18.6925i q^{65} +(-1.92829 - 3.23784i) q^{66} +5.42584i q^{67} +(0.734009 + 0.397678i) q^{68} +(-3.61238 - 3.15447i) q^{69} +(8.62623 - 5.13734i) q^{70} -1.27041i q^{71} +(0.114868 + 2.82609i) q^{72} -8.90333 q^{73} +(-6.69455 + 3.98693i) q^{74} +13.5883 q^{75} +(12.7305 + 6.89722i) q^{76} -4.38795i q^{77} +(-3.13734 - 5.26798i) q^{78} -11.1334 q^{79} +(-9.41875 - 14.4465i) q^{80} +1.00000 q^{81} +(-2.22974 + 1.32792i) q^{82} -11.0650i q^{83} +(-1.56882 + 2.89564i) q^{84} +1.79962i q^{85} +(1.21865 + 2.04627i) q^{86} -9.62409i q^{87} +(-7.53086 + 0.306095i) q^{88} -18.4228i q^{89} +(-5.23862 + 3.11985i) q^{90} -7.13922i q^{91} +(-8.98875 + 3.34699i) q^{92} -6.72959i q^{93} +(1.39679 + 2.34538i) q^{94} +31.2121i q^{95} +(5.07911 + 2.49051i) q^{96} +9.76899i q^{97} +(5.21079 - 3.10328i) q^{98} +2.66476i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 4 q^{2} + 24 q^{3} + 4 q^{4} - 4 q^{6} - 4 q^{8} + 24 q^{9}+O(q^{10}) $ 24 * q - 4 * q^2 + 24 * q^3 + 4 * q^4 - 4 * q^6 - 4 * q^8 + 24 * q^9	$ 24 q - 4 q^{2} + 24 q^{3} + 4 q^{4} - 4 q^{6} - 4 q^{8} + 24 q^{9} + 4 q^{12} + 4 q^{16} - 4 q^{18} - 4 q^{24} + 24 q^{25} + 24 q^{27} - 4 q^{32} + 4 q^{36} + 4 q^{46} + 4 q^{48} - 8 q^{49} - 44 q^{50} - 4 q^{54} + 48 q^{58} - 40 q^{62} + 4 q^{64} - 4 q^{72} - 32 q^{73} + 24 q^{75} + 24 q^{81} - 40 q^{82} - 52 q^{92} + 40 q^{94} - 4 q^{96} - 20 q^{98}+O(q^{100}) $ 24 * q - 4 * q^2 + 24 * q^3 + 4 * q^4 - 4 * q^6 - 4 * q^8 + 24 * q^9 + 4 * q^12 + 4 * q^16 - 4 * q^18 - 4 * q^24 + 24 * q^25 + 24 * q^27 - 4 * q^32 + 4 * q^36 + 4 * q^46 + 4 * q^48 - 8 * q^49 - 44 * q^50 - 4 * q^54 + 48 * q^58 - 40 * q^62 + 4 * q^64 - 4 * q^72 - 32 * q^73 + 24 * q^75 + 24 * q^81 - 40 * q^82 - 52 * q^92 + 40 * q^94 - 4 * q^96 - 20 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$-1$	$1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−1.21506	+	0.723626i	−0.859176	+	0.511681i
$2$	−1.21506	+	0.723626i	−0.859176	+	0.511681i
$3$	1.00000			0.577350
$3$	1.00000			0.577350
$4$	0.952732	−	1.75849i	0.476366	−	0.879247i
$5$	4.31142			1.92813			0.964063	−	0.265675i	$-0.0855949\pi$
$5$	4.31142			1.92813			0.964063	+	0.265675i	$0.0855949\pi$
$6$	−1.21506	+	0.723626i	−0.496045	+	0.295419i
$7$	−1.64666			−0.622379			−0.311189	−	0.950348i	$-0.600727\pi$
$7$	−1.64666			−0.622379			−0.311189	+	0.950348i	$0.600727\pi$
$8$	0.114868	+	2.82609i	0.0406119	+	0.999175i
$9$	1.00000			0.333333
$10$	−5.23862	+	3.11985i	−1.65660	+	0.986584i
$11$			2.66476i			0.803455i	0.915759	+	0.401728i	$0.131590\pi$
$11$			2.66476i			0.803455i	−0.915759	+	0.401728i	$0.868410\pi$
$12$	0.952732	−	1.75849i	0.275030	−	0.507634i
$13$			4.33558i			1.20247i	0.799071	+	0.601237i	$0.205325\pi$
$13$			4.33558i			1.20247i	−0.799071	+	0.601237i	$0.794675\pi$
$14$	2.00079	−	1.19157i	0.534733	−	0.318459i
$15$	4.31142			1.11320
$16$	−2.18460	−	3.35075i	−0.546151	−	0.837687i
$17$			0.417408i			0.101236i	0.998718	+	0.0506181i	$0.0161191\pi$
$17$			0.417408i			0.101236i	−0.998718	+	0.0506181i	$0.983881\pi$
$18$	−1.21506	+	0.723626i	−0.286392	+	0.170560i
$19$			7.23941i			1.66083i	0.557142	+	0.830417i	$0.311898\pi$
$19$			7.23941i			1.66083i	−0.557142	+	0.830417i	$0.688102\pi$
$20$	4.10762	−	7.58161i	0.918493	−	1.69530i
$21$	−1.64666			−0.359331
$22$	−1.92829	−	3.23784i	−0.411112	−	0.690309i
$23$	−3.61238	−	3.15447i	−0.753234	−	0.657753i
$23$	−3.61238	−	3.15447i	−0.753234	−	0.657753i
$24$	0.114868	+	2.82609i	0.0234473	+	0.576874i
$25$	13.5883			2.71767
$26$	−3.13734	−	5.26798i	−0.615282	−	1.03314i
$27$	1.00000			0.192450
$28$	−1.56882	+	2.89564i	−0.296480	+	0.547225i
$29$		−	9.62409i		−	1.78715i	−0.448915	−	0.893574i	$-0.648189\pi$
$29$		−	9.62409i		−	1.78715i	0.448915	−	0.893574i	$-0.351811\pi$
$30$	−5.23862	+	3.11985i	−0.956437	+	0.569605i
$31$		−	6.72959i		−	1.20867i	−0.796730	−	0.604335i	$-0.793439\pi$
$31$		−	6.72959i		−	1.20867i	0.796730	−	0.604335i	$-0.206561\pi$
$32$	5.07911	+	2.49051i	0.897868	+	0.440265i
$33$			2.66476i			0.463875i
$34$	−0.302047	−	0.507175i	−0.0518006	−	0.0869797i
$35$	−7.09944			−1.20002
$36$	0.952732	−	1.75849i	0.158789	−	0.293082i
$37$	5.50965			0.905782			0.452891	−	0.891566i	$-0.350393\pi$
$37$	5.50965			0.905782			0.452891	+	0.891566i	$0.350393\pi$
$38$	−5.23862	−	8.79630i	−0.849817	−	1.42695i
$39$			4.33558i			0.694248i
$40$	0.495243	+	12.1845i	0.0783047	+	1.92653i
$41$	1.83509			0.286592			0.143296	−	0.989680i	$-0.454230\pi$
$41$	1.83509			0.286592			0.143296	+	0.989680i	$0.454230\pi$
$42$	2.00079	−	1.19157i	0.308728	−	0.183863i
$43$		−	1.68409i		−	0.256822i	−0.991721	−	0.128411i	$-0.959012\pi$
$43$		−	1.68409i		−	0.256822i	0.991721	−	0.128411i	$-0.0409877\pi$
$44$	4.68596	+	2.53880i	0.706436	+	0.382739i
$45$	4.31142			0.642708
$46$	6.67191	+	1.21885i	0.983720	+	0.179710i
$47$		−	1.93026i		−	0.281558i	−0.990041	−	0.140779i	$-0.955039\pi$
$47$		−	1.93026i		−	0.281558i	0.990041	−	0.140779i	$-0.0449607\pi$
$48$	−2.18460	−	3.35075i	−0.315321	−	0.483639i
$49$	−4.28851			−0.612645
$50$	−16.5106	+	9.83287i	−2.33495	+	1.39058i
$51$			0.417408i			0.0584488i
$52$	7.62409	+	4.13064i	1.05727	+	0.572817i
$53$	−5.44690			−0.748189			−0.374095	−	0.927391i	$-0.622047\pi$
$53$	−5.44690			−0.748189			−0.374095	+	0.927391i	$0.622047\pi$
$54$	−1.21506	+	0.723626i	−0.165348	+	0.0984730i
$55$			11.4889i			1.54916i
$56$	−0.189148	−	4.65361i	−0.0252760	−	0.621865i
$57$			7.23941i			0.958883i
$58$	6.96424	+	11.6938i	0.914450	+	1.53547i
$59$	9.10371			1.18520			0.592601	−	0.805496i	$-0.298101\pi$
$59$	9.10371			1.18520			0.592601	+	0.805496i	$0.298101\pi$
$60$	4.10762	−	7.58161i	0.530292	−	0.978781i
$61$	0.402762			0.0515684			0.0257842	−	0.999668i	$-0.491792\pi$
$61$	0.402762			0.0515684			0.0257842	+	0.999668i	$0.491792\pi$
$62$	4.86970	+	8.17684i	0.618453	+	1.03846i
$63$	−1.64666			−0.207460
$64$	−7.97361	+	0.649254i	−0.996701	+	0.0811567i
$65$			18.6925i			2.31852i
$66$	−1.92829	−	3.23784i	−0.237356	−	0.398550i
$67$			5.42584i			0.662871i	0.943478	+	0.331436i	$0.107533\pi$
$67$			5.42584i			0.662871i	−0.943478	+	0.331436i	$0.892467\pi$
$68$	0.734009	+	0.397678i	0.0890117	+	0.0482255i
$69$	−3.61238	−	3.15447i	−0.434880	−	0.379754i
$70$	8.62623	−	5.13734i	1.03103	−	0.614029i
$71$		−	1.27041i		−	0.150770i	−0.997154	−	0.0753851i	$-0.975981\pi$
$71$		−	1.27041i		−	0.150770i	0.997154	−	0.0753851i	$-0.0240186\pi$
$72$	0.114868	+	2.82609i	0.0135373	+	0.333058i
$73$	−8.90333			−1.04206			−0.521028	−	0.853539i	$-0.674451\pi$
$73$	−8.90333			−1.04206			−0.521028	+	0.853539i	$0.674451\pi$
$74$	−6.69455	+	3.98693i	−0.778226	+	0.463471i
$75$	13.5883			1.56905
$76$	12.7305	+	6.89722i	1.46028	+	0.791165i
$77$		−	4.38795i		−	0.500053i
$78$	−3.13734	−	5.26798i	−0.355233	−	0.596481i
$79$	−11.1334			−1.25261			−0.626304	−	0.779579i	$-0.715433\pi$
$79$	−11.1334			−1.25261			−0.626304	+	0.779579i	$0.715433\pi$
$80$	−9.41875	−	14.4465i	−1.05305	−	1.61516i
$81$	1.00000			0.111111
$82$	−2.22974	+	1.32792i	−0.246233	+	0.146644i
$83$		−	11.0650i		−	1.21454i	−0.794496	−	0.607269i	$-0.792265\pi$
$83$		−	11.0650i		−	1.21454i	0.794496	−	0.607269i	$-0.207735\pi$
$84$	−1.56882	+	2.89564i	−0.171173	+	0.315940i
$85$			1.79962i			0.195196i
$86$	1.21865	+	2.04627i	0.131411	+	0.220655i
$87$		−	9.62409i		−	1.03181i
$88$	−7.53086	+	0.306095i	−0.802792	+	0.0326298i
$89$		−	18.4228i		−	1.95282i	−0.215930	−	0.976409i	$-0.569278\pi$
$89$		−	18.4228i		−	1.95282i	0.215930	−	0.976409i	$-0.430722\pi$
$90$	−5.23862	+	3.11985i	−0.552199	+	0.328861i
$91$		−	7.13922i		−	0.748394i
$92$	−8.98875	+	3.34699i	−0.937142	+	0.348948i
$93$		−	6.72959i		−	0.697826i
$94$	1.39679	+	2.34538i	0.144068	+	0.241908i
$95$			31.2121i			3.20230i
$96$	5.07911	+	2.49051i	0.518384	+	0.254187i
$97$			9.76899i			0.991891i	0.868354	+	0.495945i	$0.165178\pi$
$97$			9.76899i			0.991891i	−0.868354	+	0.495945i	$0.834822\pi$
$98$	5.21079	−	3.10328i	0.526369	−	0.313478i
$99$			2.66476i			0.267818i
$100$	12.9460	−	23.8950i	1.29460	−	2.38950i
$101$		−	8.48432i		−	0.844222i	−0.906544	−	0.422111i	$-0.861289\pi$
$101$		−	8.48432i		−	0.844222i	0.906544	−	0.422111i	$-0.138711\pi$
$102$	−0.302047	−	0.507175i	−0.0299071	−	0.0502178i
$103$	4.09449			0.403442			0.201721	−	0.979443i	$-0.435347\pi$
$103$	4.09449			0.403442			0.201721	+	0.979443i	$0.435347\pi$
$104$	−12.2528	+	0.498018i	−1.20148	+	0.0488347i
$105$	−7.09944			−0.692834
$106$	6.61830	−	3.94152i	0.642826	−	0.382834i
$107$		−	9.72333i		−	0.939990i	−0.882669	−	0.469995i	$-0.844256\pi$
$107$		−	9.72333i		−	0.939990i	0.882669	−	0.469995i	$-0.155744\pi$
$108$	0.952732	−	1.75849i	0.0916766	−	0.169211i
$109$	0.909587			0.0871226			0.0435613	−	0.999051i	$-0.486130\pi$
$109$	0.909587			0.0871226			0.0435613	+	0.999051i	$0.486130\pi$
$110$	−8.31366	−	13.9597i	−0.792676	−	1.33100i
$111$	5.50965			0.522953
$112$	3.59730	+	5.51754i	0.339913	+	0.521358i
$113$			7.19375i			0.676731i	0.941015	+	0.338365i	$0.109874\pi$
$113$			7.19375i			0.676731i	−0.941015	+	0.338365i	$0.890126\pi$
$114$	−5.23862	−	8.79630i	−0.490642	−	0.823849i
$115$	−15.5745	−	13.6003i	−1.45233	−	1.26823i
$116$	−16.9239	−	9.16918i	−1.57135	−	0.851337i
$117$			4.33558i			0.400824i
$118$	−11.0615	+	6.58768i	−1.01830	+	0.606445i
$119$		−	0.687328i		−	0.0630073i
$120$	0.495243	+	12.1845i	0.0452093	+	1.11229i
$121$	3.89906			0.354460
$122$	−0.489379	+	0.291449i	−0.0443063	+	0.0263865i
$123$	1.83509			0.165464
$124$	−11.8339	−	6.41149i	−1.06272	−	0.575769i
$125$	37.0279			3.31188
$126$	2.00079	−	1.19157i	0.178244	−	0.106153i
$127$			5.81772i			0.516239i	0.966113	+	0.258120i	$0.0831029\pi$
$127$			5.81772i			0.516239i	−0.966113	+	0.258120i	$0.916897\pi$
$128$	9.21858	−	6.55879i	0.814815	−	0.579721i
$129$		−	1.68409i		−	0.148276i
$130$	−13.5264	−	22.7125i	−1.18634	−	1.99202i
$131$	−10.5451			−0.921327			−0.460664	−	0.887575i	$-0.652389\pi$
$131$	−10.5451			−0.921327			−0.460664	+	0.887575i	$0.652389\pi$
$132$	4.68596	+	2.53880i	0.407861	+	0.220974i
$133$		−	11.9208i		−	1.03367i
$134$	−3.92628	−	6.59271i	−0.339179	−	0.569523i
$135$	4.31142			0.371068
$136$	−1.17963	+	0.0479467i	−0.101153	+	0.00411139i
$137$			12.1858i			1.04110i	0.853830	+	0.520552i	$0.174274\pi$
$137$			12.1858i			1.04110i	−0.853830	+	0.520552i	$0.825726\pi$
$138$	6.67191	+	1.21885i	0.567951	+	0.103756i
$139$	−0.585559			−0.0496664			−0.0248332	−	0.999692i	$-0.507905\pi$
$139$	−0.585559			−0.0496664			−0.0248332	+	0.999692i	$0.507905\pi$
$140$	−6.76386	+	12.4843i	−0.571650	+	1.05512i
$141$		−	1.93026i		−	0.162557i
$142$	0.919302	+	1.54362i	0.0771461	+	0.129538i
$143$	−11.5533			−0.966133
$144$	−2.18460	−	3.35075i	−0.182050	−	0.279229i
$145$		−	41.4935i		−	3.44585i
$146$	10.8181	−	6.44268i	0.895310	−	0.533200i
$147$	−4.28851			−0.353711
$148$	5.24922	−	9.68870i	0.431483	−	0.796406i
$149$	12.3817			1.01435			0.507173	−	0.861844i	$-0.330691\pi$
$149$	12.3817			1.01435			0.507173	+	0.861844i	$0.330691\pi$
$150$	−16.5106	+	9.83287i	−1.34809	+	0.802850i
$151$		−	10.4592i		−	0.851157i	−0.904922	−	0.425578i	$-0.860071\pi$
$151$		−	10.4592i		−	0.851157i	0.904922	−	0.425578i	$-0.139929\pi$
$152$	−20.4593	+	0.831574i	−1.65946	+	0.0674496i
$153$			0.417408i			0.0337454i
$154$	3.17523	+	5.33161i	0.255868	+	0.429634i
$155$		−	29.0141i		−	2.33047i
$156$	7.62409	+	4.13064i	0.610416	+	0.330716i
$157$	−11.6176			−0.927182			−0.463591	−	0.886049i	$-0.653439\pi$
$157$	−11.6176			−0.927182			−0.463591	+	0.886049i	$0.653439\pi$
$158$	13.5278	−	8.05643i	1.07621	−	0.640935i
$159$	−5.44690			−0.431967
$160$	21.8982	+	10.7377i	1.73120	+	0.848886i
$161$	5.94836	+	5.19434i	0.468797	+	0.409371i
$162$	−1.21506	+	0.723626i	−0.0954640	+	0.0568534i
$163$	−13.1349			−1.02881			−0.514403	−	0.857549i	$-0.671986\pi$
$163$	−13.1349			−1.02881			−0.514403	+	0.857549i	$0.671986\pi$
$164$	1.74834	−	3.22699i	0.136523	−	0.251985i
$165$			11.4889i			0.894409i
$166$	8.00690	+	13.4446i	0.621456	+	1.04350i
$167$			10.7842i			0.834503i	0.908791	+	0.417252i	$0.137007\pi$
$167$			10.7842i			0.834503i	−0.908791	+	0.417252i	$0.862993\pi$
$168$	−0.189148	−	4.65361i	−0.0145931	−	0.359034i
$169$	−5.79725			−0.445942
$170$	−1.30225	−	2.18664i	−0.0998781	−	0.167708i
$171$			7.23941i			0.553612i
$172$	−2.96147	−	1.60449i	−0.225810	−	0.122341i
$173$			7.69561i			0.585086i	0.956252	+	0.292543i	$0.0945015\pi$
$173$			7.69561i			0.585086i	−0.956252	+	0.292543i	$0.905498\pi$
$174$	6.96424	+	11.6938i	0.527958	+	0.886507i
$175$	−22.3754			−1.69142
$176$	8.92893	−	5.82145i	0.673044	−	0.438808i
$177$	9.10371			0.684277
$178$	13.3312	+	22.3848i	0.999219	+	1.67781i
$179$	−9.49592			−0.709759			−0.354879	−	0.934912i	$-0.615478\pi$
$179$	−9.49592			−0.709759			−0.354879	+	0.934912i	$0.615478\pi$
$180$	4.10762	−	7.58161i	0.306164	−	0.565100i
$181$	−11.1505			−0.828811			−0.414406	−	0.910092i	$-0.636010\pi$
$181$	−11.1505			−0.828811			−0.414406	+	0.910092i	$0.636010\pi$
$182$	5.16613	+	8.67457i	0.382939	+	0.643002i
$183$	0.402762			0.0297730
$184$	8.49989	−	10.5713i	0.626620	−	0.779325i
$185$	23.7544			1.74646
$186$	4.86970	+	8.17684i	0.357064	+	0.599555i
$187$	−1.11229			−0.0813388
$188$	−3.39436	−	1.83902i	−0.247559	−	0.134124i
$189$	−1.64666			−0.119777
$190$	−22.5859	−	37.9245i	−1.63855	−	2.75134i
$191$	−8.51868			−0.616390			−0.308195	−	0.951323i	$-0.599725\pi$
$191$	−8.51868			−0.616390			−0.308195	+	0.951323i	$0.599725\pi$
$192$	−7.97361	+	0.649254i	−0.575446	+	0.0468558i
$193$	−18.2663			−1.31484			−0.657418	−	0.753526i	$-0.728352\pi$
$193$	−18.2663			−1.31484			−0.657418	+	0.753526i	$0.728352\pi$
$194$	−7.06909	−	11.8699i	−0.507531	−	0.852209i
$195$			18.6925i			1.33860i
$196$	−4.08580	+	7.54132i	−0.291843	+	0.538666i
$197$		−	4.86247i		−	0.346437i	−0.984883	−	0.173218i	$-0.944583\pi$
$197$		−	4.86247i		−	0.346437i	0.984883	−	0.173218i	$-0.0554166\pi$
$198$	−1.92829	−	3.23784i	−0.137037	−	0.230103i
$199$	24.4964			1.73650			0.868252	−	0.496124i	$-0.165244\pi$
$199$	24.4964			1.73650			0.868252	+	0.496124i	$0.165244\pi$
$200$	1.56086	+	38.4019i	0.110369	+	2.71542i
$201$			5.42584i			0.382709i
$202$	6.13947	+	10.3089i	0.431972	+	0.725335i
$203$			15.8476i			1.11228i
$204$	0.734009	+	0.397678i	0.0513909	+	0.0278430i
$205$	7.91182			0.552586
$206$	−4.97504	+	2.96288i	−0.346628	+	0.206434i
$207$	−3.61238	−	3.15447i	−0.251078	−	0.219251i
$208$	14.5274	−	9.47153i	1.00730	−	0.656732i
$209$	−19.2913			−1.33441
$210$	8.62623	−	5.13734i	0.595266	−	0.354510i
$211$	4.47841			0.308307			0.154153	−	0.988047i	$-0.450735\pi$
$211$	4.47841			0.308307			0.154153	+	0.988047i	$0.450735\pi$
$212$	−5.18943	+	9.57834i	−0.356412	+	0.657843i
$213$		−	1.27041i		−	0.0870472i
$214$	7.03605	+	11.8144i	0.480975	+	0.807616i
$215$		−	7.26083i		−	0.495185i
$216$	0.114868	+	2.82609i	0.00781576	+	0.192291i
$217$			11.0813i			0.752250i
$218$	−1.10520	+	0.658200i	−0.0748536	+	0.0445789i
$219$	−8.90333			−0.601632
$220$	20.2032	+	10.9458i	1.36210	+	0.737968i
$221$	−1.80970			−0.121734
$222$	−6.69455	+	3.98693i	−0.449309	+	0.267585i
$223$		−	3.13035i		−	0.209624i	−0.994492	−	0.104812i	$-0.966576\pi$
$223$		−	3.13035i		−	0.209624i	0.994492	−	0.104812i	$-0.0334240\pi$
$224$	−8.36356	−	4.10103i	−0.558814	−	0.274012i
$225$	13.5883			0.905889
$226$	−5.20558	−	8.74082i	−0.346270	−	0.581431i
$227$			11.7467i			0.779655i	0.920888	+	0.389828i	$0.127465\pi$
$227$			11.7467i			0.779655i	−0.920888	+	0.389828i	$0.872535\pi$
$228$	12.7305	+	6.89722i	0.843095	+	0.456779i
$229$	−12.9570			−0.856226			−0.428113	−	0.903725i	$-0.640821\pi$
$229$	−12.9570			−0.856226			−0.428113	+	0.903725i	$0.640821\pi$
$230$	28.7654	+	5.25499i	1.89673	+	0.346504i
$231$		−	4.38795i		−	0.288706i
$232$	27.1986	−	1.10550i	1.78567	−	0.0725794i
$233$	5.95168			0.389908			0.194954	−	0.980812i	$-0.437544\pi$
$233$	5.95168			0.389908			0.194954	+	0.980812i	$0.437544\pi$
$234$	−3.13734	−	5.26798i	−0.205094	−	0.344379i
$235$		−	8.32217i		−	0.542879i
$236$	8.67340	−	16.0088i	0.564590	−	1.04209i
$237$	−11.1334			−0.723193
$238$	0.497369	+	0.835144i	0.0322396	+	0.0541343i
$239$		−	4.87556i		−	0.315374i	−0.987489	−	0.157687i	$-0.949596\pi$
$239$		−	4.87556i		−	0.315374i	0.987489	−	0.157687i	$-0.0504037\pi$
$240$	−9.41875	−	14.4465i	−0.607977	−	0.932516i
$241$		−	6.55054i		−	0.421958i	−0.977491	−	0.210979i	$-0.932335\pi$
$241$		−	6.55054i		−	0.421958i	0.977491	−	0.210979i	$-0.0676651\pi$
$242$	−4.73758	+	2.82146i	−0.304543	+	0.181370i
$243$	1.00000			0.0641500
$244$	0.383724	−	0.708254i	0.0245654	−	0.0453413i
$245$	−18.4896			−1.18126
$246$	−2.22974	+	1.32792i	−0.142163	+	0.0846648i
$247$	−31.3870			−1.99711
$248$	19.0184	−	0.773012i	1.20767	−	0.0490863i
$249$		−	11.0650i		−	0.701214i
$250$	−44.9910	+	26.7943i	−2.84548	+	1.69462i
$251$			11.6282i			0.733967i	0.930227	+	0.366984i	$0.119609\pi$
$251$			11.6282i			0.733967i	−0.930227	+	0.366984i	$0.880391\pi$
$252$	−1.56882	+	2.89564i	−0.0988267	+	0.182408i
$253$	8.40591	−	9.62613i	0.528475	−	0.605190i
$254$	−4.20985	−	7.06887i	−0.264150	−	0.443540i
$255$			1.79962i			0.112697i
$256$	−6.45500	+	14.6401i	−0.403438	+	0.915007i
$257$	17.2051			1.07322			0.536612	−	0.843829i	$-0.319704\pi$
$257$	17.2051			1.07322			0.536612	+	0.843829i	$0.319704\pi$
$258$	1.21865	+	2.04627i	0.0758701	+	0.127395i
$259$	−9.07252			−0.563739
$260$	32.8707	+	17.8089i	2.03855	+	1.10446i
$261$		−	9.62409i		−	0.595716i
$262$	12.8129	−	7.63068i	0.791582	−	0.471425i
$263$	−26.1527			−1.61265			−0.806323	−	0.591476i	$-0.798545\pi$
$263$	−26.1527			−1.61265			−0.806323	+	0.591476i	$0.798545\pi$
$264$	−7.53086	+	0.306095i	−0.463492	+	0.0188388i
$265$	−23.4839			−1.44260
$266$	8.62623	+	14.4845i	0.528908	+	0.888103i
$267$		−	18.4228i		−	1.12746i
$268$	9.54130	+	5.16937i	0.582828	+	0.315769i
$269$		−	10.8942i		−	0.664233i	−0.943238	−	0.332116i	$-0.892237\pi$
$269$		−	10.8942i		−	0.664233i	0.943238	−	0.332116i	$-0.107763\pi$
$270$	−5.23862	+	3.11985i	−0.318812	+	0.189868i
$271$			24.1199i			1.46518i	0.680671	+	0.732589i	$0.261688\pi$
$271$			24.1199i			1.46518i	−0.680671	+	0.732589i	$0.738312\pi$
$272$	1.39863	−	0.911871i	0.0848042	−	0.0552903i
$273$		−	7.13922i		−	0.432085i
$274$	−8.81796	−	14.8065i	−0.532713	−	0.894491i
$275$			36.2096i			2.18352i
$276$	−8.98875	+	3.34699i	−0.541059	+	0.201465i
$277$			13.1405i			0.789534i	0.918781	+	0.394767i	$0.129175\pi$
$277$			13.1405i			0.789534i	−0.918781	+	0.394767i	$0.870825\pi$
$278$	0.711488	−	0.423725i	0.0426722	−	0.0254134i
$279$		−	6.72959i		−	0.402890i
$280$	−0.815496	−	20.0637i	−0.0487352	−	1.19903i
$281$		−	16.4508i		−	0.981375i	−0.871336	−	0.490688i	$-0.836746\pi$
$281$		−	16.4508i		−	0.981375i	0.871336	−	0.490688i	$-0.163254\pi$
$282$	1.39679	+	2.34538i	0.0831775	+	0.139665i
$283$		−	18.4998i		−	1.09970i	−0.835264	−	0.549849i	$-0.814685\pi$
$283$		−	18.4998i		−	1.09970i	0.835264	−	0.549849i	$-0.185315\pi$
$284$	−2.23401	−	1.21036i	−0.132564	−	0.0718217i
$285$			31.2121i			1.84885i
$286$	14.0379	−	8.36025i	0.830078	−	0.494352i
$287$	−3.02176			−0.178369
$288$	5.07911	+	2.49051i	0.299289	+	0.146755i
$289$	16.8258			0.989751
$290$	30.0258	+	50.4170i	1.76317	+	2.96059i
$291$			9.76899i			0.572668i
$292$	−8.48249	+	15.6565i	−0.496400	+	0.916225i
$293$	13.6213			0.795766			0.397883	−	0.917436i	$-0.369745\pi$
$293$	13.6213			0.795766			0.397883	+	0.917436i	$0.369745\pi$
$294$	5.21079	−	3.10328i	0.303900	−	0.180987i
$295$	39.2499			2.28522
$296$	0.632881	+	15.5708i	0.0367855	+	0.905034i
$297$			2.66476i			0.154625i
$298$	−15.0444	+	8.95970i	−0.871502	+	0.519021i
$299$	13.6765	−	15.6618i	0.790930	−	0.905743i
$300$	12.9460	−	23.8950i	0.747440	−	1.37958i
$301$			2.77313i			0.159841i
$302$	7.56854	+	12.7085i	0.435521	+	0.731293i
$303$		−	8.48432i		−	0.487412i
$304$	24.2574	−	15.8153i	1.39126	−	0.907067i
$305$	1.73647			0.0994303
$306$	−0.302047	−	0.507175i	−0.0172669	−	0.0289932i
$307$	30.7521			1.75511			0.877557	−	0.479472i	$-0.159172\pi$
$307$	30.7521			1.75511			0.877557	+	0.479472i	$0.159172\pi$
$308$	−7.71619	−	4.18054i	−0.439671	−	0.238208i
$309$	4.09449			0.232927
$310$	20.9953	+	35.2538i	1.19245	+	2.00228i
$311$		−	15.2477i		−	0.864620i	−0.901725	−	0.432310i	$-0.857699\pi$
$311$		−	15.2477i		−	0.864620i	0.901725	−	0.432310i	$-0.142301\pi$
$312$	−12.2528	+	0.498018i	−0.693676	+	0.0281947i
$313$			12.2079i			0.690029i	0.938597	+	0.345014i	$0.112126\pi$
$313$			12.2079i			0.690029i	−0.938597	+	0.345014i	$0.887874\pi$
$314$	14.1160	−	8.40676i	0.796612	−	0.474421i
$315$	−7.09944			−0.400008
$316$	−10.6072	+	19.5781i	−0.596700	+	1.10135i
$317$		−	10.5516i		−	0.592636i	−0.955089	−	0.296318i	$-0.904241\pi$
$317$		−	10.5516i		−	0.592636i	0.955089	−	0.296318i	$-0.0957588\pi$
$318$	6.61830	−	3.94152i	0.371136	−	0.221029i
$319$	25.6459			1.43589
$320$	−34.3776	+	2.79920i	−1.92176	+	0.156480i
$321$		−	9.72333i		−	0.542703i
$322$	−10.9864	−	2.00704i	−0.612246	−	0.111848i
$323$	−3.02179			−0.168137
$324$	0.952732	−	1.75849i	0.0529295	−	0.0976941i
$325$			58.9133i			3.26792i
$326$	15.9597	−	9.50476i	0.883924	−	0.526420i
$327$	0.909587			0.0503002
$328$	0.210792	+	5.18612i	0.0116390	+	0.286356i
$329$			3.17849i			0.175236i
$330$	−8.31366	−	13.9597i	−0.457652	−	0.768455i
$331$	16.9416			0.931192			0.465596	−	0.884997i	$-0.345840\pi$
$331$	16.9416			0.931192			0.465596	+	0.884997i	$0.345840\pi$
$332$	−19.4577	−	10.5419i	−1.06788	−	0.578565i
$333$	5.50965			0.301927
$334$	−7.80369	−	13.1034i	−0.426999	−	0.716985i
$335$			23.3931i			1.27810i
$336$	3.59730	+	5.51754i	0.196249	+	0.301006i
$337$			14.8650i			0.809750i	0.914372	+	0.404875i	$0.132685\pi$
$337$			14.8650i			0.809750i	−0.914372	+	0.404875i	$0.867315\pi$
$338$	7.04399	−	4.19504i	0.383143	−	0.228180i
$339$			7.19375i			0.390711i
$340$	3.16462	+	1.71455i	0.171626	+	0.0929848i
$341$	17.9327			0.971112
$342$	−5.23862	−	8.79630i	−0.283272	−	0.475650i
$343$	18.5883			1.00368
$344$	4.75941	−	0.193448i	0.256610	−	0.0104300i
$345$	−15.5745	−	13.6003i	−0.838502	−	0.732213i
$346$	−5.56874	−	9.35061i	−0.299377	−	0.502692i
$347$	7.78401			0.417868			0.208934	−	0.977930i	$-0.433001\pi$
$347$	7.78401			0.417868			0.208934	+	0.977930i	$0.433001\pi$
$348$	−16.9239	−	9.16918i	−0.907217	−	0.491519i
$349$			17.3637i			0.929455i	0.885454	+	0.464728i	$0.153848\pi$
$349$			17.3637i			0.929455i	−0.885454	+	0.464728i	$0.846152\pi$
$350$	27.1874	−	16.1914i	1.45323	−	0.865466i
$351$			4.33558i			0.231416i
$352$	−6.63662	+	13.5346i	−0.353733	+	0.721397i
$353$	−28.6706			−1.52598			−0.762990	−	0.646410i	$-0.776270\pi$
$353$	−28.6706			−1.52598			−0.762990	+	0.646410i	$0.776270\pi$
$354$	−11.0615	+	6.58768i	−0.587914	+	0.350131i
$355$		−	5.47728i		−	0.290704i
$356$	−32.3965	−	17.5520i	−1.71701	−	0.930256i
$357$		−	0.687328i		−	0.0363773i
$358$	11.5381	−	6.87149i	0.609807	−	0.363170i
$359$	−0.668622			−0.0352885			−0.0176443	−	0.999844i	$-0.505617\pi$
$359$	−0.668622			−0.0352885			−0.0176443	+	0.999844i	$0.505617\pi$
$360$	0.495243	+	12.1845i	0.0261016	+	0.642178i
$361$	−33.4091			−1.75837
$362$	13.5485	−	8.06880i	0.712094	−	0.424087i
$363$	3.89906			0.204647
$364$	−12.5543	−	6.80176i	−0.658023	−	0.356509i
$365$	−38.3860			−2.00922
$366$	−0.489379	+	0.291449i	−0.0255802	+	0.0152343i
$367$	−9.31985			−0.486492			−0.243246	−	0.969965i	$-0.578212\pi$
$367$	−9.31985			−0.486492			−0.243246	+	0.969965i	$0.578212\pi$
$368$	−2.67821	+	18.9955i	−0.139611	+	0.990206i
$369$	1.83509			0.0955307
$370$	−28.8630	+	17.1893i	−1.50052	+	0.893630i
$371$	8.96919			0.465657
$372$	−11.8339	−	6.41149i	−0.613561	−	0.332420i
$373$	−27.3610			−1.41670			−0.708349	−	0.705862i	$-0.750560\pi$
$373$	−27.3610			−1.41670			−0.708349	+	0.705862i	$0.750560\pi$
$374$	1.35150	−	0.804882i	0.0698843	−	0.0416195i
$375$	37.0279			1.91211
$376$	5.45510	−	0.221725i	0.281325	−	0.0114346i
$377$	41.7260			2.14900
$378$	2.00079	−	1.19157i	0.102909	−	0.0612875i
$379$		−	21.2570i		−	1.09190i	−0.837819	−	0.545949i	$-0.816169\pi$
$379$		−	21.2570i		−	1.09190i	0.837819	−	0.545949i	$-0.183831\pi$
$380$	54.8864	+	29.7368i	2.81561	+	1.52546i
$381$			5.81772i			0.298051i
$382$	10.3507	−	6.16433i	0.529587	−	0.315395i
$383$	12.1458			0.620623			0.310311	−	0.950635i	$-0.399567\pi$
$383$	12.1458			0.620623			0.310311	+	0.950635i	$0.399567\pi$
$384$	9.21858	−	6.55879i	0.470434	−	0.334702i
$385$		−	18.9183i		−	0.964166i
$386$	22.1946	−	13.2180i	1.12968	−	0.672777i
$387$		−	1.68409i		−	0.0856073i
$388$	17.1787	+	9.30723i	0.872117	+	0.472503i
$389$	−6.03367			−0.305919			−0.152960	−	0.988232i	$-0.548880\pi$
$389$	−6.03367			−0.305919			−0.152960	+	0.988232i	$0.548880\pi$
$390$	−13.5264	−	22.7125i	−0.684934	−	1.15009i
$391$	1.31670	−	1.50784i	0.0665884	−	0.0762546i
$392$	−0.492611	−	12.1197i	−0.0248806	−	0.612139i
$393$	−10.5451			−0.531928
$394$	3.51861	+	5.90818i	0.177265	+	0.297650i
$395$	−48.0008			−2.41518
$396$	4.68596	+	2.53880i	0.235479	+	0.127580i
$397$			1.29653i			0.0650710i	0.999471	+	0.0325355i	$0.0103582\pi$
$397$			1.29653i			0.0650710i	−0.999471	+	0.0325355i	$0.989642\pi$
$398$	−29.7645	+	17.7262i	−1.49196	+	0.888535i
$399$		−	11.9208i		−	0.596789i
$400$	−29.6851	−	45.5311i	−1.48426	−	2.27655i
$401$			36.4362i			1.81954i	0.415114	+	0.909769i	$0.363742\pi$
$401$			36.4362i			1.81954i	−0.415114	+	0.909769i	$0.636258\pi$
$402$	−3.92628	−	6.59271i	−0.195825	−	0.328814i
$403$	29.1767			1.45339
$404$	−14.9196	−	8.08328i	−0.742280	−	0.402158i
$405$	4.31142			0.214236
$406$	−11.4677	−	19.2558i	−0.569134	−	0.955647i
$407$			14.6819i			0.727755i
$408$	−1.17963	+	0.0479467i	−0.0584006	+	0.00237371i
$409$	−14.2577			−0.705000			−0.352500	−	0.935812i	$-0.614668\pi$
$409$	−14.2577			−0.705000			−0.352500	+	0.935812i	$0.614668\pi$
$410$	−9.61332	+	5.72520i	−0.474768	+	0.282747i
$411$			12.1858i			0.601082i
$412$	3.90095	−	7.20014i	0.192186	−	0.354725i
$413$	−14.9907			−0.737645
$414$	6.67191	+	1.21885i	0.327907	+	0.0599034i
$415$		−	47.7057i		−	2.34178i
$416$	−10.7978	+	22.0209i	−0.529407	+	1.07966i
$417$	−0.585559			−0.0286749
$418$	23.4400	−	13.9597i	1.14649	−	0.682790i
$419$		−	33.4135i		−	1.63236i	−0.577801	−	0.816178i	$-0.696089\pi$
$419$		−	33.4135i		−	1.63236i	0.577801	−	0.816178i	$-0.303911\pi$
$420$	−6.76386	+	12.4843i	−0.330043	+	0.609173i
$421$	−39.4972			−1.92497			−0.962487	−	0.271327i	$-0.912537\pi$
$421$	−39.4972			−1.92497			−0.962487	+	0.271327i	$0.912537\pi$
$422$	−5.44153	+	3.24070i	−0.264890	+	0.157755i
$423$		−	1.93026i		−	0.0938526i
$424$	−0.625673	−	15.3935i	−0.0303854	−	0.747572i
$425$			5.67187i			0.275126i
$426$	0.919302	+	1.54362i	0.0445403	+	0.0747888i
$427$	−0.663212			−0.0320951
$428$	−17.0984	−	9.26372i	−0.826483	−	0.447779i
$429$	−11.5533			−0.557797
$430$	5.25413	+	8.82233i	0.253376	+	0.425451i
$431$	−2.63753			−0.127045			−0.0635227	−	0.997980i	$-0.520234\pi$
$431$	−2.63753			−0.127045			−0.0635227	+	0.997980i	$0.520234\pi$
$432$	−2.18460	−	3.35075i	−0.105107	−	0.161213i
$433$		−	29.0705i		−	1.39704i	−0.715591	−	0.698520i	$-0.753842\pi$
$433$		−	29.0705i		−	1.39704i	0.715591	−	0.698520i	$-0.246158\pi$
$434$	−8.01874	−	13.4645i	−0.384912	−	0.646315i
$435$		−	41.4935i		−	1.98946i
$436$	0.866592	−	1.59950i	0.0415022	−	0.0766023i
$437$	22.8365	−	26.1515i	1.09242	−	1.25100i
$438$	10.8181	−	6.44268i	0.516907	−	0.307843i
$439$		−	3.54435i		−	0.169162i	−0.996417	−	0.0845812i	$-0.973045\pi$
$439$		−	3.54435i		−	0.169162i	0.996417	−	0.0845812i	$-0.0269552\pi$
$440$	−32.4687	+	1.31970i	−1.54788	+	0.0629143i
$441$	−4.28851			−0.204215
$442$	2.19890	−	1.30955i	0.104591	−	0.0622889i
$443$	6.36453			0.302388			0.151194	−	0.988504i	$-0.451688\pi$
$443$	6.36453			0.302388			0.151194	+	0.988504i	$0.451688\pi$
$444$	5.24922	−	9.68870i	0.249117	−	0.459805i
$445$		−	79.4286i		−	3.76528i
$446$	2.26520	+	3.80356i	0.107260	+	0.180104i
$447$	12.3817			0.585633
$448$	13.1298	−	1.06910i	0.620326	−	0.0505102i
$449$	−34.1069			−1.60960			−0.804801	−	0.593544i	$-0.797728\pi$
$449$	−34.1069			−1.60960			−0.804801	+	0.593544i	$0.797728\pi$
$450$	−16.5106	+	9.83287i	−0.778318	+	0.463526i
$451$			4.89006i			0.230264i
$452$	12.6502	+	6.85371i	0.595014	+	0.322371i
$453$		−	10.4592i		−	0.491416i
$454$	−8.50021	−	14.2729i	−0.398935	−	0.669861i
$455$		−	30.7802i		−	1.44300i
$456$	−20.4593	+	0.831574i	−0.958092	+	0.0389420i
$457$			13.5565i			0.634146i	0.948401	+	0.317073i	$0.102700\pi$
$457$			13.5565i			0.634146i	−0.948401	+	0.317073i	$0.897300\pi$
$458$	15.7436	−	9.37605i	0.735648	−	0.438114i
$459$			0.417408i			0.0194829i
$460$	−38.7543	+	14.4303i	−1.80693	+	0.672815i
$461$		−	17.8479i		−	0.831258i	−0.909534	−	0.415629i	$-0.863561\pi$
$461$		−	17.8479i		−	0.831258i	0.909534	−	0.415629i	$-0.136439\pi$
$462$	3.17523	+	5.33161i	0.147725	+	0.248049i
$463$			36.1254i			1.67889i	0.543444	+	0.839445i	$0.317120\pi$
$463$			36.1254i			1.67889i	−0.543444	+	0.839445i	$0.682880\pi$
$464$	−32.2479	+	21.0248i	−1.49707	+	0.976054i
$465$		−	29.0141i		−	1.34550i
$466$	−7.23164	+	4.30679i	−0.334999	+	0.199508i
$467$			25.0922i			1.16113i	0.814214	+	0.580564i	$0.197168\pi$
$467$			25.0922i			1.16113i	−0.814214	+	0.580564i	$0.802832\pi$
$468$	7.62409	+	4.13064i	0.352424	+	0.190939i
$469$		−	8.93451i		−	0.412557i
$470$	6.02214	+	10.1119i	0.277780	+	0.466428i
$471$	−11.6176			−0.535309
$472$	1.04572	+	25.7280i	0.0481333	+	1.18422i
$473$	4.48770			0.206345
$474$	13.5278	−	8.05643i	0.621350	−	0.370044i
$475$			98.3715i			4.51359i
$476$	−1.20866	−	0.654839i	−0.0553990	−	0.0300145i
$477$	−5.44690			−0.249396
$478$	3.52808	+	5.92409i	0.161371	+	0.270961i
$479$	−16.9870			−0.776154			−0.388077	−	0.921627i	$-0.626860\pi$
$479$	−16.9870			−0.776154			−0.388077	+	0.921627i	$0.626860\pi$
$480$	21.8982	+	10.7377i	0.999510	+	0.490104i
$481$			23.8875i			1.08918i
$482$	4.74014	+	7.95929i	0.215908	+	0.362536i
$483$	5.94836	+	5.19434i	0.270660	+	0.236351i
$484$	3.71476	−	6.85647i	0.168853	−	0.311658i
$485$			42.1182i			1.91249i
$486$	−1.21506	+	0.723626i	−0.0551161	+	0.0328243i
$487$		−	21.7347i		−	0.984892i	−0.870343	−	0.492446i	$-0.836103\pi$
$487$		−	21.7347i		−	0.984892i	0.870343	−	0.492446i	$-0.163897\pi$
$488$	0.0462643	+	1.13824i	0.00209429	+	0.0515258i
$489$	−13.1349			−0.593981
$490$	22.4659	−	13.3795i	1.01491	−	0.604426i
$491$	6.71536			0.303060			0.151530	−	0.988453i	$-0.451580\pi$
$491$	6.71536			0.303060			0.151530	+	0.988453i	$0.451580\pi$
$492$	1.74834	−	3.22699i	0.0788214	−	0.145484i
$493$	4.01717			0.180924
$494$	38.1371	−	22.7125i	1.71587	−	1.02188i
$495$			11.4889i			0.516387i
$496$	−22.5491	+	14.7015i	−1.01249	+	0.660117i
$497$			2.09194i			0.0938361i
$498$	8.00690	+	13.4446i	0.358798	+	0.602466i
$499$	−4.53724			−0.203115			−0.101557	−	0.994830i	$-0.532383\pi$
$499$	−4.53724			−0.203115			−0.101557	+	0.994830i	$0.532383\pi$
$500$	35.2776	−	65.1133i	1.57766	−	2.91196i
$501$			10.7842i			0.481801i
$502$	−8.41449	−	14.1290i	−0.375557	−	0.630607i
$503$	25.3014			1.12814			0.564068	−	0.825729i	$-0.309236\pi$
$503$	25.3014			1.12814			0.564068	+	0.825729i	$0.309236\pi$
$504$	−0.189148	−	4.65361i	−0.00842532	−	0.207288i
$505$		−	36.5795i		−	1.62777i
$506$	−3.24795	+	17.7790i	−0.144389	+	0.790375i
$507$	−5.79725			−0.257465
$508$	10.2304	+	5.54273i	0.453902	+	0.245919i
$509$			32.5510i			1.44280i	0.692520	+	0.721399i	$0.256500\pi$
$509$			32.5510i			1.44280i	−0.692520	+	0.721399i	$0.743500\pi$
$510$	−1.30225	−	2.18664i	−0.0576646	−	0.0968261i
$511$	14.6608			0.648554
$512$	−2.75076	−	22.4596i	−0.121568	−	0.992583i
$513$			7.23941i			0.319628i
$514$	−20.9052	+	12.4500i	−0.922088	+	0.549148i
$515$	17.6531			0.777887
$516$	−2.96147	−	1.60449i	−0.130371	−	0.0706337i
$517$	5.14369			0.226219
$518$	11.0236	−	6.56511i	0.484351	−	0.288454i
$519$			7.69561i			0.337800i
$520$	−52.8267	+	2.14716i	−2.31661	+	0.0941594i
$521$		−	26.7666i		−	1.17267i	−0.810070	−	0.586334i	$-0.800571\pi$
$521$		−	26.7666i		−	1.17267i	0.810070	−	0.586334i	$-0.199429\pi$
$522$	6.96424	+	11.6938i	0.304817	+	0.511825i
$523$			5.03702i			0.220253i	0.993918	+	0.110127i	$0.0351257\pi$
$523$			5.03702i			0.220253i	−0.993918	+	0.110127i	$0.964874\pi$
$524$	−10.0466	+	18.5434i	−0.438889	+	0.810074i
$525$	−22.3754			−0.976541
$526$	31.7771	−	18.9248i	1.38555	−	0.825159i
$527$	2.80898			0.122361
$528$	8.92893	−	5.82145i	0.388582	−	0.253346i
$529$	3.09861	+	22.7903i	0.134722	+	0.990883i
$530$	28.5343	−	16.9935i	1.23945	−	0.738152i
$531$	9.10371			0.395068
$532$	−20.9627	−	11.3574i	−0.908850	−	0.492404i
$533$			7.95616i			0.344619i
$534$	13.3312	+	22.3848i	0.576899	+	0.968686i
$535$		−	41.9213i		−	1.81242i
$536$	−15.3339	+	0.623253i	−0.662325	+	0.0269204i
$537$	−9.49592			−0.409779
$538$	7.88334	+	13.2371i	0.339875	+	0.570692i
$539$		−	11.4279i		−	0.492232i
$540$	4.10762	−	7.58161i	0.176764	−	0.326260i
$541$			6.51918i			0.280282i	0.990132	+	0.140141i	$0.0447555\pi$
$541$			6.51918i			0.280282i	−0.990132	+	0.140141i	$0.955244\pi$
$542$	−17.4538	−	29.3070i	−0.749703	−	1.25885i
$543$	−11.1505			−0.478514
$544$	−1.03956	+	2.12006i	−0.0445708	+	0.0908968i
$545$	3.92161			0.167983
$546$	5.16613	+	8.67457i	0.221090	+	0.371237i
$547$	12.8015			0.547354			0.273677	−	0.961822i	$-0.411760\pi$
$547$	12.8015			0.547354			0.273677	+	0.961822i	$0.411760\pi$
$548$	21.4287	+	11.6098i	0.915388	+	0.495946i
$549$	0.402762			0.0171895
$550$	−26.2022	−	43.9968i	−1.11727	−	1.87603i
$551$	69.6727			2.96816
$552$	8.49989	−	10.5713i	0.361779	−	0.449943i
$553$	18.3330			0.779597
$554$	−9.50878	−	15.9664i	−0.403989	−	0.678348i
$555$	23.7544			1.00832
$556$	−0.557880	+	1.02970i	−0.0236594	+	0.0436691i
$557$	14.7294			0.624104			0.312052	−	0.950065i	$-0.398984\pi$
$557$	14.7294			0.624104			0.312052	+	0.950065i	$0.398984\pi$
$558$	4.86970	+	8.17684i	0.206151	+	0.346153i
$559$	7.30152			0.308821
$560$	15.5095	+	23.7884i	0.655395	+	1.00524i
$561$	−1.11229			−0.0469610
$562$	11.9043	+	19.9887i	0.502151	+	0.843174i
$563$		−	0.721786i		−	0.0304196i	−0.999884	−	0.0152098i	$-0.995158\pi$
$563$		−	0.721786i		−	0.0304196i	0.999884	−	0.0152098i	$-0.00484162\pi$
$564$	−3.39436	−	1.83902i	−0.142928	−	0.0774368i
$565$			31.0153i			1.30482i
$566$	13.3869	+	22.4783i	0.562694	+	0.944834i
$567$	−1.64666			−0.0691532
$568$	3.59030	−	0.145929i	0.150646	−	0.00612305i
$569$			3.22041i			0.135007i	0.997719	+	0.0675033i	$0.0215033\pi$
$569$			3.22041i			0.135007i	−0.997719	+	0.0675033i	$0.978497\pi$
$570$	−22.5859	−	37.9245i	−0.946019	−	1.58848i
$571$			16.7232i			0.699843i	0.936779	+	0.349922i	$0.113792\pi$
$571$			16.7232i			0.699843i	−0.936779	+	0.349922i	$0.886208\pi$
$572$	−11.0072	+	20.3164i	−0.460233	+	0.849470i
$573$	−8.51868			−0.355873
$574$	3.67161	−	2.18662i	0.153250	−	0.0912679i
$575$	−49.0862	−	42.8640i	−2.04704	−	1.78755i
$576$	−7.97361	+	0.649254i	−0.332234	+	0.0270522i
$577$	−7.73849			−0.322158			−0.161079	−	0.986942i	$-0.551497\pi$
$577$	−7.73849			−0.322158			−0.161079	+	0.986942i	$0.551497\pi$
$578$	−20.4443	+	12.1756i	−0.850370	+	0.506437i
$579$	−18.2663			−0.759121
$580$	−72.9661	−	39.5322i	−3.02975	−	1.64148i
$581$			18.2202i			0.755903i
$582$	−7.06909	−	11.8699i	−0.293023	−	0.492023i
$583$		−	14.5147i		−	0.601137i
$584$	−1.02271	−	25.1617i	−0.0423198	−	1.04120i
$585$			18.6925i			0.772840i
$586$	−16.5507	+	9.85673i	−0.683703	+	0.407178i
$587$	3.45027			0.142408			0.0712039	−	0.997462i	$-0.477316\pi$
$587$	3.45027			0.142408			0.0712039	+	0.997462i	$0.477316\pi$
$588$	−4.08580	+	7.54132i	−0.168496	+	0.310999i
$589$	48.7183			2.00740
$590$	−47.6909	+	28.4023i	−1.96340	+	1.16930i
$591$		−	4.86247i		−	0.200015i
$592$	−12.0364	−	18.4615i	−0.494694	−	0.758761i
$593$	19.7197			0.809792			0.404896	−	0.914363i	$-0.367308\pi$
$593$	19.7197			0.809792			0.404896	+	0.914363i	$0.367308\pi$
$594$	−1.92829	−	3.23784i	−0.0791186	−	0.132850i
$595$		−	2.96336i		−	0.121486i
$596$	11.7964	−	21.7731i	0.483200	−	0.891861i
$597$	24.4964			1.00257
$598$	−5.28444	+	28.9266i	−0.216097	+	1.18290i
$599$		−	21.0323i		−	0.859355i	−0.902983	−	0.429677i	$-0.858627\pi$
$599$		−	21.0323i		−	0.859355i	0.902983	−	0.429677i	$-0.141373\pi$
$600$	1.56086	+	38.4019i	0.0637218	+	1.56775i
$601$	21.9715			0.896238			0.448119	−	0.893974i	$-0.352094\pi$
$601$	21.9715			0.896238			0.448119	+	0.893974i	$0.352094\pi$
$602$	−2.00671	−	3.36951i	−0.0817873	−	0.137331i
$603$			5.42584i			0.220957i
$604$	−18.3924	−	9.96480i	−0.748377	−	0.405462i
$605$	16.8105			0.683443
$606$	6.13947	+	10.3089i	0.249399	+	0.418772i
$607$			15.8786i			0.644493i	0.946656	+	0.322246i	$0.104438\pi$
$607$			15.8786i			0.644493i	−0.946656	+	0.322246i	$0.895562\pi$
$608$	−18.0299	+	36.7697i	−0.731207	+	1.49121i
$609$			15.8476i			0.642177i
$610$	−2.10992	+	1.25656i	−0.0854281	+	0.0508765i
$611$	8.36881			0.338566
$612$	0.734009	+	0.397678i	0.0296706	+	0.0160752i
$613$	−36.0023			−1.45412			−0.727059	−	0.686575i	$-0.759113\pi$
$613$	−36.0023			−1.45412			−0.727059	+	0.686575i	$0.759113\pi$
$614$	−37.3656	+	22.2530i	−1.50795	+	0.898058i
$615$	7.91182			0.319035
$616$	12.4008	−	0.504034i	0.499641	−	0.0203081i
$617$			22.9141i			0.922487i	0.887274	+	0.461243i	$0.152597\pi$
$617$			22.9141i			0.922487i	−0.887274	+	0.461243i	$0.847403\pi$
$618$	−4.97504	+	2.96288i	−0.200126	+	0.119184i
$619$			10.3547i			0.416189i	0.978109	+	0.208094i	$0.0667261\pi$
$619$			10.3547i			0.416189i	−0.978109	+	0.208094i	$0.933274\pi$
$620$	−51.0211	−	27.6426i	−2.04906	−	1.11015i
$621$	−3.61238	−	3.15447i	−0.144960	−	0.126585i
$622$	11.0337	+	18.5269i	0.442409	+	0.742861i
$623$			30.3362i			1.21539i
$624$	14.5274	−	9.47153i	0.581562	−	0.379165i
$625$	91.7011			3.66804
$626$	−8.83392	−	14.8333i	−0.353074	−	0.592856i
$627$	−19.2913			−0.770420
$628$	−11.0684	+	20.4294i	−0.441678	+	0.815222i
$629$			2.29977i			0.0916979i
$630$	8.62623	−	5.13734i	0.343677	−	0.204676i
$631$	19.1276			0.761458			0.380729	−	0.924687i	$-0.375673\pi$
$631$	19.1276			0.761458			0.380729	+	0.924687i	$0.375673\pi$
$632$	−1.27887	−	31.4641i	−0.0508707	−	1.25157i
$633$	4.47841			0.178001
$634$	7.63540	+	12.8208i	0.303240	+	0.509179i
$635$			25.0826i			0.995374i
$636$	−5.18943	+	9.57834i	−0.205774	+	0.379806i
$637$		−	18.5932i		−	0.736689i
$638$	−31.1612	+	18.5580i	−1.23369	+	0.734719i
$639$		−	1.27041i		−	0.0502567i
$640$	39.7452	−	28.2777i	1.57107	−	1.11777i
$641$		−	14.5810i		−	0.575915i	−0.957643	−	0.287957i	$-0.907024\pi$
$641$		−	14.5810i		−	0.575915i	0.957643	−	0.287957i	$-0.0929761\pi$
$642$	7.03605	+	11.8144i	0.277691	+	0.466278i
$643$		−	26.4659i		−	1.04371i	−0.853034	−	0.521856i	$-0.825240\pi$
$643$		−	26.4659i		−	1.04371i	0.853034	−	0.521856i	$-0.174760\pi$
$644$	14.8014	−	5.51135i	0.583257	−	0.217178i
$645$		−	7.26083i		−	0.285895i
$646$	3.67164	−	2.18664i	0.144459	−	0.0860323i
$647$			26.7134i			1.05021i	0.851037	+	0.525106i	$0.175974\pi$
$647$			26.7134i			1.05021i	−0.851037	+	0.525106i	$0.824026\pi$
$648$	0.114868	+	2.82609i	0.00451243	+	0.111019i
$649$			24.2592i			0.952257i
$650$	−42.6312	−	71.5831i	−1.67213	−	2.80772i
$651$			11.0813i			0.434312i
$652$	−12.5140	+	23.0977i	−0.490088	+	0.904574i
$653$			28.6072i			1.11949i	0.828666	+	0.559743i	$0.189100\pi$
$653$			28.6072i			1.11949i	−0.828666	+	0.559743i	$0.810900\pi$
$654$	−1.10520	+	0.658200i	−0.0432168	+	0.0257377i
$655$	−45.4642			−1.77643
$656$	−4.00894	−	6.14891i	−0.156523	−	0.240074i
$657$	−8.90333			−0.347352
$658$	−2.30003	−	3.86204i	−0.0896647	−	0.150558i
$659$		−	27.6549i		−	1.07728i	−0.842536	−	0.538640i	$-0.818938\pi$
$659$		−	27.6549i		−	1.07728i	0.842536	−	0.538640i	$-0.181062\pi$
$660$	20.2032	+	10.9458i	0.786407	+	0.426066i
$661$	39.1587			1.52310			0.761548	−	0.648108i	$-0.224440\pi$
$661$	39.1587			1.52310			0.761548	+	0.648108i	$0.224440\pi$
$662$	−20.5850	+	12.2593i	−0.800058	+	0.476473i
$663$	−1.80970			−0.0702831
$664$	31.2706	−	1.27101i	1.21354	−	0.0493247i
$665$		−	51.3958i		−	1.99304i
$666$	−6.69455	+	3.98693i	−0.259409	+	0.154490i
$667$	−30.3589	+	34.7659i	−1.17550	+	1.34614i
$668$	18.9639	+	10.2744i	0.733735	+	0.397529i
$669$		−	3.13035i		−	0.121026i
$670$	−16.9278	−	28.4239i	−0.653979	−	1.09811i
$671$			1.07326i			0.0414329i
$672$	−8.36356	−	4.10103i	−0.322631	−	0.158201i
$673$	−12.9976			−0.501022			−0.250511	−	0.968114i	$-0.580599\pi$
$673$	−12.9976			−0.501022			−0.250511	+	0.968114i	$0.580599\pi$
$674$	−10.7567	−	18.0619i	−0.414333	−	0.695717i
$675$	13.5883			0.523015
$676$	−5.52322	+	10.1944i	−0.212432	+	0.392093i
$677$	8.30126			0.319044			0.159522	−	0.987194i	$-0.449005\pi$
$677$	8.30126			0.319044			0.159522	+	0.987194i	$0.449005\pi$
$678$	−5.20558	−	8.74082i	−0.199919	−	0.335689i
$679$		−	16.0862i		−	0.617332i
$680$	−5.08589	+	0.206718i	−0.195035	+	0.00792728i
$681$			11.7467i			0.450134i
$682$	−21.7893	+	12.9766i	−0.834356	+	0.496899i
$683$	15.4882			0.592638			0.296319	−	0.955089i	$-0.404241\pi$
$683$	15.4882			0.592638			0.296319	+	0.955089i	$0.404241\pi$
$684$	12.7305	+	6.89722i	0.486761	+	0.263722i
$685$			52.5381i			2.00738i
$686$	−22.5859	+	13.4510i	−0.862334	+	0.513562i
$687$	−12.9570			−0.494342
$688$	−5.64297	+	3.67908i	−0.215136	+	0.140264i
$689$		−	23.6155i		−	0.899678i
$690$	28.7654	+	5.25499i	1.09508	+	0.200054i
$691$	−2.05029			−0.0779968			−0.0389984	−	0.999239i	$-0.512417\pi$
$691$	−2.05029			−0.0779968			−0.0389984	+	0.999239i	$0.512417\pi$
$692$	13.5327	+	7.33185i	0.514436	+	0.278715i
$693$		−	4.38795i		−	0.166684i
$694$	−9.45803	+	5.63271i	−0.359022	+	0.213815i
$695$	−2.52459			−0.0957631
$696$	27.1986	−	1.10550i	1.03096	−	0.0419038i
$697$			0.765979i			0.0290135i
$698$	−12.5648	−	21.0978i	−0.475584	−	0.798565i
$699$	5.95168			0.225113
$700$	−21.3177	+	39.3469i	−0.805734	+	1.48717i
$701$	−3.71009			−0.140128			−0.0700640	−	0.997542i	$-0.522320\pi$
$701$	−3.71009			−0.140128			−0.0700640	+	0.997542i	$0.522320\pi$
$702$	−3.13734	−	5.26798i	−0.118411	−	0.198827i
$703$			39.8866i			1.50435i
$704$	−1.73010	−	21.2478i	−0.0652058	−	0.800805i
$705$		−	8.32217i		−	0.313431i
$706$	34.8364	−	20.7468i	1.31109	−	0.780815i
$707$			13.9708i			0.525426i
$708$	8.67340	−	16.0088i	0.325966	−	0.601649i
$709$	−11.3909			−0.427793			−0.213897	−	0.976856i	$-0.568616\pi$
$709$	−11.3909			−0.427793			−0.213897	+	0.976856i	$0.568616\pi$
$710$	3.96350	+	6.65521i	0.148747	+	0.249765i
$711$	−11.1334			−0.417536
$712$	52.0647	−	2.11619i	1.95121	−	0.0793076i
$713$	−21.2283	+	24.3098i	−0.795006	+	0.910411i
$714$	0.497369	+	0.835144i	0.0186135	+	0.0312545i
$715$	−49.8110			−1.86283
$716$	−9.04707	+	16.6985i	−0.338105	+	0.624053i
$717$		−	4.87556i		−	0.182081i
$718$	0.812415	−	0.483832i	0.0303191	−	0.0180565i
$719$			43.1732i			1.61009i	0.593213	+	0.805045i	$0.297859\pi$
$719$			43.1732i			1.61009i	−0.593213	+	0.805045i	$0.702141\pi$
$720$	−9.41875	−	14.4465i	−0.351016	−	0.538388i
$721$	−6.74223			−0.251094
$722$	40.5939	−	24.1757i	1.51075	−	0.899725i
$723$		−	6.55054i		−	0.243617i
$724$	−10.6234	+	19.6081i	−0.394817	+	0.728730i
$725$		−	130.775i		−	4.85687i
$726$	−4.73758	+	2.82146i	−0.175828	+	0.104714i
$727$	14.5183			0.538452			0.269226	−	0.963077i	$-0.413232\pi$
$727$	14.5183			0.538452			0.269226	+	0.963077i	$0.413232\pi$
$728$	20.1761	−	0.820066i	0.747776	−	0.0303937i
$729$	1.00000			0.0370370
$730$	46.6412	−	27.7771i	1.72627	−	1.02808i
$731$	0.702954			0.0259997
$732$	0.383724	−	0.708254i	0.0141828	−	0.0261778i
$733$	−7.89030			−0.291435			−0.145717	−	0.989326i	$-0.546549\pi$
$733$	−7.89030			−0.291435			−0.145717	+	0.989326i	$0.546549\pi$
$734$	11.3242	−	6.74408i	0.417982	−	0.248929i
$735$	−18.4896			−0.681998
$736$	−10.4914	−	25.0186i	−0.386719	−	0.922198i
$737$	−14.4585			−0.532588
$738$	−2.22974	+	1.32792i	−0.0820777	+	0.0488812i
$739$	16.7236			0.615186			0.307593	−	0.951518i	$-0.400477\pi$
$739$	16.7236			0.615186			0.307593	+	0.951518i	$0.400477\pi$
$740$	22.6316	−	41.7720i	0.831954	−	1.53557i
$741$	−31.3870			−1.15303
$742$	−10.8981	+	6.49034i	−0.400081	+	0.238268i
$743$	26.1360			0.958838			0.479419	−	0.877586i	$-0.340848\pi$
$743$	26.1360			0.958838			0.479419	+	0.877586i	$0.340848\pi$
$744$	19.0184	−	0.773012i	0.697250	−	0.0283400i
$745$	53.3826			1.95579
$746$	33.2452	−	19.7991i	1.21719	−	0.724897i
$747$		−	11.0650i		−	0.404846i
$748$	−1.05971	+	1.95596i	−0.0387470	+	0.0715169i
$749$			16.0110i			0.585030i
$750$	−44.9910	+	26.7943i	−1.64284	+	0.978391i
$751$	34.5328			1.26012			0.630059	−	0.776547i	$-0.283031\pi$
$751$	34.5328			1.26012			0.630059	+	0.776547i	$0.283031\pi$
$752$	−6.46782	+	4.21686i	−0.235857	+	0.153773i
$753$			11.6282i			0.423756i
$754$	−50.6995	+	30.1940i	−1.84637	+	1.09960i
$755$		−	45.0940i		−	1.64114i
$756$	−1.56882	+	2.89564i	−0.0570576	+	0.105313i
$757$	31.2740			1.13667			0.568337	−	0.822796i	$-0.307587\pi$
$757$	31.2740			1.13667			0.568337	+	0.822796i	$0.307587\pi$
$758$	15.3821	+	25.8285i	0.558703	+	0.938132i
$759$	8.40591	−	9.62613i	0.305115	−	0.349406i
$760$	−88.2084	+	3.58526i	−3.19966	+	0.130051i
$761$	46.9560			1.70215			0.851076	−	0.525042i	$-0.175950\pi$
$761$	46.9560			1.70215			0.851076	+	0.525042i	$0.175950\pi$
$762$	−4.20985	−	7.06887i	−0.152507	−	0.256078i
$763$	−1.49778			−0.0542233
$764$	−8.11601	+	14.9800i	−0.293627	+	0.541959i
$765$			1.79962i			0.0650654i
$766$	−14.7579	+	8.78903i	−0.533224	+	0.317561i
$767$			39.4699i			1.42517i
$768$	−6.45500	+	14.6401i	−0.232925	+	0.528280i
$769$		−	22.6189i		−	0.815657i	−0.913058	−	0.407829i	$-0.866286\pi$
$769$		−	22.6189i		−	0.815657i	0.913058	−	0.407829i	$-0.133714\pi$
$770$	13.6898	+	22.9868i	0.493345	+	0.828388i
$771$	17.2051			0.619626
$772$	−17.4029	+	32.1212i	−0.626343	+	1.15607i
$773$	−23.1449			−0.832463			−0.416232	−	0.909259i	$-0.636649\pi$
$773$	−23.1449			−0.832463			−0.416232	+	0.909259i	$0.636649\pi$
$774$	1.21865	+	2.04627i	0.0438036	+	0.0735517i
$775$		−	91.4439i		−	3.28476i
$776$	−27.6081	+	1.12214i	−0.991073	+	0.0402825i
$777$	−9.07252			−0.325475
$778$	7.33126	−	4.36612i	0.262838	−	0.156533i
$779$			13.2849i			0.475982i
$780$	32.8707	+	17.8089i	1.17696	+	0.637662i
$781$	3.38534			0.121137
$782$	−0.508759	+	2.78491i	−0.0181932	+	0.0995881i
$783$		−	9.62409i		−	0.343937i
$784$	9.36871	+	14.3697i	0.334597	+	0.513204i
$785$	−50.0881			−1.78772
$786$	12.8129	−	7.63068i	0.457020	−	0.272177i
$787$			33.0697i			1.17881i	0.807839	+	0.589403i	$0.200637\pi$
$787$			33.0697i			1.17881i	−0.807839	+	0.589403i	$0.799363\pi$
$788$	−8.55063	−	4.63263i	−0.304603	−	0.165031i
$789$	−26.1527			−0.931061
$790$	58.3238	−	34.7346i	2.07507	−	1.23580i
$791$		−	11.8457i		−	0.421183i
$792$	−7.53086	+	0.306095i	−0.267597	+	0.0108766i
$793$			1.74621i			0.0620096i
$794$	−0.938202	−	1.57536i	−0.0332956	−	0.0559074i
$795$	−23.4839			−0.832887
$796$	23.3385	−	43.0768i	0.827211	−	1.52682i
$797$	0.883626			0.0312996			0.0156498	−	0.999878i	$-0.495018\pi$
$797$	0.883626			0.0312996			0.0156498	+	0.999878i	$0.495018\pi$
$798$	8.62623	+	14.4845i	0.305365	+	0.512746i
$799$	0.805707			0.0285038
$800$	69.0166	+	33.8419i	2.44011	+	1.19649i
$801$		−	18.4228i		−	0.650939i
$802$	−26.3662	−	44.2721i	−0.931023	−	1.56330i
$803$		−	23.7252i		−	0.837246i
$804$	9.54130	+	5.16937i	0.336496	+	0.182309i
$805$	25.6459	+	22.3950i	0.903899	+	0.789319i
$806$	−35.4513	+	21.1130i	−1.24872	+	0.743673i
$807$		−	10.8942i		−	0.383495i
$808$	23.9775	−	0.974575i	0.843525	−	0.0342854i
$809$	−12.1139			−0.425901			−0.212951	−	0.977063i	$-0.568307\pi$
$809$	−12.1139			−0.425901			−0.212951	+	0.977063i	$0.568307\pi$
$810$	−5.23862	+	3.11985i	−0.184066	+	0.109620i
$811$	50.7073			1.78058			0.890288	−	0.455399i	$-0.150503\pi$
$811$	50.7073			1.78058			0.890288	+	0.455399i	$0.150503\pi$
$812$	27.8679	+	15.0985i	0.977972	+	0.529854i
$813$			24.1199i			0.845921i
$814$	−10.6242	−	17.8394i	−0.372378	−	0.625269i
$815$	−56.6301			−1.98367
$816$	1.39863	−	0.911871i	0.0489618	−	0.0319219i
$817$	12.1918			0.426539
$818$	17.3240	−	10.3173i	0.605719	−	0.360735i
$819$		−	7.13922i		−	0.249465i
$820$	7.53784	−	13.9129i	0.263233	−	0.485859i
$821$			41.8226i			1.45962i	0.683651	+	0.729809i	$0.260391\pi$
$821$			41.8226i			1.45962i	−0.683651	+	0.729809i	$0.739609\pi$
$822$	−8.81796	−	14.8065i	−0.307562	−	0.516435i
$823$			31.8941i			1.11176i	0.831263	+	0.555880i	$0.187619\pi$
$823$			31.8941i			1.11176i	−0.831263	+	0.555880i	$0.812381\pi$
$824$	0.470325	+	11.5714i	0.0163845	+	0.403109i
$825$			36.2096i			1.26066i
$826$	18.2146	−	10.8477i	0.633767	−	0.377439i
$827$			2.34058i			0.0813901i	0.999172	+	0.0406950i	$0.0129572\pi$
$827$			2.34058i			0.0813901i	−0.999172	+	0.0406950i	$0.987043\pi$
$828$	−8.98875	+	3.34699i	−0.312381	+	0.116316i
$829$		−	13.0929i		−	0.454737i	−0.973809	−	0.227368i	$-0.926988\pi$
$829$		−	13.0929i		−	0.454737i	0.973809	−	0.227368i	$-0.0730121\pi$
$830$	34.5211	+	57.9652i	1.19824	+	2.01200i
$831$			13.1405i			0.455838i
$832$	−2.81489	−	34.5702i	−0.0975888	−	1.19851i
$833$		−	1.79006i		−	0.0620218i
$834$	0.711488	−	0.423725i	0.0246368	−	0.0146724i
$835$			46.4950i			1.60903i
$836$	−18.3794	+	33.9236i	−0.635665	+	1.17327i
$837$		−	6.72959i		−	0.232609i
$838$	24.1789	+	40.5993i	0.835245	+	1.40248i
$839$	−1.94749			−0.0672347			−0.0336173	−	0.999435i	$-0.510703\pi$
$839$	−1.94749			−0.0672347			−0.0336173	+	0.999435i	$0.510703\pi$
$840$	−0.815496	−	20.0637i	−0.0281373	−	0.692263i
$841$	−63.6231			−2.19390
$842$	47.9913	−	28.5812i	1.65389	−	0.984972i
$843$		−	16.4508i		−	0.566597i
$844$	4.26673	−	7.87527i	0.146867	−	0.271078i
$845$	−24.9944			−0.859832
$846$	1.39679	+	2.34538i	0.0480226	+	0.0806359i
$847$	−6.42042			−0.220608
$848$	11.8993	+	18.2512i	0.408625	+	0.626748i
$849$		−	18.4998i		−	0.634911i
$850$	−4.10431	−	6.89166i	−0.140777	−	0.236382i
$851$	−19.9030	−	17.3801i	−0.682265	−	0.595780i
$852$	−2.23401	−	1.21036i	−0.0765360	−	0.0414663i
$853$		−	29.1925i		−	0.999531i	−0.866161	−	0.499766i	$-0.833420\pi$
$853$		−	29.1925i		−	0.999531i	0.866161	−	0.499766i	$-0.166580\pi$
$854$	0.805841	−	0.479917i	0.0275753	−	0.0164224i
$855$			31.2121i			1.06743i
$856$	27.4790	−	1.11690i	0.939214	−	0.0381747i
$857$	5.32136			0.181774			0.0908871	−	0.995861i	$-0.471030\pi$
$857$	5.32136			0.181774			0.0908871	+	0.995861i	$0.471030\pi$
$858$	14.0379	−	8.36025i	0.479246	−	0.285414i
$859$	12.9902			0.443220			0.221610	−	0.975135i	$-0.428869\pi$
$859$	12.9902			0.443220			0.221610	+	0.975135i	$0.428869\pi$
$860$	−12.7681	−	6.91763i	−0.435390	−	0.235889i
$861$	−3.02176			−0.102981
$862$	3.20476	−	1.90859i	0.109154	−	0.0650067i
$863$		−	17.6253i		−	0.599972i	−0.953944	−	0.299986i	$-0.903018\pi$
$863$		−	17.6253i		−	0.599972i	0.953944	−	0.299986i	$-0.0969821\pi$
$864$	5.07911	+	2.49051i	0.172795	+	0.0847290i
$865$			33.1790i			1.12812i
$866$	21.0362	+	35.3224i	0.714838	+	1.20030i
$867$	16.8258			0.571433
$868$	19.4865	+	10.5575i	0.661414	+	0.358346i
$869$		−	29.6679i		−	1.00641i
$870$	30.0258	+	50.4170i	1.01797	+	1.70930i
$871$	−23.5241			−0.797085
$872$	0.104482	+	2.57058i	0.00353821	+	0.0870507i
$873$			9.76899i			0.330630i
$874$	−8.82378	+	48.3007i	−0.298469	+	1.63380i
$875$	−60.9723			−2.06124
$876$	−8.48249	+	15.6565i	−0.286597	+	0.528983i
$877$		−	30.9003i		−	1.04343i	−0.853120	−	0.521715i	$-0.825293\pi$
$877$		−	30.9003i		−	1.04343i	0.853120	−	0.521715i	$-0.174707\pi$
$878$	2.56478	+	4.30659i	0.0865571	+	0.145340i
$879$	13.6213			0.459436
$880$	38.4964	−	25.0987i	1.29771	−	0.846077i
$881$			48.3699i			1.62962i	0.579725	+	0.814812i	$0.303160\pi$
$881$			48.3699i			1.62962i	−0.579725	+	0.814812i	$0.696840\pi$
$882$	5.21079	−	3.10328i	0.175456	−	0.104493i
$883$	−13.3766			−0.450158			−0.225079	−	0.974341i	$-0.572264\pi$
$883$	−13.3766			−0.450158			−0.225079	+	0.974341i	$0.572264\pi$
$884$	−1.72416	+	3.18235i	−0.0579899	+	0.107034i
$885$	39.2499			1.31937
$886$	−7.73327	+	4.60554i	−0.259804	+	0.154726i
$887$			11.0793i			0.372006i	0.982549	+	0.186003i	$0.0595534\pi$
$887$			11.0793i			0.372006i	−0.982549	+	0.186003i	$0.940447\pi$
$888$	0.632881	+	15.5708i	0.0212381	+	0.522522i
$889$		−	9.57980i		−	0.321296i
$890$	57.4766	+	96.5104i	1.92662	+	3.23503i
$891$			2.66476i			0.0892728i
$892$	−5.50470	−	2.98238i	−0.184311	−	0.0998576i
$893$	13.9740			0.467621
$894$	−15.0444	+	8.95970i	−0.503162	+	0.299657i
$895$	−40.9409			−1.36850
$896$	−15.1799	+	10.8001i	−0.507124	+	0.360806i
$897$	13.6765	−	15.6618i	0.456644	−	0.522931i
$898$	41.4418	−	24.6806i	1.38293	−	0.823603i
$899$	−64.7662			−2.16007
$900$	12.9460	−	23.8950i	0.431534	−	0.796500i
$901$		−	2.27358i		−	0.0757439i
$902$	−3.53857	−	5.94171i	−0.117822	−	0.197837i
$903$			2.77313i			0.0922840i
$904$	−20.3302	+	0.826329i	−0.676173	+	0.0274833i
$905$	−48.0745			−1.59805
$906$	7.56854	+	12.7085i	0.251448	+	0.422212i
$907$		−	49.8453i		−	1.65508i	−0.561404	−	0.827542i	$-0.689738\pi$
$907$		−	49.8453i		−	1.65508i	0.561404	−	0.827542i	$-0.310262\pi$
$908$	20.6565	+	11.1914i	0.685510	+	0.371401i
$909$		−	8.48432i		−	0.281407i
$910$	22.2733	+	37.3997i	0.738354	+	1.23979i
$911$	16.1751			0.535906			0.267953	−	0.963432i	$-0.413653\pi$
$911$	16.1751			0.535906			0.267953	+	0.963432i	$0.413653\pi$
$912$	24.2574	−	15.8153i	0.803244	−	0.523695i
$913$	29.4855			0.975827
$914$	−9.80983	−	16.4719i	−0.324480	−	0.544843i
$915$	1.73647			0.0574061
$916$	−12.3446	+	22.7849i	−0.407877	+	0.752834i
$917$	17.3641			0.573414
$918$	−0.302047	−	0.507175i	−0.00996904	−	0.0167393i
$919$	−14.2499			−0.470060			−0.235030	−	0.971988i	$-0.575519\pi$
$919$	−14.2499			−0.470060			−0.235030	+	0.971988i	$0.575519\pi$
$920$	36.6466	−	45.5772i	1.20820	−	1.50264i
$921$	30.7521			1.01332
$922$	12.9152	+	21.6862i	0.425339	+	0.714197i
$923$	5.50797			0.181297
$924$	−7.71619	−	4.18054i	−0.253844	−	0.137530i
$925$	74.8670			2.46161
$926$	−26.1413	−	43.8945i	−0.859056	−	1.44246i
$927$	4.09449			0.134481
$928$	23.9689	−	48.8818i	0.786819	−	1.60462i
$929$	−45.1397			−1.48099			−0.740493	−	0.672064i	$-0.765408\pi$
$929$	−45.1397			−1.48099			−0.740493	+	0.672064i	$0.765408\pi$
$930$	20.9953	+	35.2538i	0.688464	+	1.15602i
$931$		−	31.0463i		−	1.01750i
$932$	5.67036	−	10.4660i	0.185739	−	0.342825i
$933$		−	15.2477i		−	0.499189i
$934$	−18.1574	−	30.4885i	−0.594127	−	0.997613i
$935$	−4.79555			−0.156831
$936$	−12.2528	+	0.498018i	−0.400494	+	0.0162782i
$937$			12.1020i			0.395355i	0.980267	+	0.197677i	$0.0633398\pi$
$937$			12.1020i			0.395355i	−0.980267	+	0.197677i	$0.936660\pi$
$938$	6.46524	+	10.8559i	0.211098	+	0.354459i
$939$			12.2079i			0.398388i
$940$	−14.6345	−	7.92880i	−0.477324	−	0.258609i
$941$	−44.5566			−1.45250			−0.726251	−	0.687429i	$-0.758739\pi$
$941$	−44.5566			−1.45250			−0.726251	+	0.687429i	$0.758739\pi$
$942$	14.1160	−	8.40676i	0.459924	−	0.273907i
$943$	−6.62903	−	5.78873i	−0.215871	−	0.188507i
$944$	−19.8880	−	30.5042i	−0.647300	−	0.992828i
$945$	−7.09944			−0.230945
$946$	−5.45282	+	3.24742i	−0.177287	+	0.105583i
$947$	58.1441			1.88943			0.944714	−	0.327895i	$-0.106339\pi$
$947$	58.1441			1.88943			0.944714	+	0.327895i	$0.106339\pi$
$948$	−10.6072	+	19.5781i	−0.344505	+	0.635866i
$949$		−	38.6011i		−	1.25305i
$950$	−71.1842	−	119.527i	−2.30952	−	3.87797i
$951$		−	10.5516i		−	0.342159i
$952$	1.94245	−	0.0789518i	0.0629553	−	0.00255884i
$953$		−	28.6717i		−	0.928768i	−0.885634	−	0.464384i	$-0.846276\pi$
$953$		−	28.6717i		−	0.928768i	0.885634	−	0.464384i	$-0.153724\pi$
$954$	6.61830	−	3.94152i	0.214275	−	0.127611i
$955$	−36.7276			−1.18848
$956$	−8.57364	−	4.64510i	−0.277291	−	0.150233i
$957$	25.6459			0.829014
$958$	20.6401	−	12.2922i	0.666852	−	0.397143i
$959$		−	20.0659i		−	0.647961i
$960$	−34.3776	+	2.79920i	−1.10953	+	0.0903439i
$961$	−14.2874			−0.460883
$962$	−17.2856	−	29.0247i	−0.557311	−	0.935795i
$963$		−	9.72333i		−	0.313330i
$964$	−11.5191	−	6.24091i	−0.371005	−	0.201006i
$965$	−78.7537			−2.53517
$966$	−10.9864	−	2.00704i	−0.353481	−	0.0645754i
$967$			31.1257i			1.00093i	0.865756	+	0.500467i	$0.166838\pi$
$967$			31.1257i			1.00093i	−0.865756	+	0.500467i	$0.833162\pi$
$968$	0.447876	+	11.0191i	0.0143953	+	0.354167i
$969$	−3.02179			−0.0970737
$970$	−30.4778	−	51.1761i	−0.978584	−	1.64316i
$971$			42.4715i			1.36297i	0.731830	+	0.681487i	$0.238666\pi$
$971$			42.4715i			1.36297i	−0.731830	+	0.681487i	$0.761334\pi$
$972$	0.952732	−	1.75849i	0.0305589	−	0.0564037i
$973$	0.964216			0.0309113
$974$	15.7278	+	26.4089i	0.503950	+	0.846195i
$975$			58.9133i			1.88674i
$976$	−0.879876	−	1.34955i	−0.0281641	−	0.0431981i
$977$			13.4438i			0.430105i	0.976602	+	0.215053i	$0.0689923\pi$
$977$			13.4438i			0.430105i	−0.976602	+	0.215053i	$0.931008\pi$
$978$	15.9597	−	9.50476i	0.510334	−	0.303929i
$979$	49.0925			1.56900
$980$	−17.6156	+	32.5138i	−0.562710	+	1.03862i
$981$	0.909587			0.0290409
$982$	−8.15955	+	4.85941i	−0.260382	+	0.155070i
$983$	−11.7247			−0.373961			−0.186980	−	0.982364i	$-0.559870\pi$
$983$	−11.7247			−0.373961			−0.186980	+	0.982364i	$0.559870\pi$
$984$	0.210792	+	5.18612i	0.00671980	+	0.165328i
$985$		−	20.9641i		−	0.667973i
$986$	−4.88109	+	2.90693i	−0.155446	+	0.0925754i
$987$			3.17849i			0.101172i
$988$	−29.9034	+	55.1939i	−0.951355	+	1.75595i
$989$	−5.31243	+	6.08359i	−0.168925	+	0.193447i
$990$	−8.31366	−	13.9597i	−0.264225	−	0.443667i
$991$		−	43.2139i		−	1.37273i	−0.727255	−	0.686367i	$-0.759204\pi$
$991$		−	43.2139i		−	1.37273i	0.727255	−	0.686367i	$-0.240796\pi$
$992$	16.7601	−	34.1803i	0.532135	−	1.08523i
$993$	16.9416			0.537624
$994$	−1.51378	−	2.54182i	−0.0480141	−	0.0806217i
$995$	105.614			3.34820
$996$	−19.4577	−	10.5419i	−0.616540	−	0.334034i
$997$		−	26.1396i		−	0.827848i	−0.910311	−	0.413924i	$-0.864158\pi$
$997$		−	26.1396i		−	0.827848i	0.910311	−	0.413924i	$-0.135842\pi$
$998$	5.51301	−	3.28326i	0.174511	−	0.103930i
$999$	5.50965			0.174318

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.n.a.91.8	yes	24
4.3	odd	2		2208.2.n.a.367.24		24
8.3	odd	2	inner	552.2.n.a.91.5	✓	24
8.5	even	2		2208.2.n.a.367.2		24
23.22	odd	2	inner	552.2.n.a.91.7	yes	24
92.91	even	2		2208.2.n.a.367.1		24
184.45	odd	2		2208.2.n.a.367.23		24
184.91	even	2	inner	552.2.n.a.91.6	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.n.a.91.5	✓	24	8.3	odd	2	inner
552.2.n.a.91.6	yes	24	184.91	even	2	inner
552.2.n.a.91.7	yes	24	23.22	odd	2	inner
552.2.n.a.91.8	yes	24	1.1	even	1	trivial
2208.2.n.a.367.1		24	92.91	even	2
2208.2.n.a.367.2		24	8.5	even	2
2208.2.n.a.367.23		24	184.45	odd	2
2208.2.n.a.367.24		24	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	552.n (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.21506 + 0.723626i) q^{2} +1.00000 q^{3} +(0.952732 - 1.75849i) q^{4} +4.31142 q^{5} +(-1.21506 + 0.723626i) q^{6} -1.64666 q^{7} +(0.114868 + 2.82609i) q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(-1.21506 + 0.723626i) q^{2} +1.00000 q^{3} +(0.952732 - 1.75849i) q^{4} +4.31142 q^{5} +(-1.21506 + 0.723626i) q^{6} -1.64666 q^{7} +(0.114868 + 2.82609i) q^{8} +1.00000 q^{9} +(-5.23862 + 3.11985i) q^{10} +2.66476i q^{11} +(0.952732 - 1.75849i) q^{12} +4.33558i q^{13} +(2.00079 - 1.19157i) q^{14} +4.31142 q^{15} +(-2.18460 - 3.35075i) q^{16} +0.417408i q^{17} +(-1.21506 + 0.723626i) q^{18} +7.23941i q^{19} +(4.10762 - 7.58161i) q^{20} -1.64666 q^{21} +(-1.92829 - 3.23784i) q^{22} +(-3.61238 - 3.15447i) q^{23} +(0.114868 + 2.82609i) q^{24} +13.5883 q^{25} +(-3.13734 - 5.26798i) q^{26} +1.00000 q^{27} +(-1.56882 + 2.89564i) q^{28} -9.62409i q^{29} +(-5.23862 + 3.11985i) q^{30} -6.72959i q^{31} +(5.07911 + 2.49051i) q^{32} +2.66476i q^{33} +(-0.302047 - 0.507175i) q^{34} -7.09944 q^{35} +(0.952732 - 1.75849i) q^{36} +5.50965 q^{37} +(-5.23862 - 8.79630i) q^{38} +4.33558i q^{39} +(0.495243 + 12.1845i) q^{40} +1.83509 q^{41} +(2.00079 - 1.19157i) q^{42} -1.68409i q^{43} +(4.68596 + 2.53880i) q^{44} +4.31142 q^{45} +(6.67191 + 1.21885i) q^{46} -1.93026i q^{47} +(-2.18460 - 3.35075i) q^{48} -4.28851 q^{49} +(-16.5106 + 9.83287i) q^{50} +0.417408i q^{51} +(7.62409 + 4.13064i) q^{52} -5.44690 q^{53} +(-1.21506 + 0.723626i) q^{54} +11.4889i q^{55} +(-0.189148 - 4.65361i) q^{56} +7.23941i q^{57} +(6.96424 + 11.6938i) q^{58} +9.10371 q^{59} +(4.10762 - 7.58161i) q^{60} +0.402762 q^{61} +(4.86970 + 8.17684i) q^{62} -1.64666 q^{63} +(-7.97361 + 0.649254i) q^{64} +18.6925i q^{65} +(-1.92829 - 3.23784i) q^{66} +5.42584i q^{67} +(0.734009 + 0.397678i) q^{68} +(-3.61238 - 3.15447i) q^{69} +(8.62623 - 5.13734i) q^{70} -1.27041i q^{71} +(0.114868 + 2.82609i) q^{72} -8.90333 q^{73} +(-6.69455 + 3.98693i) q^{74} +13.5883 q^{75} +(12.7305 + 6.89722i) q^{76} -4.38795i q^{77} +(-3.13734 - 5.26798i) q^{78} -11.1334 q^{79} +(-9.41875 - 14.4465i) q^{80} +1.00000 q^{81} +(-2.22974 + 1.32792i) q^{82} -11.0650i q^{83} +(-1.56882 + 2.89564i) q^{84} +1.79962i q^{85} +(1.21865 + 2.04627i) q^{86} -9.62409i q^{87} +(-7.53086 + 0.306095i) q^{88} -18.4228i q^{89} +(-5.23862 + 3.11985i) q^{90} -7.13922i q^{91} +(-8.98875 + 3.34699i) q^{92} -6.72959i q^{93} +(1.39679 + 2.34538i) q^{94} +31.2121i q^{95} +(5.07911 + 2.49051i) q^{96} +9.76899i q^{97} +(5.21079 - 3.10328i) q^{98} +2.66476i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 4 q^{2} + 24 q^{3} + 4 q^{4} - 4 q^{6} - 4 q^{8} + 24 q^{9}+O(q^{10}) \) 24 * q - 4 * q^2 + 24 * q^3 + 4 * q^4 - 4 * q^6 - 4 * q^8 + 24 * q^9	\( 24 q - 4 q^{2} + 24 q^{3} + 4 q^{4} - 4 q^{6} - 4 q^{8} + 24 q^{9} + 4 q^{12} + 4 q^{16} - 4 q^{18} - 4 q^{24} + 24 q^{25} + 24 q^{27} - 4 q^{32} + 4 q^{36} + 4 q^{46} + 4 q^{48} - 8 q^{49} - 44 q^{50} - 4 q^{54} + 48 q^{58} - 40 q^{62} + 4 q^{64} - 4 q^{72} - 32 q^{73} + 24 q^{75} + 24 q^{81} - 40 q^{82} - 52 q^{92} + 40 q^{94} - 4 q^{96} - 20 q^{98}+O(q^{100}) \) 24 * q - 4 * q^2 + 24 * q^3 + 4 * q^4 - 4 * q^6 - 4 * q^8 + 24 * q^9 + 4 * q^12 + 4 * q^16 - 4 * q^18 - 4 * q^24 + 24 * q^25 + 24 * q^27 - 4 * q^32 + 4 * q^36 + 4 * q^46 + 4 * q^48 - 8 * q^49 - 44 * q^50 - 4 * q^54 + 48 * q^58 - 40 * q^62 + 4 * q^64 - 4 * q^72 - 32 * q^73 + 24 * q^75 + 24 * q^81 - 40 * q^82 - 52 * q^92 + 40 * q^94 - 4 * q^96 - 20 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more