LMFDB - Embedded newform 552.2.n.a.91.7

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			91.7
Character	$\chi$	$=$	552.91
Dual form			552.2.n.a.91.5

$q$-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} +(-2.10660 + 6.44688i) 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} +(-2.10549 - 9.35772i) 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	$-0.914405\pi$
$5$	−4.31142			−1.92813			−0.964063	+	0.265675i	$0.914405\pi$
$6$	−1.21506	+	0.723626i	−0.496045	+	0.295419i
$7$	1.64666			0.622379			0.311189	−	0.950348i	$-0.399273\pi$
$7$	1.64666			0.622379			0.311189	+	0.950348i	$0.399273\pi$
$8$	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	$-0.868410\pi$
$11$		−	2.66476i		−	0.803455i	0.915759	−	0.401728i	$-0.131590\pi$
$12$	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	$-0.983881\pi$
$17$		−	0.417408i		−	0.101236i	0.998718	−	0.0506181i	$-0.0161191\pi$
$18$	−1.21506	+	0.723626i	−0.286392	+	0.170560i
$19$		−	7.23941i		−	1.66083i	−0.557142	−	0.830417i	$-0.688102\pi$
$19$		−	7.23941i		−	1.66083i	0.557142	−	0.830417i	$-0.311898\pi$
$20$	−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	$-0.649607\pi$
$37$	−5.50965			−0.905782			−0.452891	+	0.891566i	$0.649607\pi$
$38$	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	$0.0409877\pi$
$43$			1.68409i			0.256822i	−0.991721	+	0.128411i	$0.959012\pi$
$44$	−4.68596	−	2.53880i	−0.706436	−	0.382739i
$45$	−4.31142			−0.642708
$46$	−2.10660	+	6.44688i	−0.310601	+	0.950540i
$47$		−	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	$-0.377953\pi$
$53$	5.44690			0.748189			0.374095	+	0.927391i	$0.377953\pi$
$54$	−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	$-0.508208\pi$
$61$	−0.402762			−0.0515684			−0.0257842	+	0.999668i	$0.508208\pi$
$62$	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	$-0.892467\pi$
$67$		−	5.42584i		−	0.662871i	0.943478	−	0.331436i	$-0.107533\pi$
$68$	−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	$-0.284567\pi$
$79$	11.1334			1.25261			0.626304	+	0.779579i	$0.284567\pi$
$80$	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	$0.207735\pi$
$83$			11.0650i			1.21454i	−0.794496	+	0.607269i	$0.792265\pi$
$84$	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	$0.430722\pi$
$89$			18.4228i			1.95282i	−0.215930	+	0.976409i	$0.569278\pi$
$90$	5.23862	−	3.11985i	0.552199	−	0.328861i
$91$			7.13922i			0.748394i
$92$	−2.10549	−	9.35772i	−0.219513	−	0.975610i
$93$		−	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	$-0.834822\pi$
$97$		−	9.76899i		−	0.991891i	0.868354	−	0.495945i	$-0.165178\pi$
$98$	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	$-0.564653\pi$
$103$	−4.09449			−0.403442			−0.201721	+	0.979443i	$0.564653\pi$
$104$	−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	$0.155744\pi$
$107$			9.72333i			0.939990i	−0.882669	+	0.469995i	$0.844256\pi$
$108$	0.952732	−	1.75849i	0.0916766	−	0.169211i
$109$	−0.909587			−0.0871226			−0.0435613	−	0.999051i	$-0.513870\pi$
$109$	−0.909587			−0.0871226			−0.0435613	+	0.999051i	$0.513870\pi$
$110$	−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	$-0.890126\pi$
$113$		−	7.19375i		−	0.676731i	0.941015	−	0.338365i	$-0.109874\pi$
$114$	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	$-0.825726\pi$
$137$		−	12.1858i		−	1.04110i	0.853830	−	0.520552i	$-0.174274\pi$
$138$	−2.10660	+	6.44688i	−0.179325	+	0.548795i
$139$	−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	$-0.669309\pi$
$149$	−12.3817			−1.01435			−0.507173	+	0.861844i	$0.669309\pi$
$150$	−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	$-0.346561\pi$
$157$	11.6176			0.927182			0.463591	+	0.886049i	$0.346561\pi$
$158$	−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	$-0.363990\pi$
$181$	11.1505			0.828811			0.414406	+	0.910092i	$0.363990\pi$
$182$	−5.16613	−	8.67457i	−0.382939	−	0.643002i
$183$	−0.402762			−0.0297730
$184$	9.32978	+	9.84658i	0.687800	+	0.725900i
$185$	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	$-0.400275\pi$
$191$	8.51868			0.616390			0.308195	+	0.951323i	$0.400275\pi$
$192$	−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	$-0.834756\pi$
$199$	−24.4964			−1.73650			−0.868252	+	0.496124i	$0.834756\pi$
$200$	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	$-0.872535\pi$
$227$		−	11.7467i		−	0.779655i	0.920888	−	0.389828i	$-0.127465\pi$
$228$	−12.7305	−	6.89722i	−0.843095	−	0.456779i
$229$	12.9570			0.856226			0.428113	−	0.903725i	$-0.359179\pi$
$229$	12.9570			0.856226			0.428113	+	0.903725i	$0.359179\pi$
$230$	9.08242	−	27.7952i	0.598877	−	1.83276i
$231$		−	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	$0.0676651\pi$
$241$			6.55054i			0.421958i	−0.977491	+	0.210979i	$0.932335\pi$
$242$	−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	$-0.880391\pi$
$251$		−	11.6282i		−	0.733967i	0.930227	−	0.366984i	$-0.119609\pi$
$252$	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	$-0.201455\pi$
$263$	26.1527			1.61265			0.806323	+	0.591476i	$0.201455\pi$
$264$	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
$276$	−2.10549	−	9.35772i	−0.126736	−	0.563269i
$277$			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	$0.163254\pi$
$281$			16.4508i			0.981375i	−0.871336	+	0.490688i	$0.836746\pi$
$282$	1.39679	+	2.34538i	0.0831775	+	0.139665i
$283$			18.4998i			1.09970i	0.835264	+	0.549849i	$0.185315\pi$
$283$			18.4998i			1.09970i	−0.835264	+	0.549849i	$0.814685\pi$
$284$	−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	$-0.630255\pi$
$293$	−13.6213			−0.795766			−0.397883	+	0.917436i	$0.630255\pi$
$294$	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	$-0.887874\pi$
$313$		−	12.2079i		−	0.690029i	0.938597	−	0.345014i	$-0.112126\pi$
$314$	−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
$322$	−3.46885	+	10.6158i	−0.193311	+	0.591596i
$323$	−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	$-0.867315\pi$
$337$		−	14.8650i		−	0.809750i	0.914372	−	0.404875i	$-0.132685\pi$
$338$	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	$-0.494383\pi$
$359$	0.668622			0.0352885			0.0176443	+	0.999844i	$0.494383\pi$
$360$	−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	$-0.421788\pi$
$367$	9.31985			0.486492			0.243246	+	0.969965i	$0.421788\pi$
$368$	−18.4615	−	5.21290i	−0.962370	−	0.271741i
$369$	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	$-0.249440\pi$
$373$	27.3610			1.41670			0.708349	+	0.705862i	$0.249440\pi$
$374$	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	$0.183831\pi$
$379$			21.2570i			1.09190i	−0.837819	+	0.545949i	$0.816169\pi$
$380$	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	$-0.600433\pi$
$383$	−12.1458			−0.620623			−0.310311	+	0.950635i	$0.600433\pi$
$384$	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	$-0.451120\pi$
$389$	6.03367			0.305919			0.152960	+	0.988232i	$0.451120\pi$
$390$	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	$-0.636258\pi$
$401$		−	36.4362i		−	1.81954i	0.415114	−	0.909769i	$-0.363742\pi$
$402$	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
$414$	−2.10660	+	6.44688i	−0.103534	+	0.316847i
$415$		−	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	$0.303911\pi$
$419$			33.4135i			1.63236i	−0.577801	+	0.816178i	$0.696089\pi$
$420$	−6.76386	+	12.4843i	−0.330043	+	0.609173i
$421$	39.4972			1.92497			0.962487	−	0.271327i	$-0.0874626\pi$
$421$	39.4972			1.92497			0.962487	+	0.271327i	$0.0874626\pi$
$422$	−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	$-0.479766\pi$
$431$	2.63753			0.127045			0.0635227	+	0.997980i	$0.479766\pi$
$432$	−2.18460	−	3.35075i	−0.105107	−	0.161213i
$433$			29.0705i			1.39704i	0.715591	+	0.698520i	$0.246158\pi$
$433$			29.0705i			1.39704i	−0.715591	+	0.698520i	$0.753842\pi$
$434$	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	$-0.897300\pi$
$457$		−	13.5565i		−	0.634146i	0.948401	−	0.317073i	$-0.102700\pi$
$458$	−15.7436	+	9.37605i	−0.735648	+	0.438114i
$459$		−	0.417408i		−	0.0194829i
$460$	9.07765	+	40.3450i	0.423248	+	1.88110i
$461$		−	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	$-0.802832\pi$
$467$		−	25.0922i		−	1.16113i	0.814214	−	0.580564i	$-0.197168\pi$
$468$	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	$-0.373140\pi$
$479$	16.9870			0.776154			0.388077	+	0.921627i	$0.373140\pi$
$480$	−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	$-0.690764\pi$
$503$	−25.3014			−1.12814			−0.564068	+	0.825729i	$0.690764\pi$
$504$	0.189148	+	4.65361i	0.00842532	+	0.207288i
$505$			36.5795i			1.62777i
$506$	17.1794	+	5.61357i	0.763717	+	0.249554i
$507$	−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	$0.199429\pi$
$521$			26.7666i			1.17267i	−0.810070	+	0.586334i	$0.800571\pi$
$522$	6.96424	+	11.6938i	0.304817	+	0.511825i
$523$		−	5.03702i		−	0.220253i	−0.993918	−	0.110127i	$-0.964874\pi$
$523$		−	5.03702i		−	0.220253i	0.993918	−	0.110127i	$-0.0351257\pi$
$524$	−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
$552$	9.32978	+	9.84658i	0.397102	+	0.419098i
$553$	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	$-0.601016\pi$
$557$	−14.7294			−0.624104			−0.312052	+	0.950065i	$0.601016\pi$
$558$	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	$0.00484162\pi$
$563$			0.721786i			0.0304196i	−0.999884	+	0.0152098i	$0.995158\pi$
$564$	−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	$-0.978497\pi$
$569$		−	3.22041i		−	0.135007i	0.997719	−	0.0675033i	$-0.0215033\pi$
$570$	−22.5859	−	37.9245i	−0.946019	−	1.58848i
$571$		−	16.7232i		−	0.699843i	−0.936779	−	0.349922i	$-0.886208\pi$
$571$		−	16.7232i		−	0.699843i	0.936779	−	0.349922i	$-0.113792\pi$
$572$	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
$598$	−27.9510	−	9.13332i	−1.14300	−	0.373489i
$599$		−	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	$-0.240887\pi$
$613$	36.0023			1.45412			0.727059	+	0.686575i	$0.240887\pi$
$614$	−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	$-0.847403\pi$
$617$		−	22.9141i		−	0.922487i	0.887274	−	0.461243i	$-0.152597\pi$
$618$	4.97504	−	2.96288i	0.200126	−	0.119184i
$619$		−	10.3547i		−	0.416189i	−0.978109	−	0.208094i	$-0.933274\pi$
$619$		−	10.3547i		−	0.416189i	0.978109	−	0.208094i	$-0.0667261\pi$
$620$	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	$-0.624327\pi$
$631$	−19.1276			−0.761458			−0.380729	+	0.924687i	$0.624327\pi$
$632$	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	$0.0929761\pi$
$641$			14.5810i			0.575915i	−0.957643	+	0.287957i	$0.907024\pi$
$642$	−7.03605	−	11.8144i	−0.277691	−	0.466278i
$643$			26.4659i			1.04371i	0.853034	+	0.521856i	$0.174760\pi$
$643$			26.4659i			1.04371i	−0.853034	+	0.521856i	$0.825240\pi$
$644$	−3.46703	−	15.4090i	−0.136620	−	0.607199i
$645$		−	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	$0.181062\pi$
$659$			27.6549i			1.07728i	−0.842536	+	0.538640i	$0.818938\pi$
$660$	20.2032	+	10.9458i	0.786407	+	0.426066i
$661$	−39.1587			−1.52310			−0.761548	−	0.648108i	$-0.775560\pi$
$661$	−39.1587			−1.52310			−0.761548	+	0.648108i	$0.775560\pi$
$662$	−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	$-0.550995\pi$
$677$	−8.30126			−0.319044			−0.159522	+	0.987194i	$0.550995\pi$
$678$	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
$690$	9.08242	−	27.7952i	0.345762	−	1.05815i
$691$	−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	$-0.477680\pi$
$701$	3.71009			0.140128			0.0700640	+	0.997542i	$0.477680\pi$
$702$	−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	$-0.431384\pi$
$709$	11.3909			0.427793			0.213897	+	0.976856i	$0.431384\pi$
$710$	−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	$-0.586768\pi$
$727$	−14.5183			−0.538452			−0.269226	+	0.963077i	$0.586768\pi$
$728$	−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	$-0.453451\pi$
$733$	7.89030			0.291435			0.145717	+	0.989326i	$0.453451\pi$
$734$	−11.3242	+	6.74408i	−0.417982	+	0.248929i
$735$	18.4896			0.681998
$736$	26.2039	−	7.02521i	0.965890	−	0.258953i
$737$	−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	$-0.659152\pi$
$743$	−26.1360			−0.958838			−0.479419	+	0.877586i	$0.659152\pi$
$744$	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	$-0.716969\pi$
$751$	−34.5328			−1.26012			−0.630059	+	0.776547i	$0.716969\pi$
$752$	−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	$-0.692413\pi$
$757$	−31.2740			−1.13667			−0.568337	+	0.822796i	$0.692413\pi$
$758$	−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	$0.133714\pi$
$769$			22.6189i			0.815657i	−0.913058	+	0.407829i	$0.866286\pi$
$770$	−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	$-0.363351\pi$
$773$	23.1449			0.832463			0.416232	+	0.909259i	$0.363351\pi$
$774$	−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
$782$	2.69098	+	0.879310i	0.0962291	+	0.0314440i
$783$		−	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	$-0.799363\pi$
$787$		−	33.0697i		−	1.17881i	0.807839	−	0.589403i	$-0.200637\pi$
$788$	−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	$-0.504982\pi$
$797$	−0.883626			−0.0312996			−0.0156498	+	0.999878i	$0.504982\pi$
$798$	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	$-0.987043\pi$
$827$		−	2.34058i		−	0.0813901i	0.999172	−	0.0406950i	$-0.0129572\pi$
$828$	−2.10549	−	9.35772i	−0.0731709	−	0.325203i
$829$		−	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	$-0.489297\pi$
$839$	1.94749			0.0672347			0.0336173	+	0.999435i	$0.489297\pi$
$840$	−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
$874$	46.6716	+	15.2505i	1.57869	+	0.515856i
$875$	−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	$-0.696840\pi$
$881$		−	48.3699i		−	1.62962i	0.579725	−	0.814812i	$-0.303160\pi$
$882$	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	$0.310262\pi$
$907$			49.8453i			1.65508i	−0.561404	+	0.827542i	$0.689738\pi$
$908$	−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	$-0.586347\pi$
$911$	−16.1751			−0.535906			−0.267953	+	0.963432i	$0.586347\pi$
$912$	−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	$-0.424481\pi$
$919$	14.2499			0.470060			0.235030	+	0.971988i	$0.424481\pi$
$920$	−40.2246	−	42.4527i	−1.32617	−	1.39963i
$921$	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	$-0.936660\pi$
$937$		−	12.1020i		−	0.395355i	0.980267	−	0.197677i	$-0.0633398\pi$
$938$	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	$-0.241261\pi$
$941$	44.5566			1.45250			0.726251	+	0.687429i	$0.241261\pi$
$942$	−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	$0.153724\pi$
$953$			28.6717i			0.928768i	−0.885634	+	0.464384i	$0.846276\pi$
$954$	−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
$966$	−3.46885	+	10.6158i	−0.111608	+	0.341558i
$967$			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	$-0.761334\pi$
$971$		−	42.4715i		−	1.36297i	0.731830	−	0.681487i	$-0.238666\pi$
$972$	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	$-0.931008\pi$
$977$		−	13.4438i		−	0.430105i	0.976602	−	0.215053i	$-0.0689923\pi$
$978$	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	$-0.440130\pi$
$983$	11.7247			0.373961			0.186980	+	0.982364i	$0.440130\pi$
$984$	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.91.7	yes	24
4.3	odd	2		2208.2.n.a.367.1		24
8.3	odd	2	inner	552.2.n.a.91.6	yes	24
8.5	even	2		2208.2.n.a.367.23		24
23.22	odd	2	inner	552.2.n.a.91.8	yes	24
92.91	even	2		2208.2.n.a.367.24		24
184.45	odd	2		2208.2.n.a.367.2		24
184.91	even	2	inner	552.2.n.a.91.5	✓	24

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 552 = 2^{3} \cdot 3 \cdot 23 \)
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} +(-2.10660 + 6.44688i) 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} +(-2.10549 - 9.35772i) 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

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