LMFDB - Embedded newform 1224.2.l.d.1189.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1224,2,Mod(1189,1224)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1224, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("1224.1189");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1224 = 2^{3} \cdot 3^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1224.l (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:	$9.77368920740$
Analytic rank:	$0$
Dimension:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - x^{16} - 2x^{14} + 2x^{12} - 4x^{11} + 4x^{10} + 8x^{8} - 16x^{7} + 16x^{6} - 64x^{4} - 128x^{2} + 512 $ x^18 - x^16 - 2x^14 + 2x^12 - 4x^11 + 4x^10 + 8x^8 - 16x^7 + 16x^6 - 64x^4 - 128*x^2 + 512
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	no (minimal twist has level 408)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1189.18
Root			$1.40931 - 0.117654i$ of defining polynomial
Character	$\chi$	$=$	1224.1189
Dual form			1224.2.l.d.1189.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.40931 + 0.117654i) q^{2} +(1.97232 + 0.331622i) q^{4} -1.46472 q^{5} -3.26018i q^{7} +(2.74059 + 0.699408i) q^{8} +(-2.06424 - 0.172330i) q^{10} -0.312167 q^{11} -6.39254i q^{13} +(0.383572 - 4.59460i) q^{14} +(3.78005 + 1.30812i) q^{16} +(3.01195 + 2.81570i) q^{17} +2.24353i q^{19} +(-2.88888 - 0.485732i) q^{20} +(-0.439940 - 0.0367276i) q^{22} -7.34630i q^{23} -2.85460 q^{25} +(0.752107 - 9.00908i) q^{26} +(1.08115 - 6.43010i) q^{28} -5.39236 q^{29} -0.606910i q^{31} +(5.17337 + 2.28829i) q^{32} +(3.91349 + 4.32257i) q^{34} +4.77524i q^{35} +11.2816 q^{37} +(-0.263960 + 3.16184i) q^{38} +(-4.01419 - 1.02444i) q^{40} -5.36742i q^{41} -7.51199i q^{43} +(-0.615692 - 0.103521i) q^{44} +(0.864321 - 10.3532i) q^{46} +4.24122 q^{47} -3.62875 q^{49} +(-4.02302 - 0.335855i) q^{50} +(2.11991 - 12.6081i) q^{52} +8.91746i q^{53} +0.457236 q^{55} +(2.28019 - 8.93480i) q^{56} +(-7.59952 - 0.634432i) q^{58} -5.15579i q^{59} +6.41607 q^{61} +(0.0714053 - 0.855325i) q^{62} +(7.02166 + 3.83358i) q^{64} +9.36327i q^{65} +11.8427i q^{67} +(5.00676 + 6.55228i) q^{68} +(-0.561825 + 6.72979i) q^{70} +6.62295i q^{71} +4.81332i q^{73} +(15.8993 + 1.32733i) q^{74} +(-0.744004 + 4.42496i) q^{76} +1.01772i q^{77} +11.5068i q^{79} +(-5.53671 - 1.91603i) q^{80} +(0.631497 - 7.56436i) q^{82} -13.3845i q^{83} +(-4.41165 - 4.12421i) q^{85} +(0.883814 - 10.5867i) q^{86} +(-0.855521 - 0.218332i) q^{88} -9.54739 q^{89} -20.8408 q^{91} +(2.43619 - 14.4892i) q^{92} +(5.97720 + 0.498996i) q^{94} -3.28614i q^{95} +13.0210i q^{97} +(-5.11404 - 0.426936i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 2 q^{4} + 4 q^{5} - 8 q^{10} + 6 q^{14} + 10 q^{16} + 2 q^{17} + 2 q^{20} + 2 q^{22} + 22 q^{25} - 2 q^{26} - 10 q^{28} - 12 q^{29} + 6 q^{34} - 16 q^{37} + 34 q^{38} - 10 q^{40} - 12 q^{44} + 32 q^{46}+ \cdots + 60 q^{98}+O(q^{100}) $ 18 * q + 2 * q^4 + 4 * q^5 - 8 * q^10 + 6 * q^14 + 10 * q^16 + 2 * q^17 + 2 * q^20 + 2 * q^22 + 22 * q^25 - 2 * q^26 - 10 * q^28 - 12 * q^29 + 6 * q^34 - 16 * q^37 + 34 * q^38 - 10 * q^40 - 12 * q^44 + 32 * q^46 - 18 * q^49 + 14 * q^50 + 8 * q^52 - 16 * q^55 + 14 * q^56 - 6 * q^58 - 16 * q^61 + 6 * q^62 + 2 * q^64 + 36 * q^68 - 32 * q^70 + 6 * q^74 + 62 * q^80 + 34 * q^82 + 16 * q^85 - 14 * q^86 + 16 * q^88 - 20 * q^89 + 2 * q^92 + 12 * q^94 + 60 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1224\mathbb{Z}\right)^\times$.

$n$	$137$	$613$	$649$	$919$
$\chi(n)$	$1$	$-1$	$-1$	$1$

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 $

$2$	1.40931	+	0.117654i	0.996533	+	0.0831938i
$2$	1.40931	+	0.117654i	0.996533	+	0.0831938i
$3$		0			0
$3$		0			0
$4$	1.97232	+	0.331622i	0.986158	+	0.165811i
$5$	−1.46472			−0.655041			−0.327521	−	0.944844i	$-0.606213\pi$
$5$	−1.46472			−0.655041			−0.327521	+	0.944844i	$0.606213\pi$
$6$		0			0
$7$		−	3.26018i		−	1.23223i	−0.787656	−	0.616115i	$-0.788705\pi$
$7$		−	3.26018i		−	1.23223i	0.787656	−	0.616115i	$-0.211295\pi$
$8$	2.74059	+	0.699408i	0.968945	+	0.247278i
$9$		0			0
$10$	−2.06424	−	0.172330i	−0.652771	−	0.0544954i
$11$	−0.312167			−0.0941219			−0.0470609	−	0.998892i	$-0.514985\pi$
$11$	−0.312167			−0.0941219			−0.0470609	+	0.998892i	$0.514985\pi$
$12$		0			0
$13$		−	6.39254i		−	1.77297i	−0.462755	−	0.886486i	$-0.653139\pi$
$13$		−	6.39254i		−	1.77297i	0.462755	−	0.886486i	$-0.346861\pi$
$14$	0.383572	−	4.59460i	0.102514	−	1.22796i
$15$		0			0
$16$	3.78005	+	1.30812i	0.945014	+	0.327031i
$17$	3.01195	+	2.81570i	0.730505	+	0.682908i
$17$	3.01195	+	2.81570i	0.730505	+	0.682908i
$18$		0			0
$19$			2.24353i			0.514702i	0.966318	+	0.257351i	$0.0828496\pi$
$19$			2.24353i			0.514702i	−0.966318	+	0.257351i	$0.917150\pi$
$20$	−2.88888	−	0.485732i	−0.645974	−	0.108613i
$21$		0			0
$22$	−0.439940	−	0.0367276i	−0.0937956	−	0.00783036i
$23$		−	7.34630i		−	1.53181i	−0.642954	−	0.765905i	$-0.722291\pi$
$23$		−	7.34630i		−	1.53181i	0.642954	−	0.765905i	$-0.277709\pi$
$24$		0			0
$25$	−2.85460			−0.570921
$26$	0.752107	−	9.00908i	0.147500	−	1.76683i
$27$		0			0
$28$	1.08115	−	6.43010i	0.204317	−	1.21517i
$29$	−5.39236			−1.00134			−0.500668	−	0.865639i	$-0.666912\pi$
$29$	−5.39236			−1.00134			−0.500668	+	0.865639i	$0.666912\pi$
$30$		0			0
$31$		−	0.606910i		−	0.109004i	−0.998514	−	0.0545021i	$-0.982643\pi$
$31$		−	0.606910i		−	0.109004i	0.998514	−	0.0545021i	$-0.0173572\pi$
$32$	5.17337	+	2.28829i	0.914531	+	0.404517i
$33$		0			0
$34$	3.91349	+	4.32257i	0.671159	+	0.741314i
$35$			4.77524i			0.807162i
$36$		0			0
$37$	11.2816			1.85469			0.927344	−	0.374211i	$-0.122086\pi$
$37$	11.2816			1.85469			0.927344	+	0.374211i	$0.122086\pi$
$38$	−0.263960	+	3.16184i	−0.0428200	+	0.512918i
$39$		0			0
$40$	−4.01419	−	1.02444i	−0.634699	−	0.161977i
$41$		−	5.36742i		−	0.838249i	−0.907929	−	0.419125i	$-0.862337\pi$
$41$		−	5.36742i		−	0.838249i	0.907929	−	0.419125i	$-0.137663\pi$
$42$		0			0
$43$		−	7.51199i		−	1.14557i	−0.819707	−	0.572784i	$-0.805863\pi$
$43$		−	7.51199i		−	1.14557i	0.819707	−	0.572784i	$-0.194137\pi$
$44$	−0.615692	−	0.103521i	−0.0928190	−	0.0156064i
$45$		0			0
$46$	0.864321	−	10.3532i	0.127437	−	1.52650i
$47$	4.24122			0.618646			0.309323	−	0.950957i	$-0.399898\pi$
$47$	4.24122			0.618646			0.309323	+	0.950957i	$0.399898\pi$
$48$		0			0
$49$	−3.62875			−0.518393
$50$	−4.02302	−	0.335855i	−0.568942	−	0.0474971i
$51$		0			0
$52$	2.11991	−	12.6081i	0.293978	−	1.74843i
$53$			8.91746i			1.22491i	0.790507	+	0.612454i	$0.209817\pi$
$53$			8.91746i			1.22491i	−0.790507	+	0.612454i	$0.790183\pi$
$54$		0			0
$55$	0.457236			0.0616537
$56$	2.28019	−	8.93480i	0.304704	−	1.19396i
$57$		0			0
$58$	−7.59952	−	0.634432i	−0.997865	−	0.0833050i
$59$		−	5.15579i		−	0.671226i	−0.942000	−	0.335613i	$-0.891057\pi$
$59$		−	5.15579i		−	0.671226i	0.942000	−	0.335613i	$-0.108943\pi$
$60$		0			0
$61$	6.41607			0.821493			0.410747	−	0.911750i	$-0.365268\pi$
$61$	6.41607			0.821493			0.410747	+	0.911750i	$0.365268\pi$
$62$	0.0714053	−	0.855325i	0.00906848	−	0.108626i
$63$		0			0
$64$	7.02166	+	3.83358i	0.877707	+	0.479198i
$65$			9.36327i			1.16137i
$66$		0			0
$67$			11.8427i			1.44682i	0.690421	+	0.723408i	$0.257425\pi$
$67$			11.8427i			1.44682i	−0.690421	+	0.723408i	$0.742575\pi$
$68$	5.00676	+	6.55228i	0.607159	+	0.794580i
$69$		0			0
$70$	−0.561825	+	6.72979i	−0.0671509	+	0.804364i
$71$			6.62295i			0.785999i	0.919539	+	0.393000i	$0.128563\pi$
$71$			6.62295i			0.785999i	−0.919539	+	0.393000i	$0.871437\pi$
$72$		0			0
$73$			4.81332i			0.563356i	0.959509	+	0.281678i	$0.0908910\pi$
$73$			4.81332i			0.563356i	−0.959509	+	0.281678i	$0.909109\pi$
$74$	15.8993	+	1.32733i	1.84826	+	0.154299i
$75$		0			0
$76$	−0.744004	+	4.42496i	−0.0853432	+	0.507577i
$77$			1.01772i			0.115980i
$78$		0			0
$79$			11.5068i			1.29461i	0.762230	+	0.647306i	$0.224104\pi$
$79$			11.5068i			1.29461i	−0.762230	+	0.647306i	$0.775896\pi$
$80$	−5.53671	−	1.91603i	−0.619023	−	0.214219i
$81$		0			0
$82$	0.631497	−	7.56436i	0.0697372	−	0.835344i
$83$		−	13.3845i		−	1.46914i	−0.678535	−	0.734568i	$-0.737385\pi$
$83$		−	13.3845i		−	1.46914i	0.678535	−	0.734568i	$-0.262615\pi$
$84$		0			0
$85$	−4.41165	−	4.12421i	−0.478511	−	0.447333i
$86$	0.883814	−	10.5867i	0.0953041	−	1.14160i
$87$		0			0
$88$	−0.855521	−	0.218332i	−0.0911989	−	0.0232743i
$89$	−9.54739			−1.01202			−0.506011	−	0.862527i	$-0.668880\pi$
$89$	−9.54739			−1.01202			−0.506011	+	0.862527i	$0.668880\pi$
$90$		0			0
$91$	−20.8408			−2.18471
$92$	2.43619	−	14.4892i	0.253991	−	1.51061i
$93$		0			0
$94$	5.97720	+	0.498996i	0.616501	+	0.0514675i
$95$		−	3.28614i		−	0.337151i
$96$		0			0
$97$			13.0210i			1.32208i	0.750351	+	0.661040i	$0.229885\pi$
$97$			13.0210i			1.32208i	−0.750351	+	0.661040i	$0.770115\pi$
$98$	−5.11404	−	0.426936i	−0.516596	−	0.0431271i
$99$		0			0
$100$	−5.63018	−	0.946648i	−0.563018	−	0.0946648i
$101$		−	1.94347i		−	0.193383i	−0.995314	−	0.0966913i	$-0.969174\pi$
$101$		−	1.94347i		−	0.193383i	0.995314	−	0.0966913i	$-0.0308259\pi$
$102$		0			0
$103$	6.97083			0.686856			0.343428	−	0.939179i	$-0.388412\pi$
$103$	6.97083			0.686856			0.343428	+	0.939179i	$0.388412\pi$
$104$	4.47100	−	17.5193i	0.438418	−	1.71791i
$105$		0			0
$106$	−1.04917	+	12.5675i	−0.101905	+	1.22066i
$107$	7.39946			0.715333			0.357667	−	0.933849i	$-0.383572\pi$
$107$	7.39946			0.715333			0.357667	+	0.933849i	$0.383572\pi$
$108$		0			0
$109$	−10.6455			−1.01966			−0.509828	−	0.860277i	$-0.670291\pi$
$109$	−10.6455			−1.01966			−0.509828	+	0.860277i	$0.670291\pi$
$110$	0.644388	+	0.0537956i	0.0614400	+	0.00512921i
$111$		0			0
$112$	4.26472	−	12.3236i	0.402978	−	1.16447i
$113$			11.0887i			1.04313i	0.853211	+	0.521567i	$0.174652\pi$
$113$			11.0887i			1.04313i	−0.853211	+	0.521567i	$0.825348\pi$
$114$		0			0
$115$			10.7603i			1.00340i
$116$	−10.6354	−	1.78822i	−0.987476	−	0.166032i
$117$		0			0
$118$	0.606598	−	7.26611i	0.0558419	−	0.668899i
$119$	9.17968	−	9.81948i	0.841500	−	0.900150i
$120$		0			0
$121$	−10.9026			−0.991141
$122$	9.04224	+	0.754875i	0.818646	+	0.0683432i
$123$		0			0
$124$	0.201265	−	1.19702i	0.0180741	−	0.107495i
$125$	11.5048			1.02902
$126$		0			0
$127$	−16.9758			−1.50636			−0.753179	−	0.657816i	$-0.771480\pi$
$127$	−16.9758			−1.50636			−0.753179	+	0.657816i	$0.771480\pi$
$128$	9.44466	+	6.22883i	0.834798	+	0.550556i
$129$		0			0
$130$	−1.10162	+	13.1958i	−0.0966189	+	1.15734i
$131$	0.168506			0.0147225			0.00736123	−	0.999973i	$-0.497657\pi$
$131$	0.168506			0.0147225			0.00736123	+	0.999973i	$0.497657\pi$
$132$		0			0
$133$	7.31432			0.634232
$134$	−1.39334	+	16.6900i	−0.120366	+	1.44180i
$135$		0			0
$136$	6.28519	+	9.82326i	0.538950	+	0.842338i
$137$	−6.02753			−0.514966			−0.257483	−	0.966283i	$-0.582893\pi$
$137$	−6.02753			−0.514966			−0.257483	+	0.966283i	$0.582893\pi$
$138$		0			0
$139$	3.56380			0.302278			0.151139	−	0.988513i	$-0.451706\pi$
$139$	3.56380			0.302278			0.151139	+	0.988513i	$0.451706\pi$
$140$	−1.58357	+	9.41827i	−0.133836	+	0.795989i
$141$		0			0
$142$	−0.779215	+	9.33379i	−0.0653903	+	0.783274i
$143$			1.99554i			0.166875i
$144$		0			0
$145$	7.89829			0.655917
$146$	−0.566305	+	6.78346i	−0.0468677	+	0.561403i
$147$		0			0
$148$	22.2509	+	3.74123i	1.82901	+	0.307527i
$149$			5.50380i			0.450889i	0.974256	+	0.225444i	$0.0723834\pi$
$149$			5.50380i			0.450889i	−0.974256	+	0.225444i	$0.927617\pi$
$150$		0			0
$151$	0.619725			0.0504325			0.0252162	−	0.999682i	$-0.491973\pi$
$151$	0.619725			0.0504325			0.0252162	+	0.999682i	$0.491973\pi$
$152$	−1.56915	+	6.14860i	−0.127275	+	0.498718i
$153$		0			0
$154$	−0.119739	+	1.43428i	−0.00964881	+	0.115578i
$155$			0.888952i			0.0714023i
$156$		0			0
$157$			18.7631i			1.49746i	0.662875	+	0.748730i	$0.269336\pi$
$157$			18.7631i			1.49746i	−0.662875	+	0.748730i	$0.730664\pi$
$158$	−1.35381	+	16.2166i	−0.107704	+	1.29012i
$159$		0			0
$160$	−7.57752	−	3.35170i	−0.599055	−	0.264975i
$161$	−23.9502			−1.88754
$162$		0			0
$163$	15.9222			1.24712			0.623561	−	0.781775i	$-0.285685\pi$
$163$	15.9222			1.24712			0.623561	+	0.781775i	$0.285685\pi$
$164$	1.77995	−	10.5862i	0.138991	−	0.826646i
$165$		0			0
$166$	1.57473	−	18.8629i	0.122223	−	1.46404i
$167$		−	7.08898i		−	0.548561i	−0.961650	−	0.274281i	$-0.911560\pi$
$167$		−	7.08898i		−	0.548561i	0.961650	−	0.274281i	$-0.0884397\pi$
$168$		0			0
$169$	−27.8646			−2.14343
$170$	−5.73216	−	6.33134i	−0.439637	−	0.485591i
$171$		0			0
$172$	2.49114	−	14.8160i	0.189947	−	1.12971i
$173$	−10.1123			−0.768827			−0.384414	−	0.923161i	$-0.625596\pi$
$173$	−10.1123			−0.768827			−0.384414	+	0.923161i	$0.625596\pi$
$174$		0			0
$175$			9.30651i			0.703506i
$176$	−1.18001	−	0.408353i	−0.0889464	−	0.0307808i
$177$		0			0
$178$	−13.4552	−	1.12329i	−1.00851	−	0.0841939i
$179$		−	2.38313i		−	0.178124i	−0.996026	−	0.0890618i	$-0.971613\pi$
$179$		−	2.38313i		−	0.178124i	0.996026	−	0.0890618i	$-0.0283869\pi$
$180$		0			0
$181$	−10.5481			−0.784038			−0.392019	−	0.919957i	$-0.628223\pi$
$181$	−10.5481			−0.784038			−0.392019	+	0.919957i	$0.628223\pi$
$182$	−29.3712	−	2.45200i	−2.17714	−	0.181754i
$183$		0			0
$184$	5.13807	−	20.1332i	0.378783	−	1.48424i
$185$	−16.5244			−1.21490
$186$		0			0
$187$	−0.940230	−	0.878969i	−0.0687565	−	0.0642765i
$188$	8.36502	+	1.40648i	0.610082	+	0.102578i
$189$		0			0
$190$	0.386627	−	4.63120i	0.0280489	−	0.335982i
$191$	16.9179			1.22414			0.612069	−	0.790804i	$-0.290338\pi$
$191$	16.9179			1.22414			0.612069	+	0.790804i	$0.290338\pi$
$192$		0			0
$193$		−	3.08185i		−	0.221836i	−0.993830	−	0.110918i	$-0.964621\pi$
$193$		−	3.08185i		−	0.221836i	0.993830	−	0.110918i	$-0.0353791\pi$
$194$	−1.53197	+	18.3506i	−0.109989	+	1.31750i
$195$		0			0
$196$	−7.15704	−	1.20337i	−0.511217	−	0.0859551i
$197$	−22.7820			−1.62315			−0.811577	−	0.584246i	$-0.801390\pi$
$197$	−22.7820			−1.62315			−0.811577	+	0.584246i	$0.801390\pi$
$198$		0			0
$199$		−	14.9021i		−	1.05638i	−0.849126	−	0.528190i	$-0.822871\pi$
$199$		−	14.9021i		−	1.05638i	0.849126	−	0.528190i	$-0.177129\pi$
$200$	−7.82329	−	1.99653i	−0.553190	−	0.141176i
$201$		0			0
$202$	0.228657	−	2.73895i	0.0160882	−	0.192712i
$203$			17.5801i			1.23388i
$204$		0			0
$205$			7.86175i			0.549088i
$206$	9.82407	+	0.820145i	0.684475	+	0.0571422i
$207$		0			0
$208$	8.36225	−	24.1642i	0.579817	−	1.67548i
$209$		−	0.700357i		−	0.0484447i
$210$		0			0
$211$	11.1308			0.766278			0.383139	−	0.923691i	$-0.374843\pi$
$211$	11.1308			0.766278			0.383139	+	0.923691i	$0.374843\pi$
$212$	−2.95722	+	17.5880i	−0.203103	+	1.20795i
$213$		0			0
$214$	10.4281	+	0.870575i	0.712853	+	0.0595113i
$215$			11.0029i			0.750394i
$216$		0			0
$217$	−1.97863			−0.134318
$218$	−15.0028	−	1.25249i	−1.01612	−	0.0848290i
$219$		0			0
$220$	0.901814	+	0.151629i	0.0608003	+	0.0102229i
$221$	17.9995	−	19.2540i	1.21078	−	1.29516i
$222$		0			0
$223$	−0.320676			−0.0214741			−0.0107370	−	0.999942i	$-0.503418\pi$
$223$	−0.320676			−0.0214741			−0.0107370	+	0.999942i	$0.503418\pi$
$224$	7.46024	−	16.8661i	0.498458	−	1.12691i
$225$		0			0
$226$	−1.30462	+	15.6274i	−0.0867822	+	1.03952i
$227$	26.1137			1.73323			0.866613	−	0.498980i	$-0.166292\pi$
$227$	26.1137			1.73323			0.866613	+	0.498980i	$0.166292\pi$
$228$		0			0
$229$		−	14.6905i		−	0.970772i	−0.874300	−	0.485386i	$-0.838679\pi$
$229$		−	14.6905i		−	0.970772i	0.874300	−	0.485386i	$-0.161321\pi$
$230$	−1.26599	+	15.1645i	−0.0834766	+	0.999921i
$231$		0			0
$232$	−14.7782	−	3.77146i	−0.970240	−	0.247609i
$233$			27.5228i			1.80308i	0.432694	+	0.901541i	$0.357563\pi$
$233$			27.5228i			1.80308i	−0.432694	+	0.901541i	$0.642437\pi$
$234$		0			0
$235$	−6.21219			−0.405239
$236$	1.70977	−	10.1688i	0.111297	−	0.661935i
$237$		0			0
$238$	14.0923	−	12.7587i	0.913470	−	0.827022i
$239$	−5.80155			−0.375271			−0.187636	−	0.982239i	$-0.560082\pi$
$239$	−5.80155			−0.375271			−0.187636	+	0.982239i	$0.560082\pi$
$240$		0			0
$241$			17.1627i			1.10554i	0.833333	+	0.552772i	$0.186430\pi$
$241$			17.1627i			1.10554i	−0.833333	+	0.552772i	$0.813570\pi$
$242$	−15.3651	−	1.28273i	−0.987705	−	0.0824568i
$243$		0			0
$244$	12.6545	+	2.12771i	0.810122	+	0.136212i
$245$	5.31509			0.339569
$246$		0			0
$247$	14.3419			0.912552
$248$	0.424478	−	1.66329i	0.0269544	−	0.105619i
$249$		0			0
$250$	16.2138	+	1.35358i	1.02545	+	0.0856079i
$251$		−	6.91981i		−	0.436774i	−0.975862	−	0.218387i	$-0.929920\pi$
$251$		−	6.91981i		−	0.436774i	0.975862	−	0.218387i	$-0.0700796\pi$
$252$		0			0
$253$			2.29327i			0.144177i
$254$	−23.9242	−	1.99727i	−1.50114	−	0.125320i
$255$		0			0
$256$	12.5776	+	9.88957i	0.786101	+	0.618098i
$257$	0.288958			0.0180247			0.00901234	−	0.999959i	$-0.497131\pi$
$257$	0.288958			0.0180247			0.00901234	+	0.999959i	$0.497131\pi$
$258$		0			0
$259$		−	36.7801i		−	2.28540i
$260$	−3.10506	+	18.4673i	−0.192568	+	1.14529i
$261$		0			0
$262$	0.237478	+	0.0198254i	0.0146714	+	0.00122482i
$263$	1.38062			0.0851326			0.0425663	−	0.999094i	$-0.486447\pi$
$263$	1.38062			0.0851326			0.0425663	+	0.999094i	$0.486447\pi$
$264$		0			0
$265$		−	13.0616i		−	0.802365i
$266$	10.3081	+	0.860557i	0.632033	+	0.0527641i
$267$		0			0
$268$	−3.92729	+	23.3575i	−0.239898	+	1.42679i
$269$	17.5243			1.06847			0.534237	−	0.845335i	$-0.320599\pi$
$269$	17.5243			1.06847			0.534237	+	0.845335i	$0.320599\pi$
$270$		0			0
$271$	0.927991			0.0563715			0.0281857	−	0.999603i	$-0.491027\pi$
$271$	0.927991			0.0563715			0.0281857	+	0.999603i	$0.491027\pi$
$272$	7.70204	+	14.5835i	0.467005	+	0.884255i
$273$		0			0
$274$	−8.49466	−	0.709161i	−0.513181	−	0.0428420i
$275$	0.891113			0.0537361
$276$		0			0
$277$	9.97435			0.599301			0.299650	−	0.954049i	$-0.403130\pi$
$277$	9.97435			0.599301			0.299650	+	0.954049i	$0.403130\pi$
$278$	5.02251	+	0.419295i	0.301230	+	0.0251476i
$279$		0			0
$280$	−3.33984	+	13.0870i	−0.199594	+	0.782096i
$281$	19.4670			1.16131			0.580653	−	0.814151i	$-0.302797\pi$
$281$	19.4670			1.16131			0.580653	+	0.814151i	$0.302797\pi$
$282$		0			0
$283$	2.02405			0.120317			0.0601587	−	0.998189i	$-0.480839\pi$
$283$	2.02405			0.120317			0.0601587	+	0.998189i	$0.480839\pi$
$284$	−2.19631	+	13.0625i	−0.130327	+	0.775119i
$285$		0			0
$286$	−0.234783	+	2.81234i	−0.0138830	+	0.166297i
$287$	−17.4987			−1.03292
$288$		0			0
$289$	1.14366	+	16.9615i	0.0672742	+	0.997735i
$290$	11.1311	+	0.929264i	0.653643	+	0.0545682i
$291$		0			0
$292$	−1.59620	+	9.49337i	−0.0934105	+	0.555558i
$293$		−	1.29056i		−	0.0753952i	−0.999289	−	0.0376976i	$-0.987998\pi$
$293$		−	1.29056i		−	0.0753952i	0.999289	−	0.0376976i	$-0.0120024\pi$
$294$		0			0
$295$			7.55177i			0.439681i
$296$	30.9183	+	7.89046i	1.79709	+	0.458624i
$297$		0			0
$298$	−0.647543	+	7.75657i	−0.0375112	+	0.449326i
$299$	−46.9616			−2.71586
$300$		0			0
$301$	−24.4904			−1.41160
$302$	0.873385	+	0.0729130i	0.0502577	+	0.00419567i
$303$		0			0
$304$	−2.93482	+	8.48068i	−0.168324	+	0.486400i
$305$	−9.39773			−0.538112
$306$		0			0
$307$		−	7.42682i		−	0.423871i	−0.977284	−	0.211936i	$-0.932023\pi$
$307$		−	7.42682i		−	0.423871i	0.977284	−	0.211936i	$-0.0679767\pi$
$308$	−0.337498	+	2.00726i	−0.0192307	+	0.114374i
$309$		0			0
$310$	−0.104589	+	1.25281i	−0.00594023	+	0.0711548i
$311$		−	3.73279i		−	0.211667i	−0.994384	−	0.105834i	$-0.966249\pi$
$311$		−	3.73279i		−	0.211667i	0.994384	−	0.105834i	$-0.0337511\pi$
$312$		0			0
$313$		−	1.09676i		−	0.0619925i	−0.999520	−	0.0309963i	$-0.990132\pi$
$313$		−	1.09676i		−	0.0619925i	0.999520	−	0.0309963i	$-0.00986800\pi$
$314$	−2.20755	+	26.4431i	−0.124579	+	1.49227i
$315$		0			0
$316$	−3.81589	+	22.6950i	−0.214661	+	1.27669i
$317$	19.9349			1.11965			0.559827	−	0.828610i	$-0.310868\pi$
$317$	19.9349			1.11965			0.559827	+	0.828610i	$0.310868\pi$
$318$		0			0
$319$	1.68332			0.0942477
$320$	−10.2847	−	5.61511i	−0.574934	−	0.313894i
$321$		0			0
$322$	−33.7533	−	2.81784i	−1.88100	−	0.157032i
$323$	−6.31712	+	6.75741i	−0.351494	+	0.375992i
$324$		0			0
$325$			18.2482i			1.01223i
$326$	22.4393	+	1.87331i	1.24280	+	0.103753i
$327$		0			0
$328$	3.75402	−	14.7099i	0.207281	−	0.812217i
$329$		−	13.8271i		−	0.762314i
$330$		0			0
$331$			26.9222i			1.47978i	0.672728	+	0.739890i	$0.265122\pi$
$331$			26.9222i			1.47978i	−0.672728	+	0.739890i	$0.734878\pi$
$332$	4.43858	−	26.3984i	0.243599	−	1.44880i
$333$		0			0
$334$	0.834045	−	9.99057i	0.0456369	−	0.546660i
$335$		−	17.3462i		−	0.947724i
$336$		0			0
$337$			12.2109i			0.665170i	0.943073	+	0.332585i	$0.107921\pi$
$337$			12.2109i			0.665170i	−0.943073	+	0.332585i	$0.892079\pi$
$338$	−39.2699	−	3.27838i	−2.13600	−	0.178320i
$339$		0			0
$340$	−7.33349	−	9.59723i	−0.397714	−	0.520483i
$341$			0.189457i			0.0102597i
$342$		0			0
$343$		−	10.9909i		−	0.593451i
$344$	5.25395	−	20.5873i	0.283274	−	1.10999i
$345$		0			0
$346$	−14.2514	−	1.18976i	−0.766162	−	0.0639617i
$347$	−14.2507			−0.765018			−0.382509	−	0.923952i	$-0.624940\pi$
$347$	−14.2507			−0.765018			−0.382509	+	0.923952i	$0.624940\pi$
$348$		0			0
$349$			18.5830i			0.994725i	0.867543	+	0.497363i	$0.165698\pi$
$349$			18.5830i			0.994725i	−0.867543	+	0.497363i	$0.834302\pi$
$350$	−1.09495	+	13.1158i	−0.0585274	+	0.701067i
$351$		0			0
$352$	−1.61495	−	0.714329i	−0.0860773	−	0.0380739i
$353$	3.89576			0.207350			0.103675	−	0.994611i	$-0.466940\pi$
$353$	3.89576			0.207350			0.103675	+	0.994611i	$0.466940\pi$
$354$		0			0
$355$		−	9.70074i		−	0.514862i
$356$	−18.8305	−	3.16612i	−0.998012	−	0.167804i
$357$		0			0
$358$	0.280385	−	3.35857i	0.0148188	−	0.177506i
$359$	−8.66787			−0.457472			−0.228736	−	0.973488i	$-0.573459\pi$
$359$	−8.66787			−0.457472			−0.228736	+	0.973488i	$0.573459\pi$
$360$		0			0
$361$	13.9666			0.735082
$362$	−14.8656	−	1.24103i	−0.781320	−	0.0652271i
$363$		0			0
$364$	−41.1047	−	6.91127i	−2.15447	−	0.362249i
$365$		−	7.05015i		−	0.369022i
$366$		0			0
$367$		−	32.3753i		−	1.68998i	−0.534785	−	0.844988i	$-0.679608\pi$
$367$		−	32.3753i		−	1.68998i	0.534785	−	0.844988i	$-0.320392\pi$
$368$	9.60988	−	27.7694i	0.500950	−	1.44758i
$369$		0			0
$370$	−23.2880	−	1.94416i	−1.21069	−	0.101072i
$371$	29.0725			1.50937
$372$		0			0
$373$		−	11.7221i		−	0.606947i	−0.952840	−	0.303473i	$-0.901854\pi$
$373$		−	11.7221i		−	0.606947i	0.952840	−	0.303473i	$-0.0981464\pi$
$374$	−1.22166	−	1.34936i	−0.0631707	−	0.0697738i
$375$		0			0
$376$	11.6234	+	2.96635i	0.599433	+	0.152978i
$377$			34.4709i			1.77534i
$378$		0			0
$379$	27.7442			1.42512			0.712562	−	0.701609i	$-0.247535\pi$
$379$	27.7442			1.42512			0.712562	+	0.701609i	$0.247535\pi$
$380$	1.08976	−	6.48131i	0.0559033	−	0.332484i
$381$		0			0
$382$	23.8426	+	1.99046i	1.21989	+	0.101841i
$383$	25.2288			1.28913			0.644566	−	0.764549i	$-0.277038\pi$
$383$	25.2288			1.28913			0.644566	+	0.764549i	$0.277038\pi$
$384$		0			0
$385$		−	1.49067i		−	0.0759716i
$386$	0.362591	−	4.34328i	0.0184554	−	0.221067i
$387$		0			0
$388$	−4.31804	+	25.6815i	−0.219215	+	1.30378i
$389$			26.3923i			1.33814i	0.743198	+	0.669072i	$0.233308\pi$
$389$			26.3923i			1.33814i	−0.743198	+	0.669072i	$0.766692\pi$
$390$		0			0
$391$	20.6850	−	22.1267i	1.04608	−	1.11899i
$392$	−9.94491	−	2.53798i	−0.502294	−	0.128187i
$393$		0			0
$394$	−32.1070	−	2.68039i	−1.61753	−	0.135036i
$395$		−	16.8542i		−	0.848025i
$396$		0			0
$397$	−21.2037			−1.06418			−0.532091	−	0.846687i	$-0.678594\pi$
$397$	−21.2037			−1.06418			−0.532091	+	0.846687i	$0.678594\pi$
$398$	1.75329	−	21.0017i	0.0878843	−	1.05272i
$399$		0			0
$400$	−10.7906	−	3.73418i	−0.539528	−	0.186709i
$401$		−	7.21971i		−	0.360535i	−0.983618	−	0.180268i	$-0.942304\pi$
$401$		−	7.21971i		−	0.360535i	0.983618	−	0.180268i	$-0.0576964\pi$
$402$		0			0
$403$	−3.87970			−0.193262
$404$	0.644497	−	3.83314i	0.0320649	−	0.190706i
$405$		0			0
$406$	−2.06836	+	24.7758i	−0.102651	+	1.22960i
$407$	−3.52175			−0.174567
$408$		0			0
$409$	24.5533			1.21408			0.607042	−	0.794670i	$-0.292356\pi$
$409$	24.5533			1.21408			0.607042	+	0.794670i	$0.292356\pi$
$410$	−0.924964	+	11.0796i	−0.0456807	+	0.547185i
$411$		0			0
$412$	13.7487	+	2.31168i	0.677349	+	0.113888i
$413$	−16.8088			−0.827106
$414$		0			0
$415$			19.6045i			0.962345i
$416$	14.6280	−	33.0710i	0.717197	−	1.62144i
$417$		0			0
$418$	0.0823997	−	0.987021i	0.00403030	−	0.0482768i
$419$	−39.0863			−1.90949			−0.954745	−	0.297426i	$-0.903872\pi$
$419$	−39.0863			−1.90949			−0.954745	+	0.297426i	$0.903872\pi$
$420$		0			0
$421$		−	9.66214i		−	0.470904i	−0.971886	−	0.235452i	$-0.924343\pi$
$421$		−	9.66214i		−	0.470904i	0.971886	−	0.235452i	$-0.0756570\pi$
$422$	15.6868	+	1.30958i	0.763621	+	0.0637496i
$423$		0			0
$424$	−6.23695	+	24.4391i	−0.302893	+	1.18687i
$425$	−8.59792	−	8.03771i	−0.417060	−	0.389886i
$426$		0			0
$427$		−	20.9175i		−	1.01227i
$428$	14.5941	+	2.45382i	0.705431	+	0.118610i
$429$		0			0
$430$	−1.29454	+	15.5066i	−0.0624282	+	0.747793i
$431$		−	6.07054i		−	0.292408i	−0.989254	−	0.146204i	$-0.953294\pi$
$431$		−	6.07054i		−	0.292408i	0.989254	−	0.146204i	$-0.0467055\pi$
$432$		0			0
$433$	20.5097			0.985634			0.492817	−	0.870133i	$-0.335967\pi$
$433$	20.5097			0.985634			0.492817	+	0.870133i	$0.335967\pi$
$434$	−2.78851	−	0.232794i	−0.133853	−	0.0111745i
$435$		0			0
$436$	−20.9963	−	3.53028i	−1.00554	−	0.169070i
$437$	16.4817			0.788426
$438$		0			0
$439$		−	7.36907i		−	0.351706i	−0.984416	−	0.175853i	$-0.943732\pi$
$439$		−	7.36907i		−	0.351706i	0.984416	−	0.175853i	$-0.0562684\pi$
$440$	1.25310	+	0.319795i	0.0597390	+	0.0152456i
$441$		0			0
$442$	27.6322	−	25.0172i	1.31433	−	1.18995i
$443$			18.9079i			0.898342i	0.893446	+	0.449171i	$0.148281\pi$
$443$			18.9079i			0.898342i	−0.893446	+	0.449171i	$0.851719\pi$
$444$		0			0
$445$	13.9842			0.662916
$446$	−0.451933	−	0.0377288i	−0.0213996	−	0.00178651i
$447$		0			0
$448$	12.4982	−	22.8918i	0.590482	−	1.08154i
$449$			19.0187i			0.897550i	0.893645	+	0.448775i	$0.148139\pi$
$449$			19.0187i			0.897550i	−0.893645	+	0.448775i	$0.851861\pi$
$450$		0			0
$451$			1.67553i			0.0788976i
$452$	−3.67724	+	21.8703i	−0.172963	+	1.02869i
$453$		0			0
$454$	36.8023	+	3.07238i	1.72722	+	0.144194i
$455$	30.5259			1.43108
$456$		0			0
$457$	−20.5126			−0.959539			−0.479769	−	0.877395i	$-0.659280\pi$
$457$	−20.5126			−0.959539			−0.479769	+	0.877395i	$0.659280\pi$
$458$	1.72839	−	20.7034i	0.0807623	−	0.967407i
$459$		0			0
$460$	−3.56833	+	21.2226i	−0.166374	+	0.989510i
$461$		−	8.07937i		−	0.376294i	−0.982141	−	0.188147i	$-0.939752\pi$
$461$		−	8.07937i		−	0.376294i	0.982141	−	0.188147i	$-0.0602481\pi$
$462$		0			0
$463$	12.6813			0.589350			0.294675	−	0.955597i	$-0.404789\pi$
$463$	12.6813			0.589350			0.294675	+	0.955597i	$0.404789\pi$
$464$	−20.3834	−	7.05388i	−0.946277	−	0.327468i
$465$		0			0
$466$	−3.23817	+	38.7883i	−0.150005	+	1.79683i
$467$			32.1472i			1.48760i	0.668405	+	0.743798i	$0.266977\pi$
$467$			32.1472i			1.48760i	−0.668405	+	0.743798i	$0.733023\pi$
$468$		0			0
$469$	38.6093			1.78281
$470$	−8.75491	−	0.730888i	−0.403834	−	0.0337133i
$471$		0			0
$472$	3.60600	−	14.1299i	0.165980	−	0.650381i
$473$			2.34499i			0.107823i
$474$		0			0
$475$		−	6.40440i		−	0.293854i
$476$	21.3616	−	16.3229i	0.979106	−	0.748160i
$477$		0			0
$478$	−8.17619	−	0.682574i	−0.373970	−	0.0312202i
$479$		−	25.4835i		−	1.16437i	−0.813056	−	0.582185i	$-0.802198\pi$
$479$		−	25.4835i		−	1.16437i	0.813056	−	0.582185i	$-0.197802\pi$
$480$		0			0
$481$		−	72.1183i		−	3.28831i
$482$	−2.01925	+	24.1875i	−0.0919744	+	1.10171i
$483$		0			0
$484$	−21.5033	−	3.61552i	−0.977421	−	0.164342i
$485$		−	19.0721i		−	0.866017i
$486$		0			0
$487$			3.09673i			0.140326i	0.997536	+	0.0701630i	$0.0223520\pi$
$487$			3.09673i			0.140326i	−0.997536	+	0.0701630i	$0.977648\pi$
$488$	17.5838	+	4.48745i	0.795982	+	0.203137i
$489$		0			0
$490$	7.49062	+	0.625341i	0.338392	+	0.0282500i
$491$			37.4349i			1.68941i	0.535231	+	0.844706i	$0.320225\pi$
$491$			37.4349i			1.68941i	−0.535231	+	0.844706i	$0.679775\pi$
$492$		0			0
$493$	−16.2415	−	15.1833i	−0.731481	−	0.683820i
$494$	20.2122	+	1.68738i	0.909389	+	0.0759187i
$495$		0			0
$496$	0.793914	−	2.29415i	0.0356478	−	0.103011i
$497$	21.5920			0.968532
$498$		0			0
$499$	−19.7963			−0.886204			−0.443102	−	0.896471i	$-0.646122\pi$
$499$	−19.7963			−0.886204			−0.443102	+	0.896471i	$0.646122\pi$
$500$	22.6910	+	3.81523i	1.01477	+	0.170622i
$501$		0			0
$502$	0.814142	−	9.75216i	0.0363369	−	0.435260i
$503$		−	10.8162i		−	0.482268i	−0.970492	−	0.241134i	$-0.922481\pi$
$503$		−	10.8162i		−	0.482268i	0.970492	−	0.241134i	$-0.0775194\pi$
$504$		0			0
$505$			2.84663i			0.126674i
$506$	−0.269812	+	3.23193i	−0.0119946	+	0.143677i
$507$		0			0
$508$	−33.4816	−	5.62954i	−1.48551	−	0.249770i
$509$			2.63717i			0.116890i	0.998291	+	0.0584452i	$0.0186143\pi$
$509$			2.63717i			0.116890i	−0.998291	+	0.0584452i	$0.981386\pi$
$510$		0			0
$511$	15.6923			0.694185
$512$	16.5622	+	15.4173i	0.731954	+	0.681354i
$513$		0			0
$514$	0.407231	+	0.0339970i	0.0179622	+	0.00149954i
$515$	−10.2103			−0.449919
$516$		0			0
$517$	−1.32397			−0.0582281
$518$	4.32732	−	51.8346i	0.190131	−	2.27748i
$519$		0			0
$520$	−6.54875	+	25.6609i	−0.287182	+	1.12530i
$521$		−	38.5194i		−	1.68757i	−0.536684	−	0.843783i	$-0.680323\pi$
$521$		−	38.5194i		−	1.68757i	0.536684	−	0.843783i	$-0.319677\pi$
$522$		0			0
$523$		−	0.305975i		−	0.0133793i	−0.999978	−	0.00668967i	$-0.997871\pi$
$523$		−	0.305975i		−	0.0133793i	0.999978	−	0.00668967i	$-0.00212940\pi$
$524$	0.332347	+	0.0558803i	0.0145187	+	0.00244114i
$525$		0			0
$526$	1.94572	+	0.162435i	0.0848375	+	0.00708250i
$527$	1.70888	−	1.82798i	0.0744399	−	0.0796281i
$528$		0			0
$529$	−30.9682			−1.34644
$530$	1.53674	−	18.4078i	0.0667518	−	0.799584i
$531$		0			0
$532$	14.4261	+	2.42559i	0.625452	+	0.105162i
$533$	−34.3114			−1.48619
$534$		0			0
$535$	−10.8381			−0.468573
$536$	−8.28288	+	32.4560i	−0.357766	+	1.40188i
$537$		0			0
$538$	24.6972	+	2.06180i	1.06477	+	0.0888905i
$539$	1.13278			0.0487921
$540$		0			0
$541$	1.50556			0.0647292			0.0323646	−	0.999476i	$-0.489696\pi$
$541$	1.50556			0.0647292			0.0323646	+	0.999476i	$0.489696\pi$
$542$	1.30783	+	0.109182i	0.0561760	+	0.00468976i
$543$		0			0
$544$	9.13876	+	21.4589i	0.391821	+	0.920041i
$545$	15.5927			0.667916
$546$		0			0
$547$	−3.68763			−0.157672			−0.0788358	−	0.996888i	$-0.525120\pi$
$547$	−3.68763			−0.157672			−0.0788358	+	0.996888i	$0.525120\pi$
$548$	−11.8882	−	1.99886i	−0.507838	−	0.0853870i
$549$		0			0
$550$	1.25585	+	0.104843i	0.0535498	+	0.00447051i
$551$		−	12.0979i		−	0.515390i
$552$		0			0
$553$	37.5141			1.59526
$554$	14.0570	+	1.17352i	0.597223	+	0.0498581i
$555$		0			0
$556$	7.02894	+	1.18183i	0.298094	+	0.0501209i
$557$		−	29.3032i		−	1.24162i	−0.783962	−	0.620809i	$-0.786804\pi$
$557$		−	29.3032i		−	1.24162i	0.783962	−	0.620809i	$-0.213196\pi$
$558$		0			0
$559$	−48.0207			−2.03106
$560$	−6.24661	+	18.0507i	−0.263967	+	0.762779i
$561$		0			0
$562$	27.4351	+	2.29037i	1.15728	+	0.0966135i
$563$		−	27.2285i		−	1.14754i	−0.819015	−	0.573772i	$-0.805480\pi$
$563$		−	27.2285i		−	1.14754i	0.819015	−	0.573772i	$-0.194520\pi$
$564$		0			0
$565$		−	16.2417i		−	0.683296i
$566$	2.85252	+	0.238138i	0.119900	+	0.0100097i
$567$		0			0
$568$	−4.63214	+	18.1508i	−0.194360	+	0.761589i
$569$	−8.50233			−0.356436			−0.178218	−	0.983991i	$-0.557033\pi$
$569$	−8.50233			−0.356436			−0.178218	+	0.983991i	$0.557033\pi$
$570$		0			0
$571$	3.89571			0.163030			0.0815151	−	0.996672i	$-0.474024\pi$
$571$	3.89571			0.163030			0.0815151	+	0.996672i	$0.474024\pi$
$572$	−0.661764	+	3.93584i	−0.0276698	+	0.164566i
$573$		0			0
$574$	−24.6611	−	2.05879i	−1.02934	−	0.0859323i
$575$			20.9708i			0.874542i
$576$		0			0
$577$	3.69131			0.153671			0.0768355	−	0.997044i	$-0.475518\pi$
$577$	3.69131			0.153671			0.0768355	+	0.997044i	$0.475518\pi$
$578$	−0.383810	+	24.0386i	−0.0159644	+	0.999873i
$579$		0			0
$580$	15.5779	+	2.61924i	0.646837	+	0.108758i
$581$	−43.6357			−1.81032
$582$		0			0
$583$		−	2.78374i		−	0.115291i
$584$	−3.36647	+	13.1913i	−0.139306	+	0.545861i
$585$		0			0
$586$	0.151839	−	1.81880i	0.00627241	−	0.0751338i
$587$		−	18.6727i		−	0.770704i	−0.922770	−	0.385352i	$-0.874080\pi$
$587$		−	18.6727i		−	0.770704i	0.922770	−	0.385352i	$-0.125920\pi$
$588$		0			0
$589$	1.36162			0.0561047
$590$	−0.888495	+	10.6428i	−0.0365787	+	0.438157i
$591$		0			0
$592$	42.6451	+	14.7578i	1.75270	+	0.606541i
$593$	−18.0541			−0.741393			−0.370697	−	0.928754i	$-0.620881\pi$
$593$	−18.0541			−0.741393			−0.370697	+	0.928754i	$0.620881\pi$
$594$		0			0
$595$	−13.4456	+	14.3828i	−0.551217	+	0.589636i
$596$	−1.82518	+	10.8552i	−0.0747623	+	0.444648i
$597$		0			0
$598$	−66.1835	−	5.52521i	−2.70644	−	0.225943i
$599$	43.6498			1.78348			0.891741	−	0.452546i	$-0.149484\pi$
$599$	43.6498			1.78348			0.891741	+	0.452546i	$0.149484\pi$
$600$		0			0
$601$		−	10.1680i		−	0.414760i	−0.978260	−	0.207380i	$-0.933506\pi$
$601$		−	10.1680i		−	0.414760i	0.978260	−	0.207380i	$-0.0664937\pi$
$602$	−34.5146	−	2.88139i	−1.40671	−	0.117437i
$603$		0			0
$604$	1.22229	+	0.205514i	0.0497344	+	0.00836225i
$605$	15.9692			0.649239
$606$		0			0
$607$			10.9378i			0.443952i	0.975052	+	0.221976i	$0.0712506\pi$
$607$			10.9378i			0.443952i	−0.975052	+	0.221976i	$0.928749\pi$
$608$	−5.13386	+	11.6066i	−0.208206	+	0.470711i
$609$		0			0
$610$	−13.2443	−	1.10568i	−0.536247	−	0.0447676i
$611$		−	27.1122i		−	1.09684i
$612$		0			0
$613$		−	35.0085i		−	1.41398i	−0.707224	−	0.706990i	$-0.750053\pi$
$613$		−	35.0085i		−	1.41398i	0.707224	−	0.706990i	$-0.249947\pi$
$614$	0.873794	−	10.4667i	0.0352635	−	0.422402i
$615$		0			0
$616$	−0.711801	+	2.78915i	−0.0286793	+	0.112378i
$617$		−	24.5518i		−	0.988419i	−0.869343	−	0.494209i	$-0.835458\pi$
$617$		−	24.5518i		−	0.988419i	0.869343	−	0.494209i	$-0.164542\pi$
$618$		0			0
$619$	37.2040			1.49536			0.747678	−	0.664061i	$-0.231168\pi$
$619$	37.2040			1.49536			0.747678	+	0.664061i	$0.231168\pi$
$620$	−0.294796	+	1.75329i	−0.0118393	+	0.0704139i
$621$		0			0
$622$	0.439177	−	5.26067i	0.0176094	−	0.210933i
$623$			31.1262i			1.24704i
$624$		0			0
$625$	−2.57822			−0.103129
$626$	0.129038	−	1.54568i	0.00515740	−	0.0617776i
$627$		0			0
$628$	−6.22226	+	37.0068i	−0.248295	+	1.47673i
$629$	33.9797	+	31.7657i	1.35486	+	1.26658i
$630$		0			0
$631$	12.3656			0.492266			0.246133	−	0.969236i	$-0.420840\pi$
$631$	12.3656			0.492266			0.246133	+	0.969236i	$0.420840\pi$
$632$	−8.04793	+	31.5353i	−0.320129	+	1.25441i
$633$		0			0
$634$	28.0944	+	2.34541i	1.11577	+	0.0931483i
$635$	24.8647			0.986726
$636$		0			0
$637$			23.1969i			0.919096i
$638$	2.37232	+	0.198049i	0.0939209	+	0.00784082i
$639$		0			0
$640$	−13.8338	−	9.12348i	−0.546827	−	0.360637i
$641$		−	37.6527i		−	1.48719i	−0.668629	−	0.743596i	$-0.733118\pi$
$641$		−	37.6527i		−	1.48719i	0.668629	−	0.743596i	$-0.266882\pi$
$642$		0			0
$643$	−29.1814			−1.15080			−0.575400	−	0.817872i	$-0.695154\pi$
$643$	−29.1814			−1.15080			−0.575400	+	0.817872i	$0.695154\pi$
$644$	−47.2374	−	7.94242i	−1.86142	−	0.312975i
$645$		0			0
$646$	−9.69782	+	8.78005i	−0.381556	+	0.345447i
$647$	−32.6928			−1.28529			−0.642643	−	0.766166i	$-0.722162\pi$
$647$	−32.6928			−1.28529			−0.642643	+	0.766166i	$0.722162\pi$
$648$		0			0
$649$			1.60947i			0.0631771i
$650$	−2.14697	+	25.7174i	−0.0842110	+	1.00872i
$651$		0			0
$652$	31.4036	+	5.28014i	1.22986	+	0.206786i
$653$	5.75472			0.225200			0.112600	−	0.993640i	$-0.464082\pi$
$653$	5.75472			0.225200			0.112600	+	0.993640i	$0.464082\pi$
$654$		0			0
$655$	−0.246814			−0.00964382
$656$	7.02125	−	20.2891i	0.274134	−	0.792157i
$657$		0			0
$658$	1.62681	−	19.4867i	0.0634198	−	0.759672i
$659$			16.3764i			0.637933i	0.947766	+	0.318966i	$0.103336\pi$
$659$			16.3764i			0.637933i	−0.947766	+	0.318966i	$0.896664\pi$
$660$		0			0
$661$			26.9352i			1.04766i	0.851823	+	0.523829i	$0.175497\pi$
$661$			26.9352i			1.04766i	−0.851823	+	0.523829i	$0.824503\pi$
$662$	−3.16750	+	37.9418i	−0.123108	+	1.47465i
$663$		0			0
$664$	9.36121	−	36.6813i	0.363285	−	1.42351i
$665$	−10.7134			−0.415448
$666$		0			0
$667$			39.6139i			1.53386i
$668$	2.35086	−	13.9817i	0.0909574	−	0.540968i
$669$		0			0
$670$	2.04085	−	24.4462i	0.0788448	−	0.944439i
$671$	−2.00288			−0.0773205
$672$		0			0
$673$			48.5604i			1.87187i	0.352179	+	0.935933i	$0.385441\pi$
$673$			48.5604i			1.87187i	−0.352179	+	0.935933i	$0.614559\pi$
$674$	−1.43666	+	17.2089i	−0.0553380	+	0.662864i
$675$		0			0
$676$	−54.9578	−	9.24051i	−2.11376	−	0.355404i
$677$	−18.4217			−0.708002			−0.354001	−	0.935245i	$-0.615179\pi$
$677$	−18.4217			−0.708002			−0.354001	+	0.935245i	$0.615179\pi$
$678$		0			0
$679$	42.4507			1.62911
$680$	−9.20602	−	14.3883i	−0.353035	−	0.551766i
$681$		0			0
$682$	−0.0222904	+	0.267004i	−0.000853542	+	0.0102241i
$683$	35.1819			1.34620			0.673099	−	0.739552i	$-0.264963\pi$
$683$	35.1819			1.34620			0.673099	+	0.739552i	$0.264963\pi$
$684$		0			0
$685$	8.82862			0.337324
$686$	1.29312	−	15.4896i	0.0493715	−	0.591394i
$687$		0			0
$688$	9.82662	−	28.3957i	0.374636	−	1.08258i
$689$	57.0052			2.17173
$690$		0			0
$691$	16.9759			0.645792			0.322896	−	0.946434i	$-0.395344\pi$
$691$	16.9759			0.645792			0.322896	+	0.946434i	$0.395344\pi$
$692$	−19.9447	−	3.35347i	−0.758185	−	0.127480i
$693$		0			0
$694$	−20.0837	−	1.67665i	−0.762366	−	0.0636447i
$695$	−5.21996			−0.198004
$696$		0			0
$697$	15.1130	−	16.1664i	0.572447	−	0.612345i
$698$	−2.18636	+	26.1892i	−0.0827550	+	0.991277i
$699$		0			0
$700$	−3.08624	+	18.3554i	−0.116649	+	0.693768i
$701$			25.1119i			0.948462i	0.880400	+	0.474231i	$0.157274\pi$
$701$			25.1119i			0.948462i	−0.880400	+	0.474231i	$0.842726\pi$
$702$		0			0
$703$			25.3107i			0.954611i
$704$	−2.19193	−	1.19672i	−0.0826114	−	0.0451030i
$705$		0			0
$706$	5.49033	+	0.458351i	0.206631	+	0.0172503i
$707$	−6.33606			−0.238292
$708$		0			0
$709$	−32.3694			−1.21566			−0.607830	−	0.794067i	$-0.707960\pi$
$709$	−32.3694			−1.21566			−0.607830	+	0.794067i	$0.707960\pi$
$710$	1.14133	−	13.6714i	0.0428333	−	0.513077i
$711$		0			0
$712$	−26.1655	−	6.67752i	−0.980592	−	0.250251i
$713$	−4.45855			−0.166974
$714$		0			0
$715$		−	2.92290i		−	0.109310i
$716$	0.790298	−	4.70029i	0.0295348	−	0.175658i
$717$		0			0
$718$	−12.2157	−	1.01981i	−0.455887	−	0.0380589i
$719$			14.6515i			0.546410i	0.961956	+	0.273205i	$0.0880838\pi$
$719$			14.6515i			0.546410i	−0.961956	+	0.273205i	$0.911916\pi$
$720$		0			0
$721$		−	22.7261i		−	0.846366i
$722$	19.6832	+	1.64322i	0.732534	+	0.0611543i
$723$		0			0
$724$	−20.8043	−	3.49799i	−0.773185	−	0.130002i
$725$	15.3931			0.571684
$726$		0			0
$727$	5.77315			0.214114			0.107057	−	0.994253i	$-0.465857\pi$
$727$	5.77315			0.214114			0.107057	+	0.994253i	$0.465857\pi$
$728$	−57.1161	−	14.5762i	−2.11686	−	0.540232i
$729$		0			0
$730$	0.829477	−	9.93585i	0.0307003	−	0.367742i
$731$	21.1515	−	22.6257i	0.782317	−	0.836842i
$732$		0			0
$733$			9.97415i			0.368403i	0.982888	+	0.184202i	$0.0589700\pi$
$733$			9.97415i			0.368403i	−0.982888	+	0.184202i	$0.941030\pi$
$734$	3.80907	−	45.6268i	0.140596	−	1.68412i
$735$		0			0
$736$	16.8105	−	38.0051i	0.619643	−	1.40089i
$737$		−	3.69690i		−	0.136177i
$738$		0			0
$739$		−	31.2897i		−	1.15101i	−0.817798	−	0.575506i	$-0.804805\pi$
$739$		−	31.2897i		−	1.15101i	0.817798	−	0.575506i	$-0.195195\pi$
$740$	−32.5913	−	5.47984i	−1.19808	−	0.201443i
$741$		0			0
$742$	40.9722	+	3.42049i	1.50414	+	0.125570i
$743$		−	0.432434i		−	0.0158645i	−0.999969	−	0.00793223i	$-0.997475\pi$
$743$		−	0.432434i		−	0.0158645i	0.999969	−	0.00793223i	$-0.00252493\pi$
$744$		0			0
$745$		−	8.06151i		−	0.295351i
$746$	1.37915	−	16.5201i	0.0504942	−	0.604843i
$747$		0			0
$748$	−1.56295	−	2.04540i	−0.0571470	−	0.0747874i
$749$		−	24.1236i		−	0.881455i
$750$		0			0
$751$		−	44.0064i		−	1.60582i	−0.596103	−	0.802908i	$-0.703285\pi$
$751$		−	44.0064i		−	1.60582i	0.596103	−	0.802908i	$-0.296715\pi$
$752$	16.0320	+	5.54805i	0.584628	+	0.202316i
$753$		0			0
$754$	−4.05563	+	48.5802i	−0.147697	+	1.76919i
$755$	−0.907721			−0.0330354
$756$		0			0
$757$		−	48.4044i		−	1.75929i	−0.475634	−	0.879643i	$-0.657781\pi$
$757$		−	48.4044i		−	1.75929i	0.475634	−	0.879643i	$-0.342219\pi$
$758$	39.1002	+	3.26421i	1.42018	+	0.118562i
$759$		0			0
$760$	2.29836	−	9.00597i	0.0833701	−	0.326681i
$761$	37.9787			1.37673			0.688363	−	0.725366i	$-0.258329\pi$
$761$	37.9787			1.37673			0.688363	+	0.725366i	$0.258329\pi$
$762$		0			0
$763$			34.7062i			1.25645i
$764$	33.3675	+	5.61035i	1.20719	+	0.202975i
$765$		0			0
$766$	35.5552	+	2.96826i	1.28466	+	0.107248i
$767$	−32.9586			−1.19007
$768$		0			0
$769$	−3.04684			−0.109872			−0.0549358	−	0.998490i	$-0.517495\pi$
$769$	−3.04684			−0.109872			−0.0549358	+	0.998490i	$0.517495\pi$
$770$	0.175383	−	2.10082i	0.00632037	−	0.0757083i
$771$		0			0
$772$	1.02201	−	6.07837i	0.0367828	−	0.218765i
$773$			21.3814i			0.769036i	0.923118	+	0.384518i	$0.125632\pi$
$773$			21.3814i			0.769036i	−0.923118	+	0.384518i	$0.874368\pi$
$774$		0			0
$775$			1.73249i			0.0622328i
$776$	−9.10698	+	35.6851i	−0.326922	+	1.28102i
$777$		0			0
$778$	−3.10516	+	37.1950i	−0.111325	+	1.33351i
$779$	12.0420			0.431449
$780$		0			0
$781$		−	2.06746i		−	0.0739797i
$782$	31.7549	−	28.7497i	1.13555	−	1.02809i
$783$		0			0
$784$	−13.7169	−	4.74686i	−0.489888	−	0.169531i
$785$		−	27.4827i		−	0.980899i
$786$		0			0
$787$	−38.9140			−1.38713			−0.693567	−	0.720392i	$-0.743962\pi$
$787$	−38.9140			−1.38713			−0.693567	+	0.720392i	$0.743962\pi$
$788$	−44.9334	−	7.55502i	−1.60069	−	0.269136i
$789$		0			0
$790$	1.98296	−	23.7528i	0.0705504	−	0.845085i
$791$	36.1510			1.28538
$792$		0			0
$793$		−	41.0150i		−	1.45649i
$794$	−29.8826	−	2.49469i	−1.06049	−	0.0885334i
$795$		0			0
$796$	4.94185	−	29.3916i	0.175159	−	1.04176i
$797$		−	18.6530i		−	0.660722i	−0.943855	−	0.330361i	$-0.892829\pi$
$797$		−	18.6530i		−	0.660722i	0.943855	−	0.330361i	$-0.107171\pi$
$798$		0			0
$799$	12.7743	+	11.9420i	0.451924	+	0.422478i
$800$	−14.7679	−	6.53217i	−0.522124	−	0.230947i
$801$		0			0
$802$	0.849427	−	10.1748i	0.0299943	−	0.359285i
$803$		−	1.50256i		−	0.0530241i
$804$		0			0
$805$	35.0803			1.23642
$806$	−5.46770	−	0.456461i	−0.192592	−	0.0160782i
$807$		0			0
$808$	1.35928	−	5.32625i	0.0478193	−	0.187377i
$809$			32.7083i			1.14996i	0.818166	+	0.574982i	$0.194991\pi$
$809$			32.7083i			1.14996i	−0.818166	+	0.574982i	$0.805009\pi$
$810$		0			0
$811$	−31.1576			−1.09409			−0.547045	−	0.837103i	$-0.684247\pi$
$811$	−31.1576			−1.09409			−0.547045	+	0.837103i	$0.684247\pi$
$812$	−5.82993	+	34.6734i	−0.204590	+	1.21680i
$813$		0			0
$814$	−4.96324	−	0.414347i	−0.173961	−	0.0145229i
$815$	−23.3215			−0.816916
$816$		0			0
$817$	16.8534			0.589626
$818$	34.6033	+	2.88879i	1.20987	+	0.101004i
$819$		0			0
$820$	−2.60713	+	15.5058i	−0.0910448	+	0.541487i
$821$	−28.5075			−0.994917			−0.497459	−	0.867488i	$-0.665733\pi$
$821$	−28.5075			−0.994917			−0.497459	+	0.867488i	$0.665733\pi$
$822$		0			0
$823$		−	23.6353i		−	0.823876i	−0.911212	−	0.411938i	$-0.864852\pi$
$823$		−	23.6353i		−	0.823876i	0.911212	−	0.411938i	$-0.135148\pi$
$824$	19.1042	+	4.87546i	0.665526	+	0.169845i
$825$		0			0
$826$	−23.6888	−	1.97762i	−0.824239	−	0.0688101i
$827$	−33.1756			−1.15363			−0.576814	−	0.816875i	$-0.695704\pi$
$827$	−33.1756			−1.15363			−0.576814	+	0.816875i	$0.695704\pi$
$828$		0			0
$829$			24.0031i			0.833662i	0.908984	+	0.416831i	$0.136859\pi$
$829$			24.0031i			0.833662i	−0.908984	+	0.416831i	$0.863141\pi$
$830$	−2.30654	+	27.6288i	−0.0800612	+	0.959009i
$831$		0			0
$832$	24.5063	−	44.8862i	0.849605	−	1.55615i
$833$	−10.9296	−	10.2175i	−0.378688	−	0.354014i
$834$		0			0
$835$			10.3833i			0.359330i
$836$	0.232254	−	1.38132i	0.00803266	−	0.0477741i
$837$		0			0
$838$	−55.0847	−	4.59865i	−1.90287	−	0.158858i
$839$			27.2563i			0.940993i	0.882402	+	0.470496i	$0.155925\pi$
$839$			27.2563i			0.940993i	−0.882402	+	0.470496i	$0.844075\pi$
$840$		0			0
$841$	0.0775701			0.00267483
$842$	1.13679	−	13.6170i	0.0391763	−	0.469271i
$843$		0			0
$844$	21.9535	+	3.69122i	0.755671	+	0.127057i
$845$	40.8138			1.40404
$846$		0			0
$847$			35.5442i			1.22131i
$848$	−11.6651	+	33.7085i	−0.400583	+	1.15755i
$849$		0			0
$850$	−11.1715	−	12.3392i	−0.383178	−	0.423231i
$851$		−	82.8782i		−	2.84103i
$852$		0			0
$853$	35.1320			1.20290			0.601449	−	0.798911i	$-0.294590\pi$
$853$	35.1320			1.20290			0.601449	+	0.798911i	$0.294590\pi$
$854$	2.46103	−	29.4793i	0.0842146	−	1.00876i
$855$		0			0
$856$	20.2789	+	5.17525i	0.693118	+	0.176886i
$857$		−	27.2840i		−	0.932005i	−0.884783	−	0.466002i	$-0.845694\pi$
$857$		−	27.2840i		−	0.932005i	0.884783	−	0.466002i	$-0.154306\pi$
$858$		0			0
$859$		−	3.90819i		−	0.133346i	−0.997775	−	0.0666728i	$-0.978762\pi$
$859$		−	3.90819i		−	0.133346i	0.997775	−	0.0666728i	$-0.0212384\pi$
$860$	−3.64881	+	21.7013i	−0.124423	+	0.740007i
$861$		0			0
$862$	0.714222	−	8.55528i	0.0243265	−	0.291394i
$863$	−30.8940			−1.05164			−0.525821	−	0.850595i	$-0.676242\pi$
$863$	−30.8940			−1.05164			−0.525821	+	0.850595i	$0.676242\pi$
$864$		0			0
$865$	14.8117			0.503614
$866$	28.9046	+	2.41305i	0.982217	+	0.0819986i
$867$		0			0
$868$	−3.90249	−	0.656158i	−0.132459	−	0.0222714i
$869$		−	3.59203i		−	0.121851i
$870$		0			0
$871$	75.7049			2.56516
$872$	−29.1750	−	7.44556i	−0.987989	−	0.252139i
$873$		0			0
$874$	23.2278	+	1.93913i	0.785692	+	0.0655921i
$875$		−	37.5076i		−	1.26799i
$876$		0			0
$877$	−17.7726			−0.600137			−0.300068	−	0.953918i	$-0.597010\pi$
$877$	−17.7726			−0.600137			−0.300068	+	0.953918i	$0.597010\pi$
$878$	0.866999	−	10.3853i	0.0292598	−	0.350487i
$879$		0			0
$880$	1.72838	+	0.598122i	0.0582636	+	0.0201627i
$881$		−	34.8223i		−	1.17319i	−0.809879	−	0.586597i	$-0.800467\pi$
$881$		−	34.8223i		−	1.17319i	0.809879	−	0.586597i	$-0.199533\pi$
$882$		0			0
$883$			7.89791i			0.265786i	0.991130	+	0.132893i	$0.0424266\pi$
$883$			7.89791i			0.265786i	−0.991130	+	0.132893i	$0.957573\pi$
$884$	41.8857	−	32.0060i	1.40877	−	1.07648i
$885$		0			0
$886$	−2.22459	+	26.6471i	−0.0747365	+	0.895228i
$887$		−	21.4557i		−	0.720412i	−0.932873	−	0.360206i	$-0.882706\pi$
$887$		−	21.4557i		−	0.720412i	0.932873	−	0.360206i	$-0.117294\pi$
$888$		0			0
$889$			55.3440i			1.85618i
$890$	19.7081	+	1.64530i	0.660618	+	0.0551505i
$891$		0			0
$892$	−0.632475	−	0.106343i	−0.0211768	−	0.00356063i
$893$			9.51532i			0.318418i
$894$		0			0
$895$			3.49061i			0.116678i
$896$	20.3071	−	30.7913i	0.678413	−	1.02866i
$897$		0			0
$898$	−2.23763	+	26.8033i	−0.0746706	+	0.894438i
$899$			3.27268i			0.109150i
$900$		0			0
$901$	−25.1089	+	26.8589i	−0.836499	+	0.894800i
$902$	−0.197132	+	2.36134i	−0.00656379	+	0.0786241i
$903$		0			0
$904$	−7.75550	+	30.3895i	−0.257944	+	1.01074i
$905$	15.4501			0.513577
$906$		0			0
$907$	−46.9549			−1.55911			−0.779557	−	0.626332i	$-0.784556\pi$
$907$	−46.9549			−1.55911			−0.779557	+	0.626332i	$0.784556\pi$
$908$	51.5044	+	8.65987i	1.70923	+	0.287388i
$909$		0			0
$910$	43.0205	+	3.59149i	1.42612	+	0.119057i
$911$			20.5297i			0.680181i	0.940393	+	0.340090i	$0.110458\pi$
$911$			20.5297i			0.680181i	−0.940393	+	0.340090i	$0.889542\pi$
$912$		0			0
$913$			4.17819i			0.138278i
$914$	−28.9086	−	2.41339i	−0.956212	−	0.0798277i
$915$		0			0
$916$	4.87167	−	28.9742i	0.160965	−	0.957335i
$917$		−	0.549360i		−	0.0181415i
$918$		0			0
$919$	−53.2755			−1.75740			−0.878698	−	0.477379i	$-0.841587\pi$
$919$	−53.2755			−1.75740			−0.878698	+	0.477379i	$0.841587\pi$
$920$	−7.52581	+	29.4894i	−0.248119	+	0.972238i
$921$		0			0
$922$	0.950569	−	11.3863i	0.0313053	−	0.374989i
$923$	42.3375			1.39355
$924$		0			0
$925$	−32.2046			−1.05888
$926$	17.8719	+	1.49200i	0.587307	+	0.0490303i
$927$		0			0
$928$	−27.8967	−	12.3393i	−0.915753	−	0.405057i
$929$			40.7355i			1.33649i	0.743942	+	0.668244i	$0.232954\pi$
$929$			40.7355i			1.33649i	−0.743942	+	0.668244i	$0.767046\pi$
$930$		0			0
$931$		−	8.14122i		−	0.266818i
$932$	−9.12717	+	54.2837i	−0.298970	+	1.77812i
$933$		0			0
$934$	−3.78224	+	45.3054i	−0.123759	+	1.48244i
$935$	1.37717	+	1.28744i	0.0450383	+	0.0421038i
$936$		0			0
$937$	−21.3186			−0.696449			−0.348225	−	0.937411i	$-0.613215\pi$
$937$	−21.3186			−0.696449			−0.348225	+	0.937411i	$0.613215\pi$
$938$	54.4125	+	4.54253i	1.77663	+	0.148319i
$939$		0			0
$940$	−12.2524	−	2.06010i	−0.399629	−	0.0671929i
$941$	−27.9682			−0.911738			−0.455869	−	0.890047i	$-0.650671\pi$
$941$	−27.9682			−0.911738			−0.455869	+	0.890047i	$0.650671\pi$
$942$		0			0
$943$	−39.4307			−1.28404
$944$	6.74441	−	19.4892i	0.219512	−	0.634318i
$945$		0			0
$946$	−0.275898	+	3.30483i	−0.00897020	+	0.107449i
$947$	50.2968			1.63443			0.817214	−	0.576335i	$-0.195518\pi$
$947$	50.2968			1.63443			0.817214	+	0.576335i	$0.195518\pi$
$948$		0			0
$949$	30.7693			0.998815
$950$	0.753502	−	9.02579i	0.0244468	−	0.292835i
$951$		0			0
$952$	32.0256	−	20.4908i	1.03795	−	0.664111i
$953$	15.4664			0.501006			0.250503	−	0.968116i	$-0.419404\pi$
$953$	15.4664			0.501006			0.250503	+	0.968116i	$0.419404\pi$
$954$		0			0
$955$	−24.7800			−0.801861
$956$	−11.4425	−	1.92392i	−0.370076	−	0.0622240i
$957$		0			0
$958$	2.99823	−	35.9142i	0.0968684	−	1.16033i
$959$			19.6508i			0.634557i
$960$		0			0
$961$	30.6317			0.988118
$962$	8.48499	−	101.637i	0.273567	−	3.27691i
$963$		0			0
$964$	−5.69151	+	33.8502i	−0.183311	+	1.09024i
$965$			4.51403i			0.145312i
$966$		0			0
$967$	−50.1822			−1.61375			−0.806876	−	0.590721i	$-0.798843\pi$
$967$	−50.1822			−1.61375			−0.806876	+	0.590721i	$0.798843\pi$
$968$	−29.8794	−	7.62534i	−0.960361	−	0.245088i
$969$		0			0
$970$	2.24390	−	26.8785i	0.0720473	−	0.863015i
$971$			30.8673i			0.990579i	0.868728	+	0.495290i	$0.164938\pi$
$971$			30.8673i			0.990579i	−0.868728	+	0.495290i	$0.835062\pi$
$972$		0			0
$973$		−	11.6186i		−	0.372476i
$974$	−0.364342	+	4.36425i	−0.0116743	+	0.139840i
$975$		0			0
$976$	24.2531	+	8.39302i	0.776322	+	0.268654i
$977$	31.1825			0.997617			0.498809	−	0.866712i	$-0.333771\pi$
$977$	31.1825			0.997617			0.498809	+	0.866712i	$0.333771\pi$
$978$		0			0
$979$	2.98038			0.0952533
$980$	10.4830	+	1.76260i	0.334868	+	0.0563042i
$981$		0			0
$982$	−4.40435	+	52.7574i	−0.140549	+	1.68356i
$983$		−	2.61279i		−	0.0833350i	−0.999132	−	0.0416675i	$-0.986733\pi$
$983$		−	2.61279i		−	0.0833350i	0.999132	−	0.0416675i	$-0.0132670\pi$
$984$		0			0
$985$	33.3693			1.06323
$986$	−21.1030	−	23.3088i	−0.672056	−	0.742305i
$987$		0			0
$988$	28.2867	+	4.75608i	0.899921	+	0.151311i
$989$	−55.1853			−1.75479
$990$		0			0
$991$			35.6087i			1.13115i	0.824698	+	0.565573i	$0.191345\pi$
$991$			35.6087i			1.13115i	−0.824698	+	0.565573i	$0.808655\pi$
$992$	1.38879	−	3.13977i	0.0440941	−	0.0996877i
$993$		0			0
$994$	30.4298	+	2.54038i	0.965175	+	0.0805759i
$995$			21.8273i			0.691973i
$996$		0			0
$997$	−4.13227			−0.130870			−0.0654351	−	0.997857i	$-0.520844\pi$
$997$	−4.13227			−0.130870			−0.0654351	+	0.997857i	$0.520844\pi$
$998$	−27.8991	−	2.32911i	−0.883132	−	0.0737267i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1224.2.l.d.1189.18		18
3.2	odd	2		408.2.l.b.373.1	yes	18
4.3	odd	2		4896.2.l.d.3025.6		18
8.3	odd	2		4896.2.l.c.3025.14		18
8.5	even	2		1224.2.l.c.1189.17		18
12.11	even	2		1632.2.l.a.1393.14		18
17.16	even	2		1224.2.l.c.1189.18		18
24.5	odd	2		408.2.l.a.373.2	yes	18
24.11	even	2		1632.2.l.b.1393.6		18
51.50	odd	2		408.2.l.a.373.1	✓	18
68.67	odd	2		4896.2.l.c.3025.13		18
136.67	odd	2		4896.2.l.d.3025.5		18
136.101	even	2	inner	1224.2.l.d.1189.17		18
204.203	even	2		1632.2.l.b.1393.5		18
408.101	odd	2		408.2.l.b.373.2	yes	18
408.203	even	2		1632.2.l.a.1393.13		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
408.2.l.a.373.1	✓	18	51.50	odd	2
408.2.l.a.373.2	yes	18	24.5	odd	2
408.2.l.b.373.1	yes	18	3.2	odd	2
408.2.l.b.373.2	yes	18	408.101	odd	2
1224.2.l.c.1189.17		18	8.5	even	2
1224.2.l.c.1189.18		18	17.16	even	2
1224.2.l.d.1189.17		18	136.101	even	2	inner
1224.2.l.d.1189.18		18	1.1	even	1	trivial
1632.2.l.a.1393.13		18	408.203	even	2
1632.2.l.a.1393.14		18	12.11	even	2
1632.2.l.b.1393.5		18	204.203	even	2
1632.2.l.b.1393.6		18	24.11	even	2
4896.2.l.c.3025.13		18	68.67	odd	2
4896.2.l.c.3025.14		18	8.3	odd	2
4896.2.l.d.3025.5		18	136.67	odd	2
4896.2.l.d.3025.6		18	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:	\( N \)	\(=\)	\( 1224 = 2^{3} \cdot 3^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1224.l (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.40931 + 0.117654i) q^{2} +(1.97232 + 0.331622i) q^{4} -1.46472 q^{5} -3.26018i q^{7} +(2.74059 + 0.699408i) q^{8} +(-2.06424 - 0.172330i) q^{10} -0.312167 q^{11} -6.39254i q^{13} +(0.383572 - 4.59460i) q^{14} +(3.78005 + 1.30812i) q^{16} +(3.01195 + 2.81570i) q^{17} +2.24353i q^{19} +(-2.88888 - 0.485732i) q^{20} +(-0.439940 - 0.0367276i) q^{22} -7.34630i q^{23} -2.85460 q^{25} +(0.752107 - 9.00908i) q^{26} +(1.08115 - 6.43010i) q^{28} -5.39236 q^{29} -0.606910i q^{31} +(5.17337 + 2.28829i) q^{32} +(3.91349 + 4.32257i) q^{34} +4.77524i q^{35} +11.2816 q^{37} +(-0.263960 + 3.16184i) q^{38} +(-4.01419 - 1.02444i) q^{40} -5.36742i q^{41} -7.51199i q^{43} +(-0.615692 - 0.103521i) q^{44} +(0.864321 - 10.3532i) q^{46} +4.24122 q^{47} -3.62875 q^{49} +(-4.02302 - 0.335855i) q^{50} +(2.11991 - 12.6081i) q^{52} +8.91746i q^{53} +0.457236 q^{55} +(2.28019 - 8.93480i) q^{56} +(-7.59952 - 0.634432i) q^{58} -5.15579i q^{59} +6.41607 q^{61} +(0.0714053 - 0.855325i) q^{62} +(7.02166 + 3.83358i) q^{64} +9.36327i q^{65} +11.8427i q^{67} +(5.00676 + 6.55228i) q^{68} +(-0.561825 + 6.72979i) q^{70} +6.62295i q^{71} +4.81332i q^{73} +(15.8993 + 1.32733i) q^{74} +(-0.744004 + 4.42496i) q^{76} +1.01772i q^{77} +11.5068i q^{79} +(-5.53671 - 1.91603i) q^{80} +(0.631497 - 7.56436i) q^{82} -13.3845i q^{83} +(-4.41165 - 4.12421i) q^{85} +(0.883814 - 10.5867i) q^{86} +(-0.855521 - 0.218332i) q^{88} -9.54739 q^{89} -20.8408 q^{91} +(2.43619 - 14.4892i) q^{92} +(5.97720 + 0.498996i) q^{94} -3.28614i q^{95} +13.0210i q^{97} +(-5.11404 - 0.426936i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 2 q^{4} + 4 q^{5} - 8 q^{10} + 6 q^{14} + 10 q^{16} + 2 q^{17} + 2 q^{20} + 2 q^{22} + 22 q^{25} - 2 q^{26} - 10 q^{28} - 12 q^{29} + 6 q^{34} - 16 q^{37} + 34 q^{38} - 10 q^{40} - 12 q^{44} + 32 q^{46}+ \cdots + 60 q^{98}+O(q^{100}) \) 18 * q + 2 * q^4 + 4 * q^5 - 8 * q^10 + 6 * q^14 + 10 * q^16 + 2 * q^17 + 2 * q^20 + 2 * q^22 + 22 * q^25 - 2 * q^26 - 10 * q^28 - 12 * q^29 + 6 * q^34 - 16 * q^37 + 34 * q^38 - 10 * q^40 - 12 * q^44 + 32 * q^46 - 18 * q^49 + 14 * q^50 + 8 * q^52 - 16 * q^55 + 14 * q^56 - 6 * q^58 - 16 * q^61 + 6 * q^62 + 2 * q^64 + 36 * q^68 - 32 * q^70 + 6 * q^74 + 62 * q^80 + 34 * q^82 + 16 * q^85 - 14 * q^86 + 16 * q^88 - 20 * q^89 + 2 * q^92 + 12 * q^94 + 60 * q^98

Introduction

L-functions

Modular forms

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Database

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