LMFDB - Embedded newform 1512.2.j.d.323.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1512,2,Mod(323,1512)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1512, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1512.323");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1512 = 2^{3} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1512.j (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$12.0733807856$
Analytic rank:	$0$
Dimension:	$48$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			323.13
Character	$\chi$	$=$	1512.323
Dual form			1512.2.j.d.323.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.908924 - 1.08345i) q^{2} +(-0.347713 + 1.96954i) q^{4} +0.863507 q^{5} -1.00000i q^{7} +(2.44994 - 1.41344i) q^{8} +O(q^{10})$	\(q+(-0.908924 - 1.08345i) q^{2} +(-0.347713 + 1.96954i) q^{4} +0.863507 q^{5} -1.00000i q^{7} +(2.44994 - 1.41344i) q^{8} +(-0.784863 - 0.935564i) q^{10} -2.62979i q^{11} -1.01906i q^{13} +(-1.08345 + 0.908924i) q^{14} +(-3.75819 - 1.36967i) q^{16} -2.34382i q^{17} -4.09641 q^{19} +(-0.300253 + 1.70071i) q^{20} +(-2.84923 + 2.39028i) q^{22} +6.23450 q^{23} -4.25435 q^{25} +(-1.10410 + 0.926249i) q^{26} +(1.96954 + 0.347713i) q^{28} -1.57590 q^{29} +6.29822i q^{31} +(1.93194 + 5.31673i) q^{32} +(-2.53941 + 2.13036i) q^{34} -0.863507i q^{35} -5.18085i q^{37} +(3.72332 + 4.43824i) q^{38} +(2.11554 - 1.22051i) q^{40} -10.1388i q^{41} -0.496156 q^{43} +(5.17948 + 0.914412i) q^{44} +(-5.66669 - 6.75475i) q^{46} -5.24394 q^{47} -1.00000 q^{49} +(3.86689 + 4.60937i) q^{50} +(2.00708 + 0.354341i) q^{52} +10.5477 q^{53} -2.27084i q^{55} +(-1.41344 - 2.44994i) q^{56} +(1.43238 + 1.70741i) q^{58} +4.40654i q^{59} -9.59653i q^{61} +(6.82379 - 5.72461i) q^{62} +(4.00440 - 6.92566i) q^{64} -0.879966i q^{65} -12.6840 q^{67} +(4.61625 + 0.814978i) q^{68} +(-0.935564 + 0.784863i) q^{70} -2.11023 q^{71} -8.27702 q^{73} +(-5.61318 + 4.70900i) q^{74} +(1.42438 - 8.06805i) q^{76} -2.62979 q^{77} -9.44227i q^{79} +(-3.24523 - 1.18272i) q^{80} +(-10.9849 + 9.21541i) q^{82} -6.62600i q^{83} -2.02391i q^{85} +(0.450968 + 0.537558i) q^{86} +(-3.71704 - 6.44282i) q^{88} -10.2551i q^{89} -1.01906 q^{91} +(-2.16782 + 12.2791i) q^{92} +(4.76634 + 5.68153i) q^{94} -3.53728 q^{95} +15.1206 q^{97} +(0.908924 + 1.08345i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 4 q^{4}+O(q^{10}) $ 48 * q - 4 * q^4	$ 48 q - 4 q^{4} - 12 q^{10} - 12 q^{16} + 16 q^{19} - 24 q^{22} + 48 q^{25} + 8 q^{28} + 12 q^{34} + 32 q^{40} + 64 q^{43} + 60 q^{46} - 48 q^{49} + 16 q^{52} + 36 q^{58} - 4 q^{64} + 32 q^{67} + 12 q^{70} - 32 q^{76} + 36 q^{82} + 24 q^{88} - 60 q^{94}+O(q^{100}) $ 48 * q - 4 * q^4 - 12 * q^10 - 12 * q^16 + 16 * q^19 - 24 * q^22 + 48 * q^25 + 8 * q^28 + 12 * q^34 + 32 * q^40 + 64 * q^43 + 60 * q^46 - 48 * q^49 + 16 * q^52 + 36 * q^58 - 4 * q^64 + 32 * q^67 + 12 * q^70 - 32 * q^76 + 36 * q^82 + 24 * q^88 - 60 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times$.

$n$	$757$	$785$	$1081$	$1135$
$\chi(n)$	$-1$	$-1$	$1$	$-1$

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 $

$2$	−0.908924	−	1.08345i	−0.642707	−	0.766112i
$2$	−0.908924	−	1.08345i	−0.642707	−	0.766112i
$3$		0			0
$3$		0			0
$4$	−0.347713	+	1.96954i	−0.173857	+	0.984771i
$5$	0.863507			0.386172			0.193086	−	0.981182i	$-0.438150\pi$
$5$	0.863507			0.386172			0.193086	+	0.981182i	$0.438150\pi$
$6$		0			0
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$	2.44994	−	1.41344i	0.866184	−	0.499725i
$9$		0			0
$10$	−0.784863	−	0.935564i	−0.248195	−	0.295851i
$11$		−	2.62979i		−	0.792911i	−0.918054	−	0.396455i	$-0.870240\pi$
$11$		−	2.62979i		−	0.792911i	0.918054	−	0.396455i	$-0.129760\pi$
$12$		0			0
$13$		−	1.01906i		−	0.282636i	−0.989964	−	0.141318i	$-0.954866\pi$
$13$		−	1.01906i		−	0.282636i	0.989964	−	0.141318i	$-0.0451341\pi$
$14$	−1.08345	+	0.908924i	−0.289563	+	0.242920i
$15$		0			0
$16$	−3.75819	−	1.36967i	−0.939548	−	0.342418i
$17$		−	2.34382i		−	0.568460i	−0.958756	−	0.284230i	$-0.908262\pi$
$17$		−	2.34382i		−	0.568460i	0.958756	−	0.284230i	$-0.0917379\pi$
$18$		0			0
$19$	−4.09641			−0.939780			−0.469890	−	0.882725i	$-0.655706\pi$
$19$	−4.09641			−0.939780			−0.469890	+	0.882725i	$0.655706\pi$
$20$	−0.300253	+	1.70071i	−0.0671386	+	0.380291i
$21$		0			0
$22$	−2.84923	+	2.39028i	−0.607459	+	0.509609i
$23$	6.23450			1.29998			0.649992	−	0.759941i	$-0.274772\pi$
$23$	6.23450			1.29998			0.649992	+	0.759941i	$0.274772\pi$
$24$		0			0
$25$	−4.25435			−0.850871
$26$	−1.10410	+	0.926249i	−0.216531	+	0.181652i
$27$		0			0
$28$	1.96954	+	0.347713i	0.372208	+	0.0657117i
$29$	−1.57590			−0.292638			−0.146319	−	0.989237i	$-0.546743\pi$
$29$	−1.57590			−0.292638			−0.146319	+	0.989237i	$0.546743\pi$
$30$		0			0
$31$			6.29822i			1.13119i	0.824682	+	0.565597i	$0.191354\pi$
$31$			6.29822i			1.13119i	−0.824682	+	0.565597i	$0.808646\pi$
$32$	1.93194	+	5.31673i	0.341523	+	0.939874i
$33$		0			0
$34$	−2.53941	+	2.13036i	−0.435504	+	0.365353i
$35$		−	0.863507i		−	0.145959i
$36$		0			0
$37$		−	5.18085i		−	0.851727i	−0.904787	−	0.425863i	$-0.859970\pi$
$37$		−	5.18085i		−	0.851727i	0.904787	−	0.425863i	$-0.140030\pi$
$38$	3.72332	+	4.43824i	0.604003	+	0.719977i
$39$		0			0
$40$	2.11554	−	1.22051i	0.334496	−	0.192980i
$41$		−	10.1388i		−	1.58342i	−0.610899	−	0.791708i	$-0.709192\pi$
$41$		−	10.1388i		−	1.58342i	0.610899	−	0.791708i	$-0.290808\pi$
$42$		0			0
$43$	−0.496156			−0.0756630			−0.0378315	−	0.999284i	$-0.512045\pi$
$43$	−0.496156			−0.0756630			−0.0378315	+	0.999284i	$0.512045\pi$
$44$	5.17948	+	0.914412i	0.780836	+	0.137853i
$45$		0			0
$46$	−5.66669	−	6.75475i	−0.835508	−	0.995933i
$47$	−5.24394			−0.764907			−0.382453	−	0.923975i	$-0.624921\pi$
$47$	−5.24394			−0.764907			−0.382453	+	0.923975i	$0.624921\pi$
$48$		0			0
$49$	−1.00000			−0.142857
$50$	3.86689	+	4.60937i	0.546860	+	0.651863i
$51$		0			0
$52$	2.00708	+	0.354341i	0.278332	+	0.0491382i
$53$	10.5477			1.44884			0.724419	−	0.689360i	$-0.242108\pi$
$53$	10.5477			1.44884			0.724419	+	0.689360i	$0.242108\pi$
$54$		0			0
$55$		−	2.27084i		−	0.306200i
$56$	−1.41344	−	2.44994i	−0.188878	−	0.327387i
$57$		0			0
$58$	1.43238	+	1.70741i	0.188080	+	0.224194i
$59$			4.40654i			0.573683i	0.957978	+	0.286841i	$0.0926053\pi$
$59$			4.40654i			0.573683i	−0.957978	+	0.286841i	$0.907395\pi$
$60$		0			0
$61$		−	9.59653i		−	1.22871i	−0.789030	−	0.614355i	$-0.789416\pi$
$61$		−	9.59653i		−	1.22871i	0.789030	−	0.614355i	$-0.210584\pi$
$62$	6.82379	−	5.72461i	0.866622	−	0.727026i
$63$		0			0
$64$	4.00440	−	6.92566i	0.500550	−	0.865708i
$65$		−	0.879966i		−	0.109146i
$66$		0			0
$67$	−12.6840			−1.54959			−0.774796	−	0.632212i	$-0.782147\pi$
$67$	−12.6840			−1.54959			−0.774796	+	0.632212i	$0.782147\pi$
$68$	4.61625	+	0.814978i	0.559803	+	0.0988306i
$69$		0			0
$70$	−0.935564	+	0.784863i	−0.111821	+	0.0938091i
$71$	−2.11023			−0.250438			−0.125219	−	0.992129i	$-0.539963\pi$
$71$	−2.11023			−0.250438			−0.125219	+	0.992129i	$0.539963\pi$
$72$		0			0
$73$	−8.27702			−0.968752			−0.484376	−	0.874860i	$-0.660953\pi$
$73$	−8.27702			−0.968752			−0.484376	+	0.874860i	$0.660953\pi$
$74$	−5.61318	+	4.70900i	−0.652519	+	0.547410i
$75$		0			0
$76$	1.42438	−	8.06805i	0.163387	−	0.925468i
$77$	−2.62979			−0.299692
$78$		0			0
$79$		−	9.44227i		−	1.06234i	−0.847266	−	0.531169i	$-0.821753\pi$
$79$		−	9.44227i		−	1.06234i	0.847266	−	0.531169i	$-0.178247\pi$
$80$	−3.24523	−	1.18272i	−0.362827	−	0.132232i
$81$		0			0
$82$	−10.9849	+	9.21541i	−1.21308	+	1.01767i
$83$		−	6.62600i		−	0.727298i	−0.931536	−	0.363649i	$-0.881531\pi$
$83$		−	6.62600i		−	0.727298i	0.931536	−	0.363649i	$-0.118469\pi$
$84$		0			0
$85$		−	2.02391i		−	0.219524i
$86$	0.450968	+	0.537558i	0.0486291	+	0.0579664i
$87$		0			0
$88$	−3.71704	−	6.44282i	−0.396237	−	0.686807i
$89$		−	10.2551i		−	1.08704i	−0.839395	−	0.543522i	$-0.817091\pi$
$89$		−	10.2551i		−	1.08704i	0.839395	−	0.543522i	$-0.182909\pi$
$90$		0			0
$91$	−1.01906			−0.106827
$92$	−2.16782	+	12.2791i	−0.226011	+	1.28019i
$93$		0			0
$94$	4.76634	+	5.68153i	0.491611	+	0.586005i
$95$	−3.53728			−0.362917
$96$		0			0
$97$	15.1206			1.53526			0.767631	−	0.640892i	$-0.221435\pi$
$97$	15.1206			1.53526			0.767631	+	0.640892i	$0.221435\pi$
$98$	0.908924	+	1.08345i	0.0918152	+	0.109445i
$99$		0			0
$100$	1.47930	−	8.37913i	0.147930	−	0.837913i
$101$	−7.58948			−0.755181			−0.377591	−	0.925973i	$-0.623247\pi$
$101$	−7.58948			−0.755181			−0.377591	+	0.925973i	$0.623247\pi$
$102$		0			0
$103$			7.33678i			0.722914i	0.932389	+	0.361457i	$0.117721\pi$
$103$			7.33678i			0.722914i	−0.932389	+	0.361457i	$0.882279\pi$
$104$	−1.44038	−	2.49664i	−0.141240	−	0.244815i
$105$		0			0
$106$	−9.58705	−	11.4279i	−0.931177	−	1.10997i
$107$		−	19.1057i		−	1.84702i	−0.383578	−	0.923508i	$-0.625308\pi$
$107$		−	19.1057i		−	1.84702i	0.383578	−	0.923508i	$-0.374692\pi$
$108$		0			0
$109$		−	5.46494i		−	0.523446i	−0.965143	−	0.261723i	$-0.915709\pi$
$109$		−	5.46494i		−	0.523446i	0.965143	−	0.261723i	$-0.0842907\pi$
$110$	−2.46034	+	2.06402i	−0.234584	+	0.196797i
$111$		0			0
$112$	−1.36967	+	3.75819i	−0.129422	+	0.355116i
$113$			5.25502i			0.494351i	0.968971	+	0.247175i	$0.0795024\pi$
$113$			5.25502i			0.494351i	−0.968971	+	0.247175i	$0.920498\pi$
$114$		0			0
$115$	5.38354			0.502017
$116$	0.547963	−	3.10381i	0.0508771	−	0.288181i
$117$		0			0
$118$	4.77425	−	4.00521i	0.439506	−	0.368710i
$119$	−2.34382			−0.214858
$120$		0			0
$121$	4.08422			0.371293
$122$	−10.3973	+	8.72252i	−0.941330	+	0.789700i
$123$		0			0
$124$	−12.4046	−	2.18998i	−1.11397	−	0.196666i
$125$	−7.99120			−0.714755
$126$		0			0
$127$			8.49723i			0.754007i	0.926212	+	0.377004i	$0.123046\pi$
$127$			8.49723i			0.754007i	−0.926212	+	0.377004i	$0.876954\pi$
$128$	−11.1433	+	1.95635i	−0.984936	+	0.172918i
$129$		0			0
$130$	−0.953396	+	0.799823i	−0.0836184	+	0.0701491i
$131$		−	5.91940i		−	0.517180i	−0.965987	−	0.258590i	$-0.916742\pi$
$131$		−	5.91940i		−	0.517180i	0.965987	−	0.258590i	$-0.0832579\pi$
$132$		0			0
$133$			4.09641i			0.355204i
$134$	11.5288	+	13.7424i	0.995933	+	1.18716i
$135$		0			0
$136$	−3.31284	−	5.74222i	−0.284074	−	0.492391i
$137$		−	0.115119i		−	0.00983532i	−0.999988	−	0.00491766i	$-0.998435\pi$
$137$		−	0.115119i		−	0.00983532i	0.999988	−	0.00491766i	$-0.00156535\pi$
$138$		0			0
$139$	−9.05579			−0.768102			−0.384051	−	0.923312i	$-0.625471\pi$
$139$	−9.05579			−0.768102			−0.384051	+	0.923312i	$0.625471\pi$
$140$	1.70071	+	0.300253i	0.143737	+	0.0253760i
$141$		0			0
$142$	1.91804	+	2.28632i	0.160958	+	0.191863i
$143$	−2.67991			−0.224105
$144$		0			0
$145$	−1.36081			−0.113009
$146$	7.52319	+	8.96771i	0.622624	+	0.742173i
$147$		0			0
$148$	10.2039	+	1.80145i	0.838756	+	0.148078i
$149$	−7.56092			−0.619415			−0.309707	−	0.950832i	$-0.600231\pi$
$149$	−7.56092			−0.619415			−0.309707	+	0.950832i	$0.600231\pi$
$150$		0			0
$151$			11.0274i			0.897401i	0.893682	+	0.448700i	$0.148113\pi$
$151$			11.0274i			0.897401i	−0.893682	+	0.448700i	$0.851887\pi$
$152$	−10.0359	+	5.79001i	−0.814023	+	0.469632i
$153$		0			0
$154$	2.39028	+	2.84923i	0.192614	+	0.229598i
$155$			5.43856i			0.436836i
$156$		0			0
$157$		−	6.90136i		−	0.550788i	−0.961331	−	0.275394i	$-0.911192\pi$
$157$		−	6.90136i		−	0.550788i	0.961331	−	0.275394i	$-0.0888083\pi$
$158$	−10.2302	+	8.58230i	−0.813870	+	0.682771i
$159$		0			0
$160$	1.66825	+	4.59103i	0.131887	+	0.362953i
$161$		−	6.23450i		−	0.491347i
$162$		0			0
$163$	−14.0095			−1.09731			−0.548653	−	0.836050i	$-0.684859\pi$
$163$	−14.0095			−1.09731			−0.548653	+	0.836050i	$0.684859\pi$
$164$	19.9688	+	3.52540i	1.55930	+	0.275288i
$165$		0			0
$166$	−7.17892	+	6.02253i	−0.557192	+	0.467439i
$167$	−5.97129			−0.462072			−0.231036	−	0.972945i	$-0.574212\pi$
$167$	−5.97129			−0.462072			−0.231036	+	0.972945i	$0.574212\pi$
$168$		0			0
$169$	11.9615			0.920117
$170$	−2.19280	+	1.83958i	−0.168180	+	0.141089i
$171$		0			0
$172$	0.172520	−	0.977200i	0.0131545	−	0.0745108i
$173$	3.37661			0.256719			0.128359	−	0.991728i	$-0.459029\pi$
$173$	3.37661			0.256719			0.128359	+	0.991728i	$0.459029\pi$
$174$		0			0
$175$			4.25435i			0.321599i
$176$	−3.60195	+	9.88324i	−0.271507	+	0.744977i
$177$		0			0
$178$	−11.1109	+	9.32115i	−0.832797	+	0.698650i
$179$		−	11.3901i		−	0.851335i	−0.904880	−	0.425668i	$-0.860039\pi$
$179$		−	11.3901i		−	0.851335i	0.904880	−	0.425668i	$-0.139961\pi$
$180$		0			0
$181$		−	11.4514i		−	0.851175i	−0.904917	−	0.425588i	$-0.860067\pi$
$181$		−	11.4514i		−	0.851175i	0.904917	−	0.425588i	$-0.139933\pi$
$182$	0.926249	+	1.10410i	0.0686581	+	0.0818411i
$183$		0			0
$184$	15.2741	−	8.81206i	1.12602	−	0.649634i
$185$		−	4.47371i		−	0.328913i
$186$		0			0
$187$	−6.16375			−0.450738
$188$	1.82339	−	10.3282i	0.132984	−	0.753258i
$189$		0			0
$190$	3.21512	+	3.83245i	0.233249	+	0.278035i
$191$	−12.1088			−0.876160			−0.438080	−	0.898936i	$-0.644341\pi$
$191$	−12.1088			−0.876160			−0.438080	+	0.898936i	$0.644341\pi$
$192$		0			0
$193$	1.69048			0.121683			0.0608416	−	0.998147i	$-0.480622\pi$
$193$	1.69048			0.121683			0.0608416	+	0.998147i	$0.480622\pi$
$194$	−13.7435	−	16.3823i	−0.986723	−	1.17618i
$195$		0			0
$196$	0.347713	−	1.96954i	0.0248367	−	0.140682i
$197$	7.38828			0.526393			0.263197	−	0.964742i	$-0.415223\pi$
$197$	7.38828			0.526393			0.263197	+	0.964742i	$0.415223\pi$
$198$		0			0
$199$			21.1249i			1.49750i	0.662851	+	0.748751i	$0.269346\pi$
$199$			21.1249i			1.49750i	−0.662851	+	0.748751i	$0.730654\pi$
$200$	−10.4229	+	6.01326i	−0.737011	+	0.425201i
$201$		0			0
$202$	6.89826	+	8.22279i	0.485360	+	0.578554i
$203$			1.57590i			0.110607i
$204$		0			0
$205$		−	8.75494i		−	0.611472i
$206$	7.94900	−	6.66857i	0.553833	−	0.464621i
$207$		0			0
$208$	−1.39578	+	3.82982i	−0.0967798	+	0.265550i
$209$			10.7727i			0.745162i
$210$		0			0
$211$	5.02364			0.345841			0.172921	−	0.984936i	$-0.444680\pi$
$211$	5.02364			0.345841			0.172921	+	0.984936i	$0.444680\pi$
$212$	−3.66757	+	20.7741i	−0.251890	+	1.42677i
$213$		0			0
$214$	−20.7000	+	17.3656i	−1.41502	+	1.18709i
$215$	−0.428434			−0.0292190
$216$		0			0
$217$	6.29822			0.427551
$218$	−5.92097	+	4.96721i	−0.401019	+	0.336422i
$219$		0			0
$220$	4.47252	+	0.789602i	0.301537	+	0.0532349i
$221$	−2.38849			−0.160668
$222$		0			0
$223$			6.37320i			0.426781i	0.976967	+	0.213390i	$0.0684507\pi$
$223$			6.37320i			0.426781i	−0.976967	+	0.213390i	$0.931549\pi$
$224$	5.31673	−	1.93194i	0.355239	−	0.129083i
$225$		0			0
$226$	5.69354	−	4.77642i	0.378728	−	0.317723i
$227$			7.87985i			0.523004i	0.965203	+	0.261502i	$0.0842177\pi$
$227$			7.87985i			0.523004i	−0.965203	+	0.261502i	$0.915782\pi$
$228$		0			0
$229$			21.7103i			1.43466i	0.696736	+	0.717328i	$0.254635\pi$
$229$			21.7103i			1.43466i	−0.696736	+	0.717328i	$0.745365\pi$
$230$	−4.89323	−	5.83278i	−0.322650	−	0.384602i
$231$		0			0
$232$	−3.86087	+	2.22744i	−0.253478	+	0.146239i
$233$		−	2.68586i		−	0.175956i	−0.996122	−	0.0879782i	$-0.971959\pi$
$233$		−	2.68586i		−	0.175956i	0.996122	−	0.0879782i	$-0.0280406\pi$
$234$		0			0
$235$	−4.52818			−0.295386
$236$	−8.67887	−	1.53221i	−0.564946	−	0.0997386i
$237$		0			0
$238$	2.13036	+	2.53941i	0.138090	+	0.164605i
$239$	3.96640			0.256565			0.128283	−	0.991738i	$-0.459054\pi$
$239$	3.96640			0.256565			0.128283	+	0.991738i	$0.459054\pi$
$240$		0			0
$241$	17.4310			1.12283			0.561414	−	0.827535i	$-0.310258\pi$
$241$	17.4310			1.12283			0.561414	+	0.827535i	$0.310258\pi$
$242$	−3.71224	−	4.42503i	−0.238632	−	0.284452i
$243$		0			0
$244$	18.9008	+	3.33684i	1.21000	+	0.213619i
$245$	−0.863507			−0.0551675
$246$		0			0
$247$			4.17449i			0.265616i
$248$	8.90213	+	15.4303i	0.565286	+	0.979822i
$249$		0			0
$250$	7.26340	+	8.65804i	0.459378	+	0.547583i
$251$		−	19.8413i		−	1.25237i	−0.779673	−	0.626187i	$-0.784615\pi$
$251$		−	19.8413i		−	1.25237i	0.779673	−	0.626187i	$-0.215385\pi$
$252$		0			0
$253$		−	16.3954i		−	1.03077i
$254$	9.20629	−	7.72334i	0.577654	−	0.484605i
$255$		0			0
$256$	12.2480	+	10.2950i	0.765500	+	0.643436i
$257$		−	23.6701i		−	1.47650i	−0.674525	−	0.738252i	$-0.735652\pi$
$257$		−	23.6701i		−	1.47650i	0.674525	−	0.738252i	$-0.264348\pi$
$258$		0			0
$259$	−5.18085			−0.321923
$260$	1.73313	+	0.305976i	0.107484	+	0.0189758i
$261$		0			0
$262$	−6.41335	+	5.38028i	−0.396218	+	0.332395i
$263$	30.1325			1.85805			0.929025	−	0.370017i	$-0.120648\pi$
$263$	30.1325			1.85805			0.929025	+	0.370017i	$0.120648\pi$
$264$		0			0
$265$	9.10801			0.559501
$266$	4.43824	−	3.72332i	0.272126	−	0.228292i
$267$		0			0
$268$	4.41038	−	24.9816i	0.269407	−	1.52599i
$269$	3.73011			0.227429			0.113714	−	0.993513i	$-0.463725\pi$
$269$	3.73011			0.227429			0.113714	+	0.993513i	$0.463725\pi$
$270$		0			0
$271$		−	7.25451i		−	0.440680i	−0.975423	−	0.220340i	$-0.929283\pi$
$271$		−	7.25451i		−	0.440680i	0.975423	−	0.220340i	$-0.0707167\pi$
$272$	−3.21027	+	8.80853i	−0.194651	+	0.534095i
$273$		0			0
$274$	−0.124726	+	0.104635i	−0.00753496	+	0.00632122i
$275$			11.1880i			0.674665i
$276$		0			0
$277$			3.00503i			0.180555i	0.995917	+	0.0902774i	$0.0287754\pi$
$277$			3.00503i			0.180555i	−0.995917	+	0.0902774i	$0.971225\pi$
$278$	8.23102	+	9.81146i	0.493664	+	0.588452i
$279$		0			0
$280$	−1.22051	−	2.11554i	−0.0729395	−	0.126428i
$281$			7.67039i			0.457577i	0.973476	+	0.228789i	$0.0734764\pi$
$281$			7.67039i			0.457577i	−0.973476	+	0.228789i	$0.926524\pi$
$282$		0			0
$283$	−17.3124			−1.02912			−0.514558	−	0.857455i	$-0.672044\pi$
$283$	−17.3124			−1.02912			−0.514558	+	0.857455i	$0.672044\pi$
$284$	0.733754	−	4.15618i	0.0435403	−	0.246624i
$285$		0			0
$286$	2.43584	+	2.90354i	0.144034	+	0.171690i
$287$	−10.1388			−0.598475
$288$		0			0
$289$	11.5065			0.676853
$290$	1.23687	+	1.47436i	0.0726314	+	0.0865774i
$291$		0			0
$292$	2.87803	−	16.3019i	0.168424	−	0.953999i
$293$	−22.9400			−1.34017			−0.670084	−	0.742286i	$-0.733742\pi$
$293$	−22.9400			−1.34017			−0.670084	+	0.742286i	$0.733742\pi$
$294$		0			0
$295$			3.80508i			0.221540i
$296$	−7.32280	−	12.6928i	−0.425629	−	0.737752i
$297$		0			0
$298$	6.87231	+	8.19186i	0.398102	+	0.474542i
$299$		−	6.35333i		−	0.367423i
$300$		0			0
$301$			0.496156i			0.0285979i
$302$	11.9476	−	10.0231i	0.687510	−	0.576765i
$303$		0			0
$304$	15.3951	+	5.61073i	0.882968	+	0.321798i
$305$		−	8.28668i		−	0.474494i
$306$		0			0
$307$	1.46235			0.0834608			0.0417304	−	0.999129i	$-0.486713\pi$
$307$	1.46235			0.0834608			0.0417304	+	0.999129i	$0.486713\pi$
$308$	0.914412	−	5.17948i	0.0521035	−	0.295128i
$309$		0			0
$310$	5.89239	−	4.94324i	0.334665	−	0.280757i
$311$	5.83176			0.330689			0.165344	−	0.986236i	$-0.447126\pi$
$311$	5.83176			0.330689			0.165344	+	0.986236i	$0.447126\pi$
$312$		0			0
$313$	30.4020			1.71842			0.859211	−	0.511621i	$-0.170955\pi$
$313$	30.4020			1.71842			0.859211	+	0.511621i	$0.170955\pi$
$314$	−7.47725	+	6.27281i	−0.421966	+	0.353995i
$315$		0			0
$316$	18.5969	+	3.28320i	1.04616	+	0.184695i
$317$	−8.85186			−0.497170			−0.248585	−	0.968610i	$-0.579965\pi$
$317$	−8.85186			−0.497170			−0.248585	+	0.968610i	$0.579965\pi$
$318$		0			0
$319$			4.14429i			0.232036i
$320$	3.45783	−	5.98036i	0.193299	−	0.334312i
$321$		0			0
$322$	−6.75475	+	5.66669i	−0.376427	+	0.315792i
$323$			9.60124i			0.534228i
$324$		0			0
$325$			4.33544i			0.240487i
$326$	12.7336	+	15.1785i	0.705246	+	0.840660i
$327$		0			0
$328$	−14.3306	−	24.8395i	−0.791273	−	1.37153i
$329$			5.24394i			0.289108i
$330$		0			0
$331$	27.0721			1.48802			0.744010	−	0.668169i	$-0.232922\pi$
$331$	27.0721			1.48802			0.744010	+	0.668169i	$0.232922\pi$
$332$	13.0502	+	2.30395i	0.716222	+	0.126446i
$333$		0			0
$334$	5.42745	+	6.46957i	0.296977	+	0.353999i
$335$	−10.9527			−0.598409
$336$		0			0
$337$	−21.8651			−1.19107			−0.595533	−	0.803331i	$-0.703059\pi$
$337$	−21.8651			−1.19107			−0.595533	+	0.803331i	$0.703059\pi$
$338$	−10.8721	−	12.9597i	−0.591365	−	0.704913i
$339$		0			0
$340$	3.98617	+	0.703740i	0.216180	+	0.0381656i
$341$	16.5630			0.896936
$342$		0			0
$343$			1.00000i			0.0539949i
$344$	−1.21555	+	0.701284i	−0.0655381	+	0.0378107i
$345$		0			0
$346$	−3.06908	−	3.65837i	−0.164995	−	0.196675i
$347$			16.3033i			0.875206i	0.899168	+	0.437603i	$0.144172\pi$
$347$			16.3033i			0.875206i	−0.899168	+	0.437603i	$0.855828\pi$
$348$		0			0
$349$		−	10.3171i		−	0.552260i	−0.961120	−	0.276130i	$-0.910948\pi$
$349$		−	10.3171i		−	0.552260i	0.961120	−	0.276130i	$-0.0890521\pi$
$350$	4.60937	−	3.86689i	0.246381	−	0.206694i
$351$		0			0
$352$	13.9819	−	5.08060i	0.745236	−	0.270797i
$353$			1.62441i			0.0864586i	0.999065	+	0.0432293i	$0.0137646\pi$
$353$			1.62441i			0.0864586i	−0.999065	+	0.0432293i	$0.986235\pi$
$354$		0			0
$355$	−1.82220			−0.0967121
$356$	20.1979	+	3.56585i	1.07049	+	0.188990i
$357$		0			0
$358$	−12.3406	+	10.3527i	−0.652219	+	0.547159i
$359$	26.5784			1.40275			0.701376	−	0.712791i	$-0.252569\pi$
$359$	26.5784			1.40275			0.701376	+	0.712791i	$0.252569\pi$
$360$		0			0
$361$	−2.21945			−0.116813
$362$	−12.4070	+	10.4084i	−0.652096	+	0.547056i
$363$		0			0
$364$	0.354341	−	2.00708i	0.0185725	−	0.105200i
$365$	−7.14727			−0.374105
$366$		0			0
$367$			14.5506i			0.759534i	0.925082	+	0.379767i	$0.123996\pi$
$367$			14.5506i			0.759534i	−0.925082	+	0.379767i	$0.876004\pi$
$368$	−23.4304	−	8.53922i	−1.22140	−	0.445138i
$369$		0			0
$370$	−4.84702	+	4.06626i	−0.251985	+	0.211395i
$371$		−	10.5477i		−	0.547609i
$372$		0			0
$373$		−	38.2468i		−	1.98034i	−0.139856	−	0.990172i	$-0.544664\pi$
$373$		−	38.2468i		−	1.98034i	0.139856	−	0.990172i	$-0.455336\pi$
$374$	5.60238	+	6.67810i	0.289692	+	0.345316i
$375$		0			0
$376$	−12.8473	+	7.41197i	−0.662550	+	0.382243i
$377$			1.60594i			0.0827102i
$378$		0			0
$379$	28.9922			1.48923			0.744614	−	0.667495i	$-0.232633\pi$
$379$	28.9922			1.48923			0.744614	+	0.667495i	$0.232633\pi$
$380$	1.22996	−	6.96682i	0.0630956	−	0.357390i
$381$		0			0
$382$	11.0060	+	13.1192i	0.563114	+	0.671237i
$383$	33.7127			1.72264			0.861320	−	0.508063i	$-0.169638\pi$
$383$	33.7127			1.72264			0.861320	+	0.508063i	$0.169638\pi$
$384$		0			0
$385$	−2.27084			−0.115733
$386$	−1.53651	−	1.83154i	−0.0782065	−	0.0932230i
$387$		0			0
$388$	−5.25763	+	29.7806i	−0.266916	+	1.51188i
$389$	32.7096			1.65844			0.829221	−	0.558922i	$-0.188785\pi$
$389$	32.7096			1.65844			0.829221	+	0.558922i	$0.188785\pi$
$390$		0			0
$391$		−	14.6126i		−	0.738988i
$392$	−2.44994	+	1.41344i	−0.123741	+	0.0713893i
$393$		0			0
$394$	−6.71539	−	8.00481i	−0.338316	−	0.403276i
$395$		−	8.15347i		−	0.410245i
$396$		0			0
$397$			16.5435i			0.830292i	0.909755	+	0.415146i	$0.136270\pi$
$397$			16.5435i			0.830292i	−0.909755	+	0.415146i	$0.863730\pi$
$398$	22.8877	−	19.2009i	1.14726	−	0.962454i
$399$		0			0
$400$	15.9887	+	5.82707i	0.799434	+	0.291354i
$401$		−	0.431420i		−	0.0215441i	−0.999942	−	0.0107720i	$-0.996571\pi$
$401$		−	0.431420i		−	0.0215441i	0.999942	−	0.0107720i	$-0.00342892\pi$
$402$		0			0
$403$	6.41827			0.319717
$404$	2.63896	−	14.9478i	0.131293	−	0.743681i
$405$		0			0
$406$	1.70741	−	1.43238i	0.0847373	−	0.0710877i
$407$	−13.6245			−0.675343
$408$		0			0
$409$	−7.04622			−0.348413			−0.174207	−	0.984709i	$-0.555736\pi$
$409$	−7.04622			−0.348413			−0.174207	+	0.984709i	$0.555736\pi$
$410$	−9.48551	+	7.95758i	−0.468456	+	0.392997i
$411$		0			0
$412$	−14.4501	−	2.55109i	−0.711905	−	0.125683i
$413$	4.40654			0.216832
$414$		0			0
$415$		−	5.72160i		−	0.280862i
$416$	5.41807	−	1.96877i	0.265643	−	0.0965268i
$417$		0			0
$418$	11.6716	−	9.79155i	0.570878	−	0.478920i
$419$			6.00287i			0.293259i	0.989191	+	0.146630i	$0.0468426\pi$
$419$			6.00287i			0.293259i	−0.989191	+	0.146630i	$0.953157\pi$
$420$		0			0
$421$		−	30.8156i		−	1.50186i	−0.660381	−	0.750931i	$-0.729605\pi$
$421$		−	30.8156i		−	1.50186i	0.660381	−	0.750931i	$-0.270395\pi$
$422$	−4.56610	−	5.44284i	−0.222275	−	0.264953i
$423$		0			0
$424$	25.8412	−	14.9085i	1.25496	−	0.724020i
$425$			9.97145i			0.483686i
$426$		0			0
$427$	−9.59653			−0.464409
$428$	37.6295	+	6.64330i	1.81889	+	0.321116i
$429$		0			0
$430$	0.389414	+	0.464186i	0.0187792	+	0.0223850i
$431$	4.16376			0.200561			0.100281	−	0.994959i	$-0.468026\pi$
$431$	4.16376			0.200561			0.100281	+	0.994959i	$0.468026\pi$
$432$		0			0
$433$	18.1624			0.872827			0.436414	−	0.899746i	$-0.356248\pi$
$433$	18.1624			0.872827			0.436414	+	0.899746i	$0.356248\pi$
$434$	−5.72461	−	6.82379i	−0.274790	−	0.327552i
$435$		0			0
$436$	10.7634	+	1.90023i	0.515474	+	0.0910046i
$437$	−25.5390			−1.22170
$438$		0			0
$439$			20.8931i			0.997173i	0.866840	+	0.498586i	$0.166147\pi$
$439$			20.8931i			0.997173i	−0.866840	+	0.498586i	$0.833853\pi$
$440$	−3.20969	−	5.56342i	−0.153016	−	0.265226i
$441$		0			0
$442$	2.17096	+	2.58781i	0.103262	+	0.123089i
$443$		−	2.40982i		−	0.114494i	−0.998360	−	0.0572469i	$-0.981768\pi$
$443$		−	2.40982i		−	0.114494i	0.998360	−	0.0572469i	$-0.0182322\pi$
$444$		0			0
$445$		−	8.85539i		−	0.419786i
$446$	6.90502	−	5.79275i	0.326962	−	0.274295i
$447$		0			0
$448$	−6.92566	−	4.00440i	−0.327207	−	0.189190i
$449$			37.5452i			1.77187i	0.463810	+	0.885935i	$0.346482\pi$
$449$			37.5452i			1.77187i	−0.463810	+	0.885935i	$0.653518\pi$
$450$		0			0
$451$	−26.6629			−1.25551
$452$	−10.3500	−	1.82724i	−0.486822	−	0.0859462i
$453$		0			0
$454$	8.53739	−	7.16218i	0.400680	−	0.336138i
$455$	−0.879966			−0.0412534
$456$		0			0
$457$	41.1990			1.92721			0.963603	−	0.267336i	$-0.0861433\pi$
$457$	41.1990			1.92721			0.963603	+	0.267336i	$0.0861433\pi$
$458$	23.5219	−	19.7330i	1.09911	−	0.922062i
$459$		0			0
$460$	−1.87193	+	10.6031i	−0.0872791	+	0.494372i
$461$	22.9421			1.06852			0.534260	−	0.845320i	$-0.320590\pi$
$461$	22.9421			1.06852			0.534260	+	0.845320i	$0.320590\pi$
$462$		0			0
$463$			28.5381i			1.32628i	0.748497	+	0.663138i	$0.230776\pi$
$463$			28.5381i			1.32628i	−0.748497	+	0.663138i	$0.769224\pi$
$464$	5.92255	+	2.15847i	0.274947	+	0.100205i
$465$		0			0
$466$	−2.90998	+	2.44124i	−0.134802	+	0.113088i
$467$		−	3.49880i		−	0.161905i	−0.996718	−	0.0809525i	$-0.974204\pi$
$467$		−	3.49880i		−	0.161905i	0.996718	−	0.0809525i	$-0.0257962\pi$
$468$		0			0
$469$			12.6840i			0.585691i
$470$	4.11577	+	4.90604i	0.189846	+	0.226299i
$471$		0			0
$472$	6.22836	+	10.7958i	0.286684	+	0.496915i
$473$			1.30478i			0.0599940i
$474$		0			0
$475$	17.4276			0.799632
$476$	0.814978	−	4.61625i	0.0373545	−	0.211586i
$477$		0			0
$478$	−3.60516	−	4.29738i	−0.164896	−	0.196558i
$479$	−31.3664			−1.43317			−0.716583	−	0.697502i	$-0.754295\pi$
$479$	−31.3664			−1.43317			−0.716583	+	0.697502i	$0.754295\pi$
$480$		0			0
$481$	−5.27960			−0.240729
$482$	−15.8434	−	18.8855i	−0.721648	−	0.860212i
$483$		0			0
$484$	−1.42014	+	8.04404i	−0.0645517	+	0.365638i
$485$	13.0567			0.592876
$486$		0			0
$487$			39.7445i			1.80100i	0.434861	+	0.900498i	$0.356798\pi$
$487$			39.7445i			1.80100i	−0.434861	+	0.900498i	$0.643202\pi$
$488$	−13.5641	−	23.5109i	−0.614017	−	1.06429i
$489$		0			0
$490$	0.784863	+	0.935564i	0.0354565	+	0.0422645i
$491$			6.77799i			0.305886i	0.988235	+	0.152943i	$0.0488751\pi$
$491$			6.77799i			0.305886i	−0.988235	+	0.152943i	$0.951125\pi$
$492$		0			0
$493$			3.69364i			0.166353i
$494$	4.52283	−	3.79429i	0.203492	−	0.170713i
$495$		0			0
$496$	8.62650	−	23.6699i	0.387341	−	1.06281i
$497$			2.11023i			0.0946566i
$498$		0			0
$499$	−8.19185			−0.366718			−0.183359	−	0.983046i	$-0.558697\pi$
$499$	−8.19185			−0.366718			−0.183359	+	0.983046i	$0.558697\pi$
$500$	2.77865	−	15.7390i	0.124265	−	0.703870i
$501$		0			0
$502$	−21.4970	+	18.0343i	−0.959460	+	0.804909i
$503$	−37.5183			−1.67286			−0.836429	−	0.548075i	$-0.815361\pi$
$503$	−37.5183			−1.67286			−0.836429	+	0.548075i	$0.815361\pi$
$504$		0			0
$505$	−6.55357			−0.291630
$506$	−17.7636	+	14.9022i	−0.789686	+	0.662483i
$507$		0			0
$508$	−16.7356	−	2.95460i	−0.742524	−	0.131089i
$509$	−6.84007			−0.303181			−0.151590	−	0.988443i	$-0.548439\pi$
$509$	−6.84007			−0.303181			−0.151590	+	0.988443i	$0.548439\pi$
$510$		0			0
$511$			8.27702i			0.366154i
$512$	0.0215603	−	22.6274i	0.000952839	−	1.00000i
$513$		0			0
$514$	−25.6453	+	21.5144i	−1.13117	+	0.948958i
$515$			6.33536i			0.279169i
$516$		0			0
$517$			13.7904i			0.606503i
$518$	4.70900	+	5.61318i	0.206902	+	0.246629i
$519$		0			0
$520$	−1.24378	−	2.15586i	−0.0545432	−	0.0945409i
$521$			20.2860i			0.888746i	0.895842	+	0.444373i	$0.146574\pi$
$521$			20.2860i			0.888746i	−0.895842	+	0.444373i	$0.853426\pi$
$522$		0			0
$523$	−36.4847			−1.59537			−0.797683	−	0.603077i	$-0.793941\pi$
$523$	−36.4847			−1.59537			−0.797683	+	0.603077i	$0.793941\pi$
$524$	11.6585	+	2.05825i	0.509304	+	0.0899152i
$525$		0			0
$526$	−27.3882	−	32.6470i	−1.19418	−	1.42348i
$527$	14.7619			0.643038
$528$		0			0
$529$	15.8690			0.689956
$530$	−8.27849	−	9.86805i	−0.359595	−	0.428641i
$531$		0			0
$532$	−8.06805	−	1.42438i	−0.349794	−	0.0617545i
$533$	−10.3321			−0.447531
$534$		0			0
$535$		−	16.4979i		−	0.713267i
$536$	−31.0749	+	17.9280i	−1.34223	+	0.774370i
$537$		0			0
$538$	−3.39038	−	4.04137i	−0.146170	−	0.174236i
$539$			2.62979i			0.113273i
$540$		0			0
$541$			16.1841i			0.695810i	0.937530	+	0.347905i	$0.113107\pi$
$541$			16.1841i			0.695810i	−0.937530	+	0.347905i	$0.886893\pi$
$542$	−7.85988	+	6.59380i	−0.337611	+	0.283228i
$543$		0			0
$544$	12.4615	−	4.52813i	0.534281	−	0.194142i
$545$		−	4.71901i		−	0.202140i
$546$		0			0
$547$	7.35520			0.314486			0.157243	−	0.987560i	$-0.449739\pi$
$547$	7.35520			0.314486			0.157243	+	0.987560i	$0.449739\pi$
$548$	0.226733	+	0.0400286i	0.00968554	+	0.00170994i
$549$		0			0
$550$	12.1217	−	10.1691i	0.516869	−	0.433611i
$551$	6.45555			0.275015
$552$		0			0
$553$	−9.44227			−0.401526
$554$	3.25579	−	2.73134i	0.138325	−	0.116044i
$555$		0			0
$556$	3.14882	−	17.8358i	0.133540	−	0.756404i
$557$	36.2146			1.53446			0.767231	−	0.641371i	$-0.221634\pi$
$557$	36.2146			1.53446			0.767231	+	0.641371i	$0.221634\pi$
$558$		0			0
$559$			0.505613i			0.0213851i
$560$	−1.18272	+	3.24523i	−0.0499791	+	0.137136i
$561$		0			0
$562$	8.31046	−	6.97180i	0.350555	−	0.294088i
$563$			39.2015i			1.65215i	0.563562	+	0.826074i	$0.309430\pi$
$563$			39.2015i			1.65215i	−0.563562	+	0.826074i	$0.690570\pi$
$564$		0			0
$565$			4.53775i			0.190905i
$566$	15.7357	+	18.7571i	0.661420	+	0.788419i
$567$		0			0
$568$	−5.16992	+	2.98267i	−0.216925	+	0.125150i
$569$		−	29.8748i		−	1.25242i	−0.779655	−	0.626209i	$-0.784606\pi$
$569$		−	29.8748i		−	1.25242i	0.779655	−	0.626209i	$-0.215394\pi$
$570$		0			0
$571$	4.67642			0.195702			0.0978511	−	0.995201i	$-0.468803\pi$
$571$	4.67642			0.195702			0.0978511	+	0.995201i	$0.468803\pi$
$572$	0.931841	−	5.27820i	0.0389622	−	0.220693i
$573$		0			0
$574$	9.21541	+	10.9849i	0.384644	+	0.458499i
$575$	−26.5238			−1.10612
$576$		0			0
$577$	−39.3888			−1.63978			−0.819889	−	0.572522i	$-0.805965\pi$
$577$	−39.3888			−1.63978			−0.819889	+	0.572522i	$0.805965\pi$
$578$	−10.4585	−	12.4667i	−0.435018	−	0.518546i
$579$		0			0
$580$	0.473170	−	2.68016i	0.0196473	−	0.111288i
$581$	−6.62600			−0.274893
$582$		0			0
$583$		−	27.7382i		−	1.14880i
$584$	−20.2782	+	11.6990i	−0.839118	+	0.484110i
$585$		0			0
$586$	20.8507	+	24.8542i	0.861334	+	1.02672i
$587$			41.1486i			1.69838i	0.528085	+	0.849191i	$0.322910\pi$
$587$			41.1486i			1.69838i	−0.528085	+	0.849191i	$0.677090\pi$
$588$		0			0
$589$		−	25.8001i		−	1.06307i
$590$	4.12260	−	3.45853i	0.169725	−	0.142385i
$591$		0			0
$592$	−7.09607	+	19.4706i	−0.291647	+	0.800238i
$593$			30.7274i			1.26182i	0.775854	+	0.630912i	$0.217319\pi$
$593$			30.7274i			1.26182i	−0.775854	+	0.630912i	$0.782681\pi$
$594$		0			0
$595$	−2.02391			−0.0829721
$596$	2.62903	−	14.8916i	0.107689	−	0.609982i
$597$		0			0
$598$	−6.88350	+	5.77470i	−0.281487	+	0.236145i
$599$	44.7307			1.82765			0.913824	−	0.406110i	$-0.133115\pi$
$599$	44.7307			1.82765			0.913824	+	0.406110i	$0.133115\pi$
$600$		0			0
$601$	−20.8116			−0.848923			−0.424461	−	0.905446i	$-0.639537\pi$
$601$	−20.8116			−0.848923			−0.424461	+	0.905446i	$0.639537\pi$
$602$	0.537558	−	0.450968i	0.0219092	−	0.0183801i
$603$		0			0
$604$	−21.7190	−	3.83439i	−0.883734	−	0.156019i
$605$	3.52675			0.143383
$606$		0			0
$607$			21.1941i			0.860243i	0.902771	+	0.430121i	$0.141529\pi$
$607$			21.1941i			0.860243i	−0.902771	+	0.430121i	$0.858471\pi$
$608$	−7.91403	−	21.7795i	−0.320956	−	0.883275i
$609$		0			0
$610$	−8.97817	+	7.53196i	−0.363516	+	0.304960i
$611$			5.34389i			0.216191i
$612$		0			0
$613$			3.95265i			0.159646i	0.996809	+	0.0798229i	$0.0254355\pi$
$613$			3.95265i			0.159646i	−0.996809	+	0.0798229i	$0.974565\pi$
$614$	−1.32917	−	1.58438i	−0.0536408	−	0.0639404i
$615$		0			0
$616$	−6.44282	+	3.71704i	−0.259589	+	0.149764i
$617$		−	17.1751i		−	0.691445i	−0.938337	−	0.345722i	$-0.887634\pi$
$617$		−	17.1751i		−	0.691445i	0.938337	−	0.345722i	$-0.112366\pi$
$618$		0			0
$619$	22.4666			0.903007			0.451504	−	0.892269i	$-0.350888\pi$
$619$	22.4666			0.903007			0.451504	+	0.892269i	$0.350888\pi$
$620$	−10.7115	−	1.89106i	−0.430183	−	0.0759468i
$621$		0			0
$622$	−5.30063	−	6.31840i	−0.212536	−	0.253345i
$623$	−10.2551			−0.410864
$624$		0			0
$625$	14.3713			0.574852
$626$	−27.6331	−	32.9389i	−1.10444	−	1.31650i
$627$		0			0
$628$	13.5925	+	2.39969i	0.542400	+	0.0957582i
$629$	−12.1430			−0.484173
$630$		0			0
$631$		−	19.1896i		−	0.763926i	−0.924178	−	0.381963i	$-0.875248\pi$
$631$		−	19.1896i		−	0.763926i	0.924178	−	0.381963i	$-0.124752\pi$
$632$	−13.3460	−	23.1330i	−0.530877	−	0.920180i
$633$		0			0
$634$	8.04567	+	9.59051i	0.319534	+	0.380888i
$635$			7.33742i			0.291177i
$636$		0			0
$637$			1.01906i			0.0403766i
$638$	4.49012	−	3.76685i	0.177766	−	0.149131i
$639$		0			0
$640$	−9.62231	+	1.68932i	−0.380355	+	0.0667763i
$641$			15.7596i			0.622467i	0.950333	+	0.311234i	$0.100742\pi$
$641$			15.7596i			0.622467i	−0.950333	+	0.311234i	$0.899258\pi$
$642$		0			0
$643$	−47.6538			−1.87928			−0.939642	−	0.342160i	$-0.888842\pi$
$643$	−47.6538			−1.87928			−0.939642	+	0.342160i	$0.888842\pi$
$644$	12.2791	+	2.16782i	0.483865	+	0.0854240i
$645$		0			0
$646$	10.4024	−	8.72680i	0.409278	−	0.343352i
$647$	2.45095			0.0963567			0.0481783	−	0.998839i	$-0.484658\pi$
$647$	2.45095			0.0963567			0.0481783	+	0.998839i	$0.484658\pi$
$648$		0			0
$649$	11.5883			0.454879
$650$	4.69722	−	3.94059i	0.184240	−	0.154563i
$651$		0			0
$652$	4.87128	−	27.5923i	0.190774	−	1.08060i
$653$	26.8786			1.05184			0.525920	−	0.850534i	$-0.323721\pi$
$653$	26.8786			1.05184			0.525920	+	0.850534i	$0.323721\pi$
$654$		0			0
$655$		−	5.11144i		−	0.199721i
$656$	−13.8869	+	38.1036i	−0.542191	+	1.48770i
$657$		0			0
$658$	5.68153	−	4.76634i	0.221489	−	0.185811i
$659$		−	38.9485i		−	1.51722i	−0.651545	−	0.758610i	$-0.725879\pi$
$659$		−	38.9485i		−	1.51722i	0.651545	−	0.758610i	$-0.274121\pi$
$660$		0			0
$661$			5.36184i			0.208552i	0.994548	+	0.104276i	$0.0332525\pi$
$661$			5.36184i			0.208552i	−0.994548	+	0.104276i	$0.966748\pi$
$662$	−24.6065	−	29.3312i	−0.956360	−	1.13999i
$663$		0			0
$664$	−9.36543	−	16.2333i	−0.363449	−	0.629974i
$665$			3.53728i			0.137170i
$666$		0			0
$667$	−9.82498			−0.380425
$668$	2.07630	−	11.7607i	0.0803343	−	0.455035i
$669$		0			0
$670$	9.95517	+	11.8667i	0.384602	+	0.458449i
$671$	−25.2368			−0.974258
$672$		0			0
$673$	−36.5666			−1.40954			−0.704770	−	0.709436i	$-0.748950\pi$
$673$	−36.5666			−1.40954			−0.704770	+	0.709436i	$0.748950\pi$
$674$	19.8737	+	23.6896i	0.765506	+	0.912491i
$675$		0			0
$676$	−4.15918	+	23.5587i	−0.159968	+	0.906104i
$677$	−18.9463			−0.728166			−0.364083	−	0.931367i	$-0.618618\pi$
$677$	−18.9463			−0.728166			−0.364083	+	0.931367i	$0.618618\pi$
$678$		0			0
$679$		−	15.1206i		−	0.580275i
$680$	−2.86066	−	4.95845i	−0.109701	−	0.190148i
$681$		0			0
$682$	−15.0545	−	17.9451i	−0.576466	−	0.687154i
$683$			15.1090i			0.578130i	0.957309	+	0.289065i	$0.0933444\pi$
$683$			15.1090i			0.578130i	−0.957309	+	0.289065i	$0.906656\pi$
$684$		0			0
$685$		−	0.0994065i		−	0.00379813i
$686$	1.08345	−	0.908924i	0.0413662	−	0.0347029i
$687$		0			0
$688$	1.86465	+	0.679571i	0.0710890	+	0.0259084i
$689$		−	10.7487i		−	0.409494i
$690$		0			0
$691$	−12.9717			−0.493467			−0.246733	−	0.969083i	$-0.579357\pi$
$691$	−12.9717			−0.493467			−0.246733	+	0.969083i	$0.579357\pi$
$692$	−1.17409	+	6.65037i	−0.0446322	+	0.252809i
$693$		0			0
$694$	17.6637	−	14.8184i	0.670506	−	0.562501i
$695$	−7.81974			−0.296620
$696$		0			0
$697$	−23.7636			−0.900109
$698$	−11.1780	+	9.37744i	−0.423093	+	0.354941i
$699$		0			0
$700$	−8.37913	−	1.47930i	−0.316701	−	0.0559121i
$701$	9.31510			0.351826			0.175913	−	0.984406i	$-0.443712\pi$
$701$	9.31510			0.351826			0.175913	+	0.984406i	$0.443712\pi$
$702$		0			0
$703$			21.2229i			0.800436i
$704$	−18.2130	−	10.5307i	−0.686429	−	0.396892i
$705$		0			0
$706$	1.75996	−	1.47647i	0.0662370	−	0.0555675i
$707$			7.58948i			0.285432i
$708$		0			0
$709$			19.1984i			0.721012i	0.932757	+	0.360506i	$0.117396\pi$
$709$			19.1984i			0.721012i	−0.932757	+	0.360506i	$0.882604\pi$
$710$	1.65624	+	1.97425i	0.0621575	+	0.0740924i
$711$		0			0
$712$	−14.4950	−	25.1245i	−0.543223	−	0.941580i
$713$			39.2663i			1.47053i
$714$		0			0
$715$	−2.31412			−0.0865433
$716$	22.4333	+	3.96049i	0.838370	+	0.148010i
$717$		0			0
$718$	−24.1577	−	28.7962i	−0.901558	−	1.07467i
$719$	−2.53286			−0.0944596			−0.0472298	−	0.998884i	$-0.515039\pi$
$719$	−2.53286			−0.0944596			−0.0472298	+	0.998884i	$0.515039\pi$
$720$		0			0
$721$	7.33678			0.273236
$722$	2.01731	+	2.40466i	0.0750766	+	0.0894920i
$723$		0			0
$724$	22.5540	+	3.98180i	0.838213	+	0.147983i
$725$	6.70446			0.248997
$726$		0			0
$727$		−	38.2306i		−	1.41790i	−0.705261	−	0.708948i	$-0.749170\pi$
$727$		−	38.2306i		−	1.41790i	0.705261	−	0.708948i	$-0.250830\pi$
$728$	−2.49664	+	1.44038i	−0.0925315	+	0.0533839i
$729$		0			0
$730$	6.49633	+	7.74369i	0.240440	+	0.286607i
$731$			1.16290i			0.0430114i
$732$		0			0
$733$			20.4492i			0.755307i	0.925947	+	0.377654i	$0.123269\pi$
$733$			20.4492i			0.755307i	−0.925947	+	0.377654i	$0.876731\pi$
$734$	15.7648	−	13.2254i	0.581888	−	0.488157i
$735$		0			0
$736$	12.0447	+	33.1471i	0.443974	+	1.22182i
$737$			33.3561i			1.22869i
$738$		0			0
$739$	43.3758			1.59560			0.797802	−	0.602920i	$-0.205996\pi$
$739$	43.3758			1.59560			0.797802	+	0.602920i	$0.205996\pi$
$740$	8.81115	+	1.55557i	0.323904	+	0.0571838i
$741$		0			0
$742$	−11.4279	+	9.58705i	−0.419530	+	0.351952i
$743$	28.3974			1.04180			0.520900	−	0.853618i	$-0.325596\pi$
$743$	28.3974			1.04180			0.520900	+	0.853618i	$0.325596\pi$
$744$		0			0
$745$	−6.52891			−0.239201
$746$	−41.4384	+	34.7634i	−1.51717	+	1.27278i
$747$		0			0
$748$	2.14322	−	12.1398i	0.0783638	−	0.443874i
$749$	−19.1057			−0.698107
$750$		0			0
$751$		−	48.3659i		−	1.76490i	−0.470409	−	0.882448i	$-0.655894\pi$
$751$		−	48.3659i		−	1.76490i	0.470409	−	0.882448i	$-0.344106\pi$
$752$	19.7077	+	7.18248i	0.718667	+	0.261918i
$753$		0			0
$754$	1.73995	−	1.45968i	0.0633653	−	0.0531584i
$755$			9.52228i			0.346551i
$756$		0			0
$757$		−	38.1581i		−	1.38688i	−0.720515	−	0.693439i	$-0.756095\pi$
$757$		−	38.1581i		−	1.38688i	0.720515	−	0.693439i	$-0.243905\pi$
$758$	−26.3517	−	31.4115i	−0.957137	−	1.14092i
$759$		0			0
$760$	−8.66611	+	4.99971i	−0.314353	+	0.181359i
$761$			17.9144i			0.649396i	0.945818	+	0.324698i	$0.105263\pi$
$761$			17.9144i			0.649396i	−0.945818	+	0.324698i	$0.894737\pi$
$762$		0			0
$763$	−5.46494			−0.197844
$764$	4.21038	−	23.8487i	0.152326	−	0.862817i
$765$		0			0
$766$	−30.6423	−	36.5259i	−1.10715	−	1.31974i
$767$	4.49053			0.162144
$768$		0			0
$769$	11.7804			0.424811			0.212405	−	0.977182i	$-0.431870\pi$
$769$	11.7804			0.424811			0.212405	+	0.977182i	$0.431870\pi$
$770$	2.06402	+	2.46034i	0.0743822	+	0.0886643i
$771$		0			0
$772$	−0.587801	+	3.32946i	−0.0211554	+	0.119830i
$773$	−38.7391			−1.39335			−0.696675	−	0.717387i	$-0.745338\pi$
$773$	−38.7391			−1.39335			−0.696675	+	0.717387i	$0.745338\pi$
$774$		0			0
$775$		−	26.7949i		−	0.962500i
$776$	37.0445	−	21.3720i	1.32982	−	0.767209i
$777$		0			0
$778$	−29.7305	−	35.4391i	−1.06589	−	1.27055i
$779$			41.5327i			1.48806i
$780$		0			0
$781$			5.54945i			0.198575i
$782$	−15.8319	+	13.2817i	−0.566148	+	0.474953i
$783$		0			0
$784$	3.75819	+	1.36967i	0.134221	+	0.0489169i
$785$		−	5.95937i		−	0.212699i
$786$		0			0
$787$	30.0068			1.06963			0.534814	−	0.844970i	$-0.320382\pi$
$787$	30.0068			1.06963			0.534814	+	0.844970i	$0.320382\pi$
$788$	−2.56900	+	14.5515i	−0.0915170	+	0.518377i
$789$		0			0
$790$	−8.83385	+	7.41088i	−0.314294	+	0.263667i
$791$	5.25502			0.186847
$792$		0			0
$793$	−9.77945			−0.347278
$794$	17.9239	−	15.0367i	0.636097	−	0.533634i
$795$		0			0
$796$	−41.6063	−	7.34540i	−1.47470	−	0.260351i
$797$	−46.9406			−1.66272			−0.831361	−	0.555733i	$-0.812438\pi$
$797$	−46.9406			−1.66272			−0.831361	+	0.555733i	$0.812438\pi$
$798$		0			0
$799$			12.2909i			0.434819i
$800$	−8.21918	−	22.6192i	−0.290592	−	0.799711i
$801$		0			0
$802$	−0.467421	+	0.392128i	−0.0165052	+	0.0138465i
$803$			21.7668i			0.768134i
$804$		0			0
$805$		−	5.38354i		−	0.189745i
$806$	−5.83372	−	6.95385i	−0.205484	−	0.244939i
$807$		0			0
$808$	−18.5938	+	10.7272i	−0.654126	+	0.377383i
$809$		−	0.613418i		−	0.0215666i	−0.999942	−	0.0107833i	$-0.996567\pi$
$809$		−	0.613418i		−	0.0215666i	0.999942	−	0.0107833i	$-0.00343250\pi$
$810$		0			0
$811$	−7.41924			−0.260525			−0.130262	−	0.991480i	$-0.541582\pi$
$811$	−7.41924			−0.260525			−0.130262	+	0.991480i	$0.541582\pi$
$812$	−3.10381	−	0.547963i	−0.108922	−	0.0192297i
$813$		0			0
$814$	12.3837	+	14.7615i	0.434048	+	0.517389i
$815$	−12.0973			−0.423749
$816$		0			0
$817$	2.03246			0.0711066
$818$	6.40448	+	7.63420i	0.223927	+	0.266924i
$819$		0			0
$820$	17.2432	+	3.04421i	0.602160	+	0.106308i
$821$	37.6799			1.31504			0.657519	−	0.753438i	$-0.271606\pi$
$821$	37.6799			1.31504			0.657519	+	0.753438i	$0.271606\pi$
$822$		0			0
$823$		−	11.9871i		−	0.417844i	−0.977932	−	0.208922i	$-0.933005\pi$
$823$		−	11.9871i		−	0.417844i	0.977932	−	0.208922i	$-0.0669955\pi$
$824$	10.3701	+	17.9746i	0.361258	+	0.626177i
$825$		0			0
$826$	−4.00521	−	4.77425i	−0.139359	−	0.166117i
$827$			36.1978i			1.25872i	0.777113	+	0.629361i	$0.216683\pi$
$827$			36.1978i			1.25872i	−0.777113	+	0.629361i	$0.783317\pi$
$828$		0			0
$829$			23.3923i			0.812449i	0.913773	+	0.406225i	$0.133155\pi$
$829$			23.3923i			0.812449i	−0.913773	+	0.406225i	$0.866845\pi$
$830$	−6.19905	+	5.20050i	−0.215172	+	0.180512i
$831$		0			0
$832$	−7.05767	−	4.08072i	−0.244681	−	0.141474i
$833$			2.34382i			0.0812086i
$834$		0			0
$835$	−5.15625			−0.178439
$836$	−21.2172	−	3.74581i	−0.733814	−	0.129551i
$837$		0			0
$838$	6.50379	−	5.45616i	0.224670	−	0.188480i
$839$	54.5591			1.88359			0.941794	−	0.336190i	$-0.109139\pi$
$839$	54.5591			1.88359			0.941794	+	0.336190i	$0.109139\pi$
$840$		0			0
$841$	−26.5165			−0.914363
$842$	−33.3871	+	28.0091i	−1.15059	+	0.965256i
$843$		0			0
$844$	−1.74679	+	9.89426i	−0.0601268	+	0.340575i
$845$	10.3289			0.355324
$846$		0			0
$847$		−	4.08422i		−	0.140335i
$848$	−39.6402	−	14.4469i	−1.36125	−	0.496108i
$849$		0			0
$850$	10.8035	−	9.06329i	0.370558	−	0.310868i
$851$		−	32.3000i		−	1.10723i
$852$		0			0
$853$			8.05394i			0.275762i	0.990449	+	0.137881i	$0.0440291\pi$
$853$			8.05394i			0.275762i	−0.990449	+	0.137881i	$0.955971\pi$
$854$	8.72252	+	10.3973i	0.298479	+	0.355789i
$855$		0			0
$856$	−27.0047	−	46.8078i	−0.923000	−	1.59986i
$857$			7.83566i			0.267661i	0.991004	+	0.133830i	$0.0427278\pi$
$857$			7.83566i			0.267661i	−0.991004	+	0.133830i	$0.957272\pi$
$858$		0			0
$859$	−16.4766			−0.562173			−0.281087	−	0.959682i	$-0.590695\pi$
$859$	−16.4766			−0.562173			−0.281087	+	0.959682i	$0.590695\pi$
$860$	0.148972	−	0.843819i	0.00507991	−	0.0287740i
$861$		0			0
$862$	−3.78454	−	4.51121i	−0.128902	−	0.153652i
$863$	−36.1099			−1.22920			−0.614598	−	0.788841i	$-0.710682\pi$
$863$	−36.1099			−1.22920			−0.614598	+	0.788841i	$0.710682\pi$
$864$		0			0
$865$	2.91572			0.0991376
$866$	−16.5082	−	19.6779i	−0.560972	−	0.668684i
$867$		0			0
$868$	−2.18998	+	12.4046i	−0.0743326	+	0.421040i
$869$	−24.8312			−0.842339
$870$		0			0
$871$			12.9257i			0.437971i
$872$	−7.72434	−	13.3888i	−0.261579	−	0.453401i
$873$		0			0
$874$	23.2131	+	27.6702i	0.785193	+	0.935958i
$875$			7.99120i			0.270152i
$876$		0			0
$877$		−	30.7080i		−	1.03694i	−0.855097	−	0.518468i	$-0.826503\pi$
$877$		−	30.7080i		−	1.03694i	0.855097	−	0.518468i	$-0.173497\pi$
$878$	22.6365	−	18.9902i	0.763946	−	0.640889i
$879$		0			0
$880$	−3.11031	+	8.53425i	−0.104848	+	0.287690i
$881$		−	8.54573i		−	0.287913i	−0.989584	−	0.143956i	$-0.954017\pi$
$881$		−	8.54573i		−	0.287913i	0.989584	−	0.143956i	$-0.0459825\pi$
$882$		0			0
$883$	2.67385			0.0899823			0.0449912	−	0.998987i	$-0.485674\pi$
$883$	2.67385			0.0899823			0.0449912	+	0.998987i	$0.485674\pi$
$884$	0.830512	−	4.70424i	0.0279331	−	0.158221i
$885$		0			0
$886$	−2.61091	+	2.19034i	−0.0877152	+	0.0735859i
$887$	25.4850			0.855704			0.427852	−	0.903849i	$-0.359270\pi$
$887$	25.4850			0.855704			0.427852	+	0.903849i	$0.359270\pi$
$888$		0			0
$889$	8.49723			0.284988
$890$	−9.59435	+	8.04888i	−0.321603	+	0.269799i
$891$		0			0
$892$	−12.5523	−	2.21605i	−0.420281	−	0.0741987i
$893$	21.4813			0.718844
$894$		0			0
$895$		−	9.83543i		−	0.328762i
$896$	1.95635	+	11.1433i	0.0653570	+	0.372271i
$897$		0			0
$898$	40.6783	−	34.1258i	1.35745	−	1.13879i
$899$		−	9.92539i		−	0.331030i
$900$		0			0
$901$		−	24.7219i		−	0.823606i
$902$	24.2346	+	28.8879i	0.806923	+	0.961861i
$903$		0			0
$904$	7.42763	+	12.8745i	0.247039	+	0.428199i
$905$		−	9.88836i		−	0.328700i
$906$		0			0
$907$	−9.90655			−0.328942			−0.164471	−	0.986382i	$-0.552592\pi$
$907$	−9.90655			−0.328942			−0.164471	+	0.986382i	$0.552592\pi$
$908$	−15.5197	−	2.73993i	−0.515039	−	0.0909277i
$909$		0			0
$910$	0.799823	+	0.953396i	0.0265139	+	0.0316048i
$911$	−43.7839			−1.45062			−0.725312	−	0.688420i	$-0.758304\pi$
$911$	−43.7839			−1.45062			−0.725312	+	0.688420i	$0.758304\pi$
$912$		0			0
$913$	−17.4250			−0.576683
$914$	−37.4467	−	44.6369i	−1.23863	−	1.47646i
$915$		0			0
$916$	−42.7593	−	7.54895i	−1.41281	−	0.249424i
$917$	−5.91940			−0.195476
$918$		0			0
$919$		−	8.90469i		−	0.293739i	−0.989156	−	0.146869i	$-0.953080\pi$
$919$		−	8.90469i		−	0.293739i	0.989156	−	0.146869i	$-0.0469197\pi$
$920$	13.1893	−	7.60928i	0.434840	−	0.250871i
$921$		0			0
$922$	−20.8526	−	24.8565i	−0.686745	−	0.818607i
$923$			2.15045i			0.0707828i
$924$		0			0
$925$			22.0412i			0.724710i
$926$	30.9195	−	25.9389i	1.01608	−	0.852406i
$927$		0			0
$928$	−3.04456	−	8.37865i	−0.0999425	−	0.275043i
$929$		−	27.2093i		−	0.892709i	−0.894856	−	0.446354i	$-0.852722\pi$
$929$		−	27.2093i		−	0.892709i	0.894856	−	0.446354i	$-0.147278\pi$
$930$		0			0
$931$	4.09641			0.134254
$932$	5.28991	+	0.933909i	0.173277	+	0.0305912i
$933$		0			0
$934$	−3.79076	+	3.18014i	−0.124038	+	0.104057i
$935$	−5.32245			−0.174063
$936$		0			0
$937$	11.2863			0.368708			0.184354	−	0.982860i	$-0.440981\pi$
$937$	11.2863			0.368708			0.184354	+	0.982860i	$0.440981\pi$
$938$	13.7424	−	11.5288i	0.448705	−	0.376427i
$939$		0			0
$940$	1.57451	−	8.91844i	0.0513548	−	0.290887i
$941$	−42.7661			−1.39414			−0.697068	−	0.717005i	$-0.745512\pi$
$941$	−42.7661			−1.39414			−0.697068	+	0.717005i	$0.745512\pi$
$942$		0			0
$943$		−	63.2104i		−	2.05842i
$944$	6.03552	−	16.5606i	0.196439	−	0.539002i
$945$		0			0
$946$	1.41366	−	1.18595i	0.0459622	−	0.0385586i
$947$			1.63182i			0.0530271i	0.999648	+	0.0265135i	$0.00844051\pi$
$947$			1.63182i			0.0530271i	−0.999648	+	0.0265135i	$0.991559\pi$
$948$		0			0
$949$			8.43479i			0.273805i
$950$	−15.8403	−	18.8818i	−0.513928	−	0.612608i
$951$		0			0
$952$	−5.74222	+	3.31284i	−0.186106	+	0.107370i
$953$		−	30.4300i		−	0.985723i	−0.870108	−	0.492862i	$-0.835951\pi$
$953$		−	30.4300i		−	0.985723i	0.870108	−	0.492862i	$-0.164049\pi$
$954$		0			0
$955$	−10.4560			−0.338349
$956$	−1.37917	+	7.81199i	−0.0446055	+	0.252658i
$957$		0			0
$958$	28.5097	+	33.9838i	0.921105	+	1.09797i
$959$	−0.115119			−0.00371740
$960$		0			0
$961$	−8.66758			−0.279599
$962$	4.79876	+	5.72017i	0.154718	+	0.184426i
$963$		0			0
$964$	−6.06098	+	34.3310i	−0.195211	+	1.10573i
$965$	1.45974			0.0469906
$966$		0			0
$967$			55.0276i			1.76957i	0.466003	+	0.884783i	$0.345694\pi$
$967$			55.0276i			1.76957i	−0.466003	+	0.884783i	$0.654306\pi$
$968$	10.0061	−	5.77278i	0.321608	−	0.185544i
$969$		0			0
$970$	−11.8676	−	14.1463i	−0.381045	−	0.454210i
$971$		−	19.1605i		−	0.614891i	−0.951566	−	0.307445i	$-0.900526\pi$
$971$		−	19.1605i		−	0.614891i	0.951566	−	0.307445i	$-0.0994741\pi$
$972$		0			0
$973$			9.05579i			0.290315i
$974$	43.0610	−	36.1247i	1.37977	−	1.15751i
$975$		0			0
$976$	−13.1441	+	36.0656i	−0.420733	+	1.15443i
$977$		−	19.0482i		−	0.609405i	−0.952448	−	0.304703i	$-0.901443\pi$
$977$		−	19.0482i		−	0.609405i	0.952448	−	0.304703i	$-0.0985571\pi$
$978$		0			0
$979$	−26.9689			−0.861928
$980$	0.300253	−	1.70071i	0.00959123	−	0.0543273i
$981$		0			0
$982$	7.34359	−	6.16068i	0.234343	−	0.196595i
$983$	22.5016			0.717689			0.358845	−	0.933397i	$-0.383171\pi$
$983$	22.5016			0.717689			0.358845	+	0.933397i	$0.383171\pi$
$984$		0			0
$985$	6.37984			0.203279
$986$	4.00186	−	3.35724i	0.127445	−	0.106916i
$987$		0			0
$988$	−8.22182	−	1.45152i	−0.261571	−	0.0461791i
$989$	−3.09328			−0.0983607
$990$		0			0
$991$		−	30.0467i		−	0.954466i	−0.878777	−	0.477233i	$-0.841640\pi$
$991$		−	30.0467i		−	0.954466i	0.878777	−	0.477233i	$-0.158360\pi$
$992$	−33.4859	+	12.1678i	−1.06318	+	0.386328i
$993$		0			0
$994$	2.28632	−	1.91804i	0.0725176	−	0.0608364i
$995$			18.2415i			0.578294i
$996$		0			0
$997$		−	61.6652i		−	1.95296i	−0.215619	−	0.976478i	$-0.569177\pi$
$997$		−	61.6652i		−	1.95296i	0.215619	−	0.976478i	$-0.430823\pi$
$998$	7.44577	+	8.87543i	0.235692	+	0.280947i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1512.2.j.d.323.13	✓	48
3.2	odd	2	inner	1512.2.j.d.323.36	yes	48
4.3	odd	2		6048.2.j.d.5615.30		48
8.3	odd	2	inner	1512.2.j.d.323.35	yes	48
8.5	even	2		6048.2.j.d.5615.20		48
12.11	even	2		6048.2.j.d.5615.19		48
24.5	odd	2		6048.2.j.d.5615.29		48
24.11	even	2	inner	1512.2.j.d.323.14	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1512.2.j.d.323.13	✓	48	1.1	even	1	trivial
1512.2.j.d.323.14	yes	48	24.11	even	2	inner
1512.2.j.d.323.35	yes	48	8.3	odd	2	inner
1512.2.j.d.323.36	yes	48	3.2	odd	2	inner
6048.2.j.d.5615.19		48	12.11	even	2
6048.2.j.d.5615.20		48	8.5	even	2
6048.2.j.d.5615.29		48	24.5	odd	2
6048.2.j.d.5615.30		48	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:	\( N \)	\(=\)	\( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1512.j (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.908924 - 1.08345i) q^{2} +(-0.347713 + 1.96954i) q^{4} +0.863507 q^{5} -1.00000i q^{7} +(2.44994 - 1.41344i) q^{8} +O(q^{10})\)	\(q+(-0.908924 - 1.08345i) q^{2} +(-0.347713 + 1.96954i) q^{4} +0.863507 q^{5} -1.00000i q^{7} +(2.44994 - 1.41344i) q^{8} +(-0.784863 - 0.935564i) q^{10} -2.62979i q^{11} -1.01906i q^{13} +(-1.08345 + 0.908924i) q^{14} +(-3.75819 - 1.36967i) q^{16} -2.34382i q^{17} -4.09641 q^{19} +(-0.300253 + 1.70071i) q^{20} +(-2.84923 + 2.39028i) q^{22} +6.23450 q^{23} -4.25435 q^{25} +(-1.10410 + 0.926249i) q^{26} +(1.96954 + 0.347713i) q^{28} -1.57590 q^{29} +6.29822i q^{31} +(1.93194 + 5.31673i) q^{32} +(-2.53941 + 2.13036i) q^{34} -0.863507i q^{35} -5.18085i q^{37} +(3.72332 + 4.43824i) q^{38} +(2.11554 - 1.22051i) q^{40} -10.1388i q^{41} -0.496156 q^{43} +(5.17948 + 0.914412i) q^{44} +(-5.66669 - 6.75475i) q^{46} -5.24394 q^{47} -1.00000 q^{49} +(3.86689 + 4.60937i) q^{50} +(2.00708 + 0.354341i) q^{52} +10.5477 q^{53} -2.27084i q^{55} +(-1.41344 - 2.44994i) q^{56} +(1.43238 + 1.70741i) q^{58} +4.40654i q^{59} -9.59653i q^{61} +(6.82379 - 5.72461i) q^{62} +(4.00440 - 6.92566i) q^{64} -0.879966i q^{65} -12.6840 q^{67} +(4.61625 + 0.814978i) q^{68} +(-0.935564 + 0.784863i) q^{70} -2.11023 q^{71} -8.27702 q^{73} +(-5.61318 + 4.70900i) q^{74} +(1.42438 - 8.06805i) q^{76} -2.62979 q^{77} -9.44227i q^{79} +(-3.24523 - 1.18272i) q^{80} +(-10.9849 + 9.21541i) q^{82} -6.62600i q^{83} -2.02391i q^{85} +(0.450968 + 0.537558i) q^{86} +(-3.71704 - 6.44282i) q^{88} -10.2551i q^{89} -1.01906 q^{91} +(-2.16782 + 12.2791i) q^{92} +(4.76634 + 5.68153i) q^{94} -3.53728 q^{95} +15.1206 q^{97} +(0.908924 + 1.08345i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{4}+O(q^{10}) \) 48 * q - 4 * q^4	\( 48 q - 4 q^{4} - 12 q^{10} - 12 q^{16} + 16 q^{19} - 24 q^{22} + 48 q^{25} + 8 q^{28} + 12 q^{34} + 32 q^{40} + 64 q^{43} + 60 q^{46} - 48 q^{49} + 16 q^{52} + 36 q^{58} - 4 q^{64} + 32 q^{67} + 12 q^{70} - 32 q^{76} + 36 q^{82} + 24 q^{88} - 60 q^{94}+O(q^{100}) \) 48 * q - 4 * q^4 - 12 * q^10 - 12 * q^16 + 16 * q^19 - 24 * q^22 + 48 * q^25 + 8 * q^28 + 12 * q^34 + 32 * q^40 + 64 * q^43 + 60 * q^46 - 48 * q^49 + 16 * q^52 + 36 * q^58 - 4 * q^64 + 32 * q^67 + 12 * q^70 - 32 * q^76 + 36 * q^82 + 24 * q^88 - 60 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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