LMFDB - Embedded newform 735.2.d.f.589.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [735,2,Mod(589,735)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(735, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("735.589");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 735 = 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	735.d (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:	$5.86900454856$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			589.4
Root			$0.965926 + 0.258819i$ of defining polynomial
Character	$\chi$	$=$	735.589
Dual form			735.2.d.f.589.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.517638i q^{2} +1.00000i q^{3} +1.73205 q^{4} +(1.41421 - 1.73205i) q^{5} +0.517638 q^{6} -1.93185i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q-0.517638i q^{2} +1.00000i q^{3} +1.73205 q^{4} +(1.41421 - 1.73205i) q^{5} +0.517638 q^{6} -1.93185i q^{8} -1.00000 q^{9} +(-0.896575 - 0.732051i) q^{10} +3.46410 q^{11} +1.73205i q^{12} -4.00000i q^{13} +(1.73205 + 1.41421i) q^{15} +2.46410 q^{16} +4.00000i q^{17} +0.517638i q^{18} -5.27792 q^{19} +(2.44949 - 3.00000i) q^{20} -1.79315i q^{22} -3.48477i q^{23} +1.93185 q^{24} +(-1.00000 - 4.89898i) q^{25} -2.07055 q^{26} -1.00000i q^{27} +4.92820 q^{29} +(0.732051 - 0.896575i) q^{30} -7.34847 q^{31} -5.13922i q^{32} +3.46410i q^{33} +2.07055 q^{34} -1.73205 q^{36} +10.5558i q^{37} +2.73205i q^{38} +4.00000 q^{39} +(-3.34607 - 2.73205i) q^{40} +8.48528 q^{41} +6.00000 q^{44} +(-1.41421 + 1.73205i) q^{45} -1.80385 q^{46} +6.00000i q^{47} +2.46410i q^{48} +(-2.53590 + 0.517638i) q^{50} -4.00000 q^{51} -6.92820i q^{52} +7.34847i q^{53} -0.517638 q^{54} +(4.89898 - 6.00000i) q^{55} -5.27792i q^{57} -2.55103i q^{58} +0.757875 q^{59} +(3.00000 + 2.44949i) q^{60} +0.656339 q^{61} +3.80385i q^{62} +2.26795 q^{64} +(-6.92820 - 5.65685i) q^{65} +1.79315 q^{66} -12.6264i q^{67} +6.92820i q^{68} +3.48477 q^{69} -6.39230 q^{71} +1.93185i q^{72} +2.92820i q^{73} +5.46410 q^{74} +(4.89898 - 1.00000i) q^{75} -9.14162 q^{76} -2.07055i q^{78} +4.53590 q^{79} +(3.48477 - 4.26795i) q^{80} +1.00000 q^{81} -4.39230i q^{82} -6.00000i q^{83} +(6.92820 + 5.65685i) q^{85} +4.92820i q^{87} -6.69213i q^{88} +15.4548 q^{89} +(0.896575 + 0.732051i) q^{90} -6.03579i q^{92} -7.34847i q^{93} +3.10583 q^{94} +(-7.46410 + 9.14162i) q^{95} +5.13922 q^{96} +18.9282i q^{97} -3.46410 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{9}+O(q^{10}) $ 8 * q - 8 * q^9	$ 8 q - 8 q^{9} - 8 q^{16} - 8 q^{25} - 16 q^{29} - 8 q^{30} + 32 q^{39} + 48 q^{44} - 56 q^{46} - 48 q^{50} - 32 q^{51} + 24 q^{60} + 32 q^{64} + 32 q^{71} + 16 q^{74} + 64 q^{79} + 8 q^{81} - 32 q^{95}+O(q^{100}) $ 8 * q - 8 * q^9 - 8 * q^16 - 8 * q^25 - 16 * q^29 - 8 * q^30 + 32 * q^39 + 48 * q^44 - 56 * q^46 - 48 * q^50 - 32 * q^51 + 24 * q^60 + 32 * q^64 + 32 * q^71 + 16 * q^74 + 64 * q^79 + 8 * q^81 - 32 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/735\mathbb{Z}\right)^\times$.

$n$	$346$	$442$	$491$
$\chi(n)$	$1$	$-1$	$1$

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 $

$2$		−	0.517638i		−	0.366025i	−0.983111	−	0.183013i	$-0.941415\pi$
$2$		−	0.517638i		−	0.366025i	0.983111	−	0.183013i	$-0.0585849\pi$
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	1.73205			0.866025
$5$	1.41421	−	1.73205i	0.632456	−	0.774597i
$5$	1.41421	−	1.73205i	0.632456	−	0.774597i
$6$	0.517638			0.211325
$7$		0			0
$7$		0			0
$8$		−	1.93185i		−	0.683013i
$9$	−1.00000			−0.333333
$10$	−0.896575	−	0.732051i	−0.283522	−	0.231495i
$11$	3.46410			1.04447			0.522233	−	0.852803i	$-0.325099\pi$
$11$	3.46410			1.04447			0.522233	+	0.852803i	$0.325099\pi$
$12$			1.73205i			0.500000i
$13$		−	4.00000i		−	1.10940i	−0.832050	−	0.554700i	$-0.812833\pi$
$13$		−	4.00000i		−	1.10940i	0.832050	−	0.554700i	$-0.187167\pi$
$14$		0			0
$15$	1.73205	+	1.41421i	0.447214	+	0.365148i
$16$	2.46410			0.616025
$17$			4.00000i			0.970143i	0.874475	+	0.485071i	$0.161206\pi$
$17$			4.00000i			0.970143i	−0.874475	+	0.485071i	$0.838794\pi$
$18$			0.517638i			0.122008i
$19$	−5.27792			−1.21084			−0.605419	−	0.795907i	$-0.706994\pi$
$19$	−5.27792			−1.21084			−0.605419	+	0.795907i	$0.706994\pi$
$20$	2.44949	−	3.00000i	0.547723	−	0.670820i
$21$		0			0
$22$		−	1.79315i		−	0.382301i
$23$		−	3.48477i		−	0.726624i	−0.931668	−	0.363312i	$-0.881646\pi$
$23$		−	3.48477i		−	0.726624i	0.931668	−	0.363312i	$-0.118354\pi$
$24$	1.93185			0.394338
$25$	−1.00000	−	4.89898i	−0.200000	−	0.979796i
$26$	−2.07055			−0.406069
$27$		−	1.00000i		−	0.192450i
$28$		0			0
$29$	4.92820			0.915144			0.457572	−	0.889172i	$-0.348719\pi$
$29$	4.92820			0.915144			0.457572	+	0.889172i	$0.348719\pi$
$30$	0.732051	−	0.896575i	0.133654	−	0.163692i
$31$	−7.34847			−1.31982			−0.659912	−	0.751343i	$-0.729406\pi$
$31$	−7.34847			−1.31982			−0.659912	+	0.751343i	$0.729406\pi$
$32$		−	5.13922i		−	0.908494i
$33$			3.46410i			0.603023i
$34$	2.07055			0.355097
$35$		0			0
$36$	−1.73205			−0.288675
$37$			10.5558i			1.73537i	0.497116	+	0.867684i	$0.334392\pi$
$37$			10.5558i			1.73537i	−0.497116	+	0.867684i	$0.665608\pi$
$38$			2.73205i			0.443197i
$39$	4.00000			0.640513
$40$	−3.34607	−	2.73205i	−0.529059	−	0.431975i
$41$	8.48528			1.32518			0.662589	−	0.748983i	$-0.269458\pi$
$41$	8.48528			1.32518			0.662589	+	0.748983i	$0.269458\pi$
$42$		0			0
$43$		0			0		1.00000			$0$
$43$		0			0		−1.00000			$\pi$
$44$	6.00000			0.904534
$45$	−1.41421	+	1.73205i	−0.210819	+	0.258199i
$46$	−1.80385			−0.265963
$47$			6.00000i			0.875190i	0.899172	+	0.437595i	$0.144170\pi$
$47$			6.00000i			0.875190i	−0.899172	+	0.437595i	$0.855830\pi$
$48$			2.46410i			0.355662i
$49$		0			0
$50$	−2.53590	+	0.517638i	−0.358630	+	0.0732051i
$51$	−4.00000			−0.560112
$52$		−	6.92820i		−	0.960769i
$53$			7.34847i			1.00939i	0.863298	+	0.504695i	$0.168395\pi$
$53$			7.34847i			1.00939i	−0.863298	+	0.504695i	$0.831605\pi$
$54$	−0.517638			−0.0704416
$55$	4.89898	−	6.00000i	0.660578	−	0.809040i
$56$		0			0
$57$		−	5.27792i		−	0.699077i
$58$		−	2.55103i		−	0.334966i
$59$	0.757875			0.0986669			0.0493334	−	0.998782i	$-0.484290\pi$
$59$	0.757875			0.0986669			0.0493334	+	0.998782i	$0.484290\pi$
$60$	3.00000	+	2.44949i	0.387298	+	0.316228i
$61$	0.656339			0.0840356			0.0420178	−	0.999117i	$-0.486621\pi$
$61$	0.656339			0.0840356			0.0420178	+	0.999117i	$0.486621\pi$
$62$			3.80385i			0.483089i
$63$		0			0
$64$	2.26795			0.283494
$65$	−6.92820	−	5.65685i	−0.859338	−	0.701646i
$66$	1.79315			0.220722
$67$		−	12.6264i		−	1.54256i	−0.636497	−	0.771279i	$-0.719617\pi$
$67$		−	12.6264i		−	1.54256i	0.636497	−	0.771279i	$-0.280383\pi$
$68$			6.92820i			0.840168i
$69$	3.48477			0.419517
$70$		0			0
$71$	−6.39230			−0.758627			−0.379314	−	0.925268i	$-0.623840\pi$
$71$	−6.39230			−0.758627			−0.379314	+	0.925268i	$0.623840\pi$
$72$			1.93185i			0.227671i
$73$			2.92820i			0.342720i	0.985208	+	0.171360i	$0.0548162\pi$
$73$			2.92820i			0.342720i	−0.985208	+	0.171360i	$0.945184\pi$
$74$	5.46410			0.635189
$75$	4.89898	−	1.00000i	0.565685	−	0.115470i
$76$	−9.14162			−1.04862
$77$		0			0
$78$		−	2.07055i		−	0.234444i
$79$	4.53590			0.510328			0.255164	−	0.966898i	$-0.417870\pi$
$79$	4.53590			0.510328			0.255164	+	0.966898i	$0.417870\pi$
$80$	3.48477	−	4.26795i	0.389609	−	0.477171i
$81$	1.00000			0.111111
$82$		−	4.39230i		−	0.485049i
$83$		−	6.00000i		−	0.658586i	−0.944228	−	0.329293i	$-0.893190\pi$
$83$		−	6.00000i		−	0.658586i	0.944228	−	0.329293i	$-0.106810\pi$
$84$		0			0
$85$	6.92820	+	5.65685i	0.751469	+	0.613572i
$86$		0			0
$87$			4.92820i			0.528359i
$88$		−	6.69213i		−	0.713384i
$89$	15.4548			1.63821			0.819103	−	0.573646i	$-0.194471\pi$
$89$	15.4548			1.63821			0.819103	+	0.573646i	$0.194471\pi$
$90$	0.896575	+	0.732051i	0.0945074	+	0.0771649i
$91$		0			0
$92$		−	6.03579i		−	0.629275i
$93$		−	7.34847i		−	0.762001i
$94$	3.10583			0.320342
$95$	−7.46410	+	9.14162i	−0.765801	+	0.937910i
$96$	5.13922			0.524519
$97$			18.9282i			1.92187i	0.276778	+	0.960934i	$0.410733\pi$
$97$			18.9282i			1.92187i	−0.276778	+	0.960934i	$0.589267\pi$
$98$		0			0
$99$	−3.46410			−0.348155
$100$	−1.73205	−	8.48528i	−0.173205	−	0.848528i
$101$	−6.96953			−0.693494			−0.346747	−	0.937959i	$-0.612714\pi$
$101$	−6.96953			−0.693494			−0.346747	+	0.937959i	$0.612714\pi$
$102$			2.07055i			0.205015i
$103$		−	13.8564i		−	1.36531i	−0.730740	−	0.682656i	$-0.760825\pi$
$103$		−	13.8564i		−	1.36531i	0.730740	−	0.682656i	$-0.239175\pi$
$104$	−7.72741			−0.757735
$105$		0			0
$106$	3.80385			0.369462
$107$			15.5563i			1.50389i	0.659226	+	0.751945i	$0.270884\pi$
$107$			15.5563i			1.50389i	−0.659226	+	0.751945i	$0.729116\pi$
$108$		−	1.73205i		−	0.166667i
$109$	−15.8564			−1.51877			−0.759384	−	0.650643i	$-0.774500\pi$
$109$	−15.8564			−1.51877			−0.759384	+	0.650643i	$0.774500\pi$
$110$	−3.10583	−	2.53590i	−0.296129	−	0.241788i
$111$	−10.5558			−1.00192
$112$		0			0
$113$			5.27792i			0.496505i	0.968695	+	0.248252i	$0.0798562\pi$
$113$			5.27792i			0.496505i	−0.968695	+	0.248252i	$0.920144\pi$
$114$	−2.73205			−0.255880
$115$	−6.03579	−	4.92820i	−0.562840	−	0.459557i
$116$	8.53590			0.792538
$117$			4.00000i			0.369800i
$118$		−	0.392305i		−	0.0361146i
$119$		0			0
$120$	2.73205	−	3.34607i	0.249401	−	0.305453i
$121$	1.00000			0.0909091
$122$		−	0.339746i		−	0.0307592i
$123$			8.48528i			0.765092i
$124$	−12.7279			−1.14300
$125$	−9.89949	−	5.19615i	−0.885438	−	0.464758i
$126$		0			0
$127$			2.82843i			0.250982i	0.992095	+	0.125491i	$0.0400507\pi$
$127$			2.82843i			0.250982i	−0.992095	+	0.125491i	$0.959949\pi$
$128$		−	11.4524i		−	1.01226i
$129$		0			0
$130$	−2.92820	+	3.58630i	−0.256820	+	0.314539i
$131$	−5.65685			−0.494242			−0.247121	−	0.968985i	$-0.579484\pi$
$131$	−5.65685			−0.494242			−0.247121	+	0.968985i	$0.579484\pi$
$132$			6.00000i			0.522233i
$133$		0			0
$134$	−6.53590			−0.564616
$135$	−1.73205	−	1.41421i	−0.149071	−	0.121716i
$136$	7.72741			0.662620
$137$			10.1769i			0.869471i	0.900558	+	0.434735i	$0.143158\pi$
$137$			10.1769i			0.869471i	−0.900558	+	0.434735i	$0.856842\pi$
$138$		−	1.80385i		−	0.153554i
$139$	0.378937			0.0321410			0.0160705	−	0.999871i	$-0.494884\pi$
$139$	0.378937			0.0321410			0.0160705	+	0.999871i	$0.494884\pi$
$140$		0			0
$141$	−6.00000			−0.505291
$142$			3.30890i			0.277677i
$143$		−	13.8564i		−	1.15873i
$144$	−2.46410			−0.205342
$145$	6.96953	−	8.53590i	0.578788	−	0.708868i
$146$	1.51575			0.125444
$147$		0			0
$148$			18.2832i			1.50287i
$149$	−7.07180			−0.579344			−0.289672	−	0.957126i	$-0.593546\pi$
$149$	−7.07180			−0.579344			−0.289672	+	0.957126i	$0.593546\pi$
$150$	−0.517638	−	2.53590i	−0.0422650	−	0.207055i
$151$	−19.4641			−1.58397			−0.791983	−	0.610543i	$-0.790951\pi$
$151$	−19.4641			−1.58397			−0.791983	+	0.610543i	$0.790951\pi$
$152$			10.1962i			0.827017i
$153$		−	4.00000i		−	0.323381i
$154$		0			0
$155$	−10.3923	+	12.7279i	−0.834730	+	1.02233i
$156$	6.92820			0.554700
$157$			5.07180i			0.404773i	0.979306	+	0.202387i	$0.0648698\pi$
$157$			5.07180i			0.404773i	−0.979306	+	0.202387i	$0.935130\pi$
$158$		−	2.34795i		−	0.186793i
$159$	−7.34847			−0.582772
$160$	−8.90138	−	7.26795i	−0.703716	−	0.574582i
$161$		0			0
$162$		−	0.517638i		−	0.0406695i
$163$			22.4243i			1.75641i	0.478284	+	0.878205i	$0.341259\pi$
$163$			22.4243i			1.75641i	−0.478284	+	0.878205i	$0.658741\pi$
$164$	14.6969			1.14764
$165$	6.00000	+	4.89898i	0.467099	+	0.381385i
$166$	−3.10583			−0.241059
$167$			18.9282i			1.46471i	0.680924	+	0.732354i	$0.261578\pi$
$167$			18.9282i			1.46471i	−0.680924	+	0.732354i	$0.738422\pi$
$168$		0			0
$169$	−3.00000			−0.230769
$170$	2.92820	−	3.58630i	0.224583	−	0.275057i
$171$	5.27792			0.403612
$172$		0			0
$173$		−	16.0000i		−	1.21646i	−0.793762	−	0.608229i	$-0.791880\pi$
$173$		−	16.0000i		−	1.21646i	0.793762	−	0.608229i	$-0.208120\pi$
$174$	2.55103			0.193393
$175$		0			0
$176$	8.53590			0.643418
$177$			0.757875i			0.0569654i
$178$		−	8.00000i		−	0.599625i
$179$	−10.3923			−0.776757			−0.388379	−	0.921500i	$-0.626965\pi$
$179$	−10.3923			−0.776757			−0.388379	+	0.921500i	$0.626965\pi$
$180$	−2.44949	+	3.00000i	−0.182574	+	0.223607i
$181$	−6.31319			−0.469256			−0.234628	−	0.972085i	$-0.575387\pi$
$181$	−6.31319			−0.469256			−0.234628	+	0.972085i	$0.575387\pi$
$182$		0			0
$183$			0.656339i			0.0485180i
$184$	−6.73205			−0.496293
$185$	18.2832	+	14.9282i	1.34421	+	1.09754i
$186$	−3.80385			−0.278912
$187$			13.8564i			1.01328i
$188$			10.3923i			0.757937i
$189$		0			0
$190$	4.73205	+	3.86370i	0.343299	+	0.280302i
$191$	−7.46410			−0.540083			−0.270042	−	0.962849i	$-0.587037\pi$
$191$	−7.46410			−0.540083			−0.270042	+	0.962849i	$0.587037\pi$
$192$			2.26795i			0.163675i
$193$			6.41473i			0.461742i	0.972984	+	0.230871i	$0.0741576\pi$
$193$			6.41473i			0.461742i	−0.972984	+	0.230871i	$0.925842\pi$
$194$	9.79796			0.703452
$195$	5.65685	−	6.92820i	0.405096	−	0.496139i
$196$		0			0
$197$		−	22.8033i		−	1.62467i	−0.583193	−	0.812333i	$-0.698197\pi$
$197$		−	22.8033i		−	1.62467i	0.583193	−	0.812333i	$-0.301803\pi$
$198$			1.79315i			0.127434i
$199$	−8.10634			−0.574643			−0.287322	−	0.957834i	$-0.592765\pi$
$199$	−8.10634			−0.574643			−0.287322	+	0.957834i	$0.592765\pi$
$200$	−9.46410	+	1.93185i	−0.669213	+	0.136603i
$201$	12.6264			0.890597
$202$			3.60770i			0.253837i
$203$		0			0
$204$	−6.92820			−0.485071
$205$	12.0000	−	14.6969i	0.838116	−	1.02648i
$206$	−7.17260			−0.499739
$207$			3.48477i			0.242208i
$208$		−	9.85641i		−	0.683419i
$209$	−18.2832			−1.26468
$210$		0			0
$211$	−26.9282			−1.85381			−0.926907	−	0.375291i	$-0.877543\pi$
$211$	−26.9282			−1.85381			−0.926907	+	0.375291i	$0.877543\pi$
$212$			12.7279i			0.874157i
$213$		−	6.39230i		−	0.437994i
$214$	8.05256			0.550462
$215$		0			0
$216$	−1.93185			−0.131446
$217$		0			0
$218$			8.20788i			0.555908i
$219$	−2.92820			−0.197870
$220$	8.48528	−	10.3923i	0.572078	−	0.700649i
$221$	16.0000			1.07628
$222$			5.46410i			0.366726i
$223$		−	8.00000i		−	0.535720i	−0.963458	−	0.267860i	$-0.913684\pi$
$223$		−	8.00000i		−	0.535720i	0.963458	−	0.267860i	$-0.0863164\pi$
$224$		0			0
$225$	1.00000	+	4.89898i	0.0666667	+	0.326599i
$226$	2.73205			0.181733
$227$			4.00000i			0.265489i	0.991150	+	0.132745i	$0.0423790\pi$
$227$			4.00000i			0.265489i	−0.991150	+	0.132745i	$0.957621\pi$
$228$		−	9.14162i		−	0.605419i
$229$	13.4858			0.891167			0.445583	−	0.895240i	$-0.352996\pi$
$229$	13.4858			0.891167			0.445583	+	0.895240i	$0.352996\pi$
$230$	−2.55103	+	3.12436i	−0.168210	+	0.206014i
$231$		0			0
$232$		−	9.52056i		−	0.625055i
$233$			5.27792i			0.345768i	0.984942	+	0.172884i	$0.0553085\pi$
$233$			5.27792i			0.345768i	−0.984942	+	0.172884i	$0.944691\pi$
$234$	2.07055			0.135356
$235$	10.3923	+	8.48528i	0.677919	+	0.553519i
$236$	1.31268			0.0854480
$237$			4.53590i			0.294638i
$238$		0			0
$239$	8.53590			0.552141			0.276071	−	0.961137i	$-0.410968\pi$
$239$	8.53590			0.552141			0.276071	+	0.961137i	$0.410968\pi$
$240$	4.26795	+	3.48477i	0.275495	+	0.224941i
$241$	14.0406			0.904435			0.452217	−	0.891908i	$-0.350633\pi$
$241$	14.0406			0.904435			0.452217	+	0.891908i	$0.350633\pi$
$242$		−	0.517638i		−	0.0332750i
$243$			1.00000i			0.0641500i
$244$	1.13681			0.0727769
$245$		0			0
$246$	4.39230			0.280043
$247$			21.1117i			1.34330i
$248$			14.1962i			0.901457i
$249$	6.00000			0.380235
$250$	−2.68973	+	5.12436i	−0.170113	+	0.324093i
$251$	20.3538			1.28472			0.642360	−	0.766403i	$-0.277955\pi$
$251$	20.3538			1.28472			0.642360	+	0.766403i	$0.277955\pi$
$252$		0			0
$253$		−	12.0716i		−	0.758934i
$254$	1.46410			0.0918659
$255$	−5.65685	+	6.92820i	−0.354246	+	0.433861i
$256$	−1.39230			−0.0870191
$257$		−	3.46410i		−	0.216085i	−0.994146	−	0.108042i	$-0.965542\pi$
$257$		−	3.46410i		−	0.216085i	0.994146	−	0.108042i	$-0.0344582\pi$
$258$		0			0
$259$		0			0
$260$	−12.0000	−	9.79796i	−0.744208	−	0.607644i
$261$	−4.92820			−0.305048
$262$			2.92820i			0.180905i
$263$		−	7.62587i		−	0.470231i	−0.971967	−	0.235116i	$-0.924453\pi$
$263$		−	7.62587i		−	0.470231i	0.971967	−	0.235116i	$-0.0755469\pi$
$264$	6.69213			0.411872
$265$	12.7279	+	10.3923i	0.781870	+	0.638394i
$266$		0			0
$267$			15.4548i			0.945819i
$268$		−	21.8695i		−	1.33589i
$269$	−30.9096			−1.88459			−0.942297	−	0.334779i	$-0.891338\pi$
$269$	−30.9096			−1.88459			−0.942297	+	0.334779i	$0.891338\pi$
$270$	−0.732051	+	0.896575i	−0.0445512	+	0.0545638i
$271$	−1.69161			−0.102758			−0.0513791	−	0.998679i	$-0.516362\pi$
$271$	−1.69161			−0.102758			−0.0513791	+	0.998679i	$0.516362\pi$
$272$			9.85641i			0.597632i
$273$		0			0
$274$	5.26795			0.318248
$275$	−3.46410	−	16.9706i	−0.208893	−	1.02336i
$276$	6.03579			0.363312
$277$		−	11.3137i		−	0.679775i	−0.940466	−	0.339887i	$-0.889611\pi$
$277$		−	11.3137i		−	0.679775i	0.940466	−	0.339887i	$-0.110389\pi$
$278$		−	0.196152i		−	0.0117644i
$279$	7.34847			0.439941
$280$		0			0
$281$	27.8564			1.66177			0.830887	−	0.556441i	$-0.187834\pi$
$281$	27.8564			1.66177			0.830887	+	0.556441i	$0.187834\pi$
$282$			3.10583i			0.184949i
$283$		−	2.14359i		−	0.127423i	−0.997968	−	0.0637117i	$-0.979706\pi$
$283$		−	2.14359i		−	0.127423i	0.997968	−	0.0637117i	$-0.0202938\pi$
$284$	−11.0718			−0.656990
$285$	−9.14162	−	7.46410i	−0.541503	−	0.442135i
$286$	−7.17260			−0.424125
$287$		0			0
$288$			5.13922i			0.302831i
$289$	1.00000			0.0588235
$290$	−4.41851	−	3.60770i	−0.259464	−	0.211851i
$291$	−18.9282			−1.10959
$292$			5.07180i			0.296804i
$293$		−	11.4641i		−	0.669740i	−0.942264	−	0.334870i	$-0.891308\pi$
$293$		−	11.4641i		−	0.669740i	0.942264	−	0.334870i	$-0.108692\pi$
$294$		0			0
$295$	1.07180	−	1.31268i	0.0624024	−	0.0764270i
$296$	20.3923			1.18528
$297$		−	3.46410i		−	0.201008i
$298$			3.66063i			0.212055i
$299$	−13.9391			−0.806117
$300$	8.48528	−	1.73205i	0.489898	−	0.100000i
$301$		0			0
$302$			10.0754i			0.579772i
$303$		−	6.96953i		−	0.400389i
$304$	−13.0053			−0.745906
$305$	0.928203	−	1.13681i	0.0531488	−	0.0650937i
$306$	−2.07055			−0.118366
$307$		−	4.00000i		−	0.228292i	−0.993464	−	0.114146i	$-0.963587\pi$
$307$		−	4.00000i		−	0.228292i	0.993464	−	0.114146i	$-0.0364132\pi$
$308$		0			0
$309$	13.8564			0.788263
$310$	6.58846	+	5.37945i	0.374199	+	0.305532i
$311$	4.14110			0.234821			0.117410	−	0.993083i	$-0.462541\pi$
$311$	4.14110			0.234821			0.117410	+	0.993083i	$0.462541\pi$
$312$		−	7.72741i		−	0.437478i
$313$			2.92820i			0.165512i	0.996570	+	0.0827559i	$0.0263722\pi$
$313$			2.92820i			0.165512i	−0.996570	+	0.0827559i	$0.973628\pi$
$314$	2.62536			0.148157
$315$		0			0
$316$	7.85641			0.441957
$317$		−	4.72311i		−	0.265277i	−0.991165	−	0.132638i	$-0.957655\pi$
$317$		−	4.72311i		−	0.265277i	0.991165	−	0.132638i	$-0.0423449\pi$
$318$			3.80385i			0.213309i
$319$	17.0718			0.955837
$320$	3.20736	−	3.92820i	0.179297	−	0.219593i
$321$	−15.5563			−0.868271
$322$		0			0
$323$		−	21.1117i		−	1.17468i
$324$	1.73205			0.0962250
$325$	−19.5959	+	4.00000i	−1.08699	+	0.221880i
$326$	11.6077			0.642891
$327$		−	15.8564i		−	0.876861i
$328$		−	16.3923i		−	0.905114i
$329$		0			0
$330$	2.53590	−	3.10583i	0.139597	−	0.170970i
$331$	−8.78461			−0.482846			−0.241423	−	0.970420i	$-0.577614\pi$
$331$	−8.78461			−0.482846			−0.241423	+	0.970420i	$0.577614\pi$
$332$		−	10.3923i		−	0.570352i
$333$		−	10.5558i		−	0.578456i
$334$	9.79796			0.536120
$335$	−21.8695	−	17.8564i	−1.19486	−	0.975600i
$336$		0			0
$337$		−	17.7284i		−	0.965730i	−0.875695	−	0.482865i	$-0.839596\pi$
$337$		−	17.7284i		−	0.965730i	0.875695	−	0.482865i	$-0.160404\pi$
$338$			1.55291i			0.0844674i
$339$	−5.27792			−0.286657
$340$	12.0000	+	9.79796i	0.650791	+	0.531369i
$341$	−25.4558			−1.37851
$342$		−	2.73205i		−	0.147732i
$343$		0			0
$344$		0			0
$345$	4.92820	−	6.03579i	0.265326	−	0.324956i
$346$	−8.28221			−0.445254
$347$		−	31.0112i		−	1.66477i	−0.554200	−	0.832383i	$-0.686976\pi$
$347$		−	31.0112i		−	1.66477i	0.554200	−	0.832383i	$-0.313024\pi$
$348$			8.53590i			0.457572i
$349$	17.6269			0.943546			0.471773	−	0.881720i	$-0.343614\pi$
$349$	17.6269			0.943546			0.471773	+	0.881720i	$0.343614\pi$
$350$		0			0
$351$	−4.00000			−0.213504
$352$		−	17.8028i		−	0.948891i
$353$		−	11.4641i		−	0.610173i	−0.952325	−	0.305086i	$-0.901315\pi$
$353$		−	11.4641i		−	0.610173i	0.952325	−	0.305086i	$-0.0986853\pi$
$354$	0.392305			0.0208508
$355$	−9.04008	+	11.0718i	−0.479798	+	0.587630i
$356$	26.7685			1.41873
$357$		0			0
$358$			5.37945i			0.284313i
$359$	−15.4641			−0.816164			−0.408082	−	0.912945i	$-0.633802\pi$
$359$	−15.4641			−0.816164			−0.408082	+	0.912945i	$0.633802\pi$
$360$	3.34607	+	2.73205i	0.176353	+	0.143992i
$361$	8.85641			0.466127
$362$			3.26795i			0.171760i
$363$			1.00000i			0.0524864i
$364$		0			0
$365$	5.07180	+	4.14110i	0.265470	+	0.216755i
$366$	0.339746			0.0177588
$367$			4.00000i			0.208798i	0.994535	+	0.104399i	$0.0332919\pi$
$367$			4.00000i			0.208798i	−0.994535	+	0.104399i	$0.966708\pi$
$368$		−	8.58682i		−	0.447619i
$369$	−8.48528			−0.441726
$370$	7.72741	−	9.46410i	0.401729	−	0.492015i
$371$		0			0
$372$		−	12.7279i		−	0.659912i
$373$		−	7.17260i		−	0.371383i	−0.982608	−	0.185692i	$-0.940547\pi$
$373$		−	7.17260i		−	0.371383i	0.982608	−	0.185692i	$-0.0594526\pi$
$374$	7.17260			0.370887
$375$	5.19615	−	9.89949i	0.268328	−	0.511208i
$376$	11.5911			0.597766
$377$		−	19.7128i		−	1.01526i
$378$		0			0
$379$	−11.4641			−0.588871			−0.294436	−	0.955671i	$-0.595132\pi$
$379$	−11.4641			−0.588871			−0.294436	+	0.955671i	$0.595132\pi$
$380$	−12.9282	+	15.8338i	−0.663203	+	0.812254i
$381$	−2.82843			−0.144905
$382$			3.86370i			0.197684i
$383$			23.8564i			1.21901i	0.792784	+	0.609503i	$0.208631\pi$
$383$			23.8564i			1.21901i	−0.792784	+	0.609503i	$0.791369\pi$
$384$	11.4524			0.584428
$385$		0			0
$386$	3.32051			0.169009
$387$		0			0
$388$			32.7846i			1.66439i
$389$	−11.0718			−0.561362			−0.280681	−	0.959801i	$-0.590560\pi$
$389$	−11.0718			−0.561362			−0.280681	+	0.959801i	$0.590560\pi$
$390$	−3.58630	−	2.92820i	−0.181599	−	0.148275i
$391$	13.9391			0.704929
$392$		0			0
$393$		−	5.65685i		−	0.285351i
$394$	−11.8038			−0.594669
$395$	6.41473	−	7.85641i	0.322760	−	0.395299i
$396$	−6.00000			−0.301511
$397$			23.7128i			1.19011i	0.803684	+	0.595056i	$0.202870\pi$
$397$			23.7128i			1.19011i	−0.803684	+	0.595056i	$0.797130\pi$
$398$			4.19615i			0.210334i
$399$		0			0
$400$	−2.46410	−	12.0716i	−0.123205	−	0.603579i
$401$	2.00000			0.0998752			0.0499376	−	0.998752i	$-0.484098\pi$
$401$	2.00000			0.0998752			0.0499376	+	0.998752i	$0.484098\pi$
$402$		−	6.53590i		−	0.325981i
$403$			29.3939i			1.46421i
$404$	−12.0716			−0.600584
$405$	1.41421	−	1.73205i	0.0702728	−	0.0860663i
$406$		0			0
$407$			36.5665i			1.81253i
$408$			7.72741i			0.382564i
$409$	11.4152			0.564448			0.282224	−	0.959349i	$-0.408928\pi$
$409$	11.4152			0.564448			0.282224	+	0.959349i	$0.408928\pi$
$410$	−7.60770	−	6.21166i	−0.375717	−	0.306772i
$411$	−10.1769			−0.501989
$412$		−	24.0000i		−	1.18240i
$413$		0			0
$414$	1.80385			0.0886543
$415$	−10.3923	−	8.48528i	−0.510138	−	0.416526i
$416$	−20.5569			−1.00788
$417$			0.378937i			0.0185566i
$418$			9.46410i			0.462904i
$419$	21.1117			1.03137			0.515686	−	0.856778i	$-0.327537\pi$
$419$	21.1117			1.03137			0.515686	+	0.856778i	$0.327537\pi$
$420$		0			0
$421$	12.7846			0.623084			0.311542	−	0.950232i	$-0.399155\pi$
$421$	12.7846			0.623084			0.311542	+	0.950232i	$0.399155\pi$
$422$			13.9391i			0.678543i
$423$		−	6.00000i		−	0.291730i
$424$	14.1962			0.689426
$425$	19.5959	−	4.00000i	0.950542	−	0.194029i
$426$	−3.30890			−0.160317
$427$		0			0
$428$			26.9444i			1.30241i
$429$	13.8564			0.668994
$430$		0			0
$431$	37.3205			1.79767			0.898833	−	0.438292i	$-0.144416\pi$
$431$	37.3205			1.79767			0.898833	+	0.438292i	$0.144416\pi$
$432$		−	2.46410i		−	0.118554i
$433$			17.8564i			0.858124i	0.903275	+	0.429062i	$0.141156\pi$
$433$			17.8564i			0.858124i	−0.903275	+	0.429062i	$0.858844\pi$
$434$		0			0
$435$	8.53590	+	6.96953i	0.409265	+	0.334163i
$436$	−27.4641			−1.31529
$437$			18.3923i			0.879823i
$438$			1.51575i			0.0724253i
$439$	−13.0053			−0.620710			−0.310355	−	0.950621i	$-0.600448\pi$
$439$	−13.0053			−0.620710			−0.310355	+	0.950621i	$0.600448\pi$
$440$	−11.5911	−	9.46410i	−0.552584	−	0.451183i
$441$		0			0
$442$		−	8.28221i		−	0.393945i
$443$		−	12.5249i		−	0.595074i	−0.954710	−	0.297537i	$-0.903835\pi$
$443$		−	12.5249i		−	0.595074i	0.954710	−	0.297537i	$-0.0961651\pi$
$444$	−18.2832			−0.867684
$445$	21.8564	−	26.7685i	1.03609	−	1.26895i
$446$	−4.14110			−0.196087
$447$		−	7.07180i		−	0.334485i
$448$		0			0
$449$	−35.8564			−1.69217			−0.846084	−	0.533049i	$-0.821046\pi$
$449$	−35.8564			−1.69217			−0.846084	+	0.533049i	$0.821046\pi$
$450$	2.53590	−	0.517638i	0.119543	−	0.0244017i
$451$	29.3939			1.38410
$452$			9.14162i			0.429986i
$453$		−	19.4641i		−	0.914503i
$454$	2.07055			0.0971758
$455$		0			0
$456$	−10.1962			−0.477479
$457$		−	21.8695i		−	1.02301i	−0.859279	−	0.511507i	$-0.829087\pi$
$457$		−	21.8695i		−	1.02301i	0.859279	−	0.511507i	$-0.170913\pi$
$458$		−	6.98076i		−	0.326190i
$459$	4.00000			0.186704
$460$	−10.4543	−	8.53590i	−0.487434	−	0.397988i
$461$	32.4254			1.51020			0.755100	−	0.655609i	$-0.227588\pi$
$461$	32.4254			1.51020			0.755100	+	0.655609i	$0.227588\pi$
$462$		0			0
$463$		−	22.4243i		−	1.04215i	−0.853512	−	0.521074i	$-0.825532\pi$
$463$		−	22.4243i		−	1.04215i	0.853512	−	0.521074i	$-0.174468\pi$
$464$	12.1436			0.563752
$465$	−12.7279	−	10.3923i	−0.590243	−	0.481932i
$466$	2.73205			0.126560
$467$		−	9.85641i		−	0.456100i	−0.973649	−	0.228050i	$-0.926765\pi$
$467$		−	9.85641i		−	0.456100i	0.973649	−	0.228050i	$-0.0732350\pi$
$468$			6.92820i			0.320256i
$469$		0			0
$470$	4.39230	−	5.37945i	0.202602	−	0.248136i
$471$	−5.07180			−0.233696
$472$		−	1.46410i		−	0.0673907i
$473$		0			0
$474$	2.34795			0.107845
$475$	5.27792	+	25.8564i	0.242167	+	1.18637i
$476$		0			0
$477$		−	7.34847i		−	0.336463i
$478$		−	4.41851i		−	0.202098i
$479$	25.2528			1.15383			0.576914	−	0.816805i	$-0.304257\pi$
$479$	25.2528			1.15383			0.576914	+	0.816805i	$0.304257\pi$
$480$	7.26795	−	8.90138i	0.331735	−	0.406291i
$481$	42.2233			1.92522
$482$		−	7.26795i		−	0.331046i
$483$		0			0
$484$	1.73205			0.0787296
$485$	32.7846	+	26.7685i	1.48867	+	1.21550i
$486$	0.517638			0.0234805
$487$			15.4548i			0.700324i	0.936689	+	0.350162i	$0.113874\pi$
$487$			15.4548i			0.700324i	−0.936689	+	0.350162i	$0.886126\pi$
$488$		−	1.26795i		−	0.0573974i
$489$	−22.4243			−1.01406
$490$		0			0
$491$	41.3205			1.86477			0.932384	−	0.361469i	$-0.117725\pi$
$491$	41.3205			1.86477			0.932384	+	0.361469i	$0.117725\pi$
$492$			14.6969i			0.662589i
$493$			19.7128i			0.887820i
$494$	10.9282			0.491683
$495$	−4.89898	+	6.00000i	−0.220193	+	0.269680i
$496$	−18.1074			−0.813045
$497$		0			0
$498$		−	3.10583i		−	0.139176i
$499$	32.2487			1.44365			0.721825	−	0.692075i	$-0.243303\pi$
$499$	32.2487			1.44365			0.721825	+	0.692075i	$0.243303\pi$
$500$	−17.1464	−	9.00000i	−0.766812	−	0.402492i
$501$	−18.9282			−0.845650
$502$		−	10.5359i		−	0.470240i
$503$		−	23.8564i		−	1.06370i	−0.846837	−	0.531852i	$-0.821496\pi$
$503$		−	23.8564i		−	1.06370i	0.846837	−	0.531852i	$-0.178504\pi$
$504$		0			0
$505$	−9.85641	+	12.0716i	−0.438604	+	0.537178i
$506$	−6.24871			−0.277789
$507$		−	3.00000i		−	0.133235i
$508$			4.89898i			0.217357i
$509$	3.03150			0.134369			0.0671844	−	0.997741i	$-0.478598\pi$
$509$	3.03150			0.134369			0.0671844	+	0.997741i	$0.478598\pi$
$510$	3.58630	+	2.92820i	0.158804	+	0.129663i
$511$		0			0
$512$		−	22.1841i		−	0.980408i
$513$			5.27792i			0.233026i
$514$	−1.79315			−0.0790925
$515$	−24.0000	−	19.5959i	−1.05757	−	0.863499i
$516$		0			0
$517$			20.7846i			0.914106i
$518$		0			0
$519$	16.0000			0.702322
$520$	−10.9282	+	13.3843i	−0.479233	+	0.586939i
$521$	−28.2843			−1.23916			−0.619578	−	0.784935i	$-0.712696\pi$
$521$	−28.2843			−1.23916			−0.619578	+	0.784935i	$0.712696\pi$
$522$			2.55103i			0.111655i
$523$			43.7128i			1.91143i	0.294297	+	0.955714i	$0.404914\pi$
$523$			43.7128i			1.91143i	−0.294297	+	0.955714i	$0.595086\pi$
$524$	−9.79796			−0.428026
$525$		0			0
$526$	−3.94744			−0.172117
$527$		−	29.3939i		−	1.28042i
$528$			8.53590i			0.371477i
$529$	10.8564			0.472018
$530$	5.37945	−	6.58846i	0.233668	−	0.286184i
$531$	−0.757875			−0.0328890
$532$		0			0
$533$		−	33.9411i		−	1.47015i
$534$	8.00000			0.346194
$535$	26.9444	+	22.0000i	1.16491	+	0.951143i
$536$	−24.3923			−1.05359
$537$		−	10.3923i		−	0.448461i
$538$			16.0000i			0.689809i
$539$		0			0
$540$	−3.00000	−	2.44949i	−0.129099	−	0.105409i
$541$	26.6410			1.14539			0.572693	−	0.819770i	$-0.305899\pi$
$541$	26.6410			1.14539			0.572693	+	0.819770i	$0.305899\pi$
$542$			0.875644i			0.0376121i
$543$		−	6.31319i		−	0.270925i
$544$	20.5569			0.881368
$545$	−22.4243	+	27.4641i	−0.960553	+	1.17643i
$546$		0			0
$547$			10.0010i			0.427613i	0.976876	+	0.213807i	$0.0685862\pi$
$547$			10.0010i			0.427613i	−0.976876	+	0.213807i	$0.931414\pi$
$548$			17.6269i			0.752984i
$549$	−0.656339			−0.0280119
$550$	−8.78461	+	1.79315i	−0.374577	+	0.0764602i
$551$	−26.0106			−1.10809
$552$		−	6.73205i		−	0.286535i
$553$		0			0
$554$	−5.85641			−0.248815
$555$	−14.9282	+	18.2832i	−0.633667	+	0.776080i
$556$	0.656339			0.0278350
$557$			8.86422i			0.375589i	0.982208	+	0.187795i	$0.0601339\pi$
$557$			8.86422i			0.375589i	−0.982208	+	0.187795i	$0.939866\pi$
$558$		−	3.80385i		−	0.161030i
$559$		0			0
$560$		0			0
$561$	−13.8564			−0.585018
$562$		−	14.4195i		−	0.608251i
$563$		−	4.14359i		−	0.174632i	−0.996181	−	0.0873158i	$-0.972171\pi$
$563$		−	4.14359i		−	0.174632i	0.996181	−	0.0873158i	$-0.0278289\pi$
$564$	−10.3923			−0.437595
$565$	9.14162	+	7.46410i	0.384591	+	0.314017i
$566$	−1.10961			−0.0466402
$567$		0			0
$568$			12.3490i			0.518152i
$569$	15.8564			0.664735			0.332368	−	0.943150i	$-0.392153\pi$
$569$	15.8564			0.664735			0.332368	+	0.943150i	$0.392153\pi$
$570$	−3.86370	+	4.73205i	−0.161833	+	0.198204i
$571$	−15.7128			−0.657561			−0.328780	−	0.944406i	$-0.606638\pi$
$571$	−15.7128			−0.657561			−0.328780	+	0.944406i	$0.606638\pi$
$572$		−	24.0000i		−	1.00349i
$573$		−	7.46410i		−	0.311817i
$574$		0			0
$575$	−17.0718	+	3.48477i	−0.711943	+	0.145325i
$576$	−2.26795			−0.0944979
$577$			4.00000i			0.166522i	0.996528	+	0.0832611i	$0.0265335\pi$
$577$			4.00000i			0.166522i	−0.996528	+	0.0832611i	$0.973466\pi$
$578$		−	0.517638i		−	0.0215309i
$579$	−6.41473			−0.266587
$580$	12.0716	−	14.7846i	0.501245	−	0.613898i
$581$		0			0
$582$			9.79796i			0.406138i
$583$			25.4558i			1.05427i
$584$	5.65685			0.234082
$585$	6.92820	+	5.65685i	0.286446	+	0.233882i
$586$	−5.93426			−0.245142
$587$		−	4.14359i		−	0.171024i	−0.996337	−	0.0855122i	$-0.972747\pi$
$587$		−	4.14359i		−	0.171024i	0.996337	−	0.0855122i	$-0.0272527\pi$
$588$		0			0
$589$	38.7846			1.59809
$590$	−0.679492	−	0.554803i	−0.0279742	−	0.0228409i
$591$	22.8033			0.938002
$592$			26.0106i			1.06903i
$593$		−	25.3205i		−	1.03979i	−0.854231	−	0.519894i	$-0.825971\pi$
$593$		−	25.3205i		−	1.03979i	0.854231	−	0.519894i	$-0.174029\pi$
$594$	−1.79315			−0.0735739
$595$		0			0
$596$	−12.2487			−0.501727
$597$		−	8.10634i		−	0.331771i
$598$			7.21539i			0.295059i
$599$	−29.3205			−1.19800			−0.599002	−	0.800748i	$-0.704436\pi$
$599$	−29.3205			−1.19800			−0.599002	+	0.800748i	$0.704436\pi$
$600$	−1.93185	−	9.46410i	−0.0788675	−	0.386370i
$601$	−25.1512			−1.02594			−0.512970	−	0.858406i	$-0.671455\pi$
$601$	−25.1512			−1.02594			−0.512970	+	0.858406i	$0.671455\pi$
$602$		0			0
$603$			12.6264i			0.514186i
$604$	−33.7128			−1.37175
$605$	1.41421	−	1.73205i	0.0574960	−	0.0704179i
$606$	−3.60770			−0.146553
$607$		−	12.0000i		−	0.487065i	−0.969893	−	0.243532i	$-0.921694\pi$
$607$		−	12.0000i		−	0.487065i	0.969893	−	0.243532i	$-0.0783062\pi$
$608$			27.1244i			1.10004i
$609$		0			0
$610$	−0.588457	−	0.480473i	−0.0238259	−	0.0194538i
$611$	24.0000			0.970936
$612$		−	6.92820i		−	0.280056i
$613$		−	9.79796i		−	0.395736i	−0.980229	−	0.197868i	$-0.936598\pi$
$613$		−	9.79796i		−	0.395736i	0.980229	−	0.197868i	$-0.0634017\pi$
$614$	−2.07055			−0.0835607
$615$	14.6969	+	12.0000i	0.592638	+	0.483887i
$616$		0			0
$617$			27.1475i			1.09292i	0.837487	+	0.546458i	$0.184024\pi$
$617$			27.1475i			1.09292i	−0.837487	+	0.546458i	$0.815976\pi$
$618$		−	7.17260i		−	0.288524i
$619$	20.7327			0.833319			0.416659	−	0.909063i	$-0.363201\pi$
$619$	20.7327			0.833319			0.416659	+	0.909063i	$0.363201\pi$
$620$	−18.0000	+	22.0454i	−0.722897	+	0.885365i
$621$	−3.48477			−0.139839
$622$		−	2.14359i		−	0.0859503i
$623$		0			0
$624$	9.85641			0.394572
$625$	−23.0000	+	9.79796i	−0.920000	+	0.391918i
$626$	1.51575			0.0605815
$627$		−	18.2832i		−	0.730162i
$628$			8.78461i			0.350544i
$629$	−42.2233			−1.68355
$630$		0			0
$631$	−25.3205			−1.00799			−0.503997	−	0.863706i	$-0.668138\pi$
$631$	−25.3205			−1.00799			−0.503997	+	0.863706i	$0.668138\pi$
$632$		−	8.76268i		−	0.348561i
$633$		−	26.9282i		−	1.07030i
$634$	−2.44486			−0.0970979
$635$	4.89898	+	4.00000i	0.194410	+	0.158735i
$636$	−12.7279			−0.504695
$637$		0			0
$638$		−	8.83701i		−	0.349861i
$639$	6.39230			0.252876
$640$	−19.8362	−	16.1962i	−0.784093	−	0.640209i
$641$	10.0000			0.394976			0.197488	−	0.980305i	$-0.436722\pi$
$641$	10.0000			0.394976			0.197488	+	0.980305i	$0.436722\pi$
$642$			8.05256i			0.317809i
$643$			4.00000i			0.157745i	0.996885	+	0.0788723i	$0.0251319\pi$
$643$			4.00000i			0.157745i	−0.996885	+	0.0788723i	$0.974868\pi$
$644$		0			0
$645$		0			0
$646$	−10.9282			−0.429964
$647$		−	42.9282i		−	1.68768i	−0.536593	−	0.843841i	$-0.680289\pi$
$647$		−	42.9282i		−	1.68768i	0.536593	−	0.843841i	$-0.319711\pi$
$648$		−	1.93185i		−	0.0758903i
$649$	2.62536			0.103054
$650$	2.07055	+	10.1436i	0.0812137	+	0.397864i
$651$		0			0
$652$			38.8401i			1.52110i
$653$			3.96524i			0.155172i	0.996986	+	0.0775859i	$0.0247212\pi$
$653$			3.96524i			0.155172i	−0.996986	+	0.0775859i	$0.975279\pi$
$654$	−8.20788			−0.320954
$655$	−8.00000	+	9.79796i	−0.312586	+	0.382838i
$656$	20.9086			0.816344
$657$		−	2.92820i		−	0.114240i
$658$		0			0
$659$	−10.3923			−0.404827			−0.202413	−	0.979300i	$-0.564878\pi$
$659$	−10.3923			−0.404827			−0.202413	+	0.979300i	$0.564878\pi$
$660$	10.3923	+	8.48528i	0.404520	+	0.330289i
$661$	13.4858			0.524537			0.262268	−	0.964995i	$-0.415529\pi$
$661$	13.4858			0.524537			0.262268	+	0.964995i	$0.415529\pi$
$662$			4.54725i			0.176734i
$663$			16.0000i			0.621389i
$664$	−11.5911			−0.449822
$665$		0			0
$666$	−5.46410			−0.211730
$667$		−	17.1736i		−	0.664966i
$668$			32.7846i			1.26847i
$669$	8.00000			0.309298
$670$	−9.24316	+	11.3205i	−0.357094	+	0.437349i
$671$	2.27362			0.0877723
$672$		0			0
$673$		−	21.8695i		−	0.843009i	−0.906826	−	0.421504i	$-0.861502\pi$
$673$		−	21.8695i		−	0.843009i	0.906826	−	0.421504i	$-0.138498\pi$
$674$	−9.17691			−0.353482
$675$	−4.89898	+	1.00000i	−0.188562	+	0.0384900i
$676$	−5.19615			−0.199852
$677$		−	23.1769i		−	0.890761i	−0.895341	−	0.445381i	$-0.853068\pi$
$677$		−	23.1769i		−	0.890761i	0.895341	−	0.445381i	$-0.146932\pi$
$678$			2.73205i			0.104924i
$679$		0			0
$680$	10.9282	−	13.3843i	0.419077	−	0.513263i
$681$	−4.00000			−0.153280
$682$			13.1769i			0.504570i
$683$			42.3249i			1.61952i	0.586764	+	0.809758i	$0.300402\pi$
$683$			42.3249i			1.61952i	−0.586764	+	0.809758i	$0.699598\pi$
$684$	9.14162			0.349539
$685$	17.6269	+	14.3923i	0.673489	+	0.549902i
$686$		0			0
$687$			13.4858i			0.514515i
$688$		0			0
$689$	29.3939			1.11982
$690$	−3.12436	−	2.55103i	−0.118942	−	0.0971159i
$691$	10.9348			0.415978			0.207989	−	0.978131i	$-0.433308\pi$
$691$	10.9348			0.415978			0.207989	+	0.978131i	$0.433308\pi$
$692$		−	27.7128i		−	1.05348i
$693$		0			0
$694$	−16.0526			−0.609347
$695$	0.535898	−	0.656339i	0.0203278	−	0.0248963i
$696$	9.52056			0.360876
$697$			33.9411i			1.28561i
$698$		−	9.12436i		−	0.345362i
$699$	−5.27792			−0.199629
$700$		0			0
$701$	−11.0718			−0.418176			−0.209088	−	0.977897i	$-0.567050\pi$
$701$	−11.0718			−0.418176			−0.209088	+	0.977897i	$0.567050\pi$
$702$			2.07055i			0.0781480i
$703$		−	55.7128i		−	2.10125i
$704$	7.85641			0.296099
$705$	−8.48528	+	10.3923i	−0.319574	+	0.391397i
$706$	−5.93426			−0.223339
$707$		0			0
$708$			1.31268i			0.0493334i
$709$	10.9282			0.410417			0.205209	−	0.978718i	$-0.434213\pi$
$709$	10.9282			0.410417			0.205209	+	0.978718i	$0.434213\pi$
$710$	5.73118	+	4.67949i	0.215087	+	0.175618i
$711$	−4.53590			−0.170109
$712$		−	29.8564i		−	1.11892i
$713$			25.6077i			0.959016i
$714$		0			0
$715$	−24.0000	−	19.5959i	−0.897549	−	0.732846i
$716$	−18.0000			−0.672692
$717$			8.53590i			0.318779i
$718$			8.00481i			0.298737i
$719$	−14.6969			−0.548103			−0.274052	−	0.961715i	$-0.588364\pi$
$719$	−14.6969			−0.548103			−0.274052	+	0.961715i	$0.588364\pi$
$720$	−3.48477	+	4.26795i	−0.129870	+	0.159057i
$721$		0			0
$722$		−	4.58441i		−	0.170614i
$723$			14.0406i			0.522176i
$724$	−10.9348			−0.406388
$725$	−4.92820	−	24.1432i	−0.183029	−	0.896655i
$726$	0.517638			0.0192114
$727$		−	23.7128i		−	0.879460i	−0.898130	−	0.439730i	$-0.855074\pi$
$727$		−	23.7128i		−	0.879460i	0.898130	−	0.439730i	$-0.144926\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$	2.14359	−	2.62536i	0.0793380	−	0.0971688i
$731$		0			0
$732$			1.13681i			0.0420178i
$733$		−	17.8564i		−	0.659541i	−0.944061	−	0.329771i	$-0.893029\pi$
$733$		−	17.8564i		−	0.659541i	0.944061	−	0.329771i	$-0.106971\pi$
$734$	2.07055			0.0764255
$735$		0			0
$736$	−17.9090			−0.660133
$737$		−	43.7391i		−	1.61115i
$738$			4.39230i			0.161683i
$739$	25.8564			0.951143			0.475572	−	0.879677i	$-0.342241\pi$
$739$	25.8564			0.951143			0.475572	+	0.879677i	$0.342241\pi$
$740$	31.6675	+	25.8564i	1.16412	+	0.950500i
$741$	−21.1117			−0.775556
$742$		0			0
$743$			51.1619i			1.87695i	0.345351	+	0.938474i	$0.387760\pi$
$743$			51.1619i			1.87695i	−0.345351	+	0.938474i	$0.612240\pi$
$744$	−14.1962			−0.520456
$745$	−10.0010	+	12.2487i	−0.366409	+	0.448758i
$746$	−3.71281			−0.135936
$747$			6.00000i			0.219529i
$748$			24.0000i			0.877527i
$749$		0			0
$750$	−5.12436	−	2.68973i	−0.187115	−	0.0982149i
$751$	−36.7846			−1.34229			−0.671145	−	0.741326i	$-0.734197\pi$
$751$	−36.7846			−1.34229			−0.671145	+	0.741326i	$0.734197\pi$
$752$			14.7846i			0.539139i
$753$			20.3538i			0.741733i
$754$	−10.2041			−0.371612
$755$	−27.5264	+	33.7128i	−1.00179	+	1.22693i
$756$		0			0
$757$			34.2929i			1.24640i	0.782064	+	0.623198i	$0.214167\pi$
$757$			34.2929i			1.24640i	−0.782064	+	0.623198i	$0.785833\pi$
$758$			5.93426i			0.215542i
$759$	12.0716			0.438171
$760$	17.6603	+	14.4195i	0.640605	+	0.523052i
$761$	18.0802			0.655406			0.327703	−	0.944781i	$-0.393726\pi$
$761$	18.0802			0.655406			0.327703	+	0.944781i	$0.393726\pi$
$762$			1.46410i			0.0530388i
$763$		0			0
$764$	−12.9282			−0.467726
$765$	−6.92820	−	5.65685i	−0.250490	−	0.204524i
$766$	12.3490			0.446187
$767$		−	3.03150i		−	0.109461i
$768$		−	1.39230i		−	0.0502405i
$769$	−39.2934			−1.41696			−0.708478	−	0.705733i	$-0.750618\pi$
$769$	−39.2934			−1.41696			−0.708478	+	0.705733i	$0.750618\pi$
$770$		0			0
$771$	3.46410			0.124757
$772$			11.1106i			0.399881i
$773$		−	37.8564i		−	1.36160i	−0.732469	−	0.680800i	$-0.761632\pi$
$773$		−	37.8564i		−	1.36160i	0.732469	−	0.680800i	$-0.238368\pi$
$774$		0			0
$775$	7.34847	+	36.0000i	0.263965	+	1.29316i
$776$	36.5665			1.31266
$777$		0			0
$778$			5.73118i			0.205473i
$779$	−44.7846			−1.60458
$780$	9.79796	−	12.0000i	0.350823	−	0.429669i
$781$	−22.1436			−0.792360
$782$		−	7.21539i		−	0.258022i
$783$		−	4.92820i		−	0.176120i
$784$		0			0
$785$	8.78461	+	7.17260i	0.313536	+	0.256001i
$786$	−2.92820			−0.104446
$787$		−	45.8564i		−	1.63460i	−0.576209	−	0.817302i	$-0.695469\pi$
$787$		−	45.8564i		−	1.63460i	0.576209	−	0.817302i	$-0.304531\pi$
$788$		−	39.4964i		−	1.40700i
$789$	7.62587			0.271488
$790$	−4.06678	−	3.32051i	−0.144689	−	0.118138i
$791$		0			0
$792$			6.69213i			0.237795i
$793$		−	2.62536i		−	0.0932291i
$794$	12.2747			0.435611
$795$	−10.3923	+	12.7279i	−0.368577	+	0.451413i
$796$	−14.0406			−0.497656
$797$		−	10.1436i		−	0.359305i	−0.983730	−	0.179652i	$-0.942503\pi$
$797$		−	10.1436i		−	0.359305i	0.983730	−	0.179652i	$-0.0574973\pi$
$798$		0			0
$799$	−24.0000			−0.849059
$800$	−25.1769	+	5.13922i	−0.890138	+	0.181699i
$801$	−15.4548			−0.546069
$802$		−	1.03528i		−	0.0365569i
$803$			10.1436i			0.357960i
$804$	21.8695			0.771279
$805$		0			0
$806$	15.2154			0.535939
$807$		−	30.9096i		−	1.08807i
$808$			13.4641i			0.473665i
$809$	−21.7128			−0.763382			−0.381691	−	0.924290i	$-0.624658\pi$
$809$	−21.7128			−0.763382			−0.381691	+	0.924290i	$0.624658\pi$
$810$	−0.896575	−	0.732051i	−0.0315025	−	0.0257216i
$811$	−25.6317			−0.900051			−0.450026	−	0.893016i	$-0.648585\pi$
$811$	−25.6317			−0.900051			−0.450026	+	0.893016i	$0.648585\pi$
$812$		0			0
$813$		−	1.69161i		−	0.0593275i
$814$	18.9282			0.663433
$815$	38.8401	+	31.7128i	1.36051	+	1.11085i
$816$	−9.85641			−0.345043
$817$		0			0
$818$		−	5.90897i		−	0.206602i
$819$		0			0
$820$	20.7846	−	25.4558i	0.725830	−	0.888957i
$821$	18.7846			0.655587			0.327794	−	0.944749i	$-0.393695\pi$
$821$	18.7846			0.655587			0.327794	+	0.944749i	$0.393695\pi$
$822$			5.26795i			0.183741i
$823$		−	30.7066i		−	1.07036i	−0.844737	−	0.535182i	$-0.820243\pi$
$823$		−	30.7066i		−	1.07036i	0.844737	−	0.535182i	$-0.179757\pi$
$824$	−26.7685			−0.932526
$825$	16.9706	−	3.46410i	0.590839	−	0.120605i
$826$		0			0
$827$		−	8.18067i		−	0.284470i	−0.989833	−	0.142235i	$-0.954571\pi$
$827$		−	8.18067i		−	0.284470i	0.989833	−	0.142235i	$-0.0454289\pi$
$828$			6.03579i			0.209758i
$829$	6.51626			0.226319			0.113160	−	0.993577i	$-0.463903\pi$
$829$	6.51626			0.226319			0.113160	+	0.993577i	$0.463903\pi$
$830$	−4.39230	+	5.37945i	−0.152459	+	0.186724i
$831$	11.3137			0.392468
$832$		−	9.07180i		−	0.314508i
$833$		0			0
$834$	0.196152			0.00679220
$835$	32.7846	+	26.7685i	1.13456	+	0.926363i
$836$	−31.6675			−1.09524
$837$			7.34847i			0.254000i
$838$		−	10.9282i		−	0.377509i
$839$	20.3538			0.702691			0.351345	−	0.936246i	$-0.385724\pi$
$839$	20.3538			0.702691			0.351345	+	0.936246i	$0.385724\pi$
$840$		0			0
$841$	−4.71281			−0.162511
$842$		−	6.61780i		−	0.228064i
$843$			27.8564i			0.959426i
$844$	−46.6410			−1.60545
$845$	−4.24264	+	5.19615i	−0.145951	+	0.178753i
$846$	−3.10583			−0.106781
$847$		0			0
$848$			18.1074i			0.621810i
$849$	2.14359			0.0735679
$850$	−2.07055	−	10.1436i	−0.0710194	−	0.347922i
$851$	36.7846			1.26096
$852$		−	11.0718i		−	0.379314i
$853$		−	13.0718i		−	0.447570i	−0.974639	−	0.223785i	$-0.928159\pi$
$853$		−	13.0718i		−	0.447570i	0.974639	−	0.223785i	$-0.0718413\pi$
$854$		0			0
$855$	7.46410	−	9.14162i	0.255267	−	0.312637i
$856$	30.0526			1.02718
$857$		−	9.85641i		−	0.336688i	−0.985728	−	0.168344i	$-0.946158\pi$
$857$		−	9.85641i		−	0.336688i	0.985728	−	0.168344i	$-0.0538420\pi$
$858$		−	7.17260i		−	0.244869i
$859$	3.41044			0.116363			0.0581813	−	0.998306i	$-0.481470\pi$
$859$	3.41044			0.116363			0.0581813	+	0.998306i	$0.481470\pi$
$860$		0			0
$861$		0			0
$862$		−	19.3185i		−	0.657991i
$863$			15.9081i			0.541517i	0.962647	+	0.270759i	$0.0872745\pi$
$863$			15.9081i			0.541517i	−0.962647	+	0.270759i	$0.912725\pi$
$864$	−5.13922			−0.174840
$865$	−27.7128	−	22.6274i	−0.942264	−	0.769355i
$866$	9.24316			0.314095
$867$			1.00000i			0.0339618i
$868$		0			0
$869$	15.7128			0.533021
$870$	3.60770	−	4.41851i	0.122312	−	0.149801i
$871$	−50.5055			−1.71132
$872$			30.6322i			1.03734i
$873$		−	18.9282i		−	0.640623i
$874$	9.52056			0.322038
$875$		0			0
$876$	−5.07180			−0.171360
$877$		−	33.9411i		−	1.14611i	−0.819517	−	0.573055i	$-0.805758\pi$
$877$		−	33.9411i		−	1.14611i	0.819517	−	0.573055i	$-0.194242\pi$
$878$			6.73205i			0.227196i
$879$	11.4641			0.386675
$880$	12.0716	−	14.7846i	0.406933	−	0.498389i
$881$	−29.5969			−0.997147			−0.498573	−	0.866848i	$-0.666143\pi$
$881$	−29.5969			−0.997147			−0.498573	+	0.866848i	$0.666143\pi$
$882$		0			0
$883$		−	29.3939i		−	0.989183i	−0.869126	−	0.494591i	$-0.835318\pi$
$883$		−	29.3939i		−	0.989183i	0.869126	−	0.494591i	$-0.164682\pi$
$884$	27.7128			0.932083
$885$	1.31268	+	1.07180i	0.0441252	+	0.0360281i
$886$	−6.48334			−0.217812
$887$			13.7128i			0.460431i	0.973140	+	0.230216i	$0.0739431\pi$
$887$			13.7128i			0.460431i	−0.973140	+	0.230216i	$0.926057\pi$
$888$			20.3923i			0.684321i
$889$		0			0
$890$	−13.8564	−	11.3137i	−0.464468	−	0.379236i
$891$	3.46410			0.116052
$892$		−	13.8564i		−	0.463947i
$893$		−	31.6675i		−	1.05971i
$894$	−3.66063			−0.122430
$895$	−14.6969	+	18.0000i	−0.491264	+	0.601674i
$896$		0			0
$897$		−	13.9391i		−	0.465412i
$898$			18.5606i			0.619377i
$899$	−36.2147			−1.20783
$900$	1.73205	+	8.48528i	0.0577350	+	0.282843i
$901$	−29.3939			−0.979252
$902$		−	15.2154i		−	0.506617i
$903$		0			0
$904$	10.1962			0.339119
$905$	−8.92820	+	10.9348i	−0.296784	+	0.363484i
$906$	−10.0754			−0.334731
$907$			6.76646i			0.224677i	0.993670	+	0.112338i	$0.0358340\pi$
$907$			6.76646i			0.224677i	−0.993670	+	0.112338i	$0.964166\pi$
$908$			6.92820i			0.229920i
$909$	6.96953			0.231165
$910$		0			0
$911$	9.60770			0.318317			0.159159	−	0.987253i	$-0.449122\pi$
$911$	9.60770			0.318317			0.159159	+	0.987253i	$0.449122\pi$
$912$		−	13.0053i		−	0.430649i
$913$		−	20.7846i		−	0.687870i
$914$	−11.3205			−0.374449
$915$	1.13681	+	0.928203i	0.0375819	+	0.0306855i
$916$	23.3581			0.771773
$917$		0			0
$918$		−	2.07055i		−	0.0683384i
$919$	9.07180			0.299251			0.149625	−	0.988743i	$-0.452193\pi$
$919$	9.07180			0.299251			0.149625	+	0.988743i	$0.452193\pi$
$920$	−9.52056	+	11.6603i	−0.313883	+	0.384427i
$921$	4.00000			0.131804
$922$		−	16.7846i		−	0.552772i
$923$			25.5692i			0.841621i
$924$		0			0
$925$	51.7128	−	10.5558i	1.70031	−	0.347074i
$926$	−11.6077			−0.381453
$927$			13.8564i			0.455104i
$928$		−	25.3271i		−	0.831403i
$929$	18.0802			0.593191			0.296596	−	0.955003i	$-0.404149\pi$
$929$	18.0802			0.593191			0.296596	+	0.955003i	$0.404149\pi$
$930$	−5.37945	+	6.58846i	−0.176399	+	0.216044i
$931$		0			0
$932$			9.14162i			0.299444i
$933$			4.14110i			0.135574i
$934$	−5.10205			−0.166944
$935$	24.0000	+	19.5959i	0.784884	+	0.640855i
$936$	7.72741			0.252578
$937$		−	16.7846i		−	0.548329i	−0.961683	−	0.274165i	$-0.911599\pi$
$937$		−	16.7846i		−	0.548329i	0.961683	−	0.274165i	$-0.0884013\pi$
$938$		0			0
$939$	−2.92820			−0.0955583
$940$	18.0000	+	14.6969i	0.587095	+	0.479361i
$941$	0.203072			0.00661996			0.00330998	−	0.999995i	$-0.498946\pi$
$941$	0.203072			0.00661996			0.00330998	+	0.999995i	$0.498946\pi$
$942$			2.62536i			0.0855387i
$943$		−	29.5692i		−	0.962906i
$944$	1.86748			0.0607813
$945$		0			0
$946$		0			0
$947$			18.3848i			0.597425i	0.954343	+	0.298712i	$0.0965572\pi$
$947$			18.3848i			0.597425i	−0.954343	+	0.298712i	$0.903443\pi$
$948$			7.85641i			0.255164i
$949$	11.7128			0.380214
$950$	13.3843	−	2.73205i	0.434243	−	0.0886394i
$951$	4.72311			0.153157
$952$		0			0
$953$		−	53.9160i		−	1.74651i	−0.487264	−	0.873255i	$-0.662005\pi$
$953$		−	53.9160i		−	1.74651i	0.487264	−	0.873255i	$-0.337995\pi$
$954$	−3.80385			−0.123154
$955$	−10.5558	+	12.9282i	−0.341579	+	0.418347i
$956$	14.7846			0.478168
$957$			17.0718i			0.551853i
$958$		−	13.0718i		−	0.422331i
$959$		0			0
$960$	3.92820	+	3.20736i	0.126782	+	0.103517i
$961$	23.0000			0.741935
$962$		−	21.8564i		−	0.704679i
$963$		−	15.5563i		−	0.501296i
$964$	24.3190			0.783263
$965$	11.1106	+	9.07180i	0.357664	+	0.292031i
$966$		0			0
$967$			10.0010i			0.321611i	0.986986	+	0.160806i	$0.0514093\pi$
$967$			10.0010i			0.321611i	−0.986986	+	0.160806i	$0.948591\pi$
$968$		−	1.93185i		−	0.0620921i
$969$	21.1117			0.678204
$970$	13.8564	−	16.9706i	0.444902	−	0.544892i
$971$	−11.6654			−0.374362			−0.187181	−	0.982325i	$-0.559935\pi$
$971$	−11.6654			−0.374362			−0.187181	+	0.982325i	$0.559935\pi$
$972$			1.73205i			0.0555556i
$973$		0			0
$974$	8.00000			0.256337
$975$	−4.00000	−	19.5959i	−0.128103	−	0.627572i
$976$	1.61729			0.0517680
$977$			45.6338i			1.45995i	0.683472	+	0.729977i	$0.260469\pi$
$977$			45.6338i			1.45995i	−0.683472	+	0.729977i	$0.739531\pi$
$978$			11.6077i			0.371173i
$979$	53.5370			1.71105
$980$		0			0
$981$	15.8564			0.506256
$982$		−	21.3891i		−	0.682553i
$983$			24.7846i			0.790506i	0.918572	+	0.395253i	$0.129343\pi$
$983$			24.7846i			0.790506i	−0.918572	+	0.395253i	$0.870657\pi$
$984$	16.3923			0.522568
$985$	−39.4964	−	32.2487i	−1.25846	−	1.02753i
$986$	10.2041			0.324965
$987$		0			0
$988$			36.5665i			1.16333i
$989$		0			0
$990$	3.10583	+	2.53590i	0.0987097	+	0.0805961i
$991$	12.7846			0.406117			0.203058	−	0.979167i	$-0.434912\pi$
$991$	12.7846			0.406117			0.203058	+	0.979167i	$0.434912\pi$
$992$			37.7654i			1.19905i
$993$		−	8.78461i		−	0.278771i
$994$		0			0
$995$	−11.4641	+	14.0406i	−0.363436	+	0.445117i
$996$	10.3923			0.329293
$997$			41.8564i			1.32561i	0.748794	+	0.662803i	$0.230633\pi$
$997$			41.8564i			1.32561i	−0.748794	+	0.662803i	$0.769367\pi$
$998$		−	16.6932i		−	0.528413i
$999$	10.5558			0.333972

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	735.2.d.f.589.4	yes	8
3.2	odd	2		2205.2.d.t.1324.5		8
5.2	odd	4		3675.2.a.bu.1.3		4
5.3	odd	4		3675.2.a.bs.1.2		4
5.4	even	2	inner	735.2.d.f.589.5	yes	8
7.2	even	3		735.2.q.c.214.2		8
7.3	odd	6		735.2.q.c.79.3		8
7.4	even	3		735.2.q.d.79.3		8
7.5	odd	6		735.2.q.d.214.2		8
7.6	odd	2	inner	735.2.d.f.589.3	✓	8
15.14	odd	2		2205.2.d.t.1324.3		8
21.20	even	2		2205.2.d.t.1324.6		8
35.4	even	6		735.2.q.c.79.2		8
35.9	even	6		735.2.q.d.214.3		8
35.13	even	4		3675.2.a.bu.1.2		4
35.19	odd	6		735.2.q.c.214.3		8
35.24	odd	6		735.2.q.d.79.2		8
35.27	even	4		3675.2.a.bs.1.3		4
35.34	odd	2	inner	735.2.d.f.589.6	yes	8
105.104	even	2		2205.2.d.t.1324.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
735.2.d.f.589.3	✓	8	7.6	odd	2	inner
735.2.d.f.589.4	yes	8	1.1	even	1	trivial
735.2.d.f.589.5	yes	8	5.4	even	2	inner
735.2.d.f.589.6	yes	8	35.34	odd	2	inner
735.2.q.c.79.2		8	35.4	even	6
735.2.q.c.79.3		8	7.3	odd	6
735.2.q.c.214.2		8	7.2	even	3
735.2.q.c.214.3		8	35.19	odd	6
735.2.q.d.79.2		8	35.24	odd	6
735.2.q.d.79.3		8	7.4	even	3
735.2.q.d.214.2		8	7.5	odd	6
735.2.q.d.214.3		8	35.9	even	6
2205.2.d.t.1324.3		8	15.14	odd	2
2205.2.d.t.1324.4		8	105.104	even	2
2205.2.d.t.1324.5		8	3.2	odd	2
2205.2.d.t.1324.6		8	21.20	even	2
3675.2.a.bs.1.2		4	5.3	odd	4
3675.2.a.bs.1.3		4	35.27	even	4
3675.2.a.bu.1.2		4	35.13	even	4
3675.2.a.bu.1.3		4	5.2	odd	4

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:	\( N \)	\(=\)	\( 735 = 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	735.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-0.517638i q^{2} +1.00000i q^{3} +1.73205 q^{4} +(1.41421 - 1.73205i) q^{5} +0.517638 q^{6} -1.93185i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q-0.517638i q^{2} +1.00000i q^{3} +1.73205 q^{4} +(1.41421 - 1.73205i) q^{5} +0.517638 q^{6} -1.93185i q^{8} -1.00000 q^{9} +(-0.896575 - 0.732051i) q^{10} +3.46410 q^{11} +1.73205i q^{12} -4.00000i q^{13} +(1.73205 + 1.41421i) q^{15} +2.46410 q^{16} +4.00000i q^{17} +0.517638i q^{18} -5.27792 q^{19} +(2.44949 - 3.00000i) q^{20} -1.79315i q^{22} -3.48477i q^{23} +1.93185 q^{24} +(-1.00000 - 4.89898i) q^{25} -2.07055 q^{26} -1.00000i q^{27} +4.92820 q^{29} +(0.732051 - 0.896575i) q^{30} -7.34847 q^{31} -5.13922i q^{32} +3.46410i q^{33} +2.07055 q^{34} -1.73205 q^{36} +10.5558i q^{37} +2.73205i q^{38} +4.00000 q^{39} +(-3.34607 - 2.73205i) q^{40} +8.48528 q^{41} +6.00000 q^{44} +(-1.41421 + 1.73205i) q^{45} -1.80385 q^{46} +6.00000i q^{47} +2.46410i q^{48} +(-2.53590 + 0.517638i) q^{50} -4.00000 q^{51} -6.92820i q^{52} +7.34847i q^{53} -0.517638 q^{54} +(4.89898 - 6.00000i) q^{55} -5.27792i q^{57} -2.55103i q^{58} +0.757875 q^{59} +(3.00000 + 2.44949i) q^{60} +0.656339 q^{61} +3.80385i q^{62} +2.26795 q^{64} +(-6.92820 - 5.65685i) q^{65} +1.79315 q^{66} -12.6264i q^{67} +6.92820i q^{68} +3.48477 q^{69} -6.39230 q^{71} +1.93185i q^{72} +2.92820i q^{73} +5.46410 q^{74} +(4.89898 - 1.00000i) q^{75} -9.14162 q^{76} -2.07055i q^{78} +4.53590 q^{79} +(3.48477 - 4.26795i) q^{80} +1.00000 q^{81} -4.39230i q^{82} -6.00000i q^{83} +(6.92820 + 5.65685i) q^{85} +4.92820i q^{87} -6.69213i q^{88} +15.4548 q^{89} +(0.896575 + 0.732051i) q^{90} -6.03579i q^{92} -7.34847i q^{93} +3.10583 q^{94} +(-7.46410 + 9.14162i) q^{95} +5.13922 q^{96} +18.9282i q^{97} -3.46410 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{9}+O(q^{10}) \) 8 * q - 8 * q^9	\( 8 q - 8 q^{9} - 8 q^{16} - 8 q^{25} - 16 q^{29} - 8 q^{30} + 32 q^{39} + 48 q^{44} - 56 q^{46} - 48 q^{50} - 32 q^{51} + 24 q^{60} + 32 q^{64} + 32 q^{71} + 16 q^{74} + 64 q^{79} + 8 q^{81} - 32 q^{95}+O(q^{100}) \) 8 * q - 8 * q^9 - 8 * q^16 - 8 * q^25 - 16 * q^29 - 8 * q^30 + 32 * q^39 + 48 * q^44 - 56 * q^46 - 48 * q^50 - 32 * q^51 + 24 * q^60 + 32 * q^64 + 32 * q^71 + 16 * q^74 + 64 * q^79 + 8 * q^81 - 32 * q^95

Introduction

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