LMFDB - Embedded newform 378.3.r.a.305.14

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [378,3,Mod(233,378)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("378.233"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(378, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5, 2])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	378.r (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$10.2997539928$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			305.14
Character	$\chi$	$=$	378.305
Dual form			378.3.r.a.233.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.41421i q^{2} -2.00000 q^{4} +(2.07383 + 1.19732i) q^{5} +(-5.45012 - 4.39274i) q^{7} -2.82843i q^{8} +(-1.69327 + 2.93283i) q^{10} +(-5.05707 + 2.91970i) q^{11} +(-2.87005 - 4.97107i) q^{13} +(6.21227 - 7.70764i) q^{14} +4.00000 q^{16} +(-21.4241 - 12.3692i) q^{17} +(-1.06883 - 1.85127i) q^{19} +(-4.14765 - 2.39465i) q^{20} +(-4.12908 - 7.15177i) q^{22} +(0.123600 + 0.0713603i) q^{23} +(-9.63283 - 16.6845i) q^{25} +(7.03015 - 4.05886i) q^{26} +(10.9002 + 8.78548i) q^{28} +(-31.4557 - 18.1610i) q^{29} +13.0465 q^{31} +5.65685i q^{32} +(17.4927 - 30.2982i) q^{34} +(-6.04307 - 15.6353i) q^{35} +(16.0604 + 27.8173i) q^{37} +(2.61809 - 1.51156i) q^{38} +(3.38655 - 5.86567i) q^{40} +(-27.3943 + 15.8161i) q^{41} +(40.1194 - 69.4888i) q^{43} +(10.1141 - 5.83940i) q^{44} +(-0.100919 + 0.174796i) q^{46} -61.1758i q^{47} +(10.4077 + 47.8819i) q^{49} +(23.5955 - 13.6229i) q^{50} +(5.74010 + 9.94214i) q^{52} +(-22.5819 - 13.0377i) q^{53} -13.9833 q^{55} +(-12.4245 + 15.4153i) q^{56} +(25.6835 - 44.4851i) q^{58} -22.7566i q^{59} -102.664 q^{61} +18.4505i q^{62} -8.00000 q^{64} -13.7455i q^{65} +70.2380 q^{67} +(42.8481 + 24.7384i) q^{68} +(22.1117 - 8.54620i) q^{70} +100.792i q^{71} +(-4.36953 + 7.56824i) q^{73} +(-39.3397 + 22.7128i) q^{74} +(2.13766 + 3.70254i) q^{76} +(40.3871 + 6.30167i) q^{77} -62.2922 q^{79} +(8.29531 + 4.78930i) q^{80} +(-22.3674 - 38.7414i) q^{82} +(51.5381 + 29.7555i) q^{83} +(-29.6199 - 51.3031i) q^{85} +(98.2720 + 56.7374i) q^{86} +(8.25816 + 14.3035i) q^{88} +(94.6860 - 54.6670i) q^{89} +(-6.19450 + 39.7003i) q^{91} +(-0.247199 - 0.142721i) q^{92} +86.5157 q^{94} -5.11896i q^{95} +(-79.8603 + 138.322i) q^{97} +(-67.7153 + 14.7187i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 64 q^{4} + 2 q^{7} + 36 q^{11} + 10 q^{13} - 36 q^{14} + 128 q^{16} + 54 q^{17} + 28 q^{19} + 126 q^{23} + 80 q^{25} + 72 q^{26} - 4 q^{28} - 36 q^{29} + 16 q^{31} + 90 q^{35} + 22 q^{37} - 72 q^{41}+ \cdots - 288 q^{98}+O(q^{100}) $ 32 * q - 64 * q^4 + 2 * q^7 + 36 * q^11 + 10 * q^13 - 36 * q^14 + 128 * q^16 + 54 * q^17 + 28 * q^19 + 126 * q^23 + 80 * q^25 + 72 * q^26 - 4 * q^28 - 36 * q^29 + 16 * q^31 + 90 * q^35 + 22 * q^37 - 72 * q^41 + 16 * q^43 - 72 * q^44 - 12 * q^46 + 2 * q^49 + 288 * q^50 - 20 * q^52 + 72 * q^53 - 24 * q^55 + 72 * q^56 - 24 * q^58 + 124 * q^61 - 256 * q^64 - 140 * q^67 - 108 * q^68 + 72 * q^70 + 196 * q^73 - 216 * q^74 - 56 * q^76 - 486 * q^77 + 76 * q^79 + 60 * q^85 + 144 * q^86 + 486 * q^89 - 122 * q^91 - 252 * q^92 - 336 * q^94 - 38 * q^97 - 288 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$.

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$			1.41421i			0.707107i
$2$			1.41421i			0.707107i
$3$		0			0
$3$		0			0
$4$	−2.00000			−0.500000
$5$	2.07383	+	1.19732i	0.414765	+	0.239465i	0.692835	−	0.721096i	$-0.256361\pi$
$5$	2.07383	+	1.19732i	0.414765	+	0.239465i	−0.278070	+	0.960561i	$0.589695\pi$
$6$		0			0
$7$	−5.45012	−	4.39274i	−0.778589	−	0.627534i
$7$	−5.45012	−	4.39274i	−0.778589	−	0.627534i
$8$		−	2.82843i		−	0.353553i
$9$		0			0
$10$	−1.69327	+	2.93283i	−0.169327	+	0.293283i
$11$	−5.05707	+	2.91970i	−0.459733	+	0.265427i	−0.711932	−	0.702248i	$-0.752180\pi$
$11$	−5.05707	+	2.91970i	−0.459733	+	0.265427i	0.252199	+	0.967675i	$0.418846\pi$
$12$		0			0
$13$	−2.87005	−	4.97107i	−0.220773	−	0.382390i	0.734270	−	0.678858i	$-0.237525\pi$
$13$	−2.87005	−	4.97107i	−0.220773	−	0.382390i	−0.955043	+	0.296468i	$0.904191\pi$
$14$	6.21227	−	7.70764i	0.443734	−	0.550545i
$15$		0			0
$16$	4.00000			0.250000
$17$	−21.4241	−	12.3692i	−1.26024	−	0.727600i	−0.287119	−	0.957895i	$-0.592697\pi$
$17$	−21.4241	−	12.3692i	−1.26024	−	0.727600i	−0.973121	+	0.230296i	$0.926031\pi$
$18$		0			0
$19$	−1.06883	−	1.85127i	−0.0562543	−	0.0974353i	0.836527	−	0.547926i	$-0.184582\pi$
$19$	−1.06883	−	1.85127i	−0.0562543	−	0.0974353i	−0.892781	+	0.450491i	$0.851249\pi$
$20$	−4.14765	−	2.39465i	−0.207383	−	0.119732i
$21$		0			0
$22$	−4.12908	−	7.15177i	−0.187685	−	0.325081i
$23$	0.123600	+	0.0713603i	0.00537389	+	0.00310262i	0.502685	−	0.864470i	$-0.332346\pi$
$23$	0.123600	+	0.0713603i	0.00537389	+	0.00310262i	−0.497311	+	0.867573i	$0.665679\pi$
$24$		0			0
$25$	−9.63283	−	16.6845i	−0.385313	−	0.667382i
$26$	7.03015	−	4.05886i	0.270391	−	0.156110i
$27$		0			0
$28$	10.9002	+	8.78548i	0.389294	+	0.313767i
$29$	−31.4557	−	18.1610i	−1.08468	−	0.626240i	−0.152524	−	0.988300i	$-0.548740\pi$
$29$	−31.4557	−	18.1610i	−1.08468	−	0.626240i	−0.932155	+	0.362060i	$0.882074\pi$
$30$		0			0
$31$	13.0465			0.420855			0.210427	−	0.977609i	$-0.432514\pi$
$31$	13.0465			0.420855			0.210427	+	0.977609i	$0.432514\pi$
$32$			5.65685i			0.176777i
$33$		0			0
$34$	17.4927	−	30.2982i	0.514491	−	0.891124i
$35$	−6.04307	−	15.6353i	−0.172659	−	0.446724i
$36$		0			0
$37$	16.0604	+	27.8173i	0.434064	+	0.751820i	0.997219	−	0.0745311i	$-0.0237460\pi$
$37$	16.0604	+	27.8173i	0.434064	+	0.751820i	−0.563155	+	0.826351i	$0.690413\pi$
$38$	2.61809	−	1.51156i	0.0688972	−	0.0397778i
$39$		0			0
$40$	3.38655	−	5.86567i	0.0846636	−	0.146642i
$41$	−27.3943	+	15.8161i	−0.668155	+	0.385759i	−0.795377	−	0.606115i	$-0.792727\pi$
$41$	−27.3943	+	15.8161i	−0.668155	+	0.385759i	0.127222	+	0.991874i	$0.459394\pi$
$42$		0			0
$43$	40.1194	−	69.4888i	0.933009	−	1.61602i	0.154863	−	0.987936i	$-0.450506\pi$
$43$	40.1194	−	69.4888i	0.933009	−	1.61602i	0.778146	−	0.628083i	$-0.216160\pi$
$44$	10.1141	−	5.83940i	0.229867	−	0.132714i
$45$		0			0
$46$	−0.100919	+	0.174796i	−0.00219388	+	0.00379992i
$47$		−	61.1758i		−	1.30161i	−0.759244	−	0.650807i	$-0.774431\pi$
$47$		−	61.1758i		−	1.30161i	0.759244	−	0.650807i	$-0.225569\pi$
$48$		0			0
$49$	10.4077	+	47.8819i	0.212401	+	0.977183i
$50$	23.5955	−	13.6229i	0.471910	−	0.272458i
$51$		0			0
$52$	5.74010	+	9.94214i	0.110386	+	0.191195i
$53$	−22.5819	−	13.0377i	−0.426074	−	0.245994i	0.271599	−	0.962411i	$-0.412448\pi$
$53$	−22.5819	−	13.0377i	−0.426074	−	0.245994i	−0.697673	+	0.716417i	$0.745781\pi$
$54$		0			0
$55$	−13.9833			−0.254242
$56$	−12.4245	+	15.4153i	−0.221867	+	0.275273i
$57$		0			0
$58$	25.6835	−	44.4851i	0.442818	−	0.766984i
$59$		−	22.7566i		−	0.385706i	−0.981228	−	0.192853i	$-0.938226\pi$
$59$		−	22.7566i		−	0.385706i	0.981228	−	0.192853i	$-0.0617740\pi$
$60$		0			0
$61$	−102.664			−1.68302			−0.841508	−	0.540244i	$-0.818332\pi$
$61$	−102.664			−1.68302			−0.841508	+	0.540244i	$0.818332\pi$
$62$			18.4505i			0.297589i
$63$		0			0
$64$	−8.00000			−0.125000
$65$		−	13.7455i		−	0.211469i
$66$		0			0
$67$	70.2380			1.04833			0.524164	−	0.851617i	$-0.324378\pi$
$67$	70.2380			1.04833			0.524164	+	0.851617i	$0.324378\pi$
$68$	42.8481	+	24.7384i	0.630120	+	0.363800i
$69$		0			0
$70$	22.1117	−	8.54620i	0.315882	−	0.122089i
$71$			100.792i			1.41961i	0.704399	+	0.709804i	$0.251216\pi$
$71$			100.792i			1.41961i	−0.704399	+	0.709804i	$0.748784\pi$
$72$		0			0
$73$	−4.36953	+	7.56824i	−0.0598565	+	0.103675i	−0.894401	−	0.447266i	$-0.852398\pi$
$73$	−4.36953	+	7.56824i	−0.0598565	+	0.103675i	0.834544	+	0.550941i	$0.185731\pi$
$74$	−39.3397	+	22.7128i	−0.531617	+	0.306929i
$75$		0			0
$76$	2.13766	+	3.70254i	0.0281272	+	0.0487177i
$77$	40.3871	+	6.30167i	0.524508	+	0.0818398i
$78$		0			0
$79$	−62.2922			−0.788508			−0.394254	−	0.919001i	$-0.628997\pi$
$79$	−62.2922			−0.788508			−0.394254	+	0.919001i	$0.628997\pi$
$80$	8.29531	+	4.78930i	0.103691	+	0.0598662i
$81$		0			0
$82$	−22.3674	−	38.7414i	−0.272773	−	0.472457i
$83$	51.5381	+	29.7555i	0.620941	+	0.358501i	0.777235	−	0.629210i	$-0.216621\pi$
$83$	51.5381	+	29.7555i	0.620941	+	0.358501i	−0.156294	+	0.987711i	$0.549955\pi$
$84$		0			0
$85$	−29.6199	−	51.3031i	−0.348469	−	0.603566i
$86$	98.2720	+	56.7374i	1.14270	+	0.659737i
$87$		0			0
$88$	8.25816	+	14.3035i	0.0938427	+	0.162540i
$89$	94.6860	−	54.6670i	1.06389	−	0.614236i	0.137382	−	0.990518i	$-0.456131\pi$
$89$	94.6860	−	54.6670i	1.06389	−	0.614236i	0.926505	+	0.376282i	$0.122798\pi$
$90$		0			0
$91$	−6.19450	+	39.7003i	−0.0680715	+	0.436267i
$92$	−0.247199	−	0.142721i	−0.00268695	−	0.00155131i
$93$		0			0
$94$	86.5157			0.920380
$95$		−	5.11896i		−	0.0538837i
$96$		0			0
$97$	−79.8603	+	138.322i	−0.823302	+	1.42600i	0.0799082	+	0.996802i	$0.474537\pi$
$97$	−79.8603	+	138.322i	−0.823302	+	1.42600i	−0.903210	+	0.429199i	$0.858796\pi$
$98$	−67.7153	+	14.7187i	−0.690972	+	0.150190i
$99$		0			0
$100$	19.2657	+	33.3691i	0.192657	+	0.333691i
$101$	110.263	−	63.6601i	1.09171	−	0.630298i	0.157678	−	0.987491i	$-0.449599\pi$
$101$	110.263	−	63.6601i	1.09171	−	0.630298i	0.934031	+	0.357192i	$0.116266\pi$
$102$		0			0
$103$	24.4892	−	42.4165i	0.237759	−	0.411811i	−0.722312	−	0.691567i	$-0.756920\pi$
$103$	24.4892	−	42.4165i	0.237759	−	0.411811i	0.960071	+	0.279757i	$0.0902538\pi$
$104$	−14.0603	+	8.11772i	−0.135195	+	0.0780550i
$105$		0			0
$106$	18.4380	−	31.9356i	0.173944	−	0.301280i
$107$	−116.454	+	67.2350i	−1.08836	+	0.628364i	−0.933139	−	0.359516i	$-0.882942\pi$
$107$	−116.454	+	67.2350i	−1.08836	+	0.628364i	−0.155220	+	0.987880i	$0.549608\pi$
$108$		0			0
$109$	−83.0714	+	143.884i	−0.762123	+	1.32004i	0.179631	+	0.983734i	$0.442510\pi$
$109$	−83.0714	+	143.884i	−0.762123	+	1.32004i	−0.941754	+	0.336302i	$0.890824\pi$
$110$		−	19.7754i		−	0.179776i
$111$		0			0
$112$	−21.8005	−	17.5710i	−0.194647	−	0.156884i
$113$	−174.655	+	100.837i	−1.54562	+	0.892363i	−0.547149	+	0.837035i	$0.684287\pi$
$113$	−174.655	+	100.837i	−1.54562	+	0.892363i	−0.998468	+	0.0553276i	$0.982380\pi$
$114$		0			0
$115$	0.170883	+	0.295978i	0.00148594	+	0.00257372i
$116$	62.9114	+	36.3219i	0.542340	+	0.313120i
$117$		0			0
$118$	32.1827			0.272735
$119$	62.4291	+	161.524i	0.524615	+	1.35734i
$120$		0			0
$121$	−43.4507	+	75.2588i	−0.359097	+	0.621974i
$122$		−	145.189i		−	1.19007i
$123$		0			0
$124$	−26.0930			−0.210427
$125$		−	106.001i		−	0.848006i
$126$		0			0
$127$	−32.4486			−0.255501			−0.127750	−	0.991806i	$-0.540776\pi$
$127$	−32.4486			−0.255501			−0.127750	+	0.991806i	$0.540776\pi$
$128$		−	11.3137i		−	0.0883883i
$129$		0			0
$130$	19.4391			0.149532
$131$	−158.483	−	91.5000i	−1.20979	−	0.698473i	−0.247077	−	0.968996i	$-0.579470\pi$
$131$	−158.483	−	91.5000i	−1.20979	−	0.698473i	−0.962714	+	0.270523i	$0.912803\pi$
$132$		0			0
$133$	−2.30689	+	14.7848i	−0.0173450	+	0.111164i
$134$			99.3315i			0.741280i
$135$		0			0
$136$	−34.9854	+	60.5964i	−0.257245	+	0.445562i
$137$	−26.6948	+	15.4123i	−0.194853	+	0.112498i	−0.594252	−	0.804279i	$-0.702552\pi$
$137$	−26.6948	+	15.4123i	−0.194853	+	0.112498i	0.399400	+	0.916777i	$0.369219\pi$
$138$		0			0
$139$	27.7854	+	48.1257i	0.199895	+	0.346228i	0.948494	−	0.316795i	$-0.102607\pi$
$139$	27.7854	+	48.1257i	0.199895	+	0.346228i	−0.748599	+	0.663023i	$0.769273\pi$
$140$	12.0861	+	31.2707i	0.0863296	+	0.223362i
$141$		0			0
$142$	−142.542			−1.00381
$143$	29.0281	+	16.7594i	0.202993	+	0.117198i
$144$		0			0
$145$	−43.4891	−	75.3253i	−0.299925	−	0.519485i
$146$	−10.7031	−	6.17945i	−0.0733090	−	0.0423250i
$147$		0			0
$148$	−32.1207	−	55.6347i	−0.217032	−	0.375910i
$149$	−6.39250	−	3.69071i	−0.0429027	−	0.0247699i	0.478395	−	0.878145i	$-0.341219\pi$
$149$	−6.39250	−	3.69071i	−0.0429027	−	0.0247699i	−0.521298	+	0.853375i	$0.674552\pi$
$150$		0			0
$151$	−17.2684	−	29.9097i	−0.114360	−	0.198078i	0.803164	−	0.595759i	$-0.203148\pi$
$151$	−17.2684	−	29.9097i	−0.114360	−	0.198078i	−0.917524	+	0.397681i	$0.869815\pi$
$152$	−5.23619	+	3.02311i	−0.0344486	+	0.0198889i
$153$		0			0
$154$	−8.91190	+	57.1160i	−0.0578695	+	0.370883i
$155$	27.0562	+	15.6209i	0.174556	+	0.100780i
$156$		0			0
$157$	192.632			1.22696			0.613478	−	0.789712i	$-0.289770\pi$
$157$	192.632			1.22696			0.613478	+	0.789712i	$0.289770\pi$
$158$		−	88.0944i		−	0.557560i
$159$		0			0
$160$	−6.77309	+	11.7313i	−0.0423318	+	0.0733209i
$161$	−0.360166	−	0.931863i	−0.00223705	−	0.00578797i
$162$		0			0
$163$	113.038	+	195.787i	0.693484	+	1.20115i	0.970689	+	0.240339i	$0.0772586\pi$
$163$	113.038	+	195.787i	0.693484	+	1.20115i	−0.277205	+	0.960811i	$0.589408\pi$
$164$	54.7887	−	31.6323i	0.334077	−	0.192880i
$165$		0			0
$166$	−42.0807	+	72.8859i	−0.253498	+	0.439072i
$167$	113.351	−	65.4431i	0.678747	−	0.391875i	−0.120636	−	0.992697i	$-0.538493\pi$
$167$	113.351	−	65.4431i	0.678747	−	0.391875i	0.799383	+	0.600822i	$0.205160\pi$
$168$		0			0
$169$	68.0256	−	117.824i	0.402519	−	0.697183i
$170$	72.5536	−	41.8888i	0.426786	−	0.246405i
$171$		0			0
$172$	−80.2388	+	138.978i	−0.466505	+	0.808010i
$173$			80.1752i			0.463440i	0.972782	+	0.231720i	$0.0744354\pi$
$173$			80.1752i			0.463440i	−0.972782	+	0.231720i	$0.925565\pi$
$174$		0			0
$175$	−20.7908	+	133.247i	−0.118805	+	0.761413i
$176$	−20.2283	+	11.6788i	−0.114933	+	0.0663568i
$177$		0			0
$178$	77.3108	+	133.906i	0.434330	+	0.752282i
$179$	90.6710	+	52.3489i	0.506542	+	0.292452i	0.731411	−	0.681937i	$-0.238862\pi$
$179$	90.6710	+	52.3489i	0.506542	+	0.292452i	−0.224869	+	0.974389i	$0.572195\pi$
$180$		0			0
$181$	−177.386			−0.980033			−0.490016	−	0.871713i	$-0.663009\pi$
$181$	−177.386			−0.980033			−0.490016	+	0.871713i	$0.663009\pi$
$182$	−56.1447	−	8.76035i	−0.308487	−	0.0481338i
$183$		0			0
$184$	0.201837	−	0.349592i	0.00109694	−	0.00189996i
$185$			76.9178i			0.415772i
$186$		0			0
$187$	144.457			0.772499
$188$			122.352i			0.650807i
$189$		0			0
$190$	7.23930			0.0381016
$191$			175.715i			0.919971i	0.887926	+	0.459986i	$0.152145\pi$
$191$			175.715i			0.919971i	−0.887926	+	0.459986i	$0.847855\pi$
$192$		0			0
$193$	81.6816			0.423221			0.211610	−	0.977354i	$-0.432129\pi$
$193$	81.6816			0.423221			0.211610	+	0.977354i	$0.432129\pi$
$194$	−195.617	−	112.940i	−1.00833	−	0.582162i
$195$		0			0
$196$	−20.8153	−	95.7639i	−0.106201	−	0.488591i
$197$		−	318.861i		−	1.61858i	−0.587407	−	0.809292i	$-0.699851\pi$
$197$		−	318.861i		−	1.61858i	0.587407	−	0.809292i	$-0.300149\pi$
$198$		0			0
$199$	187.878	−	325.414i	0.944109	−	1.63524i	0.186583	−	0.982439i	$-0.440259\pi$
$199$	187.878	−	325.414i	0.944109	−	1.63524i	0.757525	−	0.652806i	$-0.226408\pi$
$200$	−47.1910	+	27.2458i	−0.235955	+	0.136229i
$201$		0			0
$202$	90.0290	+	155.935i	0.445688	+	0.771955i
$203$	91.6610	+	237.156i	0.451532	+	1.16826i
$204$		0			0
$205$	−75.7481			−0.369503
$206$	59.9860	+	34.6329i	0.291194	+	0.168121i
$207$		0			0
$208$	−11.4802	−	19.8843i	−0.0551932	−	0.0955975i
$209$	10.8103	+	6.24134i	0.0517240	+	0.0298629i
$210$		0			0
$211$	−130.248	−	225.596i	−0.617289	−	1.06918i	−0.989978	−	0.141220i	$-0.954898\pi$
$211$	−130.248	−	225.596i	−0.617289	−	1.06918i	0.372689	−	0.927956i	$-0.378436\pi$
$212$	45.1638	+	26.0753i	0.213037	+	0.122997i
$213$		0			0
$214$	−95.0846	−	164.691i	−0.444320	−	0.769586i
$215$	166.401	−	96.0719i	0.773960	−	0.446846i
$216$		0			0
$217$	−71.1050	−	57.3099i	−0.327673	−	0.264101i
$218$	−203.483	−	117.481i	−0.933406	−	0.538902i
$219$		0			0
$220$	27.9666			0.127121
$221$			142.001i			0.642537i
$222$		0			0
$223$	118.795	−	205.760i	0.532715	−	0.922690i	−0.466555	−	0.884492i	$-0.654505\pi$
$223$	118.795	−	205.760i	0.532715	−	0.922690i	0.999270	−	0.0381976i	$-0.0121616\pi$
$224$	24.8491	−	30.8305i	0.110933	−	0.137636i
$225$		0			0
$226$	−142.605	−	246.999i	−0.630996	−	1.09292i
$227$	204.405	−	118.013i	0.900462	−	0.519882i	0.0231118	−	0.999733i	$-0.492643\pi$
$227$	204.405	−	118.013i	0.900462	−	0.519882i	0.877350	+	0.479851i	$0.159309\pi$
$228$		0			0
$229$	199.129	−	344.901i	0.869559	−	1.50612i	0.00711031	−	0.999975i	$-0.497737\pi$
$229$	199.129	−	344.901i	0.869559	−	1.50612i	0.862448	−	0.506145i	$-0.168930\pi$
$230$	−0.418576	+	0.241665i	−0.00181989	+	0.00105072i
$231$		0			0
$232$	−51.3669	+	88.9701i	−0.221409	+	0.383492i
$233$	−131.868	+	76.1339i	−0.565956	+	0.326755i	−0.755532	−	0.655111i	$-0.772622\pi$
$233$	−131.868	+	76.1339i	−0.565956	+	0.326755i	0.189577	+	0.981866i	$0.439288\pi$
$234$		0			0
$235$	73.2473	−	126.868i	0.311691	−	0.539864i
$236$			45.5133i			0.192853i
$237$		0			0
$238$	−228.429	+	88.2881i	−0.959787	+	0.370959i
$239$	60.0571	−	34.6740i	0.251285	−	0.145079i	−0.369067	−	0.929403i	$-0.620323\pi$
$239$	60.0571	−	34.6740i	0.251285	−	0.145079i	0.620353	+	0.784323i	$0.286990\pi$
$240$		0			0
$241$	15.3762	+	26.6324i	0.0638018	+	0.110508i	0.896162	−	0.443727i	$-0.146344\pi$
$241$	15.3762	+	26.6324i	0.0638018	+	0.110508i	−0.832360	+	0.554235i	$0.813011\pi$
$242$	−106.432	−	61.4486i	−0.439802	−	0.253920i
$243$		0			0
$244$	205.328			0.841508
$245$	−35.7465	+	111.760i	−0.145904	+	0.456164i
$246$		0			0
$247$	−6.13520	+	10.6265i	−0.0248389	+	0.0430222i
$248$		−	36.9011i		−	0.148795i
$249$		0			0
$250$	149.908			0.599631
$251$		−	297.840i		−	1.18661i	−0.804976	−	0.593307i	$-0.797822\pi$
$251$		−	297.840i		−	1.18661i	0.804976	−	0.593307i	$-0.202178\pi$
$252$		0			0
$253$	−0.833402			−0.00329408
$254$		−	45.8893i		−	0.180666i
$255$		0			0
$256$	16.0000			0.0625000
$257$	−91.4268	−	52.7853i	−0.355746	−	0.205390i	0.311467	−	0.950257i	$-0.399180\pi$
$257$	−91.4268	−	52.7853i	−0.355746	−	0.205390i	−0.667213	+	0.744867i	$0.732513\pi$
$258$		0			0
$259$	34.6635	−	222.157i	0.133836	−	0.857749i
$260$			27.4910i			0.105735i
$261$		0			0
$262$	129.400	−	224.128i	0.493895	−	0.855451i
$263$	91.8938	−	53.0549i	0.349406	−	0.201730i	−0.315018	−	0.949086i	$-0.602010\pi$
$263$	91.8938	−	53.0549i	0.349406	−	0.201730i	0.664424	+	0.747356i	$0.268677\pi$
$264$		0			0
$265$	−31.2206	−	54.0757i	−0.117814	−	0.204059i
$266$	−20.9088	−	3.26244i	−0.0786045	−	0.0122648i
$267$		0			0
$268$	−140.476			−0.524164
$269$	−195.184	−	112.689i	−0.725591	−	0.418920i	0.0912161	−	0.995831i	$-0.470925\pi$
$269$	−195.184	−	112.689i	−0.725591	−	0.418920i	−0.816807	+	0.576911i	$0.804258\pi$
$270$		0			0
$271$	84.0102	+	145.510i	0.310001	+	0.536937i	0.978362	−	0.206900i	$-0.0663374\pi$
$271$	84.0102	+	145.510i	0.310001	+	0.536937i	−0.668362	+	0.743837i	$0.733004\pi$
$272$	−85.6963	−	49.4768i	−0.315060	−	0.181900i
$273$		0			0
$274$	−21.7962	−	37.7522i	−0.0795483	−	0.137782i
$275$	97.4277	+	56.2499i	0.354283	+	0.204545i
$276$		0			0
$277$	167.769	+	290.584i	0.605663	+	1.04904i	0.991946	+	0.126659i	$0.0404255\pi$
$277$	167.769	+	290.584i	0.605663	+	1.04904i	−0.386283	+	0.922380i	$0.626241\pi$
$278$	−68.0600	+	39.2944i	−0.244820	+	0.141347i
$279$		0			0
$280$	−44.2234	+	17.0924i	−0.157941	+	0.0610443i
$281$	−468.870	−	270.702i	−1.66858	−	0.963353i	−0.968406	−	0.249377i	$-0.919774\pi$
$281$	−468.870	−	270.702i	−1.66858	−	0.963353i	−0.700170	−	0.713976i	$-0.746893\pi$
$282$		0			0
$283$	−316.510			−1.11841			−0.559204	−	0.829030i	$-0.688893\pi$
$283$	−316.510			−1.11841			−0.559204	+	0.829030i	$0.688893\pi$
$284$		−	201.584i		−	0.709804i
$285$		0			0
$286$	−23.7013	+	41.0519i	−0.0828717	+	0.143538i
$287$	218.779	+	34.1364i	0.762295	+	0.118942i
$288$		0			0
$289$	161.494	+	279.715i	0.558802	+	0.967874i
$290$	106.526	−	61.5029i	0.367331	−	0.212079i
$291$		0			0
$292$	8.73906	−	15.1365i	0.0299283	−	0.0518373i
$293$	224.604	−	129.675i	0.766568	−	0.442578i	−0.0650812	−	0.997880i	$-0.520731\pi$
$293$	224.604	−	129.675i	0.766568	−	0.442578i	0.831649	+	0.555302i	$0.187397\pi$
$294$		0			0
$295$	27.2471	−	47.1933i	0.0923629	−	0.159977i
$296$	78.6793	−	45.4255i	0.265809	−	0.153465i
$297$		0			0
$298$	5.21945	−	9.04035i	0.0175149	−	0.0303368i
$299$		−	0.819229i		−	0.00273990i
$300$		0			0
$301$	−523.902	+	202.489i	−1.74054	+	0.672719i
$302$	42.2987	−	24.4212i	0.140062	−	0.0808649i
$303$		0			0
$304$	−4.27533	−	7.40509i	−0.0140636	−	0.0243588i
$305$	−212.907	−	122.922i	−0.698057	−	0.403023i
$306$		0			0
$307$	185.899			0.605534			0.302767	−	0.953065i	$-0.402090\pi$
$307$	185.899			0.605534			0.302767	+	0.953065i	$0.402090\pi$
$308$	−80.7742	−	12.6033i	−0.262254	−	0.0409199i
$309$		0			0
$310$	−22.0913	+	38.2632i	−0.0712622	+	0.123430i
$311$		−	6.94024i		−	0.0223159i	−0.999938	−	0.0111579i	$-0.996448\pi$
$311$		−	6.94024i		−	0.0223159i	0.999938	−	0.0111579i	$-0.00355176\pi$
$312$		0			0
$313$	396.112			1.26553			0.632767	−	0.774342i	$-0.281919\pi$
$313$	396.112			1.26553			0.632767	+	0.774342i	$0.281919\pi$
$314$			272.423i			0.867589i
$315$		0			0
$316$	124.584			0.394254
$317$			56.4970i			0.178224i	0.996022	+	0.0891120i	$0.0284029\pi$
$317$			56.4970i			0.178224i	−0.996022	+	0.0891120i	$0.971597\pi$
$318$		0			0
$319$	212.098			0.664884
$320$	−16.5906	−	9.57860i	−0.0518457	−	0.0299331i
$321$		0			0
$322$	1.31785	−	0.509351i	0.00409271	−	0.00158184i
$323$			52.8824i			0.163722i
$324$		0			0
$325$	−55.2934	+	95.7709i	−0.170133	+	0.294680i
$326$	−276.885	+	159.860i	−0.849341	+	0.490367i
$327$		0			0
$328$	44.7348	+	77.4829i	0.136386	+	0.236228i
$329$	−268.730	+	333.416i	−0.816807	+	1.01342i
$330$		0			0
$331$	−220.862			−0.667256			−0.333628	−	0.942705i	$-0.608273\pi$
$331$	−220.862			−0.667256			−0.333628	+	0.942705i	$0.608273\pi$
$332$	−103.076	−	59.5111i	−0.310471	−	0.179250i
$333$		0			0
$334$	92.5505	+	160.302i	0.277097	+	0.479946i
$335$	145.661	+	84.0977i	0.434810	+	0.251038i
$336$		0			0
$337$	−171.431	−	296.928i	−0.508698	−	0.881092i	−0.999949	−	0.0100734i	$-0.996793\pi$
$337$	−171.431	−	296.928i	−0.508698	−	0.881092i	0.491251	−	0.871018i	$-0.336540\pi$
$338$	166.628	+	96.2028i	0.492983	+	0.284624i
$339$		0			0
$340$	59.2397	+	102.606i	0.174235	+	0.301783i
$341$	−65.9770	+	38.0919i	−0.193481	+	0.111706i
$342$		0			0
$343$	153.610	−	306.681i	0.447842	−	0.894113i
$344$	−196.544	−	113.475i	−0.571349	−	0.329869i
$345$		0			0
$346$	−113.385			−0.327702
$347$		−	365.443i		−	1.05315i	−0.850129	−	0.526574i	$-0.823476\pi$
$347$		−	365.443i		−	1.05315i	0.850129	−	0.526574i	$-0.176524\pi$
$348$		0			0
$349$	−2.62605	+	4.54846i	−0.00752451	+	0.0130328i	−0.869763	−	0.493469i	$-0.835728\pi$
$349$	−2.62605	+	4.54846i	−0.00752451	+	0.0130328i	0.862239	+	0.506502i	$0.169062\pi$
$350$	−188.440	−	29.4026i	−0.538401	−	0.0840075i
$351$		0			0
$352$	−16.5163	−	28.6071i	−0.0469213	−	0.0812701i
$353$	129.987	−	75.0482i	0.368236	−	0.212601i	−0.304452	−	0.952528i	$-0.598473\pi$
$353$	129.987	−	75.0482i	0.368236	−	0.212601i	0.672687	+	0.739927i	$0.265140\pi$
$354$		0			0
$355$	−120.681	+	209.026i	−0.339946	+	0.588804i
$356$	−189.372	+	109.334i	−0.531944	+	0.307118i
$357$		0			0
$358$	−74.0325	+	128.228i	−0.206795	+	0.358179i
$359$	−21.1053	+	12.1852i	−0.0587893	+	0.0339420i	−0.529107	−	0.848555i	$-0.677473\pi$
$359$	−21.1053	+	12.1852i	−0.0587893	+	0.0339420i	0.470317	+	0.882497i	$0.344139\pi$
$360$		0			0
$361$	178.215	−	308.678i	0.493671	−	0.855063i
$362$		−	250.862i		−	0.692988i
$363$		0			0
$364$	12.3890	−	79.4006i	0.0340357	−	0.218134i
$365$	−18.1233	+	10.4635i	−0.0496528	+	0.0286671i
$366$		0			0
$367$	271.890	+	470.927i	0.740845	+	1.28318i	0.952111	+	0.305752i	$0.0989079\pi$
$367$	271.890	+	470.927i	0.740845	+	1.28318i	−0.211266	+	0.977429i	$0.567759\pi$
$368$	0.494398	+	0.285441i	0.00134347	+	0.000775655i
$369$		0			0
$370$	−108.778			−0.293995
$371$	65.8030	+	170.253i	0.177367	+	0.458904i
$372$		0			0
$373$	−145.946	+	252.785i	−0.391275	+	0.677709i	−0.992618	−	0.121283i	$-0.961299\pi$
$373$	−145.946	+	252.785i	−0.391275	+	0.677709i	0.601343	+	0.798991i	$0.294633\pi$
$374$			204.293i			0.546239i
$375$		0			0
$376$	−173.031			−0.460190
$377$			208.491i			0.553027i
$378$		0			0
$379$	−387.585			−1.02265			−0.511325	−	0.859387i	$-0.670845\pi$
$379$	−387.585			−1.02265			−0.511325	+	0.859387i	$0.670845\pi$
$380$			10.2379i			0.0269419i
$381$		0			0
$382$	−248.498			−0.650518
$383$	−303.470	−	175.208i	−0.792350	−	0.457463i	0.0484394	−	0.998826i	$-0.484575\pi$
$383$	−303.470	−	175.208i	−0.792350	−	0.457463i	−0.840789	+	0.541363i	$0.817909\pi$
$384$		0			0
$385$	76.2107	+	61.4251i	0.197950	+	0.159546i
$386$			115.515i			0.299262i
$387$		0			0
$388$	159.721	−	276.644i	0.411651	−	0.713000i
$389$	445.087	−	256.971i	1.14418	−	0.660594i	0.196720	−	0.980460i	$-0.436971\pi$
$389$	445.087	−	256.971i	1.14418	−	0.660594i	0.947463	+	0.319866i	$0.103638\pi$
$390$		0			0
$391$	−1.76534	−	3.05765i	−0.00451493	−	0.00782009i
$392$	135.431	−	29.4373i	0.345486	−	0.0750952i
$393$		0			0
$394$	450.937			1.14451
$395$	−129.183	−	74.5839i	−0.327046	−	0.188820i
$396$		0			0
$397$	−223.785	−	387.607i	−0.563690	−	0.976339i	−0.997170	−	0.0751762i	$-0.976048\pi$
$397$	−223.785	−	387.607i	−0.563690	−	0.976339i	0.433481	−	0.901163i	$-0.357285\pi$
$398$	460.204	+	265.699i	1.15629	+	0.667586i
$399$		0			0
$400$	−38.5313	−	66.7382i	−0.0963283	−	0.166845i
$401$	269.976	+	155.871i	0.673257	+	0.388705i	0.797309	−	0.603571i	$-0.206256\pi$
$401$	269.976	+	155.871i	0.673257	+	0.388705i	−0.124053	+	0.992276i	$0.539589\pi$
$402$		0			0
$403$	−37.4441	−	64.8551i	−0.0929134	−	0.160931i
$404$	−220.525	+	127.320i	−0.545854	+	0.315149i
$405$		0			0
$406$	−335.389	+	129.628i	−0.826082	+	0.319281i
$407$	−162.437	−	93.7828i	−0.399107	−	0.230425i
$408$		0			0
$409$	−295.889			−0.723444			−0.361722	−	0.932286i	$-0.617811\pi$
$409$	−295.889			−0.723444			−0.361722	+	0.932286i	$0.617811\pi$
$410$		−	107.124i		−	0.261278i
$411$		0			0
$412$	−48.9784	+	84.8330i	−0.118880	+	0.205905i
$413$	−99.9640	+	124.026i	−0.242043	+	0.300306i
$414$		0			0
$415$	71.2541	+	123.416i	0.171697	+	0.297387i
$416$	28.1206	−	16.2354i	0.0675976	−	0.0390275i
$417$		0			0
$418$	−8.82658	+	15.2881i	−0.0211162	+	0.0365744i
$419$	327.219	−	188.920i	0.780952	−	0.450883i	−0.0558158	−	0.998441i	$-0.517776\pi$
$419$	327.219	−	188.920i	0.780952	−	0.450883i	0.836767	+	0.547558i	$0.184443\pi$
$420$		0			0
$421$	−282.035	+	488.499i	−0.669918	+	1.16033i	0.308009	+	0.951383i	$0.400337\pi$
$421$	−282.035	+	488.499i	−0.669918	+	1.16033i	−0.977927	+	0.208948i	$0.932996\pi$
$422$	319.041	−	184.199i	0.756022	−	0.436489i
$423$		0			0
$424$	−36.8761	+	63.8713i	−0.0869719	+	0.150640i
$425$			476.601i			1.12141i
$426$		0			0
$427$	559.531	+	450.976i	1.31038	+	1.05615i
$428$	232.909	−	134.470i	0.544179	−	0.314182i
$429$		0			0
$430$	135.866	+	235.327i	0.315968	+	0.547272i
$431$	651.482	+	376.134i	1.51156	+	0.872700i	0.999909	+	0.0135064i	$0.00429935\pi$
$431$	651.482	+	376.134i	1.51156	+	0.872700i	0.511651	+	0.859193i	$0.329034\pi$
$432$		0			0
$433$	−451.261			−1.04217			−0.521087	−	0.853503i	$-0.674473\pi$
$433$	−451.261			−1.04217			−0.521087	+	0.853503i	$0.674473\pi$
$434$	81.0484	−	100.558i	0.186748	−	0.231700i
$435$		0			0
$436$	166.143	−	287.768i	0.381061	−	0.660018i
$437$		−	0.305089i		−	0.000698143i
$438$		0			0
$439$	−132.928			−0.302798			−0.151399	−	0.988473i	$-0.548378\pi$
$439$	−132.928			−0.302798			−0.151399	+	0.988473i	$0.548378\pi$
$440$			39.5508i			0.0898881i
$441$		0			0
$442$	−200.819			−0.454342
$443$			415.252i			0.937364i	0.883367	+	0.468682i	$0.155271\pi$
$443$			415.252i			0.937364i	−0.883367	+	0.468682i	$0.844729\pi$
$444$		0			0
$445$	261.816			0.588351
$446$	290.988	+	168.002i	0.652440	+	0.376687i
$447$		0			0
$448$	43.6010	+	35.1419i	0.0973236	+	0.0784418i
$449$			262.832i			0.585372i	0.956209	+	0.292686i	$0.0945490\pi$
$449$			262.832i			0.585372i	−0.956209	+	0.292686i	$0.905451\pi$
$450$		0			0
$451$	92.3567	−	159.966i	0.204782	−	0.354693i
$452$	349.310	−	201.674i	0.772809	−	0.446181i
$453$		0			0
$454$	166.896	+	289.072i	0.367612	+	0.636723i
$455$	−60.3805	+	74.9147i	−0.132704	+	0.164648i
$456$		0			0
$457$	−506.026			−1.10728			−0.553639	−	0.832757i	$-0.686761\pi$
$457$	−506.026			−1.10728			−0.553639	+	0.832757i	$0.686761\pi$
$458$	487.764	+	281.611i	1.06499	+	0.614871i
$459$		0			0
$460$	−0.341766	−	0.591955i	−0.000742969	−	0.00128686i
$461$	−660.234	−	381.186i	−1.43218	−	0.826868i	−0.434891	−	0.900483i	$-0.643213\pi$
$461$	−660.234	−	381.186i	−1.43218	−	0.826868i	−0.997287	+	0.0736145i	$0.976547\pi$
$462$		0			0
$463$	−14.2110	−	24.6141i	−0.0306932	−	0.0531622i	0.850271	−	0.526346i	$-0.176438\pi$
$463$	−14.2110	−	24.6141i	−0.0306932	−	0.0531622i	−0.880964	+	0.473183i	$0.843105\pi$
$464$	−125.823	−	72.6438i	−0.271170	−	0.156560i
$465$		0			0
$466$	−107.670	−	186.489i	−0.231050	−	0.400191i
$467$	126.660	−	73.1271i	0.271220	−	0.156589i	−0.358222	−	0.933637i	$-0.616617\pi$
$467$	126.660	−	73.1271i	0.271220	−	0.156589i	0.629442	+	0.777047i	$0.283283\pi$
$468$		0			0
$469$	−382.806	−	308.537i	−0.816217	−	0.657862i
$470$	179.419	+	103.587i	0.381742	+	0.220399i
$471$		0			0
$472$	−64.3655			−0.136368
$473$			468.546i			0.990584i
$474$		0			0
$475$	−20.5918	+	35.6660i	−0.0433511	+	0.0750862i
$476$	−124.858	−	323.048i	−0.262307	−	0.678672i
$477$		0			0
$478$	49.0364	+	84.9336i	0.102587	+	0.177685i
$479$	47.7197	−	27.5510i	0.0996236	−	0.0575177i	−0.449360	−	0.893351i	$-0.648348\pi$
$479$	47.7197	−	27.5510i	0.0996236	−	0.0575177i	0.548984	+	0.835833i	$0.315015\pi$
$480$		0			0
$481$	92.1880	−	159.674i	0.191659	−	0.331963i
$482$	−37.6639	+	21.7453i	−0.0781409	+	0.0451147i
$483$		0			0
$484$	86.9014	−	150.518i	0.179548	−	0.310987i
$485$	−331.233	+	191.237i	−0.682954	+	0.394304i
$486$		0			0
$487$	238.930	−	413.839i	0.490616	−	0.849772i	−0.509326	−	0.860574i	$-0.670105\pi$
$487$	238.930	−	413.839i	0.490616	−	0.849772i	0.999942	+	0.0108019i	$0.00343842\pi$
$488$			290.378i			0.595036i
$489$		0			0
$490$	−158.053	−	50.5532i	−0.322557	−	0.103170i
$491$	−412.348	+	238.069i	−0.839813	+	0.484866i	−0.857201	−	0.514982i	$-0.827798\pi$
$491$	−412.348	+	238.069i	−0.839813	+	0.484866i	0.0173875	+	0.999849i	$0.494465\pi$
$492$		0			0
$493$	449.273	+	778.163i	0.911303	+	1.57842i
$494$	−15.0281	−	8.67648i	−0.0304213	−	0.0175637i
$495$		0			0
$496$	52.1860			0.105214
$497$	442.754	−	549.330i	0.890853	−	1.10529i
$498$		0			0
$499$	−24.9779	+	43.2630i	−0.0500560	+	0.0866995i	−0.889968	−	0.456023i	$-0.849273\pi$
$499$	−24.9779	+	43.2630i	−0.0500560	+	0.0866995i	0.839912	+	0.542723i	$0.182607\pi$
$500$			212.001i			0.424003i
$501$		0			0
$502$	421.209			0.839063
$503$			807.461i			1.60529i	0.596457	+	0.802645i	$0.296575\pi$
$503$			807.461i			1.60529i	−0.596457	+	0.802645i	$0.703425\pi$
$504$		0			0
$505$	304.887			0.603737
$506$		−	1.17861i		−	0.00232927i
$507$		0			0
$508$	64.8972			0.127750
$509$	214.257	+	123.701i	0.420937	+	0.243028i	0.695478	−	0.718547i	$-0.255193\pi$
$509$	214.257	+	123.701i	0.420937	+	0.243028i	−0.274541	+	0.961575i	$0.588526\pi$
$510$		0			0
$511$	57.0598	−	22.0537i	0.111663	−	0.0431578i
$512$			22.6274i			0.0441942i
$513$		0			0
$514$	74.6497	−	129.297i	0.145233	−	0.251551i
$515$	101.573	−	58.6430i	0.197228	−	0.113870i
$516$		0			0
$517$	178.615	+	309.370i	0.345484	+	0.598395i
$518$	314.177	+	49.0216i	0.606520	+	0.0946363i
$519$		0			0
$520$	−38.8782			−0.0747658
$521$	−451.108	−	260.448i	−0.865851	−	0.499899i	0.000116349	−	1.00000i	$-0.499963\pi$
$521$	−451.108	−	260.448i	−0.865851	−	0.499899i	−0.865967	+	0.500101i	$0.833296\pi$
$522$		0			0
$523$	232.863	+	403.331i	0.445245	+	0.771187i	0.998069	−	0.0621107i	$-0.0197832\pi$
$523$	232.863	+	403.331i	0.445245	+	0.771187i	−0.552824	+	0.833298i	$0.686450\pi$
$524$	316.965	+	183.000i	0.604895	+	0.349236i
$525$		0			0
$526$	75.0310	+	129.957i	0.142644	+	0.247067i
$527$	−279.509	−	161.375i	−0.530378	−	0.306214i
$528$		0			0
$529$	−264.490	−	458.110i	−0.499981	−	0.865992i
$530$	76.4746	−	44.1526i	0.144292	−	0.0833069i
$531$		0			0
$532$	4.61378	−	29.5695i	0.00867252	−	0.0555818i
$533$	157.246	+	90.7861i	0.295021	+	0.170330i
$534$		0			0
$535$	−322.008			−0.601885
$536$		−	198.663i		−	0.370640i
$537$		0			0
$538$	159.367	−	276.032i	0.296221	−	0.513070i
$539$	−192.433	−	211.755i	−0.357019	−	0.392866i
$540$		0			0
$541$	272.202	+	471.468i	0.503147	+	0.871476i	0.999993	+	0.00363728i	$0.00115778\pi$
$541$	272.202	+	471.468i	0.503147	+	0.871476i	−0.496847	+	0.867838i	$0.665509\pi$
$542$	−205.782	+	118.808i	−0.379672	+	0.219204i
$543$		0			0
$544$	69.9707	−	121.193i	0.128623	−	0.222781i
$545$	−344.551	+	198.927i	−0.632204	+	0.365003i
$546$		0			0
$547$	−166.024	+	287.563i	−0.303518	+	0.525709i	−0.976930	−	0.213558i	$-0.931495\pi$
$547$	−166.024	+	287.563i	−0.303518	+	0.525709i	0.673412	+	0.739267i	$0.264828\pi$
$548$	53.3897	−	30.8245i	0.0974264	−	0.0562492i
$549$		0			0
$550$	−79.5494	+	137.784i	−0.144635	+	0.250516i
$551$			77.6440i			0.140915i
$552$		0			0
$553$	339.500	+	273.633i	0.613924	+	0.494816i
$554$	−410.948	+	237.261i	−0.741783	+	0.428269i
$555$		0			0
$556$	−55.5707	−	96.2513i	−0.0999474	−	0.173114i
$557$	384.372	+	221.918i	0.690076	+	0.398416i	0.803641	−	0.595115i	$-0.202893\pi$
$557$	384.372	+	221.918i	0.690076	+	0.398416i	−0.113564	+	0.993531i	$0.536227\pi$
$558$		0			0
$559$	−460.578			−0.823933
$560$	−24.1723	−	62.5414i	−0.0431648	−	0.111681i
$561$		0			0
$562$	382.831	−	663.082i	0.681194	−	1.17986i
$563$		−	805.689i		−	1.43106i	−0.698580	−	0.715532i	$-0.746184\pi$
$563$		−	805.689i		−	1.43106i	0.698580	−	0.715532i	$-0.253816\pi$
$564$		0			0
$565$	−482.938			−0.854758
$566$		−	447.612i		−	0.790834i
$567$		0			0
$568$	285.083			0.501907
$569$		−	762.194i		−	1.33953i	−0.742572	−	0.669767i	$-0.766394\pi$
$569$		−	762.194i		−	1.33953i	0.742572	−	0.669767i	$-0.233606\pi$
$570$		0			0
$571$	−895.261			−1.56788			−0.783941	−	0.620835i	$-0.786794\pi$
$571$	−895.261			−1.56788			−0.783941	+	0.620835i	$0.786794\pi$
$572$	−58.0561	−	33.5187i	−0.101497	−	0.0585991i
$573$		0			0
$574$	−48.2761	+	309.400i	−0.0841048	+	0.539024i
$575$		−	2.74960i		−	0.00478192i
$576$		0			0
$577$	−0.145650	+	0.252273i	−0.000252426	+	0.000437215i	−0.866152	−	0.499781i	$-0.833414\pi$
$577$	−0.145650	+	0.252273i	−0.000252426	+	0.000437215i	0.865899	+	0.500219i	$0.166747\pi$
$578$	−395.577	+	228.387i	−0.684390	+	0.395133i
$579$		0			0
$580$	86.9782	+	150.651i	0.149962	+	0.259743i
$581$	−150.181	−	388.565i	−0.258486	−	0.668786i
$582$		0			0
$583$	152.264			0.261174
$584$	21.4062	+	12.3589i	0.0366545	+	0.0211625i
$585$		0			0
$586$	183.389	+	317.638i	0.312950	+	0.542045i
$587$	−316.757	−	182.880i	−0.539621	−	0.311550i	0.205304	−	0.978698i	$-0.434182\pi$
$587$	−316.757	−	182.880i	−0.539621	−	0.311550i	−0.744925	+	0.667148i	$0.767515\pi$
$588$		0			0
$589$	−13.9445	−	24.1526i	−0.0236749	−	0.0410061i
$590$	66.7414	+	38.5332i	0.113121	+	0.0653105i
$591$		0			0
$592$	64.2414	+	111.269i	0.108516	+	0.187955i
$593$	248.305	−	143.359i	0.418726	−	0.241752i	−0.275806	−	0.961213i	$-0.588945\pi$
$593$	248.305	−	143.359i	0.418726	−	0.241752i	0.694532	+	0.719462i	$0.255611\pi$
$594$		0			0
$595$	−63.9294	+	409.721i	−0.107444	+	0.688606i
$596$	12.7850	+	7.38142i	0.0214513	+	0.0123849i
$597$		0			0
$598$	1.15857			0.00193740
$599$			36.1773i			0.0603961i	0.999544	+	0.0301980i	$0.00961380\pi$
$599$			36.1773i			0.0603961i	−0.999544	+	0.0301980i	$0.990386\pi$
$600$		0			0
$601$	450.390	−	780.099i	0.749402	−	1.29800i	−0.198708	−	0.980059i	$-0.563675\pi$
$601$	450.390	−	780.099i	0.749402	−	1.29800i	0.948110	−	0.317943i	$-0.102992\pi$
$602$	−286.362	−	740.909i	−0.475684	−	1.23075i
$603$		0			0
$604$	34.5368	+	59.8194i	0.0571801	+	0.0990388i
$605$	−180.219	+	104.049i	−0.297882	+	0.171982i
$606$		0			0
$607$	−7.88292	+	13.6536i	−0.0129867	+	0.0224936i	−0.872446	−	0.488711i	$-0.837467\pi$
$607$	−7.88292	+	13.6536i	−0.0129867	+	0.0224936i	0.859459	+	0.511205i	$0.170801\pi$
$608$	10.4724	−	6.04623i	0.0172243	−	0.00994445i
$609$		0			0
$610$	173.838	−	301.097i	0.284981	−	0.493601i
$611$	−304.109	+	175.578i	−0.497724	+	0.287361i
$612$		0			0
$613$	44.9747	−	77.8984i	0.0733681	−	0.127077i	−0.827007	−	0.562191i	$-0.809959\pi$
$613$	44.9747	−	77.8984i	0.0733681	−	0.127077i	0.900375	+	0.435114i	$0.143292\pi$
$614$			262.901i			0.428178i
$615$		0			0
$616$	17.8238	−	114.232i	0.0289348	−	0.185442i
$617$	871.820	−	503.346i	1.41300	−	0.815795i	0.417329	−	0.908755i	$-0.362966\pi$
$617$	871.820	−	503.346i	1.41300	−	0.815795i	0.995670	+	0.0929603i	$0.0296330\pi$
$618$		0			0
$619$	−75.5436	−	130.845i	−0.122041	−	0.211382i	0.798531	−	0.601953i	$-0.205611\pi$
$619$	−75.5436	−	130.845i	−0.122041	−	0.211382i	−0.920573	+	0.390572i	$0.872277\pi$
$620$	−54.1124	−	31.2418i	−0.0872780	−	0.0503900i
$621$		0			0
$622$	9.81499			0.0157797
$623$	−756.188	−	117.989i	−1.21378	−	0.189389i
$624$		0			0
$625$	−113.903	+	197.287i	−0.182246	+	0.315658i
$626$			560.187i			0.894868i
$627$		0			0
$628$	−385.264			−0.613478
$629$		−	794.614i		−	1.26330i
$630$		0			0
$631$	318.002			0.503965			0.251982	−	0.967732i	$-0.418917\pi$
$631$	318.002			0.503965			0.251982	+	0.967732i	$0.418917\pi$
$632$			176.189i			0.278780i
$633$		0			0
$634$	−79.8988			−0.126023
$635$	−67.2928	−	38.8515i	−0.105973	−	0.0611835i
$636$		0			0
$637$	208.154	−	189.161i	0.326772	−	0.296956i
$638$			299.952i			0.470144i
$639$		0			0
$640$	13.5462	−	23.4627i	0.0211659	−	0.0366604i
$641$	−376.730	+	217.505i	−0.587722	+	0.339321i	−0.764196	−	0.644984i	$-0.776864\pi$
$641$	−376.730	+	217.505i	−0.587722	+	0.339321i	0.176474	+	0.984305i	$0.443531\pi$
$642$		0			0
$643$	−267.589	−	463.477i	−0.416157	−	0.720805i	0.579392	−	0.815049i	$-0.303290\pi$
$643$	−267.589	−	463.477i	−0.416157	−	0.720805i	−0.995549	+	0.0942441i	$0.969957\pi$
$644$	0.720331	+	1.86373i	0.00111853	+	0.00289398i
$645$		0			0
$646$	−74.7869			−0.115769
$647$	217.880	+	125.793i	0.336755	+	0.194425i	0.658836	−	0.752287i	$-0.271049\pi$
$647$	217.880	+	125.793i	0.336755	+	0.194425i	−0.322081	+	0.946712i	$0.604382\pi$
$648$		0			0
$649$	66.4425	+	115.082i	0.102377	+	0.177322i
$650$	−135.441	−	78.1966i	−0.208370	−	0.120302i
$651$		0			0
$652$	−226.076	−	391.575i	−0.346742	−	0.600575i
$653$	−580.813	−	335.333i	−0.889454	−	0.513526i	−0.0156901	−	0.999877i	$-0.504995\pi$
$653$	−580.813	−	335.333i	−0.889454	−	0.513526i	−0.873764	+	0.486350i	$0.838328\pi$
$654$		0			0
$655$	−219.110	−	379.510i	−0.334520	−	0.579405i
$656$	−109.577	+	63.2645i	−0.167039	+	0.0964398i
$657$		0			0
$658$	−471.521	−	380.041i	−0.716597	−	0.577570i
$659$	240.616	+	138.920i	0.365123	+	0.210804i	0.671326	−	0.741162i	$-0.265725\pi$
$659$	240.616	+	138.920i	0.365123	+	0.210804i	−0.306203	+	0.951966i	$0.599058\pi$
$660$		0			0
$661$	−783.234			−1.18492			−0.592462	−	0.805599i	$-0.701844\pi$
$661$	−783.234			−1.18492			−0.592462	+	0.805599i	$0.701844\pi$
$662$		−	312.346i		−	0.471822i
$663$		0			0
$664$	84.1614	−	145.772i	0.126749	−	0.219536i
$665$	−22.4862	+	27.8989i	−0.0338139	+	0.0419533i
$666$		0			0
$667$	−2.59194	−	4.48937i	−0.00388597	−	0.00673069i
$668$	−226.701	+	130.886i	−0.339373	+	0.195937i
$669$		0			0
$670$	−118.932	+	205.996i	−0.177511	+	0.307457i
$671$	519.179	−	299.748i	0.773739	−	0.446718i
$672$		0			0
$673$	292.102	−	505.936i	0.434030	−	0.751762i	−0.563186	−	0.826330i	$-0.690425\pi$
$673$	292.102	−	505.936i	0.434030	−	0.751762i	0.997216	+	0.0745684i	$0.0237579\pi$
$674$	419.919	−	242.441i	0.623026	−	0.359704i
$675$		0			0
$676$	−136.051	+	235.648i	−0.201259	+	0.348591i
$677$		−	192.330i		−	0.284091i	−0.989860	−	0.142046i	$-0.954632\pi$
$677$		−	192.330i		−	0.284091i	0.989860	−	0.142046i	$-0.0453680\pi$
$678$		0			0
$679$	1042.86	−	403.067i	1.53588	−	0.593618i
$680$	−145.107	+	83.7777i	−0.213393	+	0.123202i
$681$		0			0
$682$	−53.8700	−	93.3056i	−0.0789883	−	0.136812i
$683$	−715.412	−	413.043i	−1.04746	−	0.604749i	−0.125519	−	0.992091i	$-0.540060\pi$
$683$	−715.412	−	413.043i	−1.04746	−	0.604749i	−0.921936	+	0.387343i	$0.873393\pi$
$684$		0			0
$685$	−73.8140			−0.107758
$686$	433.712	+	217.237i	0.632233	+	0.316672i
$687$		0			0
$688$	160.478	−	277.955i	0.233252	−	0.404005i
$689$			149.675i			0.217235i
$690$		0			0
$691$	−950.291			−1.37524			−0.687620	−	0.726070i	$-0.741345\pi$
$691$	−950.291			−1.37524			−0.687620	+	0.726070i	$0.741345\pi$
$692$		−	160.350i		−	0.231720i
$693$		0			0
$694$	516.814			0.744689
$695$			133.072i			0.191471i
$696$		0			0
$697$	782.531			1.12271
$698$	−6.43249	−	3.71380i	−0.00921560	−	0.00532063i
$699$		0			0
$700$	41.5816	−	266.495i	0.0594023	−	0.380707i
$701$		−	275.965i		−	0.393673i	−0.980436	−	0.196836i	$-0.936933\pi$
$701$		−	275.965i		−	0.393673i	0.980436	−	0.196836i	$-0.0630668\pi$
$702$		0			0
$703$	34.3316	−	59.4641i	0.0488359	−	0.0845863i
$704$	40.4565	−	23.3576i	0.0574667	−	0.0331784i
$705$		0			0
$706$	106.134	+	183.830i	0.150332	+	0.260382i
$707$	−880.587	−	137.399i	−1.24553	−	0.194341i
$708$		0			0
$709$	−468.543			−0.660851			−0.330425	−	0.943832i	$-0.607192\pi$
$709$	−468.543			−0.660851			−0.330425	+	0.943832i	$0.607192\pi$
$710$	−295.607	−	170.669i	−0.416347	−	0.240378i
$711$		0			0
$712$	−154.622	−	267.812i	−0.217165	−	0.376141i
$713$	1.61254	+	0.931002i	0.00226163	+	0.00130575i
$714$		0			0
$715$	40.1328	+	69.5120i	0.0561297	+	0.0972196i
$716$	−181.342	−	104.698i	−0.253271	−	0.146226i
$717$		0			0
$718$	−17.2324	−	29.8475i	−0.0240006	−	0.0415703i
$719$	946.861	−	546.670i	1.31691	−	0.760321i	0.333683	−	0.942685i	$-0.391709\pi$
$719$	946.861	−	546.670i	1.31691	−	0.760321i	0.983231	+	0.182365i	$0.0583752\pi$
$720$		0			0
$721$	−319.794	+	123.601i	−0.443542	+	0.171429i
$722$	436.536	+	252.034i	0.604621	+	0.349078i
$723$		0			0
$724$	354.772			0.490016
$725$			699.765i			0.965194i
$726$		0			0
$727$	437.186	−	757.228i	0.601356	−	1.04158i	−0.391260	−	0.920280i	$-0.627961\pi$
$727$	437.186	−	757.228i	0.601356	−	1.04158i	0.992616	−	0.121299i	$-0.0387061\pi$
$728$	112.289	+	17.5207i	0.154244	+	0.0240669i
$729$		0			0
$730$	−14.7976	−	25.6302i	−0.0202707	−	0.0351099i
$731$	−1719.04	+	992.489i	−2.35163	+	1.35771i
$732$		0			0
$733$	−165.614	+	286.852i	−0.225940	+	0.391340i	−0.956601	−	0.291401i	$-0.905879\pi$
$733$	−165.614	+	286.852i	−0.225940	+	0.391340i	0.730661	+	0.682741i	$0.239212\pi$
$734$	−665.992	+	384.511i	−0.907346	+	0.523856i
$735$		0			0
$736$	−0.403675	+	0.699185i	−0.000548471	+	0.000949979i
$737$	−355.198	+	205.074i	−0.481952	+	0.278255i
$738$		0			0
$739$	−626.471	+	1085.08i	−0.847729	+	1.46831i	0.0355017	+	0.999370i	$0.488697\pi$
$739$	−626.471	+	1085.08i	−0.847729	+	1.46831i	−0.883230	+	0.468939i	$0.844636\pi$
$740$		−	153.836i		−	0.207886i
$741$		0			0
$742$	−240.775	+	93.0595i	−0.324494	+	0.125417i
$743$	567.386	−	327.580i	0.763642	−	0.440889i	−0.0669598	−	0.997756i	$-0.521330\pi$
$743$	567.386	−	327.580i	0.763642	−	0.440889i	0.830602	+	0.556867i	$0.187997\pi$
$744$		0			0
$745$	−8.83795	−	15.3078i	−0.0118630	−	0.0205474i
$746$	−357.492	−	206.398i	−0.479212	−	0.276673i
$747$		0			0
$748$	−288.915			−0.386249
$749$	930.036	+	145.115i	1.24170	+	0.193745i
$750$		0			0
$751$	748.509	−	1296.46i	0.996683	−	1.72631i	0.427867	−	0.903842i	$-0.359265\pi$
$751$	748.509	−	1296.46i	0.996683	−	1.72631i	0.568817	−	0.822464i	$-0.307401\pi$
$752$		−	244.703i		−	0.325403i
$753$		0			0
$754$	−294.851			−0.391049
$755$		−	82.7035i		−	0.109541i
$756$		0			0
$757$	1042.92			1.37771			0.688853	−	0.724901i	$-0.258115\pi$
$757$	1042.92			1.37771			0.688853	+	0.724901i	$0.258115\pi$
$758$		−	548.127i		−	0.723123i
$759$		0			0
$760$	−14.4786			−0.0190508
$761$	949.011	+	547.912i	1.24706	+	0.719989i	0.970522	−	0.241014i	$-0.0774800\pi$
$761$	949.011	+	547.912i	1.24706	+	0.719989i	0.276536	+	0.961003i	$0.410813\pi$
$762$		0			0
$763$	1084.79	−	419.274i	1.42175	−	0.549507i
$764$		−	351.429i		−	0.459986i
$765$		0			0
$766$	247.782	−	429.171i	0.323475	−	0.560276i
$767$	−113.125	+	65.3126i	−0.147490	+	0.0851533i
$768$		0			0
$769$	176.993	+	306.561i	0.230160	+	0.398649i	0.957855	−	0.287252i	$-0.0927418\pi$
$769$	176.993	+	306.561i	0.230160	+	0.398649i	−0.727695	+	0.685901i	$0.759408\pi$
$770$	−86.8681	+	107.778i	−0.112816	+	0.139972i
$771$		0			0
$772$	−163.363			−0.211610
$773$	40.8414	+	23.5798i	0.0528349	+	0.0305043i	0.526185	−	0.850370i	$-0.323622\pi$
$773$	40.8414	+	23.5798i	0.0528349	+	0.0305043i	−0.473350	+	0.880875i	$0.656955\pi$
$774$		0			0
$775$	−125.675	−	217.675i	−0.162161	−	0.280871i
$776$	391.234	+	225.879i	0.504167	+	0.291081i
$777$		0			0
$778$	363.412	+	629.448i	0.467111	+	0.809059i
$779$	58.5599	+	33.8096i	0.0751732	+	0.0434012i
$780$		0			0
$781$	−294.283	−	509.713i	−0.376803	−	0.652641i
$782$	4.32418	−	2.49656i	0.00552964	−	0.00319254i
$783$		0			0
$784$	41.6306	+	191.528i	0.0531003	+	0.244296i
$785$	399.486	+	230.643i	0.508899	+	0.293813i
$786$		0			0
$787$	−683.837			−0.868916			−0.434458	−	0.900692i	$-0.643060\pi$
$787$	−683.837			−0.868916			−0.434458	+	0.900692i	$0.643060\pi$
$788$			637.722i			0.809292i
$789$		0			0
$790$	105.478	−	182.693i	0.133516	−	0.231256i
$791$	1394.84	+	217.639i	1.76339	+	0.275144i
$792$		0			0
$793$	294.651	+	510.350i	0.371564	+	0.643569i
$794$	548.159	−	316.479i	0.690376	−	0.398589i
$795$		0			0
$796$	−375.755	+	650.827i	−0.472054	+	0.817622i
$797$	−173.916	+	100.410i	−0.218213	+	0.125985i	−0.605123	−	0.796132i	$-0.706876\pi$
$797$	−173.916	+	100.410i	−0.218213	+	0.125985i	0.386910	+	0.922118i	$0.373543\pi$
$798$		0			0
$799$	−756.695	+	1310.64i	−0.947053	+	1.64034i
$800$	94.3821	−	54.4915i	0.117978	−	0.0681144i
$801$		0			0
$802$	−220.434	+	381.804i	−0.274856	+	0.476064i
$803$		−	51.0308i		−	0.0635502i
$804$		0			0
$805$	0.368821	−	2.36376i	0.000458163	−	0.00293635i
$806$	91.7189	−	52.9539i	0.113795	−	0.0656997i
$807$		0			0
$808$	−180.058	−	311.870i	−0.222844	−	0.385977i
$809$	−264.760	−	152.859i	−0.327268	−	0.188948i	0.327359	−	0.944900i	$-0.393841\pi$
$809$	−264.760	−	152.859i	−0.327268	−	0.188948i	−0.654628	+	0.755951i	$0.727175\pi$
$810$		0			0
$811$	−902.926			−1.11335			−0.556674	−	0.830731i	$-0.687923\pi$
$811$	−902.926			−1.11335			−0.556674	+	0.830731i	$0.687923\pi$
$812$	−183.322	−	474.312i	−0.225766	−	0.584128i
$813$		0			0
$814$	132.629	−	229.720i	0.162935	−	0.282211i
$815$			541.372i			0.664260i
$816$		0			0
$817$	−171.524			−0.209943
$818$		−	418.450i		−	0.511552i
$819$		0			0
$820$	151.496			0.184752
$821$			47.7520i			0.0581632i	0.999577	+	0.0290816i	$0.00925827\pi$
$821$			47.7520i			0.0581632i	−0.999577	+	0.0290816i	$0.990742\pi$
$822$		0			0
$823$	1480.15			1.79848			0.899239	−	0.437457i	$-0.144121\pi$
$823$	1480.15			1.79848			0.899239	+	0.437457i	$0.144121\pi$
$824$	−119.972	−	69.2659i	−0.145597	−	0.0840605i
$825$		0			0
$826$	−175.400	−	141.370i	−0.212348	−	0.171151i
$827$			1050.14i			1.26982i	0.772587	+	0.634909i	$0.218962\pi$
$827$			1050.14i			1.26982i	−0.772587	+	0.634909i	$0.781038\pi$
$828$		0			0
$829$	182.182	−	315.549i	0.219762	−	0.380638i	−0.734973	−	0.678096i	$-0.762805\pi$
$829$	182.182	−	315.549i	0.219762	−	0.380638i	0.954735	+	0.297458i	$0.0961387\pi$
$830$	−174.536	+	100.769i	−0.210285	+	0.121408i
$831$		0			0
$832$	22.9604	+	39.7686i	0.0275966	+	0.0477987i
$833$	369.287	−	1154.56i	0.443321	−	1.38603i
$834$		0			0
$835$	313.426			0.375361
$836$	−21.6206	−	12.4827i	−0.0258620	−	0.0149314i
$837$		0			0
$838$	267.173	+	462.757i	0.318822	+	0.552216i
$839$	−1021.16	−	589.566i	−1.21711	−	0.702701i	−0.252814	−	0.967515i	$-0.581356\pi$
$839$	−1021.16	−	589.566i	−1.21711	−	0.702701i	−0.964299	+	0.264814i	$0.914689\pi$
$840$		0			0
$841$	239.140	+	414.203i	0.284352	+	0.492513i
$842$	−690.843	−	398.858i	−0.820478	−	0.473703i
$843$		0			0
$844$	260.496	+	451.192i	0.308645	+	0.534588i
$845$	282.147	−	162.898i	0.333902	−	0.192778i
$846$		0			0
$847$	567.404	−	219.302i	0.669899	−	0.258916i
$848$	−90.3276	−	52.1507i	−0.106518	−	0.0614984i
$849$		0			0
$850$	−674.016			−0.792960
$851$			4.58428i			0.00538694i
$852$		0			0
$853$	152.043	−	263.345i	0.178244	−	0.308729i	−0.763035	−	0.646357i	$-0.776292\pi$
$853$	152.043	−	263.345i	0.178244	−	0.308729i	0.941279	+	0.337629i	$0.109625\pi$
$854$	−637.777	+	791.297i	−0.746811	+	0.926577i
$855$		0			0
$856$	190.169	+	329.383i	0.222160	+	0.384793i
$857$	1324.10	−	764.468i	1.54504	−	0.892028i	0.546529	−	0.837440i	$-0.315949\pi$
$857$	1324.10	−	764.468i	1.54504	−	0.892028i	0.998509	−	0.0545873i	$-0.0173843\pi$
$858$		0			0
$859$	227.177	−	393.483i	0.264467	−	0.458071i	−0.702957	−	0.711233i	$-0.748137\pi$
$859$	227.177	−	393.483i	0.264467	−	0.458071i	0.967424	+	0.253162i	$0.0814705\pi$
$860$	−332.803	+	192.144i	−0.386980	+	0.223423i
$861$		0			0
$862$	−531.933	+	921.335i	−0.617092	+	1.06883i
$863$	190.804	−	110.161i	0.221094	−	0.127649i	−0.385363	−	0.922765i	$-0.625924\pi$
$863$	190.804	−	110.161i	0.221094	−	0.127649i	0.606457	+	0.795116i	$0.292590\pi$
$864$		0			0
$865$	−95.9957	+	166.269i	−0.110978	+	0.192219i
$866$		−	638.180i		−	0.736929i
$867$		0			0
$868$	142.210	+	114.620i	0.163836	+	0.132050i
$869$	315.016	−	181.874i	0.362504	−	0.209292i
$870$		0			0
$871$	−201.586	−	349.158i	−0.231443	−	0.400870i
$872$	406.965	+	234.961i	0.466703	+	0.269451i
$873$		0			0
$874$	0.431460			0.000493662
$875$	−465.634	+	577.717i	−0.532153	+	0.660248i
$876$		0			0
$877$	824.034	−	1427.27i	0.939606	−	1.62744i	0.173398	−	0.984852i	$-0.444525\pi$
$877$	824.034	−	1427.27i	0.939606	−	1.62744i	0.766208	−	0.642593i	$-0.222141\pi$
$878$		−	187.989i		−	0.214110i
$879$		0			0
$880$	−55.9332			−0.0635605
$881$			1387.66i			1.57510i	0.616252	+	0.787549i	$0.288650\pi$
$881$			1387.66i			1.57510i	−0.616252	+	0.787549i	$0.711350\pi$
$882$		0			0
$883$	−117.311			−0.132855			−0.0664274	−	0.997791i	$-0.521160\pi$
$883$	−117.311			−0.132855			−0.0664274	+	0.997791i	$0.521160\pi$
$884$		−	284.001i		−	0.321269i
$885$		0			0
$886$	−587.255			−0.662816
$887$	−319.904	−	184.697i	−0.360658	−	0.208226i	0.308711	−	0.951156i	$-0.400102\pi$
$887$	−319.904	−	184.697i	−0.360658	−	0.208226i	−0.669370	+	0.742930i	$0.733436\pi$
$888$		0			0
$889$	176.849	+	142.538i	0.198930	+	0.160336i
$890$			370.264i			0.416027i
$891$		0			0
$892$	−237.591	+	411.520i	−0.266358	+	0.461345i
$893$	−113.253	+	65.3867i	−0.126823	+	0.0732214i
$894$		0			0
$895$	125.357	+	217.125i	0.140064	+	0.242598i
$896$	−49.6982	+	61.6611i	−0.0554667	+	0.0688182i
$897$		0			0
$898$	−371.701			−0.413920
$899$	−410.387	−	236.937i	−0.456493	−	0.263556i
$900$		0			0
$901$	322.531	+	558.640i	0.357970	+	0.620022i
$902$	226.227	+	130.612i	0.250806	+	0.144803i
$903$		0			0
$904$	285.210	+	493.998i	0.315498	+	0.546458i
$905$	−367.868	−	212.389i	−0.406484	−	0.234683i
$906$		0			0
$907$	297.608	+	515.472i	0.328124	+	0.568327i	0.982140	−	0.188154i	$-0.0602504\pi$
$907$	297.608	+	515.472i	0.328124	+	0.568327i	−0.654016	+	0.756481i	$0.726917\pi$
$908$	−408.810	+	236.026i	−0.450231	+	0.259941i
$909$		0			0
$910$	−105.945	−	85.3909i	−0.116424	−	0.0938362i
$911$	451.079	+	260.431i	0.495148	+	0.285874i	0.726707	−	0.686947i	$-0.241050\pi$
$911$	451.079	+	260.431i	0.495148	+	0.285874i	−0.231560	+	0.972821i	$0.574383\pi$
$912$		0			0
$913$	−347.509			−0.380623
$914$		−	715.629i		−	0.782964i
$915$		0			0
$916$	−398.258	+	689.803i	−0.434779	+	0.753060i
$917$	461.814	+	1194.86i	0.503614	+	1.30301i
$918$		0			0
$919$	−430.710	−	746.012i	−0.468673	−	0.811765i	0.530686	−	0.847568i	$-0.321934\pi$
$919$	−430.710	−	746.012i	−0.468673	−	0.811765i	−0.999359	+	0.0358037i	$0.988601\pi$
$920$	0.837151	−	0.483329i	0.000909947	−	0.000525358i
$921$		0			0
$922$	539.079	−	933.712i	0.584684	−	1.01270i
$923$	501.045	−	289.278i	0.542844	−	0.313411i
$924$		0			0
$925$	309.413	−	535.919i	0.334501	−	0.579372i
$926$	34.8096	−	20.0973i	0.0375913	−	0.0217034i
$927$		0			0
$928$	102.734	−	177.940i	0.110705	−	0.191746i
$929$			854.333i			0.919627i	0.888016	+	0.459813i	$0.152084\pi$
$929$			854.333i			0.919627i	−0.888016	+	0.459813i	$0.847916\pi$
$930$		0			0
$931$	77.5184	−	70.4452i	0.0832636	−	0.0756661i
$932$	263.735	−	152.268i	0.282978	−	0.163377i
$933$		0			0
$934$	103.417	+	179.124i	0.110725	+	0.191782i
$935$	299.579	+	172.962i	0.320406	+	0.184986i
$936$		0			0
$937$	−336.030			−0.358623			−0.179311	−	0.983792i	$-0.557387\pi$
$937$	−336.030			−0.358623			−0.179311	+	0.983792i	$0.557387\pi$
$938$	436.338	−	541.369i	0.465179	−	0.577152i
$939$		0			0
$940$	−146.495	+	253.736i	−0.155845	+	0.269932i
$941$			1399.91i			1.48768i	0.668356	+	0.743842i	$0.266998\pi$
$941$			1399.91i			1.48768i	−0.668356	+	0.743842i	$0.733002\pi$
$942$		0			0
$943$	−4.51457			−0.00478746
$944$		−	91.0265i		−	0.0964264i
$945$		0			0
$946$	−662.624			−0.700449
$947$		−	804.331i		−	0.849347i	−0.905347	−	0.424673i	$-0.860389\pi$
$947$		−	804.331i		−	0.849347i	0.905347	−	0.424673i	$-0.139611\pi$
$948$		0			0
$949$	50.1630			0.0528588
$950$	−50.4393	−	29.1211i	−0.0530940	−	0.0306538i
$951$		0			0
$952$	456.859	−	176.576i	0.479894	−	0.185479i
$953$		−	998.754i		−	1.04801i	−0.851715	−	0.524005i	$-0.824437\pi$
$953$		−	998.754i		−	1.04801i	0.851715	−	0.524005i	$-0.175563\pi$
$954$		0			0
$955$	−210.387	+	364.402i	−0.220301	+	0.381572i
$956$	−120.114	+	69.3480i	−0.125643	+	0.0725397i
$957$		0			0
$958$	38.9630	+	67.4858i	0.0406712	+	0.0704445i
$959$	213.192	+	33.2647i	0.222307	+	0.0346869i
$960$		0			0
$961$	−790.789			−0.822881
$962$	225.813	+	130.373i	0.234733	+	0.135523i
$963$		0			0
$964$	−30.7525	−	53.2648i	−0.0319009	−	0.0552540i
$965$	169.393	+	97.7994i	0.175537	+	0.101347i
$966$		0			0
$967$	568.912	+	985.384i	0.588327	+	1.01901i	0.994452	+	0.105194i	$0.0335464\pi$
$967$	568.912	+	985.384i	0.588327	+	1.01901i	−0.406125	+	0.913818i	$0.633120\pi$
$968$	212.864	+	122.897i	0.219901	+	0.126960i
$969$		0			0
$970$	−270.450	−	468.434i	−0.278815	−	0.482922i
$971$	−1389.34	+	802.138i	−1.43084	+	0.826095i	−0.997185	−	0.0749853i	$-0.976109\pi$
$971$	−1389.34	+	802.138i	−1.43084	+	0.826095i	−0.433653	+	0.901080i	$0.642776\pi$
$972$		0			0
$973$	59.9699	−	384.345i	0.0616341	−	0.395010i
$974$	585.257	+	337.898i	0.600880	+	0.346918i
$975$		0			0
$976$	−410.656			−0.420754
$977$			1129.63i			1.15622i	0.815958	+	0.578111i	$0.196210\pi$
$977$			1129.63i			1.15622i	−0.815958	+	0.578111i	$0.803790\pi$
$978$		0			0
$979$	−319.222	+	552.909i	−0.326070	+	0.564769i
$980$	71.4931	−	223.520i	0.0729521	−	0.228082i
$981$		0			0
$982$	−336.681	−	583.149i	−0.342852	−	0.593838i
$983$	−484.590	+	279.778i	−0.492970	+	0.284617i	−0.725806	−	0.687900i	$-0.758533\pi$
$983$	−484.590	+	279.778i	−0.492970	+	0.284617i	0.232836	+	0.972516i	$0.425200\pi$
$984$		0			0
$985$	381.780	−	661.262i	0.387594	−	0.671332i
$986$	−1100.49	+	635.367i	−1.11611	+	0.644389i
$987$		0			0
$988$	12.2704	−	21.2530i	0.0124194	−	0.0215111i
$989$	9.91748	−	5.72586i	0.0100278	−	0.00578955i
$990$		0			0
$991$	−820.211	+	1420.65i	−0.827660	+	1.43355i	0.0722098	+	0.997389i	$0.476995\pi$
$991$	−820.211	+	1420.65i	−0.827660	+	1.43355i	−0.899870	+	0.436159i	$0.856338\pi$
$992$			73.8022i			0.0743973i
$993$		0			0
$994$	776.869	+	626.148i	0.781559	+	0.629928i
$995$	779.252	−	449.901i	0.783167	−	0.452162i
$996$		0			0
$997$	−39.1528	−	67.8146i	−0.0392706	−	0.0680187i	0.845722	−	0.533624i	$-0.179170\pi$
$997$	−39.1528	−	67.8146i	−0.0392706	−	0.0680187i	−0.884993	+	0.465605i	$0.845837\pi$
$998$	−61.1832	−	35.3241i	−0.0613058	−	0.0353949i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.3.r.a.305.14		32
3.2	odd	2		126.3.r.a.11.6	yes	32
7.2	even	3		378.3.i.a.359.11		32
9.4	even	3		126.3.i.a.95.5	yes	32
9.5	odd	6		378.3.i.a.179.14		32
21.2	odd	6		126.3.i.a.65.5	✓	32
63.23	odd	6	inner	378.3.r.a.233.6		32
63.58	even	3		126.3.r.a.23.14	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.3.i.a.65.5	✓	32	21.2	odd	6
126.3.i.a.95.5	yes	32	9.4	even	3
126.3.r.a.11.6	yes	32	3.2	odd	2
126.3.r.a.23.14	yes	32	63.58	even	3
378.3.i.a.179.14		32	9.5	odd	6
378.3.i.a.359.11		32	7.2	even	3
378.3.r.a.233.6		32	63.23	odd	6	inner
378.3.r.a.305.14		32	1.1	even	1	trivial

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	378.r (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+1.41421i q^{2} -2.00000 q^{4} +(2.07383 + 1.19732i) q^{5} +(-5.45012 - 4.39274i) q^{7} -2.82843i q^{8} +(-1.69327 + 2.93283i) q^{10} +(-5.05707 + 2.91970i) q^{11} +(-2.87005 - 4.97107i) q^{13} +(6.21227 - 7.70764i) q^{14} +4.00000 q^{16} +(-21.4241 - 12.3692i) q^{17} +(-1.06883 - 1.85127i) q^{19} +(-4.14765 - 2.39465i) q^{20} +(-4.12908 - 7.15177i) q^{22} +(0.123600 + 0.0713603i) q^{23} +(-9.63283 - 16.6845i) q^{25} +(7.03015 - 4.05886i) q^{26} +(10.9002 + 8.78548i) q^{28} +(-31.4557 - 18.1610i) q^{29} +13.0465 q^{31} +5.65685i q^{32} +(17.4927 - 30.2982i) q^{34} +(-6.04307 - 15.6353i) q^{35} +(16.0604 + 27.8173i) q^{37} +(2.61809 - 1.51156i) q^{38} +(3.38655 - 5.86567i) q^{40} +(-27.3943 + 15.8161i) q^{41} +(40.1194 - 69.4888i) q^{43} +(10.1141 - 5.83940i) q^{44} +(-0.100919 + 0.174796i) q^{46} -61.1758i q^{47} +(10.4077 + 47.8819i) q^{49} +(23.5955 - 13.6229i) q^{50} +(5.74010 + 9.94214i) q^{52} +(-22.5819 - 13.0377i) q^{53} -13.9833 q^{55} +(-12.4245 + 15.4153i) q^{56} +(25.6835 - 44.4851i) q^{58} -22.7566i q^{59} -102.664 q^{61} +18.4505i q^{62} -8.00000 q^{64} -13.7455i q^{65} +70.2380 q^{67} +(42.8481 + 24.7384i) q^{68} +(22.1117 - 8.54620i) q^{70} +100.792i q^{71} +(-4.36953 + 7.56824i) q^{73} +(-39.3397 + 22.7128i) q^{74} +(2.13766 + 3.70254i) q^{76} +(40.3871 + 6.30167i) q^{77} -62.2922 q^{79} +(8.29531 + 4.78930i) q^{80} +(-22.3674 - 38.7414i) q^{82} +(51.5381 + 29.7555i) q^{83} +(-29.6199 - 51.3031i) q^{85} +(98.2720 + 56.7374i) q^{86} +(8.25816 + 14.3035i) q^{88} +(94.6860 - 54.6670i) q^{89} +(-6.19450 + 39.7003i) q^{91} +(-0.247199 - 0.142721i) q^{92} +86.5157 q^{94} -5.11896i q^{95} +(-79.8603 + 138.322i) q^{97} +(-67.7153 + 14.7187i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 64 q^{4} + 2 q^{7} + 36 q^{11} + 10 q^{13} - 36 q^{14} + 128 q^{16} + 54 q^{17} + 28 q^{19} + 126 q^{23} + 80 q^{25} + 72 q^{26} - 4 q^{28} - 36 q^{29} + 16 q^{31} + 90 q^{35} + 22 q^{37} - 72 q^{41}+ \cdots - 288 q^{98}+O(q^{100}) \) 32 * q - 64 * q^4 + 2 * q^7 + 36 * q^11 + 10 * q^13 - 36 * q^14 + 128 * q^16 + 54 * q^17 + 28 * q^19 + 126 * q^23 + 80 * q^25 + 72 * q^26 - 4 * q^28 - 36 * q^29 + 16 * q^31 + 90 * q^35 + 22 * q^37 - 72 * q^41 + 16 * q^43 - 72 * q^44 - 12 * q^46 + 2 * q^49 + 288 * q^50 - 20 * q^52 + 72 * q^53 - 24 * q^55 + 72 * q^56 - 24 * q^58 + 124 * q^61 - 256 * q^64 - 140 * q^67 - 108 * q^68 + 72 * q^70 + 196 * q^73 - 216 * q^74 - 56 * q^76 - 486 * q^77 + 76 * q^79 + 60 * q^85 + 144 * q^86 + 486 * q^89 - 122 * q^91 - 252 * q^92 - 336 * q^94 - 38 * q^97 - 288 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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