LMFDB - Embedded newform 378.3.j.a.199.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [378,3,Mod(19,378)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(378, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 5]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("378.19");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	378.j (of order $6$, degree $2$, not 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:	$10.2997539928$
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			199.10
Character	$\chi$	$=$	378.199
Dual form			378.3.j.a.19.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 1.22474i) q^{2} +(-1.00000 - 1.73205i) q^{4} -6.94216i q^{5} +(3.95343 - 5.77671i) q^{7} -2.82843 q^{8} +O(q^{10})$	\(q+(0.707107 - 1.22474i) q^{2} +(-1.00000 - 1.73205i) q^{4} -6.94216i q^{5} +(3.95343 - 5.77671i) q^{7} -2.82843 q^{8} +(-8.50237 - 4.90885i) q^{10} -17.4571 q^{11} +(13.3362 + 7.69965i) q^{13} +(-4.27951 - 8.92669i) q^{14} +(-2.00000 + 3.46410i) q^{16} +(-12.3517 - 7.13128i) q^{17} +(1.25450 - 0.724286i) q^{19} +(-12.0242 + 6.94216i) q^{20} +(-12.3440 + 21.3805i) q^{22} +12.8615 q^{23} -23.1935 q^{25} +(18.8602 - 10.8890i) q^{26} +(-13.9590 - 1.07082i) q^{28} +(2.98967 + 5.17826i) q^{29} +(-14.2616 + 8.23395i) q^{31} +(2.82843 + 4.89898i) q^{32} +(-17.4680 + 10.0852i) q^{34} +(-40.1029 - 27.4453i) q^{35} +(-0.732115 - 1.26806i) q^{37} -2.04859i q^{38} +19.6354i q^{40} +(10.5856 + 6.11162i) q^{41} +(-40.1499 - 69.5416i) q^{43} +(17.4571 + 30.2366i) q^{44} +(9.09448 - 15.7521i) q^{46} +(-72.4407 - 41.8237i) q^{47} +(-17.7409 - 45.6756i) q^{49} +(-16.4003 + 28.4062i) q^{50} -30.7986i q^{52} +(-6.51752 + 11.2887i) q^{53} +121.190i q^{55} +(-11.1820 + 16.3390i) q^{56} +8.45607 q^{58} +(88.1154 - 50.8735i) q^{59} +(58.1268 + 33.5595i) q^{61} +23.2891i q^{62} +8.00000 q^{64} +(53.4522 - 92.5819i) q^{65} +(19.7417 + 34.1937i) q^{67} +28.5251i q^{68} +(-61.9705 + 29.7090i) q^{70} +93.8955 q^{71} +(17.2189 + 9.94134i) q^{73} -2.07073 q^{74} +(-2.50900 - 1.44857i) q^{76} +(-69.0153 + 100.845i) q^{77} +(61.3930 - 106.336i) q^{79} +(24.0483 + 13.8843i) q^{80} +(14.9703 - 8.64313i) q^{82} +(7.01741 - 4.05150i) q^{83} +(-49.5065 + 85.7477i) q^{85} -113.561 q^{86} +49.3761 q^{88} +(43.7047 - 25.2329i) q^{89} +(97.2023 - 46.5994i) q^{91} +(-12.8615 - 22.2768i) q^{92} +(-102.447 + 59.1476i) q^{94} +(-5.02811 - 8.70894i) q^{95} +(-80.8837 + 46.6982i) q^{97} +(-68.4857 - 10.5695i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 32 q^{4} - 2 q^{7}+O(q^{10}) $ 32 * q - 32 * q^4 - 2 * q^7	$ 32 q - 32 q^{4} - 2 q^{7} - 24 q^{11} - 30 q^{13} + 12 q^{14} - 64 q^{16} - 54 q^{17} - 84 q^{23} - 160 q^{25} + 72 q^{26} - 4 q^{28} + 84 q^{29} - 24 q^{31} + 66 q^{35} - 22 q^{37} - 396 q^{41} - 16 q^{43} + 24 q^{44} + 12 q^{46} - 108 q^{47} - 22 q^{49} + 96 q^{50} + 252 q^{53} - 48 q^{56} + 48 q^{58} + 90 q^{59} - 102 q^{61} + 256 q^{64} + 6 q^{65} + 70 q^{67} - 108 q^{70} - 300 q^{71} - 144 q^{74} + 114 q^{77} + 106 q^{79} + 756 q^{83} - 60 q^{85} - 240 q^{86} - 414 q^{89} - 186 q^{91} + 84 q^{92} + 552 q^{95} + 114 q^{97} + 96 q^{98}+O(q^{100}) $ 32 * q - 32 * q^4 - 2 * q^7 - 24 * q^11 - 30 * q^13 + 12 * q^14 - 64 * q^16 - 54 * q^17 - 84 * q^23 - 160 * q^25 + 72 * q^26 - 4 * q^28 + 84 * q^29 - 24 * q^31 + 66 * q^35 - 22 * q^37 - 396 * q^41 - 16 * q^43 + 24 * q^44 + 12 * q^46 - 108 * q^47 - 22 * q^49 + 96 * q^50 + 252 * q^53 - 48 * q^56 + 48 * q^58 + 90 * q^59 - 102 * q^61 + 256 * q^64 + 6 * q^65 + 70 * q^67 - 108 * q^70 - 300 * q^71 - 144 * q^74 + 114 * q^77 + 106 * q^79 + 756 * q^83 - 60 * q^85 - 240 * q^86 - 414 * q^89 - 186 * q^91 + 84 * q^92 + 552 * q^95 + 114 * q^97 + 96 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	0.707107	−	1.22474i	0.353553	−	0.612372i
$2$	0.707107	−	1.22474i	0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−1.00000	−	1.73205i	−0.250000	−	0.433013i
$5$		−	6.94216i		−	1.38843i	−0.719767	−	0.694216i	$-0.755751\pi$
$5$		−	6.94216i		−	1.38843i	0.719767	−	0.694216i	$-0.244249\pi$
$6$		0			0
$7$	3.95343	−	5.77671i	0.564775	−	0.825245i
$7$	3.95343	−	5.77671i	0.564775	−	0.825245i
$8$	−2.82843			−0.353553
$9$		0			0
$10$	−8.50237	−	4.90885i	−0.850237	−	0.490885i
$11$	−17.4571			−1.58701			−0.793504	−	0.608565i	$-0.791746\pi$
$11$	−17.4571			−1.58701			−0.793504	+	0.608565i	$0.791746\pi$
$12$		0			0
$13$	13.3362	+	7.69965i	1.02586	+	0.592281i	0.915796	−	0.401643i	$-0.131561\pi$
$13$	13.3362	+	7.69965i	1.02586	+	0.592281i	0.110065	+	0.993924i	$0.464894\pi$
$14$	−4.27951	−	8.92669i	−0.305679	−	0.637621i
$15$		0			0
$16$	−2.00000	+	3.46410i	−0.125000	+	0.216506i
$17$	−12.3517	−	7.13128i	−0.726573	−	0.419487i	0.0905943	−	0.995888i	$-0.471123\pi$
$17$	−12.3517	−	7.13128i	−0.726573	−	0.419487i	−0.817167	+	0.576401i	$0.804457\pi$
$18$		0			0
$19$	1.25450	−	0.724286i	0.0660264	−	0.0381203i	−0.466623	−	0.884456i	$-0.654530\pi$
$19$	1.25450	−	0.724286i	0.0660264	−	0.0381203i	0.532650	+	0.846336i	$0.321196\pi$
$20$	−12.0242	+	6.94216i	−0.601208	+	0.347108i
$21$		0			0
$22$	−12.3440	+	21.3805i	−0.561092	+	0.971840i
$23$	12.8615			0.559197			0.279599	−	0.960117i	$-0.409799\pi$
$23$	12.8615			0.559197			0.279599	+	0.960117i	$0.409799\pi$
$24$		0			0
$25$	−23.1935			−0.927741
$26$	18.8602	−	10.8890i	0.725393	−	0.418806i
$27$		0			0
$28$	−13.9590	−	1.07082i	−0.498535	−	0.0382435i
$29$	2.98967	+	5.17826i	0.103092	+	0.178561i	0.912957	−	0.408056i	$-0.133793\pi$
$29$	2.98967	+	5.17826i	0.103092	+	0.178561i	−0.809865	+	0.586616i	$0.800460\pi$
$30$		0			0
$31$	−14.2616	+	8.23395i	−0.460052	+	0.265611i	−0.712066	−	0.702112i	$-0.752240\pi$
$31$	−14.2616	+	8.23395i	−0.460052	+	0.265611i	0.252014	+	0.967724i	$0.418907\pi$
$32$	2.82843	+	4.89898i	0.0883883	+	0.153093i
$33$		0			0
$34$	−17.4680	+	10.0852i	−0.513765	+	0.296622i
$35$	−40.1029	−	27.4453i	−1.14580	−	0.784151i
$36$		0			0
$37$	−0.732115	−	1.26806i	−0.0197869	−	0.0342719i	0.855962	−	0.517038i	$-0.172965\pi$
$37$	−0.732115	−	1.26806i	−0.0197869	−	0.0342719i	−0.875749	+	0.482766i	$0.839632\pi$
$38$		−	2.04859i		−	0.0539103i
$39$		0			0
$40$			19.6354i			0.490885i
$41$	10.5856	+	6.11162i	0.258186	+	0.149064i	0.623507	−	0.781818i	$-0.285707\pi$
$41$	10.5856	+	6.11162i	0.258186	+	0.149064i	−0.365321	+	0.930882i	$0.619041\pi$
$42$		0			0
$43$	−40.1499	−	69.5416i	−0.933718	−	1.61725i	−0.776904	−	0.629619i	$-0.783211\pi$
$43$	−40.1499	−	69.5416i	−0.933718	−	1.61725i	−0.156814	−	0.987628i	$-0.550122\pi$
$44$	17.4571	+	30.2366i	0.396752	+	0.687195i
$45$		0			0
$46$	9.09448	−	15.7521i	0.197706	−	0.342437i
$47$	−72.4407	−	41.8237i	−1.54129	−	0.889866i	−0.998758	−	0.0498323i	$-0.984131\pi$
$47$	−72.4407	−	41.8237i	−1.54129	−	0.889866i	−0.542535	−	0.840033i	$-0.682535\pi$
$48$		0			0
$49$	−17.7409	−	45.6756i	−0.362058	−	0.932155i
$50$	−16.4003	+	28.4062i	−0.328006	+	0.568123i
$51$		0			0
$52$		−	30.7986i		−	0.592281i
$53$	−6.51752	+	11.2887i	−0.122972	+	0.212994i	−0.920938	−	0.389708i	$-0.872576\pi$
$53$	−6.51752	+	11.2887i	−0.122972	+	0.212994i	0.797966	+	0.602702i	$0.205909\pi$
$54$		0			0
$55$			121.190i			2.20345i
$56$	−11.1820	+	16.3390i	−0.199678	+	0.291768i
$57$		0			0
$58$	8.45607			0.145794
$59$	88.1154	−	50.8735i	1.49348	−	0.862262i	0.493510	−	0.869740i	$-0.335714\pi$
$59$	88.1154	−	50.8735i	1.49348	−	0.862262i	0.999972	+	0.00747778i	$0.00238027\pi$
$60$		0			0
$61$	58.1268	+	33.5595i	0.952899	+	0.550156i	0.893980	−	0.448106i	$-0.147901\pi$
$61$	58.1268	+	33.5595i	0.952899	+	0.550156i	0.0589187	+	0.998263i	$0.481235\pi$
$62$			23.2891i			0.375631i
$63$		0			0
$64$	8.00000			0.125000
$65$	53.4522	−	92.5819i	0.822341	−	1.42434i
$66$		0			0
$67$	19.7417	+	34.1937i	0.294653	+	0.510354i	0.974904	−	0.222625i	$-0.0714627\pi$
$67$	19.7417	+	34.1937i	0.294653	+	0.510354i	−0.680251	+	0.732979i	$0.738129\pi$
$68$			28.5251i			0.419487i
$69$		0			0
$70$	−61.9705	+	29.7090i	−0.885293	+	0.424414i
$71$	93.8955			1.32247			0.661236	−	0.750178i	$-0.270032\pi$
$71$	93.8955			1.32247			0.661236	+	0.750178i	$0.270032\pi$
$72$		0			0
$73$	17.2189	+	9.94134i	0.235875	+	0.136183i	0.613280	−	0.789866i	$-0.289850\pi$
$73$	17.2189	+	9.94134i	0.235875	+	0.136183i	−0.377404	+	0.926049i	$0.623183\pi$
$74$	−2.07073			−0.0279829
$75$		0			0
$76$	−2.50900	−	1.44857i	−0.0330132	−	0.0190602i
$77$	−69.0153	+	100.845i	−0.896303	+	1.30967i
$78$		0			0
$79$	61.3930	−	106.336i	0.777126	−	1.34602i	−0.156466	−	0.987683i	$-0.550010\pi$
$79$	61.3930	−	106.336i	0.777126	−	1.34602i	0.933592	−	0.358338i	$-0.116657\pi$
$80$	24.0483	+	13.8843i	0.300604	+	0.173554i
$81$		0			0
$82$	14.9703	−	8.64313i	0.182565	−	0.105404i
$83$	7.01741	−	4.05150i	0.0845471	−	0.0488133i	−0.457130	−	0.889400i	$-0.651123\pi$
$83$	7.01741	−	4.05150i	0.0845471	−	0.0488133i	0.541678	+	0.840586i	$0.317789\pi$
$84$		0			0
$85$	−49.5065	+	85.7477i	−0.582429	+	1.00880i
$86$	−113.561			−1.32048
$87$		0			0
$88$	49.3761			0.561092
$89$	43.7047	−	25.2329i	0.491064	−	0.283516i	−0.233952	−	0.972248i	$-0.575166\pi$
$89$	43.7047	−	25.2329i	0.491064	−	0.283516i	0.725016	+	0.688732i	$0.241832\pi$
$90$		0			0
$91$	97.2023	−	46.5994i	1.06816	−	0.512081i
$92$	−12.8615	−	22.2768i	−0.139799	−	0.242139i
$93$		0			0
$94$	−102.447	+	59.1476i	−1.08986	+	0.629230i
$95$	−5.02811	−	8.70894i	−0.0529275	−	0.0916731i
$96$		0			0
$97$	−80.8837	+	46.6982i	−0.833853	+	0.481425i	−0.855170	−	0.518348i	$-0.826547\pi$
$97$	−80.8837	+	46.6982i	−0.833853	+	0.481425i	0.0213173	+	0.999773i	$0.493214\pi$
$98$	−68.4857	−	10.5695i	−0.698833	−	0.107852i
$99$		0			0
$100$	23.1935	+	40.1724i	0.231935	+	0.401724i
$101$			140.546i			1.39155i	0.718262	+	0.695773i	$0.244938\pi$
$101$			140.546i			1.39155i	−0.718262	+	0.695773i	$0.755062\pi$
$102$		0			0
$103$			36.1065i			0.350548i	0.984520	+	0.175274i	$0.0560811\pi$
$103$			36.1065i			0.350548i	−0.984520	+	0.175274i	$0.943919\pi$
$104$	−37.7204	−	21.7779i	−0.362697	−	0.209403i
$105$		0			0
$106$	9.21716	+	15.9646i	0.0869544	+	0.150609i
$107$	−11.3624	−	19.6803i	−0.106191	−	0.183928i	0.808033	−	0.589137i	$-0.200532\pi$
$107$	−11.3624	−	19.6803i	−0.106191	−	0.183928i	−0.914224	+	0.405209i	$0.867199\pi$
$108$		0			0
$109$	78.3438	−	135.695i	0.718751	−	1.24491i	−0.242744	−	0.970090i	$-0.578048\pi$
$109$	78.3438	−	135.695i	0.718751	−	1.24491i	0.961495	−	0.274823i	$-0.0886191\pi$
$110$	148.427	+	85.6942i	1.34933	+	0.779038i
$111$		0			0
$112$	12.1043	+	25.2485i	0.108074	+	0.225433i
$113$	66.4505	−	115.096i	0.588058	−	1.01855i	−0.406429	−	0.913682i	$-0.633226\pi$
$113$	66.4505	−	115.096i	0.588058	−	1.01855i	0.994487	−	0.104863i	$-0.0334405\pi$
$114$		0			0
$115$		−	89.2868i		−	0.776407i
$116$	5.97934	−	10.3565i	0.0515460	−	0.0892804i
$117$		0			0
$118$		−	143.892i		−	1.21942i
$119$	−90.0270	+	43.1595i	−0.756530	+	0.362685i
$120$		0			0
$121$	183.750			1.51860
$122$	82.2038	−	47.4604i	0.673801	−	0.389019i
$123$		0			0
$124$	28.5232	+	16.4679i	0.230026	+	0.132806i
$125$		−	12.5408i		−	0.100326i
$126$		0			0
$127$	245.690			1.93457			0.967284	−	0.253694i	$-0.0816458\pi$
$127$	245.690			1.93457			0.967284	+	0.253694i	$0.0816458\pi$
$128$	5.65685	−	9.79796i	0.0441942	−	0.0765466i
$129$		0			0
$130$	−75.5928	−	130.931i	−0.581483	−	1.00716i
$131$			216.313i			1.65124i	0.564226	+	0.825620i	$0.309175\pi$
$131$			216.313i			1.65124i	−0.564226	+	0.825620i	$0.690825\pi$
$132$		0			0
$133$	0.775579	−	10.1103i	0.00583142	−	0.0760173i
$134$	55.8381			0.416702
$135$		0			0
$136$	34.9360	+	20.1703i	0.256882	+	0.148311i
$137$	100.744			0.735356			0.367678	−	0.929953i	$-0.380153\pi$
$137$	100.744			0.735356			0.367678	+	0.929953i	$0.380153\pi$
$138$		0			0
$139$	−152.411	−	87.9944i	−1.09648	−	0.633054i	−0.161187	−	0.986924i	$-0.551532\pi$
$139$	−152.411	−	87.9944i	−1.09648	−	0.633054i	−0.935294	+	0.353870i	$0.884865\pi$
$140$	−7.43379	+	96.9055i	−0.0530985	+	0.692182i
$141$		0			0
$142$	66.3941	−	114.998i	0.467564	−	0.809845i
$143$	−232.811	−	134.414i	−1.62805	−	0.939955i
$144$		0			0
$145$	35.9483	−	20.7548i	0.247919	−	0.143136i
$146$	24.3512	−	14.0592i	0.166789	−	0.0962957i
$147$		0			0
$148$	−1.46423	+	2.53612i	−0.00989344	+	0.0171359i
$149$	200.929			1.34852			0.674258	−	0.738495i	$-0.264463\pi$
$149$	200.929			1.34852			0.674258	+	0.738495i	$0.264463\pi$
$150$		0			0
$151$	−236.955			−1.56924			−0.784619	−	0.619979i	$-0.787141\pi$
$151$	−236.955			−1.56924			−0.784619	+	0.619979i	$0.787141\pi$
$152$	−3.54826	+	2.04859i	−0.0233438	+	0.0134776i
$153$		0			0
$154$	74.7078	+	155.834i	0.485115	+	1.01191i
$155$	57.1614	+	99.0064i	0.368783	+	0.638751i
$156$		0			0
$157$	11.3929	−	6.57767i	0.0725659	−	0.0418960i	−0.463278	−	0.886213i	$-0.653327\pi$
$157$	11.3929	−	6.57767i	0.0725659	−	0.0418960i	0.535844	+	0.844317i	$0.319994\pi$
$158$	−86.8228	−	150.381i	−0.549511	−	0.951781i
$159$		0			0
$160$	34.0095	−	19.6354i	0.212559	−	0.122721i
$161$	50.8471	−	74.2974i	0.315821	−	0.461475i
$162$		0			0
$163$	−91.5446	−	158.560i	−0.561623	−	0.972760i	−0.997355	−	0.0726836i	$-0.976844\pi$
$163$	−91.5446	−	158.560i	−0.561623	−	0.972760i	0.435732	−	0.900077i	$-0.356490\pi$
$164$		−	24.4465i		−	0.149064i
$165$		0			0
$166$		−	11.4594i		−	0.0690324i
$167$	−178.551	−	103.087i	−1.06917	−	0.617285i	−0.141215	−	0.989979i	$-0.545101\pi$
$167$	−178.551	−	103.087i	−1.06917	−	0.617285i	−0.927954	+	0.372694i	$0.878434\pi$
$168$		0			0
$169$	34.0693	+	59.0098i	0.201593	+	0.349170i
$170$	70.0127	+	121.266i	0.411839	+	0.713327i
$171$		0			0
$172$	−80.2998	+	139.083i	−0.466859	+	0.808624i
$173$	158.871	+	91.7244i	0.918332	+	0.530199i	0.883102	−	0.469180i	$-0.155451\pi$
$173$	158.871	+	91.7244i	0.918332	+	0.530199i	0.0352292	+	0.999379i	$0.488784\pi$
$174$		0			0
$175$	−91.6939	+	133.982i	−0.523965	+	0.765614i
$176$	34.9142	−	60.4731i	0.198376	−	0.343597i
$177$		0			0
$178$		−	71.3694i		−	0.400952i
$179$	−19.7815	+	34.2626i	−0.110511	+	0.191411i	−0.915976	−	0.401232i	$-0.868582\pi$
$179$	−19.7815	+	34.2626i	−0.110511	+	0.191411i	0.805465	+	0.592643i	$0.201915\pi$
$180$		0			0
$181$			3.67614i			0.0203102i	0.999948	+	0.0101551i	$0.00323252\pi$
$181$			3.67614i			0.0203102i	−0.999948	+	0.0101551i	$0.996767\pi$
$182$	11.6601	−	151.999i	0.0640664	−	0.835158i
$183$		0			0
$184$	−36.3779			−0.197706
$185$	−8.80307	+	5.08245i	−0.0475841	+	0.0274727i
$186$		0			0
$187$	215.625	+	124.491i	1.15308	+	0.665729i
$188$			167.295i			0.889866i
$189$		0			0
$190$	−14.2216			−0.0748507
$191$	−23.9390	+	41.4635i	−0.125335	+	0.217087i	−0.921864	−	0.387514i	$-0.873334\pi$
$191$	−23.9390	+	41.4635i	−0.125335	+	0.217087i	0.796529	+	0.604601i	$0.206667\pi$
$192$		0			0
$193$	−29.2435	−	50.6512i	−0.151521	−	0.262442i	0.780266	−	0.625448i	$-0.215084\pi$
$193$	−29.2435	−	50.6512i	−0.151521	−	0.262442i	−0.931787	+	0.363006i	$0.881750\pi$
$194$			132.083i			0.680838i
$195$		0			0
$196$	−61.3716	+	76.4037i	−0.313121	+	0.389815i
$197$	203.981			1.03544			0.517718	−	0.855552i	$-0.326782\pi$
$197$	203.981			1.03544			0.517718	+	0.855552i	$0.326782\pi$
$198$		0			0
$199$	−146.130	−	84.3682i	−0.734321	−	0.423961i	0.0856795	−	0.996323i	$-0.472694\pi$
$199$	−146.130	−	84.3682i	−0.734321	−	0.423961i	−0.820001	+	0.572362i	$0.806027\pi$
$200$	65.6012			0.328006
$201$		0			0
$202$	172.133	+	99.3811i	0.852145	+	0.491986i
$203$	41.7328	+	3.20139i	0.205580	+	0.0157704i
$204$		0			0
$205$	42.4278	−	73.4871i	0.206965	−	0.358474i
$206$	44.2212	+	25.5311i	0.214666	+	0.123937i
$207$		0			0
$208$	−53.3448	+	30.7986i	−0.256465	+	0.148070i
$209$	−21.8999	+	12.6439i	−0.104784	+	0.0604973i
$210$		0			0
$211$	24.3937	−	42.2511i	0.115610	−	0.200242i	−0.802413	−	0.596768i	$-0.796451\pi$
$211$	24.3937	−	42.2511i	0.115610	−	0.200242i	0.918023	+	0.396526i	$0.129784\pi$
$212$	26.0701			0.122972
$213$		0			0
$214$	−32.1378			−0.150177
$215$	−482.769	+	278.727i	−2.24544	+	1.29640i
$216$		0			0
$217$	−8.81707	+	114.938i	−0.0406316	+	0.529666i
$218$	−110.795	−	191.902i	−0.508234	−	0.880286i
$219$		0			0
$220$	209.907	−	121.190i	0.954123	−	0.550863i
$221$	−109.817	−	190.208i	−0.496908	−	0.860670i
$222$		0			0
$223$	−158.969	+	91.7807i	−0.712865	+	0.411573i	−0.812121	−	0.583489i	$-0.801687\pi$
$223$	−158.969	+	91.7807i	−0.712865	+	0.411573i	0.0992560	+	0.995062i	$0.468354\pi$
$224$	39.4820	+	3.02873i	0.176259	+	0.0135211i
$225$		0			0
$226$	−93.9752	−	162.770i	−0.415820	−	0.720221i
$227$			81.1795i			0.357619i	0.983884	+	0.178809i	$0.0572245\pi$
$227$			81.1795i			0.357619i	−0.983884	+	0.178809i	$0.942775\pi$
$228$		0			0
$229$			203.648i			0.889292i	0.895706	+	0.444646i	$0.146671\pi$
$229$			203.648i			0.889292i	−0.895706	+	0.444646i	$0.853329\pi$
$230$	−109.354	−	63.1353i	−0.475450	−	0.274501i
$231$		0			0
$232$	−8.45607	−	14.6463i	−0.0364486	−	0.0631308i
$233$	−11.3573	−	19.6715i	−0.0487439	−	0.0844270i	0.840624	−	0.541619i	$-0.182188\pi$
$233$	−11.3573	−	19.6715i	−0.0487439	−	0.0844270i	−0.889368	+	0.457192i	$0.848855\pi$
$234$		0			0
$235$	−290.347	+	502.895i	−1.23552	+	2.13998i
$236$	−176.231	−	101.747i	−0.746741	−	0.431131i
$237$		0			0
$238$	−10.7994	+	140.779i	−0.0453755	+	0.591506i
$239$	17.2294	−	29.8421i	0.0720894	−	0.124863i	−0.827727	−	0.561130i	$-0.810367\pi$
$239$	17.2294	−	29.8421i	0.0720894	−	0.124863i	0.899817	+	0.436268i	$0.143700\pi$
$240$		0			0
$241$			122.907i			0.509987i	0.966943	+	0.254994i	$0.0820734\pi$
$241$			122.907i			0.509987i	−0.966943	+	0.254994i	$0.917927\pi$
$242$	129.931	−	225.047i	0.536905	−	0.929947i
$243$		0			0
$244$		−	134.238i		−	0.550156i
$245$	−317.087	+	123.160i	−1.29423	+	0.502693i
$246$		0			0
$247$	22.3070			0.0903118
$248$	40.3380	−	23.2891i	0.162653	−	0.0939078i
$249$		0			0
$250$	−15.3592	−	8.86766i	−0.0614369	−	0.0354706i
$251$			63.3749i			0.252490i	0.991999	+	0.126245i	$0.0402925\pi$
$251$			63.3749i			0.252490i	−0.991999	+	0.126245i	$0.959708\pi$
$252$		0			0
$253$	−224.525			−0.887451
$254$	173.729	−	300.908i	0.683973	−	1.18468i
$255$		0			0
$256$	−8.00000	−	13.8564i	−0.0312500	−	0.0541266i
$257$		−	131.248i		−	0.510691i	−0.966850	−	0.255346i	$-0.917811\pi$
$257$		−	131.248i		−	0.510691i	0.966850	−	0.255346i	$-0.0821892\pi$
$258$		0			0
$259$	−10.2196	−	0.783962i	−0.0394578	−	0.00302688i
$260$	−213.809			−0.822341
$261$		0			0
$262$	264.928	+	152.956i	1.01117	+	0.583802i
$263$	−273.993			−1.04180			−0.520899	−	0.853618i	$-0.674403\pi$
$263$	−273.993			−1.04180			−0.520899	+	0.853618i	$0.674403\pi$
$264$		0			0
$265$	78.3677	+	45.2456i	0.295727	+	0.170738i
$266$	−11.8341	−	8.09895i	−0.0444892	−	0.0304472i
$267$		0			0
$268$	39.4835	−	68.3874i	0.147326	−	0.255177i
$269$	142.473	+	82.2566i	0.529638	+	0.305787i	0.740869	−	0.671649i	$-0.234414\pi$
$269$	142.473	+	82.2566i	0.529638	+	0.305787i	−0.211231	+	0.977436i	$0.567747\pi$
$270$		0			0
$271$	−62.3327	+	35.9878i	−0.230010	+	0.132796i	−0.610577	−	0.791957i	$-0.709062\pi$
$271$	−62.3327	+	35.9878i	−0.230010	+	0.132796i	0.380567	+	0.924753i	$0.375729\pi$
$272$	49.4069	−	28.5251i	0.181643	−	0.104872i
$273$		0			0
$274$	71.2366	−	123.385i	0.259988	−	0.450312i
$275$	404.892			1.47233
$276$		0			0
$277$	75.0174			0.270821			0.135411	−	0.990790i	$-0.456765\pi$
$277$	75.0174			0.270821			0.135411	+	0.990790i	$0.456765\pi$
$278$	−215.542	+	124.443i	−0.775329	+	0.447636i
$279$		0			0
$280$	113.428	+	77.6270i	0.405100	+	0.277239i
$281$	−185.301	−	320.950i	−0.659433	−	1.14217i	−0.980763	−	0.195205i	$-0.937463\pi$
$281$	−185.301	−	320.950i	−0.659433	−	1.14217i	0.321329	−	0.946968i	$-0.395870\pi$
$282$		0			0
$283$	120.496	−	69.5681i	0.425779	−	0.245824i	−0.271768	−	0.962363i	$-0.587608\pi$
$283$	120.496	−	69.5681i	0.425779	−	0.245824i	0.697547	+	0.716539i	$0.254275\pi$
$284$	−93.8955	−	162.632i	−0.330618	−	0.572647i
$285$		0			0
$286$	−329.245	+	190.089i	−1.15121	+	0.664649i
$287$	77.1546	−	36.9884i	0.268831	−	0.128879i
$288$		0			0
$289$	−42.7897	−	74.1140i	−0.148061	−	0.256450i
$290$		−	58.7033i		−	0.202425i
$291$		0			0
$292$		−	39.7653i		−	0.136183i
$293$	89.4372	+	51.6366i	0.305247	+	0.176234i	0.644797	−	0.764354i	$-0.276942\pi$
$293$	89.4372	+	51.6366i	0.305247	+	0.176234i	−0.339551	+	0.940588i	$0.610275\pi$
$294$		0			0
$295$	−353.172	−	611.711i	−1.19719	−	2.07360i
$296$	2.07073	+	3.58661i	0.00699572	+	0.0121169i
$297$		0			0
$298$	142.078	−	246.087i	0.476773	−	0.825795i
$299$	171.524	+	99.0293i	0.573658	+	0.331202i
$300$		0			0
$301$	−560.452	−	42.9932i	−1.86197	−	0.142835i
$302$	−167.552	+	290.209i	−0.554809	+	0.960957i
$303$		0			0
$304$			5.79429i			0.0190602i
$305$	232.976	−	403.526i	0.763854	−	1.32303i
$306$		0			0
$307$		−	190.081i		−	0.619158i	−0.950874	−	0.309579i	$-0.899812\pi$
$307$		−	190.081i		−	0.619158i	0.950874	−	0.309579i	$-0.100188\pi$
$308$	243.683	+	18.6934i	0.791180	+	0.0606928i
$309$		0			0
$310$	161.677			0.521538
$311$	−134.578	+	77.6989i	−0.432728	+	0.249836i	−0.700508	−	0.713644i	$-0.747043\pi$
$311$	−134.578	+	77.6989i	−0.432728	+	0.249836i	0.267780	+	0.963480i	$0.413710\pi$
$312$		0			0
$313$	490.945	+	283.447i	1.56852	+	0.905583i	0.996343	+	0.0854495i	$0.0272326\pi$
$313$	490.945	+	283.447i	1.56852	+	0.905583i	0.572173	+	0.820133i	$0.306101\pi$
$314$		−	18.6044i		−	0.0592498i
$315$		0			0
$316$	−245.572			−0.777126
$317$	−95.7038	+	165.764i	−0.301905	+	0.522914i	−0.976567	−	0.215212i	$-0.930956\pi$
$317$	−95.7038	+	165.764i	−0.301905	+	0.522914i	0.674663	+	0.738126i	$0.264289\pi$
$318$		0			0
$319$	−52.1910	−	90.3974i	−0.163608	−	0.283377i
$320$		−	55.5373i		−	0.173554i
$321$		0			0
$322$	−55.0410	−	114.811i	−0.170935	−	0.356556i
$323$	−20.6604			−0.0639639
$324$		0			0
$325$	−309.313	−	178.582i	−0.951733	−	0.549484i
$326$	−258.927			−0.794255
$327$		0			0
$328$	−29.9407	−	17.2863i	−0.0912826	−	0.0527020i
$329$	−527.993	+	253.123i	−1.60484	+	0.769370i
$330$		0			0
$331$	−263.424	+	456.263i	−0.795842	+	1.37844i	0.126461	+	0.991972i	$0.459638\pi$
$331$	−263.424	+	456.263i	−0.795842	+	1.37844i	−0.922303	+	0.386467i	$0.873695\pi$
$332$	−14.0348	−	8.10301i	−0.0422736	−	0.0244067i
$333$		0			0
$334$	−252.510	+	145.786i	−0.756017	+	0.436486i
$335$	237.378	−	137.050i	0.708591	−	0.409105i
$336$		0			0
$337$	−168.251	+	291.419i	−0.499261	+	0.864746i	−1.00000		0.000852644i	$-0.999729\pi$
$337$	−168.251	+	291.419i	−0.499261	+	0.864746i	0.500738	+	0.865599i	$0.333062\pi$
$338$	96.3625			0.285096
$339$		0			0
$340$	198.026			0.582429
$341$	248.966	−	143.741i	0.730107	−	0.421527i
$342$		0			0
$343$	−333.992	−	78.0912i	−0.973738	−	0.227671i
$344$	113.561	+	196.693i	0.330119	+	0.571783i
$345$		0			0
$346$	224.678	−	129.718i	0.649359	−	0.374907i
$347$	92.9133	+	160.931i	0.267762	+	0.463777i	0.968283	−	0.249854i	$-0.0803827\pi$
$347$	92.9133	+	160.931i	0.267762	+	0.463777i	−0.700522	+	0.713631i	$0.747049\pi$
$348$		0			0
$349$	217.753	−	125.720i	0.623935	−	0.360229i	−0.154464	−	0.987998i	$-0.549365\pi$
$349$	217.753	−	125.720i	0.623935	−	0.360229i	0.778400	+	0.627769i	$0.216032\pi$
$350$	99.2569	+	207.042i	0.283591	+	0.591547i
$351$		0			0
$352$	−49.3761	−	85.5219i	−0.140273	−	0.242960i
$353$			76.6421i			0.217116i	0.994090	+	0.108558i	$0.0346234\pi$
$353$			76.6421i			0.217116i	−0.994090	+	0.108558i	$0.965377\pi$
$354$		0			0
$355$		−	651.837i		−	1.83616i
$356$	−87.4094	−	50.4658i	−0.245532	−	0.141758i
$357$		0			0
$358$	27.9753	+	48.4546i	0.0781432	+	0.135348i
$359$	236.702	+	409.979i	0.659336	+	1.14200i	0.980788	+	0.195078i	$0.0624960\pi$
$359$	236.702	+	409.979i	0.659336	+	1.14200i	−0.321451	+	0.946926i	$0.604171\pi$
$360$		0			0
$361$	−179.451	+	310.818i	−0.497094	+	0.860992i
$362$	4.50233	+	2.59942i	0.0124374	+	0.00718073i
$363$		0			0
$364$	−177.915	−	121.760i	−0.488777	−	0.334505i
$365$	69.0143	−	119.536i	0.189080	−	0.327497i
$366$		0			0
$367$		−	48.9039i		−	0.133253i	−0.997778	−	0.0666266i	$-0.978776\pi$
$367$		−	48.9039i		−	0.133253i	0.997778	−	0.0666266i	$-0.0212236\pi$
$368$	−25.7231	+	44.5537i	−0.0698996	+	0.121070i
$369$		0			0
$370$			14.3753i			0.0388523i
$371$	39.4449	+	82.2788i	0.106321	+	0.221776i
$372$		0			0
$373$	546.162			1.46424			0.732121	−	0.681174i	$-0.238530\pi$
$373$	546.162			1.46424			0.732121	+	0.681174i	$0.238530\pi$
$374$	304.940	−	176.057i	0.815349	−	0.470742i
$375$		0			0
$376$	204.893	+	118.295i	0.544929	+	0.314615i
$377$			92.0777i			0.244238i
$378$		0			0
$379$	385.626			1.01748			0.508741	−	0.860920i	$-0.330111\pi$
$379$	385.626			1.01748			0.508741	+	0.860920i	$0.330111\pi$
$380$	−10.0562	+	17.4179i	−0.0264637	+	0.0458365i
$381$		0			0
$382$	33.8548	+	58.6383i	0.0886252	+	0.153503i
$383$		−	48.6214i		−	0.126949i	−0.997983	−	0.0634744i	$-0.979782\pi$
$383$		−	48.6214i		−	0.126949i	0.997983	−	0.0634744i	$-0.0202181\pi$
$384$		0			0
$385$	700.079	+	479.115i	1.81839	+	1.24445i
$386$	−82.7131			−0.214283
$387$		0			0
$388$	161.767	+	93.3965i	0.416926	+	0.240713i
$389$	−369.796			−0.950632			−0.475316	−	0.879815i	$-0.657666\pi$
$389$	−369.796			−0.950632			−0.475316	+	0.879815i	$0.657666\pi$
$390$		0			0
$391$	−158.862	−	91.7192i	−0.406297	−	0.234576i
$392$	50.1787	+	129.190i	0.128007	+	0.329567i
$393$		0			0
$394$	144.236	−	249.824i	0.366082	−	0.634072i
$395$	−738.199	−	426.199i	−1.86886	−	1.07899i
$396$		0			0
$397$	570.204	−	329.208i	1.43628	−	0.829238i	0.438694	−	0.898637i	$-0.355441\pi$
$397$	570.204	−	329.208i	1.43628	−	0.829238i	0.997589	+	0.0693984i	$0.0221080\pi$
$398$	−206.659	+	119.315i	−0.519244	+	0.299785i
$399$		0			0
$400$	46.3871	−	80.3448i	0.115968	−	0.200862i
$401$	−21.9525			−0.0547444			−0.0273722	−	0.999625i	$-0.508714\pi$
$401$	−21.9525			−0.0547444			−0.0273722	+	0.999625i	$0.508714\pi$
$402$		0			0
$403$	−253.594			−0.629266
$404$	243.433	−	140.546i	0.602557	−	0.347887i
$405$		0			0
$406$	33.4304	−	48.8483i	0.0823409	−	0.120316i
$407$	12.7806	+	22.1366i	0.0314019	+	0.0543898i
$408$		0			0
$409$	198.892	−	114.830i	0.486288	−	0.280758i	−0.236745	−	0.971572i	$-0.576081\pi$
$409$	198.892	−	114.830i	0.486288	−	0.280758i	0.723033	+	0.690813i	$0.242747\pi$
$410$	−60.0020	−	103.926i	−0.146346	−	0.253479i
$411$		0			0
$412$	62.5382	−	36.1065i	0.151792	−	0.0876370i
$413$	54.4763	−	710.142i	0.131904	−	1.71947i
$414$		0			0
$415$	−28.1262	−	48.7160i	−0.0677739	−	0.117388i
$416$			87.1116i			0.209403i
$417$		0			0
$418$			35.7624i			0.0855561i
$419$	504.537	+	291.295i	1.20415	+	0.695214i	0.961474	−	0.274894i	$-0.0886429\pi$
$419$	504.537	+	291.295i	1.20415	+	0.695214i	0.242672	+	0.970108i	$0.421976\pi$
$420$		0			0
$421$	31.2793	+	54.1774i	0.0742977	+	0.128687i	0.900781	−	0.434274i	$-0.142995\pi$
$421$	31.2793	+	54.1774i	0.0742977	+	0.128687i	−0.826483	+	0.562962i	$0.809662\pi$
$422$	−34.4979	−	59.7521i	−0.0817486	−	0.141593i
$423$		0			0
$424$	18.4343	−	31.9292i	0.0434772	−	0.0753047i
$425$	286.480	+	165.400i	0.674072	+	0.389175i
$426$		0			0
$427$	423.664	−	203.107i	0.992187	−	0.475660i
$428$	−22.7249	+	39.3606i	−0.0530955	+	0.0919641i
$429$		0			0
$430$			788.358i			1.83339i
$431$	162.412	−	281.305i	0.376826	−	0.652681i	−0.613773	−	0.789483i	$-0.710349\pi$
$431$	162.412	−	281.305i	0.376826	−	0.652681i	0.990598	+	0.136802i	$0.0436823\pi$
$432$		0			0
$433$			222.186i			0.513131i	0.966527	+	0.256566i	$0.0825909\pi$
$433$			222.186i			0.513131i	−0.966527	+	0.256566i	$0.917409\pi$
$434$	134.535	+	92.0718i	0.309988	+	0.212147i
$435$		0			0
$436$	−313.375			−0.718751
$437$	16.1348	−	9.31543i	0.0369217	−	0.0213168i
$438$		0			0
$439$	331.024	+	191.117i	0.754042	+	0.435346i	0.827153	−	0.561977i	$-0.189959\pi$
$439$	331.024	+	191.117i	0.754042	+	0.435346i	−0.0731104	+	0.997324i	$0.523293\pi$
$440$		−	342.777i		−	0.779038i
$441$		0			0
$442$	−310.609			−0.702734
$443$	9.21294	−	15.9573i	0.0207967	−	0.0360209i	−0.855440	−	0.517902i	$-0.826713\pi$
$443$	9.21294	−	15.9573i	0.0207967	−	0.0360209i	0.876236	+	0.481881i	$0.160046\pi$
$444$		0			0
$445$	−175.171	−	303.405i	−0.393642	−	0.681808i
$446$			259.595i			0.582052i
$447$		0			0
$448$	31.6274	−	46.2137i	0.0705969	−	0.103156i
$449$	−383.046			−0.853109			−0.426554	−	0.904462i	$-0.640273\pi$
$449$	−383.046			−0.853109			−0.426554	+	0.904462i	$0.640273\pi$
$450$		0			0
$451$	−184.794	−	106.691i	−0.409744	−	0.236566i
$452$	−265.802			−0.588058
$453$		0			0
$454$	99.4241	+	57.4025i	0.218996	+	0.126437i
$455$	−323.500	−	674.794i	−0.710989	−	1.48306i
$456$		0			0
$457$	−60.1327	+	104.153i	−0.131581	+	0.227906i	−0.924286	−	0.381700i	$-0.875339\pi$
$457$	−60.1327	+	104.153i	−0.131581	+	0.227906i	0.792705	+	0.609605i	$0.208672\pi$
$458$	249.417	+	144.001i	0.544578	+	0.314412i
$459$		0			0
$460$	−154.649	+	89.2868i	−0.336194	+	0.194102i
$461$	17.9439	−	10.3599i	0.0389239	−	0.0224727i	−0.480412	−	0.877043i	$-0.659513\pi$
$461$	17.9439	−	10.3599i	0.0389239	−	0.0224727i	0.519336	+	0.854570i	$0.326179\pi$
$462$		0			0
$463$	181.356	−	314.119i	0.391699	−	0.678442i	−0.600975	−	0.799268i	$-0.705221\pi$
$463$	181.356	−	314.119i	0.391699	−	0.678442i	0.992674	+	0.120826i	$0.0385542\pi$
$464$	−23.9174			−0.0515460
$465$		0			0
$466$	−32.1234			−0.0689343
$467$	−359.265	+	207.422i	−0.769304	+	0.444158i	−0.832626	−	0.553835i	$-0.813164\pi$
$467$	−359.265	+	207.422i	−0.769304	+	0.444158i	0.0633224	+	0.997993i	$0.479830\pi$
$468$		0			0
$469$	275.575	+	21.1398i	0.587579	+	0.0450742i
$470$	410.612	+	711.201i	0.873643	+	1.51319i
$471$		0			0
$472$	−249.228	+	143.892i	−0.528026	+	0.304856i
$473$	700.900	+	1213.99i	1.48182	+	2.56659i
$474$		0			0
$475$	−29.0963	+	16.7988i	−0.0612554	+	0.0353658i
$476$	164.781	+	112.772i	0.346180	+	0.236916i
$477$		0			0
$478$	−24.3660	−	42.2032i	−0.0509749	−	0.0882911i
$479$			149.629i			0.312377i	0.987727	+	0.156189i	$0.0499208\pi$
$479$			149.629i			0.312377i	−0.987727	+	0.156189i	$0.950079\pi$
$480$		0			0
$481$		−	22.5481i		−	0.0468776i
$482$	150.530	+	86.9084i	0.312302	+	0.180308i
$483$		0			0
$484$	−183.750	−	318.265i	−0.379649	−	0.657571i
$485$	324.186	+	561.507i	0.668426	+	1.15775i
$486$		0			0
$487$	−46.3139	+	80.2181i	−0.0951004	+	0.164719i	−0.909651	−	0.415374i	$-0.863651\pi$
$487$	−46.3139	+	80.2181i	−0.0951004	+	0.164719i	0.814550	+	0.580093i	$0.196984\pi$
$488$	−164.408	−	94.9207i	−0.336901	−	0.194510i
$489$		0			0
$490$	−73.3752	+	475.438i	−0.149745	+	0.970282i
$491$	164.023	−	284.097i	0.334060	−	0.578609i	−0.649244	−	0.760580i	$-0.724915\pi$
$491$	164.023	−	284.097i	0.334060	−	0.578609i	0.983304	+	0.181972i	$0.0582479\pi$
$492$		0			0
$493$		−	85.2807i		−	0.172983i
$494$	15.7734	−	27.3204i	0.0319300	−	0.0553045i
$495$		0			0
$496$		−	65.8716i		−	0.132806i
$497$	371.209	−	542.407i	0.746899	−	1.09136i
$498$		0			0
$499$	167.753			0.336178			0.168089	−	0.985772i	$-0.446240\pi$
$499$	167.753			0.336178			0.168089	+	0.985772i	$0.446240\pi$
$500$	−21.7212	+	12.5408i	−0.0434425	+	0.0250815i
$501$		0			0
$502$	77.6181	+	44.8128i	0.154618	+	0.0892686i
$503$		−	320.995i		−	0.638161i	−0.947728	−	0.319080i	$-0.896626\pi$
$503$		−	320.995i		−	0.638161i	0.947728	−	0.319080i	$-0.103374\pi$
$504$		0			0
$505$	975.693			1.93207
$506$	−158.763	+	274.986i	−0.313761	+	0.543450i
$507$		0			0
$508$	−245.690	−	425.548i	−0.483642	−	0.837693i
$509$			401.681i			0.789156i	0.918862	+	0.394578i	$0.129109\pi$
$509$			401.681i			0.789156i	−0.918862	+	0.394578i	$0.870891\pi$
$510$		0			0
$511$	125.502	−	60.1663i	0.245601	−	0.117742i
$512$	−22.6274			−0.0441942
$513$		0			0
$514$	−160.745	−	92.8061i	−0.312733	−	0.180557i
$515$	250.657			0.486712
$516$		0			0
$517$	1264.60	+	730.120i	2.44604	+	1.41222i
$518$	−8.18649	+	11.9620i	−0.0158040	+	0.0230927i
$519$		0			0
$520$	−151.186	+	261.861i	−0.290742	+	0.503579i
$521$	807.871	+	466.425i	1.55062	+	0.895249i	0.998091	+	0.0617529i	$0.0196691\pi$
$521$	807.871	+	466.425i	1.55062	+	0.895249i	0.552525	+	0.833496i	$0.313664\pi$
$522$		0			0
$523$	−631.376	+	364.525i	−1.20722	+	0.696989i	−0.962151	−	0.272517i	$-0.912144\pi$
$523$	−631.376	+	364.525i	−1.20722	+	0.696989i	−0.245069	+	0.969506i	$0.578810\pi$
$524$	374.664	−	216.313i	0.715008	−	0.412810i
$525$		0			0
$526$	−193.742	+	335.572i	−0.368331	+	0.637969i
$527$	234.874			0.445682
$528$		0			0
$529$	−363.581			−0.687299
$530$	110.829	−	63.9870i	0.209111	−	0.120730i
$531$		0			0
$532$	−18.2871	+	8.76696i	−0.0343743	+	0.0164793i
$533$	94.1147	+	163.011i	0.176575	+	0.305838i
$534$		0			0
$535$	−136.624	+	78.8798i	−0.255372	+	0.147439i
$536$	−55.8381	−	96.7144i	−0.104175	−	0.180437i
$537$		0			0
$538$	201.487	−	116.328i	0.374511	−	0.216224i
$539$	309.704	+	797.364i	0.574590	+	1.47934i
$540$		0			0
$541$	222.378	+	385.171i	0.411051	+	0.711960i	0.995005	−	0.0998261i	$-0.0318286\pi$
$541$	222.378	+	385.171i	0.411051	+	0.711960i	−0.583954	+	0.811786i	$0.698495\pi$
$542$			101.789i			0.187802i
$543$		0			0
$544$		−	80.6812i		−	0.148311i
$545$	−942.019	−	543.875i	−1.72848	−	0.997936i
$546$		0			0
$547$	−32.0268	−	55.4721i	−0.0585500	−	0.101411i	0.835265	−	0.549848i	$-0.185314\pi$
$547$	−32.0268	−	55.4721i	−0.0585500	−	0.101411i	−0.893815	+	0.448436i	$0.851981\pi$
$548$	−100.744	−	174.493i	−0.183839	−	0.318419i
$549$		0			0
$550$	286.302	−	495.889i	0.520549	−	0.901617i
$551$	7.50109	+	4.33076i	0.0136136	+	0.00785981i
$552$		0			0
$553$	−371.559	−	775.040i	−0.671896	−	1.40152i
$554$	53.0453	−	91.8772i	0.0957497	−	0.165843i
$555$		0			0
$556$			351.978i			0.633054i
$557$	−321.689	+	557.182i	−0.577539	+	1.00033i	0.418222	+	0.908345i	$0.362654\pi$
$557$	−321.689	+	557.182i	−0.577539	+	1.00033i	−0.995761	+	0.0919818i	$0.970680\pi$
$558$		0			0
$559$		−	1236.56i		−	2.21209i
$560$	175.279	−	84.0298i	0.312998	−	0.150053i
$561$		0			0
$562$	−524.110			−0.932580
$563$	−488.401	+	281.979i	−0.867498	+	0.500850i	−0.866516	−	0.499150i	$-0.833646\pi$
$563$	−488.401	+	281.979i	−0.867498	+	0.500850i	−0.000981736		1.00000i	$0.500312\pi$
$564$		0			0
$565$	−799.012	−	461.310i	−1.41418	−	0.816478i
$566$		−	196.768i		−	0.347647i
$567$		0			0
$568$	−265.576			−0.467564
$569$	304.482	−	527.379i	0.535118	−	0.926852i	−0.464039	−	0.885815i	$-0.653600\pi$
$569$	304.482	−	527.379i	0.535118	−	0.926852i	0.999158	−	0.0410374i	$-0.0130663\pi$
$570$		0			0
$571$	353.067	+	611.529i	0.618330	+	1.07098i	0.989790	+	0.142530i	$0.0455239\pi$
$571$	353.067	+	611.529i	0.618330	+	1.07098i	−0.371460	+	0.928449i	$0.621143\pi$
$572$			537.654i			0.939955i
$573$		0			0
$574$	9.25523	−	120.649i	0.0161241	−	0.210191i
$575$	−298.304			−0.518790
$576$		0			0
$577$	−774.773	−	447.315i	−1.34276	−	0.775243i	−0.355548	−	0.934658i	$-0.615706\pi$
$577$	−774.773	−	447.315i	−1.34276	−	0.775243i	−0.987212	+	0.159415i	$0.949039\pi$
$578$	−121.028			−0.209390
$579$		0			0
$580$	−71.8966	−	41.5095i	−0.123960	−	0.0715681i
$581$	4.33843	−	56.5549i	0.00746717	−	0.0973406i
$582$		0			0
$583$	113.777	−	197.067i	0.195158	−	0.338023i
$584$	−48.7024	−	28.1183i	−0.0833945	−	0.0481479i
$585$		0			0
$586$	126.483	−	73.0252i	0.215842	−	0.124616i
$587$	98.0159	−	56.5895i	0.166978	−	0.0964046i	−0.414182	−	0.910194i	$-0.635932\pi$
$587$	98.0159	−	56.5895i	0.166978	−	0.0964046i	0.581160	+	0.813789i	$0.302599\pi$
$588$		0			0
$589$	−11.9275	+	20.6590i	−0.0202504	+	0.0350747i
$590$	−998.920			−1.69309
$591$		0			0
$592$	5.85692			0.00989344
$593$	416.988	−	240.748i	0.703184	−	0.405983i	−0.105348	−	0.994435i	$-0.533596\pi$
$593$	416.988	−	240.748i	0.703184	−	0.405983i	0.808532	+	0.588452i	$0.200262\pi$
$594$		0			0
$595$	299.620	+	624.982i	0.503563	+	1.05039i
$596$	−200.929	−	348.019i	−0.337129	−	0.583925i
$597$		0			0
$598$	242.571	−	140.049i	0.405638	−	0.234195i
$599$	90.9166	+	157.472i	0.151781	+	0.262892i	0.931882	−	0.362761i	$-0.118166\pi$
$599$	90.9166	+	157.472i	0.151781	+	0.262892i	−0.780101	+	0.625653i	$0.784833\pi$
$600$		0			0
$601$	−873.672	+	504.415i	−1.45370	+	0.839292i	−0.998689	−	0.0511946i	$-0.983697\pi$
$601$	−873.672	+	504.415i	−1.45370	+	0.839292i	−0.455008	+	0.890487i	$0.650364\pi$
$602$	−448.955	+	656.010i	−0.745772	+	1.08972i
$603$		0			0
$604$	236.955	+	410.418i	0.392309	+	0.679500i
$605$		−	1275.62i		−	2.10847i
$606$		0			0
$607$		−	501.420i		−	0.826063i	−0.910717	−	0.413032i	$-0.864470\pi$
$607$		−	501.420i		−	0.826063i	0.910717	−	0.413032i	$-0.135530\pi$
$608$	7.09653	+	4.09718i	0.0116719	+	0.00673879i
$609$		0			0
$610$	−329.477	−	570.671i	−0.540127	−	0.935527i
$611$	−644.056	−	1115.54i	−1.05410	−	1.82576i
$612$		0			0
$613$	212.902	−	368.757i	0.347311	−	0.601561i	−0.638460	−	0.769655i	$-0.720428\pi$
$613$	212.902	−	368.757i	0.347311	−	0.601561i	0.985771	+	0.168095i	$0.0537614\pi$
$614$	−232.801	−	134.408i	−0.379155	−	0.218905i
$615$		0			0
$616$	195.205	−	285.232i	0.316891	−	0.463039i
$617$	227.440	−	393.937i	0.368622	−	0.638472i	−0.620729	−	0.784026i	$-0.713163\pi$
$617$	227.440	−	393.937i	0.368622	−	0.638472i	0.989350	+	0.145554i	$0.0464964\pi$
$618$		0			0
$619$			500.678i			0.808850i	0.914571	+	0.404425i	$0.132528\pi$
$619$			500.678i			0.808850i	−0.914571	+	0.404425i	$0.867472\pi$
$620$	114.323	−	198.013i	0.184392	−	0.319375i
$621$		0			0
$622$			219.766i			0.353321i
$623$	27.0199	−	352.226i	0.0433706	−	0.565371i
$624$		0			0
$625$	−666.898			−1.06704
$626$	694.301	−	400.855i	1.10911	−	0.640344i
$627$		0			0
$628$	−22.7857	−	13.1553i	−0.0362830	−	0.0209480i
$629$			20.8837i			0.0332014i
$630$		0			0
$631$	790.195			1.25229			0.626145	−	0.779706i	$-0.284632\pi$
$631$	790.195			1.25229			0.626145	+	0.779706i	$0.284632\pi$
$632$	−173.646	+	300.763i	−0.274756	+	0.475891i
$633$		0			0
$634$	135.346	+	234.425i	0.213479	+	0.369756i
$635$		−	1705.62i		−	2.68602i
$636$		0			0
$637$	115.091	−	745.737i	0.180676	−	1.17070i
$638$	−147.618			−0.231377
$639$		0			0
$640$	−68.0190	−	39.2708i	−0.106280	−	0.0613606i
$641$	−372.894			−0.581738			−0.290869	−	0.956763i	$-0.593944\pi$
$641$	−372.894			−0.581738			−0.290869	+	0.956763i	$0.593944\pi$
$642$		0			0
$643$	356.344	+	205.735i	0.554190	+	0.319962i	0.750810	−	0.660518i	$-0.229663\pi$
$643$	356.344	+	205.735i	0.554190	+	0.319962i	−0.196620	+	0.980480i	$0.562997\pi$
$644$	−179.534	−	13.7724i	−0.278780	−	0.0213857i
$645$		0			0
$646$	−14.6091	+	25.3037i	−0.0226147	+	0.0391698i
$647$	508.421	+	293.537i	0.785813	+	0.453689i	0.838486	−	0.544923i	$-0.183441\pi$
$647$	508.421	+	293.537i	0.785813	+	0.453689i	−0.0526736	+	0.998612i	$0.516774\pi$
$648$		0			0
$649$	−1538.24	+	888.103i	−2.37017	+	1.36842i
$650$	−437.435	+	252.553i	−0.672977	+	0.388544i
$651$		0			0
$652$	−183.089	+	317.120i	−0.280812	+	0.486380i
$653$	−566.107			−0.866933			−0.433466	−	0.901170i	$-0.642710\pi$
$653$	−566.107			−0.866933			−0.433466	+	0.901170i	$0.642710\pi$
$654$		0			0
$655$	1501.68			2.29263
$656$	−42.3425	+	24.4465i	−0.0645466	+	0.0372660i
$657$		0			0
$658$	−63.3364	+	825.641i	−0.0962559	+	1.25477i
$659$	−368.775	−	638.738i	−0.559599	−	0.969253i	−0.997530	−	0.0702447i	$-0.977622\pi$
$659$	−368.775	−	638.738i	−0.559599	−	0.969253i	0.437931	−	0.899008i	$-0.355711\pi$
$660$		0			0
$661$	−875.032	+	505.200i	−1.32380	+	0.764297i	−0.984333	−	0.176321i	$-0.943580\pi$
$661$	−875.032	+	505.200i	−1.32380	+	0.764297i	−0.339468	+	0.940618i	$0.610247\pi$
$662$	372.537	+	645.254i	0.562745	+	0.974703i
$663$		0			0
$664$	−19.8482	+	11.4594i	−0.0298919	+	0.0172581i
$665$	−70.1873	−	5.38419i	−0.105545	−	0.00809653i
$666$		0			0
$667$	38.4518	+	66.6004i	0.0576488	+	0.0998507i
$668$			412.346i			0.617285i
$669$		0			0
$670$		−	387.637i		−	0.578562i
$671$	−1014.73	−	585.852i	−1.51226	−	0.873103i
$672$		0			0
$673$	−78.3833	−	135.764i	−0.116468	−	0.201729i	0.801897	−	0.597462i	$-0.203824\pi$
$673$	−78.3833	−	135.764i	−0.116468	−	0.201729i	−0.918366	+	0.395733i	$0.870491\pi$
$674$	237.943	+	412.129i	0.353031	+	0.611468i
$675$		0			0
$676$	68.1386	−	118.020i	0.100797	−	0.174585i
$677$	−206.518	−	119.233i	−0.305049	−	0.176120i	0.339660	−	0.940548i	$-0.389688\pi$
$677$	−206.518	−	119.233i	−0.305049	−	0.176120i	−0.644709	+	0.764428i	$0.723021\pi$
$678$		0			0
$679$	−50.0053	+	651.860i	−0.0736455	+	0.960029i
$680$	140.025	−	242.531i	0.205920	−	0.356663i
$681$		0			0
$682$		−	406.561i		−	0.596130i
$683$	−324.836	+	562.632i	−0.475602	+	0.823766i	−0.999609	−	0.0279474i	$-0.991103\pi$
$683$	−324.836	+	562.632i	−0.475602	+	0.823766i	0.524008	+	0.851713i	$0.324436\pi$
$684$		0			0
$685$		−	699.379i		−	1.02099i
$686$	−331.810	+	353.836i	−0.483688	+	0.515796i
$687$		0			0
$688$	321.199			0.466859
$689$	−173.838	+	100.365i	−0.252304	+	0.145668i
$690$		0			0
$691$	−432.840	−	249.900i	−0.626396	−	0.361650i	0.152959	−	0.988233i	$-0.451120\pi$
$691$	−432.840	−	249.900i	−0.626396	−	0.361650i	−0.779355	+	0.626583i	$0.784453\pi$
$692$		−	366.898i		−	0.530199i
$693$		0			0
$694$	262.799			0.378672
$695$	−610.871	+	1058.06i	−0.878951	+	1.52239i
$696$		0			0
$697$	−87.1673	−	150.978i	−0.125061	−	0.216612i
$698$		−	355.590i		−	0.509441i
$699$		0			0
$700$	323.758	+	24.8361i	0.462512	+	0.0354801i
$701$	−142.184			−0.202830			−0.101415	−	0.994844i	$-0.532337\pi$
$701$	−142.184			−0.202830			−0.101415	+	0.994844i	$0.532337\pi$
$702$		0			0
$703$	−1.83688	−	1.06052i	−0.00261291	−	0.00150856i
$704$	−139.657			−0.198376
$705$		0			0
$706$	93.8670	+	54.1941i	0.132956	+	0.0767622i
$707$	811.895	+	555.639i	1.14837	+	0.785910i
$708$		0			0
$709$	286.893	−	496.913i	0.404645	−	0.700865i	−0.589635	−	0.807670i	$-0.700729\pi$
$709$	286.893	−	496.913i	0.404645	−	0.700865i	0.994280	+	0.106804i	$0.0340619\pi$
$710$	−798.334	−	460.918i	−1.12441	−	0.649181i
$711$		0			0
$712$	−123.616	+	71.3694i	−0.173617	+	0.100238i
$713$	−183.426	+	105.901i	−0.257260	+	0.148529i
$714$		0			0
$715$	−933.120	+	1616.21i	−1.30506	+	2.26044i
$716$	79.1260			0.110511
$717$		0			0
$718$	669.494			0.932442
$719$	−161.137	+	93.0327i	−0.224113	+	0.129392i	−0.607853	−	0.794049i	$-0.707969\pi$
$719$	−161.137	+	93.0327i	−0.224113	+	0.129392i	0.383740	+	0.923441i	$0.374636\pi$
$720$		0			0
$721$	208.577	+	142.744i	0.289288	+	0.197981i
$722$	253.782	+	439.563i	0.351498	+	0.608813i
$723$		0			0
$724$	6.36726	−	3.67614i	0.00879456	−	0.00507754i
$725$	−69.3410	−	120.102i	−0.0956428	−	0.165658i
$726$		0			0
$727$	47.5157	−	27.4332i	0.0653587	−	0.0377348i	−0.466965	−	0.884276i	$-0.654652\pi$
$727$	47.5157	−	27.4332i	0.0653587	−	0.0377348i	0.532323	+	0.846541i	$0.321319\pi$
$728$	−274.930	+	131.803i	−0.377651	+	0.181048i
$729$		0			0
$730$	−97.6010	−	169.050i	−0.133700	−	0.231575i
$731$			1145.28i			1.56673i
$732$		0			0
$733$			369.204i			0.503689i	0.967768	+	0.251845i	$0.0810372\pi$
$733$			369.204i			0.503689i	−0.967768	+	0.251845i	$0.918963\pi$
$734$	−59.8948	−	34.5803i	−0.0816006	−	0.0471121i
$735$		0			0
$736$	36.3779	+	63.0084i	0.0494265	+	0.0856092i
$737$	−344.633	−	596.923i	−0.467617	−	0.809936i
$738$		0			0
$739$	−552.319	+	956.645i	−0.747387	+	1.29451i	0.201684	+	0.979451i	$0.435359\pi$
$739$	−552.319	+	956.645i	−0.747387	+	1.29451i	−0.949071	+	0.315062i	$0.897975\pi$
$740$	17.6061	+	10.1649i	0.0237921	+	0.0137364i
$741$		0			0
$742$	128.662	+	9.86991i	0.173399	+	0.0133018i
$743$	184.560	−	319.667i	0.248398	−	0.430238i	−0.714683	−	0.699448i	$-0.753429\pi$
$743$	184.560	−	319.667i	0.248398	−	0.430238i	0.963082	+	0.269210i	$0.0867625\pi$
$744$		0			0
$745$		−	1394.88i		−	1.87232i
$746$	386.195	−	668.910i	0.517688	−	0.896662i
$747$		0			0
$748$		−	497.966i		−	0.665729i
$749$	−158.608	−	12.1671i	−0.211760	−	0.0162445i
$750$		0			0
$751$	−655.318			−0.872595			−0.436297	−	0.899803i	$-0.643710\pi$
$751$	−655.318			−0.872595			−0.436297	+	0.899803i	$0.643710\pi$
$752$	289.763	−	167.295i	0.385323	−	0.222466i
$753$		0			0
$754$	112.772	+	65.1088i	0.149565	+	0.0863511i
$755$			1644.98i			2.17878i
$756$		0			0
$757$	251.264			0.331921			0.165961	−	0.986132i	$-0.446928\pi$
$757$	251.264			0.331921			0.165961	+	0.986132i	$0.446928\pi$
$758$	272.679	−	472.293i	0.359734	−	0.623078i
$759$		0			0
$760$	14.2216	+	24.6326i	0.0187127	+	0.0324113i
$761$		−	866.967i		−	1.13925i	−0.821906	−	0.569624i	$-0.807089\pi$
$761$		−	866.967i		−	1.13925i	0.821906	−	0.569624i	$-0.192911\pi$
$762$		0			0
$763$	−474.148	−	989.032i	−0.621426	−	1.29624i
$764$	95.7559			0.125335
$765$		0			0
$766$	−59.5488	−	34.3805i	−0.0777400	−	0.0448832i
$767$	1566.83			2.04281
$768$		0			0
$769$	−40.8679	−	23.5951i	−0.0531442	−	0.0306828i	0.473193	−	0.880959i	$-0.343102\pi$
$769$	−40.8679	−	23.5951i	−0.0531442	−	0.0306828i	−0.526337	+	0.850276i	$0.676435\pi$
$770$	1081.82	−	518.633i	1.40497	−	0.673549i
$771$		0			0
$772$	−58.4870	+	101.302i	−0.0757604	+	0.131221i
$773$	190.903	+	110.218i	0.246963	+	0.142584i	0.618373	−	0.785885i	$-0.287792\pi$
$773$	190.903	+	110.218i	0.246963	+	0.142584i	−0.371410	+	0.928469i	$0.621125\pi$
$774$		0			0
$775$	330.777	−	190.974i	0.426810	−	0.246419i
$776$	228.774	−	132.083i	0.294811	−	0.170209i
$777$		0			0
$778$	−261.485	+	452.906i	−0.336099	+	0.582141i
$779$	17.7062			0.0227295
$780$		0			0
$781$	−1639.14			−2.09877
$782$	−224.665	+	129.711i	−0.287296	+	0.165870i
$783$		0			0
$784$	193.707	+	29.8951i	0.247075	+	0.0381315i
$785$	−45.6632	−	79.0910i	−0.0581697	−	0.100753i
$786$		0			0
$787$	844.530	−	487.590i	1.07310	−	0.619555i	0.144074	−	0.989567i	$-0.453980\pi$
$787$	844.530	−	487.590i	1.07310	−	0.619555i	0.929027	+	0.370012i	$0.120646\pi$
$788$	−203.981	−	353.305i	−0.258859	−	0.448357i
$789$		0			0
$790$	−1043.97	+	602.737i	−1.32148	+	0.762958i
$791$	−402.168	−	838.888i	−0.508429	−	1.06054i
$792$		0			0
$793$	516.794	+	895.113i	0.651694	+	1.12877i
$794$		−	931.140i		−	1.17272i
$795$		0			0
$796$			337.473i			0.423961i
$797$	1053.12	+	608.022i	1.32136	+	0.762888i	0.983946	−	0.178468i	$-0.0571140\pi$
$797$	1053.12	+	608.022i	1.32136	+	0.762888i	0.337415	+	0.941356i	$0.390447\pi$
$798$		0			0
$799$	596.513	+	1033.19i	0.746574	+	1.29310i
$800$	−65.6012	−	113.625i	−0.0820015	−	0.142031i
$801$		0			0
$802$	−15.5228	+	26.8862i	−0.0193551	+	0.0335240i
$803$	−300.592	−	173.547i	−0.374336	−	0.216123i
$804$		0			0
$805$	−515.784	−	352.989i	−0.640726	−	0.438495i
$806$	−179.318	+	310.588i	−0.222479	+	0.385345i
$807$		0			0
$808$		−	397.525i		−	0.491986i
$809$	−677.925	+	1174.20i	−0.837979	+	1.45142i	0.0536018	+	0.998562i	$0.482930\pi$
$809$	−677.925	+	1174.20i	−0.837979	+	1.45142i	−0.891581	+	0.452861i	$0.850404\pi$
$810$		0			0
$811$			838.233i			1.03358i	0.856112	+	0.516790i	$0.172873\pi$
$811$			838.233i			1.03358i	−0.856112	+	0.516790i	$0.827127\pi$
$812$	−36.1878	−	75.4847i	−0.0445663	−	0.0929614i
$813$		0			0
$814$	36.1490			0.0444091
$815$	−1100.75	+	635.517i	−1.35061	+	0.779775i
$816$		0			0
$817$	−100.736	−	58.1600i	−0.123300	−	0.0711873i
$818$		−	324.789i		−	0.397052i
$819$		0			0
$820$	−169.711			−0.206965
$821$	394.189	−	682.755i	0.480133	−	0.831614i	−0.519608	−	0.854405i	$-0.673922\pi$
$821$	394.189	−	682.755i	0.480133	−	0.831614i	0.999740	+	0.0227909i	$0.00725519\pi$
$822$		0			0
$823$	−200.344	−	347.006i	−0.243432	−	0.421636i	0.718258	−	0.695777i	$-0.244940\pi$
$823$	−200.344	−	347.006i	−0.243432	−	0.421636i	−0.961689	+	0.274141i	$0.911606\pi$
$824$		−	102.124i		−	0.123937i
$825$		0			0
$826$	−831.223	−	568.866i	−1.00632	−	0.688700i
$827$	1250.02			1.51151			0.755757	−	0.654852i	$-0.227269\pi$
$827$	1250.02			1.51151			0.755757	+	0.654852i	$0.227269\pi$
$828$		0			0
$829$	916.487	+	529.134i	1.10553	+	0.638280i	0.937669	−	0.347530i	$-0.112980\pi$
$829$	916.487	+	529.134i	1.10553	+	0.638280i	0.167864	+	0.985810i	$0.446313\pi$
$830$	−79.5528			−0.0958468
$831$		0			0
$832$	106.690	+	61.5972i	0.128233	+	0.0740351i
$833$	−106.595	+	690.688i	−0.127965	+	0.829158i
$834$		0			0
$835$	−715.643	+	1239.53i	−0.857058	+	1.48447i
$836$	43.7999	+	25.2879i	0.0523922	+	0.0302486i
$837$		0			0
$838$	713.523	−	411.953i	0.851460	−	0.491591i
$839$	677.714	−	391.278i	0.807764	−	0.466363i	−0.0384146	−	0.999262i	$-0.512231\pi$
$839$	677.714	−	391.278i	0.807764	−	0.466363i	0.846179	+	0.532899i	$0.178897\pi$
$840$		0			0
$841$	402.624	−	697.365i	0.478744	−	0.829209i
$842$	88.4713			0.105073
$843$		0			0
$844$	−97.5748			−0.115610
$845$	409.655	−	236.514i	0.484799	−	0.279899i
$846$		0			0
$847$	726.442	−	1061.47i	0.857665	−	1.25321i
$848$	−26.0701	−	45.1547i	−0.0307430	−	0.0532485i
$849$		0			0
$850$	405.145	−	233.910i	0.476641	−	0.275189i
$851$	−9.41612	−	16.3092i	−0.0110648	−	0.0191647i
$852$		0			0
$853$	72.1792	−	41.6727i	0.0846180	−	0.0488542i	−0.457094	−	0.889418i	$-0.651110\pi$
$853$	72.1792	−	41.6727i	0.0846180	−	0.0488542i	0.541712	+	0.840564i	$0.317776\pi$
$854$	50.8214	−	662.499i	0.0595099	−	0.775759i
$855$		0			0
$856$	32.1378	+	55.6643i	0.0375442	+	0.0650284i
$857$			258.376i			0.301489i	0.988573	+	0.150744i	$0.0481670\pi$
$857$			258.376i			0.301489i	−0.988573	+	0.150744i	$0.951833\pi$
$858$		0			0
$859$			396.614i			0.461716i	0.972987	+	0.230858i	$0.0741533\pi$
$859$			396.614i			0.461716i	−0.972987	+	0.230858i	$0.925847\pi$
$860$	965.538	+	557.454i	1.12272	+	0.648202i
$861$		0			0
$862$	−229.685	−	397.826i	−0.266456	−	0.461515i
$863$	−195.031	−	337.804i	−0.225992	−	0.391430i	0.730624	−	0.682780i	$-0.239229\pi$
$863$	−195.031	−	337.804i	−0.225992	−	0.391430i	−0.956617	+	0.291349i	$0.905896\pi$
$864$		0			0
$865$	636.765	−	1102.91i	0.736145	−	1.27504i
$866$	272.121	+	157.109i	0.314227	+	0.181419i
$867$		0			0
$868$	207.895	−	99.6660i	0.239510	−	0.114823i
$869$	−1071.74	+	1856.31i	−1.23331	+	2.13615i
$870$		0			0
$871$			608.018i			0.698069i
$872$	−221.590	+	383.805i	−0.254117	+	0.440143i
$873$		0			0
$874$		−	26.3480i		−	0.0301465i
$875$	−72.4444	−	49.5790i	−0.0827936	−	0.0566617i
$876$		0			0
$877$	−397.853			−0.453652			−0.226826	−	0.973935i	$-0.572835\pi$
$877$	−397.853			−0.453652			−0.226826	+	0.973935i	$0.572835\pi$
$878$	468.139	−	270.280i	0.533188	−	0.307836i
$879$		0			0
$880$	−419.814	−	242.380i	−0.477061	−	0.275432i
$881$			845.162i			0.959321i	0.877454	+	0.479660i	$0.159240\pi$
$881$			845.162i			0.959321i	−0.877454	+	0.479660i	$0.840760\pi$
$882$		0			0
$883$	16.3649			0.0185333			0.00926666	−	0.999957i	$-0.497050\pi$
$883$	16.3649			0.0185333			0.00926666	+	0.999957i	$0.497050\pi$
$884$	−219.633	+	380.416i	−0.248454	+	0.430335i
$885$		0			0
$886$	−13.0291	−	22.5670i	−0.0147055	−	0.0254706i
$887$		−	644.522i		−	0.726631i	−0.931666	−	0.363315i	$-0.881645\pi$
$887$		−	644.522i		−	0.726631i	0.931666	−	0.363315i	$-0.118355\pi$
$888$		0			0
$889$	971.318	−	1419.28i	1.09260	−	1.59649i
$890$	−495.458			−0.556694
$891$		0			0
$892$	317.938	+	183.561i	0.356432	+	0.205786i
$893$	−121.169			−0.135688
$894$		0			0
$895$	237.856	+	137.326i	0.265761	+	0.153437i
$896$	−34.2361	−	71.4135i	−0.0382099	−	0.0797026i
$897$		0			0
$898$	−270.854	+	469.133i	−0.301620	+	0.522420i
$899$	−85.2751	−	49.2336i	−0.0948555	−	0.0547649i
$900$		0			0
$901$	161.005	−	92.9565i	0.178696	−	0.103170i
$902$	−261.339	+	150.884i	−0.289733	+	0.167277i
$903$		0			0
$904$	−187.950	+	325.540i	−0.207910	+	0.360110i
$905$	25.5203			0.0281993
$906$		0			0
$907$	1587.94			1.75077			0.875383	−	0.483430i	$-0.160609\pi$
$907$	1587.94			1.75077			0.875383	+	0.483430i	$0.160609\pi$
$908$	140.607	−	81.1795i	0.154853	−	0.0894047i
$909$		0			0
$910$	−1055.20	−	80.9462i	−1.15956	−	0.0889519i
$911$	752.842	+	1303.96i	0.826391	+	1.43135i	0.900852	+	0.434127i	$0.142943\pi$
$911$	752.842	+	1303.96i	0.826391	+	1.43135i	−0.0744605	+	0.997224i	$0.523723\pi$
$912$		0			0
$913$	−122.504	+	70.7275i	−0.134177	+	0.0774671i
$914$	85.0404	+	147.294i	0.0930420	+	0.161154i
$915$		0			0
$916$	352.728	−	203.648i	0.385075	−	0.222323i
$917$	1249.58	+	855.176i	1.36268	+	0.932580i
$918$		0			0
$919$	−583.949	−	1011.43i	−0.635418	−	1.10058i	−0.986426	−	0.164204i	$-0.947494\pi$
$919$	−583.949	−	1011.43i	−0.635418	−	1.10058i	0.351008	−	0.936372i	$-0.385839\pi$
$920$			252.541i			0.274501i
$921$		0			0
$922$		−	29.3023i		−	0.0317812i
$923$	1252.21	+	722.962i	1.35667	+	0.783275i
$924$		0			0
$925$	16.9803	+	29.4108i	0.0183571	+	0.0317954i
$926$	−256.477	−	444.231i	−0.276973	−	0.479731i
$927$		0			0
$928$	−16.9121	+	29.2927i	−0.0182243	+	0.0315654i
$929$	518.105	+	299.128i	0.557702	+	0.321989i	0.752222	−	0.658909i	$-0.228982\pi$
$929$	518.105	+	299.128i	0.557702	+	0.321989i	−0.194521	+	0.980898i	$0.562315\pi$
$930$		0			0
$931$	−55.3381	−	44.4506i	−0.0594395	−	0.0477450i
$932$	−22.7147	+	39.3430i	−0.0243720	+	0.0422135i
$933$		0			0
$934$			586.677i			0.628134i
$935$	864.239	−	1496.91i	0.924320	−	1.60097i
$936$		0			0
$937$		−	56.5072i		−	0.0603066i	−0.999545	−	0.0301533i	$-0.990400\pi$
$937$		−	56.5072i		−	0.0603066i	0.999545	−	0.0301533i	$-0.00959954\pi$
$938$	220.752	−	322.561i	0.235343	−	0.343881i
$939$		0			0
$940$	1161.39			1.23552
$941$	−1458.39	+	842.000i	−1.54983	+	0.894792i	−0.551671	+	0.834062i	$0.686010\pi$
$941$	−1458.39	+	842.000i	−1.54983	+	0.894792i	−0.998154	+	0.0607307i	$0.980657\pi$
$942$		0			0
$943$	136.147	+	78.6048i	0.144377	+	0.0833561i
$944$			406.988i			0.431131i
$945$		0			0
$946$	1982.45			2.09561
$947$	−444.108	+	769.218i	−0.468964	+	0.812269i	−0.999371	−	0.0354744i	$-0.988706\pi$
$947$	−444.108	+	769.218i	−0.468964	+	0.812269i	0.530407	+	0.847743i	$0.322039\pi$
$948$		0			0
$949$	153.090	+	265.159i	0.161317	+	0.279409i
$950$			47.5141i			0.0500148i
$951$		0			0
$952$	254.635	−	122.073i	0.267474	−	0.128228i
$953$	455.922			0.478407			0.239204	−	0.970969i	$-0.423114\pi$
$953$	455.922			0.478407			0.239204	+	0.970969i	$0.423114\pi$
$954$		0			0
$955$	287.846	+	166.188i	0.301410	+	0.174019i
$956$	−68.9175			−0.0720894
$957$		0			0
$958$	183.257	+	105.804i	0.191291	+	0.110442i
$959$	398.283	−	581.968i	0.415311	−	0.606849i
$960$		0			0
$961$	−344.904	+	597.391i	−0.358901	+	0.621635i
$962$	−27.6157	−	15.9439i	−0.0287065	−	0.0165737i
$963$		0			0
$964$	212.881	−	122.907i	0.220831	−	0.127497i
$965$	−351.629	+	203.013i	−0.364382	+	0.210376i
$966$		0			0
$967$	−761.975	+	1319.78i	−0.787979	+	1.36482i	0.139225	+	0.990261i	$0.455539\pi$
$967$	−761.975	+	1319.78i	−0.787979	+	1.36482i	−0.927203	+	0.374558i	$0.877794\pi$
$968$	−519.724			−0.536905
$969$		0			0
$970$	916.938			0.945296
$971$	294.389	−	169.966i	0.303182	−	0.175042i	−0.340690	−	0.940176i	$-0.610661\pi$
$971$	294.389	−	169.966i	0.303182	−	0.175042i	0.643871	+	0.765134i	$0.277327\pi$
$972$		0			0
$973$	−1110.86	+	532.555i	−1.14169	+	0.547333i
$974$	65.4978	+	113.445i	0.0672462	+	0.116474i
$975$		0			0
$976$	−232.507	+	134.238i	−0.238225	+	0.137539i
$977$	−226.166	−	391.731i	−0.231490	−	0.400953i	0.726757	−	0.686895i	$-0.241027\pi$
$977$	−226.166	−	391.731i	−0.231490	−	0.400953i	−0.958247	+	0.285942i	$0.907693\pi$
$978$		0			0
$979$	−762.957	+	440.493i	−0.779323	+	0.449942i
$980$	530.406	+	426.051i	0.541231	+	0.434746i
$981$		0			0
$982$	−231.964	−	401.774i	−0.236216	−	0.409138i
$983$		−	889.893i		−	0.905283i	−0.891693	−	0.452642i	$-0.850482\pi$
$983$		−	889.893i		−	0.905283i	0.891693	−	0.452642i	$-0.149518\pi$
$984$		0			0
$985$		−	1416.07i		−	1.43763i
$986$	−104.447	−	60.3026i	−0.105930	−	0.0611588i
$987$		0			0
$988$	−22.3070	−	38.6369i	−0.0225779	−	0.0391062i
$989$	−516.389	−	894.412i	−0.522133	−	0.904360i
$990$		0			0
$991$	−152.141	+	263.517i	−0.153523	+	0.265910i	−0.932520	−	0.361118i	$-0.882395\pi$
$991$	−152.141	+	263.517i	−0.153523	+	0.265910i	0.778997	+	0.627027i	$0.215729\pi$
$992$	−80.6759	−	46.5783i	−0.0813265	−	0.0469539i
$993$		0			0
$994$	−401.826	−	838.176i	−0.404252	−	0.843235i
$995$	−585.697	+	1014.46i	−0.588640	+	1.01955i
$996$		0			0
$997$			1827.05i			1.83255i	0.400549	+	0.916275i	$0.368819\pi$
$997$			1827.05i			1.83255i	−0.400549	+	0.916275i	$0.631181\pi$
$998$	118.619	−	205.454i	0.118857	−	0.205866i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.3.j.a.199.10		32
3.2	odd	2		126.3.j.a.31.3	✓	32
7.5	odd	6		378.3.p.a.145.7		32
9.2	odd	6		126.3.p.a.115.9	yes	32
9.7	even	3		378.3.p.a.73.7		32
21.5	even	6		126.3.p.a.103.9	yes	32
63.47	even	6		126.3.j.a.61.3	yes	32
63.61	odd	6	inner	378.3.j.a.19.15		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.3.j.a.31.3	✓	32	3.2	odd	2
126.3.j.a.61.3	yes	32	63.47	even	6
126.3.p.a.103.9	yes	32	21.5	even	6
126.3.p.a.115.9	yes	32	9.2	odd	6
378.3.j.a.19.15		32	63.61	odd	6	inner
378.3.j.a.199.10		32	1.1	even	1	trivial
378.3.p.a.73.7		32	9.7	even	3
378.3.p.a.145.7		32	7.5	odd	6

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

\(f(q)\)	\(=\)	\(q+(0.707107 - 1.22474i) q^{2} +(-1.00000 - 1.73205i) q^{4} -6.94216i q^{5} +(3.95343 - 5.77671i) q^{7} -2.82843 q^{8} +O(q^{10})\)	\(q+(0.707107 - 1.22474i) q^{2} +(-1.00000 - 1.73205i) q^{4} -6.94216i q^{5} +(3.95343 - 5.77671i) q^{7} -2.82843 q^{8} +(-8.50237 - 4.90885i) q^{10} -17.4571 q^{11} +(13.3362 + 7.69965i) q^{13} +(-4.27951 - 8.92669i) q^{14} +(-2.00000 + 3.46410i) q^{16} +(-12.3517 - 7.13128i) q^{17} +(1.25450 - 0.724286i) q^{19} +(-12.0242 + 6.94216i) q^{20} +(-12.3440 + 21.3805i) q^{22} +12.8615 q^{23} -23.1935 q^{25} +(18.8602 - 10.8890i) q^{26} +(-13.9590 - 1.07082i) q^{28} +(2.98967 + 5.17826i) q^{29} +(-14.2616 + 8.23395i) q^{31} +(2.82843 + 4.89898i) q^{32} +(-17.4680 + 10.0852i) q^{34} +(-40.1029 - 27.4453i) q^{35} +(-0.732115 - 1.26806i) q^{37} -2.04859i q^{38} +19.6354i q^{40} +(10.5856 + 6.11162i) q^{41} +(-40.1499 - 69.5416i) q^{43} +(17.4571 + 30.2366i) q^{44} +(9.09448 - 15.7521i) q^{46} +(-72.4407 - 41.8237i) q^{47} +(-17.7409 - 45.6756i) q^{49} +(-16.4003 + 28.4062i) q^{50} -30.7986i q^{52} +(-6.51752 + 11.2887i) q^{53} +121.190i q^{55} +(-11.1820 + 16.3390i) q^{56} +8.45607 q^{58} +(88.1154 - 50.8735i) q^{59} +(58.1268 + 33.5595i) q^{61} +23.2891i q^{62} +8.00000 q^{64} +(53.4522 - 92.5819i) q^{65} +(19.7417 + 34.1937i) q^{67} +28.5251i q^{68} +(-61.9705 + 29.7090i) q^{70} +93.8955 q^{71} +(17.2189 + 9.94134i) q^{73} -2.07073 q^{74} +(-2.50900 - 1.44857i) q^{76} +(-69.0153 + 100.845i) q^{77} +(61.3930 - 106.336i) q^{79} +(24.0483 + 13.8843i) q^{80} +(14.9703 - 8.64313i) q^{82} +(7.01741 - 4.05150i) q^{83} +(-49.5065 + 85.7477i) q^{85} -113.561 q^{86} +49.3761 q^{88} +(43.7047 - 25.2329i) q^{89} +(97.2023 - 46.5994i) q^{91} +(-12.8615 - 22.2768i) q^{92} +(-102.447 + 59.1476i) q^{94} +(-5.02811 - 8.70894i) q^{95} +(-80.8837 + 46.6982i) q^{97} +(-68.4857 - 10.5695i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 32 q^{4} - 2 q^{7}+O(q^{10}) \) 32 * q - 32 * q^4 - 2 * q^7	\( 32 q - 32 q^{4} - 2 q^{7} - 24 q^{11} - 30 q^{13} + 12 q^{14} - 64 q^{16} - 54 q^{17} - 84 q^{23} - 160 q^{25} + 72 q^{26} - 4 q^{28} + 84 q^{29} - 24 q^{31} + 66 q^{35} - 22 q^{37} - 396 q^{41} - 16 q^{43} + 24 q^{44} + 12 q^{46} - 108 q^{47} - 22 q^{49} + 96 q^{50} + 252 q^{53} - 48 q^{56} + 48 q^{58} + 90 q^{59} - 102 q^{61} + 256 q^{64} + 6 q^{65} + 70 q^{67} - 108 q^{70} - 300 q^{71} - 144 q^{74} + 114 q^{77} + 106 q^{79} + 756 q^{83} - 60 q^{85} - 240 q^{86} - 414 q^{89} - 186 q^{91} + 84 q^{92} + 552 q^{95} + 114 q^{97} + 96 q^{98}+O(q^{100}) \) 32 * q - 32 * q^4 - 2 * q^7 - 24 * q^11 - 30 * q^13 + 12 * q^14 - 64 * q^16 - 54 * q^17 - 84 * q^23 - 160 * q^25 + 72 * q^26 - 4 * q^28 + 84 * q^29 - 24 * q^31 + 66 * q^35 - 22 * q^37 - 396 * q^41 - 16 * q^43 + 24 * q^44 + 12 * q^46 - 108 * q^47 - 22 * q^49 + 96 * q^50 + 252 * q^53 - 48 * q^56 + 48 * q^58 + 90 * q^59 - 102 * q^61 + 256 * q^64 + 6 * q^65 + 70 * q^67 - 108 * q^70 - 300 * q^71 - 144 * q^74 + 114 * q^77 + 106 * q^79 + 756 * q^83 - 60 * q^85 - 240 * q^86 - 414 * q^89 - 186 * q^91 + 84 * q^92 + 552 * q^95 + 114 * q^97 + 96 * q^98

Introduction

L-functions

Modular forms

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