LMFDB - Embedded newform 378.3.p.a.73.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [378,3,Mod(73,378)]

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, 1]))

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

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

chi := DirichletCharacter("378.73");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	378.p (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			73.7
Character	$\chi$	$=$	378.73
Dual form			378.3.p.a.145.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.41421 q^{2} +2.00000 q^{4} +(6.01208 + 3.47108i) q^{5} +(-6.97949 - 0.535409i) q^{7} -2.82843 q^{8} +O(q^{10})$	\(q-1.41421 q^{2} +2.00000 q^{4} +(6.01208 + 3.47108i) q^{5} +(-6.97949 - 0.535409i) q^{7} -2.82843 q^{8} +(-8.50237 - 4.90885i) q^{10} +(8.72855 + 15.1183i) q^{11} +(-13.3362 + 7.69965i) q^{13} +(9.87050 + 0.757183i) q^{14} +4.00000 q^{16} +(-12.3517 - 7.13128i) q^{17} +(1.25450 - 0.724286i) q^{19} +(12.0242 + 6.94216i) q^{20} +(-12.3440 - 21.3805i) q^{22} +(-6.43077 + 11.1384i) q^{23} +(11.5968 + 20.0862i) q^{25} +(18.8602 - 10.8890i) q^{26} +(-13.9590 - 1.07082i) q^{28} +(2.98967 - 5.17826i) q^{29} -16.4679i q^{31} -5.65685 q^{32} +(17.4680 + 10.0852i) q^{34} +(-40.1029 - 27.4453i) q^{35} +(-0.732115 - 1.26806i) q^{37} +(-1.77413 + 1.02430i) q^{38} +(-17.0047 - 9.81769i) q^{40} +(-10.5856 + 6.11162i) q^{41} +(-40.1499 + 69.5416i) q^{43} +(17.4571 + 30.2366i) q^{44} +(9.09448 - 15.7521i) q^{46} +83.6474i q^{47} +(48.4267 + 7.47377i) q^{49} +(-16.4003 - 28.4062i) q^{50} +(-26.6724 + 15.3993i) q^{52} +(-6.51752 + 11.2887i) q^{53} +121.190i q^{55} +(19.7410 + 1.51437i) q^{56} +(-4.22803 + 7.32317i) q^{58} +101.747i q^{59} -67.1191i q^{61} +23.2891i q^{62} +8.00000 q^{64} -106.904 q^{65} -39.4835 q^{67} +(-24.7035 - 14.2626i) q^{68} +(56.7140 + 38.8135i) q^{70} +93.8955 q^{71} +(17.2189 + 9.94134i) q^{73} +(1.03537 + 1.79331i) q^{74} +(2.50900 - 1.44857i) q^{76} +(-52.8264 - 110.191i) q^{77} -122.786 q^{79} +(24.0483 + 13.8843i) q^{80} +(14.9703 - 8.64313i) q^{82} +(-7.01741 - 4.05150i) q^{83} +(-49.5065 - 85.7477i) q^{85} +(56.7805 - 98.3467i) q^{86} +(-24.6881 - 42.7610i) q^{88} +(43.7047 - 25.2329i) q^{89} +(97.2023 - 46.5994i) q^{91} +(-12.8615 + 22.2768i) q^{92} -118.295i q^{94} +10.0562 q^{95} +(80.8837 + 46.6982i) q^{97} +(-68.4857 - 10.5695i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 64 q^{4} - 2 q^{7}+O(q^{10}) $ 32 * q + 64 * q^4 - 2 * q^7	$ 32 q + 64 q^{4} - 2 q^{7} + 12 q^{11} + 30 q^{13} + 12 q^{14} + 128 q^{16} - 54 q^{17} + 42 q^{23} + 80 q^{25} + 72 q^{26} - 4 q^{28} + 84 q^{29} + 66 q^{35} - 22 q^{37} + 396 q^{41} - 16 q^{43} + 24 q^{44} + 12 q^{46} + 50 q^{49} + 96 q^{50} + 60 q^{52} + 252 q^{53} + 24 q^{56} - 24 q^{58} + 256 q^{64} - 12 q^{65} - 140 q^{67} - 108 q^{68} + 72 q^{70} - 300 q^{71} + 72 q^{74} - 570 q^{77} - 212 q^{79} - 756 q^{83} - 60 q^{85} + 120 q^{86} - 414 q^{89} - 186 q^{91} + 84 q^{92} - 1104 q^{95} - 114 q^{97} + 96 q^{98}+O(q^{100}) $ 32 * q + 64 * q^4 - 2 * q^7 + 12 * q^11 + 30 * q^13 + 12 * q^14 + 128 * q^16 - 54 * q^17 + 42 * q^23 + 80 * q^25 + 72 * q^26 - 4 * q^28 + 84 * q^29 + 66 * q^35 - 22 * q^37 + 396 * q^41 - 16 * q^43 + 24 * q^44 + 12 * q^46 + 50 * q^49 + 96 * q^50 + 60 * q^52 + 252 * q^53 + 24 * q^56 - 24 * q^58 + 256 * q^64 - 12 * q^65 - 140 * q^67 - 108 * q^68 + 72 * q^70 - 300 * q^71 + 72 * q^74 - 570 * q^77 - 212 * q^79 - 756 * q^83 - 60 * q^85 + 120 * q^86 - 414 * q^89 - 186 * q^91 + 84 * q^92 - 1104 * q^95 - 114 * q^97 + 96 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−1.41421			−0.707107
$2$	−1.41421			−0.707107
$3$		0			0
$3$		0			0
$4$	2.00000			0.500000
$5$	6.01208	+	3.47108i	1.20242	+	0.694216i	0.961092	−	0.276229i	$-0.0890847\pi$
$5$	6.01208	+	3.47108i	1.20242	+	0.694216i	0.241325	+	0.970444i	$0.422418\pi$
$6$		0			0
$7$	−6.97949	−	0.535409i	−0.997071	−	0.0764870i
$7$	−6.97949	−	0.535409i	−0.997071	−	0.0764870i
$8$	−2.82843			−0.353553
$9$		0			0
$10$	−8.50237	−	4.90885i	−0.850237	−	0.490885i
$11$	8.72855	+	15.1183i	0.793504	+	1.37439i	0.923785	+	0.382913i	$0.125079\pi$
$11$	8.72855	+	15.1183i	0.793504	+	1.37439i	−0.130280	+	0.991477i	$0.541588\pi$
$12$		0			0
$13$	−13.3362	+	7.69965i	−1.02586	+	0.592281i	−0.915796	−	0.401643i	$-0.868439\pi$
$13$	−13.3362	+	7.69965i	−1.02586	+	0.592281i	−0.110065	+	0.993924i	$0.535106\pi$
$14$	9.87050	+	0.757183i	0.705035	+	0.0540845i
$15$		0			0
$16$	4.00000			0.250000
$17$	−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
$23$	−6.43077	+	11.1384i	−0.279599	+	0.484279i	−0.971285	−	0.237919i	$-0.923535\pi$
$23$	−6.43077	+	11.1384i	−0.279599	+	0.484279i	0.691686	+	0.722198i	$0.256868\pi$
$24$		0			0
$25$	11.5968	+	20.0862i	0.463871	+	0.803448i
$26$	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	−0.809865	−	0.586616i	$-0.800460\pi$
$29$	2.98967	−	5.17826i	0.103092	−	0.178561i	0.912957	+	0.408056i	$0.133793\pi$
$30$		0			0
$31$		−	16.4679i		−	0.531223i	−0.964080	−	0.265611i	$-0.914426\pi$
$31$		−	16.4679i		−	0.531223i	0.964080	−	0.265611i	$-0.0855738\pi$
$32$	−5.65685			−0.176777
$33$		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	$0.839632\pi$
$38$	−1.77413	+	1.02430i	−0.0466877	+	0.0269551i
$39$		0			0
$40$	−17.0047	−	9.81769i	−0.425119	−	0.245442i
$41$	−10.5856	+	6.11162i	−0.258186	+	0.149064i	−0.623507	−	0.781818i	$-0.714293\pi$
$41$	−10.5856	+	6.11162i	−0.258186	+	0.149064i	0.365321	+	0.930882i	$0.380959\pi$
$42$		0			0
$43$	−40.1499	+	69.5416i	−0.933718	+	1.61725i	−0.156814	+	0.987628i	$0.550122\pi$
$43$	−40.1499	+	69.5416i	−0.933718	+	1.61725i	−0.776904	+	0.629619i	$0.783211\pi$
$44$	17.4571	+	30.2366i	0.396752	+	0.687195i
$45$		0			0
$46$	9.09448	−	15.7521i	0.197706	−	0.342437i
$47$			83.6474i			1.77973i	0.456223	+	0.889866i	$0.349202\pi$
$47$			83.6474i			1.77973i	−0.456223	+	0.889866i	$0.650798\pi$
$48$		0			0
$49$	48.4267	+	7.47377i	0.988299	+	0.152526i
$50$	−16.4003	−	28.4062i	−0.328006	−	0.568123i
$51$		0			0
$52$	−26.6724	+	15.3993i	−0.512930	+	0.296140i
$53$	−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
$56$	19.7410	+	1.51437i	0.352518	+	0.0270423i
$57$		0			0
$58$	−4.22803	+	7.32317i	−0.0728971	+	0.126262i
$59$			101.747i			1.72452i	0.506462	+	0.862262i	$0.330953\pi$
$59$			101.747i			1.72452i	−0.506462	+	0.862262i	$0.669047\pi$
$60$		0			0
$61$		−	67.1191i		−	1.10031i	−0.835062	−	0.550156i	$-0.814568\pi$
$61$		−	67.1191i		−	1.10031i	0.835062	−	0.550156i	$-0.185432\pi$
$62$			23.2891i			0.375631i
$63$		0			0
$64$	8.00000			0.125000
$65$	−106.904			−1.64468
$66$		0			0
$67$	−39.4835			−0.589306			−0.294653	−	0.955604i	$-0.595204\pi$
$67$	−39.4835			−0.589306			−0.294653	+	0.955604i	$0.595204\pi$
$68$	−24.7035	−	14.2626i	−0.363286	−	0.209743i
$69$		0			0
$70$	56.7140	+	38.8135i	0.810200	+	0.554479i
$71$	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	$0.623183\pi$
$74$	1.03537	+	1.79331i	0.0139914	+	0.0242339i
$75$		0			0
$76$	2.50900	−	1.44857i	0.0330132	−	0.0190602i
$77$	−52.8264	−	110.191i	−0.686057	−	1.43106i
$78$		0			0
$79$	−122.786			−1.55425			−0.777126	−	0.629345i	$-0.783323\pi$
$79$	−122.786			−1.55425			−0.777126	+	0.629345i	$0.783323\pi$
$80$	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	$-0.348877\pi$
$83$	−7.01741	−	4.05150i	−0.0845471	−	0.0488133i	−0.541678	+	0.840586i	$0.682211\pi$
$84$		0			0
$85$	−49.5065	−	85.7477i	−0.582429	−	1.00880i
$86$	56.7805	−	98.3467i	0.660238	−	1.14357i
$87$		0			0
$88$	−24.6881	−	42.7610i	−0.280546	−	0.485920i
$89$	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
$94$		−	118.295i		−	1.25846i
$95$	10.0562			0.105855
$96$		0			0
$97$	80.8837	+	46.6982i	0.833853	+	0.481425i	0.855170	−	0.518348i	$-0.173453\pi$
$97$	80.8837	+	46.6982i	0.833853	+	0.481425i	−0.0213173	+	0.999773i	$0.506786\pi$
$98$	−68.4857	−	10.5695i	−0.698833	−	0.107852i
$99$		0			0
$100$	23.1935	+	40.1724i	0.231935	+	0.401724i
$101$	121.717	−	70.2731i	1.20511	−	0.695773i	0.243426	−	0.969919i	$-0.421729\pi$
$101$	121.717	−	70.2731i	1.20511	−	0.695773i	0.961688	+	0.274146i	$0.0883953\pi$
$102$		0			0
$103$	−31.2691	−	18.0532i	−0.303584	−	0.175274i	0.340468	−	0.940256i	$-0.389414\pi$
$103$	−31.2691	−	18.0532i	−0.303584	−	0.175274i	−0.644052	+	0.764982i	$0.722748\pi$
$104$	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	$-0.0886191\pi$
$110$		−	171.388i		−	1.55808i
$111$		0			0
$112$	−27.9180	−	2.14164i	−0.249268	−	0.0191218i
$113$	66.4505	+	115.096i	0.588058	+	1.01855i	0.994487	+	0.104863i	$0.0334405\pi$
$113$	66.4505	+	115.096i	0.588058	+	1.01855i	−0.406429	+	0.913682i	$0.633226\pi$
$114$		0			0
$115$	−77.3246	+	44.6434i	−0.672388	+	0.388203i
$116$	5.97934	−	10.3565i	0.0515460	−	0.0892804i
$117$		0			0
$118$		−	143.892i		−	1.21942i
$119$	82.3907	+	56.3860i	0.692359	+	0.473832i
$120$		0			0
$121$	−91.8751	+	159.132i	−0.759298	+	1.31514i
$122$			94.9207i			0.778039i
$123$		0			0
$124$		−	32.9358i		−	0.265611i
$125$		−	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	$0.0816458\pi$
$128$	−11.3137			−0.0883883
$129$		0			0
$130$	151.186			1.16297
$131$	−187.332	−	108.156i	−1.43002	−	0.825620i	−0.432895	−	0.901444i	$-0.642508\pi$
$131$	−187.332	−	108.156i	−1.43002	−	0.825620i	−0.997121	+	0.0758237i	$0.975841\pi$
$132$		0			0
$133$	−9.14357	+	4.38348i	−0.0687486	+	0.0329585i
$134$	55.8381			0.416702
$135$		0			0
$136$	34.9360	+	20.1703i	0.256882	+	0.148311i
$137$	−50.3719	−	87.2467i	−0.367678	−	0.636837i	0.621524	−	0.783395i	$-0.286514\pi$
$137$	−50.3719	−	87.2467i	−0.367678	−	0.636837i	−0.989202	+	0.146558i	$0.953181\pi$
$138$		0			0
$139$	152.411	−	87.9944i	1.09648	−	0.633054i	0.161187	−	0.986924i	$-0.448468\pi$
$139$	152.411	−	87.9944i	1.09648	−	0.633054i	0.935294	+	0.353870i	$0.115135\pi$
$140$	−80.2057	−	54.8906i	−0.572898	−	0.392076i
$141$		0			0
$142$	−132.788			−0.935128
$143$	−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
$149$	−100.465	+	174.010i	−0.674258	+	1.16785i	0.302427	+	0.953173i	$0.402203\pi$
$149$	−100.465	+	174.010i	−0.674258	+	1.16785i	−0.976685	+	0.214677i	$0.931130\pi$
$150$		0			0
$151$	118.477	+	205.209i	0.784619	+	1.35900i	0.929227	+	0.369510i	$0.120474\pi$
$151$	118.477	+	205.209i	0.784619	+	1.35900i	−0.144608	+	0.989489i	$0.546192\pi$
$152$	−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
$157$			13.1553i			0.0837919i	0.999122	+	0.0418960i	$0.0133398\pi$
$157$			13.1553i			0.0837919i	−0.999122	+	0.0418960i	$0.986660\pi$
$158$	173.646			1.09902
$159$		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	$-0.356490\pi$
$164$	−21.1713	+	12.2232i	−0.129093	+	0.0745319i
$165$		0			0
$166$	9.92412	+	5.72969i	0.0597838	+	0.0345162i
$167$	178.551	−	103.087i	1.06917	−	0.617285i	0.141215	−	0.989979i	$-0.454899\pi$
$167$	178.551	−	103.087i	1.06917	−	0.617285i	0.927954	+	0.372694i	$0.121566\pi$
$168$		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
$173$		−	183.449i		−	1.06040i	−0.847873	−	0.530199i	$-0.822117\pi$
$173$		−	183.449i		−	1.06040i	0.847873	−	0.530199i	$-0.177883\pi$
$174$		0			0
$175$	−70.1852	−	146.400i	−0.401059	−	0.836574i
$176$	34.9142	+	60.4731i	0.198376	+	0.343597i
$177$		0			0
$178$	−61.8078	+	35.6847i	−0.347235	+	0.200476i
$179$	−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	$0.996767\pi$
$182$	−137.465	+	65.9014i	−0.755301	+	0.362096i
$183$		0			0
$184$	18.1890	−	31.5042i	0.0988530	−	0.171218i
$185$		−	10.1649i		−	0.0549454i
$186$		0			0
$187$		−	248.983i		−	1.33146i
$188$			167.295i			0.889866i
$189$		0			0
$190$	−14.2216			−0.0748507
$191$	47.8780			0.250670			0.125335	−	0.992114i	$-0.459999\pi$
$191$	47.8780			0.250670			0.125335	+	0.992114i	$0.459999\pi$
$192$		0			0
$193$	58.4870			0.303041			0.151521	−	0.988454i	$-0.451583\pi$
$193$	58.4870			0.303041			0.151521	+	0.988454i	$0.451583\pi$
$194$	−114.387	−	66.0413i	−0.589623	−	0.340419i
$195$		0			0
$196$	96.8533	+	14.9475i	0.494150	+	0.0762630i
$197$	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	$0.806027\pi$
$200$	−32.8006	−	56.8123i	−0.164003	−	0.284062i
$201$		0			0
$202$	−172.133	+	99.3811i	−0.852145	+	0.491986i
$203$	−23.6389	+	34.5409i	−0.116448	+	0.170152i
$204$		0			0
$205$	−84.8556			−0.413930
$206$	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	0.918023	−	0.396526i	$-0.129784\pi$
$211$	24.3937	+	42.2511i	0.115610	+	0.200242i	−0.802413	+	0.596768i	$0.796451\pi$
$212$	−13.0350	+	22.5773i	−0.0614860	+	0.106497i
$213$		0			0
$214$	16.0689	+	27.8322i	0.0750884	+	0.130057i
$215$	−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
$220$			242.380i			1.10173i
$221$	219.633			0.993817
$222$		0			0
$223$	158.969	+	91.7807i	0.712865	+	0.411573i	0.812121	−	0.583489i	$-0.198313\pi$
$223$	158.969	+	91.7807i	0.712865	+	0.411573i	−0.0992560	+	0.995062i	$0.531646\pi$
$224$	39.4820	+	3.02873i	0.176259	+	0.0135211i
$225$		0			0
$226$	−93.9752	−	162.770i	−0.415820	−	0.720221i
$227$	70.3035	−	40.5897i	0.309707	−	0.178809i	−0.337088	−	0.941473i	$-0.609442\pi$
$227$	70.3035	−	40.5897i	0.309707	−	0.178809i	0.646795	+	0.762664i	$0.276109\pi$
$228$		0			0
$229$	−176.364	−	101.824i	−0.770149	−	0.444646i	0.0627785	−	0.998027i	$-0.480004\pi$
$229$	−176.364	−	101.824i	−0.770149	−	0.444646i	−0.832928	+	0.553382i	$0.813337\pi$
$230$	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
$236$			203.494i			0.862262i
$237$		0			0
$238$	−116.518	−	79.7418i	−0.489572	−	0.335049i
$239$	17.2294	+	29.8421i	0.0720894	+	0.124863i	0.899817	−	0.436268i	$-0.143700\pi$
$239$	17.2294	+	29.8421i	0.0720894	+	0.124863i	−0.827727	+	0.561130i	$0.810367\pi$
$240$		0			0
$241$	106.441	−	61.4535i	0.441662	−	0.254994i	−0.262640	−	0.964894i	$-0.584593\pi$
$241$	106.441	−	61.4535i	0.441662	−	0.254994i	0.704302	+	0.709900i	$0.251260\pi$
$242$	129.931	−	225.047i	0.536905	−	0.929947i
$243$		0			0
$244$		−	134.238i		−	0.550156i
$245$	265.203	+	213.026i	1.08246	+	0.869493i
$246$		0			0
$247$	−11.1535	+	19.3184i	−0.0451559	+	0.0782123i
$248$			46.5783i			0.187816i
$249$		0			0
$250$			17.7353i			0.0709413i
$251$			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
$254$	−347.458			−1.36795
$255$		0			0
$256$	16.0000			0.0625000
$257$	113.664	+	65.6238i	0.442272	+	0.255346i	0.704561	−	0.709644i	$-0.251144\pi$
$257$	113.664	+	65.6238i	0.442272	+	0.255346i	−0.262289	+	0.964989i	$0.584477\pi$
$258$		0			0
$259$	4.43086	+	9.24239i	0.0171076	+	0.0356849i
$260$	−213.809			−0.822341
$261$		0			0
$262$	264.928	+	152.956i	1.01117	+	0.583802i
$263$	136.997	+	237.285i	0.520899	+	0.902224i	0.999705	+	0.0243030i	$0.00773665\pi$
$263$	136.997	+	237.285i	0.520899	+	0.902224i	−0.478805	+	0.877921i	$0.658930\pi$
$264$		0			0
$265$	−78.3677	+	45.2456i	−0.295727	+	0.170738i
$266$	12.9310	−	6.19918i	0.0486126	−	0.0233052i
$267$		0			0
$268$	−78.9669			−0.294653
$269$	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
$275$	−202.446	+	350.647i	−0.736167	+	1.27508i
$276$		0			0
$277$	−37.5087	−	64.9670i	−0.135411	−	0.234538i	0.790344	−	0.612664i	$-0.209902\pi$
$277$	−37.5087	−	64.9670i	−0.135411	−	0.234538i	−0.925754	+	0.378126i	$0.876569\pi$
$278$	−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	0.321329	+	0.946968i	$0.395870\pi$
$281$	−185.301	+	320.950i	−0.659433	+	1.14217i	−0.980763	+	0.195205i	$0.937463\pi$
$282$		0			0
$283$			139.136i			0.491648i	0.969315	+	0.245824i	$0.0790585\pi$
$283$			139.136i			0.491648i	−0.969315	+	0.245824i	$0.920942\pi$
$284$	187.791			0.661236
$285$		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
$290$	−50.8386	+	29.3517i	−0.175305	+	0.101213i
$291$		0			0
$292$	34.4378	+	19.8827i	0.117938	+	0.0680913i
$293$	−89.4372	+	51.6366i	−0.305247	+	0.176234i	−0.644797	−	0.764354i	$-0.723058\pi$
$293$	−89.4372	+	51.6366i	−0.305247	+	0.176234i	0.339551	+	0.940588i	$0.389725\pi$
$294$		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
$299$		−	198.059i		−	0.662404i
$300$		0			0
$301$	317.459	−	463.869i	1.05468	−	1.54109i
$302$	−167.552	−	290.209i	−0.554809	−	0.960957i
$303$		0			0
$304$	5.01800	−	2.89715i	0.0165066	−	0.00953008i
$305$	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	$-0.100188\pi$
$308$	−105.653	−	220.383i	−0.343028	−	0.715528i
$309$		0			0
$310$	−80.8384	+	140.016i	−0.260769	+	0.451665i
$311$		−	155.398i		−	0.499671i	−0.968288	−	0.249836i	$-0.919623\pi$
$311$		−	155.398i		−	0.499671i	0.968288	−	0.249836i	$-0.0803766\pi$
$312$		0			0
$313$		−	566.895i		−	1.81117i	−0.424170	−	0.905583i	$-0.639434\pi$
$313$		−	566.895i		−	1.81117i	0.424170	−	0.905583i	$-0.360566\pi$
$314$		−	18.6044i		−	0.0592498i
$315$		0			0
$316$	−245.572			−0.777126
$317$	191.408			0.603809			0.301905	−	0.953338i	$-0.402378\pi$
$317$	191.408			0.603809			0.301905	+	0.953338i	$0.402378\pi$
$318$		0			0
$319$	104.382			0.327216
$320$	48.0967	+	27.7686i	0.150302	+	0.0867770i
$321$		0			0
$322$	−71.9087	+	105.072i	−0.223319	+	0.326312i
$323$	−20.6604			−0.0639639
$324$		0			0
$325$	−309.313	−	178.582i	−0.951733	−	0.549484i
$326$	129.464	+	224.238i	0.397128	+	0.687845i
$327$		0			0
$328$	29.9407	−	17.2863i	0.0912826	−	0.0527020i
$329$	44.7856	−	583.816i	0.136126	−	1.77452i
$330$		0			0
$331$	526.847			1.59168			0.795842	−	0.605504i	$-0.207029\pi$
$331$	526.847			1.59168			0.795842	+	0.605504i	$0.207029\pi$
$332$	−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	0.500738	−	0.865599i	$-0.333062\pi$
$337$	−168.251	−	291.419i	−0.499261	−	0.864746i	−1.00000		0.000852644i	$0.999729\pi$
$338$	−48.1813	+	83.4524i	−0.142548	+	0.246901i
$339$		0			0
$340$	−99.0129	−	171.495i	−0.291214	−	0.504398i
$341$	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
$346$			259.436i			0.749815i
$347$	−185.827			−0.535523			−0.267762	−	0.963485i	$-0.586284\pi$
$347$	−185.827			−0.535523			−0.267762	+	0.963485i	$0.586284\pi$
$348$		0			0
$349$	−217.753	−	125.720i	−0.623935	−	0.360229i	0.154464	−	0.987998i	$-0.450635\pi$
$349$	−217.753	−	125.720i	−0.623935	−	0.360229i	−0.778400	+	0.627769i	$0.783968\pi$
$350$	99.2569	+	207.042i	0.283591	+	0.591547i
$351$		0			0
$352$	−49.3761	−	85.5219i	−0.140273	−	0.242960i
$353$	66.3740	−	38.3210i	0.188028	−	0.108558i	−0.403031	−	0.915186i	$-0.632043\pi$
$353$	66.3740	−	38.3210i	0.188028	−	0.108558i	0.591059	+	0.806628i	$0.298710\pi$
$354$		0			0
$355$	564.507	+	325.919i	1.59016	+	0.918080i
$356$	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
$362$		−	5.19885i		−	0.0143615i
$363$		0			0
$364$	194.405	−	93.1987i	0.534079	−	0.256040i
$365$	69.0143	+	119.536i	0.189080	+	0.327497i
$366$		0			0
$367$	−42.3520	+	24.4520i	−0.115401	+	0.0666266i	−0.556589	−	0.830788i	$-0.687890\pi$
$367$	−42.3520	+	24.4520i	−0.115401	+	0.0666266i	0.441189	+	0.897414i	$0.354557\pi$
$368$	−25.7231	+	44.5537i	−0.0698996	+	0.121070i
$369$		0			0
$370$			14.3753i			0.0388523i
$371$	51.5330	−	75.2997i	0.138903	−	0.202964i
$372$		0			0
$373$	−273.081	+	472.991i	−0.732121	+	1.26807i	0.223854	+	0.974623i	$0.428136\pi$
$373$	−273.081	+	472.991i	−0.732121	+	1.26807i	−0.955975	+	0.293448i	$0.905197\pi$
$374$			352.115i			0.941484i
$375$		0			0
$376$		−	236.590i		−	0.629230i
$377$			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	$0.330111\pi$
$380$	20.1124			0.0529275
$381$		0			0
$382$	−67.7097			−0.177250
$383$	42.1074	+	24.3107i	0.109941	+	0.0634744i	0.553962	−	0.832542i	$-0.313115\pi$
$383$	42.1074	+	24.3107i	0.109941	+	0.0634744i	−0.444021	+	0.896016i	$0.646449\pi$
$384$		0			0
$385$	64.8862	−	845.844i	0.168536	−	2.19700i
$386$	−82.7131			−0.214283
$387$		0			0
$388$	161.767	+	93.3965i	0.416926	+	0.240713i
$389$	184.898	+	320.253i	0.475316	+	0.823272i	0.999600	−	0.0282716i	$-0.00900032\pi$
$389$	184.898	+	320.253i	0.475316	+	0.823272i	−0.524284	+	0.851543i	$0.675667\pi$
$390$		0			0
$391$	158.862	−	91.7192i	0.406297	−	0.234576i
$392$	−136.971	−	21.1390i	−0.349417	−	0.0539261i
$393$		0			0
$394$	−288.472			−0.732163
$395$	−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
$401$	10.9763	−	19.0114i	0.0273722	−	0.0474101i	−0.852015	−	0.523518i	$-0.824619\pi$
$401$	10.9763	−	19.0114i	0.0273722	−	0.0474101i	0.879387	+	0.476108i	$0.157953\pi$
$402$		0			0
$403$	126.797	+	219.619i	0.314633	+	0.544960i
$404$	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
$409$			229.660i			0.561517i	0.959778	+	0.280758i	$0.0905860\pi$
$409$			229.660i			0.561517i	−0.959778	+	0.280758i	$0.909414\pi$
$410$	120.004			0.292693
$411$		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
$416$	75.4409	−	43.5558i	0.181348	−	0.104701i
$417$		0			0
$418$	−30.9712	−	17.8812i	−0.0740938	−	0.0427780i
$419$	−504.537	+	291.295i	−1.20415	+	0.695214i	−0.961474	−	0.274894i	$-0.911357\pi$
$419$	−504.537	+	291.295i	−1.20415	+	0.695214i	−0.242672	+	0.970108i	$0.578024\pi$
$420$		0			0
$421$	31.2793	−	54.1774i	0.0742977	−	0.128687i	−0.826483	−	0.562962i	$-0.809662\pi$
$421$	31.2793	−	54.1774i	0.0742977	−	0.128687i	0.900781	+	0.434274i	$0.142995\pi$
$422$	−34.4979	−	59.7521i	−0.0817486	−	0.141593i
$423$		0			0
$424$	18.4343	−	31.9292i	0.0434772	−	0.0753047i
$425$		−	330.799i		−	0.778351i
$426$		0			0
$427$	−35.9362	+	468.457i	−0.0841597	+	1.09709i
$428$	−22.7249	−	39.3606i	−0.0530955	−	0.0919641i
$429$		0			0
$430$	682.738	−	394.179i	1.58776	−	0.916696i
$431$	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	$0.917409\pi$
$434$	12.4692	−	162.546i	0.0287309	−	0.374531i
$435$		0			0
$436$	156.688	−	271.391i	0.359375	−	0.622456i
$437$			18.6309i			0.0426336i
$438$		0			0
$439$		−	382.234i		−	0.870693i	−0.900263	−	0.435346i	$-0.856626\pi$
$439$		−	382.234i		−	0.870693i	0.900263	−	0.435346i	$-0.143374\pi$
$440$		−	342.777i		−	0.779038i
$441$		0			0
$442$	−310.609			−0.702734
$443$	−18.4259			−0.0415934			−0.0207967	−	0.999784i	$-0.506620\pi$
$443$	−18.4259			−0.0415934			−0.0207967	+	0.999784i	$0.506620\pi$
$444$		0			0
$445$	350.342			0.787285
$446$	−224.816	−	129.798i	−0.504072	−	0.291026i
$447$		0			0
$448$	−55.8360	−	4.28327i	−0.124634	−	0.00956088i
$449$	−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
$452$	132.901	+	230.191i	0.294029	+	0.509273i
$453$		0			0
$454$	−99.4241	+	57.4025i	−0.218996	+	0.126437i
$455$	746.139	+	57.2376i	1.63986	+	0.125797i
$456$		0			0
$457$	120.265			0.263163			0.131581	−	0.991305i	$-0.457995\pi$
$457$	120.265			0.263163			0.131581	+	0.991305i	$0.457995\pi$
$458$	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	$-0.340487\pi$
$461$	−17.9439	−	10.3599i	−0.0389239	−	0.0224727i	−0.519336	+	0.854570i	$0.673821\pi$
$462$		0			0
$463$	181.356	+	314.119i	0.391699	+	0.678442i	0.992674	−	0.120826i	$-0.0385542\pi$
$463$	181.356	+	314.119i	0.391699	+	0.678442i	−0.600975	+	0.799268i	$0.705221\pi$
$464$	11.9587	−	20.7130i	0.0257730	−	0.0446402i
$465$		0			0
$466$	16.0617	+	27.8197i	0.0344672	+	0.0596989i
$467$	−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
$472$		−	287.784i		−	0.609712i
$473$	−1401.80			−2.96364
$474$		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
$479$	129.582	−	74.8144i	0.270527	−	0.156189i	−0.358600	−	0.933491i	$-0.616746\pi$
$479$	129.582	−	74.8144i	0.270527	−	0.156189i	0.629127	+	0.777303i	$0.283413\pi$
$480$		0			0
$481$	19.5272	+	11.2741i	0.0405972	+	0.0234388i
$482$	−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	$0.196984\pi$
$488$			189.841i			0.389019i
$489$		0			0
$490$	−375.054	−	301.264i	−0.765416	−	0.614824i
$491$	164.023	+	284.097i	0.334060	+	0.578609i	0.983304	−	0.181972i	$-0.0582479\pi$
$491$	164.023	+	284.097i	0.334060	+	0.578609i	−0.649244	+	0.760580i	$0.724915\pi$
$492$		0			0
$493$	−73.8553	+	42.6403i	−0.149808	+	0.0864916i
$494$	15.7734	−	27.3204i	0.0319300	−	0.0553045i
$495$		0			0
$496$		−	65.8716i		−	0.132806i
$497$	−655.343	−	50.2725i	−1.31860	−	0.101152i
$498$		0			0
$499$	−83.8764	+	145.278i	−0.168089	+	0.291139i	−0.937748	−	0.347317i	$-0.887093\pi$
$499$	−83.8764	+	145.278i	−0.168089	+	0.291139i	0.769659	+	0.638455i	$0.220426\pi$
$500$		−	25.0815i		−	0.0501630i
$501$		0			0
$502$		−	89.6256i		−	0.178537i
$503$		−	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
$506$	317.526			0.627522
$507$		0			0
$508$	491.380			0.967284
$509$	−347.866	−	200.840i	−0.683429	−	0.394578i	0.117716	−	0.993047i	$-0.462443\pi$
$509$	−347.866	−	200.840i	−0.683429	−	0.394578i	−0.801146	+	0.598469i	$0.795776\pi$
$510$		0			0
$511$	−114.857	−	78.6047i	−0.224768	−	0.153825i
$512$	−22.6274			−0.0441942
$513$		0			0
$514$	−160.745	−	92.8061i	−0.312733	−	0.180557i
$515$	−125.328	−	217.075i	−0.243356	−	0.421505i
$516$		0			0
$517$	−1264.60	+	730.120i	−2.44604	+	1.41222i
$518$	−6.26618	−	13.0707i	−0.0120969	−	0.0252331i
$519$		0			0
$520$	302.371			0.581483
$521$	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
$527$	−117.437	+	203.407i	−0.222841	+	0.385972i
$528$		0			0
$529$	181.790	+	314.870i	0.343649	+	0.595218i
$530$	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
$535$		−	157.760i		−	0.294878i
$536$	111.676			0.208351
$537$		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	$0.698495\pi$
$542$	88.1517	−	50.8944i	0.162642	−	0.0939011i
$543$		0			0
$544$	69.8720	+	40.3406i	0.128441	+	0.0741555i
$545$	942.019	−	543.875i	1.72848	−	0.997936i
$546$		0			0
$547$	−32.0268	+	55.4721i	−0.0585500	+	0.101411i	−0.893815	−	0.448436i	$-0.851981\pi$
$547$	−32.0268	+	55.4721i	−0.0585500	+	0.101411i	0.835265	+	0.549848i	$0.185314\pi$
$548$	−100.744	−	174.493i	−0.183839	−	0.318419i
$549$		0			0
$550$	286.302	−	495.889i	0.520549	−	0.901617i
$551$		−	8.66151i		−	0.0157196i
$552$		0			0
$553$	856.984	+	65.7407i	1.54970	+	0.118880i
$554$	53.0453	+	91.8772i	0.0957497	+	0.165843i
$555$		0			0
$556$	304.822	−	175.989i	0.548240	−	0.316527i
$557$	−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
$560$	−160.411	−	109.781i	−0.286449	−	0.196038i
$561$		0			0
$562$	262.055	−	453.892i	0.466290	−	0.807638i
$563$		−	563.957i		−	1.00170i	−0.865534	−	0.500850i	$-0.833021\pi$
$563$		−	563.957i		−	1.00170i	0.865534	−	0.500850i	$-0.166979\pi$
$564$		0			0
$565$			922.620i			1.63296i
$566$		−	196.768i		−	0.347647i
$567$		0			0
$568$	−265.576			−0.467564
$569$	−608.965			−1.07024			−0.535118	−	0.844777i	$-0.679733\pi$
$569$	−608.965			−1.07024			−0.535118	+	0.844777i	$0.679733\pi$
$570$		0			0
$571$	−706.133			−1.23666			−0.618330	−	0.785918i	$-0.712191\pi$
$571$	−706.133			−1.23666			−0.618330	+	0.785918i	$0.712191\pi$
$572$	−465.622	−	268.827i	−0.814025	−	0.469977i
$573$		0			0
$574$	−109.113	+	52.3094i	−0.190092	+	0.0911314i
$575$	−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	$0.949039\pi$
$578$	60.5138	+	104.813i	0.104695	+	0.181337i
$579$		0			0
$580$	71.8966	−	41.5095i	0.123960	−	0.0715681i
$581$	46.8088	+	32.0346i	0.0805659	+	0.0551371i
$582$		0			0
$583$	−227.554			−0.390315
$584$	−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	$-0.364068\pi$
$587$	−98.0159	−	56.5895i	−0.166978	−	0.0964046i	−0.581160	+	0.813789i	$0.697401\pi$
$588$		0			0
$589$	−11.9275	−	20.6590i	−0.0202504	−	0.0350747i
$590$	499.460	−	865.090i	0.846543	−	1.46625i
$591$		0			0
$592$	−2.92846	−	5.07224i	−0.00494672	−	0.00856797i
$593$	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
$598$			280.097i			0.468390i
$599$	−181.833			−0.303561			−0.151781	−	0.988414i	$-0.548501\pi$
$599$	−181.833			−0.303561			−0.151781	+	0.988414i	$0.548501\pi$
$600$		0			0
$601$	873.672	+	504.415i	1.45370	+	0.839292i	0.998689	−	0.0511946i	$-0.0163029\pi$
$601$	873.672	+	504.415i	1.45370	+	0.839292i	0.455008	+	0.890487i	$0.349636\pi$
$602$	−448.955	+	656.010i	−0.745772	+	1.08972i
$603$		0			0
$604$	236.955	+	410.418i	0.392309	+	0.679500i
$605$	−1104.72	+	637.811i	−1.82599	+	1.05423i
$606$		0			0
$607$	434.243	+	250.710i	0.715392	+	0.413032i	0.813054	−	0.582188i	$-0.197803\pi$
$607$	434.243	+	250.710i	0.715392	+	0.413032i	−0.0976624	+	0.995220i	$0.531137\pi$
$608$	−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	$0.0537614\pi$
$614$			268.816i			0.437811i
$615$		0			0
$616$	149.416	+	311.668i	0.242558	+	0.505955i
$617$	227.440	+	393.937i	0.368622	+	0.638472i	0.989350	−	0.145554i	$-0.0464964\pi$
$617$	227.440	+	393.937i	0.368622	+	0.638472i	−0.620729	+	0.784026i	$0.713163\pi$
$618$		0			0
$619$	433.600	−	250.339i	0.700485	−	0.404425i	−0.107043	−	0.994254i	$-0.534138\pi$
$619$	433.600	−	250.339i	0.700485	−	0.404425i	0.807528	+	0.589829i	$0.200805\pi$
$620$	114.323	−	198.013i	0.184392	−	0.319375i
$621$		0			0
$622$			219.766i			0.353321i
$623$	−318.547	+	152.713i	−0.511311	+	0.245125i
$624$		0			0
$625$	333.449	−	577.551i	0.533519	−	0.924081i
$626$			801.710i			1.28069i
$627$		0			0
$628$			26.3107i			0.0418960i
$629$			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	$0.284632\pi$
$632$	347.291			0.549511
$633$		0			0
$634$	−270.691			−0.426958
$635$	1477.11	+	852.810i	2.32616	+	1.34301i
$636$		0			0
$637$	−703.373	+	273.197i	−1.10420	+	0.428881i
$638$	−147.618			−0.231377
$639$		0			0
$640$	−68.0190	−	39.2708i	−0.106280	−	0.0613606i
$641$	186.447	+	322.936i	0.290869	+	0.503800i	0.974015	−	0.226481i	$-0.0727223\pi$
$641$	186.447	+	322.936i	0.290869	+	0.503800i	−0.683146	+	0.730281i	$0.739389\pi$
$642$		0			0
$643$	−356.344	+	205.735i	−0.554190	+	0.319962i	−0.750810	−	0.660518i	$-0.770337\pi$
$643$	−356.344	+	205.735i	−0.554190	+	0.319962i	0.196620	+	0.980480i	$0.437003\pi$
$644$	101.694	−	148.595i	0.157910	−	0.230737i
$645$		0			0
$646$	29.2181			0.0452293
$647$	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
$653$	283.053	−	490.263i	0.433466	−	0.750786i	−0.563703	−	0.825978i	$-0.690624\pi$
$653$	283.053	−	490.263i	0.433466	−	0.750786i	0.997169	+	0.0751921i	$0.0239570\pi$
$654$		0			0
$655$	−750.838	−	1300.49i	−1.14632	−	1.98548i
$656$	−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	0.437931	+	0.899008i	$0.355711\pi$
$659$	−368.775	+	638.738i	−0.559599	+	0.969253i	−0.997530	+	0.0702447i	$0.977622\pi$
$660$		0			0
$661$		−	1010.40i		−	1.52859i	−0.644865	−	0.764297i	$-0.723086\pi$
$661$		−	1010.40i		−	1.52859i	0.644865	−	0.764297i	$-0.276914\pi$
$662$	−745.075			−1.12549
$663$		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
$668$	357.102	−	206.173i	0.534584	−	0.308642i
$669$		0			0
$670$	335.703	+	193.818i	0.501049	+	0.289281i
$671$	1014.73	−	585.852i	1.51226	−	0.873103i
$672$		0			0
$673$	−78.3833	+	135.764i	−0.116468	+	0.201729i	−0.918366	−	0.395733i	$-0.870491\pi$
$673$	−78.3833	+	135.764i	−0.116468	+	0.201729i	0.801897	+	0.597462i	$0.203824\pi$
$674$	237.943	+	412.129i	0.353031	+	0.611468i
$675$		0			0
$676$	68.1386	−	118.020i	0.100797	−	0.174585i
$677$			238.466i			0.352240i	0.984369	+	0.176120i	$0.0563547\pi$
$677$			238.466i			0.352240i	−0.984369	+	0.176120i	$0.943645\pi$
$678$		0			0
$679$	−539.525	−	369.236i	−0.794587	−	0.543794i
$680$	140.025	+	242.531i	0.205920	+	0.356663i
$681$		0			0
$682$	−352.092	+	203.280i	−0.516264	+	0.298065i
$683$	−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
$686$	472.336	+	110.438i	0.688537	+	0.160988i
$687$		0			0
$688$	−160.600	+	278.167i	−0.233430	+	0.404312i
$689$		−	200.731i		−	0.291336i
$690$		0			0
$691$			499.800i			0.723300i	0.932314	+	0.361650i	$0.117786\pi$
$691$			499.800i			0.723300i	−0.932314	+	0.361650i	$0.882214\pi$
$692$		−	366.898i		−	0.530199i
$693$		0			0
$694$	262.799			0.378672
$695$	1221.74			1.75790
$696$		0			0
$697$	174.335			0.250121
$698$	307.950	+	177.795i	0.441189	+	0.254721i
$699$		0			0
$700$	−140.370	−	292.801i	−0.200529	−	0.418287i
$701$	−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
$704$	69.8284	+	120.946i	0.0991880	+	0.171799i
$705$		0			0
$706$	−93.8670	+	54.1941i	−0.132956	+	0.0767622i
$707$	−887.145	+	425.302i	−1.25480	+	0.601559i
$708$		0			0
$709$	−573.786			−0.809289			−0.404645	−	0.914474i	$-0.632605\pi$
$709$	−573.786			−0.809289			−0.404645	+	0.914474i	$0.632605\pi$
$710$	−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
$716$	−39.5630	+	68.5251i	−0.0552556	+	0.0957055i
$717$		0			0
$718$	−334.747	−	579.799i	−0.466221	−	0.807519i
$719$	−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
$724$			7.35228i			0.0101551i
$725$	138.682			0.191286
$726$		0			0
$727$	−47.5157	−	27.4332i	−0.0653587	−	0.0377348i	0.466965	−	0.884276i	$-0.345348\pi$
$727$	−47.5157	−	27.4332i	−0.0653587	−	0.0377348i	−0.532323	+	0.846541i	$0.678681\pi$
$728$	−274.930	+	131.803i	−0.377651	+	0.181048i
$729$		0			0
$730$	−97.6010	−	169.050i	−0.133700	−	0.231575i
$731$	991.842	−	572.640i	1.35683	−	0.783365i
$732$		0			0
$733$	−319.740	−	184.602i	−0.436208	−	0.251845i	0.265780	−	0.964034i	$-0.414370\pi$
$733$	−319.740	−	184.602i	−0.436208	−	0.251845i	−0.701988	+	0.712189i	$0.747704\pi$
$734$	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	$0.897975\pi$
$740$		−	20.3298i		−	0.0274727i
$741$		0			0
$742$	−72.8787	+	106.490i	−0.0982193	+	0.143517i
$743$	184.560	+	319.667i	0.248398	+	0.430238i	0.963082	−	0.269210i	$-0.0867625\pi$
$743$	184.560	+	319.667i	0.248398	+	0.430238i	−0.714683	+	0.699448i	$0.753429\pi$
$744$		0			0
$745$	−1208.00	+	697.440i	−1.62148	+	0.936161i
$746$	386.195	−	668.910i	0.517688	−	0.896662i
$747$		0			0
$748$		−	497.966i		−	0.665729i
$749$	68.7670	+	143.442i	0.0918118	+	0.191512i
$750$		0			0
$751$	327.659	−	567.522i	0.436297	−	0.755689i	−0.561103	−	0.827746i	$-0.689623\pi$
$751$	327.659	−	567.522i	0.436297	−	0.755689i	0.997401	+	0.0720568i	$0.0229563\pi$
$752$			334.589i			0.444933i
$753$		0			0
$754$		−	130.218i		−	0.172702i
$755$			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	$0.446928\pi$
$758$	−545.357			−0.719468
$759$		0			0
$760$	−28.4433			−0.0374254
$761$	750.816	+	433.484i	0.986617	+	0.569624i	0.904261	−	0.426979i	$-0.140422\pi$
$761$	750.816	+	433.484i	0.986617	+	0.569624i	0.0823559	+	0.996603i	$0.473756\pi$
$762$		0			0
$763$	−619.453	+	905.140i	−0.811865	+	1.18629i
$764$	95.7559			0.125335
$765$		0			0
$766$	−59.5488	−	34.3805i	−0.0777400	−	0.0448832i
$767$	−783.416	−	1356.92i	−1.02140	−	1.76912i
$768$		0			0
$769$	40.8679	−	23.5951i	0.0531442	−	0.0306828i	−0.473193	−	0.880959i	$-0.656898\pi$
$769$	40.8679	−	23.5951i	0.0531442	−	0.0306828i	0.526337	+	0.850276i	$0.323565\pi$
$770$	−91.7629	+	1196.20i	−0.119173	+	1.55351i
$771$		0			0
$772$	116.974			0.151521
$773$	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
$779$	−8.85312	+	15.3341i	−0.0113647	+	0.0196843i
$780$		0			0
$781$	819.571	+	1419.54i	1.04939	+	1.81759i
$782$	−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
$787$			975.179i			1.23911i	0.784953	+	0.619555i	$0.212687\pi$
$787$			975.179i			1.23911i	−0.784953	+	0.619555i	$0.787313\pi$
$788$	407.962			0.517718
$789$		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
$794$	−806.391	+	465.570i	−1.01561	+	0.586360i
$795$		0			0
$796$	−292.260	−	168.736i	−0.367161	−	0.211980i
$797$	−1053.12	+	608.022i	−1.32136	+	0.762888i	−0.983946	−	0.178468i	$-0.942886\pi$
$797$	−1053.12	+	608.022i	−1.32136	+	0.762888i	−0.337415	+	0.941356i	$0.609553\pi$
$798$		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
$803$			347.094i			0.432246i
$804$		0			0
$805$	563.589	−	270.188i	0.700111	−	0.335637i
$806$	−179.318	−	310.588i	−0.222479	−	0.385345i
$807$		0			0
$808$	−344.266	+	198.762i	−0.426072	+	0.245993i
$809$	−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	$0.827127\pi$
$812$	−47.2778	+	69.0819i	−0.0582238	+	0.0850762i
$813$		0			0
$814$	−18.0745	+	31.3059i	−0.0222045	+	0.0384594i
$815$		−	1271.03i		−	1.55955i
$816$		0			0
$817$			116.320i			0.142375i
$818$		−	324.789i		−	0.397052i
$819$		0			0
$820$	−169.711			−0.206965
$821$	−788.378			−0.960265			−0.480133	−	0.877196i	$-0.659411\pi$
$821$	−788.378			−0.960265			−0.480133	+	0.877196i	$0.659411\pi$
$822$		0			0
$823$	400.688			0.486863			0.243432	−	0.969918i	$-0.421727\pi$
$823$	400.688			0.486863			0.243432	+	0.969918i	$0.421727\pi$
$824$	88.4424	+	51.0622i	0.107333	+	0.0619687i
$825$		0			0
$826$	−77.0411	+	1004.29i	−0.0932701	+	1.21585i
$827$	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	$0.446313\pi$
$830$	39.7764	+	68.8948i	0.0479234	+	0.0830058i
$831$		0			0
$832$	−106.690	+	61.5972i	−0.128233	+	0.0740351i
$833$	−544.856	−	437.658i	−0.654089	−	0.525400i
$834$		0			0
$835$	1431.29			1.71412
$836$	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	$-0.487769\pi$
$839$	−677.714	−	391.278i	−0.807764	−	0.466363i	−0.846179	+	0.532899i	$0.821103\pi$
$840$		0			0
$841$	402.624	+	697.365i	0.478744	+	0.829209i
$842$	−44.2356	+	76.6184i	−0.0525364	+	0.0909957i
$843$		0			0
$844$	48.7874	+	84.5022i	0.0578050	+	0.100121i
$845$	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
$850$			467.821i			0.550377i
$851$	18.8322			0.0221295
$852$		0			0
$853$	−72.1792	−	41.6727i	−0.0846180	−	0.0488542i	0.457094	−	0.889418i	$-0.348890\pi$
$853$	−72.1792	−	41.6727i	−0.0846180	−	0.0488542i	−0.541712	+	0.840564i	$0.682224\pi$
$854$	50.8214	−	662.499i	0.0595099	−	0.775759i
$855$		0			0
$856$	32.1378	+	55.6643i	0.0375442	+	0.0650284i
$857$	223.760	−	129.188i	0.261097	−	0.150744i	−0.363738	−	0.931501i	$-0.618500\pi$
$857$	223.760	−	129.188i	0.261097	−	0.150744i	0.624835	+	0.780757i	$0.285166\pi$
$858$		0			0
$859$	−343.478	−	198.307i	−0.399858	−	0.230858i	0.286565	−	0.958061i	$-0.407487\pi$
$859$	−343.478	−	198.307i	−0.399858	−	0.230858i	−0.686423	+	0.727203i	$0.740820\pi$
$860$	−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
$866$		−	314.218i		−	0.362838i
$867$		0			0
$868$	−17.6341	+	229.875i	−0.0203158	+	0.264833i
$869$	−1071.74	−	1856.31i	−1.23331	−	2.13615i
$870$		0			0
$871$	526.559	−	304.009i	0.604545	−	0.349034i
$872$	−221.590	+	383.805i	−0.254117	+	0.440143i
$873$		0			0
$874$		−	26.3480i		−	0.0301465i
$875$	−6.71444	+	87.5282i	−0.00767365	+	0.100032i
$876$		0			0
$877$	198.926	−	344.551i	0.226826	−	0.392874i	−0.730040	−	0.683405i	$-0.760498\pi$
$877$	198.926	−	344.551i	0.226826	−	0.392874i	0.956866	+	0.290530i	$0.0938318\pi$
$878$			540.561i			0.615673i
$879$		0			0
$880$			484.760i			0.550863i
$881$			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	$0.497050\pi$
$884$	439.267			0.496908
$885$		0			0
$886$	26.0581			0.0294110
$887$	558.172	+	322.261i	0.629281	+	0.363315i	0.780473	−	0.625189i	$-0.214978\pi$
$887$	558.172	+	322.261i	0.629281	+	0.363315i	−0.151193	+	0.988504i	$0.548311\pi$
$888$		0			0
$889$	−1714.79	−	131.545i	−1.92890	−	0.147969i
$890$	−495.458			−0.556694
$891$		0			0
$892$	317.938	+	183.561i	0.356432	+	0.205786i
$893$	60.5846	+	104.936i	0.0678439	+	0.117509i
$894$		0			0
$895$	−237.856	+	137.326i	−0.265761	+	0.153437i
$896$	78.9640	+	6.05746i	0.0881294	+	0.00676056i
$897$		0			0
$898$	541.709			0.603239
$899$	−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
$905$	−12.7602	+	22.1013i	−0.0140996	+	0.0244213i
$906$		0			0
$907$	−793.972	−	1375.20i	−0.875383	−	1.51621i	−0.856354	−	0.516389i	$-0.827276\pi$
$907$	−793.972	−	1375.20i	−0.875383	−	1.51621i	−0.0190283	−	0.999819i	$-0.506057\pi$
$908$	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	−0.0744605	−	0.997224i	$-0.523723\pi$
$911$	752.842	−	1303.96i	0.826391	−	1.43135i	0.900852	−	0.434127i	$-0.142943\pi$
$912$		0			0
$913$		−	141.455i		−	0.154934i
$914$	−170.081			−0.186084
$915$		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	$-0.385839\pi$
$920$	218.707	−	126.271i	0.237725	−	0.137251i
$921$		0			0
$922$	25.3765	+	14.6512i	0.0275234	+	0.0158906i
$923$	−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
$929$		−	598.256i		−	0.643978i	−0.946743	−	0.321989i	$-0.895649\pi$
$929$		−	598.256i		−	0.643978i	0.946743	−	0.321989i	$-0.104351\pi$
$930$		0			0
$931$	66.1644	−	25.6989i	0.0710682	−	0.0276036i
$932$	−22.7147	−	39.3430i	−0.0243720	−	0.0422135i
$933$		0			0
$934$	508.077	−	293.339i	0.543980	−	0.314067i
$935$	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	$-0.00959954\pi$
$938$	−389.721	−	29.8962i	−0.415481	−	0.0318723i
$939$		0			0
$940$	−580.693	+	1005.79i	−0.617759	+	1.06999i
$941$		−	1684.00i		−	1.78958i	−0.446483	−	0.894792i	$-0.647324\pi$
$941$		−	1684.00i		−	1.78958i	0.446483	−	0.894792i	$-0.352676\pi$
$942$		0			0
$943$		−	157.210i		−	0.166712i
$944$			406.988i			0.431131i
$945$		0			0
$946$	1982.45			2.09561
$947$	888.217			0.937927			0.468964	−	0.883218i	$-0.344628\pi$
$947$	888.217			0.937927			0.468964	+	0.883218i	$0.344628\pi$
$948$		0			0
$949$	−306.179			−0.322634
$950$	−41.1484	−	23.7570i	−0.0433141	−	0.0250074i
$951$		0			0
$952$	−233.036	−	159.484i	−0.244786	−	0.167525i
$953$	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
$956$	34.4587	+	59.6843i	0.0360447	+	0.0624313i
$957$		0			0
$958$	−183.257	+	105.804i	−0.191291	+	0.110442i
$959$	304.858	+	635.907i	0.317891	+	0.663094i
$960$		0			0
$961$	689.808			0.717803
$962$	−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	−0.927203	−	0.374558i	$-0.877794\pi$
$967$	−761.975	−	1319.78i	−0.787979	−	1.36482i	0.139225	−	0.990261i	$-0.455539\pi$
$968$	259.862	−	450.094i	0.268452	−	0.464973i
$969$		0			0
$970$	−458.469	−	794.091i	−0.472648	−	0.818651i
$971$	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
$976$		−	268.476i		−	0.275078i
$977$	452.332			0.462981			0.231490	−	0.972837i	$-0.425640\pi$
$977$	452.332			0.462981			0.231490	+	0.972837i	$0.425640\pi$
$978$		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
$983$	−770.670	+	444.947i	−0.783998	+	0.452642i	−0.837845	−	0.545908i	$-0.816185\pi$
$983$	−770.670	+	444.947i	−0.783998	+	0.452642i	0.0538472	+	0.998549i	$0.482852\pi$
$984$		0			0
$985$	1226.35	+	708.033i	1.24502	+	0.718815i
$986$	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	$0.215729\pi$
$992$			93.1565i			0.0939078i
$993$		0			0
$994$	926.795	+	71.0961i	0.932389	+	0.0715252i
$995$	−585.697	−	1014.46i	−0.588640	−	1.01955i
$996$		0			0
$997$	1582.27	−	913.526i	1.58704	−	0.916275i	0.593243	−	0.805023i	$-0.297847\pi$
$997$	1582.27	−	913.526i	1.58704	−	0.916275i	0.993792	−	0.111252i	$-0.0354860\pi$
$998$	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.p.a.73.7		32
3.2	odd	2		126.3.p.a.115.9	yes	32
7.5	odd	6		378.3.j.a.19.15		32
9.4	even	3		378.3.j.a.199.10		32
9.5	odd	6		126.3.j.a.31.3	✓	32
21.5	even	6		126.3.j.a.61.3	yes	32
63.5	even	6		126.3.p.a.103.9	yes	32
63.40	odd	6	inner	378.3.p.a.145.7		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.3.j.a.31.3	✓	32	9.5	odd	6
126.3.j.a.61.3	yes	32	21.5	even	6
126.3.p.a.103.9	yes	32	63.5	even	6
126.3.p.a.115.9	yes	32	3.2	odd	2
378.3.j.a.19.15		32	7.5	odd	6
378.3.j.a.199.10		32	9.4	even	3
378.3.p.a.73.7		32	1.1	even	1	trivial
378.3.p.a.145.7		32	63.40	odd	6	inner

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.p (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-1.41421 q^{2} +2.00000 q^{4} +(6.01208 + 3.47108i) q^{5} +(-6.97949 - 0.535409i) q^{7} -2.82843 q^{8} +O(q^{10})\)	\(q-1.41421 q^{2} +2.00000 q^{4} +(6.01208 + 3.47108i) q^{5} +(-6.97949 - 0.535409i) q^{7} -2.82843 q^{8} +(-8.50237 - 4.90885i) q^{10} +(8.72855 + 15.1183i) q^{11} +(-13.3362 + 7.69965i) q^{13} +(9.87050 + 0.757183i) q^{14} +4.00000 q^{16} +(-12.3517 - 7.13128i) q^{17} +(1.25450 - 0.724286i) q^{19} +(12.0242 + 6.94216i) q^{20} +(-12.3440 - 21.3805i) q^{22} +(-6.43077 + 11.1384i) q^{23} +(11.5968 + 20.0862i) q^{25} +(18.8602 - 10.8890i) q^{26} +(-13.9590 - 1.07082i) q^{28} +(2.98967 - 5.17826i) q^{29} -16.4679i q^{31} -5.65685 q^{32} +(17.4680 + 10.0852i) q^{34} +(-40.1029 - 27.4453i) q^{35} +(-0.732115 - 1.26806i) q^{37} +(-1.77413 + 1.02430i) q^{38} +(-17.0047 - 9.81769i) q^{40} +(-10.5856 + 6.11162i) q^{41} +(-40.1499 + 69.5416i) q^{43} +(17.4571 + 30.2366i) q^{44} +(9.09448 - 15.7521i) q^{46} +83.6474i q^{47} +(48.4267 + 7.47377i) q^{49} +(-16.4003 - 28.4062i) q^{50} +(-26.6724 + 15.3993i) q^{52} +(-6.51752 + 11.2887i) q^{53} +121.190i q^{55} +(19.7410 + 1.51437i) q^{56} +(-4.22803 + 7.32317i) q^{58} +101.747i q^{59} -67.1191i q^{61} +23.2891i q^{62} +8.00000 q^{64} -106.904 q^{65} -39.4835 q^{67} +(-24.7035 - 14.2626i) q^{68} +(56.7140 + 38.8135i) q^{70} +93.8955 q^{71} +(17.2189 + 9.94134i) q^{73} +(1.03537 + 1.79331i) q^{74} +(2.50900 - 1.44857i) q^{76} +(-52.8264 - 110.191i) q^{77} -122.786 q^{79} +(24.0483 + 13.8843i) q^{80} +(14.9703 - 8.64313i) q^{82} +(-7.01741 - 4.05150i) q^{83} +(-49.5065 - 85.7477i) q^{85} +(56.7805 - 98.3467i) q^{86} +(-24.6881 - 42.7610i) q^{88} +(43.7047 - 25.2329i) q^{89} +(97.2023 - 46.5994i) q^{91} +(-12.8615 + 22.2768i) q^{92} -118.295i q^{94} +10.0562 q^{95} +(80.8837 + 46.6982i) q^{97} +(-68.4857 - 10.5695i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 64 q^{4} - 2 q^{7}+O(q^{10}) \) 32 * q + 64 * q^4 - 2 * q^7	\( 32 q + 64 q^{4} - 2 q^{7} + 12 q^{11} + 30 q^{13} + 12 q^{14} + 128 q^{16} - 54 q^{17} + 42 q^{23} + 80 q^{25} + 72 q^{26} - 4 q^{28} + 84 q^{29} + 66 q^{35} - 22 q^{37} + 396 q^{41} - 16 q^{43} + 24 q^{44} + 12 q^{46} + 50 q^{49} + 96 q^{50} + 60 q^{52} + 252 q^{53} + 24 q^{56} - 24 q^{58} + 256 q^{64} - 12 q^{65} - 140 q^{67} - 108 q^{68} + 72 q^{70} - 300 q^{71} + 72 q^{74} - 570 q^{77} - 212 q^{79} - 756 q^{83} - 60 q^{85} + 120 q^{86} - 414 q^{89} - 186 q^{91} + 84 q^{92} - 1104 q^{95} - 114 q^{97} + 96 q^{98}+O(q^{100}) \) 32 * q + 64 * q^4 - 2 * q^7 + 12 * q^11 + 30 * q^13 + 12 * q^14 + 128 * q^16 - 54 * q^17 + 42 * q^23 + 80 * q^25 + 72 * q^26 - 4 * q^28 + 84 * q^29 + 66 * q^35 - 22 * q^37 + 396 * q^41 - 16 * q^43 + 24 * q^44 + 12 * q^46 + 50 * q^49 + 96 * q^50 + 60 * q^52 + 252 * q^53 + 24 * q^56 - 24 * q^58 + 256 * q^64 - 12 * q^65 - 140 * q^67 - 108 * q^68 + 72 * q^70 - 300 * q^71 + 72 * q^74 - 570 * q^77 - 212 * q^79 - 756 * q^83 - 60 * q^85 + 120 * q^86 - 414 * q^89 - 186 * q^91 + 84 * q^92 - 1104 * q^95 - 114 * q^97 + 96 * q^98

Introduction

L-functions

Modular forms

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Database

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