LMFDB - Embedded newform 912.3.be.d.145.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [912,3,Mod(145,912)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(912, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 5]))

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

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

chi := DirichletCharacter("912.145");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 912 = 2^{4} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	912.be (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:	$24.8502001097$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{6})$
Coefficient field:	6.0.6967728.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 8x^{4} + 5x^{3} + 50x^{2} - 7x + 1 $ x^6 - x^5 + 8x^4 + 5x^3 + 50x^2 - 7x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 57)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			145.2
Root			$0.0702177 + 0.121621i$ of defining polynomial
Character	$\chi$	$=$	912.145
Dual form			912.3.be.d.673.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.50000 + 0.866025i) q^{3} +(-0.140435 - 0.243241i) q^{5} +5.24143 q^{7} +(1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(q+(-1.50000 + 0.866025i) q^{3} +(-0.140435 - 0.243241i) q^{5} +5.24143 q^{7} +(1.50000 - 2.59808i) q^{9} +1.15739 q^{11} +(-6.32289 - 3.65052i) q^{13} +(0.421306 + 0.243241i) q^{15} +(7.52230 + 13.0290i) q^{17} +(-1.52230 + 18.9389i) q^{19} +(-7.86214 + 4.53921i) q^{21} +(13.3819 - 23.1781i) q^{23} +(12.4606 - 21.5823i) q^{25} +5.19615i q^{27} +(-7.76372 - 4.48239i) q^{29} +11.7968i q^{31} +(-1.73608 + 1.00233i) q^{33} +(-0.736082 - 1.27493i) q^{35} -36.1681i q^{37} +12.6458 q^{39} +(40.3701 - 23.3077i) q^{41} +(-1.64044 - 2.84132i) q^{43} -0.842612 q^{45} +(-26.3199 + 45.5874i) q^{47} -21.5274 q^{49} +(-22.5669 - 13.0290i) q^{51} +(88.0273 + 50.8226i) q^{53} +(-0.162538 - 0.281524i) q^{55} +(-14.1181 - 29.7267i) q^{57} +(39.8304 - 22.9961i) q^{59} +(-50.7162 + 87.8430i) q^{61} +(7.86214 - 13.6176i) q^{63} +2.05065i q^{65} +(50.9209 + 29.3992i) q^{67} +46.3561i q^{69} +(90.7243 - 52.3797i) q^{71} +(63.1115 + 109.312i) q^{73} +43.1646i q^{75} +6.06636 q^{77} +(55.9406 - 32.2973i) q^{79} +(-4.50000 - 7.79423i) q^{81} +22.0789 q^{83} +(2.11279 - 3.65947i) q^{85} +15.5274 q^{87} +(107.579 + 62.1106i) q^{89} +(-33.1410 - 19.1339i) q^{91} +(-10.2164 - 17.6953i) q^{93} +(4.82051 - 2.28941i) q^{95} +(162.700 - 93.9348i) q^{97} +(1.73608 - 3.00698i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 9 q^{3} - 2 q^{5} - 26 q^{7} + 9 q^{9}+O(q^{10}) $ 6 * q - 9 * q^3 - 2 * q^5 - 26 * q^7 + 9 * q^9	$ 6 q - 9 q^{3} - 2 q^{5} - 26 q^{7} + 9 q^{9} - 15 q^{13} + 6 q^{15} - 10 q^{17} + 46 q^{19} + 39 q^{21} + 24 q^{23} + 15 q^{25} + 66 q^{29} + 6 q^{35} + 30 q^{39} + 24 q^{41} - 11 q^{43} - 12 q^{45} + 26 q^{47} + 96 q^{49} + 30 q^{51} + 180 q^{53} + 176 q^{55} - 141 q^{57} - 162 q^{59} - 141 q^{61} - 39 q^{63} + 63 q^{67} + 372 q^{71} + 103 q^{73} - 16 q^{77} + 123 q^{79} - 27 q^{81} + 252 q^{83} + 116 q^{85} - 132 q^{87} + 642 q^{89} - 87 q^{91} - 21 q^{93} + 214 q^{95} - 12 q^{97}+O(q^{100}) $ 6 * q - 9 * q^3 - 2 * q^5 - 26 * q^7 + 9 * q^9 - 15 * q^13 + 6 * q^15 - 10 * q^17 + 46 * q^19 + 39 * q^21 + 24 * q^23 + 15 * q^25 + 66 * q^29 + 6 * q^35 + 30 * q^39 + 24 * q^41 - 11 * q^43 - 12 * q^45 + 26 * q^47 + 96 * q^49 + 30 * q^51 + 180 * q^53 + 176 * q^55 - 141 * q^57 - 162 * q^59 - 141 * q^61 - 39 * q^63 + 63 * q^67 + 372 * q^71 + 103 * q^73 - 16 * q^77 + 123 * q^79 - 27 * q^81 + 252 * q^83 + 116 * q^85 - 132 * q^87 + 642 * q^89 - 87 * q^91 - 21 * q^93 + 214 * q^95 - 12 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/912\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$305$	$799$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.50000	+	0.866025i	−0.500000	+	0.288675i
$3$	−1.50000	+	0.866025i	−0.500000	+	0.288675i
$4$		0			0
$5$	−0.140435	−	0.243241i	−0.0280871	−	0.0486482i	0.851640	−	0.524127i	$-0.175608\pi$
$5$	−0.140435	−	0.243241i	−0.0280871	−	0.0486482i	−0.879727	+	0.475479i	$0.842275\pi$
$6$		0			0
$7$	5.24143			0.748775			0.374388	−	0.927272i	$-0.377853\pi$
$7$	5.24143			0.748775			0.374388	+	0.927272i	$0.377853\pi$
$8$		0			0
$9$	1.50000	−	2.59808i	0.166667	−	0.288675i
$10$		0			0
$11$	1.15739			0.105217			0.0526085	−	0.998615i	$-0.483246\pi$
$11$	1.15739			0.105217			0.0526085	+	0.998615i	$0.483246\pi$
$12$		0			0
$13$	−6.32289	−	3.65052i	−0.486376	−	0.280809i	0.236694	−	0.971584i	$-0.423936\pi$
$13$	−6.32289	−	3.65052i	−0.486376	−	0.280809i	−0.723070	+	0.690775i	$0.757270\pi$
$14$		0			0
$15$	0.421306	+	0.243241i	0.0280871	+	0.0162161i
$16$		0			0
$17$	7.52230	+	13.0290i	0.442488	+	0.766412i	0.997873	−	0.0651813i	$-0.0207626\pi$
$17$	7.52230	+	13.0290i	0.442488	+	0.766412i	−0.555385	+	0.831593i	$0.687429\pi$
$18$		0			0
$19$	−1.52230	+	18.9389i	−0.0801209	+	0.996785i
$19$	−1.52230	+	18.9389i	−0.0801209	+	0.996785i
$20$		0			0
$21$	−7.86214	+	4.53921i	−0.374388	+	0.216153i
$22$		0			0
$23$	13.3819	−	23.1781i	0.581820	−	1.00774i	−0.413444	−	0.910530i	$-0.635674\pi$
$23$	13.3819	−	23.1781i	0.581820	−	1.00774i	0.995264	−	0.0972122i	$-0.0309926\pi$
$24$		0			0
$25$	12.4606	−	21.5823i	0.498422	−	0.863293i
$26$		0			0
$27$			5.19615i			0.192450i
$28$		0			0
$29$	−7.76372	−	4.48239i	−0.267715	−	0.154565i	0.360134	−	0.932901i	$-0.382731\pi$
$29$	−7.76372	−	4.48239i	−0.267715	−	0.154565i	−0.627849	+	0.778335i	$0.716064\pi$
$30$		0			0
$31$			11.7968i			0.380543i	0.981732	+	0.190272i	$0.0609368\pi$
$31$			11.7968i			0.380543i	−0.981732	+	0.190272i	$0.939063\pi$
$32$		0			0
$33$	−1.73608	+	1.00233i	−0.0526085	+	0.0303736i
$34$		0			0
$35$	−0.736082	−	1.27493i	−0.0210309	−	0.0364266i
$36$		0			0
$37$		−	36.1681i		−	0.977516i	−0.872419	−	0.488758i	$-0.837450\pi$
$37$		−	36.1681i		−	0.977516i	0.872419	−	0.488758i	$-0.162550\pi$
$38$		0			0
$39$	12.6458			0.324251
$40$		0			0
$41$	40.3701	−	23.3077i	0.984636	−	0.568480i	0.0809691	−	0.996717i	$-0.474198\pi$
$41$	40.3701	−	23.3077i	0.984636	−	0.568480i	0.903666	+	0.428237i	$0.140865\pi$
$42$		0			0
$43$	−1.64044	−	2.84132i	−0.0381497	−	0.0660771i	0.846320	−	0.532675i	$-0.178813\pi$
$43$	−1.64044	−	2.84132i	−0.0381497	−	0.0660771i	−0.884470	+	0.466597i	$0.845480\pi$
$44$		0			0
$45$	−0.842612			−0.0187247
$46$		0			0
$47$	−26.3199	+	45.5874i	−0.559998	+	0.969946i	0.437497	+	0.899220i	$0.355865\pi$
$47$	−26.3199	+	45.5874i	−0.559998	+	0.969946i	−0.997496	+	0.0707260i	$0.977468\pi$
$48$		0			0
$49$	−21.5274			−0.439336
$50$		0			0
$51$	−22.5669	−	13.0290i	−0.442488	−	0.255471i
$52$		0			0
$53$	88.0273	+	50.8226i	1.66089	+	0.958916i	0.972291	+	0.233776i	$0.0751082\pi$
$53$	88.0273	+	50.8226i	1.66089	+	0.958916i	0.688601	+	0.725140i	$0.258225\pi$
$54$		0			0
$55$	−0.162538	−	0.281524i	−0.00295524	−	0.00511863i
$56$		0			0
$57$	−14.1181	−	29.7267i	−0.247687	−	0.521521i
$58$		0			0
$59$	39.8304	−	22.9961i	0.675092	−	0.389764i	−0.122911	−	0.992418i	$-0.539223\pi$
$59$	39.8304	−	22.9961i	0.675092	−	0.389764i	0.798003	+	0.602653i	$0.205890\pi$
$60$		0			0
$61$	−50.7162	+	87.8430i	−0.831413	+	1.44005i	0.0655056	+	0.997852i	$0.479134\pi$
$61$	−50.7162	+	87.8430i	−0.831413	+	1.44005i	−0.896918	+	0.442197i	$0.854199\pi$
$62$		0			0
$63$	7.86214	−	13.6176i	0.124796	−	0.216153i
$64$		0			0
$65$			2.05065i			0.0315485i
$66$		0			0
$67$	50.9209	+	29.3992i	0.760014	+	0.438794i	0.829301	−	0.558803i	$-0.188739\pi$
$67$	50.9209	+	29.3992i	0.760014	+	0.438794i	−0.0692870	+	0.997597i	$0.522072\pi$
$68$		0			0
$69$			46.3561i			0.671828i
$70$		0			0
$71$	90.7243	−	52.3797i	1.27781	−	0.737742i	0.301362	−	0.953510i	$-0.402559\pi$
$71$	90.7243	−	52.3797i	1.27781	−	0.737742i	0.976445	+	0.215768i	$0.0692254\pi$
$72$		0			0
$73$	63.1115	+	109.312i	0.864541	+	1.49743i	0.867502	+	0.497433i	$0.165724\pi$
$73$	63.1115	+	109.312i	0.864541	+	1.49743i	−0.00296139	+	0.999996i	$0.500943\pi$
$74$		0			0
$75$			43.1646i			0.575528i
$76$		0			0
$77$	6.06636			0.0787839
$78$		0			0
$79$	55.9406	−	32.2973i	0.708109	−	0.408827i	−0.102251	−	0.994759i	$-0.532605\pi$
$79$	55.9406	−	32.2973i	0.708109	−	0.408827i	0.810361	+	0.585931i	$0.199271\pi$
$80$		0			0
$81$	−4.50000	−	7.79423i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	22.0789			0.266011			0.133005	−	0.991115i	$-0.457537\pi$
$83$	22.0789			0.266011			0.133005	+	0.991115i	$0.457537\pi$
$84$		0			0
$85$	2.11279	−	3.65947i	0.0248564	−	0.0430525i
$86$		0			0
$87$	15.5274			0.178476
$88$		0			0
$89$	107.579	+	62.1106i	1.20875	+	0.697872i	0.962486	−	0.271331i	$-0.0874639\pi$
$89$	107.579	+	62.1106i	1.20875	+	0.697872i	0.246263	+	0.969203i	$0.420797\pi$
$90$		0			0
$91$	−33.1410	−	19.1339i	−0.364186	−	0.210263i
$92$		0			0
$93$	−10.2164	−	17.6953i	−0.109853	−	0.190272i
$94$		0			0
$95$	4.82051	−	2.28941i	0.0507422	−	0.0240990i
$96$		0			0
$97$	162.700	−	93.9348i	1.67732	−	0.968400i	0.713959	−	0.700188i	$-0.246900\pi$
$97$	162.700	−	93.9348i	1.67732	−	0.968400i	0.963360	−	0.268213i	$-0.0864330\pi$
$98$		0			0
$99$	1.73608	−	3.00698i	0.0175362	−	0.0303736i
$100$		0			0
$101$	19.8478	−	34.3773i	0.196513	−	0.340370i	−0.750883	−	0.660435i	$-0.770372\pi$
$101$	19.8478	−	34.3773i	0.196513	−	0.340370i	0.947395	+	0.320066i	$0.103705\pi$
$102$		0			0
$103$			26.7360i			0.259573i	0.991542	+	0.129787i	$0.0414292\pi$
$103$			26.7360i			0.259573i	−0.991542	+	0.129787i	$0.958571\pi$
$104$		0			0
$105$	2.20825	+	1.27493i	0.0210309	+	0.0121422i
$106$		0			0
$107$		−	61.9439i		−	0.578915i	−0.957191	−	0.289458i	$-0.906525\pi$
$107$		−	61.9439i		−	0.578915i	0.957191	−	0.289458i	$-0.0934749\pi$
$108$		0			0
$109$	30.9996	−	17.8976i	0.284400	−	0.164198i	−0.351014	−	0.936370i	$-0.614163\pi$
$109$	30.9996	−	17.8976i	0.284400	−	0.164198i	0.635414	+	0.772172i	$0.280830\pi$
$110$		0			0
$111$	31.3225	+	54.2522i	0.282185	+	0.488758i
$112$		0			0
$113$			106.018i			0.938215i	0.883141	+	0.469108i	$0.155424\pi$
$113$			106.018i			0.938215i	−0.883141	+	0.469108i	$0.844576\pi$
$114$		0			0
$115$	−7.51715			−0.0653665
$116$		0			0
$117$	−18.9687	+	10.9516i	−0.162125	+	0.0936031i
$118$		0			0
$119$	39.4276	+	68.2906i	0.331324	+	0.573870i
$120$		0			0
$121$	−119.660			−0.988929
$122$		0			0
$123$	−40.3701	+	69.9230i	−0.328212	+	0.568480i
$124$		0			0
$125$	−14.0214			−0.112171
$126$		0			0
$127$	97.9362	+	56.5435i	0.771151	+	0.445224i	0.833285	−	0.552844i	$-0.186457\pi$
$127$	97.9362	+	56.5435i	0.771151	+	0.445224i	−0.0621341	+	0.998068i	$0.519791\pi$
$128$		0			0
$129$	4.92131	+	2.84132i	0.0381497	+	0.0220257i
$130$		0			0
$131$	64.7582	+	112.164i	0.494337	+	0.856217i	0.999979	−	0.00652644i	$-0.00207745\pi$
$131$	64.7582	+	112.164i	0.494337	+	0.856217i	−0.505641	+	0.862744i	$0.668744\pi$
$132$		0			0
$133$	−7.97901	+	99.2669i	−0.0599926	+	0.746368i
$134$		0			0
$135$	1.26392	−	0.729724i	0.00936236	−	0.00540536i
$136$		0			0
$137$	21.4880	−	37.2183i	0.156847	−	0.271667i	−0.776883	−	0.629645i	$-0.783200\pi$
$137$	21.4880	−	37.2183i	0.156847	−	0.271667i	0.933730	+	0.357978i	$0.116534\pi$
$138$		0			0
$139$	−104.196	+	180.473i	−0.749613	+	1.29837i	0.198395	+	0.980122i	$0.436427\pi$
$139$	−104.196	+	180.473i	−0.749613	+	1.29837i	−0.948008	+	0.318246i	$0.896906\pi$
$140$		0			0
$141$		−	91.1749i		−	0.646630i
$142$		0			0
$143$	−7.31804	−	4.22507i	−0.0511751	−	0.0295459i
$144$		0			0
$145$			2.51794i			0.0173651i
$146$		0			0
$147$	32.2912	−	18.6433i	0.219668	−	0.126825i
$148$		0			0
$149$	−69.2344	−	119.917i	−0.464660	−	0.804815i	0.534526	−	0.845152i	$-0.320490\pi$
$149$	−69.2344	−	119.917i	−0.464660	−	0.804815i	−0.999186	+	0.0403369i	$0.987157\pi$
$150$		0			0
$151$		−	265.635i		−	1.75917i	−0.475739	−	0.879586i	$-0.657819\pi$
$151$		−	265.635i		−	1.75917i	0.475739	−	0.879586i	$-0.342181\pi$
$152$		0			0
$153$	45.1338			0.294992
$154$		0			0
$155$	2.86948	−	1.65669i	0.0185128	−	0.0106883i
$156$		0			0
$157$	−52.4464	−	90.8398i	−0.334053	−	0.578597i	0.649249	−	0.760576i	$-0.275083\pi$
$157$	−52.4464	−	90.8398i	−0.334053	−	0.578597i	−0.983303	+	0.181978i	$0.941750\pi$
$158$		0			0
$159$	−176.055			−1.10726
$160$		0			0
$161$	70.1400	−	121.486i	0.435652	−	0.754572i
$162$		0			0
$163$	−89.1556			−0.546967			−0.273483	−	0.961877i	$-0.588176\pi$
$163$	−89.1556			−0.546967			−0.273483	+	0.961877i	$0.588176\pi$
$164$		0			0
$165$	0.487615	+	0.281524i	0.00295524	+	0.00170621i
$166$		0			0
$167$	−20.7589	−	11.9852i	−0.124305	−	0.0717674i	0.436558	−	0.899676i	$-0.356197\pi$
$167$	−20.7589	−	11.9852i	−0.124305	−	0.0717674i	−0.560863	+	0.827909i	$0.689531\pi$
$168$		0			0
$169$	−57.8474	−	100.195i	−0.342292	−	0.592867i
$170$		0			0
$171$	46.9213	+	32.3634i	0.274394	+	0.189260i
$172$		0			0
$173$	48.4169	−	27.9535i	0.279866	−	0.161581i	−0.353497	−	0.935436i	$-0.615007\pi$
$173$	48.4169	−	27.9535i	0.279866	−	0.161581i	0.633363	+	0.773855i	$0.281674\pi$
$174$		0			0
$175$	65.3111	−	113.122i	0.373206	−	0.646412i
$176$		0			0
$177$	−39.8304	+	68.9883i	−0.225031	+	0.389764i
$178$		0			0
$179$			191.121i			1.06771i	0.845575	+	0.533856i	$0.179258\pi$
$179$			191.121i			1.06771i	−0.845575	+	0.533856i	$0.820742\pi$
$180$		0			0
$181$	74.2912	+	42.8920i	0.410448	+	0.236973i	0.690982	−	0.722872i	$-0.257178\pi$
$181$	74.2912	+	42.8920i	0.410448	+	0.236973i	−0.280534	+	0.959844i	$0.590512\pi$
$182$		0			0
$183$		−	175.686i		−	0.960033i
$184$		0			0
$185$	−8.79757	+	5.07928i	−0.0475545	+	0.0274556i
$186$		0			0
$187$	8.70621	+	15.0796i	0.0465573	+	0.0806396i
$188$		0			0
$189$			27.2353i			0.144102i
$190$		0			0
$191$	328.175			1.71820			0.859098	−	0.511811i	$-0.171025\pi$
$191$	328.175			1.71820			0.859098	+	0.511811i	$0.171025\pi$
$192$		0			0
$193$	−187.491	+	108.248i	−0.971456	+	0.560871i	−0.899680	−	0.436550i	$-0.856200\pi$
$193$	−187.491	+	108.248i	−0.971456	+	0.560871i	−0.0717764	+	0.997421i	$0.522867\pi$
$194$		0			0
$195$	−1.77591	−	3.07597i	−0.00910726	−	0.0157742i
$196$		0			0
$197$	86.2234			0.437682			0.218841	−	0.975761i	$-0.429772\pi$
$197$	86.2234			0.437682			0.218841	+	0.975761i	$0.429772\pi$
$198$		0			0
$199$	−21.2768	+	36.8525i	−0.106919	+	0.185188i	−0.914520	−	0.404540i	$-0.867432\pi$
$199$	−21.2768	+	36.8525i	−0.106919	+	0.185188i	0.807602	+	0.589728i	$0.200765\pi$
$200$		0			0
$201$	−101.842			−0.506676
$202$		0			0
$203$	−40.6930	−	23.4941i	−0.200458	−	0.115735i
$204$		0			0
$205$	−11.3388	−	6.54644i	−0.0553111	−	0.0319339i
$206$		0			0
$207$	−40.1456	−	69.5342i	−0.193940	−	0.335914i
$208$		0			0
$209$	−1.76189	+	21.9197i	−0.00843009	+	0.104879i
$210$		0			0
$211$	−278.518	+	160.803i	−1.31999	+	0.762098i	−0.983727	−	0.179670i	$-0.942497\pi$
$211$	−278.518	+	160.803i	−1.31999	+	0.762098i	−0.336265	+	0.941767i	$0.609164\pi$
$212$		0			0
$213$	−90.7243	+	157.139i	−0.425936	+	0.737742i
$214$		0			0
$215$	−0.460750	+	0.798043i	−0.00214302	+	0.00371183i
$216$		0			0
$217$			61.8322i			0.284941i
$218$		0			0
$219$	−189.334	−	109.312i	−0.864541	−	0.499143i
$220$		0			0
$221$		−	109.841i		−	0.497019i
$222$		0			0
$223$	−227.577	+	131.392i	−1.02053	+	0.589201i	−0.914257	−	0.405136i	$-0.867224\pi$
$223$	−227.577	+	131.392i	−1.02053	+	0.589201i	−0.106270	+	0.994337i	$0.533891\pi$
$224$		0			0
$225$	−37.3817	−	64.7469i	−0.166141	−	0.287764i
$226$		0			0
$227$		−	424.986i		−	1.87219i	−0.351752	−	0.936093i	$-0.614414\pi$
$227$		−	424.986i		−	1.87219i	0.351752	−	0.936093i	$-0.385586\pi$
$228$		0			0
$229$	65.9830			0.288135			0.144068	−	0.989568i	$-0.453982\pi$
$229$	65.9830			0.288135			0.144068	+	0.989568i	$0.453982\pi$
$230$		0			0
$231$	−9.09954	+	5.25362i	−0.0393920	+	0.0227430i
$232$		0			0
$233$	−25.7144	−	44.5386i	−0.110362	−	0.191153i	0.805554	−	0.592522i	$-0.201868\pi$
$233$	−25.7144	−	44.5386i	−0.110362	−	0.191153i	−0.915916	+	0.401369i	$0.868534\pi$
$234$		0			0
$235$	14.7850			0.0629149
$236$		0			0
$237$	−55.9406	+	96.8920i	−0.236036	+	0.408827i
$238$		0			0
$239$	239.866			1.00362			0.501811	−	0.864977i	$-0.332667\pi$
$239$	239.866			1.00362			0.501811	+	0.864977i	$0.332667\pi$
$240$		0			0
$241$	−165.208	−	95.3831i	−0.685512	−	0.395781i	0.116416	−	0.993200i	$-0.462859\pi$
$241$	−165.208	−	95.3831i	−0.685512	−	0.395781i	−0.801929	+	0.597420i	$0.796193\pi$
$242$		0			0
$243$	13.5000	+	7.79423i	0.0555556	+	0.0320750i
$244$		0			0
$245$	3.02322	+	5.23636i	0.0123397	+	0.0213729i
$246$		0			0
$247$	78.7623	−	114.192i	0.318876	−	0.462314i
$248$		0			0
$249$	−33.1183	+	19.1209i	−0.133005	+	0.0767907i
$250$		0			0
$251$	−103.899	+	179.959i	−0.413942	+	0.716968i	−0.995317	−	0.0966678i	$-0.969182\pi$
$251$	−103.899	+	179.959i	−0.413942	+	0.716968i	0.581375	+	0.813636i	$0.302515\pi$
$252$		0			0
$253$	15.4880	−	26.8260i	0.0612174	−	0.106032i
$254$		0			0
$255$			7.31893i			0.0287017i
$256$		0			0
$257$	−58.1843	−	33.5927i	−0.226398	−	0.130711i	0.382511	−	0.923951i	$-0.375059\pi$
$257$	−58.1843	−	33.5927i	−0.226398	−	0.130711i	−0.608909	+	0.793240i	$0.708393\pi$
$258$		0			0
$259$		−	189.572i		−	0.731940i
$260$		0			0
$261$	−23.2912	+	13.4472i	−0.0892382	+	0.0515217i
$262$		0			0
$263$	−142.093	−	246.111i	−0.540276	−	0.935785i	−0.998888	−	0.0471484i	$-0.984987\pi$
$263$	−142.093	−	246.111i	−0.540276	−	0.935785i	0.458612	−	0.888637i	$-0.348347\pi$
$264$		0			0
$265$		−	28.5491i		−	0.107733i
$266$		0			0
$267$	−215.157			−0.805833
$268$		0			0
$269$	61.8223	−	35.6931i	0.229823	−	0.132688i	−0.380667	−	0.924712i	$-0.624306\pi$
$269$	61.8223	−	35.6931i	0.229823	−	0.132688i	0.610490	+	0.792024i	$0.290972\pi$
$270$		0			0
$271$	−35.5404	−	61.5577i	−0.131145	−	0.227150i	0.792973	−	0.609257i	$-0.208532\pi$
$271$	−35.5404	−	61.5577i	−0.131145	−	0.227150i	−0.924118	+	0.382106i	$0.875199\pi$
$272$		0			0
$273$	66.2819			0.242791
$274$		0			0
$275$	14.4217	−	24.9791i	0.0524425	−	0.0908331i
$276$		0			0
$277$	−476.997			−1.72201			−0.861005	−	0.508597i	$-0.830164\pi$
$277$	−476.997			−1.72201			−0.861005	+	0.508597i	$0.830164\pi$
$278$		0			0
$279$	30.6491	+	17.6953i	0.109853	+	0.0634238i
$280$		0			0
$281$	126.681	+	73.1394i	0.450822	+	0.260282i	0.708177	−	0.706034i	$-0.249518\pi$
$281$	126.681	+	73.1394i	0.450822	+	0.260282i	−0.257355	+	0.966317i	$0.582851\pi$
$282$		0			0
$283$	−76.0571	−	131.735i	−0.268753	−	0.465494i	0.699787	−	0.714352i	$-0.253278\pi$
$283$	−76.0571	−	131.735i	−0.268753	−	0.465494i	−0.968540	+	0.248858i	$0.919945\pi$
$284$		0			0
$285$	−5.24808	+	7.60880i	−0.0184143	+	0.0266975i
$286$		0			0
$287$	211.597	−	122.165i	0.737271	−	0.425663i
$288$		0			0
$289$	31.3301	−	54.2653i	0.108409	−	0.187769i
$290$		0			0
$291$	−162.700	+	281.804i	−0.559106	+	0.968400i
$292$		0			0
$293$		−	350.693i		−	1.19690i	−0.801159	−	0.598452i	$-0.795783\pi$
$293$		−	350.693i		−	1.19690i	0.801159	−	0.598452i	$-0.204217\pi$
$294$		0			0
$295$	−11.1872	−	6.45893i	−0.0379227	−	0.0218947i
$296$		0			0
$297$			6.01396i			0.0202490i
$298$		0			0
$299$	−169.224	+	97.7016i	−0.565967	+	0.326761i
$300$		0			0
$301$	−8.59822	−	14.8926i	−0.0285655	−	0.0494769i
$302$		0			0
$303$			68.7547i			0.226913i
$304$		0			0
$305$	28.4894			0.0934078
$306$		0			0
$307$	−412.362	+	238.077i	−1.34320	+	0.775497i	−0.987276	−	0.159018i	$-0.949167\pi$
$307$	−412.362	+	238.077i	−1.34320	+	0.775497i	−0.355924	+	0.934515i	$0.615834\pi$
$308$		0			0
$309$	−23.1541	−	40.1041i	−0.0749323	−	0.129787i
$310$		0			0
$311$	468.952			1.50788			0.753942	−	0.656942i	$-0.228150\pi$
$311$	468.952			1.50788			0.753942	+	0.656942i	$0.228150\pi$
$312$		0			0
$313$	−17.6786	+	30.6203i	−0.0564812	+	0.0978284i	−0.892884	−	0.450288i	$-0.851321\pi$
$313$	−17.6786	+	30.6203i	−0.0564812	+	0.0978284i	0.836402	+	0.548116i	$0.184655\pi$
$314$		0			0
$315$	−4.41649			−0.0140206
$316$		0			0
$317$	377.554	+	217.981i	1.19102	+	0.687637i	0.958539	−	0.284963i	$-0.0919812\pi$
$317$	377.554	+	217.981i	1.19102	+	0.687637i	0.232484	+	0.972600i	$0.425315\pi$
$318$		0			0
$319$	−8.98564	−	5.18786i	−0.0281681	−	0.0162629i
$320$		0			0
$321$	53.6450	+	92.9159i	0.167118	+	0.289458i
$322$		0			0
$323$	−258.206	+	122.630i	−0.799400	+	0.379660i
$324$		0			0
$325$	−157.573	+	90.9751i	−0.484841	+	0.279923i
$326$		0			0
$327$	−30.9996	+	53.6929i	−0.0948000	+	0.164198i
$328$		0			0
$329$	−137.954	+	238.943i	−0.419313	+	0.726271i
$330$		0			0
$331$			9.06641i			0.0273910i	0.999906	+	0.0136955i	$0.00435954\pi$
$331$			9.06641i			0.0273910i	−0.999906	+	0.0136955i	$0.995640\pi$
$332$		0			0
$333$	−93.9675	−	54.2522i	−0.282185	−	0.162919i
$334$		0			0
$335$		−	16.5148i		−	0.0492978i
$336$		0			0
$337$	364.175	−	210.256i	1.08064	−	0.623906i	0.149569	−	0.988751i	$-0.452211\pi$
$337$	364.175	−	210.256i	1.08064	−	0.623906i	0.931068	+	0.364845i	$0.118878\pi$
$338$		0			0
$339$	−91.8146	−	159.028i	−0.270839	−	0.469108i
$340$		0			0
$341$			13.6535i			0.0400396i
$342$		0			0
$343$	−369.664			−1.07774
$344$		0			0
$345$	11.2757	−	6.51004i	0.0326832	−	0.0188697i
$346$		0			0
$347$	32.2864	+	55.9216i	0.0930443	+	0.161157i	0.908791	−	0.417252i	$-0.137007\pi$
$347$	32.2864	+	55.9216i	0.0930443	+	0.161157i	−0.815746	+	0.578410i	$0.803674\pi$
$348$		0			0
$349$	−242.722			−0.695477			−0.347739	−	0.937592i	$-0.613050\pi$
$349$	−242.722			−0.695477			−0.347739	+	0.937592i	$0.613050\pi$
$350$		0			0
$351$	18.9687	−	32.8547i	0.0540418	−	0.0936031i
$352$		0			0
$353$	−560.267			−1.58716			−0.793579	−	0.608467i	$-0.791785\pi$
$353$	−560.267			−1.58716			−0.793579	+	0.608467i	$0.791785\pi$
$354$		0			0
$355$	−25.4818	−	14.7119i	−0.0717797	−	0.0414420i
$356$		0			0
$357$	−118.283	−	68.2906i	−0.331324	−	0.191290i
$358$		0			0
$359$	−219.906	−	380.889i	−0.612552	−	1.06097i	−0.990809	−	0.135271i	$-0.956810\pi$
$359$	−219.906	−	380.889i	−0.612552	−	1.06097i	0.378256	−	0.925701i	$-0.376524\pi$
$360$		0			0
$361$	−356.365	−	57.6613i	−0.987161	−	0.159727i
$362$		0			0
$363$	179.491	−	103.629i	0.494465	−	0.285479i
$364$		0			0
$365$	17.7262	−	30.7026i	0.0485648	−	0.0841168i
$366$		0			0
$367$	66.5853	−	115.329i	0.181431	−	0.314248i	−0.760937	−	0.648826i	$-0.775260\pi$
$367$	66.5853	−	115.329i	0.181431	−	0.314248i	0.942368	+	0.334578i	$0.108594\pi$
$368$		0			0
$369$		−	139.846i		−	0.378986i
$370$		0			0
$371$	461.388	+	266.383i	1.24363	+	0.718013i
$372$		0			0
$373$			340.051i			0.911666i	0.890065	+	0.455833i	$0.150659\pi$
$373$			340.051i			0.911666i	−0.890065	+	0.455833i	$0.849341\pi$
$374$		0			0
$375$	21.0321	−	12.1429i	0.0560855	−	0.0323810i
$376$		0			0
$377$	32.7261	+	56.6833i	0.0868067	+	0.150354i
$378$		0			0
$379$			71.0281i			0.187409i	0.995600	+	0.0937046i	$0.0298709\pi$
$379$			71.0281i			0.187409i	−0.995600	+	0.0937046i	$0.970129\pi$
$380$		0			0
$381$	−195.872			−0.514101
$382$		0			0
$383$	−296.523	+	171.198i	−0.774213	+	0.446992i	−0.834375	−	0.551197i	$-0.814171\pi$
$383$	−296.523	+	171.198i	−0.774213	+	0.446992i	0.0601627	+	0.998189i	$0.480838\pi$
$384$		0			0
$385$	−0.851932	−	1.47559i	−0.00221281	−	0.00383270i
$386$		0			0
$387$	−9.84261			−0.0254331
$388$		0			0
$389$	38.8478	−	67.2864i	0.0998659	−	0.172973i	−0.811763	−	0.583987i	$-0.801492\pi$
$389$	38.8478	−	67.2864i	0.0998659	−	0.172973i	0.911629	+	0.411014i	$0.134825\pi$
$390$		0			0
$391$	402.649			1.02979
$392$		0			0
$393$	−194.275	−	112.164i	−0.494337	−	0.285406i
$394$		0			0
$395$	−15.7121	−	9.07138i	−0.0397774	−	0.0229655i
$396$		0			0
$397$	47.6985	+	82.6162i	0.120147	+	0.208101i	0.919826	−	0.392327i	$-0.128330\pi$
$397$	47.6985	+	82.6162i	0.120147	+	0.208101i	−0.799678	+	0.600429i	$0.794997\pi$
$398$		0			0
$399$	−73.9992	−	155.810i	−0.185462	−	0.390502i
$400$		0			0
$401$	−93.1614	+	53.7868i	−0.232323	+	0.134132i	−0.611643	−	0.791134i	$-0.709491\pi$
$401$	−93.1614	+	53.7868i	−0.232323	+	0.134132i	0.379320	+	0.925265i	$0.376158\pi$
$402$		0			0
$403$	43.0646	−	74.5901i	0.106860	−	0.185087i
$404$		0			0
$405$	−1.26392	+	2.18917i	−0.00312079	+	0.00540536i
$406$		0			0
$407$		−	41.8605i		−	0.102851i
$408$		0			0
$409$	423.796	+	244.679i	1.03618	+	0.598237i	0.918748	−	0.394845i	$-0.129202\pi$
$409$	423.796	+	244.679i	1.03618	+	0.598237i	0.117428	+	0.993081i	$0.462535\pi$
$410$		0			0
$411$			74.4366i			0.181111i
$412$		0			0
$413$	208.768	−	120.532i	0.505492	−	0.291846i
$414$		0			0
$415$	−3.10066	−	5.37050i	−0.00747146	−	0.0129410i
$416$		0			0
$417$		−	360.946i		−	0.865579i
$418$		0			0
$419$	160.772			0.383705			0.191853	−	0.981424i	$-0.438550\pi$
$419$	160.772			0.383705			0.191853	+	0.981424i	$0.438550\pi$
$420$		0			0
$421$	304.122	−	175.585i	0.722381	−	0.417067i	−0.0932477	−	0.995643i	$-0.529725\pi$
$421$	304.122	−	175.585i	0.722381	−	0.417067i	0.815628	+	0.578576i	$0.196392\pi$
$422$		0			0
$423$	78.9598	+	136.762i	0.186666	+	0.323315i
$424$		0			0
$425$	374.928			0.882184
$426$		0			0
$427$	−265.825	+	460.423i	−0.622541	+	1.07827i
$428$		0			0
$429$	14.6361			0.0341167
$430$		0			0
$431$	−14.5476	−	8.39908i	−0.0337532	−	0.0194874i	0.483028	−	0.875605i	$-0.339537\pi$
$431$	−14.5476	−	8.39908i	−0.0337532	−	0.0194874i	−0.516782	+	0.856117i	$0.672870\pi$
$432$		0			0
$433$	−360.314	−	208.027i	−0.832133	−	0.480432i	0.0224496	−	0.999748i	$-0.492853\pi$
$433$	−360.314	−	208.027i	−0.832133	−	0.480432i	−0.854582	+	0.519316i	$0.826187\pi$
$434$		0			0
$435$	−2.18060	−	3.77691i	−0.00501288	−	0.00868256i
$436$		0			0
$437$	418.596	+	288.722i	0.957886	+	0.660691i
$438$		0			0
$439$	561.428	−	324.140i	1.27888	−	0.738361i	0.302237	−	0.953233i	$-0.402267\pi$
$439$	561.428	−	324.140i	1.27888	−	0.738361i	0.976642	+	0.214872i	$0.0689334\pi$
$440$		0			0
$441$	−32.2912	+	55.9299i	−0.0732226	+	0.126825i
$442$		0			0
$443$	−341.171	+	590.925i	−0.770137	+	1.33392i	0.167351	+	0.985897i	$0.446479\pi$
$443$	−341.171	+	590.925i	−0.770137	+	1.33392i	−0.937488	+	0.348019i	$0.886855\pi$
$444$		0			0
$445$		−	34.8901i		−	0.0784047i
$446$		0			0
$447$	207.703	+	119.917i	0.464660	+	0.268272i
$448$		0			0
$449$		−	185.741i		−	0.413677i	−0.978375	−	0.206839i	$-0.933682\pi$
$449$		−	185.741i		−	0.413677i	0.978375	−	0.206839i	$-0.0663175\pi$
$450$		0			0
$451$	46.7238	−	26.9760i	0.103600	−	0.0598138i
$452$		0			0
$453$	230.047	+	398.453i	0.507829	+	0.879586i
$454$		0			0
$455$			10.7483i			0.0236227i
$456$		0			0
$457$	−311.871			−0.682430			−0.341215	−	0.939985i	$-0.610838\pi$
$457$	−311.871			−0.682430			−0.341215	+	0.939985i	$0.610838\pi$
$458$		0			0
$459$	−67.7007	+	39.0870i	−0.147496	+	0.0851569i
$460$		0			0
$461$	−428.769	−	742.649i	−0.930084	−	1.61095i	−0.783174	−	0.621803i	$-0.786400\pi$
$461$	−428.769	−	742.649i	−0.930084	−	1.61095i	−0.146910	−	0.989150i	$-0.546933\pi$
$462$		0			0
$463$	−140.408			−0.303258			−0.151629	−	0.988438i	$-0.548452\pi$
$463$	−140.408			−0.303258			−0.151629	+	0.988438i	$0.548452\pi$
$464$		0			0
$465$	−2.86948	+	4.97008i	−0.00617092	+	0.0106883i
$466$		0			0
$467$	−416.647			−0.892178			−0.446089	−	0.894989i	$-0.647183\pi$
$467$	−416.647			−0.892178			−0.446089	+	0.894989i	$0.647183\pi$
$468$		0			0
$469$	266.898	+	154.094i	0.569079	+	0.328558i
$470$		0			0
$471$	157.339	+	90.8398i	0.334053	+	0.192866i
$472$		0			0
$473$	−1.89862	−	3.28851i	−0.00401400	−	0.00695244i
$474$		0			0
$475$	389.777	+	268.844i	0.820583	+	0.565988i
$476$		0			0
$477$	264.082	−	152.468i	0.553631	−	0.319639i
$478$		0			0
$479$	78.9373	−	136.723i	0.164796	−	0.285435i	−0.771787	−	0.635881i	$-0.780637\pi$
$479$	78.9373	−	136.723i	0.164796	−	0.285435i	0.936583	+	0.350446i	$0.113970\pi$
$480$		0			0
$481$	−132.032	+	228.687i	−0.274496	+	0.475441i
$482$		0			0
$483$			242.972i			0.503048i
$484$		0			0
$485$	−45.6976	−	26.3835i	−0.0942219	−	0.0543991i
$486$		0			0
$487$		−	69.9652i		−	0.143666i	−0.997417	−	0.0718329i	$-0.977115\pi$
$487$		−	69.9652i		−	0.143666i	0.997417	−	0.0718329i	$-0.0228848\pi$
$488$		0			0
$489$	133.733	−	77.2110i	0.273483	−	0.157896i
$490$		0			0
$491$	−187.193	−	324.228i	−0.381249	−	0.660342i	0.609992	−	0.792407i	$-0.291172\pi$
$491$	−187.193	−	324.228i	−0.381249	−	0.660342i	−0.991241	+	0.132065i	$0.957839\pi$
$492$		0			0
$493$		−	134.871i		−	0.273573i
$494$		0			0
$495$	−0.975229			−0.00197016
$496$		0			0
$497$	475.525	−	274.544i	0.956790	−	0.552403i
$498$		0			0
$499$	−269.212	−	466.288i	−0.539502	−	0.934446i	−0.998931	−	0.0462308i	$-0.985279\pi$
$499$	−269.212	−	466.288i	−0.539502	−	0.934446i	0.459428	−	0.888215i	$-0.348054\pi$
$500$		0			0
$501$	41.5178			0.0828699
$502$		0			0
$503$	370.028	−	640.906i	0.735641	−	1.27417i	−0.218800	−	0.975770i	$-0.570214\pi$
$503$	370.028	−	640.906i	0.735641	−	1.27417i	0.954441	−	0.298398i	$-0.0964523\pi$
$504$		0			0
$505$	−11.1493			−0.0220778
$506$		0			0
$507$	173.542	+	100.195i	0.342292	+	0.197622i
$508$		0			0
$509$	36.2456	+	20.9264i	0.0712094	+	0.0411128i	0.535182	−	0.844737i	$-0.320243\pi$
$509$	36.2456	+	20.9264i	0.0712094	+	0.0411128i	−0.463973	+	0.885850i	$0.653576\pi$
$510$		0			0
$511$	330.794	+	572.952i	0.647347	+	1.12124i
$512$		0			0
$513$	−98.4095	−	7.91009i	−0.191831	−	0.0154193i
$514$		0			0
$515$	6.50331	−	3.75469i	0.0126278	−	0.00729065i
$516$		0			0
$517$	−30.4624	+	52.7624i	−0.0589214	+	0.102055i
$518$		0			0
$519$	−48.4169	+	83.8605i	−0.0932888	+	0.161581i
$520$		0			0
$521$			881.594i			1.69212i	0.533089	+	0.846059i	$0.321031\pi$
$521$			881.594i			1.69212i	−0.533089	+	0.846059i	$0.678969\pi$
$522$		0			0
$523$	−447.114	−	258.142i	−0.854903	−	0.493578i	0.00739916	−	0.999973i	$-0.497645\pi$
$523$	−447.114	−	258.142i	−0.854903	−	0.493578i	−0.862302	+	0.506394i	$0.830978\pi$
$524$		0			0
$525$			226.244i			0.430941i
$526$		0			0
$527$	−153.701	+	88.7393i	−0.291653	+	0.168386i
$528$		0			0
$529$	−93.6485	−	162.204i	−0.177029	−	0.306624i
$530$		0			0
$531$		−	137.977i		−	0.259843i
$532$		0			0
$533$	−340.341			−0.638538
$534$		0			0
$535$	−15.0673	+	8.69912i	−0.0281632	+	0.0162600i
$536$		0			0
$537$	−165.515	−	286.681i	−0.308222	−	0.533856i
$538$		0			0
$539$	−24.9156			−0.0462256
$540$		0			0
$541$	163.097	−	282.493i	0.301474	−	0.522168i	−0.674996	−	0.737821i	$-0.735855\pi$
$541$	163.097	−	282.493i	0.301474	−	0.522168i	0.976470	+	0.215654i	$0.0691882\pi$
$542$		0			0
$543$	−148.582			−0.273632
$544$		0			0
$545$	−8.70688	−	5.02692i	−0.0159759	−	0.00922371i
$546$		0			0
$547$	420.124	+	242.559i	0.768052	+	0.443435i	0.832179	−	0.554507i	$-0.187093\pi$
$547$	420.124	+	242.559i	0.768052	+	0.443435i	−0.0641274	+	0.997942i	$0.520426\pi$
$548$		0			0
$549$	152.148	+	263.529i	0.277138	+	0.480016i
$550$		0			0
$551$	96.7103	−	140.213i	0.175518	−	0.254470i
$552$		0			0
$553$	293.209	−	169.284i	0.530215	−	0.306120i
$554$		0			0
$555$	8.79757	−	15.2378i	0.0158515	−	0.0274556i
$556$		0			0
$557$	45.2381	−	78.3548i	0.0812175	−	0.140673i	−0.822556	−	0.568685i	$-0.807452\pi$
$557$	45.2381	−	78.3548i	0.0812175	−	0.140673i	0.903773	+	0.428012i	$0.140786\pi$
$558$		0			0
$559$			23.9538i			0.0428511i
$560$		0			0
$561$	−26.1186	−	15.0796i	−0.0465573	−	0.0268799i
$562$		0			0
$563$		−	126.463i		−	0.224624i	−0.993673	−	0.112312i	$-0.964174\pi$
$563$		−	126.463i		−	0.224624i	0.993673	−	0.112312i	$-0.0358256\pi$
$564$		0			0
$565$	25.7880	−	14.8887i	0.0456425	−	0.0263517i
$566$		0			0
$567$	−23.5864	−	40.8529i	−0.0415986	−	0.0720509i
$568$		0			0
$569$			857.322i			1.50672i	0.657610	+	0.753359i	$0.271568\pi$
$569$			857.322i			1.50672i	−0.657610	+	0.753359i	$0.728432\pi$
$570$		0			0
$571$	99.1009			0.173557			0.0867784	−	0.996228i	$-0.472343\pi$
$571$	99.1009			0.173557			0.0867784	+	0.996228i	$0.472343\pi$
$572$		0			0
$573$	−492.263	+	284.208i	−0.859098	+	0.496000i
$574$		0			0
$575$	−333.491	−	577.623i	−0.579984	−	1.00456i
$576$		0			0
$577$	777.423			1.34735			0.673677	−	0.739026i	$-0.264714\pi$
$577$	777.423			1.34735			0.673677	+	0.739026i	$0.264714\pi$
$578$		0			0
$579$	187.491	−	324.744i	0.323819	−	0.560871i
$580$		0			0
$581$	115.725			0.199182
$582$		0			0
$583$	101.882	+	58.8214i	0.174754	+	0.100894i
$584$		0			0
$585$	5.32774	+	3.07597i	0.00910726	+	0.00525808i
$586$		0			0
$587$	265.805	+	460.388i	0.452820	+	0.784307i	0.998560	−	0.0536475i	$-0.0170847\pi$
$587$	265.805	+	460.388i	0.452820	+	0.784307i	−0.545740	+	0.837955i	$0.683751\pi$
$588$		0			0
$589$	−223.419	−	17.9583i	−0.379320	−	0.0304895i
$590$		0			0
$591$	−129.335	+	74.6716i	−0.218841	+	0.126348i
$592$		0			0
$593$	−340.521	+	589.799i	−0.574234	+	0.994603i	0.421890	+	0.906647i	$0.361367\pi$
$593$	−340.521	+	589.799i	−0.574234	+	0.994603i	−0.996124	+	0.0879557i	$0.971967\pi$
$594$		0			0
$595$	11.0741	−	19.1808i	0.0186118	−	0.0322367i
$596$		0			0
$597$		−	73.7050i		−	0.123459i
$598$		0			0
$599$	281.589	+	162.575i	0.470098	+	0.271411i	0.716281	−	0.697812i	$-0.245843\pi$
$599$	281.589	+	162.575i	0.470098	+	0.271411i	−0.246183	+	0.969223i	$0.579176\pi$
$600$		0			0
$601$		−	331.221i		−	0.551117i	−0.961284	−	0.275558i	$-0.911137\pi$
$601$		−	331.221i		−	0.551117i	0.961284	−	0.275558i	$-0.0888628\pi$
$602$		0			0
$603$	152.763	−	88.1976i	0.253338	−	0.146265i
$604$		0			0
$605$	16.8046	+	29.1064i	0.0277761	+	0.0481097i
$606$		0			0
$607$		−	819.129i		−	1.34947i	−0.738060	−	0.674735i	$-0.764258\pi$
$607$		−	819.129i		−	1.34947i	0.738060	−	0.674735i	$-0.235742\pi$
$608$		0			0
$609$	81.3860			0.133639
$610$		0			0
$611$	332.836	−	192.163i	0.544740	−	0.314506i
$612$		0			0
$613$	161.068	+	278.978i	0.262754	+	0.455103i	0.966973	−	0.254880i	$-0.0820359\pi$
$613$	161.068	+	278.978i	0.262754	+	0.455103i	−0.704219	+	0.709983i	$0.748703\pi$
$614$		0			0
$615$	22.6775			0.0368740
$616$		0			0
$617$	−570.525	+	988.179i	−0.924676	+	1.60159i	−0.132595	+	0.991170i	$0.542331\pi$
$617$	−570.525	+	988.179i	−0.924676	+	1.60159i	−0.792081	+	0.610416i	$0.791002\pi$
$618$		0			0
$619$	56.7606			0.0916972			0.0458486	−	0.998948i	$-0.485401\pi$
$619$	56.7606			0.0916972			0.0458486	+	0.998948i	$0.485401\pi$
$620$		0			0
$621$	120.437	+	69.5342i	0.193940	+	0.111971i
$622$		0			0
$623$	563.866	+	325.548i	0.905082	+	0.522549i
$624$		0			0
$625$	−309.545	−	536.147i	−0.495272	−	0.857836i
$626$		0			0
$627$	−16.3402	−	34.4053i	−0.0260609	−	0.0548730i
$628$		0			0
$629$	471.234	−	272.067i	0.749180	−	0.432539i
$630$		0			0
$631$	−568.803	+	985.195i	−0.901430	+	1.56132i	−0.0757921	+	0.997124i	$0.524149\pi$
$631$	−568.803	+	985.195i	−0.901430	+	1.56132i	−0.825638	+	0.564200i	$0.809185\pi$
$632$		0			0
$633$	278.518	−	482.408i	0.439997	−	0.762098i
$634$		0			0
$635$		−	31.7628i		−	0.0500202i
$636$		0			0
$637$	136.116	+	78.5864i	0.213682	+	0.123370i
$638$		0			0
$639$		−	314.278i		−	0.491828i
$640$		0			0
$641$	65.0480	−	37.5555i	0.101479	−	0.0585889i	−0.448402	−	0.893832i	$-0.648007\pi$
$641$	65.0480	−	37.5555i	0.101479	−	0.0585889i	0.549881	+	0.835243i	$0.314673\pi$
$642$		0			0
$643$	154.393	+	267.417i	0.240114	+	0.415889i	0.960746	−	0.277428i	$-0.0894820\pi$
$643$	154.393	+	267.417i	0.240114	+	0.415889i	−0.720633	+	0.693317i	$0.756149\pi$
$644$		0			0
$645$		−	1.59609i		−	0.00247455i
$646$		0			0
$647$	−121.571			−0.187900			−0.0939498	−	0.995577i	$-0.529949\pi$
$647$	−121.571			−0.187900			−0.0939498	+	0.995577i	$0.529949\pi$
$648$		0			0
$649$	46.0992	−	26.6154i	0.0710312	−	0.0410099i
$650$		0			0
$651$	−53.5483	−	92.7484i	−0.0822555	−	0.142471i
$652$		0			0
$653$	1258.75			1.92764			0.963819	−	0.266559i	$-0.0858867\pi$
$653$	1258.75			1.92764			0.963819	+	0.266559i	$0.0858867\pi$
$654$		0			0
$655$	18.1887	−	31.5037i	0.0277690	−	0.0480973i
$656$		0			0
$657$	378.669			0.576361
$658$		0			0
$659$	−851.135	−	491.403i	−1.29156	−	0.745680i	−0.312625	−	0.949876i	$-0.601208\pi$
$659$	−851.135	−	491.403i	−1.29156	−	0.745680i	−0.978930	+	0.204197i	$0.934542\pi$
$660$		0			0
$661$	249.208	+	143.880i	0.377017	+	0.217671i	0.676519	−	0.736425i	$-0.263487\pi$
$661$	249.208	+	143.880i	0.377017	+	0.217671i	−0.299503	+	0.954095i	$0.596821\pi$
$662$		0			0
$663$	95.1253	+	164.762i	0.143477	+	0.248510i
$664$		0			0
$665$	25.2663	−	11.9998i	0.0379945	−	0.0180448i
$666$		0			0
$667$	−207.786	+	119.965i	−0.311523	+	0.179858i
$668$		0			0
$669$	227.577	−	394.176i	0.340176	−	0.589201i
$670$		0			0
$671$	−58.6983	+	101.668i	−0.0874788	+	0.151518i
$672$		0			0
$673$			252.012i			0.374460i	0.982316	+	0.187230i	$0.0599510\pi$
$673$			252.012i			0.374460i	−0.982316	+	0.187230i	$0.940049\pi$
$674$		0			0
$675$	112.145	+	64.7469i	0.166141	+	0.0959214i
$676$		0			0
$677$		−	293.002i		−	0.432795i	−0.976305	−	0.216397i	$-0.930569\pi$
$677$		−	293.002i		−	0.432795i	0.976305	−	0.216397i	$-0.0694306\pi$
$678$		0			0
$679$	852.780	−	492.353i	1.25593	−	0.725114i
$680$		0			0
$681$	368.049	+	637.479i	0.540454	+	0.936093i
$682$		0			0
$683$			532.042i			0.778979i	0.921031	+	0.389489i	$0.127349\pi$
$683$			532.042i			0.778979i	−0.921031	+	0.389489i	$0.872651\pi$
$684$		0			0
$685$	−12.0707			−0.0176215
$686$		0			0
$687$	−98.9745	+	57.1429i	−0.144068	+	0.0831775i
$688$		0			0
$689$	−371.058	−	642.691i	−0.538545	−	0.932788i
$690$		0			0
$691$	806.065			1.16652			0.583260	−	0.812286i	$-0.301777\pi$
$691$	806.065			1.16652			0.583260	+	0.812286i	$0.301777\pi$
$692$		0			0
$693$	9.09954	−	15.7609i	0.0131307	−	0.0227430i
$694$		0			0
$695$	58.5314			0.0842178
$696$		0			0
$697$	607.351	+	350.654i	0.871379	+	0.503091i
$698$		0			0
$699$	77.1431	+	44.5386i	0.110362	+	0.0637176i
$700$		0			0
$701$	−395.041	−	684.230i	−0.563539	−	0.976077i	−0.997184	−	0.0749939i	$-0.976106\pi$
$701$	−395.041	−	684.230i	−0.563539	−	0.976077i	0.433645	−	0.901084i	$-0.357227\pi$
$702$		0			0
$703$	684.985	+	55.0586i	0.974374	+	0.0783195i
$704$		0			0
$705$	−22.1775	+	12.8042i	−0.0314574	+	0.0181620i
$706$		0			0
$707$	104.031	−	180.186i	0.147144	−	0.254860i
$708$		0			0
$709$	−497.856	+	862.312i	−0.702195	+	1.21624i	0.265499	+	0.964111i	$0.414463\pi$
$709$	−497.856	+	862.312i	−0.702195	+	1.21624i	−0.967694	+	0.252126i	$0.918870\pi$
$710$		0			0
$711$		−	193.784i		−	0.272551i
$712$		0			0
$713$	273.428	+	157.864i	0.383489	+	0.221408i
$714$		0			0
$715$			2.37340i			0.00331944i
$716$		0			0
$717$	−359.799	+	207.730i	−0.501811	+	0.289721i
$718$		0			0
$719$	600.858	+	1040.72i	0.835686	+	1.44745i	0.893471	+	0.449122i	$0.148263\pi$
$719$	600.858	+	1040.72i	0.835686	+	1.44745i	−0.0577845	+	0.998329i	$0.518404\pi$
$720$		0			0
$721$			140.135i			0.194362i
$722$		0			0
$723$	330.417			0.457008
$724$		0			0
$725$	−193.481	+	111.706i	−0.266870	+	0.154077i
$726$		0			0
$727$	−12.3246	−	21.3468i	−0.0169527	−	0.0293629i	0.857425	−	0.514610i	$-0.172063\pi$
$727$	−12.3246	−	21.3468i	−0.0169527	−	0.0293629i	−0.874377	+	0.485247i	$0.838730\pi$
$728$		0			0
$729$	−27.0000			−0.0370370
$730$		0			0
$731$	24.6797	−	42.7465i	0.0337615	−	0.0584767i
$732$		0			0
$733$	68.8594			0.0939419			0.0469710	−	0.998896i	$-0.485043\pi$
$733$	68.8594			0.0939419			0.0469710	+	0.998896i	$0.485043\pi$
$734$		0			0
$735$	−9.06965	−	5.23636i	−0.0123397	−	0.00712430i
$736$		0			0
$737$	58.9352	+	34.0263i	0.0799664	+	0.0461686i
$738$		0			0
$739$	497.408	+	861.536i	0.673083	+	1.16581i	0.977025	+	0.213123i	$0.0683635\pi$
$739$	497.408	+	861.536i	0.673083	+	1.16581i	−0.303943	+	0.952690i	$0.598303\pi$
$740$		0			0
$741$	−19.2506	+	239.497i	−0.0259793	+	0.323208i
$742$		0			0
$743$	−341.188	+	196.985i	−0.459204	+	0.265121i	−0.711709	−	0.702474i	$-0.752079\pi$
$743$	−341.188	+	196.985i	−0.459204	+	0.265121i	0.252506	+	0.967595i	$0.418745\pi$
$744$		0			0
$745$	−19.4459	+	33.6813i	−0.0261019	+	0.0452098i
$746$		0			0
$747$	33.1183	−	57.3626i	0.0443351	−	0.0767907i
$748$		0			0
$749$		−	324.674i		−	0.433477i
$750$		0			0
$751$	−153.043	−	88.3594i	−0.203786	−	0.117656i	0.394634	−	0.918838i	$-0.370871\pi$
$751$	−153.043	−	88.3594i	−0.203786	−	0.117656i	−0.598420	+	0.801183i	$0.704205\pi$
$752$		0			0
$753$		−	359.918i		−	0.477979i
$754$		0			0
$755$	−64.6134	+	37.3046i	−0.0855807	+	0.0494100i
$756$		0			0
$757$	591.818	+	1025.06i	0.781793	+	1.35411i	0.930896	+	0.365284i	$0.119028\pi$
$757$	591.818	+	1025.06i	0.781793	+	1.35411i	−0.149103	+	0.988822i	$0.547639\pi$
$758$		0			0
$759$			53.6520i			0.0706878i
$760$		0			0
$761$	−517.695			−0.680282			−0.340141	−	0.940374i	$-0.610475\pi$
$761$	−517.695			−0.680282			−0.340141	+	0.940374i	$0.610475\pi$
$762$		0			0
$763$	162.482	−	93.8091i	0.212952	−	0.122948i
$764$		0			0
$765$	−6.33838	−	10.9784i	−0.00828546	−	0.0143508i
$766$		0			0
$767$	−335.791			−0.437798
$768$		0			0
$769$	476.376	−	825.107i	0.619474	−	1.07296i	−0.370107	−	0.928989i	$-0.620679\pi$
$769$	476.376	−	825.107i	0.619474	−	1.07296i	0.989582	−	0.143972i	$-0.0459875\pi$
$770$		0			0
$771$	116.369			0.150932
$772$		0			0
$773$	−1088.18	−	628.259i	−1.40773	−	0.812754i	−0.412561	−	0.910930i	$-0.635366\pi$
$773$	−1088.18	−	628.259i	−1.40773	−	0.812754i	−0.995169	+	0.0981762i	$0.968699\pi$
$774$		0			0
$775$	254.603	+	146.995i	0.328520	+	0.189671i
$776$		0			0
$777$	164.175	+	284.359i	0.211293	+	0.365970i
$778$		0			0
$779$	379.967	+	800.046i	0.487762	+	1.02702i
$780$		0			0
$781$	105.003	−	60.6236i	0.134447	−	0.0776231i
$782$		0			0
$783$	23.2912	−	40.3415i	0.0297461	−	0.0515217i
$784$		0			0
$785$	−14.7307	+	25.5142i	−0.0187652	+	0.0325022i
$786$		0			0
$787$		−	981.332i		−	1.24693i	−0.781852	−	0.623464i	$-0.785725\pi$
$787$		−	981.332i		−	1.24693i	0.781852	−	0.623464i	$-0.214275\pi$
$788$		0			0
$789$	426.278	+	246.111i	0.540276	+	0.311928i
$790$		0			0
$791$			555.687i			0.702512i
$792$		0			0
$793$	641.345	−	370.281i	0.808758	−	0.466937i
$794$		0			0
$795$	24.7243	+	42.8237i	0.0310997	+	0.0538663i
$796$		0			0
$797$		−	943.008i		−	1.18320i	−0.806233	−	0.591599i	$-0.798497\pi$
$797$		−	943.008i		−	1.18320i	0.806233	−	0.591599i	$-0.201503\pi$
$798$		0			0
$799$	−791.945			−0.991171
$800$		0			0
$801$	322.736	−	186.332i	0.402916	−	0.232624i
$802$		0			0
$803$	73.0445	+	126.517i	0.0909645	+	0.157555i
$804$		0			0
$805$	−39.4006			−0.0489448
$806$		0			0
$807$	−61.8223	+	107.079i	−0.0766076	+	0.132688i
$808$		0			0
$809$	942.078			1.16450			0.582249	−	0.813011i	$-0.302173\pi$
$809$	942.078			1.16450			0.582249	+	0.813011i	$0.302173\pi$
$810$		0			0
$811$	−556.679	−	321.399i	−0.686411	−	0.396300i	0.115855	−	0.993266i	$-0.463039\pi$
$811$	−556.679	−	321.399i	−0.686411	−	0.396300i	−0.802266	+	0.596967i	$0.796373\pi$
$812$		0			0
$813$	106.621	+	61.5577i	0.131145	+	0.0757167i
$814$		0			0
$815$	12.5206	+	21.6863i	0.0153627	+	0.0266090i
$816$		0			0
$817$	56.3087	−	26.7427i	0.0689213	−	0.0327329i
$818$		0			0
$819$	−99.4229	+	57.4018i	−0.121395	+	0.0700877i
$820$		0			0
$821$	−428.109	+	741.507i	−0.521449	+	0.903176i	0.478240	+	0.878229i	$0.341275\pi$
$821$	−428.109	+	741.507i	−0.521449	+	0.903176i	−0.999689	+	0.0249465i	$0.992058\pi$
$822$		0			0
$823$	−705.555	+	1222.06i	−0.857297	+	1.48488i	0.0172014	+	0.999852i	$0.494524\pi$
$823$	−705.555	+	1222.06i	−0.857297	+	1.48488i	−0.874498	+	0.485029i	$0.838809\pi$
$824$		0			0
$825$			49.9582i			0.0605554i
$826$		0			0
$827$	790.058	+	456.140i	0.955330	+	0.551560i	0.894733	−	0.446602i	$-0.147366\pi$
$827$	790.058	+	456.140i	0.955330	+	0.551560i	0.0605975	+	0.998162i	$0.480699\pi$
$828$		0			0
$829$		−	1182.75i		−	1.42672i	−0.700799	−	0.713359i	$-0.747173\pi$
$829$		−	1182.75i		−	1.42672i	0.700799	−	0.713359i	$-0.252827\pi$
$830$		0			0
$831$	715.495	−	413.091i	0.861005	−	0.497101i
$832$		0			0
$833$	−161.936	−	280.481i	−0.194401	−	0.336712i
$834$		0			0
$835$			6.73256i			0.00806295i
$836$		0			0
$837$	−61.2982			−0.0732356
$838$		0			0
$839$	−791.646	+	457.057i	−0.943559	+	0.544764i	−0.891074	−	0.453858i	$-0.850047\pi$
$839$	−791.646	+	457.057i	−0.943559	+	0.544764i	−0.0524848	+	0.998622i	$0.516714\pi$
$840$		0			0
$841$	−380.316	−	658.727i	−0.452219	−	0.783267i
$842$		0			0
$843$	−253.362			−0.300548
$844$		0			0
$845$	−16.2476	+	28.1417i	−0.0192280	+	0.0333038i
$846$		0			0
$847$	−627.191			−0.740486
$848$		0			0
$849$	228.171	+	131.735i	0.268753	+	0.155165i
$850$		0			0
$851$	−838.307	−	483.997i	−0.985084	−	0.568739i
$852$		0			0
$853$	241.160	+	417.701i	0.282720	+	0.489685i	0.972054	−	0.234759i	$-0.0754301\pi$
$853$	241.160	+	417.701i	0.282720	+	0.489685i	−0.689334	+	0.724444i	$0.742097\pi$
$854$		0			0
$855$	1.28271	−	15.9582i	0.00150024	−	0.0186645i
$856$		0			0
$857$	−965.678	+	557.534i	−1.12681	+	0.650565i	−0.943131	−	0.332421i	$-0.892135\pi$
$857$	−965.678	+	557.534i	−1.12681	+	0.650565i	−0.183681	+	0.982986i	$0.558801\pi$
$858$		0			0
$859$	103.471	−	179.217i	0.120455	−	0.208635i	−0.799492	−	0.600677i	$-0.794898\pi$
$859$	103.471	−	179.217i	0.120455	−	0.208635i	0.919947	+	0.392042i	$0.128231\pi$
$860$		0			0
$861$	−211.597	+	366.496i	−0.245757	+	0.425663i
$862$		0			0
$863$			562.589i			0.651899i	0.945387	+	0.325949i	$0.105684\pi$
$863$			562.589i			0.651899i	−0.945387	+	0.325949i	$0.894316\pi$
$864$		0			0
$865$	−13.5989	−	7.85132i	−0.0157213	−	0.00907667i
$866$		0			0
$867$			108.531i			0.125179i
$868$		0			0
$869$	64.7450	−	37.3806i	0.0745052	−	0.0430156i
$870$		0			0
$871$	−214.645	−	371.776i	−0.246435	−	0.426838i
$872$		0			0
$873$		−	563.609i		−	0.645600i
$874$		0			0
$875$	−73.4920			−0.0839909
$876$		0			0
$877$	−446.560	+	257.821i	−0.509190	+	0.293981i	−0.732501	−	0.680766i	$-0.761647\pi$
$877$	−446.560	+	257.821i	−0.509190	+	0.293981i	0.223311	+	0.974747i	$0.428314\pi$
$878$		0			0
$879$	303.709	+	526.039i	0.345516	+	0.598452i
$880$		0			0
$881$	−830.527			−0.942709			−0.471355	−	0.881944i	$-0.656235\pi$
$881$	−830.527			−0.942709			−0.471355	+	0.881944i	$0.656235\pi$
$882$		0			0
$883$	387.441	−	671.068i	0.438778	−	0.759986i	−0.558817	−	0.829291i	$-0.688745\pi$
$883$	387.441	−	671.068i	0.438778	−	0.759986i	0.997596	+	0.0693046i	$0.0220780\pi$
$884$		0			0
$885$	22.3744			0.0252818
$886$		0			0
$887$	−419.897	−	242.428i	−0.473390	−	0.273312i	0.244268	−	0.969708i	$-0.421452\pi$
$887$	−419.897	−	242.428i	−0.473390	−	0.273312i	−0.717658	+	0.696396i	$0.754786\pi$
$888$		0			0
$889$	513.325	+	296.368i	0.577419	+	0.333373i
$890$		0			0
$891$	−5.20825	−	9.02094i	−0.00584539	−	0.0101245i
$892$		0			0
$893$	−823.310	−	567.869i	−0.921960	−	0.635911i
$894$		0			0
$895$	46.4884	−	26.8401i	0.0519423	−	0.0299889i
$896$		0			0
$897$	169.224	−	293.105i	0.188656	−	0.326761i
$898$		0			0
$899$	52.8780	−	91.5874i	0.0588187	−	0.101877i
$900$		0			0
$901$			1529.21i			1.69724i
$902$		0			0
$903$	25.7947	+	14.8926i	0.0285655	+	0.0164923i
$904$		0			0
$905$		−	24.0942i		−	0.0266235i
$906$		0			0
$907$	606.666	−	350.259i	0.668871	−	0.386173i	−0.126778	−	0.991931i	$-0.540464\pi$
$907$	606.666	−	350.259i	0.668871	−	0.386173i	0.795649	+	0.605759i	$0.207130\pi$
$908$		0			0
$909$	−59.5433	−	103.132i	−0.0655042	−	0.113457i
$910$		0			0
$911$		−	1216.56i		−	1.33541i	−0.744426	−	0.667706i	$-0.767277\pi$
$911$		−	1216.56i		−	1.33541i	0.744426	−	0.667706i	$-0.232723\pi$
$912$		0			0
$913$	25.5538			0.0279889
$914$		0			0
$915$	−42.7341	+	24.6725i	−0.0467039	+	0.0269645i
$916$		0			0
$917$	339.425	+	587.902i	0.370148	+	0.641114i
$918$		0			0
$919$	1332.61			1.45006			0.725030	−	0.688717i	$-0.241826\pi$
$919$	1332.61			1.45006			0.725030	+	0.688717i	$0.241826\pi$
$920$		0			0
$921$	412.362	−	714.232i	0.447733	−	0.775497i
$922$		0			0
$923$	−764.853			−0.828660
$924$		0			0
$925$	−780.592	−	450.675i	−0.843883	−	0.487216i
$926$		0			0
$927$	69.4623	+	40.1041i	0.0749323	+	0.0432622i
$928$		0			0
$929$	297.945	+	516.056i	0.320716	+	0.555497i	0.980636	−	0.195839i	$-0.0627431\pi$
$929$	297.945	+	516.056i	0.320716	+	0.555497i	−0.659920	+	0.751336i	$0.729410\pi$
$930$		0			0
$931$	32.7712	−	407.707i	0.0352000	−	0.437923i
$932$		0			0
$933$	−703.427	+	406.124i	−0.753942	+	0.435288i
$934$		0			0
$935$	2.44532	−	4.23542i	0.00261532	−	0.00452986i
$936$		0			0
$937$	−330.843	+	573.037i	−0.353087	+	0.611565i	−0.986789	−	0.162013i	$-0.948201\pi$
$937$	−330.843	+	573.037i	−0.353087	+	0.611565i	0.633701	+	0.773578i	$0.281535\pi$
$938$		0			0
$939$		−	61.2406i		−	0.0652189i
$940$		0			0
$941$	−289.896	−	167.371i	−0.308072	−	0.177865i	0.337992	−	0.941149i	$-0.390252\pi$
$941$	−289.896	−	167.371i	−0.308072	−	0.177865i	−0.646063	+	0.763284i	$0.723586\pi$
$942$		0			0
$943$		−	1247.60i		−	1.32301i
$944$		0			0
$945$	6.62474	−	3.82479i	0.00701030	−	0.00404740i
$946$		0			0
$947$	−523.600	−	906.901i	−0.552904	−	0.957657i	−0.998063	−	0.0622060i	$-0.980186\pi$
$947$	−523.600	−	906.901i	−0.552904	−	0.957657i	0.445160	−	0.895451i	$-0.353147\pi$
$948$		0			0
$949$		−	921.560i		−	0.971085i
$950$		0			0
$951$	−755.109			−0.794015
$952$		0			0
$953$	−1349.22	+	778.975i	−1.41577	+	0.817393i	−0.995923	−	0.0902041i	$-0.971248\pi$
$953$	−1349.22	+	778.975i	−1.41577	+	0.817393i	−0.419843	+	0.907597i	$0.637915\pi$
$954$		0			0
$955$	−46.0874	−	79.8258i	−0.0482591	−	0.0835872i
$956$		0			0
$957$	17.9713			0.0187788
$958$		0			0
$959$	112.628	−	195.077i	0.117443	−	0.203417i
$960$		0			0
$961$	821.835			0.855187
$962$		0			0
$963$	−160.935	−	92.9159i	−0.167118	−	0.0964858i
$964$		0			0
$965$	52.6608	+	30.4037i	0.0545707	+	0.0315064i
$966$		0			0
$967$	−575.086	−	996.077i	−0.594711	−	1.03007i	−0.993588	−	0.113065i	$-0.963933\pi$
$967$	−575.086	−	996.077i	−0.594711	−	1.03007i	0.398877	−	0.917005i	$-0.369400\pi$
$968$		0			0
$969$	281.109	−	407.558i	0.290102	−	0.420597i
$970$		0			0
$971$	970.030	−	560.047i	0.999001	−	0.576774i	0.0910487	−	0.995846i	$-0.470978\pi$
$971$	970.030	−	560.047i	0.999001	−	0.576774i	0.907953	+	0.419073i	$0.137645\pi$
$972$		0			0
$973$	−546.137	+	945.937i	−0.561292	+	0.972186i
$974$		0			0
$975$	157.573	−	272.925i	0.161614	−	0.279923i
$976$		0			0
$977$			106.000i			0.108496i	0.998528	+	0.0542478i	$0.0172761\pi$
$977$			106.000i			0.108496i	−0.998528	+	0.0542478i	$0.982724\pi$
$978$		0			0
$979$	124.510	+	71.8860i	0.127181	+	0.0734280i
$980$		0			0
$981$		−	107.386i		−	0.109466i
$982$		0			0
$983$	−1529.14	+	882.852i	−1.55559	+	0.898120i	−0.557919	+	0.829896i	$0.688400\pi$
$983$	−1529.14	+	882.852i	−1.55559	+	0.898120i	−0.997670	+	0.0682241i	$0.978267\pi$
$984$		0			0
$985$	−12.1088	−	20.9731i	−0.0122932	−	0.0212925i
$986$		0			0
$987$		−	477.887i		−	0.484181i
$988$		0			0
$989$	−87.8083			−0.0887850
$990$		0			0
$991$	−1144.85	+	660.979i	−1.15525	+	0.666982i	−0.950160	−	0.311762i	$-0.899081\pi$
$991$	−1144.85	+	660.979i	−1.15525	+	0.666982i	−0.205087	+	0.978744i	$0.565748\pi$
$992$		0			0
$993$	−7.85174	−	13.5996i	−0.00790709	−	0.0136955i
$994$		0			0
$995$	11.9521			0.0120121
$996$		0			0
$997$	42.4622	−	73.5468i	0.0425900	−	0.0737681i	−0.843945	−	0.536430i	$-0.819772\pi$
$997$	42.4622	−	73.5468i	0.0425900	−	0.0737681i	0.886535	+	0.462662i	$0.153106\pi$
$998$		0			0
$999$	187.935			0.188123

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	912.3.be.d.145.2		6
4.3	odd	2		57.3.g.a.31.3	✓	6
12.11	even	2		171.3.p.e.145.1		6
19.8	odd	6	inner	912.3.be.d.673.2		6
76.27	even	6		57.3.g.a.46.3	yes	6
228.179	odd	6		171.3.p.e.46.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
57.3.g.a.31.3	✓	6	4.3	odd	2
57.3.g.a.46.3	yes	6	76.27	even	6
171.3.p.e.46.1		6	228.179	odd	6
171.3.p.e.145.1		6	12.11	even	2
912.3.be.d.145.2		6	1.1	even	1	trivial
912.3.be.d.673.2		6	19.8	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:	\( N \)	\(=\)	\( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	912.be (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.50000 + 0.866025i) q^{3} +(-0.140435 - 0.243241i) q^{5} +5.24143 q^{7} +(1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+(-1.50000 + 0.866025i) q^{3} +(-0.140435 - 0.243241i) q^{5} +5.24143 q^{7} +(1.50000 - 2.59808i) q^{9} +1.15739 q^{11} +(-6.32289 - 3.65052i) q^{13} +(0.421306 + 0.243241i) q^{15} +(7.52230 + 13.0290i) q^{17} +(-1.52230 + 18.9389i) q^{19} +(-7.86214 + 4.53921i) q^{21} +(13.3819 - 23.1781i) q^{23} +(12.4606 - 21.5823i) q^{25} +5.19615i q^{27} +(-7.76372 - 4.48239i) q^{29} +11.7968i q^{31} +(-1.73608 + 1.00233i) q^{33} +(-0.736082 - 1.27493i) q^{35} -36.1681i q^{37} +12.6458 q^{39} +(40.3701 - 23.3077i) q^{41} +(-1.64044 - 2.84132i) q^{43} -0.842612 q^{45} +(-26.3199 + 45.5874i) q^{47} -21.5274 q^{49} +(-22.5669 - 13.0290i) q^{51} +(88.0273 + 50.8226i) q^{53} +(-0.162538 - 0.281524i) q^{55} +(-14.1181 - 29.7267i) q^{57} +(39.8304 - 22.9961i) q^{59} +(-50.7162 + 87.8430i) q^{61} +(7.86214 - 13.6176i) q^{63} +2.05065i q^{65} +(50.9209 + 29.3992i) q^{67} +46.3561i q^{69} +(90.7243 - 52.3797i) q^{71} +(63.1115 + 109.312i) q^{73} +43.1646i q^{75} +6.06636 q^{77} +(55.9406 - 32.2973i) q^{79} +(-4.50000 - 7.79423i) q^{81} +22.0789 q^{83} +(2.11279 - 3.65947i) q^{85} +15.5274 q^{87} +(107.579 + 62.1106i) q^{89} +(-33.1410 - 19.1339i) q^{91} +(-10.2164 - 17.6953i) q^{93} +(4.82051 - 2.28941i) q^{95} +(162.700 - 93.9348i) q^{97} +(1.73608 - 3.00698i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 9 q^{3} - 2 q^{5} - 26 q^{7} + 9 q^{9}+O(q^{10}) \) 6 * q - 9 * q^3 - 2 * q^5 - 26 * q^7 + 9 * q^9	\( 6 q - 9 q^{3} - 2 q^{5} - 26 q^{7} + 9 q^{9} - 15 q^{13} + 6 q^{15} - 10 q^{17} + 46 q^{19} + 39 q^{21} + 24 q^{23} + 15 q^{25} + 66 q^{29} + 6 q^{35} + 30 q^{39} + 24 q^{41} - 11 q^{43} - 12 q^{45} + 26 q^{47} + 96 q^{49} + 30 q^{51} + 180 q^{53} + 176 q^{55} - 141 q^{57} - 162 q^{59} - 141 q^{61} - 39 q^{63} + 63 q^{67} + 372 q^{71} + 103 q^{73} - 16 q^{77} + 123 q^{79} - 27 q^{81} + 252 q^{83} + 116 q^{85} - 132 q^{87} + 642 q^{89} - 87 q^{91} - 21 q^{93} + 214 q^{95} - 12 q^{97}+O(q^{100}) \) 6 * q - 9 * q^3 - 2 * q^5 - 26 * q^7 + 9 * q^9 - 15 * q^13 + 6 * q^15 - 10 * q^17 + 46 * q^19 + 39 * q^21 + 24 * q^23 + 15 * q^25 + 66 * q^29 + 6 * q^35 + 30 * q^39 + 24 * q^41 - 11 * q^43 - 12 * q^45 + 26 * q^47 + 96 * q^49 + 30 * q^51 + 180 * q^53 + 176 * q^55 - 141 * q^57 - 162 * q^59 - 141 * q^61 - 39 * q^63 + 63 * q^67 + 372 * q^71 + 103 * q^73 - 16 * q^77 + 123 * q^79 - 27 * q^81 + 252 * q^83 + 116 * q^85 - 132 * q^87 + 642 * q^89 - 87 * q^91 - 21 * q^93 + 214 * q^95 - 12 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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