LMFDB - Embedded newform 336.4.bc.c.257.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [336,4,Mod(17,336)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(336, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 3, 1]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("336.17");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	336.bc (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:	$19.8246417619$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 14 x^{10} - 32 x^{9} + 70 x^{8} + 224 x^{7} - 50 x^{6} + 2016 x^{5} + 5670 x^{4} + \cdots + 531441 $ x^12 - 14x^10 - 32x^9 + 70x^8 + 224x^7 - 50x^6 + 2016x^5 + 5670x^4 - 23328x^3 - 91854*x^2 + 531441
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{7} $
Twist minimal:	no (minimal twist has level 84)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			257.6
Root			$0.865250 - 2.87252i$ of defining polynomial
Character	$\chi$	$=$	336.257
Dual form			336.4.bc.c.17.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(4.97534 + 1.49866i) q^{3} +(-0.619556 + 1.07310i) q^{5} +(-8.82127 - 16.2845i) q^{7} +(22.5081 + 14.9127i) q^{9} +O(q^{10})$	\(q+(4.97534 + 1.49866i) q^{3} +(-0.619556 + 1.07310i) q^{5} +(-8.82127 - 16.2845i) q^{7} +(22.5081 + 14.9127i) q^{9} +(-56.1748 + 32.4325i) q^{11} +54.9296i q^{13} +(-4.69072 + 4.41055i) q^{15} +(47.9159 + 82.9928i) q^{17} +(-23.2913 - 13.4472i) q^{19} +(-19.4839 - 94.2411i) q^{21} +(150.137 + 86.6815i) q^{23} +(61.7323 + 106.923i) q^{25} +(89.6363 + 107.927i) q^{27} +16.9397i q^{29} +(-66.1489 + 38.1911i) q^{31} +(-328.094 + 77.1762i) q^{33} +(22.9402 + 0.623042i) q^{35} +(69.3842 - 120.177i) q^{37} +(-82.3207 + 273.294i) q^{39} -100.811 q^{41} -197.789 q^{43} +(-29.9478 + 14.9142i) q^{45} +(161.676 - 280.031i) q^{47} +(-187.370 + 287.300i) q^{49} +(114.020 + 484.727i) q^{51} +(248.397 - 143.412i) q^{53} -80.3751i q^{55} +(-95.7292 - 101.810i) q^{57} +(84.2538 + 145.932i) q^{59} +(-166.581 - 96.1756i) q^{61} +(44.2958 - 498.081i) q^{63} +(-58.9452 - 34.0320i) q^{65} +(-442.197 - 765.908i) q^{67} +(617.076 + 656.274i) q^{69} +661.451i q^{71} +(125.139 - 72.2493i) q^{73} +(146.898 + 624.496i) q^{75} +(1023.68 + 628.683i) q^{77} +(-228.592 + 395.933i) q^{79} +(284.225 + 671.310i) q^{81} -967.789 q^{83} -118.746 q^{85} +(-25.3868 + 84.2808i) q^{87} +(-605.448 + 1048.67i) q^{89} +(894.502 - 484.549i) q^{91} +(-386.349 + 90.8792i) q^{93} +(28.8605 - 16.6626i) q^{95} -777.582i q^{97} +(-1748.04 - 107.722i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 42 q^{7} - 84 q^{9}+O(q^{10}) $ 12 * q + 42 * q^7 - 84 * q^9	$ 12 q + 42 q^{7} - 84 q^{9} - 132 q^{15} - 204 q^{19} - 378 q^{21} - 444 q^{25} - 1458 q^{31} - 108 q^{33} + 240 q^{37} + 432 q^{39} - 342 q^{45} - 1218 q^{49} + 300 q^{51} + 180 q^{57} + 2148 q^{61} - 1596 q^{63} - 1980 q^{67} - 3084 q^{73} + 3384 q^{75} + 438 q^{79} + 1008 q^{81} - 6144 q^{85} + 2898 q^{87} - 3780 q^{91} + 882 q^{93} - 9216 q^{99}+O(q^{100}) $ 12 * q + 42 * q^7 - 84 * q^9 - 132 * q^15 - 204 * q^19 - 378 * q^21 - 444 * q^25 - 1458 * q^31 - 108 * q^33 + 240 * q^37 + 432 * q^39 - 342 * q^45 - 1218 * q^49 + 300 * q^51 + 180 * q^57 + 2148 * q^61 - 1596 * q^63 - 1980 * q^67 - 3084 * q^73 + 3384 * q^75 + 438 * q^79 + 1008 * q^81 - 6144 * q^85 + 2898 * q^87 - 3780 * q^91 + 882 * q^93 - 9216 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$1$	$-1$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	4.97534	+	1.49866i	0.957505	+	0.288417i
$3$	4.97534	+	1.49866i	0.957505	+	0.288417i
$4$		0			0
$5$	−0.619556	+	1.07310i	−0.0554148	+	0.0959812i	−0.892402	−	0.451241i	$-0.850981\pi$
$5$	−0.619556	+	1.07310i	−0.0554148	+	0.0959812i	0.836987	+	0.547222i	$0.184315\pi$
$6$		0			0
$7$	−8.82127	−	16.2845i	−0.476304	−	0.879281i
$7$	−8.82127	−	16.2845i	−0.476304	−	0.879281i
$8$		0			0
$9$	22.5081	+	14.9127i	0.833632	+	0.552321i
$10$		0			0
$11$	−56.1748	+	32.4325i	−1.53976	+	0.888980i	−0.540906	+	0.841083i	$0.681918\pi$
$11$	−56.1748	+	32.4325i	−1.53976	+	0.888980i	−0.998852	+	0.0478964i	$0.984748\pi$
$12$		0			0
$13$			54.9296i			1.17190i	0.810346	+	0.585952i	$0.199279\pi$
$13$			54.9296i			1.17190i	−0.810346	+	0.585952i	$0.800721\pi$
$14$		0			0
$15$	−4.69072	+	4.41055i	−0.0807425	+	0.0759200i
$16$		0			0
$17$	47.9159	+	82.9928i	0.683607	+	1.18404i	0.973872	+	0.227096i	$0.0729232\pi$
$17$	47.9159	+	82.9928i	0.683607	+	1.18404i	−0.290265	+	0.956946i	$0.593744\pi$
$18$		0			0
$19$	−23.2913	−	13.4472i	−0.281231	−	0.162369i	0.352750	−	0.935718i	$-0.385247\pi$
$19$	−23.2913	−	13.4472i	−0.281231	−	0.162369i	−0.633980	+	0.773349i	$0.718580\pi$
$20$		0			0
$21$	−19.4839	−	94.2411i	−0.202464	−	0.979290i
$22$		0			0
$23$	150.137	+	86.6815i	1.36112	+	0.785841i	0.989773	−	0.142654i	$-0.0455635\pi$
$23$	150.137	+	86.6815i	1.36112	+	0.785841i	0.371345	+	0.928495i	$0.378897\pi$
$24$		0			0
$25$	61.7323	+	106.923i	0.493858	+	0.855388i
$26$		0			0
$27$	89.6363	+	107.927i	0.638908	+	0.769283i
$28$		0			0
$29$			16.9397i			0.108470i	0.998528	+	0.0542349i	$0.0172720\pi$
$29$			16.9397i			0.108470i	−0.998528	+	0.0542349i	$0.982728\pi$
$30$		0			0
$31$	−66.1489	+	38.1911i	−0.383248	+	0.221268i	−0.679231	−	0.733925i	$-0.737686\pi$
$31$	−66.1489	+	38.1911i	−0.383248	+	0.221268i	0.295982	+	0.955193i	$0.404353\pi$
$32$		0			0
$33$	−328.094	+	77.1762i	−1.73072	+	0.407111i
$34$		0			0
$35$	22.9402	+	0.623042i	0.110789	+	0.00300895i
$36$		0			0
$37$	69.3842	−	120.177i	0.308289	−	0.533972i	−0.669699	−	0.742632i	$-0.733577\pi$
$37$	69.3842	−	120.177i	0.308289	−	0.533972i	0.977988	+	0.208660i	$0.0669103\pi$
$38$		0			0
$39$	−82.3207	+	273.294i	−0.337996	+	1.12210i
$40$		0			0
$41$	−100.811			−0.383999			−0.192000	−	0.981395i	$-0.561497\pi$
$41$	−100.811			−0.383999			−0.192000	+	0.981395i	$0.561497\pi$
$42$		0			0
$43$	−197.789			−0.701454			−0.350727	−	0.936478i	$-0.614066\pi$
$43$	−197.789			−0.701454			−0.350727	+	0.936478i	$0.614066\pi$
$44$		0			0
$45$	−29.9478	+	14.9142i	−0.0992080	+	0.0494063i
$46$		0			0
$47$	161.676	−	280.031i	0.501762	−	0.869078i	−0.498235	−	0.867042i	$-0.666018\pi$
$47$	161.676	−	280.031i	0.501762	−	0.869078i	0.999998	−	0.00203631i	$-0.000648178\pi$
$48$		0			0
$49$	−187.370	+	287.300i	−0.546270	+	0.837609i
$50$		0			0
$51$	114.020	+	484.727i	0.313060	+	1.33089i
$52$		0			0
$53$	248.397	−	143.412i	0.643772	−	0.371682i	−0.142294	−	0.989824i	$-0.545448\pi$
$53$	248.397	−	143.412i	0.643772	−	0.371682i	0.786066	+	0.618143i	$0.212115\pi$
$54$		0			0
$55$		−	80.3751i		−	0.197051i
$56$		0			0
$57$	−95.7292	−	101.810i	−0.222450	−	0.236580i
$58$		0			0
$59$	84.2538	+	145.932i	0.185914	+	0.322012i	0.943884	−	0.330277i	$-0.107142\pi$
$59$	84.2538	+	145.932i	0.185914	+	0.322012i	−0.757970	+	0.652289i	$0.773809\pi$
$60$		0			0
$61$	−166.581	−	96.1756i	−0.349648	−	0.201869i	0.314882	−	0.949131i	$-0.398035\pi$
$61$	−166.581	−	96.1756i	−0.349648	−	0.201869i	−0.664530	+	0.747261i	$0.731368\pi$
$62$		0			0
$63$	44.2958	−	498.081i	0.0885832	−	0.996069i
$64$		0			0
$65$	−58.9452	−	34.0320i	−0.112481	−	0.0649408i
$66$		0			0
$67$	−442.197	−	765.908i	−0.806313	−	1.39657i	−0.915401	−	0.402543i	$-0.868126\pi$
$67$	−442.197	−	765.908i	−0.806313	−	1.39657i	0.109088	−	0.994032i	$-0.465207\pi$
$68$		0			0
$69$	617.076	+	656.274i	1.07663	+	1.14502i
$70$		0			0
$71$			661.451i			1.10563i	0.833304	+	0.552815i	$0.186446\pi$
$71$			661.451i			1.10563i	−0.833304	+	0.552815i	$0.813554\pi$
$72$		0			0
$73$	125.139	−	72.2493i	0.200637	−	0.115838i	−0.396316	−	0.918114i	$-0.629711\pi$
$73$	125.139	−	72.2493i	0.200637	−	0.115838i	0.596952	+	0.802277i	$0.296378\pi$
$74$		0			0
$75$	146.898	+	624.496i	0.226164	+	0.961475i
$76$		0			0
$77$	1023.68	+	628.683i	1.51506	+	0.930455i
$78$		0			0
$79$	−228.592	+	395.933i	−0.325552	+	0.563872i	−0.981624	−	0.190826i	$-0.938883\pi$
$79$	−228.592	+	395.933i	−0.325552	+	0.563872i	0.656072	+	0.754698i	$0.272217\pi$
$80$		0			0
$81$	284.225	+	671.310i	0.389884	+	0.920864i
$82$		0			0
$83$	−967.789			−1.27986			−0.639931	−	0.768432i	$-0.721037\pi$
$83$	−967.789			−1.27986			−0.639931	+	0.768432i	$0.721037\pi$
$84$		0			0
$85$	−118.746			−0.151528
$86$		0			0
$87$	−25.3868	+	84.2808i	−0.0312845	+	0.103860i
$88$		0			0
$89$	−605.448	+	1048.67i	−0.721094	+	1.24897i	0.239468	+	0.970904i	$0.423027\pi$
$89$	−605.448	+	1048.67i	−0.721094	+	1.24897i	−0.960562	+	0.278067i	$0.910306\pi$
$90$		0			0
$91$	894.502	−	484.549i	1.03043	−	0.558182i
$92$		0			0
$93$	−386.349	+	90.8792i	−0.430779	+	0.101330i
$94$		0			0
$95$	28.8605	−	16.6626i	0.0311687	−	0.0179952i
$96$		0			0
$97$		−	777.582i		−	0.813933i	−0.913443	−	0.406967i	$-0.866587\pi$
$97$		−	777.582i		−	0.813933i	0.913443	−	0.406967i	$-0.133413\pi$
$98$		0			0
$99$	−1748.04	−	107.722i	−1.77459	−	0.109359i
$100$		0			0
$101$	−866.580	−	1500.96i	−0.853742	−	1.47872i	−0.877807	−	0.479014i	$-0.840994\pi$
$101$	−866.580	−	1500.96i	−0.853742	−	1.47872i	0.0240654	−	0.999710i	$-0.492339\pi$
$102$		0			0
$103$	1106.65	+	638.925i	1.05866	+	0.611215i	0.925060	−	0.379821i	$-0.124014\pi$
$103$	1106.65	+	638.925i	1.05866	+	0.611215i	0.133595	+	0.991036i	$0.457348\pi$
$104$		0			0
$105$	113.202	+	37.4794i	0.105213	+	0.0348344i
$106$		0			0
$107$	1131.68	+	653.374i	1.02246	+	0.590318i	0.914816	−	0.403871i	$-0.132336\pi$
$107$	1131.68	+	653.374i	1.02246	+	0.590318i	0.107645	+	0.994189i	$0.465669\pi$
$108$		0			0
$109$	−508.523	−	880.787i	−0.446859	−	0.773983i	0.551320	−	0.834294i	$-0.314124\pi$
$109$	−508.523	−	880.787i	−0.446859	−	0.773983i	−0.998180	+	0.0603107i	$0.980791\pi$
$110$		0			0
$111$	525.314	−	493.938i	0.449194	−	0.422365i
$112$		0			0
$113$			114.438i			0.0952693i	0.998865	+	0.0476346i	$0.0151683\pi$
$113$			114.438i			0.0952693i	−0.998865	+	0.0476346i	$0.984832\pi$
$114$		0			0
$115$	−186.036	+	107.408i	−0.150852	+	0.0870945i
$116$		0			0
$117$	−819.147	+	1236.36i	−0.647266	+	0.976936i
$118$		0			0
$119$	928.818	−	1512.39i	0.715501	−	1.16505i
$120$		0			0
$121$	1438.24	−	2491.10i	1.08057	−	1.87160i
$122$		0			0
$123$	−501.567	−	151.081i	−0.367681	−	0.110752i
$124$		0			0
$125$	−307.876			−0.220298
$126$		0			0
$127$	2154.75			1.50554			0.752768	−	0.658286i	$-0.228718\pi$
$127$	2154.75			1.50554			0.752768	+	0.658286i	$0.228718\pi$
$128$		0			0
$129$	−984.068	−	296.418i	−0.671646	−	0.202311i
$130$		0			0
$131$	−449.460	+	778.487i	−0.299767	+	0.519212i	−0.976083	−	0.217400i	$-0.930242\pi$
$131$	−449.460	+	778.487i	−0.299767	+	0.519212i	0.676315	+	0.736612i	$0.263576\pi$
$132$		0			0
$133$	−13.5229	+	497.908i	−0.00881641	+	0.324617i
$134$		0			0
$135$	−171.352	+	29.3219i	−0.109242	+	0.0186935i
$136$		0			0
$137$	494.836	−	285.694i	0.308589	−	0.178164i	−0.337706	−	0.941252i	$-0.609651\pi$
$137$	494.836	−	285.694i	0.308589	−	0.178164i	0.646295	+	0.763088i	$0.276318\pi$
$138$		0			0
$139$			1078.72i			0.658244i	0.944287	+	0.329122i	$0.106753\pi$
$139$			1078.72i			0.658244i	−0.944287	+	0.329122i	$0.893247\pi$
$140$		0			0
$141$	1224.06	−	1150.95i	0.731097	−	0.687430i
$142$		0			0
$143$	−1781.51	−	3085.66i	−1.04180	−	1.80445i
$144$		0			0
$145$	−18.1780	−	10.4951i	−0.0104111	−	0.00601083i
$146$		0			0
$147$	−1362.80	+	1148.61i	−0.764636	+	0.644462i
$148$		0			0
$149$	−841.243	−	485.692i	−0.462532	−	0.267043i	0.250576	−	0.968097i	$-0.419380\pi$
$149$	−841.243	−	485.692i	−0.462532	−	0.267043i	−0.713108	+	0.701054i	$0.752713\pi$
$150$		0			0
$151$	−730.013	−	1264.42i	−0.393428	−	0.681437i	0.599471	−	0.800396i	$-0.295378\pi$
$151$	−730.013	−	1264.42i	−0.393428	−	0.681437i	−0.992899	+	0.118959i	$0.962044\pi$
$152$		0			0
$153$	−159.149	+	2582.56i	−0.0840946	+	1.36463i
$154$		0			0
$155$		−	94.6461i		−	0.0490462i
$156$		0			0
$157$	1878.50	−	1084.55i	0.954909	−	0.551317i	0.0603065	−	0.998180i	$-0.480792\pi$
$157$	1878.50	−	1084.55i	0.954909	−	0.551317i	0.894602	+	0.446863i	$0.147459\pi$
$158$		0			0
$159$	1450.78	−	341.262i	0.723614	−	0.170213i
$160$		0			0
$161$	87.1693	−	3209.55i	0.0426702	−	1.57110i
$162$		0			0
$163$	1693.30	−	2932.89i	0.813680	−	1.40933i	−0.0965924	−	0.995324i	$-0.530794\pi$
$163$	1693.30	−	2932.89i	0.813680	−	1.40933i	0.910272	−	0.414011i	$-0.135872\pi$
$164$		0			0
$165$	120.455	−	399.894i	0.0568326	−	0.188677i
$166$		0			0
$167$	1261.28			0.584436			0.292218	−	0.956352i	$-0.405607\pi$
$167$	1261.28			0.584436			0.292218	+	0.956352i	$0.405607\pi$
$168$		0			0
$169$	−820.265			−0.373357
$170$		0			0
$171$	−323.707	−	650.005i	−0.144763	−	0.290685i
$172$		0			0
$173$	−67.8201	+	117.468i	−0.0298050	+	0.0516238i	−0.880543	−	0.473966i	$-0.842822\pi$
$173$	−67.8201	+	117.468i	−0.0298050	+	0.0516238i	0.850738	+	0.525590i	$0.176155\pi$
$174$		0			0
$175$	1196.64	−	1948.48i	0.516900	−	0.841665i
$176$		0			0
$177$	200.490	+	852.328i	0.0851397	+	0.361949i
$178$		0			0
$179$	−2940.82	+	1697.88i	−1.22797	+	0.708971i	−0.966606	−	0.256268i	$-0.917507\pi$
$179$	−2940.82	+	1697.88i	−1.22797	+	0.708971i	−0.261368	+	0.965239i	$0.584174\pi$
$180$		0			0
$181$		−	1271.84i		−	0.522294i	−0.965299	−	0.261147i	$-0.915899\pi$
$181$		−	1271.84i		−	0.522294i	0.965299	−	0.261147i	$-0.0841007\pi$
$182$		0			0
$183$	−684.664	−	728.154i	−0.276567	−	0.294135i
$184$		0			0
$185$	85.9748	+	148.913i	0.0341675	+	0.0591799i
$186$		0			0
$187$	−5383.34	−	3108.07i	−2.10518	−	1.21543i
$188$		0			0
$189$	966.839	−	2411.74i	0.372102	−	0.928192i
$190$		0			0
$191$	−2509.87	−	1449.08i	−0.950827	−	0.548960i	−0.0574895	−	0.998346i	$-0.518310\pi$
$191$	−2509.87	−	1449.08i	−0.950827	−	0.548960i	−0.893338	+	0.449386i	$0.851643\pi$
$192$		0			0
$193$	636.386	+	1102.25i	0.237348	+	0.411098i	0.959952	−	0.280163i	$-0.0903887\pi$
$193$	636.386	+	1102.25i	0.237348	+	0.411098i	−0.722605	+	0.691261i	$0.757055\pi$
$194$		0			0
$195$	−242.270	−	257.659i	−0.0889709	−	0.0946224i
$196$		0			0
$197$			1931.73i			0.698630i	0.937005	+	0.349315i	$0.113586\pi$
$197$			1931.73i			0.698630i	−0.937005	+	0.349315i	$0.886414\pi$
$198$		0			0
$199$	2875.45	−	1660.14i	1.02430	−	0.591378i	0.108951	−	0.994047i	$-0.465251\pi$
$199$	2875.45	−	1660.14i	1.02430	−	0.591378i	0.915346	+	0.402669i	$0.131917\pi$
$200$		0			0
$201$	−1052.25	−	4473.35i	−0.369253	−	1.56978i
$202$		0			0
$203$	275.855	−	149.430i	0.0953754	−	0.0516645i
$204$		0			0
$205$	62.4579	−	108.180i	0.0212793	−	0.0368567i
$206$		0			0
$207$	2086.64	+	4189.97i	0.700634	+	1.40688i
$208$		0			0
$209$	1744.51			0.577370
$210$		0			0
$211$	−1337.20			−0.436288			−0.218144	−	0.975917i	$-0.570000\pi$
$211$	−1337.20			−0.436288			−0.218144	+	0.975917i	$0.570000\pi$
$212$		0			0
$213$	−991.287	+	3290.94i	−0.318882	+	1.05865i
$214$		0			0
$215$	122.541	−	212.248i	0.0388709	−	0.0673264i
$216$		0			0
$217$	1205.44	+	740.309i	0.377100	+	0.231592i
$218$		0			0
$219$	730.889	−	171.924i	0.225520	−	0.0530481i
$220$		0			0
$221$	−4558.77	+	2632.01i	−1.38758	+	0.801121i
$222$		0			0
$223$			3883.82i			1.16628i	0.812373	+	0.583138i	$0.198175\pi$
$223$			3883.82i			1.16628i	−0.812373	+	0.583138i	$0.801825\pi$
$224$		0			0
$225$	−205.039	+	3327.23i	−0.0607524	+	0.985847i
$226$		0			0
$227$	2196.76	+	3804.90i	0.642309	+	1.11251i	0.984916	+	0.173033i	$0.0553566\pi$
$227$	2196.76	+	3804.90i	0.642309	+	1.11251i	−0.342607	+	0.939479i	$0.611310\pi$
$228$		0			0
$229$	4125.28	+	2381.73i	1.19042	+	0.687290i	0.958402	−	0.285422i	$-0.0921337\pi$
$229$	4125.28	+	2381.73i	1.19042	+	0.687290i	0.232018	+	0.972711i	$0.425467\pi$
$230$		0			0
$231$	4150.98	+	4662.06i	1.18231	+	1.32788i
$232$		0			0
$233$	977.023	+	564.085i	0.274708	+	0.158603i	0.631025	−	0.775762i	$-0.282634\pi$
$233$	977.023	+	564.085i	0.274708	+	0.158603i	−0.356317	+	0.934365i	$0.615968\pi$
$234$		0			0
$235$	200.334	+	346.989i	0.0556101	+	0.0963196i
$236$		0			0
$237$	−1730.69	+	1627.32i	−0.474348	+	0.446016i
$238$		0			0
$239$			2668.99i			0.722355i	0.932497	+	0.361177i	$0.117625\pi$
$239$			2668.99i			0.722355i	−0.932497	+	0.361177i	$0.882375\pi$
$240$		0			0
$241$	4978.44	−	2874.31i	1.33066	−	0.768259i	0.345262	−	0.938506i	$-0.387790\pi$
$241$	4978.44	−	2874.31i	1.33066	−	0.768259i	0.985401	+	0.170248i	$0.0544568\pi$
$242$		0			0
$243$	408.054	+	3765.95i	0.107723	+	0.994181i
$244$		0			0
$245$	−192.216	−	379.066i	−0.0501234	−	0.0988476i
$246$		0			0
$247$	738.651	−	1279.38i	0.190280	−	0.329575i
$248$		0			0
$249$	−4815.08	−	1450.38i	−1.22548	−	0.369134i
$250$		0			0
$251$	7376.76			1.85505			0.927524	−	0.373763i	$-0.121933\pi$
$251$	7376.76			1.85505			0.927524	+	0.373763i	$0.121933\pi$
$252$		0			0
$253$	−11245.2			−2.79439
$254$		0			0
$255$	−590.804	−	177.960i	−0.145089	−	0.0437031i
$256$		0			0
$257$	1148.07	−	1988.51i	0.278655	−	0.482645i	−0.692396	−	0.721518i	$-0.743445\pi$
$257$	1148.07	−	1988.51i	0.278655	−	0.482645i	0.971051	+	0.238873i	$0.0767780\pi$
$258$		0			0
$259$	−2569.08	−	69.7746i	−0.616350	−	0.0167397i
$260$		0			0
$261$	−252.616	+	381.280i	−0.0599101	+	0.0904238i
$262$		0			0
$263$	6321.86	−	3649.93i	1.48222	−	0.855758i	0.482420	−	0.875940i	$-0.339758\pi$
$263$	6321.86	−	3649.93i	1.48222	−	0.855758i	0.999796	+	0.0201823i	$0.00642467\pi$
$264$		0			0
$265$			355.407i			0.0823867i
$266$		0			0
$267$	−4583.90	+	4310.12i	−1.05068	+	0.987921i
$268$		0			0
$269$	801.460	+	1388.17i	0.181657	+	0.314640i	0.942445	−	0.334361i	$-0.108520\pi$
$269$	801.460	+	1388.17i	0.181657	+	0.314640i	−0.760788	+	0.649001i	$0.775187\pi$
$270$		0			0
$271$	−1676.27	−	967.793i	−0.375741	−	0.216934i	0.300222	−	0.953869i	$-0.402939\pi$
$271$	−1676.27	−	967.793i	−0.375741	−	0.216934i	−0.675964	+	0.736935i	$0.736272\pi$
$272$		0			0
$273$	5176.63	−	1070.25i	1.14763	−	0.237268i
$274$		0			0
$275$	−6935.60	−	4004.27i	−1.52084	−	0.878060i
$276$		0			0
$277$	−1429.42	−	2475.83i	−0.310056	−	0.537033i	0.668318	−	0.743876i	$-0.267014\pi$
$277$	−1429.42	−	2475.83i	−0.310056	−	0.537033i	−0.978374	+	0.206843i	$0.933681\pi$
$278$		0			0
$279$	−2058.41	−	126.849i	−0.441699	−	0.0272195i
$280$		0			0
$281$			3286.82i			0.697777i	0.937164	+	0.348889i	$0.113441\pi$
$281$			3286.82i			0.697777i	−0.937164	+	0.348889i	$0.886559\pi$
$282$		0			0
$283$	−1070.70	+	618.169i	−0.224900	+	0.129846i	−0.608217	−	0.793771i	$-0.708115\pi$
$283$	−1070.70	+	618.169i	−0.224900	+	0.129846i	0.383317	+	0.923617i	$0.374782\pi$
$284$		0			0
$285$	168.562	−	39.6502i	0.0350343	−	0.00824097i
$286$		0			0
$287$	889.278	+	1641.65i	0.182900	+	0.337643i
$288$		0			0
$289$	−2135.37	+	3698.58i	−0.434638	+	0.752814i
$290$		0			0
$291$	1165.33	−	3868.74i	0.234752	−	0.779345i
$292$		0			0
$293$	9667.17			1.92752			0.963758	−	0.266778i	$-0.0859589\pi$
$293$	9667.17			1.92752			0.963758	+	0.266778i	$0.0859589\pi$
$294$		0			0
$295$	−208.800			−0.0412095
$296$		0			0
$297$	−8535.66	−	3155.67i	−1.66764	−	0.616534i
$298$		0			0
$299$	−4761.39	+	8246.96i	−0.920930	+	1.59510i
$300$		0			0
$301$	1744.75	+	3220.90i	0.334105	+	0.616775i
$302$		0			0
$303$	−2062.11	−	8766.50i	−0.390973	−	1.66212i
$304$		0			0
$305$	206.413	−	119.172i	0.0387513	−	0.0223731i
$306$		0			0
$307$			8175.07i			1.51979i	0.650045	+	0.759896i	$0.274750\pi$
$307$			8175.07i			1.51979i	−0.650045	+	0.759896i	$0.725250\pi$
$308$		0			0
$309$	4548.43	+	4837.36i	0.837383	+	0.890575i
$310$		0			0
$311$	359.769	+	623.138i	0.0655969	+	0.113617i	0.896959	−	0.442115i	$-0.145772\pi$
$311$	359.769	+	623.138i	0.0655969	+	0.113617i	−0.831362	+	0.555732i	$0.812438\pi$
$312$		0			0
$313$	6310.26	+	3643.23i	1.13954	+	0.657915i	0.946317	−	0.323239i	$-0.104772\pi$
$313$	6310.26	+	3643.23i	1.13954	+	0.657915i	0.193226	+	0.981154i	$0.438105\pi$
$314$		0			0
$315$	507.049	+	356.123i	0.0906951	+	0.0636993i
$316$		0			0
$317$	−2155.25	−	1244.34i	−0.381864	−	0.220470i	0.296765	−	0.954951i	$-0.404092\pi$
$317$	−2155.25	−	1244.34i	−0.381864	−	0.220470i	−0.678629	+	0.734481i	$0.737426\pi$
$318$		0			0
$319$	−549.397	−	951.584i	−0.0964274	−	0.167017i
$320$		0			0
$321$	4651.30	+	4946.75i	0.808754	+	0.860127i
$322$		0			0
$323$		−	2577.34i		−	0.443985i
$324$		0			0
$325$	−5873.27	+	3390.93i	−1.00243	+	0.578754i
$326$		0			0
$327$	−1210.08	−	5144.32i	−0.204640	−	0.869974i
$328$		0			0
$329$	−5986.35	−	162.585i	−1.00316	−	0.0272451i
$330$		0			0
$331$	−1853.27	+	3209.96i	−0.307749	+	0.533037i	−0.977870	−	0.209215i	$-0.932909\pi$
$331$	−1853.27	+	3209.96i	−0.307749	+	0.533037i	0.670121	+	0.742252i	$0.266242\pi$
$332$		0			0
$333$	3353.86	−	1670.25i	0.551923	−	0.274862i
$334$		0			0
$335$	1095.86			0.178727
$336$		0			0
$337$	−5344.50			−0.863898			−0.431949	−	0.901898i	$-0.642174\pi$
$337$	−5344.50			−0.863898			−0.431949	+	0.901898i	$0.642174\pi$
$338$		0			0
$339$	−171.503	+	569.369i	−0.0274772	+	0.0912208i
$340$		0			0
$341$	2477.27	−	4290.75i	0.393406	−	0.681400i
$342$		0			0
$343$	6331.38	+	516.886i	0.996684	+	0.0813680i
$344$		0			0
$345$	−1086.56	+	255.588i	−0.169561	+	0.0398852i
$346$		0			0
$347$	−2720.97	+	1570.95i	−0.420949	+	0.243035i	−0.695483	−	0.718542i	$-0.744810\pi$
$347$	−2720.97	+	1570.95i	−0.420949	+	0.243035i	0.274534	+	0.961577i	$0.411476\pi$
$348$		0			0
$349$			1019.37i			0.156348i	0.996940	+	0.0781741i	$0.0249090\pi$
$349$			1019.37i			0.156348i	−0.996940	+	0.0781741i	$0.975091\pi$
$350$		0			0
$351$	−5928.41	+	4923.69i	−0.901525	+	0.748738i
$352$		0			0
$353$	3352.27	+	5806.30i	0.505448	+	0.875462i	0.999980	+	0.00630284i	$0.00200627\pi$
$353$	3352.27	+	5806.30i	0.505448	+	0.875462i	−0.494532	+	0.869160i	$0.664660\pi$
$354$		0			0
$355$	−709.805	−	409.806i	−0.106120	−	0.0612683i
$356$		0			0
$357$	6887.74	−	6132.68i	1.02111	−	0.909175i
$358$		0			0
$359$	1032.81	+	596.291i	0.151837	+	0.0876631i	0.573994	−	0.818860i	$-0.305393\pi$
$359$	1032.81	+	596.291i	0.151837	+	0.0876631i	−0.422157	+	0.906523i	$0.638727\pi$
$360$		0			0
$361$	−3067.84	−	5313.66i	−0.447273	−	0.774699i
$362$		0			0
$363$	10889.0	−	10238.7i	1.57445	−	1.48041i
$364$		0			0
$365$			179.050i			0.0256765i
$366$		0			0
$367$	−3581.98	+	2068.05i	−0.509476	+	0.294146i	−0.732618	−	0.680640i	$-0.761702\pi$
$367$	−3581.98	+	2068.05i	−0.509476	+	0.294146i	0.223142	+	0.974786i	$0.428369\pi$
$368$		0			0
$369$	−2269.05	−	1503.36i	−0.320114	−	0.212091i
$370$		0			0
$371$	−4526.56	−	2779.94i	−0.633443	−	0.389023i
$372$		0			0
$373$	696.094	−	1205.67i	0.0966283	−	0.167365i	−0.813659	−	0.581343i	$-0.802528\pi$
$373$	696.094	−	1205.67i	0.0966283	−	0.167365i	0.910287	+	0.413978i	$0.135861\pi$
$374$		0			0
$375$	−1531.79	−	461.400i	−0.210936	−	0.0635376i
$376$		0			0
$377$	−930.491			−0.127116
$378$		0			0
$379$	6840.24			0.927070			0.463535	−	0.886079i	$-0.346581\pi$
$379$	6840.24			0.927070			0.463535	+	0.886079i	$0.346581\pi$
$380$		0			0
$381$	10720.6	+	3229.23i	1.44156	+	0.434222i
$382$		0			0
$383$	4912.29	−	8508.33i	0.655369	−	1.13513i	−0.326432	−	0.945221i	$-0.605847\pi$
$383$	4912.29	−	8508.33i	0.655369	−	1.13513i	0.981801	−	0.189912i	$-0.0608201\pi$
$384$		0			0
$385$	−1308.87	+	709.010i	−0.173263	+	0.0938559i
$386$		0			0
$387$	−4451.84	−	2949.56i	−0.584754	−	0.387428i
$388$		0			0
$389$	−246.932	+	142.566i	−0.0321850	+	0.0185820i	−0.516006	−	0.856585i	$-0.672582\pi$
$389$	−246.932	+	142.566i	−0.0321850	+	0.0185820i	0.483821	+	0.875167i	$0.339249\pi$
$390$		0			0
$391$			16613.7i			2.14883i
$392$		0			0
$393$	−3402.90	+	3199.65i	−0.436778	+	0.410690i
$394$		0			0
$395$	−283.251	−	490.605i	−0.0360808	−	0.0624938i
$396$		0			0
$397$	−10717.4	−	6187.70i	−1.35489	−	0.782247i	−0.365961	−	0.930630i	$-0.619260\pi$
$397$	−10717.4	−	6187.70i	−1.35489	−	0.782247i	−0.988930	+	0.148384i	$0.952593\pi$
$398$		0			0
$399$	−813.475	+	2457.00i	−0.102067	+	0.308280i
$400$		0			0
$401$	−8479.92	−	4895.88i	−1.05603	−	0.609697i	−0.131696	−	0.991290i	$-0.542042\pi$
$401$	−8479.92	−	4895.88i	−1.05603	−	0.609697i	−0.924331	+	0.381593i	$0.875376\pi$
$402$		0			0
$403$	−2097.82	−	3633.53i	−0.259305	−	0.449130i
$404$		0			0
$405$	−896.478	−	110.911i	−0.109991	−	0.0136080i
$406$		0			0
$407$			9001.22i			1.09625i
$408$		0			0
$409$	7947.38	−	4588.42i	0.960813	−	0.554726i	0.0643901	−	0.997925i	$-0.479490\pi$
$409$	7947.38	−	4588.42i	0.960813	−	0.554726i	0.896423	+	0.443199i	$0.146156\pi$
$410$		0			0
$411$	2890.14	−	679.835i	0.346861	−	0.0815907i
$412$		0			0
$413$	1633.20	−	2659.33i	0.194588	−	0.316846i
$414$		0			0
$415$	599.600	−	1038.54i	0.0709233	−	0.122843i
$416$		0			0
$417$	−1616.63	+	5367.01i	−0.189849	+	0.630272i
$418$		0			0
$419$	11642.2			1.35742			0.678711	−	0.734405i	$-0.262539\pi$
$419$	11642.2			1.35742			0.678711	+	0.734405i	$0.262539\pi$
$420$		0			0
$421$	4218.54			0.488359			0.244179	−	0.969730i	$-0.421481\pi$
$421$	4218.54			0.488359			0.244179	+	0.969730i	$0.421481\pi$
$422$		0			0
$423$	7815.01	−	3891.93i	0.898295	−	0.447357i
$424$		0			0
$425$	−5915.92	+	10246.7i	−0.675210	+	1.16950i
$426$		0			0
$427$	−96.7168	+	3561.08i	−0.0109612	+	0.403590i
$428$		0			0
$429$	−4239.26	−	18022.1i	−0.477094	−	2.02824i
$430$		0			0
$431$	−7697.77	+	4444.31i	−0.860298	+	0.496693i	−0.864112	−	0.503300i	$-0.832119\pi$
$431$	−7697.77	+	4444.31i	−0.860298	+	0.496693i	0.00381421	+	0.999993i	$0.498786\pi$
$432$		0			0
$433$			8521.56i			0.945774i	0.881123	+	0.472887i	$0.156788\pi$
$433$			8521.56i			0.945774i	−0.881123	+	0.472887i	$0.843212\pi$
$434$		0			0
$435$	−74.7134	−	79.4593i	−0.00823502	−	0.00875812i
$436$		0			0
$437$	−2331.25	−	4037.85i	−0.255192	−	0.442005i
$438$		0			0
$439$	530.773	+	306.442i	0.0577048	+	0.0333159i	0.528575	−	0.848887i	$-0.322727\pi$
$439$	530.773	+	306.442i	0.0577048	+	0.0333159i	−0.470870	+	0.882203i	$0.656060\pi$
$440$		0			0
$441$	−8501.75	+	3672.37i	−0.918017	+	0.396542i
$442$		0			0
$443$	319.307	+	184.352i	0.0342454	+	0.0197716i	0.517025	−	0.855970i	$-0.327039\pi$
$443$	319.307	+	184.352i	0.0342454	+	0.0197716i	−0.482780	+	0.875742i	$0.660373\pi$
$444$		0			0
$445$	−750.218	−	1299.42i	−0.0799185	−	0.138423i
$446$		0			0
$447$	−3457.59	−	3677.22i	−0.365857	−	0.389097i
$448$		0			0
$449$			6042.70i			0.635128i	0.948237	+	0.317564i	$0.102865\pi$
$449$			6042.70i			0.635128i	−0.948237	+	0.317564i	$0.897135\pi$
$450$		0			0
$451$	5663.02	−	3269.54i	0.591266	−	0.341368i
$452$		0			0
$453$	−1737.13	−	7384.96i	−0.180171	−	0.765951i
$454$		0			0
$455$	−34.2235	+	1260.10i	−0.00352620	+	0.129834i
$456$		0			0
$457$	6521.04	−	11294.8i	0.667487	−	1.15612i	−0.311118	−	0.950371i	$-0.600703\pi$
$457$	6521.04	−	11294.8i	0.667487	−	1.15612i	0.978605	−	0.205750i	$-0.0659633\pi$
$458$		0			0
$459$	−4662.20	+	12610.6i	−0.474102	+	1.28238i
$460$		0			0
$461$	−2429.28			−0.245429			−0.122714	−	0.992442i	$-0.539160\pi$
$461$	−2429.28			−0.245429			−0.122714	+	0.992442i	$0.539160\pi$
$462$		0			0
$463$	−9114.64			−0.914889			−0.457444	−	0.889238i	$-0.651235\pi$
$463$	−9114.64			−0.914889			−0.457444	+	0.889238i	$0.651235\pi$
$464$		0			0
$465$	141.842	−	470.897i	0.0141457	−	0.0469620i
$466$		0			0
$467$	5344.99	−	9257.79i	0.529629	−	0.917344i	−0.469774	−	0.882787i	$-0.655665\pi$
$467$	5344.99	−	9257.79i	0.529629	−	0.917344i	0.999403	−	0.0345570i	$-0.0110020\pi$
$468$		0			0
$469$	−8571.69	+	13957.2i	−0.843932	+	1.37417i
$470$		0			0
$471$	10971.6	−	2580.79i	1.07334	−	0.252477i
$472$		0			0
$473$	11110.8	−	6414.80i	1.08007	−	0.623578i
$474$		0			0
$475$		−	3320.51i		−	0.320748i
$476$		0			0
$477$	7729.58	+	476.332i	0.741956	+	0.0457228i
$478$		0			0
$479$	−3221.06	−	5579.04i	−0.307253	−	0.532177i	0.670508	−	0.741903i	$-0.266076\pi$
$479$	−3221.06	−	5579.04i	−0.307253	−	0.532177i	−0.977760	+	0.209725i	$0.932743\pi$
$480$		0			0
$481$	6601.27	+	3811.25i	0.625763	+	0.361285i
$482$		0			0
$483$	5243.70	−	15838.0i	0.493989	−	1.49203i
$484$		0			0
$485$	834.426	+	481.756i	0.0781223	+	0.0451039i
$486$		0			0
$487$	−7920.17	−	13718.1i	−0.736956	−	1.27644i	−0.953860	−	0.300252i	$-0.902929\pi$
$487$	−7920.17	−	13718.1i	−0.736956	−	1.27644i	0.216905	−	0.976193i	$-0.430404\pi$
$488$		0			0
$489$	12820.2	−	12054.4i	1.18558	−	1.11477i
$490$		0			0
$491$			174.783i			0.0160649i	0.999968	+	0.00803244i	$0.00255683\pi$
$491$			174.783i			0.0160649i	−0.999968	+	0.00803244i	$0.997443\pi$
$492$		0			0
$493$	−1405.87	+	811.681i	−0.128433	+	0.0741507i
$494$		0			0
$495$	1198.61	−	1809.09i	0.108835	−	0.164268i
$496$		0			0
$497$	10771.4	−	5834.83i	0.972159	−	0.526616i
$498$		0			0
$499$	1298.61	−	2249.26i	0.116501	−	0.201785i	−0.801878	−	0.597488i	$-0.796166\pi$
$499$	1298.61	−	2249.26i	0.116501	−	0.201785i	0.918379	+	0.395703i	$0.129499\pi$
$500$		0			0
$501$	6275.30	+	1890.22i	0.559600	+	0.168561i
$502$		0			0
$503$	−21636.9			−1.91797			−0.958987	−	0.283449i	$-0.908521\pi$
$503$	−21636.9			−1.91797			−0.958987	+	0.283449i	$0.908521\pi$
$504$		0			0
$505$	2147.58			0.189240
$506$		0			0
$507$	−4081.10	−	1229.30i	−0.357491	−	0.107682i
$508$		0			0
$509$	2572.24	−	4455.26i	0.223994	−	0.387968i	−0.732023	−	0.681279i	$-0.761424\pi$
$509$	2572.24	−	4455.26i	0.223994	−	0.387968i	0.956017	+	0.293311i	$0.0947572\pi$
$510$		0			0
$511$	−2280.43	−	1400.50i	−0.197418	−	0.121242i
$512$		0			0
$513$	−636.419	−	3719.13i	−0.0547731	−	0.320085i
$514$		0			0
$515$	−1371.26	+	791.700i	−0.117330	+	0.0677407i
$516$		0			0
$517$			20974.2i			1.78423i
$518$		0			0
$519$	−513.472	+	482.804i	−0.0434276	+	0.0408338i
$520$		0			0
$521$	−10107.3	−	17506.4i	−0.849924	−	1.47211i	−0.881275	−	0.472603i	$-0.843314\pi$
$521$	−10107.3	−	17506.4i	−0.849924	−	1.47211i	0.0313516	−	0.999508i	$-0.490019\pi$
$522$		0			0
$523$	11073.3	+	6393.15i	0.925813	+	0.534518i	0.885485	−	0.464668i	$-0.153826\pi$
$523$	11073.3	+	6393.15i	0.925813	+	0.534518i	0.0403281	+	0.999186i	$0.487160\pi$
$524$		0			0
$525$	8873.79	−	7901.01i	0.737684	−	0.656816i
$526$		0			0
$527$	−6339.17	−	3659.92i	−0.523982	−	0.302521i
$528$		0			0
$529$	8943.88	+	15491.3i	0.735093	+	1.27322i
$530$		0			0
$531$	−279.843	+	4541.09i	−0.0228703	+	0.371123i
$532$		0			0
$533$		−	5537.49i		−	0.450010i
$534$		0			0
$535$	−1402.27	+	809.604i	−0.113319	+	0.0654247i
$536$		0			0
$537$	−17176.1	+	4040.27i	−1.38027	+	0.324675i
$538$		0			0
$539$	1207.63	−	22215.9i	0.0965053	−	1.77534i
$540$		0			0
$541$	652.252	−	1129.73i	0.0518346	−	0.0897801i	−0.838944	−	0.544218i	$-0.816826\pi$
$541$	652.252	−	1129.73i	0.0518346	−	0.0897801i	0.890778	+	0.454438i	$0.150160\pi$
$542$		0			0
$543$	1906.05	−	6327.85i	0.150638	−	0.500099i
$544$		0			0
$545$	1260.23			0.0990504
$546$		0			0
$547$	−5425.06			−0.424056			−0.212028	−	0.977264i	$-0.568007\pi$
$547$	−5425.06			−0.424056			−0.212028	+	0.977264i	$0.568007\pi$
$548$		0			0
$549$	−2315.18	−	4648.89i	−0.179981	−	0.361402i
$550$		0			0
$551$	227.792	−	394.547i	0.0176121	−	0.0305050i
$552$		0			0
$553$	8464.04	+	229.878i	0.650864	+	0.0176771i
$554$		0			0
$555$	204.585	+	869.738i	0.0156471	+	0.0665195i
$556$		0			0
$557$	−21651.8	+	12500.7i	−1.64707	+	0.950936i	−0.668842	+	0.743405i	$0.733210\pi$
$557$	−21651.8	+	12500.7i	−1.64707	+	0.950936i	−0.978228	+	0.207531i	$0.933457\pi$
$558$		0			0
$559$		−	10864.5i		−	0.822036i
$560$		0			0
$561$	−22126.0	−	23531.5i	−1.66517	−	1.77095i
$562$		0			0
$563$	−252.273	−	436.949i	−0.0188846	−	0.0327091i	0.856429	−	0.516265i	$-0.172678\pi$
$563$	−252.273	−	436.949i	−0.0188846	−	0.0327091i	−0.875313	+	0.483556i	$0.839345\pi$
$564$		0			0
$565$	−122.804	−	70.9008i	−0.00914406	−	0.00527933i
$566$		0			0
$567$	8424.73	−	10550.3i	0.623995	−	0.781428i
$568$		0			0
$569$	−13368.2	−	7718.14i	−0.984928	−	0.568649i	−0.0811739	−	0.996700i	$-0.525867\pi$
$569$	−13368.2	−	7718.14i	−0.984928	−	0.568649i	−0.903754	+	0.428051i	$0.859200\pi$
$570$		0			0
$571$	200.620	+	347.484i	0.0147035	+	0.0254672i	0.873284	−	0.487212i	$-0.161986\pi$
$571$	200.620	+	347.484i	0.0147035	+	0.0254672i	−0.858580	+	0.512680i	$0.828653\pi$
$572$		0			0
$573$	−10315.8	−	10971.1i	−0.752093	−	0.799867i
$574$		0			0
$575$			21404.2i			1.55238i
$576$		0			0
$577$	13087.8	−	7556.24i	0.944284	−	0.545182i	0.0529832	−	0.998595i	$-0.483127\pi$
$577$	13087.8	−	7556.24i	0.944284	−	0.545182i	0.891301	+	0.453413i	$0.149794\pi$
$578$		0			0
$579$	1514.34	+	6437.81i	0.108694	+	0.462083i
$580$		0			0
$581$	8537.12	+	15760.0i	0.609603	+	1.12536i
$582$		0			0
$583$	−9302.42	+	16112.3i	−0.660835	+	1.14460i
$584$		0			0
$585$	−819.233	−	1645.02i	−0.0578994	−	0.116262i
$586$		0			0
$587$	92.4546			0.00650087			0.00325043	−	0.999995i	$-0.498965\pi$
$587$	92.4546			0.00650087			0.00325043	+	0.999995i	$0.498965\pi$
$588$		0			0
$589$	2054.26			0.143708
$590$		0			0
$591$	−2895.00	+	9611.02i	−0.201496	+	0.668942i
$592$		0			0
$593$	−183.749	+	318.262i	−0.0127245	+	0.0220396i	−0.872318	−	0.488940i	$-0.837384\pi$
$593$	−183.749	+	318.262i	−0.0127245	+	0.0220396i	0.859593	+	0.510979i	$0.170717\pi$
$594$		0			0
$595$	1047.49	+	1933.73i	0.0721733	+	0.133236i
$596$		0			0
$597$	16794.3	−	3950.46i	1.15133	−	0.270823i
$598$		0			0
$599$	−3689.70	+	2130.25i	−0.251681	+	0.145308i	−0.620534	−	0.784180i	$-0.713084\pi$
$599$	−3689.70	+	2130.25i	−0.251681	+	0.145308i	0.368853	+	0.929488i	$0.379751\pi$
$600$		0			0
$601$			799.579i			0.0542687i	0.999632	+	0.0271343i	$0.00863819\pi$
$601$			799.579i			0.0542687i	−0.999632	+	0.0271343i	$0.991362\pi$
$602$		0			0
$603$	1468.73	−	23833.4i	0.0991893	−	1.60957i
$604$		0			0
$605$	1782.14	+	3086.76i	0.119759	+	0.207429i
$606$		0			0
$607$	11078.7	+	6396.27i	0.740806	+	0.427704i	0.822362	−	0.568964i	$-0.192656\pi$
$607$	11078.7	+	6396.27i	0.740806	+	0.427704i	−0.0815566	+	0.996669i	$0.525989\pi$
$608$		0			0
$609$	1596.41	−	330.052i	0.106223	−	0.0219612i
$610$		0			0
$611$	15382.0	+	8880.79i	1.01848	+	0.588017i
$612$		0			0
$613$	−10022.5	−	17359.4i	−0.660365	−	1.14379i	−0.980520	−	0.196420i	$-0.937068\pi$
$613$	−10022.5	−	17359.4i	−0.660365	−	1.14379i	0.320155	−	0.947365i	$-0.396265\pi$
$614$		0			0
$615$	472.874	−	444.631i	0.0310051	−	0.0291532i
$616$		0			0
$617$			17082.6i			1.11462i	0.830305	+	0.557309i	$0.188166\pi$
$617$			17082.6i			1.11462i	−0.830305	+	0.557309i	$0.811834\pi$
$618$		0			0
$619$	14708.7	−	8492.05i	0.955074	−	0.551412i	0.0604206	−	0.998173i	$-0.480756\pi$
$619$	14708.7	−	8492.05i	0.955074	−	0.551412i	0.894653	+	0.446761i	$0.147422\pi$
$620$		0			0
$621$	4102.40	+	23973.7i	0.265094	+	1.54916i
$622$		0			0
$623$	22417.8	+	608.855i	1.44166	+	0.0391545i
$624$		0			0
$625$	−7525.79	+	13035.1i	−0.481651	+	0.834243i
$626$		0			0
$627$	8679.53	+	2614.42i	0.552834	+	0.166523i
$628$		0			0
$629$	13298.4			0.842994
$630$		0			0
$631$	−20829.5			−1.31412			−0.657061	−	0.753837i	$-0.728201\pi$
$631$	−20829.5			−1.31412			−0.657061	+	0.753837i	$0.728201\pi$
$632$		0			0
$633$	−6653.04	−	2004.01i	−0.417748	−	0.125833i
$634$		0			0
$635$	−1334.99	+	2312.27i	−0.0834290	+	0.144503i
$636$		0			0
$637$	−15781.3	−	10292.2i	−0.981597	−	0.640175i
$638$		0			0
$639$	−9863.99	+	14888.0i	−0.610662	+	0.921688i
$640$		0			0
$641$	21862.6	−	12622.4i	1.34714	−	0.777774i	0.359299	−	0.933222i	$-0.383016\pi$
$641$	21862.6	−	12622.4i	1.34714	−	0.777774i	0.987844	+	0.155449i	$0.0496823\pi$
$642$		0			0
$643$			17905.6i			1.09818i	0.835764	+	0.549089i	$0.185025\pi$
$643$			17905.6i			1.09818i	−0.835764	+	0.549089i	$0.814975\pi$
$644$		0			0
$645$	927.772	−	872.358i	0.0566372	−	0.0532544i
$646$		0			0
$647$	3777.94	+	6543.58i	0.229561	+	0.397612i	0.957678	−	0.287841i	$-0.0929376\pi$
$647$	3777.94	+	6543.58i	0.229561	+	0.397612i	−0.728117	+	0.685453i	$0.759604\pi$
$648$		0			0
$649$	−9465.88	−	5465.13i	−0.572524	−	0.330547i
$650$		0			0
$651$	4888.01	+	5489.83i	0.294280	+	0.330512i
$652$		0			0
$653$	−8162.19	−	4712.44i	−0.489144	−	0.282408i	0.235075	−	0.971977i	$-0.424466\pi$
$653$	−8162.19	−	4712.44i	−0.489144	−	0.282408i	−0.724219	+	0.689570i	$0.757800\pi$
$654$		0			0
$655$	−556.931	−	964.633i	−0.0332231	−	0.0575440i
$656$		0			0
$657$	3894.08	+	239.971i	0.231236	+	0.0142499i
$658$		0			0
$659$		−	14519.0i		−	0.858240i	−0.903248	−	0.429120i	$-0.858824\pi$
$659$		−	14519.0i		−	0.858240i	0.903248	−	0.429120i	$-0.141176\pi$
$660$		0			0
$661$	−13331.6	+	7696.97i	−0.784474	+	0.452916i	−0.838013	−	0.545650i	$-0.816283\pi$
$661$	−13331.6	+	7696.97i	−0.784474	+	0.452916i	0.0535396	+	0.998566i	$0.482950\pi$
$662$		0			0
$663$	−26625.9	+	6263.10i	−1.55967	+	0.366876i
$664$		0			0
$665$	−525.929	−	322.994i	−0.0306686	−	0.0188348i
$666$		0			0
$667$	−1468.36	+	2543.27i	−0.0852400	+	0.147640i
$668$		0			0
$669$	−5820.51	+	19323.3i	−0.336373	+	1.11671i
$670$		0			0
$671$	12476.9			0.717831
$672$		0			0
$673$	9948.76			0.569831			0.284916	−	0.958553i	$-0.408034\pi$
$673$	9948.76			0.569831			0.284916	+	0.958553i	$0.408034\pi$
$674$		0			0
$675$	−6006.52	+	16246.8i	−0.342505	+	0.926431i
$676$		0			0
$677$	−7731.79	+	13391.9i	−0.438932	+	0.760252i	−0.997607	−	0.0691341i	$-0.977976\pi$
$677$	−7731.79	+	13391.9i	−0.438932	+	0.760252i	0.558676	+	0.829386i	$0.311310\pi$
$678$		0			0
$679$	−12662.5	+	6859.26i	−0.715676	+	0.387679i
$680$		0			0
$681$	5227.39	+	22222.9i	0.294147	+	1.25049i
$682$		0			0
$683$	10282.5	−	5936.60i	0.576060	−	0.332588i	−0.183506	−	0.983019i	$-0.558745\pi$
$683$	10282.5	−	5936.60i	0.576060	−	0.332588i	0.759566	+	0.650430i	$0.225411\pi$
$684$		0			0
$685$			708.014i			0.0394917i
$686$		0			0
$687$	16955.3	+	18032.3i	0.941608	+	1.00142i
$688$		0			0
$689$	7877.56	+	13644.3i	0.435575	+	0.754438i
$690$		0			0
$691$	4156.18	+	2399.57i	0.228811	+	0.132104i	0.610024	−	0.792383i	$-0.291160\pi$
$691$	4156.18	+	2399.57i	0.228811	+	0.132104i	−0.381212	+	0.924488i	$0.624493\pi$
$692$		0			0
$693$	13665.7	+	29416.2i	0.749088	+	1.61245i
$694$		0			0
$695$	−1157.58	−	668.329i	−0.0631791	−	0.0364765i
$696$		0			0
$697$	−4830.44	−	8366.56i	−0.262505	−	0.454672i
$698$		0			0
$699$	4015.66	+	4270.74i	0.217291	+	0.231093i
$700$		0			0
$701$		−	8788.82i		−	0.473536i	−0.971566	−	0.236768i	$-0.923912\pi$
$701$		−	8788.82i		−	0.473536i	0.971566	−	0.236768i	$-0.0760882\pi$
$702$		0			0
$703$	−3232.09	+	1866.05i	−0.173401	+	0.100113i
$704$		0			0
$705$	476.714	+	2026.62i	0.0254668	+	0.108265i
$706$		0			0
$707$	−16798.1	+	27352.2i	−0.893574	+	1.45500i
$708$		0			0
$709$	−8501.87	+	14725.7i	−0.450345	+	0.780020i	−0.998407	−	0.0564176i	$-0.982032\pi$
$709$	−8501.87	+	14725.7i	−0.450345	+	0.780020i	0.548063	+	0.836437i	$0.315366\pi$
$710$		0			0
$711$	−11049.6	+	5502.76i	−0.582829	+	0.290253i
$712$		0			0
$713$	−13241.8			−0.695527
$714$		0			0
$715$	4414.98			0.230924
$716$		0			0
$717$	−3999.90	+	13279.2i	−0.208339	+	0.691658i
$718$		0			0
$719$	−11003.9	+	19059.3i	−0.570760	+	0.988586i	0.425728	+	0.904851i	$0.360018\pi$
$719$	−11003.9	+	19059.3i	−0.570760	+	0.988586i	−0.996488	+	0.0837345i	$0.973315\pi$
$720$		0			0
$721$	642.520	−	23657.4i	0.0331882	−	1.22198i
$722$		0			0
$723$	29077.1	−	6839.68i	1.49569	−	0.351826i
$724$		0			0
$725$	−1811.25	+	1045.73i	−0.0927837	+	0.0535687i
$726$		0			0
$727$		−	20005.6i		−	1.02059i	−0.860001	−	0.510293i	$-0.829537\pi$
$727$		−	20005.6i		−	1.02059i	0.860001	−	0.510293i	$-0.170463\pi$
$728$		0			0
$729$	−3613.66	+	19348.4i	−0.183593	+	0.983002i
$730$		0			0
$731$	−9477.24	−	16415.1i	−0.479519	−	0.830551i
$732$		0			0
$733$	−7493.92	−	4326.62i	−0.377619	−	0.218018i	0.299163	−	0.954202i	$-0.403293\pi$
$733$	−7493.92	−	4326.62i	−0.377619	−	0.218018i	−0.676782	+	0.736184i	$0.736626\pi$
$734$		0			0
$735$	−388.250	−	2174.05i	−0.0194841	−	0.109103i
$736$		0			0
$737$	49680.6	+	28683.1i	2.48305	+	1.43359i
$738$		0			0
$739$	−2518.09	−	4361.46i	−0.125344	−	0.217103i	0.796523	−	0.604608i	$-0.206670\pi$
$739$	−2518.09	−	4361.46i	−0.125344	−	0.217103i	−0.921867	+	0.387505i	$0.873337\pi$
$740$		0			0
$741$	5592.39	−	5258.37i	0.277249	−	0.260690i
$742$		0			0
$743$			4822.04i			0.238093i	0.992889	+	0.119047i	$0.0379838\pi$
$743$			4822.04i			0.238093i	−0.992889	+	0.119047i	$0.962016\pi$
$744$		0			0
$745$	1042.39	−	601.827i	0.0512623	−	0.0295963i
$746$		0			0
$747$	−21783.0	−	14432.3i	−1.06693	−	0.706895i
$748$		0			0
$749$	657.050	−	24192.4i	0.0320535	−	1.18020i
$750$		0			0
$751$	10017.2	−	17350.3i	0.486729	−	0.843039i	−0.513155	−	0.858296i	$-0.671523\pi$
$751$	10017.2	−	17350.3i	0.486729	−	0.843039i	0.999884	+	0.0152569i	$0.00485662\pi$
$752$		0			0
$753$	36701.9	+	11055.2i	1.77622	+	0.535027i
$754$		0			0
$755$	1809.14			0.0872069
$756$		0			0
$757$	6092.75			0.292530			0.146265	−	0.989245i	$-0.453275\pi$
$757$	6092.75			0.292530			0.146265	+	0.989245i	$0.453275\pi$
$758$		0			0
$759$	−55948.8	−	16852.7i	−2.67564	−	0.805948i
$760$		0			0
$761$	3738.26	−	6474.85i	0.178071	−	0.308427i	−0.763149	−	0.646223i	$-0.776348\pi$
$761$	3738.26	−	6474.85i	0.178071	−	0.308427i	0.941220	+	0.337795i	$0.109681\pi$
$762$		0			0
$763$	−9857.37	+	16050.7i	−0.467708	+	0.761566i
$764$		0			0
$765$	−2672.75	−	1770.83i	−0.126318	−	0.0836920i
$766$		0			0
$767$	−8015.98	+	4628.03i	−0.377367	+	0.217873i
$768$		0			0
$769$			24997.9i			1.17223i	0.810227	+	0.586117i	$0.199344\pi$
$769$			24997.9i			1.17223i	−0.810227	+	0.586117i	$0.800656\pi$
$770$		0			0
$771$	8692.11	−	8172.95i	0.406017	−	0.381766i
$772$		0			0
$773$	2912.70	+	5044.94i	0.135527	+	0.234740i	0.925799	−	0.378017i	$-0.123394\pi$
$773$	2912.70	+	5044.94i	0.135527	+	0.234740i	−0.790272	+	0.612757i	$0.790061\pi$
$774$		0			0
$775$	−8167.05	−	4715.25i	−0.378541	−	0.218551i
$776$		0			0
$777$	−12677.5	−	4197.32i	−0.585331	−	0.193794i
$778$		0			0
$779$	2348.01	+	1355.62i	0.107992	+	0.0623495i
$780$		0			0
$781$	−21452.5	−	37156.8i	−0.982883	−	1.70240i
$782$		0			0
$783$	−1828.26	+	1518.41i	−0.0834439	+	0.0693022i
$784$		0			0
$785$			2687.77i			0.122204i
$786$		0			0
$787$	15489.8	−	8943.04i	0.701590	−	0.405063i	−0.106349	−	0.994329i	$-0.533916\pi$
$787$	15489.8	−	8943.04i	0.701590	−	0.405063i	0.807940	+	0.589265i	$0.200583\pi$
$788$		0			0
$789$	36923.4	−	8685.34i	1.66604	−	0.391897i
$790$		0			0
$791$	1863.57	−	1009.49i	0.0837684	−	0.0453771i
$792$		0			0
$793$	5282.89	−	9150.24i	0.236571	−	0.409753i
$794$		0			0
$795$	−532.633	+	1768.27i	−0.0237617	+	0.0788857i
$796$		0			0
$797$	−25339.1			−1.12617			−0.563085	−	0.826399i	$-0.690386\pi$
$797$	−25339.1			−1.12617			−0.563085	+	0.826399i	$0.690386\pi$
$798$		0			0
$799$	30987.4			1.37203
$800$		0			0
$801$	−29265.9	+	14574.6i	−1.29096	+	0.642907i
$802$		0			0
$803$	−4686.46	+	8117.18i	−0.205954	+	0.356724i
$804$		0			0
$805$	3390.17	+	2082.04i	0.148432	+	0.0911579i
$806$		0			0
$807$	1907.15	+	8107.73i	0.0831905	+	0.353662i
$808$		0			0
$809$	−17555.7	+	10135.8i	−0.762947	+	0.440487i	−0.830353	−	0.557238i	$-0.811861\pi$
$809$	−17555.7	+	10135.8i	−0.762947	+	0.440487i	0.0674061	+	0.997726i	$0.478528\pi$
$810$		0			0
$811$			881.011i			0.0381461i	0.999818	+	0.0190731i	$0.00607151\pi$
$811$			881.011i			0.0381461i	−0.999818	+	0.0190731i	$0.993928\pi$
$812$		0			0
$813$	−6889.61	−	7327.25i	−0.297207	−	0.316086i
$814$		0			0
$815$	2098.19	+	3634.18i	0.0901798	+	0.156196i
$816$		0			0
$817$	4606.75	+	2659.71i	0.197270	+	0.113894i
$818$		0			0
$819$	27359.4	+	2433.15i	1.16730	+	0.103811i
$820$		0			0
$821$	29088.6	+	16794.3i	1.23654	+	0.713916i	0.968385	−	0.249460i	$-0.0802530\pi$
$821$	29088.6	+	16794.3i	1.23654	+	0.713916i	0.268154	+	0.963376i	$0.413586\pi$
$822$		0			0
$823$	15791.4	+	27351.5i	0.668838	+	1.15846i	0.978229	+	0.207526i	$0.0665413\pi$
$823$	15791.4	+	27351.5i	0.668838	+	1.15846i	−0.309392	+	0.950935i	$0.600125\pi$
$824$		0			0
$825$	−28505.9	−	30316.7i	−1.20297	−	1.27938i
$826$		0			0
$827$		−	29539.1i		−	1.24205i	−0.783791	−	0.621024i	$-0.786717\pi$
$827$		−	29539.1i		−	1.24205i	0.783791	−	0.621024i	$-0.213283\pi$
$828$		0			0
$829$	4256.59	−	2457.54i	0.178332	−	0.102960i	−0.408177	−	0.912903i	$-0.633835\pi$
$829$	4256.59	−	2457.54i	0.178332	−	0.102960i	0.586509	+	0.809943i	$0.300502\pi$
$830$		0			0
$831$	−3401.44	−	14460.3i	−0.141991	−	0.603637i
$832$		0			0
$833$	−32821.9	−	1784.16i	−1.36520	−	0.0742106i
$834$		0			0
$835$	−781.434	+	1353.48i	−0.0323864	+	0.0560948i
$836$		0			0
$837$	−10051.2	−	3715.97i	−0.415078	−	0.153456i
$838$		0			0
$839$	−6724.37			−0.276700			−0.138350	−	0.990383i	$-0.544180\pi$
$839$	−6724.37			−0.276700			−0.138350	+	0.990383i	$0.544180\pi$
$840$		0			0
$841$	24102.0			0.988234
$842$		0			0
$843$	−4925.82	+	16353.1i	−0.201251	+	0.668125i
$844$		0			0
$845$	508.200	−	880.229i	0.0206895	−	0.0358353i
$846$		0			0
$847$	−53253.5	−	1446.33i	−2.16034	−	0.0586736i
$848$		0			0
$849$	−6253.53	+	1470.99i	−0.252792	+	0.0594632i
$850$		0			0
$851$	20834.2	−	12028.7i	0.839234	−	0.484532i
$852$		0			0
$853$		−	8582.65i		−	0.344507i	−0.985053	−	0.172253i	$-0.944895\pi$
$853$		−	8582.65i		−	0.344507i	0.985053	−	0.172253i	$-0.0551048\pi$
$854$		0			0
$855$	898.078	+	55.3437i	0.0359223	+	0.00221370i
$856$		0			0
$857$	−20184.4	−	34960.3i	−0.804532	−	1.39349i	−0.916606	−	0.399791i	$-0.869083\pi$
$857$	−20184.4	−	34960.3i	−0.804532	−	1.39349i	0.112074	−	0.993700i	$-0.464251\pi$
$858$		0			0
$859$	22420.1	+	12944.2i	0.890528	+	0.514146i	0.874115	−	0.485719i	$-0.161442\pi$
$859$	22420.1	+	12944.2i	0.890528	+	0.514146i	0.0164125	+	0.999865i	$0.494775\pi$
$860$		0			0
$861$	1964.19	+	9500.50i	0.0777460	+	0.376047i
$862$		0			0
$863$	19554.1	+	11289.6i	0.771298	+	0.445309i	0.833338	−	0.552764i	$-0.186427\pi$
$863$	19554.1	+	11289.6i	0.771298	+	0.445309i	−0.0620392	+	0.998074i	$0.519760\pi$
$864$		0			0
$865$	−84.0367	−	145.556i	−0.00330328	−	0.00572144i
$866$		0			0
$867$	−16167.1	+	15201.5i	−0.633292	+	0.595467i
$868$		0			0
$869$		−	29655.3i		−	1.15764i
$870$		0			0
$871$	42071.0	−	24289.7i	1.63665	−	0.944921i
$872$		0			0
$873$	11595.8	−	17501.9i	0.449552	−	0.678520i
$874$		0			0
$875$	2715.85	+	5013.60i	0.104929	+	0.193704i
$876$		0			0
$877$	−7718.29	+	13368.5i	−0.297182	+	0.514734i	−0.975490	−	0.220044i	$-0.929380\pi$
$877$	−7718.29	+	13368.5i	−0.297182	+	0.514734i	0.678308	+	0.734777i	$0.262713\pi$
$878$		0			0
$879$	48097.5	+	14487.8i	1.84561	+	0.555928i
$880$		0			0
$881$	−12878.8			−0.492505			−0.246253	−	0.969206i	$-0.579199\pi$
$881$	−12878.8			−0.492505			−0.246253	+	0.969206i	$0.579199\pi$
$882$		0			0
$883$	−29072.1			−1.10799			−0.553994	−	0.832521i	$-0.686897\pi$
$883$	−29072.1			−1.10799			−0.553994	+	0.832521i	$0.686897\pi$
$884$		0			0
$885$	−1038.85	−	312.919i	−0.0394583	−	0.0118855i
$886$		0			0
$887$	6245.78	−	10818.0i	0.236429	−	0.409507i	−0.723258	−	0.690578i	$-0.757356\pi$
$887$	6245.78	−	10818.0i	0.236429	−	0.409507i	0.959687	+	0.281071i	$0.0906895\pi$
$888$		0			0
$889$	−19007.6	−	35089.0i	−0.717092	−	1.32379i
$890$		0			0
$891$	−37738.6	−	28492.6i	−1.41896	−	1.07131i
$892$		0			0
$893$	−7531.27	+	4348.18i	−0.282222	+	0.162941i
$894$		0			0
$895$		−	4207.74i		−	0.157150i
$896$		0			0
$897$	−36048.9	+	33895.8i	−1.34185	+	1.26170i
$898$		0			0
$899$	−646.945	−	1120.54i	−0.0240009	−	0.0415708i
$900$		0			0
$901$	23804.3	+	13743.4i	0.880174	+	0.508169i
$902$		0			0
$903$	3853.71	+	18639.8i	0.142019	+	0.686927i
$904$		0			0
$905$	1364.82	+	787.977i	0.0501304	+	0.0289428i
$906$		0			0
$907$	−6202.64	−	10743.3i	−0.227073	−	0.393302i	0.729866	−	0.683590i	$-0.239582\pi$
$907$	−6202.64	−	10743.3i	−0.227073	−	0.393302i	−0.956939	+	0.290288i	$0.906249\pi$
$908$		0			0
$909$	2878.28	−	46706.7i	0.105024	−	1.70425i
$910$		0			0
$911$		−	42362.8i		−	1.54066i	−0.637645	−	0.770331i	$-0.720091\pi$
$911$		−	42362.8i		−	1.54066i	0.637645	−	0.770331i	$-0.279909\pi$
$912$		0			0
$913$	54365.3	−	31387.8i	1.97068	−	1.13777i
$914$		0			0
$915$	1205.57	−	283.582i	0.0435574	−	0.0102458i
$916$		0			0
$917$	16642.1	+	451.989i	0.599313	+	0.0162770i
$918$		0			0
$919$	17133.8	−	29676.6i	0.615007	−	1.06522i	−0.375376	−	0.926873i	$-0.622486\pi$
$919$	17133.8	−	29676.6i	0.615007	−	1.06522i	0.990383	−	0.138351i	$-0.0441802\pi$
$920$		0			0
$921$	−12251.6	+	40673.8i	−0.438333	+	1.45521i
$922$		0			0
$923$	−36333.2			−1.29569
$924$		0			0
$925$	17133.0			0.609004
$926$		0			0
$927$	15380.5	+	30884.1i	0.544942	+	1.09425i
$928$		0			0
$929$	11062.6	−	19160.9i	0.390690	−	0.676695i	−0.601851	−	0.798609i	$-0.705570\pi$
$929$	11062.6	−	19160.9i	0.390690	−	0.676695i	0.992541	+	0.121914i	$0.0389032\pi$
$930$		0			0
$931$	8227.48	−	4171.97i	0.289629	−	0.146864i
$932$		0			0
$933$	856.103	+	3639.49i	0.0300403	+	0.127708i
$934$		0			0
$935$	6670.56	−	3851.25i	0.233316	−	0.134705i
$936$		0			0
$937$		−	4555.00i		−	0.158810i	−0.996842	−	0.0794052i	$-0.974698\pi$
$937$		−	4555.00i		−	0.158810i	0.996842	−	0.0794052i	$-0.0253021\pi$
$938$		0			0
$939$	25935.7	+	27583.2i	0.901364	+	0.958620i
$940$		0			0
$941$	26750.6	+	46333.4i	0.926721	+	1.60513i	0.788770	+	0.614689i	$0.210718\pi$
$941$	26750.6	+	46333.4i	0.926721	+	1.60513i	0.137951	+	0.990439i	$0.455948\pi$
$942$		0			0
$943$	−15135.4	−	8738.42i	−0.522668	−	0.301763i
$944$		0			0
$945$	1989.03	+	2531.73i	0.0684691	+	0.0871504i
$946$		0			0
$947$	−108.948	−	62.9013i	−0.00373848	−	0.00215841i	0.498130	−	0.867103i	$-0.334020\pi$
$947$	−108.948	−	62.9013i	−0.00373848	−	0.00215841i	−0.501868	+	0.864944i	$0.667354\pi$
$948$		0			0
$949$	3968.63	+	6873.87i	0.135750	+	0.235127i
$950$		0			0
$951$	−8858.28	−	9420.98i	−0.302050	−	0.321237i
$952$		0			0
$953$		−	24924.7i		−	0.847209i	−0.905847	−	0.423604i	$-0.860765\pi$
$953$		−	24924.7i		−	0.847209i	0.905847	−	0.423604i	$-0.139235\pi$
$954$		0			0
$955$	3110.01	−	1795.57i	0.105380	−	0.0608411i
$956$		0			0
$957$	−1307.34	−	5557.81i	−0.0441592	−	0.187731i
$958$		0			0
$959$	−9017.47	−	5537.99i	−0.303639	−	0.186476i
$960$		0			0
$961$	−11978.4	+	20747.2i	−0.402081	+	0.696424i
$962$		0			0
$963$	15728.3	+	31582.5i	0.526311	+	1.05683i
$964$		0			0
$965$	−1577.11			−0.0526103
$966$		0			0
$967$	19897.4			0.661692			0.330846	−	0.943685i	$-0.392666\pi$
$967$	19897.4			0.661692			0.330846	+	0.943685i	$0.392666\pi$
$968$		0			0
$969$	3862.55	−	12823.2i	0.128053	−	0.425118i
$970$		0			0
$971$	−19064.3	+	33020.3i	−0.630075	+	1.09132i	0.357462	+	0.933928i	$0.383642\pi$
$971$	−19064.3	+	33020.3i	−0.630075	+	1.09132i	−0.987536	+	0.157393i	$0.949691\pi$
$972$		0			0
$973$	17566.5	−	9515.69i	0.578782	−	0.313524i
$974$		0			0
$975$	−34303.4	+	8069.04i	−1.12676	+	0.265042i
$976$		0			0
$977$	−4321.33	+	2494.92i	−0.141506	+	0.0816986i	−0.569082	−	0.822281i	$-0.692701\pi$
$977$	−4321.33	+	2494.92i	−0.141506	+	0.0816986i	0.427575	+	0.903980i	$0.359368\pi$
$978$		0			0
$979$		−	78544.8i		−	2.56415i
$980$		0			0
$981$	1689.02	−	27408.2i	0.0549708	−	0.892026i
$982$		0			0
$983$	8880.48	+	15381.4i	0.288142	+	0.499076i	0.973366	−	0.229256i	$-0.0736293\pi$
$983$	8880.48	+	15381.4i	0.288142	+	0.499076i	−0.685225	+	0.728332i	$0.740296\pi$
$984$		0			0
$985$	−2072.95	−	1196.82i	−0.0670554	−	0.0387144i
$986$		0			0
$987$	−29540.5	−	9780.40i	−0.952668	−	0.315414i
$988$		0			0
$989$	−29695.4	−	17144.6i	−0.954761	−	0.551232i
$990$		0			0
$991$	−23134.6	−	40070.2i	−0.741568	−	1.28443i	−0.951781	−	0.306777i	$-0.900749\pi$
$991$	−23134.6	−	40070.2i	−0.741568	−	1.28443i	0.210214	−	0.977655i	$-0.432584\pi$
$992$		0			0
$993$	−14031.3	+	13193.2i	−0.448408	+	0.421626i
$994$		0			0
$995$			4114.20i			0.131084i
$996$		0			0
$997$	−41387.9	+	23895.3i	−1.31471	+	0.759049i	−0.982872	−	0.184288i	$-0.941002\pi$
$997$	−41387.9	+	23895.3i	−1.31471	+	0.759049i	−0.331839	+	0.943336i	$0.607669\pi$
$998$		0			0
$999$	19189.7	−	3283.76i	0.607744	−	0.103998i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.4.bc.c.257.6		12
3.2	odd	2	inner	336.4.bc.c.257.4		12
4.3	odd	2		84.4.k.c.5.1	✓	12
7.3	odd	6	inner	336.4.bc.c.17.4		12
12.11	even	2		84.4.k.c.5.3	yes	12
21.17	even	6	inner	336.4.bc.c.17.6		12
28.3	even	6		84.4.k.c.17.3	yes	12
28.11	odd	6		588.4.k.c.521.4		12
28.19	even	6		588.4.f.c.293.6		12
28.23	odd	6		588.4.f.c.293.7		12
28.27	even	2		588.4.k.c.509.6		12
84.11	even	6		588.4.k.c.521.6		12
84.23	even	6		588.4.f.c.293.5		12
84.47	odd	6		588.4.f.c.293.8		12
84.59	odd	6		84.4.k.c.17.1	yes	12
84.83	odd	2		588.4.k.c.509.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.4.k.c.5.1	✓	12	4.3	odd	2
84.4.k.c.5.3	yes	12	12.11	even	2
84.4.k.c.17.1	yes	12	84.59	odd	6
84.4.k.c.17.3	yes	12	28.3	even	6
336.4.bc.c.17.4		12	7.3	odd	6	inner
336.4.bc.c.17.6		12	21.17	even	6	inner
336.4.bc.c.257.4		12	3.2	odd	2	inner
336.4.bc.c.257.6		12	1.1	even	1	trivial
588.4.f.c.293.5		12	84.23	even	6
588.4.f.c.293.6		12	28.19	even	6
588.4.f.c.293.7		12	28.23	odd	6
588.4.f.c.293.8		12	84.47	odd	6
588.4.k.c.509.4		12	84.83	odd	2
588.4.k.c.509.6		12	28.27	even	2
588.4.k.c.521.4		12	28.11	odd	6
588.4.k.c.521.6		12	84.11	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	336.bc (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(4.97534 + 1.49866i) q^{3} +(-0.619556 + 1.07310i) q^{5} +(-8.82127 - 16.2845i) q^{7} +(22.5081 + 14.9127i) q^{9} +O(q^{10})\)	\(q+(4.97534 + 1.49866i) q^{3} +(-0.619556 + 1.07310i) q^{5} +(-8.82127 - 16.2845i) q^{7} +(22.5081 + 14.9127i) q^{9} +(-56.1748 + 32.4325i) q^{11} +54.9296i q^{13} +(-4.69072 + 4.41055i) q^{15} +(47.9159 + 82.9928i) q^{17} +(-23.2913 - 13.4472i) q^{19} +(-19.4839 - 94.2411i) q^{21} +(150.137 + 86.6815i) q^{23} +(61.7323 + 106.923i) q^{25} +(89.6363 + 107.927i) q^{27} +16.9397i q^{29} +(-66.1489 + 38.1911i) q^{31} +(-328.094 + 77.1762i) q^{33} +(22.9402 + 0.623042i) q^{35} +(69.3842 - 120.177i) q^{37} +(-82.3207 + 273.294i) q^{39} -100.811 q^{41} -197.789 q^{43} +(-29.9478 + 14.9142i) q^{45} +(161.676 - 280.031i) q^{47} +(-187.370 + 287.300i) q^{49} +(114.020 + 484.727i) q^{51} +(248.397 - 143.412i) q^{53} -80.3751i q^{55} +(-95.7292 - 101.810i) q^{57} +(84.2538 + 145.932i) q^{59} +(-166.581 - 96.1756i) q^{61} +(44.2958 - 498.081i) q^{63} +(-58.9452 - 34.0320i) q^{65} +(-442.197 - 765.908i) q^{67} +(617.076 + 656.274i) q^{69} +661.451i q^{71} +(125.139 - 72.2493i) q^{73} +(146.898 + 624.496i) q^{75} +(1023.68 + 628.683i) q^{77} +(-228.592 + 395.933i) q^{79} +(284.225 + 671.310i) q^{81} -967.789 q^{83} -118.746 q^{85} +(-25.3868 + 84.2808i) q^{87} +(-605.448 + 1048.67i) q^{89} +(894.502 - 484.549i) q^{91} +(-386.349 + 90.8792i) q^{93} +(28.8605 - 16.6626i) q^{95} -777.582i q^{97} +(-1748.04 - 107.722i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 42 q^{7} - 84 q^{9}+O(q^{10}) \) 12 * q + 42 * q^7 - 84 * q^9	\( 12 q + 42 q^{7} - 84 q^{9} - 132 q^{15} - 204 q^{19} - 378 q^{21} - 444 q^{25} - 1458 q^{31} - 108 q^{33} + 240 q^{37} + 432 q^{39} - 342 q^{45} - 1218 q^{49} + 300 q^{51} + 180 q^{57} + 2148 q^{61} - 1596 q^{63} - 1980 q^{67} - 3084 q^{73} + 3384 q^{75} + 438 q^{79} + 1008 q^{81} - 6144 q^{85} + 2898 q^{87} - 3780 q^{91} + 882 q^{93} - 9216 q^{99}+O(q^{100}) \) 12 * q + 42 * q^7 - 84 * q^9 - 132 * q^15 - 204 * q^19 - 378 * q^21 - 444 * q^25 - 1458 * q^31 - 108 * q^33 + 240 * q^37 + 432 * q^39 - 342 * q^45 - 1218 * q^49 + 300 * q^51 + 180 * q^57 + 2148 * q^61 - 1596 * q^63 - 1980 * q^67 - 3084 * q^73 + 3384 * q^75 + 438 * q^79 + 1008 * q^81 - 6144 * q^85 + 2898 * q^87 - 3780 * q^91 + 882 * q^93 - 9216 * q^99

Introduction

L-functions

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