LMFDB - Embedded newform 588.4.k.c.521.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [588,4,Mod(509,588)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(588, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 5]))

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

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

chi := DirichletCharacter("588.509");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 588 = 2^{2} \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	588.k (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:	$34.6931230834$
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:	$\Z[a_1, \ldots, a_{19}]$
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			521.4
Root			$0.865250 + 2.87252i$ of defining polynomial
Character	$\chi$	$=$	588.521
Dual form			588.4.k.c.509.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.18980 + 5.05810i) q^{3} +(-0.619556 - 1.07310i) q^{5} +(-24.1688 + 12.0362i) q^{9} +O(q^{10})$	\(q+(1.18980 + 5.05810i) q^{3} +(-0.619556 - 1.07310i) q^{5} +(-24.1688 + 12.0362i) q^{9} +(-56.1748 - 32.4325i) q^{11} +54.9296i q^{13} +(4.69072 - 4.41055i) q^{15} +(47.9159 - 82.9928i) q^{17} +(-23.2913 + 13.4472i) q^{19} +(150.137 - 86.6815i) q^{23} +(61.7323 - 106.923i) q^{25} +(-89.6363 - 107.927i) q^{27} +16.9397i q^{29} +(-66.1489 - 38.1911i) q^{31} +(97.2105 - 322.726i) q^{33} +(69.3842 + 120.177i) q^{37} +(-277.840 + 65.3551i) q^{39} -100.811 q^{41} +197.789 q^{43} +(27.8900 + 18.4785i) q^{45} +(-161.676 - 280.031i) q^{47} +(476.796 + 143.619i) q^{51} +(-248.397 - 143.412i) q^{53} +80.3751i q^{55} +(-95.7292 - 101.810i) q^{57} +(-84.2538 + 145.932i) q^{59} +(166.581 - 96.1756i) q^{61} +(58.9452 - 34.0320i) q^{65} +(442.197 - 765.908i) q^{67} +(617.076 + 656.274i) q^{69} -661.451i q^{71} +(-125.139 - 72.2493i) q^{73} +(614.279 + 185.031i) q^{75} +(228.592 + 395.933i) q^{79} +(439.259 - 581.801i) q^{81} +967.789 q^{83} -118.746 q^{85} +(-85.6827 + 20.1548i) q^{87} +(-605.448 - 1048.67i) q^{89} +(114.471 - 380.027i) q^{93} +(28.8605 + 16.6626i) q^{95} -777.582i q^{97} +(1748.04 + 107.722i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 84 q^{9}+O(q^{10}) $ 12 * q - 84 * q^9	$ 12 q - 84 q^{9} + 132 q^{15} - 204 q^{19} - 444 q^{25} - 1458 q^{31} + 108 q^{33} + 240 q^{37} - 432 q^{39} + 342 q^{45} - 300 q^{51} + 180 q^{57} - 2148 q^{61} + 1980 q^{67} + 3084 q^{73} + 3384 q^{75} - 438 q^{79} + 1008 q^{81} - 6144 q^{85} + 2898 q^{87} + 882 q^{93} + 9216 q^{99}+O(q^{100}) $ 12 * q - 84 * q^9 + 132 * q^15 - 204 * q^19 - 444 * q^25 - 1458 * q^31 + 108 * q^33 + 240 * q^37 - 432 * q^39 + 342 * q^45 - 300 * q^51 + 180 * q^57 - 2148 * q^61 + 1980 * q^67 + 3084 * q^73 + 3384 * q^75 - 438 * q^79 + 1008 * q^81 - 6144 * q^85 + 2898 * q^87 + 882 * q^93 + 9216 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/588\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$493$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.18980	+	5.05810i	0.228976	+	0.973432i
$3$	1.18980	+	5.05810i	0.228976	+	0.973432i
$4$		0			0
$5$	−0.619556	−	1.07310i	−0.0554148	−	0.0959812i	0.836987	−	0.547222i	$-0.184315\pi$
$5$	−0.619556	−	1.07310i	−0.0554148	−	0.0959812i	−0.892402	+	0.451241i	$0.850981\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	−24.1688	+	12.0362i	−0.895140	+	0.445786i
$10$		0			0
$11$	−56.1748	−	32.4325i	−1.53976	−	0.888980i	−0.998852	−	0.0478964i	$-0.984748\pi$
$11$	−56.1748	−	32.4325i	−1.53976	−	0.888980i	−0.540906	−	0.841083i	$-0.681918\pi$
$12$		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	−0.290265	−	0.956946i	$-0.593744\pi$
$17$	47.9159	−	82.9928i	0.683607	−	1.18404i	0.973872	−	0.227096i	$-0.0729232\pi$
$18$		0			0
$19$	−23.2913	+	13.4472i	−0.281231	+	0.162369i	−0.633980	−	0.773349i	$-0.718580\pi$
$19$	−23.2913	+	13.4472i	−0.281231	+	0.162369i	0.352750	+	0.935718i	$0.385247\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	150.137	−	86.6815i	1.36112	−	0.785841i	0.371345	−	0.928495i	$-0.378897\pi$
$23$	150.137	−	86.6815i	1.36112	−	0.785841i	0.989773	+	0.142654i	$0.0455635\pi$
$24$		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	0.295982	−	0.955193i	$-0.404353\pi$
$31$	−66.1489	−	38.1911i	−0.383248	−	0.221268i	−0.679231	+	0.733925i	$0.737686\pi$
$32$		0			0
$33$	97.2105	−	322.726i	0.512793	−	1.70241i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	69.3842	+	120.177i	0.308289	+	0.533972i	0.977988	−	0.208660i	$-0.0669103\pi$
$37$	69.3842	+	120.177i	0.308289	+	0.533972i	−0.669699	+	0.742632i	$0.733577\pi$
$38$		0			0
$39$	−277.840	+	65.3551i	−1.14077	+	0.268338i
$40$		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	$-0.385934\pi$
$43$	197.789			0.701454			0.350727	+	0.936478i	$0.385934\pi$
$44$		0			0
$45$	27.8900	+	18.4785i	0.0923911	+	0.0612135i
$46$		0			0
$47$	−161.676	−	280.031i	−0.501762	−	0.869078i	−0.999998	−	0.00203631i	$-0.999352\pi$
$47$	−161.676	−	280.031i	−0.501762	−	0.869078i	0.498235	−	0.867042i	$-0.333982\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	476.796	+	143.619i	1.30911	+	0.394327i
$52$		0			0
$53$	−248.397	−	143.412i	−0.643772	−	0.371682i	0.142294	−	0.989824i	$-0.454552\pi$
$53$	−248.397	−	143.412i	−0.643772	−	0.371682i	−0.786066	+	0.618143i	$0.787885\pi$
$54$		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	$-0.892858\pi$
$59$	−84.2538	+	145.932i	−0.185914	+	0.322012i	0.757970	+	0.652289i	$0.226191\pi$
$60$		0			0
$61$	166.581	−	96.1756i	0.349648	−	0.201869i	−0.314882	−	0.949131i	$-0.601965\pi$
$61$	166.581	−	96.1756i	0.349648	−	0.201869i	0.664530	+	0.747261i	$0.268632\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	58.9452	−	34.0320i	0.112481	−	0.0649408i
$66$		0			0
$67$	442.197	−	765.908i	0.806313	−	1.39657i	−0.109088	−	0.994032i	$-0.534793\pi$
$67$	442.197	−	765.908i	0.806313	−	1.39657i	0.915401	−	0.402543i	$-0.131874\pi$
$68$		0			0
$69$	617.076	+	656.274i	1.07663	+	1.14502i
$70$		0			0
$71$		−	661.451i		−	1.10563i	−0.833304	−	0.552815i	$-0.813554\pi$
$71$		−	661.451i		−	1.10563i	0.833304	−	0.552815i	$-0.186446\pi$
$72$		0			0
$73$	−125.139	−	72.2493i	−0.200637	−	0.115838i	0.396316	−	0.918114i	$-0.370289\pi$
$73$	−125.139	−	72.2493i	−0.200637	−	0.115838i	−0.596952	+	0.802277i	$0.703622\pi$
$74$		0			0
$75$	614.279	+	185.031i	0.945744	+	0.284874i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	228.592	+	395.933i	0.325552	+	0.563872i	0.981624	−	0.190826i	$-0.0611166\pi$
$79$	228.592	+	395.933i	0.325552	+	0.563872i	−0.656072	+	0.754698i	$0.727783\pi$
$80$		0			0
$81$	439.259	−	581.801i	0.602550	−	0.798081i
$82$		0			0
$83$	967.789			1.27986			0.639931	−	0.768432i	$-0.278963\pi$
$83$	967.789			1.27986			0.639931	+	0.768432i	$0.278963\pi$
$84$		0			0
$85$	−118.746			−0.151528
$86$		0			0
$87$	−85.6827	+	20.1548i	−0.105588	+	0.0248370i
$88$		0			0
$89$	−605.448	−	1048.67i	−0.721094	−	1.24897i	−0.960562	−	0.278067i	$-0.910306\pi$
$89$	−605.448	−	1048.67i	−0.721094	−	1.24897i	0.239468	−	0.970904i	$-0.423027\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	114.471	−	380.027i	0.127635	−	0.423731i
$94$		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	0.0240654	+	0.999710i	$0.492339\pi$
$101$	−866.580	+	1500.96i	−0.853742	+	1.47872i	−0.877807	+	0.479014i	$0.840994\pi$
$102$		0			0
$103$	1106.65	−	638.925i	1.05866	−	0.611215i	0.133595	−	0.991036i	$-0.457348\pi$
$103$	1106.65	−	638.925i	1.05866	−	0.611215i	0.925060	+	0.379821i	$0.124014\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	1131.68	−	653.374i	1.02246	−	0.590318i	0.107645	−	0.994189i	$-0.465669\pi$
$107$	1131.68	−	653.374i	1.02246	−	0.590318i	0.914816	+	0.403871i	$0.132336\pi$
$108$		0			0
$109$	−508.523	+	880.787i	−0.446859	+	0.773983i	−0.998180	−	0.0603107i	$-0.980791\pi$
$109$	−508.523	+	880.787i	−0.446859	+	0.773983i	0.551320	+	0.834294i	$0.314124\pi$
$110$		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
$117$	−661.145	−	1327.58i	−0.522418	−	1.04902i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	1438.24	+	2491.10i	1.08057	+	1.87160i
$122$		0			0
$123$	−119.944	−	509.910i	−0.0879268	−	0.373797i
$124$		0			0
$125$	−307.876			−0.220298
$126$		0			0
$127$	−2154.75			−1.50554			−0.752768	−	0.658286i	$-0.771282\pi$
$127$	−2154.75			−1.50554			−0.752768	+	0.658286i	$0.771282\pi$
$128$		0			0
$129$	235.328	+	1000.44i	0.160616	+	0.682818i
$130$		0			0
$131$	449.460	+	778.487i	0.299767	+	0.519212i	0.976083	−	0.217400i	$-0.0697577\pi$
$131$	449.460	+	778.487i	0.299767	+	0.519212i	−0.676315	+	0.736612i	$0.736424\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−60.2825	+	163.056i	−0.0384318	+	0.103953i
$136$		0			0
$137$	−494.836	−	285.694i	−0.308589	−	0.178164i	0.337706	−	0.941252i	$-0.390349\pi$
$137$	−494.836	−	285.694i	−0.308589	−	0.178164i	−0.646295	+	0.763088i	$0.723682\pi$
$138$		0			0
$139$		−	1078.72i		−	0.658244i	−0.944287	−	0.329122i	$-0.893247\pi$
$139$		−	1078.72i		−	0.658244i	0.944287	−	0.329122i	$-0.106753\pi$
$140$		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
$147$		0			0
$148$		0			0
$149$	841.243	−	485.692i	0.462532	−	0.267043i	−0.250576	−	0.968097i	$-0.580620\pi$
$149$	841.243	−	485.692i	0.462532	−	0.267043i	0.713108	+	0.701054i	$0.247287\pi$
$150$		0			0
$151$	730.013	−	1264.42i	0.393428	−	0.681437i	−0.599471	−	0.800396i	$-0.704622\pi$
$151$	730.013	−	1264.42i	0.393428	−	0.681437i	0.992899	+	0.118959i	$0.0379557\pi$
$152$		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	$-0.519208\pi$
$157$	−1878.50	−	1084.55i	−0.954909	−	0.551317i	−0.894602	+	0.446863i	$0.852541\pi$
$158$		0			0
$159$	429.850	−	1427.05i	0.214398	−	0.711774i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−1693.30	−	2932.89i	−0.813680	−	1.40933i	−0.910272	−	0.414011i	$-0.864128\pi$
$163$	−1693.30	−	2932.89i	−0.813680	−	1.40933i	0.0965924	−	0.995324i	$-0.469206\pi$
$164$		0			0
$165$	−406.545	+	95.6300i	−0.191815	+	0.0451199i
$166$		0			0
$167$	−1261.28			−0.584436			−0.292218	−	0.956352i	$-0.594393\pi$
$167$	−1261.28			−0.584436			−0.292218	+	0.956352i	$0.594393\pi$
$168$		0			0
$169$	−820.265			−0.373357
$170$		0			0
$171$	401.068	−	605.341i	0.179359	−	0.270711i
$172$		0			0
$173$	−67.8201	−	117.468i	−0.0298050	−	0.0516238i	0.850738	−	0.525590i	$-0.176155\pi$
$173$	−67.8201	−	117.468i	−0.0298050	−	0.0516238i	−0.880543	+	0.473966i	$0.842822\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−838.383	−	252.535i	−0.356027	−	0.107241i
$178$		0			0
$179$	−2940.82	−	1697.88i	−1.22797	−	0.708971i	−0.261368	−	0.965239i	$-0.584174\pi$
$179$	−2940.82	−	1697.88i	−1.22797	−	0.708971i	−0.966606	+	0.256268i	$0.917507\pi$
$180$		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
$189$		0			0
$190$		0			0
$191$	−2509.87	+	1449.08i	−0.950827	+	0.548960i	−0.893338	−	0.449386i	$-0.851643\pi$
$191$	−2509.87	+	1449.08i	−0.950827	+	0.548960i	−0.0574895	+	0.998346i	$0.518310\pi$
$192$		0			0
$193$	636.386	−	1102.25i	0.237348	−	0.411098i	−0.722605	−	0.691261i	$-0.757055\pi$
$193$	636.386	−	1102.25i	0.237348	−	0.411098i	0.959952	+	0.280163i	$0.0903887\pi$
$194$		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	0.915346	−	0.402669i	$-0.131917\pi$
$199$	2875.45	+	1660.14i	1.02430	+	0.591378i	0.108951	+	0.994047i	$0.465251\pi$
$200$		0			0
$201$	4400.16	+	1325.40i	1.54410	+	0.465108i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	62.4579	+	108.180i	0.0212793	+	0.0368567i
$206$		0			0
$207$	−2585.30	+	3902.07i	−0.868073	+	1.31020i
$208$		0			0
$209$	1744.51			0.577370
$210$		0			0
$211$	1337.20			0.436288			0.218144	−	0.975917i	$-0.430000\pi$
$211$	1337.20			0.436288			0.218144	+	0.975917i	$0.430000\pi$
$212$		0			0
$213$	3345.68	−	786.991i	1.07626	−	0.253163i
$214$		0			0
$215$	−122.541	−	212.248i	−0.0388709	−	0.0673264i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	216.554	−	718.930i	0.0668190	−	0.221830i
$220$		0			0
$221$	4558.77	+	2632.01i	1.38758	+	0.801121i
$222$		0			0
$223$		−	3883.82i		−	1.16628i	−0.812373	−	0.583138i	$-0.801825\pi$
$223$		−	3883.82i		−	1.16628i	0.812373	−	0.583138i	$-0.198175\pi$
$224$		0			0
$225$	−205.039	+	3327.23i	−0.0607524	+	0.985847i
$226$		0			0
$227$	−2196.76	+	3804.90i	−0.642309	+	1.11251i	0.342607	+	0.939479i	$0.388690\pi$
$227$	−2196.76	+	3804.90i	−0.642309	+	1.11251i	−0.984916	+	0.173033i	$0.944643\pi$
$228$		0			0
$229$	−4125.28	+	2381.73i	−1.19042	+	0.687290i	−0.958402	−	0.285422i	$-0.907866\pi$
$229$	−4125.28	+	2381.73i	−1.19042	+	0.687290i	−0.232018	+	0.972711i	$0.574533\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−977.023	+	564.085i	−0.274708	+	0.158603i	−0.631025	−	0.775762i	$-0.717366\pi$
$233$	−977.023	+	564.085i	−0.274708	+	0.158603i	0.356317	+	0.934365i	$0.384032\pi$
$234$		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	$-0.882375\pi$
$239$		−	2668.99i		−	0.722355i	0.932497	−	0.361177i	$-0.117625\pi$
$240$		0			0
$241$	−4978.44	−	2874.31i	−1.33066	−	0.768259i	−0.345262	−	0.938506i	$-0.612210\pi$
$241$	−4978.44	−	2874.31i	−1.33066	−	0.768259i	−0.985401	+	0.170248i	$0.945543\pi$
$242$		0			0
$243$	3465.44	+	1529.59i	0.914847	+	0.403800i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−738.651	−	1279.38i	−0.190280	−	0.329575i
$248$		0			0
$249$	1151.47	+	4895.17i	0.293058	+	1.24586i
$250$		0			0
$251$	−7376.76			−1.85505			−0.927524	−	0.373763i	$-0.878067\pi$
$251$	−7376.76			−1.85505			−0.927524	+	0.373763i	$0.878067\pi$
$252$		0			0
$253$	−11245.2			−2.79439
$254$		0			0
$255$	−141.284	−	600.632i	−0.0346963	−	0.147502i
$256$		0			0
$257$	1148.07	+	1988.51i	0.278655	+	0.482645i	0.971051	−	0.238873i	$-0.0767780\pi$
$257$	1148.07	+	1988.51i	0.278655	+	0.482645i	−0.692396	+	0.721518i	$0.743445\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−203.890	−	409.412i	−0.0483543	−	0.0970956i
$262$		0			0
$263$	6321.86	+	3649.93i	1.48222	+	0.855758i	0.999796	−	0.0201823i	$-0.00642467\pi$
$263$	6321.86	+	3649.93i	1.48222	+	0.855758i	0.482420	+	0.875940i	$0.339758\pi$
$264$		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	−0.760788	−	0.649001i	$-0.775187\pi$
$269$	801.460	−	1388.17i	0.181657	−	0.314640i	0.942445	+	0.334361i	$0.108520\pi$
$270$		0			0
$271$	−1676.27	+	967.793i	−0.375741	+	0.216934i	−0.675964	−	0.736935i	$-0.736272\pi$
$271$	−1676.27	+	967.793i	−0.375741	+	0.216934i	0.300222	+	0.953869i	$0.402939\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−6935.60	+	4004.27i	−1.52084	+	0.878060i
$276$		0			0
$277$	−1429.42	+	2475.83i	−0.310056	+	0.537033i	−0.978374	−	0.206843i	$-0.933681\pi$
$277$	−1429.42	+	2475.83i	−0.310056	+	0.537033i	0.668318	+	0.743876i	$0.267014\pi$
$278$		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	0.383317	−	0.923617i	$-0.374782\pi$
$283$	−1070.70	−	618.169i	−0.224900	−	0.129846i	−0.608217	+	0.793771i	$0.708115\pi$
$284$		0			0
$285$	−49.9431	+	165.804i	−0.0103803	+	0.0344611i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−2135.37	−	3698.58i	−0.434638	−	0.752814i
$290$		0			0
$291$	3933.09	−	925.164i	0.792308	−	0.186371i
$292$		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
$297$	1534.94	+	8969.93i	0.299887	+	1.75249i
$298$		0			0
$299$	4761.39	+	8246.96i	0.920930	+	1.59510i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	−8623.06	−	2597.41i	−1.63492	−	0.492467i
$304$		0			0
$305$	−206.413	−	119.172i	−0.0387513	−	0.0223731i
$306$		0			0
$307$		−	8175.07i		−	1.51979i	−0.650045	−	0.759896i	$-0.725250\pi$
$307$		−	8175.07i		−	1.51979i	0.650045	−	0.759896i	$-0.274750\pi$
$308$		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	$-0.854228\pi$
$311$	−359.769	+	623.138i	−0.0655969	+	0.113617i	0.831362	+	0.555732i	$0.187562\pi$
$312$		0			0
$313$	−6310.26	+	3643.23i	−1.13954	+	0.657915i	−0.946317	−	0.323239i	$-0.895228\pi$
$313$	−6310.26	+	3643.23i	−1.13954	+	0.657915i	−0.193226	+	0.981154i	$0.561895\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	2155.25	−	1244.34i	0.381864	−	0.220470i	−0.296765	−	0.954951i	$-0.595908\pi$
$317$	2155.25	−	1244.34i	0.381864	−	0.220470i	0.678629	+	0.734481i	$0.262574\pi$
$318$		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
$327$	−5060.15	−	1524.20i	−0.855740	−	0.257763i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	1853.27	+	3209.96i	0.307749	+	0.533037i	0.977870	−	0.209215i	$-0.0670910\pi$
$331$	1853.27	+	3209.96i	0.307749	+	0.533037i	−0.670121	+	0.742252i	$0.733758\pi$
$332$		0			0
$333$	−3123.41	−	2069.41i	−0.513999	−	0.340549i
$334$		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
$339$	−578.839	+	136.158i	−0.0927382	+	0.0218144i
$340$		0			0
$341$	2477.27	+	4290.75i	0.393406	+	0.681400i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	321.936	−	1068.78i	0.0502390	−	0.166787i
$346$		0			0
$347$	−2720.97	−	1570.95i	−0.420949	−	0.243035i	0.274534	−	0.961577i	$-0.411476\pi$
$347$	−2720.97	−	1570.95i	−0.420949	−	0.243035i	−0.695483	+	0.718542i	$0.744810\pi$
$348$		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	−0.494532	−	0.869160i	$-0.664660\pi$
$353$	3352.27	−	5806.30i	0.505448	−	0.875462i	0.999980	−	0.00630284i	$-0.00200627\pi$
$354$		0			0
$355$	−709.805	+	409.806i	−0.106120	+	0.0612683i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	1032.81	−	596.291i	0.151837	−	0.0876631i	−0.422157	−	0.906523i	$-0.638727\pi$
$359$	1032.81	−	596.291i	0.151837	−	0.0876631i	0.573994	+	0.818860i	$0.305393\pi$
$360$		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	0.223142	−	0.974786i	$-0.428369\pi$
$367$	−3581.98	−	2068.05i	−0.509476	−	0.294146i	−0.732618	+	0.680640i	$0.761702\pi$
$368$		0			0
$369$	2436.47	−	1213.38i	0.343733	−	0.171182i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	696.094	+	1205.67i	0.0966283	+	0.167365i	0.910287	−	0.413978i	$-0.135861\pi$
$373$	696.094	+	1205.67i	0.0966283	+	0.167365i	−0.813659	+	0.581343i	$0.802528\pi$
$374$		0			0
$375$	−366.309	−	1557.27i	−0.0504430	−	0.214445i
$376$		0			0
$377$	−930.491			−0.127116
$378$		0			0
$379$	−6840.24			−0.927070			−0.463535	−	0.886079i	$-0.653419\pi$
$379$	−6840.24			−0.927070			−0.463535	+	0.886079i	$0.653419\pi$
$380$		0			0
$381$	−2563.71	−	10898.9i	−0.344732	−	1.46554i
$382$		0			0
$383$	−4912.29	−	8508.33i	−0.655369	−	1.13513i	−0.981801	−	0.189912i	$-0.939180\pi$
$383$	−4912.29	−	8508.33i	−0.655369	−	1.13513i	0.326432	−	0.945221i	$-0.394153\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−4780.32	+	2380.63i	−0.627899	+	0.312698i
$388$		0			0
$389$	246.932	+	142.566i	0.0321850	+	0.0185820i	0.516006	−	0.856585i	$-0.327418\pi$
$389$	246.932	+	142.566i	0.0321850	+	0.0185820i	−0.483821	+	0.875167i	$0.660751\pi$
$390$		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	$-0.380740\pi$
$397$	10717.4	−	6187.70i	1.35489	−	0.782247i	0.988930	+	0.148384i	$0.0474070\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	8479.92	−	4895.88i	1.05603	−	0.609697i	0.131696	−	0.991290i	$-0.457958\pi$
$401$	8479.92	−	4895.88i	1.05603	−	0.609697i	0.924331	+	0.381593i	$0.124624\pi$
$402$		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	$-0.520510\pi$
$409$	−7947.38	−	4588.42i	−0.960813	−	0.554726i	−0.896423	+	0.443199i	$0.853844\pi$
$410$		0			0
$411$	856.314	−	2842.85i	0.102771	−	0.341186i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−599.600	−	1038.54i	−0.0709233	−	0.122843i
$416$		0			0
$417$	5456.28	−	1283.46i	0.640756	−	0.150722i
$418$		0			0
$419$	−11642.2			−1.35742			−0.678711	−	0.734405i	$-0.737461\pi$
$419$	−11642.2			−1.35742			−0.678711	+	0.734405i	$0.737461\pi$
$420$		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
$423$	7278.01	+	4822.03i	0.836570	+	0.554268i
$424$		0			0
$425$	−5915.92	−	10246.7i	−0.675210	−	1.16950i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	17727.2	+	5339.74i	1.99505	+	0.600944i
$430$		0			0
$431$	−7697.77	−	4444.31i	−0.860298	−	0.496693i	0.00381421	−	0.999993i	$-0.498786\pi$
$431$	−7697.77	−	4444.31i	−0.860298	−	0.496693i	−0.864112	+	0.503300i	$0.832119\pi$
$432$		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	−0.470870	−	0.882203i	$-0.656060\pi$
$439$	530.773	−	306.442i	0.0577048	−	0.0333159i	0.528575	+	0.848887i	$0.322727\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	319.307	−	184.352i	0.0342454	−	0.0197716i	−0.482780	−	0.875742i	$-0.660373\pi$
$443$	319.307	−	184.352i	0.0342454	−	0.0197716i	0.517025	+	0.855970i	$0.327039\pi$
$444$		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
$453$	7264.13	+	2188.08i	0.753419	+	0.226942i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	6521.04	+	11294.8i	0.667487	+	1.15612i	0.978605	+	0.205750i	$0.0659633\pi$
$457$	6521.04	+	11294.8i	0.667487	+	1.15612i	−0.311118	+	0.950371i	$0.600703\pi$
$458$		0			0
$459$	−13252.2	+	2267.73i	−1.34763	+	0.230607i
$460$		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	$-0.348765\pi$
$463$	9114.64			0.914889			0.457444	+	0.889238i	$0.348765\pi$
$464$		0			0
$465$	−478.730	+	112.610i	−0.0477431	+	0.0112304i
$466$		0			0
$467$	−5344.99	−	9257.79i	−0.529629	−	0.917344i	−0.999403	−	0.0345570i	$-0.988998\pi$
$467$	−5344.99	−	9257.79i	−0.529629	−	0.917344i	0.469774	−	0.882787i	$-0.344335\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	3250.75	−	10792.0i	0.318018	−	1.05578i
$472$		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	$-0.733924\pi$
$479$	3221.06	−	5579.04i	0.307253	−	0.532177i	0.977760	+	0.209725i	$0.0672570\pi$
$480$		0			0
$481$	−6601.27	+	3811.25i	−0.625763	+	0.361285i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−834.426	+	481.756i	−0.0781223	+	0.0451039i
$486$		0			0
$487$	7920.17	−	13718.1i	0.736956	−	1.27644i	−0.216905	−	0.976193i	$-0.569596\pi$
$487$	7920.17	−	13718.1i	0.736956	−	1.27644i	0.953860	−	0.300252i	$-0.0970706\pi$
$488$		0			0
$489$	12820.2	−	12054.4i	1.18558	−	1.11477i
$490$		0			0
$491$		−	174.783i		−	0.0160649i	−0.999968	−	0.00803244i	$-0.997443\pi$
$491$		−	174.783i		−	0.0160649i	0.999968	−	0.00803244i	$-0.00255683\pi$
$492$		0			0
$493$	1405.87	+	811.681i	0.128433	+	0.0741507i
$494$		0			0
$495$	−967.412	−	1942.57i	−0.0878423	−	0.176388i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−1298.61	−	2249.26i	−0.116501	−	0.201785i	0.801878	−	0.597488i	$-0.203834\pi$
$499$	−1298.61	−	2249.26i	−0.116501	−	0.201785i	−0.918379	+	0.395703i	$0.870501\pi$
$500$		0			0
$501$	−1500.67	−	6379.68i	−0.133822	−	0.568908i
$502$		0			0
$503$	21636.9			1.91797			0.958987	−	0.283449i	$-0.0914787\pi$
$503$	21636.9			1.91797			0.958987	+	0.283449i	$0.0914787\pi$
$504$		0			0
$505$	2147.58			0.189240
$506$		0			0
$507$	−975.948	−	4148.98i	−0.0854899	−	0.363438i
$508$		0			0
$509$	2572.24	+	4455.26i	0.223994	+	0.387968i	0.956017	−	0.293311i	$-0.0947572\pi$
$509$	2572.24	+	4455.26i	0.223994	+	0.387968i	−0.732023	+	0.681279i	$0.761424\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	3539.07	+	1308.41i	0.304588	+	0.112607i
$514$		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	0.0313516	+	0.999508i	$0.490019\pi$
$521$	−10107.3	+	17506.4i	−0.849924	+	1.47211i	−0.881275	+	0.472603i	$0.843314\pi$
$522$		0			0
$523$	11073.3	−	6393.15i	0.925813	−	0.534518i	0.0403281	−	0.999186i	$-0.487160\pi$
$523$	11073.3	−	6393.15i	0.925813	−	0.534518i	0.885485	+	0.464668i	$0.153826\pi$
$524$		0			0
$525$		0			0
$526$		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
$537$	5089.09	−	16895.1i	0.408958	−	1.35769i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	652.252	+	1129.73i	0.0518346	+	0.0897801i	0.890778	−	0.454438i	$-0.150160\pi$
$541$	652.252	+	1129.73i	0.0518346	+	0.0897801i	−0.838944	+	0.544218i	$0.816826\pi$
$542$		0			0
$543$	6433.10	−	1513.23i	0.508418	−	0.119593i
$544$		0			0
$545$	1260.23			0.0990504
$546$		0			0
$547$	5425.06			0.424056			0.212028	−	0.977264i	$-0.431993\pi$
$547$	5425.06			0.424056			0.212028	+	0.977264i	$0.431993\pi$
$548$		0			0
$549$	−2868.47	+	4329.45i	−0.222993	+	0.336569i
$550$		0			0
$551$	−227.792	−	394.547i	−0.0176121	−	0.0305050i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	855.508	+	257.693i	0.0654312	+	0.0197090i
$556$		0			0
$557$	21651.8	+	12500.7i	1.64707	+	0.950936i	0.978228	+	0.207531i	$0.0665429\pi$
$557$	21651.8	+	12500.7i	1.64707	+	0.950936i	0.668842	+	0.743405i	$0.266790\pi$
$558$		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	$-0.827322\pi$
$563$	252.273	−	436.949i	0.0188846	−	0.0327091i	0.875313	+	0.483556i	$0.160655\pi$
$564$		0			0
$565$	122.804	−	70.9008i	0.00914406	−	0.00527933i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	13368.2	−	7718.14i	0.984928	−	0.568649i	0.0811739	−	0.996700i	$-0.474133\pi$
$569$	13368.2	−	7718.14i	0.984928	−	0.568649i	0.903754	+	0.428051i	$0.140800\pi$
$570$		0			0
$571$	−200.620	+	347.484i	−0.0147035	+	0.0254672i	−0.873284	−	0.487212i	$-0.838014\pi$
$571$	−200.620	+	347.484i	−0.0147035	+	0.0254672i	0.858580	+	0.512680i	$0.171347\pi$
$572$		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	$-0.516873\pi$
$577$	−13087.8	−	7556.24i	−0.944284	−	0.545182i	−0.891301	+	0.453413i	$0.850206\pi$
$578$		0			0
$579$	6332.48	+	1907.45i	0.454523	+	0.136910i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	9302.42	+	16112.3i	0.660835	+	1.14460i
$584$		0			0
$585$	−1015.02	+	1531.99i	−0.0717363	+	0.108273i
$586$		0			0
$587$	−92.4546			−0.00650087			−0.00325043	−	0.999995i	$-0.501035\pi$
$587$	−92.4546			−0.00650087			−0.00325043	+	0.999995i	$0.501035\pi$
$588$		0			0
$589$	2054.26			0.143708
$590$		0			0
$591$	−9770.89	+	2298.37i	−0.680069	+	0.159970i
$592$		0			0
$593$	−183.749	−	318.262i	−0.0127245	−	0.0220396i	0.859593	−	0.510979i	$-0.170717\pi$
$593$	−183.749	−	318.262i	−0.0127245	−	0.0220396i	−0.872318	+	0.488940i	$0.837384\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−4975.96	+	16519.5i	−0.341126	+	1.13249i
$598$		0			0
$599$	−3689.70	−	2130.25i	−0.251681	−	0.145308i	0.368853	−	0.929488i	$-0.379751\pi$
$599$	−3689.70	−	2130.25i	−0.251681	−	0.145308i	−0.620534	+	0.784180i	$0.713084\pi$
$600$		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	−0.0815566	−	0.996669i	$-0.525989\pi$
$607$	11078.7	−	6396.27i	0.740806	−	0.427704i	0.822362	+	0.568964i	$0.192656\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	15382.0	−	8880.79i	1.01848	−	0.588017i
$612$		0			0
$613$	−10022.5	+	17359.4i	−0.660365	+	1.14379i	0.320155	+	0.947365i	$0.396265\pi$
$613$	−10022.5	+	17359.4i	−0.660365	+	1.14379i	−0.980520	+	0.196420i	$0.937068\pi$
$614$		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	0.894653	−	0.446761i	$-0.147422\pi$
$619$	14708.7	+	8492.05i	0.955074	+	0.551412i	0.0604206	+	0.998173i	$0.480756\pi$
$620$		0			0
$621$	−22813.0	−	8434.07i	−1.47416	−	0.545004i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−7525.79	−	13035.1i	−0.481651	−	0.834243i
$626$		0			0
$627$	2075.61	+	8823.90i	0.132204	+	0.562030i
$628$		0			0
$629$	13298.4			0.842994
$630$		0			0
$631$	20829.5			1.31412			0.657061	−	0.753837i	$-0.271799\pi$
$631$	20829.5			1.31412			0.657061	+	0.753837i	$0.271799\pi$
$632$		0			0
$633$	1591.00	+	6763.71i	0.0998998	+	0.424697i
$634$		0			0
$635$	1334.99	+	2312.27i	0.0834290	+	0.144503i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	7961.36	+	15986.4i	0.492874	+	0.989693i
$640$		0			0
$641$	−21862.6	−	12622.4i	−1.34714	−	0.777774i	−0.359299	−	0.933222i	$-0.616984\pi$
$641$	−21862.6	−	12622.4i	−1.34714	−	0.777774i	−0.987844	+	0.155449i	$0.950318\pi$
$642$		0			0
$643$		−	17905.6i		−	1.09818i	−0.835764	−	0.549089i	$-0.814975\pi$
$643$		−	17905.6i		−	1.09818i	0.835764	−	0.549089i	$-0.185025\pi$
$644$		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	$-0.907062\pi$
$647$	−3777.94	+	6543.58i	−0.229561	+	0.397612i	0.728117	+	0.685453i	$0.240396\pi$
$648$		0			0
$649$	9465.88	−	5465.13i	0.572524	−	0.330547i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	8162.19	−	4712.44i	0.489144	−	0.282408i	−0.235075	−	0.971977i	$-0.575534\pi$
$653$	8162.19	−	4712.44i	0.489144	−	0.282408i	0.724219	+	0.689570i	$0.242200\pi$
$654$		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	$0.141176\pi$
$659$			14519.0i			0.858240i	−0.903248	+	0.429120i	$0.858824\pi$
$660$		0			0
$661$	13331.6	+	7696.97i	0.784474	+	0.452916i	0.838013	−	0.545650i	$-0.183717\pi$
$661$	13331.6	+	7696.97i	0.784474	+	0.452916i	−0.0535396	+	0.998566i	$0.517050\pi$
$662$		0			0
$663$	−7888.94	+	26190.3i	−0.462113	+	1.53416i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	1468.36	+	2543.27i	0.0852400	+	0.147640i
$668$		0			0
$669$	19644.7	−	4620.95i	1.13529	−	0.267050i
$670$		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
$675$	−17073.4	+	2921.62i	−0.973566	+	0.166597i
$676$		0			0
$677$	−7731.79	−	13391.9i	−0.438932	−	0.760252i	0.558676	−	0.829386i	$-0.311310\pi$
$677$	−7731.79	−	13391.9i	−0.438932	−	0.760252i	−0.997607	+	0.0691341i	$0.977976\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−21859.3	−	6584.38i	−1.23003	−	0.370505i
$682$		0			0
$683$	10282.5	+	5936.60i	0.576060	+	0.332588i	0.759566	−	0.650430i	$-0.225411\pi$
$683$	10282.5	+	5936.60i	0.576060	+	0.332588i	−0.183506	+	0.983019i	$0.558745\pi$
$684$		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	−0.381212	−	0.924488i	$-0.624493\pi$
$691$	4156.18	−	2399.57i	0.228811	−	0.132104i	0.610024	+	0.792383i	$0.291160\pi$
$692$		0			0
$693$		0			0
$694$		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
$705$	−1993.47	−	600.465i	−0.106494	−	0.0320778i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−8501.87	−	14725.7i	−0.450345	−	0.780020i	0.548063	−	0.836437i	$-0.315366\pi$
$709$	−8501.87	−	14725.7i	−0.450345	−	0.780020i	−0.998407	+	0.0564176i	$0.982032\pi$
$710$		0			0
$711$	−10290.3	−	6817.83i	−0.542781	−	0.359618i
$712$		0			0
$713$	−13241.8			−0.695527
$714$		0			0
$715$	−4414.98			−0.230924
$716$		0			0
$717$	13500.0	−	3175.56i	0.703163	−	0.165402i
$718$		0			0
$719$	11003.9	+	19059.3i	0.570760	+	0.988586i	0.996488	+	0.0837345i	$0.0266848\pi$
$719$	11003.9	+	19059.3i	0.570760	+	0.988586i	−0.425728	+	0.904851i	$0.639982\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	8615.20	−	28601.3i	0.443157	−	1.47122i
$724$		0			0
$725$	1811.25	+	1045.73i	0.0927837	+	0.0535687i
$726$		0			0
$727$			20005.6i			1.02059i	0.860001	+	0.510293i	$0.170463\pi$
$727$			20005.6i			1.02059i	−0.860001	+	0.510293i	$0.829537\pi$
$728$		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	$-0.596707\pi$
$733$	7493.92	−	4326.62i	0.377619	−	0.218018i	0.676782	+	0.736184i	$0.263374\pi$
$734$		0			0
$735$		0			0
$736$		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	$-0.793330\pi$
$739$	2518.09	−	4361.46i	0.125344	−	0.217103i	0.921867	+	0.387505i	$0.126663\pi$
$740$		0			0
$741$	5592.39	−	5258.37i	0.277249	−	0.260690i
$742$		0			0
$743$		−	4822.04i		−	0.238093i	−0.992889	−	0.119047i	$-0.962016\pi$
$743$		−	4822.04i		−	0.238093i	0.992889	−	0.119047i	$-0.0379838\pi$
$744$		0			0
$745$	−1042.39	−	601.827i	−0.0512623	−	0.0295963i
$746$		0			0
$747$	−23390.3	+	11648.5i	−1.14566	+	0.570545i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−10017.2	−	17350.3i	−0.486729	−	0.843039i	0.513155	−	0.858296i	$-0.328477\pi$
$751$	−10017.2	−	17350.3i	−0.486729	−	0.843039i	−0.999884	+	0.0152569i	$0.995143\pi$
$752$		0			0
$753$	−8776.85	−	37312.4i	−0.424762	−	1.80576i
$754$		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
$759$	−13379.5	−	56879.4i	−0.639849	−	2.72015i
$760$		0			0
$761$	3738.26	+	6474.85i	0.178071	+	0.308427i	0.941220	−	0.337795i	$-0.109681\pi$
$761$	3738.26	+	6474.85i	0.178071	+	0.308427i	−0.763149	+	0.646223i	$0.776348\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	2869.96	−	1429.26i	0.135639	−	0.0675490i
$766$		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	−0.790272	−	0.612757i	$-0.790061\pi$
$773$	2912.70	−	5044.94i	0.135527	−	0.234740i	0.925799	+	0.378017i	$0.123394\pi$
$774$		0			0
$775$	−8167.05	+	4715.25i	−0.378541	+	0.218551i
$776$		0			0
$777$		0			0
$778$		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	0.807940	−	0.589265i	$-0.200583\pi$
$787$	15489.8	+	8943.04i	0.701590	+	0.405063i	−0.106349	+	0.994329i	$0.533916\pi$
$788$		0			0
$789$	−10940.0	+	36319.3i	−0.493630	+	1.63878i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	5282.89	+	9150.24i	0.236571	+	0.409753i
$794$		0			0
$795$	−1797.68	+	422.862i	−0.0801978	+	0.0188646i
$796$		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
$801$	27254.9	+	18057.7i	1.20225	+	0.796550i
$802$		0			0
$803$	4686.46	+	8117.18i	0.205954	+	0.356724i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	7975.07	+	2402.23i	0.347876	+	0.104786i
$808$		0			0
$809$	17555.7	+	10135.8i	0.762947	+	0.440487i	0.830353	−	0.557238i	$-0.188139\pi$
$809$	17555.7	+	10135.8i	0.762947	+	0.440487i	−0.0674061	+	0.997726i	$0.521472\pi$
$810$		0			0
$811$		−	881.011i		−	0.0381461i	−0.999818	−	0.0190731i	$-0.993928\pi$
$811$		−	881.011i		−	0.0381461i	0.999818	−	0.0190731i	$-0.00607151\pi$
$812$		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
$819$		0			0
$820$		0			0
$821$	−29088.6	+	16794.3i	−1.23654	+	0.713916i	−0.968385	−	0.249460i	$-0.919747\pi$
$821$	−29088.6	+	16794.3i	−1.23654	+	0.713916i	−0.268154	+	0.963376i	$0.586414\pi$
$822$		0			0
$823$	−15791.4	+	27351.5i	−0.668838	+	1.15846i	0.309392	+	0.950935i	$0.399875\pi$
$823$	−15791.4	+	27351.5i	−0.668838	+	1.15846i	−0.978229	+	0.207526i	$0.933459\pi$
$824$		0			0
$825$	−28505.9	−	30316.7i	−1.20297	−	1.27938i
$826$		0			0
$827$			29539.1i			1.24205i	0.783791	+	0.621024i	$0.213283\pi$
$827$			29539.1i			1.24205i	−0.783791	+	0.621024i	$0.786717\pi$
$828$		0			0
$829$	−4256.59	−	2457.54i	−0.178332	−	0.102960i	0.408177	−	0.912903i	$-0.366165\pi$
$829$	−4256.59	−	2457.54i	−0.178332	−	0.102960i	−0.586509	+	0.809943i	$0.699498\pi$
$830$		0			0
$831$	−14223.7	−	4284.42i	−0.593760	−	0.178851i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	781.434	+	1353.48i	0.0323864	+	0.0560948i
$836$		0			0
$837$	1807.48	+	10562.6i	0.0746422	+	0.436196i
$838$		0			0
$839$	6724.37			0.276700			0.138350	−	0.990383i	$-0.455820\pi$
$839$	6724.37			0.276700			0.138350	+	0.990383i	$0.455820\pi$
$840$		0			0
$841$	24102.0			0.988234
$842$		0			0
$843$	−16625.1	+	3910.65i	−0.679238	+	0.159774i
$844$		0			0
$845$	508.200	+	880.229i	0.0206895	+	0.0358353i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	1852.85	−	6151.21i	0.0748994	−	0.248656i
$850$		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	0.112074	+	0.993700i	$0.464251\pi$
$857$	−20184.4	+	34960.3i	−0.804532	+	1.39349i	−0.916606	+	0.399791i	$0.869083\pi$
$858$		0			0
$859$	22420.1	−	12944.2i	0.890528	−	0.514146i	0.0164125	−	0.999865i	$-0.494775\pi$
$859$	22420.1	−	12944.2i	0.890528	−	0.514146i	0.874115	+	0.485719i	$0.161442\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	19554.1	−	11289.6i	0.771298	−	0.445309i	−0.0620392	−	0.998074i	$-0.519760\pi$
$863$	19554.1	−	11289.6i	0.771298	−	0.445309i	0.833338	+	0.552764i	$0.186427\pi$
$864$		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
$873$	9359.15	+	18793.2i	0.362840	+	0.728584i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−7718.29	−	13368.5i	−0.297182	−	0.514734i	0.678308	−	0.734777i	$-0.262713\pi$
$877$	−7718.29	−	13368.5i	−0.297182	−	0.514734i	−0.975490	+	0.220044i	$0.929380\pi$
$878$		0			0
$879$	11502.0	+	48897.5i	0.441356	+	1.87631i
$880$		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	$-0.313103\pi$
$883$	29072.1			1.10799			0.553994	+	0.832521i	$0.313103\pi$
$884$		0			0
$885$	248.429	+	1056.13i	0.00943600	+	0.0401146i
$886$		0			0
$887$	−6245.78	−	10818.0i	−0.236429	−	0.409507i	0.723258	−	0.690578i	$-0.242644\pi$
$887$	−6245.78	−	10818.0i	−0.236429	−	0.409507i	−0.959687	+	0.281071i	$0.909310\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−43544.6	+	18436.3i	−1.63726	+	0.693197i
$892$		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
$903$		0			0
$904$		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	$-0.760418\pi$
$907$	6202.64	−	10743.3i	0.227073	−	0.393302i	0.956939	+	0.290288i	$0.0937510\pi$
$908$		0			0
$909$	2878.28	−	46706.7i	0.105024	−	1.70425i
$910$		0			0
$911$			42362.8i			1.54066i	0.637645	+	0.770331i	$0.279909\pi$
$911$			42362.8i			1.54066i	−0.637645	+	0.770331i	$0.720091\pi$
$912$		0			0
$913$	−54365.3	−	31387.8i	−1.97068	−	1.13777i
$914$		0			0
$915$	357.197	−	1185.85i	0.0129055	−	0.0428447i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−17133.8	−	29676.6i	−0.615007	−	1.06522i	−0.990383	−	0.138351i	$-0.955820\pi$
$919$	−17133.8	−	29676.6i	−0.615007	−	1.06522i	0.375376	−	0.926873i	$-0.377514\pi$
$920$		0			0
$921$	41350.3	−	9726.67i	1.47941	−	0.347996i
$922$		0			0
$923$	36333.2			1.29569
$924$		0			0
$925$	17133.0			0.609004
$926$		0			0
$927$	−19056.1	+	28761.9i	−0.675173	+	1.01906i
$928$		0			0
$929$	11062.6	+	19160.9i	0.390690	+	0.676695i	0.992541	−	0.121914i	$-0.0389032\pi$
$929$	11062.6	+	19160.9i	0.390690	+	0.676695i	−0.601851	+	0.798609i	$0.705570\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−3579.95	−	1078.34i	−0.125619	−	0.0378385i
$934$		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	0.137951	−	0.990439i	$-0.455948\pi$
$941$	26750.6	−	46333.4i	0.926721	−	1.60513i	0.788770	−	0.614689i	$-0.210718\pi$
$942$		0			0
$943$	−15135.4	+	8738.42i	−0.522668	+	0.301763i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−108.948	+	62.9013i	−0.00373848	+	0.00215841i	−0.501868	−	0.864944i	$-0.667354\pi$
$947$	−108.948	+	62.9013i	−0.00373848	+	0.00215841i	0.498130	+	0.867103i	$0.334020\pi$
$948$		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
$957$	5466.88	+	1646.72i	0.184659	+	0.0556225i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−11978.4	−	20747.2i	−0.402081	−	0.696424i
$962$		0			0
$963$	−19487.1	+	29412.3i	−0.652090	+	0.984216i
$964$		0			0
$965$	−1577.11			−0.0526103
$966$		0			0
$967$	−19897.4			−0.661692			−0.330846	−	0.943685i	$-0.607334\pi$
$967$	−19897.4			−0.661692			−0.330846	+	0.943685i	$0.607334\pi$
$968$		0			0
$969$	−13036.5	+	3066.51i	−0.432190	+	0.101662i
$970$		0			0
$971$	19064.3	+	33020.3i	0.630075	+	1.09132i	0.987536	+	0.157393i	$0.0503090\pi$
$971$	19064.3	+	33020.3i	0.630075	+	1.09132i	−0.357462	+	0.933928i	$0.616358\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	−10163.7	+	33742.1i	−0.333845	+	1.10832i
$976$		0			0
$977$	4321.33	+	2494.92i	0.141506	+	0.0816986i	0.569082	−	0.822281i	$-0.307299\pi$
$977$	4321.33	+	2494.92i	0.141506	+	0.0816986i	−0.427575	+	0.903980i	$0.640632\pi$
$978$		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	$-0.926371\pi$
$983$	−8880.48	+	15381.4i	−0.288142	+	0.499076i	0.685225	+	0.728332i	$0.259704\pi$
$984$		0			0
$985$	2072.95	−	1196.82i	0.0670554	−	0.0387144i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	29695.4	−	17144.6i	0.954761	−	0.551232i
$990$		0			0
$991$	23134.6	−	40070.2i	0.741568	−	1.28443i	−0.210214	−	0.977655i	$-0.567416\pi$
$991$	23134.6	−	40070.2i	0.741568	−	1.28443i	0.951781	−	0.306777i	$-0.0992507\pi$
$992$		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	$-0.0589978\pi$
$997$	41387.9	+	23895.3i	1.31471	+	0.759049i	0.331839	+	0.943336i	$0.392331\pi$
$998$		0			0
$999$	6751.04	−	18260.7i	0.213807	−	0.578320i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	588.4.k.c.521.4		12
3.2	odd	2	inner	588.4.k.c.521.6		12
7.2	even	3		84.4.k.c.5.1	✓	12
7.3	odd	6		588.4.f.c.293.6		12
7.4	even	3		588.4.f.c.293.7		12
7.5	odd	6	inner	588.4.k.c.509.6		12
7.6	odd	2		84.4.k.c.17.3	yes	12
21.2	odd	6		84.4.k.c.5.3	yes	12
21.5	even	6	inner	588.4.k.c.509.4		12
21.11	odd	6		588.4.f.c.293.5		12
21.17	even	6		588.4.f.c.293.8		12
21.20	even	2		84.4.k.c.17.1	yes	12
28.23	odd	6		336.4.bc.c.257.6		12
28.27	even	2		336.4.bc.c.17.4		12
84.23	even	6		336.4.bc.c.257.4		12
84.83	odd	2		336.4.bc.c.17.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.4.k.c.5.1	✓	12	7.2	even	3
84.4.k.c.5.3	yes	12	21.2	odd	6
84.4.k.c.17.1	yes	12	21.20	even	2
84.4.k.c.17.3	yes	12	7.6	odd	2
336.4.bc.c.17.4		12	28.27	even	2
336.4.bc.c.17.6		12	84.83	odd	2
336.4.bc.c.257.4		12	84.23	even	6
336.4.bc.c.257.6		12	28.23	odd	6
588.4.f.c.293.5		12	21.11	odd	6
588.4.f.c.293.6		12	7.3	odd	6
588.4.f.c.293.7		12	7.4	even	3
588.4.f.c.293.8		12	21.17	even	6
588.4.k.c.509.4		12	21.5	even	6	inner
588.4.k.c.509.6		12	7.5	odd	6	inner
588.4.k.c.521.4		12	1.1	even	1	trivial
588.4.k.c.521.6		12	3.2	odd	2	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:	\( N \)	\(=\)	\( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	588.k (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.18980 + 5.05810i) q^{3} +(-0.619556 - 1.07310i) q^{5} +(-24.1688 + 12.0362i) q^{9} +O(q^{10})\)	\(q+(1.18980 + 5.05810i) q^{3} +(-0.619556 - 1.07310i) q^{5} +(-24.1688 + 12.0362i) q^{9} +(-56.1748 - 32.4325i) q^{11} +54.9296i q^{13} +(4.69072 - 4.41055i) q^{15} +(47.9159 - 82.9928i) q^{17} +(-23.2913 + 13.4472i) q^{19} +(150.137 - 86.6815i) q^{23} +(61.7323 - 106.923i) q^{25} +(-89.6363 - 107.927i) q^{27} +16.9397i q^{29} +(-66.1489 - 38.1911i) q^{31} +(97.2105 - 322.726i) q^{33} +(69.3842 + 120.177i) q^{37} +(-277.840 + 65.3551i) q^{39} -100.811 q^{41} +197.789 q^{43} +(27.8900 + 18.4785i) q^{45} +(-161.676 - 280.031i) q^{47} +(476.796 + 143.619i) q^{51} +(-248.397 - 143.412i) q^{53} +80.3751i q^{55} +(-95.7292 - 101.810i) q^{57} +(-84.2538 + 145.932i) q^{59} +(166.581 - 96.1756i) q^{61} +(58.9452 - 34.0320i) q^{65} +(442.197 - 765.908i) q^{67} +(617.076 + 656.274i) q^{69} -661.451i q^{71} +(-125.139 - 72.2493i) q^{73} +(614.279 + 185.031i) q^{75} +(228.592 + 395.933i) q^{79} +(439.259 - 581.801i) q^{81} +967.789 q^{83} -118.746 q^{85} +(-85.6827 + 20.1548i) q^{87} +(-605.448 - 1048.67i) q^{89} +(114.471 - 380.027i) q^{93} +(28.8605 + 16.6626i) q^{95} -777.582i q^{97} +(1748.04 + 107.722i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 84 q^{9}+O(q^{10}) \) 12 * q - 84 * q^9	\( 12 q - 84 q^{9} + 132 q^{15} - 204 q^{19} - 444 q^{25} - 1458 q^{31} + 108 q^{33} + 240 q^{37} - 432 q^{39} + 342 q^{45} - 300 q^{51} + 180 q^{57} - 2148 q^{61} + 1980 q^{67} + 3084 q^{73} + 3384 q^{75} - 438 q^{79} + 1008 q^{81} - 6144 q^{85} + 2898 q^{87} + 882 q^{93} + 9216 q^{99}+O(q^{100}) \) 12 * q - 84 * q^9 + 132 * q^15 - 204 * q^19 - 444 * q^25 - 1458 * q^31 + 108 * q^33 + 240 * q^37 - 432 * q^39 + 342 * q^45 - 300 * q^51 + 180 * q^57 - 2148 * q^61 + 1980 * q^67 + 3084 * q^73 + 3384 * q^75 - 438 * q^79 + 1008 * q^81 - 6144 * q^85 + 2898 * q^87 + 882 * q^93 + 9216 * q^99

Introduction

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