LMFDB - Embedded newform 336.4.q.d.289.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [336,4,Mod(193,336)]

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, 0, 4]))

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

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

chi := DirichletCharacter("336.193");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	336.q (of order $3$, 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:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 42)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			289.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	336.289
Dual form			336.4.q.d.193.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.50000 - 2.59808i) q^{3} +(7.50000 - 12.9904i) q^{5} +(-17.5000 - 6.06218i) q^{7} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})$	\(q+(-1.50000 - 2.59808i) q^{3} +(7.50000 - 12.9904i) q^{5} +(-17.5000 - 6.06218i) q^{7} +(-4.50000 + 7.79423i) q^{9} +(-4.50000 - 7.79423i) q^{11} -88.0000 q^{13} -45.0000 q^{15} +(42.0000 + 72.7461i) q^{17} +(52.0000 - 90.0666i) q^{19} +(10.5000 + 54.5596i) q^{21} +(-42.0000 + 72.7461i) q^{23} +(-50.0000 - 86.6025i) q^{25} +27.0000 q^{27} +51.0000 q^{29} +(92.5000 + 160.215i) q^{31} +(-13.5000 + 23.3827i) q^{33} +(-210.000 + 181.865i) q^{35} +(-22.0000 + 38.1051i) q^{37} +(132.000 + 228.631i) q^{39} -168.000 q^{41} -326.000 q^{43} +(67.5000 + 116.913i) q^{45} +(-69.0000 + 119.512i) q^{47} +(269.500 + 212.176i) q^{49} +(126.000 - 218.238i) q^{51} +(-319.500 - 553.390i) q^{53} -135.000 q^{55} -312.000 q^{57} +(79.5000 + 137.698i) q^{59} +(-361.000 + 625.270i) q^{61} +(126.000 - 109.119i) q^{63} +(-660.000 + 1143.15i) q^{65} +(-83.0000 - 143.760i) q^{67} +252.000 q^{69} -1086.00 q^{71} +(-109.000 - 188.794i) q^{73} +(-150.000 + 259.808i) q^{75} +(31.5000 + 163.679i) q^{77} +(-291.500 + 504.893i) q^{79} +(-40.5000 - 70.1481i) q^{81} +597.000 q^{83} +1260.00 q^{85} +(-76.5000 - 132.502i) q^{87} +(519.000 - 898.934i) q^{89} +(1540.00 + 533.472i) q^{91} +(277.500 - 480.644i) q^{93} +(-780.000 - 1351.00i) q^{95} -169.000 q^{97} +81.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 3 q^{3} + 15 q^{5} - 35 q^{7} - 9 q^{9}+O(q^{10}) $ 2 * q - 3 * q^3 + 15 * q^5 - 35 * q^7 - 9 * q^9	$ 2 q - 3 q^{3} + 15 q^{5} - 35 q^{7} - 9 q^{9} - 9 q^{11} - 176 q^{13} - 90 q^{15} + 84 q^{17} + 104 q^{19} + 21 q^{21} - 84 q^{23} - 100 q^{25} + 54 q^{27} + 102 q^{29} + 185 q^{31} - 27 q^{33} - 420 q^{35} - 44 q^{37} + 264 q^{39} - 336 q^{41} - 652 q^{43} + 135 q^{45} - 138 q^{47} + 539 q^{49} + 252 q^{51} - 639 q^{53} - 270 q^{55} - 624 q^{57} + 159 q^{59} - 722 q^{61} + 252 q^{63} - 1320 q^{65} - 166 q^{67} + 504 q^{69} - 2172 q^{71} - 218 q^{73} - 300 q^{75} + 63 q^{77} - 583 q^{79} - 81 q^{81} + 1194 q^{83} + 2520 q^{85} - 153 q^{87} + 1038 q^{89} + 3080 q^{91} + 555 q^{93} - 1560 q^{95} - 338 q^{97} + 162 q^{99}+O(q^{100}) $ 2 * q - 3 * q^3 + 15 * q^5 - 35 * q^7 - 9 * q^9 - 9 * q^11 - 176 * q^13 - 90 * q^15 + 84 * q^17 + 104 * q^19 + 21 * q^21 - 84 * q^23 - 100 * q^25 + 54 * q^27 + 102 * q^29 + 185 * q^31 - 27 * q^33 - 420 * q^35 - 44 * q^37 + 264 * q^39 - 336 * q^41 - 652 * q^43 + 135 * q^45 - 138 * q^47 + 539 * q^49 + 252 * q^51 - 639 * q^53 - 270 * q^55 - 624 * q^57 + 159 * q^59 - 722 * q^61 + 252 * q^63 - 1320 * q^65 - 166 * q^67 + 504 * q^69 - 2172 * q^71 - 218 * q^73 - 300 * q^75 + 63 * q^77 - 583 * q^79 - 81 * q^81 + 1194 * q^83 + 2520 * q^85 - 153 * q^87 + 1038 * q^89 + 3080 * q^91 + 555 * q^93 - 1560 * q^95 - 338 * q^97 + 162 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{1}{3}\right)$

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
$3$	−1.50000	−	2.59808i	−0.288675	−	0.500000i
$3$	−1.50000	−	2.59808i	−0.288675	−	0.500000i
$4$		0			0
$5$	7.50000	−	12.9904i	0.670820	−	1.16190i	−0.306851	−	0.951757i	$-0.599275\pi$
$5$	7.50000	−	12.9904i	0.670820	−	1.16190i	0.977672	−	0.210138i	$-0.0673912\pi$
$6$		0			0
$7$	−17.5000	−	6.06218i	−0.944911	−	0.327327i
$7$	−17.5000	−	6.06218i	−0.944911	−	0.327327i
$8$		0			0
$9$	−4.50000	+	7.79423i	−0.166667	+	0.288675i
$10$		0			0
$11$	−4.50000	−	7.79423i	−0.123346	−	0.213641i	0.797739	−	0.603002i	$-0.206029\pi$
$11$	−4.50000	−	7.79423i	−0.123346	−	0.213641i	−0.921085	+	0.389362i	$0.872696\pi$
$12$		0			0
$13$	−88.0000			−1.87745			−0.938723	−	0.344671i	$-0.887990\pi$
$13$	−88.0000			−1.87745			−0.938723	+	0.344671i	$0.887990\pi$
$14$		0			0
$15$	−45.0000			−0.774597
$16$		0			0
$17$	42.0000	+	72.7461i	0.599206	+	1.03785i	0.992939	+	0.118630i	$0.0378502\pi$
$17$	42.0000	+	72.7461i	0.599206	+	1.03785i	−0.393733	+	0.919225i	$0.628817\pi$
$18$		0			0
$19$	52.0000	−	90.0666i	0.627875	−	1.08751i	−0.360103	−	0.932913i	$-0.617258\pi$
$19$	52.0000	−	90.0666i	0.627875	−	1.08751i	0.987977	−	0.154598i	$-0.0494083\pi$
$20$		0			0
$21$	10.5000	+	54.5596i	0.109109	+	0.566947i
$22$		0			0
$23$	−42.0000	+	72.7461i	−0.380765	+	0.659505i	−0.991172	−	0.132583i	$-0.957673\pi$
$23$	−42.0000	+	72.7461i	−0.380765	+	0.659505i	0.610406	+	0.792088i	$0.291006\pi$
$24$		0			0
$25$	−50.0000	−	86.6025i	−0.400000	−	0.692820i
$26$		0			0
$27$	27.0000			0.192450
$28$		0			0
$29$	51.0000			0.326568			0.163284	−	0.986579i	$-0.447791\pi$
$29$	51.0000			0.326568			0.163284	+	0.986579i	$0.447791\pi$
$30$		0			0
$31$	92.5000	+	160.215i	0.535919	+	0.928239i	0.999118	+	0.0419848i	$0.0133681\pi$
$31$	92.5000	+	160.215i	0.535919	+	0.928239i	−0.463199	+	0.886254i	$0.653299\pi$
$32$		0			0
$33$	−13.5000	+	23.3827i	−0.0712136	+	0.123346i
$34$		0			0
$35$	−210.000	+	181.865i	−1.01419	+	0.878310i
$36$		0			0
$37$	−22.0000	+	38.1051i	−0.0977507	+	0.169309i	−0.910753	−	0.412951i	$-0.864498\pi$
$37$	−22.0000	+	38.1051i	−0.0977507	+	0.169309i	0.813003	+	0.582260i	$0.197831\pi$
$38$		0			0
$39$	132.000	+	228.631i	0.541972	+	0.938723i
$40$		0			0
$41$	−168.000			−0.639932			−0.319966	−	0.947429i	$-0.603671\pi$
$41$	−168.000			−0.639932			−0.319966	+	0.947429i	$0.603671\pi$
$42$		0			0
$43$	−326.000			−1.15615			−0.578076	−	0.815983i	$-0.696196\pi$
$43$	−326.000			−1.15615			−0.578076	+	0.815983i	$0.696196\pi$
$44$		0			0
$45$	67.5000	+	116.913i	0.223607	+	0.387298i
$46$		0			0
$47$	−69.0000	+	119.512i	−0.214142	+	0.370905i	−0.953007	−	0.302949i	$-0.902029\pi$
$47$	−69.0000	+	119.512i	−0.214142	+	0.370905i	0.738865	+	0.673854i	$0.235362\pi$
$48$		0			0
$49$	269.500	+	212.176i	0.785714	+	0.618590i
$50$		0			0
$51$	126.000	−	218.238i	0.345952	−	0.599206i
$52$		0			0
$53$	−319.500	−	553.390i	−0.828051	−	1.43423i	−0.899565	−	0.436787i	$-0.856116\pi$
$53$	−319.500	−	553.390i	−0.828051	−	1.43423i	0.0715141	−	0.997440i	$-0.477217\pi$
$54$		0			0
$55$	−135.000			−0.330971
$56$		0			0
$57$	−312.000			−0.725007
$58$		0			0
$59$	79.5000	+	137.698i	0.175424	+	0.303843i	0.940308	−	0.340325i	$-0.110537\pi$
$59$	79.5000	+	137.698i	0.175424	+	0.303843i	−0.764884	+	0.644168i	$0.777204\pi$
$60$		0			0
$61$	−361.000	+	625.270i	−0.757726	+	1.31242i	0.186281	+	0.982497i	$0.440357\pi$
$61$	−361.000	+	625.270i	−0.757726	+	1.31242i	−0.944007	+	0.329924i	$0.892977\pi$
$62$		0			0
$63$	126.000	−	109.119i	0.251976	−	0.218218i
$64$		0			0
$65$	−660.000	+	1143.15i	−1.25943	+	2.18140i
$66$		0			0
$67$	−83.0000	−	143.760i	−0.151344	−	0.262136i	0.780378	−	0.625309i	$-0.215027\pi$
$67$	−83.0000	−	143.760i	−0.151344	−	0.262136i	−0.931722	+	0.363173i	$0.881694\pi$
$68$		0			0
$69$	252.000			0.439670
$70$		0			0
$71$	−1086.00			−1.81527			−0.907637	−	0.419755i	$-0.862116\pi$
$71$	−1086.00			−1.81527			−0.907637	+	0.419755i	$0.862116\pi$
$72$		0			0
$73$	−109.000	−	188.794i	−0.174760	−	0.302693i	0.765318	−	0.643652i	$-0.222582\pi$
$73$	−109.000	−	188.794i	−0.174760	−	0.302693i	−0.940078	+	0.340959i	$0.889248\pi$
$74$		0			0
$75$	−150.000	+	259.808i	−0.230940	+	0.400000i
$76$		0			0
$77$	31.5000	+	163.679i	0.0466202	+	0.242246i
$78$		0			0
$79$	−291.500	+	504.893i	−0.415143	+	0.719049i	−0.995443	−	0.0953535i	$-0.969602\pi$
$79$	−291.500	+	504.893i	−0.415143	+	0.719049i	0.580300	+	0.814403i	$0.302935\pi$
$80$		0			0
$81$	−40.5000	−	70.1481i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	597.000			0.789509			0.394755	−	0.918787i	$-0.370830\pi$
$83$	597.000			0.789509			0.394755	+	0.918787i	$0.370830\pi$
$84$		0			0
$85$	1260.00			1.60784
$86$		0			0
$87$	−76.5000	−	132.502i	−0.0942720	−	0.163284i
$88$		0			0
$89$	519.000	−	898.934i	0.618134	−	1.07064i	−0.371692	−	0.928356i	$-0.621222\pi$
$89$	519.000	−	898.934i	0.618134	−	1.07064i	0.989826	−	0.142283i	$-0.0454443\pi$
$90$		0			0
$91$	1540.00	+	533.472i	1.77402	+	0.614539i
$92$		0			0
$93$	277.500	−	480.644i	0.309413	−	0.535919i
$94$		0			0
$95$	−780.000	−	1351.00i	−0.842382	−	1.45905i
$96$		0			0
$97$	−169.000			−0.176901			−0.0884503	−	0.996081i	$-0.528191\pi$
$97$	−169.000			−0.176901			−0.0884503	+	0.996081i	$0.528191\pi$
$98$		0			0
$99$	81.0000			0.0822304
$100$		0			0
$101$	−321.000	−	555.988i	−0.316244	−	0.547752i	0.663457	−	0.748215i	$-0.269089\pi$
$101$	−321.000	−	555.988i	−0.316244	−	0.547752i	−0.979701	+	0.200463i	$0.935755\pi$
$102$		0			0
$103$	232.000	−	401.836i	0.221938	−	0.384408i	−0.733458	−	0.679735i	$-0.762095\pi$
$103$	232.000	−	401.836i	0.221938	−	0.384408i	0.955396	+	0.295326i	$0.0954283\pi$
$104$		0			0
$105$	787.500	+	272.798i	0.731925	+	0.253546i
$106$		0			0
$107$	196.500	−	340.348i	0.177536	−	0.307502i	−0.763500	−	0.645808i	$-0.776521\pi$
$107$	196.500	−	340.348i	0.177536	−	0.307502i	0.941036	+	0.338306i	$0.109854\pi$
$108$		0			0
$109$	−7.00000	−	12.1244i	−0.00615118	−	0.0106542i	0.862933	−	0.505318i	$-0.168625\pi$
$109$	−7.00000	−	12.1244i	−0.00615118	−	0.0106542i	−0.869085	+	0.494663i	$0.835291\pi$
$110$		0			0
$111$	132.000			0.112873
$112$		0			0
$113$	−2184.00			−1.81817			−0.909086	−	0.416608i	$-0.863219\pi$
$113$	−2184.00			−1.81817			−0.909086	+	0.416608i	$0.863219\pi$
$114$		0			0
$115$	630.000	+	1091.19i	0.510850	+	0.884819i
$116$		0			0
$117$	396.000	−	685.892i	0.312908	−	0.541972i
$118$		0			0
$119$	−294.000	−	1527.67i	−0.226478	−	1.17682i
$120$		0			0
$121$	625.000	−	1082.53i	0.469572	−	0.813322i
$122$		0			0
$123$	252.000	+	436.477i	0.184732	+	0.319966i
$124$		0			0
$125$	375.000			0.268328
$126$		0			0
$127$	373.000			0.260617			0.130309	−	0.991473i	$-0.458403\pi$
$127$	373.000			0.260617			0.130309	+	0.991473i	$0.458403\pi$
$128$		0			0
$129$	489.000	+	846.973i	0.333752	+	0.578076i
$130$		0			0
$131$	−586.500	+	1015.85i	−0.391166	+	0.677519i	−0.992604	−	0.121400i	$-0.961261\pi$
$131$	−586.500	+	1015.85i	−0.391166	+	0.677519i	0.601438	+	0.798920i	$0.294595\pi$
$132$		0			0
$133$	−1456.00	+	1260.93i	−0.949257	+	0.822081i
$134$		0			0
$135$	202.500	−	350.740i	0.129099	−	0.223607i
$136$		0			0
$137$	−15.0000	−	25.9808i	−0.00935428	−	0.0162021i	0.861310	−	0.508079i	$-0.169644\pi$
$137$	−15.0000	−	25.9808i	−0.00935428	−	0.0162021i	−0.870665	+	0.491877i	$0.836311\pi$
$138$		0			0
$139$	82.0000			0.0500370			0.0250185	−	0.999687i	$-0.492036\pi$
$139$	82.0000			0.0500370			0.0250185	+	0.999687i	$0.492036\pi$
$140$		0			0
$141$	414.000			0.247270
$142$		0			0
$143$	396.000	+	685.892i	0.231575	+	0.401099i
$144$		0			0
$145$	382.500	−	662.509i	0.219068	−	0.379437i
$146$		0			0
$147$	147.000	−	1018.45i	0.0824786	−	0.571429i
$148$		0			0
$149$	717.000	−	1241.88i	0.394221	−	0.682811i	−0.598780	−	0.800913i	$-0.704348\pi$
$149$	717.000	−	1241.88i	0.394221	−	0.682811i	0.993001	+	0.118102i	$0.0376811\pi$
$150$		0			0
$151$	−1335.50	−	2313.15i	−0.719745	−	1.24663i	−0.961101	−	0.276198i	$-0.910926\pi$
$151$	−1335.50	−	2313.15i	−0.719745	−	1.24663i	0.241356	−	0.970437i	$-0.422408\pi$
$152$		0			0
$153$	−756.000			−0.399470
$154$		0			0
$155$	2775.00			1.43802
$156$		0			0
$157$	−1126.00	−	1950.29i	−0.572386	−	0.991401i	−0.996320	−	0.0857085i	$-0.972685\pi$
$157$	−1126.00	−	1950.29i	−0.572386	−	0.991401i	0.423934	−	0.905693i	$-0.360649\pi$
$158$		0			0
$159$	−958.500	+	1660.17i	−0.478075	+	0.828051i
$160$		0			0
$161$	1176.00	−	1018.45i	0.575663	−	0.498539i
$162$		0			0
$163$	838.000	−	1451.46i	0.402682	−	0.697466i	−0.591366	−	0.806403i	$-0.701411\pi$
$163$	838.000	−	1451.46i	0.402682	−	0.697466i	0.994049	+	0.108937i	$0.0347446\pi$
$164$		0			0
$165$	202.500	+	350.740i	0.0955431	+	0.165485i
$166$		0			0
$167$	−3030.00			−1.40400			−0.702001	−	0.712176i	$-0.747710\pi$
$167$	−3030.00			−1.40400			−0.702001	+	0.712176i	$0.747710\pi$
$168$		0			0
$169$	5547.00			2.52481
$170$		0			0
$171$	468.000	+	810.600i	0.209292	+	0.362504i
$172$		0			0
$173$	−1719.00	+	2977.40i	−0.755452	+	1.30848i	0.189698	+	0.981843i	$0.439249\pi$
$173$	−1719.00	+	2977.40i	−0.755452	+	1.30848i	−0.945149	+	0.326638i	$0.894084\pi$
$174$		0			0
$175$	350.000	+	1818.65i	0.151186	+	0.785584i
$176$		0			0
$177$	238.500	−	413.094i	0.101281	−	0.175424i
$178$		0			0
$179$	−606.000	−	1049.62i	−0.253042	−	0.438282i	0.711320	−	0.702869i	$-0.248098\pi$
$179$	−606.000	−	1049.62i	−0.253042	−	0.438282i	−0.964362	+	0.264587i	$0.914765\pi$
$180$		0			0
$181$	3032.00			1.24512			0.622560	−	0.782572i	$-0.286093\pi$
$181$	3032.00			1.24512			0.622560	+	0.782572i	$0.286093\pi$
$182$		0			0
$183$	2166.00			0.874947
$184$		0			0
$185$	330.000	+	571.577i	0.131146	+	0.227152i
$186$		0			0
$187$	378.000	−	654.715i	0.147819	−	0.256030i
$188$		0			0
$189$	−472.500	−	163.679i	−0.181848	−	0.0629941i
$190$		0			0
$191$	1260.00	−	2182.38i	0.477332	−	0.826763i	−0.522331	−	0.852743i	$-0.674937\pi$
$191$	1260.00	−	2182.38i	0.477332	−	0.826763i	0.999662	+	0.0259799i	$0.00827060\pi$
$192$		0			0
$193$	−182.500	−	316.099i	−0.0680655	−	0.117893i	0.829984	−	0.557787i	$-0.188349\pi$
$193$	−182.500	−	316.099i	−0.0680655	−	0.117893i	−0.898050	+	0.439894i	$0.855016\pi$
$194$		0			0
$195$	3960.00			1.45426
$196$		0			0
$197$	−1590.00			−0.575040			−0.287520	−	0.957775i	$-0.592831\pi$
$197$	−1590.00			−0.575040			−0.287520	+	0.957775i	$0.592831\pi$
$198$		0			0
$199$	−2690.00	−	4659.22i	−0.958236	−	1.65971i	−0.726782	−	0.686868i	$-0.758985\pi$
$199$	−2690.00	−	4659.22i	−0.958236	−	1.65971i	−0.231455	−	0.972846i	$-0.574348\pi$
$200$		0			0
$201$	−249.000	+	431.281i	−0.0873786	+	0.151344i
$202$		0			0
$203$	−892.500	−	309.171i	−0.308577	−	0.106894i
$204$		0			0
$205$	−1260.00	+	2182.38i	−0.429279	+	0.743533i
$206$		0			0
$207$	−378.000	−	654.715i	−0.126922	−	0.219835i
$208$		0			0
$209$	−936.000			−0.309782
$210$		0			0
$211$	5362.00			1.74946			0.874728	−	0.484614i	$-0.161040\pi$
$211$	5362.00			1.74946			0.874728	+	0.484614i	$0.161040\pi$
$212$		0			0
$213$	1629.00	+	2821.51i	0.524025	+	0.907637i
$214$		0			0
$215$	−2445.00	+	4234.86i	−0.775570	+	1.34333i
$216$		0			0
$217$	−647.500	−	3364.51i	−0.202558	−	1.05252i
$218$		0			0
$219$	−327.000	+	566.381i	−0.100898	+	0.174760i
$220$		0			0
$221$	−3696.00	−	6401.66i	−1.12498	−	1.94852i
$222$		0			0
$223$	1573.00			0.472358			0.236179	−	0.971710i	$-0.424105\pi$
$223$	1573.00			0.472358			0.236179	+	0.971710i	$0.424105\pi$
$224$		0			0
$225$	900.000			0.266667
$226$		0			0
$227$	460.500	+	797.609i	0.134645	+	0.233212i	0.925462	−	0.378841i	$-0.123677\pi$
$227$	460.500	+	797.609i	0.134645	+	0.233212i	−0.790817	+	0.612053i	$0.790344\pi$
$228$		0			0
$229$	−2026.00	+	3509.13i	−0.584637	+	1.01262i	0.410284	+	0.911958i	$0.365430\pi$
$229$	−2026.00	+	3509.13i	−0.584637	+	1.01262i	−0.994921	+	0.100663i	$0.967904\pi$
$230$		0			0
$231$	378.000	−	327.358i	0.107665	−	0.0932405i
$232$		0			0
$233$	234.000	−	405.300i	0.0657933	−	0.113957i	−0.831252	−	0.555895i	$-0.812376\pi$
$233$	234.000	−	405.300i	0.0657933	−	0.113957i	0.897046	+	0.441938i	$0.145709\pi$
$234$		0			0
$235$	1035.00	+	1792.67i	0.287302	+	0.497622i
$236$		0			0
$237$	1749.00			0.479366
$238$		0			0
$239$	−4932.00			−1.33483			−0.667415	−	0.744686i	$-0.732599\pi$
$239$	−4932.00			−1.33483			−0.667415	+	0.744686i	$0.732599\pi$
$240$		0			0
$241$	768.500	+	1331.08i	0.205408	+	0.355778i	0.950263	−	0.311449i	$-0.100814\pi$
$241$	768.500	+	1331.08i	0.205408	+	0.355778i	−0.744854	+	0.667227i	$0.767481\pi$
$242$		0			0
$243$	−121.500	+	210.444i	−0.0320750	+	0.0555556i
$244$		0			0
$245$	4777.50	−	1909.59i	1.24581	−	0.497955i
$246$		0			0
$247$	−4576.00	+	7925.86i	−1.17880	+	2.04174i
$248$		0			0
$249$	−895.500	−	1551.05i	−0.227912	−	0.394755i
$250$		0			0
$251$	−5319.00			−1.33758			−0.668789	−	0.743452i	$-0.733187\pi$
$251$	−5319.00			−1.33758			−0.668789	+	0.743452i	$0.733187\pi$
$252$		0			0
$253$	756.000			0.187863
$254$		0			0
$255$	−1890.00	−	3273.58i	−0.464143	−	0.803919i
$256$		0			0
$257$	−2673.00	+	4629.77i	−0.648783	+	1.12372i	0.334631	+	0.942349i	$0.391388\pi$
$257$	−2673.00	+	4629.77i	−0.648783	+	1.12372i	−0.983414	+	0.181375i	$0.941945\pi$
$258$		0			0
$259$	616.000	−	533.472i	0.147785	−	0.127986i
$260$		0			0
$261$	−229.500	+	397.506i	−0.0544279	+	0.0942720i
$262$		0			0
$263$	387.000	+	670.304i	0.0907355	+	0.157159i	0.907821	−	0.419358i	$-0.137745\pi$
$263$	387.000	+	670.304i	0.0907355	+	0.157159i	−0.817085	+	0.576517i	$0.804412\pi$
$264$		0			0
$265$	−9585.00			−2.22189
$266$		0			0
$267$	−3114.00			−0.713759
$268$		0			0
$269$	−1207.50	−	2091.45i	−0.273690	−	0.474045i	0.696114	−	0.717931i	$-0.254911\pi$
$269$	−1207.50	−	2091.45i	−0.273690	−	0.474045i	−0.969804	+	0.243887i	$0.921578\pi$
$270$		0			0
$271$	−237.500	+	411.362i	−0.0532365	+	0.0922084i	−0.891416	−	0.453187i	$-0.850287\pi$
$271$	−237.500	+	411.362i	−0.0532365	+	0.0922084i	0.838179	+	0.545395i	$0.183620\pi$
$272$		0			0
$273$	−924.000	−	4801.24i	−0.204846	−	1.06441i
$274$		0			0
$275$	−450.000	+	779.423i	−0.0986764	+	0.170913i
$276$		0			0
$277$	−1864.00	−	3228.54i	−0.404321	−	0.700304i	0.589921	−	0.807461i	$-0.299159\pi$
$277$	−1864.00	−	3228.54i	−0.404321	−	0.700304i	−0.994242	+	0.107156i	$0.965825\pi$
$278$		0			0
$279$	−1665.00			−0.357279
$280$		0			0
$281$	1602.00			0.340097			0.170049	−	0.985436i	$-0.445608\pi$
$281$	1602.00			0.340097			0.170049	+	0.985436i	$0.445608\pi$
$282$		0			0
$283$	343.000	+	594.093i	0.0720468	+	0.124789i	0.899798	−	0.436306i	$-0.143714\pi$
$283$	343.000	+	594.093i	0.0720468	+	0.124789i	−0.827751	+	0.561095i	$0.810380\pi$
$284$		0			0
$285$	−2340.00	+	4053.00i	−0.486350	+	0.842382i
$286$		0			0
$287$	2940.00	+	1018.45i	0.604678	+	0.209467i
$288$		0			0
$289$	−1071.50	+	1855.89i	−0.218095	+	0.377751i
$290$		0			0
$291$	253.500	+	439.075i	0.0510668	+	0.0884503i
$292$		0			0
$293$	−1101.00			−0.219526			−0.109763	−	0.993958i	$-0.535009\pi$
$293$	−1101.00			−0.219526			−0.109763	+	0.993958i	$0.535009\pi$
$294$		0			0
$295$	2385.00			0.470712
$296$		0			0
$297$	−121.500	−	210.444i	−0.0237379	−	0.0411152i
$298$		0			0
$299$	3696.00	−	6401.66i	0.714867	−	1.23819i
$300$		0			0
$301$	5705.00	+	1976.27i	1.09246	+	0.378440i
$302$		0			0
$303$	−963.000	+	1667.96i	−0.182584	+	0.316244i
$304$		0			0
$305$	5415.00	+	9379.06i	1.01660	+	1.76080i
$306$		0			0
$307$	−2780.00			−0.516818			−0.258409	−	0.966036i	$-0.583198\pi$
$307$	−2780.00			−0.516818			−0.258409	+	0.966036i	$0.583198\pi$
$308$		0			0
$309$	−1392.00			−0.256272
$310$		0			0
$311$	2148.00	+	3720.45i	0.391646	+	0.678351i	0.992667	−	0.120883i	$-0.0385725\pi$
$311$	2148.00	+	3720.45i	0.391646	+	0.678351i	−0.601021	+	0.799233i	$0.705239\pi$
$312$		0			0
$313$	−2744.50	+	4753.61i	−0.495618	+	0.858435i	−0.999987	−	0.00505298i	$-0.998392\pi$
$313$	−2744.50	+	4753.61i	−0.495618	+	0.858435i	0.504370	+	0.863488i	$0.331725\pi$
$314$		0			0
$315$	−472.500	−	2455.18i	−0.0845154	−	0.439155i
$316$		0			0
$317$	−2245.50	+	3889.32i	−0.397854	+	0.689104i	−0.993461	−	0.114172i	$-0.963578\pi$
$317$	−2245.50	+	3889.32i	−0.397854	+	0.689104i	0.595607	+	0.803276i	$0.296912\pi$
$318$		0			0
$319$	−229.500	−	397.506i	−0.0402807	−	0.0697682i
$320$		0			0
$321$	−1179.00			−0.205001
$322$		0			0
$323$	8736.00			1.50490
$324$		0			0
$325$	4400.00	+	7621.02i	0.750979	+	1.30073i
$326$		0			0
$327$	−21.0000	+	36.3731i	−0.00355138	+	0.00615118i
$328$		0			0
$329$	1932.00	−	1673.16i	0.323753	−	0.280378i
$330$		0			0
$331$	−1982.00	+	3432.92i	−0.329126	+	0.570062i	−0.982339	−	0.187112i	$-0.940087\pi$
$331$	−1982.00	+	3432.92i	−0.329126	+	0.570062i	0.653213	+	0.757174i	$0.273421\pi$
$332$		0			0
$333$	−198.000	−	342.946i	−0.0325836	−	0.0564364i
$334$		0			0
$335$	−2490.00			−0.406099
$336$		0			0
$337$	161.000			0.0260244			0.0130122	−	0.999915i	$-0.495858\pi$
$337$	161.000			0.0260244			0.0130122	+	0.999915i	$0.495858\pi$
$338$		0			0
$339$	3276.00	+	5674.20i	0.524861	+	0.909086i
$340$		0			0
$341$	832.500	−	1441.93i	0.132206	−	0.228988i
$342$		0			0
$343$	−3430.00	−	5346.84i	−0.539949	−	0.841698i
$344$		0			0
$345$	1890.00	−	3273.58i	0.294940	−	0.510850i
$346$		0			0
$347$	−2958.00	−	5123.41i	−0.457619	−	0.792619i	0.541216	−	0.840884i	$-0.317964\pi$
$347$	−2958.00	−	5123.41i	−0.457619	−	0.792619i	−0.998835	+	0.0482646i	$0.984631\pi$
$348$		0			0
$349$	−142.000			−0.0217796			−0.0108898	−	0.999941i	$-0.503466\pi$
$349$	−142.000			−0.0217796			−0.0108898	+	0.999941i	$0.503466\pi$
$350$		0			0
$351$	−2376.00			−0.361315
$352$		0			0
$353$	2220.00	+	3845.15i	0.334727	+	0.579764i	0.983432	−	0.181275i	$-0.0580225\pi$
$353$	2220.00	+	3845.15i	0.334727	+	0.579764i	−0.648705	+	0.761040i	$0.724689\pi$
$354$		0			0
$355$	−8145.00	+	14107.6i	−1.21772	+	2.10916i
$356$		0			0
$357$	−3528.00	+	3055.34i	−0.523030	+	0.452957i
$358$		0			0
$359$	1143.00	−	1979.73i	0.168037	−	0.291048i	−0.769693	−	0.638415i	$-0.779591\pi$
$359$	1143.00	−	1979.73i	0.168037	−	0.291048i	0.937730	+	0.347366i	$0.112924\pi$
$360$		0			0
$361$	−1978.50	−	3426.86i	−0.288453	−	0.499615i
$362$		0			0
$363$	−3750.00			−0.542215
$364$		0			0
$365$	−3270.00			−0.468930
$366$		0			0
$367$	−1434.50	−	2484.63i	−0.204033	−	0.353396i	0.745791	−	0.666180i	$-0.232072\pi$
$367$	−1434.50	−	2484.63i	−0.204033	−	0.353396i	−0.949824	+	0.312784i	$0.898738\pi$
$368$		0			0
$369$	756.000	−	1309.43i	0.106655	−	0.184732i
$370$		0			0
$371$	2236.50	+	11621.2i	0.312974	+	1.62626i
$372$		0			0
$373$	1532.00	−	2653.50i	0.212665	−	0.368346i	−0.739883	−	0.672736i	$-0.765119\pi$
$373$	1532.00	−	2653.50i	0.212665	−	0.368346i	0.952548	+	0.304390i	$0.0984524\pi$
$374$		0			0
$375$	−562.500	−	974.279i	−0.0774597	−	0.134164i
$376$		0			0
$377$	−4488.00			−0.613113
$378$		0			0
$379$	6040.00			0.818612			0.409306	−	0.912397i	$-0.365771\pi$
$379$	6040.00			0.818612			0.409306	+	0.912397i	$0.365771\pi$
$380$		0			0
$381$	−559.500	−	969.082i	−0.0752337	−	0.130309i
$382$		0			0
$383$	921.000	−	1595.22i	0.122874	−	0.212825i	−0.798026	−	0.602623i	$-0.794122\pi$
$383$	921.000	−	1595.22i	0.122874	−	0.212825i	0.920900	+	0.389799i	$0.127455\pi$
$384$		0			0
$385$	2362.50	+	818.394i	0.312738	+	0.108336i
$386$		0			0
$387$	1467.00	−	2540.92i	0.192692	−	0.333752i
$388$		0			0
$389$	−3915.00	−	6780.98i	−0.510279	−	0.883828i	−0.999929	−	0.0119097i	$-0.996209\pi$
$389$	−3915.00	−	6780.98i	−0.510279	−	0.883828i	0.489650	−	0.871919i	$-0.337124\pi$
$390$		0			0
$391$	−7056.00			−0.912627
$392$		0			0
$393$	3519.00			0.451680
$394$		0			0
$395$	4372.50	+	7573.39i	0.556973	+	0.964706i
$396$		0			0
$397$	7382.00	−	12786.0i	0.933229	−	1.61640i	0.155467	−	0.987841i	$-0.450312\pi$
$397$	7382.00	−	12786.0i	0.933229	−	1.61640i	0.777762	−	0.628559i	$-0.216355\pi$
$398$		0			0
$399$	5460.00	+	1891.40i	0.685067	+	0.237314i
$400$		0			0
$401$	−3132.00	+	5424.78i	−0.390036	+	0.675563i	−0.992454	−	0.122618i	$-0.960871\pi$
$401$	−3132.00	+	5424.78i	−0.390036	+	0.675563i	0.602417	+	0.798181i	$0.294204\pi$
$402$		0			0
$403$	−8140.00	−	14098.9i	−1.00616	−	1.74272i
$404$		0			0
$405$	−1215.00			−0.149071
$406$		0			0
$407$	396.000			0.0482285
$408$		0			0
$409$	−2375.50	−	4114.49i	−0.287191	−	0.497429i	0.685948	−	0.727651i	$-0.259388\pi$
$409$	−2375.50	−	4114.49i	−0.287191	−	0.497429i	−0.973138	+	0.230222i	$0.926055\pi$
$410$		0			0
$411$	−45.0000	+	77.9423i	−0.00540070	+	0.00935428i
$412$		0			0
$413$	−556.500	−	2891.66i	−0.0663041	−	0.344526i
$414$		0			0
$415$	4477.50	−	7755.26i	0.529619	−	0.917327i
$416$		0			0
$417$	−123.000	−	213.042i	−0.0144445	−	0.0250185i
$418$		0			0
$419$	4704.00			0.548462			0.274231	−	0.961664i	$-0.411577\pi$
$419$	4704.00			0.548462			0.274231	+	0.961664i	$0.411577\pi$
$420$		0			0
$421$	−4474.00			−0.517932			−0.258966	−	0.965886i	$-0.583382\pi$
$421$	−4474.00			−0.517932			−0.258966	+	0.965886i	$0.583382\pi$
$422$		0			0
$423$	−621.000	−	1075.60i	−0.0713807	−	0.123635i
$424$		0			0
$425$	4200.00	−	7274.61i	0.479365	−	0.830284i
$426$		0			0
$427$	10108.0	−	8753.78i	1.14557	−	0.992097i
$428$		0			0
$429$	1188.00	−	2057.68i	0.133700	−	0.231575i
$430$		0			0
$431$	−6402.00	−	11088.6i	−0.715484	−	1.23925i	−0.962773	−	0.270312i	$-0.912873\pi$
$431$	−6402.00	−	11088.6i	−0.715484	−	1.23925i	0.247289	−	0.968942i	$-0.420460\pi$
$432$		0			0
$433$	−5074.00			−0.563143			−0.281571	−	0.959540i	$-0.590856\pi$
$433$	−5074.00			−0.563143			−0.281571	+	0.959540i	$0.590856\pi$
$434$		0			0
$435$	−2295.00			−0.252958
$436$		0			0
$437$	4368.00	+	7565.60i	0.478146	+	0.828173i
$438$		0			0
$439$	−633.500	+	1097.25i	−0.0688731	+	0.119292i	−0.898406	−	0.439167i	$-0.855274\pi$
$439$	−633.500	+	1097.25i	−0.0688731	+	0.119292i	0.829532	+	0.558459i	$0.188607\pi$
$440$		0			0
$441$	−2866.50	+	1145.75i	−0.309524	+	0.123718i
$442$		0			0
$443$	−3466.50	+	6004.15i	−0.371780	+	0.643941i	−0.989839	−	0.142190i	$-0.954586\pi$
$443$	−3466.50	+	6004.15i	−0.371780	+	0.643941i	0.618060	+	0.786131i	$0.287919\pi$
$444$		0			0
$445$	−7785.00	−	13484.0i	−0.829313	−	1.43641i
$446$		0			0
$447$	−4302.00			−0.455207
$448$		0			0
$449$	11688.0			1.22849			0.614244	−	0.789116i	$-0.289461\pi$
$449$	11688.0			1.22849			0.614244	+	0.789116i	$0.289461\pi$
$450$		0			0
$451$	756.000	+	1309.43i	0.0789327	+	0.136715i
$452$		0			0
$453$	−4006.50	+	6939.46i	−0.415545	+	0.719745i
$454$		0			0
$455$	18480.0	−	16004.1i	1.90408	−	1.64898i
$456$		0			0
$457$	−275.500	+	477.180i	−0.0281999	+	0.0488436i	−0.879781	−	0.475379i	$-0.842311\pi$
$457$	−275.500	+	477.180i	−0.0281999	+	0.0488436i	0.851581	+	0.524223i	$0.175644\pi$
$458$		0			0
$459$	1134.00	+	1964.15i	0.115317	+	0.199735i
$460$		0			0
$461$	13386.0			1.35238			0.676191	−	0.736726i	$-0.263629\pi$
$461$	13386.0			1.35238			0.676191	+	0.736726i	$0.263629\pi$
$462$		0			0
$463$	6376.00			0.639995			0.319998	−	0.947418i	$-0.396318\pi$
$463$	6376.00			0.639995			0.319998	+	0.947418i	$0.396318\pi$
$464$		0			0
$465$	−4162.50	−	7209.66i	−0.415121	−	0.719011i
$466$		0			0
$467$	2850.00	−	4936.34i	0.282403	−	0.489137i	−0.689573	−	0.724216i	$-0.742202\pi$
$467$	2850.00	−	4936.34i	0.282403	−	0.489137i	0.971976	+	0.235080i	$0.0755351\pi$
$468$		0			0
$469$	581.000	+	3018.96i	0.0572027	+	0.297234i
$470$		0			0
$471$	−3378.00	+	5850.87i	−0.330467	+	0.572386i
$472$		0			0
$473$	1467.00	+	2540.92i	0.142606	+	0.247001i
$474$		0			0
$475$	−10400.0			−1.00460
$476$		0			0
$477$	5751.00			0.552034
$478$		0			0
$479$	9897.00	+	17142.1i	0.944062	+	1.63516i	0.757619	+	0.652697i	$0.226362\pi$
$479$	9897.00	+	17142.1i	0.944062	+	1.63516i	0.186442	+	0.982466i	$0.440304\pi$
$480$		0			0
$481$	1936.00	−	3353.25i	0.183522	−	0.317869i
$482$		0			0
$483$	−4410.00	−	1527.67i	−0.415449	−	0.143916i
$484$		0			0
$485$	−1267.50	+	2195.37i	−0.118668	+	0.205540i
$486$		0			0
$487$	7967.50	+	13800.1i	0.741359	+	1.28407i	0.951877	+	0.306482i	$0.0991518\pi$
$487$	7967.50	+	13800.1i	0.741359	+	1.28407i	−0.210517	+	0.977590i	$0.567515\pi$
$488$		0			0
$489$	−5028.00			−0.464978
$490$		0			0
$491$	−9963.00			−0.915731			−0.457865	−	0.889021i	$-0.651386\pi$
$491$	−9963.00			−0.915731			−0.457865	+	0.889021i	$0.651386\pi$
$492$		0			0
$493$	2142.00	+	3710.05i	0.195681	+	0.338930i
$494$		0			0
$495$	607.500	−	1052.22i	0.0551618	−	0.0955431i
$496$		0			0
$497$	19005.0	+	6583.53i	1.71527	+	0.594188i
$498$		0			0
$499$	9571.00	−	16577.5i	0.858631	−	1.48719i	−0.0146043	−	0.999893i	$-0.504649\pi$
$499$	9571.00	−	16577.5i	0.858631	−	1.48719i	0.873235	−	0.487299i	$-0.162018\pi$
$500$		0			0
$501$	4545.00	+	7872.17i	0.405301	+	0.702001i
$502$		0			0
$503$	12192.0			1.08074			0.540372	−	0.841426i	$-0.318283\pi$
$503$	12192.0			1.08074			0.540372	+	0.841426i	$0.318283\pi$
$504$		0			0
$505$	−9630.00			−0.848573
$506$		0			0
$507$	−8320.50	−	14411.5i	−0.728849	−	1.26240i
$508$		0			0
$509$	9904.50	−	17155.1i	0.862494	−	1.49388i	−0.00702091	−	0.999975i	$-0.502235\pi$
$509$	9904.50	−	17155.1i	0.862494	−	1.49388i	0.869515	−	0.493907i	$-0.164432\pi$
$510$		0			0
$511$	763.000	+	3964.66i	0.0660531	+	0.343222i
$512$		0			0
$513$	1404.00	−	2431.80i	0.120835	−	0.209292i
$514$		0			0
$515$	−3480.00	−	6027.54i	−0.297761	−	0.515738i
$516$		0			0
$517$	1242.00			0.105654
$518$		0			0
$519$	10314.0			0.872321
$520$		0			0
$521$	897.000	+	1553.65i	0.0754286	+	0.130646i	0.901273	−	0.433253i	$-0.142634\pi$
$521$	897.000	+	1553.65i	0.0754286	+	0.130646i	−0.825844	+	0.563899i	$0.809301\pi$
$522$		0			0
$523$	−3224.00	+	5584.13i	−0.269552	+	0.466878i	−0.968746	−	0.248054i	$-0.920209\pi$
$523$	−3224.00	+	5584.13i	−0.269552	+	0.466878i	0.699194	+	0.714932i	$0.253542\pi$
$524$		0			0
$525$	4200.00	−	3637.31i	0.349149	−	0.302372i
$526$		0			0
$527$	−7770.00	+	13458.0i	−0.642251	+	1.11241i
$528$		0			0
$529$	2555.50	+	4426.26i	0.210035	+	0.363792i
$530$		0			0
$531$	−1431.00			−0.116949
$532$		0			0
$533$	14784.0			1.20144
$534$		0			0
$535$	−2947.50	−	5105.22i	−0.238190	−	0.412557i
$536$		0			0
$537$	−1818.00	+	3148.87i	−0.146094	+	0.253042i
$538$		0			0
$539$	441.000	−	3055.34i	0.0352416	−	0.244161i
$540$		0			0
$541$	−3631.00	+	6289.08i	−0.288556	+	0.499794i	−0.973465	−	0.228835i	$-0.926509\pi$
$541$	−3631.00	+	6289.08i	−0.288556	+	0.499794i	0.684909	+	0.728628i	$0.259842\pi$
$542$		0			0
$543$	−4548.00	−	7877.37i	−0.359435	−	0.622560i
$544$		0			0
$545$	−210.000			−0.0165053
$546$		0			0
$547$	−14204.0			−1.11027			−0.555136	−	0.831759i	$-0.687334\pi$
$547$	−14204.0			−1.11027			−0.555136	+	0.831759i	$0.687334\pi$
$548$		0			0
$549$	−3249.00	−	5627.43i	−0.252575	−	0.437474i
$550$		0			0
$551$	2652.00	−	4593.40i	0.205044	−	0.355146i
$552$		0			0
$553$	8162.00	−	7068.50i	0.627638	−	0.543550i
$554$		0			0
$555$	990.000	−	1714.73i	0.0757174	−	0.131146i
$556$		0			0
$557$	−7912.50	−	13704.9i	−0.601909	−	1.04254i	−0.992532	−	0.121986i	$-0.961074\pi$
$557$	−7912.50	−	13704.9i	−0.601909	−	1.04254i	0.390623	−	0.920551i	$-0.372260\pi$
$558$		0			0
$559$	28688.0			2.17061
$560$		0			0
$561$	−2268.00			−0.170686
$562$		0			0
$563$	529.500	+	917.121i	0.0396372	+	0.0686537i	0.885163	−	0.465280i	$-0.154046\pi$
$563$	529.500	+	917.121i	0.0396372	+	0.0686537i	−0.845526	+	0.533934i	$0.820713\pi$
$564$		0			0
$565$	−16380.0	+	28371.0i	−1.21967	+	2.11252i
$566$		0			0
$567$	283.500	+	1473.11i	0.0209980	+	0.109109i
$568$		0			0
$569$	−1980.00	+	3429.46i	−0.145880	+	0.252672i	−0.929701	−	0.368315i	$-0.879935\pi$
$569$	−1980.00	+	3429.46i	−0.145880	+	0.252672i	0.783821	+	0.620987i	$0.213268\pi$
$570$		0			0
$571$	−1265.00	−	2191.04i	−0.0927121	−	0.160582i	0.815939	−	0.578138i	$-0.196220\pi$
$571$	−1265.00	−	2191.04i	−0.0927121	−	0.160582i	−0.908651	+	0.417555i	$0.862887\pi$
$572$		0			0
$573$	−7560.00			−0.551175
$574$		0			0
$575$	8400.00			0.609225
$576$		0			0
$577$	−5915.50	−	10245.9i	−0.426803	−	0.739245i	0.569784	−	0.821795i	$-0.307027\pi$
$577$	−5915.50	−	10245.9i	−0.426803	−	0.739245i	−0.996587	+	0.0825498i	$0.973694\pi$
$578$		0			0
$579$	−547.500	+	948.298i	−0.0392976	+	0.0680655i
$580$		0			0
$581$	−10447.5	−	3619.12i	−0.746016	−	0.258428i
$582$		0			0
$583$	−2875.50	+	4980.51i	−0.204273	+	0.353811i
$584$		0			0
$585$	−5940.00	−	10288.4i	−0.419810	−	0.727132i
$586$		0			0
$587$	−4809.00			−0.338141			−0.169070	−	0.985604i	$-0.554077\pi$
$587$	−4809.00			−0.338141			−0.169070	+	0.985604i	$0.554077\pi$
$588$		0			0
$589$	19240.0			1.34596
$590$		0			0
$591$	2385.00	+	4130.94i	0.166000	+	0.287520i
$592$		0			0
$593$	−10902.0	+	18882.8i	−0.754960	+	1.30763i	0.190434	+	0.981700i	$0.439011\pi$
$593$	−10902.0	+	18882.8i	−0.754960	+	1.30763i	−0.945394	+	0.325930i	$0.894323\pi$
$594$		0			0
$595$	−22050.0	−	7638.34i	−1.51926	−	0.526288i
$596$		0			0
$597$	−8070.00	+	13977.7i	−0.553238	+	0.958236i
$598$		0			0
$599$	7083.00	+	12268.1i	0.483144	+	0.836831i	0.999813	−	0.0193549i	$-0.00616125\pi$
$599$	7083.00	+	12268.1i	0.483144	+	0.836831i	−0.516668	+	0.856186i	$0.672828\pi$
$600$		0			0
$601$	5891.00			0.399832			0.199916	−	0.979813i	$-0.435933\pi$
$601$	5891.00			0.399832			0.199916	+	0.979813i	$0.435933\pi$
$602$		0			0
$603$	1494.00			0.100896
$604$		0			0
$605$	−9375.00	−	16238.0i	−0.629997	−	1.09119i
$606$		0			0
$607$	−1368.50	+	2370.31i	−0.0915086	+	0.158497i	−0.908146	−	0.418653i	$-0.862502\pi$
$607$	−1368.50	+	2370.31i	−0.0915086	+	0.158497i	0.816638	+	0.577151i	$0.195836\pi$
$608$		0			0
$609$	535.500	+	2782.54i	0.0356315	+	0.185146i
$610$		0			0
$611$	6072.00	−	10517.0i	0.402041	−	0.696355i
$612$		0			0
$613$	13094.0	+	22679.5i	0.862743	+	1.49432i	0.869271	+	0.494337i	$0.164589\pi$
$613$	13094.0	+	22679.5i	0.862743	+	1.49432i	−0.00652719	+	0.999979i	$0.502078\pi$
$614$		0			0
$615$	7560.00			0.495689
$616$		0			0
$617$	−2358.00			−0.153857			−0.0769283	−	0.997037i	$-0.524511\pi$
$617$	−2358.00			−0.153857			−0.0769283	+	0.997037i	$0.524511\pi$
$618$		0			0
$619$	6883.00	+	11921.7i	0.446932	+	0.774110i	0.998185	−	0.0602291i	$-0.0191831\pi$
$619$	6883.00	+	11921.7i	0.446932	+	0.774110i	−0.551252	+	0.834339i	$0.685850\pi$
$620$		0			0
$621$	−1134.00	+	1964.15i	−0.0732783	+	0.126922i
$622$		0			0
$623$	−14532.0	+	12585.1i	−0.934530	+	0.809327i
$624$		0			0
$625$	9062.50	−	15696.7i	0.580000	−	1.00459i
$626$		0			0
$627$	1404.00	+	2431.80i	0.0894264	+	0.154891i
$628$		0			0
$629$	−3696.00			−0.234291
$630$		0			0
$631$	−21287.0			−1.34298			−0.671491	−	0.741012i	$-0.734346\pi$
$631$	−21287.0			−1.34298			−0.671491	+	0.741012i	$0.734346\pi$
$632$		0			0
$633$	−8043.00	−	13930.9i	−0.505025	−	0.874728i
$634$		0			0
$635$	2797.50	−	4845.41i	0.174827	−	0.302810i
$636$		0			0
$637$	−23716.0	−	18671.5i	−1.47514	−	1.16137i
$638$		0			0
$639$	4887.00	−	8464.53i	0.302546	−	0.524025i
$640$		0			0
$641$	−10713.0	−	18555.5i	−0.660122	−	1.14336i	−0.980583	−	0.196103i	$-0.937171\pi$
$641$	−10713.0	−	18555.5i	−0.660122	−	1.14336i	0.320462	−	0.947262i	$-0.396162\pi$
$642$		0			0
$643$	−9962.00			−0.610984			−0.305492	−	0.952195i	$-0.598821\pi$
$643$	−9962.00			−0.610984			−0.305492	+	0.952195i	$0.598821\pi$
$644$		0			0
$645$	14670.0			0.895551
$646$		0			0
$647$	−9087.00	−	15739.1i	−0.552159	−	0.956367i	−0.998119	−	0.0613142i	$-0.980471\pi$
$647$	−9087.00	−	15739.1i	−0.552159	−	0.956367i	0.445960	−	0.895053i	$-0.352863\pi$
$648$		0			0
$649$	715.500	−	1239.28i	0.0432755	−	0.0749555i
$650$		0			0
$651$	−7770.00	+	6729.02i	−0.467788	+	0.405117i
$652$		0			0
$653$	9583.50	−	16599.1i	0.574321	−	0.994752i	−0.421795	−	0.906691i	$-0.638600\pi$
$653$	9583.50	−	16599.1i	0.574321	−	0.994752i	0.996115	−	0.0880610i	$-0.0280670\pi$
$654$		0			0
$655$	8797.50	+	15237.7i	0.524804	+	0.908988i
$656$		0			0
$657$	1962.00			0.116507
$658$		0			0
$659$	−13080.0			−0.773178			−0.386589	−	0.922252i	$-0.626347\pi$
$659$	−13080.0			−0.773178			−0.386589	+	0.922252i	$0.626347\pi$
$660$		0			0
$661$	7595.00	+	13154.9i	0.446916	+	0.774081i	0.998183	−	0.0602477i	$-0.0191891\pi$
$661$	7595.00	+	13154.9i	0.446916	+	0.774081i	−0.551268	+	0.834328i	$0.685856\pi$
$662$		0			0
$663$	−11088.0	+	19205.0i	−0.649506	+	1.12498i
$664$		0			0
$665$	5460.00	+	28371.0i	0.318391	+	1.65441i
$666$		0			0
$667$	−2142.00	+	3710.05i	−0.124346	+	0.215373i
$668$		0			0
$669$	−2359.50	−	4086.77i	−0.136358	−	0.236179i
$670$		0			0
$671$	6498.00			0.373849
$672$		0			0
$673$	4397.00			0.251845			0.125923	−	0.992040i	$-0.459811\pi$
$673$	4397.00			0.251845			0.125923	+	0.992040i	$0.459811\pi$
$674$		0			0
$675$	−1350.00	−	2338.27i	−0.0769800	−	0.133333i
$676$		0			0
$677$	−2014.50	+	3489.22i	−0.114363	+	0.198082i	−0.917525	−	0.397679i	$-0.869816\pi$
$677$	−2014.50	+	3489.22i	−0.114363	+	0.198082i	0.803162	+	0.595761i	$0.203149\pi$
$678$		0			0
$679$	2957.50	+	1024.51i	0.167155	+	0.0579043i
$680$		0			0
$681$	1381.50	−	2392.83i	0.0777374	−	0.134645i
$682$		0			0
$683$	7510.50	+	13008.6i	0.420763	+	0.728783i	0.996014	−	0.0891936i	$-0.0284290\pi$
$683$	7510.50	+	13008.6i	0.420763	+	0.728783i	−0.575251	+	0.817977i	$0.695096\pi$
$684$		0			0
$685$	−450.000			−0.0251002
$686$		0			0
$687$	12156.0			0.675081
$688$		0			0
$689$	28116.0	+	48698.3i	1.55462	+	2.69268i
$690$		0			0
$691$	−6992.00	+	12110.5i	−0.384932	+	0.666722i	−0.991760	−	0.128111i	$-0.959109\pi$
$691$	−6992.00	+	12110.5i	−0.384932	+	0.666722i	0.606828	+	0.794834i	$0.292442\pi$
$692$		0			0
$693$	−1417.50	−	491.036i	−0.0777004	−	0.0269162i
$694$		0			0
$695$	615.000	−	1065.21i	0.0335659	−	0.0581378i
$696$		0			0
$697$	−7056.00	−	12221.4i	−0.383451	−	0.664156i
$698$		0			0
$699$	−1404.00			−0.0759716
$700$		0			0
$701$	−31053.0			−1.67312			−0.836559	−	0.547877i	$-0.815436\pi$
$701$	−31053.0			−1.67312			−0.836559	+	0.547877i	$0.815436\pi$
$702$		0			0
$703$	2288.00	+	3962.93i	0.122750	+	0.212610i
$704$		0			0
$705$	3105.00	−	5378.02i	0.165874	−	0.287302i
$706$		0			0
$707$	2247.00	+	11675.8i	0.119529	+	0.621092i
$708$		0			0
$709$	−7543.00	+	13064.9i	−0.399553	+	0.692047i	−0.993671	−	0.112332i	$-0.964168\pi$
$709$	−7543.00	+	13064.9i	−0.399553	+	0.692047i	0.594117	+	0.804378i	$0.297501\pi$
$710$		0			0
$711$	−2623.50	−	4544.04i	−0.138381	−	0.239683i
$712$		0			0
$713$	−15540.0			−0.816238
$714$		0			0
$715$	11880.0			0.621380
$716$		0			0
$717$	7398.00	+	12813.7i	0.385332	+	0.667415i
$718$		0			0
$719$	−3189.00	+	5523.51i	−0.165410	+	0.286498i	−0.936801	−	0.349863i	$-0.886228\pi$
$719$	−3189.00	+	5523.51i	−0.165410	+	0.286498i	0.771391	+	0.636362i	$0.219561\pi$
$720$		0			0
$721$	−6496.00	+	5625.70i	−0.335539	+	0.290585i
$722$		0			0
$723$	2305.50	−	3993.24i	0.118593	−	0.205408i
$724$		0			0
$725$	−2550.00	−	4416.73i	−0.130627	−	0.226253i
$726$		0			0
$727$	7363.00			0.375624			0.187812	−	0.982205i	$-0.439860\pi$
$727$	7363.00			0.375624			0.187812	+	0.982205i	$0.439860\pi$
$728$		0			0
$729$	729.000			0.0370370
$730$		0			0
$731$	−13692.0	−	23715.2i	−0.692773	−	1.19992i
$732$		0			0
$733$	−16405.0	+	28414.3i	−0.826647	+	1.43180i	0.0740064	+	0.997258i	$0.476421\pi$
$733$	−16405.0	+	28414.3i	−0.826647	+	1.43180i	−0.900654	+	0.434537i	$0.856912\pi$
$734$		0			0
$735$	−12127.5	−	9547.93i	−0.608612	−	0.479157i
$736$		0			0
$737$	−747.000	+	1293.84i	−0.0373353	+	0.0646666i
$738$		0			0
$739$	−12017.0	−	20814.1i	−0.598177	−	1.03607i	−0.993090	−	0.117354i	$-0.962559\pi$
$739$	−12017.0	−	20814.1i	−0.598177	−	1.03607i	0.394914	−	0.918718i	$-0.370775\pi$
$740$		0			0
$741$	27456.0			1.36116
$742$		0			0
$743$	8022.00			0.396095			0.198048	−	0.980192i	$-0.436540\pi$
$743$	8022.00			0.396095			0.198048	+	0.980192i	$0.436540\pi$
$744$		0			0
$745$	−10755.0	−	18628.2i	−0.528903	−	0.916087i
$746$		0			0
$747$	−2686.50	+	4653.15i	−0.131585	+	0.227912i
$748$		0			0
$749$	−5502.00	+	4764.87i	−0.268409	+	0.232449i
$750$		0			0
$751$	14759.5	−	25564.2i	0.717153	−	1.24215i	−0.244970	−	0.969531i	$-0.578778\pi$
$751$	14759.5	−	25564.2i	0.717153	−	1.24215i	0.962123	−	0.272615i	$-0.0878884\pi$
$752$		0			0
$753$	7978.50	+	13819.2i	0.386126	+	0.668789i
$754$		0			0
$755$	−40065.0			−1.93128
$756$		0			0
$757$	−3742.00			−0.179664			−0.0898318	−	0.995957i	$-0.528633\pi$
$757$	−3742.00			−0.179664			−0.0898318	+	0.995957i	$0.528633\pi$
$758$		0			0
$759$	−1134.00	−	1964.15i	−0.0542313	−	0.0939314i
$760$		0			0
$761$	5448.00	−	9436.21i	0.259514	−	0.449491i	−0.706598	−	0.707615i	$-0.749771\pi$
$761$	5448.00	−	9436.21i	0.259514	−	0.449491i	0.966112	+	0.258124i	$0.0831044\pi$
$762$		0			0
$763$	49.0000	+	254.611i	0.00232493	+	0.0120807i
$764$		0			0
$765$	−5670.00	+	9820.73i	−0.267973	+	0.464143i
$766$		0			0
$767$	−6996.00	−	12117.4i	−0.329349	−	0.570450i
$768$		0			0
$769$	17285.0			0.810550			0.405275	−	0.914195i	$-0.367176\pi$
$769$	17285.0			0.810550			0.405275	+	0.914195i	$0.367176\pi$
$770$		0			0
$771$	16038.0			0.749150
$772$		0			0
$773$	−5913.00	−	10241.6i	−0.275130	−	0.476540i	0.695038	−	0.718973i	$-0.255388\pi$
$773$	−5913.00	−	10241.6i	−0.275130	−	0.476540i	−0.970168	+	0.242434i	$0.922054\pi$
$774$		0			0
$775$	9250.00	−	16021.5i	0.428735	−	0.742591i
$776$		0			0
$777$	−2310.00	−	800.207i	−0.106655	−	0.0369463i
$778$		0			0
$779$	−8736.00	+	15131.2i	−0.401797	+	0.695932i
$780$		0			0
$781$	4887.00	+	8464.53i	0.223906	+	0.387817i
$782$		0			0
$783$	1377.00			0.0628480
$784$		0			0
$785$	−33780.0			−1.53587
$786$		0			0
$787$	8857.00	+	15340.8i	0.401166	+	0.694841i	0.993867	−	0.110582i	$-0.0352716\pi$
$787$	8857.00	+	15340.8i	0.401166	+	0.694841i	−0.592701	+	0.805423i	$0.701938\pi$
$788$		0			0
$789$	1161.00	−	2010.91i	0.0523862	−	0.0907355i
$790$		0			0
$791$	38220.0	+	13239.8i	1.71801	+	0.595136i
$792$		0			0
$793$	31768.0	−	55023.8i	1.42259	−	2.46400i
$794$		0			0
$795$	14377.5	+	24902.6i	0.641406	+	1.11095i
$796$		0			0
$797$	−24939.0			−1.10839			−0.554194	−	0.832388i	$-0.686973\pi$
$797$	−24939.0			−1.10839			−0.554194	+	0.832388i	$0.686973\pi$
$798$		0			0
$799$	−11592.0			−0.513261
$800$		0			0
$801$	4671.00	+	8090.41i	0.206045	+	0.356880i
$802$		0			0
$803$	−981.000	+	1699.14i	−0.0431118	+	0.0746717i
$804$		0			0
$805$	−4410.00	−	22915.0i	−0.193083	−	1.00329i
$806$		0			0
$807$	−3622.50	+	6274.35i	−0.158015	+	0.273690i
$808$		0			0
$809$	14532.0	+	25170.2i	0.631543	+	1.09386i	0.987236	+	0.159261i	$0.0509112\pi$
$809$	14532.0	+	25170.2i	0.631543	+	1.09386i	−0.355694	+	0.934602i	$0.615755\pi$
$810$		0			0
$811$	15370.0			0.665492			0.332746	−	0.943017i	$-0.392025\pi$
$811$	15370.0			0.665492			0.332746	+	0.943017i	$0.392025\pi$
$812$		0			0
$813$	1425.00			0.0614722
$814$		0			0
$815$	−12570.0	−	21771.9i	−0.540255	−	0.935749i
$816$		0			0
$817$	−16952.0	+	29361.7i	−0.725918	+	1.25733i
$818$		0			0
$819$	−11088.0	+	9602.49i	−0.473072	+	0.409692i
$820$		0			0
$821$	−22015.5	+	38132.0i	−0.935866	+	1.62097i	−0.162785	+	0.986662i	$0.552048\pi$
$821$	−22015.5	+	38132.0i	−0.935866	+	1.62097i	−0.773082	+	0.634306i	$0.781286\pi$
$822$		0			0
$823$	−2096.00	−	3630.38i	−0.0887752	−	0.153763i	0.818218	−	0.574907i	$-0.194962\pi$
$823$	−2096.00	−	3630.38i	−0.0887752	−	0.153763i	−0.906994	+	0.421144i	$0.861629\pi$
$824$		0			0
$825$	2700.00			0.113942
$826$		0			0
$827$	−33195.0			−1.39577			−0.697886	−	0.716209i	$-0.745876\pi$
$827$	−33195.0			−1.39577			−0.697886	+	0.716209i	$0.745876\pi$
$828$		0			0
$829$	−8224.00	−	14244.4i	−0.344549	−	0.596777i	0.640723	−	0.767773i	$-0.278635\pi$
$829$	−8224.00	−	14244.4i	−0.344549	−	0.596777i	−0.985272	+	0.170996i	$0.945302\pi$
$830$		0			0
$831$	−5592.00	+	9685.63i	−0.233435	+	0.404321i
$832$		0			0
$833$	−4116.00	+	28516.5i	−0.171202	+	1.18612i
$834$		0			0
$835$	−22725.0	+	39360.9i	−0.941834	+	1.63130i
$836$		0			0
$837$	2497.50	+	4325.80i	0.103138	+	0.178640i
$838$		0			0
$839$	−16860.0			−0.693769			−0.346884	−	0.937908i	$-0.612760\pi$
$839$	−16860.0			−0.693769			−0.346884	+	0.937908i	$0.612760\pi$
$840$		0			0
$841$	−21788.0			−0.893354
$842$		0			0
$843$	−2403.00	−	4162.12i	−0.0981776	−	0.170049i
$844$		0			0
$845$	41602.5	−	72057.6i	1.69369	−	2.93356i
$846$		0			0
$847$	−17500.0	+	15155.4i	−0.709926	+	0.614814i
$848$		0			0
$849$	1029.00	−	1782.28i	0.0415962	−	0.0720468i
$850$		0			0
$851$	−1848.00	−	3200.83i	−0.0744402	−	0.128934i
$852$		0			0
$853$	29054.0			1.16623			0.583113	−	0.812391i	$-0.301835\pi$
$853$	29054.0			1.16623			0.583113	+	0.812391i	$0.301835\pi$
$854$		0			0
$855$	14040.0			0.561588
$856$		0			0
$857$	−20979.0	−	36336.7i	−0.836207	−	1.44835i	−0.893044	−	0.449969i	$-0.851435\pi$
$857$	−20979.0	−	36336.7i	−0.836207	−	1.44835i	0.0568378	−	0.998383i	$-0.481898\pi$
$858$		0			0
$859$	2773.00	−	4802.98i	0.110144	−	0.190775i	−0.805684	−	0.592345i	$-0.798202\pi$
$859$	2773.00	−	4802.98i	0.110144	−	0.190775i	0.915828	+	0.401570i	$0.131536\pi$
$860$		0			0
$861$	−1764.00	−	9166.01i	−0.0698223	−	0.362807i
$862$		0			0
$863$	−16269.0	+	28178.7i	−0.641719	+	1.11149i	0.343330	+	0.939215i	$0.388445\pi$
$863$	−16269.0	+	28178.7i	−0.641719	+	1.11149i	−0.985049	+	0.172275i	$0.944888\pi$
$864$		0			0
$865$	25785.0	+	44660.9i	1.01354	+	1.75551i
$866$		0			0
$867$	6429.00			0.251834
$868$		0			0
$869$	5247.00			0.204824
$870$		0			0
$871$	7304.00	+	12650.9i	0.284141	+	0.492146i
$872$		0			0
$873$	760.500	−	1317.22i	0.0294834	−	0.0510668i
$874$		0			0
$875$	−6562.50	−	2273.32i	−0.253546	−	0.0878310i
$876$		0			0
$877$	−16048.0	+	27796.0i	−0.617905	+	1.07024i	0.371963	+	0.928248i	$0.378685\pi$
$877$	−16048.0	+	27796.0i	−0.617905	+	1.07024i	−0.989867	+	0.141995i	$0.954648\pi$
$878$		0			0
$879$	1651.50	+	2860.48i	0.0633717	+	0.109763i
$880$		0			0
$881$	−8490.00			−0.324671			−0.162336	−	0.986736i	$-0.551903\pi$
$881$	−8490.00			−0.324671			−0.162336	+	0.986736i	$0.551903\pi$
$882$		0			0
$883$	48352.0			1.84278			0.921390	−	0.388640i	$-0.127055\pi$
$883$	48352.0			1.84278			0.921390	+	0.388640i	$0.127055\pi$
$884$		0			0
$885$	−3577.50	−	6196.41i	−0.135883	−	0.235356i
$886$		0			0
$887$	7746.00	−	13416.5i	0.293219	−	0.507870i	−0.681350	−	0.731958i	$-0.738607\pi$
$887$	7746.00	−	13416.5i	0.293219	−	0.507870i	0.974569	+	0.224088i	$0.0719402\pi$
$888$		0			0
$889$	−6527.50	−	2261.19i	−0.246260	−	0.0853070i
$890$		0			0
$891$	−364.500	+	631.333i	−0.0137051	+	0.0237379i
$892$		0			0
$893$	7176.00	+	12429.2i	0.268909	+	0.465764i
$894$		0			0
$895$	−18180.0			−0.678984
$896$		0			0
$897$	−22176.0			−0.825457
$898$		0			0
$899$	4717.50	+	8170.95i	0.175014	+	0.303133i
$900$		0			0
$901$	26838.0	−	46484.8i	0.992346	−	1.71879i
$902$		0			0
$903$	−3423.00	−	17786.4i	−0.126147	−	0.655477i
$904$		0			0
$905$	22740.0	−	39386.8i	0.835252	−	1.44670i
$906$		0			0
$907$	−4058.00	−	7028.66i	−0.148560	−	0.257313i	0.782136	−	0.623108i	$-0.214130\pi$
$907$	−4058.00	−	7028.66i	−0.148560	−	0.257313i	−0.930695	+	0.365795i	$0.880797\pi$
$908$		0			0
$909$	5778.00			0.210830
$910$		0			0
$911$	4446.00			0.161693			0.0808466	−	0.996727i	$-0.474238\pi$
$911$	4446.00			0.161693			0.0808466	+	0.996727i	$0.474238\pi$
$912$		0			0
$913$	−2686.50	−	4653.15i	−0.0973824	−	0.168671i
$914$		0			0
$915$	16245.0	−	28137.2i	0.586932	−	1.01660i
$916$		0			0
$917$	16422.0	−	14221.9i	0.591387	−	0.512156i
$918$		0			0
$919$	13252.0	−	22953.1i	0.475673	−	0.823889i	−0.523939	−	0.851756i	$-0.675538\pi$
$919$	13252.0	−	22953.1i	0.475673	−	0.823889i	0.999612	+	0.0278666i	$0.00887137\pi$
$920$		0			0
$921$	4170.00	+	7222.65i	0.149192	+	0.258409i
$922$		0			0
$923$	95568.0			3.40808
$924$		0			0
$925$	4400.00			0.156401
$926$		0			0
$927$	2088.00	+	3616.52i	0.0739794	+	0.128136i
$928$		0			0
$929$	2715.00	−	4702.52i	0.0958840	−	0.166076i	−0.814093	−	0.580734i	$-0.802766\pi$
$929$	2715.00	−	4702.52i	0.0958840	−	0.166076i	0.909977	+	0.414658i	$0.136099\pi$
$930$		0			0
$931$	33124.0	−	13239.8i	1.16605	−	0.466076i
$932$		0			0
$933$	6444.00	−	11161.3i	0.226117	−	0.391646i
$934$		0			0
$935$	−5670.00	−	9820.73i	−0.198320	−	0.343500i
$936$		0			0
$937$	33803.0			1.17854			0.589272	−	0.807935i	$-0.299415\pi$
$937$	33803.0			1.17854			0.589272	+	0.807935i	$0.299415\pi$
$938$		0			0
$939$	16467.0			0.572290
$940$		0			0
$941$	24241.5	+	41987.5i	0.839798	+	1.45457i	0.890063	+	0.455838i	$0.150660\pi$
$941$	24241.5	+	41987.5i	0.839798	+	1.45457i	−0.0502645	+	0.998736i	$0.516006\pi$
$942$		0			0
$943$	7056.00	−	12221.4i	0.243664	−	0.422038i
$944$		0			0
$945$	−5670.00	+	4910.36i	−0.195180	+	0.169031i
$946$		0			0
$947$	18648.0	−	32299.3i	0.639893	−	1.10833i	−0.345563	−	0.938396i	$-0.612312\pi$
$947$	18648.0	−	32299.3i	0.639893	−	1.10833i	0.985456	−	0.169931i	$-0.0543546\pi$
$948$		0			0
$949$	9592.00	+	16613.8i	0.328103	+	0.568291i
$950$		0			0
$951$	13473.0			0.459403
$952$		0			0
$953$	−38478.0			−1.30790			−0.653948	−	0.756540i	$-0.726888\pi$
$953$	−38478.0			−1.30790			−0.653948	+	0.756540i	$0.726888\pi$
$954$		0			0
$955$	−18900.0	−	32735.8i	−0.640408	−	1.10922i
$956$		0			0
$957$	−688.500	+	1192.52i	−0.0232561	+	0.0402807i
$958$		0			0
$959$	105.000	+	545.596i	0.00353559	+	0.0183714i
$960$		0			0
$961$	−2217.00	+	3839.96i	−0.0744184	+	0.128897i
$962$		0			0
$963$	1768.50	+	3063.13i	0.0591787	+	0.102501i
$964$		0			0
$965$	−5475.00			−0.182639
$966$		0			0
$967$	−27257.0			−0.906438			−0.453219	−	0.891399i	$-0.649725\pi$
$967$	−27257.0			−0.906438			−0.453219	+	0.891399i	$0.649725\pi$
$968$		0			0
$969$	−13104.0	−	22696.8i	−0.434428	−	0.752452i
$970$		0			0
$971$	17170.5	−	29740.2i	0.567485	−	0.982912i	−0.429329	−	0.903148i	$-0.641250\pi$
$971$	17170.5	−	29740.2i	0.567485	−	0.982912i	0.996814	−	0.0797641i	$-0.0254167\pi$
$972$		0			0
$973$	−1435.00	−	497.099i	−0.0472806	−	0.0163785i
$974$		0			0
$975$	13200.0	−	22863.1i	0.433578	−	0.750979i
$976$		0			0
$977$	−13713.0	−	23751.6i	−0.449046	−	0.777770i	0.549278	−	0.835639i	$-0.314903\pi$
$977$	−13713.0	−	23751.6i	−0.449046	−	0.777770i	−0.998324	+	0.0578693i	$0.981569\pi$
$978$		0			0
$979$	−9342.00			−0.304976
$980$		0			0
$981$	126.000			0.00410079
$982$		0			0
$983$	6162.00	+	10672.9i	0.199936	+	0.346300i	0.948508	−	0.316755i	$-0.102593\pi$
$983$	6162.00	+	10672.9i	0.199936	+	0.346300i	−0.748571	+	0.663054i	$0.769260\pi$
$984$		0			0
$985$	−11925.0	+	20654.7i	−0.385748	+	0.668136i
$986$		0			0
$987$	−7245.00	−	2509.74i	−0.233648	−	0.0809382i
$988$		0			0
$989$	13692.0	−	23715.2i	0.440223	−	0.762488i
$990$		0			0
$991$	23798.5	+	41220.2i	0.762850	+	1.32129i	0.941376	+	0.337360i	$0.109534\pi$
$991$	23798.5	+	41220.2i	0.762850	+	1.32129i	−0.178526	+	0.983935i	$0.557133\pi$
$992$		0			0
$993$	11892.0			0.380042
$994$		0			0
$995$	−80700.0			−2.57122
$996$		0			0
$997$	5621.00	+	9735.86i	0.178555	+	0.309266i	0.941386	−	0.337332i	$-0.109525\pi$
$997$	5621.00	+	9735.86i	0.178555	+	0.309266i	−0.762831	+	0.646598i	$0.776191\pi$
$998$		0			0
$999$	−594.000	+	1028.84i	−0.0188121	+	0.0325836i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.4.q.d.289.1		2
4.3	odd	2		42.4.e.b.37.1	yes	2
7.2	even	3		2352.4.a.u.1.1		1
7.4	even	3	inner	336.4.q.d.193.1		2
7.5	odd	6		2352.4.a.q.1.1		1
12.11	even	2		126.4.g.a.37.1		2
28.3	even	6		294.4.e.e.67.1		2
28.11	odd	6		42.4.e.b.25.1	✓	2
28.19	even	6		294.4.a.g.1.1		1
28.23	odd	6		294.4.a.a.1.1		1
28.27	even	2		294.4.e.e.79.1		2
84.11	even	6		126.4.g.a.109.1		2
84.23	even	6		882.4.a.r.1.1		1
84.47	odd	6		882.4.a.h.1.1		1
84.59	odd	6		882.4.g.l.361.1		2
84.83	odd	2		882.4.g.l.667.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.4.e.b.25.1	✓	2	28.11	odd	6
42.4.e.b.37.1	yes	2	4.3	odd	2
126.4.g.a.37.1		2	12.11	even	2
126.4.g.a.109.1		2	84.11	even	6
294.4.a.a.1.1		1	28.23	odd	6
294.4.a.g.1.1		1	28.19	even	6
294.4.e.e.67.1		2	28.3	even	6
294.4.e.e.79.1		2	28.27	even	2
336.4.q.d.193.1		2	7.4	even	3	inner
336.4.q.d.289.1		2	1.1	even	1	trivial
882.4.a.h.1.1		1	84.47	odd	6
882.4.a.r.1.1		1	84.23	even	6
882.4.g.l.361.1		2	84.59	odd	6
882.4.g.l.667.1		2	84.83	odd	2
2352.4.a.q.1.1		1	7.5	odd	6
2352.4.a.u.1.1		1	7.2	even	3

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.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.50000 - 2.59808i) q^{3} +(7.50000 - 12.9904i) q^{5} +(-17.5000 - 6.06218i) q^{7} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})\)	\(q+(-1.50000 - 2.59808i) q^{3} +(7.50000 - 12.9904i) q^{5} +(-17.5000 - 6.06218i) q^{7} +(-4.50000 + 7.79423i) q^{9} +(-4.50000 - 7.79423i) q^{11} -88.0000 q^{13} -45.0000 q^{15} +(42.0000 + 72.7461i) q^{17} +(52.0000 - 90.0666i) q^{19} +(10.5000 + 54.5596i) q^{21} +(-42.0000 + 72.7461i) q^{23} +(-50.0000 - 86.6025i) q^{25} +27.0000 q^{27} +51.0000 q^{29} +(92.5000 + 160.215i) q^{31} +(-13.5000 + 23.3827i) q^{33} +(-210.000 + 181.865i) q^{35} +(-22.0000 + 38.1051i) q^{37} +(132.000 + 228.631i) q^{39} -168.000 q^{41} -326.000 q^{43} +(67.5000 + 116.913i) q^{45} +(-69.0000 + 119.512i) q^{47} +(269.500 + 212.176i) q^{49} +(126.000 - 218.238i) q^{51} +(-319.500 - 553.390i) q^{53} -135.000 q^{55} -312.000 q^{57} +(79.5000 + 137.698i) q^{59} +(-361.000 + 625.270i) q^{61} +(126.000 - 109.119i) q^{63} +(-660.000 + 1143.15i) q^{65} +(-83.0000 - 143.760i) q^{67} +252.000 q^{69} -1086.00 q^{71} +(-109.000 - 188.794i) q^{73} +(-150.000 + 259.808i) q^{75} +(31.5000 + 163.679i) q^{77} +(-291.500 + 504.893i) q^{79} +(-40.5000 - 70.1481i) q^{81} +597.000 q^{83} +1260.00 q^{85} +(-76.5000 - 132.502i) q^{87} +(519.000 - 898.934i) q^{89} +(1540.00 + 533.472i) q^{91} +(277.500 - 480.644i) q^{93} +(-780.000 - 1351.00i) q^{95} -169.000 q^{97} +81.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 3 q^{3} + 15 q^{5} - 35 q^{7} - 9 q^{9}+O(q^{10}) \) 2 * q - 3 * q^3 + 15 * q^5 - 35 * q^7 - 9 * q^9	\( 2 q - 3 q^{3} + 15 q^{5} - 35 q^{7} - 9 q^{9} - 9 q^{11} - 176 q^{13} - 90 q^{15} + 84 q^{17} + 104 q^{19} + 21 q^{21} - 84 q^{23} - 100 q^{25} + 54 q^{27} + 102 q^{29} + 185 q^{31} - 27 q^{33} - 420 q^{35} - 44 q^{37} + 264 q^{39} - 336 q^{41} - 652 q^{43} + 135 q^{45} - 138 q^{47} + 539 q^{49} + 252 q^{51} - 639 q^{53} - 270 q^{55} - 624 q^{57} + 159 q^{59} - 722 q^{61} + 252 q^{63} - 1320 q^{65} - 166 q^{67} + 504 q^{69} - 2172 q^{71} - 218 q^{73} - 300 q^{75} + 63 q^{77} - 583 q^{79} - 81 q^{81} + 1194 q^{83} + 2520 q^{85} - 153 q^{87} + 1038 q^{89} + 3080 q^{91} + 555 q^{93} - 1560 q^{95} - 338 q^{97} + 162 q^{99}+O(q^{100}) \) 2 * q - 3 * q^3 + 15 * q^5 - 35 * q^7 - 9 * q^9 - 9 * q^11 - 176 * q^13 - 90 * q^15 + 84 * q^17 + 104 * q^19 + 21 * q^21 - 84 * q^23 - 100 * q^25 + 54 * q^27 + 102 * q^29 + 185 * q^31 - 27 * q^33 - 420 * q^35 - 44 * q^37 + 264 * q^39 - 336 * q^41 - 652 * q^43 + 135 * q^45 - 138 * q^47 + 539 * q^49 + 252 * q^51 - 639 * q^53 - 270 * q^55 - 624 * q^57 + 159 * q^59 - 722 * q^61 + 252 * q^63 - 1320 * q^65 - 166 * q^67 + 504 * q^69 - 2172 * q^71 - 218 * q^73 - 300 * q^75 + 63 * q^77 - 583 * q^79 - 81 * q^81 + 1194 * q^83 + 2520 * q^85 - 153 * q^87 + 1038 * q^89 + 3080 * q^91 + 555 * q^93 - 1560 * q^95 - 338 * q^97 + 162 * q^99

Introduction

L-functions

Modular forms

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