LMFDB - Embedded newform 29.3.c.a.17.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [29,3,Mod(12,29)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(29, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("29.12");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 29 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	29.c (of order $4$, degree $2$, 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:	$0.790192766645$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 18x^{6} + 91x^{4} + 126x^{2} + 25 $ x^8 + 18x^6 + 91x^4 + 126*x^2 + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			17.4
Root			$0.486981i$ of defining polynomial
Character	$\chi$	$=$	29.17
Dual form			29.3.c.a.12.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.62492 - 2.62492i) q^{2} +(-3.11190 + 3.11190i) q^{3} -9.78036i q^{4} +4.53053i q^{5} +16.3369i q^{6} -0.745339 q^{7} +(-15.1730 - 15.1730i) q^{8} -10.3678i q^{9} +O(q^{10})$	\(q+(2.62492 - 2.62492i) q^{2} +(-3.11190 + 3.11190i) q^{3} -9.78036i q^{4} +4.53053i q^{5} +16.3369i q^{6} -0.745339 q^{7} +(-15.1730 - 15.1730i) q^{8} -10.3678i q^{9} +(11.8923 + 11.8923i) q^{10} +(0.0423096 - 0.0423096i) q^{11} +(30.4355 + 30.4355i) q^{12} -8.30191i q^{13} +(-1.95645 + 1.95645i) q^{14} +(-14.0985 - 14.0985i) q^{15} -40.5340 q^{16} +(15.2625 - 15.2625i) q^{17} +(-27.2146 - 27.2146i) q^{18} +(-25.1348 + 25.1348i) q^{19} +44.3102 q^{20} +(2.31942 - 2.31942i) q^{21} -0.222118i q^{22} +8.64367 q^{23} +94.4333 q^{24} +4.47430 q^{25} +(-21.7918 - 21.7918i) q^{26} +(4.25644 + 4.25644i) q^{27} +7.28968i q^{28} +(22.0908 + 18.7882i) q^{29} -74.0149 q^{30} +(-5.09325 + 5.09325i) q^{31} +(-45.7065 + 45.7065i) q^{32} +0.263326i q^{33} -80.1256i q^{34} -3.37678i q^{35} -101.401 q^{36} +(10.0725 + 10.0725i) q^{37} +131.953i q^{38} +(25.8347 + 25.8347i) q^{39} +(68.7415 - 68.7415i) q^{40} +(2.50571 + 2.50571i) q^{41} -12.1765i q^{42} +(-11.2668 + 11.2668i) q^{43} +(-0.413803 - 0.413803i) q^{44} +46.9716 q^{45} +(22.6889 - 22.6889i) q^{46} +(-23.0132 - 23.0132i) q^{47} +(126.138 - 126.138i) q^{48} -48.4445 q^{49} +(11.7447 - 11.7447i) q^{50} +94.9907i q^{51} -81.1956 q^{52} -42.8979 q^{53} +22.3456 q^{54} +(0.191685 + 0.191685i) q^{55} +(11.3090 + 11.3090i) q^{56} -156.434i q^{57} +(107.304 - 8.66900i) q^{58} +106.413 q^{59} +(-137.889 + 137.889i) q^{60} +(-42.3211 + 42.3211i) q^{61} +26.7387i q^{62} +7.72752i q^{63} +77.8154i q^{64} +37.6120 q^{65} +(0.691208 + 0.691208i) q^{66} -75.7926i q^{67} +(-149.273 - 149.273i) q^{68} +(-26.8982 + 26.8982i) q^{69} +(-8.86376 - 8.86376i) q^{70} -71.2051i q^{71} +(-157.310 + 157.310i) q^{72} +(-73.7928 - 73.7928i) q^{73} +52.8790 q^{74} +(-13.9236 + 13.9236i) q^{75} +(245.827 + 245.827i) q^{76} +(-0.0315350 + 0.0315350i) q^{77} +135.628 q^{78} +(-78.7399 + 78.7399i) q^{79} -183.641i q^{80} +66.8190 q^{81} +13.1546 q^{82} +15.1749 q^{83} +(-22.6847 - 22.6847i) q^{84} +(69.1473 + 69.1473i) q^{85} +59.1487i q^{86} +(-127.211 + 10.2773i) q^{87} -1.28392 q^{88} +(-22.8417 + 22.8417i) q^{89} +(123.296 - 123.296i) q^{90} +6.18773i q^{91} -84.5382i q^{92} -31.6993i q^{93} -120.816 q^{94} +(-113.874 - 113.874i) q^{95} -284.468i q^{96} +(42.8298 + 42.8298i) q^{97} +(-127.163 + 127.163i) q^{98} +(-0.438657 - 0.438657i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{2} - 2 q^{3} - 4 q^{7} - 42 q^{8}+O(q^{10}) $ 8 * q + 2 * q^2 - 2 * q^3 - 4 * q^7 - 42 * q^8	$ 8 q + 2 q^{2} - 2 q^{3} - 4 q^{7} - 42 q^{8} + 6 q^{10} - 6 q^{11} + 54 q^{12} - 40 q^{14} - 10 q^{15} - 32 q^{16} + 12 q^{17} + 20 q^{18} - 16 q^{19} + 108 q^{20} - 36 q^{21} + 168 q^{24} + 104 q^{25} - 54 q^{26} - 98 q^{27} + 128 q^{29} - 220 q^{30} - 10 q^{31} - 106 q^{32} - 252 q^{36} - 84 q^{37} - 90 q^{39} + 226 q^{40} + 20 q^{41} - 190 q^{43} + 42 q^{44} + 292 q^{45} + 12 q^{46} + 58 q^{47} + 354 q^{48} - 72 q^{49} - 60 q^{50} - 144 q^{52} + 252 q^{53} + 400 q^{54} - 74 q^{55} - 192 q^{56} + 326 q^{58} - 40 q^{59} - 258 q^{60} - 208 q^{61} + 36 q^{65} - 414 q^{66} - 296 q^{68} + 120 q^{69} + 44 q^{70} - 636 q^{72} - 188 q^{73} - 64 q^{74} - 12 q^{75} + 592 q^{76} + 180 q^{77} + 600 q^{78} - 382 q^{79} - 124 q^{81} + 228 q^{82} + 280 q^{83} - 124 q^{84} + 32 q^{85} + 34 q^{87} + 20 q^{88} - 64 q^{89} + 128 q^{90} - 460 q^{94} - 380 q^{95} - 44 q^{97} - 66 q^{98} + 552 q^{99}+O(q^{100}) $ 8 * q + 2 * q^2 - 2 * q^3 - 4 * q^7 - 42 * q^8 + 6 * q^10 - 6 * q^11 + 54 * q^12 - 40 * q^14 - 10 * q^15 - 32 * q^16 + 12 * q^17 + 20 * q^18 - 16 * q^19 + 108 * q^20 - 36 * q^21 + 168 * q^24 + 104 * q^25 - 54 * q^26 - 98 * q^27 + 128 * q^29 - 220 * q^30 - 10 * q^31 - 106 * q^32 - 252 * q^36 - 84 * q^37 - 90 * q^39 + 226 * q^40 + 20 * q^41 - 190 * q^43 + 42 * q^44 + 292 * q^45 + 12 * q^46 + 58 * q^47 + 354 * q^48 - 72 * q^49 - 60 * q^50 - 144 * q^52 + 252 * q^53 + 400 * q^54 - 74 * q^55 - 192 * q^56 + 326 * q^58 - 40 * q^59 - 258 * q^60 - 208 * q^61 + 36 * q^65 - 414 * q^66 - 296 * q^68 + 120 * q^69 + 44 * q^70 - 636 * q^72 - 188 * q^73 - 64 * q^74 - 12 * q^75 + 592 * q^76 + 180 * q^77 + 600 * q^78 - 382 * q^79 - 124 * q^81 + 228 * q^82 + 280 * q^83 - 124 * q^84 + 32 * q^85 + 34 * q^87 + 20 * q^88 - 64 * q^89 + 128 * q^90 - 460 * q^94 - 380 * q^95 - 44 * q^97 - 66 * q^98 + 552 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/29\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	2.62492	−	2.62492i	1.31246	−	1.31246i	0.392859	−	0.919599i	$-0.371486\pi$
$2$	2.62492	−	2.62492i	1.31246	−	1.31246i	0.919599	−	0.392859i	$-0.128514\pi$
$3$	−3.11190	+	3.11190i	−1.03730	+	1.03730i	−0.0380218	+	0.999277i	$0.512106\pi$
$3$	−3.11190	+	3.11190i	−1.03730	+	1.03730i	−0.999277	+	0.0380218i	$0.987894\pi$
$4$		−	9.78036i		−	2.44509i
$5$			4.53053i			0.906106i	0.891484	+	0.453053i	$0.149665\pi$
$5$			4.53053i			0.906106i	−0.891484	+	0.453053i	$0.850335\pi$
$6$			16.3369i			2.72282i
$7$	−0.745339			−0.106477			−0.0532385	−	0.998582i	$-0.516954\pi$
$7$	−0.745339			−0.106477			−0.0532385	+	0.998582i	$0.516954\pi$
$8$	−15.1730	−	15.1730i	−1.89662	−	1.89662i
$9$		−	10.3678i		−	1.15198i
$10$	11.8923	+	11.8923i	1.18923	+	1.18923i
$11$	0.0423096	−	0.0423096i	0.00384632	−	0.00384632i	−0.705181	−	0.709027i	$-0.749134\pi$
$11$	0.0423096	−	0.0423096i	0.00384632	−	0.00384632i	0.709027	+	0.705181i	$0.249134\pi$
$12$	30.4355	+	30.4355i	2.53629	+	2.53629i
$13$		−	8.30191i		−	0.638608i	−0.947652	−	0.319304i	$-0.896551\pi$
$13$		−	8.30191i		−	0.638608i	0.947652	−	0.319304i	$-0.103449\pi$
$14$	−1.95645	+	1.95645i	−0.139747	+	0.139747i
$15$	−14.0985	−	14.0985i	−0.939903	−	0.939903i
$16$	−40.5340			−2.53338
$17$	15.2625	−	15.2625i	0.897795	−	0.897795i	−0.0974461	−	0.995241i	$-0.531067\pi$
$17$	15.2625	−	15.2625i	0.897795	−	0.897795i	0.995241	+	0.0974461i	$0.0310673\pi$
$18$	−27.2146	−	27.2146i	−1.51192	−	1.51192i
$19$	−25.1348	+	25.1348i	−1.32288	+	1.32288i	−0.411453	+	0.911431i	$0.634979\pi$
$19$	−25.1348	+	25.1348i	−1.32288	+	1.32288i	−0.911431	+	0.411453i	$0.865021\pi$
$20$	44.3102			2.21551
$21$	2.31942	−	2.31942i	0.110448	−	0.110448i
$22$		−	0.222118i		−	0.0100963i
$23$	8.64367			0.375812			0.187906	−	0.982187i	$-0.439830\pi$
$23$	8.64367			0.375812			0.187906	+	0.982187i	$0.439830\pi$
$24$	94.4333			3.93472
$25$	4.47430			0.178972
$26$	−21.7918	−	21.7918i	−0.838146	−	0.838146i
$27$	4.25644	+	4.25644i	0.157646	+	0.157646i
$28$			7.28968i			0.260346i
$29$	22.0908	+	18.7882i	0.761752	+	0.647869i
$29$	22.0908	+	18.7882i	0.761752	+	0.647869i
$30$	−74.0149			−2.46716
$31$	−5.09325	+	5.09325i	−0.164298	+	0.164298i	−0.784468	−	0.620169i	$-0.787064\pi$
$31$	−5.09325	+	5.09325i	−0.164298	+	0.164298i	0.620169	+	0.784468i	$0.287064\pi$
$32$	−45.7065	+	45.7065i	−1.42833	+	1.42833i
$33$			0.263326i			0.00797957i
$34$		−	80.1256i		−	2.35664i
$35$		−	3.37678i		−	0.0964794i
$36$	−101.401			−2.81669
$37$	10.0725	+	10.0725i	0.272230	+	0.272230i	0.829997	−	0.557767i	$-0.188342\pi$
$37$	10.0725	+	10.0725i	0.272230	+	0.272230i	−0.557767	+	0.829997i	$0.688342\pi$
$38$			131.953i			3.47246i
$39$	25.8347	+	25.8347i	0.662427	+	0.662427i
$40$	68.7415	−	68.7415i	1.71854	−	1.71854i
$41$	2.50571	+	2.50571i	0.0611149	+	0.0611149i	0.737004	−	0.675889i	$-0.236240\pi$
$41$	2.50571	+	2.50571i	0.0611149	+	0.0611149i	−0.675889	+	0.737004i	$0.736240\pi$
$42$		−	12.1765i		−	0.289918i
$43$	−11.2668	+	11.2668i	−0.262018	+	0.262018i	−0.825874	−	0.563855i	$-0.809318\pi$
$43$	−11.2668	+	11.2668i	−0.262018	+	0.262018i	0.563855	+	0.825874i	$0.309318\pi$
$44$	−0.413803	−	0.413803i	−0.00940461	−	0.00940461i
$45$	46.9716			1.04381
$46$	22.6889	−	22.6889i	0.493237	−	0.493237i
$47$	−23.0132	−	23.0132i	−0.489643	−	0.489643i	0.418550	−	0.908194i	$-0.362538\pi$
$47$	−23.0132	−	23.0132i	−0.489643	−	0.489643i	−0.908194	+	0.418550i	$0.862538\pi$
$48$	126.138	−	126.138i	2.62787	−	2.62787i
$49$	−48.4445			−0.988663
$50$	11.7447	−	11.7447i	0.234893	−	0.234893i
$51$			94.9907i			1.86256i
$52$	−81.1956			−1.56145
$53$	−42.8979			−0.809394			−0.404697	−	0.914451i	$-0.632623\pi$
$53$	−42.8979			−0.809394			−0.404697	+	0.914451i	$0.632623\pi$
$54$	22.3456			0.413807
$55$	0.191685	+	0.191685i	0.00348518	+	0.00348518i
$56$	11.3090	+	11.3090i	0.201946	+	0.201946i
$57$		−	156.434i		−	2.74445i
$58$	107.304	−	8.66900i	1.85007	−	0.149466i
$59$	106.413			1.80361			0.901806	−	0.432140i	$-0.142241\pi$
$59$	106.413			1.80361			0.901806	+	0.432140i	$0.142241\pi$
$60$	−137.889	+	137.889i	−2.29815	+	2.29815i
$61$	−42.3211	+	42.3211i	−0.693788	+	0.693788i	−0.963063	−	0.269275i	$-0.913216\pi$
$61$	−42.3211	+	42.3211i	−0.693788	+	0.693788i	0.269275	+	0.963063i	$0.413216\pi$
$62$			26.7387i			0.431269i
$63$			7.72752i			0.122659i
$64$			77.8154i			1.21587i
$65$	37.6120			0.578647
$66$	0.691208	+	0.691208i	0.0104729	+	0.0104729i
$67$		−	75.7926i		−	1.13123i	−0.824668	−	0.565616i	$-0.808638\pi$
$67$		−	75.7926i		−	1.13123i	0.824668	−	0.565616i	$-0.191362\pi$
$68$	−149.273	−	149.273i	−2.19519	−	2.19519i
$69$	−26.8982	+	26.8982i	−0.389829	+	0.389829i
$70$	−8.86376	−	8.86376i	−0.126625	−	0.126625i
$71$		−	71.2051i		−	1.00289i	−0.865190	−	0.501445i	$-0.832802\pi$
$71$		−	71.2051i		−	1.00289i	0.865190	−	0.501445i	$-0.167198\pi$
$72$	−157.310	+	157.310i	−2.18486	+	2.18486i
$73$	−73.7928	−	73.7928i	−1.01086	−	1.01086i	−0.999940	−	0.0109201i	$-0.996524\pi$
$73$	−73.7928	−	73.7928i	−1.01086	−	1.01086i	−0.0109201	−	0.999940i	$-0.503476\pi$
$74$	52.8790			0.714581
$75$	−13.9236	+	13.9236i	−0.185647	+	0.185647i
$76$	245.827	+	245.827i	3.23457	+	3.23457i
$77$	−0.0315350	+	0.0315350i	−0.000409545	+	0.000409545i
$78$	135.628			1.73882
$79$	−78.7399	+	78.7399i	−0.996707	+	0.996707i	−0.999995	−	0.00328762i	$-0.998954\pi$
$79$	−78.7399	+	78.7399i	−0.996707	+	0.996707i	0.00328762	+	0.999995i	$0.498954\pi$
$80$		−	183.641i		−	2.29551i
$81$	66.8190			0.824925
$82$	13.1546			0.160421
$83$	15.1749			0.182830			0.0914152	−	0.995813i	$-0.470861\pi$
$83$	15.1749			0.182830			0.0914152	+	0.995813i	$0.470861\pi$
$84$	−22.6847	−	22.6847i	−0.270056	−	0.270056i
$85$	69.1473	+	69.1473i	0.813497	+	0.813497i
$86$			59.1487i			0.687775i
$87$	−127.211	+	10.2773i	−1.46220	+	0.118130i
$88$	−1.28392			−0.0145900
$89$	−22.8417	+	22.8417i	−0.256648	+	0.256648i	−0.823689	−	0.567041i	$-0.808088\pi$
$89$	−22.8417	+	22.8417i	−0.256648	+	0.256648i	0.567041	+	0.823689i	$0.308088\pi$
$90$	123.296	−	123.296i	1.36996	−	1.36996i
$91$			6.18773i			0.0679971i
$92$		−	84.5382i		−	0.918893i
$93$		−	31.6993i		−	0.340853i
$94$	−120.816			−1.28527
$95$	−113.874	−	113.874i	−1.19867	−	1.19867i
$96$		−	284.468i		−	2.96321i
$97$	42.8298	+	42.8298i	0.441544	+	0.441544i	0.892531	−	0.450987i	$-0.148928\pi$
$97$	42.8298	+	42.8298i	0.441544	+	0.441544i	−0.450987	+	0.892531i	$0.648928\pi$
$98$	−127.163	+	127.163i	−1.29758	+	1.29758i
$99$	−0.438657	−	0.438657i	−0.00443088	−	0.00443088i
$100$		−	43.7603i		−	0.437603i
$101$	36.4365	−	36.4365i	0.360757	−	0.360757i	−0.503334	−	0.864092i	$-0.667894\pi$
$101$	36.4365	−	36.4365i	0.360757	−	0.360757i	0.864092	+	0.503334i	$0.167894\pi$
$102$	249.343	+	249.343i	2.44453	+	2.44453i
$103$	111.751			1.08496			0.542479	−	0.840070i	$-0.317486\pi$
$103$	111.751			1.08496			0.542479	+	0.840070i	$0.317486\pi$
$104$	−125.964	+	125.964i	−1.21120	+	1.21120i
$105$	10.5082	+	10.5082i	0.100078	+	0.100078i
$106$	−112.603	+	112.603i	−1.06230	+	1.06230i
$107$	88.9678			0.831475			0.415737	−	0.909485i	$-0.363524\pi$
$107$	88.9678			0.831475			0.415737	+	0.909485i	$0.363524\pi$
$108$	41.6295	−	41.6295i	0.385459	−	0.385459i
$109$		−	41.1196i		−	0.377244i	−0.982050	−	0.188622i	$-0.939598\pi$
$109$		−	41.1196i		−	0.377244i	0.982050	−	0.188622i	$-0.0604020\pi$
$110$	1.00631			0.00914829
$111$	−62.6893			−0.564768
$112$	30.2116			0.269746
$113$	104.104	+	104.104i	0.921275	+	0.921275i	0.997120	−	0.0758450i	$-0.0241654\pi$
$113$	104.104	+	104.104i	0.921275	+	0.921275i	−0.0758450	+	0.997120i	$0.524165\pi$
$114$	−410.625	−	410.625i	−3.60198	−	3.60198i
$115$			39.1604i			0.340525i
$116$	183.755	−	216.056i	1.58410	−	1.86255i
$117$	−86.0725			−0.735662
$118$	279.326	−	279.326i	2.36717	−	2.36717i
$119$	−11.3757	+	11.3757i	−0.0955945	+	0.0955945i
$120$			427.833i			3.56527i
$121$			120.996i			0.999970i
$122$			222.179i			1.82114i
$123$	−15.5950			−0.126789
$124$	49.8138	+	49.8138i	0.401724	+	0.401724i
$125$			133.534i			1.06827i
$126$	20.2841	+	20.2841i	0.160985	+	0.160985i
$127$	8.26743	−	8.26743i	0.0650978	−	0.0650978i	−0.673808	−	0.738906i	$-0.735343\pi$
$127$	8.26743	−	8.26743i	0.0650978	−	0.0650978i	0.738906	+	0.673808i	$0.235343\pi$
$128$	21.4328	+	21.4328i	0.167443	+	0.167443i
$129$		−	70.1221i		−	0.543582i
$130$	98.7284	−	98.7284i	0.759449	−	0.759449i
$131$	−0.361622	−	0.361622i	−0.00276047	−	0.00276047i	0.705725	−	0.708486i	$-0.250621\pi$
$131$	−0.361622	−	0.361622i	−0.00276047	−	0.00276047i	−0.708486	+	0.705725i	$0.750621\pi$
$132$	2.57542			0.0195108
$133$	18.7339	−	18.7339i	0.140857	−	0.140857i
$134$	−198.949	−	198.949i	−1.48470	−	1.48470i
$135$	−19.2839	+	19.2839i	−0.142844	+	0.142844i
$136$	−463.155			−3.40555
$137$	−69.5740	+	69.5740i	−0.507840	+	0.507840i	−0.913863	−	0.406023i	$-0.866915\pi$
$137$	−69.5740	+	69.5740i	−0.507840	+	0.507840i	0.406023	+	0.913863i	$0.366915\pi$
$138$			141.211i			1.02327i
$139$	111.380			0.801297			0.400649	−	0.916232i	$-0.368785\pi$
$139$	111.380			0.801297			0.400649	+	0.916232i	$0.368785\pi$
$140$	−33.0261			−0.235901
$141$	143.230			1.01581
$142$	−186.907	−	186.907i	−1.31625	−	1.31625i
$143$	−0.351250	−	0.351250i	−0.00245629	−	0.00245629i
$144$			420.248i			2.91839i
$145$	−85.1205	+	100.083i	−0.587038	+	0.690228i
$146$	−387.400			−2.65342
$147$	150.754	−	150.754i	1.02554	−	1.02554i
$148$	98.5129	−	98.5129i	0.665628	−	0.665628i
$149$		−	44.5177i		−	0.298776i	−0.988779	−	0.149388i	$-0.952270\pi$
$149$		−	44.5177i		−	0.298776i	0.988779	−	0.149388i	$-0.0477304\pi$
$150$			73.0963i			0.487309i
$151$		−	70.6402i		−	0.467816i	−0.972259	−	0.233908i	$-0.924849\pi$
$151$		−	70.6402i		−	0.467816i	0.972259	−	0.233908i	$-0.0751514\pi$
$152$	762.738			5.01802
$153$	−158.239	−	158.239i	−1.03424	−	1.03424i
$154$			0.165553i			0.00107502i
$155$	−23.0751	−	23.0751i	−0.148872	−	0.148872i
$156$	252.672	−	252.672i	1.61969	−	1.61969i
$157$	−127.354	−	127.354i	−0.811173	−	0.811173i	0.173636	−	0.984810i	$-0.444448\pi$
$157$	−127.354	−	127.354i	−0.811173	−	0.811173i	−0.984810	+	0.173636i	$0.944448\pi$
$158$			413.371i			2.61627i
$159$	133.494	−	133.494i	0.839583	−	0.839583i
$160$	−207.075	−	207.075i	−1.29422	−	1.29422i
$161$	−6.44246			−0.0400153
$162$	175.394	−	175.394i	1.08268	−	1.08268i
$163$	83.4261	+	83.4261i	0.511817	+	0.511817i	0.915083	−	0.403266i	$-0.132125\pi$
$163$	83.4261	+	83.4261i	0.511817	+	0.511817i	−0.403266	+	0.915083i	$0.632125\pi$
$164$	24.5067	−	24.5067i	0.149431	−	0.149431i
$165$	−1.19301			−0.00723034
$166$	39.8329	−	39.8329i	0.239957	−	0.239957i
$167$		−	221.605i		−	1.32697i	−0.748188	−	0.663487i	$-0.769076\pi$
$167$		−	221.605i		−	1.32697i	0.748188	−	0.663487i	$-0.230924\pi$
$168$	−70.3848			−0.418957
$169$	100.078			0.592180
$170$	363.011			2.13536
$171$	260.592	+	260.592i	1.52393	+	1.52393i
$172$	110.193	+	110.193i	0.640658	+	0.640658i
$173$		−	6.62034i		−	0.0382679i	−0.999817	−	0.0191339i	$-0.993909\pi$
$173$		−	6.62034i		−	0.0382679i	0.999817	−	0.0191339i	$-0.00609089\pi$
$174$	−306.942	+	360.896i	−1.76403	+	2.07411i
$175$	−3.33487			−0.0190564
$176$	−1.71498	+	1.71498i	−0.00974418	+	0.00974418i
$177$	−331.147	+	331.147i	−1.87089	+	1.87089i
$178$			119.915i			0.673679i
$179$			36.9603i			0.206482i	0.994656	+	0.103241i	$0.0329213\pi$
$179$			36.9603i			0.206482i	−0.994656	+	0.103241i	$0.967079\pi$
$180$		−	459.399i		−	2.55222i
$181$	−192.039			−1.06099			−0.530494	−	0.847689i	$-0.677994\pi$
$181$	−192.039			−1.06099			−0.530494	+	0.847689i	$0.677994\pi$
$182$	16.2423	+	16.2423i	0.0892433	+	0.0892433i
$183$		−	263.398i		−	1.43933i
$184$	−131.150	−	131.150i	−0.712771	−	0.712771i
$185$	−45.6339	+	45.6339i	−0.246669	+	0.246669i
$186$	−83.2081	−	83.2081i	−0.447355	−	0.447355i
$187$		−	1.29150i		−	0.00690642i
$188$	−225.078	+	225.078i	−1.19722	+	1.19722i
$189$	−3.17249	−	3.17249i	−0.0167857	−	0.0167857i
$190$	−597.819			−3.14642
$191$	−215.351	+	215.351i	−1.12749	+	1.12749i	−0.136906	+	0.990584i	$0.543716\pi$
$191$	−215.351	+	215.351i	−1.12749	+	1.12749i	−0.990584	+	0.136906i	$0.956284\pi$
$192$	−242.153	−	242.153i	−1.26122	−	1.26122i
$193$	130.679	−	130.679i	0.677095	−	0.677095i	−0.282247	−	0.959342i	$-0.591080\pi$
$193$	130.679	−	130.679i	0.677095	−	0.677095i	0.959342	+	0.282247i	$0.0910797\pi$
$194$	224.849			1.15902
$195$	−117.045	+	117.045i	−0.600229	+	0.600229i
$196$			473.804i			2.41737i
$197$	−254.953			−1.29418			−0.647090	−	0.762414i	$-0.724014\pi$
$197$	−254.953			−1.29418			−0.647090	+	0.762414i	$0.724014\pi$
$198$	−2.30287			−0.0116307
$199$	168.018			0.844311			0.422155	−	0.906524i	$-0.361274\pi$
$199$	168.018			0.844311			0.422155	+	0.906524i	$0.361274\pi$
$200$	−67.8884	−	67.8884i	−0.339442	−	0.339442i
$201$	235.859	+	235.859i	1.17343	+	1.17343i
$202$		−	191.285i		−	0.946957i
$203$	−16.4651	−	14.0036i	−0.0811090	−	0.0689832i
$204$	929.043			4.55413
$205$	−11.3522	+	11.3522i	−0.0553766	+	0.0553766i
$206$	293.336	−	293.336i	1.42396	−	1.42396i
$207$		−	89.6158i		−	0.432926i
$208$			336.510i			1.61783i
$209$			2.12688i			0.0101765i
$210$	55.1662			0.262696
$211$	−111.890	−	111.890i	−0.530285	−	0.530285i	0.390372	−	0.920657i	$-0.372346\pi$
$211$	−111.890	−	111.890i	−0.530285	−	0.530285i	−0.920657	+	0.390372i	$0.872346\pi$
$212$			419.557i			1.97904i
$213$	221.583	+	221.583i	1.04030	+	1.04030i
$214$	233.533	−	233.533i	1.09128	−	1.09128i
$215$	−51.0445	−	51.0445i	−0.237416	−	0.237416i
$216$		−	129.166i		−	0.597989i
$217$	3.79620	−	3.79620i	0.0174940	−	0.0174940i
$218$	−107.935	−	107.935i	−0.495116	−	0.495116i
$219$	459.271			2.09713
$220$	1.87475	−	1.87475i	0.00852157	−	0.00852157i
$221$	−126.708	−	126.708i	−0.573339	−	0.573339i
$222$	−164.554	+	164.554i	−0.741234	+	0.741234i
$223$	−57.0256			−0.255720			−0.127860	−	0.991792i	$-0.540811\pi$
$223$	−57.0256			−0.255720			−0.127860	+	0.991792i	$0.540811\pi$
$224$	34.0668	−	34.0668i	0.152084	−	0.152084i
$225$		−	46.3886i		−	0.206172i
$226$	546.528			2.41827
$227$	−173.750			−0.765418			−0.382709	−	0.923869i	$-0.625009\pi$
$227$	−173.750			−0.765418			−0.382709	+	0.923869i	$0.625009\pi$
$228$	−1529.98			−6.71043
$229$	−144.696	−	144.696i	−0.631859	−	0.631859i	0.316675	−	0.948534i	$-0.397433\pi$
$229$	−144.696	−	144.696i	−0.631859	−	0.631859i	−0.948534	+	0.316675i	$0.897433\pi$
$230$	102.793	+	102.793i	0.446925	+	0.446925i
$231$		−	0.196267i		−	0.000849641i
$232$	−50.1100	−	620.255i	−0.215991	−	2.67351i
$233$	102.871			0.441507			0.220754	−	0.975330i	$-0.429148\pi$
$233$	102.871			0.441507			0.220754	+	0.975330i	$0.429148\pi$
$234$	−225.933	+	225.933i	−0.965525	+	0.965525i
$235$	104.262	−	104.262i	0.443669	−	0.443669i
$236$		−	1040.76i		−	4.41000i
$237$		−	490.060i		−	2.06777i
$238$			59.7207i			0.250927i
$239$	−312.152			−1.30607			−0.653037	−	0.757326i	$-0.726505\pi$
$239$	−312.152			−1.30607			−0.653037	+	0.757326i	$0.726505\pi$
$240$	571.470	+	571.470i	2.38113	+	2.38113i
$241$			313.004i			1.29877i	0.760460	+	0.649385i	$0.224974\pi$
$241$			313.004i			1.29877i	−0.760460	+	0.649385i	$0.775026\pi$
$242$	317.605	+	317.605i	1.31242	+	1.31242i
$243$	−246.242	+	246.242i	−1.01334	+	1.01334i
$244$	413.916	+	413.916i	1.69638	+	1.69638i
$245$		−	219.479i		−	0.895833i
$246$	−40.9356	+	40.9356i	−0.166405	+	0.166405i
$247$	208.667	+	208.667i	0.844805	+	0.844805i
$248$	154.559			0.623223
$249$	−47.2228	+	47.2228i	−0.189650	+	0.189650i
$250$	350.516	+	350.516i	1.40206	+	1.40206i
$251$	7.83425	−	7.83425i	0.0312121	−	0.0312121i	−0.691328	−	0.722541i	$-0.742974\pi$
$251$	7.83425	−	7.83425i	0.0312121	−	0.0312121i	0.722541	+	0.691328i	$0.242974\pi$
$252$	75.5779			0.299912
$253$	0.365710	−	0.365710i	0.00144549	−	0.00144549i
$254$		−	43.4026i		−	0.170876i
$255$	−430.358			−1.68768
$256$	−198.743			−0.776340
$257$	68.5603			0.266771			0.133386	−	0.991064i	$-0.457415\pi$
$257$	68.5603			0.266771			0.133386	+	0.991064i	$0.457415\pi$
$258$	−184.065	−	184.065i	−0.713429	−	0.713429i
$259$	−7.50744	−	7.50744i	−0.0289863	−	0.0289863i
$260$		−	367.859i		−	1.41484i
$261$	194.792	−	229.033i	0.746331	−	0.877521i
$262$	−1.89845			−0.00724600
$263$	153.717	−	153.717i	0.584477	−	0.584477i	−0.351653	−	0.936130i	$-0.614380\pi$
$263$	153.717	−	153.717i	0.584477	−	0.584477i	0.936130	+	0.351653i	$0.114380\pi$
$264$	3.99543	−	3.99543i	0.0151342	−	0.0151342i
$265$		−	194.350i		−	0.733397i
$266$		−	98.3500i		−	0.369737i
$267$		−	142.162i		−	0.532441i
$268$	−741.279			−2.76597
$269$	272.419	+	272.419i	1.01271	+	1.01271i	0.999918	+	0.0127932i	$0.00407231\pi$
$269$	272.419	+	272.419i	1.01271	+	1.01271i	0.0127932	+	0.999918i	$0.495928\pi$
$270$			101.237i			0.374953i
$271$	−304.778	−	304.778i	−1.12464	−	1.12464i	−0.991034	−	0.133607i	$-0.957344\pi$
$271$	−304.778	−	304.778i	−1.12464	−	1.12464i	−0.133607	−	0.991034i	$-0.542656\pi$
$272$	−618.651	+	618.651i	−2.27445	+	2.27445i
$273$	−19.2556	−	19.2556i	−0.0705333	−	0.0705333i
$274$			365.252i			1.33304i
$275$	0.189306	−	0.189306i	0.000688384	−	0.000688384i
$276$	263.074	+	263.074i	0.953167	+	0.953167i
$277$	−26.7259			−0.0964834			−0.0482417	−	0.998836i	$-0.515362\pi$
$277$	−26.7259			−0.0964834			−0.0482417	+	0.998836i	$0.515362\pi$
$278$	292.364	−	292.364i	1.05167	−	1.05167i
$279$	52.8058	+	52.8058i	0.189268	+	0.189268i
$280$	−51.2357	+	51.2357i	−0.182985	+	0.182985i
$281$	468.922			1.66876			0.834380	−	0.551189i	$-0.185826\pi$
$281$	468.922			1.66876			0.834380	+	0.551189i	$0.185826\pi$
$282$	375.966	−	375.966i	1.33321	−	1.33321i
$283$			263.495i			0.931079i	0.885027	+	0.465540i	$0.154140\pi$
$283$			263.495i			0.931079i	−0.885027	+	0.465540i	$0.845860\pi$
$284$	−696.412			−2.45215
$285$	708.728			2.48676
$286$	−1.84400			−0.00644756
$287$	−1.86760	−	1.86760i	−0.00650733	−	0.00650733i
$288$	473.876	+	473.876i	1.64540	+	1.64540i
$289$		−	176.888i		−	0.612071i
$290$	39.2752	+	486.144i	0.135432	+	1.67636i
$291$	−266.564			−0.916026
$292$	−721.720	+	721.720i	−2.47164	+	2.47164i
$293$	−84.4413	+	84.4413i	−0.288196	+	0.288196i	−0.836366	−	0.548171i	$-0.815324\pi$
$293$	−84.4413	+	84.4413i	−0.288196	+	0.288196i	0.548171	+	0.836366i	$0.315324\pi$
$294$		−	791.434i		−	2.69195i
$295$			482.108i			1.63426i
$296$		−	305.660i		−	1.03263i
$297$	0.360176			0.00121271
$298$	−116.855	−	116.855i	−0.392131	−	0.392131i
$299$		−	71.7589i		−	0.239996i
$300$	136.177	+	136.177i	0.453925	+	0.453925i
$301$	8.39757	−	8.39757i	0.0278989	−	0.0278989i
$302$	−185.424	−	185.424i	−0.613988	−	0.613988i
$303$			226.773i			0.748426i
$304$	1018.81	−	1018.81i	3.35136	−	3.35136i
$305$	−191.737	−	191.737i	−0.628646	−	0.628646i
$306$	−830.726			−2.71479
$307$	193.086	−	193.086i	0.628945	−	0.628945i	−0.318858	−	0.947803i	$-0.603299\pi$
$307$	193.086	−	193.086i	0.628945	−	0.628945i	0.947803	+	0.318858i	$0.103299\pi$
$308$	0.308423	+	0.308423i	0.00100137	+	0.00100137i
$309$	−347.756	+	347.756i	−1.12542	+	1.12542i
$310$	−121.141			−0.390776
$311$	−138.374	+	138.374i	−0.444932	+	0.444932i	−0.893666	−	0.448734i	$-0.851875\pi$
$311$	−138.374	+	138.374i	−0.444932	+	0.444932i	0.448734	+	0.893666i	$0.351875\pi$
$312$		−	783.977i		−	2.51275i
$313$	316.089			1.00987			0.504934	−	0.863158i	$-0.331517\pi$
$313$	316.089			1.00987			0.504934	+	0.863158i	$0.331517\pi$
$314$	−668.588			−2.12926
$315$	−35.0098			−0.111142
$316$	770.104	+	770.104i	2.43704	+	2.43704i
$317$	222.503	+	222.503i	0.701902	+	0.701902i	0.964819	−	0.262916i	$-0.0846843\pi$
$317$	222.503	+	222.503i	0.701902	+	0.701902i	−0.262916	+	0.964819i	$0.584684\pi$
$318$		−	700.820i		−	2.20384i
$319$	1.72957	−	0.139731i	0.00542186	−	0.000438028i
$320$	−352.545			−1.10170
$321$	−276.859	+	276.859i	−0.862488	+	0.862488i
$322$	−16.9109	+	16.9109i	−0.0525184	+	0.0525184i
$323$			767.240i			2.37536i
$324$		−	653.514i		−	2.01702i
$325$		−	37.1452i		−	0.114293i
$326$	437.973			1.34348
$327$	127.960	+	127.960i	0.391314	+	0.391314i
$328$		−	76.0381i		−	0.231823i
$329$	17.1527	+	17.1527i	0.0521358	+	0.0521358i
$330$	−3.13154	+	3.13154i	−0.00948951	+	0.00948951i
$331$	240.645	+	240.645i	0.727024	+	0.727024i	0.970026	−	0.243002i	$-0.0781322\pi$
$331$	240.645	+	240.645i	0.727024	+	0.727024i	−0.243002	+	0.970026i	$0.578132\pi$
$332$		−	148.416i		−	0.447037i
$333$	104.430	−	104.430i	0.313603	−	0.313603i
$334$	−581.693	−	581.693i	−1.74160	−	1.74160i
$335$	343.381			1.02502
$336$	−94.0153	+	94.0153i	−0.279807	+	0.279807i
$337$	−294.375	−	294.375i	−0.873517	−	0.873517i	0.119336	−	0.992854i	$-0.461923\pi$
$337$	−294.375	−	294.375i	−0.873517	−	0.873517i	−0.992854	+	0.119336i	$0.961923\pi$
$338$	262.697	−	262.697i	0.777211	−	0.777211i
$339$	−647.922			−1.91127
$340$	676.285	−	676.285i	1.98907	−	1.98907i
$341$			0.430987i			0.00126389i
$342$	1368.07			4.00019
$343$	72.6291			0.211747
$344$	341.901			0.993897
$345$	−121.863	−	121.863i	−0.353226	−	0.353226i
$346$	−17.3778	−	17.3778i	−0.0502250	−	0.0502250i
$347$			355.572i			1.02470i	0.858776	+	0.512351i	$0.171225\pi$
$347$			355.572i			1.02470i	−0.858776	+	0.512351i	$0.828775\pi$
$348$	100.516	+	1244.17i	0.288838	+	3.57521i
$349$	−239.336			−0.685775			−0.342888	−	0.939376i	$-0.611405\pi$
$349$	−239.336			−0.685775			−0.342888	+	0.939376i	$0.611405\pi$
$350$	−8.75375	+	8.75375i	−0.0250107	+	0.0250107i
$351$	35.3366	−	35.3366i	0.100674	−	0.100674i
$352$			3.86764i			0.0109876i
$353$			31.2450i			0.0885128i	0.999020	+	0.0442564i	$0.0140919\pi$
$353$			31.2450i			0.0885128i	−0.999020	+	0.0442564i	$0.985908\pi$
$354$			1738.46i			4.91092i
$355$	322.597			0.908724
$356$	223.400	+	223.400i	0.627527	+	0.627527i
$357$		−	70.8003i		−	0.198320i
$358$	97.0177	+	97.0177i	0.270999	+	0.270999i
$359$	259.580	−	259.580i	0.723064	−	0.723064i	−0.246164	−	0.969228i	$-0.579170\pi$
$359$	259.580	−	259.580i	0.723064	−	0.723064i	0.969228	+	0.246164i	$0.0791702\pi$
$360$	−712.698	−	712.698i	−1.97972	−	1.97972i
$361$		−	902.516i		−	2.50004i
$362$	−504.086	+	504.086i	−1.39250	+	1.39250i
$363$	−376.528	−	376.528i	−1.03727	−	1.03727i
$364$	60.5183			0.166259
$365$	334.321	−	334.321i	0.915947	−	0.915947i
$366$	−691.397	−	691.397i	−1.88906	−	1.88906i
$367$	130.207	−	130.207i	0.354786	−	0.354786i	−0.507100	−	0.861887i	$-0.669283\pi$
$367$	130.207	−	130.207i	0.354786	−	0.354786i	0.861887	+	0.507100i	$0.169283\pi$
$368$	−350.362			−0.952072
$369$	25.9787	−	25.9787i	0.0704030	−	0.0704030i
$370$			239.570i			0.647486i
$371$	31.9735			0.0861818
$372$	−310.031			−0.833417
$373$	−638.263			−1.71116			−0.855581	−	0.517669i	$-0.826800\pi$
$373$	−638.263			−1.71116			−0.855581	+	0.517669i	$0.826800\pi$
$374$	−3.39008	−	3.39008i	−0.00906438	−	0.00906438i
$375$	−415.545	−	415.545i	−1.10812	−	1.10812i
$376$			698.358i			1.85733i
$377$	155.978	−	183.396i	0.413735	−	0.486461i
$378$	−16.6550			−0.0440609
$379$	91.7710	−	91.7710i	0.242140	−	0.242140i	−0.575595	−	0.817735i	$-0.695229\pi$
$379$	91.7710	−	91.7710i	0.242140	−	0.242140i	0.817735	+	0.575595i	$0.195229\pi$
$380$	−1113.73	+	1113.73i	−2.93086	+	2.93086i
$381$			51.4547i			0.135052i
$382$			1130.55i			2.95957i
$383$		−	290.256i		−	0.757848i	−0.925428	−	0.378924i	$-0.876294\pi$
$383$		−	290.256i		−	0.757848i	0.925428	−	0.378924i	$-0.123706\pi$
$384$	−133.393			−0.347378
$385$	−0.142870	−	0.142870i	−0.000371091	−	0.000371091i
$386$		−	686.044i		−	1.77732i
$387$	116.812	+	116.812i	0.301839	+	0.301839i
$388$	418.891	−	418.891i	1.07962	−	1.07962i
$389$	404.811	+	404.811i	1.04065	+	1.04065i	0.999138	+	0.0415071i	$0.0132159\pi$
$389$	404.811	+	404.811i	1.04065	+	1.04065i	0.0415071	+	0.999138i	$0.486784\pi$
$390$			614.465i			1.57555i
$391$	131.924	−	131.924i	0.337402	−	0.337402i
$392$	735.046	+	735.046i	1.87512	+	1.87512i
$393$	2.25066			0.00572686
$394$	−669.231	+	669.231i	−1.69856	+	1.69856i
$395$	−356.733	−	356.733i	−0.903122	−	0.903122i
$396$	−4.29022	+	4.29022i	−0.0108339	+	0.0108339i
$397$	−485.501			−1.22292			−0.611462	−	0.791274i	$-0.709418\pi$
$397$	−485.501			−1.22292			−0.611462	+	0.791274i	$0.709418\pi$
$398$	441.032	−	441.032i	1.10812	−	1.10812i
$399$			116.596i			0.292221i
$400$	−181.361			−0.453403
$401$	−144.170			−0.359527			−0.179763	−	0.983710i	$-0.557533\pi$
$401$	−144.170			−0.359527			−0.179763	+	0.983710i	$0.557533\pi$
$402$	1238.22			3.08015
$403$	42.2837	+	42.2837i	0.104922	+	0.104922i
$404$	−356.362	−	356.362i	−0.882084	−	0.882084i
$405$			302.725i			0.747470i
$406$	−79.9778	+	6.46135i	−0.196990	+	0.0159146i
$407$	0.852328			0.00209417
$408$	1441.29	−	1441.29i	3.53257	−	3.53257i
$409$	118.758	−	118.758i	0.290361	−	0.290361i	−0.546862	−	0.837223i	$-0.684178\pi$
$409$	118.758	−	118.758i	0.290361	−	0.290361i	0.837223	+	0.546862i	$0.184178\pi$
$410$			59.5971i			0.145359i
$411$		−	433.014i		−	1.05356i
$412$		−	1092.96i		−	2.65282i
$413$	−79.3139			−0.192043
$414$	−235.234	−	235.234i	−0.568198	−	0.568198i
$415$			68.7504i			0.165664i
$416$	379.451	+	379.451i	0.912142	+	0.912142i
$417$	−346.604	+	346.604i	−0.831185	+	0.831185i
$418$	5.58289	+	5.58289i	0.0133562	+	0.0133562i
$419$			20.8124i			0.0496715i	0.999692	+	0.0248357i	$0.00790628\pi$
$419$			20.8124i			0.0496715i	−0.999692	+	0.0248357i	$0.992094\pi$
$420$	102.774	−	102.774i	0.244700	−	0.244700i
$421$	199.204	+	199.204i	0.473168	+	0.473168i	0.902938	−	0.429770i	$-0.141405\pi$
$421$	199.204	+	199.204i	0.473168	+	0.473168i	−0.429770	+	0.902938i	$0.641405\pi$
$422$	−587.404			−1.39195
$423$	−238.597	+	238.597i	−0.564058	+	0.564058i
$424$	650.888	+	650.888i	1.53511	+	1.53511i
$425$	68.2891	−	68.2891i	0.160680	−	0.160680i
$426$	1163.27			2.73069
$427$	31.5436	−	31.5436i	0.0738725	−	0.0738725i
$428$		−	870.137i		−	2.03303i
$429$	2.18611			0.00509582
$430$	−267.975			−0.623197
$431$	−193.044			−0.447898			−0.223949	−	0.974601i	$-0.571895\pi$
$431$	−193.044			−0.447898			−0.223949	+	0.974601i	$0.571895\pi$
$432$	−172.531	−	172.531i	−0.399376	−	0.399376i
$433$	118.795	+	118.795i	0.274353	+	0.274353i	0.830850	−	0.556497i	$-0.187855\pi$
$433$	118.795	+	118.795i	0.274353	+	0.274353i	−0.556497	+	0.830850i	$0.687855\pi$
$434$		−	19.9294i		−	0.0459203i
$435$	−46.5616	−	576.334i	−0.107038	−	1.32491i
$436$	−402.164			−0.922395
$437$	−217.257	+	217.257i	−0.497155	+	0.497155i
$438$	1205.55	−	1205.55i	2.75239	−	2.75239i
$439$			660.370i			1.50426i	0.659015	+	0.752130i	$0.270973\pi$
$439$			660.370i			1.50426i	−0.659015	+	0.752130i	$0.729027\pi$
$440$		−	5.81685i		−	0.0132201i
$441$			502.262i			1.13892i
$442$	−665.195			−1.50497
$443$	222.343	+	222.343i	0.501904	+	0.501904i	0.912029	−	0.410125i	$-0.134515\pi$
$443$	222.343	+	222.343i	0.501904	+	0.501904i	−0.410125	+	0.912029i	$0.634515\pi$
$444$			613.124i			1.38091i
$445$	−103.485	−	103.485i	−0.232550	−	0.232550i
$446$	−149.687	+	149.687i	−0.335622	+	0.335622i
$447$	138.534	+	138.534i	0.309920	+	0.309920i
$448$		−	57.9988i		−	0.129462i
$449$	289.500	−	289.500i	0.644765	−	0.644765i	−0.306958	−	0.951723i	$-0.599311\pi$
$449$	289.500	−	289.500i	0.644765	−	0.644765i	0.951723	+	0.306958i	$0.0993111\pi$
$450$	−121.766	−	121.766i	−0.270592	−	0.270592i
$451$	0.212031			0.000470135
$452$	1018.17	−	1018.17i	2.25260	−	2.25260i
$453$	219.825	+	219.825i	0.485265	+	0.485265i
$454$	−456.079	+	456.079i	−1.00458	+	1.00458i
$455$	−28.0337			−0.0616125
$456$	−2373.56	+	2373.56i	−5.20518	+	5.20518i
$457$		−	263.854i		−	0.577361i	−0.957426	−	0.288680i	$-0.906784\pi$
$457$		−	263.854i		−	0.577361i	0.957426	−	0.288680i	$-0.0932165\pi$
$458$	−759.628			−1.65858
$459$	129.928			0.283067
$460$	383.003			0.832614
$461$	−489.859	−	489.859i	−1.06260	−	1.06260i	−0.997905	−	0.0646957i	$-0.979392\pi$
$461$	−489.859	−	489.859i	−1.06260	−	1.06260i	−0.0646957	−	0.997905i	$-0.520608\pi$
$462$	−0.515184	−	0.515184i	−0.00111512	−	0.00111512i
$463$			606.327i			1.30956i	0.755819	+	0.654781i	$0.227239\pi$
$463$			606.327i			1.30956i	−0.755819	+	0.654781i	$0.772761\pi$
$464$	−895.428	−	761.561i	−1.92980	−	1.64130i
$465$	143.615			0.308849
$466$	270.028	−	270.028i	0.579459	−	0.579459i
$467$	337.667	−	337.667i	0.723056	−	0.723056i	−0.246171	−	0.969227i	$-0.579172\pi$
$467$	337.667	−	337.667i	0.723056	−	0.723056i	0.969227	+	0.246171i	$0.0791724\pi$
$468$			841.820i			1.79876i
$469$			56.4912i			0.120450i
$470$		−	547.359i		−	1.16459i
$471$	792.626			1.68286
$472$	−1614.60	−	1614.60i	−3.42077	−	3.42077i
$473$			0.953385i			0.00201561i
$474$	−1286.37	−	1286.37i	−2.71385	−	2.71385i
$475$	−112.461	+	112.461i	−0.236759	+	0.236759i
$476$	111.259	+	111.259i	0.233737	+	0.233737i
$477$			444.757i			0.932404i
$478$	−819.372	+	819.372i	−1.71417	+	1.71417i
$479$	431.509	+	431.509i	0.900854	+	0.900854i	0.995510	−	0.0946564i	$-0.0301753\pi$
$479$	431.509	+	431.509i	0.900854	+	0.900854i	−0.0946564	+	0.995510i	$0.530175\pi$
$480$	1288.79			2.68498
$481$	83.6211	−	83.6211i	0.173848	−	0.173848i
$482$	821.608	+	821.608i	1.70458	+	1.70458i
$483$	20.0483	−	20.0483i	0.0415078	−	0.0415078i
$484$	1183.39			2.44502
$485$	−194.042	+	194.042i	−0.400086	+	0.400086i
$486$			1292.73i			2.65993i
$487$	−317.203			−0.651341			−0.325670	−	0.945483i	$-0.605590\pi$
$487$	−317.203			−0.651341			−0.325670	+	0.945483i	$0.605590\pi$
$488$	1284.27			2.63171
$489$	−519.227			−1.06181
$490$	−576.114	−	576.114i	−1.17574	−	1.17574i
$491$	−440.067	−	440.067i	−0.896266	−	0.896266i	0.0988377	−	0.995104i	$-0.468488\pi$
$491$	−440.067	−	440.067i	−0.896266	−	0.896266i	−0.995104	+	0.0988377i	$0.968488\pi$
$492$			152.525i			0.310010i
$493$	623.916	−	50.4057i	1.26555	−	0.102243i
$494$	1095.47			2.21754
$495$	1.98735	−	1.98735i	0.00401485	−	0.00401485i
$496$	206.450	−	206.450i	0.416230	−	0.416230i
$497$			53.0720i			0.106785i
$498$			247.912i			0.497814i
$499$		−	847.151i		−	1.69770i	−0.528635	−	0.848849i	$-0.677296\pi$
$499$		−	847.151i		−	1.69770i	0.528635	−	0.848849i	$-0.322704\pi$
$500$	1306.01			2.61203
$501$	689.610	+	689.610i	1.37647	+	1.37647i
$502$		−	41.1285i		−	0.0819292i
$503$	−6.42815	−	6.42815i	−0.0127796	−	0.0127796i	0.700688	−	0.713468i	$-0.252876\pi$
$503$	−6.42815	−	6.42815i	−0.0127796	−	0.0127796i	−0.713468	+	0.700688i	$0.752876\pi$
$504$	117.249	−	117.249i	0.232638	−	0.232638i
$505$	165.077	+	165.077i	0.326884	+	0.326884i
$506$		−	1.91991i		−	0.00379430i
$507$	−311.433	+	311.433i	−0.614267	+	0.614267i
$508$	−80.8584	−	80.8584i	−0.159170	−	0.159170i
$509$	−476.056			−0.935277			−0.467638	−	0.883920i	$-0.654895\pi$
$509$	−476.056			−0.935277			−0.467638	+	0.883920i	$0.654895\pi$
$510$	−1129.65	+	1129.65i	−2.21501	+	2.21501i
$511$	55.0007	+	55.0007i	0.107633	+	0.107633i
$512$	−607.415	+	607.415i	−1.18636	+	1.18636i
$513$	−213.970			−0.417095
$514$	179.965	−	179.965i	0.350126	−	0.350126i
$515$			506.289i			0.983086i
$516$	−685.819			−1.32911
$517$	−1.94736			−0.00376665
$518$	−39.4128			−0.0760865
$519$	20.6018	+	20.6018i	0.0396952	+	0.0396952i
$520$	−570.686	−	570.686i	−1.09747	−	1.09747i
$521$		−	557.186i		−	1.06946i	−0.845024	−	0.534728i	$-0.820414\pi$
$521$		−	557.186i		−	1.06946i	0.845024	−	0.534728i	$-0.179586\pi$
$522$	−89.8785	−	1112.51i	−0.172181	−	2.13124i
$523$	456.134			0.872149			0.436074	−	0.899911i	$-0.356368\pi$
$523$	456.134			0.872149			0.436074	+	0.899911i	$0.356368\pi$
$524$	−3.53679	+	3.53679i	−0.00674960	+	0.00674960i
$525$	10.3778	−	10.3778i	0.0197672	−	0.0197672i
$526$		−	806.990i		−	1.53420i
$527$			155.472i			0.295013i
$528$		−	10.6737i		−	0.0202153i
$529$	−454.287			−0.858766
$530$	−510.153	−	510.153i	−0.962552	−	0.962552i
$531$		−	1103.27i		−	2.07772i
$532$	−183.225	−	183.225i	−0.344407	−	0.344407i
$533$	20.8022	−	20.8022i	0.0390285	−	0.0390285i
$534$	−373.163	−	373.163i	−0.698806	−	0.698806i
$535$			403.071i			0.753404i
$536$	−1150.00	+	1150.00i	−2.14552	+	2.14552i
$537$	−115.017	−	115.017i	−0.214184	−	0.214184i
$538$	1430.16			2.65828
$539$	−2.04966	+	2.04966i	−0.00380272	+	0.00380272i
$540$	188.604	+	188.604i	0.349266	+	0.349266i
$541$	537.048	−	537.048i	0.992694	−	0.992694i	−0.00727934	−	0.999974i	$-0.502317\pi$
$541$	537.048	−	537.048i	0.992694	−	0.992694i	0.999974	+	0.00727934i	$0.00231711\pi$
$542$	−1600.03			−2.95209
$543$	597.605	−	597.605i	1.10056	−	1.10056i
$544$			1395.19i			2.56469i
$545$	186.293			0.341823
$546$	−101.089			−0.185144
$547$	353.235			0.645768			0.322884	−	0.946439i	$-0.395348\pi$
$547$	353.235			0.645768			0.322884	+	0.946439i	$0.395348\pi$
$548$	680.459	+	680.459i	1.24171	+	1.24171i
$549$	438.776	+	438.776i	0.799229	+	0.799229i
$550$		−	0.993823i		−	0.00180695i
$551$	−1027.49	+	83.0098i	−1.86477	+	0.150653i
$552$	816.250			1.47871
$553$	58.6879	−	58.6879i	0.106126	−	0.106126i
$554$	−70.1532	+	70.1532i	−0.126630	+	0.126630i
$555$		−	284.016i		−	0.511740i
$556$		−	1089.34i		−	1.95924i
$557$			916.424i			1.64529i	0.568558	+	0.822643i	$0.307501\pi$
$557$			916.424i			1.64529i	−0.568558	+	0.822643i	$0.692499\pi$
$558$	277.221			0.496813
$559$	93.5358	+	93.5358i	0.167327	+	0.167327i
$560$			136.874i			0.244419i
$561$	4.01902	+	4.01902i	0.00716402	+	0.00716402i
$562$	1230.88	−	1230.88i	2.19018	−	2.19018i
$563$	−526.927	−	526.927i	−0.935928	−	0.935928i	0.0621396	−	0.998067i	$-0.480208\pi$
$563$	−526.927	−	526.927i	−0.935928	−	0.935928i	−0.998067	+	0.0621396i	$0.980208\pi$
$564$		−	1400.84i		−	2.48375i
$565$	−471.646	+	471.646i	−0.834772	+	0.834772i
$566$	691.653	+	691.653i	1.22200	+	1.22200i
$567$	−49.8028			−0.0878356
$568$	−1080.39	+	1080.39i	−1.90210	+	1.90210i
$569$	394.074	+	394.074i	0.692573	+	0.692573i	0.962797	−	0.270224i	$-0.0870979\pi$
$569$	394.074	+	394.074i	0.692573	+	0.692573i	−0.270224	+	0.962797i	$0.587098\pi$
$570$	1860.35	−	1860.35i	3.26377	−	3.26377i
$571$	−552.975			−0.968432			−0.484216	−	0.874949i	$-0.660895\pi$
$571$	−552.975			−0.968432			−0.484216	+	0.874949i	$0.660895\pi$
$572$	−3.43535	+	3.43535i	−0.00600586	+	0.00600586i
$573$		−	1340.30i		−	2.33909i
$574$	−9.80460			−0.0170812
$575$	38.6744			0.0672598
$576$	806.774			1.40065
$577$	167.445	+	167.445i	0.290200	+	0.290200i	0.837159	−	0.546959i	$-0.184215\pi$
$577$	167.445	+	167.445i	0.290200	+	0.290200i	−0.546959	+	0.837159i	$0.684215\pi$
$578$	−464.317	−	464.317i	−0.803317	−	0.803317i
$579$			813.321i			1.40470i
$580$	978.848	+	832.510i	1.68767	+	1.43536i
$581$	−11.3105			−0.0194672
$582$	−699.707	+	699.707i	−1.20225	+	1.20225i
$583$	−1.81499	+	1.81499i	−0.00311319	+	0.00311319i
$584$			2239.31i			3.83444i
$585$		−	389.954i		−	0.666588i
$586$			443.303i			0.756489i
$587$	38.0082			0.0647500			0.0323750	−	0.999476i	$-0.489693\pi$
$587$	38.0082			0.0647500			0.0323750	+	0.999476i	$0.489693\pi$
$588$	−1474.43	−	1474.43i	−2.50753	−	2.50753i
$589$		−	256.036i		−	0.434696i
$590$	1265.49	+	1265.49i	2.14490	+	2.14490i
$591$	793.388	−	793.388i	1.34245	−	1.34245i
$592$	−408.280	−	408.280i	−0.689661	−	0.689661i
$593$			627.850i			1.05877i	0.848382	+	0.529385i	$0.177577\pi$
$593$			627.850i			1.05877i	−0.848382	+	0.529385i	$0.822423\pi$
$594$	0.945432	−	0.945432i	0.00159164	−	0.00159164i
$595$	−51.5381	−	51.5381i	−0.0866187	−	0.0866187i
$596$	−435.399			−0.730535
$597$	−522.854	+	522.854i	−0.875802	+	0.875802i
$598$	−188.361	−	188.361i	−0.314985	−	0.314985i
$599$	674.702	−	674.702i	1.12638	−	1.12638i	0.135619	−	0.990761i	$-0.456698\pi$
$599$	674.702	−	674.702i	1.12638	−	1.12638i	0.990761	−	0.135619i	$-0.0433024\pi$
$600$	422.523			0.704205
$601$	−500.527	+	500.527i	−0.832823	+	0.832823i	−0.987902	−	0.155079i	$-0.950437\pi$
$601$	−500.527	+	500.527i	−0.832823	+	0.832823i	0.155079	+	0.987902i	$0.450437\pi$
$602$		−	44.0858i		−	0.0732322i
$603$	−785.802			−1.30315
$604$	−690.886			−1.14385
$605$	−548.178			−0.906079
$606$	595.260	+	595.260i	0.982278	+	0.982278i
$607$	780.373	+	780.373i	1.28562	+	1.28562i	0.937419	+	0.348204i	$0.113208\pi$
$607$	780.373	+	780.373i	1.28562	+	1.28562i	0.348204	+	0.937419i	$0.386792\pi$
$608$		−	2297.65i		−	3.77903i
$609$	94.8155	−	7.66007i	0.155690	−	0.0125781i
$610$	−1006.59			−1.65014
$611$	−191.054	+	191.054i	−0.312690	+	0.312690i
$612$	−1547.63	+	1547.63i	−2.52881	+	2.52881i
$613$		−	830.453i		−	1.35473i	−0.735645	−	0.677367i	$-0.763121\pi$
$613$		−	830.453i		−	1.35473i	0.735645	−	0.677367i	$-0.236879\pi$
$614$		−	1013.67i		−	1.65093i
$615$		−	70.6537i		−	0.114884i
$616$	0.956957			0.00155350
$617$	69.2239	+	69.2239i	0.112194	+	0.112194i	0.760975	−	0.648781i	$-0.224721\pi$
$617$	69.2239	+	69.2239i	0.112194	+	0.112194i	−0.648781	+	0.760975i	$0.724721\pi$
$618$			1825.66i			2.95414i
$619$	−331.072	−	331.072i	−0.534849	−	0.534849i	0.387162	−	0.922012i	$-0.373455\pi$
$619$	−331.072	−	331.072i	−0.534849	−	0.534849i	−0.922012	+	0.387162i	$0.873455\pi$
$620$	−225.683	+	225.683i	−0.364005	+	0.364005i
$621$	36.7912	+	36.7912i	0.0592452	+	0.0592452i
$622$			726.439i			1.16791i
$623$	17.0248	−	17.0248i	0.0273271	−	0.0273271i
$624$	−1047.18	−	1047.18i	−1.67818	−	1.67818i
$625$	−493.123			−0.788997
$626$	829.706	−	829.706i	1.32541	−	1.32541i
$627$	−6.61864	−	6.61864i	−0.0105561	−	0.0105561i
$628$	−1245.57	+	1245.57i	−1.98339	+	1.98339i
$629$	307.464			0.488814
$630$	−91.8977	+	91.8977i	−0.145869	+	0.145869i
$631$		−	681.376i		−	1.07984i	−0.841718	−	0.539918i	$-0.818455\pi$
$631$		−	681.376i		−	1.07984i	0.841718	−	0.539918i	$-0.181545\pi$
$632$	2389.43			3.78075
$633$	696.381			1.10013
$634$	1168.10			1.84243
$635$	37.4558	+	37.4558i	0.0589855	+	0.0589855i
$636$	−1305.62	−	1305.62i	−2.05286	−	2.05286i
$637$			402.181i			0.631368i
$638$	4.17320	−	4.90676i	0.00654107	−	0.00769085i
$639$	−738.240			−1.15531
$640$	−97.1018	+	97.1018i	−0.151722	+	0.151722i
$641$	−517.626	+	517.626i	−0.807529	+	0.807529i	−0.984259	−	0.176730i	$-0.943448\pi$
$641$	−517.626	+	517.626i	−0.807529	+	0.807529i	0.176730	+	0.984259i	$0.443448\pi$
$642$			1453.46i			2.26396i
$643$			867.657i			1.34939i	0.738097	+	0.674694i	$0.235725\pi$
$643$			867.657i			1.34939i	−0.738097	+	0.674694i	$0.764275\pi$
$644$			63.0096i			0.0978410i
$645$	317.690			0.492543
$646$	2013.94	+	2013.94i	3.11756	+	3.11756i
$647$		−	357.347i		−	0.552314i	−0.961113	−	0.276157i	$-0.910939\pi$
$647$		−	357.347i		−	0.552314i	0.961113	−	0.276157i	$-0.0890609\pi$
$648$	−1013.84	−	1013.84i	−1.56457	−	1.56457i
$649$	4.50229	−	4.50229i	0.00693728	−	0.00693728i
$650$	−97.5031	−	97.5031i	−0.150005	−	0.150005i
$651$			23.6268i			0.0362930i
$652$	815.937	−	815.937i	1.25144	−	1.25144i
$653$	−700.906	−	700.906i	−1.07336	−	1.07336i	−0.997087	−	0.0762758i	$-0.975697\pi$
$653$	−700.906	−	700.906i	−1.07336	−	1.07336i	−0.0762758	−	0.997087i	$-0.524303\pi$
$654$	671.767			1.02717
$655$	1.63834	−	1.63834i	0.00250128	−	0.00250128i
$656$	−101.566	−	101.566i	−0.154827	−	0.154827i
$657$	−765.069	+	765.069i	−1.16449	+	1.16449i
$658$	90.0486			0.136852
$659$	760.878	−	760.878i	1.15459	−	1.15459i	0.168974	−	0.985621i	$-0.445955\pi$
$659$	760.878	−	760.878i	1.15459	−	1.15459i	0.985621	−	0.168974i	$-0.0540453\pi$
$660$			11.6680i			0.0176788i
$661$	−204.176			−0.308889			−0.154444	−	0.988001i	$-0.549359\pi$
$661$	−204.176			−0.308889			−0.154444	+	0.988001i	$0.549359\pi$
$662$	1263.34			1.90838
$663$	788.604			1.18945
$664$	−230.248	−	230.248i	−0.346760	−	0.346760i
$665$	84.8747	+	84.8747i	0.127631	+	0.127631i
$666$		−	548.239i		−	0.823182i
$667$	190.945	+	162.399i	0.286275	+	0.243477i
$668$	−2167.37			−3.24457
$669$	177.458	−	177.458i	0.265258	−	0.265258i
$670$	901.345	−	901.345i	1.34529	−	1.34529i
$671$			3.58117i			0.00533707i
$672$			212.025i			0.315513i
$673$			255.714i			0.379962i	0.981788	+	0.189981i	$0.0608426\pi$
$673$			255.714i			0.379962i	−0.981788	+	0.189981i	$0.939157\pi$
$674$	−1545.42			−2.29291
$675$	19.0446	+	19.0446i	0.0282142	+	0.0282142i
$676$		−	978.802i		−	1.44793i
$677$	−778.876	−	778.876i	−1.15048	−	1.15048i	−0.986456	−	0.164026i	$-0.947552\pi$
$677$	−778.876	−	778.876i	−1.15048	−	1.15048i	−0.164026	−	0.986456i	$-0.552448\pi$
$678$	−1700.74	+	1700.74i	−2.50847	+	2.50847i
$679$	−31.9227	−	31.9227i	−0.0470143	−	0.0470143i
$680$		−	2098.34i		−	3.08579i
$681$	540.692	−	540.692i	0.793967	−	0.793967i
$682$	1.13130	+	1.13130i	0.00165880	+	0.00165880i
$683$	−712.500			−1.04319			−0.521596	−	0.853193i	$-0.674663\pi$
$683$	−712.500			−1.04319			−0.521596	+	0.853193i	$0.674663\pi$
$684$	2548.69	−	2548.69i	3.72615	−	3.72615i
$685$	−315.207	−	315.207i	−0.460156	−	0.460156i
$686$	190.645	−	190.645i	0.277909	−	0.277909i
$687$	900.556			1.31085
$688$	456.688	−	456.688i	0.663790	−	0.663790i
$689$			356.134i			0.516886i
$690$	−639.760			−0.927189
$691$	85.2702			0.123401			0.0617006	−	0.998095i	$-0.480348\pi$
$691$	85.2702			0.123401			0.0617006	+	0.998095i	$0.480348\pi$
$692$	−64.7493			−0.0935684
$693$	0.326948	+	0.326948i	0.000471787	+	0.000471787i
$694$	933.346	+	933.346i	1.34488	+	1.34488i
$695$			504.612i			0.726060i
$696$	2086.11	+	1774.23i	2.99728	+	2.54919i
$697$	76.4869			0.109737
$698$	−628.235	+	628.235i	−0.900051	+	0.900051i
$699$	−320.124	+	320.124i	−0.457975	+	0.457975i
$700$			32.6162i			0.0465946i
$701$			389.567i			0.555731i	0.960620	+	0.277865i	$0.0896269\pi$
$701$			389.567i			0.555731i	−0.960620	+	0.277865i	$0.910373\pi$
$702$		−	185.511i		−	0.264261i
$703$	−506.342			−0.720258
$704$	3.29233	+	3.29233i	0.00467661	+	0.00467661i
$705$			648.906i			0.920434i
$706$	82.0155	+	82.0155i	0.116169	+	0.116169i
$707$	−27.1575	+	27.1575i	−0.0384123	+	0.0384123i
$708$	3238.73	+	3238.73i	4.57448	+	4.57448i
$709$			616.933i			0.870145i	0.900396	+	0.435072i	$0.143277\pi$
$709$			616.933i			0.870145i	−0.900396	+	0.435072i	$0.856723\pi$
$710$	846.790	−	846.790i	1.19266	−	1.19266i
$711$	816.359	+	816.359i	1.14818	+	1.14818i
$712$	693.151			0.973527
$713$	−44.0244	+	44.0244i	−0.0617452	+	0.0617452i
$714$	−185.845	−	185.845i	−0.260287	−	0.260287i
$715$	1.59135	−	1.59135i	0.00222566	−	0.00222566i
$716$	361.485			0.504868
$717$	971.384	−	971.384i	1.35479	−	1.35479i
$718$		−	1362.75i		−	1.89798i
$719$	273.210			0.379986			0.189993	−	0.981785i	$-0.439153\pi$
$719$	273.210			0.379986			0.189993	+	0.981785i	$0.439153\pi$
$720$	−1903.95			−2.64437
$721$	−83.2920			−0.115523
$722$	−2369.03	−	2369.03i	−3.28120	−	3.28120i
$723$	−974.035	−	974.035i	−1.34721	−	1.34721i
$724$			1878.21i			2.59421i
$725$	98.8409	+	84.0641i	0.136332	+	0.115950i
$726$	−1976.71			−2.72274
$727$	136.415	−	136.415i	0.187641	−	0.187641i	−0.607034	−	0.794676i	$-0.707641\pi$
$727$	136.415	−	136.415i	0.187641	−	0.187641i	0.794676	+	0.607034i	$0.207641\pi$
$728$	93.8862	−	93.8862i	0.128965	−	0.128965i
$729$		−	931.186i		−	1.27735i
$730$		−	1755.13i		−	2.40428i
$731$			343.919i			0.470477i
$732$	−2576.12			−3.51930
$733$	−580.859	−	580.859i	−0.792441	−	0.792441i	0.189449	−	0.981890i	$-0.439330\pi$
$733$	−580.859	−	580.859i	−0.792441	−	0.792441i	−0.981890	+	0.189449i	$0.939330\pi$
$734$		−	683.563i		−	0.931284i
$735$	682.996	+	682.996i	0.929247	+	0.929247i
$736$	−395.072	+	395.072i	−0.536782	+	0.536782i
$737$	−3.20675	−	3.20675i	−0.00435109	−	0.00435109i
$738$		−	136.384i		−	0.184802i
$739$	−688.432	+	688.432i	−0.931572	+	0.931572i	−0.997804	−	0.0662318i	$-0.978902\pi$
$739$	−688.432	+	688.432i	−0.931572	+	0.931572i	0.0662318	+	0.997804i	$0.478902\pi$
$740$	446.316	+	446.316i	0.603129	+	0.603129i
$741$	−1298.70			−1.75263
$742$	83.9276	−	83.9276i	0.113110	−	0.113110i
$743$	108.284	+	108.284i	0.145739	+	0.145739i	0.776212	−	0.630472i	$-0.217139\pi$
$743$	108.284	+	108.284i	0.145739	+	0.145739i	−0.630472	+	0.776212i	$0.717139\pi$
$744$	−480.973	+	480.973i	−0.646469	+	0.646469i
$745$	201.689			0.270723
$746$	−1675.39	+	1675.39i	−2.24583	+	2.24583i
$747$		−	157.330i		−	0.210616i
$748$	−12.6313			−0.0168868
$749$	−66.3112			−0.0885329
$750$	−2181.54			−2.90872
$751$	474.687	+	474.687i	0.632074	+	0.632074i	0.948588	−	0.316514i	$-0.102512\pi$
$751$	474.687	+	474.687i	0.632074	+	0.632074i	−0.316514	+	0.948588i	$0.602512\pi$
$752$	932.819	+	932.819i	1.24045	+	1.24045i
$753$			48.7587i			0.0647526i
$754$	−71.9693	−	890.827i	−0.0954500	−	1.18147i
$755$	320.037			0.423891
$756$	−31.0281	+	31.0281i	−0.0410425	+	0.0410425i
$757$	144.571	−	144.571i	0.190979	−	0.190979i	−0.605140	−	0.796119i	$-0.706883\pi$
$757$	144.571	−	144.571i	0.190979	−	0.190979i	0.796119	+	0.605140i	$0.206883\pi$
$758$		−	481.782i		−	0.635597i
$759$			2.27610i			0.00299882i
$760$			3455.61i			4.54685i
$761$	279.009			0.366635			0.183318	−	0.983054i	$-0.441316\pi$
$761$	279.009			0.366635			0.183318	+	0.983054i	$0.441316\pi$
$762$	135.064	+	135.064i	0.177250	+	0.177250i
$763$			30.6480i			0.0401678i
$764$	2106.21	+	2106.21i	2.75681	+	2.75681i
$765$	716.905	−	716.905i	0.937130	−	0.937130i
$766$	−761.897	−	761.897i	−0.994644	−	0.994644i
$767$		−	883.432i		−	1.15180i
$768$	618.468	−	618.468i	0.805297	−	0.805297i
$769$	270.425	+	270.425i	0.351658	+	0.351658i	0.860726	−	0.509068i	$-0.170010\pi$
$769$	270.425	+	270.425i	0.351658	+	0.351658i	−0.509068	+	0.860726i	$0.670010\pi$
$770$	−0.750044			−0.000974083
$771$	−213.352	+	213.352i	−0.276722	+	0.276722i
$772$	−1278.09	−	1278.09i	−1.65556	−	1.65556i
$773$	933.705	−	933.705i	1.20790	−	1.20790i	0.236191	−	0.971707i	$-0.424101\pi$
$773$	933.705	−	933.705i	1.20790	−	1.20790i	0.971707	−	0.236191i	$-0.0758991\pi$
$774$	613.242			0.792302
$775$	−22.7887	+	22.7887i	−0.0294048	+	0.0294048i
$776$		−	1299.71i		−	1.67488i
$777$	46.7248			0.0601348
$778$	2125.19			2.73161
$779$	−125.961			−0.161696
$780$	1144.74	+	1144.74i	1.46762	+	1.46762i
$781$	−3.01266	−	3.01266i	−0.00385744	−	0.00385744i
$782$		−	692.579i		−	0.885651i
$783$	14.0573	+	173.999i	0.0179531	+	0.222221i
$784$	1963.65			2.50465
$785$	576.982	−	576.982i	0.735009	−	0.735009i
$786$	5.90779	−	5.90779i	0.00751627	−	0.00751627i
$787$		−	377.592i		−	0.479786i	−0.970799	−	0.239893i	$-0.922888\pi$
$787$		−	377.592i		−	0.479786i	0.970799	−	0.239893i	$-0.0771124\pi$
$788$			2493.54i			3.16438i
$789$			956.705i			1.21255i
$790$	−1872.79			−2.37062
$791$	−77.5928	−	77.5928i	−0.0980945	−	0.0980945i
$792$			13.3114i			0.0168074i
$793$	351.346	+	351.346i	0.443059	+	0.443059i
$794$	−1274.40	+	1274.40i	−1.60504	+	1.60504i
$795$	604.797	+	604.797i	0.760751	+	0.760751i
$796$		−	1643.27i		−	2.06442i
$797$	350.486	−	350.486i	0.439756	−	0.439756i	−0.452174	−	0.891930i	$-0.649351\pi$
$797$	350.486	−	350.486i	0.439756	−	0.439756i	0.891930	+	0.452174i	$0.149351\pi$
$798$	306.055	+	306.055i	0.383528	+	0.383528i
$799$	−702.480			−0.879199
$800$	−204.505	+	204.505i	−0.255631	+	0.255631i
$801$	236.818	+	236.818i	0.295653	+	0.295653i
$802$	−378.434	+	378.434i	−0.471863	+	0.471863i
$803$	−6.24428			−0.00777619
$804$	2306.78	−	2306.78i	2.86913	−	2.86913i
$805$		−	29.1878i		−	0.0362581i
$806$	221.982			0.275412
$807$	−1695.48			−2.10097
$808$	−1105.70			−1.36844
$809$	−303.271	−	303.271i	−0.374872	−	0.374872i	0.494376	−	0.869248i	$-0.335397\pi$
$809$	−303.271	−	303.271i	−0.374872	−	0.374872i	−0.869248	+	0.494376i	$0.835397\pi$
$810$	794.628	+	794.628i	0.981023	+	0.981023i
$811$		−	1521.59i		−	1.87619i	−0.346380	−	0.938094i	$-0.612589\pi$
$811$		−	1521.59i		−	1.87619i	0.346380	−	0.938094i	$-0.387411\pi$
$812$	−136.960	+	161.035i	−0.168670	+	0.198319i
$813$	1896.87			2.33318
$814$	2.23729	−	2.23729i	0.00274851	−	0.00274851i
$815$	−377.964	+	377.964i	−0.463760	+	0.463760i
$816$		−	3850.35i		−	4.71857i
$817$		−	566.376i		−	0.693239i
$818$		−	623.458i		−	0.762174i
$819$	64.1532			0.0783311
$820$	111.029	+	111.029i	0.135401	+	0.135401i
$821$			307.159i			0.374128i	0.982348	+	0.187064i	$0.0598972\pi$
$821$			307.159i			0.374128i	−0.982348	+	0.187064i	$0.940103\pi$
$822$	−1136.63	−	1136.63i	−1.38276	−	1.38276i
$823$	−861.491	+	861.491i	−1.04677	+	1.04677i	−0.0479183	+	0.998851i	$0.515259\pi$
$823$	−861.491	+	861.491i	−1.04677	+	1.04677i	−0.998851	+	0.0479183i	$0.984741\pi$
$824$	−1695.59	−	1695.59i	−2.05775	−	2.05775i
$825$			1.17820i			0.00142812i
$826$	−208.192	+	208.192i	−0.252049	+	0.252049i
$827$	18.3000	+	18.3000i	0.0221282	+	0.0221282i	0.718084	−	0.695956i	$-0.245019\pi$
$827$	18.3000	+	18.3000i	0.0221282	+	0.0221282i	−0.695956	+	0.718084i	$0.745019\pi$
$828$	−876.474			−1.05854
$829$	−211.234	+	211.234i	−0.254806	+	0.254806i	−0.822938	−	0.568132i	$-0.807666\pi$
$829$	−211.234	+	211.234i	−0.254806	+	0.254806i	0.568132	+	0.822938i	$0.307666\pi$
$830$	180.464	+	180.464i	0.217426	+	0.217426i
$831$	83.1683	−	83.1683i	0.100082	−	0.100082i
$832$	646.016			0.776462
$833$	−739.384	+	739.384i	−0.887616	+	0.887616i
$834$			1819.61i			2.18179i
$835$	1003.99			1.20238
$836$	20.8017			0.0248824
$837$	−43.3582			−0.0518020
$838$	54.6307	+	54.6307i	0.0651917	+	0.0651917i
$839$	479.471	+	479.471i	0.571479	+	0.571479i	0.932542	−	0.361063i	$-0.117586\pi$
$839$	479.471	+	479.471i	0.571479	+	0.571479i	−0.361063	+	0.932542i	$0.617586\pi$
$840$		−	318.881i		−	0.379620i
$841$	135.006	+	830.093i	0.160531	+	0.987031i
$842$	1045.79			1.24203
$843$	−1459.24	+	1459.24i	−1.73100	+	1.73100i
$844$	−1094.33	+	1094.33i	−1.29659	+	1.29659i
$845$			453.408i			0.536577i
$846$			1252.59i			1.48060i
$847$		−	90.1833i		−	0.106474i
$848$	1738.82			2.05050
$849$	−819.970	−	819.970i	−0.965807	−	0.965807i
$850$		−	358.506i		−	0.421772i
$851$	87.0635	+	87.0635i	0.102307	+	0.102307i
$852$	2167.16	−	2167.16i	2.54362	−	2.54362i
$853$	−74.8941	−	74.8941i	−0.0878008	−	0.0878008i	0.661842	−	0.749643i	$-0.269775\pi$
$853$	−74.8941	−	74.8941i	−0.0878008	−	0.0878008i	−0.749643	+	0.661842i	$0.769775\pi$
$854$		−	165.598i		−	0.193909i
$855$	−1180.62	+	1180.62i	−1.38084	+	1.38084i
$856$	−1349.90	−	1349.90i	−1.57699	−	1.57699i
$857$	1145.50			1.33664			0.668321	−	0.743873i	$-0.267013\pi$
$857$	1145.50			1.33664			0.668321	+	0.743873i	$0.267013\pi$
$858$	5.73835	−	5.73835i	0.00668805	−	0.00668805i
$859$	−307.151	−	307.151i	−0.357568	−	0.357568i	0.505348	−	0.862916i	$-0.331364\pi$
$859$	−307.151	−	307.151i	−0.357568	−	0.357568i	−0.862916	+	0.505348i	$0.831364\pi$
$860$	−499.233	+	499.233i	−0.580504	+	0.580504i
$861$	11.6236			0.0135001
$862$	−506.724	+	506.724i	−0.587847	+	0.587847i
$863$			181.269i			0.210046i	0.994470	+	0.105023i	$0.0334916\pi$
$863$			181.269i			0.210046i	−0.994470	+	0.105023i	$0.966508\pi$
$864$	−389.094			−0.450340
$865$	29.9937			0.0346747
$866$	623.653			0.720153
$867$	550.459	+	550.459i	0.634900	+	0.634900i
$868$	−37.1282	−	37.1282i	−0.0427744	−	0.0427744i
$869$			6.66290i			0.00766732i
$870$	−1635.05	−	1390.61i	−1.87937	−	1.59840i
$871$	−629.223			−0.722415
$872$	−623.905	+	623.905i	−0.715488	+	0.715488i
$873$	444.050	−	444.050i	0.508649	−	0.508649i
$874$			1140.56i			1.30499i
$875$		−	99.5282i		−	0.113747i
$876$		−	4491.84i		−	5.12767i
$877$	1730.81			1.97355			0.986777	−	0.162083i	$-0.0518211\pi$
$877$	1730.81			1.97355			0.986777	+	0.162083i	$0.0518211\pi$
$878$	1733.41	+	1733.41i	1.97428	+	1.97428i
$879$		−	525.545i		−	0.597890i
$880$	−7.76975	−	7.76975i	−0.00882926	−	0.00882926i
$881$	433.391	−	433.391i	0.491931	−	0.491931i	−0.416983	−	0.908914i	$-0.636913\pi$
$881$	433.391	−	433.391i	0.491931	−	0.491931i	0.908914	+	0.416983i	$0.136913\pi$
$882$	1318.40	+	1318.40i	1.49478	+	1.49478i
$883$			589.072i			0.667126i	0.942728	+	0.333563i	$0.108251\pi$
$883$			589.072i			0.667126i	−0.942728	+	0.333563i	$0.891749\pi$
$884$	−1239.25	+	1239.25i	−1.40187	+	1.40187i
$885$	−1500.27	−	1500.27i	−1.69522	−	1.69522i
$886$	1167.26			1.31745
$887$	136.134	−	136.134i	0.153477	−	0.153477i	−0.626192	−	0.779669i	$-0.715387\pi$
$887$	136.134	−	136.134i	0.153477	−	0.153477i	0.779669	+	0.626192i	$0.215387\pi$
$888$	951.182	+	951.182i	1.07115	+	1.07115i
$889$	−6.16203	+	6.16203i	−0.00693142	+	0.00693142i
$890$	−543.278			−0.610425
$891$	2.82708	−	2.82708i	0.00317293	−	0.00317293i
$892$			557.731i			0.625259i
$893$	1156.87			1.29548
$894$	727.282			0.813514
$895$	−167.450			−0.187095
$896$	−15.9747	−	15.9747i	−0.0178289	−	0.0178289i
$897$	223.306	+	223.306i	0.248948	+	0.248948i
$898$		−	1519.82i		−	1.69245i
$899$	−208.207	+	16.8209i	−0.231599	+	0.0187107i
$900$	−453.698			−0.504108
$901$	−654.729	+	654.729i	−0.726670	+	0.726670i
$902$	0.556563	−	0.556563i	0.000617033	−	0.000617033i
$903$			52.2647i			0.0578790i
$904$		−	3159.13i		−	3.49461i
$905$		−	870.038i		−	0.961368i
$906$	1154.04			1.27378
$907$	−490.744	−	490.744i	−0.541063	−	0.541063i	0.382778	−	0.923840i	$-0.374967\pi$
$907$	−490.744	−	490.744i	−0.541063	−	0.541063i	−0.923840	+	0.382778i	$0.874967\pi$
$908$			1699.34i			1.87152i
$909$	−377.766	−	377.766i	−0.415584	−	0.415584i
$910$	−73.5861	+	73.5861i	−0.0808639	+	0.0808639i
$911$	686.245	+	686.245i	0.753287	+	0.753287i	0.975091	−	0.221804i	$-0.0711945\pi$
$911$	686.245	+	686.245i	0.753287	+	0.753287i	−0.221804	+	0.975091i	$0.571195\pi$
$912$			6340.89i			6.95273i
$913$	0.642044	−	0.642044i	0.000703225	−	0.000703225i
$914$	−692.594	−	692.594i	−0.757762	−	0.757762i
$915$	1193.33			1.30419
$916$	−1415.18	+	1415.18i	−1.54495	+	1.54495i
$917$	0.269531	+	0.269531i	0.000293927	+	0.000293927i
$918$	341.050	−	341.050i	0.371514	−	0.371514i
$919$	94.8391			0.103198			0.0515991	−	0.998668i	$-0.483568\pi$
$919$	94.8391			0.103198			0.0515991	+	0.998668i	$0.483568\pi$
$920$	594.179	−	594.179i	0.645846	−	0.645846i
$921$			1201.73i			1.30481i
$922$	−2571.68			−2.78924
$923$	−591.138			−0.640453
$924$	−1.91956			−0.00207745
$925$	45.0675	+	45.0675i	0.0487216	+	0.0487216i
$926$	1591.56	+	1591.56i	1.71874	+	1.71874i
$927$		−	1158.61i		−	1.24985i
$928$	−1868.44	+	150.950i	−2.01340	+	0.162661i
$929$	−382.605			−0.411846			−0.205923	−	0.978568i	$-0.566020\pi$
$929$	−382.605			−0.411846			−0.205923	+	0.978568i	$0.566020\pi$
$930$	376.977	−	376.977i	0.405351	−	0.405351i
$931$	1217.64	−	1217.64i	1.30789	−	1.30789i
$932$		−	1006.12i		−	1.07952i
$933$		−	861.210i		−	0.923054i
$934$		−	1772.70i		−	1.89796i
$935$	5.85118			0.00625795
$936$	1305.97	+	1305.97i	1.39527	+	1.39527i
$937$			1462.55i			1.56089i	0.625227	+	0.780443i	$0.285006\pi$
$937$			1462.55i			1.56089i	−0.625227	+	0.780443i	$0.714994\pi$
$938$	148.285	+	148.285i	0.158086	+	0.158086i
$939$	−983.635	+	983.635i	−1.04753	+	1.04753i
$940$	−1019.72	−	1019.72i	−1.08481	−	1.08481i
$941$		−	828.617i		−	0.880571i	−0.897858	−	0.440285i	$-0.854877\pi$
$941$		−	828.617i		−	0.880571i	0.897858	−	0.440285i	$-0.145123\pi$
$942$	2080.58	−	2080.58i	2.20868	−	2.20868i
$943$	21.6585	+	21.6585i	0.0229677	+	0.0229677i
$944$	−4313.35			−4.56923
$945$	14.3731	−	14.3731i	0.0152096	−	0.0152096i
$946$	2.50256	+	2.50256i	0.00264541	+	0.00264541i
$947$	−612.076	+	612.076i	−0.646331	+	0.646331i	−0.952104	−	0.305773i	$-0.901085\pi$
$947$	−612.076	+	612.076i	−0.646331	+	0.646331i	0.305773	+	0.952104i	$0.401085\pi$
$948$	−4792.97			−5.05587
$949$	−612.621	+	612.621i	−0.645544	+	0.645544i
$950$			590.399i			0.621473i
$951$	−1384.81			−1.45617
$952$	345.207			0.362613
$953$	884.227			0.927835			0.463917	−	0.885878i	$-0.346443\pi$
$953$	884.227			0.927835			0.463917	+	0.885878i	$0.346443\pi$
$954$	1167.45	+	1167.45i	1.22374	+	1.22374i
$955$	−975.652	−	975.652i	−1.02163	−	1.02163i
$956$			3052.96i			3.19347i
$957$	−4.94742	+	5.81708i	−0.00516972	+	0.00607845i
$958$	2265.35			2.36466
$959$	51.8562	−	51.8562i	0.0540732	−	0.0540732i
$960$	1097.08	−	1097.08i	1.14279	−	1.14279i
$961$			909.118i			0.946012i
$962$		−	438.997i		−	0.456338i
$963$		−	922.400i		−	0.957840i
$964$	3061.29			3.17561
$965$	592.047	+	592.047i	0.613520	+	0.613520i
$966$		−	105.250i		−	0.108954i
$967$	−1022.14	−	1022.14i	−1.05702	−	1.05702i	−0.998273	−	0.0587468i	$-0.981290\pi$
$967$	−1022.14	−	1022.14i	−1.05702	−	1.05702i	−0.0587468	−	0.998273i	$-0.518710\pi$
$968$	1835.87	−	1835.87i	1.89656	−	1.89656i
$969$	−2387.57	−	2387.57i	−2.46395	−	2.46395i
$970$			1018.69i			1.05019i
$971$	118.570	−	118.570i	0.122111	−	0.122111i	−0.643410	−	0.765522i	$-0.722481\pi$
$971$	118.570	−	118.570i	0.122111	−	0.122111i	0.765522	+	0.643410i	$0.222481\pi$
$972$	2408.33	+	2408.33i	2.47771	+	2.47771i
$973$	−83.0161			−0.0853197
$974$	−832.631	+	832.631i	−0.854857	+	0.854857i
$975$	115.592	+	115.592i	0.118556	+	0.118556i
$976$	1715.44	−	1715.44i	1.75763	−	1.75763i
$977$	722.204			0.739205			0.369603	−	0.929190i	$-0.379494\pi$
$977$	722.204			0.739205			0.369603	+	0.929190i	$0.379494\pi$
$978$	−1362.93	+	1362.93i	−1.39359	+	1.39359i
$979$			1.93284i			0.00197430i
$980$	−2146.58			−2.19039
$981$	−426.319			−0.434576
$982$	−2310.27			−2.35262
$983$	−295.211	−	295.211i	−0.300317	−	0.300317i	0.540821	−	0.841138i	$-0.318114\pi$
$983$	−295.211	−	295.211i	−0.300317	−	0.300317i	−0.841138	+	0.540821i	$0.818114\pi$
$984$	236.623	+	236.623i	0.240470	+	0.240470i
$985$		−	1155.07i		−	1.17266i
$986$	1505.42	−	1770.04i	1.52679	−	1.79517i
$987$	−106.755			−0.108161
$988$	2040.84	−	2040.84i	2.06562	−	2.06562i
$989$	−97.3863	+	97.3863i	−0.0984694	+	0.0984694i
$990$		−	10.4332i		−	0.0105386i
$991$			1627.14i			1.64191i	0.570991	+	0.820956i	$0.306559\pi$
$991$			1627.14i			1.64191i	−0.570991	+	0.820956i	$0.693441\pi$
$992$		−	465.589i		−	0.469344i
$993$	−1497.72			−1.50828
$994$	139.309	+	139.309i	0.140150	+	0.140150i
$995$			761.210i			0.765035i
$996$	461.856	+	461.856i	0.463710	+	0.463710i
$997$	472.423	−	472.423i	0.473845	−	0.473845i	−0.429312	−	0.903156i	$-0.641244\pi$
$997$	472.423	−	472.423i	0.473845	−	0.473845i	0.903156	+	0.429312i	$0.141244\pi$
$998$	−2223.70	−	2223.70i	−2.22816	−	2.22816i
$999$			85.7462i			0.0858320i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.3.c.a.17.4	yes	8
3.2	odd	2		261.3.f.a.46.1		8
4.3	odd	2		464.3.l.c.17.4		8
29.12	odd	4	inner	29.3.c.a.12.4	✓	8
87.41	even	4		261.3.f.a.244.1		8
116.99	even	4		464.3.l.c.273.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.3.c.a.12.4	✓	8	29.12	odd	4	inner
29.3.c.a.17.4	yes	8	1.1	even	1	trivial
261.3.f.a.46.1		8	3.2	odd	2
261.3.f.a.244.1		8	87.41	even	4
464.3.l.c.17.4		8	4.3	odd	2
464.3.l.c.273.4		8	116.99	even	4

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:	\( N \)	\(=\)	\( 29 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	29.c (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.62492 - 2.62492i) q^{2} +(-3.11190 + 3.11190i) q^{3} -9.78036i q^{4} +4.53053i q^{5} +16.3369i q^{6} -0.745339 q^{7} +(-15.1730 - 15.1730i) q^{8} -10.3678i q^{9} +O(q^{10})\)	\(q+(2.62492 - 2.62492i) q^{2} +(-3.11190 + 3.11190i) q^{3} -9.78036i q^{4} +4.53053i q^{5} +16.3369i q^{6} -0.745339 q^{7} +(-15.1730 - 15.1730i) q^{8} -10.3678i q^{9} +(11.8923 + 11.8923i) q^{10} +(0.0423096 - 0.0423096i) q^{11} +(30.4355 + 30.4355i) q^{12} -8.30191i q^{13} +(-1.95645 + 1.95645i) q^{14} +(-14.0985 - 14.0985i) q^{15} -40.5340 q^{16} +(15.2625 - 15.2625i) q^{17} +(-27.2146 - 27.2146i) q^{18} +(-25.1348 + 25.1348i) q^{19} +44.3102 q^{20} +(2.31942 - 2.31942i) q^{21} -0.222118i q^{22} +8.64367 q^{23} +94.4333 q^{24} +4.47430 q^{25} +(-21.7918 - 21.7918i) q^{26} +(4.25644 + 4.25644i) q^{27} +7.28968i q^{28} +(22.0908 + 18.7882i) q^{29} -74.0149 q^{30} +(-5.09325 + 5.09325i) q^{31} +(-45.7065 + 45.7065i) q^{32} +0.263326i q^{33} -80.1256i q^{34} -3.37678i q^{35} -101.401 q^{36} +(10.0725 + 10.0725i) q^{37} +131.953i q^{38} +(25.8347 + 25.8347i) q^{39} +(68.7415 - 68.7415i) q^{40} +(2.50571 + 2.50571i) q^{41} -12.1765i q^{42} +(-11.2668 + 11.2668i) q^{43} +(-0.413803 - 0.413803i) q^{44} +46.9716 q^{45} +(22.6889 - 22.6889i) q^{46} +(-23.0132 - 23.0132i) q^{47} +(126.138 - 126.138i) q^{48} -48.4445 q^{49} +(11.7447 - 11.7447i) q^{50} +94.9907i q^{51} -81.1956 q^{52} -42.8979 q^{53} +22.3456 q^{54} +(0.191685 + 0.191685i) q^{55} +(11.3090 + 11.3090i) q^{56} -156.434i q^{57} +(107.304 - 8.66900i) q^{58} +106.413 q^{59} +(-137.889 + 137.889i) q^{60} +(-42.3211 + 42.3211i) q^{61} +26.7387i q^{62} +7.72752i q^{63} +77.8154i q^{64} +37.6120 q^{65} +(0.691208 + 0.691208i) q^{66} -75.7926i q^{67} +(-149.273 - 149.273i) q^{68} +(-26.8982 + 26.8982i) q^{69} +(-8.86376 - 8.86376i) q^{70} -71.2051i q^{71} +(-157.310 + 157.310i) q^{72} +(-73.7928 - 73.7928i) q^{73} +52.8790 q^{74} +(-13.9236 + 13.9236i) q^{75} +(245.827 + 245.827i) q^{76} +(-0.0315350 + 0.0315350i) q^{77} +135.628 q^{78} +(-78.7399 + 78.7399i) q^{79} -183.641i q^{80} +66.8190 q^{81} +13.1546 q^{82} +15.1749 q^{83} +(-22.6847 - 22.6847i) q^{84} +(69.1473 + 69.1473i) q^{85} +59.1487i q^{86} +(-127.211 + 10.2773i) q^{87} -1.28392 q^{88} +(-22.8417 + 22.8417i) q^{89} +(123.296 - 123.296i) q^{90} +6.18773i q^{91} -84.5382i q^{92} -31.6993i q^{93} -120.816 q^{94} +(-113.874 - 113.874i) q^{95} -284.468i q^{96} +(42.8298 + 42.8298i) q^{97} +(-127.163 + 127.163i) q^{98} +(-0.438657 - 0.438657i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{2} - 2 q^{3} - 4 q^{7} - 42 q^{8}+O(q^{10}) \) 8 * q + 2 * q^2 - 2 * q^3 - 4 * q^7 - 42 * q^8	\( 8 q + 2 q^{2} - 2 q^{3} - 4 q^{7} - 42 q^{8} + 6 q^{10} - 6 q^{11} + 54 q^{12} - 40 q^{14} - 10 q^{15} - 32 q^{16} + 12 q^{17} + 20 q^{18} - 16 q^{19} + 108 q^{20} - 36 q^{21} + 168 q^{24} + 104 q^{25} - 54 q^{26} - 98 q^{27} + 128 q^{29} - 220 q^{30} - 10 q^{31} - 106 q^{32} - 252 q^{36} - 84 q^{37} - 90 q^{39} + 226 q^{40} + 20 q^{41} - 190 q^{43} + 42 q^{44} + 292 q^{45} + 12 q^{46} + 58 q^{47} + 354 q^{48} - 72 q^{49} - 60 q^{50} - 144 q^{52} + 252 q^{53} + 400 q^{54} - 74 q^{55} - 192 q^{56} + 326 q^{58} - 40 q^{59} - 258 q^{60} - 208 q^{61} + 36 q^{65} - 414 q^{66} - 296 q^{68} + 120 q^{69} + 44 q^{70} - 636 q^{72} - 188 q^{73} - 64 q^{74} - 12 q^{75} + 592 q^{76} + 180 q^{77} + 600 q^{78} - 382 q^{79} - 124 q^{81} + 228 q^{82} + 280 q^{83} - 124 q^{84} + 32 q^{85} + 34 q^{87} + 20 q^{88} - 64 q^{89} + 128 q^{90} - 460 q^{94} - 380 q^{95} - 44 q^{97} - 66 q^{98} + 552 q^{99}+O(q^{100}) \) 8 * q + 2 * q^2 - 2 * q^3 - 4 * q^7 - 42 * q^8 + 6 * q^10 - 6 * q^11 + 54 * q^12 - 40 * q^14 - 10 * q^15 - 32 * q^16 + 12 * q^17 + 20 * q^18 - 16 * q^19 + 108 * q^20 - 36 * q^21 + 168 * q^24 + 104 * q^25 - 54 * q^26 - 98 * q^27 + 128 * q^29 - 220 * q^30 - 10 * q^31 - 106 * q^32 - 252 * q^36 - 84 * q^37 - 90 * q^39 + 226 * q^40 + 20 * q^41 - 190 * q^43 + 42 * q^44 + 292 * q^45 + 12 * q^46 + 58 * q^47 + 354 * q^48 - 72 * q^49 - 60 * q^50 - 144 * q^52 + 252 * q^53 + 400 * q^54 - 74 * q^55 - 192 * q^56 + 326 * q^58 - 40 * q^59 - 258 * q^60 - 208 * q^61 + 36 * q^65 - 414 * q^66 - 296 * q^68 + 120 * q^69 + 44 * q^70 - 636 * q^72 - 188 * q^73 - 64 * q^74 - 12 * q^75 + 592 * q^76 + 180 * q^77 + 600 * q^78 - 382 * q^79 - 124 * q^81 + 228 * q^82 + 280 * q^83 - 124 * q^84 + 32 * q^85 + 34 * q^87 + 20 * q^88 - 64 * q^89 + 128 * q^90 - 460 * q^94 - 380 * q^95 - 44 * q^97 - 66 * q^98 + 552 * q^99

Introduction

L-functions

Modular forms

Varieties

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