LMFDB - Embedded newform 29.3.f.a.27.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [29,3,Mod(2,29)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(29, base_ring=CyclotomicField(28))

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("29.2");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 29 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	29.f (of order $28$, degree $12$, 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:	$48$
Relative dimension:	$4$ over $\Q(\zeta_{28})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{28}]$

Embedding invariants

Embedding label			27.3
Character	$\chi$	$=$	29.27
Dual form			29.3.f.a.14.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0361447 + 0.320793i) q^{2} +(-2.40292 + 3.82423i) q^{3} +(3.79811 + 0.866894i) q^{4} +(1.11585 - 0.889864i) q^{5} +(-1.13993 - 0.909068i) q^{6} +(-2.06382 - 9.04217i) q^{7} +(-0.841863 + 2.40591i) q^{8} +(-4.94574 - 10.2699i) q^{9} +O(q^{10})$	\(q+(-0.0361447 + 0.320793i) q^{2} +(-2.40292 + 3.82423i) q^{3} +(3.79811 + 0.866894i) q^{4} +(1.11585 - 0.889864i) q^{5} +(-1.13993 - 0.909068i) q^{6} +(-2.06382 - 9.04217i) q^{7} +(-0.841863 + 2.40591i) q^{8} +(-4.94574 - 10.2699i) q^{9} +(0.245130 + 0.390122i) q^{10} +(3.02175 + 8.63567i) q^{11} +(-12.4418 + 12.4418i) q^{12} +(7.25544 - 15.0661i) q^{13} +(2.97526 - 0.335232i) q^{14} +(0.721732 + 6.40555i) q^{15} +(13.2986 + 6.40425i) q^{16} +(-13.4875 - 13.4875i) q^{17} +(3.47329 - 1.21536i) q^{18} +(-6.13512 + 3.85495i) q^{19} +(5.00955 - 2.41247i) q^{20} +(39.5385 + 13.8351i) q^{21} +(-2.87949 + 0.657224i) q^{22} +(-26.9938 + 33.8491i) q^{23} +(-7.17780 - 9.00068i) q^{24} +(-5.10975 + 22.3873i) q^{25} +(4.57085 + 2.87206i) q^{26} +(10.7659 + 1.21302i) q^{27} -36.1322i q^{28} +(8.81918 - 27.6265i) q^{29} -2.08095 q^{30} +(2.27501 - 20.1913i) q^{31} +(-7.95959 + 12.6676i) q^{32} +(-40.2858 - 9.19497i) q^{33} +(4.81419 - 3.83919i) q^{34} +(-10.3492 - 8.25322i) q^{35} +(-9.88152 - 43.2937i) q^{36} +(5.54261 - 15.8399i) q^{37} +(-1.01489 - 2.10744i) q^{38} +(40.1818 + 63.9490i) q^{39} +(1.20153 + 3.43378i) q^{40} +(-11.0137 + 11.0137i) q^{41} +(-5.86733 + 12.1836i) q^{42} +(-1.43070 + 0.161201i) q^{43} +(3.99073 + 35.4187i) q^{44} +(-14.6576 - 7.05871i) q^{45} +(-9.88290 - 9.88290i) q^{46} +(52.6538 - 18.4244i) q^{47} +(-56.4467 + 35.4678i) q^{48} +(-33.3540 + 16.0624i) q^{49} +(-6.99700 - 2.44836i) q^{50} +(83.9885 - 19.1698i) q^{51} +(40.6176 - 50.9329i) q^{52} +(26.2579 + 32.9263i) q^{53} +(-0.778260 + 3.40978i) q^{54} +(11.0564 + 6.94719i) q^{55} +(23.4920 + 2.64692i) q^{56} -32.7252i q^{57} +(8.54363 + 3.82769i) q^{58} -40.0225 q^{59} +(-2.81171 + 24.9547i) q^{60} +(-31.5754 + 50.2519i) q^{61} +(6.39500 + 1.45962i) q^{62} +(-82.6553 + 65.9154i) q^{63} +(42.3842 + 33.8003i) q^{64} +(-5.31074 - 23.2679i) q^{65} +(4.40581 - 12.5911i) q^{66} +(27.0064 + 56.0793i) q^{67} +(-39.5347 - 62.9191i) q^{68} +(-64.5829 - 184.567i) q^{69} +(3.02165 - 3.02165i) q^{70} +(16.5027 - 34.2683i) q^{71} +(28.8721 - 3.25311i) q^{72} +(10.1706 + 90.2664i) q^{73} +(4.88099 + 2.35056i) q^{74} +(-73.3358 - 73.3358i) q^{75} +(-26.6437 + 9.32302i) q^{76} +(71.8488 - 45.1456i) q^{77} +(-21.9668 + 10.5787i) q^{78} +(-68.6869 - 24.0346i) q^{79} +(20.5381 - 4.68770i) q^{80} +(33.4546 - 41.9508i) q^{81} +(-3.13504 - 3.93121i) q^{82} +(14.4041 - 63.1083i) q^{83} +(138.178 + 86.8230i) q^{84} +(-27.0520 - 3.04803i) q^{85} -0.464786i q^{86} +(84.4582 + 100.111i) q^{87} -23.3205 q^{88} +(-3.18582 + 28.2750i) q^{89} +(2.79418 - 4.44691i) q^{90} +(-151.204 - 34.5113i) q^{91} +(-131.869 + 105.162i) q^{92} +(71.7494 + 57.2182i) q^{93} +(4.00726 + 17.5569i) q^{94} +(-3.41551 + 9.76097i) q^{95} +(-29.3176 - 60.8786i) q^{96} +(59.0040 + 93.9044i) q^{97} +(-3.94715 - 11.2803i) q^{98} +(73.7429 - 73.7429i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 16 q^{2} - 12 q^{3} - 14 q^{4} - 14 q^{5} - 14 q^{6} - 10 q^{7} + 28 q^{8} - 14 q^{9}+O(q^{10}) $ 48 * q - 16 * q^2 - 12 * q^3 - 14 * q^4 - 14 * q^5 - 14 * q^6 - 10 * q^7 + 28 * q^8 - 14 * q^9	\( 48 q - 16 q^{2} - 12 q^{3} - 14 q^{4} - 14 q^{5} - 14 q^{6} - 10 q^{7} + 28 q^{8} - 14 q^{9} - 20 q^{10} - 8 q^{11} - 68 q^{12} - 14 q^{13} + 26 q^{14} - 4 q^{15} + 18 q^{16} - 26 q^{17} - 34 q^{18} + 2 q^{19} + 46 q^{20} + 218 q^{21} + 154 q^{22} + 56 q^{23} + 154 q^{24} - 34 q^{25} + 110 q^{26} + 126 q^{27} - 170 q^{29} + 24 q^{30} - 88 q^{31} - 132 q^{32} - 224 q^{33} - 224 q^{34} - 210 q^{35} - 434 q^{36} - 56 q^{37} - 294 q^{38} - 232 q^{39} - 492 q^{40} - 34 q^{41} - 14 q^{42} + 176 q^{43} + 126 q^{44} + 114 q^{45} + 744 q^{46} + 208 q^{47} + 640 q^{48} + 506 q^{49} + 732 q^{50} + 322 q^{51} + 690 q^{52} - 14 q^{53} - 36 q^{54} + 284 q^{55} + 332 q^{56} - 508 q^{58} - 44 q^{59} - 316 q^{60} - 30 q^{61} - 504 q^{62} - 686 q^{63} - 896 q^{64} - 554 q^{65} - 608 q^{66} - 574 q^{67} - 796 q^{68} - 806 q^{69} - 1066 q^{70} + 224 q^{71} + 748 q^{72} - 22 q^{73} + 820 q^{74} + 768 q^{75} + 514 q^{76} + 436 q^{77} + 282 q^{78} + 564 q^{79} + 1162 q^{80} + 670 q^{81} - 18 q^{82} - 126 q^{83} + 572 q^{84} + 38 q^{85} - 118 q^{87} - 384 q^{88} - 160 q^{89} - 828 q^{90} - 434 q^{91} - 1022 q^{92} - 406 q^{93} - 2 q^{94} - 642 q^{95} - 1176 q^{96} + 604 q^{97} - 102 q^{98} + 316 q^{99}+O(q^{100}) \) 48 * q - 16 * q^2 - 12 * q^3 - 14 * q^4 - 14 * q^5 - 14 * q^6 - 10 * q^7 + 28 * q^8 - 14 * q^9 - 20 * q^10 - 8 * q^11 - 68 * q^12 - 14 * q^13 + 26 * q^14 - 4 * q^15 + 18 * q^16 - 26 * q^17 - 34 * q^18 + 2 * q^19 + 46 * q^20 + 218 * q^21 + 154 * q^22 + 56 * q^23 + 154 * q^24 - 34 * q^25 + 110 * q^26 + 126 * q^27 - 170 * q^29 + 24 * q^30 - 88 * q^31 - 132 * q^32 - 224 * q^33 - 224 * q^34 - 210 * q^35 - 434 * q^36 - 56 * q^37 - 294 * q^38 - 232 * q^39 - 492 * q^40 - 34 * q^41 - 14 * q^42 + 176 * q^43 + 126 * q^44 + 114 * q^45 + 744 * q^46 + 208 * q^47 + 640 * q^48 + 506 * q^49 + 732 * q^50 + 322 * q^51 + 690 * q^52 - 14 * q^53 - 36 * q^54 + 284 * q^55 + 332 * q^56 - 508 * q^58 - 44 * q^59 - 316 * q^60 - 30 * q^61 - 504 * q^62 - 686 * q^63 - 896 * q^64 - 554 * q^65 - 608 * q^66 - 574 * q^67 - 796 * q^68 - 806 * q^69 - 1066 * q^70 + 224 * q^71 + 748 * q^72 - 22 * q^73 + 820 * q^74 + 768 * q^75 + 514 * q^76 + 436 * q^77 + 282 * q^78 + 564 * q^79 + 1162 * q^80 + 670 * q^81 - 18 * q^82 - 126 * q^83 + 572 * q^84 + 38 * q^85 - 118 * q^87 - 384 * q^88 - 160 * q^89 - 828 * q^90 - 434 * q^91 - 1022 * q^92 - 406 * q^93 - 2 * q^94 - 642 * q^95 - 1176 * q^96 + 604 * q^97 - 102 * q^98 + 316 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{15}{28}\right)$

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 $

$2$	−0.0361447	+	0.320793i	−0.0180724	+	0.160397i	−0.999507	−	0.0314009i	$-0.990003\pi$
$2$	−0.0361447	+	0.320793i	−0.0180724	+	0.160397i	0.981434	+	0.191798i	$0.0614317\pi$
$3$	−2.40292	+	3.82423i	−0.800974	+	1.27474i	0.156917	+	0.987612i	$0.449844\pi$
$3$	−2.40292	+	3.82423i	−0.800974	+	1.27474i	−0.957891	+	0.287131i	$0.907298\pi$
$4$	3.79811	+	0.866894i	0.949527	+	0.216723i
$5$	1.11585	−	0.889864i	0.223171	−	0.177973i	−0.505522	−	0.862814i	$-0.668700\pi$
$5$	1.11585	−	0.889864i	0.223171	−	0.177973i	0.728692	+	0.684841i	$0.240128\pi$
$6$	−1.13993	−	0.909068i	−0.189989	−	0.151511i
$7$	−2.06382	−	9.04217i	−0.294831	−	1.29174i	−0.877715	−	0.479183i	$-0.840933\pi$
$7$	−2.06382	−	9.04217i	−0.294831	−	1.29174i	0.582884	−	0.812555i	$-0.301924\pi$
$8$	−0.841863	+	2.40591i	−0.105233	+	0.300738i
$9$	−4.94574	−	10.2699i	−0.549526	−	1.14110i
$10$	0.245130	+	0.390122i	0.0245130	+	0.0390122i
$11$	3.02175	+	8.63567i	0.274705	+	0.785061i	0.995744	+	0.0921662i	$0.0293791\pi$
$11$	3.02175	+	8.63567i	0.274705	+	0.785061i	−0.721039	+	0.692894i	$0.756335\pi$
$12$	−12.4418	+	12.4418i	−1.03681	+	1.03681i
$13$	7.25544	−	15.0661i	0.558110	−	1.15893i	−0.410848	−	0.911704i	$-0.634767\pi$
$13$	7.25544	−	15.0661i	0.558110	−	1.15893i	0.968958	−	0.247224i	$-0.0795185\pi$
$14$	2.97526	−	0.335232i	0.212519	−	0.0239451i
$15$	0.721732	+	6.40555i	0.0481155	+	0.427037i
$16$	13.2986	+	6.40425i	0.831160	+	0.400265i
$17$	−13.4875	−	13.4875i	−0.793380	−	0.793380i	0.188662	−	0.982042i	$-0.439585\pi$
$17$	−13.4875	−	13.4875i	−0.793380	−	0.793380i	−0.982042	+	0.188662i	$0.939585\pi$
$18$	3.47329	−	1.21536i	0.192960	−	0.0675198i
$19$	−6.13512	+	3.85495i	−0.322901	+	0.202892i	−0.683721	−	0.729743i	$-0.739640\pi$
$19$	−6.13512	+	3.85495i	−0.322901	+	0.202892i	0.360820	+	0.932635i	$0.382497\pi$
$20$	5.00955	−	2.41247i	0.250478	−	0.120624i
$21$	39.5385	+	13.8351i	1.88279	+	0.658815i
$22$	−2.87949	+	0.657224i	−0.130886	+	0.0298738i
$23$	−26.9938	+	33.8491i	−1.17364	+	1.47170i	−0.322654	+	0.946517i	$0.604575\pi$
$23$	−26.9938	+	33.8491i	−1.17364	+	1.47170i	−0.850988	+	0.525184i	$0.823996\pi$
$24$	−7.17780	−	9.00068i	−0.299075	−	0.375028i
$25$	−5.10975	+	22.3873i	−0.204390	+	0.895491i
$26$	4.57085	+	2.87206i	0.175802	+	0.110464i
$27$	10.7659	+	1.21302i	0.398736	+	0.0449268i
$28$		−	36.1322i		−	1.29044i
$29$	8.81918	−	27.6265i	0.304110	−	0.952637i
$29$	8.81918	−	27.6265i	0.304110	−	0.952637i
$30$	−2.08095			−0.0693649
$31$	2.27501	−	20.1913i	0.0733874	−	0.651331i	−0.902138	−	0.431447i	$-0.858003\pi$
$31$	2.27501	−	20.1913i	0.0733874	−	0.651331i	0.975526	−	0.219885i	$-0.0705681\pi$
$32$	−7.95959	+	12.6676i	−0.248737	+	0.395863i
$33$	−40.2858	−	9.19497i	−1.22078	−	0.278635i
$34$	4.81419	−	3.83919i	0.141594	−	0.112917i
$35$	−10.3492	−	8.25322i	−0.295692	−	0.235806i
$36$	−9.88152	−	43.2937i	−0.274487	−	1.20260i
$37$	5.54261	−	15.8399i	0.149800	−	0.428104i	−0.844392	−	0.535726i	$-0.820038\pi$
$37$	5.54261	−	15.8399i	0.149800	−	0.428104i	0.994192	+	0.107622i	$0.0343236\pi$
$38$	−1.01489	−	2.10744i	−0.0267076	−	0.0554590i
$39$	40.1818	+	63.9490i	1.03030	+	1.63972i
$40$	1.20153	+	3.43378i	0.0300383	+	0.0858445i
$41$	−11.0137	+	11.0137i	−0.268627	+	0.268627i	−0.828547	−	0.559920i	$-0.810832\pi$
$41$	−11.0137	+	11.0137i	−0.268627	+	0.268627i	0.559920	+	0.828547i	$0.310832\pi$
$42$	−5.86733	+	12.1836i	−0.139698	+	0.290086i
$43$	−1.43070	+	0.161201i	−0.0332721	+	0.00374887i	−0.128585	−	0.991699i	$-0.541043\pi$
$43$	−1.43070	+	0.161201i	−0.0332721	+	0.00374887i	0.0953127	+	0.995447i	$0.469615\pi$
$44$	3.99073	+	35.4187i	0.0906985	+	0.804971i
$45$	−14.6576	−	7.05871i	−0.325723	−	0.156860i
$46$	−9.88290	−	9.88290i	−0.214846	−	0.214846i
$47$	52.6538	−	18.4244i	1.12029	−	0.392008i	0.294314	−	0.955709i	$-0.404909\pi$
$47$	52.6538	−	18.4244i	1.12029	−	0.392008i	0.825979	+	0.563701i	$0.190623\pi$
$48$	−56.4467	+	35.4678i	−1.17597	+	0.738913i
$49$	−33.3540	+	16.0624i	−0.680693	+	0.327805i
$50$	−6.99700	−	2.44836i	−0.139940	−	0.0489671i
$51$	83.9885	−	19.1698i	1.64683	−	0.375879i
$52$	40.6176	−	50.9329i	0.781108	−	0.979479i
$53$	26.2579	+	32.9263i	0.495432	+	0.621252i	0.965192	−	0.261542i	$-0.0842311\pi$
$53$	26.2579	+	32.9263i	0.495432	+	0.621252i	−0.469760	+	0.882794i	$0.655660\pi$
$54$	−0.778260	+	3.40978i	−0.0144122	+	0.0631441i
$55$	11.0564	+	6.94719i	0.201025	+	0.126313i
$56$	23.4920	+	2.64692i	0.419501	+	0.0472664i
$57$		−	32.7252i		−	0.574127i
$58$	8.54363	+	3.82769i	0.147304	+	0.0659946i
$59$	−40.0225			−0.678348			−0.339174	−	0.940724i	$-0.610147\pi$
$59$	−40.0225			−0.678348			−0.339174	+	0.940724i	$0.610147\pi$
$60$	−2.81171	+	24.9547i	−0.0468619	+	0.415911i
$61$	−31.5754	+	50.2519i	−0.517629	+	0.823802i	−0.998598	−	0.0529356i	$-0.983142\pi$
$61$	−31.5754	+	50.2519i	−0.517629	+	0.823802i	0.480969	+	0.876738i	$0.340285\pi$
$62$	6.39500	+	1.45962i	0.103145	+	0.0235422i
$63$	−82.6553	+	65.9154i	−1.31199	+	1.04628i
$64$	42.3842	+	33.8003i	0.662253	+	0.528129i
$65$	−5.31074	−	23.2679i	−0.0817037	−	0.357967i
$66$	4.40581	−	12.5911i	0.0667546	−	0.190774i
$67$	27.0064	+	56.0793i	0.403080	+	0.837004i	0.999413	+	0.0342668i	$0.0109096\pi$
$67$	27.0064	+	56.0793i	0.403080	+	0.837004i	−0.596333	+	0.802737i	$0.703376\pi$
$68$	−39.5347	−	62.9191i	−0.581392	−	0.925280i
$69$	−64.5829	−	184.567i	−0.935984	−	2.67489i
$70$	3.02165	−	3.02165i	0.0431664	−	0.0431664i
$71$	16.5027	−	34.2683i	0.232433	−	0.482652i	−0.751831	−	0.659356i	$-0.770829\pi$
$71$	16.5027	−	34.2683i	0.232433	−	0.482652i	0.984264	+	0.176704i	$0.0565434\pi$
$72$	28.8721	−	3.25311i	0.401002	−	0.0451820i
$73$	10.1706	+	90.2664i	0.139323	+	1.23653i	0.847617	+	0.530609i	$0.178037\pi$
$73$	10.1706	+	90.2664i	0.139323	+	1.23653i	−0.708294	+	0.705918i	$0.750535\pi$
$74$	4.88099	+	2.35056i	0.0659593	+	0.0317643i
$75$	−73.3358	−	73.3358i	−0.977810	−	0.977810i
$76$	−26.6437	+	9.32302i	−0.350575	+	0.122671i
$77$	71.8488	−	45.1456i	0.933101	−	0.586306i
$78$	−21.9668	+	10.5787i	−0.281626	+	0.135624i
$79$	−68.6869	−	24.0346i	−0.869454	−	0.304235i	−0.141564	−	0.989929i	$-0.545213\pi$
$79$	−68.6869	−	24.0346i	−0.869454	−	0.304235i	−0.727890	+	0.685694i	$0.759499\pi$
$80$	20.5381	−	4.68770i	0.256727	−	0.0585962i
$81$	33.4546	−	41.9508i	0.413020	−	0.517911i
$82$	−3.13504	−	3.93121i	−0.0382321	−	0.0479416i
$83$	14.4041	−	63.1083i	0.173543	−	0.760341i	−0.810978	−	0.585076i	$-0.801065\pi$
$83$	14.4041	−	63.1083i	0.173543	−	0.760341i	0.984521	−	0.175265i	$-0.0560782\pi$
$84$	138.178	+	86.8230i	1.64498	+	1.03361i
$85$	−27.0520	−	3.04803i	−0.318259	−	0.0358592i
$86$		−	0.464786i		−	0.00540449i
$87$	84.4582	+	100.111i	0.970784	+	1.15070i
$88$	−23.3205			−0.265006
$89$	−3.18582	+	28.2750i	−0.0357958	+	0.317696i	0.963036	+	0.269373i	$0.0868164\pi$
$89$	−3.18582	+	28.2750i	−0.0357958	+	0.317696i	−0.998832	+	0.0483234i	$0.984612\pi$
$90$	2.79418	−	4.44691i	0.0310465	−	0.0494101i
$91$	−151.204	−	34.5113i	−1.66158	−	0.379245i
$92$	−131.869	+	105.162i	−1.43336	+	1.14306i
$93$	71.7494	+	57.2182i	0.771499	+	0.615250i
$94$	4.00726	+	17.5569i	0.0426304	+	0.186776i
$95$	−3.41551	+	9.76097i	−0.0359528	+	0.102747i
$96$	−29.3176	−	60.8786i	−0.305392	−	0.634152i
$97$	59.0040	+	93.9044i	0.608289	+	0.968086i	0.998870	+	0.0475179i	$0.0151311\pi$
$97$	59.0040	+	93.9044i	0.608289	+	0.968086i	−0.390581	+	0.920568i	$0.627726\pi$
$98$	−3.94715	−	11.2803i	−0.0402770	−	0.115105i
$99$	73.7429	−	73.7429i	0.744878	−	0.744878i
$100$	−38.8148	+	80.5997i	−0.388148	+	0.805997i
$101$	81.6300	−	9.19750i	0.808218	−	0.0910643i	0.301821	−	0.953365i	$-0.402406\pi$
$101$	81.6300	−	9.19750i	0.808218	−	0.0910643i	0.506397	+	0.862300i	$0.330977\pi$
$102$	3.11381	+	27.6358i	0.0305276	+	0.270940i
$103$	−33.0306	−	15.9067i	−0.320686	−	0.154434i	0.266614	−	0.963803i	$-0.414095\pi$
$103$	−33.0306	−	15.9067i	−0.320686	−	0.154434i	−0.587300	+	0.809369i	$0.699809\pi$
$104$	30.1395	+	30.1395i	0.289802	+	0.289802i
$105$	56.4306	−	19.7459i	0.537434	−	0.188056i
$106$	−11.5116	+	7.23324i	−0.108600	+	0.0682381i
$107$	58.0912	−	27.9752i	0.542908	−	0.261451i	−0.142268	−	0.989828i	$-0.545439\pi$
$107$	58.0912	−	27.9752i	0.542908	−	0.261451i	0.685176	+	0.728377i	$0.259725\pi$
$108$	39.8384	+	13.9401i	0.368874	+	0.129075i
$109$	47.8026	−	10.9106i	0.438556	−	0.100098i	0.00245858	−	0.999997i	$-0.499217\pi$
$109$	47.8026	−	10.9106i	0.438556	−	0.100098i	0.436098	+	0.899899i	$0.356360\pi$
$110$	−2.62825	+	3.29572i	−0.0238931	+	0.0299610i
$111$	47.2568	+	59.2581i	0.425737	+	0.533857i
$112$	30.4625	−	133.465i	0.271987	−	1.19165i
$113$	−168.394	−	105.809i	−1.49021	−	0.936361i	−0.997820	−	0.0659868i	$-0.978980\pi$
$113$	−168.394	−	105.809i	−1.49021	−	0.936361i	−0.492390	−	0.870375i	$-0.663877\pi$
$114$	10.4980	+	1.18284i	0.0920881	+	0.0103758i
$115$			61.7915i			0.537317i
$116$	57.4454	−	97.2831i	0.495219	−	0.838647i
$117$	−190.611			−1.62915
$118$	1.44660	−	12.8390i	0.0122594	−	0.108805i
$119$	−94.1202	+	149.791i	−0.790926	+	1.25875i
$120$	−16.0188	−	3.65618i	−0.133490	−	0.0304681i
$121$	29.1579	−	23.2526i	0.240974	−	0.192170i
$122$	−14.9792	−	11.9455i	−0.122780	−	0.0979141i
$123$	−15.6538	−	68.5840i	−0.127267	−	0.557593i
$124$	26.1444	−	74.7165i	0.210842	−	0.602552i
$125$	29.7012	+	61.6752i	0.237610	+	0.493401i
$126$	−18.1577	−	28.8978i	−0.144109	−	0.229347i
$127$	−2.18644	−	6.24848i	−0.0172161	−	0.0492007i	0.934955	−	0.354767i	$-0.115440\pi$
$127$	−2.18644	−	6.24848i	−0.0172161	−	0.0492007i	−0.952171	+	0.305567i	$0.901154\pi$
$128$	−54.6902	+	54.6902i	−0.427267	+	0.427267i
$129$	2.82139	−	5.85868i	0.0218713	−	0.0454162i
$130$	7.65614	−	0.862640i	0.0588934	−	0.00663569i
$131$	−9.20832	−	81.7261i	−0.0702925	−	0.623863i	−0.978631	−	0.205627i	$-0.934077\pi$
$131$	−9.20832	−	81.7261i	−0.0702925	−	0.623863i	0.908338	−	0.418237i	$-0.137352\pi$
$132$	−145.039	−	69.8470i	−1.09878	−	0.529144i
$133$	47.5188	+	47.5188i	0.357284	+	0.357284i
$134$	−18.9660	+	6.63649i	−0.141537	+	0.0495261i
$135$	13.0926	−	8.22661i	0.0969821	−	0.0609379i
$136$	43.8041	−	21.0950i	0.322089	−	0.155110i
$137$	54.9656	+	19.2333i	0.401209	+	0.140389i	0.523338	−	0.852125i	$-0.324686\pi$
$137$	54.9656	+	19.2333i	0.401209	+	0.140389i	−0.122129	+	0.992514i	$0.538972\pi$
$138$	61.5423	−	14.0466i	0.445959	−	0.101787i
$139$	−12.9334	+	16.2180i	−0.0930462	+	0.116676i	−0.826175	−	0.563414i	$-0.809488\pi$
$139$	−12.9334	+	16.2180i	−0.0930462	+	0.116676i	0.733129	+	0.680090i	$0.238059\pi$
$140$	−32.1528	−	40.3183i	−0.229663	−	0.287988i
$141$	−56.0640	+	245.632i	−0.397617	+	1.74207i
$142$	10.3966	+	6.53259i	0.0732152	+	0.0460042i
$143$	152.030	+	17.1296i	1.06314	+	0.119788i
$144$		−	168.249i		−	1.16840i
$145$	−14.7429	−	38.6750i	−0.101675	−	0.266724i
$146$	−29.3245			−0.200853
$147$	18.7206	−	166.150i	0.127351	−	1.13027i
$148$	34.7829	−	55.3567i	0.235020	−	0.374032i
$149$	59.1793	+	13.5073i	0.397177	+	0.0906530i	0.416444	−	0.909161i	$-0.363276\pi$
$149$	59.1793	+	13.5073i	0.397177	+	0.0906530i	−0.0192673	+	0.999814i	$0.506133\pi$
$150$	26.1763	−	20.8749i	0.174509	−	0.139166i
$151$	−68.4936	−	54.6219i	−0.453600	−	0.361734i	0.369880	−	0.929080i	$-0.379399\pi$
$151$	−68.4936	−	54.6219i	−0.453600	−	0.361734i	−0.823480	+	0.567346i	$0.807970\pi$
$152$	−4.10972	−	18.0058i	−0.0270376	−	0.118459i
$153$	−71.8098	+	205.221i	−0.469345	+	1.34131i
$154$	11.8855	+	24.6804i	0.0771783	+	0.160262i
$155$	−15.4289	−	24.5550i	−0.0995413	−	0.158419i
$156$	97.1780	+	277.719i	0.622936	+	1.78025i
$157$	−78.9251	+	78.9251i	−0.502708	+	0.502708i	−0.912278	−	0.409571i	$-0.865679\pi$
$157$	−78.9251	+	78.9251i	−0.502708	+	0.502708i	0.409571	+	0.912278i	$0.365679\pi$
$158$	10.1928	−	21.1656i	0.0645114	−	0.133959i
$159$	−189.013	+	21.2967i	−1.18876	+	0.133942i
$160$	2.39071	+	21.2182i	0.0149420	+	0.132614i
$161$	361.780	+	174.224i	2.24708	+	1.08214i
$162$	12.2483	+	12.2483i	0.0756070	+	0.0756070i
$163$	262.325	−	91.7915i	1.60936	−	0.563138i	0.632042	−	0.774934i	$-0.282217\pi$
$163$	262.325	−	91.7915i	1.60936	−	0.563138i	0.977314	+	0.211796i	$0.0679311\pi$
$164$	−51.3789	+	32.2835i	−0.313286	+	0.196851i
$165$	−53.1353	+	25.5886i	−0.322032	+	0.155083i
$166$	19.7241	+	6.90176i	0.118820	+	0.0415769i
$167$	−285.956	+	65.2676i	−1.71231	+	0.390824i	−0.962597	−	0.270937i	$-0.912666\pi$
$167$	−285.956	+	65.2676i	−1.71231	+	0.390824i	−0.749715	+	0.661761i	$0.769809\pi$
$168$	−66.5720	+	83.4786i	−0.396262	+	0.496897i
$169$	−68.9753	−	86.4923i	−0.408138	−	0.511789i
$170$	1.95558	−	8.56795i	0.0115034	−	0.0503997i
$171$	69.9327	+	43.9416i	0.408963	+	0.256969i
$172$	−5.57371	−	0.628006i	−0.0324053	−	0.00365120i
$173$			14.6046i			0.0844195i	0.999109	+	0.0422097i	$0.0134398\pi$
$173$			14.6046i			0.0844195i	−0.999109	+	0.0422097i	$0.986560\pi$
$174$	−35.1676	+	23.4752i	−0.202113	+	0.134915i
$175$	212.975			1.21700
$176$	−15.1200	+	134.194i	−0.0859092	+	0.762465i
$177$	96.1710	−	153.055i	0.543339	−	0.864719i
$178$	−8.95528	−	2.04398i	−0.0503105	−	0.0114831i
$179$	86.0623	−	68.6324i	0.480795	−	0.383421i	−0.352887	−	0.935666i	$-0.614800\pi$
$179$	86.0623	−	68.6324i	0.480795	−	0.383421i	0.833682	+	0.552245i	$0.186229\pi$
$180$	−49.5519	−	39.5163i	−0.275288	−	0.219535i
$181$	−17.4302	−	76.3667i	−0.0962995	−	0.421916i	0.903681	−	0.428207i	$-0.140855\pi$
$181$	−17.4302	−	76.3667i	−0.0962995	−	0.421916i	−0.999980	+	0.00629122i	$0.997997\pi$
$182$	16.5362	−	47.2578i	0.0908583	−	0.259658i
$183$	−116.302	−	241.503i	−0.635528	−	1.31969i
$184$	−58.7127	−	93.4408i	−0.319091	−	0.507830i
$185$	−7.91058	−	22.6071i	−0.0427599	−	0.122201i
$186$	−20.9486	+	20.9486i	−0.112627	+	0.112627i
$187$	75.7175	−	157.229i	0.404906	−	0.840797i
$188$	215.957	−	24.3325i	1.14871	−	0.129428i
$189$	−11.2504	−	99.8504i	−0.0595261	−	0.528309i
$190$	−3.00780	−	1.44848i	−0.0158305	−	0.00762359i
$191$	−187.870	−	187.870i	−0.983612	−	0.983612i	0.0162561	−	0.999868i	$-0.494825\pi$
$191$	−187.870	−	187.870i	−0.983612	−	0.983612i	−0.999868	+	0.0162561i	$0.994825\pi$
$192$	−231.106	+	80.8675i	−1.20368	+	0.421185i
$193$	−77.8526	+	48.9180i	−0.403381	+	0.253461i	−0.718409	−	0.695621i	$-0.755129\pi$
$193$	−77.8526	+	48.9180i	−0.403381	+	0.253461i	0.315027	+	0.949083i	$0.397986\pi$
$194$	−32.2566	+	15.5340i	−0.166271	+	0.0800719i
$195$	101.743	+	35.6014i	0.521759	+	0.182571i
$196$	−140.606	+	32.0925i	−0.717380	+	0.163737i
$197$	−102.116	+	128.049i	−0.518354	+	0.649995i	−0.970259	−	0.242071i	$-0.922173\pi$
$197$	−102.116	+	128.049i	−0.518354	+	0.649995i	0.451905	+	0.892066i	$0.350745\pi$
$198$	20.9908	+	26.3217i	0.106014	+	0.132938i
$199$	−44.0784	+	193.120i	−0.221499	+	0.970452i	0.734851	+	0.678229i	$0.237252\pi$
$199$	−44.0784	+	193.120i	−0.221499	+	0.970452i	−0.956350	+	0.292223i	$0.905605\pi$
$200$	−49.5600	−	31.1406i	−0.247800	−	0.155703i
$201$	−279.354	−	31.4757i	−1.38982	−	0.156595i
$202$			26.5188i			0.131281i
$203$	−268.004	−	22.7285i	−1.32022	−	0.111963i
$204$	335.616			1.64517
$205$	−2.48899	+	22.0904i	−0.0121414	+	0.107758i
$206$	6.29666	−	10.0211i	0.0305663	−	0.0486460i
$207$	481.132	+	109.815i	2.32431	+	0.530509i
$208$	192.974	−	153.891i	0.927758	−	0.739862i
$209$	−51.8288	−	41.3321i	−0.247985	−	0.197761i
$210$	4.29469	+	18.8163i	0.0204509	+	0.0896013i
$211$	63.5268	−	181.549i	0.301075	−	0.860423i	−0.689602	−	0.724189i	$-0.742214\pi$
$211$	63.5268	−	181.549i	0.301075	−	0.860423i	0.990677	−	0.136234i	$-0.0434998\pi$
$212$	71.1867	+	147.821i	0.335786	+	0.697267i
$213$	91.3950	+	145.454i	0.429085	+	0.682884i
$214$	6.87458	+	19.6464i	0.0321242	+	0.0918058i
$215$	−1.45301	+	1.45301i	−0.00675817	+	0.00675817i
$216$	−11.9818	+	24.8805i	−0.0554714	+	0.115187i
$217$	−187.268	+	21.1000i	−0.862986	+	0.0972352i
$218$	1.77225	+	15.7291i	0.00812957	+	0.0721520i
$219$	−369.639	−	178.009i	−1.68785	−	0.812824i
$220$	35.9709	+	35.9709i	0.163504	+	0.163504i
$221$	−301.060	+	105.346i	−1.36226	+	0.476677i
$222$	−20.7177	+	13.0178i	−0.0933230	+	0.0586387i
$223$	221.904	−	106.863i	0.995084	−	0.479207i	0.135817	−	0.990734i	$-0.456634\pi$
$223$	221.904	−	106.863i	0.995084	−	0.479207i	0.859267	+	0.511527i	$0.170920\pi$
$224$	130.970	+	45.8283i	0.584687	+	0.204591i
$225$	255.187	−	58.2448i	1.13417	−	0.258866i
$226$	40.0293	−	50.1952i	0.177121	−	0.222103i
$227$	−98.4607	−	123.466i	−0.433748	−	0.543902i	0.516136	−	0.856507i	$-0.327370\pi$
$227$	−98.4607	−	123.466i	−0.433748	−	0.543902i	−0.949883	+	0.312604i	$0.898799\pi$
$228$	28.3693	−	124.294i	0.124427	−	0.545149i
$229$	−67.0912	−	42.1562i	−0.292975	−	0.184088i	0.377522	−	0.926001i	$-0.376776\pi$
$229$	−67.0912	−	42.1562i	−0.292975	−	0.184088i	−0.670497	+	0.741912i	$0.733919\pi$
$230$	−19.8223	−	2.23344i	−0.0861839	−	0.00971059i
$231$			383.248i			1.65908i
$232$	59.0422	+	44.4758i	0.254492	+	0.191706i
$233$	266.277			1.14282			0.571409	−	0.820666i	$-0.306397\pi$
$233$	266.277			1.14282			0.571409	+	0.820666i	$0.306397\pi$
$234$	6.88958	−	61.1467i	0.0294427	−	0.261311i
$235$	42.3588	−	67.4136i	0.180250	−	0.286866i
$236$	−152.010	−	34.6953i	−0.644110	−	0.147014i
$237$	256.963	−	204.921i	1.08423	−	0.864646i
$238$	−44.6502	−	35.6073i	−0.187606	−	0.149611i
$239$	98.7830	+	432.796i	0.413318	+	1.81086i	0.568152	+	0.822924i	$0.307659\pi$
$239$	98.7830	+	432.796i	0.413318	+	1.81086i	−0.154834	+	0.987940i	$0.549484\pi$
$240$	−31.4247	+	89.8067i	−0.130936	+	0.374195i
$241$	−57.9406	−	120.315i	−0.240417	−	0.499232i	0.745491	−	0.666515i	$-0.232215\pi$
$241$	−57.9406	−	120.315i	−0.240417	−	0.499232i	−0.985909	+	0.167283i	$0.946501\pi$
$242$	6.40538	+	10.1941i	0.0264685	+	0.0421244i
$243$	112.245	+	320.777i	0.461913	+	1.32007i
$244$	−163.490	+	163.490i	−0.670040	+	0.670040i
$245$	−22.9248	+	47.6038i	−0.0935705	+	0.194301i
$246$	22.5671	−	2.54270i	0.0917361	−	0.0103362i
$247$	13.5660	+	120.401i	0.0549230	+	0.487455i
$248$	46.6630	+	22.4717i	0.188157	+	0.0906119i
$249$	206.729	+	206.729i	0.830236	+	0.830236i
$250$	−20.8585	+	7.29872i	−0.0834341	+	0.0291949i
$251$	157.929	−	99.2334i	0.629199	−	0.395352i	−0.179346	−	0.983786i	$-0.557398\pi$
$251$	157.929	−	99.2334i	0.629199	−	0.395352i	0.808545	+	0.588434i	$0.200255\pi$
$252$	−371.076	+	178.701i	−1.47252	+	0.709129i
$253$	−373.878	−	130.826i	−1.47778	−	0.517097i
$254$	2.08350	−	0.475546i	0.00820276	−	0.00187223i
$255$	76.6603	−	96.1290i	0.300629	−	0.376976i
$256$	119.634	+	150.016i	0.467319	+	0.585999i
$257$	60.5477	−	265.277i	0.235594	−	1.03221i	−0.709320	−	0.704887i	$-0.750998\pi$
$257$	60.5477	−	265.277i	0.235594	−	1.03221i	0.944914	−	0.327319i	$-0.106145\pi$
$258$	1.77745	+	1.11685i	0.00688934	+	0.00432886i
$259$	−154.666	−	17.4266i	−0.597164	−	0.0672843i
$260$		−	92.9778i		−	0.357607i
$261$	−327.339	+	46.0610i	−1.25417	+	0.176479i
$262$	26.5500			0.101336
$263$	20.1675	−	178.992i	0.0766826	−	0.680577i	−0.895290	−	0.445483i	$-0.853032\pi$
$263$	20.1675	−	178.992i	0.0766826	−	0.680577i	0.971973	−	0.235093i	$-0.0755396\pi$
$264$	56.0373	−	89.1829i	0.212263	−	0.337814i
$265$	58.5999	+	13.3750i	0.221132	+	0.0504719i
$266$	−16.9613	+	13.5262i	−0.0637642	+	0.0508503i
$267$	−100.475	−	80.1259i	−0.376310	−	0.300097i
$268$	53.9583	+	236.407i	0.201337	+	0.882115i
$269$	19.6598	−	56.1843i	0.0730846	−	0.208864i	−0.901546	−	0.432683i	$-0.857567\pi$
$269$	19.6598	−	56.1843i	0.0730846	−	0.208864i	0.974631	+	0.223819i	$0.0718526\pi$
$270$	2.16582	+	4.49736i	0.00802154	+	0.0166569i
$271$	6.36322	+	10.1270i	0.0234805	+	0.0373691i	0.858258	−	0.513218i	$-0.171547\pi$
$271$	6.36322	+	10.1270i	0.0234805	+	0.0373691i	−0.834778	+	0.550587i	$0.814404\pi$
$272$	−92.9867	−	265.741i	−0.341863	−	0.976988i
$273$	495.310	−	495.310i	1.81432	−	1.81432i
$274$	−8.15664	+	16.9374i	−0.0297688	+	0.0618155i
$275$	−208.769	+	23.5227i	−0.759162	+	0.0855370i
$276$	−85.2926	−	756.993i	−0.309031	−	2.74273i
$277$	302.145	+	145.505i	1.09078	+	0.525290i	0.890747	−	0.454500i	$-0.150182\pi$
$277$	302.145	+	145.505i	1.09078	+	0.525290i	0.200030	+	0.979790i	$0.435896\pi$
$278$	−4.73515	−	4.73515i	−0.0170329	−	0.0170329i
$279$	−218.615	+	76.4965i	−0.783565	+	0.274181i
$280$	28.5691	−	17.9511i	0.102032	−	0.0641112i
$281$	−17.7067	+	8.52710i	−0.0630132	+	0.0303456i	−0.465125	−	0.885245i	$-0.653991\pi$
$281$	−17.7067	+	8.52710i	−0.0630132	+	0.0303456i	0.402112	+	0.915591i	$0.368276\pi$
$282$	−76.7709	−	26.8633i	−0.272237	−	0.0952599i
$283$	−352.519	+	80.4602i	−1.24565	+	0.284312i	−0.794019	−	0.607892i	$-0.792015\pi$
$283$	−352.519	+	80.4602i	−1.24565	+	0.284312i	−0.451632	+	0.892204i	$0.649158\pi$
$284$	92.3862	−	115.849i	0.325304	−	0.407918i
$285$	−29.1210	−	36.5166i	−0.102179	−	0.128128i
$286$	−10.9901	+	48.1510i	−0.0384271	+	0.168360i
$287$	122.318	+	76.8574i	0.426195	+	0.267796i
$288$	169.462	+	19.0937i	0.588408	+	0.0662977i
$289$			74.8232i			0.258904i
$290$	12.9396	−	3.33152i	0.0446192	−	0.0114880i
$291$	−500.894			−1.72128
$292$	−39.6224	+	351.659i	−0.135693	+	1.20431i
$293$	240.077	−	382.081i	0.819377	−	1.30403i	−0.130513	−	0.991447i	$-0.541663\pi$
$293$	240.077	−	382.081i	0.819377	−	1.30403i	0.949890	−	0.312584i	$-0.101195\pi$
$294$	52.6232	+	12.0109i	0.178990	+	0.0408534i
$295$	−44.6593	+	35.6146i	−0.151387	+	0.120727i
$296$	33.4431	+	26.6700i	0.112983	+	0.0901013i
$297$	22.0565	+	96.6360i	0.0742645	+	0.325374i
$298$	−6.47207	+	18.4961i	−0.0217184	+	0.0620675i
$299$	314.122	+	652.280i	1.05057	+	2.18154i
$300$	−214.963	−	342.112i	−0.716543	−	1.14037i
$301$	4.41031	+	12.6039i	0.0146522	+	0.0418736i
$302$	19.9980	−	19.9980i	0.0662186	−	0.0662186i
$303$	−160.977	+	334.273i	−0.531278	+	1.10321i
$304$	−106.276	+	11.9745i	−0.349593	+	0.0393896i
$305$	9.48386	+	84.1716i	0.0310946	+	0.275972i
$306$	−63.2379	−	30.4538i	−0.206660	−	0.0995222i
$307$	306.449	+	306.449i	0.998206	+	0.998206i	0.999998	−	0.00179262i	$-0.000570608\pi$
$307$	306.449	+	306.449i	0.998206	+	0.998206i	−0.00179262	+	0.999998i	$0.500571\pi$
$308$	312.026	−	109.183i	1.01307	−	0.354489i
$309$	140.201	−	88.0941i	0.453725	−	0.285094i
$310$	8.43474	−	4.06196i	0.0272088	−	0.0131031i
$311$	−450.383	−	157.596i	−1.44818	−	0.506739i	−0.512219	−	0.858855i	$-0.671176\pi$
$311$	−450.383	−	157.596i	−1.44818	−	0.506739i	−0.935956	+	0.352116i	$0.885462\pi$
$312$	−187.683	+	42.8374i	−0.601548	+	0.137299i
$313$	3.32825	−	4.17350i	0.0106334	−	0.0133339i	−0.776486	−	0.630134i	$-0.783000\pi$
$313$	3.32825	−	4.17350i	0.0106334	−	0.0133339i	0.787120	+	0.616800i	$0.211571\pi$
$314$	−22.4659	−	28.1714i	−0.0715476	−	0.0897178i
$315$	−33.5755	+	147.104i	−0.106589	+	0.466997i
$316$	−240.045	−	150.830i	−0.759635	−	0.477311i
$317$	113.076	+	12.7406i	0.356705	+	0.0401910i	0.288499	−	0.957480i	$-0.406844\pi$
$317$	113.076	+	12.7406i	0.356705	+	0.0401910i	0.0682062	+	0.997671i	$0.478272\pi$
$318$		−	61.4041i		−	0.193094i
$319$	265.222	−	7.32085i	0.831418	−	0.0229494i
$320$	77.3722			0.241788
$321$	−32.6049	+	289.376i	−0.101573	+	0.901484i
$322$	−68.9663	+	109.759i	−0.214181	+	0.340867i
$323$	134.741	+	30.7537i	0.417154	+	0.0952126i
$324$	163.431	−	130.332i	0.504418	−	0.402260i
$325$	300.215	+	239.413i	0.923738	+	0.736656i
$326$	19.9644	+	87.4700i	0.0612406	+	0.268313i
$327$	−73.1412	+	209.026i	−0.223673	+	0.639222i
$328$	−17.2259	−	35.7699i	−0.0525180	−	0.109055i
$329$	−275.264	−	438.080i	−0.836668	−	1.33155i
$330$	−6.28810	−	17.9704i	−0.0190549	−	0.0544556i
$331$	166.103	−	166.103i	0.501820	−	0.501820i	−0.410183	−	0.912003i	$-0.634535\pi$
$331$	166.103	−	166.103i	0.501820	−	0.501820i	0.912003	+	0.410183i	$0.134535\pi$
$332$	109.416	−	227.205i	0.329567	−	0.684354i
$333$	−190.087	+	21.4176i	−0.570830	+	0.0643171i
$334$	−10.6016	−	94.0919i	−0.0317414	−	0.281712i
$335$	80.0381	+	38.5443i	0.238920	+	0.115058i
$336$	437.201	+	437.201i	1.30119	+	1.30119i
$337$	−310.333	+	108.590i	−0.920868	+	0.322226i	−0.748751	−	0.662851i	$-0.769346\pi$
$337$	−310.333	+	108.590i	−0.920868	+	0.322226i	−0.172117	+	0.985077i	$0.555061\pi$
$338$	30.2392	−	19.0006i	0.0894652	−	0.0562147i
$339$	809.274	−	389.726i	2.38724	−	1.14963i
$340$	−100.104	−	35.0280i	−0.294424	−	0.103024i
$341$	181.240	−	41.3668i	0.531494	−	0.121310i
$342$	−16.6239	+	20.8457i	−0.0486079	+	0.0609523i
$343$	−69.2759	−	86.8693i	−0.201971	−	0.253263i
$344$	0.816619	−	3.57784i	0.00237389	−	0.0104007i
$345$	−236.305	−	148.480i	−0.684941	−	0.430377i
$346$	−4.68505	−	0.527878i	−0.0135406	−	0.00152566i
$347$			484.864i			1.39730i	0.715463	+	0.698651i	$0.246216\pi$
$347$			484.864i			1.39730i	−0.715463	+	0.698651i	$0.753784\pi$
$348$	233.996	+	453.448i	0.672402	+	1.30301i
$349$	−297.414			−0.852190			−0.426095	−	0.904678i	$-0.640111\pi$
$349$	−297.414			−0.852190			−0.426095	+	0.904678i	$0.640111\pi$
$350$	−7.69793	+	68.3210i	−0.0219941	+	0.195203i
$351$	96.3867	−	153.399i	0.274606	−	0.437033i
$352$	−133.445	−	30.4580i	−0.379106	−	0.0865284i
$353$	−307.816	+	245.475i	−0.871999	+	0.695396i	−0.953538	−	0.301274i	$-0.902588\pi$
$353$	−307.816	+	245.475i	−0.871999	+	0.695396i	0.0815384	+	0.996670i	$0.474017\pi$
$354$	45.6231	+	36.3832i	0.128879	+	0.102777i
$355$	−12.0795	−	52.9236i	−0.0340267	−	0.149081i
$356$	−36.6115	+	104.630i	−0.102841	+	0.293904i
$357$	−346.673	−	719.875i	−0.971074	−	2.01646i
$358$	18.9061	+	30.0889i	0.0528104	+	0.0840472i
$359$	−45.0091	−	128.629i	−0.125374	−	0.358297i	0.864039	−	0.503424i	$-0.167927\pi$
$359$	−45.0091	−	128.629i	−0.125374	−	0.358297i	−0.989413	+	0.145127i	$0.953641\pi$
$360$	29.3222	−	29.3222i	0.0814506	−	0.0814506i
$361$	−133.853	+	277.949i	−0.370784	+	0.769941i
$362$	25.1280	−	2.83124i	0.0694143	−	0.00782111i
$363$	18.8593	+	167.381i	0.0519539	+	0.461103i
$364$	−544.371	−	262.155i	−1.49552	−	0.720207i
$365$	91.6737	+	91.6737i	0.251161	+	0.251161i
$366$	81.6763	−	28.5798i	0.223159	−	0.0780868i
$367$	12.1503	−	7.63452i	0.0331070	−	0.0208025i	−0.515377	−	0.856964i	$-0.672348\pi$
$367$	12.1503	−	7.63452i	0.0331070	−	0.0208025i	0.548484	+	0.836161i	$0.315205\pi$
$368$	−575.756	+	277.270i	−1.56456	+	0.753450i
$369$	167.581	+	58.6390i	0.454148	+	0.158913i
$370$	7.53815	−	1.72053i	0.0203734	−	0.00465009i
$371$	243.534	−	305.382i	0.656426	−	0.823132i
$372$	222.910	+	279.520i	0.599220	+	0.751398i
$373$	147.677	−	647.015i	0.395917	−	1.73462i	−0.247300	−	0.968939i	$-0.579543\pi$
$373$	147.677	−	647.015i	0.395917	−	1.73462i	0.643216	−	0.765685i	$-0.277600\pi$
$374$	47.7012	+	29.9727i	0.127543	+	0.0801408i
$375$	−307.230	−	34.6165i	−0.819279	−	0.0923106i
$376$			142.191i			0.378167i
$377$	−352.235	−	333.312i	−0.934311	−	0.884118i
$378$	32.4380			0.0858148
$379$	56.5377	−	501.786i	0.149176	−	1.32397i	−0.666517	−	0.745489i	$-0.732216\pi$
$379$	56.5377	−	501.786i	0.149176	−	1.32397i	0.815693	−	0.578484i	$-0.196356\pi$
$380$	−21.4342	+	34.1124i	−0.0564058	+	0.0897694i
$381$	29.1495	+	6.65318i	0.0765078	+	0.0174624i
$382$	67.0579	−	53.4769i	0.175544	−	0.139992i
$383$	−201.835	−	160.958i	−0.526984	−	0.420256i	0.323522	−	0.946220i	$-0.395133\pi$
$383$	−201.835	−	160.958i	−0.526984	−	0.420256i	−0.850506	+	0.525965i	$0.823704\pi$
$384$	−77.7316	−	340.564i	−0.202426	−	0.886886i
$385$	39.9993	−	114.312i	0.103894	−	0.296913i
$386$	−12.8786	−	26.7427i	−0.0333643	−	0.0692817i
$387$	8.73140	+	13.8959i	0.0225618	+	0.0359068i
$388$	142.699	+	407.809i	0.367780	+	1.05105i
$389$	−161.691	+	161.691i	−0.415657	+	0.415657i	−0.883704	−	0.468046i	$-0.844958\pi$
$389$	−161.691	+	161.691i	−0.415657	+	0.415657i	0.468046	+	0.883704i	$0.344958\pi$
$390$	−15.0982	+	31.3517i	−0.0387133	+	0.0803889i
$391$	820.616	−	92.4613i	2.09876	−	0.236474i
$392$	−10.5652	−	93.7688i	−0.0269521	−	0.239206i
$393$	334.666	+	161.167i	0.851568	+	0.410094i
$394$	−37.3864	−	37.3864i	−0.0948893	−	0.0948893i
$395$	−98.0320	+	34.3029i	−0.248182	+	0.0868427i
$396$	344.011	−	216.156i	0.868714	−	0.545849i
$397$	167.789	−	80.8031i	0.422643	−	0.203534i	−0.210458	−	0.977603i	$-0.567496\pi$
$397$	167.789	−	80.8031i	0.422643	−	0.203534i	0.633102	+	0.774068i	$0.281781\pi$
$398$	−60.3584	−	21.1203i	−0.151654	−	0.0530662i
$399$	−295.907	+	67.5388i	−0.741621	+	0.169270i
$400$	−211.326	+	264.994i	−0.528315	+	0.662486i
$401$	−75.3765	−	94.5192i	−0.187971	−	0.235709i	0.678912	−	0.734220i	$-0.262452\pi$
$401$	−75.3765	−	94.5192i	−0.187971	−	0.235709i	−0.866883	+	0.498511i	$0.833880\pi$
$402$	20.1944	−	88.4773i	0.0502348	−	0.220093i
$403$	−287.697	−	180.772i	−0.713888	−	0.448566i
$404$	318.013	+	35.8315i	0.787161	+	0.0886918i
$405$		−	76.5810i		−	0.189089i
$406$	16.9781	−	85.1525i	0.0418180	−	0.209735i
$407$	153.536			0.377239
$408$	−24.5860	+	218.207i	−0.0602598	+	0.534820i
$409$	−369.388	+	587.877i	−0.903148	+	1.43735i	−0.00386193	+	0.999993i	$0.501229\pi$
$409$	−369.388	+	587.877i	−0.903148	+	1.43735i	−0.899287	+	0.437360i	$0.855914\pi$
$410$	−6.99648	−	1.59690i	−0.0170646	−	0.00389488i
$411$	−205.631	+	163.985i	−0.500318	+	0.398990i
$412$	−111.665	−	89.0495i	−0.271031	−	0.216140i
$413$	82.5991	+	361.890i	0.199998	+	0.876247i
$414$	−52.6184	+	150.375i	−0.127098	+	0.363224i
$415$	−40.0850	−	83.2373i	−0.0965903	−	0.200572i
$416$	133.101	+	211.829i	0.319954	+	0.509204i
$417$	−30.9433	−	88.4310i	−0.0742046	−	0.212065i
$418$	15.1324	−	15.1324i	0.0362019	−	0.0362019i
$419$	−54.7621	+	113.715i	−0.130697	+	0.271395i	−0.956040	−	0.293237i	$-0.905268\pi$
$419$	−54.7621	+	113.715i	−0.130697	+	0.271395i	0.825343	+	0.564632i	$0.190982\pi$
$420$	231.447	−	26.0778i	0.551064	−	0.0620900i
$421$	48.8429	+	433.493i	0.116016	+	1.02967i	0.907953	+	0.419071i	$0.137644\pi$
$421$	48.8429	+	433.493i	0.116016	+	1.02967i	−0.791937	+	0.610603i	$0.790927\pi$
$422$	55.9436	+	26.9410i	0.132568	+	0.0638413i
$423$	−449.629	−	449.629i	−1.06295	−	1.06295i
$424$	−101.323	+	35.4545i	−0.238970	+	0.0836191i
$425$	370.865	−	233.030i	0.872624	−	0.548306i
$426$	−49.9643	+	24.0615i	−0.117287	+	0.0564825i
$427$	519.552	+	181.799i	1.21675	+	0.425759i
$428$	244.888	−	55.8941i	0.572169	−	0.130594i
$429$	−430.823	+	540.235i	−1.00425	+	1.25929i
$430$	−0.413596	−	0.518633i	−0.000961852	−	0.00120612i
$431$	−11.3639	+	49.7884i	−0.0263663	+	0.115518i	−0.986399	−	0.164371i	$-0.947441\pi$
$431$	−11.3639	+	49.7884i	−0.0263663	+	0.115518i	0.960032	+	0.279889i	$0.0902978\pi$
$432$	135.402	+	85.0788i	0.313431	+	0.196942i
$433$	−270.069	−	30.4294i	−0.623716	−	0.0702759i	−0.205550	−	0.978647i	$-0.565898\pi$
$433$	−270.069	−	30.4294i	−0.623716	−	0.0702759i	−0.418166	+	0.908371i	$0.637327\pi$
$434$		−	60.8370i		−	0.140177i
$435$	183.328	+	36.5528i	0.421444	+	0.0840294i
$436$	191.018			0.438115
$437$	35.1233	−	311.728i	0.0803737	−	0.713336i
$438$	70.4645	−	112.144i	0.160878	−	0.256036i
$439$	516.826	+	117.962i	1.17728	+	0.268706i	0.766023	−	0.642813i	$-0.222233\pi$
$439$	516.826	+	117.962i	1.17728	+	0.268706i	0.411257	+	0.911520i	$0.365090\pi$
$440$	−26.0223	+	20.7521i	−0.0591415	+	0.0471638i
$441$	329.920	+	263.102i	0.748118	+	0.596604i
$442$	−22.9124	−	100.386i	−0.0518381	−	0.227117i
$443$	−148.288	+	423.784i	−0.334737	+	0.956623i	0.646348	+	0.763043i	$0.276296\pi$
$443$	−148.288	+	423.784i	−0.334737	+	0.956623i	−0.981084	+	0.193580i	$0.937990\pi$
$444$	128.116	+	266.036i	0.288549	+	0.599179i
$445$	21.6060	+	34.3857i	0.0485527	+	0.0772712i
$446$	26.2604	+	75.0478i	0.0588797	+	0.168269i
$447$	−193.858	+	193.858i	−0.433687	+	0.433687i
$448$	218.155	−	453.003i	0.486952	−	1.01117i
$449$	−754.738	+	85.0385i	−1.68093	+	0.189395i	−0.900201	−	0.435474i	$-0.856581\pi$
$449$	−754.738	+	85.0385i	−1.68093	+	0.189395i	−0.780729	+	0.624869i	$0.785152\pi$
$450$	9.46088	+	83.9677i	0.0210242	+	0.186595i
$451$	−128.391	−	61.8300i	−0.284681	−	0.137095i
$452$	−547.853	−	547.853i	−1.21206	−	1.21206i
$453$	373.471	−	130.683i	0.824440	−	0.288484i
$454$	43.1659	−	27.1229i	0.0950790	−	0.0597421i
$455$	−199.432	+	96.0412i	−0.438311	+	0.211080i
$456$	78.7338	+	27.5501i	0.172662	+	0.0604170i
$457$	224.303	−	51.1956i	0.490815	−	0.112025i	0.0300518	−	0.999548i	$-0.490433\pi$
$457$	224.303	−	51.1956i	0.490815	−	0.112025i	0.460763	+	0.887523i	$0.347576\pi$
$458$	15.9484	−	19.9987i	0.0348219	−	0.0436653i
$459$	−128.844	−	161.565i	−0.280706	−	0.351994i
$460$	−53.5666	+	234.691i	−0.116449	+	0.510197i
$461$	670.322	+	421.191i	1.45406	+	0.913646i	0.999740	+	0.0228077i	$0.00726055\pi$
$461$	670.322	+	421.191i	1.45406	+	0.913646i	0.454320	+	0.890839i	$0.349882\pi$
$462$	−122.943	−	13.8524i	−0.266111	−	0.0299835i
$463$		−	582.383i		−	1.25785i	−0.777467	−	0.628923i	$-0.783496\pi$
$463$		−	582.383i		−	1.25785i	0.777467	−	0.628923i	$-0.216504\pi$
$464$	294.209	−	310.912i	0.634071	−	0.670069i
$465$	130.978			0.281674
$466$	−9.62450	+	85.4198i	−0.0206534	+	0.183304i
$467$	112.967	−	179.786i	0.241899	−	0.384980i	−0.703605	−	0.710592i	$-0.748427\pi$
$467$	112.967	−	179.786i	0.241899	−	0.384980i	0.945504	+	0.325612i	$0.105570\pi$
$468$	−723.961	−	165.239i	−1.54693	−	0.353076i
$469$	451.342	−	359.933i	0.962350	−	0.767448i
$470$	20.0948	+	16.0251i	0.0427549	+	0.0340959i
$471$	−112.177	−	491.479i	−0.238167	−	1.04348i
$472$	33.6935	−	96.2904i	0.0713845	−	0.204005i
$473$	−5.71530	−	11.8679i	−0.0120831	−	0.0250908i
$474$	56.4495	+	89.8388i	0.119092	+	0.189533i
$475$	−54.9529	−	157.046i	−0.115690	−	0.330624i
$476$	−487.332	+	487.332i	−1.02381	+	1.02381i
$477$	208.287	−	432.512i	0.436659	−	0.906733i
$478$	−142.409	+	16.0456i	−0.297926	+	0.0335682i
$479$	−15.9968	−	141.976i	−0.0333963	−	0.296400i	−0.999297	−	0.0374877i	$-0.988064\pi$
$479$	−15.9968	−	141.976i	−0.0333963	−	0.296400i	0.965901	−	0.258912i	$-0.0833641\pi$
$480$	−86.8878	−	41.8430i	−0.181016	−	0.0871728i
$481$	−198.430	−	198.430i	−0.412537	−	0.412537i
$482$	40.6905	−	14.2382i	0.0844201	−	0.0295399i
$483$	−1535.60	+	964.882i	−3.17930	+	1.99768i
$484$	130.902	−	63.0392i	0.270459	−	0.130246i
$485$	149.402	+	52.2780i	0.308045	+	0.107790i
$486$	−106.960	+	24.4130i	−0.220083	+	0.0502325i
$487$	237.781	−	298.169i	0.488258	−	0.612256i	−0.475278	−	0.879836i	$-0.657653\pi$
$487$	237.781	−	298.169i	0.488258	−	0.612256i	0.963536	+	0.267580i	$0.0862239\pi$
$488$	−94.3193	−	118.273i	−0.193277	−	0.242362i
$489$	−279.315	+	1223.76i	−0.571196	+	2.50257i
$490$	−14.4424	−	9.07475i	−0.0294742	−	0.0185199i
$491$	364.670	+	41.0885i	0.742709	+	0.0836832i	0.475207	−	0.879874i	$-0.342373\pi$
$491$	364.670	+	41.0885i	0.742709	+	0.0836832i	0.267502	+	0.963557i	$0.413802\pi$
$492$		−	274.060i		−	0.557032i
$493$	−491.559	+	253.663i	−0.997078	+	0.514529i
$494$	−39.1143			−0.0791788
$495$	16.6652	−	147.907i	0.0336670	−	0.298803i
$496$	159.564	−	253.945i	0.321702	−	0.511986i
$497$	−343.918	−	78.4971i	−0.691989	−	0.157942i
$498$	−73.7894	+	58.8451i	−0.148171	+	0.118163i
$499$	−246.893	−	196.890i	−0.494775	−	0.394570i	0.344067	−	0.938945i	$-0.388195\pi$
$499$	−246.893	−	196.890i	−0.494775	−	0.394570i	−0.838842	+	0.544375i	$0.816767\pi$
$500$	59.3426	+	259.997i	0.118685	+	0.519994i
$501$	437.532	−	1250.39i	0.873317	−	2.49580i
$502$	26.1251	+	54.2494i	0.0520421	+	0.108066i
$503$	371.635	+	591.454i	0.738838	+	1.17585i	0.978750	+	0.205059i	$0.0657386\pi$
$503$	371.635	+	591.454i	0.738838	+	1.17585i	−0.239912	+	0.970795i	$0.577118\pi$
$504$	−89.0018	−	254.353i	−0.176591	−	0.504668i
$505$	82.9027	−	82.9027i	0.164164	−	0.164164i
$506$	55.4818	−	115.209i	0.109648	−	0.227686i
$507$	496.508	−	55.9431i	0.979307	−	0.110341i
$508$	−2.88756	−	25.6278i	−0.00568418	−	0.0504485i
$509$	540.877	+	260.473i	1.06263	+	0.511734i	0.881723	−	0.471767i	$-0.156384\pi$
$509$	540.877	+	260.473i	1.06263	+	0.511734i	0.180904	+	0.983501i	$0.442098\pi$
$510$	28.0667	+	28.0667i	0.0550327	+	0.0550327i
$511$	795.214	−	278.257i	1.55619	−	0.544535i
$512$	−314.403	+	197.553i	−0.614069	+	0.385845i
$513$	−70.7261	+	34.0599i	−0.137868	+	0.0663935i
$514$	82.9106	+	29.0117i	0.161305	+	0.0564429i
$515$	−51.0122	+	11.6432i	−0.0990528	+	0.0226082i
$516$	15.7948	−	19.8061i	0.0306101	−	0.0383839i
$517$	318.213	+	399.027i	0.615499	+	0.771812i
$518$	11.1807	−	48.9858i	0.0215844	−	0.0945672i
$519$	−55.8512	−	35.0936i	−0.107613	−	0.0676178i
$520$	60.4512	+	6.81122i	0.116252	+	0.0130985i
$521$		−	453.443i		−	0.870331i	−0.900350	−	0.435166i	$-0.856690\pi$
$521$		−	453.443i		−	0.870331i	0.900350	−	0.435166i	$-0.143310\pi$
$522$	−2.94447	−	106.673i	−0.00564074	−	0.204355i
$523$	−131.985			−0.252361			−0.126180	−	0.992007i	$-0.540272\pi$
$523$	−131.985			−0.252361			−0.126180	+	0.992007i	$0.540272\pi$
$524$	35.8736	−	318.387i	0.0684612	−	0.607610i
$525$	−511.763	+	814.466i	−0.974786	+	1.55136i
$526$	56.6904	+	12.9392i	0.107776	+	0.0245993i
$527$	−303.013	+	241.645i	−0.574977	+	0.458529i
$528$	−476.856	−	380.280i	−0.903136	−	0.720227i
$529$	−299.386	−	1311.70i	−0.565947	−	2.47958i
$530$	−6.40870	+	18.3150i	−0.0120919	+	0.0345567i
$531$	197.941	+	411.028i	0.372770	+	0.774065i
$532$	139.288	+	221.675i	0.261819	+	0.416683i
$533$	86.0239	+	245.842i	0.161396	+	0.461243i
$534$	29.3355	−	29.3355i	0.0549354	−	0.0549354i
$535$	39.9271	−	82.9095i	0.0746301	−	0.154971i
$536$	−157.657	+	17.7637i	−0.294136	+	0.0331412i
$537$	55.6649	+	494.040i	0.103659	+	0.920000i
$538$	17.3130	+	8.33749i	0.0321803	+	0.0154972i
$539$	−239.497	−	239.497i	−0.444336	−	0.444336i
$540$	56.8586	−	19.8957i	0.105294	−	0.0368439i
$541$	−413.693	+	259.940i	−0.764682	+	0.480481i	−0.857043	−	0.515244i	$-0.827701\pi$
$541$	−413.693	+	259.940i	−0.764682	+	0.480481i	0.0923617	+	0.995726i	$0.470558\pi$
$542$	−3.47868	+	1.67524i	−0.00641822	+	0.00309085i
$543$	333.927	+	116.846i	0.614968	+	0.215186i
$544$	278.209	−	63.4993i	0.511413	−	0.116727i
$545$	43.6317	−	54.7125i	0.0800583	−	0.100390i
$546$	140.989	+	176.795i	0.258222	+	0.323800i
$547$	−96.3497	+	422.136i	−0.176142	+	0.771729i	0.807246	+	0.590215i	$0.200957\pi$
$547$	−96.3497	+	422.136i	−0.176142	+	0.771729i	−0.983388	+	0.181514i	$0.941900\pi$
$548$	192.092	+	120.700i	0.350533	+	0.220255i
$549$	672.247	+	75.7441i	1.22449	+	0.137967i
$550$		−	67.8221i		−	0.123313i
$551$	52.3920	+	203.489i	0.0950853	+	0.369309i
$552$	498.421			0.902937
$553$	−75.5676	+	670.681i	−0.136650	+	1.21280i
$554$	−57.5981	+	91.6669i	−0.103968	+	0.165464i
$555$	105.463	+	24.0713i	0.190024	+	0.0433717i
$556$	−63.1818	+	50.3858i	−0.113636	+	0.0906220i
$557$	67.2366	+	53.6194i	0.120712	+	0.0962647i	0.681985	−	0.731366i	$-0.261117\pi$
$557$	67.2366	+	53.6194i	0.120712	+	0.0962647i	−0.561273	+	0.827631i	$0.689688\pi$
$558$	−16.6378	−	72.8951i	−0.0298169	−	0.130636i
$559$	−7.95169	+	22.7246i	−0.0142249	+	0.0406523i
$560$	−84.7739	−	176.035i	−0.151382	−	0.314348i
$561$	419.336	+	667.370i	0.747480	+	1.18961i
$562$	−2.09543	−	5.98841i	−0.00372853	−	0.0106555i
$563$	−243.097	+	243.097i	−0.431788	+	0.431788i	−0.889236	−	0.457448i	$-0.848764\pi$
$563$	−243.097	+	243.097i	−0.431788	+	0.431788i	0.457448	+	0.889236i	$0.348764\pi$
$564$	−425.874	+	884.337i	−0.755097	+	1.56797i
$565$	−282.058	+	31.7803i	−0.499218	+	0.0562484i
$566$	−13.0694	−	115.994i	−0.0230908	−	0.204937i
$567$	−448.370	−	215.924i	−0.790777	−	0.380818i
$568$	68.5533	+	68.5533i	0.120692	+	0.120692i
$569$	−135.305	+	47.3452i	−0.237794	+	0.0832077i	−0.446545	−	0.894761i	$-0.647346\pi$
$569$	−135.305	+	47.3452i	−0.237794	+	0.0832077i	0.208751	+	0.977969i	$0.433060\pi$
$570$	12.7668	−	8.02194i	0.0223980	−	0.0140736i
$571$	−515.966	+	248.476i	−0.903618	+	0.435159i	−0.827194	−	0.561916i	$-0.810064\pi$
$571$	−515.966	+	248.476i	−0.903618	+	0.435159i	−0.0764234	+	0.997075i	$0.524350\pi$
$572$	562.576	+	196.854i	0.983524	+	0.344150i
$573$	1169.89	−	267.021i	2.04170	−	0.466005i
$574$	−29.0765	+	36.4608i	−0.0506560	+	0.0635206i
$575$	−619.859	−	777.278i	−1.07801	−	1.35179i
$576$	137.505	−	602.450i	0.238725	−	1.04592i
$577$	569.679	+	357.953i	0.987312	+	0.620369i	0.925910	−	0.377744i	$-0.123300\pi$
$577$	569.679	+	357.953i	0.987312	+	0.620369i	0.0614016	+	0.998113i	$0.480443\pi$
$578$	−24.0028	−	2.70447i	−0.0415273	−	0.00467901i
$579$		−	415.272i		−	0.717224i
$580$	−22.4680	−	159.672i	−0.0387379	−	0.275297i
$581$	−600.363			−1.03333
$582$	18.1047	−	160.683i	0.0311077	−	0.276088i
$583$	−204.996	+	326.249i	−0.351623	+	0.559604i
$584$	−225.735	−	51.5225i	−0.386532	−	0.0882234i
$585$	−212.694	+	169.618i	−0.363579	+	0.289945i
$586$	113.892	+	90.8255i	0.194354	+	0.154992i
$587$	64.3062	+	281.744i	0.109551	+	0.479973i	0.999704	+	0.0243124i	$0.00773965\pi$
$587$	64.3062	+	281.744i	0.109551	+	0.479973i	−0.890154	+	0.455660i	$0.849403\pi$
$588$	215.137	−	614.827i	0.365880	−	1.04562i
$589$	63.8789	+	132.646i	0.108453	+	0.225205i
$590$	−9.81073	−	15.6137i	−0.0166284	−	0.0264639i
$591$	−244.313	−	698.206i	−0.413389	−	1.18140i
$592$	175.151	−	175.151i	0.295863	−	0.295863i
$593$	91.1724	−	189.321i	0.153748	−	0.319260i	−0.809841	−	0.586650i	$-0.800447\pi$
$593$	91.1724	−	189.321i	0.153748	−	0.319260i	0.963589	+	0.267389i	$0.0861609\pi$
$594$	−31.7974	+	3.58271i	−0.0535310	+	0.00603150i
$595$	28.2696	+	250.900i	0.0475119	+	0.421680i
$596$	213.060	+	102.604i	0.357483	+	0.172155i
$597$	−632.618	−	632.618i	−1.05966	−	1.05966i
$598$	−220.601	+	77.1917i	−0.368898	+	0.129083i
$599$	886.781	−	557.202i	1.48044	−	0.930220i	0.481895	−	0.876229i	$-0.339949\pi$
$599$	886.781	−	557.202i	1.48044	−	0.930220i	0.998541	−	0.0539909i	$-0.0171942\pi$
$600$	238.178	−	114.700i	0.396963	−	0.191167i
$601$	−513.064	−	179.529i	−0.853683	−	0.298717i	−0.132263	−	0.991215i	$-0.542224\pi$
$601$	−513.064	−	179.529i	−0.853683	−	0.298717i	−0.721420	+	0.692498i	$0.756510\pi$
$602$	−4.20267	+	0.959233i	−0.00698119	+	0.00159341i
$603$	442.364	−	554.707i	0.733605	−	0.919912i
$604$	−212.795	−	266.837i	−0.352310	−	0.441782i
$605$	11.8442	−	51.8930i	0.0195773	−	0.0857736i
$606$	−101.414	−	63.7227i	−0.167350	−	0.105153i
$607$	−281.310	−	31.6961i	−0.463444	−	0.0522176i	−0.122844	−	0.992426i	$-0.539202\pi$
$607$	−281.310	−	31.6961i	−0.463444	−	0.0522176i	−0.340600	+	0.940208i	$0.610630\pi$
$608$		−	108.401i		−	0.178291i
$609$	730.913	−	970.295i	1.20018	−	1.59326i
$610$	−27.3445			−0.0448270
$611$	104.444	−	926.962i	0.170939	−	1.51712i
$612$	−450.646	+	717.199i	−0.736350	+	1.17189i
$613$	−561.152	−	128.079i	−0.915419	−	0.208938i	−0.261236	−	0.965275i	$-0.584130\pi$
$613$	−561.152	−	128.079i	−0.915419	−	0.208938i	−0.654183	+	0.756336i	$0.726987\pi$
$614$	−109.383	+	87.2304i	−0.178149	+	0.142069i
$615$	−78.4978	−	62.5999i	−0.127639	−	0.101788i
$616$	48.1292	+	210.868i	0.0781318	+	0.342318i
$617$	−370.898	+	1059.96i	−0.601131	+	1.71793i	0.0907049	+	0.995878i	$0.471088\pi$
$617$	−370.898	+	1059.96i	−0.601131	+	1.71793i	−0.691836	+	0.722055i	$0.743198\pi$
$618$	23.1925	+	48.1597i	0.0375283	+	0.0779283i
$619$	−78.0793	−	124.263i	−0.126138	−	0.200747i	0.777685	−	0.628654i	$-0.216394\pi$
$619$	−78.0793	−	124.263i	−0.126138	−	0.200747i	−0.903823	+	0.427907i	$0.859251\pi$
$620$	−37.3141	−	106.638i	−0.0601841	−	0.171996i
$621$	−331.672	+	331.672i	−0.534093	+	0.534093i
$622$	66.8346	−	138.784i	0.107451	−	0.223125i
$623$	262.242	−	29.5476i	0.420934	−	0.0474279i
$624$	124.815	+	1107.76i	0.200024	+	1.77526i
$625$	−429.199	−	206.692i	−0.686719	−	0.330706i
$626$	1.21853	+	1.21853i	0.00194654	+	0.00194654i
$627$	282.604	−	98.8875i	0.450724	−	0.157715i
$628$	−368.186	+	231.347i	−0.586284	+	0.368386i
$629$	−288.395	+	138.884i	−0.458498	+	0.220801i
$630$	−45.9764	−	16.0878i	−0.0729784	−	0.0255363i
$631$	−314.703	+	71.8288i	−0.498736	+	0.113833i	−0.464487	−	0.885580i	$-0.653761\pi$
$631$	−314.703	+	71.8288i	−0.498736	+	0.113833i	−0.0342495	+	0.999413i	$0.510904\pi$
$632$	115.650	−	145.020i	0.182990	−	0.229462i
$633$	541.636	+	679.190i	0.855664	+	1.07297i
$634$	−8.17417	+	35.8134i	−0.0128930	+	0.0564880i
$635$	−8.00004	−	5.02676i	−0.0125985	−	0.00791616i
$636$	−736.356	−	82.9674i	−1.15779	−	0.130452i
$637$			619.053i			0.971826i
$638$	−7.23791	+	85.3462i	−0.0113447	+	0.133772i
$639$	−433.551			−0.678484
$640$	−12.3594	+	109.693i	−0.0193116	+	0.171396i
$641$	642.548	−	1022.61i	1.00241	−	1.59533i	0.217183	−	0.976131i	$-0.430313\pi$
$641$	642.548	−	1022.61i	1.00241	−	1.59533i	0.785231	−	0.619203i	$-0.212544\pi$
$642$	−91.6515	−	20.9189i	−0.142759	−	0.0325839i
$643$	−789.054	+	629.250i	−1.22714	+	0.978615i	−0.227156	+	0.973858i	$0.572943\pi$
$643$	−789.054	+	629.250i	−1.22714	+	0.978615i	−0.999989	+	0.00475703i	$0.998486\pi$
$644$	1223.05	+	975.346i	1.89914	+	1.51451i
$645$	−2.06517	−	9.04809i	−0.00320181	−	0.0140280i
$646$	−14.7357	+	42.1123i	−0.0228107	+	0.0651894i
$647$	−216.567	−	449.706i	−0.334725	−	0.695063i	0.663882	−	0.747837i	$-0.268908\pi$
$647$	−216.567	−	449.706i	−0.334725	−	0.695063i	−0.998606	+	0.0527747i	$0.983193\pi$
$648$	72.7654	+	115.806i	0.112292	+	0.178712i
$649$	−120.938	−	345.621i	−0.186345	−	0.532544i
$650$	−87.6534	+	87.6534i	−0.134851	+	0.134851i
$651$	369.299	−	766.858i	0.567280	−	1.17797i
$652$	1075.91	−	121.226i	1.65017	−	0.185930i
$653$	−44.5435	−	395.334i	−0.0682136	−	0.605413i	−0.980591	−	0.196063i	$-0.937184\pi$
$653$	−44.5435	−	395.334i	−0.0682136	−	0.605413i	0.912378	−	0.409349i	$-0.134244\pi$
$654$	−64.4104	−	31.0184i	−0.0984868	−	0.0474287i
$655$	−83.0002	−	83.0002i	−0.126718	−	0.126718i
$656$	−217.001	+	75.9318i	−0.330794	+	0.115750i
$657$	876.729	−	550.885i	1.33444	−	0.838486i
$658$	150.482	−	72.4685i	0.228697	−	0.110135i
$659$	600.803	+	210.230i	0.911688	+	0.319013i	0.745053	−	0.667005i	$-0.232424\pi$
$659$	600.803	+	210.230i	0.911688	+	0.319013i	0.166635	+	0.986019i	$0.446710\pi$
$660$	−223.996	+	51.1257i	−0.339388	+	0.0774632i
$661$	−638.575	+	800.748i	−0.966074	+	1.21142i	0.0113074	+	0.999936i	$0.496401\pi$
$661$	−638.575	+	800.748i	−0.966074	+	1.21142i	−0.977382	+	0.211483i	$0.932171\pi$
$662$	47.2809	+	59.2883i	0.0714213	+	0.0895594i
$663$	320.559	−	1404.46i	0.483498	−	2.11834i
$664$	139.706	+	87.7833i	0.210401	+	0.132204i
$665$	95.3093	+	10.7388i	0.143322	+	0.0161485i
$666$		−	61.7526i		−	0.0927217i
$667$	697.069	+	1044.26i	1.04508	+	1.56561i
$668$	−1142.67			−1.71059
$669$	−124.548	+	1105.39i	−0.186170	+	1.65231i
$670$	−15.2577	+	24.2825i	−0.0227727	+	0.0362426i
$671$	−529.372	−	120.826i	−0.788930	−	0.180068i
$672$	−489.968	+	390.737i	−0.729120	+	0.581453i
$673$	−148.207	−	118.191i	−0.220218	−	0.175618i	0.507166	−	0.861848i	$-0.330693\pi$
$673$	−148.207	−	118.191i	−0.220218	−	0.175618i	−0.727385	+	0.686230i	$0.759264\pi$
$674$	−23.6181	−	103.478i	−0.0350417	−	0.153528i
$675$	−82.1673	+	234.821i	−0.121729	+	0.347882i
$676$	−186.996	−	388.301i	−0.276621	−	0.574410i
$677$	−574.645	−	914.543i	−0.848812	−	1.35088i	−0.935019	−	0.354599i	$-0.884617\pi$
$677$	−574.645	−	914.543i	−0.848812	−	1.35088i	0.0862069	−	0.996277i	$-0.472525\pi$
$678$	95.7706	+	273.697i	0.141255	+	0.403682i
$679$	727.325	−	727.325i	1.07117	−	1.07117i
$680$	30.1074	−	62.5186i	0.0442756	−	0.0919391i
$681$	708.755	−	79.8575i	1.04076	−	0.117265i
$682$	6.71933	+	59.6357i	0.00985239	+	0.0874423i
$683$	639.821	+	308.122i	0.936781	+	0.451130i	0.839032	−	0.544081i	$-0.183122\pi$
$683$	639.821	+	308.122i	0.936781	+	0.451130i	0.0977481	+	0.995211i	$0.468836\pi$
$684$	227.519	+	227.519i	0.332631	+	0.332631i
$685$	78.4486	−	27.4504i	0.114524	−	0.0400735i
$686$	30.3711	−	19.0834i	0.0442727	−	0.0278184i
$687$	322.430	−	155.274i	0.469330	−	0.226017i
$688$	−20.0586	−	7.01882i	−0.0291550	−	0.0102018i
$689$	686.583	−	156.708i	0.996492	−	0.227443i
$690$	56.1726	−	70.4382i	0.0814096	−	0.102084i
$691$	808.584	+	1013.93i	1.17016	+	1.46734i	0.855246	+	0.518222i	$0.173406\pi$
$691$	808.584	+	1013.93i	1.17016	+	1.46734i	0.314919	+	0.949119i	$0.398023\pi$
$692$	−12.6606	+	55.4697i	−0.0182957	+	0.0801586i
$693$	−818.987	−	514.604i	−1.18180	−	0.742574i
$694$	−155.541	−	17.5253i	−0.224123	−	0.0252526i
$695$			29.6059i			0.0425984i
$696$	−311.959	+	118.919i	−0.448217	+	0.170860i
$697$	297.094			0.426246
$698$	10.7500	−	95.4085i	0.0154011	−	0.136688i
$699$	−639.842	+	1018.30i	−0.915367	+	1.45680i
$700$	808.903	+	184.627i	1.15558	+	0.263753i
$701$	−507.886	+	405.025i	−0.724516	+	0.577782i	−0.914781	−	0.403951i	$-0.867637\pi$
$701$	−507.886	+	405.025i	−0.724516	+	0.577782i	0.190265	+	0.981733i	$0.439065\pi$
$702$	45.7254	+	36.4648i	0.0651359	+	0.0519441i
$703$	27.0573	+	118.546i	0.0384883	+	0.168628i
$704$	−163.813	+	468.152i	−0.232690	+	0.664989i
$705$	156.020	+	323.979i	0.221305	+	0.459545i
$706$	−67.6208	−	107.618i	−0.0957802	−	0.152433i
$707$	−251.635	−	719.130i	−0.355919	−	1.01716i
$708$	497.951	−	497.951i	0.703320	−	0.703320i
$709$	−389.499	+	808.804i	−0.549365	+	1.14077i	0.422747	+	0.906248i	$0.361066\pi$
$709$	−389.499	+	808.804i	−0.549365	+	1.14077i	−0.972111	+	0.234519i	$0.924648\pi$
$710$	17.4142	−	1.96210i	0.0245270	−	0.00276353i
$711$	92.8738	+	824.278i	0.130624	+	1.15932i
$712$	−65.3449	−	31.4684i	−0.0917765	−	0.0441972i
$713$	622.046	+	622.046i	0.872435	+	0.872435i
$714$	243.462	−	85.1909i	0.340983	−	0.119315i
$715$	184.886	−	116.171i	0.258582	−	0.162478i
$716$	386.371	−	186.066i	0.539624	−	0.259869i
$717$	−1892.48	−	662.208i	−2.63944	−	0.923581i
$718$	42.8901	−	9.78938i	0.0597355	−	0.0136342i
$719$	−338.821	+	424.868i	−0.471239	+	0.590916i	−0.959474	−	0.281797i	$-0.909070\pi$
$719$	−338.821	+	424.868i	−0.471239	+	0.590916i	0.488235	+	0.872712i	$0.337641\pi$
$720$	−149.719	−	187.741i	−0.207943	−	0.260752i
$721$	−75.6621	+	331.497i	−0.104940	+	0.459774i
$722$	−84.3260	−	52.9856i	−0.116795	−	0.0733872i
$723$	599.339	+	67.5292i	0.828961	+	0.0934014i
$724$		−	305.159i		−	0.421491i
$725$	573.418	+	338.602i	0.790921	+	0.467037i
$726$	−54.3762			−0.0748984
$727$	−27.9681	+	248.224i	−0.0384706	+	0.341436i	0.959703	+	0.281018i	$0.0906720\pi$
$727$	−27.9681	+	248.224i	−0.0384706	+	0.341436i	−0.998173	+	0.0604182i	$0.980757\pi$
$728$	210.324	−	334.728i	0.288906	−	0.459791i
$729$	−1025.63	−	234.094i	−1.40691	−	0.321117i
$730$	−32.7218	+	26.0948i	−0.0448244	+	0.0357463i
$731$	21.4707	+	17.1223i	0.0293717	+	0.0234232i
$732$	−232.369	−	1018.08i	−0.317444	−	1.39081i
$733$	375.536	−	1073.22i	0.512327	−	1.46415i	−0.339642	−	0.940555i	$-0.610306\pi$
$733$	375.536	−	1073.22i	0.512327	−	1.46415i	0.851969	−	0.523592i	$-0.175408\pi$
$734$	2.00994	+	4.17368i	0.00273833	+	0.00568621i
$735$	−126.961	−	202.058i	−0.172736	−	0.274909i
$736$	−213.928	−	611.372i	−0.290664	−	0.830669i
$737$	−402.675	+	402.675i	−0.546371	+	0.546371i
$738$	−24.8682	+	51.6393i	−0.0336967	+	0.0699720i
$739$	−1294.80	+	145.889i	−1.75209	+	0.197414i	−0.928896	−	0.370340i	$-0.879241\pi$
$739$	−1294.80	+	145.889i	−1.75209	+	0.197414i	−0.823198	+	0.567754i	$0.807813\pi$
$740$	−10.4473	−	92.7220i	−0.0141179	−	0.125300i
$741$	−493.040	−	237.436i	−0.665372	−	0.320426i
$742$	89.1621	+	89.1621i	0.120165	+	0.120165i
$743$	493.579	−	172.711i	0.664305	−	0.232450i	0.0229990	−	0.999735i	$-0.492679\pi$
$743$	493.579	−	172.711i	0.664305	−	0.232450i	0.641306	+	0.767285i	$0.278393\pi$
$744$	−198.065	+	124.452i	−0.266216	+	0.167275i
$745$	78.0551	−	37.5894i	0.104772	−	0.0504555i
$746$	202.220	+	70.7600i	0.271073	+	0.0948525i
$747$	−719.357	+	164.188i	−0.962994	+	0.219797i
$748$	423.884	−	531.534i	0.566690	−	0.710607i
$749$	−372.846	−	467.534i	−0.497792	−	0.624212i
$750$	22.2095	−	97.3061i	0.0296126	−	0.129741i
$751$	−18.4139	−	11.5702i	−0.0245192	−	0.0154064i	0.519717	−	0.854339i	$-0.326038\pi$
$751$	−18.4139	−	11.5702i	−0.0245192	−	0.0154064i	−0.544236	+	0.838932i	$0.683180\pi$
$752$	818.213	+	92.1905i	1.08805	+	0.122594i
$753$			842.407i			1.11873i
$754$	119.656	−	100.947i	0.158695	−	0.133882i
$755$	−125.035			−0.165609
$756$	43.8293	−	388.996i	0.0579752	−	0.514544i
$757$	−65.6056	+	104.411i	−0.0866653	+	0.137927i	−0.887244	−	0.461301i	$-0.847383\pi$
$757$	−65.6056	+	104.411i	−0.0866653	+	0.137927i	0.800578	+	0.599228i	$0.204526\pi$
$758$	158.926	+	36.2739i	0.209665	+	0.0478547i
$759$	1398.71	−	1115.43i	1.84283	−	1.46961i
$760$	−20.6086	−	16.4348i	−0.0271166	−	0.0216247i
$761$	−130.200	−	570.442i	−0.171090	−	0.749596i	−0.985551	−	0.169377i	$-0.945824\pi$
$761$	−130.200	−	570.442i	−0.171090	−	0.749596i	0.814461	−	0.580218i	$-0.197033\pi$
$762$	−3.18790	+	9.11048i	−0.00418359	+	0.0119560i
$763$	−197.312	−	409.722i	−0.258600	−	0.536988i
$764$	−550.687	−	876.413i	−0.720795	−	1.14714i
$765$	102.489	+	292.897i	0.133973	+	0.382872i
$766$	58.9295	−	58.9295i	0.0769315	−	0.0769315i
$767$	−290.381	+	602.982i	−0.378593	+	0.786156i
$768$	−861.165	+	97.0300i	−1.12131	+	0.126341i
$769$	−150.151	−	1332.62i	−0.195255	−	1.73293i	−0.584146	−	0.811648i	$-0.698571\pi$
$769$	−150.151	−	1332.62i	−0.195255	−	1.73293i	0.388892	−	0.921283i	$-0.372858\pi$
$770$	35.2246	+	16.9633i	0.0457463	+	0.0220302i
$771$	868.988	+	868.988i	1.12709	+	1.12709i
$772$	−338.099	+	118.306i	−0.437953	+	0.153246i
$773$	647.110	−	406.606i	0.837140	−	0.526010i	−0.0439084	−	0.999036i	$-0.513981\pi$
$773$	647.110	−	406.606i	0.837140	−	0.526010i	0.881049	+	0.473025i	$0.156838\pi$
$774$	−4.77332	+	2.29871i	−0.00616708	+	0.00296991i
$775$	440.403	+	154.104i	0.568262	+	0.198843i
$776$	−275.598	+	62.9035i	−0.355152	+	0.0810612i
$777$	438.293	−	549.602i	0.564083	−	0.707338i
$778$	−46.0251	−	57.7136i	−0.0591582	−	0.0741820i
$779$	25.1131	−	110.028i	0.0322376	−	0.141242i
$780$	355.568	+	223.418i	0.455857	+	0.286434i
$781$	345.797	+	38.9620i	0.442762	+	0.0498873i
$782$			266.590i			0.340908i
$783$	128.458	−	286.726i	0.164058	−	0.366188i
$784$	−546.427			−0.696973
$785$	−17.8363	+	158.302i	−0.0227214	+	0.201658i
$786$	−63.7977	+	101.533i	−0.0811675	+	0.129177i
$787$	−114.188	−	26.0626i	−0.145092	−	0.0331163i	0.149358	−	0.988783i	$-0.452279\pi$
$787$	−114.188	−	26.0626i	−0.145092	−	0.0331163i	−0.294450	+	0.955667i	$0.595136\pi$
$788$	−498.852	+	397.821i	−0.633061	+	0.504849i
$789$	636.044	+	507.228i	0.806140	+	0.642875i
$790$	−7.46080	−	32.6879i	−0.00944405	−	0.0413771i
$791$	−609.207	+	1741.01i	−0.770174	+	2.20103i
$792$	115.337	+	239.500i	0.145628	+	0.302399i
$793$	528.006	+	840.317i	0.665833	+	1.05967i
$794$	19.8564	+	56.7464i	0.0250081	+	0.0714690i
$795$	−191.960	+	191.960i	−0.241459	+	0.241459i
$796$	−334.829	+	695.280i	−0.420640	+	0.873467i
$797$	776.435	−	87.4832i	0.974197	−	0.109766i	0.389508	−	0.921023i	$-0.372645\pi$
$797$	776.435	−	87.4832i	0.974197	−	0.109766i	0.584689	+	0.811257i	$0.301217\pi$
$798$	−10.9705	−	97.3662i	−0.0137475	−	0.122013i
$799$	−958.664	−	461.668i	−1.19983	−	0.577807i
$800$	−242.922	−	242.922i	−0.303653	−	0.303653i
$801$	306.138	−	107.122i	0.382195	−	0.133736i
$802$	33.0456	−	20.7639i	0.0412040	−	0.0258902i
$803$	−748.778	+	360.592i	−0.932475	+	0.449056i
$804$	−1033.73	−	361.718i	−1.28574	−	0.449898i
$805$	558.729	−	127.526i	0.694073	−	0.158418i
$806$	68.3892	−	85.7573i	0.0848501	−	0.106399i
$807$	167.621	+	210.190i	0.207709	+	0.260458i
$808$	−46.5930	+	204.137i	−0.0576646	+	0.252645i
$809$	−476.117	−	299.164i	−0.588526	−	0.369795i	0.204607	−	0.978844i	$-0.434408\pi$
$809$	−476.117	−	299.164i	−0.588526	−	0.369795i	−0.793133	+	0.609049i	$0.791551\pi$
$810$	24.5667	+	2.76800i	0.0303292	+	0.00341729i
$811$		−	503.652i		−	0.621026i	−0.950569	−	0.310513i	$-0.899499\pi$
$811$		−	503.652i		−	0.621026i	0.950569	−	0.310513i	$-0.100501\pi$
$812$	−998.207	−	318.657i	−1.22932	−	0.392434i
$813$	−54.0184			−0.0664432
$814$	−5.54952	+	49.2534i	−0.00681760	+	0.0605078i
$815$	211.034	−	335.859i	0.258938	−	0.412097i
$816$	1239.69	+	282.952i	1.51923	+	0.346755i
$817$	8.15609	−	6.50427i	0.00998298	−	0.00796116i
$818$	−175.236	−	139.746i	−0.214225	−	0.170838i
$819$	393.386	+	1723.54i	0.480325	+	2.10444i
$820$	−28.6034	+	81.7439i	−0.0348822	+	0.0996877i
$821$	53.3309	+	110.743i	0.0649585	+	0.134888i	0.930920	−	0.365223i	$-0.119007\pi$
$821$	53.3309	+	110.743i	0.0649585	+	0.134888i	−0.865962	+	0.500110i	$0.833293\pi$
$822$	−45.1729	−	71.8922i	−0.0549548	−	0.0874601i
$823$	178.958	+	511.434i	0.217446	+	0.621426i	0.999999	−	0.00115806i	$-0.000368624\pi$
$823$	178.958	+	511.434i	0.217446	+	0.621426i	−0.782553	+	0.622584i	$0.786083\pi$
$824$	66.0773	−	66.0773i	0.0801909	−	0.0801909i
$825$	411.701	−	854.905i	0.499031	−	1.03625i
$826$	−119.078	+	13.4168i	−0.144162	+	0.0162431i
$827$	−57.9236	−	514.086i	−0.0700406	−	0.621628i	−0.978873	−	0.204467i	$-0.934454\pi$
$827$	−57.9236	−	514.086i	−0.0700406	−	0.621628i	0.908833	−	0.417161i	$-0.136975\pi$
$828$	1732.20	+	834.181i	2.09202	+	1.00747i
$829$	319.300	+	319.300i	0.385163	+	0.385163i	0.872958	−	0.487795i	$-0.162199\pi$
$829$	319.300	+	319.300i	0.385163	+	0.385163i	−0.487795	+	0.872958i	$0.662199\pi$
$830$	28.1508	−	9.85040i	0.0339167	−	0.0118680i
$831$	−1282.48	+	805.834i	−1.54329	+	0.969716i
$832$	816.753	−	393.328i	0.981675	−	0.472750i
$833$	666.502	+	233.219i	0.800122	+	0.279975i
$834$	29.4865	−	6.73011i	0.0353555	−	0.00806967i
$835$	−261.006	+	327.291i	−0.312582	+	0.391965i
$836$	−161.021	−	201.914i	−0.192609	−	0.241524i
$837$	48.9850	−	214.617i	0.0585245	−	0.256413i
$838$	−34.4996	−	21.6775i	−0.0411689	−	0.0258681i
$839$	809.054	+	91.1585i	0.964307	+	0.108651i	0.580055	−	0.814577i	$-0.303031\pi$
$839$	809.054	+	91.1585i	0.964307	+	0.108651i	0.384252	+	0.923228i	$0.374459\pi$
$840$			152.390i			0.181417i
$841$	−685.444	−	487.285i	−0.815035	−	0.579412i
$842$	−140.827			−0.167253
$843$	9.93826	−	88.2045i	0.0117892	−	0.104632i
$844$	398.666	−	634.473i	0.472353	−	0.751745i
$845$	−153.933	−	35.1341i	−0.182169	−	0.0415788i
$846$	160.490	−	127.986i	0.189704	−	0.151284i
$847$	−270.430	−	215.661i	−0.319280	−	0.254618i
$848$	138.323	+	606.035i	0.163117	+	0.714663i
$849$	539.378	−	1541.45i	0.635310	−	1.81561i
$850$	61.3497	+	127.394i	0.0721761	+	0.149875i
$851$	386.550	+	615.190i	0.454230	+	0.722903i
$852$	221.035	+	631.682i	0.259431	+	0.741410i
$853$	410.706	−	410.706i	0.481484	−	0.481484i	−0.424121	−	0.905605i	$-0.639417\pi$
$853$	410.706	−	410.706i	0.481484	−	0.481484i	0.905605	+	0.424121i	$0.139417\pi$
$854$	−77.0991	+	160.098i	−0.0902799	+	0.187468i
$855$	117.137	−	13.1981i	0.137002	−	0.0154364i
$856$	18.4010	+	163.313i	0.0214965	+	0.190786i
$857$	72.5636	+	34.9448i	0.0846717	+	0.0407757i	0.475740	−	0.879586i	$-0.342180\pi$
$857$	72.5636	+	34.9448i	0.0846717	+	0.0407757i	−0.391069	+	0.920362i	$0.627894\pi$
$858$	−157.732	−	157.732i	−0.183837	−	0.183837i
$859$	−1227.43	+	429.496i	−1.42891	+	0.499996i	−0.930289	−	0.366827i	$-0.880444\pi$
$859$	−1227.43	+	429.496i	−1.42891	+	0.499996i	−0.498617	+	0.866822i	$0.666159\pi$
$860$	−6.77828	+	4.25907i	−0.00788172	+	0.00495241i
$861$	−587.841	+	283.089i	−0.682742	+	0.328791i
$862$	−15.5611	−	5.44505i	−0.0180523	−	0.00631676i
$863$	−562.427	+	128.370i	−0.651711	+	0.148749i	−0.535579	−	0.844485i	$-0.679907\pi$
$863$	−562.427	+	128.370i	−0.651711	+	0.148749i	−0.116132	+	0.993234i	$0.537050\pi$
$864$	−101.058	+	126.723i	−0.116965	+	0.146670i
$865$	12.9961	+	16.2966i	0.0150244	+	0.0188400i
$866$	19.5231	−	85.5365i	0.0225440	−	0.0987719i
$867$	−286.141	−	179.794i	−0.330036	−	0.207375i
$868$	−729.556	−	82.2012i	−0.840502	−	0.0947019i
$869$		−	665.783i		−	0.766149i
$870$	−18.3522	+	57.4892i	−0.0210945	+	0.0660796i
$871$	1040.84			1.19499
$872$	−13.9933	+	124.194i	−0.0160473	+	0.142424i
$873$	672.573	−	1070.39i	0.770416	−	1.22611i
$874$	98.7308	+	22.5347i	0.112964	+	0.0257834i
$875$	496.379	−	395.849i	0.567291	−	0.452399i
$876$	−1249.61	−	996.533i	−1.42650	−	1.13760i
$877$	189.702	+	831.137i	0.216308	+	0.947705i	0.960180	+	0.279383i	$0.0901300\pi$
$877$	189.702	+	831.137i	0.216308	+	0.947705i	−0.743872	+	0.668322i	$0.767013\pi$
$878$	−56.5220	+	161.531i	−0.0643759	+	0.183976i
$879$	884.278	+	1836.22i	1.00600	+	2.08899i
$880$	102.543	+	163.196i	0.116526	+	0.185449i
$881$	379.541	+	1084.67i	0.430807	+	1.23118i	0.930923	+	0.365217i	$0.119005\pi$
$881$	379.541	+	1084.67i	0.430807	+	1.23118i	−0.500116	+	0.865959i	$0.666709\pi$
$882$	−96.3264	+	96.3264i	−0.109214	+	0.109214i
$883$	266.951	−	554.329i	0.302322	−	0.627779i	−0.693361	−	0.720590i	$-0.743871\pi$
$883$	266.951	−	554.329i	0.302322	−	0.627779i	0.995684	+	0.0928113i	$0.0295853\pi$
$884$	−1234.78	+	139.127i	−1.39681	+	0.157383i
$885$	−28.8855	−	256.366i	−0.0326390	−	0.289679i
$886$	−130.587	−	62.8875i	−0.147390	−	0.0709792i
$887$	−594.479	−	594.479i	−0.670214	−	0.670214i	0.287552	−	0.957765i	$-0.407159\pi$
$887$	−594.479	−	594.479i	−0.670214	−	0.670214i	−0.957765	+	0.287552i	$0.907159\pi$
$888$	−182.353	+	63.8082i	−0.205353	+	0.0718560i
$889$	−51.9874	+	32.6659i	−0.0584785	+	0.0367445i
$890$	−11.8116	+	5.68819i	−0.0132715	+	0.00639122i
$891$	463.365	+	162.138i	0.520050	+	0.181973i
$892$	935.454	−	213.511i	1.04871	−	0.239362i
$893$	−252.012	+	316.013i	−0.282208	+	0.353878i
$894$	−55.1815	−	69.1954i	−0.0617243	−	0.0773998i
$895$	34.9595	−	153.167i	0.0390608	−	0.171137i
$896$	607.389	+	381.648i	0.677889	+	0.425946i
$897$	−3249.28	−	366.106i	−3.62238	−	0.408145i
$898$		−	245.189i		−	0.273039i
$899$	−537.750	−	240.921i	−0.598165	−	0.267988i
$900$	1019.72			1.13302
$901$	89.9406	−	798.245i	0.0998231	−	0.885954i
$902$	24.4753	−	38.9523i	0.0271345	−	0.0431843i
$903$	−58.7980	−	13.4203i	−0.0651141	−	0.0148619i
$904$	396.331	−	316.063i	0.438419	−	0.349627i
$905$	−87.4056	−	69.7036i	−0.0965807	−	0.0770206i
$906$	28.4233	+	124.531i	0.0313723	+	0.137451i
$907$	185.619	−	530.468i	0.204651	−	0.584860i	−0.795115	−	0.606458i	$-0.792590\pi$
$907$	185.619	−	530.468i	0.204651	−	0.584860i	0.999767	+	0.0215982i	$0.00687545\pi$
$908$	−266.933	−	554.292i	−0.293979	−	0.610453i
$909$	−498.178	−	792.846i	−0.548051	−	0.872218i
$910$	−23.6010	−	67.4477i	−0.0259351	−	0.0741184i
$911$	−184.062	+	184.062i	−0.202044	+	0.202044i	−0.800875	−	0.598831i	$-0.795632\pi$
$911$	−184.062	+	184.062i	−0.202044	+	0.202044i	0.598831	+	0.800875i	$0.295632\pi$
$912$	209.580	−	435.198i	0.229803	−	0.477191i
$913$	588.508	−	66.3089i	0.644587	−	0.0726275i
$914$	8.31585	+	73.8052i	0.00909831	+	0.0807497i
$915$	−344.680	−	165.989i	−0.376700	−	0.181409i
$916$	−218.275	−	218.275i	−0.238291	−	0.238291i
$917$	−719.977	+	251.931i	−0.785144	+	0.274734i
$918$	56.4860	−	35.4925i	0.0615316	−	0.0386629i
$919$	−486.005	+	234.047i	−0.528841	+	0.254676i	−0.679198	−	0.733956i	$-0.737672\pi$
$919$	−486.005	+	234.047i	−0.528841	+	0.254676i	0.150357	+	0.988632i	$0.451958\pi$
$920$	−148.664	−	52.0199i	−0.161592	−	0.0565434i
$921$	−1908.31	+	435.558i	−2.07199	+	0.472919i
$922$	−159.344	+	199.811i	−0.172824	+	0.216715i
$923$	−396.554	−	497.263i	−0.429636	−	0.538747i
$924$	−332.235	+	1455.62i	−0.359562	+	1.57534i
$925$	326.290	+	205.022i	0.352746	+	0.221645i
$926$	186.825	+	21.0501i	0.201755	+	0.0227323i
$927$			417.893i			0.450801i
$928$	279.765	+	331.613i	0.301470	+	0.357342i
$929$	1567.53			1.68733			0.843666	−	0.536869i	$-0.180393\pi$
$929$	1567.53			1.68733			0.843666	+	0.536869i	$0.180393\pi$
$930$	−4.73417	+	42.0170i	−0.00509051	+	0.0451795i
$931$	142.711	−	227.123i	0.153287	−	0.243956i
$932$	1011.35	+	230.833i	1.08514	+	0.247675i
$933$	1684.92	−	1343.68i	1.80591	−	1.44017i
$934$	53.5909	+	42.7373i	0.0573778	+	0.0457573i
$935$	−55.4227	−	242.823i	−0.0592756	−	0.259703i
$936$	160.468	−	458.592i	0.171440	−	0.489949i
$937$	−729.434	−	1514.69i	−0.778478	−	1.61653i	−0.787304	−	0.616565i	$-0.788524\pi$
$937$	−729.434	−	1514.69i	−0.778478	−	1.61653i	0.00882555	−	0.999961i	$-0.497191\pi$
$938$	99.1506	+	157.797i	0.105704	+	0.168227i
$939$	7.96287	+	22.7566i	0.00848016	+	0.0242349i
$940$	219.324	−	219.324i	0.233323	−	0.233323i
$941$	2.80284	−	5.82016i	0.00297858	−	0.00618508i	−0.899474	−	0.436974i	$-0.856050\pi$
$941$	2.80284	−	5.82016i	0.00297858	−	0.00618508i	0.902453	+	0.430789i	$0.141765\pi$
$942$	161.718	−	18.2212i	0.171675	−	0.0193431i
$943$	−75.5028	−	670.105i	−0.0800665	−	0.710610i
$944$	−532.242	−	256.314i	−0.563815	−	0.271519i
$945$	−101.407	−	101.407i	−0.107309	−	0.107309i
$946$	4.01374	−	1.40447i	0.00424285	−	0.00148464i
$947$	1038.57	−	652.574i	1.09669	−	0.689096i	0.142951	−	0.989730i	$-0.454341\pi$
$947$	1038.57	−	652.574i	1.09669	−	0.689096i	0.953740	+	0.300634i	$0.0971982\pi$
$948$	1153.62	−	555.553i	1.21690	−	0.586027i
$949$	1433.75	+	501.692i	1.51080	+	0.528653i
$950$	52.3657	−	11.9521i	0.0551218	−	0.0125812i
$951$	−320.434	+	401.812i	−0.336945	+	0.422515i
$952$	−281.148	−	352.548i	−0.295323	−	0.370324i
$953$	−247.527	+	1084.49i	−0.259735	+	1.13797i	0.661802	+	0.749679i	$0.269792\pi$
$953$	−247.527	+	1084.49i	−0.259735	+	1.13797i	−0.921536	+	0.388292i	$0.873065\pi$
$954$	131.218	+	82.4500i	0.137546	+	0.0864256i
$955$	−376.814	−	42.4567i	−0.394569	−	0.0444573i
$956$			1729.44i			1.80904i
$957$	−609.312	+	1031.86i	−0.636690	+	1.07823i
$958$	46.1231			0.0481452
$959$	60.4718	−	536.702i	0.0630572	−	0.559648i
$960$	−185.919	+	295.889i	−0.193666	+	0.308218i
$961$	534.394	+	121.972i	0.556081	+	0.126922i
$962$	70.8274	−	56.4830i	0.0736251	−	0.0587141i
$963$	−574.608	−	458.234i	−0.596685	−	0.475840i
$964$	−115.765	−	507.198i	−0.120088	−	0.526139i
$965$	−43.3417	+	123.864i	−0.0449137	+	0.128356i
$966$	−254.024	−	527.486i	−0.262965	−	0.546052i
$967$	−54.4142	−	86.5997i	−0.0562711	−	0.0895550i	0.817404	−	0.576065i	$-0.195413\pi$
$967$	−54.4142	−	86.5997i	−0.0562711	−	0.0895550i	−0.873675	+	0.486510i	$0.838270\pi$
$968$	31.3967	+	89.7265i	0.0324346	+	0.0926927i
$969$	−441.380	+	441.380i	−0.455501	+	0.455501i
$970$	−22.1705	+	46.0376i	−0.0228562	+	0.0474614i
$971$	−689.238	+	77.6584i	−0.709823	+	0.0799778i	−0.459491	−	0.888182i	$-0.651968\pi$
$971$	−689.238	+	77.6584i	−0.709823	+	0.0799778i	−0.250332	+	0.968160i	$0.580540\pi$
$972$	148.238	+	1315.65i	0.152508	+	1.35355i
$973$	173.338	+	83.4752i	0.178148	+	0.0857916i
$974$	87.0560	+	87.0560i	0.0893799	+	0.0893799i
$975$	−1636.96	+	572.799i	−1.67894	+	0.587486i
$976$	−741.733	+	466.062i	−0.759972	+	0.477522i
$977$	−1193.77	+	574.889i	−1.22187	+	0.588423i	−0.929832	−	0.367983i	$-0.880048\pi$
$977$	−1193.77	+	574.889i	−1.22187	+	0.588423i	−0.292040	+	0.956406i	$0.594334\pi$
$978$	−382.478	−	133.835i	−0.391082	−	0.136845i
$979$	−253.800	+	57.9282i	−0.259244	+	0.0591708i
$980$	−128.338	+	160.931i	−0.130957	+	0.164215i
$981$	−348.471	−	436.968i	−0.355220	−	0.445432i
$982$	−26.3618	+	115.499i	−0.0268450	+	0.117616i
$983$	895.500	+	562.680i	0.910987	+	0.572411i	0.903985	−	0.427564i	$-0.140628\pi$
$983$	895.500	+	562.680i	0.910987	+	0.572411i	0.00700229	+	0.999975i	$0.497771\pi$
$984$	178.185	+	20.0766i	0.181082	+	0.0204031i
$985$			233.753i			0.237313i
$986$	−63.6061	−	166.858i	−0.0645092	−	0.169227i
$987$	2336.75			2.36753
$988$	−52.8501	+	469.058i	−0.0534920	+	0.474755i
$989$	33.1635	−	52.7794i	0.0335324	−	0.0533665i
$990$	46.8454	+	10.6922i	0.0473186	+	0.0108002i
$991$	1276.10	−	1017.65i	1.28769	−	1.02690i	0.290132	−	0.956987i	$-0.406301\pi$
$991$	1276.10	−	1017.65i	1.28769	−	1.02690i	0.997553	−	0.0699086i	$-0.0222708\pi$
$992$	237.667	+	189.533i	0.239584	+	0.191062i
$993$	236.083	+	1034.35i	0.237747	+	1.04164i
$994$	37.6122	−	107.490i	0.0378392	−	0.108138i
$995$	122.665	+	254.717i	0.123282	+	0.255997i
$996$	605.967	+	964.390i	0.608400	+	0.968263i
$997$	395.022	+	1128.91i	0.396211	+	1.13230i	0.953345	+	0.301883i	$0.0976150\pi$
$997$	395.022	+	1128.91i	0.396211	+	1.13230i	−0.557135	+	0.830422i	$0.688099\pi$
$998$	72.0850	−	72.0850i	0.0722294	−	0.0722294i
$999$	78.8852	−	163.807i	0.0789641	−	0.163971i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.3.f.a.27.3	yes	48
3.2	odd	2		261.3.s.a.172.2		48
29.14	odd	28	inner	29.3.f.a.14.3	✓	48
87.14	even	28		261.3.s.a.217.2		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.3.f.a.14.3	✓	48	29.14	odd	28	inner
29.3.f.a.27.3	yes	48	1.1	even	1	trivial
261.3.s.a.172.2		48	3.2	odd	2
261.3.s.a.217.2		48	87.14	even	28

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.f (of order \(28\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0361447 + 0.320793i) q^{2} +(-2.40292 + 3.82423i) q^{3} +(3.79811 + 0.866894i) q^{4} +(1.11585 - 0.889864i) q^{5} +(-1.13993 - 0.909068i) q^{6} +(-2.06382 - 9.04217i) q^{7} +(-0.841863 + 2.40591i) q^{8} +(-4.94574 - 10.2699i) q^{9} +O(q^{10})\)	\(q+(-0.0361447 + 0.320793i) q^{2} +(-2.40292 + 3.82423i) q^{3} +(3.79811 + 0.866894i) q^{4} +(1.11585 - 0.889864i) q^{5} +(-1.13993 - 0.909068i) q^{6} +(-2.06382 - 9.04217i) q^{7} +(-0.841863 + 2.40591i) q^{8} +(-4.94574 - 10.2699i) q^{9} +(0.245130 + 0.390122i) q^{10} +(3.02175 + 8.63567i) q^{11} +(-12.4418 + 12.4418i) q^{12} +(7.25544 - 15.0661i) q^{13} +(2.97526 - 0.335232i) q^{14} +(0.721732 + 6.40555i) q^{15} +(13.2986 + 6.40425i) q^{16} +(-13.4875 - 13.4875i) q^{17} +(3.47329 - 1.21536i) q^{18} +(-6.13512 + 3.85495i) q^{19} +(5.00955 - 2.41247i) q^{20} +(39.5385 + 13.8351i) q^{21} +(-2.87949 + 0.657224i) q^{22} +(-26.9938 + 33.8491i) q^{23} +(-7.17780 - 9.00068i) q^{24} +(-5.10975 + 22.3873i) q^{25} +(4.57085 + 2.87206i) q^{26} +(10.7659 + 1.21302i) q^{27} -36.1322i q^{28} +(8.81918 - 27.6265i) q^{29} -2.08095 q^{30} +(2.27501 - 20.1913i) q^{31} +(-7.95959 + 12.6676i) q^{32} +(-40.2858 - 9.19497i) q^{33} +(4.81419 - 3.83919i) q^{34} +(-10.3492 - 8.25322i) q^{35} +(-9.88152 - 43.2937i) q^{36} +(5.54261 - 15.8399i) q^{37} +(-1.01489 - 2.10744i) q^{38} +(40.1818 + 63.9490i) q^{39} +(1.20153 + 3.43378i) q^{40} +(-11.0137 + 11.0137i) q^{41} +(-5.86733 + 12.1836i) q^{42} +(-1.43070 + 0.161201i) q^{43} +(3.99073 + 35.4187i) q^{44} +(-14.6576 - 7.05871i) q^{45} +(-9.88290 - 9.88290i) q^{46} +(52.6538 - 18.4244i) q^{47} +(-56.4467 + 35.4678i) q^{48} +(-33.3540 + 16.0624i) q^{49} +(-6.99700 - 2.44836i) q^{50} +(83.9885 - 19.1698i) q^{51} +(40.6176 - 50.9329i) q^{52} +(26.2579 + 32.9263i) q^{53} +(-0.778260 + 3.40978i) q^{54} +(11.0564 + 6.94719i) q^{55} +(23.4920 + 2.64692i) q^{56} -32.7252i q^{57} +(8.54363 + 3.82769i) q^{58} -40.0225 q^{59} +(-2.81171 + 24.9547i) q^{60} +(-31.5754 + 50.2519i) q^{61} +(6.39500 + 1.45962i) q^{62} +(-82.6553 + 65.9154i) q^{63} +(42.3842 + 33.8003i) q^{64} +(-5.31074 - 23.2679i) q^{65} +(4.40581 - 12.5911i) q^{66} +(27.0064 + 56.0793i) q^{67} +(-39.5347 - 62.9191i) q^{68} +(-64.5829 - 184.567i) q^{69} +(3.02165 - 3.02165i) q^{70} +(16.5027 - 34.2683i) q^{71} +(28.8721 - 3.25311i) q^{72} +(10.1706 + 90.2664i) q^{73} +(4.88099 + 2.35056i) q^{74} +(-73.3358 - 73.3358i) q^{75} +(-26.6437 + 9.32302i) q^{76} +(71.8488 - 45.1456i) q^{77} +(-21.9668 + 10.5787i) q^{78} +(-68.6869 - 24.0346i) q^{79} +(20.5381 - 4.68770i) q^{80} +(33.4546 - 41.9508i) q^{81} +(-3.13504 - 3.93121i) q^{82} +(14.4041 - 63.1083i) q^{83} +(138.178 + 86.8230i) q^{84} +(-27.0520 - 3.04803i) q^{85} -0.464786i q^{86} +(84.4582 + 100.111i) q^{87} -23.3205 q^{88} +(-3.18582 + 28.2750i) q^{89} +(2.79418 - 4.44691i) q^{90} +(-151.204 - 34.5113i) q^{91} +(-131.869 + 105.162i) q^{92} +(71.7494 + 57.2182i) q^{93} +(4.00726 + 17.5569i) q^{94} +(-3.41551 + 9.76097i) q^{95} +(-29.3176 - 60.8786i) q^{96} +(59.0040 + 93.9044i) q^{97} +(-3.94715 - 11.2803i) q^{98} +(73.7429 - 73.7429i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 16 q^{2} - 12 q^{3} - 14 q^{4} - 14 q^{5} - 14 q^{6} - 10 q^{7} + 28 q^{8} - 14 q^{9}+O(q^{10}) \) 48 * q - 16 * q^2 - 12 * q^3 - 14 * q^4 - 14 * q^5 - 14 * q^6 - 10 * q^7 + 28 * q^8 - 14 * q^9	\( 48 q - 16 q^{2} - 12 q^{3} - 14 q^{4} - 14 q^{5} - 14 q^{6} - 10 q^{7} + 28 q^{8} - 14 q^{9} - 20 q^{10} - 8 q^{11} - 68 q^{12} - 14 q^{13} + 26 q^{14} - 4 q^{15} + 18 q^{16} - 26 q^{17} - 34 q^{18} + 2 q^{19} + 46 q^{20} + 218 q^{21} + 154 q^{22} + 56 q^{23} + 154 q^{24} - 34 q^{25} + 110 q^{26} + 126 q^{27} - 170 q^{29} + 24 q^{30} - 88 q^{31} - 132 q^{32} - 224 q^{33} - 224 q^{34} - 210 q^{35} - 434 q^{36} - 56 q^{37} - 294 q^{38} - 232 q^{39} - 492 q^{40} - 34 q^{41} - 14 q^{42} + 176 q^{43} + 126 q^{44} + 114 q^{45} + 744 q^{46} + 208 q^{47} + 640 q^{48} + 506 q^{49} + 732 q^{50} + 322 q^{51} + 690 q^{52} - 14 q^{53} - 36 q^{54} + 284 q^{55} + 332 q^{56} - 508 q^{58} - 44 q^{59} - 316 q^{60} - 30 q^{61} - 504 q^{62} - 686 q^{63} - 896 q^{64} - 554 q^{65} - 608 q^{66} - 574 q^{67} - 796 q^{68} - 806 q^{69} - 1066 q^{70} + 224 q^{71} + 748 q^{72} - 22 q^{73} + 820 q^{74} + 768 q^{75} + 514 q^{76} + 436 q^{77} + 282 q^{78} + 564 q^{79} + 1162 q^{80} + 670 q^{81} - 18 q^{82} - 126 q^{83} + 572 q^{84} + 38 q^{85} - 118 q^{87} - 384 q^{88} - 160 q^{89} - 828 q^{90} - 434 q^{91} - 1022 q^{92} - 406 q^{93} - 2 q^{94} - 642 q^{95} - 1176 q^{96} + 604 q^{97} - 102 q^{98} + 316 q^{99}+O(q^{100}) \) 48 * q - 16 * q^2 - 12 * q^3 - 14 * q^4 - 14 * q^5 - 14 * q^6 - 10 * q^7 + 28 * q^8 - 14 * q^9 - 20 * q^10 - 8 * q^11 - 68 * q^12 - 14 * q^13 + 26 * q^14 - 4 * q^15 + 18 * q^16 - 26 * q^17 - 34 * q^18 + 2 * q^19 + 46 * q^20 + 218 * q^21 + 154 * q^22 + 56 * q^23 + 154 * q^24 - 34 * q^25 + 110 * q^26 + 126 * q^27 - 170 * q^29 + 24 * q^30 - 88 * q^31 - 132 * q^32 - 224 * q^33 - 224 * q^34 - 210 * q^35 - 434 * q^36 - 56 * q^37 - 294 * q^38 - 232 * q^39 - 492 * q^40 - 34 * q^41 - 14 * q^42 + 176 * q^43 + 126 * q^44 + 114 * q^45 + 744 * q^46 + 208 * q^47 + 640 * q^48 + 506 * q^49 + 732 * q^50 + 322 * q^51 + 690 * q^52 - 14 * q^53 - 36 * q^54 + 284 * q^55 + 332 * q^56 - 508 * q^58 - 44 * q^59 - 316 * q^60 - 30 * q^61 - 504 * q^62 - 686 * q^63 - 896 * q^64 - 554 * q^65 - 608 * q^66 - 574 * q^67 - 796 * q^68 - 806 * q^69 - 1066 * q^70 + 224 * q^71 + 748 * q^72 - 22 * q^73 + 820 * q^74 + 768 * q^75 + 514 * q^76 + 436 * q^77 + 282 * q^78 + 564 * q^79 + 1162 * q^80 + 670 * q^81 - 18 * q^82 - 126 * q^83 + 572 * q^84 + 38 * q^85 - 118 * q^87 - 384 * q^88 - 160 * q^89 - 828 * q^90 - 434 * q^91 - 1022 * q^92 - 406 * q^93 - 2 * q^94 - 642 * q^95 - 1176 * q^96 + 604 * q^97 - 102 * q^98 + 316 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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