LMFDB - Embedded newform 128.3.l.a.43.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [128,3,Mod(3,128)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(128, base_ring=CyclotomicField(32))

chi = DirichletCharacter(H, H._module([16, 3]))

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

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

chi := DirichletCharacter("128.3");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 128 = 2^{7} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	128.l (of order $32$, degree $16$, 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:	$3.48774738381$
Analytic rank:	$0$
Dimension:	$496$
Relative dimension:	$31$ over $\Q(\zeta_{32})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{32}]$

Embedding invariants

Embedding label			43.1
Character	$\chi$	$=$	128.43
Dual form			128.3.l.a.3.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.99185 + 0.180370i) q^{2} +(1.05127 + 0.862751i) q^{3} +(3.93493 - 0.718539i) q^{4} +(-7.90123 + 2.39681i) q^{5} +(-2.24958 - 1.52885i) q^{6} +(1.29801 - 6.52556i) q^{7} +(-7.70819 + 2.14097i) q^{8} +(-1.39499 - 7.01311i) q^{9} +O(q^{10})$	\(q+(-1.99185 + 0.180370i) q^{2} +(1.05127 + 0.862751i) q^{3} +(3.93493 - 0.718539i) q^{4} +(-7.90123 + 2.39681i) q^{5} +(-2.24958 - 1.52885i) q^{6} +(1.29801 - 6.52556i) q^{7} +(-7.70819 + 2.14097i) q^{8} +(-1.39499 - 7.01311i) q^{9} +(15.3057 - 6.19923i) q^{10} +(0.0388787 - 0.394742i) q^{11} +(4.75658 + 2.63949i) q^{12} +(-1.94755 + 6.42020i) q^{13} +(-1.40844 + 13.2321i) q^{14} +(-10.3741 - 4.29711i) q^{15} +(14.9674 - 5.65481i) q^{16} +(-11.7599 - 28.3908i) q^{17} +(4.04357 + 13.7174i) q^{18} +(-7.55037 - 14.1257i) q^{19} +(-29.3686 + 15.1086i) q^{20} +(6.99449 - 5.74023i) q^{21} +(-0.00624099 + 0.793280i) q^{22} +(-19.3042 - 12.8987i) q^{23} +(-9.95048 - 4.39953i) q^{24} +(35.8979 - 23.9862i) q^{25} +(2.72121 - 13.1394i) q^{26} +(10.3538 - 19.3706i) q^{27} +(0.418730 - 26.6103i) q^{28} +(2.58223 + 26.2178i) q^{29} +(21.4388 + 6.68801i) q^{30} +(-40.1489 + 40.1489i) q^{31} +(-28.7929 + 13.9632i) q^{32} +(0.381436 - 0.381436i) q^{33} +(28.5447 + 54.4291i) q^{34} +(5.38462 + 54.6710i) q^{35} +(-10.5284 - 26.5938i) q^{36} +(19.9517 - 37.3269i) q^{37} +(17.5871 + 26.7745i) q^{38} +(-7.58643 + 5.06909i) q^{39} +(55.7727 - 35.3913i) q^{40} +(24.1411 + 16.1305i) q^{41} +(-12.8966 + 12.6953i) q^{42} +(-38.9814 + 31.9912i) q^{43} +(-0.130653 - 1.58122i) q^{44} +(27.8313 + 52.0686i) q^{45} +(40.7776 + 22.2103i) q^{46} +(18.1618 + 43.8464i) q^{47} +(20.6134 + 6.96844i) q^{48} +(4.37204 + 1.81096i) q^{49} +(-67.1769 + 54.2519i) q^{50} +(12.1315 - 39.9921i) q^{51} +(-3.05030 + 26.6625i) q^{52} +(2.86524 - 29.0913i) q^{53} +(-17.1293 + 40.4508i) q^{54} +(0.638933 + 3.21213i) q^{55} +(3.96565 + 53.0793i) q^{56} +(4.24956 - 21.3640i) q^{57} +(-9.87231 - 51.7561i) q^{58} +(58.5036 - 17.7469i) q^{59} +(-43.9092 - 9.45461i) q^{60} +(-54.0901 - 44.3906i) q^{61} +(72.7290 - 87.2123i) q^{62} -47.5752 q^{63} +(54.8325 - 33.0060i) q^{64} -55.3954i q^{65} +(-0.690964 + 0.828563i) q^{66} +(-25.5848 + 31.1751i) q^{67} +(-66.6741 - 103.266i) q^{68} +(-9.16551 - 30.2146i) q^{69} +(-20.5864 - 107.925i) q^{70} +(-5.17915 - 1.03020i) q^{71} +(25.7677 + 51.0718i) q^{72} +(-26.9577 + 5.36223i) q^{73} +(-33.0080 + 77.9483i) q^{74} +(58.4324 + 5.75509i) q^{75} +(-39.8601 - 50.1586i) q^{76} +(-2.52545 - 0.766086i) q^{77} +(14.1967 - 11.4652i) q^{78} +(17.2775 - 41.7116i) q^{79} +(-104.707 + 80.5540i) q^{80} +(-31.8593 + 13.1965i) q^{81} +(-50.9948 - 27.7753i) q^{82} +(-47.4557 + 25.3656i) q^{83} +(23.3983 - 27.6132i) q^{84} +(160.965 + 196.136i) q^{85} +(71.8748 - 70.7527i) q^{86} +(-19.9048 + 29.7897i) q^{87} +(0.545445 + 3.12599i) q^{88} +(-13.9882 - 20.9348i) q^{89} +(-64.8273 - 98.6930i) q^{90} +(39.3675 + 21.0423i) q^{91} +(-85.2290 - 36.8846i) q^{92} +(-76.8457 + 7.56864i) q^{93} +(-44.0841 - 84.0596i) q^{94} +(93.5139 + 93.5139i) q^{95} +(-42.3157 - 10.1621i) q^{96} +(56.7531 + 56.7531i) q^{97} +(-9.03510 - 2.81858i) q^{98} +(-2.82260 + 0.278002i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 496 q - 16 q^{2} - 16 q^{3} - 16 q^{4} - 16 q^{5} - 16 q^{6} - 16 q^{7} - 16 q^{8} - 16 q^{9}+O(q^{10}) $ 496 * q - 16 * q^2 - 16 * q^3 - 16 * q^4 - 16 * q^5 - 16 * q^6 - 16 * q^7 - 16 * q^8 - 16 * q^9	\( 496 q - 16 q^{2} - 16 q^{3} - 16 q^{4} - 16 q^{5} - 16 q^{6} - 16 q^{7} - 16 q^{8} - 16 q^{9} - 16 q^{10} - 16 q^{11} - 16 q^{12} - 16 q^{13} - 16 q^{14} - 16 q^{15} - 16 q^{16} - 16 q^{17} - 16 q^{18} - 16 q^{19} - 16 q^{20} - 16 q^{21} - 16 q^{22} - 16 q^{23} - 16 q^{24} - 16 q^{25} - 16 q^{26} - 16 q^{27} - 16 q^{28} - 16 q^{29} - 16 q^{30} - 16 q^{31} - 16 q^{32} - 16 q^{33} - 16 q^{34} - 16 q^{35} - 16 q^{36} - 16 q^{37} - 16 q^{38} - 16 q^{39} - 16 q^{40} - 16 q^{41} - 16 q^{42} - 16 q^{43} - 16 q^{44} - 16 q^{45} - 16 q^{46} - 16 q^{47} - 16 q^{48} - 16 q^{49} - 640 q^{50} - 16 q^{51} - 1072 q^{52} - 16 q^{53} - 1168 q^{54} - 16 q^{55} - 800 q^{56} - 16 q^{57} - 736 q^{58} - 16 q^{59} - 592 q^{60} - 16 q^{61} - 112 q^{62} - 32 q^{63} + 176 q^{64} + 560 q^{66} - 16 q^{67} + 464 q^{68} - 16 q^{69} + 1328 q^{70} - 16 q^{71} + 1280 q^{72} - 16 q^{73} + 1216 q^{74} - 16 q^{75} + 1648 q^{76} - 16 q^{77} + 1424 q^{78} - 16 q^{79} + 800 q^{80} - 16 q^{81} - 16 q^{82} - 16 q^{83} - 16 q^{84} - 16 q^{85} - 16 q^{86} - 16 q^{87} - 16 q^{88} - 16 q^{89} - 16 q^{90} - 16 q^{91} - 16 q^{92} - 16 q^{93} - 16 q^{94} - 16 q^{95} - 16 q^{96} - 16 q^{97} - 16 q^{98} - 16 q^{99}+O(q^{100}) \) 496 * q - 16 * q^2 - 16 * q^3 - 16 * q^4 - 16 * q^5 - 16 * q^6 - 16 * q^7 - 16 * q^8 - 16 * q^9 - 16 * q^10 - 16 * q^11 - 16 * q^12 - 16 * q^13 - 16 * q^14 - 16 * q^15 - 16 * q^16 - 16 * q^17 - 16 * q^18 - 16 * q^19 - 16 * q^20 - 16 * q^21 - 16 * q^22 - 16 * q^23 - 16 * q^24 - 16 * q^25 - 16 * q^26 - 16 * q^27 - 16 * q^28 - 16 * q^29 - 16 * q^30 - 16 * q^31 - 16 * q^32 - 16 * q^33 - 16 * q^34 - 16 * q^35 - 16 * q^36 - 16 * q^37 - 16 * q^38 - 16 * q^39 - 16 * q^40 - 16 * q^41 - 16 * q^42 - 16 * q^43 - 16 * q^44 - 16 * q^45 - 16 * q^46 - 16 * q^47 - 16 * q^48 - 16 * q^49 - 640 * q^50 - 16 * q^51 - 1072 * q^52 - 16 * q^53 - 1168 * q^54 - 16 * q^55 - 800 * q^56 - 16 * q^57 - 736 * q^58 - 16 * q^59 - 592 * q^60 - 16 * q^61 - 112 * q^62 - 32 * q^63 + 176 * q^64 + 560 * q^66 - 16 * q^67 + 464 * q^68 - 16 * q^69 + 1328 * q^70 - 16 * q^71 + 1280 * q^72 - 16 * q^73 + 1216 * q^74 - 16 * q^75 + 1648 * q^76 - 16 * q^77 + 1424 * q^78 - 16 * q^79 + 800 * q^80 - 16 * q^81 - 16 * q^82 - 16 * q^83 - 16 * q^84 - 16 * q^85 - 16 * q^86 - 16 * q^87 - 16 * q^88 - 16 * q^89 - 16 * q^90 - 16 * q^91 - 16 * q^92 - 16 * q^93 - 16 * q^94 - 16 * q^95 - 16 * q^96 - 16 * q^97 - 16 * q^98 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/128\mathbb{Z}\right)^\times$.

$n$	$5$	$127$
$\chi(n)$	$e\left(\frac{29}{32}\right)$	$-1$

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 $

$2$	−1.99185	+	0.180370i	−0.995925	+	0.0901849i
$2$	−1.99185	+	0.180370i	−0.995925	+	0.0901849i
$3$	1.05127	+	0.862751i	0.350422	+	0.287584i	0.793093	−	0.609100i	$-0.208469\pi$
$3$	1.05127	+	0.862751i	0.350422	+	0.287584i	−0.442672	+	0.896684i	$0.645969\pi$
$4$	3.93493	−	0.718539i	0.983733	−	0.179635i
$5$	−7.90123	+	2.39681i	−1.58025	+	0.479362i	−0.953885	−	0.300172i	$-0.902956\pi$
$5$	−7.90123	+	2.39681i	−1.58025	+	0.479362i	−0.626360	+	0.779534i	$0.715456\pi$
$6$	−2.24958	−	1.52885i	−0.374929	−	0.254809i
$7$	1.29801	−	6.52556i	0.185431	−	0.932222i	−0.770233	−	0.637762i	$-0.779860\pi$
$7$	1.29801	−	6.52556i	0.185431	−	0.932222i	0.955664	−	0.294460i	$-0.0951398\pi$
$8$	−7.70819	+	2.14097i	−0.963524	+	0.267621i
$9$	−1.39499	−	7.01311i	−0.154999	−	0.779234i
$10$	15.3057	−	6.19923i	1.53057	−	0.619923i
$11$	0.0388787	−	0.394742i	0.00353443	−	0.0358856i	−0.993256	−	0.115944i	$-0.963011\pi$
$11$	0.0388787	−	0.394742i	0.00353443	−	0.0358856i	0.996790	+	0.0800584i	$0.0255107\pi$
$12$	4.75658	+	2.63949i	0.396382	+	0.219958i
$13$	−1.94755	+	6.42020i	−0.149811	+	0.493862i	−0.999438	−	0.0335229i	$-0.989327\pi$
$13$	−1.94755	+	6.42020i	−0.149811	+	0.493862i	0.849627	+	0.527385i	$0.176827\pi$
$14$	−1.40844	+	13.2321i	−0.100603	+	0.945147i
$15$	−10.3741	−	4.29711i	−0.691609	−	0.286474i
$16$	14.9674	−	5.65481i	0.935463	−	0.353426i
$17$	−11.7599	−	28.3908i	−0.691756	−	1.67005i	−0.741212	−	0.671271i	$-0.765749\pi$
$17$	−11.7599	−	28.3908i	−0.691756	−	1.67005i	0.0494563	−	0.998776i	$-0.484251\pi$
$18$	4.04357	+	13.7174i	0.224643	+	0.762080i
$19$	−7.55037	−	14.1257i	−0.397388	−	0.743460i	0.601057	−	0.799206i	$-0.294746\pi$
$19$	−7.55037	−	14.1257i	−0.397388	−	0.743460i	−0.998445	+	0.0557458i	$0.982246\pi$
$20$	−29.3686	+	15.1086i	−1.46843	+	0.755432i
$21$	6.99449	−	5.74023i	0.333071	−	0.273344i
$22$	−0.00624099	+	0.793280i	−0.000283681	+	0.0360582i
$23$	−19.3042	−	12.8987i	−0.839314	−	0.560812i	0.0599585	−	0.998201i	$-0.480903\pi$
$23$	−19.3042	−	12.8987i	−0.839314	−	0.560812i	−0.899272	+	0.437389i	$0.855903\pi$
$24$	−9.95048	−	4.39953i	−0.414603	−	0.183314i
$25$	35.8979	−	23.9862i	1.43592	−	0.959449i
$26$	2.72121	−	13.1394i	0.104662	−	0.505360i
$27$	10.3538	−	19.3706i	0.383474	−	0.717429i
$28$	0.418730	−	26.6103i	0.0149546	−	0.950368i
$29$	2.58223	+	26.2178i	0.0890423	+	0.904062i	0.931122	+	0.364708i	$0.118831\pi$
$29$	2.58223	+	26.2178i	0.0890423	+	0.904062i	−0.842080	+	0.539353i	$0.818669\pi$
$30$	21.4388	+	6.68801i	0.714626	+	0.222934i
$31$	−40.1489	+	40.1489i	−1.29513	+	1.29513i	−0.363553	+	0.931573i	$0.618437\pi$
$31$	−40.1489	+	40.1489i	−1.29513	+	1.29513i	−0.931573	+	0.363553i	$0.881563\pi$
$32$	−28.7929	+	13.9632i	−0.899777	+	0.436350i
$33$	0.381436	−	0.381436i	0.0115587	−	0.0115587i
$34$	28.5447	+	54.4291i	0.839550	+	1.60086i
$35$	5.38462	+	54.6710i	0.153846	+	1.56203i
$36$	−10.5284	−	26.5938i	−0.292456	−	0.738715i
$37$	19.9517	−	37.3269i	0.539234	−	1.00884i	−0.453811	−	0.891098i	$-0.649936\pi$
$37$	19.9517	−	37.3269i	0.539234	−	1.00884i	0.993045	−	0.117738i	$-0.0375641\pi$
$38$	17.5871	+	26.7745i	0.462817	+	0.704592i
$39$	−7.58643	+	5.06909i	−0.194524	+	0.129977i
$40$	55.7727	−	35.3913i	1.39432	−	0.884783i
$41$	24.1411	+	16.1305i	0.588806	+	0.393428i	0.813982	−	0.580890i	$-0.197295\pi$
$41$	24.1411	+	16.1305i	0.588806	+	0.393428i	−0.225175	+	0.974318i	$0.572295\pi$
$42$	−12.8966	+	12.6953i	−0.307062	+	0.302268i
$43$	−38.9814	+	31.9912i	−0.906544	+	0.743981i	−0.967157	−	0.254180i	$-0.918194\pi$
$43$	−38.9814	+	31.9912i	−0.906544	+	0.743981i	0.0606133	+	0.998161i	$0.480694\pi$
$44$	−0.130653	−	1.58122i	−0.00296938	−	0.0359368i
$45$	27.8313	+	52.0686i	0.618472	+	1.15708i
$46$	40.7776	+	22.2103i	0.886470	+	0.482833i
$47$	18.1618	+	43.8464i	0.386421	+	0.932902i	0.990692	+	0.136123i	$0.0434643\pi$
$47$	18.1618	+	43.8464i	0.386421	+	0.932902i	−0.604271	+	0.796779i	$0.706536\pi$
$48$	20.6134	+	6.96844i	0.429446	+	0.145176i
$49$	4.37204	+	1.81096i	0.0892254	+	0.0369584i
$50$	−67.1769	+	54.2519i	−1.34354	+	1.08504i
$51$	12.1315	−	39.9921i	0.237872	−	0.784158i
$52$	−3.05030	+	26.6625i	−0.0586596	+	0.512740i
$53$	2.86524	−	29.0913i	0.0540611	−	0.548892i	−0.929563	−	0.368662i	$-0.879816\pi$
$53$	2.86524	−	29.0913i	0.0540611	−	0.548892i	0.983625	−	0.180230i	$-0.0576840\pi$
$54$	−17.1293	+	40.4508i	−0.317210	+	0.749089i
$55$	0.638933	+	3.21213i	0.0116170	+	0.0584024i
$56$	3.96565	+	53.0793i	0.0708152	+	0.947844i
$57$	4.24956	−	21.3640i	0.0745537	−	0.374807i
$58$	−9.87231	−	51.7561i	−0.170212	−	0.892347i
$59$	58.5036	−	17.7469i	0.991586	−	0.300794i	0.247507	−	0.968886i	$-0.420389\pi$
$59$	58.5036	−	17.7469i	0.991586	−	0.300794i	0.744079	+	0.668092i	$0.232889\pi$
$60$	−43.9092	−	9.45461i	−0.731820	−	0.157577i
$61$	−54.0901	−	44.3906i	−0.886723	−	0.727715i	0.0763143	−	0.997084i	$-0.475685\pi$
$61$	−54.0901	−	44.3906i	−0.886723	−	0.727715i	−0.963037	+	0.269369i	$0.913185\pi$
$62$	72.7290	−	87.2123i	1.17305	−	1.40665i
$63$	−47.5752			−0.755161
$64$	54.8325	−	33.0060i	0.856758	−	0.515718i
$65$		−	55.3954i		−	0.852237i
$66$	−0.690964	+	0.828563i	−0.0104691	+	0.0125540i
$67$	−25.5848	+	31.1751i	−0.381862	+	0.465301i	−0.928101	−	0.372329i	$-0.878559\pi$
$67$	−25.5848	+	31.1751i	−0.381862	+	0.465301i	0.546238	+	0.837630i	$0.316059\pi$
$68$	−66.6741	−	103.266i	−0.980502	−	1.51862i
$69$	−9.16551	−	30.2146i	−0.132834	−	0.437893i
$70$	−20.5864	−	107.925i	−0.294091	−	1.54179i
$71$	−5.17915	−	1.03020i	−0.0729458	−	0.0145098i	0.158482	−	0.987362i	$-0.449340\pi$
$71$	−5.17915	−	1.03020i	−0.0729458	−	0.0145098i	−0.231428	+	0.972852i	$0.574340\pi$
$72$	25.7677	+	51.0718i	0.357885	+	0.709330i
$73$	−26.9577	+	5.36223i	−0.369284	+	0.0734552i	−0.376244	−	0.926521i	$-0.622785\pi$
$73$	−26.9577	+	5.36223i	−0.369284	+	0.0734552i	0.00695986	+	0.999976i	$0.497785\pi$
$74$	−33.0080	+	77.9483i	−0.446055	+	1.05336i
$75$	58.4324	+	5.75509i	0.779099	+	0.0767345i
$76$	−39.8601	−	50.1586i	−0.524475	−	0.659982i
$77$	−2.52545	−	0.766086i	−0.0327980	−	0.00994917i
$78$	14.1967	−	11.4652i	0.182009	−	0.146990i
$79$	17.2775	−	41.7116i	0.218703	−	0.527995i	−0.776007	−	0.630725i	$-0.782758\pi$
$79$	17.2775	−	41.7116i	0.218703	−	0.527995i	0.994709	+	0.102730i	$0.0327576\pi$
$80$	−104.707	+	80.5540i	−1.30884	+	1.00692i
$81$	−31.8593	+	13.1965i	−0.393324	+	0.162920i
$82$	−50.9948	−	27.7753i	−0.621888	−	0.338723i
$83$	−47.4557	+	25.3656i	−0.571756	+	0.305610i	−0.731821	−	0.681497i	$-0.761329\pi$
$83$	−47.4557	+	25.3656i	−0.571756	+	0.305610i	0.160065	+	0.987106i	$0.448829\pi$
$84$	23.3983	−	27.6132i	0.278551	−	0.328729i
$85$	160.965	+	196.136i	1.89370	+	2.30748i
$86$	71.8748	−	70.7527i	0.835754	−	0.822706i
$87$	−19.9048	+	29.7897i	−0.228791	+	0.342410i
$88$	0.545445	+	3.12599i	0.00619823	+	0.0355226i
$89$	−13.9882	−	20.9348i	−0.157171	−	0.235223i	0.744524	−	0.667596i	$-0.232676\pi$
$89$	−13.9882	−	20.9348i	−0.157171	−	0.235223i	−0.901695	+	0.432373i	$0.857676\pi$
$90$	−64.8273	−	98.6930i	−0.720303	−	1.09659i
$91$	39.3675	+	21.0423i	0.432609	+	0.231235i
$92$	−85.2290	−	36.8846i	−0.926402	−	0.400919i
$93$	−76.8457	+	7.56864i	−0.826298	+	0.0813832i
$94$	−44.0841	−	84.0596i	−0.468980	−	0.894251i
$95$	93.5139	+	93.5139i	0.984357	+	0.984357i
$96$	−42.3157	−	10.1621i	−0.440789	−	0.105855i
$97$	56.7531	+	56.7531i	0.585084	+	0.585084i	0.936296	−	0.351212i	$-0.114230\pi$
$97$	56.7531	+	56.7531i	0.585084	+	0.585084i	−0.351212	+	0.936296i	$0.614230\pi$
$98$	−9.03510	−	2.81858i	−0.0921949	−	0.0287610i
$99$	−2.82260	+	0.278002i	−0.0285112	+	0.00280810i
$100$	124.021	−	120.178i	1.24021	−	1.20178i
$101$	31.6797	+	16.9332i	0.313661	+	0.167655i	0.620714	−	0.784037i	$-0.286843\pi$
$101$	31.6797	+	16.9332i	0.313661	+	0.167655i	−0.307053	+	0.951692i	$0.599343\pi$
$102$	−16.9507	+	81.8464i	−0.166183	+	0.802415i
$103$	−111.280	−	166.542i	−1.08039	−	1.61691i	−0.734461	−	0.678651i	$-0.762565\pi$
$103$	−111.280	−	166.542i	−1.08039	−	1.61691i	−0.345926	−	0.938262i	$-0.612435\pi$
$104$	1.26664	−	53.6578i	0.0121792	−	0.515941i
$105$	−41.5068	+	62.1193i	−0.395303	+	0.591612i
$106$	−0.459941	+	58.4622i	−0.00433907	+	0.551530i
$107$	−75.5164	−	92.0170i	−0.705761	−	0.859972i	0.289503	−	0.957177i	$-0.406510\pi$
$107$	−75.5164	−	92.0170i	−0.705761	−	0.859972i	−0.995264	+	0.0972047i	$0.969010\pi$
$108$	26.8230	−	83.6616i	0.248361	−	0.774644i
$109$	22.5115	−	12.0326i	0.206527	−	0.110391i	−0.364890	−	0.931050i	$-0.618894\pi$
$109$	22.5115	−	12.0326i	0.206527	−	0.110391i	0.571418	+	0.820659i	$0.306394\pi$
$110$	−1.85203	−	6.28284i	−0.0168366	−	0.0571167i
$111$	53.1783	−	22.0272i	0.479084	−	0.198443i
$112$	−17.4729	−	105.011i	−0.156008	−	0.937595i
$113$	67.3042	−	162.487i	0.595613	−	1.43794i	−0.282399	−	0.959297i	$-0.591130\pi$
$113$	67.3042	−	162.487i	0.595613	−	1.43794i	0.878012	−	0.478639i	$-0.158870\pi$
$114$	−4.61107	+	43.3204i	−0.0404480	+	0.380003i
$115$	183.443	+	55.6467i	1.59515	+	0.483885i
$116$	28.9994	+	101.310i	0.249995	+	0.873361i
$117$	47.7424	+	4.70222i	0.408055	+	0.0401899i
$118$	−113.329	+	45.9014i	−0.960419	+	0.388995i
$119$	−200.530	+	39.8879i	−1.68513	+	0.335193i
$120$	89.1658	+	10.9123i	0.743048	+	0.0909356i
$121$	118.521	+	23.5752i	0.979510	+	0.194837i
$122$	115.746	+	78.6632i	0.948738	+	0.644780i
$123$	11.4620	+	37.7852i	0.0931871	+	0.307197i
$124$	−129.135	+	186.832i	−1.04141	+	1.50671i
$125$	−95.1964	+	115.997i	−0.761572	+	0.927978i
$126$	94.7626	−	8.58112i	0.752084	−	0.0681041i
$127$		−	151.538i		−	1.19322i	−0.802533	−	0.596608i	$-0.796515\pi$
$127$		−	151.538i		−	1.19322i	0.802533	−	0.596608i	$-0.203485\pi$
$128$	−103.265	+	75.6331i	−0.806757	+	0.590883i
$129$	−68.5802			−0.531629
$130$	9.99166	+	110.339i	0.0768589	+	0.848764i
$131$	163.916	+	134.522i	1.25127	+	1.02689i	0.998232	+	0.0594319i	$0.0189289\pi$
$131$	163.916	+	134.522i	1.25127	+	1.02689i	0.253035	+	0.967457i	$0.418571\pi$
$132$	1.22685	−	1.77500i	0.00929431	−	0.0134470i
$133$	−101.979	+	30.9349i	−0.766758	+	0.232594i
$134$	45.3380	−	66.7109i	0.338343	−	0.497843i
$135$	−35.3800	+	177.867i	−0.262074	+	1.31754i
$136$	151.431	+	193.664i	1.11346	+	1.42400i
$137$	−43.1225	−	216.792i	−0.314763	−	1.58242i	−0.736973	−	0.675923i	$-0.763745\pi$
$137$	−43.1225	−	216.792i	−0.314763	−	1.58242i	0.422209	−	0.906498i	$-0.361255\pi$
$138$	23.7061	+	58.5299i	0.171784	+	0.424129i
$139$	5.00138	−	50.7798i	0.0359811	−	0.365323i	−0.960287	−	0.279013i	$-0.909993\pi$
$139$	5.00138	−	50.7798i	0.0359811	−	0.365323i	0.996268	−	0.0863094i	$-0.0275074\pi$
$140$	60.4714	+	211.258i	0.431939	+	1.50898i
$141$	−18.7357	+	61.7633i	−0.132877	+	0.438037i
$142$	10.5019	+	1.11784i	0.0739571	+	0.00787208i
$143$	2.45861	+	1.01839i	0.0171931	+	0.00712160i
$144$	−60.5372	−	97.0796i	−0.420397	−	0.674164i
$145$	−83.2418	−	200.964i	−0.574082	−	1.38596i
$146$	52.7286	−	15.5431i	0.361155	−	0.106460i
$147$	3.03377	+	5.67578i	0.0206379	+	0.0386108i
$148$	51.6876	−	161.215i	0.349240	−	1.08929i
$149$	−1.25076	+	1.02647i	−0.00839436	+	0.00688907i	−0.638581	−	0.769555i	$-0.720478\pi$
$149$	−1.25076	+	1.02647i	−0.00839436	+	0.00688907i	0.630187	+	0.776444i	$0.282978\pi$
$150$	−117.427	−	0.923834i	−0.782844	−	0.00615889i
$151$	−12.6443	−	8.44864i	−0.0837370	−	0.0559513i	0.512997	−	0.858390i	$-0.328535\pi$
$151$	−12.6443	−	8.44864i	−0.0837370	−	0.0559513i	−0.596734	+	0.802439i	$0.703535\pi$
$152$	88.4424	+	92.7189i	0.581858	+	0.609993i
$153$	−182.703	+	122.078i	−1.19414	+	0.797896i
$154$	5.16849	+	1.07041i	0.0335616	+	0.00695074i
$155$	220.996	−	413.455i	1.42578	−	2.66745i
$156$	−26.2097	+	25.3977i	−0.168011	+	0.162806i
$157$	23.6835	+	240.463i	0.150850	+	1.53161i	0.710984	+	0.703208i	$0.248250\pi$
$157$	23.6835	+	240.463i	0.150850	+	1.53161i	−0.560134	+	0.828402i	$0.689250\pi$
$158$	−26.8907	+	86.1996i	−0.170194	+	0.545567i
$159$	28.1106	−	28.1106i	0.176796	−	0.176796i
$160$	194.032	−	179.337i	1.21270	−	1.12086i
$161$	−109.228	+	109.228i	−0.678436	+	0.678436i
$162$	61.0786	−	32.0320i	0.377028	−	0.197728i
$163$	5.78614	+	58.7476i	0.0354978	+	0.360415i	0.996482	+	0.0838107i	$0.0267091\pi$
$163$	5.78614	+	58.7476i	0.0354978	+	0.360415i	−0.960984	+	0.276604i	$0.910791\pi$
$164$	106.584	+	46.1263i	0.649902	+	0.281258i
$165$	−2.09958	+	3.92804i	−0.0127247	+	0.0238063i
$166$	89.9495	−	59.0841i	0.541865	−	0.355928i
$167$	−49.9309	+	33.3628i	−0.298988	+	0.199777i	−0.696011	−	0.718032i	$-0.745043\pi$
$167$	−49.9309	+	33.3628i	−0.298988	+	0.199777i	0.397023	+	0.917809i	$0.370043\pi$
$168$	−41.6252	+	59.2218i	−0.247769	+	0.352510i
$169$	103.092	+	68.8841i	0.610014	+	0.407598i
$170$	−355.994	−	361.640i	−2.09408	−	2.12730i
$171$	−88.5326	+	72.6569i	−0.517735	+	0.424894i
$172$	−130.402	+	153.893i	−0.758152	+	0.894726i
$173$	−88.9182	−	166.354i	−0.513978	−	0.961585i	−0.996329	−	0.0856071i	$-0.972717\pi$
$173$	−88.9182	−	166.354i	−0.513978	−	0.961585i	0.482351	−	0.875978i	$-0.339783\pi$
$174$	34.2743	−	62.9268i	0.196978	−	0.361648i
$175$	−109.928	−	265.389i	−0.628157	−	1.51651i
$176$	−1.65028	−	6.12812i	−0.00937658	−	0.0348188i
$177$	76.8139	+	31.8174i	0.433977	+	0.179759i
$178$	31.6384	+	39.1760i	0.177744	+	0.220090i
$179$	−2.50526	+	8.25873i	−0.0139958	+	0.0461381i	−0.963660	−	0.267131i	$-0.913924\pi$
$179$	−2.50526	+	8.25873i	−0.0139958	+	0.0461381i	0.949664	+	0.313269i	$0.101424\pi$
$180$	146.927	+	184.889i	0.816264	+	1.02716i
$181$	9.30995	−	94.5256i	0.0514362	−	0.522241i	−0.934599	−	0.355703i	$-0.884241\pi$
$181$	9.30995	−	94.5256i	0.0514362	−	0.522241i	0.986035	−	0.166537i	$-0.0532586\pi$
$182$	−82.2095	−	34.8125i	−0.451700	−	0.191277i
$183$	−18.5650	−	93.3325i	−0.101448	−	0.510014i
$184$	176.416	+	58.0958i	0.958784	+	0.315738i
$185$	−68.1770	+	342.749i	−0.368524	+	1.85270i
$186$	151.700	−	28.9362i	0.815591	−	0.155571i
$187$	−11.6642	+	3.53831i	−0.0623757	+	0.0189215i
$188$	102.971	+	159.483i	0.547717	+	0.848312i
$189$	−112.964	−	92.7076i	−0.597696	−	0.490516i
$190$	−203.133	−	169.399i	−1.06912	−	0.891571i
$191$	263.273			1.37839			0.689196	−	0.724575i	$-0.257964\pi$
$191$	263.273			1.37839			0.689196	+	0.724575i	$0.257964\pi$
$192$	86.1195	+	12.6088i	0.448539	+	0.0656709i
$193$		−	221.333i		−	1.14681i	−0.819274	−	0.573403i	$-0.805623\pi$
$193$		−	221.333i		−	1.14681i	0.819274	−	0.573403i	$-0.194377\pi$
$194$	−123.280	−	102.807i	−0.635465	−	0.529934i
$195$	47.7924	−	58.2352i	0.245089	−	0.298642i
$196$	18.5049	+	3.98452i	0.0944130	+	0.0203292i
$197$	−3.32383	−	10.9572i	−0.0168723	−	0.0556204i	0.948100	−	0.317972i	$-0.103002\pi$
$197$	−3.32383	−	10.9572i	−0.0168723	−	0.0556204i	−0.964972	+	0.262352i	$0.915502\pi$
$198$	5.57206	−	1.06285i	0.0281417	−	0.00536794i
$199$	−35.7966	−	7.12039i	−0.179883	−	0.0357809i	0.104327	−	0.994543i	$-0.466731\pi$
$199$	−35.7966	−	7.12039i	−0.179883	−	0.0357809i	−0.284210	+	0.958762i	$0.591731\pi$
$200$	−225.355	+	261.747i	−1.12677	+	1.30873i
$201$	−53.7928	+	10.7000i	−0.267626	+	0.0532341i
$202$	−66.1555	−	28.0143i	−0.327503	−	0.138685i
$203$	174.437	+	17.1806i	0.859298	+	0.0846334i
$204$	19.0006	−	166.083i	0.0931403	−	0.814133i
$205$	−229.406	−	69.5895i	−1.11905	−	0.339461i
$206$	251.692	+	311.655i	1.22181	+	1.51289i
$207$	−63.5305	+	153.376i	−0.306910	+	0.740947i
$208$	7.15529	+	107.107i	0.0344004	+	0.514936i
$209$	−5.86957	+	2.43126i	−0.0280841	+	0.0116328i
$210$	71.4709	−	131.219i	0.340337	−	0.624852i
$211$	−89.1592	+	47.6566i	−0.422555	+	0.225861i	−0.668947	−	0.743310i	$-0.733255\pi$
$211$	−89.1592	+	47.6566i	−0.422555	+	0.225861i	0.246392	+	0.969170i	$0.420755\pi$
$212$	−9.62869	−	116.531i	−0.0454183	−	0.549674i
$213$	−4.55586	−	5.55133i	−0.0213890	−	0.0260626i
$214$	167.015	+	169.663i	0.780442	+	0.792819i
$215$	231.324	−	346.201i	1.07592	−	1.61024i
$216$	−38.3373	+	171.479i	−0.177487	+	0.793886i
$217$	209.880	+	314.108i	0.967190	+	1.44750i
$218$	−42.6692	+	28.0276i	−0.195730	+	0.128567i
$219$	−32.9660	−	17.6207i	−0.150530	−	0.0804598i
$220$	4.82220	+	12.1804i	0.0219191	+	0.0553656i
$221$	205.178	−	20.2082i	0.928405	−	0.0914399i
$222$	−101.950	+	53.4666i	−0.459235	+	0.240841i
$223$	294.768	+	294.768i	1.32183	+	1.32183i	0.912295	+	0.409534i	$0.134309\pi$
$223$	294.768	+	294.768i	1.32183	+	1.32183i	0.409534	+	0.912295i	$0.365691\pi$
$224$	53.7441	+	206.014i	0.239929	+	0.919705i
$225$	−218.295	−	218.295i	−0.970202	−	0.970202i
$226$	−104.752	+	335.789i	−0.463505	+	1.48579i
$227$	−355.599	+	35.0235i	−1.56652	+	0.154288i	−0.843724	−	0.536777i	$-0.819642\pi$
$227$	−355.599	+	35.0235i	−1.56652	+	0.154288i	−0.722792	+	0.691066i	$0.757142\pi$
$228$	1.37088	−	87.1193i	0.00601262	−	0.382102i
$229$	−178.338	−	95.3238i	−0.778770	−	0.416261i	0.0335768	−	0.999436i	$-0.489310\pi$
$229$	−178.338	−	95.3238i	−0.778770	−	0.416261i	−0.812347	+	0.583175i	$0.801810\pi$
$230$	−375.427	−	77.7524i	−1.63229	−	0.338054i
$231$	−1.99397	−	2.98419i	−0.00863192	−	0.0129186i
$232$	−76.0357	−	196.563i	−0.327740	−	0.847256i
$233$	170.005	−	254.431i	0.729637	−	1.09198i	−0.262268	−	0.964995i	$-0.584471\pi$
$233$	170.005	−	254.431i	0.729637	−	1.09198i	0.991905	−	0.126983i	$-0.0405294\pi$
$234$	−95.9438	−	0.754822i	−0.410016	−	0.00322573i
$235$	−248.592	−	302.910i	−1.05784	−	1.28898i
$236$	217.456	−	111.870i	0.921423	−	0.474025i
$237$	54.1500	−	28.9438i	0.228481	−	0.122126i
$238$	392.232	−	115.620i	1.64803	−	0.485800i
$239$	1.38267	−	0.572721i	0.00578524	−	0.00239632i	−0.379789	−	0.925073i	$-0.624003\pi$
$239$	1.38267	−	0.572721i	0.00578524	−	0.00239632i	0.385574	+	0.922677i	$0.374003\pi$
$240$	−179.573	−	5.65279i	−0.748222	−	0.0235533i
$241$	−5.09900	+	12.3101i	−0.0211577	+	0.0510791i	−0.934105	−	0.356998i	$-0.883800\pi$
$241$	−5.09900	+	12.3101i	−0.0211577	+	0.0510791i	0.912948	+	0.408077i	$0.133800\pi$
$242$	−240.328	−	25.5808i	−0.993090	−	0.105706i
$243$	−234.043	−	70.9961i	−0.963138	−	0.292165i
$244$	−244.737	−	135.808i	−1.00302	−	0.556591i
$245$	−38.8850	−	3.82984i	−0.158714	−	0.0156320i
$246$	−29.6459	−	73.1951i	−0.120512	−	0.297541i
$247$	105.395	−	20.9643i	0.426700	−	0.0848759i
$248$	223.518	−	395.433i	0.901283	−	1.59449i
$249$	−71.7728	−	14.2765i	−0.288244	−	0.0573353i
$250$	168.695	−	248.220i	0.674779	−	0.992878i
$251$	54.3380	+	179.128i	0.216486	+	0.713659i	0.996166	+	0.0874809i	$0.0278817\pi$
$251$	54.3380	+	179.128i	0.216486	+	0.713659i	−0.779680	+	0.626178i	$0.784618\pi$
$252$	−187.205	+	34.1846i	−0.742877	+	0.135653i
$253$	−5.84217	+	7.11870i	−0.0230916	+	0.0281372i
$254$	27.3329	+	301.842i	0.107610	+	1.18835i
$255$			345.063i			1.35319i
$256$	192.046	−	169.276i	0.750181	−	0.661233i
$257$	20.9577			0.0815473			0.0407736	−	0.999168i	$-0.487018\pi$
$257$	20.9577			0.0815473			0.0407736	+	0.999168i	$0.487018\pi$
$258$	136.601	−	12.3698i	0.529463	−	0.0479449i
$259$	−217.681	−	178.646i	−0.840469	−	0.689755i
$260$	−39.8038	−	217.977i	−0.153091	−	0.838374i
$261$	180.266	−	54.6831i	0.690674	−	0.209514i
$262$	−350.760	−	238.383i	−1.33878	−	0.909859i
$263$	−5.70349	+	28.6734i	−0.0216863	+	0.109024i	−0.990112	−	0.140277i	$-0.955201\pi$
$263$	−5.70349	+	28.6734i	−0.0216863	+	0.109024i	0.968426	+	0.249301i	$0.0802008\pi$
$264$	−2.12354	+	3.75682i	−0.00804372	+	0.0142304i
$265$	47.0873	+	236.724i	0.177688	+	0.893298i
$266$	197.547	−	80.0117i	0.742657	−	0.300796i
$267$	3.35623	−	34.0764i	0.0125702	−	0.127627i
$268$	−78.2738	+	141.056i	−0.292067	+	0.526328i
$269$	44.2491	−	145.870i	0.164495	−	0.542267i	−0.835479	−	0.549523i	$-0.814810\pi$
$269$	44.2491	−	145.870i	0.164495	−	0.542267i	0.999974	+	0.00725570i	$0.00230958\pi$
$270$	38.3898	−	360.667i	0.142184	−	1.33580i
$271$	24.1334	+	9.99637i	0.0890530	+	0.0368870i	0.426765	−	0.904362i	$-0.359653\pi$
$271$	24.1334	+	9.99637i	0.0890530	+	0.0368870i	−0.337712	+	0.941249i	$0.609653\pi$
$272$	−336.559	−	358.437i	−1.23735	−	1.31778i
$273$	23.2313	+	56.0854i	0.0850965	+	0.205441i
$274$	124.996	+	424.039i	0.456191	+	1.54759i
$275$	−8.07271	−	15.1030i	−0.0293553	−	0.0549199i
$276$	−57.7761	−	112.307i	−0.209334	−	0.406909i
$277$	290.519	−	238.423i	1.04881	−	0.860733i	0.0583132	−	0.998298i	$-0.481428\pi$
$277$	290.519	−	238.423i	1.04881	−	0.860733i	0.990493	+	0.137566i	$0.0439278\pi$
$278$	−0.802845	+	102.048i	−0.00288793	+	0.367079i
$279$	337.576	+	225.561i	1.20995	+	0.808463i
$280$	−158.554	−	409.886i	−0.566266	−	1.46388i
$281$	155.472	−	103.883i	0.553280	−	0.369690i	−0.247279	−	0.968944i	$-0.579536\pi$
$281$	155.472	−	103.883i	0.553280	−	0.369690i	0.800558	+	0.599255i	$0.204536\pi$
$282$	26.1784	−	126.403i	0.0928314	−	0.448236i
$283$	−241.302	+	451.444i	−0.852657	+	1.59521i	−0.0500154	+	0.998748i	$0.515927\pi$
$283$	−241.302	+	451.444i	−0.852657	+	1.59521i	−0.802642	+	0.596461i	$0.796573\pi$
$284$	−21.1199	−	0.332334i	−0.0743657	−	0.00117019i
$285$	17.6287	+	178.987i	0.0618551	+	0.628025i
$286$	−5.08086	−	1.58502i	−0.0177653	−	0.00554202i
$287$	136.596	−	136.596i	0.475945	−	0.475945i
$288$	138.091	+	182.449i	0.479484	+	0.633503i
$289$	−463.389	+	463.389i	−1.60342	+	1.60342i
$290$	202.053	+	385.275i	0.696735	+	1.32853i
$291$	10.6988	+	108.626i	0.0367655	+	0.373286i
$292$	−102.224	+	40.4702i	−0.350082	+	0.138597i
$293$	109.137	−	204.180i	0.372480	−	0.696860i	−0.623934	−	0.781477i	$-0.714467\pi$
$293$	109.137	−	204.180i	0.372480	−	0.696860i	0.996414	+	0.0846168i	$0.0269666\pi$
$294$	−7.06655	−	10.7581i	−0.0240359	−	0.0365922i
$295$	−419.714	+	280.444i	−1.42276	+	0.950658i
$296$	−73.8756	+	330.439i	−0.249580	+	1.11635i
$297$	−7.24384	−	4.84018i	−0.0243900	−	0.0162969i
$298$	2.30618	−	2.27018i	0.00773886	−	0.00761804i
$299$	120.408	−	98.8162i	0.402702	−	0.330489i
$300$	234.063	−	19.3401i	0.780210	−	0.0644669i
$301$	158.162	+	295.900i	0.525455	+	0.983057i
$302$	26.7094	+	14.5478i	0.0884417	+	0.0481715i
$303$	18.6947	+	45.1330i	0.0616987	+	0.148954i
$304$	−192.888	−	168.730i	−0.634499	−	0.555032i
$305$	533.774	+	221.096i	1.75008	+	0.724906i
$306$	341.897	−	276.115i	1.11731	−	0.902338i
$307$	−28.3067	+	93.3145i	−0.0922041	+	0.303956i	−0.990897	−	0.134622i	$-0.957018\pi$
$307$	−28.3067	+	93.3145i	−0.0922041	+	0.303956i	0.898693	+	0.438578i	$0.144518\pi$
$308$	−10.4879	−	1.19986i	−0.0340517	−	0.00389566i
$309$	26.6997	−	271.087i	0.0864068	−	0.877303i
$310$	−365.617	+	863.402i	−1.17941	+	2.78517i
$311$	−38.1368	−	191.727i	−0.122626	−	0.616485i	−0.992402	−	0.123037i	$-0.960737\pi$
$311$	−38.1368	−	191.727i	−0.122626	−	0.616485i	0.869776	−	0.493447i	$-0.164263\pi$
$312$	47.6249	−	55.3158i	0.152644	−	0.177294i
$313$	−45.1858	+	227.165i	−0.144364	+	0.725765i	0.839002	+	0.544128i	$0.183140\pi$
$313$	−45.1858	+	227.165i	−0.144364	+	0.725765i	−0.983366	+	0.181637i	$0.941860\pi$
$314$	−90.5463	−	474.694i	−0.288364	−	1.51176i
$315$	375.902	−	114.029i	1.19334	−	0.361996i
$316$	38.0145	−	176.547i	0.120299	−	0.558693i
$317$	207.301	+	170.127i	0.653946	+	0.536679i	0.901819	−	0.432113i	$-0.142232\pi$
$317$	207.301	+	170.127i	0.653946	+	0.536679i	−0.247874	+	0.968792i	$0.579732\pi$
$318$	−50.9219	+	61.0625i	−0.160132	+	0.192020i
$319$	10.4497			0.0327575
$320$	−354.135	+	392.211i	−1.10667	+	1.22566i
$321$		−	161.886i		−	0.504318i
$322$	197.865	−	237.267i	0.614486	−	0.736856i
$323$	−312.250	+	380.478i	−0.966718	+	1.17795i
$324$	−115.882	+	74.8196i	−0.357660	+	0.230925i
$325$	84.0836	+	277.186i	0.258719	+	0.852881i
$326$	−22.1214	−	115.973i	−0.0678571	−	0.355745i
$327$	34.0467	+	6.77231i	0.104118	+	0.0207104i
$328$	−220.619	−	72.6522i	−0.672619	−	0.221501i
$329$	309.696	−	61.6024i	0.941326	−	0.187241i
$330$	3.47355	−	8.20277i	0.0105259	−	0.0248569i
$331$	−213.232	−	21.0015i	−0.644205	−	0.0634487i	−0.229362	−	0.973341i	$-0.573664\pi$
$331$	−213.232	−	21.0015i	−0.644205	−	0.0634487i	−0.414844	+	0.909893i	$0.636164\pi$
$332$	−168.509	+	133.911i	−0.507557	+	0.403346i
$333$	−289.610	−	87.8523i	−0.869700	−	0.263821i
$334$	93.4373	−	75.4597i	0.279752	−	0.225927i
$335$	127.430	−	307.644i	0.380389	−	0.918340i
$336$	72.2294	−	125.469i	0.214969	−	0.373419i
$337$	−124.559	+	51.5942i	−0.369612	+	0.153098i	−0.559755	−	0.828658i	$-0.689105\pi$
$337$	−124.559	+	51.5942i	−0.369612	+	0.153098i	0.190143	+	0.981756i	$0.439105\pi$
$338$	−217.769	−	118.612i	−0.644287	−	0.350923i
$339$	210.940	−	112.750i	0.622242	−	0.332596i
$340$	774.317	+	656.123i	2.27740	+	1.92977i
$341$	14.2875	+	17.4094i	0.0418989	+	0.0510540i
$342$	163.239	−	160.690i	0.477306	−	0.469854i
$343$	198.618	−	297.252i	0.579060	−	0.866625i
$344$	231.984	−	330.052i	0.674372	−	0.959454i
$345$	144.838	+	216.765i	0.419819	+	0.628304i
$346$	207.117	+	315.315i	0.598604	+	0.911314i
$347$	21.3578	+	11.4160i	0.0615500	+	0.0328992i	0.501885	−	0.864935i	$-0.332640\pi$
$347$	21.3578	+	11.4160i	0.0615500	+	0.0328992i	−0.440335	+	0.897834i	$0.645140\pi$
$348$	−56.9191	+	131.523i	−0.163561	+	0.377939i
$349$	−537.213	+	52.9109i	−1.53929	+	0.151607i	−0.831785	−	0.555098i	$-0.812681\pi$
$349$	−537.213	+	52.9109i	−1.53929	+	0.151607i	−0.707508	+	0.706705i	$0.750181\pi$
$350$	266.827	+	508.787i	0.762363	+	1.45368i
$351$	104.199	+	104.199i	0.296862	+	0.296862i
$352$	4.39243	+	11.9086i	0.0124785	+	0.0338313i
$353$	−60.9968	−	60.9968i	−0.172796	−	0.172796i	0.615411	−	0.788206i	$-0.288990\pi$
$353$	−60.9968	−	60.9968i	−0.172796	−	0.172796i	−0.788206	+	0.615411i	$0.788990\pi$
$354$	−158.741	−	49.5205i	−0.448420	−	0.139888i
$355$	43.3908	−	4.27362i	0.122228	−	0.0120384i
$356$	−70.0852	−	72.3261i	−0.196869	−	0.203163i
$357$	−245.224	−	131.075i	−0.686901	−	0.367156i
$358$	3.50047	−	16.9020i	0.00977785	−	0.0472123i
$359$	−14.6590	−	21.9388i	−0.0408329	−	0.0611107i	0.810492	−	0.585750i	$-0.199200\pi$
$359$	−14.6590	−	21.9388i	−0.0408329	−	0.0611107i	−0.851324	+	0.524640i	$0.824200\pi$
$360$	−326.006	−	341.769i	−0.905572	−	0.949359i
$361$	58.0323	−	86.8515i	0.160754	−	0.240586i
$362$	−1.49448	+	189.960i	−0.00412839	+	0.524751i
$363$	104.257	+	127.038i	0.287210	+	0.349966i
$364$	170.028	+	54.5132i	0.467110	+	0.149761i
$365$	200.147	−	106.981i	0.548348	−	0.293098i
$366$	53.8131	+	182.556i	0.147030	+	0.498787i
$367$	−371.232	+	153.769i	−1.01153	+	0.418990i	−0.826013	−	0.563650i	$-0.809396\pi$
$367$	−371.232	+	153.769i	−1.01153	+	0.418990i	−0.185519	+	0.982641i	$0.559396\pi$
$368$	−361.873	−	83.8979i	−0.983352	−	0.227983i
$369$	79.4486	−	191.806i	0.215308	−	0.519799i
$370$	73.9768	−	695.001i	0.199937	−	1.87838i
$371$	−186.118	−	56.4581i	−0.501664	−	0.152178i
$372$	−296.944	+	84.9987i	−0.798237	+	0.228491i
$373$	335.439	+	33.0378i	0.899299	+	0.0885733i	0.537091	−	0.843524i	$-0.319523\pi$
$373$	335.439	+	33.0378i	0.899299	+	0.0885733i	0.362208	+	0.932097i	$0.382023\pi$
$374$	22.5952	−	9.15166i	0.0604151	−	0.0244697i
$375$	−200.153	+	39.8130i	−0.533742	+	0.106168i
$376$	−233.868	−	299.093i	−0.621990	−	0.795460i
$377$	−173.353	−	34.4820i	−0.459821	−	0.0914641i
$378$	241.730	+	164.284i	0.639497	+	0.434614i
$379$	18.2903	+	60.2951i	0.0482594	+	0.159090i	0.977758	−	0.209735i	$-0.0672602\pi$
$379$	18.2903	+	60.2951i	0.0482594	+	0.159090i	−0.929499	+	0.368825i	$0.879760\pi$
$380$	435.164	+	300.778i	1.14517	+	0.791520i
$381$	130.740	−	159.307i	0.343149	−	0.418129i
$382$	−524.400	+	47.4865i	−1.37278	+	0.124310i
$383$			487.705i			1.27338i	0.771119	+	0.636691i	$0.219697\pi$
$383$			487.705i			1.27338i	−0.771119	+	0.636691i	$0.780303\pi$
$384$	−173.811	−	9.58150i	−0.452634	−	0.0249518i
$385$	21.7903			0.0565982
$386$	39.9219	+	440.863i	0.103425	+	1.14213i
$387$	278.736	+	228.753i	0.720249	+	0.591093i
$388$	264.099	+	182.540i	0.680668	+	0.470465i
$389$	−411.191	+	124.733i	−1.05705	+	0.320652i	−0.770517	−	0.637420i	$-0.780002\pi$
$389$	−411.191	+	124.733i	−1.05705	+	0.320652i	−0.286530	+	0.958071i	$0.592502\pi$
$390$	−84.6915	+	124.616i	−0.217158	+	0.319529i
$391$	−139.189	+	699.749i	−0.355981	+	1.78964i
$392$	−37.5778	−	4.59883i	−0.0958616	−	0.0117317i
$393$	56.2599	+	282.838i	0.143155	+	0.719688i
$394$	8.59693	+	21.2256i	0.0218196	+	0.0538721i
$395$	−36.5387	+	370.984i	−0.0925031	+	0.939200i
$396$	−10.9070	+	3.12207i	−0.0275429	+	0.00788402i
$397$	181.368	−	597.889i	0.456846	−	1.50602i	−0.362096	−	0.932141i	$-0.617939\pi$
$397$	181.368	−	597.889i	0.456846	−	1.50602i	0.818941	−	0.573877i	$-0.194561\pi$
$398$	72.5858	+	7.72612i	0.182376	+	0.0194124i
$399$	−133.896	−	55.4615i	−0.335579	−	0.139001i
$400$	401.661	−	562.008i	1.00415	−	1.40502i
$401$	126.992	+	306.587i	0.316689	+	0.764555i	0.999426	+	0.0338905i	$0.0107898\pi$
$401$	126.992	+	306.587i	0.316689	+	0.764555i	−0.682736	+	0.730665i	$0.739210\pi$
$402$	105.217	−	31.0155i	0.261734	−	0.0771529i
$403$	−179.572	−	335.956i	−0.445589	−	0.833638i
$404$	136.825	+	43.8678i	0.338675	+	0.108584i
$405$	220.098	−	180.629i	0.543451	−	0.445999i
$406$	−350.552	−	2.75791i	−0.863429	−	0.00679288i
$407$	−13.9588	−	9.32698i	−0.0342968	−	0.0229164i
$408$	−7.89002	+	334.240i	−0.0193383	+	0.819215i
$409$	570.748	−	381.362i	1.39547	−	0.932425i	0.395570	−	0.918436i	$-0.370547\pi$
$409$	570.748	−	381.362i	1.39547	−	0.932425i	0.999902	−	0.0139887i	$-0.00445288\pi$
$410$	469.494	+	97.2340i	1.14511	+	0.237156i
$411$	141.704	−	265.110i	0.344779	−	0.645035i
$412$	−557.546	−	575.373i	−1.35327	−	1.39654i
$413$	−39.8697	−	404.804i	−0.0965369	−	0.980156i
$414$	98.8787	−	316.961i	0.238838	−	0.765607i
$415$	314.162	−	314.162i	0.757017	−	0.757017i
$416$	−33.5711	−	212.050i	−0.0806998	−	0.509736i
$417$	49.0681	−	49.0681i	0.117669	−	0.117669i
$418$	11.2528	−	5.90139i	0.0269205	−	0.0141182i
$419$	28.3512	+	287.854i	0.0676639	+	0.687003i	0.967855	+	0.251508i	$0.0809266\pi$
$419$	28.3512	+	287.854i	0.0676639	+	0.687003i	−0.900191	+	0.435495i	$0.856573\pi$
$420$	−118.691	+	274.260i	−0.282598	+	0.652999i
$421$	270.116	−	505.352i	0.641606	−	1.20036i	−0.325393	−	0.945579i	$-0.605497\pi$
$421$	270.116	−	505.352i	0.641606	−	1.20036i	0.966999	−	0.254781i	$-0.0820034\pi$
$422$	168.996	−	111.006i	0.400464	−	0.263048i
$423$	282.164	−	188.536i	0.667054	−	0.445711i
$424$	40.1976	+	230.375i	0.0948056	+	0.543338i
$425$	−1103.14	−	737.096i	−2.59563	−	1.73434i
$426$	10.0759	+	10.2357i	0.0236523	+	0.0240274i
$427$	−359.883	+	295.348i	−0.842817	+	0.691682i
$428$	−363.270	−	307.819i	−0.848762	−	0.719204i
$429$	1.70603	+	3.19176i	0.00397676	+	0.00744000i
$430$	−398.318	+	731.303i	−0.926322	+	1.70071i
$431$	−307.517	−	742.411i	−0.713496	−	1.72253i	−0.691075	−	0.722783i	$-0.742863\pi$
$431$	−307.517	−	742.411i	−0.713496	−	1.72253i	−0.0224206	−	0.999749i	$-0.507137\pi$
$432$	45.4325	−	348.476i	0.105168	−	0.806658i
$433$	−79.5989	−	32.9709i	−0.183831	−	0.0761453i	0.288869	−	0.957369i	$-0.406721\pi$
$433$	−79.5989	−	32.9709i	−0.183831	−	0.0761453i	−0.472700	+	0.881223i	$0.656721\pi$
$434$	−474.706	−	587.800i	−1.09379	−	1.35438i
$435$	85.8723	−	283.083i	0.197408	−	0.650765i
$436$	79.9353	−	63.5230i	0.183338	−	0.145695i
$437$	−36.4493	+	370.076i	−0.0834080	+	0.846856i
$438$	68.8416	+	29.1517i	0.157173	+	0.0665564i
$439$	−116.820	−	587.295i	−0.266105	−	1.33780i	−0.850347	−	0.526222i	$-0.823608\pi$
$439$	−116.820	−	587.295i	−0.266105	−	1.33780i	0.584242	−	0.811579i	$-0.301392\pi$
$440$	−11.8021	−	23.3918i	−0.0268229	−	0.0531632i
$441$	6.60148	−	33.1879i	0.0149693	−	0.0752560i
$442$	−405.038	+	77.2596i	−0.916376	+	0.174795i
$443$	−319.893	+	97.0384i	−0.722106	+	0.219048i	−0.629883	−	0.776690i	$-0.716897\pi$
$443$	−319.893	+	97.0384i	−0.722106	+	0.219048i	−0.0922226	+	0.995738i	$0.529397\pi$
$444$	193.426	−	124.886i	0.435643	−	0.281275i
$445$	160.701	+	131.884i	0.361126	+	0.296368i
$446$	−640.301	−	533.966i	−1.43565	−	1.19723i
$447$	−2.20047			−0.00492275
$448$	−144.209	−	400.655i	−0.321895	−	0.894319i
$449$			226.325i			0.504065i	0.967719	+	0.252032i	$0.0810990\pi$
$449$			226.325i			0.504065i	−0.967719	+	0.252032i	$0.918901\pi$
$450$	474.186	+	395.438i	1.05375	+	0.878751i
$451$	7.30598	−	8.90236i	0.0161995	−	0.0197392i
$452$	148.085	−	687.735i	0.327621	−	1.52154i
$453$	−6.00342	−	19.7906i	−0.0132526	−	0.0436879i
$454$	701.983	−	133.901i	1.54622	−	0.294936i
$455$	−361.486	−	71.9040i	−0.794474	−	0.158031i
$456$	12.9831	+	173.776i	0.0284717	+	0.381088i
$457$	−343.170	+	68.2607i	−0.750919	+	0.149367i	−0.555689	−	0.831390i	$-0.687545\pi$
$457$	−343.170	+	68.2607i	−0.750919	+	0.149367i	−0.195230	+	0.980757i	$0.562545\pi$
$458$	372.417	+	157.704i	0.813137	+	0.344332i
$459$	−671.705	−	66.1572i	−1.46341	−	0.144133i
$460$	761.819	+	87.1554i	1.65613	+	0.189468i
$461$	−272.408	−	82.6341i	−0.590907	−	0.179250i	−0.0193510	−	0.999813i	$-0.506160\pi$
$461$	−272.408	−	82.6341i	−0.590907	−	0.179250i	−0.571556	+	0.820563i	$0.693660\pi$
$462$	4.50995	+	5.58441i	0.00976180	+	0.0120875i
$463$	−138.927	+	335.400i	−0.300059	+	0.724405i	0.699890	+	0.714251i	$0.253232\pi$
$463$	−138.927	+	335.400i	−0.300059	+	0.724405i	−0.999948	+	0.0101547i	$0.996768\pi$
$464$	186.906	+	377.810i	0.402814	+	0.814246i
$465$	589.035	−	243.986i	1.26674	−	0.524701i
$466$	−292.733	+	537.452i	−0.628183	+	1.15333i
$467$	465.110	−	248.606i	0.995953	−	0.532348i	0.108918	−	0.994051i	$-0.465261\pi$
$467$	465.110	−	248.606i	0.995953	−	0.532348i	0.887035	+	0.461703i	$0.152761\pi$
$468$	191.242	−	15.8019i	0.408636	−	0.0337647i
$469$	170.226	+	207.421i	0.362955	+	0.442262i
$470$	549.793	+	558.513i	1.16977	+	1.18832i
$471$	−182.562	+	273.223i	−0.387605	+	0.580092i
$472$	−412.962	+	262.051i	−0.874919	+	0.555192i
$473$	11.1127	+	16.6314i	0.0234941	+	0.0351614i
$474$	−102.638	+	67.4187i	−0.216536	+	0.142234i
$475$	−609.866	−	325.980i	−1.28393	−	0.686274i
$476$	−760.412	+	301.045i	−1.59750	+	0.632448i
$477$	−208.017	+	20.4879i	−0.436095	+	0.0429516i
$478$	−2.65077	+	1.39017i	−0.00554555	+	0.00290830i
$479$	−594.791	−	594.791i	−1.24173	−	1.24173i	−0.959281	−	0.282453i	$-0.908852\pi$
$479$	−594.791	−	594.791i	−1.24173	−	1.24173i	−0.282453	−	0.959281i	$-0.591148\pi$
$480$	358.702	−	21.1301i	0.747297	−	0.0440210i
$481$	200.790	+	200.790i	0.417442	+	0.417442i
$482$	7.93607	−	25.4395i	0.0164649	−	0.0527791i
$483$	−209.064	+	20.5910i	−0.432846	+	0.0426316i
$484$	483.311	+	7.60520i	0.998576	+	0.0157132i
$485$	−584.446	−	312.393i	−1.20504	−	0.644109i
$486$	478.983	+	99.1993i	0.985563	+	0.204114i
$487$	233.449	+	349.381i	0.479361	+	0.717414i	0.989794	−	0.142503i	$-0.0455151\pi$
$487$	233.449	+	349.381i	0.479361	+	0.717414i	−0.510434	+	0.859917i	$0.670515\pi$
$488$	511.976	+	226.366i	1.04913	+	0.463865i
$489$	−44.6018	+	66.7513i	−0.0912103	+	0.136506i
$490$	78.1439	+	0.614784i	0.159477	+	0.00125466i
$491$	−301.407	−	367.266i	−0.613864	−	0.747996i	0.369582	−	0.929198i	$-0.379501\pi$
$491$	−301.407	−	367.266i	−0.613864	−	0.747996i	−0.983446	+	0.181202i	$0.942001\pi$
$492$	72.2524	+	140.446i	0.146855	+	0.285460i
$493$	713.977	−	381.629i	1.44823	−	0.774095i
$494$	−206.149	+	60.7679i	−0.417306	+	0.123012i
$495$	21.6357	−	8.96181i	0.0437085	−	0.0181047i
$496$	−373.891	+	827.960i	−0.753812	+	1.66927i
$497$	−13.4452	+	32.4596i	−0.0270528	+	0.0653111i
$498$	145.536	+	15.4910i	0.292240	+	0.0311064i
$499$	−563.086	−	170.810i	−1.12843	−	0.342305i	−0.329754	−	0.944067i	$-0.606966\pi$
$499$	−563.086	−	170.810i	−1.12843	−	0.342305i	−0.798676	+	0.601762i	$0.794466\pi$
$500$	−291.243	+	524.844i	−0.582486	+	1.04969i
$501$	−81.2744	−	8.00483i	−0.162224	−	0.0159777i
$502$	−140.543	−	346.996i	−0.279965	−	0.691227i
$503$	555.595	−	110.515i	1.10456	−	0.219711i	0.391061	−	0.920365i	$-0.372108\pi$
$503$	555.595	−	110.515i	1.10456	−	0.219711i	0.713502	+	0.700654i	$0.247108\pi$
$504$	366.719	−	101.857i	0.727616	−	0.202097i
$505$	−290.894	−	57.8625i	−0.576029	−	0.114579i
$506$	10.3527	−	15.2331i	0.0204599	−	0.0301050i
$507$	48.9475	+	161.358i	0.0965435	+	0.318261i
$508$	−108.886	−	596.293i	−0.214343	−	1.17381i
$509$	−118.634	+	144.556i	−0.233073	+	0.284000i	−0.876392	−	0.481598i	$-0.840057\pi$
$509$	−118.634	+	144.556i	−0.233073	+	0.284000i	0.643320	+	0.765598i	$0.277557\pi$
$510$	−62.2390	−	687.314i	−0.122037	−	1.34768i
$511$			182.875i			0.357876i
$512$	−351.995	+	371.811i	−0.687491	+	0.726193i
$513$	−351.799			−0.685768
$514$	−41.7445	+	3.78013i	−0.0812150	+	0.00735433i
$515$	1278.42	+	1049.17i	2.48236	+	2.03722i
$516$	−269.858	+	49.2776i	−0.522982	+	0.0954991i
$517$	18.0141	−	5.46452i	0.0348436	−	0.0105697i
$518$	465.811	+	316.574i	0.899249	+	0.611146i
$519$	50.0457	−	251.597i	0.0964271	−	0.484772i
$520$	118.600	+	426.998i	0.228076	+	0.821151i
$521$	48.2465	+	242.551i	0.0926036	+	0.465550i	0.999064	+	0.0432587i	$0.0137740\pi$
$521$	48.2465	+	242.551i	0.0926036	+	0.465550i	−0.906460	+	0.422291i	$0.861226\pi$
$522$	−349.200	+	141.435i	−0.668965	+	0.270948i
$523$	82.0901	−	833.475i	0.156960	−	1.59364i	−0.517732	−	0.855543i	$-0.673223\pi$
$523$	82.0901	−	833.475i	0.156960	−	1.59364i	0.674692	−	0.738100i	$-0.264277\pi$
$524$	741.659	+	411.557i	1.41538	+	0.785414i
$525$	113.401	−	373.834i	0.216002	−	0.712064i
$526$	6.18869	−	58.1419i	0.0117656	−	0.110536i
$527$	1612.01	+	667.715i	3.05883	+	1.26701i
$528$	3.55216	−	7.86605i	0.00672757	−	0.0148978i
$529$	3.83769	+	9.26500i	0.00725461	+	0.0175142i
$530$	−136.489	−	463.026i	−0.257526	−	0.873633i
$531$	−206.073	−	385.535i	−0.388085	−	0.726055i
$532$	−379.052	+	195.003i	−0.712504	+	0.366546i
$533$	−150.577	+	123.576i	−0.282509	+	0.231849i
$534$	−0.538758	+	68.4805i	−0.00100891	+	0.128241i
$535$	817.220	+	546.049i	1.52751	+	1.02065i
$536$	130.468	−	295.080i	0.243410	−	0.550523i
$537$	−9.75891	+	6.52070i	−0.0181730	+	0.0121428i
$538$	−61.8271	+	298.532i	−0.114920	+	0.554892i
$539$	0.884841	−	1.65542i	0.00164163	−	0.00307128i
$540$	−11.4133	+	725.319i	−0.0211358	+	1.34318i
$541$	48.0541	+	487.901i	0.0888245	+	0.901850i	0.931576	+	0.363547i	$0.118434\pi$
$541$	48.0541	+	487.901i	0.0888245	+	0.901850i	−0.842751	+	0.538303i	$0.819066\pi$
$542$	−49.8731	−	15.5583i	−0.0920168	−	0.0287054i
$543$	91.3393	−	91.3393i	0.168212	−	0.168212i
$544$	735.026	+	653.247i	1.35115	+	1.20082i
$545$	−149.028	+	149.028i	−0.273447	+	0.273447i
$546$	−56.3894	−	107.523i	−0.103277	−	0.196929i
$547$	−73.1273	−	742.474i	−0.133688	−	1.35736i	−0.794710	−	0.606990i	$-0.792377\pi$
$547$	−73.1273	−	742.474i	−0.133688	−	1.35736i	0.661022	−	0.750367i	$-0.270123\pi$
$548$	−325.458	−	822.076i	−0.593901	−	1.50014i
$549$	−235.861	+	441.264i	−0.429619	+	0.803760i
$550$	18.8038	+	28.6268i	0.0341886	+	0.0520487i
$551$	350.849	−	234.430i	0.636749	−	0.425462i
$552$	135.338	+	213.277i	0.245178	+	0.386372i
$553$	−249.765	−	166.888i	−0.451655	−	0.301786i
$554$	−535.666	+	527.304i	−0.966907	+	0.951812i
$555$	−367.379	+	301.500i	−0.661944	+	0.543243i
$556$	−16.8072	−	203.409i	−0.0302288	−	0.365844i
$557$	−140.004	−	261.929i	−0.251354	−	0.470250i	0.724324	−	0.689460i	$-0.242152\pi$
$557$	−140.004	−	261.929i	−0.251354	−	0.470250i	−0.975678	+	0.219210i	$0.929652\pi$
$558$	−713.086	−	388.396i	−1.27793	−	0.696049i
$559$	−129.472	−	312.573i	−0.231613	−	0.559164i
$560$	389.748	+	787.834i	0.695978	+	1.40685i
$561$	−15.3149	−	6.34364i	−0.0272993	−	0.0113077i
$562$	−290.939	+	234.961i	−0.517685	+	0.418081i
$563$	−230.821	+	760.916i	−0.409985	+	1.35154i	0.472555	+	0.881301i	$0.343332\pi$
$563$	−230.821	+	760.916i	−0.409985	+	1.35154i	−0.882540	+	0.470238i	$0.844168\pi$
$564$	−29.3443	+	256.497i	−0.0520290	+	0.454781i
$565$	−142.336	+	1445.16i	−0.251922	+	2.55781i
$566$	399.211	−	942.733i	0.705319	−	1.66561i
$567$	44.7610	+	225.029i	0.0789435	+	0.396876i
$568$	42.1275	−	3.14742i	0.0741682	−	0.00554124i
$569$	−163.913	+	824.048i	−0.288073	+	1.44824i	0.517470	+	0.855701i	$0.326874\pi$
$569$	−163.913	+	824.048i	−0.288073	+	1.44824i	−0.805543	+	0.592538i	$0.798126\pi$
$570$	−67.3976	−	353.336i	−0.118241	−	0.619887i
$571$	857.303	−	260.060i	1.50141	−	0.455446i	0.570682	−	0.821171i	$-0.306679\pi$
$571$	857.303	−	260.060i	1.50141	−	0.455446i	0.930723	+	0.365724i	$0.119179\pi$
$572$	10.4062	+	2.24068i	0.0181927	+	0.00391728i
$573$	276.770	+	227.139i	0.483019	+	0.396403i
$574$	−247.441	+	296.717i	−0.431083	+	0.516929i
$575$	−1002.37			−1.74326
$576$	−307.965	−	338.503i	−0.534662	−	0.587679i
$577$			631.698i			1.09480i	0.836872	+	0.547398i	$0.184382\pi$
$577$			631.698i			1.09480i	−0.836872	+	0.547398i	$0.815618\pi$
$578$	839.421	−	1006.58i	1.45228	−	1.74149i
$579$	190.956	−	232.680i	0.329803	−	0.401866i
$580$	−471.951	−	730.966i	−0.813709	−	1.26029i
$581$	103.927	+	342.600i	0.178875	+	0.589673i
$582$	−40.9032	−	214.438i	−0.0702805	−	0.368450i
$583$	−11.3721	−	2.26206i	−0.0195063	−	0.00388003i
$584$	196.315	−	99.0487i	0.336156	−	0.169604i
$585$	−388.494	+	77.2762i	−0.664092	+	0.132096i
$586$	−180.556	+	426.381i	−0.308115	+	0.727613i
$587$	897.421	+	88.3882i	1.52883	+	0.150576i	0.827175	−	0.561945i	$-0.189947\pi$
$587$	897.421	+	88.3882i	1.52883	+	0.150576i	0.701651	+	0.712521i	$0.252447\pi$
$588$	16.0160	+	20.1539i	0.0272380	+	0.0342754i
$589$	870.273	+	263.994i	1.47754	+	0.448208i
$590$	785.424	−	634.306i	1.33123	−	1.07510i
$591$	5.95911	−	14.3866i	0.0100831	−	0.0243428i
$592$	87.5479	−	671.510i	0.147885	−	1.13431i
$593$	163.016	−	67.5232i	0.274900	−	0.113867i	−0.240975	−	0.970531i	$-0.577467\pi$
$593$	163.016	−	67.5232i	0.274900	−	0.113867i	0.515874	+	0.856664i	$0.327467\pi$
$594$	15.3017	+	8.33434i	0.0257604	+	0.0140309i
$595$	1488.83	−	795.797i	2.50224	−	1.33747i
$596$	−4.18409	+	4.93782i	−0.00702029	+	0.00828493i
$597$	−31.4886	−	38.3690i	−0.0527448	−	0.0642697i
$598$	−222.011	+	218.545i	−0.371256	+	0.365460i
$599$	−165.672	+	247.945i	−0.276581	+	0.413932i	−0.943590	−	0.331118i	$-0.892574\pi$
$599$	−165.672	+	247.945i	−0.276581	+	0.413932i	0.667009	+	0.745050i	$0.267574\pi$
$600$	−462.730	+	80.7404i	−0.771216	+	0.134567i
$601$	−354.404	−	530.403i	−0.589690	−	0.882534i	0.409871	−	0.912143i	$-0.365574\pi$
$601$	−354.404	−	530.403i	−0.589690	−	0.882534i	−0.999562	+	0.0296095i	$0.990574\pi$
$602$	−368.406	−	560.861i	−0.611971	−	0.931663i
$603$	254.325	+	135.940i	0.421767	+	0.225439i
$604$	−55.8251	−	24.1594i	−0.0924257	−	0.0399991i
$605$	−992.964	+	97.7985i	−1.64126	+	0.161650i
$606$	−45.3777	−	86.5262i	−0.0748806	−	0.142782i
$607$	92.8053	+	92.8053i	0.152892	+	0.152892i	0.779408	−	0.626516i	$-0.215520\pi$
$607$	92.8053	+	92.8053i	0.152892	+	0.152892i	−0.626516	+	0.779408i	$0.715520\pi$
$608$	414.637	+	301.293i	0.681969	+	0.495548i
$609$	168.557	+	168.557i	0.276777	+	0.276777i
$610$	−1103.08	−	344.114i	−1.80832	−	0.564122i
$611$	−316.874	+	31.2093i	−0.518615	+	0.0510791i
$612$	−631.205	+	611.648i	−1.03138	+	0.999425i
$613$	−413.044	−	220.777i	−0.673808	−	0.360158i	0.0987409	−	0.995113i	$-0.468518\pi$
$613$	−413.044	−	220.777i	−0.673808	−	0.360158i	−0.772549	+	0.634955i	$0.781018\pi$
$614$	39.5515	−	190.974i	0.0644161	−	0.311033i
$615$	−181.128	−	271.077i	−0.294517	−	0.440776i
$616$	21.1068	+	0.498245i	0.0342643	+	0.000808839i
$617$	418.924	−	626.964i	0.678969	−	1.01615i	−0.318696	−	0.947857i	$-0.603245\pi$
$617$	418.924	−	626.964i	0.678969	−	1.01615i	0.997665	−	0.0682921i	$-0.0217550\pi$
$618$	−4.28596	+	544.780i	−0.00693521	+	0.881521i
$619$	313.594	+	382.116i	0.506615	+	0.617312i	0.962022	−	0.272971i	$-0.0880064\pi$
$619$	313.594	+	382.116i	0.506615	+	0.617312i	−0.455408	+	0.890283i	$0.650506\pi$
$620$	572.522	−	1785.71i	0.923423	−	2.88018i
$621$	−449.727	+	240.384i	−0.724197	+	0.387092i
$622$	110.545	+	375.012i	0.177724	+	0.602913i
$623$	−154.768	+	64.1072i	−0.248424	+	0.102901i
$624$	−84.8844	+	118.771i	−0.136033	+	0.190338i
$625$	61.0951	−	147.497i	0.0977522	−	0.235995i
$626$	49.0298	−	460.628i	0.0783224	−	0.735827i
$627$	−8.26805	−	2.50808i	−0.0131867	−	0.00400013i
$628$	265.975	+	929.188i	0.423527	+	1.47960i
$629$	−1294.37	−	127.484i	−2.05782	−	0.202678i
$630$	−728.173	+	294.929i	−1.15583	+	0.468142i
$631$	−270.313	+	53.7686i	−0.428388	+	0.0852117i	−0.404575	−	0.914505i	$-0.632581\pi$
$631$	−270.313	+	53.7686i	−0.428388	+	0.0852117i	−0.0238130	+	0.999716i	$0.507581\pi$
$632$	−43.8753	+	358.512i	−0.0694230	+	0.567266i
$633$	−134.846	−	26.8225i	−0.213026	−	0.0423736i
$634$	−443.598	−	301.477i	−0.699681	−	0.475516i
$635$	363.209	+	1197.34i	0.571982	+	1.88557i
$636$	90.4149	−	130.812i	0.142162	−	0.205679i
$637$	−20.1415	+	24.5425i	−0.0316193	+	0.0385282i
$638$	−20.8142	+	1.88480i	−0.0326241	+	0.00295424i
$639$			37.7591i			0.0590909i
$640$	634.641	−	845.100i	0.991627	−	1.32047i
$641$	640.723			0.999568			0.499784	−	0.866150i	$-0.333413\pi$
$641$	640.723			0.999568			0.499784	+	0.866150i	$0.333413\pi$
$642$	29.1994	+	322.453i	0.0454819	+	0.502263i
$643$	105.576	+	86.6442i	0.164193	+	0.134750i	0.712902	−	0.701264i	$-0.247380\pi$
$643$	105.576	+	86.6442i	0.164193	+	0.134750i	−0.548709	+	0.836014i	$0.684880\pi$
$644$	−351.321	+	508.290i	−0.545529	+	0.789270i
$645$	541.868	−	164.374i	0.840105	−	0.254843i
$646$	553.328	−	814.175i	0.856545	−	1.26033i
$647$	164.339	−	826.186i	0.254001	−	1.27695i	−0.617506	−	0.786566i	$-0.711857\pi$
$647$	164.339	−	826.186i	0.254001	−	1.27695i	0.871507	−	0.490383i	$-0.163143\pi$
$648$	217.324	−	169.931i	0.335377	−	0.262239i
$649$	−4.73089	−	23.7838i	−0.00728951	−	0.0366469i
$650$	−217.478	−	536.948i	−0.334581	−	0.826073i
$651$	−50.3572	+	511.285i	−0.0773536	+	0.785384i
$652$	64.9805	+	227.010i	0.0996634	+	0.348176i
$653$	181.606	−	598.676i	0.278111	−	0.916809i	−0.700945	−	0.713216i	$-0.747238\pi$
$653$	181.606	−	598.676i	0.278111	−	0.916809i	0.979056	−	0.203593i	$-0.0652620\pi$
$654$	−69.0375	−	7.34843i	−0.105562	−	0.0112361i
$655$	−1617.56	−	670.016i	−2.46956	−	1.02293i
$656$	452.544	+	104.919i	0.689854	+	0.159938i
$657$	75.2118	+	181.577i	0.114478	+	0.276373i
$658$	−605.757	+	178.563i	−0.920604	+	0.271372i
$659$	−389.312	−	728.352i	−0.590762	−	1.10524i	−0.982693	−	0.185243i	$-0.940693\pi$
$659$	−389.312	−	728.352i	−0.590762	−	1.10524i	0.391931	−	0.919995i	$-0.371807\pi$
$660$	−5.43926	+	16.9652i	−0.00824131	+	0.0257049i
$661$	153.927	−	126.324i	0.232869	−	0.191111i	−0.510721	−	0.859747i	$-0.670621\pi$
$661$	153.927	−	126.324i	0.232869	−	0.191111i	0.743590	+	0.668636i	$0.233121\pi$
$662$	428.514	+	3.37126i	0.647302	+	0.00509254i
$663$	233.131	+	155.773i	0.351630	+	0.234952i
$664$	311.491	−	297.124i	0.469113	−	0.447476i
$665$	731.613	−	488.848i	1.10017	−	0.735110i
$666$	592.706	+	122.752i	0.889949	+	0.184312i
$667$	288.327	−	539.421i	0.432274	−	0.808727i
$668$	−172.502	+	167.158i	−0.258237	+	0.250236i
$669$	55.5679	+	564.190i	0.0830611	+	0.843334i
$670$	−198.332	+	635.765i	−0.296018	+	0.948903i
$671$	−19.6258	+	19.6258i	−0.0292486	+	0.0292486i
$672$	−121.239	+	262.943i	−0.180416	+	0.391284i
$673$	127.555	−	127.555i	0.189532	−	0.189532i	−0.605962	−	0.795494i	$-0.707212\pi$
$673$	127.555	−	127.555i	0.189532	−	0.189532i	0.795494	+	0.605962i	$0.207212\pi$
$674$	238.797	−	125.235i	0.354299	−	0.185808i
$675$	−92.9476	−	943.713i	−0.137700	−	1.39809i
$676$	455.157	+	196.978i	0.673309	+	0.291388i
$677$	−324.431	+	606.967i	−0.479218	+	0.896554i	0.519886	+	0.854236i	$0.325974\pi$
$677$	−324.431	+	606.967i	−0.479218	+	0.896554i	−0.999104	+	0.0423186i	$0.986526\pi$
$678$	−399.825	+	262.628i	−0.589712	+	0.387357i
$679$	444.012	−	296.679i	0.653920	−	0.436936i
$680$	−1660.67	−	1167.23i	−2.44216	−	1.71652i
$681$	−404.046	−	269.975i	−0.593312	−	0.396438i
$682$	−31.5988	−	32.0999i	−0.0463325	−	0.0470673i
$683$	−919.339	+	754.482i	−1.34603	+	1.10466i	−0.360946	+	0.932587i	$0.617546\pi$
$683$	−919.339	+	754.482i	−1.34603	+	1.10466i	−0.985084	+	0.172072i	$0.944954\pi$
$684$	−296.163	+	349.514i	−0.432987	+	0.510985i
$685$	860.330	+	1609.56i	1.25596	+	2.34973i
$686$	−342.001	+	627.907i	−0.498544	+	0.915316i
$687$	−105.240	−	254.072i	−0.153188	−	0.369828i
$688$	−402.546	+	699.257i	−0.585096	+	1.01636i
$689$	181.192	+	75.0520i	0.262978	+	0.108929i
$690$	−327.593	−	405.639i	−0.474772	−	0.587882i
$691$	−39.9721	+	131.770i	−0.0578467	+	0.190695i	−0.981102	−	0.193493i	$-0.938018\pi$
$691$	−39.9721	+	131.770i	−0.0578467	+	0.190695i	0.923255	+	0.384188i	$0.125518\pi$
$692$	−469.419	−	590.702i	−0.678351	−	0.853615i
$693$	−1.84966	+	18.7799i	−0.00266906	+	0.0270994i
$694$	−44.6007	−	18.8867i	−0.0642662	−	0.0272142i
$695$	82.1927	+	413.210i	0.118263	+	0.594547i
$696$	89.6516	−	272.240i	0.128810	−	0.391150i
$697$	174.064	−	875.077i	0.249733	−	1.25549i
$698$	1060.50	−	202.288i	1.51935	−	0.289810i
$699$	398.231	−	120.802i	0.569716	−	0.172821i
$700$	−623.250	−	965.299i	−0.890356	−	1.37900i
$701$	−101.653	−	83.4246i	−0.145012	−	0.119008i	0.559091	−	0.829107i	$-0.311150\pi$
$701$	−101.653	−	83.4246i	−0.145012	−	0.119008i	−0.704102	+	0.710099i	$0.748650\pi$
$702$	−226.342	−	188.754i	−0.322425	−	0.268880i
$703$	−677.913			−0.964314
$704$	−10.8970	−	22.9279i	−0.0154787	−	0.0325681i
$705$		−	532.911i		−	0.755903i
$706$	132.499	+	110.495i	0.187675	+	0.156508i
$707$	151.619	−	184.748i	0.214454	−	0.261313i
$708$	325.120	+	70.0054i	0.459209	+	0.0988777i
$709$	−116.121	−	382.801i	−0.163782	−	0.539917i	0.836182	−	0.548453i	$-0.184783\pi$
$709$	−116.121	−	382.801i	−0.163782	−	0.539917i	−0.999964	+	0.00853593i	$0.997283\pi$
$710$	−85.6572	+	16.3388i	−0.120644	+	0.0230124i
$711$	−316.630	−	62.9817i	−0.445331	−	0.0885818i
$712$	152.645	+	131.422i	0.214389	+	0.184581i
$713$	1292.91	−	257.176i	1.81334	−	0.360696i
$714$	512.091	+	216.850i	0.717214	+	0.303712i
$715$	−21.8669	−	2.15370i	−0.0305831	−	0.00301217i
$716$	−3.92380	+	34.2977i	−0.00548017	+	0.0479018i
$717$	1.94767	+	0.590820i	0.00271642	+	0.000824016i
$718$	33.1556	+	41.0547i	0.0461778	+	0.0571792i
$719$	−300.459	+	725.372i	−0.417884	+	1.00886i	0.565075	+	0.825039i	$0.308847\pi$
$719$	−300.459	+	725.372i	−0.417884	+	1.00886i	−0.982959	+	0.183823i	$0.941153\pi$
$720$	711.000	+	621.952i	0.987499	+	0.863822i
$721$	−1231.22	+	509.989i	−1.70766	+	0.707336i
$722$	−99.9263	+	183.462i	−0.138402	+	0.254103i
$723$	−15.9809	+	8.54198i	−0.0221036	+	0.0118146i
$724$	−31.2863	−	378.641i	−0.0432131	−	0.522985i
$725$	721.563	+	879.227i	0.995259	+	1.21273i
$726$	−230.578	−	234.235i	−0.317601	−	0.322638i
$727$	144.447	−	216.180i	0.198689	−	0.297360i	−0.718724	−	0.695296i	$-0.755273\pi$
$727$	144.447	−	216.180i	0.198689	−	0.297360i	0.917413	+	0.397936i	$0.130273\pi$
$728$	−348.503	−	77.9141i	−0.478713	−	0.107025i
$729$	−12.3634	−	18.5031i	−0.0169593	−	0.0253815i
$730$	−379.367	+	249.190i	−0.519681	+	0.341356i
$731$	1366.67	+	730.501i	1.86959	+	0.999317i
$732$	−140.115	−	353.918i	−0.191414	−	0.483494i
$733$	125.760	−	12.3863i	0.171569	−	0.0168981i	−0.0118677	−	0.999930i	$-0.503778\pi$
$733$	125.760	−	12.3863i	0.171569	−	0.0168981i	0.183437	+	0.983031i	$0.441278\pi$
$734$	711.704	−	373.245i	0.969623	−	0.508508i
$735$	−37.5743	−	37.5743i	−0.0511215	−	0.0511215i
$736$	735.930	+	101.841i	0.999905	+	0.138371i
$737$	11.3114	+	11.3114i	0.0153479	+	0.0153479i
$738$	−123.654	+	396.379i	−0.167552	+	0.537099i
$739$	287.398	−	28.3062i	0.388901	−	0.0383034i	0.0983226	−	0.995155i	$-0.468652\pi$
$739$	287.398	−	28.3062i	0.388901	−	0.0383034i	0.290578	+	0.956851i	$0.406152\pi$
$740$	−21.9934	+	1397.68i	−0.0297208	+	1.88876i
$741$	128.885	+	68.8904i	0.173934	+	0.0929695i
$742$	380.902	+	78.8862i	0.513344	+	0.106316i
$743$	−123.639	−	185.039i	−0.166405	−	0.249043i	0.738890	−	0.673826i	$-0.235350\pi$
$743$	−123.639	−	185.039i	−0.166405	−	0.249043i	−0.905295	+	0.424783i	$0.860350\pi$
$744$	576.137	−	222.865i	0.774378	−	0.299549i
$745$	7.42227	−	11.1082i	0.00996278	−	0.0149104i
$746$	−674.103	−	5.30339i	−0.903623	−	0.00710910i
$747$	244.092	+	297.427i	0.326763	+	0.398162i
$748$	−43.3556	+	22.3042i	−0.0579621	+	0.0298185i
$749$	−698.484	+	373.347i	−0.932555	+	0.498461i
$750$	391.494	−	115.403i	0.521993	−	0.153871i
$751$	−1045.30	+	432.976i	−1.39187	+	0.576533i	−0.947629	−	0.319373i	$-0.896528\pi$
$751$	−1045.30	+	432.976i	−1.39187	+	0.576533i	−0.444244	+	0.895906i	$0.646528\pi$
$752$	519.777	+	553.565i	0.691193	+	0.736124i
$753$	−97.4196	+	235.192i	−0.129375	+	0.312339i
$754$	351.512	+	37.4153i	0.466196	+	0.0496225i
$755$	120.155	+	36.4487i	0.159146	+	0.0482764i
$756$	−511.122	−	283.629i	−0.676087	−	0.375170i
$757$	−214.539	−	21.1303i	−0.283407	−	0.0279132i	−0.0446853	−	0.999001i	$-0.514229\pi$
$757$	−214.539	−	21.1303i	−0.283407	−	0.0279132i	−0.238722	+	0.971088i	$0.576729\pi$
$758$	−47.3070	−	116.800i	−0.0624103	−	0.154089i
$759$	−12.2833	+	2.44331i	−0.0161836	+	0.00321911i
$760$	−921.033	−	520.613i	−1.21189	−	0.685017i
$761$	−259.621	−	51.6418i	−0.341157	−	0.0678604i	0.0215385	−	0.999768i	$-0.493144\pi$
$761$	−259.621	−	51.6418i	−0.341157	−	0.0678604i	−0.362696	+	0.931908i	$0.618144\pi$
$762$	−231.680	+	340.897i	−0.304042	+	0.447372i
$763$	−49.2995	−	162.519i	−0.0646127	−	0.212999i
$764$	1035.96	−	189.172i	1.35597	−	0.247607i
$765$	1150.98	−	1402.47i	1.50455	−	1.83330i
$766$	−87.9673	−	971.436i	−0.114840	−	1.26819i
$767$			410.168i			0.534769i
$768$	347.934	−	12.2654i	0.453039	−	0.0159706i
$769$	−767.147			−0.997590			−0.498795	−	0.866720i	$-0.666224\pi$
$769$	−767.147			−0.997590			−0.498795	+	0.866720i	$0.666224\pi$
$770$	−43.4030	+	3.93031i	−0.0563675	+	0.00510430i
$771$	22.0320	+	18.0812i	0.0285759	+	0.0234517i
$772$	−159.037	−	870.932i	−0.206006	−	1.12815i
$773$	−1064.10	+	322.791i	−1.37658	+	0.417582i	−0.889964	−	0.456031i	$-0.849271\pi$
$773$	−1064.10	+	322.791i	−1.37658	+	0.417582i	−0.486621	+	0.873613i	$0.661771\pi$
$774$	−596.461	−	405.366i	−0.770622	−	0.523729i
$775$	−478.242	+	2404.29i	−0.617087	+	3.10230i
$776$	−558.970	−	315.958i	−0.720323	−	0.407162i
$777$	−74.7134	−	375.610i	−0.0961563	−	0.483410i
$778$	796.533	−	322.617i	1.02382	−	0.414674i
$779$	45.5820	−	462.802i	0.0585135	−	0.594098i
$780$	146.216	−	263.493i	0.187456	−	0.337811i
$781$	−0.608021	+	2.00438i	−0.000778516	+	0.00256642i
$782$	151.029	−	1418.90i	0.193132	−	1.81445i
$783$	534.590	+	221.434i	0.682746	+	0.282802i
$784$	75.6788	+	2.38230i	0.0965290	+	0.00303864i
$785$	−763.473	−	1843.19i	−0.972577	−	2.34801i
$786$	−163.077	−	553.222i	−0.207477	−	0.703845i
$787$	−7.83134	−	14.6514i	−0.00995087	−	0.0186168i	0.876897	−	0.480679i	$-0.159610\pi$
$787$	−7.83134	−	14.6514i	−0.00995087	−	0.0186168i	−0.886848	+	0.462062i	$0.847110\pi$
$788$	−20.9522	−	40.7276i	−0.0265891	−	0.0516848i
$789$	−30.7339	+	25.2227i	−0.0389530	+	0.0319679i
$790$	5.86537	−	745.535i	0.00742452	−	0.943715i
$791$	−972.955	−	650.108i	−1.23003	−	0.821881i
$792$	21.1620	−	8.18599i	0.0267197	−	0.0103359i
$793$	390.340	−	260.817i	0.492232	−	0.328899i
$794$	−253.416	+	1223.62i	−0.319164	+	1.54108i
$795$	−154.733	+	289.484i	−0.194632	+	0.364131i
$796$	−145.974	−	2.29699i	−0.183384	−	0.00288566i
$797$	128.345	+	1303.11i	0.161036	+	1.63502i	0.648028	+	0.761617i	$0.275594\pi$
$797$	128.345	+	1303.11i	0.161036	+	1.63502i	−0.486992	+	0.873406i	$0.661906\pi$
$798$	276.704	+	86.3202i	0.346747	+	0.108171i
$799$	1031.25	−	1031.25i	1.29068	−	1.29068i
$800$	−698.680	+	1191.88i	−0.873350	+	1.48985i
$801$	−127.305	+	127.305i	−0.158932	+	0.158932i
$802$	−308.249	−	587.769i	−0.384350	−	0.732879i
$803$	1.06862	+	10.8498i	0.00133078	+	0.0135116i
$804$	−203.983	+	80.7562i	−0.253710	+	0.100443i
$805$	601.237	−	1124.84i	0.746878	−	1.39731i
$806$	418.278	+	636.785i	0.518955	+	0.790056i
$807$	172.367	−	115.172i	0.213590	−	0.142716i
$808$	−280.447	−	62.6990i	−0.347088	−	0.0775977i
$809$	−566.044	−	378.218i	−0.699683	−	0.467513i	0.154158	−	0.988046i	$-0.450733\pi$
$809$	−566.044	−	378.218i	−0.699683	−	0.467513i	−0.853842	+	0.520533i	$0.825733\pi$
$810$	−405.821	+	399.486i	−0.501014	+	0.493192i
$811$	358.504	−	294.217i	0.442052	−	0.362783i	−0.386882	−	0.922129i	$-0.626448\pi$
$811$	358.504	−	294.217i	0.442052	−	0.362783i	0.828934	+	0.559347i	$0.188948\pi$
$812$	698.745	−	57.7357i	0.860523	−	0.0711030i
$813$	16.7462	+	31.3299i	0.0205980	+	0.0385362i
$814$	29.4862	+	16.0602i	0.0362238	+	0.0197300i
$815$	−186.525	−	450.310i	−0.228864	−	0.552528i
$816$	−44.5710	−	667.179i	−0.0546213	−	0.817621i
$817$	746.223	+	309.096i	0.913370	+	0.378330i
$818$	−1068.06	+	862.561i	−1.30569	+	1.05448i
$819$	92.6549	−	305.442i	0.113132	−	0.372945i
$820$	−952.700	−	108.993i	−1.16183	−	0.132918i
$821$	89.2087	−	905.752i	0.108659	−	1.10323i	−0.773990	−	0.633197i	$-0.781742\pi$
$821$	89.2087	−	905.752i	0.108659	−	1.10323i	0.882649	−	0.470033i	$-0.155758\pi$
$822$	−234.435	+	553.618i	−0.285201	+	0.673501i
$823$	−21.8559	−	109.877i	−0.0265563	−	0.133508i	0.965233	−	0.261392i	$-0.0841815\pi$
$823$	−21.8559	−	109.877i	−0.0265563	−	0.133508i	−0.991789	+	0.127884i	$0.959181\pi$
$824$	1214.33	+	1045.49i	1.47370	+	1.26880i
$825$	4.54355	−	22.8420i	0.00550733	−	0.0276872i
$826$	152.429	+	799.118i	0.184539	+	0.967455i
$827$	−942.749	+	285.980i	−1.13996	+	0.345804i	−0.803155	−	0.595770i	$-0.796847\pi$
$827$	−942.749	+	285.980i	−1.13996	+	0.345804i	−0.336807	+	0.941574i	$0.609347\pi$
$828$	−139.781	+	649.174i	−0.168818	+	0.784026i
$829$	636.902	+	522.692i	0.768277	+	0.630509i	0.934656	−	0.355553i	$-0.115707\pi$
$829$	636.902	+	522.692i	0.768277	+	0.630509i	−0.166379	+	0.986062i	$0.553207\pi$
$830$	−569.098	+	682.429i	−0.685660	+	0.822203i
$831$	511.112			0.615057
$832$	105.116	+	416.317i	0.126341	+	0.500381i
$833$		−	145.422i		−	0.174577i
$834$	−88.8860	+	106.587i	−0.106578	+	0.127802i
$835$	314.551	−	383.282i	0.376708	−	0.459020i
$836$	−21.3494	+	13.7844i	−0.0255376	+	0.0164885i
$837$	362.015	+	1193.40i	0.432514	+	1.42581i
$838$	−108.392	−	568.249i	−0.129346	−	0.678102i
$839$	68.8400	+	13.6931i	0.0820501	+	0.0163208i	0.235945	−	0.971767i	$-0.424182\pi$
$839$	68.8400	+	13.6931i	0.0820501	+	0.0163208i	−0.153895	+	0.988087i	$0.549182\pi$
$840$	186.947	−	567.692i	0.222556	−	0.675824i
$841$	144.136	−	28.6704i	0.171386	−	0.0340909i
$842$	−446.880	+	1055.31i	−0.530737	+	1.25333i
$843$	253.067	+	24.9249i	0.300198	+	0.0295669i
$844$	−316.592	+	251.590i	−0.375109	+	0.298092i
$845$	−979.658	−	297.176i	−1.15936	−	0.351687i
$846$	−528.022	+	426.429i	−0.624139	+	0.504053i
$847$	307.683	−	742.813i	0.363262	−	0.876993i
$848$	−121.620	−	451.623i	−0.143420	−	0.532574i
$849$	−643.156	+	266.404i	−0.757546	+	0.313786i
$850$	2330.24	+	1269.21i	2.74146	+	1.49319i
$851$	−866.618	+	463.217i	−1.01835	+	0.544321i
$852$	−21.9158	−	18.5705i	−0.0257228	−	0.0217964i
$853$	−584.920	−	712.727i	−0.685721	−	0.835553i	0.307530	−	0.951538i	$-0.400498\pi$
$853$	−584.920	−	712.727i	−0.685721	−	0.835553i	−0.993251	+	0.115985i	$0.962998\pi$
$854$	663.561	−	653.202i	0.777004	−	0.764873i
$855$	525.372	−	786.274i	0.614470	−	0.919619i
$856$	779.101	+	547.607i	0.910164	+	0.639728i
$857$	47.0145	+	70.3622i	0.0548594	+	0.0821029i	0.857885	−	0.513841i	$-0.171778\pi$
$857$	47.0145	+	70.3622i	0.0548594	+	0.0821029i	−0.803026	+	0.595944i	$0.796778\pi$
$858$	−3.97386	−	6.04979i	−0.00463153	−	0.00705104i
$859$	−1231.71	−	658.363i	−1.43389	−	0.766430i	−0.442424	−	0.896806i	$-0.645881\pi$
$859$	−1231.71	−	658.363i	−1.43389	−	0.766430i	−0.991465	+	0.130376i	$0.958381\pi$
$860$	661.485	−	1528.49i	0.769169	−	1.77732i
$861$	261.447	−	25.7503i	0.303656	−	0.0299075i
$862$	746.436	+	1423.30i	0.865935	+	1.65117i
$863$	43.6303	+	43.6303i	0.0505566	+	0.0505566i	0.731933	−	0.681377i	$-0.238618\pi$
$863$	43.6303	+	43.6303i	0.0505566	+	0.0505566i	−0.681377	+	0.731933i	$0.738618\pi$
$864$	−27.6401	+	702.307i	−0.0319908	+	0.812855i
$865$	1101.28	+	1101.28i	1.27316	+	1.27316i
$866$	164.496	+	51.3159i	0.189949	+	0.0592563i
$867$	−886.935	+	87.3554i	−1.02299	+	0.100756i
$868$	1051.56	+	1085.19i	1.21148	+	1.25022i
$869$	−15.7936	−	8.44186i	−0.0181745	−	0.00971445i
$870$	−119.985	+	579.348i	−0.137914	+	0.665917i
$871$	−150.323	−	224.975i	−0.172587	−	0.258295i
$872$	−147.761	+	140.946i	−0.169451	+	0.161636i
$873$	318.845	−	477.186i	0.365230	−	0.546605i
$874$	5.85101	−	743.710i	0.00669452	−	0.850927i
$875$	633.380	+	771.776i	0.723863	+	0.882029i
$876$	−142.380	−	45.6489i	−0.162535	−	0.0521106i
$877$	793.981	−	424.392i	0.905338	−	0.483913i	0.0481050	−	0.998842i	$-0.484682\pi$
$877$	793.981	−	424.392i	0.905338	−	0.483913i	0.857233	+	0.514929i	$0.172182\pi$
$878$	338.619	+	1148.73i	0.385670	+	1.30835i
$879$	290.888	−	120.490i	0.330931	−	0.137076i
$880$	27.7271	+	44.4642i	0.0315081	+	0.0505275i
$881$	−154.624	+	373.294i	−0.175509	+	0.423717i	−0.987015	−	0.160628i	$-0.948648\pi$
$881$	−154.624	+	373.294i	−0.175509	+	0.423717i	0.811506	+	0.584344i	$0.198648\pi$
$882$	−7.16307	+	67.2960i	−0.00812139	+	0.0762993i
$883$	1009.45	+	306.213i	1.14321	+	0.346788i	0.804411	−	0.594073i	$-0.202481\pi$
$883$	1009.45	+	306.213i	1.14321	+	0.346788i	0.338794	+	0.940860i	$0.389981\pi$
$884$	792.840	−	226.946i	0.896877	−	0.256726i
$885$	−683.184	−	67.2878i	−0.771960	−	0.0760314i
$886$	619.676	−	250.985i	0.699408	−	0.283279i
$887$	−113.317	+	22.5402i	−0.127753	+	0.0254117i	−0.258553	−	0.965997i	$-0.583246\pi$
$887$	−113.317	+	22.5402i	−0.127753	+	0.0254117i	0.130800	+	0.991409i	$0.458246\pi$
$888$	−362.749	+	283.643i	−0.408501	+	0.319417i
$889$	−988.872	−	196.699i	−1.11234	−	0.221259i
$890$	−343.880	−	233.707i	−0.386382	−	0.262592i
$891$	3.97058	+	13.0893i	0.00445632	+	0.0146905i
$892$	1371.69	+	948.090i	1.53777	+	1.06288i
$893$	482.235	−	587.605i	0.540017	−	0.658012i
$894$	4.38300	−	0.396898i	0.00490269	−	0.000443958i
$895$		−	71.2587i		−	0.0796186i
$896$	359.509	+	772.034i	0.401237	+	0.861645i
$897$	211.834			0.236159
$898$	−40.8222	−	450.806i	−0.0454590	−	0.502011i
$899$	−1156.29	−	948.942i	−1.28620	−	1.05555i
$900$	−1015.83	−	702.124i	−1.12870	−	0.780138i
$901$	−859.619	+	260.762i	−0.954072	+	0.289415i
$902$	−12.9467	+	19.0499i	−0.0143533	+	0.0211197i
$903$	−89.0180	+	447.524i	−0.0985803	+	0.495597i
$904$	−170.915	+	1396.58i	−0.189066	+	1.54488i
$905$	153.000	+	769.182i	0.169061	+	0.849925i
$906$	15.5276	+	38.3371i	0.0171386	+	0.0423147i
$907$	−23.0333	+	233.861i	−0.0253950	+	0.257840i	0.974101	+	0.226111i	$0.0726013\pi$
$907$	−23.0333	+	233.861i	−0.0253950	+	0.257840i	−0.999497	+	0.0317289i	$0.989899\pi$
$908$	−1374.09	+	393.327i	−1.51332	+	0.433179i
$909$	74.5611	−	245.795i	0.0820255	−	0.270402i
$910$	732.995	+	78.0208i	0.805489	+	0.0857372i
$911$	−750.394	−	310.823i	−0.823703	−	0.341189i	−0.0692964	−	0.997596i	$-0.522075\pi$
$911$	−750.394	−	310.823i	−0.823703	−	0.341189i	−0.754407	+	0.656407i	$0.772075\pi$
$912$	−57.2044	−	343.794i	−0.0627241	−	0.376967i
$913$	8.16786	+	19.7190i	0.00894618	+	0.0215980i
$914$	671.231	−	197.863i	0.734388	−	0.216480i
$915$	370.387	+	692.945i	0.404794	+	0.757317i
$916$	−770.243	−	246.950i	−0.840877	−	0.269596i
$917$	1090.60	−	895.032i	1.18931	−	0.976043i
$918$	1349.87	+	10.6199i	1.47045	+	0.0115685i
$919$	590.828	+	394.779i	0.642903	+	0.429574i	0.833823	−	0.552031i	$-0.186147\pi$
$919$	590.828	+	394.779i	0.642903	+	0.429574i	−0.190920	+	0.981606i	$0.561147\pi$
$920$	−1533.15	−	36.1913i	−1.66647	−	0.0393384i
$921$	−110.265	+	73.6767i	−0.119723	+	0.0799964i
$922$	557.501	+	115.461i	0.604665	+	0.125228i
$923$	16.7007	−	31.2448i	0.0180940	−	0.0338514i
$924$	−9.99041	−	10.3098i	−0.0108121	−	0.0111578i
$925$	−179.109	−	1818.52i	−0.193631	−	1.96597i
$926$	216.226	−	693.124i	0.233505	−	0.748514i
$927$	−1012.74	+	1012.74i	−1.09249	+	1.09249i
$928$	−440.434	−	718.829i	−0.474605	−	0.774600i
$929$	−357.083	+	357.083i	−0.384374	+	0.384374i	−0.872675	−	0.488301i	$-0.837617\pi$
$929$	−357.083	+	357.083i	−0.384374	+	0.384374i	0.488301	+	0.872675i	$0.337617\pi$
$930$	−1129.26	+	592.228i	−1.21426	+	0.636804i
$931$	−7.42938	−	75.4318i	−0.00798000	−	0.0810223i
$932$	486.141	−	1123.32i	0.521610	−	1.20528i
$933$	125.321	−	234.458i	0.134320	−	0.251295i
$934$	−881.588	+	579.079i	−0.943885	+	0.619999i
$935$	83.6812	−	55.9140i	0.0894986	−	0.0598011i
$936$	−378.075	+	65.9692i	−0.403926	+	0.0704800i
$937$	951.683	+	635.894i	1.01567	+	0.678649i	0.947741	−	0.319041i	$-0.103361\pi$
$937$	951.683	+	635.894i	1.01567	+	0.678649i	0.0679295	+	0.997690i	$0.478361\pi$
$938$	−376.477	−	382.447i	−0.401361	−	0.407726i
$939$	−243.489	+	199.826i	−0.259306	+	0.212807i
$940$	−1195.84	−	1013.31i	−1.27218	−	1.07799i
$941$	−317.554	−	594.101i	−0.337464	−	0.631351i	0.654757	−	0.755840i	$-0.272771\pi$
$941$	−317.554	−	594.101i	−0.337464	−	0.631351i	−0.992221	+	0.124489i	$0.960271\pi$
$942$	314.355	−	577.148i	0.333710	−	0.612684i
$943$	−257.962	−	622.775i	−0.273554	−	0.660419i
$944$	775.292	−	596.451i	0.821284	−	0.631834i
$945$	1114.76	+	461.749i	1.17964	+	0.488623i
$946$	−25.1347	−	31.1228i	−0.0265694	−	0.0328993i
$947$	−90.7786	+	299.257i	−0.0958591	+	0.316005i	−0.991736	−	0.128298i	$-0.959049\pi$
$947$	−90.7786	+	299.257i	−0.0958591	+	0.316005i	0.895877	+	0.444303i	$0.146549\pi$
$948$	192.279	−	152.801i	0.202826	−	0.161182i
$949$	18.0749	−	183.517i	0.0190462	−	0.193380i
$950$	1273.56	+	539.302i	1.34059	+	0.567686i
$951$	71.1505	+	357.698i	0.0748165	+	0.376128i
$952$	1460.33	−	736.792i	1.53396	−	0.773942i
$953$	−276.517	+	1390.14i	−0.290154	+	1.45870i	0.510657	+	0.859785i	$0.329402\pi$
$953$	−276.517	+	1390.14i	−0.290154	+	1.45870i	−0.800811	+	0.598917i	$0.795598\pi$
$954$	410.643	−	78.3288i	0.430444	−	0.0821057i
$955$	−2080.18	+	631.016i	−2.17820	+	0.660749i
$956$	5.02920	−	3.24713i	0.00526067	−	0.00339657i
$957$	10.9854	+	9.01545i	0.0114790	+	0.00942054i
$958$	1292.02	+	1077.45i	1.34866	+	1.12469i
$959$	−1470.66			−1.53354
$960$	−710.670	+	106.787i	−0.740281	+	0.111236i
$961$		−	2262.87i		−	2.35471i
$962$	−436.159	−	363.726i	−0.453388	−	0.378094i
$963$	−539.980	+	657.968i	−0.560727	+	0.683248i
$964$	−11.2189	+	52.1031i	−0.0116379	+	0.0540489i
$965$	530.494	+	1748.81i	0.549735	+	1.81223i
$966$	412.711	−	78.7232i	0.427237	−	0.0814940i
$967$	1452.59	+	288.939i	1.50216	+	0.298799i	0.876541	−	0.481327i	$-0.159845\pi$
$967$	1452.59	+	288.939i	1.50216	+	0.298799i	0.625623	+	0.780126i	$0.284845\pi$
$968$	−964.054	+	72.0263i	−0.995924	+	0.0744073i
$969$	−656.515	+	130.589i	−0.677518	+	0.134767i
$970$	1220.47	+	516.823i	1.25822	+	0.532807i
$971$	1096.64	+	108.010i	1.12940	+	0.111236i	0.645407	−	0.763839i	$-0.276688\pi$
$971$	1096.64	+	108.010i	1.12940	+	0.111236i	0.483988	+	0.875074i	$0.339188\pi$
$972$	−971.956	−	111.196i	−0.999954	−	0.114399i
$973$	−324.875	−	98.5497i	−0.333890	−	0.101284i
$974$	−528.013	−	653.807i	−0.542107	−	0.671260i
$975$	−150.749	+	363.940i	−0.154614	+	0.373271i
$976$	−1060.61	−	358.543i	−1.08669	−	0.367359i
$977$	1592.89	−	659.798i	1.63039	−	0.675331i	0.635117	−	0.772416i	$-0.280952\pi$
$977$	1592.89	−	659.798i	1.63039	−	0.675331i	0.995276	+	0.0970853i	$0.0309520\pi$
$978$	76.8002	−	141.003i	0.0785278	−	0.144175i
$979$	−8.80771	+	4.70782i	−0.00899664	+	0.00480880i
$980$	−155.762	+	12.8702i	−0.158941	+	0.0131329i
$981$	−115.790	−	141.090i	−0.118032	−	0.143823i
$982$	666.602	+	677.174i	0.678821	+	0.689586i
$983$	−303.858	+	454.756i	−0.309113	+	0.462620i	−0.953204	−	0.302329i	$-0.902236\pi$
$983$	−303.858	+	454.756i	−0.309113	+	0.462620i	0.644091	+	0.764949i	$0.277236\pi$
$984$	−169.248	−	266.716i	−0.172000	−	0.271053i
$985$	52.5247	+	78.6088i	0.0533246	+	0.0798059i
$986$	−1353.30	+	888.927i	−1.37252	+	0.901549i
$987$	378.721	+	202.430i	0.383709	+	0.205097i
$988$	399.658	−	158.224i	0.404512	−	0.160145i
$989$	1165.15	−	114.757i	1.17811	−	0.116033i
$990$	−41.4787	+	21.7530i	−0.0418976	+	0.0219727i
$991$	426.823	+	426.823i	0.430699	+	0.430699i	0.888866	−	0.458167i	$-0.151494\pi$
$991$	426.823	+	426.823i	0.430699	+	0.430699i	−0.458167	+	0.888866i	$0.651494\pi$
$992$	595.395	−	1716.61i	0.600197	−	1.73045i
$993$	−206.044	−	206.044i	−0.207497	−	0.207497i
$994$	20.9261	−	67.0798i	0.0210524	−	0.0674847i
$995$	299.904	−	29.5379i	0.301411	−	0.0296864i
$996$	−292.679	−	4.60549i	−0.293855	−	0.00462399i
$997$	833.355	+	445.438i	0.835863	+	0.446778i	0.833036	−	0.553218i	$-0.186600\pi$
$997$	833.355	+	445.438i	0.835863	+	0.446778i	0.00282629	+	0.999996i	$0.499100\pi$
$998$	1152.39	+	238.665i	1.15470	+	0.239143i
$999$	−516.469	−	772.950i	−0.516986	−	0.773724i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	128.3.l.a.43.1	yes	496
128.3	odd	32	inner	128.3.l.a.3.1	✓	496

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
128.3.l.a.3.1	✓	496	128.3	odd	32	inner
128.3.l.a.43.1	yes	496	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 128 = 2^{7} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	128.l (of order \(32\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.99185 + 0.180370i) q^{2} +(1.05127 + 0.862751i) q^{3} +(3.93493 - 0.718539i) q^{4} +(-7.90123 + 2.39681i) q^{5} +(-2.24958 - 1.52885i) q^{6} +(1.29801 - 6.52556i) q^{7} +(-7.70819 + 2.14097i) q^{8} +(-1.39499 - 7.01311i) q^{9} +O(q^{10})\)	\(q+(-1.99185 + 0.180370i) q^{2} +(1.05127 + 0.862751i) q^{3} +(3.93493 - 0.718539i) q^{4} +(-7.90123 + 2.39681i) q^{5} +(-2.24958 - 1.52885i) q^{6} +(1.29801 - 6.52556i) q^{7} +(-7.70819 + 2.14097i) q^{8} +(-1.39499 - 7.01311i) q^{9} +(15.3057 - 6.19923i) q^{10} +(0.0388787 - 0.394742i) q^{11} +(4.75658 + 2.63949i) q^{12} +(-1.94755 + 6.42020i) q^{13} +(-1.40844 + 13.2321i) q^{14} +(-10.3741 - 4.29711i) q^{15} +(14.9674 - 5.65481i) q^{16} +(-11.7599 - 28.3908i) q^{17} +(4.04357 + 13.7174i) q^{18} +(-7.55037 - 14.1257i) q^{19} +(-29.3686 + 15.1086i) q^{20} +(6.99449 - 5.74023i) q^{21} +(-0.00624099 + 0.793280i) q^{22} +(-19.3042 - 12.8987i) q^{23} +(-9.95048 - 4.39953i) q^{24} +(35.8979 - 23.9862i) q^{25} +(2.72121 - 13.1394i) q^{26} +(10.3538 - 19.3706i) q^{27} +(0.418730 - 26.6103i) q^{28} +(2.58223 + 26.2178i) q^{29} +(21.4388 + 6.68801i) q^{30} +(-40.1489 + 40.1489i) q^{31} +(-28.7929 + 13.9632i) q^{32} +(0.381436 - 0.381436i) q^{33} +(28.5447 + 54.4291i) q^{34} +(5.38462 + 54.6710i) q^{35} +(-10.5284 - 26.5938i) q^{36} +(19.9517 - 37.3269i) q^{37} +(17.5871 + 26.7745i) q^{38} +(-7.58643 + 5.06909i) q^{39} +(55.7727 - 35.3913i) q^{40} +(24.1411 + 16.1305i) q^{41} +(-12.8966 + 12.6953i) q^{42} +(-38.9814 + 31.9912i) q^{43} +(-0.130653 - 1.58122i) q^{44} +(27.8313 + 52.0686i) q^{45} +(40.7776 + 22.2103i) q^{46} +(18.1618 + 43.8464i) q^{47} +(20.6134 + 6.96844i) q^{48} +(4.37204 + 1.81096i) q^{49} +(-67.1769 + 54.2519i) q^{50} +(12.1315 - 39.9921i) q^{51} +(-3.05030 + 26.6625i) q^{52} +(2.86524 - 29.0913i) q^{53} +(-17.1293 + 40.4508i) q^{54} +(0.638933 + 3.21213i) q^{55} +(3.96565 + 53.0793i) q^{56} +(4.24956 - 21.3640i) q^{57} +(-9.87231 - 51.7561i) q^{58} +(58.5036 - 17.7469i) q^{59} +(-43.9092 - 9.45461i) q^{60} +(-54.0901 - 44.3906i) q^{61} +(72.7290 - 87.2123i) q^{62} -47.5752 q^{63} +(54.8325 - 33.0060i) q^{64} -55.3954i q^{65} +(-0.690964 + 0.828563i) q^{66} +(-25.5848 + 31.1751i) q^{67} +(-66.6741 - 103.266i) q^{68} +(-9.16551 - 30.2146i) q^{69} +(-20.5864 - 107.925i) q^{70} +(-5.17915 - 1.03020i) q^{71} +(25.7677 + 51.0718i) q^{72} +(-26.9577 + 5.36223i) q^{73} +(-33.0080 + 77.9483i) q^{74} +(58.4324 + 5.75509i) q^{75} +(-39.8601 - 50.1586i) q^{76} +(-2.52545 - 0.766086i) q^{77} +(14.1967 - 11.4652i) q^{78} +(17.2775 - 41.7116i) q^{79} +(-104.707 + 80.5540i) q^{80} +(-31.8593 + 13.1965i) q^{81} +(-50.9948 - 27.7753i) q^{82} +(-47.4557 + 25.3656i) q^{83} +(23.3983 - 27.6132i) q^{84} +(160.965 + 196.136i) q^{85} +(71.8748 - 70.7527i) q^{86} +(-19.9048 + 29.7897i) q^{87} +(0.545445 + 3.12599i) q^{88} +(-13.9882 - 20.9348i) q^{89} +(-64.8273 - 98.6930i) q^{90} +(39.3675 + 21.0423i) q^{91} +(-85.2290 - 36.8846i) q^{92} +(-76.8457 + 7.56864i) q^{93} +(-44.0841 - 84.0596i) q^{94} +(93.5139 + 93.5139i) q^{95} +(-42.3157 - 10.1621i) q^{96} +(56.7531 + 56.7531i) q^{97} +(-9.03510 - 2.81858i) q^{98} +(-2.82260 + 0.278002i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 496 q - 16 q^{2} - 16 q^{3} - 16 q^{4} - 16 q^{5} - 16 q^{6} - 16 q^{7} - 16 q^{8} - 16 q^{9}+O(q^{10}) \) 496 * q - 16 * q^2 - 16 * q^3 - 16 * q^4 - 16 * q^5 - 16 * q^6 - 16 * q^7 - 16 * q^8 - 16 * q^9	\( 496 q - 16 q^{2} - 16 q^{3} - 16 q^{4} - 16 q^{5} - 16 q^{6} - 16 q^{7} - 16 q^{8} - 16 q^{9} - 16 q^{10} - 16 q^{11} - 16 q^{12} - 16 q^{13} - 16 q^{14} - 16 q^{15} - 16 q^{16} - 16 q^{17} - 16 q^{18} - 16 q^{19} - 16 q^{20} - 16 q^{21} - 16 q^{22} - 16 q^{23} - 16 q^{24} - 16 q^{25} - 16 q^{26} - 16 q^{27} - 16 q^{28} - 16 q^{29} - 16 q^{30} - 16 q^{31} - 16 q^{32} - 16 q^{33} - 16 q^{34} - 16 q^{35} - 16 q^{36} - 16 q^{37} - 16 q^{38} - 16 q^{39} - 16 q^{40} - 16 q^{41} - 16 q^{42} - 16 q^{43} - 16 q^{44} - 16 q^{45} - 16 q^{46} - 16 q^{47} - 16 q^{48} - 16 q^{49} - 640 q^{50} - 16 q^{51} - 1072 q^{52} - 16 q^{53} - 1168 q^{54} - 16 q^{55} - 800 q^{56} - 16 q^{57} - 736 q^{58} - 16 q^{59} - 592 q^{60} - 16 q^{61} - 112 q^{62} - 32 q^{63} + 176 q^{64} + 560 q^{66} - 16 q^{67} + 464 q^{68} - 16 q^{69} + 1328 q^{70} - 16 q^{71} + 1280 q^{72} - 16 q^{73} + 1216 q^{74} - 16 q^{75} + 1648 q^{76} - 16 q^{77} + 1424 q^{78} - 16 q^{79} + 800 q^{80} - 16 q^{81} - 16 q^{82} - 16 q^{83} - 16 q^{84} - 16 q^{85} - 16 q^{86} - 16 q^{87} - 16 q^{88} - 16 q^{89} - 16 q^{90} - 16 q^{91} - 16 q^{92} - 16 q^{93} - 16 q^{94} - 16 q^{95} - 16 q^{96} - 16 q^{97} - 16 q^{98} - 16 q^{99}+O(q^{100}) \) 496 * q - 16 * q^2 - 16 * q^3 - 16 * q^4 - 16 * q^5 - 16 * q^6 - 16 * q^7 - 16 * q^8 - 16 * q^9 - 16 * q^10 - 16 * q^11 - 16 * q^12 - 16 * q^13 - 16 * q^14 - 16 * q^15 - 16 * q^16 - 16 * q^17 - 16 * q^18 - 16 * q^19 - 16 * q^20 - 16 * q^21 - 16 * q^22 - 16 * q^23 - 16 * q^24 - 16 * q^25 - 16 * q^26 - 16 * q^27 - 16 * q^28 - 16 * q^29 - 16 * q^30 - 16 * q^31 - 16 * q^32 - 16 * q^33 - 16 * q^34 - 16 * q^35 - 16 * q^36 - 16 * q^37 - 16 * q^38 - 16 * q^39 - 16 * q^40 - 16 * q^41 - 16 * q^42 - 16 * q^43 - 16 * q^44 - 16 * q^45 - 16 * q^46 - 16 * q^47 - 16 * q^48 - 16 * q^49 - 640 * q^50 - 16 * q^51 - 1072 * q^52 - 16 * q^53 - 1168 * q^54 - 16 * q^55 - 800 * q^56 - 16 * q^57 - 736 * q^58 - 16 * q^59 - 592 * q^60 - 16 * q^61 - 112 * q^62 - 32 * q^63 + 176 * q^64 + 560 * q^66 - 16 * q^67 + 464 * q^68 - 16 * q^69 + 1328 * q^70 - 16 * q^71 + 1280 * q^72 - 16 * q^73 + 1216 * q^74 - 16 * q^75 + 1648 * q^76 - 16 * q^77 + 1424 * q^78 - 16 * q^79 + 800 * q^80 - 16 * q^81 - 16 * q^82 - 16 * q^83 - 16 * q^84 - 16 * q^85 - 16 * q^86 - 16 * q^87 - 16 * q^88 - 16 * q^89 - 16 * q^90 - 16 * q^91 - 16 * q^92 - 16 * q^93 - 16 * q^94 - 16 * q^95 - 16 * q^96 - 16 * q^97 - 16 * q^98 - 16 * q^99

Introduction

L-functions

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