LMFDB - Embedded newform 43.4.g.a.9.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [43,4,Mod(9,43)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(43, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([2]))

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

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

chi := DirichletCharacter("43.9");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 43 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	43.g (of order $21$, 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:	$2.53708213025$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$10$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			9.2
Character	$\chi$	$=$	43.9
Dual form			43.4.g.a.24.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.34805 - 2.94437i) q^{2} +(6.79273 + 1.02384i) q^{3} +(-1.37577 + 6.02765i) q^{4} +(14.9228 + 10.1742i) q^{5} +(-12.9351 - 22.4043i) q^{6} +(3.09950 - 5.36848i) q^{7} +(-6.16631 + 2.96954i) q^{8} +(19.2924 + 5.95092i) q^{9} +O(q^{10})$	\(q+(-2.34805 - 2.94437i) q^{2} +(6.79273 + 1.02384i) q^{3} +(-1.37577 + 6.02765i) q^{4} +(14.9228 + 10.1742i) q^{5} +(-12.9351 - 22.4043i) q^{6} +(3.09950 - 5.36848i) q^{7} +(-6.16631 + 2.96954i) q^{8} +(19.2924 + 5.95092i) q^{9} +(-5.08298 - 67.8276i) q^{10} +(-14.8001 - 64.8435i) q^{11} +(-15.5166 + 39.5356i) q^{12} +(-3.02268 + 40.3349i) q^{13} +(-23.0846 + 3.47944i) q^{14} +(90.9496 + 84.3889i) q^{15} +(67.7853 + 32.6437i) q^{16} +(-44.0213 + 30.0132i) q^{17} +(-27.7779 - 70.7770i) q^{18} +(-88.2846 + 27.2322i) q^{19} +(-81.8566 + 75.9519i) q^{20} +(26.5505 - 33.2933i) q^{21} +(-156.172 + 195.833i) q^{22} +(101.595 - 94.2662i) q^{23} +(-44.9264 + 13.8579i) q^{24} +(73.5077 + 187.294i) q^{25} +(125.858 - 85.8086i) q^{26} +(-42.1521 - 20.2994i) q^{27} +(28.0951 + 26.0685i) q^{28} +(-17.3939 + 2.62171i) q^{29} +(34.9173 - 465.939i) q^{30} +(-46.6987 + 118.986i) q^{31} +(-50.8650 - 222.854i) q^{32} +(-34.1438 - 455.617i) q^{33} +(191.734 + 59.1422i) q^{34} +(100.873 - 48.5779i) q^{35} +(-62.4120 + 108.101i) q^{36} +(-16.4542 - 28.4995i) q^{37} +(287.479 + 196.000i) q^{38} +(-61.8287 + 270.889i) q^{39} +(-122.231 - 18.4234i) q^{40} +(-66.5083 - 83.3988i) q^{41} -160.370 q^{42} +(-215.053 + 182.371i) q^{43} +411.215 q^{44} +(227.351 + 285.089i) q^{45} +(-516.104 - 77.7902i) q^{46} +(-60.0662 + 263.167i) q^{47} +(427.025 + 291.141i) q^{48} +(152.286 + 263.768i) q^{49} +(378.864 - 656.211i) q^{50} +(-329.753 + 158.801i) q^{51} +(-238.966 - 73.7112i) q^{52} +(-34.2377 - 456.870i) q^{53} +(39.2066 + 171.775i) q^{54} +(438.871 - 1118.22i) q^{55} +(-3.17053 + 42.3078i) q^{56} +(-627.575 + 94.5916i) q^{57} +(48.5611 + 45.0581i) q^{58} +(-2.77045 - 1.33418i) q^{59} +(-633.792 + 432.112i) q^{60} +(211.224 + 538.191i) q^{61} +(459.990 - 141.888i) q^{62} +(91.7442 - 85.1262i) q^{63} +(-161.459 + 202.464i) q^{64} +(-455.481 + 571.155i) q^{65} +(-1261.33 + 1170.35i) q^{66} +(667.449 - 205.881i) q^{67} +(-120.346 - 306.636i) q^{68} +(786.619 - 536.308i) q^{69} +(-379.886 - 182.944i) q^{70} +(-517.355 - 480.035i) q^{71} +(-136.634 + 20.5943i) q^{72} +(40.2931 - 537.674i) q^{73} +(-45.2777 + 115.366i) q^{74} +(307.558 + 1347.50i) q^{75} +(-42.6866 - 569.614i) q^{76} +(-393.984 - 121.528i) q^{77} +(942.774 - 454.016i) q^{78} +(352.610 - 610.739i) q^{79} +(679.422 + 1176.79i) q^{80} +(-715.938 - 488.118i) q^{81} +(-89.3916 + 391.650i) q^{82} +(1355.60 + 204.323i) q^{83} +(164.153 + 205.841i) q^{84} -962.279 q^{85} +(1041.92 + 204.979i) q^{86} -120.836 q^{87} +(283.817 + 355.896i) q^{88} +(-489.470 - 73.7758i) q^{89} +(305.574 - 1338.81i) q^{90} +(207.168 + 141.245i) q^{91} +(428.432 + 742.066i) q^{92} +(-439.034 + 760.429i) q^{93} +(915.900 - 441.074i) q^{94} +(-1594.52 - 491.843i) q^{95} +(-117.345 - 1565.86i) q^{96} +(-84.1275 - 368.587i) q^{97} +(419.052 - 1067.73i) q^{98} +(100.349 - 1339.06i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q - 12 q^{2} - 9 q^{3} - 92 q^{4} + 5 q^{5} - 22 q^{6} - 54 q^{7} + 2 q^{8} + 201 q^{9}+O(q^{10}) $ 120 * q - 12 * q^2 - 9 * q^3 - 92 * q^4 + 5 * q^5 - 22 * q^6 - 54 * q^7 + 2 * q^8 + 201 * q^9	\( 120 q - 12 q^{2} - 9 q^{3} - 92 q^{4} + 5 q^{5} - 22 q^{6} - 54 q^{7} + 2 q^{8} + 201 q^{9} - 41 q^{10} - 68 q^{11} + 114 q^{12} - 167 q^{13} + 254 q^{14} - 163 q^{15} - 344 q^{16} + 68 q^{17} - 72 q^{18} - 407 q^{19} + 621 q^{20} + 193 q^{21} - 520 q^{22} - 219 q^{23} + 1072 q^{24} - 87 q^{25} - 133 q^{26} + 180 q^{27} + 1228 q^{28} - 17 q^{29} - 1796 q^{30} - 953 q^{31} - 2730 q^{32} + 473 q^{33} - 1043 q^{34} - 241 q^{35} - 175 q^{36} - 228 q^{37} + 1512 q^{38} + 1250 q^{39} + 2673 q^{40} - 236 q^{41} + 5286 q^{42} + 1789 q^{43} - 2756 q^{44} + 856 q^{45} + 4331 q^{46} + 962 q^{47} + 5243 q^{48} - 1264 q^{49} - 3273 q^{50} - 4803 q^{51} - 3538 q^{52} - 1375 q^{53} - 2646 q^{54} - 1460 q^{55} - 3305 q^{56} - 719 q^{57} + 142 q^{58} + 1202 q^{59} + 4043 q^{60} + 837 q^{61} - 3959 q^{62} + 3279 q^{63} + 5718 q^{64} + 54 q^{65} - 3457 q^{66} + 1384 q^{67} - 747 q^{68} - 4715 q^{69} - 2553 q^{70} - 1619 q^{71} - 20137 q^{72} - 3630 q^{73} - 5006 q^{74} - 1186 q^{75} + 1092 q^{76} + 3515 q^{77} + 2980 q^{78} + 4422 q^{79} - 1610 q^{80} - 4089 q^{81} + 5292 q^{82} + 10398 q^{83} + 17399 q^{84} + 8666 q^{85} + 1858 q^{86} + 2754 q^{87} + 7290 q^{88} + 11478 q^{89} + 29113 q^{90} + 11920 q^{91} + 3286 q^{92} - 4 q^{93} - 14736 q^{94} - 1741 q^{95} - 6200 q^{96} + 2236 q^{97} - 5254 q^{98} - 7417 q^{99}+O(q^{100}) \) 120 * q - 12 * q^2 - 9 * q^3 - 92 * q^4 + 5 * q^5 - 22 * q^6 - 54 * q^7 + 2 * q^8 + 201 * q^9 - 41 * q^10 - 68 * q^11 + 114 * q^12 - 167 * q^13 + 254 * q^14 - 163 * q^15 - 344 * q^16 + 68 * q^17 - 72 * q^18 - 407 * q^19 + 621 * q^20 + 193 * q^21 - 520 * q^22 - 219 * q^23 + 1072 * q^24 - 87 * q^25 - 133 * q^26 + 180 * q^27 + 1228 * q^28 - 17 * q^29 - 1796 * q^30 - 953 * q^31 - 2730 * q^32 + 473 * q^33 - 1043 * q^34 - 241 * q^35 - 175 * q^36 - 228 * q^37 + 1512 * q^38 + 1250 * q^39 + 2673 * q^40 - 236 * q^41 + 5286 * q^42 + 1789 * q^43 - 2756 * q^44 + 856 * q^45 + 4331 * q^46 + 962 * q^47 + 5243 * q^48 - 1264 * q^49 - 3273 * q^50 - 4803 * q^51 - 3538 * q^52 - 1375 * q^53 - 2646 * q^54 - 1460 * q^55 - 3305 * q^56 - 719 * q^57 + 142 * q^58 + 1202 * q^59 + 4043 * q^60 + 837 * q^61 - 3959 * q^62 + 3279 * q^63 + 5718 * q^64 + 54 * q^65 - 3457 * q^66 + 1384 * q^67 - 747 * q^68 - 4715 * q^69 - 2553 * q^70 - 1619 * q^71 - 20137 * q^72 - 3630 * q^73 - 5006 * q^74 - 1186 * q^75 + 1092 * q^76 + 3515 * q^77 + 2980 * q^78 + 4422 * q^79 - 1610 * q^80 - 4089 * q^81 + 5292 * q^82 + 10398 * q^83 + 17399 * q^84 + 8666 * q^85 + 1858 * q^86 + 2754 * q^87 + 7290 * q^88 + 11478 * q^89 + 29113 * q^90 + 11920 * q^91 + 3286 * q^92 - 4 * q^93 - 14736 * q^94 - 1741 * q^95 - 6200 * q^96 + 2236 * q^97 - 5254 * q^98 - 7417 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/43\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{1}{21}\right)$

Coefficient data

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

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

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

$2$	−2.34805	−	2.94437i	−0.830163	−	1.04099i	−0.998472	−	0.0552568i	$-0.982402\pi$
$2$	−2.34805	−	2.94437i	−0.830163	−	1.04099i	0.168310	−	0.985734i	$-0.446169\pi$
$3$	6.79273	+	1.02384i	1.30726	+	0.197038i	0.765468	−	0.643474i	$-0.222508\pi$
$3$	6.79273	+	1.02384i	1.30726	+	0.197038i	0.541793	+	0.840512i	$0.317746\pi$
$4$	−1.37577	+	6.02765i	−0.171971	+	0.753456i
$5$	14.9228	+	10.1742i	1.33473	+	0.910006i	0.999484	−	0.0321238i	$-0.0102271\pi$
$5$	14.9228	+	10.1742i	1.33473	+	0.910006i	0.335249	+	0.942129i	$0.391179\pi$
$6$	−12.9351	−	22.4043i	−0.880124	−	1.52442i
$7$	3.09950	−	5.36848i	0.167357	−	0.289871i	−0.770133	−	0.637884i	$-0.779810\pi$
$7$	3.09950	−	5.36848i	0.167357	−	0.289871i	0.937490	+	0.348013i	$0.113143\pi$
$8$	−6.16631	+	2.96954i	−0.272515	+	0.131236i
$9$	19.2924	+	5.95092i	0.714534	+	0.220404i
$10$	−5.08298	−	67.8276i	−0.160738	−	2.14490i
$11$	−14.8001	−	64.8435i	−0.405673	−	1.77737i	−0.603741	−	0.797181i	$-0.706324\pi$
$11$	−14.8001	−	64.8435i	−0.405673	−	1.77737i	0.198068	−	0.980188i	$-0.436533\pi$
$12$	−15.5166	+	39.5356i	−0.373271	+	0.951078i
$13$	−3.02268	+	40.3349i	−0.0644878	+	0.860529i	0.867360	+	0.497681i	$0.165815\pi$
$13$	−3.02268	+	40.3349i	−0.0644878	+	0.860529i	−0.931848	+	0.362849i	$0.881804\pi$
$14$	−23.0846	+	3.47944i	−0.440687	+	0.0664228i
$15$	90.9496	+	84.3889i	1.56554	+	1.45261i
$16$	67.7853	+	32.6437i	1.05915	+	0.510057i
$17$	−44.0213	+	30.0132i	−0.628043	+	0.428192i	−0.835071	−	0.550143i	$-0.814573\pi$
$17$	−44.0213	+	30.0132i	−0.628043	+	0.428192i	0.207028	+	0.978335i	$0.433621\pi$
$18$	−27.7779	−	70.7770i	−0.363740	−	0.926795i
$19$	−88.2846	+	27.2322i	−1.06599	+	0.328816i	−0.777641	−	0.628709i	$-0.783584\pi$
$19$	−88.2846	+	27.2322i	−1.06599	+	0.328816i	−0.288353	+	0.957524i	$0.593108\pi$
$20$	−81.8566	+	75.9519i	−0.915185	+	0.849168i
$21$	26.5505	−	33.2933i	0.275895	−	0.345961i
$22$	−156.172	+	195.833i	−1.51345	+	1.89781i
$23$	101.595	−	94.2662i	0.921042	−	0.854602i	−0.0686750	−	0.997639i	$-0.521877\pi$
$23$	101.595	−	94.2662i	0.921042	−	0.854602i	0.989717	+	0.143037i	$0.0456867\pi$
$24$	−44.9264	+	13.8579i	−0.382106	+	0.117864i
$25$	73.5077	+	187.294i	0.588061	+	1.49836i
$26$	125.858	−	85.8086i	0.949339	−	0.647248i
$27$	−42.1521	−	20.2994i	−0.300451	−	0.144690i
$28$	28.0951	+	26.0685i	0.189624	+	0.175946i
$29$	−17.3939	+	2.62171i	−0.111378	+	0.0167876i	−0.204495	−	0.978868i	$-0.565555\pi$
$29$	−17.3939	+	2.62171i	−0.111378	+	0.0167876i	0.0931166	+	0.995655i	$0.470317\pi$
$30$	34.9173	−	465.939i	0.212500	−	2.83561i
$31$	−46.6987	+	118.986i	−0.270559	+	0.689373i	0.729427	+	0.684059i	$0.239787\pi$
$31$	−46.6987	+	118.986i	−0.270559	+	0.689373i	−0.999986	+	0.00531432i	$0.998308\pi$
$32$	−50.8650	−	222.854i	−0.280992	−	1.23111i
$33$	−34.1438	−	455.617i	−0.180111	−	2.40342i
$34$	191.734	+	59.1422i	0.967122	+	0.298318i
$35$	100.873	−	48.5779i	0.487161	−	0.234604i
$36$	−62.4120	+	108.101i	−0.288944	+	0.500466i
$37$	−16.4542	−	28.4995i	−0.0731096	−	0.126630i	0.827153	−	0.561977i	$-0.189959\pi$
$37$	−16.4542	−	28.4995i	−0.0731096	−	0.126630i	−0.900263	+	0.435347i	$0.856626\pi$
$38$	287.479	+	196.000i	1.22724	+	0.836720i
$39$	−61.8287	+	270.889i	−0.253859	+	1.11223i
$40$	−122.231	−	18.4234i	−0.483160	−	0.0728247i
$41$	−66.5083	−	83.3988i	−0.253338	−	0.317676i	0.638858	−	0.769325i	$-0.279407\pi$
$41$	−66.5083	−	83.3988i	−0.253338	−	0.317676i	−0.892196	+	0.451649i	$0.850836\pi$
$42$	−160.370			−0.589180
$43$	−215.053	+	182.371i	−0.762682	+	0.646774i
$43$	−215.053	+	182.371i	−0.762682	+	0.646774i
$44$	411.215			1.40893
$45$	227.351	+	285.089i	0.753143	+	0.944411i
$46$	−516.104	−	77.7902i	−1.65425	−	0.249338i
$47$	−60.0662	+	263.167i	−0.186416	+	0.816743i	0.792070	+	0.610430i	$0.209003\pi$
$47$	−60.0662	+	263.167i	−0.186416	+	0.816743i	−0.978486	+	0.206312i	$0.933854\pi$
$48$	427.025	+	291.141i	1.28408	+	0.875470i
$49$	152.286	+	263.768i	0.443983	+	0.769002i
$50$	378.864	−	656.211i	1.07159	−	1.85605i
$51$	−329.753	+	158.801i	−0.905386	+	0.436011i
$52$	−238.966	−	73.7112i	−0.637281	−	0.196575i
$53$	−34.2377	−	456.870i	−0.0887341	−	1.18407i	−0.846806	−	0.531902i	$-0.821477\pi$
$53$	−34.2377	−	456.870i	−0.0887341	−	1.18407i	0.758072	−	0.652171i	$-0.226142\pi$
$54$	39.2066	+	171.775i	0.0988026	+	0.432883i
$55$	438.871	−	1118.22i	1.07595	−	2.74148i
$56$	−3.17053	+	42.3078i	−0.00756571	+	0.100957i
$57$	−627.575	+	94.5916i	−1.45832	+	0.219806i
$58$	48.5611	+	45.0581i	0.109938	+	0.102007i
$59$	−2.77045	−	1.33418i	−0.00611325	−	0.00294399i	0.430825	−	0.902436i	$-0.358223\pi$
$59$	−2.77045	−	1.33418i	−0.00611325	−	0.00294399i	−0.436938	+	0.899492i	$0.643937\pi$
$60$	−633.792	+	432.112i	−1.36370	+	0.929757i
$61$	211.224	+	538.191i	0.443353	+	1.12964i	0.961610	+	0.274419i	$0.0884856\pi$
$61$	211.224	+	538.191i	0.443353	+	1.12964i	−0.518257	+	0.855225i	$0.673419\pi$
$62$	459.990	−	141.888i	0.942239	−	0.290642i
$63$	91.7442	−	85.1262i	0.183471	−	0.170236i
$64$	−161.459	+	202.464i	−0.315350	+	0.395437i
$65$	−455.481	+	571.155i	−0.869161	+	1.08989i
$66$	−1261.33	+	1170.35i	−2.35241	+	2.18272i
$67$	667.449	−	205.881i	1.21704	−	0.375408i	0.381260	−	0.924468i	$-0.375490\pi$
$67$	667.449	−	205.881i	1.21704	−	0.375408i	0.835783	+	0.549060i	$0.185014\pi$
$68$	−120.346	−	306.636i	−0.214619	−	0.546839i
$69$	786.619	−	536.308i	1.37243	−	0.935708i
$70$	−379.886	−	182.944i	−0.648644	−	0.312371i
$71$	−517.355	−	480.035i	−0.864771	−	0.802390i	0.116867	−	0.993148i	$-0.462715\pi$
$71$	−517.355	−	480.035i	−0.864771	−	0.802390i	−0.981637	+	0.190758i	$0.938906\pi$
$72$	−136.634	+	20.5943i	−0.223646	+	0.0337092i
$73$	40.2931	−	537.674i	0.0646021	−	0.862055i	−0.866938	−	0.498416i	$-0.833915\pi$
$73$	40.2931	−	537.674i	0.0646021	−	0.862055i	0.931540	−	0.363639i	$-0.118466\pi$
$74$	−45.2777	+	115.366i	−0.0711274	+	0.181230i
$75$	307.558	+	1347.50i	0.473517	+	2.07461i
$76$	−42.6866	−	569.614i	−0.0644276	−	0.859726i
$77$	−393.984	−	121.528i	−0.583100	−	0.179862i
$78$	942.774	−	454.016i	1.36857	−	0.659066i
$79$	352.610	−	610.739i	0.502174	−	0.869791i	−0.497823	−	0.867279i	$-0.665867\pi$
$79$	352.610	−	610.739i	0.502174	−	0.869791i	0.999997	−	0.00251201i	$-0.000799600\pi$
$80$	679.422	+	1176.79i	0.949521	+	1.64462i
$81$	−715.938	−	488.118i	−0.982082	−	0.669572i
$82$	−89.3916	+	391.650i	−0.120386	+	0.527445i
$83$	1355.60	+	204.323i	1.79272	+	0.270210i	0.959293	−	0.282413i	$-0.0911348\pi$
$83$	1355.60	+	204.323i	1.79272	+	0.270210i	0.833432	+	0.552623i	$0.186373\pi$
$84$	164.153	+	205.841i	0.213220	+	0.267370i
$85$	−962.279			−1.22793
$86$	1041.92	+	204.979i	1.30644	+	0.257017i
$87$	−120.836			−0.148908
$88$	283.817	+	355.896i	0.343807	+	0.431120i
$89$	−489.470	−	73.7758i	−0.582963	−	0.0878676i	−0.149062	−	0.988828i	$-0.547625\pi$
$89$	−489.470	−	73.7758i	−0.582963	−	0.0878676i	−0.433902	+	0.900960i	$0.642863\pi$
$90$	305.574	−	1338.81i	0.357892	−	1.56803i
$91$	207.168	+	141.245i	0.238650	+	0.162709i
$92$	428.432	+	742.066i	0.485512	+	0.840932i
$93$	−439.034	+	760.429i	−0.489524	+	0.847880i
$94$	915.900	−	441.074i	1.00498	−	0.483972i
$95$	−1594.52	−	491.843i	−1.72204	−	0.531179i
$96$	−117.345	−	1565.86i	−0.124755	−	1.66474i
$97$	−84.1275	−	368.587i	−0.0880603	−	0.385818i	0.911622	−	0.411030i	$-0.134831\pi$
$97$	−84.1275	−	368.587i	−0.0880603	−	0.385818i	−0.999682	+	0.0252125i	$0.991974\pi$
$98$	419.052	−	1067.73i	0.431945	−	1.10058i
$99$	100.349	−	1339.06i	0.101873	−	1.35940i
$100$	−1230.07	+	185.404i	−1.23007	+	0.185404i
$101$	−116.963	−	108.526i	−0.115230	−	0.106918i	0.620453	−	0.784243i	$-0.286949\pi$
$101$	−116.963	−	108.526i	−0.115230	−	0.106918i	−0.735684	+	0.677325i	$0.763139\pi$
$102$	1241.85	+	598.041i	1.20550	+	0.580538i
$103$	254.276	−	173.362i	0.243248	−	0.165844i	−0.435559	−	0.900160i	$-0.643449\pi$
$103$	254.276	−	173.362i	0.243248	−	0.165844i	0.678808	+	0.734316i	$0.262497\pi$
$104$	−101.137	−	257.693i	−0.0953588	−	0.242970i
$105$	734.938	−	226.698i	0.683073	−	0.210700i
$106$	−1264.80	+	1173.56i	−1.15895	+	1.07535i
$107$	605.160	−	758.846i	0.546757	−	0.685612i	−0.429291	−	0.903166i	$-0.641237\pi$
$107$	605.160	−	758.846i	0.546757	−	0.685612i	0.976048	+	0.217554i	$0.0698080\pi$
$108$	180.349	−	226.151i	0.160686	−	0.201494i
$109$	−899.530	+	834.642i	−0.790453	+	0.733433i	−0.968074	−	0.250666i	$-0.919350\pi$
$109$	−899.530	+	834.642i	−0.790453	+	0.733433i	0.177621	+	0.984099i	$0.443160\pi$
$110$	−4322.95	+	1333.45i	−3.74707	+	1.15582i
$111$	−82.5900	−	210.436i	−0.0706225	−	0.179943i
$112$	385.347	−	262.725i	0.325106	−	0.221654i
$113$	1861.16	+	896.289i	1.54941	+	0.746157i	0.996217	−	0.0868952i	$-0.0276945\pi$
$113$	1861.16	+	896.289i	1.54941	+	0.746157i	0.553194	+	0.833052i	$0.313409\pi$
$114$	1752.09	+	1625.70i	1.43946	+	1.33562i
$115$	2475.16	−	373.070i	2.00704	−	0.302512i
$116$	8.12729	−	108.451i	0.00650517	−	0.0868055i
$117$	−298.344	+	760.169i	−0.235743	+	0.600664i
$118$	2.57686	+	11.2899i	0.00201033	+	0.00880782i
$119$	24.6816	+	329.353i	0.0190131	+	0.253712i
$120$	−811.419	−	250.290i	−0.617267	−	0.190402i
$121$	−2786.45	+	1341.88i	−2.09350	+	1.00818i
$122$	1088.67	−	1885.62i	0.807895	−	1.39931i
$123$	−366.386	−	634.599i	−0.268585	−	0.465202i
$124$	−652.961	−	445.181i	−0.472884	−	0.322407i
$125$	−306.257	+	1341.80i	−0.219140	+	0.960114i
$126$	−466.063	−	70.2477i	−0.329525	−	0.0496680i
$127$	−154.184	−	193.340i	−0.107729	−	0.135088i	0.725044	−	0.688703i	$-0.241819\pi$
$127$	−154.184	−	193.340i	−0.107729	−	0.135088i	−0.832773	+	0.553615i	$0.813248\pi$
$128$	−853.439			−0.589328
$129$	−1647.52	+	1018.61i	−1.12446	+	0.695225i
$130$	2751.18			1.85611
$131$	1423.14	+	1784.57i	0.949166	+	1.19022i	0.981640	+	0.190744i	$0.0610900\pi$
$131$	1423.14	+	1784.57i	0.949166	+	1.19022i	−0.0324740	+	0.999473i	$0.510339\pi$
$132$	2793.27	+	421.018i	1.84184	+	0.277613i
$133$	−127.442	+	558.361i	−0.0830875	+	0.364030i
$134$	−2173.40	−	1481.80i	−1.40114	−	0.955281i
$135$	−422.497	−	731.786i	−0.269354	−	0.466534i
$136$	182.323	−	315.793i	0.114957	−	0.199111i
$137$	519.403	−	250.131i	0.323909	−	0.155987i	−0.264862	−	0.964286i	$-0.585326\pi$
$137$	519.403	−	250.131i	0.323909	−	0.155987i	0.588771	+	0.808300i	$0.299612\pi$
$138$	−3426.11	−	1056.82i	−2.11341	−	0.651899i
$139$	−137.397	−	1833.44i	−0.0838407	−	1.11878i	−0.867451	−	0.497523i	$-0.834243\pi$
$139$	−137.397	−	1833.44i	−0.0838407	−	1.11878i	0.783610	−	0.621253i	$-0.213376\pi$
$140$	154.032	+	674.859i	0.0929863	+	0.407400i
$141$	−677.454	+	1726.13i	−0.404624	+	1.03096i
$142$	−198.622	+	2650.43i	−0.117380	+	1.56633i
$143$	2660.19	−	400.959i	1.55564	−	0.234475i
$144$	1113.48	+	1033.16i	0.644376	+	0.597894i
$145$	−286.239	−	137.845i	−0.163937	−	0.0789478i
$146$	−1677.72	+	1143.85i	−0.951022	+	0.648396i
$147$	764.383	+	1947.62i	0.428879	+	1.09277i
$148$	194.422	−	59.9713i	0.107983	−	0.0333082i
$149$	−98.0682	+	90.9940i	−0.0539199	+	0.0500303i	−0.706673	−	0.707541i	$-0.749805\pi$
$149$	−98.0682	+	90.9940i	−0.0539199	+	0.0500303i	0.652753	+	0.757571i	$0.273614\pi$
$150$	3245.37	−	4069.57i	1.76656	−	2.21519i
$151$	531.951	−	667.046i	0.286686	−	0.359493i	−0.617546	−	0.786535i	$-0.711873\pi$
$151$	531.951	−	667.046i	0.286686	−	0.359493i	0.904232	+	0.427042i	$0.140444\pi$
$152$	463.523	−	430.086i	0.247347	−	0.229504i
$153$	−1027.88	+	317.060i	−0.543133	+	0.167534i
$154$	567.274	+	1445.39i	0.296832	+	0.756317i
$155$	−1907.46	+	1300.48i	−0.988458	+	0.673919i
$156$	−1547.76	−	745.363i	−0.794359	−	0.382543i
$157$	471.311	+	437.313i	0.239584	+	0.222302i	0.790821	−	0.612047i	$-0.209654\pi$
$157$	471.311	+	437.313i	0.239584	+	0.222302i	−0.551237	+	0.834348i	$0.685844\pi$
$158$	−2626.19	+	395.834i	−1.32233	+	0.199309i
$159$	235.194	−	3138.45i	0.117309	−	1.56538i
$160$	1508.31	−	3843.11i	0.745264	−	1.89890i
$161$	−191.174	−	837.588i	−0.0935815	−	0.410007i
$162$	243.862	+	3254.11i	0.118269	+	1.57819i
$163$	−670.288	−	206.757i	−0.322092	−	0.0993523i	0.129493	−	0.991580i	$-0.458665\pi$
$163$	−670.288	−	206.757i	−0.322092	−	0.0993523i	−0.451585	+	0.892228i	$0.649141\pi$
$164$	594.199	−	286.151i	0.282922	−	0.136248i
$165$	4126.01	−	7146.46i	1.94672	−	3.37182i
$166$	−2581.41	−	4471.14i	−1.20697	−	2.09053i
$167$	96.9660	+	66.1103i	0.0449308	+	0.0306333i	0.585577	−	0.810617i	$-0.300868\pi$
$167$	96.9660	+	66.1103i	0.0449308	+	0.0306333i	−0.540646	+	0.841250i	$0.681820\pi$
$168$	−64.8529	+	284.139i	−0.0297828	+	0.130487i
$169$	554.696	+	83.6069i	0.252479	+	0.0380550i
$170$	2259.48	+	2833.30i	1.01938	+	1.27826i
$171$	−1865.28			−0.834161
$172$	−803.402	−	1547.17i	−0.356156	−	0.685874i
$173$	−69.6613			−0.0306142			−0.0153071	−	0.999883i	$-0.504873\pi$
$173$	−69.6613			−0.0306142			−0.0153071	+	0.999883i	$0.504873\pi$
$174$	283.730	+	355.786i	0.123618	+	0.155012i
$175$	1233.32	+	185.894i	0.532746	+	0.0802985i
$176$	1113.50	−	4878.57i	0.476894	−	2.08941i
$177$	−17.4529	−	11.8992i	−0.00741153	−	0.00505310i
$178$	932.080	+	1614.41i	0.392485	+	0.679804i
$179$	−1711.90	+	2965.11i	−0.714825	+	1.23811i	0.248202	+	0.968708i	$0.420160\pi$
$179$	−1711.90	+	2965.11i	−0.714825	+	1.23811i	−0.963027	+	0.269405i	$0.913173\pi$
$180$	−2031.20	+	978.172i	−0.841091	+	0.405048i
$181$	3038.83	+	937.354i	1.24792	+	0.384934i	0.847204	−	0.531267i	$-0.178284\pi$
$181$	3038.83	+	937.354i	1.24792	+	0.384934i	0.400720	+	0.916201i	$0.368760\pi$
$182$	−70.5655	−	941.631i	−0.0287399	−	0.383507i
$183$	883.769	+	3872.04i	0.356995	+	1.56410i
$184$	−346.538	+	882.964i	−0.138843	+	0.353766i
$185$	44.4167	−	592.700i	0.0176518	−	0.235547i
$186$	3269.86	−	492.852i	1.28902	−	0.194288i
$187$	2597.68	+	2410.30i	1.01584	+	0.942558i
$188$	−1503.64	−	724.116i	−0.583321	−	0.280913i
$189$	−239.627	+	163.375i	−0.0922239	+	0.0628772i
$190$	2295.84	+	5849.72i	0.876621	+	2.23359i
$191$	−2030.21	+	626.238i	−0.769115	+	0.237241i	−0.654391	−	0.756157i	$-0.727075\pi$
$191$	−2030.21	+	626.238i	−0.769115	+	0.237241i	−0.114725	+	0.993397i	$0.536599\pi$
$192$	−1304.04	+	1209.97i	−0.490161	+	0.454803i
$193$	212.294	−	266.209i	0.0791776	−	0.0992856i	−0.740665	−	0.671874i	$-0.765489\pi$
$193$	212.294	−	266.209i	0.0791776	−	0.0992856i	0.819843	+	0.572589i	$0.194061\pi$
$194$	−887.718	+	1113.16i	−0.328528	+	0.411961i
$195$	−3678.73	+	3413.36i	−1.35097	+	1.25352i
$196$	−1799.41	+	555.044i	−0.655761	+	0.202276i
$197$	−1580.47	−	4026.98i	−0.571595	−	1.45640i	−0.865669	−	0.500617i	$-0.833107\pi$
$197$	−1580.47	−	4026.98i	−0.571595	−	1.45640i	0.294074	−	0.955783i	$-0.404989\pi$
$198$	−4178.32	+	2848.73i	−1.49970	+	1.02248i
$199$	110.890	+	53.4019i	0.0395015	+	0.0190229i	0.453530	−	0.891241i	$-0.350164\pi$
$199$	110.890	+	53.4019i	0.0395015	+	0.0190229i	−0.414029	+	0.910264i	$0.635879\pi$
$200$	−1009.45	−	936.631i	−0.356894	−	0.331149i
$201$	4744.59	−	715.131i	1.66496	−	0.250953i
$202$	−44.9044	+	599.207i	−0.0156409	+	0.208713i
$203$	−39.8377	+	101.505i	−0.0137737	+	0.0350948i
$204$	−503.530	−	2206.11i	−0.172814	−	0.757149i
$205$	−143.975	−	1921.21i	−0.0490519	−	0.654552i
$206$	−1107.50	−	341.617i	−0.374577	−	0.115542i
$207$	2520.98	−	1214.04i	0.846474	−	0.407640i
$208$	−1521.57	+	2635.44i	−0.507221	+	0.878533i
$209$	3072.45	+	5321.65i	1.01687	+	1.76127i
$210$	−2393.16	−	1631.63i	−0.786398	−	0.536157i
$211$	53.0095	−	232.250i	0.0172954	−	0.0757760i	−0.965544	−	0.260241i	$-0.916198\pi$
$211$	53.0095	−	232.250i	0.0172954	−	0.0757760i	0.982839	+	0.184465i	$0.0590552\pi$
$212$	2800.95	+	422.176i	0.907407	+	0.136770i
$213$	−3022.77	−	3790.43i	−0.972379	−	1.21933i
$214$	−3655.27			−1.16761
$215$	−5064.66	+	533.488i	−1.60654	+	0.169226i
$216$	320.203			0.100866
$217$	494.034	+	619.499i	0.154549	+	0.193799i
$218$	4569.64	+	688.762i	1.41970	+	0.213986i
$219$	824.192	−	3611.02i	0.254309	−	1.11420i
$220$	6136.47	+	4183.78i	1.88055	+	1.28214i
$221$	−1077.52	−	1866.31i	−0.327971	−	0.568062i
$222$	−425.675	+	737.290i	−0.128691	+	0.222899i
$223$	−302.900	+	145.869i	−0.0909583	+	0.0438032i	−0.478810	−	0.877919i	$-0.658932\pi$
$223$	−302.900	+	145.869i	−0.0909583	+	0.0438032i	0.387851	+	0.921722i	$0.373217\pi$
$224$	−1354.04	−	417.667i	−0.403888	−	0.124583i
$225$	303.566	+	4050.80i	0.0899453	+	1.20024i
$226$	−1731.11	−	7584.48i	−0.509521	−	2.23236i
$227$	819.575	−	2088.24i	0.239635	−	0.610580i	−0.759571	−	0.650424i	$-0.774591\pi$
$227$	819.575	−	2088.24i	0.239635	−	0.610580i	0.999206	+	0.0398448i	$0.0126863\pi$
$228$	293.234	−	3912.93i	0.0851749	−	1.13658i
$229$	−2223.44	+	335.130i	−0.641613	+	0.0967076i	−0.461787	−	0.886991i	$-0.652792\pi$
$229$	−2223.44	+	335.130i	−0.641613	+	0.0967076i	−0.179826	+	0.983698i	$0.557553\pi$
$230$	−6910.26	−	6411.78i	−1.98108	−	1.83818i
$231$	−2551.80	−	1228.88i	−0.726824	−	0.350020i
$232$	99.4709	−	67.8181i	0.0281491	−	0.0191917i
$233$	972.635	+	2478.23i	0.273474	+	0.696800i	0.999954	+	0.00961245i	$0.00305978\pi$
$233$	972.635	+	2478.23i	0.273474	+	0.696800i	−0.726480	+	0.687188i	$0.758845\pi$
$234$	2938.75	−	906.483i	0.820991	−	0.253242i
$235$	−3573.87	+	3316.06i	−0.992056	+	0.920494i
$236$	11.8535	−	14.8638i	0.00326947	−	0.00409978i
$237$	3020.48	−	3787.56i	0.827854	−	1.03810i
$238$	911.783	−	846.011i	0.248328	−	0.230415i
$239$	3698.74	−	1140.91i	1.00105	−	0.308784i	0.249441	−	0.968390i	$-0.419753\pi$
$239$	3698.74	−	1140.91i	1.00105	−	0.308784i	0.751611	+	0.659607i	$0.229277\pi$
$240$	3410.28	+	8689.25i	0.917219	+	2.33704i
$241$	905.232	−	617.177i	0.241955	−	0.164962i	−0.436272	−	0.899815i	$-0.643701\pi$
$241$	905.232	−	617.177i	0.241955	−	0.164962i	0.678226	+	0.734853i	$0.262749\pi$
$242$	10493.7	+	5053.52i	2.78745	+	1.34237i
$243$	−3437.42	−	3189.46i	−0.907451	−	0.841992i
$244$	−3534.62	+	532.758i	−0.927381	+	0.139780i
$245$	−411.084	+	5485.53i	−0.107197	+	1.43044i
$246$	−1008.20	+	2568.85i	−0.261302	+	0.665788i
$247$	−831.551	−	3643.26i	−0.214212	−	0.938524i
$248$	−65.3758	−	872.379i	−0.0167394	−	0.223372i
$249$	8999.01	+	2775.83i	2.29032	+	0.706469i
$250$	4669.86	−	2248.89i	1.18139	−	0.568928i
$251$	−3576.99	+	6195.53i	−0.899513	+	1.55800i	−0.0713954	+	0.997448i	$0.522745\pi$
$251$	−3576.99	+	6195.53i	−0.899513	+	1.55800i	−0.828118	+	0.560554i	$0.810588\pi$
$252$	386.891	+	670.116i	0.0967138	+	0.167513i
$253$	−7616.17	−	5192.61i	−1.89259	−	1.29034i
$254$	−207.233	+	907.946i	−0.0511927	+	0.224290i
$255$	−6536.50	−	985.218i	−1.60522	−	0.241948i
$256$	3295.59	+	4132.55i	0.804589	+	1.00892i
$257$	−6720.05			−1.63107			−0.815535	−	0.578708i	$-0.803557\pi$
$257$	−6720.05			−1.63107			−0.815535	+	0.578708i	$0.803557\pi$
$258$	6867.63	+	2459.13i	1.65721	+	0.593406i
$259$	−203.999			−0.0489416
$260$	−2816.08	−	3531.26i	−0.671715	−	0.842305i
$261$	−351.172	−	52.9306i	−0.0832835	−	0.0125530i
$262$	1912.80	−	8380.52i	0.451043	−	1.97615i
$263$	1879.89	+	1281.69i	0.440756	+	0.300502i	0.763291	−	0.646055i	$-0.223583\pi$
$263$	1879.89	+	1281.69i	0.440756	+	0.300502i	−0.322535	+	0.946558i	$0.604535\pi$
$264$	1563.51	+	2708.08i	0.364498	+	0.631330i
$265$	4137.35	−	7166.11i	0.959078	−	1.66117i
$266$	1943.26	−	935.825i	0.447928	−	0.215711i
$267$	−3249.30	−	1002.28i	−0.744772	−	0.229732i
$268$	322.719	+	4306.39i	0.0735568	+	0.981548i
$269$	−803.148	−	3518.82i	−0.182040	−	0.797570i	−0.980658	−	0.195731i	$-0.937292\pi$
$269$	−803.148	−	3518.82i	−0.182040	−	0.797570i	0.798617	−	0.601839i	$-0.205565\pi$
$270$	−1162.60	+	2962.26i	−0.262050	+	0.667694i
$271$	−123.444	+	1647.25i	−0.0276705	+	0.369238i	0.966130	+	0.258057i	$0.0830822\pi$
$271$	−123.444	+	1647.25i	−0.0276705	+	0.369238i	−0.993800	+	0.111181i	$0.964537\pi$
$272$	−3963.74	+	597.437i	−0.883591	+	0.133180i
$273$	1262.63	+	1171.55i	0.279918	+	0.259726i
$274$	−1956.06	−	941.991i	−0.431278	−	0.207693i
$275$	11056.9	−	7538.48i	2.42457	−	1.65304i
$276$	2150.47	+	5479.30i	0.468996	+	1.19498i
$277$	2367.64	−	730.319i	0.513565	−	0.158414i	−0.0271311	−	0.999632i	$-0.508637\pi$
$277$	2367.64	−	730.319i	0.513565	−	0.158414i	0.540696	+	0.841218i	$0.318161\pi$
$278$	−5075.69	+	4709.55i	−1.09503	+	1.01604i
$279$	−1609.01	+	2017.63i	−0.345264	+	0.432948i
$280$	−477.760	+	599.092i	−0.101970	+	0.127866i
$281$	−685.992	+	636.508i	−0.145633	+	0.135128i	−0.749625	−	0.661863i	$-0.769766\pi$
$281$	−685.992	+	636.508i	−0.145633	+	0.135128i	0.603992	+	0.796990i	$0.293576\pi$
$282$	6673.05	−	2058.36i	1.40913	−	0.434659i
$283$	1242.70	+	3166.34i	0.261027	+	0.665087i	0.999962	−	0.00868981i	$-0.00276609\pi$
$283$	1242.70	+	3166.34i	0.261027	+	0.665087i	−0.738935	+	0.673777i	$0.764671\pi$
$284$	3605.24	−	2458.01i	0.753281	−	0.513578i
$285$	−10327.5	−	4973.48i	−2.14649	−	1.03370i
$286$	−7426.85	−	6891.11i	−1.53552	−	1.42475i
$287$	−653.868	+	98.5547i	−0.134483	+	0.0202700i
$288$	344.879	−	4602.09i	0.0705631	−	0.941599i
$289$	−757.840	+	1930.95i	−0.154252	+	0.393028i
$290$	266.237	+	1166.46i	0.0539103	+	0.236196i
$291$	−194.082	−	2589.84i	−0.0390972	−	0.521715i
$292$	3185.48	+	982.590i	0.638411	+	0.196924i
$293$	5673.83	−	2732.37i	1.13129	−	0.544802i	0.227929	−	0.973678i	$-0.426805\pi$
$293$	5673.83	−	2732.37i	1.13129	−	0.544802i	0.903363	+	0.428876i	$0.141090\pi$
$294$	3939.69	−	6823.74i	0.781521	−	1.35363i
$295$	−27.7686	−	48.0967i	−0.00548051	−	0.00949253i
$296$	186.092	+	126.875i	0.0365418	+	0.0249138i
$297$	−692.428	+	3033.72i	−0.135282	+	0.592709i
$298$	498.189	+	75.0900i	0.0968434	+	0.0145968i
$299$	3495.13	+	4382.75i	0.676015	+	0.847695i
$300$	−8545.38			−1.64456
$301$	312.498	+	1719.77i	0.0598408	+	0.329321i
$302$	−3213.08			−0.612225
$303$	−683.385	−	856.938i	−0.129569	−	0.162475i
$304$	−6873.36	−	1035.99i	−1.29676	−	0.195455i
$305$	−2323.59	+	10180.3i	−0.436225	+	1.91123i
$306$	3347.06	+	2281.99i	0.625291	+	0.426316i
$307$	−4042.83	−	7002.38i	−0.751584	−	1.30178i	−0.947055	−	0.321072i	$-0.895957\pi$
$307$	−4042.83	−	7002.38i	−0.751584	−	1.30178i	0.195470	−	0.980710i	$-0.437377\pi$
$308$	1274.56	−	2207.60i	0.235795	−	0.408409i
$309$	1904.72	−	917.266i	0.350666	−	0.168872i
$310$	8307.93	+	2562.66i	1.52212	+	0.469513i
$311$	221.101	+	2950.39i	0.0403134	+	0.537945i	0.980401	+	0.197012i	$0.0631239\pi$
$311$	221.101	+	2950.39i	0.0403134	+	0.537945i	−0.940088	+	0.340933i	$0.889257\pi$
$312$	−423.160	−	1853.99i	−0.0767844	−	0.336415i
$313$	−2288.96	+	5832.19i	−0.413354	+	1.05321i	0.560925	+	0.827866i	$0.310446\pi$
$313$	−2288.96	+	5832.19i	−0.413354	+	1.05321i	−0.974279	+	0.225343i	$0.927650\pi$
$314$	180.945	−	2414.55i	0.0325202	−	0.433951i
$315$	2235.17	−	336.897i	0.399801	−	0.0602603i
$316$	3196.21	+	2965.65i	0.568989	+	0.527945i
$317$	−3162.49	−	1522.97i	−0.560325	−	0.269838i	0.132211	−	0.991222i	$-0.457792\pi$
$317$	−3162.49	−	1522.97i	−0.560325	−	0.269838i	−0.692536	+	0.721383i	$0.743507\pi$
$318$	−9792.99	+	6676.75i	−1.72693	+	1.17740i
$319$	427.433	+	1089.08i	0.0750208	+	0.191150i
$320$	−4469.32	+	1378.60i	−0.780758	+	0.240832i
$321$	4887.62	−	4535.05i	0.849846	−	0.788541i
$322$	−2017.28	+	2529.59i	−0.349126	+	0.437790i
$323$	3069.08	−	3848.50i	0.528693	−	0.662960i
$324$	3927.17	−	3643.88i	0.673383	−	0.624808i
$325$	−7776.69	+	2398.79i	−1.32730	+	0.409418i
$326$	965.106	+	2459.05i	0.163964	+	0.417774i
$327$	−6964.80	+	4748.52i	−1.17784	+	0.803039i
$328$	657.767	+	316.764i	0.110729	+	0.0533242i
$329$	1226.63	+	1138.15i	0.205552	+	0.190724i
$330$	−30729.9	+	4631.79i	−5.12614	+	0.772641i
$331$	261.212	−	3485.64i	0.0433762	−	0.578815i	−0.932596	−	0.360921i	$-0.882462\pi$
$331$	261.212	−	3485.64i	0.0433762	−	0.578815i	0.975972	−	0.217894i	$-0.0699187\pi$
$332$	−3096.58	+	7889.96i	−0.511888	+	1.30427i
$333$	−147.843	−	647.742i	−0.0243296	−	0.106595i
$334$	−33.0284	−	440.734i	−0.00541089	−	0.0722032i
$335$	12054.9	+	3718.43i	1.96605	+	0.606447i
$336$	2886.55	−	1390.09i	0.468673	−	0.225701i
$337$	−3452.05	+	5979.13i	−0.557997	+	0.966480i	0.439666	+	0.898161i	$0.355097\pi$
$337$	−3452.05	+	5979.13i	−0.557997	+	0.966480i	−0.997664	+	0.0683186i	$0.978237\pi$
$338$	−1056.29	−	1829.54i	−0.169983	−	0.294420i
$339$	11724.7	+	7993.78i	1.87846	+	1.28071i
$340$	1323.88	−	5800.28i	0.211168	−	0.925189i
$341$	8406.64	+	1267.10i	1.33503	+	0.201223i
$342$	4379.78	+	5492.07i	0.692489	+	0.868354i
$343$	4014.30			0.631929
$344$	784.528	−	1763.16i	0.122962	−	0.276347i
$345$	17195.0			2.68333
$346$	163.569	+	205.109i	0.0254147	+	0.0318691i
$347$	4551.94	+	686.094i	0.704209	+	0.106142i	0.491378	−	0.870946i	$-0.336493\pi$
$347$	4551.94	+	686.094i	0.704209	+	0.106142i	0.212831	+	0.977089i	$0.431731\pi$
$348$	166.243	−	728.358i	0.0256079	−	0.112196i
$349$	8715.68	+	5942.25i	1.33679	+	0.911408i	0.999550	−	0.0300110i	$-0.00955423\pi$
$349$	8715.68	+	5942.25i	1.33679	+	0.911408i	0.337240	+	0.941419i	$0.390507\pi$
$350$	−2348.57	−	4067.85i	−0.358676	−	0.621245i
$351$	946.185	−	1638.84i	0.143885	−	0.249216i
$352$	−13697.8	+	6596.53i	−2.07414	+	0.998853i
$353$	−4071.17	−	1255.79i	−0.613843	−	0.189346i	−0.0277843	−	0.999614i	$-0.508845\pi$
$353$	−4071.17	−	1255.79i	−0.613843	−	0.189346i	−0.586059	+	0.810268i	$0.699321\pi$
$354$	5.94479	+	79.3278i	0.000892549	+	0.0119102i
$355$	−2836.41	−	12427.1i	−0.424059	−	1.85792i
$356$	1118.09	−	2848.86i	0.166457	−	0.424126i
$357$	−169.549	+	2262.48i	−0.0251358	+	0.335414i
$358$	12750.0	−	1921.75i	1.88229	−	0.283709i
$359$	−5552.55	−	5152.01i	−0.816302	−	0.757418i	0.156840	−	0.987624i	$-0.449869\pi$
$359$	−5552.55	−	5152.01i	−0.816302	−	0.757418i	−0.973142	+	0.230207i	$0.926060\pi$
$360$	−2248.49	−	1082.82i	−0.329183	−	0.158526i
$361$	1385.41	−	944.556i	0.201984	−	0.137710i
$362$	−4375.42	−	11148.4i	−0.635268	−	1.61864i
$363$	−20301.5	+	6262.17i	−2.93540	+	0.905452i
$364$	−1136.39	+	1054.42i	−0.163635	+	0.151831i
$365$	6071.68	−	7613.64i	0.870702	−	1.09183i
$366$	9325.58	−	11693.9i	1.33185	−	1.67008i
$367$	3152.17	−	2924.79i	0.448343	−	0.416002i	−0.423417	−	0.905935i	$-0.639169\pi$
$367$	3152.17	−	2924.79i	0.448343	−	0.416002i	0.871760	+	0.489933i	$0.162979\pi$
$368$	9963.83	−	3073.43i	1.41141	−	0.435364i
$369$	−786.807	−	2004.75i	−0.111001	−	0.282827i
$370$	−1849.42	+	1260.91i	−0.259856	+	0.177167i
$371$	−2558.82	−	1232.26i	−0.358079	−	0.172442i
$372$	−3979.59	−	3692.52i	−0.554656	−	0.514646i
$373$	2772.47	−	417.883i	0.384861	−	0.0580085i	0.0462378	−	0.998930i	$-0.485277\pi$
$373$	2772.47	−	417.883i	0.384861	−	0.0580085i	0.338624	+	0.940922i	$0.390039\pi$
$374$	997.299	−	13308.0i	0.137885	−	1.83995i
$375$	−3454.11	+	8800.92i	−0.475652	+	1.21194i
$376$	−411.098	−	1801.14i	−0.0563851	−	0.247039i
$377$	−53.1701	−	709.506i	−0.00726366	−	0.0969268i
$378$	1043.69	+	321.937i	0.142015	+	0.0438059i
$379$	−12050.6	+	5803.27i	−1.63324	+	0.786528i	−0.633322	+	0.773888i	$0.718309\pi$
$379$	−12050.6	+	5803.27i	−1.63324	+	0.786528i	−0.999920	+	0.0126394i	$0.995977\pi$
$380$	5158.35	−	8934.52i	0.696362	−	1.20613i
$381$	−849.378	−	1471.17i	−0.114212	−	0.197822i
$382$	6610.92	+	4507.25i	0.885456	+	0.603694i
$383$	−224.212	+	982.336i	−0.0299130	+	0.131058i	−0.987680	−	0.156489i	$-0.949982\pi$
$383$	−224.212	+	982.336i	−0.0299130	+	0.131058i	0.957767	+	0.287546i	$0.0928396\pi$
$384$	−5797.17	−	873.783i	−0.770406	−	0.116120i
$385$	−4642.89	−	5822.00i	−0.614607	−	0.770693i
$386$	−1282.29			−0.169086
$387$	−5234.17	+	2238.61i	−0.687514	+	0.294043i
$388$	2337.45			0.305840
$389$	−2963.23	−	3715.77i	−0.386225	−	0.484311i	0.550272	−	0.834985i	$-0.314524\pi$
$389$	−2963.23	−	3715.77i	−0.386225	−	0.484311i	−0.936497	+	0.350674i	$0.885952\pi$
$390$	18688.0	+	2816.77i	2.42642	+	0.365725i
$391$	−1643.10	+	7198.90i	−0.212520	+	0.931110i
$392$	−1722.31	−	1174.25i	−0.221913	−	0.151298i
$393$	7839.92	+	13579.1i	1.00629	+	1.74294i
$394$	−8145.88	+	14109.1i	−1.04158	+	1.80407i
$395$	11475.7	−	5526.40i	1.46178	−	0.703957i
$396$	7933.34	+	2447.11i	1.00673	+	0.310535i
$397$	−11.0202	−	147.054i	−0.00139317	−	0.0185906i	0.996464	−	0.0840221i	$-0.0267766\pi$
$397$	−11.0202	−	147.054i	−0.00139317	−	0.0185906i	−0.997857	+	0.0654316i	$0.979158\pi$
$398$	−103.141	−	451.892i	−0.0129900	−	0.0569128i
$399$	−1437.35	+	3662.31i	−0.180345	+	0.459511i
$400$	−1131.24	+	15095.4i	−0.141405	+	1.88692i
$401$	−5242.31	+	790.151i	−0.652839	+	0.0983997i	−0.467107	−	0.884201i	$-0.654704\pi$
$401$	−5242.31	+	790.151i	−0.652839	+	0.0983997i	−0.185732	+	0.982600i	$0.559466\pi$
$402$	−13246.2	−	12290.6i	−1.64343	−	1.52488i
$403$	−4658.14	−	2243.24i	−0.575778	−	0.277280i
$404$	815.070	−	555.706i	0.100374	−	0.0684341i
$405$	−5717.58	−	14568.2i	−0.701503	−	1.78740i
$406$	392.409	−	121.042i	0.0479678	−	0.0147961i
$407$	−1604.49	+	1488.75i	−0.195409	+	0.181313i
$408$	1561.79	−	1958.43i	0.189511	−	0.237639i
$409$	1185.20	−	1486.19i	0.143286	−	0.179676i	−0.705010	−	0.709198i	$-0.749057\pi$
$409$	1185.20	−	1486.19i	0.143286	−	0.179676i	0.848296	+	0.529522i	$0.177629\pi$
$410$	−5318.68	+	4935.02i	−0.640661	+	0.594447i
$411$	3784.25	−	1167.29i	0.454169	−	0.140093i
$412$	695.142	+	1771.19i	0.0831242	+	0.211797i
$413$	−15.7495	+	10.7378i	−0.00187647	+	0.00127936i
$414$	−9493.97	−	4572.06i	−1.12706	−	0.542764i
$415$	18150.4	+	16841.2i	2.14692	+	1.99205i
$416$	9142.54	−	1378.02i	1.07752	−	0.162411i
$417$	943.842	−	12594.7i	0.110840	−	1.47905i
$418$	8454.59	−	21542.0i	0.989301	−	2.52070i
$419$	−567.969	−	2488.44i	−0.0662222	−	0.290139i	0.930963	−	0.365113i	$-0.118970\pi$
$419$	−567.969	−	2488.44i	−0.0662222	−	0.290139i	−0.997185	+	0.0749744i	$0.976112\pi$
$420$	355.351	+	4741.83i	0.0412842	+	0.550899i
$421$	−3497.33	−	1078.78i	−0.404868	−	0.124885i	0.0856314	−	0.996327i	$-0.472709\pi$
$421$	−3497.33	−	1078.78i	−0.404868	−	0.124885i	−0.490499	+	0.871442i	$0.663185\pi$
$422$	−808.297	+	389.256i	−0.0932401	+	0.0449020i
$423$	−2724.91	+	4719.68i	−0.313214	+	0.542503i
$424$	1567.81	+	2715.53i	0.179575	+	0.311033i
$425$	−8857.21	−	6038.74i	−1.01091	−	0.689228i
$426$	−4062.80	+	17800.3i	−0.462074	+	2.02448i
$427$	3543.96	+	534.166i	0.401649	+	0.0605389i
$428$	3741.50	+	4691.69i	0.422552	+	0.529863i
$429$	18480.5			2.07983
$430$	13462.9	+	13659.6i	1.50986	+	1.53191i
$431$	−11434.2			−1.27788			−0.638939	−	0.769257i	$-0.720626\pi$
$431$	−11434.2			−1.27788			−0.638939	+	0.769257i	$0.720626\pi$
$432$	−2194.65	−	2752.00i	−0.244421	−	0.306494i
$433$	3611.46	+	544.339i	0.400821	+	0.0604141i	0.346360	−	0.938102i	$-0.387418\pi$
$433$	3611.46	+	544.339i	0.400821	+	0.0604141i	0.0544614	+	0.998516i	$0.482656\pi$
$434$	664.013	−	2909.23i	0.0734416	−	0.321769i
$435$	−1803.21	−	1229.41i	−0.198753	−	0.135507i
$436$	−3793.38	−	6570.32i	−0.416674	−	0.721701i
$437$	−6402.18	+	11088.9i	−0.700819	+	1.21385i
$438$	−12567.4	+	6052.15i	−1.37099	+	0.660235i
$439$	−12092.1	−	3729.93i	−1.31464	−	0.405512i	−0.443378	−	0.896335i	$-0.646220\pi$
$439$	−12092.1	−	3729.93i	−1.31464	−	0.405512i	−0.871259	+	0.490823i	$0.836696\pi$
$440$	614.397	+	8198.55i	0.0665687	+	0.888297i
$441$	1368.31	+	5994.96i	0.147750	+	0.647333i
$442$	−2965.04	+	7554.81i	−0.319079	+	0.812999i
$443$	635.123	−	8475.12i	0.0681165	−	0.908951i	−0.853561	−	0.520993i	$-0.825562\pi$
$443$	635.123	−	8475.12i	0.0681165	−	0.908951i	0.921677	−	0.387958i	$-0.126819\pi$
$444$	1382.06	−	208.312i	0.147724	−	0.0222659i
$445$	−6553.65	−	6080.89i	−0.698141	−	0.647780i
$446$	1140.72	+	549.341i	0.121109	+	0.0583230i
$447$	−759.314	+	517.691i	−0.0803452	+	0.0547784i
$448$	586.480	+	1494.33i	0.0618495	+	0.157590i
$449$	573.090	−	176.775i	0.0602356	−	0.0185802i	−0.264491	−	0.964388i	$-0.585204\pi$
$449$	573.090	−	176.775i	0.0602356	−	0.0185802i	0.324727	+	0.945808i	$0.394728\pi$
$450$	11214.3	−	10405.3i	1.17477	−	1.09002i
$451$	−4423.54	+	5546.95i	−0.461855	+	0.579148i
$452$	−7963.05	+	9985.35i	−0.828651	+	1.03910i
$453$	4296.35	−	3986.43i	0.445607	−	0.413463i
$454$	−8072.96	+	2490.18i	−0.834544	+	0.257423i
$455$	1654.48	+	4215.53i	0.170468	+	0.434346i
$456$	3588.92	−	2446.89i	0.368567	−	0.251285i
$457$	−8742.00	−	4209.93i	−0.894822	−	0.430924i	−0.0708059	−	0.997490i	$-0.522557\pi$
$457$	−8742.00	−	4209.93i	−0.894822	−	0.430924i	−0.824016	+	0.566567i	$0.808271\pi$
$458$	6207.52	+	5759.73i	0.633315	+	0.587630i
$459$	2464.84	−	371.515i	0.250651	−	0.0377796i
$460$	−1156.52	+	15432.6i	−0.117223	+	1.56424i
$461$	−5218.66	+	13296.9i	−0.527239	+	1.34338i	0.380861	+	0.924632i	$0.375628\pi$
$461$	−5218.66	+	13296.9i	−0.527239	+	1.34338i	−0.908101	+	0.418752i	$0.862468\pi$
$462$	2373.49	+	10398.9i	0.239014	+	1.04719i
$463$	−380.785	−	5081.22i	−0.0382215	−	0.510031i	−0.983156	−	0.182770i	$-0.941494\pi$
$463$	−380.785	−	5081.22i	−0.0382215	−	0.510031i	0.944934	−	0.327261i	$-0.106125\pi$
$464$	−1264.63	−	390.088i	−0.126528	−	0.0390288i
$465$	−14288.3	+	6880.90i	−1.42496	+	0.686224i
$466$	5013.03	−	8682.82i	0.498335	−	0.863141i
$467$	709.395	+	1228.71i	0.0702931	+	0.121751i	0.899030	−	0.437888i	$-0.144273\pi$
$467$	709.395	+	1228.71i	0.0702931	+	0.121751i	−0.828737	+	0.559639i	$0.810940\pi$
$468$	−4171.58	−	2844.13i	−0.412033	−	0.280919i
$469$	963.488	−	4221.32i	0.0948609	−	0.415613i
$470$	18155.3	+	2736.48i	1.78179	+	0.268562i
$471$	2753.75	+	3453.09i	0.269397	+	0.337813i
$472$	21.0453			0.00205231
$473$	15008.4	+	11245.7i	1.45896	+	1.09319i
$474$	−18244.2			−1.76790
$475$	−11590.0	−	14533.4i	−1.11955	−	1.40387i
$476$	−2019.18	−	304.343i	−0.194431	−	0.0293057i
$477$	2058.27	−	9017.87i	0.197572	−	0.865618i
$478$	−12044.1	−	8211.52i	−1.15248	−	0.785745i
$479$	−4404.16	−	7628.23i	−0.420107	−	0.727647i	0.575842	−	0.817561i	$-0.304674\pi$
$479$	−4404.16	−	7628.23i	−0.420107	−	0.727647i	−0.995950	+	0.0899138i	$0.971341\pi$
$480$	14180.3	−	24560.9i	1.34841	−	2.33552i
$481$	1199.26	−	577.533i	0.113683	−	0.0547469i
$482$	−3942.73	−	1216.17i	−0.372586	−	0.114927i
$483$	−441.037	−	5885.23i	−0.0415484	−	0.554425i
$484$	−4254.88	−	18641.9i	−0.399595	−	1.75074i
$485$	2494.65	−	6356.26i	0.233559	−	0.595099i
$486$	−1319.69	+	17610.1i	−0.123174	+	1.64364i
$487$	9965.66	−	1502.08i	0.927284	−	0.139766i	0.331999	−	0.943280i	$-0.392277\pi$
$487$	9965.66	−	1502.08i	0.927284	−	0.139766i	0.595285	+	0.803514i	$0.297039\pi$
$488$	−2900.65	−	2691.41i	−0.269070	−	0.249661i
$489$	−4341.40	−	2090.71i	−0.401482	−	0.193344i
$490$	17116.7	−	11669.9i	1.57806	−	1.07591i
$491$	3014.50	+	7680.81i	0.277072	+	0.705968i	0.999889	+	0.0149279i	$0.00475187\pi$
$491$	3014.50	+	7680.81i	0.277072	+	0.705968i	−0.722817	+	0.691040i	$0.757153\pi$
$492$	4329.20	−	1335.38i	0.396698	−	0.122365i
$493$	687.016	−	637.457i	0.0627619	−	0.0582346i
$494$	−8774.58	+	11003.0i	−0.799164	+	1.00212i
$495$	15121.3	−	18961.6i	1.37304	−	1.72173i
$496$	−7049.63	+	6541.10i	−0.638181	+	0.592146i
$497$	−4180.60	+	1289.54i	−0.377315	+	0.116386i
$498$	−12957.1	−	33014.2i	−1.16591	−	2.97068i
$499$	−10595.0	+	7223.53i	−0.950494	+	0.648036i	−0.936053	−	0.351860i	$-0.885549\pi$
$499$	−10595.0	+	7223.53i	−0.950494	+	0.648036i	−0.0144412	+	0.999896i	$0.504597\pi$
$500$	−7666.56	−	3692.02i	−0.685718	−	0.330224i
$501$	590.977	+	548.346i	0.0527004	+	0.0488988i
$502$	26640.9	−	4015.47i	2.36861	−	0.357010i
$503$	−776.547	+	10362.3i	−0.0688360	+	0.918553i	0.850726	+	0.525609i	$0.176162\pi$
$503$	−776.547	+	10362.3i	−0.0688360	+	0.918553i	−0.919562	+	0.392944i	$0.871457\pi$
$504$	−312.937	+	797.352i	−0.0276574	+	0.0704700i
$505$	−641.252	−	2809.51i	−0.0565057	−	0.247567i
$506$	2594.21	+	34617.3i	0.227918	+	3.04136i
$507$	3682.29	+	1135.84i	0.322557	+	0.0994957i
$508$	1377.51	−	663.373i	0.120309	−	0.0579378i
$509$	−274.997	+	476.309i	−0.0239470	+	0.0414774i	−0.877751	−	0.479118i	$-0.840957\pi$
$509$	−274.997	+	476.309i	−0.0239470	+	0.0414774i	0.853804	+	0.520595i	$0.174290\pi$
$510$	12447.2	+	21559.2i	1.08073	+	1.87188i
$511$	−2761.61	−	1882.83i	−0.239073	−	0.162997i
$512$	2910.23	−	12750.6i	0.251202	−	1.10059i
$513$	4274.18	+	644.229i	0.367855	+	0.0554452i
$514$	15779.0	+	19786.3i	1.35405	+	1.69793i
$515$	5558.32			0.475590
$516$	−3873.24	−	11332.0i	−0.330446	−	0.966792i
$517$	17953.7			1.52728
$518$	479.001	+	600.648i	0.0406295	+	0.0509478i
$519$	−473.190	−	71.3220i	−0.0400207	−	0.00603215i
$520$	1112.57	−	4874.48i	0.0938257	−	0.411077i
$521$	−9358.88	−	6380.78i	−0.786986	−	0.536558i	0.101841	−	0.994801i	$-0.467527\pi$
$521$	−9358.88	−	6380.78i	−0.786986	−	0.536558i	−0.888827	+	0.458242i	$0.848479\pi$
$522$	668.724	+	1158.26i	0.0560713	+	0.0971184i
$523$	−7107.96	+	12311.4i	−0.594282	+	1.02933i	0.399366	+	0.916792i	$0.369230\pi$
$523$	−7107.96	+	12311.4i	−0.594282	+	1.02933i	−0.993648	+	0.112535i	$0.964103\pi$
$524$	−12714.7	+	6123.06i	−1.06000	+	0.510471i
$525$	8187.31	+	2525.45i	0.680616	+	0.209942i
$526$	−640.325	−	8544.54i	−0.0530789	−	0.708289i
$527$	−1515.42	−	6639.50i	−0.125262	−	0.548807i
$528$	12558.6	−	31998.7i	1.03512	−	2.63744i
$529$	526.145	−	7020.92i	0.0432436	−	0.577046i
$530$	−30814.4	+	4644.52i	−2.52545	+	0.380651i
$531$	−45.5091	−	42.2262i	−0.00371926	−	0.00345096i
$532$	−3190.27	−	1536.35i	−0.259992	−	0.125206i
$533$	3564.92	−	2430.52i	0.289707	−	0.197519i
$534$	4678.47	+	11920.5i	0.379133	+	0.966016i
$535$	16751.3	−	5167.09i	1.35369	−	0.417557i
$536$	−3504.33	+	3251.54i	−0.282395	+	0.262024i
$537$	−14664.3	+	18388.4i	−1.17842	+	1.47769i
$538$	−8474.87	+	10627.1i	−0.679140	+	0.851615i
$539$	14849.8	−	13778.6i	1.18669	−	1.10109i
$540$	4992.20	−	1539.89i	0.397834	−	0.122715i
$541$	1086.14	+	2767.44i	0.0863158	+	0.219929i	0.967514	−	0.252818i	$-0.0813575\pi$
$541$	1086.14	+	2767.44i	0.0863158	+	0.219929i	−0.881198	+	0.472748i	$0.843262\pi$
$542$	5139.97	−	3504.37i	0.407344	−	0.277722i
$543$	19682.2	+	9478.46i	1.55552	+	0.749097i
$544$	8927.70	+	8283.70i	0.703625	+	0.652869i
$545$	−21915.3	+	3303.20i	−1.72247	+	0.259621i
$546$	484.746	−	6468.49i	0.0379949	−	0.507007i
$547$	3782.20	−	9636.90i	0.295640	−	0.753280i	−0.703454	−	0.710740i	$-0.748360\pi$
$547$	3782.20	−	9636.90i	0.295640	−	0.753280i	0.999095	−	0.0425391i	$-0.0135447\pi$
$548$	793.123	+	3474.90i	0.0618258	+	0.270877i
$549$	872.296	+	11640.0i	0.0678118	+	0.904886i
$550$	−48158.3	−	14854.9i	−3.73359	−	1.15166i
$551$	1464.22	−	705.131i	0.113208	−	0.0545183i
$552$	−3257.95	+	5642.93i	−0.251209	+	0.435107i
$553$	−2185.83	−	3785.96i	−0.168085	−	0.291131i
$554$	−7709.67	−	5256.36i	−0.591250	−	0.403107i
$555$	908.539	−	3980.57i	0.0694871	−	0.304443i
$556$	11240.3	+	1694.21i	0.857367	+	0.129227i
$557$	−15440.0	−	19361.2i	−1.17453	−	1.47282i	−0.849873	−	0.526988i	$-0.823321\pi$
$557$	−15440.0	−	19361.2i	−1.17453	−	1.47282i	−0.324661	−	0.945830i	$-0.605250\pi$
$558$	9718.69			0.737321
$559$	−6705.86	−	9225.40i	−0.507384	−	0.698019i
$560$	8423.46			0.635636
$561$	15177.6	+	19032.1i	1.14224	+	1.43233i
$562$	3484.86	+	525.258i	0.261566	+	0.0394247i
$563$	−772.246	+	3383.43i	−0.0578087	+	0.253276i	−0.995572	−	0.0939975i	$-0.970035\pi$
$563$	−772.246	+	3383.43i	−0.0578087	+	0.253276i	0.937764	+	0.347274i	$0.112893\pi$
$564$	−9472.45	−	6458.21i	−0.707203	−	0.482163i
$565$	18654.7	+	32310.9i	1.38904	+	2.40589i
$566$	6404.96	−	11093.7i	0.475655	−	0.823858i
$567$	−4839.50	+	2330.58i	−0.358448	+	0.172619i
$568$	4615.65	+	1423.74i	0.340965	+	0.105174i
$569$	−559.939	−	7471.86i	−0.0412546	−	0.550504i	−0.979091	−	0.203425i	$-0.934793\pi$
$569$	−559.939	−	7471.86i	−0.0412546	−	0.550504i	0.937836	−	0.347079i	$-0.112826\pi$
$570$	9605.88	+	42086.1i	0.705870	+	3.09262i
$571$	942.906	−	2402.49i	0.0691058	−	0.176079i	−0.892148	−	0.451743i	$-0.850802\pi$
$571$	942.906	−	2402.49i	0.0691058	−	0.176079i	0.961254	+	0.275664i	$0.0888977\pi$
$572$	−1242.97	+	16586.3i	−0.0908590	+	1.21243i
$573$	−14431.8	+	2175.25i	−1.05218	+	0.158591i
$574$	1825.50	+	1693.81i	0.132744	+	0.123168i
$575$	25123.5	+	12098.9i	1.82213	+	0.877491i
$576$	−4319.79	+	2945.18i	−0.312484	+	0.213048i
$577$	−6434.22	−	16394.1i	−0.464229	−	1.18284i	−0.950968	−	0.309288i	$-0.899909\pi$
$577$	−6434.22	−	16394.1i	−0.464229	−	1.18284i	0.486740	−	0.873547i	$-0.338186\pi$
$578$	7464.86	−	2302.60i	0.537193	−	0.165702i
$579$	1714.61	−	1590.93i	0.123069	−	0.114191i
$580$	1224.68	−	1535.70i	0.0876762	−	0.109942i
$581$	5298.58	−	6644.20i	0.378351	−	0.474437i
$582$	−7169.73	+	6652.54i	−0.510644	+	0.473808i
$583$	−29118.3	+	8981.82i	−2.06854	+	0.638060i
$584$	1348.18	+	3435.12i	0.0955278	+	0.243401i
$585$	−12186.2	+	8308.42i	−0.861262	+	0.587198i
$586$	−21367.6	−	10290.1i	−1.50629	−	0.725391i
$587$	−12454.9	−	11556.5i	−0.875757	−	0.812584i	0.107614	−	0.994193i	$-0.465679\pi$
$587$	−12454.9	−	11556.5i	−0.875757	−	0.812584i	−0.983371	+	0.181609i	$0.941870\pi$
$588$	−12791.2	+	1927.96i	−0.897107	+	0.135217i
$589$	882.517	−	11776.4i	0.0617376	−	0.823831i
$590$	−76.4120	+	194.695i	−0.00533192	+	0.0135855i
$591$	−6612.75	−	28972.3i	−0.460257	−	2.01652i
$592$	−185.024	−	2468.97i	−0.0128453	−	0.171409i
$593$	13541.9	+	4177.12i	0.937772	+	0.289264i	0.725717	−	0.687993i	$-0.241508\pi$
$593$	13541.9	+	4177.12i	0.937772	+	0.289264i	0.212055	+	0.977258i	$0.431984\pi$
$594$	10558.3	−	5084.59i	0.729311	−	0.351217i
$595$	−2982.58	+	5165.98i	−0.205502	+	0.355940i
$596$	−413.560	−	716.308i	−0.0284230	−	0.0492300i
$597$	698.572	+	476.278i	0.0478905	+	0.0326512i
$598$	4697.68	−	20581.9i	0.321241	−	1.40745i
$599$	−18335.8	−	2763.68i	−1.25072	−	0.188516i	−0.509909	−	0.860228i	$-0.670321\pi$
$599$	−18335.8	−	2763.68i	−1.25072	−	0.188516i	−0.740812	+	0.671712i	$0.765559\pi$
$600$	−5897.95	−	7395.79i	−0.401305	−	0.503220i
$601$	14490.6			0.983499			0.491750	−	0.870737i	$-0.336358\pi$
$601$	14490.6			0.983499			0.491750	+	0.870737i	$0.336358\pi$
$602$	4329.87	−	4958.22i	0.293143	−	0.335684i
$603$	14101.9			0.952360
$604$	3288.87	+	4124.12i	0.221560	+	0.277828i
$605$	−55234.1	−	8325.21i	−3.71171	−	0.559451i
$606$	−918.515	+	4024.28i	−0.0615711	+	0.269761i
$607$	3808.14	+	2596.34i	0.254642	+	0.173612i	0.683912	−	0.729564i	$-0.260277\pi$
$607$	3808.14	+	2596.34i	0.254642	+	0.173612i	−0.429271	+	0.903176i	$0.641229\pi$
$608$	10559.4	+	18289.4i	0.704342	+	1.21996i
$609$	−374.531	+	648.707i	−0.0249208	+	0.0431641i
$610$	35430.6	−	17062.5i	2.35171	−	1.13252i
$611$	−10433.3	−	3218.24i	−0.690810	−	0.213087i
$612$	−496.993	−	6631.91i	−0.0328264	−	0.438038i
$613$	−688.417	−	3016.15i	−0.0453587	−	0.198729i	0.947172	−	0.320727i	$-0.103927\pi$
$613$	−688.417	−	3016.15i	−0.0453587	−	0.198729i	−0.992530	+	0.121997i	$0.961070\pi$
$614$	−11124.8	+	28345.5i	−0.731206	+	1.86308i
$615$	989.027	−	13197.7i	0.0648479	−	0.865335i
$616$	2790.31	−	420.572i	0.182508	−	0.0275086i
$617$	16161.9	+	14996.0i	1.05454	+	0.978473i	0.999799	−	0.0200276i	$-0.00637541\pi$
$617$	16161.9	+	14996.0i	1.05454	+	0.978473i	0.0547435	+	0.998500i	$0.482566\pi$
$618$	−7173.16	−	3454.41i	−0.466904	−	0.224849i
$619$	8346.67	−	5690.67i	0.541973	−	0.369511i	−0.261174	−	0.965292i	$-0.584110\pi$
$619$	8346.67	−	5690.67i	0.541973	−	0.369511i	0.803147	+	0.595781i	$0.203157\pi$
$620$	−5214.63	−	13286.7i	−0.337782	−	0.860654i
$621$	−6195.98	+	1911.21i	−0.400380	+	0.123501i
$622$	8167.86	−	7578.67i	0.526530	−	0.488548i
$623$	−1913.18	+	2399.05i	−0.123033	+	0.154279i
$624$	−13033.9	+	16344.0i	−0.836175	+	1.04853i
$625$	214.607	−	199.127i	0.0137349	−	0.0127441i
$626$	22546.7	−	6954.74i	1.43953	−	0.444037i
$627$	15421.8	+	39294.2i	0.982279	+	2.50280i
$628$	−3284.38	+	2239.25i	−0.208696	+	0.142287i
$629$	1579.70	+	760.742i	0.100138	+	0.0482238i
$630$	−6240.24	−	5790.10i	−0.394630	−	0.366163i
$631$	19322.9	−	2912.46i	1.21907	−	0.183745i	0.492177	−	0.870495i	$-0.336201\pi$
$631$	19322.9	−	2912.46i	1.21907	−	0.183745i	0.726894	+	0.686750i	$0.240963\pi$
$632$	−360.691	+	4813.09i	−0.0227018	+	0.302934i
$633$	597.865	−	1523.34i	0.0375403	−	0.0956511i
$634$	2941.50	+	12887.6i	0.184262	+	0.807303i
$635$	−333.771	−	4453.86i	−0.0208587	−	0.278340i
$636$	18593.9	+	5735.45i	1.15927	+	0.357587i
$637$	−11099.3	+	5345.16i	−0.690380	+	0.332469i
$638$	2203.02	−	3815.74i	0.136706	−	0.236781i
$639$	−7124.37	−	12339.8i	−0.441058	−	0.763934i
$640$	−12735.7	−	8683.03i	−0.786596	−	0.536292i
$641$	−3750.77	+	16433.2i	−0.231118	+	1.01259i	0.717596	+	0.696459i	$0.245242\pi$
$641$	−3750.77	+	16433.2i	−0.231118	+	1.01259i	−0.948714	+	0.316135i	$0.897615\pi$
$642$	−24829.3	−	3742.41i	−1.52637	−	0.230064i
$643$	−2425.41	−	3041.37i	−0.148754	−	0.186532i	0.701872	−	0.712303i	$-0.252348\pi$
$643$	−2425.41	−	3041.37i	−0.148754	−	0.186532i	−0.850626	+	0.525772i	$0.823777\pi$
$644$	5311.69			0.325016
$645$	−34949.1	−	1561.56i	−2.13352	−	0.0953277i
$646$	−18537.8			−1.12904
$647$	19297.7	+	24198.5i	1.17260	+	1.47039i	0.852286	+	0.523076i	$0.175216\pi$
$647$	19297.7	+	24198.5i	1.17260	+	1.47039i	0.320310	+	0.947313i	$0.396213\pi$
$648$	5864.18	+	883.882i	0.355504	+	0.0535836i
$649$	−45.5098	+	199.392i	−0.00275257	+	0.0120598i
$650$	25323.0	+	17264.9i	1.52808	+	1.04183i
$651$	2721.57	+	4713.89i	0.163850	+	0.283797i
$652$	2168.42	−	3755.81i	0.130248	−	0.225596i
$653$	−26870.7	+	12940.2i	−1.61031	+	0.775483i	−0.999863	−	0.0165754i	$-0.994724\pi$
$653$	−26870.7	+	12940.2i	−1.61031	+	0.775483i	−0.610445	+	0.792059i	$0.709009\pi$
$654$	30335.1	+	9357.14i	1.81376	+	0.559470i
$655$	3080.77	+	41110.0i	0.183780	+	2.45237i
$656$	−1785.84	−	7824.29i	−0.106289	−	0.465682i
$657$	3977.01	−	10133.3i	0.236161	−	0.601729i
$658$	470.929	−	6284.10i	0.0279008	−	0.372310i
$659$	−3235.29	+	487.641i	−0.191243	+	0.0288252i	−0.243965	−	0.969784i	$-0.578448\pi$
$659$	−3235.29	+	487.641i	−0.191243	+	0.0288252i	0.0527224	+	0.998609i	$0.483210\pi$
$660$	37399.9	+	34702.0i	2.20574	+	2.04663i
$661$	19267.2	+	9278.61i	1.13375	+	0.545985i	0.904114	−	0.427292i	$-0.140532\pi$
$661$	19267.2	+	9278.61i	1.13375	+	0.545985i	0.229635	+	0.973277i	$0.426247\pi$
$662$	−10876.3	+	7415.36i	−0.638551	+	0.435357i
$663$	−5408.47	−	13780.6i	−0.316814	−	0.807228i
$664$	−8965.77	+	2765.58i	−0.524005	+	0.161634i
$665$	−7582.65	+	7035.67i	−0.442169	+	0.410273i
$666$	−1560.05	+	1956.24i	−0.0907667	+	0.113818i
$667$	−1519.99	+	1906.01i	−0.0882373	+	0.110646i
$668$	−531.892	+	493.524i	−0.0308077	+	0.0285853i
$669$	−2206.86	+	680.728i	−0.127537	+	0.0393400i
$670$	−17357.0	−	44225.0i	−1.00084	−	2.55009i
$671$	31772.1	−	21661.8i	1.82794	−	1.24627i
$672$	−8770.03	−	4223.42i	−0.503439	−	0.242444i
$673$	24747.3	+	22962.2i	1.41744	+	1.31519i	0.882505	+	0.470303i	$0.155855\pi$
$673$	24747.3	+	22962.2i	1.41744	+	1.31519i	0.534937	+	0.844892i	$0.320335\pi$
$674$	25710.3	−	3875.21i	1.46933	−	0.221465i
$675$	703.460	−	9387.02i	0.0401128	−	0.535269i
$676$	−1267.09	+	3228.48i	−0.0720919	+	0.183687i
$677$	−5204.37	−	22801.8i	−0.295451	−	1.29445i	−0.876822	−	0.480816i	$-0.840341\pi$
$677$	−5204.37	−	22801.8i	−0.295451	−	1.29445i	0.581371	−	0.813639i	$-0.302517\pi$
$678$	−3993.66	−	53291.7i	−0.226218	−	3.01867i
$679$	−2239.50	−	690.796i	−0.126575	−	0.0390432i
$680$	5933.71	−	2857.52i	0.334628	−	0.161148i
$681$	7705.17	−	13345.7i	0.433572	−	0.750969i
$682$	−16008.4	−	27727.4i	−0.898820	−	1.55680i
$683$	−6229.71	−	4247.34i	−0.349009	−	0.237950i	0.376108	−	0.926576i	$-0.377262\pi$
$683$	−6229.71	−	4247.34i	−0.349009	−	0.237950i	−0.725117	+	0.688625i	$0.758214\pi$
$684$	2566.20	−	11243.2i	0.143452	−	0.628503i
$685$	10295.8	+	1551.84i	0.574281	+	0.0865590i
$686$	−9425.79	−	11819.6i	−0.524604	−	0.657832i
$687$	−15446.4			−0.857810
$688$	−20530.7	+	5341.93i	−1.13768	+	0.296016i
$689$	18531.3			1.02465
$690$	−40374.8	−	50628.5i	−2.22760	−	2.79332i
$691$	10298.4	+	1552.24i	0.566961	+	0.0854557i	0.426267	−	0.904597i	$-0.359828\pi$
$691$	10298.4	+	1552.24i	0.566961	+	0.0854557i	0.140694	+	0.990053i	$0.455067\pi$
$692$	95.8380	−	419.894i	0.00526476	−	0.0230664i
$693$	−6877.71	−	4689.14i	−0.377002	−	0.257036i
$694$	−8668.08	−	15013.6i	−0.474115	−	0.821191i
$695$	16603.3	−	28757.8i	0.906188	−	1.56956i
$696$	745.113	−	358.828i	0.0405797	−	0.0195421i
$697$	5430.85	+	1675.19i	0.295133	+	0.0910366i
$698$	−2968.73	−	39614.9i	−0.160986	−	2.14820i
$699$	4069.53	+	17829.8i	0.220206	+	0.964784i
$700$	−2817.27	+	7178.30i	−0.152118	+	0.387592i
$701$	−5.20328	+	69.4330i	−0.000280350	+	0.00374101i	−0.997342	−	0.0728595i	$-0.976788\pi$
$701$	−5.20328	+	69.4330i	−0.000280350	+	0.00374101i	0.997062	+	0.0766005i	$0.0244066\pi$
$702$	−7047.05	+	1062.17i	−0.378880	+	0.0571069i
$703$	2228.76	+	2067.99i	0.119572	+	0.110947i
$704$	15518.1	+	7473.11i	0.830766	+	0.400076i
$705$	−27671.4	+	18866.0i	−1.47825	+	1.00785i
$706$	5861.83	+	14935.7i	0.312483	+	0.796193i
$707$	−945.146	+	291.539i	−0.0502771	+	0.0155084i
$708$	95.7354	−	88.8294i	0.00508186	−	0.00471528i
$709$	18420.4	−	23098.5i	0.975731	−	1.22353i	0.00103310	−	0.999999i	$-0.499671\pi$
$709$	18420.4	−	23098.5i	0.975731	−	1.22353i	0.974698	−	0.223528i	$-0.0717574\pi$
$710$	−29929.9	+	37531.0i	−1.58204	+	1.98382i
$711$	10437.2	−	9684.27i	0.550526	−	0.510813i
$712$	3237.30	−	998.576i	0.170398	−	0.0525607i
$713$	6472.04	+	16490.5i	0.339944	+	0.866162i
$714$	7059.67	−	4813.20i	0.370030	−	0.252282i
$715$	43776.9	+	21081.8i	2.28974	+	1.10268i
$716$	−15517.4	−	14398.1i	−0.809935	−	0.751509i
$717$	26292.6	−	3962.97i	1.36948	−	0.206416i
$718$	−2131.73	+	28446.0i	−0.110801	+	1.47854i
$719$	6466.73	−	16476.9i	0.335422	−	0.854640i	−0.659286	−	0.751892i	$-0.729141\pi$
$719$	6466.73	−	16476.9i	0.335422	−	0.854640i	0.994707	−	0.102748i	$-0.0327635\pi$
$720$	6104.68	+	26746.4i	0.315984	+	1.38441i
$721$	−142.566	−	1902.41i	−0.00736399	−	0.0982657i
$722$	−6034.14	−	1861.28i	−0.311035	−	0.0959416i
$723$	6780.88	−	3265.50i	0.348802	−	0.167974i
$724$	−9830.77	+	17027.4i	−0.504638	+	0.874058i
$725$	−1769.62	−	3065.07i	−0.0906509	−	0.157012i
$726$	66107.1	+	45071.1i	3.37943	+	2.30405i
$727$	−101.092	+	442.915i	−0.00515723	+	0.0225953i	−0.977441	−	0.211208i	$-0.932260\pi$
$727$	−101.092	+	442.915i	−0.00515723	+	0.0225953i	0.972284	+	0.233804i	$0.0751173\pi$
$728$	−1696.90	−	255.766i	−0.0863889	−	0.0130210i
$729$	−5497.07	−	6893.11i	−0.279280	−	0.350206i
$730$	−36674.0			−1.85940
$731$	3993.39	−	14482.6i	0.202053	−	0.732776i
$732$	−24555.2			−1.23987
$733$	9916.76	+	12435.2i	0.499705	+	0.626611i	0.966163	−	0.257933i	$-0.0830414\pi$
$733$	9916.76	+	12435.2i	0.499705	+	0.626611i	−0.466458	+	0.884544i	$0.654470\pi$
$734$	−16013.1	−	2413.59i	−0.805252	−	0.121372i
$735$	−8408.67	+	36840.8i	−0.421985	+	1.84884i
$736$	−26175.2	−	17846.0i	−1.31091	−	0.893765i
$737$	−23228.4	−	40232.7i	−1.16096	−	2.01084i
$738$	−4055.26	+	7023.91i	−0.202271	+	0.350344i
$739$	−6068.64	+	2922.50i	−0.302082	+	0.145475i	−0.578784	−	0.815481i	$-0.696473\pi$
$739$	−6068.64	+	2922.50i	−0.302082	+	0.145475i	0.276702	+	0.960956i	$0.410758\pi$
$740$	3511.48	+	1083.15i	0.174438	+	0.0538071i
$741$	−1918.38	−	25599.1i	−0.0951061	−	1.26910i
$742$	2380.01	+	10427.5i	0.117753	+	0.515912i
$743$	−12269.9	+	31263.3i	−0.605841	+	1.54366i	0.217470	+	0.976067i	$0.430220\pi$
$743$	−12269.9	+	31263.3i	−0.605841	+	1.54366i	−0.823311	+	0.567591i	$0.807876\pi$
$744$	449.096	−	5992.77i	0.0221299	−	0.295303i
$745$	−2389.24	+	360.120i	−0.117497	+	0.0177098i
$746$	−7740.32	−	7181.97i	−0.379884	−	0.352481i
$747$	24936.8	+	12008.9i	1.22141	+	0.588199i
$748$	−18102.2	+	12341.9i	−0.884870	+	0.603294i
$749$	−2198.16	−	5600.83i	−0.107235	−	0.273231i
$750$	34023.6	−	10494.9i	1.65649	−	0.510959i
$751$	−19593.3	+	18180.0i	−0.952026	+	0.883351i	−0.993273	−	0.115798i	$-0.963057\pi$
$751$	−19593.3	+	18180.0i	−0.952026	+	0.883351i	0.0412471	+	0.999149i	$0.486867\pi$
$752$	−12662.4	+	15878.1i	−0.614028	+	0.769966i
$753$	−30640.8	+	38422.3i	−1.48288	+	1.85948i
$754$	−1964.20	+	1822.51i	−0.0948699	+	0.0880264i
$755$	14724.8	−	4542.01i	0.709790	−	0.218941i
$756$	−655.095	−	1669.15i	−0.0315153	−	0.0802997i
$757$	7031.67	−	4794.11i	0.337610	−	0.230178i	−0.382633	−	0.923900i	$-0.624983\pi$
$757$	7031.67	−	4794.11i	0.337610	−	0.230178i	0.720243	+	0.693722i	$0.244030\pi$
$758$	45382.5	+	21855.0i	2.17462	+	1.04724i
$759$	−46418.1	−	43069.7i	−2.21986	−	2.05973i
$760$	11292.8	−	1702.12i	0.538992	−	0.0812399i
$761$	−633.854	+	8458.20i	−0.0301934	+	0.402903i	0.961547	+	0.274641i	$0.0885590\pi$
$761$	−633.854	+	8458.20i	−0.0301934	+	0.402903i	−0.991740	+	0.128262i	$0.959060\pi$
$762$	−2337.27	+	5955.26i	−0.111116	+	0.283118i
$763$	1692.67	+	7416.08i	0.0803130	+	0.351874i
$764$	−981.632	−	13099.0i	−0.0464845	−	0.620293i
$765$	−18564.7	−	5726.44i	−0.877395	−	0.270641i
$766$	3418.82	−	1646.42i	0.161262	−	0.0776599i
$767$	62.1881	−	107.713i	0.00292762	−	0.00507078i
$768$	18155.0	+	31445.4i	0.853011	+	1.47746i
$769$	15270.5	+	10411.3i	0.716084	+	0.488218i	0.865723	−	0.500523i	$-0.166859\pi$
$769$	15270.5	+	10411.3i	0.716084	+	0.488218i	−0.149640	+	0.988741i	$0.547811\pi$
$770$	−6240.35	+	27340.8i	−0.292060	+	1.27960i
$771$	−45647.4	−	6880.24i	−2.13223	−	0.321383i
$772$	1312.54	+	1645.88i	0.0611910	+	0.0767311i
$773$	19577.9			0.910956			0.455478	−	0.890247i	$-0.349468\pi$
$773$	19577.9			0.910956			0.455478	+	0.890247i	$0.349468\pi$
$774$	18881.4	+	10154.9i	0.876845	+	0.471592i
$775$	−25718.2			−1.19203
$776$	1613.29	+	2023.00i	0.0746310	+	0.0935843i
$777$	−1385.71	−	208.862i	−0.0639795	−	0.00964335i
$778$	−3982.77	+	17449.7i	−0.183534	+	0.804113i
$779$	8142.80	+	5551.67i	0.374513	+	0.255339i
$780$	−15513.4	−	26870.1i	−0.712141	−	1.23346i
$781$	−23470.3	+	40651.7i	−1.07533	+	1.86252i
$782$	25054.3	−	12065.5i	1.14570	−	0.551742i
$783$	786.409	+	242.575i	0.0358927	+	0.0110714i
$784$	1712.43	+	22850.7i	0.0780078	+	1.04094i
$785$	2583.97	+	11321.1i	0.117485	+	0.514736i
$786$	21573.4	−	54968.2i	0.979006	−	2.49447i
$787$	−380.551	+	5078.10i	−0.0172366	+	0.230006i	0.981932	+	0.189234i	$0.0606006\pi$
$787$	−380.551	+	5078.10i	−0.0172366	+	0.230006i	−0.999168	+	0.0407715i	$0.987018\pi$
$788$	26447.6	−	3986.33i	1.19563	−	0.180212i
$789$	11457.3	+	10630.8i	0.516973	+	0.479680i
$790$	−43217.3	−	20812.3i	−1.94633	−	0.937303i
$791$	10580.4	−	7213.58i	0.475594	−	0.324255i
$792$	3357.61	+	8555.06i	0.150641	+	0.383827i
$793$	−22346.3	+	6892.93i	−1.00068	+	0.308670i
$794$	−407.106	+	377.739i	−0.0181960	+	0.0168835i
$795$	35440.8	−	44441.4i	1.58108	−	1.98261i
$796$	−474.447	+	594.938i	−0.0211260	+	0.0264912i
$797$	−18582.4	+	17242.0i	−0.825876	+	0.766301i	−0.974926	−	0.222529i	$-0.928569\pi$
$797$	−18582.4	+	17242.0i	−0.825876	+	0.766301i	0.149050	+	0.988830i	$0.452378\pi$
$798$	14158.2	−	4367.22i	0.628062	−	0.193732i
$799$	−5254.30	−	13387.7i	−0.232646	−	0.592771i
$800$	38000.4	−	25908.2i	1.67939	−	1.14499i
$801$	−9004.03	−	4336.11i	−0.397181	−	0.191272i
$802$	14635.7	+	13580.0i	0.644396	+	0.597912i
$803$	−35461.1	+	5344.89i	−1.55840	+	0.234891i
$804$	−2216.91	+	29582.6i	−0.0972441	+	1.29763i
$805$	5668.92	−	14444.2i	0.248203	−	0.632410i
$806$	4332.64	+	18982.5i	0.189343	+	0.829567i
$807$	−1852.86	−	24724.7i	−0.0808225	−	1.07850i
$808$	1043.50	+	321.878i	0.0454335	+	0.0140144i
$809$	24172.8	−	11641.0i	1.05052	−	0.505903i	0.172738	−	0.984968i	$-0.444738\pi$
$809$	24172.8	−	11641.0i	1.05052	−	0.505903i	0.877779	+	0.479065i	$0.159024\pi$
$810$	−29468.8	+	51041.5i	−1.27831	+	2.21409i
$811$	−15002.8	−	25985.6i	−0.649593	−	1.12513i	−0.983220	−	0.182423i	$-0.941606\pi$
$811$	−15002.8	−	25985.6i	−0.649593	−	1.12513i	0.333627	−	0.942705i	$-0.391727\pi$
$812$	−557.028	−	379.775i	−0.0240737	−	0.0164132i
$813$	−2525.04	+	11062.9i	−0.108926	+	0.477238i
$814$	8150.83	+	1228.54i	0.350966	+	0.0528996i
$815$	−7898.98	−	9905.01i	−0.339496	−	0.425715i
$816$	−27536.2			−1.18133
$817$	14019.5	−	21956.9i	0.600345	−	0.940239i
$818$	−7158.79			−0.305992
$819$	3156.24	+	3957.80i	0.134662	+	0.168860i
$820$	11778.4	+	1775.32i	0.501611	+	0.0756057i
$821$	4233.99	−	18550.3i	0.179984	−	0.788563i	−0.801650	−	0.597793i	$-0.796044\pi$
$821$	4233.99	−	18550.3i	0.179984	−	0.788563i	0.981635	−	0.190770i	$-0.0610985\pi$
$822$	−12322.6	−	8401.38i	−0.522869	−	0.356486i
$823$	−2365.36	−	4096.92i	−0.100184	−	0.173523i	0.811577	−	0.584246i	$-0.198610\pi$
$823$	−2365.36	−	4096.92i	−0.100184	−	0.173523i	−0.911760	+	0.410723i	$0.865276\pi$
$824$	−1053.14	+	1824.09i	−0.0445240	+	0.0771178i
$825$	82824.8	−	39886.3i	3.49526	−	1.68323i
$826$	68.5968	+	21.1593i	0.00288957	+	0.000891316i
$827$	2631.93	+	35120.6i	0.110666	+	1.47674i	0.725576	+	0.688142i	$0.241573\pi$
$827$	2631.93	+	35120.6i	0.110666	+	1.47674i	−0.614910	+	0.788597i	$0.710808\pi$
$828$	3849.51	+	16865.8i	0.161570	+	0.707883i
$829$	7328.88	−	18673.7i	0.307048	−	0.782345i	−0.691171	−	0.722691i	$-0.742905\pi$
$829$	7328.88	−	18673.7i	0.307048	−	0.782345i	0.998219	−	0.0596539i	$-0.0189997\pi$
$830$	6968.30	−	92985.5i	0.291414	−	3.88864i
$831$	16830.4	−	2536.78i	0.702577	−	0.105896i
$832$	−7678.30	−	7124.43i	−0.319949	−	0.296869i
$833$	−14620.3	−	7040.78i	−0.608121	−	0.292856i
$834$	−39299.6	+	26794.0i	−1.63170	+	1.11247i
$835$	774.383	+	1973.10i	0.0320942	+	0.0817746i
$836$	−36304.0	+	11198.3i	−1.50191	+	0.463279i
$837$	4383.79	−	4067.57i	0.181035	−	0.167976i
$838$	−5993.25	+	7515.29i	−0.247056	+	0.309799i
$839$	24980.1	−	31324.0i	1.02790	−	1.28895i	0.0713266	−	0.997453i	$-0.477277\pi$
$839$	24980.1	−	31324.0i	1.02790	−	1.28895i	0.956573	−	0.291492i	$-0.0941518\pi$
$840$	−3858.66	+	3580.32i	−0.158496	+	0.147063i
$841$	−23009.8	+	7097.58i	−0.943450	+	0.291016i
$842$	5035.58	+	12830.5i	0.206102	+	0.525139i
$843$	−5311.44	+	3621.28i	−0.217006	+	0.147952i
$844$	1326.99	+	639.045i	0.0541195	+	0.0260626i
$845$	7426.96	+	6891.21i	0.302361	+	0.280550i
$846$	20294.7	−	3058.94i	0.824760	−	0.124313i
$847$	−1432.71	+	19118.2i	−0.0581210	+	0.775571i
$848$	12593.1	−	32086.7i	0.509963	−	1.29937i
$849$	5199.49	+	22780.4i	0.210184	+	0.920875i
$850$	3016.93	+	40258.2i	0.121741	+	1.62452i
$851$	−4358.20	−	1344.33i	−0.175555	−	0.0541515i
$852$	27006.0	−	13005.4i	1.08593	−	0.522956i
$853$	1549.99	−	2684.67i	0.0622166	−	0.107762i	−0.833239	−	0.552912i	$-0.813516\pi$
$853$	1549.99	−	2684.67i	0.0622166	−	0.107762i	0.895456	+	0.445150i	$0.146850\pi$
$854$	−6748.63	−	11689.0i	−0.270414	−	0.468370i
$855$	−27835.1	−	18977.7i	−1.11338	−	0.759091i
$856$	−1478.18	+	6476.32i	−0.0590223	+	0.258594i
$857$	−5101.25	−	768.889i	−0.203332	−	0.0306473i	0.0465866	−	0.998914i	$-0.485166\pi$
$857$	−5101.25	−	768.889i	−0.203332	−	0.0306473i	−0.249918	+	0.968267i	$0.580404\pi$
$858$	−43393.2	−	54413.3i	−1.72659	−	2.16508i
$859$	17601.3			0.699127			0.349563	−	0.936913i	$-0.386330\pi$
$859$	17601.3			0.699127			0.349563	+	0.936913i	$0.386330\pi$
$860$	3752.14	−	31262.0i	0.148775	−	1.23956i
$861$	−4542.45			−0.179798
$862$	26848.1	+	33666.4i	1.06085	+	1.33026i
$863$	−46260.0	−	6972.58i	−1.82469	−	0.275028i	−0.854871	−	0.518841i	$-0.826364\pi$
$863$	−46260.0	−	6972.58i	−1.82469	−	0.275028i	−0.969822	+	0.243813i	$0.921602\pi$
$864$	−2379.73	+	10426.3i	−0.0937039	+	0.410544i
$865$	−1039.54	−	708.746i	−0.0408618	−	0.0278591i
$866$	−6877.16	−	11911.6i	−0.269856	−	0.467405i
$867$	−7124.78	+	12340.5i	−0.279089	+	0.483396i
$868$	−4413.80	+	2125.57i	−0.172597	+	0.0831182i
$869$	−44821.1	−	13825.5i	−1.74966	−	0.539698i
$870$	614.208	+	8196.03i	0.0239352	+	0.319393i
$871$	6286.69	+	27543.8i	0.244565	+	1.07151i
$872$	3068.28	−	7817.84i	0.119157	−	0.303607i
$873$	570.408	−	7611.56i	0.0221138	−	0.295089i
$874$	47682.5	−	7186.98i	1.84540	−	0.278150i
$875$	6254.19	+	5803.04i	0.241635	+	0.224204i
$876$	20632.1	+	9935.88i	0.795768	+	0.383222i
$877$	10085.7	−	6876.31i	0.388335	−	0.264762i	−0.353377	−	0.935481i	$-0.614967\pi$
$877$	10085.7	−	6876.31i	0.388335	−	0.264762i	0.741712	+	0.670719i	$0.234014\pi$
$878$	17410.7	+	44361.7i	0.669229	+	1.70517i
$879$	41338.3	−	12751.2i	1.58624	−	0.489290i
$880$	66251.9	−	61472.8i	2.53790	−	2.35483i
$881$	−3893.33	+	4882.08i	−0.148887	+	0.186698i	−0.850682	−	0.525680i	$-0.823811\pi$
$881$	−3893.33	+	4882.08i	−0.148887	+	0.186698i	0.701795	+	0.712379i	$0.252382\pi$
$882$	14438.5	−	18105.3i	0.551212	−	0.691198i
$883$	−8457.79	+	7847.68i	−0.322341	+	0.299089i	−0.824700	−	0.565570i	$-0.808656\pi$
$883$	−8457.79	+	7847.68i	−0.322341	+	0.299089i	0.502359	+	0.864659i	$0.332466\pi$
$884$	12731.9	−	3927.27i	0.484412	−	0.149421i
$885$	−139.381	−	355.138i	−0.00529407	−	0.0134891i
$886$	−26445.2	+	18030.0i	−1.00276	+	0.683668i
$887$	−13097.2	−	6307.27i	−0.495784	−	0.238757i	0.169246	−	0.985574i	$-0.445867\pi$
$887$	−13097.2	−	6307.27i	−0.495784	−	0.238757i	−0.665030	+	0.746817i	$0.731581\pi$
$888$	1134.17	+	1052.36i	0.0428607	+	0.0397689i
$889$	−1515.84	+	228.475i	−0.0571873	+	0.00861959i
$890$	−2516.07	+	33574.6i	−0.0947627	+	1.26452i
$891$	−21055.3	+	53648.1i	−0.791673	+	2.01715i
$892$	−462.526	−	2026.46i	−0.0173616	−	0.0760660i
$893$	−1863.70	−	24869.4i	−0.0698392	−	0.931939i
$894$	3307.18	+	1020.13i	0.123723	+	0.0381636i
$895$	−55713.8	+	26830.4i	−2.08079	+	1.00206i
$896$	−2645.23	+	4581.67i	−0.0986282	+	0.170829i
$897$	19254.2	+	33349.3i	0.716699	+	1.24136i
$898$	−1866.14	−	1272.31i	−0.0693472	−	0.0472801i
$899$	500.325	−	2192.07i	0.0185615	−	0.0813231i
$900$	−24834.4	−	3743.19i	−0.919794	−	0.138637i
$901$	15219.3	+	19084.4i	0.562740	+	0.705654i
$902$	26719.0			0.986302
$903$	361.948	+	12001.9i	0.0133387	+	0.442300i
$904$	−14138.1			−0.520160
$905$	35810.9	+	44905.5i	1.31535	+	1.64940i
$906$	−21825.6	−	3289.67i	−0.800337	−	0.120631i
$907$	3959.47	−	17347.6i	0.144953	−	0.635079i	−0.849290	−	0.527926i	$-0.822970\pi$
$907$	3959.47	−	17347.6i	0.144953	−	0.635079i	0.994243	−	0.107152i	$-0.0341732\pi$
$908$	11459.6	+	7813.05i	0.418834	+	0.285556i
$909$	−1610.67	−	2789.77i	−0.0587707	−	0.101794i
$910$	8527.28	−	14769.7i	0.310634	−	0.538033i
$911$	32421.8	−	15613.5i	1.17913	−	0.567837i	0.261469	−	0.965212i	$-0.415793\pi$
$911$	32421.8	−	15613.5i	1.17913	−	0.567837i	0.917656	+	0.397375i	$0.130079\pi$
$912$	−45628.1	−	14074.4i	−1.65669	−	0.511020i
$913$	−6813.94	−	90925.7i	−0.246997	−	3.29595i
$914$	8131.13	+	35624.8i	0.294260	+	1.28924i
$915$	−26206.6	+	66773.2i	−0.946844	+	2.41252i
$916$	1038.90	−	13863.2i	0.0374742	−	0.500058i
$917$	13991.5	−	2108.87i	0.503859	−	0.0759445i
$918$	−6881.45	−	6385.05i	−0.247409	−	0.229562i
$919$	−9835.38	−	4736.47i	−0.353035	−	0.170013i	0.248958	−	0.968514i	$-0.419912\pi$
$919$	−9835.38	−	4736.47i	−0.353035	−	0.170013i	−0.601993	+	0.798502i	$0.705626\pi$
$920$	−14154.7	+	9650.53i	−0.507247	+	0.345835i
$921$	−20292.5	−	51704.5i	−0.726016	−	1.84986i
$922$	51404.8	−	15856.3i	1.83615	−	0.566376i
$923$	20926.0	−	19416.4i	0.746247	−	0.692416i
$924$	10918.0	−	13690.7i	0.388717	−	0.487436i
$925$	4128.29	−	5176.72i	0.146743	−	0.184010i
$926$	−14066.9	+	13052.1i	−0.499207	+	0.463197i
$927$	5937.26	−	1831.40i	0.210362	−	0.0648880i
$928$	1469.00	+	3742.95i	0.0519636	+	0.132401i
$929$	1448.44	−	987.528i	0.0511536	−	0.0348759i	−0.537473	−	0.843281i	$-0.680621\pi$
$929$	1448.44	−	987.528i	0.0511536	−	0.0348759i	0.588627	+	0.808405i	$0.299669\pi$
$930$	53809.7	+	25913.4i	1.89730	+	0.913692i
$931$	−20627.5	−	19139.5i	−0.726143	−	0.673762i
$932$	−16276.0	+	2453.22i	−0.572038	+	0.0862208i
$933$	−1518.84	+	20267.5i	−0.0532954	+	0.711178i
$934$	1952.07	−	4973.79i	0.0683872	−	0.174248i
$935$	14241.8	+	62397.6i	0.498137	+	2.18248i
$936$	−417.667	−	5573.38i	−0.0145853	−	0.194628i
$937$	−30486.0	−	9403.69i	−1.06290	−	0.327861i	−0.286485	−	0.958085i	$-0.592487\pi$
$937$	−30486.0	−	9403.69i	−1.06290	−	0.327861i	−0.776413	+	0.630224i	$0.782963\pi$
$938$	−14691.4	+	7075.02i	−0.511399	+	0.246277i
$939$	−21519.5	+	37272.9i	−0.747884	+	1.29537i
$940$	−15071.2	−	26104.1i	−0.522946	−	0.905769i
$941$	25493.7	+	17381.3i	0.883177	+	0.602140i	0.917704	−	0.397264i	$-0.130040\pi$
$941$	25493.7	+	17381.3i	0.883177	+	0.602140i	−0.0345276	+	0.999404i	$0.510993\pi$
$942$	3701.22	−	16216.1i	0.128017	−	0.560880i
$943$	−14618.6	−	2203.40i	−0.504822	−	0.0760896i
$944$	−144.243	−	180.875i	−0.00497322	−	0.00623622i
$945$	−5238.11			−0.180313
$946$	−2129.00	−	70595.7i	−0.0731710	−	2.42628i
$947$	6834.85			0.234533			0.117267	−	0.993100i	$-0.462587\pi$
$947$	6834.85			0.234533			0.117267	+	0.993100i	$0.462587\pi$
$948$	18674.6	+	23417.2i	0.639792	+	0.802274i
$949$	21565.2	+	3250.44i	0.737658	+	0.111184i
$950$	−15577.8	+	68250.6i	−0.532010	+	2.33089i
$951$	−19922.6	−	13583.0i	−0.679323	−	0.463154i
$952$	−1130.22	−	1957.60i	−0.0384776	−	0.0666452i
$953$	−1692.65	+	2931.75i	−0.0575343	+	0.0996523i	−0.893358	−	0.449346i	$-0.851657\pi$
$953$	−1692.65	+	2931.75i	−0.0575343	+	0.0996523i	0.835824	+	0.548998i	$0.184991\pi$
$954$	−31384.8	+	15114.1i	−1.06512	+	0.512934i
$955$	−36667.9	−	11310.5i	−1.24245	−	0.383246i
$956$	1788.38	+	23864.3i	0.0605025	+	0.807350i
$957$	1788.39	+	7835.45i	0.0604080	+	0.264665i
$958$	−12119.1	+	30879.0i	−0.408717	+	1.04139i
$959$	267.061	−	3563.69i	0.00899256	−	0.119997i
$960$	−31770.3	+	4788.61i	−1.06811	+	0.160991i
$961$	9861.38	+	9150.02i	0.331019	+	0.307141i
$962$	−4516.40	−	2174.98i	−0.151367	−	0.0728943i
$963$	16190.8	−	11038.7i	0.541788	−	0.369385i
$964$	2474.73	+	6305.51i	0.0826823	+	0.210671i
$965$	5876.47	−	1812.65i	0.196031	−	0.0604677i
$966$	−16292.7	+	15117.4i	−0.542660	+	0.503515i
$967$	32699.0	−	41003.2i	1.08741	−	1.36357i	0.161047	−	0.986947i	$-0.448513\pi$
$967$	32699.0	−	41003.2i	1.08741	−	1.36357i	0.926366	−	0.376625i	$-0.122916\pi$
$968$	13197.3	−	16548.9i	0.438201	−	0.549487i
$969$	24787.6	−	22999.6i	0.821768	−	0.762490i
$970$	−24572.7	+	7579.69i	−0.813385	+	0.250896i
$971$	−16479.5	−	41989.2i	−0.544648	−	1.38774i	−0.892864	−	0.450327i	$-0.851308\pi$
$971$	−16479.5	−	41989.2i	−0.544648	−	1.38774i	0.348216	−	0.937414i	$-0.386788\pi$
$972$	23954.1	−	16331.6i	0.790459	−	0.538926i
$973$	−10268.6	−	4945.11i	−0.338332	−	0.162932i
$974$	−27822.6	−	25815.6i	−0.915291	−	0.849266i
$975$	−55280.9	+	8332.26i	−1.81580	+	0.273688i
$976$	−3250.62	+	43376.6i	−0.106609	+	1.42259i
$977$	−12489.1	+	31821.6i	−0.408967	+	1.04203i	0.566924	+	0.823770i	$0.308133\pi$
$977$	−12489.1	+	31821.6i	−0.408967	+	1.04203i	−0.975891	+	0.218260i	$0.929962\pi$
$978$	4038.03	+	17691.8i	0.132027	+	0.578446i
$979$	2460.33	+	32830.9i	0.0803193	+	1.07179i
$980$	−32499.3	−	10024.7i	−1.05934	−	0.326762i
$981$	−22321.0	+	10749.2i	−0.726457	+	0.349843i
$982$	15536.9	−	26910.7i	0.504891	−	0.874497i
$983$	−7172.38	−	12422.9i	−0.232720	−	0.403082i	0.725888	−	0.687813i	$-0.241429\pi$
$983$	−7172.38	−	12422.9i	−0.232720	−	0.403082i	−0.958607	+	0.284731i	$0.908096\pi$
$984$	4143.71	+	2825.14i	0.134245	+	0.0915265i
$985$	17386.2	−	76173.8i	0.562405	−	2.46406i
$986$	−3490.06	−	526.042i	−0.112724	−	0.0169905i
$987$	7166.91	+	8987.02i	0.231130	+	0.289828i
$988$	23104.3			0.743974
$989$	−4656.89	+	38800.2i	−0.149728	+	1.24750i
$990$	−91335.5			−2.93215
$991$	−13594.6	−	17047.1i	−0.435769	−	0.546437i	0.514653	−	0.857398i	$-0.327921\pi$
$991$	−13594.6	−	17047.1i	−0.435769	−	0.546437i	−0.950423	+	0.310961i	$0.899349\pi$
$992$	28891.9	+	4354.75i	0.924716	+	0.139379i
$993$	5343.07	−	23409.5i	0.170753	−	0.748116i
$994$	13613.2	+	9281.30i	0.434390	+	0.296162i
$995$	1111.47	+	1925.12i	0.0354130	+	0.0613371i
$996$	−29112.3	+	50423.9i	−0.926162	+	1.60416i
$997$	−20582.7	+	9912.09i	−0.653821	+	0.314864i	−0.731225	−	0.682136i	$-0.761051\pi$
$997$	−20582.7	+	9912.09i	−0.653821	+	0.314864i	0.0774041	+	0.997000i	$0.475337\pi$
$998$	46146.3	+	14234.3i	1.46366	+	0.451481i
$999$	115.057	+	1535.32i	0.00364388	+	0.0486242i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.4.g.a.9.2	✓	120
43.14	even	21		1849.4.a.l.1.11		60
43.24	even	21	inner	43.4.g.a.24.2	yes	120
43.29	odd	42		1849.4.a.k.1.50		60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.4.g.a.9.2	✓	120	1.1	even	1	trivial
43.4.g.a.24.2	yes	120	43.24	even	21	inner
1849.4.a.k.1.50		60	43.29	odd	42
1849.4.a.l.1.11		60	43.14	even	21

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:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	43.g (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.34805 - 2.94437i) q^{2} +(6.79273 + 1.02384i) q^{3} +(-1.37577 + 6.02765i) q^{4} +(14.9228 + 10.1742i) q^{5} +(-12.9351 - 22.4043i) q^{6} +(3.09950 - 5.36848i) q^{7} +(-6.16631 + 2.96954i) q^{8} +(19.2924 + 5.95092i) q^{9} +O(q^{10})\)	\(q+(-2.34805 - 2.94437i) q^{2} +(6.79273 + 1.02384i) q^{3} +(-1.37577 + 6.02765i) q^{4} +(14.9228 + 10.1742i) q^{5} +(-12.9351 - 22.4043i) q^{6} +(3.09950 - 5.36848i) q^{7} +(-6.16631 + 2.96954i) q^{8} +(19.2924 + 5.95092i) q^{9} +(-5.08298 - 67.8276i) q^{10} +(-14.8001 - 64.8435i) q^{11} +(-15.5166 + 39.5356i) q^{12} +(-3.02268 + 40.3349i) q^{13} +(-23.0846 + 3.47944i) q^{14} +(90.9496 + 84.3889i) q^{15} +(67.7853 + 32.6437i) q^{16} +(-44.0213 + 30.0132i) q^{17} +(-27.7779 - 70.7770i) q^{18} +(-88.2846 + 27.2322i) q^{19} +(-81.8566 + 75.9519i) q^{20} +(26.5505 - 33.2933i) q^{21} +(-156.172 + 195.833i) q^{22} +(101.595 - 94.2662i) q^{23} +(-44.9264 + 13.8579i) q^{24} +(73.5077 + 187.294i) q^{25} +(125.858 - 85.8086i) q^{26} +(-42.1521 - 20.2994i) q^{27} +(28.0951 + 26.0685i) q^{28} +(-17.3939 + 2.62171i) q^{29} +(34.9173 - 465.939i) q^{30} +(-46.6987 + 118.986i) q^{31} +(-50.8650 - 222.854i) q^{32} +(-34.1438 - 455.617i) q^{33} +(191.734 + 59.1422i) q^{34} +(100.873 - 48.5779i) q^{35} +(-62.4120 + 108.101i) q^{36} +(-16.4542 - 28.4995i) q^{37} +(287.479 + 196.000i) q^{38} +(-61.8287 + 270.889i) q^{39} +(-122.231 - 18.4234i) q^{40} +(-66.5083 - 83.3988i) q^{41} -160.370 q^{42} +(-215.053 + 182.371i) q^{43} +411.215 q^{44} +(227.351 + 285.089i) q^{45} +(-516.104 - 77.7902i) q^{46} +(-60.0662 + 263.167i) q^{47} +(427.025 + 291.141i) q^{48} +(152.286 + 263.768i) q^{49} +(378.864 - 656.211i) q^{50} +(-329.753 + 158.801i) q^{51} +(-238.966 - 73.7112i) q^{52} +(-34.2377 - 456.870i) q^{53} +(39.2066 + 171.775i) q^{54} +(438.871 - 1118.22i) q^{55} +(-3.17053 + 42.3078i) q^{56} +(-627.575 + 94.5916i) q^{57} +(48.5611 + 45.0581i) q^{58} +(-2.77045 - 1.33418i) q^{59} +(-633.792 + 432.112i) q^{60} +(211.224 + 538.191i) q^{61} +(459.990 - 141.888i) q^{62} +(91.7442 - 85.1262i) q^{63} +(-161.459 + 202.464i) q^{64} +(-455.481 + 571.155i) q^{65} +(-1261.33 + 1170.35i) q^{66} +(667.449 - 205.881i) q^{67} +(-120.346 - 306.636i) q^{68} +(786.619 - 536.308i) q^{69} +(-379.886 - 182.944i) q^{70} +(-517.355 - 480.035i) q^{71} +(-136.634 + 20.5943i) q^{72} +(40.2931 - 537.674i) q^{73} +(-45.2777 + 115.366i) q^{74} +(307.558 + 1347.50i) q^{75} +(-42.6866 - 569.614i) q^{76} +(-393.984 - 121.528i) q^{77} +(942.774 - 454.016i) q^{78} +(352.610 - 610.739i) q^{79} +(679.422 + 1176.79i) q^{80} +(-715.938 - 488.118i) q^{81} +(-89.3916 + 391.650i) q^{82} +(1355.60 + 204.323i) q^{83} +(164.153 + 205.841i) q^{84} -962.279 q^{85} +(1041.92 + 204.979i) q^{86} -120.836 q^{87} +(283.817 + 355.896i) q^{88} +(-489.470 - 73.7758i) q^{89} +(305.574 - 1338.81i) q^{90} +(207.168 + 141.245i) q^{91} +(428.432 + 742.066i) q^{92} +(-439.034 + 760.429i) q^{93} +(915.900 - 441.074i) q^{94} +(-1594.52 - 491.843i) q^{95} +(-117.345 - 1565.86i) q^{96} +(-84.1275 - 368.587i) q^{97} +(419.052 - 1067.73i) q^{98} +(100.349 - 1339.06i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q - 12 q^{2} - 9 q^{3} - 92 q^{4} + 5 q^{5} - 22 q^{6} - 54 q^{7} + 2 q^{8} + 201 q^{9}+O(q^{10}) \) 120 * q - 12 * q^2 - 9 * q^3 - 92 * q^4 + 5 * q^5 - 22 * q^6 - 54 * q^7 + 2 * q^8 + 201 * q^9	\( 120 q - 12 q^{2} - 9 q^{3} - 92 q^{4} + 5 q^{5} - 22 q^{6} - 54 q^{7} + 2 q^{8} + 201 q^{9} - 41 q^{10} - 68 q^{11} + 114 q^{12} - 167 q^{13} + 254 q^{14} - 163 q^{15} - 344 q^{16} + 68 q^{17} - 72 q^{18} - 407 q^{19} + 621 q^{20} + 193 q^{21} - 520 q^{22} - 219 q^{23} + 1072 q^{24} - 87 q^{25} - 133 q^{26} + 180 q^{27} + 1228 q^{28} - 17 q^{29} - 1796 q^{30} - 953 q^{31} - 2730 q^{32} + 473 q^{33} - 1043 q^{34} - 241 q^{35} - 175 q^{36} - 228 q^{37} + 1512 q^{38} + 1250 q^{39} + 2673 q^{40} - 236 q^{41} + 5286 q^{42} + 1789 q^{43} - 2756 q^{44} + 856 q^{45} + 4331 q^{46} + 962 q^{47} + 5243 q^{48} - 1264 q^{49} - 3273 q^{50} - 4803 q^{51} - 3538 q^{52} - 1375 q^{53} - 2646 q^{54} - 1460 q^{55} - 3305 q^{56} - 719 q^{57} + 142 q^{58} + 1202 q^{59} + 4043 q^{60} + 837 q^{61} - 3959 q^{62} + 3279 q^{63} + 5718 q^{64} + 54 q^{65} - 3457 q^{66} + 1384 q^{67} - 747 q^{68} - 4715 q^{69} - 2553 q^{70} - 1619 q^{71} - 20137 q^{72} - 3630 q^{73} - 5006 q^{74} - 1186 q^{75} + 1092 q^{76} + 3515 q^{77} + 2980 q^{78} + 4422 q^{79} - 1610 q^{80} - 4089 q^{81} + 5292 q^{82} + 10398 q^{83} + 17399 q^{84} + 8666 q^{85} + 1858 q^{86} + 2754 q^{87} + 7290 q^{88} + 11478 q^{89} + 29113 q^{90} + 11920 q^{91} + 3286 q^{92} - 4 q^{93} - 14736 q^{94} - 1741 q^{95} - 6200 q^{96} + 2236 q^{97} - 5254 q^{98} - 7417 q^{99}+O(q^{100}) \) 120 * q - 12 * q^2 - 9 * q^3 - 92 * q^4 + 5 * q^5 - 22 * q^6 - 54 * q^7 + 2 * q^8 + 201 * q^9 - 41 * q^10 - 68 * q^11 + 114 * q^12 - 167 * q^13 + 254 * q^14 - 163 * q^15 - 344 * q^16 + 68 * q^17 - 72 * q^18 - 407 * q^19 + 621 * q^20 + 193 * q^21 - 520 * q^22 - 219 * q^23 + 1072 * q^24 - 87 * q^25 - 133 * q^26 + 180 * q^27 + 1228 * q^28 - 17 * q^29 - 1796 * q^30 - 953 * q^31 - 2730 * q^32 + 473 * q^33 - 1043 * q^34 - 241 * q^35 - 175 * q^36 - 228 * q^37 + 1512 * q^38 + 1250 * q^39 + 2673 * q^40 - 236 * q^41 + 5286 * q^42 + 1789 * q^43 - 2756 * q^44 + 856 * q^45 + 4331 * q^46 + 962 * q^47 + 5243 * q^48 - 1264 * q^49 - 3273 * q^50 - 4803 * q^51 - 3538 * q^52 - 1375 * q^53 - 2646 * q^54 - 1460 * q^55 - 3305 * q^56 - 719 * q^57 + 142 * q^58 + 1202 * q^59 + 4043 * q^60 + 837 * q^61 - 3959 * q^62 + 3279 * q^63 + 5718 * q^64 + 54 * q^65 - 3457 * q^66 + 1384 * q^67 - 747 * q^68 - 4715 * q^69 - 2553 * q^70 - 1619 * q^71 - 20137 * q^72 - 3630 * q^73 - 5006 * q^74 - 1186 * q^75 + 1092 * q^76 + 3515 * q^77 + 2980 * q^78 + 4422 * q^79 - 1610 * q^80 - 4089 * q^81 + 5292 * q^82 + 10398 * q^83 + 17399 * q^84 + 8666 * q^85 + 1858 * q^86 + 2754 * q^87 + 7290 * q^88 + 11478 * q^89 + 29113 * q^90 + 11920 * q^91 + 3286 * q^92 - 4 * q^93 - 14736 * q^94 - 1741 * q^95 - 6200 * q^96 + 2236 * q^97 - 5254 * q^98 - 7417 * q^99

Introduction

L-functions

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