LMFDB - Embedded newform 121.4.c.i.81.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [121,4,Mod(3,121)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(121, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([8]))

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

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

chi := DirichletCharacter("121.3");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 121 = 11^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	121.c (of order $5$, degree $4$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.13923111069$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.29283765625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 10x^{6} - 19x^{5} + 109x^{4} + 171x^{3} + 810x^{2} + 729x + 6561 $ x^8 - x^7 + 10x^6 - 19x^5 + 109x^4 + 171x^3 + 810x^2 + 729x + 6561
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 11)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			81.1
Root			$2.86504 + 2.08157i$ of defining polynomial
Character	$\chi$	$=$	121.81
Dual form			121.4.c.i.3.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.747004 - 0.542730i) q^{2} +(-0.476313 + 1.46594i) q^{3} +(-2.20868 - 6.79761i) q^{4} +(-7.05908 + 5.12872i) q^{5} +(1.15142 - 0.836554i) q^{6} +(-0.239524 - 0.737179i) q^{7} +(-4.32202 + 13.3018i) q^{8} +(19.9214 + 14.4737i) q^{9} +O(q^{10})$	\(q+(-0.747004 - 0.542730i) q^{2} +(-0.476313 + 1.46594i) q^{3} +(-2.20868 - 6.79761i) q^{4} +(-7.05908 + 5.12872i) q^{5} +(1.15142 - 0.836554i) q^{6} +(-0.239524 - 0.737179i) q^{7} +(-4.32202 + 13.3018i) q^{8} +(19.9214 + 14.4737i) q^{9} +8.05666 q^{10} +11.0169 q^{12} +(52.2644 + 37.9723i) q^{13} +(-0.221164 + 0.680672i) q^{14} +(-4.15607 - 12.7911i) q^{15} +(-35.8113 + 26.0184i) q^{16} +(56.7325 - 41.2186i) q^{17} +(-7.02601 - 21.6238i) q^{18} +(-40.0535 + 123.272i) q^{19} +(50.4542 + 36.6572i) q^{20} +1.19475 q^{21} +103.308 q^{23} +(-17.4410 - 12.6716i) q^{24} +(-15.1003 + 46.4740i) q^{25} +(-18.4330 - 56.7309i) q^{26} +(-64.3755 + 46.7715i) q^{27} +(-4.48202 + 3.25638i) q^{28} +(21.2472 + 65.3921i) q^{29} +(-3.83749 + 11.8106i) q^{30} +(-4.63339 - 3.36636i) q^{31} +152.763 q^{32} -64.7499 q^{34} +(5.47160 + 3.97535i) q^{35} +(54.3868 - 167.385i) q^{36} +(53.2416 + 163.861i) q^{37} +(96.8236 - 70.3464i) q^{38} +(-80.5593 + 58.5298i) q^{39} +(-37.7117 - 116.065i) q^{40} +(65.3332 - 201.075i) q^{41} +(-0.892481 - 0.648426i) q^{42} -300.793 q^{43} -214.858 q^{45} +(-77.1713 - 56.0682i) q^{46} +(-59.0277 + 181.669i) q^{47} +(-21.0841 - 64.8901i) q^{48} +(277.007 - 201.257i) q^{49} +(36.5029 - 26.5209i) q^{50} +(33.4015 + 102.799i) q^{51} +(142.686 - 439.141i) q^{52} +(-519.068 - 377.125i) q^{53} +73.4730 q^{54} +10.8410 q^{56} +(-161.632 - 117.432i) q^{57} +(19.6185 - 60.3796i) q^{58} +(16.0697 + 49.4574i) q^{59} +(-77.7692 + 56.5027i) q^{60} +(-398.663 + 289.646i) q^{61} +(1.63414 + 5.02936i) q^{62} +(5.89807 - 18.1524i) q^{63} +(172.376 + 125.238i) q^{64} -563.687 q^{65} -320.988 q^{67} +(-405.491 - 294.607i) q^{68} +(-49.2068 + 151.443i) q^{69} +(-1.92976 - 5.93920i) q^{70} +(147.737 - 107.337i) q^{71} +(-278.627 + 202.434i) q^{72} +(64.2516 + 197.746i) q^{73} +(49.1605 - 151.300i) q^{74} +(-60.9357 - 44.2724i) q^{75} +926.421 q^{76} +91.9439 q^{78} +(528.180 + 383.745i) q^{79} +(119.353 - 367.332i) q^{80} +(167.549 + 515.663i) q^{81} +(-157.933 + 114.745i) q^{82} +(972.740 - 706.737i) q^{83} +(-2.63881 - 8.12143i) q^{84} +(-189.080 + 581.930i) q^{85} +(224.694 + 163.249i) q^{86} -105.981 q^{87} +716.942 q^{89} +(160.500 + 116.610i) q^{90} +(15.4738 - 47.6234i) q^{91} +(-228.174 - 702.246i) q^{92} +(7.14183 - 5.18884i) q^{93} +(142.691 - 103.671i) q^{94} +(-349.487 - 1075.61i) q^{95} +(-72.7629 + 223.941i) q^{96} +(508.361 + 369.346i) q^{97} -316.153 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 7 q^{2} - 3 q^{3} + 3 q^{4} - 7 q^{5} + 29 q^{6} + 35 q^{7} - 47 q^{8} + 31 q^{9}+O(q^{10}) $ 8 * q + 7 * q^2 - 3 * q^3 + 3 * q^4 - 7 * q^5 + 29 * q^6 + 35 * q^7 - 47 * q^8 + 31 * q^9	\( 8 q + 7 q^{2} - 3 q^{3} + 3 q^{4} - 7 q^{5} + 29 q^{6} + 35 q^{7} - 47 q^{8} + 31 q^{9} - 40 q^{10} + 190 q^{12} + 65 q^{13} - 196 q^{14} - 121 q^{15} - 377 q^{16} + 31 q^{17} + 102 q^{18} - 148 q^{19} + 342 q^{20} - 334 q^{21} - 12 q^{23} + 447 q^{24} - 201 q^{25} - 140 q^{26} + 72 q^{27} + 42 q^{28} + 199 q^{29} + 114 q^{30} - 361 q^{31} - 324 q^{32} - 298 q^{34} - 237 q^{35} + 120 q^{36} + 81 q^{37} - 52 q^{38} - 365 q^{39} - 532 q^{40} + 31 q^{41} + 170 q^{42} + 650 q^{43} + 452 q^{45} - 1204 q^{46} + 857 q^{47} + 644 q^{48} + 1375 q^{49} + 147 q^{50} + 246 q^{51} + 590 q^{52} - 1493 q^{53} + 3100 q^{54} - 1560 q^{56} - 102 q^{57} + 1392 q^{58} + 676 q^{59} + 1068 q^{60} + 525 q^{61} - 2456 q^{62} + 68 q^{63} + 471 q^{64} - 1790 q^{65} + 86 q^{67} - 710 q^{68} - 42 q^{69} - 144 q^{70} + 1143 q^{71} - 919 q^{72} + 2155 q^{73} + 1476 q^{74} - 160 q^{75} + 242 q^{76} - 1340 q^{78} + 861 q^{79} - 1916 q^{80} - 26 q^{81} - 3497 q^{82} - 52 q^{83} + 84 q^{84} - 2383 q^{85} + 1061 q^{86} - 2310 q^{87} + 3782 q^{89} + 1682 q^{90} + 135 q^{91} - 2450 q^{92} - 2077 q^{93} - 702 q^{94} + 1317 q^{95} - 1252 q^{96} - 1344 q^{97} - 2740 q^{98}+O(q^{100}) \) 8 * q + 7 * q^2 - 3 * q^3 + 3 * q^4 - 7 * q^5 + 29 * q^6 + 35 * q^7 - 47 * q^8 + 31 * q^9 - 40 * q^10 + 190 * q^12 + 65 * q^13 - 196 * q^14 - 121 * q^15 - 377 * q^16 + 31 * q^17 + 102 * q^18 - 148 * q^19 + 342 * q^20 - 334 * q^21 - 12 * q^23 + 447 * q^24 - 201 * q^25 - 140 * q^26 + 72 * q^27 + 42 * q^28 + 199 * q^29 + 114 * q^30 - 361 * q^31 - 324 * q^32 - 298 * q^34 - 237 * q^35 + 120 * q^36 + 81 * q^37 - 52 * q^38 - 365 * q^39 - 532 * q^40 + 31 * q^41 + 170 * q^42 + 650 * q^43 + 452 * q^45 - 1204 * q^46 + 857 * q^47 + 644 * q^48 + 1375 * q^49 + 147 * q^50 + 246 * q^51 + 590 * q^52 - 1493 * q^53 + 3100 * q^54 - 1560 * q^56 - 102 * q^57 + 1392 * q^58 + 676 * q^59 + 1068 * q^60 + 525 * q^61 - 2456 * q^62 + 68 * q^63 + 471 * q^64 - 1790 * q^65 + 86 * q^67 - 710 * q^68 - 42 * q^69 - 144 * q^70 + 1143 * q^71 - 919 * q^72 + 2155 * q^73 + 1476 * q^74 - 160 * q^75 + 242 * q^76 - 1340 * q^78 + 861 * q^79 - 1916 * q^80 - 26 * q^81 - 3497 * q^82 - 52 * q^83 + 84 * q^84 - 2383 * q^85 + 1061 * q^86 - 2310 * q^87 + 3782 * q^89 + 1682 * q^90 + 135 * q^91 - 2450 * q^92 - 2077 * q^93 - 702 * q^94 + 1317 * q^95 - 1252 * q^96 - 1344 * q^97 - 2740 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/121\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{5}\right)$

Coefficient data

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

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

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

$2$	−0.747004	−	0.542730i	−0.264106	−	0.191884i	0.447849	−	0.894109i	$-0.352190\pi$
$2$	−0.747004	−	0.542730i	−0.264106	−	0.191884i	−0.711955	+	0.702225i	$0.752190\pi$
$3$	−0.476313	+	1.46594i	−0.0916665	+	0.282120i	−0.986371	−	0.164539i	$-0.947386\pi$
$3$	−0.476313	+	1.46594i	−0.0916665	+	0.282120i	0.894704	+	0.446659i	$0.147386\pi$
$4$	−2.20868	−	6.79761i	−0.276085	−	0.849701i
$5$	−7.05908	+	5.12872i	−0.631383	+	0.458727i	−0.856879	−	0.515518i	$-0.827600\pi$
$5$	−7.05908	+	5.12872i	−0.631383	+	0.458727i	0.225496	+	0.974244i	$0.427600\pi$
$6$	1.15142	−	0.836554i	0.0783440	−	0.0569203i
$7$	−0.239524	−	0.737179i	−0.0129331	−	0.0398039i	0.944382	−	0.328851i	$-0.106661\pi$
$7$	−0.239524	−	0.737179i	−0.0129331	−	0.0398039i	−0.957315	+	0.289047i	$0.906661\pi$
$8$	−4.32202	+	13.3018i	−0.191008	+	0.587862i
$9$	19.9214	+	14.4737i	0.737828	+	0.536063i
$10$	8.05666			0.254774
$11$		0			0
$11$		0			0
$12$	11.0169			0.265026
$13$	52.2644	+	37.9723i	1.11504	+	0.810124i	0.983450	−	0.181180i	$-0.0579917\pi$
$13$	52.2644	+	37.9723i	1.11504	+	0.810124i	0.131590	+	0.991304i	$0.457992\pi$
$14$	−0.221164	+	0.680672i	−0.00422203	+	0.0129941i
$15$	−4.15607	−	12.7911i	−0.0715395	−	0.220176i
$16$	−35.8113	+	26.0184i	−0.559551	+	0.406538i
$17$	56.7325	−	41.2186i	0.809391	−	0.588057i	−0.104263	−	0.994550i	$-0.533248\pi$
$17$	56.7325	−	41.2186i	0.809391	−	0.588057i	0.913654	+	0.406493i	$0.133248\pi$
$18$	−7.02601	−	21.6238i	−0.0920025	−	0.283155i
$19$	−40.0535	+	123.272i	−0.483627	+	1.48845i	0.350333	+	0.936625i	$0.386068\pi$
$19$	−40.0535	+	123.272i	−0.483627	+	1.48845i	−0.833960	+	0.551825i	$0.813932\pi$
$20$	50.4542	+	36.6572i	0.564096	+	0.409839i
$21$	1.19475			0.0124150
$22$		0			0
$23$	103.308			0.936572			0.468286	−	0.883577i	$-0.344872\pi$
$23$	103.308			0.936572			0.468286	+	0.883577i	$0.344872\pi$
$24$	−17.4410	−	12.6716i	−0.148339	−	0.107774i
$25$	−15.1003	+	46.4740i	−0.120803	+	0.371792i
$26$	−18.4330	−	56.7309i	−0.139039	−	0.427917i
$27$	−64.3755	+	46.7715i	−0.458854	+	0.333377i
$28$	−4.48202	+	3.25638i	−0.0302508	+	0.0219785i
$29$	21.2472	+	65.3921i	0.136052	+	0.418724i	0.995752	−	0.0920744i	$-0.0293498\pi$
$29$	21.2472	+	65.3921i	0.136052	+	0.418724i	−0.859700	+	0.510799i	$0.829350\pi$
$30$	−3.83749	+	11.8106i	−0.0233542	+	0.0718770i
$31$	−4.63339	−	3.36636i	−0.0268446	−	0.0195037i	0.574282	−	0.818658i	$-0.305281\pi$
$31$	−4.63339	−	3.36636i	−0.0268446	−	0.0195037i	−0.601127	+	0.799154i	$0.705281\pi$
$32$	152.763			0.843903
$33$		0			0
$34$	−64.7499			−0.326604
$35$	5.47160	+	3.97535i	0.0264248	+	0.0191988i
$36$	54.3868	−	167.385i	0.251791	−	0.774932i
$37$	53.2416	+	163.861i	0.236564	+	0.728069i	0.996910	+	0.0785508i	$0.0250293\pi$
$37$	53.2416	+	163.861i	0.236564	+	0.728069i	−0.760346	+	0.649518i	$0.774971\pi$
$38$	96.8236	−	70.3464i	0.413338	−	0.300308i
$39$	−80.5593	+	58.5298i	−0.330764	+	0.240314i
$40$	−37.7117	−	116.065i	−0.149069	−	0.458786i
$41$	65.3332	−	201.075i	0.248862	−	0.765917i	−0.746116	−	0.665816i	$-0.768083\pi$
$41$	65.3332	−	201.075i	0.248862	−	0.765917i	0.994977	−	0.100101i	$-0.0319166\pi$
$42$	−0.892481	−	0.648426i	−0.00327888	−	0.00238224i
$43$	−300.793			−1.06676			−0.533378	−	0.845877i	$-0.679078\pi$
$43$	−300.793			−1.06676			−0.533378	+	0.845877i	$0.679078\pi$
$44$		0			0
$45$	−214.858			−0.711758
$46$	−77.1713	−	56.0682i	−0.247354	−	0.179713i
$47$	−59.0277	+	181.669i	−0.183193	+	0.563811i	−0.999913	−	0.0132245i	$-0.995790\pi$
$47$	−59.0277	+	181.669i	−0.183193	+	0.563811i	0.816719	+	0.577035i	$0.195790\pi$
$48$	−21.0841	−	64.8901i	−0.0634005	−	0.195127i
$49$	277.007	−	201.257i	0.807600	−	0.586756i
$50$	36.5029	−	26.5209i	0.103246	−	0.0750124i
$51$	33.4015	+	102.799i	0.0917089	+	0.282251i
$52$	142.686	−	439.141i	0.380518	−	1.17111i
$53$	−519.068	−	377.125i	−1.34527	−	0.977398i	−0.999232	−	0.0391779i	$-0.987526\pi$
$53$	−519.068	−	377.125i	−1.34527	−	0.977398i	−0.346040	−	0.938220i	$-0.612474\pi$
$54$	73.4730			0.185156
$55$		0			0
$56$	10.8410			0.0258695
$57$	−161.632	−	117.432i	−0.375590	−	0.272882i
$58$	19.6185	−	60.3796i	0.0444145	−	0.136694i
$59$	16.0697	+	49.4574i	0.0354592	+	0.109132i	0.967219	−	0.253942i	$-0.0817272\pi$
$59$	16.0697	+	49.4574i	0.0354592	+	0.109132i	−0.931760	+	0.363074i	$0.881727\pi$
$60$	−77.7692	+	56.5027i	−0.167333	+	0.121574i
$61$	−398.663	+	289.646i	−0.836780	+	0.607956i	−0.921469	−	0.388451i	$-0.873010\pi$
$61$	−398.663	+	289.646i	−0.836780	+	0.607956i	0.0846894	+	0.996407i	$0.473010\pi$
$62$	1.63414	+	5.02936i	0.00334735	+	0.0103021i
$63$	5.89807	−	18.1524i	0.0117950	−	0.0363014i
$64$	172.376	+	125.238i	0.336672	+	0.244606i
$65$	−563.687			−1.07564
$66$		0			0
$67$	−320.988			−0.585298			−0.292649	−	0.956220i	$-0.594537\pi$
$67$	−320.988			−0.585298			−0.292649	+	0.956220i	$0.594537\pi$
$68$	−405.491	−	294.607i	−0.723133	−	0.525387i
$69$	−49.2068	+	151.443i	−0.0858523	+	0.264226i
$70$	−1.92976	−	5.93920i	−0.00329501	−	0.0101410i
$71$	147.737	−	107.337i	0.246945	−	0.179416i	−0.457427	−	0.889247i	$-0.651229\pi$
$71$	147.737	−	107.337i	0.246945	−	0.179416i	0.704372	+	0.709831i	$0.251229\pi$
$72$	−278.627	+	202.434i	−0.456062	+	0.331349i
$73$	64.2516	+	197.746i	0.103015	+	0.317047i	0.989259	−	0.146171i	$-0.0466948\pi$
$73$	64.2516	+	197.746i	0.103015	+	0.317047i	−0.886245	+	0.463218i	$0.846695\pi$
$74$	49.1605	−	151.300i	0.0772269	−	0.237680i
$75$	−60.9357	−	44.2724i	−0.0938167	−	0.0681618i
$76$	926.421			1.39826
$77$		0			0
$78$	91.9439			0.133469
$79$	528.180	+	383.745i	0.752214	+	0.546516i	0.896512	−	0.443019i	$-0.146092\pi$
$79$	528.180	+	383.745i	0.752214	+	0.546516i	−0.144298	+	0.989534i	$0.546092\pi$
$80$	119.353	−	367.332i	0.166801	−	0.513362i
$81$	167.549	+	515.663i	0.229834	+	0.707357i
$82$	−157.933	+	114.745i	−0.212693	+	0.154531i
$83$	972.740	−	706.737i	1.28641	−	0.934632i	0.286684	−	0.958025i	$-0.407447\pi$
$83$	972.740	−	706.737i	1.28641	−	0.934632i	0.999726	+	0.0233931i	$0.00744694\pi$
$84$	−2.63881	−	8.12143i	−0.00342760	−	0.0105491i
$85$	−189.080	+	581.930i	−0.241278	+	0.742578i
$86$	224.694	+	163.249i	0.281736	+	0.204693i
$87$	−105.981			−0.130602
$88$		0			0
$89$	716.942			0.853885			0.426942	−	0.904279i	$-0.359591\pi$
$89$	716.942			0.853885			0.426942	+	0.904279i	$0.359591\pi$
$90$	160.500	+	116.610i	0.187979	+	0.136575i
$91$	15.4738	−	47.6234i	0.0178252	−	0.0548603i
$92$	−228.174	−	702.246i	−0.258573	−	0.795807i
$93$	7.14183	−	5.18884i	0.00796315	−	0.00578557i
$94$	142.691	−	103.671i	0.156569	−	0.113754i
$95$	−349.487	−	1075.61i	−0.377438	−	1.16163i
$96$	−72.7629	+	223.941i	−0.0773577	+	0.238082i
$97$	508.361	+	369.346i	0.532126	+	0.386612i	0.821152	−	0.570709i	$-0.193332\pi$
$97$	508.361	+	369.346i	0.532126	+	0.386612i	−0.289026	+	0.957321i	$0.593332\pi$
$98$	−316.153			−0.325881
$99$		0			0
$100$	349.264			0.349264
$101$	411.960	+	299.307i	0.405857	+	0.294872i	0.771922	−	0.635717i	$-0.219295\pi$
$101$	411.960	+	299.307i	0.405857	+	0.294872i	−0.366065	+	0.930589i	$0.619295\pi$
$102$	30.8412	−	94.9195i	0.0299386	−	0.0921415i
$103$	−54.0555	−	166.366i	−0.0517111	−	0.159150i	0.921866	−	0.387509i	$-0.126664\pi$
$103$	−54.0555	−	166.366i	−0.0517111	−	0.159150i	−0.973577	+	0.228358i	$0.926664\pi$
$104$	−730.987	+	531.093i	−0.689223	+	0.500750i
$105$	−8.43382	+	6.12753i	−0.00783863	+	0.00569510i
$106$	183.069	+	563.427i	0.167747	+	0.516273i
$107$	−546.753	+	1682.73i	−0.493987	+	1.52034i	0.324543	+	0.945871i	$0.394790\pi$
$107$	−546.753	+	1682.73i	−0.493987	+	1.52034i	−0.818530	+	0.574464i	$0.805210\pi$
$108$	460.119	+	334.296i	0.409954	+	0.297849i
$109$	823.593			0.723724			0.361862	−	0.932232i	$-0.382141\pi$
$109$	823.593			0.723724			0.361862	+	0.932232i	$0.382141\pi$
$110$		0			0
$111$	−265.570			−0.227088
$112$	27.7579	+	20.1673i	0.0234185	+	0.0170145i
$113$	−336.492	+	1035.62i	−0.280128	+	0.862146i	0.707689	+	0.706525i	$0.249738\pi$
$113$	−336.492	+	1035.62i	−0.280128	+	0.862146i	−0.987817	+	0.155621i	$0.950262\pi$
$114$	57.0054	+	175.445i	0.0468337	+	0.144139i
$115$	−729.257	+	529.837i	−0.591336	+	0.429631i
$116$	397.582	−	288.860i	0.318229	−	0.231207i
$117$	491.577	+	1512.92i	0.388430	+	1.19546i
$118$	14.8379	−	45.6663i	0.0115758	−	0.0356265i
$119$	−43.9742	−	31.9491i	−0.0338749	−	0.0246115i
$120$	188.107			0.143098
$121$		0			0
$122$	455.002			0.337655
$123$	263.645	+	191.549i	0.193269	+	0.140418i
$124$	−12.6495	+	38.9312i	−0.00916097	+	0.0281946i
$125$	−468.799	−	1442.81i	−0.335445	−	1.03239i
$126$	−14.2577	+	10.3588i	−0.0100808	+	0.00732412i
$127$	−1015.52	+	737.819i	−0.709551	+	0.515519i	−0.883029	−	0.469319i	$-0.844499\pi$
$127$	−1015.52	+	737.819i	−0.709551	+	0.515519i	0.173478	+	0.984838i	$0.444499\pi$
$128$	−438.445	−	1349.40i	−0.302761	−	0.931804i
$129$	143.272	−	440.945i	0.0977858	−	0.300954i
$130$	421.076	+	305.930i	0.284083	+	0.206399i
$131$	−1401.18			−0.934519			−0.467259	−	0.884120i	$-0.654759\pi$
$131$	−1401.18			−0.934519			−0.467259	+	0.884120i	$0.654759\pi$
$132$		0			0
$133$	100.467			0.0655009
$134$	239.779	+	174.210i	0.154581	+	0.112309i
$135$	214.553	−	660.328i	0.136784	−	0.420977i
$136$	303.082	+	932.791i	0.191096	+	0.588134i
$137$	331.158	−	240.600i	0.206516	−	0.150043i	−0.479720	−	0.877422i	$-0.659262\pi$
$137$	331.158	−	240.600i	0.206516	−	0.150043i	0.686236	+	0.727379i	$0.259262\pi$
$138$	118.950	−	86.4225i	0.0733748	−	0.0533099i
$139$	−183.982	−	566.240i	−0.112268	−	0.345524i	0.879100	−	0.476638i	$-0.158145\pi$
$139$	−183.982	−	566.240i	−0.112268	−	0.345524i	−0.991367	+	0.131114i	$0.958145\pi$
$140$	14.9379	−	45.9741i	0.00901772	−	0.0277537i
$141$	−238.200	−	173.062i	−0.142270	−	0.103365i
$142$	−168.615			−0.0996468
$143$		0			0
$144$	−1089.99			−0.630783
$145$	−485.363	−	352.637i	−0.277981	−	0.201965i
$146$	59.3265	−	182.588i	0.0336294	−	0.103501i
$147$	163.089	+	501.937i	0.0915059	+	0.281626i
$148$	996.268	−	723.831i	0.553329	−	0.402017i
$149$	1755.64	−	1275.54i	0.965283	−	0.701319i	0.0109117	−	0.999940i	$-0.496527\pi$
$149$	1755.64	−	1275.54i	0.965283	−	0.701319i	0.954372	+	0.298621i	$0.0965266\pi$
$150$	21.4912	+	66.1433i	0.0116984	+	0.0360038i
$151$	555.847	−	1710.72i	0.299564	−	0.921963i	−0.682086	−	0.731272i	$-0.738927\pi$
$151$	555.847	−	1710.72i	0.299564	−	0.921963i	0.981650	−	0.190691i	$-0.0610729\pi$
$152$	−1466.63	−	1065.57i	−0.782627	−	0.568612i
$153$	1726.77			0.912427
$154$		0			0
$155$	49.9726			0.0258961
$156$	575.792	+	418.337i	0.295514	+	0.214704i
$157$	−24.2312	+	74.5758i	−0.0123176	+	0.0379095i	−0.957026	−	0.290001i	$-0.906344\pi$
$157$	−24.2312	+	74.5758i	−0.0123176	+	0.0379095i	0.944709	+	0.327910i	$0.106344\pi$
$158$	−186.282	−	573.318i	−0.0937964	−	0.288676i
$159$	800.081	−	581.293i	0.399060	−	0.289934i
$160$	−1078.36	+	783.478i	−0.532826	+	0.387121i
$161$	−24.7447	−	76.1563i	−0.0121128	−	0.0372792i
$162$	154.706	−	476.136i	0.0750300	−	0.230918i
$163$	−266.032	−	193.283i	−0.127836	−	0.0928780i	0.522030	−	0.852927i	$-0.325175\pi$
$163$	−266.032	−	193.283i	−0.127836	−	0.0928780i	−0.649866	+	0.760049i	$0.725175\pi$
$164$	−1511.13			−0.719508
$165$		0			0
$166$	−1110.21			−0.519089
$167$	−2850.77	−	2071.21i	−1.32095	−	0.959729i	−0.999920	−	0.0126616i	$-0.995970\pi$
$167$	−2850.77	−	2071.21i	−1.32095	−	0.959729i	−0.321034	−	0.947068i	$-0.604030\pi$
$168$	−5.16372	+	15.8923i	−0.00237137	+	0.00729832i
$169$	610.758	+	1879.72i	0.277997	+	0.855585i
$170$	457.075	−	332.084i	0.206212	−	0.149822i
$171$	−2582.12	+	1876.02i	−1.15474	+	0.838965i
$172$	664.355	+	2044.67i	0.294515	+	0.906424i
$173$	836.578	−	2574.72i	0.367652	−	1.13152i	−0.580651	−	0.814152i	$-0.697202\pi$
$173$	836.578	−	2574.72i	0.367652	−	1.13152i	0.948304	−	0.317365i	$-0.102798\pi$
$174$	79.1684	+	57.5192i	0.0344927	+	0.0250604i
$175$	37.8766			0.0163611
$176$		0			0
$177$	−80.1558			−0.0340389
$178$	−535.559	−	389.106i	−0.225516	−	0.163847i
$179$	455.234	−	1401.07i	0.190088	−	0.585032i	−0.809910	−	0.586554i	$-0.800484\pi$
$179$	455.234	−	1401.07i	0.190088	−	0.585032i	0.999999	+	0.00152166i	$0.000484359\pi$
$180$	474.552	+	1460.52i	0.196506	+	0.604782i
$181$	398.134	−	289.261i	0.163498	−	0.118788i	−0.503028	−	0.864270i	$-0.667781\pi$
$181$	398.134	−	289.261i	0.163498	−	0.118788i	0.666526	+	0.745482i	$0.267781\pi$
$182$	−37.4056	+	27.1768i	−0.0152346	+	0.0110686i
$183$	−234.715	−	722.378i	−0.0948122	−	0.291802i
$184$	−446.498	+	1374.18i	−0.178893	+	0.550575i
$185$	−1216.23	−	883.644i	−0.483347	−	0.351172i
$186$	−8.15111			−0.00321327
$187$		0			0
$188$	1365.29			0.529647
$189$	49.8984	+	36.2533i	0.0192041	+	0.0139526i
$190$	−322.698	+	993.162i	−0.123216	+	0.379219i
$191$	−399.844	−	1230.59i	−0.151475	−	0.466192i	0.846312	−	0.532688i	$-0.178818\pi$
$191$	−399.844	−	1230.59i	−0.151475	−	0.466192i	−0.997787	+	0.0664961i	$0.978818\pi$
$192$	−265.697	+	193.040i	−0.0998700	+	0.0725598i
$193$	−424.037	+	308.081i	−0.158149	+	0.114902i	−0.664046	−	0.747692i	$-0.731162\pi$
$193$	−424.037	+	308.081i	−0.158149	+	0.114902i	0.505896	+	0.862594i	$0.331162\pi$
$194$	−179.292	−	551.805i	−0.0663528	−	0.204213i
$195$	268.491	−	826.332i	0.0986004	−	0.303461i
$196$	−1979.89	−	1438.47i	−0.721533	−	0.524224i
$197$	1177.35			0.425801			0.212900	−	0.977074i	$-0.431709\pi$
$197$	1177.35			0.425801			0.212900	+	0.977074i	$0.431709\pi$
$198$		0			0
$199$	−3054.83			−1.08820			−0.544098	−	0.839022i	$-0.683128\pi$
$199$	−3054.83			−1.08820			−0.544098	+	0.839022i	$0.683128\pi$
$200$	−552.924	−	401.723i	−0.195488	−	0.142031i
$201$	152.891	−	470.550i	0.0536522	−	0.165125i
$202$	−145.293	−	447.166i	−0.0506079	−	0.155755i
$203$	43.1164	−	31.3259i	0.0149073	−	0.0108308i
$204$	625.017	−	454.101i	0.214509	−	0.155850i
$205$	570.064	+	1754.48i	0.194220	+	0.597747i
$206$	−49.9120	+	153.613i	−0.0168812	+	0.0519551i
$207$	2058.03	+	1495.25i	0.691029	+	0.502062i
$208$	−2859.63			−0.953269
$209$		0			0
$210$	9.62569			0.00316303
$211$	1379.08	+	1001.96i	0.449953	+	0.326910i	0.789577	−	0.613651i	$-0.210300\pi$
$211$	1379.08	+	1001.96i	0.449953	+	0.326910i	−0.339624	+	0.940561i	$0.610300\pi$
$212$	−1417.09	+	4361.37i	−0.459087	+	1.41292i
$213$	86.9808	+	267.699i	0.0279804	+	0.0861148i
$214$	1321.70	−	960.268i	0.422193	−	0.306741i
$215$	2123.32	−	1542.68i	0.673532	−	0.489349i
$216$	−343.914	−	1058.46i	−0.108335	−	0.333421i
$217$	−1.37180	+	4.22196i	−0.000429142	+	0.00132076i
$218$	−615.227	−	446.989i	−0.191140	−	0.138871i
$219$	−320.488			−0.0988884
$220$		0			0
$221$	4530.25			1.37890
$222$	198.382	+	144.133i	0.0599752	+	0.0435746i
$223$	1422.26	−	4377.26i	0.427092	−	1.31445i	−0.473886	−	0.880586i	$-0.657149\pi$
$223$	1422.26	−	4377.26i	0.427092	−	1.31445i	0.900977	−	0.433866i	$-0.142851\pi$
$224$	−36.5903	−	112.614i	−0.0109143	−	0.0335907i
$225$	−973.471	+	707.268i	−0.288436	+	0.209561i
$226$	813.420	−	590.984i	0.239415	−	0.173946i
$227$	−1015.88	−	3126.56i	−0.297032	−	0.914171i	−0.982531	−	0.186097i	$-0.940416\pi$
$227$	−1015.88	−	3126.56i	−0.297032	−	0.914171i	0.685499	−	0.728073i	$-0.259584\pi$
$228$	−441.266	+	1358.08i	−0.128174	+	0.394478i
$229$	2387.40	+	1734.55i	0.688925	+	0.500533i	0.876307	−	0.481754i	$-0.160000\pi$
$229$	2387.40	+	1734.55i	0.688925	+	0.500533i	−0.187382	+	0.982287i	$0.560000\pi$
$230$	832.316			0.238614
$231$		0			0
$232$	−961.663			−0.272139
$233$	2283.62	+	1659.14i	0.642080	+	0.466498i	0.860564	−	0.509342i	$-0.170111\pi$
$233$	2283.62	+	1659.14i	0.642080	+	0.466498i	−0.218484	+	0.975840i	$0.570111\pi$
$234$	453.896	−	1396.95i	0.126804	−	0.390262i
$235$	−515.046	−	1585.15i	−0.142970	−	0.440016i
$236$	300.699	−	218.471i	0.0829401	−	0.0602595i
$237$	−814.127	+	591.498i	−0.223136	+	0.162118i
$238$	15.5092	+	47.7323i	0.00422399	+	0.0130001i
$239$	−636.935	+	1960.28i	−0.172385	+	0.530545i	−0.999504	−	0.0314806i	$-0.989978\pi$
$239$	−636.935	+	1960.28i	−0.172385	+	0.530545i	0.827120	+	0.562026i	$0.189978\pi$
$240$	481.637	+	349.930i	0.129540	+	0.0941162i
$241$	3089.45			0.825763			0.412881	−	0.910785i	$-0.364522\pi$
$241$	3089.45			0.825763			0.412881	+	0.910785i	$0.364522\pi$
$242$		0			0
$243$	−2984.19			−0.787803
$244$	2849.42	+	2070.22i	0.747603	+	0.543166i
$245$	−923.220	+	2841.38i	−0.240744	+	0.740935i
$246$	−92.9841	−	286.176i	−0.0240994	−	0.0741703i
$247$	−6774.29	+	4921.81i	−1.74509	+	1.26788i
$248$	64.8042	−	47.0830i	0.0165930	−	0.0120555i
$249$	572.706	+	1762.61i	0.145758	+	0.448597i
$250$	−432.864	+	1332.22i	−0.109507	+	0.337028i
$251$	3259.66	+	2368.28i	0.819712	+	0.595555i	0.916630	−	0.399737i	$-0.130899\pi$
$251$	3259.66	+	2368.28i	0.819712	+	0.595555i	−0.0969183	+	0.995292i	$0.530899\pi$
$252$	−136.420			−0.0341017
$253$		0			0
$254$	1159.03			0.286316
$255$	−763.013	−	554.362i	−0.187379	−	0.136139i
$256$	121.897	−	375.159i	0.0297599	−	0.0915917i
$257$	−1358.89	−	4182.25i	−0.329827	−	1.01510i	−0.969215	−	0.246218i	$-0.920812\pi$
$257$	−1358.89	−	4182.25i	−0.329827	−	1.01510i	0.639388	−	0.768884i	$-0.279188\pi$
$258$	−346.338	+	251.630i	−0.0835740	+	0.0607201i
$259$	108.042	−	78.4971i	0.0259205	−	0.0188323i
$260$	1245.00	+	3831.72i	0.296968	+	0.913975i
$261$	−523.194	+	1610.22i	−0.124080	+	0.381879i
$262$	1046.69	+	760.464i	0.246812	+	0.179319i
$263$	914.661			0.214450			0.107225	−	0.994235i	$-0.465803\pi$
$263$	914.661			0.214450			0.107225	+	0.994235i	$0.465803\pi$
$264$		0			0
$265$	5598.31			1.29774
$266$	−75.0495	−	54.5266i	−0.0172992	−	0.0125686i
$267$	−341.489	+	1051.00i	−0.0782726	+	0.240898i
$268$	708.960	+	2181.95i	0.161592	+	0.497328i
$269$	1430.97	−	1039.66i	0.324341	−	0.235648i	−0.413685	−	0.910420i	$-0.635758\pi$
$269$	1430.97	−	1039.66i	0.324341	−	0.235648i	0.738026	+	0.674773i	$0.235758\pi$
$270$	−518.652	+	376.823i	−0.116904	+	0.0849359i
$271$	−1241.80	−	3821.86i	−0.278353	−	0.856684i	−0.988313	−	0.152441i	$-0.951287\pi$
$271$	−1241.80	−	3821.86i	−0.278353	−	0.856684i	0.709959	−	0.704243i	$-0.248713\pi$
$272$	−959.221	+	2952.18i	−0.213828	+	0.658096i
$273$	62.4428	+	45.3673i	0.0138433	+	0.0100577i
$274$	−377.957			−0.0833330
$275$		0			0
$276$	1138.13			0.248216
$277$	−5376.57	−	3906.30i	−1.16623	−	0.847318i	−0.175680	−	0.984447i	$-0.556212\pi$
$277$	−5376.57	−	3906.30i	−1.16623	−	0.847318i	−0.990553	+	0.137129i	$0.956212\pi$
$278$	−169.880	+	522.836i	−0.0366500	+	0.112797i
$279$	−43.5798	−	134.125i	−0.00935145	−	0.0287808i
$280$	−76.5276	+	55.6006i	−0.0163336	+	0.0118670i
$281$	3545.96	−	2576.29i	0.752792	−	0.546935i	−0.143899	−	0.989592i	$-0.545964\pi$
$281$	3545.96	−	2576.29i	0.752792	−	0.546935i	0.896691	+	0.442657i	$0.145964\pi$
$282$	84.0100	+	258.556i	0.0177402	+	0.0545986i
$283$	−1154.14	+	3552.07i	−0.242425	+	0.746108i	0.753624	+	0.657306i	$0.228304\pi$
$283$	−1154.14	+	3552.07i	−0.242425	+	0.746108i	−0.996049	+	0.0888023i	$0.971696\pi$
$284$	−1055.94	−	767.184i	−0.220628	−	0.160296i
$285$	1743.25			0.362319
$286$		0			0
$287$	−163.877			−0.0337050
$288$	3043.24	+	2211.04i	0.622655	+	0.452386i
$289$	1.40440	−	4.32230i	0.000285854	−	0.000879768i
$290$	171.181	+	526.842i	0.0346625	+	0.106680i
$291$	−783.578	+	569.303i	−0.157849	+	0.114684i
$292$	1202.29	−	873.515i	0.240954	−	0.175064i
$293$	690.705	+	2125.77i	0.137718	+	0.423853i	0.996003	−	0.0893208i	$-0.0284696\pi$
$293$	690.705	+	2125.77i	0.137718	+	0.423853i	−0.858285	+	0.513174i	$0.828470\pi$
$294$	150.588	−	463.462i	0.0298723	−	0.0919376i
$295$	−367.090	−	266.707i	−0.0724502	−	0.0526382i
$296$	−2409.75			−0.473190
$297$		0			0
$298$	−2003.74			−0.389509
$299$	5399.31	+	3922.83i	1.04432	+	0.758740i
$300$	−166.359	+	512.001i	−0.0320158	+	0.0985345i
$301$	72.0471	+	221.738i	0.0137964	+	0.0424611i
$302$	−1343.68	+	976.240i	−0.256027	+	0.186014i
$303$	−634.988	+	461.345i	−0.120393	+	0.0874706i
$304$	−1772.98	−	5456.66i	−0.334497	−	1.02948i
$305$	1328.68	−	4089.26i	0.249443	−	0.767706i
$306$	−1289.91	−	937.171i	−0.240977	−	0.175080i
$307$	−1022.51			−0.190090			−0.0950451	−	0.995473i	$-0.530300\pi$
$307$	−1022.51			−0.190090			−0.0950451	+	0.995473i	$0.530300\pi$
$308$		0			0
$309$	269.629			0.0496398
$310$	−37.3297	−	27.1216i	−0.00683930	−	0.00496905i
$311$	1643.78	−	5059.04i	0.299711	−	0.922417i	−0.681887	−	0.731458i	$-0.738840\pi$
$311$	1643.78	−	5059.04i	0.299711	−	0.922417i	0.981598	−	0.190959i	$-0.0611597\pi$
$312$	−430.372	−	1324.55i	−0.0780931	−	0.240346i
$313$	5657.83	−	4110.65i	1.02172	−	0.742325i	0.0550879	−	0.998482i	$-0.482456\pi$
$313$	5657.83	−	4110.65i	1.02172	−	0.742325i	0.966635	+	0.256156i	$0.0824561\pi$
$314$	58.5753	−	42.5574i	0.0105274	−	0.00764858i
$315$	51.4636	+	158.389i	0.00920522	+	0.0283308i
$316$	1441.97	−	4437.93i	0.256700	−	0.790042i
$317$	−3490.64	−	2536.10i	−0.618467	−	0.449343i	0.233919	−	0.972256i	$-0.424845\pi$
$317$	−3490.64	−	2536.10i	−0.618467	−	0.449343i	−0.852386	+	0.522913i	$0.824845\pi$
$318$	−913.149			−0.161028
$319$		0			0
$320$	−1859.13			−0.324776
$321$	−2206.36	−	1603.01i	−0.383636	−	0.278728i
$322$	−22.8479	+	70.3187i	−0.00395424	+	0.0121699i
$323$	2808.76	+	8644.48i	0.483850	+	1.48914i
$324$	3135.22	−	2277.87i	0.537588	−	0.390581i
$325$	−2553.93	+	1855.54i	−0.435898	+	0.316698i
$326$	93.8260	+	288.767i	0.0159403	+	0.0490592i
$327$	−392.288	+	1207.34i	−0.0663412	+	0.204177i
$328$	2392.29	+	1738.10i	0.402719	+	0.292593i
$329$	148.061			0.0248111
$330$		0			0
$331$	−3886.73			−0.645420			−0.322710	−	0.946498i	$-0.604594\pi$
$331$	−3886.73			−0.645420			−0.322710	+	0.946498i	$0.604594\pi$
$332$	−6952.59	−	5051.35i	−1.14932	−	0.835027i
$333$	−1311.03	+	4034.93i	−0.215748	+	0.664003i
$334$	1005.43	+	3094.40i	0.164715	+	0.506940i
$335$	2265.88	−	1646.26i	0.369547	−	0.268492i
$336$	−42.7855	+	31.0855i	−0.00694684	+	0.00504718i
$337$	2812.70	+	8656.61i	0.454652	+	1.39928i	0.871543	+	0.490319i	$0.163120\pi$
$337$	2812.70	+	8656.61i	0.454652	+	1.39928i	−0.416891	+	0.908956i	$0.636880\pi$
$338$	563.942	−	1735.64i	0.0907527	−	0.279308i
$339$	−1357.88	−	986.554i	−0.217551	−	0.158060i
$340$	4373.35			0.697583
$341$		0			0
$342$	2947.03			0.465957
$343$	−429.801	−	312.269i	−0.0676591	−	0.0491572i
$344$	1300.03	−	4001.09i	0.203759	−	0.627105i
$345$	−429.354	−	1321.42i	−0.0670019	−	0.206211i
$346$	−2022.30	+	1469.29i	−0.314219	+	0.228293i
$347$	−8213.72	+	5967.62i	−1.27071	+	0.923223i	−0.999231	−	0.0392218i	$-0.987512\pi$
$347$	−8213.72	+	5967.62i	−1.27071	+	0.923223i	−0.271477	+	0.962445i	$0.587512\pi$
$348$	234.078	+	720.419i	0.0360572	+	0.110973i
$349$	3297.87	−	10149.8i	0.505820	−	1.55675i	−0.293568	−	0.955938i	$-0.594843\pi$
$349$	3297.87	−	10149.8i	0.505820	−	1.55675i	0.799388	−	0.600815i	$-0.205157\pi$
$350$	−28.2939	−	20.5567i	−0.00432107	−	0.00313944i
$351$	−5140.56			−0.781718
$352$		0			0
$353$	−9301.69			−1.40249			−0.701245	−	0.712920i	$-0.747372\pi$
$353$	−9301.69			−1.40249			−0.701245	+	0.712920i	$0.747372\pi$
$354$	59.8767	+	43.5029i	0.00898986	+	0.00653151i
$355$	−492.383	+	1515.40i	−0.0736141	+	0.226561i
$356$	−1583.49	−	4873.50i	−0.235745	−	0.725547i
$357$	67.7811	−	49.2458i	0.0100486	−	0.00730074i
$358$	−1100.46	+	799.533i	−0.162462	+	0.118035i
$359$	−2594.94	−	7986.40i	−0.381492	−	1.17411i	−0.938993	−	0.343936i	$-0.888240\pi$
$359$	−2594.94	−	7986.40i	−0.381492	−	1.17411i	0.557501	−	0.830176i	$-0.311760\pi$
$360$	928.619	−	2858.00i	0.135951	−	0.418416i
$361$	−8042.67	−	5843.34i	−1.17257	−	0.851924i
$362$	−454.398			−0.0659742
$363$		0			0
$364$	−357.902			−0.0515362
$365$	−1467.74	−	1066.38i	−0.210480	−	0.152922i
$366$	−216.723	+	667.006i	−0.0309517	+	0.0952595i
$367$	−2894.86	−	8909.46i	−0.411745	−	1.26722i	−0.915130	−	0.403158i	$-0.867912\pi$
$367$	−2894.86	−	8909.46i	−0.411745	−	1.26722i	0.503385	−	0.864062i	$-0.332088\pi$
$368$	−3699.59	+	2687.91i	−0.524060	+	0.380752i
$369$	4211.82	−	3060.07i	0.594197	−	0.431710i
$370$	428.950	+	1320.17i	0.0602704	+	0.185493i
$371$	−153.679	+	472.976i	−0.0215057	+	0.0661879i
$372$	−51.0457	−	37.0869i	−0.00711451	−	0.00516899i
$373$	−2639.31			−0.366376			−0.183188	−	0.983078i	$-0.558642\pi$
$373$	−2639.31			−0.366376			−0.183188	+	0.983078i	$0.558642\pi$
$374$		0			0
$375$	2338.38			0.322008
$376$	−2161.40	−	1570.35i	−0.296451	−	0.215385i
$377$	−1372.62	+	4224.48i	−0.187515	+	0.577113i
$378$	−17.5985	−	54.1628i	−0.00239463	−	0.00736992i
$379$	5959.64	−	4329.93i	0.807721	−	0.586843i	−0.105448	−	0.994425i	$-0.533628\pi$
$379$	5959.64	−	4329.93i	0.807721	−	0.586843i	0.913169	+	0.407581i	$0.133628\pi$
$380$	−6539.67	+	4751.35i	−0.882837	+	0.641419i
$381$	−597.893	−	1840.13i	−0.0803963	−	0.247434i
$382$	−369.195	+	1136.27i	−0.0494494	+	0.152189i
$383$	2605.34	+	1892.89i	0.347589	+	0.252538i	0.747857	−	0.663860i	$-0.231083\pi$
$383$	2605.34	+	1892.89i	0.347589	+	0.252538i	−0.400268	+	0.916398i	$0.631083\pi$
$384$	2186.97			0.290634
$385$		0			0
$386$	483.962			0.0638160
$387$	−5992.20	−	4353.59i	−0.787082	−	0.571849i
$388$	1387.86	−	4271.40i	0.181593	−	0.558886i
$389$	3778.65	+	11629.5i	0.492507	+	1.51578i	0.820807	+	0.571206i	$0.193524\pi$
$389$	3778.65	+	11629.5i	0.492507	+	1.51578i	−0.328300	+	0.944574i	$0.606476\pi$
$390$	−649.039	+	471.555i	−0.0842702	+	0.0612259i
$391$	5860.91	−	4258.20i	0.758053	−	0.550758i
$392$	1479.85	+	4554.52i	0.190673	+	0.586832i
$393$	667.402	−	2054.05i	0.0856640	−	0.263647i
$394$	−879.485	−	638.983i	−0.112456	−	0.0817044i
$395$	−5696.59			−0.725636
$396$		0			0
$397$	8381.55			1.05959			0.529796	−	0.848125i	$-0.322269\pi$
$397$	8381.55			1.05959			0.529796	+	0.848125i	$0.322269\pi$
$398$	2281.97	+	1657.95i	0.287399	+	0.208807i
$399$	−47.8539	+	147.279i	−0.00600424	+	0.0184791i
$400$	−668.419	−	2057.18i	−0.0835524	−	0.257148i
$401$	3503.32	−	2545.31i	0.436279	−	0.316975i	−0.347876	−	0.937541i	$-0.613097\pi$
$401$	3503.32	−	2545.31i	0.436279	−	0.316975i	0.784154	+	0.620566i	$0.213097\pi$
$402$	−369.592	+	268.524i	−0.0458546	+	0.0333153i
$403$	−114.333	−	351.881i	−0.0141323	−	0.0434949i
$404$	1124.68	−	3461.42i	0.138503	−	0.426267i
$405$	−3827.43	−	2780.79i	−0.469597	−	0.341182i
$406$	−49.2097			−0.00601536
$407$		0			0
$408$	−1511.78			−0.183442
$409$	9657.95	+	7016.91i	1.16762	+	0.848323i	0.990722	−	0.135907i	$-0.0433948\pi$
$409$	9657.95	+	7016.91i	1.16762	+	0.848323i	0.176895	+	0.984230i	$0.443395\pi$
$410$	526.367	−	1619.99i	0.0634035	−	0.195136i
$411$	194.971	+	600.059i	0.0233995	+	0.0720164i
$412$	−1011.50	+	734.896i	−0.120954	+	0.0878780i
$413$	32.6099	−	23.6924i	0.00388529	−	0.00282283i
$414$	−725.841	−	2233.91i	−0.0861670	−	0.265195i
$415$	−3241.99	+	9977.82i	−0.383477	+	1.18022i
$416$	7984.05	+	5800.75i	0.940986	+	0.683667i
$417$	917.707			0.107770
$418$		0			0
$419$	−11888.5			−1.38614			−0.693070	−	0.720870i	$-0.743743\pi$
$419$	−11888.5			−1.38614			−0.693070	+	0.720870i	$0.743743\pi$
$420$	60.2801	+	43.7961i	0.00700326	+	0.00508817i
$421$	−2622.15	+	8070.15i	−0.303553	+	0.934240i	0.676660	+	0.736295i	$0.263427\pi$
$421$	−2622.15	+	8070.15i	−0.303553	+	0.934240i	−0.980213	+	0.197944i	$0.936573\pi$
$422$	−486.386	−	1496.94i	−0.0561063	−	0.172678i
$423$	−3805.33	+	2764.73i	−0.437403	+	0.317792i
$424$	7259.86	−	5274.59i	0.831533	−	0.604144i
$425$	1058.91	+	3259.00i	0.120859	+	0.371964i
$426$	80.3135	−	247.179i	0.00913427	−	0.0281124i
$427$	309.010	+	224.509i	0.0350212	+	0.0254444i
$428$	12646.2			1.42821
$429$		0			0
$430$	−2423.39			−0.271782
$431$	9271.93	+	6736.45i	1.03623	+	0.752862i	0.969545	−	0.244913i	$-0.0787593\pi$
$431$	9271.93	+	6736.45i	1.03623	+	0.752862i	0.0666800	+	0.997774i	$0.478759\pi$
$432$	1088.45	−	3349.90i	0.121222	−	0.373083i
$433$	1019.16	+	3136.66i	0.113113	+	0.348125i	0.991549	−	0.129735i	$-0.0414126\pi$
$433$	1019.16	+	3136.66i	0.113113	+	0.348125i	−0.878436	+	0.477860i	$0.841413\pi$
$434$	3.31612	−	2.40931i	0.000366772	−	0.000266475i
$435$	748.129	−	543.548i	0.0824599	−	0.0599106i
$436$	−1819.05	−	5598.47i	−0.199809	−	0.614949i
$437$	−4137.84	+	12735.0i	−0.452951	+	1.39404i
$438$	239.406	+	173.938i	0.0261170	+	0.0189751i
$439$	−5549.93			−0.603380			−0.301690	−	0.953406i	$-0.597551\pi$
$439$	−5549.93			−0.603380			−0.301690	+	0.953406i	$0.597551\pi$
$440$		0			0
$441$	8431.29			0.910408
$442$	−3384.11	−	2458.70i	−0.364176	−	0.264589i
$443$	3362.36	−	10348.3i	0.360611	−	1.10985i	−0.592073	−	0.805884i	$-0.701690\pi$
$443$	3362.36	−	10348.3i	0.360611	−	1.10985i	0.952684	−	0.303962i	$-0.0983097\pi$
$444$	586.558	+	1805.24i	0.0626955	+	0.192957i
$445$	−5060.95	+	3677.00i	−0.539128	+	0.391700i
$446$	−3438.10	+	2497.93i	−0.365020	+	0.265202i
$447$	1033.64	+	3181.21i	0.109372	+	0.336614i
$448$	51.0350	−	157.069i	0.00538209	−	0.0165644i
$449$	6104.61	+	4435.26i	0.641636	+	0.466176i	0.860412	−	0.509599i	$-0.170206\pi$
$449$	6104.61	+	4435.26i	0.641636	+	0.466176i	−0.218776	+	0.975775i	$0.570206\pi$
$450$	1111.04			0.116389
$451$		0			0
$452$	7782.91			0.809906
$453$	2243.06	+	1629.68i	0.232645	+	0.169026i
$454$	−938.010	+	2886.90i	−0.0969669	+	0.298433i
$455$	135.017	+	415.538i	0.0139114	+	0.0428148i
$456$	2260.63	−	1642.45i	0.232158	−	0.168672i
$457$	−2620.61	+	1903.98i	−0.268242	+	0.194890i	−0.713773	−	0.700377i	$-0.753015\pi$
$457$	−2620.61	+	1903.98i	−0.268242	+	0.194890i	0.445530	+	0.895267i	$0.353015\pi$
$458$	−842.005	−	2591.43i	−0.0859046	−	0.264387i
$459$	−1724.33	+	5306.93i	−0.175348	+	0.539665i
$460$	5212.32	+	3786.97i	0.528316	+	0.383844i
$461$	4837.43			0.488724			0.244362	−	0.969684i	$-0.421422\pi$
$461$	4837.43			0.488724			0.244362	+	0.969684i	$0.421422\pi$
$462$		0			0
$463$	14089.7			1.41427			0.707133	−	0.707081i	$-0.249988\pi$
$463$	14089.7			1.41427			0.707133	+	0.707081i	$0.249988\pi$
$464$	−2462.29	−	1788.96i	−0.246355	−	0.178988i
$465$	−23.8026	+	73.2568i	−0.00237380	+	0.00730582i
$466$	−805.402	−	2478.77i	−0.0800634	−	0.246410i
$467$	−11767.4	+	8549.52i	−1.16602	+	0.847162i	−0.990527	−	0.137319i	$-0.956151\pi$
$467$	−11767.4	+	8549.52i	−1.16602	+	0.847162i	−0.175491	+	0.984481i	$0.556151\pi$
$468$	9198.49	−	6683.09i	0.908548	−	0.660099i
$469$	76.8844	+	236.626i	0.00756970	+	0.0232971i
$470$	−475.567	+	1463.64i	−0.0466729	+	0.143644i
$471$	−97.7821	−	71.0429i	−0.00956595	−	0.00695007i
$472$	−727.326			−0.0709277
$473$		0			0
$474$	929.179			0.0900393
$475$	−5124.13	−	3722.90i	−0.494971	−	0.359617i
$476$	−120.053	+	369.485i	−0.0115601	+	0.0355784i
$477$	−4882.14	−	15025.7i	−0.468632	−	1.44230i
$478$	1539.70	−	1118.66i	0.147331	−	0.107042i
$479$	2289.58	−	1663.47i	0.218400	−	0.158677i	−0.473206	−	0.880952i	$-0.656904\pi$
$479$	2289.58	−	1663.47i	0.218400	−	0.158677i	0.691606	+	0.722275i	$0.256904\pi$
$480$	−634.893	−	1954.00i	−0.0603724	−	0.185807i
$481$	−3439.53	+	10585.8i	−0.326048	+	1.00347i
$482$	−2307.83	−	1676.74i	−0.218089	−	0.158451i
$483$	123.427			0.0116276
$484$		0			0
$485$	−5482.83			−0.513325
$486$	2229.20	+	1619.61i	0.208063	+	0.151167i
$487$	−5912.90	+	18198.0i	−0.550183	+	1.69329i	0.158155	+	0.987414i	$0.449445\pi$
$487$	−5912.90	+	18198.0i	−0.550183	+	1.69329i	−0.708338	+	0.705874i	$0.750555\pi$
$488$	−2129.78	−	6554.79i	−0.197563	−	0.608036i
$489$	410.056	−	297.923i	0.0379210	−	0.0275512i
$490$	2231.75	−	1621.46i	0.205756	−	0.149490i
$491$	3489.95	+	10740.9i	0.320772	+	0.987235i	0.973313	+	0.229481i	$0.0737030\pi$
$491$	3489.95	+	10740.9i	0.320772	+	0.987235i	−0.652541	+	0.757753i	$0.726297\pi$
$492$	719.770	−	2215.22i	0.0659547	−	0.202988i
$493$	3900.77	+	2834.08i	0.356353	+	0.258906i
$494$	7731.64			0.704176
$495$		0			0
$496$	253.515			0.0229499
$497$	−114.513	−	83.1986i	−0.0103352	−	0.00750899i
$498$	528.806	−	1627.50i	0.0475831	−	0.146446i
$499$	267.665	+	823.790i	0.0240127	+	0.0739036i	0.962345	−	0.271832i	$-0.0876295\pi$
$499$	267.665	+	823.790i	0.0240127	+	0.0739036i	−0.938332	+	0.345735i	$0.887629\pi$
$500$	−8772.26	+	6373.42i	−0.784615	+	0.570056i
$501$	4394.13	−	3192.52i	0.391846	−	0.284693i
$502$	−1149.64	−	3538.22i	−0.102213	−	0.314579i
$503$	1849.01	−	5690.65i	0.163903	−	0.504441i	−0.835051	−	0.550173i	$-0.814562\pi$
$503$	1849.01	−	5690.65i	0.163903	−	0.504441i	0.998954	+	0.0457317i	$0.0145619\pi$
$504$	215.968	+	156.910i	0.0190873	+	0.0138677i
$505$	−4443.12			−0.391517
$506$		0			0
$507$	−3046.47			−0.266861
$508$	7258.37	+	5273.51i	0.633933	+	0.460579i
$509$	3419.92	−	10525.4i	0.297810	−	0.916566i	−0.684453	−	0.729057i	$-0.739959\pi$
$509$	3419.92	−	10525.4i	0.297810	−	0.916566i	0.982263	−	0.187509i	$-0.0600412\pi$
$510$	269.105	+	828.220i	0.0233650	+	0.0719102i
$511$	130.384	−	94.7298i	0.0112874	−	0.00820078i
$512$	−9477.59	+	6885.87i	−0.818074	+	0.594366i
$513$	−3187.16	−	9809.07i	−0.274301	−	0.844212i
$514$	−1254.73	+	3861.66i	−0.107673	+	0.331383i
$515$	1234.82	+	897.152i	0.105656	+	0.0767636i
$516$	−3313.81			−0.282718
$517$		0			0
$518$	−123.311			−0.0104594
$519$	3375.92	+	2452.75i	0.285523	+	0.207444i
$520$	2436.26	−	7498.05i	0.205456	−	0.632329i
$521$	4605.23	+	14173.4i	0.387253	+	1.19184i	0.934833	+	0.355088i	$0.115549\pi$
$521$	4605.23	+	14173.4i	0.387253	+	1.19184i	−0.547580	+	0.836753i	$0.684451\pi$
$522$	1264.74	−	918.890i	0.106047	−	0.0770474i
$523$	−1204.98	+	875.470i	−0.100746	+	0.0731963i	−0.637018	−	0.770849i	$-0.719832\pi$
$523$	−1204.98	+	875.470i	−0.100746	+	0.0731963i	0.536272	+	0.844045i	$0.319832\pi$
$524$	3094.76	+	9524.70i	0.258006	+	0.794062i
$525$	−18.0411	+	55.5248i	−0.00149977	+	0.00461581i
$526$	−683.255	−	496.414i	−0.0566375	−	0.0411496i
$527$	−401.620			−0.0331971
$528$		0			0
$529$	−1494.50			−0.122832
$530$	−4181.95	−	3038.37i	−0.342741	−	0.249016i
$531$	−395.702	+	1217.85i	−0.0323390	+	0.0995292i
$532$	−221.900	−	682.938i	−0.0180838	−	0.0556562i
$533$	11049.9	−	8028.20i	0.897979	−	0.652420i
$534$	825.500	−	599.761i	0.0668968	−	0.0486034i
$535$	−4770.69	−	14682.7i	−0.385523	−	1.18652i
$536$	1387.32	−	4269.72i	0.111797	−	0.344074i
$537$	1837.05	+	1334.69i	0.147625	+	0.107256i
$538$	−1633.19			−0.130877
$539$		0			0
$540$	−4962.53			−0.395469
$541$	431.634	+	313.600i	0.0343020	+	0.0249219i	0.604804	−	0.796374i	$-0.293251\pi$
$541$	431.634	+	313.600i	0.0343020	+	0.0249219i	−0.570502	+	0.821296i	$0.693251\pi$
$542$	−1146.61	+	3528.90i	−0.0908692	+	0.279667i
$543$	234.404	+	721.420i	0.0185253	+	0.0570149i
$544$	8666.62	−	6296.67i	0.683048	−	0.496263i
$545$	−5813.81	+	4223.98i	−0.456947	+	0.331991i
$546$	−22.0228	−	67.7791i	−0.00172617	−	0.00531260i
$547$	5716.57	−	17593.8i	0.446842	−	1.37524i	−0.433609	−	0.901101i	$-0.642760\pi$
$547$	5716.57	−	17593.8i	0.446842	−	1.37524i	0.880451	−	0.474138i	$-0.157240\pi$
$548$	−2366.93	−	1719.67i	−0.184508	−	0.134053i
$549$	−12134.2			−0.943302
$550$		0			0
$551$	−8912.04			−0.689049
$552$	−1801.79	−	1309.08i	−0.138930	−	0.100939i
$553$	156.377	−	481.279i	0.0120250	−	0.0370092i
$554$	1896.25	+	5836.05i	0.145422	+	0.447563i
$555$	1874.68	−	1362.03i	0.143380	−	0.104171i
$556$	−3442.72	+	2501.28i	−0.262597	+	0.190788i
$557$	4865.09	+	14973.2i	0.370091	+	1.13902i	0.946732	+	0.322024i	$0.104363\pi$
$557$	4865.09	+	14973.2i	0.370091	+	1.13902i	−0.576641	+	0.816998i	$0.695637\pi$
$558$	−40.2393	+	123.844i	−0.00305280	+	0.00939556i
$559$	−15720.8	−	11421.8i	−1.18948	−	0.864205i
$560$	−299.377			−0.0225911
$561$		0			0
$562$	−4047.08			−0.303765
$563$	4880.11	+	3545.61i	0.365314	+	0.265416i	0.755265	−	0.655419i	$-0.227508\pi$
$563$	4880.11	+	3545.61i	0.365314	+	0.265416i	−0.389951	+	0.920836i	$0.627508\pi$
$564$	−650.303	+	2001.43i	−0.0485509	+	0.149424i
$565$	−2936.06	−	9036.26i	−0.218621	−	0.672846i
$566$	2789.96	−	2027.02i	0.207192	−	0.150534i
$567$	340.004	−	247.027i	0.0251831	−	0.0182966i
$568$	789.255	+	2429.08i	0.0583035	+	0.179440i
$569$	4829.81	−	14864.6i	0.355845	−	1.09518i	−0.599672	−	0.800246i	$-0.704702\pi$
$569$	4829.81	−	14864.6i	0.355845	−	1.09518i	0.955518	−	0.294934i	$-0.0952976\pi$
$570$	−1302.21	−	946.112i	−0.0956906	−	0.0695233i
$571$	7252.67			0.531550			0.265775	−	0.964035i	$-0.414372\pi$
$571$	7252.67			0.531550			0.265775	+	0.964035i	$0.414372\pi$
$572$		0			0
$573$	1994.43			0.145407
$574$	122.417	+	88.9409i	0.00890169	+	0.00646746i
$575$	−1559.98	+	4801.13i	−0.113140	+	0.348210i
$576$	1621.30	+	4989.84i	0.117281	+	0.360955i
$577$	−10515.4	+	7639.85i	−0.758683	+	0.551215i	−0.898506	−	0.438961i	$-0.855347\pi$
$577$	−10515.4	+	7639.85i	−0.758683	+	0.551215i	0.139823	+	0.990176i	$0.455347\pi$
$578$	−3.39493	+	2.46656i	−0.000244309	+	0.000177501i
$579$	−249.654	−	768.355i	−0.0179193	−	0.0551498i
$580$	−1325.08	+	4078.17i	−0.0948635	+	0.291960i
$581$	−753.986	−	547.803i	−0.0538392	−	0.0391165i
$582$	894.313			0.0636950
$583$		0			0
$584$	−2908.08			−0.206057
$585$	−11229.4	−	8158.64i	−0.793639	−	0.576613i
$586$	637.761	−	1962.83i	0.0449584	−	0.138368i
$587$	3131.18	+	9636.79i	0.220166	+	0.677603i	0.998746	+	0.0500572i	$0.0159404\pi$
$587$	3131.18	+	9636.79i	0.220166	+	0.677603i	−0.778580	+	0.627546i	$0.784060\pi$
$588$	3051.76	−	2217.23i	0.214035	−	0.155505i
$589$	600.562	−	436.334i	0.0420131	−	0.0305243i
$590$	129.468	+	398.462i	0.00903409	+	0.0278041i
$591$	−560.787	+	1725.93i	−0.0390317	+	0.120127i
$592$	−6170.05	−	4482.80i	−0.428357	−	0.311220i
$593$	838.751			0.0580833			0.0290416	−	0.999578i	$-0.490754\pi$
$593$	838.751			0.0580833			0.0290416	+	0.999578i	$0.490754\pi$
$594$		0			0
$595$	474.276			0.0326780
$596$	−12548.3	−	9116.86i	−0.862412	−	0.626579i
$597$	1455.05	−	4478.20i	0.0997511	−	0.307002i
$598$	−1904.27	−	5860.74i	−0.130220	−	0.400775i
$599$	20801.8	−	15113.4i	1.41893	−	1.03091i	0.426978	−	0.904262i	$-0.359578\pi$
$599$	20801.8	−	15113.4i	1.41893	−	1.03091i	0.991948	−	0.126648i	$-0.0404219\pi$
$600$	852.267	−	619.208i	0.0579894	−	0.0421318i
$601$	439.880	+	1353.81i	0.0298554	+	0.0918853i	0.964874	−	0.262714i	$-0.0846174\pi$
$601$	439.880	+	1353.81i	0.0298554	+	0.0918853i	−0.935019	+	0.354599i	$0.884617\pi$
$602$	66.5245	−	204.741i	0.00450388	−	0.0138615i
$603$	−6394.52	−	4645.89i	−0.431849	−	0.313757i
$604$	−12856.5			−0.866098
$605$		0			0
$606$	724.724			0.0485807
$607$	−20688.0	−	15030.7i	−1.38336	−	1.00507i	−0.996557	−	0.0829067i	$-0.973580\pi$
$607$	−20688.0	−	15030.7i	−1.38336	−	1.00507i	−0.386802	−	0.922163i	$-0.626420\pi$
$608$	−6118.69	+	18831.4i	−0.408134	+	1.25611i
$609$	25.3850	+	78.1271i	0.00168909	+	0.00519847i
$610$	−3211.89	+	2333.58i	−0.213190	+	0.154891i
$611$	−9983.42	+	7253.38i	−0.661024	+	0.480262i
$612$	−3813.88	−	11737.9i	−0.251907	−	0.775290i
$613$	1499.35	−	4614.51i	0.0987895	−	0.304043i	−0.889433	−	0.457065i	$-0.848901\pi$
$613$	1499.35	−	4614.51i	0.0987895	−	0.304043i	0.988223	+	0.153022i	$0.0489006\pi$
$614$	763.818	+	554.947i	0.0502039	+	0.0364753i
$615$	−2843.49			−0.186440
$616$		0			0
$617$	3850.99			0.251272			0.125636	−	0.992076i	$-0.459903\pi$
$617$	3850.99			0.251272			0.125636	+	0.992076i	$0.459903\pi$
$618$	−201.414	−	146.336i	−0.0131101	−	0.00952508i
$619$	7443.43	−	22908.5i	0.483323	−	1.48751i	−0.351073	−	0.936348i	$-0.614183\pi$
$619$	7443.43	−	22908.5i	0.483323	−	1.48751i	0.834396	−	0.551166i	$-0.185817\pi$
$620$	−110.373	−	339.694i	−0.00714951	−	0.0220039i
$621$	−6650.49	+	4831.86i	−0.429750	+	0.312232i
$622$	−3973.60	+	2886.99i	−0.256153	+	0.186106i
$623$	−171.725	−	528.515i	−0.0110434	−	0.0339880i
$624$	1362.08	−	4192.05i	0.0873828	−	0.268937i
$625$	5767.43	+	4190.28i	0.369115	+	0.268178i
$626$	−6457.39			−0.412283
$627$		0			0
$628$	560.456			0.0356125
$629$	9774.63	+	7101.69i	0.619619	+	0.450179i
$630$	47.5188	−	146.248i	0.00300507	−	0.00924865i
$631$	−899.970	−	2769.82i	−0.0567785	−	0.174746i	0.918645	−	0.395083i	$-0.129284\pi$
$631$	−899.970	−	2769.82i	−0.0567785	−	0.174746i	−0.975424	+	0.220337i	$0.929284\pi$
$632$	−7387.31	+	5367.19i	−0.464955	+	0.337809i
$633$	−2125.69	+	1544.41i	−0.133474	+	0.0969742i
$634$	1231.11	+	3788.95i	0.0771190	+	0.237348i
$635$	3384.57	−	10416.6i	0.211516	−	0.650979i
$636$	−5718.52	−	4154.75i	−0.356532	−	0.259036i
$637$	22119.8			1.37585
$638$		0			0
$639$	4496.68			0.278382
$640$	10015.7	+	7276.83i	0.618601	+	0.449440i
$641$	1900.65	−	5849.60i	0.117116	−	0.360445i	−0.875267	−	0.483641i	$-0.839314\pi$
$641$	1900.65	−	5849.60i	0.117116	−	0.360445i	0.992382	+	0.123195i	$0.0393142\pi$
$642$	778.155	+	2394.92i	0.0478370	+	0.147227i
$643$	7892.25	−	5734.05i	0.484043	−	0.351678i	−0.318846	−	0.947807i	$-0.603295\pi$
$643$	7892.25	−	5734.05i	0.484043	−	0.351678i	0.802889	+	0.596129i	$0.203295\pi$
$644$	−463.028	+	336.409i	−0.0283321	+	0.0205844i
$645$	1250.12	+	3847.46i	0.0763152	+	0.234874i
$646$	2593.46	−	7981.86i	0.157954	−	0.486133i
$647$	1473.76	+	1070.75i	0.0895507	+	0.0650624i	0.631660	−	0.775246i	$-0.282374\pi$
$647$	1473.76	+	1070.75i	0.0895507	+	0.0650624i	−0.542109	+	0.840308i	$0.682374\pi$
$648$	−7583.40			−0.459728
$649$		0			0
$650$	2914.86			0.175892
$651$	−5.53574	−	4.02195i	−0.000333276	−	0.000242139i
$652$	−726.286	+	2235.28i	−0.0436251	+	0.134264i
$653$	1971.95	+	6069.03i	0.118175	+	0.363705i	0.992596	−	0.121463i	$-0.0387585\pi$
$653$	1971.95	+	6069.03i	0.118175	+	0.363705i	−0.874421	+	0.485168i	$0.838759\pi$
$654$	948.300	−	688.980i	0.0566995	−	0.0411946i
$655$	9891.06	−	7186.27i	0.590039	−	0.428689i
$656$	2891.99	+	8900.62i	0.172124	+	0.529742i
$657$	−1582.14	+	4869.33i	−0.0939501	+	0.289149i
$658$	−110.602	−	80.3570i	−0.00655276	−	0.00476086i
$659$	27285.6			1.61289			0.806445	−	0.591309i	$-0.201389\pi$
$659$	27285.6			1.61289			0.806445	+	0.591309i	$0.201389\pi$
$660$		0			0
$661$	−23925.0			−1.40783			−0.703913	−	0.710286i	$-0.748566\pi$
$661$	−23925.0			−1.40783			−0.703913	+	0.710286i	$0.748566\pi$
$662$	2903.40	+	2109.44i	0.170459	+	0.123846i
$663$	−2157.82	+	6641.08i	−0.126399	+	0.389017i
$664$	5196.67	+	15993.7i	0.303720	+	0.934754i
$665$	−709.206	+	515.269i	−0.0413562	+	0.0300470i
$666$	3169.22	−	2302.57i	0.184392	−	0.133968i
$667$	2195.00	+	6755.51i	0.127422	+	0.392166i
$668$	−7782.82	+	23953.1i	−0.450788	+	1.38738i
$669$	5739.36	+	4169.89i	0.331684	+	0.240982i
$670$	−2586.10			−0.149119
$671$		0			0
$672$	182.513			0.0104771
$673$	−6744.56	−	4900.21i	−0.386306	−	0.280667i	0.377634	−	0.925955i	$-0.376738\pi$
$673$	−6744.56	−	4900.21i	−0.386306	−	0.280667i	−0.763940	+	0.645287i	$0.776738\pi$
$674$	2597.10	−	7993.06i	0.148422	−	0.456797i
$675$	−1201.57	−	3698.06i	−0.0685163	−	0.210871i
$676$	11428.6	−	8303.40i	0.650241	−	0.472428i
$677$	−898.252	+	652.618i	−0.0509935	+	0.0370490i	−0.612990	−	0.790091i	$-0.710033\pi$
$677$	−898.252	+	652.618i	−0.0509935	+	0.0370490i	0.561997	+	0.827140i	$0.310033\pi$
$678$	478.905	+	1473.92i	0.0271272	+	0.0834890i
$679$	150.509	−	463.220i	0.00850665	−	0.0261808i
$680$	−6923.50	−	5030.22i	−0.390447	−	0.283677i
$681$	5067.22			0.285134
$682$		0			0
$683$	8337.88			0.467116			0.233558	−	0.972343i	$-0.424963\pi$
$683$	8337.88			0.467116			0.233558	+	0.972343i	$0.424963\pi$
$684$	18455.6	+	13408.7i	1.03168	+	0.749556i
$685$	−1103.70	+	3396.83i	−0.0615622	+	0.189469i
$686$	151.585	+	466.532i	0.00843667	+	0.0259654i
$687$	−3679.89	+	2673.60i	−0.204362	+	0.148478i
$688$	10771.8	−	7826.16i	0.596905	−	0.433677i
$689$	−12808.5	−	39420.4i	−0.708219	−	2.17968i
$690$	−396.443	+	1220.13i	−0.0218729	+	0.0673180i
$691$	26998.5	+	19615.5i	1.48635	+	1.07990i	0.975440	+	0.220266i	$0.0706926\pi$
$691$	26998.5	+	19615.5i	1.48635	+	1.07990i	0.510913	+	0.859632i	$0.329307\pi$
$692$	−19349.7			−1.06295
$693$		0			0
$694$	9374.48			0.512753
$695$	4202.83	+	3053.53i	0.229385	+	0.166658i
$696$	458.053	−	1409.74i	0.0249460	−	0.0767760i
$697$	−4581.50	−	14100.4i	−0.248977	−	0.766272i
$698$	−7972.13	+	5792.09i	−0.432306	+	0.314089i
$699$	−3519.92	+	2557.37i	−0.190466	+	0.138382i
$700$	−83.6571	−	257.470i	−0.00451706	−	0.0139021i
$701$	−2413.07	+	7426.67i	−0.130015	+	0.400145i	−0.994781	−	0.102030i	$-0.967466\pi$
$701$	−2413.07	+	7426.67i	−0.130015	+	0.400145i	0.864767	+	0.502174i	$0.167466\pi$
$702$	3840.02	+	2789.94i	0.206456	+	0.149999i
$703$	−22332.0			−1.19810
$704$		0			0
$705$	2569.06			0.137243
$706$	6948.40	+	5048.31i	0.370406	+	0.269116i
$707$	121.968	−	375.379i	0.00648809	−	0.0199683i
$708$	177.038	+	544.868i	0.00939761	+	0.0289229i
$709$	−22613.7	+	16429.8i	−1.19785	+	0.870288i	−0.994071	−	0.108730i	$-0.965322\pi$
$709$	−22613.7	+	16429.8i	−1.19785	+	0.870288i	−0.203777	+	0.979017i	$0.565322\pi$
$710$	1190.27	−	864.778i	0.0629153	−	0.0457106i
$711$	4967.84	+	15289.5i	0.262038	+	0.806469i
$712$	−3098.64	+	9536.62i	−0.163099	+	0.501966i
$713$	−478.666	−	347.771i	−0.0251419	−	0.0182667i
$714$	−77.3599			−0.00405479
$715$		0			0
$716$	−10529.4			−0.549583
$717$	−2570.28	−	1867.42i	−0.133876	−	0.0972664i
$718$	−2396.03	+	7374.22i	−0.124539	+	0.383292i
$719$	−7720.14	−	23760.2i	−0.400435	−	1.23241i	−0.924647	−	0.380824i	$-0.875640\pi$
$719$	−7720.14	−	23760.2i	−0.400435	−	1.23241i	0.524212	−	0.851588i	$-0.324360\pi$
$720$	7694.34	−	5590.26i	0.398265	−	0.289357i
$721$	−109.694	+	79.6971i	−0.00566602	+	0.00411661i
$722$	2836.55	+	8730.00i	0.146212	+	0.449996i
$723$	−1471.54	+	4528.95i	−0.0756948	+	0.232965i
$724$	−2845.64	−	2067.47i	−0.146073	−	0.106129i
$725$	−3359.87			−0.172114
$726$		0			0
$727$	31671.2			1.61571			0.807855	−	0.589381i	$-0.200628\pi$
$727$	31671.2			1.61571			0.807855	+	0.589381i	$0.200628\pi$
$728$	566.599	+	411.658i	0.0288456	+	0.0209575i
$729$	−3102.42	+	9548.25i	−0.157619	+	0.485102i
$730$	517.654	+	1593.17i	0.0262455	+	0.0807754i
$731$	−17064.7	+	12398.3i	−0.863423	+	0.627314i
$732$	−4392.04	+	3191.00i	−0.221768	+	0.161124i
$733$	−3656.22	−	11252.7i	−0.184237	−	0.567023i	0.815698	−	0.578479i	$-0.196353\pi$
$733$	−3656.22	−	11252.7i	−0.184237	−	0.567023i	−0.999934	+	0.0114559i	$0.996353\pi$
$734$	−2672.96	+	8226.52i	−0.134415	+	0.413687i
$735$	−3725.55	−	2706.77i	−0.186965	−	0.135838i
$736$	15781.6			0.790377
$737$		0			0
$738$	−4807.04			−0.239769
$739$	4490.16	+	3262.29i	0.223509	+	0.162389i	0.693905	−	0.720067i	$-0.255889\pi$
$739$	4490.16	+	3262.29i	0.223509	+	0.162389i	−0.470396	+	0.882456i	$0.655889\pi$
$740$	−3320.41	+	10219.2i	−0.164947	+	0.507654i
$741$	−3988.40	−	12275.0i	−0.197729	−	0.608549i
$742$	371.497	−	269.909i	0.0183802	−	0.0133540i
$743$	30176.1	−	21924.2i	1.48998	−	1.08253i	0.515813	−	0.856701i	$-0.327490\pi$
$743$	30176.1	−	21924.2i	1.48998	−	1.08253i	0.974166	−	0.225832i	$-0.0725101\pi$
$744$	38.1538	+	117.425i	0.00188009	+	0.00578632i
$745$	−5851.26	+	18008.3i	−0.287750	+	0.885602i
$746$	1971.57	+	1432.43i	0.0967619	+	0.0703016i
$747$	29607.4			1.45017
$748$		0			0
$749$	1371.43			0.0669041
$750$	−1746.77	−	1269.11i	−0.0850443	−	0.0617883i
$751$	−1606.66	+	4944.80i	−0.0780665	+	0.240264i	−0.982472	−	0.186410i	$-0.940315\pi$
$751$	−1606.66	+	4944.80i	−0.0780665	+	0.240264i	0.904406	+	0.426674i	$0.140315\pi$
$752$	−2612.87	−	8041.60i	−0.126704	−	0.389956i
$753$	−5024.37	+	3650.42i	−0.243158	+	0.176665i
$754$	3318.10	−	2410.74i	0.160263	−	0.116438i
$755$	4850.04	+	14926.9i	0.233789	+	0.719530i
$756$	136.227	−	419.262i	0.00655358	−	0.0201699i
$757$	−127.874	−	92.9061i	−0.00613959	−	0.00446067i	0.584711	−	0.811242i	$-0.301208\pi$
$757$	−127.874	−	92.9061i	−0.00613959	−	0.00446067i	−0.590851	+	0.806781i	$0.701208\pi$
$758$	−6801.86			−0.325929
$759$		0			0
$760$	15818.0			0.754974
$761$	5383.00	+	3910.98i	0.256417	+	0.186298i	0.708566	−	0.705644i	$-0.249342\pi$
$761$	5383.00	+	3910.98i	0.256417	+	0.186298i	−0.452149	+	0.891943i	$0.649342\pi$
$762$	−552.063	+	1699.08i	−0.0262456	+	0.0807756i
$763$	−197.270	−	607.135i	−0.00935998	−	0.0288070i
$764$	−7481.97	+	5435.97i	−0.354304	+	0.257417i
$765$	−12189.4	+	8856.13i	−0.576091	+	0.418554i
$766$	−918.870	−	2827.99i	−0.0433422	−	0.133394i
$767$	−1038.14	+	3195.06i	−0.0488722	+	0.150413i
$768$	491.900	+	357.387i	0.0231119	+	0.0167918i
$769$	−5519.26			−0.258816			−0.129408	−	0.991591i	$-0.541308\pi$
$769$	−5519.26			−0.258816			−0.129408	+	0.991591i	$0.541308\pi$
$770$		0			0
$771$	6778.18			0.316615
$772$	3030.77	+	2201.98i	0.141295	+	0.102657i
$773$	9540.72	−	29363.3i	0.443927	−	1.36627i	−0.439729	−	0.898131i	$-0.644925\pi$
$773$	9540.72	−	29363.3i	0.443927	−	1.36627i	0.883656	−	0.468137i	$-0.155075\pi$
$774$	2113.37	+	6504.30i	0.0981443	+	0.302057i
$775$	226.414	−	164.499i	0.0104942	−	0.00762451i
$776$	−7110.11	+	5165.80i	−0.328915	+	0.238971i
$777$	63.6103	+	195.772i	0.00293695	+	0.00903899i
$778$	3489.00	−	10738.1i	0.160780	−	0.494830i
$779$	22170.1	+	16107.5i	1.01967	+	0.740836i
$780$	−6210.09			−0.285073
$781$		0			0
$782$	−6689.17			−0.305888
$783$	−4426.29	−	3215.88i	−0.202021	−	0.146777i
$784$	−4683.57	+	14414.6i	−0.213355	+	0.656640i
$785$	−211.429	−	650.711i	−0.00961302	−	0.0295858i
$786$	−1613.35	+	1172.17i	−0.0732140	+	0.0531931i
$787$	−20220.4	+	14690.9i	−0.915855	+	0.665408i	−0.942489	−	0.334238i	$-0.891521\pi$
$787$	−20220.4	+	14690.9i	−0.915855	+	0.665408i	0.0266338	+	0.999645i	$0.491521\pi$
$788$	−2600.39	−	8003.17i	−0.117557	−	0.361803i
$789$	−435.665	+	1340.84i	−0.0196579	+	0.0605008i
$790$	4255.37	+	3091.71i	0.191645	+	0.139238i
$791$	844.031			0.0379397
$792$		0			0
$793$	−31834.4			−1.42556
$794$	−6261.04	−	4548.92i	−0.279844	−	0.203319i
$795$	−2666.55	+	8206.78i	−0.118959	+	0.366119i
$796$	6747.13	+	20765.5i	0.300434	+	0.924641i
$797$	16563.4	−	12034.0i	0.736141	−	0.534838i	−0.155359	−	0.987858i	$-0.549654\pi$
$797$	16563.4	−	12034.0i	0.736141	−	0.534838i	0.891500	+	0.453020i	$0.149654\pi$
$798$	115.680	−	84.0463i	0.00513161	−	0.00372833i
$799$	4139.33	+	12739.6i	0.183278	+	0.564071i
$800$	−2306.77	+	7099.51i	−0.101946	+	0.313757i
$801$	14282.5	+	10376.8i	0.630020	+	0.457736i
$802$	−3998.41			−0.176046
$803$		0			0
$804$	−3536.30			−0.155119
$805$	565.259	+	410.685i	0.0247488	+	0.0179810i
$806$	−105.569	+	324.908i	−0.00461354	+	0.0141990i
$807$	842.491	+	2592.92i	0.0367498	+	0.113104i
$808$	−5761.81	+	4186.20i	−0.250866	+	0.182265i
$809$	11872.0	−	8625.48i	0.515941	−	0.374853i	−0.299132	−	0.954212i	$-0.596697\pi$
$809$	11872.0	−	8625.48i	0.515941	−	0.374853i	0.815072	+	0.579359i	$0.196697\pi$
$810$	1349.89	+	4154.52i	0.0585558	+	0.180216i
$811$	−1459.87	+	4493.01i	−0.0632095	+	0.194539i	−0.977674	−	0.210127i	$-0.932612\pi$
$811$	−1459.87	+	4493.01i	−0.0632095	+	0.194539i	0.914465	+	0.404666i	$0.132612\pi$
$812$	−308.172	−	223.900i	−0.0133186	−	0.00967653i
$813$	6194.10			0.267204
$814$		0			0
$815$	2869.23			0.123319
$816$	−3870.83	−	2812.32i	−0.166062	−	0.120651i
$817$	12047.8	−	37079.4i	0.515912	−	1.58781i
$818$	−3406.24	−	10483.3i	−0.145595	−	0.448094i
$819$	997.546	−	724.760i	0.0425606	−	0.0309221i
$820$	10667.2	−	7750.15i	0.454285	−	0.330057i
$821$	−13881.5	−	42723.0i	−0.590097	−	1.81613i	−0.577760	−	0.816207i	$-0.696073\pi$
$821$	−13881.5	−	42723.0i	−0.590097	−	1.81613i	−0.0123363	−	0.999924i	$-0.503927\pi$
$822$	180.026	−	554.063i	0.00763884	−	0.0235099i
$823$	−32002.7	−	23251.3i	−1.35546	−	0.984800i	−0.998719	−	0.0505967i	$-0.983888\pi$
$823$	−32002.7	−	23251.3i	−1.35546	−	0.984800i	−0.356742	−	0.934203i	$-0.616112\pi$
$824$	2446.59			0.103436
$825$		0			0
$826$	−37.2183			−0.00156778
$827$	12752.3	+	9265.07i	0.536203	+	0.389574i	0.822673	−	0.568515i	$-0.192482\pi$
$827$	12752.3	+	9265.07i	0.536203	+	0.389574i	−0.286470	+	0.958089i	$0.592482\pi$
$828$	5618.58	−	17292.2i	0.235820	−	0.725780i
$829$	6977.80	+	21475.5i	0.292339	+	0.899727i	0.984102	+	0.177603i	$0.0568342\pi$
$829$	6977.80	+	21475.5i	0.292339	+	0.899727i	−0.691763	+	0.722124i	$0.743166\pi$
$830$	7837.04	−	5693.94i	0.327744	−	0.238120i
$831$	8287.34	−	6021.10i	0.345950	−	0.251348i
$832$	4253.53	+	13091.0i	0.177241	+	0.545492i
$833$	7419.75	−	22835.6i	0.308618	−	0.949830i
$834$	−685.530	−	498.067i	−0.0284628	−	0.0206794i
$835$	30746.4			1.27428
$836$		0			0
$837$	455.727			0.0188199
$838$	8880.78	+	6452.26i	0.366088	+	0.265978i
$839$	−7245.74	+	22300.1i	−0.298153	+	0.917621i	0.683991	+	0.729491i	$0.260243\pi$
$839$	−7245.74	+	22300.1i	−0.298153	+	0.917621i	−0.982144	+	0.188131i	$0.939757\pi$
$840$	−45.0560	−	138.668i	−0.00185069	−	0.00569584i
$841$	15906.4	−	11556.7i	0.652197	−	0.473849i
$842$	6338.67	−	4605.31i	0.259436	−	0.188491i
$843$	2087.71	+	6425.30i	0.0852958	+	0.262514i
$844$	3765.00	−	11587.5i	0.153551	−	0.472580i
$845$	−13952.0	−	10136.7i	−0.568002	−	0.412678i
$846$	4343.10			0.176500
$847$		0			0
$848$	28400.7			1.15010
$849$	−4657.39	−	3383.79i	−0.188270	−	0.136786i
$850$	977.745	−	3009.19i	0.0394546	−	0.121429i
$851$	5500.27	+	16928.1i	0.221559	+	0.681889i
$852$	1627.60	−	1182.52i	0.0654469	−	0.0475500i
$853$	−12132.7	+	8814.90i	−0.487004	+	0.353829i	−0.804031	−	0.594587i	$-0.797315\pi$
$853$	−12132.7	+	8814.90i	−0.487004	+	0.353829i	0.317027	+	0.948417i	$0.397315\pi$
$854$	−108.984	−	335.418i	−0.00436692	−	0.0134400i
$855$	8605.82	−	26486.0i	0.344225	−	1.05942i
$856$	−20020.3	−	14545.6i	−0.799392	−	0.580792i
$857$	−46121.7			−1.83838			−0.919188	−	0.393819i	$-0.871154\pi$
$857$	−46121.7			−1.83838			−0.919188	+	0.393819i	$0.871154\pi$
$858$		0			0
$859$	−17398.7			−0.691080			−0.345540	−	0.938404i	$-0.612304\pi$
$859$	−17398.7			−0.691080			−0.345540	+	0.938404i	$0.612304\pi$
$860$	−15176.3	−	11026.2i	−0.601753	−	0.437199i
$861$	78.0567	−	240.234i	0.00308962	−	0.00950888i
$862$	−3270.09	−	10064.3i	−0.129211	−	0.397670i
$863$	8989.57	−	6531.30i	0.354587	−	0.257622i	−0.396204	−	0.918163i	$-0.629673\pi$
$863$	8989.57	−	6531.30i	0.354587	−	0.257622i	0.750791	+	0.660540i	$0.229673\pi$
$864$	−9834.18	+	7144.95i	−0.387229	+	0.281338i
$865$	7299.56	+	22465.7i	0.286928	+	0.883072i
$866$	941.042	−	2896.23i	0.0369260	−	0.113646i
$867$	5.66730	+	4.11754i	0.000221997	+	0.000161291i
$868$	31.7291			0.00124073
$869$		0			0
$870$	−853.855			−0.0332740
$871$	−16776.2	−	12188.7i	−0.652631	−	0.474164i
$872$	−3559.58	+	10955.3i	−0.138237	+	0.425450i
$873$	4781.43	+	14715.7i	0.185369	+	0.570507i
$874$	10002.6	−	7267.34i	0.387121	−	0.281260i
$875$	−951.323	+	691.177i	−0.0367550	+	0.0267040i
$876$	707.854	+	2178.55i	0.0273016	+	0.0840256i
$877$	−493.384	+	1518.48i	−0.0189970	+	0.0584668i	−0.960106	−	0.279638i	$-0.909786\pi$
$877$	−493.384	+	1518.48i	−0.0189970	+	0.0584668i	0.941109	+	0.338104i	$0.109786\pi$
$878$	4145.82	+	3012.11i	0.159356	+	0.115779i
$879$	−3445.25			−0.132202
$880$		0			0
$881$	4924.45			0.188319			0.0941594	−	0.995557i	$-0.469984\pi$
$881$	4924.45			0.188319			0.0941594	+	0.995557i	$0.469984\pi$
$882$	−6298.20	−	4575.91i	−0.240444	−	0.174693i
$883$	−6665.86	+	20515.4i	−0.254048	+	0.781878i	0.739968	+	0.672642i	$0.234841\pi$
$883$	−6665.86	+	20515.4i	−0.254048	+	0.781878i	−0.994016	+	0.109236i	$0.965159\pi$
$884$	−10005.9	−	30794.9i	−0.380694	−	1.17166i
$885$	565.826	−	411.097i	0.0214916	−	0.0156145i
$886$	−8128.02	+	5905.35i	−0.308201	+	0.223921i
$887$	−6836.67	−	21041.1i	−0.258797	−	0.796495i	−0.993058	−	0.117628i	$-0.962471\pi$
$887$	−6836.67	−	21041.1i	−0.258797	−	0.796495i	0.734261	−	0.678868i	$-0.237529\pi$
$888$	1147.80	−	3532.56i	0.0433756	−	0.133496i
$889$	787.146	+	571.895i	0.0296963	+	0.0215756i
$890$	5776.16			0.217548
$891$		0			0
$892$	−32896.2			−1.23481
$893$	−20030.4	−	14552.9i	−0.750607	−	0.545348i
$894$	954.408	−	2937.37i	0.0357049	−	0.109888i
$895$	3972.15	+	12225.0i	0.148351	+	0.456578i
$896$	−889.728	+	646.425i	−0.0331738	+	0.0241022i
$897$	−8322.40	+	6046.58i	−0.309785	+	0.225072i
$898$	−2153.02	−	6626.31i	−0.0800080	−	0.246239i
$899$	121.687	−	374.513i	0.00451443	−	0.0138940i
$900$	6957.81	+	5055.15i	0.257697	+	0.187228i
$901$	−44992.5			−1.66362
$902$		0			0
$903$	−359.372			−0.0132438
$904$	−12321.2	−	8951.89i	−0.453316	−	0.329353i
$905$	−1326.92	+	4083.83i	−0.0487384	+	0.150001i
$906$	−791.098	−	2434.75i	−0.0290093	−	0.0892816i
$907$	1648.63	−	1197.80i	0.0603548	−	0.0438504i	−0.557199	−	0.830379i	$-0.688124\pi$
$907$	1648.63	−	1197.80i	0.0603548	−	0.0438504i	0.617554	+	0.786529i	$0.288124\pi$
$908$	−19009.4	+	13811.1i	−0.694766	+	0.504777i
$909$	3874.73	+	11925.2i	0.141382	+	0.435130i
$910$	124.667	−	383.686i	0.00454140	−	0.0139770i
$911$	−35177.4	−	25557.9i	−1.27934	−	0.929495i	−0.279808	−	0.960056i	$-0.590271\pi$
$911$	−35177.4	−	25557.9i	−1.27934	−	0.929495i	−0.999533	+	0.0305606i	$0.990271\pi$
$912$	8843.64			0.321099
$913$		0			0
$914$	2990.95			0.108241
$915$	5361.75	+	3895.54i	0.193720	+	0.140746i
$916$	6517.78	−	20059.7i	0.235102	−	0.723570i
$917$	335.617	+	1032.92i	0.0120862	+	0.0371975i
$918$	4168.31	−	3028.45i	0.149863	−	0.108882i
$919$	−7796.33	+	5664.36i	−0.279845	+	0.203319i	−0.718850	−	0.695166i	$-0.755331\pi$
$919$	−7796.33	+	5664.36i	−0.279845	+	0.203319i	0.439005	+	0.898485i	$0.355331\pi$
$920$	−3895.92	−	11990.4i	−0.139614	−	0.429687i
$921$	487.035	−	1498.94i	0.0174249	−	0.0536283i
$922$	−3613.58	−	2625.42i	−0.129075	−	0.0937783i
$923$	11797.2			0.420704
$924$		0			0
$925$	−8419.24			−0.299268
$926$	−10525.1	−	7646.92i	−0.373516	−	0.271375i
$927$	1331.07	−	4096.61i	0.0471608	−	0.145146i
$928$	3245.78	+	9989.48i	0.114815	+	0.353363i
$929$	−5085.28	+	3694.67i	−0.179594	+	0.130482i	−0.673950	−	0.738777i	$-0.735404\pi$
$929$	−5085.28	+	3694.67i	−0.179594	+	0.130482i	0.494356	+	0.869259i	$0.335404\pi$
$930$	57.5393	−	41.8047i	0.00202880	−	0.00147401i
$931$	13714.3	+	42208.3i	0.482780	+	1.48584i
$932$	6234.44	−	19187.6i	0.219116	−	0.674369i
$933$	6633.29	+	4819.37i	0.232759	+	0.169109i
$934$	13430.4			0.470509
$935$		0			0
$936$	−22249.1			−0.776961
$937$	19912.9	+	14467.6i	0.694266	+	0.504413i	0.878060	−	0.478551i	$-0.158838\pi$
$937$	19912.9	+	14467.6i	0.694266	+	0.504413i	−0.183794	+	0.982965i	$0.558838\pi$
$938$	70.9910	−	218.488i	0.00247115	−	0.00760541i
$939$	3331.08	+	10252.0i	0.115767	+	0.356295i
$940$	−9637.65	+	7002.17i	−0.334410	+	0.242963i
$941$	15898.0	−	11550.6i	0.550754	−	0.400146i	−0.277310	−	0.960781i	$-0.589443\pi$
$941$	15898.0	−	11550.6i	0.550754	−	0.400146i	0.828063	+	0.560635i	$0.189443\pi$
$942$	34.4865	+	106.139i	0.00119281	+	0.00367111i
$943$	6749.43	−	20772.6i	0.233077	−	0.717337i
$944$	−1862.28	−	1353.03i	−0.0642077	−	0.0466496i
$945$	−538.170			−0.0185256
$946$		0			0
$947$	3025.82			0.103829			0.0519144	−	0.998652i	$-0.483468\pi$
$947$	3025.82			0.103829			0.0519144	+	0.998652i	$0.483468\pi$
$948$	5818.92	+	4227.69i	0.199356	+	0.144841i
$949$	−4150.80	+	12774.9i	−0.141982	+	0.436975i
$950$	1807.22	+	5562.04i	0.0617198	+	0.189954i
$951$	5380.41	−	3909.10i	0.183461	−	0.133293i
$952$	615.038	−	446.852i	0.0209386	−	0.0152128i
$953$	3617.77	+	11134.3i	0.122971	+	0.378465i	0.993526	−	0.113606i	$-0.0362402\pi$
$953$	3617.77	+	11134.3i	0.122971	+	0.378465i	−0.870555	+	0.492071i	$0.836240\pi$
$954$	−4507.91	+	13873.9i	−0.152986	+	0.470843i
$955$	9133.90	+	6636.16i	0.309493	+	0.224860i
$956$	14732.0			0.498398
$957$		0			0
$958$	−2613.14			−0.0881281
$959$	−256.686	−	186.493i	−0.00864319	−	0.00627964i
$960$	885.527	−	2725.37i	0.0297711	−	0.0916260i
$961$	−9195.79	−	28301.7i	−0.308677	−	0.950009i
$962$	8314.56	−	6040.88i	0.278661	−	0.202459i
$963$	−35247.4	+	25608.8i	−1.17947	+	0.856938i
$964$	−6823.59	−	21000.9i	−0.227980	−	0.701652i
$965$	1413.25	−	4349.53i	0.0471441	−	0.145095i
$966$	−92.2003	−	66.9874i	−0.00307091	−	0.00223114i
$967$	−12352.3			−0.410779			−0.205390	−	0.978680i	$-0.565846\pi$
$967$	−12352.3			−0.410779			−0.205390	+	0.978680i	$0.565846\pi$
$968$		0			0
$969$	−14010.1			−0.464469
$970$	4095.69	+	2975.70i	0.135572	+	0.0984988i
$971$	−5225.07	+	16081.1i	−0.172688	+	0.531481i	−0.999520	−	0.0309686i	$-0.990141\pi$
$971$	−5225.07	+	16081.1i	−0.172688	+	0.531481i	0.826832	+	0.562449i	$0.190141\pi$
$972$	6591.12	+	20285.4i	0.217500	+	0.669397i
$973$	−373.352	+	271.256i	−0.0123012	+	0.00893737i
$974$	14293.6	−	10384.9i	0.470221	−	0.341636i
$975$	−1503.64	−	4627.73i	−0.0493898	−	0.152006i
$976$	6740.51	−	20745.2i	0.221064	−	0.680365i
$977$	−19980.0	−	14516.3i	−0.654266	−	0.475352i	0.210456	−	0.977603i	$-0.432505\pi$
$977$	−19980.0	−	14516.3i	−0.654266	−	0.475352i	−0.864722	+	0.502251i	$0.832505\pi$
$978$	−468.005			−0.0153018
$979$		0			0
$980$	21353.7			0.696039
$981$	16407.1	+	11920.4i	0.533984	+	0.387962i
$982$	3222.43	−	9917.63i	0.104717	−	0.322285i
$983$	−9496.51	−	29227.2i	−0.308130	−	0.948326i	−0.978491	−	0.206291i	$-0.933861\pi$
$983$	−9496.51	−	29227.2i	−0.308130	−	0.948326i	0.670361	−	0.742035i	$-0.266139\pi$
$984$	−3687.42	+	2679.07i	−0.119462	+	0.0867944i
$985$	−8311.01	+	6038.30i	−0.268843	+	0.195326i
$986$	−1375.75	−	4234.13i	−0.0444350	−	0.136757i
$987$	−70.5233	+	217.048i	−0.00227435	+	0.00699972i
$988$	48418.8	+	35178.3i	1.55912	+	1.13276i
$989$	−31074.3			−0.999094
$990$		0			0
$991$	40862.5			1.30983			0.654915	−	0.755703i	$-0.272705\pi$
$991$	40862.5			1.30983			0.654915	+	0.755703i	$0.272705\pi$
$992$	−707.810	−	514.254i	−0.0226542	−	0.0164593i
$993$	1851.30	−	5697.71i	0.0591633	−	0.182086i
$994$	40.3873	+	124.299i	0.00128874	+	0.00396633i
$995$	21564.3	−	15667.3i	0.687068	−	0.499184i
$996$	10716.6	−	7786.06i	0.340932	−	0.247702i
$997$	−17934.9	−	55198.1i	−0.569715	−	1.75340i	−0.653509	−	0.756918i	$-0.726704\pi$
$997$	−17934.9	−	55198.1i	−0.569715	−	1.75340i	0.0837946	−	0.996483i	$-0.473296\pi$
$998$	247.148	−	760.644i	0.00783902	−	0.0241260i
$999$	−11091.5	−	8058.43i	−0.351270	−	0.255213i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	121.4.c.i.81.1		8
11.2	odd	10		121.4.c.h.27.1		8
11.3	even	5	inner	121.4.c.i.3.1		8
11.4	even	5		121.4.c.b.9.2		8
11.5	even	5		121.4.a.f.1.3		4
11.6	odd	10		121.4.a.g.1.2		4
11.7	odd	10		121.4.c.h.9.1		8
11.8	odd	10		11.4.c.a.3.2	✓	8
11.9	even	5		121.4.c.b.27.2		8
11.10	odd	2		11.4.c.a.4.2	yes	8
33.5	odd	10		1089.4.a.bh.1.2		4
33.8	even	10		99.4.f.c.91.1		8
33.17	even	10		1089.4.a.y.1.3		4
33.32	even	2		99.4.f.c.37.1		8
44.19	even	10		176.4.m.c.113.2		8
44.27	odd	10		1936.4.a.bl.1.4		4
44.39	even	10		1936.4.a.bk.1.4		4
44.43	even	2		176.4.m.c.81.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
11.4.c.a.3.2	✓	8	11.8	odd	10
11.4.c.a.4.2	yes	8	11.10	odd	2
99.4.f.c.37.1		8	33.32	even	2
99.4.f.c.91.1		8	33.8	even	10
121.4.a.f.1.3		4	11.5	even	5
121.4.a.g.1.2		4	11.6	odd	10
121.4.c.b.9.2		8	11.4	even	5
121.4.c.b.27.2		8	11.9	even	5
121.4.c.h.9.1		8	11.7	odd	10
121.4.c.h.27.1		8	11.2	odd	10
121.4.c.i.3.1		8	11.3	even	5	inner
121.4.c.i.81.1		8	1.1	even	1	trivial
176.4.m.c.81.2		8	44.43	even	2
176.4.m.c.113.2		8	44.19	even	10
1089.4.a.y.1.3		4	33.17	even	10
1089.4.a.bh.1.2		4	33.5	odd	10
1936.4.a.bk.1.4		4	44.39	even	10
1936.4.a.bl.1.4		4	44.27	odd	10

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:	\( N \)	\(=\)	\( 121 = 11^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	121.c (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.747004 - 0.542730i) q^{2} +(-0.476313 + 1.46594i) q^{3} +(-2.20868 - 6.79761i) q^{4} +(-7.05908 + 5.12872i) q^{5} +(1.15142 - 0.836554i) q^{6} +(-0.239524 - 0.737179i) q^{7} +(-4.32202 + 13.3018i) q^{8} +(19.9214 + 14.4737i) q^{9} +O(q^{10})\)	\(q+(-0.747004 - 0.542730i) q^{2} +(-0.476313 + 1.46594i) q^{3} +(-2.20868 - 6.79761i) q^{4} +(-7.05908 + 5.12872i) q^{5} +(1.15142 - 0.836554i) q^{6} +(-0.239524 - 0.737179i) q^{7} +(-4.32202 + 13.3018i) q^{8} +(19.9214 + 14.4737i) q^{9} +8.05666 q^{10} +11.0169 q^{12} +(52.2644 + 37.9723i) q^{13} +(-0.221164 + 0.680672i) q^{14} +(-4.15607 - 12.7911i) q^{15} +(-35.8113 + 26.0184i) q^{16} +(56.7325 - 41.2186i) q^{17} +(-7.02601 - 21.6238i) q^{18} +(-40.0535 + 123.272i) q^{19} +(50.4542 + 36.6572i) q^{20} +1.19475 q^{21} +103.308 q^{23} +(-17.4410 - 12.6716i) q^{24} +(-15.1003 + 46.4740i) q^{25} +(-18.4330 - 56.7309i) q^{26} +(-64.3755 + 46.7715i) q^{27} +(-4.48202 + 3.25638i) q^{28} +(21.2472 + 65.3921i) q^{29} +(-3.83749 + 11.8106i) q^{30} +(-4.63339 - 3.36636i) q^{31} +152.763 q^{32} -64.7499 q^{34} +(5.47160 + 3.97535i) q^{35} +(54.3868 - 167.385i) q^{36} +(53.2416 + 163.861i) q^{37} +(96.8236 - 70.3464i) q^{38} +(-80.5593 + 58.5298i) q^{39} +(-37.7117 - 116.065i) q^{40} +(65.3332 - 201.075i) q^{41} +(-0.892481 - 0.648426i) q^{42} -300.793 q^{43} -214.858 q^{45} +(-77.1713 - 56.0682i) q^{46} +(-59.0277 + 181.669i) q^{47} +(-21.0841 - 64.8901i) q^{48} +(277.007 - 201.257i) q^{49} +(36.5029 - 26.5209i) q^{50} +(33.4015 + 102.799i) q^{51} +(142.686 - 439.141i) q^{52} +(-519.068 - 377.125i) q^{53} +73.4730 q^{54} +10.8410 q^{56} +(-161.632 - 117.432i) q^{57} +(19.6185 - 60.3796i) q^{58} +(16.0697 + 49.4574i) q^{59} +(-77.7692 + 56.5027i) q^{60} +(-398.663 + 289.646i) q^{61} +(1.63414 + 5.02936i) q^{62} +(5.89807 - 18.1524i) q^{63} +(172.376 + 125.238i) q^{64} -563.687 q^{65} -320.988 q^{67} +(-405.491 - 294.607i) q^{68} +(-49.2068 + 151.443i) q^{69} +(-1.92976 - 5.93920i) q^{70} +(147.737 - 107.337i) q^{71} +(-278.627 + 202.434i) q^{72} +(64.2516 + 197.746i) q^{73} +(49.1605 - 151.300i) q^{74} +(-60.9357 - 44.2724i) q^{75} +926.421 q^{76} +91.9439 q^{78} +(528.180 + 383.745i) q^{79} +(119.353 - 367.332i) q^{80} +(167.549 + 515.663i) q^{81} +(-157.933 + 114.745i) q^{82} +(972.740 - 706.737i) q^{83} +(-2.63881 - 8.12143i) q^{84} +(-189.080 + 581.930i) q^{85} +(224.694 + 163.249i) q^{86} -105.981 q^{87} +716.942 q^{89} +(160.500 + 116.610i) q^{90} +(15.4738 - 47.6234i) q^{91} +(-228.174 - 702.246i) q^{92} +(7.14183 - 5.18884i) q^{93} +(142.691 - 103.671i) q^{94} +(-349.487 - 1075.61i) q^{95} +(-72.7629 + 223.941i) q^{96} +(508.361 + 369.346i) q^{97} -316.153 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 7 q^{2} - 3 q^{3} + 3 q^{4} - 7 q^{5} + 29 q^{6} + 35 q^{7} - 47 q^{8} + 31 q^{9}+O(q^{10}) \) 8 * q + 7 * q^2 - 3 * q^3 + 3 * q^4 - 7 * q^5 + 29 * q^6 + 35 * q^7 - 47 * q^8 + 31 * q^9	\( 8 q + 7 q^{2} - 3 q^{3} + 3 q^{4} - 7 q^{5} + 29 q^{6} + 35 q^{7} - 47 q^{8} + 31 q^{9} - 40 q^{10} + 190 q^{12} + 65 q^{13} - 196 q^{14} - 121 q^{15} - 377 q^{16} + 31 q^{17} + 102 q^{18} - 148 q^{19} + 342 q^{20} - 334 q^{21} - 12 q^{23} + 447 q^{24} - 201 q^{25} - 140 q^{26} + 72 q^{27} + 42 q^{28} + 199 q^{29} + 114 q^{30} - 361 q^{31} - 324 q^{32} - 298 q^{34} - 237 q^{35} + 120 q^{36} + 81 q^{37} - 52 q^{38} - 365 q^{39} - 532 q^{40} + 31 q^{41} + 170 q^{42} + 650 q^{43} + 452 q^{45} - 1204 q^{46} + 857 q^{47} + 644 q^{48} + 1375 q^{49} + 147 q^{50} + 246 q^{51} + 590 q^{52} - 1493 q^{53} + 3100 q^{54} - 1560 q^{56} - 102 q^{57} + 1392 q^{58} + 676 q^{59} + 1068 q^{60} + 525 q^{61} - 2456 q^{62} + 68 q^{63} + 471 q^{64} - 1790 q^{65} + 86 q^{67} - 710 q^{68} - 42 q^{69} - 144 q^{70} + 1143 q^{71} - 919 q^{72} + 2155 q^{73} + 1476 q^{74} - 160 q^{75} + 242 q^{76} - 1340 q^{78} + 861 q^{79} - 1916 q^{80} - 26 q^{81} - 3497 q^{82} - 52 q^{83} + 84 q^{84} - 2383 q^{85} + 1061 q^{86} - 2310 q^{87} + 3782 q^{89} + 1682 q^{90} + 135 q^{91} - 2450 q^{92} - 2077 q^{93} - 702 q^{94} + 1317 q^{95} - 1252 q^{96} - 1344 q^{97} - 2740 q^{98}+O(q^{100}) \) 8 * q + 7 * q^2 - 3 * q^3 + 3 * q^4 - 7 * q^5 + 29 * q^6 + 35 * q^7 - 47 * q^8 + 31 * q^9 - 40 * q^10 + 190 * q^12 + 65 * q^13 - 196 * q^14 - 121 * q^15 - 377 * q^16 + 31 * q^17 + 102 * q^18 - 148 * q^19 + 342 * q^20 - 334 * q^21 - 12 * q^23 + 447 * q^24 - 201 * q^25 - 140 * q^26 + 72 * q^27 + 42 * q^28 + 199 * q^29 + 114 * q^30 - 361 * q^31 - 324 * q^32 - 298 * q^34 - 237 * q^35 + 120 * q^36 + 81 * q^37 - 52 * q^38 - 365 * q^39 - 532 * q^40 + 31 * q^41 + 170 * q^42 + 650 * q^43 + 452 * q^45 - 1204 * q^46 + 857 * q^47 + 644 * q^48 + 1375 * q^49 + 147 * q^50 + 246 * q^51 + 590 * q^52 - 1493 * q^53 + 3100 * q^54 - 1560 * q^56 - 102 * q^57 + 1392 * q^58 + 676 * q^59 + 1068 * q^60 + 525 * q^61 - 2456 * q^62 + 68 * q^63 + 471 * q^64 - 1790 * q^65 + 86 * q^67 - 710 * q^68 - 42 * q^69 - 144 * q^70 + 1143 * q^71 - 919 * q^72 + 2155 * q^73 + 1476 * q^74 - 160 * q^75 + 242 * q^76 - 1340 * q^78 + 861 * q^79 - 1916 * q^80 - 26 * q^81 - 3497 * q^82 - 52 * q^83 + 84 * q^84 - 2383 * q^85 + 1061 * q^86 - 2310 * q^87 + 3782 * q^89 + 1682 * q^90 + 135 * q^91 - 2450 * q^92 - 2077 * q^93 - 702 * q^94 + 1317 * q^95 - 1252 * q^96 - 1344 * q^97 - 2740 * q^98

Introduction

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