LMFDB - Embedded newform 128.4.k.a.5.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [128,4,Mod(5,128)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("128.5");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 128 = 2^{7} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	128.k (of order $32$, degree $16$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.55224448073$
Analytic rank:	$0$
Dimension:	$752$
Relative dimension:	$47$ over $\Q(\zeta_{32})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{32}]$

Embedding invariants

Embedding label			5.16
Character	$\chi$	$=$	128.5
Dual form			128.4.k.a.77.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.35278 + 2.48395i) q^{2} +(6.26012 + 1.89899i) q^{3} +(-4.33998 - 6.72046i) q^{4} +(-18.2007 - 1.79261i) q^{5} +(-13.1855 + 12.9809i) q^{6} +(-7.34552 - 10.9934i) q^{7} +(22.5643 - 1.68898i) q^{8} +(13.1332 + 8.77534i) q^{9} +O(q^{10})$	\(q+(-1.35278 + 2.48395i) q^{2} +(6.26012 + 1.89899i) q^{3} +(-4.33998 - 6.72046i) q^{4} +(-18.2007 - 1.79261i) q^{5} +(-13.1855 + 12.9809i) q^{6} +(-7.34552 - 10.9934i) q^{7} +(22.5643 - 1.68898i) q^{8} +(13.1332 + 8.77534i) q^{9} +(29.0742 - 42.7844i) q^{10} +(32.0828 - 60.0227i) q^{11} +(-14.4067 - 50.3124i) q^{12} +(-0.252210 - 2.56073i) q^{13} +(37.2438 - 3.37431i) q^{14} +(-110.534 - 45.7847i) q^{15} +(-26.3292 + 58.3333i) q^{16} +(-41.0739 + 17.0134i) q^{17} +(-39.5638 + 20.7511i) q^{18} +(-12.2353 + 14.9088i) q^{19} +(66.9433 + 130.097i) q^{20} +(-25.1076 - 82.7687i) q^{21} +(105.692 + 160.889i) q^{22} +(-38.3284 - 192.690i) q^{23} +(144.462 + 32.2760i) q^{24} +(205.452 + 40.8670i) q^{25} +(6.70189 + 2.83762i) q^{26} +(-46.5008 - 56.6614i) q^{27} +(-42.0010 + 97.0762i) q^{28} +(-153.780 + 82.1971i) q^{29} +(263.255 - 212.624i) q^{30} +(30.3540 + 30.3540i) q^{31} +(-109.279 - 144.312i) q^{32} +(314.824 - 314.824i) q^{33} +(13.3036 - 125.041i) q^{34} +(113.987 + 213.254i) q^{35} +(1.97639 - 126.346i) q^{36} +(-53.1205 + 43.5949i) q^{37} +(-20.4809 - 50.5601i) q^{38} +(3.28392 - 16.5094i) q^{39} +(-413.713 - 9.70836i) q^{40} +(-166.455 + 33.1099i) q^{41} +(239.558 + 49.6018i) q^{42} +(338.088 - 102.558i) q^{43} +(-542.619 + 44.8861i) q^{44} +(-223.302 - 183.260i) q^{45} +(530.481 + 165.461i) q^{46} +(84.3929 + 203.743i) q^{47} +(-275.598 + 315.175i) q^{48} +(64.3633 - 155.387i) q^{49} +(-379.443 + 455.048i) q^{50} +(-289.436 + 28.5069i) q^{51} +(-16.1147 + 12.8085i) q^{52} +(-419.041 - 223.982i) q^{53} +(203.649 - 38.8552i) q^{54} +(-691.525 + 1034.94i) q^{55} +(-184.314 - 235.651i) q^{56} +(-104.906 + 70.0960i) q^{57} +(3.85706 - 493.176i) q^{58} +(4.86748 - 49.4203i) q^{59} +(172.021 + 941.544i) q^{60} +(72.5847 - 239.280i) q^{61} +(-116.460 + 34.3354i) q^{62} -208.838i q^{63} +(506.295 - 76.2214i) q^{64} +47.0590i q^{65} +(356.119 + 1207.89i) q^{66} +(-315.821 + 1041.12i) q^{67} +(292.598 + 202.198i) q^{68} +(125.975 - 1279.05i) q^{69} +(-683.910 - 5.34877i) q^{70} +(98.5107 - 65.8228i) q^{71} +(311.163 + 175.828i) q^{72} +(-284.203 + 425.340i) q^{73} +(-36.4270 - 190.923i) q^{74} +(1208.55 + 645.983i) q^{75} +(153.295 + 17.5232i) q^{76} +(-895.515 + 88.2005i) q^{77} +(36.5660 + 30.4906i) q^{78} +(291.910 - 704.734i) q^{79} +(583.777 - 1014.51i) q^{80} +(-346.704 - 837.018i) q^{81} +(142.933 - 458.255i) q^{82} +(-477.063 - 391.515i) q^{83} +(-447.277 + 527.949i) q^{84} +(778.071 - 236.025i) q^{85} +(-202.610 + 978.530i) q^{86} +(-1118.77 + 222.538i) q^{87} +(622.548 - 1408.56i) q^{88} +(238.905 - 1201.06i) q^{89} +(757.286 - 306.762i) q^{90} +(-26.2984 + 21.5825i) q^{91} +(-1128.62 + 1093.85i) q^{92} +(132.378 + 247.661i) q^{93} +(-620.251 - 65.9911i) q^{94} +(249.416 - 249.416i) q^{95} +(-410.054 - 1110.93i) q^{96} +(553.968 + 553.968i) q^{97} +(298.903 + 370.079i) q^{98} +(948.069 - 506.754i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 752 q - 16 q^{2} - 16 q^{3} - 16 q^{4} - 16 q^{5} - 16 q^{6} - 16 q^{7} - 16 q^{8} - 16 q^{9}+O(q^{10}) $ 752 * q - 16 * q^2 - 16 * q^3 - 16 * q^4 - 16 * q^5 - 16 * q^6 - 16 * q^7 - 16 * q^8 - 16 * q^9	\( 752 q - 16 q^{2} - 16 q^{3} - 16 q^{4} - 16 q^{5} - 16 q^{6} - 16 q^{7} - 16 q^{8} - 16 q^{9} - 16 q^{10} - 16 q^{11} - 16 q^{12} - 16 q^{13} - 16 q^{14} - 16 q^{15} - 16 q^{16} - 16 q^{17} - 16 q^{18} - 16 q^{19} - 16 q^{20} - 16 q^{21} - 16 q^{22} - 16 q^{23} - 16 q^{24} - 16 q^{25} - 16 q^{26} - 16 q^{27} - 16 q^{28} - 16 q^{29} - 16 q^{30} - 16 q^{31} - 16 q^{32} - 16 q^{33} - 16 q^{34} - 16 q^{35} - 16 q^{36} - 16 q^{37} - 16 q^{38} - 16 q^{39} - 16 q^{40} - 16 q^{41} - 16 q^{42} - 16 q^{43} - 16 q^{44} - 16 q^{45} - 16 q^{46} - 16 q^{47} - 16 q^{48} - 16 q^{49} + 5696 q^{50} - 16 q^{51} + 6608 q^{52} - 16 q^{53} + 3440 q^{54} - 16 q^{55} - 800 q^{56} - 16 q^{57} - 4768 q^{58} - 16 q^{59} - 9808 q^{60} - 16 q^{61} - 5872 q^{62} - 12112 q^{64} - 10960 q^{66} - 16 q^{67} - 4144 q^{68} - 16 q^{69} - 4048 q^{70} - 16 q^{71} + 1280 q^{72} - 16 q^{73} + 5248 q^{74} - 16 q^{75} + 11888 q^{76} - 16 q^{77} + 14096 q^{78} - 16 q^{79} + 10016 q^{80} - 16 q^{81} - 16 q^{82} - 16 q^{83} - 16 q^{84} - 16 q^{85} - 16 q^{86} - 16 q^{87} - 16 q^{88} - 16 q^{89} - 16 q^{90} - 16 q^{91} - 16 q^{92} - 16 q^{93} - 16 q^{94} - 16 q^{95} - 16 q^{96} - 16 q^{97} - 16 q^{98} - 16 q^{99}+O(q^{100}) \) 752 * q - 16 * q^2 - 16 * q^3 - 16 * q^4 - 16 * q^5 - 16 * q^6 - 16 * q^7 - 16 * q^8 - 16 * q^9 - 16 * q^10 - 16 * q^11 - 16 * q^12 - 16 * q^13 - 16 * q^14 - 16 * q^15 - 16 * q^16 - 16 * q^17 - 16 * q^18 - 16 * q^19 - 16 * q^20 - 16 * q^21 - 16 * q^22 - 16 * q^23 - 16 * q^24 - 16 * q^25 - 16 * q^26 - 16 * q^27 - 16 * q^28 - 16 * q^29 - 16 * q^30 - 16 * q^31 - 16 * q^32 - 16 * q^33 - 16 * q^34 - 16 * q^35 - 16 * q^36 - 16 * q^37 - 16 * q^38 - 16 * q^39 - 16 * q^40 - 16 * q^41 - 16 * q^42 - 16 * q^43 - 16 * q^44 - 16 * q^45 - 16 * q^46 - 16 * q^47 - 16 * q^48 - 16 * q^49 + 5696 * q^50 - 16 * q^51 + 6608 * q^52 - 16 * q^53 + 3440 * q^54 - 16 * q^55 - 800 * q^56 - 16 * q^57 - 4768 * q^58 - 16 * q^59 - 9808 * q^60 - 16 * q^61 - 5872 * q^62 - 12112 * q^64 - 10960 * q^66 - 16 * q^67 - 4144 * q^68 - 16 * q^69 - 4048 * q^70 - 16 * q^71 + 1280 * q^72 - 16 * q^73 + 5248 * q^74 - 16 * q^75 + 11888 * q^76 - 16 * q^77 + 14096 * q^78 - 16 * q^79 + 10016 * q^80 - 16 * q^81 - 16 * q^82 - 16 * q^83 - 16 * q^84 - 16 * q^85 - 16 * q^86 - 16 * q^87 - 16 * q^88 - 16 * q^89 - 16 * q^90 - 16 * q^91 - 16 * q^92 - 16 * q^93 - 16 * q^94 - 16 * q^95 - 16 * q^96 - 16 * q^97 - 16 * q^98 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−1.35278	+	2.48395i	−0.478280	+	0.878208i
$2$	−1.35278	+	2.48395i	−0.478280	+	0.878208i
$3$	6.26012	+	1.89899i	1.20476	+	0.365460i	0.827935	−	0.560825i	$-0.189516\pi$
$3$	6.26012	+	1.89899i	1.20476	+	0.365460i	0.376825	+	0.926284i	$0.377016\pi$
$4$	−4.33998	−	6.72046i	−0.542497	−	0.840057i
$5$	−18.2007	−	1.79261i	−1.62792	−	0.160336i	−0.757562	−	0.652763i	$-0.773610\pi$
$5$	−18.2007	−	1.79261i	−1.62792	−	0.160336i	−0.870354	+	0.492427i	$0.836110\pi$
$6$	−13.1855	+	12.9809i	−0.897162	+	0.883237i
$7$	−7.34552	−	10.9934i	−0.396621	−	0.593585i	0.578385	−	0.815764i	$-0.303683\pi$
$7$	−7.34552	−	10.9934i	−0.396621	−	0.593585i	−0.975006	+	0.222179i	$0.928683\pi$
$8$	22.5643	−	1.68898i	0.997210	−	0.0746431i
$9$	13.1332	+	8.77534i	0.486416	+	0.325012i
$10$	29.0742	−	42.7844i	0.919407	−	1.35296i
$11$	32.0828	−	60.0227i	0.879393	−	1.64523i	0.121749	−	0.992561i	$-0.461150\pi$
$11$	32.0828	−	60.0227i	0.879393	−	1.64523i	0.757644	−	0.652668i	$-0.226350\pi$
$12$	−14.4067	−	50.3124i	−0.346572	−	1.21033i
$13$	−0.252210	−	2.56073i	−0.00538080	−	0.0546321i	0.992119	−	0.125296i	$-0.0399881\pi$
$13$	−0.252210	−	2.56073i	−0.00538080	−	0.0546321i	−0.997500	+	0.0706641i	$0.977488\pi$
$14$	37.2438	−	3.37431i	0.710987	−	0.0644159i
$15$	−110.534	−	45.7847i	−1.90265	−	0.788104i
$16$	−26.3292	+	58.3333i	−0.411393	+	0.911458i
$17$	−41.0739	+	17.0134i	−0.585993	+	0.242726i	−0.655926	−	0.754825i	$-0.727722\pi$
$17$	−41.0739	+	17.0134i	−0.585993	+	0.242726i	0.0699324	+	0.997552i	$0.477722\pi$
$18$	−39.5638	+	20.7511i	−0.518071	+	0.271727i
$19$	−12.2353	+	14.9088i	−0.147735	+	0.180016i	−0.841620	−	0.540070i	$-0.818398\pi$
$19$	−12.2353	+	14.9088i	−0.147735	+	0.180016i	0.693885	+	0.720086i	$0.255898\pi$
$20$	66.9433	+	130.097i	0.748449	+	1.45452i
$21$	−25.1076	−	82.7687i	−0.260901	−	0.860077i
$22$	105.692	+	160.889i	1.02426	+	1.55917i
$23$	−38.3284	−	192.690i	−0.347479	−	1.74690i	−0.619866	−	0.784707i	$-0.712813\pi$
$23$	−38.3284	−	192.690i	−0.347479	−	1.74690i	0.272387	−	0.962188i	$-0.412187\pi$
$24$	144.462	+	32.2760i	1.22868	+	0.274513i
$25$	205.452	+	40.8670i	1.64362	+	0.326936i
$26$	6.70189	+	2.83762i	0.0505519	+	0.0214040i
$27$	−46.5008	−	56.6614i	−0.331448	−	0.403870i
$28$	−42.0010	+	97.0762i	−0.283480	+	0.655203i
$29$	−153.780	+	82.1971i	−0.984698	+	0.526332i	−0.883448	−	0.468529i	$-0.844784\pi$
$29$	−153.780	+	82.1971i	−0.984698	+	0.526332i	−0.101250	+	0.994861i	$0.532284\pi$
$30$	263.255	−	212.624i	1.60212	−	1.29399i
$31$	30.3540	+	30.3540i	0.175862	+	0.175862i	0.789549	−	0.613687i	$-0.210314\pi$
$31$	30.3540	+	30.3540i	0.175862	+	0.175862i	−0.613687	+	0.789549i	$0.710314\pi$
$32$	−109.279	−	144.312i	−0.603689	−	0.797220i
$33$	314.824	−	314.824i	1.66072	−	1.66072i
$34$	13.3036	−	125.041i	0.0671044	−	0.630715i
$35$	113.987	+	213.254i	0.550493	+	1.02990i
$36$	1.97639	−	126.346i	0.00914997	−	0.584935i
$37$	−53.1205	+	43.5949i	−0.236026	+	0.193701i	−0.744970	−	0.667098i	$-0.767536\pi$
$37$	−53.1205	+	43.5949i	−0.236026	+	0.193701i	0.508944	+	0.860800i	$0.330036\pi$
$38$	−20.4809	−	50.5601i	−0.0874327	−	0.215840i
$39$	3.28392	−	16.5094i	0.0134833	−	0.0677851i
$40$	−413.713	−	9.70836i	−1.63534	−	0.0383757i
$41$	−166.455	+	33.1099i	−0.634045	+	0.126119i	−0.501640	−	0.865076i	$-0.667270\pi$
$41$	−166.455	+	33.1099i	−0.634045	+	0.126119i	−0.132405	+	0.991196i	$0.542270\pi$
$42$	239.558	+	49.6018i	0.880110	+	0.182231i
$43$	338.088	−	102.558i	1.19902	−	0.363719i	0.373253	−	0.927729i	$-0.378242\pi$
$43$	338.088	−	102.558i	1.19902	−	0.363719i	0.825768	+	0.564010i	$0.190742\pi$
$44$	−542.619	+	44.8861i	−1.85915	+	0.153792i
$45$	−223.302	−	183.260i	−0.739733	−	0.607083i
$46$	530.481	+	165.461i	1.70033	+	0.530345i
$47$	84.3929	+	203.743i	0.261914	+	0.632317i	0.999057	−	0.0434201i	$-0.0138254\pi$
$47$	84.3929	+	203.743i	0.261914	+	0.632317i	−0.737143	+	0.675737i	$0.763825\pi$
$48$	−275.598	+	315.175i	−0.828731	+	0.947740i
$49$	64.3633	−	155.387i	0.187648	−	0.453023i
$50$	−379.443	+	455.048i	−1.07323	+	1.28707i
$51$	−289.436	+	28.5069i	−0.794688	+	0.0782699i
$52$	−16.1147	+	12.8085i	−0.0429751	+	0.0341580i
$53$	−419.041	−	223.982i	−1.08603	−	0.580496i	−0.171572	−	0.985172i	$-0.554884\pi$
$53$	−419.041	−	223.982i	−1.08603	−	0.580496i	−0.914460	+	0.404676i	$0.867384\pi$
$54$	203.649	−	38.8552i	0.513206	−	0.0979171i
$55$	−691.525	+	1034.94i	−1.69537	+	2.53730i
$56$	−184.314	−	235.651i	−0.439822	−	0.562324i
$57$	−104.906	+	70.0960i	−0.243774	+	0.162885i
$58$	3.85706	−	493.176i	0.00873202	−	1.11650i
$59$	4.86748	−	49.4203i	0.0107405	−	0.109050i	−0.988320	−	0.152395i	$-0.951301\pi$
$59$	4.86748	−	49.4203i	0.0107405	−	0.109050i	0.999060	+	0.0433447i	$0.0138014\pi$
$60$	172.021	+	941.544i	0.370131	+	2.02588i
$61$	72.5847	−	239.280i	0.152353	−	0.502240i	−0.847227	−	0.531231i	$-0.821730\pi$
$61$	72.5847	−	239.280i	0.152353	−	0.502240i	0.999580	+	0.0289913i	$0.00922952\pi$
$62$	−116.460	+	34.3354i	−0.238555	+	0.0703324i
$63$		−	208.838i		−	0.417636i
$64$	506.295	−	76.2214i	0.988857	−	0.148870i
$65$			47.0590i			0.0897993i
$66$	356.119	+	1207.89i	0.664170	+	2.25275i
$67$	−315.821	+	1041.12i	−0.575875	+	1.89841i	−0.166492	+	0.986043i	$0.553244\pi$
$67$	−315.821	+	1041.12i	−0.575875	+	1.89841i	−0.409383	+	0.912363i	$0.634256\pi$
$68$	292.598	+	202.198i	0.521804	+	0.360590i
$69$	125.975	−	1279.05i	0.219791	−	2.23158i
$70$	−683.910	−	5.34877i	−1.16776	−	0.00913286i
$71$	98.5107	−	65.8228i	0.164663	−	0.110024i	−0.470508	−	0.882396i	$-0.655929\pi$
$71$	98.5107	−	65.8228i	0.164663	−	0.110024i	0.635171	+	0.772371i	$0.280929\pi$
$72$	311.163	+	175.828i	0.509319	+	0.287798i
$73$	−284.203	+	425.340i	−0.455664	+	0.681949i	−0.986171	−	0.165731i	$-0.947002\pi$
$73$	−284.203	+	425.340i	−0.455664	+	0.681949i	0.530507	+	0.847680i	$0.322002\pi$
$74$	−36.4270	−	190.923i	−0.0572238	−	0.299923i
$75$	1208.55	+	645.983i	1.86068	+	0.994556i
$76$	153.295	+	17.5232i	0.231370	+	0.0264480i
$77$	−895.515	+	88.2005i	−1.32537	+	0.130537i
$78$	36.5660	+	30.4906i	0.0530806	+	0.0442613i
$79$	291.910	−	704.734i	0.415727	−	1.00365i	−0.567844	−	0.823136i	$-0.692222\pi$
$79$	291.910	−	704.734i	0.415727	−	1.00365i	0.983572	−	0.180519i	$-0.0577776\pi$
$80$	583.777	−	1014.51i	0.815853	−	1.41782i
$81$	−346.704	−	837.018i	−0.475589	−	1.14817i
$82$	142.933	−	458.255i	0.192492	−	0.617144i
$83$	−477.063	−	391.515i	−0.630897	−	0.517764i	0.263719	−	0.964600i	$-0.415051\pi$
$83$	−477.063	−	391.515i	−0.630897	−	0.517764i	−0.894616	+	0.446836i	$0.852551\pi$
$84$	−447.277	+	527.949i	−0.580976	+	0.685762i
$85$	778.071	−	236.025i	0.992866	−	0.301183i
$86$	−202.610	+	978.530i	−0.254046	+	1.22695i
$87$	−1118.77	+	222.538i	−1.37868	+	0.274236i
$88$	622.548	−	1408.56i	0.754135	−	1.70628i
$89$	238.905	−	1201.06i	0.284539	−	1.43047i	−0.528832	−	0.848726i	$-0.677370\pi$
$89$	238.905	−	1201.06i	0.284539	−	1.43047i	0.813371	−	0.581746i	$-0.197630\pi$
$90$	757.286	−	306.762i	0.886944	−	0.359284i
$91$	−26.2984	+	21.5825i	−0.0302947	+	0.0248622i
$92$	−1128.62	+	1093.85i	−1.27899	+	1.23959i
$93$	132.378	+	247.661i	0.147601	+	0.276143i
$94$	−620.251	−	65.9911i	−0.680574	−	0.0724092i
$95$	249.416	−	249.416i	0.269364	−	0.269364i
$96$	−410.054	−	1110.93i	−0.435948	−	1.18108i
$97$	553.968	+	553.968i	0.579865	+	0.579865i	0.934866	−	0.355001i	$-0.115519\pi$
$97$	553.968	+	553.968i	0.579865	+	0.579865i	−0.355001	+	0.934866i	$0.615519\pi$
$98$	298.903	+	370.079i	0.308100	+	0.381466i
$99$	948.069	−	506.754i	0.962470	−	0.514451i
$100$	−617.014	−	1558.10i	−0.617014	−	1.55810i
$101$	1218.18	+	1484.36i	1.20014	+	1.46237i	0.850894	+	0.525337i	$0.176061\pi$
$101$	1218.18	+	1484.36i	1.20014	+	1.46237i	0.349241	+	0.937033i	$0.386439\pi$
$102$	320.733	−	757.506i	0.311346	−	0.735336i
$103$	1910.54	+	380.030i	1.82768	+	0.363548i	0.984680	−	0.174369i	$-0.0557885\pi$
$103$	1910.54	+	380.030i	1.82768	+	0.363548i	0.842998	+	0.537917i	$0.180789\pi$
$104$	−10.0160	−	57.3550i	−0.00944370	−	0.0540781i
$105$	308.603	+	1551.45i	0.286825	+	1.44196i
$106$	1123.23	−	737.877i	1.02922	−	0.676122i
$107$	−288.387	−	950.683i	−0.260555	−	0.858935i	−0.985434	−	0.170058i	$-0.945604\pi$
$107$	−288.387	−	950.683i	−0.260555	−	0.858935i	0.724879	−	0.688876i	$-0.241896\pi$
$108$	−178.978	+	558.416i	−0.159465	+	0.497534i
$109$	−512.061	+	623.948i	−0.449968	+	0.548288i	−0.947750	−	0.319015i	$-0.896648\pi$
$109$	−512.061	+	623.948i	−0.449968	+	0.548288i	0.497782	+	0.867302i	$0.334148\pi$
$110$	−1635.26	−	3117.76i	−1.41741	−	2.70242i
$111$	−415.327	+	172.034i	−0.355145	+	0.147106i
$112$	834.680	−	139.043i	0.704195	−	0.117307i
$113$	1366.19	+	565.892i	1.13734	+	0.471103i	0.870271	−	0.492573i	$-0.163944\pi$
$113$	1366.19	+	565.892i	1.13734	+	0.471103i	0.267073	+	0.963676i	$0.413944\pi$
$114$	−32.2000	−	355.405i	−0.0264544	−	0.291989i
$115$	352.184	+	3575.79i	0.285577	+	2.89951i
$116$	1219.80	+	676.739i	0.976345	+	0.541669i
$117$	19.1589	−	35.8438i	0.0151388	−	0.0283228i
$118$	116.173	+	78.9453i	0.0906320	+	0.0615890i
$119$	488.743	+	326.568i	0.376496	+	0.251567i
$120$	−2571.45	−	846.410i	−1.95617	−	0.643886i
$121$	−1833.95	−	2744.70i	−1.37787	−	2.06214i
$122$	496.167	+	503.989i	0.368204	+	0.374009i
$123$	−1104.90	−	108.823i	−0.809964	−	0.0797744i
$124$	72.2571	−	335.728i	0.0523296	−	0.243140i
$125$	−1478.46	−	448.484i	−1.05790	−	0.320909i
$126$	518.741	+	282.511i	0.366771	+	0.199747i
$127$	218.861			0.152919			0.0764597	−	0.997073i	$-0.475638\pi$
$127$	218.861			0.152919			0.0764597	+	0.997073i	$0.475638\pi$
$128$	−495.575	+	1360.72i	−0.342211	+	0.939623i
$129$	2311.22			1.57746
$130$	−116.892	−	63.6604i	−0.0788624	−	0.0429492i
$131$	533.231	+	161.754i	0.355638	+	0.107882i	0.463048	−	0.886333i	$-0.346756\pi$
$131$	533.231	+	161.754i	0.355638	+	0.107882i	−0.107410	+	0.994215i	$0.534256\pi$
$132$	−3482.09	−	749.432i	−2.29604	−	0.494165i
$133$	253.772	+	24.9944i	0.165450	+	0.0162954i
$134$	−2158.85	−	2192.89i	−1.39177	−	1.41371i
$135$	744.774	+	1114.63i	0.474814	+	0.710610i
$136$	−898.069	+	453.268i	−0.566241	+	0.285790i
$137$	−367.434	−	245.512i	−0.229139	−	0.153106i	0.435701	−	0.900091i	$-0.356500\pi$
$137$	−367.434	−	245.512i	−0.229139	−	0.153106i	−0.664840	+	0.746986i	$0.731500\pi$
$138$	3006.66	+	2043.18i	1.85467	+	1.26034i
$139$	−824.924	+	1543.32i	−0.503375	+	0.941748i	0.494009	+	0.869457i	$0.335531\pi$
$139$	−824.924	+	1543.32i	−0.503375	+	0.941748i	−0.997384	+	0.0722913i	$0.976969\pi$
$140$	938.465	−	1691.56i	0.566534	−	1.02116i
$141$	141.405	+	1435.71i	0.0844573	+	0.857509i
$142$	30.2370	+	333.739i	0.0178692	+	0.197231i
$143$	−161.793	−	67.0170i	−0.0946142	−	0.0391905i
$144$	−857.681	+	535.057i	−0.496343	+	0.309639i
$145$	2946.24	−	1220.37i	1.68739	−	0.698942i
$146$	−672.058	−	1281.34i	−0.380958	−	0.726330i
$147$	697.999	−	850.514i	0.391633	−	0.477206i
$148$	523.520	+	167.793i	0.290764	+	0.0931928i
$149$	−394.072	−	1299.08i	−0.216669	−	0.714261i	−0.996136	−	0.0878187i	$-0.972010\pi$
$149$	−394.072	−	1299.08i	−0.216669	−	0.714261i	0.779468	−	0.626442i	$-0.215490\pi$
$150$	−3239.49	+	2128.10i	−1.76335	+	1.15839i
$151$	−587.247	−	2952.29i	−0.316487	−	1.59109i	−0.731873	−	0.681441i	$-0.761354\pi$
$151$	−587.247	−	2952.29i	−0.316487	−	1.59109i	0.415387	−	0.909645i	$-0.363646\pi$
$152$	−250.901	+	357.071i	−0.133886	+	0.190541i
$153$	−688.731	−	136.997i	−0.363925	−	0.0723893i
$154$	992.348	−	2343.73i	0.519258	−	1.22638i
$155$	−498.050	−	606.875i	−0.258092	−	0.314486i
$156$	−125.203	+	49.5809i	−0.0642580	+	0.0254465i
$157$	1264.00	−	675.623i	0.642537	−	0.343443i	−0.117738	−	0.993045i	$-0.537564\pi$
$157$	1264.00	−	675.623i	0.642537	−	0.343443i	0.760275	+	0.649601i	$0.225064\pi$
$158$	1355.63	+	1678.44i	0.682583	+	0.845122i
$159$	−2197.91	−	2197.91i	−1.09626	−	1.09626i
$160$	1730.26	+	2822.47i	0.854931	+	1.39460i
$161$	−1836.76	+	1836.76i	−0.899114	+	0.899114i
$162$	2548.12	+	271.106i	1.23580	+	0.131482i
$163$	418.131	+	782.267i	0.200923	+	0.375901i	0.962123	−	0.272617i	$-0.0878891\pi$
$163$	418.131	+	782.267i	0.200923	+	0.375901i	−0.761199	+	0.648518i	$0.775389\pi$
$164$	944.923	+	974.955i	0.449915	+	0.464215i
$165$	−6294.36	+	5165.65i	−2.96979	+	2.43724i
$166$	1617.86	−	655.365i	0.756449	−	0.306423i
$167$	−74.6804	+	375.444i	−0.0346045	+	0.173968i	−0.994223	−	0.107337i	$-0.965767\pi$
$167$	−74.6804	+	375.444i	−0.0346045	+	0.173968i	0.959618	+	0.281306i	$0.0907675\pi$
$168$	−706.330	−	1825.21i	−0.324372	−	0.838203i
$169$	2148.29	−	427.322i	0.977830	−	0.194502i
$170$	−466.284	+	2251.98i	−0.210367	+	1.01599i
$171$	−291.519	+	88.4312i	−0.130368	+	0.0395468i
$172$	−2156.53	−	1827.01i	−0.956011	−	0.809930i
$173$	499.884	+	410.244i	0.219685	+	0.180291i	0.737798	−	0.675021i	$-0.235866\pi$
$173$	499.884	+	410.244i	0.219685	+	0.180291i	−0.518114	+	0.855312i	$0.673366\pi$
$174$	960.679	−	3080.01i	0.418557	−	1.34193i
$175$	−1059.89	−	2558.80i	−0.457829	−	1.10530i
$176$	2656.61	+	3451.84i	1.13778	+	1.47837i
$177$	124.319	−	300.134i	0.0527933	−	0.127454i
$178$	2660.18	+	2218.20i	1.12016	+	0.934049i
$179$	−996.699	+	98.1663i	−0.416183	+	0.0409905i	−0.303942	−	0.952691i	$-0.598303\pi$
$179$	−996.699	+	98.1663i	−0.416183	+	0.0409905i	−0.112241	+	0.993681i	$0.535803\pi$
$180$	−262.461	+	2296.04i	−0.108681	+	0.950759i
$181$	−238.798	−	127.640i	−0.0980645	−	0.0524166i	0.421635	−	0.906765i	$-0.361456\pi$
$181$	−238.798	−	127.640i	−0.0980645	−	0.0524166i	−0.519700	+	0.854349i	$0.673956\pi$
$182$	−18.0339	−	94.5201i	−0.00734486	−	0.0384961i
$183$	908.778	−	1360.08i	0.367097	−	0.549400i
$184$	−1190.30	−	4283.17i	−0.476903	−	1.71608i
$185$	1044.98	−	698.231i	0.415288	−	0.277486i
$186$	−794.255	−	6.21176i	−0.313105	−	0.00244876i
$187$	−296.578	+	3011.20i	−0.115978	+	1.17755i
$188$	1002.98	−	1451.40i	0.389095	−	0.563054i
$189$	−281.326	+	927.408i	−0.108272	+	0.356926i
$190$	282.132	+	956.942i	0.107726	+	0.365389i
$191$		−	3906.72i		−	1.48000i	−0.672605	−	0.740001i	$-0.734825\pi$
$191$		−	3906.72i		−	1.48000i	0.672605	−	0.740001i	$-0.265175\pi$
$192$	3314.21	+	484.292i	1.24574	+	0.182035i
$193$		−	3941.94i		−	1.47019i	−0.677964	−	0.735095i	$-0.737137\pi$
$193$		−	3941.94i		−	1.47019i	0.677964	−	0.735095i	$-0.262863\pi$
$194$	−2125.42	+	626.631i	−0.786580	+	0.231904i
$195$	−89.3644	+	294.595i	−0.0328180	+	0.108187i
$196$	−1323.61	+	241.824i	−0.482364	+	0.0881284i
$197$	−295.367	+	2998.91i	−0.106822	+	1.08459i	0.781041	+	0.624479i	$0.214689\pi$
$197$	−295.367	+	2998.91i	−0.106822	+	1.08459i	−0.887864	+	0.460107i	$0.847811\pi$
$198$	−23.7792	+	3040.48i	−0.00853492	+	1.09130i
$199$	2808.45	−	1876.55i	1.00043	−	0.668467i	0.0564297	−	0.998407i	$-0.482028\pi$
$199$	2808.45	−	1876.55i	1.00043	−	0.668467i	0.944002	+	0.329939i	$0.107028\pi$
$200$	4704.91	+	575.130i	1.66344	+	0.203339i
$201$	−3954.15	+	5917.80i	−1.38758	+	2.07666i
$202$	−5335.00	+	1017.89i	−1.85826	+	0.354547i
$203$	2033.22	+	1086.78i	0.702975	+	0.375748i
$204$	1447.72	+	1821.42i	0.496868	+	0.625122i
$205$	3088.94	−	304.234i	1.05239	−	0.103652i
$206$	−3528.51	+	4231.58i	−1.19341	+	1.43120i
$207$	1187.54	−	2866.98i	0.398744	−	0.962652i
$208$	156.016	+	52.7096i	0.0520085	+	0.0175709i
$209$	502.321	+	1212.71i	0.166250	+	0.401364i
$210$	−4271.20	−	1332.22i	−1.40353	−	0.437771i
$211$	2281.02	+	1871.99i	0.744228	+	0.610772i	0.928166	−	0.372166i	$-0.121385\pi$
$211$	2281.02	+	1871.99i	0.744228	+	0.610772i	−0.183939	+	0.982938i	$0.558885\pi$
$212$	313.367	+	3788.22i	0.101519	+	1.22725i
$213$	741.685	−	224.988i	0.238589	−	0.0723751i
$214$	2751.57	+	569.727i	0.878941	+	0.181989i
$215$	−6337.27	+	1260.56i	−2.01022	+	0.399858i
$216$	−1144.96	−	1199.99i	−0.360669	−	0.378003i
$217$	110.726	−	556.658i	0.0346386	−	0.174140i
$218$	−857.148	−	2115.99i	−0.266300	−	0.657400i
$219$	−2586.86	+	2122.98i	−0.798191	+	0.655058i
$220$	9956.48	+	155.746i	3.05121	+	0.0477291i
$221$	53.9258	+	100.888i	0.0164138	+	0.0307080i
$222$	134.522	−	1264.37i	0.0406690	−	0.382248i
$223$	1230.89	−	1230.89i	0.369627	−	0.369627i	−0.497714	−	0.867341i	$-0.665827\pi$
$223$	1230.89	−	1230.89i	0.369627	−	0.369627i	0.867341	+	0.497714i	$0.165827\pi$
$224$	−783.762	+	2261.40i	−0.233783	+	0.674535i
$225$	2339.63	+	2339.63i	0.693223	+	0.693223i
$226$	−3253.79	+	2628.00i	−0.957695	+	0.773505i
$227$	1021.85	−	546.191i	0.298778	−	0.159700i	−0.315195	−	0.949027i	$-0.602070\pi$
$227$	1021.85	−	546.191i	0.298778	−	0.159700i	0.613974	+	0.789326i	$0.289570\pi$
$228$	926.367	+	400.802i	0.269080	+	0.116420i
$229$	1106.00	+	1347.67i	0.319156	+	0.388893i	0.907733	−	0.419548i	$-0.137812\pi$
$229$	1106.00	+	1347.67i	0.319156	+	0.388893i	−0.588577	+	0.808441i	$0.700312\pi$
$230$	−9358.49	−	3962.44i	−2.68296	−	1.13598i
$231$	−5773.52	−	1148.42i	−1.64446	−	0.327103i
$232$	−3331.11	+	2114.45i	−0.942664	+	0.598364i
$233$	−967.432	−	4863.61i	−0.272011	−	1.36749i	−0.839164	−	0.543879i	$-0.816955\pi$
$233$	−967.432	−	4863.61i	−0.272011	−	1.36749i	0.567153	−	0.823613i	$-0.308045\pi$
$234$	63.1163	+	96.0785i	0.0176327	+	0.0268412i
$235$	−1170.78	−	3859.53i	−0.324992	−	1.07135i
$236$	−353.252	+	181.772i	−0.0974354	+	0.0501369i
$237$	3165.67	−	3857.38i	0.867647	−	1.05723i
$238$	−1472.34	+	772.238i	−0.400998	+	0.210323i
$239$	−696.111	+	288.339i	−0.188400	+	0.0780380i	−0.474889	−	0.880046i	$-0.657512\pi$
$239$	−696.111	+	288.339i	−0.188400	+	0.0780380i	0.286489	+	0.958084i	$0.407512\pi$
$240$	5581.04	−	5242.35i	1.50106	−	1.40997i
$241$	−347.201	−	143.816i	−0.0928017	−	0.0384397i	0.335800	−	0.941933i	$-0.390994\pi$
$241$	−347.201	−	143.816i	−0.0928017	−	0.0384397i	−0.428601	+	0.903494i	$0.640994\pi$
$242$	9298.62	−	842.462i	2.46999	−	0.223783i
$243$	−386.939	−	3928.66i	−0.102149	−	1.03713i
$244$	−1923.09	+	550.667i	−0.504561	+	0.144479i
$245$	−1450.00	+	2712.76i	−0.378111	+	0.707396i
$246$	1765.00	−	2597.30i	0.457448	−	0.673162i
$247$	41.2632	+	27.5712i	0.0106296	+	0.00710247i
$248$	736.184	+	633.649i	0.188499	+	0.162245i
$249$	−2242.99	−	3356.87i	−0.570857	−	0.854348i
$250$	3114.03	−	3065.70i	0.787795	−	0.775568i
$251$	−5723.49	−	563.715i	−1.43930	−	0.141758i	−0.651947	−	0.758264i	$-0.726048\pi$
$251$	−5723.49	−	563.715i	−1.43930	−	0.141758i	−0.787350	+	0.616506i	$0.788548\pi$
$252$	−1403.48	+	906.351i	−0.350838	+	0.226566i
$253$	−12795.4	−	3881.45i	−3.17961	−	0.964525i
$254$	−296.070	+	543.638i	−0.0731382	+	0.134295i
$255$	5319.02			1.30624
$256$	−2709.55	−	3071.73i	−0.661511	−	0.749935i
$257$	3018.35			0.732605			0.366303	−	0.930496i	$-0.380623\pi$
$257$	3018.35			0.732605			0.366303	+	0.930496i	$0.380623\pi$
$258$	−3126.58	+	5740.96i	−0.754465	+	1.38534i
$259$	869.452	+	263.745i	0.208591	+	0.0632754i
$260$	316.258	−	204.235i	0.0754366	−	0.0487159i
$261$	−2740.93	−	269.958i	−0.650037	−	0.0640230i
$262$	−1123.13	+	1105.70i	−0.264837	+	0.260726i
$263$	4122.52	+	6169.79i	0.966561	+	1.44656i	0.893411	+	0.449240i	$0.148305\pi$
$263$	4122.52	+	6169.79i	0.966561	+	1.44656i	0.0731499	+	0.997321i	$0.476695\pi$
$264$	6572.05	−	7635.51i	1.53213	−	1.78005i
$265$	7225.31	+	4827.80i	1.67489	+	1.11913i
$266$	−405.382	+	596.545i	−0.0934420	+	0.137506i
$267$	3776.37	−	7065.09i	0.865581	−	1.61939i
$268$	8367.47	−	2395.98i	1.90718	−	0.546112i
$269$	−385.282	−	3911.84i	−0.0873274	−	0.886650i	−0.934649	−	0.355571i	$-0.884287\pi$
$269$	−385.282	−	3911.84i	−0.0873274	−	0.886650i	0.847322	−	0.531079i	$-0.178213\pi$
$270$	−3776.20	+	342.127i	−0.851157	+	0.0771154i
$271$	−5135.46	−	2127.18i	−1.15113	−	0.476815i	−0.276219	−	0.961095i	$-0.589082\pi$
$271$	−5135.46	−	2127.18i	−1.15113	−	0.476815i	−0.874913	+	0.484280i	$0.839082\pi$
$272$	88.9951	−	2843.93i	0.0198387	−	0.633964i
$273$	−205.616	+	85.1688i	−0.0455840	+	0.0188815i
$274$	1106.89	−	580.564i	0.244051	−	0.128004i
$275$	9044.43	−	11020.7i	1.98327	−	2.41662i
$276$	−9142.50	+	4704.42i	−1.99389	+	1.02599i
$277$	323.055	+	1064.97i	0.0700739	+	0.231003i	0.984981	−	0.172661i	$-0.0552366\pi$
$277$	323.055	+	1064.97i	0.0700739	+	0.231003i	−0.914907	+	0.403664i	$0.867737\pi$
$278$	−2717.59	−	4136.84i	−0.586297	−	0.892487i
$279$	132.279	+	665.012i	0.0283847	+	0.142700i
$280$	2932.21	+	4619.40i	0.625832	+	0.985936i
$281$	951.667	+	189.298i	0.202034	+	0.0401871i	0.295070	−	0.955476i	$-0.404657\pi$
$281$	951.667	+	189.298i	0.202034	+	0.0401871i	−0.0930356	+	0.995663i	$0.529657\pi$
$282$	−3757.52	−	1590.96i	−0.793466	−	0.335958i
$283$	975.502	+	1188.65i	0.204903	+	0.249675i	0.865315	−	0.501228i	$-0.167118\pi$
$283$	975.502	+	1188.65i	0.204903	+	0.249675i	−0.660412	+	0.750903i	$0.729618\pi$
$284$	−869.894	−	376.368i	−0.181756	−	0.0786385i
$285$	2035.01	−	1087.74i	0.422961	−	0.226077i
$286$	385.337	−	311.227i	0.0796694	−	0.0643469i
$287$	1586.69	+	1586.69i	0.326338	+	0.326338i
$288$	−168.800	−	2854.25i	−0.0345370	−	0.583987i
$289$	−2076.40	+	2076.40i	−0.422635	+	0.422635i
$290$	−954.272	+	8969.21i	−0.193230	+	1.81617i
$291$	2415.93	+	4519.88i	0.486681	+	0.910516i
$292$	4091.92	+	64.0086i	0.820073	+	0.0128282i
$293$	2793.14	−	2292.27i	0.556919	−	0.457051i	−0.313344	−	0.949640i	$-0.601449\pi$
$293$	2793.14	−	2292.27i	0.556919	−	0.457051i	0.870262	+	0.492589i	$0.163949\pi$
$294$	1168.39	+	2884.35i	0.231776	+	0.572172i
$295$	−177.183	+	890.757i	−0.0349694	+	0.175803i
$296$	−1125.00	+	1073.41i	−0.220909	+	0.210779i
$297$	−4892.84	+	973.247i	−0.955931	+	0.190147i
$298$	3759.94	+	778.516i	0.730898	+	0.151336i
$299$	−483.759	+	146.747i	−0.0935669	+	0.0283832i
$300$	−903.776	−	10925.6i	−0.173932	−	2.10262i
$301$	−3610.89	−	2963.38i	−0.691455	−	0.567463i
$302$	8127.74	+	2535.10i	1.54867	+	0.483043i
$303$	4807.19	+	11605.6i	0.911438	+	2.20041i
$304$	−547.533	−	1106.26i	−0.103300	−	0.208712i
$305$	−1750.02	+	4224.93i	−0.328545	+	0.793177i
$306$	1271.99	−	1525.44i	0.237631	−	0.284980i
$307$	−7493.97	+	738.092i	−1.39317	+	0.137215i	−0.766588	−	0.642139i	$-0.778047\pi$
$307$	−7493.97	+	738.092i	−1.39317	+	0.137215i	−0.626583	+	0.779354i	$0.715547\pi$
$308$	4479.27	+	5635.49i	0.828668	+	1.04257i
$309$	11238.5	+	6007.11i	2.06905	+	1.10593i
$310$	2181.20	−	416.161i	0.399625	−	0.0762462i
$311$	−128.911	+	192.929i	−0.0235045	+	0.0351769i	−0.843036	−	0.537857i	$-0.819234\pi$
$311$	−128.911	+	192.929i	−0.0235045	+	0.0351769i	0.819531	+	0.573034i	$0.194234\pi$
$312$	46.2153	−	378.069i	0.00838598	−	0.0686024i
$313$	574.882	−	384.124i	0.103816	−	0.0693673i	−0.502579	−	0.864531i	$-0.667615\pi$
$313$	574.882	−	384.124i	0.103816	−	0.0693673i	0.606394	+	0.795164i	$0.292615\pi$
$314$	−31.7033	+	4053.68i	−0.00569784	+	0.728543i
$315$	−374.364	+	3800.98i	−0.0669620	+	0.679876i
$316$	−6003.02	+	1096.76i	−1.06866	+	0.195245i
$317$	1535.62	−	5062.26i	0.272079	−	0.896924i	−0.709311	−	0.704896i	$-0.750994\pi$
$317$	1535.62	−	5062.26i	0.272079	−	0.896924i	0.981389	−	0.192028i	$-0.0615064\pi$
$318$	8432.76	−	2486.20i	1.48706	−	0.438425i
$319$			11867.4i			2.08291i
$320$	−9351.53	+	479.691i	−1.63365	+	0.0837985i
$321$		−	6499.03i		−	1.13003i
$322$	−2077.69	−	7047.16i	−0.359581	−	1.21964i
$323$	248.904	−	820.526i	0.0428773	−	0.141348i
$324$	−4120.46	+	5962.65i	−0.706526	+	1.02240i
$325$	52.8322	−	536.414i	0.00901724	−	0.0915536i
$326$	−2508.75	−	19.6206i	−0.426217	−	0.00333339i
$327$	−4390.43	+	2933.59i	−0.742480	+	0.496110i
$328$	−3700.01	+	1028.24i	−0.622862	+	0.173095i
$329$	1619.90	−	2424.36i	0.271453	−	0.406259i
$330$	−4316.32	−	22622.8i	−0.720016	−	3.77378i
$331$	−7797.93	−	4168.08i	−1.29490	−	0.692140i	−0.327373	−	0.944895i	$-0.606163\pi$
$331$	−7797.93	−	4168.08i	−1.29490	−	0.692140i	−0.967530	+	0.252755i	$0.918663\pi$
$332$	−560.720	+	4905.25i	−0.0926913	+	0.810875i
$333$	−1080.20	+	106.391i	−0.177762	+	0.0175080i
$334$	−831.556	−	693.395i	−0.136230	−	0.113595i
$335$	7614.46	−	18382.9i	1.24186	−	2.99811i
$336$	5489.23	+	714.620i	0.891257	+	0.116029i
$337$	834.484	+	2014.62i	0.134888	+	0.325648i	0.976862	−	0.213869i	$-0.0686067\pi$
$337$	834.484	+	2014.62i	0.134888	+	0.325648i	−0.841974	+	0.539518i	$0.818607\pi$
$338$	−1844.72	+	5914.31i	−0.296862	+	0.951764i
$339$	7477.86	+	6136.92i	1.19806	+	0.983220i
$340$	−4963.01	−	4204.65i	−0.791638	−	0.670674i
$341$	2795.77	−	848.087i	0.443986	−	0.134682i
$342$	174.702	−	843.744i	0.0276222	−	0.133405i
$343$	−6628.87	+	1318.56i	−1.04351	+	0.207568i
$344$	7455.50	−	2885.17i	1.16853	−	0.452203i
$345$	−4585.65	+	23053.6i	−0.715604	+	3.59758i
$346$	−1695.26	+	686.715i	−0.263403	+	0.106699i
$347$	1513.37	−	1241.99i	0.234126	−	0.192143i	−0.510013	−	0.860166i	$-0.670360\pi$
$347$	1513.37	−	1241.99i	0.234126	−	0.192143i	0.744140	+	0.668024i	$0.232860\pi$
$348$	6351.00	+	6552.85i	0.978303	+	1.00940i
$349$	2253.95	+	4216.84i	0.345705	+	0.646769i	0.993345	−	0.115178i	$-0.0367439\pi$
$349$	2253.95	+	4216.84i	0.345705	+	0.646769i	−0.647640	+	0.761947i	$0.724244\pi$
$350$	7789.71	+	828.781i	1.18965	+	0.126572i
$351$	−133.366	+	133.366i	−0.0202808	+	0.0202808i
$352$	−12168.0	+	1929.30i	−1.84249	+	0.292136i
$353$	−7149.94	−	7149.94i	−1.07805	−	1.07805i	−0.996684	−	0.0813694i	$-0.974071\pi$
$353$	−7149.94	−	7149.94i	−1.07805	−	1.07805i	−0.0813694	−	0.996684i	$-0.525929\pi$
$354$	577.339	+	714.817i	0.0866815	+	0.107322i
$355$	−1910.95	+	1021.43i	−0.285698	+	0.152709i
$356$	−9108.51	+	3607.02i	−1.35604	+	0.536999i
$357$	2439.44	+	2972.47i	0.361650	+	0.440672i
$358$	1104.47	−	2608.54i	0.163054	−	0.385100i
$359$	−3995.92	−	794.839i	−0.587456	−	0.116852i	−0.107592	−	0.994195i	$-0.534314\pi$
$359$	−3995.92	−	794.839i	−0.587456	−	0.116852i	−0.479864	+	0.877343i	$0.659314\pi$
$360$	−5348.18	−	3757.97i	−0.782984	−	0.550173i
$361$	1265.56	+	6362.38i	0.184510	+	0.927596i
$362$	640.091	−	420.492i	0.0929349	−	0.0610512i
$363$	−6268.60	−	20664.8i	−0.906380	−	2.98794i
$364$	259.179	+	83.0695i	0.0373205	+	0.0119616i
$365$	5935.15	−	7232.00i	0.851123	−	1.03710i
$366$	2149.00	+	4097.24i	0.306912	+	0.585154i
$367$	−926.756	+	383.875i	−0.131815	+	0.0545998i	−0.447616	−	0.894226i	$-0.647727\pi$
$367$	−926.756	+	383.875i	−0.131815	+	0.0545998i	0.315801	+	0.948826i	$0.397727\pi$
$368$	12249.4	+	2837.54i	1.73517	+	0.401948i
$369$	−2476.64	−	1025.86i	−0.349400	−	0.144726i
$370$	320.746	+	3540.22i	0.0450671	+	0.497425i
$371$	615.761	+	6251.93i	0.0861691	+	0.874890i
$372$	1089.88	−	1964.48i	0.151902	−	0.273800i
$373$	−1746.67	+	3267.79i	−0.242465	+	0.453619i	−0.973490	−	0.228731i	$-0.926542\pi$
$373$	−1746.67	+	3267.79i	−0.242465	+	0.453619i	0.731025	+	0.682351i	$0.239042\pi$
$374$	−7078.46	−	4810.17i	−0.978659	−	0.665049i
$375$	−8403.63	−	5615.13i	−1.15723	−	0.773237i
$376$	2248.38	+	4454.77i	0.308382	+	0.611003i
$377$	249.269	+	373.058i	0.0340531	+	0.0509641i
$378$	−1923.06	−	1953.38i	−0.261671	−	0.265796i
$379$	4431.80	+	436.494i	0.600649	+	0.0591588i	0.393772	−	0.919208i	$-0.371170\pi$
$379$	4431.80	+	436.494i	0.600649	+	0.0591588i	0.206877	+	0.978367i	$0.433670\pi$
$380$	−2758.65	−	593.731i	−0.372410	−	0.0801519i
$381$	1370.09	+	415.613i	0.184231	+	0.0558859i
$382$	9704.09	+	5284.93i	1.29975	+	0.707855i
$383$	−1593.29			−0.212567			−0.106284	−	0.994336i	$-0.533895\pi$
$383$	−1593.29			−0.212567			−0.106284	+	0.994336i	$0.533895\pi$
$384$	−5686.34	+	7577.17i	−0.755677	+	1.00696i
$385$	16457.1			2.17852
$386$	9791.56	+	5332.57i	1.29113	+	0.703162i
$387$	5340.16	+	1619.92i	0.701436	+	0.212778i
$388$	1318.71	−	6127.13i	0.172545	−	0.801696i
$389$	−11497.3	−	1132.39i	−1.49856	−	0.147595i	−0.684770	−	0.728759i	$-0.740097\pi$
$389$	−11497.3	−	1132.39i	−1.49856	−	0.147595i	−0.813786	+	0.581164i	$0.802597\pi$
$390$	−610.868	−	620.498i	−0.0793141	−	0.0805645i
$391$	4852.60	+	7262.43i	0.627638	+	0.939327i
$392$	1189.87	−	3614.90i	0.153310	−	0.465766i
$393$	3030.92	+	2025.19i	0.389032	+	0.259943i
$394$	−7049.56	−	4790.54i	−0.901401	−	0.612548i
$395$	−6576.27	+	12303.3i	−0.837691	+	1.56721i
$396$	−7520.22	−	4172.16i	−0.954306	−	0.529442i
$397$	−441.609	−	4483.73i	−0.0558280	−	0.566831i	−0.981889	−	0.189457i	$-0.939327\pi$
$397$	−441.609	−	4483.73i	−0.0558280	−	0.566831i	0.926061	−	0.377374i	$-0.123173\pi$
$398$	862.030	+	9514.60i	0.108567	+	1.19830i
$399$	1541.18	+	638.377i	0.193372	+	0.0800973i
$400$	−7793.29	+	10908.7i	−0.974161	+	1.36359i
$401$	−633.213	+	262.285i	−0.0788557	+	0.0326631i	−0.421763	−	0.906706i	$-0.638588\pi$
$401$	−633.213	+	262.285i	−0.0788557	+	0.0326631i	0.342907	+	0.939369i	$0.388588\pi$
$402$	−9350.41	−	17827.4i	−1.16009	−	2.21181i
$403$	70.0727	−	85.3838i	0.00866146	−	0.0105540i
$404$	4688.69	−	14628.8i	0.577404	−	1.80151i
$405$	4809.80	+	15855.8i	0.590126	+	1.94538i
$406$	−5449.99	+	3580.23i	−0.666203	+	0.437645i
$407$	912.427	+	4587.08i	0.111124	+	0.558656i
$408$	−6482.76	+	1132.09i	−0.786629	+	0.137370i
$409$	−9132.41	−	1816.55i	−1.10408	−	0.219615i	−0.390787	−	0.920481i	$-0.627797\pi$
$409$	−9132.41	−	1816.55i	−1.10408	−	0.219615i	−0.713293	+	0.700866i	$0.752797\pi$
$410$	−3422.95	+	8084.31i	−0.412311	+	0.973795i
$411$	−1833.96	−	2234.68i	−0.220103	−	0.268196i
$412$	−5737.72	−	14489.0i	−0.686110	−	1.73258i
$413$	−579.049	+	309.508i	−0.0689907	+	0.0368763i
$414$	5514.95	+	6828.18i	0.654698	+	0.810596i
$415$	7981.02	+	7981.02i	0.944031	+	0.944031i
$416$	−341.983	+	316.231i	−0.0403055	+	0.0372705i
$417$	−8094.87	+	8094.87i	−0.950617	+	0.950617i
$418$	−3691.84	−	392.790i	−0.431995	−	0.0459617i
$419$	−456.457	−	853.972i	−0.0532205	−	0.0995686i	0.853905	−	0.520429i	$-0.174228\pi$
$419$	−456.457	−	853.972i	−0.0532205	−	0.0995686i	−0.907125	+	0.420861i	$0.861728\pi$
$420$	9087.14	−	8807.23i	1.05573	−	1.02321i
$421$	1608.34	−	1319.93i	0.186189	−	0.152801i	−0.536681	−	0.843785i	$-0.680322\pi$
$421$	1608.34	−	1319.93i	0.186189	−	0.152801i	0.722870	+	0.690984i	$0.242822\pi$
$422$	−7735.63	+	3133.55i	−0.892333	+	0.361467i
$423$	−679.559	+	3416.37i	−0.0781118	+	0.392694i
$424$	−9833.66	−	4346.24i	−1.12633	−	0.497812i
$425$	−9134.01	+	1816.87i	−1.04251	+	0.207367i
$426$	−444.478	+	2146.66i	−0.0505517	+	0.244146i
$427$	−3163.66	+	959.686i	−0.358549	+	0.108765i
$428$	−5137.44	+	6064.04i	−0.580204	+	0.684851i
$429$	−885.580	−	726.777i	−0.0996648	−	0.0817928i
$430$	5441.75	−	17446.7i	0.610290	−	1.95664i
$431$	4268.26	+	10304.5i	0.477018	+	1.15162i	0.961001	+	0.276546i	$0.0891899\pi$
$431$	4268.26	+	10304.5i	0.477018	+	1.15162i	−0.483982	+	0.875078i	$0.660810\pi$
$432$	4529.58	−	1220.70i	0.504466	−	0.135951i
$433$	6248.46	−	15085.1i	0.693491	−	1.67424i	−0.0441348	−	0.999026i	$-0.514053\pi$
$433$	6248.46	−	15085.1i	0.693491	−	1.67424i	0.737626	−	0.675210i	$-0.235947\pi$
$434$	1232.92	+	1028.07i	0.136364	+	0.113708i
$435$	20761.3	−	2044.81i	2.28834	−	0.225382i
$436$	6415.55	+	733.363i	0.704700	+	0.0805544i
$437$	3341.73	+	1786.19i	0.365804	+	0.195526i
$438$	−1773.92	−	9297.54i	−0.193519	−	1.01428i
$439$	5463.25	−	8176.33i	0.593956	−	0.888918i	−0.405729	−	0.913993i	$-0.632982\pi$
$439$	5463.25	−	8176.33i	0.593956	−	0.888918i	0.999686	+	0.0250749i	$0.00798244\pi$
$440$	−13855.8	+	24520.7i	−1.50125	+	2.65677i
$441$	2208.87	−	1475.92i	0.238513	−	0.159369i
$442$	−323.551	−	2.53045i	−0.0348184	−	0.000272310i
$443$	−979.541	+	9945.45i	−0.105055	+	1.06664i	0.787687	+	0.616075i	$0.211278\pi$
$443$	−979.541	+	9945.45i	−0.105055	+	1.06664i	−0.892743	+	0.450567i	$0.851222\pi$
$444$	2958.66	+	2044.56i	0.316242	+	0.218537i
$445$	−6501.26	+	21431.8i	−0.692561	+	2.28307i
$446$	1392.35	+	4722.60i	0.147824	+	0.501394i
$447$		−	8880.74i		−	0.939697i
$448$	−4556.93	−	5005.99i	−0.480568	−	0.527926i
$449$		−	6727.25i		−	0.707079i	−0.935420	−	0.353539i	$-0.884978\pi$
$449$		−	6727.25i		−	0.707079i	0.935420	−	0.353539i	$-0.115022\pi$
$450$	−8976.51	+	2646.51i	−0.940348	+	0.277239i
$451$	−3352.98	+	11053.3i	−0.350080	+	1.15406i
$452$	−2126.16	−	11637.4i	−0.221252	−	1.21101i
$453$	1930.12	−	19596.8i	0.200188	−	2.03254i
$454$	−25.6298	+	3277.10i	−0.00264948	+	0.338771i
$455$	517.336	−	345.673i	0.0533035	−	0.0356163i
$456$	−2248.74	+	1758.85i	−0.230936	+	0.180627i
$457$	5086.74	−	7612.85i	0.520674	−	0.779243i	−0.474195	−	0.880420i	$-0.657261\pi$
$457$	5086.74	−	7612.85i	0.520674	−	0.779243i	0.994868	+	0.101177i	$0.0322607\pi$
$458$	−4843.72	+	924.155i	−0.494175	+	0.0942859i
$459$	2873.97	+	1536.17i	0.292256	+	0.156214i
$460$	22502.5	−	17885.7i	2.28083	−	1.81288i
$461$	10777.8	−	1061.52i	1.08887	−	0.107245i	0.462388	−	0.886678i	$-0.346993\pi$
$461$	10777.8	−	1061.52i	1.08887	−	0.107245i	0.626485	+	0.779433i	$0.284493\pi$
$462$	10662.9	−	12787.5i	1.07377	−	1.28773i
$463$	−3419.40	+	8255.15i	−0.343224	+	0.828616i	0.654162	+	0.756355i	$0.273022\pi$
$463$	−3419.40	+	8255.15i	−0.343224	+	0.828616i	−0.997386	+	0.0722616i	$0.976978\pi$
$464$	−745.933	−	11134.7i	−0.0746316	−	1.11404i
$465$	−1965.40	−	4744.90i	−0.196007	−	0.473203i
$466$	13389.7	+	4176.34i	1.33104	+	0.415161i
$467$	−4401.38	−	3612.12i	−0.436128	−	0.357921i	0.390564	−	0.920576i	$-0.372280\pi$
$467$	−4401.38	−	3612.12i	−0.436128	−	0.357921i	−0.826692	+	0.562655i	$0.809780\pi$
$468$	−324.036	+	26.8047i	−0.0320055	+	0.00264754i
$469$	13765.3	−	4175.65i	1.35527	−	0.411117i
$470$	11170.7	+	2312.95i	1.09631	+	0.226996i
$471$	9195.80	−	1829.16i	0.899618	−	0.178945i
$472$	26.3612	−	1123.36i	0.00257070	−	0.109548i
$473$	4691.00	−	23583.3i	0.456010	−	2.29252i
$474$	5299.07	+	13081.5i	0.513491	+	1.26763i
$475$	−3123.05	+	2563.02i	−0.301674	+	0.247578i
$476$	73.5501	−	4701.88i	0.00708227	−	0.452753i
$477$	−3537.84	−	6618.83i	−0.339594	−	0.635336i
$478$	225.466	−	2119.16i	0.0215745	−	0.202779i
$479$	9528.57	−	9528.57i	0.908918	−	0.908918i	−0.0872671	−	0.996185i	$-0.527813\pi$
$479$	9528.57	−	9528.57i	0.908918	−	0.908918i	0.996185	+	0.0872671i	$0.0278133\pi$
$480$	5471.79	+	20954.7i	0.520316	+	1.99260i
$481$	125.032	+	125.032i	0.0118523	+	0.0118523i
$482$	826.917	−	667.879i	0.0781432	−	0.0631142i
$483$	−14986.3	+	8010.37i	−1.41181	+	0.754626i
$484$	−10486.3	+	24236.9i	−0.984819	+	2.27620i
$485$	−9089.53	−	11075.6i	−0.850999	−	1.03695i
$486$	10282.0	+	4353.47i	0.959674	+	0.406332i
$487$	5829.47	+	1159.55i	0.542420	+	0.107894i	0.458693	−	0.888595i	$-0.348318\pi$
$487$	5829.47	+	1159.55i	0.542420	+	0.107894i	0.0837270	+	0.996489i	$0.473318\pi$
$488$	1233.68	−	5521.77i	0.114439	−	0.512211i
$489$	1132.03	+	5691.11i	0.104688	+	0.526300i
$490$	−4776.83	−	7271.50i	−0.440398	−	0.670393i
$491$	−2229.45	−	7349.52i	−0.204916	−	0.675518i	−0.997809	−	0.0661570i	$-0.978926\pi$
$491$	−2229.45	−	7349.52i	−0.204916	−	0.675518i	0.792893	−	0.609361i	$-0.208574\pi$
$492$	4063.90	+	7897.73i	0.372388	+	0.723693i
$493$	4917.90	−	5992.48i	0.449272	−	0.547439i
$494$	−124.305	+	65.1978i	−0.0113214	+	0.00593803i
$495$	−18163.9	+	7523.73i	−1.64931	+	0.683165i
$496$	−2569.84	+	971.454i	−0.232640	+	0.0879427i
$497$	−1447.23	−	599.461i	−0.130618	−	0.0541036i
$498$	11372.5	−	1030.36i	1.02332	−	0.0927140i
$499$	696.867	+	7075.41i	0.0625172	+	0.634748i	0.974480	+	0.224475i	$0.0720666\pi$
$499$	696.867	+	7075.41i	0.0625172	+	0.634748i	−0.911963	+	0.410273i	$0.865433\pi$
$500$	3402.44	+	11882.3i	0.304324	+	1.06279i
$501$	−1180.47	+	2208.50i	−0.105269	+	0.196944i
$502$	9142.86	−	13454.3i	0.812880	−	1.19620i
$503$	9477.75	+	6332.83i	0.840143	+	0.561366i	0.899525	−	0.436869i	$-0.143913\pi$
$503$	9477.75	+	6332.83i	0.840143	+	0.561366i	−0.0593815	+	0.998235i	$0.518913\pi$
$504$	−352.723	−	4712.27i	−0.0311737	−	0.416471i
$505$	−19510.8	−	29200.0i	−1.71925	−	2.57304i
$506$	26950.7	−	26532.4i	2.36780	−	2.33105i
$507$	14260.0	+	1404.49i	1.24913	+	0.123029i
$508$	−949.851	−	1470.84i	−0.0829583	−	0.128461i
$509$	−7327.40	−	2222.74i	−0.638077	−	0.193559i	−0.0453617	−	0.998971i	$-0.514444\pi$
$509$	−7327.40	−	2222.74i	−0.638077	−	0.193559i	−0.592715	+	0.805412i	$0.701944\pi$
$510$	−7195.46	+	13212.2i	−0.624745	+	1.14715i
$511$	6763.53			0.585521
$512$	11295.4	−	2575.00i	0.974986	−	0.222266i
$513$	1413.70			0.121670
$514$	−4083.16	+	7497.42i	−0.350390	+	0.643380i
$515$	−34091.8	−	10341.6i	−2.91702	−	0.884868i
$516$	−10030.7	−	15532.5i	−0.855767	−	1.32515i
$517$	14936.7	+	1471.14i	1.27063	+	0.125146i
$518$	−1831.31	+	1802.88i	−0.155334	+	0.152923i
$519$	2350.28	+	3517.45i	0.198778	+	0.297493i
$520$	79.4818	+	1061.85i	0.00670290	+	0.0895488i
$521$	−14126.7	−	9439.16i	−1.18791	−	0.793737i	−0.205171	−	0.978726i	$-0.565775\pi$
$521$	−14126.7	−	9439.16i	−1.18791	−	0.793737i	−0.982741	+	0.184989i	$0.940775\pi$
$522$	4378.44	−	6443.14i	0.367125	−	0.540246i
$523$	−3944.08	+	7378.85i	−0.329756	+	0.616930i	−0.991095	−	0.133157i	$-0.957488\pi$
$523$	−3944.08	+	7378.85i	−0.329756	+	0.616930i	0.661339	+	0.750087i	$0.269988\pi$
$524$	−1227.15	−	4285.56i	−0.102306	−	0.357282i
$525$	−1775.91	−	18031.1i	−0.147632	−	1.49894i
$526$	−20902.3	+	1893.76i	−1.73267	+	0.156981i
$527$	−1763.18	−	730.333i	−0.145741	−	0.0603678i
$528$	10075.7	+	26653.8i	0.830469	+	2.19689i
$529$	−24419.4	+	10114.9i	−2.00702	+	0.831336i
$530$	−21766.2	+	11416.3i	−1.78390	+	0.935649i
$531$	497.606	−	606.334i	0.0406671	−	0.0495530i
$532$	−933.392	−	1813.94i	−0.0760671	−	0.147828i
$533$	126.767	+	417.894i	0.0103018	+	0.0339606i
$534$	12440.7	+	18937.8i	1.00817	+	1.53468i
$535$	3544.62	+	17820.0i	0.286444	+	1.44005i
$536$	−5367.83	+	24025.6i	−0.432566	+	1.93609i
$537$	−6425.87	−	1278.18i	−0.516381	−	0.102715i
$538$	10238.0	+	4334.83i	0.820430	+	0.347375i
$539$	−7261.78	−	8848.50i	−0.580310	−	0.707109i
$540$	4258.54	−	9842.70i	0.339367	−	0.784375i
$541$	4916.69	−	2628.02i	0.390730	−	0.208850i	−0.264320	−	0.964435i	$-0.585148\pi$
$541$	4916.69	−	2628.02i	0.390730	−	0.208850i	0.655050	+	0.755585i	$0.272648\pi$
$542$	12230.9	−	9878.61i	0.969306	−	0.782883i
$543$	−1252.51	−	1252.51i	−0.0989880	−	0.0989880i
$544$	6943.77	+	4068.26i	0.547264	+	0.320635i
$545$	10438.3	−	10438.3i	0.820420	−	0.820420i
$546$	66.5978	−	625.953i	0.00522000	−	0.0490628i
$547$	−4734.20	−	8857.07i	−0.370055	−	0.692324i	0.626118	−	0.779728i	$-0.284643\pi$
$547$	−4734.20	−	8857.07i	−0.370055	−	0.692324i	−0.996173	+	0.0874045i	$0.972143\pi$
$548$	−55.2944	+	3534.84i	−0.00431033	+	0.275549i
$549$	3053.03	−	2505.56i	0.237341	−	0.194781i
$550$	15139.6	+	37374.4i	1.17374	+	2.89754i
$551$	656.088	−	3298.38i	0.0507265	−	0.255019i
$552$	682.252	−	29073.5i	0.0526061	−	2.24176i
$553$	−9891.62	+	1967.57i	−0.760641	+	0.151301i
$554$	−3082.35	−	638.216i	−0.236383	−	0.0489444i
$555$	7867.61	−	2386.61i	0.601732	−	0.182533i
$556$	13952.0	−	1154.13i	1.06420	−	0.0880322i
$557$	−1297.55	−	1064.87i	−0.0987056	−	0.0810056i	0.583746	−	0.811936i	$-0.301586\pi$
$557$	−1297.55	−	1064.87i	−0.0987056	−	0.0810056i	−0.682452	+	0.730931i	$0.739086\pi$
$558$	−1830.80	−	571.040i	−0.138896	−	0.0433227i
$559$	−347.892	−	839.885i	−0.0263224	−	0.0635480i
$560$	−15441.0	+	1034.42i	−1.16518	+	0.0780575i
$561$	−7574.84	+	18287.3i	−0.570071	+	1.37627i
$562$	−1757.60	+	2107.81i	−0.131922	+	0.158208i
$563$	19496.1	−	1920.20i	1.45944	−	0.143742i	0.663071	−	0.748557i	$-0.269253\pi$
$563$	19496.1	−	1920.20i	1.45944	−	0.143742i	0.796366	+	0.604815i	$0.206753\pi$
$564$	9034.95	−	7181.27i	0.674539	−	0.536146i
$565$	−23851.0	−	12748.6i	−1.77597	−	0.949274i
$566$	−4272.19	+	815.111i	−0.317268	+	0.0605330i
$567$	−6654.91	+	9959.78i	−0.492910	+	0.737692i
$568$	2111.65	−	1651.63i	0.155991	−	0.122008i
$569$	−2828.88	+	1890.20i	−0.208423	+	0.139264i	−0.655401	−	0.755281i	$-0.727500\pi$
$569$	−2828.88	+	1890.20i	−0.208423	+	0.139264i	0.446978	+	0.894545i	$0.352500\pi$
$570$	−51.0416	+	6526.33i	−0.00375070	+	0.479575i
$571$	2101.84	−	21340.4i	0.154044	−	1.56404i	−0.538476	−	0.842641i	$-0.681000\pi$
$571$	2101.84	−	21340.4i	0.154044	−	1.56404i	0.692520	−	0.721398i	$-0.256500\pi$
$572$	251.795	+	1378.18i	0.0184057	+	0.100742i
$573$	7418.81	−	24456.5i	0.540882	−	1.78305i
$574$	−6087.68	+	1794.81i	−0.442674	+	0.130512i
$575$		−	41154.9i		−	2.98483i
$576$	7318.15	+	3441.87i	0.529380	+	0.248978i
$577$			7968.43i			0.574922i	0.957792	+	0.287461i	$0.0928112\pi$
$577$			7968.43i			0.574922i	−0.957792	+	0.287461i	$0.907189\pi$
$578$	−2348.76	−	7966.59i	−0.169023	−	0.573298i
$579$	7485.68	−	24677.0i	0.537296	−	1.77123i
$580$	−20988.1	−	14503.7i	−1.50256	−	1.03833i
$581$	−799.790	+	8120.41i	−0.0571100	+	0.579847i
$582$	−14495.4	−	113.366i	−1.03239	−	0.00807420i
$583$	−26888.0	+	17966.0i	−1.91010	+	1.27629i
$584$	−5694.45	+	10077.5i	−0.403490	+	0.714059i
$585$	−412.959	+	618.037i	−0.0291859	+	0.0436798i
$586$	1915.38	+	10039.0i	0.135023	+	0.707688i
$587$	150.316	+	80.3456i	0.0105693	+	0.00564943i	0.476673	−	0.879081i	$-0.341843\pi$
$587$	150.316	+	80.3456i	0.0105693	+	0.00564943i	−0.466104	+	0.884730i	$0.654343\pi$
$588$	−8745.15	−	999.660i	−0.613340	−	0.0701110i
$589$	−823.931	+	81.1501i	−0.0576392	+	0.00567697i
$590$	−1972.90	−	1645.11i	−0.137666	−	0.114793i
$591$	−7543.91	+	18212.6i	−0.525068	+	1.26763i
$592$	−1144.42	−	4246.51i	−0.0794513	−	0.294815i
$593$	9202.11	+	22215.9i	0.637243	+	1.53844i	0.830337	+	0.557261i	$0.188148\pi$
$593$	9202.11	+	22215.9i	0.637243	+	1.53844i	−0.193094	+	0.981180i	$0.561852\pi$
$594$	4201.44	−	13470.2i	0.290214	−	0.930450i
$595$	−8310.04	−	6819.88i	−0.572569	−	0.469895i
$596$	−7020.16	+	8286.33i	−0.482478	+	0.569499i
$597$	21144.8	−	6414.20i	1.44958	−	0.439725i
$598$	289.908	−	1400.15i	0.0198248	−	0.0957463i
$599$	9541.75	−	1897.97i	0.650860	−	0.129464i	0.141392	−	0.989954i	$-0.454842\pi$
$599$	9541.75	−	1897.97i	0.650860	−	0.129464i	0.509468	+	0.860489i	$0.329842\pi$
$600$	28361.1	+	12534.9i	1.92973	+	0.852894i
$601$	−3321.35	+	16697.5i	−0.225425	+	1.13329i	0.687821	+	0.725880i	$0.258567\pi$
$601$	−3321.35	+	16697.5i	−0.225425	+	1.13329i	−0.913246	+	0.407408i	$0.866433\pi$
$602$	12245.6	−	4960.45i	0.829059	−	0.335836i
$603$	−13283.9	+	10901.8i	−0.897120	+	0.736247i
$604$	−17292.1	+	16759.4i	−1.16491	+	1.12903i
$605$	28458.9	+	53242.9i	1.91243	+	3.57791i
$606$	−35330.7	−	3758.98i	−2.36834	−	0.251977i
$607$	8346.86	−	8346.86i	0.558136	−	0.558136i	−0.370641	−	0.928776i	$-0.620862\pi$
$607$	8346.86	−	8346.86i	0.558136	−	0.558136i	0.928776	+	0.370641i	$0.120862\pi$
$608$	3488.59	+	136.486i	0.232699	+	0.00910399i
$609$	10664.4	+	10664.4i	0.709595	+	0.709595i
$610$	−8127.11	−	10062.4i	−0.539438	−	0.667891i
$611$	500.444	−	267.493i	0.0331355	−	0.0177113i
$612$	2068.39	+	5223.15i	0.136617	+	0.344989i
$613$	13509.3	+	16461.1i	0.890106	+	1.08460i	0.995923	+	0.0902112i	$0.0287542\pi$
$613$	13509.3	+	16461.1i	0.890106	+	1.08460i	−0.105817	+	0.994386i	$0.533746\pi$
$614$	8304.31	−	19613.1i	0.545822	−	1.28912i
$615$	19914.8	+	3961.31i	1.30576	+	0.259732i
$616$	−20057.7	+	3502.69i	−1.31193	+	0.229103i
$617$	4158.59	+	20906.6i	0.271343	+	1.36413i	0.840459	+	0.541875i	$0.182285\pi$
$617$	4158.59	+	20906.6i	0.271343	+	1.36413i	−0.569116	+	0.822257i	$0.692715\pi$
$618$	−30124.6	+	19789.6i	−1.96082	+	1.28811i
$619$	−21.4240	−	70.6254i	−0.00139112	−	0.00458590i	0.956242	−	0.292577i	$-0.0945127\pi$
$619$	−21.4240	−	70.6254i	−0.00139112	−	0.00458590i	−0.957633	+	0.287991i	$0.907013\pi$
$620$	−1916.96	+	5980.95i	−0.124172	+	0.387420i
$621$	−9135.77	+	11132.0i	−0.590348	+	0.719341i
$622$	−304.838	−	581.199i	−0.0196509	−	0.0374662i
$623$	−14958.6	+	6196.03i	−0.961961	+	0.398457i
$624$	876.585	+	626.240i	0.0562363	+	0.0401758i
$625$	1913.42	+	792.566i	0.122459	+	0.0507242i
$626$	176.455	+	1947.61i	0.0112661	+	0.124349i
$627$	841.669	+	8545.61i	0.0536093	+	0.544304i
$628$	−10026.2	−	5562.48i	−0.637087	−	0.353451i
$629$	1440.17	−	2694.37i	0.0912932	−	0.170798i
$630$	−8935.00	−	6071.79i	−0.565046	−	0.383977i
$631$	−2181.70	−	1457.77i	−0.137642	−	0.0919696i	0.484843	−	0.874601i	$-0.338877\pi$
$631$	−2181.70	−	1457.77i	−0.137642	−	0.0919696i	−0.622485	+	0.782632i	$0.713877\pi$
$632$	5396.47	−	16394.8i	0.339652	−	1.03189i
$633$	10724.6	+	16050.5i	0.673403	+	1.00782i
$634$	10497.0	+	10662.5i	0.657556	+	0.667922i
$635$	−3983.41	−	392.332i	−0.248940	−	0.0245184i
$636$	−5232.07	+	24309.8i	−0.326203	+	1.51564i
$637$	−414.136	−	125.627i	−0.0257593	−	0.00781400i
$638$	−29478.0	−	16054.0i	−1.82922	−	0.996211i
$639$	1871.38			0.115854
$640$	11459.0	−	23877.6i	0.707746	−	1.47476i
$641$	9280.13			0.571830			0.285915	−	0.958255i	$-0.407702\pi$
$641$	9280.13			0.571830			0.285915	+	0.958255i	$0.407702\pi$
$642$	16143.2	+	8791.75i	0.992403	+	0.540471i
$643$	−6003.55	−	1821.16i	−0.368207	−	0.111694i	0.100758	−	0.994911i	$-0.467873\pi$
$643$	−6003.55	−	1821.16i	−0.368207	−	0.111694i	−0.468965	+	0.883217i	$0.655373\pi$
$644$	20315.4	+	4372.38i	1.24307	+	0.267540i
$645$	−42065.8	−	4143.12i	−2.56797	−	0.252923i
$646$	1701.43	+	1728.25i	0.103625	+	0.105259i
$647$	7532.53	+	11273.2i	0.457704	+	0.685002i	0.986503	−	0.163745i	$-0.0523575\pi$
$647$	7532.53	+	11273.2i	0.457704	+	0.685002i	−0.528799	+	0.848747i	$0.677357\pi$
$648$	−9236.85	−	18301.1i	−0.559965	−	1.10947i
$649$	−2810.18	−	1877.70i	−0.169968	−	0.113569i
$650$	1260.95	+	856.882i	0.0760903	+	0.0517072i
$651$	1750.24	−	3274.48i	0.105372	−	0.197138i
$652$	3442.52	−	6205.05i	0.206778	−	0.372713i
$653$	94.9170	+	963.709i	0.00568819	+	0.0577532i	0.997610	−	0.0690993i	$-0.0220125\pi$
$653$	94.9170	+	963.709i	0.00568819	+	0.0577532i	−0.991922	+	0.126852i	$0.959513\pi$
$654$	−1347.60	−	14874.1i	−0.0805741	−	0.889331i
$655$	−9415.19	−	3899.90i	−0.561652	−	0.232644i
$656$	2451.20	−	10581.6i	0.145889	−	0.629790i
$657$	−7465.00	+	3092.11i	−0.443284	+	0.183614i
$658$	3830.60	+	7303.37i	0.226949	+	0.432698i
$659$	2674.11	−	3258.41i	0.158070	−	0.192609i	−0.687953	−	0.725755i	$-0.741490\pi$
$659$	2674.11	−	3258.41i	0.158070	−	0.192609i	0.846023	+	0.533146i	$0.178990\pi$
$660$	62032.9	+	19882.2i	3.65853	+	1.17260i
$661$	2477.54	+	8167.34i	0.145787	+	0.480594i	0.999172	−	0.0406864i	$-0.0129545\pi$
$661$	2477.54	+	8167.34i	0.145787	+	0.480594i	−0.853385	+	0.521281i	$0.825454\pi$
$662$	20902.2	−	13731.1i	1.22717	−	0.806157i
$663$	145.997	+	733.976i	0.00855211	+	0.0429944i
$664$	−11425.8	−	8028.52i	−0.667784	−	0.469227i
$665$	−4574.02	−	909.828i	−0.266726	−	0.0530551i
$666$	1197.01	−	2827.09i	0.0696443	−	0.164486i
$667$	21732.7	+	26481.3i	1.26161	+	1.53727i
$668$	2847.27	−	1127.53i	0.164916	−	0.0653076i
$669$	10043.0	−	5368.09i	0.580395	−	0.310228i
$670$	35361.6	+	43782.0i	2.03901	+	2.52454i
$671$	−12033.5	−	12033.5i	−0.692322	−	0.692322i
$672$	−9200.80	+	12668.2i	−0.528167	+	0.727214i
$673$	13923.8	−	13923.8i	0.797507	−	0.797507i	−0.185195	−	0.982702i	$-0.559292\pi$
$673$	13923.8	−	13923.8i	0.797507	−	0.797507i	0.982702	+	0.185195i	$0.0592915\pi$
$674$	−6133.08	−	652.525i	−0.350501	−	0.0372913i
$675$	−7238.12	−	13541.6i	−0.412734	−	0.772170i
$676$	−12195.3	−	12582.9i	−0.693863	−	0.715916i
$677$	8861.99	−	7272.85i	0.503093	−	0.412878i	−0.348318	−	0.937376i	$-0.613247\pi$
$677$	8861.99	−	7272.85i	0.503093	−	0.412878i	0.851411	+	0.524499i	$0.175747\pi$
$678$	−25359.7	+	10272.7i	−1.43648	+	0.581889i
$679$	2020.78	−	10159.2i	0.114213	−	0.574186i
$680$	17158.0	−	6639.89i	0.967615	−	0.374453i
$681$	7434.12	−	1478.74i	0.418320	−	0.0832090i
$682$	−1675.45	+	8091.81i	−0.0940710	+	0.454328i
$683$	21115.6	−	6405.35i	1.18297	−	0.358849i	0.363290	−	0.931676i	$-0.381653\pi$
$683$	21115.6	−	6405.35i	1.18297	−	0.358849i	0.819676	+	0.572827i	$0.194153\pi$
$684$	1859.48	+	1575.35i	0.103946	+	0.0880628i
$685$	6247.43	+	5127.14i	0.348470	+	0.285982i
$686$	5692.15	−	18249.5i	0.316804	−	1.01570i
$687$	4364.51	+	10536.9i	0.242382	+	0.585161i
$688$	−2919.03	+	22422.0i	−0.161754	+	1.24249i
$689$	−467.871	+	1129.54i	−0.0258700	+	0.0624558i
$690$	−51060.6	−	42577.0i	−2.81717	−	2.34910i
$691$	−14960.5	+	1473.48i	−0.823622	+	0.0811197i	−0.501043	−	0.865423i	$-0.667050\pi$
$691$	−14960.5	+	1473.48i	−0.823622	+	0.0811197i	−0.322580	+	0.946542i	$0.604550\pi$
$692$	587.543	−	5139.90i	0.0322760	−	0.282355i
$693$	−12535.0	−	6700.09i	−0.687106	−	0.367266i
$694$	1037.78	+	5439.26i	0.0567632	+	0.297509i
$695$	17780.7	−	26610.7i	0.970448	−	1.45238i
$696$	−24868.4	+	6910.99i	−1.35436	+	0.376380i
$697$	6273.63	−	4191.91i	0.340934	−	0.227805i
$698$	−13523.5	−	105.766i	−0.733341	−	0.00573536i
$699$	3179.68	−	32283.9i	0.172055	−	1.74691i
$700$	−12596.4	+	18228.1i	−0.680142	+	0.984224i
$701$	−6838.67	+	22544.1i	−0.368464	+	1.21466i	0.555284	+	0.831661i	$0.312609\pi$
$701$	−6838.67	+	22544.1i	−0.368464	+	1.21466i	−0.923748	+	0.383001i	$0.874891\pi$
$702$	−150.860	−	511.690i	−0.00811088	−	0.0275107i
$703$		−	1325.36i		−	0.0711050i
$704$	11668.3	−	32834.5i	0.624669	−	1.75781i
$705$		−	26384.4i		−	1.40950i
$706$	27432.4	−	8087.78i	1.46237	−	0.431144i
$707$	7369.90	−	24295.3i	0.392042	−	1.29239i
$708$	−2556.58	+	467.090i	−0.135709	+	0.0247942i
$709$	112.847	−	1145.75i	0.00597751	−	0.0606907i	−0.991733	−	0.128317i	$-0.959043\pi$
$709$	112.847	−	1145.75i	0.00597751	−	0.0606907i	0.997711	+	0.0676262i	$0.0215425\pi$
$710$	47.9300	−	6128.47i	0.00253349	−	0.323940i
$711$	10018.0	−	6693.81i	0.528417	−	0.353077i
$712$	3362.17	−	27504.6i	0.176970	−	1.44772i
$713$	4685.48	−	7012.32i	0.246105	−	0.368322i
$714$	−10683.5	+	2038.35i	−0.559971	+	0.106839i
$715$	2824.61	+	1509.78i	0.147740	+	0.0789689i
$716$	4985.38	+	6272.24i	0.260213	+	0.327381i
$717$	−4905.29	+	483.129i	−0.255497	+	0.0251642i
$718$	7379.94	−	8850.42i	0.383589	−	0.460021i
$719$	−5.49450	+	13.2649i	−0.000284994	+	0.000688035i	−0.924022	−	0.382339i	$-0.875119\pi$
$719$	−5.49450	+	13.2649i	−0.000284994	+	0.000688035i	0.923737	+	0.383027i	$0.125119\pi$
$720$	16569.5	−	8200.90i	0.857651	−	0.424486i
$721$	−9856.10	−	23794.7i	−0.509099	−	1.22907i
$722$	−17515.8	−	5463.32i	−0.902869	−	0.281612i
$723$	−1900.42	−	1559.63i	−0.0977556	−	0.0802259i
$724$	178.577	+	2158.78i	0.00916681	+	0.110816i
$725$	−34953.6	+	10603.1i	−1.79054	+	0.543155i
$726$	59810.3	+	12384.0i	3.05753	+	0.633078i
$727$	−7267.96	+	1445.69i	−0.370775	+	0.0737518i	−0.376961	−	0.926229i	$-0.623031\pi$
$727$	−7267.96	+	1445.69i	−0.370775	+	0.0737518i	0.00618591	+	0.999981i	$0.498031\pi$
$728$	−556.952	+	531.412i	−0.0283544	+	0.0270542i
$729$	265.973	−	1337.14i	0.0135128	−	0.0679337i
$730$	9934.96	+	24525.9i	0.503711	+	1.24349i
$731$	−12141.7	+	9964.47i	−0.614334	+	0.504171i
$732$	−13084.5	−	204.676i	−0.660677	−	0.0103348i
$733$	4957.74	+	9275.27i	0.249820	+	0.467381i	0.975306	−	0.220856i	$-0.0708851\pi$
$733$	4957.74	+	9275.27i	0.249820	+	0.467381i	−0.725486	+	0.688237i	$0.758385\pi$
$734$	300.171	−	2821.31i	0.0150947	−	0.141875i
$735$	−14228.7	+	14228.7i	−0.714058	+	0.714058i
$736$	−23619.0	+	26588.3i	−1.18289	+	1.33160i
$737$	52358.4	+	52358.4i	2.61689	+	2.61689i
$738$	5898.51	−	4764.07i	0.294210	−	0.237626i
$739$	−14284.7	+	7635.34i	−0.711058	+	0.380069i	−0.786924	−	0.617049i	$-0.788328\pi$
$739$	−14284.7	+	7635.34i	−0.711058	+	0.380069i	0.0758661	+	0.997118i	$0.475828\pi$
$740$	−9227.61	−	3992.42i	−0.458397	−	0.198330i
$741$	205.955	+	250.957i	0.0102104	+	0.0124415i
$742$	−16362.4	−	6927.96i	−0.809548	−	0.342767i
$743$	24622.1	+	4897.64i	1.21574	+	0.241826i	0.760973	−	0.648783i	$-0.224722\pi$
$743$	24622.1	+	4897.64i	1.21574	+	0.241826i	0.454769	+	0.890609i	$0.349722\pi$
$744$	3405.30	+	5364.72i	0.167802	+	0.264355i
$745$	4843.63	+	24350.6i	0.238197	+	1.19750i
$746$	−5754.16	−	8759.24i	−0.282406	−	0.429891i
$747$	−2829.69	−	9328.24i	−0.138598	−	0.456898i
$748$	21523.8	−	11075.4i	1.05212	−	0.541387i
$749$	−8332.84	+	10153.6i	−0.406509	+	0.495333i
$750$	25315.9	−	13278.2i	1.23254	−	0.646466i
$751$	−9481.91	+	3927.54i	−0.460719	+	0.190836i	−0.600956	−	0.799282i	$-0.705213\pi$
$751$	−9481.91	+	3927.54i	−0.460719	+	0.190836i	0.140237	+	0.990118i	$0.455213\pi$
$752$	−14107.0	−	441.450i	−0.684080	−	0.0214070i
$753$	−34759.2	−	14397.7i	−1.68220	−	0.696790i
$754$	−1263.86	+	114.507i	−0.0610439	+	0.00553063i
$755$	5395.98	+	54786.3i	0.260106	+	2.64090i
$756$	7453.55	−	2134.29i	0.358576	−	0.102676i
$757$	16232.1	−	30368.2i	0.779349	−	1.45806i	−0.106613	−	0.994301i	$-0.534000\pi$
$757$	16232.1	−	30368.2i	0.779349	−	1.45806i	0.885962	−	0.463759i	$-0.153500\pi$
$758$	−7079.47	+	10417.9i	−0.339232	+	0.499200i
$759$	−72730.1	−	48596.7i	−3.47817	−	2.32404i
$760$	5206.64	−	6049.16i	0.248506	−	0.288719i
$761$	13572.4	+	20312.5i	0.646516	+	0.967579i	0.999490	+	0.0319457i	$0.0101704\pi$
$761$	13572.4	+	20312.5i	0.646516	+	0.967579i	−0.352974	+	0.935633i	$0.614830\pi$
$762$	−2885.79	+	2841.01i	−0.137193	+	0.135064i
$763$	10620.6	+	1046.04i	0.503922	+	0.0496320i
$764$	−26255.0	+	16955.1i	−1.24329	+	0.802898i
$765$	12289.8	+	3728.06i	0.580834	+	0.176194i
$766$	2155.37	−	3957.65i	0.101667	−	0.186678i
$767$	−127.780			−0.00601545
$768$	−11128.9	−	24374.8i	−0.522891	−	1.14525i
$769$	−11001.7			−0.515908			−0.257954	−	0.966157i	$-0.583048\pi$
$769$	−11001.7			−0.515908			−0.257954	+	0.966157i	$0.583048\pi$
$770$	−22262.8	+	40878.5i	−1.04194	+	1.91319i
$771$	18895.2	+	5731.81i	0.882614	+	0.267738i
$772$	−26491.6	+	17107.9i	−1.23504	+	0.797575i
$773$	−35694.4	−	3515.59i	−1.66085	−	0.163579i	−0.776408	−	0.630230i	$-0.782961\pi$
$773$	−35694.4	−	3515.59i	−1.66085	−	0.163579i	−0.884442	+	0.466651i	$0.845461\pi$
$774$	−11247.9	+	11073.3i	−0.522346	+	0.514239i
$775$	4995.82	+	7476.77i	0.231555	+	0.346546i
$776$	13435.5	+	11564.3i	0.621531	+	0.534965i
$777$	4942.02	+	3302.15i	0.228178	+	0.152463i
$778$	18366.2	−	27026.9i	0.846348	−	1.24545i
$779$	1543.00	−	2886.74i	0.0709674	−	0.132771i
$780$	2367.65	−	677.966i	0.108687	−	0.0311219i
$781$	−790.359	−	8024.65i	−0.0362116	−	0.367663i
$782$	−24604.0	+	2229.14i	−1.12511	+	0.101936i
$783$	11808.3	+	4891.16i	0.538945	+	0.223239i
$784$	7369.60	+	7845.73i	0.335714	+	0.357404i
$785$	−24216.8	+	10030.9i	−1.10106	+	0.456075i
$786$	−9130.64	+	4789.00i	−0.414350	+	0.217326i
$787$	7860.69	−	9578.28i	0.356040	−	0.433836i	−0.563931	−	0.825822i	$-0.690712\pi$
$787$	7860.69	−	9578.28i	0.356040	−	0.433836i	0.919971	+	0.391986i	$0.128212\pi$
$788$	21435.9	−	11030.2i	0.969065	−	0.498648i
$789$	14091.1	+	46452.2i	0.635814	+	2.09600i
$790$	−21664.6	−	32978.8i	−0.975685	−	1.48523i
$791$	−3814.29	−	19175.7i	−0.171455	−	0.861960i
$792$	20536.6	−	13035.8i	0.921385	−	0.584858i
$793$	−631.037	−	125.521i	−0.0282582	−	0.00562091i
$794$	11734.7	+	4968.56i	0.524497	+	0.222075i
$795$	36063.3	+	43943.3i	1.60885	+	1.96039i
$796$	−24799.9	−	10729.9i	−1.10428	−	0.477778i
$797$	−34783.2	+	18592.0i	−1.54590	+	0.826301i	−0.999934	−	0.0115050i	$-0.996338\pi$
$797$	−34783.2	+	18592.0i	−1.54590	+	0.826301i	−0.545967	+	0.837806i	$0.683838\pi$
$798$	−3670.57	+	2964.62i	−0.162828	+	0.131512i
$799$	−6932.70	−	6932.70i	−0.306960	−	0.306960i
$800$	−16554.1	−	34115.2i	−0.731593	−	1.50769i
$801$	13677.3	−	13677.3i	0.603325	−	0.603325i
$802$	205.094	−	1927.68i	0.00903008	−	0.0848738i
$803$	16412.0	+	30704.7i	0.721255	+	1.34937i
$804$	56931.2	+	890.558i	2.49728	+	0.0390641i
$805$	36722.9	−	30137.7i	1.60784	−	1.31952i
$806$	117.296	+	289.562i	0.00512602	+	0.0126543i
$807$	5016.61	−	25220.2i	0.218826	−	1.10011i
$808$	29994.5	+	31436.0i	1.30594	+	1.36871i
$809$	25124.8	−	4997.63i	1.09189	−	0.217191i	0.383873	−	0.923386i	$-0.374590\pi$
$809$	25124.8	−	4997.63i	1.09189	−	0.217191i	0.708017	+	0.706195i	$0.249590\pi$
$810$	−45891.5	−	9502.08i	−1.99070	−	0.412184i
$811$	2701.32	−	819.435i	0.116962	−	0.0354800i	−0.231261	−	0.972892i	$-0.574285\pi$
$811$	2701.32	−	819.435i	0.116962	−	0.0354800i	0.348223	+	0.937412i	$0.386785\pi$
$812$	−1520.48	−	18380.7i	−0.0657122	−	0.794381i
$813$	−28109.1	−	23068.5i	−1.21258	−	0.995140i
$814$	−12628.4	−	3938.88i	−0.543764	−	0.169604i
$815$	−6207.95	−	14987.3i	−0.266816	−	0.644151i
$816$	5957.69	−	17634.3i	0.255589	−	0.756525i
$817$	−2607.60	+	6295.30i	−0.111663	+	0.269577i
$818$	16866.3	−	20227.0i	0.720927	−	0.864574i
$819$	−534.776	+	52.6708i	−0.0228163	+	0.00224721i
$820$	−15450.5	−	19438.7i	−0.657994	−	0.827840i
$821$	6710.89	+	3587.05i	0.285276	+	0.152483i	0.607829	−	0.794068i	$-0.292041\pi$
$821$	6710.89	+	3587.05i	0.285276	+	0.152483i	−0.322552	+	0.946552i	$0.604541\pi$
$822$	8031.77	−	1532.42i	0.340803	−	0.0650234i
$823$	−4442.16	+	6648.16i	−0.188146	+	0.281580i	−0.913536	−	0.406758i	$-0.866659\pi$
$823$	−4442.16	+	6648.16i	−0.188146	+	0.281580i	0.725390	+	0.688338i	$0.241659\pi$
$824$	43751.8	+	5348.24i	1.84972	+	0.226110i
$825$	77547.2	−	51815.4i	3.27254	−	2.18664i
$826$	14.5235	−	1857.02i	0.000611790	−	0.0782253i
$827$	−424.998	+	4315.08i	−0.0178702	+	0.181439i	−0.999976	−	0.00688958i	$-0.997807\pi$
$827$	−424.998	+	4315.08i	−0.0178702	+	0.181439i	0.982106	+	0.188328i	$0.0603070\pi$
$828$	−24421.3	+	4461.81i	−1.02500	+	0.187269i
$829$	10772.3	−	35511.6i	0.451313	−	1.48778i	−0.376310	−	0.926494i	$-0.622807\pi$
$829$	10772.3	−	35511.6i	0.451313	−	1.48778i	0.827623	−	0.561285i	$-0.189693\pi$
$830$	−30621.0	+	9027.87i	−1.28057	+	0.377545i
$831$			7280.30i			0.303912i
$832$	−322.874	−	1277.26i	−0.0134539	−	0.0532223i
$833$			7477.38i			0.311016i
$834$	−9156.65	−	31057.8i	−0.380179	−	1.28950i
$835$	2032.26	−	6699.45i	0.0842265	−	0.277658i
$836$	5969.91	−	8638.97i	0.246978	−	0.357398i
$837$	308.414	−	3131.38i	0.0127364	−	0.129315i
$838$	2738.71	+	21.4191i	0.112896	+	0.000882946i
$839$	−5864.03	+	3918.22i	−0.241298	+	0.161230i	−0.670339	−	0.742055i	$-0.733851\pi$
$839$	−5864.03	+	3918.22i	−0.241298	+	0.161230i	0.429042	+	0.903285i	$0.358851\pi$
$840$	9583.79	+	34486.2i	0.393657	+	1.41653i
$841$	3342.12	−	5001.84i	0.137034	−	0.205086i
$842$	1102.91	+	5780.60i	0.0451410	+	0.236594i
$843$	5598.07	+	2992.23i	0.228716	+	0.122251i
$844$	2681.02	−	23453.9i	0.109342	−	0.956536i
$845$	−39866.3	+	3926.49i	−1.62301	+	0.159853i
$846$	−7566.79	−	6309.58i	−0.307508	−	0.256416i
$847$	−16702.1	+	40322.5i	−0.677559	+	1.63577i
$848$	24098.6	−	18546.8i	0.975884	−	0.751060i
$849$	3849.52	+	9293.57i	0.155613	+	0.375682i
$850$	7843.30	−	25146.2i	0.316497	−	1.01472i
$851$	10436.3	+	8564.86i	0.420390	+	0.345005i
$852$	−4730.92	−	4008.02i	−0.190233	−	0.161165i
$853$	16939.4	−	5138.52i	0.679947	−	0.206260i	0.0686263	−	0.997642i	$-0.478138\pi$
$853$	16939.4	−	5138.52i	0.679947	−	0.206260i	0.611321	+	0.791383i	$0.290638\pi$
$854$	1895.92	−	9156.61i	0.0759686	−	0.366900i
$855$	5464.35	−	1086.93i	0.218569	−	0.0434762i
$856$	−8112.93	−	20964.4i	−0.323942	−	0.837090i
$857$	−270.827	+	1361.54i	−0.0107949	+	0.0542699i	−0.985807	−	0.167881i	$-0.946308\pi$
$857$	−270.827	+	1361.54i	−0.0107949	+	0.0542699i	0.975012	+	0.222151i	$0.0713077\pi$
$858$	3003.27	−	1216.57i	0.119499	−	0.0484066i
$859$	29678.5	−	24356.5i	1.17883	−	0.967443i	0.178967	−	0.983855i	$-0.442724\pi$
$859$	29678.5	−	24356.5i	1.17883	−	0.967443i	0.999865	+	0.0164123i	$0.00522445\pi$
$860$	35975.2	+	37118.5i	1.42644	+	1.47178i
$861$	6919.74	+	12945.9i	0.273896	+	0.512423i
$862$	−31369.8	−	3337.57i	−1.23951	−	0.131877i
$863$	6104.65	−	6104.65i	0.240793	−	0.240793i	−0.576385	−	0.817178i	$-0.695537\pi$
$863$	6104.65	−	6104.65i	0.240793	−	0.240793i	0.817178	+	0.576385i	$0.195537\pi$
$864$	−3095.36	+	12902.6i	−0.121882	+	0.508049i
$865$	−8362.80	−	8362.80i	−0.328721	−	0.328721i
$866$	29017.8	+	35927.6i	1.13864	+	1.40978i
$867$	−16941.6	+	9055.47i	−0.663629	+	0.354717i
$868$	−4221.55	+	1671.75i	−0.165079	+	0.0653721i
$869$	−32934.7	−	40131.0i	−1.28565	−	1.56657i
$870$	−23006.2	+	54336.1i	−0.896534	+	2.11743i
$871$	2745.68	+	546.150i	0.106813	+	0.0212464i
$872$	−10500.5	+	14943.8i	−0.407787	+	0.580345i
$873$	2414.13	+	12136.6i	0.0935920	+	0.470519i
$874$	−8957.42	+	5884.35i	−0.346670	+	0.227736i
$875$	5929.68	+	19547.5i	0.229097	+	0.755231i
$876$	25494.3	+	8171.19i	0.983303	+	0.315159i
$877$	−25774.8	+	31406.6i	−0.992419	+	1.20927i	−0.0145833	+	0.999894i	$0.504642\pi$
$877$	−25774.8	+	31406.6i	−0.992419	+	1.20927i	−0.977836	+	0.209373i	$0.932858\pi$
$878$	12919.0	+	24631.2i	0.496578	+	0.946768i
$879$	21838.4	−	9045.76i	0.837987	−	0.347106i
$880$	−42164.2	−	67588.0i	−1.61518	−	2.58908i
$881$	12672.6	+	5249.17i	0.484621	+	0.200737i	0.611598	−	0.791169i	$-0.290527\pi$
$881$	12672.6	+	5249.17i	0.484621	+	0.200737i	−0.126976	+	0.991906i	$0.540527\pi$
$882$	677.993	+	7483.30i	0.0258835	+	0.285687i
$883$	−3553.46	−	36078.9i	−0.135429	−	1.37503i	−0.787239	−	0.616648i	$-0.788490\pi$
$883$	−3553.46	−	36078.9i	−0.135429	−	1.37503i	0.651810	−	0.758382i	$-0.274010\pi$
$884$	443.978	−	800.259i	0.0168921	−	0.0304475i
$885$	−2800.72	+	5239.77i	−0.106379	+	0.199020i
$886$	−23378.9	−	15887.1i	−0.886488	−	0.602413i
$887$	13090.9	+	8747.05i	0.495546	+	0.331113i	0.778102	−	0.628138i	$-0.216183\pi$
$887$	13090.9	+	8747.05i	0.495546	+	0.331113i	−0.282557	+	0.959251i	$0.591183\pi$
$888$	−9080.99	+	4583.30i	−0.343173	+	0.173204i
$889$	−1607.65	−	2406.01i	−0.0606510	−	0.0907707i
$890$	−44440.7	−	45141.3i	−1.67377	−	1.70016i
$891$	−61363.3	−	6043.76i	−2.30724	−	0.227243i
$892$	−13614.2	−	2930.12i	−0.511029	−	0.109986i
$893$	−4070.13	−	1234.66i	−0.152521	−	0.0462668i
$894$	22059.3	+	12013.7i	0.825249	+	0.449438i
$895$	18316.5			0.684083
$896$	18599.1	−	4547.17i	0.693475	−	0.169543i
$897$	−3307.06			−0.123099
$898$	16710.1	+	9100.48i	0.620962	+	0.338181i
$899$	−7162.85	−	2172.83i	−0.265733	−	0.0806093i
$900$	5569.44	−	25877.3i	0.206275	−	0.958419i
$901$	21022.3	+	2070.52i	0.777309	+	0.0765583i
$902$	−22920.0	−	23281.3i	−0.846066	−	0.859405i
$903$	−16977.2	−	25408.1i	−0.625653	−	0.936355i
$904$	31782.8	+	10461.5i	1.16934	+	0.384894i
$905$	4117.46	+	2751.20i	0.151237	+	0.101053i
$906$	46066.5	+	31304.5i	1.68925	+	1.14793i
$907$	6056.02	−	11330.0i	0.221706	−	0.414782i	−0.746337	−	0.665568i	$-0.768189\pi$
$907$	6056.02	−	11330.0i	0.221706	−	0.414782i	0.968042	+	0.250786i	$0.0806892\pi$
$908$	−8105.47	−	4496.85i	−0.296244	−	0.164354i
$909$	2972.90	+	30184.4i	0.108476	+	1.10138i
$910$	158.792	+	1752.66i	0.00578451	+	0.0638461i
$911$	7195.88	+	2980.63i	0.261701	+	0.108400i	0.509676	−	0.860366i	$-0.329765\pi$
$911$	7195.88	+	2980.63i	0.261701	+	0.108400i	−0.247975	+	0.968766i	$0.579765\pi$
$912$	−1326.84	−	7965.08i	−0.0481756	−	0.289200i
$913$	−38805.3	+	16073.7i	−1.40665	+	0.582652i
$914$	12028.7	+	22933.7i	0.435310	+	0.829956i
$915$	−18978.4	+	23125.3i	−0.685692	+	0.835518i
$916$	4256.92	−	13281.7i	0.153551	−	0.479083i
$917$	−2138.64	−	7050.16i	−0.0770166	−	0.253890i
$918$	−7703.61	+	5060.70i	−0.276969	+	0.181948i
$919$	−5090.12	−	25589.8i	−0.182707	−	0.918530i	−0.957965	−	0.286885i	$-0.907380\pi$
$919$	−5090.12	−	25589.8i	−0.182707	−	0.918530i	0.775258	−	0.631645i	$-0.217620\pi$
$920$	13986.2	+	80090.3i	0.501209	+	2.87011i
$921$	−48314.8	−	9610.41i	−1.72858	−	0.343837i
$922$	−11943.2	+	28207.4i	−0.426603	+	1.00755i
$923$	−193.399	−	235.658i	−0.00689688	−	0.00840387i
$924$	17339.0	+	43784.8i	0.617329	+	1.55889i
$925$	−12695.3	+	6785.79i	−0.451264	+	0.241206i
$926$	−15879.7	−	19661.0i	−0.563540	−	0.697732i
$927$	21756.6	+	21756.6i	0.770854	+	0.770854i
$928$	28667.0	+	13209.9i	1.01405	+	0.467280i
$929$	−12718.1	+	12718.1i	−0.449157	+	0.449157i	−0.895074	−	0.445917i	$-0.852878\pi$
$929$	−12718.1	+	12718.1i	−0.449157	+	0.449157i	0.445917	+	0.895074i	$0.352878\pi$
$930$	14444.8	+	1536.85i	0.509317	+	0.0541883i
$931$	1529.12	+	2860.78i	0.0538291	+	0.100707i
$932$	−28487.0	+	27609.5i	−1.00121	+	0.970365i
$933$	−1173.37	+	962.959i	−0.0411730	+	0.0337898i
$934$	14926.4	−	6046.40i	0.522920	−	0.211825i
$935$	10795.8	−	54274.2i	0.377605	−	1.89835i
$936$	371.768	−	841.149i	0.0129825	−	0.0293737i
$937$	50227.6	−	9990.90i	1.75119	−	0.348333i	0.787696	−	0.616064i	$-0.211274\pi$
$937$	50227.6	−	9990.90i	1.75119	−	0.348333i	0.963494	+	0.267731i	$0.0862737\pi$
$938$	−8249.28	+	39840.9i	−0.287152	+	1.38684i
$939$	4328.28	−	1312.97i	0.150424	−	0.0456306i
$940$	−20856.7	+	24618.4i	−0.723691	+	0.854218i
$941$	29417.2	+	24142.0i	1.01910	+	0.836353i	0.986606	−	0.163119i	$-0.0521555\pi$
$941$	29417.2	+	24142.0i	1.01910	+	0.836353i	0.0324925	+	0.999472i	$0.489655\pi$
$942$	−7896.35	+	25316.3i	−0.273118	+	0.875637i
$943$	12759.9	+	30805.1i	0.440635	+	1.06379i
$944$	2754.69	+	1585.13i	0.0949764	+	0.0546522i
$945$	6782.80	−	16375.1i	0.233486	−	0.563685i
$946$	52233.7	+	43555.2i	1.79521	+	1.49693i
$947$	22650.2	−	2230.85i	0.777225	−	0.0765500i	0.298377	−	0.954448i	$-0.403555\pi$
$947$	22650.2	−	2230.85i	0.777225	−	0.0765500i	0.478848	+	0.877898i	$0.341055\pi$
$948$	−39662.3	−	4533.81i	−1.35883	−	0.155328i
$949$	1160.86	+	620.492i	0.0397082	+	0.0212245i
$950$	−2141.61	−	11224.7i	−0.0731400	−	0.383344i
$951$	19226.3	−	28774.2i	0.655579	−	0.981144i
$952$	11579.7	+	6543.30i	0.394224	+	0.222762i
$953$	−21226.9	+	14183.4i	−0.721519	+	0.482104i	−0.861312	−	0.508077i	$-0.830356\pi$
$953$	−21226.9	+	14183.4i	−0.721519	+	0.482104i	0.139792	+	0.990181i	$0.455356\pi$
$954$	21226.7	+	166.012i	0.720378	+	0.00563398i
$955$	−7003.22	+	71104.9i	−0.237297	+	2.40932i
$956$	4958.88	+	3426.80i	0.167763	+	0.115932i
$957$	−22536.0	+	74291.3i	−0.761218	+	2.50940i
$958$	10778.4	+	36558.5i	0.363502	+	1.23294i
$959$			5842.74i			0.196738i
$960$	−59452.6	−	14755.5i	−1.99877	−	0.496075i
$961$		−	27948.3i		−	0.938145i
$962$	−479.714	+	141.432i	−0.0160775	+	0.00474008i
$963$	4555.12	−	15016.2i	0.152426	−	0.502483i
$964$	540.341	+	2957.51i	0.0180531	+	0.0988122i
$965$	−7066.35	+	71745.8i	−0.235724	+	2.39335i
$966$	375.883	−	48061.5i	0.0125195	−	1.60078i
$967$	−26552.4	+	17741.7i	−0.883006	+	0.590006i	−0.912281	−	0.409566i	$-0.865680\pi$
$967$	−26552.4	+	17741.7i	−0.883006	+	0.590006i	0.0292746	+	0.999571i	$0.490680\pi$
$968$	−46017.6	−	58834.8i	−1.52796	−	1.95353i
$969$	3116.33	−	4663.92i	0.103314	−	0.154620i
$970$	39807.4	−	7595.04i	1.31767	−	0.251404i
$971$	−12404.9	−	6630.54i	−0.409981	−	0.219139i	0.253496	−	0.967337i	$-0.418420\pi$
$971$	−12404.9	−	6630.54i	−0.409981	−	0.219139i	−0.663476	+	0.748197i	$0.730920\pi$
$972$	−24723.1	+	19650.7i	−0.815836	+	0.648453i
$973$	23025.8	−	2267.84i	0.758657	−	0.0747212i
$974$	−10766.3	+	12911.5i	−0.354182	+	0.424754i
$975$	1349.38	−	3257.69i	0.0443228	−	0.107005i
$976$	12046.9	+	10534.1i	0.395094	+	0.345481i
$977$	−11940.0	−	28825.7i	−0.390987	−	0.943925i	−0.989725	−	0.142981i	$-0.954331\pi$
$977$	−11940.0	−	28825.7i	−0.390987	−	0.943925i	0.598739	−	0.800944i	$-0.295669\pi$
$978$	−15667.8	−	4886.90i	−0.512271	−	0.159781i
$979$	−64426.0	−	52873.1i	−2.10323	−	1.72608i
$980$	24524.0	−	2028.66i	0.799378	−	0.0661255i
$981$	−12200.4	+	3700.94i	−0.397072	+	0.120450i
$982$	21271.8	+	4404.43i	0.691252	+	0.143127i
$983$	−24080.7	+	4789.96i	−0.781339	+	0.155418i	−0.569615	−	0.821911i	$-0.692908\pi$
$983$	−24080.7	+	4789.96i	−0.781339	+	0.155418i	−0.211724	+	0.977329i	$0.567908\pi$
$984$	−25115.1	−	589.362i	−0.813659	−	0.0190937i
$985$	10751.7	−	54052.6i	0.347796	−	1.74849i
$986$	8232.16	+	20322.3i	0.265888	+	0.656383i
$987$	14744.6	−	12100.6i	0.475507	−	0.390239i
$988$	6.20961	−	396.966i	0.000199954	−	0.0127826i
$989$	−32720.2	−	61215.2i	−1.05201	−	1.96818i
$990$	5883.18	−	55296.1i	0.188869	−	1.77518i
$991$	−9664.16	+	9664.16i	−0.309780	+	0.309780i	−0.844824	−	0.535044i	$-0.820295\pi$
$991$	−9664.16	+	9664.16i	−0.309780	+	0.309780i	0.535044	+	0.844824i	$0.320295\pi$
$992$	1063.39	−	7697.51i	0.0340350	−	0.246367i
$993$	−40900.8	−	40900.8i	−1.30710	−	1.30710i
$994$	3446.80	−	2783.89i	0.109986	−	0.0888327i
$995$	−54479.6	+	29119.9i	−1.73580	+	0.927803i
$996$	−12825.2	+	29642.6i	−0.408013	+	0.943035i
$997$	13901.6	+	16939.1i	0.441592	+	0.538081i	0.945477	−	0.325690i	$-0.105596\pi$
$997$	13901.6	+	16939.1i	0.441592	+	0.538081i	−0.503885	+	0.863771i	$0.668096\pi$
$998$	−18517.7	−	7840.49i	−0.587341	−	0.248684i
$999$	4940.29	+	982.686i	0.156460	+	0.0311219i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	128.4.k.a.5.16	✓	752
128.77	even	32	inner	128.4.k.a.77.16	yes	752

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
128.4.k.a.5.16	✓	752	1.1	even	1	trivial
128.4.k.a.77.16	yes	752	128.77	even	32	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 128 = 2^{7} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	128.k (of order \(32\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.35278 + 2.48395i) q^{2} +(6.26012 + 1.89899i) q^{3} +(-4.33998 - 6.72046i) q^{4} +(-18.2007 - 1.79261i) q^{5} +(-13.1855 + 12.9809i) q^{6} +(-7.34552 - 10.9934i) q^{7} +(22.5643 - 1.68898i) q^{8} +(13.1332 + 8.77534i) q^{9} +O(q^{10})\)	\(q+(-1.35278 + 2.48395i) q^{2} +(6.26012 + 1.89899i) q^{3} +(-4.33998 - 6.72046i) q^{4} +(-18.2007 - 1.79261i) q^{5} +(-13.1855 + 12.9809i) q^{6} +(-7.34552 - 10.9934i) q^{7} +(22.5643 - 1.68898i) q^{8} +(13.1332 + 8.77534i) q^{9} +(29.0742 - 42.7844i) q^{10} +(32.0828 - 60.0227i) q^{11} +(-14.4067 - 50.3124i) q^{12} +(-0.252210 - 2.56073i) q^{13} +(37.2438 - 3.37431i) q^{14} +(-110.534 - 45.7847i) q^{15} +(-26.3292 + 58.3333i) q^{16} +(-41.0739 + 17.0134i) q^{17} +(-39.5638 + 20.7511i) q^{18} +(-12.2353 + 14.9088i) q^{19} +(66.9433 + 130.097i) q^{20} +(-25.1076 - 82.7687i) q^{21} +(105.692 + 160.889i) q^{22} +(-38.3284 - 192.690i) q^{23} +(144.462 + 32.2760i) q^{24} +(205.452 + 40.8670i) q^{25} +(6.70189 + 2.83762i) q^{26} +(-46.5008 - 56.6614i) q^{27} +(-42.0010 + 97.0762i) q^{28} +(-153.780 + 82.1971i) q^{29} +(263.255 - 212.624i) q^{30} +(30.3540 + 30.3540i) q^{31} +(-109.279 - 144.312i) q^{32} +(314.824 - 314.824i) q^{33} +(13.3036 - 125.041i) q^{34} +(113.987 + 213.254i) q^{35} +(1.97639 - 126.346i) q^{36} +(-53.1205 + 43.5949i) q^{37} +(-20.4809 - 50.5601i) q^{38} +(3.28392 - 16.5094i) q^{39} +(-413.713 - 9.70836i) q^{40} +(-166.455 + 33.1099i) q^{41} +(239.558 + 49.6018i) q^{42} +(338.088 - 102.558i) q^{43} +(-542.619 + 44.8861i) q^{44} +(-223.302 - 183.260i) q^{45} +(530.481 + 165.461i) q^{46} +(84.3929 + 203.743i) q^{47} +(-275.598 + 315.175i) q^{48} +(64.3633 - 155.387i) q^{49} +(-379.443 + 455.048i) q^{50} +(-289.436 + 28.5069i) q^{51} +(-16.1147 + 12.8085i) q^{52} +(-419.041 - 223.982i) q^{53} +(203.649 - 38.8552i) q^{54} +(-691.525 + 1034.94i) q^{55} +(-184.314 - 235.651i) q^{56} +(-104.906 + 70.0960i) q^{57} +(3.85706 - 493.176i) q^{58} +(4.86748 - 49.4203i) q^{59} +(172.021 + 941.544i) q^{60} +(72.5847 - 239.280i) q^{61} +(-116.460 + 34.3354i) q^{62} -208.838i q^{63} +(506.295 - 76.2214i) q^{64} +47.0590i q^{65} +(356.119 + 1207.89i) q^{66} +(-315.821 + 1041.12i) q^{67} +(292.598 + 202.198i) q^{68} +(125.975 - 1279.05i) q^{69} +(-683.910 - 5.34877i) q^{70} +(98.5107 - 65.8228i) q^{71} +(311.163 + 175.828i) q^{72} +(-284.203 + 425.340i) q^{73} +(-36.4270 - 190.923i) q^{74} +(1208.55 + 645.983i) q^{75} +(153.295 + 17.5232i) q^{76} +(-895.515 + 88.2005i) q^{77} +(36.5660 + 30.4906i) q^{78} +(291.910 - 704.734i) q^{79} +(583.777 - 1014.51i) q^{80} +(-346.704 - 837.018i) q^{81} +(142.933 - 458.255i) q^{82} +(-477.063 - 391.515i) q^{83} +(-447.277 + 527.949i) q^{84} +(778.071 - 236.025i) q^{85} +(-202.610 + 978.530i) q^{86} +(-1118.77 + 222.538i) q^{87} +(622.548 - 1408.56i) q^{88} +(238.905 - 1201.06i) q^{89} +(757.286 - 306.762i) q^{90} +(-26.2984 + 21.5825i) q^{91} +(-1128.62 + 1093.85i) q^{92} +(132.378 + 247.661i) q^{93} +(-620.251 - 65.9911i) q^{94} +(249.416 - 249.416i) q^{95} +(-410.054 - 1110.93i) q^{96} +(553.968 + 553.968i) q^{97} +(298.903 + 370.079i) q^{98} +(948.069 - 506.754i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 752 q - 16 q^{2} - 16 q^{3} - 16 q^{4} - 16 q^{5} - 16 q^{6} - 16 q^{7} - 16 q^{8} - 16 q^{9}+O(q^{10}) \) 752 * q - 16 * q^2 - 16 * q^3 - 16 * q^4 - 16 * q^5 - 16 * q^6 - 16 * q^7 - 16 * q^8 - 16 * q^9	\( 752 q - 16 q^{2} - 16 q^{3} - 16 q^{4} - 16 q^{5} - 16 q^{6} - 16 q^{7} - 16 q^{8} - 16 q^{9} - 16 q^{10} - 16 q^{11} - 16 q^{12} - 16 q^{13} - 16 q^{14} - 16 q^{15} - 16 q^{16} - 16 q^{17} - 16 q^{18} - 16 q^{19} - 16 q^{20} - 16 q^{21} - 16 q^{22} - 16 q^{23} - 16 q^{24} - 16 q^{25} - 16 q^{26} - 16 q^{27} - 16 q^{28} - 16 q^{29} - 16 q^{30} - 16 q^{31} - 16 q^{32} - 16 q^{33} - 16 q^{34} - 16 q^{35} - 16 q^{36} - 16 q^{37} - 16 q^{38} - 16 q^{39} - 16 q^{40} - 16 q^{41} - 16 q^{42} - 16 q^{43} - 16 q^{44} - 16 q^{45} - 16 q^{46} - 16 q^{47} - 16 q^{48} - 16 q^{49} + 5696 q^{50} - 16 q^{51} + 6608 q^{52} - 16 q^{53} + 3440 q^{54} - 16 q^{55} - 800 q^{56} - 16 q^{57} - 4768 q^{58} - 16 q^{59} - 9808 q^{60} - 16 q^{61} - 5872 q^{62} - 12112 q^{64} - 10960 q^{66} - 16 q^{67} - 4144 q^{68} - 16 q^{69} - 4048 q^{70} - 16 q^{71} + 1280 q^{72} - 16 q^{73} + 5248 q^{74} - 16 q^{75} + 11888 q^{76} - 16 q^{77} + 14096 q^{78} - 16 q^{79} + 10016 q^{80} - 16 q^{81} - 16 q^{82} - 16 q^{83} - 16 q^{84} - 16 q^{85} - 16 q^{86} - 16 q^{87} - 16 q^{88} - 16 q^{89} - 16 q^{90} - 16 q^{91} - 16 q^{92} - 16 q^{93} - 16 q^{94} - 16 q^{95} - 16 q^{96} - 16 q^{97} - 16 q^{98} - 16 q^{99}+O(q^{100}) \) 752 * q - 16 * q^2 - 16 * q^3 - 16 * q^4 - 16 * q^5 - 16 * q^6 - 16 * q^7 - 16 * q^8 - 16 * q^9 - 16 * q^10 - 16 * q^11 - 16 * q^12 - 16 * q^13 - 16 * q^14 - 16 * q^15 - 16 * q^16 - 16 * q^17 - 16 * q^18 - 16 * q^19 - 16 * q^20 - 16 * q^21 - 16 * q^22 - 16 * q^23 - 16 * q^24 - 16 * q^25 - 16 * q^26 - 16 * q^27 - 16 * q^28 - 16 * q^29 - 16 * q^30 - 16 * q^31 - 16 * q^32 - 16 * q^33 - 16 * q^34 - 16 * q^35 - 16 * q^36 - 16 * q^37 - 16 * q^38 - 16 * q^39 - 16 * q^40 - 16 * q^41 - 16 * q^42 - 16 * q^43 - 16 * q^44 - 16 * q^45 - 16 * q^46 - 16 * q^47 - 16 * q^48 - 16 * q^49 + 5696 * q^50 - 16 * q^51 + 6608 * q^52 - 16 * q^53 + 3440 * q^54 - 16 * q^55 - 800 * q^56 - 16 * q^57 - 4768 * q^58 - 16 * q^59 - 9808 * q^60 - 16 * q^61 - 5872 * q^62 - 12112 * q^64 - 10960 * q^66 - 16 * q^67 - 4144 * q^68 - 16 * q^69 - 4048 * q^70 - 16 * q^71 + 1280 * q^72 - 16 * q^73 + 5248 * q^74 - 16 * q^75 + 11888 * q^76 - 16 * q^77 + 14096 * q^78 - 16 * q^79 + 10016 * q^80 - 16 * q^81 - 16 * q^82 - 16 * q^83 - 16 * q^84 - 16 * q^85 - 16 * q^86 - 16 * q^87 - 16 * q^88 - 16 * q^89 - 16 * q^90 - 16 * q^91 - 16 * q^92 - 16 * q^93 - 16 * q^94 - 16 * q^95 - 16 * q^96 - 16 * q^97 - 16 * q^98 - 16 * q^99

Introduction

L-functions

Modular forms

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