LMFDB - Embedded newform 128.3.l.a.43.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("128.3");

S:= CuspForms(chi, 3);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.48774738381$
Analytic rank:	$0$
Dimension:	$496$
Relative dimension:	$31$ over $\Q(\zeta_{32})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{32}]$

Embedding invariants

Embedding label			43.19
Character	$\chi$	$=$	128.43
Dual form			128.3.l.a.3.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.359443 + 1.96744i) q^{2} +(1.06123 + 0.870929i) q^{3} +(-3.74160 + 1.41436i) q^{4} +(-6.51407 + 1.97602i) q^{5} +(-1.33205 + 2.40095i) q^{6} +(-0.702367 + 3.53104i) q^{7} +(-4.12755 - 6.85298i) q^{8} +(-1.38812 - 6.97855i) q^{9} +O(q^{10})$	\(q+(0.359443 + 1.96744i) q^{2} +(1.06123 + 0.870929i) q^{3} +(-3.74160 + 1.41436i) q^{4} +(-6.51407 + 1.97602i) q^{5} +(-1.33205 + 2.40095i) q^{6} +(-0.702367 + 3.53104i) q^{7} +(-4.12755 - 6.85298i) q^{8} +(-1.38812 - 6.97855i) q^{9} +(-6.22913 - 12.1057i) q^{10} +(-0.787497 + 7.99559i) q^{11} +(-5.20251 - 1.75771i) q^{12} +(-2.30539 + 7.59984i) q^{13} +(-7.19955 - 0.112656i) q^{14} +(-8.63390 - 3.57628i) q^{15} +(11.9992 - 10.5839i) q^{16} +(7.94744 + 19.1868i) q^{17} +(13.2309 - 5.23943i) q^{18} +(7.19499 + 13.4609i) q^{19} +(21.5782 - 16.6067i) q^{20} +(-3.82066 + 3.13553i) q^{21} +(-16.0139 + 1.32461i) q^{22} +(-20.1780 - 13.4825i) q^{23} +(1.58817 - 10.8674i) q^{24} +(17.7417 - 11.8546i) q^{25} +(-15.7808 - 1.80399i) q^{26} +(10.4291 - 19.5116i) q^{27} +(-2.36618 - 14.2051i) q^{28} +(3.83729 + 38.9607i) q^{29} +(3.93270 - 18.2721i) q^{30} +(6.89353 - 6.89353i) q^{31} +(25.1362 + 19.8033i) q^{32} +(-7.79931 + 7.79931i) q^{33} +(-34.8922 + 22.5326i) q^{34} +(-2.40214 - 24.3893i) q^{35} +(15.0640 + 24.1477i) q^{36} +(-18.2260 + 34.0985i) q^{37} +(-23.8972 + 18.9941i) q^{38} +(-9.06547 + 6.05735i) q^{39} +(40.4288 + 36.4846i) q^{40} +(-0.962894 - 0.643385i) q^{41} +(-7.54226 - 6.38985i) q^{42} +(59.6302 - 48.9372i) q^{43} +(-8.36214 - 31.0301i) q^{44} +(22.8321 + 42.7158i) q^{45} +(19.2732 - 44.5452i) q^{46} +(8.29527 + 20.0266i) q^{47} +(21.9518 - 0.781576i) q^{48} +(33.2952 + 13.7913i) q^{49} +(29.7003 + 30.6446i) q^{50} +(-8.27630 + 27.2833i) q^{51} +(-2.12307 - 31.6962i) q^{52} +(1.21081 - 12.2936i) q^{53} +(42.1364 + 13.5054i) q^{54} +(-10.6696 - 53.6399i) q^{55} +(27.0972 - 9.76124i) q^{56} +(-4.08793 + 20.5514i) q^{57} +(-75.2734 + 21.5538i) q^{58} +(-105.206 + 31.9140i) q^{59} +(37.3628 + 1.16957i) q^{60} +(38.0299 + 31.2103i) q^{61} +(16.0404 + 11.0847i) q^{62} +25.6165 q^{63} +(-29.9266 + 56.5721i) q^{64} -54.0614i q^{65} +(-18.1480 - 12.5412i) q^{66} +(26.0326 - 31.7208i) q^{67} +(-56.8732 - 60.5489i) q^{68} +(-9.67122 - 31.8817i) q^{69} +(47.1209 - 13.4926i) q^{70} +(-81.2684 - 16.1653i) q^{71} +(-42.0943 + 38.3171i) q^{72} +(74.7208 - 14.8629i) q^{73} +(-73.6377 - 23.6020i) q^{74} +(29.1525 + 2.87127i) q^{75} +(-45.9593 - 40.1889i) q^{76} +(-27.6796 - 8.39652i) q^{77} +(-15.1760 - 15.6584i) q^{78} +(32.3206 - 78.0289i) q^{79} +(-57.2493 + 92.6552i) q^{80} +(-31.1020 + 12.8829i) q^{81} +(0.919713 - 2.12569i) q^{82} +(26.3421 - 14.0801i) q^{83} +(9.86060 - 17.1357i) q^{84} +(-89.6837 - 109.280i) q^{85} +(117.714 + 99.7284i) q^{86} +(-29.8598 + 44.6883i) q^{87} +(58.0440 - 27.6055i) q^{88} +(-43.7143 - 65.4230i) q^{89} +(-75.8338 + 60.2745i) q^{90} +(-25.2161 - 13.4783i) q^{91} +(94.5674 + 21.9073i) q^{92} +(13.3194 - 1.31185i) q^{93} +(-36.4193 + 23.5188i) q^{94} +(-73.4676 - 73.4676i) q^{95} +(9.42810 + 42.9077i) q^{96} +(-112.520 - 112.520i) q^{97} +(-15.1658 + 70.4633i) q^{98} +(56.8908 - 5.60325i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 496 q - 16 q^{2} - 16 q^{3} - 16 q^{4} - 16 q^{5} - 16 q^{6} - 16 q^{7} - 16 q^{8} - 16 q^{9}+O(q^{10}) $ 496 * q - 16 * q^2 - 16 * q^3 - 16 * q^4 - 16 * q^5 - 16 * q^6 - 16 * q^7 - 16 * q^8 - 16 * q^9	\( 496 q - 16 q^{2} - 16 q^{3} - 16 q^{4} - 16 q^{5} - 16 q^{6} - 16 q^{7} - 16 q^{8} - 16 q^{9} - 16 q^{10} - 16 q^{11} - 16 q^{12} - 16 q^{13} - 16 q^{14} - 16 q^{15} - 16 q^{16} - 16 q^{17} - 16 q^{18} - 16 q^{19} - 16 q^{20} - 16 q^{21} - 16 q^{22} - 16 q^{23} - 16 q^{24} - 16 q^{25} - 16 q^{26} - 16 q^{27} - 16 q^{28} - 16 q^{29} - 16 q^{30} - 16 q^{31} - 16 q^{32} - 16 q^{33} - 16 q^{34} - 16 q^{35} - 16 q^{36} - 16 q^{37} - 16 q^{38} - 16 q^{39} - 16 q^{40} - 16 q^{41} - 16 q^{42} - 16 q^{43} - 16 q^{44} - 16 q^{45} - 16 q^{46} - 16 q^{47} - 16 q^{48} - 16 q^{49} - 640 q^{50} - 16 q^{51} - 1072 q^{52} - 16 q^{53} - 1168 q^{54} - 16 q^{55} - 800 q^{56} - 16 q^{57} - 736 q^{58} - 16 q^{59} - 592 q^{60} - 16 q^{61} - 112 q^{62} - 32 q^{63} + 176 q^{64} + 560 q^{66} - 16 q^{67} + 464 q^{68} - 16 q^{69} + 1328 q^{70} - 16 q^{71} + 1280 q^{72} - 16 q^{73} + 1216 q^{74} - 16 q^{75} + 1648 q^{76} - 16 q^{77} + 1424 q^{78} - 16 q^{79} + 800 q^{80} - 16 q^{81} - 16 q^{82} - 16 q^{83} - 16 q^{84} - 16 q^{85} - 16 q^{86} - 16 q^{87} - 16 q^{88} - 16 q^{89} - 16 q^{90} - 16 q^{91} - 16 q^{92} - 16 q^{93} - 16 q^{94} - 16 q^{95} - 16 q^{96} - 16 q^{97} - 16 q^{98} - 16 q^{99}+O(q^{100}) \) 496 * q - 16 * q^2 - 16 * q^3 - 16 * q^4 - 16 * q^5 - 16 * q^6 - 16 * q^7 - 16 * q^8 - 16 * q^9 - 16 * q^10 - 16 * q^11 - 16 * q^12 - 16 * q^13 - 16 * q^14 - 16 * q^15 - 16 * q^16 - 16 * q^17 - 16 * q^18 - 16 * q^19 - 16 * q^20 - 16 * q^21 - 16 * q^22 - 16 * q^23 - 16 * q^24 - 16 * q^25 - 16 * q^26 - 16 * q^27 - 16 * q^28 - 16 * q^29 - 16 * q^30 - 16 * q^31 - 16 * q^32 - 16 * q^33 - 16 * q^34 - 16 * q^35 - 16 * q^36 - 16 * q^37 - 16 * q^38 - 16 * q^39 - 16 * q^40 - 16 * q^41 - 16 * q^42 - 16 * q^43 - 16 * q^44 - 16 * q^45 - 16 * q^46 - 16 * q^47 - 16 * q^48 - 16 * q^49 - 640 * q^50 - 16 * q^51 - 1072 * q^52 - 16 * q^53 - 1168 * q^54 - 16 * q^55 - 800 * q^56 - 16 * q^57 - 736 * q^58 - 16 * q^59 - 592 * q^60 - 16 * q^61 - 112 * q^62 - 32 * q^63 + 176 * q^64 + 560 * q^66 - 16 * q^67 + 464 * q^68 - 16 * q^69 + 1328 * q^70 - 16 * q^71 + 1280 * q^72 - 16 * q^73 + 1216 * q^74 - 16 * q^75 + 1648 * q^76 - 16 * q^77 + 1424 * q^78 - 16 * q^79 + 800 * q^80 - 16 * q^81 - 16 * q^82 - 16 * q^83 - 16 * q^84 - 16 * q^85 - 16 * q^86 - 16 * q^87 - 16 * q^88 - 16 * q^89 - 16 * q^90 - 16 * q^91 - 16 * q^92 - 16 * q^93 - 16 * q^94 - 16 * q^95 - 16 * q^96 - 16 * q^97 - 16 * q^98 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	0.359443	+	1.96744i	0.179721	+	0.983718i
$2$	0.359443	+	1.96744i	0.179721	+	0.983718i
$3$	1.06123	+	0.870929i	0.353743	+	0.290310i	0.794435	−	0.607349i	$-0.207767\pi$
$3$	1.06123	+	0.870929i	0.353743	+	0.290310i	−0.440692	+	0.897658i	$0.645267\pi$
$4$	−3.74160	+	1.41436i	−0.935400	+	0.353590i
$5$	−6.51407	+	1.97602i	−1.30281	+	0.395204i	−0.864053	−	0.503400i	$-0.832082\pi$
$5$	−6.51407	+	1.97602i	−1.30281	+	0.395204i	−0.438760	+	0.898604i	$0.644582\pi$
$6$	−1.33205	+	2.40095i	−0.222008	+	0.400159i
$7$	−0.702367	+	3.53104i	−0.100338	+	0.504434i	0.897632	+	0.440746i	$0.145286\pi$
$7$	−0.702367	+	3.53104i	−0.100338	+	0.504434i	−0.997970	+	0.0636876i	$0.979714\pi$
$8$	−4.12755	−	6.85298i	−0.515944	−	0.856622i
$9$	−1.38812	−	6.97855i	−0.154236	−	0.775395i
$10$	−6.22913	−	12.1057i	−0.622913	−	1.21057i
$11$	−0.787497	+	7.99559i	−0.0715906	+	0.726872i	0.890653	+	0.454683i	$0.150247\pi$
$11$	−0.787497	+	7.99559i	−0.0715906	+	0.726872i	−0.962244	+	0.272189i	$0.912253\pi$
$12$	−5.20251	−	1.75771i	−0.433542	−	0.146476i
$13$	−2.30539	+	7.59984i	−0.177337	+	0.584603i	0.822536	+	0.568712i	$0.192558\pi$
$13$	−2.30539	+	7.59984i	−0.177337	+	0.584603i	−0.999874	+	0.0158904i	$0.994942\pi$
$14$	−7.19955	−	0.112656i	−0.514253	−	0.00804686i
$15$	−8.63390	−	3.57628i	−0.575593	−	0.238419i
$16$	11.9992	−	10.5839i	0.749948	−	0.661497i
$17$	7.94744	+	19.1868i	0.467496	+	1.12864i	0.965252	+	0.261319i	$0.0841575\pi$
$17$	7.94744	+	19.1868i	0.467496	+	1.12864i	−0.497756	+	0.867317i	$0.665842\pi$
$18$	13.2309	−	5.23943i	0.735050	−	0.291079i
$19$	7.19499	+	13.4609i	0.378684	+	0.708467i	0.996995	−	0.0774661i	$-0.0246829\pi$
$19$	7.19499	+	13.4609i	0.378684	+	0.708467i	−0.618311	+	0.785933i	$0.712183\pi$
$20$	21.5782	−	16.6067i	1.07891	−	0.830336i
$21$	−3.82066	+	3.13553i	−0.181936	+	0.149311i
$22$	−16.0139	+	1.32461i	−0.727903	+	0.0602094i
$23$	−20.1780	−	13.4825i	−0.877306	−	0.586197i	0.0333123	−	0.999445i	$-0.489394\pi$
$23$	−20.1780	−	13.4825i	−0.877306	−	0.586197i	−0.910619	+	0.413248i	$0.864394\pi$
$24$	1.58817	−	10.8674i	0.0661739	−	0.452808i
$25$	17.7417	−	11.8546i	0.709667	−	0.474184i
$26$	−15.7808	−	1.80399i	−0.606955	−	0.0693843i
$27$	10.4291	−	19.5116i	0.386264	−	0.722650i
$28$	−2.36618	−	14.2051i	−0.0845065	−	0.507326i
$29$	3.83729	+	38.9607i	0.132320	+	1.34347i	0.800437	+	0.599416i	$0.204601\pi$
$29$	3.83729	+	38.9607i	0.132320	+	1.34347i	−0.668117	+	0.744056i	$0.732899\pi$
$30$	3.93270	−	18.2721i	0.131090	−	0.609070i
$31$	6.89353	−	6.89353i	0.222372	−	0.222372i	−0.587125	−	0.809497i	$-0.699740\pi$
$31$	6.89353	−	6.89353i	0.222372	−	0.222372i	0.809497	+	0.587125i	$0.199740\pi$
$32$	25.1362	+	19.8033i	0.785508	+	0.618852i
$33$	−7.79931	+	7.79931i	−0.236343	+	0.236343i
$34$	−34.8922	+	22.5326i	−1.02624	+	0.662725i
$35$	−2.40214	−	24.3893i	−0.0686325	−	0.696837i
$36$	15.0640	+	24.1477i	0.418444	+	0.670769i
$37$	−18.2260	+	34.0985i	−0.492595	+	0.921580i	0.505672	+	0.862726i	$0.331245\pi$
$37$	−18.2260	+	34.0985i	−0.492595	+	0.921580i	−0.998267	+	0.0588541i	$0.981255\pi$
$38$	−23.8972	+	18.9941i	−0.628874	+	0.499844i
$39$	−9.06547	+	6.05735i	−0.232448	+	0.155317i
$40$	40.4288	+	36.4846i	1.01072	+	0.912116i
$41$	−0.962894	−	0.643385i	−0.0234852	−	0.0156923i	0.543772	−	0.839233i	$-0.316996\pi$
$41$	−0.962894	−	0.643385i	−0.0234852	−	0.0156923i	−0.567257	+	0.823541i	$0.691996\pi$
$42$	−7.54226	−	6.38985i	−0.179578	−	0.152139i
$43$	59.6302	−	48.9372i	1.38675	−	1.13808i	0.412927	−	0.910764i	$-0.364507\pi$
$43$	59.6302	−	48.9372i	1.38675	−	1.13808i	0.973822	−	0.227311i	$-0.0729935\pi$
$44$	−8.36214	−	31.0301i	−0.190049	−	0.705230i
$45$	22.8321	+	42.7158i	0.507380	+	0.949240i
$46$	19.2732	−	44.5452i	0.418982	−	0.968374i
$47$	8.29527	+	20.0266i	0.176495	+	0.426097i	0.987227	−	0.159321i	$-0.0509305\pi$
$47$	8.29527	+	20.0266i	0.176495	+	0.426097i	−0.810732	+	0.585418i	$0.800930\pi$
$48$	21.9518	−	0.781576i	0.457328	−	0.0162828i
$49$	33.2952	+	13.7913i	0.679494	+	0.281456i
$50$	29.7003	+	30.6446i	0.594006	+	0.612891i
$51$	−8.27630	+	27.2833i	−0.162280	+	0.534967i
$52$	−2.12307	−	31.6962i	−0.0408283	−	0.609543i
$53$	1.21081	−	12.2936i	0.0228455	−	0.231954i	−0.976981	−	0.213326i	$-0.931570\pi$
$53$	1.21081	−	12.2936i	0.0228455	−	0.231954i	0.999826	−	0.0186278i	$-0.00592977\pi$
$54$	42.1364	+	13.5054i	0.780303	+	0.250100i
$55$	−10.6696	−	53.6399i	−0.193994	−	0.975271i
$56$	27.0972	−	9.76124i	0.483878	−	0.174308i
$57$	−4.08793	+	20.5514i	−0.0717181	+	0.360551i
$58$	−75.2734	+	21.5538i	−1.29782	+	0.371617i
$59$	−105.206	+	31.9140i	−1.78316	+	0.540916i	−0.997021	−	0.0771342i	$-0.975423\pi$
$59$	−105.206	+	31.9140i	−1.78316	+	0.540916i	−0.786139	+	0.618050i	$0.787923\pi$
$60$	37.3628	+	1.16957i	0.622713	+	0.0194928i
$61$	38.0299	+	31.2103i	0.623441	+	0.511645i	0.892246	−	0.451550i	$-0.149129\pi$
$61$	38.0299	+	31.2103i	0.623441	+	0.511645i	−0.268805	+	0.963195i	$0.586629\pi$
$62$	16.0404	+	11.0847i	0.258716	+	0.178786i
$63$	25.6165			0.406611
$64$	−29.9266	+	56.5721i	−0.467603	+	0.883938i
$65$		−	54.0614i		−	0.831713i
$66$	−18.1480	−	12.5412i	−0.274970	−	0.190019i
$67$	26.0326	−	31.7208i	0.388546	−	0.473445i	−0.541599	−	0.840637i	$-0.682181\pi$
$67$	26.0326	−	31.7208i	0.388546	−	0.473445i	0.930145	+	0.367192i	$0.119681\pi$
$68$	−56.8732	−	60.5489i	−0.836371	−	0.890425i
$69$	−9.67122	−	31.8817i	−0.140163	−	0.462054i
$70$	47.1209	−	13.4926i	0.673156	−	0.192751i
$71$	−81.2684	−	16.1653i	−1.14463	−	0.227680i	−0.413881	−	0.910331i	$-0.635827\pi$
$71$	−81.2684	−	16.1653i	−1.14463	−	0.227680i	−0.730744	+	0.682651i	$0.760827\pi$
$72$	−42.0943	+	38.3171i	−0.584644	+	0.532182i
$73$	74.7208	−	14.8629i	1.02357	−	0.203601i	0.345363	−	0.938469i	$-0.387756\pi$
$73$	74.7208	−	14.8629i	1.02357	−	0.203601i	0.678210	+	0.734868i	$0.262756\pi$
$74$	−73.6377	−	23.6020i	−0.995104	−	0.318947i
$75$	29.1525	+	2.87127i	0.388701	+	0.0382837i
$76$	−45.9593	−	40.1889i	−0.604728	−	0.528802i
$77$	−27.6796	−	8.39652i	−0.359475	−	0.109046i
$78$	−15.1760	−	15.6584i	−0.194564	−	0.200749i
$79$	32.3206	−	78.0289i	0.409122	−	0.987707i	−0.576248	−	0.817275i	$-0.695484\pi$
$79$	32.3206	−	78.0289i	0.409122	−	0.987707i	0.985369	−	0.170432i	$-0.0545163\pi$
$80$	−57.2493	+	92.6552i	−0.715616	+	1.15819i
$81$	−31.1020	+	12.8829i	−0.383975	+	0.159048i
$82$	0.919713	−	2.12569i	0.0112160	−	0.0259231i
$83$	26.3421	−	14.0801i	0.317375	−	0.169640i	−0.305016	−	0.952347i	$-0.598662\pi$
$83$	26.3421	−	14.0801i	0.317375	−	0.169640i	0.622390	+	0.782707i	$0.286162\pi$
$84$	9.86060	−	17.1357i	0.117388	−	0.203996i
$85$	−89.6837	−	109.280i	−1.05510	−	1.28565i
$86$	117.714	+	99.7284i	1.36877	+	1.15963i
$87$	−29.8598	+	44.6883i	−0.343216	+	0.513659i
$88$	58.0440	−	27.6055i	0.659591	−	0.313699i
$89$	−43.7143	−	65.4230i	−0.491172	−	0.735090i	0.500237	−	0.865888i	$-0.333246\pi$
$89$	−43.7143	−	65.4230i	−0.491172	−	0.735090i	−0.991409	+	0.130798i	$0.958246\pi$
$90$	−75.8338	+	60.2745i	−0.842598	+	0.669717i
$91$	−25.2161	−	13.4783i	−0.277100	−	0.148113i
$92$	94.5674	+	21.9073i	1.02791	+	0.238123i
$93$	13.3194	−	1.31185i	0.143219	−	0.0141059i
$94$	−36.4193	+	23.5188i	−0.387439	+	0.250200i
$95$	−73.4676	−	73.4676i	−0.773343	−	0.773343i
$96$	9.42810	+	42.9077i	0.0982093	+	0.446955i
$97$	−112.520	−	112.520i	−1.16000	−	1.16000i	−0.984475	−	0.175525i	$-0.943838\pi$
$97$	−112.520	−	112.520i	−1.16000	−	1.16000i	−0.175525	−	0.984475i	$-0.556162\pi$
$98$	−15.1658	+	70.4633i	−0.154753	+	0.719014i
$99$	56.8908	−	5.60325i	0.574654	−	0.0565985i
$100$	−49.6156	+	69.4484i	−0.496156	+	0.694484i
$101$	150.679	+	80.5394i	1.49187	+	0.797420i	0.997420	−	0.0717867i	$-0.0228701\pi$
$101$	150.679	+	80.5394i	1.49187	+	0.797420i	0.494448	+	0.869207i	$0.335370\pi$
$102$	−56.6530	−	6.47630i	−0.555421	−	0.0634931i
$103$	−8.16492	−	12.2197i	−0.0792710	−	0.118637i	0.789715	−	0.613473i	$-0.210228\pi$
$103$	−8.16492	−	12.2197i	−0.0792710	−	0.118637i	−0.868986	+	0.494836i	$0.835228\pi$
$104$	61.5971	−	15.5700i	0.592280	−	0.149711i
$105$	18.6921	−	27.9748i	0.178020	−	0.266426i
$106$	24.6220	−	2.03664i	0.232283	−	0.0192136i
$107$	−6.00696	−	7.31950i	−0.0561398	−	0.0684065i	0.744184	−	0.667975i	$-0.232839\pi$
$107$	−6.00696	−	7.31950i	−0.0561398	−	0.0684065i	−0.800323	+	0.599569i	$0.795339\pi$
$108$	−11.4253	+	87.7550i	−0.105790	+	0.812546i
$109$	−168.472	+	90.0501i	−1.54561	+	0.826147i	−0.999930	−	0.0118440i	$-0.996230\pi$
$109$	−168.472	+	90.0501i	−1.54561	+	0.826147i	−0.545683	+	0.837991i	$0.683730\pi$
$110$	101.698	−	40.2723i	0.924527	−	0.366112i
$111$	−49.0393	+	20.3128i	−0.441796	+	0.182998i
$112$	28.9445	+	49.8033i	0.258433	+	0.444673i
$113$	−32.5613	+	78.6100i	−0.288153	+	0.695664i	−0.999978	−	0.00669401i	$-0.997869\pi$
$113$	−32.5613	+	78.6100i	−0.288153	+	0.695664i	0.711824	+	0.702358i	$0.247869\pi$
$114$	−41.9030	−	0.655683i	−0.367570	−	0.00575161i
$115$	158.083	+	47.9539i	1.37463	+	0.416991i
$116$	−69.4621	−	140.348i	−0.598811	−	1.20990i
$117$	56.2360	+	5.53877i	0.480650	+	0.0473399i
$118$	−100.604	−	195.516i	−0.852580	−	1.65691i
$119$	−73.3314	+	14.5865i	−0.616230	+	0.122576i
$120$	11.1287	+	73.9292i	0.0927394	+	0.616077i
$121$	55.3657	+	11.0129i	0.457568	+	0.0910159i
$122$	−47.7347	+	86.0397i	−0.391268	+	0.705243i
$123$	−0.461509	−	1.52139i	−0.00375211	−	0.0123690i
$124$	−16.0429	+	35.5428i	−0.129378	+	0.286635i
$125$	15.8152	−	19.2709i	0.126522	−	0.154167i
$126$	9.20766	+	50.3988i	0.0730767	+	0.399991i
$127$		−	134.679i		−	1.06046i	−0.847852	−	0.530232i	$-0.822105\pi$
$127$		−	134.679i		−	1.06046i	0.847852	−	0.530232i	$-0.177895\pi$
$128$	−122.059	−	38.5442i	−0.953584	−	0.301127i
$129$	105.902			0.820948
$130$	106.362	−	19.4320i	0.818171	−	0.149477i
$131$	182.914	+	150.114i	1.39629	+	1.14591i	0.970504	+	0.241084i	$0.0775030\pi$
$131$	182.914	+	150.114i	1.39629	+	1.14591i	0.425788	+	0.904823i	$0.359997\pi$
$132$	18.1509	−	40.2129i	0.137507	−	0.304643i
$133$	−52.5844	+	15.9513i	−0.395371	+	0.119935i
$134$	71.7658	+	39.8156i	0.535566	+	0.297131i
$135$	−29.3809	+	147.708i	−0.217636	+	1.09413i
$136$	98.6834	−	133.658i	0.725613	−	0.982781i
$137$	9.37113	+	47.1119i	0.0684024	+	0.343882i	0.999797	−	0.0201279i	$-0.00640735\pi$
$137$	9.37113	+	47.1119i	0.0684024	+	0.343882i	−0.931395	+	0.364010i	$0.881407\pi$
$138$	59.2490	−	30.4871i	0.429341	−	0.220921i
$139$	−11.9891	+	121.728i	−0.0862529	+	0.875740i	0.850553	+	0.525890i	$0.176268\pi$
$139$	−11.9891	+	121.728i	−0.0862529	+	0.875740i	−0.936806	+	0.349850i	$0.886232\pi$
$140$	43.4831	+	87.8576i	0.310594	+	0.627554i
$141$	−8.63852	+	28.4774i	−0.0612661	+	0.201967i
$142$	2.59283	−	165.701i	0.0182594	−	1.16691i
$143$	−58.9497	−	24.4178i	−0.412236	−	0.170754i
$144$	−90.5169	−	69.0451i	−0.628590	−	0.479480i
$145$	−101.984	−	246.210i	−0.703335	−	1.69800i
$146$	56.0996	+	141.666i	0.384244	+	0.970315i
$147$	23.3226	+	43.6335i	0.158657	+	0.296827i
$148$	19.9670	−	153.361i	0.134912	−	1.03622i
$149$	−116.625	+	95.7118i	−0.782720	+	0.642361i	−0.938441	−	0.345440i	$-0.887730\pi$
$149$	−116.625	+	95.7118i	−0.782720	+	0.642361i	0.155721	+	0.987801i	$0.450230\pi$
$150$	4.82962	+	58.3878i	0.0321975	+	0.389252i
$151$	148.564	+	99.2671i	0.983866	+	0.657398i	0.939834	−	0.341632i	$-0.110980\pi$
$151$	148.564	+	99.2671i	0.983866	+	0.657398i	0.0440322	+	0.999030i	$0.485980\pi$
$152$	62.5494	−	104.868i	0.411509	−	0.689918i
$153$	122.864	−	82.0953i	0.803034	−	0.536570i
$154$	6.57037	−	57.4759i	0.0426647	−	0.373220i
$155$	−31.2832	+	58.5267i	−0.201827	+	0.377592i
$156$	25.3521	−	35.4860i	0.162513	−	0.227475i
$157$	4.87922	+	49.5396i	0.0310779	+	0.315539i	0.998138	+	0.0609918i	$0.0194264\pi$
$157$	4.87922	+	49.5396i	0.0310779	+	0.315539i	−0.967060	+	0.254547i	$0.918074\pi$
$158$	165.134	+	35.5418i	1.04515	+	0.224948i
$159$	11.9918	−	11.9918i	0.0754200	−	0.0754200i
$160$	−202.871	−	79.3301i	−1.26794	−	0.495813i
$161$	61.7797	−	61.7797i	0.383725	−	0.383725i
$162$	−36.5256	−	56.5605i	−0.225467	−	0.349139i
$163$	−1.54344	−	15.6709i	−0.00946898	−	0.0961402i	0.989289	−	0.145973i	$-0.0466312\pi$
$163$	−1.54344	−	15.6709i	−0.00946898	−	0.0961402i	−0.998758	+	0.0498326i	$0.984131\pi$
$164$	4.51274	+	1.04541i	0.0275167	+	0.00637446i
$165$	35.3936	−	66.2168i	0.214507	−	0.401314i
$166$	37.1702	+	46.7653i	0.223917	+	0.281719i
$167$	−4.56876	+	3.05275i	−0.0273578	+	0.0182799i	−0.569174	−	0.822217i	$-0.692737\pi$
$167$	−4.56876	+	3.05275i	−0.0273578	+	0.0182799i	0.541816	+	0.840497i	$0.317737\pi$
$168$	37.2577	+	13.2408i	0.221772	+	0.0788143i
$169$	88.0756	+	58.8503i	0.521158	+	0.348226i
$170$	182.765	−	215.727i	1.07509	−	1.26898i
$171$	83.9499	−	68.8959i	0.490935	−	0.402900i
$172$	−153.898	+	267.442i	−0.894754	+	1.55490i
$173$	74.8143	+	139.968i	0.432453	+	0.809062i	0.999897	−	0.0143498i	$-0.00456784\pi$
$173$	74.8143	+	139.968i	0.432453	+	0.809062i	−0.567444	+	0.823412i	$0.692068\pi$
$174$	−98.6542	−	42.6843i	−0.566978	−	0.245312i
$175$	29.3979	+	70.9728i	0.167988	+	0.405559i
$176$	75.1756	+	104.275i	0.427134	+	0.592473i
$177$	−139.443	−	57.7592i	−0.787814	−	0.326323i
$178$	113.003	−	109.521i	0.634847	−	0.615286i
$179$	−63.4435	+	209.145i	−0.354433	+	1.16841i	0.580702	+	0.814117i	$0.302778\pi$
$179$	−63.4435	+	209.145i	−0.354433	+	1.16841i	−0.935135	+	0.354293i	$0.884722\pi$
$180$	−145.844	−	127.533i	−0.810245	−	0.708516i
$181$	27.5511	−	279.731i	0.152216	−	1.54548i	−0.551003	−	0.834503i	$-0.685755\pi$
$181$	27.5511	−	279.731i	0.152216	−	1.54548i	0.703219	−	0.710973i	$-0.251745\pi$
$182$	17.4539	−	54.4557i	0.0959005	−	0.299207i
$183$	13.1765	+	66.2427i	0.0720027	+	0.361982i
$184$	−9.10958	+	193.930i	−0.0495086	+	1.05397i
$185$	51.3462	−	258.135i	0.277547	−	1.39532i
$186$	7.36853	+	25.7335i	0.0396158	+	0.138352i
$187$	−159.668	+	48.4349i	−0.853842	+	0.259010i
$188$	−59.3624	−	63.1989i	−0.315757	−	0.336164i
$189$	61.5709	+	50.5299i	0.325772	+	0.267354i
$190$	118.135	−	170.950i	0.621765	−	0.899738i
$191$	133.082			0.696763			0.348382	−	0.937353i	$-0.386731\pi$
$191$	133.082			0.696763			0.348382	+	0.937353i	$0.386731\pi$
$192$	−81.0293	+	33.9720i	−0.422028	+	0.176938i
$193$			302.677i			1.56827i	0.620589	+	0.784136i	$0.286894\pi$
$193$			302.677i			1.56827i	−0.620589	+	0.784136i	$0.713106\pi$
$194$	180.931	−	261.820i	0.932636	−	1.34959i
$195$	47.0836	−	57.3715i	0.241454	−	0.294213i
$196$	−144.083	−	4.51024i	−0.735119	−	0.0230114i
$197$	−21.8477	−	72.0221i	−0.110902	−	0.365595i	0.883868	−	0.467737i	$-0.154930\pi$
$197$	−21.8477	−	72.0221i	−0.110902	−	0.365595i	−0.994770	+	0.102142i	$0.967430\pi$
$198$	31.4730	+	109.915i	0.158955	+	0.555126i
$199$	152.973	+	30.4282i	0.768708	+	0.152906i	0.563840	−	0.825884i	$-0.309323\pi$
$199$	152.973	+	30.4282i	0.768708	+	0.152906i	0.204868	+	0.978790i	$0.434323\pi$
$200$	−154.469	−	72.6528i	−0.772346	−	0.363264i
$201$	55.2531	−	10.9905i	0.274891	−	0.0546792i
$202$	−104.296	+	325.400i	−0.516316	+	1.61089i
$203$	−140.267	−	13.8151i	−0.690970	−	0.0680546i
$204$	−7.62180	−	113.789i	−0.0373618	−	0.557789i
$205$	7.54370	+	2.28836i	0.0367985	+	0.0111627i
$206$	21.1066	−	20.4562i	0.102459	−	0.0993020i
$207$	−66.0791	+	159.529i	−0.319223	+	0.770671i
$208$	52.7736	+	115.592i	0.253719	+	0.555730i
$209$	−113.294	+	46.9278i	−0.542075	+	0.224535i
$210$	61.7573	+	26.7202i	0.294082	+	0.127239i
$211$	−41.9183	+	22.4058i	−0.198665	+	0.106189i	−0.567730	−	0.823215i	$-0.692178\pi$
$211$	−41.9183	+	22.4058i	−0.198665	+	0.106189i	0.369065	+	0.929404i	$0.379678\pi$
$212$	12.8572	+	47.7102i	0.0606470	+	0.225048i
$213$	−72.1657	−	87.9341i	−0.338806	−	0.412836i
$214$	12.2415	−	14.4492i	0.0572032	−	0.0675198i
$215$	−291.734	+	436.611i	−1.35690	+	2.03075i
$216$	−176.759	+	9.06429i	−0.818329	+	0.0419643i
$217$	19.4995	+	29.1831i	0.0898596	+	0.134484i
$218$	−237.724	−	299.090i	−1.09048	−	1.37197i
$219$	92.2406	+	49.3036i	0.421190	+	0.225131i
$220$	115.788	+	185.609i	0.526308	+	0.843675i
$221$	−164.139	+	16.1662i	−0.742709	+	0.0731504i
$222$	−57.5909	−	89.1805i	−0.259418	−	0.401714i
$223$	−137.593	−	137.593i	−0.617010	−	0.617010i	0.327754	−	0.944763i	$-0.393708\pi$
$223$	−137.593	−	137.593i	−0.617010	−	0.617010i	−0.944763	+	0.327754i	$0.893708\pi$
$224$	−87.5809	+	74.8478i	−0.390986	+	0.334142i
$225$	−107.356	−	107.356i	−0.477136	−	0.477136i
$226$	−166.364	−	35.8065i	−0.736124	−	0.158436i
$227$	−37.7993	+	3.72290i	−0.166517	+	0.0164005i	−0.180932	−	0.983496i	$-0.557911\pi$
$227$	−37.7993	+	3.72290i	−0.166517	+	0.0164005i	0.0144152	+	0.999896i	$0.495411\pi$
$228$	−13.7717	−	82.6770i	−0.0604022	−	0.362619i
$229$	3.66577	+	1.95939i	0.0160077	+	0.00855630i	0.479381	−	0.877607i	$-0.340861\pi$
$229$	3.66577	+	1.95939i	0.0160077	+	0.00855630i	−0.463373	+	0.886163i	$0.653361\pi$
$230$	−37.5245	+	328.255i	−0.163150	+	1.42719i
$231$	−22.0617	−	33.0176i	−0.0955051	−	0.142933i
$232$	251.158	−	187.109i	1.08258	−	0.806505i
$233$	−159.972	+	239.414i	−0.686573	+	1.02753i	0.310462	+	0.950586i	$0.399516\pi$
$233$	−159.972	+	239.414i	−0.686573	+	1.02753i	−0.997035	+	0.0769439i	$0.975484\pi$
$234$	9.31647	+	112.632i	0.0398140	+	0.481332i
$235$	−93.6089	−	114.063i	−0.398336	−	0.485373i
$236$	348.503	−	268.209i	1.47671	−	1.13648i
$237$	102.257	−	54.6576i	0.431465	−	0.230623i
$238$	−55.0565	−	139.032i	−0.231330	−	0.584167i
$239$	415.021	−	171.907i	1.73649	−	0.719277i	0.737452	−	0.675399i	$-0.236029\pi$
$239$	415.021	−	171.907i	1.73649	−	0.719277i	0.999037	−	0.0438783i	$-0.0139714\pi$
$240$	−141.451	+	48.4684i	−0.589378	+	0.201952i
$241$	−180.990	+	436.949i	−0.750996	+	1.81306i	−0.197306	+	0.980342i	$0.563219\pi$
$241$	−180.990	+	436.949i	−0.750996	+	1.81306i	−0.553690	+	0.832723i	$0.686781\pi$
$242$	−1.76642	+	112.887i	−0.00729924	+	0.466475i
$243$	−234.768	−	71.2160i	−0.966123	−	0.293070i
$244$	−186.435	−	62.9887i	−0.764080	−	0.258150i
$245$	−244.139	−	24.0456i	−0.996486	−	0.0981453i
$246$	2.82735	−	1.45484i	0.0114933	−	0.00591399i
$247$	−118.888	+	23.6482i	−0.481327	+	0.0957418i
$248$	−75.6946	−	18.7878i	−0.305220	−	0.0757572i
$249$	40.2178	+	7.99982i	0.161517	+	0.0321278i
$250$	43.5989	+	24.1886i	0.174396	+	0.0967546i
$251$	−116.073	−	382.642i	−0.462442	−	1.52447i	−0.809783	−	0.586729i	$-0.800415\pi$
$251$	−116.073	−	382.642i	−0.462442	−	1.52447i	0.347341	−	0.937739i	$-0.387085\pi$
$252$	−95.8468	+	36.2310i	−0.380344	+	0.143774i
$253$	123.691	−	150.718i	0.488897	−	0.595723i
$254$	264.972	−	48.4094i	1.04320	−	0.190588i
$255$		−	194.079i		−	0.761096i
$256$	31.9602	−	253.997i	0.124844	−	0.992176i
$257$	210.594			0.819431			0.409716	−	0.912213i	$-0.365628\pi$
$257$	210.594			0.819431			0.409716	+	0.912213i	$0.365628\pi$
$258$	38.0658	+	208.356i	0.147542	+	0.807581i
$259$	−107.602	−	88.3063i	−0.415450	−	0.340951i
$260$	76.4622	+	202.276i	0.294085	+	0.777985i
$261$	266.563	−	80.8609i	1.02131	−	0.309812i
$262$	−229.592	+	413.829i	−0.876306	+	1.57950i
$263$	8.38563	−	42.1574i	0.0318845	−	0.160294i	−0.961563	−	0.274585i	$-0.911460\pi$
$263$	8.38563	−	42.1574i	0.0318845	−	0.160294i	0.993447	+	0.114291i	$0.0364595\pi$
$264$	85.6405	+	21.2564i	0.324396	+	0.0805168i
$265$	16.4051	+	82.4738i	0.0619059	+	0.311222i
$266$	−50.2842	−	97.7228i	−0.189038	−	0.367379i
$267$	10.5879	−	107.501i	0.0396551	−	0.402625i
$268$	−52.5389	+	155.506i	−0.196041	+	0.580246i
$269$	40.3422	−	132.990i	0.149971	−	0.494388i	−0.849476	−	0.527627i	$-0.823082\pi$
$269$	40.3422	−	132.990i	0.149971	−	0.494388i	0.999447	+	0.0332384i	$0.0105821\pi$
$270$	−301.166	−	4.71255i	−1.11543	−	0.0174539i
$271$	369.053	+	152.867i	1.36182	+	0.564083i	0.939558	−	0.342391i	$-0.111237\pi$
$271$	369.053	+	152.867i	1.36182	+	0.564083i	0.422260	+	0.906475i	$0.361237\pi$
$272$	298.435	+	146.111i	1.09719	+	0.537171i
$273$	−15.0214	−	36.2650i	−0.0550236	−	0.132839i
$274$	−89.3211	+	35.3711i	−0.325990	+	0.129092i
$275$	80.8131	+	151.191i	0.293866	+	0.549784i
$276$	81.2781	+	105.610i	0.294486	+	0.382646i
$277$	−131.189	+	107.664i	−0.473605	+	0.388677i	−0.840696	−	0.541508i	$-0.817854\pi$
$277$	−131.189	+	107.664i	−0.473605	+	0.388677i	0.367091	+	0.930185i	$0.380354\pi$
$278$	−243.801	+	20.1663i	−0.876982	+	0.0725407i
$279$	−57.6759	−	38.5378i	−0.206724	−	0.138128i
$280$	−157.224	+	117.130i	−0.561516	+	0.418321i
$281$	87.1233	−	58.2139i	0.310047	−	0.207167i	−0.390805	−	0.920474i	$-0.627803\pi$
$281$	87.1233	−	58.2139i	0.310047	−	0.207167i	0.700852	+	0.713307i	$0.252803\pi$
$282$	−59.1325	−	6.75974i	−0.209690	−	0.0239707i
$283$	147.873	−	276.652i	0.522521	−	0.977568i	−0.472821	−	0.881159i	$-0.656764\pi$
$283$	147.873	−	276.652i	0.522521	−	0.977568i	0.995342	−	0.0964096i	$-0.0307359\pi$
$284$	326.937	−	54.4587i	1.15119	−	0.191756i
$285$	−13.9810	−	141.951i	−0.0490560	−	0.498074i
$286$	26.8513	−	124.756i	0.0938858	−	0.436211i
$287$	2.94812	−	2.94812i	0.0102722	−	0.0102722i
$288$	103.306	−	202.904i	0.358702	−	0.704528i
$289$	−100.618	+	100.618i	−0.348160	+	0.348160i
$290$	447.745	−	289.144i	1.54395	−	0.997050i
$291$	−21.4127	−	217.407i	−0.0735831	−	0.747102i
$292$	−258.554	+	161.293i	−0.885459	+	0.552374i
$293$	174.588	−	326.632i	0.595865	−	1.11479i	−0.385514	−	0.922702i	$-0.625976\pi$
$293$	174.588	−	326.632i	0.595865	−	1.11479i	0.981379	−	0.192083i	$-0.0615243\pi$
$294$	−77.4630	+	61.5695i	−0.263480	+	0.209420i
$295$	622.259	−	415.780i	2.10935	−	1.40942i
$296$	308.905	−	15.8408i	1.04360	−	0.0535162i
$297$	147.793	+	98.7524i	0.497621	+	0.332500i
$298$	−230.227	−	195.050i	−0.772573	−	0.654529i
$299$	148.983	−	122.267i	0.498272	−	0.408921i
$300$	−113.138	+	30.4890i	−0.377127	+	0.101630i
$301$	130.917	+	244.928i	0.434940	+	0.813715i
$302$	−141.902	+	327.970i	−0.469873	+	1.08599i
$303$	89.7607	+	216.701i	0.296240	+	0.715186i
$304$	228.803	+	85.3680i	0.752642	+	0.280816i
$305$	−309.402	−	128.158i	−1.01443	−	0.420191i
$306$	205.680	+	212.219i	0.672156	+	0.693526i
$307$	−13.4499	+	44.3382i	−0.0438106	+	0.144424i	−0.976117	−	0.217245i	$-0.930293\pi$
$307$	−13.4499	+	44.3382i	−0.0438106	+	0.144424i	0.932307	+	0.361669i	$0.117793\pi$
$308$	115.442	−	7.73251i	0.374811	−	0.0251056i
$309$	1.97760	−	20.0789i	0.00640001	−	0.0649804i
$310$	−126.392	−	40.5106i	−0.407716	−	0.130679i
$311$	−56.3807	−	283.445i	−0.181288	−	0.911399i	−0.959136	−	0.282946i	$-0.908688\pi$
$311$	−56.3807	−	283.445i	−0.181288	−	0.911399i	0.777848	−	0.628453i	$-0.216312\pi$
$312$	78.9291	+	37.1234i	0.252978	+	0.118985i
$313$	54.0466	−	271.711i	0.172673	−	0.868085i	−0.793179	−	0.608989i	$-0.791575\pi$
$313$	54.0466	−	271.711i	0.172673	−	0.868085i	0.965852	−	0.259096i	$-0.0834246\pi$
$314$	−95.7121	+	27.4062i	−0.304816	+	0.0872809i
$315$	−166.868	+	50.6187i	−0.529739	+	0.160694i
$316$	−10.5699	+	337.666i	−0.0334492	+	1.06856i
$317$	−141.300	−	115.962i	−0.445740	−	0.365809i	0.384584	−	0.923090i	$-0.374345\pi$
$317$	−141.300	−	115.962i	−0.445740	−	0.365809i	−0.830324	+	0.557281i	$0.811845\pi$
$318$	27.9034	+	19.2827i	0.0877466	+	0.0606374i
$319$	−314.536			−0.986005
$320$	83.1564	−	427.650i	0.259864	−	1.33641i
$321$		−	12.9993i		−	0.0404963i
$322$	143.754	+	99.3414i	0.446441	+	0.308514i
$323$	−201.090	+	245.028i	−0.622569	+	0.758602i
$324$	98.1502	−	92.1920i	0.302933	−	0.284543i
$325$	49.1917	+	162.163i	0.151359	+	0.498964i
$326$	30.2766	−	8.66940i	0.0928730	−	0.0265933i
$327$	−257.215	−	51.1632i	−0.786589	−	0.156462i
$328$	−0.434708	+	9.25429i	−0.00132533	+	0.0282143i
$329$	−76.5408	+	15.2249i	−0.232647	+	0.0462763i
$330$	142.999	+	45.8335i	0.433331	+	0.138889i
$331$	78.7395	+	7.75516i	0.237884	+	0.0234295i	0.216256	−	0.976337i	$-0.430615\pi$
$331$	78.7395	+	7.75516i	0.237884	+	0.0234295i	0.0216273	+	0.999766i	$0.493115\pi$
$332$	−78.6472	+	89.9395i	−0.236889	+	0.270902i
$333$	263.258	+	79.8584i	0.790564	+	0.239815i
$334$	−7.64829	−	7.89145i	−0.0228991	−	0.0236271i
$335$	−106.897	+	258.072i	−0.319096	+	0.770365i
$336$	−12.6584	+	78.0614i	−0.0376738	+	0.232326i
$337$	−136.918	+	56.7131i	−0.406284	+	0.168288i	−0.576460	−	0.817125i	$-0.695566\pi$
$337$	−136.918	+	56.7131i	−0.406284	+	0.168288i	0.170176	+	0.985414i	$0.445566\pi$
$338$	−84.1259	+	194.436i	−0.248893	+	0.575256i
$339$	−103.019	+	55.0647i	−0.303890	+	0.162433i
$340$	490.122	+	282.037i	1.44154	+	0.829520i
$341$	49.6892	+	60.5465i	0.145716	+	0.177556i
$342$	165.723	+	140.402i	0.484572	+	0.410532i
$343$	−170.092	+	254.560i	−0.495894	+	0.742157i
$344$	−581.493	−	206.653i	−1.69039	−	0.600737i
$345$	125.998	+	188.569i	0.365211	+	0.546578i
$346$	−248.486	+	197.503i	−0.718167	+	0.570817i
$347$	−546.338	−	292.024i	−1.57446	−	0.841567i	−0.999730	−	0.0232236i	$-0.992607\pi$
$347$	−546.338	−	292.024i	−1.57446	−	0.841567i	−0.574730	−	0.818343i	$-0.694893\pi$
$348$	48.5180	−	209.438i	0.139420	−	0.601834i
$349$	360.649	−	35.5208i	1.03338	−	0.101779i	0.432918	−	0.901433i	$-0.357484\pi$
$349$	360.649	−	35.5208i	1.03338	−	0.101779i	0.600461	+	0.799654i	$0.294984\pi$
$350$	−129.068	+	83.3491i	−0.368764	+	0.238140i
$351$	124.241	+	124.241i	0.353964	+	0.353964i
$352$	−178.133	+	185.384i	−0.506061	+	0.526659i
$353$	317.983	+	317.983i	0.900800	+	0.900800i	0.995505	−	0.0947050i	$-0.0301908\pi$
$353$	317.983	+	317.983i	0.900800	+	0.900800i	−0.0947050	+	0.995505i	$0.530191\pi$
$354$	63.5157	−	295.106i	0.179423	−	0.833634i
$355$	561.331	−	55.2862i	1.58121	−	0.155736i
$356$	256.093	+	182.959i	0.719363	+	0.513930i
$357$	−90.5253	−	48.3868i	−0.253572	−	0.135537i
$358$	−434.284	−	49.6453i	−1.21308	−	0.138674i
$359$	203.077	+	303.926i	0.565674	+	0.846591i	0.998492	−	0.0548902i	$-0.0174809\pi$
$359$	203.077	+	303.926i	0.565674	+	0.846591i	−0.432818	+	0.901481i	$0.642481\pi$
$360$	198.490	−	332.780i	0.551361	−	0.924388i
$361$	71.1335	−	106.459i	0.197046	−	0.294900i
$362$	560.256	−	46.3423i	1.54767	−	0.128017i
$363$	49.1643	+	59.9069i	0.135439	+	0.165033i
$364$	113.412	+	14.7657i	0.311571	+	0.0405652i
$365$	−457.367	+	244.468i	−1.25306	+	0.669775i
$366$	−125.592	+	49.7344i	−0.343148	+	0.135886i
$367$	424.043	−	175.645i	1.15543	−	0.478595i	0.279080	−	0.960268i	$-0.409970\pi$
$367$	424.043	−	175.645i	1.15543	−	0.478595i	0.876351	+	0.481672i	$0.159970\pi$
$368$	−384.818	+	51.7841i	−1.04570	+	0.140718i
$369$	−3.15328	+	7.61270i	−0.00854548	+	0.0206306i
$370$	526.319	+	8.23566i	1.42248	+	0.0222585i
$371$	42.5586	+	12.9100i	0.114713	+	0.0347979i
$372$	−47.9805	+	23.7468i	−0.128980	+	0.0638356i
$373$	38.5301	+	3.79489i	0.103298	+	0.0101740i	0.149534	−	0.988757i	$-0.452223\pi$
$373$	38.5301	+	3.79489i	0.103298	+	0.0101740i	−0.0462361	+	0.998931i	$0.514723\pi$
$374$	−152.684	−	296.728i	−0.408247	−	0.793390i
$375$	33.5672	−	6.67693i	0.0895125	−	0.0178051i
$376$	103.002	−	139.508i	0.273942	−	0.371032i
$377$	−304.941	−	60.6566i	−0.808863	−	0.160893i
$378$	−77.2832	+	139.299i	−0.204453	+	0.368517i
$379$	32.0529	+	105.664i	0.0845723	+	0.278798i	0.989019	−	0.147789i	$-0.0472158\pi$
$379$	32.0529	+	105.664i	0.0845723	+	0.278798i	−0.904447	+	0.426587i	$0.859716\pi$
$380$	378.796	+	170.977i	0.996832	+	0.449939i
$381$	117.296	−	142.925i	0.307863	−	0.375132i
$382$	47.8353	+	261.830i	0.125223	+	0.685418i
$383$		−	681.785i		−	1.78012i	−0.455845	−	0.890059i	$-0.650663\pi$
$383$		−	681.785i		−	1.78012i	0.455845	−	0.890059i	$-0.349337\pi$
$384$	−95.9632	−	147.209i	−0.249904	−	0.383356i
$385$	196.899			0.511425
$386$	−595.497	+	108.795i	−1.54274	+	0.281852i
$387$	−424.285	−	348.202i	−1.09634	−	0.899746i
$388$	580.149	+	261.861i	1.49523	+	0.674900i
$389$	−414.510	+	125.740i	−1.06558	+	0.323239i	−0.773920	−	0.633284i	$-0.781707\pi$
$389$	−414.510	+	125.740i	−1.06558	+	0.323239i	−0.291657	+	0.956523i	$0.594207\pi$
$390$	129.799	+	72.0122i	0.332817	+	0.184647i
$391$	98.3232	−	494.304i	0.251466	−	1.26421i
$392$	−42.9161	−	285.096i	−0.109480	−	0.727285i
$393$	63.3756	+	318.611i	0.161261	+	0.810714i
$394$	133.846	−	68.8717i	0.339710	−	0.174801i
$395$	−56.3520	+	572.152i	−0.142663	+	1.44848i
$396$	−204.938	+	101.429i	−0.517519	+	0.256134i
$397$	−63.9315	+	210.754i	−0.161037	+	0.530866i	−0.999909	−	0.0134611i	$-0.995715\pi$
$397$	−63.9315	+	210.754i	−0.161037	+	0.530866i	0.838873	+	0.544327i	$0.183215\pi$
$398$	−4.88053	+	311.901i	−0.0122626	+	0.783672i
$399$	−69.6966	−	28.8693i	−0.174678	−	0.0723541i
$400$	87.4169	−	330.023i	0.218542	−	0.825056i
$401$	29.8121	+	71.9727i	0.0743444	+	0.179483i	0.956683	−	0.291132i	$-0.0940320\pi$
$401$	29.8121	+	71.9727i	0.0743444	+	0.179483i	−0.882338	+	0.470615i	$0.844032\pi$
$402$	41.4835	+	104.756i	0.103193	+	0.260588i
$403$	36.4975	+	68.2820i	0.0905644	+	0.169434i
$404$	−677.692	−	88.2326i	−1.67745	−	0.218397i
$405$	177.144	−	145.378i	0.437392	−	0.358958i
$406$	−23.2376	−	280.932i	−0.0572355	−	0.691950i
$407$	−258.284	−	172.580i	−0.634605	−	0.424030i
$408$	221.133	−	55.8960i	0.541992	−	0.137000i
$409$	−313.717	+	209.619i	−0.767033	+	0.512515i	−0.876457	−	0.481480i	$-0.840099\pi$
$409$	−313.717	+	209.619i	−0.767033	+	0.512515i	0.109424	+	0.993995i	$0.465099\pi$
$410$	−1.79066	+	15.6643i	−0.00436747	+	0.0382055i
$411$	−31.0862	+	58.1581i	−0.0756354	+	0.141504i
$412$	47.8329	+	34.1730i	0.116099	+	0.0829441i
$413$	−38.7961	−	393.903i	−0.0939372	−	0.953760i
$414$	−337.615	−	72.6648i	−0.815494	−	0.175519i
$415$	−143.772	+	143.772i	−0.346437	+	0.346437i
$416$	−208.450	+	145.377i	−0.501083	+	0.349464i
$417$	−118.740	+	118.740i	−0.284747	+	0.284747i
$418$	−133.050	−	206.030i	−0.318301	−	0.492895i
$419$	−38.4067	−	389.950i	−0.0916628	−	0.930668i	−0.925523	−	0.378692i	$-0.876374\pi$
$419$	−38.4067	−	389.950i	−0.0916628	−	0.930668i	0.833860	−	0.551976i	$-0.186126\pi$
$420$	−30.3722	+	131.108i	−0.0723146	+	0.312162i
$421$	−61.2662	+	114.621i	−0.145525	+	0.272259i	−0.944114	−	0.329618i	$-0.893080\pi$
$421$	−61.2662	+	114.621i	−0.145525	+	0.272259i	0.798589	+	0.601877i	$0.205580\pi$
$422$	−59.1492	−	74.4179i	−0.140164	−	0.176346i
$423$	128.242	−	85.6883i	0.303172	−	0.202573i
$424$	−89.2453	+	42.4447i	−0.210484	+	0.100105i
$425$	368.453	+	246.193i	0.866949	+	0.579277i
$426$	147.065	−	173.589i	0.345224	−	0.407485i
$427$	−136.916	+	112.364i	−0.320646	+	0.263147i
$428$	32.8280	+	18.8906i	0.0767010	+	0.0441370i
$429$	−41.2931	−	77.2539i	−0.0962542	−	0.180079i
$430$	−963.866	−	417.031i	−2.24155	−	0.969841i
$431$	−270.765	−	653.685i	−0.628226	−	1.51667i	−0.841825	−	0.539750i	$-0.818519\pi$
$431$	−270.765	−	653.685i	−0.628226	−	1.51667i	0.213599	−	0.976921i	$-0.431481\pi$
$432$	−81.3682	−	344.504i	−0.188352	−	0.797463i
$433$	194.169	+	80.4276i	0.448428	+	0.185745i	0.595457	−	0.803387i	$-0.296971\pi$
$433$	194.169	+	80.4276i	0.448428	+	0.185745i	−0.147029	+	0.989132i	$0.546971\pi$
$434$	−50.4069	+	48.8537i	−0.116145	+	0.112566i
$435$	106.204	−	350.106i	0.244146	−	0.804842i
$436$	502.991	−	575.211i	1.15365	−	1.31929i
$437$	36.3060	−	368.621i	0.0830801	−	0.843526i
$438$	−63.8464	+	199.199i	−0.145768	+	0.454793i
$439$	57.8466	+	290.815i	0.131769	+	0.662448i	0.989048	+	0.147595i	$0.0471533\pi$
$439$	57.8466	+	290.815i	0.131769	+	0.662448i	−0.857279	+	0.514852i	$0.827847\pi$
$440$	−323.554	+	294.520i	−0.735349	+	0.669365i
$441$	50.0257	−	251.496i	0.113437	−	0.570287i
$442$	−90.8045	−	317.121i	−0.205440	−	0.717469i
$443$	−500.389	+	151.791i	−1.12955	+	0.342644i	−0.799111	−	0.601184i	$-0.794696\pi$
$443$	−500.389	+	151.791i	−1.12955	+	0.342644i	−0.330436	+	0.943828i	$0.607196\pi$
$444$	154.756	−	145.362i	0.348550	−	0.327391i
$445$	414.035	+	339.790i	0.930416	+	0.763573i
$446$	221.249	−	320.162i	0.496073	−	0.717853i
$447$	−207.124			−0.463366
$448$	−178.739	−	145.406i	−0.398970	−	0.324568i
$449$			261.887i			0.583267i	0.956530	+	0.291633i	$0.0941988\pi$
$449$			261.887i			0.583267i	−0.956530	+	0.291633i	$0.905801\pi$
$450$	172.627	−	249.803i	0.383616	−	0.555119i
$451$	5.90252	−	7.19224i	0.0130876	−	0.0159473i
$452$	10.6487	−	340.181i	0.0235590	−	0.752612i
$453$	71.2057	+	234.734i	0.157187	+	0.518176i
$454$	−20.9112	−	73.0295i	−0.0460600	−	0.160858i
$455$	190.893	+	37.9709i	0.419544	+	0.0834525i
$456$	157.712	−	56.8126i	0.345859	−	0.124589i
$457$	−799.016	+	158.934i	−1.74839	+	0.347777i	−0.962645	−	0.270768i	$-0.912722\pi$
$457$	−799.016	+	158.934i	−1.74839	+	0.347777i	−0.785749	+	0.618545i	$0.787722\pi$
$458$	−2.53735	+	7.91645i	−0.00554006	+	0.0172848i
$459$	457.250	+	45.0352i	0.996186	+	0.0981158i
$460$	−659.308	+	44.1617i	−1.43328	+	0.0960037i
$461$	−8.30914	−	2.52055i	−0.0180242	−	0.00546757i	0.281260	−	0.959632i	$-0.409248\pi$
$461$	−8.30914	−	2.52055i	−0.0180242	−	0.00546757i	−0.299284	+	0.954164i	$0.596748\pi$
$462$	57.0301	−	55.2728i	0.123442	−	0.119638i
$463$	−260.460	+	628.805i	−0.562548	+	1.35811i	0.345174	+	0.938539i	$0.387820\pi$
$463$	−260.460	+	628.805i	−0.562548	+	1.35811i	−0.907722	+	0.419572i	$0.862180\pi$
$464$	458.402	+	426.882i	0.987936	+	0.920005i
$465$	−84.1713	+	34.8649i	−0.181013	+	0.0749782i
$466$	−528.533	−	228.678i	−1.13419	−	0.490725i
$467$	−114.962	+	61.4486i	−0.246172	+	0.131581i	−0.589869	−	0.807499i	$-0.700821\pi$
$467$	−114.962	+	61.4486i	−0.246172	+	0.131581i	0.343697	+	0.939081i	$0.388321\pi$
$468$	−218.247	+	58.8142i	−0.466339	+	0.125671i
$469$	93.7228	+	114.202i	0.199835	+	0.243500i
$470$	190.764	−	225.168i	0.405881	−	0.479082i
$471$	−37.9675	+	56.8224i	−0.0806104	+	0.120642i
$472$	652.951	+	589.250i	1.38337	+	1.24841i
$473$	344.323	+	515.317i	0.727957	+	1.08946i
$474$	144.291	+	181.538i	0.304411	+	0.382992i
$475$	287.225	+	153.525i	0.604683	+	0.323210i
$476$	253.746	−	158.294i	0.533080	−	0.332550i
$477$	−87.4721	+	8.61525i	−0.183380	+	0.0180613i
$478$	487.393	+	754.736i	1.01965	+	1.57895i
$479$	454.748	+	454.748i	0.949369	+	0.949369i	0.998779	−	0.0494093i	$-0.0157339\pi$
$479$	454.748	+	454.748i	0.949369	+	0.949369i	−0.0494093	+	0.998779i	$0.515734\pi$
$480$	−146.202	−	260.874i	−0.304587	−	0.543487i
$481$	−217.125	−	217.125i	−0.451403	−	0.451403i
$482$	−924.724	−	199.028i	−1.91851	−	0.412922i
$483$	119.368	−	11.7568i	0.247139	−	0.0243411i
$484$	−222.733	+	37.1011i	−0.460192	+	0.0766552i
$485$	955.305	+	510.621i	1.96970	+	1.05283i
$486$	55.7274	−	487.489i	0.114665	−	1.00306i
$487$	218.005	+	326.267i	0.447649	+	0.669954i	0.984832	−	0.173512i	$-0.0555116\pi$
$487$	218.005	+	326.267i	0.447649	+	0.669954i	−0.537183	+	0.843466i	$0.680512\pi$
$488$	56.9133	−	389.440i	0.116626	−	0.798034i
$489$	12.0103	−	17.9746i	0.0245609	−	0.0367579i
$490$	−40.4458	−	488.971i	−0.0825425	−	0.997900i
$491$	−137.393	−	167.413i	−0.279822	−	0.340964i	0.614066	−	0.789255i	$-0.289533\pi$
$491$	−137.393	−	167.413i	−0.279822	−	0.340964i	−0.893888	+	0.448291i	$0.852033\pi$
$492$	3.87858	+	5.03970i	0.00788329	+	0.0102433i
$493$	−717.035	+	383.263i	−1.45443	+	0.777410i
$494$	−89.2597	−	225.404i	−0.180688	−	0.456283i
$495$	−359.518	+	148.917i	−0.726300	+	0.300843i
$496$	9.75589	−	155.677i	0.0196691	−	0.313866i
$497$	114.160	−	275.608i	0.229699	−	0.554543i
$498$	−1.28313	+	82.0015i	−0.00257657	+	0.164662i
$499$	−433.704	−	131.563i	−0.869146	−	0.263653i	−0.175948	−	0.984399i	$-0.556299\pi$
$499$	−433.704	−	131.563i	−0.869146	−	0.263653i	−0.693198	+	0.720747i	$0.743799\pi$
$500$	−31.9183	+	94.4725i	−0.0638365	+	0.188945i
$501$	−7.50723	−	0.739398i	−0.0149845	−	0.00147584i
$502$	711.101	−	365.904i	1.41654	−	0.728892i
$503$	314.007	−	62.4599i	0.624268	−	0.124175i	0.127187	−	0.991879i	$-0.459405\pi$
$503$	314.007	−	62.4599i	0.624268	−	0.124175i	0.497081	+	0.867704i	$0.334405\pi$
$504$	−105.733	−	175.549i	−0.209789	−	0.348312i
$505$	−1140.68	−	226.895i	−2.25877	−	0.449297i
$506$	340.988	+	189.180i	0.673888	+	0.373873i
$507$	42.2141	+	139.161i	0.0832626	+	0.274480i
$508$	190.485	+	503.915i	0.374970	+	0.991959i
$509$	192.120	−	234.099i	0.377447	−	0.459920i	−0.549290	−	0.835632i	$-0.685102\pi$
$509$	192.120	−	234.099i	0.377447	−	0.459920i	0.926737	+	0.375712i	$0.122602\pi$
$510$	381.839	−	69.7604i	0.748703	−	0.136785i
$511$			274.281i			0.536754i
$512$	511.211	−	28.4178i	0.998458	−	0.0555036i
$513$	337.680			0.658246
$514$	75.6964	+	414.330i	0.147269	+	0.806089i
$515$	77.3331	+	63.4656i	0.150161	+	0.123234i
$516$	−396.244	+	149.784i	−0.767915	+	0.290279i
$517$	−166.657	+	50.5547i	−0.322353	+	0.0977848i
$518$	135.060	−	243.440i	0.260734	−	0.469962i
$519$	−42.5068	+	213.696i	−0.0819013	+	0.411746i
$520$	−370.481	+	223.141i	−0.712464	+	0.429118i
$521$	106.016	+	532.978i	0.203486	+	1.02299i	0.938589	+	0.345036i	$0.112133\pi$
$521$	106.016	+	532.978i	0.203486	+	1.02299i	−0.735104	+	0.677955i	$0.762867\pi$
$522$	254.903	+	495.380i	0.488319	+	0.949004i
$523$	−12.6234	+	128.167i	−0.0241365	+	0.245062i	0.975544	+	0.219802i	$0.0705412\pi$
$523$	−12.6234	+	128.167i	−0.0241365	+	0.245062i	−0.999681	+	0.0252596i	$0.991959\pi$
$524$	−896.707	−	302.960i	−1.71127	−	0.578167i
$525$	−30.6144	+	100.922i	−0.0583131	+	0.192232i
$526$	85.9562	+	1.34501i	0.163415	+	0.00255706i
$527$	187.051	+	77.4790i	0.354935	+	0.147019i
$528$	−11.0378	+	176.133i	−0.0209049	+	0.333585i
$529$	22.9352	+	55.3704i	0.0433557	+	0.104670i
$530$	−156.365	+	61.9205i	−0.295029	+	0.116831i
$531$	368.753	+	689.888i	0.694450	+	1.29922i
$532$	174.189	−	134.057i	0.327423	−	0.251986i
$533$	7.10946	−	5.83458i	0.0133386	−	0.0109467i
$534$	215.307	−	17.8094i	0.403196	−	0.0333509i
$535$	53.5932	+	35.8098i	0.100174	+	0.0669343i
$536$	−324.833	−	47.4714i	−0.606031	−	0.0885661i
$537$	−249.479	+	166.696i	−0.464579	+	0.310422i
$538$	276.151	+	31.5682i	0.513291	+	0.0586770i
$539$	−136.490	+	255.354i	−0.253227	+	0.473755i
$540$	−98.9803	−	594.219i	−0.183297	−	1.10041i
$541$	−101.846	−	1034.06i	−0.188255	−	1.91139i	−0.371696	−	0.928355i	$-0.621224\pi$
$541$	−101.846	−	1034.06i	−0.188255	−	1.91139i	0.183441	−	0.983031i	$-0.441276\pi$
$542$	−168.102	+	781.034i	−0.310151	+	1.44102i
$543$	272.864	−	272.864i	0.502512	−	0.502512i
$544$	−180.193	+	639.670i	−0.331237	+	1.17586i
$545$	919.496	−	919.496i	1.68715	−	1.68715i
$546$	65.9496	−	42.5889i	0.120787	−	0.0780016i
$547$	−96.8011	−	982.838i	−0.176967	−	1.79678i	−0.516606	−	0.856223i	$-0.672805\pi$
$547$	−96.8011	−	982.838i	−0.176967	−	1.79678i	0.339639	−	0.940556i	$-0.389695\pi$
$548$	−101.696	−	163.020i	−0.185577	−	0.297481i
$549$	165.013	−	308.718i	0.300570	−	0.562327i
$550$	−268.410	+	213.339i	−0.488018	+	0.387889i
$551$	−496.836	+	331.975i	−0.901698	+	0.602496i
$552$	−178.566	+	197.870i	−0.323490	+	0.358461i
$553$	252.822	+	168.930i	0.457182	+	0.305479i
$554$	−258.976	−	219.406i	−0.467466	−	0.396040i
$555$	279.307	−	229.221i	0.503256	−	0.413012i
$556$	−127.308	−	472.414i	−0.228972	−	0.849666i
$557$	−356.258	−	666.511i	−0.639601	−	1.19661i	−0.967733	−	0.251977i	$-0.918919\pi$
$557$	−356.258	−	666.511i	−0.639601	−	1.19661i	0.328133	−	0.944632i	$-0.393581\pi$
$558$	55.0895	−	127.326i	0.0987267	−	0.228182i
$559$	234.445	+	565.999i	0.419400	+	1.01252i
$560$	−286.959	−	267.227i	−0.512426	−	0.477192i
$561$	−211.628	−	87.6594i	−0.377234	−	0.156256i
$562$	145.848	+	150.485i	0.259516	+	0.267767i
$563$	−162.580	+	535.956i	−0.288775	+	0.951964i	0.685779	+	0.727810i	$0.259462\pi$
$563$	−162.580	+	535.956i	−0.288775	+	0.951964i	−0.974554	+	0.224154i	$0.928038\pi$
$564$	−7.95538	−	118.769i	−0.0141053	−	0.210583i
$565$	56.7717	−	576.413i	0.100481	−	1.02020i
$566$	597.447	+	191.491i	1.05556	+	0.338323i
$567$	−23.6449	−	118.871i	−0.0417017	−	0.209649i
$568$	224.659	+	623.653i	0.395527	+	1.09798i
$569$	129.572	−	651.400i	0.227718	−	1.14482i	−0.682564	−	0.730826i	$-0.739135\pi$
$569$	129.572	−	651.400i	0.227718	−	1.14482i	0.910282	−	0.413989i	$-0.135865\pi$
$570$	274.254	−	78.5299i	0.481148	−	0.137772i
$571$	168.344	−	51.0665i	0.294822	−	0.0894334i	−0.139409	−	0.990235i	$-0.544520\pi$
$571$	168.344	−	51.0665i	0.294822	−	0.0894334i	0.434231	+	0.900802i	$0.357020\pi$
$572$	255.102	+	7.98545i	0.445982	+	0.0139606i
$573$	141.230	+	115.905i	0.246475	+	0.202277i
$574$	6.85992	+	4.74056i	0.0119511	+	0.00825881i
$575$	−517.823			−0.900561
$576$	436.333	+	130.316i	0.757522	+	0.226242i
$577$		−	784.680i		−	1.35993i	−0.733244	−	0.679966i	$-0.761995\pi$
$577$		−	784.680i		−	1.35993i	0.733244	−	0.679966i	$-0.238005\pi$
$578$	−234.127	−	161.794i	−0.405063	−	0.279920i
$579$	−263.610	+	321.210i	−0.455285	+	0.554766i
$580$	729.812	+	776.979i	1.25830	+	1.33962i
$581$	31.2157	+	102.904i	0.0537275	+	0.177116i
$582$	420.037	−	120.273i	0.721713	−	0.206655i
$583$	97.3409	+	19.3623i	0.166965	+	0.0332115i
$584$	−410.269	−	450.713i	−0.702516	−	0.771768i
$585$	−377.270	+	75.0437i	−0.644906	+	0.128280i
$586$	705.382	+	226.086i	1.20372	+	0.385812i
$587$	850.682	+	83.7849i	1.44920	+	0.142734i	0.791789	−	0.610795i	$-0.209150\pi$
$587$	850.682	+	83.7849i	1.44920	+	0.142734i	0.657414	+	0.753529i	$0.271650\pi$
$588$	−148.977	−	130.273i	−0.253363	−	0.221552i
$589$	142.392	+	43.1941i	0.241752	+	0.0733346i
$590$	1041.69	+	1074.81i	1.76557	+	1.82170i
$591$	39.5408	−	95.4598i	0.0669048	−	0.161523i
$592$	142.199	+	602.056i	0.240202	+	1.01699i
$593$	716.905	−	296.952i	1.20895	−	0.500762i	0.315066	−	0.949070i	$-0.397973\pi$
$593$	716.905	−	296.952i	1.20895	−	0.500762i	0.893879	+	0.448308i	$0.147973\pi$
$594$	−141.166	+	326.270i	−0.237653	+	0.549276i
$595$	448.862	−	239.922i	0.754390	−	0.403230i
$596$	300.994	−	523.066i	0.505024	−	0.877627i
$597$	135.839	+	165.520i	0.227535	+	0.277253i
$598$	294.104	+	249.167i	0.491813	+	0.416667i
$599$	451.850	−	676.241i	0.754340	−	1.12895i	−0.233330	−	0.972398i	$-0.574962\pi$
$599$	451.850	−	676.241i	0.754340	−	1.12895i	0.987670	−	0.156552i	$-0.0500378\pi$
$600$	−100.652	−	211.633i	−0.167753	−	0.352722i
$601$	−234.584	−	351.080i	−0.390323	−	0.584160i	0.583318	−	0.812244i	$-0.301754\pi$
$601$	−234.584	−	351.080i	−0.390323	−	0.584160i	−0.973642	+	0.228084i	$0.926754\pi$
$602$	−434.824	+	345.608i	−0.722298	+	0.574100i
$603$	−257.502	−	137.637i	−0.427034	−	0.228254i
$604$	−696.266	−	161.295i	−1.15276	−	0.267045i
$605$	−382.418	+	37.6649i	−0.632096	+	0.0622560i
$606$	−394.082	+	254.490i	−0.650301	+	0.419951i
$607$	239.601	+	239.601i	0.394730	+	0.394730i	0.876369	−	0.481640i	$-0.159959\pi$
$607$	239.601	+	239.601i	0.394730	+	0.394730i	−0.481640	+	0.876369i	$0.659959\pi$
$608$	−85.7144	+	480.840i	−0.140978	+	0.790855i
$609$	−136.823	−	136.823i	−0.224669	−	0.224669i
$610$	140.931	−	654.793i	0.231035	−	1.07343i
$611$	−171.322	+	16.8738i	−0.280397	+	0.0276167i
$612$	−343.597	+	480.942i	−0.561433	+	0.785853i
$613$	334.146	+	178.605i	0.545099	+	0.291362i	0.720871	−	0.693069i	$-0.243742\pi$
$613$	334.146	+	178.605i	0.545099	+	0.291362i	−0.175772	+	0.984431i	$0.556242\pi$
$614$	−92.0670	−	10.5247i	−0.149946	−	0.0171411i
$615$	6.01260	+	8.99850i	0.00977659	+	0.0146317i
$616$	56.7079	+	224.345i	0.0920583	+	0.364196i
$617$	566.485	−	847.804i	0.918127	−	1.37407i	−0.00925385	−	0.999957i	$-0.502946\pi$
$617$	566.485	−	847.804i	0.918127	−	1.37407i	0.927381	−	0.374118i	$-0.122054\pi$
$618$	40.2148	−	3.32642i	0.0650726	−	0.00538256i
$619$	335.615	+	408.948i	0.542188	+	0.660658i	0.969970	−	0.243224i	$-0.0782049\pi$
$619$	335.615	+	408.948i	0.542188	+	0.660658i	−0.427782	+	0.903882i	$0.640705\pi$
$620$	34.2713	−	263.229i	0.0552764	−	0.424563i
$621$	−473.505	+	253.094i	−0.762488	+	0.407558i
$622$	537.394	−	212.808i	0.863977	−	0.342134i
$623$	261.715	−	108.406i	0.420088	−	0.174006i
$624$	−44.6674	+	168.632i	−0.0715824	+	0.270243i
$625$	−269.082	+	649.621i	−0.430531	+	1.03939i
$626$	554.000	+	8.66880i	0.884984	+	0.0138479i
$627$	−161.101	−	48.8696i	−0.256940	−	0.0779419i
$628$	−88.3229	−	178.456i	−0.140642	−	0.284166i
$629$	−799.091	−	78.7036i	−1.27042	−	0.125125i
$630$	−159.568	−	310.107i	−0.253283	−	0.492233i
$631$	−218.287	+	43.4200i	−0.345938	+	0.0688114i	−0.365002	−	0.931007i	$-0.618932\pi$
$631$	−218.287	+	43.4200i	−0.345938	+	0.0688114i	0.0190633	+	0.999818i	$0.493932\pi$
$632$	−668.135	+	100.576i	−1.05718	+	0.159139i
$633$	−63.9988	−	12.7302i	−0.101104	−	0.0201108i
$634$	177.358	−	319.679i	0.279744	−	0.504226i
$635$	266.128	+	877.308i	0.419100	+	1.38159i
$636$	−27.9078	+	61.8292i	−0.0438802	+	0.0972157i
$637$	−181.570	+	221.244i	−0.285039	+	0.347321i
$638$	−113.058	−	618.828i	−0.177206	−	0.969950i
$639$			589.575i			0.922653i
$640$	871.263	+	9.88917i	1.36135	+	0.0154518i
$641$	779.310			1.21577			0.607886	−	0.794024i	$-0.292018\pi$
$641$	779.310			1.21577			0.607886	+	0.794024i	$0.292018\pi$
$642$	25.5753	−	4.67251i	0.0398369	−	0.00727805i
$643$	−349.448	−	286.785i	−0.543465	−	0.446010i	0.322173	−	0.946681i	$-0.395587\pi$
$643$	−349.448	−	286.785i	−0.543465	−	0.446010i	−0.865638	+	0.500671i	$0.833087\pi$
$644$	−143.776	+	318.534i	−0.223255	+	0.494618i
$645$	−689.855	+	209.265i	−1.06954	+	0.324442i
$646$	−554.358	−	307.557i	−0.858139	−	0.476095i
$647$	179.142	−	900.608i	0.276881	−	1.39197i	−0.552603	−	0.833445i	$-0.686365\pi$
$647$	179.142	−	900.608i	0.276881	−	1.39197i	0.829484	−	0.558530i	$-0.188635\pi$
$648$	216.661	+	159.967i	0.334354	+	0.246862i
$649$	−172.322	−	866.319i	−0.265519	−	1.33485i
$650$	−301.364	+	155.070i	−0.463637	+	0.238569i
$651$	−4.72293	+	47.9527i	−0.00725488	+	0.0736601i
$652$	27.9392	+	56.4511i	0.0428515	+	0.0865815i
$653$	137.846	−	454.417i	0.211096	−	0.695891i	−0.785894	−	0.618362i	$-0.787797\pi$
$653$	137.846	−	454.417i	0.211096	−	0.695891i	0.996990	−	0.0775297i	$-0.0247033\pi$
$654$	8.20631	−	524.443i	0.0125479	−	0.801901i
$655$	−1488.14	−	616.409i	−2.27198	−	0.941083i
$656$	−18.3635	+	2.47113i	−0.0279931	+	0.00376696i
$657$	−207.443	−	500.812i	−0.315743	−	0.762271i
$658$	−57.4661	−	145.117i	−0.0873345	−	0.220542i
$659$	558.356	+	1044.61i	0.847278	+	1.58515i	0.810438	+	0.585824i	$0.199229\pi$
$659$	558.356	+	1044.61i	0.847278	+	1.58515i	0.0368397	+	0.999321i	$0.488271\pi$
$660$	−38.7744	+	297.816i	−0.0587491	+	0.451237i
$661$	−775.881	+	636.749i	−1.17380	+	0.963311i	−0.999770	−	0.0214293i	$-0.993178\pi$
$661$	−775.881	+	636.749i	−1.17380	+	0.963311i	−0.174028	+	0.984741i	$0.555678\pi$
$662$	13.0446	+	157.702i	0.0197048	+	0.238221i
$663$	−188.269	−	125.797i	−0.283965	−	0.189739i
$664$	−205.219	−	122.405i	−0.309065	−	0.184345i
$665$	311.018	−	207.816i	0.467696	−	0.312505i
$666$	−62.4901	+	546.647i	−0.0938290	+	0.820792i
$667$	447.860	−	837.887i	0.671454	−	1.25620i
$668$	12.7768	−	17.8840i	0.0191269	−	0.0267725i
$669$	−26.1841	−	265.852i	−0.0391392	−	0.397387i
$670$	−546.164	−	117.551i	−0.815170	−	0.175449i
$671$	−279.493	+	279.493i	−0.416533	+	0.416533i
$672$	−158.131	+	3.15400i	−0.235314	+	0.00469345i
$673$	−445.900	+	445.900i	−0.662556	+	0.662556i	−0.955982	−	0.293426i	$-0.905205\pi$
$673$	−445.900	+	445.900i	−0.662556	+	0.662556i	0.293426	+	0.955982i	$0.405205\pi$
$674$	−160.793	−	248.991i	−0.238566	−	0.369423i
$675$	−46.2714	−	469.801i	−0.0685502	−	0.696002i
$676$	−412.779	−	95.6236i	−0.610620	−	0.141455i
$677$	−202.167	+	378.228i	−0.298622	+	0.558682i	−0.985824	−	0.167784i	$-0.946339\pi$
$677$	−202.167	+	378.228i	−0.298622	+	0.558682i	0.687202	+	0.726466i	$0.258839\pi$
$678$	−145.366	−	182.890i	−0.214403	−	0.269750i
$679$	476.343	−	318.282i	0.701535	−	0.468751i
$680$	−378.719	+	1065.66i	−0.556939	+	1.56715i
$681$	−43.3561	−	28.9696i	−0.0636654	−	0.0425398i
$682$	−101.261	+	119.523i	−0.148476	+	0.175254i
$683$	166.214	−	136.408i	0.243359	−	0.199719i	−0.504805	−	0.863233i	$-0.668436\pi$
$683$	166.214	−	136.408i	0.243359	−	0.199719i	0.748164	+	0.663514i	$0.230936\pi$
$684$	−216.664	+	376.517i	−0.316760	+	0.550463i
$685$	−154.138	−	288.372i	−0.225019	−	0.420981i
$686$	−561.968	−	243.144i	−0.819196	−	0.354438i
$687$	2.18373	+	5.27199i	0.00317865	+	0.00767393i
$688$	197.564	−	1218.33i	0.287157	−	1.77083i
$689$	90.6378	+	37.5434i	0.131550	+	0.0544897i
$690$	−325.709	+	315.673i	−0.472042	+	0.457497i
$691$	209.560	−	690.828i	0.303271	−	0.999751i	−0.664367	−	0.747407i	$-0.731299\pi$
$691$	209.560	−	690.828i	0.303271	−	0.999751i	0.967638	−	0.252344i	$-0.0812014\pi$
$692$	−477.890	−	417.889i	−0.690593	−	0.603886i
$693$	−20.1729	+	204.819i	−0.0291095	+	0.295554i
$694$	378.160	−	1179.85i	0.544900	−	1.70007i
$695$	−162.439	−	816.634i	−0.233725	−	1.17501i
$696$	429.496	+	20.1750i	0.617091	+	0.0289870i
$697$	4.69197	−	23.5881i	0.00673166	−	0.0338424i
$698$	199.518	+	696.786i	0.285842	+	0.998261i
$699$	−378.280	+	114.750i	−0.541173	+	0.164163i
$700$	−210.376	−	223.973i	−0.300538	−	0.319961i
$701$	399.966	+	328.243i	0.570564	+	0.468250i	0.874892	−	0.484317i	$-0.160932\pi$
$701$	399.966	+	328.243i	0.570564	+	0.468250i	−0.304328	+	0.952567i	$0.598432\pi$
$702$	−199.779	+	289.095i	−0.284586	+	0.411816i
$703$	−590.131			−0.839447
$704$	−428.760	−	283.831i	−0.609034	−	0.403169i
$705$		−	202.574i		−	0.287338i
$706$	−511.314	+	739.907i	−0.724240	+	1.04803i
$707$	−390.219	+	475.484i	−0.551937	+	0.672537i
$708$	603.433	+	18.8892i	0.852306	+	0.0266797i
$709$	237.034	+	781.396i	0.334322	+	1.10211i	0.949512	+	0.313732i	$0.101579\pi$
$709$	237.034	+	781.396i	0.334322	+	1.10211i	−0.615190	+	0.788379i	$0.710921\pi$
$710$	310.538	+	1084.51i	0.437378	+	1.52748i
$711$	−589.394	−	117.238i	−0.828964	−	0.164891i
$712$	−267.910	+	569.610i	−0.376278	+	0.800014i
$713$	−232.040	+	46.1557i	−0.325442	+	0.0647345i
$714$	62.6592	−	195.495i	0.0877580	−	0.273802i
$715$	432.252	+	42.5731i	0.604549	+	0.0595428i
$716$	−58.4263	−	872.270i	−0.0816010	−	1.21825i
$717$	590.152	+	179.021i	0.823085	+	0.249680i
$718$	−524.960	+	508.785i	−0.731143	+	0.708614i
$719$	−358.317	+	865.054i	−0.498355	+	1.20313i	0.452015	+	0.892011i	$0.350706\pi$
$719$	−358.317	+	865.054i	−0.498355	+	1.20313i	−0.950369	+	0.311124i	$0.899294\pi$
$720$	726.068	+	270.901i	1.00843	+	0.376251i
$721$	48.8828	−	20.2479i	0.0677987	−	0.0280831i
$722$	235.019	+	101.685i	0.325512	+	0.140838i
$723$	−572.624	+	306.074i	−0.792010	+	0.423338i
$724$	292.555	+	1085.61i	0.404082	+	1.49946i
$725$	529.944	+	645.739i	0.730957	+	0.890674i
$726$	−100.191	+	118.261i	−0.138004	+	0.162894i
$727$	−555.967	+	832.064i	−0.764742	+	1.14452i	0.220838	+	0.975310i	$0.429121\pi$
$727$	−555.967	+	832.064i	−0.764742	+	1.14452i	−0.985581	+	0.169207i	$0.945879\pi$
$728$	11.7144	+	228.438i	0.0160912	+	0.313788i
$729$	−18.7914	−	28.1234i	−0.0257770	−	0.0385780i
$730$	−645.372	−	811.968i	−0.884071	−	1.11229i
$731$	1412.86	+	755.188i	1.93277	+	1.03309i
$732$	−142.992	−	229.218i	−0.195345	−	0.313139i
$733$	435.252	−	42.8686i	0.593795	−	0.0584837i	0.203344	−	0.979107i	$-0.434819\pi$
$733$	435.252	−	42.8686i	0.593795	−	0.0584837i	0.390451	+	0.920624i	$0.372319\pi$
$734$	497.989	+	771.144i	0.678458	+	1.05060i
$735$	−238.146	−	238.146i	−0.324008	−	0.324008i
$736$	−240.202	−	738.492i	−0.326361	−	1.00339i
$737$	233.126	+	233.126i	0.316317	+	0.316317i
$738$	−16.1109	−	3.46755i	−0.0218305	−	0.00469858i
$739$	958.815	−	94.4350i	1.29745	−	0.127788i	0.574395	−	0.818579i	$-0.305238\pi$
$739$	958.815	−	94.4350i	1.29745	−	0.127788i	0.723054	+	0.690791i	$0.242738\pi$
$740$	172.978	+	1038.46i	0.233755	+	1.40332i
$741$	−146.763	−	78.4466i	−0.198061	−	0.105866i
$742$	−10.1022	+	88.3718i	−0.0136149	+	0.119099i
$743$	−214.897	−	321.616i	−0.289228	−	0.432861i	0.658193	−	0.752849i	$-0.271321\pi$
$743$	−214.897	−	321.616i	−0.289228	−	0.432861i	−0.947421	+	0.319988i	$0.896321\pi$
$744$	−63.9666	−	85.8629i	−0.0859766	−	0.115407i
$745$	570.576	−	853.927i	0.765874	−	1.14621i
$746$	6.38318	+	77.1696i	0.00855654	+	0.103445i
$747$	−134.825	−	164.285i	−0.180489	−	0.219926i
$748$	528.912	−	407.053i	0.707101	−	0.544188i
$749$	30.0645	−	16.0698i	0.0401395	−	0.0214550i
$750$	25.2019	+	63.6413i	0.0336025	+	0.0848551i
$751$	59.4811	−	24.6379i	0.0792026	−	0.0328068i	−0.342730	−	0.939434i	$-0.611352\pi$
$751$	59.4811	−	24.6379i	0.0792026	−	0.0328068i	0.421933	+	0.906627i	$0.361352\pi$
$752$	311.496	+	152.505i	0.414224	+	0.202800i
$753$	210.074	−	507.162i	0.278982	−	0.673522i
$754$	9.72901	−	621.755i	0.0129032	−	0.824609i
$755$	−1163.91	−	353.068i	−1.54160	−	0.467639i
$756$	−301.841	−	101.979i	−0.399261	−	0.134894i
$757$	−354.279	−	34.8934i	−0.468004	−	0.0460943i	−0.138733	−	0.990330i	$-0.544303\pi$
$757$	−354.279	−	34.8934i	−0.468004	−	0.0460943i	−0.329271	+	0.944236i	$0.606803\pi$
$758$	−196.366	+	101.042i	−0.259059	+	0.133301i
$759$	262.529	−	52.2203i	0.345888	−	0.0688015i
$760$	−200.230	+	806.713i	−0.263461	+	1.06146i
$761$	267.310	+	53.1714i	0.351262	+	0.0698704i	0.367568	−	0.929997i	$-0.380191\pi$
$761$	267.310	+	53.1714i	0.351262	+	0.0698704i	−0.0163058	+	0.999867i	$0.505191\pi$
$762$	323.358	+	179.399i	0.424354	+	0.235431i
$763$	−199.641	−	658.128i	−0.261653	−	0.862554i
$764$	−497.939	+	188.226i	−0.651753	+	0.246368i
$765$	−638.124	+	777.556i	−0.834149	+	1.01641i
$766$	1341.37	−	245.063i	1.75113	−	0.319925i
$767$		−	873.126i		−	1.13836i
$768$	255.131	−	241.714i	0.332201	−	0.314732i
$769$	−55.8591			−0.0726386			−0.0363193	−	0.999340i	$-0.511563\pi$
$769$	−55.8591			−0.0726386			−0.0363193	+	0.999340i	$0.511563\pi$
$770$	70.7737	+	387.385i	0.0919139	+	0.503097i
$771$	223.489	+	183.412i	0.289868	+	0.237889i
$772$	−428.094	−	1132.50i	−0.554526	−	1.46696i
$773$	−219.690	+	66.6421i	−0.284204	+	0.0862123i	−0.429168	−	0.903225i	$-0.641193\pi$
$773$	−219.690	+	66.6421i	−0.284204	+	0.0862123i	0.144964	+	0.989437i	$0.453693\pi$
$774$	532.558	−	959.912i	0.688060	−	1.24020i
$775$	40.5827	−	204.023i	0.0523648	−	0.263255i
$776$	−306.665	+	1235.53i	−0.395187	+	1.59218i
$777$	−37.2815	−	187.427i	−0.0479813	−	0.241218i
$778$	−396.378	−	770.324i	−0.509483	−	0.990134i
$779$	1.73252	−	17.5905i	0.00222403	−	0.0225809i
$780$	−95.0241	+	281.255i	−0.121826	+	0.360583i
$781$	193.250	−	637.058i	0.247439	−	0.815696i
$782$	1007.85	+	15.7705i	1.28881	+	0.0201669i
$783$	800.203	+	331.455i	1.02197	+	0.423314i
$784$	545.481	−	186.910i	0.695767	−	0.238406i
$785$	−129.675	−	313.063i	−0.165191	−	0.398806i
$786$	−604.066	+	239.210i	−0.768532	+	0.304338i
$787$	−151.272	−	283.009i	−0.192213	−	0.359605i	0.767292	−	0.641298i	$-0.221604\pi$
$787$	−151.272	−	283.009i	−0.192213	−	0.359605i	−0.959504	+	0.281693i	$0.909104\pi$
$788$	183.611	+	238.578i	0.233008	+	0.302763i
$789$	45.6152	−	37.4354i	0.0578140	−	0.0474467i
$790$	−1145.93	+	94.7867i	−1.45054	+	0.119983i
$791$	−254.705	−	170.188i	−0.322003	−	0.215156i
$792$	−273.219	−	366.744i	−0.344973	−	0.463060i
$793$	−324.867	+	217.069i	−0.409669	+	0.273732i
$794$	−437.624	−	50.0271i	−0.551164	−	0.0630065i
$795$	−54.4193	+	101.811i	−0.0684519	+	0.128065i
$796$	−615.400	+	102.509i	−0.773116	+	0.128780i
$797$	−64.0929	−	650.746i	−0.0804177	−	0.816495i	−0.947803	−	0.318857i	$-0.896701\pi$
$797$	−64.0929	−	650.746i	−0.0804177	−	0.816495i	0.867385	−	0.497638i	$-0.165799\pi$
$798$	31.7465	−	147.500i	0.0397826	−	0.184838i
$799$	−318.320	+	318.320i	−0.398398	+	0.398398i
$800$	680.719	+	53.3629i	0.850899	+	0.0667036i
$801$	−395.878	+	395.878i	−0.494229	+	0.494229i
$802$	−130.886	+	84.5234i	−0.163199	+	0.105391i
$803$	59.9952	+	609.142i	0.0747138	+	0.758582i
$804$	−191.191	+	119.270i	−0.237799	+	0.148346i
$805$	−280.359	+	524.515i	−0.348272	+	0.651572i
$806$	−121.222	+	96.3499i	−0.150399	+	0.119541i
$807$	158.638	−	105.998i	0.196577	−	0.131349i
$808$	−69.9994	−	1365.03i	−0.0866329	−	1.68939i
$809$	−193.485	−	129.283i	−0.239166	−	0.159806i	0.430211	−	0.902728i	$-0.358439\pi$
$809$	−193.485	−	129.283i	−0.239166	−	0.159806i	−0.669377	+	0.742923i	$0.733439\pi$
$810$	349.695	+	296.264i	0.431722	+	0.365757i
$811$	−134.388	+	110.289i	−0.165707	+	0.135992i	−0.713592	−	0.700561i	$-0.752933\pi$
$811$	−134.388	+	110.289i	−0.165707	+	0.135992i	0.547885	+	0.836553i	$0.315433\pi$
$812$	544.362	−	146.697i	0.670397	−	0.180662i
$813$	258.514	+	483.645i	0.317975	+	0.594890i
$814$	246.702	−	570.190i	0.303073	−	0.700480i
$815$	41.0200	+	99.0311i	0.0503313	+	0.121511i
$816$	189.456	+	414.973i	0.232177	+	0.508545i
$817$	1087.78	+	450.572i	1.33143	+	0.551496i
$818$	−525.174	−	541.871i	−0.642022	−	0.662434i
$819$	−59.0559	+	194.681i	−0.0721073	+	0.237706i
$820$	−31.4621	+	2.10739i	−0.0383684	+	0.00256999i
$821$	2.90944	−	29.5400i	0.00354377	−	0.0359805i	−0.993250	−	0.115991i	$-0.962995\pi$
$821$	2.90944	−	29.5400i	0.00354377	−	0.0359805i	0.996794	+	0.0800109i	$0.0254955\pi$
$822$	−125.596	−	40.2555i	−0.152793	−	0.0489726i
$823$	−128.021	−	643.604i	−0.155554	−	0.782022i	−0.977249	−	0.212095i	$-0.931971\pi$
$823$	−128.021	−	643.604i	−0.155554	−	0.782022i	0.821695	−	0.569927i	$-0.193029\pi$
$824$	−50.0399	+	106.391i	−0.0607281	+	0.129116i
$825$	−45.9151	+	230.831i	−0.0556546	+	0.279795i
$826$	761.034	−	217.914i	0.921348	−	0.263819i
$827$	220.822	−	66.9856i	0.267016	−	0.0809983i	−0.153938	−	0.988081i	$-0.549196\pi$
$827$	220.822	−	66.9856i	0.267016	−	0.0809983i	0.420954	+	0.907082i	$0.361696\pi$
$828$	21.6101	−	690.354i	0.0260992	−	0.833760i
$829$	246.707	+	202.467i	0.297596	+	0.244231i	0.771327	−	0.636439i	$-0.219593\pi$
$829$	246.707	+	202.467i	0.297596	+	0.244231i	−0.473731	+	0.880670i	$0.657093\pi$
$830$	−334.539	−	231.184i	−0.403059	−	0.278534i
$831$	−232.989			−0.280371
$832$	−360.946	−	357.858i	−0.433829	−	0.430118i
$833$			748.435i			0.898481i
$834$	−276.293	−	190.932i	−0.331286	−	0.228936i
$835$	23.7289	−	28.9138i	0.0284179	−	0.0346273i
$836$	357.527	−	335.823i	0.427664	−	0.401702i
$837$	−62.6099	−	206.397i	−0.0748027	−	0.246591i
$838$	753.396	−	215.727i	0.899040	−	0.257431i
$839$	−316.280	−	62.9121i	−0.376973	−	0.0749846i	0.00296736	−	0.999996i	$-0.499055\pi$
$839$	−316.280	−	62.9121i	−0.376973	−	0.0749846i	−0.379940	+	0.925011i	$0.624055\pi$
$840$	−268.863	−	12.6295i	−0.320075	−	0.0150351i
$841$	−678.371	+	134.936i	−0.806624	+	0.160448i
$842$	−247.531	−	79.3376i	−0.293980	−	0.0942252i
$843$	143.158	+	14.0998i	0.169820	+	0.0167258i
$844$	125.152	−	143.121i	0.148284	−	0.169575i
$845$	−690.020	−	209.315i	−0.816592	−	0.247710i
$846$	214.682	+	221.507i	0.253761	+	0.261829i
$847$	−77.7741	+	187.763i	−0.0918230	+	0.221680i
$848$	−115.586	−	160.328i	−0.136304	−	0.189066i
$849$	397.872	−	164.804i	0.468636	−	0.194115i
$850$	−351.930	+	813.400i	−0.414035	+	0.956941i
$851$	827.499	−	442.308i	0.972384	−	0.519750i
$852$	394.386	+	226.946i	0.462894	+	0.266369i
$853$	313.144	+	381.567i	0.367109	+	0.447324i	0.923501	−	0.383596i	$-0.125315\pi$
$853$	313.144	+	381.567i	0.367109	+	0.447324i	−0.556392	+	0.830920i	$0.687815\pi$
$854$	−270.282	−	228.985i	−0.316490	−	0.268132i
$855$	−410.716	+	614.680i	−0.480369	+	0.718924i
$856$	−25.3663	+	71.3772i	−0.0296336	+	0.0833845i
$857$	207.632	+	310.743i	0.242278	+	0.362594i	0.932602	−	0.360905i	$-0.117532\pi$
$857$	207.632	+	310.743i	0.242278	+	0.362594i	−0.690325	+	0.723500i	$0.742532\pi$
$858$	137.150	−	109.010i	0.159848	−	0.127051i
$859$	893.996	+	477.851i	1.04074	+	0.556288i	0.900963	−	0.433895i	$-0.142861\pi$
$859$	893.996	+	477.851i	1.04074	+	0.556288i	0.139778	+	0.990183i	$0.455361\pi$
$860$	474.028	−	2046.24i	0.551195	−	2.37935i
$861$	5.69624	−	0.561031i	0.00661584	−	0.000651603i
$862$	1188.76	−	767.676i	1.37907	−	0.890575i
$863$	1073.06	+	1073.06i	1.24340	+	1.24340i	0.958580	+	0.284825i	$0.0919355\pi$
$863$	1073.06	+	1073.06i	1.24340	+	1.24340i	0.284825	+	0.958580i	$0.408064\pi$
$864$	648.542	−	283.916i	0.750627	−	0.328606i
$865$	−763.925	−	763.925i	−0.883150	−	0.883150i
$866$	−88.4433	+	410.925i	−0.102129	+	0.474509i
$867$	−194.411	+	19.1478i	−0.224234	+	0.0220851i
$868$	−114.235	−	81.6122i	−0.131607	−	0.0940233i
$869$	598.434	+	319.870i	0.688647	+	0.368090i
$870$	726.985	+	83.1055i	0.835615	+	0.0955235i
$871$	181.058	+	270.972i	0.207873	+	0.311104i
$872$	1312.49	+	782.847i	1.50515	+	0.897761i
$873$	−629.036	+	941.418i	−0.720545	+	1.07837i
$874$	738.288	−	61.0684i	0.844723	−	0.0698723i
$875$	56.9382	+	69.3794i	0.0650722	+	0.0792907i
$876$	−414.860	−	54.0131i	−0.473585	−	0.0616588i
$877$	1069.32	−	571.564i	1.21930	−	0.651727i	0.269019	−	0.963135i	$-0.413301\pi$
$877$	1069.32	−	571.564i	1.21930	−	0.651727i	0.950276	+	0.311408i	$0.100801\pi$
$878$	−551.366	+	218.341i	−0.627980	+	0.248680i
$879$	469.752	−	194.578i	0.534416	−	0.221363i
$880$	−695.749	−	530.708i	−0.790624	−	0.603077i
$881$	−364.693	+	880.448i	−0.413954	+	0.999373i	0.570112	+	0.821567i	$0.306900\pi$
$881$	−364.693	+	880.448i	−0.413954	+	0.999373i	−0.984066	+	0.177806i	$0.943100\pi$
$882$	512.784	+	8.02387i	0.581388	+	0.00909736i
$883$	−949.859	−	288.137i	−1.07572	−	0.326315i	−0.297766	−	0.954639i	$-0.596241\pi$
$883$	−949.859	−	288.137i	−1.07572	−	0.326315i	−0.777952	+	0.628323i	$0.783741\pi$
$884$	591.277	−	292.639i	0.668865	−	0.331039i
$885$	1022.48	+	100.705i	1.15534	+	0.113791i
$886$	−478.501	−	929.923i	−0.540069	−	1.04957i
$887$	388.472	−	77.2718i	0.437961	−	0.0871159i	0.0288151	−	0.999585i	$-0.490827\pi$
$887$	388.472	−	77.2718i	0.437961	−	0.0871159i	0.409146	+	0.912469i	$0.365827\pi$
$888$	341.615	+	252.224i	0.384702	+	0.284036i
$889$	475.556	+	94.5941i	0.534934	+	0.106405i
$890$	−519.693	+	936.722i	−0.583924	+	1.05250i
$891$	−78.5134	−	258.824i	−0.0881183	−	0.290487i
$892$	709.425	+	320.213i	0.795320	+	0.358983i
$893$	−209.891	+	255.752i	−0.235040	+	0.286397i
$894$	−74.4494	−	407.504i	−0.0832767	−	0.455821i
$895$		−	1487.75i		−	1.66229i
$896$	221.831	−	403.922i	0.247579	−	0.450806i
$897$	264.592			0.294974
$898$	−515.245	+	94.1333i	−0.573770	+	0.104826i
$899$	295.029	+	242.124i	0.328175	+	0.269326i
$900$	553.522	+	249.843i	0.615024	+	0.277603i
$901$	245.497	−	74.4708i	0.272472	−	0.0826535i
$902$	16.2719	+	9.02762i	0.0180398	+	0.0100084i
$903$	−74.3822	+	373.945i	−0.0823724	+	0.414114i
$904$	673.111	−	101.325i	0.744592	−	0.112085i
$905$	373.285	+	1876.63i	0.412470	+	2.07362i
$906$	−436.229	+	224.466i	−0.481489	+	0.247755i
$907$	−145.552	+	1477.82i	−0.160477	+	1.62935i	0.491337	+	0.870969i	$0.336508\pi$
$907$	−145.552	+	1477.82i	−0.160477	+	1.62935i	−0.651814	+	0.758379i	$0.725992\pi$
$908$	136.164	−	67.3914i	0.149961	−	0.0742196i
$909$	352.889	−	1163.32i	0.388216	−	1.27978i
$910$	−6.09034	+	389.217i	−0.00669268	+	0.427711i
$911$	−1343.70	−	556.579i	−1.47497	−	0.610954i	−0.506987	−	0.861954i	$-0.669241\pi$
$911$	−1343.70	−	556.579i	−1.47497	−	0.610954i	−0.967987	+	0.251000i	$0.919241\pi$
$912$	168.463	+	289.866i	0.184719	+	0.317836i
$913$	91.8347	+	221.709i	0.100586	+	0.242835i
$914$	−599.893	−	1514.88i	−0.656338	−	1.65742i
$915$	−216.730	−	405.473i	−0.236863	−	0.443139i
$916$	−16.4871	−	2.14655i	−0.0179990	−	0.00234340i
$917$	−658.530	+	540.442i	−0.718136	+	0.589359i
$918$	75.7513	+	915.796i	0.0825177	+	0.997600i
$919$	1376.04	+	919.441i	1.49732	+	1.00048i	0.990361	+	0.138513i	$0.0442323\pi$
$919$	1376.04	+	919.441i	1.49732	+	1.00048i	0.506964	+	0.861967i	$0.330768\pi$
$920$	−323.869	−	1281.27i	−0.352031	−	1.39269i
$921$	−52.8888	+	35.3392i	−0.0574254	+	0.0383705i
$922$	1.97236	−	17.2537i	0.00213922	−	0.0187133i
$923$	310.209	−	580.359i	0.336087	−	0.628775i
$924$	129.245	+	92.3356i	0.139875	+	0.0999303i
$925$	80.8640	+	821.026i	0.0874206	+	0.887596i
$926$	−1330.75	−	286.418i	−1.43710	−	0.309307i
$927$	−73.9417	+	73.9417i	−0.0797645	+	0.0797645i
$928$	−675.094	+	1055.32i	−0.727472	+	1.13719i
$929$	191.666	−	191.666i	0.206314	−	0.206314i	−0.596385	−	0.802699i	$-0.703397\pi$
$929$	191.666	−	191.666i	0.206314	−	0.206314i	0.802699	+	0.596385i	$0.203397\pi$
$930$	−98.8491	−	153.070i	−0.106289	−	0.164591i
$931$	53.9153	+	547.411i	0.0579111	+	0.587982i
$932$	259.932	−	1122.05i	0.278897	−	1.20392i
$933$	187.028	−	349.904i	0.200458	−	0.375031i
$934$	−162.218	−	204.093i	−0.173681	−	0.218515i
$935$	944.383	−	631.017i	1.01004	−	0.674884i
$936$	−194.160	−	408.246i	−0.207436	−	0.436160i
$937$	−675.381	−	451.275i	−0.720791	−	0.481617i	0.140273	−	0.990113i	$-0.455202\pi$
$937$	−675.381	−	451.275i	−0.720791	−	0.481617i	−0.861065	+	0.508496i	$0.830202\pi$
$938$	−190.996	+	225.443i	−0.203621	+	0.240344i
$939$	293.997	−	241.277i	0.313095	−	0.256951i
$940$	511.573	+	294.381i	0.544226	+	0.313171i
$941$	778.218	+	1455.94i	0.827011	+	1.54723i	0.836951	+	0.547279i	$0.184336\pi$
$941$	778.218	+	1455.94i	0.827011	+	1.54723i	−0.00993930	+	0.999951i	$0.503164\pi$
$942$	−125.441	−	54.2742i	−0.133165	−	0.0576159i
$943$	10.7548	+	25.9645i	0.0114049	+	0.0275339i
$944$	−924.614	+	1496.44i	−0.979463	+	1.58521i
$945$	−500.925	−	207.490i	−0.530080	−	0.219566i
$946$	−890.087	+	862.661i	−0.940896	+	0.911904i
$947$	175.177	−	577.483i	0.184981	−	0.609802i	−0.814576	−	0.580057i	$-0.803030\pi$
$947$	175.177	−	577.483i	0.184981	−	0.609802i	0.999558	−	0.0297454i	$-0.00946967\pi$
$948$	−305.300	+	349.136i	−0.322047	+	0.368287i
$949$	−59.3047	+	602.131i	−0.0624918	+	0.634490i
$950$	−198.809	+	620.279i	−0.209273	+	0.652925i
$951$	−48.9571	−	246.124i	−0.0514796	−	0.258805i
$952$	402.640	+	442.332i	0.422941	+	0.464634i
$953$	−15.5921	+	78.3866i	−0.0163610	+	0.0822524i	−0.988103	−	0.153793i	$-0.950851\pi$
$953$	−15.5921	+	78.3866i	−0.0163610	+	0.0822524i	0.971742	+	0.236045i	$0.0758513\pi$
$954$	−48.3912	−	168.999i	−0.0507245	−	0.177148i
$955$	−866.904	+	262.972i	−0.907752	+	0.275364i
$956$	−1309.70	+	1230.20i	−1.36998	+	1.28682i
$957$	−333.795	−	273.938i	−0.348793	−	0.286247i
$958$	−731.231	+	1058.14i	−0.763289	+	1.10453i
$959$	−172.936			−0.180329
$960$	460.701	−	381.412i	0.479897	−	0.397304i
$961$			865.958i			0.901101i
$962$	349.135	−	505.223i	0.362926	−	0.525180i
$963$	−42.7411	+	52.0802i	−0.0443833	+	0.0540812i
$964$	59.1900	−	1890.87i	0.0614004	−	1.96149i
$965$	−598.095	−	1971.66i	−0.619788	−	2.04317i
$966$	66.0367	+	230.624i	0.0683610	+	0.238741i
$967$	−1489.16	−	296.213i	−1.53998	−	0.306321i	−0.649152	−	0.760659i	$-0.724876\pi$
$967$	−1489.16	−	296.213i	−1.53998	−	0.306321i	−0.890830	+	0.454337i	$0.849876\pi$
$968$	−153.054	−	424.877i	−0.158113	−	0.438922i
$969$	−426.805	+	84.8968i	−0.440459	+	0.0876128i
$970$	−661.237	+	2063.04i	−0.681687	+	2.12684i
$971$	−1380.73	−	135.990i	−1.42196	−	0.140051i	−0.642397	−	0.766372i	$-0.722060\pi$
$971$	−1380.73	−	135.990i	−1.42196	−	0.140051i	−0.779565	+	0.626321i	$0.784560\pi$
$972$	979.133	−	65.5842i	1.00734	−	0.0674735i
$973$	−421.405	−	127.832i	−0.433098	−	0.131379i
$974$	−563.550	+	546.185i	−0.578593	+	0.560765i
$975$	−89.0291	+	214.935i	−0.0913119	+	0.220446i
$976$	786.656	−	28.0083i	0.806000	−	0.0286970i
$977$	985.692	−	408.287i	1.00890	−	0.417899i	0.183844	−	0.982955i	$-0.441146\pi$
$977$	985.692	−	408.287i	1.00890	−	0.417899i	0.825052	+	0.565057i	$0.191146\pi$
$978$	39.6809	+	17.1686i	0.0405735	+	0.0175548i
$979$	557.521	−	298.001i	0.569480	−	0.304393i
$980$	947.481	−	255.332i	0.966817	−	0.260542i
$981$	862.279	+	1050.69i	0.878979	+	1.07104i
$982$	279.990	−	330.487i	0.285122	−	0.336544i
$983$	617.926	−	924.791i	0.628612	−	0.940784i	−0.371313	−	0.928508i	$-0.621092\pi$
$983$	617.926	−	924.791i	0.628612	−	0.940784i	0.999925	−	0.0122764i	$-0.00390781\pi$
$984$	−8.52116	+	9.44234i	−0.00865972	+	0.00959587i
$985$	284.634	+	425.986i	0.288969	+	0.432473i
$986$	−1011.78	−	1272.96i	−1.02614	−	1.29103i
$987$	−94.4873	−	50.5045i	−0.0957318	−	0.0511697i
$988$	411.383	−	256.632i	0.416380	−	0.259749i
$989$	−1863.02	+	183.491i	−1.88374	+	0.185532i
$990$	−422.211	−	653.802i	−0.426476	−	0.660406i
$991$	−858.404	−	858.404i	−0.866199	−	0.866199i	0.125850	−	0.992049i	$-0.459834\pi$
$991$	−858.404	−	858.404i	−0.866199	−	0.866199i	−0.992049	+	0.125850i	$0.959834\pi$
$992$	309.792	−	36.7630i	0.312290	−	0.0370595i
$993$	76.8065	+	76.8065i	0.0773480	+	0.0773480i
$994$	583.274	+	125.538i	0.586795	+	0.126296i
$995$	−1056.60	+	104.066i	−1.06191	+	0.104589i
$996$	−161.794	+	26.9503i	−0.162444	+	0.0270586i
$997$	286.229	+	152.992i	0.287090	+	0.153453i	0.608656	−	0.793434i	$-0.291709\pi$
$997$	286.229	+	152.992i	0.287090	+	0.153453i	−0.321566	+	0.946887i	$0.604209\pi$
$998$	102.949	−	900.574i	0.103156	−	0.902378i
$999$	475.232	+	711.235i	0.475708	+	0.711947i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	128.3.l.a.43.19	yes	496
128.3	odd	32	inner	128.3.l.a.3.19	✓	496

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
128.3.l.a.3.19	✓	496	128.3	odd	32	inner
128.3.l.a.43.19	yes	496	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.359443 + 1.96744i) q^{2} +(1.06123 + 0.870929i) q^{3} +(-3.74160 + 1.41436i) q^{4} +(-6.51407 + 1.97602i) q^{5} +(-1.33205 + 2.40095i) q^{6} +(-0.702367 + 3.53104i) q^{7} +(-4.12755 - 6.85298i) q^{8} +(-1.38812 - 6.97855i) q^{9} +O(q^{10})\)	\(q+(0.359443 + 1.96744i) q^{2} +(1.06123 + 0.870929i) q^{3} +(-3.74160 + 1.41436i) q^{4} +(-6.51407 + 1.97602i) q^{5} +(-1.33205 + 2.40095i) q^{6} +(-0.702367 + 3.53104i) q^{7} +(-4.12755 - 6.85298i) q^{8} +(-1.38812 - 6.97855i) q^{9} +(-6.22913 - 12.1057i) q^{10} +(-0.787497 + 7.99559i) q^{11} +(-5.20251 - 1.75771i) q^{12} +(-2.30539 + 7.59984i) q^{13} +(-7.19955 - 0.112656i) q^{14} +(-8.63390 - 3.57628i) q^{15} +(11.9992 - 10.5839i) q^{16} +(7.94744 + 19.1868i) q^{17} +(13.2309 - 5.23943i) q^{18} +(7.19499 + 13.4609i) q^{19} +(21.5782 - 16.6067i) q^{20} +(-3.82066 + 3.13553i) q^{21} +(-16.0139 + 1.32461i) q^{22} +(-20.1780 - 13.4825i) q^{23} +(1.58817 - 10.8674i) q^{24} +(17.7417 - 11.8546i) q^{25} +(-15.7808 - 1.80399i) q^{26} +(10.4291 - 19.5116i) q^{27} +(-2.36618 - 14.2051i) q^{28} +(3.83729 + 38.9607i) q^{29} +(3.93270 - 18.2721i) q^{30} +(6.89353 - 6.89353i) q^{31} +(25.1362 + 19.8033i) q^{32} +(-7.79931 + 7.79931i) q^{33} +(-34.8922 + 22.5326i) q^{34} +(-2.40214 - 24.3893i) q^{35} +(15.0640 + 24.1477i) q^{36} +(-18.2260 + 34.0985i) q^{37} +(-23.8972 + 18.9941i) q^{38} +(-9.06547 + 6.05735i) q^{39} +(40.4288 + 36.4846i) q^{40} +(-0.962894 - 0.643385i) q^{41} +(-7.54226 - 6.38985i) q^{42} +(59.6302 - 48.9372i) q^{43} +(-8.36214 - 31.0301i) q^{44} +(22.8321 + 42.7158i) q^{45} +(19.2732 - 44.5452i) q^{46} +(8.29527 + 20.0266i) q^{47} +(21.9518 - 0.781576i) q^{48} +(33.2952 + 13.7913i) q^{49} +(29.7003 + 30.6446i) q^{50} +(-8.27630 + 27.2833i) q^{51} +(-2.12307 - 31.6962i) q^{52} +(1.21081 - 12.2936i) q^{53} +(42.1364 + 13.5054i) q^{54} +(-10.6696 - 53.6399i) q^{55} +(27.0972 - 9.76124i) q^{56} +(-4.08793 + 20.5514i) q^{57} +(-75.2734 + 21.5538i) q^{58} +(-105.206 + 31.9140i) q^{59} +(37.3628 + 1.16957i) q^{60} +(38.0299 + 31.2103i) q^{61} +(16.0404 + 11.0847i) q^{62} +25.6165 q^{63} +(-29.9266 + 56.5721i) q^{64} -54.0614i q^{65} +(-18.1480 - 12.5412i) q^{66} +(26.0326 - 31.7208i) q^{67} +(-56.8732 - 60.5489i) q^{68} +(-9.67122 - 31.8817i) q^{69} +(47.1209 - 13.4926i) q^{70} +(-81.2684 - 16.1653i) q^{71} +(-42.0943 + 38.3171i) q^{72} +(74.7208 - 14.8629i) q^{73} +(-73.6377 - 23.6020i) q^{74} +(29.1525 + 2.87127i) q^{75} +(-45.9593 - 40.1889i) q^{76} +(-27.6796 - 8.39652i) q^{77} +(-15.1760 - 15.6584i) q^{78} +(32.3206 - 78.0289i) q^{79} +(-57.2493 + 92.6552i) q^{80} +(-31.1020 + 12.8829i) q^{81} +(0.919713 - 2.12569i) q^{82} +(26.3421 - 14.0801i) q^{83} +(9.86060 - 17.1357i) q^{84} +(-89.6837 - 109.280i) q^{85} +(117.714 + 99.7284i) q^{86} +(-29.8598 + 44.6883i) q^{87} +(58.0440 - 27.6055i) q^{88} +(-43.7143 - 65.4230i) q^{89} +(-75.8338 + 60.2745i) q^{90} +(-25.2161 - 13.4783i) q^{91} +(94.5674 + 21.9073i) q^{92} +(13.3194 - 1.31185i) q^{93} +(-36.4193 + 23.5188i) q^{94} +(-73.4676 - 73.4676i) q^{95} +(9.42810 + 42.9077i) q^{96} +(-112.520 - 112.520i) q^{97} +(-15.1658 + 70.4633i) q^{98} +(56.8908 - 5.60325i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 496 q - 16 q^{2} - 16 q^{3} - 16 q^{4} - 16 q^{5} - 16 q^{6} - 16 q^{7} - 16 q^{8} - 16 q^{9}+O(q^{10}) \) 496 * q - 16 * q^2 - 16 * q^3 - 16 * q^4 - 16 * q^5 - 16 * q^6 - 16 * q^7 - 16 * q^8 - 16 * q^9	\( 496 q - 16 q^{2} - 16 q^{3} - 16 q^{4} - 16 q^{5} - 16 q^{6} - 16 q^{7} - 16 q^{8} - 16 q^{9} - 16 q^{10} - 16 q^{11} - 16 q^{12} - 16 q^{13} - 16 q^{14} - 16 q^{15} - 16 q^{16} - 16 q^{17} - 16 q^{18} - 16 q^{19} - 16 q^{20} - 16 q^{21} - 16 q^{22} - 16 q^{23} - 16 q^{24} - 16 q^{25} - 16 q^{26} - 16 q^{27} - 16 q^{28} - 16 q^{29} - 16 q^{30} - 16 q^{31} - 16 q^{32} - 16 q^{33} - 16 q^{34} - 16 q^{35} - 16 q^{36} - 16 q^{37} - 16 q^{38} - 16 q^{39} - 16 q^{40} - 16 q^{41} - 16 q^{42} - 16 q^{43} - 16 q^{44} - 16 q^{45} - 16 q^{46} - 16 q^{47} - 16 q^{48} - 16 q^{49} - 640 q^{50} - 16 q^{51} - 1072 q^{52} - 16 q^{53} - 1168 q^{54} - 16 q^{55} - 800 q^{56} - 16 q^{57} - 736 q^{58} - 16 q^{59} - 592 q^{60} - 16 q^{61} - 112 q^{62} - 32 q^{63} + 176 q^{64} + 560 q^{66} - 16 q^{67} + 464 q^{68} - 16 q^{69} + 1328 q^{70} - 16 q^{71} + 1280 q^{72} - 16 q^{73} + 1216 q^{74} - 16 q^{75} + 1648 q^{76} - 16 q^{77} + 1424 q^{78} - 16 q^{79} + 800 q^{80} - 16 q^{81} - 16 q^{82} - 16 q^{83} - 16 q^{84} - 16 q^{85} - 16 q^{86} - 16 q^{87} - 16 q^{88} - 16 q^{89} - 16 q^{90} - 16 q^{91} - 16 q^{92} - 16 q^{93} - 16 q^{94} - 16 q^{95} - 16 q^{96} - 16 q^{97} - 16 q^{98} - 16 q^{99}+O(q^{100}) \) 496 * q - 16 * q^2 - 16 * q^3 - 16 * q^4 - 16 * q^5 - 16 * q^6 - 16 * q^7 - 16 * q^8 - 16 * q^9 - 16 * q^10 - 16 * q^11 - 16 * q^12 - 16 * q^13 - 16 * q^14 - 16 * q^15 - 16 * q^16 - 16 * q^17 - 16 * q^18 - 16 * q^19 - 16 * q^20 - 16 * q^21 - 16 * q^22 - 16 * q^23 - 16 * q^24 - 16 * q^25 - 16 * q^26 - 16 * q^27 - 16 * q^28 - 16 * q^29 - 16 * q^30 - 16 * q^31 - 16 * q^32 - 16 * q^33 - 16 * q^34 - 16 * q^35 - 16 * q^36 - 16 * q^37 - 16 * q^38 - 16 * q^39 - 16 * q^40 - 16 * q^41 - 16 * q^42 - 16 * q^43 - 16 * q^44 - 16 * q^45 - 16 * q^46 - 16 * q^47 - 16 * q^48 - 16 * q^49 - 640 * q^50 - 16 * q^51 - 1072 * q^52 - 16 * q^53 - 1168 * q^54 - 16 * q^55 - 800 * q^56 - 16 * q^57 - 736 * q^58 - 16 * q^59 - 592 * q^60 - 16 * q^61 - 112 * q^62 - 32 * q^63 + 176 * q^64 + 560 * q^66 - 16 * q^67 + 464 * q^68 - 16 * q^69 + 1328 * q^70 - 16 * q^71 + 1280 * q^72 - 16 * q^73 + 1216 * q^74 - 16 * q^75 + 1648 * q^76 - 16 * q^77 + 1424 * q^78 - 16 * q^79 + 800 * q^80 - 16 * q^81 - 16 * q^82 - 16 * q^83 - 16 * q^84 - 16 * q^85 - 16 * q^86 - 16 * q^87 - 16 * q^88 - 16 * q^89 - 16 * q^90 - 16 * q^91 - 16 * q^92 - 16 * q^93 - 16 * q^94 - 16 * q^95 - 16 * q^96 - 16 * q^97 - 16 * q^98 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more