LMFDB - Embedded newform 169.4.e.g.147.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [169,4,Mod(23,169)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(169, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5]))

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

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

chi := DirichletCharacter("169.23");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 169 = 13^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	169.e (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$9.97132279097$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.1731891456.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 9x^{6} + 65x^{4} - 144x^{2} + 256 $ x^8 - 9x^6 + 65x^4 - 144*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 13)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			147.2
Root			$-1.35234 + 0.780776i$ of defining polynomial
Character	$\chi$	$=$	169.147
Dual form			169.4.e.g.23.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.379706 - 0.219224i) q^{2} +(1.84233 - 3.19101i) q^{3} +(-3.90388 - 6.76172i) q^{4} +17.8078i q^{5} +(-1.39909 + 0.807764i) q^{6} +(4.70983 - 2.71922i) q^{7} +6.93087i q^{8} +(6.71165 + 11.6249i) q^{9} +O(q^{10})$	\(q+(-0.379706 - 0.219224i) q^{2} +(1.84233 - 3.19101i) q^{3} +(-3.90388 - 6.76172i) q^{4} +17.8078i q^{5} +(-1.39909 + 0.807764i) q^{6} +(4.70983 - 2.71922i) q^{7} +6.93087i q^{8} +(6.71165 + 11.6249i) q^{9} +(3.90388 - 6.76172i) q^{10} +(19.4191 + 11.2116i) q^{11} -28.7689 q^{12} -2.38447 q^{14} +(56.8247 + 32.8078i) q^{15} +(-29.7116 + 51.4621i) q^{16} +(33.9924 + 58.8766i) q^{17} -5.88540i q^{18} +(69.9816 - 40.4039i) q^{19} +(120.411 - 69.5194i) q^{20} -20.0388i q^{21} +(-4.91571 - 8.51427i) q^{22} +(70.2656 - 121.704i) q^{23} +(22.1165 + 12.7689i) q^{24} -192.116 q^{25} +148.946 q^{27} +(-36.7733 - 21.2311i) q^{28} +(53.3466 - 92.3990i) q^{29} +(-14.3845 - 24.9146i) q^{30} +276.155i q^{31} +(70.5819 - 40.7505i) q^{32} +(71.5529 - 41.3111i) q^{33} -29.8078i q^{34} +(48.4233 + 83.8716i) q^{35} +(52.4029 - 90.7646i) q^{36} +(3.71670 + 2.14584i) q^{37} -35.4299 q^{38} -123.423 q^{40} +(197.254 + 113.884i) q^{41} +(-4.39298 + 7.60887i) q^{42} +(13.7647 + 23.8411i) q^{43} -175.076i q^{44} +(-207.014 + 119.519i) q^{45} +(-53.3606 + 30.8078i) q^{46} +318.617i q^{47} +(109.477 + 189.620i) q^{48} +(-156.712 + 271.433i) q^{49} +(72.9479 + 42.1165i) q^{50} +250.501 q^{51} -67.6562 q^{53} +(-56.5558 - 32.6525i) q^{54} +(-199.654 + 345.811i) q^{55} +(18.8466 + 32.6432i) q^{56} -297.749i q^{57} +(-40.5121 + 23.3897i) q^{58} +(-252.113 + 145.557i) q^{59} -512.311i q^{60} +(-331.655 - 574.444i) q^{61} +(60.5398 - 104.858i) q^{62} +(63.2215 + 36.5009i) q^{63} +439.652 q^{64} -36.2255 q^{66} +(-368.149 - 212.551i) q^{67} +(265.405 - 459.695i) q^{68} +(-258.905 - 448.436i) q^{69} -42.4621i q^{70} +(132.470 - 76.4815i) q^{71} +(-80.5708 + 46.5175i) q^{72} +117.268i q^{73} +(-0.940837 - 1.62958i) q^{74} +(-353.942 + 613.045i) q^{75} +(-546.400 - 315.464i) q^{76} +121.948 q^{77} +202.462 q^{79} +(-916.425 - 529.098i) q^{80} +(93.1932 - 161.415i) q^{81} +(-49.9323 - 86.4853i) q^{82} -336.155i q^{83} +(-135.497 + 78.2292i) q^{84} +(-1048.46 + 605.329i) q^{85} -12.0702i q^{86} +(-196.564 - 340.459i) q^{87} +(-77.7065 + 134.592i) q^{88} +(-621.974 - 359.097i) q^{89} +104.806 q^{90} -1097.23 q^{92} +(881.214 + 508.769i) q^{93} +(69.8485 - 120.981i) q^{94} +(719.503 + 1246.22i) q^{95} -300.303i q^{96} +(-657.632 + 379.684i) q^{97} +(119.009 - 68.7098i) q^{98} +300.994i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 10 q^{3} + 10 q^{4} - 70 q^{9}+O(q^{10}) $ 8 * q - 10 * q^3 + 10 * q^4 - 70 * q^9	$ 8 q - 10 q^{3} + 10 q^{4} - 70 q^{9} - 10 q^{10} - 560 q^{12} - 184 q^{14} - 114 q^{16} + 140 q^{17} + 340 q^{22} + 290 q^{23} - 300 q^{25} + 1340 q^{27} - 68 q^{29} - 280 q^{30} + 140 q^{35} + 1450 q^{36} - 1240 q^{38} - 740 q^{40} + 740 q^{42} + 910 q^{43} + 480 q^{48} - 1130 q^{49} + 932 q^{51} + 2180 q^{53} - 1020 q^{55} - 344 q^{56} - 1004 q^{61} - 1000 q^{62} + 5084 q^{64} - 6392 q^{66} + 1010 q^{68} - 958 q^{69} - 1698 q^{74} - 3450 q^{75} - 1020 q^{77} + 960 q^{79} - 244 q^{81} - 3030 q^{82} - 3230 q^{87} - 2040 q^{88} + 2900 q^{90} - 4160 q^{92} - 2080 q^{94} + 2540 q^{95}+O(q^{100}) $ 8 * q - 10 * q^3 + 10 * q^4 - 70 * q^9 - 10 * q^10 - 560 * q^12 - 184 * q^14 - 114 * q^16 + 140 * q^17 + 340 * q^22 + 290 * q^23 - 300 * q^25 + 1340 * q^27 - 68 * q^29 - 280 * q^30 + 140 * q^35 + 1450 * q^36 - 1240 * q^38 - 740 * q^40 + 740 * q^42 + 910 * q^43 + 480 * q^48 - 1130 * q^49 + 932 * q^51 + 2180 * q^53 - 1020 * q^55 - 344 * q^56 - 1004 * q^61 - 1000 * q^62 + 5084 * q^64 - 6392 * q^66 + 1010 * q^68 - 958 * q^69 - 1698 * q^74 - 3450 * q^75 - 1020 * q^77 + 960 * q^79 - 244 * q^81 - 3030 * q^82 - 3230 * q^87 - 2040 * q^88 + 2900 * q^90 - 4160 * q^92 - 2080 * q^94 + 2540 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/169\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−0.379706	−	0.219224i	−0.134246	−	0.0775072i	0.431373	−	0.902174i	$-0.358029\pi$
$2$	−0.379706	−	0.219224i	−0.134246	−	0.0775072i	−0.565619	+	0.824667i	$0.691363\pi$
$3$	1.84233	−	3.19101i	0.354556	−	0.614110i	−0.632486	−	0.774572i	$-0.717965\pi$
$3$	1.84233	−	3.19101i	0.354556	−	0.614110i	0.987042	+	0.160462i	$0.0512985\pi$
$4$	−3.90388	−	6.76172i	−0.487985	−	0.845215i
$5$			17.8078i			1.59277i	0.604787	+	0.796387i	$0.293258\pi$
$5$			17.8078i			1.59277i	−0.604787	+	0.796387i	$0.706742\pi$
$6$	−1.39909	+	0.807764i	−0.0951959	+	0.0549614i
$7$	4.70983	−	2.71922i	0.254307	−	0.146824i	−0.367428	−	0.930052i	$-0.619761\pi$
$7$	4.70983	−	2.71922i	0.254307	−	0.146824i	0.621735	+	0.783228i	$0.286428\pi$
$8$			6.93087i			0.306304i
$9$	6.71165	+	11.6249i	0.248579	+	0.430552i
$10$	3.90388	−	6.76172i	0.123452	−	0.213824i
$11$	19.4191	+	11.2116i	0.532281	+	0.307313i	0.741945	−	0.670461i	$-0.233904\pi$
$11$	19.4191	+	11.2116i	0.532281	+	0.307313i	−0.209664	+	0.977774i	$0.567237\pi$
$12$	−28.7689			−0.692073
$13$		0			0
$13$		0			0
$14$	−2.38447			−0.0455198
$15$	56.8247	+	32.8078i	0.978139	+	0.564729i
$16$	−29.7116	+	51.4621i	−0.464244	+	0.804095i
$17$	33.9924	+	58.8766i	0.484963	+	0.839981i	0.999851	−	0.0172769i	$-0.00549968\pi$
$17$	33.9924	+	58.8766i	0.484963	+	0.839981i	−0.514888	+	0.857258i	$0.672166\pi$
$18$		−	5.88540i		−	0.0770668i
$19$	69.9816	−	40.4039i	0.844993	−	0.487857i	−0.0139650	−	0.999902i	$-0.504445\pi$
$19$	69.9816	−	40.4039i	0.844993	−	0.487857i	0.858958	+	0.512045i	$0.171112\pi$
$20$	120.411	−	69.5194i	1.34624	−	0.777251i
$21$		−	20.0388i		−	0.208230i
$22$	−4.91571	−	8.51427i	−0.0476379	−	0.0825113i
$23$	70.2656	−	121.704i	0.637017	−	1.10335i	−0.349067	−	0.937098i	$-0.613501\pi$
$23$	70.2656	−	121.704i	0.637017	−	1.10335i	0.986084	−	0.166248i	$-0.0531653\pi$
$24$	22.1165	+	12.7689i	0.188104	+	0.108602i
$25$	−192.116			−1.53693
$26$		0			0
$27$	148.946			1.06165
$28$	−36.7733	−	21.2311i	−0.248196	−	0.143296i
$29$	53.3466	−	92.3990i	0.341594	−	0.591657i	−0.643135	−	0.765753i	$-0.722367\pi$
$29$	53.3466	−	92.3990i	0.341594	−	0.591657i	0.984729	+	0.174095i	$0.0557001\pi$
$30$	−14.3845	−	24.9146i	−0.0875411	−	0.151626i
$31$			276.155i			1.59997i	0.600023	+	0.799983i	$0.295158\pi$
$31$			276.155i			1.59997i	−0.600023	+	0.799983i	$0.704842\pi$
$32$	70.5819	−	40.7505i	0.389913	−	0.225117i
$33$	71.5529	−	41.3111i	0.377447	−	0.217919i
$34$		−	29.8078i		−	0.150353i
$35$	48.4233	+	83.8716i	0.233858	+	0.405054i
$36$	52.4029	−	90.7646i	0.242606	−	0.420206i
$37$	3.71670	+	2.14584i	0.0165141	+	0.00953442i	0.508234	−	0.861219i	$-0.330298\pi$
$37$	3.71670	+	2.14584i	0.0165141	+	0.00953442i	−0.491720	+	0.870753i	$0.663632\pi$
$38$	−35.4299			−0.151250
$39$		0			0
$40$	−123.423			−0.487873
$41$	197.254	+	113.884i	0.751362	+	0.433799i	0.826186	−	0.563398i	$-0.190506\pi$
$41$	197.254	+	113.884i	0.751362	+	0.433799i	−0.0748237	+	0.997197i	$0.523839\pi$
$42$	−4.39298	+	7.60887i	−0.0161393	+	0.0279541i
$43$	13.7647	+	23.8411i	0.0488162	+	0.0845521i	0.889401	−	0.457128i	$-0.151122\pi$
$43$	13.7647	+	23.8411i	0.0488162	+	0.0845521i	−0.840585	+	0.541680i	$0.817788\pi$
$44$		−	175.076i		−	0.599856i
$45$	−207.014	+	119.519i	−0.685773	+	0.395931i
$46$	−53.3606	+	30.8078i	−0.171035	+	0.0987469i
$47$			318.617i			0.988832i	0.869225	+	0.494416i	$0.164618\pi$
$47$			318.617i			0.988832i	−0.869225	+	0.494416i	$0.835382\pi$
$48$	109.477	+	189.620i	0.329202	+	0.570194i
$49$	−156.712	+	271.433i	−0.456885	+	0.791348i
$50$	72.9479	+	42.1165i	0.206328	+	0.119123i
$51$	250.501			0.687787
$52$		0			0
$53$	−67.6562			−0.175345			−0.0876726	−	0.996149i	$-0.527943\pi$
$53$	−67.6562			−0.175345			−0.0876726	+	0.996149i	$0.527943\pi$
$54$	−56.5558	−	32.6525i	−0.142523	−	0.0822859i
$55$	−199.654	+	345.811i	−0.489480	+	0.847804i
$56$	18.8466	+	32.6432i	0.0449729	+	0.0778953i
$57$		−	297.749i		−	0.691892i
$58$	−40.5121	+	23.3897i	−0.0917155	+	0.0529519i
$59$	−252.113	+	145.557i	−0.556310	+	0.321186i	−0.751663	−	0.659547i	$-0.770748\pi$
$59$	−252.113	+	145.557i	−0.556310	+	0.321186i	0.195353	+	0.980733i	$0.437415\pi$
$60$		−	512.311i		−	1.10232i
$61$	−331.655	−	574.444i	−0.696133	−	1.20574i	−0.969797	−	0.243912i	$-0.921569\pi$
$61$	−331.655	−	574.444i	−0.696133	−	1.20574i	0.273664	−	0.961825i	$-0.411764\pi$
$62$	60.5398	−	104.858i	0.124009	−	0.214790i
$63$	63.2215	+	36.5009i	0.126431	+	0.0729950i
$64$	439.652			0.858696
$65$		0			0
$66$	−36.2255			−0.0675613
$67$	−368.149	−	212.551i	−0.671291	−	0.387570i	0.125275	−	0.992122i	$-0.460019\pi$
$67$	−368.149	−	212.551i	−0.671291	−	0.387570i	−0.796566	+	0.604552i	$0.793352\pi$
$68$	265.405	−	459.695i	0.473310	−	0.819796i
$69$	−258.905	−	448.436i	−0.451717	−	0.782397i
$70$		−	42.4621i		−	0.0725028i
$71$	132.470	−	76.4815i	0.221427	−	0.127841i	−0.385184	−	0.922840i	$-0.625862\pi$
$71$	132.470	−	76.4815i	0.221427	−	0.127841i	0.606611	+	0.794999i	$0.292529\pi$
$72$	−80.5708	+	46.5175i	−0.131880	+	0.0761409i
$73$			117.268i			0.188016i	0.995571	+	0.0940081i	$0.0299680\pi$
$73$			117.268i			0.188016i	−0.995571	+	0.0940081i	$0.970032\pi$
$74$	−0.940837	−	1.62958i	−0.00147797	−	0.00255993i
$75$	−353.942	+	613.045i	−0.544929	+	0.943845i
$76$	−546.400	−	315.464i	−0.824689	−	0.476134i
$77$	121.948			0.180484
$78$		0			0
$79$	202.462			0.288339			0.144169	−	0.989553i	$-0.453949\pi$
$79$	202.462			0.288339			0.144169	+	0.989553i	$0.453949\pi$
$80$	−916.425	−	529.098i	−1.28074	−	0.739437i
$81$	93.1932	−	161.415i	0.127837	−	0.221420i
$82$	−49.9323	−	86.4853i	−0.0672452	−	0.116472i
$83$		−	336.155i		−	0.444552i	−0.974984	−	0.222276i	$-0.928651\pi$
$83$		−	336.155i		−	0.444552i	0.974984	−	0.222276i	$-0.0713486\pi$
$84$	−135.497	+	78.2292i	−0.175999	+	0.101613i
$85$	−1048.46	+	605.329i	−1.33790	+	0.772437i
$86$		−	12.0702i		−	0.0151344i
$87$	−196.564	−	340.459i	−0.242228	−	0.419552i
$88$	−77.7065	+	134.592i	−0.0941311	+	0.163040i
$89$	−621.974	−	359.097i	−0.740777	−	0.427688i	0.0815748	−	0.996667i	$-0.474005\pi$
$89$	−621.974	−	359.097i	−0.740777	−	0.427688i	−0.822352	+	0.568979i	$0.807338\pi$
$90$	104.806			0.122750
$91$		0			0
$92$	−1097.23			−1.24342
$93$	881.214	+	508.769i	0.982555	+	0.567278i
$94$	69.8485	−	120.981i	0.0766417	−	0.132747i
$95$	719.503	+	1246.22i	0.777047	+	1.34588i
$96$		−	300.303i		−	0.319266i
$97$	−657.632	+	379.684i	−0.688376	+	0.397434i	−0.803003	−	0.595975i	$-0.796766\pi$
$97$	−657.632	+	379.684i	−0.688376	+	0.397434i	0.114628	+	0.993409i	$0.463433\pi$
$98$	119.009	−	68.7098i	0.122670	−	0.0708238i
$99$			300.994i			0.305566i
$100$	750.000	+	1299.04i	0.750000	+	1.29904i
$101$	−174.348	+	301.980i	−0.171766	+	0.297507i	−0.939037	−	0.343816i	$-0.888280\pi$
$101$	−174.348	+	301.980i	−0.171766	+	0.297507i	0.767272	+	0.641322i	$0.221614\pi$
$102$	−95.1168	−	54.9157i	−0.0923330	−	0.0533085i
$103$	580.303			0.555136			0.277568	−	0.960706i	$-0.410472\pi$
$103$	580.303			0.555136			0.277568	+	0.960706i	$0.410472\pi$
$104$		0			0
$105$	356.847			0.331663
$106$	25.6895	+	14.8318i	0.0235395	+	0.0135905i
$107$	−285.747	+	494.928i	−0.258170	+	0.447163i	−0.965752	−	0.259468i	$-0.916453\pi$
$107$	−285.747	+	494.928i	−0.258170	+	0.447163i	0.707582	+	0.706631i	$0.249786\pi$
$108$	−581.468	−	1007.13i	−0.518072	−	0.897327i
$109$		−	176.004i		−	0.154661i	−0.997005	−	0.0773307i	$-0.975360\pi$
$109$		−	176.004i		−	0.154661i	0.997005	−	0.0773307i	$-0.0246397\pi$
$110$	151.620	−	87.5379i	0.131422	−	0.0758765i
$111$	13.6948	−	7.90668i	0.0117104	−	0.00676098i
$112$			323.170i			0.272649i
$113$	−632.441	−	1095.42i	−0.526505	−	0.911933i	−0.999523	−	0.0308807i	$-0.990169\pi$
$113$	−632.441	−	1095.42i	−0.526505	−	0.911933i	0.473018	−	0.881053i	$-0.343165\pi$
$114$	−65.2736	+	113.057i	−0.0536266	+	0.0928840i
$115$	2167.27	+	1251.27i	1.75738	+	1.01462i
$116$	−833.035			−0.666770
$117$		0			0
$118$	127.638			0.0995768
$119$	320.197	+	184.866i	0.246659	+	0.142409i
$120$	−227.386	+	393.845i	−0.172979	+	0.299608i
$121$	−414.098	−	717.239i	−0.311118	−	0.538872i
$122$			290.827i			0.215821i
$123$	726.812	−	419.625i	0.532801	−	0.307613i
$124$	1867.29	−	1078.08i	1.35232	−	0.780760i
$125$		−	1195.19i		−	0.855211i
$126$	−16.0037	−	27.7193i	−0.0113153	−	0.0195986i
$127$	1302.05	−	2255.22i	0.909752	−	1.57574i	0.0953448	−	0.995444i	$-0.469605\pi$
$127$	1302.05	−	2255.22i	0.909752	−	1.57574i	0.814408	−	0.580293i	$-0.197062\pi$
$128$	−731.594	−	422.386i	−0.505190	−	0.291672i
$129$	101.436			0.0692323
$130$		0			0
$131$	2131.70			1.42174			0.710870	−	0.703324i	$-0.248302\pi$
$131$	2131.70			1.42174			0.710870	+	0.703324i	$0.248302\pi$
$132$	−558.668	−	322.547i	−0.368377	−	0.212683i
$133$	219.734	−	380.591i	0.143259	−	0.248131i
$134$	93.1922	+	161.414i	0.0600790	+	0.104060i
$135$			2652.40i			1.69098i
$136$	−408.066	+	235.597i	−0.257290	+	0.148546i
$137$	595.812	−	343.992i	0.371560	−	0.214520i	−0.302580	−	0.953124i	$-0.597848\pi$
$137$	595.812	−	343.992i	0.371560	−	0.214520i	0.674140	+	0.738604i	$0.264515\pi$
$138$			227.032i			0.140045i
$139$	339.790	+	588.534i	0.207343	+	0.359128i	0.950877	−	0.309570i	$-0.100185\pi$
$139$	339.790	+	588.534i	0.207343	+	0.359128i	−0.743534	+	0.668698i	$0.766852\pi$
$140$	378.078	−	654.850i	0.228239	−	0.395321i
$141$	1016.71	+	586.998i	0.607252	+	0.350597i
$142$	−67.0662			−0.0396343
$143$		0			0
$144$	−797.656			−0.461607
$145$	1645.42	+	949.983i	0.942377	+	0.544082i
$146$	25.7079	−	44.5274i	0.0145726	−	0.0252405i
$147$	577.429	+	1000.14i	0.323983	+	0.561155i
$148$		−	33.5084i		−	0.0186106i
$149$	1710.80	−	987.731i	0.940632	−	0.543074i	0.0504739	−	0.998725i	$-0.483927\pi$
$149$	1710.80	−	987.731i	0.940632	−	0.543074i	0.890159	+	0.455651i	$0.150593\pi$
$150$	268.788	−	155.185i	0.146310	−	0.0844719i
$151$			1803.24i			0.971824i	0.874008	+	0.485912i	$0.161513\pi$
$151$			1803.24i			0.971824i	−0.874008	+	0.485912i	$0.838487\pi$
$152$	280.034	+	485.033i	0.149433	+	0.258825i
$153$	−456.290	+	790.318i	−0.241104	+	0.417604i
$154$	−46.3044	−	26.7339i	−0.0242293	−	0.0139888i
$155$	−4917.71			−2.54839
$156$		0			0
$157$	−397.168			−0.201894			−0.100947	−	0.994892i	$-0.532187\pi$
$157$	−397.168			−0.201894			−0.100947	+	0.994892i	$0.532187\pi$
$158$	−76.8762	−	44.3845i	−0.0387085	−	0.0223483i
$159$	−124.645	+	215.892i	−0.0621698	+	0.107681i
$160$	725.675	+	1256.91i	0.358560	+	0.621044i
$161$		−	764.272i		−	0.374118i
$162$	−70.7721	+	40.8603i	−0.0343233	+	0.0198166i
$163$	815.270	−	470.696i	0.391760	−	0.226183i	−0.291162	−	0.956674i	$-0.594042\pi$
$163$	815.270	−	470.696i	0.391760	−	0.226183i	0.682922	+	0.730491i	$0.260709\pi$
$164$		−	1778.37i		−	0.846750i
$165$	735.658	+	1274.20i	0.347096	+	0.601189i
$166$	−73.6932	+	127.640i	−0.0344560	+	0.0596796i
$167$	−3187.35	−	1840.22i	−1.47691	−	0.852696i	−0.477252	−	0.878766i	$-0.658367\pi$
$167$	−3187.35	−	1840.22i	−1.47691	−	0.852696i	−0.999660	+	0.0260704i	$0.991701\pi$
$168$	138.886			0.0637817
$169$		0			0
$170$	530.810			0.239478
$171$	939.383	+	542.353i	0.420096	+	0.242543i
$172$	107.471	−	186.146i	0.0476431	−	0.0825203i
$173$	711.387	+	1232.16i	0.312634	+	0.541499i	0.978932	−	0.204187i	$-0.0654552\pi$
$173$	711.387	+	1232.16i	0.312634	+	0.541499i	−0.666297	+	0.745686i	$0.732122\pi$
$174$			172.366i			0.0750978i
$175$	−904.837	+	522.408i	−0.390853	+	0.225659i
$176$	−1153.95	+	666.233i	−0.494217	+	0.285336i
$177$			1072.66i			0.455514i
$178$	157.445	+	272.703i	0.0662978	+	0.114831i
$179$	583.946	−	1011.42i	0.243833	−	0.422331i	−0.717970	−	0.696074i	$-0.754928\pi$
$179$	583.946	−	1011.42i	0.243833	−	0.422331i	0.961803	+	0.273743i	$0.0882617\pi$
$180$	1616.31	+	933.179i	0.669294	+	0.386417i
$181$	1133.96			0.465673			0.232836	−	0.972516i	$-0.425199\pi$
$181$	1133.96			0.465673			0.232836	+	0.972516i	$0.425199\pi$
$182$		0			0
$183$	−2444.07			−0.987274
$184$	843.512	+	487.002i	0.337959	+	0.195121i
$185$	−38.2126	+	66.1861i	−0.0151862	+	0.0263032i
$186$	−223.068	−	386.366i	−0.0879364	−	0.152310i
$187$			1524.44i			0.596141i
$188$	2154.40	−	1243.84i	0.835776	−	0.482536i
$189$	701.511	−	405.018i	0.269986	−	0.155877i
$190$		−	630.928i		−	0.240907i
$191$	−1341.06	−	2322.78i	−0.508040	−	0.879952i	−0.999957	−	0.00930919i	$-0.997037\pi$
$191$	−1341.06	−	2322.78i	−0.508040	−	0.879952i	0.491916	−	0.870642i	$-0.336297\pi$
$192$	809.985	−	1402.93i	0.304456	−	0.527334i
$193$	1706.65	+	985.333i	0.636514	+	0.367491i	0.783270	−	0.621681i	$-0.213550\pi$
$193$	1706.65	+	985.333i	0.636514	+	0.367491i	−0.146757	+	0.989173i	$0.546883\pi$
$194$	332.943			0.123216
$195$		0			0
$196$	2447.14			0.891813
$197$	−3478.00	−	2008.02i	−1.25785	−	0.726222i	−0.285197	−	0.958469i	$-0.592059\pi$
$197$	−3478.00	−	2008.02i	−1.25785	−	0.726222i	−0.972657	+	0.232247i	$0.925392\pi$
$198$	65.9851	−	114.290i	0.0236836	−	0.0410212i
$199$	−2113.03	−	3659.87i	−0.752707	−	1.30373i	−0.946506	−	0.322685i	$-0.895415\pi$
$199$	−2113.03	−	3659.87i	−0.752707	−	1.30373i	0.193800	−	0.981041i	$-0.437919\pi$
$200$		−	1331.53i		−	0.470768i
$201$	−1356.50	+	783.177i	−0.476021	+	0.274831i
$202$	132.402	−	76.4426i	0.0461178	−	0.0266261i
$203$		−	580.245i		−	0.200617i
$204$	−977.926	−	1693.82i	−0.335630	−	0.581328i
$205$	−2028.03	+	3512.65i	−0.690944	+	1.19675i
$206$	−220.345	−	127.216i	−0.0745250	−	0.0430270i
$207$	1886.39			0.633398
$208$		0			0
$209$	1811.98			0.599699
$210$	−135.497	−	78.2292i	−0.0445247	−	0.0257063i
$211$	−682.334	+	1181.84i	−0.222625	+	0.385597i	−0.955604	−	0.294654i	$-0.904796\pi$
$211$	−682.334	+	1181.84i	−0.222625	+	0.385597i	0.732980	+	0.680251i	$0.238129\pi$
$212$	264.122	+	457.473i	0.0855659	+	0.148204i
$213$		−	563.617i		−	0.181307i
$214$	217.000	−	125.285i	0.0693168	−	0.0400201i
$215$	−424.557	+	245.118i	−0.134672	+	0.0777532i
$216$			1032.33i			0.325189i
$217$	750.928	+	1300.65i	0.234914	+	0.406883i
$218$	−38.5842	+	66.8297i	−0.0119874	+	0.0207628i
$219$	374.203	+	216.046i	0.115463	+	0.0666624i
$220$	3117.71			0.955436
$221$		0			0
$222$	−6.93332			−0.00209610
$223$	−917.527	−	529.734i	−0.275525	−	0.159075i	0.355871	−	0.934535i	$-0.384184\pi$
$223$	−917.527	−	529.734i	−0.275525	−	0.159075i	−0.631396	+	0.775461i	$0.717518\pi$
$224$	221.619	−	383.856i	0.0661052	−	0.114498i
$225$	−1289.42	−	2233.34i	−0.382050	−	0.661729i
$226$			554.584i			0.163232i
$227$	−3000.08	+	1732.10i	−0.877190	+	0.506446i	−0.869731	−	0.493526i	$-0.835708\pi$
$227$	−3000.08	+	1732.10i	−0.877190	+	0.506446i	−0.00745930	+	0.999972i	$0.502374\pi$
$228$	−2013.30	+	1162.38i	−0.584797	+	0.337633i
$229$		−	2324.64i		−	0.670815i	−0.942073	−	0.335407i	$-0.891126\pi$
$229$		−	2324.64i		−	0.670815i	0.942073	−	0.335407i	$-0.108874\pi$
$230$	−548.617	−	950.233i	−0.157282	−	0.272420i
$231$	224.668	−	389.137i	0.0639917	−	0.110837i
$232$	640.405	+	369.738i	0.181227	+	0.104631i
$233$	3731.01			1.04904			0.524521	−	0.851398i	$-0.324245\pi$
$233$	3731.01			1.04904			0.524521	+	0.851398i	$0.324245\pi$
$234$		0			0
$235$	−5673.86			−1.57499
$236$	1968.44	+	1136.48i	0.542942	+	0.313468i
$237$	373.002	−	646.058i	0.102232	−	0.177072i
$238$	−81.0540	−	140.390i	−0.0220754	−	0.0382357i
$239$		−	6044.47i		−	1.63592i	−0.575278	−	0.817958i	$-0.695106\pi$
$239$		−	6044.47i		−	1.63592i	0.575278	−	0.817958i	$-0.304894\pi$
$240$	−3376.71	+	1949.55i	−0.908191	+	0.524344i
$241$	−4480.78	+	2586.98i	−1.19765	+	0.691461i	−0.960030	−	0.279898i	$-0.909699\pi$
$241$	−4480.78	+	2586.98i	−1.19765	+	0.691461i	−0.237616	+	0.971359i	$0.576366\pi$
$242$			363.120i			0.0964556i
$243$	1667.39	+	2888.00i	0.440176	+	0.762408i
$244$	−2589.49	+	4485.12i	−0.679405	+	1.17676i
$245$	−4833.61	−	2790.68i	−1.26044	−	0.727715i
$246$	−367.967			−0.0953688
$247$		0			0
$248$	−1914.00			−0.490076
$249$	−1072.67	−	619.309i	−0.273004	−	0.157619i
$250$	−262.015	+	453.823i	−0.0662851	+	0.114809i
$251$	2810.37	+	4867.70i	0.706728	+	1.22409i	0.966064	+	0.258301i	$0.0831628\pi$
$251$	2810.37	+	4867.70i	0.706728	+	1.22409i	−0.259337	+	0.965787i	$0.583504\pi$
$252$		−	569.981i		−	0.142482i
$253$	2729.00	−	1575.59i	0.678144	−	0.391527i
$254$	−988.796	+	570.882i	−0.244262	+	0.141025i
$255$			4460.86i			1.09549i
$256$	−1573.42	−	2725.24i	−0.384135	−	0.665341i
$257$	−837.070	+	1449.85i	−0.203171	+	0.351903i	−0.949549	−	0.313620i	$-0.898458\pi$
$257$	−837.070	+	1449.85i	−0.203171	+	0.351903i	0.746377	+	0.665523i	$0.231791\pi$
$258$	−38.5160	−	22.2372i	−0.00929420	−	0.00536601i
$259$	23.3401			0.00559954
$260$		0			0
$261$	1432.17			0.339653
$262$	−809.422	−	467.320i	−0.190864	−	0.110195i
$263$	3154.59	−	5463.91i	0.739622	−	1.28106i	−0.213044	−	0.977043i	$-0.568338\pi$
$263$	3154.59	−	5463.91i	0.739622	−	1.28106i	0.952666	−	0.304020i	$-0.0983289\pi$
$264$	286.322	+	495.924i	0.0667496	+	0.115614i
$265$		−	1204.81i		−	0.279285i
$266$	−166.869	+	96.3419i	−0.0384639	+	0.0222072i
$267$	−2291.76	+	1323.15i	−0.525294	+	0.303279i
$268$			3319.09i			0.756514i
$269$	1241.37	+	2150.11i	0.281366	+	0.487340i	0.971721	−	0.236131i	$-0.0758793\pi$
$269$	1241.37	+	2150.11i	0.281366	+	0.487340i	−0.690356	+	0.723470i	$0.742546\pi$
$270$	581.468	−	1007.13i	0.131063	−	0.227008i
$271$	−2455.81	−	1417.86i	−0.550478	−	0.317819i	0.198837	−	0.980033i	$-0.436284\pi$
$271$	−2455.81	−	1417.86i	−0.550478	−	0.317819i	−0.749315	+	0.662214i	$0.769617\pi$
$272$	−4039.88			−0.900566
$273$		0			0
$274$	−301.645			−0.0665075
$275$	−3730.74	−	2153.94i	−0.818080	−	0.472318i
$276$	−2021.47	+	3501.28i	−0.440863	+	0.763596i
$277$	−1918.76	−	3323.38i	−0.416198	−	0.720876i	0.579355	−	0.815075i	$-0.303304\pi$
$277$	−1918.76	−	3323.38i	−0.416198	−	0.720876i	−0.995553	+	0.0941989i	$0.969971\pi$
$278$		−	297.960i		−	0.0642822i
$279$	−3210.28	+	1853.46i	−0.688869	+	0.397719i
$280$	−581.303	+	335.616i	−0.124070	+	0.0716317i
$281$		−	9122.13i		−	1.93659i	−0.249819	−	0.968293i	$-0.580371\pi$
$281$		−	9122.13i		−	1.93659i	0.249819	−	0.968293i	$-0.419629\pi$
$282$	−257.368	−	445.774i	−0.0543476	−	0.0941328i
$283$	1063.92	−	1842.77i	0.223476	−	0.387072i	−0.732385	−	0.680891i	$-0.761593\pi$
$283$	1063.92	−	1842.77i	0.223476	−	0.387072i	0.955861	+	0.293819i	$0.0949262\pi$
$284$	−1034.29	−	597.150i	−0.216106	−	0.124769i
$285$	5302.24			1.10203
$286$		0			0
$287$	1238.71			0.254769
$288$	947.441	+	547.005i	0.193849	+	0.111919i
$289$	145.530	−	252.066i	0.0296215	−	0.0513059i
$290$	−416.518	−	721.430i	−0.0843405	−	0.146082i
$291$			2798.01i			0.563651i
$292$	792.934	−	457.800i	0.158914	−	0.0917491i
$293$	7166.16	−	4137.38i	1.42884	−	0.824944i	0.431815	−	0.901962i	$-0.357873\pi$
$293$	7166.16	−	4137.38i	1.42884	−	0.824944i	0.997030	+	0.0770183i	$0.0245400\pi$
$294$		−	506.344i		−	0.100444i
$295$	−2592.05	−	4489.56i	−0.511576	−	0.886076i
$296$	−14.8725	+	25.7600i	−0.00292043	+	0.00505834i
$297$	2892.40	+	1669.93i	0.565099	+	0.326260i
$298$	−866.136			−0.168369
$299$		0			0
$300$	5526.99			1.06367
$301$	129.659	+	74.8585i	0.0248286	+	0.0143348i
$302$	395.312	−	684.701i	0.0753234	−	0.130464i
$303$	642.414	+	1112.69i	0.121801	+	0.210966i
$304$			4801.86i			0.905940i
$305$	10229.6	−	5906.04i	1.92047	−	1.10878i
$306$	346.513	−	200.059i	0.0647347	−	0.0373746i
$307$		−	3610.49i		−	0.671211i	−0.942003	−	0.335605i	$-0.891059\pi$
$307$		−	3610.49i		−	0.671211i	0.942003	−	0.335605i	$-0.108941\pi$
$308$	−476.070	−	824.578i	−0.0880734	−	0.152548i
$309$	1069.11	−	1851.75i	0.196827	−	0.340914i
$310$	1867.29	+	1078.08i	0.342112	+	0.197518i
$311$	−3331.06			−0.607354			−0.303677	−	0.952775i	$-0.598214\pi$
$311$	−3331.06			−0.607354			−0.303677	+	0.952775i	$0.598214\pi$
$312$		0			0
$313$	−358.125			−0.0646724			−0.0323362	−	0.999477i	$-0.510295\pi$
$313$	−358.125			−0.0646724			−0.0323362	+	0.999477i	$0.510295\pi$
$314$	150.807	+	87.0685i	0.0271036	+	0.0156483i
$315$	−650.000	+	1125.83i	−0.116265	+	0.201376i
$316$	−790.388	−	1368.99i	−0.140705	−	0.243708i
$317$		−	3047.46i		−	0.539944i	−0.962868	−	0.269972i	$-0.912986\pi$
$317$		−	3047.46i		−	0.539944i	0.962868	−	0.269972i	$-0.0870144\pi$
$318$	94.6570	−	54.6503i	0.0166921	−	0.00963721i
$319$	2071.89	−	1196.21i	0.363647	−	0.209952i
$320$			7829.23i			1.36771i
$321$	1052.88	+	1823.64i	0.183072	+	0.317089i
$322$	−167.546	+	290.199i	−0.0289969	+	0.0502241i
$323$	4757.69	+	2746.85i	0.819581	+	0.473185i
$324$	−1455.26			−0.249530
$325$		0			0
$326$	−412.751			−0.0701232
$327$	−561.629	−	324.257i	−0.0949791	−	0.0548362i
$328$	−789.318	+	1367.14i	−0.132874	+	0.230145i
$329$	866.392	+	1500.63i	0.145185	+	0.251467i
$330$		−	645.094i		−	0.107610i
$331$	−6663.87	+	3847.39i	−1.10658	+	0.638887i	−0.937942	−	0.346791i	$-0.887271\pi$
$331$	−6663.87	+	3847.39i	−1.10658	+	0.638887i	−0.168641	+	0.985677i	$0.553938\pi$
$332$	−2272.99	+	1312.31i	−0.375742	+	0.216935i
$333$			57.6084i			0.00948025i
$334$	806.838	+	1397.48i	0.132180	+	0.228943i
$335$	3785.05	−	6555.90i	0.617312	−	1.06922i
$336$	1031.24	+	595.386i	0.167437	+	0.0966696i
$337$	−4712.21			−0.761693			−0.380846	−	0.924638i	$-0.624367\pi$
$337$	−4712.21			−0.761693			−0.380846	+	0.924638i	$0.624367\pi$
$338$		0			0
$339$	−4660.66			−0.746703
$340$	8186.13	+	4726.27i	1.30575	+	0.753876i
$341$	−3096.16	+	5362.70i	−0.491690	+	0.851632i
$342$	−237.793	−	411.870i	−0.0375976	−	0.0651210i
$343$			3569.92i			0.561976i
$344$	−165.240	+	95.4013i	−0.0258986	+	0.0149526i
$345$	7985.65	−	4610.52i	1.24618	−	0.719484i
$346$		−	623.811i		−	0.0969257i
$347$	2630.99	+	4557.01i	0.407029	+	0.704995i	0.994555	−	0.104210i	$-0.0332315\pi$
$347$	2630.99	+	4557.01i	0.407029	+	0.704995i	−0.587526	+	0.809205i	$0.699898\pi$
$348$	−1534.72	+	2658.22i	−0.236408	+	0.409470i
$349$	−43.5909	−	25.1672i	−0.00668587	−	0.00386009i	0.496653	−	0.867949i	$-0.334562\pi$
$349$	−43.5909	−	25.1672i	−0.00668587	−	0.00386009i	−0.503339	+	0.864089i	$0.667895\pi$
$350$	458.096			0.0699608
$351$		0			0
$352$	1827.52			0.276725
$353$	7844.14	+	4528.82i	1.18272	+	0.682846i	0.956643	−	0.291263i	$-0.0940753\pi$
$353$	7844.14	+	4528.82i	1.18272	+	0.682846i	0.226081	+	0.974109i	$0.427409\pi$
$354$	235.152	−	407.295i	0.0353056	−	0.0611511i
$355$	1361.96	+	2358.99i	0.203621	+	0.352683i
$356$			5607.49i			0.834821i
$357$	1179.82	−	681.168i	0.174909	−	0.100984i
$358$	−443.456	+	256.029i	−0.0654675	+	0.0377977i
$359$			7177.86i			1.05525i	0.849479	+	0.527623i	$0.176917\pi$
$359$			7177.86i			1.05525i	−0.849479	+	0.527623i	$0.823083\pi$
$360$	−828.373	−	1434.78i	−0.121275	−	0.210055i
$361$	−164.553	+	285.014i	−0.0239908	+	0.0415532i
$362$	−430.573	−	248.591i	−0.0625150	−	0.0360930i
$363$	−3051.62			−0.441235
$364$		0			0
$365$	−2088.28			−0.299467
$366$	928.030	+	535.798i	0.132538	+	0.0765209i
$367$	−2002.07	+	3467.69i	−0.284761	+	0.493221i	−0.972551	−	0.232689i	$-0.925248\pi$
$367$	−2002.07	+	3467.69i	−0.284761	+	0.493221i	0.687790	+	0.725910i	$0.258581\pi$
$368$	4175.41	+	7232.03i	0.591463	+	1.02444i
$369$			3057.41i			0.431334i
$370$	29.0191	−	16.7542i	0.00407738	−	0.00235408i
$371$	−318.649	+	183.972i	−0.0445915	+	0.0257449i
$372$		−	7944.70i		−	1.10729i
$373$	5007.09	+	8672.53i	0.695060	+	1.20388i	0.970161	+	0.242464i	$0.0779555\pi$
$373$	5007.09	+	8672.53i	0.695060	+	1.20388i	−0.275101	+	0.961415i	$0.588711\pi$
$374$	334.194	−	578.841i	0.0462053	−	0.0800299i
$375$	−3813.87	−	2201.94i	−0.525194	−	0.303221i
$376$	−2208.30			−0.302883
$377$		0			0
$378$	−355.158			−0.0483263
$379$	−7074.66	−	4084.56i	−0.958842	−	0.553587i	−0.0630252	−	0.998012i	$-0.520075\pi$
$379$	−7074.66	−	4084.56i	−0.958842	−	0.553587i	−0.895816	+	0.444425i	$0.853408\pi$
$380$	5617.71	−	9730.16i	0.758375	−	1.31354i
$381$	−4797.62	−	8309.73i	−0.645117	−	1.11738i
$382$			1175.97i			0.157507i
$383$	6330.86	−	3655.12i	0.844626	−	0.487645i	−0.0142079	−	0.999899i	$-0.504523\pi$
$383$	6330.86	−	3655.12i	0.844626	−	0.487645i	0.858834	+	0.512254i	$0.171189\pi$
$384$	−2695.67	+	1556.35i	−0.358237	+	0.206828i
$385$			2171.62i			0.287470i
$386$	−432.017	−	748.275i	−0.0569665	−	0.0986689i
$387$	−184.767	+	320.027i	−0.0242694	+	0.0420358i
$388$	5134.64	+	2964.48i	0.671834	+	0.387884i
$389$	−8785.47			−1.14509			−0.572546	−	0.819872i	$-0.694044\pi$
$389$	−8785.47			−1.14509			−0.572546	+	0.819872i	$0.694044\pi$
$390$		0			0
$391$	9553.99			1.23572
$392$	−1881.26	−	1086.15i	−0.242393	−	0.139946i
$393$	3927.30	−	6802.29i	0.504087	−	0.873104i
$394$	880.412	+	1524.92i	0.112575	+	0.194986i
$395$			3605.40i			0.459259i
$396$	2035.24	−	1175.05i	0.258269	−	0.149112i
$397$	9757.33	−	5633.40i	1.23352	−	0.712171i	0.265756	−	0.964040i	$-0.414379\pi$
$397$	9757.33	−	5633.40i	1.23352	−	0.712171i	0.967761	+	0.251869i	$0.0810452\pi$
$398$			1852.90i			0.233361i
$399$	−809.646	−	1402.35i	−0.101586	−	0.175953i
$400$	5708.10	−	9886.71i	0.713512	−	1.23584i
$401$	−1365.06	−	788.117i	−0.169995	−	0.0981464i	0.412589	−	0.910917i	$-0.364625\pi$
$401$	−1365.06	−	788.117i	−0.169995	−	0.0981464i	−0.582583	+	0.812771i	$0.697958\pi$
$402$	686.763			0.0852055
$403$		0			0
$404$	2722.54			0.335276
$405$	2874.45	+	1659.56i	0.352672	+	0.203616i
$406$	−127.203	+	220.323i	−0.0155493	+	0.0269321i
$407$	48.1168	+	83.3407i	0.00586010	+	0.0101500i
$408$			1736.19i			0.210672i
$409$	−5850.68	+	3377.89i	−0.707329	+	0.408377i	−0.810071	−	0.586331i	$-0.800572\pi$
$409$	−5850.68	+	3377.89i	−0.707329	+	0.408377i	0.102742	+	0.994708i	$0.467238\pi$
$410$	1540.11	−	889.183i	0.185514	−	0.107106i
$411$		−	2534.99i		−	0.304238i
$412$	−2265.43	−	3923.85i	−0.270898	−	0.469209i
$413$	−791.606	+	1371.10i	−0.0943157	+	0.163360i
$414$	−716.275	−	413.542i	−0.0850314	−	0.0490929i
$415$	5986.17			0.708072
$416$		0			0
$417$	2504.02			0.294059
$418$	−688.019	−	397.228i	−0.0805074	−	0.0464810i
$419$	−5378.09	+	9315.13i	−0.627057	+	1.08610i	0.361082	+	0.932534i	$0.382408\pi$
$419$	−5378.09	+	9315.13i	−0.627057	+	1.08610i	−0.988139	+	0.153561i	$0.950926\pi$
$420$	−1393.09	−	2412.90i	−0.161847	−	0.280327i
$421$		−	7886.03i		−	0.912925i	−0.889743	−	0.456463i	$-0.849116\pi$
$421$		−	7886.03i		−	0.912925i	0.889743	−	0.456463i	$-0.150884\pi$
$422$	518.173	−	299.167i	0.0597731	−	0.0345100i
$423$	−3703.90	+	2138.45i	−0.425744	+	0.245803i
$424$		−	468.916i		−	0.0537089i
$425$	−6530.50	−	11311.2i	−0.745355	−	1.29099i
$426$	−123.558	+	214.009i	−0.0140526	+	0.0243398i
$427$	−3124.08	−	1803.69i	−0.354063	−	0.204418i
$428$	4462.08			0.503932
$429$		0			0
$430$	214.943			0.0241057
$431$	−12197.6	−	7042.31i	−1.36320	−	0.787044i	−0.373152	−	0.927770i	$-0.621723\pi$
$431$	−12197.6	−	7042.31i	−1.36320	−	0.787044i	−0.990049	+	0.140726i	$0.955056\pi$
$432$	−4425.43	+	7665.07i	−0.492867	+	0.853671i
$433$	932.072	+	1614.40i	0.103447	+	0.179175i	0.913103	−	0.407730i	$-0.133679\pi$
$433$	932.072	+	1614.40i	0.103447	+	0.179175i	−0.809656	+	0.586905i	$0.800346\pi$
$434$		−	658.485i		−	0.0728301i
$435$	6062.81	−	3500.36i	0.668252	−	0.385815i
$436$	−1190.09	+	687.098i	−0.130722	+	0.0754725i
$437$		−	11356.0i		−	1.24309i
$438$	−94.7249	−	164.068i	−0.0103336	−	0.0178984i
$439$	3077.24	−	5329.94i	0.334553	−	0.579463i	−0.648846	−	0.760920i	$-0.724748\pi$
$439$	3077.24	−	5329.94i	0.334553	−	0.579463i	0.983399	+	0.181457i	$0.0580813\pi$
$440$	−2396.77	−	1383.78i	−0.259686	−	0.149930i
$441$	−4207.17			−0.454289
$442$		0			0
$443$	−14539.3			−1.55933			−0.779663	−	0.626200i	$-0.784609\pi$
$443$	−14539.3			−1.55933			−0.779663	+	0.626200i	$0.784609\pi$
$444$	−106.926	−	61.7335i	−0.0114290	−	0.00659852i
$445$	6394.72	−	11076.0i	0.681210	−	1.17989i
$446$	232.261	+	402.287i	0.0246589	+	0.0427104i
$447$		−	7278.90i		−	0.770202i
$448$	2070.69	−	1195.51i	0.218373	−	0.126077i
$449$	−6100.17	+	3521.93i	−0.641169	+	0.370179i	−0.785065	−	0.619414i	$-0.787370\pi$
$449$	−6100.17	+	3521.93i	−0.641169	+	0.370179i	0.143896	+	0.989593i	$0.454037\pi$
$450$			1130.68i			0.118446i
$451$	2553.66	+	4423.08i	0.266624	+	0.461806i
$452$	−4937.95	+	8552.78i	−0.513853	+	0.890020i
$453$	5754.15	+	3322.16i	0.596807	+	0.344567i
$454$	1518.87			0.157013
$455$		0			0
$456$	2063.66			0.211929
$457$	12210.0	+	7049.43i	1.24980	+	0.721572i	0.971069	−	0.238798i	$-0.0767533\pi$
$457$	12210.0	+	7049.43i	1.24980	+	0.721572i	0.278730	+	0.960370i	$0.410087\pi$
$458$	−509.616	+	882.681i	−0.0519930	+	0.0900545i
$459$	5063.04	+	8769.44i	0.514863	+	0.891770i
$460$		−	19539.3i		−	1.98049i
$461$	−12513.8	+	7224.85i	−1.26426	+	0.729924i	−0.973897	−	0.226991i	$-0.927111\pi$
$461$	−12513.8	+	7224.85i	−1.26426	+	0.729924i	−0.290368	+	0.956915i	$0.593778\pi$
$462$	−170.616	+	98.5051i	−0.0171813	+	0.00991964i
$463$			15806.5i			1.58659i	0.608840	+	0.793293i	$0.291635\pi$
$463$			15806.5i			1.58659i	−0.608840	+	0.793293i	$0.708365\pi$
$464$	3170.03	+	5490.65i	0.317166	+	0.549347i
$465$	−9060.04	+	15692.4i	−0.903547	+	1.56499i
$466$	−1416.69	−	817.926i	−0.140830	−	0.0813083i
$467$	15071.3			1.49340			0.746699	−	0.665162i	$-0.231638\pi$
$467$	15071.3			1.49340			0.746699	+	0.665162i	$0.231638\pi$
$468$		0			0
$469$	−2311.89			−0.227619
$470$	2154.40	+	1243.84i	0.211437	+	0.122073i
$471$	−731.713	+	1267.36i	−0.0715830	+	0.123985i
$472$	−1008.84	−	1747.36i	−0.0983804	−	0.170400i
$473$			617.299i			0.0600073i
$474$	−283.262	+	163.542i	−0.0274487	+	0.0158475i
$475$	−13444.6	+	7762.25i	−1.29870	+	0.749803i
$476$		−	2886.78i		−	0.277973i
$477$	−454.085	−	786.498i	−0.0435872	−	0.0754953i
$478$	−1325.09	+	2295.12i	−0.126795	+	0.219616i
$479$	339.954	+	196.272i	0.0324277	+	0.0187222i	0.516126	−	0.856513i	$-0.327374\pi$
$479$	339.954	+	196.272i	0.0324277	+	0.0187222i	−0.483698	+	0.875235i	$0.660707\pi$
$480$	5347.73			0.508519
$481$		0			0
$482$	2268.51			0.214373
$483$	−2438.80	−	1408.04i	−0.229750	−	0.132646i
$484$	−3233.18	+	5600.03i	−0.303642	+	0.525923i
$485$	−6761.33	−	11711.0i	−0.633023	−	1.09643i
$486$		−	1462.12i		−	0.136467i
$487$	−8225.41	+	4748.94i	−0.765357	+	0.441879i	−0.831216	−	0.555950i	$-0.812355\pi$
$487$	−8225.41	+	4748.94i	−0.765357	+	0.441879i	0.0658588	+	0.997829i	$0.479021\pi$
$488$	3981.40	−	2298.66i	0.369322	−	0.213228i
$489$		−	3468.71i		−	0.320778i
$490$	1223.57	+	2119.28i	0.112806	+	0.195386i
$491$	−946.912	+	1640.10i	−0.0870337	+	0.150747i	−0.906256	−	0.422729i	$-0.861072\pi$
$491$	−946.912	+	1640.10i	−0.0870337	+	0.150747i	0.819222	+	0.573476i	$0.194405\pi$
$492$	−5674.78	−	3276.34i	−0.519998	−	0.300221i
$493$	7253.52			0.662641
$494$		0			0
$495$	−5360.04			−0.486699
$496$	−14211.5	−	8205.03i	−1.28652	−	0.742775i
$497$	415.941	−	720.430i	0.0375402	−	0.0650216i
$498$	271.534	+	470.311i	0.0244332	+	0.0423196i
$499$			13370.1i			1.19945i	0.800205	+	0.599727i	$0.204724\pi$
$499$			13370.1i			1.19945i	−0.800205	+	0.599727i	$0.795276\pi$
$500$	−8081.57	+	4665.90i	−0.722838	+	0.417330i
$501$	−11744.3	+	6780.57i	−1.04730	+	0.604658i
$502$		−	2464.39i		−	0.219106i
$503$	−2777.36	−	4810.52i	−0.246195	−	0.426423i	0.716272	−	0.697822i	$-0.245847\pi$
$503$	−2777.36	−	4810.52i	−0.246195	−	0.426423i	−0.962467	+	0.271399i	$0.912514\pi$
$504$	−252.983	+	438.180i	−0.0223587	+	0.0387263i
$505$	−5377.60	−	3104.76i	−0.473861	−	0.273584i
$506$	−1381.62			−0.121385
$507$		0			0
$508$	−20332.3			−1.77578
$509$	1903.13	+	1098.78i	0.165727	+	0.0956824i	0.580569	−	0.814211i	$-0.302830\pi$
$509$	1903.13	+	1098.78i	0.165727	+	0.0956824i	−0.414843	+	0.909893i	$0.636163\pi$
$510$	977.926	−	1693.82i	0.0849084	−	0.147066i
$511$	318.878	+	552.313i	0.0276053	+	0.0478139i
$512$			8137.89i			0.702437i
$513$	10423.5	−	6018.00i	0.897091	−	0.517936i
$514$	635.682	−	367.011i	0.0545500	−	0.0314945i
$515$			10333.9i			0.884206i
$516$	−395.996	−	685.884i	−0.0337844	−	0.0585162i
$517$	−3572.23	+	6187.28i	−0.303881	+	0.526337i
$518$	−8.86237	−	5.11669i	−0.000751718	−	0.000434005i
$519$	5242.44			0.443386
$520$		0			0
$521$	17005.2			1.42997			0.714983	−	0.699142i	$-0.246435\pi$
$521$	17005.2			1.42997			0.714983	+	0.699142i	$0.246435\pi$
$522$	−543.805	−	313.966i	−0.0455972	−	0.0263255i
$523$	7243.11	−	12545.4i	0.605581	−	1.04890i	−0.386378	−	0.922341i	$-0.626274\pi$
$523$	7243.11	−	12545.4i	0.605581	−	1.04890i	0.991959	−	0.126557i	$-0.0403928\pi$
$524$	−8321.92	−	14414.0i	−0.693788	−	1.20168i
$525$			3849.79i			0.320035i
$526$	−2395.64	+	1383.12i	−0.198583	+	0.114652i
$527$	−16259.1	+	9387.19i	−1.34394	+	0.775925i
$528$			4909.68i			0.404671i
$529$	−3791.02	−	6566.23i	−0.311582	−	0.539675i
$530$	−264.122	+	457.473i	−0.0216466	+	0.0374931i
$531$	−3384.18	−	1953.86i	−0.276574	−	0.159680i
$532$	−3431.27			−0.279632
$533$		0			0
$534$	1160.26			0.0940252
$535$	−8813.56	−	5088.51i	−0.712230	−	0.411206i
$536$	1473.16	−	2551.59i	0.118714	−	0.205619i
$537$	−2151.64	−	3726.75i	−0.172905	−	0.299481i
$538$		−	1088.55i		−	0.0872315i
$539$	−6086.41	+	3513.99i	−0.486383	+	0.280813i
$540$	17934.8	−	10354.6i	1.42924	−	0.825172i
$541$		−	15266.7i		−	1.21325i	−0.794990	−	0.606623i	$-0.792524\pi$
$541$		−	15266.7i		−	1.21325i	0.794990	−	0.606623i	$-0.207476\pi$
$542$	621.657	+	1076.74i	0.0492665	+	0.0853321i
$543$	2089.13	−	3618.48i	0.165107	−	0.285974i
$544$	4798.50	+	2770.41i	0.378187	+	0.218347i
$545$	3134.23			0.246341
$546$		0			0
$547$	15260.5			1.19286			0.596430	−	0.802665i	$-0.296586\pi$
$547$	15260.5			1.19286			0.596430	+	0.802665i	$0.296586\pi$
$548$	−4651.96	−	2685.81i	−0.362631	−	0.209365i
$549$	4451.91	−	7710.93i	0.346089	−	0.599443i
$550$	944.390	+	1635.73i	0.0732162	+	0.126814i
$551$		−	8621.64i		−	0.666595i
$552$	3108.05	−	1794.44i	0.239651	−	0.138363i
$553$	953.563	−	550.540i	0.0733266	−	0.0423351i
$554$			1682.55i			0.129033i
$555$	140.800	+	243.873i	0.0107687	+	0.0186520i
$556$	2653.00	−	4595.13i	0.202360	−	0.350498i
$557$	9043.12	+	5221.05i	0.687916	+	0.397169i	0.802831	−	0.596207i	$-0.203326\pi$
$557$	9043.12	+	5221.05i	0.687916	+	0.397169i	−0.114915	+	0.993375i	$0.536659\pi$
$558$	1625.29			0.123304
$559$		0			0
$560$	−5754.94			−0.434269
$561$	4864.51	+	2808.53i	0.366096	+	0.211366i
$562$	−1999.79	+	3463.73i	−0.150099	+	0.259980i
$563$	3572.63	+	6187.98i	0.267440	+	0.463219i	0.968200	−	0.250178i	$-0.0804891\pi$
$563$	3572.63	+	6187.98i	0.267440	+	0.463219i	−0.700760	+	0.713397i	$0.747156\pi$
$564$		−	9166.29i		−	0.684344i
$565$	19507.0	−	11262.4i	1.45250	−	0.838604i
$566$	−807.958	+	466.475i	−0.0600018	+	0.0346420i
$567$		−	1013.65i		−	0.0750783i
$568$	530.083	+	918.131i	0.0391581	+	0.0678238i
$569$	2219.43	−	3844.17i	0.163521	−	0.283226i	−0.772608	−	0.634883i	$-0.781048\pi$
$569$	2219.43	−	3844.17i	0.163521	−	0.283226i	0.936129	+	0.351657i	$0.114382\pi$
$570$	−2013.30	−	1162.38i	−0.147943	−	0.0854151i
$571$	−10117.3			−0.741497			−0.370748	−	0.928733i	$-0.620899\pi$
$571$	−10117.3			−0.741497			−0.370748	+	0.928733i	$0.620899\pi$
$572$		0			0
$573$	−9882.70			−0.720516
$574$	−470.346	−	271.554i	−0.0342018	−	0.0197464i
$575$	−13499.2	+	23381.3i	−0.979052	+	1.69577i
$576$	2950.79	+	5110.92i	0.213454	+	0.369714i
$577$		−	3105.60i		−	0.224069i	−0.993704	−	0.112035i	$-0.964263\pi$
$577$		−	3105.60i		−	0.224069i	0.993704	−	0.112035i	$-0.0357368\pi$
$578$	−110.518	+	63.8074i	−0.00795316	+	0.00459176i
$579$	6288.41	−	3630.62i	0.451360	−	0.260593i
$580$		−	14834.5i		−	1.06202i
$581$	−914.081	−	1583.24i	−0.0652711	−	0.113053i
$582$	613.390	−	1062.42i	0.0436870	−	0.0756682i
$583$	−1313.83	−	758.538i	−0.0933329	−	0.0538858i
$584$	−812.769			−0.0575901
$585$		0			0
$586$	−3628.05			−0.255757
$587$	17028.1	+	9831.16i	1.19731	+	0.691270i	0.959956	−	0.280152i	$-0.0903848\pi$
$587$	17028.1	+	9831.16i	1.19731	+	0.691270i	0.237359	+	0.971422i	$0.423718\pi$
$588$	4508.43	−	7808.83i	0.316198	−	0.547671i
$589$	11157.7	+	19325.8i	0.780555	+	1.35196i
$590$			2272.95i			0.158603i
$591$	−12815.2	+	7398.88i	−0.891960	+	0.514974i
$592$	−220.859	+	127.513i	−0.0153332	+	0.00885261i
$593$			6395.51i			0.442888i	0.975173	+	0.221444i	$0.0710769\pi$
$593$			6395.51i			0.442888i	−0.975173	+	0.221444i	$0.928923\pi$
$594$	−732.176	−	1268.17i	−0.0505750	−	0.0875985i
$595$	−3292.05	+	5702.00i	−0.226825	+	0.392872i
$596$	−13357.5	−	7711.97i	−0.918029	−	0.530025i
$597$	−15571.6			−1.06751
$598$		0			0
$599$	8878.48			0.605618			0.302809	−	0.953051i	$-0.402076\pi$
$599$	8878.48			0.605618			0.302809	+	0.953051i	$0.402076\pi$
$600$	−4248.94	−	2453.12i	−0.289103	−	0.166914i
$601$	−9550.29	+	16541.6i	−0.648194	+	1.12270i	0.335360	+	0.942090i	$0.391142\pi$
$601$	−9550.29	+	16541.6i	−0.648194	+	1.12270i	−0.983554	+	0.180615i	$0.942191\pi$
$602$	−32.8215	−	56.8485i	−0.00222210	−	0.00384879i
$603$		−	5706.26i		−	0.385368i
$604$	12193.0	−	7039.63i	0.821401	−	0.474236i
$605$	12772.4	−	7374.16i	0.858302	−	0.495541i
$606$		−	563.330i		−	0.0377619i
$607$	−8297.88	−	14372.4i	−0.554861	−	0.961047i	−0.997914	−	0.0645522i	$-0.979438\pi$
$607$	−8297.88	−	14372.4i	−0.554861	−	0.961047i	0.443053	−	0.896495i	$-0.353895\pi$
$608$	3292.95	−	5703.56i	0.219650	−	0.380444i
$609$	−1851.57	−	1069.00i	−0.123201	−	0.0711300i
$610$	−5178.97			−0.343755
$611$		0			0
$612$	7125.21			0.470620
$613$	14262.7	+	8234.58i	0.939748	+	0.542564i	0.889881	−	0.456192i	$-0.150787\pi$
$613$	14262.7	+	8234.58i	0.939748	+	0.542564i	0.0498668	+	0.998756i	$0.484120\pi$
$614$	−791.505	+	1370.93i	−0.0520237	+	0.0901077i
$615$	7472.59	+	12942.9i	0.489958	+	0.848631i
$616$			845.205i			0.0552829i
$617$	−8760.69	+	5057.99i	−0.571624	+	0.330027i	−0.757798	−	0.652489i	$-0.773725\pi$
$617$	−8760.69	+	5057.99i	−0.571624	+	0.330027i	0.186174	+	0.982517i	$0.440391\pi$
$618$	−811.895	+	468.748i	−0.0528466	+	0.0305110i
$619$			18854.8i			1.22430i	0.790743	+	0.612148i	$0.209694\pi$
$619$			18854.8i			1.22430i	−0.790743	+	0.612148i	$0.790306\pi$
$620$	19198.2	+	33252.2i	1.24357	+	2.15393i
$621$	10465.8	−	18127.3i	0.676292	−	1.17137i
$622$	1264.83	+	730.247i	0.0815352	+	0.0470743i
$623$	−3905.86			−0.251180
$624$		0			0
$625$	−2730.82			−0.174773
$626$	135.983	+	78.5095i	0.00868204	+	0.00501258i
$627$	3338.26	−	5782.03i	0.212627	−	0.368281i
$628$	1550.50	+	2685.54i	0.0985215	+	0.170644i
$629$			291.769i			0.0184954i
$630$	493.618	−	284.991i	0.0312162	−	0.0180227i
$631$	16407.9	−	9473.12i	1.03517	−	0.597653i	0.116705	−	0.993167i	$-0.462767\pi$
$631$	16407.9	−	9473.12i	1.03517	−	0.597653i	0.918460	+	0.395514i	$0.129433\pi$
$632$			1403.24i			0.0883194i
$633$	2514.17	+	4354.66i	0.157866	+	0.273432i
$634$	−668.074	+	1157.14i	−0.0418496	+	0.0724856i
$635$	40160.5	+	23186.7i	2.50979	+	1.44903i
$636$	1946.40			0.121352
$637$		0			0
$638$	−1048.95			−0.0650912
$639$	1778.18	+	1026.63i	0.110084	+	0.0635571i
$640$	7521.75	−	13028.1i	0.464568	−	0.804655i
$641$	−11793.5	−	20426.9i	−0.726698	−	1.25868i	−0.958271	−	0.285861i	$-0.907721\pi$
$641$	−11793.5	−	20426.9i	−0.726698	−	1.25868i	0.231573	−	0.972818i	$-0.425613\pi$
$642$		−	923.263i		−	0.0567575i
$643$	23515.2	−	13576.5i	1.44222	−	0.832669i	0.444226	−	0.895915i	$-0.353479\pi$
$643$	23515.2	−	13576.5i	1.44222	−	0.832669i	0.997998	+	0.0632461i	$0.0201453\pi$
$644$	−5167.79	+	2983.63i	−0.316211	+	0.182564i
$645$			1806.35i			0.110272i
$646$	−1204.35	−	2085.99i	−0.0733506	−	0.127047i
$647$	3428.36	−	5938.09i	0.208319	−	0.360820i	−0.742866	−	0.669440i	$-0.766534\pi$
$647$	3428.36	−	5938.09i	0.208319	−	0.360820i	0.951185	+	0.308620i	$0.0998673\pi$
$648$	1118.75	+	645.910i	0.0678219	+	0.0391570i
$649$	−6527.75			−0.394817
$650$		0			0
$651$	5533.83			0.333161
$652$	−6365.44	−	3675.09i	−0.382346	−	0.220748i
$653$	4036.95	−	6992.20i	0.241926	−	0.419029i	−0.719337	−	0.694662i	$-0.755554\pi$
$653$	4036.95	−	6992.20i	0.241926	−	0.419029i	0.961263	+	0.275633i	$0.0888874\pi$
$654$	142.169	+	246.245i	0.00850041	+	0.0147231i
$655$			37960.9i			2.26451i
$656$	−11721.5	+	6767.39i	−0.697632	+	0.402778i
$657$	−1363.23	+	787.061i	−0.0809508	+	0.0467370i
$658$		−	759.734i		−	0.0450114i
$659$	−2652.86	−	4594.89i	−0.156815	−	0.271611i	0.776904	−	0.629620i	$-0.216789\pi$
$659$	−2652.86	−	4594.89i	−0.156815	−	0.271611i	−0.933718	+	0.358008i	$0.883456\pi$
$660$	5743.84	−	9948.63i	0.338756	−	0.586742i
$661$	−22385.3	−	12924.2i	−1.31723	−	0.760502i	−0.333946	−	0.942592i	$-0.608380\pi$
$661$	−22385.3	−	12924.2i	−1.31723	−	0.760502i	−0.983282	+	0.182091i	$0.941714\pi$
$662$	3373.75			0.198073
$663$		0			0
$664$	2329.85			0.136168
$665$	6777.48	+	3912.98i	0.395217	+	0.228179i
$666$	12.6291	−	21.8743i	0.000734788	−	0.00127269i
$667$	−7496.86	−	12984.9i	−0.435202	−	0.753792i
$668$			28735.9i			1.66441i
$669$	−3380.77	+	1951.89i	−0.195379	+	0.112802i
$670$	−2874.42	+	1659.55i	−0.165744	+	0.0956923i
$671$		−	14873.6i		−	0.855722i
$672$	−816.591	−	1414.38i	−0.0468760	−	0.0811917i
$673$	−7264.55	+	12582.6i	−0.416089	+	0.720687i	−0.995542	−	0.0943186i	$-0.969933\pi$
$673$	−7264.55	+	12582.6i	−0.416089	+	0.720687i	0.579453	+	0.815005i	$0.303266\pi$
$674$	1789.26	+	1033.03i	0.102255	+	0.0590367i
$675$	−28615.0			−1.63169
$676$		0			0
$677$	12058.1			0.684535			0.342267	−	0.939603i	$-0.388805\pi$
$677$	12058.1			0.684535			0.342267	+	0.939603i	$0.388805\pi$
$678$	1769.68	+	1021.73i	0.100242	+	0.0578749i
$679$	−2064.89	+	3576.50i	−0.116706	+	0.202140i
$680$	−4195.46	−	7266.74i	−0.236601	−	0.409804i
$681$			12764.4i			0.718255i
$682$	2351.26	−	1357.50i	0.132015	−	0.0762190i
$683$	26005.7	−	15014.4i	1.45693	−	0.841156i	0.458067	−	0.888918i	$-0.348542\pi$
$683$	26005.7	−	15014.4i	1.45693	−	0.841156i	0.998859	+	0.0477615i	$0.0152087\pi$
$684$		−	8469.13i		−	0.473429i
$685$	6125.74	+	10610.1i	0.341682	+	0.591811i
$686$	782.611	−	1355.52i	0.0435572	−	0.0754433i
$687$	−7417.94	−	4282.75i	−0.411954	−	0.237842i
$688$	−1635.89			−0.0906505
$689$		0			0
$690$	−4042.94			−0.223061
$691$	389.448	+	224.848i	0.0214404	+	0.0123786i	0.510682	−	0.859770i	$-0.329393\pi$
$691$	389.448	+	224.848i	0.0214404	+	0.0123786i	−0.489241	+	0.872148i	$0.662726\pi$
$692$	5554.34	−	9620.40i	0.305122	−	0.528487i
$693$	818.471	+	1417.63i	0.0448646	+	0.0777077i
$694$		−	2307.10i		−	0.126191i
$695$	−10480.5	+	6050.90i	−0.572010	+	0.330250i
$696$	2359.68	−	1362.36i	0.128510	−	0.0741955i
$697$			15484.8i			0.841506i
$698$	11.0345	+	19.1123i	0.000598370	+	0.00103641i
$699$	6873.75	−	11905.7i	0.371944	−	0.644227i
$700$	7064.75	+	4078.84i	0.381461	+	0.220236i
$701$	26986.0			1.45399			0.726994	−	0.686644i	$-0.240917\pi$
$701$	26986.0			1.45399			0.726994	+	0.686644i	$0.240917\pi$
$702$		0			0
$703$	346.801			0.0186057
$704$	8537.67	+	4929.23i	0.457068	+	0.263888i
$705$	−10453.1	+	18105.3i	−0.558422	+	0.967215i
$706$	−1985.65	−	3439.24i	−0.105851	−	0.183339i
$707$			1896.37i			0.100877i
$708$	7253.01	−	4187.53i	0.385007	−	0.222284i
$709$	−7879.85	+	4549.44i	−0.417396	+	0.240984i	−0.693963	−	0.720011i	$-0.744137\pi$
$709$	−7879.85	+	4549.44i	−0.417396	+	0.240984i	0.276566	+	0.960995i	$0.410803\pi$
$710$		−	1194.30i		−	0.0631285i
$711$	1358.85	+	2353.60i	0.0716751	+	0.124145i
$712$	2488.85	−	4310.82i	0.131002	−	0.226903i
$713$	33609.1	+	19404.2i	1.76532	+	1.01921i
$714$	−597.312			−0.0313079
$715$		0			0
$716$	−9118.62			−0.475948
$717$	−19287.9	−	11135.9i	−1.00463	−	0.580025i
$718$	1573.56	−	2725.48i	0.0817892	−	0.141663i
$719$	−3146.78	−	5450.38i	−0.163220	−	0.282705i	0.772802	−	0.634647i	$-0.218855\pi$
$719$	−3146.78	−	5450.38i	−0.163220	−	0.282705i	−0.936022	+	0.351942i	$0.885521\pi$
$720$		−	14204.5i		−	0.735235i
$721$	2733.13	−	1577.97i	0.141175	−	0.0815074i
$722$	124.963	−	72.1476i	0.00644135	−	0.00371892i
$723$			19064.3i			0.980648i
$724$	−4426.86	−	7667.54i	−0.227242	−	0.393594i
$725$	−10248.8	+	17751.4i	−0.525006	+	0.909337i
$726$	1158.72	+	668.987i	0.0592343	+	0.0341989i
$727$	−18070.7			−0.921878			−0.460939	−	0.887432i	$-0.652487\pi$
$727$	−18070.7			−0.921878			−0.460939	+	0.887432i	$0.652487\pi$
$728$		0			0
$729$	17319.9			0.879944
$730$	792.934	+	457.800i	0.0402025	+	0.0232109i
$731$	−935.790	+	1620.84i	−0.0473481	+	0.0820093i
$732$	9541.37	+	16526.1i	0.481775	+	0.834459i
$733$		−	34771.5i		−	1.75214i	−0.482188	−	0.876068i	$-0.660158\pi$
$733$		−	34771.5i		−	1.75214i	0.482188	−	0.876068i	$-0.339842\pi$
$734$	1520.40	−	877.803i	0.0764563	−	0.0441421i
$735$	−17810.2	+	10282.7i	−0.893794	+	0.516032i
$736$		−	11453.4i		−	0.573613i
$737$	−4766.09	−	8255.10i	−0.238210	−	0.412592i
$738$	670.256	−	1160.92i	0.0334315	−	0.0579051i
$739$	−20465.4	−	11815.7i	−1.01872	−	0.588158i	−0.104986	−	0.994474i	$-0.533480\pi$
$739$	−20465.4	−	11815.7i	−1.01872	−	0.588158i	−0.913733	+	0.406316i	$0.866813\pi$
$740$	596.710			0.0296425
$741$		0			0
$742$	161.324			0.00798167
$743$	28148.3	+	16251.4i	1.38985	+	0.802431i	0.993298	−	0.115581i	$-0.0368730\pi$
$743$	28148.3	+	16251.4i	1.38985	+	0.802431i	0.396553	+	0.918012i	$0.370206\pi$
$744$	−3526.21	+	6107.58i	−0.173760	+	0.300961i
$745$	17589.3	+	30465.5i	0.864995	+	1.49822i
$746$		−	4390.69i		−	0.215489i
$747$	3907.78	−	2256.16i	0.191403	−	0.110507i
$748$	10307.9	−	5951.25i	0.503868	−	0.290908i
$749$			3108.04i			0.151622i
$750$	965.435	+	1672.18i	0.0470036	+	0.0814126i
$751$	1010.43	−	1750.12i	0.0490960	−	0.0850368i	−0.840433	−	0.541915i	$-0.817699\pi$
$751$	1010.43	−	1750.12i	0.0490960	−	0.0850368i	0.889529	+	0.456879i	$0.151033\pi$
$752$	−16396.7	−	9466.65i	−0.795115	−	0.459060i
$753$	20710.5			1.00230
$754$		0			0
$755$	−32111.6			−1.54790
$756$	−5477.23	−	3162.28i	−0.263499	−	0.152131i
$757$	−6284.11	+	10884.4i	−0.301717	+	0.522589i	−0.976525	−	0.215404i	$-0.930893\pi$
$757$	−6284.11	+	10884.4i	−0.301717	+	0.522589i	0.674808	+	0.737993i	$0.264226\pi$
$758$	1790.86	+	3101.87i	0.0858141	+	0.148634i
$759$		−	11611.0i		−	0.555273i
$760$	−8637.36	+	4986.78i	−0.412250	+	0.238013i
$761$	−7538.59	+	4352.40i	−0.359098	+	0.207325i	−0.668685	−	0.743546i	$-0.733143\pi$
$761$	−7538.59	+	4352.40i	−0.359098	+	0.207325i	0.309587	+	0.950871i	$0.399809\pi$
$762$			4207.01i			0.200005i
$763$	−478.593	−	828.948i	−0.0227081	−	0.0393315i
$764$	−10470.7	+	18135.8i	−0.495832	+	0.858807i
$765$	−14073.8	−	8125.51i	−0.665149	−	0.384024i
$766$	−3205.16			−0.151184
$767$		0			0
$768$	−11595.0			−0.544790
$769$	−18979.7	−	10957.9i	−0.890020	−	0.513853i	−0.0160706	−	0.999871i	$-0.505116\pi$
$769$	−18979.7	−	10957.9i	−0.890020	−	0.513853i	−0.873949	+	0.486018i	$0.838449\pi$
$770$	476.070	−	824.578i

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:	\( N \)	\(=\)	\( 169 = 13^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	169.e (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.379706 - 0.219224i) q^{2} +(1.84233 - 3.19101i) q^{3} +(-3.90388 - 6.76172i) q^{4} +17.8078i q^{5} +(-1.39909 + 0.807764i) q^{6} +(4.70983 - 2.71922i) q^{7} +6.93087i q^{8} +(6.71165 + 11.6249i) q^{9} +O(q^{10})\)	\(q+(-0.379706 - 0.219224i) q^{2} +(1.84233 - 3.19101i) q^{3} +(-3.90388 - 6.76172i) q^{4} +17.8078i q^{5} +(-1.39909 + 0.807764i) q^{6} +(4.70983 - 2.71922i) q^{7} +6.93087i q^{8} +(6.71165 + 11.6249i) q^{9} +(3.90388 - 6.76172i) q^{10} +(19.4191 + 11.2116i) q^{11} -28.7689 q^{12} -2.38447 q^{14} +(56.8247 + 32.8078i) q^{15} +(-29.7116 + 51.4621i) q^{16} +(33.9924 + 58.8766i) q^{17} -5.88540i q^{18} +(69.9816 - 40.4039i) q^{19} +(120.411 - 69.5194i) q^{20} -20.0388i q^{21} +(-4.91571 - 8.51427i) q^{22} +(70.2656 - 121.704i) q^{23} +(22.1165 + 12.7689i) q^{24} -192.116 q^{25} +148.946 q^{27} +(-36.7733 - 21.2311i) q^{28} +(53.3466 - 92.3990i) q^{29} +(-14.3845 - 24.9146i) q^{30} +276.155i q^{31} +(70.5819 - 40.7505i) q^{32} +(71.5529 - 41.3111i) q^{33} -29.8078i q^{34} +(48.4233 + 83.8716i) q^{35} +(52.4029 - 90.7646i) q^{36} +(3.71670 + 2.14584i) q^{37} -35.4299 q^{38} -123.423 q^{40} +(197.254 + 113.884i) q^{41} +(-4.39298 + 7.60887i) q^{42} +(13.7647 + 23.8411i) q^{43} -175.076i q^{44} +(-207.014 + 119.519i) q^{45} +(-53.3606 + 30.8078i) q^{46} +318.617i q^{47} +(109.477 + 189.620i) q^{48} +(-156.712 + 271.433i) q^{49} +(72.9479 + 42.1165i) q^{50} +250.501 q^{51} -67.6562 q^{53} +(-56.5558 - 32.6525i) q^{54} +(-199.654 + 345.811i) q^{55} +(18.8466 + 32.6432i) q^{56} -297.749i q^{57} +(-40.5121 + 23.3897i) q^{58} +(-252.113 + 145.557i) q^{59} -512.311i q^{60} +(-331.655 - 574.444i) q^{61} +(60.5398 - 104.858i) q^{62} +(63.2215 + 36.5009i) q^{63} +439.652 q^{64} -36.2255 q^{66} +(-368.149 - 212.551i) q^{67} +(265.405 - 459.695i) q^{68} +(-258.905 - 448.436i) q^{69} -42.4621i q^{70} +(132.470 - 76.4815i) q^{71} +(-80.5708 + 46.5175i) q^{72} +117.268i q^{73} +(-0.940837 - 1.62958i) q^{74} +(-353.942 + 613.045i) q^{75} +(-546.400 - 315.464i) q^{76} +121.948 q^{77} +202.462 q^{79} +(-916.425 - 529.098i) q^{80} +(93.1932 - 161.415i) q^{81} +(-49.9323 - 86.4853i) q^{82} -336.155i q^{83} +(-135.497 + 78.2292i) q^{84} +(-1048.46 + 605.329i) q^{85} -12.0702i q^{86} +(-196.564 - 340.459i) q^{87} +(-77.7065 + 134.592i) q^{88} +(-621.974 - 359.097i) q^{89} +104.806 q^{90} -1097.23 q^{92} +(881.214 + 508.769i) q^{93} +(69.8485 - 120.981i) q^{94} +(719.503 + 1246.22i) q^{95} -300.303i q^{96} +(-657.632 + 379.684i) q^{97} +(119.009 - 68.7098i) q^{98} +300.994i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 10 q^{3} + 10 q^{4} - 70 q^{9}+O(q^{10}) \) 8 * q - 10 * q^3 + 10 * q^4 - 70 * q^9	\( 8 q - 10 q^{3} + 10 q^{4} - 70 q^{9} - 10 q^{10} - 560 q^{12} - 184 q^{14} - 114 q^{16} + 140 q^{17} + 340 q^{22} + 290 q^{23} - 300 q^{25} + 1340 q^{27} - 68 q^{29} - 280 q^{30} + 140 q^{35} + 1450 q^{36} - 1240 q^{38} - 740 q^{40} + 740 q^{42} + 910 q^{43} + 480 q^{48} - 1130 q^{49} + 932 q^{51} + 2180 q^{53} - 1020 q^{55} - 344 q^{56} - 1004 q^{61} - 1000 q^{62} + 5084 q^{64} - 6392 q^{66} + 1010 q^{68} - 958 q^{69} - 1698 q^{74} - 3450 q^{75} - 1020 q^{77} + 960 q^{79} - 244 q^{81} - 3030 q^{82} - 3230 q^{87} - 2040 q^{88} + 2900 q^{90} - 4160 q^{92} - 2080 q^{94} + 2540 q^{95}+O(q^{100}) \) 8 * q - 10 * q^3 + 10 * q^4 - 70 * q^9 - 10 * q^10 - 560 * q^12 - 184 * q^14 - 114 * q^16 + 140 * q^17 + 340 * q^22 + 290 * q^23 - 300 * q^25 + 1340 * q^27 - 68 * q^29 - 280 * q^30 + 140 * q^35 + 1450 * q^36 - 1240 * q^38 - 740 * q^40 + 740 * q^42 + 910 * q^43 + 480 * q^48 - 1130 * q^49 + 932 * q^51 + 2180 * q^53 - 1020 * q^55 - 344 * q^56 - 1004 * q^61 - 1000 * q^62 + 5084 * q^64 - 6392 * q^66 + 1010 * q^68 - 958 * q^69 - 1698 * q^74 - 3450 * q^75 - 1020 * q^77 + 960 * q^79 - 244 * q^81 - 3030 * q^82 - 3230 * q^87 - 2040 * q^88 + 2900 * q^90 - 4160 * q^92 - 2080 * q^94 + 2540 * q^95

Introduction

L-functions

Modular forms

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