LMFDB - Embedded newform 725.2.l.e.401.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [725,2,Mod(226,725)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(725, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([0, 10]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("725.226");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 725 = 5^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	725.l (of order $7$, degree $6$, 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:	$5.78915414654$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$6$ over $\Q(\zeta_{7})$
Twist minimal:	no (minimal twist has level 145)
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			401.6
Character	$\chi$	$=$	725.401
Dual form			725.2.l.e.226.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.74641 + 2.18993i) q^{2} +(-0.157624 - 0.690597i) q^{3} +(-1.30080 + 5.69919i) q^{4} +(1.23708 - 1.55125i) q^{6} +(0.404594 + 1.77264i) q^{7} +(-9.70531 + 4.67383i) q^{8} +(2.25083 - 1.08394i) q^{9} +O(q^{10})$	\(q+(1.74641 + 2.18993i) q^{2} +(-0.157624 - 0.690597i) q^{3} +(-1.30080 + 5.69919i) q^{4} +(1.23708 - 1.55125i) q^{6} +(0.404594 + 1.77264i) q^{7} +(-9.70531 + 4.67383i) q^{8} +(2.25083 - 1.08394i) q^{9} +(3.09974 + 1.49276i) q^{11} +4.14088 q^{12} +(1.13604 + 0.547090i) q^{13} +(-3.17538 + 3.98180i) q^{14} +(-16.6512 - 8.01877i) q^{16} -6.04532 q^{17} +(6.30463 + 3.03615i) q^{18} +(-0.717470 + 3.14344i) q^{19} +(1.16041 - 0.558823i) q^{21} +(2.14439 + 9.39519i) q^{22} +(-0.429904 + 0.539083i) q^{23} +(4.75752 + 5.96575i) q^{24} +(0.785912 + 3.44330i) q^{26} +(-2.42831 - 3.04501i) q^{27} -10.6289 q^{28} +(-0.718081 - 5.33707i) q^{29} +(0.304181 + 0.381431i) q^{31} +(-6.72519 - 29.4650i) q^{32} +(0.542299 - 2.37597i) q^{33} +(-10.5576 - 13.2388i) q^{34} +(3.24971 + 14.2379i) q^{36} +(4.86199 - 2.34141i) q^{37} +(-8.13692 + 3.91853i) q^{38} +(0.198751 - 0.870783i) q^{39} +3.37890 q^{41} +(3.25033 + 1.56528i) q^{42} +(1.82152 - 2.28412i) q^{43} +(-12.5397 + 15.7242i) q^{44} -1.93134 q^{46} +(7.87732 + 3.79352i) q^{47} +(-2.91311 + 12.7632i) q^{48} +(3.32822 - 1.60279i) q^{49} +(0.952888 + 4.17488i) q^{51} +(-4.59574 + 5.76288i) q^{52} +(3.43501 + 4.30737i) q^{53} +(2.42752 - 10.6357i) q^{54} +(-12.2117 - 15.3130i) q^{56} +2.28394 q^{57} +(10.4338 - 10.8933i) q^{58} -11.4694 q^{59} +(1.82638 + 8.00189i) q^{61} +(-0.304082 + 1.33227i) q^{62} +(2.83211 + 3.55136i) q^{63} +(29.7354 - 37.2870i) q^{64} +(6.15028 - 2.96182i) q^{66} +(12.9974 - 6.25922i) q^{67} +(7.86377 - 34.4534i) q^{68} +(0.440052 + 0.211918i) q^{69} +(3.47791 + 1.67487i) q^{71} +(-16.7788 + 21.0400i) q^{72} +(-1.53445 + 1.92414i) q^{73} +(13.6186 + 6.55835i) q^{74} +(-16.9818 - 8.17800i) q^{76} +(-1.39199 + 6.09869i) q^{77} +(2.25406 - 1.08550i) q^{78} +(-0.240998 + 0.116059i) q^{79} +(2.95275 - 3.70264i) q^{81} +(5.90095 + 7.39955i) q^{82} +(-1.23269 + 5.40078i) q^{83} +(1.67538 + 7.34030i) q^{84} +8.18319 q^{86} +(-3.57258 + 1.33716i) q^{87} -37.0608 q^{88} +(-0.696833 - 0.873801i) q^{89} +(-0.510158 + 2.23515i) q^{91} +(-2.51312 - 3.15135i) q^{92} +(0.215468 - 0.270189i) q^{93} +(5.44950 + 23.8758i) q^{94} +(-19.2884 + 9.28879i) q^{96} +(0.252772 - 1.10746i) q^{97} +(9.32243 + 4.48945i) q^{98} +8.59505 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 2 q^{2} + 2 q^{3} - 10 q^{4} + 2 q^{6} + 8 q^{7} - 9 q^{8} - 18 q^{9}+O(q^{10}) $ 36 * q + 2 * q^2 + 2 * q^3 - 10 * q^4 + 2 * q^6 + 8 * q^7 - 9 * q^8 - 18 * q^9	$ 36 q + 2 q^{2} + 2 q^{3} - 10 q^{4} + 2 q^{6} + 8 q^{7} - 9 q^{8} - 18 q^{9} + 4 q^{11} + 14 q^{12} + 8 q^{13} + 16 q^{14} - 20 q^{16} - 28 q^{17} + 42 q^{18} - 6 q^{19} + 31 q^{21} + 19 q^{22} + 16 q^{24} - 32 q^{26} - 7 q^{27} - 60 q^{28} - 21 q^{29} - 7 q^{31} - 32 q^{32} - 56 q^{33} - 48 q^{34} - 12 q^{36} + 16 q^{37} + 34 q^{38} + 19 q^{39} - 28 q^{41} - 31 q^{42} - 15 q^{43} - 31 q^{44} + 76 q^{46} + 22 q^{47} + 101 q^{48} + 50 q^{49} - 14 q^{51} - 7 q^{52} + 15 q^{53} + 43 q^{54} + 6 q^{56} - 20 q^{57} + 70 q^{58} + 2 q^{59} - 4 q^{61} + 19 q^{62} + 43 q^{63} + 87 q^{64} + 66 q^{66} + 43 q^{67} - 46 q^{68} - 48 q^{69} + 27 q^{71} - 181 q^{72} + 44 q^{73} - 23 q^{74} - 40 q^{76} + 43 q^{77} - 10 q^{78} + 82 q^{79} - 49 q^{81} - 70 q^{82} + 25 q^{83} - 34 q^{84} - 126 q^{86} + 47 q^{87} - 40 q^{88} + 36 q^{89} - 45 q^{91} - 45 q^{92} - 122 q^{93} - 89 q^{96} - 21 q^{97} + 32 q^{98} - 8 q^{99}+O(q^{100}) $ 36 * q + 2 * q^2 + 2 * q^3 - 10 * q^4 + 2 * q^6 + 8 * q^7 - 9 * q^8 - 18 * q^9 + 4 * q^11 + 14 * q^12 + 8 * q^13 + 16 * q^14 - 20 * q^16 - 28 * q^17 + 42 * q^18 - 6 * q^19 + 31 * q^21 + 19 * q^22 + 16 * q^24 - 32 * q^26 - 7 * q^27 - 60 * q^28 - 21 * q^29 - 7 * q^31 - 32 * q^32 - 56 * q^33 - 48 * q^34 - 12 * q^36 + 16 * q^37 + 34 * q^38 + 19 * q^39 - 28 * q^41 - 31 * q^42 - 15 * q^43 - 31 * q^44 + 76 * q^46 + 22 * q^47 + 101 * q^48 + 50 * q^49 - 14 * q^51 - 7 * q^52 + 15 * q^53 + 43 * q^54 + 6 * q^56 - 20 * q^57 + 70 * q^58 + 2 * q^59 - 4 * q^61 + 19 * q^62 + 43 * q^63 + 87 * q^64 + 66 * q^66 + 43 * q^67 - 46 * q^68 - 48 * q^69 + 27 * q^71 - 181 * q^72 + 44 * q^73 - 23 * q^74 - 40 * q^76 + 43 * q^77 - 10 * q^78 + 82 * q^79 - 49 * q^81 - 70 * q^82 + 25 * q^83 - 34 * q^84 - 126 * q^86 + 47 * q^87 - 40 * q^88 + 36 * q^89 - 45 * q^91 - 45 * q^92 - 122 * q^93 - 89 * q^96 - 21 * q^97 + 32 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/725\mathbb{Z}\right)^\times$.

$n$	$176$	$552$
$\chi(n)$	$e\left(\frac{2}{7}\right)$	$1$

Coefficient data

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

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

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

$2$	1.74641	+	2.18993i	1.23490	+	1.54852i	0.726009	+	0.687685i	$0.241373\pi$
$2$	1.74641	+	2.18993i	1.23490	+	1.54852i	0.508891	+	0.860831i	$0.330056\pi$
$3$	−0.157624	−	0.690597i	−0.0910044	−	0.398716i	0.908825	−	0.417177i	$-0.136981\pi$
$3$	−0.157624	−	0.690597i	−0.0910044	−	0.398716i	−0.999830	+	0.0184609i	$0.994123\pi$
$4$	−1.30080	+	5.69919i	−0.650402	+	2.84960i
$5$		0			0
$5$		0			0
$6$	1.23708	−	1.55125i	0.505037	−	0.633297i
$7$	0.404594	+	1.77264i	0.152922	+	0.669996i	0.992027	+	0.126026i	$0.0402222\pi$
$7$	0.404594	+	1.77264i	0.152922	+	0.669996i	−0.839105	+	0.543970i	$0.816921\pi$
$8$	−9.70531	+	4.67383i	−3.43135	+	1.65245i
$9$	2.25083	−	1.08394i	0.750276	−	0.361314i
$10$		0			0
$11$	3.09974	+	1.49276i	0.934607	+	0.450083i	0.838264	−	0.545265i	$-0.183571\pi$
$11$	3.09974	+	1.49276i	0.934607	+	0.450083i	0.0963435	+	0.995348i	$0.469285\pi$
$12$	4.14088			1.19537
$13$	1.13604	+	0.547090i	0.315082	+	0.151735i	0.584740	−	0.811221i	$-0.301196\pi$
$13$	1.13604	+	0.547090i	0.315082	+	0.151735i	−0.269658	+	0.962956i	$0.586911\pi$
$14$	−3.17538	+	3.98180i	−0.848655	+	1.06418i
$15$		0			0
$16$	−16.6512	−	8.01877i	−4.16279	−	2.00469i
$17$	−6.04532			−1.46620			−0.733102	−	0.680118i	$-0.761928\pi$
$17$	−6.04532			−1.46620			−0.733102	+	0.680118i	$0.761928\pi$
$18$	6.30463	+	3.03615i	1.48602	+	0.715628i
$19$	−0.717470	+	3.14344i	−0.164599	+	0.721154i	0.823498	+	0.567320i	$0.192020\pi$
$19$	−0.717470	+	3.14344i	−0.164599	+	0.721154i	−0.988097	+	0.153835i	$0.950838\pi$
$20$		0			0
$21$	1.16041	−	0.558823i	0.253222	−	0.121945i
$22$	2.14439	+	9.39519i	0.457186	+	2.00306i
$23$	−0.429904	+	0.539083i	−0.0896412	+	0.112407i	−0.824629	−	0.565673i	$-0.808616\pi$
$23$	−0.429904	+	0.539083i	−0.0896412	+	0.112407i	0.734988	+	0.678080i	$0.237188\pi$
$24$	4.75752	+	5.96575i	0.971126	+	1.21775i
$25$		0			0
$26$	0.785912	+	3.44330i	0.154130	+	0.675288i
$27$	−2.42831	−	3.04501i	−0.467329	−	0.586012i
$28$	−10.6289			−2.00868
$29$	−0.718081	−	5.33707i	−0.133344	−	0.991070i
$29$	−0.718081	−	5.33707i	−0.133344	−	0.991070i
$30$		0			0
$31$	0.304181	+	0.381431i	0.0546325	+	0.0685070i	0.808397	−	0.588638i	$-0.200336\pi$
$31$	0.304181	+	0.381431i	0.0546325	+	0.0685070i	−0.753765	+	0.657145i	$0.771764\pi$
$32$	−6.72519	−	29.4650i	−1.18886	−	5.20872i
$33$	0.542299	−	2.37597i	0.0944021	−	0.413603i
$34$	−10.5576	−	13.2388i	−1.81062	−	2.27044i
$35$		0			0
$36$	3.24971	+	14.2379i	0.541618	+	2.37298i
$37$	4.86199	−	2.34141i	0.799306	−	0.384925i	0.0107913	−	0.999942i	$-0.496565\pi$
$37$	4.86199	−	2.34141i	0.799306	−	0.384925i	0.788514	+	0.615017i	$0.210851\pi$
$38$	−8.13692	+	3.91853i	−1.31998	+	0.635670i
$39$	0.198751	−	0.870783i	0.0318256	−	0.139437i
$40$		0			0
$41$	3.37890			0.527695			0.263848	−	0.964564i	$-0.415008\pi$
$41$	3.37890			0.527695			0.263848	+	0.964564i	$0.415008\pi$
$42$	3.25033	+	1.56528i	0.501537	+	0.241528i
$43$	1.82152	−	2.28412i	0.277779	−	0.348324i	−0.623297	−	0.781986i	$-0.714207\pi$
$43$	1.82152	−	2.28412i	0.277779	−	0.348324i	0.901076	+	0.433661i	$0.142778\pi$
$44$	−12.5397	+	15.7242i	−1.89043	+	2.37052i
$45$		0			0
$46$	−1.93134			−0.284761
$47$	7.87732	+	3.79352i	1.14902	+	0.553341i	0.908741	−	0.417362i	$-0.137045\pi$
$47$	7.87732	+	3.79352i	1.14902	+	0.553341i	0.240284	+	0.970703i	$0.422759\pi$
$48$	−2.91311	+	12.7632i	−0.420472	+	1.84221i
$49$	3.32822	−	1.60279i	0.475460	−	0.228969i
$50$		0			0
$51$	0.952888	+	4.17488i	0.133431	+	0.584600i
$52$	−4.59574	+	5.76288i	−0.637315	+	0.799168i
$53$	3.43501	+	4.30737i	0.471835	+	0.591663i	0.959619	−	0.281302i	$-0.0907662\pi$
$53$	3.43501	+	4.30737i	0.471835	+	0.591663i	−0.487784	+	0.872964i	$0.662195\pi$
$54$	2.42752	−	10.6357i	0.330344	−	1.44733i
$55$		0			0
$56$	−12.2117	−	15.3130i	−1.63186	−	2.04629i
$57$	2.28394			0.302515
$58$	10.4338	−	10.8933i	1.37002	−	1.43036i
$59$	−11.4694			−1.49318			−0.746591	−	0.665283i	$-0.768311\pi$
$59$	−11.4694			−1.49318			−0.746591	+	0.665283i	$0.768311\pi$
$60$		0			0
$61$	1.82638	+	8.00189i	0.233844	+	1.02454i	0.946419	+	0.322941i	$0.104672\pi$
$61$	1.82638	+	8.00189i	0.233844	+	1.02454i	−0.712575	+	0.701596i	$0.752471\pi$
$62$	−0.304082	+	1.33227i	−0.0386185	+	0.169198i
$63$	2.83211	+	3.55136i	0.356813	+	0.447429i
$64$	29.7354	−	37.2870i	3.71693	−	4.66088i
$65$		0			0
$66$	6.15028	−	2.96182i	0.757047	−	0.364575i
$67$	12.9974	−	6.25922i	1.58789	−	0.764686i	0.588836	−	0.808252i	$-0.299586\pi$
$67$	12.9974	−	6.25922i	1.58789	−	0.764686i	0.999051	+	0.0435665i	$0.0138720\pi$
$68$	7.86377	−	34.4534i	0.953622	−	4.17809i
$69$	0.440052	+	0.211918i	0.0529761	+	0.0255119i
$70$		0			0
$71$	3.47791	+	1.67487i	0.412752	+	0.198771i	0.628724	−	0.777629i	$-0.283578\pi$
$71$	3.47791	+	1.67487i	0.412752	+	0.198771i	−0.215972	+	0.976400i	$0.569292\pi$
$72$	−16.7788	+	21.0400i	−1.97740	+	2.47959i
$73$	−1.53445	+	1.92414i	−0.179594	+	0.225204i	−0.863477	−	0.504387i	$-0.831718\pi$
$73$	−1.53445	+	1.92414i	−0.179594	+	0.225204i	0.683883	+	0.729591i	$0.260290\pi$
$74$	13.6186	+	6.55835i	1.58313	+	0.762393i
$75$		0			0
$76$	−16.9818	−	8.17800i	−1.94794	−	0.938080i
$77$	−1.39199	+	6.09869i	−0.158632	+	0.695010i
$78$	2.25406	−	1.08550i	0.255222	−	0.122908i
$79$	−0.240998	+	0.116059i	−0.0271144	+	0.0130576i	−0.447392	−	0.894338i	$-0.647647\pi$
$79$	−0.240998	+	0.116059i	−0.0271144	+	0.0130576i	0.420277	+	0.907396i	$0.361933\pi$
$80$		0			0
$81$	2.95275	−	3.70264i	0.328084	−	0.411404i
$82$	5.90095	+	7.39955i	0.651651	+	0.817144i
$83$	−1.23269	+	5.40078i	−0.135306	+	0.592813i	0.861125	+	0.508394i	$0.169761\pi$
$83$	−1.23269	+	5.40078i	−0.135306	+	0.592813i	−0.996430	+	0.0844191i	$0.973097\pi$
$84$	1.67538	+	7.34030i	0.182799	+	0.800893i
$85$		0			0
$86$	8.18319			0.882416
$87$	−3.57258	+	1.33716i	−0.383021	+	0.143358i
$88$	−37.0608			−3.95070
$89$	−0.696833	−	0.873801i	−0.0738641	−	0.0926227i	0.743527	−	0.668706i	$-0.233152\pi$
$89$	−0.696833	−	0.873801i	−0.0738641	−	0.0926227i	−0.817391	+	0.576084i	$0.804580\pi$
$90$		0			0
$91$	−0.510158	+	2.23515i	−0.0534791	+	0.234307i
$92$	−2.51312	−	3.15135i	−0.262010	−	0.328551i
$93$	0.215468	−	0.270189i	0.0223430	−	0.0280173i
$94$	5.44950	+	23.8758i	0.562073	+	2.46260i
$95$		0			0
$96$	−19.2884	+	9.28879i	−1.96861	+	0.948033i
$97$	0.252772	−	1.10746i	0.0256651	−	0.112446i	−0.960473	−	0.278374i	$-0.910205\pi$
$97$	0.252772	−	1.10746i	0.0256651	−	0.112446i	0.986138	+	0.165928i	$0.0530618\pi$
$98$	9.32243	+	4.48945i	0.941708	+	0.453503i
$99$	8.59505			0.863835
$100$		0			0
$101$	−5.98735	+	7.50790i	−0.595763	+	0.747064i	−0.984711	−	0.174196i	$-0.944267\pi$
$101$	−5.98735	+	7.50790i	−0.595763	+	0.747064i	0.388948	+	0.921260i	$0.372839\pi$
$102$	−7.47856	+	9.37782i	−0.740488	+	0.928542i
$103$	4.41538	+	2.12634i	0.435060	+	0.209514i	0.638578	−	0.769557i	$-0.279523\pi$
$103$	4.41538	+	2.12634i	0.435060	+	0.209514i	−0.203517	+	0.979071i	$0.565237\pi$
$104$	−13.5827			−1.33189
$105$		0			0
$106$	−3.43390	+	15.0449i	−0.333530	+	1.46129i
$107$	10.7029	−	5.15423i	1.03469	−	0.498278i	0.162118	−	0.986771i	$-0.448168\pi$
$107$	10.7029	−	5.15423i	1.03469	−	0.498278i	0.872568	+	0.488493i	$0.162453\pi$
$108$	20.5128	−	9.87846i	1.97385	−	0.950555i
$109$	−3.12370	−	13.6858i	−0.299196	−	1.31086i	−0.871328	−	0.490701i	$-0.836741\pi$
$109$	−3.12370	−	13.6858i	−0.299196	−	1.31086i	0.572132	−	0.820162i	$-0.306117\pi$
$110$		0			0
$111$	−2.38334	−	2.98861i	−0.226216	−	0.283666i
$112$	7.47746	−	32.7609i	0.706553	−	3.09561i
$113$	−0.927048	−	4.06166i	−0.0872093	−	0.382089i	0.912422	−	0.409251i	$-0.134210\pi$
$113$	−0.927048	−	4.06166i	−0.0872093	−	0.382089i	−0.999631	+	0.0271623i	$0.991353\pi$
$114$	3.98870	+	5.00167i	0.373576	+	0.468450i
$115$		0			0
$116$	31.3511	+	2.85000i	2.91088	+	0.264616i
$117$	3.15005			0.291223
$118$	−20.0302	−	25.1171i	−1.84393	−	2.31222i
$119$	−2.44590	−	10.7162i	−0.224215	−	0.982351i
$120$		0			0
$121$	0.521685	+	0.654173i	0.0474259	+	0.0594703i
$122$	−14.3340	+	17.9743i	−1.29774	+	1.62731i
$123$	−0.532596	−	2.33346i	−0.0480226	−	0.210401i
$124$	−2.56953	+	1.23742i	−0.230750	+	0.111123i
$125$		0			0
$126$	−2.83119	+	12.4043i	−0.252223	+	1.10506i
$127$	−4.03441	−	1.94287i	−0.357996	−	0.172402i	0.246236	−	0.969210i	$-0.420806\pi$
$127$	−4.03441	−	1.94287i	−0.357996	−	0.172402i	−0.604233	+	0.796808i	$0.706520\pi$
$128$	73.1410			6.46481
$129$	−1.86452	−	0.897905i	−0.164162	−	0.0790561i
$130$		0			0
$131$	12.2530	−	15.3647i	1.07055	−	1.34242i	0.134355	−	0.990933i	$-0.457104\pi$
$131$	12.2530	−	15.3647i	1.07055	−	1.34242i	0.936192	−	0.351490i	$-0.114325\pi$
$132$	12.8357	+	6.18133i	1.11720	+	0.538016i
$133$	−5.86248			−0.508341
$134$	36.4061	+	17.5323i	3.14501	+	1.51456i
$135$		0			0
$136$	58.6717	−	28.2548i	5.03105	−	2.42283i
$137$	−4.33116	+	2.08578i	−0.370036	+	0.178200i	−0.609655	−	0.792667i	$-0.708692\pi$
$137$	−4.33116	+	2.08578i	−0.370036	+	0.178200i	0.239619	+	0.970867i	$0.422978\pi$
$138$	0.304427	+	1.33378i	0.0259145	+	0.113539i
$139$	−3.12690	+	3.92101i	−0.265220	+	0.332576i	−0.896553	−	0.442936i	$-0.853937\pi$
$139$	−3.12690	+	3.92101i	−0.265220	+	0.332576i	0.631333	+	0.775512i	$0.282508\pi$
$140$		0			0
$141$	1.37813	−	6.03800i	0.116060	−	0.508491i
$142$	2.40601	+	10.5414i	0.201908	+	0.884616i
$143$	2.70477	+	3.39167i	0.226184	+	0.283626i
$144$	−46.1708			−3.84756
$145$		0			0
$146$	−6.89353			−0.570513
$147$	−1.63149	−	2.04582i	−0.134563	−	0.168736i
$148$	7.01965	+	30.7551i	0.577012	+	2.52805i
$149$	2.56850	−	11.2533i	0.210420	−	0.921909i	−0.753863	−	0.657032i	$-0.771812\pi$
$149$	2.56850	−	11.2533i	0.210420	−	0.921909i	0.964282	−	0.264877i	$-0.0853312\pi$
$150$		0			0
$151$	−3.37357	+	4.23032i	−0.274537	+	0.344258i	−0.899916	−	0.436062i	$-0.856373\pi$
$151$	−3.37357	+	4.23032i	−0.274537	+	0.344258i	0.625380	+	0.780321i	$0.284944\pi$
$152$	−7.72864	−	33.8614i	−0.626875	−	2.74652i
$153$	−13.6070	+	6.55277i	−1.10006	+	0.529760i
$154$	−15.7867	+	7.60248i	−1.27213	+	0.612625i
$155$		0			0
$156$	4.70423	+	2.26544i	0.376640	+	0.181380i
$157$	−3.21678			−0.256727			−0.128364	−	0.991727i	$-0.540972\pi$
$157$	−3.21678			−0.256727			−0.128364	+	0.991727i	$0.540972\pi$
$158$	−0.675043	−	0.325084i	−0.0537035	−	0.0258623i
$159$	2.43321	−	3.05115i	0.192966	−	0.241972i
$160$		0			0
$161$	−1.12954	−	0.543957i	−0.0890200	−	0.0428698i
$162$	13.2652			1.04222
$163$	10.6995	+	5.15261i	0.838050	+	0.403584i	0.803128	−	0.595806i	$-0.203167\pi$
$163$	10.6995	+	5.15261i	0.838050	+	0.403584i	0.0349221	+	0.999390i	$0.488882\pi$
$164$	−4.39528	+	19.2570i	−0.343214	+	1.50372i
$165$		0			0
$166$	−13.9801	+	6.73248i	−1.08507	+	0.522542i
$167$	−3.42589	−	15.0098i	−0.265103	−	1.16149i	−0.915634	−	0.402013i	$-0.868311\pi$
$167$	−3.42589	−	15.0098i	−0.265103	−	1.16149i	0.650531	−	0.759480i	$-0.274546\pi$
$168$	−8.65027	+	10.8471i	−0.667383	+	0.836871i
$169$	−7.11408	−	8.92077i	−0.547237	−	0.686213i
$170$		0			0
$171$	1.79240	+	7.85304i	0.137069	+	0.600537i
$172$	10.6482	+	13.3524i	0.811916	+	1.01811i
$173$	−24.9271			−1.89517			−0.947587	−	0.319499i	$-0.896485\pi$
$173$	−24.9271			−1.89517			−0.947587	+	0.319499i	$0.896485\pi$
$174$	−9.16748	−	5.48848i	−0.694985	−	0.416081i
$175$		0			0
$176$	−39.6442	−	49.7122i	−2.98829	−	3.74720i
$177$	1.80785	+	7.92070i	0.135886	+	0.595356i
$178$	0.696607	−	3.05203i	0.0522129	−	0.228760i
$179$	4.11700	+	5.16255i	0.307719	+	0.385867i	0.911512	−	0.411274i	$-0.134916\pi$
$179$	4.11700	+	5.16255i	0.307719	+	0.385867i	−0.603793	+	0.797141i	$0.706345\pi$
$180$		0			0
$181$	−2.06054	−	9.02783i	−0.153159	−	0.671033i	−0.991955	−	0.126588i	$-0.959597\pi$
$181$	−2.06054	−	9.02783i	−0.153159	−	0.671033i	0.838796	−	0.544445i	$-0.183260\pi$
$182$	−5.78577	+	2.78628i	−0.428870	+	0.206533i
$183$	5.23820	−	2.52258i	0.387219	−	0.186475i
$184$	1.65277	−	7.24126i	0.121844	−	0.533833i
$185$		0			0
$186$	0.967992			0.0709766
$187$	−18.7389	−	9.02419i	−1.37033	−	0.659914i
$188$	−31.8668	+	39.9597i	−2.32413	+	2.91436i
$189$	4.41523	−	5.53652i	0.321160	−	0.402722i
$190$		0			0
$191$	−2.58646			−0.187149			−0.0935747	−	0.995612i	$-0.529829\pi$
$191$	−2.58646			−0.187149			−0.0935747	+	0.995612i	$0.529829\pi$
$192$	−30.4373	−	14.6578i	−2.19663	−	1.05784i
$193$	−1.61776	+	7.08788i	−0.116449	+	0.510197i	0.882737	+	0.469867i	$0.155698\pi$
$193$	−1.61776	+	7.08788i	−0.116449	+	0.510197i	−0.999186	+	0.0403299i	$0.987159\pi$
$194$	2.86672	−	1.38054i	0.205818	−	0.0991168i
$195$		0			0
$196$	4.80523	+	21.0531i	0.343230	+	1.50379i
$197$	12.7696	−	16.0126i	0.909799	−	1.14085i	−0.0797725	−	0.996813i	$-0.525419\pi$
$197$	12.7696	−	16.0126i	0.909799	−	1.14085i	0.989572	−	0.144039i	$-0.0460092\pi$
$198$	15.0105	+	18.8226i	1.06675	+	1.33766i
$199$	−2.41093	+	10.5630i	−0.170907	+	0.748791i	0.814720	+	0.579854i	$0.196890\pi$
$199$	−2.41093	+	10.5630i	−0.170907	+	0.748791i	−0.985627	+	0.168937i	$0.945967\pi$
$200$		0			0
$201$	−6.37131	−	7.98937i	−0.449397	−	0.563526i
$202$	−26.8982			−1.89255
$203$	9.17019	−	3.43225i	0.643621	−	0.240897i
$204$	−25.0329			−1.75266
$205$		0			0
$206$	3.05455	+	13.3828i	0.212820	+	0.932427i
$207$	−0.383306	+	1.67937i	−0.0266416	+	0.116725i
$208$	−14.5295	−	18.2194i	−1.00744	−	1.26329i
$209$	−6.91636	+	8.67284i	−0.478415	+	0.599913i
$210$		0			0
$211$	−12.6081	+	6.07175i	−0.867978	+	0.417996i	−0.814219	−	0.580558i	$-0.802835\pi$
$211$	−12.6081	+	6.07175i	−0.867978	+	0.417996i	−0.0537590	+	0.998554i	$0.517120\pi$
$212$	−29.0168	+	13.9738i	−1.99288	+	0.959722i
$213$	0.608460	−	2.66584i	0.0416910	−	0.182660i
$214$	29.9790	+	14.4371i	2.04933	+	0.986903i
$215$		0			0
$216$	37.7994	+	18.2032i	2.57192	+	1.23857i
$217$	−0.553070	+	0.693528i	−0.0375448	+	0.0470798i
$218$	24.5157	−	30.7418i	1.66042	−	2.08209i
$219$	1.57067	+	0.756397i	0.106136	+	0.0511126i
$220$		0			0
$221$	−6.86775	−	3.30733i	−0.461975	−	0.222475i
$222$	2.38256	−	10.4387i	0.159907	−	0.700599i
$223$	15.1407	−	7.29137i	1.01390	−	0.488266i	0.148264	−	0.988948i	$-0.452632\pi$
$223$	15.1407	−	7.29137i	1.01390	−	0.488266i	0.865632	+	0.500682i	$0.166917\pi$
$224$	49.5099	−	23.8427i	3.30802	−	1.59306i
$225$		0			0
$226$	7.27575	−	9.12351i	0.483976	−	0.606887i
$227$	−3.86745	−	4.84963i	−0.256692	−	0.321881i	0.636741	−	0.771077i	$-0.280282\pi$
$227$	−3.86745	−	4.84963i	−0.256692	−	0.321881i	−0.893433	+	0.449196i	$0.851710\pi$
$228$	−2.97096	+	13.0166i	−0.196756	+	0.862046i
$229$	5.63524	+	24.6896i	0.372387	+	1.63153i	0.720055	+	0.693917i	$0.244116\pi$
$229$	5.63524	+	24.6896i	0.372387	+	1.63153i	−0.347668	+	0.937618i	$0.613026\pi$
$230$		0			0
$231$	4.43115			0.291548
$232$	31.9138	+	48.4418i	2.09524	+	3.18036i
$233$	−14.6568			−0.960201			−0.480101	−	0.877213i	$-0.659400\pi$
$233$	−14.6568			−0.960201			−0.480101	+	0.877213i	$0.659400\pi$
$234$	5.50129	+	6.89840i	0.359631	+	0.450963i
$235$		0			0
$236$	14.9194	−	65.3661i	0.971169	−	4.25497i
$237$	0.118137	+	0.148139i	0.00767382	+	0.00962266i
$238$	19.1962	−	24.0712i	1.24430	−	1.56031i
$239$	−2.83553	−	12.4233i	−0.183415	−	0.803594i	−0.979989	−	0.199053i	$-0.936213\pi$
$239$	−2.83553	−	12.4233i	−0.183415	−	0.803594i	0.796574	−	0.604542i	$-0.206644\pi$
$240$		0			0
$241$	−15.2323	+	7.33551i	−0.981201	+	0.472521i	−0.854518	−	0.519422i	$-0.826147\pi$
$241$	−15.2323	+	7.33551i	−0.981201	+	0.472521i	−0.126683	+	0.991943i	$0.540433\pi$
$242$	−0.521516	+	2.28491i	−0.0335243	+	0.146880i
$243$	−13.5495	−	6.52509i	−0.869200	−	0.418585i
$244$	−47.9801			−3.07161
$245$		0			0
$246$	4.17998	−	5.24153i	0.266506	−	0.334187i
$247$	−2.53482	+	3.17857i	−0.161287	+	0.202247i
$248$	−4.73491	−	2.28021i	−0.300667	−	0.144794i
$249$	3.92407			0.248678
$250$		0			0
$251$	−0.953932	+	4.17945i	−0.0602116	+	0.263804i	−0.996070	−	0.0885727i	$-0.971769\pi$
$251$	−0.953932	+	4.17945i	−0.0602116	+	0.263804i	0.935858	+	0.352377i	$0.114627\pi$
$252$	−23.9239	+	11.5211i	−1.50706	+	0.725763i
$253$	−2.13731	+	1.02927i	−0.134372	+	0.0647099i
$254$	−2.79100	−	12.2281i	−0.175123	−	0.767262i
$255$		0			0
$256$	68.2635	+	85.5997i	4.26647	+	5.34998i
$257$	−1.88563	+	8.26148i	−0.117622	+	0.515337i	0.881450	+	0.472277i	$0.156568\pi$
$257$	−1.88563	+	8.26148i	−0.117622	+	0.515337i	−0.999072	+	0.0430598i	$0.986289\pi$
$258$	−1.28987	−	5.65128i	−0.0803037	−	0.351834i
$259$	6.11761	+	7.67124i	0.380130	+	0.476668i
$260$		0			0
$261$	−7.40135	−	11.2345i	−0.458132	−	0.695397i
$262$	55.0465			3.40078
$263$	4.40328	+	5.52154i	0.271518	+	0.340473i	0.898832	−	0.438294i	$-0.144417\pi$
$263$	4.40328	+	5.52154i	0.271518	+	0.340473i	−0.627314	+	0.778767i	$0.715846\pi$
$264$	5.84169	+	25.5941i	0.359531	+	1.57521i
$265$		0			0
$266$	−10.2383	−	12.8384i	−0.627751	−	0.787174i
$267$	−0.493606	+	0.618963i	−0.0302082	+	0.0378799i
$268$	18.7654	+	82.2168i	1.14628	+	5.02219i
$269$	−21.1126	+	10.1673i	−1.28726	+	0.619912i	−0.947246	−	0.320508i	$-0.896146\pi$
$269$	−21.1126	+	10.1673i	−1.28726	+	0.619912i	−0.340015	+	0.940420i	$0.610432\pi$
$270$		0			0
$271$	3.34691	−	14.6638i	0.203311	−	0.890762i	−0.765594	−	0.643325i	$-0.777555\pi$
$271$	3.34691	−	14.6638i	0.203311	−	0.890762i	0.968904	−	0.247437i	$-0.0795883\pi$
$272$	100.661	+	48.4760i	6.10350	+	2.93929i
$273$	1.62400			0.0982889
$274$	−12.1317	−	5.84232i	−0.732903	−	0.352948i
$275$		0			0
$276$	−1.78018	+	2.23228i	−0.107154	+	0.134367i
$277$	2.48894	+	1.19861i	0.149546	+	0.0720174i	0.507160	−	0.861852i	$-0.330695\pi$
$277$	2.48894	+	1.19861i	0.149546	+	0.0720174i	−0.357614	+	0.933869i	$0.616410\pi$
$278$	−14.0476			−0.842519
$279$	1.09811	+	0.528820i	0.0657419	+	0.0316597i
$280$		0			0
$281$	−26.7047	+	12.8603i	−1.59307	+	0.767181i	−0.999298	−	0.0374541i	$-0.988075\pi$
$281$	−26.7047	+	12.8603i	−1.59307	+	0.767181i	−0.593770	+	0.804635i	$0.702361\pi$
$282$	15.6296	−	7.52682i	0.930729	−	0.448215i
$283$	−0.725560	−	3.17889i	−0.0431301	−	0.188965i	0.948774	−	0.315956i	$-0.102325\pi$
$283$	−0.725560	−	3.17889i	−0.0431301	−	0.188965i	−0.991904	+	0.126991i	$0.959468\pi$
$284$	−14.0695	+	17.6426i	−0.834872	+	1.04690i
$285$		0			0
$286$	−2.70389	+	11.8465i	−0.159885	+	0.700500i
$287$	1.36708	+	5.98957i	0.0806963	+	0.353553i
$288$	−47.0756	−	59.0309i	−2.77395	−	3.47843i
$289$	19.5458			1.14976
$290$		0			0
$291$	−0.804655			−0.0471697
$292$	−8.97005	−	11.2481i	−0.524932	−	0.658244i
$293$	2.26702	+	9.93245i	0.132441	+	0.580260i	0.996978	+	0.0776908i	$0.0247547\pi$
$293$	2.26702	+	9.93245i	0.132441	+	0.580260i	−0.864537	+	0.502569i	$0.832388\pi$
$294$	1.63096	−	7.14569i	0.0951193	−	0.416745i
$295$		0			0
$296$	−36.2437	+	45.4482i	−2.10662	+	2.64162i
$297$	−2.98168	−	13.0636i	−0.173015	−	0.758028i
$298$	29.1297	−	14.0281i	1.68744	−	0.812627i
$299$	−0.783317	+	0.377226i	−0.0453004	+	0.0218155i
$300$		0			0
$301$	4.78590	+	2.30477i	0.275855	+	0.132845i
$302$	−15.1557			−0.872115
$303$	6.12868	+	2.95142i	0.352083	+	0.169554i
$304$	37.1532	−	46.5887i	2.13088	−	2.67204i
$305$		0			0
$306$	−38.1135	−	18.3545i	−2.17880	−	1.04926i
$307$	−30.1707			−1.72193			−0.860966	−	0.508663i	$-0.830140\pi$
$307$	−30.1707			−1.72193			−0.860966	+	0.508663i	$0.830140\pi$
$308$	−32.9469	−	15.8664i	−1.87733	−	0.904072i
$309$	0.772469	−	3.38441i	0.0439443	−	0.192532i
$310$		0			0
$311$	26.9819	−	12.9938i	1.53000	−	0.736811i	0.535803	−	0.844343i	$-0.320009\pi$
$311$	26.9819	−	12.9938i	1.53000	−	0.736811i	0.994202	+	0.107532i	$0.0342948\pi$
$312$	2.14096	+	9.38015i	0.121208	+	0.531046i
$313$	10.4536	−	13.1084i	0.590871	−	0.740928i	−0.393054	−	0.919516i	$-0.628581\pi$
$313$	10.4536	−	13.1084i	0.590871	−	0.740928i	0.983924	+	0.178587i	$0.0571527\pi$
$314$	−5.61783	−	7.04454i	−0.317033	−	0.397546i
$315$		0			0
$316$	−0.347949	−	1.52447i	−0.0195737	−	0.0857579i
$317$	−7.96916	−	9.99301i	−0.447593	−	0.561263i	0.505934	−	0.862572i	$-0.331148\pi$
$317$	−7.96916	−	9.99301i	−0.447593	−	0.561263i	−0.953527	+	0.301309i	$0.902576\pi$
$318$	10.9312			0.612992
$319$	5.74109	−	17.6155i	0.321439	−	0.986277i
$320$		0			0
$321$	−5.24653	−	6.57894i	−0.292833	−	0.367200i
$322$	−0.781410	−	3.42358i	−0.0435463	−	0.190789i
$323$	4.33733	−	19.0031i	0.241335	−	1.05736i
$324$	17.2611	+	21.6447i	0.958949	+	1.20248i
$325$		0			0
$326$	7.40189	+	32.4298i	0.409953	+	1.79612i
$327$	−8.95901	+	4.31443i	−0.495434	+	0.238589i
$328$	−32.7932	+	15.7924i	−1.81070	+	0.871989i
$329$	−3.53743	+	15.4985i	−0.195025	+	0.854460i
$330$		0			0
$331$	13.2637			0.729037			0.364518	−	0.931196i	$-0.381234\pi$
$331$	13.2637			0.729037			0.364518	+	0.931196i	$0.381234\pi$
$332$	−29.1766	−	14.0507i	−1.60128	−	0.771134i
$333$	8.40554	−	10.5402i	0.460621	−	0.577600i
$334$	26.8874	−	33.7157i	1.47121	−	1.84484i
$335$		0			0
$336$	−23.8032			−1.29857
$337$	4.05115	+	1.95093i	0.220680	+	0.106274i	0.540958	−	0.841050i	$-0.318062\pi$
$337$	4.05115	+	1.95093i	0.220680	+	0.106274i	−0.320277	+	0.947324i	$0.603776\pi$
$338$	7.11177	−	31.1587i	0.386829	−	1.69481i
$339$	−2.65884	+	1.28043i	−0.144409	+	0.0695435i
$340$		0			0
$341$	0.373499	+	1.63640i	0.0202261	+	0.0886162i
$342$	−14.0673	+	17.6399i	−0.760675	+	0.953856i
$343$	12.1233	+	15.2021i	0.654595	+	0.820836i
$344$	−7.00286	+	30.6815i	−0.377569	+	1.65424i
$345$		0			0
$346$	−43.5330	−	54.5887i	−2.34035	−	2.93471i
$347$	−8.91901			−0.478798			−0.239399	−	0.970921i	$-0.576950\pi$
$347$	−8.91901			−0.478798			−0.239399	+	0.970921i	$0.576950\pi$
$348$	−2.97349	−	22.1002i	−0.159396	−	1.18470i
$349$	16.4945			0.882933			0.441466	−	0.897278i	$-0.354458\pi$
$349$	16.4945			0.882933			0.441466	+	0.897278i	$0.354458\pi$
$350$		0			0
$351$	−1.09278	−	4.78777i	−0.0583281	−	0.255552i
$352$	23.1377	−	101.373i	1.23324	−	5.40319i
$353$	−14.1787	−	17.7796i	−0.754658	−	0.946311i	0.245073	−	0.969505i	$-0.421188\pi$
$353$	−14.1787	−	17.7796i	−0.754658	−	0.946311i	−0.999731	+	0.0231933i	$0.992617\pi$
$354$	−14.1885	+	17.7919i	−0.754113	+	0.945628i
$355$		0			0
$356$	5.88640	−	2.83474i	0.311979	−	0.150241i
$357$	−7.01503	+	3.37826i	−0.371275	+	0.178796i
$358$	−4.11566	+	18.0319i	−0.217519	+	0.953014i
$359$	−13.6918	−	6.59362i	−0.722625	−	0.347998i	0.0361538	−	0.999346i	$-0.488489\pi$
$359$	−13.6918	−	6.59362i	−0.722625	−	0.347998i	−0.758779	+	0.651348i	$0.774204\pi$
$360$		0			0
$361$	7.75196	+	3.73315i	0.407998	+	0.196481i
$362$	16.1718	−	20.2788i	0.849969	−	1.06583i
$363$	0.369539	−	0.463388i	0.0193958	−	0.0243216i
$364$	−12.0749	−	5.81498i	−0.632898	−	0.304788i
$365$		0			0
$366$	14.6723	+	7.06583i	0.766936	+	0.369337i
$367$	5.82850	−	25.5363i	0.304245	−	1.33299i	−0.559405	−	0.828894i	$-0.688970\pi$
$367$	5.82850	−	25.5363i	0.304245	−	1.33299i	0.863650	−	0.504091i	$-0.168172\pi$
$368$	11.4812	−	5.52905i	0.598498	−	0.288221i
$369$	7.60532	−	3.66253i	0.395917	−	0.190664i
$370$		0			0
$371$	−6.24564	+	7.83178i	−0.324257	+	0.406606i
$372$	1.25958	+	1.57946i	0.0653060	+	0.0818912i
$373$	−4.03038	+	17.6582i	−0.208685	+	0.914309i	0.756758	+	0.653695i	$0.226782\pi$
$373$	−4.03038	+	17.6582i	−0.208685	+	0.914309i	−0.965443	+	0.260614i	$0.916075\pi$
$374$	−12.9635	−	56.7969i	−0.670328	−	2.93690i
$375$		0			0
$376$	−94.1820			−4.85707
$377$	2.10409	−	6.45601i	0.108366	−	0.332501i
$378$	19.8354			1.02022
$379$	3.11944	+	3.91166i	0.160235	+	0.200928i	0.855467	−	0.517857i	$-0.173270\pi$
$379$	3.11944	+	3.91166i	0.160235	+	0.200928i	−0.695232	+	0.718785i	$0.744699\pi$
$380$		0			0
$381$	−0.705820	+	3.09240i	−0.0361602	+	0.158428i
$382$	−4.51702	−	5.66416i	−0.231111	−	0.289804i
$383$	−14.3119	+	17.9465i	−0.731303	+	0.917025i	−0.998918	−	0.0465008i	$-0.985193\pi$
$383$	−14.3119	+	17.9465i	−0.731303	+	0.917025i	0.267615	+	0.963526i	$0.413764\pi$
$384$	−11.5288	−	50.5109i	−0.588326	−	2.57763i
$385$		0			0
$386$	−18.3473	+	8.83557i	−0.933851	+	0.449719i
$387$	1.62408	−	7.11558i	0.0825568	−	0.361705i
$388$	5.98285	+	2.88119i	0.303733	+	0.146270i
$389$	8.54415			0.433205			0.216603	−	0.976260i	$-0.430502\pi$
$389$	8.54415			0.433205			0.216603	+	0.976260i	$0.430502\pi$
$390$		0			0
$391$	2.59891	−	3.25893i	0.131432	−	0.164811i
$392$	−24.8102	+	31.1111i	−1.25311	+	1.57135i
$393$	−12.5422	−	6.04001i	−0.632670	−	0.304678i
$394$	57.3676			2.89014
$395$		0			0
$396$	−11.1805	+	48.9848i	−0.561840	+	2.46158i
$397$	1.83429	−	0.883346i	0.0920602	−	0.0443339i	−0.387287	−	0.921959i	$-0.626588\pi$
$397$	1.83429	−	0.883346i	0.0920602	−	0.0443339i	0.479347	+	0.877625i	$0.340873\pi$
$398$	−27.3427	+	13.1676i	−1.37057	+	0.660030i
$399$	0.924068	+	4.04861i	0.0462613	+	0.202684i
$400$		0			0
$401$	−15.3418	−	19.2380i	−0.766132	−	0.960699i	0.233801	−	0.972285i	$-0.424884\pi$
$401$	−15.3418	−	19.2380i	−0.766132	−	0.960699i	−0.999933	+	0.0115852i	$0.996312\pi$
$402$	6.36924	−	27.9055i	0.317669	−	1.39180i
$403$	0.136886	+	0.599736i	0.00681877	+	0.0298750i
$404$	−35.0006	−	43.8894i	−1.74134	−	2.18358i
$405$		0			0
$406$	23.5313	+	14.0880i	1.16784	+	0.699174i
$407$	18.5661			0.920285
$408$	−28.7607	−	36.0648i	−1.42387	−	1.78547i
$409$	−1.96847	−	8.62445i	−0.0973348	−	0.426452i	0.902658	−	0.430360i	$-0.141613\pi$
$409$	−1.96847	−	8.62445i	−0.0973348	−	0.426452i	−0.999992	+	0.00390791i	$0.998756\pi$
$410$		0			0
$411$	2.12313	+	2.66232i	0.104726	+	0.131322i
$412$	−17.8619	+	22.3982i	−0.879995	+	1.10348i
$413$	−4.64043	−	20.3311i	−0.228341	−	1.00043i
$414$	−4.34712	+	2.09346i	−0.213650	+	0.102888i
$415$		0			0
$416$	8.47988	−	37.1528i	0.415760	−	1.82157i
$417$	3.20071	+	1.54138i	0.156739	+	0.0754817i
$418$	−31.0718			−1.51977
$419$	−5.04772	−	2.43086i	−0.246597	−	0.118755i	0.306503	−	0.951870i	$-0.400841\pi$
$419$	−5.04772	−	2.43086i	−0.246597	−	0.118755i	−0.553100	+	0.833115i	$0.686555\pi$
$420$		0			0
$421$	−11.5526	+	14.4865i	−0.563040	+	0.706030i	−0.979117	−	0.203299i	$-0.934834\pi$
$421$	−11.5526	+	14.4865i	−0.563040	+	0.706030i	0.416076	+	0.909330i	$0.363405\pi$
$422$	−35.3157	−	17.0071i	−1.71914	−	0.827894i
$423$	21.8424			1.06202
$424$	−53.4698	−	25.7497i	−2.59672	−	1.25051i
$425$		0			0
$426$	6.90062	−	3.32317i	0.334336	−	0.161008i
$427$	−13.4455	+	6.47503i	−0.650676	+	0.313349i
$428$	15.4526	+	67.7024i	0.746931	+	3.27252i
$429$	1.91594	−	2.40252i	0.0925026	−	0.115995i
$430$		0			0
$431$	5.61452	−	24.5988i	0.270442	−	1.18488i	−0.639051	−	0.769164i	$-0.720673\pi$
$431$	5.61452	−	24.5988i	0.270442	−	1.18488i	0.909493	−	0.415719i	$-0.136470\pi$
$432$	16.0170	+	70.1749i	0.770617	+	3.37629i
$433$	−3.74715	−	4.69878i	−0.180076	−	0.225809i	0.683598	−	0.729859i	$-0.260414\pi$
$433$	−3.74715	−	4.69878i	−0.180076	−	0.225809i	−0.863674	+	0.504050i	$0.831843\pi$
$434$	−2.48467			−0.119268
$435$		0			0
$436$	82.0614			3.93003
$437$	−1.38613	−	1.73815i	−0.0663076	−	0.0831471i
$438$	1.08659	+	4.76065i	0.0519192	+	0.227473i
$439$	0.359081	−	1.57324i	0.0171380	−	0.0750864i	−0.965636	−	0.259899i	$-0.916311\pi$
$439$	0.359081	−	1.57324i	0.0171380	−	0.0750864i	0.982774	+	0.184813i	$0.0591678\pi$
$440$		0			0
$441$	5.75392	−	7.21519i	0.273996	−	0.343580i
$442$	−4.75108	−	20.8159i	−0.225986	−	0.990110i
$443$	−17.4076	+	8.38304i	−0.827059	+	0.398290i	−0.799011	−	0.601316i	$-0.794643\pi$
$443$	−17.4076	+	8.38304i	−0.827059	+	0.398290i	−0.0280475	+	0.999607i	$0.508929\pi$
$444$	20.1329	−	9.69550i	0.955466	−	0.460128i
$445$		0			0
$446$	42.4095	+	20.4233i	2.00815	+	0.967073i
$447$	−8.17637			−0.386729
$448$	78.1274	+	37.6242i	3.69117	+	1.77757i
$449$	−21.7030	+	27.2147i	−1.02423	+	1.28434i	−0.0661551	+	0.997809i	$0.521073\pi$
$449$	−21.7030	+	27.2147i	−1.02423	+	1.28434i	−0.958071	+	0.286530i	$0.907498\pi$
$450$		0			0
$451$	10.4737	+	5.04387i	0.493188	+	0.237507i
$452$	24.3541			1.14552
$453$	3.45320	+	1.66297i	0.162245	+	0.0781333i
$454$	3.86620	−	16.9389i	0.181450	−	0.794983i
$455$		0			0
$456$	−22.1663	+	10.6747i	−1.03803	+	0.499891i
$457$	1.53782	+	6.73762i	0.0719361	+	0.315173i	0.998076	−	0.0620084i	$-0.0197506\pi$
$457$	1.53782	+	6.73762i	0.0719361	+	0.315173i	−0.926140	+	0.377181i	$0.876893\pi$
$458$	−44.2271	+	55.4590i	−2.06660	+	2.59143i
$459$	14.6799	+	18.4080i	0.685199	+	0.859213i
$460$		0			0
$461$	−2.98798	−	13.0912i	−0.139164	−	0.609718i	−0.995620	−	0.0934970i	$-0.970195\pi$
$461$	−2.98798	−	13.0912i	−0.139164	−	0.609718i	0.856455	−	0.516221i	$-0.172662\pi$
$462$	7.73861	+	9.70391i	0.360033	+	0.451467i
$463$	11.0362			0.512896			0.256448	−	0.966558i	$-0.417448\pi$
$463$	11.0362			0.512896			0.256448	+	0.966558i	$0.417448\pi$
$464$	−30.8399	+	94.6266i	−1.43171	+	4.39293i
$465$		0			0
$466$	−25.5969	−	32.0975i	−1.18575	−	1.48689i
$467$	2.66034	+	11.6557i	0.123106	+	0.539361i	0.998440	+	0.0558422i	$0.0177844\pi$
$467$	2.66034	+	11.6557i	0.123106	+	0.539361i	−0.875334	+	0.483519i	$0.839358\pi$
$468$	−4.09760	+	17.9528i	−0.189412	+	0.829867i
$469$	16.3540	+	20.5073i	0.755159	+	0.946940i
$470$		0			0
$471$	0.507043	+	2.22150i	0.0233633	+	0.102361i
$472$	111.314	−	53.6058i	5.12363	−	2.46741i
$473$	9.05588	−	4.36108i	0.416390	−	0.200523i
$474$	−0.118099	+	0.517424i	−0.00542445	+	0.0237660i
$475$		0			0
$476$	64.2552			2.94513
$477$	12.4006	+	5.97179i	0.567782	+	0.273430i
$478$	22.2541	−	27.9058i	1.01788	−	1.27638i
$479$	22.0796	−	27.6869i	1.00884	−	1.26505i	0.0448823	−	0.998992i	$-0.485709\pi$
$479$	22.0796	−	27.6869i	1.00884	−	1.26505i	0.963958	−	0.266054i	$-0.0857198\pi$
$480$		0			0
$481$	6.80439			0.310254
$482$	−42.6662	−	20.5470i	−1.94339	−	0.935888i
$483$	−0.197612	+	0.865796i	−0.00899167	+	0.0393951i
$484$	−4.40687	+	2.12224i	−0.200312	+	0.0964653i
$485$		0			0
$486$	−9.37349	−	41.0680i	−0.425190	−	1.86288i
$487$	−9.18266	+	11.5147i	−0.416106	+	0.521780i	−0.945072	−	0.326863i	$-0.894009\pi$
$487$	−9.18266	+	11.5147i	−0.416106	+	0.521780i	0.528966	+	0.848643i	$0.322580\pi$
$488$	−55.1251	−	69.1246i	−2.49539	−	3.12913i
$489$	1.87188	−	8.20122i	0.0846492	−	0.370872i
$490$		0			0
$491$	11.6547	+	14.6146i	0.525970	+	0.659546i	0.971865	−	0.235540i	$-0.0756858\pi$
$491$	11.6547	+	14.6146i	0.525970	+	0.659546i	−0.445895	+	0.895085i	$0.647114\pi$
$492$	13.9916			0.630791
$493$	4.34103	+	32.2643i	0.195510	+	1.45311i
$494$	−11.3877			−0.512356
$495$		0			0
$496$	−2.00635	−	8.79041i	−0.0900880	−	0.394701i
$497$	−1.56181	+	6.84274i	−0.0700568	+	0.306939i
$498$	6.85304	+	8.59344i	0.307092	+	0.385081i
$499$	4.50786	−	5.65268i	0.201800	−	0.253049i	−0.670626	−	0.741796i	$-0.733974\pi$
$499$	4.50786	−	5.65268i	0.201800	−	0.253049i	0.872426	+	0.488747i	$0.162546\pi$
$500$		0			0
$501$	−9.82571	+	4.73181i	−0.438980	+	0.211402i
$502$	−10.8187	+	5.21000i	−0.482861	+	0.232533i
$503$	1.29045	−	5.65385i	0.0575385	−	0.252093i	−0.937976	−	0.346700i	$-0.887302\pi$
$503$	1.29045	−	5.65385i	0.0575385	−	0.252093i	0.995515	+	0.0946070i	$0.0301594\pi$
$504$	−44.0850	−	21.2302i	−1.96370	−	0.945668i
$505$		0			0
$506$	−5.98667	−	2.88303i	−0.266140	−	0.128166i
$507$	−5.03931	+	6.31909i	−0.223803	+	0.280641i
$508$	16.3208	−	20.4656i	0.724118	−	0.908015i
$509$	−32.2732	−	15.5420i	−1.43048	−	0.688885i	−0.451397	−	0.892323i	$-0.649074\pi$
$509$	−32.2732	−	15.5420i	−1.43048	−	0.688885i	−0.979088	+	0.203438i	$0.934788\pi$
$510$		0			0
$511$	−4.03165	−	1.94154i	−0.178350	−	0.0858887i
$512$	−35.6905	+	156.370i	−1.57731	+	6.91066i
$513$	11.3140	−	5.44855i	0.499527	−	0.240559i
$514$	−21.3852	+	10.2985i	−0.943259	+	0.454250i
$515$		0			0
$516$	7.54271	−	9.45826i	0.332049	−	0.416377i
$517$	18.7548	+	23.5178i	0.824837	+	1.03431i
$518$	−6.11562	+	26.7943i	−0.268705	+	1.17727i
$519$	3.92912	+	17.2146i	0.172469	+	0.755636i
$520$		0			0
$521$	−10.6623			−0.467125			−0.233562	−	0.972342i	$-0.575038\pi$
$521$	−10.6623			−0.467125			−0.233562	+	0.972342i	$0.575038\pi$
$522$	11.6769	−	35.8285i	0.511085	−	1.56817i
$523$	7.23345			0.316297			0.158148	−	0.987415i	$-0.449448\pi$
$523$	7.23345			0.316297			0.158148	+	0.987415i	$0.449448\pi$
$524$	71.6279	+	89.8185i	3.12908	+	3.92374i
$525$		0			0
$526$	−4.40185	+	19.2858i	−0.191930	+	0.840899i
$527$	−1.83887	−	2.30587i	−0.0801024	−	0.100445i
$528$	−28.0822	+	35.2140i	−1.22212	+	1.53249i
$529$	5.01219	+	21.9598i	0.217921	+	0.954775i
$530$		0			0
$531$	−25.8155	+	12.4321i	−1.12030	+	0.539508i
$532$	7.62593	−	33.4114i	0.330626	−	1.44857i
$533$	3.83858	+	1.84856i	0.166267	+	0.0800701i
$534$	−2.21753			−0.0959617
$535$		0			0
$536$	−96.8894	+	121.495i	−4.18498	+	5.24780i
$537$	2.91630	−	3.65693i	0.125848	−	0.157808i
$538$	−59.1371	−	28.4789i	−2.54958	−	1.22781i
$539$	12.7092			0.547423
$540$		0			0
$541$	0.153391	−	0.672049i	0.00659479	−	0.0288937i	−0.971523	−	0.236943i	$-0.923854\pi$
$541$	0.153391	−	0.672049i	0.00659479	−	0.0288937i	0.978118	+	0.208050i	$0.0667116\pi$
$542$	37.9578	−	18.2795i	1.63043	−	0.785172i
$543$	−5.90980	+	2.84601i	−0.253614	+	0.122134i
$544$	40.6559	+	178.125i	1.74311	+	7.63705i
$545$		0			0
$546$	2.83617	+	3.55645i	0.121377	+	0.152202i
$547$	−6.14533	+	26.9245i	−0.262756	+	1.15121i	0.655493	+	0.755202i	$0.272461\pi$
$547$	−6.14533	+	26.9245i	−0.262756	+	1.15121i	−0.918248	+	0.396006i	$0.870396\pi$
$548$	−6.25326	−	27.3973i	−0.267126	−	1.17036i
$549$	12.7845	+	16.0312i	0.545627	+	0.684195i
$550$		0			0
$551$	17.2920	+	1.57194i	0.736663	+	0.0669670i
$552$	−5.26131			−0.223936
$553$	−0.303237	−	0.380247i	−0.0128949	−	0.0161697i
$554$	1.72184	+	7.54386i	0.0731539	+	0.320508i
$555$		0			0
$556$	−18.2791	−	22.9213i	−0.775207	−	0.972078i
$557$	−0.0514036	+	0.0644581i	−0.00217804	+	0.00273118i	−0.782919	−	0.622123i	$-0.786270\pi$
$557$	−0.0514036	+	0.0644581i	−0.00217804	+	0.00273118i	0.780741	+	0.624854i	$0.214842\pi$
$558$	0.759667	+	3.32832i	0.0321593	+	0.140899i
$559$	3.31895	−	1.59832i	0.140376	−	0.0676017i
$560$		0			0
$561$	−3.27837	+	14.3635i	−0.138413	+	0.606426i
$562$	−74.8006	−	36.0221i	−3.15527	−	1.51950i
$563$	−11.1085			−0.468167			−0.234083	−	0.972217i	$-0.575209\pi$
$563$	−11.1085			−0.468167			−0.234083	+	0.972217i	$0.575209\pi$
$564$	32.6190	+	15.7085i	1.37351	+	0.661447i
$565$		0			0
$566$	5.69442	−	7.14057i	0.239354	−	0.300141i
$567$	7.75811	+	3.73611i	0.325810	+	0.156902i
$568$	−41.5823			−1.74475
$569$	−25.8173	−	12.4330i	−1.08232	−	0.521217i	−0.194262	−	0.980950i	$-0.562231\pi$
$569$	−25.8173	−	12.4330i	−1.08232	−	0.521217i	−0.888058	+	0.459732i	$0.847945\pi$
$570$		0			0
$571$	18.3904	−	8.85636i	0.769616	−	0.370627i	−0.00751092	−	0.999972i	$-0.502391\pi$
$571$	18.3904	−	8.85636i	0.769616	−	0.370627i	0.777126	+	0.629344i	$0.216677\pi$
$572$	−22.8482	+	11.0031i	−0.955331	+	0.460063i
$573$	0.407688	+	1.78620i	0.0170314	+	0.0746195i
$574$	−10.7293	+	13.4541i	−0.447831	+	0.561563i
$575$		0			0
$576$	26.5123	−	116.158i	1.10468	−	4.83992i
$577$	−2.47287	−	10.8343i	−0.102947	−	0.451039i	−0.999959	−	0.00903403i	$-0.997124\pi$
$577$	−2.47287	−	10.8343i	−0.102947	−	0.451039i	0.897012	−	0.442005i	$-0.145733\pi$
$578$	34.1351	+	42.8041i	1.41983	+	1.78041i
$579$	5.14986			0.214021
$580$		0			0
$581$	−10.0724			−0.417873
$582$	−1.40526	−	1.76214i	−0.0582499	−	0.0730430i
$583$	4.21779	+	18.4794i	0.174683	+	0.765337i
$584$	5.89922	−	25.8462i	0.244112	−	1.06952i
$585$		0			0
$586$	−17.7922	+	22.3108i	−0.734991	+	0.921650i
$587$	8.27164	+	36.2404i	0.341407	+	1.49580i	0.796106	+	0.605157i	$0.206890\pi$
$587$	8.27164	+	36.2404i	0.341407	+	1.49580i	−0.454699	+	0.890645i	$0.650253\pi$
$588$	13.7818	−	6.63695i	0.568350	−	0.273703i
$589$	−1.41724	+	0.682509i	−0.0583965	+	0.0281223i
$590$		0			0
$591$	−13.0711	−	6.29470i	−0.537672	−	0.258929i
$592$	−99.7329			−4.09900
$593$	−34.7808	−	16.7495i	−1.42828	−	0.687821i	−0.449600	−	0.893230i	$-0.648433\pi$
$593$	−34.7808	−	16.7495i	−1.42828	−	0.687821i	−0.978676	+	0.205409i	$0.934148\pi$
$594$	23.4012	−	29.3441i	0.960162	−	1.20400i
$595$		0			0
$596$	60.7938	+	29.2767i	2.49021	+	1.19922i
$597$	7.67479			0.314108
$598$	−2.19409	−	1.05662i	−0.0897231	−	0.0432084i
$599$	3.04410	−	13.3371i	0.124379	−	0.544938i	−0.873890	−	0.486123i	$-0.838411\pi$
$599$	3.04410	−	13.3371i	0.124379	−	0.544938i	0.998269	−	0.0588148i	$-0.0187322\pi$
$600$		0			0
$601$	3.45201	−	1.66240i	0.140811	−	0.0678108i	−0.362152	−	0.932119i	$-0.617958\pi$
$601$	3.45201	−	1.66240i	0.140811	−	0.0678108i	0.502962	+	0.864308i	$0.332243\pi$
$602$	3.31087	+	14.5059i	0.134941	+	0.591215i
$603$	22.4703	−	28.1769i	0.915062	−	1.14745i
$604$	−19.7211	−	24.7294i	−0.802438	−	1.00623i
$605$		0			0
$606$	4.23980	+	18.5758i	0.172230	+	0.754590i
$607$	17.7307	+	22.2336i	0.719665	+	0.902432i	0.998319	−	0.0579597i	$-0.0184595\pi$
$607$	17.7307	+	22.2336i	0.719665	+	0.902432i	−0.278653	+	0.960392i	$0.589888\pi$
$608$	97.4465			3.95198
$609$	−3.81574	−	5.79190i	−0.154622	−	0.234700i
$610$		0			0
$611$	6.87358	+	8.61920i	0.278075	+	0.348696i
$612$	−19.6455	−	86.0726i	−0.794123	−	3.47928i
$613$	10.5696	−	46.3083i	0.426901	−	1.87038i	−0.0620623	−	0.998072i	$-0.519768\pi$
$613$	10.5696	−	46.3083i	0.426901	−	1.87038i	0.488964	−	0.872304i	$-0.337375\pi$
$614$	−52.6904	−	66.0717i	−2.12641	−	2.66644i
$615$		0			0
$616$	−14.9946	−	65.6956i	−0.604149	−	2.64695i
$617$	20.1373	−	9.69761i	0.810697	−	0.390411i	0.0178568	−	0.999841i	$-0.494316\pi$
$617$	20.1373	−	9.69761i	0.810697	−	0.390411i	0.792840	+	0.609429i	$0.208601\pi$
$618$	8.76068	−	4.21892i	0.352406	−	0.169710i
$619$	−6.41964	+	28.1263i	−0.258027	+	1.13049i	0.665330	+	0.746549i	$0.268291\pi$
$619$	−6.41964	+	28.1263i	−0.258027	+	1.13049i	−0.923357	+	0.383941i	$0.874566\pi$
$620$		0			0
$621$	2.68545			0.107763
$622$	75.5771	+	36.3960i	3.03037	+	1.45935i
$623$	1.26700	−	1.58877i	0.0507613	−	0.0636527i
$624$	−10.2920	+	12.9058i	−0.412011	+	0.516646i
$625$		0			0
$626$	46.9627			1.87701
$627$	7.07962	+	3.40937i	0.282733	+	0.136157i
$628$	4.18440	−	18.3331i	0.166976	−	0.731569i
$629$	−29.3922	+	14.1546i	−1.17195	+	0.564379i
$630$		0			0
$631$	−5.51970	−	24.1834i	−0.219736	−	0.962726i	−0.957673	−	0.287857i	$-0.907057\pi$
$631$	−5.51970	−	24.1834i	−0.219736	−	0.962726i	0.737938	−	0.674869i	$-0.235800\pi$
$632$	1.79652	−	2.25277i	0.0714619	−	0.0896104i
$633$	6.18047	+	7.75007i	0.245652	+	0.308037i
$634$	7.96657	−	34.9038i	0.316393	−	1.38621i
$635$		0			0
$636$	14.2240	+	17.8363i	0.564018	+	0.707256i
$637$	4.65787			0.184552
$638$	48.6030	−	18.1913i	1.92421	−	0.720200i
$639$	9.64365			0.381497
$640$		0			0
$641$	−2.82243	−	12.3659i	−0.111479	−	0.488423i	−0.999586	−	0.0287849i	$-0.990836\pi$
$641$	−2.82243	−	12.3659i	−0.111479	−	0.488423i	0.888106	−	0.459638i	$-0.152021\pi$
$642$	5.24482	−	22.9791i	0.206997	−	0.906912i
$643$	1.02859	+	1.28982i	0.0405638	+	0.0508654i	0.801700	−	0.597727i	$-0.203929\pi$
$643$	1.02859	+	1.28982i	0.0405638	+	0.0508654i	−0.761136	+	0.648593i	$0.775358\pi$
$644$	4.56942	−	5.72987i	0.180060	−	0.225789i
$645$		0			0
$646$	49.1902	−	23.6888i	1.93536	−	0.932022i
$647$	20.0945	−	9.67703i	0.789998	−	0.380443i	0.00503650	−	0.999987i	$-0.498397\pi$
$647$	20.0945	−	9.67703i	0.789998	−	0.380443i	0.784962	+	0.619544i	$0.212683\pi$
$648$	−11.3519	+	49.7359i	−0.445944	+	1.95381i
$649$	−35.5520	−	17.1210i	−1.39554	−	0.672056i
$650$		0			0
$651$	0.566126	+	0.272632i	0.0221882	+	0.0106853i
$652$	−43.2837	+	54.2760i	−1.69512	+	2.12561i
$653$	15.3840	−	19.2909i	0.602021	−	0.754911i	−0.383670	−	0.923470i	$-0.625340\pi$
$653$	15.3840	−	19.2909i	0.602021	−	0.754911i	0.985692	+	0.168559i	$0.0539115\pi$
$654$	−25.0944	−	12.0848i	−0.981270	−	0.472555i
$655$		0			0
$656$	−56.2625	−	27.0946i	−2.19668	−	1.05787i
$657$	−1.36813	+	5.99417i	−0.0533759	+	0.233855i
$658$	−40.1185	+	19.3200i	−1.56398	+	0.753173i
$659$	−24.5652	+	11.8300i	−0.956924	+	0.460830i	−0.846109	−	0.533011i	$-0.821061\pi$
$659$	−24.5652	+	11.8300i	−0.956924	+	0.460830i	−0.110816	+	0.993841i	$0.535346\pi$
$660$		0			0
$661$	−2.56656	+	3.21837i	−0.0998278	+	0.125180i	−0.829236	−	0.558899i	$-0.811224\pi$
$661$	−2.56656	+	3.21837i	−0.0998278	+	0.125180i	0.729408	+	0.684079i	$0.239796\pi$
$662$	23.1638	+	29.0465i	0.900288	+	1.12893i
$663$	−1.20151	+	5.26416i	−0.0466628	+	0.204443i
$664$	−13.2787	−	58.1777i	−0.515313	−	2.25773i
$665$		0			0
$666$	37.7619			1.46324
$667$	3.18583	+	1.90733i	0.123356	+	0.0738519i
$668$	90.0001			3.48221
$669$	−7.42194	−	9.30681i	−0.286949	−	0.359822i
$670$		0			0
$671$	−6.28357	+	27.5301i	−0.242575	+	1.06279i
$672$	−24.2696	−	30.4332i	−0.936222	−	1.17399i
$673$	−17.8748	+	22.4143i	−0.689023	+	0.864008i	−0.996150	−	0.0876605i	$-0.972061\pi$
$673$	−17.8748	+	22.4143i	−0.689023	+	0.864008i	0.307127	+	0.951669i	$0.400632\pi$
$674$	2.80258	+	12.2789i	0.107951	+	0.472965i
$675$		0			0
$676$	60.0952	−	28.9403i	2.31136	−	1.11309i
$677$	−5.82430	+	25.5179i	−0.223846	+	0.980734i	0.730706	+	0.682692i	$0.239191\pi$
$677$	−5.82430	+	25.5179i	−0.223846	+	0.980734i	−0.954553	+	0.298042i	$0.903666\pi$
$678$	−7.44750	−	3.58653i	−0.286020	−	0.137740i
$679$	2.06541			0.0792631
$680$		0			0
$681$	−2.73954	+	3.43527i	−0.104979	+	0.131640i
$682$	−2.93133	+	3.67577i	−0.112246	+	0.140753i
$683$	18.5933	+	8.95404i	0.711451	+	0.342617i	0.754359	−	0.656462i	$-0.227948\pi$
$683$	18.5933	+	8.95404i	0.711451	+	0.342617i	−0.0429078	+	0.999079i	$0.513662\pi$
$684$	−47.0875			−1.80044
$685$		0			0
$686$	−12.1193	+	53.0983i	−0.462718	+	2.02730i
$687$	16.1623	−	7.78336i	0.616630	−	0.296954i
$688$	−48.6462	+	23.4268i	−1.85462	+	0.893138i
$689$	1.54581	+	6.77262i	0.0588905	+	0.258016i
$690$		0			0
$691$	31.6231	+	39.6541i	1.20300	+	1.50851i	0.807310	+	0.590128i	$0.200923\pi$
$691$	31.6231	+	39.6541i	1.20300	+	1.50851i	0.395689	+	0.918385i	$0.370506\pi$
$692$	32.4253	−	142.064i	1.23262	−	5.40048i
$693$	3.47750	+	15.2359i	0.132099	+	0.578765i
$694$	−15.5763	−	19.5320i	−0.591267	−	0.741426i
$695$		0			0
$696$	28.4233	−	29.6752i	1.07738	−	1.12483i
$697$	−20.4265			−0.773709
$698$	28.8063	+	36.1219i	1.09033	+	1.36724i
$699$	2.31027	+	10.1220i	0.0873825	+	0.382848i
$700$		0			0
$701$	13.8465	+	17.3630i	0.522976	+	0.655792i	0.971238	−	0.238111i	$-0.0765281\pi$
$701$	13.8465	+	17.3630i	0.522976	+	0.655792i	−0.448262	+	0.893902i	$0.647957\pi$
$702$	8.57644	−	10.7545i	0.323697	−	0.405903i
$703$	3.87175	+	16.9632i	0.146026	+	0.639781i
$704$	147.833	−	71.1924i	5.57165	−	2.68317i
$705$		0			0
$706$	14.1741	−	62.1009i	0.533451	−	2.33720i
$707$	−15.7313	−	7.57577i	−0.591635	−	0.284916i
$708$	−47.4933			−1.78491
$709$	−12.0714	−	5.81327i	−0.453350	−	0.218322i	0.193252	−	0.981149i	$-0.438096\pi$
$709$	−12.0714	−	5.81327i	−0.453350	−	0.218322i	−0.646602	+	0.762827i	$0.723811\pi$
$710$		0			0
$711$	−0.416645	+	0.522456i	−0.0156254	+	0.0195936i
$712$	10.8470	+	5.22363i	0.406508	+	0.195764i
$713$	−0.336391			−0.0125979
$714$	−19.6493	−	9.46260i	−0.735356	−	0.354129i
$715$		0			0
$716$	−34.7778	+	16.7481i	−1.29971	+	0.625906i
$717$	−8.13252	+	3.91642i	−0.303715	+	0.146261i
$718$	−9.47194	−	41.4993i	−0.353490	−	1.54874i
$719$	20.1882	−	25.3152i	0.752892	−	0.944097i	−0.246796	−	0.969067i	$-0.579378\pi$
$719$	20.1882	−	25.3152i	0.752892	−	0.944097i	0.999688	+	0.0249704i	$0.00794916\pi$
$720$		0			0
$721$	−1.98279	+	8.68719i	−0.0738431	+	0.323528i
$722$	5.36278	+	23.4959i	0.199582	+	0.874426i
$723$	7.46686	+	9.36315i	0.277696	+	0.348219i
$724$	54.1317			2.01179
$725$		0			0
$726$	1.66016			0.0616142
$727$	−12.8191	−	16.0746i	−0.475434	−	0.596175i	0.485058	−	0.874482i	$-0.338798\pi$
$727$	−12.8191	−	16.0746i	−0.475434	−	0.596175i	−0.960492	+	0.278306i	$0.910227\pi$
$728$	−5.49546	−	24.0772i	−0.203675	−	0.892361i
$729$	0.790997	−	3.46559i	0.0292962	−	0.128355i
$730$		0			0
$731$	−11.0117	+	13.8082i	−0.407282	+	0.510715i
$732$	7.56283	+	33.1349i	0.279530	+	1.22470i
$733$	−38.4982	+	18.5398i	−1.42197	+	0.684782i	−0.977485	−	0.211006i	$-0.932326\pi$
$733$	−38.4982	+	18.5398i	−1.42197	+	0.684782i	−0.444480	+	0.895789i	$0.646612\pi$
$734$	66.1018	−	31.8329i	2.43986	−	1.17498i
$735$		0			0
$736$	18.7752	+	9.04168i	0.692065	+	0.333281i
$737$	49.6321			1.82822
$738$	21.3027	+	10.2588i	0.784163	+	0.377633i
$739$	−22.1975	+	27.8348i	−0.816549	+	1.02392i	0.182621	+	0.983183i	$0.441542\pi$
$739$	−22.1975	+	27.8348i	−0.816549	+	1.02392i	−0.999170	+	0.0407362i	$0.987030\pi$
$740$		0			0
$741$	2.59466	+	1.24952i	0.0953171	+	0.0459023i
$742$	−28.0585			−1.03006
$743$	−33.8547	−	16.3036i	−1.24201	−	0.598120i	−0.306650	−	0.951822i	$-0.599208\pi$
$743$	−33.8547	−	16.3036i	−1.24201	−	0.598120i	−0.935358	+	0.353703i	$0.884922\pi$
$744$	−0.828371	+	3.62933i	−0.0303696	+	0.133058i
$745$		0			0
$746$	−45.7091	+	22.0123i	−1.67353	+	0.805928i
$747$	3.07955	+	13.4924i	0.112675	+	0.493661i
$748$	75.8062	−	95.0580i	2.77175	−	3.47567i
$749$	13.4669	+	16.8870i	0.492071	+	0.617037i
$750$		0			0
$751$	6.15586	+	26.9706i	0.224631	+	0.984171i	0.953942	+	0.299990i	$0.0969832\pi$
$751$	6.15586	+	26.9706i	0.224631	+	0.984171i	−0.729312	+	0.684181i	$0.760160\pi$
$752$	−100.747	−	126.333i	−3.67387	−	4.60688i
$753$	3.03668			0.110663
$754$	17.8128	−	6.66704i	0.648705	−	0.242799i
$755$		0			0
$756$	25.8103	+	32.3652i	0.938713	+	1.17711i
$757$	−0.813259	−	3.56312i	−0.0295584	−	0.129504i	0.957996	−	0.286781i	$-0.0925854\pi$
$757$	−0.813259	−	3.56312i	−0.0295584	−	0.129504i	−0.987554	+	0.157278i	$0.949728\pi$
$758$	−3.11843	+	13.6627i	−0.113267	+	0.496253i
$759$	1.04771	+	1.31378i	0.0380293	+	0.0476873i
$760$		0			0
$761$	−2.91296	−	12.7625i	−0.105595	−	0.462640i	−0.999885	−	0.0151534i	$-0.995176\pi$
$761$	−2.91296	−	12.7625i	−0.105595	−	0.462640i	0.894291	−	0.447487i	$-0.147681\pi$
$762$	−8.00479	+	3.85491i	−0.289983	+	0.139648i
$763$	22.9962	−	11.0744i	0.832519	−	0.400920i
$764$	3.36447	−	14.7407i	0.121722	−	0.533300i
$765$		0			0
$766$	−64.2961			−2.32311
$767$	−13.0297	−	6.27477i	−0.470475	−	0.226569i
$768$	48.3549	−	60.6351i	1.74486	−	2.18798i
$769$	17.1156	−	21.4623i	0.617204	−	0.773949i	−0.370744	−	0.928735i	$-0.620897\pi$
$769$	17.1156	−	21.4623i	0.617204	−	0.773949i	0.987948	+	0.154786i	$0.0494687\pi$
$770$		0			0
$771$	6.00257			0.216177
$772$	−38.2908	−	18.4399i	−1.37812	−	0.663666i
$773$	10.3414	−	45.3087i	0.371955	−	1.62964i	−0.349329	−	0.937000i	$-0.613590\pi$
$773$	10.3414	−	45.3087i	0.371955	−	1.62964i	0.721283	−	0.692640i	$-0.243553\pi$
$774$	18.4189	−	8.87010i	0.662055	−	0.318829i
$775$		0			0
$776$	2.72288	+	11.9297i	0.0977456	+	0.428251i
$777$	4.33345	−	5.43398i	0.155462	−	0.194943i
$778$	14.9216	+	18.7111i	0.534965	+	0.670825i
$779$	−2.42426	+	10.6214i	−0.0868580	+	0.380550i
$780$		0			0
$781$	8.28045	+	10.3834i	0.296298	+	0.371546i
$782$	11.6756			0.417518
$783$	−14.5077	+	15.1466i	−0.518463	+	0.541297i
$784$	−68.2710			−2.43825
$785$		0			0
$786$	−8.67666	−	38.0149i	−0.309486	−	1.35595i
$787$	−2.12568	+	9.31321i	−0.0757722	+	0.331980i	−0.998580	−	0.0532820i	$-0.983032\pi$
$787$	−2.12568	+	9.31321i	−0.0757722	+	0.331980i	0.922807	+	0.385262i	$0.125889\pi$
$788$	74.6483	+	93.6060i	2.65923	+	3.33457i
$789$	3.11909	−	3.91122i	0.111043	−	0.139243i
$790$		0			0
$791$	6.82479	−	3.28665i	0.242662	−	0.116860i
$792$	−83.4176	+	40.1718i	−2.96411	+	1.42744i
$793$	−2.30291	+	10.0897i	−0.0817786	+	0.358296i
$794$	5.13789	+	2.47428i	0.182337	+	0.0878088i
$795$		0			0
$796$	−57.0644	−	27.4808i	−2.02259	−	0.974030i
$797$	−15.7525	+	19.7530i	−0.557982	+	0.699688i	−0.978183	−	0.207743i	$-0.933388\pi$
$797$	−15.7525	+	19.7530i	−0.557982	+	0.699688i	0.420201	+	0.907431i	$0.361960\pi$
$798$	−7.25237	+	9.09419i	−0.256731	+	0.321931i
$799$	−47.6209	−	22.9330i	−1.68471	−	0.811311i
$800$		0			0
$801$	−2.51560	−	1.21145i	−0.0888843	−	0.0428044i
$802$	15.3368	−	67.1949i	0.541561	−	2.37274i
$803$	−7.62869	+	3.67378i	−0.269211	+	0.129645i
$804$	53.8208	−	25.9187i	1.89811	−	0.914083i
$805$		0			0
$806$	−1.07432	+	1.34716i	−0.0378414	+	0.0474516i
$807$	10.3494	+	12.9777i	0.364315	+	0.456837i
$808$	23.0184	−	100.850i	0.809785	−	3.54790i
$809$	−0.146459	−	0.641681i	−0.00514924	−	0.0225603i	0.972288	−	0.233786i	$-0.0751116\pi$
$809$	−0.146459	−	0.641681i	−0.00514924	−	0.0225603i	−0.977437	+	0.211226i	$0.932254\pi$
$810$		0			0
$811$	16.0989			0.565311			0.282655	−	0.959222i	$-0.408785\pi$
$811$	16.0989			0.565311			0.282655	+	0.959222i	$0.408785\pi$
$812$	7.63243	+	56.7274i	0.267846	+	1.99074i
$813$	−10.6543			−0.373663
$814$	32.4240	+	40.6584i	1.13646	+	1.42508i
$815$		0			0
$816$	17.6107	−	77.1575i	0.616498	−	2.70105i
$817$	5.87309	+	7.36463i	0.205474	+	0.257656i
$818$	15.4492	−	19.3727i	0.540168	−	0.677350i
$819$	1.27449	+	5.58392i	0.0445344	+	0.195118i
$820$		0			0
$821$	5.26138	−	2.53375i	0.183624	−	0.0884284i	−0.339813	−	0.940493i	$-0.610364\pi$
$821$	5.26138	−	2.53375i	0.183624	−	0.0884284i	0.523437	+	0.852064i	$0.324650\pi$
$822$	−2.12244	+	9.29901i	−0.0740286	+	0.324340i
$823$	21.3783	+	10.2952i	0.745199	+	0.358869i	0.767642	−	0.640879i	$-0.221430\pi$
$823$	21.3783	+	10.2952i	0.745199	+	0.358869i	−0.0224426	+	0.999748i	$0.507144\pi$
$824$	−52.7908			−1.83905
$825$		0			0
$826$	36.4195	−	45.6687i	1.26720	−	1.58902i
$827$	−26.8628	+	33.6848i	−0.934110	+	1.17134i	0.0508766	+	0.998705i	$0.483798\pi$
$827$	−26.8628	+	33.6848i	−0.934110	+	1.17134i	−0.984986	+	0.172632i	$0.944773\pi$
$828$	−9.07247	−	4.36907i	−0.315290	−	0.151836i
$829$	37.8281			1.31382			0.656912	−	0.753967i	$-0.271862\pi$
$829$	37.8281			1.31382			0.656912	+	0.753967i	$0.271862\pi$
$830$		0			0
$831$	0.435438	−	1.90778i	0.0151052	−	0.0661802i
$832$	54.1801	−	26.0918i	1.87836	−	0.904569i
$833$	−20.1201	+	9.68935i	−0.697121	+	0.335716i
$834$	2.21424	+	9.70123i	0.0766729	+	0.335926i
$835$		0			0
$836$	−40.4314	−	50.6993i	−1.39835	−	1.75347i
$837$	0.422813	−	1.85246i	0.0146146	−	0.0640305i
$838$	−3.49200	−	15.2994i	−0.120629	−	0.528511i
$839$	14.1276	+	17.7155i	0.487740	+	0.611607i	0.963415	−	0.268014i	$-0.0863675\pi$
$839$	14.1276	+	17.7155i	0.487740	+	0.611607i	−0.475675	+	0.879621i	$0.657796\pi$
$840$		0			0
$841$	−27.9687	+	7.66490i	−0.964439	+	0.264307i
$842$	−51.9002			−1.78860
$843$	13.0906	+	16.4151i	0.450864	+	0.565365i
$844$	−18.2034	−	79.7542i	−0.626586	−	2.74525i
$845$		0			0
$846$	38.1459	+	47.8334i	1.31148	+	1.64455i
$847$	−0.948543	+	1.18944i	−0.0325923	+	0.0408695i
$848$	−22.6571	−	99.2672i	−0.778048	−	3.40885i
$849$	−2.08096	+	1.00214i	−0.0714185	+	0.0343933i
$850$		0			0
$851$	−0.827975	+	3.62759i	−0.0283826	+	0.124352i
$852$	14.4016	+	6.93546i	0.493392	+	0.237605i
$853$	−1.64615			−0.0563630			−0.0281815	−	0.999603i	$-0.508972\pi$
$853$	−1.64615			−0.0563630			−0.0281815	+	0.999603i	$0.508972\pi$
$854$	−37.6614	−	18.1368i	−1.28875	−	0.620627i
$855$		0			0
$856$	−79.7847	+	100.047i	−2.72698	+	3.41953i
$857$	−9.06517	−	4.36555i	−0.309660	−	0.149124i	0.272599	−	0.962128i	$-0.412117\pi$
$857$	−9.06517	−	4.36555i	−0.309660	−	0.149124i	−0.582259	+	0.813003i	$0.697831\pi$
$858$	8.60737			0.293851
$859$	35.0681	+	16.8879i	1.19651	+	0.576208i	0.922678	−	0.385570i	$-0.125995\pi$
$859$	35.0681	+	16.8879i	1.19651	+	0.576208i	0.273830	+	0.961778i	$0.411710\pi$
$860$		0			0
$861$	3.92090	−	1.88820i	0.133624	−	0.0643498i
$862$	63.6750	−	30.6643i	2.16878	−	1.04443i
$863$	−5.38247	−	23.5821i	−0.183221	−	0.802745i	−0.980084	−	0.198585i	$-0.936366\pi$
$863$	−5.38247	−	23.5821i	−0.183221	−	0.802745i	0.796862	−	0.604161i	$-0.206492\pi$
$864$	−73.3902	+	92.0284i	−2.49678	+	3.13087i
$865$		0			0
$866$	3.74593	−	16.4120i	0.127292	−	0.557703i
$867$	−3.08090	−	13.4983i	−0.104633	−	0.458426i
$868$	−3.23312	−	4.05420i	−0.109739	−	0.137608i
$869$	−0.920280			−0.0312183
$870$		0			0
$871$	18.1900			0.616344
$872$	94.2816	+	118.225i	3.19278	+	4.00362i
$873$	−0.631482	−	2.76670i	−0.0213724	−	0.0936387i
$874$	1.38568	−	6.07106i	0.0468714	−	0.205357i
$875$		0			0
$876$	−6.35399	+	7.96766i	−0.214682	+	0.269202i
$877$	−0.498604	−	2.18453i	−0.0168367	−	0.0737663i	0.965812	−	0.259245i	$-0.0834736\pi$
$877$	−0.498604	−	2.18453i	−0.0168367	−	0.0737663i	−0.982648	+	0.185478i	$0.940616\pi$
$878$	4.07238	−	1.96116i	0.137436	−	0.0661858i
$879$	6.50198	−	3.13119i	0.219306	−	0.105612i
$880$		0			0
$881$	50.6838	+	24.4081i	1.70758	+	0.822328i	0.992352	+	0.123439i	$0.0393923\pi$
$881$	50.6838	+	24.4081i	1.70758	+	0.822328i	0.715230	+	0.698889i	$0.246322\pi$
$882$	25.8495			0.870398
$883$	−52.2552	−	25.1648i	−1.75853	−	0.846862i	−0.973928	−	0.226857i	$-0.927155\pi$
$883$	−52.2552	−	25.1648i	−1.75853	−	0.846862i	−0.784598	−	0.620005i	$-0.787131\pi$
$884$	27.7827	−	34.8384i	0.934434	−	1.17174i
$885$		0			0
$886$	−48.7591	−	23.4811i	−1.63809	−	0.788864i
$887$	4.31316			0.144822			0.0724108	−	0.997375i	$-0.476931\pi$
$887$	4.31316			0.144822			0.0724108	+	0.997375i	$0.476931\pi$
$888$	37.0993	+	17.8661i	1.24497	+	0.599546i
$889$	1.81172	−	7.93765i	0.0607630	−	0.266220i
$890$		0			0
$891$	14.6799	−	7.06947i	0.491795	−	0.236836i
$892$	21.8599	+	95.7744i	0.731923	+	3.20676i
$893$	−17.5764	+	22.0401i	−0.588172	+	0.737545i
$894$	−14.2793	−	17.9057i	−0.477572	−	0.598856i
$895$		0			0
$896$	29.5924	+	129.653i	0.988613	+	4.33140i
$897$	0.383980	+	0.481496i	0.0128207	+	0.0160767i
$898$	−97.5006			−3.25364
$899$	1.81730	−	1.89733i	0.0606102	−	0.0632796i
$900$		0			0
$901$	−20.7657	−	26.0394i	−0.691807	−	0.867498i
$902$	7.24568	+	31.7454i	0.241255	+	1.05701i
$903$	0.837291	−	3.66841i	0.0278633	−	0.122077i
$904$	27.9808	+	35.0868i	0.930628	+	1.16697i
$905$		0			0
$906$	2.38891	+	10.4665i	0.0793663	+	0.347726i
$907$	−11.7170	+	5.64261i	−0.389057	+	0.187360i	−0.618178	−	0.786038i	$-0.712129\pi$
$907$	−11.7170	+	5.64261i	−0.389057	+	0.187360i	0.229121	+	0.973398i	$0.426415\pi$
$908$	32.6698	−	15.7329i	1.08418	−	0.522116i
$909$	−5.33837	+	23.3889i	−0.177062	+	0.775761i
$910$		0			0
$911$	15.9042			0.526928			0.263464	−	0.964669i	$-0.415135\pi$
$911$	15.9042			0.526928			0.263464	+	0.964669i	$0.415135\pi$
$912$	−38.0302	−	18.3144i	−1.25931	−	0.606450i
$913$	−11.8831	+	14.9009i	−0.393273	+	0.493149i
$914$	−12.0693	+	15.1344i	−0.399216	+	0.500601i
$915$		0			0
$916$	−148.041			−4.89142
$917$	32.1937	+	15.5036i	1.06313	+	0.511975i
$918$	−14.6751	+	64.2960i	−0.484352	+	2.12208i
$919$	−6.11088	+	2.94284i	−0.201579	+	0.0970755i	−0.531950	−	0.846776i	$-0.678541\pi$
$919$	−6.11088	+	2.94284i	−0.201579	+	0.0970755i	0.330371	+	0.943851i	$0.392826\pi$
$920$		0			0
$921$	4.75563	+	20.8358i	0.156703	+	0.686562i
$922$	23.4506	−	29.4061i	0.772304	−	0.968439i
$923$	3.03476	+	3.80546i	0.0998902	+	0.125258i
$924$	−5.76405	+	25.2540i	−0.189623	+	0.830795i
$925$		0			0
$926$	19.2738	+	24.1686i	0.633376	+	0.794228i
$927$	12.2431			0.402116
$928$	−152.428	+	57.0511i	−5.00368	+	1.87279i
$929$	−1.28775			−0.0422498			−0.0211249	−	0.999777i	$-0.506725\pi$
$929$	−1.28775			−0.0422498			−0.0211249	+	0.999777i	$0.506725\pi$
$930$		0			0
$931$	2.65036	+	11.6120i	0.0868622	+	0.380568i
$932$	19.0657	−	83.5321i	0.624517	−	2.73619i
$933$	−13.2265	−	16.5855i	−0.433016	−	0.542985i
$934$	−20.8791	+	26.1816i	−0.683186	+	0.856688i
$935$		0			0
$936$	−30.5722	+	14.7228i	−0.999285	+	0.481230i
$937$	27.4931	−	13.2400i	0.898159	−	0.432531i	0.0729354	−	0.997337i	$-0.476763\pi$
$937$	27.4931	−	13.2400i	0.898159	−	0.432531i	0.825224	+	0.564806i	$0.191049\pi$
$938$	−16.3487	+	71.6285i	−0.533805	+	2.33875i
$939$	−10.7003	−	5.15301i	−0.349192	−	0.168162i
$940$		0			0
$941$	49.7489	+	23.9578i	1.62177	+	0.781003i	0.999998	−	0.00219594i	$-0.000698991\pi$
$941$	49.7489	+	23.9578i	1.62177	+	0.781003i	0.621771	+	0.783199i	$0.286413\pi$
$942$	−3.97943	+	4.99005i	−0.129657	+	0.162584i
$943$	−1.45260	+	1.82151i	−0.0473032	+	0.0593164i
$944$	190.978	+	91.9702i	6.21580	+	2.99337i
$945$		0			0
$946$	25.3658	+	12.2155i	0.824712	+	0.397160i
$947$	−8.06558	+	35.3376i	−0.262096	+	1.14832i	0.656877	+	0.753998i	$0.271877\pi$
$947$	−8.06558	+	35.3376i	−0.262096	+	1.14832i	−0.918973	+	0.394320i	$0.870980\pi$
$948$	−0.997946	+	0.480585i	−0.0324118	+	0.0156087i
$949$	−2.79589	+	1.34643i	−0.0907583	+	0.0437069i
$950$		0			0
$951$	−5.64501	+	7.07862i	−0.183052	+	0.229540i
$952$	73.8238	+	92.5721i	2.39264	+	3.00028i
$953$	10.7981	−	47.3095i	0.349784	−	1.53250i	−0.427886	−	0.903833i	$-0.640742\pi$
$953$	10.7981	−	47.3095i	0.349784	−	1.53250i	0.777670	−	0.628672i	$-0.216401\pi$
$954$	8.57867	+	37.5856i	0.277745	+	1.21688i
$955$		0			0
$956$	74.4911			2.40921
$957$	−13.0701	−	1.18815i	−0.422497	−	0.0384075i
$958$	99.1924			3.20476
$959$	−5.44970	−	6.83371i	−0.175980	−	0.220672i
$960$		0			0
$961$	6.84519	−	29.9907i	0.220812	−	0.967443i
$962$	11.8833	+	14.9012i	0.383132	+	0.480433i
$963$	18.5034	−	23.2026i	0.596265	−	0.747692i
$964$	−21.9922	−	96.3541i	−0.708321	−	3.10336i
$965$		0			0
$966$	−2.24115	+	1.07928i	−0.0721077	+	0.0347252i
$967$	7.37547	−	32.3141i	0.237179	−	1.03915i	−0.706351	−	0.707862i	$-0.749660\pi$
$967$	7.37547	−	32.3141i	0.237179	−	1.03915i	0.943530	−	0.331288i	$-0.107483\pi$
$968$	−8.12061	−	3.91068i	−0.261006	−	0.125694i
$969$	−13.8071			−0.443549
$970$		0			0
$971$	31.9199	−	40.0262i	1.02436	−	1.28450i	0.0663388	−	0.997797i	$-0.478868\pi$
$971$	31.9199	−	40.0262i	1.02436	−	1.28450i	0.958019	−	0.286706i	$-0.0925604\pi$
$972$	54.8130	−	68.7333i	1.75813	−	2.20462i
$973$	−8.21567	−	3.95646i	−0.263382	−	0.126838i
$974$	−41.2531			−1.32183
$975$		0			0
$976$	33.7540	−	147.886i	1.08044	−	4.73372i
$977$	−42.1234	+	20.2855i	−1.34765	+	0.648992i	−0.961846	−	0.273591i	$-0.911789\pi$
$977$	−42.1234	+	20.2855i	−1.34765	+	0.648992i	−0.385799	+	0.922583i	$0.626074\pi$
$978$	21.2292	−	10.2234i	0.678835	−	0.326910i
$979$	−0.855629	−	3.74876i	−0.0273460	−	0.119811i
$980$		0			0
$981$	−21.8655	−	27.4185i	−0.698113	−	0.875406i
$982$	−11.6509	+	51.0461i	−0.371796	+	1.62895i
$983$	5.89073	+	25.8090i	0.187885	+	0.823178i	0.977729	+	0.209870i	$0.0673042\pi$
$983$	5.89073	+	25.8090i	0.187885	+	0.823178i	−0.789844	+	0.613308i	$0.789839\pi$
$984$	16.0752	+	20.1576i	0.512458	+	0.642602i
$985$		0			0
$986$	−63.0754	+	65.8533i	−2.00873	+	2.09720i
$987$	11.2608			0.358435
$988$	−14.8180	−	18.5811i	−0.471422	−	0.591144i
$989$	0.448248	+	1.96390i	0.0142535	+	0.0624485i
$990$		0			0
$991$	14.3938	+	18.0493i	0.457235	+	0.573354i	0.955994	−	0.293386i	$-0.0947822\pi$
$991$	14.3938	+	18.0493i	0.457235	+	0.573354i	−0.498759	+	0.866741i	$0.666211\pi$
$992$	9.19317	−	11.5279i	0.291883	−	0.366010i
$993$	−2.09067	−	9.15984i	−0.0663456	−	0.290679i
$994$	−17.7127	+	8.52999i	−0.561813	+	0.270555i
$995$		0			0
$996$	−5.10444	+	22.3640i	−0.161740	+	0.708631i
$997$	42.8441	+	20.6327i	1.35689	+	0.653443i	0.963940	−	0.266118i	$-0.0857412\pi$
$997$	42.8441	+	20.6327i	1.35689	+	0.653443i	0.392947	+	0.919561i	$0.371455\pi$
$998$	20.2516			0.641052
$999$	−18.9360	−	9.11911i	−0.599109	−	0.288516i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	725.2.l.e.401.6		36
5.2	odd	4		725.2.r.d.24.1		72
5.3	odd	4		725.2.r.d.24.12		72
5.4	even	2		145.2.k.b.111.1	yes	36
29.23	even	7	inner	725.2.l.e.226.6		36
145.9	even	14		4205.2.a.t.1.18		18
145.23	odd	28		725.2.r.d.574.1		72
145.49	even	14		4205.2.a.s.1.1		18
145.52	odd	28		725.2.r.d.574.12		72
145.139	even	14		145.2.k.b.81.1	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
145.2.k.b.81.1	✓	36	145.139	even	14
145.2.k.b.111.1	yes	36	5.4	even	2
725.2.l.e.226.6		36	29.23	even	7	inner
725.2.l.e.401.6		36	1.1	even	1	trivial
725.2.r.d.24.1		72	5.2	odd	4
725.2.r.d.24.12		72	5.3	odd	4
725.2.r.d.574.1		72	145.23	odd	28
725.2.r.d.574.12		72	145.52	odd	28
4205.2.a.s.1.1		18	145.49	even	14
4205.2.a.t.1.18		18	145.9	even	14

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:	\( N \)	\(=\)	\( 725 = 5^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	725.l (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.74641 + 2.18993i) q^{2} +(-0.157624 - 0.690597i) q^{3} +(-1.30080 + 5.69919i) q^{4} +(1.23708 - 1.55125i) q^{6} +(0.404594 + 1.77264i) q^{7} +(-9.70531 + 4.67383i) q^{8} +(2.25083 - 1.08394i) q^{9} +O(q^{10})\)	\(q+(1.74641 + 2.18993i) q^{2} +(-0.157624 - 0.690597i) q^{3} +(-1.30080 + 5.69919i) q^{4} +(1.23708 - 1.55125i) q^{6} +(0.404594 + 1.77264i) q^{7} +(-9.70531 + 4.67383i) q^{8} +(2.25083 - 1.08394i) q^{9} +(3.09974 + 1.49276i) q^{11} +4.14088 q^{12} +(1.13604 + 0.547090i) q^{13} +(-3.17538 + 3.98180i) q^{14} +(-16.6512 - 8.01877i) q^{16} -6.04532 q^{17} +(6.30463 + 3.03615i) q^{18} +(-0.717470 + 3.14344i) q^{19} +(1.16041 - 0.558823i) q^{21} +(2.14439 + 9.39519i) q^{22} +(-0.429904 + 0.539083i) q^{23} +(4.75752 + 5.96575i) q^{24} +(0.785912 + 3.44330i) q^{26} +(-2.42831 - 3.04501i) q^{27} -10.6289 q^{28} +(-0.718081 - 5.33707i) q^{29} +(0.304181 + 0.381431i) q^{31} +(-6.72519 - 29.4650i) q^{32} +(0.542299 - 2.37597i) q^{33} +(-10.5576 - 13.2388i) q^{34} +(3.24971 + 14.2379i) q^{36} +(4.86199 - 2.34141i) q^{37} +(-8.13692 + 3.91853i) q^{38} +(0.198751 - 0.870783i) q^{39} +3.37890 q^{41} +(3.25033 + 1.56528i) q^{42} +(1.82152 - 2.28412i) q^{43} +(-12.5397 + 15.7242i) q^{44} -1.93134 q^{46} +(7.87732 + 3.79352i) q^{47} +(-2.91311 + 12.7632i) q^{48} +(3.32822 - 1.60279i) q^{49} +(0.952888 + 4.17488i) q^{51} +(-4.59574 + 5.76288i) q^{52} +(3.43501 + 4.30737i) q^{53} +(2.42752 - 10.6357i) q^{54} +(-12.2117 - 15.3130i) q^{56} +2.28394 q^{57} +(10.4338 - 10.8933i) q^{58} -11.4694 q^{59} +(1.82638 + 8.00189i) q^{61} +(-0.304082 + 1.33227i) q^{62} +(2.83211 + 3.55136i) q^{63} +(29.7354 - 37.2870i) q^{64} +(6.15028 - 2.96182i) q^{66} +(12.9974 - 6.25922i) q^{67} +(7.86377 - 34.4534i) q^{68} +(0.440052 + 0.211918i) q^{69} +(3.47791 + 1.67487i) q^{71} +(-16.7788 + 21.0400i) q^{72} +(-1.53445 + 1.92414i) q^{73} +(13.6186 + 6.55835i) q^{74} +(-16.9818 - 8.17800i) q^{76} +(-1.39199 + 6.09869i) q^{77} +(2.25406 - 1.08550i) q^{78} +(-0.240998 + 0.116059i) q^{79} +(2.95275 - 3.70264i) q^{81} +(5.90095 + 7.39955i) q^{82} +(-1.23269 + 5.40078i) q^{83} +(1.67538 + 7.34030i) q^{84} +8.18319 q^{86} +(-3.57258 + 1.33716i) q^{87} -37.0608 q^{88} +(-0.696833 - 0.873801i) q^{89} +(-0.510158 + 2.23515i) q^{91} +(-2.51312 - 3.15135i) q^{92} +(0.215468 - 0.270189i) q^{93} +(5.44950 + 23.8758i) q^{94} +(-19.2884 + 9.28879i) q^{96} +(0.252772 - 1.10746i) q^{97} +(9.32243 + 4.48945i) q^{98} +8.59505 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 2 q^{2} + 2 q^{3} - 10 q^{4} + 2 q^{6} + 8 q^{7} - 9 q^{8} - 18 q^{9}+O(q^{10}) \) 36 * q + 2 * q^2 + 2 * q^3 - 10 * q^4 + 2 * q^6 + 8 * q^7 - 9 * q^8 - 18 * q^9	\( 36 q + 2 q^{2} + 2 q^{3} - 10 q^{4} + 2 q^{6} + 8 q^{7} - 9 q^{8} - 18 q^{9} + 4 q^{11} + 14 q^{12} + 8 q^{13} + 16 q^{14} - 20 q^{16} - 28 q^{17} + 42 q^{18} - 6 q^{19} + 31 q^{21} + 19 q^{22} + 16 q^{24} - 32 q^{26} - 7 q^{27} - 60 q^{28} - 21 q^{29} - 7 q^{31} - 32 q^{32} - 56 q^{33} - 48 q^{34} - 12 q^{36} + 16 q^{37} + 34 q^{38} + 19 q^{39} - 28 q^{41} - 31 q^{42} - 15 q^{43} - 31 q^{44} + 76 q^{46} + 22 q^{47} + 101 q^{48} + 50 q^{49} - 14 q^{51} - 7 q^{52} + 15 q^{53} + 43 q^{54} + 6 q^{56} - 20 q^{57} + 70 q^{58} + 2 q^{59} - 4 q^{61} + 19 q^{62} + 43 q^{63} + 87 q^{64} + 66 q^{66} + 43 q^{67} - 46 q^{68} - 48 q^{69} + 27 q^{71} - 181 q^{72} + 44 q^{73} - 23 q^{74} - 40 q^{76} + 43 q^{77} - 10 q^{78} + 82 q^{79} - 49 q^{81} - 70 q^{82} + 25 q^{83} - 34 q^{84} - 126 q^{86} + 47 q^{87} - 40 q^{88} + 36 q^{89} - 45 q^{91} - 45 q^{92} - 122 q^{93} - 89 q^{96} - 21 q^{97} + 32 q^{98} - 8 q^{99}+O(q^{100}) \) 36 * q + 2 * q^2 + 2 * q^3 - 10 * q^4 + 2 * q^6 + 8 * q^7 - 9 * q^8 - 18 * q^9 + 4 * q^11 + 14 * q^12 + 8 * q^13 + 16 * q^14 - 20 * q^16 - 28 * q^17 + 42 * q^18 - 6 * q^19 + 31 * q^21 + 19 * q^22 + 16 * q^24 - 32 * q^26 - 7 * q^27 - 60 * q^28 - 21 * q^29 - 7 * q^31 - 32 * q^32 - 56 * q^33 - 48 * q^34 - 12 * q^36 + 16 * q^37 + 34 * q^38 + 19 * q^39 - 28 * q^41 - 31 * q^42 - 15 * q^43 - 31 * q^44 + 76 * q^46 + 22 * q^47 + 101 * q^48 + 50 * q^49 - 14 * q^51 - 7 * q^52 + 15 * q^53 + 43 * q^54 + 6 * q^56 - 20 * q^57 + 70 * q^58 + 2 * q^59 - 4 * q^61 + 19 * q^62 + 43 * q^63 + 87 * q^64 + 66 * q^66 + 43 * q^67 - 46 * q^68 - 48 * q^69 + 27 * q^71 - 181 * q^72 + 44 * q^73 - 23 * q^74 - 40 * q^76 + 43 * q^77 - 10 * q^78 + 82 * q^79 - 49 * q^81 - 70 * q^82 + 25 * q^83 - 34 * q^84 - 126 * q^86 + 47 * q^87 - 40 * q^88 + 36 * q^89 - 45 * q^91 - 45 * q^92 - 122 * q^93 - 89 * q^96 - 21 * q^97 + 32 * q^98 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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