LMFDB - Embedded newform 520.2.by.c.61.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [520,2,Mod(61,520)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(520, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 0, 4]))

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

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

chi := DirichletCharacter("520.61");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 520 = 2^{3} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	520.by (of order $6$, degree $2$, 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:	$4.15222090511$
Analytic rank:	$0$
Dimension:	$104$
Relative dimension:	$52$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			61.17
Character	$\chi$	$=$	520.61
Dual form			520.2.by.c.341.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.885292 - 1.10284i) q^{2} +(-1.75135 - 1.01114i) q^{3} +(-0.432517 + 1.95267i) q^{4} -1.00000i q^{5} +(0.435326 + 2.82661i) q^{6} +(-1.47683 - 2.55794i) q^{7} +(2.53639 - 1.25169i) q^{8} +(0.544814 + 0.943646i) q^{9} +O(q^{10})$	\(q+(-0.885292 - 1.10284i) q^{2} +(-1.75135 - 1.01114i) q^{3} +(-0.432517 + 1.95267i) q^{4} -1.00000i q^{5} +(0.435326 + 2.82661i) q^{6} +(-1.47683 - 2.55794i) q^{7} +(2.53639 - 1.25169i) q^{8} +(0.544814 + 0.943646i) q^{9} +(-1.10284 + 0.885292i) q^{10} +(-1.24190 - 0.717013i) q^{11} +(2.73192 - 2.98247i) q^{12} +(2.00168 - 2.99888i) q^{13} +(-1.51358 + 3.89323i) q^{14} +(-1.01114 + 1.75135i) q^{15} +(-3.62586 - 1.68913i) q^{16} +(-1.37139 - 2.37531i) q^{17} +(0.558372 - 1.43625i) q^{18} +(-3.75031 + 2.16524i) q^{19} +(1.95267 + 0.432517i) q^{20} +5.97313i q^{21} +(0.308695 + 2.00439i) q^{22} +(-1.58450 + 2.74444i) q^{23} +(-5.70774 - 0.372509i) q^{24} -1.00000 q^{25} +(-5.07936 + 0.447342i) q^{26} +3.86331i q^{27} +(5.63358 - 1.77741i) q^{28} +(6.81137 + 3.93255i) q^{29} +(2.82661 - 0.435326i) q^{30} -2.91661 q^{31} +(1.34710 + 5.49412i) q^{32} +(1.45000 + 2.51148i) q^{33} +(-1.40551 + 3.61527i) q^{34} +(-2.55794 + 1.47683i) q^{35} +(-2.07827 + 0.655701i) q^{36} +(-1.91697 - 1.10676i) q^{37} +(5.70804 + 2.21913i) q^{38} +(-6.53793 + 3.22809i) q^{39} +(-1.25169 - 2.53639i) q^{40} +(-0.730409 + 1.26511i) q^{41} +(6.58742 - 5.28797i) q^{42} +(6.42836 - 3.71142i) q^{43} +(1.93723 - 2.11491i) q^{44} +(0.943646 - 0.544814i) q^{45} +(4.42942 - 0.682174i) q^{46} -5.79800 q^{47} +(4.64219 + 6.62451i) q^{48} +(-0.862049 + 1.49311i) q^{49} +(0.885292 + 1.10284i) q^{50} +5.54667i q^{51} +(4.99006 + 5.20570i) q^{52} +13.7392i q^{53} +(4.26062 - 3.42016i) q^{54} +(-0.717013 + 1.24190i) q^{55} +(-6.94756 - 4.63942i) q^{56} +8.75747 q^{57} +(-1.69308 - 10.9933i) q^{58} +(-0.541074 + 0.312389i) q^{59} +(-2.98247 - 2.73192i) q^{60} +(-9.48398 + 5.47558i) q^{61} +(2.58205 + 3.21656i) q^{62} +(1.60919 - 2.78721i) q^{63} +(4.86656 - 6.34954i) q^{64} +(-2.99888 - 2.00168i) q^{65} +(1.48609 - 3.82251i) q^{66} +(-6.36790 - 3.67651i) q^{67} +(5.23136 - 1.65051i) q^{68} +(5.55002 - 3.20431i) q^{69} +(3.89323 + 1.51358i) q^{70} +(1.50229 + 2.60204i) q^{71} +(2.56301 + 1.71152i) q^{72} +4.76130 q^{73} +(0.476495 + 3.09393i) q^{74} +(1.75135 + 1.01114i) q^{75} +(-2.60594 - 8.25963i) q^{76} +4.23562i q^{77} +(9.34805 + 4.35250i) q^{78} +8.05187 q^{79} +(-1.68913 + 3.62586i) q^{80} +(5.54080 - 9.59694i) q^{81} +(2.04184 - 0.314463i) q^{82} -8.89091i q^{83} +(-11.6636 - 2.58348i) q^{84} +(-2.37531 + 1.37139i) q^{85} +(-9.78408 - 3.80377i) q^{86} +(-7.95272 - 13.7745i) q^{87} +(-4.04743 - 0.264151i) q^{88} +(-8.28220 + 14.3452i) q^{89} +(-1.43625 - 0.558372i) q^{90} +(-10.6271 - 0.691365i) q^{91} +(-4.67366 - 4.28102i) q^{92} +(5.10800 + 2.94911i) q^{93} +(5.13292 + 6.39428i) q^{94} +(2.16524 + 3.75031i) q^{95} +(3.19608 - 10.9842i) q^{96} +(-8.29183 - 14.3619i) q^{97} +(2.40983 - 0.371137i) q^{98} -1.56255i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 104 q + 2 q^{6} - 4 q^{7} + 12 q^{8} + 60 q^{9}+O(q^{10}) $ 104 * q + 2 * q^6 - 4 * q^7 + 12 * q^8 + 60 * q^9	$ 104 q + 2 q^{6} - 4 q^{7} + 12 q^{8} + 60 q^{9} - 28 q^{12} - 24 q^{14} + 4 q^{15} - 20 q^{16} + 4 q^{17} - 40 q^{18} - 4 q^{20} + 24 q^{22} + 32 q^{23} + 24 q^{24} - 104 q^{25} - 10 q^{26} + 22 q^{28} - 12 q^{30} - 40 q^{31} + 30 q^{32} + 12 q^{33} - 4 q^{34} + 18 q^{36} + 56 q^{39} - 16 q^{41} - 20 q^{42} - 32 q^{44} - 30 q^{46} - 56 q^{47} - 24 q^{48} - 80 q^{49} - 6 q^{52} - 10 q^{54} + 16 q^{55} - 38 q^{56} + 104 q^{57} - 68 q^{58} - 12 q^{62} + 12 q^{63} - 108 q^{64} + 180 q^{66} - 6 q^{68} + 8 q^{70} - 72 q^{71} - 80 q^{72} + 24 q^{73} + 40 q^{74} - 20 q^{76} - 52 q^{78} - 40 q^{79} - 24 q^{80} - 60 q^{81} + 64 q^{82} - 70 q^{84} + 140 q^{86} - 8 q^{87} + 86 q^{88} + 36 q^{89} - 20 q^{90} + 76 q^{92} + 46 q^{94} - 32 q^{95} + 12 q^{96} + 12 q^{97} - 8 q^{98}+O(q^{100}) $ 104 * q + 2 * q^6 - 4 * q^7 + 12 * q^8 + 60 * q^9 - 28 * q^12 - 24 * q^14 + 4 * q^15 - 20 * q^16 + 4 * q^17 - 40 * q^18 - 4 * q^20 + 24 * q^22 + 32 * q^23 + 24 * q^24 - 104 * q^25 - 10 * q^26 + 22 * q^28 - 12 * q^30 - 40 * q^31 + 30 * q^32 + 12 * q^33 - 4 * q^34 + 18 * q^36 + 56 * q^39 - 16 * q^41 - 20 * q^42 - 32 * q^44 - 30 * q^46 - 56 * q^47 - 24 * q^48 - 80 * q^49 - 6 * q^52 - 10 * q^54 + 16 * q^55 - 38 * q^56 + 104 * q^57 - 68 * q^58 - 12 * q^62 + 12 * q^63 - 108 * q^64 + 180 * q^66 - 6 * q^68 + 8 * q^70 - 72 * q^71 - 80 * q^72 + 24 * q^73 + 40 * q^74 - 20 * q^76 - 52 * q^78 - 40 * q^79 - 24 * q^80 - 60 * q^81 + 64 * q^82 - 70 * q^84 + 140 * q^86 - 8 * q^87 + 86 * q^88 + 36 * q^89 - 20 * q^90 + 76 * q^92 + 46 * q^94 - 32 * q^95 + 12 * q^96 + 12 * q^97 - 8 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/520\mathbb{Z}\right)^\times$.

$n$	$41$	$261$	$391$	$417$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$	$1$	$1$

Coefficient data

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

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

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

$2$	−0.885292	−	1.10284i	−0.625996	−	0.779826i
$2$	−0.885292	−	1.10284i	−0.625996	−	0.779826i
$3$	−1.75135	−	1.01114i	−1.01114	−	0.583783i	−0.0996158	−	0.995026i	$-0.531761\pi$
$3$	−1.75135	−	1.01114i	−1.01114	−	0.583783i	−0.911526	+	0.411243i	$0.865095\pi$
$4$	−0.432517	+	1.95267i	−0.216258	+	0.976336i
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$	0.435326	+	2.82661i	0.177721	+	1.15396i
$7$	−1.47683	−	2.55794i	−0.558189	−	0.966812i	−0.997648	−	0.0685489i	$-0.978163\pi$
$7$	−1.47683	−	2.55794i	−0.558189	−	0.966812i	0.439459	−	0.898263i	$-0.355170\pi$
$8$	2.53639	−	1.25169i	0.896750	−	0.442538i
$9$	0.544814	+	0.943646i	0.181605	+	0.314549i
$10$	−1.10284	+	0.885292i	−0.348749	+	0.279954i
$11$	−1.24190	−	0.717013i	−0.374448	−	0.216188i	0.300952	−	0.953639i	$-0.402696\pi$
$11$	−1.24190	−	0.717013i	−0.374448	−	0.216188i	−0.675400	+	0.737452i	$0.736029\pi$
$12$	2.73192	−	2.98247i	0.788636	−	0.860966i
$13$	2.00168	−	2.99888i	0.555167	−	0.831739i
$13$	2.00168	−	2.99888i	0.555167	−	0.831739i
$14$	−1.51358	+	3.89323i	−0.404521	+	1.04051i
$15$	−1.01114	+	1.75135i	−0.261076	+	0.452196i
$16$	−3.62586	−	1.68913i	−0.906465	−	0.422282i
$17$	−1.37139	−	2.37531i	−0.332610	−	0.576098i	0.650412	−	0.759581i	$-0.274596\pi$
$17$	−1.37139	−	2.37531i	−0.332610	−	0.576098i	−0.983023	+	0.183483i	$0.941263\pi$
$18$	0.558372	−	1.43625i	0.131610	−	0.338526i
$19$	−3.75031	+	2.16524i	−0.860380	+	0.496741i	−0.864140	−	0.503252i	$-0.832137\pi$
$19$	−3.75031	+	2.16524i	−0.860380	+	0.496741i	0.00375925	+	0.999993i	$0.498803\pi$
$20$	1.95267	+	0.432517i	0.436631	+	0.0967137i
$21$			5.97313i			1.30344i
$22$	0.308695	+	2.00439i	0.0658140	+	0.427337i
$23$	−1.58450	+	2.74444i	−0.330391	+	0.572254i	−0.982589	−	0.185795i	$-0.940514\pi$
$23$	−1.58450	+	2.74444i	−0.330391	+	0.572254i	0.652197	+	0.758049i	$0.273847\pi$
$24$	−5.70774	−	0.372509i	−1.16509	−	0.0760381i
$25$	−1.00000			−0.200000
$26$	−5.07936	+	0.447342i	−0.996144	+	0.0877309i
$27$			3.86331i			0.743495i
$28$	5.63358	−	1.77741i	1.06465	−	0.335899i
$29$	6.81137	+	3.93255i	1.26484	+	0.730255i	0.974007	−	0.226519i	$-0.0727344\pi$
$29$	6.81137	+	3.93255i	1.26484	+	0.730255i	0.290833	+	0.956774i	$0.406068\pi$
$30$	2.82661	−	0.435326i	0.516067	−	0.0794793i
$31$	−2.91661			−0.523839			−0.261919	−	0.965090i	$-0.584355\pi$
$31$	−2.91661			−0.523839			−0.261919	+	0.965090i	$0.584355\pi$
$32$	1.34710	+	5.49412i	0.238137	+	0.971232i
$33$	1.45000	+	2.51148i	0.252413	+	0.437192i
$34$	−1.40551	+	3.61527i	−0.241044	+	0.620013i
$35$	−2.55794	+	1.47683i	−0.432371	+	0.249630i
$36$	−2.07827	+	0.655701i	−0.346379	+	0.109283i
$37$	−1.91697	−	1.10676i	−0.315148	−	0.181951i	0.334080	−	0.942545i	$-0.391575\pi$
$37$	−1.91697	−	1.10676i	−0.315148	−	0.181951i	−0.649228	+	0.760594i	$0.724908\pi$
$38$	5.70804	+	2.21913i	0.925966	+	0.359990i
$39$	−6.53793	+	3.22809i	−1.04691	+	0.516908i
$40$	−1.25169	−	2.53639i	−0.197909	−	0.401039i
$41$	−0.730409	+	1.26511i	−0.114071	+	0.197576i	−0.917408	−	0.397948i	$-0.869722\pi$
$41$	−0.730409	+	1.26511i	−0.114071	+	0.197576i	0.803337	+	0.595524i	$0.203056\pi$
$42$	6.58742	−	5.28797i	1.01646	−	0.815951i
$43$	6.42836	−	3.71142i	0.980316	−	0.565986i	0.0779504	−	0.996957i	$-0.475162\pi$
$43$	6.42836	−	3.71142i	0.980316	−	0.565986i	0.902365	+	0.430972i	$0.141829\pi$
$44$	1.93723	−	2.11491i	0.292049	−	0.318834i
$45$	0.943646	−	0.544814i	0.140670	−	0.0812161i
$46$	4.42942	−	0.682174i	0.653083	−	0.100581i
$47$	−5.79800			−0.845726			−0.422863	−	0.906194i	$-0.638975\pi$
$47$	−5.79800			−0.845726			−0.422863	+	0.906194i	$0.638975\pi$
$48$	4.64219	+	6.62451i	0.670043	+	0.956165i
$49$	−0.862049	+	1.49311i	−0.123150	+	0.213302i
$50$	0.885292	+	1.10284i	0.125199	+	0.155965i
$51$			5.54667i			0.776689i
$52$	4.99006	+	5.20570i	0.691997	+	0.721900i
$53$			13.7392i			1.88722i	0.331057	+	0.943611i	$0.392595\pi$
$53$			13.7392i			1.88722i	−0.331057	+	0.943611i	$0.607405\pi$
$54$	4.26062	−	3.42016i	0.579797	−	0.465425i
$55$	−0.717013	+	1.24190i	−0.0966820	+	0.167458i
$56$	−6.94756	−	4.63942i	−0.928407	−	0.619968i
$57$	8.75747			1.15996
$58$	−1.69308	−	10.9933i	−0.222312	−	1.44349i
$59$	−0.541074	+	0.312389i	−0.0704418	+	0.0406696i	−0.534807	−	0.844974i	$-0.679616\pi$
$59$	−0.541074	+	0.312389i	−0.0704418	+	0.0406696i	0.464365	+	0.885644i	$0.346282\pi$
$60$	−2.98247	−	2.73192i	−0.385036	−	0.352689i
$61$	−9.48398	+	5.47558i	−1.21430	+	0.701076i	−0.963693	−	0.267013i	$-0.913963\pi$
$61$	−9.48398	+	5.47558i	−1.21430	+	0.701076i	−0.250606	+	0.968089i	$0.580630\pi$
$62$	2.58205	+	3.21656i	0.327921	+	0.408503i
$63$	1.60919	−	2.78721i	0.202739	−	0.351155i
$64$	4.86656	−	6.34954i	0.608320	−	0.793692i
$65$	−2.99888	−	2.00168i	−0.371965	−	0.248278i
$66$	1.48609	−	3.82251i	0.182925	−	0.470519i
$67$	−6.36790	−	3.67651i	−0.777963	−	0.449157i	0.0577450	−	0.998331i	$-0.481609\pi$
$67$	−6.36790	−	3.67651i	−0.777963	−	0.449157i	−0.835708	+	0.549174i	$0.814942\pi$
$68$	5.23136	−	1.65051i	0.634395	−	0.200153i
$69$	5.55002	−	3.20431i	0.668144	−	0.385753i
$70$	3.89323	+	1.51358i	0.465330	+	0.180907i
$71$	1.50229	+	2.60204i	0.178289	+	0.308805i	0.941295	−	0.337586i	$-0.109611\pi$
$71$	1.50229	+	2.60204i	0.178289	+	0.308805i	−0.763006	+	0.646392i	$0.776277\pi$
$72$	2.56301	+	1.71152i	0.302054	+	0.201704i
$73$	4.76130			0.557268			0.278634	−	0.960397i	$-0.410118\pi$
$73$	4.76130			0.557268			0.278634	+	0.960397i	$0.410118\pi$
$74$	0.476495	+	3.09393i	0.0553914	+	0.359662i
$75$	1.75135	+	1.01114i	0.202228	+	0.116757i
$76$	−2.60594	−	8.25963i	−0.298922	−	0.947445i
$77$			4.23562i			0.482694i
$78$	9.34805	+	4.35250i	1.05846	+	0.492824i
$79$	8.05187			0.905906			0.452953	−	0.891534i	$-0.350371\pi$
$79$	8.05187			0.905906			0.452953	+	0.891534i	$0.350371\pi$
$80$	−1.68913	+	3.62586i	−0.188850	+	0.405383i
$81$	5.54080	−	9.59694i	0.615644	−	1.06633i
$82$	2.04184	−	0.314463i	0.225483	−	0.0347266i
$83$		−	8.89091i		−	0.975904i	−0.872870	−	0.487952i	$-0.837744\pi$
$83$		−	8.89091i		−	0.975904i	0.872870	−	0.487952i	$-0.162256\pi$
$84$	−11.6636	−	2.58348i	−1.27260	−	0.281881i
$85$	−2.37531	+	1.37139i	−0.257639	+	0.148748i
$86$	−9.78408	−	3.80377i	−1.05504	−	0.410172i
$87$	−7.95272	−	13.7745i	−0.852621	−	1.47678i
$88$	−4.04743	−	0.264151i	−0.431457	−	0.0281586i
$89$	−8.28220	+	14.3452i	−0.877911	+	1.52059i	−0.0242824	+	0.999705i	$0.507730\pi$
$89$	−8.28220	+	14.3452i	−0.877911	+	1.52059i	−0.853629	+	0.520882i	$0.825603\pi$
$90$	−1.43625	−	0.558372i	−0.151394	−	0.0588576i
$91$	−10.6271	−	0.691365i	−1.11402	−	0.0724748i
$92$	−4.67366	−	4.28102i	−0.487263	−	0.446328i
$93$	5.10800	+	2.94911i	0.529675	+	0.305808i
$94$	5.13292	+	6.39428i	0.529421	+	0.659519i
$95$	2.16524	+	3.75031i	0.222149	+	0.384774i
$96$	3.19608	−	10.9842i	0.326199	−	1.12107i
$97$	−8.29183	−	14.3619i	−0.841908	−	1.45823i	−0.888279	−	0.459303i	$-0.848099\pi$
$97$	−8.29183	−	14.3619i	−0.841908	−	1.45823i	0.0463712	−	0.998924i	$-0.485234\pi$
$98$	2.40983	−	0.371137i	0.243430	−	0.0374905i
$99$		−	1.56255i		−	0.157043i
$100$	0.432517	−	1.95267i	0.0432517	−	0.195267i
$101$	2.10848	+	1.21733i	0.209802	+	0.121129i	0.601219	−	0.799084i	$-0.294682\pi$
$101$	2.10848	+	1.21733i	0.209802	+	0.121129i	−0.391418	+	0.920213i	$0.628015\pi$
$102$	6.11709	−	4.91042i	0.605683	−	0.486204i
$103$	−5.47755			−0.539719			−0.269860	−	0.962900i	$-0.586977\pi$
$103$	−5.47755			−0.539719			−0.269860	+	0.962900i	$0.586977\pi$
$104$	1.32340	−	10.1118i	0.129770	−	0.991544i
$105$	5.97313			0.582918
$106$	15.1521	−	12.1632i	1.47171	−	1.18139i
$107$	−15.5621	−	8.98478i	−1.50445	−	0.868592i	−0.999987	−	0.00515595i	$-0.998359\pi$
$107$	−15.5621	−	8.98478i	−1.50445	−	0.868592i	−0.504459	−	0.863436i	$-0.668308\pi$
$108$	−7.54378	−	1.67095i	−0.725901	−	0.160787i
$109$		−	19.0052i		−	1.82036i	−0.414209	−	0.910182i	$-0.635942\pi$
$109$		−	19.0052i		−	1.82036i	0.414209	−	0.910182i	$-0.364058\pi$
$110$	2.00439	−	0.308695i	0.191111	−	0.0294329i
$111$	2.23819	+	3.87666i	0.212440	+	0.367956i
$112$	1.03408	+	11.7693i	0.0977115	+	1.11209i
$113$	−0.626143	−	1.08451i	−0.0589026	−	0.102022i	0.835070	−	0.550143i	$-0.185427\pi$
$113$	−0.626143	−	1.08451i	−0.0589026	−	0.102022i	−0.893973	+	0.448121i	$0.852093\pi$
$114$	−7.75292	−	9.65810i	−0.726127	−	0.904564i
$115$	2.74444	+	1.58450i	0.255920	+	0.147755i
$116$	−10.6250	+	11.5995i	−0.986507	+	1.07698i
$117$	3.92042	+	0.255050i	0.362443	+	0.0235794i
$118$	0.823524	+	0.320163i	0.0758115	+	0.0294734i
$119$	−4.05061	+	7.01586i	−0.371319	+	0.643143i
$120$	−0.372509	+	5.70774i	−0.0340053	+	0.521043i
$121$	−4.47179	−	7.74536i	−0.406526	−	0.704124i
$122$	14.4348	+	5.61184i	1.30686	+	0.508072i
$123$	2.55840	−	1.47709i	0.230683	−	0.133185i
$124$	1.26148	−	5.69519i	0.113285	−	0.511443i
$125$			1.00000i			0.0894427i
$126$	−4.49845	+	0.692806i	−0.400754	+	0.0617200i
$127$	−2.82647	+	4.89559i	−0.250809	+	0.434413i	−0.963749	−	0.266812i	$-0.914030\pi$
$127$	−2.82647	+	4.89559i	−0.250809	+	0.434413i	0.712940	+	0.701225i	$0.247363\pi$
$128$	−11.3109	+	0.254154i	−0.999748	+	0.0224642i
$129$	−15.0111			−1.32165
$130$	0.447342	+	5.07936i	0.0392344	+	0.445489i
$131$		−	5.83322i		−	0.509650i	−0.966987	−	0.254825i	$-0.917982\pi$
$131$		−	5.83322i		−	0.509650i	0.966987	−	0.254825i	$-0.0820179\pi$
$132$	−5.53125	+	1.74512i	−0.481433	+	0.151894i
$133$	11.0771	+	6.39539i	0.960510	+	0.554551i
$134$	1.58284	+	10.2776i	0.136737	+	0.887846i
$135$	3.86331			0.332501
$136$	−6.45153	−	4.30817i	−0.553214	−	0.369423i
$137$	−3.53163	−	6.11696i	−0.301727	−	0.522607i	0.674800	−	0.738001i	$-0.264230\pi$
$137$	−3.53163	−	6.11696i	−0.301727	−	0.522607i	−0.976527	+	0.215394i	$0.930896\pi$
$138$	−8.44723	−	3.28405i	−0.719076	−	0.279557i
$139$	0.284522	−	0.164269i	0.0241329	−	0.0139331i	−0.487885	−	0.872908i	$-0.662231\pi$
$139$	0.284522	−	0.164269i	0.0241329	−	0.0139331i	0.512018	+	0.858975i	$0.328898\pi$
$140$	−1.77741	−	5.63358i	−0.150219	−	0.476124i
$141$	10.1543	+	5.86260i	0.855148	+	0.493720i
$142$	1.53967	−	3.96035i	0.129207	−	0.332345i
$143$	−4.63613	+	2.28908i	−0.387693	+	0.191422i
$144$	−0.381481	−	4.34179i	−0.0317901	−	0.361816i
$145$	3.93255	−	6.81137i	0.326580	−	0.565653i
$146$	−4.21514	−	5.25096i	−0.348848	−	0.434573i
$147$	3.01950	−	1.74331i	0.249044	−	0.143785i
$148$	2.99027	−	3.26453i	0.245799	−	0.268342i
$149$	−4.40274	+	2.54192i	−0.360686	+	0.208242i	−0.669382	−	0.742919i	$-0.733441\pi$
$149$	−4.40274	+	2.54192i	−0.360686	+	0.208242i	0.308696	+	0.951161i	$0.400108\pi$
$150$	−0.435326	−	2.82661i	−0.0355442	−	0.230792i
$151$	18.8539			1.53431			0.767155	−	0.641462i	$-0.221672\pi$
$151$	18.8539			1.53431			0.767155	+	0.641462i	$0.221672\pi$
$152$	−6.80205	+	10.1861i	−0.551719	+	0.826203i
$153$	1.49430	−	2.58821i	0.120807	−	0.209244i
$154$	4.67122	−	3.74976i	0.376417	−	0.302164i
$155$			2.91661i			0.234268i
$156$	−3.47564	−	14.1626i	−0.278274	−	1.13392i
$157$		−	3.38032i		−	0.269779i	−0.990861	−	0.134890i	$-0.956932\pi$
$157$		−	3.38032i		−	0.269779i	0.990861	−	0.134890i	$-0.0430680\pi$
$158$	−7.12825	−	8.87993i	−0.567093	−	0.706449i
$159$	13.8923	−	24.0621i	1.10173	−	1.90825i
$160$	5.49412	−	1.34710i	0.434348	−	0.106498i
$161$	9.36015			0.737683
$162$	−15.4891	+	2.38548i	−1.21694	+	0.187421i
$163$	10.2351	−	5.90921i	0.801672	−	0.462845i	−0.0423838	−	0.999101i	$-0.513495\pi$
$163$	10.2351	−	5.90921i	0.801672	−	0.462845i	0.844055	+	0.536256i	$0.180162\pi$
$164$	−2.15442	−	1.97343i	−0.168232	−	0.154099i
$165$	2.51148	−	1.45000i	0.195518	−	0.112883i
$166$	−9.80526	+	7.87105i	−0.761036	+	0.610912i
$167$	−12.4305	+	21.5302i	−0.961897	+	1.66606i	−0.244168	+	0.969733i	$0.578515\pi$
$167$	−12.4305	+	21.5302i	−0.961897	+	1.66606i	−0.717729	+	0.696322i	$0.754818\pi$
$168$	7.47650	+	15.1502i	0.576824	+	1.16886i
$169$	−4.98652	−	12.0056i	−0.383579	−	0.923508i
$170$	3.61527	+	1.40551i	0.277278	+	0.107798i
$171$	−4.08645	−	2.35931i	−0.312498	−	0.180421i
$172$	4.46680	+	14.1577i	0.340591	+	1.07952i
$173$	13.1646	−	7.60060i	1.00089	−	0.577863i	0.0923773	−	0.995724i	$-0.470553\pi$
$173$	13.1646	−	7.60060i	1.00089	−	0.577863i	0.908511	+	0.417861i	$0.137220\pi$
$174$	−8.15062	+	20.9651i	−0.617897	+	1.58936i
$175$	1.47683	+	2.55794i	0.111638	+	0.193362i
$176$	3.29184	+	4.69752i	0.248132	+	0.354089i
$177$	1.26348			0.0949688
$178$	23.1526	−	3.56573i	1.73536	−	0.267263i
$179$	−2.68996	−	1.55305i	−0.201057	−	0.116080i	0.396092	−	0.918211i	$-0.370366\pi$
$179$	−2.68996	−	1.55305i	−0.201057	−	0.116080i	−0.597148	+	0.802131i	$0.703700\pi$
$180$	0.655701	+	2.07827i	0.0488731	+	0.154905i
$181$			21.5561i			1.60225i	0.598497	+	0.801125i	$0.295765\pi$
$181$			21.5561i			1.60225i	−0.598497	+	0.801125i	$0.704235\pi$
$182$	8.64562	+	12.3321i	0.640856	+	0.914113i
$183$	22.1463			1.63710
$184$	−0.583737	+	8.94426i	−0.0430337	+	0.659380i
$185$	−1.10676	+	1.91697i	−0.0813710	+	0.140939i
$186$	−1.26968	−	8.24413i	−0.0930972	−	0.604489i
$187$			3.93321i			0.287625i
$188$	2.50773	−	11.3216i	0.182895	−	0.825712i
$189$	9.88213	−	5.70545i	0.718819	−	0.415011i
$190$	2.21913	−	5.70804i	0.160992	−	0.414105i
$191$	−0.150019	−	0.259840i	−0.0108550	−	0.0188014i	0.860547	−	0.509371i	$-0.170122\pi$
$191$	−0.150019	−	0.259840i	−0.0108550	−	0.0188014i	−0.871402	+	0.490570i	$0.836789\pi$
$192$	−14.9433	+	6.19947i	−1.07844	+	0.447408i
$193$	−8.54347	+	14.7977i	−0.614973	+	1.06516i	0.375417	+	0.926856i	$0.377500\pi$
$193$	−8.54347	+	14.7977i	−0.614973	+	1.06516i	−0.990389	+	0.138308i	$0.955834\pi$
$194$	−8.49818	+	21.8590i	−0.610133	+	1.56939i
$195$	3.22809	+	6.53793i	0.231168	+	0.468191i
$196$	−2.54271	−	2.32909i	−0.181622	−	0.166364i
$197$	−8.04183	−	4.64295i	−0.572957	−	0.330797i	0.185373	−	0.982668i	$-0.440651\pi$
$197$	−8.04183	−	4.64295i	−0.572957	−	0.330797i	−0.758329	+	0.651872i	$0.773984\pi$
$198$	−1.72325	+	1.38332i	−0.122466	+	0.0983081i
$199$	0.537790	+	0.931479i	0.0381229	+	0.0660308i	0.884457	−	0.466621i	$-0.154529\pi$
$199$	0.537790	+	0.931479i	0.0381229	+	0.0660308i	−0.846334	+	0.532652i	$0.821195\pi$
$200$	−2.53639	+	1.25169i	−0.179350	+	0.0885077i
$201$	7.43494	+	12.8777i	0.524420	+	0.908323i
$202$	−0.524097	−	3.40301i	−0.0368753	−	0.239435i
$203$		−	23.2308i		−	1.63048i
$204$	−10.8308	−	2.39903i	−0.758309	−	0.167966i
$205$	1.26511	+	0.730409i	0.0883588	+	0.0510140i
$206$	4.84923	+	6.04087i	0.337862	+	0.420887i
$207$	−3.45303			−0.240002
$208$	−12.3233	+	7.49240i	−0.854468	+	0.519505i
$209$	6.21003			0.429557
$210$	−5.28797	−	6.58742i	−0.364904	−	0.454575i
$211$	−1.94828	−	1.12484i	−0.134125	−	0.0774373i	0.431436	−	0.902144i	$-0.358007\pi$
$211$	−1.94828	−	1.12484i	−0.134125	−	0.0774373i	−0.565561	+	0.824706i	$0.691340\pi$
$212$	−26.8281	−	5.94243i	−1.84256	−	0.408128i
$213$		−	6.07611i		−	0.416328i
$214$	3.86821	+	25.1167i	0.264426	+	1.71694i
$215$	−3.71142	−	6.42836i	−0.253116	−	0.438411i
$216$	4.83566	+	9.79887i	0.329025	+	0.666729i
$217$	4.30734	+	7.46052i	0.292401	+	0.506453i
$218$	−20.9597	+	16.8251i	−1.41957	+	1.13954i
$219$	−8.33870	−	4.81435i	−0.563477	−	0.325324i
$220$	−2.11491	−	1.93723i	−0.142587	−	0.130608i
$221$	−9.86836	−	0.642004i	−0.663818	−	0.0431859i
$222$	2.29389	−	5.90035i	0.153956	−	0.396005i
$223$	8.85641	−	15.3397i	0.593069	−	1.02723i	−0.400747	−	0.916189i	$-0.631249\pi$
$223$	8.85641	−	15.3397i	0.593069	−	1.02723i	0.993816	−	0.111037i	$-0.0354172\pi$
$224$	12.0642	−	11.5597i	0.806073	−	0.772364i
$225$	−0.544814	−	0.943646i	−0.0363209	−	0.0629097i
$226$	−0.641725	+	1.65065i	−0.0426869	+	0.109799i
$227$	16.8780	−	9.74452i	1.12023	−	0.646767i	0.178772	−	0.983890i	$-0.442787\pi$
$227$	16.8780	−	9.74452i	1.12023	−	0.646767i	0.941460	+	0.337124i	$0.109454\pi$
$228$	−3.78775	+	17.1005i	−0.250850	+	1.13251i
$229$		−	8.70672i		−	0.575357i	−0.957727	−	0.287678i	$-0.907117\pi$
$229$		−	8.70672i		−	0.575357i	0.957727	−	0.287678i	$-0.0928834\pi$
$230$	−0.682174	−	4.42942i	−0.0449812	−	0.292067i
$231$	4.28281	−	7.41805i	0.281788	−	0.488072i
$232$	22.1986	+	1.44877i	1.45741	+	0.0951163i
$233$	1.22945			0.0805438			0.0402719	−	0.999189i	$-0.487178\pi$
$233$	1.22945			0.0805438			0.0402719	+	0.999189i	$0.487178\pi$
$234$	−3.18944	−	4.54940i	−0.208500	−	0.297403i
$235$			5.79800i			0.378220i
$236$	−0.375970	−	1.19165i	−0.0244736	−	0.0775700i
$237$	−14.1016	−	8.14158i	−0.915999	−	0.528852i
$238$	11.3234	−	1.74391i	0.733984	−	0.113041i
$239$	19.4898			1.26069			0.630344	−	0.776316i	$-0.282914\pi$
$239$	19.4898			1.26069			0.630344	+	0.776316i	$0.282914\pi$
$240$	6.62451	−	4.64219i	0.427610	−	0.299652i
$241$	−0.572420	−	0.991460i	−0.0368728	−	0.0638656i	0.847000	−	0.531593i	$-0.178406\pi$
$241$	−0.572420	−	0.991460i	−0.0368728	−	0.0638656i	−0.883873	+	0.467727i	$0.845073\pi$
$242$	−4.58307	+	11.7886i	−0.294611	+	0.757798i
$243$	−9.37055	+	5.41009i	−0.601121	+	0.347058i
$244$	−6.59003	−	20.8874i	−0.421883	−	1.33718i
$245$	1.49311	+	0.862049i	0.0953914	+	0.0550743i
$246$	−3.89393	−	1.51385i	−0.248268	−	0.0965197i
$247$	−1.01364	+	15.5809i	−0.0644964	+	0.991386i
$248$	−7.39766	+	3.65069i	−0.469752	+	0.231819i
$249$	−8.98997	+	15.5711i	−0.569716	+	0.986777i
$250$	1.10284	−	0.885292i	0.0697498	−	0.0559908i
$251$	1.38095	−	0.797294i	0.0871650	−	0.0503248i	−0.455784	−	0.890090i	$-0.650641\pi$
$251$	1.38095	−	0.797294i	0.0871650	−	0.0503248i	0.542949	+	0.839766i	$0.317308\pi$
$252$	4.74650	+	4.34774i	0.299001	+	0.273882i
$253$	3.93559	−	2.27221i	0.247428	−	0.142853i
$254$	7.90131	−	1.21688i	0.495772	−	0.0763537i
$255$	5.54667			0.347346
$256$	10.2937	+	12.2491i	0.643356	+	0.765567i
$257$	4.37045	−	7.56984i	0.272621	−	0.472194i	−0.696911	−	0.717158i	$-0.745443\pi$
$257$	4.37045	−	7.56984i	0.272621	−	0.472194i	0.969532	+	0.244964i	$0.0787761\pi$
$258$	13.2892	+	16.5548i	0.827348	+	1.03066i
$259$			6.53801i			0.406252i
$260$	5.20570	−	4.99006i	0.322844	−	0.309470i
$261$			8.57003i			0.530471i
$262$	−6.43311	+	5.16410i	−0.397439	+	0.319039i
$263$	−12.6443	+	21.9006i	−0.779681	+	1.35045i	0.152445	+	0.988312i	$0.451285\pi$
$263$	−12.6443	+	21.9006i	−0.779681	+	1.35045i	−0.932126	+	0.362135i	$0.882048\pi$
$264$	6.82136	+	4.55514i	0.419826	+	0.280350i
$265$	13.7392			0.843991
$266$	−2.75340	−	17.8781i	−0.168822	−	1.09618i
$267$	29.0100	−	16.7489i	1.77538	−	1.02502i
$268$	9.93324	−	10.8443i	0.606769	−	0.662419i
$269$	−3.78760	+	2.18677i	−0.230934	+	0.133330i	−0.611003	−	0.791628i	$-0.709234\pi$
$269$	−3.78760	+	2.18677i	−0.230934	+	0.133330i	0.380069	+	0.924958i	$0.375900\pi$
$270$	−3.42016	−	4.26062i	−0.208144	−	0.259293i
$271$	7.24823	−	12.5543i	0.440299	−	0.762620i	−0.557413	−	0.830236i	$-0.688206\pi$
$271$	7.24823	−	12.5543i	0.440299	−	0.762620i	0.997711	+	0.0676158i	$0.0215392\pi$
$272$	0.960251	+	10.9290i	0.0582238	+	0.662668i
$273$	17.9127	+	11.9563i	1.08413	+	0.723630i
$274$	−3.61951	+	9.31011i	−0.218663	+	0.562444i
$275$	1.24190	+	0.717013i	0.0748895	+	0.0432375i
$276$	3.85648	+	12.2233i	0.232133	+	0.735756i
$277$	−3.71904	+	2.14719i	−0.223456	+	0.129012i	−0.607549	−	0.794282i	$-0.707847\pi$
$277$	−3.71904	+	2.14719i	−0.223456	+	0.129012i	0.384094	+	0.923294i	$0.374514\pi$
$278$	−0.433048	−	0.168357i	−0.0259725	−	0.0100974i
$279$	−1.58901	−	2.75225i	−0.0951316	−	0.164773i
$280$	−4.63942	+	6.94756i	−0.277258	+	0.415196i
$281$	8.79421			0.524618			0.262309	−	0.964984i	$-0.415516\pi$
$281$	8.79421			0.524618			0.262309	+	0.964984i	$0.415516\pi$
$282$	−2.52402	−	16.3887i	−0.150303	−	0.975934i
$283$	−19.6741	−	11.3588i	−1.16950	−	0.675212i	−0.215939	−	0.976407i	$-0.569281\pi$
$283$	−19.6741	−	11.3588i	−1.16950	−	0.675212i	−0.953563	+	0.301194i	$0.902615\pi$
$284$	−5.73070	+	1.80805i	−0.340054	+	0.107288i
$285$		−	8.75747i		−	0.518748i
$286$	6.62882	+	3.08641i	0.391970	+	0.182503i
$287$	4.31476			0.254692
$288$	−4.45058	+	4.26446i	−0.262253	+	0.251286i
$289$	4.73859	−	8.20748i	0.278741	−	0.482793i
$290$	−10.9933	+	1.69308i	−0.645549	+	0.0994209i
$291$			33.5369i			1.96597i
$292$	−2.05934	+	9.29726i	−0.120514	+	0.544081i
$293$	−21.7868	+	12.5786i	−1.27280	+	0.734849i	−0.975513	−	0.219941i	$-0.929414\pi$
$293$	−21.7868	+	12.5786i	−1.27280	+	0.734849i	−0.297282	+	0.954790i	$0.596080\pi$
$294$	−4.59572	−	1.78669i	−0.268028	−	0.104202i
$295$	0.312389	+	0.541074i	0.0181880	+	0.0315025i
$296$	−6.24752	−	0.407737i	−0.363130	−	0.0236993i
$297$	2.77004	−	4.79786i	0.160734	−	0.278400i
$298$	6.70104	+	2.60518i	0.388181	+	0.150914i
$299$	5.05855	+	10.2452i	0.292544	+	0.592496i
$300$	−2.73192	+	2.98247i	−0.157727	+	0.172193i
$301$	−18.9872	−	10.9623i	−1.09440	−	0.631854i
$302$	−16.6912	−	20.7929i	−0.960472	−	1.19650i
$303$	−2.46179	−	4.26394i	−0.141426	−	0.244957i
$304$	17.2555	−	1.51611i	0.989669	−	0.0869550i
$305$	5.47558	+	9.48398i	0.313531	+	0.543051i
$306$	−4.17728	+	0.643341i	−0.238799	+	0.0367774i
$307$			8.88918i			0.507332i	0.967292	+	0.253666i	$0.0816365\pi$
$307$			8.88918i			0.507332i	−0.967292	+	0.253666i	$0.918364\pi$
$308$	−8.27078	−	1.83198i	−0.471272	−	0.104387i
$309$	9.59311	+	5.53858i	0.545733	+	0.315079i
$310$	3.21656	−	2.58205i	0.182688	−	0.146651i
$311$	−26.1302			−1.48171			−0.740854	−	0.671666i	$-0.765579\pi$
$311$	−26.1302			−1.48171			−0.740854	+	0.671666i	$0.765579\pi$
$312$	−12.5422	+	16.3712i	−0.710062	+	0.926834i
$313$	−27.5229			−1.55569			−0.777843	−	0.628459i	$-0.783686\pi$
$313$	−27.5229			−1.55569			−0.777843	+	0.628459i	$0.783686\pi$
$314$	−3.72796	+	2.99257i	−0.210381	+	0.168881i
$315$	−2.78721	−	1.60919i	−0.157041	−	0.0906679i
$316$	−3.48257	+	15.7227i	−0.195910	+	0.884469i
$317$		−	32.8088i		−	1.84273i	−0.388701	−	0.921364i	$-0.627076\pi$
$317$		−	32.8088i		−	1.84273i	0.388701	−	0.921364i	$-0.372924\pi$
$318$	−38.8354	+	5.98102i	−2.17778	+	0.335399i
$319$	−5.63937	−	9.76768i	−0.315744	−	0.546885i
$320$	−6.34954	−	4.86656i	−0.354950	−	0.272049i
$321$	18.1698	+	31.4710i	1.01414	+	1.75654i
$322$	−8.28646	−	10.3228i	−0.461786	−	0.575265i
$323$	10.2863	+	5.93878i	0.572343	+	0.330442i
$324$	16.3432	+	14.9702i	0.907955	+	0.831678i
$325$	−2.00168	+	2.99888i	−0.111033	+	0.166348i
$326$	−15.5779	−	6.05626i	−0.862782	−	0.335425i
$327$	−19.2169	+	33.2847i	−1.06270	+	1.84065i
$328$	−0.269086	+	4.12305i	−0.0148578	+	0.227657i
$329$	8.56266	+	14.8310i	0.472075	+	0.817657i
$330$	−3.82251	−	1.48609i	−0.210422	−	0.0818063i
$331$	−20.2922	+	11.7157i	−1.11536	+	0.643953i	−0.940212	−	0.340589i	$-0.889374\pi$
$331$	−20.2922	+	11.7157i	−1.11536	+	0.643953i	−0.175148	+	0.984542i	$0.556040\pi$
$332$	17.3610	+	3.84547i	0.952811	+	0.211048i
$333$		−	2.41192i		−	0.132173i
$334$	34.7489	−	5.35167i	1.90138	−	0.292831i
$335$	−3.67651	+	6.36790i	−0.200869	+	0.347916i
$336$	10.0894	−	21.6577i	0.550421	−	1.18153i
$337$	−11.3949			−0.620721			−0.310360	−	0.950619i	$-0.600450\pi$
$337$	−11.3949			−0.620721			−0.310360	+	0.950619i	$0.600450\pi$
$338$	−8.82575	+	16.1278i	−0.480057	+	0.877237i
$339$			2.53248i			0.137545i
$340$	−1.65051	−	5.23136i	−0.0895114	−	0.283710i
$341$	3.62215	+	2.09125i	0.196150	+	0.113247i
$342$	1.01575	+	6.59538i	0.0549256	+	0.356637i
$343$	−15.5832			−0.841414
$344$	11.6593	−	17.4599i	0.628628	−	0.941375i
$345$	−3.20431	−	5.55002i	−0.172514	−	0.298803i
$346$	−20.0368	−	7.78974i	−1.07718	−	0.418779i
$347$	−2.44656	+	1.41252i	−0.131338	+	0.0758280i	−0.564229	−	0.825618i	$-0.690827\pi$
$347$	−2.44656	+	1.41252i	−0.131338	+	0.0758280i	0.432891	+	0.901446i	$0.357493\pi$
$348$	30.3368	−	9.57135i	1.62622	−	0.513078i
$349$	−26.3259	−	15.1993i	−1.40919	−	0.813598i	−0.413883	−	0.910330i	$-0.635828\pi$
$349$	−26.3259	−	15.1993i	−1.40919	−	0.813598i	−0.995310	+	0.0967323i	$0.969161\pi$
$350$	1.51358	−	3.89323i	0.0809043	−	0.208102i
$351$	11.5856	+	7.73313i	0.618393	+	0.412764i
$352$	2.26638	−	7.78905i	0.120798	−	0.415158i
$353$	1.09425	−	1.89530i	0.0582412	−	0.100877i	−0.835435	−	0.549590i	$-0.814784\pi$
$353$	1.09425	−	1.89530i	0.0582412	−	0.100877i	0.893676	+	0.448713i	$0.148117\pi$
$354$	−1.11855	−	1.39342i	−0.0594501	−	0.0740592i
$355$	2.60204	−	1.50229i	0.138102	−	0.0797332i
$356$	−24.4293	−	22.3770i	−1.29475	−	1.18598i
$357$	14.1881	−	8.19148i	0.750912	−	0.433539i
$358$	0.668632	+	4.34150i	0.0353383	+	0.229455i
$359$	21.4704			1.13316			0.566581	−	0.824006i	$-0.308266\pi$
$359$	21.4704			1.13316			0.566581	+	0.824006i	$0.308266\pi$
$360$	1.71152	−	2.56301i	0.0902049	−	0.135083i
$361$	−0.123444	+	0.213811i	−0.00649704	+	0.0112532i
$362$	23.7729	−	19.0834i	1.24948	−	1.00300i
$363$			18.0864i			0.949291i
$364$	5.94641	−	20.4522i	0.311677	−	1.07199i
$365$		−	4.76130i		−	0.249218i
$366$	−19.6060	−	24.4239i	−1.02482	−	1.27666i
$367$	−5.62577	+	9.74412i	−0.293663	+	0.508639i	−0.974673	−	0.223635i	$-0.928208\pi$
$367$	−5.62577	+	9.74412i	−0.293663	+	0.508639i	0.681010	+	0.732274i	$0.261541\pi$
$368$	10.3809	−	7.27451i	0.541141	−	0.379210i
$369$	−1.59175			−0.0828632
$370$	3.09393	−	0.476495i	0.160846	−	0.0247718i
$371$	35.1440	−	20.2904i	1.82459	−	1.05343i
$372$	−7.96793	+	8.69872i	−0.413118	+	0.451007i
$373$	−23.9902	+	13.8507i	−1.24216	+	0.717164i	−0.969534	−	0.244955i	$-0.921227\pi$
$373$	−23.9902	+	13.8507i	−1.24216	+	0.717164i	−0.272630	+	0.962119i	$0.587893\pi$
$374$	4.33771	−	3.48204i	0.224297	−	0.180052i
$375$	1.01114	−	1.75135i	0.0522151	−	0.0904392i
$376$	−14.7060	+	7.25729i	−0.758404	+	0.374266i
$377$	25.4274	−	12.5547i	1.30958	−	0.646602i
$378$	−15.0408	−	5.84743i	−0.773614	−	0.300759i
$379$	4.20765	+	2.42929i	0.216132	+	0.124784i	0.604158	−	0.796864i	$-0.293510\pi$
$379$	4.20765	+	2.42929i	0.216132	+	0.124784i	−0.388026	+	0.921648i	$0.626843\pi$
$380$	−8.25963	+	2.60594i	−0.423710	+	0.133682i
$381$	9.90026	−	5.71592i	0.507206	−	0.292835i
$382$	−0.153752	+	0.395481i	−0.00786664	+	0.0202346i
$383$	−6.94602	−	12.0309i	−0.354925	−	0.614748i	0.632180	−	0.774821i	$-0.282160\pi$
$383$	−6.94602	−	12.0309i	−0.354925	−	0.614748i	−0.987105	+	0.160073i	$0.948827\pi$
$384$	20.0662	+	10.9918i	1.02400	+	0.560921i
$385$	4.23562			0.215867
$386$	23.8830	−	3.67822i	1.21561	−	0.187216i
$387$	7.00452	+	4.04406i	0.356060	+	0.205571i
$388$	31.6304	−	9.97948i	1.60579	−	0.506631i
$389$			18.0019i			0.912731i	0.889792	+	0.456366i	$0.150849\pi$
$389$			18.0019i			0.912731i	−0.889792	+	0.456366i	$0.849151\pi$
$390$	4.35250	−	9.34805i	0.220397	−	0.473357i
$391$	8.69186			0.439566
$392$	−0.317583	+	4.86613i	−0.0160404	+	0.245777i
$393$	−5.89821	+	10.2160i	−0.297525	+	0.515329i
$394$	1.99893	+	12.9792i	0.100704	+	0.653884i
$395$		−	8.05187i		−	0.405133i
$396$	3.05116	+	0.675831i	0.153326	+	0.0339618i
$397$	6.98375	−	4.03207i	0.350504	−	0.202364i	−0.314403	−	0.949290i	$-0.601804\pi$
$397$	6.98375	−	4.03207i	0.350504	−	0.202364i	0.664907	+	0.746926i	$0.268471\pi$
$398$	0.551172	−	1.41773i	0.0276278	−	0.0710642i
$399$	−12.9333	−	22.4011i	−0.647474	−	1.12146i
$400$	3.62586	+	1.68913i	0.181293	+	0.0844564i
$401$	−8.60260	+	14.9001i	−0.429593	+	0.744078i	−0.996837	−	0.0794723i	$-0.974676\pi$
$401$	−8.60260	+	14.9001i	−0.429593	+	0.744078i	0.567244	+	0.823550i	$0.308010\pi$
$402$	7.61996	−	19.6001i	0.380049	−	0.977563i
$403$	−5.83813	+	8.74656i	−0.290818	+	0.435697i
$404$	−3.28900	+	3.59065i	−0.163634	+	0.178642i
$405$	−9.59694	−	5.54080i	−0.476876	−	0.275324i
$406$	−25.6199	+	20.5660i	−1.27149	+	1.02067i
$407$	1.58713	+	2.74899i	0.0786711	+	0.136262i
$408$	6.94270	+	14.0685i	0.343715	+	0.696495i
$409$	−18.9551	−	32.8313i	−0.937272	−	1.62340i	−0.770532	−	0.637401i	$-0.780009\pi$
$409$	−18.9551	−	32.8313i	−0.937272	−	1.62340i	−0.166740	−	0.986001i	$-0.553324\pi$
$410$	−0.314463	−	2.04184i	−0.0155302	−	0.100839i
$411$			14.2839i			0.704572i
$412$	2.36913	−	10.6959i	0.116719	−	0.526948i
$413$	1.59815	+	0.922691i	0.0786397	+	0.0454026i
$414$	3.05694	+	3.80815i	0.150240	+	0.187160i
$415$	−8.89091			−0.436438
$416$	19.1727	+	6.95769i	0.940017	+	0.341129i
$417$	−0.664397			−0.0325356
$418$	−5.49769	−	6.84867i	−0.268901	−	0.334980i
$419$	−33.2578	−	19.2014i	−1.62475	−	0.938051i	−0.985625	−	0.168950i	$-0.945962\pi$
$419$	−33.2578	−	19.2014i	−1.62475	−	0.938051i	−0.639128	−	0.769101i	$-0.720704\pi$
$420$	−2.58348	+	11.6636i	−0.126061	+	0.569124i
$421$		−	18.4451i		−	0.898959i	−0.893291	−	0.449480i	$-0.851609\pi$
$421$		−	18.4451i		−	0.898959i	0.893291	−	0.449480i	$-0.148391\pi$
$422$	0.484277	+	3.14446i	0.0235742	+	0.153070i
$423$	−3.15883	−	5.47126i	−0.153588	−	0.266022i
$424$	17.1972	+	34.8479i	0.835168	+	1.69237i
$425$	1.37139	+	2.37531i	0.0665221	+	0.115220i
$426$	−6.70098	+	5.37913i	−0.324664	+	0.260620i
$427$	28.0124	+	16.1730i	1.35562	+	0.782666i
$428$	24.2752	−	26.5016i	1.17339	−	1.28100i
$429$	10.4341	+	0.678807i	0.503761	+	0.0327731i
$430$	−3.80377	+	9.78408i	−0.183434	+	0.471830i
$431$	9.97432	−	17.2760i	0.480446	−	0.832157i	−0.519302	−	0.854591i	$-0.673808\pi$
$431$	9.97432	−	17.2760i	0.480446	−	0.832157i	0.999748	+	0.0224338i	$0.00714151\pi$
$432$	6.52563	−	14.0078i	0.313964	−	0.673952i
$433$	2.34321	+	4.05856i	0.112608	+	0.195042i	0.916821	−	0.399299i	$-0.130746\pi$
$433$	2.34321	+	4.05856i	0.112608	+	0.195042i	−0.804213	+	0.594341i	$0.797413\pi$
$434$	4.41452	−	11.3550i	0.211904	−	0.545060i
$435$	−13.7745	+	7.95272i	−0.660437	+	0.381304i
$436$	37.1108	+	8.22005i	1.77729	+	0.393669i
$437$		−	13.7233i		−	0.656475i
$438$	2.07272	+	13.4584i	0.0990383	+	0.643066i
$439$	10.6251	−	18.4032i	0.507108	−	0.878337i	−0.492858	−	0.870110i	$-0.664048\pi$
$439$	10.6251	−	18.4032i	0.507108	−	0.878337i	0.999966	−	0.00822722i	$-0.00261884\pi$
$440$	−0.264151	+	4.04743i	−0.0125929	+	0.192953i
$441$	−1.87863			−0.0894584
$442$	8.02835	+	11.4516i	0.381870	+	0.544697i
$443$			34.4195i			1.63532i	0.575700	+	0.817661i	$0.304730\pi$
$443$			34.4195i			1.63532i	−0.575700	+	0.817661i	$0.695270\pi$
$444$	−8.53791	+	2.69373i	−0.405191	+	0.127839i
$445$	14.3452	+	8.28220i	0.680027	+	0.392614i
$446$	−24.7578	+	3.81294i	−1.17232	+	0.180548i
$447$	10.2810			0.486273
$448$	−23.4288	−	3.07120i	−1.10691	−	0.145100i
$449$	−4.37574	−	7.57901i	−0.206504	−	0.357675i	0.744107	−	0.668061i	$-0.232875\pi$
$449$	−4.37574	−	7.57901i	−0.206504	−	0.357675i	−0.950611	+	0.310385i	$0.899542\pi$
$450$	−0.558372	+	1.43625i	−0.0263219	+	0.0677053i
$451$	1.81419	−	1.04743i	0.0854271	−	0.0493214i
$452$	2.38851	−	0.753583i	0.112346	−	0.0354456i
$453$	−33.0198	−	19.0640i	−1.55140	−	0.895704i
$454$	−25.6886	−	9.98701i	−1.20563	−	0.468714i
$455$	−0.691365	+	10.6271i	−0.0324117	+	0.498206i
$456$	22.2124	−	10.9616i	1.04019	−	0.513325i
$457$	20.9459	−	36.2794i	0.979809	−	1.69708i	0.316753	−	0.948508i	$-0.397407\pi$
$457$	20.9459	−	36.2794i	0.979809	−	1.69708i	0.663056	−	0.748570i	$-0.269259\pi$
$458$	−9.60213	+	7.70799i	−0.448678	+	0.360171i
$459$	9.17658	−	5.29810i	0.428326	−	0.247294i
$460$	−4.28102	+	4.67366i	−0.199604	+	0.217911i
$461$	−3.16621	+	1.82801i	−0.147465	+	0.0851390i	−0.571917	−	0.820311i	$-0.693800\pi$
$461$	−3.16621	+	1.82801i	−0.147465	+	0.0851390i	0.424452	+	0.905450i	$0.360467\pi$
$462$	−11.9725	+	1.84388i	−0.557010	+	0.0857849i
$463$	3.86291			0.179525			0.0897623	−	0.995963i	$-0.471389\pi$
$463$	3.86291			0.179525			0.0897623	+	0.995963i	$0.471389\pi$
$464$	−18.0545	−	25.7641i	−0.838159	−	1.19607i
$465$	2.94911	−	5.10800i	0.136762	−	0.236878i
$466$	−1.08842	−	1.35589i	−0.0504201	−	0.0628102i
$467$		−	35.5795i		−	1.64642i	−0.567734	−	0.823212i	$-0.692180\pi$
$467$		−	35.5795i		−	1.64642i	0.567734	−	0.823212i	$-0.307820\pi$
$468$	−2.19368	+	7.54499i	−0.101403	+	0.348767i
$469$			21.7183i			1.00286i
$470$	6.39428	−	5.13292i	0.294946	−	0.236764i
$471$	−3.41798	+	5.92012i	−0.157492	+	0.272785i
$472$	−0.981361	+	1.46960i	−0.0451708	+	0.0676436i
$473$	−10.6445			−0.489436
$474$	3.50519	+	22.7595i	0.160999	+	1.04538i
$475$	3.75031	−	2.16524i	0.172076	−	0.0993482i
$476$	−11.9477	−	10.9440i	−0.547623	−	0.501617i
$477$	−12.9649	+	7.48530i	−0.593623	+	0.342728i
$478$	−17.2541	−	21.4941i	−0.789186	−	0.983118i
$479$	0.372422	−	0.645053i	0.0170164	−	0.0294732i	−0.857392	−	0.514664i	$-0.827917\pi$
$479$	0.372422	−	0.645053i	0.0170164	−	0.0294732i	0.874408	+	0.485191i	$0.161250\pi$
$480$	−10.9842	−	3.19608i	−0.501359	−	0.145880i
$481$	−7.15623	+	3.53337i	−0.326296	+	0.161108i
$482$	−0.586664	+	1.50902i	−0.0267218	+	0.0687339i
$483$	−16.3929	−	9.46443i	−0.745902	−	0.430647i
$484$	17.0583	−	5.38193i	0.775376	−	0.244633i
$485$	−14.3619	+	8.29183i	−0.652139	+	0.376513i
$486$	14.2621	+	5.54472i	0.646944	+	0.251514i
$487$	−11.3703	−	19.6939i	−0.515236	−	0.892415i	−0.999844	−	0.0176832i	$-0.994371\pi$
$487$	−11.3703	−	19.6939i	−0.515236	−	0.892415i	0.484608	−	0.874732i	$-0.338962\pi$
$488$	−17.2014	+	25.7592i	−0.778669	+	1.16606i
$489$	−23.9002			−1.08080
$490$	−0.371137	−	2.40983i	−0.0167663	−	0.108865i
$491$	22.6530	+	13.0787i	1.02232	+	0.590234i	0.914774	−	0.403966i	$-0.132369\pi$
$491$	22.6530	+	13.0787i	1.02232	+	0.590234i	0.107542	+	0.994201i	$0.465702\pi$
$492$	1.77773	+	5.63459i	0.0801462	+	0.254027i
$493$		−	21.5722i		−	0.971562i
$494$	18.0806	−	12.6757i	0.813483	−	0.570307i
$495$	−1.56255			−0.0702316
$496$	10.5752	+	4.92653i	0.474841	+	0.221208i
$497$	4.43725	−	7.68554i	0.199038	−	0.344744i
$498$	25.1312	−	3.87045i	1.12615	−	0.173439i
$499$			23.9912i			1.07399i	0.843584	+	0.536997i	$0.180441\pi$
$499$			23.9912i			1.07399i	−0.843584	+	0.536997i	$0.819559\pi$
$500$	−1.95267	−	0.432517i	−0.0873262	−	0.0193427i
$501$	43.5401	−	25.1379i	1.94523	−	1.12308i
$502$	−2.10184	−	0.817135i	−0.0938095	−	0.0364705i
$503$	−9.88309	−	17.1180i	−0.440665	−	0.763255i	0.557074	−	0.830463i	$-0.311924\pi$
$503$	−9.88309	−	17.1180i	−0.440665	−	0.763255i	−0.997739	+	0.0672084i	$0.978591\pi$
$504$	0.592835	−	9.08366i	0.0264070	−	0.404618i
$505$	1.21733	−	2.10848i	0.0541705	−	0.0938261i
$506$	−5.99004	−	2.32876i	−0.266290	−	0.103526i
$507$	−3.40623	+	26.0681i	−0.151276	+	1.15772i
$508$	−8.33698	−	7.63659i	−0.369894	−	0.338819i
$509$	8.96887	+	5.17818i	0.397538	+	0.229519i	0.685421	−	0.728147i	$-0.259618\pi$
$509$	8.96887	+	5.17818i	0.397538	+	0.229519i	−0.287883	+	0.957666i	$0.592951\pi$
$510$	−4.91042	−	6.11709i	−0.217437	−	0.270869i
$511$	−7.03163	−	12.1791i	−0.311061	−	0.538774i
$512$	4.39586	−	22.1963i	0.194271	−	0.980948i
$513$	−8.36501	−	14.4886i	−0.369324	−	0.639688i
$514$	−12.2175	+	1.88161i	−0.538889	+	0.0829941i
$515$			5.47755i			0.241370i
$516$	6.49254	−	29.3117i	0.285818	−	1.29038i
$517$	7.20055	+	4.15724i	0.316680	+	0.182835i
$518$	7.21039	−	5.78805i	0.316806	−	0.254312i
$519$	−30.7411			−1.34939
$520$	−10.1118	−	1.32340i	−0.443432	−	0.0580348i
$521$	−23.6589			−1.03651			−0.518257	−	0.855225i	$-0.673419\pi$
$521$	−23.6589			−1.03651			−0.518257	+	0.855225i	$0.673419\pi$
$522$	9.45138	−	7.58697i	0.413676	−	0.332073i
$523$	21.1903	+	12.2342i	0.926586	+	0.534965i	0.885730	−	0.464200i	$-0.153658\pi$
$523$	21.1903	+	12.2342i	0.926586	+	0.534965i	0.0408559	+	0.999165i	$0.486992\pi$
$524$	11.3904	+	2.52296i	0.497590	+	0.110216i
$525$		−	5.97313i		−	0.260689i
$526$	35.3467	−	5.44374i	1.54119	−	0.237358i
$527$	3.99980	+	6.92786i	0.174234	+	0.301783i
$528$	−1.01530	−	11.5555i	−0.0441852	−	0.502889i
$529$	6.47872	+	11.2215i	0.281683	+	0.487890i
$530$	−12.1632	−	15.1521i	−0.528335	−	0.658167i
$531$	−0.589569	−	0.340388i	−0.0255851	−	0.0147716i
$532$	−17.2791	+	18.8639i	−0.749146	+	0.817854i
$533$	2.33185	+	4.72275i	0.101004	+	0.204565i
$534$	−44.1538	−	17.1657i	−1.91072	−	0.742834i
$535$	−8.98478	+	15.5621i	−0.388446	+	0.672808i
$536$	−20.7533	−	1.35444i	−0.896407	−	0.0585030i
$537$	3.14070	+	5.43985i	0.135531	+	0.234747i
$538$	5.76479	+	2.24119i	0.248538	+	0.0966245i
$539$	2.14116	−	1.23620i	0.0922263	−	0.0532469i
$540$	−1.67095	+	7.54378i	−0.0719061	+	0.324633i
$541$			29.6849i			1.27625i	0.769931	+	0.638127i	$0.220291\pi$
$541$			29.6849i			1.27625i	−0.769931	+	0.638127i	$0.779709\pi$
$542$	−20.2622	+	3.12058i	−0.870336	+	0.134040i
$543$	21.7962	−	37.7522i	0.935366	−	1.62010i
$544$	11.2028	−	10.7344i	0.480318	−	0.460232i
$545$	−19.0052			−0.814091
$546$	−2.67203	−	30.3397i	−0.114352	−	1.29842i
$547$			34.3918i			1.47049i	0.677804	+	0.735243i	$0.262932\pi$
$547$			34.3918i			1.47049i	−0.677804	+	0.735243i	$0.737068\pi$
$548$	13.4719	−	4.25042i	0.575491	−	0.181569i
$549$	−10.3340	−	5.96635i	−0.441045	−	0.254637i
$550$	−0.308695	−	2.00439i	−0.0131628	−	0.0854673i
$551$	−34.0597			−1.45099
$552$	10.0662	−	15.0743i	0.428448	−	0.641604i
$553$	−11.8912	−	20.5962i	−0.505667	−	0.875840i
$554$	5.66045	+	2.20062i	0.240489	+	0.0934955i
$555$	3.87666	−	2.23819i	0.164555	−	0.0950060i
$556$	0.197703	+	0.626628i	0.00838447	+	0.0265749i
$557$	8.85555	+	5.11276i	0.375222	+	0.216634i	0.675737	−	0.737142i	$-0.263825\pi$
$557$	8.85555	+	5.11276i	0.375222	+	0.216634i	−0.300515	+	0.953777i	$0.597159\pi$
$558$	−1.62855	+	4.18897i	−0.0689422	+	0.177333i
$559$	1.73747	−	26.7069i	0.0734871	−	1.12958i
$560$	11.7693	−	1.03408i	0.497343	−	0.0436979i
$561$	3.97703	−	6.88842i	0.167910	−	0.290829i
$562$	−7.78544	−	9.69861i	−0.328409	−	0.409111i
$563$	17.3608	−	10.0233i	0.731670	−	0.422430i	−0.0873627	−	0.996177i	$-0.527844\pi$
$563$	17.3608	−	10.0233i	0.731670	−	0.422430i	0.819033	+	0.573747i	$0.194511\pi$
$564$	−15.8397	+	17.2924i	−0.666970	+	0.728141i
$565$	−1.08451	+	0.626143i	−0.0456258	+	0.0263420i
$566$	4.89031	+	31.7532i	0.205555	+	1.33469i
$567$	−32.7312			−1.37458
$568$	7.06733	+	4.71940i	0.296539	+	0.198021i
$569$	−19.9763	+	34.5999i	−0.837449	+	1.45050i	0.0545718	+	0.998510i	$0.482621\pi$
$569$	−19.9763	+	34.5999i	−0.837449	+	1.45050i	−0.892021	+	0.451994i	$0.850713\pi$
$570$	−9.65810	+	7.75292i	−0.404533	+	0.324734i
$571$		−	22.4689i		−	0.940294i	−0.882588	−	0.470147i	$-0.844201\pi$
$571$		−	22.4689i		−	0.940294i	0.882588	−	0.470147i	$-0.155799\pi$
$572$	−2.46462	−	10.0429i	−0.103051	−	0.419915i
$573$			0.606761i			0.0253478i
$574$	−3.81982	−	4.75849i	−0.159436	−	0.198616i
$575$	1.58450	−	2.74444i	0.0660782	−	0.114451i
$576$	8.64308	+	1.13299i	0.360128	+	0.0472079i
$577$	−38.0639			−1.58462			−0.792310	−	0.610119i	$-0.791122\pi$
$577$	−38.0639			−1.58462			−0.792310	+	0.610119i	$0.791122\pi$
$578$	−13.2466	+	2.04010i	−0.550985	+	0.0848571i
$579$	29.9252	−	17.2773i	1.24365	−	0.718021i
$580$	11.5995	+	10.6250i	0.481642	+	0.441179i
$581$	−22.7424	+	13.1304i	−0.943516	+	0.544739i
$582$	36.9858	−	29.6899i	1.53311	−	1.23069i
$583$	9.85117	−	17.0627i	0.407994	−	0.706666i
$584$	12.0765	−	5.95966i	0.499730	−	0.246613i
$585$	0.255050	−	3.92042i	0.0105450	−	0.162090i
$586$	33.1598	+	12.8916i	1.36982	+	0.532547i
$587$	35.3069	+	20.3845i	1.45727	+	0.841356i	0.998876	−	0.0473917i	$-0.0150909\pi$
$587$	35.3069	+	20.3845i	1.45727	+	0.841356i	0.458396	+	0.888748i	$0.348424\pi$
$588$	2.09812	+	6.65009i	0.0865252	+	0.274245i
$589$	10.9382	−	6.31517i	0.450701	−	0.260212i
$590$	0.320163	−	0.823524i	0.0131809	−	0.0339039i
$591$	9.38936	+	16.2629i	0.386227	+	0.668964i
$592$	5.08121	+	7.25098i	0.208836	+	0.298014i
$593$	−23.7184			−0.973998			−0.486999	−	0.873402i	$-0.661909\pi$
$593$	−23.7184			−0.973998			−0.486999	+	0.873402i	$0.661909\pi$
$594$	−7.74357	+	1.19259i	−0.317723	+	0.0489324i
$595$	7.01586	+	4.05061i	0.287622	+	0.166059i
$596$	−3.05928	−	9.69652i	−0.125313	−	0.397185i
$597$		−	2.17513i		−	0.0890220i
$598$	6.82055	−	14.6488i	0.278913	−	0.599033i
$599$	33.3185			1.36136			0.680678	−	0.732583i	$-0.261685\pi$
$599$	33.3185			1.36136			0.680678	+	0.732583i	$0.261685\pi$
$600$	5.70774	+	0.372509i	0.233017	+	0.0152076i
$601$	10.4294	−	18.0643i	0.425426	−	0.736859i	−0.571034	−	0.820926i	$-0.693458\pi$
$601$	10.4294	−	18.0643i	0.425426	−	0.736859i	0.996460	+	0.0840669i	$0.0267909\pi$
$602$	4.71957	+	30.6446i	0.192355	+	1.24898i
$603$		−	8.01206i		−	0.326276i
$604$	−8.15464	+	36.8155i	−0.331808	+	1.49800i
$605$	−7.74536	+	4.47179i	−0.314894	+	0.181804i
$606$	−2.52305	+	6.48980i	−0.102492	+	0.263630i
$607$	0.285836	+	0.495082i	0.0116017	+	0.0200948i	0.871768	−	0.489919i	$-0.162974\pi$
$607$	0.285836	+	0.495082i	0.0116017	+	0.0200948i	−0.860166	+	0.510014i	$0.829640\pi$
$608$	−16.9482	−	17.6878i	−0.687338	−	0.717337i
$609$	−23.4896	+	40.6852i	−0.951847	+	1.64865i
$610$	5.61184	−	14.4348i	0.227217	−	0.584447i
$611$	−11.6058	+	17.3875i	−0.469519	+	0.703423i
$612$	4.40761	+	4.03733i	0.178167	+	0.163199i
$613$	−13.9694	−	8.06522i	−0.564218	−	0.325751i	0.190619	−	0.981664i	$-0.438951\pi$
$613$	−13.9694	−	8.06522i	−0.564218	−	0.325751i	−0.754837	+	0.655913i	$0.772284\pi$
$614$	9.80335	−	7.86952i	0.395631	−	0.317588i
$615$	−1.47709	−	2.55840i	−0.0595622	−	0.103165i
$616$	5.30167	+	10.7432i	0.213611	+	0.432856i
$617$	14.7068	+	25.4729i	0.592074	+	1.02550i	0.993953	+	0.109809i	$0.0350240\pi$
$617$	14.7068	+	25.4729i	0.592074	+	1.02550i	−0.401879	+	0.915693i	$0.631643\pi$
$618$	−2.38452	−	15.4829i	−0.0959195	−	0.622815i
$619$		−	25.3087i		−	1.01724i	−0.860990	−	0.508622i	$-0.830155\pi$
$619$		−	25.3087i		−	1.01724i	0.860990	−	0.508622i	$-0.169845\pi$
$620$	−5.69519	−	1.26148i	−0.228724	−	0.0506624i
$621$	−10.6026	−	6.12142i	−0.425468	−	0.245644i
$622$	23.1329	+	28.8175i	0.927543	+	1.15547i
$623$	48.9256			1.96016
$624$	29.1583	−	0.661200i	1.16727	−	0.0264692i
$625$	1.00000			0.0400000
$626$	24.3658	+	30.3534i	0.973853	+	1.21317i
$627$	−10.8759	−	6.27922i	−0.434343	−	0.250768i
$628$	6.60066	+	1.46205i	0.263395	+	0.0583420i
$629$			6.07122i			0.242075i
$630$	0.692806	+	4.49845i	0.0276020	+	0.179223i
$631$	22.6813	+	39.2852i	0.902928	+	1.56392i	0.823675	+	0.567063i	$0.191920\pi$
$631$	22.6813	+	39.2852i	0.902928	+	1.56392i	0.0792533	+	0.996855i	$0.474746\pi$
$632$	20.4227	−	10.0784i	0.812371	−	0.400898i
$633$	2.27475	+	3.93998i	0.0904131	+	0.156600i
$634$	−36.1829	+	29.0454i	−1.43701	+	1.15354i
$635$	4.89559	+	2.82647i	0.194275	+	0.112165i
$636$	40.9767	+	37.5343i	1.62483	+	1.48833i
$637$	2.75211	+	5.57392i	0.109043	+	0.220847i
$638$	−5.77971	+	14.8666i	−0.228821	+	0.588573i
$639$	−1.63694	+	2.83526i	−0.0647562	+	0.112161i
$640$	0.254154	+	11.3109i	0.0100463	+	0.447101i
$641$	−9.40375	−	16.2878i	−0.371426	−	0.643328i	0.618359	−	0.785896i	$-0.287798\pi$
$641$	−9.40375	−	16.2878i	−0.371426	−	0.643328i	−0.989785	+	0.142567i	$0.954464\pi$
$642$	18.6219	−	47.8994i	0.734949	−	1.89044i
$643$	−26.1835	+	15.1171i	−1.03258	+	0.596159i	−0.917722	−	0.397224i	$-0.869974\pi$
$643$	−26.1835	+	15.1171i	−1.03258	+	0.596159i	−0.114855	+	0.993382i	$0.536640\pi$
$644$	−4.04842	+	18.2773i	−0.159530	+	0.720226i
$645$			15.0111i			0.591060i
$646$	−2.55682	−	16.6017i	−0.100597	−	0.653184i
$647$	−0.0369857	+	0.0640610i	−0.00145406	+	0.00251850i	−0.866752	−	0.498740i	$-0.833796\pi$
$647$	−0.0369857	+	0.0640610i	−0.00145406	+	0.00251850i	0.865297	+	0.501259i	$0.167130\pi$
$648$	2.04126	−	31.2769i	0.0801881	−	1.22867i
$649$	0.895948			0.0351690
$650$	5.07936	−	0.447342i	0.199229	−	0.0175462i
$651$		−	17.4213i		−	0.682795i
$652$	7.11192	+	22.5415i	0.278524	+	0.882795i
$653$	31.9916	+	18.4703i	1.25193	+	0.722800i	0.971492	−	0.237073i	$-0.0761881\pi$
$653$	31.9916	+	18.4703i	1.25193	+	0.722800i	0.280435	+	0.959873i	$0.409521\pi$
$654$	53.7202	−	8.27344i	2.10063	−	0.323517i
$655$	−5.83322			−0.227923
$656$	4.78529	−	3.35334i	0.186834	−	0.130926i
$657$	2.59403	+	4.49298i	0.101203	+	0.175288i
$658$	8.77574	−	22.5730i	0.342114	−	0.879986i
$659$	23.1055	−	13.3399i	0.900061	−	0.519650i	0.0228409	−	0.999739i	$-0.492729\pi$
$659$	23.1055	−	13.3399i	0.900061	−	0.519650i	0.877220	+	0.480089i	$0.159396\pi$
$660$	1.74512	+	5.53125i	0.0679288	+	0.215303i
$661$	−2.88995	−	1.66852i	−0.112406	−	0.0648977i	0.442743	−	0.896649i	$-0.354005\pi$
$661$	−2.88995	−	1.66852i	−0.112406	−	0.0648977i	−0.555149	+	0.831751i	$0.687339\pi$
$662$	30.8851	+	12.0073i	1.20038	+	0.466675i
$663$	16.6338	+	11.1027i	0.646002	+	0.431192i
$664$	−11.1286	−	22.5508i	−0.431875	−	0.875142i
$665$	6.39539	−	11.0771i	0.248003	−	0.429553i
$666$	−2.65997	+	2.13526i	−0.103072	+	0.0827395i
$667$	−21.5852	+	12.4622i	−0.835784	+	0.482540i
$668$	−36.6650	−	33.5848i	−1.41861	−	1.29943i
$669$	−31.0213	+	17.9102i	−1.19935	+	0.692447i
$670$	10.2776	−	1.58284i	0.397057	−	0.0611506i
$671$	15.7042			0.606256
$672$	−32.8171	+	8.04643i	−1.26595	+	0.310398i
$673$	14.4277	−	24.9895i	0.556147	−	0.963275i	−0.441666	−	0.897180i	$-0.645612\pi$
$673$	14.4277	−	24.9895i	0.556147	−	0.963275i	0.997813	−	0.0660957i	$-0.0210543\pi$
$674$	10.0878	+	12.5668i	0.388569	+	0.484054i
$675$		−	3.86331i		−	0.148699i
$676$	25.5998	−	4.54442i	0.984607	−	0.174785i
$677$			28.5538i			1.09741i	0.836016	+	0.548705i	$0.184879\pi$
$677$			28.5538i			1.09741i	−0.836016	+	0.548705i	$0.815121\pi$
$678$	2.79292	−	2.24198i	0.107261	−	0.0861028i
$679$	−24.4912	+	42.4201i	−0.939888	+	1.62793i
$680$	−4.30817	+	6.45153i	−0.165211	+	0.247405i
$681$	−39.4124			−1.51029
$682$	−0.900343	−	5.84602i	−0.0344759	−	0.223856i
$683$	2.67626	−	1.54514i	0.102404	−	0.0591232i	−0.447923	−	0.894072i	$-0.647836\pi$
$683$	2.67626	−	1.54514i	0.102404	−	0.0591232i	0.550328	+	0.834949i	$0.314503\pi$
$684$	6.37442	−	6.95905i	0.243732	−	0.266086i
$685$	−6.11696	+	3.53163i	−0.233717	+	0.134936i
$686$	13.7957	+	17.1858i	0.526722	+	0.656157i
$687$	−8.80373	+	15.2485i	−0.335883	+	0.581767i
$688$	−29.5774	+	2.59875i	−1.12763	+	0.0990763i
$689$	41.2021	+	27.5015i	1.56968	+	1.04772i
$690$	−3.28405	+	8.44723i	−0.125022	+	0.321581i
$691$	31.2899	+	18.0652i	1.19032	+	0.687233i	0.958380	−	0.285496i	$-0.0921583\pi$
$691$	31.2899	+	18.0652i	1.19032	+	0.687233i	0.231943	+	0.972729i	$0.425492\pi$
$692$	9.14756	+	28.9936i	0.347738	+	1.10217i
$693$	−3.99693	+	2.30763i	−0.151831	+	0.0876595i
$694$	3.72370	+	1.44767i	0.141350	+	0.0549528i
$695$	−0.164269	−	0.284522i	−0.00623108	−	0.0107925i
$696$	−37.4126	−	24.9832i	−1.41812	−	0.946987i
$697$	4.00670			0.151764
$698$	6.54373	+	42.4891i	0.247684	+	1.60823i
$699$	−2.15319	−	1.24315i	−0.0814412	−	0.0470201i
$700$	−5.63358	+	1.77741i	−0.212929	+	0.0671798i
$701$		−	14.6511i		−	0.553363i	−0.960962	−	0.276682i	$-0.910765\pi$
$701$		−	14.6511i		−	0.553363i	0.960962	−	0.276682i	$-0.0892347\pi$
$702$	−1.72822	−	19.6231i	−0.0652275	−	0.740628i
$703$	9.58566			0.361530
$704$	−10.5965	+	4.39612i	−0.399370	+	0.165685i
$705$	5.86260	−	10.1543i	0.220798	−	0.382434i
$706$	−3.05895	+	0.471108i	−0.115125	+	0.0177304i
$707$		−	7.19116i		−	0.270451i
$708$	−0.546476	+	2.46716i	−0.0205378	+	0.0927215i
$709$	−15.9046	+	9.18252i	−0.597309	+	0.344857i	−0.767982	−	0.640471i	$-0.778739\pi$
$709$	−15.9046	+	9.18252i	−0.597309	+	0.344857i	0.170673	+	0.985328i	$0.445406\pi$
$710$	−3.96035	−	1.53967i	−0.148629	−	0.0577829i
$711$	4.38677	+	7.59811i	0.164517	+	0.284951i
$712$	−3.05120	+	46.7517i	−0.114349	+	1.75210i
$713$	4.62137	−	8.00445i	0.173072	−	0.299769i
$714$	−21.5945	−	8.39533i	−0.808153	−	0.314187i
$715$	2.28908	+	4.63613i	0.0856067	+	0.173381i
$716$	4.19604	−	4.58089i	0.156814	−	0.171196i
$717$	−34.1334	−	19.7069i	−1.27473	−	0.735968i
$718$	−19.0075	−	23.6784i	−0.709355	−	0.883670i
$719$	−11.9817	−	20.7529i	−0.446841	−	0.773951i	0.551338	−	0.834282i	$-0.314118\pi$
$719$	−11.9817	−	20.7529i	−0.446841	−	0.773951i	−0.998178	+	0.0603313i	$0.980784\pi$
$720$	−4.34179	+	0.381481i	−0.161809	+	0.0142170i
$721$	8.08941	+	14.0113i	0.301265	+	0.521807i
$722$	0.345083	−	0.0531461i	0.0128427	−	0.00197789i
$723$			2.31519i			0.0861028i
$724$	−42.0919	−	9.32336i	−1.56433	−	0.346500i
$725$	−6.81137	−	3.93255i	−0.252968	−	0.146051i
$726$	19.9465	−	16.0118i	0.740282	−	0.594252i
$727$	33.7901			1.25321			0.626603	−	0.779339i	$-0.284445\pi$
$727$	33.7901			1.25321			0.626603	+	0.779339i	$0.284445\pi$
$728$	−27.8199	+	11.5482i	−1.03107	+	0.428006i
$729$	−11.3633			−0.420863
$730$	−5.25096	+	4.21514i	−0.194347	+	0.156009i
$731$	−17.6316	−	10.1796i	−0.652127	−	0.376505i
$732$	−9.57867	+	43.2445i	−0.354038	+	1.59836i
$733$		−	0.451256i		−	0.0166675i	−0.999965	−	0.00833377i	$-0.997347\pi$
$733$		−	0.451256i		−	0.0166675i	0.999965	−	0.00833377i	$-0.00265275\pi$
$734$	15.7267	−	2.42206i	0.580481	−	0.0893998i
$735$	−1.74331	−	3.01950i	−0.0643028	−	0.111376i
$736$	−17.2127	−	5.00839i	−0.634470	−	0.184612i
$737$	5.27221	+	9.13173i	0.194204	+	0.336372i
$738$	1.40916	+	1.75545i	0.0518720	+	0.0646189i
$739$	−43.4646	−	25.0943i	−1.59887	−	0.923109i	−0.991705	−	0.128534i	$-0.958973\pi$
$739$	−43.4646	−	25.0943i	−1.59887	−	0.923109i	−0.607166	−	0.794575i	$-0.707694\pi$
$740$	−3.26453	−	2.99027i	−0.120006	−	0.109925i
$741$	17.5297	−	26.2626i	0.643969	−	0.964780i
$742$	−53.4898	−	20.7954i	−1.96367	−	0.763421i
$743$	−16.7042	+	28.9324i	−0.612816	+	1.06143i	0.377948	+	0.925827i	$0.376630\pi$
$743$	−16.7042	+	28.9324i	−0.612816	+	1.06143i	−0.990763	+	0.135601i	$0.956703\pi$
$744$	16.6472	+	1.08646i	0.610318	+	0.0398317i
$745$	2.54192	+	4.40274i	0.0931288	+	0.161304i
$746$	36.5135	+	14.1954i	1.33685	+	0.519731i
$747$	8.38987	−	4.84389i	0.306969	−	0.177229i
$748$	−7.68027	−	1.70118i	−0.280819	−	0.0622013i
$749$			53.0760i			1.93935i
$750$	−2.82661	+	0.435326i	−0.103213	+	0.0158959i
$751$	24.1298	−	41.7941i	0.880510	−	1.52509i	0.0297359	−	0.999558i	$-0.490533\pi$
$751$	24.1298	−	41.7941i	0.880510	−	1.52509i	0.850774	−	0.525531i	$-0.176133\pi$
$752$	21.0227	+	9.79356i	0.766620	+	0.357135i
$753$	−3.22471			−0.117515
$754$	−36.3566	−	16.9278i	−1.32403	−	0.616474i
$755$		−	18.8539i		−	0.686164i
$756$	6.86669	+	21.7643i	0.249739	+	0.791559i
$757$	−14.9106	−	8.60861i	−0.541933	−	0.312885i	0.203929	−	0.978986i	$-0.434629\pi$
$757$	−14.9106	−	8.60861i	−0.541933	−	0.312885i	−0.745862	+	0.666100i	$0.767962\pi$
$758$	−1.04588	−	6.79099i	−0.0379880	−	0.246660i
$759$	−9.19012			−0.333580
$760$	10.1861	+	6.80205i	0.369489	+	0.246736i
$761$	−7.67188	−	13.2881i	−0.278105	−	0.481693i	0.692808	−	0.721122i	$-0.256373\pi$
$761$	−7.67188	−	13.2881i	−0.278105	−	0.481693i	−0.970914	+	0.239429i	$0.923040\pi$
$762$	−15.0684	−	5.85816i	−0.545870	−	0.212219i
$763$	−48.6141	+	28.0674i	−1.75995	+	1.01611i
$764$	0.572268	−	0.180552i	0.0207039	−	0.00653215i
$765$	−2.58821	−	1.49430i	−0.0935769	−	0.0540266i
$766$	−7.11887	+	18.3112i	−0.257215	+	0.661610i
$767$	−0.146242	+	2.24792i	−0.00528051	+	0.0811676i
$768$	−5.64230	−	31.8608i	−0.203599	−	1.14968i
$769$	1.21031	−	2.09632i	0.0436450	−	0.0755954i	−0.843378	−	0.537321i	$-0.819436\pi$
$769$	1.21031	−	2.09632i	0.0436450	−	0.0755954i	0.887023	+	0.461726i	$0.152770\pi$
$770$	−3.74976	−	4.67122i	−0.135132	−	0.168339i
$771$	−15.3084	+	8.83829i	−0.551317	+	0.318303i
$772$	−25.1999	−	23.0829i	−0.906965	−	0.830771i
$773$	36.3061	−	20.9614i	1.30584	−	0.753927i	0.324441	−	0.945906i	$-0.394824\pi$
$773$	36.3061	−	20.9614i	1.30584	−	0.753927i	0.981399	+	0.191978i	$0.0614903\pi$
$774$	−1.74109	−	11.3051i	−0.0625821	−	0.406352i
$775$	2.91661			0.104768
$776$	−39.0079	−	26.0486i	−1.40030	−	0.935088i
$777$	6.61085	−	11.4503i	0.237163	−	0.410778i
$778$	19.8532	−	15.9369i	0.711772	−	0.571366i
$779$		−	6.32606i		−	0.226654i
$780$	−14.1626	+	3.47564i	−0.507104	+	0.124448i
$781$		−	4.30864i		−	0.154175i
$782$	−7.69483	−	9.58574i	−0.275167	−	0.342785i
$783$	−15.1927	+	26.3144i	−0.542941	+	0.940402i
$784$	5.64772	−	3.95770i	0.201704	−	0.141347i
$785$	−3.38032			−0.120649
$786$	16.4883	−	2.53935i	0.588116	−	0.0905756i
$787$	−34.6665	+	20.0147i	−1.23573	+	0.713448i	−0.968218	−	0.250107i	$-0.919534\pi$
$787$	−34.6665	+	20.0147i	−1.23573	+	0.713448i	−0.267510	+	0.963555i	$0.586201\pi$
$788$	12.5444	−	13.6949i	0.446875	−	0.487861i
$789$	44.2892	−	25.5704i	1.57674	−	0.910329i
$790$	−8.87993	+	7.12825i	−0.315934	+	0.253612i
$791$	−1.84941	+	3.20328i	−0.0657576	+	0.113895i
$792$	−1.95583	−	3.96325i	−0.0694974	−	0.140828i
$793$	−2.56335	+	39.4017i	−0.0910271	+	1.39919i
$794$	−10.6294	−	4.13241i	−0.377223	−	0.146654i
$795$	−24.0621	−	13.8923i	−0.853395	−	0.492708i
$796$	−2.05148	+	0.647247i	−0.0727126	+	0.0229410i
$797$	−18.2955	+	10.5629i	−0.648061	+	0.374158i	−0.787713	−	0.616043i	$-0.788735\pi$
$797$	−18.2955	+	10.5629i	−0.648061	+	0.374158i	0.139652	+	0.990201i	$0.455402\pi$
$798$	−13.2551	+	34.0949i	−0.469227	+	1.20695i
$799$	7.95131	+	13.7721i	0.281297	+	0.487221i
$800$	−1.34710	−	5.49412i	−0.0476273	−	0.194246i
$801$	−18.0490			−0.637731
$802$	24.0483	−	3.70367i	0.849175	−	0.130781i
$803$	−5.91307	−	3.41392i	−0.208668	−	0.120474i
$804$	−28.3617	+	8.94818i	−1.00024	+	0.315578i
$805$		−	9.36015i		−	0.329902i
$806$	14.8145	−	1.30472i	0.521819	−	0.0459568i
$807$	8.84454			0.311343
$808$	6.87165	+	0.448471i	0.241744	+	0.0157771i
$809$	−0.874694	+	1.51502i	−0.0307526	+	0.0532651i	−0.880992	−	0.473131i	$-0.843124\pi$
$809$	−0.874694	+	1.51502i	−0.0307526	+	0.0532651i	0.850239	+	0.526396i	$0.176457\pi$
$810$	2.38548	+	15.4891i	0.0838171	+	0.544232i
$811$		−	33.0837i		−	1.16173i	−0.814001	−	0.580863i	$-0.802715\pi$
$811$		−	33.0837i		−	1.16173i	0.814001	−	0.580863i	$-0.197285\pi$
$812$	45.3621	+	10.0477i	1.59190	+	0.352605i
$813$	−25.3884	+	14.6580i	−0.890409	+	0.514078i
$814$	1.62663	−	4.18401i	0.0570132	−	0.146649i
$815$	−5.90921	−	10.2351i	−0.206991	−	0.358518i
$816$	9.36903	−	20.1114i	0.327982	−	0.704041i
$817$	−16.0722	+	27.8379i	−0.562296	+	0.973926i
$818$	−19.4268	+	49.9698i	−0.679244	+	1.74715i
$819$	−5.13739	−	10.4049i	−0.179515	−	0.363576i
$820$	−1.97343	+	2.15442i	−0.0689152	+	0.0752357i
$821$	−13.2589	−	7.65503i	−0.462739	−	0.267162i	0.250456	−	0.968128i	$-0.419419\pi$
$821$	−13.2589	−	7.65503i	−0.462739	−	0.267162i	−0.713195	+	0.700965i	$0.752753\pi$
$822$	15.7529	−	12.6454i	0.549444	−	0.441059i
$823$	−18.0178	−	31.2077i	−0.628060	−	1.08783i	−0.987941	−	0.154833i	$-0.950516\pi$
$823$	−18.0178	−	31.2077i	−0.628060	−	1.08783i	0.359881	−	0.932998i	$-0.382817\pi$
$824$	−13.8932	+	6.85619i	−0.483993	+	0.238847i
$825$	−1.45000	−	2.51148i	−0.0504826	−	0.0874385i
$826$	−0.397245	−	2.57935i	−0.0138219	−	0.0897472i
$827$		−	10.2039i		−	0.354825i	−0.984137	−	0.177412i	$-0.943227\pi$
$827$		−	10.2039i		−	0.354825i	0.984137	−	0.177412i	$-0.0567726\pi$
$828$	1.49350	−	6.74264i	0.0519025	−	0.234323i
$829$	15.8247	+	9.13638i	0.549614	+	0.317320i	0.748966	−	0.662608i	$-0.230551\pi$
$829$	15.8247	+	9.13638i	0.549614	+	0.317320i	−0.199353	+	0.979928i	$0.563884\pi$
$830$	7.87105	+	9.80526i	0.273208	+	0.340346i
$831$	8.68445			0.301260
$832$	−9.30017	−	27.3040i	−0.322425	−	0.946595i
$833$	4.72881			0.163844
$834$	0.588185	+	0.732724i	0.0203672	+	0.0253721i
$835$	21.5302	+	12.4305i	0.745083	+	0.430174i
$836$	−2.68594	+	12.1262i	−0.0928953	+	0.419392i
$837$		−	11.2678i		−	0.389471i
$838$	8.26678	+	53.6770i	0.285571	+	1.85424i
$839$	8.17203	+	14.1544i	0.282130	+	0.488663i	0.971909	−	0.235356i	$-0.0756258\pi$
$839$	8.17203	+	14.1544i	0.282130	+	0.488663i	−0.689779	+	0.724020i	$0.742292\pi$
$840$	15.1502	−	7.47650i	0.522732	−	0.257964i
$841$	16.4298	+	28.4573i	0.566546	+	0.981286i
$842$	−20.3420	+	16.3293i	−0.701032	+	0.562745i
$843$	−15.4017	−	8.89219i	−0.530464	−	0.306263i
$844$	3.03911	−	3.31784i	0.104611	−	0.114205i
$845$	−12.0056	+	4.98652i	−0.413005	+	0.171542i
$846$	−3.23744	+	8.32735i	−0.111306	+	0.286300i
$847$	−13.2081	+	22.8771i	−0.453837	+	0.786068i
$848$	23.2072	−	49.8163i	0.796940	−	1.71070i
$849$	22.9708	+	39.7865i	0.788355	+	1.36547i
$850$	1.40551	−	3.61527i	0.0482088	−	0.124003i
$851$	6.07489	−	3.50734i	0.208245	−	0.120230i
$852$	11.8646	+	2.62802i	0.406476	+	0.0900344i
$853$		−	7.33568i		−	0.251169i	−0.992083	−	0.125584i	$-0.959919\pi$
$853$		−	7.33568i		−	0.251169i	0.992083	−	0.125584i	$-0.0400806\pi$
$854$	−6.96295	−	45.2111i	−0.238267	−	1.54709i
$855$	−2.35931	+	4.08645i	−0.0806867	+	0.139753i
$856$	−50.7177	−	3.31004i	−1.73350	−	0.113135i
$857$	27.7142			0.946700			0.473350	−	0.880874i	$-0.343045\pi$
$857$	27.7142			0.946700			0.473350	+	0.880874i	$0.343045\pi$
$858$	−8.48857	−	12.1081i	−0.289795	−	0.413362i
$859$		−	6.17249i		−	0.210603i	−0.994440	−	0.105301i	$-0.966419\pi$
$859$		−	6.17249i		−	0.210603i	0.994440	−	0.105301i	$-0.0335807\pi$
$860$	14.1577	−	4.46680i	0.482775	−	0.152317i
$861$	−7.55665	−	4.36283i	−0.257530	−	0.148685i
$862$	−27.8829	+	4.29424i	−0.949695	+	0.146262i
$863$	15.9559			0.543146			0.271573	−	0.962418i	$-0.412456\pi$
$863$	15.9559			0.543146			0.271573	+	0.962418i	$0.412456\pi$
$864$	−21.2255	+	5.20428i	−0.722106	+	0.177053i
$865$	−7.60060	−	13.1646i	−0.258428	−	0.447611i
$866$	2.40152	−	6.17720i	0.0816071	−	0.209910i
$867$	−16.5978	+	9.58277i	−0.563692	+	0.325448i
$868$	−16.4310	+	5.18401i	−0.557703	+	0.175957i
$869$	−9.99964	−	5.77329i	−0.339214	−	0.195846i
$870$	20.9651	+	8.15062i	0.710782	+	0.276332i
$871$	−23.7719	+	11.7373i	−0.805481	+	0.397705i
$872$	−23.7885	−	48.2045i	−0.805581	−	1.63241i
$873$	9.03502	−	15.6491i	0.305789	−	0.529642i
$874$	−15.1346	+	12.1491i	−0.511937	+	0.410951i
$875$	2.55794	−	1.47683i	0.0864743	−	0.0499259i
$876$	13.0075	−	14.2005i	0.439482	−	0.479789i
$877$	10.3978	−	6.00317i	0.351109	−	0.202713i	−0.314065	−	0.949402i	$-0.601691\pi$
$877$	10.3978	−	6.00317i	0.351109	−	0.202713i	0.665173	+	0.746689i	$0.268358\pi$
$878$	−29.7021	+	4.57441i	−1.00240	+	0.154379i
$879$	50.8749			1.71597
$880$	4.69752	−	3.29184i	0.158353	−	0.110968i
$881$	23.4156	−	40.5571i	0.788893	−	1.36640i	−0.137753	−	0.990467i	$-0.543988\pi$
$881$	23.4156	−	40.5571i	0.788893	−	1.36640i	0.926646	−	0.375936i	$-0.122679\pi$
$882$	1.66313	+	2.07183i	0.0560006	+	0.0697620i
$883$			34.4995i			1.16100i	0.814260	+	0.580500i	$0.197143\pi$
$883$			34.4995i			1.16100i	−0.814260	+	0.580500i	$0.802857\pi$
$884$	5.52185	−	18.9920i	0.185720	−	0.638770i
$885$		−	1.26348i		−	0.0424714i
$886$	37.9593	−	30.4713i	1.27527	−	1.02370i
$887$	10.8241	−	18.7479i	0.363437	−	0.629492i	−0.625087	−	0.780555i	$-0.714936\pi$
$887$	10.8241	−	18.7479i	0.363437	−	0.629492i	0.988524	+	0.151063i	$0.0482698\pi$
$888$	10.5293	+	7.03121i	0.353340	+	0.235952i
$889$	16.6968			0.559994
$890$	−3.56573	−	23.1526i	−0.119524	−	0.776078i
$891$	−13.7623	+	7.94565i	−0.461053	+	0.266189i
$892$	26.1230	+	23.9284i	0.874661	+	0.801181i
$893$	21.7443	−	12.5541i	0.727646	−	0.420106i
$894$	−9.10165	−	11.3383i	−0.304405	−	0.379209i
$895$	−1.55305	+	2.68996i	−0.0519126	+	0.0899153i
$896$	17.3543	+	28.5572i	0.579767	+	0.954028i
$897$	1.50007	−	23.0579i	0.0500859	−	0.769879i
$898$	−4.48463	+	11.5354i	−0.149654	+	0.384941i
$899$	−19.8661	−	11.4697i	−0.662572	−	0.382536i
$900$	2.07827	−	0.655701i	0.0692757	−	0.0218567i
$901$	32.6349	−	18.8417i	1.08722	−	0.627710i
$902$	−2.76124	−	1.07349i	−0.0919391	−	0.0357433i
$903$	22.1688	+	38.3975i	0.737731	+	1.27779i
$904$	−2.94561	−	1.96701i	−0.0979696	−	0.0654218i
$905$	21.5561			0.716548
$906$	8.20760	+	53.2928i	0.272679	+	1.77053i
$907$	−3.97167	−	2.29305i	−0.131877	−	0.0761393i	0.432610	−	0.901581i	$-0.357593\pi$
$907$	−3.97167	−	2.29305i	−0.131877	−	0.0761393i	−0.564487	+	0.825442i	$0.690926\pi$
$908$	11.7278	+	37.1719i	0.389202	+	1.23359i
$909$			2.65288i			0.0879904i
$910$	12.3321	−	8.64562i	0.408804	−	0.286599i
$911$	−1.21715			−0.0403261			−0.0201631	−	0.999797i	$-0.506419\pi$
$911$	−1.21715			−0.0403261			−0.0201631	+	0.999797i	$0.506419\pi$
$912$	−31.7533	−	14.7925i	−1.05146	−	0.489828i
$913$	−6.37490	+	11.0416i	−0.210978	+	0.365425i
$914$	−58.5536	+	9.01783i	−1.93678	+	0.298283i
$915$		−	22.1463i		−	0.732135i
$916$	17.0014	+	3.76581i	0.561741	+	0.124426i
$917$	−14.9210	+	8.61466i	−0.492736	+	0.284481i
$918$	−13.9669	−	5.42994i	−0.460977	−	0.179215i
$919$	0.546458	+	0.946493i	0.0180260	+	0.0312219i	0.874898	−	0.484308i	$-0.160929\pi$
$919$	0.546458	+	0.946493i	0.0180260	+	0.0312219i	−0.856872	+	0.515530i	$0.827595\pi$
$920$	8.94426	+	0.583737i	0.294884	+	0.0192452i
$921$	8.98822	−	15.5681i	0.296172	−	0.512985i
$922$	4.81903	+	1.87350i	0.158706	+	0.0617005i
$923$	10.8103	+	0.703284i	0.355826	+	0.0231489i
$924$	12.6326	+	11.5714i	0.415583	+	0.380670i
$925$	1.91697	+	1.10676i	0.0630297	+	0.0363902i
$926$	−3.41980	−	4.26018i	−0.112382	−	0.139998i
$927$	−2.98425	−	5.16887i	−0.0980156	−	0.169768i
$928$	−12.4302	+	42.7200i	−0.408043	+	1.40235i
$929$	4.95450	+	8.58145i	0.162552	+	0.281548i	0.935783	−	0.352576i	$-0.114694\pi$
$929$	4.95450	+	8.58145i	0.162552	+	0.281548i	−0.773231	+	0.634124i	$0.781361\pi$
$930$	−8.24413	+	1.26968i	−0.270336	+	0.0416343i
$931$		−	7.46618i		−	0.244694i
$932$	−0.531757	+	2.40071i	−0.0174183	+	0.0786378i
$933$	45.7631	+	26.4213i	1.49822	+	0.864996i
$934$	−39.2386	+	31.4983i	−1.28392	+	1.03065i
$935$	3.93321			0.128630
$936$	10.2630	−	4.26024i	0.335456	−	0.139250i
$937$	50.8388			1.66083			0.830416	−	0.557144i	$-0.188103\pi$
$937$	50.8388			1.66083			0.830416	+	0.557144i	$0.188103\pi$
$938$	23.9518	−	19.2270i	0.782055	−	0.627785i
$939$	48.2022	+	27.8295i	1.57302	+	0.908183i
$940$	−11.3216	−	2.50773i	−0.369270	−	0.0817933i
$941$			26.5864i			0.866693i	0.901227	+	0.433347i	$0.142667\pi$
$941$			26.5864i			0.866693i	−0.901227	+	0.433347i	$0.857333\pi$
$942$	9.55487	−	1.47154i	0.311314	−	0.0479454i
$943$	−2.31467	−	4.00912i	−0.0753760	−	0.130555i
$944$	2.48952	−	0.218736i	0.0810270	−	0.00711925i
$945$	−5.70545	−	9.88213i	−0.185598	−	0.321466i
$946$	9.42352	+	11.7392i	0.306385	+	0.381675i
$947$	−31.9714	−	18.4587i	−1.03893	−	0.599827i	−0.119400	−	0.992846i	$-0.538097\pi$
$947$	−31.9714	−	18.4587i	−1.03893	−	0.599827i	−0.919530	+	0.393019i	$0.871431\pi$
$948$	21.9970	−	24.0145i	0.714430	−	0.779954i
$949$	9.53062	−	14.2786i	0.309377	−	0.463502i
$950$	−5.70804	−	2.21913i	−0.185193	−	0.0719979i
$951$	−33.1744	+	57.4597i	−1.07575	+	1.86326i
$952$	−1.49226	+	22.8651i	−0.0483646	+	0.741061i
$953$	4.08785	+	7.08037i	0.132419	+	0.229356i	0.924608	−	0.380919i	$-0.124392\pi$
$953$	4.08785	+	7.08037i	0.132419	+	0.229356i	−0.792190	+	0.610275i	$0.791059\pi$
$954$	19.7328	+	7.67157i	0.638874	+	0.248376i
$955$	−0.259840	+	0.150019i	−0.00840823	+	0.00485449i
$956$	−8.42965	+	38.0571i	−0.272634	+	1.23086i
$957$			22.8088i			0.737304i
$958$	−1.04109	+	0.160338i	−0.0336362	+	0.00518030i
$959$	−10.4312	+	18.0674i	−0.336842	+	0.583427i
$960$	6.19947	+	14.9433i	0.200087	+	0.482293i
$961$	−22.4934			−0.725593
$962$	10.2321	+	4.76411i	0.329896	+	0.153601i
$963$		−	19.5802i		−	0.630962i
$964$	2.18358	−	0.688925i	0.0703283	−	0.0221888i
$965$	14.7977	+	8.54347i	0.476356	+	0.275024i
$966$	4.07472	+	26.4575i	0.131102	+	0.851257i
$967$	−38.5017			−1.23813			−0.619066	−	0.785339i	$-0.712489\pi$
$967$	−38.5017			−1.23813			−0.619066	+	0.785339i	$0.712489\pi$
$968$	−21.0370	−	14.0480i	−0.676154	−	0.451519i
$969$	−12.0099	−	20.8017i	−0.385813	−	0.668248i
$970$	21.8590	+	8.49818i	0.701851	+	0.272860i
$971$	44.6075	−	25.7541i	1.43152	−	0.826489i	0.434285	−	0.900776i	$-0.357001\pi$
$971$	44.6075	−	25.7541i	1.43152	−	0.826489i	0.997237	+	0.0742863i	$0.0236679\pi$
$972$	−6.51121	−	20.6376i	−0.208847	−	0.661951i
$973$	−0.840381	−	0.485194i	−0.0269414	−	0.0155546i
$974$	−11.6532	+	29.9744i	−0.373393	+	0.960442i
$975$	6.53793	−	3.22809i	0.209381	−	0.103382i
$976$	43.6365	−	3.83402i	1.39677	−	0.122724i
$977$	28.9684	−	50.1748i	0.926782	−	1.60523i	0.138112	−	0.990417i	$-0.455897\pi$
$977$	28.9684	−	50.1748i	0.926782	−	1.60523i	0.788670	−	0.614817i	$-0.210770\pi$
$978$	21.1587	+	26.3581i	0.676579	+	0.842840i
$979$	20.5714	−	11.8769i	0.657464	−	0.379587i
$980$	−2.32909	+	2.54271i	−0.0744002	+	0.0812238i
$981$	17.9341	−	10.3543i	0.572593	−	0.330587i
$982$	−5.63077	−	36.5612i	−0.179685	−	1.16671i
$983$	−21.2236			−0.676927			−0.338464	−	0.940979i	$-0.609907\pi$
$983$	−21.2236			−0.676927			−0.338464	+	0.940979i	$0.609907\pi$
$984$	4.64025	−	6.94881i	0.147926	−	0.221520i
$985$	−4.64295	+	8.04183i	−0.147937	+	0.256234i
$986$	−23.7907	+	19.0977i	−0.757650	+	0.608194i
$987$		−	34.6322i		−	1.10236i
$988$	−29.9859	−	8.71829i	−0.953978	−	0.277366i
$989$			23.5230i			0.747987i
$990$	1.38332	+	1.72325i	0.0439647	+	0.0547685i
$991$	7.31173	−	12.6643i	0.232265	−	0.402294i	−0.726210	−	0.687473i	$-0.758720\pi$
$991$	7.31173	−	12.6643i	0.232265	−	0.402294i	0.958474	+	0.285179i	$0.0920531\pi$
$992$	−3.92898	−	16.0242i	−0.124745	−	0.508769i
$993$	47.3849			1.50372
$994$	−12.4042	+	1.91037i	−0.393437	+	0.0605931i
$995$	0.931479	−	0.537790i	0.0295299	−	0.0170491i
$996$	−26.5169	−	24.2892i	−0.840220	−	0.769633i
$997$	46.8148	−	27.0285i	1.48264	−	0.856002i	0.482833	−	0.875712i	$-0.339608\pi$
$997$	46.8148	−	27.0285i	1.48264	−	0.856002i	0.999806	+	0.0197105i	$0.00627444\pi$
$998$	26.4585	−	21.2392i	0.837528	−	0.672315i
$999$	4.27578	−	7.40587i	0.135280	−	0.234311i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	520.2.by.c.61.17	✓	104
8.5	even	2	inner	520.2.by.c.61.50	yes	104
13.3	even	3	inner	520.2.by.c.341.50	yes	104
104.29	even	6	inner	520.2.by.c.341.17	yes	104

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
520.2.by.c.61.17	✓	104	1.1	even	1	trivial
520.2.by.c.61.50	yes	104	8.5	even	2	inner
520.2.by.c.341.17	yes	104	104.29	even	6	inner
520.2.by.c.341.50	yes	104	13.3	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 520 = 2^{3} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	520.by (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.885292 - 1.10284i) q^{2} +(-1.75135 - 1.01114i) q^{3} +(-0.432517 + 1.95267i) q^{4} -1.00000i q^{5} +(0.435326 + 2.82661i) q^{6} +(-1.47683 - 2.55794i) q^{7} +(2.53639 - 1.25169i) q^{8} +(0.544814 + 0.943646i) q^{9} +O(q^{10})\)	\(q+(-0.885292 - 1.10284i) q^{2} +(-1.75135 - 1.01114i) q^{3} +(-0.432517 + 1.95267i) q^{4} -1.00000i q^{5} +(0.435326 + 2.82661i) q^{6} +(-1.47683 - 2.55794i) q^{7} +(2.53639 - 1.25169i) q^{8} +(0.544814 + 0.943646i) q^{9} +(-1.10284 + 0.885292i) q^{10} +(-1.24190 - 0.717013i) q^{11} +(2.73192 - 2.98247i) q^{12} +(2.00168 - 2.99888i) q^{13} +(-1.51358 + 3.89323i) q^{14} +(-1.01114 + 1.75135i) q^{15} +(-3.62586 - 1.68913i) q^{16} +(-1.37139 - 2.37531i) q^{17} +(0.558372 - 1.43625i) q^{18} +(-3.75031 + 2.16524i) q^{19} +(1.95267 + 0.432517i) q^{20} +5.97313i q^{21} +(0.308695 + 2.00439i) q^{22} +(-1.58450 + 2.74444i) q^{23} +(-5.70774 - 0.372509i) q^{24} -1.00000 q^{25} +(-5.07936 + 0.447342i) q^{26} +3.86331i q^{27} +(5.63358 - 1.77741i) q^{28} +(6.81137 + 3.93255i) q^{29} +(2.82661 - 0.435326i) q^{30} -2.91661 q^{31} +(1.34710 + 5.49412i) q^{32} +(1.45000 + 2.51148i) q^{33} +(-1.40551 + 3.61527i) q^{34} +(-2.55794 + 1.47683i) q^{35} +(-2.07827 + 0.655701i) q^{36} +(-1.91697 - 1.10676i) q^{37} +(5.70804 + 2.21913i) q^{38} +(-6.53793 + 3.22809i) q^{39} +(-1.25169 - 2.53639i) q^{40} +(-0.730409 + 1.26511i) q^{41} +(6.58742 - 5.28797i) q^{42} +(6.42836 - 3.71142i) q^{43} +(1.93723 - 2.11491i) q^{44} +(0.943646 - 0.544814i) q^{45} +(4.42942 - 0.682174i) q^{46} -5.79800 q^{47} +(4.64219 + 6.62451i) q^{48} +(-0.862049 + 1.49311i) q^{49} +(0.885292 + 1.10284i) q^{50} +5.54667i q^{51} +(4.99006 + 5.20570i) q^{52} +13.7392i q^{53} +(4.26062 - 3.42016i) q^{54} +(-0.717013 + 1.24190i) q^{55} +(-6.94756 - 4.63942i) q^{56} +8.75747 q^{57} +(-1.69308 - 10.9933i) q^{58} +(-0.541074 + 0.312389i) q^{59} +(-2.98247 - 2.73192i) q^{60} +(-9.48398 + 5.47558i) q^{61} +(2.58205 + 3.21656i) q^{62} +(1.60919 - 2.78721i) q^{63} +(4.86656 - 6.34954i) q^{64} +(-2.99888 - 2.00168i) q^{65} +(1.48609 - 3.82251i) q^{66} +(-6.36790 - 3.67651i) q^{67} +(5.23136 - 1.65051i) q^{68} +(5.55002 - 3.20431i) q^{69} +(3.89323 + 1.51358i) q^{70} +(1.50229 + 2.60204i) q^{71} +(2.56301 + 1.71152i) q^{72} +4.76130 q^{73} +(0.476495 + 3.09393i) q^{74} +(1.75135 + 1.01114i) q^{75} +(-2.60594 - 8.25963i) q^{76} +4.23562i q^{77} +(9.34805 + 4.35250i) q^{78} +8.05187 q^{79} +(-1.68913 + 3.62586i) q^{80} +(5.54080 - 9.59694i) q^{81} +(2.04184 - 0.314463i) q^{82} -8.89091i q^{83} +(-11.6636 - 2.58348i) q^{84} +(-2.37531 + 1.37139i) q^{85} +(-9.78408 - 3.80377i) q^{86} +(-7.95272 - 13.7745i) q^{87} +(-4.04743 - 0.264151i) q^{88} +(-8.28220 + 14.3452i) q^{89} +(-1.43625 - 0.558372i) q^{90} +(-10.6271 - 0.691365i) q^{91} +(-4.67366 - 4.28102i) q^{92} +(5.10800 + 2.94911i) q^{93} +(5.13292 + 6.39428i) q^{94} +(2.16524 + 3.75031i) q^{95} +(3.19608 - 10.9842i) q^{96} +(-8.29183 - 14.3619i) q^{97} +(2.40983 - 0.371137i) q^{98} -1.56255i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 104 q + 2 q^{6} - 4 q^{7} + 12 q^{8} + 60 q^{9}+O(q^{10}) \) 104 * q + 2 * q^6 - 4 * q^7 + 12 * q^8 + 60 * q^9	\( 104 q + 2 q^{6} - 4 q^{7} + 12 q^{8} + 60 q^{9} - 28 q^{12} - 24 q^{14} + 4 q^{15} - 20 q^{16} + 4 q^{17} - 40 q^{18} - 4 q^{20} + 24 q^{22} + 32 q^{23} + 24 q^{24} - 104 q^{25} - 10 q^{26} + 22 q^{28} - 12 q^{30} - 40 q^{31} + 30 q^{32} + 12 q^{33} - 4 q^{34} + 18 q^{36} + 56 q^{39} - 16 q^{41} - 20 q^{42} - 32 q^{44} - 30 q^{46} - 56 q^{47} - 24 q^{48} - 80 q^{49} - 6 q^{52} - 10 q^{54} + 16 q^{55} - 38 q^{56} + 104 q^{57} - 68 q^{58} - 12 q^{62} + 12 q^{63} - 108 q^{64} + 180 q^{66} - 6 q^{68} + 8 q^{70} - 72 q^{71} - 80 q^{72} + 24 q^{73} + 40 q^{74} - 20 q^{76} - 52 q^{78} - 40 q^{79} - 24 q^{80} - 60 q^{81} + 64 q^{82} - 70 q^{84} + 140 q^{86} - 8 q^{87} + 86 q^{88} + 36 q^{89} - 20 q^{90} + 76 q^{92} + 46 q^{94} - 32 q^{95} + 12 q^{96} + 12 q^{97} - 8 q^{98}+O(q^{100}) \) 104 * q + 2 * q^6 - 4 * q^7 + 12 * q^8 + 60 * q^9 - 28 * q^12 - 24 * q^14 + 4 * q^15 - 20 * q^16 + 4 * q^17 - 40 * q^18 - 4 * q^20 + 24 * q^22 + 32 * q^23 + 24 * q^24 - 104 * q^25 - 10 * q^26 + 22 * q^28 - 12 * q^30 - 40 * q^31 + 30 * q^32 + 12 * q^33 - 4 * q^34 + 18 * q^36 + 56 * q^39 - 16 * q^41 - 20 * q^42 - 32 * q^44 - 30 * q^46 - 56 * q^47 - 24 * q^48 - 80 * q^49 - 6 * q^52 - 10 * q^54 + 16 * q^55 - 38 * q^56 + 104 * q^57 - 68 * q^58 - 12 * q^62 + 12 * q^63 - 108 * q^64 + 180 * q^66 - 6 * q^68 + 8 * q^70 - 72 * q^71 - 80 * q^72 + 24 * q^73 + 40 * q^74 - 20 * q^76 - 52 * q^78 - 40 * q^79 - 24 * q^80 - 60 * q^81 + 64 * q^82 - 70 * q^84 + 140 * q^86 - 8 * q^87 + 86 * q^88 + 36 * q^89 - 20 * q^90 + 76 * q^92 + 46 * q^94 - 32 * q^95 + 12 * q^96 + 12 * q^97 - 8 * q^98

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