LMFDB - Embedded newform 861.2.bw.a.824.92

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [861,2,Mod(236,861)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(861, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([15, 25, 21]))

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

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

chi := DirichletCharacter("861.236");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 861 = 3 \cdot 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	861.bw (of order $30$, degree $8$, 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:	$6.87511961403$
Analytic rank:	$0$
Dimension:	$864$
Relative dimension:	$108$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			824.92
Character	$\chi$	$=$	861.824
Dual form			861.2.bw.a.605.92

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.10072 - 0.220794i) q^{2} +(1.39356 - 1.02858i) q^{3} +(2.40798 - 0.511831i) q^{4} +(-1.58817 - 1.76385i) q^{5} +(2.70038 - 2.46846i) q^{6} +(-0.338439 - 2.62402i) q^{7} +(0.927655 - 0.301413i) q^{8} +(0.884034 - 2.86679i) q^{9} +O(q^{10})$	\(q+(2.10072 - 0.220794i) q^{2} +(1.39356 - 1.02858i) q^{3} +(2.40798 - 0.511831i) q^{4} +(-1.58817 - 1.76385i) q^{5} +(2.70038 - 2.46846i) q^{6} +(-0.338439 - 2.62402i) q^{7} +(0.927655 - 0.301413i) q^{8} +(0.884034 - 2.86679i) q^{9} +(-3.72575 - 3.35468i) q^{10} +(-2.61402 + 2.90317i) q^{11} +(2.82920 - 3.19007i) q^{12} +(2.12311 - 1.54253i) q^{13} +(-1.29033 - 5.43759i) q^{14} +(-4.02748 - 0.824461i) q^{15} +(-2.61569 + 1.16458i) q^{16} +(3.84529 + 3.46231i) q^{17} +(1.22413 - 6.21751i) q^{18} +(0.472784 - 0.210497i) q^{19} +(-4.72707 - 3.43442i) q^{20} +(-3.17065 - 3.30862i) q^{21} +(-4.85032 + 6.67590i) q^{22} +(6.67084 - 0.701133i) q^{23} +(0.982717 - 1.37421i) q^{24} +(-0.0662131 + 0.629975i) q^{25} +(4.11947 - 3.70919i) q^{26} +(-1.71678 - 4.90435i) q^{27} +(-2.15801 - 6.14534i) q^{28} +(0.169272 - 0.520964i) q^{29} +(-8.64264 - 0.842715i) q^{30} +(-1.44495 - 1.30104i) q^{31} +(-6.92712 + 3.99938i) q^{32} +(-0.656657 + 6.73448i) q^{33} +(8.84233 + 6.42433i) q^{34} +(-4.09086 + 4.76435i) q^{35} +(0.661419 - 7.35564i) q^{36} +(1.48113 + 1.64496i) q^{37} +(0.946711 - 0.546584i) q^{38} +(1.37207 - 4.33340i) q^{39} +(-2.00492 - 1.15754i) q^{40} +(5.76396 + 2.78869i) q^{41} +(-7.39118 - 6.25041i) q^{42} +(-6.12990 + 4.45363i) q^{43} +(-4.80857 + 8.32869i) q^{44} +(-6.46057 + 2.99366i) q^{45} +(13.8588 - 2.94577i) q^{46} +(10.5659 - 1.11052i) q^{47} +(-2.44726 + 4.31336i) q^{48} +(-6.77092 + 1.77614i) q^{49} +1.33802i q^{50} +(8.91992 + 0.869751i) q^{51} +(4.32288 - 4.80104i) q^{52} +(4.29602 - 0.913146i) q^{53} +(-4.68932 - 9.92361i) q^{54} +9.27226 q^{55} +(-1.10487 - 2.33217i) q^{56} +(0.442341 - 0.779639i) q^{57} +(0.240566 - 1.13177i) q^{58} +(-3.13256 - 1.39471i) q^{59} +(-10.1201 + 0.0761087i) q^{60} +(5.57771 + 12.5277i) q^{61} +(-3.32270 - 2.41408i) q^{62} +(-7.82169 - 1.34948i) q^{63} +(-9.03610 + 6.56511i) q^{64} +(-6.09265 - 1.29503i) q^{65} +(0.107486 + 14.2922i) q^{66} +(-2.86747 - 13.4904i) q^{67} +(11.0315 + 6.36903i) q^{68} +(8.57506 - 7.83859i) q^{69} +(-7.54180 + 10.9118i) q^{70} +(4.75666 + 14.6395i) q^{71} +(-0.0440107 - 2.92585i) q^{72} +(3.33086 - 1.92307i) q^{73} +(3.47464 + 3.12858i) q^{74} +(0.555710 + 0.946016i) q^{75} +(1.03071 - 0.748858i) q^{76} +(8.50264 + 5.87669i) q^{77} +(1.92553 - 9.40621i) q^{78} +(-11.1101 - 6.41445i) q^{79} +(6.20830 + 2.76411i) q^{80} +(-7.43697 - 5.06868i) q^{81} +(12.7242 + 4.58560i) q^{82} +11.8609 q^{83} +(-9.32831 - 6.34423i) q^{84} -12.2812i q^{85} +(-11.8939 + 10.7093i) q^{86} +(-0.299965 - 0.900107i) q^{87} +(-1.54986 + 3.48104i) q^{88} +(1.28077 + 2.87665i) q^{89} +(-12.9109 + 7.71530i) q^{90} +(-4.76616 - 5.04902i) q^{91} +(15.7044 - 5.10265i) q^{92} +(-3.35186 - 0.326828i) q^{93} +(21.9508 - 4.66578i) q^{94} +(-1.12215 - 0.499613i) q^{95} +(-5.53969 + 12.6985i) q^{96} +(-1.18877 + 3.65867i) q^{97} +(-13.8316 + 5.22615i) q^{98} +(6.01188 + 10.0604i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 864 q - 110 q^{4} - 20 q^{7} - 12 q^{9}+O(q^{10}) $ 864 * q - 110 * q^4 - 20 * q^7 - 12 * q^9	$ 864 q - 110 q^{4} - 20 q^{7} - 12 q^{9} - 18 q^{10} - 15 q^{12} - 50 q^{15} + 82 q^{16} - 15 q^{18} - 30 q^{19} - 14 q^{21} + 30 q^{24} + 78 q^{25} + 15 q^{30} - 18 q^{31} + 36 q^{33} + 16 q^{36} - 10 q^{37} - 2 q^{39} - 144 q^{40} - 24 q^{42} - 8 q^{43} + 69 q^{45} - 12 q^{46} + 52 q^{49} - 18 q^{51} - 30 q^{52} + 15 q^{54} - 38 q^{57} - 10 q^{58} - 126 q^{61} + 65 q^{63} - 16 q^{64} - 70 q^{67} - 260 q^{70} - 33 q^{72} - 48 q^{73} + 60 q^{75} - 2 q^{78} + 68 q^{81} - 150 q^{82} + 115 q^{84} - 138 q^{87} + 30 q^{88} + 64 q^{91} - 15 q^{93} + 60 q^{94} - 30 q^{99}+O(q^{100}) $ 864 * q - 110 * q^4 - 20 * q^7 - 12 * q^9 - 18 * q^10 - 15 * q^12 - 50 * q^15 + 82 * q^16 - 15 * q^18 - 30 * q^19 - 14 * q^21 + 30 * q^24 + 78 * q^25 + 15 * q^30 - 18 * q^31 + 36 * q^33 + 16 * q^36 - 10 * q^37 - 2 * q^39 - 144 * q^40 - 24 * q^42 - 8 * q^43 + 69 * q^45 - 12 * q^46 + 52 * q^49 - 18 * q^51 - 30 * q^52 + 15 * q^54 - 38 * q^57 - 10 * q^58 - 126 * q^61 + 65 * q^63 - 16 * q^64 - 70 * q^67 - 260 * q^70 - 33 * q^72 - 48 * q^73 + 60 * q^75 - 2 * q^78 + 68 * q^81 - 150 * q^82 + 115 * q^84 - 138 * q^87 + 30 * q^88 + 64 * q^91 - 15 * q^93 + 60 * q^94 - 30 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/861\mathbb{Z}\right)^\times$.

$n$	$211$	$493$	$575$
$\chi(n)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{5}{6}\right)$	$-1$

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 $

$2$	2.10072	−	0.220794i	1.48543	−	0.156125i	0.673201	−	0.739460i	$-0.264919\pi$
$2$	2.10072	−	0.220794i	1.48543	−	0.156125i	0.812232	+	0.583335i	$0.198252\pi$
$3$	1.39356	−	1.02858i	0.804574	−	0.593853i
$3$	1.39356	−	1.02858i	0.804574	−	0.593853i
$4$	2.40798	−	0.511831i	1.20399	−	0.255915i
$5$	−1.58817	−	1.76385i	−0.710253	−	0.788816i	0.274720	−	0.961524i	$-0.411415\pi$
$5$	−1.58817	−	1.76385i	−0.710253	−	0.788816i	−0.984973	+	0.172709i	$0.944748\pi$
$6$	2.70038	−	2.46846i	1.10242	−	1.00774i
$7$	−0.338439	−	2.62402i	−0.127918	−	0.991785i
$7$	−0.338439	−	2.62402i	−0.127918	−	0.991785i
$8$	0.927655	−	0.301413i	0.327976	−	0.106566i
$9$	0.884034	−	2.86679i	0.294678	−	0.955597i
$10$	−3.72575	−	3.35468i	−1.17819	−	1.06084i
$11$	−2.61402	+	2.90317i	−0.788158	+	0.875338i	−0.994670	−	0.103106i	$-0.967122\pi$
$11$	−2.61402	+	2.90317i	−0.788158	+	0.875338i	0.206513	+	0.978444i	$0.433788\pi$
$12$	2.82920	−	3.19007i	0.816721	−	0.920894i
$13$	2.12311	−	1.54253i	0.588844	−	0.427821i	−0.253057	−	0.967451i	$-0.581436\pi$
$13$	2.12311	−	1.54253i	0.588844	−	0.427821i	0.841902	+	0.539631i	$0.181436\pi$
$14$	−1.29033	−	5.43759i	−0.344856	−	1.45326i
$15$	−4.02748	−	0.824461i	−1.03989	−	0.212875i
$16$	−2.61569	+	1.16458i	−0.653922	+	0.291145i
$17$	3.84529	+	3.46231i	0.932619	+	0.839734i	0.987316	−	0.158769i	$-0.0507525\pi$
$17$	3.84529	+	3.46231i	0.932619	+	0.839734i	−0.0546967	+	0.998503i	$0.517419\pi$
$18$	1.22413	−	6.21751i	0.288531	−	1.46548i
$19$	0.472784	−	0.210497i	0.108464	−	0.0482914i	−0.351787	−	0.936080i	$-0.614426\pi$
$19$	0.472784	−	0.210497i	0.108464	−	0.0482914i	0.460251	+	0.887789i	$0.347759\pi$
$20$	−4.72707	−	3.43442i	−1.05701	−	0.767960i
$21$	−3.17065	−	3.30862i	−0.691893	−	0.722000i
$22$	−4.85032	+	6.67590i	−1.03409	+	1.42331i
$23$	6.67084	−	0.701133i	1.39097	−	0.146196i	0.620765	−	0.783997i	$-0.286822\pi$
$23$	6.67084	−	0.701133i	1.39097	−	0.146196i	0.770201	+	0.637801i	$0.220156\pi$
$24$	0.982717	−	1.37421i	0.200596	−	0.280509i
$25$	−0.0662131	+	0.629975i	−0.0132426	+	0.125995i
$26$	4.11947	−	3.70919i	0.807895	−	0.727432i
$27$	−1.71678	−	4.90435i	−0.330394	−	0.943843i
$28$	−2.15801	−	6.14534i	−0.407825	−	1.16136i
$29$	0.169272	−	0.520964i	0.0314330	−	0.0967407i	−0.934109	−	0.356987i	$-0.883804\pi$
$29$	0.169272	−	0.520964i	0.0314330	−	0.0967407i	0.965542	+	0.260247i	$0.0838039\pi$
$30$	−8.64264	−	0.842715i	−1.57792	−	0.153858i
$31$	−1.44495	−	1.30104i	−0.259521	−	0.233674i	0.529091	−	0.848565i	$-0.322533\pi$
$31$	−1.44495	−	1.30104i	−0.259521	−	0.233674i	−0.788612	+	0.614892i	$0.789200\pi$
$32$	−6.92712	+	3.99938i	−1.22455	+	0.706997i
$33$	−0.656657	+	6.73448i	−0.114309	+	1.17232i
$34$	8.84233	+	6.42433i	1.51645	+	1.10176i
$35$	−4.09086	+	4.76435i	−0.691481	+	0.805322i
$36$	0.661419	−	7.35564i	0.110237	−	1.22594i
$37$	1.48113	+	1.64496i	0.243497	+	0.270431i	0.852488	−	0.522746i	$-0.175092\pi$
$37$	1.48113	+	1.64496i	0.243497	+	0.270431i	−0.608992	+	0.793177i	$0.708426\pi$
$38$	0.946711	−	0.546584i	0.153577	−	0.0886676i
$39$	1.37207	−	4.33340i	0.219706	−	0.693900i
$40$	−2.00492	−	1.15754i	−0.317006	−	0.183024i
$41$	5.76396	+	2.78869i	0.900179	+	0.435520i
$41$	5.76396	+	2.78869i	0.900179	+	0.435520i
$42$	−7.39118	−	6.25041i	−1.14048	−	0.964460i
$43$	−6.12990	+	4.45363i	−0.934801	+	0.679172i	−0.947163	−	0.320751i	$-0.896065\pi$
$43$	−6.12990	+	4.45363i	−0.934801	+	0.679172i	0.0123629	+	0.999924i	$0.496065\pi$
$44$	−4.80857	+	8.32869i	−0.724920	+	1.25560i
$45$	−6.46057	+	2.99366i	−0.963085	+	0.446269i
$46$	13.8588	−	2.94577i	2.04336	−	0.434330i
$47$	10.5659	−	1.11052i	1.54119	−	0.161986i	0.704518	−	0.709686i	$-0.251163\pi$
$47$	10.5659	−	1.11052i	1.54119	−	0.161986i	0.836675	+	0.547700i	$0.184497\pi$
$48$	−2.44726	+	4.31336i	−0.353231	+	0.622581i
$49$	−6.77092	+	1.77614i	−0.967274	+	0.253734i
$50$			1.33802i			0.189225i
$51$	8.91992	+	0.869751i	1.24904	+	0.121790i
$52$	4.32288	−	4.80104i	0.599476	−	0.665785i
$53$	4.29602	−	0.913146i	0.590103	−	0.125430i	0.0968242	−	0.995301i	$-0.469132\pi$
$53$	4.29602	−	0.913146i	0.590103	−	0.125430i	0.493279	+	0.869871i	$0.335798\pi$
$54$	−4.68932	−	9.92361i	−0.638135	−	1.35043i
$55$	9.27226			1.25027
$56$	−1.10487	−	2.33217i	−0.147644	−	0.311650i
$57$	0.442341	−	0.779639i	0.0585895	−	0.103266i
$58$	0.240566	−	1.13177i	0.0315879	−	0.148609i
$59$	−3.13256	−	1.39471i	−0.407825	−	0.181575i	0.192562	−	0.981285i	$-0.438320\pi$
$59$	−3.13256	−	1.39471i	−0.407825	−	0.181575i	−0.600387	+	0.799709i	$0.704987\pi$
$60$	−10.1201	+	0.0761087i	−1.30649	+	0.00982558i
$61$	5.57771	+	12.5277i	0.714153	+	1.60401i	0.794513	+	0.607248i	$0.207726\pi$
$61$	5.57771	+	12.5277i	0.714153	+	1.60401i	−0.0803598	+	0.996766i	$0.525607\pi$
$62$	−3.32270	−	2.41408i	−0.421983	−	0.306589i
$63$	−7.82169	−	1.34948i	−0.985441	−	0.170019i
$64$	−9.03610	+	6.56511i	−1.12951	+	0.820639i
$65$	−6.09265	−	1.29503i	−0.755700	−	0.160629i
$66$	0.107486	+	14.2922i	0.0132306	+	1.75925i
$67$	−2.86747	−	13.4904i	−0.350317	−	1.64811i	−0.702135	−	0.712044i	$-0.747770\pi$
$67$	−2.86747	−	13.4904i	−0.350317	−	1.64811i	0.351818	−	0.936068i	$-0.385564\pi$
$68$	11.0315	+	6.36903i	1.33776	+	0.772358i
$69$	8.57506	−	7.83859i	1.03232	−	0.943655i
$70$	−7.54180	+	10.9118i	−0.901418	+	1.30421i
$71$	4.75666	+	14.6395i	0.564511	+	1.73739i	0.669399	+	0.742903i	$0.266552\pi$
$71$	4.75666	+	14.6395i	0.564511	+	1.73739i	−0.104887	+	0.994484i	$0.533448\pi$
$72$	−0.0440107	−	2.92585i	−0.00518671	−	0.344815i
$73$	3.33086	−	1.92307i	0.389848	−	0.225079i	−0.292246	−	0.956343i	$-0.594403\pi$
$73$	3.33086	−	1.92307i	0.389848	−	0.225079i	0.682094	+	0.731264i	$0.261069\pi$
$74$	3.47464	+	3.12858i	0.403919	+	0.363690i
$75$	0.555710	+	0.946016i	0.0641678	+	0.109236i
$76$	1.03071	−	0.748858i	0.118231	−	0.0858999i
$77$	8.50264	+	5.87669i	0.968966	+	0.669711i
$78$	1.92553	−	9.40621i	0.218024	−	1.06504i
$79$	−11.1101	−	6.41445i	−1.24999	−	0.721682i	−0.278882	−	0.960325i	$-0.589964\pi$
$79$	−11.1101	−	6.41445i	−1.24999	−	0.721682i	−0.971107	+	0.238644i	$0.923297\pi$
$80$	6.20830	+	2.76411i	0.694109	+	0.309037i
$81$	−7.43697	−	5.06868i	−0.826330	−	0.563186i
$82$	12.7242	+	4.58560i	1.40515	+	0.506395i
$83$	11.8609			1.30190			0.650949	−	0.759121i	$-0.274371\pi$
$83$	11.8609			1.30190			0.650949	+	0.759121i	$0.274371\pi$
$84$	−9.32831	−	6.34423i	−1.01780	−	0.692212i
$85$		−	12.2812i		−	1.33209i
$86$	−11.8939	+	10.7093i	−1.28255	+	1.15481i
$87$	−0.299965	−	0.900107i	−0.0321596	−	0.0965016i
$88$	−1.54986	+	3.48104i	−0.165215	+	0.371080i
$89$	1.28077	+	2.87665i	0.135761	+	0.304925i	0.968614	−	0.248570i	$-0.0799606\pi$
$89$	1.28077	+	2.87665i	0.135761	+	0.304925i	−0.832853	+	0.553495i	$0.813294\pi$
$90$	−12.9109	+	7.71530i	−1.36092	+	0.813264i
$91$	−4.76616	−	5.04902i	−0.499630	−	0.529281i
$92$	15.7044	−	5.10265i	1.63729	−	0.531988i
$93$	−3.35186	−	0.326828i	−0.347572	−	0.0338905i
$94$	21.9508	−	4.66578i	2.26405	−	0.481238i
$95$	−1.12215	−	0.499613i	−0.115130	−	0.0512592i
$96$	−5.53969	+	12.6985i	−0.565392	+	1.29604i
$97$	−1.18877	+	3.65867i	−0.120702	+	0.371482i	−0.993094	−	0.117326i	$-0.962568\pi$
$97$	−1.18877	+	3.65867i	−0.120702	+	0.371482i	0.872392	+	0.488807i	$0.162568\pi$
$98$	−13.8316	+	5.22615i	−1.39721	+	0.527921i
$99$	6.01188	+	10.0604i	0.604217	+	1.01110i
$100$	0.163001	+	1.55085i	0.0163001	+	0.155085i
$101$	−11.2744	−	1.18499i	−1.12184	−	0.117911i	−0.474606	−	0.880198i	$-0.657409\pi$
$101$	−11.2744	−	1.18499i	−1.12184	−	0.117911i	−0.647238	+	0.762288i	$0.724076\pi$
$102$	18.9303	−	0.142367i	1.87438	−	0.0140964i
$103$	1.42322	+	3.19660i	0.140234	+	0.314970i	0.969986	−	0.243162i	$-0.0781848\pi$
$103$	1.42322	+	3.19660i	0.140234	+	0.314970i	−0.829752	+	0.558132i	$0.811518\pi$
$104$	1.50457	−	2.07087i	0.147536	−	0.203065i
$105$	−0.800341	+	10.8472i	−0.0781053	+	1.05858i
$106$	8.82310	−	2.86680i	0.856976	−	0.278448i
$107$	−0.858446	−	1.92810i	−0.0829891	−	0.186397i	0.867285	−	0.497813i	$-0.165863\pi$
$107$	−0.858446	−	1.92810i	−0.0829891	−	0.186397i	−0.950274	+	0.311416i	$0.899197\pi$
$108$	−6.64415	−	10.9309i	−0.639334	−	1.05182i
$109$	−8.25874	+	4.76818i	−0.791043	+	0.456709i	−0.840330	−	0.542076i	$-0.817639\pi$
$109$	−8.25874	+	4.76818i	−0.791043	+	0.456709i	0.0492863	+	0.998785i	$0.484305\pi$
$110$	19.4784	−	2.04726i	1.85719	−	0.195199i
$111$	3.75603	+	0.768893i	0.356507	+	0.0729801i
$112$	3.94112	+	6.46946i	0.372401	+	0.611307i
$113$	−8.95115	+	2.90841i	−0.842054	+	0.273600i	−0.698114	−	0.715987i	$-0.745977\pi$
$113$	−8.95115	+	2.90841i	−0.842054	+	0.273600i	−0.143940	+	0.989586i	$0.545977\pi$
$114$	0.757094	−	1.73547i	0.0709083	−	0.162542i
$115$	−11.8311	−	10.6528i	−1.10326	−	0.993379i
$116$	0.140956	−	1.34111i	0.0130874	−	0.124519i
$117$	−2.54521	−	7.45015i	−0.235304	−	0.688767i
$118$	−6.88857	−	2.23823i	−0.634145	−	0.206046i
$119$	7.78377	−	11.2619i	0.713537	−	1.03237i
$120$	−3.98462	+	0.449122i	−0.363744	+	0.0409990i
$121$	−0.445447	−	4.23815i	−0.0404952	−	0.385286i
$122$	14.4833	+	25.0857i	1.31125	+	2.27116i
$123$	10.9008	−	2.04250i	0.982895	−	0.184166i
$124$	−4.14532	−	2.39330i	−0.372261	−	0.214925i
$125$	−8.38462	+	6.09179i	−0.749944	+	0.544866i
$126$	−16.7291	−	1.10790i	−1.49035	−	0.0986997i
$127$	2.14263	−	6.59433i	0.190127	−	0.585152i	−0.809872	−	0.586607i	$-0.800463\pi$
$127$	2.14263	−	6.59433i	0.190127	−	0.585152i	0.999999	+	0.00145529i	$0.000463233\pi$
$128$	−5.64431	+	5.08216i	−0.498891	+	0.449204i
$129$	−3.96147	+	12.5115i	−0.348788	+	1.10158i
$130$	−13.0849	−	1.37528i	−1.14762	−	0.120620i
$131$	−18.2258	−	3.87400i	−1.59239	−	0.338473i	−0.675423	−	0.737431i	$-0.736039\pi$
$131$	−18.2258	−	3.87400i	−1.59239	−	0.338473i	−0.916969	+	0.398958i	$0.869372\pi$
$132$	1.86570	+	16.5526i	0.162389	+	1.44072i
$133$	−0.712357	−	1.16935i	−0.0617692	−	0.101396i
$134$	−9.00235	−	27.7064i	−0.777684	−	2.39347i
$135$	−5.92398	+	10.8171i	−0.509855	+	0.930987i
$136$	4.61069	+	2.05281i	0.395363	+	0.176027i
$137$	9.54682	+	16.5356i	0.815640	+	1.41273i	0.908867	+	0.417085i	$0.136948\pi$
$137$	9.54682	+	16.5356i	0.815640	+	1.41273i	−0.0932274	+	0.995645i	$0.529718\pi$
$138$	16.2831	−	18.3600i	1.38611	−	1.56291i
$139$	−4.53559	+	6.24271i	−0.384704	+	0.529499i	−0.956823	−	0.290671i	$-0.906121\pi$
$139$	−4.53559	+	6.24271i	−0.384704	+	0.529499i	0.572119	+	0.820171i	$0.306121\pi$
$140$	−7.41215	+	13.5663i	−0.626441	+	1.14656i
$141$	13.5820	−	12.4155i	1.14381	−	1.04557i
$142$	13.2247	+	29.7032i	1.10979	+	2.49264i
$143$	−1.07164	+	10.1959i	−0.0896148	+	0.852628i
$144$	1.02625	+	8.52815i	0.0855206	+	0.710679i
$145$	−1.18773	+	0.528813i	−0.0986359	+	0.0439155i
$146$	6.57260	−	4.77528i	0.543952	−	0.395205i
$147$	−7.60879	+	9.43961i	−0.627563	+	0.778566i
$148$	4.40848	+	3.20295i	0.362374	+	0.263280i
$149$	−14.1065	−	15.6668i	−1.15565	−	1.28347i	−0.952573	−	0.304311i	$-0.901574\pi$
$149$	−14.1065	−	15.6668i	−1.15565	−	1.28347i	−0.203073	−	0.979164i	$-0.565093\pi$
$150$	1.37627	+	1.86462i	0.112372	+	0.152245i
$151$	−5.28777	+	11.8765i	−0.430313	+	0.966498i	0.560108	+	0.828419i	$0.310759\pi$
$151$	−5.28777	+	11.8765i	−0.430313	+	0.966498i	−0.990421	+	0.138079i	$0.955907\pi$
$152$	0.375134	−	0.337772i	0.0304274	−	0.0273970i
$153$	13.3251	−	7.96283i	1.07727	−	0.643757i
$154$	19.1592	+	10.4679i	1.54389	+	0.843531i
$155$			4.61495i			0.370682i
$156$	1.08593	−	11.1370i	0.0869440	−	0.891673i
$157$	−0.316654	+	3.01276i	−0.0252718	+	0.240445i	0.974593	+	0.223984i	$0.0719064\pi$
$157$	−0.316654	+	3.01276i	−0.0252718	+	0.240445i	−0.999865	+	0.0164605i	$0.994760\pi$
$158$	−24.7556	−	11.0219i	−1.96945	−	0.876855i
$159$	5.04752	−	5.69134i	0.400294	−	0.451352i
$160$	18.0558	+	5.86667i	1.42743	+	0.463801i
$161$	−4.09746	−	17.2671i	−0.322925	−	1.36084i
$162$	−16.7421	−	9.00583i	−1.31539	−	0.707564i
$163$	6.39416	−	11.0750i	0.500829	−	0.867461i	−0.499171	−	0.866504i	$-0.666362\pi$
$163$	6.39416	−	11.0750i	0.500829	−	0.867461i	1.00000		0.000957403i	$-0.000304751\pi$
$164$	15.3068	+	3.76492i	1.19526	+	0.293991i
$165$	12.9215	−	9.53729i	1.00594	−	0.742477i
$166$	24.9163	−	2.61881i	1.93388	−	0.203259i
$167$		−	5.52225i		−	0.427324i	−0.976908	−	0.213662i	$-0.931461\pi$
$167$		−	5.52225i		−	0.427324i	0.976908	−	0.213662i	$-0.0685392\pi$
$168$	−3.93854	−	2.11358i	−0.303865	−	0.163066i
$169$	−1.88903	+	5.81382i	−0.145310	+	0.447217i
$170$	−2.71163	−	25.7994i	−0.207973	−	1.97873i
$171$	−0.185494	−	1.54146i	−0.0141851	−	0.117878i
$172$	−12.4811	+	13.8617i	−0.951678	+	1.05695i
$173$	6.20539	−	10.7481i	0.471787	−	0.817160i	−0.527692	−	0.849436i	$-0.676942\pi$
$173$	6.20539	−	10.7481i	0.471787	−	0.817160i	0.999479	+	0.0322763i	$0.0102756\pi$
$174$	−0.828880	−	1.82464i	−0.0628372	−	0.138326i
$175$	1.67547	−	0.0394641i	0.126654	−	0.00298320i
$176$	3.45650	−	10.6380i	0.260543	−	0.801870i
$177$	−5.79999	+	1.27849i	−0.435954	+	0.0960971i
$178$	3.32568	+	5.76026i	0.249271	+	0.431749i
$179$	−13.0215	+	2.76781i	−0.973273	+	0.206876i	−0.666992	−	0.745065i	$-0.732418\pi$
$179$	−13.0215	+	2.76781i	−0.973273	+	0.206876i	−0.306282	+	0.951941i	$0.599085\pi$
$180$	−14.0247	+	10.5154i	−1.04534	+	0.783770i
$181$	−4.57906	−	14.0929i	−0.340359	−	1.04752i	−0.964022	−	0.265823i	$-0.914356\pi$
$181$	−4.57906	−	14.0929i	−0.340359	−	1.04752i	0.623663	−	0.781693i	$-0.285644\pi$
$182$	−11.1272	−	9.55423i	−0.824800	−	0.708207i
$183$	20.6587	+	11.7211i	1.52714	+	0.866446i
$184$	5.97691	−	2.66109i	0.440623	−	0.196178i
$185$	0.549167	−	5.22498i	0.0403756	−	0.384148i
$186$	−7.11347	+	0.0534974i	−0.521585	+	0.00392262i
$187$	−20.1033	+	2.11295i	−1.47010	+	0.154514i
$188$	24.8740	−	8.08205i	1.81412	−	0.589444i
$189$	−12.2881	+	6.16467i	−0.893826	+	0.448414i
$190$	−2.46763	−	0.801781i	−0.179021	−	0.0581673i
$191$	−6.35192	+	11.0018i	−0.459609	+	0.796066i	−0.998940	−	0.0460278i	$-0.985344\pi$
$191$	−6.35192	+	11.0018i	−0.459609	+	0.796066i	0.539331	+	0.842094i	$0.318677\pi$
$192$	−5.83961	+	18.4433i	−0.421438	+	1.33103i
$193$	−2.59990	−	12.2315i	−0.187145	−	0.880446i	−0.967058	−	0.254558i	$-0.918070\pi$
$193$	−2.59990	−	12.2315i	−0.187145	−	0.880446i	0.779913	−	0.625888i	$-0.215263\pi$
$194$	−1.68947	+	7.94832i	−0.121297	+	0.570656i
$195$	−9.82253	+	4.46209i	−0.703406	+	0.319537i
$196$	−15.3951	+	7.74246i	−1.09965	+	0.553033i
$197$	12.3769	−	4.02150i	0.881817	−	0.286520i	0.167106	−	0.985939i	$-0.446558\pi$
$197$	12.3769	−	4.02150i	0.881817	−	0.286520i	0.714712	+	0.699419i	$0.246558\pi$
$198$	14.8506	+	19.8066i	1.05538	+	1.40759i
$199$	9.11007	+	4.05606i	0.645796	+	0.287527i	0.703380	−	0.710814i	$-0.251673\pi$
$199$	9.11007	+	4.05606i	0.645796	+	0.287527i	−0.0575845	+	0.998341i	$0.518340\pi$
$200$	0.128460	+	0.604357i	0.00908350	+	0.0427345i
$201$	−17.8720	−	15.8503i	−1.26059	−	1.11799i
$202$	−23.9460			−1.68483
$203$	−1.42431	−	0.267857i	−0.0999668	−	0.0187999i
$204$	21.9241	−	2.47115i	1.53500	−	0.173015i
$205$	−4.23535	−	14.5957i	−0.295809	−	1.01940i
$206$	3.69557	+	6.40091i	0.257483	+	0.445973i
$207$	3.88724	−	19.7437i	0.270182	−	1.37228i
$208$	−3.75699	+	6.50730i	−0.260500	+	0.451200i
$209$	−0.624761	+	1.92282i	−0.0432156	+	0.133004i
$210$	0.713711	+	22.9636i	0.0492507	+	1.58464i
$211$	2.53552	+	3.48984i	0.174552	+	0.240251i	0.887325	−	0.461144i	$-0.152561\pi$
$211$	2.53552	+	3.48984i	0.174552	+	0.240251i	−0.712773	+	0.701395i	$0.752561\pi$
$212$	9.87732	−	4.39767i	0.678377	−	0.302033i
$213$	21.6866	+	15.5084i	1.48594	+	1.06262i
$214$	−2.22907	−	3.86086i	−0.152376	−	0.263923i
$215$	17.5909	+	3.73905i	1.19969	+	0.255001i
$216$	−3.07081	−	4.03209i	−0.208942	−	0.274349i
$217$	−2.92492	+	4.23190i	−0.198557	+	0.287280i
$218$	−16.2965	+	11.8401i	−1.10374	+	0.801913i
$219$	2.66372	−	6.10599i	0.179998	−	0.412605i
$220$	22.3274	−	4.74583i	1.50531	−	0.319964i
$221$	13.5047	+	1.41940i	0.908423	+	0.0954791i
$222$	8.06014	+	0.785917i	0.540961	+	0.0527473i
$223$	3.98503	+	5.48492i	0.266857	+	0.367298i	0.921326	−	0.388792i	$-0.127107\pi$
$223$	3.98503	+	5.48492i	0.266857	+	0.367298i	−0.654468	+	0.756089i	$0.727107\pi$
$224$	12.8388	+	16.8233i	0.857831	+	1.12406i
$225$	1.74747	+	0.746738i	0.116498	+	0.0497825i
$226$	−18.1617	+	8.08611i	−1.20810	+	0.537880i
$227$	3.35178	+	0.352286i	0.222465	+	0.0233820i	0.215105	−	0.976591i	$-0.430991\pi$
$227$	3.35178	+	0.352286i	0.222465	+	0.0233820i	0.00735999	+	0.999973i	$0.497657\pi$
$228$	0.666102	−	2.10376i	0.0441137	−	0.139325i
$229$	23.7354	+	5.04512i	1.56848	+	0.333391i	0.908498	−	0.417890i	$-0.137230\pi$
$229$	23.7354	+	5.04512i	1.56848	+	0.333391i	0.659982	+	0.751281i	$0.270564\pi$
$230$	−27.2060	−	19.7663i	−1.79391	−	1.30335i
$231$	17.8936	−	0.556135i	1.17731	−	0.0365910i
$232$		−	0.534296i		−	0.0350783i
$233$	−0.991837	−	9.43670i	−0.0649774	−	0.618219i	−0.977753	−	0.209758i	$-0.932732\pi$
$233$	−0.991837	−	9.43670i	−0.0649774	−	0.618219i	0.912776	−	0.408461i	$-0.133934\pi$
$234$	−6.99172	−	15.0887i	−0.457063	−	0.986380i
$235$	−18.7392	−	16.8729i	−1.22241	−	1.10067i
$236$	−8.25698	−	1.75508i	−0.537484	−	0.114246i
$237$	−22.0805	+	2.48878i	−1.43428	+	0.161663i
$238$	13.8649	−	25.3767i	0.898731	−	1.64492i
$239$	18.6848	+	13.5753i	1.20862	+	0.878112i	0.995104	−	0.0988284i	$-0.0315095\pi$
$239$	18.6848	+	13.5753i	1.20862	+	0.878112i	0.213513	+	0.976940i	$0.431509\pi$
$240$	11.4948	−	2.53379i	0.741985	−	0.163555i
$241$	−2.75216	−	12.9479i	−0.177282	−	0.834048i	−0.973437	−	0.228955i	$-0.926469\pi$
$241$	−2.75216	−	12.9479i	−0.177282	−	0.834048i	0.796155	−	0.605093i	$-0.206864\pi$
$242$	−1.87152	−	8.80480i	−0.120306	−	0.565994i
$243$	−15.5774	+	0.586022i	−0.999293	+	0.0375933i
$244$	19.8431	+	27.3117i	1.27032	+	1.74845i
$245$	13.8862	+	9.12204i	0.887158	+	0.582785i
$246$	22.4486	−	6.69755i	1.43127	−	0.427020i
$247$	0.679075	−	1.17619i	0.0432085	−	0.0748393i
$248$	−1.73257	−	0.771389i	−0.110018	−	0.0489832i
$249$	16.5289	−	12.1999i	1.04747	−	0.773136i
$250$	−16.2687	+	14.6484i	−1.02892	+	0.926447i
$251$	−6.88059	+	21.1763i	−0.434299	+	1.33663i	0.459504	+	0.888175i	$0.348027\pi$
$251$	−6.88059	+	21.1763i	−0.434299	+	1.33663i	−0.893803	+	0.448459i	$0.851973\pi$
$252$	−19.5252	+	0.753859i	−1.22997	+	0.0474887i
$253$	−15.4022	+	21.1993i	−0.968329	+	1.33279i
$254$	3.04507	−	14.3259i	0.191064	−	0.898888i
$255$	−12.6323	−	17.1147i	−0.791064	−	1.07176i
$256$	4.21236	−	4.67830i	0.263272	−	0.292394i
$257$	−0.0212842	+	0.100134i	−0.00132767	+	0.00624621i	−0.978806	−	0.204788i	$-0.934350\pi$
$257$	−0.0212842	+	0.100134i	−0.00132767	+	0.00624621i	0.977479	+	0.211034i	$0.0676830\pi$
$258$	−5.55945	+	27.1579i	−0.346116	+	1.69077i
$259$	3.81514	−	4.44324i	0.237061	−	0.276089i
$260$	−15.3338			−0.950961
$261$	−1.34385	−	0.945816i	−0.0831825	−	0.0585446i
$262$	−39.1426	−	4.11405i	−2.41824	−	0.254167i
$263$	−8.99637	+	9.99148i	−0.554740	+	0.616101i	−0.953661	−	0.300884i	$-0.902718\pi$
$263$	−8.99637	+	9.99148i	−0.554740	+	0.616101i	0.398921	+	0.916985i	$0.369385\pi$
$264$	1.42071	+	6.44520i	0.0874389	+	0.396675i
$265$	−8.43347	−	6.12727i	−0.518064	−	0.376395i
$266$	−1.75465	−	2.29920i	−0.107584	−	0.140973i
$267$	4.74371	+	2.69142i	0.290310	+	0.164712i
$268$	−13.8096	−	31.0168i	−0.843555	−	1.89466i
$269$	1.40622	+	0.626087i	0.0857384	+	0.0381732i	0.449158	−	0.893452i	$-0.351724\pi$
$269$	1.40622	+	0.626087i	0.0857384	+	0.0381732i	−0.363419	+	0.931626i	$0.618391\pi$
$270$	−10.0563	+	24.0317i	−0.612005	+	1.46252i
$271$	−5.85147	−	13.1426i	−0.355451	−	0.798357i	−0.999445	−	0.0333255i	$-0.989390\pi$
$271$	−5.85147	−	13.1426i	−0.355451	−	0.798357i	0.643993	−	0.765031i	$-0.277276\pi$
$272$	−14.0902	−	4.57818i	−0.854344	−	0.277593i
$273$	−11.8353	−	2.13373i	−0.716304	−	0.129139i
$274$	23.7062	+	32.6287i	1.43214	+	1.97117i
$275$	−1.65584	−	1.83900i	−0.0998509	−	0.110896i
$276$	16.6365	−	23.2641i	1.00140	−	1.40033i
$277$	−2.14379	+	2.38092i	−0.128808	+	0.143055i	−0.804098	−	0.594496i	$-0.797351\pi$
$277$	−2.14379	+	2.38092i	−0.128808	+	0.143055i	0.675291	+	0.737552i	$0.264018\pi$
$278$	−8.14965	+	14.1156i	−0.488783	+	0.846598i
$279$	−5.00719	+	2.99221i	−0.299773	+	0.179139i
$280$	−2.35887	+	5.65271i	−0.140969	+	0.337814i
$281$	−20.4884	+	14.8857i	−1.22224	+	0.888007i	−0.996284	−	0.0861312i	$-0.972550\pi$
$281$	−20.4884	+	14.8857i	−1.22224	+	0.888007i	−0.225953	+	0.974138i	$0.572550\pi$
$282$	25.7906	−	29.0802i	1.53581	−	1.73170i
$283$	−3.32779	−	15.6560i	−0.197817	−	0.930654i	−0.959282	−	0.282449i	$-0.908853\pi$
$283$	−3.32779	−	15.6560i	−0.197817	−	0.930654i	0.761466	−	0.648205i	$-0.224480\pi$
$284$	18.9469	+	32.8169i	1.12429	+	1.94733i
$285$	−2.07768	+	0.457981i	−0.123071	+	0.0271285i
$286$			21.6554i			1.28051i
$287$	5.36682	−	16.0685i	0.316793	−	0.948495i
$288$	5.34156	+	23.3942i	0.314755	+	1.37852i
$289$	1.02164	+	9.72030i	0.0600967	+	0.571782i
$290$	−2.37834	+	1.37313i	−0.139661	+	0.0806331i
$291$	2.10662	+	6.32134i	0.123492	+	0.370564i
$292$	7.03635	−	6.33555i	0.411771	−	0.370760i
$293$	6.94504	+	9.55902i	0.405733	+	0.558444i	0.962171	−	0.272445i	$-0.0878323\pi$
$293$	6.94504	+	9.55902i	0.405733	+	0.558444i	−0.556438	+	0.830889i	$0.687832\pi$
$294$	−13.8997	+	21.5100i	−0.810648	+	1.25449i
$295$	2.51500	+	7.74039i	0.146429	+	0.450663i
$296$	1.86980	+	1.07953i	0.108680	+	0.0627462i
$297$	18.7258	+	7.83601i	1.08658	+	0.454691i
$298$	−33.0928	−	29.7969i	−1.91702	−	1.72609i
$299$	13.0814	−	11.7785i	0.756517	−	0.681171i
$300$	1.82234	+	1.99355i	0.105213	+	0.115098i
$301$	13.7610	+	14.5777i	0.793171	+	0.840243i
$302$	−8.48585	+	26.1168i	−0.488306	+	1.50285i
$303$	−16.9304	+	9.94530i	−0.972628	+	0.571343i
$304$	−0.991515	+	1.10119i	−0.0568673	+	0.0631575i
$305$	13.2386	−	29.7345i	0.758042	−	1.70259i
$306$	26.2341	−	19.6698i	1.49970	−	1.12445i
$307$	3.34668	−	4.60631i	0.191005	−	0.262896i	−0.702764	−	0.711423i	$-0.748051\pi$
$307$	3.34668	−	4.60631i	0.191005	−	0.262896i	0.893769	+	0.448527i	$0.148051\pi$
$308$	23.4820	+	9.79902i	1.33801	+	0.558351i
$309$	5.27131	+	2.99076i	0.299874	+	0.170139i
$310$	1.01896	+	9.69471i	0.0578728	+	0.550623i
$311$	−10.7131	−	9.64609i	−0.607482	−	0.546980i	0.306946	−	0.951727i	$-0.400693\pi$
$311$	−10.7131	−	9.64609i	−0.607482	−	0.546980i	−0.914429	+	0.404747i	$0.867359\pi$
$312$	−0.0333422	−	4.43346i	−0.00188763	−	0.250996i
$313$	7.46453	+	8.29020i	0.421920	+	0.468590i	0.916205	−	0.400710i	$-0.131237\pi$
$313$	7.46453	+	8.29020i	0.421920	+	0.468590i	−0.494285	+	0.869300i	$0.664570\pi$
$314$			6.39889i			0.361110i
$315$	10.0419	+	15.9395i	0.565798	+	0.898088i
$316$	−30.0361	−	9.75931i	−1.68966	−	0.549004i
$317$	5.42176	+	1.15243i	0.304517	+	0.0647270i	0.357636	−	0.933861i	$-0.383583\pi$
$317$	5.42176	+	1.15243i	0.304517	+	0.0647270i	−0.0531191	+	0.998588i	$0.516916\pi$
$318$	9.34681	−	13.0704i	0.524143	−	0.732950i
$319$	1.06997	+	1.85324i	0.0599066	+	0.103761i
$320$	25.9307	+	5.51175i	1.44957	+	0.308116i
$321$	−3.17951	−	1.80395i	−0.177463	−	0.100686i
$322$	−12.4201	−	35.3686i	−0.692144	−	1.97102i
$323$	2.54680	+	0.827505i	0.141708	+	0.0460436i
$324$	−20.5023	−	8.39878i	−1.13902	−	0.466599i
$325$	0.831177	+	1.43964i	0.0461054	+	0.0798569i
$326$	10.9870	−	24.6773i	0.608515	−	1.36675i
$327$	−6.60459	+	15.1396i	−0.365235	+	0.837220i
$328$	6.18751	+	0.849608i	0.341648	+	0.0469118i
$329$	−6.48993	−	27.3492i	−0.357801	−	1.50781i
$330$	25.0386	−	22.8882i	1.37833	−	1.25995i
$331$	−27.8854	−	16.0996i	−1.53272	−	0.884916i	−0.999235	−	0.0391063i	$-0.987549\pi$
$331$	−27.8854	−	16.0996i	−1.53272	−	0.884916i	−0.533485	−	0.845810i	$-0.679118\pi$
$332$	28.5607	−	6.07076i	1.56747	−	0.333176i
$333$	6.02514	−	2.79189i	0.330176	−	0.152995i
$334$	−1.21928	−	11.6007i	−0.0667161	−	0.634762i
$335$	−19.2409	+	26.4828i	−1.05124	+	1.44691i
$336$	12.1466	+	4.96183i	0.662650	+	0.270690i
$337$	6.95676			0.378959			0.189479	−	0.981885i	$-0.439320\pi$
$337$	6.95676			0.378959			0.189479	+	0.981885i	$0.439320\pi$
$338$	−2.68465	+	12.6303i	−0.146026	+	0.686997i
$339$	−9.48246	+	13.2601i	−0.515016	+	0.720187i
$340$	−6.28592	−	29.5729i	−0.340902	−	1.60382i
$341$	7.55427	−	0.793986i	0.409087	−	0.0429968i
$342$	−0.730016	−	3.19722i	−0.0394748	−	0.172886i
$343$	6.95216	+	17.1659i	0.375381	+	0.926870i
$344$	−4.34405	+	5.97907i	−0.234215	+	0.322370i
$345$	−27.4447	−	2.67604i	−1.47757	−	0.144073i
$346$	10.6627	−	23.9488i	0.573229	−	1.28749i
$347$	0.307124	−	2.92209i	0.0164873	−	0.156866i	−0.983181	−	0.182636i	$-0.941537\pi$
$347$	0.307124	−	2.92209i	0.0164873	−	0.156866i	0.999668	+	0.0257698i	$0.00820370\pi$
$348$	−1.18301	−	2.01390i	−0.0634160	−	0.107957i
$349$	3.76638	−	5.18398i	0.201610	−	0.277492i	−0.696226	−	0.717823i	$-0.745139\pi$
$349$	3.76638	−	5.18398i	0.201610	−	0.277492i	0.897836	+	0.440331i	$0.145139\pi$
$350$	3.51099	−	0.452838i	0.187670	−	0.0242052i
$351$	−11.2100	−	7.76430i	−0.598346	−	0.414428i
$352$	6.49680	−	30.5651i	0.346281	−	1.62912i
$353$	0.407345	−	3.87563i	0.0216808	−	0.206279i	−0.978319	−	0.207104i	$-0.933596\pi$
$353$	0.407345	−	3.87563i	0.0216808	−	0.206279i	1.00000		0.000825286i	$0.000262697\pi$
$354$	−11.9019	+	3.96635i	−0.632577	+	0.210809i
$355$	18.2674	−	31.6401i	0.969532	−	1.67928i
$356$	4.55642	+	6.27137i	0.241490	+	0.332382i
$357$	−0.736609	−	23.7004i	−0.0389855	−	1.25436i
$358$	−26.7434	+	8.68946i	−1.41343	+	0.459252i
$359$	−1.29749	+	6.10421i	−0.0684789	+	0.322168i	−0.999032	−	0.0439890i	$-0.985993\pi$
$359$	−1.29749	+	6.10421i	−0.0684789	+	0.322168i	0.930553	+	0.366157i	$0.119327\pi$
$360$	−5.09085	+	4.72439i	−0.268312	+	0.248997i
$361$	−12.5343	+	13.9207i	−0.659698	+	0.732669i
$362$	−12.7309	−	28.5942i	−0.669124	−	1.50288i
$363$	−4.98004	−	5.44794i	−0.261384	−	0.285943i
$364$	−14.0610	−	9.71844i	−0.736999	−	0.509385i
$365$	−8.68199	−	2.82095i	−0.454436	−	0.147655i
$366$	45.9861	+	20.0613i	2.40373	+	1.04862i
$367$	0.669956	−	1.50475i	0.0349714	−	0.0785471i	−0.895215	−	0.445634i	$-0.852978\pi$
$367$	0.669956	−	1.50475i	0.0349714	−	0.0785471i	0.930187	+	0.367087i	$0.119645\pi$
$368$	−16.6323	+	9.60266i	−0.867019	+	0.500573i
$369$	13.0901	−	14.0588i	0.681444	−	0.731870i
$370$		−	11.0975i		−	0.576930i
$371$	−3.85005	−	10.9638i	−0.199885	−	0.569211i
$372$	−8.23847	+	0.928590i	−0.427145	+	0.0481452i
$373$	1.49286	+	1.65799i	0.0772973	+	0.0858474i	0.780553	−	0.625090i	$-0.214938\pi$
$373$	1.49286	+	1.65799i	0.0772973	+	0.0858474i	−0.703256	+	0.710937i	$0.748271\pi$
$374$	−41.7649	+	8.87741i	−2.15961	+	0.459040i
$375$	−5.41859	+	17.1136i	−0.279815	+	0.883741i
$376$	9.46677	−	4.21488i	0.488212	−	0.217366i
$377$	−0.444221	−	1.36717i	−0.0228785	−	0.0704129i
$378$	−24.4527	+	15.6634i	−1.25771	+	0.805637i
$379$	1.09397	+	3.36691i	0.0561937	+	0.172946i	0.975214	−	0.221264i	$-0.0710182\pi$
$379$	1.09397	+	3.36691i	0.0561937	+	0.172946i	−0.919020	+	0.394210i	$0.871018\pi$
$380$	−2.95782	−	0.628705i	−0.151733	−	0.0322519i
$381$	−3.79693	−	11.3935i	−0.194523	−	0.583706i
$382$	−10.9145	+	24.5143i	−0.558432	+	1.25426i
$383$	−7.09790	−	4.09798i	−0.362686	−	0.209397i	0.307572	−	0.951525i	$-0.400483\pi$
$383$	−7.09790	−	4.09798i	−0.362686	−	0.209397i	−0.670258	+	0.742128i	$0.733817\pi$
$384$	−2.63828	+	12.8880i	−0.134634	+	0.657686i
$385$	−3.13809	−	24.3306i	−0.159932	−	1.24000i
$386$	−8.16231	−	25.1210i	−0.415451	−	1.27863i
$387$	7.34859	+	21.5103i	0.373550	+	1.09343i
$388$	−0.989918	+	9.41844i	−0.0502555	+	0.478149i
$389$	19.7413	+	2.07489i	1.00092	+	0.105201i	0.590791	−	0.806825i	$-0.298816\pi$
$389$	19.7413	+	2.07489i	1.00092	+	0.105201i	0.410132	+	0.912026i	$0.365483\pi$
$390$	−19.6492	+	11.5424i	−0.994975	+	0.584470i
$391$	28.0788	+	20.4005i	1.42001	+	1.03170i
$392$	−5.74573	+	3.68849i	−0.290203	+	0.186297i
$393$	−29.3835	+	13.3480i	−1.48220	+	0.673320i
$394$	25.1125	−	11.1808i	1.26515	−	0.563280i
$395$	6.33075	+	29.7838i	0.318535	+	1.49859i
$396$	19.6257	+	21.1480i	0.986227	+	1.06273i
$397$	−0.922727	−	8.77916i	−0.0463103	−	0.440613i	−0.992969	−	0.118375i	$-0.962231\pi$
$397$	−0.922727	−	8.77916i	−0.0463103	−	0.440613i	0.946659	−	0.322238i	$-0.104435\pi$
$398$	20.0333	+	6.50920i	1.00418	+	0.326277i
$399$	−2.19549	−	0.896849i	−0.109912	−	0.0448986i
$400$	−0.560463	−	1.72493i	−0.0280232	−	0.0862464i
$401$	−1.53920	−	0.888660i	−0.0768642	−	0.0443776i	0.461075	−	0.887361i	$-0.347464\pi$
$401$	−1.53920	−	0.888660i	−0.0768642	−	0.0443776i	−0.537940	+	0.842983i	$0.680797\pi$
$402$	−41.0436	−	29.3509i	−2.04707	−	1.46389i
$403$	−5.07468	−	0.533370i	−0.252788	−	0.0265691i
$404$	−27.7550	+	2.91717i	−1.38086	+	0.145134i
$405$	2.87083	+	21.1676i	0.142653	+	1.05183i
$406$	−3.05121	−	0.248213i	−0.151429	−	0.0123186i
$407$	−8.64732			−0.428632
$408$	8.53677	−	1.88176i	0.422633	−	0.0931608i
$409$	25.5162	−	14.7318i	1.26169	−	0.728440i	0.288292	−	0.957542i	$-0.406913\pi$
$409$	25.5162	−	14.7318i	1.26169	−	0.728440i	0.973402	+	0.229103i	$0.0735792\pi$
$410$	−12.1199	−	29.7262i	−0.598560	−	1.46807i
$411$	30.3123	+	13.2237i	1.49520	+	0.652275i
$412$	5.06319	+	6.96888i	0.249445	+	0.343332i
$413$	−2.59955	+	8.69191i	−0.127915	+	0.427701i
$414$	3.80670	−	42.3343i	0.187089	−	2.08062i
$415$	−18.8371	−	20.9207i	−0.924677	−	1.02696i
$416$	−8.53788	+	19.1764i	−0.418604	+	0.940200i
$417$	0.100511	+	13.3648i	0.00492206	+	0.654479i
$418$	−0.887900	+	4.17724i	−0.0434286	+	0.204316i
$419$	26.8445			1.31144			0.655720	−	0.755004i	$-0.272365\pi$
$419$	26.8445			1.31144			0.655720	+	0.755004i	$0.272365\pi$
$420$	3.62473	+	26.5294i	0.176869	+	1.29450i
$421$	−21.8918	+	7.11306i	−1.06694	+	0.346669i	−0.789295	−	0.614015i	$-0.789554\pi$
$421$	−21.8918	+	7.11306i	−1.06694	+	0.346669i	−0.277644	+	0.960684i	$0.589554\pi$
$422$	6.09695	+	6.77135i	0.296795	+	0.329624i
$423$	6.15697	−	31.2719i	0.299362	−	1.52049i
$424$	3.70999	−	2.14196i	0.180173	−	0.104023i
$425$	−2.43578	+	2.19319i	−0.118153	+	0.106385i
$426$	48.9817	+	27.7906i	2.37317	+	1.34646i
$427$	30.9853	−	18.8759i	1.49948	−	0.913468i
$428$	−3.05398	−	4.20344i	−0.147620	−	0.203181i
$429$	8.99398	+	15.3110i	0.434234	+	0.739220i
$430$	37.7790	+	3.97073i	1.82187	+	0.191486i
$431$	−8.34687	−	0.877291i	−0.402054	−	0.0422576i	−0.0986565	−	0.995122i	$-0.531454\pi$
$431$	−8.34687	−	0.877291i	−0.402054	−	0.0422576i	−0.303398	+	0.952864i	$0.598121\pi$
$432$	10.2021	+	10.8289i	0.490846	+	0.521007i
$433$	9.49752	+	13.0722i	0.456422	+	0.628211i	0.973762	−	0.227569i	$-0.0730778\pi$
$433$	9.49752	+	13.0722i	0.456422	+	0.628211i	−0.517340	+	0.855780i	$0.673078\pi$
$434$	−5.21006	+	9.53584i	−0.250091	+	0.457735i
$435$	−1.11125	+	1.95862i	−0.0532805	+	0.0939085i
$436$	−17.4463	+	15.7087i	−0.835528	+	0.752313i
$437$	3.00628	−	1.73568i	0.143810	−	0.0830287i
$438$	4.24757	−	13.4151i	0.202957	−	0.640999i
$439$	−23.0475	−	25.5969i	−1.10000	−	1.22167i	−0.973253	−	0.229736i	$-0.926214\pi$
$439$	−23.0475	−	25.5969i	−1.10000	−	1.22167i	−0.126745	−	0.991935i	$-0.540453\pi$
$440$	8.60146	−	2.79478i	0.410058	−	0.133236i
$441$	−0.893903	+	20.9810i	−0.0425668	+	0.999094i
$442$	28.6829			1.36431
$443$	−4.73963	+	22.2982i	−0.225187	+	1.05942i	0.709709	+	0.704495i	$0.248827\pi$
$443$	−4.73963	+	22.2982i	−0.225187	+	1.05942i	−0.934895	+	0.354924i	$0.884507\pi$
$444$	9.43798	−	0.0709790i	0.447907	−	0.00336852i
$445$	3.03989	−	6.82770i	0.144105	−	0.323664i
$446$	9.58247	+	10.6424i	0.453743	+	0.503933i
$447$	−35.7728	−	7.32301i	−1.69200	−	0.346367i
$448$	20.2851	+	21.4890i	0.958382	+	1.01526i
$449$	8.59559	+	11.8308i	0.405651	+	0.558331i	0.962151	−	0.272517i	$-0.0878561\pi$
$449$	8.59559	+	11.8308i	0.405651	+	0.558331i	−0.556500	+	0.830848i	$0.687856\pi$
$450$	3.83582	+	1.18286i	0.180822	+	0.0557603i
$451$	−23.1631	+	9.44403i	−1.09071	+	0.444702i
$452$	−20.0655	+	11.5848i	−0.943804	+	0.544905i
$453$	4.84716	+	21.9896i	0.227739	+	1.03316i
$454$	7.11892			0.334108
$455$	−1.33620	+	16.4255i	−0.0626418	+	0.770039i
$456$	0.175346	−	0.856564i	0.00821133	−	0.0401123i
$457$	−17.2826	+	1.81648i	−0.808447	+	0.0849712i	−0.499728	−	0.866182i	$-0.666567\pi$
$457$	−17.2826	+	1.81648i	−0.808447	+	0.0849712i	−0.308719	+	0.951153i	$0.599900\pi$
$458$	50.9754	+	5.35773i	2.38192	+	0.250350i
$459$	10.3789	−	24.8027i	0.484446	−	1.15769i
$460$	−33.9415	−	19.5962i	−1.58253	−	0.913675i
$461$	6.94697	+	21.3806i	0.323552	+	0.995792i	0.972090	+	0.234609i	$0.0753810\pi$
$461$	6.94697	+	21.3806i	0.323552	+	0.995792i	−0.648537	+	0.761183i	$0.724619\pi$
$462$	37.4667	−	5.11910i	1.74311	−	0.238162i
$463$	21.9343	+	7.12688i	1.01937	+	0.331214i	0.770581	−	0.637342i	$-0.219966\pi$
$463$	21.9343	+	7.12688i	1.01937	+	0.331214i	0.248792	+	0.968557i	$0.419966\pi$
$464$	0.163943	+	1.55981i	0.00761085	+	0.0724124i
$465$	4.74686	+	6.43122i	0.220130	+	0.298241i
$466$	−4.16714	−	19.6049i	−0.193039	−	0.908178i
$467$	−1.97051	+	0.877327i	−0.0911842	+	0.0405978i	−0.451822	−	0.892108i	$-0.649226\pi$
$467$	−1.97051	+	0.877327i	−0.0911842	+	0.0405978i	0.360638	+	0.932706i	$0.382559\pi$
$468$	−9.94201	−	16.6371i	−0.459570	−	0.769049i
$469$	−34.4285	+	12.0900i	−1.58976	+	0.558262i
$470$	−43.0913	−	31.3077i	−1.98765	−	1.44412i
$471$	2.65760	+	4.52418i	0.122456	+	0.208463i
$472$	−3.32632	−	0.349610i	−0.153106	−	0.0160921i
$473$	3.09406	−	29.4380i	0.142265	−	1.35356i
$474$	−45.8354	+	10.1035i	−2.10529	+	0.464068i
$475$	0.101304	+	0.311780i	0.00464812	+	0.0143055i
$476$	12.9789	−	31.1023i	0.594889	−	1.42557i
$477$	1.18002	−	13.1230i	0.0540296	−	0.600862i
$478$	42.2488	+	24.3924i	1.93242	+	1.11568i
$479$	12.8586	−	28.8809i	0.587525	−	1.31960i	−0.338081	−	0.941117i	$-0.609778\pi$
$479$	12.8586	−	28.8809i	0.587525	−	1.31960i	0.925607	−	0.378487i	$-0.123555\pi$
$480$	31.1962	−	10.3963i	1.42390	−	0.474523i
$481$	5.68201	+	1.20775i	0.259077	+	0.0550686i
$482$	−8.64035	−	26.5923i	−0.393557	−	1.21124i
$483$	−23.4707	−	19.8482i	−1.06795	−	0.903125i
$484$	−3.24184	−	9.97736i	−0.147356	−	0.453516i
$485$	8.34131	−	3.71379i	0.378759	−	0.168635i
$486$	−32.5944	+	4.67048i	−1.47851	+	0.211857i
$487$	29.5368	−	6.27825i	1.33844	−	0.284494i	0.517586	−	0.855631i	$-0.326831\pi$
$487$	29.5368	−	6.27825i	1.33844	−	0.284494i	0.820855	+	0.571137i	$0.193497\pi$
$488$	8.95023	+	9.94023i	0.405158	+	0.449973i
$489$	−2.48090	−	22.0106i	−0.112190	−	0.995355i
$490$	31.1852	+	16.0968i	1.40880	+	0.727181i
$491$		−	31.4654i		−	1.42001i	−0.704195	−	0.710007i	$-0.748692\pi$
$491$		−	31.4654i		−	1.42001i	0.704195	−	0.710007i	$-0.251308\pi$
$492$	25.2035	−	10.4977i	1.13626	−	0.473271i
$493$	2.45464	−	1.41719i	0.110551	−	0.0638269i
$494$	1.16685	−	2.62078i	0.0524990	−	0.117915i
$495$	8.19699	−	26.5816i	0.368427	−	1.19475i
$496$	5.29470	+	1.72035i	0.237739	+	0.0772462i
$497$	36.8044	−	17.4361i	1.65090	−	0.782117i
$498$	32.0288	−	29.2780i	1.43525	−	1.31198i
$499$	−8.75009	−	19.6530i	−0.391708	−	0.879791i	−0.996515	−	0.0834182i	$-0.973416\pi$
$499$	−8.75009	−	19.6530i	−0.391708	−	0.879791i	0.604807	−	0.796372i	$-0.293250\pi$
$500$	−17.0720	+	18.9604i	−0.763483	+	0.847934i
$501$	−5.68009	−	7.69560i	−0.253768	−	0.343814i
$502$	−9.77858	+	46.0046i	−0.436439	+	2.05329i
$503$	−24.2742	+	7.88715i	−1.08233	+	0.351671i	−0.795279	−	0.606244i	$-0.792676\pi$
$503$	−24.2742	+	7.88715i	−1.08233	+	0.351671i	−0.287053	+	0.957915i	$0.592676\pi$
$504$	−7.66259	+	1.10571i	−0.341319	+	0.0492521i
$505$	15.8156	+	21.7683i	0.703783	+	0.968675i
$506$	−27.6750	+	47.9346i	−1.23031	+	2.13095i
$507$	3.34752	+	10.0449i	0.148669	+	0.446112i
$508$	1.78421	−	16.9756i	0.0791616	−	0.753172i
$509$	−6.46697	+	30.4247i	−0.286643	+	1.34855i	0.565286	+	0.824895i	$0.308766\pi$
$509$	−6.46697	+	30.4247i	−0.286643	+	1.34855i	−0.851930	+	0.523656i	$0.824568\pi$
$510$	−30.3157	−	33.1640i	−1.34240	−	1.46853i
$511$	−6.17347	−	8.08939i	−0.273098	−	0.357854i
$512$	16.7447	−	23.0471i	0.740018	−	1.01855i
$513$	−1.84402	−	1.95733i	−0.0814153	−	0.0864180i
$514$	−0.0226030	+	0.215054i	−0.000996977	+	0.00948561i
$515$	3.37799	−	7.58709i	0.148852	−	0.334327i
$516$	−3.13533	+	32.1550i	−0.138025	+	1.41555i
$517$	−24.3954	+	33.5774i	−1.07291	+	1.47673i
$518$	7.03350	−	10.1764i	0.309034	−	0.447123i
$519$	−2.40767	−	21.3609i	−0.105685	−	0.937638i
$520$	−6.04222	+	0.635063i	−0.264969	+	0.0278493i
$521$	−4.24823	−	19.9864i	−0.186118	−	0.875619i	−0.967757	−	0.251887i	$-0.918949\pi$
$521$	−4.24823	−	19.9864i	−0.186118	−	0.875619i	0.781638	−	0.623732i	$-0.214384\pi$
$522$	−3.03189	−	1.69018i	−0.132702	−	0.0739771i
$523$	6.80446	−	32.0125i	0.297538	−	1.39981i	−0.534538	−	0.845145i	$-0.679514\pi$
$523$	6.80446	−	32.0125i	0.297538	−	1.39981i	0.832076	−	0.554662i	$-0.187152\pi$
$524$	−45.8700			−2.00384
$525$	2.29429	−	1.77836i	0.100131	−	0.0776140i
$526$	−16.6928	+	22.9756i	−0.727840	+	1.00179i
$527$	−1.05165	−	10.0057i	−0.0458104	−	0.435857i
$528$	−6.12523	−	18.3800i	−0.266566	−	0.799888i
$529$	21.5111	−	4.57233i	0.935265	−	0.198797i
$530$	−19.0692	−	11.0096i	−0.828314	−	0.478227i
$531$	−6.76762	+	7.74743i	−0.293690	+	0.336210i
$532$	−2.31385	−	2.45117i	−0.100318	−	0.106272i
$533$	16.5391	−	2.97038i	0.716390	−	0.128661i
$534$	10.5595	+	4.60653i	0.456952	+	0.199344i
$535$	−2.03751	+	4.57633i	−0.0880893	+	0.197852i
$536$	−6.72620	−	11.6501i	−0.290528	−	0.503209i
$537$	−15.2994	+	17.2508i	−0.660217	+	0.744428i
$538$	3.09230	+	1.00475i	0.133319	+	0.0433178i
$539$	12.5429	−	24.3000i	0.540261	−	1.04667i
$540$	−8.72828	+	29.0794i	−0.375606	+	1.25138i
$541$	11.2509	+	2.39145i	0.483713	+	0.102816i	0.443312	−	0.896367i	$-0.353803\pi$
$541$	11.2509	+	2.39145i	0.483713	+	0.102816i	0.0404008	+	0.999184i	$0.487137\pi$
$542$	−15.1941	−	26.3170i	−0.652643	−	1.13041i
$543$	−20.8769	−	14.9294i	−0.895914	−	0.640681i
$544$	−40.4839	−	8.60511i	−1.73573	−	0.368941i
$545$	21.5266	+	6.99443i	0.922100	+	0.299609i
$546$	−25.3337	−	1.86920i	−1.08418	−	0.0799945i
$547$		−	3.52767i		−	0.150832i	−0.997152	−	0.0754161i	$-0.975972\pi$
$547$		−	3.52767i		−	0.150832i	0.997152	−	0.0754161i	$-0.0240285\pi$
$548$	31.4519	+	34.9309i	1.34356	+	1.49217i
$549$	40.8453	−	4.91518i	1.74323	−	0.209775i
$550$	−3.88450	−	3.49762i	−0.165635	−	0.149139i
$551$	−0.0296326	−	0.281935i	−0.00126239	−	0.0120108i
$552$	5.59204	−	9.85614i	0.238013	−	0.419505i
$553$	−13.0715	+	31.3241i	−0.555857	+	1.33204i
$554$	−3.97780	+	5.47497i	−0.169000	+	0.232609i
$555$	−4.60903	−	7.84620i	−0.195642	−	0.333053i
$556$	−7.72638	+	17.3537i	−0.327672	+	0.735963i
$557$	−7.88077	+	8.75248i	−0.333919	+	0.370854i	−0.886599	−	0.462539i	$-0.846938\pi$
$557$	−7.88077	+	8.75248i	−0.333919	+	0.370854i	0.552680	+	0.833394i	$0.313605\pi$
$558$	−9.85805	+	7.39135i	−0.417324	+	0.312901i
$559$	−6.14458	+	18.9111i	−0.259888	+	0.799854i
$560$	5.15195	−	17.2262i	0.217709	−	0.727938i
$561$	−25.8419	+	23.6225i	−1.09105	+	0.997342i
$562$	−39.7537	+	35.7944i	−1.67691	+	1.50990i
$563$	−24.9328	−	22.4496i	−1.05079	−	0.946136i	−0.0521701	−	0.998638i	$-0.516614\pi$
$563$	−24.9328	−	22.4496i	−1.05079	−	0.946136i	−0.998621	+	0.0525019i	$0.983280\pi$
$564$	26.3504	−	36.8478i	1.10955	−	1.55157i
$565$	19.3460	+	11.1694i	0.813891	+	0.469900i
$566$	−10.4475	−	32.1542i	−0.439142	−	1.35154i
$567$	−10.7833	+	21.2302i	−0.452857	+	0.891583i
$568$	8.82508	+	12.1467i	0.370292	+	0.509663i
$569$	−17.0399	+	15.3428i	−0.714349	+	0.643203i	−0.943953	−	0.330081i	$-0.892924\pi$
$569$	−17.0399	+	15.3428i	−0.714349	+	0.643203i	0.229603	+	0.973284i	$0.426257\pi$
$570$	−4.26350	+	1.42083i	−0.178578	+	0.0595120i
$571$	6.40475	−	3.69779i	0.268031	−	0.154748i	−0.359962	−	0.932967i	$-0.617210\pi$
$571$	6.40475	−	3.69779i	0.268031	−	0.154748i	0.627992	+	0.778220i	$0.283877\pi$
$572$	2.63812	+	25.1001i	0.110306	+	1.04949i
$573$	2.46452	+	21.8652i	0.102957	+	0.913434i
$574$	7.72634	−	34.9404i	0.322491	−	1.45838i
$575$			4.24889i			0.177191i
$576$	10.8326	+	31.7084i	0.451358	+	1.32118i
$577$	−6.82004	−	11.8127i	−0.283922	−	0.491767i	0.688425	−	0.725307i	$-0.258302\pi$
$577$	−6.82004	−	11.8127i	−0.283922	−	0.491767i	−0.972347	+	0.233540i	$0.924969\pi$
$578$	4.29238	+	20.1940i	0.178539	+	0.839961i
$579$	−16.2043	−	14.3712i	−0.673427	−	0.597247i
$580$	−2.58937	+	1.88129i	−0.107518	+	0.0781162i
$581$	−4.01418	−	31.1231i	−0.166536	−	1.29120i
$582$	5.82113	+	12.8142i	0.241293	+	0.531167i
$583$	−8.57887	+	14.8590i	−0.355300	+	0.615398i
$584$	2.51025	−	2.78792i	0.103875	−	0.115365i
$585$	−9.09869	+	16.3215i	−0.376185	+	0.674810i
$586$	16.7002	+	18.5474i	0.689877	+	0.766186i
$587$	−26.6851	−	36.7289i	−1.10141	−	1.51596i	−0.833499	−	0.552521i	$-0.813666\pi$
$587$	−26.6851	−	36.7289i	−1.10141	−	1.51596i	−0.267914	−	0.963443i	$-0.586334\pi$
$588$	−13.4903	+	26.6248i	−0.556331	+	1.09799i
$589$	−0.957016	−	0.310953i	−0.0394331	−	0.0128126i
$590$	6.99235	+	15.7051i	0.287871	+	0.646568i
$591$	13.1115	−	18.3349i	0.539337	−	0.754196i
$592$	−5.78987	−	2.57782i	−0.237962	−	0.105948i
$593$	4.82866	+	10.8453i	0.198289	+	0.445365i	0.985134	−	0.171786i	$-0.0549537\pi$
$593$	4.82866	+	10.8453i	0.198289	+	0.445365i	−0.786845	+	0.617150i	$0.788287\pi$
$594$	41.0679	+	12.3267i	1.68504	+	0.505770i
$595$	−32.2262	+	4.15645i	−1.32114	+	0.170398i
$596$	−41.9868	−	30.5052i	−1.71984	−	1.24954i
$597$	16.8675	−	3.71808i	0.690339	−	0.152171i
$598$	24.8797	−	27.6317i	1.01741	−	1.12994i
$599$	28.9366	+	3.04136i	1.18232	+	0.124267i	0.675216	−	0.737620i	$-0.264050\pi$
$599$	28.9366	+	3.04136i	1.18232	+	0.124267i	0.507101	+	0.861887i	$0.330717\pi$
$600$	0.800649	+	0.710078i	0.0326864	+	0.0289888i
$601$	6.36225			0.259522			0.129761	−	0.991545i	$-0.458579\pi$
$601$	6.36225			0.259522			0.129761	+	0.991545i	$0.458579\pi$
$602$	32.1267	+	27.5852i	1.30938	+	1.12429i
$603$	−41.2090	−	3.70552i	−1.67816	−	0.150900i
$604$	−6.65405	+	31.3048i	−0.270749	+	1.27378i
$605$	−6.76799	+	7.51661i	−0.275158	+	0.305594i
$606$	−33.3702	+	24.6304i	−1.35557	+	1.00054i
$607$	−3.33428	+	15.6865i	−0.135334	+	0.636697i	0.857226	+	0.514941i	$0.172186\pi$
$607$	−3.33428	+	15.6865i	−0.135334	+	0.636697i	−0.992560	+	0.121757i	$0.961147\pi$
$608$	−2.43318	+	3.34898i	−0.0986784	+	0.135819i
$609$	−2.26037	+	1.09174i	−0.0915950	+	0.0442397i
$610$	21.2454	−	65.3868i	0.860203	−	2.64743i
$611$	20.7195	−	18.6559i	0.838222	−	0.754738i
$612$	28.0109	−	25.9945i	1.13227	−	1.05076i
$613$	22.9496	+	10.2178i	0.926926	+	0.412694i	0.813971	−	0.580906i	$-0.197302\pi$
$613$	22.9496	+	10.2178i	0.926926	+	0.412694i	0.112955	+	0.993600i	$0.463968\pi$
$614$	6.01339	−	10.4155i	0.242680	−	0.420335i
$615$	−20.9151	−	15.9836i	−0.843377	−	0.644519i
$616$	9.65883	+	2.88873i	0.389166	+	0.116390i
$617$	23.6047	+	32.4891i	0.950290	+	1.30796i	0.951398	+	0.307963i	$0.0996473\pi$
$617$	23.6047	+	32.4891i	0.950290	+	1.30796i	−0.00110793	+	0.999999i	$0.500353\pi$
$618$	11.7339	+	5.11888i	0.472006	+	0.205911i
$619$	−0.277863	−	1.30724i	−0.0111683	−	0.0525425i	0.972211	−	0.234108i	$-0.0752169\pi$
$619$	−0.277863	−	1.30724i	−0.0111683	−	0.0525425i	−0.983379	+	0.181565i	$0.941884\pi$
$620$	2.36207	+	11.1127i	0.0948632	+	0.446296i
$621$	−14.8909	−	31.5125i	−0.597553	−	1.26455i
$622$	−24.6350	−	17.8983i	−0.987772	−	0.717658i
$623$	7.11492	−	4.33433i	0.285053	−	0.173651i
$624$	1.45770	+	12.9327i	0.0583545	+	0.517723i
$625$	27.1592	+	5.77287i	1.08637	+	0.230915i
$626$	17.5113	+	15.7673i	0.699893	+	0.630186i
$627$	1.10713	+	3.32218i	0.0442146	+	0.132675i
$628$	0.779530	+	7.41674i	0.0311066	+	0.295960i
$629$			11.4535i			0.456681i
$630$	24.6146	+	31.2672i	0.980670	+	1.24571i
$631$	−34.3348	−	24.9457i	−1.36685	−	0.993072i	−0.997976	−	0.0635909i	$-0.979745\pi$
$631$	−34.3348	−	24.9457i	−1.36685	−	0.993072i	−0.368870	−	0.929481i	$-0.620255\pi$
$632$	−12.2398	−	2.60165i	−0.486873	−	0.103488i
$633$	7.12300	+	2.25532i	0.283114	+	0.0896410i
$634$	11.6441	+	1.22384i	0.462444	+	0.0486049i
$635$	−15.0342	+	6.69367i	−0.596616	+	0.265630i
$636$	9.24130	−	16.2881i	0.366441	−	0.645864i
$637$	−11.6357	+	14.2153i	−0.461021	+	0.563230i
$638$	2.65688	+	3.65689i	0.105187	+	0.144778i
$639$	46.1734	−	0.694540i	1.82659	−	0.0274756i
$640$	17.9283	+	1.88434i	0.708678	+	0.0744851i
$641$	−34.9605	+	7.43108i	−1.38086	+	0.293510i	−0.837704	−	0.546124i	$-0.816103\pi$
$641$	−34.9605	+	7.43108i	−1.38086	+	0.293510i	−0.543153	+	0.839634i	$0.682769\pi$
$642$	−7.07756	−	3.08757i	−0.279329	−	0.121857i
$643$	36.0587	−	26.1982i	1.42202	−	1.03316i	0.430582	−	0.902551i	$-0.358308\pi$
$643$	36.0587	−	26.1982i	1.42202	−	1.03316i	0.991435	−	0.130604i	$-0.0416917\pi$
$644$	−18.7044	−	39.4815i	−0.737057	−	1.55579i
$645$	28.3599	−	12.8831i	1.11667	−	0.507270i
$646$	5.53282	+	1.17604i	0.217686	+	0.0462705i
$647$	−21.9432	−	38.0067i	−0.862675	−	1.49420i	−0.869337	−	0.494220i	$-0.835454\pi$
$647$	−21.9432	−	38.0067i	−0.862675	−	1.49420i	0.00666154	−	0.999978i	$-0.497880\pi$
$648$	−8.42671	−	2.46038i	−0.331032	−	0.0966530i
$649$	12.2376	−	5.44855i	0.480370	−	0.213874i
$650$	2.06394	+	2.84076i	0.0809542	+	0.111424i
$651$	0.276797	+	8.90594i	0.0108485	+	0.349051i
$652$	9.72844	−	29.9411i	0.380995	−	1.17258i
$653$	−15.5911	+	27.0047i	−0.610129	+	1.05677i	0.381090	+	0.924538i	$0.375549\pi$
$653$	−15.5911	+	27.0047i	−0.610129	+	1.05677i	−0.991218	+	0.132236i	$0.957784\pi$
$654$	−10.5317	+	33.2622i	−0.411821	+	1.30066i
$655$	22.1125	+	38.3000i	0.864008	+	1.49651i
$656$	−18.3244	−	0.581756i	−0.715446	−	0.0227138i
$657$	−2.56846	−	11.2489i	−0.100205	−	0.438863i
$658$	−19.6721	−	56.0201i	−0.766897	−	2.18389i
$659$	3.09258			0.120470			0.0602350	−	0.998184i	$-0.480815\pi$
$659$	3.09258			0.120470			0.0602350	+	0.998184i	$0.480815\pi$
$660$	26.2331	−	29.5792i	1.02112	−	1.15137i
$661$	1.00654	+	4.73540i	0.0391499	+	0.184186i	0.993378	−	0.114895i	$-0.0366533\pi$
$661$	1.00654	+	4.73540i	0.0391499	+	0.184186i	−0.954228	+	0.299081i	$0.903320\pi$
$662$	−62.1341	−	27.6639i	−2.41491	−	1.07519i
$663$	20.2796	−	11.9127i	0.787594	−	0.462650i
$664$	11.0028	−	3.57502i	0.426991	−	0.138738i
$665$	−0.931212	+	3.11362i	−0.0361109	+	0.120741i
$666$	12.0407	−	7.19530i	0.466567	−	0.278812i
$667$	0.763918	−	3.59395i	0.0295790	−	0.139158i
$668$	−2.82646	−	13.2974i	−0.109359	−	0.514493i
$669$	11.1951	+	3.54465i	0.432827	+	0.137044i
$670$	−34.5725	+	59.8813i	−1.33565	+	2.31342i
$671$	−50.9504	−	16.5548i	−1.96692	−	0.639091i
$672$	35.1959	+	10.2386i	1.35771	+	0.394961i
$673$	5.24093	−	1.70288i	0.202023	−	0.0656413i	−0.206258	−	0.978498i	$-0.566128\pi$
$673$	5.24093	−	1.70288i	0.202023	−	0.0656413i	0.408281	+	0.912856i	$0.366128\pi$
$674$	14.6142	−	1.53601i	0.562918	−	0.0591651i
$675$	3.20329	−	0.756794i	0.123295	−	0.0291290i
$676$	−1.57303	+	14.9664i	−0.0605012	+	0.575631i
$677$	12.6759	−	5.64366i	0.487173	−	0.216903i	−0.148425	−	0.988924i	$-0.547420\pi$
$677$	12.6759	−	5.64366i	0.487173	−	0.216903i	0.635598	+	0.772020i	$0.280754\pi$
$678$	−16.9922	+	29.9493i	−0.652583	+	1.15020i
$679$	10.0027	+	1.88113i	0.383870	+	0.0721910i
$680$	−3.70173	−	11.3928i	−0.141955	−	0.436892i
$681$	5.03327	−	2.95665i	0.192875	−	0.113299i
$682$	15.6941	−	3.33588i	0.600958	−	0.127738i
$683$	−16.5674	−	28.6955i	−0.633932	−	1.09800i	−0.986740	−	0.162307i	$-0.948106\pi$
$683$	−16.5674	−	28.6955i	−0.633932	−	1.09800i	0.352808	−	0.935696i	$-0.385227\pi$
$684$	−1.23563	−	3.61686i	−0.0472456	−	0.138294i
$685$	14.0042	−	43.1005i	0.535073	−	1.64678i
$686$	18.3947	+	34.5257i	0.702312	+	1.31820i
$687$	38.2661	−	17.3832i	1.45994	−	0.663209i
$688$	10.8473	−	18.7881i	0.413549	−	0.716288i
$689$	7.71235	−	8.56544i	0.293817	−	0.326317i
$690$	−58.2445	+	0.438032i	−2.21733	+	0.0166756i
$691$	0.0104461	+	0.0993877i	0.000397387	+	0.00378089i	0.994719	−	0.102638i	$-0.0327283\pi$
$691$	0.0104461	+	0.0993877i	0.000397387	+	0.00378089i	−0.994321	+	0.106419i	$0.966062\pi$
$692$	9.44125	−	29.0572i	0.358902	−	1.10459i
$693$	24.3639	−	19.1801i	0.925507	−	0.728592i
$694$		−	6.20631i		−	0.235588i
$695$	18.2145	−	1.91442i	0.690914	−	0.0726180i
$696$	−0.549568	−	0.744575i	−0.0208313	−	0.0282231i
$697$	12.5088	+	30.6799i	0.473803	+	1.16209i
$698$	6.76751	−	11.7217i	0.256154	−	0.443672i
$699$	−11.0886	−	12.1304i	−0.419410	−	0.458816i
$700$	4.01430	−	0.952588i	0.151726	−	0.0360044i
$701$	−19.6979	−	6.40023i	−0.743979	−	0.241734i	−0.0875907	−	0.996157i	$-0.527917\pi$
$701$	−19.6979	−	6.40023i	−0.743979	−	0.241734i	−0.656389	+	0.754423i	$0.727917\pi$
$702$	−25.2634	−	13.8355i	−0.953505	−	0.522188i
$703$	1.04652	+	0.465939i	0.0394701	+	0.0175732i
$704$	4.56096	−	43.3947i	0.171898	−	1.63550i
$705$	−43.4695	−	4.23856i	−1.63716	−	0.159633i
$706$		−	8.23155i		−	0.309799i
$707$	0.706271	+	29.9852i	0.0265621	+	1.12771i
$708$	−13.3119	+	6.04719i	−0.500291	+	0.227267i
$709$	−1.44119	+	1.29765i	−0.0541250	+	0.0487343i	−0.695749	−	0.718285i	$-0.744928\pi$
$709$	−1.44119	+	1.29765i	−0.0541250	+	0.0487343i	0.641624	+	0.767019i	$0.278261\pi$
$710$	31.3887	−	70.5002i	1.17800	−	2.64583i
$711$	−28.2106	+	26.1799i	−1.05798	+	0.981822i
$712$	2.05517	+	2.28250i	0.0770209	+	0.0855404i
$713$	−10.5512	−	7.66593i	−0.395147	−	0.287091i
$714$	−6.78032	−	49.6252i	−0.253747	−	1.85718i
$715$	19.6860	−	14.3027i	0.736215	−	0.534892i
$716$	−29.9388	+	13.3296i	−1.11887	+	0.498151i
$717$	40.0017	−	0.300836i	1.49389	−	0.0112349i
$718$	−1.37789	+	13.1097i	−0.0514223	+	0.489250i
$719$	−8.75198	−	19.6573i	−0.326394	−	0.733093i	0.673588	−	0.739107i	$-0.264752\pi$
$719$	−8.75198	−	19.6573i	−0.326394	−	0.733093i	−0.999982	+	0.00601432i	$0.998086\pi$
$720$	13.4125	−	15.3543i	0.499854	−	0.572222i
$721$	7.90625	−	4.81640i	0.294444	−	0.179372i
$722$	−23.2574	+	32.0110i	−0.865549	+	1.19133i
$723$	−17.1533	−	15.2129i	−0.637938	−	0.565773i
$724$	−18.2394	−	31.5916i	−0.677863	−	1.17409i
$725$	0.316987	+	0.141132i	0.0117726	+	0.00524150i
$726$	−11.6645	−	10.3450i	−0.432912	−	0.383940i
$727$	2.70266	+	8.31795i	0.100236	+	0.308496i	0.988583	−	0.150678i	$-0.0481456\pi$
$727$	2.70266	+	8.31795i	0.100236	+	0.308496i	−0.888347	+	0.459173i	$0.848146\pi$
$728$	−5.94320	−	3.24716i	−0.220270	−	0.120348i
$729$	−21.1054	+	16.8393i	−0.781680	+	0.623680i
$730$	−18.8613	−	4.00909i	−0.698087	−	0.148383i
$731$	−38.9911	−	4.09813i	−1.44214	−	0.151575i
$732$	55.7449	+	17.6502i	2.06039	+	0.652372i
$733$	−2.53477	+	2.28231i	−0.0936237	+	0.0842992i	−0.714614	−	0.699519i	$-0.753397\pi$
$733$	−2.53477	+	2.28231i	−0.0936237	+	0.0842992i	0.620990	+	0.783819i	$0.286731\pi$
$734$	1.07515	−	3.30897i	0.0396845	−	0.122136i
$735$	28.7341	−	1.57101i	1.05987	−	0.0579476i
$736$	−43.4056	+	31.5360i	−1.59995	+	1.16243i
$737$	46.6604	+	26.9394i	1.71876	+	0.992326i
$738$	24.3946	−	32.4237i	0.897977	−	1.19353i
$739$	11.3765	+	19.7047i	0.418492	+	0.724849i	0.995788	−	0.0916859i	$-0.0292256\pi$
$739$	11.3765	+	19.7047i	0.418492	+	0.724849i	−0.577296	+	0.816535i	$0.695892\pi$
$740$	−1.35192	−	12.8627i	−0.0496977	−	0.472842i
$741$	−0.263478	−	2.33758i	−0.00967911	−	0.0858732i
$742$	−10.5086	−	22.1817i	−0.385783	−	0.814317i
$743$	30.8807	+	10.0337i	1.13290	+	0.368102i	0.814678	−	0.579913i	$-0.196913\pi$
$743$	30.8807	+	10.0337i	1.13290	+	0.368102i	0.318224	+	0.948015i	$0.396913\pi$
$744$	−3.20788	+	0.707111i	−0.117607	+	0.0259240i
$745$	−5.23032	+	49.7632i	−0.191624	+	1.82318i
$746$	3.50215	+	3.15335i	0.128223	+	0.115452i
$747$	10.4854	−	34.0026i	0.383641	−	1.24409i
$748$	−47.3269	+	15.3774i	−1.73044	+	0.562255i
$749$	−4.76884	+	2.90512i	−0.174249	+	0.106151i
$750$	−7.60436	+	37.1472i	−0.277672	+	1.35642i
$751$	44.9342	−	4.72278i	1.63967	−	0.172337i	0.760665	−	0.649145i	$-0.224873\pi$
$751$	44.9342	−	4.72278i	1.63967	−	0.172337i	0.879007	+	0.476808i	$0.158206\pi$
$752$	−26.3438	+	15.2096i	−0.960658	+	0.554636i
$753$	12.1930	+	36.5877i	0.444339	+	1.33333i
$754$	−1.23505	−	2.77396i	−0.0449777	−	0.101022i
$755$	29.3463	−	9.53518i	1.06802	−	0.347021i
$756$	−26.4341	+	21.1338i	−0.961400	+	0.768629i
$757$	−27.3692	+	37.6705i	−0.994752	+	1.36916i	−0.0662611	+	0.997802i	$0.521107\pi$
$757$	−27.3692	+	37.6705i	−0.994752	+	1.36916i	−0.928491	+	0.371356i	$0.878893\pi$
$758$	3.04153	+	6.83138i	0.110473	+	0.248127i
$759$	0.341322	+	45.3851i	0.0123892	+	1.64737i
$760$	−1.19156	−	0.125238i	−0.0432223	−	0.00454285i
$761$	−1.12089	−	10.6645i	−0.0406321	−	0.386588i	−0.995873	−	0.0907591i	$-0.971071\pi$
$761$	−1.12089	−	10.6645i	−0.0406321	−	0.386588i	0.955241	−	0.295829i	$-0.0955960\pi$
$762$	−10.4919	−	23.0962i	−0.380081	−	0.836686i
$763$	15.3069	+	20.0573i	0.554146	+	0.726124i
$764$	−9.66418	+	29.7433i	−0.349638	+	1.07607i
$765$	−35.2077	−	10.8570i	−1.27294	−	0.392537i
$766$	−15.8155	−	7.04152i	−0.571438	−	0.254420i
$767$	−8.80214	+	1.87095i	−0.317827	+	0.0675562i
$768$	1.05817	−	10.8523i	0.0381833	−	0.391597i
$769$	38.5592	−	12.5286i	1.39048	−	0.451794i	0.484379	−	0.874858i	$-0.339045\pi$
$769$	38.5592	−	12.5286i	1.39048	−	0.451794i	0.906100	+	0.423064i	$0.139045\pi$
$770$	−11.9643	−	50.4188i	−0.431164	−	1.81697i
$771$	0.0733356	+	0.161436i	0.00264112	+	0.00581398i
$772$	−12.5210	−	28.1226i	−0.450640	−	1.01215i
$773$	−19.2737	+	43.2895i	−0.693228	+	1.55701i	0.131394	+	0.991330i	$0.458055\pi$
$773$	−19.2737	+	43.2895i	−0.693228	+	1.55701i	−0.824622	+	0.565685i	$0.808612\pi$
$774$	20.1867	+	43.5645i	0.725595	+	1.56590i
$775$	0.915298	−	0.824138i	0.0328785	−	0.0296039i
$776$			3.75230i			0.134700i
$777$	0.746399	−	10.1161i	0.0267769	−	0.362914i
$778$	41.9290			1.50323
$779$	3.31212	+	0.105152i	0.118669	+	0.00376747i
$780$	−21.3686	+	15.7721i	−0.765118	+	0.564731i
$781$	−54.9349	−	24.4586i	−1.96572	−	0.875197i
$782$	63.4901	+	36.6560i	2.27040	+	1.31082i
$783$	−2.84560	+	0.0642112i	−0.101693	+	0.00229472i
$784$	15.6421	−	12.5311i	0.558648	−	0.447539i
$785$	5.81695	−	4.22626i	0.207616	−	0.150842i
$786$	−58.7792	+	34.5282i	−2.09659	+	1.23158i
$787$	8.16804	+	7.35454i	0.291159	+	0.262161i	0.801746	−	0.597666i	$-0.203905\pi$
$787$	8.16804	+	7.35454i	0.291159	+	0.262161i	−0.510586	+	0.859827i	$0.670572\pi$
$788$	27.7449	−	16.0185i	0.988372	−	0.570637i
$789$	−2.25994	+	23.1773i	−0.0804559	+	0.825133i
$790$	19.8752	+	61.1697i	0.707129	+	2.17632i
$791$	10.6611	+	22.5037i	0.379066	+	0.800138i
$792$	8.60928	+	7.52047i	0.305917	+	0.267228i
$793$	31.1665	+	17.9940i	1.10675	+	0.638985i
$794$	−3.87678	−	18.2388i	−0.137582	−	0.647271i
$795$	−18.0550	+	0.135784i	−0.640344	+	0.00481575i
$796$	24.0128	+	5.10409i	0.851113	+	0.180910i
$797$	24.9683	−	18.1405i	0.884422	−	0.642570i	−0.0499957	−	0.998749i	$-0.515921\pi$
$797$	24.9683	−	18.1405i	0.884422	−	0.642570i	0.934418	+	0.356179i	$0.115921\pi$
$798$	−4.81013	−	1.39928i	−0.170277	−	0.0495338i
$799$	44.4738	+	32.3121i	1.57337	+	1.14312i
$800$	−2.06084	−	4.62873i	−0.0728618	−	0.163650i
$801$	9.37901	−	1.12864i	0.331391	−	0.0398784i
$802$	−3.42965	−	1.52698i	−0.121105	−	0.0539195i
$803$	−3.12395	+	14.6970i	−0.110242	+	0.518646i
$804$	−51.1479	−	29.0196i	−1.80385	−	1.02344i
$805$	−23.9490	+	34.6504i	−0.844092	+	1.22127i
$806$	−10.7782			−0.379647
$807$	2.60363	−	0.573917i	0.0916522	−	0.0202028i
$808$	−10.8159	+	2.29900i	−0.380503	+	0.0808784i
$809$	5.46565	−	6.07021i	0.192162	−	0.213417i	−0.639363	−	0.768905i	$-0.720802\pi$
$809$	5.46565	−	6.07021i	0.192162	−	0.213417i	0.831525	+	0.555488i	$0.187468\pi$
$810$	10.7045	+	43.8333i	0.376118	+	1.54015i
$811$			27.6300i			0.970219i	0.874453	+	0.485109i	$0.161220\pi$
$811$			27.6300i			0.970219i	−0.874453	+	0.485109i	$0.838780\pi$
$812$	−3.56679	+	0.0840122i	−0.125170	+	0.00294825i
$813$	−21.6727	−	12.2963i	−0.760093	−	0.431251i
$814$	−18.1656	+	1.90928i	−0.636704	+	0.0669203i
$815$	−29.6896	+	6.31072i	−1.03998	+	0.221055i
$816$	−24.3446	+	8.11296i	−0.852232	+	0.284010i
$817$	−1.96064	+	3.39593i	−0.0685942	+	0.118809i
$818$	50.3497	−	36.5812i	1.76043	−	1.27903i
$819$	−18.6879	+	9.20009i	−0.653009	+	0.321477i
$820$	−17.6691	−	32.9782i	−0.617032	−	1.15165i
$821$	28.3230	+	16.3523i	0.988479	+	0.570699i	0.904819	−	0.425796i	$-0.140006\pi$
$821$	28.3230	+	16.3523i	0.988479	+	0.570699i	0.0836598	+	0.996494i	$0.473339\pi$
$822$	66.5974	+	21.0864i	2.32285	+	0.735473i
$823$	22.4711	−	12.9737i	0.783294	−	0.452235i	−0.0543022	−	0.998525i	$-0.517293\pi$
$823$	22.4711	−	12.9737i	0.783294	−	0.452235i	0.837597	+	0.546289i	$0.183960\pi$
$824$	2.28375	+	2.53636i	0.0795583	+	0.0883584i
$825$	−4.19908	−	0.859588i	−0.146193	−	0.0299270i
$826$	−3.54180	+	18.8332i	−0.123235	+	0.655292i
$827$	9.19718	+	6.68214i	0.319817	+	0.232361i	0.736098	−	0.676876i	$-0.236666\pi$
$827$	9.19718	+	6.68214i	0.319817	+	0.232361i	−0.416280	+	0.909236i	$0.636666\pi$
$828$	−0.745060	−	49.5320i	−0.0258926	−	1.72136i
$829$	−41.2335	+	23.8062i	−1.43210	+	0.826822i	−0.997281	−	0.0736972i	$-0.976520\pi$
$829$	−41.2335	+	23.8062i	−1.43210	+	0.826822i	−0.434817	+	0.900519i	$0.643187\pi$
$830$	−44.1906	−	39.7894i	−1.53388	−	1.38111i
$831$	−0.538530	+	5.52302i	−0.0186814	+	0.191591i
$832$	−9.05775	+	27.8769i	−0.314021	+	0.966458i
$833$	−32.1857	−	16.6133i	−1.11517	−	0.575616i
$834$	3.16203	+	28.0536i	0.109492	+	0.971416i
$835$	−9.74039	+	8.77029i	−0.337080	+	0.303508i
$836$	−0.520252	+	4.94987i	−0.0179933	+	0.171195i
$837$	−3.90010	+	9.32015i	−0.134807	+	0.322151i
$838$	56.3928	−	5.92712i	1.94806	−	0.204749i
$839$	−30.7925	+	42.3823i	−1.06308	+	1.46320i	−0.186183	+	0.982515i	$0.559612\pi$
$839$	−30.7925	+	42.3823i	−1.06308	+	1.46320i	−0.876894	+	0.480684i	$0.840388\pi$
$840$	2.52705	+	10.3037i	0.0871916	+	0.355511i
$841$	23.2187	+	16.8694i	0.800646	+	0.581704i
$842$	−44.4179	+	19.7761i	−1.53074	+	0.681530i
$843$	−13.2407	+	41.8182i	−0.456034	+	1.44030i
$844$	7.89168	+	7.10570i	0.271643	+	0.244588i
$845$	13.2548	−	5.90141i	0.455978	−	0.203015i
$846$	6.02940	−	67.0529i	0.207295	−	2.30533i
$847$	−10.9702	+	2.60321i	−0.376941	+	0.0894475i
$848$	−10.1736	+	7.39155i	−0.349363	+	0.253827i
$849$	−20.7410	−	18.3947i	−0.711830	−	0.631306i
$850$	−4.63264	+	5.14507i	−0.158898	+	0.176475i
$851$	11.0337	+	9.93482i	0.378232	+	0.340561i
$852$	60.1586	+	26.2440i	2.06100	+	0.899105i
$853$	41.3135	−	13.4236i	1.41455	−	0.459615i	0.500683	−	0.865631i	$-0.333082\pi$
$853$	41.3135	−	13.4236i	1.41455	−	0.459615i	0.913866	+	0.406016i	$0.133082\pi$
$854$	60.9237	−	46.4943i	2.08477	−	1.59100i
$855$	−2.42430	+	2.77529i	−0.0829093	+	0.0949129i
$856$	−1.37750	−	1.52987i	−0.0470819	−	0.0522897i
$857$	−2.70483	+	0.574929i	−0.0923951	+	0.0196392i	−0.253877	−	0.967236i	$-0.581706\pi$
$857$	−2.70483	+	0.574929i	−0.0923951	+	0.0196392i	0.161482	+	0.986876i	$0.448373\pi$
$858$	22.2744	+	30.1782i	0.760436	+	1.03027i
$859$	−44.8544	+	4.71438i	−1.53041	+	0.160853i	−0.831972	−	0.554817i	$-0.812788\pi$
$859$	−44.8544	+	4.71438i	−1.53041	+	0.160853i	−0.698439	+	0.715670i	$0.746122\pi$
$860$	44.2721			1.50967
$861$	−9.04881	−	27.9127i	−0.308383	−	0.951262i
$862$	−17.7281			−0.603822
$863$	−4.99964	+	0.525483i	−0.170190	+	0.0178877i	−0.189240	−	0.981931i	$-0.560602\pi$
$863$	−4.99964	+	0.525483i	−0.170190	+	0.0178877i	0.0190503	+	0.999819i	$0.493936\pi$
$864$	31.5067	+	27.1070i	1.07188	+	0.922200i
$865$	−28.8132	+	6.12443i	−0.979677	+	0.208237i
$866$	22.8379	+	25.3641i	0.776064	+	0.861906i
$867$	11.4219	+	12.4950i	0.387907	+	0.424352i
$868$	−4.87712	+	11.6874i	−0.165540	+	0.396695i
$869$	47.6644	−	15.4871i	1.61690	−	0.525364i
$870$	−1.90198	+	4.35986i	−0.0644831	+	0.147813i
$871$	−26.8972	−	24.2184i	−0.911378	−	0.820609i
$872$	−6.22407	+	6.91253i	−0.210773	+	0.234088i
$873$	9.43773	+	6.64236i	0.319419	+	0.224810i
$874$	5.93213	−	4.30994i	0.200657	−	0.145786i
$875$	18.8226	+	19.9397i	0.636321	+	0.674084i
$876$	3.28894	−	16.0665i	0.111123	−	0.542835i
$877$	−8.87487	+	3.95135i	−0.299683	+	0.133427i	−0.551070	−	0.834459i	$-0.685780\pi$
$877$	−8.87487	+	3.95135i	−0.299683	+	0.133427i	0.251387	+	0.967887i	$0.419113\pi$
$878$	−54.0680	−	48.6830i	−1.82471	−	1.64297i
$879$	19.5106	+	6.17755i	0.658076	+	0.208364i
$880$	−24.2533	+	10.7983i	−0.817579	+	0.364010i
$881$	−24.0782	−	17.4939i	−0.811216	−	0.589383i	0.102967	−	0.994685i	$-0.467166\pi$
$881$	−24.0782	−	17.4939i	−0.811216	−	0.589383i	−0.914183	+	0.405302i	$0.867166\pi$
$882$	2.75464	+	44.2725i	0.0927537	+	1.49073i
$883$	−26.0379	+	35.8380i	−0.876243	+	1.20605i	0.101204	+	0.994866i	$0.467731\pi$
$883$	−26.0379	+	35.8380i	−0.876243	+	1.20605i	−0.977447	+	0.211180i	$0.932269\pi$
$884$	33.2454	−	3.49424i	1.11816	−	0.117524i
$885$	11.4664	+	8.19982i	0.385440	+	0.275634i
$886$	−5.03331	+	47.8887i	−0.169097	+	1.60885i
$887$	−15.4747	+	13.9335i	−0.519591	+	0.467842i	−0.886706	−	0.462334i	$-0.847012\pi$
$887$	−15.4747	+	13.9335i	−0.519591	+	0.467842i	0.367115	+	0.930176i	$0.380346\pi$
$888$	3.71606	−	0.418852i	0.124703	−	0.0140557i
$889$	−18.0288	−	3.39051i	−0.604666	−	0.113714i
$890$	4.87843	−	15.0143i	0.163526	−	0.503280i
$891$	34.1556	−	8.34112i	1.14426	−	0.279438i
$892$	12.4032	+	11.1679i	0.415290	+	0.373929i
$893$	4.76162	−	2.74912i	0.159342	−	0.0919960i
$894$	−76.7656	−	7.48515i	−2.56742	−	0.250341i
$895$	25.5624	+	18.5722i	0.854457	+	0.620799i
$896$	15.2459	+	13.0908i	0.509331	+	0.437332i
$897$	6.11454	−	29.8694i	0.204158	−	0.997312i
$898$	20.6691	+	22.9554i	0.689737	+	0.766030i
$899$	−0.922385	+	0.532539i	−0.0307633	+	0.0177612i
$900$	4.59007	+	0.903717i	0.153002	+	0.0301239i
$901$	19.6810	+	11.3628i	0.655670	+	0.378551i
$902$	−46.5741	+	24.9535i	−1.55075	+	0.830862i
$903$	34.1711	+	6.16056i	1.13714	+	0.205011i
$904$	−7.42695	+	5.39600i	−0.247017	+	0.179468i
$905$	−17.5853	+	30.4587i	−0.584557	+	1.01248i
$906$	15.0377	+	45.1238i	0.499594	+	1.49914i
$907$	−29.3440	+	6.23726i	−0.974352	+	0.207105i	−0.667465	−	0.744641i	$-0.732621\pi$
$907$	−29.3440	+	6.23726i	−0.974352	+	0.207105i	−0.306887	+	0.951746i	$0.599287\pi$
$908$	8.25131	−	0.867247i	0.273829	−	0.0287806i
$909$	−13.3641	+	31.2738i	−0.443258	+	1.03729i
$910$	0.819687	+	34.8004i	0.0271724	+	1.15362i
$911$			27.3092i			0.904793i	0.891817	+	0.452396i	$0.149431\pi$
$911$			27.3092i			0.904793i	−0.891817	+	0.452396i	$0.850569\pi$
$912$	−0.249074	+	2.55443i	−0.00824766	+	0.0845857i
$913$	−31.0046	+	34.4340i	−1.02610	+	1.13960i
$914$	−35.9049	+	7.63181i	−1.18763	+	0.252438i
$915$	−12.1355	−	55.0539i	−0.401187	−	1.82002i
$916$	59.7365			1.97375
$917$	−3.99714	+	49.1358i	−0.131997	+	1.62261i
$918$	16.3269	−	54.3950i	0.538867	−	1.79530i
$919$	−7.90369	+	37.1839i	−0.260719	+	1.22659i	0.631641	+	0.775261i	$0.282382\pi$
$919$	−7.90369	+	37.1839i	−0.260719	+	1.22659i	−0.892360	+	0.451324i	$0.850952\pi$
$920$	−14.1861	−	6.31607i	−0.467702	−	0.208235i
$921$	−0.0741643	−	9.86152i	−0.00244380	−	0.324948i
$922$	19.3143	+	43.3807i	0.636084	+	1.42867i
$923$	32.6807	+	23.7439i	1.07570	+	0.781541i
$924$	42.8028	−	10.4977i	1.40811	−	0.345348i
$925$	−1.13436	+	0.824159i	−0.0372974	+	0.0270982i
$926$	47.6514	+	10.1286i	1.56592	+	0.332847i
$927$	10.4221	−	1.25416i	0.342308	−	0.0411922i
$928$	0.910968	+	4.28577i	0.0299040	+	0.140687i
$929$	5.92668	+	3.42177i	0.194448	+	0.112265i	0.594063	−	0.804418i	$-0.297523\pi$
$929$	5.92668	+	3.42177i	0.194448	+	0.112265i	−0.399615	+	0.916683i	$0.630856\pi$
$930$	11.3918	+	12.4621i	0.373552	+	0.408649i
$931$	−2.82731	+	2.26499i	−0.0926614	+	0.0742320i
$932$	−7.21831	−	22.2157i	−0.236444	−	0.727699i
$933$	−24.8511	−	2.42315i	−0.813590	−	0.0793304i
$934$	−3.94577	+	2.27809i	−0.129110	+	0.0745415i
$935$	35.6545	+	32.1035i	1.16603	+	1.04990i
$936$	−4.60665	−	6.14402i	−0.150573	−	0.200823i
$937$	−16.8055	+	12.2099i	−0.549013	+	0.398881i	−0.827421	−	0.561582i	$-0.810193\pi$
$937$	−16.8055	+	12.2099i	−0.549013	+	0.398881i	0.278409	+	0.960463i	$0.410193\pi$
$938$	−69.6552	+	32.9992i	−2.27432	+	1.07746i
$939$	18.9295	+	3.87503i	0.617739	+	0.126457i
$940$	−53.7597	−	31.0382i	−1.75345	−	1.01235i
$941$	11.3703	+	5.06238i	0.370661	+	0.165029i	0.583609	−	0.812035i	$-0.301640\pi$
$941$	11.3703	+	5.06238i	0.370661	+	0.165029i	−0.212949	+	0.977063i	$0.568307\pi$
$942$	6.58179	+	8.91725i	0.214446	+	0.290540i
$943$	40.4057	+	14.5616i	1.31579	+	0.474191i
$944$	9.81804			0.319550
$945$	30.3891	+	11.8837i	0.988558	+	0.386577i
$946$		−	62.5241i		−	2.03283i
$947$	−8.15134	+	7.33950i	−0.264883	+	0.238502i	−0.790860	−	0.611997i	$-0.790366\pi$
$947$	−8.15134	+	7.33950i	−0.264883	+	0.238502i	0.525977	+	0.850499i	$0.323700\pi$
$948$	−51.8954	+	17.2944i	−1.68548	+	0.561696i
$949$	4.10539	−	9.22085i	0.133266	−	0.299321i
$950$	0.281650	+	0.632595i	0.00913792	+	0.0205241i
$951$	8.74094	−	3.97075i	0.283444	−	0.128760i
$952$	3.82617	−	12.7933i	0.124007	−	0.414632i
$953$	−25.2226	+	8.19532i	−0.817040	+	0.265473i	−0.687577	−	0.726112i	$-0.741326\pi$
$953$	−25.2226	+	8.19532i	−0.817040	+	0.265473i	−0.129464	+	0.991584i	$0.541326\pi$
$954$	−0.418594	−	27.8283i	−0.0135525	−	0.900976i
$955$	29.4935	−	6.26904i	0.954388	−	0.202861i
$956$	51.9407	+	23.1255i	1.67988	+	0.747932i
$957$	3.39727	+	1.48205i	0.109818	+	0.0479079i
$958$	20.6356	−	63.5099i	0.666706	−	2.05191i
$959$	40.1586	−	30.6473i	1.29679	−	0.989653i
$960$	41.8054	−	18.9910i	1.34926	−	0.612931i
$961$	−2.84520	−	27.0703i	−0.0917807	−	0.873235i
$962$	12.2030	+	1.28258i	0.393440	+	0.0413522i
$963$	−6.28636	+	0.756478i	−0.202575	+	0.0243772i
$964$	−13.2543	−	29.7696i	−0.426892	−	0.958814i
$965$	−17.4455	+	24.0116i	−0.561590	+	0.772962i
$966$	−53.6877	−	36.5133i	−1.72737	−	1.17480i
$967$	7.31377	−	2.37639i	0.235195	−	0.0764195i	−0.189048	−	0.981968i	$-0.560540\pi$
$967$	7.31377	−	2.37639i	0.235195	−	0.0764195i	0.424243	+	0.905548i	$0.360540\pi$
$968$	−1.69066	−	3.79727i	−0.0543397	−	0.122049i
$969$	4.40028	−	1.46641i	0.141357	−	0.0471080i
$970$	16.7028	−	9.64335i	0.536294	−	0.309629i
$971$	−44.3520	+	4.66159i	−1.42332	+	0.149597i	−0.784678	−	0.619903i	$-0.787172\pi$
$971$	−44.3520	+	4.66159i	−1.42332	+	0.149597i	−0.638646	+	0.769501i	$0.720505\pi$
$972$	−37.2101	+	9.38414i	−1.19352	+	0.300996i
$973$	17.9160	+	9.78869i	0.574360	+	0.313811i
$974$	60.6624	−	19.7104i	1.94375	−	0.631562i
$975$	2.63909	+	1.15130i	0.0845185	+	0.0368710i
$976$	−29.1791	−	26.2730i	−0.934000	−	0.840977i
$977$	−2.83355	+	26.9594i	−0.0906533	+	0.862508i	0.850828	+	0.525444i	$0.176101\pi$
$977$	−2.83355	+	26.9594i	−0.0906533	+	0.862508i	−0.941482	+	0.337064i	$0.890566\pi$
$978$	−10.0715	−	45.6904i	−0.322051	−	1.46102i
$979$	−11.6994	−	3.80135i	−0.373913	−	0.121492i
$980$	38.1066	+	14.8582i	1.21727	+	0.474629i
$981$	6.36838	+	27.8913i	0.203327	+	0.890501i
$982$	−6.94739	−	66.1000i	−0.221700	−	2.10933i
$983$	2.57532	+	4.46059i	0.0821401	+	0.142271i	0.904169	−	0.427175i	$-0.140491\pi$
$983$	2.57532	+	4.46059i	0.0821401	+	0.142271i	−0.822029	+	0.569446i	$0.807158\pi$
$984$	9.49658	−	5.18039i	0.302740	−	0.165145i
$985$	−26.7500	−	15.4441i	−0.852324	−	0.492090i
$986$	4.84360	−	3.51908i	0.154252	−	0.112070i
$987$	−37.1750	−	31.4374i	−1.18329	−	1.00066i
$988$	1.03318	−	3.17981i	0.0328700	−	0.101163i
$989$	−37.7690	+	34.0073i	−1.20098	+	1.08137i
$990$	11.3505	−	57.6504i	0.360742	−	1.83225i
$991$	−53.6950	−	5.64357i	−1.70568	−	0.179274i	−0.799067	−	0.601242i	$-0.794673\pi$
$991$	−53.6950	−	5.64357i	−1.70568	−	0.179274i	−0.906611	+	0.421968i	$0.861339\pi$
$992$	15.2127	+	3.23356i	0.483004	+	0.102666i
$993$	−55.4199	+	6.24659i	−1.75870	+	0.198229i
$994$	73.4659	−	44.7546i	2.33020	−	1.41953i
$995$	−7.31410	−	22.5105i	−0.231873	−	0.713630i
$996$	33.5568	−	37.8370i	1.06329	−	1.19891i
$997$	24.5555	+	10.9328i	0.777681	+	0.346246i	0.756894	−	0.653538i	$-0.226716\pi$
$997$	24.5555	+	10.9328i	0.777681	+	0.346246i	0.0207873	+	0.999784i	$0.493383\pi$
$998$	−22.7208	−	39.3535i	−0.719213	−	1.24571i
$999$	5.52472	−	10.0880i	0.174794	−	0.319171i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	861.2.bw.a.824.92	yes	864
3.2	odd	2	inner	861.2.bw.a.824.17	yes	864
7.3	odd	6	inner	861.2.bw.a.332.17	yes	864
21.17	even	6	inner	861.2.bw.a.332.92	yes	864
41.31	even	10	inner	861.2.bw.a.236.92	yes	864
123.113	odd	10	inner	861.2.bw.a.236.17	✓	864
287.31	odd	30	inner	861.2.bw.a.605.17	yes	864
861.605	even	30	inner	861.2.bw.a.605.92	yes	864

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
861.2.bw.a.236.17	✓	864	123.113	odd	10	inner
861.2.bw.a.236.92	yes	864	41.31	even	10	inner
861.2.bw.a.332.17	yes	864	7.3	odd	6	inner
861.2.bw.a.332.92	yes	864	21.17	even	6	inner
861.2.bw.a.605.17	yes	864	287.31	odd	30	inner
861.2.bw.a.605.92	yes	864	861.605	even	30	inner
861.2.bw.a.824.17	yes	864	3.2	odd	2	inner
861.2.bw.a.824.92	yes	864	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 861 = 3 \cdot 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	861.bw (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(2.10072 - 0.220794i) q^{2} +(1.39356 - 1.02858i) q^{3} +(2.40798 - 0.511831i) q^{4} +(-1.58817 - 1.76385i) q^{5} +(2.70038 - 2.46846i) q^{6} +(-0.338439 - 2.62402i) q^{7} +(0.927655 - 0.301413i) q^{8} +(0.884034 - 2.86679i) q^{9} +O(q^{10})\)	\(q+(2.10072 - 0.220794i) q^{2} +(1.39356 - 1.02858i) q^{3} +(2.40798 - 0.511831i) q^{4} +(-1.58817 - 1.76385i) q^{5} +(2.70038 - 2.46846i) q^{6} +(-0.338439 - 2.62402i) q^{7} +(0.927655 - 0.301413i) q^{8} +(0.884034 - 2.86679i) q^{9} +(-3.72575 - 3.35468i) q^{10} +(-2.61402 + 2.90317i) q^{11} +(2.82920 - 3.19007i) q^{12} +(2.12311 - 1.54253i) q^{13} +(-1.29033 - 5.43759i) q^{14} +(-4.02748 - 0.824461i) q^{15} +(-2.61569 + 1.16458i) q^{16} +(3.84529 + 3.46231i) q^{17} +(1.22413 - 6.21751i) q^{18} +(0.472784 - 0.210497i) q^{19} +(-4.72707 - 3.43442i) q^{20} +(-3.17065 - 3.30862i) q^{21} +(-4.85032 + 6.67590i) q^{22} +(6.67084 - 0.701133i) q^{23} +(0.982717 - 1.37421i) q^{24} +(-0.0662131 + 0.629975i) q^{25} +(4.11947 - 3.70919i) q^{26} +(-1.71678 - 4.90435i) q^{27} +(-2.15801 - 6.14534i) q^{28} +(0.169272 - 0.520964i) q^{29} +(-8.64264 - 0.842715i) q^{30} +(-1.44495 - 1.30104i) q^{31} +(-6.92712 + 3.99938i) q^{32} +(-0.656657 + 6.73448i) q^{33} +(8.84233 + 6.42433i) q^{34} +(-4.09086 + 4.76435i) q^{35} +(0.661419 - 7.35564i) q^{36} +(1.48113 + 1.64496i) q^{37} +(0.946711 - 0.546584i) q^{38} +(1.37207 - 4.33340i) q^{39} +(-2.00492 - 1.15754i) q^{40} +(5.76396 + 2.78869i) q^{41} +(-7.39118 - 6.25041i) q^{42} +(-6.12990 + 4.45363i) q^{43} +(-4.80857 + 8.32869i) q^{44} +(-6.46057 + 2.99366i) q^{45} +(13.8588 - 2.94577i) q^{46} +(10.5659 - 1.11052i) q^{47} +(-2.44726 + 4.31336i) q^{48} +(-6.77092 + 1.77614i) q^{49} +1.33802i q^{50} +(8.91992 + 0.869751i) q^{51} +(4.32288 - 4.80104i) q^{52} +(4.29602 - 0.913146i) q^{53} +(-4.68932 - 9.92361i) q^{54} +9.27226 q^{55} +(-1.10487 - 2.33217i) q^{56} +(0.442341 - 0.779639i) q^{57} +(0.240566 - 1.13177i) q^{58} +(-3.13256 - 1.39471i) q^{59} +(-10.1201 + 0.0761087i) q^{60} +(5.57771 + 12.5277i) q^{61} +(-3.32270 - 2.41408i) q^{62} +(-7.82169 - 1.34948i) q^{63} +(-9.03610 + 6.56511i) q^{64} +(-6.09265 - 1.29503i) q^{65} +(0.107486 + 14.2922i) q^{66} +(-2.86747 - 13.4904i) q^{67} +(11.0315 + 6.36903i) q^{68} +(8.57506 - 7.83859i) q^{69} +(-7.54180 + 10.9118i) q^{70} +(4.75666 + 14.6395i) q^{71} +(-0.0440107 - 2.92585i) q^{72} +(3.33086 - 1.92307i) q^{73} +(3.47464 + 3.12858i) q^{74} +(0.555710 + 0.946016i) q^{75} +(1.03071 - 0.748858i) q^{76} +(8.50264 + 5.87669i) q^{77} +(1.92553 - 9.40621i) q^{78} +(-11.1101 - 6.41445i) q^{79} +(6.20830 + 2.76411i) q^{80} +(-7.43697 - 5.06868i) q^{81} +(12.7242 + 4.58560i) q^{82} +11.8609 q^{83} +(-9.32831 - 6.34423i) q^{84} -12.2812i q^{85} +(-11.8939 + 10.7093i) q^{86} +(-0.299965 - 0.900107i) q^{87} +(-1.54986 + 3.48104i) q^{88} +(1.28077 + 2.87665i) q^{89} +(-12.9109 + 7.71530i) q^{90} +(-4.76616 - 5.04902i) q^{91} +(15.7044 - 5.10265i) q^{92} +(-3.35186 - 0.326828i) q^{93} +(21.9508 - 4.66578i) q^{94} +(-1.12215 - 0.499613i) q^{95} +(-5.53969 + 12.6985i) q^{96} +(-1.18877 + 3.65867i) q^{97} +(-13.8316 + 5.22615i) q^{98} +(6.01188 + 10.0604i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 864 q - 110 q^{4} - 20 q^{7} - 12 q^{9}+O(q^{10}) \) 864 * q - 110 * q^4 - 20 * q^7 - 12 * q^9	\( 864 q - 110 q^{4} - 20 q^{7} - 12 q^{9} - 18 q^{10} - 15 q^{12} - 50 q^{15} + 82 q^{16} - 15 q^{18} - 30 q^{19} - 14 q^{21} + 30 q^{24} + 78 q^{25} + 15 q^{30} - 18 q^{31} + 36 q^{33} + 16 q^{36} - 10 q^{37} - 2 q^{39} - 144 q^{40} - 24 q^{42} - 8 q^{43} + 69 q^{45} - 12 q^{46} + 52 q^{49} - 18 q^{51} - 30 q^{52} + 15 q^{54} - 38 q^{57} - 10 q^{58} - 126 q^{61} + 65 q^{63} - 16 q^{64} - 70 q^{67} - 260 q^{70} - 33 q^{72} - 48 q^{73} + 60 q^{75} - 2 q^{78} + 68 q^{81} - 150 q^{82} + 115 q^{84} - 138 q^{87} + 30 q^{88} + 64 q^{91} - 15 q^{93} + 60 q^{94} - 30 q^{99}+O(q^{100}) \) 864 * q - 110 * q^4 - 20 * q^7 - 12 * q^9 - 18 * q^10 - 15 * q^12 - 50 * q^15 + 82 * q^16 - 15 * q^18 - 30 * q^19 - 14 * q^21 + 30 * q^24 + 78 * q^25 + 15 * q^30 - 18 * q^31 + 36 * q^33 + 16 * q^36 - 10 * q^37 - 2 * q^39 - 144 * q^40 - 24 * q^42 - 8 * q^43 + 69 * q^45 - 12 * q^46 + 52 * q^49 - 18 * q^51 - 30 * q^52 + 15 * q^54 - 38 * q^57 - 10 * q^58 - 126 * q^61 + 65 * q^63 - 16 * q^64 - 70 * q^67 - 260 * q^70 - 33 * q^72 - 48 * q^73 + 60 * q^75 - 2 * q^78 + 68 * q^81 - 150 * q^82 + 115 * q^84 - 138 * q^87 + 30 * q^88 + 64 * q^91 - 15 * q^93 + 60 * q^94 - 30 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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