LMFDB - Embedded newform 676.2.l.l.427.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [676,2,Mod(19,676)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(676, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 5]))

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

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

chi := DirichletCharacter("676.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 676 = 2^{2} \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	676.l (of order $12$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.39788717664$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	16.0.2353561680715186176.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 2 x^{14} + 41 x^{12} - 92 x^{11} + 66 x^{10} - 104 x^{9} + 291 x^{8} - 388 x^{7} + \cdots + 4 $ x^16 - 4x^15 + 2x^14 + 41x^12 - 92x^11 + 66x^10 - 104x^9 + 291x^8 - 388x^7 + 366x^6 - 344x^5 + 286x^4 - 184x^3 + 84x^2 - 24x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 52)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			427.4
Root			$2.07391 - 0.620024i$ of defining polynomial
Character	$\chi$	$=$	676.427
Dual form			676.2.l.l.19.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.29769 + 0.562129i) q^{2} +(-2.42308 + 1.39897i) q^{3} +(1.36802 + 1.45894i) q^{4} +(-0.707107 - 0.707107i) q^{5} +(-3.93082 + 0.453347i) q^{6} +(-2.70260 + 0.724158i) q^{7} +(0.955161 + 2.66227i) q^{8} +(2.41421 - 4.18154i) q^{9} +O(q^{10})$	\(q+(1.29769 + 0.562129i) q^{2} +(-2.42308 + 1.39897i) q^{3} +(1.36802 + 1.45894i) q^{4} +(-0.707107 - 0.707107i) q^{5} +(-3.93082 + 0.453347i) q^{6} +(-2.70260 + 0.724158i) q^{7} +(0.955161 + 2.66227i) q^{8} +(2.41421 - 4.18154i) q^{9} +(-0.520123 - 1.31509i) q^{10} +(-0.424202 + 1.58314i) q^{11} +(-5.35584 - 1.62132i) q^{12} +(-3.91421 - 0.579471i) q^{14} +(2.70260 + 0.724158i) q^{15} +(-0.257031 + 3.99173i) q^{16} +(-5.04757 - 2.91421i) q^{17} +(5.48348 - 4.06926i) q^{18} +(-0.599912 - 2.23890i) q^{19} +(0.0642909 - 1.99897i) q^{20} +(5.53553 - 5.53553i) q^{21} +(-1.44042 + 1.81598i) q^{22} +(-1.97844 - 3.42675i) q^{23} +(-6.03885 - 5.11465i) q^{24} -4.00000i q^{25} +5.11582i q^{27} +(-4.75372 - 2.95227i) q^{28} +(0.292893 + 0.507306i) q^{29} +(3.10007 + 2.45894i) q^{30} +(-3.95687 + 3.95687i) q^{31} +(-2.57742 + 5.03557i) q^{32} +(-1.18689 - 4.42953i) q^{33} +(-4.91203 - 6.61914i) q^{34} +(2.42308 + 1.39897i) q^{35} +(9.40333 - 2.19824i) q^{36} +(2.56632 + 0.687644i) q^{37} +(0.480049 - 3.24264i) q^{38} +(1.20711 - 2.55791i) q^{40} +(-1.55291 + 5.79555i) q^{41} +(10.2951 - 4.07175i) q^{42} +(2.55791 - 4.43043i) q^{43} +(-2.89003 + 1.54689i) q^{44} +(-4.66390 + 1.24969i) q^{45} +(-0.641130 - 5.55902i) q^{46} +(-1.97844 - 1.97844i) q^{47} +(-4.96149 - 10.0319i) q^{48} +(0.717439 - 0.414214i) q^{49} +(2.24852 - 5.19078i) q^{50} +16.3075 q^{51} -0.242641 q^{53} +(-2.87575 + 6.63877i) q^{54} +(1.41941 - 0.819496i) q^{55} +(-4.50932 - 6.50334i) q^{56} +(4.58579 + 4.58579i) q^{57} +(0.0949146 + 0.822972i) q^{58} +(-3.16629 + 0.848404i) q^{59} +(2.64070 + 4.93360i) q^{60} +(-0.414214 + 0.717439i) q^{61} +(-7.35909 + 2.91054i) q^{62} +(-3.49655 + 13.0493i) q^{63} +(-6.17534 + 5.08579i) q^{64} +(0.949747 - 6.41536i) q^{66} +(-3.82205 - 1.02411i) q^{67} +(-2.65351 - 11.3508i) q^{68} +(9.58783 + 5.53553i) q^{69} +(2.35802 + 3.17751i) q^{70} +(1.92398 + 7.18040i) q^{71} +(13.4383 + 2.43324i) q^{72} +(-9.65685 + 9.65685i) q^{73} +(2.94376 + 2.33496i) q^{74} +(5.59587 + 9.69232i) q^{75} +(2.44574 - 3.93811i) q^{76} -4.58579i q^{77} +9.55274i q^{79} +(3.00433 - 2.64083i) q^{80} +(0.0857864 + 0.148586i) q^{81} +(-5.27306 + 6.64792i) q^{82} +(-6.75481 + 6.75481i) q^{83} +(15.6488 + 0.503297i) q^{84} +(1.50851 + 5.62983i) q^{85} +(5.80985 - 4.31147i) q^{86} +(-1.41941 - 0.819496i) q^{87} +(-4.61993 + 0.382817i) q^{88} +(-8.52761 - 2.28497i) q^{89} +(-6.75481 - 1.00000i) q^{90} +(2.29289 - 7.57430i) q^{92} +(4.05229 - 15.1234i) q^{93} +(-1.45527 - 3.67954i) q^{94} +(-1.15894 + 2.00735i) q^{95} +(-0.799300 - 15.8073i) q^{96} +(-0.565826 + 0.151613i) q^{97} +(1.16386 - 0.134230i) q^{98} +(5.59587 + 5.59587i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{2} - 8 q^{6} - 8 q^{8} + 16 q^{9}+O(q^{10}) $ 16 * q + 4 * q^2 - 8 * q^6 - 8 * q^8 + 16 * q^9	$ 16 q + 4 q^{2} - 8 q^{6} - 8 q^{8} + 16 q^{9} - 40 q^{14} + 4 q^{16} + 8 q^{20} + 32 q^{21} - 24 q^{22} - 32 q^{24} - 12 q^{28} + 16 q^{29} + 4 q^{32} - 8 q^{33} + 8 q^{34} + 32 q^{37} + 8 q^{40} - 4 q^{42} - 56 q^{44} - 16 q^{45} + 20 q^{46} + 44 q^{48} + 16 q^{50} + 64 q^{53} + 32 q^{54} + 96 q^{57} - 12 q^{58} - 24 q^{60} + 16 q^{61} - 64 q^{66} - 44 q^{68} + 16 q^{70} - 16 q^{72} - 64 q^{73} - 44 q^{74} - 32 q^{76} - 16 q^{80} + 24 q^{81} + 48 q^{84} - 16 q^{85} + 64 q^{86} - 16 q^{89} + 48 q^{92} - 32 q^{93} - 20 q^{94} - 48 q^{96} + 8 q^{97} + 16 q^{98}+O(q^{100}) $ 16 * q + 4 * q^2 - 8 * q^6 - 8 * q^8 + 16 * q^9 - 40 * q^14 + 4 * q^16 + 8 * q^20 + 32 * q^21 - 24 * q^22 - 32 * q^24 - 12 * q^28 + 16 * q^29 + 4 * q^32 - 8 * q^33 + 8 * q^34 + 32 * q^37 + 8 * q^40 - 4 * q^42 - 56 * q^44 - 16 * q^45 + 20 * q^46 + 44 * q^48 + 16 * q^50 + 64 * q^53 + 32 * q^54 + 96 * q^57 - 12 * q^58 - 24 * q^60 + 16 * q^61 - 64 * q^66 - 44 * q^68 + 16 * q^70 - 16 * q^72 - 64 * q^73 - 44 * q^74 - 32 * q^76 - 16 * q^80 + 24 * q^81 + 48 * q^84 - 16 * q^85 + 64 * q^86 - 16 * q^89 + 48 * q^92 - 32 * q^93 - 20 * q^94 - 48 * q^96 + 8 * q^97 + 16 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/676\mathbb{Z}\right)^\times$.

$n$	$339$	$509$
$\chi(n)$	$-1$	$e\left(\frac{7}{12}\right)$

Coefficient data

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

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

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

$2$	1.29769	+	0.562129i	0.917609	+	0.397485i
$2$	1.29769	+	0.562129i	0.917609	+	0.397485i
$3$	−2.42308	+	1.39897i	−1.39897	+	0.807694i	−0.994284	−	0.106764i	$-0.965951\pi$
$3$	−2.42308	+	1.39897i	−1.39897	+	0.807694i	−0.404682	+	0.914458i	$0.632618\pi$
$4$	1.36802	+	1.45894i	0.684011	+	0.729472i
$5$	−0.707107	−	0.707107i	−0.316228	−	0.316228i	0.531089	−	0.847316i	$-0.321783\pi$
$5$	−0.707107	−	0.707107i	−0.316228	−	0.316228i	−0.847316	+	0.531089i	$0.821783\pi$
$6$	−3.93082	+	0.453347i	−1.60475	+	0.185078i
$7$	−2.70260	+	0.724158i	−1.02149	+	0.273706i	−0.730421	−	0.682997i	$-0.760676\pi$
$7$	−2.70260	+	0.724158i	−1.02149	+	0.273706i	−0.291064	+	0.956704i	$0.594009\pi$
$8$	0.955161	+	2.66227i	0.337700	+	0.941254i
$9$	2.41421	−	4.18154i	0.804738	−	1.39385i
$10$	−0.520123	−	1.31509i	−0.164477	−	0.415869i
$11$	−0.424202	+	1.58314i	−0.127902	+	0.477336i	−0.999926	−	0.0121260i	$-0.996140\pi$
$11$	−0.424202	+	1.58314i	−0.127902	+	0.477336i	0.872025	+	0.489462i	$0.162807\pi$
$12$	−5.35584	−	1.62132i	−1.54610	−	0.468035i
$13$		0			0
$13$		0			0
$14$	−3.91421	−	0.579471i	−1.04612	−	0.154870i
$15$	2.70260	+	0.724158i	0.697807	+	0.186977i
$16$	−0.257031	+	3.99173i	−0.0642577	+	0.997933i
$17$	−5.04757	−	2.91421i	−1.22421	−	0.706801i	−0.258401	−	0.966038i	$-0.583196\pi$
$17$	−5.04757	−	2.91421i	−1.22421	−	0.706801i	−0.965814	+	0.259237i	$0.916529\pi$
$18$	5.48348	−	4.06926i	1.29247	−	0.959134i
$19$	−0.599912	−	2.23890i	−0.137629	−	0.513640i	−0.999973	−	0.00731664i	$-0.997671\pi$
$19$	−0.599912	−	2.23890i	−0.137629	−	0.513640i	0.862344	−	0.506323i	$-0.168996\pi$
$20$	0.0642909	−	1.99897i	0.0143759	−	0.446982i
$21$	5.53553	−	5.53553i	1.20795	−	1.20795i
$22$	−1.44042	+	1.81598i	−0.307098	+	0.387168i
$23$	−1.97844	−	3.42675i	−0.412533	−	0.714528i	0.582633	−	0.812735i	$-0.302022\pi$
$23$	−1.97844	−	3.42675i	−0.412533	−	0.714528i	−0.995166	+	0.0982076i	$0.968689\pi$
$24$	−6.03885	−	5.11465i	−1.23268	−	1.04402i
$25$		−	4.00000i		−	0.800000i
$26$		0			0
$27$			5.11582i			0.984539i
$28$	−4.75372	−	2.95227i	−0.898368	−	0.557926i
$29$	0.292893	+	0.507306i	0.0543889	+	0.0942043i	0.891938	−	0.452158i	$-0.149346\pi$
$29$	0.292893	+	0.507306i	0.0543889	+	0.0942043i	−0.837549	+	0.546362i	$0.816012\pi$
$30$	3.10007	+	2.45894i	0.565993	+	0.448940i
$31$	−3.95687	+	3.95687i	−0.710676	+	0.710676i	−0.966677	−	0.256001i	$-0.917595\pi$
$31$	−3.95687	+	3.95687i	−0.710676	+	0.710676i	0.256001	+	0.966677i	$0.417595\pi$
$32$	−2.57742	+	5.03557i	−0.455627	+	0.890171i
$33$	−1.18689	−	4.42953i	−0.206611	−	0.771082i
$34$	−4.91203	−	6.61914i	−0.842407	−	1.13517i
$35$	2.42308	+	1.39897i	0.409575	+	0.236468i
$36$	9.40333	−	2.19824i	1.56722	−	0.366373i
$37$	2.56632	+	0.687644i	0.421901	+	0.113048i	0.463522	−	0.886085i	$-0.346586\pi$
$37$	2.56632	+	0.687644i	0.421901	+	0.113048i	−0.0416209	+	0.999133i	$0.513252\pi$
$38$	0.480049	−	3.24264i	0.0778743	−	0.526026i
$39$		0			0
$40$	1.20711	−	2.55791i	0.190860	−	0.404441i
$41$	−1.55291	+	5.79555i	−0.242524	+	0.905114i	0.732087	+	0.681211i	$0.238546\pi$
$41$	−1.55291	+	5.79555i	−0.242524	+	0.905114i	−0.974612	+	0.223903i	$0.928120\pi$
$42$	10.2951	−	4.07175i	1.58857	−	0.628284i
$43$	2.55791	−	4.43043i	0.390077	−	0.675634i	−0.602382	−	0.798208i	$-0.705782\pi$
$43$	2.55791	−	4.43043i	0.390077	−	0.675634i	0.992459	+	0.122574i	$0.0391149\pi$
$44$	−2.89003	+	1.54689i	−0.435689	+	0.233202i
$45$	−4.66390	+	1.24969i	−0.695254	+	0.186293i
$46$	−0.641130	−	5.55902i	−0.0945294	−	0.819632i
$47$	−1.97844	−	1.97844i	−0.288585	−	0.288585i	0.547936	−	0.836520i	$-0.315414\pi$
$47$	−1.97844	−	1.97844i	−0.288585	−	0.288585i	−0.836520	+	0.547936i	$0.815414\pi$
$48$	−4.96149	−	10.0319i	−0.716130	−	1.44798i
$49$	0.717439	−	0.414214i	0.102491	−	0.0591734i
$50$	2.24852	−	5.19078i	0.317988	−	0.734087i
$51$	16.3075			2.28351
$52$		0			0
$53$	−0.242641			−0.0333293			−0.0166646	−	0.999861i	$-0.505305\pi$
$53$	−0.242641			−0.0333293			−0.0166646	+	0.999861i	$0.505305\pi$
$54$	−2.87575	+	6.63877i	−0.391340	+	0.903422i
$55$	1.41941	−	0.819496i	0.191393	−	0.110501i
$56$	−4.50932	−	6.50334i	−0.602583	−	0.869046i
$57$	4.58579	+	4.58579i	0.607402	+	0.607402i
$58$	0.0949146	+	0.822972i	0.0124629	+	0.108062i
$59$	−3.16629	+	0.848404i	−0.412216	+	0.110453i	−0.458966	−	0.888454i	$-0.651780\pi$
$59$	−3.16629	+	0.848404i	−0.412216	+	0.110453i	0.0467506	+	0.998907i	$0.485113\pi$
$60$	2.64070	+	4.93360i	0.340914	+	0.636925i
$61$	−0.414214	+	0.717439i	−0.0530346	+	0.0918586i	−0.891324	−	0.453367i	$-0.850223\pi$
$61$	−0.414214	+	0.717439i	−0.0530346	+	0.0918586i	0.838289	+	0.545226i	$0.183556\pi$
$62$	−7.35909	+	2.91054i	−0.934605	+	0.369639i
$63$	−3.49655	+	13.0493i	−0.440523	+	1.64406i
$64$	−6.17534	+	5.08579i	−0.771917	+	0.635723i
$65$		0			0
$66$	0.949747	−	6.41536i	0.116906	−	0.789676i
$67$	−3.82205	−	1.02411i	−0.466937	−	0.125115i	0.0176763	−	0.999844i	$-0.494373\pi$
$67$	−3.82205	−	1.02411i	−0.466937	−	0.125115i	−0.484614	+	0.874728i	$0.661040\pi$
$68$	−2.65351	−	11.3508i	−0.321785	−	1.37649i
$69$	9.58783	+	5.53553i	1.15424	+	0.666400i
$70$	2.35802	+	3.17751i	0.281837	+	0.379786i
$71$	1.92398	+	7.18040i	0.228335	+	0.852157i	0.981041	+	0.193800i	$0.0620814\pi$
$71$	1.92398	+	7.18040i	0.228335	+	0.852157i	−0.752706	+	0.658357i	$0.771252\pi$
$72$	13.4383	+	2.43324i	1.58372	+	0.286760i
$73$	−9.65685	+	9.65685i	−1.13025	+	1.13025i	−0.140114	+	0.990135i	$0.544747\pi$
$73$	−9.65685	+	9.65685i	−1.13025	+	1.13025i	−0.990135	+	0.140114i	$0.955253\pi$
$74$	2.94376	+	2.33496i	0.342205	+	0.271433i
$75$	5.59587	+	9.69232i	0.646155	+	1.11917i
$76$	2.44574	−	3.93811i	0.280546	−	0.451732i
$77$		−	4.58579i		−	0.522599i
$78$		0			0
$79$			9.55274i			1.07477i	0.843338	+	0.537384i	$0.180587\pi$
$79$			9.55274i			1.07477i	−0.843338	+	0.537384i	$0.819413\pi$
$80$	3.00433	−	2.64083i	0.335894	−	0.295254i
$81$	0.0857864	+	0.148586i	0.00953183	+	0.0165096i
$82$	−5.27306	+	6.64792i	−0.582312	+	0.734140i
$83$	−6.75481	+	6.75481i	−0.741436	+	0.741436i	−0.972854	−	0.231418i	$-0.925663\pi$
$83$	−6.75481	+	6.75481i	−0.741436	+	0.741436i	0.231418	+	0.972854i	$0.425663\pi$
$84$	15.6488	+	0.503297i	1.70742	+	0.0549142i
$85$	1.50851	+	5.62983i	0.163621	+	0.610641i
$86$	5.80985	−	4.31147i	0.626493	−	0.464917i
$87$	−1.41941	−	0.819496i	−0.152176	−	0.0878591i
$88$	−4.61993	+	0.382817i	−0.492487	+	0.0408085i
$89$	−8.52761	−	2.28497i	−0.903924	−	0.242206i	−0.223224	−	0.974767i	$-0.571658\pi$
$89$	−8.52761	−	2.28497i	−0.903924	−	0.242206i	−0.680701	+	0.732561i	$0.738325\pi$
$90$	−6.75481	−	1.00000i	−0.712019	−	0.105409i
$91$		0			0
$92$	2.29289	−	7.57430i	0.239051	−	0.789676i
$93$	4.05229	−	15.1234i	0.420203	−	1.56822i
$94$	−1.45527	−	3.67954i	−0.150100	−	0.379516i
$95$	−1.15894	+	2.00735i	−0.118905	+	0.205949i
$96$	−0.799300	−	15.8073i	−0.0815782	−	1.61333i
$97$	−0.565826	+	0.151613i	−0.0574510	+	0.0153939i	−0.287430	−	0.957802i	$-0.592801\pi$
$97$	−0.565826	+	0.151613i	−0.0574510	+	0.0153939i	0.229979	+	0.973196i	$0.426134\pi$
$98$	1.16386	−	0.134230i	0.117567	−	0.0135592i
$99$	5.59587	+	5.59587i	0.562406	+	0.562406i
$100$	5.83577	−	5.47209i	0.583577	−	0.547209i
$101$	9.37769	−	5.41421i	0.933115	−	0.538734i	0.0453198	−	0.998973i	$-0.485569\pi$
$101$	9.37769	−	5.41421i	0.933115	−	0.538734i	0.887796	+	0.460238i	$0.152236\pi$
$102$	21.1622	+	9.16694i	2.09537	+	0.907663i
$103$	−4.91697			−0.484484			−0.242242	−	0.970216i	$-0.577883\pi$
$103$	−4.91697			−0.484484			−0.242242	+	0.970216i	$0.577883\pi$
$104$		0			0
$105$	−7.82843			−0.763976
$106$	−0.314873	−	0.136395i	−0.0305832	−	0.0132479i
$107$	−8.86085	+	5.11582i	−0.856611	+	0.494565i	−0.862876	−	0.505416i	$-0.831339\pi$
$107$	−8.86085	+	5.11582i	−0.856611	+	0.494565i	0.00626493	+	0.999980i	$0.498006\pi$
$108$	−7.46369	+	6.99855i	−0.718193	+	0.673436i
$109$	−4.70711	−	4.70711i	−0.450859	−	0.450859i	0.444781	−	0.895640i	$-0.353282\pi$
$109$	−4.70711	−	4.70711i	−0.450859	−	0.450859i	−0.895640	+	0.444781i	$0.853282\pi$
$110$	2.30262	−	0.265565i	0.219546	−	0.0253206i
$111$	−7.18040	+	1.92398i	−0.681534	+	0.182616i
$112$	−2.19600	−	10.9742i	−0.207502	−	1.03696i
$113$	−7.65685	+	13.2621i	−0.720296	+	1.24759i	0.240585	+	0.970628i	$0.422661\pi$
$113$	−7.65685	+	13.2621i	−0.720296	+	1.24759i	−0.960881	+	0.276962i	$0.910673\pi$
$114$	3.37315	+	8.52875i	0.315924	+	0.798791i
$115$	−1.02411	+	3.82205i	−0.0954992	+	0.356408i
$116$	−0.339446	+	1.12132i	−0.0315168	+	0.104112i
$117$		0			0
$118$	−4.58579	−	0.678892i	−0.422156	−	0.0624971i
$119$	15.7519	+	4.22070i	1.44397	+	0.386911i
$120$	0.653510	+	7.88672i	0.0596570	+	0.719956i
$121$	7.19988	+	4.15685i	0.654535	+	0.377896i
$122$	−0.940816	+	0.698175i	−0.0851775	+	0.0632098i
$123$	−4.34495	−	16.2156i	−0.391771	−	1.46211i
$124$	−11.1859	−	0.359763i	−1.00453	−	0.0323077i
$125$	−6.36396	+	6.36396i	−0.569210	+	0.569210i
$126$	−11.8728	+	14.9685i	−1.05772	+	1.33350i
$127$	−9.21329	−	15.9579i	−0.817548	−	1.41603i	−0.907484	−	0.420086i	$-0.862000\pi$
$127$	−9.21329	−	15.9579i	−0.817548	−	1.41603i	0.0899365	−	0.995948i	$-0.471334\pi$
$128$	−10.8726	+	3.12846i	−0.961008	+	0.276520i
$129$			14.3137i			1.26025i
$130$		0			0
$131$		−	10.7117i		−	0.935884i	−0.883759	−	0.467942i	$-0.844996\pi$
$131$		−	10.7117i		−	0.935884i	0.883759	−	0.467942i	$-0.155004\pi$
$132$	4.83874	−	7.79130i	0.421158	−	0.678145i
$133$	3.24264	+	5.61642i	0.281173	+	0.487005i
$134$	−4.38417	−	3.47747i	−0.378734	−	0.300408i
$135$	3.61743	−	3.61743i	0.311339	−	0.311339i
$136$	2.93718	−	16.2215i	0.251861	−	1.39098i
$137$	3.16863	+	11.8255i	0.270714	+	1.01032i	0.958659	+	0.284556i	$0.0918463\pi$
$137$	3.16863	+	11.8255i	0.270714	+	1.01032i	−0.687945	+	0.725763i	$0.741487\pi$
$138$	9.33039	+	12.5730i	0.794255	+	1.07029i
$139$	18.9689	+	10.9517i	1.60892	+	0.928912i	0.989612	+	0.143765i	$0.0459210\pi$
$139$	18.9689	+	10.9517i	1.60892	+	0.928912i	0.619310	+	0.785146i	$0.287412\pi$
$140$	1.27382	+	5.44895i	0.107657	+	0.460521i
$141$	7.56168	+	2.02615i	0.636808	+	0.170632i
$142$	−1.53957	+	10.3995i	−0.129198	+	0.872706i
$143$		0			0
$144$	16.0711	+	10.7117i	1.33926	+	0.892640i
$145$	0.151613	−	0.565826i	0.0125907	−	0.0469893i
$146$	−17.9600	+	7.10325i	−1.48638	+	0.587869i
$147$	−1.15894	+	2.00735i	−0.0955879	+	0.165563i
$148$	2.50755	+	4.68483i	0.206120	+	0.385091i
$149$	8.85906	−	2.37378i	0.725762	−	0.194467i	0.123021	−	0.992404i	$-0.460742\pi$
$149$	8.85906	−	2.37378i	0.725762	−	0.194467i	0.602741	+	0.797937i	$0.294075\pi$
$150$	1.81339	+	15.7233i	0.148063	+	1.28380i
$151$	−1.29954	−	1.29954i	−0.105755	−	0.105755i	0.652249	−	0.758005i	$-0.273826\pi$
$151$	−1.29954	−	1.29954i	−0.105755	−	0.105755i	−0.758005	+	0.652249i	$0.773826\pi$
$152$	5.38755	−	3.73564i	0.436988	−	0.303000i
$153$	−24.3718	+	14.0711i	−1.97034	+	1.13758i
$154$	2.57780	−	5.95095i	0.207725	−	0.479541i
$155$	5.59587			0.449471
$156$		0			0
$157$	12.0000			0.957704			0.478852	−	0.877896i	$-0.341053\pi$
$157$	12.0000			0.957704			0.478852	+	0.877896i	$0.341053\pi$
$158$	−5.36987	+	12.3965i	−0.427204	+	0.986216i
$159$	0.587938	−	0.339446i	0.0466265	−	0.0269198i
$160$	5.38319	−	1.73817i	0.425579	−	0.137415i
$161$	7.82843	+	7.82843i	0.616966	+	0.616966i
$162$	0.0277998	+	0.241043i	0.00218416	+	0.0189381i
$163$	14.6324	−	3.92075i	1.14610	−	0.307097i	0.364699	−	0.931125i	$-0.381172\pi$
$163$	14.6324	−	3.92075i	1.14610	−	0.307097i	0.781401	+	0.624029i	$0.214505\pi$
$164$	−10.5798	+	5.66283i	−0.826144	+	0.442193i
$165$	−2.29289	+	3.97141i	−0.178501	+	0.309174i
$166$	−12.5627	+	4.96860i	−0.975058	+	0.385638i
$167$	3.49655	−	13.0493i	0.270571	−	1.00978i	−0.688181	−	0.725539i	$-0.741590\pi$
$167$	3.49655	−	13.0493i	0.270571	−	1.00978i	0.958752	−	0.284245i	$-0.0917429\pi$
$168$	20.0244	+	9.44975i	1.54492	+	0.729064i
$169$		0			0
$170$	−1.20711	+	8.15377i	−0.0925809	+	0.625366i
$171$	−10.8104	−	2.89663i	−0.826691	−	0.221511i
$172$	9.96302	−	2.32908i	0.759673	−	0.177591i
$173$	−10.7255	−	6.19239i	−0.815447	−	0.470799i	0.0333969	−	0.999442i	$-0.489367\pi$
$173$	−10.7255	−	6.19239i	−0.815447	−	0.470799i	−0.848844	+	0.528644i	$0.822701\pi$
$174$	−1.38130	−	1.86135i	−0.104716	−	0.141108i
$175$	2.89663	+	10.8104i	0.218965	+	0.817188i
$176$	−6.21045	−	2.10022i	−0.468131	−	0.158310i
$177$	6.48528	−	6.48528i	0.487464	−	0.487464i
$178$	−9.78178	−	7.75880i	−0.733176	−	0.581547i
$179$	3.71685	+	6.43777i	0.277810	+	0.481182i	0.970840	−	0.239727i	$-0.0770580\pi$
$179$	3.71685	+	6.43777i	0.277810	+	0.481182i	−0.693030	+	0.720909i	$0.743725\pi$
$180$	−8.20355	−	5.09477i	−0.611456	−	0.379741i
$181$			11.4142i			0.848412i	0.905566	+	0.424206i	$0.139447\pi$
$181$			11.4142i			0.848412i	−0.905566	+	0.424206i	$0.860553\pi$
$182$		0			0
$183$		−	2.31788i		−	0.171343i
$184$	7.23321	−	8.54023i	0.533239	−	0.629594i
$185$	−1.32843	−	2.30090i	−0.0976679	−	0.169166i
$186$	13.7599	−	17.3476i	1.00893	−	1.27199i
$187$	6.75481	−	6.75481i	0.493960	−	0.493960i
$188$	0.179882	−	5.59297i	0.0131192	−	0.407910i
$189$	−3.70466	−	13.8260i	−0.269474	−	1.00569i
$190$	−2.63234	+	1.95345i	−0.190970	+	0.141718i
$191$	−20.8041	−	12.0112i	−1.50533	−	0.869102i	−0.999981	−	0.00618597i	$-0.998031\pi$
$191$	−20.8041	−	12.0112i	−1.50533	−	0.869102i	−0.505348	−	0.862916i	$-0.668636\pi$
$192$	7.84849	−	20.9624i	0.566416	−	1.51283i
$193$	8.29323	+	2.22217i	0.596960	+	0.159955i	0.544632	−	0.838675i	$-0.316669\pi$
$193$	8.29323	+	2.22217i	0.596960	+	0.159955i	0.0523278	+	0.998630i	$0.483336\pi$
$194$	−0.819496	−	0.121320i	−0.0588363	−	0.00871029i
$195$		0			0
$196$	1.58579	+	0.480049i	0.113270	+	0.0342892i
$197$	−6.81049	+	25.4171i	−0.485227	+	1.81089i	0.0938081	+	0.995590i	$0.470096\pi$
$197$	−6.81049	+	25.4171i	−0.485227	+	1.81089i	−0.579035	+	0.815302i	$0.696571\pi$
$198$	4.11613	+	10.4073i	0.292520	+	0.739616i
$199$	8.25319	−	14.2950i	0.585053	−	1.01334i	−0.409815	−	0.912169i	$-0.634407\pi$
$199$	8.25319	−	14.2950i	0.585053	−	1.01334i	0.994869	−	0.101174i	$-0.0322598\pi$
$200$	10.6491	−	3.82064i	0.753003	−	0.270160i
$201$	10.6938	−	2.86540i	0.754285	−	0.202110i
$202$	15.2129	−	1.75452i	1.07037	−	0.123448i
$203$	−1.15894	−	1.15894i	−0.0813418	−	0.0813418i
$204$	22.3091	+	23.7918i	1.56195	+	1.66576i
$205$	5.19615	−	3.00000i	0.362915	−	0.209529i
$206$	−6.38073	−	2.76397i	−0.444566	−	0.192575i
$207$	−19.1055			−1.32792
$208$		0			0
$209$	3.79899			0.262782
$210$	−10.1589	−	4.40059i	−0.701031	−	0.303669i
$211$	8.44512	−	4.87579i	0.581386	−	0.335663i	−0.180298	−	0.983612i	$-0.557706\pi$
$211$	8.44512	−	4.87579i	0.581386	−	0.335663i	0.761684	+	0.647949i	$0.224373\pi$
$212$	−0.331938	−	0.353999i	−0.0227976	−	0.0243128i
$213$	−14.7071	−	14.7071i	−1.00771	−	1.00771i
$214$	−14.3744	+	1.65782i	−0.982616	+	0.113327i
$215$	−4.94150	+	1.32407i	−0.337007	+	0.0903009i
$216$	−13.6197	+	4.88643i	−0.926701	+	0.332479i
$217$	7.82843	−	13.5592i	0.531428	−	0.920461i
$218$	−3.46239	−	8.75439i	−0.234502	−	0.592922i
$219$	9.88972	−	36.9090i	0.668286	−	2.49408i
$220$	3.13738	+	0.949747i	0.211522	+	0.0640320i
$221$		0			0
$222$	−10.3995	−	1.53957i	−0.697968	−	0.103329i
$223$	−24.3234	−	6.51742i	−1.62881	−	0.436439i	−0.675239	−	0.737599i	$-0.735959\pi$
$223$	−24.3234	−	6.51742i	−1.62881	−	0.436439i	−0.953574	+	0.301160i	$0.902626\pi$
$224$	3.31917	−	15.4756i	0.221771	−	1.03400i
$225$	−16.7262	−	9.65685i	−1.11508	−	0.643790i
$226$	−17.3912	+	12.9060i	−1.15685	+	0.858492i
$227$	−4.69637	−	17.5271i	−0.311709	−	1.16331i	−0.927015	−	0.375025i	$-0.877634\pi$
$227$	−4.69637	−	17.5271i	−0.311709	−	1.16331i	0.615306	−	0.788289i	$-0.289033\pi$
$228$	−0.416945	+	12.9639i	−0.0276128	+	0.858553i
$229$	14.7071	−	14.7071i	0.971873	−	0.971873i	−0.0277421	−	0.999615i	$-0.508832\pi$
$229$	14.7071	−	14.7071i	0.971873	−	0.971873i	0.999615	+	0.0277421i	$0.00883173\pi$
$230$	−3.47747	+	4.38417i	−0.229298	+	0.289083i
$231$	6.41536	+	11.1117i	0.422100	+	0.731098i
$232$	−1.07082	+	1.26432i	−0.0703030	+	0.0830066i
$233$		−	11.9706i		−	0.784218i	−0.919919	−	0.392109i	$-0.871746\pi$
$233$		−	11.9706i		−	0.784218i	0.919919	−	0.392109i	$-0.128254\pi$
$234$		0			0
$235$			2.79793i			0.182517i
$236$	−5.56932	−	3.45880i	−0.362532	−	0.225149i
$237$	−13.3640	−	23.1471i	−0.868083	−	1.50356i
$238$	18.0685	+	14.3318i	1.17121	+	0.928991i
$239$	8.25319	−	8.25319i	0.533855	−	0.533855i	−0.387862	−	0.921717i	$-0.626786\pi$
$239$	8.25319	−	8.25319i	0.533855	−	0.533855i	0.921717	+	0.387862i	$0.126786\pi$
$240$	−3.58530	+	10.6019i	−0.231430	+	0.684350i
$241$	4.78434	+	17.8554i	0.308187	+	1.15017i	0.930167	+	0.367136i	$0.119662\pi$
$241$	4.78434	+	17.8554i	0.308187	+	1.15017i	−0.621981	+	0.783032i	$0.713672\pi$
$242$	7.00656	+	9.44159i	0.450399	+	0.606928i
$243$	−13.7070	−	7.91375i	−0.879305	−	0.507667i
$244$	−1.61336	+	0.377158i	−0.103285	+	0.0241451i
$245$	−0.800199	−	0.214413i	−0.0511228	−	0.0136983i
$246$	3.47682	−	23.4853i	0.221674	−	1.49737i
$247$		0			0
$248$	−14.3137	−	6.75481i	−0.908921	−	0.428931i
$249$	6.91770	−	25.8172i	0.438391	−	1.63610i
$250$	−11.8358	+	4.68111i	−0.748564	+	0.296059i
$251$	−9.07269	+	15.7144i	−0.572663	+	0.991882i	0.423628	+	0.905836i	$0.360756\pi$
$251$	−9.07269	+	15.7144i	−0.572663	+	0.991882i	−0.996291	+	0.0860454i	$0.972577\pi$
$252$	−23.8215	+	12.7504i	−1.50061	+	0.803203i
$253$	6.26430	−	1.67851i	0.393833	−	0.105527i
$254$	−2.98565	−	25.8875i	−0.187336	−	1.62433i
$255$	−11.5312	−	11.5312i	−0.722110	−	0.722110i
$256$	−15.8679	−	2.05200i	−0.991742	−	0.128250i
$257$	0.568852	−	0.328427i	0.0354840	−	0.0204867i	−0.482153	−	0.876087i	$-0.660145\pi$
$257$	0.568852	−	0.328427i	0.0354840	−	0.0204867i	0.517637	+	0.855600i	$0.326812\pi$
$258$	−8.04615	+	18.5748i	−0.500931	+	1.15642i
$259$	−7.43370			−0.461908
$260$		0			0
$261$	2.82843			0.175075
$262$	6.02135	−	13.9005i	0.372000	−	0.858775i
$263$	7.68498	−	4.43692i	0.473876	−	0.273592i	−0.243985	−	0.969779i	$-0.578455\pi$
$263$	7.68498	−	4.43692i	0.473876	−	0.273592i	0.717861	+	0.696187i	$0.245121\pi$
$264$	10.6589	−	7.39073i	0.656011	−	0.454868i
$265$	0.171573	+	0.171573i	0.0105396	+	0.0105396i
$266$	1.05081	+	9.11118i	0.0644290	+	0.558642i
$267$	23.8597	−	6.39318i	1.46019	−	0.391256i
$268$	−3.73452	−	6.97716i	−0.228122	−	0.426198i
$269$	4.07107	−	7.05130i	0.248217	−	0.429925i	−0.714814	−	0.699315i	$-0.753489\pi$
$269$	4.07107	−	7.05130i	0.248217	−	0.429925i	0.963031	+	0.269390i	$0.0868219\pi$
$270$	6.72778	−	2.66086i	0.409440	−	0.161935i
$271$	−4.82062	+	17.9908i	−0.292832	+	1.09286i	0.650093	+	0.759855i	$0.274730\pi$
$271$	−4.82062	+	17.9908i	−0.292832	+	1.09286i	−0.942924	+	0.333007i	$0.891937\pi$
$272$	12.9301	−	19.3995i	0.784005	−	1.17627i
$273$		0			0
$274$	−2.53553	+	17.1270i	−0.153177	+	1.03468i
$275$	6.33257	+	1.69681i	0.381869	+	0.102321i
$276$	5.04033	+	21.5608i	0.303392	+	1.29781i
$277$	−5.19615	−	3.00000i	−0.312207	−	0.180253i	0.335707	−	0.941966i	$-0.391025\pi$
$277$	−5.19615	−	3.00000i	−0.312207	−	0.180253i	−0.647913	+	0.761714i	$0.724358\pi$
$278$	18.4596	+	24.8749i	1.10713	+	1.49190i
$279$	6.99309	+	26.0986i	0.418665	+	1.56248i
$280$	−1.40999	+	7.78713i	−0.0842631	+	0.465370i
$281$	−7.75736	+	7.75736i	−0.462765	+	0.462765i	−0.899561	−	0.436796i	$-0.856113\pi$
$281$	−7.75736	+	7.75736i	−0.462765	+	0.462765i	0.436796	+	0.899561i	$0.356113\pi$
$282$	8.67380	+	6.87996i	0.516517	+	0.409696i
$283$	−0.678892	−	1.17588i	−0.0403560	−	0.0698986i	0.845142	−	0.534542i	$-0.179516\pi$
$283$	−0.678892	−	1.17588i	−0.0403560	−	0.0698986i	−0.885498	+	0.464643i	$0.846183\pi$
$284$	−7.84375	+	12.6299i	−0.465441	+	0.749449i
$285$		−	6.48528i		−	0.384155i
$286$		0			0
$287$		−	16.7876i		−	0.990940i
$288$	14.8340	+	22.9345i	0.874101	+	1.35143i
$289$	8.48528	+	14.6969i	0.499134	+	0.864526i
$290$	0.514814	−	0.649044i	0.0302309	−	0.0381132i
$291$	1.15894	−	1.15894i	0.0679384	−	0.0679384i
$292$	−27.2996	−	0.878012i	−1.59759	−	0.0513817i
$293$	−7.02490	−	26.2173i	−0.410399	−	1.53163i	−0.793876	−	0.608080i	$-0.791940\pi$
$293$	−7.02490	−	26.2173i	−0.410399	−	1.53163i	0.383477	−	0.923551i	$-0.374727\pi$
$294$	−2.63234	+	1.95345i	−0.153521	+	0.113927i
$295$	2.83882	+	1.63899i	0.165282	+	0.0954257i
$296$	0.620558	+	7.48905i	0.0360692	+	0.435292i
$297$	−8.09907	−	2.17014i	−0.469956	−	0.125924i
$298$	12.8307	+	1.89949i	0.743264	+	0.110035i
$299$		0			0
$300$	−6.48528	+	21.4234i	−0.374428	+	1.23688i
$301$	−3.70466	+	13.8260i	−0.213533	+	0.796916i
$302$	−0.955900	−	2.41692i	−0.0550059	−	0.139078i
$303$	−15.1486	+	26.2382i	−0.870265	+	1.50734i
$304$	9.09130	−	1.81922i	0.521422	−	0.104340i
$305$	0.800199	−	0.214413i	0.0458193	−	0.0122772i
$306$	−39.5369	+	4.55985i	−2.26017	+	0.260669i
$307$	19.1055	+	19.1055i	1.09041	+	1.09041i	0.995485	+	0.0949226i	$0.0302604\pi$
$307$	19.1055	+	19.1055i	1.09041	+	1.09041i	0.0949226	+	0.995485i	$0.469740\pi$
$308$	6.69040	−	6.27346i	0.381221	−	0.357463i
$309$	11.9142	−	6.87868i	0.677776	−	0.391314i
$310$	7.26172	+	3.14560i	0.412438	+	0.178658i
$311$	−22.7811			−1.29180			−0.645900	−	0.763422i	$-0.723518\pi$
$311$	−22.7811			−1.29180			−0.645900	+	0.763422i	$0.723518\pi$
$312$		0			0
$313$	−13.4853			−0.762233			−0.381117	−	0.924527i	$-0.624460\pi$
$313$	−13.4853			−0.762233			−0.381117	+	0.924527i	$0.624460\pi$
$314$	15.5723	+	6.74555i	0.878798	+	0.380673i
$315$	11.6997	−	6.75481i	0.659202	−	0.380590i
$316$	−13.9369	+	13.0684i	−0.784012	+	0.735153i
$317$	−4.34315	−	4.34315i	−0.243935	−	0.243935i	0.574541	−	0.818476i	$-0.305181\pi$
$317$	−4.34315	−	4.34315i	−0.243935	−	0.243935i	−0.818476	+	0.574541i	$0.805181\pi$
$318$	0.953776	−	0.110000i	0.0534851	−	0.00616852i
$319$	−0.927384	+	0.248492i	−0.0519235	+	0.0139129i
$320$	7.96282	+	0.770428i	0.445135	+	0.0430682i
$321$	14.3137	−	24.7921i	0.798913	−	1.38376i
$322$	5.75832	+	14.5595i	0.320899	+	0.811369i
$323$	−3.49655	+	13.0493i	−0.194553	+	0.726082i
$324$	−0.0994215	+	0.328427i	−0.00552342	+	0.0182460i
$325$		0			0
$326$	21.1924	+	3.13738i	1.17374	+	0.173763i
$327$	17.9908	+	4.82062i	0.994893	+	0.266581i
$328$	−16.9126	+	1.40141i	−0.933842	+	0.0773801i
$329$	6.77962	+	3.91421i	0.373772	+	0.215798i
$330$	−5.20792	+	3.86477i	−0.286686	+	0.212749i
$331$	5.36906	+	20.0376i	0.295110	+	1.10137i	0.941130	+	0.338046i	$0.109766\pi$
$331$	5.36906	+	20.0376i	0.295110	+	1.10137i	−0.646019	+	0.763321i	$0.723567\pi$
$332$	−19.0956	−	0.614154i	−1.04801	−	0.0337061i
$333$	9.07107	−	9.07107i	0.497091	−	0.497091i
$334$	11.8728	−	14.9685i	0.649652	−	0.819039i
$335$	1.97844	+	3.42675i	0.108094	+	0.187224i
$336$	20.6736	+	23.5192i	1.12784	+	1.28308i
$337$			8.17157i			0.445134i	0.974917	+	0.222567i	$0.0714436\pi$
$337$			8.17157i			0.445134i	−0.974917	+	0.222567i	$0.928556\pi$
$338$		0			0
$339$		−	42.8467i		−	2.32711i
$340$	−6.14993	+	9.90256i	−0.333527	+	0.537042i
$341$	−4.58579	−	7.94282i	−0.248334	−	0.430128i
$342$	−12.4003	−	9.83577i	−0.670531	−	0.531858i
$343$	12.2101	−	12.2101i	0.659282	−	0.659282i
$344$	14.2382	+	2.57807i	0.767672	+	0.139000i
$345$	−2.86540	−	10.6938i	−0.154268	−	0.575736i
$346$	−10.4375	−	14.0650i	−0.561126	−	0.756137i
$347$	8.10071	+	4.67695i	0.434869	+	0.251072i	0.701419	−	0.712749i	$-0.252550\pi$
$347$	8.10071	+	4.67695i	0.434869	+	0.251072i	−0.266550	+	0.963821i	$0.585884\pi$
$348$	−0.746184	−	3.19192i	−0.0399997	−	0.171105i
$349$	0.634472	+	0.170006i	0.0339625	+	0.00910023i	0.275760	−	0.961226i	$-0.411070\pi$
$349$	0.634472	+	0.170006i	0.0339625	+	0.00910023i	−0.241798	+	0.970327i	$0.577737\pi$
$350$	−2.31788	+	15.6569i	−0.123896	+	0.836894i
$351$		0			0
$352$	−6.87868	−	6.21652i	−0.366635	−	0.331342i
$353$	−1.61571	+	6.02993i	−0.0859958	+	0.320941i	−0.995501	−	0.0947521i	$-0.969794\pi$
$353$	−1.61571	+	6.02993i	−0.0859958	+	0.320941i	0.909505	+	0.415693i	$0.136461\pi$
$354$	12.0615	−	4.77035i	0.641060	−	0.253541i
$355$	3.71685	−	6.43777i	0.197270	−	0.341681i
$356$	−8.33232	−	15.5672i	−0.441612	−	0.825059i
$357$	−44.0727	+	11.8092i	−2.33257	+	0.625011i
$358$	1.20448	+	10.4436i	0.0636586	+	0.551962i
$359$	−3.95687	−	3.95687i	−0.208836	−	0.208836i	0.594937	−	0.803773i	$-0.297177\pi$
$359$	−3.95687	−	3.95687i	−0.208836	−	0.208836i	−0.803773	+	0.594937i	$0.797177\pi$
$360$	−7.78178	−	11.2229i	−0.410136	−	0.591499i
$361$	11.8017	−	6.81371i	0.621142	−	0.358616i
$362$	−6.41626	+	14.8122i	−0.337231	+	0.778510i
$363$	−23.2612			−1.22090
$364$		0			0
$365$	13.6569			0.714832
$366$	1.30295	−	3.00790i	0.0681062	−	0.157226i
$367$	13.1191	−	7.57430i	0.684810	−	0.395375i	−0.116855	−	0.993149i	$-0.537281\pi$
$367$	13.1191	−	7.57430i	0.684810	−	0.395375i	0.801665	+	0.597774i	$0.203948\pi$
$368$	14.1872	−	7.01661i	0.739559	−	0.365766i
$369$	20.4853	+	20.4853i	1.06642	+	1.06642i
$370$	−0.430488	−	3.73262i	−0.0223800	−	0.194050i
$371$	0.655760	−	0.175710i	0.0340453	−	0.00912242i
$372$	27.6077	−	14.7770i	1.43140	−	0.766153i
$373$	−15.3137	+	26.5241i	−0.792914	+	1.37337i	0.131242	+	0.991350i	$0.458104\pi$
$373$	−15.3137	+	26.5241i	−0.792914	+	1.37337i	−0.924155	+	0.382017i	$0.875230\pi$
$374$	12.5627	−	4.96860i	0.649604	−	0.256920i
$375$	6.51742	−	24.3234i	0.336558	−	1.25605i
$376$	3.37740	−	7.15685i	0.174176	−	0.369087i
$377$		0			0
$378$	2.96447	−	20.0244i	0.152476	−	1.02994i
$379$	19.1102	+	5.12057i	0.981627	+	0.263026i	0.713730	−	0.700421i	$-0.247005\pi$
$379$	19.1102	+	5.12057i	0.981627	+	0.263026i	0.267897	+	0.963447i	$0.413671\pi$
$380$	−4.51406	+	1.05526i	−0.231566	+	0.0541339i
$381$	44.6491	+	25.7782i	2.28744	+	1.32066i
$382$	−20.2454	−	27.2815i	−1.03585	−	1.39584i
$383$	−4.22070	−	15.7519i	−0.215668	−	0.804883i	−0.985930	−	0.167157i	$-0.946541\pi$
$383$	−4.22070	−	15.7519i	−0.215668	−	0.804883i	0.770262	−	0.637727i	$-0.220125\pi$
$384$	21.9685	−	22.7909i	1.12108	−	1.16304i
$385$	−3.24264	+	3.24264i	−0.165260	+	0.165260i
$386$	9.51294	+	7.54556i	0.484196	+	0.384059i
$387$	−12.3507	−	21.3920i	−0.627820	−	1.08742i
$388$	−0.995257	−	0.618099i	−0.0505265	−	0.0313792i
$389$		−	22.1421i		−	1.12265i	−0.827595	−	0.561325i	$-0.810292\pi$
$389$		−	22.1421i		−	1.12265i	0.827595	−	0.561325i	$-0.189708\pi$
$390$		0			0
$391$			23.0624i			1.16631i
$392$	1.78802	+	1.51437i	0.0903085	+	0.0764874i
$393$	14.9853	+	25.9553i	0.755907	+	1.30927i
$394$	−23.1256	+	29.1552i	−1.16505	+	1.46882i
$395$	6.75481	−	6.75481i	0.339871	−	0.339871i
$396$	−0.508782	+	15.8193i	−0.0255673	+	0.794951i
$397$	−0.554425	−	2.06914i	−0.0278258	−	0.103847i	0.950616	−	0.310369i	$-0.100452\pi$
$397$	−0.554425	−	2.06914i	−0.0278258	−	0.103847i	−0.978442	+	0.206521i	$0.933786\pi$
$398$	18.7457	−	13.9111i	0.939639	−	0.697302i
$399$	−15.7144	−	9.07269i	−0.786702	−	0.454203i
$400$	15.9669	+	1.02812i	0.798347	+	0.0514061i
$401$	−26.6174	−	7.13211i	−1.32921	−	0.356160i	−0.476789	−	0.879018i	$-0.658199\pi$
$401$	−26.6174	−	7.13211i	−1.32921	−	0.356160i	−0.852420	+	0.522857i	$0.824866\pi$
$402$	15.4881	+	2.29289i	0.772474	+	0.114359i
$403$		0			0
$404$	20.7279	+	6.27476i	1.03125	+	0.312181i
$405$	0.0444063	−	0.165727i	0.00220657	−	0.00823502i
$406$	−0.852478	−	2.15543i	−0.0423078	−	0.106972i
$407$	−2.17728	+	3.77116i	−0.107924	+	0.186929i
$408$	15.5763	+	43.4151i	0.771143	+	2.14937i
$409$	−7.02429	+	1.88215i	−0.347329	+	0.0930664i	−0.428266	−	0.903653i	$-0.640875\pi$
$409$	−7.02429	+	1.88215i	−0.347329	+	0.0930664i	0.0809372	+	0.996719i	$0.474209\pi$
$410$	8.42941	−	0.972176i	0.416299	−	0.0480124i
$411$	−24.2213	−	24.2213i	−1.19475	−	1.19475i
$412$	−6.72653	−	7.17358i	−0.331392	−	0.353417i
$413$	7.94282	−	4.58579i	0.390840	−	0.225652i
$414$	−24.7931	−	10.7397i	−1.21851	−	0.527830i
$415$	9.55274			0.468926
$416$		0			0
$417$	−61.2843			−3.00110
$418$	4.92993	+	2.13552i	0.241131	+	0.104452i
$419$	−4.43043	+	2.55791i	−0.216441	+	0.124962i	−0.604301	−	0.796756i	$-0.706548\pi$
$419$	−4.43043	+	2.55791i	−0.216441	+	0.124962i	0.387861	+	0.921718i	$0.373214\pi$
$420$	−10.7095	−	11.4212i	−0.522568	−	0.557299i
$421$	0.0208153	+	0.0208153i	0.00101447	+	0.00101447i	0.707614	−	0.706599i	$-0.249772\pi$
$421$	0.0208153	+	0.0208153i	0.00101447	+	0.00101447i	−0.706599	+	0.707614i	$0.749772\pi$
$422$	13.7000	−	1.58004i	0.666906	−	0.0769153i
$423$	−13.0493	+	3.49655i	−0.634478	+	0.170008i
$424$	−0.231761	−	0.645974i	−0.0112553	−	0.0313713i
$425$	−11.6569	+	20.1903i	−0.565440	+	0.979372i
$426$	−10.8180	−	27.3526i	−0.524136	−	1.32524i
$427$	0.599912	−	2.23890i	0.0290318	−	0.108348i
$428$	−19.5855	−	5.92893i	−0.946702	−	0.286586i
$429$		0			0
$430$	−7.15685	−	1.05952i	−0.345134	−	0.0510946i
$431$	−35.5179	−	9.51699i	−1.71084	−	0.458417i	−0.735207	−	0.677843i	$-0.762915\pi$
$431$	−35.5179	−	9.51699i	−1.71084	−	0.458417i	−0.975629	+	0.219426i	$0.929582\pi$
$432$	−20.4210	−	1.31492i	−0.982505	−	0.0632642i
$433$	−8.38857	−	4.84315i	−0.403129	−	0.232747i	0.284704	−	0.958615i	$-0.408105\pi$
$433$	−8.38857	−	4.84315i	−0.403129	−	0.232747i	−0.687833	+	0.725869i	$0.741438\pi$
$434$	17.7809	−	13.1952i	0.853513	−	0.633388i
$435$	0.424202	+	1.58314i	0.0203389	+	0.0759059i
$436$	0.427975	−	13.3068i	0.0204963	−	0.637281i
$437$	−6.48528	+	6.48528i	−0.310233	+	0.310233i
$438$	33.5814	−	42.3372i	1.60458	−	2.02295i
$439$	11.8706	+	20.5605i	0.566554	+	0.981300i	0.996903	+	0.0786378i	$0.0250570\pi$
$439$	11.8706	+	20.5605i	0.566554	+	0.981300i	−0.430349	+	0.902662i	$0.641610\pi$
$440$	3.53748	+	2.99609i	0.168643	+	0.142833i
$441$		−	4.00000i		−	0.190476i
$442$		0			0
$443$			27.4993i			1.30653i	0.757129	+	0.653265i	$0.226601\pi$
$443$			27.4993i			1.30653i	−0.757129	+	0.653265i	$0.773399\pi$
$444$	−12.6299	−	7.84375i	−0.599390	−	0.372248i
$445$	4.41421	+	7.64564i	0.209254	+	0.362438i
$446$	−27.9007	−	22.1305i	−1.32113	−	1.04791i
$447$	−18.1454	+	18.1454i	−0.858247	+	0.858247i
$448$	13.0065	−	18.2167i	0.614500	−	0.860660i
$449$	0.0995874	+	0.371665i	0.00469982	+	0.0175400i	0.968236	−	0.250038i	$-0.0804432\pi$
$449$	0.0995874	+	0.371665i	0.00469982	+	0.0175400i	−0.963536	+	0.267578i	$0.913777\pi$
$450$	−16.2771	−	21.9339i	−0.767308	−	1.03397i
$451$	−8.51645	−	4.91697i	−0.401024	−	0.231531i
$452$	−29.8233	+	6.97188i	−1.40277	+	0.327930i
$453$	4.96692	+	1.33088i	0.233366	+	0.0625303i
$454$	3.75803	−	25.3848i	0.176373	−	1.19137i
$455$		0			0
$456$	−7.82843	+	16.5888i	−0.366600	+	0.776840i
$457$	1.24969	−	4.66390i	0.0584580	−	0.218168i	−0.930518	−	0.366247i	$-0.880642\pi$
$457$	1.24969	−	4.66390i	0.0584580	−	0.218168i	0.988976	+	0.148079i	$0.0473091\pi$
$458$	27.3526	−	10.8180i	1.27810	−	0.505494i
$459$	14.9086	−	25.8224i	0.695873	−	1.20529i
$460$	−6.97716	+	3.73452i	−0.325312	+	0.174123i
$461$	−18.4899	+	4.95435i	−0.861160	+	0.230747i	−0.662261	−	0.749273i	$-0.730403\pi$
$461$	−18.4899	+	4.95435i	−0.861160	+	0.230747i	−0.198899	+	0.980020i	$0.563736\pi$
$462$	2.07895	+	18.0259i	0.0967217	+	0.838640i
$463$	16.1087	+	16.1087i	0.748635	+	0.748635i	0.974223	−	0.225588i	$-0.0724303\pi$
$463$	16.1087	+	16.1087i	0.748635	+	0.748635i	−0.225588	+	0.974223i	$0.572430\pi$
$464$	−2.10031	+	1.03876i	−0.0975046	+	0.0482231i
$465$	−13.5592	+	7.82843i	−0.628794	+	0.363035i
$466$	6.72900	−	15.5341i	0.311715	−	0.719605i
$467$	6.95365			0.321777			0.160888	−	0.986973i	$-0.448564\pi$
$467$	6.95365			0.321777			0.160888	+	0.986973i	$0.448564\pi$
$468$		0			0
$469$	11.0711			0.511214
$470$	−1.57280	+	3.63086i	−0.0725478	+	0.167479i
$471$	−29.0770	+	16.7876i	−1.33980	+	0.773532i
$472$	−5.28299	−	7.61914i	−0.243169	−	0.350699i
$473$	5.92893	+	5.92893i	0.272613	+	0.272613i
$474$	−4.33071	−	37.5501i	−0.198916	−	1.72473i
$475$	−8.95561	+	2.39965i	−0.410912	+	0.110103i
$476$	15.3912	+	28.7551i	0.705452	+	1.31799i
$477$	−0.585786	+	1.01461i	−0.0268213	+	0.0464559i
$478$	15.3495	−	6.07077i	0.702069	−	0.277670i
$479$	2.77239	−	10.3467i	0.126674	−	0.472752i	−0.873220	−	0.487326i	$-0.837972\pi$
$479$	2.77239	−	10.3467i	0.126674	−	0.472752i	0.999894	+	0.0145735i	$0.00463906\pi$
$480$	−10.6123	+	11.7426i	−0.484381	+	0.535976i
$481$		0			0
$482$	−3.82843	+	25.8603i	−0.174380	+	1.17790i
$483$	−29.9206	−	8.01721i	−1.36144	−	0.364795i
$484$	3.78498	+	16.1909i	0.172045	+	0.735949i
$485$	0.507306	+	0.292893i	0.0230356	+	0.0132996i
$486$	−13.3390	−	17.9747i	−0.605068	−	0.815351i
$487$	2.29672	+	8.57148i	0.104074	+	0.388411i	0.998239	−	0.0593285i	$-0.0188959\pi$
$487$	2.29672	+	8.57148i	0.104074	+	0.388411i	−0.894164	+	0.447739i	$0.852229\pi$
$488$	−2.30565	−	0.417478i	−0.104372	−	0.0188983i
$489$	−29.9706	+	29.9706i	−1.35532	+	1.35532i
$490$	−0.917886	−	0.728057i	−0.0414659	−	0.0328903i
$491$	1.39897	+	2.42308i	0.0631345	+	0.109352i	0.895865	−	0.444326i	$-0.146557\pi$
$491$	1.39897	+	2.42308i	0.0631345	+	0.109352i	−0.832730	+	0.553679i	$0.813224\pi$
$492$	17.7136	−	28.5223i	0.798591	−	1.28588i
$493$		−	3.41421i		−	0.153768i
$494$		0			0
$495$		−	7.91375i		−	0.355697i
$496$	−14.7777	−	16.8118i	−0.663541	−	0.754873i
$497$	−10.3995	−	18.0125i	−0.466481	−	0.807969i
$498$	23.4896	−	29.6142i	1.05260	−	1.32704i
$499$	3.95687	−	3.95687i	0.177134	−	0.177134i	−0.612971	−	0.790105i	$-0.710026\pi$
$499$	3.95687	−	3.95687i	0.177134	−	0.177134i	0.790105	+	0.612971i	$0.210026\pi$
$500$	−17.9907	−	0.578618i	−0.804568	−	0.0258766i
$501$	9.78310	+	36.5110i	0.437077	+	1.63119i
$502$	−20.6071	+	15.2924i	−0.919739	+	0.682534i
$503$	20.2161	+	11.6718i	0.901392	+	0.520419i	0.877652	−	0.479299i	$-0.159109\pi$
$503$	20.2161	+	11.6718i	0.901392	+	0.520419i	0.0237405	+	0.999718i	$0.492442\pi$
$504$	−38.0804	+	3.15542i	−1.69624	+	0.140554i
$505$	−10.4595	−	2.80260i	−0.465440	−	0.124714i
$506$	9.07269	+	1.34315i	0.403330	+	0.0597101i
$507$		0			0
$508$	10.6777	−	35.2724i	0.473745	−	1.56496i
$509$	3.05380	−	11.3969i	0.135357	−	0.505161i	−0.864639	−	0.502394i	$-0.832453\pi$
$509$	3.05380	−	11.3969i	0.135357	−	0.505161i	0.999996	−	0.00276674i	$-0.000880680\pi$
$510$	−8.48194	−	21.4460i	−0.375586	−	0.949643i
$511$	19.1055	−	33.0917i	0.845177	−	1.46389i
$512$	−19.4382	−	11.5827i	−0.859054	−	0.511886i
$513$	11.4538	−	3.06904i	0.505698	−	0.135501i
$514$	0.922815	−	0.106430i	0.0407036	−	0.00469441i
$515$	3.47682	+	3.47682i	0.153207	+	0.153207i
$516$	−20.8829	+	19.5815i	−0.919318	+	0.862026i
$517$	3.97141	−	2.29289i	0.174662	−	0.100841i
$518$	−9.64667	−	4.17870i	−0.423850	−	0.183601i
$519$	34.6518			1.52104
$520$		0			0
$521$	11.0000			0.481919			0.240959	−	0.970535i	$-0.422538\pi$
$521$	11.0000			0.481919			0.240959	+	0.970535i	$0.422538\pi$
$522$	3.67043	+	1.58994i	0.160651	+	0.0695898i
$523$	12.8755	−	7.43370i	0.563008	−	0.325053i	−0.191344	−	0.981523i	$-0.561285\pi$
$523$	12.8755	−	7.43370i	0.563008	−	0.325053i	0.754352	+	0.656470i	$0.227951\pi$
$524$	15.6277	−	14.6538i	0.682701	−	0.640155i
$525$	−22.1421	−	22.1421i	−0.966362	−	0.966362i
$526$	12.4669	−	1.43782i	0.543582	−	0.0626921i
$527$	31.5038	−	8.44141i	1.37233	−	0.367713i
$528$	17.9866	−	3.59922i	0.782765	−	0.156636i
$529$	3.67157	−	6.35935i	0.159634	−	0.276494i
$530$	0.126203	+	0.319095i	0.00548191	+	0.0138606i
$531$	−4.09646	+	15.2882i	−0.177771	+	0.663451i
$532$	−3.75803	+	12.4142i	−0.162931	+	0.538224i
$533$		0			0
$534$	34.5563	+	5.11582i	1.49540	+	0.221383i
$535$	9.88300	+	2.64814i	0.427279	+	0.114489i
$536$	−0.924203	−	11.1535i	−0.0399195	−	0.481758i
$537$	−18.0125	−	10.3995i	−0.777295	−	0.448771i
$538$	9.24674	−	6.86196i	0.398655	−	0.295840i
$539$	0.351421	+	1.31152i	0.0151368	+	0.0564911i
$540$	10.2263	+	0.328900i	0.440072	+	0.0141536i
$541$	16.1213	−	16.1213i	0.693110	−	0.693110i	−0.269805	−	0.962915i	$-0.586959\pi$
$541$	16.1213	−	16.1213i	0.693110	−	0.693110i	0.962915	+	0.269805i	$0.0869593\pi$
$542$	−16.3688	+	20.6367i	−0.703101	+	0.886424i
$543$	−15.9681	−	27.6576i	−0.685257	−	1.18690i
$544$	27.6844	−	17.9062i	1.18696	−	0.767722i
$545$			6.65685i			0.285148i
$546$		0			0
$547$			14.3873i			0.615159i	0.951522	+	0.307579i	$0.0995189\pi$
$547$			14.3873i			0.615159i	−0.951522	+	0.307579i	$0.900481\pi$
$548$	−12.9180	+	20.8004i	−0.551828	+	0.888548i
$549$	2.00000	+	3.46410i	0.0853579	+	0.147844i
$550$	7.26392	+	5.76166i	0.309735	+	0.245678i
$551$	0.960099	−	0.960099i	0.0409016	−	0.0409016i
$552$	−5.57916	+	30.8127i	−0.237465	+	1.31147i
$553$	−6.91770	−	25.8172i	−0.294170	−	1.09786i
$554$	−5.05663	−	6.81399i	−0.214836	−	0.289499i
$555$	6.43777	+	3.71685i	0.273268	+	0.157771i
$556$	9.97197	+	42.6567i	0.422906	+	1.80905i
$557$	11.4254	+	3.06142i	0.484109	+	0.129717i	0.492615	−	0.870247i	$-0.336041\pi$
$557$	11.4254	+	3.06142i	0.484109	+	0.129717i	−0.00850625	+	0.999964i	$0.502708\pi$
$558$	−5.59587	+	37.7990i	−0.236892	+	1.60016i
$559$		0			0
$560$	−6.20711	+	9.31271i	−0.262298	+	0.393534i
$561$	−6.91770	+	25.8172i	−0.292065	+	1.09000i
$562$	−14.4273	+	5.70605i	−0.608580	+	0.240695i
$563$	−14.2297	+	24.6465i	−0.599710	+	1.03873i	0.393154	+	0.919473i	$0.371384\pi$
$563$	−14.2297	+	24.6465i	−0.599710	+	1.03873i	−0.992864	+	0.119255i	$0.961949\pi$
$564$	7.38851	+	13.8039i	0.311113	+	0.581248i
$565$	14.7919	−	3.96348i	0.622300	−	0.166745i
$566$	−0.220001	−	1.90755i	−0.00924733	−	0.0801804i
$567$	−0.339446	−	0.339446i	−0.0142554	−	0.0142554i
$568$	−17.2784	+	11.9806i	−0.724987	+	0.502695i
$569$	−25.5350	+	14.7426i	−1.07048	+	0.618044i	−0.928313	−	0.371799i	$-0.878741\pi$
$569$	−25.5350	+	14.7426i	−1.07048	+	0.618044i	−0.142170	+	0.989842i	$0.545408\pi$
$570$	3.64556	−	8.41591i	0.152696	−	0.352504i
$571$	−11.6718			−0.488449			−0.244224	−	0.969719i	$-0.578533\pi$
$571$	−11.6718			−0.488449			−0.244224	+	0.969719i	$0.578533\pi$
$572$		0			0
$573$	67.2132			2.80787
$574$	9.43679	−	21.7852i	0.393884	−	0.909295i
$575$	−13.7070	+	7.91375i	−0.571622	+	0.330026i
$576$	6.35784	+	38.1006i	0.264910	+	1.58752i
$577$	−0.485281	−	0.485281i	−0.0202025	−	0.0202025i	0.696933	−	0.717136i	$-0.254547\pi$
$577$	−0.485281	−	0.485281i	−0.0202025	−	0.0202025i	−0.717136	+	0.696933i	$0.754547\pi$
$578$	2.74973	+	23.8420i	0.114374	+	0.991695i
$579$	−23.2039	+	6.21747i	−0.964321	+	0.258389i
$580$	1.03292	−	0.552869i	0.0428896	−	0.0229566i
$581$	13.3640	−	23.1471i	0.554431	−	0.960302i
$582$	2.15543	−	0.852478i	0.0893453	−	0.0353363i
$583$	0.102929	−	0.384135i	0.00426287	−	0.0159092i
$584$	−34.9330	−	16.4853i	−1.44554	−	0.682166i
$585$		0			0
$586$	5.62132	−	37.9709i	0.232215	−	1.56856i
$587$	34.3984	+	9.21703i	1.41977	+	0.380428i	0.885404	−	0.464823i	$-0.153882\pi$
$587$	34.3984	+	9.21703i	1.41977	+	0.380428i	0.534371	+	0.845250i	$0.320549\pi$
$588$	−4.51406	+	1.05526i	−0.186157	+	0.0435183i
$589$	11.2328	+	6.48528i	0.462841	+	0.267221i
$590$	2.76259	+	3.72269i	0.113734	+	0.153261i
$591$	−19.0553	−	71.1153i	−0.783830	−	2.92529i
$592$	−3.40452	+	10.0673i	−0.139925	+	0.413765i
$593$	−1.44365	+	1.44365i	−0.0592836	+	0.0592836i	−0.736127	−	0.676843i	$-0.763347\pi$
$593$	−1.44365	+	1.44365i	−0.0592836	+	0.0592836i	0.676843	+	0.736127i	$0.263347\pi$
$594$	−9.29022	−	7.36890i	−0.381182	−	0.302350i
$595$	−8.15377	−	14.1227i	−0.334272	−	0.578976i
$596$	15.5826	+	9.67748i	0.638288	+	0.396405i
$597$			46.1838i			1.89018i
$598$		0			0
$599$		−	13.9073i		−	0.568237i	−0.958789	−	0.284118i	$-0.908299\pi$
$599$		−	13.9073i		−	0.568237i	0.958789	−	0.284118i	$-0.0917009\pi$
$600$	−20.4586	+	24.1554i	−0.835219	+	0.986141i
$601$	−7.98528	−	13.8309i	−0.325726	−	0.564175i	0.655933	−	0.754819i	$-0.272276\pi$
$601$	−7.98528	−	13.8309i	−0.325726	−	0.564175i	−0.981659	+	0.190645i	$0.938942\pi$
$602$	−12.5795	+	15.8594i	−0.512702	+	0.646381i
$603$	−13.5096	+	13.5096i	−0.550154	+	0.550154i
$604$	0.118156	−	3.67377i	0.00480770	−	0.149484i
$605$	−2.15175	−	8.03043i	−0.0874809	−	0.326483i
$606$	−34.4075	+	25.5336i	−1.39771	+	1.03723i
$607$	21.7364	+	12.5495i	0.882253	+	0.509369i	0.871401	−	0.490572i	$-0.163212\pi$
$607$	21.7364	+	12.5495i	0.882253	+	0.509369i	0.0108525	+	0.999941i	$0.496545\pi$
$608$	12.8204	+	2.74969i	0.519935	+	0.111515i
$609$	4.42953	+	1.18689i	0.179494	+	0.0480952i
$610$	1.15894	+	0.171573i	0.0469242	+	0.00694678i
$611$		0			0
$612$	−53.8701	−	16.3075i	−2.17757	−	0.659193i
$613$	11.2992	−	42.1693i	0.456371	−	1.70320i	−0.227653	−	0.973742i	$-0.573105\pi$
$613$	11.2992	−	42.1693i	0.456371	−	1.70320i	0.684025	−	0.729459i	$-0.260228\pi$
$614$	14.0533	+	35.5328i	0.567146	+	1.43399i
$615$	−8.39380	+	14.5385i	−0.338471	+	0.586248i
$616$	12.2086	−	4.38016i	0.491898	−	0.176482i
$617$	33.4475	−	8.96224i	1.34655	−	0.360806i	0.487687	−	0.873018i	$-0.337841\pi$
$617$	33.4475	−	8.96224i	1.34655	−	0.360806i	0.858859	+	0.512212i	$0.171174\pi$
$618$	19.3277	−	2.22910i	0.777475	−	0.0896674i
$619$	21.1422	+	21.1422i	0.849775	+	0.849775i	0.990105	−	0.140330i	$-0.0448163\pi$
$619$	21.1422	+	21.1422i	0.849775	+	0.849775i	−0.140330	+	0.990105i	$0.544816\pi$
$620$	7.65527	+	8.16405i	0.307443	+	0.327876i
$621$	17.5306	−	10.1213i	0.703480	−	0.406155i
$622$	−29.5630	−	12.8059i	−1.18537	−	0.513471i
$623$	24.7013			0.989638
$624$		0			0
$625$	−11.0000			−0.440000
$626$	−17.4998	−	7.58047i	−0.699432	−	0.302976i
$627$	−9.20526	+	5.31466i	−0.367623	+	0.212247i
$628$	16.4163	+	17.5073i	0.655080	+	0.698618i
$629$	−10.9497	−	10.9497i	−0.436595	−	0.436595i
$630$	18.9797	−	2.18895i	0.756168	−	0.0872100i
$631$	2.70260	−	0.724158i	0.107589	−	0.0288283i	−0.204623	−	0.978841i	$-0.565597\pi$
$631$	2.70260	−	0.724158i	0.107589	−	0.0288283i	0.312212	+	0.950013i	$0.398930\pi$
$632$	−25.4319	+	9.12440i	−1.01163	+	0.362949i
$633$	−13.6421	+	23.6289i	−0.542226	+	0.939163i
$634$	−3.19467	−	8.07748i	−0.126877	−	0.320798i
$635$	−4.76915	+	17.7987i	−0.189258	+	0.706321i
$636$	1.29954	+	0.393398i	0.0515303	+	0.0155993i
$637$		0			0
$638$	−1.34315	−	0.198843i	−0.0531756	−	0.00787227i
$639$	34.6700	+	9.28981i	1.37153	+	0.367499i
$640$	9.90022	+	5.47591i	0.391341	+	0.216454i
$641$	−33.0321	−	19.0711i	−1.30469	−	0.753262i	−0.323484	−	0.946234i	$-0.604854\pi$
$641$	−33.0321	−	19.0711i	−1.30469	−	0.753262i	−0.981204	+	0.192972i	$0.938187\pi$
$642$	32.5112	−	24.1264i	1.28311	−	0.952192i
$643$	6.32040	+	23.5880i	0.249252	+	0.930222i	0.971198	+	0.238272i	$0.0765811\pi$
$643$	6.32040	+	23.5880i	0.249252	+	0.930222i	−0.721946	+	0.691949i	$0.756752\pi$
$644$	−0.711769	+	22.1307i	−0.0280476	+	0.872071i
$645$	10.1213	−	10.1213i	0.398527	−	0.398527i
$646$	−11.8728	+	14.9685i	−0.467130	+	0.588927i
$647$	16.7876	+	29.0770i	0.659988	+	1.14313i	0.980618	+	0.195929i	$0.0627722\pi$
$647$	16.7876	+	29.0770i	0.659988	+	1.14313i	−0.320630	+	0.947205i	$0.603894\pi$
$648$	−0.313637	+	0.370310i	−0.0123208	+	0.0145472i
$649$		−	5.37258i		−	0.210892i
$650$		0			0
$651$			43.8068i			1.71692i
$652$	25.7376	+	15.9842i	1.00796	+	0.625990i
$653$	7.41421	+	12.8418i	0.290141	+	0.502538i	0.973843	−	0.227223i	$-0.0729646\pi$
$653$	7.41421	+	12.8418i	0.290141	+	0.502538i	−0.683702	+	0.729761i	$0.739631\pi$
$654$	20.6367	+	16.3688i	0.806960	+	0.640072i
$655$	−7.57430	+	7.57430i	−0.295952	+	0.295952i
$656$	−22.7352	−	7.68846i	−0.887659	−	0.300184i
$657$	17.0668	+	63.6942i	0.665840	+	2.48495i
$658$	6.59758	+	8.89047i	0.257200	+	0.346587i
$659$	−29.9084	−	17.2676i	−1.16507	−	0.672652i	−0.212554	−	0.977149i	$-0.568178\pi$
$659$	−29.9084	−	17.2676i	−1.16507	−	0.672652i	−0.952513	+	0.304497i	$0.901512\pi$
$660$	−8.93079	+	2.08777i	−0.347630	+	0.0812664i
$661$	42.4439	+	11.3728i	1.65088	+	0.442351i	0.959858	−	0.280487i	$-0.0904961\pi$
$661$	42.4439	+	11.3728i	1.65088	+	0.442351i	0.691017	+	0.722838i	$0.257163\pi$
$662$	−4.29632	+	29.0208i	−0.166981	+	1.12793i
$663$		0			0
$664$	−24.4350	−	11.5312i	−0.948263	−	0.447496i
$665$	1.67851	−	6.26430i	0.0650900	−	0.242919i
$666$	16.8706	−	6.67237i	0.653722	−	0.258549i
$667$	1.15894	−	2.00735i	0.0448744	−	0.0777247i
$668$	23.8215	−	12.7504i	0.921682	−	0.493330i
$669$	68.0551	−	18.2353i	2.63116	−	0.705018i
$670$	0.641130	+	5.55902i	0.0247690	+	0.214764i
$671$	−0.960099	−	0.960099i	−0.0370642	−	0.0370642i
$672$	13.6072	+	42.1419i	0.524908	+	1.62566i
$673$	−37.0650	+	21.3995i	−1.42875	+	0.824890i	−0.997022	−	0.0771135i	$-0.975430\pi$
$673$	−37.0650	+	21.3995i	−1.42875	+	0.824890i	−0.431729	+	0.902003i	$0.642096\pi$
$674$	−4.59348	+	10.6042i	−0.176934	+	0.408459i
$675$	20.4633			0.787631
$676$		0			0
$677$	−31.2132			−1.19962			−0.599810	−	0.800142i	$-0.704757\pi$
$677$	−31.2132			−1.19962			−0.599810	+	0.800142i	$0.704757\pi$
$678$	24.0854	−	55.6020i	0.924994	−	2.13538i
$679$	1.41941	−	0.819496i	0.0544719	−	0.0314494i
$680$	−13.5472	+	9.39344i	−0.519513	+	0.360222i
$681$	35.8995	+	35.8995i	1.37567	+	1.37567i
$682$	−1.48606	−	12.8852i	−0.0569043	−	0.493398i
$683$	−42.9699	+	11.5138i	−1.64420	+	0.440561i	−0.957980	−	0.286835i	$-0.907397\pi$
$683$	−42.9699	+	11.5138i	−1.64420	+	0.440561i	−0.686218	+	0.727396i	$0.740730\pi$
$684$	−10.5628	−	19.7344i	−0.403879	−	0.754563i
$685$	6.12132	−	10.6024i	0.233884	−	0.405098i
$686$	22.7086	−	8.98131i	0.867017	−	0.342908i
$687$	−15.0618	+	56.2113i	−0.574642	+	2.14459i
$688$	17.0276	+	11.3492i	0.649172	+	0.432686i
$689$		0			0
$690$	2.29289	−	15.4881i	0.0872890	−	0.589620i
$691$	−3.16629	−	0.848404i	−0.120451	−	0.0322748i	0.198090	−	0.980184i	$-0.436526\pi$
$691$	−3.16629	−	0.848404i	−0.120451	−	0.0322748i	−0.318541	+	0.947909i	$0.603193\pi$
$692$	−5.63842	−	24.1193i	−0.214341	−	0.916877i
$693$	−19.1757	−	11.0711i	−0.728423	−	0.420555i
$694$	7.88320	+	10.6229i	0.299242	+	0.403240i
$695$	−5.66902	−	21.1571i	−0.215038	−	0.802533i
$696$	0.825954	−	4.56159i	0.0313077	−	0.172907i
$697$	24.7279	−	24.7279i	0.936637	−	0.936637i
$698$	0.727786	+	0.577272i	0.0275471	+	0.0218501i
$699$	16.7464	+	29.0056i	0.633408	+	1.09709i
$700$	−11.8091	+	19.0149i	−0.446341	+	0.718694i
$701$			31.3553i			1.18427i	0.805837	+	0.592137i	$0.201716\pi$
$701$			31.3553i			1.18427i	−0.805837	+	0.592137i	$0.798284\pi$
$702$		0			0
$703$		−	6.15828i		−	0.232264i
$704$	−5.43194	−	11.9338i	−0.204724	−	0.449774i
$705$	−3.91421	−	6.77962i	−0.147418	−	0.255335i
$706$	−5.48630	+	6.91676i	−0.206480	+	0.260316i
$707$	−21.4234	+	21.4234i	−0.805708	+	0.805708i
$708$	18.3337	+	0.589649i	0.689021	+	0.0221604i
$709$	−1.08730	−	4.05786i	−0.0408345	−	0.152396i	0.942498	−	0.334211i	$-0.108470\pi$
$709$	−1.08730	−	4.05786i	−0.0408345	−	0.152396i	−0.983333	+	0.181814i	$0.941803\pi$
$710$	8.44219	−	6.26491i	0.316830	−	0.235118i
$711$	39.9452	+	23.0624i	1.49806	+	0.864906i
$712$	−2.06205	−	24.8853i	−0.0772784	−	0.932615i
$713$	21.3877	+	5.73081i	0.800974	+	0.214620i
$714$	−63.8312	−	9.44975i	−2.38882	−	0.353648i
$715$		0			0
$716$	−4.30761	+	14.2297i	−0.160983	+	0.531788i
$717$	−8.45222	+	31.5441i	−0.315654	+	1.17804i
$718$	−2.91054	−	7.35909i	−0.108620	−	0.274639i
$719$	−8.53440	+	14.7820i	−0.318279	+	0.551276i	−0.980129	−	0.198360i	$-0.936438\pi$
$719$	−8.53440	+	14.7820i	−0.318279	+	0.551276i	0.661850	+	0.749637i	$0.269772\pi$
$720$	−3.78966	−	18.9383i	−0.141232	−	0.705787i
$721$	13.2886	−	3.56067i	0.494893	−	0.132606i
$722$	19.1452	−	2.20804i	0.712509	−	0.0821748i
$723$	−36.5720	−	36.5720i	−1.36013	−	1.36013i
$724$	−16.6527	+	15.6149i	−0.618892	+	0.580323i
$725$	2.02922	−	1.17157i	0.0753635	−	0.0435111i
$726$	−30.1859	−	13.0758i	−1.12030	−	0.485288i
$727$	43.1279			1.59953			0.799763	−	0.600316i	$-0.204958\pi$
$727$	43.1279			1.59953			0.799763	+	0.600316i	$0.204958\pi$
$728$		0			0
$729$	43.7696			1.62109
$730$	17.7224	+	7.67691i	0.655936	+	0.284135i
$731$	−25.8224	+	14.9086i	−0.955077	+	0.551414i
$732$	3.38166	−	3.17092i	0.124990	−	0.117200i
$733$	−14.8492	−	14.8492i	−0.548469	−	0.548469i	0.377529	−	0.925998i	$-0.376774\pi$
$733$	−14.8492	−	14.8492i	−0.548469	−	0.548469i	−0.925998	+	0.377529i	$0.876774\pi$
$734$	21.2823	−	2.45452i	0.785544	−	0.0905979i
$735$	2.23890	−	0.599912i	0.0825832	−	0.0221281i
$736$	22.3549	−	1.13038i	0.824013	−	0.0416664i
$737$	3.24264	−	5.61642i	0.119444	−	0.206883i
$738$	15.0683	+	38.0990i	0.554671	+	1.40244i
$739$	−13.7377	+	51.2698i	−0.505349	+	1.88599i	−0.0434508	+	0.999056i	$0.513835\pi$
$739$	−13.7377	+	51.2698i	−0.505349	+	1.88599i	−0.461898	+	0.886933i	$0.652832\pi$
$740$	1.53957	−	5.08579i	0.0565957	−	0.186957i
$741$		0			0
$742$	0.949747	+	0.140603i	0.0348663	+	0.00516171i
$743$	−12.5856	−	3.37230i	−0.461721	−	0.123718i	0.0204578	−	0.999791i	$-0.493488\pi$
$743$	−12.5856	−	3.37230i	−0.461721	−	0.123718i	−0.482178	+	0.876073i	$0.660154\pi$
$744$	44.1330	−	3.65695i	1.61799	−	0.134070i
$745$	−7.94282	−	4.58579i	−0.291002	−	0.168010i
$746$	−34.7825	+	25.8119i	−1.27348	+	0.945042i
$747$	11.9380	+	44.5530i	0.436787	+	1.63011i
$748$	19.0956	+	0.614154i	0.698204	+	0.0224557i
$749$	20.2426	−	20.2426i	0.739650	−	0.739650i
$750$	22.1305	−	27.9007i	0.808091	−	1.01879i
$751$	−4.15572	−	7.19791i	−0.151644	−	0.262656i	0.780188	−	0.625545i	$-0.215123\pi$
$751$	−4.15572	−	7.19791i	−0.151644	−	0.262656i	−0.931832	+	0.362890i	$0.881790\pi$
$752$	8.40591	−	7.38887i	0.306532	−	0.269445i
$753$		−	50.7696i		−	1.85015i
$754$		0			0
$755$			1.83783i			0.0668856i
$756$	15.1033	−	24.3191i	0.549300	−	0.884478i
$757$	−22.3640	−	38.7355i	−0.812832	−	1.40787i	−0.910874	−	0.412684i	$-0.864591\pi$
$757$	−22.3640	−	38.7355i	−0.812832	−	1.40787i	0.0980422	−	0.995182i	$-0.468742\pi$
$758$	21.9208	+	17.3874i	0.796200	+	0.631537i
$759$	−12.8307	+	12.8307i	−0.465726	+	0.465726i
$760$	−6.45107	−	1.16807i	−0.234005	−	0.0423705i
$761$	−0.125600	−	0.468746i	−0.00455300	−	0.0169920i	0.963612	−	0.267305i	$-0.0861331\pi$
$761$	−0.125600	−	0.468746i	−0.00455300	−	0.0169920i	−0.968165	+	0.250313i	$0.919466\pi$
$762$	43.4502	+	58.5508i	1.57404	+	2.12107i
$763$	16.1301	+	9.31271i	0.583949	+	0.337143i
$764$	−10.9367	−	46.7836i	−0.395676	−	1.69257i
$765$	27.1832	+	7.28372i	0.982811	+	0.263343i
$766$	3.37740	−	22.8137i	0.122031	−	0.824293i
$767$		0			0
$768$	41.3198	−	17.2265i	1.49100	−	0.621606i
$769$	−0.606451	+	2.26330i	−0.0218692	+	0.0816169i	−0.975998	−	0.217780i	$-0.930119\pi$
$769$	−0.606451	+	2.26330i	−0.0218692	+	0.0816169i	0.954129	+	0.299396i	$0.0967853\pi$
$770$	−6.03074	+	2.38517i	−0.217333	+	0.0859557i
$771$	−0.918917	+	1.59161i	−0.0330940	+	0.0573205i
$772$	8.10331	+	15.1393i	0.291645	+	0.544876i
$773$	−43.8785	+	11.7572i	−1.57820	+	0.422878i	−0.938369	−	0.345636i	$-0.887663\pi$
$773$	−43.8785	+	11.7572i	−1.57820	+	0.422878i	−0.639833	+	0.768514i	$0.720996\pi$
$774$	−4.00234	−	34.7029i	−0.143861	−	1.24737i
$775$	15.8275	+	15.8275i	0.568540	+	0.568540i
$776$	−0.944089	−	1.36157i	−0.0338908	−	0.0488774i
$777$	18.0125	−	10.3995i	0.646193	−	0.373080i
$778$	12.4467	−	28.7337i	0.446237	−	1.03015i
$779$	13.9073			0.498281
$780$		0			0
$781$	−12.1838			−0.435969
$782$	−12.9640	+	29.9279i	−0.463592	+	1.07022i
$783$	−2.59528	+	1.49839i	−0.0927479	+	0.0535480i
$784$	1.46903	+	2.97029i	0.0524652	+	0.106082i
$785$	−8.48528	−	8.48528i	−0.302853	−	0.302853i
$786$	4.85611	+	42.1057i	0.173212	+	1.50186i
$787$	−25.1712	+	6.74460i	−0.897256	+	0.240419i	−0.677837	−	0.735212i	$-0.737083\pi$
$787$	−25.1712	+	6.74460i	−0.897256	+	0.240419i	−0.219418	+	0.975631i	$0.570416\pi$
$788$	−46.3990	+	24.8350i	−1.65290	+	0.884711i
$789$	−12.4142	+	21.5020i	−0.441958	+	0.765493i
$790$	12.5627	−	4.96860i	0.446963	−	0.176775i
$791$	11.0895	−	41.3868i	0.394299	−	1.47154i
$792$	−9.55274	+	20.2426i	−0.339442	+	0.719291i
$793$		0			0
$794$	0.443651	−	2.99678i	0.0157446	−	0.106352i
$795$	−0.655760	−	0.175710i	−0.0232574	−	0.00623180i
$796$	32.1461	−	7.51487i	1.13939	−	0.266357i
$797$	26.9954	+	15.5858i	0.956225	+	0.552077i	0.895009	−	0.446048i	$-0.147169\pi$
$797$	26.9954	+	15.5858i	0.956225	+	0.552077i	0.0612160	+	0.998125i	$0.480502\pi$
$798$	−15.2924	−	20.6071i	−0.541346	−	0.729483i
$799$	4.22070	+	15.7519i	0.149318	+	0.557261i
$800$	20.1423	+	10.3097i	0.712137	+	0.364502i
$801$	−30.1421	+	30.1421i	−1.06502	+	1.06502i
$802$	−30.5321	−	24.2177i	−1.07813	−	0.855157i
$803$	−11.1917	−	19.3846i	−0.394948	−	0.684069i
$804$	18.8099	+	11.6818i	0.663373	+	0.411984i
$805$		−	11.0711i		−	0.390204i
$806$		0			0
$807$			22.7811i			0.801934i
$808$	23.3713	+	19.7945i	0.822199	+	0.696367i
$809$	3.42893	+	5.93908i	0.120555	+	0.208807i	0.919987	−	0.391950i	$-0.128199\pi$
$809$	3.42893	+	5.93908i	0.120555	+	0.208807i	−0.799432	+	0.600757i	$0.794866\pi$
$810$	0.150786	−	0.190101i	0.00529807	−	0.00667945i
$811$	6.55596	−	6.55596i	0.230211	−	0.230211i	−0.582570	−	0.812781i	$-0.697953\pi$
$811$	6.55596	−	6.55596i	0.230211	−	0.230211i	0.812781	+	0.582570i	$0.197953\pi$
$812$	0.105372	−	3.27629i	0.00369784	−	0.114975i
$813$	−13.4878	−	50.3370i	−0.473036	−	1.76540i
$814$	−4.94532	+	3.66990i	−0.173333	+	0.128630i
$815$	−13.1191	−	7.57430i	−0.459541	−	0.265316i
$816$	−4.19154	+	65.0954i	−0.146733	+	2.27879i
$817$	−11.4538	−	3.06904i	−0.400718	−	0.107372i
$818$	−10.1734	−	1.50610i	−0.355704	−	0.0526594i
$819$		0			0
$820$	11.4853	+	3.47682i	0.401083	+	0.121416i
$821$	−0.813245	+	3.03507i	−0.0283824	+	0.105925i	−0.978664	−	0.205467i	$-0.934129\pi$
$821$	−0.813245	+	3.03507i	−0.0283824	+	0.105925i	0.950282	+	0.311392i	$0.100795\pi$
$822$	−17.8164	−	45.0473i	−0.621417	−	1.57121i
$823$	27.0192	−	46.7987i	0.941831	−	1.63130i	0.179856	−	0.983693i	$-0.442437\pi$
$823$	27.0192	−	46.7987i	0.941831	−	1.63130i	0.761975	−	0.647606i	$-0.224230\pi$
$824$	−4.69650	−	13.0903i	−0.163610	−	0.456022i
$825$	−17.7181	+	4.74756i	−0.616866	+	0.165289i
$826$	12.8852	−	1.48606i	0.448332	−	0.0517068i
$827$	−32.3339	−	32.3339i	−1.12436	−	1.12436i	−0.991078	−	0.133281i	$-0.957449\pi$
$827$	−32.3339	−	32.3339i	−1.12436	−	1.12436i	−0.133281	−	0.991078i	$-0.542551\pi$
$828$	−26.1367	−	27.8738i	−0.908314	−	0.968682i
$829$	−19.3858	+	11.1924i	−0.673296	+	0.388728i	−0.797324	−	0.603551i	$-0.793752\pi$
$829$	−19.3858	+	11.1924i	−0.673296	+	0.388728i	0.124028	+	0.992279i	$0.460419\pi$
$830$	12.3965	+	5.36987i	0.430290	+	0.186391i
$831$	16.7876			0.582355
$832$		0			0
$833$	−4.82843			−0.167295
$834$	−79.5283	−	34.4497i	−2.75384	−	1.19289i
$835$	−11.6997	+	6.75481i	−0.404884	+	0.233760i
$836$	5.19710	+	5.54251i	0.179746	+	0.191692i
$837$	−20.2426	−	20.2426i	−0.699688	−	0.699688i
$838$	−7.18721	+	0.828912i	−0.248278	+	0.0286343i
$839$	32.8153	−	8.79283i	1.13291	−	0.303562i	0.356813	−	0.934176i	$-0.383863\pi$
$839$	32.8153	−	8.79283i	1.13291	−	0.303562i	0.776097	+	0.630614i	$0.217197\pi$
$840$	−7.47741	−	20.8414i	−0.257995	−	0.719095i
$841$	14.3284	−	24.8176i	0.494084	−	0.855778i
$842$	0.0153110	+	0.0387127i	0.000527652	+	0.00133413i
$843$	7.94442	−	29.6490i	0.273620	−	1.02117i
$844$	18.6666	+	5.65076i	0.642531	+	0.194507i
$845$		0			0
$846$	−18.8995	−	2.79793i	−0.649778	−	0.0961949i
$847$	−22.4686	−	6.02044i	−0.772030	−	0.206865i
$848$	0.0623661	−	0.968557i	0.00214166	−	0.0332604i
$849$	3.29002	+	1.89949i	0.112913	+	0.0651905i
$850$	−26.4766	+	19.6481i	−0.908139	+	0.673926i
$851$	−2.72092	−	10.1546i	−0.0932720	−	0.348096i
$852$	1.33719	−	41.5765i	0.0458112	−	1.42439i
$853$	−39.5772	+	39.5772i	−1.35510	+	1.35510i	−0.475240	+	0.879856i	$0.657639\pi$
$853$	−39.5772	+	39.5772i	−1.35510	+	1.35510i	−0.879856	+	0.475240i	$0.842361\pi$
$854$	2.03706	−	2.56818i	0.0697066	−	0.0878815i
$855$	5.59587	+	9.69232i	0.191375	+	0.331470i
$856$	−22.0832	−	18.7035i	−0.754789	−	0.639274i
$857$			30.1421i			1.02964i	0.857300	+	0.514818i	$0.172140\pi$
$857$			30.1421i			1.02964i	−0.857300	+	0.514818i	$0.827860\pi$
$858$		0			0
$859$		−	35.3307i		−	1.20547i	−0.797943	−	0.602733i	$-0.794078\pi$
$859$		−	35.3307i		−	1.20547i	0.797943	−	0.602733i	$-0.205922\pi$
$860$	−8.69182	−	5.39801i	−0.296389	−	0.184071i
$861$	23.4853	+	40.6777i	0.800376	+	1.38629i
$862$	−40.7416	−	32.3158i	−1.38766	−	1.10068i
$863$	−25.3220	+	25.3220i	−0.861971	+	0.861971i	−0.991567	−	0.129596i	$-0.958632\pi$
$863$	−25.3220	+	25.3220i	−0.861971	+	0.861971i	0.129596	+	0.991567i	$0.458632\pi$
$864$	−25.7610	−	13.1856i	−0.876408	−	0.448583i
$865$	3.20542	+	11.9628i	0.108987	+	0.406747i
$866$	−8.16333	−	11.0004i	−0.277401	−	0.373808i
$867$	−41.1210	−	23.7412i	−1.39654	−	0.806295i
$868$	30.4916	−	7.12810i	1.03495	−	0.241944i
$869$	−15.1234	−	4.05229i	−0.513025	−	0.137465i
$870$	−0.339446	+	2.29289i	−0.0115083	+	0.0777364i
$871$		0			0
$872$	8.03553	−	17.0276i	0.272118	−	0.576628i
$873$	−0.732051	+	2.73205i	−0.0247762	+	0.0924659i
$874$	−12.0615	+	4.77035i	−0.407986	+	0.161359i
$875$	12.5907	−	21.8077i	0.425643	−	0.737236i
$876$	67.3774	−	36.0637i	2.27647	−	1.21848i
$877$	−19.4842	+	5.22079i	−0.657936	+	0.176293i	−0.572314	−	0.820034i	$-0.693954\pi$
$877$	−19.4842	+	5.22079i	−0.657936	+	0.176293i	−0.0856217	+	0.996328i	$0.527288\pi$
$878$	3.84678	+	33.3541i	0.129822	+	1.12565i
$879$	53.6990	+	53.6990i	1.81122	+	1.81122i
$880$	2.90638	+	5.87653i	0.0979739	+	0.198098i
$881$	−10.6640	+	6.15685i	−0.359279	+	0.207430i	−0.668764	−	0.743474i	$-0.733176\pi$
$881$	−10.6640	+	6.15685i	−0.359279	+	0.207430i	0.309486	+	0.950904i	$0.399843\pi$
$882$	2.24852	−	5.19078i	0.0757115	−	0.174783i
$883$	−34.4529			−1.15943			−0.579717	−	0.814818i	$-0.696837\pi$
$883$	−34.4529			−1.15943			−0.579717	+	0.814818i	$0.696837\pi$
$884$		0			0
$885$	−9.17157			−0.308299
$886$	−15.4581	+	35.6857i	−0.519326	+	1.19888i
$887$	40.2896	−	23.2612i	1.35279	−	0.781035i	0.364152	−	0.931340i	$-0.381359\pi$
$887$	40.2896	−	23.2612i	1.35279	−	0.781035i	0.988640	+	0.150305i	$0.0480256\pi$
$888$	−11.9806	−	17.2784i	−0.402042	−	0.579826i
$889$	36.4558	+	36.4558i	1.22269	+	1.22269i
$890$	1.43046	+	12.4031i	0.0479493	+	0.415752i
$891$	−0.271625	+	0.0727816i	−0.00909976	+	0.00243827i
$892$	−23.7663	−	44.4024i	−0.795756	−	1.48670i
$893$	−3.24264	+	5.61642i	−0.108511	+	0.187946i
$894$	−33.7472	+	13.3471i	−1.12868	+	0.446394i
$895$	1.92398	−	7.18040i	0.0643117	−	0.240014i
$896$	27.1186	−	16.3284i	0.905970	−	0.545494i
$897$		0			0
$898$	−0.0796898	+	0.538289i	−0.00265928	+	0.0179629i
$899$	−3.16629	−	0.848404i	−0.105602	−	0.0282959i
$900$	−8.79296	−	37.6133i	−0.293099	−	1.25378i
$901$	1.22474	+	0.707107i	0.0408022	+	0.0235571i
$902$	−8.28777	−	11.1681i	−0.275953	−	0.371856i
$903$	−10.3654	−	38.6842i	−0.344939	−	1.28733i
$904$	−42.6207	−	7.71720i	−1.41754	−	0.256670i
$905$	8.07107	−	8.07107i	0.268291	−	0.268291i
$906$	5.69742	+	4.51913i	0.189284	+	0.150138i
$907$	−8.15377	−	14.1227i	−0.270742	−	0.468938i	0.698310	−	0.715795i	$-0.253936\pi$
$907$	−8.15377	−	14.1227i	−0.270742	−	0.468938i	−0.969052	+	0.246857i	$0.920602\pi$
$908$	19.1463	−	30.8292i	0.635392	−	1.02310i
$909$		−	52.2843i		−	1.73416i
$910$		0			0
$911$			4.91697i			0.162907i	0.996677	+	0.0814533i	$0.0259561\pi$
$911$			4.91697i			0.162907i	−0.996677	+	0.0814533i	$0.974044\pi$
$912$	−19.4839	+	17.1265i	−0.645177	+	0.567117i
$913$	−7.82843	−	13.5592i	−0.259083	−	0.448745i
$914$	4.24343	−	5.34983i	0.140360	−	0.176957i
$915$	−1.63899	+	1.63899i	−0.0541834	+	0.0541834i
$916$	41.5765	+	1.33719i	1.37373	+	0.0441819i
$917$	7.75695	+	28.9493i	0.256157	+	0.955991i
$918$	33.8623	−	25.1291i	1.11762	−	0.829383i
$919$	22.2235	+	12.8307i	0.733084	+	0.423246i	0.819549	−	0.573008i	$-0.194224\pi$
$919$	22.2235	+	12.8307i	0.733084	+	0.423246i	−0.0864651	+	0.996255i	$0.527557\pi$
$920$	−11.1535	+	0.924203i	−0.367720	+	0.0304701i
$921$	−73.0220	−	19.5662i	−2.40616	−	0.644728i
$922$	−26.7792	−	3.96447i	−0.881926	−	0.130563i
$923$		0			0
$924$	−7.43503	+	24.5607i	−0.244594	+	0.807989i
$925$	2.75058	−	10.2653i	0.0904384	−	0.337521i
$926$	11.8490	+	29.9593i	0.389383	+	0.984525i
$927$	−11.8706	+	20.5605i	−0.389882	+	0.675296i
$928$	−3.30948	+	0.167345i	−0.108639	+	0.00549336i
$929$	−28.1776	+	7.55016i	−0.924476	+	0.247713i	−0.689498	−	0.724288i	$-0.742169\pi$
$929$	−28.1776	+	7.55016i	−0.924476	+	0.247713i	−0.234979	+	0.972001i	$0.575502\pi$
$930$	−21.9963	+	2.53687i	−0.721288	+	0.0831872i
$931$	−1.35778	−	1.35778i	−0.0444996	−	0.0444996i
$932$	17.4644	−	16.3760i	0.572065	−	0.536414i
$933$	55.2006	−	31.8701i	1.80719	−	1.04338i
$934$	9.02371	+	3.90885i	0.295265	+	0.127901i
$935$	−9.55274			−0.312408
$936$		0			0
$937$	−8.97056			−0.293056			−0.146528	−	0.989207i	$-0.546810\pi$
$937$	−8.97056			−0.293056			−0.146528	+	0.989207i	$0.546810\pi$
$938$	14.3669	+	6.22337i	0.469095	+	0.203200i
$939$	32.6759	−	18.8655i	1.06634	−	0.615651i
$940$	−4.08202	+	3.82763i	−0.133141	+	0.124844i
$941$	34.2635	+	34.2635i	1.11696	+	1.11696i	0.992186	+	0.124771i	$0.0398197\pi$
$941$	34.2635	+	34.2635i	1.11696	+	1.11696i	0.124771	+	0.992186i	$0.460180\pi$
$942$	−47.1698	+	5.44017i	−1.53688	+	0.177250i
$943$	22.9323	−	6.14469i	0.746778	−	0.200099i
$944$	−2.57277	−	12.8570i	−0.0837365	−	0.418461i
$945$	−7.15685	+	12.3960i	−0.232812	+	0.403243i
$946$	4.36112	+	11.0268i	0.141792	+	0.358511i
$947$	−1.12704	+	4.20618i	−0.0366240	+	0.136683i	−0.981817	−	0.189829i	$-0.939207\pi$
$947$	−1.12704	+	4.20618i	−0.0366240	+	0.136683i	0.945193	+	0.326512i	$0.105873\pi$
$948$	15.4881	−	51.1630i	0.503029	−	1.66170i
$949$		0			0
$950$	−12.9706	−	1.92020i	−0.420821	−	0.0622994i
$951$	16.5997	+	4.44788i	0.538282	+	0.144232i
$952$	3.80893	+	45.9672i	0.123448	+	1.48980i
$953$	44.2904	+	25.5711i	1.43471	+	0.828328i	0.997475	−	0.0710208i	$-0.0226257\pi$
$953$	44.2904	+	25.5711i	1.43471	+	0.828328i	0.437232	+	0.899349i	$0.355959\pi$
$954$	−1.33051	+	0.987369i	−0.0430770	+	0.0319672i
$955$	6.21747	+	23.2039i	0.201193	+	0.750861i
$956$	23.3315	+	0.750389i	0.754595	+	0.0242693i
$957$	1.89949	−	1.89949i	0.0614020	−	0.0614020i
$958$	9.41388	−	11.8684i	0.304149	−	0.383451i
$959$	−17.1270	−	29.6649i	−0.553061	−	0.957930i
$960$	−20.3723	+	9.27290i	−0.657515	+	0.299282i
$961$		−	0.313708i		−	0.0101196i
$962$		0			0
$963$			49.4027i			1.59198i
$964$	−19.5049	+	31.4067i	−0.628212	+	1.01154i
$965$	−4.29289	−	7.43551i	−0.138193	−	0.239358i
$966$	−34.3211	−	27.2231i	−1.10426	−	0.875890i
$967$	7.85551	−	7.85551i	0.252616	−	0.252616i	−0.569426	−	0.822042i	$-0.692835\pi$
$967$	7.85551	−	7.85551i	0.252616	−	0.252616i	0.822042	+	0.569426i	$0.192835\pi$
$968$	−4.18961	+	23.1385i	−0.134659	+	0.743699i
$969$	−9.78310	−	36.5110i	−0.314278	−	1.17290i
$970$	0.493684	+	0.665257i	0.0158513	+	0.0213601i
$971$	−0.760141	−	0.438868i	−0.0243941	−	0.0140839i	0.487753	−	0.872981i	$-0.337817\pi$
$971$	−0.760141	−	0.438868i	−0.0243941	−	0.0140839i	−0.512147	+	0.858898i	$0.671150\pi$
$972$	−7.20579	−	30.8239i	−0.231126	−	0.988678i
$973$	−59.1961	−	15.8615i	−1.89774	−	0.508498i
$974$	−1.83783	+	12.4142i	−0.0588880	+	0.397777i
$975$		0			0
$976$	−2.75736	−	1.83783i	−0.0882609	−	0.0588276i
$977$	13.0405	−	48.6680i	0.417204	−	1.55703i	−0.363176	−	0.931720i	$-0.618308\pi$
$977$	13.0405	−	48.6680i	0.417204	−	1.55703i	0.780380	−	0.625305i	$-0.215026\pi$
$978$	−55.7400	+	22.0453i	−1.78237	+	0.704931i
$979$	7.23486	−	12.5311i	0.231227	−	0.400497i
$980$	−0.781874	−	1.46077i	−0.0249761	−	0.0466625i
$981$	−31.0469	+	8.31900i	−0.991252	+	0.265605i
$982$	0.453347	+	3.93082i	0.0144669	+	0.125437i
$983$	−31.3155	−	31.3155i	−0.998811	−	0.998811i	0.00118842	−	0.999999i	$-0.499622\pi$
$983$	−31.3155	−	31.3155i	−0.998811	−	0.998811i	−0.999999	+	0.00118842i	$0.999622\pi$
$984$	39.0201	−	27.0559i	1.24391	−	0.862510i
$985$	22.7883	−	13.1569i	0.726097	−	0.419212i
$986$	1.91923	−	4.43061i	0.0611207	−	0.141099i
$987$	−21.9034			−0.697193
$988$		0			0
$989$	−20.2426			−0.643679
$990$	4.44855	−	10.2696i	0.141384	−	0.326390i
$991$	−18.5532	+	10.7117i	−0.589361	+	0.340268i	−0.764845	−	0.644215i	$-0.777184\pi$
$991$	−18.5532	+	10.7117i	−0.589361	+	0.340268i	0.175484	+	0.984482i	$0.443851\pi$
$992$	−9.72659	−	30.1236i	−0.308820	−	0.956426i
$993$	−41.0416	−	41.0416i	−1.30242	−	1.30242i
$994$	−3.37005	−	29.2205i	−0.106891	−	0.926819i
$995$	−15.9439	+	4.27217i	−0.505457	+	0.135437i
$996$	47.1294	−	25.2260i	1.49335	−	0.799315i
$997$	8.53553	−	14.7840i	0.270323	−	0.468213i	−0.698621	−	0.715491i	$-0.746203\pi$
$997$	8.53553	−	14.7840i	0.270323	−	0.468213i	0.968945	+	0.247278i	$0.0795362\pi$
$998$	7.35909	−	2.91054i	0.232948	−	0.0921316i
$999$	−3.51786	+	13.1288i	−0.111300	+	0.415378i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	676.2.l.l.427.4		16
4.3	odd	2	inner	676.2.l.l.427.1		16
13.2	odd	12		52.2.f.b.31.4	yes	8
13.3	even	3		52.2.f.b.47.2	yes	8
13.4	even	6		676.2.l.h.319.4		16
13.5	odd	4	inner	676.2.l.l.587.2		16
13.6	odd	12	inner	676.2.l.l.19.1		16
13.7	odd	12		676.2.l.h.19.4		16
13.8	odd	4		676.2.l.h.587.3		16
13.9	even	3	inner	676.2.l.l.319.1		16
13.10	even	6		676.2.f.g.99.3		8
13.11	odd	12		676.2.f.g.239.1		8
13.12	even	2		676.2.l.h.427.1		16
39.2	even	12		468.2.n.i.343.1		8
39.29	odd	6		468.2.n.i.307.3		8
52.3	odd	6		52.2.f.b.47.4	yes	8
52.7	even	12		676.2.l.h.19.1		16
52.11	even	12		676.2.f.g.239.3		8
52.15	even	12		52.2.f.b.31.2	✓	8
52.19	even	12	inner	676.2.l.l.19.4		16
52.23	odd	6		676.2.f.g.99.1		8
52.31	even	4	inner	676.2.l.l.587.1		16
52.35	odd	6	inner	676.2.l.l.319.2		16
52.43	odd	6		676.2.l.h.319.3		16
52.47	even	4		676.2.l.h.587.4		16
52.51	odd	2		676.2.l.h.427.4		16
104.3	odd	6		832.2.k.h.255.1		8
104.29	even	6		832.2.k.h.255.4		8
104.67	even	12		832.2.k.h.447.1		8
104.93	odd	12		832.2.k.h.447.4		8
156.107	even	6		468.2.n.i.307.1		8
156.119	odd	12		468.2.n.i.343.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
52.2.f.b.31.2	✓	8	52.15	even	12
52.2.f.b.31.4	yes	8	13.2	odd	12
52.2.f.b.47.2	yes	8	13.3	even	3
52.2.f.b.47.4	yes	8	52.3	odd	6
468.2.n.i.307.1		8	156.107	even	6
468.2.n.i.307.3		8	39.29	odd	6
468.2.n.i.343.1		8	39.2	even	12
468.2.n.i.343.3		8	156.119	odd	12
676.2.f.g.99.1		8	52.23	odd	6
676.2.f.g.99.3		8	13.10	even	6
676.2.f.g.239.1		8	13.11	odd	12
676.2.f.g.239.3		8	52.11	even	12
676.2.l.h.19.1		16	52.7	even	12
676.2.l.h.19.4		16	13.7	odd	12
676.2.l.h.319.3		16	52.43	odd	6
676.2.l.h.319.4		16	13.4	even	6
676.2.l.h.427.1		16	13.12	even	2
676.2.l.h.427.4		16	52.51	odd	2
676.2.l.h.587.3		16	13.8	odd	4
676.2.l.h.587.4		16	52.47	even	4
676.2.l.l.19.1		16	13.6	odd	12	inner
676.2.l.l.19.4		16	52.19	even	12	inner
676.2.l.l.319.1		16	13.9	even	3	inner
676.2.l.l.319.2		16	52.35	odd	6	inner
676.2.l.l.427.1		16	4.3	odd	2	inner
676.2.l.l.427.4		16	1.1	even	1	trivial
676.2.l.l.587.1		16	52.31	even	4	inner
676.2.l.l.587.2		16	13.5	odd	4	inner
832.2.k.h.255.1		8	104.3	odd	6
832.2.k.h.255.4		8	104.29	even	6
832.2.k.h.447.1		8	104.67	even	12
832.2.k.h.447.4		8	104.93	odd	12

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:	\( N \)	\(=\)	\( 676 = 2^{2} \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	676.l (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.29769 + 0.562129i) q^{2} +(-2.42308 + 1.39897i) q^{3} +(1.36802 + 1.45894i) q^{4} +(-0.707107 - 0.707107i) q^{5} +(-3.93082 + 0.453347i) q^{6} +(-2.70260 + 0.724158i) q^{7} +(0.955161 + 2.66227i) q^{8} +(2.41421 - 4.18154i) q^{9} +O(q^{10})\)	\(q+(1.29769 + 0.562129i) q^{2} +(-2.42308 + 1.39897i) q^{3} +(1.36802 + 1.45894i) q^{4} +(-0.707107 - 0.707107i) q^{5} +(-3.93082 + 0.453347i) q^{6} +(-2.70260 + 0.724158i) q^{7} +(0.955161 + 2.66227i) q^{8} +(2.41421 - 4.18154i) q^{9} +(-0.520123 - 1.31509i) q^{10} +(-0.424202 + 1.58314i) q^{11} +(-5.35584 - 1.62132i) q^{12} +(-3.91421 - 0.579471i) q^{14} +(2.70260 + 0.724158i) q^{15} +(-0.257031 + 3.99173i) q^{16} +(-5.04757 - 2.91421i) q^{17} +(5.48348 - 4.06926i) q^{18} +(-0.599912 - 2.23890i) q^{19} +(0.0642909 - 1.99897i) q^{20} +(5.53553 - 5.53553i) q^{21} +(-1.44042 + 1.81598i) q^{22} +(-1.97844 - 3.42675i) q^{23} +(-6.03885 - 5.11465i) q^{24} -4.00000i q^{25} +5.11582i q^{27} +(-4.75372 - 2.95227i) q^{28} +(0.292893 + 0.507306i) q^{29} +(3.10007 + 2.45894i) q^{30} +(-3.95687 + 3.95687i) q^{31} +(-2.57742 + 5.03557i) q^{32} +(-1.18689 - 4.42953i) q^{33} +(-4.91203 - 6.61914i) q^{34} +(2.42308 + 1.39897i) q^{35} +(9.40333 - 2.19824i) q^{36} +(2.56632 + 0.687644i) q^{37} +(0.480049 - 3.24264i) q^{38} +(1.20711 - 2.55791i) q^{40} +(-1.55291 + 5.79555i) q^{41} +(10.2951 - 4.07175i) q^{42} +(2.55791 - 4.43043i) q^{43} +(-2.89003 + 1.54689i) q^{44} +(-4.66390 + 1.24969i) q^{45} +(-0.641130 - 5.55902i) q^{46} +(-1.97844 - 1.97844i) q^{47} +(-4.96149 - 10.0319i) q^{48} +(0.717439 - 0.414214i) q^{49} +(2.24852 - 5.19078i) q^{50} +16.3075 q^{51} -0.242641 q^{53} +(-2.87575 + 6.63877i) q^{54} +(1.41941 - 0.819496i) q^{55} +(-4.50932 - 6.50334i) q^{56} +(4.58579 + 4.58579i) q^{57} +(0.0949146 + 0.822972i) q^{58} +(-3.16629 + 0.848404i) q^{59} +(2.64070 + 4.93360i) q^{60} +(-0.414214 + 0.717439i) q^{61} +(-7.35909 + 2.91054i) q^{62} +(-3.49655 + 13.0493i) q^{63} +(-6.17534 + 5.08579i) q^{64} +(0.949747 - 6.41536i) q^{66} +(-3.82205 - 1.02411i) q^{67} +(-2.65351 - 11.3508i) q^{68} +(9.58783 + 5.53553i) q^{69} +(2.35802 + 3.17751i) q^{70} +(1.92398 + 7.18040i) q^{71} +(13.4383 + 2.43324i) q^{72} +(-9.65685 + 9.65685i) q^{73} +(2.94376 + 2.33496i) q^{74} +(5.59587 + 9.69232i) q^{75} +(2.44574 - 3.93811i) q^{76} -4.58579i q^{77} +9.55274i q^{79} +(3.00433 - 2.64083i) q^{80} +(0.0857864 + 0.148586i) q^{81} +(-5.27306 + 6.64792i) q^{82} +(-6.75481 + 6.75481i) q^{83} +(15.6488 + 0.503297i) q^{84} +(1.50851 + 5.62983i) q^{85} +(5.80985 - 4.31147i) q^{86} +(-1.41941 - 0.819496i) q^{87} +(-4.61993 + 0.382817i) q^{88} +(-8.52761 - 2.28497i) q^{89} +(-6.75481 - 1.00000i) q^{90} +(2.29289 - 7.57430i) q^{92} +(4.05229 - 15.1234i) q^{93} +(-1.45527 - 3.67954i) q^{94} +(-1.15894 + 2.00735i) q^{95} +(-0.799300 - 15.8073i) q^{96} +(-0.565826 + 0.151613i) q^{97} +(1.16386 - 0.134230i) q^{98} +(5.59587 + 5.59587i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{2} - 8 q^{6} - 8 q^{8} + 16 q^{9}+O(q^{10}) \) 16 * q + 4 * q^2 - 8 * q^6 - 8 * q^8 + 16 * q^9	\( 16 q + 4 q^{2} - 8 q^{6} - 8 q^{8} + 16 q^{9} - 40 q^{14} + 4 q^{16} + 8 q^{20} + 32 q^{21} - 24 q^{22} - 32 q^{24} - 12 q^{28} + 16 q^{29} + 4 q^{32} - 8 q^{33} + 8 q^{34} + 32 q^{37} + 8 q^{40} - 4 q^{42} - 56 q^{44} - 16 q^{45} + 20 q^{46} + 44 q^{48} + 16 q^{50} + 64 q^{53} + 32 q^{54} + 96 q^{57} - 12 q^{58} - 24 q^{60} + 16 q^{61} - 64 q^{66} - 44 q^{68} + 16 q^{70} - 16 q^{72} - 64 q^{73} - 44 q^{74} - 32 q^{76} - 16 q^{80} + 24 q^{81} + 48 q^{84} - 16 q^{85} + 64 q^{86} - 16 q^{89} + 48 q^{92} - 32 q^{93} - 20 q^{94} - 48 q^{96} + 8 q^{97} + 16 q^{98}+O(q^{100}) \) 16 * q + 4 * q^2 - 8 * q^6 - 8 * q^8 + 16 * q^9 - 40 * q^14 + 4 * q^16 + 8 * q^20 + 32 * q^21 - 24 * q^22 - 32 * q^24 - 12 * q^28 + 16 * q^29 + 4 * q^32 - 8 * q^33 + 8 * q^34 + 32 * q^37 + 8 * q^40 - 4 * q^42 - 56 * q^44 - 16 * q^45 + 20 * q^46 + 44 * q^48 + 16 * q^50 + 64 * q^53 + 32 * q^54 + 96 * q^57 - 12 * q^58 - 24 * q^60 + 16 * q^61 - 64 * q^66 - 44 * q^68 + 16 * q^70 - 16 * q^72 - 64 * q^73 - 44 * q^74 - 32 * q^76 - 16 * q^80 + 24 * q^81 + 48 * q^84 - 16 * q^85 + 64 * q^86 - 16 * q^89 + 48 * q^92 - 32 * q^93 - 20 * q^94 - 48 * q^96 + 8 * q^97 + 16 * q^98

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