LMFDB - Embedded newform 260.2.j.a.31.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [260,2,Mod(31,260)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(260, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 0, 3]))

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

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

chi := DirichletCharacter("260.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 260 = 2^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	260.j (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.07611045255$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$28$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			31.11
Character	$\chi$	$=$	260.31
Dual form			260.2.j.a.151.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.647340 + 1.25736i) q^{2} +0.759638i q^{3} +(-1.16190 - 1.62788i) q^{4} +(0.707107 - 0.707107i) q^{5} +(-0.955138 - 0.491744i) q^{6} +(2.17387 - 2.17387i) q^{7} +(2.79897 - 0.407140i) q^{8} +2.42295 q^{9} +O(q^{10})$	\(q+(-0.647340 + 1.25736i) q^{2} +0.759638i q^{3} +(-1.16190 - 1.62788i) q^{4} +(0.707107 - 0.707107i) q^{5} +(-0.955138 - 0.491744i) q^{6} +(2.17387 - 2.17387i) q^{7} +(2.79897 - 0.407140i) q^{8} +2.42295 q^{9} +(0.431349 + 1.34683i) q^{10} +(-2.35498 + 2.35498i) q^{11} +(1.23660 - 0.882626i) q^{12} +(2.65753 - 2.43671i) q^{13} +(1.32610 + 4.14056i) q^{14} +(0.537145 + 0.537145i) q^{15} +(-1.29996 + 3.78287i) q^{16} -0.711800i q^{17} +(-1.56847 + 3.04652i) q^{18} +(3.99929 + 3.99929i) q^{19} +(-1.97267 - 0.329493i) q^{20} +(1.65135 + 1.65135i) q^{21} +(-1.43658 - 4.48552i) q^{22} -7.44256 q^{23} +(0.309279 + 2.12620i) q^{24} -1.00000i q^{25} +(1.34350 + 4.91884i) q^{26} +4.11948i q^{27} +(-6.06460 - 1.01296i) q^{28} +7.58586 q^{29} +(-1.02310 + 0.327669i) q^{30} +(-2.87857 - 2.87857i) q^{31} +(-3.91491 - 4.08332i) q^{32} +(-1.78893 - 1.78893i) q^{33} +(0.894988 + 0.460776i) q^{34} -3.07431i q^{35} +(-2.81523 - 3.94426i) q^{36} +(-1.05129 - 1.05129i) q^{37} +(-7.61743 + 2.43964i) q^{38} +(1.85102 + 2.01876i) q^{39} +(1.69128 - 2.26706i) q^{40} +(-5.21586 + 5.21586i) q^{41} +(-3.14532 + 1.00736i) q^{42} +11.0617 q^{43} +(6.56987 + 1.09736i) q^{44} +(1.71328 - 1.71328i) q^{45} +(4.81786 - 9.35796i) q^{46} +(3.59208 - 3.59208i) q^{47} +(-2.87361 - 0.987502i) q^{48} -2.45138i q^{49} +(1.25736 + 0.647340i) q^{50} +0.540710 q^{51} +(-7.05445 - 1.49490i) q^{52} +0.920541 q^{53} +(-5.17966 - 2.66670i) q^{54} +3.33044i q^{55} +(5.19952 - 6.96965i) q^{56} +(-3.03801 + 3.03801i) q^{57} +(-4.91063 + 9.53814i) q^{58} +(-3.80422 + 3.80422i) q^{59} +(0.250295 - 1.49852i) q^{60} -8.67840 q^{61} +(5.48281 - 1.75598i) q^{62} +(5.26717 - 5.26717i) q^{63} +(7.66847 - 2.27915i) q^{64} +(0.156139 - 3.60217i) q^{65} +(3.40737 - 1.09128i) q^{66} +(-10.8530 - 10.8530i) q^{67} +(-1.15872 + 0.827042i) q^{68} -5.65365i q^{69} +(3.86551 + 1.99012i) q^{70} +(-2.08032 - 2.08032i) q^{71} +(6.78177 - 0.986480i) q^{72} +(-8.66411 - 8.66411i) q^{73} +(2.00240 - 0.641310i) q^{74} +0.759638 q^{75} +(1.86356 - 11.1571i) q^{76} +10.2388i q^{77} +(-3.73654 + 1.02057i) q^{78} -1.66567i q^{79} +(1.75568 + 3.59411i) q^{80} +4.13954 q^{81} +(-3.18177 - 9.93464i) q^{82} +(-2.77385 - 2.77385i) q^{83} +(0.769486 - 4.60690i) q^{84} +(-0.503318 - 0.503318i) q^{85} +(-7.16070 + 13.9086i) q^{86} +5.76250i q^{87} +(-5.63271 + 7.55032i) q^{88} +(-1.93603 - 1.93603i) q^{89} +(1.04514 + 3.26329i) q^{90} +(0.480021 - 11.0742i) q^{91} +(8.64753 + 12.1156i) q^{92} +(2.18667 - 2.18667i) q^{93} +(2.19124 + 6.84182i) q^{94} +5.65584 q^{95} +(3.10185 - 2.97391i) q^{96} +(-9.24834 + 9.24834i) q^{97} +(3.08226 + 1.58687i) q^{98} +(-5.70600 + 5.70600i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 12 q^{6} + 12 q^{8} - 56 q^{9}+O(q^{10}) $ 56 * q - 12 * q^6 + 12 * q^8 - 56 * q^9	$ 56 q - 12 q^{6} + 12 q^{8} - 56 q^{9} + 16 q^{14} - 12 q^{18} - 8 q^{20} - 16 q^{21} - 40 q^{24} - 16 q^{26} - 44 q^{28} + 40 q^{32} - 4 q^{34} + 16 q^{37} + 8 q^{41} + 8 q^{42} + 28 q^{44} - 12 q^{46} + 104 q^{48} + 56 q^{52} - 16 q^{53} + 20 q^{54} - 48 q^{57} - 4 q^{58} + 16 q^{61} - 8 q^{65} + 64 q^{66} + 24 q^{68} - 8 q^{70} - 32 q^{72} + 48 q^{73} - 136 q^{74} - 88 q^{76} + 52 q^{78} - 32 q^{80} + 56 q^{81} - 20 q^{84} - 64 q^{86} - 8 q^{89} - 88 q^{92} - 48 q^{93} - 16 q^{94} - 4 q^{96} - 32 q^{97} + 16 q^{98}+O(q^{100}) $ 56 * q - 12 * q^6 + 12 * q^8 - 56 * q^9 + 16 * q^14 - 12 * q^18 - 8 * q^20 - 16 * q^21 - 40 * q^24 - 16 * q^26 - 44 * q^28 + 40 * q^32 - 4 * q^34 + 16 * q^37 + 8 * q^41 + 8 * q^42 + 28 * q^44 - 12 * q^46 + 104 * q^48 + 56 * q^52 - 16 * q^53 + 20 * q^54 - 48 * q^57 - 4 * q^58 + 16 * q^61 - 8 * q^65 + 64 * q^66 + 24 * q^68 - 8 * q^70 - 32 * q^72 + 48 * q^73 - 136 * q^74 - 88 * q^76 + 52 * q^78 - 32 * q^80 + 56 * q^81 - 20 * q^84 - 64 * q^86 - 8 * q^89 - 88 * q^92 - 48 * q^93 - 16 * q^94 - 4 * q^96 - 32 * q^97 + 16 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/260\mathbb{Z}\right)^\times$.

$n$	$41$	$131$	$157$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	−0.647340	+	1.25736i	−0.457738	+	0.889087i
$2$	−0.647340	+	1.25736i	−0.457738	+	0.889087i
$3$			0.759638i			0.438577i	0.975660	+	0.219289i	$0.0703736\pi$
$3$			0.759638i			0.438577i	−0.975660	+	0.219289i	$0.929626\pi$
$4$	−1.16190	−	1.62788i	−0.580951	−	0.813938i
$5$	0.707107	−	0.707107i	0.316228	−	0.316228i
$5$	0.707107	−	0.707107i	0.316228	−	0.316228i
$6$	−0.955138	−	0.491744i	−0.389933	−	0.200754i
$7$	2.17387	−	2.17387i	0.821644	−	0.821644i	−0.164700	−	0.986344i	$-0.552666\pi$
$7$	2.17387	−	2.17387i	0.821644	−	0.821644i	0.986344	+	0.164700i	$0.0526656\pi$
$8$	2.79897	−	0.407140i	0.989586	−	0.143946i
$9$	2.42295			0.807650
$10$	0.431349	+	1.34683i	0.136404	+	0.425904i
$11$	−2.35498	+	2.35498i	−0.710053	+	0.710053i	−0.966546	−	0.256493i	$-0.917433\pi$
$11$	−2.35498	+	2.35498i	−0.710053	+	0.710053i	0.256493	+	0.966546i	$0.417433\pi$
$12$	1.23660	−	0.882626i	0.356975	−	0.254792i
$13$	2.65753	−	2.43671i	0.737065	−	0.675822i
$13$	2.65753	−	2.43671i	0.737065	−	0.675822i
$14$	1.32610	+	4.14056i	0.354415	+	1.10661i
$15$	0.537145	+	0.537145i	0.138690	+	0.138690i
$16$	−1.29996	+	3.78287i	−0.324991	+	0.945717i
$17$		−	0.711800i		−	0.172637i	−0.996268	−	0.0863184i	$-0.972490\pi$
$17$		−	0.711800i		−	0.172637i	0.996268	−	0.0863184i	$-0.0275102\pi$
$18$	−1.56847	+	3.04652i	−0.369692	+	0.718071i
$19$	3.99929	+	3.99929i	0.917499	+	0.917499i	0.996847	−	0.0793480i	$-0.0252838\pi$
$19$	3.99929	+	3.99929i	0.917499	+	0.917499i	−0.0793480	+	0.996847i	$0.525284\pi$
$20$	−1.97267	−	0.329493i	−0.441103	−	0.0736769i
$21$	1.65135	+	1.65135i	0.360354	+	0.360354i
$22$	−1.43658	−	4.48552i	−0.306280	−	0.956317i
$23$	−7.44256			−1.55188			−0.775940	−	0.630807i	$-0.782724\pi$
$23$	−7.44256			−1.55188			−0.775940	+	0.630807i	$0.782724\pi$
$24$	0.309279	+	2.12620i	0.0631313	+	0.434010i
$25$		−	1.00000i		−	0.200000i
$26$	1.34350	+	4.91884i	0.263482	+	0.964664i
$27$			4.11948i			0.792794i
$28$	−6.06460	−	1.01296i	−1.14610	−	0.191432i
$29$	7.58586			1.40866			0.704329	−	0.709874i	$-0.251248\pi$
$29$	7.58586			1.40866			0.704329	+	0.709874i	$0.251248\pi$
$30$	−1.02310	+	0.327669i	−0.186792	+	0.0598239i
$31$	−2.87857	−	2.87857i	−0.517006	−	0.517006i	0.399658	−	0.916664i	$-0.369129\pi$
$31$	−2.87857	−	2.87857i	−0.517006	−	0.517006i	−0.916664	+	0.399658i	$0.869129\pi$
$32$	−3.91491	−	4.08332i	−0.692064	−	0.721836i
$33$	−1.78893	−	1.78893i	−0.311413	−	0.311413i
$34$	0.894988	+	0.460776i	0.153489	+	0.0790225i
$35$		−	3.07431i		−	0.519653i
$36$	−2.81523	−	3.94426i	−0.469205	−	0.657377i
$37$	−1.05129	−	1.05129i	−0.172832	−	0.172832i	0.615391	−	0.788222i	$-0.288998\pi$
$37$	−1.05129	−	1.05129i	−0.172832	−	0.172832i	−0.788222	+	0.615391i	$0.788998\pi$
$38$	−7.61743	+	2.43964i	−1.23571	+	0.395762i
$39$	1.85102	+	2.01876i	0.296400	+	0.323260i
$40$	1.69128	−	2.26706i	0.267415	−	0.358454i
$41$	−5.21586	+	5.21586i	−0.814580	+	0.814580i	−0.985317	−	0.170737i	$-0.945385\pi$
$41$	−5.21586	+	5.21586i	−0.814580	+	0.814580i	0.170737	+	0.985317i	$0.445385\pi$
$42$	−3.14532	+	1.00736i	−0.485334	+	0.155438i
$43$	11.0617			1.68690			0.843449	−	0.537209i	$-0.180521\pi$
$43$	11.0617			1.68690			0.843449	+	0.537209i	$0.180521\pi$
$44$	6.56987	+	1.09736i	0.990445	+	0.165433i
$45$	1.71328	−	1.71328i	0.255401	−	0.255401i
$46$	4.81786	−	9.35796i	0.710355	−	1.37976i
$47$	3.59208	−	3.59208i	0.523958	−	0.523958i	−0.394806	−	0.918764i	$-0.629188\pi$
$47$	3.59208	−	3.59208i	0.523958	−	0.523958i	0.918764	+	0.394806i	$0.129188\pi$
$48$	−2.87361	−	0.987502i	−0.414770	−	0.142534i
$49$		−	2.45138i		−	0.350197i
$50$	1.25736	+	0.647340i	0.177817	+	0.0915476i
$51$	0.540710			0.0757146
$52$	−7.05445	−	1.49490i	−0.978276	−	0.207306i
$53$	0.920541			0.126446			0.0632230	−	0.997999i	$-0.479862\pi$
$53$	0.920541			0.126446			0.0632230	+	0.997999i	$0.479862\pi$
$54$	−5.17966	−	2.66670i	−0.704863	−	0.362892i
$55$			3.33044i			0.449077i
$56$	5.19952	−	6.96965i	0.694815	−	0.931359i
$57$	−3.03801	+	3.03801i	−0.402394	+	0.402394i
$58$	−4.91063	+	9.53814i	−0.644797	+	1.25242i
$59$	−3.80422	+	3.80422i	−0.495268	+	0.495268i	−0.909961	−	0.414694i	$-0.863889\pi$
$59$	−3.80422	+	3.80422i	−0.495268	+	0.495268i	0.414694	+	0.909961i	$0.363889\pi$
$60$	0.250295	−	1.49852i	0.0323130	−	0.193458i
$61$	−8.67840			−1.11115			−0.555577	−	0.831465i	$-0.687503\pi$
$61$	−8.67840			−1.11115			−0.555577	+	0.831465i	$0.687503\pi$
$62$	5.48281	−	1.75598i	0.696317	−	0.223010i
$63$	5.26717	−	5.26717i	0.663601	−	0.663601i
$64$	7.66847	−	2.27915i	0.958559	−	0.284893i
$65$	0.156139	−	3.60217i	0.0193667	−	0.446794i
$66$	3.40737	−	1.09128i	0.419419	−	0.134328i
$67$	−10.8530	−	10.8530i	−1.32590	−	1.32590i	−0.908911	−	0.416990i	$-0.863085\pi$
$67$	−10.8530	−	10.8530i	−1.32590	−	1.32590i	−0.416990	−	0.908911i	$-0.636915\pi$
$68$	−1.15872	+	0.827042i	−0.140516	+	0.100294i
$69$		−	5.65365i		−	0.680619i
$70$	3.86551	+	1.99012i	0.462017	+	0.237865i
$71$	−2.08032	−	2.08032i	−0.246888	−	0.246888i	0.572804	−	0.819692i	$-0.305856\pi$
$71$	−2.08032	−	2.08032i	−0.246888	−	0.246888i	−0.819692	+	0.572804i	$0.805856\pi$
$72$	6.78177	−	0.986480i	0.799239	−	0.116258i
$73$	−8.66411	−	8.66411i	−1.01406	−	1.01406i	−0.999900	−	0.0141576i	$-0.995493\pi$
$73$	−8.66411	−	8.66411i	−1.01406	−	1.01406i	−0.0141576	−	0.999900i	$-0.504507\pi$
$74$	2.00240	−	0.641310i	0.232774	−	0.0745508i
$75$	0.759638			0.0877154
$76$	1.86356	−	11.1571i	0.213765	−	1.27981i
$77$			10.2388i			1.16682i
$78$	−3.73654	+	1.02057i	−0.423080	+	0.115557i
$79$		−	1.66567i		−	0.187402i	−0.995600	−	0.0937012i	$-0.970130\pi$
$79$		−	1.66567i		−	0.187402i	0.995600	−	0.0937012i	$-0.0298698\pi$
$80$	1.75568	+	3.59411i	0.196291	+	0.401833i
$81$	4.13954			0.459949
$82$	−3.18177	−	9.93464i	−0.351368	−	1.09710i
$83$	−2.77385	−	2.77385i	−0.304470	−	0.304470i	0.538290	−	0.842760i	$-0.319071\pi$
$83$	−2.77385	−	2.77385i	−0.304470	−	0.304470i	−0.842760	+	0.538290i	$0.819071\pi$
$84$	0.769486	−	4.60690i	0.0839578	−	0.502654i
$85$	−0.503318	−	0.503318i	−0.0545925	−	0.0545925i
$86$	−7.16070	+	13.9086i	−0.772158	+	1.49980i
$87$			5.76250i			0.617805i
$88$	−5.63271	+	7.55032i	−0.600449	+	0.804867i
$89$	−1.93603	−	1.93603i	−0.205219	−	0.205219i	0.597013	−	0.802232i	$-0.296354\pi$
$89$	−1.93603	−	1.93603i	−0.205219	−	0.205219i	−0.802232	+	0.597013i	$0.796354\pi$
$90$	1.04514	+	3.26329i	0.110167	+	0.343981i
$91$	0.480021	−	11.0742i	0.0503199	−	1.16089i
$92$	8.64753	+	12.1156i	0.901567	+	1.26313i
$93$	2.18667	−	2.18667i	0.226747	−	0.226747i
$94$	2.19124	+	6.84182i	0.226009	+	0.705680i
$95$	5.65584			0.580277
$96$	3.10185	−	2.97391i	0.316581	−	0.303524i
$97$	−9.24834	+	9.24834i	−0.939027	+	0.939027i	−0.998245	−	0.0592185i	$-0.981139\pi$
$97$	−9.24834	+	9.24834i	−0.939027	+	0.939027i	0.0592185	+	0.998245i	$0.481139\pi$
$98$	3.08226	+	1.58687i	0.311356	+	0.160299i
$99$	−5.70600	+	5.70600i	−0.573474	+	0.573474i
$100$	−1.62788	+	1.16190i	−0.162788	+	0.116190i
$101$			17.1573i			1.70721i	0.520920	+	0.853605i	$0.325589\pi$
$101$			17.1573i			1.70721i	−0.520920	+	0.853605i	$0.674411\pi$
$102$	−0.350023	+	0.679867i	−0.0346574	+	0.0673168i
$103$	2.76865			0.272804			0.136402	−	0.990654i	$-0.456446\pi$
$103$	2.76865			0.272804			0.136402	+	0.990654i	$0.456446\pi$
$104$	6.44625	−	7.90227i	0.632107	−	0.774881i
$105$	2.33536			0.227908
$106$	−0.595902	+	1.15745i	−0.0578792	+	0.112421i
$107$			12.0825i			1.16806i	0.811732	+	0.584030i	$0.198525\pi$
$107$			12.0825i			1.16806i	−0.811732	+	0.584030i	$0.801475\pi$
$108$	6.70600	−	4.78643i	0.645285	−	0.460575i
$109$	−5.62999	+	5.62999i	−0.539256	+	0.539256i	−0.923310	−	0.384055i	$-0.874527\pi$
$109$	−5.62999	+	5.62999i	−0.539256	+	0.539256i	0.384055	+	0.923310i	$0.374527\pi$
$110$	−4.18756	−	2.15593i	−0.399268	−	0.205560i
$111$	0.798603	−	0.798603i	0.0758001	−	0.0758001i
$112$	5.39750	+	11.0494i	0.510016	+	1.04407i
$113$	−11.9831			−1.12728			−0.563638	−	0.826022i	$-0.690599\pi$
$113$	−11.9831			−1.12728			−0.563638	+	0.826022i	$0.690599\pi$
$114$	−1.85324	−	5.78649i	−0.173572	−	0.541955i
$115$	−5.26268	+	5.26268i	−0.490748	+	0.490748i
$116$	−8.81403	−	12.3488i	−0.818362	−	1.14656i
$117$	6.43905	−	5.90403i	0.595291	−	0.545828i
$118$	−2.32065	−	7.24590i	−0.213633	−	0.667039i
$119$	−1.54736	−	1.54736i	−0.141846	−	0.141846i
$120$	1.72215	+	1.28476i	0.157210	+	0.117282i
$121$		−	0.0918484i		−	0.00834986i
$122$	5.61787	−	10.9119i	0.508618	−	0.987913i
$123$	−3.96216	−	3.96216i	−0.357256	−	0.357256i
$124$	−1.34134	+	8.03057i	−0.120456	+	0.721167i
$125$	−0.707107	−	0.707107i	−0.0632456	−	0.0632456i
$126$	3.21307	+	10.0324i	0.286243	+	0.893754i
$127$	1.18943			0.105545			0.0527726	−	0.998607i	$-0.483194\pi$
$127$	1.18943			0.105545			0.0527726	+	0.998607i	$0.483194\pi$
$128$	−2.09840	+	11.1174i	−0.185474	+	0.982649i
$129$			8.40291i			0.739835i
$130$	4.42814	+	2.52815i	0.388374	+	0.221733i
$131$		−	1.76622i		−	0.154315i	−0.997019	−	0.0771577i	$-0.975415\pi$
$131$		−	1.76622i		−	0.154315i	0.997019	−	0.0771577i	$-0.0245845\pi$
$132$	−0.833595	+	4.99072i	−0.0725551	+	0.434387i
$133$	17.3878			1.50771
$134$	20.6716	−	6.62052i	1.78576	−	0.571926i
$135$	2.91291	+	2.91291i	0.250703	+	0.250703i
$136$	−0.289802	−	1.99231i	−0.0248503	−	0.170839i
$137$	1.41198	+	1.41198i	0.120634	+	0.120634i	0.764846	−	0.644213i	$-0.222815\pi$
$137$	1.41198	+	1.41198i	0.120634	+	0.120634i	−0.644213	+	0.764846i	$0.722815\pi$
$138$	7.10866	+	3.65983i	0.605130	+	0.311545i
$139$		−	19.0945i		−	1.61957i	−0.586724	−	0.809787i	$-0.699583\pi$
$139$		−	19.0945i		−	1.61957i	0.586724	−	0.809787i	$-0.300417\pi$
$140$	−5.00460	+	3.57205i	−0.422966	+	0.301893i
$141$	2.72868	+	2.72868i	0.229796	+	0.229796i
$142$	3.96238	−	1.26903i	0.332515	−	0.106495i
$143$	−0.520014	+	11.9968i	−0.0434857	+	1.00322i
$144$	−3.14975	+	9.16570i	−0.262479	+	0.763809i
$145$	5.36401	−	5.36401i	0.445457	−	0.445457i
$146$	16.5025	−	5.28527i	1.36576	−	0.437412i
$147$	1.86216			0.153588
$148$	−0.489876	+	2.93288i	−0.0402675	+	0.241081i
$149$	−7.65414	+	7.65414i	−0.627052	+	0.627052i	−0.947325	−	0.320273i	$-0.896225\pi$
$149$	−7.65414	+	7.65414i	−0.627052	+	0.627052i	0.320273	+	0.947325i	$0.396225\pi$
$150$	−0.491744	+	0.955138i	−0.0401507	+	0.0779867i
$151$	−11.7896	+	11.7896i	−0.959420	+	0.959420i	−0.999208	−	0.0397877i	$-0.987332\pi$
$151$	−11.7896	+	11.7896i	−0.959420	+	0.959420i	0.0397877	+	0.999208i	$0.487332\pi$
$152$	12.8222	+	9.56561i	1.04001	+	0.775874i
$153$		−	1.72466i		−	0.139430i
$154$	−12.8739	−	6.62799i	−1.03741	−	0.534098i
$155$	−4.07091			−0.326984
$156$	1.13558	−	5.35883i	0.0909195	−	0.429050i
$157$	12.2911			0.980936			0.490468	−	0.871459i	$-0.336826\pi$
$157$	12.2911			0.980936			0.490468	+	0.871459i	$0.336826\pi$
$158$	2.09434	+	1.07825i	0.166617	+	0.0857812i
$159$			0.699278i			0.0554563i
$160$	−5.65560	−	0.119088i	−0.447114	−	0.00941472i
$161$	−16.1791	+	16.1791i	−1.27509	+	1.27509i
$162$	−2.67969	+	5.20489i	−0.210536	+	0.408934i
$163$	−8.01251	+	8.01251i	−0.627588	+	0.627588i	−0.947461	−	0.319872i	$-0.896360\pi$
$163$	−8.01251	+	8.01251i	−0.627588	+	0.627588i	0.319872	+	0.947461i	$0.396360\pi$
$164$	14.5511	+	2.43045i	1.13625	+	0.189786i
$165$	−2.52993			−0.196955
$166$	5.28335	−	1.69210i	0.410067	−	0.131333i
$167$	0.240596	−	0.240596i	0.0186179	−	0.0186179i	−0.697737	−	0.716354i	$-0.745809\pi$
$167$	0.240596	−	0.240596i	0.0186179	−	0.0186179i	0.716354	+	0.697737i	$0.245809\pi$
$168$	5.29441	+	3.94975i	0.408473	+	0.304730i
$169$	1.12488	−	12.9512i	0.0865293	−	0.996249i
$170$	0.958670	−	0.307034i	0.0735266	−	0.0235484i
$171$	9.69007	+	9.69007i	0.741018	+	0.741018i
$172$	−12.8527	−	18.0071i	−0.980006	−	1.37303i
$173$		−	18.7796i		−	1.42779i	−0.700255	−	0.713893i	$-0.746930\pi$
$173$		−	18.7796i		−	1.42779i	0.700255	−	0.713893i	$-0.253070\pi$
$174$	−7.24554	−	3.73030i	−0.549283	−	0.282793i
$175$	−2.17387	−	2.17387i	−0.164329	−	0.164329i
$176$	−5.84719	−	11.9700i	−0.440748	−	0.902270i
$177$	−2.88983	−	2.88983i	−0.217213	−	0.217213i
$178$	3.68755	−	1.18102i	0.276394	−	0.0885209i
$179$	18.2890			1.36698			0.683491	−	0.729959i	$-0.260461\pi$
$179$	18.2890			1.36698			0.683491	+	0.729959i	$0.260461\pi$
$180$	−4.77969	−	0.798345i	−0.356257	−	0.0595051i
$181$			3.47325i			0.258165i	0.991634	+	0.129082i	$0.0412032\pi$
$181$			3.47325i			0.258165i	−0.991634	+	0.129082i	$0.958797\pi$
$182$	13.6135	+	7.77232i	1.00910	+	0.576122i
$183$		−	6.59244i		−	0.487327i
$184$	−20.8315	+	3.03016i	−1.53572	+	0.223387i
$185$	−1.48676			−0.109308
$186$	1.33391	+	4.16495i	0.0978071	+	0.305389i
$187$	1.67627	+	1.67627i	0.122581	+	0.122581i
$188$	−10.0211	−	1.67381i	−0.730864	−	0.122075i
$189$	8.95519	+	8.95519i	0.651394	+	0.651394i
$190$	−3.66125	+	7.11142i	−0.265615	+	0.515917i
$191$		−	9.55506i		−	0.691380i	−0.938349	−	0.345690i	$-0.887645\pi$
$191$		−	9.55506i		−	0.691380i	0.938349	−	0.345690i	$-0.112355\pi$
$192$	1.73133	+	5.82526i	0.124948	+	0.420402i
$193$	−2.86959	−	2.86959i	−0.206557	−	0.206557i	0.596245	−	0.802803i	$-0.296659\pi$
$193$	−2.86959	−	2.86959i	−0.206557	−	0.206557i	−0.802803	+	0.596245i	$0.796659\pi$
$194$	−5.64167	−	17.6153i	−0.405048	−	1.26470i
$195$	2.73634	+	0.118609i	0.195954	+	0.00849380i
$196$	−3.99054	+	2.84826i	−0.285039	+	0.203447i
$197$	7.20752	−	7.20752i	0.513515	−	0.513515i	−0.402087	−	0.915602i	$-0.631715\pi$
$197$	7.20752	−	7.20752i	0.513515	−	0.513515i	0.915602	+	0.402087i	$0.131715\pi$
$198$	−3.48077	−	10.8682i	−0.247367	−	0.772369i
$199$	0.0570233			0.00404227			0.00202114	−	0.999998i	$-0.499357\pi$
$199$	0.0570233			0.00404227			0.00202114	+	0.999998i	$0.499357\pi$
$200$	−0.407140	−	2.79897i	−0.0287891	−	0.197917i
$201$	8.24433	−	8.24433i	0.581510	−	0.581510i
$202$	−21.5728	−	11.1066i	−1.51786	−	0.781456i
$203$	16.4906	−	16.4906i	1.15742	−	1.15742i
$204$	−0.628253	−	0.880209i	−0.0439865	−	0.0616270i
$205$			7.37634i			0.515186i
$206$	−1.79226	+	3.48119i	−0.124873	+	0.242546i
$207$	−18.0329			−1.25338
$208$	5.76307	+	13.2207i	0.399597	+	0.916691i
$209$	−18.8365			−1.30295
$210$	−1.51177	+	2.93639i	−0.104322	+	0.202630i
$211$			19.2469i			1.32501i	0.749058	+	0.662504i	$0.230506\pi$
$211$			19.2469i			1.32501i	−0.749058	+	0.662504i	$0.769494\pi$
$212$	−1.06958	−	1.49853i	−0.0734590	−	0.102919i
$213$	1.58029	−	1.58029i	0.108280	−	0.108280i
$214$	−15.1921	−	7.82149i	−1.03851	−	0.534666i
$215$	7.82182	−	7.82182i	0.533444	−	0.533444i
$216$	1.67720	+	11.5303i	0.114119	+	0.784538i
$217$	−12.5152			−0.849590
$218$	−3.43440	−	10.7234i	−0.232607	−	0.726283i
$219$	6.58159	−	6.58159i	0.444742	−	0.444742i
$220$	5.42155	−	3.86965i	0.365521	−	0.260892i
$221$	−1.73445	−	1.89163i	−0.116672	−	0.127245i
$222$	0.487164	+	1.52110i	0.0326963	+	0.102089i
$223$	9.88632	+	9.88632i	0.662037	+	0.662037i	0.955860	−	0.293823i	$-0.0949276\pi$
$223$	9.88632	+	9.88632i	0.662037	+	0.662037i	−0.293823	+	0.955860i	$0.594928\pi$
$224$	−17.3871	−	0.366113i	−1.16172	−	0.0244619i
$225$		−	2.42295i		−	0.161530i
$226$	7.75714	−	15.0671i	0.515998	−	1.00225i
$227$	−11.9923	−	11.9923i	−0.795957	−	0.795957i	0.186498	−	0.982455i	$-0.440286\pi$
$227$	−11.9923	−	11.9923i	−0.795957	−	0.795957i	−0.982455	+	0.186498i	$0.940286\pi$
$228$	8.47537	+	1.41563i	0.561295	+	0.0937525i
$229$	1.98734	+	1.98734i	0.131327	+	0.131327i	0.769715	−	0.638388i	$-0.220398\pi$
$229$	1.98734	+	1.98734i	0.131327	+	0.131327i	−0.638388	+	0.769715i	$0.720398\pi$
$230$	−3.21034	−	10.0238i	−0.211683	−	0.660951i
$231$	−7.77779			−0.511741
$232$	21.2326	−	3.08851i	1.39399	−	0.202770i
$233$		−	5.37361i		−	0.352037i	−0.984387	−	0.176019i	$-0.943678\pi$
$233$		−	5.37361i		−	0.352037i	0.984387	−	0.176019i	$-0.0563219\pi$
$234$	3.25523	+	11.9181i	0.212801	+	0.779111i
$235$		−	5.07996i		−	0.331380i
$236$	10.6129	+	1.77267i	0.690844	+	0.115391i
$237$	1.26530			0.0821904
$238$	2.94725	−	0.943917i	0.191042	−	0.0611851i
$239$	−10.0021	−	10.0021i	−0.646981	−	0.646981i	0.305281	−	0.952262i	$-0.401250\pi$
$239$	−10.0021	−	10.0021i	−0.646981	−	0.646981i	−0.952262	+	0.305281i	$0.901250\pi$
$240$	−2.73022	+	1.33368i	−0.176235	+	0.0860887i
$241$	−5.10512	−	5.10512i	−0.328850	−	0.328850i	0.523299	−	0.852149i	$-0.324701\pi$
$241$	−5.10512	−	5.10512i	−0.328850	−	0.328850i	−0.852149	+	0.523299i	$0.824701\pi$
$242$	0.115486	+	0.0594571i	0.00742375	+	0.00382205i
$243$			15.5030i			0.994517i
$244$	10.0835	+	14.1274i	0.645527	+	0.904411i
$245$	−1.73339	−	1.73339i	−0.110742	−	0.110742i
$246$	7.54673	−	2.41700i	0.481162	−	0.154102i
$247$	20.3733	+	0.883100i	1.29632	+	0.0561903i
$248$	−9.22901	−	6.88505i	−0.586043	−	0.437201i
$249$	2.10712	−	2.10712i	0.133533	−	0.133533i
$250$	1.34683	−	0.431349i	0.0851807	−	0.0272809i
$251$	−2.54160			−0.160424			−0.0802122	−	0.996778i	$-0.525560\pi$
$251$	−2.54160			−0.160424			−0.0802122	+	0.996778i	$0.525560\pi$
$252$	−14.6942	−	2.45436i	−0.925650	−	0.154610i
$253$	17.5271	−	17.5271i	1.10192	−	1.10192i
$254$	−0.769968	+	1.49555i	−0.0483121	+	0.0938389i
$255$	0.382340	−	0.382340i	0.0239430	−	0.0239430i
$256$	−12.6202	−	9.83518i	−0.788762	−	0.614699i
$257$		−	8.53523i		−	0.532413i	−0.963916	−	0.266206i	$-0.914230\pi$
$257$		−	8.53523i		−	0.532413i	0.963916	−	0.266206i	$-0.0857703\pi$
$258$	−10.5655	−	5.43954i	−0.657778	−	0.338651i
$259$	−4.57075			−0.284012
$260$	−6.04530	+	3.93119i	−0.374914	+	0.243802i
$261$	18.3802			1.13770
$262$	2.22077	+	1.14335i	0.137200	+	0.0706361i
$263$		−	1.01215i		−	0.0624117i	−0.999513	−	0.0312058i	$-0.990065\pi$
$263$		−	1.01215i		−	0.0624117i	0.999513	−	0.0312058i	$-0.00993474\pi$
$264$	−5.73551	−	4.27882i	−0.352996	−	0.263343i
$265$	0.650921	−	0.650921i	0.0399857	−	0.0399857i
$266$	−11.2558	+	21.8627i	−0.690139	+	1.34049i
$267$	1.47068	−	1.47068i	0.0900043	−	0.0900043i
$268$	−5.05720	+	30.2774i	−0.308917	+	1.84949i
$269$	−9.28142			−0.565898			−0.282949	−	0.959135i	$-0.591313\pi$
$269$	−9.28142			−0.565898			−0.282949	+	0.959135i	$0.591313\pi$
$270$	−5.54822	+	1.77693i	−0.337654	+	0.108141i
$271$	18.5866	−	18.5866i	1.12905	−	1.12905i	0.138722	−	0.990331i	$-0.455701\pi$
$271$	18.5866	−	18.5866i	1.12905	−	1.12905i	0.990331	−	0.138722i	$-0.0442994\pi$
$272$	2.69264	+	0.925314i	0.163266	+	0.0561054i
$273$	8.41237	+	0.364642i	0.509140	+	0.0220691i
$274$	−2.68940	+	0.861336i	−0.162473	+	0.0520352i
$275$	2.35498	+	2.35498i	0.142011	+	0.142011i
$276$	−9.20344	+	6.56899i	−0.553982	+	0.395407i
$277$			27.9484i			1.67926i	0.543162	+	0.839628i	$0.317227\pi$
$277$			27.9484i			1.67926i	−0.543162	+	0.839628i	$0.682773\pi$
$278$	24.0086	+	12.3606i	1.43994	+	0.741341i
$279$	−6.97463	−	6.97463i	−0.417560	−	0.417560i
$280$	−1.25167	−	8.60490i	−0.0748019	−	0.514241i
$281$	−5.87304	−	5.87304i	−0.350356	−	0.350356i	0.509886	−	0.860242i	$-0.329688\pi$
$281$	−5.87304	−	5.87304i	−0.350356	−	0.350356i	−0.860242	+	0.509886i	$0.829688\pi$
$282$	−5.19731	+	1.66455i	−0.309495	+	0.0991223i
$283$	−8.50815			−0.505757			−0.252879	−	0.967498i	$-0.581377\pi$
$283$	−8.50815			−0.505757			−0.252879	+	0.967498i	$0.581377\pi$
$284$	−0.969373	+	5.80363i	−0.0575217	+	0.344382i
$285$			4.29639i			0.254496i
$286$	−14.7477	−	8.41986i	−0.872049	−	0.497877i
$287$			22.6771i			1.33859i
$288$	−9.48562	−	9.89368i	−0.558946	−	0.582991i
$289$	16.4933			0.970197
$290$	3.27215	+	10.2168i	0.192147	+	0.599952i
$291$	−7.02539	−	7.02539i	−0.411836	−	0.411836i
$292$	−4.03725	+	24.1710i	−0.236262	+	1.41450i
$293$	15.9731	+	15.9731i	0.933157	+	0.933157i	0.997902	−	0.0647451i	$-0.0206234\pi$
$293$	15.9731	+	15.9731i	0.933157	+	0.933157i	−0.0647451	+	0.997902i	$0.520623\pi$
$294$	−1.20545	+	2.34140i	−0.0703033	+	0.136553i
$295$			5.37998i			0.313235i
$296$	−3.37057	−	2.51452i	−0.195910	−	0.146153i
$297$	−9.70128	−	9.70128i	−0.562926	−	0.562926i
$298$	−4.66918	−	14.5788i	−0.270478	−	0.844529i
$299$	−19.7788	+	18.1354i	−1.14384	+	1.04879i
$300$	−0.882626	−	1.23660i	−0.0509584	−	0.0713949i
$301$	24.0467	−	24.0467i	1.38603	−	1.38603i
$302$	−7.19186	−	22.4555i	−0.413845	−	1.29217i
$303$	−13.0333			−0.748744
$304$	−20.3277	+	9.92985i	−1.16587	+	0.569516i
$305$	−6.13655	+	6.13655i	−0.351378	+	0.351378i
$306$	2.16851	+	1.11644i	0.123965	+	0.0638225i
$307$	4.72362	−	4.72362i	0.269591	−	0.269591i	−0.559344	−	0.828936i	$-0.688947\pi$
$307$	4.72362	−	4.72362i	0.269591	−	0.269591i	0.828936	+	0.559344i	$0.188947\pi$
$308$	16.6675	−	11.8965i	0.949720	−	0.677866i
$309$			2.10317i			0.119645i
$310$	2.63526	−	5.11860i	0.149673	−	0.290717i
$311$	7.71037			0.437215			0.218607	−	0.975813i	$-0.429849\pi$
$311$	7.71037			0.437215			0.218607	+	0.975813i	$0.429849\pi$
$312$	6.00286	+	4.89682i	0.339845	+	0.277228i
$313$	14.6925			0.830467			0.415234	−	0.909715i	$-0.363700\pi$
$313$	14.6925			0.830467			0.415234	+	0.909715i	$0.363700\pi$
$314$	−7.95651	+	15.4543i	−0.449012	+	0.872137i
$315$		−	7.44890i		−	0.419698i
$316$	−2.71150	+	1.93534i	−0.152534	+	0.108872i
$317$	4.90951	−	4.90951i	0.275745	−	0.275745i	−0.555663	−	0.831408i	$-0.687535\pi$
$317$	4.90951	−	4.90951i	0.275745	−	0.275745i	0.831408	+	0.555663i	$0.187535\pi$
$318$	−0.879243	−	0.452670i	−0.0493055	−	0.0253845i
$319$	−17.8645	+	17.8645i	−1.00022	+	1.00022i
$320$	3.81083	−	7.03403i	0.213032	−	0.393214i
$321$	−9.17833			−0.512285
$322$	−9.86957	−	30.8163i	−0.550010	−	1.71733i
$323$	2.84669	−	2.84669i	0.158394	−	0.158394i
$324$	−4.80974	−	6.73866i	−0.267208	−	0.374370i
$325$	−2.43671	−	2.65753i	−0.135164	−	0.147413i
$326$	−4.88779	−	15.2614i	−0.270709	−	0.845252i
$327$	−4.27676	−	4.27676i	−0.236505	−	0.236505i
$328$	−12.4754	+	16.7226i	−0.688841	+	0.923352i
$329$		−	15.6174i		−	0.861014i
$330$	1.63772	−	3.18103i	0.0901538	−	0.175110i
$331$	16.2551	+	16.2551i	0.893459	+	0.893459i	0.994847	−	0.101388i	$-0.0323282\pi$
$331$	16.2551	+	16.2551i	0.893459	+	0.893459i	−0.101388	+	0.994847i	$0.532328\pi$
$332$	−1.29254	+	7.73843i	−0.0709374	+	0.424702i
$333$	−2.54724	−	2.54724i	−0.139588	−	0.139588i
$334$	0.146768	+	0.458263i	0.00803080	+	0.0250750i
$335$	−15.3484			−0.838573
$336$	−8.39354	+	4.10015i	−0.457905	+	0.223681i
$337$			12.8579i			0.700415i	0.936672	+	0.350207i	$0.113889\pi$
$337$			12.8579i			0.700415i	−0.936672	+	0.350207i	$0.886111\pi$
$338$	15.5562	+	9.79823i	0.846145	+	0.532954i
$339$		−	9.10283i		−	0.494398i
$340$	−0.234533	+	1.40415i	−0.0127193	+	0.0761506i
$341$	13.5579			0.734204
$342$	−18.4567	+	5.91113i	−0.998022	+	0.319637i
$343$	9.88809	+	9.88809i	0.533907	+	0.533907i
$344$	30.9615	−	4.50367i	1.66933	−	0.242822i
$345$	−3.99773	−	3.99773i	−0.215231	−	0.215231i
$346$	23.6127	+	12.1568i	1.26943	+	0.653552i
$347$		−	9.03173i		−	0.484849i	−0.970170	−	0.242424i	$-0.922057\pi$
$347$		−	9.03173i		−	0.484849i	0.970170	−	0.242424i	$-0.0779426\pi$
$348$	9.38064	−	6.69547i	0.502855	−	0.358915i
$349$	−7.42335	−	7.42335i	−0.397363	−	0.397363i	0.479939	−	0.877302i	$-0.340659\pi$
$349$	−7.42335	−	7.42335i	−0.397363	−	0.397363i	−0.877302	+	0.479939i	$0.840659\pi$
$350$	4.14056	−	1.32610i	0.221322	−	0.0708830i
$351$	10.0380	+	10.9476i	0.535788	+	0.584341i
$352$	18.8357	+	0.396615i	1.00394	+	0.0211397i
$353$	−11.8608	+	11.8608i	−0.631286	+	0.631286i	−0.948391	−	0.317104i	$-0.897289\pi$
$353$	−11.8608	+	11.8608i	−0.631286	+	0.631286i	0.317104	+	0.948391i	$0.397289\pi$
$354$	5.50426	−	1.76285i	0.292548	−	0.0936946i
$355$	−2.94201			−0.156146
$356$	−0.902139	+	5.40110i	−0.0478133	+	0.286258i
$357$	1.17543	−	1.17543i	0.0622104	−	0.0622104i
$358$	−11.8392	+	22.9958i	−0.625720	+	1.21537i
$359$	5.05298	−	5.05298i	0.266686	−	0.266686i	−0.561077	−	0.827763i	$-0.689613\pi$
$359$	5.05298	−	5.05298i	0.266686	−	0.266686i	0.827763	+	0.561077i	$0.189613\pi$
$360$	4.09789	−	5.49298i	0.215978	−	0.289505i
$361$			12.9886i			0.683609i
$362$	−4.36713	−	2.24838i	−0.229531	−	0.118172i
$363$	0.0697716			0.00366206
$364$	−18.5851	+	12.0857i	−0.974126	+	0.633463i
$365$	−12.2529			−0.641346
$366$	8.28906	+	4.26755i	0.433276	+	0.223068i
$367$		−	22.5693i		−	1.17811i	−0.808094	−	0.589053i	$-0.799501\pi$
$367$		−	22.5693i		−	1.17811i	0.808094	−	0.589053i	$-0.200499\pi$
$368$	9.67505	−	28.1542i	0.504347	−	1.46764i
$369$	−12.6378	+	12.6378i	−0.657896	+	0.657896i
$370$	0.962436	−	1.86939i	0.0500346	−	0.0971847i
$371$	2.00113	−	2.00113i	0.103894	−	0.103894i
$372$	−6.10033	−	1.01893i	−0.316287	−	0.0528291i
$373$	−9.46884			−0.490278			−0.245139	−	0.969488i	$-0.578834\pi$
$373$	−9.46884			−0.490278			−0.245139	+	0.969488i	$0.578834\pi$
$374$	−3.19279	+	1.02256i	−0.165095	+	0.0528753i
$375$	0.537145	−	0.537145i	0.0277381	−	0.0277381i
$376$	8.59164	−	11.5166i	0.443080	−	0.593923i
$377$	20.1596	−	18.4845i	1.03827	−	0.952002i
$378$	−17.0569	+	5.46284i	−0.877314	+	0.280978i
$379$	22.1382	+	22.1382i	1.13716	+	1.13716i	0.988957	+	0.148206i	$0.0473497\pi$
$379$	22.1382	+	22.1382i	1.13716	+	1.13716i	0.148206	+	0.988957i	$0.452650\pi$
$380$	−6.57154	−	9.20701i	−0.337113	−	0.472310i
$381$			0.903540i			0.0462898i
$382$	12.0141	+	6.18537i	0.614697	+	0.316471i
$383$	16.8574	+	16.8574i	0.861372	+	0.861372i	0.991497	−	0.130126i	$-0.0415381\pi$
$383$	16.8574	+	16.8574i	0.861372	+	0.861372i	−0.130126	+	0.991497i	$0.541538\pi$
$384$	−8.44520	−	1.59403i	−0.430967	−	0.0813448i
$385$	7.23993	+	7.23993i	0.368981	+	0.368981i
$386$	5.46570	−	1.75050i	0.278197	−	0.0890983i
$387$	26.8020			1.36242
$388$	25.8008	+	4.30948i	1.30984	+	0.218781i
$389$			33.8842i			1.71800i	0.511980	+	0.858998i	$0.328912\pi$
$389$			33.8842i			1.71800i	−0.511980	+	0.858998i	$0.671088\pi$
$390$	−1.92048	+	3.36379i	−0.0972472	+	0.170332i
$391$			5.29761i			0.267912i
$392$	−0.998054	−	6.86134i	−0.0504093	−	0.346550i
$393$	1.34169			0.0676792
$394$	4.39673	+	13.7282i	0.221504	+	0.691615i
$395$	−1.17781	−	1.17781i	−0.0592618	−	0.0592618i
$396$	15.9185	+	2.65884i	0.799933	+	0.133612i
$397$	−8.67250	−	8.67250i	−0.435260	−	0.435260i	0.455153	−	0.890413i	$-0.349585\pi$
$397$	−8.67250	−	8.67250i	−0.435260	−	0.435260i	−0.890413	+	0.455153i	$0.849585\pi$
$398$	−0.0369134	+	0.0716987i	−0.00185030	+	0.00359393i
$399$			13.2084i			0.661249i
$400$	3.78287	+	1.29996i	0.189143	+	0.0649982i
$401$	−10.3143	−	10.3143i	−0.515072	−	0.515072i	0.401004	−	0.916076i	$-0.368661\pi$
$401$	−10.3143	−	10.3143i	−0.515072	−	0.515072i	−0.916076	+	0.401004i	$0.868661\pi$
$402$	5.02920	+	15.7030i	0.250834	+	0.783192i
$403$	−14.6641	−	0.635630i	−0.730472	−	0.0316630i
$404$	27.9299	−	19.9351i	1.38956	−	0.991806i
$405$	2.92710	−	2.92710i	0.145449	−	0.145449i
$406$	10.0596	+	31.4097i	0.499250	+	1.55884i
$407$	4.95155			0.245439
$408$	1.51343	−	0.220145i	0.0749260	−	0.0108988i
$409$	20.8109	−	20.8109i	1.02903	−	1.02903i	0.0294688	−	0.999566i	$-0.490618\pi$
$409$	20.8109	−	20.8109i	1.02903	−	1.02903i	0.999566	−	0.0294688i	$-0.00938157\pi$
$410$	−9.27470	−	4.77500i	−0.458045	−	0.235820i
$411$	−1.07260	+	1.07260i	−0.0529072	+	0.0529072i
$412$	−3.21691	−	4.50703i	−0.158486	−	0.222045i
$413$			16.5397i			0.813867i
$414$	11.6734	−	22.6739i	0.573718	−	1.11436i
$415$	−3.92282			−0.192564
$416$	−20.3538	−	1.31204i	−0.997929	−	0.0643279i
$417$	14.5049			0.710308
$418$	12.1936	−	23.6842i	0.596408	−	1.15843i
$419$		−	17.9072i		−	0.874826i	−0.899261	−	0.437413i	$-0.855895\pi$
$419$		−	17.9072i		−	0.874826i	0.899261	−	0.437413i	$-0.144105\pi$
$420$	−2.71346	−	3.80168i	−0.132403	−	0.185503i
$421$	7.06870	−	7.06870i	0.344508	−	0.344508i	−0.513551	−	0.858059i	$-0.671670\pi$
$421$	7.06870	−	7.06870i	0.344508	−	0.344508i	0.858059	+	0.513551i	$0.171670\pi$
$422$	−24.2002	−	12.4593i	−1.17805	−	0.606507i
$423$	8.70342	−	8.70342i	0.423175	−	0.423175i
$424$	2.57657	−	0.374789i	0.125129	−	0.0182014i
$425$	−0.711800			−0.0345274
$426$	0.964006	+	3.00997i	0.0467063	+	0.145834i
$427$	−18.8657	+	18.8657i	−0.912973	+	0.912973i
$428$	19.6688	−	14.0387i	0.950729	−	0.678586i
$429$	−9.11324	−	0.395022i	−0.439991	−	0.0190718i
$430$	4.77146	+	14.8982i	0.230100	+	0.718456i
$431$	−18.8239	−	18.8239i	−0.906716	−	0.906716i	0.0892898	−	0.996006i	$-0.471540\pi$
$431$	−18.8239	−	18.8239i	−0.906716	−	0.906716i	−0.996006	+	0.0892898i	$0.971540\pi$
$432$	−15.5834	−	5.35517i	−0.749759	−	0.257651i
$433$			37.5103i			1.80263i	0.433163	+	0.901316i	$0.357397\pi$
$433$			37.5103i			1.80263i	−0.433163	+	0.901316i	$0.642603\pi$
$434$	8.10161	−	15.7362i	0.388890	−	0.755360i
$435$	4.07471	+	4.07471i	0.195367	+	0.195367i
$436$	15.7064	+	2.62343i	0.752202	+	0.125639i
$437$	−29.7649	−	29.7649i	−1.42385	−	1.42385i
$438$	4.01489	+	12.5359i	0.191839	+	0.598990i
$439$	−1.37913			−0.0658224			−0.0329112	−	0.999458i	$-0.510478\pi$
$439$	−1.37913			−0.0658224			−0.0329112	+	0.999458i	$0.510478\pi$
$440$	1.35596	+	9.32181i	0.0646427	+	0.444400i
$441$		−	5.93957i		−	0.282837i
$442$	3.50123	−	0.956302i	0.166537	−	0.0454866i
$443$			5.41151i			0.257109i	0.991702	+	0.128554i	$0.0410336\pi$
$443$			5.41151i			0.257109i	−0.991702	+	0.128554i	$0.958966\pi$
$444$	−2.22793	−	0.372128i	−0.105733	−	0.0176604i
$445$	−2.73796			−0.129792
$446$	−18.8305	+	6.03085i	−0.891648	+	0.285569i
$447$	−5.81438	−	5.81438i	−0.275011	−	0.275011i
$448$	11.7157	−	21.6248i	0.553513	−	1.02167i
$449$	27.9636	+	27.9636i	1.31968	+	1.31968i	0.914026	+	0.405656i	$0.132957\pi$
$449$	27.9636	+	27.9636i	1.31968	+	1.31968i	0.405656	+	0.914026i	$0.367043\pi$
$450$	3.04652	+	1.56847i	0.143614	+	0.0739385i
$451$		−	24.5665i		−	1.15679i
$452$	13.9232	+	19.5070i	0.654893	+	0.917534i
$453$	−8.95579	−	8.95579i	−0.420780	−	0.420780i
$454$	22.8417	−	7.31554i	1.07202	−	0.343335i
$455$	−7.49120	−	8.17006i	−0.351193	−	0.383018i
$456$	−7.26640	+	9.74019i	−0.340280	+	0.456126i
$457$	0.914860	−	0.914860i	0.0427954	−	0.0427954i	−0.685385	−	0.728181i	$-0.740366\pi$
$457$	0.914860	−	0.914860i	0.0427954	−	0.0427954i	0.728181	+	0.685385i	$0.240366\pi$
$458$	−3.78529	+	1.21232i	−0.176875	+	0.0566479i
$459$	2.93224			0.136865
$460$	14.6817	+	2.45227i	0.684539	+	0.114338i
$461$	12.5558	−	12.5558i	0.584780	−	0.584780i	−0.351433	−	0.936213i	$-0.614305\pi$
$461$	12.5558	−	12.5558i	0.584780	−	0.584780i	0.936213	+	0.351433i	$0.114305\pi$
$462$	5.03487	−	9.77947i	0.234243	−	0.454982i
$463$	−16.0992	+	16.0992i	−0.748195	+	0.748195i	−0.974140	−	0.225945i	$-0.927453\pi$
$463$	−16.0992	+	16.0992i	−0.748195	+	0.748195i	0.225945	+	0.974140i	$0.427453\pi$
$464$	−9.86134	+	28.6963i	−0.457801	+	1.33219i
$465$		−	3.09242i		−	0.143408i
$466$	6.75656	+	3.47855i	0.312992	+	0.161141i
$467$	9.19091			0.425305			0.212652	−	0.977128i	$-0.431790\pi$
$467$	9.19091			0.425305			0.212652	+	0.977128i	$0.431790\pi$
$468$	−17.0926	−	3.62207i	−0.790105	−	0.167430i
$469$	−47.1858			−2.17884
$470$	6.38734	+	3.28846i	0.294626	+	0.151685i
$471$			9.33678i			0.430216i
$472$	−9.09906	+	12.1968i	−0.418818	+	0.561401i
$473$	−26.0501	+	26.0501i	−1.19779	+	1.19779i
$474$	−0.819082	+	1.59094i	−0.0376217	+	0.0730744i
$475$	3.99929	−	3.99929i	0.183500	−	0.183500i
$476$	−0.721027	+	4.31678i	−0.0330482	+	0.197859i
$477$	2.23042			0.102124
$478$	19.0510	−	6.10147i	0.871371	−	0.279075i
$479$	2.00449	−	2.00449i	0.0915876	−	0.0915876i	−0.659829	−	0.751416i	$-0.729371\pi$
$479$	2.00449	−	2.00449i	0.0915876	−	0.0915876i	0.751416	+	0.659829i	$0.229371\pi$
$480$	0.0904636	−	4.29621i	0.00412908	−	0.196094i
$481$	−5.35554	−	0.232141i	−0.244192	−	0.0105847i
$482$	9.72372	−	3.11422i	0.442903	−	0.141849i
$483$	−12.2903	−	12.2903i	−0.559227	−	0.559227i
$484$	−0.149518	+	0.106719i	−0.00679627	+	0.00485086i
$485$			13.0791i			0.593893i
$486$	−19.4928	−	10.0357i	−0.884212	−	0.455228i
$487$	−1.38289	−	1.38289i	−0.0626647	−	0.0626647i	0.675080	−	0.737745i	$-0.264109\pi$
$487$	−1.38289	−	1.38289i	−0.0626647	−	0.0626647i	−0.737745	+	0.675080i	$0.764109\pi$
$488$	−24.2906	+	3.53332i	−1.09958	+	0.159946i
$489$	−6.08661	−	6.08661i	−0.275246	−	0.275246i
$490$	3.30158	−	1.05740i	0.149150	−	0.0477684i
$491$	−39.7989			−1.79610			−0.898050	−	0.439893i	$-0.855016\pi$
$491$	−39.7989			−1.79610			−0.898050	+	0.439893i	$0.855016\pi$
$492$	−1.84626	+	11.0536i	−0.0832360	+	0.498333i
$493$		−	5.39961i		−	0.243186i
$494$	−14.2988	+	25.0449i	−0.643334	+	1.12682i
$495$			8.06950i			0.362697i
$496$	14.6313	−	7.14722i	0.656964	−	0.320919i
$497$	−9.04466			−0.405708
$498$	1.28539	+	4.01343i	0.0575995	+	0.179846i
$499$	−16.9696	−	16.9696i	−0.759664	−	0.759664i	0.216597	−	0.976261i	$-0.430504\pi$
$499$	−16.9696	−	16.9696i	−0.759664	−	0.759664i	−0.976261	+	0.216597i	$0.930504\pi$
$500$	−0.329493	+	1.97267i	−0.0147354	+	0.0882206i
$501$	0.182766	+	0.182766i	0.00816537	+	0.00816537i
$502$	1.64528	−	3.19571i	0.0734324	−	0.142631i
$503$		−	25.0262i		−	1.11586i	−0.829888	−	0.557931i	$-0.811596\pi$
$503$		−	25.0262i		−	1.11586i	0.829888	−	0.557931i	$-0.188404\pi$
$504$	12.5982	−	16.8871i	0.561167	−	0.752212i
$505$	12.1320	+	12.1320i	0.539867	+	0.539867i
$506$	10.6918	+	33.3838i	0.475310	+	1.48409i
$507$	9.83825	+	0.854503i	0.436932	+	0.0379498i
$508$	−1.38201	−	1.93625i	−0.0613167	−	0.0859073i
$509$	6.46064	−	6.46064i	0.286363	−	0.286363i	−0.549277	−	0.835640i	$-0.685097\pi$
$509$	6.46064	−	6.46064i	0.286363	−	0.286363i	0.835640	+	0.549277i	$0.185097\pi$
$510$	0.233235	+	0.728242i	0.0103278	+	0.0322471i
$511$	−37.6692			−1.66639
$512$	20.5359	−	9.50141i	0.907567	−	0.419907i
$513$	−16.4750	+	16.4750i	−0.727388	+	0.727388i
$514$	10.7318	+	5.52519i	0.473361	+	0.243706i
$515$	1.95773	−	1.95773i	0.0862681	−	0.0862681i
$516$	13.6789	−	9.76337i	0.602180	−	0.429808i
$517$			16.9185i			0.744076i
$518$	2.95883	−	5.74707i	0.130003	−	0.252512i
$519$	14.2657			0.626194
$520$	−1.02956	−	10.1459i	−0.0451491	−	0.444929i
$521$	−33.4237			−1.46432			−0.732160	−	0.681133i	$-0.761488\pi$
$521$	−33.4237			−1.46432			−0.732160	+	0.681133i	$0.761488\pi$
$522$	−11.8982	+	23.1104i	−0.520770	+	1.01152i
$523$		−	20.1901i		−	0.882850i	−0.897298	−	0.441425i	$-0.854473\pi$
$523$		−	20.1901i		−	0.882850i	0.897298	−	0.441425i	$-0.145527\pi$
$524$	−2.87519	+	2.05218i	−0.125603	+	0.0896498i
$525$	1.65135	−	1.65135i	0.0720708	−	0.0720708i
$526$	1.27263	+	0.655203i	0.0554894	+	0.0285682i
$527$	−2.04897	+	2.04897i	−0.0892543	+	0.0892543i
$528$	9.09284	−	4.44175i	0.395715	−	0.193302i
$529$	32.3916			1.40833
$530$	0.397074	+	1.23981i	0.0172478	+	0.0538538i
$531$	−9.21744	+	9.21744i	−0.400003	+	0.400003i
$532$	−20.2029	−	28.3052i	−0.875909	−	1.22719i
$533$	−1.15174	+	26.5708i	−0.0498873	+	1.15091i
$534$	0.897145	+	2.80121i	0.0388232	+	0.121220i
$535$	8.54362	+	8.54362i	0.369373	+	0.369373i
$536$	−34.7958	−	25.9585i	−1.50295	−	1.12123i
$537$			13.8930i			0.599527i
$538$	6.00823	−	11.6701i	0.259033	−	0.503133i
$539$	5.77294	+	5.77294i	0.248658	+	0.248658i
$540$	1.35734	−	8.12638i	0.0584106	−	0.349704i
$541$	−17.7357	−	17.7357i	−0.762519	−	0.762519i	0.214258	−	0.976777i	$-0.431267\pi$
$541$	−17.7357	−	17.7357i	−0.762519	−	0.762519i	−0.976777	+	0.214258i	$0.931267\pi$
$542$	11.3382	+	35.4018i	0.487016	+	1.52064i
$543$	−2.63842			−0.113225
$544$	−2.90651	+	2.78663i	−0.124615	+	0.119476i
$545$			7.96201i			0.341055i
$546$	−5.90415	+	10.3413i	−0.252674	+	0.442568i
$547$			11.5196i			0.492542i	0.969201	+	0.246271i	$0.0792053\pi$
$547$			11.5196i			0.492542i	−0.969201	+	0.246271i	$0.920795\pi$
$548$	0.657946	−	3.93912i	0.0281061	−	0.168271i
$549$	−21.0273			−0.897424
$550$	−4.48552	+	1.43658i	−0.191263	+	0.0612561i
$551$	30.3380	+	30.3380i	1.29244	+	1.29244i
$552$	−2.30183	−	15.8244i	−0.0979722	−	0.673531i
$553$	−3.62094	−	3.62094i	−0.153978	−	0.153978i
$554$	−35.1412	−	18.0921i	−1.49301	−	0.768660i
$555$		−	1.12940i		−	0.0479402i
$556$	−31.0835	+	22.1859i	−1.31823	+	0.940893i
$557$	8.08996	+	8.08996i	0.342783	+	0.342783i	0.857412	−	0.514630i	$-0.172071\pi$
$557$	8.08996	+	8.08996i	0.342783	+	0.342783i	−0.514630	+	0.857412i	$0.672071\pi$
$558$	13.2846	−	4.25466i	0.562381	−	0.180114i
$559$	29.3968	−	26.9542i	1.24335	−	1.14004i
$560$	11.6297	+	3.99649i	0.491445	+	0.168883i
$561$	−1.27336	+	1.27336i	−0.0537613	+	0.0537613i
$562$	11.1864	−	3.58267i	0.471869	−	0.151126i
$563$	−3.35387			−0.141349			−0.0706743	−	0.997499i	$-0.522515\pi$
$563$	−3.35387			−0.141349			−0.0706743	+	0.997499i	$0.522515\pi$
$564$	1.27149	−	7.61241i	0.0535395	−	0.320540i
$565$	−8.47334	+	8.47334i	−0.356476	+	0.356476i
$566$	5.50766	−	10.6978i	0.231504	−	0.449662i
$567$	8.99880	−	8.99880i	0.377914	−	0.377914i
$568$	−6.66973	−	4.97577i	−0.279856	−	0.208779i
$569$		−	38.4607i		−	1.61236i	−0.591672	−	0.806179i	$-0.701532\pi$
$569$		−	38.4607i		−	1.61236i	0.591672	−	0.806179i	$-0.298468\pi$
$570$	−5.40211	−	2.78123i	−0.226269	−	0.116493i
$571$	27.1181			1.13486			0.567428	−	0.823423i	$-0.307938\pi$
$571$	27.1181			1.13486			0.567428	+	0.823423i	$0.307938\pi$
$572$	20.1335	−	13.0926i	0.841826	−	0.547430i
$573$	7.25839			0.303223
$574$	−28.5133	−	14.6798i	−1.19012	−	0.612724i
$575$			7.44256i			0.310376i
$576$	18.5803	−	5.52226i	0.774180	−	0.230094i
$577$	−7.92664	+	7.92664i	−0.329990	+	0.329990i	−0.852583	−	0.522592i	$-0.824965\pi$
$577$	−7.92664	+	7.92664i	−0.329990	+	0.329990i	0.522592	+	0.852583i	$0.324965\pi$
$578$	−10.6768	+	20.7380i	−0.444096	+	0.862589i
$579$	2.17985	−	2.17985i	0.0905914	−	0.0905914i
$580$	−14.9644	−	2.49949i	−0.621363	−	0.103786i
$581$	−12.0600			−0.500331
$582$	13.3812	−	4.28562i	0.554671	−	0.177645i
$583$	−2.16785	+	2.16785i	−0.0897833	+	0.0897833i
$584$	−27.7781	−	20.7231i	−1.14947	−	0.857527i
$585$	0.378318	−	8.72788i	0.0156415	−	0.360853i
$586$	−30.4239	+	9.74388i	−1.25680	+	0.402516i
$587$	24.9147	+	24.9147i	1.02834	+	1.02834i	0.999587	+	0.0287520i	$0.00915330\pi$
$587$	24.9147	+	24.9147i	1.02834	+	1.02834i	0.0287520	+	0.999587i	$0.490847\pi$
$588$	−2.16365	−	3.03137i	−0.0892274	−	0.125011i
$589$		−	23.0244i		−	0.948706i
$590$	−6.76457	−	3.48268i	−0.278493	−	0.143379i
$591$	5.47511	+	5.47511i	0.225216	+	0.225216i
$592$	5.34356	−	2.61027i	0.219619	−	0.107281i
$593$	−24.1410	−	24.1410i	−0.991354	−	0.991354i	0.00860886	−	0.999963i	$-0.497260\pi$
$593$	−24.1410	−	24.1410i	−0.991354	−	0.991354i	−0.999963	+	0.00860886i	$0.997260\pi$
$594$	18.4780	−	5.91797i	0.758162	−	0.242817i
$595$	−2.18829			−0.0897112
$596$	21.3534	+	3.56663i	0.874668	+	0.146095i
$597$			0.0433170i			0.00177285i
$598$	−9.99906	−	36.6088i	−0.408892	−	1.49704i
$599$		−	22.3997i		−	0.915225i	−0.889152	−	0.457613i	$-0.848705\pi$
$599$		−	22.3997i		−	0.915225i	0.889152	−	0.457613i	$-0.151295\pi$
$600$	2.12620	−	0.309279i	0.0868019	−	0.0126263i
$601$	35.5412			1.44976			0.724878	−	0.688878i	$-0.241896\pi$
$601$	35.5412			1.44976			0.724878	+	0.688878i	$0.241896\pi$
$602$	14.6690	+	45.8017i	0.597862	+	1.86674i
$603$	−26.2962	−	26.2962i	−1.07086	−	1.07086i
$604$	32.8903	+	5.49362i	1.33829	+	0.223532i
$605$	−0.0649467	−	0.0649467i	−0.00264046	−	0.00264046i
$606$	8.43697	−	16.3875i	0.342729	−	0.665698i
$607$		−	0.244959i		−	0.00994258i	−0.999988	−	0.00497129i	$-0.998418\pi$
$607$		−	0.244959i		−	0.00994258i	0.999988	−	0.00497129i	$-0.00158242\pi$
$608$	0.673542	−	31.9872i	0.0273157	−	1.29725i
$609$	12.5269	+	12.5269i	0.507616	+	0.507616i
$610$	−3.74342	−	11.6883i	−0.151566	−	0.473245i
$611$	0.793183	−	18.2989i	0.0320887	−	0.740294i
$612$	−2.80753	+	2.00388i	−0.113487	+	0.0810021i
$613$	−22.7940	+	22.7940i	−0.920642	+	0.920642i	−0.997075	−	0.0764330i	$-0.975647\pi$
$613$	−22.7940	+	22.7940i	−0.920642	+	0.920642i	0.0764330	+	0.997075i	$0.475647\pi$
$614$	2.88150	+	8.99708i	0.116288	+	0.363092i
$615$	−5.60335			−0.225949
$616$	4.16863	+	28.6581i	0.167959	+	1.15467i
$617$	5.38617	−	5.38617i	0.216839	−	0.216839i	−0.590326	−	0.807165i	$-0.701001\pi$
$617$	5.38617	−	5.38617i	0.216839	−	0.216839i	0.807165	+	0.590326i	$0.201001\pi$
$618$	−2.64445	−	1.36147i	−0.106375	−	0.0547663i
$619$	8.24810	−	8.24810i	0.331519	−	0.331519i	−0.521644	−	0.853163i	$-0.674681\pi$
$619$	8.24810	−	8.24810i	0.331519	−	0.331519i	0.853163	+	0.521644i	$0.174681\pi$
$620$	4.73000	+	6.62694i	0.189962	+	0.266144i
$621$		−	30.6594i		−	1.23032i
$622$	−4.99123	+	9.69470i	−0.200130	+	0.388722i
$623$	−8.41734			−0.337234
$624$	−10.0429	+	4.37785i	−0.402040	+	0.175254i
$625$	−1.00000			−0.0400000
$626$	−9.51102	+	18.4737i	−0.380137	+	0.738358i
$627$		−	14.3089i		−	0.571442i
$628$	−14.2810	−	20.0084i	−0.569876	−	0.798421i
$629$	−0.748311	+	0.748311i	−0.0298371	+	0.0298371i
$630$	9.36594	+	4.82197i	0.373148	+	0.192112i
$631$	14.9116	−	14.9116i	0.593620	−	0.593620i	−0.344988	−	0.938607i	$-0.612117\pi$
$631$	14.9116	−	14.9116i	0.593620	−	0.593620i	0.938607	+	0.344988i	$0.112117\pi$
$632$	−0.678160	−	4.66216i	−0.0269758	−	0.185451i
$633$	−14.6206			−0.581119
$634$	2.99489	+	9.35113i	0.118942	+	0.371381i
$635$	0.841057	−	0.841057i	0.0333763	−	0.0333763i
$636$	1.13834	−	0.812493i	0.0451380	−	0.0322174i
$637$	−5.97330	−	6.51460i	−0.236671	−	0.258118i
$638$	−10.8977	−	34.0265i	−0.431444	−	1.34712i
$639$	−5.04051	−	5.04051i	−0.199399	−	0.199399i
$640$	6.37740	+	9.34499i	0.252089	+	0.369393i
$641$			2.65410i			0.104831i	0.998625	+	0.0524153i	$0.0166920\pi$
$641$			2.65410i			0.104831i	−0.998625	+	0.0524153i	$0.983308\pi$
$642$	5.94150	−	11.5405i	0.234492	−	0.455466i
$643$	−2.81539	−	2.81539i	−0.111028	−	0.111028i	0.649410	−	0.760438i	$-0.275016\pi$
$643$	−2.81539	−	2.81539i	−0.111028	−	0.111028i	−0.760438	+	0.649410i	$0.775016\pi$
$644$	45.1361	+	7.53904i	1.77861	+	0.297080i
$645$	5.94175	+	5.94175i	0.233956	+	0.233956i
$646$	1.73654	+	5.42209i	0.0683231	+	0.213329i
$647$	−18.2443			−0.717259			−0.358630	−	0.933480i	$-0.616756\pi$
$647$	−18.2443			−0.717259			−0.358630	+	0.933480i	$0.616756\pi$
$648$	11.5864	−	1.68537i	0.455159	−	0.0662077i
$649$		−	17.9177i		−	0.703332i
$650$	4.91884	−	1.34350i	0.192933	−	0.0526964i
$651$		−	9.50705i		−	0.372611i
$652$	22.3531	+	3.73362i	0.875416	+	0.146220i
$653$	−3.15602			−0.123505			−0.0617524	−	0.998092i	$-0.519669\pi$
$653$	−3.15602			−0.123505			−0.0617524	+	0.998092i	$0.519669\pi$
$654$	8.14593	−	2.60890i	0.318531	−	0.102016i
$655$	−1.24891	−	1.24891i	−0.0487988	−	0.0487988i
$656$	−12.9505	−	26.5113i	−0.505631	−	1.03509i
$657$	−20.9927	−	20.9927i	−0.819003	−	0.819003i
$658$	19.6367	+	10.1097i	0.765516	+	0.394119i
$659$			47.9086i			1.86625i	0.359546	+	0.933127i	$0.382931\pi$
$659$			47.9086i			1.86625i	−0.359546	+	0.933127i	$0.617069\pi$
$660$	2.93953	+	4.11841i	0.114421	+	0.160309i
$661$	−0.866294	−	0.866294i	−0.0336949	−	0.0336949i	0.690059	−	0.723754i	$-0.257585\pi$
$661$	−0.866294	−	0.866294i	−0.0336949	−	0.0336949i	−0.723754	+	0.690059i	$0.757585\pi$
$662$	−30.9610	+	9.91591i	−1.20333	+	0.385393i
$663$	1.43695	−	1.31755i	0.0558065	−	0.0511696i
$664$	−8.89327	−	6.63458i	−0.345126	−	0.257472i
$665$	12.2950	−	12.2950i	0.476781	−	0.476781i
$666$	4.85171	−	1.55386i	0.188000	−	0.0602109i
$667$	−56.4582			−2.18607
$668$	−0.671209	−	0.112111i	−0.0259699	−	0.00433772i
$669$	−7.51002	+	7.51002i	−0.290354	+	0.290354i
$670$	9.93564	−	19.2985i	0.383847	−	0.745565i
$671$	20.4374	−	20.4374i	0.788979	−	0.788979i
$672$	0.278113	−	13.2079i	0.0107285	−	0.509505i
$673$			19.2806i			0.743212i	0.928391	+	0.371606i	$0.121193\pi$
$673$			19.2806i			0.743212i	−0.928391	+	0.371606i	$0.878807\pi$
$674$	−16.1670	−	8.32343i	−0.622730	−	0.320607i
$675$	4.11948			0.158559
$676$	−22.3900	+	13.2169i	−0.861155	+	0.508343i
$677$	34.9705			1.34403			0.672013	−	0.740539i	$-0.265430\pi$
$677$	34.9705			1.34403			0.672013	+	0.740539i	$0.265430\pi$
$678$	11.4455	+	5.89262i	0.439563	+	0.226305i
$679$			40.2093i			1.54309i
$680$	−1.61369	−	1.20385i	−0.0618824	−	0.0461656i
$681$	9.10981	−	9.10981i	0.349089	−	0.349089i
$682$	−8.77659	+	17.0472i	−0.336073	+	0.652771i
$683$	−9.68877	+	9.68877i	−0.370730	+	0.370730i	−0.867743	−	0.497013i	$-0.834430\pi$
$683$	−9.68877	+	9.68877i	−0.370730	+	0.370730i	0.497013	+	0.867743i	$0.334430\pi$
$684$	4.51532	−	27.0332i	0.172647	−	1.03364i
$685$	1.99684			0.0762955
$686$	−18.8338	+	6.03193i	−0.719079	+	0.230300i
$687$	−1.50966	+	1.50966i	−0.0575972	+	0.0575972i
$688$	−14.3798	+	41.8451i	−0.548226	+	1.59533i
$689$	2.44636	−	2.24309i	0.0931989	−	0.0854550i
$690$	7.61448	−	2.43869i	0.289878	−	0.0928395i
$691$	18.1218	+	18.1218i	0.689387	+	0.689387i	0.962096	−	0.272710i	$-0.0879199\pi$
$691$	18.1218	+	18.1218i	0.689387	+	0.689387i	−0.272710	+	0.962096i	$0.587920\pi$
$692$	−30.5708	+	21.8201i	−1.16213	+	0.829474i
$693$			24.8081i			0.942383i
$694$	11.3561	+	5.84660i	0.431073	+	0.221934i
$695$	−13.5018	−	13.5018i	−0.512154	−	0.512154i
$696$	2.34615	+	16.1291i	0.0889304	+	0.611371i
$697$	3.71265	+	3.71265i	0.140627	+	0.140627i
$698$	14.1392	−	4.52839i	0.535178	−	0.171402i
$699$	4.08200			0.154395
$700$	−1.01296	+	6.06460i	−0.0382864	+	0.229220i
$701$		−	10.6153i		−	0.400935i	−0.979700	−	0.200467i	$-0.935754\pi$
$701$		−	10.6153i		−	0.400935i	0.979700	−	0.200467i	$-0.0642460\pi$
$702$	−20.2631	+	5.53451i	−0.764780	+	0.208887i
$703$		−	8.40886i		−	0.317146i
$704$	−12.6918	+	23.4264i	−0.478338	+	0.882917i
$705$	3.85893			0.145336
$706$	−7.23531	−	22.5912i	−0.272305	−	0.850232i
$707$	37.2976	+	37.2976i	1.40272	+	1.40272i
$708$	−1.34659	+	8.06199i	−0.0506078	+	0.302988i
$709$	4.69489	+	4.69489i	0.176320	+	0.176320i	0.789750	−	0.613429i	$-0.210210\pi$
$709$	4.69489	+	4.69489i	0.176320	+	0.176320i	−0.613429	+	0.789750i	$0.710210\pi$
$710$	1.90448	−	3.69917i	0.0714739	−	0.138827i
$711$		−	4.03583i		−	0.151356i
$712$	−6.20713	−	4.63066i	−0.232622	−	0.173541i
$713$	21.4239	+	21.4239i	0.802332	+	0.802332i
$714$	0.717035	+	2.23884i	0.0268344	+	0.0837865i
$715$	8.11533	+	8.85074i	0.303496	+	0.330999i
$716$	−21.2500	−	29.7722i	−0.794151	−	1.11264i
$717$	7.59797	−	7.59797i	0.283751	−	0.283751i
$718$	3.08241	+	9.62440i	0.115035	+	0.359179i
$719$	39.2158			1.46250			0.731252	−	0.682108i	$-0.238936\pi$
$719$	39.2158			1.46250			0.731252	+	0.682108i	$0.238936\pi$
$720$	4.25392	+	8.70834i	0.158534	+	0.324541i
$721$	6.01868	−	6.01868i	0.224147	−	0.224147i
$722$	−16.3313	−	8.40801i	−0.607787	−	0.312914i
$723$	3.87804	−	3.87804i	0.144226	−	0.144226i
$724$	5.65403	−	4.03558i	0.210130	−	0.149981i
$725$		−	7.58586i		−	0.281732i
$726$	−0.0451659	+	0.0877279i	−0.00167626	+	0.00325589i
$727$	−31.6876			−1.17523			−0.587613	−	0.809142i	$-0.699932\pi$
$727$	−31.6876			−1.17523			−0.587613	+	0.809142i	$0.699932\pi$
$728$	−3.16518	−	31.1917i	−0.117309	−	1.15604i
$729$	0.641958			0.0237762
$730$	7.93179	−	15.4063i	0.293569	−	0.570213i
$731$		−	7.87374i		−	0.291221i
$732$	−10.7317	+	7.65977i	−0.396654	+	0.283113i
$733$	15.6379	−	15.6379i	0.577600	−	0.577600i	−0.356642	−	0.934241i	$-0.616078\pi$
$733$	15.6379	−	15.6379i	0.577600	−	0.577600i	0.934241	+	0.356642i	$0.116078\pi$
$734$	28.3777	+	14.6100i	1.04744	+	0.539264i
$735$	1.31675	−	1.31675i	0.0485689	−	0.0485689i
$736$	29.1369	+	30.3903i	1.07400	+	1.12020i
$737$	51.1170			1.88292
$738$	−7.70928	−	24.0711i	−0.283783	−	0.886071i
$739$	−22.7608	+	22.7608i	−0.837269	+	0.837269i	−0.988499	−	0.151229i	$-0.951677\pi$
$739$	−22.7608	+	22.7608i	−0.837269	+	0.837269i	0.151229	+	0.988499i	$0.451677\pi$
$740$	1.72747	+	2.42025i	0.0635029	+	0.0889703i
$741$	−0.670837	+	15.4763i	−0.0246438	+	0.568537i
$742$	1.22073	+	3.81155i	0.0448144	+	0.139926i
$743$	−22.3331	−	22.3331i	−0.819322	−	0.819322i	0.166687	−	0.986010i	$-0.446693\pi$
$743$	−22.3331	−	22.3331i	−0.819322	−	0.819322i	−0.986010	+	0.166687i	$0.946693\pi$
$744$	5.23015	−	7.01071i	0.191746	−	0.257025i
$745$			10.8246i			0.396582i
$746$	6.12955	−	11.9057i	0.224419	−	0.435900i
$747$	−6.72090	−	6.72090i	−0.245905	−	0.245905i
$748$	0.781099	−	4.67643i	0.0285598	−	0.170987i
$749$	26.2657	+	26.2657i	0.959729	+	0.959729i
$750$	0.327669	+	1.02310i	0.0119648	+	0.0373583i
$751$	45.5248			1.66122			0.830611	−	0.556853i	$-0.187991\pi$
$751$	45.5248			1.66122			0.830611	+	0.556853i	$0.187991\pi$
$752$	8.91879	+	18.2579i	0.325235	+	0.665798i
$753$		−	1.93070i		−	0.0703585i
$754$	10.1916	+	37.3136i	0.371156	+	1.35888i
$755$			16.6729i			0.606791i
$756$	4.17288	−	24.9830i	0.151766	−	0.908623i
$757$	−35.0477			−1.27383			−0.636916	−	0.770933i	$-0.719790\pi$
$757$	−35.0477			−1.27383			−0.636916	+	0.770933i	$0.719790\pi$
$758$	−42.1666	+	13.5047i	−1.53156	+	0.490514i
$759$	13.3142	+	13.3142i	0.483276	+	0.483276i
$760$	15.8305	−	2.30272i	0.574234	−	0.0835284i
$761$	1.53925	+	1.53925i	0.0557976	+	0.0557976i	0.734455	−	0.678657i	$-0.237438\pi$
$761$	1.53925	+	1.53925i	0.0557976	+	0.0557976i	−0.678657	+	0.734455i	$0.737438\pi$
$762$	−1.13607	−	0.584897i	−0.0411556	−	0.0211886i
$763$			24.4777i			0.886152i
$764$	−15.5545	+	11.1021i	−0.562741	+	0.401658i
$765$	−1.21952	−	1.21952i	−0.0440917	−	0.0440917i
$766$	−32.1082	+	10.2833i	−1.16012	+	0.371552i
$767$	−0.840028	+	19.3796i	−0.0303316	+	0.699757i
$768$	7.47118	−	9.58678i	0.269593	−	0.345933i
$769$	36.8997	−	36.8997i	1.33064	−	1.33064i	0.425836	−	0.904801i	$-0.359980\pi$
$769$	36.8997	−	36.8997i	1.33064	−	1.33064i	0.904801	−	0.425836i	$-0.140020\pi$
$770$	−13.7899	+	4.41650i	−0.496953	+	0.159160i
$771$	6.48368			0.233504
$772$	−1.33715	+	8.00552i	−0.0481252	+	0.288125i
$773$	33.7368	−	33.7368i	1.21343	−	1.21343i	0.243535	−	0.969892i	$-0.421693\pi$
$773$	33.7368	−	33.7368i	1.21343	−	1.21343i	0.969892	−	0.243535i	$-0.0783071\pi$
$774$	−17.3500	+	33.6998i	−0.623633	+	1.21131i
$775$	−2.87857	+	2.87857i	−0.103401	+	0.103401i
$776$	−22.1205	+	29.6512i	−0.794078	+	1.06442i
$777$		−	3.47211i		−	0.124561i
$778$	−42.6046	−	21.9346i	−1.52745	−	0.786392i
$779$	−41.7194			−1.49475
$780$	−2.98628	−	4.59224i	−0.106926	−	0.164429i
$781$	9.79821			0.350607
$782$	−6.66100	−	3.42935i	−0.238197	−	0.122633i
$783$			31.2498i			1.11678i
$784$	9.27324	+	3.18670i	0.331187	+	0.113811i
$785$	8.69111	−	8.69111i	0.310199	−	0.310199i
$786$	−0.868528	+	1.68698i	−0.0309794	+	0.0601727i
$787$	13.4293	−	13.4293i	0.478702	−	0.478702i	−0.426015	−	0.904716i	$-0.640083\pi$
$787$	13.4293	−	13.4293i	0.478702	−	0.478702i	0.904716	+	0.426015i	$0.140083\pi$
$788$	−20.1074	−	3.35852i	−0.716296	−	0.119642i
$789$	0.768866			0.0273723
$790$	2.24336	−	0.718484i	0.0798153	−	0.0255625i
$791$	−26.0497	+	26.0497i	−0.926220	+	0.926220i
$792$	−13.6478	+	18.2941i	−0.484953	+	0.650051i
$793$	−23.0631	+	21.1467i	−0.818993	+	0.750943i
$794$	16.5185	−	5.29039i	0.586219	−	0.187749i
$795$	0.494464	+	0.494464i	0.0175368	+	0.0175368i
$796$	−0.0662555	−	0.0928268i	−0.00234836	−	0.00329016i
$797$		−	27.7789i		−	0.983979i	−0.870601	−	0.491989i	$-0.836270\pi$
$797$		−	27.7789i		−	0.983979i	0.870601	−	0.491989i	$-0.163730\pi$
$798$	−16.6078	−	8.55035i	−0.587908	−	0.302679i
$799$	−2.55684	−	2.55684i	−0.0904545	−	0.0904545i
$800$	−4.08332	+	3.91491i	−0.144367	+	0.138413i
$801$	−4.69091	−	4.69091i	−0.165745	−	0.165745i
$802$	19.6456	−	6.29192i	0.693712	−	0.222176i
$803$	40.8076			1.44007
$804$	−22.9999	−	3.84164i	−0.811142	−	0.135484i
$805$			22.8807i			0.806439i
$806$	10.2919	−	18.0266i	0.362516	−	0.634959i
$807$		−	7.05052i		−	0.248190i
$808$	6.98540	+	48.0227i	0.245746	+	1.68943i
$809$	36.5845			1.28624			0.643121	−	0.765765i	$-0.277639\pi$
$809$	36.5845			1.28624			0.643121	+	0.765765i	$0.277639\pi$
$810$	1.78558	+	5.57523i	0.0627391	+	0.195894i
$811$	11.5212	+	11.5212i	0.404564	+	0.404564i	0.879838	−	0.475274i	$-0.157651\pi$
$811$	11.5212	+	11.5212i	0.404564	+	0.404564i	−0.475274	+	0.879838i	$0.657651\pi$
$812$	−46.0052	−	7.68420i	−1.61447	−	0.269662i
$813$	14.1191	+	14.1191i	0.495177	+	0.495177i
$814$	−3.20534	+	6.22588i	−0.112347	+	0.218217i
$815$			11.3314i			0.396922i
$816$	−0.702903	+	2.04544i	−0.0246065	+	0.0716045i
$817$	44.2390	+	44.2390i	1.54773	+	1.54773i
$818$	12.6951	+	39.6386i	0.443873	+	1.38593i
$819$	1.16307	−	26.8322i	0.0406409	−	0.937593i
$820$	12.0078	−	8.57059i	0.419329	−	0.299298i
$821$	−15.9214	+	15.9214i	−0.555661	+	0.555661i	−0.928069	−	0.372408i	$-0.878532\pi$
$821$	−15.9214	+	15.9214i	−0.555661	+	0.555661i	0.372408	+	0.928069i	$0.378532\pi$
$822$	−0.654304	−	2.04297i	−0.0228215	−	0.0712568i
$823$	31.5004			1.09803			0.549017	−	0.835811i	$-0.315002\pi$
$823$	31.5004			1.09803			0.549017	+	0.835811i	$0.315002\pi$
$824$	7.74938	−	1.12723i	0.269962	−	0.0392689i
$825$	−1.78893	+	1.78893i	−0.0622826	+	0.0622826i
$826$	−20.7964	−	10.7068i	−0.723599	−	0.372538i
$827$	7.38794	−	7.38794i	0.256904	−	0.256904i	−0.566890	−	0.823794i	$-0.691853\pi$
$827$	7.38794	−	7.38794i	0.256904	−	0.256904i	0.823794	+	0.566890i	$0.191853\pi$
$828$	20.9525	+	29.3554i	0.728151	+	1.02017i
$829$		−	32.4357i		−	1.12654i	−0.826273	−	0.563269i	$-0.809543\pi$
$829$		−	32.4357i		−	1.12654i	0.826273	−	0.563269i	$-0.190457\pi$
$830$	2.53940	−	4.93239i	0.0881437	−	0.171206i
$831$	−21.2307			−0.736484
$832$	14.8255	−	24.7427i	0.513983	−	0.857800i
$833$	−1.74489			−0.0604569
$834$	−9.38959	+	18.2379i	−0.325135	+	0.631525i
$835$		−	0.340254i		−	0.0117750i
$836$	21.8861	+	30.6634i	0.756948	+	1.06052i
$837$	11.8582	−	11.8582i	0.409880	−	0.409880i
$838$	22.5158	+	11.5921i	0.777796	+	0.400441i
$839$	−31.9636	+	31.9636i	−1.10351	+	1.10351i	−0.109523	+	0.993984i	$0.534932\pi$
$839$	−31.9636	+	31.9636i	−1.10351	+	1.10351i	−0.993984	+	0.109523i	$0.965068\pi$
$840$	6.53661	−	0.950819i	0.225534	−	0.0328064i
$841$	28.5452			0.984318
$842$	4.31205	+	13.4638i	0.148603	+	0.463992i
$843$	4.46138	−	4.46138i	0.153658	−	0.153658i
$844$	31.3315	−	22.3630i	1.07848	−	0.769766i
$845$	−8.36250	−	9.95332i	−0.287679	−	0.342405i
$846$	5.30926	+	16.5774i	0.182536	+	0.569943i
$847$	−0.199666	−	0.199666i	−0.00686061	−	0.00686061i
$848$	−1.19667	+	3.48228i	−0.0410938	+	0.119582i
$849$		−	6.46312i		−	0.221814i
$850$	0.460776	−	0.894988i	0.0158045	−	0.0306978i
$851$	7.82432	+	7.82432i	0.268214	+	0.268214i
$852$	−4.40866	−	0.736373i	−0.151038	−	0.0252277i
$853$	−13.6990	−	13.6990i	−0.469044	−	0.469044i	0.432561	−	0.901605i	$-0.357610\pi$
$853$	−13.6990	−	13.6990i	−0.469044	−	0.469044i	−0.901605	+	0.432561i	$0.857610\pi$
$854$	−11.5084	−	35.9334i	−0.393810	−	1.22962i
$855$	13.7038			0.468661
$856$	4.91927	+	33.8186i	0.168137	+	1.15590i
$857$		−	42.0448i		−	1.43622i	−0.695928	−	0.718111i	$-0.745007\pi$
$857$		−	42.0448i		−	1.43622i	0.695928	−	0.718111i	$-0.254993\pi$
$858$	6.39604	−	11.2029i	0.218357	−	0.382461i
$859$		−	20.3642i		−	0.694818i	−0.937714	−	0.347409i	$-0.887062\pi$
$859$		−	20.3642i		−	0.694818i	0.937714	−	0.347409i	$-0.112938\pi$
$860$	−21.8212	−	3.64476i	−0.744096	−	0.124285i
$861$	−17.2264			−0.587075
$862$	35.8539	−	11.4829i	1.22119	−	0.391111i
$863$	−30.8613	−	30.8613i	−1.05053	−	1.05053i	−0.998653	−	0.0518785i	$-0.983479\pi$
$863$	−30.8613	−	30.8613i	−1.05053	−	1.05053i	−0.0518785	−	0.998653i	$-0.516521\pi$
$864$	16.8212	−	16.1274i	0.572267	−	0.548664i
$865$	−13.2792	−	13.2792i	−0.451505	−	0.451505i
$866$	−47.1639	−	24.2819i	−1.60270	−	0.825133i
$867$			12.5290i			0.425506i
$868$	14.5415	+	20.3733i	0.493571	+	0.691514i
$869$	3.92261	+	3.92261i	0.133066	+	0.133066i
$870$	−7.76109	+	2.48565i	−0.263125	+	0.0842714i
$871$	−55.2876	−	2.39649i	−1.87335	−	0.0812021i
$872$	−13.4660	+	18.0504i	−0.456016	+	0.611263i
$873$	−22.4083	+	22.4083i	−0.758405	+	0.758405i
$874$	56.6932	−	18.1572i	1.91767	−	0.614175i
$875$	−3.07431			−0.103931
$876$	−18.3612	−	3.06685i	−0.620367	−	0.103619i
$877$	−12.0540	+	12.0540i	−0.407033	+	0.407033i	−0.880703	−	0.473669i	$-0.842929\pi$
$877$	−12.0540	+	12.0540i	−0.407033	+	0.407033i	0.473669	+	0.880703i	$0.342929\pi$
$878$	0.892767	−	1.73406i	0.0301294	−	0.0585218i
$879$	−12.1337	+	12.1337i	−0.409261	+	0.409261i
$880$	−12.5986	−	4.32945i	−0.424700	−	0.145946i
$881$			16.6369i			0.560513i	0.959925	+	0.280257i	$0.0904195\pi$
$881$			16.6369i			0.560513i	−0.959925	+	0.280257i	$0.909580\pi$
$882$	7.46817	+	3.84492i	0.251466	+	0.129465i
$883$	−17.9316			−0.603445			−0.301722	−	0.953396i	$-0.597562\pi$
$883$	−17.9316			−0.603445			−0.301722	+	0.953396i	$0.597562\pi$
$884$	−1.06407	+	5.02136i	−0.0357886	+	0.168886i
$885$	−4.08684			−0.137378
$886$	−6.80421	−	3.50308i	−0.228592	−	0.117688i
$887$		−	32.4751i		−	1.09041i	−0.838304	−	0.545204i	$-0.816452\pi$
$887$		−	32.4751i		−	1.09041i	0.838304	−	0.545204i	$-0.183548\pi$
$888$	1.91012	−	2.56041i	0.0640996	−	0.0859218i
$889$	2.58567	−	2.58567i	0.0867206	−	0.0867206i
$890$	1.77239	−	3.44260i	0.0594107	−	0.115396i
$891$	−9.74852	+	9.74852i	−0.326588	+	0.326588i
$892$	4.60676	−	27.5807i	0.154246	−	0.923469i
$893$	28.7315			0.961462
$894$	11.0746	−	3.54688i	0.370391	−	0.118626i
$895$	12.9323	−	12.9323i	0.432278	−	0.432278i
$896$	19.6061	+	28.7294i	0.654994	+	0.959781i
$897$	−13.7763	−	15.0247i	−0.459977	−	0.501661i
$898$	−53.2621	+	17.0583i	−1.77738	+	0.569243i
$899$	−21.8364	−	21.8364i	−0.728285	−	0.728285i
$900$	−3.94426	+	2.81523i	−0.131475	+	0.0938411i
$901$		−	0.655241i		−	0.0218292i
$902$	30.8889	+	15.9028i	1.02849	+	0.529507i
$903$	18.2668	+	18.2668i	0.607881	+	0.607881i
$904$	−33.5404	+	4.87881i	−1.11554	+	0.162267i
$905$	2.45596	+	2.45596i	0.0816389	+	0.0816389i
$906$	17.0581	−	5.46321i	0.566717	−	0.181503i
$907$	2.42103			0.0803890			0.0401945	−	0.999192i	$-0.487202\pi$
$907$	2.42103			0.0803890			0.0401945	+	0.999192i	$0.487202\pi$
$908$	−5.58810	+	33.4559i	−0.185448	+	1.11027i
$909$			41.5712i			1.37883i
$910$	15.1220	−	4.13033i	0.501291	−	0.136919i
$911$		−	33.0139i		−	1.09380i	−0.837198	−	0.546900i	$-0.815808\pi$
$911$		−	33.0139i		−	1.09380i	0.837198	−	0.546900i	$-0.184192\pi$
$912$	−7.54309	−	15.4417i	−0.249777	−	0.511325i
$913$	13.0647			0.432379
$914$	0.558082	+	1.74253i	0.0184597	+	0.0576379i
$915$	−4.66156	−	4.66156i	−0.154106	−	0.154106i
$916$	0.926050	−	5.54425i	0.0305976	−	0.183187i
$917$	−3.83953	−	3.83953i	−0.126792	−	0.126792i
$918$	−1.89816	+	3.68688i	−0.0626485	+	0.121685i
$919$		−	4.39277i		−	0.144904i	−0.997372	−	0.0724520i	$-0.976918\pi$
$919$		−	4.39277i		−	0.144904i	0.997372	−	0.0724520i	$-0.0230824\pi$
$920$	−12.5874	+	16.8727i	−0.414996	+	0.556278i
$921$	3.58824	+	3.58824i	0.118237	+	0.118237i
$922$	7.65926	+	23.9149i	0.252244	+	0.787597i
$923$	−10.5976	−	0.459364i	−0.348825	−	0.0151202i
$924$	9.03704	+	12.6613i	0.297297	+	0.416526i
$925$	−1.05129	+	1.05129i	−0.0345664	+	0.0345664i
$926$	−9.82084	−	30.6642i	−0.322733	−	1.00769i
$927$	6.70831			0.220330
$928$	−29.6979	−	30.9755i	−0.974882	−	1.01682i
$929$	10.9501	−	10.9501i	0.359260	−	0.359260i	−0.504280	−	0.863540i	$-0.668242\pi$
$929$	10.9501	−	10.9501i	0.359260	−	0.359260i	0.863540	+	0.504280i	$0.168242\pi$
$930$	3.88828	+	2.00185i	0.127502	+	0.0656431i
$931$	9.80376	−	9.80376i	0.321305	−	0.321305i
$932$	−8.74758	+	6.24362i	−0.286536	+	0.204516i
$933$			5.85709i			0.191752i
$934$	−5.94964	+	11.5563i	−0.194678	+	0.378133i
$935$	2.37061			0.0775272
$936$	15.6189	−	19.1468i	0.510521	−	0.625833i
$937$	−9.84506			−0.321624			−0.160812	−	0.986985i	$-0.551411\pi$
$937$	−9.84506			−0.321624			−0.160812	+	0.986985i	$0.551411\pi$
$938$	30.5452	−	59.3295i	0.997337	−	1.93718i
$939$			11.1610i			0.364224i
$940$	−8.26955	+	5.90243i	−0.269723	+	0.192516i
$941$	17.3787	−	17.3787i	0.566529	−	0.566529i	−0.364625	−	0.931154i	$-0.618803\pi$
$941$	17.3787	−	17.3787i	0.566529	−	0.566529i	0.931154	+	0.364625i	$0.118803\pi$
$942$	−11.7397	−	6.04406i	−0.382499	−	0.196926i
$943$	38.8193	−	38.8193i	1.26413	−	1.26413i
$944$	−9.44552	−	19.3362i	−0.307426	−	0.629340i
$945$	12.6646			0.411978
$946$	−15.8911	−	49.6177i	−0.516664	−	1.61321i
$947$	32.2440	−	32.2440i	1.04779	−	1.04779i	0.0489909	−	0.998799i	$-0.484399\pi$
$947$	32.2440	−	32.2440i	1.04779	−	1.04779i	0.998799	−	0.0489909i	$-0.0156005\pi$
$948$	−1.47016	−	2.05976i	−0.0477486	−	0.0668979i
$949$	−44.1370	−	1.91316i	−1.43275	−	0.0621038i
$950$	2.43964	+	7.61743i	0.0791524	+	0.247142i
$951$	3.72945	+	3.72945i	0.120936	+	0.120936i
$952$	−4.96100	−	3.70101i	−0.160787	−	0.119951i
$953$		−	2.15000i		−	0.0696454i	−0.999394	−	0.0348227i	$-0.988913\pi$
$953$		−	2.15000i		−	0.0696454i	0.999394	−	0.0348227i	$-0.0110866\pi$
$954$	−1.44384	+	2.80444i	−0.0467461	+	0.0907972i
$955$	−6.75645	−	6.75645i	−0.218634	−	0.218634i
$956$	−4.66071	+	27.9036i	−0.150738	+	0.902468i
$957$	−13.5706	−	13.5706i	−0.438674	−	0.438674i
$958$	1.22278	+	3.81796i	0.0395062	+	0.123353i
$959$	6.13892			0.198236
$960$	5.34332	+	2.89485i	0.172455	+	0.0934309i
$961$		−	14.4277i		−	0.465409i
$962$	3.75874	−	6.58357i	0.121187	−	0.212263i
$963$			29.2753i			0.943384i
$964$	−2.37885	+	14.2422i	−0.0766176	+	0.458709i
$965$	−4.05821			−0.130638
$966$	23.4093	−	7.49730i	0.753180	−	0.241222i
$967$	−10.2122	−	10.2122i	−0.328401	−	0.328401i	0.523577	−	0.851978i	$-0.324597\pi$
$967$	−10.2122	−	10.2122i	−0.328401	−	0.328401i	−0.851978	+	0.523577i	$0.824597\pi$
$968$	−0.0373952	−	0.257081i	−0.00120193	−	0.00826290i
$969$	2.16245	+	2.16245i	0.0694680	+	0.0694680i
$970$	−16.4452	−	8.46664i	−0.528022	−	0.271847i
$971$			3.10518i			0.0996500i	0.998758	+	0.0498250i	$0.0158664\pi$
$971$			3.10518i			0.0996500i	−0.998758	+	0.0498250i	$0.984134\pi$
$972$	25.2369	−	18.0130i	0.809475	−	0.577766i
$973$	−41.5088	−	41.5088i	−1.33071	−	1.33071i
$974$	2.63399	−	0.843589i	0.0843983	−	0.0270303i
$975$	2.01876	−	1.85102i	0.0646520	−	0.0592800i
$976$	11.2816	−	32.8292i	0.361115	−	1.05084i
$977$	−21.3774	+	21.3774i	−0.683924	+	0.683924i	−0.960882	−	0.276958i	$-0.910674\pi$
$977$	−21.3774	+	21.3774i	−0.683924	+	0.683924i	0.276958	+	0.960882i	$0.410674\pi$
$978$	11.5932	−	3.71295i	0.370708	−	0.118727i
$979$	9.11862			0.291432
$980$	−0.807712	+	4.83577i	−0.0258014	+	0.154473i
$981$	−13.6412	+	13.6412i	−0.435530	+	0.435530i
$982$	25.7634	−	50.0415i	0.822144	−	1.59689i
$983$	5.54953	−	5.54953i	0.177003	−	0.177003i	−0.613045	−	0.790048i	$-0.710056\pi$
$983$	5.54953	−	5.54953i	0.177003	−	0.177003i	0.790048	+	0.613045i	$0.210056\pi$
$984$	−12.7031	−	9.47683i	−0.404961	−	0.302110i
$985$		−	10.1930i		−	0.324775i
$986$	6.78925	+	3.49538i	0.216214	+	0.111316i
$987$	11.8636			0.377621
$988$	−22.2342	−	34.1913i	−0.707365	−	1.08777i
$989$	−82.3275			−2.61786
$990$	−10.1463	−	5.22370i	−0.322469	−	0.166020i
$991$			16.5227i			0.524861i	0.964951	+	0.262431i	$0.0845240\pi$
$991$			16.5227i			0.524861i	−0.964951	+	0.262431i	$0.915476\pi$
$992$	−0.484796	+	23.0235i	−0.0153923	+	0.730995i
$993$	−12.3480	+	12.3480i	−0.391851	+	0.391851i
$994$	5.85497	−	11.3724i	0.185708	−	0.360710i
$995$	0.0403215	−	0.0403215i	0.00127828	−	0.00127828i
$996$	−5.87841	−	0.981863i	−0.186264	−	0.0311115i
$997$	−55.8787			−1.76970			−0.884849	−	0.465878i	$-0.845738\pi$
$997$	−55.8787			−1.76970			−0.884849	+	0.465878i	$0.845738\pi$
$998$	32.3220	−	10.3518i	1.02313	−	0.327680i
$999$	4.33079	−	4.33079i	0.137020	−	0.137020i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	260.2.j.a.31.11	yes	56
4.3	odd	2	inner	260.2.j.a.31.3	✓	56
13.8	odd	4	inner	260.2.j.a.151.3	yes	56
52.47	even	4	inner	260.2.j.a.151.11	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
260.2.j.a.31.3	✓	56	4.3	odd	2	inner
260.2.j.a.31.11	yes	56	1.1	even	1	trivial
260.2.j.a.151.3	yes	56	13.8	odd	4	inner
260.2.j.a.151.11	yes	56	52.47	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 260 = 2^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	260.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.647340 + 1.25736i) q^{2} +0.759638i q^{3} +(-1.16190 - 1.62788i) q^{4} +(0.707107 - 0.707107i) q^{5} +(-0.955138 - 0.491744i) q^{6} +(2.17387 - 2.17387i) q^{7} +(2.79897 - 0.407140i) q^{8} +2.42295 q^{9} +O(q^{10})\)	\(q+(-0.647340 + 1.25736i) q^{2} +0.759638i q^{3} +(-1.16190 - 1.62788i) q^{4} +(0.707107 - 0.707107i) q^{5} +(-0.955138 - 0.491744i) q^{6} +(2.17387 - 2.17387i) q^{7} +(2.79897 - 0.407140i) q^{8} +2.42295 q^{9} +(0.431349 + 1.34683i) q^{10} +(-2.35498 + 2.35498i) q^{11} +(1.23660 - 0.882626i) q^{12} +(2.65753 - 2.43671i) q^{13} +(1.32610 + 4.14056i) q^{14} +(0.537145 + 0.537145i) q^{15} +(-1.29996 + 3.78287i) q^{16} -0.711800i q^{17} +(-1.56847 + 3.04652i) q^{18} +(3.99929 + 3.99929i) q^{19} +(-1.97267 - 0.329493i) q^{20} +(1.65135 + 1.65135i) q^{21} +(-1.43658 - 4.48552i) q^{22} -7.44256 q^{23} +(0.309279 + 2.12620i) q^{24} -1.00000i q^{25} +(1.34350 + 4.91884i) q^{26} +4.11948i q^{27} +(-6.06460 - 1.01296i) q^{28} +7.58586 q^{29} +(-1.02310 + 0.327669i) q^{30} +(-2.87857 - 2.87857i) q^{31} +(-3.91491 - 4.08332i) q^{32} +(-1.78893 - 1.78893i) q^{33} +(0.894988 + 0.460776i) q^{34} -3.07431i q^{35} +(-2.81523 - 3.94426i) q^{36} +(-1.05129 - 1.05129i) q^{37} +(-7.61743 + 2.43964i) q^{38} +(1.85102 + 2.01876i) q^{39} +(1.69128 - 2.26706i) q^{40} +(-5.21586 + 5.21586i) q^{41} +(-3.14532 + 1.00736i) q^{42} +11.0617 q^{43} +(6.56987 + 1.09736i) q^{44} +(1.71328 - 1.71328i) q^{45} +(4.81786 - 9.35796i) q^{46} +(3.59208 - 3.59208i) q^{47} +(-2.87361 - 0.987502i) q^{48} -2.45138i q^{49} +(1.25736 + 0.647340i) q^{50} +0.540710 q^{51} +(-7.05445 - 1.49490i) q^{52} +0.920541 q^{53} +(-5.17966 - 2.66670i) q^{54} +3.33044i q^{55} +(5.19952 - 6.96965i) q^{56} +(-3.03801 + 3.03801i) q^{57} +(-4.91063 + 9.53814i) q^{58} +(-3.80422 + 3.80422i) q^{59} +(0.250295 - 1.49852i) q^{60} -8.67840 q^{61} +(5.48281 - 1.75598i) q^{62} +(5.26717 - 5.26717i) q^{63} +(7.66847 - 2.27915i) q^{64} +(0.156139 - 3.60217i) q^{65} +(3.40737 - 1.09128i) q^{66} +(-10.8530 - 10.8530i) q^{67} +(-1.15872 + 0.827042i) q^{68} -5.65365i q^{69} +(3.86551 + 1.99012i) q^{70} +(-2.08032 - 2.08032i) q^{71} +(6.78177 - 0.986480i) q^{72} +(-8.66411 - 8.66411i) q^{73} +(2.00240 - 0.641310i) q^{74} +0.759638 q^{75} +(1.86356 - 11.1571i) q^{76} +10.2388i q^{77} +(-3.73654 + 1.02057i) q^{78} -1.66567i q^{79} +(1.75568 + 3.59411i) q^{80} +4.13954 q^{81} +(-3.18177 - 9.93464i) q^{82} +(-2.77385 - 2.77385i) q^{83} +(0.769486 - 4.60690i) q^{84} +(-0.503318 - 0.503318i) q^{85} +(-7.16070 + 13.9086i) q^{86} +5.76250i q^{87} +(-5.63271 + 7.55032i) q^{88} +(-1.93603 - 1.93603i) q^{89} +(1.04514 + 3.26329i) q^{90} +(0.480021 - 11.0742i) q^{91} +(8.64753 + 12.1156i) q^{92} +(2.18667 - 2.18667i) q^{93} +(2.19124 + 6.84182i) q^{94} +5.65584 q^{95} +(3.10185 - 2.97391i) q^{96} +(-9.24834 + 9.24834i) q^{97} +(3.08226 + 1.58687i) q^{98} +(-5.70600 + 5.70600i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 12 q^{6} + 12 q^{8} - 56 q^{9}+O(q^{10}) \) 56 * q - 12 * q^6 + 12 * q^8 - 56 * q^9	\( 56 q - 12 q^{6} + 12 q^{8} - 56 q^{9} + 16 q^{14} - 12 q^{18} - 8 q^{20} - 16 q^{21} - 40 q^{24} - 16 q^{26} - 44 q^{28} + 40 q^{32} - 4 q^{34} + 16 q^{37} + 8 q^{41} + 8 q^{42} + 28 q^{44} - 12 q^{46} + 104 q^{48} + 56 q^{52} - 16 q^{53} + 20 q^{54} - 48 q^{57} - 4 q^{58} + 16 q^{61} - 8 q^{65} + 64 q^{66} + 24 q^{68} - 8 q^{70} - 32 q^{72} + 48 q^{73} - 136 q^{74} - 88 q^{76} + 52 q^{78} - 32 q^{80} + 56 q^{81} - 20 q^{84} - 64 q^{86} - 8 q^{89} - 88 q^{92} - 48 q^{93} - 16 q^{94} - 4 q^{96} - 32 q^{97} + 16 q^{98}+O(q^{100}) \) 56 * q - 12 * q^6 + 12 * q^8 - 56 * q^9 + 16 * q^14 - 12 * q^18 - 8 * q^20 - 16 * q^21 - 40 * q^24 - 16 * q^26 - 44 * q^28 + 40 * q^32 - 4 * q^34 + 16 * q^37 + 8 * q^41 + 8 * q^42 + 28 * q^44 - 12 * q^46 + 104 * q^48 + 56 * q^52 - 16 * q^53 + 20 * q^54 - 48 * q^57 - 4 * q^58 + 16 * q^61 - 8 * q^65 + 64 * q^66 + 24 * q^68 - 8 * q^70 - 32 * q^72 + 48 * q^73 - 136 * q^74 - 88 * q^76 + 52 * q^78 - 32 * q^80 + 56 * q^81 - 20 * q^84 - 64 * q^86 - 8 * q^89 - 88 * q^92 - 48 * q^93 - 16 * q^94 - 4 * q^96 - 32 * q^97 + 16 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more