LMFDB - Embedded newform 260.2.j.a.31.3

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			31.3
Character	$\chi$	$=$	260.31
Dual form			260.2.j.a.151.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.25736 + 0.647340i) q^{2} -0.759638i q^{3} +(1.16190 - 1.62788i) q^{4} +(0.707107 - 0.707107i) q^{5} +(0.491744 + 0.955138i) q^{6} +(-2.17387 + 2.17387i) q^{7} +(-0.407140 + 2.79897i) q^{8} +2.42295 q^{9} +O(q^{10})$	\(q+(-1.25736 + 0.647340i) q^{2} -0.759638i q^{3} +(1.16190 - 1.62788i) q^{4} +(0.707107 - 0.707107i) q^{5} +(0.491744 + 0.955138i) q^{6} +(-2.17387 + 2.17387i) q^{7} +(-0.407140 + 2.79897i) 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} +(-3.04652 + 1.56847i) q^{18} +(-3.99929 - 3.99929i) q^{19} +(-0.329493 - 1.97267i) q^{20} +(1.65135 + 1.65135i) q^{21} +(-1.43658 + 4.48552i) q^{22} +7.44256 q^{23} +(2.12620 + 0.309279i) q^{24} -1.00000i q^{25} +(-1.76408 + 4.78414i) q^{26} -4.11948i q^{27} +(1.01296 + 6.06460i) q^{28} +7.58586 q^{29} +(1.02310 + 0.327669i) q^{30} +(2.87857 + 2.87857i) q^{31} +(4.08332 + 3.91491i) q^{32} +(-1.78893 - 1.78893i) q^{33} +(0.460776 + 0.894988i) 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} +(-1.09736 - 6.56987i) q^{44} +(1.71328 - 1.71328i) q^{45} +(-9.35796 + 4.81786i) q^{46} +(-3.59208 + 3.59208i) q^{47} +(-2.87361 + 0.987502i) q^{48} -2.45138i q^{49} +(0.647340 + 1.25736i) q^{50} -0.540710 q^{51} +(-0.878878 - 7.15734i) q^{52} +0.920541 q^{53} +(2.66670 + 5.17966i) q^{54} -3.33044i q^{55} +(-5.19952 - 6.96965i) q^{56} +(-3.03801 + 3.03801i) q^{57} +(-9.53814 + 4.91063i) q^{58} +(3.80422 - 3.80422i) q^{59} +(-1.49852 + 0.250295i) 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} +(-1.99012 - 3.86551i) q^{70} +(2.08032 + 2.08032i) q^{71} +(-0.986480 + 6.78177i) q^{72} +(-8.66411 - 8.66411i) q^{73} +(2.00240 + 0.641310i) q^{74} -0.759638 q^{75} +(-11.1571 + 1.86356i) q^{76} +10.2388i q^{77} +(3.63422 + 1.34006i) q^{78} +1.66567i q^{79} +(-3.59411 - 1.75568i) q^{80} +4.13954 q^{81} +(3.18177 - 9.93464i) q^{82} +(2.77385 + 2.77385i) q^{83} +(4.60690 - 0.769486i) q^{84} +(-0.503318 - 0.503318i) q^{85} +(13.9086 - 7.16070i) 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} +(2.97391 - 3.10185i) q^{96} +(-9.24834 + 9.24834i) q^{97} +(1.58687 + 3.08226i) 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 $

$2$	−1.25736	+	0.647340i	−0.889087	+	0.457738i
$2$	−1.25736	+	0.647340i	−0.889087	+	0.457738i
$3$		−	0.759638i		−	0.438577i	−0.975660	−	0.219289i	$-0.929626\pi$
$3$		−	0.759638i		−	0.438577i	0.975660	−	0.219289i	$-0.0703736\pi$
$4$	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
$6$	0.491744	+	0.955138i	0.200754	+	0.389933i
$7$	−2.17387	+	2.17387i	−0.821644	+	0.821644i	−0.986344	−	0.164700i	$-0.947334\pi$
$7$	−2.17387	+	2.17387i	−0.821644	+	0.821644i	0.164700	+	0.986344i	$0.447334\pi$
$8$	−0.407140	+	2.79897i	−0.143946	+	0.989586i
$9$	2.42295			0.807650
$10$	−0.431349	+	1.34683i	−0.136404	+	0.425904i
$11$	2.35498	−	2.35498i	0.710053	−	0.710053i	−0.256493	−	0.966546i	$-0.582567\pi$
$11$	2.35498	−	2.35498i	0.710053	−	0.710053i	0.966546	+	0.256493i	$0.0825671\pi$
$12$	−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	$-0.0275102\pi$
$18$	−3.04652	+	1.56847i	−0.718071	+	0.369692i
$19$	−3.99929	−	3.99929i	−0.917499	−	0.917499i	0.0793480	−	0.996847i	$-0.474716\pi$
$19$	−3.99929	−	3.99929i	−0.917499	−	0.917499i	−0.996847	+	0.0793480i	$0.974716\pi$
$20$	−0.329493	−	1.97267i	−0.0736769	−	0.441103i
$21$	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	$-0.217276\pi$
$23$	7.44256			1.55188			0.775940	+	0.630807i	$0.217276\pi$
$24$	2.12620	+	0.309279i	0.434010	+	0.0631313i
$25$		−	1.00000i		−	0.200000i
$26$	−1.76408	+	4.78414i	−0.345965	+	0.938247i
$27$		−	4.11948i		−	0.792794i
$28$	1.01296	+	6.06460i	0.191432	+	1.14610i
$29$	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	0.916664	−	0.399658i	$-0.130871\pi$
$31$	2.87857	+	2.87857i	0.517006	+	0.517006i	−0.399658	+	0.916664i	$0.630871\pi$
$32$	4.08332	+	3.91491i	0.721836	+	0.692064i
$33$	−1.78893	−	1.78893i	−0.311413	−	0.311413i
$34$	0.460776	+	0.894988i	0.0790225	+	0.153489i
$35$			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	$-0.819479\pi$
$43$	−11.0617			−1.68690			−0.843449	+	0.537209i	$0.819479\pi$
$44$	−1.09736	−	6.56987i	−0.165433	−	0.990445i
$45$	1.71328	−	1.71328i	0.255401	−	0.255401i
$46$	−9.35796	+	4.81786i	−1.37976	+	0.710355i
$47$	−3.59208	+	3.59208i	−0.523958	+	0.523958i	−0.918764	−	0.394806i	$-0.870812\pi$
$47$	−3.59208	+	3.59208i	−0.523958	+	0.523958i	0.394806	+	0.918764i	$0.370812\pi$
$48$	−2.87361	+	0.987502i	−0.414770	+	0.142534i
$49$		−	2.45138i		−	0.350197i
$50$	0.647340	+	1.25736i	0.0915476	+	0.177817i
$51$	−0.540710			−0.0757146
$52$	−0.878878	−	7.15734i	−0.121878	−	0.992545i
$53$	0.920541			0.126446			0.0632230	−	0.997999i	$-0.479862\pi$
$53$	0.920541			0.126446			0.0632230	+	0.997999i	$0.479862\pi$
$54$	2.66670	+	5.17966i	0.362892	+	0.704863i
$55$		−	3.33044i		−	0.449077i
$56$	−5.19952	−	6.96965i	−0.694815	−	0.931359i
$57$	−3.03801	+	3.03801i	−0.402394	+	0.402394i
$58$	−9.53814	+	4.91063i	−1.25242	+	0.644797i
$59$	3.80422	−	3.80422i	0.495268	−	0.495268i	−0.414694	−	0.909961i	$-0.636111\pi$
$59$	3.80422	−	3.80422i	0.495268	−	0.495268i	0.909961	+	0.414694i	$0.136111\pi$
$60$	−1.49852	+	0.250295i	−0.193458	+	0.0323130i
$61$	−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	$0.136915\pi$
$67$	10.8530	+	10.8530i	1.32590	+	1.32590i	0.416990	+	0.908911i	$0.363085\pi$
$68$	−1.15872	−	0.827042i	−0.140516	−	0.100294i
$69$		−	5.65365i		−	0.680619i
$70$	−1.99012	−	3.86551i	−0.237865	−	0.462017i
$71$	2.08032	+	2.08032i	0.246888	+	0.246888i	0.819692	−	0.572804i	$-0.194144\pi$
$71$	2.08032	+	2.08032i	0.246888	+	0.246888i	−0.572804	+	0.819692i	$0.694144\pi$
$72$	−0.986480	+	6.78177i	−0.116258	+	0.799239i
$73$	−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
$76$	−11.1571	+	1.86356i	−1.27981	+	0.213765i
$77$			10.2388i			1.16682i
$78$	3.63422	+	1.34006i	0.411494	+	0.151732i
$79$			1.66567i			0.187402i	0.995600	+	0.0937012i	$0.0298698\pi$
$79$			1.66567i			0.187402i	−0.995600	+	0.0937012i	$0.970130\pi$
$80$	−3.59411	−	1.75568i	−0.401833	−	0.196291i
$81$	4.13954			0.459949
$82$	3.18177	−	9.93464i	0.351368	−	1.09710i
$83$	2.77385	+	2.77385i	0.304470	+	0.304470i	0.842760	−	0.538290i	$-0.180929\pi$
$83$	2.77385	+	2.77385i	0.304470	+	0.304470i	−0.538290	+	0.842760i	$0.680929\pi$
$84$	4.60690	−	0.769486i	0.502654	−	0.0839578i
$85$	−0.503318	−	0.503318i	−0.0545925	−	0.0545925i
$86$	13.9086	−	7.16070i	1.49980	−	0.772158i
$87$		−	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
$96$	2.97391	−	3.10185i	0.303524	−	0.316581i
$97$	−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	$0.481139\pi$
$98$	1.58687	+	3.08226i	0.160299	+	0.311356i
$99$	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	$0.674411\pi$
$102$	0.679867	−	0.350023i	0.0673168	−	0.0346574i
$103$	−2.76865			−0.272804			−0.136402	−	0.990654i	$-0.543554\pi$
$103$	−2.76865			−0.272804			−0.136402	+	0.990654i	$0.543554\pi$
$104$	5.73830	+	8.43042i	0.562686	+	0.826670i
$105$	2.33536			0.227908
$106$	−1.15745	+	0.595902i	−0.112421	+	0.0578792i
$107$		−	12.0825i		−	1.16806i	−0.811732	−	0.584030i	$-0.801475\pi$
$107$		−	12.0825i		−	1.16806i	0.811732	−	0.584030i	$-0.198525\pi$
$108$	−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	$0.374527\pi$
$110$	2.15593	+	4.18756i	0.205560	+	0.399268i
$111$	−0.798603	+	0.798603i	−0.0758001	+	0.0758001i
$112$	11.0494	+	5.39750i	1.04407	+	0.510016i
$113$	−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
$122$	10.9119	−	5.61787i	0.987913	−	0.508618i
$123$	3.96216	+	3.96216i	0.357256	+	0.357256i
$124$	8.03057	−	1.34134i	0.721167	−	0.120456i
$125$	−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	$-0.516806\pi$
$127$	−1.18943			−0.105545			−0.0527726	+	0.998607i	$0.516806\pi$
$128$	11.1174	−	2.09840i	0.982649	−	0.185474i
$129$			8.40291i			0.739835i
$130$	2.13550	+	4.63029i	0.187296	+	0.406104i
$131$			1.76622i			0.154315i	0.997019	+	0.0771577i	$0.0245845\pi$
$131$			1.76622i			0.154315i	−0.997019	+	0.0771577i	$0.975415\pi$
$132$	−4.99072	+	0.833595i	−0.434387	+	0.0725551i
$133$	17.3878			1.50771
$134$	−20.6716	−	6.62052i	−1.78576	−	0.571926i
$135$	−2.91291	−	2.91291i	−0.250703	−	0.250703i
$136$	1.99231	+	0.289802i	0.170839	+	0.0248503i
$137$	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	$0.722815\pi$
$138$	3.65983	+	7.10866i	0.311545	+	0.605130i
$139$			19.0945i			1.61957i	0.586724	+	0.809787i	$0.300417\pi$
$139$			19.0945i			1.61957i	−0.586724	+	0.809787i	$0.699583\pi$
$140$	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
$148$	−2.93288	+	0.489876i	−0.241081	+	0.0402675i
$149$	−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	$0.396225\pi$
$150$	0.955138	−	0.491744i	0.0779867	−	0.0401507i
$151$	11.7896	−	11.7896i	0.959420	−	0.959420i	−0.0397877	−	0.999208i	$-0.512668\pi$
$151$	11.7896	−	11.7896i	0.959420	−	0.959420i	0.999208	+	0.0397877i	$0.0126682\pi$
$152$	12.8222	−	9.56561i	1.04001	−	0.775874i
$153$		−	1.72466i		−	0.139430i
$154$	−6.62799	−	12.8739i	−0.534098	−	1.03741i
$155$	4.07091			0.326984
$156$	−5.43699	+	0.667629i	−0.435308	+	0.0534531i
$157$	12.2911			0.980936			0.490468	−	0.871459i	$-0.336826\pi$
$157$	12.2911			0.980936			0.490468	+	0.871459i	$0.336826\pi$
$158$	−1.07825	−	2.09434i	−0.0857812	−	0.166617i
$159$		−	0.699278i		−	0.0554563i
$160$	5.65560	−	0.119088i	0.447114	−	0.00941472i
$161$	−16.1791	+	16.1791i	−1.27509	+	1.27509i
$162$	−5.20489	+	2.67969i	−0.408934	+	0.210536i
$163$	8.01251	−	8.01251i	0.627588	−	0.627588i	−0.319872	−	0.947461i	$-0.603640\pi$
$163$	8.01251	−	8.01251i	0.627588	−	0.627588i	0.947461	+	0.319872i	$0.103640\pi$
$164$	2.43045	+	14.5511i	0.189786	+	1.13625i
$165$	−2.52993			−0.196955
$166$	−5.28335	−	1.69210i	−0.410067	−	0.131333i
$167$	−0.240596	+	0.240596i	−0.0186179	+	0.0186179i	−0.716354	−	0.697737i	$-0.754191\pi$
$167$	−0.240596	+	0.240596i	−0.0186179	+	0.0186179i	0.697737	+	0.716354i	$0.254191\pi$
$168$	−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	$-0.253070\pi$
$174$	3.73030	+	7.24554i	0.282793	+	0.549283i
$175$	2.17387	+	2.17387i	0.164329	+	0.164329i
$176$	−11.9700	−	5.84719i	−0.902270	−	0.440748i
$177$	−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	$-0.739539\pi$
$179$	−18.2890			−1.36698			−0.683491	+	0.729959i	$0.739539\pi$
$180$	−0.798345	−	4.77969i	−0.0595051	−	0.356257i
$181$			3.47325i			0.258165i	0.991634	+	0.129082i	$0.0412032\pi$
$181$			3.47325i			0.258165i	−0.991634	+	0.129082i	$0.958797\pi$
$182$	−6.56520	−	14.2350i	−0.486645	−	1.05517i
$183$			6.59244i			0.487327i
$184$	−3.03016	+	20.8315i	−0.223387	+	1.53572i
$185$	−1.48676			−0.109308
$186$	−1.33391	+	4.16495i	−0.0978071	+	0.305389i
$187$	−1.67627	−	1.67627i	−0.122581	−	0.122581i
$188$	1.67381	+	10.0211i	0.122075	+	0.730864i
$189$	8.95519	+	8.95519i	0.651394	+	0.651394i
$190$	7.11142	−	3.66125i	0.515917	−	0.265615i
$191$			9.55506i			0.691380i	0.938349	+	0.345690i	$0.112355\pi$
$191$			9.55506i			0.691380i	−0.938349	+	0.345690i	$0.887645\pi$
$192$	−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	$-0.500643\pi$
$199$	−0.0570233			−0.00404227			−0.00202114	+	0.999998i	$0.500643\pi$
$200$	2.79897	+	0.407140i	0.197917	+	0.0287891i
$201$	8.24433	−	8.24433i	0.581510	−	0.581510i
$202$	−11.1066	−	21.5728i	−0.781456	−	1.51786i
$203$	−16.4906	+	16.4906i	−1.15742	+	1.15742i
$204$	−0.628253	+	0.880209i	−0.0439865	+	0.0616270i
$205$			7.37634i			0.515186i
$206$	3.48119	−	1.79226i	0.242546	−	0.124873i
$207$	18.0329			1.25338
$208$	−12.6724	−	6.88543i	−0.878676	−	0.477419i
$209$	−18.8365			−1.30295
$210$	−2.93639	+	1.51177i	−0.202630	+	0.104322i
$211$		−	19.2469i		−	1.32501i	−0.749058	−	0.662504i	$-0.769494\pi$
$211$		−	19.2469i		−	1.32501i	0.749058	−	0.662504i	$-0.230506\pi$
$212$	1.06958	−	1.49853i	0.0734590	−	0.102919i
$213$	1.58029	−	1.58029i	0.108280	−	0.108280i
$214$	7.82149	+	15.1921i	0.534666	+	1.03851i
$215$	−7.82182	+	7.82182i	−0.533444	+	0.533444i
$216$	11.5303	+	1.67720i	0.784538	+	0.114119i
$217$	−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	0.293823	−	0.955860i	$-0.405072\pi$
$223$	−9.88632	−	9.88632i	−0.662037	−	0.662037i	−0.955860	+	0.293823i	$0.905072\pi$
$224$	−17.3871	+	0.366113i	−1.16172	+	0.0244619i
$225$		−	2.42295i		−	0.161530i
$226$	15.0671	−	7.75714i	1.00225	−	0.515998i
$227$	11.9923	+	11.9923i	0.795957	+	0.795957i	0.982455	−	0.186498i	$-0.0597138\pi$
$227$	11.9923	+	11.9923i	0.795957	+	0.795957i	−0.186498	+	0.982455i	$0.559714\pi$
$228$	1.41563	+	8.47537i	0.0937525	+	0.561295i
$229$	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
$232$	−3.08851	+	21.2326i	−0.202770	+	1.39399i
$233$		−	5.37361i		−	0.352037i	−0.984387	−	0.176019i	$-0.943678\pi$
$233$		−	5.37361i		−	0.352037i	0.984387	−	0.176019i	$-0.0563219\pi$
$234$	−4.27429	+	11.5917i	−0.279419	+	0.757776i
$235$			5.07996i			0.331380i
$236$	−1.77267	−	10.6129i	−0.115391	−	0.690844i
$237$	1.26530			0.0821904
$238$	−2.94725	−	0.943917i	−0.191042	−	0.0611851i
$239$	10.0021	+	10.0021i	0.646981	+	0.646981i	0.952262	−	0.305281i	$-0.0987504\pi$
$239$	10.0021	+	10.0021i	0.646981	+	0.646981i	−0.305281	+	0.952262i	$0.598750\pi$
$240$	−1.33368	+	2.73022i	−0.0860887	+	0.176235i
$241$	−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	$0.824701\pi$
$242$	0.0594571	+	0.115486i	0.00382205	+	0.00742375i
$243$		−	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	$-0.474440\pi$
$251$	2.54160			0.160424			0.0802122	+	0.996778i	$0.474440\pi$
$252$	2.45436	+	14.6942i	0.154610	+	0.925650i
$253$	17.5271	−	17.5271i	1.10192	−	1.10192i
$254$	1.49555	−	0.769968i	0.0938389	−	0.0483121i
$255$	−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	$-0.0857703\pi$
$258$	−5.43954	−	10.5655i	−0.338651	−	0.657778i
$259$	4.57075			0.284012
$260$	−5.68247	−	4.43955i	−0.352412	−	0.275329i
$261$	18.3802			1.13770
$262$	−1.14335	−	2.22077i	−0.0706361	−	0.137200i
$263$			1.01215i			0.0624117i	0.999513	+	0.0312058i	$0.00993474\pi$
$263$			1.01215i			0.0624117i	−0.999513	+	0.0312058i	$0.990065\pi$
$264$	5.73551	−	4.27882i	0.352996	−	0.263343i
$265$	0.650921	−	0.650921i	0.0399857	−	0.0399857i
$266$	−21.8627	+	11.2558i	−1.34049	+	0.690139i
$267$	−1.47068	+	1.47068i	−0.0900043	+	0.0900043i
$268$	30.2774	−	5.05720i	1.84949	−	0.308917i
$269$	−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	$0.544299\pi$
$271$	−18.5866	+	18.5866i	−1.12905	+	1.12905i	−0.990331	+	0.138722i	$0.955701\pi$
$272$	−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	$0.682773\pi$
$278$	−12.3606	−	24.0086i	−0.741341	−	1.43994i
$279$	6.97463	+	6.97463i	0.417560	+	0.417560i
$280$	−8.60490	−	1.25167i	−0.514241	−	0.0748019i
$281$	−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	$-0.418623\pi$
$283$	8.50815			0.505757			0.252879	+	0.967498i	$0.418623\pi$
$284$	5.80363	−	0.969373i	0.344382	−	0.0575217i
$285$			4.29639i			0.254496i
$286$	7.11217	+	15.4209i	0.420551	+	0.911859i
$287$		−	22.6771i		−	1.33859i
$288$	9.89368	+	9.48562i	0.582991	+	0.558946i
$289$	16.4933			0.970197
$290$	−3.27215	+	10.2168i	−0.192147	+	0.599952i
$291$	7.02539	+	7.02539i	0.411836	+	0.411836i
$292$	−24.1710	+	4.03725i	−1.41450	+	0.236262i
$293$	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	$0.520623\pi$
$294$	2.34140	−	1.20545i	0.136553	−	0.0703033i
$295$		−	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
$304$	−9.92985	+	20.3277i	−0.569516	+	1.16587i
$305$	−6.13655	+	6.13655i	−0.351378	+	0.351378i
$306$	1.11644	+	2.16851i	0.0638225	+	0.123965i
$307$	−4.72362	+	4.72362i	−0.269591	+	0.269591i	−0.828936	−	0.559344i	$-0.811053\pi$
$307$	−4.72362	+	4.72362i	−0.269591	+	0.269591i	0.559344	+	0.828936i	$0.311053\pi$
$308$	16.6675	+	11.8965i	0.949720	+	0.677866i
$309$			2.10317i			0.119645i
$310$	−5.11860	+	2.63526i	−0.290717	+	0.149673i
$311$	−7.71037			−0.437215			−0.218607	−	0.975813i	$-0.570151\pi$
$311$	−7.71037			−0.437215			−0.218607	+	0.975813i	$0.570151\pi$
$312$	6.40407	−	4.35903i	0.362559	−	0.246781i
$313$	14.6925			0.830467			0.415234	−	0.909715i	$-0.363700\pi$
$313$	14.6925			0.830467			0.415234	+	0.909715i	$0.363700\pi$
$314$	−15.4543	+	7.95651i	−0.872137	+	0.449012i
$315$			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	$0.187535\pi$
$318$	0.452670	+	0.879243i	0.0253845	+	0.0493055i
$319$	17.8645	−	17.8645i	1.00022	−	1.00022i
$320$	−7.03403	+	3.81083i	−0.393214	+	0.213032i
$321$	−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
$330$	3.18103	−	1.63772i	0.175110	−	0.0901538i
$331$	−16.2551	−	16.2551i	−0.893459	−	0.893459i	0.101388	−	0.994847i	$-0.467672\pi$
$331$	−16.2551	−	16.2551i	−0.893459	−	0.893459i	−0.994847	+	0.101388i	$0.967672\pi$
$332$	7.73843	−	1.29254i	0.424702	−	0.0709374i
$333$	−2.54724	−	2.54724i	−0.139588	−	0.139588i
$334$	0.146768	−	0.458263i	0.00803080	−	0.0250750i
$335$	15.3484			0.838573
$336$	4.10015	−	8.39354i	0.223681	−	0.457905i
$337$			12.8579i			0.700415i	0.936672	+	0.350207i	$0.113889\pi$
$337$			12.8579i			0.700415i	−0.936672	+	0.350207i	$0.886111\pi$
$338$	6.96947	+	17.0125i	0.379089	+	0.925360i
$339$			9.10283i			0.494398i
$340$	−1.40415	+	0.234533i	−0.0761506	+	0.0127193i
$341$	13.5579			0.734204
$342$	18.4567	+	5.91113i	0.998022	+	0.319637i
$343$	−9.88809	−	9.88809i	−0.533907	−	0.533907i
$344$	4.50367	−	30.9615i	0.242822	−	1.66933i
$345$	−3.99773	−	3.99773i	−0.215231	−	0.215231i
$346$	12.1568	+	23.6127i	0.653552	+	1.26943i
$347$			9.03173i			0.484849i	0.970170	+	0.242424i	$0.0779426\pi$
$347$			9.03173i			0.484849i	−0.970170	+	0.242424i	$0.922057\pi$
$348$	−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
$356$	−5.40110	+	0.902139i	−0.286258	+	0.0478133i
$357$	1.17543	−	1.17543i	0.0622104	−	0.0622104i
$358$	22.9958	−	11.8392i	1.21537	−	0.625720i
$359$	−5.05298	+	5.05298i	−0.266686	+	0.266686i	−0.827763	−	0.561077i	$-0.810387\pi$
$359$	−5.05298	+	5.05298i	−0.266686	+	0.266686i	0.561077	+	0.827763i	$0.310387\pi$
$360$	4.09789	+	5.49298i	0.215978	+	0.289505i
$361$			12.9886i			0.683609i
$362$	−2.24838	−	4.36713i	−0.118172	−	0.229531i
$363$	−0.0697716			−0.00366206
$364$	17.4697	+	13.6485i	0.915659	+	0.715378i
$365$	−12.2529			−0.641346
$366$	−4.26755	−	8.28906i	−0.223068	−	0.433276i
$367$			22.5693i			1.17811i	0.808094	+	0.589053i	$0.200499\pi$
$367$			22.5693i			1.17811i	−0.808094	+	0.589053i	$0.799501\pi$
$368$	−9.67505	−	28.1542i	−0.504347	−	1.46764i
$369$	−12.6378	+	12.6378i	−0.657896	+	0.657896i
$370$	1.86939	−	0.962436i	0.0971847	−	0.0500346i
$371$	−2.00113	+	2.00113i	−0.103894	+	0.103894i
$372$	−1.01893	−	6.10033i	−0.0528291	−	0.316287i
$373$	−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	$-0.952650\pi$
$379$	−22.1382	−	22.1382i	−1.13716	−	1.13716i	−0.148206	−	0.988957i	$-0.547350\pi$
$380$	−6.57154	+	9.20701i	−0.337113	+	0.472310i
$381$			0.903540i			0.0462898i
$382$	−6.18537	−	12.0141i	−0.316471	−	0.614697i
$383$	−16.8574	−	16.8574i	−0.861372	−	0.861372i	0.130126	−	0.991497i	$-0.458462\pi$
$383$	−16.8574	−	16.8574i	−0.861372	−	0.861372i	−0.991497	+	0.130126i	$0.958462\pi$
$384$	−1.59403	−	8.44520i	−0.0813448	−	0.430967i
$385$	7.23993	+	7.23993i	0.368981	+	0.368981i
$386$	5.46570	+	1.75050i	0.278197	+	0.0890983i
$387$	−26.8020			−1.36242
$388$	4.30948	+	25.8008i	0.218781	+	1.30984i
$389$			33.8842i			1.71800i	0.511980	+	0.858998i	$0.328912\pi$
$389$			33.8842i			1.71800i	−0.511980	+	0.858998i	$0.671088\pi$
$390$	3.51735	−	1.62221i	0.178108	−	0.0821438i
$391$		−	5.29761i		−	0.267912i
$392$	6.86134	+	0.998054i	0.346550	+	0.0504093i
$393$	1.34169			0.0676792
$394$	−4.39673	+	13.7282i	−0.221504	+	0.691615i
$395$	1.17781	+	1.17781i	0.0592618	+	0.0592618i
$396$	−2.65884	−	15.9185i	−0.133612	−	0.799933i
$397$	−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	$0.849585\pi$
$398$	0.0716987	−	0.0369134i	0.00359393	−	0.00185030i
$399$		−	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
$408$	0.220145	−	1.51343i	0.0108988	−	0.0749260i
$409$	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	$-0.00938157\pi$
$410$	−4.77500	−	9.27470i	−0.235820	−	0.458045i
$411$	1.07260	−	1.07260i	0.0529072	−	0.0529072i
$412$	−3.21691	+	4.50703i	−0.158486	+	0.222045i
$413$			16.5397i			0.813867i
$414$	−22.6739	+	11.6734i	−1.11436	+	0.573718i
$415$	3.92282			0.192564
$416$	20.3910	+	0.454088i	0.999752	+	0.0222635i
$417$	14.5049			0.710308
$418$	23.6842	−	12.1936i	1.15843	−	0.596408i
$419$			17.9072i			0.874826i	0.899261	+	0.437413i	$0.144105\pi$
$419$			17.9072i			0.874826i	−0.899261	+	0.437413i	$0.855895\pi$
$420$	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	$0.171670\pi$
$422$	12.4593	+	24.2002i	0.606507	+	1.17805i
$423$	−8.70342	+	8.70342i	−0.423175	+	0.423175i
$424$	−0.374789	+	2.57657i	−0.0182014	+	0.125129i
$425$	−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	0.996006	−	0.0892898i	$-0.0284597\pi$
$431$	18.8239	+	18.8239i	0.906716	+	0.906716i	−0.0892898	+	0.996006i	$0.528460\pi$
$432$	−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	$0.642603\pi$
$434$	15.7362	−	8.10161i	0.755360	−	0.388890i
$435$	−4.07471	−	4.07471i	−0.195367	−	0.195367i
$436$	2.62343	+	15.7064i	0.125639	+	0.752202i
$437$	−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	$-0.489522\pi$
$439$	1.37913			0.0658224			0.0329112	+	0.999458i	$0.489522\pi$
$440$	9.32181	+	1.35596i	0.444400	+	0.0646427i
$441$		−	5.93957i		−	0.282837i
$442$	3.40535	+	1.25567i	0.161976	+	0.0597263i
$443$		−	5.41151i		−	0.257109i	−0.991702	−	0.128554i	$-0.958966\pi$
$443$		−	5.41151i		−	0.257109i	0.991702	−	0.128554i	$-0.0410336\pi$
$444$	0.372128	+	2.22793i	0.0176604	+	0.105733i
$445$	−2.73796			−0.129792
$446$	18.8305	+	6.03085i	0.891648	+	0.285569i
$447$	5.81438	+	5.81438i	0.275011	+	0.275011i
$448$	21.6248	−	11.7157i	1.02167	−	0.553513i
$449$	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	$0.367043\pi$
$450$	1.56847	+	3.04652i	0.0739385	+	0.143614i
$451$			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
$460$	−2.45227	−	14.6817i	−0.114338	−	0.684539i
$461$	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	$0.114305\pi$
$462$	−9.77947	+	5.03487i	−0.454982	+	0.234243i
$463$	16.0992	−	16.0992i	0.748195	−	0.748195i	−0.225945	−	0.974140i	$-0.572547\pi$
$463$	16.0992	−	16.0992i	0.748195	−	0.748195i	0.974140	+	0.225945i	$0.0725471\pi$
$464$	−9.86134	−	28.6963i	−0.457801	−	1.33219i
$465$		−	3.09242i		−	0.143408i
$466$	3.47855	+	6.75656i	0.161141	+	0.312992i
$467$	−9.19091			−0.425305			−0.212652	−	0.977128i	$-0.568210\pi$
$467$	−9.19091			−0.425305			−0.212652	+	0.977128i	$0.568210\pi$
$468$	−2.12948	−	17.3419i	−0.0984351	−	0.801629i
$469$	−47.1858			−2.17884
$470$	−3.28846	−	6.38734i	−0.151685	−	0.294626i
$471$		−	9.33678i		−	0.430216i
$472$	9.09906	+	12.1968i	0.418818	+	0.561401i
$473$	−26.0501	+	26.0501i	−1.19779	+	1.19779i
$474$	−1.59094	+	0.819082i	−0.0730744	+	0.0376217i
$475$	−3.99929	+	3.99929i	−0.183500	+	0.183500i
$476$	4.31678	−	0.721027i	0.197859	−	0.0330482i
$477$	2.23042			0.102124
$478$	−19.0510	−	6.10147i	−0.871371	−	0.279075i
$479$	−2.00449	+	2.00449i	−0.0915876	+	0.0915876i	−0.751416	−	0.659829i	$-0.770629\pi$
$479$	−2.00449	+	2.00449i	−0.0915876	+	0.0915876i	0.659829	+	0.751416i	$0.270629\pi$
$480$	−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
$486$	10.0357	+	19.4928i	0.455228	+	0.884212i
$487$	1.38289	+	1.38289i	0.0626647	+	0.0626647i	0.737745	−	0.675080i	$-0.235891\pi$
$487$	1.38289	+	1.38289i	0.0626647	+	0.0626647i	−0.675080	+	0.737745i	$0.735891\pi$
$488$	3.53332	−	24.2906i	0.159946	−	1.09958i
$489$	−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	$-0.144984\pi$
$491$	39.7989			1.79610			0.898050	+	0.439893i	$0.144984\pi$
$492$	11.0536	−	1.84626i	0.498333	−	0.0832360i
$493$		−	5.39961i		−	0.243186i
$494$	26.1882	−	12.0781i	1.17826	−	0.543418i
$495$		−	8.06950i		−	0.362697i
$496$	7.14722	−	14.6313i	0.320919	−	0.656964i
$497$	−9.04466			−0.405708
$498$	−1.28539	+	4.01343i	−0.0575995	+	0.179846i
$499$	16.9696	+	16.9696i	0.759664	+	0.759664i	0.976261	−	0.216597i	$-0.0694959\pi$
$499$	16.9696	+	16.9696i	0.759664	+	0.759664i	−0.216597	+	0.976261i	$0.569496\pi$
$500$	−1.97267	+	0.329493i	−0.0882206	+	0.0147354i
$501$	0.182766	+	0.182766i	0.00816537	+	0.00816537i
$502$	−3.19571	+	1.64528i	−0.142631	+	0.0734324i
$503$			25.0262i			1.11586i	0.829888	+	0.557931i	$0.188404\pi$
$503$			25.0262i			1.11586i	−0.829888	+	0.557931i	$0.811596\pi$
$504$	−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
$512$	9.50141	−	20.5359i	0.419907	−	0.907567i
$513$	−16.4750	+	16.4750i	−0.727388	+	0.727388i
$514$	5.52519	+	10.7318i	0.243706	+	0.473361i
$515$	−1.95773	+	1.95773i	−0.0862681	+	0.0862681i
$516$	13.6789	+	9.76337i	0.602180	+	0.429808i
$517$			16.9185i			0.744076i
$518$	−5.74707	+	2.95883i	−0.252512	+	0.130003i
$519$	−14.2657			−0.626194
$520$	10.0188	+	1.90362i	0.439353	+	0.0834791i
$521$	−33.4237			−1.46432			−0.732160	−	0.681133i	$-0.761488\pi$
$521$	−33.4237			−1.46432			−0.732160	+	0.681133i	$0.761488\pi$
$522$	−23.1104	+	11.8982i	−1.01152	+	0.520770i
$523$			20.1901i			0.882850i	0.897298	+	0.441425i	$0.145527\pi$
$523$			20.1901i			0.882850i	−0.897298	+	0.441425i	$0.854473\pi$
$524$	2.87519	+	2.05218i	0.125603	+	0.0896498i
$525$	1.65135	−	1.65135i	0.0720708	−	0.0720708i
$526$	−0.655203	−	1.27263i	−0.0285682	−	0.0554894i
$527$	2.04897	−	2.04897i	0.0892543	−	0.0892543i
$528$	−4.44175	+	9.09284i	−0.193302	+	0.395715i
$529$	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
$538$	11.6701	−	6.00823i	0.503133	−	0.259033i
$539$	−5.77294	−	5.77294i	−0.248658	−	0.248658i
$540$	−8.12638	+	1.35734i	−0.349704	+	0.0584106i
$541$	−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
$544$	2.78663	−	2.90651i	0.119476	−	0.124615i
$545$			7.96201i			0.341055i
$546$	−10.8134	+	4.98717i	−0.462771	+	0.213431i
$547$		−	11.5196i		−	0.492542i	−0.969201	−	0.246271i	$-0.920795\pi$
$547$		−	11.5196i		−	0.492542i	0.969201	−	0.246271i	$-0.0792053\pi$
$548$	3.93912	−	0.657946i	0.168271	−	0.0281061i
$549$	−21.0273			−0.897424
$550$	4.48552	+	1.43658i	0.191263	+	0.0612561i
$551$	−30.3380	−	30.3380i	−1.29244	−	1.29244i
$552$	15.8244	+	2.30183i	0.673531	+	0.0979722i
$553$	−3.62094	−	3.62094i	−0.153978	−	0.153978i
$554$	−18.0921	−	35.1412i	−0.768660	−	1.49301i
$555$			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	$-0.477485\pi$
$563$	3.35387			0.141349			0.0706743	+	0.997499i	$0.477485\pi$
$564$	7.61241	−	1.27149i	0.320540	−	0.0535395i
$565$	−8.47334	+	8.47334i	−0.356476	+	0.356476i
$566$	−10.6978	+	5.50766i	−0.449662	+	0.231504i
$567$	−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	$-0.298468\pi$
$570$	−2.78123	−	5.40211i	−0.116493	−	0.226269i
$571$	−27.1181			−1.13486			−0.567428	−	0.823423i	$-0.692062\pi$
$571$	−27.1181			−1.13486			−0.567428	+	0.823423i	$0.692062\pi$
$572$	−18.9251	−	14.7857i	−0.791299	−	0.618219i
$573$	7.25839			0.303223
$574$	14.6798	+	28.5133i	0.612724	+	1.19012i
$575$		−	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	$0.324965\pi$
$578$	−20.7380	+	10.6768i	−0.862589	+	0.444096i
$579$	−2.17985	+	2.17985i	−0.0905914	+	0.0905914i
$580$	−2.49949	−	14.9644i	−0.103786	−	0.621363i
$581$	−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	$-0.990847\pi$
$587$	−24.9147	−	24.9147i	−1.02834	−	1.02834i	−0.0287520	−	0.999587i	$-0.509153\pi$
$588$	−2.16365	+	3.03137i	−0.0892274	+	0.125011i
$589$		−	23.0244i		−	0.948706i
$590$	3.48268	+	6.76457i	0.143379	+	0.278493i
$591$	−5.47511	−	5.47511i	−0.225216	−	0.225216i
$592$	−2.61027	+	5.34356i	−0.107281	+	0.219619i
$593$	−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
$596$	3.56663	+	21.3534i	0.146095	+	0.874668i
$597$			0.0433170i			0.00177285i
$598$	−13.1293	+	35.6062i	−0.536897	+	1.45605i
$599$			22.3997i			0.915225i	0.889152	+	0.457613i	$0.151295\pi$
$599$			22.3997i			0.915225i	−0.889152	+	0.457613i	$0.848705\pi$
$600$	0.309279	−	2.12620i	0.0126263	−	0.0868019i
$601$	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
$604$	−5.49362	−	32.8903i	−0.223532	−	1.33829i
$605$	−0.0649467	−	0.0649467i	−0.00264046	−	0.00264046i
$606$	−16.3875	+	8.43697i	−0.665698	+	0.342729i
$607$			0.244959i			0.00994258i	0.999988	+	0.00497129i	$0.00158242\pi$
$607$			0.244959i			0.00994258i	−0.999988	+	0.00497129i	$0.998418\pi$
$608$	−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
$616$	−28.6581	−	4.16863i	−1.15467	−	0.167959i
$617$	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	$0.201001\pi$
$618$	−1.36147	−	2.64445i	−0.0547663	−	0.106375i
$619$	−8.24810	+	8.24810i	−0.331519	+	0.331519i	−0.853163	−	0.521644i	$-0.825319\pi$
$619$	−8.24810	+	8.24810i	−0.331519	+	0.331519i	0.521644	+	0.853163i	$0.325319\pi$
$620$	4.73000	−	6.62694i	0.189962	−	0.266144i
$621$		−	30.6594i		−	1.23032i
$622$	9.69470	−	4.99123i	0.388722	−	0.200130i
$623$	8.41734			0.337234
$624$	−5.23044	+	9.62647i	−0.209385	+	0.385367i
$625$	−1.00000			−0.0400000
$626$	−18.4737	+	9.51102i	−0.738358	+	0.380137i
$627$			14.3089i			0.571442i
$628$	14.2810	−	20.0084i	0.569876	−	0.798421i
$629$	−0.748311	+	0.748311i	−0.0298371	+	0.0298371i
$630$	−4.82197	−	9.36594i	−0.192112	−	0.373148i
$631$	−14.9116	+	14.9116i	−0.593620	+	0.593620i	−0.938607	−	0.344988i	$-0.887883\pi$
$631$	−14.9116	+	14.9116i	−0.593620	+	0.593620i	0.344988	+	0.938607i	$0.387883\pi$
$632$	−4.66216	−	0.678160i	−0.185451	−	0.0269758i
$633$	−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	$0.983308\pi$
$642$	11.5405	−	5.94150i	0.455466	−	0.234492i
$643$	2.81539	+	2.81539i	0.111028	+	0.111028i	0.760438	−	0.649410i	$-0.224984\pi$
$643$	2.81539	+	2.81539i	0.111028	+	0.111028i	−0.649410	+	0.760438i	$0.724984\pi$
$644$	7.53904	+	45.1361i	0.297080	+	1.77861i
$645$	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	$-0.383244\pi$
$647$	18.2443			0.717259			0.358630	+	0.933480i	$0.383244\pi$
$648$	−1.68537	+	11.5864i	−0.0662077	+	0.455159i
$649$		−	17.9177i		−	0.703332i
$650$	4.78414	+	1.76408i	0.187649	+	0.0691931i
$651$			9.50705i			0.372611i
$652$	−3.73362	−	22.3531i	−0.146220	−	0.875416i
$653$	−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
$656$	26.5113	+	12.9505i	1.03509	+	0.505631i
$657$	−20.9927	−	20.9927i	−0.819003	−	0.819003i
$658$	10.1097	+	19.6367i	0.394119	+	0.765516i
$659$		−	47.9086i		−	1.86625i	−0.359546	−	0.933127i	$-0.617069\pi$
$659$		−	47.9086i		−	1.86625i	0.359546	−	0.933127i	$-0.382931\pi$
$660$	−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
$668$	0.112111	+	0.671209i	0.00433772	+	0.0259699i
$669$	−7.51002	+	7.51002i	−0.290354	+	0.290354i
$670$	−19.2985	+	9.93564i	−0.745565	+	0.383847i
$671$	−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	$0.878807\pi$
$674$	−8.32343	−	16.1670i	−0.320607	−	0.622730i
$675$	−4.11948			−0.158559
$676$	−19.7760	−	16.8793i	−0.760616	−	0.649202i
$677$	34.9705			1.34403			0.672013	−	0.740539i	$-0.265430\pi$
$677$	34.9705			1.34403			0.672013	+	0.740539i	$0.265430\pi$
$678$	−5.89262	−	11.4455i	−0.226305	−	0.439563i
$679$		−	40.2093i		−	1.54309i
$680$	1.61369	−	1.20385i	0.0618824	−	0.0461656i
$681$	9.10981	−	9.10981i	0.349089	−	0.349089i
$682$	−17.0472	+	8.77659i	−0.652771	+	0.336073i
$683$	9.68877	−	9.68877i	0.370730	−	0.370730i	−0.497013	−	0.867743i	$-0.665570\pi$
$683$	9.68877	−	9.68877i	0.370730	−	0.370730i	0.867743	+	0.497013i	$0.165570\pi$
$684$	−27.0332	+	4.51532i	−1.03364	+	0.172647i
$685$	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	0.272710	−	0.962096i	$-0.412080\pi$
$691$	−18.1218	−	18.1218i	−0.689387	−	0.689387i	−0.962096	+	0.272710i	$0.912080\pi$
$692$	−30.5708	−	21.8201i	−1.16213	−	0.829474i
$693$			24.8081i			0.942383i
$694$	−5.84660	−	11.3561i	−0.221934	−	0.431073i
$695$	13.5018	+	13.5018i	0.512154	+	0.512154i
$696$	16.1291	+	2.34615i	0.611371	+	0.0889304i
$697$	3.71265	+	3.71265i	0.140627	+	0.140627i
$698$	14.1392	+	4.52839i	0.535178	+	0.171402i
$699$	−4.08200			−0.154395
$700$	6.06460	−	1.01296i	0.229220	−	0.0382864i
$701$		−	10.6153i		−	0.400935i	−0.979700	−	0.200467i	$-0.935754\pi$
$701$		−	10.6153i		−	0.400935i	0.979700	−	0.200467i	$-0.0642460\pi$
$702$	19.7082	+	7.26711i	0.743837	+	0.274279i
$703$			8.40886i			0.317146i
$704$	−23.4264	+	12.6918i	−0.882917	+	0.478338i
$705$	3.85893			0.145336
$706$	7.23531	−	22.5912i	0.272305	−	0.850232i
$707$	−37.2976	−	37.2976i	−1.40272	−	1.40272i
$708$	−8.06199	+	1.34659i	−0.302988	+	0.0506078i
$709$	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	$0.710210\pi$
$710$	−3.69917	+	1.90448i	−0.138827	+	0.0714739i
$711$			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	$-0.761064\pi$
$719$	−39.2158			−1.46250			−0.731252	+	0.682108i	$0.761064\pi$
$720$	−8.70834	−	4.25392i	−0.324541	−	0.158534i
$721$	6.01868	−	6.01868i	0.224147	−	0.224147i
$722$	−8.40801	−	16.3313i	−0.312914	−	0.607787i
$723$	−3.87804	+	3.87804i	−0.144226	+	0.144226i
$724$	5.65403	+	4.03558i	0.210130	+	0.149981i
$725$		−	7.58586i		−	0.281732i
$726$	0.0877279	−	0.0451659i	0.00325589	−	0.00167626i
$727$	31.6876			1.17523			0.587613	−	0.809142i	$-0.300068\pi$
$727$	31.6876			1.17523			0.587613	+	0.809142i	$0.300068\pi$
$728$	−30.8009	−	5.85231i	−1.14156	−	0.216901i
$729$	0.641958			0.0237762
$730$	15.4063	−	7.93179i	0.570213	−	0.293569i
$731$			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	$0.116078\pi$
$734$	−14.6100	−	28.3777i	−0.539264	−	1.04744i
$735$	−1.31675	+	1.31675i	−0.0485689	+	0.0485689i
$736$	30.3903	+	29.1369i	1.12020	+	1.07400i
$737$	51.1170			1.88292
$738$	7.70928	−	24.0711i	0.283783	−	0.886071i
$739$	22.7608	−	22.7608i	0.837269	−	0.837269i	−0.151229	−	0.988499i	$-0.548323\pi$
$739$	22.7608	−	22.7608i	0.837269	−	0.837269i	0.988499	+	0.151229i	$0.0483232\pi$
$740$	−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	0.986010	−	0.166687i	$-0.0533071\pi$
$743$	22.3331	+	22.3331i	0.819322	+	0.819322i	−0.166687	+	0.986010i	$0.553307\pi$
$744$	5.23015	+	7.01071i	0.191746	+	0.257025i
$745$			10.8246i			0.396582i
$746$	11.9057	−	6.12955i	0.435900	−	0.224419i
$747$	6.72090	+	6.72090i	0.245905	+	0.245905i
$748$	−4.67643	+	0.781099i	−0.170987	+	0.0285598i
$749$	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	$-0.812009\pi$
$751$	−45.5248			−1.66122			−0.830611	+	0.556853i	$0.812009\pi$
$752$	18.2579	+	8.91879i	0.665798	+	0.325235i
$753$		−	1.93070i		−	0.0703585i
$754$	−13.3821	+	36.2918i	−0.487347	+	1.32167i
$755$		−	16.6729i		−	0.606791i
$756$	24.9830	−	4.17288i	0.908623	−	0.151766i
$757$	−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
$760$	2.30272	−	15.8305i	0.0835284	−	0.574234i
$761$	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	$0.737438\pi$
$762$	−0.584897	−	1.13607i	−0.0211886	−	0.0411556i
$763$		−	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
$772$	−8.00552	+	1.33715i	−0.288125	+	0.0481252i
$773$	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	$-0.0783071\pi$
$774$	33.6998	−	17.3500i	1.21131	−	0.623633i
$775$	2.87857	−	2.87857i	0.103401	−	0.103401i
$776$	−22.1205	−	29.6512i	−0.794078	−	1.06442i
$777$		−	3.47211i		−	0.124561i
$778$	−21.9346	−	42.6046i	−0.786392	−	1.52745i
$779$	41.7194			1.49475
$780$	−3.37245	+	4.31662i	−0.120753	+	0.154560i
$781$	9.79821			0.350607
$782$	3.42935	+	6.66100i	0.122633	+	0.238197i
$783$		−	31.2498i		−	1.11678i
$784$	−9.27324	+	3.18670i	−0.331187	+	0.113811i
$785$	8.69111	−	8.69111i	0.310199	−	0.310199i
$786$	−1.68698	+	0.868528i	−0.0601727	+	0.0309794i
$787$	−13.4293	+	13.4293i	−0.478702	+	0.478702i	−0.904716	−	0.426015i	$-0.859917\pi$
$787$	−13.4293	+	13.4293i	−0.478702	+	0.478702i	0.426015	+	0.904716i	$0.359917\pi$
$788$	−3.35852	−	20.1074i	−0.119642	−	0.716296i
$789$	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	$-0.163730\pi$
$798$	8.55035	+	16.6078i	0.302679	+	0.587908i
$799$	2.55684	+	2.55684i	0.0904545	+	0.0904545i
$800$	3.91491	−	4.08332i	0.138413	−	0.144367i
$801$	−4.69091	−	4.69091i	−0.165745	−	0.165745i
$802$	19.6456	+	6.29192i	0.693712	+	0.222176i
$803$	−40.8076			−1.44007
$804$	−3.84164	−	22.9999i	−0.135484	−	0.811142i
$805$			22.8807i			0.806439i
$806$	−18.8495	+	8.69345i	−0.663946	+	0.306214i
$807$			7.05052i			0.248190i
$808$	−48.0227	−	6.98540i	−1.68943	−	0.245746i
$809$	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	0.475274	−	0.879838i	$-0.342349\pi$
$811$	−11.5212	−	11.5212i	−0.404564	−	0.404564i	−0.879838	+	0.475274i	$0.842349\pi$
$812$	7.68420	+	46.0052i	0.269662	+	1.61447i
$813$	14.1191	+	14.1191i	0.495177	+	0.495177i
$814$	6.22588	−	3.20534i	0.218217	−	0.112347i
$815$		−	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	$-0.684998\pi$
$823$	−31.5004			−1.09803			−0.549017	+	0.835811i	$0.684998\pi$
$824$	1.12723	−	7.74938i	0.0392689	−	0.269962i
$825$	−1.78893	+	1.78893i	−0.0622826	+	0.0622826i
$826$	−10.7068	−	20.7964i	−0.372538	−	0.723599i
$827$	−7.38794	+	7.38794i	−0.256904	+	0.256904i	−0.823794	−	0.566890i	$-0.808147\pi$
$827$	−7.38794	+	7.38794i	−0.256904	+	0.256904i	0.566890	+	0.823794i	$0.308147\pi$
$828$	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	$-0.190457\pi$
$830$	−4.93239	+	2.53940i	−0.171206	+	0.0881437i
$831$	21.2307			0.736484
$832$	−25.9328	+	12.6290i	−0.899057	+	0.437831i
$833$	−1.74489			−0.0604569
$834$	−18.2379	+	9.38959i	−0.631525	+	0.325135i
$835$			0.340254i			0.0117750i
$836$	−21.8861	+	30.6634i	−0.756948	+	1.06052i
$837$	11.8582	−	11.8582i	0.409880	−	0.409880i
$838$	−11.5921	−	22.5158i	−0.400441	−	0.777796i
$839$	31.9636	−	31.9636i	1.10351	−	1.10351i	0.109523	−	0.993984i	$-0.465068\pi$
$839$	31.9636	−	31.9636i	1.10351	−	1.10351i	0.993984	−	0.109523i	$-0.0349324\pi$
$840$	−0.950819	+	6.53661i	−0.0328064	+	0.225534i
$841$	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
$850$	0.894988	−	0.460776i	0.0306978	−	0.0158045i
$851$	−7.82432	−	7.82432i	−0.268214	−	0.268214i
$852$	−0.736373	−	4.40866i	−0.0252277	−	0.151038i
$853$	−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
$856$	33.8186	+	4.91927i	1.15590	+	0.168137i
$857$		−	42.0448i		−	1.43622i	−0.695928	−	0.718111i	$-0.745007\pi$
$857$		−	42.0448i		−	1.43622i	0.695928	−	0.718111i	$-0.254993\pi$
$858$	11.7143	−	5.40268i	0.399920	−	0.184444i
$859$			20.3642i			0.694818i	0.937714	+	0.347409i	$0.112938\pi$
$859$			20.3642i			0.694818i	−0.937714	+	0.347409i	$0.887062\pi$
$860$	3.64476	+	21.8212i	0.124285	+	0.744096i
$861$	−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	$0.0165209\pi$
$863$	30.8613	+	30.8613i	1.05053	+	1.05053i	0.0518785	+	0.998653i	$0.483479\pi$
$864$	16.1274	−	16.8212i	0.548664	−	0.572267i
$865$	−13.2792	−	13.2792i	−0.451505	−	0.451505i
$866$	−24.2819	−	47.1639i	−0.825133	−	1.60270i
$867$		−	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
$876$	3.06685	+	18.3612i	0.103619	+	0.620367i
$877$	−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	$0.342929\pi$
$878$	−1.73406	+	0.892767i	−0.0585218	+	0.0301294i
$879$	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	$0.909580\pi$
$882$	3.84492	+	7.46817i	0.129465	+	0.251466i
$883$	17.9316			0.603445			0.301722	−	0.953396i	$-0.402438\pi$
$883$	17.9316			0.603445			0.301722	+	0.953396i	$0.402438\pi$
$884$	−5.09460	+	0.625585i	−0.171350	+	0.0210407i
$885$	−4.08684			−0.137378
$886$	3.50308	+	6.80421i	0.117688	+	0.228592i
$887$			32.4751i			1.09041i	0.838304	+	0.545204i	$0.183548\pi$
$887$			32.4751i			1.09041i	−0.838304	+	0.545204i	$0.816452\pi$
$888$	−1.91012	−	2.56041i	−0.0640996	−	0.0859218i
$889$	2.58567	−	2.58567i	0.0867206	−	0.0867206i
$890$	3.44260	−	1.77239i	0.115396	−	0.0594107i
$891$	9.74852	−	9.74852i	0.326588	−	0.326588i
$892$	−27.5807	+	4.60676i	−0.923469	+	0.154246i
$893$	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
$902$	−15.9028	−	30.8889i	−0.529507	−	1.02849i
$903$	−18.2668	−	18.2668i	−0.607881	−	0.607881i
$904$	4.87881	−	33.5404i	0.162267	−	1.11554i
$905$	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	$-0.512798\pi$
$907$	−2.42103			−0.0803890			−0.0401945	+	0.999192i	$0.512798\pi$
$908$	33.4559	−	5.58810i	1.11027	−	0.185448i
$909$			41.5712i			1.37883i
$910$	−14.7079	−	5.42334i	−0.487563	−	0.179782i
$911$			33.0139i			1.09380i	0.837198	+	0.546900i	$0.184192\pi$
$911$			33.0139i			1.09380i	−0.837198	+	0.546900i	$0.815808\pi$
$912$	15.4417	+	7.54309i	0.511325	+	0.249777i
$913$	13.0647			0.432379
$914$	−0.558082	+	1.74253i	−0.0184597	+	0.0576379i
$915$	4.66156	+	4.66156i	0.154106	+	0.154106i
$916$	5.54425	−	0.926050i	0.183187	−	0.0305976i
$917$	−3.83953	−	3.83953i	−0.126792	−	0.126792i
$918$	3.68688	−	1.89816i	0.121685	−	0.0626485i
$919$			4.39277i			0.144904i	0.997372	+	0.0724520i	$0.0230824\pi$
$919$			4.39277i			0.144904i	−0.997372	+	0.0724520i	$0.976918\pi$
$920$	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
$928$	30.9755	+	29.6979i	1.01682	+	0.974882i
$929$	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	$0.168242\pi$
$930$	2.00185	+	3.88828i	0.0656431	+	0.127502i
$931$	−9.80376	+	9.80376i	−0.321305	+	0.321305i
$932$	−8.74758	−	6.24362i	−0.286536	−	0.204516i
$933$			5.85709i			0.191752i
$934$	11.5563	−	5.94964i	0.378133	−	0.194678i
$935$	−2.37061			−0.0775272
$936$	13.9036	+	20.4265i	0.454454	+	0.667660i
$937$	−9.84506			−0.321624			−0.160812	−	0.986985i	$-0.551411\pi$
$937$	−9.84506			−0.321624			−0.160812	+	0.986985i	$0.551411\pi$
$938$	59.3295	−	30.5452i	1.93718	−	0.997337i
$939$		−	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	$0.118803\pi$
$942$	6.04406	+	11.7397i	0.196926	+	0.382499i
$943$	−38.8193	+	38.8193i	−1.26413	+	1.26413i
$944$	−19.3362	−	9.44552i	−0.629340	−	0.307426i
$945$	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	$0.515601\pi$
$947$	−32.2440	+	32.2440i	−1.04779	+	1.04779i	−0.998799	+	0.0489909i	$0.984399\pi$
$948$	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	$-0.0110866\pi$
$954$	−2.80444	+	1.44384i	−0.0907972	+	0.0467461i
$955$	6.75645	+	6.75645i	0.218634	+	0.218634i
$956$	27.9036	−	4.66071i	0.902468	−	0.150738i
$957$	−13.5706	−	13.5706i	−0.438674	−	0.438674i
$958$	1.22278	−	3.81796i	0.0395062	−	0.123353i
$959$	−6.13892			−0.198236
$960$	2.89485	+	5.34332i	0.0934309	+	0.172455i
$961$		−	14.4277i		−	0.465409i
$962$	6.88412	−	3.17497i	0.221953	−	0.102365i
$963$		−	29.2753i		−	0.943384i
$964$	−14.2422	+	2.37885i	−0.458709	+	0.0766176i
$965$	−4.05821			−0.130638
$966$	−23.4093	−	7.49730i	−0.753180	−	0.241222i
$967$	10.2122	+	10.2122i	0.328401	+	0.328401i	0.851978	−	0.523577i	$-0.175403\pi$
$967$	10.2122	+	10.2122i	0.328401	+	0.328401i	−0.523577	+	0.851978i	$0.675403\pi$
$968$	0.257081	+	0.0373952i	0.00826290	+	0.00120193i
$969$	2.16245	+	2.16245i	0.0694680	+	0.0694680i
$970$	−8.46664	−	16.4452i	−0.271847	−	0.528022i
$971$		−	3.10518i		−	0.0996500i	−0.998758	−	0.0498250i	$-0.984134\pi$
$971$		−	3.10518i		−	0.0996500i	0.998758	−	0.0498250i	$-0.0158664\pi$
$972$	−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
$980$	−4.83577	+	0.807712i	−0.154473	+	0.0258014i
$981$	−13.6412	+	13.6412i	−0.435530	+	0.435530i
$982$	−50.0415	+	25.7634i	−1.59689	+	0.822144i
$983$	−5.54953	+	5.54953i	−0.177003	+	0.177003i	−0.790048	−	0.613045i	$-0.789944\pi$
$983$	−5.54953	+	5.54953i	−0.177003	+	0.177003i	0.613045	+	0.790048i	$0.289944\pi$
$984$	−12.7031	+	9.47683i	−0.404961	+	0.302110i
$985$		−	10.1930i		−	0.324775i
$986$	3.49538	+	6.78925i	0.111316	+	0.216214i
$987$	−11.8636			−0.377621
$988$	−25.1094	+	32.1391i	−0.798836	+	1.02248i
$989$	−82.3275			−2.61786
$990$	5.22370	+	10.1463i	0.166020	+	0.322469i
$991$		−	16.5227i		−	0.524861i	−0.964951	−	0.262431i	$-0.915476\pi$
$991$		−	16.5227i		−	0.524861i	0.964951	−	0.262431i	$-0.0845240\pi$
$992$	0.484796	+	23.0235i	0.0153923	+	0.730995i
$993$	−12.3480	+	12.3480i	−0.391851	+	0.391851i
$994$	11.3724	−	5.85497i	0.360710	−	0.185708i
$995$	−0.0403215	+	0.0403215i	−0.00127828	+	0.00127828i
$996$	−0.981863	−	5.87841i	−0.0311115	−	0.186264i
$997$	−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.31.3	✓	56
4.3	odd	2	inner	260.2.j.a.31.11	yes	56
13.8	odd	4	inner	260.2.j.a.151.11	yes	56
52.47	even	4	inner	260.2.j.a.151.3	yes	56

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

\(f(q)\)	\(=\)	\(q+(-1.25736 + 0.647340i) q^{2} -0.759638i q^{3} +(1.16190 - 1.62788i) q^{4} +(0.707107 - 0.707107i) q^{5} +(0.491744 + 0.955138i) q^{6} +(-2.17387 + 2.17387i) q^{7} +(-0.407140 + 2.79897i) q^{8} +2.42295 q^{9} +O(q^{10})\)	\(q+(-1.25736 + 0.647340i) q^{2} -0.759638i q^{3} +(1.16190 - 1.62788i) q^{4} +(0.707107 - 0.707107i) q^{5} +(0.491744 + 0.955138i) q^{6} +(-2.17387 + 2.17387i) q^{7} +(-0.407140 + 2.79897i) 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} +(-3.04652 + 1.56847i) q^{18} +(-3.99929 - 3.99929i) q^{19} +(-0.329493 - 1.97267i) q^{20} +(1.65135 + 1.65135i) q^{21} +(-1.43658 + 4.48552i) q^{22} +7.44256 q^{23} +(2.12620 + 0.309279i) q^{24} -1.00000i q^{25} +(-1.76408 + 4.78414i) q^{26} -4.11948i q^{27} +(1.01296 + 6.06460i) q^{28} +7.58586 q^{29} +(1.02310 + 0.327669i) q^{30} +(2.87857 + 2.87857i) q^{31} +(4.08332 + 3.91491i) q^{32} +(-1.78893 - 1.78893i) q^{33} +(0.460776 + 0.894988i) 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} +(-1.09736 - 6.56987i) q^{44} +(1.71328 - 1.71328i) q^{45} +(-9.35796 + 4.81786i) q^{46} +(-3.59208 + 3.59208i) q^{47} +(-2.87361 + 0.987502i) q^{48} -2.45138i q^{49} +(0.647340 + 1.25736i) q^{50} -0.540710 q^{51} +(-0.878878 - 7.15734i) q^{52} +0.920541 q^{53} +(2.66670 + 5.17966i) q^{54} -3.33044i q^{55} +(-5.19952 - 6.96965i) q^{56} +(-3.03801 + 3.03801i) q^{57} +(-9.53814 + 4.91063i) q^{58} +(3.80422 - 3.80422i) q^{59} +(-1.49852 + 0.250295i) 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} +(-1.99012 - 3.86551i) q^{70} +(2.08032 + 2.08032i) q^{71} +(-0.986480 + 6.78177i) q^{72} +(-8.66411 - 8.66411i) q^{73} +(2.00240 + 0.641310i) q^{74} -0.759638 q^{75} +(-11.1571 + 1.86356i) q^{76} +10.2388i q^{77} +(3.63422 + 1.34006i) q^{78} +1.66567i q^{79} +(-3.59411 - 1.75568i) q^{80} +4.13954 q^{81} +(3.18177 - 9.93464i) q^{82} +(2.77385 + 2.77385i) q^{83} +(4.60690 - 0.769486i) q^{84} +(-0.503318 - 0.503318i) q^{85} +(13.9086 - 7.16070i) 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} +(2.97391 - 3.10185i) q^{96} +(-9.24834 + 9.24834i) q^{97} +(1.58687 + 3.08226i) 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

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