LMFDB - Embedded newform 240.2.bk.b.11.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [240,2,Mod(11,240)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(240, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 2, 0]))

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

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

chi := DirichletCharacter("240.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 240 = 2^{4} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	240.bk (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:	$1.91640964851$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$30$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			11.15
Character	$\chi$	$=$	240.11
Dual form			240.2.bk.b.131.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0794625 - 1.41198i) q^{2} +(-1.53859 + 0.795457i) q^{3} +(-1.98737 + 0.224399i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(1.24543 + 2.10924i) q^{6} +3.51098 q^{7} +(0.474768 + 2.78830i) q^{8} +(1.73450 - 2.44776i) q^{9} +O(q^{10})$	\(q+(-0.0794625 - 1.41198i) q^{2} +(-1.53859 + 0.795457i) q^{3} +(-1.98737 + 0.224399i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(1.24543 + 2.10924i) q^{6} +3.51098 q^{7} +(0.474768 + 2.78830i) q^{8} +(1.73450 - 2.44776i) q^{9} +(1.05461 + 0.942232i) q^{10} +(1.75586 + 1.75586i) q^{11} +(2.87924 - 1.92612i) q^{12} +(1.12741 - 1.12741i) q^{13} +(-0.278991 - 4.95744i) q^{14} +(0.525472 - 1.65042i) q^{15} +(3.89929 - 0.891927i) q^{16} -3.82976i q^{17} +(-3.59401 - 2.25457i) q^{18} +(5.17853 + 5.17853i) q^{19} +(1.24661 - 1.56396i) q^{20} +(-5.40195 + 2.79284i) q^{21} +(2.33972 - 2.61877i) q^{22} -1.51234i q^{23} +(-2.94844 - 3.91238i) q^{24} -1.00000i q^{25} +(-1.68147 - 1.50229i) q^{26} +(-0.721589 + 5.14581i) q^{27} +(-6.97763 + 0.787860i) q^{28} +(5.36681 + 5.36681i) q^{29} +(-2.37211 - 0.610810i) q^{30} +5.91275i q^{31} +(-1.56923 - 5.43484i) q^{32} +(-4.09826 - 1.30483i) q^{33} +(-5.40754 + 0.304322i) q^{34} +(-2.48264 + 2.48264i) q^{35} +(-2.89782 + 5.25382i) q^{36} +(-6.47214 - 6.47214i) q^{37} +(6.90048 - 7.72348i) q^{38} +(-0.837811 + 2.63142i) q^{39} +(-2.30733 - 1.63591i) q^{40} -1.94422 q^{41} +(4.37268 + 7.40552i) q^{42} +(-3.83565 + 3.83565i) q^{43} +(-3.88357 - 3.09554i) q^{44} +(0.504351 + 2.95730i) q^{45} +(-2.13539 + 0.120174i) q^{46} +9.21655 q^{47} +(-5.28991 + 4.47402i) q^{48} +5.32701 q^{49} +(-1.41198 + 0.0794625i) q^{50} +(3.04641 + 5.89242i) q^{51} +(-1.98759 + 2.49357i) q^{52} +(1.59396 - 1.59396i) q^{53} +(7.32311 + 0.609970i) q^{54} -2.48317 q^{55} +(1.66690 + 9.78966i) q^{56} +(-12.0869 - 3.84832i) q^{57} +(7.15136 - 8.00428i) q^{58} +(-7.95230 - 7.95230i) q^{59} +(-0.673957 + 3.39791i) q^{60} +(4.50816 - 4.50816i) q^{61} +(8.34868 - 0.469842i) q^{62} +(6.08979 - 8.59404i) q^{63} +(-7.54919 + 2.64759i) q^{64} +1.59440i q^{65} +(-1.51674 + 5.89035i) q^{66} +(-5.51114 - 5.51114i) q^{67} +(0.859393 + 7.61115i) q^{68} +(1.20300 + 2.32686i) q^{69} +(3.70271 + 3.30816i) q^{70} -4.74332i q^{71} +(7.64856 + 3.67418i) q^{72} +11.2777i q^{73} +(-8.62424 + 9.65282i) q^{74} +(0.795457 + 1.53859i) q^{75} +(-11.4537 - 9.12961i) q^{76} +(6.16481 + 6.16481i) q^{77} +(3.78209 + 0.973873i) q^{78} +2.03963i q^{79} +(-2.12653 + 3.38790i) q^{80} +(-2.98304 - 8.49126i) q^{81} +(0.154493 + 2.74520i) q^{82} +(-0.221380 + 0.221380i) q^{83} +(10.1090 - 6.76259i) q^{84} +(2.70805 + 2.70805i) q^{85} +(5.72065 + 5.11107i) q^{86} +(-12.5264 - 3.98824i) q^{87} +(-4.06224 + 5.72950i) q^{88} +1.54573 q^{89} +(4.13557 - 0.947128i) q^{90} +(3.95831 - 3.95831i) q^{91} +(0.339367 + 3.00558i) q^{92} +(-4.70334 - 9.09728i) q^{93} +(-0.732370 - 13.0136i) q^{94} -7.32355 q^{95} +(6.73758 + 7.11372i) q^{96} -13.4341 q^{97} +(-0.423297 - 7.52162i) q^{98} +(7.34347 - 1.25239i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q + 4 q^{3} + 8 q^{4} + 8 q^{6} + 16 q^{7}+O(q^{10}) $ 60 * q + 4 * q^3 + 8 * q^4 + 8 * q^6 + 16 * q^7	$ 60 q + 4 q^{3} + 8 q^{4} + 8 q^{6} + 16 q^{7} + 4 q^{12} + 16 q^{13} - 52 q^{16} - 20 q^{18} + 20 q^{19} - 16 q^{21} - 24 q^{22} - 28 q^{24} - 20 q^{27} - 56 q^{28} - 12 q^{34} + 12 q^{36} + 24 q^{37} - 80 q^{39} - 8 q^{40} + 36 q^{42} - 8 q^{45} + 36 q^{46} + 56 q^{48} + 28 q^{49} - 36 q^{51} - 24 q^{52} + 92 q^{54} - 80 q^{58} + 28 q^{60} + 20 q^{61} - 64 q^{64} + 24 q^{66} - 40 q^{67} + 12 q^{69} - 16 q^{70} - 56 q^{72} + 4 q^{75} - 20 q^{76} - 8 q^{78} - 28 q^{81} - 32 q^{82} + 16 q^{84} - 20 q^{85} - 24 q^{87} + 8 q^{88} + 32 q^{90} - 16 q^{91} - 48 q^{93} + 28 q^{94} + 72 q^{96} - 8 q^{97} + 32 q^{99}+O(q^{100}) $ 60 * q + 4 * q^3 + 8 * q^4 + 8 * q^6 + 16 * q^7 + 4 * q^12 + 16 * q^13 - 52 * q^16 - 20 * q^18 + 20 * q^19 - 16 * q^21 - 24 * q^22 - 28 * q^24 - 20 * q^27 - 56 * q^28 - 12 * q^34 + 12 * q^36 + 24 * q^37 - 80 * q^39 - 8 * q^40 + 36 * q^42 - 8 * q^45 + 36 * q^46 + 56 * q^48 + 28 * q^49 - 36 * q^51 - 24 * q^52 + 92 * q^54 - 80 * q^58 + 28 * q^60 + 20 * q^61 - 64 * q^64 + 24 * q^66 - 40 * q^67 + 12 * q^69 - 16 * q^70 - 56 * q^72 + 4 * q^75 - 20 * q^76 - 8 * q^78 - 28 * q^81 - 32 * q^82 + 16 * q^84 - 20 * q^85 - 24 * q^87 + 8 * q^88 + 32 * q^90 - 16 * q^91 - 48 * q^93 + 28 * q^94 + 72 * q^96 - 8 * q^97 + 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/240\mathbb{Z}\right)^\times$.

$n$	$31$	$97$	$161$	$181$
$\chi(n)$	$-1$	$1$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	−0.0794625	−	1.41198i	−0.0561884	−	0.998420i
$2$	−0.0794625	−	1.41198i	−0.0561884	−	0.998420i
$3$	−1.53859	+	0.795457i	−0.888303	+	0.459257i
$3$	−1.53859	+	0.795457i	−0.888303	+	0.459257i
$4$	−1.98737	+	0.224399i	−0.993686	+	0.112199i
$5$	−0.707107	+	0.707107i	−0.316228	+	0.316228i
$5$	−0.707107	+	0.707107i	−0.316228	+	0.316228i
$6$	1.24543	+	2.10924i	0.508444	+	0.861095i
$7$	3.51098			1.32703			0.663514	−	0.748164i	$-0.269064\pi$
$7$	3.51098			1.32703			0.663514	+	0.748164i	$0.269064\pi$
$8$	0.474768	+	2.78830i	0.167856	+	0.985812i
$9$	1.73450	−	2.44776i	0.578166	−	0.815919i
$10$	1.05461	+	0.942232i	0.333497	+	0.297960i
$11$	1.75586	+	1.75586i	0.529413	+	0.529413i	0.920397	−	0.390984i	$-0.127865\pi$
$11$	1.75586	+	1.75586i	0.529413	+	0.529413i	−0.390984	+	0.920397i	$0.627865\pi$
$12$	2.87924	−	1.92612i	0.831166	−	0.556024i
$13$	1.12741	−	1.12741i	0.312687	−	0.312687i	−0.533263	−	0.845950i	$-0.679034\pi$
$13$	1.12741	−	1.12741i	0.312687	−	0.312687i	0.845950	+	0.533263i	$0.179034\pi$
$14$	−0.278991	−	4.95744i	−0.0745636	−	1.32493i
$15$	0.525472	−	1.65042i	0.135676	−	0.426136i
$16$	3.89929	−	0.891927i	0.974823	−	0.222982i
$17$		−	3.82976i		−	0.928853i	−0.885612	−	0.464427i	$-0.846260\pi$
$17$		−	3.82976i		−	0.928853i	0.885612	−	0.464427i	$-0.153740\pi$
$18$	−3.59401	−	2.25457i	−0.847117	−	0.531407i
$19$	5.17853	+	5.17853i	1.18804	+	1.18804i	0.977610	+	0.210426i	$0.0674852\pi$
$19$	5.17853	+	5.17853i	1.18804	+	1.18804i	0.210426	+	0.977610i	$0.432515\pi$
$20$	1.24661	−	1.56396i	0.278750	−	0.349712i
$21$	−5.40195	+	2.79284i	−1.17880	+	0.609447i
$22$	2.33972	−	2.61877i	0.498830	−	0.558323i
$23$		−	1.51234i		−	0.315344i	−0.987492	−	0.157672i	$-0.949601\pi$
$23$		−	1.51234i		−	0.315344i	0.987492	−	0.157672i	$-0.0503989\pi$
$24$	−2.94844	−	3.91238i	−0.601848	−	0.798611i
$25$		−	1.00000i		−	0.200000i
$26$	−1.68147	−	1.50229i	−0.329762	−	0.294624i
$27$	−0.721589	+	5.14581i	−0.138870	+	0.990311i
$28$	−6.97763	+	0.787860i	−1.31865	+	0.148892i
$29$	5.36681	+	5.36681i	0.996592	+	0.996592i	0.999994	−	0.00340269i	$-0.00108311\pi$
$29$	5.36681	+	5.36681i	0.996592	+	0.996592i	−0.00340269	+	0.999994i	$0.501083\pi$
$30$	−2.37211	−	0.610810i	−0.433086	−	0.111518i
$31$			5.91275i			1.06196i	0.847384	+	0.530981i	$0.178176\pi$
$31$			5.91275i			1.06196i	−0.847384	+	0.530981i	$0.821824\pi$
$32$	−1.56923	−	5.43484i	−0.277403	−	0.960754i
$33$	−4.09826	−	1.30483i	−0.713416	−	0.227143i
$34$	−5.40754	+	0.304322i	−0.927386	+	0.0521908i
$35$	−2.48264	+	2.48264i	−0.419643	+	0.419643i
$36$	−2.89782	+	5.25382i	−0.482969	+	0.875637i
$37$	−6.47214	−	6.47214i	−1.06401	−	1.06401i	−0.997806	−	0.0662079i	$-0.978910\pi$
$37$	−6.47214	−	6.47214i	−1.06401	−	1.06401i	−0.0662079	−	0.997806i	$-0.521090\pi$
$38$	6.90048	−	7.72348i	1.11941	−	1.25291i
$39$	−0.837811	+	2.63142i	−0.134157	+	0.421365i
$40$	−2.30733	−	1.63591i	−0.364822	−	0.258660i
$41$	−1.94422			−0.303636			−0.151818	−	0.988408i	$-0.548513\pi$
$41$	−1.94422			−0.303636			−0.151818	+	0.988408i	$0.548513\pi$
$42$	4.37268	+	7.40552i	0.674719	+	1.14270i
$43$	−3.83565	+	3.83565i	−0.584931	+	0.584931i	−0.936254	−	0.351323i	$-0.885732\pi$
$43$	−3.83565	+	3.83565i	−0.584931	+	0.584931i	0.351323	+	0.936254i	$0.385732\pi$
$44$	−3.88357	−	3.09554i	−0.585470	−	0.466670i
$45$	0.504351	+	2.95730i	0.0751843	+	0.440848i
$46$	−2.13539	+	0.120174i	−0.314846	+	0.0177187i
$47$	9.21655			1.34437			0.672186	−	0.740382i	$-0.265356\pi$
$47$	9.21655			1.34437			0.672186	+	0.740382i	$0.265356\pi$
$48$	−5.28991	+	4.47402i	−0.763532	+	0.645770i
$49$	5.32701			0.761001
$50$	−1.41198	+	0.0794625i	−0.199684	+	0.0112377i
$51$	3.04641	+	5.89242i	0.426582	+	0.825103i
$52$	−1.98759	+	2.49357i	−0.275629	+	0.345796i
$53$	1.59396	−	1.59396i	0.218947	−	0.218947i	−0.589107	−	0.808055i	$-0.700521\pi$
$53$	1.59396	−	1.59396i	0.218947	−	0.218947i	0.808055	+	0.589107i	$0.200521\pi$
$54$	7.32311	+	0.609970i	0.996549	+	0.0830065i
$55$	−2.48317			−0.334830
$56$	1.66690	+	9.78966i	0.222749	+	1.30820i
$57$	−12.0869	−	3.84832i	−1.60095	−	0.509722i
$58$	7.15136	−	8.00428i	0.939020	−	1.05101i
$59$	−7.95230	−	7.95230i	−1.03530	−	1.03530i	−0.999354	−	0.0359472i	$-0.988555\pi$
$59$	−7.95230	−	7.95230i	−1.03530	−	1.03530i	−0.0359472	−	0.999354i	$-0.511445\pi$
$60$	−0.673957	+	3.39791i	−0.0870074	+	0.438668i
$61$	4.50816	−	4.50816i	0.577210	−	0.577210i	−0.356923	−	0.934134i	$-0.616174\pi$
$61$	4.50816	−	4.50816i	0.577210	−	0.577210i	0.934134	+	0.356923i	$0.116174\pi$
$62$	8.34868	−	0.469842i	1.06028	−	0.0596700i
$63$	6.08979	−	8.59404i	0.767242	−	1.08275i
$64$	−7.54919	+	2.64759i	−0.943649	+	0.330948i
$65$			1.59440i			0.197761i
$66$	−1.51674	+	5.89035i	−0.186698	+	0.725052i
$67$	−5.51114	−	5.51114i	−0.673293	−	0.673293i	0.285181	−	0.958474i	$-0.407946\pi$
$67$	−5.51114	−	5.51114i	−0.673293	−	0.673293i	−0.958474	+	0.285181i	$0.907946\pi$
$68$	0.859393	+	7.61115i	0.104217	+	0.922988i
$69$	1.20300	+	2.32686i	0.144824	+	0.280121i
$70$	3.70271	+	3.30816i	0.442559	+	0.395401i
$71$		−	4.74332i		−	0.562929i	−0.959572	−	0.281465i	$-0.909180\pi$
$71$		−	4.74332i		−	0.562929i	0.959572	−	0.281465i	$-0.0908202\pi$
$72$	7.64856	+	3.67418i	0.901391	+	0.433006i
$73$			11.2777i			1.31996i	0.751284	+	0.659979i	$0.229435\pi$
$73$			11.2777i			1.31996i	−0.751284	+	0.659979i	$0.770565\pi$
$74$	−8.62424	+	9.65282i	−1.00255	+	1.12212i
$75$	0.795457	+	1.53859i	0.0918514	+	0.177661i
$76$	−11.4537	−	9.12961i	−1.31383	−	1.04724i
$77$	6.16481	+	6.16481i	0.702545	+	0.702545i
$78$	3.78209	+	0.973873i	0.428237	+	0.110269i
$79$			2.03963i			0.229476i	0.993396	+	0.114738i	$0.0366029\pi$
$79$			2.03963i			0.229476i	−0.993396	+	0.114738i	$0.963397\pi$
$80$	−2.12653	+	3.38790i	−0.237753	+	0.378779i
$81$	−2.98304	−	8.49126i	−0.331449	−	0.943473i
$82$	0.154493	+	2.74520i	0.0170609	+	0.303157i
$83$	−0.221380	+	0.221380i	−0.0242996	+	0.0242996i	−0.719152	−	0.694853i	$-0.755470\pi$
$83$	−0.221380	+	0.221380i	−0.0242996	+	0.0242996i	0.694853	+	0.719152i	$0.255470\pi$
$84$	10.1090	−	6.76259i	1.10298	−	0.737859i
$85$	2.70805	+	2.70805i	0.293729	+	0.293729i
$86$	5.72065	+	5.11107i	0.616873	+	0.551140i
$87$	−12.5264	−	3.98824i	−1.34297	−	0.427584i
$88$	−4.06224	+	5.72950i	−0.433036	+	0.610766i
$89$	1.54573			0.163847			0.0819235	−	0.996639i	$-0.473894\pi$
$89$	1.54573			0.163847			0.0819235	+	0.996639i	$0.473894\pi$
$90$	4.13557	−	0.947128i	0.435927	−	0.0998361i
$91$	3.95831	−	3.95831i	0.414944	−	0.414944i
$92$	0.339367	+	3.00558i	0.0353814	+	0.313353i
$93$	−4.70334	−	9.09728i	−0.487713	−	0.943344i
$94$	−0.732370	−	13.0136i	−0.0755382	−	1.34225i
$95$	−7.32355			−0.751380
$96$	6.73758	+	7.11372i	0.687651	+	0.726041i
$97$	−13.4341			−1.36402			−0.682012	−	0.731341i	$-0.738895\pi$
$97$	−13.4341			−1.36402			−0.682012	+	0.731341i	$0.738895\pi$
$98$	−0.423297	−	7.52162i	−0.0427595	−	0.759799i
$99$	7.34347	−	1.25239i	0.738047	−	0.125870i
$100$	0.224399	+	1.98737i	0.0224399	+	0.198737i
$101$	−8.90121	+	8.90121i	−0.885703	+	0.885703i	−0.994107	−	0.108404i	$-0.965426\pi$
$101$	−8.90121	+	8.90121i	−0.885703	+	0.885703i	0.108404	+	0.994107i	$0.465426\pi$
$102$	8.07789	−	4.76969i	0.799831	−	0.472270i
$103$	15.5803			1.53517			0.767587	−	0.640945i	$-0.221457\pi$
$103$	15.5803			1.53517			0.767587	+	0.640945i	$0.221457\pi$
$104$	3.67881	+	2.60829i	0.360737	+	0.255764i
$105$	1.84492	−	5.79459i	0.180046	−	0.565494i
$106$	−2.37730	−	2.12398i	−0.230904	−	0.206299i
$107$	−12.4022	−	12.4022i	−1.19896	−	1.19896i	−0.974477	−	0.224486i	$-0.927930\pi$
$107$	−12.4022	−	12.4022i	−1.19896	−	1.19896i	−0.224486	−	0.974477i	$-0.572070\pi$
$108$	0.279353	−	10.3885i	0.0268808	−	0.999639i
$109$	7.33488	−	7.33488i	0.702554	−	0.702554i	−0.262404	−	0.964958i	$-0.584515\pi$
$109$	7.33488	−	7.33488i	0.702554	−	0.702554i	0.964958	+	0.262404i	$0.0845154\pi$
$110$	0.197319	+	3.50618i	0.0188136	+	0.334301i
$111$	15.1063	+	4.80964i	1.43382	+	0.456511i
$112$	13.6903	−	3.13154i	1.29362	−	0.295903i
$113$		−	8.40660i		−	0.790827i	−0.918503	−	0.395413i	$-0.870601\pi$
$113$		−	8.40660i		−	0.790827i	0.918503	−	0.395413i	$-0.129399\pi$
$114$	−4.47329	+	17.3723i	−0.418962	+	1.62706i
$115$	1.06938	+	1.06938i	0.0997206	+	0.0997206i
$116$	−11.8701	−	9.46154i	−1.10212	−	0.878482i
$117$	−0.804136	−	4.71511i	−0.0743424	−	0.435912i
$118$	−10.5966	+	11.8604i	−0.975493	+	1.09184i
$119$		−	13.4462i		−	1.23261i
$120$	4.85133	+	0.681607i	0.442864	+	0.0622219i
$121$		−	4.83388i		−	0.439444i
$122$	−6.72366	−	6.00720i	−0.608731	−	0.543866i
$123$	2.99135	−	1.54654i	0.269721	−	0.139447i
$124$	−1.32681	−	11.7508i	−0.119151	−	1.05526i
$125$	0.707107	+	0.707107i	0.0632456	+	0.0632456i
$126$	−12.6185	−	7.91576i	−1.12415	−	0.705192i
$127$		−	1.60514i		−	0.142433i	−0.997461	−	0.0712166i	$-0.977312\pi$
$127$		−	1.60514i		−	0.142433i	0.997461	−	0.0712166i	$-0.0226881\pi$
$128$	4.33821	+	10.4489i	0.383448	+	0.923563i
$129$	2.85038	−	8.95257i	0.250962	−	0.788230i
$130$	2.25126	−	0.126695i	0.197448	−	0.0111119i
$131$	−8.85291	+	8.85291i	−0.773482	+	0.773482i	−0.978714	−	0.205231i	$-0.934205\pi$
$131$	−8.85291	+	8.85291i	−0.773482	+	0.773482i	0.205231	+	0.978714i	$0.434205\pi$
$132$	8.43757	+	1.67355i	0.734396	+	0.145664i
$133$	18.1817	+	18.1817i	1.57656	+	1.57656i
$134$	−7.34369	+	8.21954i	−0.634398	+	0.710061i
$135$	−3.12839	−	4.14887i	−0.269249	−	0.357078i
$136$	10.6785	−	1.81825i	0.915674	−	0.155913i
$137$	7.23925			0.618491			0.309245	−	0.950982i	$-0.399924\pi$
$137$	7.23925			0.618491			0.309245	+	0.950982i	$0.399924\pi$
$138$	3.18989	−	1.88351i	0.271541	−	0.160335i
$139$	−4.43154	+	4.43154i	−0.375879	+	0.375879i	−0.869613	−	0.493734i	$-0.835632\pi$
$139$	−4.43154	+	4.43154i	−0.375879	+	0.375879i	0.493734	+	0.869613i	$0.335632\pi$
$140$	4.37683	−	5.49103i	0.369909	−	0.464077i
$141$	−14.1805	+	7.33137i	−1.19421	+	0.617412i
$142$	−6.69748	+	0.376916i	−0.562040	+	0.0316301i
$143$	3.95915			0.331081
$144$	4.58009	−	11.0916i	0.381674	−	0.924297i
$145$	−7.58981			−0.630300
$146$	15.9239	−	0.896156i	1.31787	−	0.0741664i
$147$	−8.19606	+	4.23740i	−0.676000	+	0.349495i
$148$	14.3149	+	11.4102i	1.17668	+	0.937914i
$149$	12.0515	−	12.0515i	0.987298	−	0.987298i	−0.0126223	−	0.999920i	$-0.504018\pi$
$149$	12.0515	−	12.0515i	0.987298	−	0.987298i	0.999920	+	0.0126223i	$0.00401791\pi$
$150$	2.10924	−	1.24543i	0.172219	−	0.101689i
$151$	−6.84934			−0.557392			−0.278696	−	0.960379i	$-0.589902\pi$
$151$	−6.84934			−0.557392			−0.278696	+	0.960379i	$0.589902\pi$
$152$	−11.9807	+	16.8979i	−0.971761	+	1.37060i
$153$	−9.37432	−	6.64271i	−0.757869	−	0.537031i
$154$	8.21471	−	9.19445i	0.661960	−	0.740910i
$155$	−4.18095	−	4.18095i	−0.335822	−	0.335822i
$156$	1.07455	−	5.41762i	0.0860332	−	0.433756i
$157$	1.15699	−	1.15699i	0.0923380	−	0.0923380i	−0.659429	−	0.751767i	$-0.729202\pi$
$157$	1.15699	−	1.15699i	0.0923380	−	0.0923380i	0.751767	+	0.659429i	$0.229202\pi$
$158$	2.87991	−	0.162074i	0.229114	−	0.0128939i
$159$	−1.18452	+	3.72037i	−0.0939385	+	0.295045i
$160$	4.95263	+	2.73340i	0.391540	+	0.216094i
$161$		−	5.30980i		−	0.418470i
$162$	−11.7524	+	4.88672i	−0.923359	+	0.383937i
$163$	−0.137820	−	0.137820i	−0.0107949	−	0.0107949i	0.701689	−	0.712484i	$-0.252430\pi$
$163$	−0.137820	−	0.137820i	−0.0107949	−	0.0107949i	−0.712484	+	0.701689i	$0.752430\pi$
$164$	3.86389	−	0.436281i	0.301719	−	0.0340678i
$165$	3.82057	−	1.97525i	0.297431	−	0.153773i
$166$	0.330175	+	0.294992i	0.0256266	+	0.0228958i
$167$			21.5928i			1.67090i	0.549563	+	0.835452i	$0.314794\pi$
$167$			21.5928i			1.67090i	−0.549563	+	0.835452i	$0.685206\pi$
$168$	−10.3519	−	13.7363i	−0.798668	−	1.05978i
$169$			10.4579i			0.804454i
$170$	3.60852	−	4.03890i	0.276761	−	0.309769i
$171$	21.6579	−	3.69364i	1.65622	−	0.282460i
$172$	6.76214	−	8.48357i	0.515609	−	0.646866i
$173$	6.45101	+	6.45101i	0.490461	+	0.490461i	0.908452	−	0.417990i	$-0.137265\pi$
$173$	6.45101	+	6.45101i	0.490461	+	0.490461i	−0.417990	+	0.908452i	$0.637265\pi$
$174$	−4.63593	+	18.0039i	−0.351449	+	1.36487i
$175$		−	3.51098i		−	0.265405i
$176$	8.41273	+	5.28052i	0.634133	+	0.398034i
$177$	18.5610	+	5.90959i	1.39513	+	0.444192i
$178$	−0.122828	−	2.18254i	−0.00920631	−	0.163588i
$179$	−12.2532	+	12.2532i	−0.915849	+	0.915849i	−0.996724	−	0.0808755i	$-0.974228\pi$
$179$	−12.2532	+	12.2532i	−0.915849	+	0.915849i	0.0808755	+	0.996724i	$0.474228\pi$
$180$	−1.66595	−	5.76408i	−0.124172	−	0.429629i
$181$	−5.66828	−	5.66828i	−0.421320	−	0.421320i	0.464338	−	0.885658i	$-0.346292\pi$
$181$	−5.66828	−	5.66828i	−0.421320	−	0.421320i	−0.885658	+	0.464338i	$0.846292\pi$
$182$	−5.90360	−	5.27452i	−0.437604	−	0.390974i
$183$	−3.35015	+	10.5222i	−0.247650	+	0.777826i
$184$	4.21685	−	0.718010i	0.310870	−	0.0529324i
$185$	9.15299			0.672941
$186$	−12.4714	+	7.36391i	−0.914450	+	0.539948i
$187$	6.72454	−	6.72454i	0.491747	−	0.491747i
$188$	−18.3167	+	2.06818i	−1.33588	+	0.150838i
$189$	−2.53349	+	18.0668i	−0.184284	+	1.31417i
$190$	0.581947	+	10.3407i	0.0422189	+	0.750193i
$191$	−3.90768			−0.282750			−0.141375	−	0.989956i	$-0.545152\pi$
$191$	−3.90768			−0.282750			−0.141375	+	0.989956i	$0.545152\pi$
$192$	9.50904	−	10.0786i	0.686256	−	0.727360i
$193$	−15.6827			−1.12886			−0.564431	−	0.825480i	$-0.690904\pi$
$193$	−15.6827			−1.12886			−0.564431	+	0.825480i	$0.690904\pi$
$194$	1.06751	+	18.9687i	0.0766424	+	1.36187i
$195$	−1.26827	−	2.45312i	−0.0908230	−	0.175671i
$196$	−10.5867	+	1.19537i	−0.756196	+	0.0853838i
$197$	−2.42785	+	2.42785i	−0.172977	+	0.172977i	−0.788286	−	0.615309i	$-0.789031\pi$
$197$	−2.42785	+	2.42785i	−0.172977	+	0.172977i	0.615309	+	0.788286i	$0.289031\pi$
$198$	−2.35188	−	10.2693i	−0.167141	−	0.729808i
$199$	1.79472			0.127224			0.0636122	−	0.997975i	$-0.479738\pi$
$199$	1.79472			0.127224			0.0636122	+	0.997975i	$0.479738\pi$
$200$	2.78830	−	0.474768i	0.197162	−	0.0335712i
$201$	12.8632	+	4.09549i	0.907303	+	0.288874i
$202$	13.2756	+	11.8610i	0.934070	+	0.834538i
$203$	18.8428	+	18.8428i	1.32250	+	1.32250i
$204$	−7.37659	−	11.0268i	−0.516465	−	0.772031i
$205$	1.37477	−	1.37477i	0.0960182	−	0.0960182i
$206$	−1.23805	−	21.9991i	−0.0862590	−	1.53275i
$207$	−3.70184	−	2.62315i	−0.257296	−	0.182321i
$208$	3.39053	−	5.40166i	0.235091	−	0.374538i
$209$			18.1856i			1.25792i
$210$	−8.32844	−	2.14454i	−0.574717	−	0.147988i
$211$	−14.3115	−	14.3115i	−0.985245	−	0.985245i	0.0146475	−	0.999893i	$-0.495337\pi$
$211$	−14.3115	−	14.3115i	−0.985245	−	0.985245i	−0.999893	+	0.0146475i	$0.995337\pi$
$212$	−2.81011	+	3.52547i	−0.192999	+	0.242131i
$213$	3.77311	+	7.29802i	0.258529	+	0.500052i
$214$	−16.5261	+	18.4971i	−1.12970	+	1.26444i
$215$		−	5.42443i		−	0.369943i
$216$	−14.6906	+	0.431059i	−0.999570	+	0.0293298i
$217$			20.7596i			1.40925i
$218$	−10.9395	−	9.77385i	−0.740919	−	0.661968i
$219$	−8.97095	−	17.3518i	−0.606200	−	1.17252i
$220$	4.93497	−	0.557219i	0.332716	−	0.0375677i
$221$	−4.31771	−	4.31771i	−0.290440	−	0.290440i
$222$	5.59074	−	21.7119i	0.375226	−	1.45721i
$223$		−	17.4916i		−	1.17133i	−0.810554	−	0.585663i	$-0.800834\pi$
$223$		−	17.4916i		−	1.17133i	0.810554	−	0.585663i	$-0.199166\pi$
$224$	−5.50954	−	19.0816i	−0.368122	−	1.27495i
$225$	−2.44776	−	1.73450i	−0.163184	−	0.115633i
$226$	−11.8700	+	0.668009i	−0.789577	+	0.0444353i
$227$	7.17464	−	7.17464i	0.476198	−	0.476198i	−0.427716	−	0.903913i	$-0.640682\pi$
$227$	7.17464	−	7.17464i	0.476198	−	0.476198i	0.903913	+	0.427716i	$0.140682\pi$
$228$	24.8847	+	4.93575i	1.64803	+	0.326878i
$229$	1.75012	+	1.75012i	0.115651	+	0.115651i	0.762564	−	0.646913i	$-0.223940\pi$
$229$	1.75012	+	1.75012i	0.115651	+	0.115651i	−0.646913	+	0.762564i	$0.723940\pi$
$230$	1.42497	−	1.59493i	0.0939599	−	0.105166i
$231$	−14.3889	−	4.58125i	−0.946722	−	0.301424i
$232$	−12.4163	+	17.5122i	−0.815168	+	1.14974i
$233$	−20.6184			−1.35076			−0.675378	−	0.737472i	$-0.736020\pi$
$233$	−20.6184			−1.35076			−0.675378	+	0.737472i	$0.736020\pi$
$234$	−6.59374	+	1.51010i	−0.431046	+	0.0987182i
$235$	−6.51708	+	6.51708i	−0.425128	+	0.425128i
$236$	17.5887	+	14.0197i	1.14492	+	0.912604i
$237$	−1.62244	−	3.13815i	−0.105389	−	0.203844i
$238$	−18.9858	+	1.06847i	−1.23067	+	0.0692586i
$239$	−10.6006			−0.685693			−0.342846	−	0.939391i	$-0.611391\pi$
$239$	−10.6006			−0.685693			−0.342846	+	0.939391i	$0.611391\pi$
$240$	0.576916	−	6.90414i	0.0372398	−	0.445660i
$241$	17.3589			1.11818			0.559092	−	0.829106i	$-0.311150\pi$
$241$	17.3589			1.11818			0.559092	+	0.829106i	$0.311150\pi$
$242$	−6.82534	+	0.384112i	−0.438750	+	0.0246917i
$243$	11.3441	+	10.6917i	0.727724	+	0.685870i
$244$	−7.94776	+	9.97101i	−0.508803	+	0.638328i
$245$	−3.76676	+	3.76676i	−0.240650	+	0.240650i
$246$	−2.42139	−	4.10084i	−0.154382	−	0.261460i
$247$	11.6766			0.742967
$248$	−16.4865	+	2.80718i	−1.04689	+	0.178256i
$249$	0.164514	−	0.516710i	0.0104256	−	0.0327452i
$250$	0.942232	−	1.05461i	0.0595920	−	0.0666993i
$251$	−3.93789	−	3.93789i	−0.248558	−	0.248558i	0.571821	−	0.820378i	$-0.306237\pi$
$251$	−3.93789	−	3.93789i	−0.248558	−	0.248558i	−0.820378	+	0.571821i	$0.806237\pi$
$252$	−10.1742	+	18.4461i	−0.640914	+	1.16199i
$253$	2.65546	−	2.65546i	0.166947	−	0.166947i
$254$	−2.26642	+	0.127548i	−0.142208	+	0.00800310i
$255$	−6.32070	−	2.01243i	−0.395818	−	0.126023i
$256$	14.4089	−	6.95577i	0.900558	−	0.434735i
$257$			7.62234i			0.475469i	0.971330	+	0.237734i	$0.0764048\pi$
$257$			7.62234i			0.475469i	−0.971330	+	0.237734i	$0.923595\pi$
$258$	−12.8673	−	3.31329i	−0.801086	−	0.206277i
$259$	−22.7236	−	22.7236i	−1.41198	−	1.41198i
$260$	−0.357781	−	3.16866i	−0.0221886	−	0.196512i
$261$	22.4454	−	3.82793i	1.38933	−	0.236943i
$262$	13.2036	+	11.7967i	0.815721	+	0.728800i
$263$			2.87652i			0.177374i	0.996060	+	0.0886869i	$0.0282670\pi$
$263$			2.87652i			0.177374i	−0.996060	+	0.0886869i	$0.971733\pi$
$264$	1.69254	−	12.0467i	0.104169	−	0.741421i
$265$			2.25420i			0.138474i
$266$	24.2275	−	27.1170i	1.48548	−	1.66265i
$267$	−2.37824	+	1.22956i	−0.145546	+	0.0752479i
$268$	12.1894	+	9.71599i	0.744585	+	0.593499i
$269$	9.94498	+	9.94498i	0.606356	+	0.606356i	0.941992	−	0.335636i	$-0.108951\pi$
$269$	9.94498	+	9.94498i	0.606356	+	0.606356i	−0.335636	+	0.941992i	$0.608951\pi$
$270$	−5.60953	+	4.74691i	−0.341385	+	0.288888i
$271$			0.0695552i			0.00422518i	0.999998	+	0.00211259i	$0.000672458\pi$
$271$			0.0695552i			0.00422518i	−0.999998	+	0.00211259i	$0.999328\pi$
$272$	−3.41587	−	14.9333i	−0.207117	−	0.905467i
$273$	−2.94154	+	9.23888i	−0.178030	+	0.559162i
$274$	−0.575249	−	10.2217i	−0.0347520	−	0.617514i
$275$	1.75586	−	1.75586i	0.105883	−	0.105883i
$276$	−2.91295	−	4.35439i	−0.175339	−	0.262104i
$277$	−15.9432	−	15.9432i	−0.957934	−	0.957934i	0.0412163	−	0.999150i	$-0.486877\pi$
$277$	−15.9432	−	15.9432i	−0.957934	−	0.957934i	−0.999150	+	0.0412163i	$0.986877\pi$
$278$	6.60939	+	5.90511i	0.396405	+	0.354165i
$279$	14.4730	+	10.2557i	0.866475	+	0.613990i
$280$	−8.10101	−	5.74366i	−0.484128	−	0.343249i
$281$	2.39888			0.143105			0.0715526	−	0.997437i	$-0.477205\pi$
$281$	2.39888			0.143105			0.0715526	+	0.997437i	$0.477205\pi$
$282$	11.4786	+	19.4399i	0.683538	+	1.15763i
$283$	−20.4462	+	20.4462i	−1.21540	+	1.21540i	−0.246172	+	0.969226i	$0.579173\pi$
$283$	−20.4462	+	20.4462i	−1.21540	+	1.21540i	−0.969226	+	0.246172i	$0.920827\pi$
$284$	1.06440	+	9.42675i	0.0631603	+	0.559375i
$285$	11.2679	−	5.82556i	0.667453	−	0.345077i
$286$	−0.314604	−	5.59024i	−0.0186029	−	0.330558i
$287$	−6.82613			−0.402934
$288$	−16.0250	−	5.58563i	−0.944282	−	0.329136i
$289$	2.33295			0.137232
$290$	0.603105	+	10.7167i	0.0354156	+	0.629304i
$291$	20.6695	−	10.6862i	1.21167	−	0.626438i
$292$	−2.53071	−	22.4130i	−0.148098	−	1.31162i
$293$	3.11853	−	3.11853i	0.182187	−	0.182187i	−0.610121	−	0.792308i	$-0.708879\pi$
$293$	3.11853	−	3.11853i	0.182187	−	0.182187i	0.792308	+	0.610121i	$0.208879\pi$
$294$	6.63441	+	11.2360i	0.386926	+	0.655294i
$295$	11.2462			0.654782
$296$	14.9735	−	21.1190i	0.870316	−	1.22752i
$297$	−10.3023	+	7.76832i	−0.597803	+	0.450764i
$298$	−17.9741	−	16.0588i	−1.04121	−	0.930264i
$299$	−1.70502	−	1.70502i	−0.0986041	−	0.0986041i
$300$	−1.92612	−	2.87924i	−0.111205	−	0.166233i
$301$	−13.4669	+	13.4669i	−0.776219	+	0.776219i
$302$	0.544266	+	9.67113i	0.0313190	+	0.556511i
$303$	6.61475	−	20.7758i	0.380008	−	1.19354i
$304$	24.8115	+	15.5737i	1.42303	+	0.893214i
$305$			6.37550i			0.365060i
$306$	−8.63446	+	13.7642i	−0.493599	+	0.786847i
$307$	−3.45878	−	3.45878i	−0.197403	−	0.197403i	0.601483	−	0.798886i	$-0.294577\pi$
$307$	−3.45878	−	3.45878i	−0.197403	−	0.197403i	−0.798886	+	0.601483i	$0.794577\pi$
$308$	−13.6351	−	10.8684i	−0.776934	−	0.619284i
$309$	−23.9717	+	12.3935i	−1.36370	+	0.705039i
$310$	−5.57118	+	6.23564i	−0.316422	+	0.354161i
$311$			2.12427i			0.120456i	0.998185	+	0.0602281i	$0.0191828\pi$
$311$			2.12427i			0.120456i	−0.998185	+	0.0602281i	$0.980817\pi$
$312$	−7.73495	−	1.08675i	−0.437905	−	0.0615252i
$313$		−	27.2742i		−	1.54163i	−0.637058	−	0.770816i	$-0.719849\pi$
$313$		−	27.2742i		−	1.54163i	0.637058	−	0.770816i	$-0.280151\pi$
$314$	−1.72559	−	1.54171i	−0.0973805	−	0.0870038i
$315$	1.77077	+	10.3830i	0.0997716	+	0.585018i
$316$	−0.457690	−	4.05350i	−0.0257471	−	0.228027i
$317$	−9.46006	−	9.46006i	−0.531330	−	0.531330i	0.389638	−	0.920968i	$-0.372600\pi$
$317$	−9.46006	−	9.46006i	−0.531330	−	0.531330i	−0.920968	+	0.389638i	$0.872600\pi$
$318$	5.34721	+	1.37689i	0.299857	+	0.0772120i
$319$			18.8468i			1.05522i
$320$	3.46596	−	7.21021i	0.193753	−	0.403063i
$321$	28.9472	+	9.21643i	1.61568	+	0.514411i
$322$	−7.49732	+	0.421929i	−0.417809	+	0.0235132i
$323$	19.8325	−	19.8325i	1.10351	−	1.10351i
$324$	7.83383	+	16.2059i	0.435213	+	0.900328i
$325$	−1.12741	−	1.12741i	−0.0625374	−	0.0625374i
$326$	−0.183647	+	0.205550i	−0.0101713	+	0.0113844i
$327$	−5.45077	+	17.1199i	−0.301428	+	0.946734i
$328$	−0.923054	−	5.42106i	−0.0509671	−	0.299328i
$329$	32.3592			1.78402
$330$	−3.09261	−	5.23760i	−0.170242	−	0.288321i
$331$	22.9090	−	22.9090i	1.25919	−	1.25919i	0.307713	−	0.951479i	$-0.400436\pi$
$331$	22.9090	−	22.9090i	1.25919	−	1.25919i	0.951479	−	0.307713i	$-0.0995638\pi$
$332$	0.390287	−	0.489641i	0.0214198	−	0.0268726i
$333$	−27.0682	+	4.61632i	−1.48333	+	0.252973i
$334$	30.4887	−	1.71582i	1.66826	−	0.0938855i
$335$	7.79393			0.425828
$336$	−18.5728	+	15.7082i	−1.01323	+	0.856954i
$337$	15.5272			0.845823			0.422911	−	0.906171i	$-0.361008\pi$
$337$	15.5272			0.845823			0.422911	+	0.906171i	$0.361008\pi$
$338$	14.7663	−	0.831010i	0.803183	−	0.0452010i
$339$	6.68709	+	12.9343i	0.363193	+	0.702494i
$340$	−5.98958	−	4.77422i	−0.324831	−	0.258918i
$341$	−10.3820	+	10.3820i	−0.562216	+	0.562216i
$342$	−6.93634	−	30.2870i	−0.375074	−	1.63774i
$343$	−5.87385			−0.317158
$344$	−12.5160	−	8.87388i	−0.674816	−	0.478448i
$345$	−2.49599	−	0.794692i	−0.134380	−	0.0427848i
$346$	8.59608	−	9.62131i	0.462128	−	0.517245i
$347$	18.3343	+	18.3343i	0.984235	+	0.984235i	0.999878	−	0.0156427i	$-0.00497943\pi$
$347$	18.3343	+	18.3343i	0.984235	+	0.984235i	−0.0156427	+	0.999878i	$0.504979\pi$
$348$	25.7895	+	5.11521i	1.38246	+	0.274204i
$349$	25.9981	−	25.9981i	1.39164	−	1.39164i	0.570001	−	0.821644i	$-0.306943\pi$
$349$	25.9981	−	25.9981i	1.39164	−	1.39164i	0.821644	−	0.570001i	$-0.193057\pi$
$350$	−4.95744	+	0.278991i	−0.264986	+	0.0149127i
$351$	4.98790	+	6.61495i	0.266234	+	0.353080i
$352$	6.78749	−	12.2982i	0.361774	−	0.655496i
$353$			8.80761i			0.468782i	0.972142	+	0.234391i	$0.0753095\pi$
$353$			8.80761i			0.468782i	−0.972142	+	0.234391i	$0.924690\pi$
$354$	6.86932	−	26.6773i	0.365100	−	1.41789i
$355$	3.35404	+	3.35404i	0.178014	+	0.178014i
$356$	−3.07194	+	0.346860i	−0.162813	+	0.0183835i
$357$	10.6959	+	20.6882i	0.566086	+	1.09493i
$358$	18.2750	+	16.3276i	0.965862	+	0.862942i
$359$		−	12.0480i		−	0.635870i	−0.948112	−	0.317935i	$-0.897011\pi$
$359$		−	12.0480i		−	0.635870i	0.948112	−	0.317935i	$-0.102989\pi$
$360$	−8.00638	+	2.81031i	−0.421973	+	0.148116i
$361$			34.6343i			1.82286i
$362$	−7.55308	+	8.45391i	−0.396981	+	0.444328i
$363$	3.84515	+	7.43735i	0.201818	+	0.390360i
$364$	−6.97840	+	8.75488i	−0.365768	+	0.458881i
$365$	−7.97456	−	7.97456i	−0.417408	−	0.417408i
$366$	15.1234	+	3.89422i	0.790512	+	0.203554i
$367$			2.13265i			0.111323i	0.998450	+	0.0556617i	$0.0177268\pi$
$367$			2.13265i			0.111323i	−0.998450	+	0.0556617i	$0.982273\pi$
$368$	−1.34890	−	5.89705i	−0.0703161	−	0.307405i
$369$	−3.37225	+	4.75898i	−0.175552	+	0.247743i
$370$	−0.727319	−	12.9238i	−0.0378115	−	0.671878i
$371$	5.59637	−	5.59637i	0.290549	−	0.290549i
$372$	11.3887	+	17.0243i	0.590477	+	0.882666i
$373$	−7.18805	−	7.18805i	−0.372183	−	0.372183i	0.496089	−	0.868272i	$-0.334769\pi$
$373$	−7.18805	−	7.18805i	−0.372183	−	0.372183i	−0.868272	+	0.496089i	$0.834769\pi$
$374$	−10.0293	−	8.96056i	−0.518600	−	0.463339i
$375$	−1.65042	−	0.525472i	−0.0852272	−	0.0271353i
$376$	4.37572	+	25.6985i	0.225661	+	1.32530i
$377$	12.1012			0.623242
$378$	25.7113	+	2.14160i	1.32245	+	0.110152i
$379$	−16.0037	+	16.0037i	−0.822056	+	0.822056i	−0.986403	−	0.164346i	$-0.947449\pi$
$379$	−16.0037	+	16.0037i	−0.822056	+	0.822056i	0.164346	+	0.986403i	$0.447449\pi$
$380$	14.5546	−	1.64339i	0.746636	−	0.0843044i
$381$	1.27682	+	2.46965i	0.0654134	+	0.126524i
$382$	0.310514	+	5.51756i	0.0158873	+	0.282303i
$383$	−29.7218			−1.51871			−0.759356	−	0.650676i	$-0.774486\pi$
$383$	−29.7218			−1.51871			−0.759356	+	0.650676i	$0.774486\pi$
$384$	−14.9864	−	12.6257i	−0.764771	−	0.644303i
$385$	−8.71836			−0.444329
$386$	1.24618	+	22.1436i	0.0634290	+	1.12708i
$387$	2.73582	+	16.0417i	0.139069	+	0.815443i
$388$	26.6985	−	3.01459i	1.35541	−	0.153043i
$389$	13.6529	−	13.6529i	0.692231	−	0.692231i	−0.270491	−	0.962723i	$-0.587186\pi$
$389$	13.6529	−	13.6529i	0.692231	−	0.692231i	0.962723	+	0.270491i	$0.0871860\pi$
$390$	−3.36297	+	1.98571i	−0.170291	+	0.100550i
$391$	−5.79189			−0.292909
$392$	2.52909	+	14.8533i	0.127738	+	0.750204i
$393$	6.57886	−	20.6631i	0.331860	−	1.04231i
$394$	3.62100	+	3.23516i	0.182423	+	0.162985i
$395$	−1.44224	−	1.44224i	−0.0725667	−	0.0725667i
$396$	−14.3132	+	4.13683i	−0.719264	+	0.207883i
$397$	−17.3192	+	17.3192i	−0.869228	+	0.869228i	−0.992387	−	0.123159i	$-0.960697\pi$
$397$	−17.3192	+	17.3192i	−0.869228	+	0.869228i	0.123159	+	0.992387i	$0.460697\pi$
$398$	−0.142613	−	2.53411i	−0.00714854	−	0.127023i
$399$	−42.4370	−	13.5114i	−2.12450	−	0.676416i
$400$	−0.891927	−	3.89929i	−0.0445964	−	0.194965i
$401$		−	30.4913i		−	1.52266i	−0.648364	−	0.761331i	$-0.724546\pi$
$401$		−	30.4913i		−	1.52266i	0.648364	−	0.761331i	$-0.275454\pi$
$402$	4.76061	−	18.4881i	0.237437	−	0.922101i
$403$	6.66609	+	6.66609i	0.332062	+	0.332062i
$404$	15.6926	−	19.6874i	0.780735	−	0.979486i
$405$	8.11355	+	3.89490i	0.403166	+	0.193539i
$406$	25.1083	−	28.1029i	1.24611	−	1.39472i
$407$		−	22.7284i		−	1.12661i
$408$	−14.9835	+	11.2918i	−0.741792	+	0.559028i
$409$		−	8.41558i		−	0.416124i	−0.978116	−	0.208062i	$-0.933284\pi$
$409$		−	8.41558i		−	0.416124i	0.978116	−	0.208062i	$-0.0667156\pi$
$410$	−2.05039	−	1.83191i	−0.101262	−	0.0904714i
$411$	−11.1382	+	5.75851i	−0.549408	+	0.284046i
$412$	−30.9639	+	3.49620i	−1.52548	+	0.172245i
$413$	−27.9204	−	27.9204i	−1.37387	−	1.37387i
$414$	−3.40967	+	5.43536i	−0.167576	+	0.267133i
$415$		−	0.313078i		−	0.0153684i
$416$	−7.89646	−	4.35813i	−0.387156	−	0.213675i
$417$	3.29321	−	10.3434i	0.161269	−	0.506519i
$418$	25.6777	−	1.44507i	1.25594	−	0.0706808i
$419$	5.15875	−	5.15875i	0.252022	−	0.252022i	−0.569777	−	0.821799i	$-0.692971\pi$
$419$	5.15875	−	5.15875i	0.252022	−	0.252022i	0.821799	+	0.569777i	$0.192971\pi$
$420$	−2.36625	+	11.9300i	−0.115461	+	0.582124i
$421$	−27.9926	−	27.9926i	−1.36427	−	1.36427i	−0.868386	−	0.495889i	$-0.834842\pi$
$421$	−27.9926	−	27.9926i	−1.36427	−	1.36427i	−0.495889	−	0.868386i	$-0.665158\pi$
$422$	−19.0703	+	21.3448i	−0.928329	+	1.03905i
$423$	15.9861	−	22.5599i	0.777270	−	1.09690i
$424$	5.20119	+	3.68767i	0.252592	+	0.179089i
$425$	−3.82976			−0.185771
$426$	10.0048	−	5.90747i	0.484735	−	0.286218i
$427$	15.8281	−	15.8281i	0.765974	−	0.765974i
$428$	27.4308	+	21.8647i	1.32592	+	1.05687i
$429$	−6.09150	+	3.14934i	−0.294100	+	0.152051i
$430$	−7.65918	+	0.431038i	−0.369358	+	0.0207865i
$431$	−19.9029			−0.958687			−0.479344	−	0.877627i	$-0.659125\pi$
$431$	−19.9029			−0.958687			−0.479344	+	0.877627i	$0.659125\pi$
$432$	1.77600	+	20.7086i	0.0854478	+	0.996343i
$433$	−20.4956			−0.984957			−0.492479	−	0.870325i	$-0.663909\pi$
$433$	−20.4956			−0.984957			−0.492479	+	0.870325i	$0.663909\pi$
$434$	29.3121	−	1.64961i	1.40703	−	0.0791837i
$435$	11.6776	−	6.03737i	0.559897	−	0.289470i
$436$	−12.9312	+	16.2231i	−0.619292	+	0.776944i
$437$	7.83169	−	7.83169i	0.374640	−	0.374640i
$438$	−23.7875	+	14.0456i	−1.13661	+	0.671125i
$439$	−10.3356			−0.493292			−0.246646	−	0.969106i	$-0.579328\pi$
$439$	−10.3356			−0.493292			−0.246646	+	0.969106i	$0.579328\pi$
$440$	−1.17893	−	6.92380i	−0.0562032	−	0.330079i
$441$	9.23968	−	13.0392i	0.439985	−	0.620915i
$442$	−5.75341	+	6.43961i	−0.273662	+	0.306301i
$443$	3.48167	+	3.48167i	0.165419	+	0.165419i	0.784962	−	0.619543i	$-0.212682\pi$
$443$	3.48167	+	3.48167i	0.165419	+	0.165419i	−0.619543	+	0.784962i	$0.712682\pi$
$444$	−31.1010	−	6.16872i	−1.47599	−	0.292755i
$445$	−1.09300	+	1.09300i	−0.0518130	+	0.0518130i
$446$	−24.6978	+	1.38993i	−1.16948	+	0.0658150i
$447$	−8.95584	+	28.1287i	−0.423597	+	1.33044i
$448$	−26.5051	+	9.29563i	−1.25225	+	0.439177i
$449$			22.9123i			1.08130i	0.841248	+	0.540649i	$0.181821\pi$
$449$			22.9123i			1.08130i	−0.841248	+	0.540649i	$0.818179\pi$
$450$	−2.25457	+	3.59401i	−0.106281	+	0.169423i
$451$	−3.41379	−	3.41379i	−0.160749	−	0.160749i
$452$	1.88643	+	16.7070i	0.0887303	+	0.785833i
$453$	10.5383	−	5.44836i	0.495133	−	0.255986i
$454$	−10.7006	−	9.56033i	−0.502202	−	0.448689i
$455$			5.59790i			0.262434i
$456$	4.99178	−	35.5289i	0.233761	−	1.66380i
$457$		−	6.23475i		−	0.291649i	−0.989310	−	0.145825i	$-0.953416\pi$
$457$		−	6.23475i		−	0.291649i	0.989310	−	0.145825i	$-0.0465835\pi$
$458$	2.33206	−	2.61020i	0.108970	−	0.121966i
$459$	19.7072	+	2.76351i	0.919853	+	0.128990i
$460$	−2.36523	−	1.88530i	−0.110280	−	0.0879024i
$461$	−3.04206	−	3.04206i	−0.141683	−	0.141683i	0.632708	−	0.774391i	$-0.281943\pi$
$461$	−3.04206	−	3.04206i	−0.141683	−	0.141683i	−0.774391	+	0.632708i	$0.781943\pi$
$462$	−5.32526	+	20.6809i	−0.247753	+	0.962163i
$463$			10.5968i			0.492475i	0.969210	+	0.246237i	$0.0791943\pi$
$463$			10.5968i			0.492475i	−0.969210	+	0.246237i	$0.920806\pi$
$464$	25.7136	+	16.1399i	1.19372	+	0.749278i
$465$	9.75851	+	3.10699i	0.452540	+	0.144083i
$466$	1.63839	+	29.1128i	0.0758969	+	1.34862i
$467$	21.3303	−	21.3303i	0.987050	−	0.987050i	−0.0128668	−	0.999917i	$-0.504096\pi$
$467$	21.3303	−	21.3303i	0.987050	−	0.987050i	0.999917	+	0.0128668i	$0.00409573\pi$
$468$	2.65618	+	9.19023i	0.122782	+	0.424819i
$469$	−19.3495	−	19.3495i	−0.893478	−	0.893478i
$470$	9.71985	+	8.68413i	0.448343	+	0.400569i
$471$	−0.859796	+	2.70047i	−0.0396173	+	0.124431i
$472$	18.3979	−	25.9489i	0.846830	−	1.19439i
$473$	−13.4698			−0.619340
$474$	−4.30207	+	2.54021i	−0.197601	+	0.116676i
$475$	5.17853	−	5.17853i	0.237607	−	0.237607i
$476$	3.01732	+	26.7226i	0.138298	+	1.22483i
$477$	−1.13691	−	6.66635i	−0.0520555	−	0.305231i
$478$	0.842346	+	14.9678i	0.0385280	+	0.684610i
$479$	23.7800			1.08654			0.543269	−	0.839559i	$-0.317187\pi$
$479$	23.7800			1.08654			0.543269	+	0.839559i	$0.317187\pi$
$480$	−9.79435	−	0.265974i	−0.447049	−	0.0121400i
$481$	−14.5935			−0.665407
$482$	−1.37938	−	24.5104i	−0.0628290	−	1.11642i
$483$	4.22371	+	8.16958i	0.192186	+	0.371729i
$484$	1.08472	+	9.60672i	0.0493053	+	0.436669i
$485$	9.49933	−	9.49933i	0.431342	−	0.431342i
$486$	14.1950	−	16.8672i	0.643897	−	0.765112i
$487$	9.88906			0.448116			0.224058	−	0.974576i	$-0.428069\pi$
$487$	9.88906			0.448116			0.224058	+	0.974576i	$0.428069\pi$
$488$	14.7104	+	10.4298i	0.665909	+	0.472133i
$489$	0.321677	+	0.102418i	0.0145468	+	0.00463150i
$490$	5.61791	+	5.01928i	0.253791	+	0.226748i
$491$	−7.74985	−	7.74985i	−0.349746	−	0.349746i	0.510269	−	0.860015i	$-0.329546\pi$
$491$	−7.74985	−	7.74985i	−0.349746	−	0.349746i	−0.860015	+	0.510269i	$0.829546\pi$
$492$	−5.59789	+	3.74481i	−0.252372	+	0.168829i
$493$	20.5536	−	20.5536i	0.925687	−	0.925687i
$494$	−0.927855	−	16.4872i	−0.0417462	−	0.741793i
$495$	−4.30705	+	6.07819i	−0.193587	+	0.273194i
$496$	5.27374	+	23.0555i	0.236798	+	1.03522i
$497$		−	16.6537i		−	0.747022i
$498$	−0.742657	−	0.191231i	−0.0332792	−	0.00856928i
$499$	−13.0925	−	13.0925i	−0.586102	−	0.586102i	0.350472	−	0.936573i	$-0.386021\pi$
$499$	−13.0925	−	13.0925i	−0.586102	−	0.586102i	−0.936573	+	0.350472i	$0.886021\pi$
$500$	−1.56396	−	1.24661i	−0.0699423	−	0.0557501i
$501$	−17.1762	−	33.2225i	−0.767375	−	1.48427i
$502$	−5.24731	+	5.87314i	−0.234199	+	0.262131i
$503$			11.2568i			0.501916i	0.967998	+	0.250958i	$0.0807456\pi$
$503$			11.2568i			0.501916i	−0.967998	+	0.250958i	$0.919254\pi$
$504$	26.8540	+	12.9000i	1.19617	+	0.574610i
$505$		−	12.5882i		−	0.560168i
$506$	−3.96046	−	3.53845i	−0.176064	−	0.157303i
$507$	−8.31880	−	16.0904i	−0.369451	−	0.714599i
$508$	0.360191	+	3.19001i	0.0159809	+	0.141534i
$509$	−26.0017	−	26.0017i	−1.15251	−	1.15251i	−0.986049	−	0.166457i	$-0.946767\pi$
$509$	−26.0017	−	26.0017i	−1.15251	−	1.15251i	−0.166457	−	0.986049i	$-0.553233\pi$
$510$	−2.33925	+	9.08461i	−0.103584	+	0.402273i
$511$			39.5959i			1.75162i
$512$	−10.9664	−	19.7924i	−0.484650	−	0.874708i
$513$	−30.3845	+	22.9109i	−1.34151	+	1.01154i
$514$	10.7626	−	0.605690i	0.474718	−	0.0267158i
$515$	−11.0169	+	11.0169i	−0.485464	+	0.485464i
$516$	−3.65583	+	18.4317i	−0.160939	+	0.811410i
$517$	16.1830	+	16.1830i	0.711728	+	0.711728i
$518$	−30.2796	+	33.8909i	−1.33041	+	1.48908i
$519$	−15.0569	−	4.79394i	−0.660926	−	0.210431i
$520$	−4.44565	+	0.756968i	−0.194955	+	0.0331953i
$521$	−31.9983			−1.40187			−0.700936	−	0.713224i	$-0.747234\pi$
$521$	−31.9983			−1.40187			−0.700936	+	0.713224i	$0.747234\pi$
$522$	−7.18853	−	31.3882i	−0.314633	−	1.37383i
$523$	−20.8693	+	20.8693i	−0.912549	+	0.912549i	−0.996472	−	0.0839234i	$-0.973255\pi$
$523$	−20.8693	+	20.8693i	−0.912549	+	0.912549i	0.0839234	+	0.996472i	$0.473255\pi$
$524$	15.6074	−	19.5806i	0.681814	−	0.855383i
$525$	2.79284	+	5.40195i	0.121889	+	0.235761i
$526$	4.06158	−	0.228575i	0.177093	−	0.00996635i
$527$	22.6444			0.986406
$528$	−17.1441	−	1.43258i	−0.746103	−	0.0623450i
$529$	20.7128			0.900558
$530$	3.18288	−	0.179124i	0.138256	−	0.00778066i
$531$	−33.2585	+	5.67206i	−1.44330	+	0.246146i
$532$	−40.2138	−	32.0539i	−1.74349	−	1.38971i
$533$	−2.19193	+	2.19193i	−0.0949431	+	0.0949431i
$534$	1.92510	+	3.26032i	0.0833071	+	0.141088i
$535$	17.5393			0.758291
$536$	12.7502	−	17.9832i	0.550724	−	0.776756i
$537$	9.10573	−	28.5995i	0.392941	−	1.23416i
$538$	13.2519	−	14.8324i	0.571328	−	0.639469i
$539$	9.35350	+	9.35350i	0.402884	+	0.402884i
$540$	7.14828	+	7.54335i	0.307613	+	0.324614i
$541$	6.84616	−	6.84616i	0.294339	−	0.294339i	−0.544452	−	0.838792i	$-0.683263\pi$
$541$	6.84616	−	6.84616i	0.294339	−	0.294339i	0.838792	+	0.544452i	$0.183263\pi$
$542$	0.0982105	−	0.00552702i	0.00421850	−	0.000237406i
$543$	13.2300	+	4.21227i	0.567754	+	0.180766i
$544$	−20.8141	+	6.00977i	−0.892399	+	0.257667i
$545$			10.3731i			0.444334i
$546$	13.2788	+	3.41925i	0.568282	+	0.146331i
$547$	16.2972	+	16.2972i	0.696819	+	0.696819i	0.963723	−	0.266904i	$-0.0860007\pi$
$547$	16.2972	+	16.2972i	0.696819	+	0.696819i	−0.266904	+	0.963723i	$0.586001\pi$
$548$	−14.3871	+	1.62448i	−0.614586	+	0.0693943i
$549$	−3.21549	−	18.8543i	−0.137234	−	0.804680i
$550$	−2.61877	−	2.33972i	−0.111665	−	0.0997659i
$551$			55.5844i			2.36797i
$552$	−5.91684	+	4.45904i	−0.251837	+	0.189789i
$553$			7.16110i			0.304521i
$554$	−21.2446	+	23.7784i	−0.902596	+	1.01025i
$555$	−14.0827	+	7.28081i	−0.597776	+	0.309053i
$556$	7.81269	−	9.80156i	0.331332	−	0.415679i
$557$	2.97161	+	2.97161i	0.125911	+	0.125911i	0.767254	−	0.641343i	$-0.221622\pi$
$557$	2.97161	+	2.97161i	0.125911	+	0.125911i	−0.641343	+	0.767254i	$0.721622\pi$
$558$	13.3307	−	21.2505i	0.564334	−	0.899605i
$559$			8.64869i			0.365801i
$560$	−7.46620	+	11.8949i	−0.315505	+	0.502650i
$561$	−4.99720	+	15.6954i	−0.210982	+	0.662658i
$562$	−0.190621	−	3.38717i	−0.00804086	−	0.142879i
$563$	8.75134	−	8.75134i	0.368825	−	0.368825i	−0.498224	−	0.867049i	$-0.666014\pi$
$563$	8.75134	−	8.75134i	0.368825	−	0.368825i	0.867049	+	0.498224i	$0.166014\pi$
$564$	26.5367	−	17.7522i	1.11740	−	0.747503i
$565$	5.94437	+	5.94437i	0.250081	+	0.250081i
$566$	30.4943	+	27.2449i	1.28177	+	1.14519i
$567$	−10.4734	−	29.8127i	−0.439841	−	1.25201i
$568$	13.2258	−	2.25198i	0.554942	−	0.0944909i
$569$	−18.2968			−0.767044			−0.383522	−	0.923532i	$-0.625289\pi$
$569$	−18.2968			−0.767044			−0.383522	+	0.923532i	$0.625289\pi$
$570$	−9.12095	−	15.4471i	−0.382035	−	0.647010i
$571$	0.436875	−	0.436875i	0.0182827	−	0.0182827i	−0.697906	−	0.716189i	$-0.745885\pi$
$571$	0.436875	−	0.436875i	0.0182827	−	0.0182827i	0.716189	+	0.697906i	$0.245885\pi$
$572$	−7.86831	+	0.888429i	−0.328991	+	0.0371471i
$573$	6.01230	−	3.10839i	0.251168	−	0.129855i
$574$	0.542421	+	9.63835i	0.0226402	+	0.402297i
$575$	−1.51234			−0.0630689
$576$	−6.61340	+	23.0708i	−0.275558	+	0.961284i
$577$	8.34500			0.347407			0.173703	−	0.984798i	$-0.444427\pi$
$577$	8.34500			0.347407			0.173703	+	0.984798i	$0.444427\pi$
$578$	−0.185382	−	3.29407i	−0.00771086	−	0.137015i
$579$	24.1291	−	12.4749i	1.00277	−	0.518438i
$580$	15.0838	−	1.70314i	0.626320	−	0.0707192i
$581$	−0.777261	+	0.777261i	−0.0322462	+	0.0322462i
$582$	−16.7312	−	28.3358i	−0.693530	−	1.17455i
$583$	5.59755			0.231827
$584$	−31.4457	+	5.35430i	−1.30123	+	0.221563i
$585$	3.90270	+	2.76548i	0.161357	+	0.114338i
$586$	−4.65111	−	4.15550i	−0.192136	−	0.171662i
$587$	0.0354325	+	0.0354325i	0.00146246	+	0.00146246i	0.707838	−	0.706375i	$-0.249671\pi$
$587$	0.0354325	+	0.0354325i	0.00146246	+	0.00146246i	−0.706375	+	0.707838i	$0.749671\pi$
$588$	15.3378	−	10.2605i	0.632518	−	0.423135i
$589$	−30.6194	+	30.6194i	−1.26165	+	1.26165i
$590$	−0.893654	−	15.8795i	−0.0367912	−	0.653747i
$591$	1.80421	−	5.66671i	0.0742153	−	0.233097i
$592$	−31.0094	−	19.4641i	−1.27448	−	0.799969i
$593$		−	1.04154i		−	0.0427710i	−0.999771	−	0.0213855i	$-0.993192\pi$
$593$		−	1.04154i		−	0.0427710i	0.999771	−	0.0213855i	$-0.00680773\pi$
$594$	11.7874	+	13.9294i	0.483641	+	0.571531i
$595$	9.50791	+	9.50791i	0.389787	+	0.389787i
$596$	−21.2465	+	26.6552i	−0.870290	+	1.09184i
$597$	−2.76133	+	1.42762i	−0.113014	+	0.0584287i
$598$	−2.27197	+	2.54294i	−0.0929079	+	0.103989i
$599$			30.9787i			1.26575i	0.774252	+	0.632877i	$0.218126\pi$
$599$			30.9787i			1.26575i	−0.774252	+	0.632877i	$0.781874\pi$
$600$	−3.91238	+	2.94844i	−0.159722	+	0.120370i
$601$		−	7.31426i		−	0.298355i	−0.988810	−	0.149177i	$-0.952337\pi$
$601$		−	7.31426i		−	0.298355i	0.988810	−	0.149177i	$-0.0476626\pi$
$602$	20.0851	+	17.9449i	0.818607	+	0.731378i
$603$	−23.0490	+	3.93088i	−0.938628	+	0.160078i
$604$	13.6122	−	1.53698i	0.553872	−	0.0625390i
$605$	3.41807	+	3.41807i	0.138964	+	0.138964i
$606$	−29.8606	−	7.68900i	−1.21301	−	0.312344i
$607$			38.6263i			1.56779i	0.620892	+	0.783896i	$0.286771\pi$
$607$			38.6263i			1.56779i	−0.620892	+	0.783896i	$0.713229\pi$
$608$	20.0182	−	36.2708i	0.811845	−	1.47098i
$609$	−43.9799	−	14.0026i	−1.78215	−	0.567415i
$610$	9.00207	−	0.506613i	0.364483	−	0.0205122i
$611$	10.3908	−	10.3908i	0.420368	−	0.420368i
$612$	20.1209	+	11.0979i	0.813338	+	0.448608i
$613$	23.7829	+	23.7829i	0.960584	+	0.960584i	0.999252	−	0.0386686i	$-0.0123117\pi$
$613$	23.7829	+	23.7829i	0.960584	+	0.960584i	−0.0386686	+	0.999252i	$0.512312\pi$
$614$	−4.60888	+	5.15857i	−0.185999	+	0.208183i
$615$	−1.02163	+	3.20878i	−0.0411963	+	0.129390i
$616$	−14.2625	+	20.1162i	−0.574651	+	0.810504i
$617$	1.30622			0.0525863			0.0262932	−	0.999654i	$-0.491630\pi$
$617$	1.30622			0.0525863			0.0262932	+	0.999654i	$0.491630\pi$
$618$	19.4042	+	32.8627i	0.780550	+	1.32193i
$619$	9.93310	−	9.93310i	0.399245	−	0.399245i	−0.478722	−	0.877967i	$-0.658900\pi$
$619$	9.93310	−	9.93310i	0.399245	−	0.399245i	0.877967	+	0.478722i	$0.158900\pi$
$620$	9.24729	+	7.37090i	0.371380	+	0.296022i
$621$	7.78220	+	1.09129i	0.312289	+	0.0437918i
$622$	2.99942	−	0.168800i	0.120266	−	0.00676825i
$623$	5.42703			0.217430
$624$	−0.919833	+	11.0079i	−0.0368228	+	0.440670i
$625$	−1.00000			−0.0400000
$626$	−38.5107	+	2.16728i	−1.53920	+	0.0866219i
$627$	−14.4658	−	27.9801i	−0.577710	−	1.11742i
$628$	−2.03975	+	2.55900i	−0.0813947	+	0.102115i
$629$	−24.7867	+	24.7867i	−0.988312	+	0.988312i
$630$	14.5199	−	3.32535i	0.578488	−	0.132485i
$631$	25.4152			1.01176			0.505881	−	0.862603i	$-0.331168\pi$
$631$	25.4152			1.01176			0.505881	+	0.862603i	$0.331168\pi$
$632$	−5.68709	+	0.968350i	−0.226220	+	0.0385189i
$633$	33.4037	+	10.6353i	1.32768	+	0.422716i
$634$	−12.6057	+	14.1091i	−0.500636	+	0.560345i
$635$	1.13501	+	1.13501i	0.0450413	+	0.0450413i
$636$	1.51923	−	7.65957i	0.0602415	−	0.303722i
$637$	6.00572	−	6.00572i	0.237955	−	0.237955i
$638$	26.6113	−	1.49761i	1.05355	−	0.0592910i
$639$	−11.6105	−	8.22728i	−0.459305	−	0.325466i
$640$	−10.4561	−	4.32092i	−0.413313	−	0.170799i
$641$			49.6843i			1.96241i	0.192968	+	0.981205i	$0.438188\pi$
$641$			49.6843i			1.96241i	−0.192968	+	0.981205i	$0.561812\pi$
$642$	10.7132	−	41.6052i	0.422816	−	1.64203i
$643$	−15.6741	−	15.6741i	−0.618128	−	0.618128i	0.326923	−	0.945051i	$-0.393988\pi$
$643$	−15.6741	−	15.6741i	−0.618128	−	0.618128i	−0.945051	+	0.326923i	$0.893988\pi$
$644$	1.19151	+	10.5525i	0.0469521	+	0.415828i
$645$	4.31490	+	8.34595i	0.169899	+	0.328621i
$646$	−29.5790	−	26.4272i	−1.16377	−	1.03976i
$647$		−	13.3723i		−	0.525721i	−0.964834	−	0.262860i	$-0.915334\pi$
$647$		−	13.3723i		−	0.525721i	0.964834	−	0.262860i	$-0.0846659\pi$
$648$	22.2599	−	12.3490i	0.874451	−	0.485113i
$649$		−	27.9263i		−	1.09620i
$650$	−1.50229	+	1.68147i	−0.0589247	+	0.0659525i
$651$	−16.5133	−	31.9404i	−0.647209	−	1.25184i
$652$	0.304826	+	0.242973i	0.0119379	+	0.00951554i
$653$	23.9746	+	23.9746i	0.938197	+	0.938197i	0.998198	−	0.0600013i	$-0.0191105\pi$
$653$	23.9746	+	23.9746i	0.938197	+	0.938197i	−0.0600013	+	0.998198i	$0.519110\pi$
$654$	24.6061	+	6.33598i	0.962175	+	0.247756i
$655$		−	12.5199i		−	0.489193i
$656$	−7.58108	+	1.73410i	−0.295992	+	0.0677054i
$657$	27.6052	+	19.5612i	1.07698	+	0.763155i
$658$	−2.57134	−	45.6905i	−0.100241	−	1.78120i
$659$	−0.128623	+	0.128623i	−0.00501045	+	0.00501045i	−0.709608	−	0.704597i	$-0.751128\pi$
$659$	−0.128623	+	0.128623i	−0.00501045	+	0.00501045i	0.704597	+	0.709608i	$0.251128\pi$
$660$	−7.14964	+	4.78289i	−0.278299	+	0.186174i
$661$	10.7294	+	10.7294i	0.417324	+	0.417324i	0.884280	−	0.466956i	$-0.154649\pi$
$661$	10.7294	+	10.7294i	0.417324	+	0.417324i	−0.466956	+	0.884280i	$0.654649\pi$
$662$	−34.1674	−	30.5266i	−1.32796	−	1.18645i
$663$	10.0777	+	3.20862i	0.391386	+	0.124612i
$664$	−0.722376	−	0.512168i	−0.0280336	−	0.0198760i
$665$	−25.7129			−0.997102
$666$	8.66906	+	37.8529i	0.335919	+	1.46677i
$667$	8.11643	−	8.11643i	0.314269	−	0.314269i
$668$	−4.84541	−	42.9130i	−0.187474	−	1.66035i
$669$	13.9138	+	26.9124i	0.537940	+	1.04049i
$670$	−0.619325	−	11.0049i	−0.0239266	−	0.425155i
$671$	15.8314			0.611165
$672$	23.6555	+	24.9762i	0.912532	+	0.963476i
$673$	−6.40413			−0.246861			−0.123430	−	0.992353i	$-0.539390\pi$
$673$	−6.40413			−0.246861			−0.123430	+	0.992353i	$0.539390\pi$
$674$	−1.23383	−	21.9241i	−0.0475255	−	0.844486i
$675$	5.14581	+	0.721589i	0.198062	+	0.0277740i
$676$	−2.34674	−	20.7837i	−0.0902592	−	0.799374i
$677$	7.77482	−	7.77482i	0.298811	−	0.298811i	−0.541737	−	0.840548i	$-0.682233\pi$
$677$	7.77482	−	7.77482i	0.298811	−	0.298811i	0.840548	+	0.541737i	$0.182233\pi$
$678$	17.7316	−	10.4698i	0.680977	−	0.402091i
$679$	−47.1669			−1.81010
$680$	−6.26515	+	8.83654i	−0.240257	+	0.338866i
$681$	−5.33169	+	16.7459i	−0.204311	+	0.641705i
$682$	15.4841	+	13.8342i	0.592918	+	0.529738i
$683$	4.83040	+	4.83040i	0.184830	+	0.184830i	0.793457	−	0.608627i	$-0.208279\pi$
$683$	4.83040	+	4.83040i	0.184830	+	0.184830i	−0.608627	+	0.793457i	$0.708279\pi$
$684$	−42.2135	+	12.2006i	−1.61407	+	0.466503i
$685$	−5.11892	+	5.11892i	−0.195584	+	0.195584i
$686$	0.466751	+	8.29376i	0.0178206	+	0.316657i
$687$	−4.08485	−	1.30056i	−0.155847	−	0.0496196i
$688$	−11.5352	+	18.3774i	−0.439775	+	0.700633i
$689$		−	3.59409i		−	0.136924i
$690$	−0.923751	+	3.58743i	−0.0351666	+	0.136571i
$691$	2.08824	+	2.08824i	0.0794403	+	0.0794403i	0.745710	−	0.666270i	$-0.232110\pi$
$691$	2.08824	+	2.08824i	0.0794403	+	0.0794403i	−0.666270	+	0.745710i	$0.732110\pi$
$692$	−14.2682	−	11.3730i	−0.542394	−	0.432335i
$693$	25.7828	−	4.39712i	0.979408	−	0.167033i
$694$	24.4307	−	27.3445i	0.927377	−	1.03798i
$695$		−	6.26715i		−	0.237727i
$696$	5.17327	−	36.8207i	0.196092	−	1.39569i
$697$			7.44590i			0.282034i
$698$	−38.7746	−	34.6429i	−1.46764	−	1.31125i
$699$	31.7232	−	16.4010i	1.19988	−	0.620345i
$700$	0.787860	+	6.97763i	0.0297783	+	0.263730i
$701$	7.61403	+	7.61403i	0.287578	+	0.287578i	0.836122	−	0.548544i	$-0.184818\pi$
$701$	7.61403	+	7.61403i	0.287578	+	0.287578i	−0.548544	+	0.836122i	$0.684818\pi$
$702$	8.94383	−	7.56845i	0.337563	−	0.285653i
$703$		−	67.0324i		−	2.52817i
$704$	−17.9042	−	8.60655i	−0.674788	−	0.324372i
$705$	4.84304	−	15.2112i	0.182399	−	0.572885i
$706$	12.4362	−	0.699874i	0.468041	−	0.0263401i
$707$	−31.2520	+	31.2520i	−1.17535	+	1.17535i
$708$	−38.2137	−	7.57948i	−1.43616	−	0.284854i
$709$	31.6178	+	31.6178i	1.18743	+	1.18743i	0.977775	+	0.209655i	$0.0672341\pi$
$709$	31.6178	+	31.6178i	1.18743	+	1.18743i	0.209655	+	0.977775i	$0.432766\pi$
$710$	4.46931	−	5.00235i	0.167730	−	0.187735i
$711$	4.99252	+	3.53773i	0.187234	+	0.132675i
$712$	0.733863	+	4.30995i	0.0275027	+	0.161522i
$713$	8.94208			0.334884
$714$	28.3614	−	16.7463i	1.06140	−	0.626715i
$715$	−2.79954	+	2.79954i	−0.104697	+	0.104697i
$716$	21.6021	−	27.1013i	0.807308	−	1.01282i
$717$	16.3099	−	8.43228i	0.609103	−	0.314909i
$718$	−17.0116	+	0.957366i	−0.634866	+	0.0357286i
$719$	53.0736			1.97931			0.989655	−	0.143466i	$-0.0458248\pi$
$719$	53.0736			1.97931			0.989655	+	0.143466i	$0.0458248\pi$
$720$	4.60431	+	11.0815i	0.171593	+	0.412984i
$721$	54.7022			2.03722
$722$	48.9030	−	2.75213i	1.81998	−	0.102424i
$723$	−26.7081	+	13.8082i	−0.993286	+	0.513534i
$724$	12.5369	+	9.99302i	0.465932	+	0.371388i
$725$	5.36681	−	5.36681i	0.199318	−	0.199318i
$726$	10.1958	−	6.02026i	0.378403	−	0.223433i
$727$	19.2404			0.713587			0.356794	−	0.934183i	$-0.383870\pi$
$727$	19.2404			0.713587			0.356794	+	0.934183i	$0.383870\pi$
$728$	12.9162	+	9.15767i	0.478708	+	0.339406i
$729$	−25.9586	−	7.42631i	−0.961430	−	0.275049i
$730$	−10.6262	+	11.8936i	−0.393295	+	0.440202i
$731$	14.6896	+	14.6896i	0.543315	+	0.543315i
$732$	4.29681	−	21.6634i	0.158815	−	0.800701i
$733$	17.9974	−	17.9974i	0.664751	−	0.664751i	−0.291745	−	0.956496i	$-0.594236\pi$
$733$	17.9974	−	17.9974i	0.664751	−	0.664751i	0.956496	+	0.291745i	$0.0942359\pi$
$734$	3.01126	−	0.169466i	0.111148	−	0.00625509i
$735$	2.79919	−	8.79179i	0.103250	−	0.324290i
$736$	−8.21932	+	2.37321i	−0.302968	+	0.0874776i
$737$		−	19.3536i		−	0.712900i
$738$	6.98755	+	4.38338i	0.257215	+	0.161355i
$739$	25.8918	+	25.8918i	0.952444	+	0.952444i	0.998919	−	0.0464758i	$-0.0147990\pi$
$739$	25.8918	+	25.8918i	0.952444	+	0.952444i	−0.0464758	+	0.998919i	$0.514799\pi$
$740$	−18.1904	+	2.05392i	−0.668692	+	0.0755036i
$741$	−17.9655	+	9.28826i	−0.659980	+	0.341213i
$742$	−8.34666	−	7.45726i	−0.306415	−	0.273764i
$743$			0.469261i			0.0172155i	0.999963	+	0.00860776i	$0.00273997\pi$
$743$			0.469261i			0.0172155i	−0.999963	+	0.00860776i	$0.997260\pi$
$744$	23.1329	−	17.4334i	0.848094	−	0.639139i
$745$			17.0434i			0.624422i
$746$	−9.57819	+	10.7206i	−0.350683	+	0.392507i
$747$	0.157901	+	0.925867i	0.00577731	+	0.0338757i
$748$	−11.8552	+	14.8731i	−0.433468	+	0.543815i
$749$	−43.5438	−	43.5438i	−1.59106	−	1.59106i
$750$	−0.610810	+	2.37211i	−0.0223036	+	0.0866173i
$751$			10.8501i			0.395925i	0.980210	+	0.197963i	$0.0634324\pi$
$751$			10.8501i			0.395925i	−0.980210	+	0.197963i	$0.936568\pi$
$752$	35.9380	−	8.22049i	1.31052	−	0.299770i
$753$	9.19121	+	2.92637i	0.334946	+	0.106643i
$754$	−0.961590	−	17.0866i	−0.0350190	−	0.622258i
$755$	4.84322	−	4.84322i	0.176263	−	0.176263i
$756$	0.980805	−	36.4740i	0.0356715	−	1.32655i
$757$	−13.8807	−	13.8807i	−0.504502	−	0.504502i	0.408331	−	0.912834i	$-0.366111\pi$
$757$	−13.8807	−	13.8807i	−0.504502	−	0.504502i	−0.912834	+	0.408331i	$0.866111\pi$
$758$	23.8686	+	21.3252i	0.866948	+	0.774568i
$759$	−1.97335	+	6.19796i	−0.0716281	+	0.224972i
$760$	−3.47698	−	20.4202i	−0.126123	−	0.740719i
$761$	−14.3490			−0.520152			−0.260076	−	0.965588i	$-0.583748\pi$
$761$	−14.3490			−0.520152			−0.260076	+	0.965588i	$0.583748\pi$
$762$	3.38563	−	1.99909i	0.122648	−	0.0724193i
$763$	25.7526	−	25.7526i	0.932308	−	0.932308i
$764$	7.76601	−	0.876878i	0.280964	−	0.0317243i
$765$	11.3258	−	1.93154i	0.409483	−	0.0698351i
$766$	2.36176	+	41.9665i	0.0853340	+	1.51631i
$767$	−17.9310			−0.647450
$768$	−16.6364	+	22.1637i	−0.600314	+	0.799765i
$769$	−15.4011			−0.555376			−0.277688	−	0.960671i	$-0.589568\pi$
$769$	−15.4011			−0.555376			−0.277688	+	0.960671i	$0.589568\pi$
$770$	0.692782	+	12.3101i	0.0249661	+	0.443627i
$771$	−6.06324	−	11.7276i	−0.218362	−	0.422360i
$772$	31.1673	−	3.51917i	1.12173	−	0.126658i
$773$	−18.0950	+	18.0950i	−0.650833	+	0.650833i	−0.953194	−	0.302361i	$-0.902225\pi$
$773$	−18.0950	+	18.0950i	−0.650833	+	0.650833i	0.302361	+	0.953194i	$0.402225\pi$
$774$	22.4331	−	5.13763i	0.806341	−	0.184668i
$775$	5.91275			0.212392
$776$	−6.37807	−	37.4582i	−0.228959	−	1.34467i
$777$	53.0378	+	16.8866i	1.90272	+	0.605803i
$778$	−20.3626	−	18.1928i	−0.730033	−	0.652242i
$779$	−10.0682	−	10.0682i	−0.360731	−	0.360731i
$780$	3.07101	+	4.59066i	0.109960	+	0.164372i
$781$	8.32863	−	8.32863i	0.298022	−	0.298022i
$782$	0.460238	+	8.17803i	0.0164581	+	0.292446i
$783$	−31.4892	+	23.7439i	−1.12533	+	0.848539i
$784$	20.7715	−	4.75130i	0.741841	−	0.169689i
$785$			1.63623i			0.0583997i
$786$	−29.6986	−	7.64728i	−1.05931	−	0.272769i
$787$	19.8406	+	19.8406i	0.707242	+	0.707242i	0.965954	−	0.258712i	$-0.0832981\pi$
$787$	19.8406	+	19.8406i	0.707242	+	0.707242i	−0.258712	+	0.965954i	$0.583298\pi$
$788$	4.28024	−	5.36985i	0.152477	−	0.191293i
$789$	−2.28815	−	4.42577i	−0.0814601	−	0.157562i
$790$	−1.92180	+	2.15101i	−0.0683747	+	0.0765295i
$791$		−	29.5154i		−	1.04945i
$792$	6.97847	+	19.8812i	0.247969	+	0.706447i
$793$		−	10.1651i		−	0.360972i
$794$	25.8306	+	23.0782i	0.916695	+	0.819014i
$795$	−1.79312	−	3.46828i	−0.0635954	−	0.123007i
$796$	−3.56677	+	0.402733i	−0.126421	+	0.0142745i
$797$	14.3294	+	14.3294i	0.507575	+	0.507575i	0.913781	−	0.406207i	$-0.133149\pi$
$797$	14.3294	+	14.3294i	0.507575	+	0.507575i	−0.406207	+	0.913781i	$0.633149\pi$
$798$	−15.7057	+	60.9937i	−0.555974	+	2.15916i
$799$		−	35.2972i		−	1.24872i
$800$	−5.43484	+	1.56923i	−0.192151	+	0.0554807i
$801$	2.68107	−	3.78357i	0.0947308	−	0.133686i
$802$	−43.0530	+	2.42291i	−1.52026	+	0.0855560i
$803$	−19.8022	+	19.8022i	−0.698803	+	0.698803i
$804$	−26.4831	−	5.25277i	−0.933985	−	0.185251i
$805$	3.75459	+	3.75459i	0.132332	+	0.132332i
$806$	8.88268	−	9.94209i	0.312879	−	0.350195i
$807$	−23.2120	−	7.39042i	−0.817102	−	0.260155i
$808$	−29.0452	−	20.5932i	−1.02181	−	0.724466i
$809$	11.9504			0.420155			0.210077	−	0.977685i	$-0.432628\pi$
$809$	11.9504			0.420155			0.210077	+	0.977685i	$0.432628\pi$
$810$	4.85480	−	11.7657i	0.170580	−	0.413403i
$811$	−28.2125	+	28.2125i	−0.990674	+	0.990674i	−0.999957	−	0.00928247i	$-0.997045\pi$
$811$	−28.2125	+	28.2125i	−0.990674	+	0.990674i	0.00928247	+	0.999957i	$0.497045\pi$
$812$	−41.6759	−	33.2193i	−1.46254	−	1.16577i
$813$	−0.0553281	−	0.107017i	−0.00194044	−	0.00375324i
$814$	−32.0920	+	1.80606i	−1.12483	+	0.0633022i
$815$	0.194907			0.00682728
$816$	17.1344	+	20.2591i	0.599825	+	0.709209i
$817$	−39.7260			−1.38984
$818$	−11.8826	+	0.668723i	−0.415466	+	0.0233814i
$819$	−2.82331	−	16.5547i	−0.0986544	−	0.578467i
$820$	−2.42369	+	3.04068i	−0.0846388	+	0.106185i
$821$	3.76757	−	3.76757i	0.131489	−	0.131489i	−0.638299	−	0.769788i	$-0.720362\pi$
$821$	3.76757	−	3.76757i	0.131489	−	0.131489i	0.769788	+	0.638299i	$0.220362\pi$
$822$	9.01597	+	15.2693i	0.314468	+	0.532579i
$823$	−14.2240			−0.495817			−0.247909	−	0.968783i	$-0.579743\pi$
$823$	−14.2240			−0.495817			−0.247909	+	0.968783i	$0.579743\pi$
$824$	7.39703	+	43.4425i	0.257688	+	1.51339i
$825$	−1.30483	+	4.09826i	−0.0454285	+	0.142683i
$826$	−37.2044	+	41.6416i	−1.29451	+	1.44890i
$827$	26.6691	+	26.6691i	0.927376	+	0.927376i	0.997536	−	0.0701598i	$-0.0223509\pi$
$827$	26.6691	+	26.6691i	0.927376	+	0.927376i	−0.0701598	+	0.997536i	$0.522351\pi$
$828$	7.94556	+	4.38248i	0.276127	+	0.152302i
$829$	3.85197	−	3.85197i	0.133785	−	0.133785i	−0.637043	−	0.770828i	$-0.719843\pi$
$829$	3.85197	−	3.85197i	0.133785	−	0.133785i	0.770828	+	0.637043i	$0.219843\pi$
$830$	−0.442060	+	0.0248780i	−0.0153441	+	0.000863527i
$831$	37.2121	+	11.8479i	1.29087	+	0.410998i
$832$	−5.52611	+	11.4959i	−0.191584	+	0.398550i
$833$		−	20.4012i		−	0.706858i
$834$	−14.8664	−	3.82804i	−0.514781	−	0.132554i
$835$	−15.2684	−	15.2684i	−0.528386	−	0.528386i
$836$	−4.08082	−	36.1415i	−0.141138	−	1.24998i
$837$	−30.4259	−	4.26658i	−1.05167	−	0.147474i
$838$	−7.69398	−	6.87413i	−0.265784	−	0.237463i
$839$		−	14.7894i		−	0.510587i	−0.966864	−	0.255294i	$-0.917828\pi$
$839$		−	14.7894i		−	0.510587i	0.966864	−	0.255294i	$-0.0821722\pi$
$840$	17.0329	+	2.39311i	0.587692	+	0.0825702i
$841$			28.6053i			0.986389i
$842$	−37.3006	+	41.7493i	−1.28546	+	1.43878i
$843$	−3.69089	+	1.90821i	−0.127121	+	0.0657221i
$844$	31.6538	+	25.2308i	1.08957	+	0.868480i
$845$	−7.39485	−	7.39485i	−0.254391	−	0.254391i
$846$	−33.1244	−	20.7794i	−1.13884	−	0.714409i
$847$		−	16.9717i		−	0.583154i
$848$	4.79362	−	7.63701i	0.164613	−	0.262256i
$849$	15.1942	−	47.7222i	0.521462	−	1.63782i
$850$	0.304322	+	5.40754i	0.0104382	+	0.185477i
$851$	−9.78807	+	9.78807i	−0.335531	+	0.335531i
$852$	−9.13624	−	13.6572i	−0.313002	−	0.467888i
$853$	2.02828	+	2.02828i	0.0694471	+	0.0694471i	0.740977	−	0.671530i	$-0.234363\pi$
$853$	2.02828	+	2.02828i	0.0694471	+	0.0694471i	−0.671530	+	0.740977i	$0.734363\pi$
$854$	−23.6066	−	21.0912i	−0.807803	−	0.721725i
$855$	−12.7027	+	17.9263i	−0.434422	+	0.613065i
$856$	28.6928	−	40.4691i	0.980699	−	1.38320i
$857$	−5.84248			−0.199575			−0.0997877	−	0.995009i	$-0.531816\pi$
$857$	−5.84248			−0.199575			−0.0997877	+	0.995009i	$0.531816\pi$
$858$	4.93084	+	8.35082i	0.168336	+	0.285092i
$859$	−5.81546	+	5.81546i	−0.198421	+	0.198421i	−0.799323	−	0.600902i	$-0.794808\pi$
$859$	−5.81546	+	5.81546i	−0.198421	+	0.198421i	0.600902	+	0.799323i	$0.294808\pi$
$860$	1.21723	+	10.7803i	0.0415073	+	0.367607i
$861$	10.5026	−	5.42989i	0.357927	−	0.185050i
$862$	1.58153	+	28.1024i	0.0538672	+	0.957173i
$863$	−42.6745			−1.45266			−0.726328	−	0.687348i	$-0.758775\pi$
$863$	−42.6745			−1.45266			−0.726328	+	0.687348i	$0.758775\pi$
$864$	29.0990	−	4.15323i	0.989967	−	0.141296i
$865$	−9.12311			−0.310195
$866$	1.62863	+	28.9394i	0.0553432	+	0.983401i
$867$	−3.58944	+	1.85576i	−0.121904	+	0.0630248i
$868$	−4.65842	−	41.2570i	−0.158117	−	1.40035i
$869$	−3.58131	+	3.58131i	−0.121488	+	0.121488i
$870$	−9.45257	−	16.0088i	−0.320472	−	0.542748i
$871$	−12.4266			−0.421060
$872$	23.9342	+	16.9694i	0.810513	+	0.574658i
$873$	−23.3014	+	32.8834i	−0.788632	+	1.11293i
$874$	−11.6805	−	10.4359i	−0.395099	−	0.352998i
$875$	2.48264	+	2.48264i	0.0839286	+	0.0839286i
$876$	21.7223	+	32.4713i	0.733929	+	1.09710i
$877$	−23.4883	+	23.4883i	−0.793142	+	0.793142i	−0.982004	−	0.188861i	$-0.939520\pi$
$877$	−23.4883	+	23.4883i	−0.793142	+	0.793142i	0.188861	+	0.982004i	$0.439520\pi$
$878$	0.821293	+	14.5937i	0.0277173	+	0.492512i
$879$	−2.31748	+	7.27879i	−0.0781665	+	0.245508i
$880$	−9.68259	+	2.21480i	−0.326400	+	0.0746610i
$881$		−	15.6287i		−	0.526544i	−0.964722	−	0.263272i	$-0.915198\pi$
$881$		−	15.6287i		−	0.526544i	0.964722	−	0.263272i	$-0.0848017\pi$
$882$	−19.1453	−	12.0101i	−0.644657	−	0.404401i
$883$	2.12908	+	2.12908i	0.0716492	+	0.0716492i	0.742023	−	0.670374i	$-0.233866\pi$
$883$	2.12908	+	2.12908i	0.0716492	+	0.0716492i	−0.670374	+	0.742023i	$0.733866\pi$
$884$	9.54977	+	7.61200i	0.321194	+	0.256019i
$885$	−17.3033	+	8.94590i	−0.581645	+	0.300713i
$886$	4.63938	−	5.19270i	0.155863	−	0.174452i
$887$		−	3.07143i		−	0.103128i	−0.998670	−	0.0515642i	$-0.983579\pi$
$887$		−	3.07143i		−	0.103128i	0.998670	−	0.0515642i	$-0.0164207\pi$
$888$	−6.23874	+	44.4042i	−0.209358	+	1.49011i
$889$		−	5.63562i		−	0.189013i
$890$	1.63014	+	1.45644i	0.0546424	+	0.0488198i
$891$	9.67169	−	20.1473i	0.324014	−	0.674960i
$892$	3.92510	+	34.7624i	0.131422	+	1.16393i
$893$	47.7282	+	47.7282i	1.59716	+	1.59716i
$894$	40.4289	+	10.4103i	1.35214	+	0.348172i
$895$		−	17.3287i		−	0.579234i
$896$	15.2314	+	36.6860i	0.508845	+	1.22559i
$897$	3.97960	+	1.26705i	0.132875	+	0.0423057i
$898$	32.3517	−	1.82067i	1.07959	−	0.0607564i
$899$	−31.7326	+	31.7326i	−1.05834	+	1.05834i
$900$	5.25382	+	2.89782i	0.175127	+	0.0965939i
$901$	−6.10448	−	6.10448i	−0.203370	−	0.203370i
$902$	−4.54893	+	5.09147i	−0.151463	+	0.169527i
$903$	10.0077	−	31.4323i	0.333034	−	1.04600i
$904$	23.4401	−	3.99118i	0.779606	−	0.132745i
$905$	8.01616			0.266466
$906$	−8.53037	−	14.4469i	−0.283402	−	0.479967i
$907$	13.6377	−	13.6377i	0.452833	−	0.452833i	−0.443461	−	0.896294i	$-0.646249\pi$
$907$	13.6377	−	13.6377i	0.452833	−	0.452833i	0.896294	+	0.443461i	$0.146249\pi$
$908$	−12.6487	+	15.8687i	−0.419762	+	0.526620i
$909$	6.34888	+	37.2271i	0.210579	+	1.23475i
$910$	7.90412	−	0.444823i	0.262019	−	0.0147457i
$911$	−7.46839			−0.247439			−0.123719	−	0.992317i	$-0.539482\pi$
$911$	−7.46839			−0.247439			−0.123719	+	0.992317i	$0.539482\pi$
$912$	−50.5628	−	4.22507i	−1.67430	−	0.139906i
$913$	−0.777426			−0.0257290
$914$	−8.80334	+	0.495429i	−0.291189	+	0.0163873i
$915$	−5.07143	−	9.80926i	−0.167656	−	0.324284i
$916$	−3.87085	−	3.08541i	−0.127897	−	0.101945i
$917$	−31.0824	+	31.0824i	−1.02643	+	1.02643i
$918$	2.33604	−	28.0457i	0.0771008	−	0.925648i
$919$	3.21213			0.105958			0.0529792	−	0.998596i	$-0.483128\pi$
$919$	3.21213			0.105958			0.0529792	+	0.998596i	$0.483128\pi$
$920$	−2.47405	+	3.48947i	−0.0815671	+	0.115044i
$921$	8.07294	+	2.57032i	0.266012	+	0.0846950i
$922$	−4.05359	+	4.53705i	−0.133498	+	0.149420i
$923$	−5.34767	−	5.34767i	−0.176021	−	0.176021i
$924$	29.6242	+	5.87580i	0.974564	+	0.193300i
$925$	−6.47214	+	6.47214i	−0.212803	+	0.212803i
$926$	14.9625	−	0.842048i	0.491697	−	0.0276714i
$927$	27.0240	−	38.1368i	0.887585	−	1.25258i
$928$	20.7460	−	37.5895i	0.681021	−	1.23394i
$929$		−	49.4818i		−	1.62344i	−0.584044	−	0.811722i	$-0.698530\pi$
$929$		−	49.4818i		−	1.62344i	0.584044	−	0.811722i	$-0.301470\pi$
$930$	3.61157	−	14.0257i	0.118428	−	0.459921i
$931$	27.5861	+	27.5861i	0.904097	+	0.904097i
$932$	40.9764	−	4.62674i	1.34223	−	0.151554i
$933$	−1.68976	−	3.26837i	−0.0553204	−	0.107002i
$934$	−31.8130	−	28.4230i	−1.04095	−	0.930030i
$935$			9.50993i			0.311008i
$936$	12.7654	−	4.48075i	0.417249	−	0.146458i
$937$			16.5098i			0.539351i	0.962951	+	0.269675i	$0.0869164\pi$
$937$			16.5098i			0.539351i	−0.962951	+	0.269675i	$0.913084\pi$
$938$	−25.7836	+	28.8587i	−0.841863	+	0.942270i
$939$	21.6955	+	41.9638i	0.708005	+	1.36944i
$940$	11.4894	−	14.4143i	0.374744	−	0.470142i
$941$	31.9487	+	31.9487i	1.04150	+	1.04150i	0.999101	+	0.0423968i	$0.0134994\pi$
$941$	31.9487	+	31.9487i	1.04150	+	1.04150i	0.0423968	+	0.999101i	$0.486501\pi$
$942$	3.88133	+	0.999428i	0.126461	+	0.0325631i
$943$			2.94032i			0.0957500i
$944$	−38.1012	−	23.9154i	−1.24009	−	0.778381i
$945$	−10.9837	−	14.5666i	−0.357301	−	0.473852i
$946$	1.07034	+	19.0190i	0.0347997	+	0.618361i
$947$	−1.41437	+	1.41437i	−0.0459609	+	0.0459609i	−0.729714	−	0.683753i	$-0.760347\pi$
$947$	−1.41437	+	1.41437i	−0.0459609	+	0.0459609i	0.683753	+	0.729714i	$0.260347\pi$
$948$	3.92858	+	5.87259i	0.127594	+	0.190733i
$949$	12.7146	+	12.7146i	0.412734	+	0.412734i
$950$	−7.72348	−	6.90048i	−0.250583	−	0.223881i
$951$	22.0802	+	7.03005i	0.715999	+	0.227965i
$952$	37.4920	−	6.38383i	1.21512	−	0.206901i
$953$	56.1603			1.81921			0.909606	−	0.415473i	$-0.136384\pi$
$953$	56.1603			1.81921			0.909606	+	0.415473i	$0.136384\pi$
$954$	−9.32240	+	2.13502i	−0.301824	+	0.0691237i
$955$	2.76315	−	2.76315i	0.0894133	−	0.0894133i
$956$	21.0672	−	2.37875i	0.681363	−	0.0769343i
$957$	−14.9918	−	28.9974i	−0.484616	−	0.937353i
$958$	−1.88962	−	33.5769i	−0.0610508	−	1.08482i
$959$	25.4169			0.820754
$960$	0.402734	+	13.8506i	0.0129982	+	0.447025i
$961$	−3.96064			−0.127763
$962$	1.15964	+	20.6057i	0.0373882	+	0.664355i
$963$	−51.8691	+	8.84598i	−1.67146	+	0.285058i
$964$	−34.4985	+	3.89531i	−1.11112	+	0.125459i
$965$	11.0893	−	11.0893i	0.356978	−	0.356978i
$966$	11.1997	−	6.61297i	0.360343	−	0.212769i
$967$	−13.2411			−0.425805			−0.212903	−	0.977073i	$-0.568292\pi$
$967$	−13.2411			−0.425805			−0.212903	+	0.977073i	$0.568292\pi$
$968$	13.4783	−	2.29497i	0.433209	−	0.0737632i
$969$	−14.7381	+	46.2900i	−0.473457	+	1.48705i
$970$	−14.1677	−	12.6580i	−0.454898	−	0.406425i
$971$	−39.6158	−	39.6158i	−1.27133	−	1.27133i	−0.945390	−	0.325940i	$-0.894319\pi$
$971$	−39.6158	−	39.6158i	−1.27133	−	1.27133i	−0.325940	−	0.945390i	$-0.605681\pi$
$972$	−24.9441	−	18.7027i	−0.800083	−	0.599889i
$973$	−15.5591	+	15.5591i	−0.498801	+	0.498801i
$974$	−0.785809	−	13.9631i	−0.0251789	−	0.447408i
$975$	2.63142	+	0.837811i	0.0842729	+	0.0268314i
$976$	13.5577	−	21.5996i	0.433970	−	0.691385i
$977$		−	17.8687i		−	0.571669i	−0.958279	−	0.285834i	$-0.907729\pi$
$977$		−	17.8687i		−	0.571669i	0.958279	−	0.285834i	$-0.0922707\pi$
$978$	0.119051	−	0.462340i	0.00380683	−	0.0147840i
$979$	2.71409	+	2.71409i	0.0867428	+	0.0867428i
$980$	6.64070	−	8.33121i	0.212129	−	0.266131i
$981$	−5.23168	−	30.6763i	−0.167035	−	0.979420i
$982$	−10.3268	+	11.5585i	−0.329542	+	0.368845i
$983$		−	3.81968i		−	0.121829i	−0.998143	−	0.0609144i	$-0.980598\pi$
$983$		−	3.81968i		−	0.121829i	0.998143	−	0.0609144i	$-0.0194017\pi$
$984$	5.73242	+	7.60653i	0.182743	+	0.242487i
$985$		−	3.43350i		−	0.109401i
$986$	−30.6545	−	27.3880i	−0.976238	−	0.872212i
$987$	−49.7874	+	25.7403i	−1.58475	+	0.819323i
$988$	−23.2058	+	2.62022i	−0.738276	+	0.0833604i
$989$	5.80080	+	5.80080i	0.184455	+	0.184455i
$990$	8.92453	+	5.59847i	0.283640	+	0.177931i
$991$		−	36.5313i		−	1.16045i	−0.814455	−	0.580227i	$-0.802964\pi$
$991$		−	36.5313i		−	1.16045i	0.814455	−	0.580227i	$-0.197036\pi$
$992$	32.1349	−	9.27847i	1.02028	−	0.294592i
$993$	−17.0244	+	53.4706i	−0.540252	+	1.69684i
$994$	−23.5147	+	1.32335i	−0.745842	+	0.0419740i
$995$	−1.26906	+	1.26906i	−0.0402319	+	0.0402319i
$996$	−0.211001	+	1.06381i	−0.00668583	+	0.0337082i
$997$	28.2872	+	28.2872i	0.895865	+	0.895865i	0.995067	−	0.0992026i	$-0.0316292\pi$
$997$	28.2872	+	28.2872i	0.895865	+	0.895865i	−0.0992026	+	0.995067i	$0.531629\pi$
$998$	−17.4460	+	19.5267i	−0.552244	+	0.618108i
$999$	37.9746	−	28.6342i	1.20146	−	0.905945i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	240.2.bk.b.11.15	✓	60
3.2	odd	2	inner	240.2.bk.b.11.16	yes	60
4.3	odd	2		960.2.bk.b.911.26		60
12.11	even	2		960.2.bk.b.911.12		60
16.3	odd	4	inner	240.2.bk.b.131.16	yes	60
16.13	even	4		960.2.bk.b.431.12		60
48.29	odd	4		960.2.bk.b.431.26		60
48.35	even	4	inner	240.2.bk.b.131.15	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.2.bk.b.11.15	✓	60	1.1	even	1	trivial
240.2.bk.b.11.16	yes	60	3.2	odd	2	inner
240.2.bk.b.131.15	yes	60	48.35	even	4	inner
240.2.bk.b.131.16	yes	60	16.3	odd	4	inner
960.2.bk.b.431.12		60	16.13	even	4
960.2.bk.b.431.26		60	48.29	odd	4
960.2.bk.b.911.12		60	12.11	even	2
960.2.bk.b.911.26		60	4.3	odd	2

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:	\( N \)	\(=\)	\( 240 = 2^{4} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	240.bk (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0794625 - 1.41198i) q^{2} +(-1.53859 + 0.795457i) q^{3} +(-1.98737 + 0.224399i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(1.24543 + 2.10924i) q^{6} +3.51098 q^{7} +(0.474768 + 2.78830i) q^{8} +(1.73450 - 2.44776i) q^{9} +O(q^{10})\)	\(q+(-0.0794625 - 1.41198i) q^{2} +(-1.53859 + 0.795457i) q^{3} +(-1.98737 + 0.224399i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(1.24543 + 2.10924i) q^{6} +3.51098 q^{7} +(0.474768 + 2.78830i) q^{8} +(1.73450 - 2.44776i) q^{9} +(1.05461 + 0.942232i) q^{10} +(1.75586 + 1.75586i) q^{11} +(2.87924 - 1.92612i) q^{12} +(1.12741 - 1.12741i) q^{13} +(-0.278991 - 4.95744i) q^{14} +(0.525472 - 1.65042i) q^{15} +(3.89929 - 0.891927i) q^{16} -3.82976i q^{17} +(-3.59401 - 2.25457i) q^{18} +(5.17853 + 5.17853i) q^{19} +(1.24661 - 1.56396i) q^{20} +(-5.40195 + 2.79284i) q^{21} +(2.33972 - 2.61877i) q^{22} -1.51234i q^{23} +(-2.94844 - 3.91238i) q^{24} -1.00000i q^{25} +(-1.68147 - 1.50229i) q^{26} +(-0.721589 + 5.14581i) q^{27} +(-6.97763 + 0.787860i) q^{28} +(5.36681 + 5.36681i) q^{29} +(-2.37211 - 0.610810i) q^{30} +5.91275i q^{31} +(-1.56923 - 5.43484i) q^{32} +(-4.09826 - 1.30483i) q^{33} +(-5.40754 + 0.304322i) q^{34} +(-2.48264 + 2.48264i) q^{35} +(-2.89782 + 5.25382i) q^{36} +(-6.47214 - 6.47214i) q^{37} +(6.90048 - 7.72348i) q^{38} +(-0.837811 + 2.63142i) q^{39} +(-2.30733 - 1.63591i) q^{40} -1.94422 q^{41} +(4.37268 + 7.40552i) q^{42} +(-3.83565 + 3.83565i) q^{43} +(-3.88357 - 3.09554i) q^{44} +(0.504351 + 2.95730i) q^{45} +(-2.13539 + 0.120174i) q^{46} +9.21655 q^{47} +(-5.28991 + 4.47402i) q^{48} +5.32701 q^{49} +(-1.41198 + 0.0794625i) q^{50} +(3.04641 + 5.89242i) q^{51} +(-1.98759 + 2.49357i) q^{52} +(1.59396 - 1.59396i) q^{53} +(7.32311 + 0.609970i) q^{54} -2.48317 q^{55} +(1.66690 + 9.78966i) q^{56} +(-12.0869 - 3.84832i) q^{57} +(7.15136 - 8.00428i) q^{58} +(-7.95230 - 7.95230i) q^{59} +(-0.673957 + 3.39791i) q^{60} +(4.50816 - 4.50816i) q^{61} +(8.34868 - 0.469842i) q^{62} +(6.08979 - 8.59404i) q^{63} +(-7.54919 + 2.64759i) q^{64} +1.59440i q^{65} +(-1.51674 + 5.89035i) q^{66} +(-5.51114 - 5.51114i) q^{67} +(0.859393 + 7.61115i) q^{68} +(1.20300 + 2.32686i) q^{69} +(3.70271 + 3.30816i) q^{70} -4.74332i q^{71} +(7.64856 + 3.67418i) q^{72} +11.2777i q^{73} +(-8.62424 + 9.65282i) q^{74} +(0.795457 + 1.53859i) q^{75} +(-11.4537 - 9.12961i) q^{76} +(6.16481 + 6.16481i) q^{77} +(3.78209 + 0.973873i) q^{78} +2.03963i q^{79} +(-2.12653 + 3.38790i) q^{80} +(-2.98304 - 8.49126i) q^{81} +(0.154493 + 2.74520i) q^{82} +(-0.221380 + 0.221380i) q^{83} +(10.1090 - 6.76259i) q^{84} +(2.70805 + 2.70805i) q^{85} +(5.72065 + 5.11107i) q^{86} +(-12.5264 - 3.98824i) q^{87} +(-4.06224 + 5.72950i) q^{88} +1.54573 q^{89} +(4.13557 - 0.947128i) q^{90} +(3.95831 - 3.95831i) q^{91} +(0.339367 + 3.00558i) q^{92} +(-4.70334 - 9.09728i) q^{93} +(-0.732370 - 13.0136i) q^{94} -7.32355 q^{95} +(6.73758 + 7.11372i) q^{96} -13.4341 q^{97} +(-0.423297 - 7.52162i) q^{98} +(7.34347 - 1.25239i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 4 q^{3} + 8 q^{4} + 8 q^{6} + 16 q^{7}+O(q^{10}) \) 60 * q + 4 * q^3 + 8 * q^4 + 8 * q^6 + 16 * q^7	\( 60 q + 4 q^{3} + 8 q^{4} + 8 q^{6} + 16 q^{7} + 4 q^{12} + 16 q^{13} - 52 q^{16} - 20 q^{18} + 20 q^{19} - 16 q^{21} - 24 q^{22} - 28 q^{24} - 20 q^{27} - 56 q^{28} - 12 q^{34} + 12 q^{36} + 24 q^{37} - 80 q^{39} - 8 q^{40} + 36 q^{42} - 8 q^{45} + 36 q^{46} + 56 q^{48} + 28 q^{49} - 36 q^{51} - 24 q^{52} + 92 q^{54} - 80 q^{58} + 28 q^{60} + 20 q^{61} - 64 q^{64} + 24 q^{66} - 40 q^{67} + 12 q^{69} - 16 q^{70} - 56 q^{72} + 4 q^{75} - 20 q^{76} - 8 q^{78} - 28 q^{81} - 32 q^{82} + 16 q^{84} - 20 q^{85} - 24 q^{87} + 8 q^{88} + 32 q^{90} - 16 q^{91} - 48 q^{93} + 28 q^{94} + 72 q^{96} - 8 q^{97} + 32 q^{99}+O(q^{100}) \) 60 * q + 4 * q^3 + 8 * q^4 + 8 * q^6 + 16 * q^7 + 4 * q^12 + 16 * q^13 - 52 * q^16 - 20 * q^18 + 20 * q^19 - 16 * q^21 - 24 * q^22 - 28 * q^24 - 20 * q^27 - 56 * q^28 - 12 * q^34 + 12 * q^36 + 24 * q^37 - 80 * q^39 - 8 * q^40 + 36 * q^42 - 8 * q^45 + 36 * q^46 + 56 * q^48 + 28 * q^49 - 36 * q^51 - 24 * q^52 + 92 * q^54 - 80 * q^58 + 28 * q^60 + 20 * q^61 - 64 * q^64 + 24 * q^66 - 40 * q^67 + 12 * q^69 - 16 * q^70 - 56 * q^72 + 4 * q^75 - 20 * q^76 - 8 * q^78 - 28 * q^81 - 32 * q^82 + 16 * q^84 - 20 * q^85 - 24 * q^87 + 8 * q^88 + 32 * q^90 - 16 * q^91 - 48 * q^93 + 28 * q^94 + 72 * q^96 - 8 * q^97 + 32 * q^99

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