LMFDB - Embedded newform 240.2.bk.b.11.20

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			11.20
Character	$\chi$	$=$	240.11
Dual form			240.2.bk.b.131.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.774214 - 1.18347i) q^{2} +(1.55407 + 0.764773i) q^{3} +(-0.801186 - 1.83251i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(2.10826 - 1.24709i) q^{6} +3.70081 q^{7} +(-2.78901 - 0.470579i) q^{8} +(1.83024 + 2.37702i) q^{9} +O(q^{10})$	\(q+(0.774214 - 1.18347i) q^{2} +(1.55407 + 0.764773i) q^{3} +(-0.801186 - 1.83251i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(2.10826 - 1.24709i) q^{6} +3.70081 q^{7} +(-2.78901 - 0.470579i) q^{8} +(1.83024 + 2.37702i) q^{9} +(0.289385 + 1.38429i) q^{10} +(-1.64037 - 1.64037i) q^{11} +(0.156360 - 3.46057i) q^{12} +(-1.05025 + 1.05025i) q^{13} +(2.86522 - 4.37979i) q^{14} +(-1.63967 + 0.558115i) q^{15} +(-2.71620 + 2.93637i) q^{16} -2.98027i q^{17} +(4.23012 - 0.325714i) q^{18} +(-4.72085 - 4.72085i) q^{19} +(1.86231 + 0.729258i) q^{20} +(5.75131 + 2.83028i) q^{21} +(-3.21132 + 0.671326i) q^{22} +6.79225i q^{23} +(-3.97441 - 2.86427i) q^{24} -1.00000i q^{25} +(0.429819 + 2.05606i) q^{26} +(1.02644 + 5.09376i) q^{27} +(-2.96504 - 6.78179i) q^{28} +(-1.73154 - 1.73154i) q^{29} +(-0.608943 + 2.37259i) q^{30} +8.33693i q^{31} +(1.37217 + 5.48791i) q^{32} +(-1.29473 - 3.80376i) q^{33} +(-3.52705 - 2.30737i) q^{34} +(-2.61687 + 2.61687i) q^{35} +(2.88954 - 5.25838i) q^{36} +(-1.13135 - 1.13135i) q^{37} +(-9.24192 + 1.93202i) q^{38} +(-2.43537 + 0.828959i) q^{39} +(2.30487 - 1.63938i) q^{40} -1.40357 q^{41} +(7.80229 - 4.61524i) q^{42} +(2.31521 - 2.31521i) q^{43} +(-1.69176 + 4.32024i) q^{44} +(-2.97498 - 0.386626i) q^{45} +(8.03841 + 5.25866i) q^{46} -10.4517 q^{47} +(-6.46681 + 2.48603i) q^{48} +6.69602 q^{49} +(-1.18347 - 0.774214i) q^{50} +(2.27923 - 4.63154i) q^{51} +(2.76605 + 1.08315i) q^{52} +(4.58009 - 4.58009i) q^{53} +(6.82298 + 2.72890i) q^{54} +2.31983 q^{55} +(-10.3216 - 1.74153i) q^{56} +(-3.72614 - 10.9469i) q^{57} +(-3.38980 + 0.708637i) q^{58} +(8.43378 + 8.43378i) q^{59} +(2.33643 + 2.55756i) q^{60} +(0.960744 - 0.960744i) q^{61} +(9.86647 + 6.45456i) q^{62} +(6.77339 + 8.79689i) q^{63} +(7.55711 + 2.62490i) q^{64} -1.48528i q^{65} +(-5.50402 - 1.41265i) q^{66} +(-8.74415 - 8.74415i) q^{67} +(-5.46139 + 2.38775i) q^{68} +(-5.19453 + 10.5556i) q^{69} +(1.07096 + 5.12299i) q^{70} +10.6306i q^{71} +(-3.98599 - 7.49079i) q^{72} -9.12658i q^{73} +(-2.21481 + 0.463006i) q^{74} +(0.764773 - 1.55407i) q^{75} +(-4.86874 + 12.4333i) q^{76} +(-6.07070 - 6.07070i) q^{77} +(-0.904453 + 3.52397i) q^{78} -5.11634i q^{79} +(-0.155680 - 3.99697i) q^{80} +(-2.30041 + 8.70104i) q^{81} +(-1.08666 + 1.66107i) q^{82} +(-5.15848 + 5.15848i) q^{83} +(0.578658 - 12.8069i) q^{84} +(2.10737 + 2.10737i) q^{85} +(-0.947505 - 4.53244i) q^{86} +(-1.36669 - 4.01516i) q^{87} +(3.80308 + 5.34693i) q^{88} +13.4884 q^{89} +(-2.76083 + 3.22146i) q^{90} +(-3.88679 + 3.88679i) q^{91} +(12.4469 - 5.44186i) q^{92} +(-6.37586 + 12.9561i) q^{93} +(-8.09185 + 12.3692i) q^{94} +6.67630 q^{95} +(-2.06456 + 9.57797i) q^{96} +5.93480 q^{97} +(5.18415 - 7.92451i) q^{98} +(0.896908 - 6.90147i) 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 $

$2$	0.774214	−	1.18347i	0.547452	−	0.836837i
$2$	0.774214	−	1.18347i	0.547452	−	0.836837i
$3$	1.55407	+	0.764773i	0.897241	+	0.441542i
$3$	1.55407	+	0.764773i	0.897241	+	0.441542i
$4$	−0.801186	−	1.83251i	−0.400593	−	0.916256i
$5$	−0.707107	+	0.707107i	−0.316228	+	0.316228i
$5$	−0.707107	+	0.707107i	−0.316228	+	0.316228i
$6$	2.10826	−	1.24709i	0.860695	−	0.509121i
$7$	3.70081			1.39878			0.699388	−	0.714742i	$-0.253456\pi$
$7$	3.70081			1.39878			0.699388	+	0.714742i	$0.253456\pi$
$8$	−2.78901	−	0.470579i	−0.986063	−	0.166375i
$9$	1.83024	+	2.37702i	0.610081	+	0.792339i
$10$	0.289385	+	1.38429i	0.0915117	+	0.437751i
$11$	−1.64037	−	1.64037i	−0.494590	−	0.494590i	0.415159	−	0.909749i	$-0.363726\pi$
$11$	−1.64037	−	1.64037i	−0.494590	−	0.494590i	−0.909749	+	0.415159i	$0.863726\pi$
$12$	0.156360	−	3.46057i	0.0451371	−	0.998981i
$13$	−1.05025	+	1.05025i	−0.291288	+	0.291288i	−0.837589	−	0.546301i	$-0.816036\pi$
$13$	−1.05025	+	1.05025i	−0.291288	+	0.291288i	0.546301	+	0.837589i	$0.316036\pi$
$14$	2.86522	−	4.37979i	0.765762	−	1.17055i
$15$	−1.63967	+	0.558115i	−0.423360	+	0.144105i
$16$	−2.71620	+	2.93637i	−0.679050	+	0.734092i
$17$		−	2.98027i		−	0.722823i	−0.932406	−	0.361411i	$-0.882295\pi$
$17$		−	2.98027i		−	0.722823i	0.932406	−	0.361411i	$-0.117705\pi$
$18$	4.23012	−	0.325714i	0.997049	−	0.0767716i
$19$	−4.72085	−	4.72085i	−1.08304	−	1.08304i	−0.996225	−	0.0868137i	$-0.972332\pi$
$19$	−4.72085	−	4.72085i	−1.08304	−	1.08304i	−0.0868137	−	0.996225i	$-0.527668\pi$
$20$	1.86231	+	0.729258i	0.416424	+	0.163067i
$21$	5.75131	+	2.83028i	1.25504	+	0.617618i
$22$	−3.21132	+	0.671326i	−0.684656	+	0.143127i
$23$			6.79225i			1.41628i	0.706071	+	0.708142i	$0.250466\pi$
$23$			6.79225i			1.41628i	−0.706071	+	0.708142i	$0.749534\pi$
$24$	−3.97441	−	2.86427i	−0.811274	−	0.584666i
$25$		−	1.00000i		−	0.200000i
$26$	0.429819	+	2.05606i	0.0842945	+	0.403227i
$27$	1.02644	+	5.09376i	0.197539	+	0.980295i
$28$	−2.96504	−	6.78179i	−0.560340	−	1.28164i
$29$	−1.73154	−	1.73154i	−0.321539	−	0.321539i	0.527819	−	0.849357i	$-0.323010\pi$
$29$	−1.73154	−	1.73154i	−0.321539	−	0.321539i	−0.849357	+	0.527819i	$0.823010\pi$
$30$	−0.608943	+	2.37259i	−0.111177	+	0.433174i
$31$			8.33693i			1.49736i	0.662934	+	0.748678i	$0.269311\pi$
$31$			8.33693i			1.49736i	−0.662934	+	0.748678i	$0.730689\pi$
$32$	1.37217	+	5.48791i	0.242568	+	0.970134i
$33$	−1.29473	−	3.80376i	−0.225384	−	0.662149i
$34$	−3.52705	−	2.30737i	−0.604885	−	0.395711i
$35$	−2.61687	+	2.61687i	−0.442332	+	0.442332i
$36$	2.88954	−	5.25838i	0.481591	−	0.876396i
$37$	−1.13135	−	1.13135i	−0.185992	−	0.185992i	0.607969	−	0.793961i	$-0.291985\pi$
$37$	−1.13135	−	1.13135i	−0.185992	−	0.185992i	−0.793961	+	0.607969i	$0.791985\pi$
$38$	−9.24192	+	1.93202i	−1.49924	+	0.313415i
$39$	−2.43537	+	0.828959i	−0.389971	+	0.132740i
$40$	2.30487	−	1.63938i	0.364433	−	0.259208i
$41$	−1.40357			−0.219200			−0.109600	−	0.993976i	$-0.534957\pi$
$41$	−1.40357			−0.219200			−0.109600	+	0.993976i	$0.534957\pi$
$42$	7.80229	−	4.61524i	1.20392	−	0.712147i
$43$	2.31521	−	2.31521i	0.353066	−	0.353066i	−0.508183	−	0.861249i	$-0.669683\pi$
$43$	2.31521	−	2.31521i	0.353066	−	0.353066i	0.861249	+	0.508183i	$0.169683\pi$
$44$	−1.69176	+	4.32024i	−0.255042	+	0.651301i
$45$	−2.97498	−	0.386626i	−0.443484	−	0.0576348i
$46$	8.03841	+	5.25866i	1.18520	+	0.775347i
$47$	−10.4517			−1.52454			−0.762269	−	0.647260i	$-0.775915\pi$
$47$	−10.4517			−1.52454			−0.762269	+	0.647260i	$0.775915\pi$
$48$	−6.46681	+	2.48603i	−0.933404	+	0.358828i
$49$	6.69602			0.956574
$50$	−1.18347	−	0.774214i	−0.167367	−	0.109490i
$51$	2.27923	−	4.63154i	0.319156	−	0.648546i
$52$	2.76605	+	1.08315i	0.383582	+	0.150207i
$53$	4.58009	−	4.58009i	0.629123	−	0.629123i	−0.318724	−	0.947847i	$-0.603254\pi$
$53$	4.58009	−	4.58009i	0.629123	−	0.629123i	0.947847	+	0.318724i	$0.103254\pi$
$54$	6.82298	+	2.72890i	0.928490	+	0.371356i
$55$	2.31983			0.312806
$56$	−10.3216	−	1.74153i	−1.37928	−	0.232721i
$57$	−3.72614	−	10.9469i	−0.493539	−	1.44995i
$58$	−3.38980	+	0.708637i	−0.445102	+	0.0930486i
$59$	8.43378	+	8.43378i	1.09798	+	1.09798i	0.994646	+	0.103339i	$0.0329525\pi$
$59$	8.43378	+	8.43378i	1.09798	+	1.09798i	0.103339	+	0.994646i	$0.467047\pi$
$60$	2.33643	+	2.55756i	0.301632	+	0.330179i
$61$	0.960744	−	0.960744i	0.123011	−	0.123011i	−0.642921	−	0.765932i	$-0.722278\pi$
$61$	0.960744	−	0.960744i	0.123011	−	0.123011i	0.765932	+	0.642921i	$0.222278\pi$
$62$	9.86647	+	6.45456i	1.25304	+	0.819730i
$63$	6.77339	+	8.79689i	0.853367	+	1.10830i
$64$	7.55711	+	2.62490i	0.944639	+	0.328112i
$65$		−	1.48528i		−	0.184227i
$66$	−5.50402	−	1.41265i	−0.677498	−	0.173885i
$67$	−8.74415	−	8.74415i	−1.06827	−	1.06827i	−0.997492	−	0.0707763i	$-0.977452\pi$
$67$	−8.74415	−	8.74415i	−1.06827	−	1.06827i	−0.0707763	−	0.997492i	$-0.522548\pi$
$68$	−5.46139	+	2.38775i	−0.662291	+	0.289558i
$69$	−5.19453	+	10.5556i	−0.625348	+	1.27075i
$70$	1.07096	+	5.12299i	0.128004	+	0.612315i
$71$			10.6306i			1.26162i	0.775938	+	0.630809i	$0.217277\pi$
$71$			10.6306i			1.26162i	−0.775938	+	0.630809i	$0.782723\pi$
$72$	−3.98599	−	7.49079i	−0.469753	−	0.882798i
$73$		−	9.12658i		−	1.06818i	−0.845426	−	0.534092i	$-0.820653\pi$
$73$		−	9.12658i		−	1.06818i	0.845426	−	0.534092i	$-0.179347\pi$
$74$	−2.21481	+	0.463006i	−0.257467	+	0.0538234i
$75$	0.764773	−	1.55407i	0.0883084	−	0.179448i
$76$	−4.86874	+	12.4333i	−0.558483	+	1.42620i
$77$	−6.07070	−	6.07070i	−0.691821	−	0.691821i
$78$	−0.904453	+	3.52397i	−0.102409	+	0.399011i
$79$		−	5.11634i		−	0.575633i	−0.957686	−	0.287816i	$-0.907071\pi$
$79$		−	5.11634i		−	0.575633i	0.957686	−	0.287816i	$-0.0929293\pi$
$80$	−0.155680	−	3.99697i	−0.0174055	−	0.446875i
$81$	−2.30041	+	8.70104i	−0.255601	+	0.966782i
$82$	−1.08666	+	1.66107i	−0.120002	+	0.183435i
$83$	−5.15848	+	5.15848i	−0.566216	+	0.566216i	−0.931066	−	0.364850i	$-0.881120\pi$
$83$	−5.15848	+	5.15848i	−0.566216	+	0.566216i	0.364850	+	0.931066i	$0.381120\pi$
$84$	0.578658	−	12.8069i	0.0631367	−	1.39735i
$85$	2.10737	+	2.10737i	0.228577	+	0.228577i
$86$	−0.947505	−	4.53244i	−0.102172	−	0.488745i
$87$	−1.36669	−	4.01516i	−0.146525	−	0.430470i
$88$	3.80308	+	5.34693i	0.405410	+	0.569984i
$89$	13.4884			1.42976			0.714882	−	0.699245i	$-0.246481\pi$
$89$	13.4884			1.42976			0.714882	+	0.699245i	$0.246481\pi$
$90$	−2.76083	+	3.22146i	−0.291017	+	0.339572i
$91$	−3.88679	+	3.88679i	−0.407447	+	0.407447i
$92$	12.4469	−	5.44186i	1.29768	−	0.567353i
$93$	−6.37586	+	12.9561i	−0.661146	+	1.34349i
$94$	−8.09185	+	12.3692i	−0.834611	+	1.27579i
$95$	6.67630			0.684974
$96$	−2.06456	+	9.57797i	−0.210713	+	0.977548i
$97$	5.93480			0.602588			0.301294	−	0.953531i	$-0.402581\pi$
$97$	5.93480			0.602588			0.301294	+	0.953531i	$0.402581\pi$
$98$	5.18415	−	7.92451i	0.523678	−	0.800497i
$99$	0.896908	−	6.90147i	0.0901427	−	0.693623i
$100$	−1.83251	+	0.801186i	−0.183251	+	0.0801186i
$101$	8.51168	−	8.51168i	0.846944	−	0.846944i	−0.142807	−	0.989751i	$-0.545613\pi$
$101$	8.51168	−	8.51168i	0.846944	−	0.846944i	0.989751	+	0.142807i	$0.0456128\pi$
$102$	−3.71666	−	6.28320i	−0.368004	−	0.622130i
$103$	16.2278			1.59897			0.799486	−	0.600685i	$-0.205105\pi$
$103$	16.2278			1.59897			0.799486	+	0.600685i	$0.205105\pi$
$104$	3.42339	−	2.43494i	0.335691	−	0.238765i
$105$	−6.06810	+	2.06548i	−0.592186	+	0.201570i
$106$	−1.87441	−	8.96634i	−0.182059	−	0.870888i
$107$	−7.19945	−	7.19945i	−0.695997	−	0.695997i	0.267548	−	0.963545i	$-0.413787\pi$
$107$	−7.19945	−	7.19945i	−0.695997	−	0.695997i	−0.963545	+	0.267548i	$0.913787\pi$
$108$	8.51201	−	5.96202i	0.819068	−	0.573696i
$109$	−2.14060	+	2.14060i	−0.205033	+	0.205033i	−0.802152	−	0.597120i	$-0.796312\pi$
$109$	−2.14060	+	2.14060i	−0.205033	+	0.205033i	0.597120	+	0.802152i	$0.296312\pi$
$110$	1.79605	−	2.74545i	0.171246	−	0.261768i
$111$	−0.892964	−	2.62341i	−0.0847564	−	0.249003i
$112$	−10.0522	+	10.8669i	−0.949839	+	1.02683i
$113$		−	12.9003i		−	1.21355i	−0.794872	−	0.606777i	$-0.792462\pi$
$113$		−	12.9003i		−	1.21355i	0.794872	−	0.606777i	$-0.207538\pi$
$114$	−15.8401	−	4.06548i	−1.48356	−	0.380767i
$115$	−4.80285	−	4.80285i	−0.447868	−	0.447868i
$116$	−1.78578	+	4.56035i	−0.165806	+	0.423418i
$117$	−4.41869	−	0.574249i	−0.408508	−	0.0530894i
$118$	16.5106	−	3.45155i	1.51993	−	0.317741i
$119$		−	11.0294i		−	1.01107i
$120$	4.83568	−	0.784992i	0.441435	−	0.0716596i
$121$		−	5.61837i		−	0.510761i
$122$	−0.393187	−	1.88083i	−0.0355975	−	0.170282i
$123$	−2.18123	−	1.07341i	−0.196675	−	0.0967861i
$124$	15.2775	−	6.67943i	1.37196	−	0.599830i
$125$	0.707107	+	0.707107i	0.0632456	+	0.0632456i
$126$	15.6549	−	1.20541i	1.39465	−	0.107386i
$127$		−	15.8513i		−	1.40657i	−0.710907	−	0.703287i	$-0.751715\pi$
$127$		−	15.8513i		−	1.40657i	0.710907	−	0.703287i	$-0.248285\pi$
$128$	8.95730	−	6.91136i	0.791721	−	0.610883i
$129$	5.36859	−	1.82738i	0.472678	−	0.160892i
$130$	−1.75778	−	1.14993i	−0.154168	−	0.100855i
$131$	1.49476	−	1.49476i	0.130598	−	0.130598i	−0.638786	−	0.769384i	$-0.720563\pi$
$131$	1.49476	−	1.49476i	0.130598	−	0.130598i	0.769384	+	0.638786i	$0.220563\pi$
$132$	−5.93311	+	5.42013i	−0.516411	+	0.471762i
$133$	−17.4710	−	17.4710i	−1.51493	−	1.51493i
$134$	−17.1183	+	3.57857i	−1.47879	+	0.309141i
$135$	−4.32764	−	2.87603i	−0.372464	−	0.247529i
$136$	−1.40246	+	8.31200i	−0.120260	+	0.712748i
$137$	3.26641			0.279069			0.139534	−	0.990217i	$-0.455439\pi$
$137$	3.26641			0.279069			0.139534	+	0.990217i	$0.455439\pi$
$138$	8.47054	+	14.3199i	0.721060	+	1.21899i
$139$	−12.0760	+	12.0760i	−1.02427	+	1.02427i	−0.0245738	+	0.999698i	$0.507823\pi$
$139$	−12.0760	+	12.0760i	−1.02427	+	1.02427i	−0.999698	+	0.0245738i	$0.992177\pi$
$140$	6.89205	+	2.69885i	0.582484	+	0.228094i
$141$	−16.2426	−	7.99318i	−1.36788	−	0.673147i
$142$	12.5809	+	8.23034i	1.05577	+	0.690675i
$143$	3.44561			0.288137
$144$	−11.9511	−	1.08219i	−0.995925	−	0.0901823i
$145$	2.44877			0.203359
$146$	−10.8010	−	7.06592i	−0.893897	−	0.584780i
$147$	10.4061	+	5.12093i	0.858277	+	0.422367i
$148$	−1.16679	+	2.97962i	−0.0959093	+	0.244924i
$149$	7.13471	−	7.13471i	0.584498	−	0.584498i	−0.351638	−	0.936136i	$-0.614375\pi$
$149$	7.13471	−	7.13471i	0.584498	−	0.584498i	0.936136	+	0.351638i	$0.114375\pi$
$150$	−1.24709	−	2.10826i	−0.101824	−	0.172139i
$151$	1.11742			0.0909345			0.0454672	−	0.998966i	$-0.485522\pi$
$151$	1.11742			0.0909345			0.0454672	+	0.998966i	$0.485522\pi$
$152$	10.9450	+	15.3880i	0.887753	+	1.24813i
$153$	7.08416	−	5.45463i	0.572720	−	0.440981i
$154$	−11.8845	+	2.48445i	−0.957680	+	0.200203i
$155$	−5.89510	−	5.89510i	−0.473506	−	0.473506i
$156$	3.47026	+	3.79870i	0.277843	+	0.304139i
$157$	−4.34837	+	4.34837i	−0.347037	+	0.347037i	−0.859005	−	0.511968i	$-0.828917\pi$
$157$	−4.34837	+	4.34837i	−0.347037	+	0.347037i	0.511968	+	0.859005i	$0.328917\pi$
$158$	−6.05501	−	3.96114i	−0.481711	−	0.315131i
$159$	10.6205	−	3.61503i	0.842259	−	0.286691i
$160$	−4.85081	−	2.91027i	−0.383490	−	0.230077i
$161$			25.1369i			1.98106i
$162$	8.51638	+	9.45892i	0.669110	+	0.743163i
$163$	3.76818	+	3.76818i	0.295147	+	0.295147i	0.839109	−	0.543963i	$-0.183077\pi$
$163$	3.76818	+	3.76818i	0.295147	+	0.295147i	−0.543963	+	0.839109i	$0.683077\pi$
$164$	1.12452	+	2.57205i	0.0878101	+	0.200843i
$165$	3.60518	+	1.77415i	0.280663	+	0.138117i
$166$	2.11112	+	10.0986i	0.163855	+	0.783807i
$167$		−	0.863725i		−	0.0668371i	−0.999441	−	0.0334185i	$-0.989361\pi$
$167$		−	0.863725i		−	0.0668371i	0.999441	−	0.0334185i	$-0.0106394\pi$
$168$	−14.7086	−	10.6001i	−1.13479	−	0.817817i
$169$			10.7939i			0.830302i
$170$	4.12556	−	0.862448i	0.316416	−	0.0661467i
$171$	2.58123	−	19.8619i	0.197392	−	1.51887i
$172$	−6.09756	−	2.38773i	−0.464934	−	0.182063i
$173$	10.7180	+	10.7180i	0.814872	+	0.814872i	0.985360	−	0.170488i	$-0.0545343\pi$
$173$	10.7180	+	10.7180i	0.814872	+	0.814872i	−0.170488	+	0.985360i	$0.554534\pi$
$174$	−5.80992	−	1.49116i	−0.440449	−	0.113044i
$175$		−	3.70081i		−	0.279755i
$176$	9.27231	−	0.361151i	0.698926	−	0.0272228i
$177$	6.65673	+	19.5566i	0.500350	+	1.46996i
$178$	10.4429	−	15.9630i	0.782727	−	1.19648i
$179$	7.19980	−	7.19980i	0.538138	−	0.538138i	−0.384844	−	0.922982i	$-0.625745\pi$
$179$	7.19980	−	7.19980i	0.538138	−	0.538138i	0.922982	+	0.384844i	$0.125745\pi$
$180$	1.67502	+	5.76145i	0.124848	+	0.429433i
$181$	−0.752304	−	0.752304i	−0.0559183	−	0.0559183i	0.678595	−	0.734513i	$-0.262589\pi$
$181$	−0.752304	−	0.752304i	−0.0559183	−	0.0559183i	−0.734513	+	0.678595i	$0.762589\pi$
$182$	1.59068	+	7.60910i	0.117909	+	0.564024i
$183$	2.22781	−	0.758309i	0.164685	−	0.0560558i
$184$	3.19629	−	18.9436i	0.235634	−	1.39654i
$185$	1.59996			0.117632
$186$	10.3969	+	17.5764i	0.762336	+	1.28877i
$187$	−4.88875	+	4.88875i	−0.357501	+	0.357501i
$188$	8.37376	+	19.1529i	0.610719	+	1.39687i
$189$	3.79868	+	18.8511i	0.276313	+	1.37121i
$190$	5.16888	−	7.90117i	0.374990	−	0.573211i
$191$	−8.75399			−0.633416			−0.316708	−	0.948523i	$-0.602578\pi$
$191$	−8.75399			−0.633416			−0.316708	+	0.948523i	$0.602578\pi$
$192$	9.73680	+	9.85874i	0.702693	+	0.711493i
$193$	−0.183333			−0.0131966			−0.00659830	−	0.999978i	$-0.502100\pi$
$193$	−0.183333			−0.0131966			−0.00659830	+	0.999978i	$0.502100\pi$
$194$	4.59481	−	7.02364i	0.329888	−	0.504268i
$195$	1.13590	−	2.30823i	0.0813438	−	0.165296i
$196$	−5.36476	−	12.2705i	−0.383197	−	0.876467i
$197$	−14.8704	+	14.8704i	−1.05948	+	1.05948i	−0.0613594	+	0.998116i	$0.519544\pi$
$197$	−14.8704	+	14.8704i	−1.05948	+	1.05948i	−0.998116	+	0.0613594i	$0.980456\pi$
$198$	−7.47326	−	6.40467i	−0.531101	−	0.455160i
$199$	7.88871			0.559216			0.279608	−	0.960114i	$-0.409795\pi$
$199$	7.88871			0.559216			0.279608	+	0.960114i	$0.409795\pi$
$200$	−0.470579	+	2.78901i	−0.0332750	+	0.197213i
$201$	−6.90170	−	20.2763i	−0.486809	−	1.43018i
$202$	−3.48343	−	16.6631i	−0.245093	−	1.17241i
$203$	−6.40810	−	6.40810i	−0.449760	−	0.449760i
$204$	−10.3135	−	0.465995i	−0.722086	−	0.0326262i
$205$	0.992471	−	0.992471i	0.0693172	−	0.0693172i
$206$	12.5638	−	19.2050i	0.875360	−	1.33808i
$207$	−16.1453	+	12.4315i	−1.12218	+	0.864048i
$208$	−0.231229	−	5.93663i	−0.0160328	−	0.411631i
$209$			15.4879i			1.07132i
$210$	−2.25358	+	8.78052i	−0.155512	+	0.605913i
$211$	6.47164	+	6.47164i	0.445526	+	0.445526i	0.893864	−	0.448338i	$-0.147984\pi$
$211$	6.47164	+	6.47164i	0.445526	+	0.445526i	−0.448338	+	0.893864i	$0.647984\pi$
$212$	−12.0626	−	4.72356i	−0.828460	−	0.324416i
$213$	−8.12998	+	16.5206i	−0.557057	+	1.13197i
$214$	−14.0942	+	2.94639i	−0.963461	+	0.201411i
$215$			3.27420i			0.223298i
$216$	−0.465738	−	14.6896i	−0.0316894	−	0.999498i
$217$			30.8534i			2.09447i
$218$	0.876048	+	4.19062i	0.0593335	+	0.283825i
$219$	6.97976	−	14.1833i	0.471648	−	0.958419i
$220$	−1.85862	−	4.25112i	−0.125308	−	0.286611i
$221$	3.13005	+	3.13005i	0.210550	+	0.210550i
$222$	−3.79606	−	0.974287i	−0.254775	−	0.0653899i
$223$			20.4567i			1.36988i	0.728598	+	0.684941i	$0.240172\pi$
$223$			20.4567i			1.36988i	−0.728598	+	0.684941i	$0.759828\pi$
$224$	5.07815	+	20.3097i	0.339298	+	1.35700i
$225$	2.37702	−	1.83024i	0.158468	−	0.122016i
$226$	−15.2670	−	9.98756i	−1.01555	−	0.664363i
$227$	2.16493	−	2.16493i	0.143692	−	0.143692i	−0.631602	−	0.775293i	$-0.717602\pi$
$227$	2.16493	−	2.16493i	0.143692	−	0.143692i	0.775293	+	0.631602i	$0.217602\pi$
$228$	−17.0750	+	15.5987i	−1.13082	+	1.03305i
$229$	12.4796	+	12.4796i	0.824675	+	0.824675i	0.986774	−	0.162099i	$-0.0518264\pi$
$229$	12.4796	+	12.4796i	0.824675	+	0.824675i	−0.162099	+	0.986774i	$0.551826\pi$
$230$	−9.40244	+	1.96558i	−0.619979	+	0.129606i
$231$	−4.79157	−	14.0770i	−0.315262	−	0.926198i
$232$	4.01445	+	5.64410i	0.263561	+	0.370553i
$233$	−5.18461			−0.339655			−0.169828	−	0.985474i	$-0.554321\pi$
$233$	−5.18461			−0.339655			−0.169828	+	0.985474i	$0.554321\pi$
$234$	−4.10062	+	4.78478i	−0.268066	+	0.312791i
$235$	7.39047	−	7.39047i	0.482101	−	0.482101i
$236$	8.69798	−	22.2120i	0.566190	−	1.44588i
$237$	3.91284	−	7.95113i	0.254166	−	0.516481i
$238$	−13.0530	−	8.53914i	−0.846098	−	0.553510i
$239$	−4.65199			−0.300912			−0.150456	−	0.988617i	$-0.548074\pi$
$239$	−4.65199			−0.300912			−0.150456	+	0.988617i	$0.548074\pi$
$240$	2.81484	−	6.33062i	0.181697	−	0.408639i
$241$	−27.3839			−1.76395			−0.881976	−	0.471294i	$-0.843787\pi$
$241$	−27.3839			−1.76395			−0.881976	+	0.471294i	$0.843787\pi$
$242$	−6.64915	−	4.34982i	−0.427424	−	0.279617i
$243$	−10.2293	+	11.7627i	−0.656211	+	0.754578i
$244$	−2.53031	−	0.990841i	−0.161987	−	0.0634321i
$245$	−4.73480	+	4.73480i	−0.302495	+	0.302495i
$246$	−2.95909	+	1.75037i	−0.188664	+	0.111599i
$247$	9.91619			0.630952
$248$	3.92319	−	23.2517i	0.249123	−	1.47649i
$249$	−11.9617	+	4.07155i	−0.758041	+	0.258024i
$250$	1.38429	−	0.289385i	0.0875501	−	0.0183023i
$251$	17.0804	+	17.0804i	1.07810	+	1.07810i	0.996680	+	0.0814227i	$0.0259464\pi$
$251$	17.0804	+	17.0804i	1.07810	+	1.07810i	0.0814227	+	0.996680i	$0.474054\pi$
$252$	10.6937	−	19.4603i	0.673638	−	1.22588i
$253$	11.1418	−	11.1418i	0.700480	−	0.700480i
$254$	−18.7595	−	12.2723i	−1.17707	−	0.770031i
$255$	1.66333	+	4.88666i	0.104162	+	0.306014i
$256$	−1.24449	−	15.9515i	−0.0777809	−	0.996970i
$257$		−	26.8596i		−	1.67546i	−0.546087	−	0.837728i	$-0.683883\pi$
$257$		−	26.8596i		−	1.67546i	0.546087	−	0.837728i	$-0.316117\pi$
$258$	1.99380	−	7.76833i	0.124128	−	0.483635i
$259$	−4.18690	−	4.18690i	−0.260161	−	0.260161i
$260$	−2.72180	+	1.18999i	−0.168799	+	0.0738000i
$261$	0.946756	−	7.28503i	0.0586027	−	0.450932i
$262$	−0.611736	−	2.92627i	−0.0377932	−	0.180786i
$263$		−	19.0211i		−	1.17289i	−0.809989	−	0.586445i	$-0.800527\pi$
$263$		−	19.0211i		−	1.17289i	0.809989	−	0.586445i	$-0.199473\pi$
$264$	1.82105	+	11.2180i	0.112078	+	0.690418i
$265$			6.47722i			0.397892i
$266$	−34.2026	+	7.15005i	−2.09710	+	0.438398i
$267$	20.9618	+	10.3155i	1.28284	+	0.631300i
$268$	−9.01808	+	23.0295i	−0.550867	+	1.40675i
$269$	−5.00097	−	5.00097i	−0.304914	−	0.304914i	0.538019	−	0.842933i	$-0.319173\pi$
$269$	−5.00097	−	5.00097i	−0.304914	−	0.304914i	−0.842933	+	0.538019i	$0.819173\pi$
$270$	−6.75420	+	2.89495i	−0.411048	+	0.176181i
$271$		−	2.59469i		−	0.157616i	−0.996890	−	0.0788082i	$-0.974889\pi$
$271$		−	2.59469i		−	0.157616i	0.996890	−	0.0788082i	$-0.0251115\pi$
$272$	8.75118	+	8.09503i	0.530618	+	0.490833i
$273$	−9.01285	+	3.06782i	−0.545483	+	0.185673i
$274$	2.52890	−	3.86569i	0.152777	−	0.233535i
$275$	−1.64037	+	1.64037i	−0.0989181	+	0.0989181i
$276$	23.5051	+	1.06203i	1.41484	+	0.0639270i
$277$	−3.10525	−	3.10525i	−0.186576	−	0.186576i	0.607638	−	0.794214i	$-0.292117\pi$
$277$	−3.10525	−	3.10525i	−0.186576	−	0.186576i	−0.794214	+	0.607638i	$0.792117\pi$
$278$	4.94213	+	23.6409i	0.296409	+	1.41789i
$279$	−19.8170	+	15.2586i	−1.18641	+	0.913509i
$280$	8.52991	−	6.06702i	0.509760	−	0.362574i
$281$	20.0286			1.19480			0.597402	−	0.801942i	$-0.296200\pi$
$281$	20.0286			1.19480			0.597402	+	0.801942i	$0.296200\pi$
$282$	−22.0349	+	13.0342i	−1.31216	+	0.776175i
$283$	−7.17636	+	7.17636i	−0.426590	+	0.426590i	−0.887465	−	0.460875i	$-0.847536\pi$
$283$	−7.17636	+	7.17636i	−0.426590	+	0.426590i	0.460875	+	0.887465i	$0.347536\pi$
$284$	19.4807	−	8.51707i	1.15596	−	0.505395i
$285$	10.3754	+	5.10585i	0.614586	+	0.302445i
$286$	2.66764	−	4.07777i	0.157741	−	0.241123i
$287$	−5.19433			−0.306612
$288$	−10.5334	+	13.3059i	−0.620689	+	0.784057i
$289$	8.11797			0.477527
$290$	1.89587	−	2.89803i	0.111329	−	0.170178i
$291$	9.22308	+	4.53878i	0.540666	+	0.266068i
$292$	−16.7246	+	7.31208i	−0.978731	+	0.427907i
$293$	−14.6692	+	14.6692i	−0.856985	+	0.856985i	−0.990982	−	0.133997i	$-0.957219\pi$
$293$	−14.6692	+	14.6692i	−0.856985	+	0.856985i	0.133997	+	0.990982i	$0.457219\pi$
$294$	14.1170	−	8.35052i	0.823318	−	0.487012i
$295$	−11.9272			−0.694427
$296$	2.62294	+	3.68772i	0.152455	+	0.214344i
$297$	6.67191	−	10.0394i	0.387143	−	0.582545i
$298$	−2.91990	−	13.9675i	−0.169145	−	0.809114i
$299$	−7.13359	−	7.13359i	−0.412546	−	0.412546i
$300$	−3.46057	−	0.156360i	−0.199796	−	0.00902743i
$301$	8.56815	−	8.56815i	0.493860	−	0.493860i
$302$	0.865123	−	1.32243i	0.0497822	−	0.0760973i
$303$	19.7372	−	6.71821i	1.13387	−	0.385951i
$304$	26.6850	−	1.03936i	1.53049	−	0.0596116i
$305$			1.35870i			0.0777988i
$306$	−0.970718	−	12.6069i	−0.0554923	−	0.720689i
$307$	21.0583	+	21.0583i	1.20186	+	1.20186i	0.973601	+	0.228259i	$0.0733032\pi$
$307$	21.0583	+	21.0583i	1.20186	+	1.20186i	0.228259	+	0.973601i	$0.426697\pi$
$308$	−6.26088	+	15.9884i	−0.356747	+	0.911024i
$309$	25.2191	+	12.4106i	1.43466	+	0.706013i
$310$	−11.5407	+	2.41258i	−0.655469	+	0.137026i
$311$			12.5077i			0.709245i	0.935010	+	0.354622i	$0.115391\pi$
$311$			12.5077i			0.709245i	−0.935010	+	0.354622i	$0.884609\pi$
$312$	7.18236	−	1.16594i	0.406621	−	0.0660081i
$313$			11.0251i			0.623175i	0.950218	+	0.311587i	$0.100861\pi$
$313$			11.0251i			0.623175i	−0.950218	+	0.311587i	$0.899139\pi$
$314$	1.77958	+	8.51271i	0.100428	+	0.480400i
$315$	−11.0099	−	1.43083i	−0.620335	−	0.0806182i
$316$	−9.37575	+	4.09914i	−0.527427	+	0.230594i
$317$	−4.58153	−	4.58153i	−0.257324	−	0.257324i	0.566641	−	0.823965i	$-0.308243\pi$
$317$	−4.58153	−	4.58153i	−0.257324	−	0.257324i	−0.823965	+	0.566641i	$0.808243\pi$
$318$	3.94426	−	15.3678i	0.221183	−	0.861783i
$319$			5.68073i			0.318060i
$320$	−7.19977	+	3.48760i	−0.402479	+	0.194963i
$321$	−5.68248	−	16.6944i	−0.317165	−	0.931789i
$322$	29.7486	+	19.4613i	1.65783	+	1.08454i
$323$	−14.0694	+	14.0694i	−0.782845	+	0.782845i
$324$	17.7878	−	2.75562i	0.988212	−	0.153090i
$325$	1.05025	+	1.05025i	0.0582576	+	0.0582576i
$326$	7.37690	−	1.54214i	0.408568	−	0.0854112i
$327$	−4.96372	+	1.68957i	−0.274494	+	0.0934332i
$328$	3.91455	+	0.660489i	0.216145	+	0.0364694i
$329$	−38.6798			−2.13249
$330$	4.89082	−	2.89304i	0.269231	−	0.159256i
$331$	−7.38886	+	7.38886i	−0.406129	+	0.406129i	−0.880386	−	0.474258i	$-0.842717\pi$
$331$	−7.38886	+	7.38886i	−0.406129	+	0.406129i	0.474258	+	0.880386i	$0.342717\pi$
$332$	13.5859	+	5.32007i	0.745622	+	0.291977i
$333$	0.618588	−	4.75987i	0.0338984	−	0.260839i
$334$	−1.02219	−	0.668708i	−0.0559318	−	0.0365901i
$335$	12.3661			0.675632
$336$	−23.9325	+	9.20033i	−1.30562	+	0.501919i
$337$	−20.1812			−1.09934			−0.549671	−	0.835382i	$-0.685247\pi$
$337$	−20.1812			−1.09934			−0.549671	+	0.835382i	$0.685247\pi$
$338$	12.7743	+	8.35681i	0.694828	+	0.454551i
$339$	9.86577	−	20.0479i	0.535835	−	1.08885i
$340$	2.17339	−	5.55018i	0.117869	−	0.301001i
$341$	13.6756	−	13.6756i	0.740578	−	0.740578i
$342$	−21.5074	−	18.4321i	−1.16299	−	0.996695i
$343$	−1.12498			−0.0607433
$344$	−7.54662	+	5.36764i	−0.406886	+	0.289404i
$345$	−3.79086	−	11.1370i	−0.204093	−	0.599598i
$346$	20.9824	−	4.38636i	1.12802	−	0.235812i
$347$	2.82091	+	2.82091i	0.151434	+	0.151434i	0.778758	−	0.627324i	$-0.215850\pi$
$347$	2.82091	+	2.82091i	0.151434	+	0.151434i	−0.627324	+	0.778758i	$0.715850\pi$
$348$	−6.26285	+	5.72137i	−0.335724	+	0.306698i
$349$	13.0364	−	13.0364i	0.697820	−	0.697820i	−0.266120	−	0.963940i	$-0.585742\pi$
$349$	13.0364	−	13.0364i	0.697820	−	0.697820i	0.963940	+	0.266120i	$0.0857418\pi$
$350$	−4.37979	−	2.86522i	−0.234110	−	0.153152i
$351$	−6.42777	−	4.27172i	−0.343089	−	0.228007i
$352$	6.75134	−	11.2531i	0.359847	−	0.599791i
$353$		−	33.6872i		−	1.79299i	−0.443056	−	0.896494i	$-0.646106\pi$
$353$		−	33.6872i		−	1.79299i	0.443056	−	0.896494i	$-0.353894\pi$
$354$	28.2983	+	7.26296i	1.50404	+	0.386022i
$355$	−7.51695	−	7.51695i	−0.398959	−	0.398959i
$356$	−10.8067	−	24.7176i	−0.572753	−	1.31003i
$357$	8.43502	−	17.1405i	0.446428	−	0.907170i
$358$	−2.94654	−	14.0949i	−0.155729	−	0.744939i
$359$		−	7.29801i		−	0.385174i	−0.981280	−	0.192587i	$-0.938312\pi$
$359$		−	7.29801i		−	0.385174i	0.981280	−	0.192587i	$-0.0616878\pi$
$360$	8.11531	+	2.47827i	0.427714	+	0.130616i
$361$			25.5729i			1.34594i
$362$	−1.47277	+	0.307883i	−0.0774071	+	0.0161820i
$363$	4.29678	−	8.73132i	0.225522	−	0.458275i
$364$	10.2366	+	4.00855i	0.536546	+	0.210105i
$365$	6.45346	+	6.45346i	0.337790	+	0.337790i
$366$	0.827369	−	3.22363i	0.0432473	−	0.168502i
$367$			7.97995i			0.416550i	0.978070	+	0.208275i	$0.0667849\pi$
$367$			7.97995i			0.416550i	−0.978070	+	0.208275i	$0.933215\pi$
$368$	−19.9445	−	18.4491i	−1.03968	−	0.961728i
$369$	−2.56887	−	3.33630i	−0.133730	−	0.173681i
$370$	1.23871	−	1.89350i	0.0643977	−	0.0984386i
$371$	16.9500	−	16.9500i	0.880002	−	0.880002i
$372$	28.8505	+	1.30356i	1.49583	+	0.0675864i
$373$	−3.87290	−	3.87290i	−0.200531	−	0.200531i	0.599696	−	0.800228i	$-0.295288\pi$
$373$	−3.87290	−	3.87290i	−0.200531	−	0.200531i	−0.800228	+	0.599696i	$0.795288\pi$
$374$	2.00074	+	9.57062i	0.103456	+	0.494885i
$375$	0.558115	+	1.63967i	0.0288209	+	0.0846720i
$376$	29.1499	+	4.91836i	1.50329	+	0.253645i
$377$	3.63711			0.187321
$378$	25.2506	+	10.0991i	1.29875	+	0.519444i
$379$	0.762975	−	0.762975i	0.0391914	−	0.0391914i	−0.687240	−	0.726431i	$-0.741178\pi$
$379$	0.762975	−	0.762975i	0.0391914	−	0.0391914i	0.726431	+	0.687240i	$0.241178\pi$
$380$	−5.34896	−	12.2344i	−0.274396	−	0.627611i
$381$	12.1226	−	24.6339i	0.621061	−	1.26203i
$382$	−6.77746	+	10.3601i	−0.346765	+	0.530066i
$383$	7.74701			0.395854			0.197927	−	0.980217i	$-0.436579\pi$
$383$	7.74701			0.395854			0.197927	+	0.980217i	$0.436579\pi$
$384$	19.2059	−	3.89041i	0.980095	−	0.198531i
$385$	8.58527			0.437546
$386$	−0.141939	+	0.216968i	−0.00722450	+	0.0110434i
$387$	9.74068	+	1.26589i	0.495147	+	0.0643488i
$388$	−4.75488	−	10.8756i	−0.241393	−	0.552125i
$389$	−12.4634	+	12.4634i	−0.631919	+	0.631919i	−0.948549	−	0.316630i	$-0.897449\pi$
$389$	−12.4634	+	12.4634i	−0.631919	+	0.631919i	0.316630	+	0.948549i	$0.397449\pi$
$390$	−1.85228	−	3.13137i	−0.0937938	−	0.158563i
$391$	20.2428			1.02372
$392$	−18.6752	−	3.15101i	−0.943242	−	0.159150i
$393$	3.46612	−	1.17981i	0.174843	−	0.0595134i
$394$	6.08577	+	29.1116i	0.306597	+	1.46662i
$395$	3.61780	+	3.61780i	0.182031	+	0.182031i
$396$	−13.3656	+	3.88576i	−0.671647	+	0.195267i
$397$	4.06000	−	4.06000i	0.203766	−	0.203766i	−0.597846	−	0.801611i	$-0.703976\pi$
$397$	4.06000	−	4.06000i	0.203766	−	0.203766i	0.801611	+	0.597846i	$0.203976\pi$
$398$	6.10755	−	9.33603i	0.306144	−	0.467973i
$399$	−13.7897	−	40.5124i	−0.690351	−	2.02816i
$400$	2.93637	+	2.71620i	0.146818	+	0.135810i
$401$			10.5026i			0.524475i	0.965003	+	0.262238i	$0.0844605\pi$
$401$			10.5026i			0.524475i	−0.965003	+	0.262238i	$0.915540\pi$
$402$	−29.3397	−	7.53025i	−1.46333	−	0.375575i
$403$	−8.75589	−	8.75589i	−0.436162	−	0.436162i
$404$	−22.4172	−	8.77832i	−1.11530	−	0.436738i
$405$	−4.52593	−	7.77920i	−0.224895	−	0.386552i
$406$	−12.5450	+	2.62253i	−0.622599	+	0.130154i
$407$			3.71165i			0.183980i
$408$	−8.53630	+	11.8448i	−0.422610	+	0.586407i
$409$			3.48657i			0.172400i	0.996278	+	0.0861999i	$0.0274724\pi$
$409$			3.48657i			0.172400i	−0.996278	+	0.0861999i	$0.972528\pi$
$410$	−0.406171	−	1.94294i	−0.0200594	−	0.0959550i
$411$	5.07622	+	2.49806i	0.250392	+	0.123220i
$412$	−13.0015	−	29.7376i	−0.640537	−	1.46507i
$413$	31.2118	+	31.2118i	1.53583	+	1.53583i
$414$	2.21234	+	28.7320i	0.108730	+	1.41210i
$415$		−	7.29519i		−	0.358107i
$416$	−7.20483	−	4.32257i	−0.353246	−	0.211932i
$417$	−28.0023	+	9.53150i	−1.37128	+	0.466759i
$418$	18.3294	+	11.9909i	0.896521	+	0.586496i
$419$	−25.7359	+	25.7359i	−1.25728	+	1.25728i	−0.304894	+	0.952386i	$0.598621\pi$
$419$	−25.7359	+	25.7359i	−1.25728	+	1.25728i	−0.952386	+	0.304894i	$0.901379\pi$
$420$	8.64669	+	9.46504i	0.421915	+	0.461847i
$421$	−13.0915	−	13.0915i	−0.638040	−	0.638040i	0.312032	−	0.950072i	$-0.398990\pi$
$421$	−13.0915	−	13.0915i	−0.638040	−	0.638040i	−0.950072	+	0.312032i	$0.898990\pi$
$422$	12.6694	−	2.64854i	0.616737	−	0.128929i
$423$	−19.1292	−	24.8439i	−0.930092	−	1.20795i
$424$	−14.9292	+	10.6186i	−0.725025	+	0.515684i
$425$	−2.98027			−0.144565
$426$	13.2573	+	22.4121i	0.642317	+	1.08587i
$427$	3.55553	−	3.55553i	0.172064	−	0.172064i
$428$	−7.42498	+	18.9612i	−0.358900	+	0.916523i
$429$	5.35471	+	2.63511i	0.258528	+	0.127224i
$430$	3.87490	+	2.53493i	0.186864	+	0.122245i
$431$	−23.9332			−1.15282			−0.576410	−	0.817161i	$-0.695547\pi$
$431$	−23.9332			−1.15282			−0.576410	+	0.817161i	$0.695547\pi$
$432$	−17.7452	−	10.8217i	−0.853765	−	0.520658i
$433$	26.4273			1.27001			0.635006	−	0.772507i	$-0.280997\pi$
$433$	26.4273			1.27001			0.635006	+	0.772507i	$0.280997\pi$
$434$	36.5140	+	23.8871i	1.75273	+	1.14662i
$435$	3.80554	+	1.87275i	0.182462	+	0.0897915i
$436$	5.63771	+	2.20766i	0.269997	+	0.105728i
$437$	32.0652	−	32.0652i	1.53389	−	1.53389i
$438$	−11.3816	−	19.2412i	−0.543836	−	0.919381i
$439$	−33.3846			−1.59336			−0.796680	−	0.604402i	$-0.793412\pi$
$439$	−33.3846			−1.59336			−0.796680	+	0.604402i	$0.793412\pi$
$440$	−6.47003	−	1.09167i	−0.308447	−	0.0520431i
$441$	12.2553	+	15.9165i	0.583588	+	0.757931i
$442$	6.12763	−	1.28098i	0.291462	−	0.0609300i
$443$	−5.30972	−	5.30972i	−0.252273	−	0.252273i	0.569629	−	0.821902i	$-0.307087\pi$
$443$	−5.30972	−	5.30972i	−0.252273	−	0.252273i	−0.821902	+	0.569629i	$0.807087\pi$
$444$	−4.09200	+	3.73821i	−0.194198	+	0.177407i
$445$	−9.53771	+	9.53771i	−0.452131	+	0.452131i
$446$	24.2098	+	15.8379i	1.14637	+	0.749944i
$447$	16.5442	−	5.63138i	0.782516	−	0.266355i
$448$	27.9675	+	9.71425i	1.32134	+	0.458955i
$449$		−	3.93567i		−	0.185736i	−0.995678	−	0.0928680i	$-0.970397\pi$
$449$		−	3.93567i		−	0.185736i	0.995678	−	0.0928680i	$-0.0296035\pi$
$450$	−0.325714	−	4.23012i	−0.0153543	−	0.199410i
$451$	2.30237	+	2.30237i	0.108414	+	0.108414i
$452$	−23.6399	+	10.3355i	−1.11193	+	0.486141i
$453$	1.73655	+	0.854574i	0.0815901	+	0.0401514i
$454$	−0.886004	−	4.23824i	−0.0415822	−	0.198911i
$455$		−	5.49676i		−	0.257692i
$456$	5.24084	+	32.2844i	0.245425	+	1.51186i
$457$		−	1.96560i		−	0.0919467i	−0.998943	−	0.0459734i	$-0.985361\pi$
$457$		−	1.96560i		−	0.0919467i	0.998943	−	0.0459734i	$-0.0146389\pi$
$458$	24.4311	−	5.10731i	1.14159	−	0.238649i
$459$	15.1808	−	3.05908i	0.708579	−	0.142786i
$460$	−4.95330	+	12.6493i	−0.230949	+	0.589775i
$461$	−22.3863	−	22.3863i	−1.04263	−	1.04263i	−0.999050	−	0.0435846i	$-0.986122\pi$
$461$	−22.3863	−	22.3863i	−1.04263	−	1.04263i	−0.0435846	−	0.999050i	$-0.513878\pi$
$462$	−20.3693	−	5.22794i	−0.947668	−	0.243226i
$463$			0.425933i			0.0197948i	0.999951	+	0.00989739i	$0.00315049\pi$
$463$			0.425933i			0.0197948i	−0.999951	+	0.00989739i	$0.996850\pi$
$464$	9.78764	−	0.381223i	0.454380	−	0.0176978i
$465$	−4.65296	−	13.6698i	−0.215776	−	0.633921i
$466$	−4.01400	+	6.13581i	−0.185945	+	0.284236i
$467$	3.37383	−	3.37383i	0.156122	−	0.156122i	−0.624724	−	0.780846i	$-0.714788\pi$
$467$	3.37383	−	3.37383i	0.156122	−	0.156122i	0.780846	+	0.624724i	$0.214788\pi$
$468$	2.48788	+	8.55739i	0.115002	+	0.395565i
$469$	−32.3605	−	32.3605i	−1.49427	−	1.49427i
$470$	−3.02457	−	14.4682i	−0.139513	−	0.667367i
$471$	−10.0832	+	3.43214i	−0.464607	+	0.158144i
$472$	−19.5531	−	27.4906i	−0.900005	−	1.26536i
$473$	−7.59559			−0.349246
$474$	−6.38052	−	10.7866i	−0.293067	−	0.495444i
$475$	−4.72085	+	4.72085i	−0.216608	+	0.216608i
$476$	−20.2116	+	8.83663i	−0.926396	+	0.405026i
$477$	19.2696	+	2.50426i	0.882295	+	0.114662i
$478$	−3.60164	+	5.50548i	−0.164735	+	0.251815i
$479$	−3.91064			−0.178682			−0.0893408	−	0.996001i	$-0.528476\pi$
$479$	−3.91064			−0.178682			−0.0893408	+	0.996001i	$0.528476\pi$
$480$	−5.31279	−	8.23252i	−0.242494	−	0.375761i
$481$	2.37640			0.108355
$482$	−21.2010	+	32.4079i	−0.965679	+	1.47614i
$483$	−19.2240	+	39.0644i	−0.874722	+	1.77749i
$484$	−10.2957	+	4.50136i	−0.467988	+	0.204607i
$485$	−4.19654	+	4.19654i	−0.190555	+	0.190555i
$486$	6.00109	+	21.2129i	0.272215	+	0.962236i
$487$	−15.7341			−0.712981			−0.356491	−	0.934299i	$-0.616027\pi$
$487$	−15.7341			−0.712981			−0.356491	+	0.934299i	$0.616027\pi$
$488$	−3.13163	+	2.22742i	−0.141762	+	0.100830i
$489$	2.97420	+	8.73781i	0.134498	+	0.395137i
$490$	1.93773	+	9.26922i	0.0875377	+	0.418741i
$491$	18.0662	+	18.0662i	0.815316	+	0.815316i	0.985425	−	0.170109i	$-0.0544119\pi$
$491$	18.0662	+	18.0662i	0.815316	+	0.815316i	−0.170109	+	0.985425i	$0.554412\pi$
$492$	−0.219461	+	4.85714i	−0.00989407	+	0.218977i
$493$	−5.16046	+	5.16046i	−0.232415	+	0.232415i
$494$	7.67725	−	11.7355i	0.345416	−	0.528004i
$495$	4.24586	+	5.51428i	0.190837	+	0.247849i
$496$	−24.4803	−	22.6448i	−1.09920	−	1.01678i
$497$			39.3418i			1.76472i
$498$	−4.44235	+	17.3085i	−0.199067	+	0.775612i
$499$	7.40048	+	7.40048i	0.331291	+	0.331291i	0.853077	−	0.521786i	$-0.174734\pi$
$499$	7.40048	+	7.40048i	0.331291	+	0.331291i	−0.521786	+	0.853077i	$0.674734\pi$
$500$	0.729258	−	1.86231i	0.0326134	−	0.0832849i
$501$	0.660554	−	1.34229i	0.0295114	−	0.0599689i
$502$	33.4379	−	6.99018i	1.49241	−	0.311987i
$503$			15.3725i			0.685426i	0.939440	+	0.342713i	$0.111346\pi$
$503$			15.3725i			0.685426i	−0.939440	+	0.342713i	$0.888654\pi$
$504$	−14.7514	−	27.7220i	−0.657079	−	1.23484i
$505$			12.0373i			0.535654i
$506$	−4.55982	−	21.8121i	−0.202709	−	0.969667i
$507$	−8.25491	+	16.7745i	−0.366613	+	0.744981i
$508$	−29.0477	+	12.6998i	−1.28878	+	0.563463i
$509$	−27.2034	−	27.2034i	−1.20577	−	1.20577i	−0.972385	−	0.233382i	$-0.925021\pi$
$509$	−27.2034	−	27.2034i	−1.20577	−	1.20577i	−0.233382	−	0.972385i	$-0.574979\pi$
$510$	7.07097	+	1.81482i	0.313108	+	0.0803614i
$511$		−	33.7757i		−	1.49415i
$512$	−19.8416	−	10.8771i	−0.876883	−	0.480703i
$513$	19.2012	−	28.8926i	0.847755	−	1.27564i
$514$	−31.7875	−	20.7951i	−1.40208	−	0.917232i
$515$	−11.4748	+	11.4748i	−0.505639	+	0.505639i
$516$	−7.64993	−	8.37394i	−0.336770	−	0.368642i
$517$	17.1447	+	17.1447i	0.754022	+	0.754022i
$518$	−8.19661	+	1.71350i	−0.360138	+	0.0752869i
$519$	8.45962	+	24.8533i	0.371336	+	1.09094i
$520$	−0.698944	+	4.14247i	−0.0306507	+	0.181659i
$521$	−24.2497			−1.06240			−0.531200	−	0.847246i	$-0.678259\pi$
$521$	−24.2497			−1.06240			−0.531200	+	0.847246i	$0.678259\pi$
$522$	−7.88860	−	6.76063i	−0.345275	−	0.295905i
$523$	−1.27250	+	1.27250i	−0.0556426	+	0.0556426i	−0.734381	−	0.678738i	$-0.762527\pi$
$523$	−1.27250	+	1.27250i	−0.0556426	+	0.0556426i	0.678738	+	0.734381i	$0.262527\pi$
$524$	−3.93676	−	1.54159i	−0.171978	−	0.0673447i
$525$	2.83028	−	5.75131i	0.123524	−	0.251008i
$526$	−22.5108	−	14.7264i	−0.981518	−	0.642100i
$527$	24.8463			1.08232
$528$	14.6860	+	6.52996i	0.639125	+	0.284180i
$529$	−23.1347			−1.00586
$530$	7.66557	+	5.01475i	0.332971	+	0.217827i
$531$	−4.61135	+	35.4831i	−0.200116	+	1.53984i
$532$	−18.0183	+	46.0133i	−0.781192	+	1.99493i
$533$	1.47410	−	1.47410i	0.0638504	−	0.0638504i
$534$	28.4370	−	16.8212i	1.23059	−	0.727923i
$535$	10.1816			0.440187
$536$	20.2727	+	28.5023i	0.875646	+	1.23111i
$537$	16.6952	−	5.68275i	0.720450	−	0.245229i
$538$	−9.79030	+	2.04666i	−0.422090	+	0.0882378i
$539$	−10.9839	−	10.9839i	−0.473112	−	0.473112i
$540$	−1.80311	+	10.2347i	−0.0775937	+	0.440431i
$541$	−3.67154	+	3.67154i	−0.157852	+	0.157852i	−0.781614	−	0.623762i	$-0.785603\pi$
$541$	−3.67154	+	3.67154i	−0.157852	+	0.157852i	0.623762	+	0.781614i	$0.285603\pi$
$542$	−3.07073	−	2.00885i	−0.131899	−	0.0862874i
$543$	−0.593789	−	1.74447i	−0.0254819	−	0.0748625i
$544$	16.3555	−	4.08944i	0.701235	−	0.175333i
$545$		−	3.02727i		−	0.129674i
$546$	−3.34721	+	13.0416i	−0.143247	+	0.558127i
$547$	−27.6536	−	27.6536i	−1.18238	−	1.18238i	−0.979125	−	0.203258i	$-0.934847\pi$
$547$	−27.6536	−	27.6536i	−1.18238	−	1.18238i	−0.203258	−	0.979125i	$-0.565153\pi$
$548$	−2.61700	−	5.98574i	−0.111793	−	0.255698i
$549$	4.04210	+	0.525308i	0.172513	+	0.0224196i
$550$	0.671326	+	3.21132i	0.0286254	+	0.136931i
$551$			16.3487i			0.696477i
$552$	19.4548	−	26.9952i	0.828053	−	1.14899i
$553$		−	18.9346i		−	0.805181i
$554$	−6.07909	+	1.27083i	−0.258276	+	0.0539925i
$555$	2.48645	+	1.22361i	0.105544	+	0.0519393i
$556$	31.8045	+	12.4543i	1.34881	+	0.528179i
$557$	4.63673	+	4.63673i	0.196464	+	0.196464i	0.798482	−	0.602018i	$-0.205636\pi$
$557$	4.63673	+	4.63673i	0.196464	+	0.196464i	−0.602018	+	0.798482i	$0.705636\pi$
$558$	2.71546	+	35.2662i	0.114954	+	1.49294i
$559$			4.86311i			0.205688i
$560$	−0.576142	−	14.7920i	−0.0243464	−	0.625078i
$561$	−11.3362	+	3.85866i	−0.478616	+	0.162913i
$562$	15.5064	−	23.7031i	0.654098	−	0.999857i
$563$	25.4102	−	25.4102i	1.07091	−	1.07091i	0.0736280	−	0.997286i	$-0.476542\pi$
$563$	25.4102	−	25.4102i	1.07091	−	1.07091i	0.997286	−	0.0736280i	$-0.0234577\pi$
$564$	−1.63422	+	36.1689i	−0.0688133	+	1.52298i
$565$	9.12186	+	9.12186i	0.383760	+	0.383760i
$566$	2.93695	+	14.0490i	0.123449	+	0.590524i
$567$	−8.51339	+	32.2009i	−0.357529	+	1.35231i
$568$	5.00253	−	29.6488i	0.209902	−	1.24403i
$569$	32.5082			1.36281			0.681406	−	0.731905i	$-0.261369\pi$
$569$	32.5082			1.36281			0.681406	+	0.731905i	$0.261369\pi$
$570$	14.0754	−	8.32593i	0.589553	−	0.348735i
$571$	10.2759	−	10.2759i	0.430034	−	0.430034i	−0.458606	−	0.888640i	$-0.651651\pi$
$571$	10.2759	−	10.2759i	0.430034	−	0.430034i	0.888640	+	0.458606i	$0.151651\pi$
$572$	−2.76058	−	6.31413i	−0.115425	−	0.264007i
$573$	−13.6043	−	6.69481i	−0.568327	−	0.279680i
$574$	−4.02153	+	6.14732i	−0.167855	+	0.256584i
$575$	6.79225			0.283257
$576$	7.59194	+	22.7676i	0.316331	+	0.948649i
$577$	13.2950			0.553479			0.276739	−	0.960945i	$-0.410746\pi$
$577$	13.2950			0.553479			0.276739	+	0.960945i	$0.410746\pi$
$578$	6.28504	−	9.60734i	0.261423	−	0.399613i
$579$	−0.284912	−	0.140208i	−0.0118405	−	0.00582685i
$580$	−1.96192	−	4.48739i	−0.0814642	−	0.186329i
$581$	−19.0906	+	19.0906i	−0.792010	+	0.792010i
$582$	12.5121	−	7.40122i	0.518644	−	0.306790i
$583$	−15.0261			−0.622316
$584$	−4.29478	+	25.4541i	−0.177719	+	1.05330i
$585$	3.53054	−	2.71843i	0.145970	−	0.112393i
$586$	6.00342	+	28.7176i	0.247999	+	1.18631i
$587$	4.18164	+	4.18164i	0.172595	+	0.172595i	0.788118	−	0.615524i	$-0.211055\pi$
$587$	4.18164	+	4.18164i	0.172595	+	0.172595i	−0.615524	+	0.788118i	$0.711055\pi$
$588$	1.04699	−	23.1720i	0.0431770	−	0.955599i
$589$	39.3574	−	39.3574i	1.62169	−	1.62169i
$590$	−9.23418	+	14.1154i	−0.380165	+	0.581122i
$591$	−34.4822	+	11.7371i	−1.41841	+	0.482801i
$592$	6.39501	−	0.249082i	0.262833	−	0.0102372i
$593$		−	11.5415i		−	0.473953i	−0.971515	−	0.236976i	$-0.923844\pi$
$593$		−	11.5415i		−	0.473953i	0.971515	−	0.236976i	$-0.0761564\pi$
$594$	−6.71581	−	15.6686i	−0.275553	−	0.642892i
$595$	7.79899	+	7.79899i	0.319727	+	0.319727i
$596$	−18.7907	−	7.35821i	−0.769696	−	0.301404i
$597$	12.2596	+	6.03308i	0.501751	+	0.246917i
$598$	−13.9653	+	2.91944i	−0.571083	+	0.119385i
$599$		−	30.4906i		−	1.24581i	−0.782297	−	0.622906i	$-0.785952\pi$
$599$		−	30.4906i		−	1.24581i	0.782297	−	0.622906i	$-0.214048\pi$
$600$	−2.86427	+	3.97441i	−0.116933	+	0.162255i
$601$			4.74836i			0.193690i	0.995299	+	0.0968449i	$0.0308751\pi$
$601$			4.74836i			0.193690i	−0.995299	+	0.0968449i	$0.969125\pi$
$602$	−3.50654	−	16.7737i	−0.142916	−	0.683645i
$603$	4.78106	−	36.7889i	0.194700	−	1.49816i
$604$	−0.895262	−	2.04769i	−0.0364277	−	0.0833193i
$605$	3.97279	+	3.97279i	0.161517	+	0.161517i
$606$	7.33005	−	28.5597i	0.297763	−	1.16016i
$607$		−	32.6306i		−	1.32444i	−0.749311	−	0.662219i	$-0.769615\pi$
$607$		−	32.6306i		−	1.32444i	0.749311	−	0.662219i	$-0.230385\pi$
$608$	19.4298	−	32.3854i	0.787983	−	1.31340i
$609$	−5.05787	−	14.8594i	−0.204955	−	0.602131i
$610$	1.60797	+	1.05192i	0.0651049	+	0.0425911i
$611$	10.9769	−	10.9769i	0.444080	−	0.444080i
$612$	−15.6714	−	8.61164i	−0.633479	−	0.348105i
$613$	−3.48260	−	3.48260i	−0.140661	−	0.140661i	0.633270	−	0.773931i	$-0.281712\pi$
$613$	−3.48260	−	3.48260i	−0.140661	−	0.140661i	−0.773931	+	0.633270i	$0.781712\pi$
$614$	41.2254	−	8.61816i	1.66372	−	0.347800i
$615$	2.30138	−	0.783351i	0.0928006	−	0.0315877i
$616$	14.0745	+	19.7880i	0.567077	+	0.797280i
$617$	−19.4357			−0.782450			−0.391225	−	0.920295i	$-0.627949\pi$
$617$	−19.4357			−0.782450			−0.391225	+	0.920295i	$0.627949\pi$
$618$	34.2124	−	20.2375i	1.37623	−	0.814070i
$619$	−3.75292	+	3.75292i	−0.150843	+	0.150843i	−0.778494	−	0.627652i	$-0.784016\pi$
$619$	−3.75292	+	3.75292i	−0.150843	+	0.150843i	0.627652	+	0.778494i	$0.284016\pi$
$620$	−6.07977	+	15.5259i	−0.244169	+	0.623535i
$621$	−34.5981	+	6.97187i	−1.38838	+	0.279771i
$622$	14.8024	+	9.68361i	0.593522	+	0.388277i
$623$	49.9179			1.99992
$624$	4.18083	−	9.40276i	0.167367	−	0.376412i
$625$	−1.00000			−0.0400000
$626$	13.0478	+	8.53577i	0.521496	+	0.341158i
$627$	−11.8447	+	24.0692i	−0.473033	+	0.961232i
$628$	11.4523	+	4.48458i	0.456996	+	0.178954i
$629$	−3.37172	+	3.37172i	−0.134439	+	0.134439i
$630$	−10.2173	+	11.9220i	−0.407068	+	0.474985i
$631$	−25.7871			−1.02657			−0.513285	−	0.858218i	$-0.671572\pi$
$631$	−25.7871			−1.02657			−0.513285	+	0.858218i	$0.671572\pi$
$632$	−2.40764	+	14.2695i	−0.0957709	+	0.567610i
$633$	5.10802	+	15.0067i	0.203026	+	0.596463i
$634$	−8.96918	+	1.87500i	−0.356211	+	0.0744659i
$635$	11.2085	+	11.2085i	0.444797	+	0.444797i
$636$	−15.1336	−	16.5659i	−0.600085	−	0.656879i
$637$	−7.03252	+	7.03252i	−0.278639	+	0.278639i
$638$	6.72295	+	4.39810i	0.266164	+	0.174122i
$639$	−25.2691	+	19.4566i	−0.999628	+	0.769690i
$640$	−1.44670	+	11.2208i	−0.0571858	+	0.443542i
$641$		−	2.90236i		−	0.114636i	−0.998356	−	0.0573181i	$-0.981745\pi$
$641$		−	2.90236i		−	0.114636i	0.998356	−	0.0573181i	$-0.0182549\pi$
$642$	−24.1567	−	6.19999i	−0.953388	−	0.244694i
$643$	19.1059	+	19.1059i	0.753464	+	0.753464i	0.975124	−	0.221660i	$-0.0711475\pi$
$643$	19.1059	+	19.1059i	0.753464	+	0.753464i	−0.221660	+	0.975124i	$0.571148\pi$
$644$	46.0636	−	20.1393i	1.81516	−	0.793600i
$645$	−2.50402	+	5.08832i	−0.0985956	+	0.200352i
$646$	5.75796	+	27.5435i	0.226544	+	1.08368i
$647$		−	15.4569i		−	0.607673i	−0.952724	−	0.303836i	$-0.901732\pi$
$647$		−	15.4569i		−	0.607673i	0.952724	−	0.303836i	$-0.0982677\pi$
$648$	10.5104	−	23.1847i	0.412887	−	0.910782i
$649$		−	27.6691i		−	1.08611i
$650$	2.05606	−	0.429819i	0.0806454	−	0.0168589i
$651$	−23.5959	+	47.9482i	−0.924794	+	1.87924i
$652$	3.88622	−	9.92425i	0.152196	−	0.388664i
$653$	−10.2237	−	10.2237i	−0.400084	−	0.400084i	0.478178	−	0.878263i	$-0.341297\pi$
$653$	−10.2237	−	10.2237i	−0.400084	−	0.400084i	−0.878263	+	0.478178i	$0.841297\pi$
$654$	−1.84344	+	7.18248i	−0.0720840	+	0.280857i
$655$			2.11392i			0.0825975i
$656$	3.81237	−	4.12138i	0.148848	−	0.160913i
$657$	21.6940	−	16.7039i	0.846364	−	0.651680i
$658$	−29.9464	+	45.7763i	−1.16743	+	1.78454i
$659$	−12.2198	+	12.2198i	−0.476016	+	0.476016i	−0.903855	−	0.427839i	$-0.859275\pi$
$659$	−12.2198	+	12.2198i	−0.476016	+	0.476016i	0.427839	+	0.903855i	$0.359275\pi$
$660$	0.362728	−	8.02795i	0.0141192	−	0.312488i
$661$	20.1618	+	20.1618i	0.784203	+	0.784203i	0.980537	−	0.196334i	$-0.0629036\pi$
$661$	20.1618	+	20.1618i	0.784203	+	0.784203i	−0.196334	+	0.980537i	$0.562904\pi$
$662$	3.02391	+	14.4650i	0.117528	+	0.562199i
$663$	2.47052	+	7.25807i	0.0959472	+	0.281880i
$664$	16.8145	−	11.9596i	0.652529	−	0.464121i
$665$	24.7077			0.958124
$666$	−5.15422	−	4.41723i	−0.199722	−	0.171164i
$667$	11.7611	−	11.7611i	0.455390	−	0.455390i
$668$	−1.58279	+	0.692005i	−0.0612399	+	0.0267745i
$669$	−15.6447	+	31.7911i	−0.604860	+	1.22911i
$670$	9.57401	−	14.6349i	0.369876	−	0.565394i
$671$	−3.15195			−0.121680
$672$	−7.64056	+	35.4463i	−0.294741	+	1.36737i
$673$	−43.0800			−1.66061			−0.830306	−	0.557307i	$-0.811835\pi$
$673$	−43.0800			−1.66061			−0.830306	+	0.557307i	$0.811835\pi$
$674$	−15.6246	+	23.8838i	−0.601836	+	0.919969i
$675$	5.09376	−	1.02644i	0.196059	−	0.0395078i
$676$	19.7800	−	8.64795i	0.760770	−	0.332613i
$677$	7.68277	−	7.68277i	0.295273	−	0.295273i	−0.543886	−	0.839159i	$-0.683048\pi$
$677$	7.68277	−	7.68277i	0.295273	−	0.295273i	0.839159	+	0.543886i	$0.183048\pi$
$678$	−16.0878	−	27.1971i	−0.617847	−	1.04450i
$679$	21.9636			0.842886
$680$	−4.88579	−	6.86916i	−0.187361	−	0.263420i
$681$	5.02013	−	1.70877i	0.192372	−	0.0654800i
$682$	−5.59680	−	26.7725i	−0.214312	−	1.02517i
$683$	−24.8441	−	24.8441i	−0.950634	−	0.950634i	0.0482031	−	0.998838i	$-0.484651\pi$
$683$	−24.8441	−	24.8441i	−0.950634	−	0.950634i	−0.998838	+	0.0482031i	$0.984651\pi$
$684$	−38.4652	+	11.1829i	−1.47075	+	0.427589i
$685$	−2.30970	+	2.30970i	−0.0882492	+	0.0882492i
$686$	−0.870976	+	1.33138i	−0.0332540	+	0.0508323i
$687$	9.85007	+	28.9382i	0.375804	+	1.10406i
$688$	0.509726	+	13.0869i	0.0194331	+	0.498932i
$689$			9.62051i			0.366512i
$690$	−16.1152	−	4.13609i	−0.613497	−	0.157458i
$691$	9.51097	+	9.51097i	0.361814	+	0.361814i	0.864481	−	0.502666i	$-0.167648\pi$
$691$	9.51097	+	9.51097i	0.361814	+	0.361814i	−0.502666	+	0.864481i	$0.667648\pi$
$692$	11.0537	−	28.2279i	0.420200	−	1.07306i
$693$	3.31929	−	25.5410i	0.126089	−	0.970224i
$694$	5.52244	−	1.15447i	0.209629	−	0.0438229i
$695$		−	17.0780i		−	0.647806i
$696$	1.92226	+	11.8414i	0.0728631	+	0.448849i
$697$			4.18301i			0.158443i
$698$	−5.33516	−	25.5210i	−0.201939	−	0.965984i
$699$	−8.05723	−	3.96505i	−0.304752	−	0.149972i
$700$	−6.78179	+	2.96504i	−0.256327	+	0.112068i
$701$	31.5931	+	31.5931i	1.19326	+	1.19326i	0.976147	+	0.217109i	$0.0696626\pi$
$701$	31.5931	+	31.5931i	1.19326	+	1.19326i	0.217109	+	0.976147i	$0.430337\pi$
$702$	−10.0319	+	4.29983i	−0.378630	+	0.162287i
$703$			10.6818i			0.402873i
$704$	−8.09066	−	16.7023i	−0.304928	−	0.629490i
$705$	17.1373	−	5.83325i	0.645429	−	0.219693i
$706$	−39.8677	−	26.0811i	−1.50044	−	0.981575i
$707$	31.5001	−	31.5001i	1.18468	−	1.18468i
$708$	30.5044	−	27.8670i	1.14643	−	1.04731i
$709$	−9.00516	−	9.00516i	−0.338196	−	0.338196i	0.517492	−	0.855688i	$-0.326866\pi$
$709$	−9.00516	−	9.00516i	−0.338196	−	0.338196i	−0.855688	+	0.517492i	$0.826866\pi$
$710$	−14.7158	+	3.07633i	−0.552274	+	0.115453i
$711$	12.1616	−	9.36415i	0.456096	−	0.351183i
$712$	−37.6191	−	6.34734i	−1.40984	−	0.237877i
$713$	−56.6265			−2.12068
$714$	−13.7547	−	23.2530i	−0.514756	−	0.870220i
$715$	−2.43642	+	2.43642i	−0.0911168	+	0.0911168i
$716$	−18.9621	−	7.42534i	−0.708647	−	0.277498i
$717$	−7.22950	−	3.55772i	−0.269991	−	0.132865i
$718$	−8.63695	−	5.65022i	−0.322328	−	0.210864i
$719$	43.3604			1.61707			0.808535	−	0.588447i	$-0.200261\pi$
$719$	43.3604			1.61707			0.808535	+	0.588447i	$0.200261\pi$
$720$	9.21593	−	7.68548i	0.343457	−	0.286421i
$721$	60.0560			2.23660
$722$	30.2647	+	19.7989i	1.12634	+	0.736839i
$723$	−42.5564	−	20.9425i	−1.58269	−	0.778859i
$724$	−0.775871	+	1.98134i	−0.0288350	+	0.0736360i
$725$	−1.73154	+	1.73154i	−0.0643077	+	0.0643077i
$726$	−7.00660	−	11.8450i	−0.260039	−	0.439609i
$727$	7.38841			0.274021			0.137010	−	0.990570i	$-0.456251\pi$
$727$	7.38841			0.274021			0.137010	+	0.990570i	$0.456251\pi$
$728$	12.6693	−	9.01125i	0.469557	−	0.333979i
$729$	−24.8928	+	10.4569i	−0.921957	+	0.387293i
$730$	12.6338	−	2.64110i	0.467599	−	0.0977514i
$731$	−6.89995	−	6.89995i	−0.255204	−	0.255204i
$732$	−3.17450	−	3.47495i	−0.117333	−	0.128438i
$733$	−2.07544	+	2.07544i	−0.0766582	+	0.0766582i	−0.744396	−	0.667738i	$-0.767263\pi$
$733$	−2.07544	+	2.07544i	−0.0766582	+	0.0766582i	0.667738	+	0.744396i	$0.267263\pi$
$734$	9.44400	+	6.17818i	0.348584	+	0.228041i
$735$	−10.9792	+	3.73715i	−0.404975	+	0.137847i
$736$	−37.2753	+	9.32013i	−1.37398	+	0.343545i
$737$			28.6873i			1.05671i
$738$	−5.93725	+	0.457162i	−0.218553	+	0.0168284i
$739$	37.4179	+	37.4179i	1.37644	+	1.37644i	0.850560	+	0.525878i	$0.176263\pi$
$739$	37.4179	+	37.4179i	1.37644	+	1.37644i	0.525878	+	0.850560i	$0.323737\pi$
$740$	−1.28187	−	2.93195i	−0.0471225	−	0.107781i
$741$	15.4104	+	7.58364i	0.566116	+	0.278592i
$742$	−6.93685	−	33.1828i	−0.254660	−	1.21818i
$743$			50.7202i			1.86074i	0.366617	+	0.930372i	$0.380516\pi$
$743$			50.7202i			1.86074i	−0.366617	+	0.930372i	$0.619484\pi$
$744$	23.8792	−	33.1344i	0.875454	−	1.21477i
$745$			10.0900i			0.369669i
$746$	−7.58191	+	1.58500i	−0.277593	+	0.0580308i
$747$	−21.7031	−	2.82051i	−0.794073	−	0.103197i
$748$	12.8755	+	5.04190i	0.470775	+	0.184350i
$749$	−26.6438	−	26.6438i	−0.973544	−	0.973544i
$750$	2.37259	+	0.608943i	0.0866348	+	0.0222354i
$751$			6.38457i			0.232976i	0.993192	+	0.116488i	$0.0371637\pi$
$751$			6.38457i			0.232976i	−0.993192	+	0.116488i	$0.962836\pi$
$752$	28.3889	−	30.6900i	1.03524	−	1.11915i
$753$	13.4814	+	39.6066i	0.491290	+	1.44334i
$754$	2.81590	−	4.30440i	0.102549	−	0.156757i
$755$	−0.790136	+	0.790136i	−0.0287560	+	0.0287560i
$756$	31.5014	−	22.0643i	1.14569	−	0.802472i
$757$	12.2736	+	12.2736i	0.446091	+	0.446091i	0.894053	−	0.447962i	$-0.147850\pi$
$757$	12.2736	+	12.2736i	0.446091	+	0.446091i	−0.447962	+	0.894053i	$0.647850\pi$
$758$	−0.312250	−	1.49366i	−0.0113414	−	0.0542522i
$759$	25.8361	−	8.79416i	0.937790	−	0.319208i
$760$	−18.6202	−	3.14173i	−0.675427	−	0.113962i
$761$	0.363241			0.0131675			0.00658374	−	0.999978i	$-0.497904\pi$
$761$	0.363241			0.0131675			0.00658374	+	0.999978i	$0.497904\pi$
$762$	−19.7679	−	33.4187i	−0.716116	−	1.21063i
$763$	−7.92198	+	7.92198i	−0.286795	+	0.286795i
$764$	7.01357	+	16.0418i	0.253742	+	0.580372i
$765$	−1.15225	+	8.86626i	−0.0416597	+	0.320560i
$766$	5.99784	−	9.16833i	0.216711	−	0.331265i
$767$	−17.7152			−0.639660
$768$	10.2653	−	25.7415i	0.370416	−	0.928866i
$769$	25.6145			0.923683			0.461841	−	0.886963i	$-0.347189\pi$
$769$	25.6145			0.923683			0.461841	+	0.886963i	$0.347189\pi$
$770$	6.64684	−	10.1604i	0.239535	−	0.366155i
$771$	20.5415	−	41.7416i	0.739784	−	1.50329i
$772$	0.146884	+	0.335960i	0.00528646	+	0.0120915i
$773$	−15.3046	+	15.3046i	−0.550469	+	0.550469i	−0.926576	−	0.376107i	$-0.877262\pi$
$773$	−15.3046	+	15.3046i	−0.550469	+	0.550469i	0.376107	+	0.926576i	$0.377262\pi$
$774$	9.03951	−	10.5477i	0.324918	−	0.379129i
$775$	8.33693			0.299471
$776$	−16.5522	−	2.79280i	−0.594190	−	0.100256i
$777$	−3.30469	−	9.70875i	−0.118555	−	0.348299i
$778$	5.10068	+	24.3994i	0.182868	+	0.874759i
$779$	6.62603	+	6.62603i	0.237402	+	0.237402i
$780$	−5.13993	−	0.232238i	−0.184039	−	0.00831547i
$781$	17.4381	−	17.4381i	0.623984	−	0.623984i
$782$	15.6722	−	23.9567i	0.560438	−	0.856688i
$783$	7.04272	−	10.5974i	0.251686	−	0.378719i
$784$	−18.1877	+	19.6620i	−0.649562	+	0.702213i
$785$		−	6.14952i		−	0.219486i
$786$	1.28725	−	5.01546i	0.0459148	−	0.178895i
$787$	−16.6202	−	16.6202i	−0.592445	−	0.592445i	0.345847	−	0.938291i	$-0.387592\pi$
$787$	−16.6202	−	16.6202i	−0.592445	−	0.592445i	−0.938291	+	0.345847i	$0.887592\pi$
$788$	39.1643	+	15.3363i	1.39517	+	0.546332i
$789$	14.5468	−	29.5600i	0.517880	−	1.05236i
$790$	7.08249	−	1.48059i	0.251984	−	0.0526771i
$791$		−	47.7415i		−	1.69749i
$792$	−5.74917	+	18.8262i	−0.204288	+	0.668959i
$793$			2.01805i			0.0716631i
$794$	−1.66157	−	7.94818i	−0.0589668	−	0.282070i
$795$	−4.95360	+	10.0660i	−0.175686	+	0.357005i
$796$	−6.32033	−	14.4562i	−0.224018	−	0.512385i
$797$	−7.97036	−	7.97036i	−0.282324	−	0.282324i	0.551711	−	0.834035i	$-0.313975\pi$
$797$	−7.97036	−	7.97036i	−0.282324	−	0.282324i	−0.834035	+	0.551711i	$0.813975\pi$
$798$	−58.6213	−	15.0456i	−2.07517	−	0.532608i
$799$			31.1489i			1.10197i
$800$	5.48791	−	1.37217i	0.194027	−	0.0485135i
$801$	24.6870	+	32.0620i	0.872272	+	1.13286i
$802$	12.4295	+	8.13127i	0.438901	+	0.287125i
$803$	−14.9710	+	14.9710i	−0.528314	+	0.528314i
$804$	−31.6270	+	28.8925i	−1.11540	+	1.01896i
$805$	−17.7744	−	17.7744i	−0.626467	−	0.626467i
$806$	−17.1412	+	3.58337i	−0.603774	+	0.126219i
$807$	−3.94723	−	11.5964i	−0.138949	−	0.408214i
$808$	−27.7445	+	19.7337i	−0.976050	+	0.694229i
$809$	51.4785			1.80989			0.904944	−	0.425530i	$-0.139912\pi$
$809$	51.4785			1.80989			0.904944	+	0.425530i	$0.139912\pi$
$810$	−12.7105	−	0.666479i	−0.446600	−	0.0234177i
$811$	−24.3359	+	24.3359i	−0.854549	+	0.854549i	−0.990690	−	0.136140i	$-0.956530\pi$
$811$	−24.3359	+	24.3359i	−0.854549	+	0.854549i	0.136140	+	0.990690i	$0.456530\pi$
$812$	−6.60884	+	16.8770i	−0.231925	+	0.592267i
$813$	1.98435	−	4.03232i	0.0695942	−	0.141420i
$814$	4.39262	+	2.87361i	0.153961	+	0.100720i
$815$	−5.32901			−0.186667
$816$	7.40905	+	19.2729i	0.259369	+	0.674685i
$817$	−21.8595			−0.764767
$818$	4.12624	+	2.69935i	0.144271	+	0.0943806i
$819$	−16.3528	−	2.12519i	−0.571412	−	0.0742601i
$820$	−2.61387	−	1.02356i	−0.0912803	−	0.0357443i
$821$	−8.69556	+	8.69556i	−0.303477	+	0.303477i	−0.842373	−	0.538895i	$-0.818842\pi$
$821$	−8.69556	+	8.69556i	−0.303477	+	0.303477i	0.538895	+	0.842373i	$0.318842\pi$
$822$	6.88646	−	4.07350i	0.240193	−	0.142080i
$823$	29.6784			1.03452			0.517262	−	0.855827i	$-0.326951\pi$
$823$	29.6784			1.03452			0.517262	+	0.855827i	$0.326951\pi$
$824$	−45.2594	−	7.63646i	−1.57669	−	0.266029i
$825$	−3.80376	+	1.29473i	−0.132430	+	0.0450768i
$826$	61.1028	−	12.7735i	2.12604	−	0.444448i
$827$	8.30052	+	8.30052i	0.288637	+	0.288637i	0.836541	−	0.547904i	$-0.184574\pi$
$827$	8.30052	+	8.30052i	0.288637	+	0.288637i	−0.547904	+	0.836541i	$0.684574\pi$
$828$	35.7162	+	19.6265i	1.24123	+	0.682069i
$829$	−38.9513	+	38.9513i	−1.35284	+	1.35284i	−0.470362	+	0.882474i	$0.655877\pi$
$829$	−38.9513	+	38.9513i	−1.35284	+	1.35284i	−0.882474	+	0.470362i	$0.844123\pi$
$830$	−8.63361	−	5.64804i	−0.299677	−	0.196046i
$831$	−2.45095	−	7.20057i	−0.0850226	−	0.249785i
$832$	−10.6937	+	5.18008i	−0.370737	+	0.179587i
$833$		−	19.9560i		−	0.691433i
$834$	−10.3995	+	40.5192i	−0.360107	+	1.40306i
$835$	0.610746	+	0.610746i	0.0211357	+	0.0211357i
$836$	28.3818	−	12.4087i	0.981604	−	0.429163i
$837$	−42.4663	+	8.55738i	−1.46785	+	0.295786i
$838$	10.5325	+	50.3826i	0.363839	+	1.74044i
$839$			6.20951i			0.214376i	0.994239	+	0.107188i	$0.0341847\pi$
$839$			6.20951i			0.214376i	−0.994239	+	0.107188i	$0.965815\pi$
$840$	17.8959	−	2.90511i	0.617469	−	0.100236i
$841$		−	23.0035i		−	0.793226i
$842$	−25.6289	+	5.35772i	−0.883231	+	0.184639i
$843$	31.1257	+	15.3173i	1.07203	+	0.527556i
$844$	6.67437	−	17.0444i	0.229741	−	0.586691i
$845$	−7.63246	−	7.63246i	−0.262565	−	0.262565i
$846$	−44.2120	+	3.40427i	−1.52004	+	0.117041i
$847$		−	20.7925i		−	0.714440i
$848$	1.00837	+	25.8892i	0.0346276	+	0.889040i
$849$	−16.6408	+	5.66425i	−0.571112	+	0.194397i
$850$	−2.30737	+	3.52705i	−0.0791421	+	0.120977i
$851$	7.68439	−	7.68439i	0.263417	−	0.263417i
$852$	36.7879	+	1.66219i	1.26033	+	0.0569458i
$853$	34.5462	+	34.5462i	1.18284	+	1.18284i	0.979005	+	0.203834i	$0.0653403\pi$
$853$	34.5462	+	34.5462i	1.18284	+	1.18284i	0.203834	+	0.979005i	$0.434660\pi$
$854$	−1.45511	−	6.96060i	−0.0497929	−	0.238187i
$855$	12.2193	+	15.8697i	0.417890	+	0.542731i
$856$	16.6914	+	23.4672i	0.570500	+	0.802093i
$857$	−5.49279			−0.187630			−0.0938150	−	0.995590i	$-0.529906\pi$
$857$	−5.49279			−0.187630			−0.0938150	+	0.995590i	$0.529906\pi$
$858$	7.26426	−	4.29698i	0.247998	−	0.146696i
$859$	14.8425	−	14.8425i	0.506420	−	0.506420i	−0.407005	−	0.913426i	$-0.633427\pi$
$859$	14.8425	−	14.8425i	0.506420	−	0.506420i	0.913426	+	0.407005i	$0.133427\pi$
$860$	6.00001	−	2.62324i	0.204599	−	0.0894518i
$861$	−8.07234	−	3.97249i	−0.275105	−	0.135382i
$862$	−18.5294	+	28.3241i	−0.631114	+	0.964723i
$863$	−55.1980			−1.87896			−0.939480	−	0.342604i	$-0.888691\pi$
$863$	−55.1980			−1.87896			−0.939480	+	0.342604i	$0.888691\pi$
$864$	−26.5456	+	12.6225i	−0.903101	+	0.429427i
$865$	−15.1575			−0.515370
$866$	20.4603	−	31.2758i	0.695271	−	1.06279i
$867$	12.6159	+	6.20840i	0.428457	+	0.210848i
$868$	56.5392	−	24.7193i	1.91907	−	0.839028i
$869$	−8.39269	+	8.39269i	−0.284702	+	0.284702i
$870$	5.16264	−	3.05383i	0.175030	−	0.103534i
$871$	18.3672			0.622348
$872$	6.97748	−	4.96284i	0.236287	−	0.168063i
$873$	10.8621	+	14.1071i	0.367628	+	0.477454i
$874$	−13.1228	−	62.7735i	−0.443885	−	2.12335i
$875$	2.61687	+	2.61687i	0.0884664	+	0.0884664i
$876$	−31.5832	−	1.42703i	−1.06710	−	0.0482148i
$877$	−3.99970	+	3.99970i	−0.135060	+	0.135060i	−0.771405	−	0.636345i	$-0.780446\pi$
$877$	−3.99970	+	3.99970i	−0.135060	+	0.135060i	0.636345	+	0.771405i	$0.280446\pi$
$878$	−25.8468	+	39.5095i	−0.872287	+	1.33338i
$879$	−34.0156	+	11.5783i	−1.14732	+	0.390527i
$880$	−6.30114	+	6.81188i	−0.212411	+	0.229629i
$881$			20.7548i			0.699246i	0.936890	+	0.349623i	$0.113690\pi$
$881$			20.7548i			0.699246i	−0.936890	+	0.349623i	$0.886310\pi$
$882$	28.3250	−	2.18099i	0.953751	−	0.0734377i
$883$	−27.8615	−	27.8615i	−0.937616	−	0.937616i	0.0605495	−	0.998165i	$-0.480715\pi$
$883$	−27.8615	−	27.8615i	−0.937616	−	0.937616i	−0.998165	+	0.0605495i	$0.980715\pi$
$884$	3.22810	−	8.24360i	0.108573	−	0.277262i
$885$	−18.5356	−	9.12158i	−0.623068	−	0.306618i
$886$	−10.3947	+	2.17302i	−0.349218	+	0.0730040i
$887$		−	0.494572i		−	0.0166061i	−0.999966	−	0.00830305i	$-0.997357\pi$
$887$		−	0.494572i		−	0.0166061i	0.999966	−	0.00830305i	$-0.00264297\pi$
$888$	1.25596	+	7.73692i	0.0421472	+	0.259634i
$889$		−	58.6626i		−	1.96748i
$890$	3.90333	+	18.6718i	0.130840	+	0.625880i
$891$	18.0465	−	10.4994i	0.604579	−	0.351743i
$892$	37.4872	−	16.3896i	1.25516	−	0.548765i
$893$	49.3410	+	49.3410i	1.65113	+	1.65113i
$894$	6.14423	−	23.9394i	0.205494	−	0.800655i
$895$			10.1820i			0.340348i
$896$	33.1493	−	25.5776i	1.10744	−	0.854489i
$897$	−5.63050	−	16.5417i	−0.187997	−	0.552310i
$898$	−4.65774	−	3.04705i	−0.155431	−	0.101681i
$899$	14.4357	−	14.4357i	0.481458	−	0.481458i
$900$	−5.25838	−	2.88954i	−0.175279	−	0.0963182i
$901$	−13.6499	−	13.6499i	−0.454744	−	0.454744i
$902$	4.50730	−	0.942250i	0.150077	−	0.0313735i
$903$	19.8682	−	6.76278i	0.661171	−	0.225051i
$904$	−6.07060	+	35.9789i	−0.201905	+	1.19664i
$905$	1.06392			0.0353659
$906$	2.35582	−	1.39352i	0.0782668	−	0.0462967i
$907$	35.5428	−	35.5428i	1.18018	−	1.18018i	0.200481	−	0.979698i	$-0.435750\pi$
$907$	35.5428	−	35.5428i	1.18018	−	1.18018i	0.979698	−	0.200481i	$-0.0642505\pi$
$908$	−5.70178	−	2.23275i	−0.189220	−	0.0740964i
$909$	35.8109	+	4.65395i	1.18777	+	0.154362i
$910$	−6.50523	−	4.25567i	−0.215646	−	0.141074i
$911$	−20.1029			−0.666040			−0.333020	−	0.942920i	$-0.608068\pi$
$911$	−20.1029			−0.666040			−0.333020	+	0.942920i	$0.608068\pi$
$912$	42.2651	+	18.7927i	1.39954	+	0.622288i
$913$	16.9236			0.560090
$914$	−2.32622	−	1.52179i	−0.0769444	−	0.0503364i
$915$	−1.03910	+	2.11151i	−0.0343514	+	0.0698042i
$916$	12.8705	−	32.8675i	0.425255	−	1.08597i
$917$	5.53184	−	5.53184i	0.182678	−	0.182678i
$918$	8.13287	−	20.3344i	0.268425	−	0.671134i
$919$	33.2221			1.09589			0.547947	−	0.836513i	$-0.315409\pi$
$919$	33.2221			1.09589			0.547947	+	0.836513i	$0.315409\pi$
$920$	11.1351	+	15.6553i	0.367112	+	0.516140i
$921$	16.6212	+	48.8308i	0.547686	+	1.60903i
$922$	−43.8252	+	9.16166i	−1.44331	+	0.301723i
$923$	−11.1648	−	11.1648i	−0.367494	−	0.367494i
$924$	−21.9573	+	20.0589i	−0.722343	+	0.659889i
$925$	−1.13135	+	1.13135i	−0.0371984	+	0.0371984i
$926$	0.504077	+	0.329763i	0.0165650	+	0.0108367i
$927$	29.7008	+	38.5737i	0.975503	+	1.26693i
$928$	7.12656	−	11.8785i	0.233941	−	0.389931i
$929$			22.0724i			0.724171i	0.932145	+	0.362085i	$0.117935\pi$
$929$			22.0724i			0.724171i	−0.932145	+	0.362085i	$0.882065\pi$
$930$	−19.7801	−	5.07671i	−0.648616	−	0.166472i
$931$	−31.6109	−	31.6109i	−1.03601	−	1.03601i
$932$	4.15384	+	9.50086i	0.136063	+	0.311211i
$933$	−9.56553	+	19.4377i	−0.313161	+	0.636363i
$934$	−1.38075	−	6.60487i	−0.0451795	−	0.216118i
$935$		−	6.91374i		−	0.226104i
$936$	12.0535	+	3.68093i	0.393982	+	0.120315i
$937$		−	8.25822i		−	0.269784i	−0.990860	−	0.134892i	$-0.956931\pi$
$937$		−	8.25822i		−	0.269784i	0.990860	−	0.134892i	$-0.0430688\pi$
$938$	−63.3515	+	13.2436i	−2.06850	+	0.432419i
$939$	−8.43169	+	17.1337i	−0.275158	+	0.559138i
$940$	−19.4643	−	7.62199i	−0.634855	−	0.248602i
$941$	4.79693	+	4.79693i	0.156375	+	0.156375i	0.780958	−	0.624583i	$-0.214731\pi$
$941$	4.79693	+	4.79693i	0.156375	+	0.156375i	−0.624583	+	0.780958i	$0.714731\pi$
$942$	−3.74470	+	14.5903i	−0.122009	+	0.475377i
$943$		−	9.53338i		−	0.310449i
$944$	−47.6725	+	1.85682i	−1.55161	+	0.0604343i
$945$	−16.0158	−	10.6436i	−0.520993	−	0.346238i
$946$	−5.88061	+	8.98913i	−0.191195	+	0.292262i
$947$	6.93551	−	6.93551i	0.225374	−	0.225374i	−0.585383	−	0.810757i	$-0.699056\pi$
$947$	6.93551	−	6.93551i	0.225374	−	0.225374i	0.810757	+	0.585383i	$0.199056\pi$
$948$	−17.7054	−	0.799989i	−0.575046	−	0.0259824i
$949$	9.58522	+	9.58522i	0.311150	+	0.311150i
$950$	1.93202	+	9.24192i	0.0626831	+	0.299848i
$951$	−3.61617	−	10.6238i	−0.117262	−	0.344502i
$952$	−5.19023	+	30.7612i	−0.168216	+	0.996975i
$953$	−21.8791			−0.708734			−0.354367	−	0.935106i	$-0.615304\pi$
$953$	−21.8791			−0.708734			−0.354367	+	0.935106i	$0.615304\pi$
$954$	17.8825	−	20.8661i	0.578968	−	0.675565i
$955$	6.19000	−	6.19000i	0.200304	−	0.200304i
$956$	3.72711	+	8.52483i	0.120543	+	0.275713i
$957$	−4.34447	+	8.82823i	−0.140437	+	0.285376i
$958$	−3.02767	+	4.62811i	−0.0978196	+	0.149527i
$959$	12.0884			0.390354
$960$	−13.8561	−	0.0862237i	−0.447205	−	0.00278286i
$961$	−38.5043			−1.24208
$962$	1.83984	−	2.81239i	0.0593189	−	0.0906752i
$963$	3.93645	−	30.2900i	0.126850	−	0.976080i
$964$	21.9396	+	50.1813i	0.706627	+	1.61623i
$965$	0.129636	−	0.129636i	0.00417313	−	0.00417313i
$966$	31.3479	+	52.9951i	1.00860	+	1.70509i
$967$	−31.3801			−1.00912			−0.504558	−	0.863378i	$-0.668345\pi$
$967$	−31.3801			−1.00912			−0.504558	+	0.863378i	$0.668345\pi$
$968$	−2.64389	+	15.6697i	−0.0849778	+	0.503642i
$969$	−32.6248	+	11.1049i	−1.04806	+	0.356741i
$970$	1.71745	+	8.21548i	0.0551439	+	0.263783i
$971$	−26.8216	−	26.8216i	−0.860747	−	0.860747i	0.130678	−	0.991425i	$-0.458285\pi$
$971$	−26.8216	−	26.8216i	−0.860747	−	0.860747i	−0.991425	+	0.130678i	$0.958285\pi$
$972$	29.7509	+	9.32123i	0.954260	+	0.298978i
$973$	−44.6910	+	44.6910i	−1.43273	+	1.43273i
$974$	−12.1816	+	18.6208i	−0.390323	+	0.596649i
$975$	0.828959	+	2.43537i	0.0265479	+	0.0779943i
$976$	0.211522	+	5.43067i	0.00677065	+	0.173832i
$977$			36.8627i			1.17934i	0.807643	+	0.589671i	$0.200743\pi$
$977$			36.8627i			1.17934i	−0.807643	+	0.589671i	$0.799257\pi$
$978$	12.6436	+	3.24506i	0.404297	+	0.103766i
$979$	−22.1259	−	22.1259i	−0.707147	−	0.707147i
$980$	12.4700	+	4.88312i	0.398341	+	0.155986i
$981$	−9.00608	−	1.17042i	−0.287542	−	0.0373687i
$982$	35.3679	−	7.39364i	1.12863	−	0.235941i
$983$		−	36.2140i		−	1.15505i	−0.816373	−	0.577524i	$-0.804019\pi$
$983$		−	36.2140i		−	1.15505i	0.816373	−	0.577524i	$-0.195981\pi$
$984$	5.57835	+	4.02019i	0.177831	+	0.128159i
$985$		−	21.0300i		−	0.670071i
$986$	2.11193	+	10.1025i	0.0672576	+	0.321730i
$987$	−60.1110	−	29.5813i	−1.91335	−	0.941582i
$988$	−7.94472	−	18.1715i	−0.252755	−	0.578114i
$989$	15.7255	+	15.7255i	0.500041	+	0.500041i
$990$	9.81318	−	0.755603i	0.311883	−	0.0240147i
$991$		−	27.1806i		−	0.863420i	−0.902012	−	0.431710i	$-0.857910\pi$
$991$		−	27.1806i		−	0.863420i	0.902012	−	0.431710i	$-0.142090\pi$
$992$	−45.7523	+	11.4397i	−1.45264	+	0.363210i
$993$	−17.1336	+	5.83198i	−0.543718	+	0.185072i
$994$	46.5597	+	30.4590i	1.47678	+	0.966099i
$995$	−5.57816	+	5.57816i	−0.176840	+	0.176840i
$996$	17.0447	+	18.6579i	0.540082	+	0.591197i
$997$	13.9123	+	13.9123i	0.440607	+	0.440607i	0.892216	−	0.451609i	$-0.149150\pi$
$997$	13.9123	+	13.9123i	0.440607	+	0.440607i	−0.451609	+	0.892216i	$0.649150\pi$
$998$	14.4878	−	3.02867i	0.458603	−	0.0958708i
$999$	4.60154	−	6.92407i	0.145586	−	0.219068i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	240.2.bk.b.11.20	yes	60
3.2	odd	2	inner	240.2.bk.b.11.11	✓	60
4.3	odd	2		960.2.bk.b.911.4		60
12.11	even	2		960.2.bk.b.911.14		60
16.3	odd	4	inner	240.2.bk.b.131.11	yes	60
16.13	even	4		960.2.bk.b.431.14		60
48.29	odd	4		960.2.bk.b.431.4		60
48.35	even	4	inner	240.2.bk.b.131.20	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.2.bk.b.11.11	✓	60	3.2	odd	2	inner
240.2.bk.b.11.20	yes	60	1.1	even	1	trivial
240.2.bk.b.131.11	yes	60	16.3	odd	4	inner
240.2.bk.b.131.20	yes	60	48.35	even	4	inner
960.2.bk.b.431.4		60	48.29	odd	4
960.2.bk.b.431.14		60	16.13	even	4
960.2.bk.b.911.4		60	4.3	odd	2
960.2.bk.b.911.14		60	12.11	even	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)

\(f(q)\)	\(=\)	\(q+(0.774214 - 1.18347i) q^{2} +(1.55407 + 0.764773i) q^{3} +(-0.801186 - 1.83251i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(2.10826 - 1.24709i) q^{6} +3.70081 q^{7} +(-2.78901 - 0.470579i) q^{8} +(1.83024 + 2.37702i) q^{9} +O(q^{10})\)	\(q+(0.774214 - 1.18347i) q^{2} +(1.55407 + 0.764773i) q^{3} +(-0.801186 - 1.83251i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(2.10826 - 1.24709i) q^{6} +3.70081 q^{7} +(-2.78901 - 0.470579i) q^{8} +(1.83024 + 2.37702i) q^{9} +(0.289385 + 1.38429i) q^{10} +(-1.64037 - 1.64037i) q^{11} +(0.156360 - 3.46057i) q^{12} +(-1.05025 + 1.05025i) q^{13} +(2.86522 - 4.37979i) q^{14} +(-1.63967 + 0.558115i) q^{15} +(-2.71620 + 2.93637i) q^{16} -2.98027i q^{17} +(4.23012 - 0.325714i) q^{18} +(-4.72085 - 4.72085i) q^{19} +(1.86231 + 0.729258i) q^{20} +(5.75131 + 2.83028i) q^{21} +(-3.21132 + 0.671326i) q^{22} +6.79225i q^{23} +(-3.97441 - 2.86427i) q^{24} -1.00000i q^{25} +(0.429819 + 2.05606i) q^{26} +(1.02644 + 5.09376i) q^{27} +(-2.96504 - 6.78179i) q^{28} +(-1.73154 - 1.73154i) q^{29} +(-0.608943 + 2.37259i) q^{30} +8.33693i q^{31} +(1.37217 + 5.48791i) q^{32} +(-1.29473 - 3.80376i) q^{33} +(-3.52705 - 2.30737i) q^{34} +(-2.61687 + 2.61687i) q^{35} +(2.88954 - 5.25838i) q^{36} +(-1.13135 - 1.13135i) q^{37} +(-9.24192 + 1.93202i) q^{38} +(-2.43537 + 0.828959i) q^{39} +(2.30487 - 1.63938i) q^{40} -1.40357 q^{41} +(7.80229 - 4.61524i) q^{42} +(2.31521 - 2.31521i) q^{43} +(-1.69176 + 4.32024i) q^{44} +(-2.97498 - 0.386626i) q^{45} +(8.03841 + 5.25866i) q^{46} -10.4517 q^{47} +(-6.46681 + 2.48603i) q^{48} +6.69602 q^{49} +(-1.18347 - 0.774214i) q^{50} +(2.27923 - 4.63154i) q^{51} +(2.76605 + 1.08315i) q^{52} +(4.58009 - 4.58009i) q^{53} +(6.82298 + 2.72890i) q^{54} +2.31983 q^{55} +(-10.3216 - 1.74153i) q^{56} +(-3.72614 - 10.9469i) q^{57} +(-3.38980 + 0.708637i) q^{58} +(8.43378 + 8.43378i) q^{59} +(2.33643 + 2.55756i) q^{60} +(0.960744 - 0.960744i) q^{61} +(9.86647 + 6.45456i) q^{62} +(6.77339 + 8.79689i) q^{63} +(7.55711 + 2.62490i) q^{64} -1.48528i q^{65} +(-5.50402 - 1.41265i) q^{66} +(-8.74415 - 8.74415i) q^{67} +(-5.46139 + 2.38775i) q^{68} +(-5.19453 + 10.5556i) q^{69} +(1.07096 + 5.12299i) q^{70} +10.6306i q^{71} +(-3.98599 - 7.49079i) q^{72} -9.12658i q^{73} +(-2.21481 + 0.463006i) q^{74} +(0.764773 - 1.55407i) q^{75} +(-4.86874 + 12.4333i) q^{76} +(-6.07070 - 6.07070i) q^{77} +(-0.904453 + 3.52397i) q^{78} -5.11634i q^{79} +(-0.155680 - 3.99697i) q^{80} +(-2.30041 + 8.70104i) q^{81} +(-1.08666 + 1.66107i) q^{82} +(-5.15848 + 5.15848i) q^{83} +(0.578658 - 12.8069i) q^{84} +(2.10737 + 2.10737i) q^{85} +(-0.947505 - 4.53244i) q^{86} +(-1.36669 - 4.01516i) q^{87} +(3.80308 + 5.34693i) q^{88} +13.4884 q^{89} +(-2.76083 + 3.22146i) q^{90} +(-3.88679 + 3.88679i) q^{91} +(12.4469 - 5.44186i) q^{92} +(-6.37586 + 12.9561i) q^{93} +(-8.09185 + 12.3692i) q^{94} +6.67630 q^{95} +(-2.06456 + 9.57797i) q^{96} +5.93480 q^{97} +(5.18415 - 7.92451i) q^{98} +(0.896908 - 6.90147i) 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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