LMFDB - Embedded newform 110.3.l.a.37.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [110,3,Mod(3,110)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("110.3"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(110, base_ring=CyclotomicField(20)) chi = DirichletCharacter(H, H._module([15, 16])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 110 = 2 \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	110.l (of order $20$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [48,-12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$2.99728290796$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$6$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			37.5
Character	$\chi$	$=$	110.37
Dual form			110.3.l.a.3.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.221232 - 1.39680i) q^{2} +(1.09534 + 2.14972i) q^{3} +(-1.90211 + 0.618034i) q^{4} +(1.48006 - 4.77592i) q^{5} +(2.76042 - 2.00556i) q^{6} +(1.47655 - 2.89789i) q^{7} +(1.28408 + 2.52015i) q^{8} +(1.86852 - 2.57180i) q^{9} +(-6.99845 - 1.01077i) q^{10} +(10.0869 + 4.38810i) q^{11} +(-3.41206 - 3.41206i) q^{12} +(22.7719 - 3.60671i) q^{13} +(-4.37444 - 1.42134i) q^{14} +(11.8881 - 2.04953i) q^{15} +(3.23607 - 2.35114i) q^{16} +(-25.2737 - 4.00296i) q^{17} +(-4.00567 - 2.04099i) q^{18} +(-12.6650 - 4.11512i) q^{19} +(0.136436 + 9.99907i) q^{20} +7.84699 q^{21} +(3.89777 - 15.0601i) q^{22} +(-31.6053 + 31.6053i) q^{23} +(-4.01112 + 5.52083i) q^{24} +(-20.6188 - 14.1373i) q^{25} +(-10.0757 - 31.0099i) q^{26} +(29.0222 + 4.59667i) q^{27} +(-1.01757 + 6.42468i) q^{28} +(9.21597 - 2.99445i) q^{29} +(-5.49280 - 16.1519i) q^{30} +(21.3814 + 15.5345i) q^{31} +(-4.00000 - 4.00000i) q^{32} +(1.61533 + 26.4904i) q^{33} +36.1880i q^{34} +(-11.6547 - 11.3409i) q^{35} +(-1.96468 + 6.04666i) q^{36} +(-23.7594 + 46.6304i) q^{37} +(-2.94610 + 18.6010i) q^{38} +(32.6963 + 45.0026i) q^{39} +(13.9365 - 2.40269i) q^{40} +(10.6065 - 32.6435i) q^{41} +(-1.73600 - 10.9607i) q^{42} +(-3.10574 + 3.10574i) q^{43} +(-21.8983 - 2.11264i) q^{44} +(-9.51718 - 12.7303i) q^{45} +(51.1385 + 37.1543i) q^{46} +(-32.0813 + 16.3462i) q^{47} +(8.59890 + 4.38136i) q^{48} +(22.5839 + 31.0841i) q^{49} +(-15.1855 + 31.9281i) q^{50} +(-19.0780 - 58.7161i) q^{51} +(-41.0856 + 20.9341i) q^{52} +(-74.7316 + 11.8363i) q^{53} -41.5552i q^{54} +(35.8864 - 41.6794i) q^{55} +9.19912 q^{56} +(-5.02614 - 31.7338i) q^{57} +(-6.22152 - 12.2104i) q^{58} +(46.5392 - 15.1215i) q^{59} +(-21.3458 + 11.2457i) q^{60} +(-9.53445 + 6.92718i) q^{61} +(16.9684 - 33.3023i) q^{62} +(-4.69384 - 9.21217i) q^{63} +(-4.70228 + 6.47214i) q^{64} +(16.4784 - 114.095i) q^{65} +(36.6445 - 8.11682i) q^{66} +(28.1955 + 28.1955i) q^{67} +(50.5474 - 8.00593i) q^{68} +(-102.561 - 33.3242i) q^{69} +(-13.2627 + 18.7883i) q^{70} +(-3.31366 + 2.40752i) q^{71} +(8.88064 + 1.40656i) q^{72} +(-27.5587 - 14.0419i) q^{73} +(70.3897 + 22.8710i) q^{74} +(7.80672 - 59.8100i) q^{75} +26.6336 q^{76} +(27.6100 - 22.7514i) q^{77} +(55.6263 - 55.6263i) q^{78} +(46.6732 - 64.2401i) q^{79} +(-6.43928 - 18.9350i) q^{80} +(13.0665 + 40.2147i) q^{81} +(-47.9430 - 7.59343i) q^{82} +(-1.12047 + 7.07437i) q^{83} +(-14.9259 + 4.84971i) q^{84} +(-56.5245 + 114.781i) q^{85} +(5.02519 + 3.65102i) q^{86} +(16.5319 + 16.5319i) q^{87} +(1.89367 + 31.0550i) q^{88} +59.8878i q^{89} +(-15.6763 + 16.1100i) q^{90} +(23.1719 - 71.3159i) q^{91} +(40.5837 - 79.6501i) q^{92} +(-9.97500 + 62.9796i) q^{93} +(29.9299 + 41.1949i) q^{94} +(-38.3986 + 54.3966i) q^{95} +(4.21754 - 12.9803i) q^{96} +(9.83435 + 62.0916i) q^{97} +(38.4220 - 38.4220i) q^{98} +(30.1328 - 17.7421i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 12 q^{2} + 2 q^{3} + 4 q^{5} + 4 q^{6} + 38 q^{7} + 24 q^{8} + 36 q^{10} + 80 q^{11} - 16 q^{12} - 16 q^{13} + 38 q^{15} + 48 q^{16} - 18 q^{17} - 44 q^{18} + 4 q^{20} + 24 q^{21} + 64 q^{23} + 70 q^{25}+ \cdots - 440 q^{98}+O(q^{100}) $ 48 * q - 12 * q^2 + 2 * q^3 + 4 * q^5 + 4 * q^6 + 38 * q^7 + 24 * q^8 + 36 * q^10 + 80 * q^11 - 16 * q^12 - 16 * q^13 + 38 * q^15 + 48 * q^16 - 18 * q^17 - 44 * q^18 + 4 * q^20 + 24 * q^21 + 64 * q^23 + 70 * q^25 + 8 * q^26 - 82 * q^27 + 64 * q^28 - 14 * q^30 - 116 * q^31 - 192 * q^32 - 312 * q^33 - 288 * q^35 - 88 * q^36 + 22 * q^37 - 72 * q^38 - 24 * q^40 - 196 * q^41 - 96 * q^42 - 484 * q^43 - 56 * q^45 - 132 * q^46 - 310 * q^47 - 8 * q^48 - 128 * q^50 + 256 * q^51 + 8 * q^52 - 82 * q^53 - 264 * q^55 + 48 * q^56 + 744 * q^57 + 168 * q^58 + 196 * q^60 + 528 * q^61 + 144 * q^62 + 814 * q^63 + 840 * q^65 + 436 * q^66 + 192 * q^67 + 36 * q^68 + 230 * q^70 - 292 * q^71 - 48 * q^72 - 108 * q^73 + 258 * q^75 + 96 * q^76 - 200 * q^77 + 88 * q^78 + 24 * q^80 + 628 * q^81 + 24 * q^82 + 360 * q^83 - 368 * q^85 + 532 * q^86 - 328 * q^87 - 40 * q^88 - 766 * q^90 + 72 * q^91 + 68 * q^92 - 66 * q^93 - 232 * q^95 - 16 * q^96 + 6 * q^97 - 440 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/110\mathbb{Z}\right)^\times$.

$n$	$67$	$101$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{5}\right)$

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 $

$2$	−0.221232	−	1.39680i	−0.110616	−	0.698401i
$2$	−0.221232	−	1.39680i	−0.110616	−	0.698401i
$3$	1.09534	+	2.14972i	0.365113	+	0.716575i	0.998352	−	0.0573814i	$-0.0182751\pi$
$3$	1.09534	+	2.14972i	0.365113	+	0.716575i	−0.633239	+	0.773956i	$0.718275\pi$
$4$	−1.90211	+	0.618034i	−0.475528	+	0.154508i
$5$	1.48006	−	4.77592i	0.296012	−	0.955184i
$5$	1.48006	−	4.77592i	0.296012	−	0.955184i
$6$	2.76042	−	2.00556i	0.460069	−	0.334260i
$7$	1.47655	−	2.89789i	0.210936	−	0.413985i	−0.761162	−	0.648562i	$-0.775371\pi$
$7$	1.47655	−	2.89789i	0.210936	−	0.413985i	0.972097	+	0.234577i	$0.0753706\pi$
$8$	1.28408	+	2.52015i	0.160510	+	0.315018i
$9$	1.86852	−	2.57180i	0.207614	−	0.285756i
$10$	−6.99845	−	1.01077i	−0.699845	−	0.101077i
$11$	10.0869	+	4.38810i	0.916987	+	0.398918i
$11$	10.0869	+	4.38810i	0.916987	+	0.398918i
$12$	−3.41206	−	3.41206i	−0.284338	−	0.284338i
$13$	22.7719	−	3.60671i	1.75168	−	0.277439i	0.803531	−	0.595263i	$-0.202952\pi$
$13$	22.7719	−	3.60671i	1.75168	−	0.277439i	0.948150	+	0.317824i	$0.102952\pi$
$14$	−4.37444	−	1.42134i	−0.312460	−	0.101524i
$15$	11.8881	−	2.04953i	0.792539	−	0.136635i
$16$	3.23607	−	2.35114i	0.202254	−	0.146946i
$17$	−25.2737	−	4.00296i	−1.48669	−	0.235468i	−0.640338	−	0.768093i	$-0.721206\pi$
$17$	−25.2737	−	4.00296i	−1.48669	−	0.235468i	−0.846351	+	0.532625i	$0.821206\pi$
$18$	−4.00567	−	2.04099i	−0.222537	−	0.113388i
$19$	−12.6650	−	4.11512i	−0.666582	−	0.216585i	−0.0438703	−	0.999037i	$-0.513969\pi$
$19$	−12.6650	−	4.11512i	−0.666582	−	0.216585i	−0.622711	+	0.782452i	$0.713969\pi$
$20$	0.136436	+	9.99907i	0.00682179	+	0.499953i
$21$	7.84699			0.373666
$22$	3.89777	−	15.0601i	0.177171	−	0.684551i
$23$	−31.6053	+	31.6053i	−1.37414	+	1.37414i	−0.519945	+	0.854200i	$0.674048\pi$
$23$	−31.6053	+	31.6053i	−1.37414	+	1.37414i	−0.854200	+	0.519945i	$0.825952\pi$
$24$	−4.01112	+	5.52083i	−0.167130	+	0.230035i
$25$	−20.6188	−	14.1373i	−0.824753	−	0.565493i
$26$	−10.0757	−	31.0099i	−0.387527	−	1.19269i
$27$	29.0222	+	4.59667i	1.07490	+	0.170247i
$28$	−1.01757	+	6.42468i	−0.0363418	+	0.229453i
$29$	9.21597	−	2.99445i	0.317792	−	0.103257i	−0.145778	−	0.989317i	$-0.546568\pi$
$29$	9.21597	−	2.99445i	0.317792	−	0.103257i	0.463570	+	0.886060i	$0.346568\pi$
$30$	−5.49280	−	16.1519i	−0.183093	−	0.538396i
$31$	21.3814	+	15.5345i	0.689723	+	0.501113i	0.876569	−	0.481276i	$-0.159827\pi$
$31$	21.3814	+	15.5345i	0.689723	+	0.501113i	−0.186846	+	0.982389i	$0.559827\pi$
$32$	−4.00000	−	4.00000i	−0.125000	−	0.125000i
$33$	1.61533	+	26.4904i	0.0489494	+	0.802739i
$34$			36.1880i			1.06435i
$35$	−11.6547	−	11.3409i	−0.332992	−	0.324027i
$36$	−1.96468	+	6.04666i	−0.0545745	+	0.167963i
$37$	−23.7594	+	46.6304i	−0.642145	+	1.26028i	0.308861	+	0.951107i	$0.400052\pi$
$37$	−23.7594	+	46.6304i	−0.642145	+	1.26028i	−0.951006	+	0.309173i	$0.899948\pi$
$38$	−2.94610	+	18.6010i	−0.0775290	+	0.489499i
$39$	32.6963	+	45.0026i	0.838367	+	1.15391i
$40$	13.9365	−	2.40269i	0.348413	−	0.0600671i
$41$	10.6065	−	32.6435i	0.258696	−	0.796183i	−0.734383	−	0.678735i	$-0.762529\pi$
$41$	10.6065	−	32.6435i	0.258696	−	0.796183i	0.993079	−	0.117448i	$-0.0374715\pi$
$42$	−1.73600	−	10.9607i	−0.0413334	−	0.260969i
$43$	−3.10574	+	3.10574i	−0.0722265	+	0.0722265i	−0.742297	−	0.670071i	$-0.766264\pi$
$43$	−3.10574	+	3.10574i	−0.0722265	+	0.0722265i	0.670071	+	0.742297i	$0.266264\pi$
$44$	−21.8983	−	2.11264i	−0.497689	−	0.0480144i
$45$	−9.51718	−	12.7303i	−0.211493	−	0.282896i
$46$	51.1385	+	37.1543i	1.11171	+	0.807702i
$47$	−32.0813	+	16.3462i	−0.682581	+	0.347792i	−0.760656	−	0.649155i	$-0.775123\pi$
$47$	−32.0813	+	16.3462i	−0.682581	+	0.347792i	0.0780750	+	0.996947i	$0.475123\pi$
$48$	8.59890	+	4.38136i	0.179144	+	0.0912783i
$49$	22.5839	+	31.0841i	0.460896	+	0.634369i
$50$	−15.1855	+	31.9281i	−0.303710	+	0.638561i
$51$	−19.0780	−	58.7161i	−0.374079	−	1.15130i
$52$	−41.0856	+	20.9341i	−0.790107	+	0.402580i
$53$	−74.7316	+	11.8363i	−1.41003	+	0.223327i	−0.814574	−	0.580060i	$-0.803029\pi$
$53$	−74.7316	+	11.8363i	−1.41003	+	0.223327i	−0.595457	+	0.803387i	$0.703029\pi$
$54$		−	41.5552i		−	0.769541i
$55$	35.8864	−	41.6794i	0.652479	−	0.757806i
$56$	9.19912			0.164270
$57$	−5.02614	−	31.7338i	−0.0881779	−	0.556734i
$58$	−6.22152	−	12.2104i	−0.107268	−	0.210525i
$59$	46.5392	−	15.1215i	0.788800	−	0.256297i	0.113207	−	0.993571i	$-0.463888\pi$
$59$	46.5392	−	15.1215i	0.788800	−	0.256297i	0.675593	+	0.737275i	$0.263888\pi$
$60$	−21.3458	+	11.2457i	−0.355763	+	0.187428i
$61$	−9.53445	+	6.92718i	−0.156302	+	0.113560i	−0.663188	−	0.748453i	$-0.730797\pi$
$61$	−9.53445	+	6.92718i	−0.156302	+	0.113560i	0.506885	+	0.862014i	$0.330797\pi$
$62$	16.9684	−	33.3023i	0.273683	−	0.537134i
$63$	−4.69384	−	9.21217i	−0.0745053	−	0.146225i
$64$	−4.70228	+	6.47214i	−0.0734732	+	0.101127i
$65$	16.4784	−	114.095i	0.253514	−	1.75530i
$66$	36.6445	−	8.11682i	0.555220	−	0.122982i
$67$	28.1955	+	28.1955i	0.420828	+	0.420828i	0.885489	−	0.464661i	$-0.153824\pi$
$67$	28.1955	+	28.1955i	0.420828	+	0.420828i	−0.464661	+	0.885489i	$0.653824\pi$
$68$	50.5474	−	8.00593i	0.743345	−	0.117734i
$69$	−102.561	−	33.3242i	−1.48640	−	0.482959i
$70$	−13.2627	+	18.7883i	−0.189467	+	0.268405i
$71$	−3.31366	+	2.40752i	−0.0466713	+	0.0339087i	−0.610876	−	0.791726i	$-0.709183\pi$
$71$	−3.31366	+	2.40752i	−0.0466713	+	0.0339087i	0.564205	+	0.825635i	$0.309183\pi$
$72$	8.88064	+	1.40656i	0.123342	+	0.0195355i
$73$	−27.5587	−	14.0419i	−0.377517	−	0.192354i	0.254928	−	0.966960i	$-0.417948\pi$
$73$	−27.5587	−	14.0419i	−0.377517	−	0.192354i	−0.632444	+	0.774606i	$0.717948\pi$
$74$	70.3897	+	22.8710i	0.951213	+	0.309068i
$75$	7.80672	−	59.8100i	0.104090	−	0.797466i
$76$	26.6336			0.350443
$77$	27.6100	−	22.7514i	0.358571	−	0.295472i
$78$	55.6263	−	55.6263i	0.713158	−	0.713158i
$79$	46.6732	−	64.2401i	0.590800	−	0.813166i	−0.404028	−	0.914747i	$-0.632390\pi$
$79$	46.6732	−	64.2401i	0.590800	−	0.813166i	0.994827	+	0.101581i	$0.0323900\pi$
$80$	−6.43928	−	18.9350i	−0.0804910	−	0.236688i
$81$	13.0665	+	40.2147i	0.161315	+	0.496477i
$82$	−47.9430	−	7.59343i	−0.584671	−	0.0926028i
$83$	−1.12047	+	7.07437i	−0.0134996	+	0.0852334i	−0.993518	−	0.113672i	$-0.963739\pi$
$83$	−1.12047	+	7.07437i	−0.0134996	+	0.0852334i	0.980019	+	0.198905i	$0.0637387\pi$
$84$	−14.9259	+	4.84971i	−0.177689	+	0.0577346i
$85$	−56.5245	+	114.781i	−0.664994	+	1.35036i
$86$	5.02519	+	3.65102i	0.0584325	+	0.0424537i
$87$	16.5319	+	16.5319i	0.190021	+	0.190021i
$88$	1.89367	+	31.0550i	0.0215190	+	0.352898i
$89$			59.8878i			0.672897i	0.941702	+	0.336448i	$0.109226\pi$
$89$			59.8878i			0.672897i	−0.941702	+	0.336448i	$0.890774\pi$
$90$	−15.6763	+	16.1100i	−0.174181	+	0.179000i
$91$	23.1719	−	71.3159i	0.254637	−	0.783691i
$92$	40.5837	−	79.6501i	0.441128	−	0.865762i
$93$	−9.97500	+	62.9796i	−0.107258	+	0.677201i
$94$	29.9299	+	41.1949i	0.318403	+	0.438244i
$95$	−38.3986	+	54.3966i	−0.404195	+	0.572596i
$96$	4.21754	−	12.9803i	0.0439327	−	0.135211i
$97$	9.83435	+	62.0916i	0.101385	+	0.640120i	0.985085	+	0.172067i	$0.0550445\pi$
$97$	9.83435	+	62.0916i	0.101385	+	0.640120i	−0.883700	+	0.468053i	$0.844956\pi$
$98$	38.4220	−	38.4220i	0.392061	−	0.392061i
$99$	30.1328	−	17.7421i	0.304372	−	0.179213i
$100$	47.9567	+	14.1476i	0.479567	+	0.141476i
$101$	−48.6808	−	35.3686i	−0.481988	−	0.350185i	0.320107	−	0.947381i	$-0.396281\pi$
$101$	−48.6808	−	35.3686i	−0.481988	−	0.350185i	−0.802095	+	0.597197i	$0.796281\pi$
$102$	−77.7941	+	39.6381i	−0.762688	+	0.388609i
$103$	26.1537	+	13.3260i	0.253919	+	0.129378i	0.576318	−	0.817226i	$-0.304489\pi$
$103$	26.1537	+	13.3260i	0.253919	+	0.129378i	−0.322398	+	0.946604i	$0.604489\pi$
$104$	38.3303	+	52.7571i	0.368560	+	0.507280i
$105$	11.6140	−	37.4766i	0.110610	−	0.356920i
$106$	33.0660	+	101.767i	0.311943	+	0.960063i
$107$	77.3985	−	39.4365i	0.723350	−	0.368565i	−0.0532312	−	0.998582i	$-0.516952\pi$
$107$	77.3985	−	39.4365i	0.723350	−	0.368565i	0.776581	+	0.630017i	$0.216952\pi$
$108$	−58.0444	+	9.19333i	−0.537448	+	0.0851235i
$109$		−	37.7842i		−	0.346644i	−0.984865	−	0.173322i	$-0.944550\pi$
$109$		−	37.7842i		−	0.346644i	0.984865	−	0.173322i	$-0.0554501\pi$
$110$	−66.1570	−	40.9054i	−0.601427	−	0.371867i
$111$	−126.267			−1.13754
$112$	−2.03514	−	12.8494i	−0.0181709	−	0.114726i
$113$	−89.1126	−	174.893i	−0.788607	−	1.54773i	−0.835922	−	0.548849i	$-0.815066\pi$
$113$	−89.1126	−	174.893i	−0.788607	−	1.54773i	0.0473146	−	0.998880i	$-0.484934\pi$
$114$	−43.2139	+	14.0411i	−0.379069	+	0.123167i
$115$	104.167	+	197.722i	0.905797	+	1.71933i
$116$	−15.6792	+	11.3916i	−0.135165	+	0.0982032i
$117$	33.2740	−	65.3039i	0.284393	−	0.558153i
$118$	−31.4177	−	61.6607i	−0.266252	−	0.522549i
$119$	−48.9181	+	67.3300i	−0.411076	+	0.565798i
$120$	20.4303	+	27.3280i	0.170253	+	0.227733i
$121$	82.4892	+	88.5242i	0.681729	+	0.731605i
$122$	11.7852	+	11.7852i	0.0966002	+	0.0966002i
$123$	81.7923	−	12.9546i	0.664978	−	0.105322i
$124$	−50.2707	−	16.3339i	−0.405409	−	0.131725i
$125$	−98.0359	+	77.5498i	−0.784287	+	0.620398i
$126$	−11.8292	+	8.59438i	−0.0938822	+	0.0682094i
$127$	158.759	+	25.1450i	1.25007	+	0.197992i	0.746163	−	0.665764i	$-0.231894\pi$
$127$	158.759	+	25.1450i	1.25007	+	0.197992i	0.503910	+	0.863756i	$0.331894\pi$
$128$	10.0806	+	5.13632i	0.0787546	+	0.0401275i
$129$	−10.0783	−	3.27464i	−0.0781265	−	0.0253848i
$130$	−163.013	+	2.22429i	−1.25395	+	0.0171099i
$131$	−97.8485			−0.746935			−0.373468	−	0.927643i	$-0.621831\pi$
$131$	−97.8485			−0.746935			−0.373468	+	0.927643i	$0.621831\pi$
$132$	−19.4445	−	49.3894i	−0.147307	−	0.374162i
$133$	−30.6258	+	30.6258i	−0.230269	+	0.230269i
$134$	33.1458	−	45.6213i	0.247357	−	0.340457i
$135$	64.9080	−	131.804i	0.480800	−	0.976329i
$136$	−22.3654	−	68.8336i	−0.164451	−	0.506129i
$137$	−126.467	−	20.0304i	−0.923117	−	0.146207i	−0.323256	−	0.946312i	$-0.604777\pi$
$137$	−126.467	−	20.0304i	−0.923117	−	0.146207i	−0.599861	+	0.800104i	$0.704777\pi$
$138$	−23.8575	+	150.630i	−0.172880	+	1.09152i
$139$	−178.685	+	58.0582i	−1.28550	+	0.417685i	−0.870515	−	0.492143i	$-0.836214\pi$
$139$	−178.685	+	58.0582i	−1.28550	+	0.417685i	−0.414987	+	0.909827i	$0.636214\pi$
$140$	29.1777	+	14.3688i	0.208412	+	0.102634i
$141$	−70.2798	−	51.0613i	−0.498439	−	0.362137i
$142$	4.09591	+	4.09591i	0.0288445	+	0.0288445i
$143$	245.523	+	63.5447i	1.71694	+	0.444369i
$144$		−	12.7157i		−	0.0883033i
$145$	−0.661048	−	48.4467i	−0.00455895	−	0.334115i
$146$	−13.5169	+	41.6006i	−0.0925812	+	0.284936i
$147$	−42.0851	+	82.5967i	−0.286293	+	0.561882i
$148$	16.3738	−	103.380i	0.110634	−	0.698516i
$149$	−1.61613	−	2.22441i	−0.0108465	−	0.0149289i	0.803559	−	0.595225i	$-0.202937\pi$
$149$	−1.61613	−	2.22441i	−0.0108465	−	0.0149289i	−0.814406	+	0.580296i	$0.802937\pi$
$150$	−85.2698	+	2.32742i	−0.568465	+	0.0155161i
$151$	−58.1803	+	179.061i	−0.385300	+	1.18583i	0.550962	+	0.834530i	$0.314261\pi$
$151$	−58.1803	+	179.061i	−0.385300	+	1.18583i	−0.936262	+	0.351302i	$0.885739\pi$
$152$	−5.89221	−	37.2019i	−0.0387645	−	0.244750i
$153$	−57.5193	+	57.5193i	−0.375943	+	0.375943i
$154$	−37.8874	−	33.5324i	−0.246022	−	0.217743i
$155$	105.837	−	79.1238i	0.682821	−	0.510476i
$156$	−90.0052	−	65.3926i	−0.576957	−	0.419184i
$157$	27.0952	−	13.8057i	0.172581	−	0.0879345i	−0.365566	−	0.930785i	$-0.619125\pi$
$157$	27.0952	−	13.8057i	0.172581	−	0.0879345i	0.538147	+	0.842851i	$0.319125\pi$
$158$	−100.056	−	50.9812i	−0.633268	−	0.322666i
$159$	−107.301	−	147.688i	−0.674851	−	0.928853i
$160$	−25.0239	+	13.1834i	−0.156400	+	0.0823965i
$161$	44.9220	+	138.256i	0.279019	+	0.858731i
$162$	53.2812	−	27.1481i	0.328896	−	0.167581i
$163$	−36.5899	+	5.79528i	−0.224478	+	0.0355538i	−0.267660	−	0.963513i	$-0.586250\pi$
$163$	−36.5899	+	5.79528i	−0.224478	+	0.0355538i	0.0431821	+	0.999067i	$0.486250\pi$
$164$			68.6468i			0.418578i
$165$	128.907	+	31.4927i	0.781254	+	0.190865i
$166$	10.1294			0.0610204
$167$	32.2046	+	203.332i	0.192842	+	1.21755i	0.874186	+	0.485592i	$0.161396\pi$
$167$	32.2046	+	203.332i	0.192842	+	1.21755i	−0.681344	+	0.731963i	$0.738604\pi$
$168$	10.0762	+	19.7756i	0.0599771	+	0.117712i
$169$	344.820	−	112.039i	2.04036	−	0.662952i
$170$	172.831	+	53.5604i	1.01665	+	0.315061i
$171$	−34.2482	+	24.8828i	−0.200282	+	0.145513i
$172$	3.98802	−	7.82692i	0.0231861	−	0.0455054i
$173$	15.8891	+	31.1841i	0.0918443	+	0.180255i	0.932359	−	0.361535i	$-0.117747\pi$
$173$	15.8891	+	31.1841i	0.0918443	+	0.180255i	−0.840514	+	0.541789i	$0.817747\pi$
$174$	19.4344	−	26.7491i	0.111692	−	0.153731i
$175$	−71.4132	+	38.8767i	−0.408075	+	0.222153i
$176$	42.9588	−	9.51544i	0.244084	−	0.0540650i
$177$	83.4833	+	83.4833i	0.471657	+	0.471657i
$178$	83.6514	−	13.2491i	0.469952	−	0.0744330i
$179$	−53.4490	−	17.3666i	−0.298598	−	0.0970203i	0.155887	−	0.987775i	$-0.450177\pi$
$179$	−53.4490	−	17.3666i	−0.298598	−	0.0970203i	−0.454485	+	0.890755i	$0.650177\pi$
$180$	25.9705	+	18.3326i	0.144281	+	0.101848i
$181$	149.963	−	108.954i	0.828523	−	0.601957i	−0.0906180	−	0.995886i	$-0.528884\pi$
$181$	149.963	−	108.954i	0.828523	−	0.601957i	0.919141	+	0.393928i	$0.128884\pi$
$182$	−104.741	−	16.5893i	−0.575498	−	0.0911499i
$183$	−25.3350	−	12.9088i	−0.138442	−	0.0705400i
$184$	−120.234	−	39.0663i	−0.653445	−	0.212317i
$185$	187.538	+	182.489i	1.01372	+	0.986425i
$186$	90.1769			0.484822
$187$	−237.367	−	151.281i	−1.26934	−	0.808988i
$188$	50.9198	−	50.9198i	0.270850	−	0.270850i
$189$	56.1734	−	77.3161i	0.297214	−	0.409080i
$190$	84.4763	+	41.6009i	0.444612	+	0.218952i
$191$	−62.0339	−	190.921i	−0.324785	−	0.999585i	−0.971538	−	0.236885i	$-0.923873\pi$
$191$	−62.0339	−	190.921i	−0.324785	−	0.999585i	0.646753	−	0.762700i	$-0.276127\pi$
$192$	−19.0639	−	3.01942i	−0.0992911	−	0.0157262i
$193$	34.3640	−	216.966i	0.178052	−	1.12418i	−0.723123	−	0.690719i	$-0.757294\pi$
$193$	34.3640	−	216.966i	0.178052	−	1.12418i	0.901175	−	0.433456i	$-0.142706\pi$
$194$	84.5541	−	27.4733i	0.435846	−	0.141615i
$195$	263.322	−	89.5483i	1.35037	−	0.459222i
$196$	−62.1681	−	45.1678i	−0.317184	−	0.230448i
$197$	42.0008	+	42.0008i	0.213202	+	0.213202i	0.805626	−	0.592424i	$-0.201829\pi$
$197$	42.0008	+	42.0008i	0.213202	+	0.213202i	−0.592424	+	0.805626i	$0.701829\pi$
$198$	−31.4486	−	38.1645i	−0.158831	−	0.192750i
$199$		−	149.329i		−	0.750396i	−0.926945	−	0.375198i	$-0.877575\pi$
$199$		−	149.329i		−	0.750396i	0.926945	−	0.375198i	$-0.122425\pi$
$200$	9.15191	−	70.1159i	0.0457595	−	0.350580i
$201$	−29.7289	+	91.4961i	−0.147905	+	0.455205i
$202$	−38.6333	+	75.8221i	−0.191254	+	0.375357i
$203$	4.93025	−	31.1284i	0.0242869	−	0.153342i
$204$	72.5771	+	99.8938i	0.355770	+	0.489676i
$205$	−140.205	−	98.9703i	−0.683925	−	0.482782i
$206$	12.8277	−	39.4797i	0.0622705	−	0.191649i
$207$	22.2273	+	140.338i	0.107378	+	0.677961i
$208$	65.2114	−	65.2114i	0.313516	−	0.313516i
$209$	−109.693	−	97.0841i	−0.524847	−	0.464517i
$210$	−54.9168	−	7.93150i	−0.261509	−	0.0377690i
$211$	−44.5674	−	32.3801i	−0.211220	−	0.153460i	0.477146	−	0.878824i	$-0.341671\pi$
$211$	−44.5674	−	32.3801i	−0.211220	−	0.153460i	−0.688365	+	0.725364i	$0.741671\pi$
$212$	134.833	−	68.7007i	0.636003	−	0.324060i
$213$	−8.80508	−	4.48641i	−0.0413384	−	0.0210630i
$214$	−72.2080	−	99.3858i	−0.337420	−	0.464419i
$215$	10.2361	+	19.4295i	0.0476097	+	0.0903696i
$216$	25.6825	+	79.0427i	0.118901	+	0.365939i
$217$	76.5880	−	39.0236i	0.352940	−	0.179832i
$218$	−52.7771	+	8.35907i	−0.242097	+	0.0383443i
$219$		−	74.6242i		−	0.340750i
$220$	−42.5007	+	101.458i	−0.193185	+	0.461172i
$221$	−589.967			−2.66953
$222$	27.9343	+	176.370i	0.125830	+	0.794459i
$223$	−3.50042	−	6.86995i	−0.0156969	−	0.0308070i	0.883025	−	0.469326i	$-0.155503\pi$
$223$	−3.50042	−	6.86995i	−0.0156969	−	0.0308070i	−0.898722	+	0.438519i	$0.855503\pi$
$224$	−17.4978	+	5.68537i	−0.0781151	+	0.0253811i
$225$	−74.8851	+	26.6116i	−0.332823	+	0.118274i
$226$	−224.577	+	163.165i	−0.993703	+	0.721967i
$227$	46.6567	−	91.5688i	0.205536	−	0.403387i	−0.765110	−	0.643899i	$-0.777316\pi$
$227$	46.6567	−	91.5688i	0.205536	−	0.403387i	0.970646	+	0.240512i	$0.0773155\pi$
$228$	29.1729	+	57.2550i	0.127951	+	0.251118i
$229$	−21.7257	+	29.9029i	−0.0948723	+	0.130580i	−0.853814	−	0.520578i	$-0.825717\pi$
$229$	−21.7257	+	29.9029i	−0.0948723	+	0.130580i	0.758942	+	0.651158i	$0.225717\pi$
$230$	253.134	−	189.243i	1.10058	−	0.822795i
$231$	79.1515	+	34.4334i	0.342647	+	0.149062i
$232$	19.3805	+	19.3805i	0.0835366	+	0.0835366i
$233$	331.934	−	52.5732i	1.42461	−	0.225636i	0.603936	−	0.797032i	$-0.293598\pi$
$233$	331.934	−	52.5732i	1.42461	−	0.225636i	0.820674	+	0.571396i	$0.193598\pi$
$234$	−98.5778	−	32.0299i	−0.421273	−	0.136880i
$235$	30.5860	+	177.411i	0.130153	+	0.754942i
$236$	−79.1773	+	57.5256i	−0.335497	+	0.243753i
$237$	189.221	+	29.9697i	0.798403	+	0.126455i
$238$	104.869	+	53.4334i	0.440625	+	0.224510i
$239$	−261.355	−	84.9194i	−1.09354	−	0.355311i	−0.293924	−	0.955829i	$-0.594961\pi$
$239$	−261.355	−	84.9194i	−1.09354	−	0.355311i	−0.799612	+	0.600517i	$0.794961\pi$
$240$	33.6519	−	34.5830i	0.140216	−	0.144096i
$241$	193.987			0.804924			0.402462	−	0.915437i	$-0.368155\pi$
$241$	193.987			0.804924			0.402462	+	0.915437i	$0.368155\pi$
$242$	105.402	−	134.806i	0.435543	−	0.557048i
$243$	114.860	−	114.860i	0.472676	−	0.472676i
$244$	13.8544	−	19.0689i	0.0567802	−	0.0781512i
$245$	181.881	−	61.8525i	0.742370	−	0.252459i
$246$	−36.1901	−	111.382i	−0.147114	−	0.452771i
$247$	−303.249	−	48.0299i	−1.22773	−	0.194453i
$248$	−11.6938	+	73.8318i	−0.0471525	+	0.297709i
$249$	−16.4352	+	5.34013i	−0.0660050	+	0.0214463i
$250$	130.010	+	119.780i	0.520041	+	0.479121i
$251$	130.229	+	94.6169i	0.518840	+	0.376960i	0.816167	−	0.577816i	$-0.196095\pi$
$251$	130.229	+	94.6169i	0.518840	+	0.376960i	−0.297327	+	0.954776i	$0.596095\pi$
$252$	14.6216	+	14.6216i	0.0580224	+	0.0580224i
$253$	−457.486	+	180.111i	−1.80824	+	0.711902i
$254$		−	227.318i		−	0.894953i
$255$	−308.660	+	4.21162i	−1.21043	+	0.0165162i
$256$	4.94427	−	15.2169i	0.0193136	−	0.0594410i
$257$	−28.3621	+	55.6637i	−0.110358	+	0.216590i	−0.939580	−	0.342330i	$-0.888784\pi$
$257$	−28.3621	+	55.6637i	−0.110358	+	0.216590i	0.829222	+	0.558920i	$0.188784\pi$
$258$	−2.34439	+	14.8019i	−0.00908677	+	0.0573716i
$259$	100.048	+	137.704i	0.386286	+	0.531676i
$260$	39.1706	+	227.205i	0.150656	+	0.873866i
$261$	9.51912	−	29.2968i	0.0364717	−	0.112248i
$262$	21.6472	+	136.675i	0.0826229	+	0.521660i
$263$	−296.982	+	296.982i	−1.12921	+	1.12921i	−0.138902	+	0.990306i	$0.544357\pi$
$263$	−296.982	+	296.982i	−1.12921	+	1.12921i	−0.990306	+	0.138902i	$0.955643\pi$
$264$	−64.6855	+	38.0866i	−0.245021	+	0.144268i
$265$	−54.0781	+	374.431i	−0.204068	+	1.41295i
$266$	49.5535	+	36.0028i	0.186292	+	0.135349i
$267$	−128.742	+	65.5974i	−0.482181	+	0.245683i
$268$	−71.0568	−	36.2052i	−0.265137	−	0.135094i
$269$	198.171	+	272.759i	0.736696	+	1.01397i	0.998802	+	0.0489355i	$0.0155829\pi$
$269$	198.171	+	272.759i	0.736696	+	1.01397i	−0.262106	+	0.965039i	$0.584417\pi$
$270$	−198.464	−	61.5043i	−0.735053	−	0.227794i
$271$	−81.2048	−	249.923i	−0.299649	−	0.922224i	−0.981620	−	0.190845i	$-0.938877\pi$
$271$	−81.2048	−	249.923i	−0.299649	−	0.922224i	0.681972	−	0.731379i	$-0.261123\pi$
$272$	−91.1990	+	46.4682i	−0.335290	+	0.170839i
$273$	178.691	−	28.3018i	0.654544	−	0.103670i
$274$			181.081i			0.660879i
$275$	−145.943	−	233.078i	−0.530703	−	0.847558i
$276$	215.679			0.781444
$277$	−58.2882	−	368.017i	−0.210427	−	1.32858i	−0.836134	−	0.548525i	$-0.815190\pi$
$277$	−58.2882	−	368.017i	−0.210427	−	1.32858i	0.625707	−	0.780058i	$-0.284810\pi$
$278$	120.627	+	236.743i	0.433908	+	0.851593i
$279$	79.9032	−	25.9621i	0.286392	−	0.0930543i
$280$	13.6153	−	43.9343i	0.0486260	−	0.156908i
$281$	327.095	−	237.648i	1.16404	−	0.845723i	0.173755	−	0.984789i	$-0.444410\pi$
$281$	327.095	−	237.648i	1.16404	−	0.845723i	0.990283	+	0.139066i	$0.0444100\pi$
$282$	−55.7744	+	109.463i	−0.197782	+	0.388168i
$283$	−127.289	−	249.818i	−0.449783	−	0.882750i	−0.998895	−	0.0470005i	$-0.985034\pi$
$283$	−127.289	−	249.818i	−0.449783	−	0.882750i	0.549111	−	0.835749i	$-0.314966\pi$
$284$	4.81503	−	6.62733i	0.0169543	−	0.0233357i
$285$	−158.997	−	22.9636i	−0.557885	−	0.0805739i
$286$	34.4420	−	357.005i	0.120426	−	1.24827i
$287$	−78.9364	−	78.9364i	−0.275040	−	0.275040i
$288$	−17.7613	+	2.81311i	−0.0616711	+	0.00976775i
$289$	347.882	+	113.034i	1.20374	+	0.391120i
$290$	−67.5243	+	11.6413i	−0.232842	+	0.0401424i
$291$	−122.708	+	89.1525i	−0.421677	+	0.306366i
$292$	61.0982	+	9.67700i	0.209240	+	0.0331404i
$293$	−351.695	−	179.197i	−1.20032	−	0.611595i	−0.264609	−	0.964356i	$-0.585243\pi$
$293$	−351.695	−	179.197i	−1.20032	−	0.611595i	−0.935714	+	0.352761i	$0.885243\pi$
$294$	124.682	+	40.5116i	0.424088	+	0.137795i
$295$	−3.33819	−	244.648i	−0.0113159	−	0.829317i
$296$	−148.024			−0.500082
$297$	272.572	+	173.718i	0.917751	+	0.584910i
$298$	−2.74952	+	2.74952i	−0.00922659	+	0.00922659i
$299$	−605.721	+	833.703i	−2.02582	+	2.78830i
$300$	22.1153	+	118.590i	0.0737177	+	0.395300i
$301$	4.41432	+	13.5859i	0.0146655	+	0.0451358i
$302$	262.984	+	41.6525i	0.870807	+	0.137922i
$303$	22.7109	−	143.391i	0.0749534	−	0.473237i
$304$	−50.6602	+	16.4605i	−0.166645	+	0.0541464i
$305$	18.9721	+	55.7884i	0.0622036	+	0.182913i
$306$	93.0682	+	67.6180i	0.304144	+	0.220974i
$307$	15.5350	+	15.5350i	0.0506025	+	0.0506025i	0.731955	−	0.681353i	$-0.238608\pi$
$307$	15.5350	+	15.5350i	0.0506025	+	0.0506025i	−0.681353	+	0.731955i	$0.738608\pi$
$308$	−38.4562	+	60.3396i	−0.124858	+	0.195908i
$309$			70.8197i			0.229190i
$310$	−133.935	−	130.329i	−0.432048	−	0.420416i
$311$	−139.171	+	428.325i	−0.447496	+	1.37725i	0.432228	+	0.901764i	$0.357728\pi$
$311$	−139.171	+	428.325i	−0.447496	+	1.37725i	−0.879723	+	0.475486i	$0.842272\pi$
$312$	−71.4286	+	140.186i	−0.228938	+	0.449316i
$313$	5.31448	−	33.5543i	0.0169792	−	0.107202i	−0.977743	−	0.209805i	$-0.932717\pi$
$313$	5.31448	−	33.5543i	0.0169792	−	0.107202i	0.994722	+	0.102603i	$0.0327170\pi$
$314$	−25.2782	−	34.7924i	−0.0805037	−	0.110804i
$315$	−50.9438	+	8.78280i	−0.161726	+	0.0278819i
$316$	−49.0751	+	151.038i	−0.155301	+	0.477967i
$317$	−42.6927	−	269.551i	−0.134677	−	0.850320i	−0.958836	−	0.283961i	$-0.908352\pi$
$317$	−42.6927	−	269.551i	−0.134677	−	0.850320i	0.824159	−	0.566359i	$-0.191648\pi$
$318$	−182.552	+	182.552i	−0.574062	+	0.574062i
$319$	106.100	+	10.2360i	0.332602	+	0.0320877i
$320$	23.9507	+	32.0369i	0.0748461	+	0.100115i
$321$	169.555	+	123.189i	0.528209	+	0.383766i
$322$	183.178	−	93.3337i	0.568875	−	0.289856i
$323$	303.620	+	154.702i	0.940000	+	0.478954i
$324$	−49.7080	−	68.4173i	−0.153420	−	0.211164i
$325$	−520.518	−	247.567i	−1.60159	−	0.761744i
$326$	16.1897	+	49.8268i	0.0496617	+	0.152843i
$327$	81.2256	−	41.3865i	0.248396	−	0.126564i
$328$	95.8861	−	15.1869i	0.292336	−	0.0463014i
$329$			117.104i			0.355940i
$330$	15.4709	−	187.025i	0.0468814	−	0.566741i
$331$	126.015			0.380711			0.190355	−	0.981715i	$-0.439036\pi$
$331$	126.015			0.380711			0.190355	+	0.981715i	$0.439036\pi$
$332$	−2.24094	−	14.1487i	−0.00674982	−	0.0426167i
$333$	75.5291	+	148.234i	0.226814	+	0.445148i
$334$	276.889	−	89.9668i	0.829010	−	0.269362i
$335$	176.390	−	92.9283i	0.526539	−	0.277398i
$336$	25.3934	−	18.4494i	0.0755756	−	0.0549089i
$337$	177.755	−	348.864i	0.527463	−	1.03520i	−0.461514	−	0.887133i	$-0.652694\pi$
$337$	177.755	−	348.864i	0.527463	−	1.03520i	0.988977	−	0.148071i	$-0.0473065\pi$
$338$	−232.781	−	456.859i	−0.688702	−	1.35165i
$339$	278.364	−	383.135i	0.821132	−	1.13019i
$340$	36.5777	−	253.260i	0.107581	−	0.744882i
$341$	147.504	+	250.518i	0.432564	+	0.734656i
$342$	42.3331	+	42.3331i	0.123781	+	0.123781i
$343$	280.829	−	44.4790i	0.818744	−	0.129676i
$344$	−11.8149	−	3.83891i	−0.0343457	−	0.0111596i
$345$	−310.951	+	440.503i	−0.901306	+	1.27682i
$346$	40.0428	−	29.0928i	0.115731	−	0.0840832i
$347$	−569.575	−	90.2118i	−1.64143	−	0.259976i	−0.733680	−	0.679496i	$-0.762199\pi$
$347$	−569.575	−	90.2118i	−1.64143	−	0.259976i	−0.907746	+	0.419519i	$0.862199\pi$
$348$	−41.6627	−	21.2282i	−0.119720	−	0.0610006i
$349$	157.086	+	51.0405i	0.450104	+	0.146248i	0.525293	−	0.850922i	$-0.323956\pi$
$349$	157.086	+	51.0405i	0.450104	+	0.146248i	−0.0751884	+	0.997169i	$0.523956\pi$
$350$	70.1019	+	91.1493i	0.200291	+	0.260427i
$351$	677.468			1.93011
$352$	−22.7950	−	57.8998i	−0.0647586	−	0.164488i
$353$	296.633	−	296.633i	0.840321	−	0.840321i	−0.148579	−	0.988900i	$-0.547470\pi$
$353$	296.633	−	296.633i	0.840321	−	0.840321i	0.988900	+	0.148579i	$0.0474700\pi$
$354$	98.1405	−	135.079i	0.277233	−	0.381579i
$355$	6.59368	+	19.3891i	0.0185738	+	0.0546171i
$356$	−37.0127	−	113.913i	−0.103968	−	0.319981i
$357$	−198.323	−	31.4112i	−0.555526	−	0.0879866i
$358$	−12.4331	+	78.4997i	−0.0347294	+	0.219273i
$359$	355.912	−	115.643i	0.991399	−	0.322125i	0.231976	−	0.972722i	$-0.425481\pi$
$359$	355.912	−	115.643i	0.991399	−	0.322125i	0.759424	+	0.650597i	$0.225481\pi$
$360$	19.8615	−	40.3315i	0.0551708	−	0.112032i
$361$	−148.586	−	107.954i	−0.411595	−	0.299042i
$362$	−185.364	−	185.364i	−0.512055	−	0.512055i
$363$	−99.9488	+	274.293i	−0.275341	+	0.755628i
$364$			149.972i			0.412011i
$365$	−107.851	+	110.835i	−0.295483	+	0.303659i
$366$	−12.4262	+	38.2438i	−0.0339513	+	0.104491i
$367$	19.8331	−	38.9247i	0.0540413	−	0.106062i	−0.862406	−	0.506217i	$-0.831044\pi$
$367$	19.8331	−	38.9247i	0.0540413	−	0.106062i	0.916448	+	0.400155i	$0.131044\pi$
$368$	−27.9684	+	176.586i	−0.0760011	+	0.479852i
$369$	−64.1341	−	88.2730i	−0.173805	−	0.239222i
$370$	213.411	−	302.325i	0.576787	−	0.817095i
$371$	−76.0446	+	234.041i	−0.204972	+	0.630839i
$372$	−19.9500	−	125.959i	−0.0536290	−	0.338600i
$373$	−229.523	+	229.523i	−0.615344	+	0.615344i	−0.944334	−	0.328990i	$-0.893292\pi$
$373$	−229.523	+	229.523i	−0.615344	+	0.615344i	0.328990	+	0.944334i	$0.393292\pi$
$374$	−158.796	+	365.023i	−0.424589	+	0.975997i
$375$	−274.093	−	125.807i	−0.730915	−	0.335485i
$376$	−82.3899	−	59.8598i	−0.219122	−	0.159201i
$377$	199.065	−	101.429i	0.528023	−	0.269041i
$378$	−120.423	−	61.3584i	−0.318578	−	0.162324i
$379$	−372.712	−	512.994i	−0.983408	−	1.35355i	−0.934973	−	0.354719i	$-0.884577\pi$
$379$	−372.712	−	512.994i	−0.983408	−	1.35355i	−0.0484349	−	0.998826i	$-0.515423\pi$
$380$	39.4194	−	127.200i	0.103735	−	0.334737i
$381$	119.840	+	368.831i	0.314542	+	0.968060i
$382$	−252.955	+	128.887i	−0.662185	+	0.337400i
$383$	326.373	−	51.6924i	0.852149	−	0.134967i	0.284944	−	0.958544i	$-0.408025\pi$
$383$	326.373	−	51.6924i	0.852149	−	0.134967i	0.567205	+	0.823577i	$0.308025\pi$
$384$			27.2965i			0.0710846i
$385$	−67.7943	−	165.537i	−0.176089	−	0.429965i
$386$	−310.661			−0.804821
$387$	2.18420	+	13.7905i	0.00564392	+	0.0356343i
$388$	−57.0808	−	112.027i	−0.147115	−	0.288730i
$389$	147.993	−	48.0859i	0.380445	−	0.123614i	−0.112550	−	0.993646i	$-0.535902\pi$
$389$	147.993	−	48.0859i	0.380445	−	0.123614i	0.492996	+	0.870032i	$0.335902\pi$
$390$	−183.336	−	347.997i	−0.470093	−	0.892300i
$391$	925.299	−	672.269i	2.36649	−	1.71936i
$392$	−49.3369	+	96.8291i	−0.125859	+	0.247013i
$393$	−107.177	−	210.347i	−0.272716	−	0.535235i
$394$	49.3749	−	67.9587i	0.125317	−	0.172484i
$395$	−237.726	−	317.987i	−0.601839	−	0.805030i
$396$	−46.3508	+	52.3706i	−0.117047	+	0.132249i
$397$	91.6064	+	91.6064i	0.230747	+	0.230747i	0.813004	−	0.582258i	$-0.197831\pi$
$397$	91.6064	+	91.6064i	0.230747	+	0.230747i	−0.582258	+	0.813004i	$0.697831\pi$
$398$	−208.583	+	33.0363i	−0.524078	+	0.0830057i
$399$	−99.3826	−	32.2914i	−0.249079	−	0.0809307i
$400$	−99.9628	+	2.72846i	−0.249907	+	0.00682116i
$401$	486.739	−	353.636i	1.21381	−	0.881886i	0.218241	−	0.975895i	$-0.429968\pi$
$401$	486.739	−	353.636i	1.21381	−	0.881886i	0.995571	+	0.0940086i	$0.0299681\pi$
$402$	134.379	+	21.2835i	0.334276	+	0.0529441i
$403$	542.922	+	276.633i	1.34720	+	0.686434i
$404$	114.455	+	37.1888i	0.283305	+	0.0920515i
$405$	211.401	−	2.88454i	0.521978	−	0.00712232i
$406$	−44.5709			−0.109781
$407$	−444.276	+	366.095i	−1.09159	+	0.899497i
$408$	123.476	−	123.476i	0.302636	−	0.302636i
$409$	−2.69919	+	3.71512i	−0.00659949	+	0.00908342i	−0.812304	−	0.583234i	$-0.801787\pi$
$409$	−2.69919	+	3.71512i	−0.00659949	+	0.00908342i	0.805704	+	0.592318i	$0.201787\pi$
$410$	−107.224	+	217.733i	−0.261523	+	0.531057i
$411$	−95.4644	−	293.809i	−0.232273	−	0.714864i
$412$	−57.9832	−	9.18363i	−0.140736	−	0.0222904i
$413$	24.8970	−	157.193i	0.0602833	−	0.380614i
$414$	191.107	−	62.0944i	0.461611	−	0.149986i
$415$	32.1283	+	15.8218i	0.0774175	+	0.0381248i
$416$	−105.514	−	76.6606i	−0.253640	−	0.184280i
$417$	−320.529	−	320.529i	−0.768656	−	0.768656i
$418$	−111.340	+	174.697i	−0.266363	+	0.417936i
$419$			319.685i			0.762972i	0.924375	+	0.381486i	$0.124588\pi$
$419$			319.685i			0.762972i	−0.924375	+	0.381486i	$0.875412\pi$
$420$	1.07061	+	78.4626i	0.00254907	+	0.186816i
$421$	−39.8469	+	122.636i	−0.0946481	+	0.291297i	−0.987162	−	0.159723i	$-0.948940\pi$
$421$	−39.8469	+	122.636i	−0.0946481	+	0.291297i	0.892514	+	0.451020i	$0.148940\pi$
$422$	−35.3689	+	69.4153i	−0.0838125	+	0.164491i
$423$	−17.9054	+	113.050i	−0.0423295	+	0.267258i
$424$	−125.791	−	173.136i	−0.296676	−	0.408339i
$425$	464.523	+	439.839i	1.09300	+	1.03492i
$426$	−4.31867	+	13.2915i	−0.0101377	+	0.0312007i
$427$	5.99614	+	37.8581i	0.0140425	+	0.0886608i
$428$	−122.848	+	122.848i	−0.287027	+	0.287027i
$429$	132.327	+	597.409i	0.308455	+	1.39256i
$430$	24.8746	−	18.5962i	0.0578478	−	0.0432470i
$431$	−617.459	−	448.610i	−1.43262	−	1.04086i	−0.989522	−	0.144386i	$-0.953879\pi$
$431$	−617.459	−	448.610i	−1.43262	−	1.04086i	−0.443098	−	0.896473i	$-0.646121\pi$
$432$	104.725	−	53.3602i	0.242420	−	0.123519i
$433$	24.8720	+	12.6729i	0.0574412	+	0.0292678i	0.482475	−	0.875910i	$-0.339738\pi$
$433$	24.8720	+	12.6729i	0.0574412	+	0.0292678i	−0.425034	+	0.905177i	$0.639738\pi$
$434$	−71.4519	−	98.3451i	−0.164636	−	0.226602i
$435$	103.423	−	54.4867i	0.237754	−	0.125257i
$436$	23.3519	+	71.8698i	0.0535595	+	0.164839i
$437$	530.343	−	270.223i	1.21360	−	0.618360i
$438$	−104.235	+	16.5093i	−0.237980	+	0.0376924i
$439$			463.222i			1.05518i	0.849501	+	0.527588i	$0.176903\pi$
$439$			463.222i			1.05518i	−0.849501	+	0.527588i	$0.823097\pi$
$440$	151.119	+	36.9193i	0.343452	+	0.0839076i
$441$	122.140			0.276963
$442$	130.519	+	824.067i	0.295293	+	1.86440i
$443$	182.415	+	358.010i	0.411772	+	0.808148i	1.00000		0.000547229i	$-0.000174188\pi$
$443$	182.415	+	358.010i	0.411772	+	0.808148i	−0.588228	+	0.808695i	$0.700174\pi$
$444$	240.174	−	78.0373i	0.540933	−	0.175760i
$445$	286.019	+	88.6376i	0.642740	+	0.199186i
$446$	−8.82156	+	6.40924i	−0.0197793	+	0.0143705i
$447$	3.01166	−	5.91072i	0.00673750	−	0.0132231i
$448$	11.8124	+	23.1831i	0.0263670	+	0.0517481i
$449$	−190.802	+	262.617i	−0.424949	+	0.584892i	−0.966785	−	0.255592i	$-0.917729\pi$
$449$	−190.802	+	262.617i	−0.424949	+	0.584892i	0.541836	+	0.840484i	$0.317729\pi$
$450$	53.7381	+	98.7123i	0.119418	+	0.219361i
$451$	250.229	−	282.728i	0.554832	−	0.626891i
$452$	277.592	+	277.592i	0.614142	+	0.614142i
$453$	−448.658	+	71.0605i	−0.990415	+	0.156866i
$454$	−138.225	−	44.9122i	−0.304461	−	0.0989255i
$455$	−306.303	−	216.219i	−0.673194	−	0.475207i
$456$	73.5199	−	53.4153i	0.161228	−	0.117139i
$457$	−492.623	−	78.0238i	−1.07795	−	0.170730i	−0.407885	−	0.913033i	$-0.633734\pi$
$457$	−492.623	−	78.0238i	−1.07795	−	0.170730i	−0.670064	+	0.742303i	$0.733734\pi$
$458$	46.5749	+	23.7311i	0.101692	+	0.0518146i
$459$	−715.099	−	232.350i	−1.55795	−	0.506208i
$460$	−320.336	−	311.712i	−0.696383	−	0.677634i
$461$	96.2486			0.208782			0.104391	−	0.994536i	$-0.466711\pi$
$461$	96.2486			0.208782			0.104391	+	0.994536i	$0.466711\pi$
$462$	30.5858	−	118.177i	0.0662030	−	0.255794i
$463$	−257.405	+	257.405i	−0.555950	+	0.555950i	−0.928152	−	0.372202i	$-0.878603\pi$
$463$	−257.405	+	257.405i	−0.555950	+	0.555950i	0.372202	+	0.928152i	$0.378603\pi$
$464$	22.7831	−	31.3583i	0.0491016	−	0.0675825i
$465$	286.022	+	140.854i	0.615101	+	0.302911i
$466$	−146.869	−	452.016i	−0.315169	−	0.969991i
$467$	140.681	+	22.2817i	0.301245	+	0.0477125i	0.305227	−	0.952280i	$-0.401268\pi$
$467$	140.681	+	22.2817i	0.301245	+	0.0477125i	−0.00398232	+	0.999992i	$0.501268\pi$
$468$	−22.9309	+	144.780i	−0.0489976	+	0.309358i
$469$	123.340	−	40.0755i	0.262984	−	0.0854487i
$470$	241.042	−	81.9716i	0.512855	−	0.174408i
$471$	59.3569	+	43.1253i	0.126023	+	0.0915612i
$472$	97.8685	+	97.8685i	0.207348	+	0.207348i
$473$	−44.9554	+	17.6989i	−0.0950432	+	0.0374183i
$474$		−	270.935i		−	0.571593i
$475$	202.962	+	263.899i	0.427288	+	0.555577i
$476$	51.4355	−	158.302i	0.108058	−	0.332568i
$477$	−109.197	+	214.311i	−0.228925	+	0.449290i
$478$	−60.7956	+	383.848i	−0.127187	+	0.803030i
$479$	191.350	+	263.371i	0.399479	+	0.549835i	0.960613	−	0.277889i	$-0.0896349\pi$
$479$	191.350	+	263.371i	0.399479	+	0.549835i	−0.561134	+	0.827725i	$0.689635\pi$
$480$	−55.7504	−	39.3542i	−0.116147	−	0.0819879i
$481$	−372.863	+	1147.55i	−0.775182	+	2.38576i
$482$	−42.9160	−	270.961i	−0.0890373	−	0.562160i
$483$	−248.007	+	248.007i	−0.513472	+	0.513472i
$484$	−211.615	−	117.402i	−0.437221	−	0.242566i
$485$	311.100	+	44.9314i	0.641444	+	0.0926421i
$486$	−185.848	−	135.026i	−0.382403	−	0.277832i
$487$	−84.9695	+	43.2941i	−0.174475	+	0.0888996i	−0.539047	−	0.842276i	$-0.681215\pi$
$487$	−84.9695	+	43.2941i	−0.174475	+	0.0888996i	0.364572	+	0.931175i	$0.381215\pi$
$488$	−29.7005	−	15.1332i	−0.0608617	−	0.0310106i
$489$	−52.5366	−	72.3104i	−0.107437	−	0.147874i
$490$	−126.634	−	240.367i	−0.258436	−	0.490546i
$491$	−99.1371	−	305.113i	−0.201909	−	0.621411i	−0.999826	−	0.0186442i	$-0.994065\pi$
$491$	−99.1371	−	305.113i	−0.201909	−	0.621411i	0.797918	−	0.602767i	$-0.205935\pi$
$492$	−147.572	+	75.1916i	−0.299943	+	0.152828i
$493$	−244.909	+	38.7897i	−0.496772	+	0.0786809i
$494$			434.204i			0.878956i
$495$	−40.1365	−	170.171i	−0.0810839	−	0.343781i
$496$	105.715			0.213136
$497$	2.08394	+	13.1575i	0.00419303	+	0.0264738i
$498$	11.0951	+	21.7754i	0.0222793	+	0.0437257i
$499$	−110.784	+	35.9958i	−0.222011	+	0.0721359i	−0.417911	−	0.908488i	$-0.637237\pi$
$499$	−110.784	+	35.9958i	−0.222011	+	0.0721359i	0.195899	+	0.980624i	$0.437237\pi$
$500$	138.547	−	208.098i	0.277094	−	0.416196i
$501$	−401.832	+	291.948i	−0.802060	+	0.582731i
$502$	103.350	−	202.836i	0.205877	−	0.404056i
$503$	94.0821	+	184.646i	0.187042	+	0.367090i	0.965418	−	0.260708i	$-0.0839561\pi$
$503$	94.0821	+	184.646i	0.187042	+	0.367090i	−0.778376	+	0.627799i	$0.783956\pi$
$504$	17.1888	−	23.6583i	0.0341047	−	0.0469411i
$505$	−240.968	+	180.148i	−0.477165	+	0.356728i
$506$	352.790	+	599.171i	0.697213	+	1.18413i
$507$	618.548	+	618.548i	1.22002	+	1.22002i
$508$	−317.519	+	50.2900i	−0.625037	+	0.0989961i
$509$	−260.005	−	84.4806i	−0.510815	−	0.165974i	0.0422581	−	0.999107i	$-0.486545\pi$
$509$	−260.005	−	84.4806i	−0.510815	−	0.165974i	−0.553073	+	0.833133i	$0.686545\pi$
$510$	74.1682	+	430.205i	0.145428	+	0.843540i
$511$	−81.3837	+	59.1287i	−0.159264	+	0.115712i
$512$	−22.3488	−	3.53971i	−0.0436501	−	0.00691349i
$513$	−348.652	−	177.647i	−0.679633	−	0.346290i
$514$	84.0258	+	27.3016i	0.163474	+	0.0531160i
$515$	102.353	−	105.185i	0.198743	−	0.204242i
$516$	21.1939			0.0410735
$517$	−395.328	+	24.1063i	−0.764658	+	0.0466273i
$518$	170.212	−	170.212i	0.328594	−	0.328594i
$519$	−49.6332	+	68.3142i	−0.0956324	+	0.131627i
$520$	308.695	−	104.979i	0.593644	−	0.201882i
$521$	−196.830	−	605.779i	−0.377792	−	1.16272i	−0.941576	−	0.336802i	$-0.890655\pi$
$521$	−196.830	−	605.779i	−0.377792	−	1.16272i	0.563784	−	0.825923i	$-0.309345\pi$
$522$	−43.0278	−	6.81494i	−0.0824288	−	0.0130554i
$523$	−57.1467	+	360.810i	−0.109267	+	0.689885i	0.870862	+	0.491527i	$0.163561\pi$
$523$	−57.1467	+	360.810i	−0.109267	+	0.689885i	−0.980130	+	0.198359i	$0.936439\pi$
$524$	186.119	−	60.4737i	0.355189	−	0.115408i
$525$	−161.796	−	110.935i	−0.308183	−	0.211306i
$526$	480.526	+	349.123i	0.913548	+	0.663732i
$527$	−478.203	−	478.203i	−0.907407	−	0.907407i
$528$	67.5100	+	81.9269i	0.127860	+	0.155165i
$529$		−	1468.79i		−	2.77655i
$530$	534.969	−	7.29958i	1.00938	−	0.0137728i
$531$	48.0701	−	147.944i	0.0905274	−	0.278615i
$532$	39.3259	−	77.1814i	0.0739209	−	0.145078i
$533$	123.795	−	781.608i	0.232260	−	1.46643i
$534$	120.109	+	165.315i	0.224922	+	0.309579i
$535$	−73.7910	−	428.017i	−0.137927	−	0.800033i
$536$	−34.8515	+	107.262i	−0.0650215	+	0.200116i
$537$	−21.2113	−	133.923i	−0.0394997	−	0.249391i
$538$	337.149	−	337.149i	0.626671	−	0.626671i
$539$	91.4006	+	412.641i	0.169574	+	0.765567i
$540$	−42.0027	+	290.822i	−0.0777828	+	0.538560i
$541$	−467.566	−	339.706i	−0.864262	−	0.627923i	0.0647792	−	0.997900i	$-0.479366\pi$
$541$	−467.566	−	339.706i	−0.864262	−	0.627923i	−0.929041	+	0.369977i	$0.879366\pi$
$542$	−331.127	+	168.718i	−0.610936	+	0.311287i
$543$	398.482	+	203.036i	0.733852	+	0.373916i
$544$	85.0830	+	117.107i	0.156403	+	0.215270i
$545$	−180.454	−	55.9230i	−0.331109	−	0.102611i
$546$	−79.0641	−	243.334i	−0.144806	−	0.445667i
$547$	240.624	−	122.604i	0.439897	−	0.224139i	−0.219992	−	0.975502i	$-0.570603\pi$
$547$	240.624	−	122.604i	0.439897	−	0.224139i	0.659889	+	0.751363i	$0.270603\pi$
$548$	252.934	−	40.0608i	0.461558	−	0.0731037i
$549$			37.4643i			0.0682409i
$550$	−293.277	+	255.418i	−0.533231	+	0.464397i
$551$	−129.043			−0.234198
$552$	−47.7150	−	301.260i	−0.0864401	−	0.545762i
$553$	−117.246	−	230.108i	−0.212018	−	0.416108i
$554$	−501.152	+	162.834i	−0.904607	+	0.293925i
$555$	−186.883	+	603.041i	−0.336726	+	1.08656i
$556$	303.997	−	220.866i	0.546756	−	0.397242i
$557$	−275.539	+	540.775i	−0.494683	+	0.970870i	0.499817	+	0.866131i	$0.333401\pi$
$557$	−275.539	+	540.775i	−0.494683	+	0.970870i	−0.994500	+	0.104739i	$0.966599\pi$
$558$	−53.9411	−	105.865i	−0.0966686	−	0.189723i
$559$	−59.5219	+	81.9249i	−0.106479	+	0.146556i
$560$	−64.3796	−	9.29819i	−0.114964	−	0.0166039i
$561$	65.2147	−	675.977i	0.116247	−	1.20495i
$562$	−404.311	−	404.311i	−0.719415	−	0.719415i
$563$	180.393	−	28.5715i	0.320414	−	0.0507486i	0.00584424	−	0.999983i	$-0.498140\pi$
$563$	180.393	−	28.5715i	0.320414	−	0.0507486i	0.314570	+	0.949234i	$0.398140\pi$
$564$	165.238	+	53.6890i	0.292975	+	0.0951933i
$565$	−967.169	+	166.742i	−1.71180	+	0.295118i
$566$	−320.786	+	233.065i	−0.566760	+	0.411775i
$567$	135.831	+	21.5135i	0.239561	+	0.0379428i
$568$	−10.3223	−	5.25947i	−0.0181731	−	0.00925964i
$569$	−193.684	−	62.9318i	−0.340394	−	0.110601i	0.133832	−	0.991004i	$-0.457272\pi$
$569$	−193.684	−	62.9318i	−0.340394	−	0.110601i	−0.474226	+	0.880403i	$0.657272\pi$
$570$	3.09967	+	227.168i	0.00543802	+	0.398540i
$571$	609.672			1.06773			0.533863	−	0.845571i	$-0.320740\pi$
$571$	609.672			1.06773			0.533863	+	0.845571i	$0.320740\pi$
$572$	−506.285	+	30.8722i	−0.885114	+	0.0539724i
$573$	342.479	−	342.479i	0.597694	−	0.597694i
$574$	−92.7953	+	127.722i	−0.161664	+	0.222512i
$575$	1098.48	−	204.850i	1.91040	−	0.356262i
$576$	7.85872	+	24.1867i	0.0136436	+	0.0419907i
$577$	728.522	+	115.387i	1.26260	+	0.199977i	0.751610	−	0.659608i	$-0.229278\pi$
$577$	728.522	+	115.387i	1.26260	+	0.199977i	0.510994	+	0.859584i	$0.329278\pi$
$578$	80.9231	−	510.928i	0.140005	−	0.883959i
$579$	504.057	−	163.778i	0.870565	−	0.282864i
$580$	31.1991	+	91.7426i	0.0537916	+	0.158177i
$581$	18.8463	+	13.6927i	0.0324378	+	0.0235674i
$582$	151.675	+	151.675i	0.260611	+	0.260611i
$583$	−805.746	−	208.538i	−1.38207	−	0.357698i
$584$		−	87.4829i		−	0.149799i
$585$	−262.638	−	255.568i	−0.448955	−	0.436868i
$586$	−172.497	+	530.892i	−0.294364	+	0.905959i
$587$	432.896	−	849.606i	0.737472	−	1.44737i	−0.151045	−	0.988527i	$-0.548264\pi$
$587$	432.896	−	849.606i	0.737472	−	1.44737i	0.888517	−	0.458843i	$-0.151736\pi$
$588$	29.0031	−	183.118i	0.0493250	−	0.311426i
$589$	−206.870	−	284.732i	−0.351223	−	0.483416i
$590$	−340.987	+	58.7868i	−0.577944	+	0.0996386i
$591$	−44.2850	+	136.295i	−0.0749323	+	0.230618i
$592$	32.7477	+	206.761i	0.0553170	+	0.349258i
$593$	290.951	−	290.951i	0.490643	−	0.490643i	−0.417866	−	0.908509i	$-0.637222\pi$
$593$	290.951	−	290.951i	0.490643	−	0.490643i	0.908509	+	0.417866i	$0.137222\pi$
$594$	182.348	−	419.161i	0.306984	−	0.705659i
$595$	249.161	+	333.281i	0.418758	+	0.560137i
$596$	4.44882	+	3.23226i	0.00746447	+	0.00542325i
$597$	321.016	−	163.566i	0.537715	−	0.273979i
$598$	1298.52	+	661.630i	2.17144	+	1.10641i
$599$	13.6824	+	18.8322i	0.0228421	+	0.0314394i	0.820285	−	0.571955i	$-0.193815\pi$
$599$	13.6824	+	18.8322i	0.0228421	+	0.0314394i	−0.797443	+	0.603394i	$0.793815\pi$
$600$	160.754	−	57.1266i	0.267924	−	0.0952111i
$601$	168.739	+	519.324i	0.280763	+	0.864100i	0.987637	+	0.156760i	$0.0501050\pi$
$601$	168.739	+	519.324i	0.280763	+	0.864100i	−0.706873	+	0.707340i	$0.749895\pi$
$602$	18.0002	−	9.17156i	0.0299007	−	0.0152352i
$603$	125.197	−	19.8293i	0.207624	−	0.0328844i
$604$		−	376.551i		−	0.623429i
$605$	544.874	−	262.941i	0.900617	−	0.434613i
$606$	−205.313			−0.338800
$607$	123.928	+	782.453i	0.204165	+	1.28905i	0.850492	+	0.525988i	$0.176304\pi$
$607$	123.928	+	782.453i	0.204165	+	1.28905i	−0.646326	+	0.763061i	$0.723696\pi$
$608$	34.1997	+	67.1207i	0.0562495	+	0.110396i
$609$	72.3177	−	23.4974i	0.118748	−	0.0385836i
$610$	73.7282	−	38.8424i	0.120866	−	0.0636761i
$611$	−671.595	+	487.942i	−1.09917	+	0.798596i
$612$	73.8594	−	144.957i	0.120685	−	0.236858i
$613$	73.1734	+	143.611i	0.119369	+	0.234275i	0.942958	−	0.332912i	$-0.108031\pi$
$613$	73.1734	+	143.611i	0.119369	+	0.234275i	−0.823588	+	0.567188i	$0.808031\pi$
$614$	18.2624	−	25.1361i	0.0297434	−	0.0409383i
$615$	59.1874	−	409.807i	0.0962397	−	0.666353i
$616$	92.7902	+	40.3666i	0.150633	+	0.0655303i
$617$	−399.441	−	399.441i	−0.647393	−	0.647393i	0.304969	−	0.952362i	$-0.401354\pi$
$617$	−399.441	−	399.441i	−0.647393	−	0.647393i	−0.952362	+	0.304969i	$0.901354\pi$
$618$	98.9211	−	15.6676i	0.160066	−	0.0253520i
$619$	−410.408	−	133.350i	−0.663018	−	0.215428i	−0.0418726	−	0.999123i	$-0.513332\pi$
$619$	−410.408	−	133.350i	−0.663018	−	0.215428i	−0.621145	+	0.783695i	$0.713332\pi$
$620$	−152.413	+	215.914i	−0.245828	+	0.348248i
$621$	−1062.54	+	771.977i	−1.71101	+	1.24312i
$622$	629.074	+	99.6356i	1.01137	+	0.160186i
$623$	173.548	+	88.4273i	0.278569	+	0.141938i
$624$	211.615	+	68.7579i	0.339127	+	0.110189i
$625$	225.273	+	582.990i	0.360436	+	0.932784i
$626$	−48.0445			−0.0767484
$627$	88.5530	−	342.150i	0.141233	−	0.545693i
$628$	−43.0058	+	43.0058i	−0.0684806	+	0.0684806i
$629$	787.147	−	1083.41i	1.25143	−	1.72244i
$630$	23.5382	+	69.2153i	0.0373622	+	0.109866i
$631$	306.602	+	943.625i	0.485899	+	1.49544i	0.830674	+	0.556759i	$0.187955\pi$
$631$	306.602	+	943.625i	0.485899	+	1.49544i	−0.344775	+	0.938685i	$0.612045\pi$
$632$	221.827	+	35.1339i	0.350991	+	0.0555916i
$633$	20.7919	−	131.275i	0.0328466	−	0.207385i
$634$	−367.065	+	119.267i	−0.578967	+	0.188118i
$635$	355.064	−	721.006i	0.559156	−	1.13544i
$636$	295.375	+	214.603i	0.464426	+	0.337425i
$637$	626.388	+	626.388i	0.983341	+	0.983341i
$638$	−9.17507	−	150.465i	−0.0143810	−	0.235839i
$639$			13.0206i			0.0203765i
$640$	39.4505	−	40.5420i	0.0616415	−	0.0633469i
$641$	32.0265	−	98.5675i	0.0499634	−	0.153772i	−0.922962	−	0.384891i	$-0.874239\pi$
$641$	32.0265	−	98.5675i	0.0499634	−	0.153772i	0.972925	+	0.231120i	$0.0742389\pi$
$642$	134.560	−	264.088i	0.209595	−	0.411353i
$643$	37.5514	−	237.090i	0.0584003	−	0.368725i	−0.941129	−	0.338048i	$-0.890234\pi$
$643$	37.5514	−	237.090i	0.0584003	−	0.368725i	0.999529	−	0.0306775i	$-0.00976647\pi$
$644$	−170.893	−	235.215i	−0.265363	−	0.365240i
$645$	−30.5560	+	43.2866i	−0.0473736	+	0.0671110i
$646$	148.918	−	458.322i	0.230523	−	0.709477i
$647$	−6.81953	−	43.0568i	−0.0105402	−	0.0665484i	0.981858	−	0.189620i	$-0.0607256\pi$
$647$	−6.81953	−	43.0568i	−0.0105402	−	0.0665484i	−0.992398	+	0.123071i	$0.960726\pi$
$648$	−84.5684	+	84.5684i	−0.130507	+	0.130507i
$649$	535.789	+	51.6901i	0.825561	+	0.0796458i
$650$	−230.647	+	781.831i	−0.354841	+	1.20282i
$651$	167.780	+	121.899i	0.257726	+	0.187249i
$652$	66.0165	−	33.6371i	0.101252	−	0.0515906i
$653$	562.678	+	286.699i	0.861682	+	0.439049i	0.828228	−	0.560391i	$-0.189349\pi$
$653$	562.678	+	286.699i	0.861682	+	0.439049i	0.0334541	+	0.999440i	$0.489349\pi$
$654$	−75.7785	−	104.300i	−0.115869	−	0.159480i
$655$	−144.822	+	467.317i	−0.221102	+	0.713461i
$656$	−42.4261	−	130.574i	−0.0646739	−	0.199046i
$657$	−87.6070	+	44.6380i	−0.133344	+	0.0679421i
$658$	163.572	−	25.9072i	0.248589	−	0.0393726i
$659$			141.360i			0.214508i	0.994232	+	0.107254i	$0.0342057\pi$
$659$			141.360i			0.214508i	−0.994232	+	0.107254i	$0.965794\pi$
$660$	−264.659	+	19.7660i	−0.400998	+	0.0299486i
$661$	−816.071			−1.23460			−0.617300	−	0.786727i	$-0.711774\pi$
$661$	−816.071			−1.23460			−0.617300	+	0.786727i	$0.711774\pi$
$662$	−27.8786	−	176.018i	−0.0421127	−	0.265889i
$663$	−646.214	−	1268.27i	−0.974681	−	1.91292i
$664$	−19.2672	+	6.26030i	−0.0290169	+	0.00942817i
$665$	100.938	+	191.594i	0.151787	+	0.288112i
$666$	190.344	−	138.293i	0.285802	−	0.207648i
$667$	−196.633	+	385.915i	−0.294802	+	0.578582i
$668$	−186.923	−	366.856i	−0.279824	−	0.549186i
$669$	10.9344	−	15.0499i	0.0163443	−	0.0224960i
$670$	−168.826	−	225.824i	−0.251979	−	0.337051i
$671$	−126.570	+	28.0354i	−0.188628	+	0.0417815i
$672$	−31.3880	−	31.3880i	−0.0467083	−	0.0467083i
$673$	568.805	−	90.0899i	0.845179	−	0.133863i	0.281197	−	0.959650i	$-0.409269\pi$
$673$	568.805	−	90.0899i	0.845179	−	0.133863i	0.563982	+	0.825787i	$0.309269\pi$
$674$	−526.619	−	171.109i	−0.781334	−	0.253871i
$675$	−533.420	−	505.074i	−0.790251	−	0.748258i
$676$	−586.643	+	426.221i	−0.867816	+	0.630505i
$677$	−90.3100	−	14.3037i	−0.133397	−	0.0211281i	0.0893787	−	0.995998i	$-0.471512\pi$
$677$	−90.3100	−	14.3037i	−0.133397	−	0.0211281i	−0.222776	+	0.974870i	$0.571512\pi$
$678$	−596.747	−	304.058i	−0.880157	−	0.448463i
$679$	194.456	+	63.1825i	0.286386	+	0.0930523i
$680$	−361.846	+	4.93733i	−0.532126	+	0.00726079i
$681$	247.953			0.364101
$682$	317.291	−	261.457i	0.465236	−	0.383368i
$683$	187.784	−	187.784i	0.274939	−	0.274939i	−0.556146	−	0.831085i	$-0.687720\pi$
$683$	187.784	−	187.784i	0.274939	−	0.274939i	0.831085	+	0.556146i	$0.187720\pi$
$684$	49.7655	−	68.4964i	0.0727566	−	0.100141i
$685$	−282.843	+	574.350i	−0.412909	+	0.838467i
$686$	−124.257	−	382.423i	−0.181132	−	0.557467i
$687$	−88.0801	−	13.9505i	−0.128210	−	0.0203064i
$688$	−2.74835	+	17.3524i	−0.00399470	+	0.0252215i
$689$	−1659.09	+	539.070i	−2.40796	+	0.782395i
$690$	684.087	+	336.883i	0.991431	+	0.488237i
$691$	−809.253	−	587.956i	−1.17113	−	0.850878i	−0.179989	−	0.983669i	$-0.557606\pi$
$691$	−809.253	−	587.956i	−1.17113	−	0.850878i	−0.991144	+	0.132791i	$0.957606\pi$
$692$	−49.4956	−	49.4956i	−0.0715255	−	0.0715255i
$693$	−6.92215	−	113.519i	−0.00998867	−	0.163808i
$694$			815.541i			1.17513i
$695$	12.8168	+	939.314i	0.0184414	+	1.35153i
$696$	−20.4345	+	62.8909i	−0.0293599	+	0.0903605i
$697$	−398.737	+	782.565i	−0.572076	+	1.12276i
$698$	36.5409	−	230.710i	0.0523509	−	0.330531i
$699$	476.599	+	655.982i	0.681829	+	0.938457i
$700$	111.809	−	118.084i	0.159727	−	0.168691i
$701$	5.72749	−	17.6274i	0.00817045	−	0.0251461i	−0.946888	−	0.321563i	$-0.895792\pi$
$701$	5.72749	−	17.6274i	0.00817045	−	0.0251461i	0.955059	+	0.296417i	$0.0957918\pi$
$702$	−149.877	−	946.289i	−0.213501	−	1.34799i
$703$	492.803	−	492.803i	0.701000	−	0.701000i
$704$	−75.8316	+	44.6494i	−0.107715	+	0.0634225i
$705$	−347.883	+	260.077i	−0.493451	+	0.368904i
$706$	−479.963	−	348.713i	−0.679834	−	0.493928i
$707$	−174.374	+	88.8481i	−0.246640	+	0.125669i
$708$	−210.390	−	107.199i	−0.297161	−	0.151411i
$709$	−172.221	−	237.042i	−0.242907	−	0.334333i	0.670104	−	0.742267i	$-0.266249\pi$
$709$	−172.221	−	237.042i	−0.242907	−	0.334333i	−0.913011	+	0.407934i	$0.866249\pi$
$710$	25.6240	−	13.4995i	0.0360901	−	0.0190134i
$711$	−78.0029	−	240.068i	−0.109709	−	0.337649i
$712$	−150.926	+	76.9007i	−0.211975	+	0.108007i
$713$	−1166.74	+	184.793i	−1.63638	+	0.259177i
$714$			283.967i			0.397713i
$715$	666.874	−	1078.55i	0.932691	−	1.50846i
$716$	112.399			0.156982
$717$	−103.719	−	654.857i	−0.144657	−	0.913329i
$718$	−240.269	−	471.555i	−0.334637	−	0.656762i
$719$	1304.16	−	423.747i	1.81385	−	0.589356i	0.813885	−	0.581026i	$-0.197349\pi$
$719$	1304.16	−	423.747i	1.81385	−	0.589356i	0.999965	−	0.00832949i	$-0.00265139\pi$
$720$	−60.7291	−	18.8200i	−0.0843459	−	0.0261389i
$721$	77.2345	−	56.1141i	0.107121	−	0.0778282i
$722$	−117.918	+	231.428i	−0.163322	+	0.320537i
$723$	212.481	+	417.018i	0.293888	+	0.576788i
$724$	−217.909	+	299.925i	−0.300979	+	0.414262i
$725$	−232.356	−	68.5471i	−0.320491	−	0.0945477i
$726$	405.245	+	78.9264i	0.558189	+	0.108714i
$727$	346.781	+	346.781i	0.477002	+	0.477002i	0.904172	−	0.427169i	$-0.140489\pi$
$727$	346.781	+	346.781i	0.477002	+	0.477002i	−0.427169	+	0.904172i	$0.640489\pi$
$728$	209.481	−	33.1785i	0.287749	−	0.0455749i
$729$	734.661	+	238.706i	1.00777	+	0.327443i
$730$	178.675	+	126.127i	0.244761	+	0.172777i
$731$	90.9257	−	66.0614i	0.124385	−	0.0903713i
$732$	56.1681	+	8.89615i	0.0767323	+	0.0121532i
$733$	−1168.47	−	595.367i	−1.59410	−	0.812233i	−0.999969	−	0.00786168i	$-0.997498\pi$
$733$	−1168.47	−	595.367i	−1.59410	−	0.812233i	−0.594127	−	0.804371i	$-0.702502\pi$
$734$	−58.7579	−	19.0916i	−0.0800516	−	0.0260103i
$735$	332.187	+	323.244i	0.451955	+	0.439787i
$736$	252.843			0.343536
$737$	160.679	+	408.128i	0.218018	+	0.553770i
$738$	−109.111	+	109.111i	−0.147847	+	0.147847i
$739$	216.767	−	298.354i	0.293325	−	0.403727i	−0.636766	−	0.771057i	$-0.719728\pi$
$739$	216.767	−	298.354i	0.293325	−	0.403727i	0.930090	+	0.367330i	$0.119728\pi$
$740$	−469.502	−	231.209i	−0.634462	−	0.312445i
$741$	−228.909	−	704.510i	−0.308919	−	0.950755i
$742$	343.733	+	54.4419i	0.463252	+	0.0733719i
$743$	−175.625	+	1108.86i	−0.236373	+	1.49240i	0.528893	+	0.848689i	$0.322607\pi$
$743$	−175.625	+	1108.86i	−0.236373	+	1.49240i	−0.765266	+	0.643714i	$0.777393\pi$
$744$	−171.527	+	55.7324i	−0.230547	+	0.0749091i
$745$	−13.0156	+	4.42624i	−0.0174706	+	0.00594126i
$746$	371.377	+	269.821i	0.497824	+	0.361690i
$747$	16.1002	+	16.1002i	0.0215532	+	0.0215532i
$748$	544.995	+	141.052i	0.728603	+	0.188573i
$749$		−	282.523i		−	0.377200i
$750$	−115.089	+	410.686i	−0.153452	+	0.547582i
$751$	−356.174	+	1096.19i	−0.474266	+	1.45964i	0.372679	+	0.927960i	$0.378439\pi$
$751$	−356.174	+	1096.19i	−0.474266	+	1.45964i	−0.846945	+	0.531681i	$0.821561\pi$
$752$	−65.3850	+	128.325i	−0.0869481	+	0.170645i
$753$	−60.7553	+	383.594i	−0.0806843	+	0.509421i
$754$	−185.715	−	255.615i	−0.246306	−	0.339012i
$755$	769.069	+	542.885i	1.01863	+	0.719054i
$756$	−59.0642	+	181.781i	−0.0781273	+	0.240451i
$757$	116.887	+	737.995i	0.154408	+	0.974894i	0.936229	+	0.351391i	$0.114291\pi$
$757$	116.887	+	737.995i	0.154408	+	0.974894i	−0.781821	+	0.623503i	$0.785709\pi$
$758$	−634.095	+	634.095i	−0.836537	+	0.836537i
$759$	−888.291	−	786.185i	−1.17034	−	1.03582i
$760$	−186.394	−	26.9205i	−0.245256	−	0.0354216i
$761$	650.632	+	472.712i	0.854969	+	0.621172i	0.926512	−	0.376266i	$-0.122792\pi$
$761$	650.632	+	472.712i	0.854969	+	0.621172i	−0.0715424	+	0.997438i	$0.522792\pi$
$762$	488.671	−	248.990i	0.641301	−	0.326759i
$763$	−109.495	−	55.7903i	−0.143505	−	0.0731196i
$764$	235.991	+	324.814i	0.308889	+	0.425149i
$765$	189.576	+	359.840i	0.247811	+	0.470379i
$766$	−144.408	−	444.443i	−0.188522	−	0.580212i
$767$	1005.25	−	512.198i	1.31062	−	0.667794i
$768$	38.1278	−	6.03885i	0.0496456	−	0.00786309i
$769$			749.322i			0.974411i	0.873287	+	0.487206i	$0.161984\pi$
$769$			749.322i			0.974411i	−0.873287	+	0.487206i	$0.838016\pi$
$770$	−216.224	+	131.317i	−0.280810	+	0.170542i
$771$	−150.728			−0.195496
$772$	68.7280	+	433.932i	0.0890259	+	0.562088i
$773$	378.483	+	742.815i	0.489629	+	0.960951i	0.995172	+	0.0981495i	$0.0312923\pi$
$773$	378.483	+	742.815i	0.489629	+	0.960951i	−0.505543	+	0.862802i	$0.668708\pi$
$774$	18.7794	−	6.10179i	0.0242627	−	0.00788344i
$775$	−221.243	−	622.579i	−0.285475	−	0.803328i
$776$	−143.852	+	104.515i	−0.185376	+	0.134684i
$777$	−186.440	+	365.908i	−0.239948	+	0.470924i
$778$	−99.9073	−	196.079i	−0.128416	−	0.252030i
$779$	−268.664	+	369.785i	−0.344883	+	0.474691i
$780$	−445.523	+	333.073i	−0.571184	+	0.427016i
$781$	−43.9888	+	9.74360i	−0.0563237	+	0.0124758i
$782$	−1143.73	−	1143.73i	−1.46257	−	1.46257i
$783$	281.232	−	44.5428i	0.359173	−	0.0568874i
$784$	146.166	+	47.4922i	0.186436	+	0.0605768i
$785$	−25.8323	−	149.838i	−0.0329075	−	0.190876i
$786$	−270.102	+	196.241i	−0.343642	+	0.249670i
$787$	356.685	+	56.4934i	0.453221	+	0.0717832i	0.378872	−	0.925449i	$-0.376312\pi$
$787$	356.685	+	56.4934i	0.453221	+	0.0717832i	0.0743493	+	0.997232i	$0.476312\pi$
$788$	−105.848	−	53.9323i	−0.134325	−	0.0684421i
$789$	−963.724	−	313.133i	−1.22145	−	0.396873i
$790$	−391.572	+	402.406i	−0.495661	+	0.509374i
$791$	−638.402			−0.807082
$792$	83.4057	+	53.1568i	0.105310	+	0.0671172i
$793$	−192.133	+	192.133i	−0.242286	+	0.242286i
$794$	107.690	−	148.222i	0.135629	−	0.186678i
$795$	−864.157	+	293.876i	−1.08699	+	0.369655i
$796$	92.2903	+	284.040i	0.115943	+	0.356835i
$797$	1278.25	+	202.455i	1.60383	+	0.254021i	0.893237	−	0.449585i	$-0.148428\pi$
$797$	1278.25	+	202.455i	1.60383	+	0.254021i	0.710590	+	0.703607i	$0.248428\pi$
$798$	−23.1181	+	145.962i	−0.0289700	+	0.182909i
$799$	876.247	−	284.710i	1.09668	−	0.356333i
$800$	25.9261	+	139.025i	0.0324076	+	0.173781i
$801$	154.019	+	111.902i	0.192284	+	0.139702i
$802$	−601.642	−	601.642i	−0.750177	−	0.750177i
$803$	−216.364	−	262.569i	−0.269444	−	0.326985i
$804$		−	192.409i		−	0.239315i
$805$	726.786	−	9.91688i	0.902839	−	0.0123191i
$806$	266.290	−	819.555i	0.330384	−	1.01682i
$807$	−369.292	+	724.777i	−0.457611	+	0.898113i
$808$	26.6242	−	168.099i	0.0329508	−	0.208043i
$809$	786.152	+	1082.05i	0.971758	+	1.33751i	0.941154	+	0.337979i	$0.109743\pi$
$809$	786.152	+	1082.05i	0.971758	+	1.33751i	0.0306043	+	0.999532i	$0.490257\pi$
$810$	−50.7978	−	294.648i	−0.0627133	−	0.363763i
$811$	23.0439	−	70.9218i	0.0284141	−	0.0874498i	−0.935844	−	0.352415i	$-0.885361\pi$
$811$	23.0439	−	70.9218i	0.0284141	−	0.0874498i	0.964258	+	0.264965i	$0.0853605\pi$
$812$	9.86050	+	62.2567i	0.0121435	+	0.0766709i
$813$	448.318	−	448.318i	0.551436	−	0.551436i
$814$	609.651	+	539.573i	0.748957	+	0.662867i
$815$	−26.4776	+	183.328i	−0.0324878	+	0.224942i
$816$	−199.788	−	145.154i	−0.244838	−	0.177885i
$817$	52.1148	−	26.5538i	0.0637881	−	0.0325016i
$818$	5.78644	+	2.94834i	0.00707388	+	0.00360432i
$819$	−140.113	−	192.849i	−0.171078	−	0.235469i
$820$	327.852	+	101.602i	0.399819	+	0.123904i
$821$	50.5148	+	155.468i	0.0615283	+	0.189365i	0.977096	−	0.212799i	$-0.0682581\pi$
$821$	50.5148	+	155.468i	0.0615283	+	0.189365i	−0.915568	+	0.402164i	$0.868258\pi$
$822$	−389.274	+	198.345i	−0.473569	+	0.241295i
$823$	−409.482	+	64.8555i	−0.497548	+	0.0788038i	−0.400165	−	0.916443i	$-0.631047\pi$
$823$	−409.482	+	64.8555i	−0.497548	+	0.0788038i	−0.0973828	+	0.995247i	$0.531047\pi$
$824$			83.0227i			0.100756i
$825$	341.197	−	569.038i	0.413572	−	0.689743i
$826$	−225.076			−0.272489
$827$	−37.7333	−	238.238i	−0.0456267	−	0.288076i	0.954316	−	0.298800i	$-0.0965863\pi$
$827$	−37.7333	−	238.238i	−0.0456267	−	0.288076i	−0.999942	+	0.0107243i	$0.996586\pi$
$828$	−129.012	−	253.201i	−0.155812	−	0.305799i
$829$	−829.710	+	269.589i	−1.00086	+	0.325198i	−0.763208	−	0.646153i	$-0.776377\pi$
$829$	−829.710	+	269.589i	−1.00086	+	0.325198i	−0.237649	+	0.971351i	$0.576377\pi$
$830$	14.9921	−	48.3771i	0.0180628	−	0.0582857i
$831$	727.290	−	528.407i	0.875199	−	0.635869i
$832$	−83.7366	+	164.342i	−0.100645	+	0.197527i
$833$	−446.351	−	876.012i	−0.535835	−	1.05164i
$834$	−376.805	+	518.627i	−0.451804	+	0.621855i
$835$	1018.76	+	147.137i	1.22007	+	0.176212i
$836$	268.650	+	116.871i	0.321351	+	0.139798i
$837$	549.129	+	549.129i	0.656068	+	0.656068i
$838$	446.537	−	70.7246i	0.532861	−	0.0843969i
$839$	−1285.50	−	417.683i	−1.53218	−	0.497835i	−0.582973	−	0.812492i	$-0.698111\pi$
$839$	−1285.50	−	417.683i	−1.53218	−	0.497835i	−0.949206	+	0.314657i	$0.898111\pi$
$840$	109.360	−	18.8539i	0.130190	−	0.0224451i
$841$	−604.416	+	439.134i	−0.718687	+	0.522157i
$842$	180.114	+	28.5272i	0.213912	+	0.0338803i
$843$	869.158	+	442.858i	1.03103	+	0.525336i
$844$	104.784	+	34.0464i	0.124152	+	0.0403394i
$845$	−24.7335	−	1812.66i	−0.0292704	−	2.14516i
$846$	161.870			0.191335
$847$	378.333	−	108.335i	0.446674	−	0.127904i
$848$	−214.008	+	214.008i	−0.252368	+	0.252368i
$849$	397.616	−	547.271i	0.468334	−	0.644607i
$850$	511.601	−	746.154i	0.601883	−	0.877828i
$851$	−722.846	−	2224.69i	−0.849408	−	2.61421i
$852$	19.5210	+	3.09182i	0.0229120	+	0.00362890i
$853$	−256.753	+	1621.08i	−0.301000	+	1.90044i	0.118962	+	0.992899i	$0.462043\pi$
$853$	−256.753	+	1621.08i	−0.301000	+	1.90044i	−0.419962	+	0.907542i	$0.637957\pi$
$854$	51.5538	−	16.7508i	0.0603674	−	0.0196146i
$855$	68.1487	+	200.395i	0.0797061	+	0.234380i
$856$	198.772	+	144.416i	0.232210	+	0.168710i
$857$	−894.831	−	894.831i	−1.04414	−	1.04414i	−0.998980	−	0.0451637i	$-0.985619\pi$
$857$	−894.831	−	894.831i	−1.04414	−	1.04414i	−0.0451637	−	0.998980i	$-0.514381\pi$
$858$	805.188	−	317.001i	0.938447	−	0.369465i
$859$		−	94.9702i		−	0.110559i	−0.998471	−	0.0552795i	$-0.982395\pi$
$859$		−	94.9702i		−	0.110559i	0.998471	−	0.0552795i	$-0.0176050\pi$
$860$	−31.4782	−	30.6308i	−0.0366026	−	0.0356172i
$861$	83.2293	−	256.153i	0.0966659	−	0.297507i
$862$	−490.018	+	961.715i	−0.568467	+	1.11568i
$863$	−16.4691	+	103.982i	−0.0190835	+	0.120489i	−0.995391	−	0.0958989i	$-0.969427\pi$
$863$	−16.4691	+	103.982i	−0.0190835	+	0.120489i	0.976308	+	0.216387i	$0.0694274\pi$
$864$	−97.7022	−	134.476i	−0.113081	−	0.155643i
$865$	172.449	−	29.7306i	0.199363	−	0.0343706i
$866$	12.1991	−	37.5450i	0.0140867	−	0.0433545i
$867$	138.057	+	871.660i	0.159236	+	1.00537i
$868$	−121.561	+	121.561i	−0.140047	+	0.140047i
$869$	752.677	−	443.174i	0.866142	−	0.509982i
$870$	−98.9876	−	132.407i	−0.113779	−	0.152192i
$871$	743.756	+	540.371i	0.853911	+	0.620403i
$872$	95.2218	−	48.5179i	0.109199	−	0.0556398i
$873$	178.063	+	90.7276i	0.203967	+	0.103926i
$874$	−494.777	−	681.002i	−0.566106	−	0.779179i
$875$	79.9762	+	398.604i	0.0914013	+	0.455547i
$876$	46.1203	+	141.944i	0.0526488	+	0.162036i
$877$	1143.86	−	582.827i	1.30429	−	0.664569i	0.342800	−	0.939408i	$-0.388625\pi$
$877$	1143.86	−	582.827i	1.30429	−	0.664569i	0.961490	+	0.274839i	$0.0886245\pi$
$878$	647.030	−	102.479i	0.736936	−	0.116719i
$879$		−	952.328i		−	1.08342i
$880$	18.1367	−	219.251i	0.0206099	−	0.249149i
$881$	224.310			0.254608			0.127304	−	0.991864i	$-0.459368\pi$
$881$	224.310			0.254608			0.127304	+	0.991864i	$0.459368\pi$
$882$	−27.0214	−	170.606i	−0.0306365	−	0.193431i
$883$	−609.547	−	1196.30i	−0.690313	−	1.35482i	−0.923958	−	0.382494i	$-0.875065\pi$
$883$	−609.547	−	1196.30i	−0.690313	−	1.35482i	0.233645	−	0.972322i	$-0.424935\pi$
$884$	1122.18	−	364.620i	1.26944	−	0.412466i
$885$	522.270	−	275.149i	0.590136	−	0.310903i
$886$	459.713	−	334.001i	0.518863	−	0.376976i
$887$	−528.258	+	1036.76i	−0.595555	+	1.16884i	0.374788	+	0.927111i	$0.377716\pi$
$887$	−528.258	+	1036.76i	−0.595555	+	1.16884i	−0.970343	+	0.241733i	$0.922284\pi$
$888$	−162.137	−	318.211i	−0.182586	−	0.358346i
$889$	307.284	−	422.940i	0.345651	−	0.475748i
$890$	60.5327	−	419.122i	0.0680143	−	0.470923i
$891$	−44.6655	+	462.977i	−0.0501297	+	0.519615i
$892$	10.9040	+	10.9040i	0.0122243	+	0.0122243i
$893$	473.578	−	75.0074i	0.530323	−	0.0839949i
$894$	−8.92238	−	2.89906i	−0.00998029	−	0.00324279i
$895$	−162.050	+	229.565i	−0.181061	+	0.256497i
$896$	29.7690	−	21.6284i	0.0332243	−	0.0241389i
$897$	−2455.70	−	388.945i	−2.73768	−	0.433606i
$898$	409.035	+	208.414i	0.455495	+	0.232086i
$899$	243.568	+	79.1399i	0.270932	+	0.0880311i
$900$	125.993	−	96.8999i	0.139992	−	0.107667i
$901$	1936.13			2.14886
$902$	−450.274	−	286.972i	−0.499195	−	0.318151i
$903$	−24.3707	+	24.3707i	−0.0269886	+	0.0269886i
$904$	326.329	−	449.154i	0.360984	−	0.496851i
$905$	−298.403	−	877.469i	−0.329727	−	0.969579i
$906$	198.515	+	610.966i	0.219111	+	0.674355i
$907$	−1243.02	−	196.874i	−1.37047	−	0.217061i	−0.572572	−	0.819855i	$-0.694054\pi$
$907$	−1243.02	−	196.874i	−1.37047	−	0.217061i	−0.797897	+	0.602794i	$0.794054\pi$
$908$	−32.1536	+	203.010i	−0.0354114	+	0.223579i
$909$	−181.922	+	59.1101i	−0.200134	+	0.0650276i
$910$	−234.252	+	475.679i	−0.257419	+	0.522725i
$911$	−1101.88	−	800.565i	−1.20953	−	0.878776i	−0.214343	−	0.976758i	$-0.568761\pi$
$911$	−1101.88	−	800.565i	−1.20953	−	0.878776i	−0.995188	+	0.0979828i	$0.968761\pi$
$912$	−90.8756	−	90.8756i	−0.0996443	−	0.0996443i
$913$	−42.3450	+	66.4414i	−0.0463801	+	0.0727727i
$914$			705.358i			0.771726i
$915$	−99.1488	+	101.892i	−0.108359	+	0.111357i
$916$	22.8438	−	70.3060i	0.0249387	−	0.0767533i
$917$	−144.478	+	283.555i	−0.157555	+	0.309220i
$918$	−166.344	+	1050.25i	−0.181203	+	1.14407i
$919$	−473.444	−	651.640i	−0.515173	−	0.709075i	0.469608	−	0.882875i	$-0.344395\pi$
$919$	−473.444	−	651.640i	−0.515173	−	0.709075i	−0.984781	+	0.173800i	$0.944395\pi$
$920$	−364.531	+	516.407i	−0.396230	+	0.561311i
$921$	−16.3798	+	50.4119i	−0.0177848	+	0.0547361i
$922$	−21.2932	−	134.440i	−0.0230946	−	0.145814i
$923$	−66.7750	+	66.7750i	−0.0723456	+	0.0723456i
$924$	−171.836	−	16.5778i	−0.185970	−	0.0179414i
$925$	1149.12	−	625.570i	1.24229	−	0.676292i
$926$	416.490	+	302.597i	0.449773	+	0.326779i
$927$	83.1405	−	42.3622i	0.0896877	−	0.0456982i
$928$	−48.8417	−	24.8861i	−0.0526311	−	0.0268169i
$929$	1070.37	+	1473.24i	1.15218	+	1.58584i	0.736680	+	0.676242i	$0.236392\pi$
$929$	1070.37	+	1473.24i	1.15218	+	1.58584i	0.415497	+	0.909594i	$0.363608\pi$
$930$	133.467	−	430.678i	0.143513	−	0.463094i
$931$	−158.111	−	486.617i	−0.169830	−	0.522682i
$932$	−598.885	+	305.147i	−0.642580	+	0.327411i
$933$	−1073.22	+	169.981i	−1.15029	+	0.182188i
$934$		−	201.433i		−	0.215667i
$935$	−1073.82	+	909.740i	−1.14847	+	0.972984i
$936$	207.302			0.221476
$937$	−279.721	−	1766.09i	−0.298528	−	1.88483i	−0.444862	−	0.895599i	$-0.646747\pi$
$937$	−279.721	−	1766.09i	−0.298528	−	1.88483i	0.146333	−	0.989235i	$-0.453253\pi$
$938$	−83.2641	−	163.415i	−0.0887677	−	0.174216i
$939$	77.9537	−	25.3287i	0.0830178	−	0.0269741i
$940$	−167.824	−	318.553i	−0.178536	−	0.338886i
$941$	371.392	−	269.832i	0.394678	−	0.286751i	−0.372692	−	0.927955i	$-0.621565\pi$
$941$	371.392	−	269.832i	0.394678	−	0.286751i	0.767370	+	0.641205i	$0.221565\pi$
$942$	47.1059	−	92.4506i	0.0500063	−	0.0981429i
$943$	696.486	+	1366.93i	0.738586	+	1.44956i
$944$	115.051	−	158.355i	0.121876	−	0.167748i
$945$	−286.115	−	382.712i	−0.302767	−	0.404987i
$946$	34.6674	+	58.8783i	0.0366463	+	0.0622392i
$947$	−513.242	−	513.242i	−0.541966	−	0.541966i	0.382139	−	0.924105i	$-0.375188\pi$
$947$	−513.242	−	513.242i	−0.541966	−	0.541966i	−0.924105	+	0.382139i	$0.875188\pi$
$948$	−378.443	+	59.9395i	−0.399201	+	0.0632273i
$949$	−678.208	−	220.363i	−0.714655	−	0.232206i
$950$	323.713	−	341.880i	0.340750	−	0.359874i
$951$	532.698	−	387.028i	0.560145	−	0.406969i
$952$	−232.496	−	36.8238i	−0.244219	−	0.0386804i
$953$	1038.38	+	529.079i	1.08959	+	0.555172i	0.904033	−	0.427462i	$-0.140592\pi$
$953$	1038.38	+	529.079i	1.08959	+	0.555172i	0.185554	+	0.982634i	$0.440592\pi$
$954$	323.508	+	105.114i	0.339107	+	0.110183i
$955$	−1003.64	+	13.6945i	−1.05093	+	0.0143398i
$956$	549.610			0.574906
$957$	94.2111	+	239.298i	0.0984442	+	0.250050i
$958$	325.545	−	325.545i	0.339817	−	0.339817i
$959$	−244.781	+	336.912i	−0.255246	+	0.351316i
$960$	−42.6363	+	86.5787i	−0.0444128	+	0.0901862i
$961$	−81.1216	−	249.667i	−0.0844138	−	0.259799i
$962$	1685.39	+	266.940i	1.75197	+	0.277485i
$963$	43.1980	−	272.741i	0.0448577	−	0.283221i
$964$	−368.984	+	119.890i	−0.382764	+	0.124368i
$965$	−985.351	−	485.243i	−1.02109	−	0.502842i
$966$	401.283	+	291.550i	0.415407	+	0.301811i
$967$	−527.210	−	527.210i	−0.545202	−	0.545202i	0.379847	−	0.925049i	$-0.375977\pi$
$967$	−527.210	−	527.210i	−0.545202	−	0.545202i	−0.925049	+	0.379847i	$0.875977\pi$
$968$	−117.171	+	321.557i	−0.121045	+	0.332187i
$969$			822.151i			0.848453i
$970$	−6.06494	−	444.486i	−0.00625252	−	0.458233i
$971$	−320.325	+	985.858i	−0.329891	+	1.01530i	0.639293	+	0.768964i	$0.279227\pi$
$971$	−320.325	+	985.858i	−0.329891	+	1.01530i	−0.969184	+	0.246338i	$0.920773\pi$
$972$	−147.490	+	289.465i	−0.151738	+	0.297803i
$973$	−95.5906	+	603.535i	−0.0982431	+	0.620283i
$974$	79.2713	+	109.108i	0.0813873	+	0.112020i
$975$	−37.9436	−	1390.14i	−0.0389165	−	1.42578i
$976$	−14.5673	+	44.8337i	−0.0149256	+	0.0459361i
$977$	92.5475	+	584.322i	0.0947262	+	0.598078i	0.988694	+	0.149947i	$0.0479102\pi$
$977$	92.5475	+	584.322i	0.0947262	+	0.598078i	−0.893968	+	0.448131i	$0.852090\pi$
$978$	−89.3806	+	89.3806i	−0.0913912	+	0.0913912i
$979$	−262.793	+	604.079i	−0.268430	+	0.617037i
$980$	−307.730	+	230.059i	−0.314011	+	0.234754i
$981$	−97.1734	−	70.6006i	−0.0990555	−	0.0719680i
$982$	−404.250	+	205.976i	−0.411660	+	0.209751i
$983$	224.123	+	114.196i	0.227999	+	0.116171i	0.564259	−	0.825598i	$-0.309162\pi$
$983$	224.123	+	114.196i	0.227999	+	0.116171i	−0.336260	+	0.941769i	$0.609162\pi$
$984$	137.675	+	189.494i	0.139914	+	0.192575i
$985$	262.756	−	138.429i	0.266758	−	0.140537i
$986$	108.363	+	333.507i	0.109902	+	0.338243i
$987$	−251.742	+	128.269i	−0.255058	+	0.129958i
$988$	606.497	−	96.0597i	0.613864	−	0.0972264i
$989$		−	196.316i		−	0.198499i
$990$	−228.816	+	93.7101i	−0.231128	+	0.0946566i
$991$	383.871			0.387357			0.193678	−	0.981065i	$-0.437958\pi$
$991$	383.871			0.387357			0.193678	+	0.981065i	$0.437958\pi$
$992$	−23.3876	−	147.664i	−0.0235762	−	0.148854i
$993$	138.029	+	270.898i	0.139003	+	0.272808i
$994$	17.9173	−	5.82170i	0.0180255	−	0.00585684i
$995$	−713.183	−	221.016i	−0.716767	−	0.222127i
$996$	27.9613	−	20.3151i	0.0280736	−	0.0203967i
$997$	513.324	−	1007.46i	0.514869	−	1.01049i	−0.476474	−	0.879189i	$-0.658085\pi$
$997$	513.324	−	1007.46i	0.514869	−	1.01049i	0.991343	−	0.131299i	$-0.0419147\pi$
$998$	74.7879	+	146.779i	0.0749377	+	0.147074i
$999$	−903.893	+	1244.10i	−0.904798	+	1.24535i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	110.3.l.a.37.5	yes	48
5.3	odd	4	inner	110.3.l.a.103.2	yes	48
11.3	even	5	inner	110.3.l.a.47.2	yes	48
55.3	odd	20	inner	110.3.l.a.3.5	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
110.3.l.a.3.5	✓	48	55.3	odd	20	inner
110.3.l.a.37.5	yes	48	1.1	even	1	trivial
110.3.l.a.47.2	yes	48	11.3	even	5	inner
110.3.l.a.103.2	yes	48	5.3	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 110 = 2 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	110.l (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.221232 - 1.39680i) q^{2} +(1.09534 + 2.14972i) q^{3} +(-1.90211 + 0.618034i) q^{4} +(1.48006 - 4.77592i) q^{5} +(2.76042 - 2.00556i) q^{6} +(1.47655 - 2.89789i) q^{7} +(1.28408 + 2.52015i) q^{8} +(1.86852 - 2.57180i) q^{9} +(-6.99845 - 1.01077i) q^{10} +(10.0869 + 4.38810i) q^{11} +(-3.41206 - 3.41206i) q^{12} +(22.7719 - 3.60671i) q^{13} +(-4.37444 - 1.42134i) q^{14} +(11.8881 - 2.04953i) q^{15} +(3.23607 - 2.35114i) q^{16} +(-25.2737 - 4.00296i) q^{17} +(-4.00567 - 2.04099i) q^{18} +(-12.6650 - 4.11512i) q^{19} +(0.136436 + 9.99907i) q^{20} +7.84699 q^{21} +(3.89777 - 15.0601i) q^{22} +(-31.6053 + 31.6053i) q^{23} +(-4.01112 + 5.52083i) q^{24} +(-20.6188 - 14.1373i) q^{25} +(-10.0757 - 31.0099i) q^{26} +(29.0222 + 4.59667i) q^{27} +(-1.01757 + 6.42468i) q^{28} +(9.21597 - 2.99445i) q^{29} +(-5.49280 - 16.1519i) q^{30} +(21.3814 + 15.5345i) q^{31} +(-4.00000 - 4.00000i) q^{32} +(1.61533 + 26.4904i) q^{33} +36.1880i q^{34} +(-11.6547 - 11.3409i) q^{35} +(-1.96468 + 6.04666i) q^{36} +(-23.7594 + 46.6304i) q^{37} +(-2.94610 + 18.6010i) q^{38} +(32.6963 + 45.0026i) q^{39} +(13.9365 - 2.40269i) q^{40} +(10.6065 - 32.6435i) q^{41} +(-1.73600 - 10.9607i) q^{42} +(-3.10574 + 3.10574i) q^{43} +(-21.8983 - 2.11264i) q^{44} +(-9.51718 - 12.7303i) q^{45} +(51.1385 + 37.1543i) q^{46} +(-32.0813 + 16.3462i) q^{47} +(8.59890 + 4.38136i) q^{48} +(22.5839 + 31.0841i) q^{49} +(-15.1855 + 31.9281i) q^{50} +(-19.0780 - 58.7161i) q^{51} +(-41.0856 + 20.9341i) q^{52} +(-74.7316 + 11.8363i) q^{53} -41.5552i q^{54} +(35.8864 - 41.6794i) q^{55} +9.19912 q^{56} +(-5.02614 - 31.7338i) q^{57} +(-6.22152 - 12.2104i) q^{58} +(46.5392 - 15.1215i) q^{59} +(-21.3458 + 11.2457i) q^{60} +(-9.53445 + 6.92718i) q^{61} +(16.9684 - 33.3023i) q^{62} +(-4.69384 - 9.21217i) q^{63} +(-4.70228 + 6.47214i) q^{64} +(16.4784 - 114.095i) q^{65} +(36.6445 - 8.11682i) q^{66} +(28.1955 + 28.1955i) q^{67} +(50.5474 - 8.00593i) q^{68} +(-102.561 - 33.3242i) q^{69} +(-13.2627 + 18.7883i) q^{70} +(-3.31366 + 2.40752i) q^{71} +(8.88064 + 1.40656i) q^{72} +(-27.5587 - 14.0419i) q^{73} +(70.3897 + 22.8710i) q^{74} +(7.80672 - 59.8100i) q^{75} +26.6336 q^{76} +(27.6100 - 22.7514i) q^{77} +(55.6263 - 55.6263i) q^{78} +(46.6732 - 64.2401i) q^{79} +(-6.43928 - 18.9350i) q^{80} +(13.0665 + 40.2147i) q^{81} +(-47.9430 - 7.59343i) q^{82} +(-1.12047 + 7.07437i) q^{83} +(-14.9259 + 4.84971i) q^{84} +(-56.5245 + 114.781i) q^{85} +(5.02519 + 3.65102i) q^{86} +(16.5319 + 16.5319i) q^{87} +(1.89367 + 31.0550i) q^{88} +59.8878i q^{89} +(-15.6763 + 16.1100i) q^{90} +(23.1719 - 71.3159i) q^{91} +(40.5837 - 79.6501i) q^{92} +(-9.97500 + 62.9796i) q^{93} +(29.9299 + 41.1949i) q^{94} +(-38.3986 + 54.3966i) q^{95} +(4.21754 - 12.9803i) q^{96} +(9.83435 + 62.0916i) q^{97} +(38.4220 - 38.4220i) q^{98} +(30.1328 - 17.7421i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 12 q^{2} + 2 q^{3} + 4 q^{5} + 4 q^{6} + 38 q^{7} + 24 q^{8} + 36 q^{10} + 80 q^{11} - 16 q^{12} - 16 q^{13} + 38 q^{15} + 48 q^{16} - 18 q^{17} - 44 q^{18} + 4 q^{20} + 24 q^{21} + 64 q^{23} + 70 q^{25}+ \cdots - 440 q^{98}+O(q^{100}) \) 48 * q - 12 * q^2 + 2 * q^3 + 4 * q^5 + 4 * q^6 + 38 * q^7 + 24 * q^8 + 36 * q^10 + 80 * q^11 - 16 * q^12 - 16 * q^13 + 38 * q^15 + 48 * q^16 - 18 * q^17 - 44 * q^18 + 4 * q^20 + 24 * q^21 + 64 * q^23 + 70 * q^25 + 8 * q^26 - 82 * q^27 + 64 * q^28 - 14 * q^30 - 116 * q^31 - 192 * q^32 - 312 * q^33 - 288 * q^35 - 88 * q^36 + 22 * q^37 - 72 * q^38 - 24 * q^40 - 196 * q^41 - 96 * q^42 - 484 * q^43 - 56 * q^45 - 132 * q^46 - 310 * q^47 - 8 * q^48 - 128 * q^50 + 256 * q^51 + 8 * q^52 - 82 * q^53 - 264 * q^55 + 48 * q^56 + 744 * q^57 + 168 * q^58 + 196 * q^60 + 528 * q^61 + 144 * q^62 + 814 * q^63 + 840 * q^65 + 436 * q^66 + 192 * q^67 + 36 * q^68 + 230 * q^70 - 292 * q^71 - 48 * q^72 - 108 * q^73 + 258 * q^75 + 96 * q^76 - 200 * q^77 + 88 * q^78 + 24 * q^80 + 628 * q^81 + 24 * q^82 + 360 * q^83 - 368 * q^85 + 532 * q^86 - 328 * q^87 - 40 * q^88 - 766 * q^90 + 72 * q^91 + 68 * q^92 - 66 * q^93 - 232 * q^95 - 16 * q^96 + 6 * q^97 - 440 * q^98

Introduction

L-functions

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