LMFDB - Embedded newform 144.2.u.a.11.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [144,2,Mod(11,144)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(144, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 3, 2]))

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

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

chi := DirichletCharacter("144.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$144 = 2^{4} \cdot 3^{2}$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	144.u (of order $12$ , degree $4$ , 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:	$1.14984578911$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$22$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			11.20
Character	$\chi$	$=$	144.11
Dual form			144.2.u.a.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+(1.29365 + 0.571371i) q^{2} +(1.61259 + 0.632098i) q^{3} +(1.34707 + 1.47831i) q^{4} +(-3.81396 - 1.02195i) q^{5} +(1.72497 + 1.73910i) q^{6} +(1.46715 - 2.54117i) q^{7} +(0.897978 + 2.68210i) q^{8} +(2.20090 + 2.03863i) q^{9} +(-4.35003 - 3.50123i) q^{10} +(-2.65006 + 0.710081i) q^{11} +(1.23784 + 3.23539i) q^{12} +(-2.34729 - 0.628955i) q^{13} +(3.34993 - 2.44911i) q^{14} +(-5.50439 - 4.05878i) q^{15} +(-0.370800 + 3.98278i) q^{16} -2.89808i q^{17} +(1.68239 + 3.89481i) q^{18} +(-1.99906 - 1.99906i) q^{19} +(-3.62692 - 7.01485i) q^{20} +(3.97218 - 3.17049i) q^{21} +(-3.83397 - 0.595568i) q^{22} +(-2.07141 + 1.19593i) q^{23} +(-0.247276 + 4.89273i) q^{24} +(9.17180 + 5.29534i) q^{25} +(-2.67721 - 2.15482i) q^{26} +(2.26054 + 4.67867i) q^{27} +(5.73299 - 1.25424i) q^{28} +(8.46218 - 2.26743i) q^{29} +(-4.80170 - 8.39570i) q^{30} +(-0.439075 + 0.253500i) q^{31} +(-2.75533 + 4.94046i) q^{32} +(-4.72230 - 0.530027i) q^{33} +(1.65588 - 3.74911i) q^{34} +(-8.19258 + 8.19258i) q^{35} +(-0.0489584 + 5.99980i) q^{36} +(1.36407 + 1.36407i) q^{37} +(-1.44388 - 3.72828i) q^{38} +(-3.38766 - 2.49797i) q^{39} +(-0.683892 - 11.1471i) q^{40} +(0.745739 + 1.29166i) q^{41} +(6.95014 - 1.83193i) q^{42} +(-1.27136 - 4.74478i) q^{43} +(-4.61954 - 2.96108i) q^{44} +(-6.31078 - 10.0245i) q^{45} +(-3.36300 + 0.363572i) q^{46} +(-3.25802 + 5.64306i) q^{47} +(-3.11546 + 6.18821i) q^{48} +(-0.805035 - 1.39436i) q^{49} +(8.83951 + 12.0908i) q^{50} +(1.83187 - 4.67343i) q^{51} +(-2.23218 - 4.31727i) q^{52} +(-5.17979 + 5.17979i) q^{53} +(0.251099 + 7.34418i) q^{54} +10.8329 q^{55} +(8.13313 + 1.65311i) q^{56} +(-1.96006 - 4.48726i) q^{57} +(12.2427 + 1.90177i) q^{58} +(0.664781 - 2.48100i) q^{59} +(-1.41467 - 13.6047i) q^{60} +(2.99657 + 11.1833i) q^{61} +(-0.712853 + 0.0770663i) q^{62} +(8.40956 - 2.60190i) q^{63} +(-6.38727 + 4.81693i) q^{64} +(8.30972 + 4.79762i) q^{65} +(-5.80617 - 3.38386i) q^{66} +(-2.53505 + 9.46095i) q^{67} +(4.28427 - 3.90393i) q^{68} +(-4.09628 + 0.619209i) q^{69} +(-15.2794 + 5.91735i) q^{70} -4.65399i q^{71} +(-3.49145 + 7.73368i) q^{72} -4.91897i q^{73} +(0.985240 + 2.54402i) q^{74} +(11.4432 + 14.3367i) q^{75} +(0.262354 - 5.64809i) q^{76} +(-2.08358 + 7.77604i) q^{77} +(-2.95519 - 5.16711i) q^{78} +(-3.61263 - 2.08575i) q^{79} +(5.48441 - 14.8112i) q^{80} +(0.687950 + 8.97367i) q^{81} +(0.226711 + 2.09705i) q^{82} +(-3.37411 - 12.5924i) q^{83} +(10.0378 + 1.60123i) q^{84} +(-2.96169 + 11.0532i) q^{85} +(1.06633 - 6.86451i) q^{86} +(15.0793 + 1.69249i) q^{87} +(-4.28420 - 6.47007i) q^{88} +7.33327 q^{89} +(-2.43627 - 16.5740i) q^{90} +(-5.04210 + 5.04210i) q^{91} +(-4.55828 - 1.45118i) q^{92} +(-0.868286 + 0.131254i) q^{93} +(-7.43902 + 5.43861i) q^{94} +(5.58139 + 9.66725i) q^{95} +(-7.56608 + 6.22531i) q^{96} +(2.50134 - 4.33245i) q^{97} +(-0.244738 - 2.26379i) q^{98} +(-7.28011 - 3.83968i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$88 q - 6 q^{2} - 4 q^{3} - 2 q^{4} - 6 q^{5} + 2 q^{6} - 4 q^{7} - 8 q^{10} - 6 q^{11} - 16 q^{12} - 2 q^{13} - 6 q^{14} - 2 q^{16} - 10 q^{18} - 8 q^{19} - 48 q^{20} + 2 q^{21} - 2 q^{22} - 12 q^{23} - 16 q^{27}+ \cdots + 46 q^{99}+O(q^{100})$ 88 * q - 6 * q^2 - 4 * q^3 - 2 * q^4 - 6 * q^5 + 2 * q^6 - 4 * q^7 - 8 * q^10 - 6 * q^11 - 16 * q^12 - 2 * q^13 - 6 * q^14 - 2 * q^16 - 10 * q^18 - 8 * q^19 - 48 * q^20 + 2 * q^21 - 2 * q^22 - 12 * q^23 - 16 * q^27 + 8 * q^28 - 6 * q^29 - 34 * q^30 - 6 * q^32 - 8 * q^33 + 2 * q^34 - 26 * q^36 - 8 * q^37 - 6 * q^38 - 32 * q^39 - 2 * q^40 + 48 * q^42 - 2 * q^43 + 6 * q^45 - 40 * q^46 + 42 * q^48 - 24 * q^49 + 72 * q^50 - 12 * q^51 - 2 * q^52 - 38 * q^54 - 16 * q^55 + 36 * q^56 + 16 * q^58 - 42 * q^59 + 70 * q^60 - 2 * q^61 - 44 * q^64 - 12 * q^65 + 104 * q^66 - 2 * q^67 + 96 * q^68 - 10 * q^69 - 16 * q^70 - 10 * q^72 + 78 * q^74 - 56 * q^75 - 14 * q^76 - 6 * q^77 + 12 * q^78 - 8 * q^81 - 36 * q^82 + 54 * q^83 + 158 * q^84 + 8 * q^85 + 54 * q^86 + 48 * q^87 + 22 * q^88 + 64 * q^90 + 20 * q^91 + 108 * q^92 - 34 * q^93 + 6 * q^94 - 58 * q^96 - 4 * q^97 + 46 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/144\mathbb{Z}\right)^\times$ .

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{6}\right)$	$-1$

Coefficient data

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

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$	1.29365	+	0.571371i	0.914750	+	0.404020i
$2$	1.29365	+	0.571371i	0.914750	+	0.404020i
$3$	1.61259	+	0.632098i	0.931030	+	0.364942i
$3$	1.61259	+	0.632098i	0.931030	+	0.364942i
$4$	1.34707	+	1.47831i	0.673535	+	0.739155i
$5$	−3.81396	−	1.02195i	−1.70566	−	0.457029i	−0.731302	−	0.682053i	$-0.761087\pi$
$5$	−3.81396	−	1.02195i	−1.70566	−	0.457029i	−0.974353	+	0.225024i	$0.927754\pi$
$6$	1.72497	+	1.73910i	0.704216	+	0.709986i
$7$	1.46715	−	2.54117i	0.554529	−	0.960473i	−0.443411	−	0.896318i	$-0.646232\pi$
$7$	1.46715	−	2.54117i	0.554529	−	0.960473i	0.997940	−	0.0641541i	$-0.0204349\pi$
$8$	0.897978	+	2.68210i	0.317483	+	0.948264i
$9$	2.20090	+	2.03863i	0.733634	+	0.679544i
$10$	−4.35003	−	3.50123i	−1.37560	−	1.10719i
$11$	−2.65006	+	0.710081i	−0.799022	+	0.214097i	−0.635155	−	0.772385i	$-0.719064\pi$
$11$	−2.65006	+	0.710081i	−0.799022	+	0.214097i	−0.163868	+	0.986482i	$0.552397\pi$
$12$	1.23784	+	3.23539i	0.357333	+	0.933977i
$13$	−2.34729	−	0.628955i	−0.651021	−	0.174441i	−0.0818307	−	0.996646i	$-0.526077\pi$
$13$	−2.34729	−	0.628955i	−0.651021	−	0.174441i	−0.569191	+	0.822206i	$0.692743\pi$
$14$	3.34993	−	2.44911i	0.895306	−	0.654551i
$15$	−5.50439	−	4.05878i	−1.42123	−	1.04797i
$16$	−0.370800	+	3.98278i	−0.0926999	+	0.995694i
$17$		−	2.89808i		−	0.702889i	−0.936209	−	0.351444i	$-0.885691\pi$
$17$		−	2.89808i		−	0.702889i	0.936209	−	0.351444i	$-0.114309\pi$
$18$	1.68239	+	3.89481i	0.396543	+	0.918016i
$19$	−1.99906	−	1.99906i	−0.458615	−	0.458615i	0.439586	−	0.898201i	$-0.355125\pi$
$19$	−1.99906	−	1.99906i	−0.458615	−	0.458615i	−0.898201	+	0.439586i	$0.855125\pi$
$20$	−3.62692	−	7.01485i	−0.811004	−	1.56857i
$21$	3.97218	−	3.17049i	0.866800	−	0.691858i
$22$	−3.83397	−	0.595568i	−0.817406	−	0.126976i
$23$	−2.07141	+	1.19593i	−0.431918	+	0.249368i	−0.700163	−	0.713983i	$-0.746890\pi$
$23$	−2.07141	+	1.19593i	−0.431918	+	0.249368i	0.268245	+	0.963351i	$0.413556\pi$
$24$	−0.247276	+	4.89273i	−0.0504751	+	0.998725i
$25$	9.17180	+	5.29534i	1.83436	+	1.05907i
$26$	−2.67721	−	2.15482i	−0.525044	−	0.422595i
$27$	2.26054	+	4.67867i	0.435041	+	0.900410i
$28$	5.73299	−	1.25424i	1.08343	−	0.237029i
$29$	8.46218	−	2.26743i	1.57139	−	0.421052i	0.635141	−	0.772396i	$-0.280942\pi$
$29$	8.46218	−	2.26743i	1.57139	−	0.421052i	0.936246	+	0.351344i	$0.114275\pi$
$30$	−4.80170	−	8.39570i	−0.876666	−	1.53284i
$31$	−0.439075	+	0.253500i	−0.0788602	+	0.0455300i	−0.538912	−	0.842362i	$-0.681164\pi$
$31$	−0.439075	+	0.253500i	−0.0788602	+	0.0455300i	0.460051	+	0.887892i	$0.347831\pi$
$32$	−2.75533	+	4.94046i	−0.487078	+	0.873359i
$33$	−4.72230	−	0.530027i	−0.822047	−	0.0922658i
$34$	1.65588	−	3.74911i	0.283981	−	0.642968i
$35$	−8.19258	+	8.19258i	−1.38480	+	1.38480i
$36$	−0.0489584	+	5.99980i	−0.00815973	+	0.999967i
$37$	1.36407	+	1.36407i	0.224251	+	0.224251i	0.810286	−	0.586035i	$-0.199312\pi$
$37$	1.36407	+	1.36407i	0.224251	+	0.224251i	−0.586035	+	0.810286i	$0.699312\pi$
$38$	−1.44388	−	3.72828i	−0.234228	−	0.604808i
$39$	−3.38766	−	2.49797i	−0.542460	−	0.399995i
$40$	−0.683892	−	11.1471i	−0.108133	−	1.76251i
$41$	0.745739	+	1.29166i	0.116465	+	0.201723i	0.918364	−	0.395736i	$-0.129510\pi$
$41$	0.745739	+	1.29166i	0.116465	+	0.201723i	−0.801899	+	0.597459i	$0.796177\pi$
$42$	6.95014	−	1.83193i	1.07243	−	0.282672i
$43$	−1.27136	−	4.74478i	−0.193881	−	0.723572i	−0.992554	−	0.121807i	$-0.961131\pi$
$43$	−1.27136	−	4.74478i	−0.193881	−	0.723572i	0.798673	−	0.601765i	$-0.205536\pi$
$44$	−4.61954	−	2.96108i	−0.696421	−	0.446399i
$45$	−6.31078	−	10.0245i	−0.940756	−	1.49436i
$46$	−3.36300	+	0.363572i	−0.495847	+	0.0536058i
$47$	−3.25802	+	5.64306i	−0.475231	+	0.823124i	−0.999598	−	0.0283684i	$-0.990969\pi$
$47$	−3.25802	+	5.64306i	−0.475231	+	0.823124i	0.524367	+	0.851493i	$0.324302\pi$
$48$	−3.11546	+	6.18821i	−0.449677	+	0.893191i
$49$	−0.805035	−	1.39436i	−0.115005	−	0.199195i
$50$	8.83951	+	12.0908i	1.25010	+	1.70990i
$51$	1.83187	−	4.67343i	0.256514	−	0.654411i
$52$	−2.23218	−	4.31727i	−0.309547	−	0.598698i
$53$	−5.17979	+	5.17979i	−0.711499	+	0.711499i	−0.966849	−	0.255349i	$-0.917809\pi$
$53$	−5.17979	+	5.17979i	−0.711499	+	0.711499i	0.255349	+	0.966849i	$0.417809\pi$
$54$	0.251099	+	7.34418i	0.0341702	+	0.999416i
$55$	10.8329			1.46071
$56$	8.13313	+	1.65311i	1.08684	+	0.220906i
$57$	−1.96006	−	4.48726i	−0.259616	−	0.594352i
$58$	12.2427	+	1.90177i	1.60754	+	0.249715i
$59$	0.664781	−	2.48100i	0.0865472	−	0.322998i	−0.909056	−	0.416675i	$-0.863195\pi$
$59$	0.664781	−	2.48100i	0.0865472	−	0.322998i	0.995603	+	0.0936766i	$0.0298620\pi$
$60$	−1.41467	−	13.6047i	−0.182633	−	1.75635i
$61$	2.99657	+	11.1833i	0.383671	+	1.43188i	0.840251	+	0.542198i	$0.182408\pi$
$61$	2.99657	+	11.1833i	0.383671	+	1.43188i	−0.456580	+	0.889682i	$0.650926\pi$
$62$	−0.712853	+	0.0770663i	−0.0905324	+	0.00978743i
$63$	8.40956	−	2.60190i	1.05951	−	0.327809i
$64$	−6.38727	+	4.81693i	−0.798409	+	0.602116i
$65$	8.30972	+	4.79762i	1.03069	+	0.595071i
$66$	−5.80617	−	3.38386i	−0.714691	−	0.416524i
$67$	−2.53505	+	9.46095i	−0.309706	+	1.15584i	0.619112	+	0.785303i	$0.287493\pi$
$67$	−2.53505	+	9.46095i	−0.309706	+	1.15584i	−0.928818	+	0.370536i	$0.879174\pi$
$68$	4.28427	−	3.90393i	0.519544	−	0.473421i
$69$	−4.09628	+	0.619209i	−0.493134	+	0.0745440i
$70$	−15.2794	+	5.91735i	−1.82623	+	0.707259i
$71$		−	4.65399i		−	0.552327i	−0.961111	−	0.276164i	$-0.910937\pi$
$71$		−	4.65399i		−	0.552327i	0.961111	−	0.276164i	$-0.0890632\pi$
$72$	−3.49145	+	7.73368i	−0.411471	+	0.911423i
$73$		−	4.91897i		−	0.575722i	−0.957672	−	0.287861i	$-0.907056\pi$
$73$		−	4.91897i		−	0.575722i	0.957672	−	0.287861i	$-0.0929441\pi$
$74$	0.985240	+	2.54402i	0.114532	+	0.295736i
$75$	11.4432	+	14.3367i	1.32135	+	1.65546i
$76$	0.262354	−	5.64809i	0.0300940	−	0.647881i
$77$	−2.08358	+	7.77604i	−0.237446	+	0.886162i
$78$	−2.95519	−	5.16711i	−0.334609	−	0.585060i
$79$	−3.61263	−	2.08575i	−0.406453	−	0.234666i	0.282812	−	0.959175i	$-0.408733\pi$
$79$	−3.61263	−	2.08575i	−0.406453	−	0.234666i	−0.689264	+	0.724510i	$0.742066\pi$
$80$	5.48441	−	14.8112i	0.613175	−	1.65594i
$81$	0.687950	+	8.97367i	0.0764389	+	0.997074i
$82$	0.226711	+	2.09705i	0.0250361	+	0.231580i
$83$	−3.37411	−	12.5924i	−0.370357	−	1.38219i	−0.860011	−	0.510275i	$-0.829544\pi$
$83$	−3.37411	−	12.5924i	−0.370357	−	1.38219i	0.489654	−	0.871917i	$-0.337123\pi$
$84$	10.0378	+	1.60123i	1.09521	+	0.174709i
$85$	−2.96169	+	11.0532i	−0.321241	+	1.19889i
$86$	1.06633	−	6.86451i	0.114985	−	0.740220i
$87$	15.0793	+	1.69249i	1.61667	+	0.181453i
$88$	−4.28420	−	6.47007i	−0.456697	−	0.689712i
$89$	7.33327			0.777325			0.388662	−	0.921380i	$-0.372937\pi$
$89$	7.33327			0.777325			0.388662	+	0.921380i	$0.372937\pi$
$90$	−2.43627	−	16.5740i	−0.256805	−	1.74705i
$91$	−5.04210	+	5.04210i	−0.528556	+	0.528556i
$92$	−4.55828	−	1.45118i	−0.475234	−	0.151296i
$93$	−0.868286	+	0.131254i	−0.0900371	+	0.0136104i
$94$	−7.43902	+	5.43861i	−0.767276	+	0.560950i
$95$	5.58139	+	9.66725i	0.572639	+	0.991839i
$96$	−7.56608	+	6.22531i	−0.772209	+	0.635368i
$97$	2.50134	−	4.33245i	0.253973	−	0.439893i	−0.710643	−	0.703552i	$-0.751596\pi$
$97$	2.50134	−	4.33245i	0.253973	−	0.439893i	0.964616	+	0.263659i	$0.0849294\pi$
$98$	−0.244738	−	2.26379i	−0.0247222	−	0.228678i
$99$	−7.28011	−	3.83968i	−0.731679	−	0.385902i
$100$	4.52691	+	20.6920i	0.452691	+	2.06920i
$101$	−2.82933	−	10.5592i	−0.281529	−	1.05068i	−0.951339	−	0.308147i	$-0.900291\pi$
$101$	−2.82933	−	10.5592i	−0.281529	−	1.05068i	0.669810	−	0.742533i	$-0.266376\pi$
$102$	5.04007	−	4.99911i	0.499041	−	0.494986i
$103$	−0.321949	−	0.557632i	−0.0317226	−	0.0549451i	0.849728	−	0.527221i	$-0.176766\pi$
$103$	−0.321949	−	0.557632i	−0.0317226	−	0.0549451i	−0.881451	+	0.472276i	$0.843433\pi$
$104$	−0.420899	−	6.86044i	−0.0412726	−	0.672722i
$105$	−18.3898	+	8.03277i	−1.79466	+	0.783918i
$106$	−9.66043	+	3.74127i	−0.938304	+	0.363384i
$107$	3.74155	+	3.74155i	0.361709	+	0.361709i	0.864442	−	0.502733i	$-0.167672\pi$
$107$	3.74155	+	3.74155i	0.361709	+	0.361709i	−0.502733	+	0.864442i	$0.667672\pi$
$108$	−3.87141	+	9.64428i	−0.372527	+	0.928021i
$109$	6.00859	−	6.00859i	0.575518	−	0.575518i	−0.358147	−	0.933665i	$-0.616591\pi$
$109$	6.00859	−	6.00859i	0.575518	−	0.575518i	0.933665	+	0.358147i	$0.116591\pi$
$110$	14.0140	+	6.18959i	1.33618	+	0.590155i
$111$	1.33746	+	3.06191i	0.126946	+	0.290623i
$112$	9.57690	+	6.78558i	0.904932	+	0.641177i
$113$	14.4387	−	8.33620i	1.35828	−	0.784204i	0.368889	−	0.929474i	$-0.379738\pi$
$113$	14.4387	−	8.33620i	1.35828	−	0.784204i	0.989392	+	0.145270i	$0.0464051\pi$
$114$	0.0282530	−	6.92487i	0.00264614	−	0.648574i
$115$	9.12244	−	2.44435i	0.850672	−	0.227937i
$116$	14.7511	+	9.45533i	1.36961	+	0.877905i
$117$	−3.88395	−	6.16953i	−0.359071	−	0.570374i
$118$	2.27757	−	2.82971i	0.209667	−	0.260496i
$119$	−7.36453	−	4.25191i	−0.675105	−	0.389772i
$120$	5.94322	−	18.4080i	0.542539	−	1.68041i
$121$	−3.00769	+	1.73649i	−0.273426	+	0.157863i
$122$	−2.51332	+	16.1795i	−0.227545	+	1.46482i
$123$	0.386118	+	2.55430i	0.0348151	+	0.230313i
$124$	−0.966217	−	0.307606i	−0.0867689	−	0.0276239i
$125$	−15.6093	−	15.6093i	−1.39613	−	1.39613i
$126$	12.3657	+	1.43902i	1.10162	+	0.128199i
$127$		−	17.9975i		−	1.59702i	−0.601983	−	0.798509i	$-0.705623\pi$
$127$		−	17.9975i		−	1.59702i	0.601983	−	0.798509i	$-0.294377\pi$
$128$	−11.0152	+	2.58193i	−0.973611	+	0.228212i
$129$	0.948984	−	8.45502i	0.0835533	−	0.744423i
$130$	8.00866	+	10.9544i	0.702406	+	0.960762i
$131$	17.4121	+	4.66555i	1.52130	+	0.407631i	0.920170	−	0.391520i	$-0.128051\pi$
$131$	17.4121	+	4.66555i	1.52130	+	0.407631i	0.601131	+	0.799151i	$0.294717\pi$
$132$	−5.57773	−	7.69501i	−0.485479	−	0.669765i
$133$	−8.01285	+	2.14704i	−0.694802	+	0.186172i
$134$	−8.68519	+	10.7907i	−0.750286	+	0.932176i
$135$	−3.84026	−	20.1544i	−0.330517	−	1.73462i
$136$	7.77294	−	2.60242i	0.666524	−	0.223155i
$137$	−0.396155	+	0.686161i	−0.0338458	+	0.0586227i	−0.882452	−	0.470402i	$-0.844109\pi$
$137$	−0.396155	+	0.686161i	−0.0338458	+	0.0586227i	0.848606	+	0.529025i	$0.177442\pi$
$138$	−5.65295	−	1.53945i	−0.481211	−	0.131047i
$139$	−20.5134	−	5.49654i	−1.73992	−	0.466211i	−0.757492	−	0.652844i	$-0.773576\pi$
$139$	−20.5134	−	5.49654i	−1.73992	−	0.466211i	−0.982430	+	0.186633i	$0.940242\pi$
$140$	−23.1472	−	1.07519i	−1.95629	−	0.0908697i
$141$	−8.82082	+	7.04056i	−0.742847	+	0.592922i
$142$	2.65916	−	6.02065i	0.223151	−	0.505242i
$143$	6.66706			0.557528
$144$	−8.93551	+	8.00978i	−0.744626	+	0.667482i
$145$	−34.5916			−2.87268
$146$	2.81055	−	6.36343i	0.232603	−	0.526641i
$147$	−0.416819	−	2.75740i	−0.0343787	−	0.227426i
$148$	−0.179019	+	3.85401i	−0.0147152	+	0.316798i
$149$	−11.3030	−	3.02863i	−0.925977	−	0.248115i	−0.235839	−	0.971792i	$-0.575784\pi$
$149$	−11.3030	−	3.02863i	−0.925977	−	0.248115i	−0.690139	+	0.723677i	$0.742450\pi$
$150$	6.61193	+	25.0850i	0.539862	+	2.04818i
$151$	−4.24025	+	7.34432i	−0.345066	+	0.597673i	−0.985366	−	0.170453i	$-0.945477\pi$
$151$	−4.24025	+	7.34432i	−0.345066	+	0.597673i	0.640299	+	0.768125i	$0.278810\pi$
$152$	3.56655	−	7.15677i	0.289285	−	0.580490i
$153$	5.90813	−	6.37840i	0.477644	−	0.515663i
$154$	−7.13844	+	8.86899i	−0.575232	+	0.714684i
$155$	1.93368	−	0.518128i	0.155317	−	0.0416170i
$156$	−0.870651	−	8.37295i	−0.0697079	−	0.670372i
$157$	3.53516	+	0.947242i	0.282136	+	0.0755981i	0.397112	−	0.917770i	$-0.370012\pi$
$157$	3.53516	+	0.947242i	0.282136	+	0.0755981i	−0.114976	+	0.993368i	$0.536679\pi$
$158$	−3.48175	−	4.76239i	−0.276993	−	0.378875i
$159$	−11.6270	+	5.07875i	−0.922084	+	0.402771i
$160$	15.5576	−	16.0269i	1.22994	−	1.26704i
$161$			7.01840i			0.553127i
$162$	−4.23732	+	12.0019i	−0.332916	+	0.942957i
$163$	−3.86060	−	3.86060i	−0.302385	−	0.302385i	0.539561	−	0.841946i	$-0.318590\pi$
$163$	−3.86060	−	3.86060i	−0.302385	−	0.302385i	−0.841946	+	0.539561i	$0.818590\pi$
$164$	−0.904908	+	2.84239i	−0.0706614	+	0.221953i
$165$	17.4690	+	6.84745i	1.35996	+	0.533073i
$166$	2.82998	−	18.2180i	0.219649	−	1.41399i
$167$	−5.98224	+	3.45385i	−0.462920	+	0.267267i	−0.713271	−	0.700888i	$-0.752787\pi$
$167$	−5.98224	+	3.45385i	−0.462920	+	0.267267i	0.250351	+	0.968155i	$0.419454\pi$
$168$	12.0705	+	7.80673i	0.931258	+	0.602302i
$169$	−6.14414	−	3.54732i	−0.472626	−	0.272871i
$170$	−10.1469	+	12.6067i	−0.778229	+	0.966894i
$171$	−0.324387	−	8.47507i	−0.0248065	−	0.648105i
$172$	5.30164	−	8.27102i	0.404247	−	0.630659i
$173$	3.86859	−	1.03659i	0.294123	−	0.0788101i	−0.108740	−	0.994070i	$-0.534682\pi$
$173$	3.86859	−	1.03659i	0.294123	−	0.0788101i	0.402863	+	0.915260i	$0.368015\pi$
$174$	18.5403	+	10.8053i	1.40554	+	0.819151i
$175$	26.9127	−	15.5381i	2.03441	−	1.17457i
$176$	−1.84545	−	10.8179i	−0.139106	−	0.815429i
$177$	2.64026	−	3.58063i	0.198454	−	0.269137i
$178$	9.48669	+	4.19001i	0.711058	+	0.314055i
$179$	10.0625	−	10.0625i	0.752109	−	0.752109i	−0.222764	−	0.974872i	$-0.571508\pi$
$179$	10.0625	−	10.0625i	0.752109	−	0.752109i	0.974872	+	0.222764i	$0.0715078\pi$
$180$	6.31821	−	22.8330i	0.470931	−	1.70187i
$181$	15.0346	+	15.0346i	1.11751	+	1.11751i	0.992106	+	0.125405i	$0.0400229\pi$
$181$	15.0346	+	15.0346i	1.11751	+	1.11751i	0.125405	+	0.992106i	$0.459977\pi$
$182$	−9.40363	+	3.64181i	−0.697044	+	0.269949i
$183$	−2.23673	+	19.9283i	−0.165344	+	1.47314i
$184$	−5.06767	−	4.48179i	−0.373593	−	0.330402i
$185$	−3.80849	−	6.59651i	−0.280006	−	0.484985i
$186$	−1.19825	−	0.326317i	−0.0878603	−	0.0239267i
$187$	2.05787	+	7.68009i	0.150487	+	0.561624i
$188$	−12.7310	+	2.78523i	−0.928501	+	0.203134i
$189$	15.2058	+	1.11987i	1.10606	+	0.0814585i
$190$	1.69679	+	15.6951i	0.123098	+	1.13864i
$191$	−10.9007	+	18.8806i	−0.788749	+	1.36615i	0.137984	+	0.990434i	$0.455938\pi$
$191$	−10.9007	+	18.8806i	−0.788749	+	1.36615i	−0.926734	+	0.375719i	$0.877396\pi$
$192$	−13.3448	+	3.73035i	−0.963080	+	0.269215i
$193$	−2.34723	−	4.06553i	−0.168958	−	0.292643i	0.769096	−	0.639133i	$-0.220707\pi$
$193$	−2.34723	−	4.06553i	−0.168958	−	0.292643i	−0.938054	+	0.346490i	$0.887373\pi$
$194$	5.71130	−	4.17549i	0.410047	−	0.299782i
$195$	10.3676	+	12.9892i	0.742440	+	0.930173i
$196$	0.976859	−	3.06840i	0.0697757	−	0.219171i
$197$	14.3226	−	14.3226i	1.02044	−	1.02044i	0.0206566	−	0.999787i	$-0.493424\pi$
$197$	14.3226	−	14.3226i	1.02044	−	1.02044i	0.999787	−	0.0206566i	$-0.00657567\pi$
$198$	−7.22406	−	9.12685i	−0.513391	−	0.648617i
$199$	−14.4965			−1.02763			−0.513816	−	0.857901i	$-0.671768\pi$
$199$	−14.4965			−1.02763			−0.513816	+	0.857901i	$0.671768\pi$
$200$	−5.96653	+	29.3547i	−0.421898	+	2.07569i
$201$	−10.0683	+	13.6542i	−0.710160	+	0.963096i
$202$	2.37305	−	15.2765i	0.166967	−	1.07485i
$203$	6.65332	−	24.8305i	0.466971	−	1.74276i
$204$	9.37644	−	3.58736i	0.656482	−	0.251165i
$205$	−1.52421	−	5.68844i	−0.106456	−	0.397298i
$206$	−0.0978753	−	0.905334i	−0.00681930	−	0.0630776i
$207$	−6.99702	−	1.59072i	−0.486327	−	0.110563i
$208$	3.37536	−	9.11552i	0.234039	−	0.632047i
$209$	6.71710	+	3.87812i	0.464632	+	0.268255i
$210$	−28.3797	−	0.115787i	−1.95839	−	0.00799008i
$211$	−1.71268	+	6.39179i	−0.117905	+	0.440029i	−0.999488	−	0.0320010i	$-0.989812\pi$
$211$	−1.71268	+	6.39179i	−0.117905	+	0.440029i	0.881582	+	0.472030i	$0.156479\pi$
$212$	−14.6349	−	0.679790i	−1.00513	−	0.0466882i
$213$	2.94178	−	7.50499i	0.201568	−	0.514234i
$214$	2.70245	+	6.97808i	0.184736	+	0.477012i
$215$			19.3957i			1.32277i
$216$	−10.5187	+	10.2643i	−0.715708	+	0.698399i
$217$			1.48769i			0.100991i
$218$	11.2062	−	4.33989i	0.758976	−	0.293934i
$219$	3.10927	−	7.93229i	0.210105	−	0.536014i
$220$	14.5927	+	16.0144i	0.983837	+	1.07969i
$221$	−1.82276	+	6.80265i	−0.122612	+	0.457596i
$222$	−0.0192786	+	4.72523i	−0.00129390	+	0.317137i
$223$	1.59599	+	0.921443i	0.106875	+	0.0617044i	0.552485	−	0.833523i	$-0.313680\pi$
$223$	1.59599	+	0.921443i	0.106875	+	0.0617044i	−0.445610	+	0.895227i	$0.647013\pi$
$224$	8.51209	+	14.2501i	0.568738	+	0.952128i
$225$	9.39099	+	30.3525i	0.626066	+	2.02350i
$226$	23.4417	−	2.53428i	1.55932	−	0.168578i
$227$	−0.184084	−	0.687012i	−0.0122181	−	0.0455986i	0.959548	−	0.281546i	$-0.0908473\pi$
$227$	−0.184084	−	0.687012i	−0.0122181	−	0.0455986i	−0.971766	+	0.235948i	$0.924181\pi$
$228$	3.99322	−	8.94223i	0.264457	−	0.592214i
$229$	1.98433	−	7.40562i	0.131128	−	0.489377i	−0.868856	−	0.495066i	$-0.835144\pi$
$229$	1.98433	−	7.40562i	0.131128	−	0.489377i	0.999984	+	0.00568843i	$0.00181069\pi$
$230$	13.1979	+	2.05016i	0.870243	+	0.135183i
$231$	−8.27520	+	11.2226i	−0.544468	+	0.738390i
$232$	13.6803	+	20.6603i	0.898158	+	1.35641i
$233$	1.36925			0.0897024			0.0448512	−	0.998994i	$-0.485719\pi$
$233$	1.36925			0.0897024			0.0448512	+	0.998994i	$0.485719\pi$
$234$	−1.49939	−	10.2004i	−0.0980183	−	0.666821i
$235$	18.1929	−	18.1929i	1.18677	−	1.18677i
$236$	4.56319	−	2.35933i	0.297038	−	0.153579i
$237$	−4.50730	−	5.64701i	−0.292780	−	0.366812i
$238$	−7.09772	−	9.70837i	−0.460077	−	0.629300i
$239$	−0.773627	−	1.33996i	−0.0500418	−	0.0866749i	0.839919	−	0.542711i	$-0.182602\pi$
$239$	−0.773627	−	1.33996i	−0.0500418	−	0.0866749i	−0.889961	+	0.456036i	$0.849269\pi$
$240$	18.2063	−	20.4178i	1.17521	−	1.31796i
$241$	3.83660	−	6.64519i	0.247137	−	0.428054i	−0.715593	−	0.698517i	$-0.753844\pi$
$241$	3.83660	−	6.64519i	0.247137	−	0.428054i	0.962730	+	0.270463i	$0.0871769\pi$
$242$	−4.88308	+	0.527908i	−0.313896	+	0.0339352i
$243$	−4.56286	+	14.9057i	−0.292707	+	0.956202i
$244$	−12.4959	+	19.4946i	−0.799965	+	1.24801i
$245$	1.64541	+	6.14075i	0.105121	+	0.392318i
$246$	−0.959949	+	3.52499i	−0.0612041	+	0.224745i
$247$	3.43505	+	5.94968i	0.218567	+	0.378569i
$248$	−1.07419	−	0.950004i	−0.0682112	−	0.0603253i
$249$	2.51855	−	22.4391i	0.159606	−	1.42202i
$250$	−11.2743	−	29.1116i	−0.713048	−	1.84118i
$251$	−5.46632	−	5.46632i	−0.345031	−	0.345031i	0.513224	−	0.858255i	$-0.328451\pi$
$251$	−5.46632	−	5.46632i	−0.345031	−	0.345031i	−0.858255	+	0.513224i	$0.828451\pi$
$252$	15.1747	+	8.92699i	0.955916	+	0.562348i
$253$	4.64014	−	4.64014i	0.291723	−	0.291723i
$254$	10.2832	−	23.2825i	0.645227	−	1.46087i
$255$	−11.7627	+	15.9522i	−0.736609	+	0.998965i
$256$	−15.7250	−	2.95362i	−0.982813	−	0.184602i
$257$	−20.5918	+	11.8887i	−1.28448	+	0.741596i	−0.977664	−	0.210172i	$-0.932598\pi$
$257$	−20.5918	+	11.8887i	−1.28448	+	0.741596i	−0.306818	+	0.951768i	$0.599264\pi$
$258$	6.05861	−	10.3956i	0.377192	−	0.647204i
$259$	5.46761	−	1.46504i	0.339741	−	0.0910333i
$260$	4.10141	+	18.7471i	0.254359	+	1.16264i
$261$	23.2469	+	12.2609i	1.43895	+	0.758929i
$262$	19.8594	+	15.9844i	1.22692	+	0.987517i
$263$	−6.13704	−	3.54322i	−0.378426	−	0.218484i	0.298707	−	0.954345i	$-0.403445\pi$
$263$	−6.13704	−	3.54322i	−0.378426	−	0.218484i	−0.677133	+	0.735860i	$0.736778\pi$
$264$	−2.81894	−	13.1416i	−0.173494	−	0.808811i
$265$	25.0490	−	14.4621i	1.53875	−	0.888397i
$266$	−11.5926	−	1.80079i	−0.710788	−	0.110414i
$267$	11.8256	+	4.63535i	0.723713	+	0.283679i
$268$	−17.4011	+	8.99698i	−1.06294	+	0.549578i
$269$	20.6616	+	20.6616i	1.25976	+	1.25976i	0.951207	+	0.308553i	$0.0998448\pi$
$269$	20.6616	+	20.6616i	1.25976	+	1.25976i	0.308553	+	0.951207i	$0.400155\pi$
$270$	6.54769	−	28.2670i	0.398479	−	1.72028i
$271$			16.6901i			1.01385i	0.861989	+	0.506927i	$0.169218\pi$
$271$			16.6901i			1.01385i	−0.861989	+	0.506927i	$0.830782\pi$
$272$	11.5424	+	1.07461i	0.699862	+	0.0651577i
$273$	−11.3180	+	4.94374i	−0.684994	+	0.299209i
$274$	−0.904539	+	0.661302i	−0.0546452	+	0.0399507i
$275$	−28.0659	−	7.52024i	−1.69244	−	0.453487i
$276$	−6.43336	−	5.22145i	−0.387243	−	0.314294i
$277$	4.49217	−	1.20367i	0.269908	−	0.0723217i	−0.121326	−	0.992613i	$-0.538715\pi$
$277$	4.49217	−	1.20367i	0.269908	−	0.0723217i	0.391235	+	0.920291i	$0.372048\pi$
$278$	−23.3966	−	18.8314i	−1.40324	−	1.12943i
$279$	−1.48316	−	0.337184i	−0.0887942	−	0.0201867i
$280$	−29.3301	−	14.6165i	−1.75281	−	0.873505i
$281$	−11.4153	+	19.7719i	−0.680979	+	1.17949i	0.293703	+	0.955897i	$0.405112\pi$
$281$	−11.4153	+	19.7719i	−0.680979	+	1.17949i	−0.974682	+	0.223594i	$0.928221\pi$
$282$	−15.4338	+	4.06807i	−0.919072	+	0.242250i
$283$	−24.9438	−	6.68368i	−1.48276	−	0.397303i	−0.575472	−	0.817822i	$-0.695182\pi$
$283$	−24.9438	−	6.68368i	−1.48276	−	0.397303i	−0.907284	+	0.420518i	$0.861848\pi$
$284$	6.88004	−	6.26926i	0.408256	−	0.372012i
$285$	2.88985	+	19.1173i	0.171180	+	1.13241i
$286$	8.62486	+	3.80937i	0.509999	+	0.225253i
$287$	4.37643			0.258333
$288$	−16.1360	+	5.25638i	−0.950823	+	0.309735i
$289$	8.60110			0.505947
$290$	−44.7495	−	19.7646i	−2.62778	−	1.16062i
$291$	6.77217	−	5.40538i	0.396992	−	0.316869i
$292$	7.27176	−	6.62620i	0.425547	−	0.387769i
$293$	−2.76706	−	0.741431i	−0.161653	−	0.0433149i	0.177085	−	0.984196i	$-0.443333\pi$
$293$	−2.76706	−	0.741431i	−0.161653	−	0.0433149i	−0.338738	+	0.940881i	$0.610000\pi$
$294$	1.03628	−	3.80527i	0.0604369	−	0.221928i
$295$	−5.07090	+	8.78306i	−0.295239	+	0.511370i
$296$	−2.43366	+	4.88346i	−0.141453	+	0.283845i
$297$	−9.31280	−	10.7936i	−0.540383	−	0.626307i
$298$	−12.8917	−	10.3762i	−0.746794	−	0.601077i
$299$	5.61438	−	1.50437i	0.324688	−	0.0869998i
$300$	−5.77930	+	36.2291i	−0.333668	+	2.09169i
$301$	−13.9226	−	3.73054i	−0.802484	−	0.215025i
$302$	−9.68174	+	7.07825i	−0.557121	+	0.407307i
$303$	2.11190	−	18.8161i	0.121326	−	1.08096i
$304$	8.70304	−	7.22054i	0.499154	−	0.414127i
$305$		−	45.7152i		−	2.61764i
$306$	11.2875	−	4.87570i	0.645263	−	0.278725i
$307$	−7.67329	−	7.67329i	−0.437938	−	0.437938i	0.453380	−	0.891317i	$-0.350218\pi$
$307$	−7.67329	−	7.67329i	−0.437938	−	0.437938i	−0.891317	+	0.453380i	$0.850218\pi$
$308$	−14.3021	+	7.39470i	−0.814940	+	0.421352i
$309$	−0.166694	−	1.10274i	−0.00948289	−	0.0627325i
$310$	2.79755	+	0.434571i	0.158890	+	0.0246820i
$311$	15.0777	−	8.70513i	0.854980	−	0.493623i	−0.00734815	−	0.999973i	$-0.502339\pi$
$311$	15.0777	−	8.70513i	0.854980	−	0.493623i	0.862328	+	0.506350i	$0.169006\pi$
$312$	3.65774	−	11.3291i	0.207079	−	0.641387i
$313$	−21.3027	−	12.2991i	−1.20410	−	0.695189i	−0.242638	−	0.970117i	$-0.578013\pi$
$313$	−21.3027	−	12.2991i	−1.20410	−	0.695189i	−0.961465	+	0.274928i	$0.911346\pi$
$314$	4.03203	+	3.24529i	0.227541	+	0.183142i
$315$	−34.7328	+	1.32941i	−1.95697	+	0.0749039i
$316$	−1.78308	−	8.15024i	−0.100306	−	0.458487i
$317$	−7.99342	+	2.14183i	−0.448955	+	0.120297i	−0.476211	−	0.879331i	$-0.657990\pi$
$317$	−7.99342	+	2.14183i	−0.448955	+	0.120297i	0.0272552	+	0.999629i	$0.491323\pi$
$318$	−17.9432	−	0.0732070i	−1.00620	−	0.00410524i
$319$	−20.8152	+	12.0177i	−1.16543	+	0.672860i
$320$	29.2835	−	11.8441i	1.63699	−	0.662106i
$321$	3.66857	+	8.39862i	0.204759	+	0.468765i
$322$	−4.01011	+	9.07937i	−0.223475	+	0.505973i
$323$	−5.79343	+	5.79343i	−0.322355	+	0.322355i
$324$	−12.3391	+	13.1052i	−0.685508	+	0.728065i
$325$	−18.1983	−	18.1983i	−1.00946	−	1.00946i
$326$	−2.78844	−	7.20010i	−0.154437	−	0.398777i
$327$	13.4874	−	5.89138i	0.745856	−	0.325794i
$328$	−2.79469	+	3.16003i	−0.154311	+	0.174483i
$329$	9.55998	+	16.5584i	0.527059	+	0.912893i
$330$	18.6864	+	18.8395i	1.02865	+	1.03708i
$331$	6.84245	+	25.5364i	0.376095	+	1.40361i	0.851738	+	0.523968i	$0.175549\pi$
$331$	6.84245	+	25.5364i	0.376095	+	1.40361i	−0.475643	+	0.879639i	$0.657784\pi$
$332$	14.0702	−	21.9508i	0.772205	−	1.20471i
$333$	0.221347	+	5.78301i	0.0121298	+	0.316907i
$334$	−9.71236	+	1.05000i	−0.531437	+	0.0574535i
$335$	19.3372	−	33.4930i	1.05650	−	1.82992i
$336$	11.1545	+	16.9959i	0.608526	+	0.927203i
$337$	12.3368	+	21.3679i	0.672026	+	1.16398i	0.977329	+	0.211728i	$0.0679092\pi$
$337$	12.3368	+	21.3679i	0.672026	+	1.16398i	−0.305302	+	0.952256i	$0.598757\pi$
$338$	−5.92154	−	8.09958i	−0.322090	−	0.440559i
$339$	28.5531	−	4.31619i	1.55079	−	0.234423i
$340$	−20.3296	+	10.5111i	−1.10253	+	0.570046i
$341$	0.983569	−	0.983569i	0.0532632	−	0.0532632i
$342$	4.42276	−	11.1491i	0.239156	−	0.602876i
$343$	15.8156			0.853964
$344$	11.5843	−	7.67062i	0.624584	−	0.413572i
$345$	16.2558	+	1.82454i	0.875185	+	0.0982300i
$346$	5.59688	+	0.869418i	0.300890	+	0.0467402i
$347$	6.16895	−	23.0228i	0.331166	−	1.23593i	−0.576799	−	0.816886i	$-0.695699\pi$
$347$	6.16895	−	23.0228i	0.331166	−	1.23593i	0.907966	−	0.419044i	$-0.137635\pi$
$348$	17.8108	+	24.5718i	0.954762	+	1.31718i
$349$	6.94337	+	25.9130i	0.371670	+	1.38709i	0.858149	+	0.513400i	$0.171614\pi$
$349$	6.94337	+	25.9130i	0.371670	+	1.38709i	−0.486479	+	0.873692i	$0.661719\pi$
$350$	43.6937	−	4.72371i	2.33553	−	0.252493i
$351$	−2.36348	−	12.4040i	−0.126153	−	0.662075i
$352$	3.79365	−	15.0490i	0.202202	−	0.802115i
$353$	5.54075	+	3.19895i	0.294904	+	0.170263i	0.640151	−	0.768249i	$-0.278872\pi$
$353$	5.54075	+	3.19895i	0.294904	+	0.170263i	−0.345247	+	0.938512i	$0.612205\pi$
$354$	5.46144	−	3.12352i	0.290272	−	0.166013i
$355$	−4.75614	+	17.7502i	−0.252430	+	0.942080i
$356$	9.87843	+	10.8408i	0.523556	+	0.574563i
$357$	−9.18835	−	11.5117i	−0.486299	−	0.609264i
$358$	18.7668	−	7.26798i	0.991859	−	0.384125i
$359$			17.2363i			0.909697i	0.890569	+	0.454849i	$0.150307\pi$
$359$			17.2363i			0.909697i	−0.890569	+	0.454849i	$0.849693\pi$
$360$	21.2197	−	25.9279i	1.11837	−	1.36652i
$361$		−	11.0076i		−	0.579345i
$362$	10.8592	+	28.0398i	0.570746	+	1.47374i
$363$	−5.94781	+	0.899094i	−0.312179	+	0.0471902i
$364$	−14.2459	−	0.661719i	−0.746686	−	0.0346835i
$365$	−5.02693	+	18.7608i	−0.263121	+	0.981983i
$366$	−14.2800	+	24.5023i	−0.746427	+	1.28075i
$367$	−1.26366	−	0.729575i	−0.0659625	−	0.0380835i	0.466656	−	0.884439i	$-0.345459\pi$
$367$	−1.26366	−	0.729575i	−0.0659625	−	0.0380835i	−0.532619	+	0.846355i	$0.678792\pi$
$368$	−3.99503	−	8.69340i	−0.208255	−	0.453175i
$369$	−0.991918	+	4.36310i	−0.0516372	+	0.227134i
$370$	−1.15782	−	10.7096i	−0.0601920	−	0.556768i
$371$	5.56323	+	20.7623i	0.288829	+	1.07792i
$372$	−1.36368	−	1.10679i	−0.0707033	−	0.0573843i
$373$	−2.08247	+	7.77189i	−0.107826	+	0.402413i	−0.998650	−	0.0519349i	$-0.983461\pi$
$373$	−2.08247	+	7.77189i	−0.107826	+	0.402413i	0.890824	+	0.454348i	$0.150128\pi$
$374$	−1.72601	+	11.1112i	−0.0892497	+	0.574545i
$375$	−15.3048	−	35.0379i	−0.790335	−	1.80935i
$376$	−18.0608	−	3.67098i	−0.931417	−	0.189316i
$377$	−21.2893			−1.09646
$378$	19.0312	+	10.1369i	0.978860	+	0.521386i
$379$	−16.4748	+	16.4748i	−0.846255	+	0.846255i	−0.989664	−	0.143409i	$-0.954194\pi$
$379$	−16.4748	+	16.4748i	−0.846255	+	0.846255i	0.143409	+	0.989664i	$0.454194\pi$
$380$	−6.77266	+	21.2735i	−0.347430	+	1.09131i
$381$	11.3762	−	29.0226i	0.582819	−	1.48687i
$382$	−24.8896	+	18.1966i	−1.27346	+	0.931019i
$383$	−5.19654	−	9.00067i	−0.265531	−	0.459913i	0.702172	−	0.712008i	$-0.252214\pi$
$383$	−5.19654	−	9.00067i	−0.265531	−	0.459913i	−0.967703	+	0.252095i	$0.918881\pi$
$384$	−19.3950	−	2.79907i	−0.989746	−	0.142839i
$385$	15.8934	−	27.5282i	0.810004	−	1.40297i
$386$	−0.713580	−	6.60052i	−0.0363203	−	0.335958i
$387$	6.87473	−	13.0346i	0.349462	−	0.662588i
$388$	9.77418	−	2.13836i	0.496209	−	0.108559i
$389$	6.24292	+	23.2989i	0.316529	+	1.18130i	0.922558	+	0.385859i	$0.126095\pi$
$389$	6.24292	+	23.2989i	0.316529	+	1.18130i	−0.606029	+	0.795442i	$0.707239\pi$
$390$	5.99046	+	22.7272i	0.303339	+	1.15084i
$391$	3.46590	+	6.00311i	0.175278	+	0.303590i
$392$	3.01691	−	3.41129i	0.152377	−	0.172296i
$393$	25.1295	+	18.5298i	1.26761	+	0.934704i
$394$	26.7120	−	10.3449i	1.34573	−	0.521171i
$395$	11.6469	+	11.6469i	0.586019	+	0.586019i
$396$	−4.13060	−	15.9346i	−0.207570	−	0.800743i
$397$	8.37131	−	8.37131i	0.420144	−	0.420144i	−0.465109	−	0.885253i	$-0.653985\pi$
$397$	8.37131	−	8.37131i	0.420144	−	0.420144i	0.885253	+	0.465109i	$0.153985\pi$
$398$	−18.7535	−	8.28289i	−0.940026	−	0.415184i
$399$	−14.2786	−	1.60262i	−0.714824	−	0.0802312i
$400$	−24.4911	+	34.5657i	−1.22455	+	1.72829i
$401$	−3.16266	+	1.82596i	−0.157936	+	0.0911842i	−0.576885	−	0.816825i	$-0.695732\pi$
$401$	−3.16266	+	1.82596i	−0.157936	+	0.0911842i	0.418949	+	0.908010i	$0.362399\pi$
$402$	−20.8265	+	11.9111i	−1.03873	+	0.594073i
$403$	1.19008	−	0.318880i	0.0592820	−	0.0158846i
$404$	11.7985	−	18.4066i	0.586996	−	0.915764i
$405$	6.54681	−	34.9283i	0.325313	−	1.73560i
$406$	22.7945	−	28.3205i	1.13127	−	1.40552i
$407$	−4.58345	−	2.64626i	−0.227193	−	0.131170i
$408$	14.1796	+	0.716628i	0.701993	+	0.0354784i
$409$	−12.1263	+	7.00113i	−0.599607	+	0.346184i	−0.768887	−	0.639385i	$-0.779189\pi$
$409$	−12.1263	+	7.00113i	−0.599607	+	0.346184i	0.169280	+	0.985568i	$0.445856\pi$
$410$	1.27841	−	8.22976i	0.0631361	−	0.406439i
$411$	−1.07256	+	0.856089i	−0.0529054	+	0.0422277i
$412$	0.390665	−	1.22711i	0.0192467	−	0.0604554i
$413$	−5.32931	−	5.32931i	−0.262238	−	0.262238i
$414$	−8.14282	−	6.05573i	−0.400198	−	0.297623i
$415$			51.4750i			2.52681i
$416$	9.57488	−	9.86373i	0.469447	−	0.483609i
$417$	−29.6053	−	21.8302i	−1.44978	−	1.06903i
$418$	6.47375	+	8.85490i	0.316641	+	0.433107i
$419$	0.601258	+	0.161107i	0.0293734	+	0.00787057i	0.273476	−	0.961879i	$-0.411827\pi$
$419$	0.601258	+	0.161107i	0.0293734	+	0.00787057i	−0.244102	+	0.969749i	$0.578493\pi$
$420$	−36.6473	−	16.3651i	−1.78821	−	0.798536i
$421$	17.3705	−	4.65440i	0.846585	−	0.226842i	0.190649	−	0.981658i	$-0.438941\pi$
$421$	17.3705	−	4.65440i	0.846585	−	0.226842i	0.655936	+	0.754816i	$0.272274\pi$
$422$	−5.86769	+	7.29018i	−0.285635	+	0.354881i
$423$	−18.6747	+	5.77791i	−0.907995	+	0.280932i
$424$	−18.5440	−	9.24136i	−0.900578	−	0.448800i
$425$	15.3463	−	26.5806i	0.744407	−	1.28935i
$426$	8.09377	−	8.02800i	0.392145	−	0.388958i
$427$	32.8152	+	8.79280i	1.58804	+	0.425514i
$428$	−0.491037	+	10.5713i	−0.0237352	+	0.510983i
$429$	10.7513	+	4.21424i	0.519075	+	0.203465i
$430$	−11.0821	+	25.0913i	−0.534427	+	1.21001i
$431$	6.34380			0.305570			0.152785	−	0.988259i	$-0.451176\pi$
$431$	6.34380			0.305570			0.152785	+	0.988259i	$0.451176\pi$
$432$	−19.4723	+	7.26838i	−0.936862	+	0.349700i
$433$	26.7319			1.28465			0.642327	−	0.766430i	$-0.277969\pi$
$433$	26.7319			1.28465			0.642327	+	0.766430i	$0.277969\pi$
$434$	−0.850021	+	1.92455i	−0.0408023	+	0.0923813i
$435$	−55.7822	−	21.8653i	−2.67455	−	1.04836i
$436$	16.9765	+	0.788560i	0.813029	+	0.0377652i
$437$	6.53158	+	1.75013i	0.312448	+	0.0837202i
$438$	8.55459	−	8.48507i	0.408754	−	0.405432i
$439$	0.347800	−	0.602407i	0.0165996	−	0.0287513i	−0.857606	−	0.514307i	$-0.828049\pi$
$439$	0.347800	−	0.602407i	0.0165996	−	0.0287513i	0.874206	+	0.485555i	$0.161383\pi$
$440$	9.72769	+	29.0548i	0.463750	+	1.38513i
$441$	1.07079	−	4.71003i	0.0509899	−	0.224287i
$442$	−6.24486	+	7.75878i	−0.297037	+	0.369048i
$443$	−15.8656	+	4.25119i	−0.753800	+	0.201980i	−0.615203	−	0.788369i	$-0.710926\pi$
$443$	−15.8656	+	4.25119i	−0.753800	+	0.201980i	−0.138597	+	0.990349i	$0.544259\pi$
$444$	−2.72480	+	6.10179i	−0.129313	+	0.289578i
$445$	−27.9688	−	7.49422i	−1.32585	−	0.355260i
$446$	1.53816	+	2.10393i	0.0728342	+	0.0996238i
$447$	−16.3127	−	12.0285i	−0.771565	−	0.568931i
$448$	2.86957	+	23.2983i	0.135575	+	1.10074i
$449$			12.0759i			0.569896i	0.958543	+	0.284948i	$0.0919763\pi$
$449$			12.0759i			0.569896i	−0.958543	+	0.284948i	$0.908024\pi$
$450$	−5.19384	+	44.6313i	−0.244840	+	2.10394i
$451$	−2.89343	−	2.89343i	−0.136247	−	0.136247i
$452$	31.7735	+	10.1155i	1.49450	+	0.475791i
$453$	−11.4801	+	9.16314i	−0.539383	+	0.430522i
$454$	0.154398	−	0.993935i	0.00724624	−	0.0466477i
$455$	24.3831	−	14.0776i	1.14310	−	0.659969i
$456$	10.2752	−	9.28653i	0.481179	−	0.434882i
$457$	−10.6069	−	6.12391i	−0.496171	−	0.286464i	0.230960	−	0.972963i	$-0.425813\pi$
$457$	−10.6069	−	6.12391i	−0.496171	−	0.286464i	−0.727131	+	0.686499i	$0.759147\pi$
$458$	6.79839	−	8.44651i	0.317668	−	0.394679i
$459$	13.5592	−	6.55124i	0.632888	−	0.305786i
$460$	15.9021	+	10.1931i	0.741438	+	0.475255i
$461$	−30.3154	+	8.12298i	−1.41193	+	0.378325i	−0.882613	−	0.470101i	$-0.844217\pi$
$461$	−30.3154	+	8.12298i	−1.41193	+	0.378325i	−0.529314	+	0.848426i	$0.677551\pi$
$462$	−17.1175	+	9.78987i	−0.796376	+	0.455466i
$463$	30.9163	−	17.8495i	1.43680	−	0.829538i	0.439176	−	0.898401i	$-0.355271\pi$
$463$	30.9163	−	17.8495i	1.43680	−	0.829538i	0.997626	+	0.0688633i	$0.0219372\pi$
$464$	5.89291	+	34.5437i	0.273572	+	1.60365i
$465$	3.44574	+	0.386747i	0.159793	+	0.0179350i
$466$	1.77133	+	0.782348i	0.0820553	+	0.0362416i
$467$	−7.64586	+	7.64586i	−0.353808	+	0.353808i	−0.861524	−	0.507716i	$-0.830490\pi$
$467$	−7.64586	+	7.64586i	−0.353808	+	0.353808i	0.507716	+	0.861524i	$0.330490\pi$
$468$	3.88852	−	14.0525i	0.179747	−	0.649576i
$469$	20.3226	+	20.3226i	0.938411	+	0.938411i
$470$	33.9301	−	13.1404i	1.56508	−	0.606120i
$471$	5.10201	+	3.76208i	0.235088	+	0.173348i
$472$	7.25123	−	0.444875i	0.333765	−	0.0204770i
$473$	6.73836	+	11.6712i	0.309830	+	0.536641i
$474$	−2.60434	−	9.88060i	−0.119621	−	0.453831i
$475$	−7.74926	−	28.9206i	−0.355560	−	1.32697i
$476$	−3.63490	−	16.6147i	−0.166605	−	0.761533i
$477$	−21.9599	+	0.840526i	−1.00548	+	0.0384851i
$478$	−0.235189	−	2.17547i	−0.0107573	−	0.0995038i
$479$	−3.03628	+	5.25898i	−0.138731	+	0.240289i	−0.927017	−	0.375020i	$-0.877636\pi$
$479$	−3.03628	+	5.25898i	−0.138731	+	0.240289i	0.788286	+	0.615310i	$0.210969\pi$
$480$	35.2187	−	16.0110i	1.60750	−	0.730797i
$481$	−2.34393	−	4.05980i	−0.106874	−	0.185111i
$482$	8.76009	−	6.40444i	0.399011	−	0.291714i
$483$	−4.43632	+	11.3178i	−0.201859	+	0.514978i
$484$	−6.61864	−	2.10712i	−0.300847	−	0.0957782i
$485$	−13.9675	+	13.9675i	−0.634234	+	0.634234i
$486$	−14.4194	+	16.6757i	−0.654079	+	0.756426i
$487$	−7.15811			−0.324365			−0.162183	−	0.986761i	$-0.551853\pi$
$487$	−7.15811			−0.324365			−0.162183	+	0.986761i	$0.551853\pi$
$488$	−27.3039	+	18.0795i	−1.23599	+	0.818419i
$489$	−3.78529	−	8.66584i	−0.171177	−	0.391883i
$490$	−1.38006	+	8.88413i	−0.0623446	+	0.401344i
$491$	−7.24226	+	27.0285i	−0.326838	+	1.21978i	0.585612	+	0.810591i	$0.300854\pi$
$491$	−7.24226	+	27.0285i	−0.326838	+	1.21978i	−0.912451	+	0.409187i	$0.865813\pi$
$492$	−3.25592	+	4.01162i	−0.146788	+	0.180858i
$493$	−6.57122	−	24.5241i	−0.295953	−	1.10451i
$494$	1.04429	+	9.65950i	0.0469846	+	0.434602i
$495$	23.8421	+	22.0843i	1.07162	+	0.992614i
$496$	−0.846826	−	1.84274i	−0.0380236	−	0.0827413i
$497$	−11.8266	−	6.82809i	−0.530495	−	0.306282i
$498$	16.0792	−	27.5894i	0.720525	−	1.23631i
$499$	11.4708	−	42.8097i	0.513505	−	1.91643i	0.134937	−	0.990854i	$-0.456917\pi$
$499$	11.4708	−	42.8097i	0.513505	−	1.91643i	0.378568	−	0.925573i	$-0.376416\pi$
$500$	2.04854	−	44.1021i	0.0916135	−	1.97231i
$501$	−11.8301	+	1.78828i	−0.528529	+	0.0798945i
$502$	−3.94822	−	10.1948i	−0.176218	−	0.455017i
$503$		−	3.93000i		−	0.175230i	−0.996154	−	0.0876151i	$-0.972075\pi$
$503$		−	3.93000i		−	0.175230i	0.996154	−	0.0876151i	$-0.0279245\pi$
$504$	14.5301	+	20.2188i	0.647224	+	0.900617i
$505$			43.1638i			1.92077i
$506$	8.65397	−	3.35149i	0.384716	−	0.148992i
$507$	−7.66573	−	9.60408i	−0.340447	−	0.426532i
$508$	26.6058	−	24.2439i	1.18044	−	1.07565i
$509$	10.8415	−	40.4609i	0.480539	−	1.79340i	−0.118819	−	0.992916i	$-0.537911\pi$
$509$	10.8415	−	40.4609i	0.480539	−	1.79340i	0.599358	−	0.800481i	$-0.295423\pi$
$510$	−24.3315	+	13.9157i	−1.07741	+	0.616199i
$511$	−12.4999	−	7.21684i	−0.552965	−	0.319254i
$512$	−18.6551	−	12.8058i	−0.824446	−	0.565941i
$513$	4.83397	−	13.8719i	0.213425	−	0.612458i
$514$	−33.4315	+	3.61427i	−1.47460	+	0.159418i
$515$	0.658030	+	2.45580i	0.0289963	+	0.108216i
$516$	13.7775	−	9.98662i	0.606520	−	0.439636i
$517$	4.62691	−	17.2679i	0.203491	−	0.759441i
$518$	7.91027	+	1.22878i	0.347557	+	0.0539895i
$519$	6.89368	+	0.773740i	0.302599	+	0.0339634i
$520$	−5.40572	+	26.5956i	−0.237057	+	1.16629i
$521$	−26.1826			−1.14708			−0.573540	−	0.819178i	$-0.694430\pi$
$521$	−26.1826			−1.14708			−0.573540	+	0.819178i	$0.694430\pi$
$522$	23.0679	+	29.1439i	1.00965	+	1.27559i
$523$	7.29036	−	7.29036i	0.318785	−	0.318785i	−0.529515	−	0.848300i	$-0.677626\pi$
$523$	7.29036	−	7.29036i	0.318785	−	0.318785i	0.848300	+	0.529515i	$0.177626\pi$
$524$	16.5582	+	32.0253i	0.723347	+	1.39903i
$525$	53.2208	−	8.04507i	2.32275	−	0.351116i
$526$	−5.91470	−	8.09022i	−0.257893	−	0.352750i
$527$	0.734665	+	1.27248i	0.0320025	+	0.0554300i
$528$	3.86201	−	18.6113i	0.168072	−	0.809955i
$529$	−8.63952	+	14.9641i	−0.375631	+	0.650612i
$530$	40.6679	−	4.39659i	1.76650	−	0.190976i
$531$	6.52096	−	4.10519i	0.282986	−	0.178150i
$532$	−13.9679	−	8.95326i	−0.605584	−	0.388173i
$533$	−0.938073	−	3.50093i	−0.0406324	−	0.151642i
$534$	12.6497	+	12.7533i	0.547404	+	0.551889i
$535$	−10.4465	−	18.0938i	−0.451640	−	0.782263i
$536$	−27.6516	+	1.69647i	−1.19437	+	0.0732763i
$537$	22.5873	−	9.86624i	0.974712	−	0.425760i
$538$	14.9235	+	38.5344i	0.643397	+	1.66133i
$539$	3.12350	+	3.12350i	0.134539	+	0.134539i
$540$	24.6214	−	32.8265i	1.05954	−	1.41263i
$541$	13.6906	−	13.6906i	0.588607	−	0.588607i	−0.348647	−	0.937254i	$-0.613359\pi$
$541$	13.6906	−	13.6906i	0.588607	−	0.588607i	0.937254	+	0.348647i	$0.113359\pi$
$542$	−9.53625	+	21.5912i	−0.409617	+	0.927422i
$543$	14.7413	+	33.7479i	0.632609	+	1.44826i
$544$	14.3179	+	7.98517i	0.613874	+	0.342361i
$545$	−29.0570	+	16.7761i	−1.24466	+	0.718607i
$546$	−17.4662	−	0.0712609i	−0.747484	−	0.00304969i
$547$	29.0133	−	7.77408i	1.24052	−	0.332396i	0.421851	−	0.906665i	$-0.361380\pi$
$547$	29.0133	−	7.77408i	1.24052	−	0.332396i	0.818666	+	0.574269i	$0.194714\pi$
$548$	−1.54801	+	0.338667i	−0.0661276	+	0.0144672i
$549$	−16.2036	+	30.7224i	−0.691552	+	1.31120i
$550$	−32.0107	−	25.7646i	−1.36494	−	1.09861i
$551$	−21.4491	−	12.3836i	−0.913762	−	0.527561i
$552$	−5.33914	−	10.4306i	−0.227249	−	0.443954i
$553$	−10.6005	+	6.12021i	−0.450780	+	0.260258i
$554$	6.49904	+	1.00956i	0.276118	+	0.0428921i
$555$	−1.97191	−	13.0448i	−0.0837027	−	0.553721i
$556$	−19.5074	−	37.7294i	−0.827297	−	1.60008i
$557$	−1.85284	−	1.85284i	−0.0785074	−	0.0785074i	0.666763	−	0.745270i	$-0.267679\pi$
$557$	−1.85284	−	1.85284i	−0.0785074	−	0.0785074i	−0.745270	+	0.666763i	$0.767679\pi$
$558$	−1.72603	−	1.28363i	−0.0730687	−	0.0543404i
$559$			11.9370i			0.504882i
$560$	−29.5914	−	35.6670i	−1.25047	−	1.50721i
$561$	−1.53606	+	13.6856i	−0.0648526	+	0.577808i
$562$	−26.0645	+	19.0556i	−1.09946	+	0.803810i
$563$	26.1400	+	7.00420i	1.10167	+	0.295192i	0.763445	−	0.645873i	$-0.223506\pi$
$563$	26.1400	+	7.00420i	1.10167	+	0.295192i	0.338226	+	0.941065i	$0.390173\pi$
$564$	−22.2904	−	3.55578i	−0.938595	−	0.149725i
$565$	−63.5879	+	17.0383i	−2.67516	+	0.716808i
$566$	−28.4498	−	22.8985i	−1.19583	−	0.962496i
$567$	23.8130	+	11.4175i	1.00005	+	0.479489i
$568$	12.4825	−	4.17918i	0.523752	−	0.175355i
$569$	5.84691	−	10.1271i	0.245115	−	0.424552i	−0.717049	−	0.697023i	$-0.754508\pi$
$569$	5.84691	−	10.1271i	0.245115	−	0.424552i	0.962164	+	0.272471i	$0.0878409\pi$
$570$	−7.18462	+	26.3823i	−0.300930	+	1.10503i
$571$	44.1127	+	11.8200i	1.84606	+	0.494650i	0.999303	−	0.0373319i	$-0.0118859\pi$
$571$	44.1127	+	11.8200i	1.84606	+	0.494650i	0.846756	+	0.531982i	$0.178553\pi$
$572$	8.98101	+	9.85599i	0.375515	+	0.412100i
$573$	−29.5128	+	23.5564i	−1.23292	+	0.984082i
$574$	5.66158	+	2.50057i	0.236310	+	0.104372i
$575$	−25.3314			−1.05639
$576$	−23.8777	−	2.41971i	−0.994905	−	0.100821i
$577$	−32.6884			−1.36083			−0.680417	−	0.732825i	$-0.738202\pi$
$577$	−32.6884			−1.36083			−0.680417	+	0.732825i	$0.738202\pi$
$578$	11.1268	+	4.91442i	0.462815	+	0.204413i
$579$	−1.21532	−	8.03972i	−0.0505068	−	0.334119i
$580$	−46.5974	−	51.1372i	−1.93485	−	2.12335i
$581$	−36.9497	−	9.90064i	−1.53293	−	0.410748i
$582$	11.8493	−	3.12325i	0.491170	−	0.129463i
$583$	10.0487	−	17.4048i	0.416174	−	0.720834i
$584$	13.1931	−	4.41713i	0.545936	−	0.182782i
$585$	8.50830	+	27.4996i	0.351775	+	1.13697i
$586$	−3.15598	−	2.54017i	−0.130372	−	0.104933i
$587$	28.3101	−	7.58567i	1.16848	−	0.313094i	0.378134	−	0.925751i	$-0.376566\pi$
$587$	28.3101	−	7.58567i	1.16848	−	0.313094i	0.790349	+	0.612657i	$0.209899\pi$
$588$	3.51480	−	4.33060i	0.144948	−	0.178591i
$589$	1.38450	+	0.370975i	0.0570472	+	0.0152858i
$590$	−11.5784	+	8.46486i	−0.476674	+	0.348493i
$591$	32.1498	−	14.0432i	1.32247	−	0.577661i
$592$	−5.93857	+	4.92698i	−0.244074	+	0.202498i
$593$			43.9681i			1.80555i	0.430111	+	0.902776i	$0.358474\pi$
$593$			43.9681i			1.80555i	−0.430111	+	0.902776i	$0.641526\pi$
$594$	−5.88039	−	19.2842i	−0.241275	−	0.791240i
$595$	23.7428	+	23.7428i	0.973360	+	0.973360i
$596$	−10.7487	−	20.7891i	−0.440283	−	0.851555i
$597$	−23.3770	−	9.16323i	−0.956756	−	0.375026i
$598$	8.12260	+	1.26176i	0.332158	+	0.0515973i
$599$	2.81411	−	1.62473i	0.114982	−	0.0663846i	−0.441406	−	0.897307i	$-0.645520\pi$
$599$	2.81411	−	1.62473i	0.114982	−	0.0663846i	0.556388	+	0.830923i	$0.312187\pi$
$600$	−28.1767	+	43.5658i	−1.15031	+	1.77856i
$601$	12.6206	+	7.28651i	0.514806	+	0.297223i	0.734807	−	0.678276i	$-0.237273\pi$
$601$	12.6206	+	7.28651i	0.514806	+	0.297223i	−0.220001	+	0.975500i	$0.570606\pi$
$602$	−15.8794	−	12.7810i	−0.647198	−	0.520914i
$603$	−24.8668	+	15.6546i	−1.01266	+	0.637504i
$604$	−16.5691	+	3.62493i	−0.674187	+	0.147496i
$605$	13.2458	−	3.54920i	0.538519	−	0.144296i
$606$	13.4830	−	23.1348i	0.547711	−	0.939787i
$607$	32.0317	−	18.4935i	1.30013	−	0.750629i	0.319702	−	0.947518i	$-0.396417\pi$
$607$	32.0317	−	18.4935i	1.30013	−	0.750629i	0.980426	+	0.196889i	$0.0630838\pi$
$608$	15.3843	−	4.36821i	0.623916	−	0.177154i
$609$	26.4244	−	35.8359i	1.07077	−	1.45214i
$610$	26.1203	−	59.1395i	1.05758	−	2.39449i
$611$	11.1967	−	11.1967i	0.452972	−	0.452972i
$612$	17.3879	+	0.141886i	0.702865	+	0.00573538i
$613$	3.34985	+	3.34985i	0.135299	+	0.135299i	0.771513	−	0.636214i	$-0.219500\pi$
$613$	3.34985	+	3.34985i	0.135299	+	0.135299i	−0.636214	+	0.771513i	$0.719500\pi$
$614$	−5.54227	−	14.3109i	−0.223668	−	0.577539i
$615$	1.13772	−	10.1366i	0.0458774	−	0.408747i
$616$	−22.7271	+	1.39434i	−0.915701	+	0.0561797i
$617$	−4.04358	−	7.00369i	−0.162789	−	0.281958i	0.773079	−	0.634309i	$-0.218715\pi$
$617$	−4.04358	−	7.00369i	−0.162789	−	0.281958i	−0.935868	+	0.352352i	$0.885382\pi$
$618$	0.414427	−	1.52180i	0.0166707	−	0.0612158i
$619$	11.6692	+	43.5499i	0.469023	+	1.75042i	0.643194	+	0.765703i	$0.277609\pi$
$619$	11.6692	+	43.5499i	0.469023	+	1.75042i	−0.174171	+	0.984715i	$0.555725\pi$
$620$	3.37076	+	2.16062i	0.135373	+	0.0867727i
$621$	−10.2778	−	6.98798i	−0.412436	−	0.280418i
$622$	24.4792	−	2.64644i	0.981526	−	0.106112i
$623$	10.7590	−	18.6351i	0.431049	−	0.746599i
$624$	11.2050	−	12.5660i	0.448558	−	0.503044i
$625$	17.1046	+	29.6260i	0.684182	+	1.18504i
$626$	−20.5310	−	28.0826i	−0.820583	−	1.12241i
$627$	8.38059	+	10.4997i	0.334689	+	0.419318i
$628$	3.36179	+	6.50206i	0.134150	+	0.259460i
$629$	3.95318	−	3.95318i	0.157624	−	0.157624i
$630$	−45.6917	−	18.1255i	−1.82040	−	0.722137i
$631$	−3.49919			−0.139300			−0.0696502	−	0.997571i	$-0.522188\pi$
$631$	−3.49919			−0.139300			−0.0696502	+	0.997571i	$0.522188\pi$
$632$	2.35013	−	11.5624i	0.0934830	−	0.459927i
$633$	−6.80209	+	9.22477i	−0.270359	+	0.366652i
$634$	−11.5645	−	1.79642i	−0.459284	−	0.0713451i
$635$	−18.3925	+	68.6417i	−0.729883	+	2.72396i
$636$	−23.1704	−	10.3469i	−0.918766	−	0.410282i
$637$	1.01266	+	3.77930i	0.0401231	+	0.149741i
$638$	−33.7942	+	3.65348i	−1.33792	+	0.144643i
$639$	9.48779	−	10.2430i	0.375331	−	0.405206i
$640$	44.6500	+	1.40955i	1.76495	+	0.0557174i
$641$	4.01739	+	2.31944i	0.158677	+	0.0916125i	0.577236	−	0.816577i	$-0.304131\pi$
$641$	4.01739	+	2.31944i	0.158677	+	0.0916125i	−0.418559	+	0.908190i	$0.637465\pi$
$642$	−0.0528800	+	12.9610i	−0.00208701	+	0.511530i
$643$	−10.6535	+	39.7595i	−0.420134	+	1.56796i	0.354190	+	0.935173i	$0.384757\pi$
$643$	−10.6535	+	39.7595i	−0.420134	+	1.56796i	−0.774324	+	0.632789i	$0.781910\pi$
$644$	−10.3754	+	9.45428i	−0.408847	+	0.372551i
$645$	−12.2600	+	31.2773i	−0.482736	+	1.23154i
$646$	−10.8049	+	4.18449i	−0.425112	+	0.164636i
$647$		−	2.08960i		−	0.0821505i	−0.999156	−	0.0410752i	$-0.986922\pi$
$647$		−	2.08960i		−	0.0821505i	0.999156	−	0.0410752i	$-0.0130783\pi$
$648$	−23.4505	+	9.90331i	−0.921221	+	0.389039i
$649$			7.04684i			0.276613i
$650$	−13.1443	−	33.9403i	−0.515563	−	1.33125i
$651$	−0.940365	+	2.39903i	−0.0368558	+	0.0940255i
$652$	0.506660	−	10.9077i	0.0198423	−	0.427177i
$653$	4.75454	−	17.7442i	0.186059	−	0.694383i	−0.808342	−	0.588713i	$-0.799635\pi$
$653$	4.75454	−	17.7442i	0.186059	−	0.694383i	0.994401	−	0.105670i	$-0.0336987\pi$
$654$	20.8142	+	0.0849205i	0.813899	+	0.00332065i
$655$	−61.6410	−	35.5885i	−2.40851	−	1.39056i
$656$	−5.42091	+	2.49117i	−0.211651	+	0.0972637i
$657$	10.0280	−	10.8262i	0.391228	−	0.422369i
$658$	2.90632	+	26.8831i	0.113300	+	1.04801i
$659$	−7.84088	−	29.2626i	−0.305437	−	1.13991i	−0.932568	−	0.360994i	$-0.882438\pi$
$659$	−7.84088	−	29.2626i	−0.305437	−	1.13991i	0.627131	−	0.778914i	$-0.284229\pi$
$660$	13.4094	+	35.0486i	0.521958	+	1.36427i
$661$	12.5011	−	46.6546i	0.486235	−	1.81465i	−0.0881985	−	0.996103i	$-0.528111\pi$
$661$	12.5011	−	46.6546i	0.486235	−	1.81465i	0.574434	−	0.818551i	$-0.305222\pi$
$662$	−5.73899	+	36.9448i	−0.223052	+	1.43590i
$663$	−7.23932	+	9.81773i	−0.281152	+	0.381289i
$664$	30.7440	−	20.3574i	1.19310	−	0.790019i
$665$	32.7549			1.27018
$666$	−3.01790	+	7.60768i	−0.116941	+	0.294791i
$667$	−14.8169	+	14.8169i	−0.573714	+	0.573714i
$668$	−13.1644	−	4.19103i	−0.509344	−	0.162156i
$669$	1.99123	+	2.49473i	0.0769854	+	0.0964519i
$670$	44.1525	−	32.2796i	1.70576	−	1.24707i
$671$	−15.8822	−	27.5087i	−0.613124	−	1.06196i
$672$	4.71904	+	28.3601i	0.182041	+	1.09402i
$673$	8.92590	−	15.4601i	0.344068	−	0.595944i	−0.641116	−	0.767444i	$-0.721528\pi$
$673$	8.92590	−	15.4601i	0.344068	−	0.595944i	0.985184	+	0.171500i	$0.0548615\pi$
$674$	3.75049	+	34.6915i	0.144463	+	1.33627i
$675$	−4.04192	+	54.8822i	−0.155574	+	2.11241i
$676$	−3.03255	−	13.8614i	−0.116637	−	0.533132i
$677$	0.575049	+	2.14611i	0.0221009	+	0.0824818i	0.976095	−	0.217342i	$-0.0697387\pi$
$677$	0.575049	+	2.14611i	0.0221009	+	0.0824818i	−0.953995	+	0.299824i	$0.903072\pi$
$678$	39.4039	+	10.7307i	1.51330	+	0.412111i
$679$	−7.33966	−	12.7127i	−0.281670	−	0.487867i
$680$	−32.3052	+	1.98198i	−1.23885	+	0.0760053i
$681$	0.137406	−	1.22423i	0.00526543	−	0.0469126i
$682$	1.83438	−	0.710413i	0.0702420	−	0.0272031i
$683$	0.857818	+	0.857818i	0.0328235	+	0.0328235i	0.723328	−	0.690505i	$-0.242611\pi$
$683$	0.857818	+	0.857818i	0.0328235	+	0.0328235i	−0.690505	+	0.723328i	$0.742611\pi$
$684$	12.0918	−	11.8961i	0.462342	−	0.454857i
$685$	2.21214	−	2.21214i	0.0845216	−	0.0845216i
$686$	20.4599	+	9.03659i	0.781163	+	0.345019i
$687$	7.88099	−	10.6879i	0.300679	−	0.407771i
$688$	19.3688	−	3.30418i	0.738429	−	0.125971i
$689$	15.4163	−	8.90063i	0.587316	−	0.339087i
$690$	19.9869	+	11.6484i	0.760889	+	0.443448i
$691$	−37.8791	+	10.1497i	−1.44099	+	0.386112i	−0.892880	−	0.450295i	$-0.851319\pi$
$691$	−37.8791	+	10.1497i	−1.44099	+	0.386112i	−0.548109	+	0.836407i	$0.684652\pi$
$692$	6.74366	+	4.32262i	0.256355	+	0.164321i
$693$	−20.4383	+	12.8667i	−0.776386	+	0.488764i
$694$	21.1350	−	26.2588i	0.802275	−	0.996769i
$695$	72.6201	+	41.9272i	2.75464	+	1.59039i
$696$	9.00146	+	41.9639i	0.341199	+	1.59064i
$697$	3.74334	−	2.16122i	0.141789	−	0.0818619i
$698$	−5.82363	+	37.4897i	−0.220428	+	1.41900i
$699$	2.20804	+	0.865499i	0.0835156	+	0.0327362i
$700$	59.2235	+	18.8545i	2.23844	+	0.712632i
$701$	−14.3403	−	14.3403i	−0.541627	−	0.541627i	0.382379	−	0.924006i	$-0.375105\pi$
$701$	−14.3403	−	14.3403i	−0.541627	−	0.541627i	−0.924006	+	0.382379i	$0.875105\pi$
$702$	4.02975	−	17.3969i	0.152093	−	0.656602i
$703$		−	5.45369i		−	0.205690i
$704$	13.5062	−	17.3006i	0.509035	−	0.652041i
$705$	40.8374	−	17.8380i	1.53802	−	0.671817i
$706$	5.34001	+	7.30415i	0.200974	+	0.274895i
$707$	−30.9838	−	8.30208i	−1.16527	−	0.312232i
$708$	8.84989	−	0.920246i	0.332599	−	0.0345850i
$709$	−4.26177	+	1.14194i	−0.160054	+	0.0428864i	−0.337956	−	0.941162i	$-0.609736\pi$
$709$	−4.26177	+	1.14194i	−0.160054	+	0.0428864i	0.177902	+	0.984048i	$0.443069\pi$
$710$	−16.2947	+	20.2450i	−0.611529	+	0.759781i
$711$	−3.69896	−	11.9554i	−0.138722	−	0.448361i
$712$	6.58511	+	19.6685i	0.246787	+	0.737109i
$713$	0.606335	−	1.05020i	0.0227074	−	0.0393304i
$714$	−5.30908	−	20.1421i	−0.198687	−	0.753799i
$715$	−25.4279	−	6.81339i	−0.950951	−	0.254806i
$716$	28.4305	+	1.32059i	1.06250	+	0.0493530i
$717$	−0.400557	−	2.64982i	−0.0149591	−	0.0989593i
$718$	−9.84832	+	22.2978i	−0.367536	+	0.832146i
$719$	−49.2509			−1.83675			−0.918374	−	0.395714i	$-0.870497\pi$
$719$	−49.2509			−1.83675			−0.918374	+	0.395714i	$0.870497\pi$
$720$	42.2653	−	21.4174i	1.57513	−	0.798178i
$721$	−1.88938			−0.0703644
$722$	6.28939	−	14.2399i	0.234067	−	0.529956i
$723$	10.3873	−	8.29086i	0.386307	−	0.308340i
$724$	−1.97312	+	42.4784i	−0.0733304	+	1.57870i
$725$	89.6203	+	24.0137i	3.32841	+	0.891846i
$726$	−8.20811	−	2.23529i	−0.304631	−	0.0829593i
$727$	−2.18154	+	3.77855i	−0.0809090	+	0.140139i	−0.903641	−	0.428291i	$-0.859116\pi$
$727$	−2.18154	+	3.77855i	−0.0809090	+	0.140139i	0.822732	+	0.568430i	$0.192449\pi$
$728$	−18.0511	−	8.99570i	−0.669018	−	0.333403i
$729$	−16.7799	+	21.1527i	−0.621478	+	0.783432i
$730$	−17.2224	+	21.3976i	−0.637431	+	0.791962i
$731$	−13.7508	+	3.68451i	−0.508591	+	0.136277i
$732$	−32.4732	+	23.5382i	−1.20024	+	0.869998i
$733$	30.7314	+	8.23445i	1.13509	+	0.304146i	0.776975	−	0.629532i	$-0.216753\pi$
$733$	30.7314	+	8.23445i	1.13509	+	0.304146i	0.358114	+	0.933678i	$0.383420\pi$
$734$	−1.21788	−	1.66583i	−0.0449527	−	0.0614871i
$735$	−1.22818	+	10.9426i	−0.0453023	+	0.403623i
$736$	−0.201029	−	13.5289i	−0.00741003	−	0.498681i
$737$		−	26.8722i		−	0.989849i
$738$	−3.77615	+	5.07759i	−0.139002	+	0.186909i
$739$	−32.4463	−	32.4463i	−1.19356	−	1.19356i	−0.976061	−	0.217495i	$-0.930211\pi$
$739$	−32.4463	−	32.4463i	−1.19356	−	1.19356i	−0.217495	−	0.976061i	$-0.569789\pi$
$740$	4.62137	−	14.5161i	0.169885	−	0.533622i
$741$	1.77855	+	11.7657i	0.0653366	+	0.432224i
$742$	−4.66606	+	30.0378i	−0.171297	+	1.10272i
$743$	−10.8406	+	6.25880i	−0.397702	+	0.229613i	−0.685492	−	0.728080i	$-0.740413\pi$
$743$	−10.8406	+	6.25880i	−0.397702	+	0.229613i	0.287790	+	0.957693i	$0.407079\pi$
$744$	−1.13174	−	2.21096i	−0.0414915	−	0.0810578i
$745$	40.0141	+	23.1021i	1.46600	+	0.846397i
$746$	−7.13463	+	8.86426i	−0.261217	+	0.324544i
$747$	18.2451	−	34.5932i	0.667554	−	1.26570i
$748$	−8.58145	+	13.3878i	−0.313769	+	0.489507i
$749$	14.9973	−	4.01852i	0.547990	−	0.146834i
$750$	0.220608	−	54.0716i	0.00805548	−	1.97442i
$751$	−34.0479	+	19.6575i	−1.24242	+	0.717314i	−0.969587	−	0.244747i	$-0.921295\pi$
$751$	−34.0479	+	19.6575i	−1.24242	+	0.717314i	−0.272837	+	0.962060i	$0.587962\pi$
$752$	−21.2670	−	15.0684i	−0.775526	−	0.549488i
$753$	−5.35969	−	12.2702i	−0.195318	−	0.447151i
$754$	−27.5410	−	12.1641i	−1.00298	−	0.442990i
$755$	23.6777	−	23.6777i	0.861718	−	0.861718i
$756$	18.8278	+	23.9875i	0.684762	+	0.872417i
$757$	−25.3026	−	25.3026i	−0.919640	−	0.919640i	0.0773631	−	0.997003i	$-0.475350\pi$
$757$	−25.3026	−	25.3026i	−0.919640	−	0.919640i	−0.997003	+	0.0773631i	$0.975350\pi$
$758$	−30.7259	+	11.8995i	−1.11602	+	0.432208i
$759$	10.4157	−	4.54963i	0.378065	−	0.165141i
$760$	−20.9165	+	23.6508i	−0.758722	+	0.857905i
$761$	11.0907	+	19.2097i	0.402039	+	0.696352i	0.993972	−	0.109635i	$-0.0349683\pi$
$761$	11.0907	+	19.2097i	0.402039	+	0.696352i	−0.591933	+	0.805987i	$0.701635\pi$
$762$	31.2995	−	31.0451i	1.13386	−	1.12465i
$763$	−6.45338	−	24.0843i	−0.233628	−	0.871911i
$764$	−42.5955	+	9.31888i	−1.54105	+	0.337145i
$765$	−29.0518	+	18.2892i	−1.05037	+	0.661247i
$766$	−1.57979	−	14.6129i	−0.0570803	−	0.527985i
$767$	−3.12087	+	5.40551i	−0.112688	+	0.195182i
$768$	−23.4910	−	14.7027i	−0.847660	−	0.530540i
$769$	0.792978	+	1.37348i	0.0285955	+	0.0495289i	0.879969	−	0.475031i	$-0.157563\pi$
$769$	0.792978	+	1.37348i	0.0285955	+	0.0495289i	−0.851374	+	0.524560i	$0.824230\pi$
$770$	36.2894	−	26.5309i	1.30778	−	0.956107i
$771$	−40.7210	+	6.15555i	−1.46653	+	0.221687i
$772$	2.84822	−	8.94650i	0.102510	−	0.321991i
$773$	−0.198602	+	0.198602i	−0.00714323	+	0.00714323i	−0.710669	−	0.703526i	$-0.751608\pi$
$773$	−0.198602	+	0.198602i	−0.00714323	+	0.00714323i	0.703526	+	0.710669i	$0.251608\pi$
$774$	16.3411	−	12.9343i	0.587369	−	0.464913i
$775$	−5.36948			−0.192877
$776$	13.8662	+	2.81839i	0.497767	+	0.101174i
$777$	9.74308	+	1.09355i	0.349531	+	0.0392310i
$778$	−5.23614	+	33.7077i	−0.187725	+	1.20848i
$779$	1.09132	−	4.07287i	0.0391007	−	0.145926i
$780$	−5.23609	+	32.8239i	−0.187482	+	1.17528i
$781$	3.30471	+	12.3334i	0.118252	+	0.441322i
$782$	1.05366	+	9.74625i	0.0376789	+	0.348525i
$783$	29.7377	+	34.4661i	1.06274	+	1.23172i
$784$	5.85194	−	2.68925i	0.208998	−	0.0960445i
$785$	−12.5149	−	7.22549i	−0.446676	−	0.257889i
$786$	21.9214	+	38.3293i	0.781912	+	1.36716i
$787$	−3.76684	+	14.0581i	−0.134274	+	0.501116i	0.865726	+	0.500518i	$0.166857\pi$
$787$	−3.76684	+	14.0581i	−0.134274	+	0.501116i	−1.00000		0.000597888i	$0.999810\pi$
$788$	40.4668	+	1.87968i	1.44157	+	0.0669609i
$789$	−7.65687	−	9.59298i	−0.272592	−	0.341519i
$790$	8.41234	+	21.7217i	0.299298	+	0.772825i
$791$		−	48.9217i		−	1.73946i
$792$	3.76099	−	22.9739i	0.133641	−	0.816342i
$793$		−	28.1353i		−	0.999112i
$794$	15.6127	−	6.04644i	0.554073	−	0.214580i
$795$	49.5353	−	7.48795i	1.75683	−	0.265570i
$796$	−19.5278	−	21.4304i	−0.692146	−	0.759579i
$797$	−3.12214	+	11.6520i	−0.110592	+	0.412734i	−0.998919	−	0.0464762i	$-0.985201\pi$
$797$	−3.12214	+	11.6520i	−0.110592	+	0.412734i	0.888328	+	0.459210i	$0.151868\pi$
$798$	−17.5558	−	10.2316i	−0.621470	−	0.362195i
$799$	16.3541	+	9.44202i	0.578565	+	0.334035i
$800$	−51.4327	+	30.7225i	−1.81842	+	1.08621i
$801$	16.1398	+	14.9498i	0.570272	+	0.528227i
$802$	−5.13468	+	0.555109i	−0.181312	+	0.0196016i
$803$	3.49286	+	13.0355i	0.123261	+	0.460015i
$804$	−33.7479	+	3.50923i	−1.19020	+	0.123761i
$805$	7.17244	−	26.7679i	0.252795	−	0.943445i
$806$	1.72174	+	0.267455i	0.0606459	+	0.00942071i
$807$	20.2586	+	46.3789i	0.713135	+	1.63261i
$808$	25.7801	−	17.0705i	0.906941	−	0.600537i
$809$	−5.40097			−0.189888			−0.0949441	−	0.995483i	$-0.530267\pi$
$809$	−5.40097			−0.189888			−0.0949441	+	0.995483i	$0.530267\pi$
$810$	28.4263	−	41.4444i	0.998798	−	1.45621i
$811$	19.4041	−	19.4041i	0.681371	−	0.681371i	−0.278938	−	0.960309i	$-0.589982\pi$
$811$	19.4041	−	19.4041i	0.681371	−	0.681371i	0.960309	+	0.278938i	$0.0899823\pi$
$812$	45.6697	−	23.6128i	1.60269	−	0.828647i
$813$	−10.5498	+	26.9144i	−0.369998	+	0.943928i
$814$	−4.41740	−	6.04219i	−0.154830	−	0.211779i
$815$	10.7788	+	18.6695i	0.377566	+	0.653964i
$816$	17.9340	+	9.02885i	0.627814	+	0.316073i
$817$	−6.94356	+	12.0266i	−0.242924	+	0.420758i
$818$	−19.6875	+	2.12840i	−0.688356	+	0.0744179i
$819$	−21.3762	+	0.818183i	−0.746944	+	0.0285896i
$820$	6.35606	−	9.91600i	0.221963	−	0.346282i
$821$	−5.53178	−	20.6449i	−0.193061	−	0.720512i	−0.992760	−	0.120112i	$-0.961675\pi$
$821$	−5.53178	−	20.6449i	−0.193061	−	0.720512i	0.799700	−	0.600400i	$-0.204992\pi$
$822$	−1.87666	+	0.494652i	−0.0654561	+	0.0172530i
$823$	−15.8047	−	27.3746i	−0.550918	−	0.954217i	−0.998209	−	0.0598289i	$-0.980944\pi$
$823$	−15.8047	−	27.3746i	−0.550918	−	0.954217i	0.447291	−	0.894389i	$-0.352389\pi$
$824$	1.20652	−	1.36424i	0.0420311	−	0.0475255i
$825$	−40.5053	−	29.8675i	−1.41021	−	1.03985i
$826$	−3.84926	−	9.93929i	−0.133933	−	0.345832i
$827$	−11.4058	−	11.4058i	−0.396617	−	0.396617i	0.480421	−	0.877038i	$-0.340484\pi$
$827$	−11.4058	−	11.4058i	−0.396617	−	0.396617i	−0.877038	+	0.480421i	$0.840484\pi$
$828$	−7.07391	−	12.4866i	−0.245835	−	0.433938i
$829$	−15.8083	+	15.8083i	−0.549043	+	0.549043i	−0.926164	−	0.377121i	$-0.876914\pi$
$829$	−15.8083	+	15.8083i	−0.549043	+	0.549043i	0.377121	+	0.926164i	$0.376914\pi$
$830$	−29.4113	+	66.5907i	−1.02088	+	2.31140i
$831$	8.00487	+	0.898459i	0.277686	+	0.0311672i
$832$	18.0224	−	7.28942i	0.624815	−	0.252715i
$833$	−4.04098	+	2.33306i	−0.140012	+	0.0808357i
$834$	−25.8259	−	45.1562i	−0.894278	−	1.56363i
$835$	26.3457	−	7.05931i	0.911730	−	0.244297i
$836$	3.31535	+	15.1541i	0.114664	+	0.524114i
$837$	−2.17859	−	1.48124i	−0.0753031	−	0.0511992i
$838$	0.685767	+	0.551957i	0.0236894	+	0.0190670i
$839$	−28.2922	−	16.3345i	−0.976755	−	0.563930i	−0.0754662	−	0.997148i	$-0.524044\pi$
$839$	−28.2922	−	16.3345i	−0.976755	−	0.563930i	−0.901289	+	0.433219i	$0.857378\pi$
$840$	−38.0583	−	42.1100i	−1.31314	−	1.45293i
$841$	41.3525	−	23.8749i	1.42595	−	0.823272i
$842$	25.1307	+	3.90380i	0.866062	+	0.134534i
$843$	−30.9060	+	24.6684i	−1.06446	+	0.849624i
$844$	−11.7561	+	6.07833i	−0.404663	+	0.209225i
$845$	19.8083	+	19.8083i	0.681428	+	0.681428i
$846$	−27.4599	−	3.19557i	−0.944091	−	0.109866i
$847$			10.1907i			0.350158i
$848$	−18.7093	−	22.5506i	−0.642480	−	0.774392i
$849$	−35.9994	−	26.5450i	−1.23550	−	0.911021i
$850$	35.0402	−	25.6177i	1.20187	−	0.878678i
$851$	−4.45686	−	1.19421i	−0.152779	−	0.0409371i
$852$	15.0575	−	5.76089i	0.515861	−	0.197365i
$853$	38.7224	−	10.3756i	1.32583	−	0.355255i	0.474672	−	0.880163i	$-0.342567\pi$
$853$	38.7224	−	10.3756i	1.32583	−	0.355255i	0.851159	+	0.524907i	$0.175900\pi$
$854$	37.4275	+	30.1245i	1.28074	+	1.03084i
$855$	−7.42388	+	32.6551i	−0.253891	+	1.11678i
$856$	−6.67537	+	13.3950i	−0.228159	+	0.457833i
$857$	−0.0140657	+	0.0243624i	−0.000480474	+	0.000832205i	−0.866266	−	0.499584i	$-0.833486\pi$
$857$	−0.0140657	+	0.0243624i	−0.000480474	+	0.000832205i	0.865785	+	0.500416i	$0.166820\pi$
$858$	11.5005	+	11.5947i	0.392620	+	0.395837i
$859$	11.7598	+	3.15104i	0.401240	+	0.107512i	0.453795	−	0.891106i	$-0.350070\pi$
$859$	11.7598	+	3.15104i	0.401240	+	0.107512i	−0.0525549	+	0.998618i	$0.516736\pi$
$860$	−28.6728	+	26.1274i	−0.977735	+	0.890935i
$861$	7.05740	+	2.76634i	0.240516	+	0.0942765i
$862$	8.20667	+	3.62466i	0.279520	+	0.123457i
$863$	40.1140			1.36550			0.682748	−	0.730654i	$-0.260785\pi$
$863$	40.1140			1.36550			0.682748	+	0.730654i	$0.260785\pi$
$864$	−29.3433	−	1.72315i	−0.998280	−	0.0586227i
$865$	−15.8140			−0.537692
$866$	34.5818	+	15.2738i	1.17514	+	0.519026i
$867$	13.8701	+	5.43674i	0.471052	+	0.184642i
$868$	−2.19926	+	2.00402i	−0.0746478	+	0.0680209i
$869$	11.0547	+	2.96211i	0.375006	+	0.100483i
$870$	−59.6695	−	60.1584i	−2.02299	−	2.03956i
$871$	11.9010	−	20.6132i	0.403251	−	0.698451i
$872$	21.5112	+	10.7200i	0.728461	+	0.363026i
$873$	14.3375	−	4.43598i	0.485250	−	0.150135i
$874$	7.44962	+	5.99602i	0.251987	+	0.202818i
$875$	−62.5669	+	16.7647i	−2.11515	+	0.566752i
$876$	15.9148	−	6.08889i	0.537711	−	0.205724i
$877$	−45.8849	−	12.2948i	−1.54942	−	0.415167i	−0.620127	−	0.784501i	$-0.712919\pi$
$877$	−45.8849	−	12.2948i	−1.54942	−	0.415167i	−0.929297	+	0.369334i	$0.879586\pi$
$878$	0.794129	−	0.580582i	0.0268006	−	0.0195937i
$879$	−3.99348	−	2.94468i	−0.134697	−	0.0993216i
$880$	−4.01683	+	43.1450i	−0.135407	+	1.45442i
$881$			20.6694i			0.696371i	0.937426	+	0.348186i	$0.113202\pi$
$881$			20.6694i			0.696371i	−0.937426	+	0.348186i	$0.886798\pi$
$882$	4.07640	−	5.48132i	0.137259	−	0.184566i
$883$	−37.7611	−	37.7611i	−1.27076	−	1.27076i	−0.945688	−	0.325075i	$-0.894610\pi$
$883$	−37.7611	−	37.7611i	−1.27076	−	1.27076i	−0.325075	−	0.945688i	$-0.605390\pi$
$884$	−12.5118	+	6.46904i	−0.420818	+	0.217577i
$885$	−13.7291	+	10.9582i	−0.461497	+	0.368355i
$886$	−22.9536	−	3.56561i	−0.771142	−	0.119789i
$887$	−24.4908	+	14.1398i	−0.822322	+	0.474768i	−0.851216	−	0.524815i	$-0.824135\pi$
$887$	−24.4908	+	14.1398i	−0.822322	+	0.474768i	0.0288948	+	0.999582i	$0.490801\pi$
$888$	−7.01132	+	6.33672i	−0.235285	+	0.212646i
$889$	−45.7347	−	26.4049i	−1.53389	−	0.885593i
$890$	−31.8999	−	25.6755i	−1.06929	−	0.860643i
$891$	−8.19514	−	23.2922i	−0.274547	−	0.780319i
$892$	0.787728	+	3.60061i	0.0263751	+	0.120557i
$893$	17.7937	−	4.76782i	0.595445	−	0.159549i
$894$	−14.2302	−	24.8814i	−0.475930	−	0.832157i
$895$	−48.6615	+	28.0947i	−1.62657	+	0.939103i
$896$	−9.59973	+	31.7795i	−0.320704	+	1.06168i
$897$	10.0046	+	1.12291i	0.334044	+	0.0374928i
$898$	−6.89980	+	15.6220i	−0.230249	+	0.521312i
$899$	−3.14074	+	3.14074i	−0.104750	+	0.104750i
$900$	−32.2200	+	54.7697i	−1.07400	+	1.82566i
$901$	15.0115	+	15.0115i	0.500105	+	0.500105i
$902$	−2.08987	−	5.39632i	−0.0695852	−	0.179678i
$903$	−20.0934	−	14.8163i	−0.668665	−	0.493055i
$904$	35.3241	+	31.2403i	1.17486	+	1.03904i
$905$	−41.9767	−	72.7058i	−1.39535	−	2.41682i
$906$	−20.0868	+	5.29451i	−0.667340	+	0.175898i
$907$	−9.12179	−	34.0430i	−0.302884	−	1.13038i	−0.934751	−	0.355302i	$-0.884378\pi$
$907$	−9.12179	−	34.0430i	−0.302884	−	1.13038i	0.631867	−	0.775077i	$-0.282289\pi$
$908$	0.767642	−	1.19759i	0.0254751	−	0.0397434i
$909$	15.2993	−	29.0078i	0.507444	−	0.962126i
$910$	39.5868	−	4.27972i	1.31229	−	0.141871i
$911$	−8.81619	+	15.2701i	−0.292093	+	0.505921i	−0.974305	−	0.225235i	$-0.927685\pi$
$911$	−8.81619	+	15.2701i	−0.292093	+	0.505921i	0.682211	+	0.731155i	$0.261018\pi$
$912$	18.5985	−	6.14261i	0.615859	−	0.203402i
$913$	17.8832	+	30.9746i	0.591847	+	1.02511i
$914$	−10.2226	−	13.9827i	−0.338135	−	0.462506i
$915$	28.8965	−	73.7199i	0.955288	−	2.43710i
$916$	13.6208	−	7.04244i	0.450045	−	0.232689i
$917$	37.4020	−	37.4020i	1.23512	−	1.23512i
$918$	21.2841	−	0.727706i	0.702478	−	0.0240179i
$919$	40.6483			1.34086			0.670431	−	0.741972i	$-0.266109\pi$
$919$	40.6483			1.34086			0.670431	+	0.741972i	$0.266109\pi$
$920$	14.7477	+	22.2723i	0.486218	+	0.734295i
$921$	−7.52361	−	17.2242i	−0.247911	−	0.567555i
$922$	−43.8588	−	6.81301i	−1.44441	−	0.224374i
$923$	−2.92715	+	10.9243i	−0.0963483	+	0.359577i
$924$	−27.7377	+	2.88427i	−0.912503	+	0.0948856i
$925$	5.28775	+	19.7341i	0.173860	+	0.648855i
$926$	50.1936	−	5.42641i	1.64946	−	0.178323i
$927$	0.428229	−	1.88363i	0.0140649	−	0.0618665i
$928$	−12.1139	+	48.0546i	−0.397658	+	1.57747i
$929$	−46.7331	−	26.9814i	−1.53326	−	0.885230i	−0.999208	−	0.0397807i	$-0.987334\pi$
$929$	−46.7331	−	26.9814i	−1.53326	−	0.885230i	−0.534055	−	0.845450i	$-0.679333\pi$
$930$	4.23662	+	2.46911i	0.138924	+	0.0809654i
$931$	−1.17810	+	4.39672i	−0.0386106	+	0.144097i
$932$	1.84447	+	2.02417i	0.0604177	+	0.0663040i
$933$	29.8167	−	4.50721i	0.976156	−	0.147560i
$934$	−14.2597	+	5.52246i	−0.466592	+	0.180701i
$935$		−	31.3946i		−	1.02671i
$936$	13.0596	−	15.9572i	0.426865	−	0.521579i
$937$			47.0464i			1.53694i	0.639886	+	0.768470i	$0.278982\pi$
$937$			47.0464i			1.53694i	−0.639886	+	0.768470i	$0.721018\pi$
$938$	14.6786	+	37.9021i	0.479274	+	1.23755i
$939$	−26.5784	−	33.2989i	−0.867352	−	1.08667i
$940$	51.4018	+	2.38761i	1.67654	+	0.0778753i
$941$	0.645083	−	2.40748i	0.0210291	−	0.0784816i	−0.954614	−	0.297846i	$-0.903732\pi$
$941$	0.645083	−	2.40748i	0.0210291	−	0.0784816i	0.975643	+	0.219365i	$0.0703984\pi$
$942$	4.45068	+	7.78196i	0.145011	+	0.253550i
$943$	−3.08946	−	1.78370i	−0.100607	−	0.0580853i
$944$	9.63476	+	3.56763i	0.313585	+	0.116116i
$945$	−56.8501	−	19.8107i	−1.84933	−	0.644443i
$946$	2.04852	+	18.9485i	0.0666031	+	0.616070i
$947$	13.4692	+	50.2676i	0.437689	+	1.63348i	0.734548	+	0.678557i	$0.237394\pi$
$947$	13.4692	+	50.2676i	0.437689	+	1.63348i	−0.296859	+	0.954921i	$0.595939\pi$
$948$	2.27638	−	14.2701i	0.0739333	−	0.463471i
$949$	−3.09381	+	11.5462i	−0.100429	+	0.374807i
$950$	6.49955	−	41.8409i	0.210873	−	1.35750i
$951$	−14.2440	−	1.59873i	−0.461893	−	0.0518424i
$952$	4.79085	−	23.5705i	0.155272	−	0.763924i
$953$	61.2734			1.98484			0.992420	−	0.122896i	$-0.0392181\pi$
$953$	61.2734			1.98484			0.992420	+	0.122896i	$0.0392181\pi$
$954$	−28.8888	−	11.4599i	−0.935308	−	0.371028i
$955$	60.8700	−	60.8700i	1.96971	−	1.96971i
$956$	0.938748	−	2.94868i	0.0303613	−	0.0953673i
$957$	−41.1628	+	6.22233i	−1.33060	+	0.201139i
$958$	−6.93271	+	5.06846i	−0.223986	+	0.163754i
$959$	1.16244	+	2.01340i	0.0375370	+	0.0650160i
$960$	54.7089	−	0.589690i	1.76572	−	0.0190322i
$961$	−15.3715	+	26.6242i	−0.495854	+	0.858844i
$962$	−0.712574	−	6.59122i	−0.0229743	−	0.212509i
$963$	0.607142	+	15.8624i	0.0195649	+	0.511160i
$964$	14.9918	−	3.27985i	0.482854	−	0.105637i
$965$	4.79750	+	17.9045i	0.154437	+	0.576367i
$966$	−12.2057	+	12.1065i	−0.392713	+	0.389521i
$967$	−3.75805	−	6.50913i	−0.120851	−	0.209319i	0.799253	−	0.600995i	$-0.205229\pi$
$967$	−3.75805	−	6.50913i	−0.120851	−	0.209319i	−0.920103	+	0.391676i	$0.871896\pi$
$968$	−7.35827	−	6.50758i	−0.236504	−	0.209161i
$969$	−13.0045	+	5.68042i	−0.417763	+	0.182481i
$970$	−26.0498	+	10.0885i	−0.836409	+	0.323922i
$971$	−20.5494	−	20.5494i	−0.659461	−	0.659461i	0.295791	−	0.955253i	$-0.404417\pi$
$971$	−20.5494	−	20.5494i	−0.659461	−	0.659461i	−0.955253	+	0.295791i	$0.904417\pi$
$972$	−28.1818	+	13.3337i	−0.903930	+	0.427680i
$973$	−44.0638	+	44.0638i	−1.41262	+	1.41262i
$974$	−9.26011	−	4.08994i	−0.296713	−	0.131050i
$975$	−17.8434	−	40.8496i	−0.571445	−	1.30824i
$976$	−45.6519	+	7.78788i	−1.46128	+	0.249284i
$977$	48.8661	−	28.2129i	1.56337	−	0.902610i	0.566453	−	0.824094i	$-0.308315\pi$
$977$	48.8661	−	28.2129i	1.56337	−	0.902610i	0.996913	−	0.0785154i	$-0.0250180\pi$
$978$	0.0545625	−	13.3734i	0.00174472	−	0.427634i
$979$	−19.4336	+	5.20721i	−0.621100	+	0.166423i
$980$	−6.86144	+	10.7044i	−0.219181	+	0.341941i
$981$	25.4736	−	0.975015i	0.813310	−	0.0311298i
$982$	−24.8122	+	30.8274i	−0.791790	+	0.983743i
$983$	5.17882	+	2.98999i	0.165179	+	0.0953660i	0.580311	−	0.814395i	$-0.302931\pi$
$983$	5.17882	+	2.98999i	0.165179	+	0.0953660i	−0.415132	+	0.909761i	$0.636265\pi$
$984$	−6.50415	+	3.32931i	−0.207345	+	0.106134i
$985$	−69.2628	+	39.9889i	−2.20690	+	1.27415i
$986$	5.51150	−	35.4803i	0.175522	−	1.12992i
$987$	4.94982	+	32.7447i	0.157555	+	1.04228i
$988$	−4.16822	+	13.0927i	−0.132609	+	0.416535i
$989$	8.30792	+	8.30792i	0.264176	+	0.264176i
$990$	18.2251	+	42.1921i	0.579232	+	1.34095i
$991$		−	20.2358i		−	0.642812i	−0.946942	−	0.321406i	$-0.895845\pi$
$991$		−	20.2358i		−	0.642812i	0.946942	−	0.321406i	$-0.104155\pi$
$992$	−0.0426121	−	2.86771i	−0.00135293	−	0.0910499i
$993$	−5.10742	+	45.5049i	−0.162079	+	1.44405i
$994$	−11.3981	−	15.5905i	−0.361527	−	0.494502i
$995$	55.2892	+	14.8147i	1.75278	+	0.469657i
$996$	36.5646	−	26.5039i	1.15859	−	0.839808i
$997$	0.647795	−	0.173576i	0.0205159	−	0.00549721i	−0.248547	−	0.968620i	$-0.579953\pi$
$997$	0.647795	−	0.173576i	0.0205159	−	0.00549721i	0.269062	+	0.963123i	$0.413286\pi$
$998$	39.2995	−	48.8268i	1.24400	−	1.54559i
$999$	−3.29849	+	9.46555i	−0.104360	+	0.299477i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	144.2.u.a.11.20	✓	88
3.2	odd	2		432.2.v.a.251.3		88
4.3	odd	2		576.2.y.a.335.3		88
9.4	even	3		432.2.v.a.395.5		88
9.5	odd	6	inner	144.2.u.a.59.18	yes	88
12.11	even	2		1728.2.z.a.143.22		88
16.3	odd	4	inner	144.2.u.a.83.18	yes	88
16.13	even	4		576.2.y.a.47.9		88
36.23	even	6		576.2.y.a.527.9		88
36.31	odd	6		1728.2.z.a.719.22		88
48.29	odd	4		1728.2.z.a.1007.22		88
48.35	even	4		432.2.v.a.35.5		88
144.13	even	12		1728.2.z.a.1583.22		88
144.67	odd	12		432.2.v.a.179.3		88
144.77	odd	12		576.2.y.a.239.3		88
144.131	even	12	inner	144.2.u.a.131.20	yes	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.2.u.a.11.20	✓	88	1.1	even	1	trivial
144.2.u.a.59.18	yes	88	9.5	odd	6	inner
144.2.u.a.83.18	yes	88	16.3	odd	4	inner
144.2.u.a.131.20	yes	88	144.131	even	12	inner
432.2.v.a.35.5		88	48.35	even	4
432.2.v.a.179.3		88	144.67	odd	12
432.2.v.a.251.3		88	3.2	odd	2
432.2.v.a.395.5		88	9.4	even	3
576.2.y.a.47.9		88	16.13	even	4
576.2.y.a.239.3		88	144.77	odd	12
576.2.y.a.335.3		88	4.3	odd	2
576.2.y.a.527.9		88	36.23	even	6
1728.2.z.a.143.22		88	12.11	even	2
1728.2.z.a.719.22		88	36.31	odd	6
1728.2.z.a.1007.22		88	48.29	odd	4
1728.2.z.a.1583.22		88	144.13	even	12

Overview	Random
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Classical	Maass
Hilbert	Bianchi

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

Introduction

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Modular forms

Varieties

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	144.2.u.a.11.20

Level	$144$
Weight	$2$
Character	144.11
Analytic conductor	$1.150$
Analytic rank	$0$
Dimension	$88$
Inner twists	$4$