LMFDB - Embedded newform 272.2.l.b.205.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [272,2,Mod(69,272)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(272, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 1, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("272.69"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 272 = 2^{4} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	272.l (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [30] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$2.17193093498$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$15$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			205.6
Character	$\chi$	$=$	272.205
Dual form			272.2.l.b.69.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.405142 + 1.35494i) q^{2} +(-2.04684 - 2.04684i) q^{3} +(-1.67172 - 1.09789i) q^{4} +(-0.112242 + 0.112242i) q^{5} +(3.60261 - 1.94409i) q^{6} -1.01296i q^{7} +(2.16485 - 1.82028i) q^{8} +5.37914i q^{9} +(-0.106607 - 0.197555i) q^{10} +(-4.56843 + 4.56843i) q^{11} +(1.17455 + 5.66895i) q^{12} +(3.07260 + 3.07260i) q^{13} +(1.37250 + 0.410394i) q^{14} +0.459483 q^{15} +(1.58929 + 3.67072i) q^{16} -1.00000 q^{17} +(-7.28841 - 2.17932i) q^{18} +(-2.65491 - 2.65491i) q^{19} +(0.310865 - 0.0644080i) q^{20} +(-2.07337 + 2.07337i) q^{21} +(-4.33908 - 8.04081i) q^{22} +5.91450i q^{23} +(-8.15694 - 0.705293i) q^{24} +4.97480i q^{25} +(-5.40803 + 2.91835i) q^{26} +(4.86974 - 4.86974i) q^{27} +(-1.11212 + 1.69339i) q^{28} +(-3.98716 - 3.98716i) q^{29} +(-0.186156 + 0.622571i) q^{30} +4.31396 q^{31} +(-5.61748 + 0.666231i) q^{32} +18.7017 q^{33} +(0.405142 - 1.35494i) q^{34} +(0.113697 + 0.113697i) q^{35} +(5.90569 - 8.99242i) q^{36} +(-4.49312 + 4.49312i) q^{37} +(4.67286 - 2.52163i) q^{38} -12.5783i q^{39} +(-0.0386758 + 0.447298i) q^{40} +2.83552i q^{41} +(-1.96928 - 3.64931i) q^{42} +(3.25504 - 3.25504i) q^{43} +(12.6527 - 2.62152i) q^{44} +(-0.603764 - 0.603764i) q^{45} +(-8.01379 - 2.39621i) q^{46} -0.815754 q^{47} +(4.26035 - 10.7664i) q^{48} +5.97391 q^{49} +(-6.74056 - 2.01550i) q^{50} +(2.04684 + 2.04684i) q^{51} +(-1.76316 - 8.50990i) q^{52} +(-5.94015 + 5.94015i) q^{53} +(4.62526 + 8.57113i) q^{54} -1.02554i q^{55} +(-1.84387 - 2.19291i) q^{56} +10.8684i q^{57} +(7.01773 - 3.78699i) q^{58} +(-4.40078 + 4.40078i) q^{59} +(-0.768126 - 0.504460i) q^{60} +(-9.70982 - 9.70982i) q^{61} +(-1.74777 + 5.84516i) q^{62} +5.44887 q^{63} +(1.37318 - 7.88127i) q^{64} -0.689749 q^{65} +(-7.57686 + 25.3397i) q^{66} +(1.61155 + 1.61155i) q^{67} +(1.67172 + 1.09789i) q^{68} +(12.1061 - 12.1061i) q^{69} +(-0.200115 + 0.107989i) q^{70} -0.780693i q^{71} +(9.79153 + 11.6451i) q^{72} -6.99816i q^{73} +(-4.26755 - 7.90826i) q^{74} +(10.1826 - 10.1826i) q^{75} +(1.52348 + 7.35306i) q^{76} +(4.62764 + 4.62764i) q^{77} +(17.0428 + 5.09600i) q^{78} -11.7856 q^{79} +(-0.590392 - 0.233623i) q^{80} -3.79775 q^{81} +(-3.84196 - 1.14879i) q^{82} +(3.93699 + 3.93699i) q^{83} +(5.74243 - 1.18977i) q^{84} +(0.112242 - 0.112242i) q^{85} +(3.09163 + 5.72913i) q^{86} +16.3222i q^{87} +(-1.57417 + 18.2058i) q^{88} -1.66274i q^{89} +(1.06267 - 0.573453i) q^{90} +(3.11243 - 3.11243i) q^{91} +(6.49345 - 9.88739i) q^{92} +(-8.83001 - 8.83001i) q^{93} +(0.330496 - 1.10530i) q^{94} +0.595984 q^{95} +(12.8618 + 10.1344i) q^{96} -16.9653 q^{97} +(-2.42028 + 8.09428i) q^{98} +(-24.5742 - 24.5742i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 2 q^{2} - 2 q^{3} - 2 q^{4} - 2 q^{5} + 8 q^{6} + 2 q^{8} - 6 q^{10} - 10 q^{11} - 2 q^{12} - 6 q^{13} - 22 q^{14} - 28 q^{15} + 2 q^{16} - 30 q^{17} + 8 q^{18} + 10 q^{19} - 10 q^{20} - 4 q^{21}+ \cdots + 54 q^{99}+O(q^{100}) $ 30 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 - 2 * q^5 + 8 * q^6 + 2 * q^8 - 6 * q^10 - 10 * q^11 - 2 * q^12 - 6 * q^13 - 22 * q^14 - 28 * q^15 + 2 * q^16 - 30 * q^17 + 8 * q^18 + 10 * q^19 - 10 * q^20 - 4 * q^21 + 28 * q^22 + 18 * q^24 + 6 * q^26 + 4 * q^27 + 8 * q^28 - 18 * q^29 - 56 * q^30 + 48 * q^31 - 38 * q^32 - 12 * q^33 - 2 * q^34 + 16 * q^35 + 20 * q^36 + 6 * q^37 + 42 * q^38 + 10 * q^40 + 12 * q^42 + 2 * q^43 + 22 * q^44 + 42 * q^45 - 14 * q^46 - 32 * q^47 - 62 * q^48 - 38 * q^49 - 28 * q^50 + 2 * q^51 - 10 * q^52 - 6 * q^53 + 40 * q^54 + 96 * q^56 + 62 * q^58 - 14 * q^59 - 28 * q^60 + 6 * q^61 - 74 * q^62 + 84 * q^63 - 38 * q^64 - 12 * q^65 + 26 * q^67 + 2 * q^68 + 12 * q^69 + 48 * q^70 + 44 * q^72 + 42 * q^74 - 26 * q^75 - 38 * q^76 - 28 * q^77 - 56 * q^78 - 72 * q^79 - 38 * q^80 - 10 * q^81 - 76 * q^82 - 34 * q^83 + 104 * q^84 + 2 * q^85 + 34 * q^86 - 2 * q^88 + 70 * q^90 + 16 * q^91 - 40 * q^92 - 24 * q^93 - 44 * q^94 + 76 * q^95 - 126 * q^96 - 28 * q^97 - 30 * q^98 + 54 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/272\mathbb{Z}\right)^\times$.

$n$	$69$	$239$	$241$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	−0.405142	+	1.35494i	−0.286479	+	0.958087i
$2$	−0.405142	+	1.35494i	−0.286479	+	0.958087i
$3$	−2.04684	−	2.04684i	−1.18175	−	1.18175i	−0.979292	−	0.202454i	$-0.935108\pi$
$3$	−2.04684	−	2.04684i	−1.18175	−	1.18175i	−0.202454	−	0.979292i	$-0.564892\pi$
$4$	−1.67172	−	1.09789i	−0.835860	−	0.548943i
$5$	−0.112242	+	0.112242i	−0.0501960	+	0.0501960i	−0.731759	−	0.681563i	$-0.761300\pi$
$5$	−0.112242	+	0.112242i	−0.0501960	+	0.0501960i	0.681563	+	0.731759i	$0.261300\pi$
$6$	3.60261	−	1.94409i	1.47076	−	0.793670i
$7$		−	1.01296i		−	0.382863i	−0.981506	−	0.191432i	$-0.938687\pi$
$7$		−	1.01296i		−	0.382863i	0.981506	−	0.191432i	$-0.0613131\pi$
$8$	2.16485	−	1.82028i	0.765391	−	0.643565i
$9$			5.37914i			1.79305i
$10$	−0.106607	−	0.197555i	−0.0337120	−	0.0624722i
$11$	−4.56843	+	4.56843i	−1.37743	+	1.37743i	−0.528500	+	0.848934i	$0.677245\pi$
$11$	−4.56843	+	4.56843i	−1.37743	+	1.37743i	−0.848934	+	0.528500i	$0.822755\pi$
$12$	1.17455	+	5.66895i	0.339063	+	1.63649i
$13$	3.07260	+	3.07260i	0.852187	+	0.852187i	0.990402	−	0.138215i	$-0.0441366\pi$
$13$	3.07260	+	3.07260i	0.852187	+	0.852187i	−0.138215	+	0.990402i	$0.544137\pi$
$14$	1.37250	+	0.410394i	0.366816	+	0.109682i
$15$	0.459483			0.118638
$16$	1.58929	+	3.67072i	0.397323	+	0.917679i
$17$	−1.00000			−0.242536
$17$	−1.00000			−0.242536
$18$	−7.28841	−	2.17932i	−1.71790	−	0.513670i
$19$	−2.65491	−	2.65491i	−0.609078	−	0.609078i	0.333627	−	0.942705i	$-0.391727\pi$
$19$	−2.65491	−	2.65491i	−0.609078	−	0.609078i	−0.942705	+	0.333627i	$0.891727\pi$
$20$	0.310865	−	0.0644080i	0.0695116	−	0.0144021i
$21$	−2.07337	+	2.07337i	−0.452447	+	0.452447i
$22$	−4.33908	−	8.04081i	−0.925095	−	1.71431i
$23$			5.91450i			1.23326i	0.787254	+	0.616629i	$0.211502\pi$
$23$			5.91450i			1.23326i	−0.787254	+	0.616629i	$0.788498\pi$
$24$	−8.15694	−	0.705293i	−1.66503	−	0.143967i
$25$			4.97480i			0.994961i
$26$	−5.40803	+	2.91835i	−1.06060	+	0.572335i
$27$	4.86974	−	4.86974i	0.937181	−	0.937181i
$28$	−1.11212	+	1.69339i	−0.210170	+	0.320020i
$29$	−3.98716	−	3.98716i	−0.740397	−	0.740397i	0.232257	−	0.972654i	$-0.425389\pi$
$29$	−3.98716	−	3.98716i	−0.740397	−	0.740397i	−0.972654	+	0.232257i	$0.925389\pi$
$30$	−0.186156	+	0.622571i	−0.0339873	+	0.113665i
$31$	4.31396			0.774810			0.387405	−	0.921910i	$-0.373371\pi$
$31$	4.31396			0.774810			0.387405	+	0.921910i	$0.373371\pi$
$32$	−5.61748	+	0.666231i	−0.993040	+	0.117774i
$33$	18.7017			3.25555
$34$	0.405142	−	1.35494i	0.0694813	−	0.232370i
$35$	0.113697	+	0.113697i	0.0192182	+	0.0192182i
$36$	5.90569	−	8.99242i	0.984281	−	1.49874i
$37$	−4.49312	+	4.49312i	−0.738665	+	0.738665i	−0.972320	−	0.233655i	$-0.924931\pi$
$37$	−4.49312	+	4.49312i	−0.738665	+	0.738665i	0.233655	+	0.972320i	$0.424931\pi$
$38$	4.67286	−	2.52163i	0.758038	−	0.409062i
$39$		−	12.5783i		−	2.01414i
$40$	−0.0386758	+	0.447298i	−0.00611517	+	0.0707240i
$41$			2.83552i			0.442834i	0.975179	+	0.221417i	$0.0710683\pi$
$41$			2.83552i			0.442834i	−0.975179	+	0.221417i	$0.928932\pi$
$42$	−1.96928	−	3.64931i	−0.303867	−	0.563100i
$43$	3.25504	−	3.25504i	0.496389	−	0.496389i	−0.413923	−	0.910312i	$-0.635842\pi$
$43$	3.25504	−	3.25504i	0.496389	−	0.496389i	0.910312	+	0.413923i	$0.135842\pi$
$44$	12.6527	−	2.62152i	1.90747	−	0.395208i
$45$	−0.603764	−	0.603764i	−0.0900039	−	0.0900039i
$46$	−8.01379	−	2.39621i	−1.18157	−	0.353303i
$47$	−0.815754			−0.118990			−0.0594950	−	0.998229i	$-0.518949\pi$
$47$	−0.815754			−0.118990			−0.0594950	+	0.998229i	$0.518949\pi$
$48$	4.26035	−	10.7664i	0.614929	−	1.55400i
$49$	5.97391			0.853416
$50$	−6.74056	−	2.01550i	−0.953258	−	0.285035i
$51$	2.04684	+	2.04684i	0.286616	+	0.286616i
$52$	−1.76316	−	8.50990i	−0.244507	−	1.18011i
$53$	−5.94015	+	5.94015i	−0.815942	+	0.815942i	−0.985517	−	0.169575i	$-0.945761\pi$
$53$	−5.94015	+	5.94015i	−0.815942	+	0.815942i	0.169575	+	0.985517i	$0.445761\pi$
$54$	4.62526	+	8.57113i	0.629418	+	1.16638i
$55$		−	1.02554i		−	0.138283i
$56$	−1.84387	−	2.19291i	−0.246398	−	0.293040i
$57$			10.8684i			1.43955i
$58$	7.01773	−	3.78699i	0.921473	−	0.497257i
$59$	−4.40078	+	4.40078i	−0.572933	+	0.572933i	−0.932947	−	0.360014i	$-0.882772\pi$
$59$	−4.40078	+	4.40078i	−0.572933	+	0.572933i	0.360014	+	0.932947i	$0.382772\pi$
$60$	−0.768126	−	0.504460i	−0.0991647	−	0.0651255i
$61$	−9.70982	−	9.70982i	−1.24321	−	1.24321i	−0.958660	−	0.284555i	$-0.908154\pi$
$61$	−9.70982	−	9.70982i	−1.24321	−	1.24321i	−0.284555	−	0.958660i	$-0.591846\pi$
$62$	−1.74777	+	5.84516i	−0.221967	+	0.742335i
$63$	5.44887			0.686493
$64$	1.37318	−	7.88127i	0.171647	−	0.985158i
$65$	−0.689749			−0.0855528
$66$	−7.57686	+	25.3397i	−0.932647	+	3.11910i
$67$	1.61155	+	1.61155i	0.196882	+	0.196882i	0.798662	−	0.601780i	$-0.205542\pi$
$67$	1.61155	+	1.61155i	0.196882	+	0.196882i	−0.601780	+	0.798662i	$0.705542\pi$
$68$	1.67172	+	1.09789i	0.202726	+	0.133138i
$69$	12.1061	−	12.1061i	1.45740	−	1.45740i
$70$	−0.200115	+	0.107989i	−0.0239183	+	0.0129071i
$71$		−	0.780693i		−	0.0926512i	−0.998926	−	0.0463256i	$-0.985249\pi$
$71$		−	0.780693i		−	0.0926512i	0.998926	−	0.0463256i	$-0.0147512\pi$
$72$	9.79153	+	11.6451i	1.15394	+	1.37238i
$73$		−	6.99816i		−	0.819072i	−0.912294	−	0.409536i	$-0.865691\pi$
$73$		−	6.99816i		−	0.819072i	0.912294	−	0.409536i	$-0.134309\pi$
$74$	−4.26755	−	7.90826i	−0.496093	−	0.919317i
$75$	10.1826	−	10.1826i	1.17579	−	1.17579i
$76$	1.52348	+	7.35306i	0.174755	+	0.843453i
$77$	4.62764	+	4.62764i	0.527369	+	0.527369i
$78$	17.0428	+	5.09600i	1.92972	+	0.577008i
$79$	−11.7856			−1.32598			−0.662992	−	0.748627i	$-0.730714\pi$
$79$	−11.7856			−1.32598			−0.662992	+	0.748627i	$0.730714\pi$
$80$	−0.590392	−	0.233623i	−0.0660079	−	0.0261198i
$81$	−3.79775			−0.421973
$82$	−3.84196	−	1.14879i	−0.424274	−	0.126863i
$83$	3.93699	+	3.93699i	0.432140	+	0.432140i	0.889356	−	0.457216i	$-0.151153\pi$
$83$	3.93699	+	3.93699i	0.432140	+	0.432140i	−0.457216	+	0.889356i	$0.651153\pi$
$84$	5.74243	−	1.18977i	0.626551	−	0.129815i
$85$	0.112242	−	0.112242i	0.0121743	−	0.0121743i
$86$	3.09163	+	5.72913i	0.333379	+	0.617788i
$87$			16.3222i			1.74992i
$88$	−1.57417	+	18.2058i	−0.167807	+	1.94074i
$89$		−	1.66274i		−	0.176250i	−0.996109	−	0.0881251i	$-0.971912\pi$
$89$		−	1.66274i		−	0.176250i	0.996109	−	0.0881251i	$-0.0280875\pi$
$90$	1.06267	−	0.573453i	0.112016	−	0.0604473i
$91$	3.11243	−	3.11243i	0.326271	−	0.326271i
$92$	6.49345	−	9.88739i	0.676989	−	1.03083i
$93$	−8.83001	−	8.83001i	−0.915629	−	0.915629i
$94$	0.330496	−	1.10530i	0.0340881	−	0.114003i
$95$	0.595984			0.0611466
$96$	12.8618	+	10.1344i	1.31270	+	1.03434i
$97$	−16.9653			−1.72257			−0.861285	−	0.508123i	$-0.830340\pi$
$97$	−16.9653			−1.72257			−0.861285	+	0.508123i	$0.830340\pi$
$98$	−2.42028	+	8.09428i	−0.244486	+	0.817646i
$99$	−24.5742	−	24.5742i	−2.46980	−	2.46980i
$100$	5.46177	−	8.31648i	0.546177	−	0.831648i
$101$	−2.09654	+	2.09654i	−0.208614	+	0.208614i	−0.803678	−	0.595064i	$-0.797127\pi$
$101$	−2.09654	+	2.09654i	−0.208614	+	0.208614i	0.595064	+	0.803678i	$0.297127\pi$
$102$	−3.60261	+	1.94409i	−0.356712	+	0.192493i
$103$			11.6252i			1.14547i	0.819742	+	0.572733i	$0.194117\pi$
$103$			11.6252i			1.14547i	−0.819742	+	0.572733i	$0.805883\pi$
$104$	12.2447	+	1.05874i	1.20069	+	0.103818i
$105$		−	0.465438i		−	0.0454221i
$106$	−5.64194	−	10.4551i	−0.547993	−	1.01549i
$107$	−0.709693	+	0.709693i	−0.0686086	+	0.0686086i	−0.740578	−	0.671970i	$-0.765448\pi$
$107$	−0.709693	+	0.709693i	−0.0686086	+	0.0686086i	0.671970	+	0.740578i	$0.265448\pi$
$108$	−13.4872	+	2.79442i	−1.29781	+	0.268893i
$109$	−1.02443	−	1.02443i	−0.0981229	−	0.0981229i	0.656341	−	0.754464i	$-0.272103\pi$
$109$	−1.02443	−	1.02443i	−0.0981229	−	0.0981229i	−0.754464	+	0.656341i	$0.772103\pi$
$110$	1.38954	+	0.415488i	0.132487	+	0.0396153i
$111$	18.3934			1.74583
$112$	3.71829	−	1.60989i	0.351346	−	0.152120i
$113$	8.75234			0.823351			0.411675	−	0.911331i	$-0.364944\pi$
$113$	8.75234			0.823351			0.411675	+	0.911331i	$0.364944\pi$
$114$	−14.7260	−	4.40324i	−1.37922	−	0.412401i
$115$	−0.663854	−	0.663854i	−0.0619047	−	0.0619047i
$116$	2.28797	+	11.0429i	0.212432	+	1.02530i
$117$	−16.5280	+	16.5280i	−1.52801	+	1.52801i
$118$	−4.17985	−	7.74574i	−0.384786	−	0.713053i
$119$			1.01296i			0.0928580i
$120$	0.994713	−	0.836386i	0.0908044	−	0.0763513i
$121$		−	30.7411i		−	2.79464i
$122$	17.0901	−	9.22235i	1.54726	−	0.834953i
$123$	5.80388	−	5.80388i	0.523318	−	0.523318i
$124$	−7.21173	−	4.73624i	−0.647633	−	0.425327i
$125$	−1.11959	−	1.11959i	−0.100139	−	0.100139i
$126$	−2.20757	+	7.38288i	−0.196666	+	0.657719i
$127$	−15.8565			−1.40703			−0.703517	−	0.710678i	$-0.748388\pi$
$127$	−15.8565			−1.40703			−0.703517	+	0.710678i	$0.748388\pi$
$128$	10.1223	+	5.05361i	0.894694	+	0.446680i
$129$	−13.3251			−1.17321
$130$	0.279446	−	0.934567i	0.0245091	−	0.0819670i
$131$	2.93671	+	2.93671i	0.256582	+	0.256582i	0.823662	−	0.567081i	$-0.191927\pi$
$131$	2.93671	+	2.93671i	0.256582	+	0.256582i	−0.567081	+	0.823662i	$0.691927\pi$
$132$	−31.2640	−	20.5324i	−2.72119	−	1.78711i
$133$	−2.68932	+	2.68932i	−0.233194	+	0.233194i
$134$	−2.83646	+	1.53065i	−0.245033	+	0.132228i
$135$			1.09318i			0.0940855i
$136$	−2.16485	+	1.82028i	−0.185635	+	0.156088i
$137$			2.84052i			0.242682i	0.992611	+	0.121341i	$0.0387194\pi$
$137$			2.84052i			0.242682i	−0.992611	+	0.121341i	$0.961281\pi$
$138$	11.4983	+	21.3077i	0.978800	+	1.81383i
$139$	0.172689	−	0.172689i	0.0146473	−	0.0146473i	−0.699745	−	0.714392i	$-0.746703\pi$
$139$	0.172689	−	0.172689i	0.0146473	−	0.0146473i	0.714392	+	0.699745i	$0.246703\pi$
$140$	−0.0652429	−	0.314895i	−0.00551403	−	0.0266135i
$141$	1.66972	+	1.66972i	0.140616	+	0.140616i
$142$	1.05779	+	0.316292i	0.0887679	+	0.0265426i
$143$	−28.0739			−2.34766
$144$	−19.7453	+	8.54903i	−1.64544	+	0.712419i
$145$	0.895052			0.0743300
$146$	9.48207	+	2.83525i	0.784742	+	0.234647i
$147$	−12.2277	−	12.2277i	−1.00852	−	1.00852i
$148$	12.4442	−	2.57830i	1.02291	−	0.211935i
$149$	−2.90961	+	2.90961i	−0.238365	+	0.238365i	−0.816173	−	0.577808i	$-0.803908\pi$
$149$	−2.90961	+	2.90961i	−0.238365	+	0.238365i	0.577808	+	0.816173i	$0.303908\pi$
$150$	9.67145	+	17.9223i	0.789670	+	1.46335i
$151$		−	12.1378i		−	0.987757i	−0.869531	−	0.493878i	$-0.835579\pi$
$151$		−	12.1378i		−	0.987757i	0.869531	−	0.493878i	$-0.164421\pi$
$152$	−10.5802	−	0.914818i	−0.858165	−	0.0742015i
$153$		−	5.37914i		−	0.434878i
$154$	−8.14503	+	4.39532i	−0.656345	+	0.354185i
$155$	−0.484207	+	0.484207i	−0.0388924	+	0.0388924i
$156$	−13.8095	+	21.0274i	−1.10565	+	1.68354i
$157$	17.2062	+	17.2062i	1.37321	+	1.37321i	0.855646	+	0.517562i	$0.173160\pi$
$157$	17.2062	+	17.2062i	1.37321	+	1.37321i	0.517562	+	0.855646i	$0.326840\pi$
$158$	4.77484	−	15.9688i	0.379866	−	1.27041i
$159$	24.3171			1.92847
$160$	0.555737	−	0.705295i	0.0439349	−	0.0557585i
$161$	5.99116			0.472170
$162$	1.53863	−	5.14573i	0.120886	−	0.404286i
$163$	6.71572	+	6.71572i	0.526016	+	0.526016i	0.919382	−	0.393366i	$-0.128689\pi$
$163$	6.71572	+	6.71572i	0.526016	+	0.526016i	−0.393366	+	0.919382i	$0.628689\pi$
$164$	3.11308	−	4.74020i	0.243091	−	0.370147i
$165$	−2.09911	+	2.09911i	−0.163416	+	0.163416i
$166$	−6.92942	+	3.73934i	−0.537827	+	0.290229i
$167$			2.25312i			0.174352i	0.996193	+	0.0871760i	$0.0277842\pi$
$167$			2.25312i			0.174352i	−0.996193	+	0.0871760i	$0.972216\pi$
$168$	−0.714434	+	8.26267i	−0.0551198	+	0.637479i
$169$			5.88179i			0.452445i
$170$	0.106607	+	0.197555i	0.00817637	+	0.0151517i
$171$	14.2811	−	14.2811i	1.09211	−	1.09211i
$172$	−9.01517	+	1.86785i	−0.687401	+	0.142422i
$173$	4.38630	+	4.38630i	0.333484	+	0.333484i	0.853908	−	0.520424i	$-0.174226\pi$
$173$	4.38630	+	4.38630i	0.333484	+	0.333484i	−0.520424	+	0.853908i	$0.674226\pi$
$174$	−22.1156	−	6.61281i	−1.67658	−	0.501316i
$175$	5.03928			0.380934
$176$	−24.0300	−	9.50884i	−1.81133	−	0.716756i
$177$	18.0154			1.35412
$178$	2.25291	+	0.673647i	0.168863	+	0.0504920i
$179$	4.10787	+	4.10787i	0.307037	+	0.307037i	0.843759	−	0.536722i	$-0.180338\pi$
$179$	4.10787	+	4.10787i	0.307037	+	0.307037i	−0.536722	+	0.843759i	$0.680338\pi$
$180$	0.346460	+	1.67219i	0.0258236	+	0.124638i
$181$	8.94790	−	8.94790i	0.665092	−	0.665092i	−0.291484	−	0.956576i	$-0.594149\pi$
$181$	8.94790	−	8.94790i	0.665092	−	0.665092i	0.956576	+	0.291484i	$0.0941489\pi$
$182$	2.95618	+	5.47813i	0.219126	+	0.406066i
$183$			39.7490i			2.93833i
$184$	10.7660	+	12.8040i	0.793683	+	0.943925i
$185$		−	1.00863i		−	0.0741561i
$186$	15.5415	−	8.38671i	1.13956	−	0.614944i
$187$	4.56843	−	4.56843i	0.334077	−	0.334077i
$188$	1.36371	+	0.895605i	0.0994589	+	0.0653187i
$189$	−4.93286	−	4.93286i	−0.358812	−	0.358812i
$190$	−0.241458	+	0.807521i	−0.0175172	+	0.0585838i
$191$	−26.6573			−1.92885			−0.964427	−	0.264351i	$-0.914842\pi$
$191$	−26.6573			−1.92885			−0.964427	+	0.264351i	$0.914842\pi$
$192$	−18.9424	+	13.3210i	−1.36705	+	0.961364i
$193$	13.4602			0.968888			0.484444	−	0.874822i	$-0.339022\pi$
$193$	13.4602			0.968888			0.484444	+	0.874822i	$0.339022\pi$
$194$	6.87338	−	22.9870i	0.493480	−	1.65037i
$195$	1.41181	+	1.41181i	0.101102	+	0.101102i
$196$	−9.98670	−	6.55867i	−0.713336	−	0.468477i
$197$	17.3025	−	17.3025i	1.23275	−	1.23275i	0.269847	−	0.962903i	$-0.413027\pi$
$197$	17.3025	−	17.3025i	1.23275	−	1.23275i	0.962903	−	0.269847i	$-0.0869732\pi$
$198$	43.2527	−	23.3405i	3.07383	−	1.65874i
$199$			14.3832i			1.01959i	0.860295	+	0.509797i	$0.170280\pi$
$199$			14.3832i			1.01959i	−0.860295	+	0.509797i	$0.829720\pi$
$200$	9.05552	+	10.7697i	0.640322	+	0.761534i
$201$		−	6.59718i		−	0.465330i
$202$	−1.99129	−	3.69008i	−0.140107	−	0.259633i
$203$	−4.03884	+	4.03884i	−0.283471	+	0.283471i
$204$	−1.17455	−	5.66895i	−0.0822347	−	0.396906i
$205$	−0.318264	−	0.318264i	−0.0222285	−	0.0222285i
$206$	−15.7515	−	4.70987i	−1.09746	−	0.328152i
$207$	−31.8149			−2.21129
$208$	−6.39539	+	16.1619i	−0.443441	+	1.12063i
$209$	24.2575			1.67793
$210$	0.630641	+	0.188569i	0.0435183	+	0.0130125i
$211$	10.4119	+	10.4119i	0.716788	+	0.716788i	0.967946	−	0.251158i	$-0.0808115\pi$
$211$	10.4119	+	10.4119i	0.716788	+	0.716788i	−0.251158	+	0.967946i	$0.580811\pi$
$212$	16.4519	−	3.40866i	1.12992	−	0.234107i
$213$	−1.59796	+	1.59796i	−0.109490	+	0.109490i
$214$	−0.674064	−	1.24912i	−0.0460781	−	0.0853879i
$215$			0.730702i			0.0498335i
$216$	1.67799	−	19.4065i	0.114173	−	1.32045i
$217$		−	4.36988i		−	0.296647i
$218$	1.80309	−	0.973003i	0.122120	−	0.0659001i
$219$	−14.3241	+	14.3241i	−0.967935	+	0.967935i
$220$	−1.12592	+	1.71441i	−0.0759097	+	0.115585i
$221$	−3.07260	−	3.07260i	−0.206686	−	0.206686i
$222$	−7.45196	+	24.9220i	−0.500143	+	1.67266i
$223$	18.2677			1.22329			0.611647	−	0.791131i	$-0.290507\pi$
$223$	18.2677			1.22329			0.611647	+	0.791131i	$0.290507\pi$
$224$	0.674866	+	5.69030i	0.0450914	+	0.380199i
$225$	−26.7602			−1.78401
$226$	−3.54594	+	11.8589i	−0.235873	+	0.788841i
$227$	19.9826	+	19.9826i	1.32629	+	1.32629i	0.908582	+	0.417707i	$0.137166\pi$
$227$	19.9826	+	19.9826i	1.32629	+	1.32629i	0.417707	+	0.908582i	$0.362834\pi$
$228$	11.9322	−	18.1689i	0.790232	−	1.20326i
$229$	−6.83533	+	6.83533i	−0.451691	+	0.451691i	−0.895916	−	0.444224i	$-0.853479\pi$
$229$	−6.83533	+	6.83533i	−0.451691	+	0.451691i	0.444224	+	0.895916i	$0.353479\pi$
$230$	1.16844	−	0.630526i	0.0770444	−	0.0415757i
$231$		−	18.9441i		−	1.24643i
$232$	−15.8894	−	1.37388i	−1.04319	−	0.0901996i
$233$			22.3112i			1.46166i	0.682561	+	0.730829i	$0.260866\pi$
$233$			22.3112i			1.46166i	−0.682561	+	0.730829i	$0.739134\pi$
$234$	−15.6982	−	29.0906i	−1.02622	−	1.90171i
$235$	0.0915616	−	0.0915616i	0.00597282	−	0.00597282i
$236$	12.1884	−	2.52532i	0.793400	−	0.164384i
$237$	24.1233	+	24.1233i	1.56698	+	1.56698i
$238$	−1.37250	−	0.410394i	−0.0889660	−	0.0266019i
$239$	−3.45658			−0.223587			−0.111794	−	0.993731i	$-0.535660\pi$
$239$	−3.45658			−0.223587			−0.111794	+	0.993731i	$0.535660\pi$
$240$	0.730252	+	1.68663i	0.0471376	+	0.108872i
$241$	−3.87048			−0.249320			−0.124660	−	0.992200i	$-0.539784\pi$
$241$	−3.87048			−0.249320			−0.124660	+	0.992200i	$0.539784\pi$
$242$	41.6523	+	12.4545i	2.67751	+	0.800607i
$243$	−6.83580	−	6.83580i	−0.438517	−	0.438517i
$244$	5.57181	+	26.8924i	0.356699	+	1.72161i
$245$	−0.670522	+	0.670522i	−0.0428381	+	0.0428381i
$246$	5.51250	+	10.2153i	0.351464	+	0.651303i
$247$		−	16.3150i		−	1.03810i
$248$	9.33909	−	7.85261i	0.593033	−	0.498641i
$249$		−	16.1168i		−	1.02136i
$250$	1.97057	−	1.06338i	0.124630	−	0.0672542i
$251$	5.53871	−	5.53871i	0.349600	−	0.349600i	−0.510360	−	0.859961i	$-0.670488\pi$
$251$	5.53871	−	5.53871i	0.349600	−	0.349600i	0.859961	+	0.510360i	$0.170488\pi$
$252$	−9.10897	−	5.98223i	−0.573811	−	0.376845i
$253$	−27.0200	−	27.0200i	−1.69873	−	1.69873i
$254$	6.42413	−	21.4845i	0.403086	−	1.34806i
$255$	−0.459483			−0.0287739
$256$	−10.9483	+	11.6677i	−0.684269	+	0.729230i
$257$	−25.7212			−1.60445			−0.802223	−	0.597024i	$-0.796350\pi$
$257$	−25.7212			−1.60445			−0.802223	+	0.597024i	$0.796350\pi$
$258$	5.39857	−	18.0547i	0.336100	−	1.12404i
$259$	4.55136	+	4.55136i	0.282808	+	0.282808i
$260$	1.15307	+	0.757266i	0.0715101	+	0.0469636i
$261$	21.4475	−	21.4475i	1.32757	−	1.32757i
$262$	−5.16885	+	2.78928i	−0.319333	+	0.172322i
$263$		−	17.3559i		−	1.07021i	−0.844785	−	0.535105i	$-0.820272\pi$
$263$		−	17.3559i		−	1.07021i	0.844785	−	0.535105i	$-0.179728\pi$
$264$	40.4865	−	34.0423i	2.49177	−	2.09516i
$265$		−	1.33347i		−	0.0819141i
$266$	−2.55431	−	4.73343i	−0.156615	−	0.290225i
$267$	−3.40337	+	3.40337i	−0.208283	+	0.208283i
$268$	−0.924761	−	4.46336i	−0.0564888	−	0.272643i
$269$	−4.90641	−	4.90641i	−0.299149	−	0.299149i	0.541531	−	0.840681i	$-0.317845\pi$
$269$	−4.90641	−	4.90641i	−0.299149	−	0.299149i	−0.840681	+	0.541531i	$0.817845\pi$
$270$	−1.48119	−	0.442892i	−0.0901421	−	0.0269535i
$271$	20.2369			1.22930			0.614652	−	0.788798i	$-0.289296\pi$
$271$	20.2369			1.22930			0.614652	+	0.788798i	$0.289296\pi$
$272$	−1.58929	−	3.67072i	−0.0963649	−	0.222570i
$273$	−12.7413			−0.771140
$274$	−3.84872	−	1.15081i	−0.232510	−	0.0695232i
$275$	−22.7270	−	22.7270i	−1.37049	−	1.37049i
$276$	−33.5290	+	6.94686i	−2.01821	+	0.418152i
$277$	−7.38744	+	7.38744i	−0.443868	+	0.443868i	−0.893310	−	0.449442i	$-0.851623\pi$
$277$	−7.38744	+	7.38744i	−0.443868	+	0.443868i	0.449442	+	0.893310i	$0.351623\pi$
$278$	0.164019	+	0.303946i	0.00983722	+	0.0182295i
$279$			23.2054i			1.38927i
$280$	0.453096	+	0.0391771i	0.0270776	+	0.00234128i
$281$		−	23.2693i		−	1.38813i	−0.719912	−	0.694066i	$-0.755818\pi$
$281$		−	23.2693i		−	1.38813i	0.719912	−	0.694066i	$-0.244182\pi$
$282$	−2.93884	+	1.58590i	−0.175006	+	0.0944387i
$283$	6.08235	−	6.08235i	0.361558	−	0.361558i	−0.502828	−	0.864386i	$-0.667707\pi$
$283$	6.08235	−	6.08235i	0.361558	−	0.361558i	0.864386	+	0.502828i	$0.167707\pi$
$284$	−0.857112	+	1.30510i	−0.0508603	+	0.0774434i
$285$	−1.21989	−	1.21989i	−0.0722598	−	0.0722598i
$286$	11.3739	−	38.0385i	0.672555	−	2.24926i
$287$	2.87228			0.169545
$288$	−3.58375	−	30.2173i	−0.211175	−	1.78057i
$289$	1.00000			0.0588235
$290$	−0.362623	+	1.21274i	−0.0212940	+	0.0712146i
$291$	34.7254	+	34.7254i	2.03564	+	2.03564i
$292$	−7.68318	+	11.6990i	−0.449624	+	0.684629i
$293$	2.93453	−	2.93453i	0.171437	−	0.171437i	−0.616173	−	0.787611i	$-0.711318\pi$
$293$	2.93453	−	2.93453i	0.171437	−	0.171437i	0.787611	+	0.616173i	$0.211318\pi$
$294$	21.5217	−	11.6138i	1.25517	−	0.677330i
$295$		−	0.987903i		−	0.0575180i
$296$	−1.54822	+	17.9057i	−0.0899885	+	1.04075i
$297$			44.4941i			2.58181i
$298$	−2.76354	−	5.12116i	−0.160088	−	0.296661i
$299$	−18.1729	+	18.1729i	−1.05097	+	1.05097i
$300$	−28.2019	+	5.84314i	−1.62824	+	0.337354i
$301$	−3.29723	−	3.29723i	−0.190049	−	0.190049i
$302$	16.4459	+	4.91752i	0.946357	+	0.282972i
$303$	8.58259			0.493057
$304$	5.52600	−	13.9649i	0.316938	−	0.800939i
$305$	2.17969			0.124809
$306$	7.28841	+	2.17932i	0.416651	+	0.124583i
$307$	0.197517	+	0.197517i	0.0112729	+	0.0112729i	0.712721	−	0.701448i	$-0.247463\pi$
$307$	0.197517	+	0.197517i	0.0112729	+	0.0112729i	−0.701448	+	0.712721i	$0.747463\pi$
$308$	−2.65549	−	12.8167i	−0.151311	−	0.730302i
$309$	23.7950	−	23.7950i	1.35365	−	1.35365i
$310$	−0.459898	−	0.852243i	−0.0261204	−	0.0484041i
$311$			10.3125i			0.584767i	0.956301	+	0.292383i	$0.0944484\pi$
$311$			10.3125i			0.584767i	−0.956301	+	0.292383i	$0.905552\pi$
$312$	−22.8960	−	27.2301i	−1.29623	−	1.54160i
$313$			2.95932i			0.167270i	0.996496	+	0.0836352i	$0.0266531\pi$
$313$			2.95932i			0.167270i	−0.996496	+	0.0836352i	$0.973347\pi$
$314$	−30.2844	+	16.3424i	−1.70905	+	0.922257i
$315$	−0.611590	+	0.611590i	−0.0344592	+	0.0344592i
$316$	19.7022	+	12.9392i	1.10834	+	0.727890i
$317$	−12.4351	−	12.4351i	−0.698424	−	0.698424i	0.265647	−	0.964070i	$-0.414415\pi$
$317$	−12.4351	−	12.4351i	−0.698424	−	0.698424i	−0.964070	+	0.265647i	$0.914415\pi$
$318$	−9.85190	+	32.9482i	−0.552467	+	1.84764i
$319$	36.4301			2.03970
$320$	0.730479	+	1.03874i	0.0408350	+	0.0580671i
$321$	2.90526			0.162156
$322$	−2.42727	+	8.11766i	−0.135267	+	0.452379i
$323$	2.65491	+	2.65491i	0.147723	+	0.147723i
$324$	6.34878	+	4.16950i	0.352710	+	0.231639i
$325$	−15.2856	+	15.2856i	−0.847893	+	0.847893i
$326$	−11.8202	+	6.37857i	−0.654661	+	0.353276i
$327$			4.19371i			0.231913i
$328$	5.16144	+	6.13849i	0.284993	+	0.338942i
$329$			0.826327i			0.0455569i
$330$	−1.99373	−	3.69461i	−0.109751	−	0.203382i
$331$	−6.77696	+	6.77696i	−0.372495	+	0.372495i	−0.868385	−	0.495890i	$-0.834842\pi$
$331$	−6.77696	+	6.77696i	−0.372495	+	0.372495i	0.495890	+	0.868385i	$0.334842\pi$
$332$	−2.25917	−	10.9039i	−0.123988	−	0.598429i
$333$	−24.1692	−	24.1692i	−1.32446	−	1.32446i
$334$	−3.05285	−	0.912836i	−0.167044	−	0.0499481i
$335$	−0.361766			−0.0197654
$336$	−10.9060	−	4.31557i	−0.594969	−	0.235434i
$337$	1.53987			0.0838823			0.0419412	−	0.999120i	$-0.486646\pi$
$337$	1.53987			0.0838823			0.0419412	+	0.999120i	$0.486646\pi$
$338$	−7.96947	−	2.38296i	−0.433482	−	0.129616i
$339$	−17.9147	−	17.9147i	−0.972991	−	0.972991i
$340$	−0.310865	+	0.0644080i	−0.0168590	+	0.00349302i
$341$	−19.7080	+	19.7080i	−1.06725	+	1.06725i
$342$	13.5642	+	25.1360i	0.733467	+	1.35920i
$343$		−	13.1421i		−	0.709605i
$344$	1.12161	−	12.9718i	0.0604730	−	0.699390i
$345$			2.71761i			0.146311i
$346$	−7.72024	+	4.16609i	−0.415043	+	0.223970i
$347$	18.7405	−	18.7405i	1.00604	−	1.00604i	0.00605993	−	0.999982i	$-0.498071\pi$
$347$	18.7405	−	18.7405i	1.00604	−	1.00604i	0.999982	−	0.00605993i	$-0.00192895\pi$
$348$	17.9199	−	27.2861i	0.960609	−	1.46269i
$349$	10.6170	+	10.6170i	0.568313	+	0.568313i	0.931656	−	0.363343i	$-0.118365\pi$
$349$	10.6170	+	10.6170i	0.568313	+	0.568313i	−0.363343	+	0.931656i	$0.618365\pi$
$350$	−2.04163	+	6.82792i	−0.109130	+	0.364968i
$351$	29.9255			1.59731
$352$	22.6195	−	28.7067i	1.20562	−	1.53007i
$353$	9.14327			0.486647			0.243323	−	0.969945i	$-0.421762\pi$
$353$	9.14327			0.486647			0.243323	+	0.969945i	$0.421762\pi$
$354$	−7.29882	+	24.4098i	−0.387928	+	1.29737i
$355$	0.0876263	+	0.0876263i	0.00465072	+	0.00465072i
$356$	−1.82550	+	2.77964i	−0.0967513	+	0.147320i
$357$	2.07337	−	2.07337i	0.109735	−	0.109735i
$358$	−7.23019	+	3.90164i	−0.382127	+	0.206208i
$359$			14.0524i			0.741658i	0.928701	+	0.370829i	$0.120926\pi$
$359$			14.0524i			0.741658i	−0.928701	+	0.370829i	$0.879074\pi$
$360$	−2.40608	−	0.208042i	−0.126812	−	0.0109648i
$361$		−	4.90289i		−	0.258047i
$362$	8.49869	+	15.7490i	0.446681	+	0.827751i
$363$	−62.9222	+	62.9222i	−3.30256	+	3.30256i
$364$	−8.62020	+	1.78602i	−0.451821	+	0.0936126i
$365$	0.785485	+	0.785485i	0.0411142	+	0.0411142i
$366$	−53.8574	−	16.1040i	−2.81517	−	0.841769i
$367$	26.4894			1.38274			0.691369	−	0.722502i	$-0.257008\pi$
$367$	26.4894			1.38274			0.691369	+	0.722502i	$0.257008\pi$
$368$	−21.7105	+	9.39987i	−1.13174	+	0.490002i
$369$	−15.2527			−0.794023
$370$	1.36663	+	0.408639i	0.0710480	+	0.0212442i
$371$	6.01714	+	6.01714i	0.312395	+	0.312395i
$372$	5.06695	+	24.4556i	0.262709	+	1.26797i
$373$	−6.93682	+	6.93682i	−0.359175	+	0.359175i	−0.863509	−	0.504334i	$-0.831738\pi$
$373$	−6.93682	+	6.93682i	−0.359175	+	0.359175i	0.504334	+	0.863509i	$0.331738\pi$
$374$	4.33908	+	8.04081i	0.224368	+	0.415780i
$375$			4.58325i			0.236678i
$376$	−1.76599	+	1.48490i	−0.0910738	+	0.0765778i
$377$		−	24.5019i		−	1.26191i
$378$	8.68223	−	4.68521i	0.446566	−	0.240981i
$379$	−26.0497	+	26.0497i	−1.33808	+	1.33808i	−0.440171	+	0.897914i	$0.645082\pi$
$379$	−26.0497	+	26.0497i	−1.33808	+	1.33808i	−0.897914	+	0.440171i	$0.854918\pi$
$380$	−0.996317	−	0.654322i	−0.0511100	−	0.0335660i
$381$	32.4557	+	32.4557i	1.66276	+	1.66276i
$382$	10.8000	−	36.1190i	0.552576	−	1.84801i
$383$	−21.8850			−1.11827			−0.559136	−	0.829076i	$-0.688867\pi$
$383$	−21.8850			−1.11827			−0.559136	+	0.829076i	$0.688867\pi$
$384$	−10.3748	−	31.0627i	−0.529438	−	1.58516i
$385$	−1.03883			−0.0529436
$386$	−5.45330	+	18.2378i	−0.277566	+	0.928278i
$387$	17.5093	+	17.5093i	0.890049	+	0.890049i
$388$	28.3613	+	18.6260i	1.43983	+	0.945592i
$389$	11.3552	−	11.3552i	0.575732	−	0.575732i	−0.357993	−	0.933724i	$-0.616539\pi$
$389$	11.3552	−	11.3552i	0.575732	−	0.575732i	0.933724	+	0.357993i	$0.116539\pi$
$390$	−2.48490	+	1.34093i	−0.125828	+	0.0679007i
$391$		−	5.91450i		−	0.299109i
$392$	12.9326	−	10.8742i	0.653197	−	0.549229i
$393$		−	12.0220i		−	0.606429i
$394$	16.4338	+	30.4538i	0.827925	+	1.53424i
$395$	1.32284	−	1.32284i	0.0665591	−	0.0665591i
$396$	14.1015	+	68.0609i	0.708628	+	3.42019i
$397$	−18.5828	−	18.5828i	−0.932642	−	0.932642i	0.0652287	−	0.997870i	$-0.479222\pi$
$397$	−18.5828	−	18.5828i	−0.932642	−	0.932642i	−0.997870	+	0.0652287i	$0.979222\pi$
$398$	−19.4883	−	5.82722i	−0.976860	−	0.292092i
$399$	11.0093			0.551152
$400$	−18.2611	+	7.90641i	−0.913054	+	0.395321i
$401$	15.9357			0.795792			0.397896	−	0.917431i	$-0.369741\pi$
$401$	15.9357			0.795792			0.397896	+	0.917431i	$0.369741\pi$
$402$	8.93878	+	2.67280i	0.445826	+	0.133307i
$403$	13.2551	+	13.2551i	0.660283	+	0.660283i
$404$	5.80659	−	1.20306i	0.288889	−	0.0598547i
$405$	0.426266	−	0.426266i	0.0211814	−	0.0211814i
$406$	−3.83608	−	7.10869i	−0.190381	−	0.352798i
$407$		−	41.0530i		−	2.03492i
$408$	8.15694	+	0.705293i	0.403829	+	0.0349172i
$409$			1.11106i			0.0549385i	0.999623	+	0.0274693i	$0.00874484\pi$
$409$			1.11106i			0.0549385i	−0.999623	+	0.0274693i	$0.991255\pi$
$410$	0.560171	−	0.302286i	0.0276649	−	0.0149289i
$411$	5.81409	−	5.81409i	0.286788	−	0.286788i
$412$	12.7632	−	19.4341i	0.628796	−	0.957449i
$413$	4.45783	+	4.45783i	0.219355	+	0.219355i
$414$	12.8896	−	43.1073i	0.633488	−	2.11861i
$415$	−0.883788			−0.0433835
$416$	−19.3074	−	15.2132i	−0.946622	−	0.745891i
$417$	−0.706934			−0.0346187
$418$	−9.82776	+	32.8675i	−0.480691	+	1.60760i
$419$	3.75339	+	3.75339i	0.183365	+	0.183365i	0.792820	−	0.609455i	$-0.208612\pi$
$419$	3.75339	+	3.75339i	0.183365	+	0.183365i	−0.609455	+	0.792820i	$0.708612\pi$
$420$	−0.510998	+	0.778082i	−0.0249342	+	0.0379665i
$421$	1.64504	−	1.64504i	0.0801743	−	0.0801743i	−0.665882	−	0.746057i	$-0.731945\pi$
$421$	1.64504	−	1.64504i	0.0801743	−	0.0801743i	0.746057	+	0.665882i	$0.231945\pi$
$422$	−18.3259	+	9.88923i	−0.892089	+	0.481400i
$423$		−	4.38806i		−	0.213355i
$424$	−2.04683	+	23.6723i	−0.0994029	+	1.14963i
$425$		−	4.97480i		−	0.241313i
$426$	−1.51773	−	2.81253i	−0.0735345	−	0.136268i
$427$	−9.83567	+	9.83567i	−0.475982	+	0.475982i
$428$	1.96557	−	0.407245i	0.0950094	−	0.0196849i
$429$	57.4630	+	57.4630i	2.77434	+	2.77434i
$430$	−0.990057	−	0.296038i	−0.0477448	−	0.0142762i
$431$	−14.3879			−0.693043			−0.346522	−	0.938042i	$-0.612637\pi$
$431$	−14.3879			−0.693043			−0.346522	+	0.938042i	$0.612637\pi$
$432$	25.6148	+	10.1360i	1.23239	+	0.487668i
$433$	27.4224			1.31783			0.658917	−	0.752215i	$-0.271015\pi$
$433$	27.4224			1.31783			0.658917	+	0.752215i	$0.271015\pi$
$434$	5.92092	+	1.77042i	0.284213	+	0.0849830i
$435$	−1.83203	−	1.83203i	−0.0878392	−	0.0878392i
$436$	0.587854	+	2.83728i	0.0281531	+	0.135881i
$437$	15.7025	−	15.7025i	0.751151	−	0.751151i
$438$	−13.6050	−	25.2116i	−0.650073	−	1.20466i
$439$		−	21.1786i		−	1.01080i	−0.862885	−	0.505401i	$-0.831345\pi$
$439$		−	21.1786i		−	1.01080i	0.862885	−	0.505401i	$-0.168655\pi$
$440$	−1.86676	−	2.22014i	−0.0889944	−	0.105841i
$441$			32.1345i			1.53021i
$442$	5.40803	−	2.91835i	0.257234	−	0.138812i
$443$	19.9521	−	19.9521i	0.947951	−	0.947951i	−0.0507595	−	0.998711i	$-0.516164\pi$
$443$	19.9521	−	19.9521i	0.947951	−	0.947951i	0.998711	+	0.0507595i	$0.0161642\pi$
$444$	−30.7487	−	20.1939i	−1.45927	−	0.958361i
$445$	0.186629	+	0.186629i	0.00884706	+	0.00884706i
$446$	−7.40101	+	24.7516i	−0.350448	+	1.17202i
$447$	11.9111			0.563374
$448$	−7.98342	−	1.39098i	−0.377181	−	0.0657175i
$449$	−34.6939			−1.63730			−0.818652	−	0.574290i	$-0.805278\pi$
$449$	−34.6939			−1.63730			−0.818652	+	0.574290i	$0.805278\pi$
$450$	10.8417	−	36.2584i	0.511082	−	1.70924i
$451$	−12.9539	−	12.9539i	−0.609975	−	0.609975i
$452$	−14.6315	−	9.60907i	−0.688206	−	0.451973i
$453$	−24.8441	+	24.8441i	−1.16728	+	1.16728i
$454$	−35.1709	+	18.9794i	−1.65065	+	0.890746i
$455$			0.698689i			0.0327550i
$456$	19.7835	+	23.5284i	0.926446	+	1.10182i
$457$			17.8288i			0.833995i	0.908908	+	0.416998i	$0.136918\pi$
$457$			17.8288i			0.833995i	−0.908908	+	0.416998i	$0.863082\pi$
$458$	−6.49217	−	12.0307i	−0.303359	−	0.562159i
$459$	−4.86974	+	4.86974i	−0.227300	+	0.227300i
$460$	0.380941	+	1.83861i	0.0177615	+	0.0857258i
$461$	−23.9602	−	23.9602i	−1.11594	−	1.11594i	−0.992331	−	0.123609i	$-0.960553\pi$
$461$	−23.9602	−	23.9602i	−1.11594	−	1.11594i	−0.123609	−	0.992331i	$-0.539447\pi$
$462$	25.6681	+	7.67507i	1.19419	+	0.357077i
$463$	−25.6632			−1.19267			−0.596334	−	0.802736i	$-0.703377\pi$
$463$	−25.6632			−1.19267			−0.596334	+	0.802736i	$0.703377\pi$
$464$	8.29898	−	20.9725i	0.385270	−	0.973624i
$465$	1.98219			0.0919219
$466$	−30.2304	−	9.03922i	−1.40039	−	0.418734i
$467$	9.87622	+	9.87622i	0.457017	+	0.457017i	0.897675	−	0.440658i	$-0.145255\pi$
$467$	9.87622	+	9.87622i	0.457017	+	0.457017i	−0.440658	+	0.897675i	$0.645255\pi$
$468$	45.7760	−	9.48430i	2.11600	−	0.438412i
$469$	1.63244	−	1.63244i	0.0753790	−	0.0753790i
$470$	0.0869649	+	0.161156i	0.00401139	+	0.00743357i
$471$		−	70.4370i		−	3.24557i
$472$	−1.51640	+	17.5377i	−0.0697981	+	0.807238i
$473$			29.7408i			1.36748i
$474$	−42.4589	+	22.9122i	−1.95020	+	1.05239i
$475$	13.2077	−	13.2077i	0.606009	−	0.606009i
$476$	1.11212	−	1.69339i	0.0509738	−	0.0776163i
$477$	−31.9529	−	31.9529i	−1.46302	−	1.46302i
$478$	1.40040	−	4.68345i	0.0640530	−	0.214216i
$479$	−27.3534			−1.24981			−0.624905	−	0.780701i	$-0.714862\pi$
$479$	−27.3534			−1.24981			−0.624905	+	0.780701i	$0.714862\pi$
$480$	−2.58114	+	0.306121i	−0.117812	+	0.0139725i
$481$	−27.6112			−1.25896
$482$	1.56810	−	5.24427i	0.0714248	−	0.238870i
$483$	−12.2630	−	12.2630i	−0.557985	−	0.557985i
$484$	−33.7502	+	51.3905i	−1.53410	+	2.33593i
$485$	1.90422	−	1.90422i	0.0864661	−	0.0864661i
$486$	12.0316	−	6.49262i	0.545763	−	0.294511i
$487$		−	24.7929i		−	1.12348i	−0.827315	−	0.561738i	$-0.810133\pi$
$487$		−	24.7929i		−	1.12348i	0.827315	−	0.561738i	$-0.189867\pi$
$488$	−38.6949	−	3.34577i	−1.75164	−	0.151456i
$489$		−	27.4921i		−	1.24323i
$490$	−0.636859	−	1.18017i	−0.0287704	−	0.0533148i
$491$	17.4273	−	17.4273i	0.786482	−	0.786482i	−0.194433	−	0.980916i	$-0.562287\pi$
$491$	17.4273	−	17.4273i	0.786482	−	0.786482i	0.980916	+	0.194433i	$0.0622868\pi$
$492$	−16.0744	+	3.33046i	−0.724692	+	0.150149i
$493$	3.98716	+	3.98716i	0.179573	+	0.179573i
$494$	22.1058	+	6.60989i	0.994587	+	0.297393i
$495$	5.51651			0.247949
$496$	6.85614	+	15.8353i	0.307850	+	0.711027i
$497$	−0.790812			−0.0354728
$498$	21.8373	+	6.52960i	0.978552	+	0.292598i
$499$	−15.0714	−	15.0714i	−0.674688	−	0.674688i	0.284105	−	0.958793i	$-0.408303\pi$
$499$	−15.0714	−	15.0714i	−0.674688	−	0.674688i	−0.958793	+	0.284105i	$0.908303\pi$
$500$	0.642457	+	3.10082i	0.0287316	+	0.138673i
$501$	4.61179	−	4.61179i	0.206040	−	0.206040i
$502$	5.26065	+	9.74857i	0.234794	+	0.435100i
$503$			2.23642i			0.0997169i	0.998756	+	0.0498585i	$0.0158770\pi$
$503$			2.23642i			0.0997169i	−0.998756	+	0.0498585i	$0.984123\pi$
$504$	11.7960	−	9.91845i	0.525435	−	0.441803i
$505$		−	0.470639i		−	0.0209431i
$506$	47.5574	−	25.6635i	2.11418	−	1.14088i
$507$	12.0391	−	12.0391i	0.534676	−	0.534676i
$508$	26.5076	+	17.4086i	1.17608	+	0.772382i
$509$	−21.4598	−	21.4598i	−0.951189	−	0.951189i	0.0476743	−	0.998863i	$-0.484819\pi$
$509$	−21.4598	−	21.4598i	−0.951189	−	0.951189i	−0.998863	+	0.0476743i	$0.984819\pi$
$510$	0.186156	−	0.622571i	0.00824312	−	0.0275679i
$511$	−7.08886			−0.313593
$512$	−11.3734	−	19.5614i	−0.502636	−	0.864498i
$513$	−25.8574			−1.14163
$514$	10.4208	−	34.8507i	0.459640	−	1.53720i
$515$	−1.30483	−	1.30483i	−0.0574978	−	0.0574978i
$516$	22.2759	+	14.6295i	0.980640	+	0.644026i
$517$	3.72671	−	3.72671i	0.163901	−	0.163901i
$518$	−8.01077	+	4.32287i	−0.351973	+	0.189936i
$519$		−	17.9561i		−	0.788187i
$520$	−1.49320	+	1.25553i	−0.0654814	+	0.0550588i
$521$			42.7220i			1.87168i	0.352419	+	0.935842i	$0.385359\pi$
$521$			42.7220i			1.87168i	−0.352419	+	0.935842i	$0.614641\pi$
$522$	20.3708	+	37.7494i	0.891605	+	1.65225i
$523$	3.20523	−	3.20523i	0.140155	−	0.140155i	−0.633548	−	0.773703i	$-0.718402\pi$
$523$	3.20523	−	3.20523i	0.140155	−	0.140155i	0.773703	+	0.633548i	$0.218402\pi$
$524$	−1.68518	−	8.13353i	−0.0736175	−	0.355315i
$525$	−10.3146	−	10.3146i	−0.450167	−	0.450167i
$526$	23.5162	+	7.03161i	1.02535	+	0.306593i
$527$	−4.31396			−0.187919
$528$	29.7225	+	68.6487i	1.29351	+	2.98755i
$529$	−11.9813			−0.520927
$530$	1.80676	+	0.540243i	0.0784808	+	0.0234667i
$531$	−23.6725	−	23.6725i	−1.02730	−	1.02730i
$532$	7.44836	−	1.54322i	0.322928	−	0.0669072i
$533$	−8.71244	+	8.71244i	−0.377378	+	0.377378i
$534$	−3.23251	−	5.99021i	−0.139884	−	0.259222i
$535$		−	0.159314i		−	0.00688776i
$536$	6.42224	+	0.555301i	0.277398	+	0.0239853i
$537$		−	16.8163i		−	0.725679i
$538$	8.63569	−	4.66010i	0.372311	−	0.200911i
$539$	−27.2914	+	27.2914i	−1.17552	+	1.17552i
$540$	1.20018	−	1.82748i	0.0516476	−	0.0786423i
$541$	27.0364	+	27.0364i	1.16239	+	1.16239i	0.983952	+	0.178436i	$0.0571038\pi$
$541$	27.0364	+	27.0364i	1.16239	+	1.16239i	0.178436	+	0.983952i	$0.442896\pi$
$542$	−8.19883	+	27.4198i	−0.352170	+	1.17778i
$543$	−36.6299			−1.57194
$544$	5.61748	−	0.666231i	0.240848	−	0.0285644i
$545$	0.229968			0.00985076
$546$	5.16205	−	17.2637i	0.220915	−	0.738819i
$547$	16.9275	+	16.9275i	0.723769	+	0.723769i	0.969371	−	0.245602i	$-0.0789856\pi$
$547$	16.9275	+	16.9275i	0.723769	+	0.723769i	−0.245602	+	0.969371i	$0.578986\pi$
$548$	3.11856	−	4.74854i	0.133218	−	0.202848i
$549$	52.2305	−	52.2305i	2.22914	−	2.22914i
$550$	40.0014	−	21.5861i	1.70567	−	0.920433i
$551$			21.1711i			0.901920i
$552$	4.17145	−	48.2442i	0.177549	−	2.05341i
$553$			11.9384i			0.507671i
$554$	−7.01656	−	13.0025i	−0.298105	−	0.552423i
$555$	−2.06451	+	2.06451i	−0.0876337	+	0.0876337i
$556$	−0.478280	+	0.0990945i	−0.0202836	+	0.00420254i
$557$	21.7982	+	21.7982i	0.923621	+	0.923621i	0.997283	−	0.0736625i	$-0.0234688\pi$
$557$	21.7982	+	21.7982i	0.923621	+	0.923621i	−0.0736625	+	0.997283i	$0.523469\pi$
$558$	−31.4419	−	9.40150i	−1.33104	−	0.397997i
$559$	20.0029			0.846032
$560$	−0.236651	+	0.598045i	−0.0100003	+	0.0252720i
$561$	−18.7017			−0.789587
$562$	31.5285	+	9.42739i	1.32995	+	0.397670i
$563$	−5.82606	−	5.82606i	−0.245539	−	0.245539i	0.573598	−	0.819137i	$-0.305547\pi$
$563$	−5.82606	−	5.82606i	−0.245539	−	0.245539i	−0.819137	+	0.573598i	$0.805547\pi$
$564$	−0.958141	−	4.62447i	−0.0403450	−	0.194725i
$565$	−0.982377	+	0.982377i	−0.0413289	+	0.0413289i
$566$	5.77699	+	10.7054i	0.242825	+	0.449982i
$567$			3.84698i			0.161558i
$568$	−1.42108	−	1.69009i	−0.0596271	−	0.0709144i
$569$		−	9.99322i		−	0.418938i	−0.977815	−	0.209469i	$-0.932827\pi$
$569$		−	9.99322i		−	0.418938i	0.977815	−	0.209469i	$-0.0671735\pi$
$570$	2.14710	−	1.15864i	0.0899320	−	0.0485302i
$571$	7.14084	−	7.14084i	0.298835	−	0.298835i	−0.541723	−	0.840557i	$-0.682228\pi$
$571$	7.14084	−	7.14084i	0.298835	−	0.298835i	0.840557	+	0.541723i	$0.182228\pi$
$572$	46.9318	+	30.8220i	1.96232	+	1.28873i
$573$	54.5633	+	54.5633i	2.27941	+	2.27941i
$574$	−1.16368	+	3.89176i	−0.0485711	+	0.162439i
$575$	−29.4235			−1.22704
$576$	42.3945	+	7.38653i	1.76644	+	0.307772i
$577$	3.84281			0.159978			0.0799891	−	0.996796i	$-0.474511\pi$
$577$	3.84281			0.159978			0.0799891	+	0.996796i	$0.474511\pi$
$578$	−0.405142	+	1.35494i	−0.0168517	+	0.0563580i
$579$	−27.5510	−	27.5510i	−1.14498	−	1.14498i
$580$	−1.49628	−	0.982665i	−0.0621295	−	0.0408030i
$581$	3.98802	−	3.98802i	0.165451	−	0.165451i
$582$	−61.1195	+	32.9821i	−2.53349	+	1.36715i
$583$		−	54.2743i		−	2.24781i
$584$	−12.7386	−	15.1500i	−0.527126	−	0.626911i
$585$		−	3.71026i		−	0.153400i
$586$	2.78721	+	5.16502i	0.115139	+	0.213365i
$587$	7.57085	−	7.57085i	0.312482	−	0.312482i	−0.533388	−	0.845871i	$-0.679082\pi$
$587$	7.57085	−	7.57085i	0.312482	−	0.312482i	0.845871	+	0.533388i	$0.179082\pi$
$588$	7.01664	+	33.8658i	0.289361	+	1.39660i
$589$	−11.4532	−	11.4532i	−0.471920	−	0.471920i
$590$	1.33855	+	0.400241i	0.0551072	+	0.0164777i
$591$	−70.8309			−2.91360
$592$	−23.6339	−	9.35210i	−0.971346	−	0.384369i
$593$	−0.0598069			−0.00245597			−0.00122799	−	0.999999i	$-0.500391\pi$
$593$	−0.0598069			−0.00245597			−0.00122799	+	0.999999i	$0.500391\pi$
$594$	−60.2868	−	18.0264i	−2.47360	−	0.739634i
$595$	−0.113697	−	0.113697i	−0.00466110	−	0.00466110i
$596$	8.05848	−	1.66963i	0.330088	−	0.0683908i
$597$	29.4401	−	29.4401i	1.20490	−	1.20490i
$598$	−17.2606	−	31.9858i	−0.705838	−	1.30800i
$599$			8.94011i			0.365283i	0.983180	+	0.182641i	$0.0584647\pi$
$599$			8.94011i			0.365283i	−0.983180	+	0.182641i	$0.941535\pi$
$600$	3.50869	−	40.5792i	0.143242	−	1.65664i
$601$			28.4600i			1.16091i	0.814293	+	0.580454i	$0.197125\pi$
$601$			28.4600i			1.16091i	−0.814293	+	0.580454i	$0.802875\pi$
$602$	5.80339	−	3.13170i	0.236529	−	0.127638i
$603$	−8.66876	+	8.66876i	−0.353019	+	0.353019i
$604$	−13.3259	+	20.2909i	−0.542222	+	0.825626i
$605$	3.45043	+	3.45043i	0.140280	+	0.140280i
$606$	−3.47717	+	11.6289i	−0.141250	+	0.472391i
$607$	20.8160			0.844896			0.422448	−	0.906387i	$-0.361171\pi$
$607$	20.8160			0.844896			0.422448	+	0.906387i	$0.361171\pi$
$608$	16.6827	+	13.1451i	0.676573	+	0.533106i
$609$	16.5338			0.669982
$610$	−0.883086	+	2.95335i	−0.0357551	+	0.119578i
$611$	−2.50649	−	2.50649i	−0.101402	−	0.101402i
$612$	−5.90569	+	8.99242i	−0.238723	+	0.363497i
$613$	−30.4927	+	30.4927i	−1.23159	+	1.23159i	−0.268233	+	0.963354i	$0.586440\pi$
$613$	−30.4927	+	30.4927i	−1.23159	+	1.23159i	−0.963354	+	0.268233i	$0.913560\pi$
$614$	−0.347647	+	0.187601i	−0.0140299	+	0.00757097i
$615$			1.30287i			0.0525370i
$616$	18.4418	+	1.59457i	0.743040	+	0.0642472i
$617$			24.7514i			0.996453i	0.867047	+	0.498227i	$0.166015\pi$
$617$			24.7514i			0.996453i	−0.867047	+	0.498227i	$0.833985\pi$
$618$	22.6004	+	41.8811i	0.909122	+	1.68471i
$619$	13.8910	−	13.8910i	0.558327	−	0.558327i	−0.370504	−	0.928831i	$-0.620815\pi$
$619$	13.8910	−	13.8910i	0.558327	−	0.558327i	0.928831	+	0.370504i	$0.120815\pi$
$620$	1.34106	−	0.277854i	0.0538583	−	0.0111589i
$621$	28.8021	+	28.8021i	1.15579	+	1.15579i
$622$	−13.9728	−	4.17802i	−0.560257	−	0.167523i
$623$	−1.68429			−0.0674798
$624$	46.1713	−	19.9906i	1.84833	−	0.800263i
$625$	−24.6227			−0.984908
$626$	−4.00969	−	1.19894i	−0.160260	−	0.0479195i
$627$	−49.6514	−	49.6514i	−1.98289	−	1.98289i
$628$	−9.87351	−	47.6545i	−0.393996	−	1.90162i
$629$	4.49312	−	4.49312i	0.179153	−	0.179153i
$630$	−0.580886	−	1.07645i	−0.0231431	−	0.0428867i
$631$			43.5129i			1.73222i	0.499854	+	0.866110i	$0.333387\pi$
$631$			43.5129i			1.73222i	−0.499854	+	0.866110i	$0.666613\pi$
$632$	−25.5141	+	21.4531i	−1.01490	+	0.853357i
$633$		−	42.6233i		−	1.69412i
$634$	21.8868	−	11.8108i	0.869234	−	0.469067i
$635$	1.77976	−	1.77976i	0.0706275	−	0.0706275i
$636$	−40.6514	−	26.6974i	−1.61193	−	1.05862i
$637$	18.3555	+	18.3555i	0.727270	+	0.727270i
$638$	−14.7594	+	49.3606i	−0.584330	+	1.95421i
$639$	4.19946			0.166128
$640$	−1.70337	+	0.568919i	−0.0673316	+	0.0224885i
$641$	20.1009			0.793936			0.396968	−	0.917832i	$-0.370062\pi$
$641$	20.1009			0.793936			0.396968	+	0.917832i	$0.370062\pi$
$642$	−1.17704	+	3.93645i	−0.0464543	+	0.155359i
$643$	12.2175	+	12.2175i	0.481811	+	0.481811i	0.905710	−	0.423899i	$-0.139339\pi$
$643$	12.2175	+	12.2175i	0.481811	+	0.481811i	−0.423899	+	0.905710i	$0.639339\pi$
$644$	−10.0155	−	6.57761i	−0.394668	−	0.259194i
$645$	1.49563	−	1.49563i	0.0588905	−	0.0588905i
$646$	−4.67286	+	2.52163i	−0.183851	+	0.0992120i
$647$		−	16.3854i		−	0.644178i	−0.946709	−	0.322089i	$-0.895615\pi$
$647$		−	16.3854i		−	0.644178i	0.946709	−	0.322089i	$-0.104385\pi$
$648$	−8.22158	+	6.91297i	−0.322974	+	0.271567i
$649$		−	40.2093i		−	1.57835i
$650$	−14.5182	−	26.9039i	−0.569451	−	1.05526i
$651$	−8.94446	+	8.94446i	−0.350561	+	0.350561i
$652$	−3.85370	−	18.5999i	−0.150923	−	0.728428i
$653$	18.7699	+	18.7699i	0.734523	+	0.734523i	0.971512	−	0.236989i	$-0.0761605\pi$
$653$	18.7699	+	18.7699i	0.734523	+	0.734523i	−0.236989	+	0.971512i	$0.576161\pi$
$654$	−5.68222	−	1.69905i	−0.222192	−	0.0664381i
$655$	−0.659243			−0.0257587
$656$	−10.4084	+	4.50647i	−0.406380	+	0.175948i
$657$	37.6441			1.46864
$658$	−1.11962	−	0.334780i	−0.0436474	−	0.0130511i
$659$	28.1462	+	28.1462i	1.09642	+	1.09642i	0.994826	+	0.101593i	$0.0323940\pi$
$659$	28.1462	+	28.1462i	1.09642	+	1.09642i	0.101593	+	0.994826i	$0.467606\pi$
$660$	5.81372	−	1.20454i	0.226299	−	0.0468867i
$661$	−8.99640	+	8.99640i	−0.349919	+	0.349919i	−0.860080	−	0.510160i	$-0.829586\pi$
$661$	−8.99640	+	8.99640i	−0.349919	+	0.349919i	0.510160	+	0.860080i	$0.329586\pi$
$662$	−6.43673	−	11.9280i	−0.250171	−	0.463595i
$663$			12.5783i			0.488500i
$664$	15.6894	+	1.35659i	0.608867	+	0.0526459i
$665$		−	0.603709i		−	0.0234108i
$666$	42.5397	−	22.9558i	1.64838	−	0.889519i
$667$	23.5821	−	23.5821i	0.913102	−	0.913102i
$668$	2.47367	−	3.76659i	0.0957093	−	0.145734i
$669$	−37.3911	−	37.3911i	−1.44562	−	1.44562i
$670$	0.146567	−	0.490171i	0.00566237	−	0.0189370i
$671$	88.7172			3.42489
$672$	10.2658	−	13.0285i	0.396012	−	0.502585i
$673$	18.4947			0.712919			0.356459	−	0.934311i	$-0.383984\pi$
$673$	18.4947			0.712919			0.356459	+	0.934311i	$0.383984\pi$
$674$	−0.623868	+	2.08644i	−0.0240305	+	0.0803665i
$675$	24.2260	+	24.2260i	0.932458	+	0.932458i
$676$	6.45754	−	9.83270i	0.248367	−	0.378181i
$677$	−7.27015	+	7.27015i	−0.279414	+	0.279414i	−0.832875	−	0.553461i	$-0.813307\pi$
$677$	−7.27015	+	7.27015i	−0.279414	+	0.279414i	0.553461	+	0.832875i	$0.313307\pi$
$678$	31.5313	−	17.0153i	1.21095	−	0.653468i
$679$			17.1852i			0.659509i
$680$	0.0386758	−	0.447298i	0.00148315	−	0.0171531i
$681$		−	81.8024i		−	3.13467i
$682$	−18.7186	−	34.6877i	−0.716773	−	1.32826i
$683$	1.07946	−	1.07946i	0.0413043	−	0.0413043i	−0.686153	−	0.727457i	$-0.740702\pi$
$683$	1.07946	−	1.07946i	0.0413043	−	0.0413043i	0.727457	+	0.686153i	$0.240702\pi$
$684$	−39.5531	+	8.19500i	−1.51235	+	0.313343i
$685$	−0.318824	−	0.318824i	−0.0121817	−	0.0121817i
$686$	17.8067	+	5.32441i	0.679863	+	0.203287i
$687$	27.9817			1.06757
$688$	17.1215	+	6.77512i	0.652752	+	0.258299i
$689$	−36.5035			−1.39067
$690$	−3.68220	−	1.10102i	−0.140179	−	0.0419151i
$691$	15.3729	+	15.3729i	0.584812	+	0.584812i	0.936222	−	0.351410i	$-0.114298\pi$
$691$	15.3729	+	15.3729i	0.584812	+	0.584812i	−0.351410	+	0.936222i	$0.614298\pi$
$692$	−2.51700	−	12.1483i	−0.0956821	−	0.461810i
$693$	−24.8928	+	24.8928i	−0.945598	+	0.945598i
$694$	17.7996	+	32.9848i	0.675665	+	1.25208i
$695$			0.0387658i			0.00147047i
$696$	29.7109	+	35.3352i	1.12619	+	1.33938i
$697$		−	2.83552i		−	0.107403i
$698$	−18.6867	+	10.0840i	−0.707303	+	0.381683i
$699$	45.6676	−	45.6676i	1.72731	−	1.72731i
$700$	−8.42427	−	5.53256i	−0.318407	−	0.209111i
$701$	−2.22188	−	2.22188i	−0.0839191	−	0.0839191i	0.663901	−	0.747820i	$-0.268900\pi$
$701$	−2.22188	−	2.22188i	−0.0839191	−	0.0839191i	−0.747820	+	0.663901i	$0.768900\pi$
$702$	−12.1241	+	40.5473i	−0.457595	+	1.53036i
$703$	23.8577			0.899810
$704$	29.7317	+	42.2783i	1.12056	+	1.59342i
$705$	−0.374825			−0.0141167
$706$	−3.70432	+	12.3886i	−0.139414	+	0.466250i
$707$	2.12372	+	2.12372i	0.0798705	+	0.0798705i
$708$	−30.1168	−	19.7789i	−1.13186	−	0.743337i
$709$	−14.5326	+	14.5326i	−0.545785	+	0.545785i	−0.925219	−	0.379434i	$-0.876119\pi$
$709$	−14.5326	+	14.5326i	−0.545785	+	0.545785i	0.379434	+	0.925219i	$0.376119\pi$
$710$	−0.154229	+	0.0832272i	−0.00578813	+	0.00312346i
$711$		−	63.3964i		−	2.37755i
$712$	−3.02665	−	3.59959i	−0.113428	−	0.134900i
$713$			25.5149i			0.955542i
$714$	1.96928	+	3.64931i	0.0736986	+	0.136572i
$715$	3.15107	−	3.15107i	0.117843	−	0.117843i
$716$	−2.35723	−	11.3772i	−0.0880939	−	0.425185i
$717$	7.07507	+	7.07507i	0.264223	+	0.264223i
$718$	−19.0402	−	5.69323i	−0.710573	−	0.212469i
$719$	−22.0455			−0.822158			−0.411079	−	0.911600i	$-0.634848\pi$
$719$	−22.0455			−0.822158			−0.411079	+	0.911600i	$0.634848\pi$
$720$	1.25669	−	3.17580i	0.0468341	−	0.118355i
$721$	11.7759			0.438557
$722$	6.64312	+	1.98637i	0.247231	+	0.0739250i
$723$	7.92228	+	7.92228i	0.294633	+	0.294633i
$724$	−24.7822	+	5.13460i	−0.921022	+	0.190826i
$725$	19.8353	−	19.8353i	0.736666	−	0.736666i
$726$	−59.7633	−	110.748i	−2.21802	−	4.11025i
$727$			35.0296i			1.29917i	0.760287	+	0.649587i	$0.225058\pi$
$727$			35.0296i			1.29917i	−0.760287	+	0.649587i	$0.774942\pi$
$728$	1.07247	−	12.4034i	0.0397483	−	0.459702i
$729$			39.3769i			1.45840i
$730$	−1.38252	+	0.746051i	−0.0511693	+	0.0276126i
$731$	−3.25504	+	3.25504i	−0.120392	+	0.120392i
$732$	43.6398	−	66.4491i	1.61298	−	2.45603i
$733$	33.3592	+	33.3592i	1.23215	+	1.23215i	0.963136	+	0.269015i	$0.0866983\pi$
$733$	33.3592	+	33.3592i	1.23215	+	1.23215i	0.269015	+	0.963136i	$0.413302\pi$
$734$	−10.7320	+	35.8916i	−0.396125	+	1.32478i
$735$	2.74491			0.101247
$736$	−3.94042	−	33.2246i	−0.145246	−	1.22468i
$737$	−14.7245			−0.542384
$738$	6.17951	−	20.6665i	0.227471	−	0.760743i
$739$	−30.4784	−	30.4784i	−1.12117	−	1.12117i	−0.991566	−	0.129599i	$-0.958631\pi$
$739$	−30.4784	−	30.4784i	−1.12117	−	1.12117i	−0.129599	−	0.991566i	$-0.541369\pi$
$740$	−1.10736	+	1.68615i	−0.0407075	+	0.0619841i
$741$	−33.3942	+	33.3942i	−1.22677	+	1.22677i
$742$	−10.5907	+	5.71506i	−0.388795	+	0.209807i
$743$		−	25.9320i		−	0.951354i	−0.879620	−	0.475677i	$-0.842203\pi$
$743$		−	25.9320i		−	0.951354i	0.879620	−	0.475677i	$-0.157797\pi$
$744$	−35.1887	−	3.04261i	−1.29008	−	0.111547i
$745$		−	0.653160i		−	0.0239299i
$746$	−6.58857	−	12.2094i	−0.241225	−	0.447016i
$747$	−21.1776	+	21.1776i	−0.774848	+	0.774848i
$748$	−12.6527	+	2.62152i	−0.462630	+	0.0958521i
$749$	0.718892	+	0.718892i	0.0262677	+	0.0262677i
$750$	−6.21002	−	1.85687i	−0.226758	−	0.0678032i
$751$	9.47512			0.345752			0.172876	−	0.984944i	$-0.444694\pi$
$751$	9.47512			0.345752			0.172876	+	0.984944i	$0.444694\pi$
$752$	−1.29647	−	2.99440i	−0.0472774	−	0.109195i
$753$	−22.6737			−0.826277
$754$	33.1986	+	9.92677i	1.20902	+	0.361512i
$755$	1.36236	+	1.36236i	0.0495815	+	0.0495815i
$756$	2.83064	+	13.6621i	0.102949	+	0.496885i
$757$	−11.9056	+	11.9056i	−0.432717	+	0.432717i	−0.889552	−	0.456835i	$-0.848983\pi$
$757$	−11.9056	+	11.9056i	−0.432717	+	0.432717i	0.456835	+	0.889552i	$0.348983\pi$
$758$	−24.7420	−	45.8497i	−0.898668	−	1.66533i
$759$			110.611i			4.01494i
$760$	1.29022	−	1.08486i	0.0468011	−	0.0393519i
$761$			18.8898i			0.684754i	0.939563	+	0.342377i	$0.111232\pi$
$761$			18.8898i			0.684754i	−0.939563	+	0.342377i	$0.888768\pi$
$762$	−57.1247	+	30.8263i	−2.06941	+	1.11672i
$763$	−1.03771	+	1.03771i	−0.0375677	+	0.0375677i
$764$	44.5635	+	29.2667i	1.61225	+	1.05883i
$765$	0.603764	+	0.603764i	0.0218291	+	0.0218291i
$766$	8.86655	−	29.6529i	0.320361	−	1.07140i
$767$	−27.0437			−0.976493
$768$	46.2914	−	1.47244i	1.67040	−	0.0531319i
$769$	−13.3803			−0.482506			−0.241253	−	0.970462i	$-0.577558\pi$
$769$	−13.3803			−0.482506			−0.241253	+	0.970462i	$0.577558\pi$
$770$	0.420874	−	1.40755i	0.0151672	−	0.0507246i
$771$	52.6474	+	52.6474i	1.89605	+	1.89605i
$772$	−22.5017	−	14.7778i	−0.809854	−	0.531864i
$773$	4.48902	−	4.48902i	0.161459	−	0.161459i	−0.621754	−	0.783213i	$-0.713580\pi$
$773$	4.48902	−	4.48902i	0.161459	−	0.161459i	0.783213	+	0.621754i	$0.213580\pi$
$774$	−30.8178	+	16.6303i	−1.10772	+	0.597764i
$775$			21.4611i			0.770906i
$776$	−36.7275	+	30.8816i	−1.31844	+	1.10859i
$777$		−	18.6319i		−	0.668414i
$778$	10.7851	+	19.9861i	0.386666	+	0.716536i
$779$	7.52806	−	7.52806i	0.269721	−	0.269721i
$780$	−0.810142	−	3.91015i	−0.0290077	−	0.140006i
$781$	3.56654	+	3.56654i	0.127621	+	0.127621i
$782$	8.01379	+	2.39621i	0.286572	+	0.0856885i
$783$	−38.8329			−1.38777
$784$	9.49428	+	21.9285i	0.339082	+	0.783161i
$785$	−3.86252			−0.137859
$786$	16.2890	+	4.87061i	0.581011	+	0.173729i
$787$	11.9747	+	11.9747i	0.426850	+	0.426850i	0.887554	−	0.460704i	$-0.152403\pi$
$787$	11.9747	+	11.9747i	0.426850	+	0.426850i	−0.460704	+	0.887554i	$0.652403\pi$
$788$	−47.9210	+	9.92873i	−1.70712	+	0.353696i
$789$	−35.5248	+	35.5248i	−1.26472	+	1.26472i
$790$	1.25643	+	2.32830i	0.0447016	+	0.0828372i
$791$		−	8.86578i		−	0.315231i
$792$	−97.9315	−	8.46768i	−3.47985	−	0.300886i
$793$		−	59.6688i		−	2.11890i
$794$	32.7072	−	17.6498i	1.16073	−	0.626369i
$795$	−2.72940	+	2.72940i	−0.0968017	+	0.0968017i
$796$	15.7911	−	24.0446i	0.559700	−	0.852238i
$797$	3.52687	+	3.52687i	0.124928	+	0.124928i	0.766807	−	0.641878i	$-0.221845\pi$
$797$	3.52687	+	3.52687i	0.124928	+	0.124928i	−0.641878	+	0.766807i	$0.721845\pi$
$798$	−4.46031	+	14.9169i	−0.157893	+	0.528051i
$799$	0.815754			0.0288593
$800$	−3.31437	−	27.9459i	−0.117181	−	0.988036i
$801$	8.94412			0.316025
$802$	−6.45623	+	21.5919i	−0.227978	+	0.762437i
$803$	31.9706	+	31.9706i	1.12822	+	1.12822i
$804$	−7.24296	+	11.0286i	−0.255439	+	0.388950i
$805$	−0.672458	+	0.672458i	−0.0237010	+	0.0237010i
$806$	−23.3300	+	12.5896i	−0.821766	+	0.443451i
$807$			20.0853i			0.707037i
$808$	−0.722417	+	8.35499i	−0.0254145	+	0.293928i
$809$			11.8721i			0.417402i	0.977980	+	0.208701i	$0.0669235\pi$
$809$			11.8721i			0.417402i	−0.977980	+	0.208701i	$0.933076\pi$
$810$	0.404866	+	0.750264i	0.0142256	+	0.0263616i
$811$	7.06018	−	7.06018i	0.247916	−	0.247916i	−0.572199	−	0.820115i	$-0.693909\pi$
$811$	7.06018	−	7.06018i	0.247916	−	0.247916i	0.820115	+	0.572199i	$0.193909\pi$
$812$	11.1860	−	2.31762i	0.392552	−	0.0813326i
$813$	−41.4218	−	41.4218i	−1.45273	−	1.45273i
$814$	55.6244	+	16.6323i	1.94963	+	0.582963i
$815$	−1.50757			−0.0528078
$816$	−4.26035	+	10.7664i	−0.149142	+	0.376900i
$817$	−17.2837			−0.604679
$818$	−1.50542	−	0.450139i	−0.0526359	−	0.0157387i
$819$	16.7422	+	16.7422i	0.585020	+	0.585020i
$820$	0.182630	+	0.881466i	0.00637773	+	0.0307821i
$821$	−7.90352	+	7.90352i	−0.275835	+	0.275835i	−0.831444	−	0.555609i	$-0.812485\pi$
$821$	−7.90352	+	7.90352i	−0.275835	+	0.275835i	0.555609	+	0.831444i	$0.312485\pi$
$822$	5.52221	+	10.2333i	0.192609	+	0.356926i
$823$			29.3339i			1.02252i	0.859427	+	0.511258i	$0.170820\pi$
$823$			29.3339i			1.02252i	−0.859427	+	0.511258i	$0.829180\pi$
$824$	21.1611	+	25.1669i	0.737182	+	0.876730i
$825$			93.0374i			3.23915i
$826$	−7.84614	+	4.23403i	−0.273002	+	0.147321i
$827$	−12.8238	+	12.8238i	−0.445928	+	0.445928i	−0.893998	−	0.448070i	$-0.852111\pi$
$827$	−12.8238	+	12.8238i	−0.445928	+	0.445928i	0.448070	+	0.893998i	$0.352111\pi$
$828$	53.1857	+	34.9292i	1.84833	+	1.21387i
$829$	−12.8736	−	12.8736i	−0.447118	−	0.447118i	0.447277	−	0.894395i	$-0.352394\pi$
$829$	−12.8736	−	12.8736i	−0.447118	−	0.447118i	−0.894395	+	0.447277i	$0.852394\pi$
$830$	0.358060	−	1.19748i	0.0124284	−	0.0415651i
$831$	30.2419			1.04908
$832$	28.4352	−	19.9968i	0.985815	−	0.693264i
$833$	−5.97391			−0.206984
$834$	0.286409	−	0.957852i	0.00991753	−	0.0331677i
$835$	−0.252894	−	0.252894i	−0.00875177	−	0.00875177i
$836$	−40.5518	−	26.6320i	−1.40251	−	0.921088i
$837$	21.0079	−	21.0079i	0.726138	−	0.726138i
$838$	−6.60627	+	3.56496i	−0.228210	+	0.123149i
$839$		−	32.0690i		−	1.10714i	−0.832801	−	0.553572i	$-0.813264\pi$
$839$		−	32.0690i		−	1.10714i	0.832801	−	0.553572i	$-0.186736\pi$
$840$	−0.847227	−	1.00761i	−0.0292321	−	0.0347657i
$841$			2.79492i			0.0963766i
$842$	1.56245	+	2.89540i	0.0538457	+	0.0997822i
$843$	−47.6287	+	47.6287i	−1.64042	+	1.64042i
$844$	−5.97472	−	28.8370i	−0.205658	−	0.992610i
$845$	−0.660182	−	0.660182i	−0.0227110	−	0.0227110i
$846$	5.94555	+	1.77779i	0.204412	+	0.0611216i
$847$	−31.1395			−1.06997
$848$	−31.2452	−	12.3640i	−1.07297	−	0.424581i
$849$	−24.8992			−0.854539
$850$	6.74056	+	2.01550i	0.231199	+	0.0691312i
$851$	−26.5746	−	26.5746i	−0.910965	−	0.910965i
$852$	4.42571	−	0.916961i	0.151622	−	0.0314146i
$853$	−27.3066	+	27.3066i	−0.934960	+	0.934960i	−0.998010	−	0.0630503i	$-0.979917\pi$
$853$	−27.3066	+	27.3066i	−0.934960	+	0.934960i	0.0630503	+	0.998010i	$0.479917\pi$
$854$	−9.34189	−	17.3116i	−0.319673	−	0.592390i
$855$			3.20588i			0.109639i
$856$	−0.244543	+	2.82822i	−0.00835830	+	0.0966666i
$857$		−	20.4665i		−	0.699121i	−0.936914	−	0.349560i	$-0.886331\pi$
$857$		−	20.4665i		−	0.699121i	0.936914	−	0.349560i	$-0.113669\pi$
$858$	−101.140	+	54.5782i	−3.45285	+	1.86327i
$859$	15.1127	−	15.1127i	0.515638	−	0.515638i	−0.400610	−	0.916249i	$-0.631202\pi$
$859$	15.1127	−	15.1127i	0.515638	−	0.515638i	0.916249	+	0.400610i	$0.131202\pi$
$860$	0.802228	−	1.22153i	0.0273558	−	0.0416538i
$861$	−5.87910	−	5.87910i	−0.200359	−	0.200359i
$862$	5.82917	−	19.4948i	0.198542	−	0.663995i
$863$	−7.40206			−0.251969			−0.125985	−	0.992032i	$-0.540209\pi$
$863$	−7.40206			−0.251969			−0.125985	+	0.992032i	$0.540209\pi$
$864$	−24.1113	+	30.6000i	−0.820283	+	1.04103i
$865$	−0.984651			−0.0334791
$866$	−11.1100	+	37.1556i	−0.377532	+	1.26260i
$867$	−2.04684	−	2.04684i	−0.0695145	−	0.0695145i
$868$	−4.79763	+	7.30521i	−0.162842	+	0.247955i
$869$	53.8417	−	53.8417i	1.82645	−	1.82645i
$870$	3.22453	−	1.74006i	0.109322	−	0.0589935i
$871$			9.90331i			0.335561i
$872$	−4.08250	−	0.352995i	−0.138251	−	0.0119539i
$873$		−	91.2590i		−	3.08865i
$874$	14.9142	+	27.6376i	0.504479	+	0.934857i
$875$	−1.13410	+	1.13410i	−0.0383396	+	0.0383396i
$876$	39.6722	−	8.21966i	1.34040	−	0.277717i
$877$	−0.807629	−	0.807629i	−0.0272717	−	0.0272717i	0.693339	−	0.720611i	$-0.256139\pi$
$877$	−0.807629	−	0.807629i	−0.0272717	−	0.0272717i	−0.720611	+	0.693339i	$0.756139\pi$
$878$	28.6958	+	8.58036i	0.968435	+	0.289573i
$879$	−12.0131			−0.405191
$880$	3.76445	−	1.62988i	0.126900	−	0.0549431i
$881$	22.8408			0.769526			0.384763	−	0.923015i	$-0.374283\pi$
$881$	22.8408			0.769526			0.384763	+	0.923015i	$0.374283\pi$
$882$	−43.5403	−	13.0191i	−1.46608	−	0.438374i
$883$	8.29032	+	8.29032i	0.278992	+	0.278992i	0.832706	−	0.553715i	$-0.186790\pi$
$883$	8.29032	+	8.29032i	0.278992	+	0.278992i	−0.553715	+	0.832706i	$0.686790\pi$
$884$	1.76316	+	8.50990i	0.0593016	+	0.286219i
$885$	−2.02208	+	2.02208i	−0.0679716	+	0.0679716i
$886$	18.9504	+	35.1173i	0.636651	+	1.17979i
$887$		−	20.9534i		−	0.703546i	−0.936085	−	0.351773i	$-0.885579\pi$
$887$		−	20.9534i		−	0.703546i	0.936085	−	0.351773i	$-0.114421\pi$
$888$	39.8191	−	33.4812i	1.33624	−	1.12355i
$889$			16.0620i			0.538702i
$890$	−0.328482	+	0.177260i	−0.0110107	+	0.00594175i
$891$	17.3498	−	17.3498i	0.581239	−	0.581239i
$892$	−30.5384	−	20.0558i	−1.02250	−	0.671519i
$893$	2.16575	+	2.16575i	0.0724742	+	0.0724742i
$894$	−4.82567	+	16.1388i	−0.161395	+	0.539761i
$895$	−0.922149			−0.0308240
$896$	5.11911	−	10.2535i	0.171018	−	0.342546i
$897$	74.3943			2.48395
$898$	14.0559	−	47.0081i	0.469053	−	1.56868i
$899$	−17.2005	−	17.2005i	−0.573668	−	0.573668i
$900$	44.7355	+	29.3796i	1.49118	+	0.979321i
$901$	5.94015	−	5.94015i	0.197895	−	0.197895i
$902$	22.7999	−	12.3036i	0.759154	−	0.409664i
$903$			13.4978i			0.449180i
$904$	18.9475	−	15.9317i	0.630185	−	0.529880i
$905$			2.00866i			0.0667700i
$906$	−23.5968	−	43.7276i	−0.783953	−	1.45275i
$907$	−24.8227	+	24.8227i	−0.824223	+	0.824223i	−0.986711	−	0.162488i	$-0.948048\pi$
$907$	−24.8227	+	24.8227i	−0.824223	+	0.824223i	0.162488	+	0.986711i	$0.448048\pi$
$908$	−11.4667	−	55.3438i	−0.380534	−	1.83665i
$909$	−11.2776	−	11.2776i	−0.374054	−	0.374054i
$910$	−0.946681	−	0.283068i	−0.0313822	−	0.00938363i
$911$	12.4172			0.411401			0.205701	−	0.978615i	$-0.434053\pi$
$911$	12.4172			0.411401			0.205701	+	0.978615i	$0.434053\pi$
$912$	−39.8947	+	17.2730i	−1.32105	+	0.571967i
$913$	−35.9717			−1.19049
$914$	−24.1569	−	7.22319i	−0.799040	−	0.238922i
$915$	−4.46149	−	4.46149i	−0.147492	−	0.147492i
$916$	18.9312	−	3.92234i	0.625503	−	0.129598i
$917$	2.97477	−	2.97477i	0.0982357	−	0.0982357i
$918$	−4.62526	−	8.57113i	−0.152656	−	0.282890i
$919$			20.5870i			0.679103i	0.940587	+	0.339552i	$0.110275\pi$
$919$			20.5870i			0.679103i	−0.940587	+	0.339552i	$0.889725\pi$
$920$	−2.64554	−	0.228748i	−0.0872210	−	0.00754159i
$921$		−	0.808574i		−	0.0266434i
$922$	42.1720	−	22.7574i	1.38886	−	0.749474i
$923$	2.39876	−	2.39876i	0.0789562	−	0.0789562i
$924$	−20.7985	+	31.6693i	−0.684220	+	1.04184i
$925$	−22.3524	−	22.3524i	−0.734943	−	0.734943i
$926$	10.3972	−	34.7720i	0.341674	−	1.14268i
$927$	−62.5337			−2.05388
$928$	25.0542	+	19.7415i	0.822444	+	0.648045i
$929$	27.0561			0.887681			0.443841	−	0.896106i	$-0.353616\pi$
$929$	27.0561			0.887681			0.443841	+	0.896106i	$0.353616\pi$
$930$	−0.803069	+	2.68575i	−0.0263337	+	0.0880691i
$931$	−15.8602	−	15.8602i	−0.519797	−	0.519797i
$932$	24.4952	−	37.2981i	0.802367	−	1.22174i
$933$	21.1080	−	21.1080i	0.691046	−	0.691046i
$934$	−17.3830	+	9.38041i	−0.568788	+	0.306936i
$935$			1.02554i			0.0335386i
$936$	−5.69514	+	65.8662i	−0.186151	+	2.15290i
$937$			40.2132i			1.31371i	0.754018	+	0.656854i	$0.228113\pi$
$937$			40.2132i			1.31371i	−0.754018	+	0.656854i	$0.771887\pi$
$938$	1.55048	+	2.87322i	0.0506251	+	0.0938141i
$939$	6.05726	−	6.05726i	0.197671	−	0.197671i
$940$	−0.253590	+	0.0525411i	−0.00827118	+	0.00171370i
$941$	−10.2877	−	10.2877i	−0.335370	−	0.335370i	0.519252	−	0.854621i	$-0.326211\pi$
$941$	−10.2877	−	10.2877i	−0.335370	−	0.335370i	−0.854621	+	0.519252i	$0.826211\pi$
$942$	95.4378	+	28.5370i	3.10953	+	0.929786i
$943$	−16.7707			−0.546129
$944$	−23.1482	−	9.15990i	−0.753408	−	0.298129i
$945$	1.10734			0.0360219
$946$	−40.2970	−	12.0493i	−1.31017	−	0.391755i
$947$	−21.5285	−	21.5285i	−0.699581	−	0.699581i	0.264739	−	0.964320i	$-0.414714\pi$
$947$	−21.5285	−	21.5285i	−0.699581	−	0.699581i	−0.964320	+	0.264739i	$0.914714\pi$
$948$	−13.8427	−	66.8120i	−0.449591	−	2.16995i
$949$	21.5026	−	21.5026i	0.698003	−	0.698003i
$950$	12.5446	+	23.2466i	0.407000	+	0.754218i
$951$			50.9054i			1.65072i
$952$	1.84387	+	2.19291i	0.0597602	+	0.0710727i
$953$			22.2373i			0.720338i	0.932887	+	0.360169i	$0.117281\pi$
$953$			22.2373i			0.720338i	−0.932887	+	0.360169i	$0.882719\pi$
$954$	56.2397	−	30.3488i	1.82083	−	0.982578i
$955$	2.99206	−	2.99206i	0.0968208	−	0.0968208i
$956$	5.77842	+	3.79493i	0.186888	+	0.122737i
$957$	−74.5668	−	74.5668i	−2.41040	−	2.41040i
$958$	11.0820	−	37.0622i	0.358044	−	1.19743i
$959$	2.87733			0.0929139
$960$	0.630952	−	3.62131i	0.0203639	−	0.116877i
$961$	−12.3897			−0.399669
$962$	11.1865	−	37.4115i	0.360666	−	1.20619i
$963$	−3.81754	−	3.81754i	−0.123019	−	0.123019i
$964$	6.47036	+	4.24935i	0.208396	+	0.136862i
$965$	−1.51080	+	1.51080i	−0.0486343	+	0.0486343i
$966$	21.5838	−	11.6473i	0.694449	−	0.374747i
$967$		−	14.4501i		−	0.464683i	−0.972634	−	0.232342i	$-0.925361\pi$
$967$		−	14.4501i		−	0.464683i	0.972634	−	0.232342i	$-0.0746387\pi$
$968$	−55.9573	−	66.5499i	−1.79854	−	2.13900i
$969$		−	10.8684i		−	0.349143i
$970$	1.80862	+	3.35158i	0.0580713	+	0.107613i
$971$	6.18861	−	6.18861i	0.198602	−	0.198602i	−0.600799	−	0.799400i	$-0.705151\pi$
$971$	6.18861	−	6.18861i	0.198602	−	0.198602i	0.799400	+	0.600799i	$0.205151\pi$
$972$	3.92261	+	18.9325i	0.125818	+	0.607259i
$973$	−0.174927	−	0.174927i	−0.00560790	−	0.00560790i
$974$	33.5929	+	10.0447i	1.07639	+	0.321852i
$975$	62.5745			2.00399
$976$	20.2102	−	51.0737i	0.646914	−	1.63483i
$977$	47.9589			1.53434			0.767171	−	0.641443i	$-0.221664\pi$
$977$	47.9589			1.53434			0.767171	+	0.641443i	$0.221664\pi$
$978$	37.2501	+	11.1382i	1.19113	+	0.356160i
$979$	7.59611	+	7.59611i	0.242773	+	0.242773i
$980$	1.85708	−	0.384768i	0.0593223	−	0.0122910i
$981$	5.51057	−	5.51057i	0.175939	−	0.175939i
$982$	16.5524	+	30.6734i	0.528207	+	0.978829i
$983$			32.0505i			1.02225i	0.859506	+	0.511126i	$0.170771\pi$
$983$			32.0505i			1.02225i	−0.859506	+	0.511126i	$0.829229\pi$
$984$	1.99987	−	23.1292i	0.0637537	−	0.737332i
$985$			3.88412i			0.123758i
$986$	−7.01773	+	3.78699i	−0.223490	+	0.120602i
$987$	1.69136	−	1.69136i	0.0538367	−	0.0538367i
$988$	−17.9120	+	27.2741i	−0.569856	+	0.867704i
$989$	19.2519	+	19.2519i	0.612176	+	0.612176i
$990$	−2.23497	+	7.47453i	−0.0710321	+	0.237556i
$991$	37.1875			1.18130			0.590650	−	0.806928i	$-0.298872\pi$
$991$	37.1875			1.18130			0.590650	+	0.806928i	$0.298872\pi$
$992$	−24.2336	+	2.87409i	−0.769418	+	0.0912526i
$993$	27.7428			0.880390
$994$	0.320391	−	1.07150i	0.0101622	−	0.0339860i
$995$	−1.61439	−	1.61439i	−0.0511796	−	0.0511796i
$996$	−17.6944	+	26.9428i	−0.560669	+	0.853714i
$997$	−3.51747	+	3.51747i	−0.111399	+	0.111399i	−0.760609	−	0.649210i	$-0.775100\pi$
$997$	−3.51747	+	3.51747i	−0.111399	+	0.111399i	0.649210	+	0.760609i	$0.275100\pi$
$998$	26.5269	−	14.3148i	0.839693	−	0.453126i
$999$			43.7607i			1.38453i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	272.2.l.b.205.6	yes	30
4.3	odd	2		1088.2.l.b.273.14		30
16.5	even	4	inner	272.2.l.b.69.6	✓	30
16.11	odd	4		1088.2.l.b.817.14		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
272.2.l.b.69.6	✓	30	16.5	even	4	inner
272.2.l.b.205.6	yes	30	1.1	even	1	trivial
1088.2.l.b.273.14		30	4.3	odd	2
1088.2.l.b.817.14		30	16.11	odd	4

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:	\( N \)	\(=\)	\( 272 = 2^{4} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	272.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.405142 + 1.35494i) q^{2} +(-2.04684 - 2.04684i) q^{3} +(-1.67172 - 1.09789i) q^{4} +(-0.112242 + 0.112242i) q^{5} +(3.60261 - 1.94409i) q^{6} -1.01296i q^{7} +(2.16485 - 1.82028i) q^{8} +5.37914i q^{9} +(-0.106607 - 0.197555i) q^{10} +(-4.56843 + 4.56843i) q^{11} +(1.17455 + 5.66895i) q^{12} +(3.07260 + 3.07260i) q^{13} +(1.37250 + 0.410394i) q^{14} +0.459483 q^{15} +(1.58929 + 3.67072i) q^{16} -1.00000 q^{17} +(-7.28841 - 2.17932i) q^{18} +(-2.65491 - 2.65491i) q^{19} +(0.310865 - 0.0644080i) q^{20} +(-2.07337 + 2.07337i) q^{21} +(-4.33908 - 8.04081i) q^{22} +5.91450i q^{23} +(-8.15694 - 0.705293i) q^{24} +4.97480i q^{25} +(-5.40803 + 2.91835i) q^{26} +(4.86974 - 4.86974i) q^{27} +(-1.11212 + 1.69339i) q^{28} +(-3.98716 - 3.98716i) q^{29} +(-0.186156 + 0.622571i) q^{30} +4.31396 q^{31} +(-5.61748 + 0.666231i) q^{32} +18.7017 q^{33} +(0.405142 - 1.35494i) q^{34} +(0.113697 + 0.113697i) q^{35} +(5.90569 - 8.99242i) q^{36} +(-4.49312 + 4.49312i) q^{37} +(4.67286 - 2.52163i) q^{38} -12.5783i q^{39} +(-0.0386758 + 0.447298i) q^{40} +2.83552i q^{41} +(-1.96928 - 3.64931i) q^{42} +(3.25504 - 3.25504i) q^{43} +(12.6527 - 2.62152i) q^{44} +(-0.603764 - 0.603764i) q^{45} +(-8.01379 - 2.39621i) q^{46} -0.815754 q^{47} +(4.26035 - 10.7664i) q^{48} +5.97391 q^{49} +(-6.74056 - 2.01550i) q^{50} +(2.04684 + 2.04684i) q^{51} +(-1.76316 - 8.50990i) q^{52} +(-5.94015 + 5.94015i) q^{53} +(4.62526 + 8.57113i) q^{54} -1.02554i q^{55} +(-1.84387 - 2.19291i) q^{56} +10.8684i q^{57} +(7.01773 - 3.78699i) q^{58} +(-4.40078 + 4.40078i) q^{59} +(-0.768126 - 0.504460i) q^{60} +(-9.70982 - 9.70982i) q^{61} +(-1.74777 + 5.84516i) q^{62} +5.44887 q^{63} +(1.37318 - 7.88127i) q^{64} -0.689749 q^{65} +(-7.57686 + 25.3397i) q^{66} +(1.61155 + 1.61155i) q^{67} +(1.67172 + 1.09789i) q^{68} +(12.1061 - 12.1061i) q^{69} +(-0.200115 + 0.107989i) q^{70} -0.780693i q^{71} +(9.79153 + 11.6451i) q^{72} -6.99816i q^{73} +(-4.26755 - 7.90826i) q^{74} +(10.1826 - 10.1826i) q^{75} +(1.52348 + 7.35306i) q^{76} +(4.62764 + 4.62764i) q^{77} +(17.0428 + 5.09600i) q^{78} -11.7856 q^{79} +(-0.590392 - 0.233623i) q^{80} -3.79775 q^{81} +(-3.84196 - 1.14879i) q^{82} +(3.93699 + 3.93699i) q^{83} +(5.74243 - 1.18977i) q^{84} +(0.112242 - 0.112242i) q^{85} +(3.09163 + 5.72913i) q^{86} +16.3222i q^{87} +(-1.57417 + 18.2058i) q^{88} -1.66274i q^{89} +(1.06267 - 0.573453i) q^{90} +(3.11243 - 3.11243i) q^{91} +(6.49345 - 9.88739i) q^{92} +(-8.83001 - 8.83001i) q^{93} +(0.330496 - 1.10530i) q^{94} +0.595984 q^{95} +(12.8618 + 10.1344i) q^{96} -16.9653 q^{97} +(-2.42028 + 8.09428i) q^{98} +(-24.5742 - 24.5742i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 2 q^{2} - 2 q^{3} - 2 q^{4} - 2 q^{5} + 8 q^{6} + 2 q^{8} - 6 q^{10} - 10 q^{11} - 2 q^{12} - 6 q^{13} - 22 q^{14} - 28 q^{15} + 2 q^{16} - 30 q^{17} + 8 q^{18} + 10 q^{19} - 10 q^{20} - 4 q^{21}+ \cdots + 54 q^{99}+O(q^{100}) \) 30 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 - 2 * q^5 + 8 * q^6 + 2 * q^8 - 6 * q^10 - 10 * q^11 - 2 * q^12 - 6 * q^13 - 22 * q^14 - 28 * q^15 + 2 * q^16 - 30 * q^17 + 8 * q^18 + 10 * q^19 - 10 * q^20 - 4 * q^21 + 28 * q^22 + 18 * q^24 + 6 * q^26 + 4 * q^27 + 8 * q^28 - 18 * q^29 - 56 * q^30 + 48 * q^31 - 38 * q^32 - 12 * q^33 - 2 * q^34 + 16 * q^35 + 20 * q^36 + 6 * q^37 + 42 * q^38 + 10 * q^40 + 12 * q^42 + 2 * q^43 + 22 * q^44 + 42 * q^45 - 14 * q^46 - 32 * q^47 - 62 * q^48 - 38 * q^49 - 28 * q^50 + 2 * q^51 - 10 * q^52 - 6 * q^53 + 40 * q^54 + 96 * q^56 + 62 * q^58 - 14 * q^59 - 28 * q^60 + 6 * q^61 - 74 * q^62 + 84 * q^63 - 38 * q^64 - 12 * q^65 + 26 * q^67 + 2 * q^68 + 12 * q^69 + 48 * q^70 + 44 * q^72 + 42 * q^74 - 26 * q^75 - 38 * q^76 - 28 * q^77 - 56 * q^78 - 72 * q^79 - 38 * q^80 - 10 * q^81 - 76 * q^82 - 34 * q^83 + 104 * q^84 + 2 * q^85 + 34 * q^86 - 2 * q^88 + 70 * q^90 + 16 * q^91 - 40 * q^92 - 24 * q^93 - 44 * q^94 + 76 * q^95 - 126 * q^96 - 28 * q^97 - 30 * q^98 + 54 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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