LMFDB - Embedded newform 29.3.f.a.15.2

Newspace parameters

Level:	$ N $	$=$	$ 29 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	29.f (of order $28$, degree $12$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$0.790192766645$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$4$ over $\Q(\zeta_{28})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{28}]$

Embedding invariants

Embedding label			15.2
Character	$\chi$	$=$	29.15
Dual form			29.3.f.a.2.2

$q$-expansion

$f(q)$	$=$	$q+(-1.68783 + 0.190173i) q^{2} +(-3.78594 + 2.37886i) q^{3} +(-1.08711 + 0.248126i) q^{4} +(0.141728 + 0.113024i) q^{5} +(5.93762 - 4.73509i) q^{6} +(-1.55116 + 6.79606i) q^{7} +(8.20045 - 2.86946i) q^{8} +(4.76938 - 9.90371i) q^{9} +O(q^{10})$	\(q+(-1.68783 + 0.190173i) q^{2} +(-3.78594 + 2.37886i) q^{3} +(-1.08711 + 0.248126i) q^{4} +(0.141728 + 0.113024i) q^{5} +(5.93762 - 4.73509i) q^{6} +(-1.55116 + 6.79606i) q^{7} +(8.20045 - 2.86946i) q^{8} +(4.76938 - 9.90371i) q^{9} +(-0.260707 - 0.163813i) q^{10} +(-12.2566 - 4.28875i) q^{11} +(3.52547 - 3.52547i) q^{12} +(9.66173 + 20.0628i) q^{13} +(1.32566 - 11.7656i) q^{14} +(-0.805444 - 0.0907517i) q^{15} +(-9.27670 + 4.46742i) q^{16} +(-5.90660 - 5.90660i) q^{17} +(-6.16648 + 17.6228i) q^{18} +(-10.7431 + 17.0975i) q^{19} +(-0.182118 - 0.0877036i) q^{20} +(-10.2943 - 29.4194i) q^{21} +(21.5026 + 4.90782i) q^{22} +(15.0384 + 18.8575i) q^{23} +(-24.2203 + 30.3713i) q^{24} +(-5.55571 - 24.3412i) q^{25} +(-20.1228 - 32.0252i) q^{26} +(0.997389 + 8.85208i) q^{27} -7.77294i q^{28} +(28.5764 - 4.93832i) q^{29} +1.37671 q^{30} +(35.5909 - 4.01014i) q^{31} +(-14.6174 + 9.18473i) q^{32} +(56.6049 - 12.9197i) q^{33} +(11.0926 + 8.84605i) q^{34} +(-0.987964 + 0.787875i) q^{35} +(-2.72747 + 11.9498i) q^{36} +(-23.0925 + 8.08043i) q^{37} +(14.8810 - 30.9007i) q^{38} +(-84.3053 - 52.9725i) q^{39} +(1.48655 + 0.520168i) q^{40} +(-14.1288 + 14.1288i) q^{41} +(22.9698 + 47.6973i) q^{42} +(-4.31425 + 38.2901i) q^{43} +(14.3884 + 1.62118i) q^{44} +(1.79532 - 0.864579i) q^{45} +(-28.9684 - 28.9684i) q^{46} +(1.53295 - 4.38091i) q^{47} +(24.4936 - 38.9814i) q^{48} +(0.367152 + 0.176811i) q^{49} +(14.0061 + 40.0272i) q^{50} +(36.4130 + 8.31102i) q^{51} +(-15.4815 - 19.4131i) q^{52} +(-51.0246 + 63.9828i) q^{53} +(-3.36685 - 14.7511i) q^{54} +(-1.25237 - 1.99313i) q^{55} +(6.78085 + 60.1817i) q^{56} -90.2863i q^{57} +(-47.2930 + 13.7695i) q^{58} +28.0326 q^{59} +(0.898124 - 0.101194i) q^{60} +(-3.26475 + 2.05138i) q^{61} +(-59.3088 + 13.5368i) q^{62} +(59.9082 + 47.7752i) q^{63} +(55.1251 - 43.9608i) q^{64} +(-0.898247 + 3.93548i) q^{65} +(-93.0824 + 32.5709i) q^{66} +(-2.88318 + 5.98698i) q^{67} +(7.88670 + 4.95554i) q^{68} +(-101.794 - 35.6192i) q^{69} +(1.51768 - 1.51768i) q^{70} +(-15.5711 - 32.3337i) q^{71} +(10.6927 - 94.9004i) q^{72} +(103.524 + 11.6644i) q^{73} +(37.4396 - 18.0300i) q^{74} +(78.9378 + 78.9378i) q^{75} +(7.43657 - 21.2525i) q^{76} +(48.1585 - 76.6437i) q^{77} +(152.367 + 73.3760i) q^{78} +(-28.1618 - 80.4819i) q^{79} +(-1.81970 - 0.415334i) q^{80} +(36.8483 + 46.2063i) q^{81} +(21.1601 - 26.5339i) q^{82} +(-6.13681 - 26.8871i) q^{83} +(18.4908 + 29.4279i) q^{84} +(-0.169541 - 1.50472i) q^{85} -65.4475i q^{86} +(-96.4410 + 86.6755i) q^{87} -112.816 q^{88} +(26.8243 - 3.02237i) q^{89} +(-2.86577 + 1.80068i) q^{90} +(-151.335 + 34.5412i) q^{91} +(-21.0274 - 16.7688i) q^{92} +(-125.205 + 99.8480i) q^{93} +(-1.75422 + 7.68575i) q^{94} +(-3.45503 + 1.20897i) q^{95} +(33.4914 - 69.5456i) q^{96} +(-6.09419 - 3.82923i) q^{97} +(-0.653314 - 0.228604i) q^{98} +(-100.931 + 100.931i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48q - 16q^{2} - 12q^{3} - 14q^{4} - 14q^{5} - 14q^{6} - 10q^{7} + 28q^{8} - 14q^{9} + O(q^{10}) $	\( 48q - 16q^{2} - 12q^{3} - 14q^{4} - 14q^{5} - 14q^{6} - 10q^{7} + 28q^{8} - 14q^{9} - 20q^{10} - 8q^{11} - 68q^{12} - 14q^{13} + 26q^{14} - 4q^{15} + 18q^{16} - 26q^{17} - 34q^{18} + 2q^{19} + 46q^{20} + 218q^{21} + 154q^{22} + 56q^{23} + 154q^{24} - 34q^{25} + 110q^{26} + 126q^{27} - 170q^{29} + 24q^{30} - 88q^{31} - 132q^{32} - 224q^{33} - 224q^{34} - 210q^{35} - 434q^{36} - 56q^{37} - 294q^{38} - 232q^{39} - 492q^{40} - 34q^{41} - 14q^{42} + 176q^{43} + 126q^{44} + 114q^{45} + 744q^{46} + 208q^{47} + 640q^{48} + 506q^{49} + 732q^{50} + 322q^{51} + 690q^{52} - 14q^{53} - 36q^{54} + 284q^{55} + 332q^{56} - 508q^{58} - 44q^{59} - 316q^{60} - 30q^{61} - 504q^{62} - 686q^{63} - 896q^{64} - 554q^{65} - 608q^{66} - 574q^{67} - 796q^{68} - 806q^{69} - 1066q^{70} + 224q^{71} + 748q^{72} - 22q^{73} + 820q^{74} + 768q^{75} + 514q^{76} + 436q^{77} + 282q^{78} + 564q^{79} + 1162q^{80} + 670q^{81} - 18q^{82} - 126q^{83} + 572q^{84} + 38q^{85} - 118q^{87} - 384q^{88} - 160q^{89} - 828q^{90} - 434q^{91} - 1022q^{92} - 406q^{93} - 2q^{94} - 642q^{95} - 1176q^{96} + 604q^{97} - 102q^{98} + 316q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/29\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{27}{28}\right)$

Coefficient data

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

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

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

$2$	−1.68783	+	0.190173i	−0.843915	+	0.0950863i	−0.523326	−	0.852132i	$-0.675309\pi$
$2$	−1.68783	+	0.190173i	−0.843915	+	0.0950863i	−0.320588	+	0.947219i	$0.603881\pi$
$3$	−3.78594	+	2.37886i	−1.26198	+	0.792954i	−0.985763	−	0.168142i	$-0.946223\pi$
$3$	−3.78594	+	2.37886i	−1.26198	+	0.792954i	−0.276216	+	0.961096i	$0.589080\pi$
$4$	−1.08711	+	0.248126i	−0.271777	+	0.0620314i
$5$	0.141728	+	0.113024i	0.0283456	+	0.0226049i	0.637560	−	0.770401i	$-0.279944\pi$
$5$	0.141728	+	0.113024i	0.0283456	+	0.0226049i	−0.609215	+	0.793005i	$0.708515\pi$
$6$	5.93762	−	4.73509i	0.989603	−	0.789182i
$7$	−1.55116	+	6.79606i	−0.221594	+	0.970865i	0.734685	+	0.678408i	$0.237330\pi$
$7$	−1.55116	+	6.79606i	−0.221594	+	0.970865i	−0.956279	+	0.292457i	$0.905527\pi$
$8$	8.20045	−	2.86946i	1.02506	−	0.358683i
$9$	4.76938	−	9.90371i	0.529931	−	1.10041i
$10$	−0.260707	−	0.163813i	−0.0260707	−	0.0163813i
$11$	−12.2566	−	4.28875i	−1.11423	−	0.389887i	−0.290505	−	0.956873i	$-0.593823\pi$
$11$	−12.2566	−	4.28875i	−1.11423	−	0.389887i	−0.823727	+	0.566987i	$0.808109\pi$
$12$	3.52547	−	3.52547i	0.293789	−	0.293789i
$13$	9.66173	+	20.0628i	0.743210	+	1.54329i	0.836694	+	0.547671i	$0.184486\pi$
$13$	9.66173	+	20.0628i	0.743210	+	1.54329i	−0.0934833	+	0.995621i	$0.529800\pi$
$14$	1.32566	−	11.7656i	0.0946901	−	0.840398i
$15$	−0.805444	−	0.0907517i	−0.0536962	−	0.00605011i
$16$	−9.27670	+	4.46742i	−0.579794	+	0.279214i
$17$	−5.90660	−	5.90660i	−0.347447	−	0.347447i	0.511711	−	0.859158i	$-0.329012\pi$
$17$	−5.90660	−	5.90660i	−0.347447	−	0.347447i	−0.859158	+	0.511711i	$0.829012\pi$
$18$	−6.16648	+	17.6228i	−0.342582	+	0.979043i
$19$	−10.7431	+	17.0975i	−0.565425	+	0.899868i	−1.00000		0.000767373i	$-0.999756\pi$
$19$	−10.7431	+	17.0975i	−0.565425	+	0.899868i	0.434575	+	0.900636i	$0.356899\pi$
$20$	−0.182118	−	0.0877036i	−0.00910592	−	0.00438518i
$21$	−10.2943	−	29.4194i	−0.490205	−	1.40093i
$22$	21.5026	+	4.90782i	0.977390	+	0.223083i
$23$	15.0384	+	18.8575i	0.653843	+	0.819893i	0.992657	−	0.120960i	$-0.0385973\pi$
$23$	15.0384	+	18.8575i	0.653843	+	0.819893i	−0.338814	+	0.940853i	$0.610026\pi$
$24$	−24.2203	+	30.3713i	−1.00918	+	1.26547i
$25$	−5.55571	−	24.3412i	−0.222228	−	0.973646i
$26$	−20.1228	−	32.0252i	−0.773952	−	1.23174i
$27$	0.997389	+	8.85208i	0.0369403	+	0.327855i
$28$		−	7.77294i		−	0.277605i
$29$	28.5764	−	4.93832i	0.985395	−	0.170287i
$29$	28.5764	−	4.93832i	0.985395	−	0.170287i
$30$	1.37671			0.0458903
$31$	35.5909	−	4.01014i	1.14809	−	0.129359i	0.482655	−	0.875811i	$-0.339673\pi$
$31$	35.5909	−	4.01014i	1.14809	−	0.129359i	0.665440	+	0.746451i	$0.268244\pi$
$32$	−14.6174	+	9.18473i	−0.456794	+	0.287023i
$33$	56.6049	−	12.9197i	1.71530	−	0.391506i
$34$	11.0926	+	8.84605i	0.326253	+	0.260178i
$35$	−0.987964	+	0.787875i	−0.0282275	+	0.0225107i
$36$	−2.72747	+	11.9498i	−0.0757631	+	0.331940i
$37$	−23.0925	+	8.08043i	−0.624123	+	0.218390i	−0.623767	−	0.781610i	$-0.714399\pi$
$37$	−23.0925	+	8.08043i	−0.624123	+	0.218390i	−0.000355153		1.00000i	$0.500113\pi$
$38$	14.8810	−	30.9007i	0.391605	−	0.813176i
$39$	−84.3053	−	52.9725i	−2.16167	−	1.35827i
$40$	1.48655	+	0.520168i	0.0371639	+	0.0130042i
$41$	−14.1288	+	14.1288i	−0.344605	+	0.344605i	−0.858095	−	0.513490i	$-0.828352\pi$
$41$	−14.1288	+	14.1288i	−0.344605	+	0.344605i	0.513490	+	0.858095i	$0.328352\pi$
$42$	22.9698	+	47.6973i	0.546900	+	1.13565i
$43$	−4.31425	+	38.2901i	−0.100331	+	0.890466i	0.838221	+	0.545330i	$0.183596\pi$
$43$	−4.31425	+	38.2901i	−0.100331	+	0.890466i	−0.938553	+	0.345136i	$0.887833\pi$
$44$	14.3884	+	1.62118i	0.327008	+	0.0368450i
$45$	1.79532	−	0.864579i	0.0398959	−	0.0192129i
$46$	−28.9684	−	28.9684i	−0.629748	−	0.629748i
$47$	1.53295	−	4.38091i	0.0326159	−	0.0932108i	−0.926424	−	0.376482i	$-0.877134\pi$
$47$	1.53295	−	4.38091i	0.0326159	−	0.0932108i	0.959040	+	0.283271i	$0.0914195\pi$
$48$	24.4936	−	38.9814i	0.510284	−	0.812112i
$49$	0.367152	+	0.176811i	0.00749289	+	0.00360839i
$50$	14.0061	+	40.0272i	0.280122	+	0.800544i
$51$	36.4130	+	8.31102i	0.713980	+	0.162961i
$52$	−15.4815	−	19.4131i	−0.297720	−	0.373330i
$53$	−51.0246	+	63.9828i	−0.962728	+	1.20722i	0.0155405	+	0.999879i	$0.495053\pi$
$53$	−51.0246	+	63.9828i	−0.962728	+	1.20722i	−0.978268	+	0.207343i	$0.933518\pi$
$54$	−3.36685	−	14.7511i	−0.0623490	−	0.273169i
$55$	−1.25237	−	1.99313i	−0.0227703	−	0.0362387i
$56$	6.78085	+	60.1817i	0.121087	+	1.07467i
$57$		−	90.2863i		−	1.58397i
$58$	−47.2930	+	13.7695i	−0.815397	+	0.237405i
$59$	28.0326			0.475129			0.237564	−	0.971372i	$-0.423651\pi$
$59$	28.0326			0.475129			0.237564	+	0.971372i	$0.423651\pi$
$60$	0.898124	−	0.101194i	0.0149687	−	0.00168657i
$61$	−3.26475	+	2.05138i	−0.0535205	+	0.0336292i	−0.558527	−	0.829487i	$-0.688633\pi$
$61$	−3.26475	+	2.05138i	−0.0535205	+	0.0336292i	0.505006	+	0.863116i	$0.331490\pi$
$62$	−59.3088	+	13.5368i	−0.956594	+	0.218336i
$63$	59.9082	+	47.7752i	0.950923	+	0.758336i
$64$	55.1251	−	43.9608i	0.861329	−	0.686887i
$65$	−0.898247	+	3.93548i	−0.0138192	+	0.0605458i
$66$	−93.0824	+	32.5709i	−1.41034	+	0.493499i
$67$	−2.88318	+	5.98698i	−0.0430325	+	0.0893579i	−0.921377	−	0.388671i	$-0.872934\pi$
$67$	−2.88318	+	5.98698i	−0.0430325	+	0.0893579i	0.878344	+	0.478029i	$0.158649\pi$
$68$	7.88670	+	4.95554i	0.115981	+	0.0728756i
$69$	−101.794	−	35.6192i	−1.47527	−	0.516221i
$70$	1.51768	−	1.51768i	0.0216812	−	0.0216812i
$71$	−15.5711	−	32.3337i	−0.219311	−	0.455404i	0.762065	−	0.647501i	$-0.224186\pi$
$71$	−15.5711	−	32.3337i	−0.219311	−	0.455404i	−0.981376	+	0.192096i	$0.938471\pi$
$72$	10.6927	−	94.9004i	0.148510	−	1.31806i
$73$	103.524	+	11.6644i	1.41814	+	0.159786i	0.787511	−	0.616301i	$-0.211370\pi$
$73$	103.524	+	11.6644i	1.41814	+	0.159786i	0.630626	+	0.776087i	$0.282798\pi$
$74$	37.4396	−	18.0300i	0.505940	−	0.243648i
$75$	78.9378	+	78.9378i	1.05250	+	1.05250i
$76$	7.43657	−	21.2525i	0.0978496	−	0.279638i
$77$	48.1585	−	76.6437i	0.625434	−	0.995373i
$78$	152.367	+	73.3760i	1.95342	+	0.940718i
$79$	−28.1618	−	80.4819i	−0.356479	−	1.01876i	−0.972877	−	0.231323i	$-0.925694\pi$
$79$	−28.1618	−	80.4819i	−0.356479	−	1.01876i	0.616398	−	0.787435i	$-0.288591\pi$
$80$	−1.81970	−	0.415334i	−0.0227462	−	0.00519168i
$81$	36.8483	+	46.2063i	0.454918	+	0.570449i
$82$	21.1601	−	26.5339i	0.258050	−	0.323584i
$83$	−6.13681	−	26.8871i	−0.0739375	−	0.323941i	0.924410	−	0.381399i	$-0.124558\pi$
$83$	−6.13681	−	26.8871i	−0.0739375	−	0.323941i	−0.998348	+	0.0574578i	$0.981701\pi$
$84$	18.4908	+	29.4279i	0.220128	+	0.350332i
$85$	−0.169541	−	1.50472i	−0.00199461	−	0.0177026i
$86$		−	65.4475i		−	0.761018i
$87$	−96.4410	+	86.6755i	−1.10852	+	0.996271i
$88$	−112.816			−1.28200
$89$	26.8243	−	3.02237i	0.301397	−	0.0339592i	0.0400288	−	0.999199i	$-0.487255\pi$
$89$	26.8243	−	3.02237i	0.301397	−	0.0339592i	0.261368	+	0.965239i	$0.415826\pi$
$90$	−2.86577	+	1.80068i	−0.0318419	+	0.0200076i
$91$	−151.335	+	34.5412i	−1.66302	+	0.379573i
$92$	−21.0274	−	16.7688i	−0.228559	−	0.182270i
$93$	−125.205	+	99.8480i	−1.34630	+	1.07363i
$94$	−1.75422	+	7.68575i	−0.0186619	+	0.0817633i
$95$	−3.45503	+	1.20897i	−0.0363688	+	0.0127260i
$96$	33.4914	−	69.5456i	0.348869	−	0.724433i
$97$	−6.09419	−	3.82923i	−0.0628267	−	0.0394766i	0.500252	−	0.865880i	$-0.333241\pi$
$97$	−6.09419	−	3.82923i	−0.0628267	−	0.0394766i	−0.563079	+	0.826403i	$0.690383\pi$
$98$	−0.653314	−	0.228604i	−0.00666647	−	0.00233270i
$99$	−100.931	+	100.931i	−1.01950	+	1.01950i
$100$	12.0793	+	25.0830i	0.120793	+	0.250830i
$101$	−12.4952	+	110.898i	−0.123715	+	1.09800i	0.766433	+	0.642324i	$0.222030\pi$
$101$	−12.4952	+	110.898i	−0.123715	+	1.09800i	−0.890148	+	0.455672i	$0.849399\pi$
$102$	−63.0394	−	7.10284i	−0.618033	−	0.0696356i
$103$	108.481	−	52.2416i	1.05321	−	0.507200i	0.174552	−	0.984648i	$-0.444152\pi$
$103$	108.481	−	52.2416i	1.05321	−	0.507200i	0.878660	+	0.477448i	$0.158438\pi$
$104$	136.800	+	136.800i	1.31538	+	1.31538i
$105$	1.86612	−	5.33307i	0.0177726	−	0.0507912i
$106$	73.9530	−	117.696i	0.697670	−	1.11033i
$107$	−127.998	−	61.6404i	−1.19624	−	0.576079i	−0.273638	−	0.961833i	$-0.588227\pi$
$107$	−127.998	−	61.6404i	−1.19624	−	0.576079i	−0.922602	+	0.385754i	$0.873941\pi$
$108$	−3.28070	−	9.37570i	−0.0303768	−	0.0868120i
$109$	30.7554	+	7.01972i	0.282160	+	0.0644011i	0.361259	−	0.932466i	$-0.382347\pi$
$109$	30.7554	+	7.01972i	0.282160	+	0.0644011i	−0.0790990	+	0.996867i	$0.525204\pi$
$110$	2.49282	+	3.12590i	0.0226620	+	0.0284172i
$111$	68.2046	−	85.5259i	0.614456	−	0.770504i
$112$	−15.9713	−	69.9747i	−0.142601	−	0.624774i
$113$	−51.3355	−	81.7000i	−0.454297	−	0.723009i	0.538526	−	0.842609i	$-0.318982\pi$
$113$	−51.3355	−	81.7000i	−0.454297	−	0.723009i	−0.992822	+	0.119600i	$0.961839\pi$
$114$	17.1700	+	152.388i	0.150614	+	1.33674i
$115$			4.37235i			0.0380205i
$116$	−29.8404	+	12.4590i	−0.257245	+	0.107406i
$117$	244.777			2.09211
$118$	−47.3143	+	5.33104i	−0.400968	+	0.0451783i
$119$	49.3036	−	30.9795i	0.414316	−	0.260332i
$120$	−6.86541	+	1.56698i	−0.0572117	+	0.0130582i
$121$	37.2281	+	29.6884i	0.307671	+	0.245359i
$122$	5.12023	−	4.08324i	0.0419691	−	0.0334692i
$123$	19.8803	−	87.1012i	0.161628	−	0.708140i
$124$	−37.6962	+	13.1905i	−0.304002	+	0.106375i
$125$	3.93008	−	8.16089i	0.0314406	−	0.0652871i
$126$	−110.200	−	69.2434i	−0.874605	−	0.549551i
$127$	95.5607	+	33.4381i	0.752446	+	0.263292i	0.679132	−	0.734017i	$-0.262357\pi$
$127$	95.5607	+	33.4381i	0.752446	+	0.263292i	0.0733147	+	0.997309i	$0.476642\pi$
$128$	−35.8531	+	35.8531i	−0.280102	+	0.280102i
$129$	−74.7533	−	155.227i	−0.579483	−	1.20331i
$130$	0.767667	−	6.81324i	0.00590513	−	0.0524095i
$131$	95.6113	+	10.7728i	0.729857	+	0.0822352i	0.469070	−	0.883161i	$-0.344589\pi$
$131$	95.6113	+	10.7728i	0.729857	+	0.0822352i	0.260787	+	0.965396i	$0.416018\pi$
$132$	−58.3300	+	28.0903i	−0.441894	+	0.212805i
$133$	−99.5314	−	99.5314i	−0.748356	−	0.748356i
$134$	3.72775	−	10.6533i	0.0278190	−	0.0795022i
$135$	−0.859143	+	1.36732i	−0.00636402	+	0.0101283i
$136$	−65.3855	−	31.4880i	−0.480776	−	0.231529i
$137$	60.7818	+	173.704i	0.443662	+	1.26791i	0.921127	+	0.389263i	$0.127270\pi$
$137$	60.7818	+	173.704i	0.443662	+	1.26791i	−0.477464	+	0.878651i	$0.658444\pi$
$138$	178.584	+	40.7607i	1.29409	+	0.295368i
$139$	116.483	+	146.065i	0.838009	+	1.05083i	0.997969	+	0.0637063i	$0.0202921\pi$
$139$	116.483	+	146.065i	0.838009	+	1.05083i	−0.159960	+	0.987124i	$0.551136\pi$
$140$	0.878533	−	1.10165i	0.00627524	−	0.00786890i
$141$	4.61794	+	20.2325i	0.0327513	+	0.143493i
$142$	32.4303	+	51.6126i	0.228383	+	0.363469i
$143$	−32.3752	−	287.338i	−0.226400	−	2.00935i
$144$			113.181i			0.785976i
$145$	4.60824	+	2.52994i	0.0317810	+	0.0174479i
$146$	−176.949			−1.21198
$147$	−1.81062	+	0.204008i	−0.0123172	+	0.00138781i
$148$	23.0992	−	14.5142i	0.156075	−	0.0980687i
$149$	112.412	−	25.6572i	0.754440	−	0.172196i	0.172031	−	0.985092i	$-0.444967\pi$
$149$	112.412	−	25.6572i	0.754440	−	0.172196i	0.582410	+	0.812896i	$0.302110\pi$
$150$	−148.245	−	118.222i	−0.988302	−	0.788145i
$151$	−7.95750	+	6.34590i	−0.0526987	+	0.0420258i	−0.649485	−	0.760374i	$-0.725015\pi$
$151$	−7.95750	+	6.34590i	−0.0526987	+	0.0420258i	0.596786	+	0.802400i	$0.296444\pi$
$152$	−39.0374	+	171.034i	−0.256825	+	1.12522i
$153$	−86.6680	+	30.3265i	−0.566458	+	0.198212i
$154$	−66.7077	+	138.520i	−0.433167	+	0.899480i
$155$	5.49748	+	3.45430i	0.0354676	+	0.0222858i
$156$	104.793	+	36.6687i	0.671750	+	0.235055i
$157$	−54.2399	+	54.2399i	−0.345477	+	0.345477i	−0.858422	−	0.512945i	$-0.828555\pi$
$157$	−54.2399	+	54.2399i	−0.345477	+	0.345477i	0.512945	+	0.858422i	$0.328555\pi$
$158$	62.8378	+	130.484i	0.397708	+	0.825849i
$159$	40.9696	−	363.615i	0.257670	−	2.28689i
$160$	−3.10980	−	0.350390i	−0.0194363	−	0.00218994i
$161$	−151.484	+	72.9508i	−0.940894	+	0.453111i
$162$	−70.9809	−	70.9809i	−0.438154	−	0.438154i
$163$	−9.39776	+	26.8573i	−0.0576550	+	0.164768i	−0.969109	−	0.246634i	$-0.920675\pi$
$163$	−9.39776	+	26.8573i	−0.0576550	+	0.164768i	0.911454	+	0.411403i	$0.134961\pi$
$164$	11.8538	−	18.8653i	0.0722795	−	0.115032i
$165$	9.48275	+	4.56665i	0.0574712	+	0.0276767i
$166$	15.4711	+	44.2138i	0.0931994	+	0.266348i
$167$	−41.1889	−	9.40109i	−0.246640	−	0.0562939i	0.0974137	−	0.995244i	$-0.468943\pi$
$167$	−41.1889	−	9.40109i	−0.246640	−	0.0562939i	−0.344053	+	0.938950i	$0.611800\pi$
$168$	−168.836	−	211.713i	−1.00497	−	1.26020i
$169$	−203.797	+	255.553i	−1.20590	+	1.51215i
$170$	0.572314	+	2.50747i	0.00336655	+	0.0147498i
$171$	118.091	+	187.941i	0.690590	+	1.09907i
$172$	−4.81068	−	42.6960i	−0.0279691	−	0.248232i
$173$			127.036i			0.734309i	0.930160	+	0.367155i	$0.119668\pi$
$173$			127.036i			0.734309i	−0.930160	+	0.367155i	$0.880332\pi$
$174$	146.293	−	164.634i	0.840762	−	0.946172i
$175$	174.042			0.994524
$176$	132.860	−	14.9697i	0.754887	−	0.0850553i
$177$	−106.130	+	66.6857i	−0.599603	+	0.376755i
$178$	−44.7001	+	10.2025i	−0.251124	+	0.0573174i
$179$	−114.042	−	90.9455i	−0.637106	−	0.508075i	0.250836	−	0.968030i	$-0.419294\pi$
$179$	−114.042	−	90.9455i	−0.637106	−	0.508075i	−0.887943	+	0.459954i	$0.847866\pi$
$180$	−1.73718	+	1.38536i	−0.00965102	+	0.00769643i
$181$	48.4132	−	212.112i	0.267476	−	1.17189i	−0.645462	−	0.763792i	$-0.723335\pi$
$181$	48.4132	−	212.112i	0.267476	−	1.17189i	0.912938	−	0.408098i	$-0.133808\pi$
$182$	248.859	−	87.0794i	1.36735	−	0.478458i
$183$	7.48019	−	15.5328i	0.0408754	−	0.0848786i
$184$	177.433	+	111.488i	0.964307	+	0.605914i
$185$	−4.18615	−	1.46480i	−0.0226278	−	0.00791782i
$186$	192.337	−	192.337i	1.03407	−	1.03407i
$187$	47.0626	+	97.7265i	0.251672	+	0.522602i
$188$	−0.579465	+	5.14289i	−0.00308226	+	0.0273558i
$189$	−61.7063	−	6.95263i	−0.326489	−	0.0367864i
$190$	5.60159	−	2.69758i	0.0294821	−	0.0141978i
$191$	−140.809	−	140.809i	−0.737221	−	0.737221i	0.234818	−	0.972039i	$-0.424550\pi$
$191$	−140.809	−	140.809i	−0.737221	−	0.737221i	−0.972039	+	0.234818i	$0.924550\pi$
$192$	−104.123	+	297.568i	−0.542310	+	1.54983i
$193$	−170.596	+	271.502i	−0.883916	+	1.40674i	0.0294336	+	0.999567i	$0.490630\pi$
$193$	−170.596	+	271.502i	−0.883916	+	1.40674i	−0.913349	+	0.407177i	$0.866513\pi$
$194$	11.0142	+	5.30414i	0.0567740	+	0.0273409i
$195$	−5.96125	−	17.0363i	−0.0305705	−	0.0873655i
$196$	−0.443006	−	0.101113i	−0.00226023	−	0.000515883i
$197$	−35.3554	−	44.3343i	−0.179469	−	0.225047i	0.683957	−	0.729522i	$-0.260258\pi$
$197$	−35.3554	−	44.3343i	−0.179469	−	0.225047i	−0.863426	+	0.504475i	$0.831686\pi$
$198$	151.160	−	189.548i	0.763432	−	0.957314i
$199$	−6.42619	−	28.1550i	−0.0322924	−	0.141482i	0.956212	−	0.292676i	$-0.0945456\pi$
$199$	−6.42619	−	28.1550i	−0.0322924	−	0.141482i	−0.988504	+	0.151193i	$0.951688\pi$
$200$	−115.405	−	183.666i	−0.577027	−	0.918332i
$201$	−3.32667	−	29.5250i	−0.0165506	−	0.146890i
$202$		−	189.553i		−	0.938379i
$203$	−10.7654	+	201.867i	−0.0530317	+	0.994420i
$204$	−41.6471			−0.204152
$205$	−3.59935	+	0.405549i	−0.0175578	+	0.00197829i
$206$	−173.162	+	108.805i	−0.840593	+	0.528179i
$207$	258.484	−	58.9972i	1.24871	−	0.285011i
$208$	−179.258	−	142.953i	−0.861817	−	0.687276i
$209$	205.000	−	163.482i	0.980861	−	0.782211i
$210$	−2.13549	+	9.35620i	−0.0101690	+	0.0445533i
$211$	281.518	−	98.5074i	1.33421	−	0.466860i	0.433449	−	0.901178i	$-0.357296\pi$
$211$	281.518	−	98.5074i	1.33421	−	0.466860i	0.900759	+	0.434318i	$0.143011\pi$
$212$	39.5935	−	82.2168i	0.186762	−	0.387815i
$213$	135.869	+	85.3719i	0.637881	+	0.400807i
$214$	227.761	+	79.6969i	1.06430	+	0.372415i
$215$	−4.93917	+	4.93917i	−0.0229729	+	0.0229729i
$216$	33.5797	+	69.7290i	0.155462	+	0.322819i
$217$	−27.9540	+	248.098i	−0.128820	+	1.14331i
$218$	−53.2448	−	5.99925i	−0.244242	−	0.0275195i
$219$	−419.683	+	202.109i	−1.91636	+	0.922871i
$220$	1.85601	+	1.85601i	0.00843639	+	0.00843639i
$221$	61.4349	−	175.571i	0.277986	−	0.794438i
$222$	−98.8531	+	157.324i	−0.445284	+	0.708666i
$223$	−61.9105	−	29.8145i	−0.277625	−	0.133697i	0.289890	−	0.957060i	$-0.406381\pi$
$223$	−61.9105	−	29.8145i	−0.277625	−	0.133697i	−0.567516	+	0.823363i	$0.692095\pi$
$224$	−39.7461	−	113.588i	−0.177438	−	0.507088i
$225$	−267.565	−	61.0700i	−1.18918	−	0.271422i
$226$	102.183	+	128.133i	0.452136	+	0.566960i
$227$	275.667	−	345.675i	1.21439	−	1.52280i	0.429625	−	0.903007i	$-0.358646\pi$
$227$	275.667	−	345.675i	1.21439	−	1.52280i	0.784766	−	0.619792i	$-0.212783\pi$
$228$	22.4024	+	98.1511i	0.0982559	+	0.430487i
$229$	−48.7472	−	77.5808i	−0.212870	−	0.338781i	0.723173	−	0.690667i	$-0.242683\pi$
$229$	−48.7472	−	77.5808i	−0.212870	−	0.338781i	−0.936043	+	0.351887i	$0.885540\pi$
$230$	−0.831502	−	7.37979i	−0.00361523	−	0.0320860i
$231$			404.731i			1.75208i
$232$	220.169	−	122.495i	0.949006	−	0.527997i
$233$	−115.705			−0.496587			−0.248294	−	0.968685i	$-0.579870\pi$
$233$	−115.705			−0.496587			−0.248294	+	0.968685i	$0.579870\pi$
$234$	−413.141	+	46.5498i	−1.76556	+	0.198931i
$235$	0.712412	−	0.447638i	0.00303154	−	0.00190484i
$236$	−30.4745	+	6.95561i	−0.129129	+	0.0294729i
$237$	298.074	+	237.706i	1.25770	+	1.00298i
$238$	−77.3247	+	61.6644i	−0.324893	+	0.259094i
$239$	−39.0003	+	170.872i	−0.163181	+	0.714944i	0.825436	+	0.564495i	$0.190929\pi$
$239$	−39.0003	+	170.872i	−0.163181	+	0.714944i	−0.988618	+	0.150449i	$0.951928\pi$
$240$	7.87728	−	2.75638i	0.0328220	−	0.0114849i
$241$	1.62503	−	3.37442i	0.00674288	−	0.0140017i	−0.897570	−	0.440872i	$-0.854669\pi$
$241$	1.62503	−	3.37442i	0.00674288	−	0.0140017i	0.904313	+	0.426870i	$0.140384\pi$
$242$	−68.4807	−	43.0293i	−0.282978	−	0.177807i
$243$	−325.098	−	113.757i	−1.33785	−	0.468134i
$244$	3.04014	−	3.04014i	0.0124596	−	0.0124596i
$245$	0.0320518	+	0.0665563i	0.000130824	+	0.000271658i
$246$	−16.9902	+	150.793i	−0.0690660	+	0.612978i
$247$	−446.820	−	50.3446i	−1.80899	−	0.203824i
$248$	280.355	−	135.012i	1.13046	−	0.544402i
$249$	87.1944	+	87.1944i	0.350178	+	0.350178i
$250$	−5.08132	+	14.5216i	−0.0203253	+	0.0580863i
$251$	−101.330	+	161.266i	−0.403705	+	0.642493i	−0.985270	−	0.171007i	$-0.945298\pi$
$251$	−101.330	+	161.266i	−0.403705	+	0.642493i	0.581565	+	0.813500i	$0.302441\pi$
$252$	−76.9810	−	37.0721i	−0.305480	−	0.147112i
$253$	−103.444	−	295.625i	−0.408868	−	1.16848i
$254$	−167.649	−	38.2648i	−0.660036	−	0.150649i
$255$	4.22140	+	5.29347i	0.0165545	+	0.0207587i
$256$	−122.148	+	153.168i	−0.477139	+	0.598313i
$257$	31.9955	+	140.182i	0.124496	+	0.545454i	0.998253	+	0.0590900i	$0.0188199\pi$
$257$	31.9955	+	140.182i	0.124496	+	0.545454i	−0.873756	+	0.486364i	$0.838323\pi$
$258$	155.691	+	247.780i	0.603452	+	0.960388i
$259$	−19.0949	−	169.472i	−0.0737256	−	0.654333i
$260$		−	4.50117i		−	0.0173122i
$261$	87.3842	−	306.566i	0.334805	−	1.17458i
$262$	−163.424			−0.623757
$263$	−14.2134	+	1.60147i	−0.0540434	+	0.00608923i	−0.138945	−	0.990300i	$-0.544371\pi$
$263$	−14.2134	+	1.60147i	−0.0540434	+	0.00608923i	0.0849014	+	0.996389i	$0.472942\pi$
$264$	427.113	−	268.373i	1.61785	−	1.01656i
$265$	−14.4632	+	3.30114i	−0.0545783	+	0.0124571i
$266$	186.920	+	149.064i	0.702707	+	0.560390i
$267$	−94.3653	+	75.2538i	−0.353428	+	0.281849i
$268$	1.64881	−	7.22389i	0.00615226	−	0.0269548i
$269$	115.482	−	40.4089i	0.429301	−	0.150219i	−0.106975	−	0.994262i	$-0.534116\pi$
$269$	115.482	−	40.4089i	0.429301	−	0.150219i	0.536276	+	0.844043i	$0.319831\pi$
$270$	1.19006	−	2.47119i	0.00440763	−	0.00915254i
$271$	364.109	+	228.785i	1.34358	+	0.844225i	0.995639	−	0.0932924i	$-0.0297391\pi$
$271$	364.109	+	228.785i	1.34358	+	0.844225i	0.347938	+	0.937518i	$0.386882\pi$
$272$	81.1810	+	28.4065i	0.298460	+	0.104435i
$273$	490.775	−	490.775i	1.79771	−	1.79771i
$274$	−135.623	−	281.624i	−0.494975	−	1.02783i
$275$	−36.2994	+	322.166i	−0.131998	+	1.17151i
$276$	119.499	+	13.4643i	0.432968	+	0.0487838i
$277$	363.232	−	174.923i	1.31131	−	0.631492i	0.358064	−	0.933697i	$-0.383437\pi$
$277$	363.232	−	174.923i	1.31131	−	0.631492i	0.953243	+	0.302205i	$0.0977227\pi$
$278$	−224.381	−	224.381i	−0.807127	−	0.807127i
$279$	130.031	−	371.608i	0.466062	−	1.33193i
$280$	−5.84097	+	9.29585i	−0.0208606	+	0.0331995i
$281$	55.4249	+	26.6912i	0.197242	+	0.0949865i	0.529897	−	0.848062i	$-0.322230\pi$
$281$	55.4249	+	26.6912i	0.197242	+	0.0949865i	−0.332656	+	0.943048i	$0.607945\pi$
$282$	−11.6420	−	33.2708i	−0.0412835	−	0.117982i
$283$	172.772	+	39.4340i	0.610501	+	0.139343i	0.516583	−	0.856237i	$-0.327204\pi$
$283$	172.772	+	39.4340i	0.610501	+	0.139343i	0.0939179	+	0.995580i	$0.470061\pi$
$284$	24.9503	+	31.2867i	0.0878532	+	0.110164i
$285$	10.2046	−	12.7961i	0.0358055	−	0.0448987i
$286$	109.288	+	478.820i	0.382124	+	1.67420i
$287$	−74.1042	−	117.936i	−0.258203	−	0.410927i
$288$	21.2470	+	188.572i	0.0737742	+	0.654764i
$289$		−	219.224i		−	0.758561i
$290$	−8.25905	−	3.39374i	−0.0284795	−	0.0117026i
$291$	32.1814			0.110589
$292$	−115.436	+	13.0065i	−0.395329	+	0.0445429i
$293$	−42.8502	+	26.9246i	−0.146246	+	0.0918927i	−0.603168	−	0.797614i	$-0.706095\pi$
$293$	−42.8502	+	26.9246i	−0.146246	+	0.0918927i	0.456921	+	0.889507i	$0.348952\pi$
$294$	3.01722	−	0.688662i	0.0102627	−	0.00234239i
$295$	3.97301	+	3.16837i	0.0134678	+	0.0107402i
$296$	−166.183	+	132.526i	−0.561428	+	0.447724i
$297$	25.7398	−	112.774i	0.0866661	−	0.379709i
$298$	−184.852	+	64.6826i	−0.620310	+	0.217056i
$299$	−233.038	+	483.909i	−0.779392	+	1.61842i
$300$	−105.401	−	66.2276i	−0.351335	−	0.220759i
$301$	−253.529	−	88.7138i	−0.842290	−	0.294730i
$302$	12.2241	−	12.2241i	0.0404771	−	0.0404771i
$303$	−216.504	−	449.576i	−0.714536	−	1.48375i
$304$	23.2785	−	206.602i	0.0765739	−	0.679612i
$305$	−0.694563	−	0.0782585i	−0.00227726	−	0.000256585i
$306$	140.514	−	67.6678i	0.459195	−	0.221137i
$307$	91.5953	+	91.5953i	0.298356	+	0.298356i	0.840370	−	0.542014i	$-0.182338\pi$
$307$	91.5953	+	91.5953i	0.298356	+	0.298356i	−0.542014	+	0.840370i	$0.682338\pi$
$308$	−33.3362	+	95.2695i	−0.108235	+	0.309317i
$309$	−286.426	+	455.844i	−0.926944	+	1.47522i
$310$	−9.93573	−	4.78479i	−0.0320507	−	0.0154348i
$311$	161.202	+	460.688i	0.518333	+	1.48131i	0.844269	+	0.535919i	$0.180035\pi$
$311$	161.202	+	460.688i	0.518333	+	1.48131i	−0.325936	+	0.945392i	$0.605680\pi$
$312$	−843.344	−	192.488i	−2.70303	−	0.616948i
$313$	−331.292	−	415.427i	−1.05844	−	1.32724i	−0.942581	−	0.333979i	$-0.891609\pi$
$313$	−331.292	−	415.427i	−1.05844	−	1.32724i	−0.115861	−	0.993265i	$-0.536963\pi$
$314$	81.2328	−	101.863i	0.258703	−	0.324403i
$315$	3.09091	+	13.5422i	0.00981243	+	0.0429911i
$316$	50.5846	+	80.5050i	0.160078	+	0.254763i
$317$	49.7527	+	441.567i	0.156948	+	1.39296i	0.787264	+	0.616617i	$0.211497\pi$
$317$	49.7527	+	441.567i	0.156948	+	1.39296i	−0.630315	+	0.776339i	$0.717074\pi$
$318$			621.512i			1.95444i
$319$	−371.428	−	62.0306i	−1.16435	−	0.194453i
$320$	12.7814			0.0399420
$321$	631.225	−	71.1220i	1.96643	−	0.221564i
$322$	241.806	−	151.937i	0.750949	−	0.471853i
$323$	164.443	−	37.5330i	0.509112	−	0.116201i
$324$	−51.5232	−	41.0884i	−0.159022	−	0.126816i
$325$	434.674	−	346.641i	1.33746	−	1.06659i
$326$	10.7543	−	47.1177i	0.0329886	−	0.144533i
$327$	−133.137	+	46.5866i	−0.407146	+	0.142467i
$328$	−75.3204	+	156.404i	−0.229635	+	0.476843i
$329$	27.3951	+	17.2135i	0.0832677	+	0.0523205i
$330$	−16.8737	−	5.90437i	−0.0511325	−	0.0178920i
$331$	−206.567	+	206.567i	−0.624068	+	0.624068i	−0.946569	−	0.322501i	$-0.895477\pi$
$331$	−206.567	+	206.567i	−0.624068	+	0.624068i	0.322501	+	0.946569i	$0.395477\pi$
$332$	13.3428	+	27.7066i	0.0401891	+	0.0834535i
$333$	−30.1108	+	267.240i	−0.0904227	+	0.802524i
$334$	71.3076	+	8.03443i	0.213496	+	0.0240552i
$335$	−1.08530	+	0.522654i	−0.00323971	+	0.00156016i
$336$	226.926	+	226.926i	0.675375	+	0.675375i
$337$	156.253	−	446.546i	0.463659	−	1.32506i	−0.440457	−	0.897774i	$-0.645184\pi$
$337$	156.253	−	446.546i	0.463659	−	1.32506i	0.904116	−	0.427287i	$-0.140531\pi$
$338$	295.375	−	470.087i	0.873891	−	1.39079i
$339$	388.706	+	187.191i	1.14663	+	0.552186i
$340$	0.557670	+	1.59373i	0.00164021	+	0.00468744i
$341$	−453.421	−	103.490i	−1.32968	−	0.303491i
$342$	−235.059	−	294.754i	−0.687306	−	0.861854i
$343$	−214.737	+	269.272i	−0.626055	+	0.785049i
$344$	74.4930	+	326.375i	0.216549	+	0.948765i
$345$	−10.4012	−	16.5535i	−0.0301485	−	0.0479810i
$346$	−24.1587	−	214.414i	−0.0698228	−	0.619694i
$347$		−	511.474i		−	1.47399i	−0.675899	−	0.736994i	$-0.736245\pi$
$347$		−	511.474i		−	1.47399i	0.675899	−	0.736994i	$-0.263755\pi$
$348$	83.3355	−	118.155i	0.239470	−	0.339527i
$349$	−482.022			−1.38115			−0.690576	−	0.723260i	$-0.742643\pi$
$349$	−482.022			−1.38115			−0.690576	+	0.723260i	$0.742643\pi$
$350$	−293.753	+	33.0980i	−0.839293	+	0.0945657i
$351$	−167.961	+	105.537i	−0.478521	+	0.300675i
$352$	218.550	−	49.8827i	0.620881	−	0.141712i
$353$	190.763	+	152.128i	0.540404	+	0.430958i	0.855273	−	0.518177i	$-0.173389\pi$
$353$	190.763	+	152.128i	0.540404	+	0.430958i	−0.314869	+	0.949135i	$0.601961\pi$
$354$	166.447	−	132.737i	0.470189	−	0.374963i
$355$	1.44764	−	6.34252i	0.00407785	−	0.0178662i
$356$	−28.4110	+	9.94145i	−0.0798063	+	0.0279254i
$357$	−112.964	+	234.573i	−0.316427	+	0.657067i
$358$	209.779	+	131.813i	0.585975	+	0.368192i
$359$	569.212	+	199.176i	1.58555	+	0.554808i	0.972027	−	0.234870i	$-0.0754663\pi$
$359$	569.212	+	199.176i	1.58555	+	0.554808i	0.613522	+	0.789677i	$0.289752\pi$
$360$	12.2415	−	12.2415i	0.0340043	−	0.0340043i
$361$	−20.2788	−	42.1094i	−0.0561741	−	0.116647i
$362$	−41.3753	+	367.216i	−0.114296	+	1.01441i
$363$	−211.568	−	23.8380i	−0.582832	−	0.0656694i
$364$	155.947	−	75.1001i	0.428426	−	0.206319i
$365$	13.3539	+	13.3539i	0.0365861	+	0.0365861i
$366$	−9.67138	+	27.6392i	−0.0264245	+	0.0755170i
$367$	137.681	−	219.118i	0.375153	−	0.597052i	−0.604777	−	0.796395i	$-0.706738\pi$
$367$	137.681	−	219.118i	0.375153	−	0.597052i	0.979930	+	0.199343i	$0.0638807\pi$
$368$	−223.751	−	107.753i	−0.608020	−	0.292807i
$369$	72.5420	+	207.313i	0.196591	+	0.561824i
$370$	7.34407	+	1.67624i	0.0198488	+	0.00453037i
$371$	−355.684	−	446.013i	−0.958716	−	1.20219i
$372$	111.337	−	139.612i	0.299294	−	0.375302i
$373$	−135.641	−	594.282i	−0.363649	−	1.59325i	−0.743850	−	0.668347i	$-0.767002\pi$
$373$	−135.641	−	594.282i	−0.363649	−	1.59325i	0.380201	−	0.924904i	$-0.375855\pi$
$374$	−98.0185	−	155.996i	−0.262082	−	0.417101i
$375$	4.53460	+	40.2457i	0.0120923	+	0.107322i
$376$		−	40.3241i		−	0.107245i
$377$	375.174	+	525.611i	0.995158	+	1.39419i
$378$	105.472			0.279026
$379$	−160.764	+	18.1138i	−0.424180	+	0.0477936i	−0.321475	−	0.946918i	$-0.604179\pi$
$379$	−160.764	+	18.1138i	−0.424180	+	0.0477936i	−0.102706	+	0.994712i	$0.532750\pi$
$380$	3.45602	−	2.17156i	0.00909480	−	0.00571464i
$381$	−441.331	+	100.731i	−1.15835	+	0.264386i
$382$	264.440	+	210.884i	0.692251	+	0.552052i
$383$	−272.105	+	216.997i	−0.710458	+	0.566571i	−0.910647	−	0.413186i	$-0.864416\pi$
$383$	−272.105	+	216.997i	−0.710458	+	0.566571i	0.200189	+	0.979757i	$0.435845\pi$
$384$	50.4479	−	221.027i	0.131375	−	0.575591i
$385$	15.4880	−	5.41950i	0.0402287	−	0.0140766i
$386$	236.304	−	490.691i	0.612187	−	1.27122i
$387$	358.637	+	225.347i	0.926712	+	0.582292i
$388$	7.57518	+	2.65067i	0.0195237	+	0.00683163i
$389$	254.246	−	254.246i	0.653588	−	0.653588i	−0.300267	−	0.953855i	$-0.597076\pi$
$389$	254.246	−	254.246i	0.653588	−	0.653588i	0.953855	+	0.300267i	$0.0970758\pi$
$390$	13.3014	+	27.6207i	0.0341062	+	0.0708222i
$391$	22.5582	−	200.210i	0.0576936	−	0.512045i
$392$	3.51816	+	0.396401i	0.00897490	+	0.00101123i
$393$	−387.605	+	186.661i	−0.986273	+	0.474964i
$394$	68.1051	+	68.1051i	0.172856	+	0.172856i
$395$	5.10510	−	14.5895i	0.0129243	−	0.0369355i
$396$	84.6793	−	134.766i	0.213837	−	0.340319i
$397$	110.601	+	53.2627i	0.278592	+	0.134163i	0.567963	−	0.823054i	$-0.307732\pi$
$397$	110.601	+	53.2627i	0.278592	+	0.134163i	−0.289371	+	0.957217i	$0.593446\pi$
$398$	16.2006	+	46.2987i	0.0407051	+	0.116328i
$399$	613.591	+	140.048i	1.53782	+	0.350998i
$400$	160.281	+	200.986i	0.400702	+	0.502465i
$401$	158.554	−	198.821i	0.395398	−	0.495813i	−0.543788	−	0.839223i	$-0.683010\pi$
$401$	158.554	−	198.821i	0.395398	−	0.495813i	0.939186	+	0.343410i	$0.111582\pi$
$402$	11.2297	+	49.2005i	0.0279346	+	0.122389i
$403$	424.325	+	675.309i	1.05292	+	1.67570i
$404$	−13.9329	−	123.658i	−0.0344875	−	0.306085i
$405$			10.7135i			0.0264531i
$406$	−20.2194	−	342.765i	−0.0498015	−	0.844248i
$407$	317.690			0.780565
$408$	322.451	−	36.3315i	0.790321	−	0.0890477i
$409$	−55.7403	+	35.0239i	−0.136284	+	0.0856331i	−0.598449	−	0.801161i	$-0.704216\pi$
$409$	−55.7403	+	35.0239i	−0.136284	+	0.0856331i	0.462164	+	0.886794i	$0.347073\pi$
$410$	5.99796	−	1.36900i	0.0146292	−	0.00333901i
$411$	−643.334	−	513.042i	−1.56529	−	1.24828i
$412$	−104.968	+	83.7092i	−0.254777	+	0.203178i
$413$	−43.4830	+	190.511i	−0.105286	+	0.461286i
$414$	−425.056	+	148.734i	−1.02671	+	0.359260i
$415$	2.16915	−	4.50428i	0.00522686	−	0.0108537i
$416$	−325.501	−	204.526i	−0.782454	−	0.491649i
$417$	−788.467	−	275.897i	−1.89081	−	0.661623i
$418$	−314.915	+	314.915i	−0.753386	+	0.753386i
$419$	−226.933	−	471.231i	−0.541606	−	1.12466i	−0.974743	−	0.223329i	$-0.928308\pi$
$419$	−226.933	−	471.231i	−0.541606	−	1.12466i	0.433137	−	0.901328i	$-0.357407\pi$
$420$	−0.705408	+	6.26067i	−0.00167954	+	0.0149064i
$421$	−192.380	−	21.6760i	−0.456960	−	0.0514871i	−0.119515	−	0.992832i	$-0.538134\pi$
$421$	−192.380	−	21.6760i	−0.456960	−	0.0514871i	−0.337445	+	0.941345i	$0.609563\pi$
$422$	−456.421	+	219.801i	−1.08157	+	0.520855i
$423$	−36.0761	−	36.0761i	−0.0852862	−	0.0852862i
$424$	−234.828	+	671.100i	−0.553840	+	1.58278i
$425$	−110.958	+	176.589i	−0.261078	+	0.415503i
$426$	−245.558	−	118.255i	−0.576428	−	0.277593i
$427$	−8.87715	−	25.3694i	−0.0207896	−	0.0594132i
$428$	154.442	+	35.2504i	0.360846	+	0.0823608i
$429$	806.107	+	1010.83i	1.87904	+	2.35624i
$430$	7.39717	−	9.27576i	0.0172027	−	0.0215715i
$431$	−58.0221	−	254.212i	−0.134622	−	0.589818i	−0.996565	−	0.0828129i	$-0.973610\pi$
$431$	−58.0221	−	254.212i	−0.134622	−	0.589818i	0.861943	−	0.507005i	$-0.169248\pi$
$432$	−48.7984	−	77.6623i	−0.112959	−	0.179774i
$433$	6.90278	+	61.2639i	0.0159418	+	0.141487i	0.999162	−	0.0409369i	$-0.0130343\pi$
$433$	6.90278	+	61.2639i	0.0159418	+	0.141487i	−0.983220	+	0.182424i	$0.941606\pi$
$434$		−	424.064i		−	0.977106i
$435$	−23.4649	+	1.38417i	−0.0539422	+	0.00318201i
$436$	−35.1763			−0.0806795
$437$	−483.975	+	54.5309i	−1.10750	+	0.124785i
$438$	669.918	−	420.937i	1.52949	−	0.961044i
$439$	−173.225	+	39.5375i	−0.394590	+	0.0900626i	−0.415212	−	0.909725i	$-0.636293\pi$
$439$	−173.225	+	39.5375i	−0.394590	+	0.0900626i	0.0206218	+	0.999787i	$0.493435\pi$
$440$	−15.9892	−	12.7509i	−0.0363390	−	0.0289794i
$441$	3.50217	−	2.79289i	0.00794143	−	0.00633308i
$442$	−70.3028	+	308.017i	−0.159056	+	0.696871i
$443$	632.160	−	221.202i	1.42700	−	0.499328i	0.497276	−	0.867592i	$-0.334334\pi$
$443$	632.160	−	221.202i	1.42700	−	0.499328i	0.929721	+	0.368265i	$0.120048\pi$
$444$	−52.9248	+	109.899i	−0.119200	+	0.247521i
$445$	4.14336	+	2.60345i	0.00931093	+	0.00585044i
$446$	110.164	+	38.5481i	0.247005	+	0.0864308i
$447$	−364.548	+	364.548i	−0.815544	+	0.815544i
$448$	213.252	+	442.823i	0.476010	+	0.988445i
$449$	28.7774	−	255.406i	0.0640921	−	0.568834i	−0.920094	−	0.391697i	$-0.871888\pi$
$449$	28.7774	−	255.406i	0.0640921	−	0.568834i	0.984186	−	0.177136i	$-0.0566834\pi$
$450$	463.218	+	52.1922i	1.02937	+	0.115983i
$451$	233.765	−	112.575i	0.518327	−	0.249613i
$452$	76.0792	+	76.0792i	0.168317	+	0.168317i
$453$	15.0306	−	42.9550i	0.0331801	−	0.0948233i
$454$	−399.541	+	635.865i	−0.880045	+	1.40058i
$455$	−25.3524	−	12.2091i	−0.0557196	−	0.0268331i
$456$	−259.073	−	740.388i	−0.568142	−	1.62366i
$457$	508.462	+	116.053i	1.11261	+	0.253946i	0.739043	−	0.673658i	$-0.235278\pi$
$457$	508.462	+	116.053i	1.11261	+	0.253946i	0.373566	+	0.927604i	$0.378135\pi$
$458$	97.0308	+	121.673i	0.211858	+	0.265661i
$459$	46.3945	−	58.1768i	0.101077	−	0.126747i
$460$	−1.08489	−	4.75323i	−0.00235846	−	0.0103331i
$461$	−305.337	−	485.941i	−0.662336	−	1.05410i	−0.993859	−	0.110655i	$-0.964705\pi$
$461$	−305.337	−	485.941i	−0.662336	−	1.05410i	0.331523	−	0.943447i	$-0.392438\pi$
$462$	−76.9687	−	683.116i	−0.166599	−	1.47861i
$463$			548.047i			1.18369i	0.806053	+	0.591843i	$0.201600\pi$
$463$			548.047i			1.18369i	−0.806053	+	0.591843i	$0.798400\pi$
$464$	−243.033	+	173.474i	−0.523779	+	0.373867i
$465$	−29.0304			−0.0624310
$466$	195.290	−	22.0039i	0.419077	−	0.0472187i
$467$	−696.323	+	437.528i	−1.49105	+	0.936892i	−0.493304	+	0.869857i	$0.664211\pi$
$467$	−696.323	+	437.528i	−1.49105	+	0.936892i	−0.997751	+	0.0670350i	$0.978646\pi$
$468$	−266.099	+	60.7354i	−0.568588	+	0.129776i
$469$	−36.2156	−	28.8810i	−0.0772187	−	0.0615799i
$470$	−1.11730	+	0.891017i	−0.00237724	+	0.00189578i
$471$	76.3196	−	334.378i	0.162037	−	0.709932i
$472$	229.880	−	80.4385i	0.487034	−	0.170420i
$473$	217.095	−	450.801i	0.458974	−	0.953069i
$474$	−548.304	−	344.522i	−1.15676	−	0.726840i
$475$	475.858	+	166.510i	1.00181	+	0.350547i
$476$	−45.9116	+	45.9116i	−0.0964530	+	0.0964530i
$477$	390.312	+	810.491i	0.818264	+	1.69914i
$478$	33.3308	−	295.819i	0.0697297	−	0.618868i
$479$	272.204	+	30.6701i	0.568277	+	0.0640294i	0.391428	−	0.920209i	$-0.371981\pi$
$479$	272.204	+	30.6701i	0.568277	+	0.0640294i	0.176848	+	0.984238i	$0.443410\pi$
$480$	12.6070	−	6.07123i	0.0262647	−	0.0126484i
$481$	−385.230	−	385.230i	−0.800894	−	0.800894i
$482$	−2.10106	+	6.00448i	−0.00435904	+	0.0124574i
$483$	399.968	−	636.546i	0.828092	−	1.31790i
$484$	−47.8375	−	23.0373i	−0.0988379	−	0.0475978i
$485$	−0.430922	−	1.23150i	−0.000888498	−	0.00253918i
$486$	570.343	+	130.177i	1.17354	+	0.267854i
$487$	77.1649	+	96.7617i	0.158449	+	0.198689i	0.854719	−	0.519091i	$-0.173730\pi$
$487$	77.1649	+	96.7617i	0.158449	+	0.198689i	−0.696269	+	0.717781i	$0.745158\pi$
$488$	−20.8861	+	26.1903i	−0.0427993	+	0.0536686i
$489$	−28.3104	−	124.036i	−0.0578944	−	0.253652i
$490$	−0.0667551	−	0.106240i	−0.000136235	−	0.000216817i
$491$	11.6732	+	103.602i	0.0237743	+	0.211002i	0.999983	−	0.00583045i	$-0.00185590\pi$
$491$	11.6732	+	103.602i	0.0237743	+	0.211002i	−0.976209	+	0.216833i	$0.930427\pi$
$492$			99.6214i			0.202482i
$493$	−197.958	−	139.621i	−0.401538	−	0.283207i
$494$	763.731			1.54601
$495$	−25.7124	+	2.89709i	−0.0519442	+	0.00585271i
$496$	−312.251	+	196.201i	−0.629539	+	0.395566i
$497$	243.895	−	55.6675i	0.490734	−	0.112007i
$498$	−163.751	−	130.587i	−0.328818	−	0.262223i
$499$	−276.912	+	220.830i	−0.554935	+	0.442546i	−0.860372	−	0.509666i	$-0.829769\pi$
$499$	−276.912	+	220.830i	−0.554935	+	0.442546i	0.305437	+	0.952212i	$0.401197\pi$
$500$	−2.24750	+	9.84694i	−0.00449500	+	0.0196939i
$501$	178.302	−	62.3907i	0.355893	−	0.124532i
$502$	140.359	−	291.459i	0.279600	−	0.580596i
$503$	−437.771	−	275.070i	−0.870320	−	0.546858i	0.0212333	−	0.999775i	$-0.493241\pi$
$503$	−437.771	−	275.070i	−0.870320	−	0.546858i	−0.891553	+	0.452916i	$0.850384\pi$
$504$	628.363	+	219.874i	1.24675	+	0.436257i
$505$	−14.3051	+	14.3051i	−0.0283269	+	0.0283269i
$506$	230.815	+	479.292i	0.456155	+	0.947217i
$507$	163.636	−	1452.31i	0.322754	−	2.86452i
$508$	−112.182	−	12.6399i	−0.220830	−	0.0248816i
$509$	282.331	−	135.964i	0.554679	−	0.267119i	−0.135477	−	0.990781i	$-0.543257\pi$
$509$	282.331	−	135.964i	0.554679	−	0.267119i	0.690155	+	0.723661i	$0.257542\pi$
$510$	−8.13167	−	8.13167i	−0.0159445	−	0.0159445i
$511$	−239.853	+	685.462i	−0.469381	+	1.34141i
$512$	284.940	−	453.480i	0.556524	−	0.885703i
$513$	−162.063	−	78.0456i	−0.315913	−	0.152136i
$514$	−80.6617	−	230.518i	−0.156929	−	0.448479i
$515$	21.2794	+	4.85688i	0.0413192	+	0.00943083i
$516$	119.781	+	150.200i	0.232133	+	0.291086i
$517$	−37.5773	+	47.1204i	−0.0726833	+	0.0911420i
$518$	64.4580	+	282.409i	0.124436	+	0.545191i
$519$	−302.200	−	480.948i	−0.582273	−	0.926683i
$520$	3.92667	+	34.8502i	0.00755129	+	0.0670195i
$521$			903.060i			1.73332i	0.498898	+	0.866661i	$0.333738\pi$
$521$			903.060i			1.73332i	−0.498898	+	0.866661i	$0.666262\pi$
$522$	−89.1892	+	534.048i	−0.170860	+	1.02308i
$523$	643.715			1.23081			0.615407	−	0.788210i	$-0.288992\pi$
$523$	643.715			1.23081			0.615407	+	0.788210i	$0.288992\pi$
$524$	−106.613	+	12.0124i	−0.203460	+	0.0229244i
$525$	−658.911	+	414.021i	−1.25507	+	0.788612i
$526$	23.6853	−	5.40601i	0.0450290	−	0.0102776i
$527$	−233.908	−	186.535i	−0.443847	−	0.353957i
$528$	−467.389	+	372.730i	−0.885206	+	0.705928i
$529$	−11.7403	+	51.4375i	−0.0221934	+	0.0972354i
$530$	23.7837	−	8.32228i	0.0448749	−	0.0157024i
$531$	133.698	−	277.627i	0.251785	−	0.522838i
$532$	132.898	+	83.5053i	0.249808	+	0.156965i
$533$	−419.972	−	146.955i	−0.787940	−	0.275712i
$534$	144.961	−	144.961i	0.271463	−	0.271463i
$535$	−11.1740	−	23.2031i	−0.0208860	−	0.0433702i
$536$	−6.46394	+	57.3690i	−0.0120596	+	0.107032i
$537$	648.103	+	73.0236i	1.20690	+	0.135984i
$538$	−187.229	+	90.1649i	−0.348010	+	0.167593i
$539$	−3.74172	−	3.74172i	−0.00694196	−	0.00694196i
$540$	0.594716	−	1.69960i	0.00110133	−	0.00314741i
$541$	63.1537	−	100.509i	0.116735	−	0.185783i	−0.783246	−	0.621712i	$-0.786437\pi$
$541$	63.1537	−	100.509i	0.116735	−	0.185783i	0.899981	+	0.435929i	$0.143580\pi$
$542$	−658.063	−	316.906i	−1.21414	−	0.584698i
$543$	321.296	+	918.211i	0.591705	+	1.69100i
$544$	140.590	+	32.0887i	0.258437	+	0.0589865i
$545$	3.56551	+	4.47101i	0.00654222	+	0.00820368i
$546$	−735.013	+	921.677i	−1.34618	+	1.68805i
$547$	−141.842	−	621.450i	−0.259309	−	1.13611i	−0.921993	−	0.387206i	$-0.873440\pi$
$547$	−141.842	−	621.450i	−0.259309	−	1.13611i	0.662684	−	0.748899i	$-0.269417\pi$
$548$	−109.177	−	173.754i	−0.199228	−	0.317070i
$549$	4.74544	+	42.1170i	0.00864379	+	0.0767158i
$550$		−	550.664i		−	1.00121i
$551$	−222.566	+	541.638i	−0.403931	+	0.983010i
$552$	−936.963			−1.69740
$553$	590.643	−	66.5495i	1.06807	−	0.120343i
$554$	−579.808	+	364.317i	−1.04658	+	0.657613i
$555$	19.3330	−	4.41264i	0.0348343	−	0.00795071i
$556$	−162.873	−	129.887i	−0.292936	−	0.233609i
$557$	593.908	−	473.626i	1.06626	−	0.850316i	0.0770829	−	0.997025i	$-0.475439\pi$
$557$	593.908	−	473.626i	1.06626	−	0.850316i	0.989180	+	0.146709i	$0.0468680\pi$
$558$	−148.801	+	651.940i	−0.266668	+	1.16835i
$559$	−809.889	+	283.392i	−1.44882	+	0.506963i
$560$	5.64527	−	11.7225i	0.0100808	−	0.0209331i
$561$	−410.654	−	258.031i	−0.732003	−	0.459948i
$562$	−98.6237	−	34.5099i	−0.175487	−	0.0614055i
$563$	−443.544	+	443.544i	−0.787822	+	0.787822i	−0.981137	−	0.193315i	$-0.938076\pi$
$563$	−443.544	+	443.544i	−0.787822	+	0.787822i	0.193315	+	0.981137i	$0.438076\pi$
$564$	−10.0404	−	20.8491i	−0.0178021	−	0.0369665i
$565$	1.95841	−	17.3814i	0.00346621	−	0.0307635i
$566$	−299.109	−	33.7014i	−0.528460	−	0.0595432i
$567$	−371.179	+	178.750i	−0.654636	+	0.315256i
$568$	−220.470	−	220.470i	−0.388152	−	0.388152i
$569$	92.2750	−	263.707i	0.162170	−	0.463456i	−0.833911	−	0.551899i	$-0.813903\pi$
$569$	92.2750	−	263.707i	0.162170	−	0.463456i	0.996081	+	0.0884427i	$0.0281890\pi$
$570$	−14.7901	+	23.5383i	−0.0259475	+	0.0412953i
$571$	438.799	+	211.315i	0.768475	+	0.370078i	0.776686	−	0.629888i	$-0.216899\pi$
$571$	438.799	+	211.315i	0.768475	+	0.370078i	−0.00821061	+	0.999966i	$0.502614\pi$
$572$	106.491	+	304.334i	0.186173	+	0.532053i
$573$	868.060	+	198.129i	1.51494	+	0.345775i
$574$	147.503	+	184.963i	0.256975	+	0.322236i
$575$	375.466	−	470.819i	0.652984	−	0.818816i
$576$	−172.463	−	755.609i	−0.299414	−	1.31182i
$577$	150.219	+	239.072i	0.260345	+	0.414336i	0.951161	−	0.308694i	$-0.0998918\pi$
$577$	150.219	+	239.072i	0.260345	+	0.414336i	−0.690817	+	0.723030i	$0.742749\pi$
$578$	41.6905	+	370.013i	0.0721288	+	0.640161i
$579$		−	1433.71i		−	2.47618i
$580$	−5.63741	−	1.60690i	−0.00971966	−	0.00277052i
$581$	192.246			0.330888
$582$	−54.3167	+	6.12003i	−0.0933277	+	0.0105155i
$583$	899.792	−	565.377i	1.54338	−	0.969771i
$584$	882.413	−	201.405i	1.51098	−	0.344872i
$585$	34.6918	+	27.6658i	0.0593022	+	0.0472919i
$586$	67.2035	−	53.5930i	0.114682	−	0.0914556i
$587$	36.9042	−	161.688i	0.0628691	−	0.275448i	−0.933717	−	0.358013i	$-0.883454\pi$
$587$	36.9042	−	161.688i	0.0628691	−	0.275448i	0.996586	+	0.0825656i	$0.0263114\pi$
$588$	1.91773	−	0.671041i	0.00326144	−	0.00114123i
$589$	−313.793	+	651.597i	−0.532755	+	1.10628i
$590$	−7.30830	−	4.59211i	−0.0123870	−	0.00778324i
$591$	239.319	+	83.7412i	0.404938	+	0.141694i
$592$	178.124	−	178.124i	0.300885	−	0.300885i
$593$	464.417	+	964.372i	0.783165	+	1.62626i	0.779610	+	0.626266i	$0.215418\pi$
$593$	464.417	+	964.372i	0.783165	+	1.62626i	0.00355571	+	0.999994i	$0.498868\pi$
$594$	−21.9980	+	195.237i	−0.0370336	+	0.328683i
$595$	10.4892	+	1.18184i	0.0176288	+	0.00198629i
$596$	−115.838	+	55.7844i	−0.194358	+	0.0935980i
$597$	91.3060	+	91.3060i	0.152941	+	0.152941i
$598$	301.302	−	861.073i	0.503850	−	1.43992i
$599$	19.6237	−	31.2310i	0.0327608	−	0.0521385i	−0.829942	−	0.557849i	$-0.811627\pi$
$599$	19.6237	−	31.2310i	0.0327608	−	0.0521385i	0.862703	+	0.505711i	$0.168770\pi$
$600$	873.834	+	420.816i	1.45639	+	0.701361i
$601$	−165.010	−	471.571i	−0.274559	−	0.784645i	−0.995766	−	0.0919249i	$-0.970698\pi$
$601$	−165.010	−	471.571i	−0.274559	−	0.784645i	0.721207	−	0.692720i	$-0.243588\pi$
$602$	444.785	+	101.519i	0.738846	+	0.168637i
$603$	45.5424	+	57.1083i	0.0755263	+	0.0947070i
$604$	7.07610	−	8.87315i	0.0117154	−	0.0146906i
$605$	1.92076	+	8.41538i	0.00317480	+	0.0139097i
$606$	450.919	+	717.634i	0.744091	+	1.18421i
$607$	−18.5846	−	164.942i	−0.0306171	−	0.271734i	−0.999689	−	0.0249540i	$-0.992056\pi$
$607$	−18.5846	−	164.942i	−0.0306171	−	0.271734i	0.969072	−	0.246780i	$-0.0793725\pi$
$608$		−	348.593i		−	0.573344i
$609$	−439.457	−	789.866i	−0.721604	−	1.29699i
$610$	1.18719			0.00194621
$611$	102.704	−	11.5720i	0.168092	−	0.0189394i
$612$	86.6929	−	54.4728i	0.141655	−	0.0890078i
$613$	−793.283	+	181.062i	−1.29410	+	0.295370i	−0.813497	−	0.581569i	$-0.802439\pi$
$613$	−793.283	+	181.062i	−1.29410	+	0.295370i	−0.480602	+	0.876939i	$0.659582\pi$
$614$	−172.016	−	137.178i	−0.280157	−	0.223418i
$615$	12.6622	−	10.0977i	0.0205889	−	0.0164191i
$616$	174.995	−	766.702i	0.284082	−	1.24465i
$617$	−889.197	+	311.143i	−1.44116	+	0.504284i	−0.933908	−	0.357512i	$-0.883625\pi$
$617$	−889.197	+	311.143i	−1.44116	+	0.504284i	−0.507254	+	0.861797i	$0.669339\pi$
$618$	396.749	−	823.857i	0.641988	−	1.33310i
$619$	−690.219	−	433.693i	−1.11505	−	0.700635i	−0.157108	−	0.987581i	$-0.550217\pi$
$619$	−690.219	−	433.693i	−1.11505	−	0.700635i	−0.957947	+	0.286946i	$0.907360\pi$
$620$	−6.83347	−	2.39113i	−0.0110217	−	0.00385667i
$621$	−151.929	+	151.929i	−0.244653	+	0.244653i
$622$	−359.691	−	746.906i	−0.578281	−	1.20081i
$623$	−21.0685	+	186.988i	−0.0338177	+	0.300141i
$624$	1018.73	+	114.783i	1.63257	+	0.183947i
$625$	−560.886	+	270.108i	−0.897418	+	0.432174i
$626$	638.168	+	638.168i	1.01944	+	1.01944i
$627$	−387.216	+	1106.60i	−0.617569	+	1.76491i
$628$	45.5064	−	72.4231i	0.0724625	−	0.115323i
$629$	184.126	+	88.6705i	0.292728	+	0.140971i
$630$	−7.79229	−	22.2691i	−0.0123687	−	0.0353477i
$631$	430.841	+	98.3366i	0.682791	+	0.155842i	0.549827	−	0.835278i	$-0.314694\pi$
$631$	430.841	+	98.3366i	0.682791	+	0.155842i	0.132963	+	0.991121i	$0.457551\pi$
$632$	−461.879	−	579.178i	−0.730822	−	0.916421i
$633$	−831.474	+	1042.63i	−1.31354	+	1.64713i
$634$	−167.948	−	735.828i	−0.264902	−	1.16061i
$635$	9.76432	+	15.5398i	0.0153769	+	0.0244722i
$636$	45.6838	+	405.455i	0.0718299	+	0.637508i
$637$			9.07439i			0.0142455i
$638$	638.704	+	34.0616i	1.00110	+	0.0533881i
$639$	−394.488			−0.617353
$640$	−9.13367	+	1.02912i	−0.0142714	+	0.00160800i
$641$	439.716	−	276.292i	0.685984	−	0.431032i	−0.143435	−	0.989660i	$-0.545815\pi$
$641$	439.716	−	276.292i	0.685984	−	0.431032i	0.829419	+	0.558628i	$0.188672\pi$
$642$	−1051.87	+	240.084i	−1.63843	+	0.373962i
$643$	886.679	+	707.103i	1.37897	+	1.09969i	0.983439	+	0.181241i	$0.0580115\pi$
$643$	886.679	+	707.103i	1.37897	+	1.09969i	0.395533	+	0.918452i	$0.370560\pi$
$644$	146.579	−	116.893i	0.227607	−	0.181510i
$645$	6.94978	−	30.4490i	0.0107748	−	0.0472077i
$646$	−270.414	+	94.6219i	−0.418597	+	0.146474i
$647$	−64.3196	+	133.561i	−0.0994120	+	0.206431i	−0.944743	−	0.327812i	$-0.893689\pi$
$647$	−64.3196	+	133.561i	−0.0994120	+	0.206431i	0.845331	+	0.534243i	$0.179403\pi$
$648$	434.760	+	273.178i	0.670926	+	0.421571i
$649$	−343.583	−	120.225i	−0.529404	−	0.185246i
$650$	−667.734	+	667.734i	−1.02728	+	1.02728i
$651$	−484.360	−	1005.78i	−0.744024	−	1.54498i
$652$	3.55242	−	31.5286i	0.00544850	−	0.0483568i
$653$	−828.414	−	93.3398i	−1.26863	−	0.142940i	−0.548128	−	0.836395i	$-0.684659\pi$
$653$	−828.414	−	93.3398i	−1.26863	−	0.142940i	−0.720500	+	0.693455i	$0.756088\pi$
$654$	215.853	−	103.949i	0.330050	−	0.158944i
$655$	12.3332	+	12.3332i	0.0188294	+	0.0188294i
$656$	67.9493	−	194.188i	0.103581	−	0.296018i
$657$	609.265	−	969.640i	0.927344	−	1.47586i
$658$	−49.5117	−	23.8436i	−0.0752458	−	0.0362365i
$659$	30.0943	+	86.0046i	0.0456666	+	0.130508i	0.964458	−	0.264235i	$-0.0851194\pi$
$659$	30.0943	+	86.0046i	0.0456666	+	0.130508i	−0.918792	+	0.394743i	$0.870834\pi$
$660$	−11.4419	−	2.61154i	−0.0173362	−	0.00395688i
$661$	−17.7926	−	22.3113i	−0.0269177	−	0.0337538i	0.768190	−	0.640221i	$-0.221157\pi$
$661$	−17.7926	−	22.3113i	−0.0269177	−	0.0337538i	−0.795108	+	0.606468i	$0.792586\pi$
$662$	309.366	−	387.933i	0.467320	−	0.586001i
$663$	185.070	+	810.845i	0.279140	+	1.22299i
$664$	−127.476	−	202.877i	−0.191982	−	0.305538i
$665$	−2.85692	−	25.3559i	−0.00429613	−	0.0381292i
$666$		−	456.783i		−	0.685860i
$667$	522.868	+	464.617i	0.783910	+	0.696578i
$668$	47.1095			0.0705231
$669$	305.314	−	34.4006i	0.456373	−	0.0514209i
$670$	1.73241	−	1.08855i	0.00258569	−	0.00162470i
$671$	48.8125	−	11.1411i	0.0727458	−	0.0166038i
$672$	420.686	+	335.486i	0.626020	+	0.499235i
$673$	−459.480	+	366.423i	−0.682734	+	0.544463i	−0.902286	−	0.431138i	$-0.858112\pi$
$673$	−459.480	+	366.423i	−0.682734	+	0.544463i	0.219551	+	0.975601i	$0.429541\pi$
$674$	−178.808	+	783.408i	−0.265293	+	1.16233i
$675$	209.929	−	73.4572i	0.311005	−	0.108825i
$676$	158.140	−	328.382i	0.233935	−	0.485772i
$677$	−104.008	−	65.3523i	−0.153630	−	0.0965322i	0.453023	−	0.891499i	$-0.350346\pi$
$677$	−104.008	−	65.3523i	−0.153630	−	0.0965322i	−0.606653	+	0.794967i	$0.707488\pi$
$678$	−691.668	−	242.025i	−1.02016	−	0.356969i
$679$	35.4767	−	35.4767i	0.0522485	−	0.0522485i
$680$	−5.70806	−	11.8529i	−0.00839420	−	0.0174307i
$681$	−221.344	+	1964.48i	−0.325027	+	2.88470i
$682$	784.978	+	88.4458i	1.15099	+	0.129686i
$683$	909.152	−	437.825i	1.33112	−	0.641032i	0.373112	−	0.927786i	$-0.378291\pi$
$683$	909.152	−	437.825i	1.33112	−	0.641032i	0.958004	+	0.286755i	$0.0925765\pi$
$684$	−175.011	−	175.011i	−0.255864	−	0.255864i
$685$	−11.0183	+	31.4886i	−0.0160852	+	0.0459688i
$686$	311.231	−	495.322i	0.453690	−	0.722043i
$687$	369.108	+	177.753i	0.537275	+	0.258738i
$688$	−131.036	−	374.479i	−0.190459	−	0.544301i
$689$	−1776.66	−	405.511i	−2.57861	−	0.588550i
$690$	20.7035	+	25.9614i	0.0300051	+	0.0376252i
$691$	−82.1865	+	103.059i	−0.118938	+	0.149144i	−0.837736	−	0.546075i	$-0.816121\pi$
$691$	−82.1865	+	103.059i	−0.118938	+	0.149144i	0.718798	+	0.695219i	$0.244693\pi$
$692$	−31.5208	−	138.102i	−0.0455503	−	0.199569i
$693$	−529.372	−	842.490i	−0.763884	−	1.21571i
$694$	97.2684	+	863.280i	0.140156	+	1.24392i
$695$			33.8670i			0.0487296i
$696$	−542.147	+	987.512i	−0.778947	+	1.41884i
$697$	166.906			0.239464
$698$	813.571	−	91.6674i	1.16557	−	0.131329i
$699$	438.051	−	275.246i	0.626682	−	0.393771i
$700$	−189.202	+	43.1842i	−0.270289	+	0.0616918i
$701$	205.200	+	163.642i	0.292725	+	0.233441i	0.758830	−	0.651289i	$-0.225771\pi$
$701$	205.200	+	163.642i	0.292725	+	0.233441i	−0.466104	+	0.884730i	$0.654343\pi$
$702$	263.419	−	210.070i	0.375241	−	0.299245i
$703$	109.930	−	481.633i	0.156372	−	0.685111i
$704$	−864.181	+	302.390i	−1.22753	+	0.429531i
$705$	−1.63228	+	3.38946i	−0.00231529	+	0.00480774i
$706$	−350.905	−	220.488i	−0.497033	−	0.312307i
$707$	−734.285	−	256.937i	−1.03859	−	0.363419i
$708$	98.8282	−	98.8282i	0.139588	−	0.139588i
$709$	242.106	+	502.738i	0.341475	+	0.709081i	0.999017	−	0.0443379i	$-0.0141178\pi$
$709$	242.106	+	502.738i	0.341475	+	0.709081i	−0.657541	+	0.753418i	$0.728404\pi$
$710$	−1.23719	+	10.9804i	−0.00174252	+	0.0154653i
$711$	−931.384	−	104.942i	−1.30996	−	0.147597i
$712$	211.299	−	101.756i	0.296768	−	0.142916i
$713$	610.852	+	610.852i	0.856735	+	0.856735i
$714$	146.055	−	417.402i	0.204559	−	0.584597i
$715$	27.8877	−	44.3830i	0.0390038	−	0.0620742i
$716$	146.542	+	70.5710i	0.204668	+	0.0985628i
$717$	−258.827	−	739.685i	−0.360986	−	1.03164i
$718$	−998.611	−	227.926i	−1.39082	−	0.317446i
$719$	173.291	+	217.300i	0.241017	+	0.302225i	0.887597	−	0.460620i	$-0.152373\pi$
$719$	173.291	+	217.300i	0.241017	+	0.302225i	−0.646581	+	0.762846i	$0.723802\pi$
$720$	−12.7922	+	16.0409i	−0.0177669	+	0.0222790i
$721$	186.766	+	818.277i	0.259038	+	1.13492i
$722$	42.2353	+	67.2171i	0.0584976	+	0.0930984i
$723$	1.87500	+	16.6411i	0.00259336	+	0.0230167i
$724$			242.602i			0.335085i
$725$	−278.967	−	668.148i	−0.384782	−	0.921583i
$726$	361.624			0.498105
$727$	−868.909	+	97.9026i	−1.19520	+	0.134667i	−0.687055	−	0.726606i	$-0.741097\pi$
$727$	−868.909	+	97.9026i	−1.19520	+	0.134667i	−0.508144	+	0.861272i	$0.669668\pi$
$728$	−1141.90	+	717.502i	−1.56854	+	0.985580i
$729$	982.845	−	224.328i	1.34821	−	0.307720i
$730$	−25.0787	−	19.9996i	−0.0343543	−	0.0273967i
$731$	251.647	−	200.681i	0.344250	−	0.274530i
$732$	−4.27771	+	18.7419i	−0.00584386	+	0.0256036i
$733$	121.421	−	42.4869i	0.165649	−	0.0579631i	−0.246181	−	0.969224i	$-0.579176\pi$
$733$	121.421	−	42.4869i	0.165649	−	0.0579631i	0.411830	+	0.911261i	$0.364890\pi$
$734$	−190.712	+	396.017i	−0.259825	+	0.539533i
$735$	−0.279674	−	0.175731i	−0.000380509	−	0.000239090i
$736$	−393.024	−	137.525i	−0.534000	−	0.186855i
$737$	61.0145	−	61.0145i	0.0827876	−	0.0827876i
$738$	−161.864	−	336.114i	−0.219328	−	0.455439i
$739$	61.1890	−	543.068i	0.0827998	−	0.734868i	−0.881886	−	0.471463i	$-0.843726\pi$
$739$	61.1890	−	543.068i	0.0827998	−	0.734868i	0.964685	−	0.263405i	$-0.0848455\pi$
$740$	4.91426	+	0.553704i	0.00664089	+	0.000748249i
$741$	1811.40	−	872.322i	2.44453	−	1.17722i
$742$	685.153	+	685.153i	0.923387	+	0.923387i
$743$	73.3592	−	209.649i	0.0987338	−	0.282165i	−0.883913	−	0.467651i	$-0.845100\pi$
$743$	73.3592	−	209.649i	0.0987338	−	0.282165i	0.982647	+	0.185486i	$0.0593860\pi$
$744$	−740.231	+	1178.07i	−0.994934	+	1.58343i
$745$	18.8318	+	9.06891i	0.0252776	+	0.0121730i
$746$	341.955	+	977.252i	0.458385	+	1.30999i
$747$	−295.551	−	67.4577i	−0.395651	−	0.0903048i
$748$	−75.4107	−	94.5620i	−0.100816	−	0.126420i
$749$	617.456	−	774.266i	0.824374	−	1.03373i
$750$	−15.3073	−	67.0655i	−0.0204097	−	0.0894207i
$751$	−4.56022	−	7.25755i	−0.00607220	−	0.00966385i	0.843674	−	0.536855i	$-0.180388\pi$
$751$	−4.56022	−	7.25755i	−0.00607220	−	0.00966385i	−0.849747	+	0.527191i	$0.823245\pi$
$752$	5.35069	+	47.4887i	0.00711528	+	0.0631498i
$753$		−	851.592i		−	1.13093i
$754$	−733.187	−	815.793i	−0.972397	−	1.08195i
$755$	−1.84504			−0.00244377
$756$	68.8067	−	7.75265i	0.0910141	−	0.0102548i
$757$	642.972	−	404.006i	0.849368	−	0.533693i	−0.0355886	−	0.999367i	$-0.511331\pi$
$757$	642.972	−	404.006i	0.849368	−	0.533693i	0.884957	+	0.465673i	$0.154188\pi$
$758$	267.898	−	61.1460i	0.353427	−	0.0806675i
$759$	1094.88	+	873.138i	1.44253	+	1.15038i
$760$	−24.8637	+	19.8282i	−0.0327154	+	0.0260897i
$761$	−61.0011	+	267.263i	−0.0801592	+	0.351200i	−0.999063	−	0.0432815i	$-0.986219\pi$
$761$	−61.0011	+	267.263i	−0.0801592	+	0.351200i	0.918904	+	0.394482i	$0.129076\pi$
$762$	725.736	−	253.946i	0.952409	−	0.333262i
$763$	−95.4128	+	198.127i	−0.125050	+	0.259668i
$764$	188.013	+	118.137i	0.246091	+	0.154629i
$765$	−15.7109	−	5.49750i	−0.0205372	−	0.00718627i
$766$	418.001	−	418.001i	0.545693	−	0.545693i
$767$	270.844	+	562.413i	0.353121	+	0.733263i
$768$	98.0770	−	870.457i	0.127704	−	1.13341i
$769$	1376.20	+	155.060i	1.78959	+	0.201639i	0.943494	−	0.331390i	$-0.107518\pi$
$769$	1376.20	+	155.060i	1.78959	+	0.201639i	0.846097	+	0.533028i	$0.178946\pi$
$770$	−25.1105	+	12.0926i	−0.0326111	+	0.0157047i
$771$	−454.606	−	454.606i	−0.589631	−

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 29 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	29.f (of order \(28\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.68783 + 0.190173i) q^{2} +(-3.78594 + 2.37886i) q^{3} +(-1.08711 + 0.248126i) q^{4} +(0.141728 + 0.113024i) q^{5} +(5.93762 - 4.73509i) q^{6} +(-1.55116 + 6.79606i) q^{7} +(8.20045 - 2.86946i) q^{8} +(4.76938 - 9.90371i) q^{9} +O(q^{10})\)	\(q+(-1.68783 + 0.190173i) q^{2} +(-3.78594 + 2.37886i) q^{3} +(-1.08711 + 0.248126i) q^{4} +(0.141728 + 0.113024i) q^{5} +(5.93762 - 4.73509i) q^{6} +(-1.55116 + 6.79606i) q^{7} +(8.20045 - 2.86946i) q^{8} +(4.76938 - 9.90371i) q^{9} +(-0.260707 - 0.163813i) q^{10} +(-12.2566 - 4.28875i) q^{11} +(3.52547 - 3.52547i) q^{12} +(9.66173 + 20.0628i) q^{13} +(1.32566 - 11.7656i) q^{14} +(-0.805444 - 0.0907517i) q^{15} +(-9.27670 + 4.46742i) q^{16} +(-5.90660 - 5.90660i) q^{17} +(-6.16648 + 17.6228i) q^{18} +(-10.7431 + 17.0975i) q^{19} +(-0.182118 - 0.0877036i) q^{20} +(-10.2943 - 29.4194i) q^{21} +(21.5026 + 4.90782i) q^{22} +(15.0384 + 18.8575i) q^{23} +(-24.2203 + 30.3713i) q^{24} +(-5.55571 - 24.3412i) q^{25} +(-20.1228 - 32.0252i) q^{26} +(0.997389 + 8.85208i) q^{27} -7.77294i q^{28} +(28.5764 - 4.93832i) q^{29} +1.37671 q^{30} +(35.5909 - 4.01014i) q^{31} +(-14.6174 + 9.18473i) q^{32} +(56.6049 - 12.9197i) q^{33} +(11.0926 + 8.84605i) q^{34} +(-0.987964 + 0.787875i) q^{35} +(-2.72747 + 11.9498i) q^{36} +(-23.0925 + 8.08043i) q^{37} +(14.8810 - 30.9007i) q^{38} +(-84.3053 - 52.9725i) q^{39} +(1.48655 + 0.520168i) q^{40} +(-14.1288 + 14.1288i) q^{41} +(22.9698 + 47.6973i) q^{42} +(-4.31425 + 38.2901i) q^{43} +(14.3884 + 1.62118i) q^{44} +(1.79532 - 0.864579i) q^{45} +(-28.9684 - 28.9684i) q^{46} +(1.53295 - 4.38091i) q^{47} +(24.4936 - 38.9814i) q^{48} +(0.367152 + 0.176811i) q^{49} +(14.0061 + 40.0272i) q^{50} +(36.4130 + 8.31102i) q^{51} +(-15.4815 - 19.4131i) q^{52} +(-51.0246 + 63.9828i) q^{53} +(-3.36685 - 14.7511i) q^{54} +(-1.25237 - 1.99313i) q^{55} +(6.78085 + 60.1817i) q^{56} -90.2863i q^{57} +(-47.2930 + 13.7695i) q^{58} +28.0326 q^{59} +(0.898124 - 0.101194i) q^{60} +(-3.26475 + 2.05138i) q^{61} +(-59.3088 + 13.5368i) q^{62} +(59.9082 + 47.7752i) q^{63} +(55.1251 - 43.9608i) q^{64} +(-0.898247 + 3.93548i) q^{65} +(-93.0824 + 32.5709i) q^{66} +(-2.88318 + 5.98698i) q^{67} +(7.88670 + 4.95554i) q^{68} +(-101.794 - 35.6192i) q^{69} +(1.51768 - 1.51768i) q^{70} +(-15.5711 - 32.3337i) q^{71} +(10.6927 - 94.9004i) q^{72} +(103.524 + 11.6644i) q^{73} +(37.4396 - 18.0300i) q^{74} +(78.9378 + 78.9378i) q^{75} +(7.43657 - 21.2525i) q^{76} +(48.1585 - 76.6437i) q^{77} +(152.367 + 73.3760i) q^{78} +(-28.1618 - 80.4819i) q^{79} +(-1.81970 - 0.415334i) q^{80} +(36.8483 + 46.2063i) q^{81} +(21.1601 - 26.5339i) q^{82} +(-6.13681 - 26.8871i) q^{83} +(18.4908 + 29.4279i) q^{84} +(-0.169541 - 1.50472i) q^{85} -65.4475i q^{86} +(-96.4410 + 86.6755i) q^{87} -112.816 q^{88} +(26.8243 - 3.02237i) q^{89} +(-2.86577 + 1.80068i) q^{90} +(-151.335 + 34.5412i) q^{91} +(-21.0274 - 16.7688i) q^{92} +(-125.205 + 99.8480i) q^{93} +(-1.75422 + 7.68575i) q^{94} +(-3.45503 + 1.20897i) q^{95} +(33.4914 - 69.5456i) q^{96} +(-6.09419 - 3.82923i) q^{97} +(-0.653314 - 0.228604i) q^{98} +(-100.931 + 100.931i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48q - 16q^{2} - 12q^{3} - 14q^{4} - 14q^{5} - 14q^{6} - 10q^{7} + 28q^{8} - 14q^{9} + O(q^{10}) \)	\( 48q - 16q^{2} - 12q^{3} - 14q^{4} - 14q^{5} - 14q^{6} - 10q^{7} + 28q^{8} - 14q^{9} - 20q^{10} - 8q^{11} - 68q^{12} - 14q^{13} + 26q^{14} - 4q^{15} + 18q^{16} - 26q^{17} - 34q^{18} + 2q^{19} + 46q^{20} + 218q^{21} + 154q^{22} + 56q^{23} + 154q^{24} - 34q^{25} + 110q^{26} + 126q^{27} - 170q^{29} + 24q^{30} - 88q^{31} - 132q^{32} - 224q^{33} - 224q^{34} - 210q^{35} - 434q^{36} - 56q^{37} - 294q^{38} - 232q^{39} - 492q^{40} - 34q^{41} - 14q^{42} + 176q^{43} + 126q^{44} + 114q^{45} + 744q^{46} + 208q^{47} + 640q^{48} + 506q^{49} + 732q^{50} + 322q^{51} + 690q^{52} - 14q^{53} - 36q^{54} + 284q^{55} + 332q^{56} - 508q^{58} - 44q^{59} - 316q^{60} - 30q^{61} - 504q^{62} - 686q^{63} - 896q^{64} - 554q^{65} - 608q^{66} - 574q^{67} - 796q^{68} - 806q^{69} - 1066q^{70} + 224q^{71} + 748q^{72} - 22q^{73} + 820q^{74} + 768q^{75} + 514q^{76} + 436q^{77} + 282q^{78} + 564q^{79} + 1162q^{80} + 670q^{81} - 18q^{82} - 126q^{83} + 572q^{84} + 38q^{85} - 118q^{87} - 384q^{88} - 160q^{89} - 828q^{90} - 434q^{91} - 1022q^{92} - 406q^{93} - 2q^{94} - 642q^{95} - 1176q^{96} + 604q^{97} - 102q^{98} + 316q^{99} + O(q^{100}) \)

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