LMFDB - Embedded newform 29.3.f.a.15.3

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			15.3
Character	$\chi$	$=$	29.15
Dual form			29.3.f.a.2.3

$q$-expansion

$f(q)$	$=$	$q+(0.415096 - 0.0467701i) q^{2} +(2.68233 - 1.68542i) q^{3} +(-3.72959 + 0.851255i) q^{4} +(0.738700 + 0.589093i) q^{5} +(1.03460 - 0.825065i) q^{6} +(-0.577468 + 2.53005i) q^{7} +(-3.08546 + 1.07965i) q^{8} +(0.449302 - 0.932984i) q^{9} +O(q^{10})$	\(q+(0.415096 - 0.0467701i) q^{2} +(2.68233 - 1.68542i) q^{3} +(-3.72959 + 0.851255i) q^{4} +(0.738700 + 0.589093i) q^{5} +(1.03460 - 0.825065i) q^{6} +(-0.577468 + 2.53005i) q^{7} +(-3.08546 + 1.07965i) q^{8} +(0.449302 - 0.932984i) q^{9} +(0.334184 + 0.209981i) q^{10} +(-8.65125 - 3.02720i) q^{11} +(-8.56928 + 8.56928i) q^{12} +(-4.51239 - 9.37008i) q^{13} +(-0.121374 + 1.07722i) q^{14} +(2.97431 + 0.335124i) q^{15} +(12.5564 - 6.04684i) q^{16} +(21.4949 + 21.4949i) q^{17} +(0.142868 - 0.408292i) q^{18} +(14.2589 - 22.6929i) q^{19} +(-3.25652 - 1.56826i) q^{20} +(2.71524 + 7.75971i) q^{21} +(-3.73269 - 0.851961i) q^{22} +(-2.27710 - 2.85539i) q^{23} +(-6.45655 + 8.09626i) q^{24} +(-5.36438 - 23.5029i) q^{25} +(-2.31132 - 3.67844i) q^{26} +(2.82493 + 25.0719i) q^{27} -9.92764i q^{28} +(-24.3191 + 15.7981i) q^{29} +1.25030 q^{30} +(21.7090 - 2.44602i) q^{31} +(16.0007 - 10.0539i) q^{32} +(-28.3076 + 6.46103i) q^{33} +(9.92777 + 7.91713i) q^{34} +(-1.91701 + 1.52877i) q^{35} +(-0.881504 + 3.86212i) q^{36} +(-46.0478 + 16.1128i) q^{37} +(4.85746 - 10.0866i) q^{38} +(-27.8962 - 17.5284i) q^{39} +(-2.91524 - 1.02009i) q^{40} +(-25.3355 + 25.3355i) q^{41} +(1.49001 + 3.09404i) q^{42} +(2.78030 - 24.6759i) q^{43} +(34.8426 + 3.92581i) q^{44} +(0.881514 - 0.424515i) q^{45} +(-1.07876 - 1.07876i) q^{46} +(7.49184 - 21.4104i) q^{47} +(23.4889 - 37.3824i) q^{48} +(38.0798 + 18.3383i) q^{49} +(-3.32597 - 9.50507i) q^{50} +(93.8843 + 21.4285i) q^{51} +(24.8057 + 31.1054i) q^{52} +(-18.6271 + 23.3576i) q^{53} +(2.34523 + 10.2751i) q^{54} +(-4.60737 - 7.33259i) q^{55} +(-0.949813 - 8.42982i) q^{56} -84.9020i q^{57} +(-9.35591 + 7.69514i) q^{58} +18.2577 q^{59} +(-11.3782 + 1.28202i) q^{60} +(-78.8333 + 49.5342i) q^{61} +(8.89694 - 2.03067i) q^{62} +(2.10104 + 1.67552i) q^{63} +(-37.4125 + 29.8355i) q^{64} +(2.18655 - 9.57990i) q^{65} +(-11.4482 + 4.00590i) q^{66} +(24.5454 - 50.9691i) q^{67} +(-98.4648 - 61.8696i) q^{68} +(-10.9205 - 3.82123i) q^{69} +(-0.724244 + 0.724244i) q^{70} +(56.1438 + 116.584i) q^{71} +(-0.379006 + 3.36377i) q^{72} +(47.2614 + 5.32509i) q^{73} +(-18.3607 + 8.84204i) q^{74} +(-54.0012 - 54.0012i) q^{75} +(-33.8624 + 96.7732i) q^{76} +(12.6548 - 20.1400i) q^{77} +(-12.3994 - 5.97125i) q^{78} +(-13.7375 - 39.2594i) q^{79} +(12.8375 + 2.93009i) q^{80} +(55.6449 + 69.7765i) q^{81} +(-9.33174 + 11.7016i) q^{82} +(-29.4538 - 129.046i) q^{83} +(-16.7322 - 26.6292i) q^{84} +(3.21577 + 28.5408i) q^{85} -10.3729i q^{86} +(-38.6056 + 83.3636i) q^{87} +29.9614 q^{88} +(32.3276 - 3.64244i) q^{89} +(0.346059 - 0.217443i) q^{90} +(26.3125 - 6.00567i) q^{91} +(10.9233 + 8.71105i) q^{92} +(54.1082 - 43.1499i) q^{93} +(2.10847 - 9.23779i) q^{94} +(23.9012 - 8.36341i) q^{95} +(25.9741 - 53.9358i) q^{96} +(-36.1089 - 22.6888i) q^{97} +(16.6645 + 5.83115i) q^{98} +(-6.71135 + 6.71135i) 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 $

$2$	0.415096	−	0.0467701i	0.207548	−	0.0233851i	−0.00757815	−	0.999971i	$-0.502412\pi$
$2$	0.415096	−	0.0467701i	0.207548	−	0.0233851i	0.215126	+	0.976586i	$0.430984\pi$
$3$	2.68233	−	1.68542i	0.894110	−	0.561807i	−0.00477622	−	0.999989i	$-0.501520\pi$
$3$	2.68233	−	1.68542i	0.894110	−	0.561807i	0.898886	+	0.438182i	$0.144377\pi$
$4$	−3.72959	+	0.851255i	−0.932398	+	0.212814i
$5$	0.738700	+	0.589093i	0.147740	+	0.117819i	0.694571	−	0.719425i	$-0.255594\pi$
$5$	0.738700	+	0.589093i	0.147740	+	0.117819i	−0.546831	+	0.837243i	$0.684166\pi$
$6$	1.03460	−	0.825065i	0.172433	−	0.137511i
$7$	−0.577468	+	2.53005i	−0.0824954	+	0.361436i	−0.999280	−	0.0379466i	$-0.987918\pi$
$7$	−0.577468	+	2.53005i	−0.0824954	+	0.361436i	0.916784	+	0.399383i	$0.130775\pi$
$8$	−3.08546	+	1.07965i	−0.385682	+	0.134956i
$9$	0.449302	−	0.932984i	0.0499224	−	0.103665i
$10$	0.334184	+	0.209981i	0.0334184	+	0.0209981i
$11$	−8.65125	−	3.02720i	−0.786477	−	0.275200i	−0.0929879	−	0.995667i	$-0.529642\pi$
$11$	−8.65125	−	3.02720i	−0.786477	−	0.275200i	−0.693489	+	0.720467i	$0.743928\pi$
$12$	−8.56928	+	8.56928i	−0.714107	+	0.714107i
$13$	−4.51239	−	9.37008i	−0.347107	−	0.720775i	0.652198	−	0.758049i	$-0.273847\pi$
$13$	−4.51239	−	9.37008i	−0.347107	−	0.720775i	−0.999305	+	0.0372733i	$0.988133\pi$
$14$	−0.121374	+	1.07722i	−0.00866957	+	0.0769445i
$15$	2.97431	+	0.335124i	0.198287	+	0.0223416i
$16$	12.5564	−	6.04684i	0.784774	−	0.377927i
$17$	21.4949	+	21.4949i	1.26441	+	1.26441i	0.948936	+	0.315469i	$0.102162\pi$
$17$	21.4949	+	21.4949i	1.26441	+	1.26441i	0.315469	+	0.948936i	$0.397838\pi$
$18$	0.142868	−	0.408292i	0.00793709	−	0.0226829i
$19$	14.2589	−	22.6929i	0.750467	−	1.19436i	−0.225030	−	0.974352i	$-0.572248\pi$
$19$	14.2589	−	22.6929i	0.750467	−	1.19436i	0.975498	−	0.220010i	$-0.0706090\pi$
$20$	−3.25652	−	1.56826i	−0.162826	−	0.0784128i
$21$	2.71524	+	7.75971i	0.129297	+	0.369510i
$22$	−3.73269	−	0.851961i	−0.169668	−	0.0387255i
$23$	−2.27710	−	2.85539i	−0.0990042	−	0.124147i	0.729861	−	0.683595i	$-0.239585\pi$
$23$	−2.27710	−	2.85539i	−0.0990042	−	0.124147i	−0.828866	+	0.559448i	$0.811013\pi$
$24$	−6.45655	+	8.09626i	−0.269023	+	0.337344i
$25$	−5.36438	−	23.5029i	−0.214575	−	0.940115i
$26$	−2.31132	−	3.67844i	−0.0888969	−	0.141479i
$27$	2.82493	+	25.0719i	0.104627	+	0.928589i
$28$		−	9.92764i		−	0.354558i
$29$	−24.3191	+	15.7981i	−0.838591	+	0.544761i
$29$	−24.3191	+	15.7981i	−0.838591	+	0.544761i
$30$	1.25030			0.0416766
$31$	21.7090	−	2.44602i	0.700291	−	0.0789039i	0.245362	−	0.969431i	$-0.421093\pi$
$31$	21.7090	−	2.44602i	0.700291	−	0.0789039i	0.454929	+	0.890528i	$0.349665\pi$
$32$	16.0007	−	10.0539i	0.500022	−	0.314185i
$33$	−28.3076	+	6.46103i	−0.857807	+	0.195789i
$34$	9.92777	+	7.91713i	0.291993	+	0.232857i
$35$	−1.91701	+	1.52877i	−0.0547718	+	0.0436790i
$36$	−0.881504	+	3.86212i	−0.0244862	+	0.107281i
$37$	−46.0478	+	16.1128i	−1.24454	+	0.435482i	−0.870608	−	0.491976i	$-0.836275\pi$
$37$	−46.0478	+	16.1128i	−1.24454	+	0.435482i	−0.373927	+	0.927458i	$0.621989\pi$
$38$	4.85746	−	10.0866i	0.127828	−	0.265437i
$39$	−27.8962	−	17.5284i	−0.715288	−	0.449445i
$40$	−2.91524	−	1.02009i	−0.0728810	−	0.0255021i
$41$	−25.3355	+	25.3355i	−0.617940	+	0.617940i	−0.945003	−	0.327063i	$-0.893941\pi$
$41$	−25.3355	+	25.3355i	−0.617940	+	0.617940i	0.327063	+	0.945003i	$0.393941\pi$
$42$	1.49001	+	3.09404i	0.0354764	+	0.0736675i
$43$	2.78030	−	24.6759i	0.0646582	−	0.573857i	−0.919057	−	0.394124i	$-0.871048\pi$
$43$	2.78030	−	24.6759i	0.0646582	−	0.573857i	0.983715	−	0.179733i	$-0.0575234\pi$
$44$	34.8426	+	3.92581i	0.791877	+	0.0892231i
$45$	0.881514	−	0.424515i	0.0195892	−	0.00943366i
$46$	−1.07876	−	1.07876i	−0.0234513	−	0.0234513i
$47$	7.49184	−	21.4104i	0.159401	−	0.455541i	−0.836289	−	0.548289i	$-0.815279\pi$
$47$	7.49184	−	21.4104i	0.159401	−	0.455541i	0.995690	+	0.0927479i	$0.0295651\pi$
$48$	23.4889	−	37.3824i	0.489352	−	0.778800i
$49$	38.0798	+	18.3383i	0.777138	+	0.374250i
$50$	−3.32597	−	9.50507i	−0.0665193	−	0.190101i
$51$	93.8843	+	21.4285i	1.84087	+	0.420166i
$52$	24.8057	+	31.1054i	0.477033	+	0.598181i
$53$	−18.6271	+	23.3576i	−0.351454	+	0.440709i	−0.925863	−	0.377859i	$-0.876660\pi$
$53$	−18.6271	+	23.3576i	−0.351454	+	0.440709i	0.574409	+	0.818568i	$0.305232\pi$
$54$	2.34523	+	10.2751i	0.0434303	+	0.190280i
$55$	−4.60737	−	7.33259i	−0.0837704	−	0.133320i
$56$	−0.949813	−	8.42982i	−0.0169609	−	0.150533i
$57$		−	84.9020i		−	1.48951i
$58$	−9.35591	+	7.69514i	−0.161309	+	0.132675i
$59$	18.2577			0.309453			0.154726	−	0.987957i	$-0.450550\pi$
$59$	18.2577			0.309453			0.154726	+	0.987957i	$0.450550\pi$
$60$	−11.3782	+	1.28202i	−0.189637	+	0.0213670i
$61$	−78.8333	+	49.5342i	−1.29235	+	0.812037i	−0.989987	−	0.141156i	$-0.954918\pi$
$61$	−78.8333	+	49.5342i	−1.29235	+	0.812037i	−0.302362	+	0.953193i	$0.597775\pi$
$62$	8.89694	−	2.03067i	0.143499	−	0.0327527i
$63$	2.10104	+	1.67552i	0.0333499	+	0.0265956i
$64$	−37.4125	+	29.8355i	−0.584570	+	0.466179i
$65$	2.18655	−	9.57990i	0.0336392	−	0.147383i
$66$	−11.4482	+	4.00590i	−0.173458	+	0.0606955i
$67$	24.5454	−	50.9691i	0.366349	−	0.760732i	−0.633567	−	0.773688i	$-0.718410\pi$
$67$	24.5454	−	50.9691i	0.366349	−	0.760732i	0.999916	+	0.0129558i	$0.00412406\pi$
$68$	−98.4648	−	61.8696i	−1.44801	−	0.909846i
$69$	−10.9205	−	3.82123i	−0.158267	−	0.0553802i
$70$	−0.724244	+	0.724244i	−0.0103463	+	0.0103463i
$71$	56.1438	+	116.584i	0.790758	+	1.64203i	0.766436	+	0.642321i	$0.222028\pi$
$71$	56.1438	+	116.584i	0.790758	+	1.64203i	0.0243218	+	0.999704i	$0.492257\pi$
$72$	−0.379006	+	3.36377i	−0.00526397	+	0.0467190i
$73$	47.2614	+	5.32509i	0.647417	+	0.0729464i	0.429566	−	0.903036i	$-0.358667\pi$
$73$	47.2614	+	5.32509i	0.647417	+	0.0729464i	0.217851	+	0.975982i	$0.430095\pi$
$74$	−18.3607	+	8.84204i	−0.248117	+	0.119487i
$75$	−54.0012	−	54.0012i	−0.720016	−	0.720016i
$76$	−33.8624	+	96.7732i	−0.445558	+	1.27333i
$77$	12.6548	−	20.1400i	0.164348	−	0.261558i
$78$	−12.3994	−	5.97125i	−0.158967	−	0.0765545i
$79$	−13.7375	−	39.2594i	−0.173892	−	0.496954i	0.823644	−	0.567107i	$-0.191937\pi$
$79$	−13.7375	−	39.2594i	−0.173892	−	0.496954i	−0.997536	+	0.0701522i	$0.977652\pi$
$80$	12.8375	+	2.93009i	0.160469	+	0.0366261i
$81$	55.6449	+	69.7765i	0.686974	+	0.861438i
$82$	−9.33174	+	11.7016i	−0.113802	+	0.142703i
$83$	−29.4538	−	129.046i	−0.354865	−	1.55477i	−0.765786	−	0.643095i	$-0.777650\pi$
$83$	−29.4538	−	129.046i	−0.354865	−	1.55477i	0.410921	−	0.911671i	$-0.365207\pi$
$84$	−16.7322	−	26.6292i	−0.199193	−	0.317014i
$85$	3.21577	+	28.5408i	0.0378326	+	0.335774i
$86$		−	10.3729i		−	0.120615i
$87$	−38.6056	+	83.3636i	−0.443742	+	0.958203i
$88$	29.9614			0.340470
$89$	32.3276	−	3.64244i	0.363231	−	0.0409263i	0.0715370	−	0.997438i	$-0.477210\pi$
$89$	32.3276	−	3.64244i	0.363231	−	0.0409263i	0.291694	+	0.956512i	$0.405781\pi$
$90$	0.346059	−	0.217443i	0.00384510	−	0.00241603i
$91$	26.3125	−	6.00567i	0.289149	−	0.0659963i
$92$	10.9233	+	8.71105i	0.118732	+	0.0946853i
$93$	54.1082	−	43.1499i	0.581809	−	0.463977i
$94$	2.10847	−	9.23779i	0.0224305	−	0.0982744i
$95$	23.9012	−	8.36341i	0.251592	−	0.0880359i
$96$	25.9741	−	53.9358i	0.270564	−	0.561831i
$97$	−36.1089	−	22.6888i	−0.372257	−	0.233905i	0.332890	−	0.942966i	$-0.391976\pi$
$97$	−36.1089	−	22.6888i	−0.372257	−	0.233905i	−0.705147	+	0.709061i	$0.749119\pi$
$98$	16.6645	+	5.83115i	0.170046	+	0.0595015i
$99$	−6.71135	+	6.71135i	−0.0677914	+	0.0677914i
$100$	40.0139	+	83.0897i	0.400139	+	0.830897i
$101$	10.9637	−	97.3053i	0.108551	−	0.963419i	−0.814873	−	0.579639i	$-0.803194\pi$
$101$	10.9637	−	97.3053i	0.108551	−	0.963419i	0.923425	−	0.383780i	$-0.125378\pi$
$102$	39.9733	+	4.50390i	0.391895	+	0.0441559i
$103$	−66.1244	+	31.8438i	−0.641985	+	0.309164i	−0.726405	−	0.687267i	$-0.758810\pi$
$103$	−66.1244	+	31.8438i	−0.641985	+	0.309164i	0.0844205	+	0.996430i	$0.473096\pi$
$104$	24.0392	+	24.0392i	0.231146	+	0.231146i
$105$	−2.56545	+	7.33162i	−0.0244328	+	0.0698250i
$106$	−6.63959	+	10.5668i	−0.0626376	+	0.0996872i
$107$	55.3820	+	26.6706i	0.517589	+	0.249258i	0.674394	−	0.738372i	$-0.264405\pi$
$107$	55.3820	+	26.6706i	0.517589	+	0.249258i	−0.156805	+	0.987630i	$0.550119\pi$
$108$	−31.8784	−	91.1033i	−0.295171	−	0.843549i
$109$	154.567	+	35.2790i	1.41805	+	0.323660i	0.861755	−	0.507325i	$-0.169366\pi$
$109$	154.567	+	35.2790i	1.41805	+	0.323660i	0.556294	+	0.830985i	$0.312223\pi$
$110$	−2.25545	−	2.82824i	−0.0205041	−	0.0257113i
$111$	−96.3585	+	120.830i	−0.868095	+	1.08856i
$112$	8.04790	+	35.2602i	0.0718562	+	0.314823i
$113$	−46.5316	−	74.0546i	−0.411784	−	0.655351i	0.574858	−	0.818253i	$-0.305057\pi$
$113$	−46.5316	−	74.0546i	−0.411784	−	0.655351i	−0.986642	+	0.162902i	$0.947914\pi$
$114$	−3.97088	−	35.2425i	−0.0348323	−	0.309145i
$115$		−	3.45070i		−	0.0300061i
$116$	77.2523	−	79.6222i	0.665968	−	0.686398i
$117$	−10.7696			−0.0920475
$118$	7.57871	−	0.853915i	0.0642263	−	0.00723657i
$119$	−66.7958	+	41.9706i	−0.561309	+	0.352694i
$120$	−9.53890	+	2.17719i	−0.0794909	+	0.0181433i
$121$	−28.9215	−	23.0641i	−0.239020	−	0.190612i
$122$	−30.4067	+	24.2485i	−0.249235	+	0.198759i
$123$	−25.2572	+	110.659i	−0.205343	+	0.899669i
$124$	−78.8837	+	27.6026i	−0.636159	+	0.222602i
$125$	20.1314	−	41.8033i	0.161051	−	0.334426i
$126$	0.950499	+	0.597238i	0.00754365	+	0.00473999i
$127$	−171.713	−	60.0851i	−1.35207	−	0.473111i	−0.445546	−	0.895259i	$-0.646990\pi$
$127$	−171.713	−	60.0851i	−1.35207	−	0.473111i	−0.906527	+	0.422148i	$0.861276\pi$
$128$	−67.5837	+	67.5837i	−0.527998	+	0.527998i
$129$	−34.1315	−	70.8748i	−0.264585	−	0.549417i
$130$	0.459576	−	4.07885i	0.00353520	−	0.0313757i
$131$	−72.7489	−	8.19683i	−0.555335	−	0.0625712i	−0.170163	−	0.985416i	$-0.554429\pi$
$131$	−72.7489	−	8.19683i	−0.555335	−	0.0625712i	−0.385172	+	0.922845i	$0.625858\pi$
$132$	100.076	−	48.1940i	0.758151	−	0.365106i
$133$	49.1801	+	49.1801i	0.369775	+	0.369775i
$134$	7.80488	−	22.3051i	0.0582454	−	0.166456i
$135$	−12.6829	+	20.1848i	−0.0939476	+	0.149517i
$136$	−89.5284	−	43.1146i	−0.658297	−	0.317019i
$137$	65.2470	+	186.465i	0.476255	+	1.36106i	0.892188	+	0.451664i	$0.149169\pi$
$137$	65.2470	+	186.465i	0.476255	+	1.36106i	−0.415933	+	0.909395i	$0.636545\pi$
$138$	−4.71176	−	1.07543i	−0.0341432	−	0.00779296i
$139$	−38.5551	−	48.3466i	−0.277375	−	0.347817i	0.623557	−	0.781778i	$-0.285687\pi$
$139$	−38.5551	−	48.3466i	−0.277375	−	0.347817i	−0.900932	+	0.433961i	$0.857116\pi$
$140$	5.84830	−	7.33354i	0.0417736	−	0.0523824i
$141$	−15.9900	−	70.0568i	−0.113404	−	0.496856i
$142$	28.7577	+	45.7677i	0.202519	+	0.322308i
$143$	10.6727	+	94.7228i	0.0746343	+	0.662397i
$144$		−	14.4318i		−	0.100221i
$145$	−27.2711	−	2.65621i	−0.188076	−	0.0183187i
$146$	19.8671			0.136076
$147$	133.050	−	14.9912i	0.905103	−	0.101981i
$148$	158.023	−	99.2927i	1.06773	−	0.670897i
$149$	−29.6561	+	6.76882i	−0.199034	+	0.0454283i	−0.320876	−	0.947121i	$-0.603977\pi$
$149$	−29.6561	+	6.76882i	−0.199034	+	0.0454283i	0.121841	+	0.992550i	$0.461120\pi$
$150$	−24.9414	−	19.8901i	−0.166276	−	0.132601i
$151$	110.649	−	88.2399i	0.732777	−	0.584370i	−0.184399	−	0.982851i	$-0.559034\pi$
$151$	110.649	−	88.2399i	0.732777	−	0.584370i	0.917177	+	0.398481i	$0.130463\pi$
$152$	−19.4948	+	85.4124i	−0.128255	+	0.561924i
$153$	29.7121	−	10.3967i	0.194197	−	0.0679523i
$154$	4.31101	−	8.95191i	0.0279936	−	0.0581293i
$155$	17.4774	+	10.9818i	0.112757	+	0.0708501i
$156$	118.963	+	41.6269i	0.762582	+	0.266839i
$157$	19.5784	−	19.5784i	0.124703	−	0.124703i	−0.642001	−	0.766704i	$-0.721895\pi$
$157$	19.5784	−	19.5784i	0.124703	−	0.124703i	0.766704	+	0.642001i	$0.221895\pi$
$158$	−7.53854	−	15.6539i	−0.0477123	−	0.0990755i
$159$	−10.5966	+	94.0472i	−0.0666451	+	0.591492i
$160$	17.7424	+	1.99909i	0.110890	+	0.0124943i
$161$	8.53923	−	4.11228i	0.0530387	−	0.0255421i
$162$	26.3615	+	26.3615i	0.162725	+	0.162725i
$163$	34.1257	−	97.5257i	0.209360	−	0.598317i	−0.790541	−	0.612410i	$-0.790200\pi$
$163$	34.1257	−	97.5257i	0.209360	−	0.598317i	0.999901	+	0.0140927i	$0.00448600\pi$
$164$	72.9242	−	116.058i	0.444660	−	0.707672i
$165$	−24.7170	−	11.9031i	−0.149800	−	0.0721398i
$166$	−18.2617	−	52.1888i	−0.110010	−	0.314390i
$167$	−262.410	−	59.8934i	−1.57132	−	0.358643i	−0.653904	−	0.756577i	$-0.726870\pi$
$167$	−262.410	−	59.8934i	−1.57132	−	0.358643i	−0.917414	+	0.397934i	$0.869727\pi$
$168$	−16.7555	−	21.0107i	−0.0997351	−	0.125064i
$169$	37.9331	−	47.5666i	0.224456	−	0.281459i
$170$	2.66971	+	11.6968i	0.0157042	+	0.0688045i
$171$	−14.7656	−	23.4993i	−0.0863483	−	0.137423i
$172$	10.6361	+	94.3977i	0.0618376	+	0.548824i
$173$			126.379i			0.730512i	0.930907	+	0.365256i	$0.119019\pi$
$173$			126.379i			0.730512i	−0.930907	+	0.365256i	$0.880981\pi$
$174$	−12.1261	+	36.4095i	−0.0696903	+	0.209250i
$175$	62.5612			0.357493
$176$	−126.933	+	14.3020i	−0.721213	+	0.0812612i
$177$	48.9732	−	30.7719i	0.276685	−	0.173852i
$178$	13.2487	−	3.02393i	0.0744309	−	0.0169884i
$179$	220.984	+	176.229i	1.23455	+	0.984520i	0.999923	+	0.0124338i	$0.00395789\pi$
$179$	220.984	+	176.229i	1.23455	+	0.984520i	0.234626	+	0.972086i	$0.424614\pi$
$180$	−2.92632	+	2.33366i	−0.0162573	+	0.0129648i
$181$	51.3580	−	225.014i	0.283746	−	1.24317i	−0.609204	−	0.793014i	$-0.708511\pi$
$181$	51.3580	−	225.014i	0.283746	−	1.24317i	0.892949	−	0.450157i	$-0.148632\pi$
$182$	10.6414	−	3.72357i	0.0584690	−	0.0204592i
$183$	−127.971	+	265.734i	−0.699295	+	1.45210i
$184$	10.1087	+	6.35171i	0.0549386	+	0.0345202i
$185$	−43.5075	−	15.2239i	−0.235175	−	0.0822914i
$186$	20.4420	−	20.4420i	0.109903	−	0.109903i
$187$	−120.888	−	251.027i	−0.646461	−	1.34239i
$188$	−9.71575	+	86.2297i	−0.0516795	+	0.458669i
$189$	−65.0645	−	7.33101i	−0.344257	−	0.0387884i
$190$	9.53017	−	4.58949i	0.0501588	−	0.0241552i
$191$	68.5806	+	68.5806i	0.359061	+	0.359061i	0.863467	−	0.504406i	$-0.168289\pi$
$191$	68.5806	+	68.5806i	0.359061	+	0.359061i	−0.504406	+	0.863467i	$0.668289\pi$
$192$	−50.0674	+	143.084i	−0.260767	+	0.745231i
$193$	−16.7176	+	26.6059i	−0.0866198	+	0.137855i	−0.887224	−	0.461339i	$-0.847369\pi$
$193$	−16.7176	+	26.6059i	−0.0866198	+	0.137855i	0.800604	+	0.599194i	$0.204512\pi$
$194$	−16.0499	−	7.72920i	−0.0827312	−	0.0398413i
$195$	−10.2811	−	29.3817i	−0.0527236	−	0.150675i
$196$	−157.633	−	35.9786i	−0.804248	−	0.183564i
$197$	−63.4701	−	79.5889i	−0.322183	−	0.404005i	0.594194	−	0.804322i	$-0.297471\pi$
$197$	−63.4701	−	79.5889i	−0.322183	−	0.404005i	−0.916377	+	0.400317i	$0.868900\pi$
$198$	−2.47197	+	3.09975i	−0.0124847	+	0.0156553i
$199$	34.8200	+	152.557i	0.174975	+	0.766616i	0.983902	+	0.178707i	$0.0571915\pi$
$199$	34.8200	+	152.557i	0.174975	+	0.766616i	−0.808927	+	0.587909i	$0.799951\pi$
$200$	41.9264	+	66.7254i	0.209632	+	0.333627i
$201$	−20.0654	−	178.085i	−0.0998278	−	0.885996i
$202$		−	40.9039i		−	0.202494i
$203$	−25.9264	−	70.6516i	−0.127716	−	0.348037i
$204$	−368.391			−1.80584
$205$	−33.6403	+	3.79036i	−0.164099	+	0.0184895i
$206$	−25.9587	+	16.3109i	−0.126013	+	0.0791792i
$207$	−3.68714	+	0.841565i	−0.0178123	+	0.00406553i
$208$	−113.319	−	90.3686i	−0.544801	−	0.434465i
$209$	−192.053	+	153.157i	−0.918914	+	0.732810i
$210$	−0.722007	+	3.16332i	−0.00343813	+	0.0150634i
$211$	−19.1966	+	6.71718i	−0.0909791	+	0.0318350i	−0.375385	−	0.926869i	$-0.622489\pi$
$211$	−19.1966	+	6.71718i	−0.0909791	+	0.0318350i	0.284406	+	0.958704i	$0.408204\pi$
$212$	49.5881	−	102.971i	0.233906	−	0.485711i
$213$	347.089	+	218.090i	1.62952	+	1.02390i
$214$	24.2363	+	8.48064i	0.113254	+	0.0396291i
$215$	16.5902	−	16.5902i	0.0771637	−	0.0771637i
$216$	−35.7850	−	74.3084i	−0.165671	−	0.344020i
$217$	−6.34771	+	56.3375i	−0.0292521	+	0.259620i
$218$	65.8104	+	7.41505i	0.301882	+	0.0340140i
$219$	135.746	−	65.3717i	0.619844	−	0.298501i
$220$	23.4255	+	23.4255i	0.106480	+	0.106480i
$221$	104.415	−	298.402i	0.472468	−	1.35024i
$222$	−34.3469	+	54.6627i	−0.154716	+	0.246228i
$223$	228.933	+	110.248i	1.02661	+	0.494387i	0.869884	−	0.493256i	$-0.164193\pi$
$223$	228.933	+	110.248i	1.02661	+	0.494387i	0.156721	+	0.987643i	$0.449908\pi$
$224$	16.1970	+	46.2884i	0.0723081	+	0.206645i
$225$	−24.3380	−	5.55500i	−0.108169	−	0.0246889i
$226$	−22.7787	−	28.5635i	−0.100791	−	0.126387i
$227$	261.380	−	327.760i	1.15145	−	1.44388i	0.275617	−	0.961268i	$-0.411118\pi$
$227$	261.380	−	327.760i	1.15145	−	1.44388i	0.875836	−	0.482609i	$-0.160311\pi$
$228$	72.2733	+	316.650i	0.316988	+	1.38882i
$229$	140.386	+	223.424i	0.613041	+	0.975649i	0.998596	+	0.0529641i	$0.0168669\pi$
$229$	140.386	+	223.424i	0.613041	+	0.975649i	−0.385556	+	0.922685i	$0.625990\pi$
$230$	−0.161390	−	1.43237i	−0.000701694	−	0.00622771i
$231$		−	75.3507i		−	0.326194i
$232$	57.9793	−	75.0004i	0.249911	−	0.323277i
$233$	233.305			1.00131			0.500654	−	0.865648i	$-0.333093\pi$
$233$	233.305			1.00131			0.500654	+	0.865648i	$0.333093\pi$
$234$	−4.47041	+	0.503694i	−0.0191043	+	0.00215254i
$235$	18.1470	−	11.4025i	0.0772211	−	0.0485212i
$236$	−68.0938	+	15.5420i	−0.288533	+	0.0658558i
$237$	−103.017	−	82.1533i	−0.434671	−	0.346638i
$238$	−25.7637	+	20.5459i	−0.108251	+	0.0863272i
$239$	37.0417	−	162.290i	0.154986	−	0.679038i	−0.836406	−	0.548111i	$-0.815347\pi$
$239$	37.0417	−	162.290i	0.154986	−	0.679038i	0.991392	−	0.130928i	$-0.0417956\pi$
$240$	39.3730	−	13.7772i	0.164054	−	0.0574050i
$241$	−119.624	+	248.401i	−0.496363	+	1.03071i	0.490841	+	0.871249i	$0.336689\pi$
$241$	−119.624	+	248.401i	−0.496363	+	1.03071i	−0.987204	+	0.159460i	$0.949025\pi$
$242$	−13.0839	−	8.22116i	−0.0540657	−	0.0339717i
$243$	52.5283	+	18.3804i	0.216166	+	0.0756397i
$244$	251.850	−	251.850i	1.03217	−	1.03217i
$245$	17.3266	+	35.9790i	0.0707207	+	0.146853i
$246$	−5.30865	+	47.1155i	−0.0215799	+	0.191527i
$247$	−276.976	−	31.2077i	−1.12136	−	0.126347i
$248$	−64.3414	+	30.9852i	−0.259441	+	0.124940i
$249$	−296.501	−	296.501i	−1.19077	−	1.19077i
$250$	6.40133	−	18.2940i	0.0256053	−	0.0731758i
$251$	−222.330	+	353.836i	−0.885777	+	1.40971i	0.0262849	+	0.999654i	$0.491632\pi$
$251$	−222.330	+	353.836i	−0.885777	+	1.40971i	−0.912062	+	0.410052i	$0.865511\pi$
$252$	−9.26233	−	4.46050i	−0.0367553	−	0.0177004i
$253$	11.0559	+	31.5959i	0.0436992	+	0.124885i
$254$	−74.0878	−	16.9100i	−0.291684	−	0.0665750i
$255$	56.7289	+	71.1358i	0.222466	+	0.278964i
$256$	94.4490	−	118.435i	0.368941	−	0.462638i
$257$	2.48412	+	10.8836i	0.00966583	+	0.0423487i	0.979531	−	0.201294i	$-0.0645147\pi$
$257$	2.48412	+	10.8836i	0.00966583	+	0.0423487i	−0.969865	+	0.243643i	$0.921658\pi$
$258$	−17.4827	−	27.8235i	−0.0677624	−	0.107843i
$259$	−14.1752	−	125.808i	−0.0547303	−	0.485745i
$260$			37.5904i			0.144579i
$261$	3.81273	+	29.7875i	0.0146082	+	0.114128i
$262$	−30.5812			−0.116722
$263$	−325.997	+	36.7310i	−1.23953	+	0.139662i	−0.707285	−	0.706928i	$-0.750080\pi$
$263$	−325.997	+	36.7310i	−1.23953	+	0.139662i	−0.532246	+	0.846590i	$0.678652\pi$
$264$	80.3662	−	50.4975i	0.304418	−	0.191278i
$265$	−27.5196	+	6.28117i	−0.103848	+	0.0237025i
$266$	22.7146	+	18.1143i	0.0853934	+	0.0680990i
$267$	80.5742	−	64.2558i	0.301776	−	0.240658i
$268$	−48.1567	+	210.988i	−0.179689	+	0.787270i
$269$	292.071	−	102.200i	1.08577	−	0.379926i	0.272702	−	0.962099i	$-0.412083\pi$
$269$	292.071	−	102.200i	1.08577	−	0.379926i	0.813066	+	0.582172i	$0.197797\pi$
$270$	−4.32059	+	8.97181i	−0.0160022	+	0.0332289i
$271$	16.8213	+	10.5695i	0.0620712	+	0.0390019i	0.562710	−	0.826654i	$-0.309759\pi$
$271$	16.8213	+	10.5695i	0.0620712	+	0.0390019i	−0.500639	+	0.865656i	$0.666902\pi$
$272$	399.874	+	139.922i	1.47013	+	0.514419i
$273$	60.4569	−	60.4569i	0.221454	−	0.221454i
$274$	35.8048	+	74.3494i	0.130674	+	0.271348i
$275$	−24.7394	+	219.568i	−0.0899615	+	0.798430i
$276$	43.9817	+	4.95555i	0.159354	+	0.0179549i
$277$	−278.671	+	134.201i	−1.00603	+	0.484480i	−0.862981	−	0.505236i	$-0.831406\pi$
$277$	−278.671	+	134.201i	−1.00603	+	0.484480i	−0.143051	+	0.989715i	$0.545691\pi$
$278$	−18.2653	−	18.2653i	−0.0657024	−	0.0657024i
$279$	7.47180	−	21.3532i	0.0267807	−	0.0765347i
$280$	4.26433	−	6.78663i	0.0152297	−	0.0242380i
$281$	−275.413	−	132.632i	−0.980118	−	0.472000i	−0.125972	−	0.992034i	$-0.540205\pi$
$281$	−275.413	−	132.632i	−0.980118	−	0.472000i	−0.854146	+	0.520034i	$0.825919\pi$
$282$	−9.91396	−	28.3325i	−0.0351559	−	0.100470i
$283$	−104.652	−	23.8861i	−0.369794	−	0.0844032i	0.0335853	−	0.999436i	$-0.489307\pi$
$283$	−104.652	−	23.8861i	−0.369794	−	0.0844032i	−0.403380	+	0.915033i	$0.632165\pi$
$284$	−308.636	−	387.017i	−1.08675	−	1.36274i
$285$	50.0152	−	62.7171i	0.175492	−	0.220060i
$286$	8.86040	+	38.8199i	0.0309804	+	0.135734i
$287$	−49.4697	−	78.7306i	−0.172368	−	0.274323i
$288$	−2.19100	−	19.4457i	−0.00760763	−	0.0675196i
$289$			635.060i			2.19744i
$290$	−11.4444	+	0.172888i	−0.0394633	+	0.000596165i
$291$	−135.096			−0.464248
$292$	−180.799	+	20.3712i	−0.619175	+	0.0697642i
$293$	−230.684	+	144.948i	−0.787318	+	0.494705i	−0.864695	−	0.502297i	$-0.832488\pi$
$293$	−230.684	+	144.948i	−0.787318	+	0.494705i	0.0773772	+	0.997002i	$0.475345\pi$
$294$	54.5275	−	12.4456i	0.185468	−	0.0423318i
$295$	13.4870	+	10.7555i	0.0457185	+	0.0364593i
$296$	124.682	−	99.4308i	0.421224	−	0.335915i
$297$	51.4586	−	225.455i	0.173261	−	0.759108i
$298$	−11.9936	+	4.19673i	−0.0402469	+	0.0140830i
$299$	−16.4801	+	34.2212i	−0.0551173	+	0.114452i
$300$	247.372	+	155.434i	0.824572	+	0.518113i
$301$	60.8257	+	21.2838i	0.202079	+	0.0707104i
$302$	41.8032	−	41.8032i	0.138421	−	0.138421i
$303$	−134.592	−	279.483i	−0.444198	−	0.922388i
$304$	41.8199	−	371.162i	0.137565	−	1.22093i
$305$	−87.4144	−	9.84924i	−0.286605	−	0.0322926i
$306$	11.8471	−	5.70527i	0.0387161	−	0.0186447i
$307$	−134.403	−	134.403i	−0.437796	−	0.437796i	0.453473	−	0.891270i	$-0.350185\pi$
$307$	−134.403	−	134.403i	−0.437796	−	0.437796i	−0.891270	+	0.453473i	$0.850185\pi$
$308$	−30.0530	+	85.8865i	−0.0975746	+	0.278852i
$309$	−123.697	+	196.863i	−0.400315	+	0.637097i
$310$	7.76842	+	3.74108i	0.0250594	+	0.0120680i
$311$	60.8757	+	173.973i	0.195742	+	0.559398i	0.999361	−	0.0357461i	$-0.0113808\pi$
$311$	60.8757	+	173.973i	0.195742	+	0.559398i	−0.803619	+	0.595144i	$0.797095\pi$
$312$	104.997	+	23.9649i	0.336529	+	0.0768106i
$313$	263.236	+	330.088i	0.841010	+	1.05459i	0.997756	+	0.0669540i	$0.0213281\pi$
$313$	263.236	+	330.088i	0.841010	+	1.05459i	−0.156746	+	0.987639i	$0.550101\pi$
$314$	7.21125	−	9.04262i	0.0229658	−	0.0287981i
$315$	0.564998	+	2.47542i	0.00179364	+	0.00785847i
$316$	84.6549	+	134.728i	0.267895	+	0.426353i
$317$	−45.6880	−	405.492i	−0.144126	−	1.27915i	−0.832592	−	0.553886i	$-0.813144\pi$
$317$	−45.6880	−	405.492i	−0.144126	−	1.27915i	0.688466	−	0.725268i	$-0.258284\pi$
$318$			39.5343i			0.124322i
$319$	258.215	−	63.0541i	0.809451	−	0.197662i
$320$	−45.2125			−0.141289
$321$	193.504	−	21.8027i	0.602816	−	0.0679210i
$322$	3.35227	−	2.10637i	0.0104108	−	0.00654153i
$323$	794.274	−	181.288i	2.45905	−	0.561263i
$324$	−266.930	−	212.870i	−0.823860	−	0.657006i
$325$	−196.018	+	156.319i	−0.603131	+	0.480981i
$326$	9.60417	−	42.0786i	0.0294607	−	0.129076i
$327$	474.060	−	165.881i	1.44973	−	0.507281i
$328$	50.8182	−	105.525i	0.154934	−	0.321723i
$329$	49.8432	+	31.3186i	0.151499	+	0.0951932i
$330$	−10.8166	−	3.78491i	−0.0327777	−	0.0114694i
$331$	53.9759	−	53.9759i	0.163069	−	0.163069i	−0.620856	−	0.783925i	$-0.713215\pi$
$331$	53.9759	−	53.9759i	0.163069	−	0.163069i	0.783925	+	0.620856i	$0.213215\pi$
$332$	219.702	+	456.215i	0.661752	+	1.37414i
$333$	−5.65634	+	50.2014i	−0.0169860	+	0.150755i
$334$	−111.727	−	12.5886i	−0.334511	−	0.0376904i
$335$	48.1572	−	23.1913i	0.143753	−	0.0692277i
$336$	81.0153	+	81.0153i	0.241117	+	0.241117i
$337$	−100.512	+	287.246i	−0.298255	+	0.852363i	0.693063	+	0.720877i	$0.256261\pi$
$337$	−100.512	+	287.246i	−0.298255	+	0.852363i	−0.991318	+	0.131486i	$0.958025\pi$
$338$	13.5212	−	21.5189i	0.0400035	−	0.0636652i
$339$	−249.626	−	120.214i	−0.736361	−	0.354613i
$340$	−36.2890	−	103.708i	−0.106732	−	0.305024i
$341$	−195.215	−	44.5565i	−0.572478	−	0.130664i
$342$	−7.22820	−	9.06387i	−0.0211351	−	0.0265025i
$343$	−147.670	+	185.172i	−0.430525	+	0.539861i
$344$	18.0627	+	79.1380i	0.0525080	+	0.230052i
$345$	−5.81587	−	9.25591i	−0.0168576	−	0.0268287i
$346$	5.91075	+	52.4593i	0.0170831	+	0.151617i
$347$			3.76060i			0.0108375i	0.999985	+	0.00541873i	$0.00172484\pi$
$347$			3.76060i			0.0108375i	−0.999985	+	0.00541873i	$0.998275\pi$
$348$	73.0194	−	343.776i	0.209826	−	0.987861i
$349$	227.541			0.651979			0.325989	−	0.945373i	$-0.394303\pi$
$349$	227.541			0.651979			0.325989	+	0.945373i	$0.394303\pi$
$350$	25.9689	−	2.92600i	0.0741970	−	0.00835999i
$351$	222.179	−	139.604i	0.632988	−	0.397732i
$352$	−168.861	+	38.5415i	−0.479720	+	0.109493i
$353$	−317.199	−	252.957i	−0.898579	−	0.716593i	0.0609682	−	0.998140i	$-0.480581\pi$
$353$	−317.199	−	252.957i	−0.898579	−	0.716593i	−0.959548	+	0.281547i	$0.909153\pi$
$354$	18.8894	−	15.0638i	0.0533599	−	0.0425531i
$355$	−27.2053	+	119.194i	−0.0766347	+	0.335759i
$356$	−117.468	+	41.1039i	−0.329967	+	0.115460i
$357$	−108.430	+	225.158i	−0.303726	+	0.630694i
$358$	99.9720	+	62.8166i	0.279251	+	0.175465i
$359$	−237.999	−	83.2794i	−0.662949	−	0.231976i	−0.0222319	−	0.999753i	$-0.507077\pi$
$359$	−237.999	−	83.2794i	−0.662949	−	0.231976i	−0.640717	+	0.767777i	$0.721363\pi$
$360$	−2.26155	+	2.26155i	−0.00628207	+	0.00628207i
$361$	−155.019	−	321.900i	−0.429415	−	0.891690i
$362$	10.7946	−	95.8045i	0.0298193	−	0.264653i
$363$	−116.450	−	13.1207i	−0.320798	−	0.0361452i
$364$	−93.0227	+	44.7974i	−0.255557	+	0.123070i
$365$	31.7750	+	31.7750i	0.0870549	+	0.0870549i
$366$	−40.6919	+	116.291i	−0.111180	+	0.317734i
$367$	−246.647	+	392.537i	−0.672063	+	1.06958i	0.320429	+	0.947273i	$0.396173\pi$
$367$	−246.647	+	392.537i	−0.672063	+	1.06958i	−0.992492	+	0.122310i	$0.960970\pi$
$368$	−45.8582	−	22.0841i	−0.124615	−	0.0600112i
$369$	12.2544	+	35.0209i	0.0332096	+	0.0949077i
$370$	−18.7718	−	4.28454i	−0.0507346	−	0.0115799i
$371$	−48.3394	−	60.6157i	−0.130295	−	0.163385i
$372$	−165.070	+	206.991i	−0.443737	+	0.556429i
$373$	−55.7998	−	244.475i	−0.149597	−	0.655429i	−0.992997	−	0.118142i	$-0.962306\pi$
$373$	−55.7998	−	244.475i	−0.149597	−	0.655429i	0.843399	−	0.537287i	$-0.180551\pi$
$374$	−61.9209	−	98.5465i	−0.165564	−	0.263493i
$375$	−16.4570	−	146.060i	−0.0438854	−	0.389494i
$376$			74.1495i			0.197206i
$377$	257.767	+	156.585i	0.683731	+	0.415345i
$378$	−27.3509			−0.0723570
$379$	487.332	−	54.9091i	1.28584	−	0.144879i	0.557545	−	0.830147i	$-0.311743\pi$
$379$	487.332	−	54.9091i	1.28584	−	0.144879i	0.728291	+	0.685268i	$0.240315\pi$
$380$	−82.0226	+	51.5382i	−0.215849	+	0.135627i
$381$	−561.860	+	128.241i	−1.47470	+	0.336590i
$382$	31.6751	+	25.2600i	0.0829190	+	0.0661257i
$383$	172.689	−	137.715i	0.450886	−	0.359570i	−0.371564	−	0.928407i	$-0.621178\pi$
$383$	172.689	−	137.715i	0.450886	−	0.359570i	0.822450	+	0.568838i	$0.192607\pi$
$384$	−67.3749	+	295.189i	−0.175455	+	0.768721i
$385$	21.2124	−	7.42255i	0.0550972	−	0.0192794i
$386$	−5.69506	+	11.8259i	−0.0147540	+	0.0306371i
$387$	−21.7730	−	13.6809i	−0.0562610	−	0.0353511i
$388$	153.986	+	53.8819i	0.396870	+	0.138871i
$389$	−291.445	+	291.445i	−0.749217	+	0.749217i	−0.974332	−	0.225115i	$-0.927724\pi$
$389$	−291.445	+	291.445i	−0.749217	+	0.749217i	0.225115	+	0.974332i	$0.427724\pi$
$390$	−5.64183	−	11.7154i	−0.0144662	−	0.0300395i
$391$	12.4303	−	110.322i	0.0317911	−	0.282154i
$392$	−137.292	−	15.4691i	−0.350236	−	0.0394621i
$393$	−208.952	+	100.626i	−0.531684	+	0.256045i
$394$	−30.0686	−	30.0686i	−0.0763162	−	0.0763162i
$395$	12.9796	−	37.0935i	0.0328597	−	0.0939077i
$396$	19.3175	−	30.7437i	0.0487817	−	0.0776356i
$397$	−65.4912	−	31.5389i	−0.164965	−	0.0794430i	0.349579	−	0.936907i	$-0.386325\pi$
$397$	−65.4912	−	31.5389i	−0.164965	−	0.0794430i	−0.514544	+	0.857464i	$0.672039\pi$
$398$	21.5888	+	61.6972i	0.0542431	+	0.155018i
$399$	214.806	+	49.0281i	0.538362	+	0.122878i
$400$	−209.475	−	262.674i	−0.523688	−	0.656684i
$401$	324.268	−	406.619i	0.808649	−	1.01401i	−0.190826	−	0.981624i	$-0.561117\pi$
$401$	324.268	−	406.619i	0.808649	−	1.01401i	0.999475	−	0.0323898i	$-0.0103118\pi$
$402$	−16.6581	−	72.9841i	−0.0414382	−	0.181552i
$403$	−120.879	−	192.378i	−0.299948	−	0.477365i
$404$	41.9416	+	372.242i	0.103816	+	0.921392i
$405$			84.3239i			0.208207i
$406$	−14.0663	−	28.1146i	−0.0346462	−	0.0692479i
$407$	447.148			1.09864
$408$	−312.811	+	35.2453i	−0.766694	+	0.0863856i
$409$	250.417	−	157.347i	0.612266	−	0.384712i	−0.189909	−	0.981802i	$-0.560819\pi$
$409$	250.417	−	157.347i	0.612266	−	0.384712i	0.802174	+	0.597090i	$0.203676\pi$
$410$	−13.7867	+	3.14673i	−0.0336261	+	0.00767494i
$411$	489.286	+	390.192i	1.19048	+	0.949373i
$412$	219.510	−	175.053i	0.532791	−	0.424887i
$413$	−10.5432	+	46.1929i	−0.0255284	+	0.111847i
$414$	−1.49116	+	0.521779i	−0.00360183	+	0.00126033i
$415$	54.2624	−	112.677i	0.130753	−	0.271511i
$416$	−166.407	−	104.561i	−0.400018	−	0.251348i
$417$	−184.902	−	64.6999i	−0.443410	−	0.155156i
$418$	−72.5574	+	72.5574i	−0.173582	+	0.173582i
$419$	59.7192	+	124.008i	0.142528	+	0.295962i	0.959997	−	0.280010i	$-0.0903379\pi$
$419$	59.7192	+	124.008i	0.142528	+	0.295962i	−0.817469	+	0.575972i	$0.804624\pi$
$420$	3.32699	−	29.5278i	0.00792140	−	0.0703044i
$421$	432.517	+	48.7330i	1.02736	+	0.115755i	0.609523	−	0.792768i	$-0.291361\pi$
$421$	432.517	+	48.7330i	1.02736	+	0.115755i	0.417833	+	0.908524i	$0.362790\pi$
$422$	−7.65428	+	3.68611i	−0.0181381	+	0.00873485i
$423$	−16.6095	−	16.6095i	−0.0392660	−	0.0392660i
$424$	32.2550	−	92.1795i	0.0760731	−	0.217404i
$425$	389.885	−	620.498i	0.917376	−	1.46000i
$426$	154.275	+	74.2951i	0.362149	+	0.174402i
$427$	−79.8005	−	228.057i	−0.186886	−	0.534091i
$428$	−229.256	−	52.3262i	−0.535645	−	0.122257i
$429$	188.275	+	236.090i	0.438870	+	0.550326i
$430$	6.11061	−	7.66246i	0.0142107	−	0.0178197i
$431$	38.3560	+	168.049i	0.0889930	+	0.389904i	0.999734	−	0.0230748i	$-0.00734557\pi$
$431$	38.3560	+	168.049i	0.0889930	+	0.389904i	−0.910741	+	0.412979i	$0.864488\pi$
$432$	187.077	+	297.731i	0.433048	+	0.689192i
$433$	5.55493	+	49.3014i	0.0128289	+	0.113860i	0.998495	−	0.0548506i	$-0.0174682\pi$
$433$	5.55493	+	49.3014i	0.0128289	+	0.113860i	−0.985666	+	0.168711i	$0.946040\pi$
$434$			23.6824i			0.0545677i
$435$	−77.6269	+	38.8384i	−0.178453	+	0.0892836i
$436$	−606.505			−1.39107
$437$	−97.2658	+	10.9592i	−0.222576	+	0.0250783i
$438$	53.2902	−	33.4844i	0.121667	−	0.0764485i
$439$	190.067	−	43.3816i	0.432955	−	0.0988191i	−0.000488576	−	1.00000i	$-0.500156\pi$
$439$	190.067	−	43.3816i	0.432955	−	0.0988191i	0.433443	+	0.901181i	$0.357298\pi$
$440$	22.1324	+	17.6500i	0.0503010	+	0.0401137i
$441$	34.2186	−	27.2884i	0.0775932	−	0.0618785i
$442$	29.3862	−	128.749i	0.0664845	−	0.291288i
$443$	−228.033	+	79.7920i	−0.514746	+	0.180117i	−0.575137	−	0.818057i	$-0.695051\pi$
$443$	−228.033	+	79.7920i	−0.514746	+	0.180117i	0.0603905	+	0.998175i	$0.480765\pi$
$444$	256.521	−	532.672i	0.577751	−	1.19971i
$445$	26.0261	+	16.3533i	0.0584856	+	0.0367490i
$446$	100.186	+	35.0565i	0.224631	+	0.0786019i
$447$	−68.1392	+	68.1392i	−0.152437	+	0.152437i
$448$	−53.8807	−	111.884i	−0.120269	−	0.249742i
$449$	−55.8565	+	495.740i	−0.124402	+	1.10410i	0.764059	+	0.645147i	$0.223204\pi$
$449$	−55.8565	+	495.740i	−0.124402	+	1.10410i	−0.888461	+	0.458952i	$0.848225\pi$
$450$	−10.3624	−	1.16757i	−0.0230276	−	0.00259459i
$451$	295.880	−	142.488i	0.656053	−	0.315938i
$452$	236.583	+	236.583i	0.523415	+	0.523415i
$453$	148.077	−	423.179i	0.326880	−	0.934171i
$454$	93.1685	−	148.277i	0.205217	−	0.326601i
$455$	22.9750	+	11.0642i	0.0504944	+	0.0243168i
$456$	91.6642	+	261.961i	0.201018	+	0.574476i
$457$	204.659	+	46.7120i	0.447831	+	0.102215i	0.440488	−	0.897759i	$-0.354805\pi$
$457$	204.659	+	46.7120i	0.447831	+	0.102215i	0.00734312	+	0.999973i	$0.497663\pi$
$458$	68.7234	+	86.1764i	0.150051	+	0.188158i
$459$	−478.197	+	599.639i	−1.04182	+	1.30640i
$460$	2.93743	+	12.8697i	0.00638571	+	0.0279776i
$461$	−129.473	−	206.054i	−0.280852	−	0.446973i	0.676272	−	0.736652i	$-0.263594\pi$
$461$	−129.473	−	206.054i	−0.280852	−	0.446973i	−0.957124	+	0.289679i	$0.906451\pi$
$462$	−3.52417	−	31.2778i	−0.00762806	−	0.0677009i
$463$		−	710.071i		−	1.53363i	−0.641868	−	0.766815i	$-0.721840\pi$
$463$		−	710.071i		−	1.53363i	0.641868	−	0.766815i	$-0.278160\pi$
$464$	−209.832	+	345.421i	−0.452225	+	0.744441i
$465$	65.3890			0.140622
$466$	96.8439	−	10.9117i	0.207820	−	0.0234156i
$467$	−676.037	+	424.782i	−1.44762	+	0.909598i	−0.447735	+	0.894166i	$0.647769\pi$
$467$	−676.037	+	424.782i	−1.44762	+	0.909598i	−0.999881	+	0.0154315i	$0.995088\pi$
$468$	40.1661	−	9.16765i	0.0858250	−	0.0195890i
$469$	114.780	+	91.5341i	0.244734	+	0.195169i
$470$	6.99944	−	5.58187i	0.0148924	−	0.0118763i
$471$	19.5179	−	85.5136i	0.0414393	−	0.181558i
$472$	−56.3333	+	19.7119i	−0.119350	+	0.0417625i
$473$	−98.7519	+	205.061i	−0.208778	+	0.433532i
$474$	−46.6043	−	29.2834i	−0.0983213	−	0.0617794i
$475$	−609.838	−	213.391i	−1.28387	−	0.449245i
$476$	213.393	−	213.393i	0.448306	−	0.448306i
$477$	13.4231	+	27.8734i	0.0281407	+	0.0584347i
$478$	7.78553	−	69.0985i	0.0162877	−	0.144558i
$479$	−483.953	−	54.5284i	−1.01034	−	0.113838i	−0.408753	−	0.912645i	$-0.634036\pi$
$479$	−483.953	−	54.5284i	−1.01034	−	0.113838i	−0.601587	+	0.798807i	$0.705465\pi$
$480$	50.9603	−	24.5412i	0.106167	−	0.0511275i
$481$	358.764	+	358.764i	0.745872	+	0.745872i
$482$	−38.0376	+	108.705i	−0.0789161	+	0.225529i
$483$	15.9741	−	25.4227i	0.0330727	−	0.0526349i
$484$	127.499	+	61.4001i	0.263427	+	0.126860i
$485$	−13.3079	−	38.0317i	−0.0274389	−	0.0784159i
$486$	22.6640	+	5.17290i	0.0466337	+	0.0106438i
$487$	−72.6889	−	91.1490i	−0.149259	−	0.187164i	0.701581	−	0.712589i	$-0.252478\pi$
$487$	−72.6889	−	91.1490i	−0.149259	−	0.187164i	−0.850840	+	0.525425i	$0.823906\pi$
$488$	189.757	−	237.948i	0.388847	−	0.487598i
$489$	−72.8353	−	319.112i	−0.148947	−	0.652581i
$490$	8.87495	+	14.1244i	0.0181121	+	0.0288253i
$491$	75.7150	+	671.989i	0.154206	+	1.36861i	0.797650	+	0.603120i	$0.206076\pi$
$491$	75.7150	+	671.989i	0.154206	+	1.36861i	−0.643445	+	0.765493i	$0.722495\pi$
$492$		−	434.214i		−	0.882550i
$493$	−862.315	−	183.159i	−1.74912	−	0.371520i
$494$	−116.431			−0.235691
$495$	−8.91129	+	1.00406i	−0.0180026	+	0.00202841i
$496$	257.796	−	161.984i	0.519751	−	0.326581i
$497$	−327.384	+	74.7233i	−0.658721	+	0.150349i
$498$	−136.944	−	109.209i	−0.274988	−	0.219295i
$499$	−611.573	+	487.713i	−1.22560	+	0.977381i	−0.225602	+	0.974220i	$0.572435\pi$
$499$	−611.573	+	487.713i	−1.22560	+	0.977381i	−0.999995	+	0.00316117i	$0.998994\pi$
$500$	−39.4967	+	173.046i	−0.0789934	+	0.346093i
$501$	−804.816	+	281.617i	−1.60642	+	0.562110i
$502$	−75.7395	+	157.275i	−0.150875	+	0.313296i
$503$	−418.298	−	262.834i	−0.831606	−	0.522533i	0.0476598	−	0.998864i	$-0.484824\pi$
$503$	−418.298	−	262.834i	−0.831606	−	0.522533i	−0.879266	+	0.476331i	$0.841967\pi$
$504$	−8.29164	−	2.90137i	−0.0164517	−	0.00575669i
$505$	65.4208	−	65.4208i	0.129546	−	0.129546i
$506$	6.06701	+	12.5983i	0.0119901	+	0.0248978i
$507$	21.5794	−	191.522i	0.0425629	−	0.377756i
$508$	691.569	+	77.9211i	1.36136	+	0.153388i
$509$	658.293	−	317.017i	1.29331	−	0.622823i	0.344531	−	0.938775i	$-0.388038\pi$
$509$	658.293	−	317.017i	1.29331	−	0.622823i	0.948775	+	0.315952i	$0.102324\pi$
$510$	26.8750	+	26.8750i	0.0526961	+	0.0526961i
$511$	−40.7647	+	116.499i	−0.0797744	+	0.227982i
$512$	237.068	−	377.292i	0.463023	−	0.736898i
$513$	609.234	+	293.392i	1.18759	+	0.571914i
$514$	1.54018	+	4.40157i	0.00299645	+	0.00856337i
$515$	−67.6051	−	15.4304i	−0.131272	−	0.0299620i
$516$	187.629	+	235.280i	0.363622	+	0.455968i
$517$	−129.627	+	162.548i	−0.250730	+	0.314406i
$518$	−11.7681	−	51.5595i	−0.0227184	−	0.0995356i
$519$	213.001	+	338.989i	0.410407	+	0.653158i
$520$	3.59641	+	31.9190i	0.00691618	+	0.0613828i
$521$		−	412.503i		−	0.791753i	−0.918304	−	0.395876i	$-0.870441\pi$
$521$		−	412.503i		−	0.791753i	0.918304	−	0.395876i	$-0.129559\pi$
$522$	2.97581	+	12.1864i	0.00570079	+	0.0233455i
$523$	−54.7428			−0.104671			−0.0523354	−	0.998630i	$-0.516666\pi$
$523$	−54.7428			−0.104671			−0.0523354	+	0.998630i	$0.516666\pi$
$524$	278.301	−	31.3570i	0.531110	−	0.0598417i
$525$	167.810	−	105.442i	0.319638	−	0.200842i
$526$	−133.602	+	30.4938i	−0.253996	+	0.0579730i
$527$	519.210	+	414.056i	0.985219	+	0.785686i
$528$	−316.373	+	252.299i	−0.599190	+	0.477838i
$529$	114.745	−	502.733i	0.216910	−	0.950346i
$530$	−11.1295	+	3.89439i	−0.0209991	+	0.00734790i
$531$	8.20321	−	17.0341i	0.0154486	−	0.0320794i
$532$	−225.287	−	141.557i	−0.423471	−	0.266084i
$533$	351.720	+	123.072i	0.659887	+	0.230904i
$534$	30.4408	−	30.4408i	0.0570053	−	0.0570053i
$535$	25.1992	+	52.3267i	0.0471013	+	0.0978069i
$536$	−20.7051	+	183.763i	−0.0386290	+	0.342842i
$537$	889.772	+	100.253i	1.65693	+	0.186691i
$538$	116.458	−	56.0832i	0.216465	−	0.104244i
$539$	−273.924	−	273.924i	−0.508208	−	0.508208i
$540$	30.1198	−	86.0774i	0.0557774	−	0.159403i
$541$	−6.00071	+	9.55008i	−0.0110919	+	0.0176526i	−0.852224	−	0.523177i	$-0.824747\pi$
$541$	−6.00071	+	9.55008i	−0.0110919	+	0.0176526i	0.841132	+	0.540829i	$0.181890\pi$
$542$	7.47680	+	3.60064i	0.0137948	+	0.00664324i
$543$	−241.484	−	690.121i	−0.444722	−	1.27094i
$544$	560.041	+	127.826i	1.02949	+	0.234974i
$545$	93.3962	+	117.115i	0.171369	+	0.214890i
$546$	22.2679	−	27.9230i	0.0407836	−	0.0511410i
$547$	−11.9903	−	52.5331i	−0.0219202	−	0.0960385i	0.962785	−	0.270270i	$-0.0871130\pi$
$547$	−11.9903	−	52.5331i	−0.0219202	−	0.0960385i	−0.984705	+	0.174232i	$0.944256\pi$
$548$	−402.074	−	639.897i	−0.733712	−	1.16770i
$549$	10.7948	+	95.8061i	0.0196626	+	0.174510i
$550$			92.2991i			0.167817i
$551$	11.7400	+	777.134i	0.0213068	+	1.41041i
$552$	37.8202			0.0685148
$553$	107.261	−	12.0854i	0.193962	−	0.0218543i
$554$	−109.399	+	68.7398i	−0.197471	+	0.124079i
$555$	−142.360	+	32.4928i	−0.256505	+	0.0585455i
$556$	184.950	+	147.493i	0.332644	+	0.265275i
$557$	543.971	−	433.802i	0.976608	−	0.778819i	0.00137506	−	0.999999i	$-0.499562\pi$
$557$	543.971	−	433.802i	0.976608	−	0.778819i	0.975233	+	0.221180i	$0.0709909\pi$
$558$	2.10283	−	9.21309i	0.00376851	−	0.0165109i
$559$	−243.761	+	85.2955i	−0.436066	+	0.152586i
$560$	−14.8265	+	30.7876i	−0.0264760	+	0.0549779i
$561$	−747.348	−	469.590i	−1.33217	−	0.837059i
$562$	−120.526	−	42.1740i	−0.214460	−	0.0750426i
$563$	−319.915	+	319.915i	−0.568233	+	0.568233i	−0.931633	−	0.363400i	$-0.881616\pi$
$563$	−319.915	+	319.915i	−0.568233	+	0.568233i	0.363400	+	0.931633i	$0.381616\pi$
$564$	119.272	+	247.672i	0.211476	+	0.439134i
$565$	9.25221	−	82.1156i	0.0163756	−	0.145337i
$566$	−44.5578	−	5.02045i	−0.0787239	−	0.00887006i
$567$	−208.671	+	100.491i	−0.368027	+	0.177232i
$568$	−299.099	−	299.099i	−0.526582	−	0.526582i
$569$	173.583	−	496.072i	0.305067	−	0.871832i	−0.684660	−	0.728863i	$-0.740049\pi$
$569$	173.583	−	496.072i	0.305067	−	0.871832i	0.989727	−	0.142969i	$-0.0456650\pi$
$570$	17.8278	−	28.3728i	0.0312769	−	0.0497769i
$571$	619.219	+	298.200i	1.08445	+	0.522242i	0.888736	−	0.458419i	$-0.151584\pi$
$571$	619.219	+	298.200i	1.08445	+	0.522242i	0.195711	+	0.980662i	$0.437299\pi$
$572$	−120.438	−	344.192i	−0.210556	−	0.601735i
$573$	299.543	+	68.3687i	0.522762	+	0.119317i
$574$	−24.2170	−	30.3671i	−0.0421898	−	0.0529044i
$575$	−54.8946	+	68.8357i	−0.0954689	+	0.119714i
$576$	11.0265	+	48.3104i	0.0191433	+	0.0838722i
$577$	−30.2263	−	48.1049i	−0.0523853	−	0.0833707i	0.819505	−	0.573072i	$-0.194249\pi$
$577$	−30.2263	−	48.1049i	−0.0523853	−	0.0833707i	−0.871890	+	0.489702i	$0.837106\pi$
$578$	29.7019	+	263.611i	0.0513873	+	0.456075i
$579$			99.5421i			0.171921i
$580$	103.971	−	13.3081i	0.179261	−	0.0229449i
$581$	343.501			0.591223
$582$	−56.0780	+	6.31847i	−0.0963539	+	0.0108565i
$583$	231.855	−	145.684i	0.397694	−	0.249888i
$584$	−151.572	+	34.5954i	−0.259542	+	0.0592387i
$585$	−7.95547	−	6.34428i	−0.0135991	−	0.0108449i
$586$	−88.9769	+	70.9567i	−0.151838	+	0.121087i
$587$	−71.8016	+	314.583i	−0.122320	+	0.535917i	0.876221	+	0.481910i	$0.160057\pi$
$587$	−71.8016	+	314.583i	−0.122320	+	0.535917i	−0.998541	+	0.0540076i	$0.982800\pi$
$588$	−483.462	+	169.171i	−0.822214	+	0.287705i
$589$	254.039	−	527.518i	0.431306	−	0.895616i
$590$	6.10142	+	3.83378i	0.0103414	+	0.00649793i
$591$	−304.388	−	106.510i	−0.515040	−	0.180220i
$592$	−480.762	+	480.762i	−0.812099	+	0.812099i
$593$	209.288	+	434.591i	0.352931	+	0.732869i	0.999552	−	0.0299430i	$-0.00953257\pi$
$593$	209.288	+	434.591i	0.352931	+	0.732869i	−0.646621	+	0.762812i	$0.723818\pi$
$594$	10.8157	−	95.9923i	0.0182083	−	0.161603i
$595$	−74.0666	−	8.34530i	−0.124482	−	0.0140257i
$596$	104.843	−	50.4899i	0.175912	−	0.0847146i
$597$	350.521	+	350.521i	0.587137	+	0.587137i
$598$	−5.24029	+	14.9759i	−0.00876302	+	0.0250433i
$599$	452.046	−	719.427i	0.754668	−	1.20105i	−0.219586	−	0.975593i	$-0.570471\pi$
$599$	452.046	−	719.427i	0.754668	−	1.20105i	0.974254	−	0.225454i	$-0.0723865\pi$
$600$	224.921	+	108.316i	0.374868	+	0.180527i
$601$	241.988	+	691.562i	0.402642	+	1.15069i	0.949584	+	0.313514i	$0.101506\pi$
$601$	241.988	+	691.562i	0.402642	+	1.15069i	−0.546941	+	0.837171i	$0.684208\pi$
$602$	26.2440	+	5.99001i	0.0435946	+	0.00995019i
$603$	−36.5251	−	45.8010i	−0.0605722	−	0.0759552i
$604$	−337.563	+	423.290i	−0.558878	+	0.700811i
$605$	−7.77737	−	34.0749i	−0.0128552	−	0.0563221i
$606$	−68.9402	−	109.718i	−0.113763	−	0.181052i
$607$	−27.7513	−	246.300i	−0.0457188	−	0.405766i	−0.995640	−	0.0932767i	$-0.970266\pi$
$607$	−27.7513	−	246.300i	−0.0457188	−	0.405766i	0.949921	−	0.312489i	$-0.101163\pi$
$608$		−	506.460i		−	0.832993i
$609$	−188.621	−	145.814i	−0.309722	−	0.239432i
$610$	−36.7461			−0.0602395
$611$	−234.424	+	26.4132i	−0.383672	+	0.0432295i
$612$	−101.964	+	64.0681i	−0.166607	+	0.104686i
$613$	1.19680	−	0.273162i	0.00195236	−	0.000445614i	−0.221545	−	0.975150i	$-0.571110\pi$
$613$	1.19680	−	0.273162i	0.00195236	−	0.000445614i	0.223497	+	0.974705i	$0.428253\pi$
$614$	−62.0765	−	49.5043i	−0.101102	−	0.0806260i
$615$	−83.8461	+	66.8651i	−0.136335	+	0.108724i
$616$	−17.3017	+	75.8038i	−0.0280872	+	0.123058i
$617$	−285.233	+	99.8075i	−0.462291	+	0.161762i	−0.551368	−	0.834262i	$-0.685894\pi$
$617$	−285.233	+	99.8075i	−0.462291	+	0.161762i	0.0890772	+	0.996025i	$0.471608\pi$
$618$	−42.1390	+	87.5025i	−0.0681861	+	0.141590i
$619$	−272.432	−	171.181i	−0.440117	−	0.276544i	0.293691	−	0.955900i	$-0.405116\pi$
$619$	−272.432	−	171.181i	−0.440117	−	0.276544i	−0.733808	+	0.679356i	$0.762259\pi$
$620$	−74.5319	−	26.0798i	−0.120213	−	0.0420642i
$621$	65.1574	−	65.1574i	0.104923	−	0.104923i
$622$	33.4060	+	69.3683i	0.0537074	+	0.111525i
$623$	−9.45256	+	83.8938i	−0.0151727	+	0.134661i
$624$	−456.267	−	51.4090i	−0.731197	−	0.0823862i
$625$	−503.501	+	242.473i	−0.805601	+	0.387957i
$626$	124.707	+	124.707i	0.199212	+	0.199212i
$627$	−257.016	+	734.508i	−0.409913	+	1.17146i
$628$	−56.3533	+	89.6858i	−0.0897346	+	0.142812i
$629$	−1336.14	−	643.449i	−2.12422	−	1.02297i
$630$	0.350304	+	1.00111i	0.000556039	+	0.00158907i
$631$	680.376	+	155.291i	1.07825	+	0.246103i	0.724527	−	0.689247i	$-0.242058\pi$
$631$	680.376	+	155.291i	1.07825	+	0.246103i	0.353723	+	0.935350i	$0.384916\pi$
$632$	84.7726	+	106.301i	0.134134	+	0.168199i
$633$	−40.1703	+	50.3720i	−0.0634603	+	0.0795766i
$634$	−37.9298	−	166.181i	−0.0598262	−	0.262116i
$635$	−91.4488	−	145.540i	−0.144014	−	0.229197i
$636$	−40.5373	−	359.778i	−0.0637378	−	0.565689i
$637$		−	439.560i		−	0.690047i
$638$	104.235	−	38.2503i	0.163378	−	0.0599534i
$639$	133.996			0.209697
$640$	−89.7372	+	10.1110i	−0.140214	+	0.0157984i
$641$	−989.853	+	621.966i	−1.54423	+	0.970306i	−0.553748	+	0.832684i	$0.686803\pi$
$641$	−989.853	+	621.966i	−1.54423	+	0.970306i	−0.990485	+	0.137621i	$0.956054\pi$
$642$	79.3031	−	18.1004i	0.123525	−	0.0281938i
$643$	−234.086	−	186.677i	−0.364052	−	0.290322i	0.424330	−	0.905508i	$-0.360510\pi$
$643$	−234.086	−	186.677i	−0.364052	−	0.290322i	−0.788382	+	0.615186i	$0.789081\pi$
$644$	−28.3473	+	22.6062i	−0.0440175	+	0.0351028i
$645$	16.5389	−	72.4618i	0.0256418	−	0.112344i
$646$	321.221	−	112.400i	0.497247	−	0.173994i
$647$	493.455	−	1024.67i	0.762681	−	1.58372i	−0.0484269	−	0.998827i	$-0.515421\pi$
$647$	493.455	−	1024.67i	0.762681	−	1.58372i	0.811108	−	0.584897i	$-0.198865\pi$
$648$	−247.024	−	155.215i	−0.381210	−	0.239530i
$649$	−157.952	−	55.2698i	−0.243377	−	0.0851614i
$650$	−74.0552	+	74.0552i	−0.113931	+	0.113931i
$651$	77.9256	+	161.814i	0.119701	+	0.248563i
$652$	−44.2558	+	392.781i	−0.0678770	+	0.602425i
$653$	609.259	+	68.6470i	0.933015	+	0.105126i	0.565367	−	0.824839i	$-0.308735\pi$
$653$	609.259	+	68.6470i	0.933015	+	0.105126i	0.367648	+	0.929965i	$0.380163\pi$
$654$	189.023	−	91.0285i	0.289025	−	0.139187i
$655$	−48.9109	−	48.9109i	−0.0746731	−	0.0746731i
$656$	−164.923	+	471.322i	−0.251407	+	0.718479i
$657$	26.2029	−	41.7016i	0.0398826	−	0.0634728i
$658$	22.1545	+	10.6691i	0.0336695	+	0.0162144i
$659$	176.059	+	503.147i	0.267161	+	0.763501i	0.996820	+	0.0796900i	$0.0253931\pi$
$659$	176.059	+	503.147i	0.267161	+	0.763501i	−0.729659	+	0.683811i	$0.760321\pi$
$660$	102.317	+	23.3531i	0.155026	+	0.0353836i
$661$	620.208	+	777.717i	0.938288	+	1.17658i	0.984098	+	0.177626i	$0.0568417\pi$
$661$	620.208	+	777.717i	0.938288	+	1.17658i	−0.0458100	+	0.998950i	$0.514587\pi$
$662$	19.8808	−	24.9297i	0.0300314	−	0.0376581i
$663$	−222.856	−	976.397i	−0.336133	−	1.47270i
$664$	230.202	+	366.365i	0.346690	+	0.551754i
$665$	7.35765	+	65.3010i	0.0110641	+	0.0981970i
$666$			21.1030i			0.0316861i
$667$	100.487	+	33.4669i	0.150655	+	0.0501752i
$668$	1029.67			1.54142
$669$	799.888	−	90.1258i	1.19565	−	0.134717i
$670$	18.9052	−	11.8789i	0.0282168	−	0.0177298i
$671$	831.957	−	189.889i	1.23988	−	0.282994i
$672$	121.461	+	96.8621i	0.180746	+	0.144140i
$673$	314.226	−	250.587i	0.466903	−	0.372343i	−0.361594	−	0.932336i	$-0.617767\pi$
$673$	314.226	−	250.587i	0.466903	−	0.372343i	0.828498	+	0.559992i	$0.189196\pi$
$674$	−28.2876	+	123.936i	−0.0419697	+	0.183881i
$675$	574.108	−	200.889i	0.850530	−	0.297613i
$676$	−100.984	+	209.695i	−0.149384	+	0.310199i
$677$	424.331	+	266.625i	0.626781	+	0.393833i	0.807640	−	0.589676i	$-0.200745\pi$
$677$	424.331	+	266.625i	0.626781	+	0.393833i	−0.180858	+	0.983509i	$0.557888\pi$
$678$	−109.241	−	38.2252i	−0.161123	−	0.0563794i
$679$	78.2555	−	78.2555i	0.115251	−	0.115251i
$680$	−40.7361	−	84.5893i	−0.0599060	−	0.124396i
$681$	148.694	−	1319.69i	0.218346	−	1.93788i
$682$	−83.1169	−	9.36503i	−0.121872	−	0.0137317i
$683$	−344.482	+	165.894i	−0.504366	+	0.242890i	−0.668724	−	0.743511i	$-0.733159\pi$
$683$	−344.482	+	165.894i	−0.504366	+	0.242890i	0.164358	+	0.986401i	$0.447445\pi$
$684$	75.0734	+	75.0734i	0.109756	+	0.109756i
$685$	−61.6474	+	176.178i	−0.0899963	+	0.257195i
$686$	−52.6368	+	83.7709i	−0.0767300	+	0.122115i
$687$	753.125	+	362.686i	1.09625	+	0.527927i
$688$	−114.300	−	326.652i	−0.166134	−	0.474784i
$689$	302.915	+	69.1384i	0.439645	+	0.100346i
$690$	−2.84705	−	3.57009i	−0.00412616	−	0.00517404i
$691$	−495.980	+	621.939i	−0.717771	+	0.900056i	−0.998209	−	0.0598158i	$-0.980949\pi$
$691$	−495.980	+	621.939i	−0.717771	+	0.900056i	0.280439	+	0.959872i	$0.409520\pi$
$692$	−107.580	−	471.341i	−0.155463	−	0.681129i
$693$	−13.1045	−	20.8557i	−0.0189098	−	0.0300947i
$694$	0.175884	+	1.56101i	0.000253435	+	0.00224930i
$695$		−	58.4262i		−	0.0840664i
$696$	29.1125	−	298.895i	0.0418283	−	0.429447i
$697$	−1089.17			−1.56265
$698$	94.4513	−	10.6421i	0.135317	−	0.0152466i
$699$	625.800	−	393.216i	0.895279	−	0.562541i
$700$	−233.328	+	53.2556i	−0.333326	+	0.0760794i
$701$	−825.456	−	658.279i	−1.17754	−	0.939057i	−0.178548	−	0.983931i	$-0.557140\pi$
$701$	−825.456	−	658.279i	−1.17754	−	0.939057i	−0.998993	+	0.0448739i	$0.985711\pi$
$702$	85.6963	−	68.3405i	0.122074	−	0.0973511i
$703$	−290.944	+	1274.71i	−0.413860	+	1.81324i
$704$	413.983	−	144.859i	0.588044	−	0.205765i
$705$	29.4582	−	61.1705i	0.0417846	−	0.0867667i
$706$	−143.499	−	90.1663i	−0.203256	−	0.127714i
$707$	239.856	+	83.9294i	0.339259	+	0.118712i
$708$	−156.455	+	156.455i	−0.220982	+	0.220982i
$709$	313.200	+	650.367i	0.441749	+	0.917301i	0.996364	+	0.0851945i	$0.0271512\pi$
$709$	313.200	+	650.367i	0.441749	+	0.917301i	−0.554615	+	0.832107i	$0.687135\pi$
$710$	−5.71810	+	50.7495i	−0.00805366	+	0.0714782i
$711$	−42.8007	−	4.82248i	−0.0601978	−	0.00678267i
$712$	−95.8127	+	46.1410i	−0.134568	+	0.0648048i
$713$	−56.4179	−	56.4179i	−0.0791275	−	0.0791275i
$714$	−34.4784	+	98.5335i	−0.0482890	+	0.138002i
$715$	−47.9167	+	76.2589i	−0.0670163	+	0.106656i
$716$	−974.197	−	469.149i	−1.36061	−	0.655236i
$717$	−174.169	−	497.747i	−0.242914	−	0.694207i
$718$	−102.687	−	23.4377i	−0.143019	−	0.0326431i
$719$	−684.608	−	858.472i	−0.952167	−	1.19398i	−0.980924	−	0.194394i	$-0.937726\pi$
$719$	−684.608	−	858.472i	−0.952167	−	1.19398i	0.0287562	−	0.999586i	$-0.490845\pi$
$720$	8.50166	−	10.6607i	0.0118079	−	0.0148066i
$721$	−42.3818	−	185.687i	−0.0587820	−	0.257541i
$722$	−79.4031	−	126.369i	−0.109977	−	0.175027i
$723$	97.7898	+	867.909i	0.135256	+	1.20043i
$724$			882.929i			1.21952i
$725$	501.757	+	486.823i	0.692079	+	0.671480i
$726$	−48.9515			−0.0674263
$727$	31.1294	−	3.50744i	0.0428190	−	0.00482454i	−0.0905290	−	0.995894i	$-0.528856\pi$
$727$	31.1294	−	3.50744i	0.0428190	−	0.00482454i	0.133348	+	0.991069i	$0.457427\pi$
$728$	−74.7022	+	46.9385i	−0.102613	+	0.0644759i
$729$	−611.212	+	139.505i	−0.838425	+	0.191365i
$730$	14.6758	+	11.7036i	0.0201039	+	0.0160323i
$731$	590.167	−	470.643i	0.807342	−	0.643834i
$732$	251.072	−	1100.02i	0.342994	−	1.50276i
$733$	143.446	−	50.1941i	0.195698	−	0.0684776i	−0.230651	−	0.973037i	$-0.574085\pi$
$733$	143.446	−	50.1941i	0.195698	−	0.0684776i	0.426348	+	0.904559i	$0.359800\pi$
$734$	−84.0234	+	174.476i	−0.114473	+	0.237706i
$735$	107.115	+	67.3050i	0.145735	+	0.0915715i
$736$	−65.1430	−	22.7945i	−0.0885095	−	0.0309708i
$737$	−366.642	+	366.642i	−0.497479	+	0.497479i
$738$	6.72467	+	13.9639i	0.00911203	+	0.0189213i
$739$	125.579	−	1114.55i	0.169931	−	1.50818i	−0.562191	−	0.827008i	$-0.690041\pi$
$739$	125.579	−	1114.55i	0.169931	−	1.50818i	0.732122	−	0.681174i	$-0.238530\pi$
$740$	175.225	+	19.7431i	0.236790	+	0.0266798i
$741$	−795.538	+	383.111i	−1.07360	+	0.517019i
$742$	−22.9005	−	22.9005i	−0.0308632	−	0.0308632i
$743$	−63.5004	+	181.474i	−0.0854649	+	0.244245i	−0.978682	−	0.205381i	$-0.934157\pi$
$743$	−63.5004	+	181.474i	−0.0854649	+	0.244245i	0.893217	+	0.449625i	$0.148442\pi$
$744$	−120.362	+	191.555i	−0.161777	+	0.257466i
$745$	−25.8944	−	12.4701i	−0.0347576	−	0.0167384i
$746$	−34.5965	−	98.8710i	−0.0463759	−	0.132535i
$747$	−133.631	−	30.5004i	−0.178890	−	0.0408306i
$748$	664.552	+	833.322i	0.888439	+	1.11407i
$749$	−99.4592	+	124.718i	−0.132789	+	0.166513i
$750$	−13.6625	−	59.8593i	−0.0182167	−	0.0798125i
$751$	−192.970	−	307.110i	−0.256950	−	0.408934i	0.693191	−	0.720754i	$-0.256204\pi$
$751$	−192.970	−	307.110i	−0.256950	−	0.408934i	−0.950141	+	0.311820i	$0.899061\pi$
$752$	−35.3950	−	314.140i	−0.0470679	−	0.417739i
$753$			1323.83i			1.75807i
$754$	114.322	+	52.9422i	0.151620	+	0.0702151i
$755$	133.718			0.177110
$756$	248.905	−	28.0448i	0.329239	−	0.0370964i
$757$	−145.660	+	91.5245i	−0.192418	+	0.120904i	−0.624796	−	0.780788i	$-0.714818\pi$
$757$	−145.660	+	91.5245i	−0.192418	+	0.120904i	0.432377	+	0.901693i	$0.357675\pi$
$758$	199.722	−	45.5852i	0.263485	−	0.0601387i
$759$	82.9079	+	66.1169i	0.109233	+	0.0871105i
$760$	−64.7167	+	51.6098i	−0.0851536	+	0.0679077i
$761$	−64.7556	+	283.713i	−0.0850928	+	0.372816i	−0.999488	−	0.0320077i	$-0.989810\pi$
$761$	−64.7556	+	283.713i	−0.0850928	+	0.372816i	0.914395	+	0.404824i	$0.132667\pi$
$762$	−227.228	+	79.5106i	−0.298200	+	0.104345i
$763$	−178.515	+	370.691i	−0.233965	+	0.485833i
$764$	−314.157	−	197.398i	−0.411201	−	0.258374i
$765$	28.0729	+	9.82315i	0.0366966	+	0.0128407i
$766$	65.2418	−	65.2418i	0.0851721	−	0.0851721i
$767$	−82.3859	−	171.076i	−0.107413	−	0.223046i
$768$	53.7302	−	476.869i	0.0699612	−	0.620923i
$769$	−609.620	−	68.6876i	−0.792743	−	0.0893207i	−0.293700	−	0.955898i	$-0.594887\pi$
$769$	−609.620	−	68.6876i	−0.792743	−	0.0893207i	−0.499043	+	0.866577i	$0.666315\pi$
$770$	8.45805	−	4.07318i	0.0109845	−	0.00528985i
$771$	25.0067	+

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)

\(f(q)\)	\(=\)	\(q+(0.415096 - 0.0467701i) q^{2} +(2.68233 - 1.68542i) q^{3} +(-3.72959 + 0.851255i) q^{4} +(0.738700 + 0.589093i) q^{5} +(1.03460 - 0.825065i) q^{6} +(-0.577468 + 2.53005i) q^{7} +(-3.08546 + 1.07965i) q^{8} +(0.449302 - 0.932984i) q^{9} +O(q^{10})\)	\(q+(0.415096 - 0.0467701i) q^{2} +(2.68233 - 1.68542i) q^{3} +(-3.72959 + 0.851255i) q^{4} +(0.738700 + 0.589093i) q^{5} +(1.03460 - 0.825065i) q^{6} +(-0.577468 + 2.53005i) q^{7} +(-3.08546 + 1.07965i) q^{8} +(0.449302 - 0.932984i) q^{9} +(0.334184 + 0.209981i) q^{10} +(-8.65125 - 3.02720i) q^{11} +(-8.56928 + 8.56928i) q^{12} +(-4.51239 - 9.37008i) q^{13} +(-0.121374 + 1.07722i) q^{14} +(2.97431 + 0.335124i) q^{15} +(12.5564 - 6.04684i) q^{16} +(21.4949 + 21.4949i) q^{17} +(0.142868 - 0.408292i) q^{18} +(14.2589 - 22.6929i) q^{19} +(-3.25652 - 1.56826i) q^{20} +(2.71524 + 7.75971i) q^{21} +(-3.73269 - 0.851961i) q^{22} +(-2.27710 - 2.85539i) q^{23} +(-6.45655 + 8.09626i) q^{24} +(-5.36438 - 23.5029i) q^{25} +(-2.31132 - 3.67844i) q^{26} +(2.82493 + 25.0719i) q^{27} -9.92764i q^{28} +(-24.3191 + 15.7981i) q^{29} +1.25030 q^{30} +(21.7090 - 2.44602i) q^{31} +(16.0007 - 10.0539i) q^{32} +(-28.3076 + 6.46103i) q^{33} +(9.92777 + 7.91713i) q^{34} +(-1.91701 + 1.52877i) q^{35} +(-0.881504 + 3.86212i) q^{36} +(-46.0478 + 16.1128i) q^{37} +(4.85746 - 10.0866i) q^{38} +(-27.8962 - 17.5284i) q^{39} +(-2.91524 - 1.02009i) q^{40} +(-25.3355 + 25.3355i) q^{41} +(1.49001 + 3.09404i) q^{42} +(2.78030 - 24.6759i) q^{43} +(34.8426 + 3.92581i) q^{44} +(0.881514 - 0.424515i) q^{45} +(-1.07876 - 1.07876i) q^{46} +(7.49184 - 21.4104i) q^{47} +(23.4889 - 37.3824i) q^{48} +(38.0798 + 18.3383i) q^{49} +(-3.32597 - 9.50507i) q^{50} +(93.8843 + 21.4285i) q^{51} +(24.8057 + 31.1054i) q^{52} +(-18.6271 + 23.3576i) q^{53} +(2.34523 + 10.2751i) q^{54} +(-4.60737 - 7.33259i) q^{55} +(-0.949813 - 8.42982i) q^{56} -84.9020i q^{57} +(-9.35591 + 7.69514i) q^{58} +18.2577 q^{59} +(-11.3782 + 1.28202i) q^{60} +(-78.8333 + 49.5342i) q^{61} +(8.89694 - 2.03067i) q^{62} +(2.10104 + 1.67552i) q^{63} +(-37.4125 + 29.8355i) q^{64} +(2.18655 - 9.57990i) q^{65} +(-11.4482 + 4.00590i) q^{66} +(24.5454 - 50.9691i) q^{67} +(-98.4648 - 61.8696i) q^{68} +(-10.9205 - 3.82123i) q^{69} +(-0.724244 + 0.724244i) q^{70} +(56.1438 + 116.584i) q^{71} +(-0.379006 + 3.36377i) q^{72} +(47.2614 + 5.32509i) q^{73} +(-18.3607 + 8.84204i) q^{74} +(-54.0012 - 54.0012i) q^{75} +(-33.8624 + 96.7732i) q^{76} +(12.6548 - 20.1400i) q^{77} +(-12.3994 - 5.97125i) q^{78} +(-13.7375 - 39.2594i) q^{79} +(12.8375 + 2.93009i) q^{80} +(55.6449 + 69.7765i) q^{81} +(-9.33174 + 11.7016i) q^{82} +(-29.4538 - 129.046i) q^{83} +(-16.7322 - 26.6292i) q^{84} +(3.21577 + 28.5408i) q^{85} -10.3729i q^{86} +(-38.6056 + 83.3636i) q^{87} +29.9614 q^{88} +(32.3276 - 3.64244i) q^{89} +(0.346059 - 0.217443i) q^{90} +(26.3125 - 6.00567i) q^{91} +(10.9233 + 8.71105i) q^{92} +(54.1082 - 43.1499i) q^{93} +(2.10847 - 9.23779i) q^{94} +(23.9012 - 8.36341i) q^{95} +(25.9741 - 53.9358i) q^{96} +(-36.1089 - 22.6888i) q^{97} +(16.6645 + 5.83115i) q^{98} +(-6.71135 + 6.71135i) 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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