LMFDB - Embedded newform 76.3.b.b.39.2

Newspace parameters

Level:	$ N $	$=$	$ 76 = 2^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	76.b (of order $2$, degree $1$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$2.07085000914$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
Defining polynomial:	$x^{14} - 2 x^{13} + x^{12} + 14 x^{11} - 42 x^{10} + 28 x^{9} + 132 x^{8} - 440 x^{7} + 528 x^{6} + 448 x^{5} - 2688 x^{4} + 3584 x^{3} + 1024 x^{2} - 8192 x + 16384$
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{12} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			39.2
Root			$-1.92254 - 0.551226i$ of defining polynomial
Character	$\chi$	$=$	76.39
Dual form			76.3.b.b.39.1

$q$-expansion

$f(q)$	$=$	$q+(-1.92254 + 0.551226i) q^{2} -0.644704i q^{3} +(3.39230 - 2.11950i) q^{4} -2.32715 q^{5} +(0.355377 + 1.23947i) q^{6} -8.62924i q^{7} +(-5.35350 + 5.94475i) q^{8} +8.58436 q^{9} +O(q^{10})$	\(q+(-1.92254 + 0.551226i) q^{2} -0.644704i q^{3} +(3.39230 - 2.11950i) q^{4} -2.32715 q^{5} +(0.355377 + 1.23947i) q^{6} -8.62924i q^{7} +(-5.35350 + 5.94475i) q^{8} +8.58436 q^{9} +(4.47404 - 1.28279i) q^{10} -19.2717i q^{11} +(-1.36645 - 2.18703i) q^{12} +13.8067 q^{13} +(4.75666 + 16.5900i) q^{14} +1.50032i q^{15} +(7.01540 - 14.3800i) q^{16} -12.5180 q^{17} +(-16.5037 + 4.73192i) q^{18} -4.35890i q^{19} +(-7.89440 + 4.93241i) q^{20} -5.56330 q^{21} +(10.6231 + 37.0506i) q^{22} +37.4981i q^{23} +(3.83260 + 3.45142i) q^{24} -19.5844 q^{25} +(-26.5438 + 7.61058i) q^{26} -11.3367i q^{27} +(-18.2897 - 29.2730i) q^{28} -6.36930 q^{29} +(-0.827018 - 2.88443i) q^{30} +5.44851i q^{31} +(-5.56075 + 31.5131i) q^{32} -12.4245 q^{33} +(24.0663 - 6.90025i) q^{34} +20.0816i q^{35} +(29.1207 - 18.1946i) q^{36} +20.9250 q^{37} +(2.40274 + 8.38015i) q^{38} -8.90120i q^{39} +(12.4584 - 13.8343i) q^{40} +72.8337 q^{41} +(10.6957 - 3.06664i) q^{42} -10.1553i q^{43} +(-40.8465 - 65.3755i) q^{44} -19.9771 q^{45} +(-20.6699 - 72.0914i) q^{46} +32.4450i q^{47} +(-9.27083 - 4.52286i) q^{48} -25.4638 q^{49} +(37.6517 - 10.7954i) q^{50} +8.07040i q^{51} +(46.8363 - 29.2633i) q^{52} -42.9339 q^{53} +(6.24908 + 21.7952i) q^{54} +44.8482i q^{55} +(51.2987 + 46.1966i) q^{56} -2.81020 q^{57} +(12.2452 - 3.51092i) q^{58} -38.9728i q^{59} +(3.17994 + 5.08955i) q^{60} +25.5611 q^{61} +(-3.00336 - 10.4750i) q^{62} -74.0765i q^{63} +(-6.68010 - 63.6504i) q^{64} -32.1302 q^{65} +(23.8867 - 6.84873i) q^{66} +65.3183i q^{67} +(-42.4648 + 26.5320i) q^{68} +24.1751 q^{69} +(-11.0695 - 38.6076i) q^{70} +18.7557i q^{71} +(-45.9563 + 51.0319i) q^{72} +72.8251 q^{73} +(-40.2292 + 11.5344i) q^{74} +12.6261i q^{75} +(-9.23871 - 14.7867i) q^{76} -166.300 q^{77} +(4.90657 + 17.1129i) q^{78} +139.874i q^{79} +(-16.3259 + 33.4644i) q^{80} +69.9504 q^{81} +(-140.026 + 40.1478i) q^{82} -94.7116i q^{83} +(-18.8724 + 11.7914i) q^{84} +29.1313 q^{85} +(5.59789 + 19.5240i) q^{86} +4.10631i q^{87} +(114.566 + 103.171i) q^{88} +33.3546 q^{89} +(38.4068 - 11.0119i) q^{90} -119.141i q^{91} +(79.4773 + 127.205i) q^{92} +3.51267 q^{93} +(-17.8845 - 62.3766i) q^{94} +10.1438i q^{95} +(20.3166 + 3.58504i) q^{96} -150.817 q^{97} +(48.9551 - 14.0363i) q^{98} -165.435i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14q + 2q^{2} + 2q^{4} - 40q^{8} - 68q^{9} + O(q^{10}) $	$ 14q + 2q^{2} + 2q^{4} - 40q^{8} - 68q^{9} - 12q^{10} + 4q^{12} + 54q^{13} + 30q^{14} + 58q^{16} + 34q^{17} + 36q^{18} + 32q^{20} - 38q^{21} + 36q^{22} - 98q^{24} - 86q^{25} - 16q^{26} + 18q^{28} + 54q^{29} - 204q^{30} + 72q^{32} + 20q^{33} - 82q^{34} + 96q^{36} + 100q^{37} - 148q^{40} + 224q^{41} + 224q^{42} - 96q^{44} - 168q^{45} + 46q^{46} + 296q^{48} - 220q^{49} - 58q^{50} - 288q^{52} + 14q^{53} - 128q^{54} + 12q^{56} + 38q^{57} - 72q^{58} + 188q^{60} + 28q^{61} + 396q^{62} - 118q^{64} - 472q^{65} - 32q^{66} + 30q^{68} + 122q^{69} + 156q^{70} + 80q^{72} + 70q^{73} - 224q^{74} + 228q^{77} + 274q^{78} - 348q^{80} + 334q^{81} - 400q^{82} - 216q^{84} + 48q^{85} - 124q^{86} + 472q^{88} + 416q^{90} + 126q^{92} - 176q^{93} - 88q^{94} - 106q^{96} + 308q^{97} + 68q^{98} + O(q^{100}) $

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

$n$	$21$	$39$
$\chi(n)$	$1$	$-1$

Coefficient data

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

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

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

$2$	−1.92254	+	0.551226i	−0.961269	+	0.275613i
$2$	−1.92254	+	0.551226i	−0.961269	+	0.275613i
$3$		−	0.644704i		−	0.214901i	−0.994210	−	0.107451i	$-0.965731\pi$
$3$		−	0.644704i		−	0.214901i	0.994210	−	0.107451i	$-0.0342688\pi$
$4$	3.39230	−	2.11950i	0.848075	−	0.529876i
$5$	−2.32715			−0.465431			−0.232715	−	0.972545i	$-0.574761\pi$
$5$	−2.32715			−0.465431			−0.232715	+	0.972545i	$0.574761\pi$
$6$	0.355377	+	1.23947i	0.0592296	+	0.206578i
$7$		−	8.62924i		−	1.23275i	−0.787453	−	0.616374i	$-0.788601\pi$
$7$		−	8.62924i		−	1.23275i	0.787453	−	0.616374i	$-0.211399\pi$
$8$	−5.35350	+	5.94475i	−0.669187	+	0.743094i
$9$	8.58436			0.953817
$10$	4.47404	−	1.28279i	0.447404	−	0.128279i
$11$		−	19.2717i		−	1.75197i	−0.482334	−	0.875987i	$-0.660211\pi$
$11$		−	19.2717i		−	1.75197i	0.482334	−	0.875987i	$-0.339789\pi$
$12$	−1.36645	−	2.18703i	−0.113871	−	0.182252i
$13$	13.8067			1.06205			0.531025	−	0.847356i	$-0.321807\pi$
$13$	13.8067			1.06205			0.531025	+	0.847356i	$0.321807\pi$
$14$	4.75666	+	16.5900i	0.339761	+	1.18500i
$15$			1.50032i			0.100022i
$16$	7.01540	−	14.3800i	0.438463	−	0.898749i
$17$	−12.5180			−0.736353			−0.368177	−	0.929756i	$-0.620018\pi$
$17$	−12.5180			−0.736353			−0.368177	+	0.929756i	$0.620018\pi$
$18$	−16.5037	+	4.73192i	−0.916875	+	0.262884i
$19$		−	4.35890i		−	0.229416i
$19$		−	4.35890i		−	0.229416i
$20$	−7.89440	+	4.93241i	−0.394720	+	0.246621i
$21$	−5.56330			−0.264919
$22$	10.6231	+	37.0506i	0.482867	+	1.68412i
$23$			37.4981i			1.63035i	0.579214	+	0.815175i	$0.303360\pi$
$23$			37.4981i			1.63035i	−0.579214	+	0.815175i	$0.696640\pi$
$24$	3.83260	+	3.45142i	0.159692	+	0.143809i
$25$	−19.5844			−0.783374
$26$	−26.5438	+	7.61058i	−1.02092	+	0.292715i
$27$		−	11.3367i		−	0.419878i
$28$	−18.2897	−	29.2730i	−0.653204	−	1.04546i
$29$	−6.36930			−0.219631			−0.109816	−	0.993952i	$-0.535026\pi$
$29$	−6.36930			−0.219631			−0.109816	+	0.993952i	$0.535026\pi$
$30$	−0.827018	−	2.88443i	−0.0275673	−	0.0961477i
$31$			5.44851i			0.175758i	0.996131	+	0.0878791i	$0.0280089\pi$
$31$			5.44851i			0.175758i	−0.996131	+	0.0878791i	$0.971991\pi$
$32$	−5.56075	+	31.5131i	−0.173774	+	0.984786i
$33$	−12.4245			−0.376502
$34$	24.0663	−	6.90025i	0.707833	−	0.202948i
$35$			20.0816i			0.573759i
$36$	29.1207	−	18.1946i	0.808909	−	0.505405i
$37$	20.9250			0.565542			0.282771	−	0.959187i	$-0.408746\pi$
$37$	20.9250			0.565542			0.282771	+	0.959187i	$0.408746\pi$
$38$	2.40274	+	8.38015i	0.0632299	+	0.220530i
$39$		−	8.90120i		−	0.228236i
$40$	12.4584	−	13.8343i	0.311460	−	0.345859i
$41$	72.8337			1.77643			0.888216	−	0.459425i	$-0.151945\pi$
$41$	72.8337			1.77643			0.888216	+	0.459425i	$0.151945\pi$
$42$	10.6957	−	3.06664i	0.254659	−	0.0730152i
$43$		−	10.1553i		−	0.236171i	−0.993003	−	0.118085i	$-0.962324\pi$
$43$		−	10.1553i		−	0.236171i	0.993003	−	0.118085i	$-0.0376757\pi$
$44$	−40.8465	−	65.3755i	−0.928329	−	1.48581i
$45$	−19.9771			−0.443936
$46$	−20.6699	−	72.0914i	−0.449346	−	1.56721i
$47$			32.4450i			0.690318i	0.938544	+	0.345159i	$0.112175\pi$
$47$			32.4450i			0.690318i	−0.938544	+	0.345159i	$0.887825\pi$
$48$	−9.27083	−	4.52286i	−0.193142	−	0.0942262i
$49$	−25.4638			−0.519669
$50$	37.6517	−	10.7954i	0.753033	−	0.215908i
$51$			8.07040i			0.158243i
$52$	46.8363	−	29.2633i	0.900698	−	0.562755i
$53$	−42.9339			−0.810074			−0.405037	−	0.914300i	$-0.632741\pi$
$53$	−42.9339			−0.810074			−0.405037	+	0.914300i	$0.632741\pi$
$54$	6.24908	+	21.7952i	0.115724	+	0.403615i
$55$			44.8482i			0.815423i
$56$	51.2987	+	46.1966i	0.916048	+	0.824940i
$57$	−2.81020			−0.0493017
$58$	12.2452	−	3.51092i	0.211125	−	0.0605332i
$59$		−	38.9728i		−	0.660556i	−0.943884	−	0.330278i	$-0.892858\pi$
$59$		−	38.9728i		−	0.660556i	0.943884	−	0.330278i	$-0.107142\pi$
$60$	3.17994	+	5.08955i	0.0529991	+	0.0848258i
$61$	25.5611			0.419034			0.209517	−	0.977805i	$-0.432811\pi$
$61$	25.5611			0.419034			0.209517	+	0.977805i	$0.432811\pi$
$62$	−3.00336	−	10.4750i	−0.0484412	−	0.168951i
$63$		−	74.0765i		−	1.17582i
$64$	−6.68010	−	63.6504i	−0.104377	−	0.994538i
$65$	−32.1302			−0.494311
$66$	23.8867	−	6.84873i	0.361919	−	0.103769i
$67$			65.3183i			0.974900i	0.873151	+	0.487450i	$0.162073\pi$
$67$			65.3183i			0.974900i	−0.873151	+	0.487450i	$0.837927\pi$
$68$	−42.4648	+	26.5320i	−0.624483	+	0.390176i
$69$	24.1751			0.350364
$70$	−11.0695	−	38.6076i	−0.158135	−	0.551537i
$71$			18.7557i			0.264165i	0.991239	+	0.132083i	$0.0421665\pi$
$71$			18.7557i			0.264165i	−0.991239	+	0.132083i	$0.957834\pi$
$72$	−45.9563	+	51.0319i	−0.638283	+	0.708776i
$73$	72.8251			0.997604			0.498802	−	0.866716i	$-0.333773\pi$
$73$	72.8251			0.997604			0.498802	+	0.866716i	$0.333773\pi$
$74$	−40.2292	+	11.5344i	−0.543638	+	0.155871i
$75$			12.6261i			0.168348i
$76$	−9.23871	−	14.7867i	−0.121562	−	0.194562i
$77$	−166.300			−2.15974
$78$	4.90657	+	17.1129i	0.0629048	+	0.219396i
$79$			139.874i			1.77056i	0.465060	+	0.885279i	$0.346033\pi$
$79$			139.874i			1.77056i	−0.465060	+	0.885279i	$0.653967\pi$
$80$	−16.3259	+	33.4644i	−0.204074	+	0.418306i
$81$	69.9504			0.863585
$82$	−140.026	+	40.1478i	−1.70763	+	0.489608i
$83$		−	94.7116i		−	1.14110i	−0.821262	−	0.570552i	$-0.806729\pi$
$83$		−	94.7116i		−	1.14110i	0.821262	−	0.570552i	$-0.193271\pi$
$84$	−18.8724	+	11.7914i	−0.224671	+	0.140374i
$85$	29.1313			0.342721
$86$	5.59789	+	19.5240i	0.0650917	+	0.227024i
$87$			4.10631i			0.0471990i
$88$	114.566	+	103.171i	1.30188	+	1.17240i
$89$	33.3546			0.374770			0.187385	−	0.982287i	$-0.439999\pi$
$89$	33.3546			0.374770			0.187385	+	0.982287i	$0.439999\pi$
$90$	38.4068	−	11.0119i	0.426742	−	0.122354i
$91$		−	119.141i		−	1.30924i
$92$	79.4773	+	127.205i	0.863884	+	1.38266i
$93$	3.51267			0.0377707
$94$	−17.8845	−	62.3766i	−0.190261	−	0.663581i
$95$			10.1438i			0.106777i
$96$	20.3166	+	3.58504i	0.211632	+	0.0373441i
$97$	−150.817			−1.55482			−0.777408	−	0.628996i	$-0.783466\pi$
$97$	−150.817			−1.55482			−0.777408	+	0.628996i	$0.783466\pi$
$98$	48.9551	−	14.0363i	0.499542	−	0.143228i
$99$		−	165.435i		−	1.67106i
$100$	−66.4360	+	41.5091i	−0.664360	+	0.415091i
$101$	77.7745			0.770045			0.385022	−	0.922907i	$-0.374194\pi$
$101$	77.7745			0.770045			0.385022	+	0.922907i	$0.374194\pi$
$102$	−4.44862	−	15.5157i	−0.0436139	−	0.152114i
$103$			14.9481i			0.145127i	0.997364	+	0.0725637i	$0.0231180\pi$
$103$			14.9481i			0.145127i	−0.997364	+	0.0725637i	$0.976882\pi$
$104$	−73.9139	+	82.0771i	−0.710711	+	0.789203i
$105$	12.9467			0.123302
$106$	82.5420	−	23.6663i	0.778698	−	0.223267i
$107$			80.5205i			0.752528i	0.926512	+	0.376264i	$0.122792\pi$
$107$			80.5205i			0.752528i	−0.926512	+	0.376264i	$0.877208\pi$
$108$	−24.0282	−	38.4575i	−0.222483	−	0.356088i
$109$	53.8512			0.494048			0.247024	−	0.969009i	$-0.420547\pi$
$109$	53.8512			0.494048			0.247024	+	0.969009i	$0.420547\pi$
$110$	−24.7215	−	86.2224i	−0.224741	−	0.783840i
$111$		−	13.4905i		−	0.121536i
$112$	−124.088	−	60.5376i	−1.10793	−	0.540514i
$113$	105.921			0.937355			0.468677	−	0.883369i	$-0.344731\pi$
$113$	105.921			0.937355			0.468677	+	0.883369i	$0.344731\pi$
$114$	5.40271	−	1.54905i	0.0473922	−	0.0135882i
$115$		−	87.2638i		−	0.758815i
$116$	−21.6066	+	13.4998i	−0.186264	+	0.116377i
$117$	118.521			1.01300
$118$	21.4828	+	74.9266i	0.182058	+	0.634972i
$119$			108.021i			0.907739i
$120$	−8.91905	−	8.03199i	−0.0743254	−	0.0669332i
$121$	−250.399			−2.06941
$122$	−49.1421	+	14.0899i	−0.402804	+	0.115491i
$123$		−	46.9562i		−	0.381758i
$124$	11.5481	+	18.4830i	0.0931301	+	0.149056i
$125$	103.755			0.830037
$126$	40.8329	+	142.415i	0.324070	+	1.13028i
$127$		−	17.1409i		−	0.134968i	−0.997720	−	0.0674839i	$-0.978503\pi$
$127$		−	17.1409i		−	0.134968i	0.997720	−	0.0674839i	$-0.0214971\pi$
$128$	47.9285	+	118.688i	0.374441	+	0.927251i
$129$	−6.54719			−0.0507534
$130$	61.7715	−	17.7110i	0.475166	−	0.136238i
$131$		−	229.336i		−	1.75066i	−0.483526	−	0.875330i	$-0.660644\pi$
$131$		−	229.336i		−	1.75066i	0.483526	−	0.875330i	$-0.339356\pi$
$132$	−42.1478	+	26.3339i	−0.319302	+	0.199499i
$133$	−37.6140			−0.282812
$134$	−36.0051	−	125.577i	−0.268695	−	0.937141i
$135$			26.3822i			0.195424i
$136$	67.0151	−	74.4164i	0.492758	−	0.547179i
$137$	−120.567			−0.880054			−0.440027	−	0.897985i	$-0.645031\pi$
$137$	−120.567			−0.880054			−0.440027	+	0.897985i	$0.645031\pi$
$138$	−46.4776	+	13.3260i	−0.336794	+	0.0965650i
$139$			145.864i			1.04938i	0.851292	+	0.524692i	$0.175819\pi$
$139$			145.864i			1.04938i	−0.851292	+	0.524692i	$0.824181\pi$
$140$	42.5630	+	68.1227i	0.304021	+	0.486591i
$141$	20.9174			0.148350
$142$	−10.3387	−	36.0586i	−0.0728074	−	0.253934i
$143$		−	266.078i		−	1.86069i
$144$	60.2227	−	123.443i	0.418213	−	0.857243i
$145$	14.8223			0.102223
$146$	−140.009	+	40.1431i	−0.958966	+	0.274953i
$147$			16.4166i			0.111678i
$148$	70.9840	−	44.3507i	0.479622	−	0.299667i
$149$	19.2547			0.129226			0.0646132	−	0.997910i	$-0.479419\pi$
$149$	19.2547			0.129226			0.0646132	+	0.997910i	$0.479419\pi$
$150$	−6.95984	−	24.2742i	−0.0463989	−	0.161828i
$151$			165.526i			1.09620i	0.836414	+	0.548099i	$0.184648\pi$
$151$			165.526i			1.09620i	−0.836414	+	0.548099i	$0.815352\pi$
$152$	25.9126	+	23.3354i	0.170477	+	0.153522i
$153$	−107.459			−0.702347
$154$	319.719	−	91.6690i	2.07609	−	0.595253i
$155$		−	12.6795i		−	0.0818033i
$156$	−18.8661	−	30.1956i	−0.120937	−	0.193561i
$157$	149.449			0.951907			0.475954	−	0.879470i	$-0.342103\pi$
$157$	149.449			0.951907			0.475954	+	0.879470i	$0.342103\pi$
$158$	−77.1022	−	268.913i	−0.487989	−	1.70198i
$159$			27.6796i			0.174086i
$160$	12.9407	−	73.3359i	0.0808795	−	0.458349i
$161$	323.580			2.00981
$162$	−134.482	+	38.5585i	−0.830137	+	0.238015i
$163$			146.763i			0.900384i	0.892932	+	0.450192i	$0.148644\pi$
$163$			146.763i			0.900384i	−0.892932	+	0.450192i	$0.851356\pi$
$164$	247.074	−	154.371i	1.50655	−	0.941289i
$165$	28.9138			0.175235
$166$	52.2075	+	182.087i	0.314503	+	1.09691i
$167$			213.493i			1.27840i	0.769040	+	0.639201i	$0.220735\pi$
$167$			213.493i			1.27840i	−0.769040	+	0.639201i	$0.779265\pi$
$168$	29.7831	−	33.0724i	0.177281	−	0.196860i
$169$	21.6237			0.127951
$170$	−56.0061	+	16.0579i	−0.329447	+	0.0944584i
$171$		−	37.4183i		−	0.218821i
$172$	−21.5243	−	34.4500i	−0.125141	−	0.200291i
$173$	−280.715			−1.62263			−0.811314	−	0.584610i	$-0.801247\pi$
$173$	−280.715			−1.62263			−0.811314	+	0.584610i	$0.801247\pi$
$174$	−2.26351	−	7.89454i	−0.0130087	−	0.0453709i
$175$			168.998i			0.965704i
$176$	−277.127	−	135.199i	−1.57459	−	0.768175i
$177$	−25.1259			−0.141954
$178$	−64.1254	+	18.3859i	−0.360255	+	0.103292i
$179$		−	35.1878i		−	0.196580i	−0.995158	−	0.0982899i	$-0.968663\pi$
$179$		−	35.1878i		−	0.196580i	0.995158	−	0.0982899i	$-0.0313372\pi$
$180$	−67.7684	+	42.3416i	−0.376491	+	0.235231i
$181$	−345.539			−1.90906			−0.954529	−	0.298120i	$-0.903641\pi$
$181$	−345.539			−1.90906			−0.954529	+	0.298120i	$0.903641\pi$
$182$	65.6736	+	229.053i	0.360844	+	1.25853i
$183$		−	16.4793i		−	0.0900509i
$184$	−222.917	−	200.746i	−1.21150	−	1.09101i
$185$	−48.6958			−0.263220
$186$	−6.75324	+	1.93628i	−0.0363078	+	0.0104101i
$187$			241.244i			1.29007i
$188$	68.7672	+	110.063i	0.365783	+	0.585442i
$189$	−97.8271			−0.517604
$190$	−5.59154	−	19.5019i	−0.0294292	−	0.102642i
$191$		−	100.233i		−	0.524782i	−0.964962	−	0.262391i	$-0.915489\pi$
$191$		−	100.233i		−	0.524782i	0.964962	−	0.262391i	$-0.0845110\pi$
$192$	−41.0357	+	4.30669i	−0.213727	+	0.0224307i
$193$	168.119			0.871085			0.435543	−	0.900168i	$-0.356557\pi$
$193$	168.119			0.871085			0.435543	+	0.900168i	$0.356557\pi$
$194$	289.952	−	83.1343i	1.49460	−	0.428528i
$195$			20.7145i			0.106228i
$196$	−86.3808	+	53.9706i	−0.440719	+	0.275360i
$197$	216.705			1.10002			0.550012	−	0.835157i	$-0.314623\pi$
$197$	216.705			1.10002			0.550012	+	0.835157i	$0.314623\pi$
$198$	91.1922	+	318.056i	0.460567	+	1.60634i
$199$			82.2545i			0.413339i	0.978411	+	0.206670i	$0.0662625\pi$
$199$			82.2545i			0.413339i	−0.978411	+	0.206670i	$0.933738\pi$
$200$	104.845	−	116.424i	0.524224	−	0.582121i
$201$	42.1109			0.209507
$202$	−149.524	+	42.8713i	−0.740220	+	0.212234i
$203$			54.9623i			0.270750i
$204$	17.1053	+	27.3772i	0.0838493	+	0.134202i
$205$	−169.495			−0.826806
$206$	−8.23978	−	28.7383i	−0.0399990	−	0.139506i
$207$			321.897i			1.55506i
$208$	96.8592	−	198.540i	0.465669	−	0.954517i
$209$	−84.0035			−0.401931
$210$	−24.8904	+	7.13653i	−0.118526	+	0.0339835i
$211$			16.4195i			0.0778173i	0.999243	+	0.0389087i	$0.0123881\pi$
$211$			16.4195i			0.0778173i	−0.999243	+	0.0389087i	$0.987612\pi$
$212$	−145.645	+	90.9986i	−0.687003	+	0.429239i
$213$	12.0919			0.0567695
$214$	−44.3850	−	154.804i	−0.207407	−	0.723382i
$215$			23.6331i			0.109921i
$216$	67.3938	+	60.6910i	0.312009	+	0.280977i
$217$	47.0165			0.216666
$218$	−103.531	+	29.6842i	−0.474913	+	0.136166i
$219$		−	46.9506i		−	0.214386i
$220$	95.0561	+	152.139i	0.432073	+	0.691540i
$221$	−172.832			−0.782044
$222$	7.43629	+	25.9359i	0.0334968	+	0.116828i
$223$		−	195.225i		−	0.875450i	−0.899109	−	0.437725i	$-0.855784\pi$
$223$		−	195.225i		−	0.875450i	0.899109	−	0.437725i	$-0.144216\pi$
$224$	271.934	+	47.9851i	1.21399	+	0.214219i
$225$	−168.119			−0.747196
$226$	−203.637	+	58.3864i	−0.901050	+	0.258347i
$227$		−	305.403i		−	1.34539i	−0.739920	−	0.672695i	$-0.765137\pi$
$227$		−	305.403i		−	1.34539i	0.739920	−	0.672695i	$-0.234863\pi$
$228$	−9.53304	+	5.95623i	−0.0418116	+	0.0261238i
$229$	−229.686			−1.00300			−0.501499	−	0.865158i	$-0.667218\pi$
$229$	−229.686			−1.00300			−0.501499	+	0.865158i	$0.667218\pi$
$230$	48.1020	+	167.768i	0.209139	+	0.729425i
$231$			107.214i			0.464132i
$232$	34.0981	−	37.8639i	0.146974	−	0.163207i
$233$	187.667			0.805436			0.402718	−	0.915324i	$-0.368065\pi$
$233$	187.667			0.805436			0.402718	+	0.915324i	$0.368065\pi$
$234$	−227.862	+	65.3320i	−0.973767	+	0.279196i
$235$		−	75.5044i		−	0.321295i
$236$	−82.6030	−	132.207i	−0.350013	−	0.560201i
$237$	90.1774			0.380495
$238$	−59.5439	−	207.674i	−0.250184	−	0.872581i
$239$		−	69.8504i		−	0.292261i	−0.989265	−	0.146130i	$-0.953318\pi$
$239$		−	69.8504i		−	0.292261i	0.989265	−	0.146130i	$-0.0466819\pi$
$240$	21.5747	+	10.5254i	0.0898944	+	0.0438557i
$241$	297.561			1.23469			0.617346	−	0.786691i	$-0.288208\pi$
$241$	297.561			1.23469			0.617346	+	0.786691i	$0.288208\pi$
$242$	481.402	−	138.026i	1.98926	−	0.570357i
$243$		−	147.128i		−	0.605463i
$244$	86.7109	−	54.1768i	0.355372	−	0.222036i
$245$	59.2582			0.241870
$246$	25.8835	+	90.2750i	0.105217	+	0.366972i
$247$		−	60.1818i		−	0.243651i
$248$	−32.3900	−	29.1686i	−0.130605	−	0.117615i
$249$	−61.0609			−0.245225
$250$	−199.472	+	57.1922i	−0.797889	+	0.228769i
$251$		−	36.4667i		−	0.145286i	−0.997358	−	0.0726429i	$-0.976857\pi$
$251$		−	36.4667i		−	0.145286i	0.997358	−	0.0726429i	$-0.0231433\pi$
$252$	−157.005	−	251.290i	−0.623037	−	0.997181i
$253$	722.652			2.85633
$254$	9.44851	+	32.9540i	0.0371988	+	0.129740i
$255$		−	18.7811i		−	0.0736513i
$256$	−157.568	−	201.763i	−0.615501	−	0.788136i
$257$	−175.943			−0.684604			−0.342302	−	0.939590i	$-0.611207\pi$
$257$	−175.943			−0.684604			−0.342302	+	0.939590i	$0.611207\pi$
$258$	12.5872	−	3.60898i	0.0487877	−	0.0139883i
$259$		−	180.567i		−	0.697171i
$260$	−108.995	+	68.1001i	−0.419213	+	0.261924i
$261$	−54.6764			−0.209488
$262$	126.416	+	440.908i	0.482504	+	1.68285i
$263$		−	444.887i		−	1.69158i	−0.533512	−	0.845792i	$-0.679128\pi$
$263$		−	444.887i		−	1.69158i	0.533512	−	0.845792i	$-0.320872\pi$
$264$	66.5148	−	73.8608i	0.251950	−	0.279776i
$265$	99.9138			0.377033
$266$	72.3143	−	20.7338i	0.271858	−	0.0779466i
$267$		−	21.5038i		−	0.0805386i
$268$	138.442	+	221.579i	0.516576	+	0.826788i
$269$	149.744			0.556670			0.278335	−	0.960484i	$-0.410217\pi$
$269$	149.744			0.556670			0.278335	+	0.960484i	$0.410217\pi$
$270$	−14.5426	−	50.7208i	−0.0538614	−	0.187855i
$271$		−	439.685i		−	1.62245i	−0.584731	−	0.811227i	$-0.698800\pi$
$271$		−	439.685i		−	1.62245i	0.584731	−	0.811227i	$-0.301200\pi$
$272$	−87.8188	+	180.009i	−0.322863	+	0.661797i
$273$	−76.8106			−0.281358
$274$	231.795	−	66.4598i	0.845968	−	0.242554i
$275$			377.424i			1.37245i
$276$	82.0094	−	51.2393i	0.297135	−	0.185650i
$277$	83.2452			0.300524			0.150262	−	0.988646i	$-0.451988\pi$
$277$	83.2452			0.300524			0.150262	+	0.988646i	$0.451988\pi$
$278$	−80.4042	−	280.430i	−0.289224	−	1.00874i
$279$			46.7719i			0.167641i
$280$	−119.380	−	107.507i	−0.426357	−	0.383952i
$281$	−12.9851			−0.0462105			−0.0231052	−	0.999733i	$-0.507355\pi$
$281$	−12.9851			−0.0462105			−0.0231052	+	0.999733i	$0.507355\pi$
$282$	−40.2144	+	11.5302i	−0.142604	+	0.0408872i
$283$		−	111.022i		−	0.392303i	−0.980574	−	0.196152i	$-0.937156\pi$
$283$		−	111.022i		−	0.392303i	0.980574	−	0.196152i	$-0.0628445\pi$
$284$	39.7529	+	63.6251i	0.139975	+	0.224032i
$285$	6.53976			0.0229465
$286$	146.669	+	511.545i	0.512829	+	1.78862i
$287$		−	628.500i		−	2.18990i
$288$	−47.7355	+	270.520i	−0.165748	+	0.939306i
$289$	−132.300			−0.457784
$290$	−28.4965	+	8.17046i	−0.0982639	+	0.0281740i
$291$			97.2324i			0.334132i
$292$	247.045	−	154.353i	0.846043	−	0.528607i
$293$	−141.572			−0.483179			−0.241590	−	0.970378i	$-0.577669\pi$
$293$	−141.572			−0.483179			−0.241590	+	0.970378i	$0.577669\pi$
$294$	−9.04926	−	31.5615i	−0.0307798	−	0.107352i
$295$			90.6956i			0.307443i
$296$	−112.022	+	124.394i	−0.378453	+	0.420251i
$297$	−218.478			−0.735615
$298$	−37.0179	+	10.6137i	−0.124221	+	0.0356165i
$299$			517.723i			1.73151i
$300$	26.7611	+	42.8315i	0.0892036	+	0.142772i
$301$	−87.6329			−0.291139
$302$	−91.2421	−	318.229i	−0.302126	−	1.05374i
$303$		−	50.1415i		−	0.165484i
$304$	−62.6809	−	30.5794i	−0.206187	−	0.100590i
$305$	−59.4846			−0.195031
$306$	206.594	−	59.2342i	0.675144	−	0.193576i
$307$		−	357.744i		−	1.16529i	−0.812727	−	0.582645i	$-0.802018\pi$
$307$		−	357.744i		−	1.16529i	0.812727	−	0.582645i	$-0.197982\pi$
$308$	−564.141	+	352.474i	−1.83163	+	1.14440i
$309$	9.63710			0.0311880
$310$	6.98927	+	24.3768i	0.0225460	+	0.0786349i
$311$			472.383i			1.51892i	0.650557	+	0.759458i	$0.274536\pi$
$311$			472.383i			1.51892i	−0.650557	+	0.759458i	$0.725464\pi$
$312$	52.9154	+	47.6526i	0.169601	+	0.152733i
$313$	63.7596			0.203705			0.101852	−	0.994800i	$-0.467523\pi$
$313$	63.7596			0.203705			0.101852	+	0.994800i	$0.467523\pi$
$314$	−287.322	+	82.3804i	−0.915039	+	0.262358i
$315$			172.387i			0.547261i
$316$	296.464	+	474.495i	0.938177	+	1.50157i
$317$	198.721			0.626880			0.313440	−	0.949608i	$-0.398519\pi$
$317$	198.721			0.626880			0.313440	+	0.949608i	$0.398519\pi$
$318$	−15.2577	−	53.2151i	−0.0479803	−	0.167343i
$319$			122.747i			0.384788i
$320$	15.5456	+	148.124i	0.0485801	+	0.462888i
$321$	51.9119			0.161719
$322$	−622.094	+	178.366i	−1.93197	+	0.553930i
$323$			54.5647i			0.168931i
$324$	237.293	−	148.260i	0.732385	−	0.457593i
$325$	−270.394			−0.831983
$326$	−80.8993	−	282.156i	−0.248157	−	0.865511i
$327$		−	34.7181i		−	0.106172i
$328$	−389.915	+	432.978i	−1.18877	+	1.32006i
$329$	279.975			0.850989
$330$	−55.5879	+	15.9380i	−0.168448	+	0.0482971i
$331$			438.736i			1.32549i	0.748846	+	0.662744i	$0.230608\pi$
$331$			438.736i			1.32549i	−0.748846	+	0.662744i	$0.769392\pi$
$332$	−200.742	−	321.290i	−0.604644	−	0.967742i
$333$	179.628			0.539424
$334$	−117.683	−	410.449i	−0.352344	−	1.22889i
$335$		−	152.006i		−	0.453748i
$336$	−39.0288	+	80.0003i	−0.116157	+	0.238096i
$337$	−538.699			−1.59851			−0.799257	−	0.600989i	$-0.794773\pi$
$337$	−538.699			−1.59851			−0.799257	+	0.600989i	$0.794773\pi$
$338$	−41.5724	+	11.9196i	−0.122995	+	0.0352650i
$339$		−	68.2877i		−	0.201439i
$340$	98.8222	−	61.7440i	0.290653	−	0.181600i
$341$	105.002			0.307924
$342$	20.6260	+	71.9382i	0.0603098	+	0.210346i
$343$		−	203.100i		−	0.592127i
$344$	60.3710	+	54.3666i	0.175497	+	0.158043i
$345$	−56.2593			−0.163070
$346$	539.685	−	154.737i	1.55978	−	0.447217i
$347$			584.405i			1.68417i	0.539349	+	0.842083i	$0.318671\pi$
$347$			584.405i			1.68417i	−0.539349	+	0.842083i	$0.681329\pi$
$348$	8.70335	+	13.9299i	0.0250096	+	0.0400283i
$349$	−300.832			−0.861983			−0.430991	−	0.902356i	$-0.641836\pi$
$349$	−300.832			−0.861983			−0.430991	+	0.902356i	$0.641836\pi$
$350$	−93.1561	−	324.905i	−0.266160	−	0.928301i
$351$		−	156.522i		−	0.445931i
$352$	607.312	+	107.165i	1.72532	+	0.304447i
$353$	−316.023			−0.895250			−0.447625	−	0.894221i	$-0.647730\pi$
$353$	−316.023			−0.895250			−0.447625	+	0.894221i	$0.647730\pi$
$354$	48.3055	−	13.8500i	0.136456	−	0.0391244i
$355$		−	43.6475i		−	0.122951i
$356$	113.149	−	70.6951i	0.317833	−	0.198582i
$357$	69.6415			0.195074
$358$	19.3964	+	67.6498i	0.0541799	+	0.188966i
$359$			116.055i			0.323272i	0.986850	+	0.161636i	$0.0516770\pi$
$359$			116.055i			0.323272i	−0.986850	+	0.161636i	$0.948323\pi$
$360$	106.947	−	118.759i	0.297076	−	0.329886i
$361$	−19.0000			−0.0526316
$362$	664.312	−	190.470i	1.83512	−	0.526161i
$363$			161.433i			0.444720i
$364$	−252.520	−	404.162i	−0.693736	−	1.11033i
$365$	−169.475			−0.464316
$366$	9.08383	+	31.6821i	0.0248192	+	0.0865632i
$367$			67.8773i			0.184952i	0.995715	+	0.0924759i	$0.0294781\pi$
$367$			67.8773i			0.184952i	−0.995715	+	0.0924759i	$0.970522\pi$
$368$	539.222	+	263.064i	1.46528	+	0.714848i
$369$	625.231			1.69439
$370$	93.6195	−	26.8424i	0.253026	−	0.0725470i
$371$			370.487i			0.998617i
$372$	11.9160	−	7.44512i	0.0320324	−	0.0200138i
$373$	−267.337			−0.716721			−0.358361	−	0.933583i	$-0.616664\pi$
$373$	−267.337			−0.716721			−0.358361	+	0.933583i	$0.616664\pi$
$374$	−132.980	−	463.800i	−0.355561	−	1.24011i
$375$		−	66.8910i		−	0.178376i
$376$	−192.877	−	173.694i	−0.512971	−	0.461952i
$377$	−87.9388			−0.233259
$378$	188.076	−	53.9248i	0.497556	−	0.142658i
$379$			372.834i			0.983731i	0.870671	+	0.491866i	$0.163685\pi$
$379$			372.834i			0.983731i	−0.870671	+	0.491866i	$0.836315\pi$
$380$	21.4999	+	34.4109i	0.0565786	+	0.0905550i
$381$	−11.0508			−0.0290047
$382$	55.2512	+	192.702i	0.144637	+	0.504457i
$383$		−	19.6246i		−	0.0512392i	−0.999672	−	0.0256196i	$-0.991844\pi$
$383$		−	19.6246i		−	0.0512392i	0.999672	−	0.0256196i	$-0.00815587\pi$
$384$	76.5186	−	30.8997i	0.199267	−	0.0804679i
$385$	387.006			1.00521
$386$	−323.216	+	92.6718i	−0.837347	+	0.240082i
$387$		−	87.1771i		−	0.225264i
$388$	−511.617	+	319.658i	−1.31860	+	0.823860i
$389$	198.727			0.510867			0.255434	−	0.966827i	$-0.417782\pi$
$389$	198.727			0.510867			0.255434	+	0.966827i	$0.417782\pi$
$390$	−11.4183	−	39.8243i	−0.0292778	−	0.102114i
$391$		−	469.401i		−	1.20051i
$392$	136.320	−	151.376i	0.347756	−	0.386163i
$393$	−147.854			−0.376219
$394$	−416.623	+	119.453i	−1.05742	+	0.303181i
$395$		−	325.509i		−	0.824072i
$396$	−350.641	−	561.206i	−0.885457	−	1.41719i
$397$	295.448			0.744203			0.372101	−	0.928192i	$-0.378637\pi$
$397$	295.448			0.744203			0.372101	+	0.928192i	$0.378637\pi$
$398$	−45.3408	−	158.137i	−0.113922	−	0.397330i
$399$			24.2499i			0.0607766i
$400$	−137.392	+	281.623i	−0.343480	+	0.704057i
$401$	−63.9986			−0.159597			−0.0797987	−	0.996811i	$-0.525428\pi$
$401$	−63.9986			−0.159597			−0.0797987	+	0.996811i	$0.525428\pi$
$402$	−80.9599	+	23.2126i	−0.201393	+	0.0577429i
$403$			75.2256i			0.186664i
$404$	263.835	−	164.843i	0.653056	−	0.408028i
$405$	−162.785			−0.401939
$406$	−30.2966	−	105.667i	−0.0746222	−	0.260264i
$407$		−	403.262i		−	0.990815i
$408$	−47.9765	−	43.2049i	−0.117590	−	0.105894i
$409$	504.473			1.23343			0.616715	−	0.787186i	$-0.288463\pi$
$409$	504.473			1.23343			0.616715	+	0.787186i	$0.288463\pi$
$410$	325.861	−	93.4302i	0.794783	−	0.227878i
$411$			77.7302i			0.189125i
$412$	31.6826	+	50.7085i	0.0768995	+	0.123079i
$413$	−336.306			−0.814299
$414$	−177.438	−	618.859i	−0.428594	−	1.49483i
$415$			220.408i			0.531105i
$416$	−76.7754	+	435.091i	−0.184556	+	1.04589i
$417$	94.0393			0.225514
$418$	161.500	−	46.3049i	0.386363	−	0.110777i
$419$			470.299i			1.12243i	0.827670	+	0.561215i	$0.189666\pi$
$419$			470.299i			1.12243i	−0.827670	+	0.561215i	$0.810334\pi$
$420$	43.9190	−	27.4405i	0.104569	−	0.0653345i
$421$	−470.034			−1.11647			−0.558235	−	0.829683i	$-0.688521\pi$
$421$	−470.034			−1.11647			−0.558235	+	0.829683i	$0.688521\pi$
$422$	−9.05083	−	31.5670i	−0.0214475	−	0.0748033i
$423$			278.519i			0.658437i
$424$	229.847	−	255.231i	0.542091	−	0.601961i
$425$	245.157			0.576840
$426$	−23.2471	+	6.66537i	−0.0545707	+	0.0156464i
$427$		−	220.573i		−	0.516564i
$428$	170.664	+	273.150i	0.398747	+	0.638201i
$429$	−171.541			−0.399864
$430$	−13.0271	−	45.4354i	−0.0302957	−	0.105664i
$431$			224.005i			0.519733i	0.965645	+	0.259866i	$0.0836785\pi$
$431$			224.005i			0.519733i	−0.965645	+	0.259866i	$0.916321\pi$
$432$	−163.022	−	79.5315i	−0.377365	−	0.184101i
$433$	180.128			0.415999			0.207999	−	0.978129i	$-0.433305\pi$
$433$	180.128			0.415999			0.207999	+	0.978129i	$0.433305\pi$
$434$	−90.3909	+	25.9167i	−0.208274	+	0.0597159i
$435$		−	9.55602i		−	0.0219679i
$436$	182.680	−	114.138i	0.418990	−	0.261784i
$437$	163.450			0.374028
$438$	25.8804	+	90.2643i	0.0590877	+	0.206083i
$439$			590.004i			1.34397i	0.740563	+	0.671987i	$0.234559\pi$
$439$			590.004i			1.34397i	−0.740563	+	0.671987i	$0.765441\pi$
$440$	−266.612	−	240.095i	−0.605936	−	0.545671i
$441$	−218.590			−0.495670
$442$	332.276	−	95.2693i	0.751755	−	0.215541i
$443$			157.459i			0.355439i	0.984081	+	0.177719i	$0.0568720\pi$
$443$			157.459i			0.355439i	−0.984081	+	0.177719i	$0.943128\pi$
$444$	−28.5931	−	45.7637i	−0.0643988	−	0.103071i
$445$	−77.6212			−0.174430
$446$	107.613	+	375.328i	0.241285	+	0.841543i
$447$		−	12.4136i		−	0.0277709i
$448$	−549.255	+	57.6442i	−1.22602	+	0.128670i
$449$	−715.434			−1.59339			−0.796697	−	0.604379i	$-0.793421\pi$
$449$	−715.434			−1.59339			−0.796697	+	0.604379i	$0.793421\pi$
$450$	323.215	−	92.6716i	0.718256	−	0.205937i
$451$		−	1403.63i		−	3.11226i
$452$	359.316	−	224.500i	0.794947	−	0.496682i
$453$	106.715			0.235574
$454$	168.346	+	587.149i	0.370807	+	1.29328i
$455$			277.259i			0.609361i
$456$	15.0444	−	16.7059i	0.0329921	−	0.0366358i
$457$	31.3497			0.0685988			0.0342994	−	0.999412i	$-0.489080\pi$
$457$	31.3497			0.0685988			0.0342994	+	0.999412i	$0.489080\pi$
$458$	441.581	−	126.609i	0.964150	−	0.276439i
$459$			141.913i			0.309178i
$460$	−184.956	−	296.025i	−0.402078	−	0.643532i
$461$	368.719			0.799824			0.399912	−	0.916554i	$-0.369041\pi$
$461$	368.719			0.799824			0.399912	+	0.916554i	$0.369041\pi$
$462$	−59.0994	−	206.124i	−0.127921	−	0.446155i
$463$		−	817.405i		−	1.76545i	−0.469887	−	0.882726i	$-0.655705\pi$
$463$		−	817.405i		−	1.76545i	0.469887	−	0.882726i	$-0.344295\pi$
$464$	−44.6832	+	91.5905i	−0.0963001	+	0.197393i
$465$	−8.17453			−0.0175796
$466$	−360.796	+	103.447i	−0.774241	+	0.221989i
$467$			86.9194i			0.186123i	0.995660	+	0.0930614i	$0.0296653\pi$
$467$			86.9194i			0.186123i	−0.995660	+	0.0930614i	$0.970335\pi$
$468$	402.060	−	251.206i	0.859102	−	0.536766i
$469$	563.647			1.20181
$470$	41.6200	+	145.160i	0.0885531	+	0.308851i
$471$		−	96.3506i		−	0.204566i
$472$	231.683	+	208.641i	0.490855	+	0.442036i
$473$	−195.711			−0.413765
$474$	−173.369	+	49.7081i	−0.365758	+	0.104869i
$475$			85.3662i			0.179718i
$476$	228.951	+	366.439i	0.480989	+	0.769830i
$477$	−368.560			−0.772662
$478$	38.5033	+	134.290i	0.0805509	+	0.280941i
$479$		−	333.107i		−	0.695421i	−0.937602	−	0.347710i	$-0.886959\pi$
$479$		−	333.107i		−	0.695421i	0.937602	−	0.347710i	$-0.113041\pi$
$480$	−47.2799	−	8.34293i	−0.0984999	−	0.0173811i
$481$	288.905			0.600634
$482$	−572.072	+	164.023i	−1.18687	+	0.340297i
$483$		−	208.613i		−	0.431911i
$484$	−849.429	+	530.722i	−1.75502	+	1.09653i
$485$	350.975			0.723659
$486$	81.1005	+	282.858i	0.166873	+	0.582013i
$487$		−	264.690i		−	0.543511i	−0.962366	−	0.271755i	$-0.912396\pi$
$487$		−	264.690i		−	0.543511i	0.962366	−	0.271755i	$-0.0876042\pi$
$488$	−136.841	+	151.954i	−0.280412	+	0.311382i
$489$	94.6183			0.193494
$490$	−113.926	+	32.6646i	−0.232502	+	0.0666625i
$491$			402.874i			0.820518i	0.911969	+	0.410259i	$0.134562\pi$
$491$			402.874i			0.820518i	−0.911969	+	0.410259i	$0.865438\pi$
$492$	−99.5238	−	159.289i	−0.202284	−	0.323759i
$493$	79.7310			0.161726
$494$	33.1738	+	115.702i	0.0671534	+	0.234214i
$495$			384.993i			0.777764i
$496$	78.3495	+	38.2235i	0.157963	+	0.0770634i
$497$	161.848			0.325650
$498$	117.392	−	33.6584i	0.235727	−	0.0675871i
$499$			350.536i			0.702477i	0.936286	+	0.351238i	$0.114239\pi$
$499$			350.536i			0.702477i	−0.936286	+	0.351238i	$0.885761\pi$
$500$	351.967	−	219.908i	0.703934	−	0.439817i
$501$	137.640			0.274730
$502$	20.1014	+	70.1086i	0.0400426	+	0.139659i
$503$		−	339.615i		−	0.675179i	−0.941293	−	0.337589i	$-0.890388\pi$
$503$		−	339.615i		−	0.675179i	0.941293	−	0.337589i	$-0.109612\pi$
$504$	440.366	+	396.568i	0.873742	+	0.786842i
$505$	−180.993			−0.358403
$506$	−1389.33	+	398.345i	−2.74570	+	0.787242i
$507$		−	13.9409i		−	0.0274969i
$508$	−36.3302	−	58.1471i	−0.0715162	−	0.114463i
$509$	−933.003			−1.83301			−0.916506	−	0.400020i	$-0.869003\pi$
$509$	−933.003			−1.83301			−0.916506	+	0.400020i	$0.869003\pi$
$510$	10.3526	+	36.1073i	0.0202992	+	0.0707986i
$511$		−	628.426i		−	1.22980i
$512$	414.148	+	301.041i	0.808882	+	0.587971i
$513$	−49.4155			−0.0963266
$514$	338.257	−	96.9844i	0.658088	−	0.188686i
$515$		−	34.7866i		−	0.0675467i
$516$	−22.2100	+	13.8768i	−0.0430427	+	0.0268930i
$517$	625.270			1.20942
$518$	99.5333	+	347.147i	0.192149	+	0.670169i
$519$			180.978i			0.348705i
$520$	172.009	−	191.006i	0.330787	−	0.367319i
$521$	−415.284			−0.797091			−0.398545	−	0.917149i	$-0.630485\pi$
$521$	−415.284			−0.797091			−0.398545	+	0.917149i	$0.630485\pi$
$522$	105.117	−	30.1390i	0.201374	−	0.0577376i
$523$		−	241.598i		−	0.461947i	−0.972960	−	0.230973i	$-0.925809\pi$
$523$		−	241.598i		−	0.461947i	0.972960	−	0.230973i	$-0.0741911\pi$
$524$	−486.080	−	777.978i	−0.927633	−	1.48469i
$525$	108.954			0.207531
$526$	245.233	+	855.311i	0.466223	+	1.62607i
$527$		−	68.2044i		−	0.129420i
$528$	−87.1632	+	178.665i	−0.165082	+	0.338381i
$529$	−877.105			−1.65804
$530$	−192.088	+	55.0750i	−0.362430	+	0.103915i
$531$		−	334.556i		−	0.630050i
$532$	−127.598	+	79.7230i	−0.239846	+	0.149855i
$533$	1005.59			1.88666
$534$	11.8535	+	41.3419i	0.0221975	+	0.0774192i
$535$		−	187.384i		−	0.350250i
$536$	−388.301	−	349.681i	−0.724442	−	0.652391i
$537$	−22.6857			−0.0422452
$538$	−287.889	+	82.5428i	−0.535109	+	0.153425i
$539$			490.731i			0.910447i
$540$	55.9173	+	89.4965i	0.103551	+	0.165734i
$541$	−304.787			−0.563377			−0.281689	−	0.959506i	$-0.590894\pi$
$541$	−304.787			−0.563377			−0.281689	+	0.959506i	$0.590894\pi$
$542$	242.366	+	845.311i	0.447169	+	1.55961i
$543$			222.770i			0.410259i
$544$	69.6095	−	394.482i	0.127959	−	0.725150i
$545$	−125.320			−0.229945
$546$	147.671	−	42.3400i	0.270460	−	0.0775458i
$547$			555.915i			1.01630i	0.861269	+	0.508149i	$0.169670\pi$
$547$			555.915i			1.01630i	−0.861269	+	0.508149i	$0.830330\pi$
$548$	−409.001	+	255.543i	−0.746352	+	0.466319i
$549$	219.425			0.399682
$550$	−208.046	−	725.612i	−0.378265	−	1.31930i
$551$			27.7632i			0.0503869i
$552$	−129.422	+	143.715i	−0.234459	+	0.260354i
$553$	1207.01			2.18265
$554$	−160.042	+	45.8869i	−0.288885	+	0.0828283i
$555$			31.3944i			0.0565664i
$556$	309.160	+	494.816i	0.556043	+	0.889956i
$557$	−192.055			−0.344802			−0.172401	−	0.985027i	$-0.555152\pi$
$557$	−192.055			−0.344802			−0.172401	+	0.985027i	$0.555152\pi$
$558$	−25.7819	−	89.9208i	−0.0462041	−	0.161148i
$559$		−	140.211i		−	0.250825i
$560$	288.773	+	140.880i	0.515666	+	0.251572i
$561$	155.531			0.277238
$562$	24.9644	−	7.15775i	0.0444207	−	0.0127362i
$563$		−	107.771i		−	0.191423i	−0.995409	−	0.0957114i	$-0.969487\pi$
$563$		−	107.771i		−	0.191423i	0.995409	−	0.0957114i	$-0.0305126\pi$
$564$	70.9580	−	44.3345i	0.125812	−	0.0786072i
$565$	−246.495			−0.436274
$566$	61.1981	+	213.444i	0.108124	+	0.377109i
$567$		−	603.619i		−	1.06458i
$568$	−111.498	−	100.409i	−0.196300	−	0.176776i
$569$	−647.934			−1.13872			−0.569362	−	0.822087i	$-0.692810\pi$
$569$	−647.934			−1.13872			−0.569362	+	0.822087i	$0.692810\pi$
$570$	−12.5729	+	3.60489i	−0.0220578	+	0.00632436i
$571$		−	285.402i		−	0.499828i	−0.968268	−	0.249914i	$-0.919598\pi$
$571$		−	285.402i		−	0.499828i	0.968268	−	0.249914i	$-0.0804023\pi$
$572$	−563.953	−	902.616i	−0.985933	−	1.57800i
$573$	−64.6208			−0.112776
$574$	346.445	+	1208.31i	0.603563	+	2.10508i
$575$		−	734.376i		−	1.27717i
$576$	−57.3444	−	546.398i	−0.0995562	−	0.948608i
$577$	−92.4624			−0.160247			−0.0801234	−	0.996785i	$-0.525531\pi$
$577$	−92.4624			−0.160247			−0.0801234	+	0.996785i	$0.525531\pi$
$578$	254.351	−	72.9269i	0.440053	−	0.126171i
$579$		−	108.387i		−	0.187197i
$580$	50.2819	−	31.4160i	0.0866929	−	0.0541656i
$581$	−817.289			−1.40669
$582$	−53.5970	−	186.933i	−0.0920911	−	0.321191i
$583$			827.410i			1.41923i
$584$	−389.869	+	432.927i	−0.667584	+	0.741314i
$585$	−275.817			−0.471482
$586$	272.177	−	78.0379i	0.464465	−	0.133170i
$587$			654.717i			1.11536i	0.830056	+	0.557681i	$0.188309\pi$
$587$			654.717i			1.11536i	−0.830056	+	0.557681i	$0.811691\pi$
$588$	34.7951	+	55.6901i	0.0591753	+	0.0947110i
$589$	23.7495			0.0403217
$590$	−49.9938	−	174.366i	−0.0847352	−	0.295535i
$591$		−	139.710i		−	0.236396i
$592$	146.798	−	300.902i	0.247969	−	0.508280i
$593$	106.297			0.179253			0.0896264	−	0.995975i	$-0.471433\pi$
$593$	106.297			0.179253			0.0896264	+	0.995975i	$0.471433\pi$
$594$	420.032	−	120.431i	0.707124	−	0.202745i
$595$		−	251.381i		−	0.422489i
$596$	65.3178	−	40.8105i	0.109594	−	0.0684740i
$597$	53.0298			0.0888271
$598$	−285.382	−	995.342i	−0.477228	−	1.66445i
$599$			478.675i			0.799124i	0.916706	+	0.399562i	$0.130838\pi$
$599$			478.675i			0.799124i	−0.916706	+	0.399562i	$0.869162\pi$
$600$	−75.0591	−	67.5939i	−0.125098	−	0.112656i
$601$	808.024			1.34447			0.672233	−	0.740340i	$-0.265335\pi$
$601$	808.024			1.34447			0.672233	+	0.740340i	$0.265335\pi$
$602$	168.478	−	48.3055i	0.279863	−	0.0802418i
$603$			560.715i			0.929876i
$604$	350.833	+	561.513i	0.580849	+	0.929657i
$605$	582.717			0.963169
$606$	27.6393	+	96.3990i	0.0456094	+	0.159074i
$607$		−	694.694i		−	1.14447i	−0.820089	−	0.572236i	$-0.806076\pi$
$607$		−	694.694i		−	1.14447i	0.820089	−	0.572236i	$-0.193924\pi$
$608$	137.363	+	24.2388i	0.225925	+	0.0398664i
$609$	35.4344			0.0581845
$610$	114.361	−	32.7894i	0.187478	−	0.0537531i
$611$			447.956i			0.733153i
$612$	−364.533	+	227.760i	−0.595643	+	0.372157i
$613$	−496.830			−0.810489			−0.405245	−	0.914208i	$-0.632814\pi$
$613$	−496.830			−0.810489			−0.405245	+	0.914208i	$0.632814\pi$
$614$	197.198	+	687.776i	0.321169	+	1.12016i
$615$			109.274i			0.177682i
$616$	890.289	−	988.614i	1.44527	−	1.60489i
$617$	387.951			0.628770			0.314385	−	0.949296i	$-0.398202\pi$
$617$	387.951			0.628770			0.314385	+	0.949296i	$0.398202\pi$
$618$	−18.5277	+	5.31222i	−0.0299801	+	0.00859583i
$619$		−	882.105i		−	1.42505i	−0.701647	−	0.712525i	$-0.747552\pi$
$619$		−	882.105i		−	1.42505i	0.701647	−	0.712525i	$-0.252448\pi$
$620$	−26.8743	−	43.0127i	−0.0433456	−	0.0693753i
$621$	425.104			0.684548
$622$	−260.389	−	908.173i	−0.418633	−	1.46009i
$623$		−	287.824i		−	0.461998i
$624$	−127.999	−	62.4455i	−0.205127	−	0.100073i
$625$	248.156			0.397050
$626$	−122.580	+	35.1459i	−0.195815	+	0.0561437i
$627$			54.1574i			0.0863754i
$628$	506.977	−	316.759i	0.807289	−	0.504393i
$629$	−261.940			−0.416439
$630$	−95.0243	−	331.421i	−0.150832	−	0.526065i
$631$			502.601i			0.796515i	0.917274	+	0.398258i	$0.130385\pi$
$631$			502.601i			0.796515i	−0.917274	+	0.398258i	$0.869615\pi$
$632$	−831.517	−	748.816i	−1.31569	−	1.18484i
$633$	10.5857			0.0167230
$634$	−382.048	+	109.540i	−0.602600	+	0.172776i
$635$			39.8895i			0.0628181i
$636$	58.6671	+	93.8977i	0.0922439	+	0.147638i
$637$	−351.570			−0.551915
$638$	−67.6616	−	235.987i	−0.106053	−	0.369885i
$639$			161.006i			0.251966i
$640$	−111.537	−	276.205i	−0.174277	−	0.431571i
$641$	385.625			0.601600			0.300800	−	0.953687i	$-0.402746\pi$
$641$	385.625			0.601600			0.300800	+	0.953687i	$0.402746\pi$
$642$	−99.8026	+	28.6152i	−0.155456	+	0.0445719i
$643$		−	925.293i		−	1.43902i	−0.694480	−	0.719512i	$-0.744365\pi$
$643$		−	925.293i		−	1.43902i	0.694480	−	0.719512i	$-0.255635\pi$
$644$	1097.68	−	685.829i	1.70447	−	1.06495i
$645$	15.2363			0.0236222
$646$	−30.0775	−	104.903i	−0.0465596	−	0.162388i
$647$			656.956i			1.01539i	0.861538	+	0.507694i	$0.169502\pi$
$647$			656.956i			1.01539i	−0.861538	+	0.507694i	$0.830498\pi$
$648$	−374.479	+	415.838i	−0.577900	+	0.641725i
$649$	−751.073			−1.15728
$650$	519.843	−	149.048i	0.799759	−	0.229305i
$651$		−	30.3117i		−	0.0465617i
$652$	311.064	+	497.863i	0.477092	+	0.763593i
$653$	392.897			0.601680			0.300840	−	0.953675i	$-0.402733\pi$
$653$	392.897			0.601680			0.300840	+	0.953675i	$0.402733\pi$
$654$	19.1375	+	66.7468i	0.0292622	+	0.102059i
$655$			533.701i			0.814811i
$656$	510.958	−	1047.35i	0.778899	−	1.59657i
$657$	625.157			0.951533
$658$	−538.263	+	154.330i	−0.818029	+	0.234543i
$659$		−	695.576i		−	1.05550i	−0.849399	−	0.527751i	$-0.823035\pi$
$659$		−	695.576i		−	1.05550i	0.849399	−	0.527751i	$-0.176965\pi$
$660$	98.0844	−	61.2830i	0.148613	−	0.0928530i
$661$	1179.05			1.78373			0.891866	−	0.452299i	$-0.149396\pi$
$661$	1179.05			1.78373			0.891866	+	0.452299i	$0.149396\pi$
$662$	−241.843	−	843.487i	−0.365322	−	1.27415i
$663$			111.425i			0.168062i
$664$	563.037	+	507.038i	0.847947	+	0.763612i
$665$	87.5335			0.131629
$666$	−345.342	+	99.0156i	−0.518531	+	0.148672i
$667$		−	238.837i		−	0.358076i
$668$	452.500	+	724.233i	0.677395	+	1.08418i
$669$	−125.863			−0.188135
$670$	83.7894	+	292.237i	0.125059	+	0.436174i
$671$		−	492.606i		−	0.734137i
$672$	30.9362	−	175.317i	0.0460359	−	0.260889i
$673$	−881.170			−1.30932			−0.654658	−	0.755925i	$-0.727187\pi$
$673$	−881.170			−1.30932			−0.654658	+	0.755925i	$0.727187\pi$
$674$	1035.67	−	296.945i	1.53660	−	0.440571i
$675$			222.022i			0.328921i
$676$	73.3542	−	45.8316i	0.108512	−	0.0677982i
$677$	−126.536			−0.186907			−0.0934533	−	0.995624i	$-0.529791\pi$
$677$	−126.536			−0.186907			−0.0934533	+	0.995624i	$0.529791\pi$
$678$	37.6420	+	131.286i	0.0555191	+	0.193637i
$679$			1301.44i			1.91670i
$680$	−155.954	+	173.178i	−0.229345	+	0.254674i
$681$	−196.895			−0.289126
$682$	−201.870	+	57.8798i	−0.295998	+	0.0848678i
$683$			873.042i			1.27825i	0.769105	+	0.639123i	$0.220702\pi$
$683$			873.042i			1.27825i	−0.769105	+	0.639123i	$0.779298\pi$
$684$	−79.3083	−	126.934i	−0.115948	−	0.185576i
$685$	280.579			0.409604
$686$	111.954	+	390.467i	0.163198	+	0.569193i
$687$			148.080i			0.215545i
$688$	−146.034	−	71.2439i	−0.212258	−	0.103552i
$689$	−592.774			−0.860339
$690$	108.161	−	31.0116i	0.156754	−	0.0449443i
$691$			610.841i			0.883996i	0.897016	+	0.441998i	$0.145730\pi$
$691$			610.841i			0.883996i	−0.897016	+	0.441998i	$0.854270\pi$
$692$	−952.269	+	594.976i	−1.37611	+	0.859792i
$693$	−1427.58			−2.06000
$694$	−322.139	−	1123.54i	−0.464178	−	1.61894i
$695$		−	339.449i		−	0.488415i
$696$	−24.4110	−	21.9831i	−0.0350733	−	0.0315850i
$697$	−911.733			−1.30808
$698$	578.361	−	165.826i	0.828597	−	0.237574i
$699$		−	120.989i		−	0.173089i
$700$	358.192	+	573.292i	0.511703	+	0.818989i
$701$	−506.393			−0.722387			−0.361193	−	0.932491i	$-0.617631\pi$
$701$	−506.393			−0.722387			−0.361193	+	0.932491i	$0.617631\pi$
$702$	86.2789	+	300.919i	0.122904	+	0.428660i
$703$		−	91.2102i		−	0.129744i
$704$	−1226.65	+	128.737i	−1.74241	+	0.182865i
$705$	−48.6780			−0.0690467
$706$	607.566	−	174.200i	0.860576	−	0.246742i
$707$		−	671.135i		−	0.949272i
$708$	−85.2346	+	53.2545i	−0.120388	+	0.0752182i
$709$	−1036.42			−1.46180			−0.730902	−	0.682483i	$-0.760900\pi$
$709$	−1036.42			−1.46180			−0.730902	+	0.682483i	$0.760900\pi$
$710$	24.0596	+	83.9140i	0.0338868	+	0.118189i
$711$			1200.73i			1.68879i
$712$	−178.564	+	198.284i	−0.250792	+	0.278489i
$713$	−204.308			−0.286548
$714$	−133.888	+	38.3882i	−0.187519	+	0.0537649i
$715$			619.204i			0.866020i
$716$	−74.5806	−	119.367i	−0.104163	−	0.166714i
$717$	−45.0328			−0.0628072
$718$	−63.9722	−	223.119i	−0.0890978	−	0.310751i
$719$			834.943i			1.16126i	0.814169	+	0.580628i	$0.197193\pi$
$719$			834.943i			1.16126i	−0.814169	+	0.580628i	$0.802807\pi$
$720$	−140.148	+	287.271i	−0.194649	+	0.398987i
$721$	128.991			0.178905
$722$	36.5282	−	10.4733i	0.0505931	−	0.0145059i
$723$		−	191.839i		−	0.265337i
$724$	−1172.17	+	732.372i	−1.61902	+	1.01156i
$725$	124.739			0.172053
$726$	−88.9862	−	310.362i	−0.122571	−	0.427495i
$727$			225.252i			0.309838i	0.987927	+	0.154919i	$0.0495116\pi$
$727$			225.252i			0.309838i	−0.987927	+	0.154919i	$0.950488\pi$
$728$	708.263	+	637.821i	0.972889	+	0.876128i
$729$	534.700			0.733470
$730$	325.822	−	93.4191i	0.446332	−	0.127971i
$731$			127.125i			0.173905i
$732$	−34.9280	−	55.9028i	−0.0477158	−	0.0763700i
$733$	697.401			0.951434			0.475717	−	0.879598i	$-0.342189\pi$
$733$	697.401			0.951434			0.475717	+	0.879598i	$0.342189\pi$
$734$	−37.4157	−	130.497i	−0.0509751	−	0.177788i
$735$		−	38.2040i		−	0.0519782i
$736$	−1181.68	−	208.517i	−1.60555	−	0.283312i
$737$	1258.80			1.70800
$738$	−1202.03	+	344.643i	−1.62877	+	0.466996i
$739$			1065.87i			1.44231i	0.692772	+	0.721157i	$0.256389\pi$
$739$			1065.87i			1.44231i	−0.692772	+	0.721157i	$0.743611\pi$
$740$	−165.191	+	103.211i	−0.223231	+	0.139474i
$741$	−38.7994			−0.0523609
$742$	−204.222	−	712.275i	−0.275232	−	0.959939i
$743$			1050.43i			1.41376i	0.707332	+	0.706881i	$0.249898\pi$
$743$			1050.43i			1.41376i	−0.707332	+	0.706881i	$0.750102\pi$
$744$	−18.8051	+	20.8820i	−0.0252756	+	0.0280671i
$745$	−44.8087			−0.0601459
$746$	513.966	−	147.363i	0.688962	−	0.197538i
$747$		−	813.038i		−	1.08840i
$748$	511.317	+	818.370i	0.683578	+	1.09408i
$749$	694.831			0.927678
$750$	36.8720	+	128.600i	0.0491627	+	0.171467i
$751$			26.6606i			0.0355002i	0.999842	+	0.0177501i	$0.00565033\pi$
$751$			26.6606i			0.0355002i	−0.999842	+	0.0177501i	$0.994350\pi$
$752$	466.558	+	227.614i	0.620423	+	0.302679i
$753$	−23.5102			−0.0312221
$754$	169.066	−	48.4741i	0.224225	−	0.0642893i
$755$		−	385.204i		−	0.510204i
$756$	−331.859	+	207.345i	−0.438967	+	0.274266i
$757$	445.989			0.589153			0.294577	−	0.955628i	$-0.404821\pi$
$757$	445.989			0.589153			0.294577	+	0.955628i	$0.404821\pi$
$758$	−205.516	−	716.788i	−0.271129	−	0.945630i
$759$		−	465.897i		−	0.613830i
$760$	−60.3025	−	54.3050i	−0.0793454	−	0.0714539i
$761$	294.799			0.387384			0.193692	−	0.981062i	$-0.437954\pi$
$761$	294.799			0.387384			0.193692	+	0.981062i	$0.437954\pi$
$762$	21.2456	−	6.09149i	0.0278813	−	0.00799408i
$763$		−	464.695i		−	0.609037i
$764$	−212.445	−	340.022i	−0.278070	−	0.445055i
$765$	250.074			0.326894
$766$	10.8176	+	37.7291i	0.0141222	+	0.0492547i
$767$		−	538.084i		−	0.701543i
$768$	−130.077	+	101.585i	−0.169371	+	0.132272i
$769$	−279.363			−0.363281			−0.181641	−	0.983365i	$-0.558141\pi$
$769$	−279.363			−0.363281			−0.181641	+	0.983365i	$0.558141\pi$
$770$	−744.034	+	213.328i	−0.966278	+	0.277049i
$771$			113.431i			0.147122i
$772$	570.312	−	356.330i	0.738746	−	0.461567i
$773$	−1092.48			−1.41329			−0.706647	−	0.707566i	$-0.749793\pi$
$773$	−1092.48			−1.41329			−0.706647	+	0.707566i	$0.749793\pi$
$774$	48.0543	+	167.601i	0.0620856	+	0.216539i
$775$		−	106.705i		−	0.137684i
$776$	807.400	−	896.571i	1.04046	−	1.15537i
$777$	−116.412			−0.149823
$778$	−382.061	+	109.544i	−0.491081	+	0.140802i
$779$		−	317.475i		−	0.407542i

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:	\( N \)	\(=\)	\( 76 = 2^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	76.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.92254 + 0.551226i) q^{2} -0.644704i q^{3} +(3.39230 - 2.11950i) q^{4} -2.32715 q^{5} +(0.355377 + 1.23947i) q^{6} -8.62924i q^{7} +(-5.35350 + 5.94475i) q^{8} +8.58436 q^{9} +O(q^{10})\)	\(q+(-1.92254 + 0.551226i) q^{2} -0.644704i q^{3} +(3.39230 - 2.11950i) q^{4} -2.32715 q^{5} +(0.355377 + 1.23947i) q^{6} -8.62924i q^{7} +(-5.35350 + 5.94475i) q^{8} +8.58436 q^{9} +(4.47404 - 1.28279i) q^{10} -19.2717i q^{11} +(-1.36645 - 2.18703i) q^{12} +13.8067 q^{13} +(4.75666 + 16.5900i) q^{14} +1.50032i q^{15} +(7.01540 - 14.3800i) q^{16} -12.5180 q^{17} +(-16.5037 + 4.73192i) q^{18} -4.35890i q^{19} +(-7.89440 + 4.93241i) q^{20} -5.56330 q^{21} +(10.6231 + 37.0506i) q^{22} +37.4981i q^{23} +(3.83260 + 3.45142i) q^{24} -19.5844 q^{25} +(-26.5438 + 7.61058i) q^{26} -11.3367i q^{27} +(-18.2897 - 29.2730i) q^{28} -6.36930 q^{29} +(-0.827018 - 2.88443i) q^{30} +5.44851i q^{31} +(-5.56075 + 31.5131i) q^{32} -12.4245 q^{33} +(24.0663 - 6.90025i) q^{34} +20.0816i q^{35} +(29.1207 - 18.1946i) q^{36} +20.9250 q^{37} +(2.40274 + 8.38015i) q^{38} -8.90120i q^{39} +(12.4584 - 13.8343i) q^{40} +72.8337 q^{41} +(10.6957 - 3.06664i) q^{42} -10.1553i q^{43} +(-40.8465 - 65.3755i) q^{44} -19.9771 q^{45} +(-20.6699 - 72.0914i) q^{46} +32.4450i q^{47} +(-9.27083 - 4.52286i) q^{48} -25.4638 q^{49} +(37.6517 - 10.7954i) q^{50} +8.07040i q^{51} +(46.8363 - 29.2633i) q^{52} -42.9339 q^{53} +(6.24908 + 21.7952i) q^{54} +44.8482i q^{55} +(51.2987 + 46.1966i) q^{56} -2.81020 q^{57} +(12.2452 - 3.51092i) q^{58} -38.9728i q^{59} +(3.17994 + 5.08955i) q^{60} +25.5611 q^{61} +(-3.00336 - 10.4750i) q^{62} -74.0765i q^{63} +(-6.68010 - 63.6504i) q^{64} -32.1302 q^{65} +(23.8867 - 6.84873i) q^{66} +65.3183i q^{67} +(-42.4648 + 26.5320i) q^{68} +24.1751 q^{69} +(-11.0695 - 38.6076i) q^{70} +18.7557i q^{71} +(-45.9563 + 51.0319i) q^{72} +72.8251 q^{73} +(-40.2292 + 11.5344i) q^{74} +12.6261i q^{75} +(-9.23871 - 14.7867i) q^{76} -166.300 q^{77} +(4.90657 + 17.1129i) q^{78} +139.874i q^{79} +(-16.3259 + 33.4644i) q^{80} +69.9504 q^{81} +(-140.026 + 40.1478i) q^{82} -94.7116i q^{83} +(-18.8724 + 11.7914i) q^{84} +29.1313 q^{85} +(5.59789 + 19.5240i) q^{86} +4.10631i q^{87} +(114.566 + 103.171i) q^{88} +33.3546 q^{89} +(38.4068 - 11.0119i) q^{90} -119.141i q^{91} +(79.4773 + 127.205i) q^{92} +3.51267 q^{93} +(-17.8845 - 62.3766i) q^{94} +10.1438i q^{95} +(20.3166 + 3.58504i) q^{96} -150.817 q^{97} +(48.9551 - 14.0363i) q^{98} -165.435i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14q + 2q^{2} + 2q^{4} - 40q^{8} - 68q^{9} + O(q^{10}) \)	\( 14q + 2q^{2} + 2q^{4} - 40q^{8} - 68q^{9} - 12q^{10} + 4q^{12} + 54q^{13} + 30q^{14} + 58q^{16} + 34q^{17} + 36q^{18} + 32q^{20} - 38q^{21} + 36q^{22} - 98q^{24} - 86q^{25} - 16q^{26} + 18q^{28} + 54q^{29} - 204q^{30} + 72q^{32} + 20q^{33} - 82q^{34} + 96q^{36} + 100q^{37} - 148q^{40} + 224q^{41} + 224q^{42} - 96q^{44} - 168q^{45} + 46q^{46} + 296q^{48} - 220q^{49} - 58q^{50} - 288q^{52} + 14q^{53} - 128q^{54} + 12q^{56} + 38q^{57} - 72q^{58} + 188q^{60} + 28q^{61} + 396q^{62} - 118q^{64} - 472q^{65} - 32q^{66} + 30q^{68} + 122q^{69} + 156q^{70} + 80q^{72} + 70q^{73} - 224q^{74} + 228q^{77} + 274q^{78} - 348q^{80} + 334q^{81} - 400q^{82} - 216q^{84} + 48q^{85} - 124q^{86} + 472q^{88} + 416q^{90} + 126q^{92} - 176q^{93} - 88q^{94} - 106q^{96} + 308q^{97} + 68q^{98} + O(q^{100}) \)

Introduction

L-functions

Modular forms

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