LMFDB - Embedded newform 300.2.h.c.299.4

Newspace parameters

Level:	$ N $	$=$	$ 300 = 2^{2} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	300.h (of order $2$, degree $1$, not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$2.39551206064$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
Defining polynomial:	$x^{16} - 2 x^{15} + 2 x^{14} + 10 x^{13} - 42 x^{11} + 134 x^{10} + 110 x^{9} + 92 x^{8} + 142 x^{7} + 1514 x^{6} + 1102 x^{5} + 249 x^{4} - 1056 x^{3} + 392 x^{2} - 280 x + 100$
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{6}\cdot 5^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			299.4
Root			$1.10359 - 2.13477i$ of defining polynomial
Character	$\chi$	$=$	300.299
Dual form			300.2.h.c.299.2

$q$-expansion

$f(q)$	$=$	$q+(-1.38758 + 0.273147i) q^{2} +(0.758030 + 1.55737i) q^{3} +(1.85078 - 0.758030i) q^{4} +(-1.47722 - 1.95392i) q^{6} -3.56393 q^{7} +(-2.36106 + 1.55737i) q^{8} +(-1.85078 + 2.36106i) q^{9} +O(q^{10})$	\(q+(-1.38758 + 0.273147i) q^{2} +(0.758030 + 1.55737i) q^{3} +(1.85078 - 0.758030i) q^{4} +(-1.47722 - 1.95392i) q^{6} -3.56393 q^{7} +(-2.36106 + 1.55737i) q^{8} +(-1.85078 + 2.36106i) q^{9} -4.20732 q^{11} +(2.58348 + 2.30774i) q^{12} +2.70156i q^{13} +(4.94525 - 0.973477i) q^{14} +(2.85078 - 2.80590i) q^{16} +0.828216 q^{17} +(1.92320 - 3.78171i) q^{18} +5.07999i q^{19} +(-2.70156 - 5.55034i) q^{21} +(5.83802 - 1.14922i) q^{22} +1.09259i q^{23} +(-4.21515 - 2.49651i) q^{24} +(-0.737925 - 3.74865i) q^{26} +(-5.07999 - 1.09259i) q^{27} +(-6.59605 + 2.70156i) q^{28} -5.55034i q^{29} +6.59605i q^{31} +(-3.18928 + 4.67210i) q^{32} +(-3.18928 - 6.55234i) q^{33} +(-1.14922 + 0.226225i) q^{34} +(-1.63564 + 5.77275i) q^{36} -5.40312i q^{37} +(-1.38758 - 7.04891i) q^{38} +(-4.20732 + 2.04787i) q^{39} +10.2725i q^{41} +(5.26471 + 6.96364i) q^{42} +0.531805 q^{43} +(-7.78683 + 3.18928i) q^{44} +(-0.298438 - 1.51606i) q^{46} -6.22947i q^{47} +(6.53078 + 2.31276i) q^{48} +5.70156 q^{49} +(0.627812 + 1.28984i) q^{51} +(2.04787 + 5.00000i) q^{52} +5.55034 q^{53} +(7.34735 + 0.128476i) q^{54} +(8.41464 - 5.55034i) q^{56} +(-7.91140 + 3.85078i) q^{57} +(1.51606 + 7.70156i) q^{58} +0.701562 q^{61} +(-1.80169 - 9.15257i) q^{62} +(6.59605 - 8.41464i) q^{63} +(3.14922 - 7.35408i) q^{64} +(6.21515 + 8.22079i) q^{66} +2.04787 q^{67} +(1.53285 - 0.627812i) q^{68} +(-1.70156 + 0.828216i) q^{69} +11.3663 q^{71} +(0.692770 - 8.45695i) q^{72} +7.70156i q^{73} +(1.47585 + 7.49729i) q^{74} +(3.85078 + 9.40194i) q^{76} +14.9946 q^{77} +(5.27865 - 3.99080i) q^{78} -7.12785i q^{79} +(-2.14922 - 8.73961i) q^{81} +(-2.80590 - 14.2539i) q^{82} +3.11473i q^{83} +(-9.20732 - 8.22459i) q^{84} +(-0.737925 + 0.145261i) q^{86} +(8.64391 - 4.20732i) q^{87} +(9.93375 - 6.55234i) q^{88} +4.72212i q^{89} -9.62817i q^{91} +(0.828216 + 2.02214i) q^{92} +(-10.2725 + 5.00000i) q^{93} +(1.70156 + 8.64391i) q^{94} +(-9.69374 - 1.42528i) q^{96} +8.10469i q^{97} +(-7.91140 + 1.55737i) q^{98} +(7.78683 - 9.93375i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16q + 4q^{4} + 6q^{6} - 4q^{9} + O(q^{10}) $	$ 16q + 4q^{4} + 6q^{6} - 4q^{9} + 20q^{16} + 8q^{21} - 26q^{24} - 44q^{34} - 42q^{36} - 56q^{46} + 40q^{49} + 56q^{54} - 40q^{61} + 76q^{64} + 58q^{66} + 24q^{69} + 36q^{76} - 60q^{81} - 80q^{84} - 24q^{94} - 78q^{96} + O(q^{100}) $

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/300\mathbb{Z}\right)^\times$.

$n$	$101$	$151$	$277$
$\chi(n)$	$-1$	$-1$	$-1$

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 $

$2$	−1.38758	+	0.273147i	−0.981170	+	0.193144i
$2$	−1.38758	+	0.273147i	−0.981170	+	0.193144i
$3$	0.758030	+	1.55737i	0.437649	+	0.899146i
$3$	0.758030	+	1.55737i	0.437649	+	0.899146i
$4$	1.85078	−	0.758030i	0.925391	−	0.379015i
$5$		0			0
$5$		0			0
$6$	−1.47722	−	1.95392i	−0.603073	−	0.797686i
$7$	−3.56393			−1.34704			−0.673519	−	0.739170i	$-0.735218\pi$
$7$	−3.56393			−1.34704			−0.673519	+	0.739170i	$0.735218\pi$
$8$	−2.36106	+	1.55737i	−0.834761	+	0.550612i
$9$	−1.85078	+	2.36106i	−0.616927	+	0.787020i
$10$		0			0
$11$	−4.20732			−1.26856			−0.634278	−	0.773105i	$-0.718702\pi$
$11$	−4.20732			−1.26856			−0.634278	+	0.773105i	$0.718702\pi$
$12$	2.58348	+	2.30774i	0.745786	+	0.666186i
$13$			2.70156i			0.749279i	0.927171	+	0.374639i	$0.122233\pi$
$13$			2.70156i			0.749279i	−0.927171	+	0.374639i	$0.877767\pi$
$14$	4.94525	−	0.973477i	1.32167	−	0.260173i
$15$		0			0
$16$	2.85078	−	2.80590i	0.712695	−	0.701474i
$17$	0.828216			0.200872			0.100436	−	0.994944i	$-0.467976\pi$
$17$	0.828216			0.200872			0.100436	+	0.994944i	$0.467976\pi$
$18$	1.92320	−	3.78171i	0.453302	−	0.891357i
$19$			5.07999i			1.16543i	0.812677	+	0.582714i	$0.198009\pi$
$19$			5.07999i			1.16543i	−0.812677	+	0.582714i	$0.801991\pi$
$20$		0			0
$21$	−2.70156	−	5.55034i	−0.589529	−	1.21118i
$22$	5.83802	−	1.14922i	1.24467	−	0.245014i
$23$			1.09259i			0.227821i	0.993491	+	0.113910i	$0.0363377\pi$
$23$			1.09259i			0.227821i	−0.993491	+	0.113910i	$0.963662\pi$
$24$	−4.21515	−	2.49651i	−0.860413	−	0.509597i
$25$		0			0
$26$	−0.737925	−	3.74865i	−0.144719	−	0.735170i
$27$	−5.07999	−	1.09259i	−0.977644	−	0.210269i
$28$	−6.59605	+	2.70156i	−1.24654	+	0.510547i
$29$		−	5.55034i		−	1.03067i	−0.856988	−	0.515336i	$-0.827667\pi$
$29$		−	5.55034i		−	1.03067i	0.856988	−	0.515336i	$-0.172333\pi$
$30$		0			0
$31$			6.59605i			1.18468i	0.805686	+	0.592342i	$0.201797\pi$
$31$			6.59605i			1.18468i	−0.805686	+	0.592342i	$0.798203\pi$
$32$	−3.18928	+	4.67210i	−0.563790	+	0.825918i
$33$	−3.18928	−	6.55234i	−0.555182	−	1.14062i
$34$	−1.14922	+	0.226225i	−0.197089	+	0.0387972i
$35$		0			0
$36$	−1.63564	+	5.77275i	−0.272606	+	0.962126i
$37$		−	5.40312i		−	0.888268i	−0.895960	−	0.444134i	$-0.853511\pi$
$37$		−	5.40312i		−	0.888268i	0.895960	−	0.444134i	$-0.146489\pi$
$38$	−1.38758	−	7.04891i	−0.225096	−	1.14348i
$39$	−4.20732	+	2.04787i	−0.673711	+	0.327921i
$40$		0			0
$41$			10.2725i			1.60429i	0.597130	+	0.802144i	$0.296308\pi$
$41$			10.2725i			1.60429i	−0.597130	+	0.802144i	$0.703692\pi$
$42$	5.26471	+	6.96364i	0.812362	+	1.07451i
$43$	0.531805			0.0810995			0.0405498	−	0.999178i	$-0.487089\pi$
$43$	0.531805			0.0810995			0.0405498	+	0.999178i	$0.487089\pi$
$44$	−7.78683	+	3.18928i	−1.17391	+	0.480802i
$45$		0			0
$46$	−0.298438	−	1.51606i	−0.0440023	−	0.223531i
$47$		−	6.22947i		−	0.908661i	−0.890833	−	0.454331i	$-0.849879\pi$
$47$		−	6.22947i		−	0.908661i	0.890833	−	0.454331i	$-0.150121\pi$
$48$	6.53078	+	2.31276i	0.942638	+	0.333818i
$49$	5.70156			0.814509
$50$		0			0
$51$	0.627812	+	1.28984i	0.0879113	+	0.180613i
$52$	2.04787	+	5.00000i	0.283988	+	0.693375i
$53$	5.55034			0.762398			0.381199	−	0.924493i	$-0.375511\pi$
$53$	5.55034			0.762398			0.381199	+	0.924493i	$0.375511\pi$
$54$	7.34735	+	0.128476i	0.999847	+	0.0174833i
$55$		0			0
$56$	8.41464	−	5.55034i	1.12445	−	0.741695i
$57$	−7.91140	+	3.85078i	−1.04789	+	0.510048i
$58$	1.51606	+	7.70156i	0.199068	+	1.01126i
$59$		0			0			−	1.00000i	$-0.5\pi$
$59$		0			0				1.00000i	$0.5\pi$
$60$		0			0
$61$	0.701562			0.0898258			0.0449129	−	0.998991i	$-0.485699\pi$
$61$	0.701562			0.0898258			0.0449129	+	0.998991i	$0.485699\pi$
$62$	−1.80169	−	9.15257i	−0.228815	−	1.16238i
$63$	6.59605	−	8.41464i	0.831024	−	1.06015i
$64$	3.14922	−	7.35408i	0.393652	−	0.919259i
$65$		0			0
$66$	6.21515	+	8.22079i	0.765032	+	1.01191i
$67$	2.04787			0.250187			0.125093	−	0.992145i	$-0.460077\pi$
$67$	2.04787			0.250187			0.125093	+	0.992145i	$0.460077\pi$
$68$	1.53285	−	0.627812i	0.185885	−	0.0761334i
$69$	−1.70156	+	0.828216i	−0.204844	+	0.0997054i
$70$		0			0
$71$	11.3663			1.34894			0.674468	−	0.738304i	$-0.264373\pi$
$71$	11.3663			1.34894			0.674468	+	0.738304i	$0.264373\pi$
$72$	0.692770	−	8.45695i	0.0816437	−	0.996662i
$73$			7.70156i			0.901400i	0.892676	+	0.450700i	$0.148826\pi$
$73$			7.70156i			0.901400i	−0.892676	+	0.450700i	$0.851174\pi$
$74$	1.47585	+	7.49729i	0.171564	+	0.871542i
$75$		0			0
$76$	3.85078	+	9.40194i	0.441715	+	1.07848i
$77$	14.9946			1.70879
$78$	5.27865	−	3.99080i	0.597689	−	0.451870i
$79$		−	7.12785i		−	0.801946i	−0.916090	−	0.400973i	$-0.868672\pi$
$79$		−	7.12785i		−	0.801946i	0.916090	−	0.400973i	$-0.131328\pi$
$80$		0			0
$81$	−2.14922	−	8.73961i	−0.238802	−	0.971068i
$82$	−2.80590	−	14.2539i	−0.309859	−	1.57408i
$83$			3.11473i			0.341886i	0.985281	+	0.170943i	$0.0546815\pi$
$83$			3.11473i			0.341886i	−0.985281	+	0.170943i	$0.945319\pi$
$84$	−9.20732	−	8.22459i	−1.00460	−	0.897377i
$85$		0			0
$86$	−0.737925	+	0.145261i	−0.0795724	+	0.0156639i
$87$	8.64391	−	4.20732i	0.926724	−	0.451072i
$88$	9.93375	−	6.55234i	1.05894	−	0.698482i
$89$			4.72212i			0.500544i	0.968176	+	0.250272i	$0.0805200\pi$
$89$			4.72212i			0.500544i	−0.968176	+	0.250272i	$0.919480\pi$
$90$		0			0
$91$		−	9.62817i		−	1.00931i
$92$	0.828216	+	2.02214i	0.0863474	+	0.210823i
$93$	−10.2725	+	5.00000i	−1.06520	+	0.518476i
$94$	1.70156	+	8.64391i	0.175503	+	0.891551i
$95$		0			0
$96$	−9.69374	−	1.42528i	−0.989363	−	0.145467i
$97$			8.10469i			0.822906i	0.911431	+	0.411453i	$0.134979\pi$
$97$			8.10469i			0.822906i	−0.911431	+	0.411453i	$0.865021\pi$
$98$	−7.91140	+	1.55737i	−0.799172	+	0.157318i
$99$	7.78683	−	9.93375i	0.782606	−	0.998379i
$100$		0			0
$101$			7.20677i			0.717100i	0.933510	+	0.358550i	$0.116729\pi$
$101$			7.20677i			0.717100i	−0.933510	+	0.358550i	$0.883271\pi$
$102$	−1.22346	−	1.61827i	−0.121140	−	0.160233i
$103$	−4.09573			−0.403564			−0.201782	−	0.979430i	$-0.564673\pi$
$103$	−4.09573			−0.403564			−0.201782	+	0.979430i	$0.564673\pi$
$104$	−4.20732	−	6.37855i	−0.412562	−	0.625469i
$105$		0			0
$106$	−7.70156	+	1.51606i	−0.748042	+	0.147253i
$107$			18.8514i			1.82244i	0.411924	+	0.911218i	$0.364857\pi$
$107$			18.8514i			1.82244i	−0.411924	+	0.911218i	$0.635143\pi$
$108$	−10.2302	+	1.82864i	−0.984397	+	0.175961i
$109$	−8.70156			−0.833458			−0.416729	−	0.909031i	$-0.636824\pi$
$109$	−8.70156			−0.833458			−0.416729	+	0.909031i	$0.636824\pi$
$110$		0			0
$111$	8.41464	−	4.09573i	0.798683	−	0.388750i
$112$	−10.1600	+	10.0000i	−0.960027	+	0.944911i
$113$	15.8228			1.48848			0.744242	−	0.667910i	$-0.232811\pi$
$113$	15.8228			1.48848			0.744242	+	0.667910i	$0.232811\pi$
$114$	9.92590	−	7.50426i	0.929646	−	0.702838i
$115$		0			0
$116$	−4.20732	−	10.2725i	−0.390640	−	0.953774i
$117$	−6.37855	−	5.00000i	−0.589697	−	0.462250i
$118$		0			0
$119$	−2.95170			−0.270582
$120$		0			0
$121$	6.70156			0.609233
$122$	−0.973477	+	0.191630i	−0.0881344	+	0.0173493i
$123$	−15.9980	+	7.78683i	−1.44249	+	0.702115i
$124$	5.00000	+	12.2078i	0.449013	+	1.09630i
$125$		0			0
$126$	−6.85413	+	13.4777i	−0.610615	+	1.20069i
$127$	16.2242			1.43967			0.719833	−	0.694147i	$-0.244218\pi$
$127$	16.2242			1.43967			0.719833	+	0.694147i	$0.244218\pi$
$128$	−2.36106	+	11.0646i	−0.208690	+	0.977982i
$129$	0.403124	+	0.828216i	0.0354931	+	0.0729203i
$130$		0			0
$131$	−19.7810			−1.72827			−0.864136	−	0.503258i	$-0.832135\pi$
$131$	−19.7810			−1.72827			−0.864136	+	0.503258i	$0.832135\pi$
$132$	−10.8695	−	9.70939i	−0.946071	−	0.845094i
$133$		−	18.1047i		−	1.56988i
$134$	−2.84159	+	0.559369i	−0.245476	+	0.0483221i
$135$		0			0
$136$	−1.95547	+	1.28984i	−0.167680	+	0.110602i
$137$	−6.37855			−0.544957			−0.272478	−	0.962162i	$-0.587843\pi$
$137$	−6.37855			−0.544957			−0.272478	+	0.962162i	$0.587843\pi$
$138$	2.13484	−	1.61400i	0.181729	−	0.137392i
$139$		−	1.51606i		−	0.128591i	−0.997931	−	0.0642953i	$-0.979520\pi$
$139$		−	1.51606i		−	0.128591i	0.997931	−	0.0642953i	$-0.0204799\pi$
$140$		0			0
$141$	9.70156	−	4.72212i	0.817019	−	0.397674i
$142$	−15.7718	+	3.10469i	−1.32354	+	0.260539i
$143$		−	11.3663i		−	0.950501i
$144$	1.34872	+	11.9240i	0.112393	+	0.993664i
$145$		0			0
$146$	−2.10366	−	10.6866i	−0.174100	−	0.884427i
$147$	4.32196	+	8.87942i	0.356469	+	0.732362i
$148$	−4.09573	−	10.0000i	−0.336667	−	0.821995i
$149$			1.65643i			0.135700i	0.997696	+	0.0678501i	$0.0216139\pi$
$149$			1.65643i			0.135700i	−0.997696	+	0.0678501i	$0.978386\pi$
$150$		0			0
$151$		−	4.62754i		−	0.376583i	−0.982113	−	0.188292i	$-0.939705\pi$
$151$		−	4.62754i		−	0.376583i	0.982113	−	0.188292i	$-0.0602951\pi$
$152$	−7.91140	−	11.9942i	−0.641699	−	0.972854i
$153$	−1.53285	+	1.95547i	−0.123923	+	0.158090i
$154$	−20.8062	+	4.09573i	−1.67662	+	0.330043i
$155$		0			0
$156$	−6.23449	+	6.97943i	−0.499159	+	0.558801i
$157$			8.10469i			0.646824i	0.946258	+	0.323412i	$0.104830\pi$
$157$			8.10469i			0.646824i	−0.946258	+	0.323412i	$0.895170\pi$
$158$	1.94695	+	9.89049i	0.154891	+	0.786845i
$159$	4.20732	+	8.64391i	0.333662	+	0.685507i
$160$		0			0
$161$		−	3.89391i		−	0.306883i
$162$	5.36943	+	11.5399i	0.421862	+	0.906660i
$163$	−5.07999			−0.397895			−0.198948	−	0.980010i	$-0.563752\pi$
$163$	−5.07999			−0.397895			−0.198948	+	0.980010i	$0.563752\pi$
$164$	7.78683	+	19.0121i	0.608049	+	1.48459i
$165$		0			0
$166$	−0.850781	−	4.32196i	−0.0660334	−	0.335449i
$167$			3.27777i			0.253641i	0.991926	+	0.126821i	$0.0404773\pi$
$167$			3.27777i			0.253641i	−0.991926	+	0.126821i	$0.959523\pi$
$168$	15.0225	+	8.89736i	1.15901	+	0.686447i
$169$	5.70156			0.438582
$170$		0			0
$171$	−11.9942	−	9.40194i	−0.917216	−	0.718984i
$172$	0.984255	−	0.403124i	0.0750487	−	0.0307379i
$173$	−14.9946			−1.14002			−0.570008	−	0.821639i	$-0.693060\pi$
$173$	−14.9946			−1.14002			−0.570008	+	0.821639i	$0.693060\pi$
$174$	−10.8449	+	8.19908i	−0.822152	+	0.621570i
$175$		0			0
$176$	−11.9942	+	11.8053i	−0.904093	+	0.889858i
$177$		0			0
$178$	−1.28984	−	6.55234i	−0.0966772	−	0.491119i
$179$	15.5737			1.16403			0.582015	−	0.813178i	$-0.302264\pi$
$179$	15.5737			1.16403			0.582015	+	0.813178i	$0.302264\pi$
$180$		0			0
$181$	−21.5078			−1.59866			−0.799331	−	0.600890i	$-0.794813\pi$
$181$	−21.5078			−1.59866			−0.799331	+	0.600890i	$0.794813\pi$
$182$	2.62991	+	13.3599i	0.194942	+	0.990301i
$183$	0.531805	+	1.09259i	0.0393122	+	0.0807665i
$184$	−1.70156	−	2.57967i	−0.125441	−	0.190176i
$185$		0			0
$186$	12.8882	−	9.74382i	0.945006	−	0.714451i
$187$	−3.48457			−0.254817
$188$	−4.72212	−	11.5294i	−0.344396	−	0.840866i
$189$	18.1047	+	3.89391i	1.31692	+	0.283240i
$190$		0			0
$191$	11.3663			0.822440			0.411220	−	0.911536i	$-0.365103\pi$
$191$	11.3663			0.822440			0.411220	+	0.911536i	$0.365103\pi$
$192$	13.8402	−	0.670121i	0.998830	−	0.0483618i
$193$		−	5.80625i		−	0.417943i	−0.977922	−	0.208971i	$-0.932988\pi$
$193$		−	5.80625i		−	0.417943i	0.977922	−	0.208971i	$-0.0670116\pi$
$194$	−2.21377	−	11.2459i	−0.158940	−	0.807411i
$195$		0			0
$196$	10.5523	−	4.32196i	0.753739	−	0.308711i
$197$	−9.44424			−0.672875			−0.336437	−	0.941706i	$-0.609222\pi$
$197$	−9.44424			−0.672875			−0.336437	+	0.941706i	$0.609222\pi$
$198$	−8.09151	+	15.9109i	−0.575039	+	1.13074i
$199$		−	15.6924i		−	1.11241i	−0.831047	−	0.556203i	$-0.812258\pi$
$199$		−	15.6924i		−	1.11241i	0.831047	−	0.556203i	$-0.187742\pi$
$200$		0			0
$201$	1.55234	+	3.18928i	0.109494	+	0.224954i
$202$	−1.96851	−	10.0000i	−0.138504	−	0.703598i
$203$			19.7810i			1.38835i
$204$	2.13968	+	1.91130i	0.149807	+	0.133818i
$205$		0			0
$206$	5.68317	−	1.11874i	0.395965	−	0.0779462i
$207$	−2.57967	−	2.02214i	−0.179299	−	0.140549i
$208$	7.58030	+	7.70156i	0.525599	+	0.534007i
$209$		−	21.3731i		−	1.47841i
$210$		0			0
$211$		−	14.1763i		−	0.975940i	−0.872860	−	0.487970i	$-0.837738\pi$
$211$		−	14.1763i		−	0.975940i	0.872860	−	0.487970i	$-0.162262\pi$
$212$	10.2725	−	4.20732i	0.705515	−	0.288960i
$213$	8.61603	+	17.7016i	0.590361	+	1.21289i
$214$	−5.14922	−	26.1580i	−0.351993	−	1.78812i
$215$		0			0
$216$	13.6957	−	5.33173i	0.931876	−	0.362778i
$217$		−	23.5078i		−	1.59581i
$218$	12.0742	−	2.37681i	0.817765	−	0.160978i
$219$	−11.9942	+	5.83802i	−0.810490	+	0.394497i
$220$		0			0
$221$			2.23748i			0.150509i
$222$	−10.5573	+	7.98161i	−0.708559	+	0.535691i
$223$	15.6924			1.05084			0.525421	−	0.850843i	$-0.323908\pi$
$223$	15.6924			1.05084			0.525421	+	0.850843i	$0.323908\pi$
$224$	11.3663	−	16.6510i	0.759446	−	1.11254i
$225$		0			0
$226$	−21.9555	+	4.32196i	−1.46046	+	0.287492i
$227$		−	11.6924i		−	0.776053i	−0.921648	−	0.388026i	$-0.873157\pi$
$227$		−	11.6924i		−	0.776053i	0.921648	−	0.388026i	$-0.126843\pi$
$228$	−11.7233	+	13.1240i	−0.776392	+	0.869160i
$229$	−8.70156			−0.575015			−0.287508	−	0.957778i	$-0.592827\pi$
$229$	−8.70156			−0.575015			−0.287508	+	0.957778i	$0.592827\pi$
$230$		0			0
$231$	11.3663	+	23.3521i	0.747850	+	1.53645i
$232$	8.64391	+	13.1047i	0.567501	+	0.860365i
$233$	−14.9946			−0.982328			−0.491164	−	0.871067i	$-0.663428\pi$
$233$	−14.9946			−0.982328			−0.491164	+	0.871067i	$0.663428\pi$
$234$	10.2165	+	5.19564i	0.667875	+	0.339649i
$235$		0			0
$236$		0			0
$237$	11.1007	−	5.40312i	0.721066	−	0.350971i
$238$	4.09573	−	0.806248i	0.265487	−	0.0522613i
$239$	−5.46295			−0.353369			−0.176684	−	0.984268i	$-0.556537\pi$
$239$	−5.46295			−0.353369			−0.176684	+	0.984268i	$0.556537\pi$
$240$		0			0
$241$	7.00000			0.450910			0.225455	−	0.974254i	$-0.427613\pi$
$241$	7.00000			0.450910			0.225455	+	0.974254i	$0.427613\pi$
$242$	−9.29898	+	1.83051i	−0.597761	+	0.117670i
$243$	11.9816	−	9.97201i	0.768621	−	0.639705i
$244$	1.29844	−	0.531805i	0.0831240	−	0.0340453i
$245$		0			0
$246$	20.0716	−	15.1747i	1.27972	−	0.967503i
$247$	−13.7239			−0.873231
$248$	−10.2725	−	15.5737i	−0.652302	−	0.988929i
$249$	−4.85078	+	2.36106i	−0.307406	+	0.149626i
$250$		0			0
$251$	1.25562			0.0792543			0.0396272	−	0.999215i	$-0.487383\pi$
$251$	1.25562			0.0792543			0.0396272	+	0.999215i	$0.487383\pi$
$252$	5.82928	−	20.5737i	0.367210	−	1.29602i
$253$		−	4.59688i		−	0.289003i
$254$	−22.5125	+	4.43160i	−1.41256	+	0.278063i
$255$		0			0
$256$	0.253905	−	15.9980i	0.0158691	−	0.999874i
$257$	11.1007			0.692441			0.346221	−	0.938153i	$-0.387465\pi$
$257$	11.1007			0.692441			0.346221	+	0.938153i	$0.387465\pi$
$258$	−0.785594	−	1.03911i	−0.0489089	−	0.0646920i
$259$			19.2563i			1.19653i
$260$		0			0
$261$	13.1047	+	10.2725i	0.811160	+	0.635849i
$262$	27.4478	−	5.40312i	1.69573	−	0.333806i
$263$		−	17.9219i		−	1.10511i	−0.833476	−	0.552555i	$-0.813653\pi$
$263$		−	17.9219i		−	1.10511i	0.833476	−	0.552555i	$-0.186347\pi$
$264$	17.7345	+	10.5036i	1.09148	+	0.646452i
$265$		0			0
$266$	4.94525	+	25.1218i	0.303213	+	1.54032i
$267$	−7.35408	+	3.57951i	−0.450062	+	0.219062i
$268$	3.79015	−	1.55234i	0.231520	−	0.0948245i
$269$			14.9946i			0.914236i	0.889406	+	0.457118i	$0.151118\pi$
$269$			14.9946i			0.914236i	−0.889406	+	0.457118i	$0.848882\pi$
$270$		0			0
$271$			24.4157i			1.48315i	0.670872	+	0.741573i	$0.265920\pi$
$271$			24.4157i			1.48315i	−0.670872	+	0.741573i	$0.734080\pi$
$272$	2.36106	−	2.32389i	0.143160	−	0.140906i
$273$	14.9946	−	7.29844i	0.907513	−	0.441722i
$274$	8.85078	−	1.74228i	0.534695	−	0.105255i
$275$		0			0
$276$	−2.52141	+	2.82268i	−0.151771	+	0.169905i
$277$			28.1047i			1.68865i	0.535834	+	0.844323i	$0.319997\pi$
$277$			28.1047i			1.68865i	−0.535834	+	0.844323i	$0.680003\pi$
$278$	0.414108	+	2.10366i	0.0248365	+	0.126169i
$279$	−15.5737	−	12.2078i	−0.932371	−	0.730864i
$280$		0			0
$281$		−	7.20677i		−	0.429920i	−0.976623	−	0.214960i	$-0.931038\pi$
$281$		−	7.20677i		−	0.429920i	0.976623	−	0.214960i	$-0.0689621\pi$
$282$	−12.1719	+	9.20230i	−0.724826	+	0.547989i
$283$	6.14360			0.365199			0.182599	−	0.983187i	$-0.441549\pi$
$283$	6.14360			0.365199			0.182599	+	0.983187i	$0.441549\pi$
$284$	21.0366	−	8.61603i	1.24829	−	0.511267i
$285$		0			0
$286$	3.10469	+	15.7718i	0.183584	+	0.932604i
$287$		−	36.6103i		−	2.16104i
$288$	−5.12846	−	16.1771i	−0.302197	−	0.953245i
$289$	−16.3141			−0.959651
$290$		0			0
$291$	−12.6220	+	6.14360i	−0.739913	+	0.360144i
$292$	5.83802	+	14.2539i	0.341644	+	0.834147i
$293$	18.8885			1.10348			0.551739	−	0.834017i	$-0.313965\pi$
$293$	18.8885			1.10348			0.551739	+	0.834017i	$0.313965\pi$
$294$	−8.42247	−	11.1404i	−0.491208	−	0.649722i
$295$		0			0
$296$	8.41464	+	12.7571i	0.489091	+	0.741492i
$297$	21.3731	+	4.59688i	1.24020	+	0.266738i
$298$	−0.452450	−	2.29844i	−0.0262097	−	0.133145i
$299$	−2.95170			−0.170701
$300$		0			0
$301$	−1.89531			−0.109244
$302$	1.26400	+	6.42110i	0.0727350	+	0.369493i
$303$	−11.2236	+	5.46295i	−0.644778	+	0.313838i
$304$	14.2539	+	14.4819i	0.817518	+	0.830595i
$305$		0			0
$306$	1.59282	−	3.13207i	0.0910556	−	0.179048i
$307$	−20.3993			−1.16425			−0.582125	−	0.813100i	$-0.697778\pi$
$307$	−20.3993			−1.16425			−0.582125	+	0.813100i	$0.697778\pi$
$308$	27.7517	−	11.3663i	1.58130	−	0.647657i
$309$	−3.10469	−	6.37855i	−0.176619	−	0.362863i
$310$		0			0
$311$	16.8293			0.954301			0.477151	−	0.878821i	$-0.341670\pi$
$311$	16.8293			0.954301			0.477151	+	0.878821i	$0.341670\pi$
$312$	6.74447	−	11.3875i	0.381830	−	0.644689i
$313$			22.7016i			1.28317i	0.767053	+	0.641584i	$0.221722\pi$
$313$			22.7016i			1.28317i	−0.767053	+	0.641584i	$0.778278\pi$
$314$	−2.21377	−	11.2459i	−0.124930	−	0.634645i
$315$		0			0
$316$	−5.40312	−	13.1921i	−0.303949	−	0.742113i
$317$	−29.9892			−1.68436			−0.842180	−	0.539197i	$-0.818728\pi$
$317$	−29.9892			−1.68436			−0.842180	+	0.539197i	$0.818728\pi$
$318$	−8.19908	−	10.8449i	−0.459781	−	0.608154i
$319$			23.3521i			1.30746i
$320$		0			0
$321$	−29.3586	+	14.2900i	−1.63864	+	0.797587i
$322$	1.06361	+	5.40312i	0.0592727	+	0.301104i
$323$			4.20732i			0.234102i
$324$	−10.6026	−	14.5459i	−0.589035	−	0.808108i
$325$		0			0
$326$	7.04891	−	1.38758i	0.390403	−	0.0768512i
$327$	−6.59605	−	13.5515i	−0.364762	−	0.749401i
$328$	−15.9980	−	24.2539i	−0.883341	−	1.33920i
$329$			22.2014i			1.22400i
$330$		0			0
$331$			30.0275i			1.65046i	0.564798	+	0.825229i	$0.308954\pi$
$331$			30.0275i			1.65046i	−0.564798	+	0.825229i	$0.691046\pi$
$332$	2.36106	+	5.76469i	0.129580	+	0.316378i
$333$	12.7571	+	10.0000i	0.699085	+	0.547997i
$334$	−0.895314	−	4.54818i	−0.0489894	−	0.248865i
$335$		0			0
$336$	−23.2752	−	8.24250i	−1.26977	−	0.449665i
$337$		−	0.403124i		−	0.0219596i	−0.999940	−	0.0109798i	$-0.996505\pi$
$337$		−	0.403124i		−	0.0219596i	0.999940	−	0.0109798i	$-0.00349505\pi$
$338$	−7.91140	+	1.55737i	−0.430323	+	0.0847096i
$339$	11.9942	+	24.6419i	0.651433	+	1.33836i
$340$		0			0
$341$		−	27.7517i		−	1.50284i
$342$	19.2110	+	9.76981i	1.03881	+	0.528291i
$343$	4.62754			0.249863
$344$	−1.25562	+	0.828216i	−0.0676987	+	0.0446544i
$345$		0			0
$346$	20.8062	−	4.09573i	1.11855	−	0.220188i
$347$			13.3885i			0.718732i	0.933197	+	0.359366i	$0.117007\pi$
$347$			13.3885i			0.718732i	−0.933197	+	0.359366i	$0.882993\pi$
$348$	12.8087	−	14.3392i	0.686619	−	0.768661i
$349$	12.2094			0.653553			0.326776	−	0.945102i	$-0.394038\pi$
$349$	12.2094			0.653553			0.326776	+	0.945102i	$0.394038\pi$
$350$		0			0
$351$	2.95170	−	13.7239i	0.157550	−	0.732527i
$352$	13.4183	−	19.6570i	0.715199	−	1.04772i
$353$	−29.4081			−1.56524			−0.782618	−	0.622502i	$-0.786116\pi$
$353$	−29.4081			−1.56524			−0.782618	+	0.622502i	$0.786116\pi$
$354$		0			0
$355$		0			0
$356$	3.57951	+	8.73961i	0.189714	+	0.463199i
$357$	−2.23748	−	4.59688i	−0.118420	−	0.243292i
$358$	−21.6098	+	4.25391i	−1.14211	+	0.224826i
$359$	−36.6103			−1.93222			−0.966108	−	0.258137i	$-0.916891\pi$
$359$	−36.6103			−1.93222			−0.966108	+	0.258137i	$0.916891\pi$
$360$		0			0
$361$	−6.80625			−0.358224
$362$	29.8439	−	5.87480i	1.56856	−	0.308773i
$363$	5.07999	+	10.4368i	0.266630	+	0.547789i
$364$	−7.29844	−	17.8196i	−0.382542	−	0.934002i
$365$		0			0
$366$	−1.03636	−	1.37080i	−0.0541715	−	0.0716528i
$367$	−3.56393			−0.186035			−0.0930177	−	0.995664i	$-0.529651\pi$
$367$	−3.56393			−0.186035			−0.0930177	+	0.995664i	$0.529651\pi$
$368$	3.06569	+	3.11473i	0.159810	+	0.162367i
$369$	−24.2539	−	19.0121i	−1.26261	−	0.989729i
$370$		0			0
$371$	−19.7810			−1.02698
$372$	−15.2219	+	17.0407i	−0.789220	+	0.883521i
$373$		−	17.2984i		−	0.895679i	−0.894114	−	0.447840i	$-0.852194\pi$
$373$		−	17.2984i		−	0.895679i	0.894114	−	0.447840i	$-0.147806\pi$
$374$	4.83513	−	0.951801i	0.250019	−	0.0492165i
$375$		0			0
$376$	9.70156	+	14.7082i	0.500320	+	0.758515i
$377$	14.9946			0.772260
$378$	−26.1854	−	0.457877i	−1.34683	−	0.0235507i
$379$		−	21.3042i		−	1.09432i	−0.837027	−	0.547162i	$-0.815708\pi$
$379$		−	21.3042i		−	1.09432i	0.837027	−	0.547162i	$-0.184292\pi$
$380$		0			0
$381$	12.2984	+	25.2670i	0.630068	+	1.29447i
$382$	−15.7718	+	3.10469i	−0.806953	+	0.158850i
$383$		−	12.4589i		−	0.636622i	−0.947986	−	0.318311i	$-0.896884\pi$
$383$		−	12.4589i		−	0.636622i	0.947986	−	0.318311i	$-0.103116\pi$
$384$	−19.0214	+	4.71026i	−0.970681	+	0.240370i
$385$		0			0
$386$	1.58596	+	8.05666i	0.0807233	+	0.410073i
$387$	−0.984255	+	1.25562i	−0.0500325	+	0.0638270i
$388$	6.14360	+	15.0000i	0.311894	+	0.761510i
$389$		−	19.9639i		−	1.01221i	−0.862472	−	0.506104i	$-0.831085\pi$
$389$		−	19.9639i		−	1.01221i	0.862472	−	0.506104i	$-0.168915\pi$
$390$		0			0
$391$			0.904899i			0.0457627i
$392$	−13.4617	+	8.87942i	−0.679920	+	0.448479i
$393$	−14.9946	−	30.8062i	−0.756377	−	1.55397i
$394$	13.1047	−	2.57967i	0.660205	−	0.129962i
$395$		0			0
$396$	6.88165	−	24.2878i	0.345816	−	1.22051i
$397$		−	28.9109i		−	1.45100i	−0.688223	−	0.725499i	$-0.741609\pi$
$397$		−	28.9109i		−	1.45100i	0.688223	−	0.725499i	$-0.258391\pi$
$398$	4.28634	+	21.7745i	0.214855	+	1.09146i
$399$	28.1956	−	13.7239i	1.41155	−	0.687054i
$400$		0			0
$401$		−	30.8174i		−	1.53895i	−0.638679	−	0.769473i	$-0.720519\pi$
$401$		−	30.8174i		−	1.53895i	0.638679	−	0.769473i	$-0.279481\pi$
$402$	−3.02515	−	4.00137i	−0.150881	−	0.199570i
$403$	−17.8196			−0.887659
$404$	5.46295	+	13.3382i	0.271792	+	0.663598i
$405$		0			0
$406$	−5.40312	−	27.4478i	−0.268153	−	1.36221i
$407$			22.7327i			1.12682i
$408$	−3.49105	−	2.06765i	−0.172833	−	0.102364i
$409$	27.2094			1.34542			0.672708	−	0.739908i	$-0.265131\pi$
$409$	27.2094			1.34542			0.672708	+	0.739908i	$0.265131\pi$
$410$		0			0
$411$	−4.83513	−	9.93375i	−0.238500	−	0.489996i
$412$	−7.58030	+	3.10469i	−0.373455	+	0.152957i
$413$		0			0
$414$	4.13185	+	2.10127i	0.203070	+	0.103272i
$415$		0			0
$416$	−12.6220	−	8.61603i	−0.618843	−	0.422436i
$417$	2.36106	−	1.14922i	0.115622	−	0.0562775i
$418$	5.83802	+	29.6570i	0.285547	+	1.45057i
$419$	10.1107			0.493941			0.246970	−	0.969023i	$-0.420565\pi$
$419$	10.1107			0.493941			0.246970	+	0.969023i	$0.420565\pi$
$420$		0			0
$421$	24.2094			1.17989			0.589946	−	0.807442i	$-0.299149\pi$
$421$	24.2094			1.17989			0.589946	+	0.807442i	$0.299149\pi$
$422$	3.87223	+	19.6709i	0.188497	+	0.957563i
$423$	14.7082	+	11.5294i	0.715135	+	0.560578i
$424$	−13.1047	+	8.64391i	−0.636420	+	0.419785i
$425$		0			0
$426$	−16.7906	−	22.2090i	−0.813507	−	1.07603i
$427$	−2.50031			−0.120999
$428$	14.2900	+	34.8899i	0.690731	+	1.68647i
$429$	17.7016	−	8.61603i	0.854639	−	0.415986i
$430$		0			0
$431$	−19.7810			−0.952817			−0.476408	−	0.879224i	$-0.658062\pi$
$431$	−19.7810			−0.952817			−0.476408	+	0.879224i	$0.658062\pi$
$432$	−17.5476	+	11.1392i	−0.844260	+	0.535934i
$433$			31.2094i			1.49983i	0.661536	+	0.749913i	$0.269905\pi$
$433$			31.2094i			1.49983i	−0.661536	+	0.749913i	$0.730095\pi$
$434$	6.42110	+	32.6191i	0.308222	+	1.56577i
$435$		0			0
$436$	−16.1047	+	6.59605i	−0.771275	+	0.315893i
$437$	−5.55034			−0.265509
$438$	15.0483	−	11.3769i	0.719034	−	0.543610i
$439$			21.9154i			1.04596i	0.852344	+	0.522981i	$0.175180\pi$
$439$			21.9154i			1.04596i	−0.852344	+	0.522981i	$0.824820\pi$
$440$		0			0
$441$	−10.5523	+	13.4617i	−0.502493	+	0.641035i
$442$	−0.611161	−	3.10469i	−0.0290699	−	0.147675i
$443$			11.2033i			0.532285i	0.963934	+	0.266143i	$0.0857492\pi$
$443$			11.2033i			0.532285i	−0.963934	+	0.266143i	$0.914251\pi$
$444$	12.4690	−	13.9589i	0.591752	−	0.662458i
$445$		0			0
$446$	−21.7745	+	4.28634i	−1.03105	+	0.202964i
$447$	−2.57967	+	1.25562i	−0.122014	+	0.0593890i
$448$	−11.2236	+	26.2094i	−0.530264	+	1.23828i
$449$			19.1357i			0.903068i	0.892254	+	0.451534i	$0.149123\pi$
$449$			19.1357i			0.903068i	−0.892254	+	0.451534i	$0.850877\pi$
$450$		0			0
$451$		−	43.2196i		−	2.03513i
$452$	29.2845	−	11.9942i	1.37743	−	0.564158i
$453$	7.20677	−	3.50781i	0.338604	−	0.164811i
$454$	3.19375	+	16.2242i	0.149890	+	0.761440i
$455$		0			0
$456$	12.6822	−	21.4129i	0.593899	−	1.00275i
$457$		−	16.8953i		−	0.790329i	−0.918610	−	0.395165i	$-0.870688\pi$
$457$		−	16.8953i		−	0.790329i	0.918610	−	0.395165i	$-0.129312\pi$
$458$	12.0742	−	2.37681i	0.564188	−	0.111061i
$459$	−4.20732	−	0.904899i	−0.196381	−	0.0422371i
$460$		0			0
$461$			7.20677i			0.335653i	0.985817	+	0.167826i	$0.0536748\pi$
$461$			7.20677i			0.335653i	−0.985817	+	0.167826i	$0.946325\pi$
$462$	−22.1503	−	29.2983i	−1.03053	−	1.36308i
$463$	7.12785			0.331259			0.165630	−	0.986188i	$-0.447034\pi$
$463$	7.12785			0.331259			0.165630	+	0.986188i	$0.447034\pi$
$464$	−15.5737	−	15.8228i	−0.722989	−	0.734555i
$465$		0			0
$466$	20.8062	−	4.09573i	0.963831	−	0.189731i
$467$		−	0.766519i		−	0.0354703i	−0.999843	−	0.0177351i	$-0.994354\pi$
$467$		−	0.766519i		−	0.0354703i	0.999843	−	0.0177351i	$-0.00564557\pi$
$468$	−15.5955	−	4.41877i	−0.720900	−	0.204258i
$469$	−7.29844			−0.337011
$470$		0			0
$471$	−12.6220	+	6.14360i	−0.581590	+	0.283082i
$472$		0			0
$473$	−2.23748			−0.102879
$474$	−13.9273	+	10.5294i	−0.639701	+	0.483632i
$475$		0			0
$476$	−5.46295	+	2.23748i	−0.250394	+	0.102555i
$477$	−10.2725	+	13.1047i	−0.470344	+	0.600022i
$478$	7.58030	−	1.49219i	0.346715	−	0.0682512i
$479$	42.0732			1.92237			0.961187	−	0.275897i	$-0.0889747\pi$
$479$	42.0732			1.92237			0.961187	+	0.275897i	$0.0889747\pi$
$480$		0			0
$481$	14.5969			0.665560
$482$	−9.71309	+	1.91203i	−0.442419	+	0.0870906i
$483$	6.06424	−	2.95170i	0.275932	−	0.134307i
$484$	12.4031	−	5.07999i	0.563778	−	0.230908i
$485$		0			0
$486$	−13.9017	+	17.1098i	−0.630592	+	0.776114i
$487$	34.0438			1.54267			0.771337	−	0.636427i	$-0.219588\pi$
$487$	34.0438			1.54267			0.771337	+	0.636427i	$0.219588\pi$
$488$	−1.65643	+	1.09259i	−0.0749831	+	0.0494592i
$489$	−3.85078	−	7.91140i	−0.174138	−	0.357766i
$490$		0			0
$491$	16.8293			0.759495			0.379748	−	0.925090i	$-0.376011\pi$
$491$	16.8293			0.759495			0.379748	+	0.925090i	$0.376011\pi$
$492$	−23.7061	+	26.5387i	−1.06875	+	1.19646i
$493$		−	4.59688i		−	0.207033i
$494$	19.0431	−	3.74865i	0.856788	−	0.168660i
$495$		0			0
$496$	18.5078	+	18.8039i	0.831025	+	0.844319i
$497$	−40.5088			−1.81707
$498$	6.08595	−	4.60115i	0.272718	−	0.206182i
$499$		−	22.9790i		−	1.02868i	−0.857586	−	0.514340i	$-0.828037\pi$
$499$		−	22.9790i		−	1.02868i	0.857586	−	0.514340i	$-0.171963\pi$
$500$		0			0
$501$	−5.10469	+	2.48465i	−0.228061	+	0.111006i
$502$	−1.74228	+	0.342970i	−0.0777620	+	0.0153075i
$503$			32.2399i			1.43751i	0.695265	+	0.718753i	$0.255287\pi$
$503$			32.2399i			1.43751i	−0.695265	+	0.718753i	$0.744713\pi$
$504$	−2.46898	+	30.1400i	−0.109977	+	1.34254i
$505$		0			0
$506$	1.25562	+	6.37855i	0.0558193	+	0.283561i
$507$	4.32196	+	8.87942i	0.191945	+	0.394349i
$508$	30.0275	−	12.2984i	1.33225	−	0.545655i
$509$			42.7463i			1.89470i	0.320207	+	0.947348i	$0.396247\pi$
$509$			42.7463i			1.89470i	−0.320207	+	0.947348i	$0.603753\pi$
$510$		0			0
$511$		−	27.4478i		−	1.21422i
$512$	4.01749	+	22.2679i	0.177550	+	0.984112i
$513$	5.55034	−	25.8062i	0.245053	−	1.13937i
$514$	−15.4031	+	3.03212i	−0.679403	+	0.133741i
$515$		0			0
$516$	1.37391	+	1.22727i	0.0604829	+	0.0540273i
$517$			26.2094i			1.15269i
$518$	−5.25982	−	26.7198i	−0.231103	−	1.17400i
$519$	−11.3663	−	23.3521i	−0.498927	−	1.02504i
$520$		0			0
$521$		−	10.2725i		−	0.450045i	−0.974354	−	0.225022i	$-0.927754\pi$
$521$		−	10.2725i		−	0.450045i	0.974354	−	0.225022i	$-0.0722455\pi$
$522$	−20.9898	−	10.6744i	−0.918697	−	0.467206i
$523$	−31.4642			−1.37583			−0.687916	−	0.725790i	$-0.741474\pi$
$523$	−31.4642			−1.37583			−0.687916	+	0.725790i	$0.741474\pi$
$524$	−36.6103	+	14.9946i	−1.59933	+	0.655041i
$525$		0			0
$526$	4.89531	+	24.8681i	0.213446	+	1.08430i
$527$			5.46295i			0.237970i
$528$	−27.4771	−	9.73052i	−1.19579	−	0.423467i
$529$	21.8062			0.948098
$530$		0			0
$531$		0			0
$532$	−13.7239	−	33.5078i	−0.595006	−	1.45275i
$533$	−27.7517			−1.20206
$534$	9.22667	−	6.97562i	0.399277	−	0.301865i
$535$		0			0
$536$	−4.83513	+	3.18928i	−0.208846	+	0.137756i
$537$	11.8053	+	24.2539i	0.509437	+	1.04663i
$538$	−4.09573	−	20.8062i	−0.176579	−	0.897021i
$539$	−23.9883			−1.03325
$540$		0			0
$541$	−19.2984			−0.829705			−0.414852	−	0.909889i	$-0.636167\pi$
$541$	−19.2984			−0.829705			−0.414852	+	0.909889i	$0.636167\pi$
$542$	−6.66908	−	33.8788i	−0.286461	−	1.45522i
$543$	−16.3036	−	33.4955i	−0.699653	−	1.43743i
$544$	−2.64141	+	3.86951i	−0.113249	+	0.165904i
$545$		0			0
$546$	−18.8127	+	14.2229i	−0.805109	+	0.608685i
$547$	21.8360			0.933640			0.466820	−	0.884352i	$-0.345400\pi$
$547$	21.8360			0.933640			0.466820	+	0.884352i	$0.345400\pi$
$548$	−11.8053	+	4.83513i	−0.504298	+	0.206547i
$549$	−1.29844	+	1.65643i	−0.0554160	+	0.0706948i
$550$		0			0
$551$	28.1956			1.20117
$552$	2.72766	−	4.60542i	0.116097	−	0.196020i
$553$			25.4031i			1.08025i
$554$	−7.67672	−	38.9976i	−0.326153	−	1.65685i
$555$		0			0
$556$	−1.14922	−	2.80590i	−0.0487377	−	0.118996i
$557$	17.2321			0.730146			0.365073	−	0.930979i	$-0.381044\pi$
$557$	17.2321			0.730146			0.365073	+	0.930979i	$0.381044\pi$
$558$	24.9443	+	12.6855i	1.05598	+	0.537020i
$559$			1.43670i			0.0607661i
$560$		0			0
$561$	−2.64141	−	5.42675i	−0.111520	−	0.229118i
$562$	1.96851	+	10.0000i	0.0830366	+	0.421825i
$563$		−	30.0547i		−	1.26666i	−0.773883	−	0.633328i	$-0.781688\pi$
$563$		−	30.0547i		−	1.26666i	0.773883	−	0.633328i	$-0.218312\pi$
$564$	14.3760	−	16.0937i	0.605337	−	0.677667i
$565$		0			0
$566$	−8.52476	+	1.67811i	−0.358322	+	0.0705361i
$567$	7.65966	+	31.1473i	0.321675	+	1.30806i
$568$	−26.8366	+	17.7016i	−1.12604	+	0.742741i
$569$		−	43.5745i		−	1.82674i	−0.407133	−	0.913369i	$-0.633472\pi$
$569$		−	43.5745i		−	1.82674i	0.407133	−	0.913369i	$-0.366528\pi$
$570$		0			0
$571$			32.9802i			1.38018i	0.723724	+	0.690090i	$0.242429\pi$
$571$			32.9802i			1.38018i	−0.723724	+	0.690090i	$0.757571\pi$
$572$	−8.61603	−	21.0366i	−0.360254	−	0.879585i
$573$	8.61603	+	17.7016i	0.359940	+	0.739493i
$574$	10.0000	+	50.7999i	0.417392	+	2.12034i
$575$		0			0
$576$	11.5349	+	21.0463i	0.480621	+	0.876928i
$577$		−	0.403124i		−	0.0167823i	−0.999965	−	0.00839114i	$-0.997329\pi$
$577$		−	0.403124i		−	0.0167823i	0.999965	−	0.00839114i	$-0.00267101\pi$
$578$	22.6371	−	4.45614i	0.941581	−	0.185351i
$579$	9.04246	−	4.40131i	0.375792	−	0.182912i
$580$		0			0
$581$		−	11.1007i		−	0.460534i
$582$	15.8359	−	11.9724i	0.656421	−	0.496273i
$583$	−23.3521			−0.967144
$584$	−11.9942	−	18.1839i	−0.496322	−	0.752453i
$585$		0			0
$586$	−26.2094	+	5.15934i	−1.08270	+	0.213130i
$587$			3.88125i			0.160196i	0.996787	+	0.0800982i	$0.0255234\pi$
$587$			3.88125i			0.160196i	−0.996787	+	0.0800982i	$0.974477\pi$
$588$	14.7299	+	13.1577i	0.607449	+	0.542614i
$589$	−33.5078			−1.38067
$590$		0			0
$591$	−7.15902	−	14.7082i	−0.294483	−	0.605012i
$592$	−15.1606	−	15.4031i	−0.623097	−	0.633065i
$593$	43.5745			1.78939			0.894695	−	0.446678i	$-0.147393\pi$
$593$	43.5745			1.78939			0.894695	+	0.446678i	$0.147393\pi$
$594$	−30.9127	−	0.540538i	−1.26836	−	0.0221785i
$595$		0			0
$596$	1.25562	+	3.06569i	0.0514324	+	0.125576i
$597$	24.4388	−	11.8953i	1.00021	−	0.486843i
$598$	4.09573	−	0.806248i	0.167487	−	0.0329700i
$599$		0			0			−	1.00000i	$-0.5\pi$
$599$		0			0				1.00000i	$0.5\pi$
$600$		0			0
$601$	24.0156			0.979618			0.489809	−	0.871830i	$-0.337067\pi$
$601$	24.0156			0.979618			0.489809	+	0.871830i	$0.337067\pi$
$602$	2.62991	−	0.517700i	0.107187	−	0.0210999i
$603$	−3.79015	+	4.83513i	−0.154347	+	0.196902i
$604$	−3.50781	−	8.56455i	−0.142731	−	0.348487i
$605$		0			0
$606$	14.0815	−	10.6460i	0.572021	−	0.432464i
$607$	27.4478			1.11407			0.557036	−	0.830489i	$-0.311939\pi$
$607$	27.4478			1.11407			0.557036	+	0.830489i	$0.311939\pi$
$608$	−23.7342	−	16.2015i	−0.962549	−	0.657057i
$609$	−30.8062	+	14.9946i	−1.24833	+	0.607611i
$610$		0			0
$611$	16.8293			0.680840
$612$	−1.35466	+	4.78108i	−0.0547588	+	0.193264i
$613$		−	20.8062i		−	0.840356i	−0.907442	−	0.420178i	$-0.861968\pi$
$613$		−	20.8062i		−	0.840356i	0.907442	−	0.420178i	$-0.138032\pi$
$614$	28.3057	−	5.57201i	1.14233	−	0.224868i
$615$		0			0
$616$	−35.4031	+	23.3521i	−1.42643	+	0.940881i
$617$	18.3074			0.737030			0.368515	−	0.929622i	$-0.379866\pi$
$617$	18.3074			0.737030			0.368515	+	0.929622i	$0.379866\pi$
$618$	6.05030	+	8.00274i	0.243379	+	0.321918i
$619$		−	26.9160i		−	1.08184i	−0.841073	−	0.540922i	$-0.818075\pi$
$619$		−	26.9160i		−	1.08184i	0.841073	−	0.540922i	$-0.181925\pi$
$620$		0			0
$621$	1.19375	−	5.55034i	0.0479036	−	0.222727i
$622$	−23.3521	+	4.59688i	−0.936332	+	0.184318i
$623$		−	16.8293i		−	0.674251i
$624$	−6.24806	+	17.6433i	−0.250123	+	0.706298i
$625$		0			0
$626$	−6.20087	−	31.5003i	−0.247837	−	1.25901i
$627$	33.2858	−	16.2015i	1.32931	−	0.647025i
$628$	6.14360	+	15.0000i	0.245156	+	0.598565i
$629$		−	4.47495i		−	0.178428i
$630$		0			0
$631$			2.65903i			0.105854i	0.998598	+	0.0529271i	$0.0168551\pi$
$631$			2.65903i			0.105854i	−0.998598	+	0.0529271i	$0.983145\pi$
$632$	11.1007	+	16.8293i	0.441561	+	0.669433i
$633$	22.0778	−	10.7461i	0.877512	−	0.427119i
$634$	41.6125	−	8.19146i	1.65264	−	0.325324i
$635$		0			0
$636$	14.3392	+	12.8087i	0.568585	+	0.507898i
$637$			15.4031i			0.610294i
$638$	−6.37855	−	32.4030i	−0.252529	−	1.28285i
$639$	−21.0366	+	26.8366i	−0.832196	+	1.06164i
$640$		0			0
$641$			41.0898i			1.62295i	0.584386	+	0.811476i	$0.301335\pi$
$641$			41.0898i			1.62295i	−0.584386	+	0.811476i	$0.698665\pi$
$642$	36.8343	−	27.8477i	1.45373	−	1.09906i
$643$	22.2885			0.878971			0.439485	−	0.898250i	$-0.355161\pi$
$643$	22.2885			0.878971			0.439485	+	0.898250i	$0.355161\pi$
$644$	−2.95170	−	7.20677i	−0.116313	−	0.283986i
$645$		0			0
$646$	−1.14922	−	5.83802i	−0.0452154	−	0.229694i
$647$		−	2.18518i		−	0.0859082i	−0.999077	−	0.0429541i	$-0.986323\pi$
$647$		−	2.18518i		−	0.0859082i	0.999077	−	0.0429541i	$-0.0136769\pi$
$648$	18.6852	+	17.2876i	0.734025	+	0.679123i
$649$		0			0
$650$		0			0
$651$	36.6103	−	17.8196i	1.43487	−	0.698406i
$652$	−9.40194	+	3.85078i	−0.368208	+	0.150808i
$653$	−7.78781			−0.304761			−0.152380	−	0.988322i	$-0.548694\pi$
$653$	−7.78781			−0.304761			−0.152380	+	0.988322i	$0.548694\pi$
$654$	12.8541	+	17.0022i	0.502636	+	0.664838i
$655$		0			0
$656$	28.8234	+	29.2845i	1.12537	+	1.14337i
$657$	−18.1839	−	14.2539i	−0.709420	−	0.556098i
$658$	−6.06424	−	30.8062i	−0.236409	−	1.20095i
$659$	21.0366			0.819470			0.409735	−	0.912205i	$-0.365621\pi$
$659$	21.0366			0.819470			0.409735	+	0.912205i	$0.365621\pi$
$660$		0			0
$661$	−18.0000			−0.700119			−0.350059	−	0.936727i	$-0.613839\pi$
$661$	−18.0000			−0.700119			−0.350059	+	0.936727i	$0.613839\pi$
$662$	−8.20192	−	41.6656i	−0.318777	−	1.61938i
$663$	−3.48457	+	1.69607i	−0.135329	+	0.0658700i
$664$	−4.85078	−	7.35408i	−0.188247	−	0.285393i
$665$		0			0
$666$	−20.4330	−	10.3913i	−0.791764	−	0.402654i
$667$	6.06424			0.234808
$668$	2.48465	+	6.06643i	0.0961339	+	0.234717i
$669$	11.8953	+	24.4388i	0.459899	+	0.944860i
$670$		0			0
$671$	−2.95170			−0.113949
$672$	34.5478	+	5.07959i	1.33271	+	0.195950i
$673$		−	0.806248i		−	0.0310786i	−0.999879	−	0.0155393i	$-0.995053\pi$
$673$		−	0.806248i		−	0.0310786i	0.999879	−	0.0155393i	$-0.00494651\pi$
$674$	0.110112	+	0.559369i	0.00424137	+	0.0215461i
$675$		0			0
$676$	10.5523	−	4.32196i	0.405859	−	0.166229i
$677$	3.89391			0.149655			0.0748275	−	0.997196i	$-0.476159\pi$
$677$	3.89391			0.149655			0.0748275	+	0.997196i	$0.476159\pi$
$678$	−23.3738	−	30.9165i	−0.897664	−	1.18734i
$679$		−	28.8845i		−	1.10849i
$680$		0			0
$681$	18.2094	−	8.86320i	0.697785	−	0.339639i
$682$	7.58030	+	38.5078i	0.290265	+	1.47454i
$683$		−	19.9440i		−	0.763137i	−0.924341	−	0.381568i	$-0.875384\pi$
$683$		−	19.9440i		−	0.763137i	0.924341	−	0.381568i	$-0.124616\pi$
$684$	−29.3255	−	8.30900i	−1.12129	−	0.317703i
$685$		0			0
$686$	−6.42110	+	1.26400i	−0.245159	+	0.0482597i
$687$	−6.59605	−	13.5515i	−0.251655	−	0.517023i
$688$	1.51606	−	1.49219i	0.0577992	−	0.0568892i
$689$			14.9946i			0.571248i
$690$		0			0
$691$			18.8039i			0.715333i	0.933849	+	0.357667i	$0.116428\pi$
$691$			18.8039i			0.715333i	−0.933849	+	0.357667i	$0.883572\pi$
$692$	−27.7517	+	11.3663i	−1.05496	+	0.432084i
$693$	−27.7517	+	35.4031i	−1.05420	+	1.34485i
$694$	−3.65703	−	18.5777i	−0.138819	−	0.705198i
$695$		0			0
$696$	−13.8565	+	23.3955i	−0.525228	+	0.886803i
$697$			8.50781i			0.322256i
$698$	−16.9415	+	3.33496i	−0.641247	+	0.126230i
$699$	−11.3663	−	23.3521i	−0.429915	−	0.883256i
$700$		0			0
$701$			27.7517i			1.04817i	0.851667	+	0.524083i	$0.175592\pi$
$701$			27.7517i			1.04817i	−0.851667	+	0.524083i	$0.824408\pi$
$702$	−0.347085	+	19.8493i	−0.0130999	+	0.749164i
$703$	27.4478			1.03521
$704$	−13.2498	+	30.9410i	−0.499370	+	1.16613i
$705$		0			0
$706$	40.8062	−	8.03275i	1.53576	−	0.302317i
$707$		−	25.6844i		−	0.965961i
$708$		0			0
$709$	11.2984			0.424322			0.212161	−	0.977235i	$-0.431950\pi$
$709$	11.2984			0.424322			0.212161	+	0.977235i	$0.431950\pi$
$710$		0			0
$711$	16.8293	+	13.1921i	0.631148	+	0.494742i
$712$	−7.35408	−	11.1492i	−0.275606	−	0.417835i
$713$	−7.20677			−0.269896
$714$	4.36031	+	5.76739i	0.163181	+	0.215839i
$715$		0			0
$716$	28.8234	−	11.8053i	1.07718	−	0.441185i
$717$	−4.14108	−	8.50781i	−0.154651	−	0.317730i
$718$	50.7999	−	10.0000i	1.89583	−	0.373197i
$719$	25.6844			0.957866			0.478933	−	0.877851i	$-0.341024\pi$
$719$	25.6844			0.957866			0.478933	+	0.877851i	$0.341024\pi$
$720$		0			0
$721$	14.5969			0.543616
$722$	9.44424	−	1.85911i	0.351478	−	0.0691889i
$723$	5.30621	+	10.9016i	0.197340	+	0.405434i
$724$	−39.8062	+	16.3036i	−1.47939	+	0.605917i
$725$		0			0
$726$	−9.89969	−	13.0943i	−0.367412	−	0.485977i
$727$	−45.1087			−1.67299			−0.836495	−	0.547975i	$-0.815399\pi$
$727$	−45.1087			−1.67299			−0.836495	+	0.547975i	$0.815399\pi$
$728$	14.9946	+	22.7327i	0.555736	+	0.842529i
$729$	24.6125	+	11.1007i	0.911574	+	0.411136i
$730$		0			0
$731$	0.440449			0.0162906
$732$	1.81247	+	1.61902i	0.0669908	+	0.0598407i
$733$		−	20.8062i		−	0.768496i	−0.923230	−	0.384248i	$-0.874461\pi$
$733$		−	20.8062i		−	0.768496i	0.923230	−	0.384248i	$-0.125539\pi$
$734$	4.94525	−	0.973477i	0.182532	−	0.0359317i
$735$		0			0
$736$	−5.10469	−	3.48457i	−0.188161	−	0.128443i
$737$	−8.61603			−0.317376
$738$	38.8474	+	19.7560i	1.42999	+	0.727227i
$739$			52.9271i			1.94695i	0.228785	+	0.973477i	$0.426525\pi$
$739$			52.9271i			1.94695i	−0.228785	+	0.973477i	$0.573475\pi$
$740$		0			0
$741$	−10.4031	−	21.3731i	−0.382168	−	0.785162i
$742$	27.4478	−	5.40312i	1.00764	−	0.198355i
$743$			29.6143i			1.08644i	0.839589	+	0.543222i	$0.182796\pi$
$743$			29.6143i			1.08644i	−0.839589	+	0.543222i	$0.817204\pi$
$744$	16.4671	−	27.8033i	0.603712	−	1.01932i
$745$		0			0
$746$	4.72502	+	24.0030i	0.172995	+	0.878814i
$747$	−7.35408	−	5.76469i	−0.269072	−	0.210919i
$748$	−6.44918	+	2.64141i	−0.235805	+	0.0965795i
$749$		−	67.1851i		−	2.45489i
$750$		0			0
$751$		−	28.3527i		−	1.03460i	−0.855803	−	0.517302i	$-0.826936\pi$
$751$		−	28.3527i		−	1.03460i	0.855803	−	0.517302i	$-0.173064\pi$
$752$	−17.4792	−	17.7588i	−0.637402	−	0.647598i
$753$	0.951801	+	1.95547i	0.0346856	+	0.0712612i
$754$	−20.8062	+	4.09573i	−0.757719	+	0.149158i
$755$		0			0
$756$	36.4595	−	6.51713i	1.32602	−	0.237026i
$757$		−	8.91093i		−	0.323873i	−0.986801	−	0.161937i	$-0.948226\pi$
$757$		−	8.91093i		−	0.323873i	0.986801	−	0.161937i	$-0.0517740\pi$
$758$	5.81918	+	29.5614i	0.211362	+	1.07372i
$759$	7.15902	−	3.48457i	0.259856	−	0.126482i
$760$		0			0
$761$		−	3.06569i		−	0.111131i	−0.998455	−	0.0555656i	$-0.982304\pi$
$761$		−	3.06569i		−	0.111131i	0.998455	−	0.0555656i	$-0.0176962\pi$
$762$	−23.9667	−	31.7009i	−0.868224	−	1.14840i
$763$	31.0117			1.12270
$764$	21.0366	−	8.61603i	0.761078	−	0.311717i
$765$		0			0
$766$	3.40312	+	17.2878i	0.122960	+	0.624634i
$767$		0			0
$768$	25.1072	−	11.7315i	0.905978	−	0.423325i
$769$	39.8062			1.43545			0.717725	−	0.696327i	$-0.245183\pi$
$769$	39.8062			1.43545			0.717725	+	0.696327i	$0.245183\pi$
$770$		0			0
$771$	8.41464	+	17.2878i	0.303046	+	0.622606i
$772$	−4.40131	−	10.7461i	−0.158407	−	0.386760i
$773$	5.55034			0.199632			0.0998159	−	0.995006i	$-0.468175\pi$
$773$	5.55034			0.199632			0.0998159	+	0.995006i	$0.468175\pi$
$774$	1.02277	−	2.01113i	0.0367626	−	0.0722886i
$775$		0			0
$776$	−12.6220	−	19.1357i	−0.453102	−	0.686930i
$777$	−29.9892	+	14.5969i	−1.07586	+	0.523660i
$778$	5.45308	+	27.7016i	0.195502	+	0.993149i
$779$	−52.1839			−1.86968
$780$		0			0
$781$	−47.8219			−1.71120
$782$	−0.247171	−	1.25562i	−0.00883881	−	0.0449010i
$783$	−6.06424	+	28.1956i	−0.216718	+	1.00763i
$784$	16.2539	−	15.9980i	0.580497	−	0.571357i
$785$		0			0
$786$	29.2209	+	38.6505i	1.04227	+	1.37862i
$787$	−14.7875

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:	\( N \)	\(=\)	\( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	300.h (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.38758 + 0.273147i) q^{2} +(0.758030 + 1.55737i) q^{3} +(1.85078 - 0.758030i) q^{4} +(-1.47722 - 1.95392i) q^{6} -3.56393 q^{7} +(-2.36106 + 1.55737i) q^{8} +(-1.85078 + 2.36106i) q^{9} +O(q^{10})\)	\(q+(-1.38758 + 0.273147i) q^{2} +(0.758030 + 1.55737i) q^{3} +(1.85078 - 0.758030i) q^{4} +(-1.47722 - 1.95392i) q^{6} -3.56393 q^{7} +(-2.36106 + 1.55737i) q^{8} +(-1.85078 + 2.36106i) q^{9} -4.20732 q^{11} +(2.58348 + 2.30774i) q^{12} +2.70156i q^{13} +(4.94525 - 0.973477i) q^{14} +(2.85078 - 2.80590i) q^{16} +0.828216 q^{17} +(1.92320 - 3.78171i) q^{18} +5.07999i q^{19} +(-2.70156 - 5.55034i) q^{21} +(5.83802 - 1.14922i) q^{22} +1.09259i q^{23} +(-4.21515 - 2.49651i) q^{24} +(-0.737925 - 3.74865i) q^{26} +(-5.07999 - 1.09259i) q^{27} +(-6.59605 + 2.70156i) q^{28} -5.55034i q^{29} +6.59605i q^{31} +(-3.18928 + 4.67210i) q^{32} +(-3.18928 - 6.55234i) q^{33} +(-1.14922 + 0.226225i) q^{34} +(-1.63564 + 5.77275i) q^{36} -5.40312i q^{37} +(-1.38758 - 7.04891i) q^{38} +(-4.20732 + 2.04787i) q^{39} +10.2725i q^{41} +(5.26471 + 6.96364i) q^{42} +0.531805 q^{43} +(-7.78683 + 3.18928i) q^{44} +(-0.298438 - 1.51606i) q^{46} -6.22947i q^{47} +(6.53078 + 2.31276i) q^{48} +5.70156 q^{49} +(0.627812 + 1.28984i) q^{51} +(2.04787 + 5.00000i) q^{52} +5.55034 q^{53} +(7.34735 + 0.128476i) q^{54} +(8.41464 - 5.55034i) q^{56} +(-7.91140 + 3.85078i) q^{57} +(1.51606 + 7.70156i) q^{58} +0.701562 q^{61} +(-1.80169 - 9.15257i) q^{62} +(6.59605 - 8.41464i) q^{63} +(3.14922 - 7.35408i) q^{64} +(6.21515 + 8.22079i) q^{66} +2.04787 q^{67} +(1.53285 - 0.627812i) q^{68} +(-1.70156 + 0.828216i) q^{69} +11.3663 q^{71} +(0.692770 - 8.45695i) q^{72} +7.70156i q^{73} +(1.47585 + 7.49729i) q^{74} +(3.85078 + 9.40194i) q^{76} +14.9946 q^{77} +(5.27865 - 3.99080i) q^{78} -7.12785i q^{79} +(-2.14922 - 8.73961i) q^{81} +(-2.80590 - 14.2539i) q^{82} +3.11473i q^{83} +(-9.20732 - 8.22459i) q^{84} +(-0.737925 + 0.145261i) q^{86} +(8.64391 - 4.20732i) q^{87} +(9.93375 - 6.55234i) q^{88} +4.72212i q^{89} -9.62817i q^{91} +(0.828216 + 2.02214i) q^{92} +(-10.2725 + 5.00000i) q^{93} +(1.70156 + 8.64391i) q^{94} +(-9.69374 - 1.42528i) q^{96} +8.10469i q^{97} +(-7.91140 + 1.55737i) q^{98} +(7.78683 - 9.93375i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16q + 4q^{4} + 6q^{6} - 4q^{9} + O(q^{10}) \)	\( 16q + 4q^{4} + 6q^{6} - 4q^{9} + 20q^{16} + 8q^{21} - 26q^{24} - 44q^{34} - 42q^{36} - 56q^{46} + 40q^{49} + 56q^{54} - 40q^{61} + 76q^{64} + 58q^{66} + 24q^{69} + 36q^{76} - 60q^{81} - 80q^{84} - 24q^{94} - 78q^{96} + O(q^{100}) \)

Introduction

L-functions

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