LMFDB - Embedded newform 4598.2.a.cc.1.8

Newspace parameters

Level:	$ N $	$=$	$ 4598 = 2 \cdot 11^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4598.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	$36.7152148494$
Analytic rank:	$1$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
Defining polynomial:	$ x^{10} - 2x^{9} - 19x^{8} + 36x^{7} + 118x^{6} - 220x^{5} - 270x^{4} + 512x^{3} + 176x^{2} - 392x + 44 $ x^10 - 2x^9 - 19x^8 + 36x^7 + 118x^6 - 220x^5 - 270x^4 + 512x^3 + 176x^2 - 392*x + 44
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 418)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$2.10092$ of defining polynomial
Character	$\chi$	$=$	4598.1

$q$-expansion

$f(q)$	$=$	$q-1.00000 q^{2} +2.10092 q^{3} +1.00000 q^{4} +2.46005 q^{5} -2.10092 q^{6} -3.09995 q^{7} -1.00000 q^{8} +1.41386 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +2.10092 q^{3} +1.00000 q^{4} +2.46005 q^{5} -2.10092 q^{6} -3.09995 q^{7} -1.00000 q^{8} +1.41386 q^{9} -2.46005 q^{10} +2.10092 q^{12} -3.97832 q^{13} +3.09995 q^{14} +5.16836 q^{15} +1.00000 q^{16} -2.14576 q^{17} -1.41386 q^{18} -1.00000 q^{19} +2.46005 q^{20} -6.51275 q^{21} -2.55940 q^{23} -2.10092 q^{24} +1.05183 q^{25} +3.97832 q^{26} -3.33234 q^{27} -3.09995 q^{28} +6.50365 q^{29} -5.16836 q^{30} +1.48635 q^{31} -1.00000 q^{32} +2.14576 q^{34} -7.62603 q^{35} +1.41386 q^{36} -1.74921 q^{37} +1.00000 q^{38} -8.35814 q^{39} -2.46005 q^{40} +5.48529 q^{41} +6.51275 q^{42} +4.59472 q^{43} +3.47817 q^{45} +2.55940 q^{46} -3.40634 q^{47} +2.10092 q^{48} +2.60971 q^{49} -1.05183 q^{50} -4.50808 q^{51} -3.97832 q^{52} -11.7609 q^{53} +3.33234 q^{54} +3.09995 q^{56} -2.10092 q^{57} -6.50365 q^{58} -6.65028 q^{59} +5.16836 q^{60} -6.34059 q^{61} -1.48635 q^{62} -4.38291 q^{63} +1.00000 q^{64} -9.78686 q^{65} +14.1154 q^{67} -2.14576 q^{68} -5.37710 q^{69} +7.62603 q^{70} -15.9696 q^{71} -1.41386 q^{72} -3.17623 q^{73} +1.74921 q^{74} +2.20981 q^{75} -1.00000 q^{76} +8.35814 q^{78} +7.25669 q^{79} +2.46005 q^{80} -11.2426 q^{81} -5.48529 q^{82} +11.2166 q^{83} -6.51275 q^{84} -5.27868 q^{85} -4.59472 q^{86} +13.6636 q^{87} -4.63686 q^{89} -3.47817 q^{90} +12.3326 q^{91} -2.55940 q^{92} +3.12270 q^{93} +3.40634 q^{94} -2.46005 q^{95} -2.10092 q^{96} -5.47081 q^{97} -2.60971 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 10 q^{2} + 2 q^{3} + 10 q^{4} - 3 q^{5} - 2 q^{6} - 11 q^{7} - 10 q^{8} + 12 q^{9}+O(q^{10}) $ 10 * q - 10 * q^2 + 2 * q^3 + 10 * q^4 - 3 * q^5 - 2 * q^6 - 11 * q^7 - 10 * q^8 + 12 * q^9	$ 10 q - 10 q^{2} + 2 q^{3} + 10 q^{4} - 3 q^{5} - 2 q^{6} - 11 q^{7} - 10 q^{8} + 12 q^{9} + 3 q^{10} + 2 q^{12} - 11 q^{13} + 11 q^{14} + q^{15} + 10 q^{16} - 12 q^{17} - 12 q^{18} - 10 q^{19} - 3 q^{20} + q^{21} + 14 q^{23} - 2 q^{24} + 5 q^{25} + 11 q^{26} + 2 q^{27} - 11 q^{28} - 16 q^{29} - q^{30} + 12 q^{31} - 10 q^{32} + 12 q^{34} + 12 q^{35} + 12 q^{36} - q^{37} + 10 q^{38} - 11 q^{39} + 3 q^{40} + 5 q^{41} - q^{42} - 22 q^{43} - 2 q^{45} - 14 q^{46} + 8 q^{47} + 2 q^{48} - 3 q^{49} - 5 q^{50} - 8 q^{51} - 11 q^{52} + 2 q^{53} - 2 q^{54} + 11 q^{56} - 2 q^{57} + 16 q^{58} - 7 q^{59} + q^{60} - 35 q^{61} - 12 q^{62} - 38 q^{63} + 10 q^{64} - 4 q^{65} + 9 q^{67} - 12 q^{68} + 6 q^{69} - 12 q^{70} - 4 q^{71} - 12 q^{72} - 5 q^{73} + q^{74} - 15 q^{75} - 10 q^{76} + 11 q^{78} - 18 q^{79} - 3 q^{80} - 6 q^{81} - 5 q^{82} - 7 q^{83} + q^{84} - 35 q^{85} + 22 q^{86} - 8 q^{87} + 22 q^{89} + 2 q^{90} + 11 q^{91} + 14 q^{92} - 64 q^{93} - 8 q^{94} + 3 q^{95} - 2 q^{96} + 32 q^{97} + 3 q^{98}+O(q^{100}) $ 10 * q - 10 * q^2 + 2 * q^3 + 10 * q^4 - 3 * q^5 - 2 * q^6 - 11 * q^7 - 10 * q^8 + 12 * q^9 + 3 * q^10 + 2 * q^12 - 11 * q^13 + 11 * q^14 + q^15 + 10 * q^16 - 12 * q^17 - 12 * q^18 - 10 * q^19 - 3 * q^20 + q^21 + 14 * q^23 - 2 * q^24 + 5 * q^25 + 11 * q^26 + 2 * q^27 - 11 * q^28 - 16 * q^29 - q^30 + 12 * q^31 - 10 * q^32 + 12 * q^34 + 12 * q^35 + 12 * q^36 - q^37 + 10 * q^38 - 11 * q^39 + 3 * q^40 + 5 * q^41 - q^42 - 22 * q^43 - 2 * q^45 - 14 * q^46 + 8 * q^47 + 2 * q^48 - 3 * q^49 - 5 * q^50 - 8 * q^51 - 11 * q^52 + 2 * q^53 - 2 * q^54 + 11 * q^56 - 2 * q^57 + 16 * q^58 - 7 * q^59 + q^60 - 35 * q^61 - 12 * q^62 - 38 * q^63 + 10 * q^64 - 4 * q^65 + 9 * q^67 - 12 * q^68 + 6 * q^69 - 12 * q^70 - 4 * q^71 - 12 * q^72 - 5 * q^73 + q^74 - 15 * q^75 - 10 * q^76 + 11 * q^78 - 18 * q^79 - 3 * q^80 - 6 * q^81 - 5 * q^82 - 7 * q^83 + q^84 - 35 * q^85 + 22 * q^86 - 8 * q^87 + 22 * q^89 + 2 * q^90 + 11 * q^91 + 14 * q^92 - 64 * q^93 - 8 * q^94 + 3 * q^95 - 2 * q^96 + 32 * q^97 + 3 * q^98

Display 100 coefficients 10 coefficients

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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	2.10092	1.21297	0.606483	−	0.795096i	$-0.292580\pi$
$3$	2.10092	1.21297	0.606483	+	0.795096i	$0.292580\pi$
$4$	1.00000	0.500000
$5$	2.46005	1.10017	0.550083	−	0.835110i	$-0.314596\pi$
$5$	2.46005	1.10017	0.550083	+	0.835110i	$0.314596\pi$
$6$	−2.10092	−0.857697
$7$	−3.09995	−1.17167	−0.585836	−	0.810430i	$-0.699234\pi$
$7$	−3.09995	−1.17167	−0.585836	+	0.810430i	$0.699234\pi$
$8$	−1.00000	−0.353553
$9$	1.41386	0.471288
$10$	−2.46005	−0.777935
$11$	0	0
$11$	0	0
$12$	2.10092	0.606483
$13$	−3.97832	−1.10339	−0.551694	−	0.834047i	$-0.686018\pi$
$13$	−3.97832	−1.10339	−0.551694	+	0.834047i	$0.686018\pi$
$14$	3.09995	0.828497
$15$	5.16836	1.33447
$16$	1.00000	0.250000
$17$	−2.14576	−0.520424	−0.260212	−	0.965551i	$-0.583792\pi$
$17$	−2.14576	−0.520424	−0.260212	+	0.965551i	$0.583792\pi$
$18$	−1.41386	−0.333251
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	2.46005	0.550083
$21$	−6.51275	−1.42120
$22$	0	0
$23$	−2.55940	−0.533672	−0.266836	−	0.963742i	$-0.585978\pi$
$23$	−2.55940	−0.533672	−0.266836	+	0.963742i	$0.585978\pi$
$24$	−2.10092	−0.428848
$25$	1.05183	0.210366
$26$	3.97832	0.780213
$27$	−3.33234	−0.641310
$28$	−3.09995	−0.585836
$29$	6.50365	1.20770	0.603849	−	0.797099i	$-0.293633\pi$
$29$	6.50365	1.20770	0.603849	+	0.797099i	$0.293633\pi$
$30$	−5.16836	−0.943609
$31$	1.48635	0.266956	0.133478	−	0.991052i	$-0.457385\pi$
$31$	1.48635	0.266956	0.133478	+	0.991052i	$0.457385\pi$
$32$	−1.00000	−0.176777
$33$	0	0
$34$	2.14576	0.367995
$35$	−7.62603	−1.28903
$36$	1.41386	0.235644
$37$	−1.74921	−0.287569	−0.143784	−	0.989609i	$-0.545927\pi$
$37$	−1.74921	−0.287569	−0.143784	+	0.989609i	$0.545927\pi$
$38$	1.00000	0.162221
$39$	−8.35814	−1.33837
$40$	−2.46005	−0.388968
$41$	5.48529	0.856659	0.428329	−	0.903623i	$-0.359102\pi$
$41$	5.48529	0.856659	0.428329	+	0.903623i	$0.359102\pi$
$42$	6.51275	1.00494
$43$	4.59472	0.700689	0.350344	−	0.936621i	$-0.386065\pi$
$43$	4.59472	0.700689	0.350344	+	0.936621i	$0.386065\pi$
$44$	0	0
$45$	3.47817	0.518495
$46$	2.55940	0.377363
$47$	−3.40634	−0.496866	−0.248433	−	0.968649i	$-0.579916\pi$
$47$	−3.40634	−0.496866	−0.248433	+	0.968649i	$0.579916\pi$
$48$	2.10092	0.303242
$49$	2.60971	0.372815
$50$	−1.05183	−0.148751
$51$	−4.50808	−0.631257
$52$	−3.97832	−0.551694
$53$	−11.7609	−1.61548	−0.807742	−	0.589536i	$-0.799311\pi$
$53$	−11.7609	−1.61548	−0.807742	+	0.589536i	$0.799311\pi$
$54$	3.33234	0.453475
$55$	0	0
$56$	3.09995	0.414249
$57$	−2.10092	−0.278274
$58$	−6.50365	−0.853971
$59$	−6.65028	−0.865793	−0.432896	−	0.901444i	$-0.642508\pi$
$59$	−6.65028	−0.865793	−0.432896	+	0.901444i	$0.642508\pi$
$60$	5.16836	0.667233
$61$	−6.34059	−0.811829	−0.405915	−	0.913911i	$-0.633047\pi$
$61$	−6.34059	−0.811829	−0.405915	+	0.913911i	$0.633047\pi$
$62$	−1.48635	−0.188766
$63$	−4.38291	−0.552195
$64$	1.00000	0.125000
$65$	−9.78686	−1.21391
$66$	0	0
$67$	14.1154	1.72447	0.862236	−	0.506506i	$-0.169063\pi$
$67$	14.1154	1.72447	0.862236	+	0.506506i	$0.169063\pi$
$68$	−2.14576	−0.260212
$69$	−5.37710	−0.647326
$70$	7.62603	0.911485
$71$	−15.9696	−1.89524	−0.947619	−	0.319404i	$-0.896517\pi$
$71$	−15.9696	−1.89524	−0.947619	+	0.319404i	$0.896517\pi$
$72$	−1.41386	−0.166626
$73$	−3.17623	−0.371749	−0.185875	−	0.982573i	$-0.559512\pi$
$73$	−3.17623	−0.371749	−0.185875	+	0.982573i	$0.559512\pi$
$74$	1.74921	0.203342
$75$	2.20981	0.255167
$76$	−1.00000	−0.114708
$77$	0	0
$78$	8.35814	0.946373
$79$	7.25669	0.816442	0.408221	−	0.912883i	$-0.366149\pi$
$79$	7.25669	0.816442	0.408221	+	0.912883i	$0.366149\pi$
$80$	2.46005	0.275042
$81$	−11.2426	−1.24918
$82$	−5.48529	−0.605749
$83$	11.2166	1.23118	0.615588	−	0.788068i	$-0.288918\pi$
$83$	11.2166	1.23118	0.615588	+	0.788068i	$0.288918\pi$
$84$	−6.51275	−0.710600
$85$	−5.27868	−0.572553
$86$	−4.59472	−0.495462
$87$	13.6636	1.46490
$88$	0	0
$89$	−4.63686	−0.491506	−0.245753	−	0.969332i	$-0.579035\pi$
$89$	−4.63686	−0.491506	−0.245753	+	0.969332i	$0.579035\pi$
$90$	−3.47817	−0.366632
$91$	12.3326	1.29281
$92$	−2.55940	−0.266836
$93$	3.12270	0.323809
$94$	3.40634	0.351338
$95$	−2.46005	−0.252395
$96$	−2.10092	−0.214424
$97$	−5.47081	−0.555477	−0.277738	−	0.960657i	$-0.589585\pi$
$97$	−5.47081	−0.555477	−0.277738	+	0.960657i	$0.589585\pi$
$98$	−2.60971	−0.263620
$99$	0	0
$100$	1.05183	0.105183
$101$	−5.80492	−0.577611	−0.288806	−	0.957388i	$-0.593258\pi$
$101$	−5.80492	−0.577611	−0.288806	+	0.957388i	$0.593258\pi$
$102$	4.50808	0.446366
$103$	−9.56301	−0.942271	−0.471136	−	0.882061i	$-0.656156\pi$
$103$	−9.56301	−0.942271	−0.471136	+	0.882061i	$0.656156\pi$
$104$	3.97832	0.390107
$105$	−16.0217	−1.56356
$106$	11.7609	1.14232
$107$	−14.5663	−1.40818	−0.704090	−	0.710111i	$-0.748645\pi$
$107$	−14.5663	−1.40818	−0.704090	+	0.710111i	$0.748645\pi$
$108$	−3.33234	−0.320655
$109$	−3.38080	−0.323822	−0.161911	−	0.986805i	$-0.551766\pi$
$109$	−3.38080	−0.323822	−0.161911	+	0.986805i	$0.551766\pi$
$110$	0	0
$111$	−3.67496	−0.348811
$112$	−3.09995	−0.292918
$113$	11.3668	1.06930	0.534650	−	0.845074i	$-0.320444\pi$
$113$	11.3668	1.06930	0.534650	+	0.845074i	$0.320444\pi$
$114$	2.10092	0.196769
$115$	−6.29625	−0.587128
$116$	6.50365	0.603849
$117$	−5.62481	−0.520014
$118$	6.65028	0.612208
$119$	6.65177	0.609766
$120$	−5.16836	−0.471805
$121$	0	0
$122$	6.34059	0.574050
$123$	11.5242	1.03910
$124$	1.48635	0.133478
$125$	−9.71268	−0.868729
$126$	4.38291	0.390461
$127$	−13.3466	−1.18432	−0.592160	−	0.805820i	$-0.701725\pi$
$127$	−13.3466	−1.18432	−0.592160	+	0.805820i	$0.701725\pi$
$128$	−1.00000	−0.0883883
$129$	9.65314	0.849912
$130$	9.78686	0.858364
$131$	−4.58757	−0.400818	−0.200409	−	0.979712i	$-0.564227\pi$
$131$	−4.58757	−0.400818	−0.200409	+	0.979712i	$0.564227\pi$
$132$	0	0
$133$	3.09995	0.268800
$134$	−14.1154	−1.21939
$135$	−8.19772	−0.705548
$136$	2.14576	0.183998
$137$	−13.6371	−1.16509	−0.582546	−	0.812798i	$-0.697943\pi$
$137$	−13.6371	−1.16509	−0.582546	+	0.812798i	$0.697943\pi$
$138$	5.37710	0.457729
$139$	−5.78982	−0.491086	−0.245543	−	0.969386i	$-0.578966\pi$
$139$	−5.78982	−0.491086	−0.245543	+	0.969386i	$0.578966\pi$
$140$	−7.62603	−0.644517
$141$	−7.15646	−0.602682
$142$	15.9696	1.34014
$143$	0	0
$144$	1.41386	0.117822
$145$	15.9993	1.32867
$146$	3.17623	0.262866
$147$	5.48278	0.452212
$148$	−1.74921	−0.143784
$149$	−10.3503	−0.847926	−0.423963	−	0.905679i	$-0.639361\pi$
$149$	−10.3503	−0.847926	−0.423963	+	0.905679i	$0.639361\pi$
$150$	−2.20981	−0.180430
$151$	−12.1731	−0.990632	−0.495316	−	0.868713i	$-0.664948\pi$
$151$	−12.1731	−0.990632	−0.495316	+	0.868713i	$0.664948\pi$
$152$	1.00000	0.0811107
$153$	−3.03382	−0.245270
$154$	0	0
$155$	3.65649	0.293696
$156$	−8.35814	−0.669186
$157$	3.72389	0.297199	0.148599	−	0.988897i	$-0.452524\pi$
$157$	3.72389	0.297199	0.148599	+	0.988897i	$0.452524\pi$
$158$	−7.25669	−0.577312
$159$	−24.7087	−1.95953
$160$	−2.46005	−0.194484
$161$	7.93402	0.625289
$162$	11.2426	0.883301
$163$	−19.8920	−1.55806	−0.779032	−	0.626984i	$-0.784289\pi$
$163$	−19.8920	−1.55806	−0.779032	+	0.626984i	$0.784289\pi$
$164$	5.48529	0.428329
$165$	0	0
$166$	−11.2166	−0.870573
$167$	−21.9867	−1.70138	−0.850690	−	0.525667i	$-0.823816\pi$
$167$	−21.9867	−1.70138	−0.850690	+	0.525667i	$0.823816\pi$
$168$	6.51275	0.502470
$169$	2.82705	0.217465
$170$	5.27868	0.404856
$171$	−1.41386	−0.108121
$172$	4.59472	0.350344
$173$	−25.4819	−1.93735	−0.968675	−	0.248333i	$-0.920117\pi$
$173$	−25.4819	−1.93735	−0.968675	+	0.248333i	$0.920117\pi$
$174$	−13.6636	−1.03584
$175$	−3.26062	−0.246480
$176$	0	0
$177$	−13.9717	−1.05018
$178$	4.63686	0.347547
$179$	22.7884	1.70329	0.851643	−	0.524122i	$-0.175607\pi$
$179$	22.7884	1.70329	0.851643	+	0.524122i	$0.175607\pi$
$180$	3.47817	0.259248
$181$	−1.54547	−0.114874	−0.0574368	−	0.998349i	$-0.518293\pi$
$181$	−1.54547	−0.114874	−0.0574368	+	0.998349i	$0.518293\pi$
$182$	−12.3326	−0.914154
$183$	−13.3211	−0.984722
$184$	2.55940	0.188682
$185$	−4.30315	−0.316374
$186$	−3.12270	−0.228967
$187$	0	0
$188$	−3.40634	−0.248433
$189$	10.3301	0.751405
$190$	2.46005	0.178471
$191$	7.14404	0.516925	0.258462	−	0.966021i	$-0.416784\pi$
$191$	7.14404	0.516925	0.258462	+	0.966021i	$0.416784\pi$
$192$	2.10092	0.151621
$193$	−12.0980	−0.870833	−0.435417	−	0.900229i	$-0.643399\pi$
$193$	−12.0980	−0.870833	−0.435417	+	0.900229i	$0.643399\pi$
$194$	5.47081	0.392781
$195$	−20.5614	−1.47243
$196$	2.60971	0.186408
$197$	18.2516	1.30037	0.650186	−	0.759775i	$-0.274691\pi$
$197$	18.2516	1.30037	0.650186	+	0.759775i	$0.274691\pi$
$198$	0	0
$199$	23.9705	1.69923	0.849613	−	0.527406i	$-0.176835\pi$
$199$	23.9705	1.69923	0.849613	+	0.527406i	$0.176835\pi$
$200$	−1.05183	−0.0743756
$201$	29.6554	2.09173
$202$	5.80492	0.408433
$203$	−20.1610	−1.41503
$204$	−4.50808	−0.315629
$205$	13.4941	0.942467
$206$	9.56301	0.666286
$207$	−3.61865	−0.251513
$208$	−3.97832	−0.275847
$209$	0	0
$210$	16.0217	1.10560
$211$	20.7466	1.42826	0.714129	−	0.700015i	$-0.246823\pi$
$211$	20.7466	1.42826	0.714129	+	0.700015i	$0.246823\pi$
$212$	−11.7609	−0.807742
$213$	−33.5508	−2.29886
$214$	14.5663	0.995734
$215$	11.3032	0.770874
$216$	3.33234	0.226737
$217$	−4.60761	−0.312785
$218$	3.38080	0.228977
$219$	−6.67300	−0.450920
$220$	0	0
$221$	8.53654	0.574230
$222$	3.67496	0.246647
$223$	28.3845	1.90077	0.950384	−	0.311080i	$-0.100691\pi$
$223$	28.3845	1.90077	0.950384	+	0.311080i	$0.100691\pi$
$224$	3.09995	0.207124
$225$	1.48715	0.0991430
$226$	−11.3668	−0.756109
$227$	−8.50634	−0.564585	−0.282293	−	0.959328i	$-0.591095\pi$
$227$	−8.50634	−0.564585	−0.282293	+	0.959328i	$0.591095\pi$
$228$	−2.10092	−0.139137
$229$	−1.70730	−0.112822	−0.0564109	−	0.998408i	$-0.517966\pi$
$229$	−1.70730	−0.112822	−0.0564109	+	0.998408i	$0.517966\pi$
$230$	6.29625	0.415162
$231$	0	0
$232$	−6.50365	−0.426986
$233$	9.95632	0.652260	0.326130	−	0.945325i	$-0.394255\pi$
$233$	9.95632	0.652260	0.326130	+	0.945325i	$0.394255\pi$
$234$	5.62481	0.367705
$235$	−8.37977	−0.546636
$236$	−6.65028	−0.432896
$237$	15.2457	0.990317
$238$	−6.65177	−0.431170
$239$	16.2786	1.05297	0.526487	−	0.850183i	$-0.323509\pi$
$239$	16.2786	1.05297	0.526487	+	0.850183i	$0.323509\pi$
$240$	5.16836	0.333616
$241$	−5.95144	−0.383366	−0.191683	−	0.981457i	$-0.561395\pi$
$241$	−5.95144	−0.383366	−0.191683	+	0.981457i	$0.561395\pi$
$242$	0	0
$243$	−13.6227	−0.873899
$244$	−6.34059	−0.405915
$245$	6.42000	0.410159
$246$	−11.5242	−0.734753
$247$	3.97832	0.253135
$248$	−1.48635	−0.0943832
$249$	23.5651	1.49338
$250$	9.71268	0.614284
$251$	−21.0594	−1.32926	−0.664630	−	0.747173i	$-0.731411\pi$
$251$	−21.0594	−1.32926	−0.664630	+	0.747173i	$0.731411\pi$
$252$	−4.38291	−0.276098
$253$	0	0
$254$	13.3466	0.837441
$255$	−11.0901	−0.694488
$256$	1.00000	0.0625000
$257$	1.27738	0.0796811	0.0398405	−	0.999206i	$-0.487315\pi$
$257$	1.27738	0.0796811	0.0398405	+	0.999206i	$0.487315\pi$
$258$	−9.65314	−0.600978
$259$	5.42248	0.336936
$260$	−9.78686	−0.606955
$261$	9.19528	0.569174
$262$	4.58757	0.283421
$263$	8.85896	0.546267	0.273134	−	0.961976i	$-0.411940\pi$
$263$	8.85896	0.546267	0.273134	+	0.961976i	$0.411940\pi$
$264$	0	0
$265$	−28.9324	−1.77730
$266$	−3.09995	−0.190070
$267$	−9.74167	−0.596181
$268$	14.1154	0.862236
$269$	26.0234	1.58667	0.793337	−	0.608783i	$-0.208342\pi$
$269$	26.0234	1.58667	0.793337	+	0.608783i	$0.208342\pi$
$270$	8.19772	0.498897
$271$	17.0826	1.03770	0.518848	−	0.854867i	$-0.326361\pi$
$271$	17.0826	1.03770	0.518848	+	0.854867i	$0.326361\pi$
$272$	−2.14576	−0.130106
$273$	25.9098	1.56813
$274$	13.6371	0.823845
$275$	0	0
$276$	−5.37710	−0.323663
$277$	8.49406	0.510359	0.255179	−	0.966894i	$-0.417865\pi$
$277$	8.49406	0.510359	0.255179	+	0.966894i	$0.417865\pi$
$278$	5.78982	0.347251
$279$	2.10150	0.125813
$280$	7.62603	0.455742
$281$	29.4238	1.75527	0.877637	−	0.479325i	$-0.159119\pi$
$281$	29.4238	1.75527	0.877637	+	0.479325i	$0.159119\pi$
$282$	7.15646	0.426161
$283$	−17.0589	−1.01405	−0.507024	−	0.861932i	$-0.669255\pi$
$283$	−17.0589	−1.01405	−0.507024	+	0.861932i	$0.669255\pi$
$284$	−15.9696	−0.947619
$285$	−5.16836	−0.306147
$286$	0	0
$287$	−17.0041	−1.00372
$288$	−1.41386	−0.0833128
$289$	−12.3957	−0.729159
$290$	−15.9993	−0.939510
$291$	−11.4937	−0.673775
$292$	−3.17623	−0.185875
$293$	20.5142	1.19845	0.599227	−	0.800579i	$-0.295475\pi$
$293$	20.5142	1.19845	0.599227	+	0.800579i	$0.295475\pi$
$294$	−5.48278	−0.319762
$295$	−16.3600	−0.952516
$296$	1.74921	0.101671
$297$	0	0
$298$	10.3503	0.599575
$299$	10.1821	0.588847
$300$	2.20981	0.127584
$301$	−14.2434	−0.820977
$302$	12.1731	0.700483
$303$	−12.1957	−0.700623
$304$	−1.00000	−0.0573539
$305$	−15.5982	−0.893147
$306$	3.03382	0.173432
$307$	5.64603	0.322236	0.161118	−	0.986935i	$-0.448490\pi$
$307$	5.64603	0.322236	0.161118	+	0.986935i	$0.448490\pi$
$308$	0	0
$309$	−20.0911	−1.14294
$310$	−3.65649	−0.207674
$311$	8.41613	0.477235	0.238617	−	0.971114i	$-0.423306\pi$
$311$	8.41613	0.477235	0.238617	+	0.971114i	$0.423306\pi$
$312$	8.35814	0.473186
$313$	31.3766	1.77351	0.886756	−	0.462239i	$-0.152954\pi$
$313$	31.3766	1.77351	0.886756	+	0.462239i	$0.152954\pi$
$314$	−3.72389	−0.210151
$315$	−10.7822	−0.607507
$316$	7.25669	0.408221
$317$	7.20289	0.404555	0.202277	−	0.979328i	$-0.435166\pi$
$317$	7.20289	0.404555	0.202277	+	0.979328i	$0.435166\pi$
$318$	24.7087	1.38560
$319$	0	0
$320$	2.46005	0.137521
$321$	−30.6027	−1.70808
$322$	−7.93402	−0.442146
$323$	2.14576	0.119393
$324$	−11.2426	−0.624588
$325$	−4.18452	−0.232115
$326$	19.8920	1.10172
$327$	−7.10279	−0.392785
$328$	−5.48529	−0.302875
$329$	10.5595	0.582164
$330$	0	0
$331$	20.4083	1.12174	0.560870	−	0.827904i	$-0.310467\pi$
$331$	20.4083	1.12174	0.560870	+	0.827904i	$0.310467\pi$
$332$	11.2166	0.615588
$333$	−2.47315	−0.135528
$334$	21.9867	1.20306
$335$	34.7246	1.89721
$336$	−6.51275	−0.355300
$337$	−32.1119	−1.74925	−0.874623	−	0.484803i	$-0.838891\pi$
$337$	−32.1119	−1.74925	−0.874623	+	0.484803i	$0.838891\pi$
$338$	−2.82705	−0.153771
$339$	23.8807	1.29702
$340$	−5.27868	−0.286277
$341$	0	0
$342$	1.41386	0.0764530
$343$	13.6097	0.734855
$344$	−4.59472	−0.247731
$345$	−13.2279	−0.712167
$346$	25.4819	1.36991
$347$	1.12968	0.0606444	0.0303222	−	0.999540i	$-0.490347\pi$
$347$	1.12968	0.0606444	0.0303222	+	0.999540i	$0.490347\pi$
$348$	13.6636	0.732448
$349$	−21.1559	−1.13245	−0.566225	−	0.824251i	$-0.691597\pi$
$349$	−21.1559	−1.13245	−0.566225	+	0.824251i	$0.691597\pi$
$350$	3.26062	0.174288
$351$	13.2571	0.707614
$352$	0	0
$353$	−0.0272714	−0.00145151	−0.000725755	−	1.00000i	$-0.500231\pi$
$353$	−0.0272714	−0.00145151	−0.000725755		1.00000i	$0.500231\pi$
$354$	13.9717	0.742588
$355$	−39.2858	−2.08508
$356$	−4.63686	−0.245753
$357$	13.9748	0.739626
$358$	−22.7884	−1.20441
$359$	15.1154	0.797758	0.398879	−	0.917004i	$-0.369399\pi$
$359$	15.1154	0.797758	0.398879	+	0.917004i	$0.369399\pi$
$360$	−3.47817	−0.183316
$361$	1.00000	0.0526316
$362$	1.54547	0.0812279
$363$	0	0
$364$	12.3326	0.646404
$365$	−7.81367	−0.408986
$366$	13.3211	0.696304
$367$	21.4714	1.12080	0.560399	−	0.828223i	$-0.310648\pi$
$367$	21.4714	1.12080	0.560399	+	0.828223i	$0.310648\pi$
$368$	−2.55940	−0.133418
$369$	7.75546	0.403733
$370$	4.30315	0.223710
$371$	36.4582	1.89282
$372$	3.12270	0.161904
$373$	−18.3417	−0.949697	−0.474848	−	0.880068i	$-0.657497\pi$
$373$	−18.3417	−0.949697	−0.474848	+	0.880068i	$0.657497\pi$
$374$	0	0
$375$	−20.4056	−1.05374
$376$	3.40634	0.175669
$377$	−25.8736	−1.33256
$378$	−10.3301	−0.531323
$379$	12.3232	0.633003	0.316501	−	0.948592i	$-0.397492\pi$
$379$	12.3232	0.633003	0.316501	+	0.948592i	$0.397492\pi$
$380$	−2.46005	−0.126198
$381$	−28.0402	−1.43654
$382$	−7.14404	−0.365521
$383$	28.7507	1.46909	0.734546	−	0.678558i	$-0.237395\pi$
$383$	28.7507	1.46909	0.734546	+	0.678558i	$0.237395\pi$
$384$	−2.10092	−0.107212
$385$	0	0
$386$	12.0980	0.615772
$387$	6.49631	0.330226
$388$	−5.47081	−0.277738
$389$	2.72988	0.138410	0.0692052	−	0.997602i	$-0.477954\pi$
$389$	2.72988	0.138410	0.0692052	+	0.997602i	$0.477954\pi$
$390$	20.5614	1.04117
$391$	5.49187	0.277736
$392$	−2.60971	−0.131810
$393$	−9.63812	−0.486179
$394$	−18.2516	−0.919502
$395$	17.8518	0.898222
$396$	0	0
$397$	7.21330	0.362025	0.181013	−	0.983481i	$-0.442062\pi$
$397$	7.21330	0.362025	0.181013	+	0.983481i	$0.442062\pi$
$398$	−23.9705	−1.20153
$399$	6.51275	0.326045
$400$	1.05183	0.0525915
$401$	−1.18981	−0.0594164	−0.0297082	−	0.999559i	$-0.509458\pi$
$401$	−1.18981	−0.0594164	−0.0297082	+	0.999559i	$0.509458\pi$
$402$	−29.6554	−1.47908
$403$	−5.91317	−0.294556
$404$	−5.80492	−0.288806
$405$	−27.6573	−1.37430
$406$	20.1610	1.00057
$407$	0	0
$408$	4.50808	0.223183
$409$	11.7792	0.582442	0.291221	−	0.956656i	$-0.405939\pi$
$409$	11.7792	0.582442	0.291221	+	0.956656i	$0.405939\pi$
$410$	−13.4941	−0.666425
$411$	−28.6504	−1.41322
$412$	−9.56301	−0.471136
$413$	20.6156	1.01443
$414$	3.61865	0.177847
$415$	27.5932	1.35450
$416$	3.97832	0.195053
$417$	−12.1640	−0.595672
$418$	0	0
$419$	20.0798	0.980963	0.490482	−	0.871452i	$-0.336821\pi$
$419$	20.0798	0.980963	0.490482	+	0.871452i	$0.336821\pi$
$420$	−16.0217	−0.781778
$421$	0.885182	0.0431412	0.0215706	−	0.999767i	$-0.493133\pi$
$421$	0.885182	0.0431412	0.0215706	+	0.999767i	$0.493133\pi$
$422$	−20.7466	−1.00993
$423$	−4.81611	−0.234167
$424$	11.7609	0.571160
$425$	−2.25698	−0.109480
$426$	33.5508	1.62554
$427$	19.6555	0.951198
$428$	−14.5663	−0.704090
$429$	0	0
$430$	−11.3032	−0.545090
$431$	−20.3046	−0.978038	−0.489019	−	0.872273i	$-0.662645\pi$
$431$	−20.3046	−0.978038	−0.489019	+	0.872273i	$0.662645\pi$
$432$	−3.33234	−0.160327
$433$	−36.1713	−1.73828	−0.869140	−	0.494566i	$-0.835327\pi$
$433$	−36.1713	−1.73828	−0.869140	+	0.494566i	$0.835327\pi$
$434$	4.60761	0.221172
$435$	33.6132	1.61163
$436$	−3.38080	−0.161911
$437$	2.55940	0.122433
$438$	6.67300	0.318848
$439$	21.4914	1.02573	0.512864	−	0.858470i	$-0.328584\pi$
$439$	21.4914	1.02573	0.512864	+	0.858470i	$0.328584\pi$
$440$	0	0
$441$	3.68977	0.175703
$442$	−8.53654	−0.406042
$443$	−24.5995	−1.16876	−0.584379	−	0.811481i	$-0.698662\pi$
$443$	−24.5995	−1.16876	−0.584379	+	0.811481i	$0.698662\pi$
$444$	−3.67496	−0.174406
$445$	−11.4069	−0.540739
$446$	−28.3845	−1.34405
$447$	−21.7451	−1.02851
$448$	−3.09995	−0.146459
$449$	35.2701	1.66450	0.832251	−	0.554400i	$-0.187052\pi$
$449$	35.2701	1.66450	0.832251	+	0.554400i	$0.187052\pi$
$450$	−1.48715	−0.0701047
$451$	0	0
$452$	11.3668	0.534650
$453$	−25.5747	−1.20160
$454$	8.50634	0.399222
$455$	30.3388	1.42230
$456$	2.10092	0.0983846
$457$	−7.37055	−0.344780	−0.172390	−	0.985029i	$-0.555149\pi$
$457$	−7.37055	−0.344780	−0.172390	+	0.985029i	$0.555149\pi$
$458$	1.70730	0.0797770
$459$	7.15042	0.333753
$460$	−6.29625	−0.293564
$461$	−36.4875	−1.69939	−0.849696	−	0.527272i	$-0.823215\pi$
$461$	−36.4875	−1.69939	−0.849696	+	0.527272i	$0.823215\pi$
$462$	0	0
$463$	−16.2208	−0.753844	−0.376922	−	0.926245i	$-0.623018\pi$
$463$	−16.2208	−0.753844	−0.376922	+	0.926245i	$0.623018\pi$
$464$	6.50365	0.301924
$465$	7.68199	0.356244
$466$	−9.95632	−0.461217
$467$	4.27354	0.197756	0.0988779	−	0.995100i	$-0.468475\pi$
$467$	4.27354	0.197756	0.0988779	+	0.995100i	$0.468475\pi$
$468$	−5.62481	−0.260007
$469$	−43.7571	−2.02052
$470$	8.37977	0.386530
$471$	7.82359	0.360492
$472$	6.65028	0.306104
$473$	0	0
$474$	−15.2457	−0.700260
$475$	−1.05183	−0.0482613
$476$	6.65177	0.304883
$477$	−16.6283	−0.761359
$478$	−16.2786	−0.744564
$479$	−39.1936	−1.79080	−0.895402	−	0.445260i	$-0.853111\pi$
$479$	−39.1936	−1.79080	−0.895402	+	0.445260i	$0.853111\pi$
$480$	−5.16836	−0.235902
$481$	6.95893	0.317300
$482$	5.95144	0.271081
$483$	16.6687	0.758454
$484$	0	0
$485$	−13.4585	−0.611117
$486$	13.6227	0.617940
$487$	3.27438	0.148376	0.0741882	−	0.997244i	$-0.476363\pi$
$487$	3.27438	0.148376	0.0741882	+	0.997244i	$0.476363\pi$
$488$	6.34059	0.287025
$489$	−41.7916	−1.88988
$490$	−6.42000	−0.290026
$491$	40.6503	1.83452	0.917260	−	0.398288i	$-0.130396\pi$
$491$	40.6503	1.83452	0.917260	+	0.398288i	$0.130396\pi$
$492$	11.5242	0.519549
$493$	−13.9553	−0.628515
$494$	−3.97832	−0.178993
$495$	0	0
$496$	1.48635	0.0667390
$497$	49.5049	2.22060
$498$	−23.5651	−1.05598
$499$	−14.1445	−0.633195	−0.316598	−	0.948560i	$-0.602540\pi$
$499$	−14.1445	−0.633195	−0.316598	+	0.948560i	$0.602540\pi$
$500$	−9.71268	−0.434364
$501$	−46.1923	−2.06372
$502$	21.0594	0.939928
$503$	−27.7402	−1.23688	−0.618438	−	0.785834i	$-0.712234\pi$
$503$	−27.7402	−1.23688	−0.618438	+	0.785834i	$0.712234\pi$
$504$	4.38291	0.195230
$505$	−14.2804	−0.635468
$506$	0	0
$507$	5.93940	0.263778
$508$	−13.3466	−0.592160
$509$	4.86817	0.215778	0.107889	−	0.994163i	$-0.465591\pi$
$509$	4.86817	0.215778	0.107889	+	0.994163i	$0.465591\pi$
$510$	11.0901	0.491077
$511$	9.84616	0.435568
$512$	−1.00000	−0.0441942
$513$	3.33234	0.147127
$514$	−1.27738	−0.0563430
$515$	−23.5254	−1.03666
$516$	9.65314	0.424956
$517$	0	0
$518$	−5.42248	−0.238250
$519$	−53.5353	−2.34994
$520$	9.78686	0.429182
$521$	18.6548	0.817281	0.408641	−	0.912695i	$-0.366003\pi$
$521$	18.6548	0.817281	0.408641	+	0.912695i	$0.366003\pi$
$522$	−9.19528	−0.402466
$523$	−8.39239	−0.366974	−0.183487	−	0.983022i	$-0.558738\pi$
$523$	−8.39239	−0.366974	−0.183487	+	0.983022i	$0.558738\pi$
$524$	−4.58757	−0.200409
$525$	−6.85031	−0.298972
$526$	−8.85896	−0.386269
$527$	−3.18935	−0.138930
$528$	0	0
$529$	−16.4495	−0.715194
$530$	28.9324	1.25674
$531$	−9.40259	−0.408038
$532$	3.09995	0.134400
$533$	−21.8223	−0.945227
$534$	9.74167	0.421563
$535$	−35.8338	−1.54923
$536$	−14.1154	−0.609693
$537$	47.8766	2.06603
$538$	−26.0234	−1.12195
$539$	0	0
$540$	−8.19772	−0.352774
$541$	−32.0199	−1.37664	−0.688322	−	0.725405i	$-0.741653\pi$
$541$	−32.0199	−1.37664	−0.688322	+	0.725405i	$0.741653\pi$
$542$	−17.0826	−0.733762
$543$	−3.24690	−0.139338
$544$	2.14576	0.0919989
$545$	−8.31693	−0.356258
$546$	−25.9098	−1.10884
$547$	25.7176	1.09961	0.549803	−	0.835295i	$-0.314703\pi$
$547$	25.7176	1.09961	0.549803	+	0.835295i	$0.314703\pi$
$548$	−13.6371	−0.582546
$549$	−8.96474	−0.382606
$550$	0	0
$551$	−6.50365	−0.277065
$552$	5.37710	0.228864
$553$	−22.4954	−0.956602
$554$	−8.49406	−0.360878
$555$	−9.04057	−0.383751
$556$	−5.78982	−0.245543
$557$	37.3111	1.58092	0.790461	−	0.612512i	$-0.209841\pi$
$557$	37.3111	1.58092	0.790461	+	0.612512i	$0.209841\pi$
$558$	−2.10150	−0.0889634
$559$	−18.2793	−0.773131
$560$	−7.62603	−0.322259
$561$	0	0
$562$	−29.4238	−1.24117
$563$	0.758990	0.0319876	0.0159938	−	0.999872i	$-0.494909\pi$
$563$	0.758990	0.0319876	0.0159938	+	0.999872i	$0.494909\pi$
$564$	−7.15646	−0.301341
$565$	27.9629	1.17641
$566$	17.0589	0.717041
$567$	34.8515	1.46362
$568$	15.9696	0.670068
$569$	−31.2487	−1.31001	−0.655007	−	0.755623i	$-0.727334\pi$
$569$	−31.2487	−1.31001	−0.655007	+	0.755623i	$0.727334\pi$
$570$	5.16836	0.216479
$571$	−20.5848	−0.861445	−0.430723	−	0.902484i	$-0.641741\pi$
$571$	−20.5848	−0.861445	−0.430723	+	0.902484i	$0.641741\pi$
$572$	0	0
$573$	15.0091	0.627012
$574$	17.0041	0.709739
$575$	−2.69206	−0.112267
$576$	1.41386	0.0589110
$577$	12.5133	0.520934	0.260467	−	0.965483i	$-0.416124\pi$
$577$	12.5133	0.520934	0.260467	+	0.965483i	$0.416124\pi$
$578$	12.3957	0.515593
$579$	−25.4169	−1.05629
$580$	15.9993	0.664334
$581$	−34.7708	−1.44254
$582$	11.4937	0.476431
$583$	0	0
$584$	3.17623	0.131433
$585$	−13.8373	−0.572102
$586$	−20.5142	−0.847435
$587$	12.0214	0.496178	0.248089	−	0.968737i	$-0.420197\pi$
$587$	12.0214	0.496178	0.248089	+	0.968737i	$0.420197\pi$
$588$	5.48278	0.226106
$589$	−1.48635	−0.0612439
$590$	16.3600	0.673531
$591$	38.3451	1.57731
$592$	−1.74921	−0.0718922
$593$	−33.2839	−1.36680	−0.683402	−	0.730042i	$-0.739500\pi$
$593$	−33.2839	−1.36680	−0.683402	+	0.730042i	$0.739500\pi$
$594$	0	0
$595$	16.3637	0.670844
$596$	−10.3503	−0.423963
$597$	50.3602	2.06110
$598$	−10.1821	−0.416378
$599$	−14.8580	−0.607081	−0.303541	−	0.952819i	$-0.598169\pi$
$599$	−14.8580	−0.607081	−0.303541	+	0.952819i	$0.598169\pi$
$600$	−2.20981	−0.0902152
$601$	30.9531	1.26260	0.631301	−	0.775538i	$-0.282521\pi$
$601$	30.9531	1.26260	0.631301	+	0.775538i	$0.282521\pi$
$602$	14.2434	0.580518
$603$	19.9573	0.812724
$604$	−12.1731	−0.495316
$605$	0	0
$606$	12.1957	0.495415
$607$	29.4283	1.19446	0.597229	−	0.802071i	$-0.296268\pi$
$607$	29.4283	1.19446	0.597229	+	0.802071i	$0.296268\pi$
$608$	1.00000	0.0405554
$609$	−42.3567	−1.71638
$610$	15.5982	0.631551
$611$	13.5515	0.548236
$612$	−3.03382	−0.122635
$613$	21.5787	0.871554	0.435777	−	0.900055i	$-0.356474\pi$
$613$	21.5787	0.871554	0.435777	+	0.900055i	$0.356474\pi$
$614$	−5.64603	−0.227855
$615$	28.3500	1.14318
$616$	0	0
$617$	−21.8270	−0.878721	−0.439360	−	0.898311i	$-0.644795\pi$
$617$	−21.8270	−0.878721	−0.439360	+	0.898311i	$0.644795\pi$
$618$	20.0911	0.808183
$619$	41.5379	1.66955	0.834775	−	0.550592i	$-0.185598\pi$
$619$	41.5379	1.66955	0.834775	+	0.550592i	$0.185598\pi$
$620$	3.65649	0.146848
$621$	8.52881	0.342249
$622$	−8.41613	−0.337456
$623$	14.3740	0.575884
$624$	−8.35814	−0.334593
$625$	−29.1528	−1.16611
$626$	−31.3766	−1.25406
$627$	0	0
$628$	3.72389	0.148599
$629$	3.75340	0.149658
$630$	10.7822	0.429572
$631$	1.40462	0.0559171	0.0279585	−	0.999609i	$-0.491099\pi$
$631$	1.40462	0.0559171	0.0279585	+	0.999609i	$0.491099\pi$
$632$	−7.25669	−0.288656
$633$	43.5870	1.73243
$634$	−7.20289	−0.286063
$635$	−32.8333	−1.30295
$636$	−24.7087	−0.979765
$637$	−10.3822	−0.411360
$638$	0	0
$639$	−22.5788	−0.893203
$640$	−2.46005	−0.0972419
$641$	−12.6801	−0.500832	−0.250416	−	0.968138i	$-0.580567\pi$
$641$	−12.6801	−0.500832	−0.250416	+	0.968138i	$0.580567\pi$
$642$	30.6027	1.20779
$643$	4.42309	0.174429	0.0872147	−	0.996190i	$-0.472203\pi$
$643$	4.42309	0.174429	0.0872147	+	0.996190i	$0.472203\pi$
$644$	7.93402	0.312644
$645$	23.7472	0.935044
$646$	−2.14576	−0.0844239
$647$	−24.5901	−0.966736	−0.483368	−	0.875417i	$-0.660587\pi$
$647$	−24.5901	−0.966736	−0.483368	+	0.875417i	$0.660587\pi$
$648$	11.2426	0.441650
$649$	0	0
$650$	4.18452	0.164130
$651$	−9.68022	−0.379398
$652$	−19.8920	−0.779032
$653$	19.5368	0.764533	0.382267	−	0.924052i	$-0.375144\pi$
$653$	19.5368	0.764533	0.382267	+	0.924052i	$0.375144\pi$
$654$	7.10279	0.277741
$655$	−11.2856	−0.440967
$656$	5.48529	0.214165
$657$	−4.49076	−0.175201
$658$	−10.5595	−0.411652
$659$	35.3980	1.37891	0.689456	−	0.724328i	$-0.257850\pi$
$659$	35.3980	1.37891	0.689456	+	0.724328i	$0.257850\pi$
$660$	0	0
$661$	−26.3898	−1.02644	−0.513222	−	0.858256i	$-0.671548\pi$
$661$	−26.3898	−1.02644	−0.513222	+	0.858256i	$0.671548\pi$
$662$	−20.4083	−0.793190
$663$	17.9346	0.696522
$664$	−11.2166	−0.435287
$665$	7.62603	0.295725
$666$	2.47315	0.0958326
$667$	−16.6455	−0.644514
$668$	−21.9867	−0.850690
$669$	59.6336	2.30557
$670$	−34.7246	−1.34153
$671$	0	0
$672$	6.51275	0.251235
$673$	−4.02795	−0.155266	−0.0776331	−	0.996982i	$-0.524736\pi$
$673$	−4.02795	−0.155266	−0.0776331	+	0.996982i	$0.524736\pi$
$674$	32.1119	1.23690
$675$	−3.50506	−0.134910
$676$	2.82705	0.108733
$677$	21.6069	0.830419	0.415210	−	0.909726i	$-0.363708\pi$
$677$	21.6069	0.830419	0.415210	+	0.909726i	$0.363708\pi$
$678$	−23.8807	−0.917135
$679$	16.9593	0.650837
$680$	5.27868	0.202428
$681$	−17.8711	−0.684823
$682$	0	0
$683$	3.73163	0.142787	0.0713935	−	0.997448i	$-0.477255\pi$
$683$	3.73163	0.142787	0.0713935	+	0.997448i	$0.477255\pi$
$684$	−1.41386	−0.0540605
$685$	−33.5478	−1.28180
$686$	−13.6097	−0.519621
$687$	−3.58691	−0.136849
$688$	4.59472	0.175172
$689$	46.7887	1.78251
$690$	13.2279	0.503578
$691$	42.4147	1.61353	0.806765	−	0.590872i	$-0.201216\pi$
$691$	42.4147	1.61353	0.806765	+	0.590872i	$0.201216\pi$
$692$	−25.4819	−0.968675
$693$	0	0
$694$	−1.12968	−0.0428820
$695$	−14.2432	−0.540277
$696$	−13.6636	−0.517919
$697$	−11.7701	−0.445826
$698$	21.1559	0.800763
$699$	20.9174	0.791170
$700$	−3.26062	−0.123240
$701$	−51.9082	−1.96054	−0.980272	−	0.197654i	$-0.936668\pi$
$701$	−51.9082	−1.96054	−0.980272	+	0.197654i	$0.936668\pi$
$702$	−13.2571	−0.500358
$703$	1.74921	0.0659728
$704$	0	0
$705$	−17.6052	−0.663051
$706$	0.0272714	0.00102637
$707$	17.9950	0.676771
$708$	−13.9717	−0.525089
$709$	−42.1161	−1.58170	−0.790852	−	0.612008i	$-0.790362\pi$
$709$	−42.1161	−1.58170	−0.790852	+	0.612008i	$0.790362\pi$
$710$	39.2858	1.47437
$711$	10.2600	0.384779
$712$	4.63686	0.173774
$713$	−3.80416	−0.142467
$714$	−13.9748	−0.522995
$715$	0	0
$716$	22.7884	0.851643
$717$	34.2000	1.27722
$718$	−15.1154	−0.564100
$719$	−6.37162	−0.237621	−0.118811	−	0.992917i	$-0.537908\pi$
$719$	−6.37162	−0.237621	−0.118811	+	0.992917i	$0.537908\pi$
$720$	3.47817	0.129624
$721$	29.6449	1.10403
$722$	−1.00000	−0.0372161
$723$	−12.5035	−0.465010
$724$	−1.54547	−0.0574368
$725$	6.84074	0.254059
$726$	0	0
$727$	−36.8358	−1.36616	−0.683082	−	0.730342i	$-0.739361\pi$
$727$	−36.8358	−1.36616	−0.683082	+	0.730342i	$0.739361\pi$
$728$	−12.3326	−0.457077
$729$	5.10748	0.189166
$730$	7.81367	0.289197
$731$	−9.85919	−0.364655
$732$	−13.3211	−0.492361
$733$	−7.23710	−0.267308	−0.133654	−	0.991028i	$-0.542671\pi$
$733$	−7.23710	−0.267308	−0.133654	+	0.991028i	$0.542671\pi$
$734$	−21.4714	−0.792524
$735$	13.4879	0.497509
$736$	2.55940	0.0943408
$737$	0	0
$738$	−7.75546	−0.285482
$739$	19.6497	0.722825	0.361413	−	0.932406i	$-0.382295\pi$
$739$	19.6497	0.722825	0.361413	+	0.932406i	$0.382295\pi$
$740$	−4.30315	−0.158187
$741$	8.35814	0.307044
$742$	−36.4582	−1.33842
$743$	7.72331	0.283341	0.141670	−	0.989914i	$-0.454753\pi$
$743$	7.72331	0.283341	0.141670	+	0.989914i	$0.454753\pi$
$744$	−3.12270	−0.114484
$745$	−25.4621	−0.932860
$746$	18.3417	0.671537
$747$	15.8587	0.580239
$748$	0	0
$749$	45.1549	1.64992
$750$	20.4056	0.745106
$751$	−45.4390	−1.65809	−0.829046	−	0.559181i	$-0.811116\pi$
$751$	−45.4390	−1.65809	−0.829046	+	0.559181i	$0.811116\pi$
$752$	−3.40634	−0.124217
$753$	−44.2442	−1.61235
$754$	25.8736	0.942261
$755$	−29.9464	−1.08986
$756$	10.3301	0.375702
$757$	−0.394649	−0.0143438	−0.00717189	−	0.999974i	$-0.502283\pi$
$757$	−0.394649	−0.0143438	−0.00717189	+	0.999974i	$0.502283\pi$
$758$	−12.3232	−0.447601
$759$	0	0
$760$	2.46005	0.0892353
$761$	37.5003	1.35938	0.679692	−	0.733498i	$-0.262114\pi$
$761$	37.5003	1.35938	0.679692	+	0.733498i	$0.262114\pi$
$762$	28.0402	1.01579
$763$	10.4803	0.379413
$764$	7.14404	0.258462
$765$	−7.46334	−0.269838
$766$	−28.7507	−1.03881
$767$	26.4570	0.955305
$768$	2.10092	0.0758104
$769$	0.388213	0.0139993	0.00699965	−	0.999976i	$-0.497772\pi$
$769$	0.388213	0.0139993	0.00699965	+	0.999976i	$0.497772\pi$
$770$	0	0
$771$	2.68368	0.0966505
$772$	−12.0980	−0.435417
$773$	−32.5057	−1.16915	−0.584574	−	0.811341i	$-0.698738\pi$
$773$	−32.5057	−1.16915	−0.584574	+	0.811341i	$0.698738\pi$
$774$	−6.49631	−0.233505
$775$	1.56339	0.0561585
$776$	5.47081	0.196391
$777$	11.3922	0.408693
$778$	−2.72988	−0.0978709
$779$	−5.48529	−0.196531
$780$	−20.5614	−0.736216
$781$	0	0
$782$	−5.49187	−0.196389
$783$	−21.6724	−0.774508
$784$	2.60971	0.0932038
$785$	9.16094	0.326968
$786$	9.63812	0.343781
$787$	−11.8225	−0.421425	−0.210713	−	0.977548i	$-0.567578\pi$
$787$	−11.8225	−0.421425	−0.210713	+	0.977548i	$0.567578\pi$
$788$	18.2516	0.650186
$789$	18.6120	0.662604
$790$	−17.8518	−0.635139
$791$	−35.2366	−1.25287
$792$	0	0
$793$	25.2249	0.895763
$794$	−7.21330	−0.255991
$795$	−60.7846	−2.15581
$796$	23.9705	0.849613
$797$	27.4045	0.970719	0.485359	−	0.874315i	$-0.338689\pi$
$797$	27.4045	0.970719	0.485359	+	0.874315i	$0.338689\pi$
$798$	−6.51275	−0.230549
$799$	7.30921	0.258581
$800$	−1.05183	−0.0371878
$801$	−6.55589	−0.231641
$802$	1.18981	0.0420137
$803$	0	0
$804$	29.6554	1.04586
$805$	19.5181	0.687922
$806$	5.91317	0.208283
$807$	54.6731	1.92458
$808$	5.80492	0.204216
$809$	9.23218	0.324586	0.162293	−	0.986743i	$-0.448111\pi$
$809$	9.23218	0.324586	0.162293	+	0.986743i	$0.448111\pi$
$810$	27.6573	0.971778
$811$	−28.3825	−0.996646	−0.498323	−	0.866992i	$-0.666051\pi$
$811$	−28.3825	−0.996646	−0.498323	+	0.866992i	$0.666051\pi$
$812$	−20.1610	−0.707513
$813$	35.8892	1.25869
$814$	0	0
$815$	−48.9353	−1.71413
$816$	−4.50808	−0.157814
$817$	−4.59472	−0.160749
$818$	−11.7792	−0.411849
$819$	17.4366	0.609285
$820$	13.4941	0.471233
$821$	29.3170	1.02317	0.511584	−	0.859233i	$-0.329059\pi$
$821$	29.3170	1.02317	0.511584	+	0.859233i	$0.329059\pi$
$822$	28.6504	0.999296
$823$	−19.1547	−0.667692	−0.333846	−	0.942628i	$-0.608347\pi$
$823$	−19.1547	−0.667692	−0.333846	+	0.942628i	$0.608347\pi$
$824$	9.56301	0.333143
$825$	0	0
$826$	−20.6156	−0.717307
$827$	−19.0633	−0.662896	−0.331448	−	0.943473i	$-0.607537\pi$
$827$	−19.0633	−0.662896	−0.331448	+	0.943473i	$0.607537\pi$
$828$	−3.61865	−0.125757
$829$	−3.45420	−0.119969	−0.0599847	−	0.998199i	$-0.519105\pi$
$829$	−3.45420	−0.119969	−0.0599847	+	0.998199i	$0.519105\pi$
$830$	−27.5932	−0.957775
$831$	17.8453	0.619048
$832$	−3.97832	−0.137923
$833$	−5.59981	−0.194022
$834$	12.1640	0.421203
$835$	−54.0883	−1.87180
$836$	0	0
$837$	−4.95302	−0.171202
$838$	−20.0798	−0.693646
$839$	16.7961	0.579865	0.289932	−	0.957047i	$-0.406367\pi$
$839$	16.7961	0.579865	0.289932	+	0.957047i	$0.406367\pi$
$840$	16.0217	0.552800
$841$	13.2975	0.458533
$842$	−0.885182	−0.0305054
$843$	61.8170	2.12909
$844$	20.7466	0.714129
$845$	6.95466	0.239248
$846$	4.81611	0.165581
$847$	0	0
$848$	−11.7609	−0.403871
$849$	−35.8395	−1.23001
$850$	2.25698	0.0774138
$851$	4.47694	0.153467
$852$	−33.5508	−1.14943
$853$	−5.53724	−0.189592	−0.0947958	−	0.995497i	$-0.530220\pi$
$853$	−5.53724	−0.189592	−0.0947958	+	0.995497i	$0.530220\pi$
$854$	−19.6555	−0.672598
$855$	−3.47817	−0.118951
$856$	14.5663	0.497867
$857$	26.5793	0.907932	0.453966	−	0.891019i	$-0.350009\pi$
$857$	26.5793	0.907932	0.453966	+	0.891019i	$0.350009\pi$
$858$	0	0
$859$	19.7426	0.673610	0.336805	−	0.941574i	$-0.390654\pi$
$859$	19.7426	0.673610	0.336805	+	0.941574i	$0.390654\pi$
$860$	11.3032	0.385437
$861$	−35.7243	−1.21748
$862$	20.3046	0.691577
$863$	−22.8417	−0.777539	−0.388770	−	0.921335i	$-0.627100\pi$
$863$	−22.8417	−0.777539	−0.388770	+	0.921335i	$0.627100\pi$
$864$	3.33234	0.113369
$865$	−62.6866	−2.13141
$866$	36.1713	1.22915
$867$	−26.0424	−0.884445
$868$	−4.60761	−0.156392
$869$	0	0
$870$	−33.6132	−1.13959
$871$	−56.1557	−1.90276
$872$	3.38080	0.114488
$873$	−7.73499	−0.261790
$874$	−2.55940	−0.0865730
$875$	30.1089	1.01787
$876$	−6.67300	−0.225460
$877$	39.1209	1.32102	0.660510	−	0.750817i	$-0.270340\pi$
$877$	39.1209	1.32102	0.660510	+	0.750817i	$0.270340\pi$
$878$	−21.4914	−0.725300
$879$	43.0987	1.45368
$880$	0	0
$881$	39.7517	1.33927	0.669635	−	0.742691i	$-0.266451\pi$
$881$	39.7517	1.33927	0.669635	+	0.742691i	$0.266451\pi$
$882$	−3.68977	−0.124241
$883$	−24.1017	−0.811088	−0.405544	−	0.914075i	$-0.632918\pi$
$883$	−24.1017	−0.811088	−0.405544	+	0.914075i	$0.632918\pi$
$884$	8.53654	0.287115
$885$	−34.3710	−1.15537
$886$	24.5995	0.826437
$887$	−40.9484	−1.37491	−0.687457	−	0.726225i	$-0.741273\pi$
$887$	−40.9484	−1.37491	−0.687457	+	0.726225i	$0.741273\pi$
$888$	3.67496	0.123323
$889$	41.3739	1.38764
$890$	11.4069	0.382360
$891$	0	0
$892$	28.3845	0.950384
$893$	3.40634	0.113989
$894$	21.7451	0.727264
$895$	56.0606	1.87390
$896$	3.09995	0.103562
$897$	21.3918	0.714252
$898$	−35.2701	−1.17698
$899$	9.66669	0.322402
$900$	1.48715	0.0495715
$901$	25.2361	0.840737
$902$	0	0
$903$	−29.9243	−0.995818
$904$	−11.3668	−0.378054
$905$	−3.80192	−0.126380
$906$	25.5747	0.849662
$907$	−54.8992	−1.82290	−0.911449	−	0.411413i	$-0.865035\pi$
$907$	−54.8992	−1.82290	−0.911449	+	0.411413i	$0.865035\pi$
$908$	−8.50634	−0.282293
$909$	−8.20737	−0.272221
$910$	−30.3388	−1.00572
$911$	46.8459	1.55207	0.776037	−	0.630687i	$-0.217227\pi$
$911$	46.8459	1.55207	0.776037	+	0.630687i	$0.217227\pi$
$912$	−2.10092	−0.0695684
$913$	0	0
$914$	7.37055	0.243796
$915$	−32.7705	−1.08336
$916$	−1.70730	−0.0564109
$917$	14.2213	0.469627
$918$	−7.15042	−0.235999
$919$	−1.76516	−0.0582272	−0.0291136	−	0.999576i	$-0.509268\pi$
$919$	−1.76516	−0.0582272	−0.0291136	+	0.999576i	$0.509268\pi$
$920$	6.29625	0.207581
$921$	11.8619	0.390861
$922$	36.4875	1.20165
$923$	63.5320	2.09118
$924$	0	0
$925$	−1.83988	−0.0604947
$926$	16.2208	0.533048
$927$	−13.5208	−0.444081
$928$	−6.50365	−0.213493
$929$	−28.8886	−0.947805	−0.473902	−	0.880577i	$-0.657155\pi$
$929$	−28.8886	−0.947805	−0.473902	+	0.880577i	$0.657155\pi$
$930$	−7.68199	−0.251902
$931$	−2.60971	−0.0855297
$932$	9.95632	0.326130
$933$	17.6816	0.578870
$934$	−4.27354	−0.139835
$935$	0	0
$936$	5.62481	0.183853
$937$	25.1445	0.821436	0.410718	−	0.911762i	$-0.365278\pi$
$937$	25.1445	0.821436	0.410718	+	0.911762i	$0.365278\pi$
$938$	43.7571	1.42872
$939$	65.9198	2.15121
$940$	−8.37977	−0.273318
$941$	−0.744662	−0.0242753	−0.0121376	−	0.999926i	$-0.503864\pi$
$941$	−0.744662	−0.0242753	−0.0121376	+	0.999926i	$0.503864\pi$
$942$	−7.82359	−0.254906
$943$	−14.0391	−0.457175
$944$	−6.65028	−0.216448
$945$	25.4125	0.826670
$946$	0	0
$947$	54.6088	1.77455	0.887273	−	0.461244i	$-0.152597\pi$
$947$	54.6088	1.77455	0.887273	+	0.461244i	$0.152597\pi$
$948$	15.2457	0.495158
$949$	12.6361	0.410184
$950$	1.05183	0.0341259
$951$	15.1327	0.490712
$952$	−6.65177	−0.215585
$953$	29.4684	0.954574	0.477287	−	0.878747i	$-0.341620\pi$
$953$	29.4684	0.954574	0.477287	+	0.878747i	$0.341620\pi$
$954$	16.6283	0.538362
$955$	17.5747	0.568703
$956$	16.2786	0.526487
$957$	0	0
$958$	39.1936	1.26629
$959$	42.2742	1.36511
$960$	5.16836	0.166808
$961$	−28.7908	−0.928734
$962$	−6.95893	−0.224365
$963$	−20.5948	−0.663659
$964$	−5.95144	−0.191683
$965$	−29.7616	−0.958061
$966$	−16.6687	−0.536308
$967$	−30.8647	−0.992541	−0.496271	−	0.868168i	$-0.665298\pi$
$967$	−30.8647	−0.992541	−0.496271	+	0.868168i	$0.665298\pi$
$968$	0	0
$969$	4.50808	0.144820
$970$	13.4585	0.432125
$971$	−10.8297	−0.347541	−0.173771	−	0.984786i	$-0.555595\pi$
$971$	−10.8297	−0.347541	−0.173771	+	0.984786i	$0.555595\pi$
$972$	−13.6227	−0.436949
$973$	17.9482	0.575392
$974$	−3.27438	−0.104918
$975$	−8.79134	−0.281548
$976$	−6.34059	−0.202957
$977$	5.53214	0.176989	0.0884945	−	0.996077i	$-0.471794\pi$
$977$	5.53214	0.176989	0.0884945	+	0.996077i	$0.471794\pi$
$978$	41.7916	1.33635
$979$	0	0
$980$	6.42000	0.205079
$981$	−4.77999	−0.152613
$982$	−40.6503	−1.29720
$983$	22.2474	0.709583	0.354791	−	0.934945i	$-0.384552\pi$
$983$	22.2474	0.709583	0.354791	+	0.934945i	$0.384552\pi$
$984$	−11.5242	−0.367377
$985$	44.8998	1.43063
$986$	13.9553	0.444427
$987$	22.1847	0.706146
$988$	3.97832	0.126567
$989$	−11.7597	−0.373938
$990$	0	0
$991$	−8.28887	−0.263305	−0.131652	−	0.991296i	$-0.542028\pi$
$991$	−8.28887	−0.263305	−0.131652	+	0.991296i	$0.542028\pi$
$992$	−1.48635	−0.0471916
$993$	42.8761	1.36063
$994$	−49.5049	−1.57020
$995$	58.9686	1.86943
$996$	23.5651	0.746688
$997$	−27.5534	−0.872624	−0.436312	−	0.899795i	$-0.643716\pi$
$997$	−27.5534	−0.872624	−0.436312	+	0.899795i	$0.643716\pi$
$998$	14.1445	0.447736
$999$	5.82898	0.184421

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4598.2.a.cc.1.8		10
11.3	even	5		418.2.f.h.229.2	yes	20
11.4	even	5		418.2.f.h.115.2	✓	20
11.10	odd	2		4598.2.a.cd.1.8		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.f.h.115.2	✓	20	11.4	even	5
418.2.f.h.229.2	yes	20	11.3	even	5
4598.2.a.cc.1.8		10	1.1	even	1	trivial
4598.2.a.cd.1.8		10	11.10	odd	2

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:	\( N \)	\(=\)	\( 4598 = 2 \cdot 11^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4598.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +2.10092 q^{3} +1.00000 q^{4} +2.46005 q^{5} -2.10092 q^{6} -3.09995 q^{7} -1.00000 q^{8} +1.41386 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +2.10092 q^{3} +1.00000 q^{4} +2.46005 q^{5} -2.10092 q^{6} -3.09995 q^{7} -1.00000 q^{8} +1.41386 q^{9} -2.46005 q^{10} +2.10092 q^{12} -3.97832 q^{13} +3.09995 q^{14} +5.16836 q^{15} +1.00000 q^{16} -2.14576 q^{17} -1.41386 q^{18} -1.00000 q^{19} +2.46005 q^{20} -6.51275 q^{21} -2.55940 q^{23} -2.10092 q^{24} +1.05183 q^{25} +3.97832 q^{26} -3.33234 q^{27} -3.09995 q^{28} +6.50365 q^{29} -5.16836 q^{30} +1.48635 q^{31} -1.00000 q^{32} +2.14576 q^{34} -7.62603 q^{35} +1.41386 q^{36} -1.74921 q^{37} +1.00000 q^{38} -8.35814 q^{39} -2.46005 q^{40} +5.48529 q^{41} +6.51275 q^{42} +4.59472 q^{43} +3.47817 q^{45} +2.55940 q^{46} -3.40634 q^{47} +2.10092 q^{48} +2.60971 q^{49} -1.05183 q^{50} -4.50808 q^{51} -3.97832 q^{52} -11.7609 q^{53} +3.33234 q^{54} +3.09995 q^{56} -2.10092 q^{57} -6.50365 q^{58} -6.65028 q^{59} +5.16836 q^{60} -6.34059 q^{61} -1.48635 q^{62} -4.38291 q^{63} +1.00000 q^{64} -9.78686 q^{65} +14.1154 q^{67} -2.14576 q^{68} -5.37710 q^{69} +7.62603 q^{70} -15.9696 q^{71} -1.41386 q^{72} -3.17623 q^{73} +1.74921 q^{74} +2.20981 q^{75} -1.00000 q^{76} +8.35814 q^{78} +7.25669 q^{79} +2.46005 q^{80} -11.2426 q^{81} -5.48529 q^{82} +11.2166 q^{83} -6.51275 q^{84} -5.27868 q^{85} -4.59472 q^{86} +13.6636 q^{87} -4.63686 q^{89} -3.47817 q^{90} +12.3326 q^{91} -2.55940 q^{92} +3.12270 q^{93} +3.40634 q^{94} -2.46005 q^{95} -2.10092 q^{96} -5.47081 q^{97} -2.60971 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 10 q^{2} + 2 q^{3} + 10 q^{4} - 3 q^{5} - 2 q^{6} - 11 q^{7} - 10 q^{8} + 12 q^{9}+O(q^{10}) \) 10 * q - 10 * q^2 + 2 * q^3 + 10 * q^4 - 3 * q^5 - 2 * q^6 - 11 * q^7 - 10 * q^8 + 12 * q^9	\( 10 q - 10 q^{2} + 2 q^{3} + 10 q^{4} - 3 q^{5} - 2 q^{6} - 11 q^{7} - 10 q^{8} + 12 q^{9} + 3 q^{10} + 2 q^{12} - 11 q^{13} + 11 q^{14} + q^{15} + 10 q^{16} - 12 q^{17} - 12 q^{18} - 10 q^{19} - 3 q^{20} + q^{21} + 14 q^{23} - 2 q^{24} + 5 q^{25} + 11 q^{26} + 2 q^{27} - 11 q^{28} - 16 q^{29} - q^{30} + 12 q^{31} - 10 q^{32} + 12 q^{34} + 12 q^{35} + 12 q^{36} - q^{37} + 10 q^{38} - 11 q^{39} + 3 q^{40} + 5 q^{41} - q^{42} - 22 q^{43} - 2 q^{45} - 14 q^{46} + 8 q^{47} + 2 q^{48} - 3 q^{49} - 5 q^{50} - 8 q^{51} - 11 q^{52} + 2 q^{53} - 2 q^{54} + 11 q^{56} - 2 q^{57} + 16 q^{58} - 7 q^{59} + q^{60} - 35 q^{61} - 12 q^{62} - 38 q^{63} + 10 q^{64} - 4 q^{65} + 9 q^{67} - 12 q^{68} + 6 q^{69} - 12 q^{70} - 4 q^{71} - 12 q^{72} - 5 q^{73} + q^{74} - 15 q^{75} - 10 q^{76} + 11 q^{78} - 18 q^{79} - 3 q^{80} - 6 q^{81} - 5 q^{82} - 7 q^{83} + q^{84} - 35 q^{85} + 22 q^{86} - 8 q^{87} + 22 q^{89} + 2 q^{90} + 11 q^{91} + 14 q^{92} - 64 q^{93} - 8 q^{94} + 3 q^{95} - 2 q^{96} + 32 q^{97} + 3 q^{98}+O(q^{100}) \) 10 * q - 10 * q^2 + 2 * q^3 + 10 * q^4 - 3 * q^5 - 2 * q^6 - 11 * q^7 - 10 * q^8 + 12 * q^9 + 3 * q^10 + 2 * q^12 - 11 * q^13 + 11 * q^14 + q^15 + 10 * q^16 - 12 * q^17 - 12 * q^18 - 10 * q^19 - 3 * q^20 + q^21 + 14 * q^23 - 2 * q^24 + 5 * q^25 + 11 * q^26 + 2 * q^27 - 11 * q^28 - 16 * q^29 - q^30 + 12 * q^31 - 10 * q^32 + 12 * q^34 + 12 * q^35 + 12 * q^36 - q^37 + 10 * q^38 - 11 * q^39 + 3 * q^40 + 5 * q^41 - q^42 - 22 * q^43 - 2 * q^45 - 14 * q^46 + 8 * q^47 + 2 * q^48 - 3 * q^49 - 5 * q^50 - 8 * q^51 - 11 * q^52 + 2 * q^53 - 2 * q^54 + 11 * q^56 - 2 * q^57 + 16 * q^58 - 7 * q^59 + q^60 - 35 * q^61 - 12 * q^62 - 38 * q^63 + 10 * q^64 - 4 * q^65 + 9 * q^67 - 12 * q^68 + 6 * q^69 - 12 * q^70 - 4 * q^71 - 12 * q^72 - 5 * q^73 + q^74 - 15 * q^75 - 10 * q^76 + 11 * q^78 - 18 * q^79 - 3 * q^80 - 6 * q^81 - 5 * q^82 - 7 * q^83 + q^84 - 35 * q^85 + 22 * q^86 - 8 * q^87 + 22 * q^89 + 2 * q^90 + 11 * q^91 + 14 * q^92 - 64 * q^93 - 8 * q^94 + 3 * q^95 - 2 * q^96 + 32 * q^97 + 3 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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