LMFDB - Embedded newform 5819.2.a.t.1.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [5819,2,Mod(1,5819)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(5819, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("5819.1"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 5819 = 11 \cdot 23^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5819.a (trivial)

Newform invariants

comment:select newform

sage:traces = [60,5,9,73,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$46.4649489362$
Analytic rank:	$0$
Dimension:	$60$
Twist minimal:	no (minimal twist has level 253)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Character	$\chi$	$=$	5819.1

$q$-expansion

comment:q-expansion

sage:f.q_expansion() # note that sage often uses an isomorphic number field

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.67053 q^{2} +3.39922 q^{3} +0.790674 q^{4} +1.45882 q^{5} -5.67850 q^{6} +1.59098 q^{7} +2.02022 q^{8} +8.55467 q^{9} -2.43701 q^{10} -1.00000 q^{11} +2.68767 q^{12} -1.30794 q^{13} -2.65778 q^{14} +4.95885 q^{15} -4.95618 q^{16} +2.95107 q^{17} -14.2908 q^{18} +3.43321 q^{19} +1.15345 q^{20} +5.40808 q^{21} +1.67053 q^{22} +6.86716 q^{24} -2.87184 q^{25} +2.18496 q^{26} +18.8815 q^{27} +1.25794 q^{28} +6.51587 q^{29} -8.28392 q^{30} +1.28950 q^{31} +4.23902 q^{32} -3.39922 q^{33} -4.92985 q^{34} +2.32095 q^{35} +6.76395 q^{36} +0.915746 q^{37} -5.73529 q^{38} -4.44597 q^{39} +2.94714 q^{40} +0.847520 q^{41} -9.03436 q^{42} +4.84131 q^{43} -0.790674 q^{44} +12.4797 q^{45} +4.08129 q^{47} -16.8471 q^{48} -4.46879 q^{49} +4.79749 q^{50} +10.0313 q^{51} -1.03415 q^{52} -9.11028 q^{53} -31.5422 q^{54} -1.45882 q^{55} +3.21412 q^{56} +11.6702 q^{57} -10.8850 q^{58} -7.33808 q^{59} +3.92083 q^{60} -14.6241 q^{61} -2.15415 q^{62} +13.6103 q^{63} +2.83095 q^{64} -1.90805 q^{65} +5.67850 q^{66} -14.4825 q^{67} +2.33333 q^{68} -3.87723 q^{70} +15.3390 q^{71} +17.2823 q^{72} +12.0890 q^{73} -1.52978 q^{74} -9.76199 q^{75} +2.71455 q^{76} -1.59098 q^{77} +7.42714 q^{78} +5.34111 q^{79} -7.23019 q^{80} +38.5184 q^{81} -1.41581 q^{82} -8.73373 q^{83} +4.27602 q^{84} +4.30508 q^{85} -8.08756 q^{86} +22.1489 q^{87} -2.02022 q^{88} +0.274393 q^{89} -20.8478 q^{90} -2.08091 q^{91} +4.38330 q^{93} -6.81792 q^{94} +5.00845 q^{95} +14.4094 q^{96} -13.2094 q^{97} +7.46525 q^{98} -8.55467 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q + 5 q^{2} + 9 q^{3} + 73 q^{4} - 8 q^{5} + 26 q^{6} + 30 q^{8} + 75 q^{9} + 7 q^{10} - 60 q^{11} + 41 q^{12} + 46 q^{13} - 16 q^{14} - 4 q^{15} + 99 q^{16} + 5 q^{17} + 36 q^{18} + 8 q^{19} - 82 q^{20}+ \cdots - 75 q^{99}+O(q^{100}) $ 60 * q + 5 * q^2 + 9 * q^3 + 73 * q^4 - 8 * q^5 + 26 * q^6 + 30 * q^8 + 75 * q^9 + 7 * q^10 - 60 * q^11 + 41 * q^12 + 46 * q^13 - 16 * q^14 - 4 * q^15 + 99 * q^16 + 5 * q^17 + 36 * q^18 + 8 * q^19 - 82 * q^20 + 13 * q^21 - 5 * q^22 + 54 * q^24 + 96 * q^25 + 31 * q^26 + 54 * q^27 + 29 * q^28 + 42 * q^29 + 14 * q^30 + 71 * q^31 + 40 * q^32 - 9 * q^33 - 10 * q^34 + 9 * q^35 + 93 * q^36 + 5 * q^37 + 11 * q^38 + 56 * q^39 + 40 * q^40 + 62 * q^41 - 43 * q^42 + 2 * q^43 - 73 * q^44 + q^45 - q^47 + 71 * q^48 + 138 * q^49 - 18 * q^50 + 27 * q^51 + 102 * q^52 - 11 * q^53 + 69 * q^54 + 8 * q^55 - 13 * q^56 - 38 * q^57 + 58 * q^58 + 57 * q^59 + 49 * q^60 + 26 * q^61 + 17 * q^62 + 41 * q^63 + 184 * q^64 + 19 * q^65 - 26 * q^66 - 7 * q^67 + 76 * q^68 + 43 * q^70 + 33 * q^71 + 100 * q^72 + 108 * q^73 + 63 * q^74 + q^75 + 42 * q^76 - 3 * q^78 + 25 * q^79 - 148 * q^80 + 68 * q^81 + 59 * q^82 + 41 * q^83 + 97 * q^84 + 160 * q^85 - 78 * q^86 + 41 * q^87 - 30 * q^88 - 51 * q^89 + 53 * q^90 + 65 * q^93 + 121 * q^94 - 14 * q^95 + 82 * q^96 + 13 * q^97 - 75 * q^98 - 75 * q^99

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 $

$2$	−1.67053	−1.18124	−0.590622	−	0.806948i	$-0.701118\pi$
$2$	−1.67053	−1.18124	−0.590622	+	0.806948i	$0.701118\pi$
$3$	3.39922	1.96254	0.981269	−	0.192641i	$-0.0617054\pi$
$3$	3.39922	1.96254	0.981269	+	0.192641i	$0.0617054\pi$
$4$	0.790674	0.395337
$5$	1.45882	0.652405	0.326203	−	0.945300i	$-0.394231\pi$
$5$	1.45882	0.652405	0.326203	+	0.945300i	$0.394231\pi$
$6$	−5.67850	−2.31824
$7$	1.59098	0.601333	0.300667	−	0.953729i	$-0.402791\pi$
$7$	1.59098	0.601333	0.300667	+	0.953729i	$0.402791\pi$
$8$	2.02022	0.714255
$9$	8.55467	2.85156
$10$	−2.43701	−0.770650
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	2.68767	0.775864
$13$	−1.30794	−0.362758	−0.181379	−	0.983413i	$-0.558056\pi$
$13$	−1.30794	−0.362758	−0.181379	+	0.983413i	$0.558056\pi$
$14$	−2.65778	−0.710321
$15$	4.95885	1.28037
$16$	−4.95618	−1.23905
$17$	2.95107	0.715739	0.357870	−	0.933772i	$-0.383503\pi$
$17$	2.95107	0.715739	0.357870	+	0.933772i	$0.383503\pi$
$18$	−14.2908	−3.36838
$19$	3.43321	0.787633	0.393817	−	0.919189i	$-0.371155\pi$
$19$	3.43321	0.787633	0.393817	+	0.919189i	$0.371155\pi$
$20$	1.15345	0.257920
$21$	5.40808	1.18014
$22$	1.67053	0.356158
$23$	0	0
$23$	0	0
$24$	6.86716	1.40175
$25$	−2.87184	−0.574367
$26$	2.18496	0.428505
$27$	18.8815	3.63375
$28$	1.25794	0.237729
$29$	6.51587	1.20997	0.604984	−	0.796238i	$-0.293180\pi$
$29$	6.51587	1.20997	0.604984	+	0.796238i	$0.293180\pi$
$30$	−8.28392	−1.51243
$31$	1.28950	0.231601	0.115801	−	0.993272i	$-0.463057\pi$
$31$	1.28950	0.231601	0.115801	+	0.993272i	$0.463057\pi$
$32$	4.23902	0.749360
$33$	−3.39922	−0.591728
$34$	−4.92985	−0.845462
$35$	2.32095	0.392313
$36$	6.76395	1.12733
$37$	0.915746	0.150548	0.0752739	−	0.997163i	$-0.476017\pi$
$37$	0.915746	0.150548	0.0752739	+	0.997163i	$0.476017\pi$
$38$	−5.73529	−0.930387
$39$	−4.44597	−0.711926
$40$	2.94714	0.465984
$41$	0.847520	0.132360	0.0661802	−	0.997808i	$-0.478919\pi$
$41$	0.847520	0.132360	0.0661802	+	0.997808i	$0.478919\pi$
$42$	−9.03436	−1.39403
$43$	4.84131	0.738293	0.369147	−	0.929371i	$-0.379650\pi$
$43$	4.84131	0.738293	0.369147	+	0.929371i	$0.379650\pi$
$44$	−0.790674	−0.119199
$45$	12.4797	1.86037
$46$	0	0
$47$	4.08129	0.595318	0.297659	−	0.954672i	$-0.403794\pi$
$47$	4.08129	0.595318	0.297659	+	0.954672i	$0.403794\pi$
$48$	−16.8471	−2.43167
$49$	−4.46879	−0.638398
$50$	4.79749	0.678468
$51$	10.0313	1.40467
$52$	−1.03415	−0.143411
$53$	−9.11028	−1.25139	−0.625697	−	0.780067i	$-0.715185\pi$
$53$	−9.11028	−1.25139	−0.625697	+	0.780067i	$0.715185\pi$
$54$	−31.5422	−4.29235
$55$	−1.45882	−0.196708
$56$	3.21412	0.429505
$57$	11.6702	1.54576
$58$	−10.8850	−1.42927
$59$	−7.33808	−0.955336	−0.477668	−	0.878540i	$-0.658518\pi$
$59$	−7.33808	−0.955336	−0.477668	+	0.878540i	$0.658518\pi$
$60$	3.92083	0.506178
$61$	−14.6241	−1.87243	−0.936214	−	0.351430i	$-0.885696\pi$
$61$	−14.6241	−1.87243	−0.936214	+	0.351430i	$0.885696\pi$
$62$	−2.15415	−0.273578
$63$	13.6103	1.71474
$64$	2.83095	0.353869
$65$	−1.90805	−0.236665
$66$	5.67850	0.698975
$67$	−14.4825	−1.76932	−0.884659	−	0.466239i	$-0.845609\pi$
$67$	−14.4825	−1.76932	−0.884659	+	0.466239i	$0.845609\pi$
$68$	2.33333	0.282958
$69$	0	0
$70$	−3.87723	−0.463417
$71$	15.3390	1.82040	0.910200	−	0.414170i	$-0.135928\pi$
$71$	15.3390	1.82040	0.910200	+	0.414170i	$0.135928\pi$
$72$	17.2823	2.03674
$73$	12.0890	1.41491	0.707454	−	0.706760i	$-0.249844\pi$
$73$	12.0890	1.41491	0.707454	+	0.706760i	$0.249844\pi$
$74$	−1.52978	−0.177834
$75$	−9.76199	−1.12722
$76$	2.71455	0.311380
$77$	−1.59098	−0.181309
$78$	7.42714	0.840958
$79$	5.34111	0.600922	0.300461	−	0.953794i	$-0.402859\pi$
$79$	5.34111	0.600922	0.300461	+	0.953794i	$0.402859\pi$
$80$	−7.23019	−0.808360
$81$	38.5184	4.27982
$82$	−1.41581	−0.156350
$83$	−8.73373	−0.958652	−0.479326	−	0.877637i	$-0.659119\pi$
$83$	−8.73373	−0.958652	−0.479326	+	0.877637i	$0.659119\pi$
$84$	4.27602	0.466552
$85$	4.30508	0.466952
$86$	−8.08756	−0.872104
$87$	22.1489	2.37461
$88$	−2.02022	−0.215356
$89$	0.274393	0.0290856	0.0145428	−	0.999894i	$-0.495371\pi$
$89$	0.274393	0.0290856	0.0145428	+	0.999894i	$0.495371\pi$
$90$	−20.8478	−2.19755
$91$	−2.08091	−0.218138
$92$	0	0
$93$	4.38330	0.454527
$94$	−6.81792	−0.703215
$95$	5.00845	0.513856
$96$	14.4094	1.47065
$97$	−13.2094	−1.34121	−0.670605	−	0.741815i	$-0.733965\pi$
$97$	−13.2094	−1.34121	−0.670605	+	0.741815i	$0.733965\pi$
$98$	7.46525	0.754104
$99$	−8.55467	−0.859777
$100$	−2.27069	−0.227069
$101$	−2.18688	−0.217603	−0.108801	−	0.994064i	$-0.534701\pi$
$101$	−2.18688	−0.217603	−0.108801	+	0.994064i	$0.534701\pi$
$102$	−16.7576	−1.65925
$103$	0.835944	0.0823680	0.0411840	−	0.999152i	$-0.486887\pi$
$103$	0.835944	0.0823680	0.0411840	+	0.999152i	$0.486887\pi$
$104$	−2.64232	−0.259101
$105$	7.88943	0.769929
$106$	15.2190	1.47820
$107$	18.7243	1.81015	0.905073	−	0.425256i	$-0.139816\pi$
$107$	18.7243	1.81015	0.905073	+	0.425256i	$0.139816\pi$
$108$	14.9291	1.43656
$109$	19.5235	1.87002	0.935008	−	0.354626i	$-0.115392\pi$
$109$	19.5235	1.87002	0.935008	+	0.354626i	$0.115392\pi$
$110$	2.43701	0.232360
$111$	3.11282	0.295456
$112$	−7.88518	−0.745079
$113$	−7.23233	−0.680360	−0.340180	−	0.940360i	$-0.610488\pi$
$113$	−7.23233	−0.680360	−0.340180	+	0.940360i	$0.610488\pi$
$114$	−19.4955	−1.82592
$115$	0	0
$116$	5.15193	0.478345
$117$	−11.1890	−1.03442
$118$	12.2585	1.12848
$119$	4.69508	0.430398
$120$	10.0180	0.914511
$121$	1.00000	0.0909091
$122$	24.4301	2.21179
$123$	2.88090	0.259762
$124$	1.01958	0.0915606
$125$	−11.4836	−1.02713
$126$	−22.7364	−2.02552
$127$	6.05213	0.537040	0.268520	−	0.963274i	$-0.413465\pi$
$127$	6.05213	0.537040	0.268520	+	0.963274i	$0.413465\pi$
$128$	−13.2072	−1.16737
$129$	16.4567	1.44893
$130$	3.18746	0.279559
$131$	12.3371	1.07790	0.538950	−	0.842338i	$-0.318821\pi$
$131$	12.3371	1.07790	0.538950	+	0.842338i	$0.318821\pi$
$132$	−2.68767	−0.233932
$133$	5.46217	0.473630
$134$	24.1934	2.09000
$135$	27.5448	2.37068
$136$	5.96180	0.511220
$137$	−1.45154	−0.124014	−0.0620068	−	0.998076i	$-0.519750\pi$
$137$	−1.45154	−0.124014	−0.0620068	+	0.998076i	$0.519750\pi$
$138$	0	0
$139$	−9.77385	−0.829007	−0.414504	−	0.910048i	$-0.636045\pi$
$139$	−9.77385	−0.829007	−0.414504	+	0.910048i	$0.636045\pi$
$140$	1.83512	0.155096
$141$	13.8732	1.16833
$142$	−25.6242	−2.15034
$143$	1.30794	0.109376
$144$	−42.3985	−3.53321
$145$	9.50551	0.789389
$146$	−20.1950	−1.67135
$147$	−15.1904	−1.25288
$148$	0.724056	0.0595171
$149$	−16.7206	−1.36981	−0.684903	−	0.728635i	$-0.740155\pi$
$149$	−16.7206	−1.36981	−0.684903	+	0.728635i	$0.740155\pi$
$150$	16.3077	1.33152
$151$	−0.354848	−0.0288771	−0.0144386	−	0.999896i	$-0.504596\pi$
$151$	−0.354848	−0.0288771	−0.0144386	+	0.999896i	$0.504596\pi$
$152$	6.93584	0.562571
$153$	25.2454	2.04097
$154$	2.65778	0.214170
$155$	1.88115	0.151098
$156$	−3.51531	−0.281450
$157$	0.798909	0.0637599	0.0318799	−	0.999492i	$-0.489851\pi$
$157$	0.798909	0.0637599	0.0318799	+	0.999492i	$0.489851\pi$
$158$	−8.92249	−0.709835
$159$	−30.9678	−2.45591
$160$	6.18398	0.488887
$161$	0	0
$162$	−64.3462	−5.05551
$163$	15.4842	1.21282	0.606408	−	0.795154i	$-0.292610\pi$
$163$	15.4842	1.21282	0.606408	+	0.795154i	$0.292610\pi$
$164$	0.670112	0.0523269
$165$	−4.95885	−0.386046
$166$	14.5900	1.13240
$167$	−6.09555	−0.471688	−0.235844	−	0.971791i	$-0.575785\pi$
$167$	−6.09555	−0.471688	−0.235844	+	0.971791i	$0.575785\pi$
$168$	10.9255	0.842920
$169$	−11.2893	−0.868407
$170$	−7.19178	−0.551584
$171$	29.3700	2.24598
$172$	3.82790	0.291875
$173$	−15.1301	−1.15032	−0.575160	−	0.818041i	$-0.695060\pi$
$173$	−15.1301	−1.15032	−0.575160	+	0.818041i	$0.695060\pi$
$174$	−37.0004	−2.80499
$175$	−4.56903	−0.345386
$176$	4.95618	0.373586
$177$	−24.9437	−1.87488
$178$	−0.458382	−0.0343572
$179$	1.93248	0.144441	0.0722204	−	0.997389i	$-0.476992\pi$
$179$	1.93248	0.144441	0.0722204	+	0.997389i	$0.476992\pi$
$180$	9.86741	0.735473
$181$	−6.40393	−0.476000	−0.238000	−	0.971265i	$-0.576492\pi$
$181$	−6.40393	−0.476000	−0.238000	+	0.971265i	$0.576492\pi$
$182$	3.47622	0.257674
$183$	−49.7106	−3.67471
$184$	0	0
$185$	1.33591	0.0982181
$186$	−7.32243	−0.536907
$187$	−2.95107	−0.215803
$188$	3.22697	0.235351
$189$	30.0401	2.18510
$190$	−8.36677	−0.606989
$191$	−2.79437	−0.202194	−0.101097	−	0.994877i	$-0.532235\pi$
$191$	−2.79437	−0.202194	−0.101097	+	0.994877i	$0.532235\pi$
$192$	9.62301	0.694481
$193$	5.39665	0.388459	0.194230	−	0.980956i	$-0.437779\pi$
$193$	5.39665	0.388459	0.194230	+	0.980956i	$0.437779\pi$
$194$	22.0667	1.58430
$195$	−6.48589	−0.464464
$196$	−3.53335	−0.252382
$197$	5.28974	0.376879	0.188439	−	0.982085i	$-0.439657\pi$
$197$	5.28974	0.376879	0.188439	+	0.982085i	$0.439657\pi$
$198$	14.2908	1.01561
$199$	−10.3419	−0.733116	−0.366558	−	0.930395i	$-0.619464\pi$
$199$	−10.3419	−0.733116	−0.366558	+	0.930395i	$0.619464\pi$
$200$	−5.80173	−0.410245
$201$	−49.2291	−3.47235
$202$	3.65325	0.257042
$203$	10.3666	0.727594
$204$	7.93150	0.555316
$205$	1.23638	0.0863526
$206$	−1.39647	−0.0972967
$207$	0	0
$208$	6.48239	0.449473
$209$	−3.43321	−0.237480
$210$	−13.1795	−0.909474
$211$	3.24458	0.223366	0.111683	−	0.993744i	$-0.464376\pi$
$211$	3.24458	0.223366	0.111683	+	0.993744i	$0.464376\pi$
$212$	−7.20326	−0.494722
$213$	52.1404	3.57260
$214$	−31.2795	−2.13822
$215$	7.06262	0.481667
$216$	38.1448	2.59542
$217$	2.05157	0.139270
$218$	−32.6147	−2.20894
$219$	41.0930	2.77681
$220$	−1.15345	−0.0777658
$221$	−3.85982	−0.259640
$222$	−5.20006	−0.349005
$223$	5.45173	0.365075	0.182537	−	0.983199i	$-0.441569\pi$
$223$	5.45173	0.365075	0.182537	+	0.983199i	$0.441569\pi$
$224$	6.74419	0.450615
$225$	−24.5676	−1.63784
$226$	12.0818	0.803671
$227$	−5.32468	−0.353411	−0.176706	−	0.984264i	$-0.556544\pi$
$227$	−5.32468	−0.353411	−0.176706	+	0.984264i	$0.556544\pi$
$228$	9.22735	0.611096
$229$	−17.2717	−1.14134	−0.570672	−	0.821178i	$-0.693317\pi$
$229$	−17.2717	−1.14134	−0.570672	+	0.821178i	$0.693317\pi$
$230$	0	0
$231$	−5.40808	−0.355825
$232$	13.1635	0.864225
$233$	−5.12686	−0.335872	−0.167936	−	0.985798i	$-0.553710\pi$
$233$	−5.12686	−0.335872	−0.167936	+	0.985798i	$0.553710\pi$
$234$	18.6916	1.22191
$235$	5.95388	0.388388
$236$	−5.80202	−0.377679
$237$	18.1556	1.17933
$238$	−7.84328	−0.508404
$239$	−20.4852	−1.32508	−0.662539	−	0.749027i	$-0.730521\pi$
$239$	−20.4852	−1.32508	−0.662539	+	0.749027i	$0.730521\pi$
$240$	−24.5770	−1.58644
$241$	19.3556	1.24681	0.623403	−	0.781901i	$-0.285750\pi$
$241$	19.3556	1.24681	0.623403	+	0.781901i	$0.285750\pi$
$242$	−1.67053	−0.107386
$243$	74.2878	4.76556
$244$	−11.5629	−0.740240
$245$	−6.51917	−0.416495
$246$	−4.81264	−0.306843
$247$	−4.49044	−0.285720
$248$	2.60507	0.165422
$249$	−29.6878	−1.88139
$250$	19.1837	1.21329
$251$	20.7713	1.31107	0.655535	−	0.755165i	$-0.272443\pi$
$251$	20.7713	1.31107	0.655535	+	0.755165i	$0.272443\pi$
$252$	10.7613	0.677898
$253$	0	0
$254$	−10.1103	−0.634375
$255$	14.6339	0.916411
$256$	16.4012	1.02507
$257$	−18.7383	−1.16886	−0.584431	−	0.811443i	$-0.698682\pi$
$257$	−18.7383	−1.16886	−0.584431	+	0.811443i	$0.698682\pi$
$258$	−27.4914	−1.71154
$259$	1.45693	0.0905293
$260$	−1.50865	−0.0935624
$261$	55.7412	3.45029
$262$	−20.6096	−1.27326
$263$	26.1960	1.61532	0.807659	−	0.589650i	$-0.200734\pi$
$263$	26.1960	1.61532	0.807659	+	0.589650i	$0.200734\pi$
$264$	−6.86716	−0.422644
$265$	−13.2903	−0.816416
$266$	−9.12472	−0.559472
$267$	0.932721	0.0570816
$268$	−11.4509	−0.699476
$269$	17.7600	1.08285	0.541424	−	0.840750i	$-0.317885\pi$
$269$	17.7600	1.08285	0.541424	+	0.840750i	$0.317885\pi$
$270$	−46.0145	−2.80035
$271$	13.3854	0.813107	0.406553	−	0.913627i	$-0.366731\pi$
$271$	13.3854	0.813107	0.406553	+	0.913627i	$0.366731\pi$
$272$	−14.6260	−0.886833
$273$	−7.07345	−0.428104
$274$	2.42485	0.146490
$275$	2.87184	0.173178
$276$	0	0
$277$	10.7484	0.645809	0.322905	−	0.946431i	$-0.395341\pi$
$277$	10.7484	0.645809	0.322905	+	0.946431i	$0.395341\pi$
$278$	16.3275	0.979260
$279$	11.0313	0.660425
$280$	4.68883	0.280211
$281$	−6.09616	−0.363666	−0.181833	−	0.983329i	$-0.558203\pi$
$281$	−6.09616	−0.363666	−0.181833	+	0.983329i	$0.558203\pi$
$282$	−23.1756	−1.38009
$283$	−14.0335	−0.834207	−0.417104	−	0.908859i	$-0.636955\pi$
$283$	−14.0335	−0.834207	−0.417104	+	0.908859i	$0.636955\pi$
$284$	12.1281	0.719671
$285$	17.0248	1.00846
$286$	−2.18496	−0.129199
$287$	1.34839	0.0795927
$288$	36.2634	2.13684
$289$	−8.29120	−0.487718
$290$	−15.8792	−0.932461
$291$	−44.9015	−2.63217
$292$	9.55843	0.559365
$293$	−17.1214	−1.00024	−0.500122	−	0.865955i	$-0.666711\pi$
$293$	−17.1214	−1.00024	−0.500122	+	0.865955i	$0.666711\pi$
$294$	25.3760	1.47996
$295$	−10.7050	−0.623266
$296$	1.85001	0.107529
$297$	−18.8815	−1.09562
$298$	27.9323	1.61807
$299$	0	0
$300$	−7.71855	−0.445631
$301$	7.70242	0.443960
$302$	0.592785	0.0341109
$303$	−7.43368	−0.427054
$304$	−17.0156	−0.975913
$305$	−21.3340	−1.22158
$306$	−42.1732	−2.41088
$307$	−17.1016	−0.976040	−0.488020	−	0.872833i	$-0.662281\pi$
$307$	−17.1016	−0.976040	−0.488020	+	0.872833i	$0.662281\pi$
$308$	−1.25794	−0.0716780
$309$	2.84156	0.161650
$310$	−3.14253	−0.178484
$311$	22.6738	1.28572	0.642858	−	0.765986i	$-0.277749\pi$
$311$	22.6738	1.28572	0.642858	+	0.765986i	$0.277749\pi$
$312$	−8.98183	−0.508496
$313$	13.6959	0.774141	0.387070	−	0.922050i	$-0.373487\pi$
$313$	13.6959	0.774141	0.387070	+	0.922050i	$0.373487\pi$
$314$	−1.33460	−0.0753159
$315$	19.8550	1.11870
$316$	4.22308	0.237567
$317$	−0.137911	−0.00774584	−0.00387292	−	0.999993i	$-0.501233\pi$
$317$	−0.137911	−0.00774584	−0.00387292	+	0.999993i	$0.501233\pi$
$318$	51.7327	2.90103
$319$	−6.51587	−0.364819
$320$	4.12985	0.230866
$321$	63.6479	3.55248
$322$	0	0
$323$	10.1316	0.563740
$324$	30.4555	1.69197
$325$	3.75619	0.208356
$326$	−25.8668	−1.43263
$327$	66.3647	3.66998
$328$	1.71217	0.0945390
$329$	6.49325	0.357984
$330$	8.28392	0.456015
$331$	−1.99732	−0.109783	−0.0548914	−	0.998492i	$-0.517481\pi$
$331$	−1.99732	−0.109783	−0.0548914	+	0.998492i	$0.517481\pi$
$332$	−6.90553	−0.378990
$333$	7.83391	0.429295
$334$	10.1828	0.557179
$335$	−21.1274	−1.15431
$336$	−26.8034	−1.46225
$337$	−22.0275	−1.19991	−0.599957	−	0.800033i	$-0.704815\pi$
$337$	−22.0275	−1.19991	−0.599957	+	0.800033i	$0.704815\pi$
$338$	18.8591	1.02580
$339$	−24.5843	−1.33523
$340$	3.40392	0.184603
$341$	−1.28950	−0.0698305
$342$	−49.0635	−2.65305
$343$	−18.2466	−0.985223
$344$	9.78050	0.527329
$345$	0	0
$346$	25.2753	1.35881
$347$	−16.6573	−0.894211	−0.447105	−	0.894481i	$-0.647545\pi$
$347$	−16.6573	−0.894211	−0.447105	+	0.894481i	$0.647545\pi$
$348$	17.5125	0.938770
$349$	26.8844	1.43909	0.719545	−	0.694446i	$-0.244351\pi$
$349$	26.8844	1.43909	0.719545	+	0.694446i	$0.244351\pi$
$350$	7.63270	0.407985
$351$	−24.6959	−1.31817
$352$	−4.23902	−0.225941
$353$	−8.75166	−0.465804	−0.232902	−	0.972500i	$-0.574822\pi$
$353$	−8.75166	−0.465804	−0.232902	+	0.972500i	$0.574822\pi$
$354$	41.6692	2.21469
$355$	22.3768	1.18764
$356$	0.216955	0.0114986
$357$	15.9596	0.844672
$358$	−3.22828	−0.170620
$359$	−34.9012	−1.84202	−0.921008	−	0.389544i	$-0.872633\pi$
$359$	−34.9012	−1.84202	−0.921008	+	0.389544i	$0.872633\pi$
$360$	25.2118	1.32878
$361$	−7.21304	−0.379634
$362$	10.6980	0.562273
$363$	3.39922	0.178413
$364$	−1.64532	−0.0862380
$365$	17.6357	0.923093
$366$	83.0431	4.34073
$367$	−2.94041	−0.153488	−0.0767441	−	0.997051i	$-0.524452\pi$
$367$	−2.94041	−0.153488	−0.0767441	+	0.997051i	$0.524452\pi$
$368$	0	0
$369$	7.25026	0.377433
$370$	−2.23168	−0.116020
$371$	−14.4943	−0.752504
$372$	3.46576	0.179691
$373$	3.11175	0.161120	0.0805600	−	0.996750i	$-0.474329\pi$
$373$	3.11175	0.161120	0.0805600	+	0.996750i	$0.474329\pi$
$374$	4.92985	0.254916
$375$	−39.0353	−2.01577
$376$	8.24510	0.425208
$377$	−8.52238	−0.438925
$378$	−50.1829	−2.58113
$379$	−25.0966	−1.28913	−0.644563	−	0.764551i	$-0.722961\pi$
$379$	−25.0966	−1.28913	−0.644563	+	0.764551i	$0.722961\pi$
$380$	3.96005	0.203146
$381$	20.5725	1.05396
$382$	4.66808	0.238840
$383$	−12.1717	−0.621945	−0.310972	−	0.950419i	$-0.600655\pi$
$383$	−12.1717	−0.621945	−0.310972	+	0.950419i	$0.600655\pi$
$384$	−44.8942	−2.29100
$385$	−2.32095	−0.118287
$386$	−9.01527	−0.458865
$387$	41.4158	2.10529
$388$	−10.4443	−0.530229
$389$	29.3724	1.48924	0.744621	−	0.667488i	$-0.232630\pi$
$389$	29.3724	1.48924	0.744621	+	0.667488i	$0.232630\pi$
$390$	10.8349	0.548645
$391$	0	0
$392$	−9.02793	−0.455979
$393$	41.9366	2.11542
$394$	−8.83668	−0.445185
$395$	7.79173	0.392045
$396$	−6.76395	−0.339901
$397$	17.7400	0.890346	0.445173	−	0.895445i	$-0.353142\pi$
$397$	17.7400	0.890346	0.445173	+	0.895445i	$0.353142\pi$
$398$	17.2764	0.865989
$399$	18.5671	0.929517
$400$	14.2333	0.711667
$401$	−17.0670	−0.852285	−0.426143	−	0.904656i	$-0.640128\pi$
$401$	−17.0670	−0.852285	−0.426143	+	0.904656i	$0.640128\pi$
$402$	82.2387	4.10170
$403$	−1.68659	−0.0840152
$404$	−1.72911	−0.0860264
$405$	56.1915	2.79218
$406$	−17.3177	−0.859465
$407$	−0.915746	−0.0453918
$408$	20.2654	1.00329
$409$	30.7419	1.52009	0.760046	−	0.649870i	$-0.225176\pi$
$409$	30.7419	1.52009	0.760046	+	0.649870i	$0.225176\pi$
$410$	−2.06541	−0.102003
$411$	−4.93411	−0.243382
$412$	0.660959	0.0325631
$413$	−11.6747	−0.574475
$414$	0	0
$415$	−12.7410	−0.625429
$416$	−5.54439	−0.271836
$417$	−33.2234	−1.62696
$418$	5.73529	0.280522
$419$	9.59178	0.468589	0.234294	−	0.972166i	$-0.424722\pi$
$419$	9.59178	0.468589	0.234294	+	0.972166i	$0.424722\pi$
$420$	6.23796	0.304381
$421$	1.83846	0.0896013	0.0448006	−	0.998996i	$-0.485735\pi$
$421$	1.83846	0.0896013	0.0448006	+	0.998996i	$0.485735\pi$
$422$	−5.42017	−0.263850
$423$	34.9141	1.69758
$424$	−18.4047	−0.893813
$425$	−8.47498	−0.411097
$426$	−87.1022	−4.22012
$427$	−23.2667	−1.12595
$428$	14.8048	0.715617
$429$	4.44597	0.214654
$430$	−11.7983	−0.568966
$431$	8.00207	0.385446	0.192723	−	0.981253i	$-0.438268\pi$
$431$	8.00207	0.385446	0.192723	+	0.981253i	$0.438268\pi$
$432$	−93.5803	−4.50239
$433$	−22.6248	−1.08728	−0.543640	−	0.839319i	$-0.682954\pi$
$433$	−22.6248	−1.08728	−0.543640	+	0.839319i	$0.682954\pi$
$434$	−3.42721	−0.164511
$435$	32.3113	1.54921
$436$	15.4367	0.739286
$437$	0	0
$438$	−68.6472	−3.28009
$439$	−3.22057	−0.153709	−0.0768547	−	0.997042i	$-0.524488\pi$
$439$	−3.22057	−0.153709	−0.0768547	+	0.997042i	$0.524488\pi$
$440$	−2.94714	−0.140499
$441$	−38.2290	−1.82043
$442$	6.44795	0.306698
$443$	−5.89971	−0.280304	−0.140152	−	0.990130i	$-0.544759\pi$
$443$	−5.89971	−0.280304	−0.140152	+	0.990130i	$0.544759\pi$
$444$	2.46122	0.116805
$445$	0.400291	0.0189756
$446$	−9.10728	−0.431242
$447$	−56.8370	−2.68830
$448$	4.50398	0.212793
$449$	−3.92735	−0.185343	−0.0926715	−	0.995697i	$-0.529541\pi$
$449$	−3.92735	−0.185343	−0.0926715	+	0.995697i	$0.529541\pi$
$450$	41.0410	1.93469
$451$	−0.847520	−0.0399082
$452$	−5.71841	−0.268971
$453$	−1.20621	−0.0566725
$454$	8.89504	0.417465
$455$	−3.03567	−0.142314
$456$	23.5764	1.10407
$457$	−11.8598	−0.554779	−0.277389	−	0.960758i	$-0.589469\pi$
$457$	−11.8598	−0.554779	−0.277389	+	0.960758i	$0.589469\pi$
$458$	28.8529	1.34821
$459$	55.7207	2.60082
$460$	0	0
$461$	1.79399	0.0835545	0.0417773	−	0.999127i	$-0.486698\pi$
$461$	1.79399	0.0835545	0.0417773	+	0.999127i	$0.486698\pi$
$462$	9.03436	0.420317
$463$	18.3448	0.852557	0.426278	−	0.904592i	$-0.359824\pi$
$463$	18.3448	0.852557	0.426278	+	0.904592i	$0.359824\pi$
$464$	−32.2939	−1.49920
$465$	6.39445	0.296536
$466$	8.56458	0.396747
$467$	−7.60437	−0.351888	−0.175944	−	0.984400i	$-0.556298\pi$
$467$	−7.60437	−0.351888	−0.175944	+	0.984400i	$0.556298\pi$
$468$	−8.84685	−0.408946
$469$	−23.0413	−1.06395
$470$	−9.94614	−0.458781
$471$	2.71566	0.125131
$472$	−14.8245	−0.682353
$473$	−4.84131	−0.222604
$474$	−30.3295	−1.39308
$475$	−9.85963	−0.452391
$476$	3.71228	0.170152
$477$	−77.9355	−3.56842
$478$	34.2212	1.56524
$479$	1.34460	0.0614362	0.0307181	−	0.999528i	$-0.490221\pi$
$479$	1.34460	0.0614362	0.0307181	+	0.999528i	$0.490221\pi$
$480$	21.0207	0.959459
$481$	−1.19774	−0.0546123
$482$	−32.3342	−1.47278
$483$	0	0
$484$	0.790674	0.0359397
$485$	−19.2701	−0.875012
$486$	−124.100	−5.62929
$487$	−3.48264	−0.157813	−0.0789067	−	0.996882i	$-0.525143\pi$
$487$	−3.48264	−0.157813	−0.0789067	+	0.996882i	$0.525143\pi$
$488$	−29.5439	−1.33739
$489$	52.6341	2.38020
$490$	10.8905	0.491982
$491$	−25.2303	−1.13863	−0.569314	−	0.822120i	$-0.692791\pi$
$491$	−25.2303	−1.13863	−0.569314	+	0.822120i	$0.692791\pi$
$492$	2.27785	0.102694
$493$	19.2288	0.866021
$494$	7.50142	0.337505
$495$	−12.4797	−0.560923
$496$	−6.39101	−0.286965
$497$	24.4039	1.09467
$498$	49.5945	2.22238
$499$	−15.7643	−0.705706	−0.352853	−	0.935679i	$-0.614788\pi$
$499$	−15.7643	−0.705706	−0.352853	+	0.935679i	$0.614788\pi$
$500$	−9.07979	−0.406061
$501$	−20.7201	−0.925706
$502$	−34.6990	−1.54869
$503$	−6.54121	−0.291658	−0.145829	−	0.989310i	$-0.546585\pi$
$503$	−6.54121	−0.291658	−0.145829	+	0.989310i	$0.546585\pi$
$504$	27.4958	1.22476
$505$	−3.19027	−0.141965
$506$	0	0
$507$	−38.3747	−1.70428
$508$	4.78526	0.212312
$509$	20.2932	0.899479	0.449740	−	0.893160i	$-0.351517\pi$
$509$	20.2932	0.899479	0.449740	+	0.893160i	$0.351517\pi$
$510$	−24.4464	−1.08250
$511$	19.2333	0.850831
$512$	−0.984233	−0.0434974
$513$	64.8243	2.86206
$514$	31.3029	1.38071
$515$	1.21949	0.0537374
$516$	13.0119	0.572815
$517$	−4.08129	−0.179495
$518$	−2.43385	−0.106937
$519$	−51.4305	−2.25755
$520$	−3.85468	−0.169039
$521$	−33.4891	−1.46718	−0.733591	−	0.679591i	$-0.762157\pi$
$521$	−33.4891	−1.46718	−0.733591	+	0.679591i	$0.762157\pi$
$522$	−93.1173	−4.07564
$523$	36.5090	1.59643	0.798215	−	0.602373i	$-0.205778\pi$
$523$	36.5090	1.59643	0.798215	+	0.602373i	$0.205778\pi$
$524$	9.75464	0.426133
$525$	−15.5311	−0.677833
$526$	−43.7613	−1.90808
$527$	3.80541	0.165766
$528$	16.8471	0.733178
$529$	0	0
$530$	22.2018	0.964386
$531$	−62.7748	−2.72420
$532$	4.31879	0.187243
$533$	−1.10851	−0.0480147
$534$	−1.55814	−0.0674273
$535$	27.3154	1.18095
$536$	−29.2578	−1.26374
$537$	6.56893	0.283470
$538$	−29.6687	−1.27911
$539$	4.46879	0.192484
$540$	21.7790	0.937217
$541$	1.95587	0.0840895	0.0420447	−	0.999116i	$-0.486613\pi$
$541$	1.95587	0.0840895	0.0420447	+	0.999116i	$0.486613\pi$
$542$	−22.3608	−0.960477
$543$	−21.7683	−0.934169
$544$	12.5096	0.536346
$545$	28.4814	1.22001
$546$	11.8164	0.505696
$547$	26.4000	1.12878	0.564391	−	0.825508i	$-0.309111\pi$
$547$	26.4000	1.12878	0.564391	+	0.825508i	$0.309111\pi$
$548$	−1.14770	−0.0490272
$549$	−125.105	−5.33934
$550$	−4.79749	−0.204566
$551$	22.3704	0.953011
$552$	0	0
$553$	8.49759	0.361354
$554$	−17.9555	−0.762858
$555$	4.54105	0.192757
$556$	−7.72793	−0.327737
$557$	42.5409	1.80251	0.901257	−	0.433284i	$-0.142645\pi$
$557$	42.5409	1.80251	0.901257	+	0.433284i	$0.142645\pi$
$558$	−18.4281	−0.780123
$559$	−6.33215	−0.267822
$560$	−11.5031	−0.486094
$561$	−10.0313	−0.423523
$562$	10.1838	0.429578
$563$	−18.3252	−0.772317	−0.386159	−	0.922432i	$-0.626198\pi$
$563$	−18.3252	−0.772317	−0.386159	+	0.922432i	$0.626198\pi$
$564$	10.9692	0.461885
$565$	−10.5507	−0.443871
$566$	23.4435	0.985402
$567$	61.2819	2.57360
$568$	30.9880	1.30023
$569$	−7.54526	−0.316314	−0.158157	−	0.987414i	$-0.550555\pi$
$569$	−7.54526	−0.316314	−0.158157	+	0.987414i	$0.550555\pi$
$570$	−28.4405	−1.19124
$571$	16.2373	0.679508	0.339754	−	0.940514i	$-0.389656\pi$
$571$	16.2373	0.679508	0.339754	+	0.940514i	$0.389656\pi$
$572$	1.03415	0.0432402
$573$	−9.49868	−0.396813
$574$	−2.25252	−0.0940184
$575$	0	0
$576$	24.2178	1.00908
$577$	−9.85003	−0.410062	−0.205031	−	0.978755i	$-0.565730\pi$
$577$	−9.85003	−0.410062	−0.205031	+	0.978755i	$0.565730\pi$
$578$	13.8507	0.576113
$579$	18.3444	0.762366
$580$	7.51575	0.312075
$581$	−13.8952	−0.576469
$582$	75.0094	3.10924
$583$	9.11028	0.377309
$584$	24.4224	1.01060
$585$	−16.3228	−0.674864
$586$	28.6019	1.18153
$587$	−37.6852	−1.55544	−0.777718	−	0.628614i	$-0.783623\pi$
$587$	−37.6852	−1.55544	−0.777718	+	0.628614i	$0.783623\pi$
$588$	−12.0106	−0.495310
$589$	4.42714	0.182417
$590$	17.8830	0.736230
$591$	17.9810	0.739639
$592$	−4.53860	−0.186535
$593$	−9.95792	−0.408923	−0.204461	−	0.978875i	$-0.565544\pi$
$593$	−9.95792	−0.408923	−0.204461	+	0.978875i	$0.565544\pi$
$594$	31.5422	1.29419
$595$	6.84929	0.280794
$596$	−13.2205	−0.541534
$597$	−35.1543	−1.43877
$598$	0	0
$599$	−4.01858	−0.164195	−0.0820974	−	0.996624i	$-0.526162\pi$
$599$	−4.01858	−0.164195	−0.0820974	+	0.996624i	$0.526162\pi$
$600$	−19.7213	−0.805121
$601$	−3.15220	−0.128581	−0.0642904	−	0.997931i	$-0.520478\pi$
$601$	−3.15220	−0.128581	−0.0642904	+	0.997931i	$0.520478\pi$
$602$	−12.8671	−0.524425
$603$	−123.893	−5.04531
$604$	−0.280569	−0.0114162
$605$	1.45882	0.0593096
$606$	12.4182	0.504455
$607$	−4.86550	−0.197484	−0.0987422	−	0.995113i	$-0.531482\pi$
$607$	−4.86550	−0.197484	−0.0987422	+	0.995113i	$0.531482\pi$
$608$	14.5535	0.590221
$609$	35.2384	1.42793
$610$	35.6391	1.44299
$611$	−5.33809	−0.215956
$612$	19.9609	0.806871
$613$	−7.69499	−0.310798	−0.155399	−	0.987852i	$-0.549666\pi$
$613$	−7.69499	−0.310798	−0.155399	+	0.987852i	$0.549666\pi$
$614$	28.5687	1.15294
$615$	4.20273	0.169470
$616$	−3.21412	−0.129501
$617$	33.1545	1.33475	0.667376	−	0.744721i	$-0.267417\pi$
$617$	33.1545	1.33475	0.667376	+	0.744721i	$0.267417\pi$
$618$	−4.74691	−0.190949
$619$	36.3788	1.46219	0.731095	−	0.682276i	$-0.239010\pi$
$619$	36.3788	1.46219	0.731095	+	0.682276i	$0.239010\pi$
$620$	1.48738	0.0597346
$621$	0	0
$622$	−37.8773	−1.51874
$623$	0.436553	0.0174901
$624$	22.0351	0.882108
$625$	−2.39337	−0.0957349
$626$	−22.8795	−0.914449
$627$	−11.6702	−0.466064
$628$	0.631676	0.0252066
$629$	2.70243	0.107753
$630$	−33.1684	−1.32146
$631$	9.05699	0.360553	0.180277	−	0.983616i	$-0.442301\pi$
$631$	9.05699	0.360553	0.180277	+	0.983616i	$0.442301\pi$
$632$	10.7902	0.429211
$633$	11.0290	0.438364
$634$	0.230384	0.00914973
$635$	8.82899	0.350368
$636$	−24.4854	−0.970910
$637$	5.84491	0.231584
$638$	10.8850	0.430940
$639$	131.220	5.19097
$640$	−19.2670	−0.761595
$641$	13.7489	0.543047	0.271524	−	0.962432i	$-0.412472\pi$
$641$	13.7489	0.543047	0.271524	+	0.962432i	$0.412472\pi$
$642$	−106.326	−4.19635
$643$	8.75949	0.345441	0.172720	−	0.984971i	$-0.444744\pi$
$643$	8.75949	0.345441	0.172720	+	0.984971i	$0.444744\pi$
$644$	0	0
$645$	24.0074	0.945289
$646$	−16.9252	−0.665914
$647$	−13.6240	−0.535613	−0.267807	−	0.963473i	$-0.586299\pi$
$647$	−13.6240	−0.535613	−0.267807	+	0.963473i	$0.586299\pi$
$648$	77.8155	3.05688
$649$	7.33808	0.288045
$650$	−6.27484	−0.246119
$651$	6.97373	0.273322
$652$	12.2429	0.479471
$653$	−25.1229	−0.983136	−0.491568	−	0.870839i	$-0.663576\pi$
$653$	−25.1229	−0.983136	−0.491568	+	0.870839i	$0.663576\pi$
$654$	−110.864	−4.33514
$655$	17.9977	0.703228
$656$	−4.20046	−0.164001
$657$	103.417	4.03469
$658$	−10.8472	−0.422867
$659$	−16.7202	−0.651326	−0.325663	−	0.945486i	$-0.605588\pi$
$659$	−16.7202	−0.651326	−0.325663	+	0.945486i	$0.605588\pi$
$660$	−3.92083	−0.152618
$661$	−13.1288	−0.510651	−0.255326	−	0.966855i	$-0.582183\pi$
$661$	−13.1288	−0.510651	−0.255326	+	0.966855i	$0.582183\pi$
$662$	3.33659	0.129680
$663$	−13.1204	−0.509553
$664$	−17.6440	−0.684721
$665$	7.96833	0.308999
$666$	−13.0868	−0.507103
$667$	0	0
$668$	−4.81959	−0.186476
$669$	18.5316	0.716473
$670$	35.2939	1.36352
$671$	14.6241	0.564558
$672$	22.9250	0.884350
$673$	32.4311	1.25013	0.625064	−	0.780574i	$-0.285073\pi$
$673$	32.4311	1.25013	0.625064	+	0.780574i	$0.285073\pi$
$674$	36.7976	1.41739
$675$	−54.2247	−2.08711
$676$	−8.92614	−0.343313
$677$	36.1771	1.39040	0.695200	−	0.718817i	$-0.255316\pi$
$677$	36.1771	1.39040	0.695200	+	0.718817i	$0.255316\pi$
$678$	41.0688	1.57724
$679$	−21.0158	−0.806514
$680$	8.69721	0.333523
$681$	−18.0997	−0.693583
$682$	2.15415	0.0824868
$683$	11.5573	0.442227	0.221113	−	0.975248i	$-0.429031\pi$
$683$	11.5573	0.442227	0.221113	+	0.975248i	$0.429031\pi$
$684$	23.2221	0.887919
$685$	−2.11754	−0.0809072
$686$	30.4815	1.16379
$687$	−58.7102	−2.23993
$688$	−23.9944	−0.914779
$689$	11.9157	0.453952
$690$	0	0
$691$	24.9023	0.947328	0.473664	−	0.880706i	$-0.342931\pi$
$691$	24.9023	0.947328	0.473664	+	0.880706i	$0.342931\pi$
$692$	−11.9630	−0.454764
$693$	−13.6103	−0.517012
$694$	27.8265	1.05628
$695$	−14.2583	−0.540849
$696$	44.7455	1.69607
$697$	2.50109	0.0947355
$698$	−44.9112	−1.69992
$699$	−17.4273	−0.659162
$700$	−3.61261	−0.136544
$701$	−45.5889	−1.72187	−0.860934	−	0.508717i	$-0.830120\pi$
$701$	−45.5889	−1.72187	−0.860934	+	0.508717i	$0.830120\pi$
$702$	41.2553	1.55708
$703$	3.14395	0.118576
$704$	−2.83095	−0.106695
$705$	20.2385	0.762227
$706$	14.6199	0.550228
$707$	−3.47928	−0.130852
$708$	−19.7223	−0.741211
$709$	−10.8607	−0.407881	−0.203940	−	0.978983i	$-0.565375\pi$
$709$	−10.8607	−0.407881	−0.203940	+	0.978983i	$0.565375\pi$
$710$	−37.3812	−1.40289
$711$	45.6915	1.71356
$712$	0.554333	0.0207745
$713$	0	0
$714$	−26.6610	−0.997763
$715$	1.90805	0.0713572
$716$	1.52796	0.0571027
$717$	−69.6337	−2.60052
$718$	58.3036	2.17587
$719$	−32.4082	−1.20862	−0.604311	−	0.796748i	$-0.706552\pi$
$719$	−32.4082	−1.20862	−0.604311	+	0.796748i	$0.706552\pi$
$720$	−61.8519	−2.30508
$721$	1.32997	0.0495306
$722$	12.0496	0.448440
$723$	65.7940	2.44690
$724$	−5.06342	−0.188180
$725$	−18.7125	−0.694966
$726$	−5.67850	−0.210749
$727$	27.1330	1.00631	0.503154	−	0.864197i	$-0.332173\pi$
$727$	27.1330	1.00631	0.503154	+	0.864197i	$0.332173\pi$
$728$	−4.20388	−0.155806
$729$	136.965	5.07278
$730$	−29.4609	−1.09040
$731$	14.2870	0.528425
$732$	−39.3048	−1.45275
$733$	34.7331	1.28290	0.641448	−	0.767166i	$-0.278334\pi$
$733$	34.7331	1.28290	0.641448	+	0.767166i	$0.278334\pi$
$734$	4.91204	0.181307
$735$	−22.1601	−0.817387
$736$	0	0
$737$	14.4825	0.533469
$738$	−12.1118	−0.445841
$739$	−0.820303	−0.0301753	−0.0150877	−	0.999886i	$-0.504803\pi$
$739$	−0.820303	−0.0301753	−0.0150877	+	0.999886i	$0.504803\pi$
$740$	1.05627	0.0388292
$741$	−15.2640	−0.560736
$742$	24.2131	0.888891
$743$	−21.3971	−0.784982	−0.392491	−	0.919756i	$-0.628387\pi$
$743$	−21.3971	−0.784982	−0.392491	+	0.919756i	$0.628387\pi$
$744$	8.85521	0.324648
$745$	−24.3924	−0.893668
$746$	−5.19827	−0.190322
$747$	−74.7142	−2.73365
$748$	−2.33333	−0.0853150
$749$	29.7899	1.08850
$750$	65.2097	2.38112
$751$	−11.2209	−0.409457	−0.204729	−	0.978819i	$-0.565631\pi$
$751$	−11.2209	−0.409457	−0.204729	+	0.978819i	$0.565631\pi$
$752$	−20.2276	−0.737626
$753$	70.6060	2.57303
$754$	14.2369	0.518477
$755$	−0.517661	−0.0188396
$756$	23.7519	0.863849
$757$	−21.7168	−0.789310	−0.394655	−	0.918829i	$-0.629136\pi$
$757$	−21.7168	−0.789310	−0.394655	+	0.918829i	$0.629136\pi$
$758$	41.9247	1.52277
$759$	0	0
$760$	10.1182	0.367024
$761$	29.6496	1.07480	0.537399	−	0.843328i	$-0.319407\pi$
$761$	29.6496	1.07480	0.537399	+	0.843328i	$0.319407\pi$
$762$	−34.3670	−1.24499
$763$	31.0615	1.12450
$764$	−2.20944	−0.0799346
$765$	36.8286	1.33154
$766$	20.3332	0.734668
$767$	9.59777	0.346555
$768$	55.7512	2.01175
$769$	31.9851	1.15341	0.576706	−	0.816952i	$-0.304338\pi$
$769$	31.9851	1.15341	0.576706	+	0.816952i	$0.304338\pi$
$770$	3.87723	0.139726
$771$	−63.6955	−2.29394
$772$	4.26699	0.153572
$773$	10.6542	0.383205	0.191603	−	0.981473i	$-0.438632\pi$
$773$	10.6542	0.383205	0.191603	+	0.981473i	$0.438632\pi$
$774$	−69.1865	−2.48686
$775$	−3.70324	−0.133024
$776$	−26.6858	−0.957965
$777$	4.95243	0.177667
$778$	−49.0676	−1.75916
$779$	2.90972	0.104251
$780$	−5.12822	−0.183620
$781$	−15.3390	−0.548871
$782$	0	0
$783$	123.030	4.39672
$784$	22.1481	0.791005
$785$	1.16547	0.0415973
$786$	−70.0563	−2.49883
$787$	45.9496	1.63793	0.818963	−	0.573846i	$-0.194549\pi$
$787$	45.9496	1.63793	0.818963	+	0.573846i	$0.194549\pi$
$788$	4.18246	0.148994
$789$	89.0460	3.17012
$790$	−13.0163	−0.463100
$791$	−11.5065	−0.409123
$792$	−17.2823	−0.614100
$793$	19.1275	0.679238
$794$	−29.6352	−1.05172
$795$	−45.1765	−1.60225
$796$	−8.17705	−0.289828
$797$	26.3653	0.933906	0.466953	−	0.884282i	$-0.345352\pi$
$797$	26.3653	0.933906	0.466953	+	0.884282i	$0.345352\pi$
$798$	−31.0169	−1.09799
$799$	12.0442	0.426092
$800$	−12.1738	−0.430408
$801$	2.34734	0.0829392
$802$	28.5109	1.00676
$803$	−12.0890	−0.426611
$804$	−38.9242	−1.37275
$805$	0	0
$806$	2.81751	0.0992424
$807$	60.3702	2.12513
$808$	−4.41797	−0.155424
$809$	−28.2478	−0.993141	−0.496571	−	0.867996i	$-0.665408\pi$
$809$	−28.2478	−0.993141	−0.496571	+	0.867996i	$0.665408\pi$
$810$	−93.8697	−3.29824
$811$	−29.3756	−1.03152	−0.515758	−	0.856734i	$-0.672490\pi$
$811$	−29.3756	−1.03152	−0.515758	+	0.856734i	$0.672490\pi$
$812$	8.19661	0.287644
$813$	45.4999	1.59575
$814$	1.52978	0.0536188
$815$	22.5887	0.791248
$816$	−49.7170	−1.74044
$817$	16.6213	0.581504
$818$	−51.3554	−1.79560
$819$	−17.8015	−0.622033
$820$	0.977574	0.0341384
$821$	15.1991	0.530454	0.265227	−	0.964186i	$-0.414553\pi$
$821$	15.1991	0.530454	0.265227	+	0.964186i	$0.414553\pi$
$822$	8.24258	0.287493
$823$	−13.5880	−0.473648	−0.236824	−	0.971553i	$-0.576106\pi$
$823$	−13.5880	−0.473648	−0.236824	+	0.971553i	$0.576106\pi$
$824$	1.68879	0.0588318
$825$	9.76199	0.339869
$826$	19.5030	0.678595
$827$	4.88706	0.169940	0.0849699	−	0.996384i	$-0.472921\pi$
$827$	4.88706	0.169940	0.0849699	+	0.996384i	$0.472921\pi$
$828$	0	0
$829$	41.5608	1.44347	0.721733	−	0.692171i	$-0.243346\pi$
$829$	41.5608	1.44347	0.721733	+	0.692171i	$0.243346\pi$
$830$	21.2842	0.738785
$831$	36.5362	1.26743
$832$	−3.70271	−0.128368
$833$	−13.1877	−0.456927
$834$	55.5008	1.92184
$835$	−8.89233	−0.307732
$836$	−2.71455	−0.0938847
$837$	24.3478	0.841582
$838$	−16.0234	−0.553518
$839$	0.135827	0.00468926	0.00234463	−	0.999997i	$-0.499254\pi$
$839$	0.135827	0.00468926	0.00234463	+	0.999997i	$0.499254\pi$
$840$	15.9384	0.549926
$841$	13.4566	0.464021
$842$	−3.07121	−0.105841
$843$	−20.7222	−0.713709
$844$	2.56540	0.0883048
$845$	−16.4691	−0.566553
$846$	−58.3251	−2.00526
$847$	1.59098	0.0546666
$848$	45.1522	1.55053
$849$	−47.7030	−1.63716
$850$	14.1577	0.485606
$851$	0	0
$852$	41.2261	1.41238
$853$	−44.1722	−1.51243	−0.756214	−	0.654324i	$-0.772953\pi$
$853$	−44.1722	−1.51243	−0.756214	+	0.654324i	$0.772953\pi$
$854$	38.8677	1.33003
$855$	42.8456	1.46529
$856$	37.8271	1.29291
$857$	−48.6370	−1.66141	−0.830704	−	0.556714i	$-0.812062\pi$
$857$	−48.6370	−1.66141	−0.830704	+	0.556714i	$0.812062\pi$
$858$	−7.42714	−0.253558
$859$	−41.7562	−1.42470	−0.712352	−	0.701822i	$-0.752370\pi$
$859$	−41.7562	−1.42470	−0.712352	+	0.701822i	$0.752370\pi$
$860$	5.58423	0.190420
$861$	4.58345	0.156204
$862$	−13.3677	−0.455306
$863$	22.3278	0.760048	0.380024	−	0.924977i	$-0.375916\pi$
$863$	22.3278	0.760048	0.380024	+	0.924977i	$0.375916\pi$
$864$	80.0392	2.72299
$865$	−22.0721	−0.750475
$866$	37.7955	1.28434
$867$	−28.1836	−0.957165
$868$	1.62212	0.0550584
$869$	−5.34111	−0.181185
$870$	−53.9770	−1.82999
$871$	18.9422	0.641833
$872$	39.4418	1.33567
$873$	−113.002	−3.82454
$874$	0	0
$875$	−18.2702	−0.617645
$876$	32.4912	1.09778
$877$	24.3070	0.820788	0.410394	−	0.911908i	$-0.365391\pi$
$877$	24.3070	0.820788	0.410394	+	0.911908i	$0.365391\pi$
$878$	5.38006	0.181568
$879$	−58.1994	−1.96302
$880$	7.23019	0.243730
$881$	−26.4410	−0.890819	−0.445410	−	0.895327i	$-0.646942\pi$
$881$	−26.4410	−0.890819	−0.445410	+	0.895327i	$0.646942\pi$
$882$	63.8628	2.15037
$883$	28.6462	0.964023	0.482011	−	0.876165i	$-0.339906\pi$
$883$	28.6462	0.964023	0.482011	+	0.876165i	$0.339906\pi$
$884$	−3.05186	−0.102645
$885$	−36.3884	−1.22318
$886$	9.85565	0.331107
$887$	−16.2310	−0.544985	−0.272492	−	0.962158i	$-0.587848\pi$
$887$	−16.2310	−0.544985	−0.272492	+	0.962158i	$0.587848\pi$
$888$	6.28857	0.211031
$889$	9.62881	0.322940
$890$	−0.668698	−0.0224148
$891$	−38.5184	−1.29041
$892$	4.31054	0.144327
$893$	14.0119	0.468892
$894$	94.9479	3.17553
$895$	2.81915	0.0942339
$896$	−21.0124	−0.701975
$897$	0	0
$898$	6.56075	0.218935
$899$	8.40223	0.280230
$900$	−19.4250	−0.647499
$901$	−26.8851	−0.895671
$902$	1.41581	0.0471413
$903$	26.1822	0.871289
$904$	−14.6109	−0.485951
$905$	−9.34220	−0.310545
$906$	2.01500	0.0669440
$907$	40.6192	1.34874	0.674369	−	0.738394i	$-0.264416\pi$
$907$	40.6192	1.34874	0.674369	+	0.738394i	$0.264416\pi$
$908$	−4.21008	−0.139716
$909$	−18.7080	−0.620507
$910$	5.07118	0.168108
$911$	−53.3187	−1.76653	−0.883263	−	0.468878i	$-0.844659\pi$
$911$	−53.3187	−1.76653	−0.883263	+	0.468878i	$0.844659\pi$
$912$	−57.8398	−1.91527
$913$	8.73373	0.289044
$914$	19.8122	0.655329
$915$	−72.5189	−2.39740
$916$	−13.6563	−0.451216
$917$	19.6281	0.648177
$918$	−93.0831	−3.07220
$919$	8.18610	0.270035	0.135017	−	0.990843i	$-0.456891\pi$
$919$	8.18610	0.270035	0.135017	+	0.990843i	$0.456891\pi$
$920$	0	0
$921$	−58.1320	−1.91552
$922$	−2.99692	−0.0986982
$923$	−20.0625	−0.660364
$924$	−4.27602	−0.140671
$925$	−2.62987	−0.0864697
$926$	−30.6456	−1.00708
$927$	7.15123	0.234877
$928$	27.6209	0.906702
$929$	47.1259	1.54615	0.773075	−	0.634315i	$-0.218718\pi$
$929$	47.1259	1.54615	0.773075	+	0.634315i	$0.218718\pi$
$930$	−10.6821	−0.350281
$931$	−15.3423	−0.502824
$932$	−4.05367	−0.132783
$933$	77.0733	2.52327
$934$	12.7033	0.415666
$935$	−4.30508	−0.140791
$936$	−22.6042	−0.738842
$937$	14.4769	0.472939	0.236470	−	0.971639i	$-0.424010\pi$
$937$	14.4769	0.472939	0.236470	+	0.971639i	$0.424010\pi$
$938$	38.4912	1.25678
$939$	46.5555	1.51928
$940$	4.70758	0.153544
$941$	28.7201	0.936247	0.468124	−	0.883663i	$-0.344930\pi$
$941$	28.7201	0.936247	0.468124	+	0.883663i	$0.344930\pi$
$942$	−4.53660	−0.147810
$943$	0	0
$944$	36.3688	1.18371
$945$	43.8232	1.42557
$946$	8.08756	0.262949
$947$	−11.7718	−0.382531	−0.191266	−	0.981538i	$-0.561259\pi$
$947$	−11.7718	−0.382531	−0.191266	+	0.981538i	$0.561259\pi$
$948$	14.3551	0.466234
$949$	−15.8117	−0.513268
$950$	16.4708	0.534384
$951$	−0.468789	−0.0152015
$952$	9.48509	0.307413
$953$	11.3022	0.366114	0.183057	−	0.983102i	$-0.441401\pi$
$953$	11.3022	0.366114	0.183057	+	0.983102i	$0.441401\pi$
$954$	130.194	4.21517
$955$	−4.07649	−0.131912
$956$	−16.1971	−0.523852
$957$	−22.1489	−0.715971
$958$	−2.24619	−0.0725711
$959$	−2.30937	−0.0745735
$960$	14.0383	0.453083
$961$	−29.3372	−0.946361
$962$	2.00086	0.0645105
$963$	160.180	5.16173
$964$	15.3040	0.492908
$965$	7.87275	0.253433
$966$	0	0
$967$	33.4043	1.07421	0.537105	−	0.843516i	$-0.319518\pi$
$967$	33.4043	1.07421	0.537105	+	0.843516i	$0.319518\pi$
$968$	2.02022	0.0649322
$969$	34.4397	1.10636
$970$	32.1914	1.03360
$971$	−51.8713	−1.66463	−0.832314	−	0.554304i	$-0.812984\pi$
$971$	−51.8713	−1.66463	−0.832314	+	0.554304i	$0.812984\pi$
$972$	58.7374	1.88400
$973$	−15.5500	−0.498510
$974$	5.81786	0.186416
$975$	12.7681	0.408907
$976$	72.4799	2.32002
$977$	−31.1592	−0.996870	−0.498435	−	0.866927i	$-0.666092\pi$
$977$	−31.1592	−0.996870	−0.498435	+	0.866927i	$0.666092\pi$
$978$	−87.9269	−2.81159
$979$	−0.274393	−0.00876963
$980$	−5.15454	−0.164656
$981$	167.017	5.33246
$982$	42.1480	1.34500
$983$	3.63587	0.115966	0.0579831	−	0.998318i	$-0.481533\pi$
$983$	3.63587	0.115966	0.0579831	+	0.998318i	$0.481533\pi$
$984$	5.82005	0.185536
$985$	7.71680	0.245878
$986$	−32.1223	−1.02298
$987$	22.0719	0.702558
$988$	−3.55047	−0.112956
$989$	0	0
$990$	20.8478	0.662587
$991$	26.7482	0.849684	0.424842	−	0.905267i	$-0.360330\pi$
$991$	26.7482	0.849684	0.424842	+	0.905267i	$0.360330\pi$
$992$	5.46623	0.173553
$993$	−6.78933	−0.215453
$994$	−40.7675	−1.29307
$995$	−15.0870	−0.478289
$996$	−23.4734	−0.743783
$997$	57.0396	1.80646	0.903232	−	0.429153i	$-0.141188\pi$
$997$	57.0396	1.80646	0.903232	+	0.429153i	$0.141188\pi$
$998$	26.3347	0.833611
$999$	17.2907	0.547053

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5819.2.a.t.1.13		60
23.7	odd	22		253.2.i.b.210.10	yes	120
23.10	odd	22		253.2.i.b.100.10	✓	120
23.22	odd	2		5819.2.a.u.1.13		60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
253.2.i.b.100.10	✓	120	23.10	odd	22
253.2.i.b.210.10	yes	120	23.7	odd	22
5819.2.a.t.1.13		60	1.1	even	1	trivial
5819.2.a.u.1.13		60	23.22	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 5819 = 11 \cdot 23^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5819.a (trivial)

\(f(q)\)	\(=\)	\(q-1.67053 q^{2} +3.39922 q^{3} +0.790674 q^{4} +1.45882 q^{5} -5.67850 q^{6} +1.59098 q^{7} +2.02022 q^{8} +8.55467 q^{9} -2.43701 q^{10} -1.00000 q^{11} +2.68767 q^{12} -1.30794 q^{13} -2.65778 q^{14} +4.95885 q^{15} -4.95618 q^{16} +2.95107 q^{17} -14.2908 q^{18} +3.43321 q^{19} +1.15345 q^{20} +5.40808 q^{21} +1.67053 q^{22} +6.86716 q^{24} -2.87184 q^{25} +2.18496 q^{26} +18.8815 q^{27} +1.25794 q^{28} +6.51587 q^{29} -8.28392 q^{30} +1.28950 q^{31} +4.23902 q^{32} -3.39922 q^{33} -4.92985 q^{34} +2.32095 q^{35} +6.76395 q^{36} +0.915746 q^{37} -5.73529 q^{38} -4.44597 q^{39} +2.94714 q^{40} +0.847520 q^{41} -9.03436 q^{42} +4.84131 q^{43} -0.790674 q^{44} +12.4797 q^{45} +4.08129 q^{47} -16.8471 q^{48} -4.46879 q^{49} +4.79749 q^{50} +10.0313 q^{51} -1.03415 q^{52} -9.11028 q^{53} -31.5422 q^{54} -1.45882 q^{55} +3.21412 q^{56} +11.6702 q^{57} -10.8850 q^{58} -7.33808 q^{59} +3.92083 q^{60} -14.6241 q^{61} -2.15415 q^{62} +13.6103 q^{63} +2.83095 q^{64} -1.90805 q^{65} +5.67850 q^{66} -14.4825 q^{67} +2.33333 q^{68} -3.87723 q^{70} +15.3390 q^{71} +17.2823 q^{72} +12.0890 q^{73} -1.52978 q^{74} -9.76199 q^{75} +2.71455 q^{76} -1.59098 q^{77} +7.42714 q^{78} +5.34111 q^{79} -7.23019 q^{80} +38.5184 q^{81} -1.41581 q^{82} -8.73373 q^{83} +4.27602 q^{84} +4.30508 q^{85} -8.08756 q^{86} +22.1489 q^{87} -2.02022 q^{88} +0.274393 q^{89} -20.8478 q^{90} -2.08091 q^{91} +4.38330 q^{93} -6.81792 q^{94} +5.00845 q^{95} +14.4094 q^{96} -13.2094 q^{97} +7.46525 q^{98} -8.55467 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 5 q^{2} + 9 q^{3} + 73 q^{4} - 8 q^{5} + 26 q^{6} + 30 q^{8} + 75 q^{9} + 7 q^{10} - 60 q^{11} + 41 q^{12} + 46 q^{13} - 16 q^{14} - 4 q^{15} + 99 q^{16} + 5 q^{17} + 36 q^{18} + 8 q^{19} - 82 q^{20}+ \cdots - 75 q^{99}+O(q^{100}) \) 60 * q + 5 * q^2 + 9 * q^3 + 73 * q^4 - 8 * q^5 + 26 * q^6 + 30 * q^8 + 75 * q^9 + 7 * q^10 - 60 * q^11 + 41 * q^12 + 46 * q^13 - 16 * q^14 - 4 * q^15 + 99 * q^16 + 5 * q^17 + 36 * q^18 + 8 * q^19 - 82 * q^20 + 13 * q^21 - 5 * q^22 + 54 * q^24 + 96 * q^25 + 31 * q^26 + 54 * q^27 + 29 * q^28 + 42 * q^29 + 14 * q^30 + 71 * q^31 + 40 * q^32 - 9 * q^33 - 10 * q^34 + 9 * q^35 + 93 * q^36 + 5 * q^37 + 11 * q^38 + 56 * q^39 + 40 * q^40 + 62 * q^41 - 43 * q^42 + 2 * q^43 - 73 * q^44 + q^45 - q^47 + 71 * q^48 + 138 * q^49 - 18 * q^50 + 27 * q^51 + 102 * q^52 - 11 * q^53 + 69 * q^54 + 8 * q^55 - 13 * q^56 - 38 * q^57 + 58 * q^58 + 57 * q^59 + 49 * q^60 + 26 * q^61 + 17 * q^62 + 41 * q^63 + 184 * q^64 + 19 * q^65 - 26 * q^66 - 7 * q^67 + 76 * q^68 + 43 * q^70 + 33 * q^71 + 100 * q^72 + 108 * q^73 + 63 * q^74 + q^75 + 42 * q^76 - 3 * q^78 + 25 * q^79 - 148 * q^80 + 68 * q^81 + 59 * q^82 + 41 * q^83 + 97 * q^84 + 160 * q^85 - 78 * q^86 + 41 * q^87 - 30 * q^88 - 51 * q^89 + 53 * q^90 + 65 * q^93 + 121 * q^94 - 14 * q^95 + 82 * q^96 + 13 * q^97 - 75 * q^98 - 75 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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