LMFDB - Embedded newform 1805.2.a.w.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1805,2,Mod(1,1805)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1805, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1805.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1805 = 5 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1805.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	yes
Analytic conductor:	$14.4129975648$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 29x^{14} + 339x^{12} - 2038x^{10} + 6639x^{8} - 11261x^{6} + 8701x^{4} - 2592x^{2} + 256 $ x^16 - 29x^14 + 339x^12 - 2038x^10 + 6639x^8 - 11261x^6 + 8701x^4 - 2592*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$-0.503538$ of defining polynomial
Character	$\chi$	$=$	1805.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.503538 q^{2} -3.01030 q^{3} -1.74645 q^{4} +1.00000 q^{5} +1.51580 q^{6} +2.48971 q^{7} +1.88648 q^{8} +6.06188 q^{9} +O(q^{10})$	\(q-0.503538 q^{2} -3.01030 q^{3} -1.74645 q^{4} +1.00000 q^{5} +1.51580 q^{6} +2.48971 q^{7} +1.88648 q^{8} +6.06188 q^{9} -0.503538 q^{10} +4.58103 q^{11} +5.25733 q^{12} +6.06268 q^{13} -1.25366 q^{14} -3.01030 q^{15} +2.54298 q^{16} +1.83458 q^{17} -3.05239 q^{18} -1.74645 q^{20} -7.49476 q^{21} -2.30672 q^{22} +0.125981 q^{23} -5.67886 q^{24} +1.00000 q^{25} -3.05279 q^{26} -9.21717 q^{27} -4.34815 q^{28} -3.79112 q^{29} +1.51580 q^{30} +8.09930 q^{31} -5.05345 q^{32} -13.7903 q^{33} -0.923781 q^{34} +2.48971 q^{35} -10.5868 q^{36} -1.44010 q^{37} -18.2505 q^{39} +1.88648 q^{40} -3.02823 q^{41} +3.77390 q^{42} +8.78585 q^{43} -8.00054 q^{44} +6.06188 q^{45} -0.0634361 q^{46} +5.70424 q^{47} -7.65514 q^{48} -0.801349 q^{49} -0.503538 q^{50} -5.52263 q^{51} -10.5882 q^{52} +9.24712 q^{53} +4.64120 q^{54} +4.58103 q^{55} +4.69679 q^{56} +1.90897 q^{58} -7.06307 q^{59} +5.25733 q^{60} -8.41466 q^{61} -4.07831 q^{62} +15.0923 q^{63} -2.54137 q^{64} +6.06268 q^{65} +6.94392 q^{66} +6.08737 q^{67} -3.20400 q^{68} -0.379239 q^{69} -1.25366 q^{70} +10.4060 q^{71} +11.4356 q^{72} -10.8772 q^{73} +0.725145 q^{74} -3.01030 q^{75} +11.4054 q^{77} +9.18981 q^{78} +5.23370 q^{79} +2.54298 q^{80} +9.56077 q^{81} +1.52483 q^{82} +5.03188 q^{83} +13.0892 q^{84} +1.83458 q^{85} -4.42401 q^{86} +11.4124 q^{87} +8.64202 q^{88} -14.6205 q^{89} -3.05239 q^{90} +15.0943 q^{91} -0.220019 q^{92} -24.3813 q^{93} -2.87230 q^{94} +15.2124 q^{96} -2.49726 q^{97} +0.403510 q^{98} +27.7697 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 26 q^{4} + 16 q^{5} - 2 q^{6} + 22 q^{7} + 18 q^{9}+O(q^{10}) $ 16 * q + 26 * q^4 + 16 * q^5 - 2 * q^6 + 22 * q^7 + 18 * q^9	$ 16 q + 26 q^{4} + 16 q^{5} - 2 q^{6} + 22 q^{7} + 18 q^{9} + 12 q^{11} + 42 q^{16} + 22 q^{17} + 26 q^{20} + 42 q^{23} - 14 q^{24} + 16 q^{25} - 26 q^{26} + 46 q^{28} - 2 q^{30} + 22 q^{35} - 8 q^{36} - 38 q^{39} + 74 q^{42} + 88 q^{43} - 48 q^{44} + 18 q^{45} + 32 q^{47} + 30 q^{49} - 22 q^{54} + 12 q^{55} - 2 q^{58} + 20 q^{61} + 6 q^{62} - 6 q^{63} + 24 q^{64} - 24 q^{66} + 84 q^{68} + 44 q^{73} - 122 q^{74} + 4 q^{77} + 42 q^{80} - 36 q^{81} - 50 q^{82} + 56 q^{83} + 22 q^{85} + 34 q^{87} + 6 q^{92} - 58 q^{93} - 96 q^{96} + 6 q^{99}+O(q^{100}) $ 16 * q + 26 * q^4 + 16 * q^5 - 2 * q^6 + 22 * q^7 + 18 * q^9 + 12 * q^11 + 42 * q^16 + 22 * q^17 + 26 * q^20 + 42 * q^23 - 14 * q^24 + 16 * q^25 - 26 * q^26 + 46 * q^28 - 2 * q^30 + 22 * q^35 - 8 * q^36 - 38 * q^39 + 74 * q^42 + 88 * q^43 - 48 * q^44 + 18 * q^45 + 32 * q^47 + 30 * q^49 - 22 * q^54 + 12 * q^55 - 2 * q^58 + 20 * q^61 + 6 * q^62 - 6 * q^63 + 24 * q^64 - 24 * q^66 + 84 * q^68 + 44 * q^73 - 122 * q^74 + 4 * q^77 + 42 * q^80 - 36 * q^81 - 50 * q^82 + 56 * q^83 + 22 * q^85 + 34 * q^87 + 6 * q^92 - 58 * q^93 - 96 * q^96 + 6 * q^99

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 $

$2$	−0.503538	−0.356055	−0.178028	−	0.984025i	$-0.556972\pi$
$2$	−0.503538	−0.356055	−0.178028	+	0.984025i	$0.556972\pi$
$3$	−3.01030	−1.73800	−0.868998	−	0.494816i	$-0.835235\pi$
$3$	−3.01030	−1.73800	−0.868998	+	0.494816i	$0.835235\pi$
$4$	−1.74645	−0.873225
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	1.51580	0.618822
$7$	2.48971	0.941022	0.470511	−	0.882394i	$-0.344070\pi$
$7$	2.48971	0.941022	0.470511	+	0.882394i	$0.344070\pi$
$8$	1.88648	0.666971
$9$	6.06188	2.02063
$10$	−0.503538	−0.159233
$11$	4.58103	1.38123	0.690616	−	0.723222i	$-0.257339\pi$
$11$	4.58103	1.38123	0.690616	+	0.723222i	$0.257339\pi$
$12$	5.25733	1.51766
$13$	6.06268	1.68149	0.840743	−	0.541434i	$-0.182119\pi$
$13$	6.06268	1.68149	0.840743	+	0.541434i	$0.182119\pi$
$14$	−1.25366	−0.335056
$15$	−3.01030	−0.777255
$16$	2.54298	0.635746
$17$	1.83458	0.444951	0.222475	−	0.974938i	$-0.428586\pi$
$17$	1.83458	0.444951	0.222475	+	0.974938i	$0.428586\pi$
$18$	−3.05239	−0.719455
$19$	0	0
$19$	0	0
$20$	−1.74645	−0.390518
$21$	−7.49476	−1.63549
$22$	−2.30672	−0.491795
$23$	0.125981	0.0262688	0.0131344	−	0.999914i	$-0.495819\pi$
$23$	0.125981	0.0262688	0.0131344	+	0.999914i	$0.495819\pi$
$24$	−5.67886	−1.15919
$25$	1.00000	0.200000
$26$	−3.05279	−0.598702
$27$	−9.21717	−1.77385
$28$	−4.34815	−0.821723
$29$	−3.79112	−0.703993	−0.351997	−	0.936001i	$-0.614497\pi$
$29$	−3.79112	−0.703993	−0.351997	+	0.936001i	$0.614497\pi$
$30$	1.51580	0.276746
$31$	8.09930	1.45468	0.727339	−	0.686279i	$-0.240757\pi$
$31$	8.09930	1.45468	0.727339	+	0.686279i	$0.240757\pi$
$32$	−5.05345	−0.893332
$33$	−13.7903	−2.40058
$34$	−0.923781	−0.158427
$35$	2.48971	0.420838
$36$	−10.5868	−1.76446
$37$	−1.44010	−0.236751	−0.118375	−	0.992969i	$-0.537769\pi$
$37$	−1.44010	−0.236751	−0.118375	+	0.992969i	$0.537769\pi$
$38$	0	0
$39$	−18.2505	−2.92241
$40$	1.88648	0.298279
$41$	−3.02823	−0.472930	−0.236465	−	0.971640i	$-0.575989\pi$
$41$	−3.02823	−0.472930	−0.236465	+	0.971640i	$0.575989\pi$
$42$	3.77390	0.582325
$43$	8.78585	1.33983	0.669915	−	0.742438i	$-0.266330\pi$
$43$	8.78585	1.33983	0.669915	+	0.742438i	$0.266330\pi$
$44$	−8.00054	−1.20613
$45$	6.06188	0.903652
$46$	−0.0634361	−0.00935314
$47$	5.70424	0.832048	0.416024	−	0.909354i	$-0.363423\pi$
$47$	5.70424	0.832048	0.416024	+	0.909354i	$0.363423\pi$
$48$	−7.65514	−1.10492
$49$	−0.801349	−0.114478
$50$	−0.503538	−0.0712110
$51$	−5.52263	−0.773323
$52$	−10.5882	−1.46832
$53$	9.24712	1.27019	0.635095	−	0.772434i	$-0.280961\pi$
$53$	9.24712	1.27019	0.635095	+	0.772434i	$0.280961\pi$
$54$	4.64120	0.631587
$55$	4.58103	0.617706
$56$	4.69679	0.627634
$57$	0	0
$58$	1.90897	0.250660
$59$	−7.06307	−0.919533	−0.459767	−	0.888040i	$-0.652067\pi$
$59$	−7.06307	−0.919533	−0.459767	+	0.888040i	$0.652067\pi$
$60$	5.25733	0.678718
$61$	−8.41466	−1.07739	−0.538693	−	0.842502i	$-0.681082\pi$
$61$	−8.41466	−1.07739	−0.538693	+	0.842502i	$0.681082\pi$
$62$	−4.07831	−0.517945
$63$	15.0923	1.90145
$64$	−2.54137	−0.317671
$65$	6.06268	0.751983
$66$	6.94392	0.854737
$67$	6.08737	0.743690	0.371845	−	0.928295i	$-0.378725\pi$
$67$	6.08737	0.743690	0.371845	+	0.928295i	$0.378725\pi$
$68$	−3.20400	−0.388542
$69$	−0.379239	−0.0456550
$70$	−1.25366	−0.149841
$71$	10.4060	1.23497	0.617484	−	0.786584i	$-0.288152\pi$
$71$	10.4060	1.23497	0.617484	+	0.786584i	$0.288152\pi$
$72$	11.4356	1.34770
$73$	−10.8772	−1.27308	−0.636542	−	0.771242i	$-0.719636\pi$
$73$	−10.8772	−1.27308	−0.636542	+	0.771242i	$0.719636\pi$
$74$	0.725145	0.0842964
$75$	−3.01030	−0.347599
$76$	0	0
$77$	11.4054	1.29977
$78$	9.18981	1.04054
$79$	5.23370	0.588838	0.294419	−	0.955676i	$-0.404874\pi$
$79$	5.23370	0.588838	0.294419	+	0.955676i	$0.404874\pi$
$80$	2.54298	0.284314
$81$	9.56077	1.06231
$82$	1.52483	0.168389
$83$	5.03188	0.552321	0.276160	−	0.961112i	$-0.410938\pi$
$83$	5.03188	0.552321	0.276160	+	0.961112i	$0.410938\pi$
$84$	13.0892	1.42815
$85$	1.83458	0.198988
$86$	−4.42401	−0.477053
$87$	11.4124	1.22354
$88$	8.64202	0.921242
$89$	−14.6205	−1.54977	−0.774887	−	0.632100i	$-0.782193\pi$
$89$	−14.6205	−1.54977	−0.774887	+	0.632100i	$0.782193\pi$
$90$	−3.05239	−0.321750
$91$	15.0943	1.58231
$92$	−0.220019	−0.0229386
$93$	−24.3813	−2.52822
$94$	−2.87230	−0.296255
$95$	0	0
$96$	15.2124	1.55261
$97$	−2.49726	−0.253559	−0.126779	−	0.991931i	$-0.540464\pi$
$97$	−2.49726	−0.253559	−0.126779	+	0.991931i	$0.540464\pi$
$98$	0.403510	0.0407606
$99$	27.7697	2.79096
$100$	−1.74645	−0.174645
$101$	4.95956	0.493495	0.246747	−	0.969080i	$-0.420638\pi$
$101$	4.95956	0.493495	0.246747	+	0.969080i	$0.420638\pi$
$102$	2.78085	0.275345
$103$	3.89359	0.383647	0.191823	−	0.981429i	$-0.438560\pi$
$103$	3.89359	0.383647	0.191823	+	0.981429i	$0.438560\pi$
$104$	11.4371	1.12150
$105$	−7.49476	−0.731414
$106$	−4.65628	−0.452258
$107$	−9.94642	−0.961556	−0.480778	−	0.876842i	$-0.659646\pi$
$107$	−9.94642	−0.961556	−0.480778	+	0.876842i	$0.659646\pi$
$108$	16.0973	1.54897
$109$	1.32770	0.127170	0.0635852	−	0.997976i	$-0.479747\pi$
$109$	1.32770	0.127170	0.0635852	+	0.997976i	$0.479747\pi$
$110$	−2.30672	−0.219937
$111$	4.33513	0.411472
$112$	6.33129	0.598251
$113$	−6.21032	−0.584218	−0.292109	−	0.956385i	$-0.594357\pi$
$113$	−6.21032	−0.584218	−0.292109	+	0.956385i	$0.594357\pi$
$114$	0	0
$115$	0.125981	0.0117478
$116$	6.62100	0.614744
$117$	36.7513	3.39766
$118$	3.55652	0.327405
$119$	4.56757	0.418708
$120$	−5.67886	−0.518407
$121$	9.98583	0.907802
$122$	4.23710	0.383609
$123$	9.11587	0.821950
$124$	−14.1450	−1.27026
$125$	1.00000	0.0894427
$126$	−7.59956	−0.677023
$127$	−3.53948	−0.314078	−0.157039	−	0.987592i	$-0.550195\pi$
$127$	−3.53948	−0.314078	−0.157039	+	0.987592i	$0.550195\pi$
$128$	11.3866	1.00644
$129$	−26.4480	−2.32862
$130$	−3.05279	−0.267748
$131$	−0.000573902 0	−5.01420e−5 0	−2.50710e−5	−	1.00000i	$-0.500008\pi$
$131$	−0.000573902 0	−5.01420e−5 0	−2.50710e−5		1.00000i	$0.500008\pi$
$132$	24.0840	2.09624
$133$	0	0
$134$	−3.06522	−0.264795
$135$	−9.21717	−0.793288
$136$	3.46090	0.296769
$137$	−3.90623	−0.333732	−0.166866	−	0.985980i	$-0.553365\pi$
$137$	−3.90623	−0.333732	−0.166866	+	0.985980i	$0.553365\pi$
$138$	0.190961	0.0162557
$139$	−16.6201	−1.40970	−0.704851	−	0.709356i	$-0.748986\pi$
$139$	−16.6201	−1.40970	−0.704851	+	0.709356i	$0.748986\pi$
$140$	−4.34815	−0.367486
$141$	−17.1714	−1.44610
$142$	−5.23983	−0.439717
$143$	27.7733	2.32252
$144$	15.4153	1.28461
$145$	−3.79112	−0.314835
$146$	5.47710	0.453288
$147$	2.41230	0.198963
$148$	2.51506	0.206737
$149$	−15.7959	−1.29405	−0.647025	−	0.762469i	$-0.723987\pi$
$149$	−15.7959	−1.29405	−0.647025	+	0.762469i	$0.723987\pi$
$150$	1.51580	0.123764
$151$	−17.0704	−1.38917	−0.694586	−	0.719410i	$-0.744412\pi$
$151$	−17.0704	−1.38917	−0.694586	+	0.719410i	$0.744412\pi$
$152$	0	0
$153$	11.1210	0.899080
$154$	−5.74307	−0.462790
$155$	8.09930	0.650551
$156$	31.8735	2.55192
$157$	20.9098	1.66878	0.834392	−	0.551171i	$-0.185819\pi$
$157$	20.9098	1.66878	0.834392	+	0.551171i	$0.185819\pi$
$158$	−2.63537	−0.209659
$159$	−27.8366	−2.20758
$160$	−5.05345	−0.399510
$161$	0.313655	0.0247195
$162$	−4.81421	−0.378240
$163$	−16.5302	−1.29474	−0.647372	−	0.762175i	$-0.724132\pi$
$163$	−16.5302	−1.29474	−0.647372	+	0.762175i	$0.724132\pi$
$164$	5.28865	0.412974
$165$	−13.7903	−1.07357
$166$	−2.53374	−0.196657
$167$	18.6256	1.44129	0.720647	−	0.693303i	$-0.243845\pi$
$167$	18.6256	1.44129	0.720647	+	0.693303i	$0.243845\pi$
$168$	−14.1387	−1.09083
$169$	23.7561	1.82740
$170$	−0.923781	−0.0708507
$171$	0	0
$172$	−15.3441	−1.16997
$173$	7.49526	0.569854	0.284927	−	0.958549i	$-0.408031\pi$
$173$	7.49526	0.569854	0.284927	+	0.958549i	$0.408031\pi$
$174$	−5.74657	−0.435647
$175$	2.48971	0.188204
$176$	11.6495	0.878113
$177$	21.2619	1.59814
$178$	7.36200	0.551805
$179$	3.34760	0.250212	0.125106	−	0.992143i	$-0.460073\pi$
$179$	3.34760	0.250212	0.125106	+	0.992143i	$0.460073\pi$
$180$	−10.5868	−0.789091
$181$	−1.15209	−0.0856339	−0.0428169	−	0.999083i	$-0.513633\pi$
$181$	−1.15209	−0.0856339	−0.0428169	+	0.999083i	$0.513633\pi$
$182$	−7.60056	−0.563391
$183$	25.3306	1.87249
$184$	0.237660	0.0175205
$185$	−1.44010	−0.105878
$186$	12.2769	0.900187
$187$	8.40426	0.614581
$188$	−9.96216	−0.726565
$189$	−22.9481	−1.66923
$190$	0	0
$191$	−19.2583	−1.39348	−0.696741	−	0.717323i	$-0.745367\pi$
$191$	−19.2583	−1.39348	−0.696741	+	0.717323i	$0.745367\pi$
$192$	7.65026	0.552110
$193$	3.25423	0.234245	0.117122	−	0.993117i	$-0.462633\pi$
$193$	3.25423	0.234245	0.117122	+	0.993117i	$0.462633\pi$
$194$	1.25747	0.0902809
$195$	−18.2505	−1.30694
$196$	1.39952	0.0999654
$197$	10.8657	0.774152	0.387076	−	0.922048i	$-0.373485\pi$
$197$	10.8657	0.774152	0.387076	+	0.922048i	$0.373485\pi$
$198$	−13.9831	−0.993734
$199$	2.55526	0.181137	0.0905687	−	0.995890i	$-0.471132\pi$
$199$	2.55526	0.181137	0.0905687	+	0.995890i	$0.471132\pi$
$200$	1.88648	0.133394
$201$	−18.3248	−1.29253
$202$	−2.49733	−0.175711
$203$	−9.43878	−0.662473
$204$	9.64499	0.675284
$205$	−3.02823	−0.211501
$206$	−1.96057	−0.136599
$207$	0.763680	0.0530794
$208$	15.4173	1.06900
$209$	0	0
$210$	3.77390	0.260424
$211$	24.8994	1.71415	0.857074	−	0.515193i	$-0.172280\pi$
$211$	24.8994	1.71415	0.857074	+	0.515193i	$0.172280\pi$
$212$	−16.1496	−1.10916
$213$	−31.3252	−2.14637
$214$	5.00840	0.342367
$215$	8.78585	0.599190
$216$	−17.3880	−1.18310
$217$	20.1649	1.36888
$218$	−0.668546	−0.0452797
$219$	32.7437	2.21261
$220$	−8.00054	−0.539396
$221$	11.1225	0.748179
$222$	−2.18290	−0.146507
$223$	8.59702	0.575699	0.287850	−	0.957676i	$-0.407060\pi$
$223$	8.59702	0.575699	0.287850	+	0.957676i	$0.407060\pi$
$224$	−12.5816	−0.840645
$225$	6.06188	0.404126
$226$	3.12713	0.208014
$227$	1.87301	0.124316	0.0621581	−	0.998066i	$-0.480202\pi$
$227$	1.87301	0.124316	0.0621581	+	0.998066i	$0.480202\pi$
$228$	0	0
$229$	−23.0557	−1.52356	−0.761781	−	0.647835i	$-0.775675\pi$
$229$	−23.0557	−1.52356	−0.761781	+	0.647835i	$0.775675\pi$
$230$	−0.0634361	−0.00418285
$231$	−34.3337	−2.25899
$232$	−7.15187	−0.469543
$233$	−13.2155	−0.865778	−0.432889	−	0.901447i	$-0.642506\pi$
$233$	−13.2155	−0.865778	−0.432889	+	0.901447i	$0.642506\pi$
$234$	−18.5057	−1.20975
$235$	5.70424	0.372103
$236$	12.3353	0.802959
$237$	−15.7550	−1.02340
$238$	−2.29994	−0.149083
$239$	9.15611	0.592259	0.296130	−	0.955148i	$-0.404304\pi$
$239$	9.15611	0.592259	0.296130	+	0.955148i	$0.404304\pi$
$240$	−7.65514	−0.494137
$241$	14.3985	0.927491	0.463746	−	0.885968i	$-0.346505\pi$
$241$	14.3985	0.927491	0.463746	+	0.885968i	$0.346505\pi$
$242$	−5.02824	−0.323228
$243$	−1.12924	−0.0724406
$244$	14.6958	0.940801
$245$	−0.801349	−0.0511963
$246$	−4.59019	−0.292660
$247$	0	0
$248$	15.2792	0.970228
$249$	−15.1475	−0.959931
$250$	−0.503538	−0.0318465
$251$	−28.4056	−1.79295	−0.896474	−	0.443096i	$-0.853880\pi$
$251$	−28.4056	−1.79295	−0.896474	+	0.443096i	$0.853880\pi$
$252$	−26.3580	−1.66040
$253$	0.577121	0.0362833
$254$	1.78226	0.111829
$255$	−5.52263	−0.345840
$256$	−0.650841	−0.0406776
$257$	−22.4440	−1.40002	−0.700008	−	0.714135i	$-0.746820\pi$
$257$	−22.4440	−1.40002	−0.700008	+	0.714135i	$0.746820\pi$
$258$	13.3176	0.829117
$259$	−3.58543	−0.222788
$260$	−10.5882	−0.656651
$261$	−22.9813	−1.42251
$262$	0.000288981 0	1.78533e−5 0
$263$	3.20105	0.197385	0.0986925	−	0.995118i	$-0.468534\pi$
$263$	3.20105	0.197385	0.0986925	+	0.995118i	$0.468534\pi$
$264$	−26.0150	−1.60111
$265$	9.24712	0.568046
$266$	0	0
$267$	44.0121	2.69350
$268$	−10.6313	−0.649409
$269$	−4.14244	−0.252569	−0.126285	−	0.991994i	$-0.540305\pi$
$269$	−4.14244	−0.252569	−0.126285	+	0.991994i	$0.540305\pi$
$270$	4.64120	0.282454
$271$	−0.455443	−0.0276662	−0.0138331	−	0.999904i	$-0.504403\pi$
$271$	−0.455443	−0.0276662	−0.0138331	+	0.999904i	$0.504403\pi$
$272$	4.66531	0.282876
$273$	−45.4384	−2.75006
$274$	1.96693	0.118827
$275$	4.58103	0.276246
$276$	0.662322	0.0398671
$277$	17.1987	1.03337	0.516686	−	0.856175i	$-0.327166\pi$
$277$	17.1987	1.03337	0.516686	+	0.856175i	$0.327166\pi$
$278$	8.36887	0.501931
$279$	49.0970	2.93936
$280$	4.69679	0.280687
$281$	−27.7907	−1.65785	−0.828927	−	0.559357i	$-0.811048\pi$
$281$	−27.7907	−1.65785	−0.828927	+	0.559357i	$0.811048\pi$
$282$	8.64647	0.514890
$283$	10.8066	0.642387	0.321193	−	0.947014i	$-0.395916\pi$
$283$	10.8066	0.642387	0.321193	+	0.947014i	$0.395916\pi$
$284$	−18.1736	−1.07840
$285$	0	0
$286$	−13.9849	−0.826946
$287$	−7.53941	−0.445037
$288$	−30.6334	−1.80509
$289$	−13.6343	−0.802019
$290$	1.90897	0.112099
$291$	7.51751	0.440684
$292$	18.9965	1.11169
$293$	6.42299	0.375235	0.187618	−	0.982242i	$-0.439923\pi$
$293$	6.42299	0.375235	0.187618	+	0.982242i	$0.439923\pi$
$294$	−1.21468	−0.0708418
$295$	−7.06307	−0.411228
$296$	−2.71672	−0.157906
$297$	−42.2241	−2.45009
$298$	7.95383	0.460753
$299$	0.763781	0.0441706
$300$	5.25733	0.303532
$301$	21.8742	1.26081
$302$	8.59561	0.494622
$303$	−14.9297	−0.857691
$304$	0	0
$305$	−8.41466	−0.481822
$306$	−5.59985	−0.320122
$307$	10.4182	0.594599	0.297300	−	0.954784i	$-0.403914\pi$
$307$	10.4182	0.594599	0.297300	+	0.954784i	$0.403914\pi$
$308$	−19.9190	−1.13499
$309$	−11.7209	−0.666776
$310$	−4.07831	−0.231632
$311$	18.9591	1.07507	0.537537	−	0.843240i	$-0.319355\pi$
$311$	18.9591	1.07507	0.537537	+	0.843240i	$0.319355\pi$
$312$	−34.4292	−1.94917
$313$	2.00867	0.113537	0.0567685	−	0.998387i	$-0.481920\pi$
$313$	2.00867	0.113537	0.0567685	+	0.998387i	$0.481920\pi$
$314$	−10.5289	−0.594179
$315$	15.0923	0.850356
$316$	−9.14040	−0.514188
$317$	11.9150	0.669210	0.334605	−	0.942358i	$-0.391397\pi$
$317$	11.9150	0.669210	0.334605	+	0.942358i	$0.391397\pi$
$318$	14.0168	0.786022
$319$	−17.3672	−0.972378
$320$	−2.54137	−0.142067
$321$	29.9417	1.67118
$322$	−0.157937	−0.00880150
$323$	0	0
$324$	−16.6974	−0.927634
$325$	6.06268	0.336297
$326$	8.32357	0.461000
$327$	−3.99676	−0.221021
$328$	−5.71270	−0.315431
$329$	14.2019	0.782975
$330$	6.94392	0.382250
$331$	3.75832	0.206576	0.103288	−	0.994651i	$-0.467064\pi$
$331$	3.75832	0.206576	0.103288	+	0.994651i	$0.467064\pi$
$332$	−8.78793	−0.482300
$333$	−8.72972	−0.478386
$334$	−9.37870	−0.513180
$335$	6.08737	0.332588
$336$	−19.0591	−1.03976
$337$	7.43625	0.405078	0.202539	−	0.979274i	$-0.435081\pi$
$337$	7.43625	0.405078	0.202539	+	0.979274i	$0.435081\pi$
$338$	−11.9621	−0.650654
$339$	18.6949	1.01537
$340$	−3.20400	−0.173761
$341$	37.1031	2.00925
$342$	0	0
$343$	−19.4231	−1.04875
$344$	16.5743	0.893628
$345$	−0.379239	−0.0204176
$346$	−3.77415	−0.202899
$347$	−27.3288	−1.46709	−0.733543	−	0.679643i	$-0.762135\pi$
$347$	−27.3288	−1.46709	−0.733543	+	0.679643i	$0.762135\pi$
$348$	−19.9312	−1.06842
$349$	−20.4429	−1.09428	−0.547142	−	0.837040i	$-0.684284\pi$
$349$	−20.4429	−1.09428	−0.547142	+	0.837040i	$0.684284\pi$
$350$	−1.25366	−0.0670111
$351$	−55.8808	−2.98270
$352$	−23.1500	−1.23390
$353$	−6.62289	−0.352501	−0.176250	−	0.984345i	$-0.556397\pi$
$353$	−6.62289	−0.352501	−0.176250	+	0.984345i	$0.556397\pi$
$354$	−10.7062	−0.569028
$355$	10.4060	0.552294
$356$	25.5340	1.35330
$357$	−13.7497	−0.727713
$358$	−1.68565	−0.0890892
$359$	0.848513	0.0447828	0.0223914	−	0.999749i	$-0.492872\pi$
$359$	0.848513	0.0447828	0.0223914	+	0.999749i	$0.492872\pi$
$360$	11.4356	0.602710
$361$	0	0
$362$	0.580119	0.0304904
$363$	−30.0603	−1.57776
$364$	−26.3615	−1.38172
$365$	−10.8772	−0.569340
$366$	−12.7549	−0.666711
$367$	−37.5524	−1.96022	−0.980109	−	0.198458i	$-0.936407\pi$
$367$	−37.5524	−1.96022	−0.980109	+	0.198458i	$0.936407\pi$
$368$	0.320367	0.0167003
$369$	−18.3568	−0.955616
$370$	0.725145	0.0376985
$371$	23.0226	1.19528
$372$	42.5807	2.20771
$373$	−8.81739	−0.456547	−0.228274	−	0.973597i	$-0.573308\pi$
$373$	−8.81739	−0.456547	−0.228274	+	0.973597i	$0.573308\pi$
$374$	−4.23187	−0.218825
$375$	−3.01030	−0.155451
$376$	10.7609	0.554952
$377$	−22.9844	−1.18375
$378$	11.5552	0.594337
$379$	10.1233	0.520000	0.260000	−	0.965609i	$-0.416277\pi$
$379$	10.1233	0.520000	0.260000	+	0.965609i	$0.416277\pi$
$380$	0	0
$381$	10.6549	0.545866
$382$	9.69729	0.496156
$383$	−21.6823	−1.10791	−0.553957	−	0.832545i	$-0.686883\pi$
$383$	−21.6823	−1.10791	−0.553957	+	0.832545i	$0.686883\pi$
$384$	−34.2770	−1.74919
$385$	11.4054	0.581275
$386$	−1.63863	−0.0834041
$387$	53.2588	2.70730
$388$	4.36135	0.221414
$389$	24.5644	1.24546	0.622732	−	0.782435i	$-0.286023\pi$
$389$	24.5644	1.24546	0.622732	+	0.782435i	$0.286023\pi$
$390$	9.18981	0.465344
$391$	0.231122	0.0116883
$392$	−1.51173	−0.0763538
$393$	0.00172761	8.71466e−5 0
$394$	−5.47132	−0.275641
$395$	5.23370	0.263336
$396$	−48.4983	−2.43713
$397$	31.5355	1.58272	0.791360	−	0.611350i	$-0.209373\pi$
$397$	31.5355	1.58272	0.791360	+	0.611350i	$0.209373\pi$
$398$	−1.28667	−0.0644949
$399$	0	0
$400$	2.54298	0.127149
$401$	−34.3868	−1.71719	−0.858597	−	0.512651i	$-0.828663\pi$
$401$	−34.3868	−1.71719	−0.858597	+	0.512651i	$0.828663\pi$
$402$	9.22722	0.460212
$403$	49.1035	2.44602
$404$	−8.66162	−0.430932
$405$	9.56077	0.475079
$406$	4.75279	0.235877
$407$	−6.59714	−0.327008
$408$	−10.4183	−0.515784
$409$	3.70382	0.183142	0.0915712	−	0.995799i	$-0.470811\pi$
$409$	3.70382	0.183142	0.0915712	+	0.995799i	$0.470811\pi$
$410$	1.52483	0.0753059
$411$	11.7589	0.580024
$412$	−6.79996	−0.335010
$413$	−17.5850	−0.865301
$414$	−0.384542	−0.0188992
$415$	5.03188	0.247005
$416$	−30.6375	−1.50213
$417$	50.0315	2.45005
$418$	0	0
$419$	33.3164	1.62761	0.813806	−	0.581137i	$-0.197392\pi$
$419$	33.3164	1.62761	0.813806	+	0.581137i	$0.197392\pi$
$420$	13.0892	0.638689
$421$	−8.92117	−0.434791	−0.217396	−	0.976084i	$-0.569756\pi$
$421$	−8.92117	−0.434791	−0.217396	+	0.976084i	$0.569756\pi$
$422$	−12.5378	−0.610331
$423$	34.5784	1.68126
$424$	17.4445	0.847180
$425$	1.83458	0.0889902
$426$	15.7734	0.764225
$427$	−20.9501	−1.01384
$428$	17.3709	0.839655
$429$	−83.6060	−4.03653
$430$	−4.42401	−0.213345
$431$	−3.49481	−0.168339	−0.0841696	−	0.996451i	$-0.526824\pi$
$431$	−3.49481	−0.168339	−0.0841696	+	0.996451i	$0.526824\pi$
$432$	−23.4391	−1.12772
$433$	15.3102	0.735760	0.367880	−	0.929873i	$-0.380084\pi$
$433$	15.3102	0.735760	0.367880	+	0.929873i	$0.380084\pi$
$434$	−10.1538	−0.487398
$435$	11.4124	0.547182
$436$	−2.31876	−0.111048
$437$	0	0
$438$	−16.4877	−0.787812
$439$	22.8056	1.08845	0.544225	−	0.838939i	$-0.316824\pi$
$439$	22.8056	1.08845	0.544225	+	0.838939i	$0.316824\pi$
$440$	8.64202	0.411992
$441$	−4.85768	−0.231318
$442$	−5.60059	−0.266393
$443$	−6.71988	−0.319271	−0.159635	−	0.987176i	$-0.551032\pi$
$443$	−6.71988	−0.319271	−0.159635	+	0.987176i	$0.551032\pi$
$444$	−7.57108	−0.359308
$445$	−14.6205	−0.693080
$446$	−4.32893	−0.204981
$447$	47.5503	2.24905
$448$	−6.32726	−0.298935
$449$	33.0298	1.55877	0.779385	−	0.626545i	$-0.215532\pi$
$449$	33.0298	1.55877	0.779385	+	0.626545i	$0.215532\pi$
$450$	−3.05239	−0.143891
$451$	−13.8724	−0.653226
$452$	10.8460	0.510154
$453$	51.3871	2.41437
$454$	−0.943134	−0.0442635
$455$	15.0943	0.707633
$456$	0	0
$457$	32.6810	1.52875	0.764377	−	0.644770i	$-0.223047\pi$
$457$	32.6810	1.52875	0.764377	+	0.644770i	$0.223047\pi$
$458$	11.6094	0.542472
$459$	−16.9096	−0.789274
$460$	−0.220019	−0.0102584
$461$	−30.2466	−1.40873	−0.704363	−	0.709840i	$-0.748767\pi$
$461$	−30.2466	−1.40873	−0.704363	+	0.709840i	$0.748767\pi$
$462$	17.2883	0.804326
$463$	24.3154	1.13003	0.565017	−	0.825079i	$-0.308869\pi$
$463$	24.3154	1.13003	0.565017	+	0.825079i	$0.308869\pi$
$464$	−9.64076	−0.447561
$465$	−24.3813	−1.13066
$466$	6.65452	0.308265
$467$	−27.8202	−1.28737	−0.643683	−	0.765292i	$-0.722595\pi$
$467$	−27.8202	−1.28737	−0.643683	+	0.765292i	$0.722595\pi$
$468$	−64.1843	−2.96692
$469$	15.1558	0.699829
$470$	−2.87230	−0.132489
$471$	−62.9447	−2.90034
$472$	−13.3243	−0.613302
$473$	40.2483	1.85062
$474$	7.93324	0.364386
$475$	0	0
$476$	−7.97703	−0.365627
$477$	56.0550	2.56658
$478$	−4.61045	−0.210877
$479$	1.26749	0.0579129	0.0289565	−	0.999581i	$-0.490782\pi$
$479$	1.26749	0.0579129	0.0289565	+	0.999581i	$0.490782\pi$
$480$	15.2124	0.694347
$481$	−8.73087	−0.398093
$482$	−7.25021	−0.330238
$483$	−0.944195	−0.0429624
$484$	−17.4397	−0.792716
$485$	−2.49726	−0.113395
$486$	0.568614	0.0257928
$487$	−1.36641	−0.0619178	−0.0309589	−	0.999521i	$-0.509856\pi$
$487$	−1.36641	−0.0619178	−0.0309589	+	0.999521i	$0.509856\pi$
$488$	−15.8741	−0.718586
$489$	49.7607	2.25026
$490$	0.403510	0.0182287
$491$	11.3994	0.514446	0.257223	−	0.966352i	$-0.417193\pi$
$491$	11.3994	0.514446	0.257223	+	0.966352i	$0.417193\pi$
$492$	−15.9204	−0.717747
$493$	−6.95511	−0.313242
$494$	0	0
$495$	27.7697	1.24815
$496$	20.5964	0.924805
$497$	25.9080	1.16213
$498$	7.62732	0.341788
$499$	24.1534	1.08125	0.540627	−	0.841263i	$-0.318187\pi$
$499$	24.1534	1.08125	0.540627	+	0.841263i	$0.318187\pi$
$500$	−1.74645	−0.0781036
$501$	−56.0686	−2.50496
$502$	14.3033	0.638389
$503$	2.21176	0.0986175	0.0493088	−	0.998784i	$-0.484298\pi$
$503$	2.21176	0.0986175	0.0493088	+	0.998784i	$0.484298\pi$
$504$	28.4714	1.26822
$505$	4.95956	0.220698
$506$	−0.290602	−0.0129189
$507$	−71.5130	−3.17600
$508$	6.18152	0.274261
$509$	32.7479	1.45152	0.725762	−	0.687946i	$-0.241487\pi$
$509$	32.7479	1.45152	0.725762	+	0.687946i	$0.241487\pi$
$510$	2.78085	0.123138
$511$	−27.0811	−1.19800
$512$	−22.4454	−0.991957
$513$	0	0
$514$	11.3014	0.498483
$515$	3.89359	0.171572
$516$	46.1901	2.03341
$517$	26.1313	1.14925
$518$	1.80540	0.0793247
$519$	−22.5629	−0.990403
$520$	11.4371	0.501551
$521$	−29.3834	−1.28731	−0.643655	−	0.765316i	$-0.722583\pi$
$521$	−29.3834	−1.28731	−0.643655	+	0.765316i	$0.722583\pi$
$522$	11.5720	0.506491
$523$	−23.3722	−1.02200	−0.510998	−	0.859582i	$-0.670724\pi$
$523$	−23.3722	−1.02200	−0.510998	+	0.859582i	$0.670724\pi$
$524$	0.00100229	4.37853e−5 0
$525$	−7.49476	−0.327098
$526$	−1.61185	−0.0702800
$527$	14.8588	0.647260
$528$	−35.0684	−1.52616
$529$	−22.9841	−0.999310
$530$	−4.65628	−0.202256
$531$	−42.8155	−1.85803
$532$	0	0
$533$	−18.3592	−0.795225
$534$	−22.1618	−0.959034
$535$	−9.94642	−0.430021
$536$	11.4837	0.496020
$537$	−10.0773	−0.434867
$538$	2.08588	0.0899285
$539$	−3.67100	−0.158121
$540$	16.0973	0.692719
$541$	32.4586	1.39550	0.697752	−	0.716339i	$-0.254184\pi$
$541$	32.4586	1.39550	0.697752	+	0.716339i	$0.254184\pi$
$542$	0.229333	0.00985070
$543$	3.46812	0.148831
$544$	−9.27095	−0.397489
$545$	1.32770	0.0568723
$546$	22.8799	0.979171
$547$	−0.914710	−0.0391102	−0.0195551	−	0.999809i	$-0.506225\pi$
$547$	−0.914710	−0.0391102	−0.0195551	+	0.999809i	$0.506225\pi$
$548$	6.82203	0.291423
$549$	−51.0087	−2.17700
$550$	−2.30672	−0.0983590
$551$	0	0
$552$	−0.715427	−0.0304506
$553$	13.0304	0.554109
$554$	−8.66021	−0.367937
$555$	4.33513	0.184016
$556$	29.0262	1.23099
$557$	−3.38668	−0.143498	−0.0717490	−	0.997423i	$-0.522858\pi$
$557$	−3.38668	−0.143498	−0.0717490	+	0.997423i	$0.522858\pi$
$558$	−24.7222	−1.04657
$559$	53.2659	2.25291
$560$	6.33129	0.267546
$561$	−25.2993	−1.06814
$562$	13.9937	0.590287
$563$	−36.3104	−1.53030	−0.765151	−	0.643851i	$-0.777336\pi$
$563$	−36.3104	−1.53030	−0.765151	+	0.643851i	$0.777336\pi$
$564$	29.9890	1.26277
$565$	−6.21032	−0.261270
$566$	−5.44154	−0.228725
$567$	23.8035	0.999655
$568$	19.6308	0.823688
$569$	−11.2365	−0.471057	−0.235528	−	0.971867i	$-0.575682\pi$
$569$	−11.2365	−0.471057	−0.235528	+	0.971867i	$0.575682\pi$
$570$	0	0
$571$	25.4188	1.06375	0.531873	−	0.846824i	$-0.321488\pi$
$571$	25.4188	1.06375	0.531873	+	0.846824i	$0.321488\pi$
$572$	−48.5047	−2.02808
$573$	57.9732	2.42187
$574$	3.79638	0.158458
$575$	0.125981	0.00525376
$576$	−15.4055	−0.641894
$577$	−18.2718	−0.760664	−0.380332	−	0.924850i	$-0.624190\pi$
$577$	−18.2718	−0.760664	−0.380332	+	0.924850i	$0.624190\pi$
$578$	6.86540	0.285563
$579$	−9.79620	−0.407116
$580$	6.62100	0.274922
$581$	12.5279	0.519746
$582$	−3.78535	−0.156908
$583$	42.3613	1.75443
$584$	−20.5197	−0.849110
$585$	36.7513	1.51948
$586$	−3.23422	−0.133604
$587$	10.2873	0.424601	0.212301	−	0.977204i	$-0.431904\pi$
$587$	10.2873	0.424601	0.212301	+	0.977204i	$0.431904\pi$
$588$	−4.21296	−0.173739
$589$	0	0
$590$	3.55652	0.146420
$591$	−32.7091	−1.34547
$592$	−3.66215	−0.150514
$593$	12.8804	0.528936	0.264468	−	0.964394i	$-0.414804\pi$
$593$	12.8804	0.528936	0.264468	+	0.964394i	$0.414804\pi$
$594$	21.2615	0.872368
$595$	4.56757	0.187252
$596$	27.5867	1.13000
$597$	−7.69208	−0.314816
$598$	−0.384593	−0.0157272
$599$	25.1559	1.02784	0.513922	−	0.857837i	$-0.328192\pi$
$599$	25.1559	1.02784	0.513922	+	0.857837i	$0.328192\pi$
$600$	−5.67886	−0.231839
$601$	−32.8268	−1.33903	−0.669517	−	0.742797i	$-0.733499\pi$
$601$	−32.8268	−1.33903	−0.669517	+	0.742797i	$0.733499\pi$
$602$	−11.0145	−0.448918
$603$	36.9009	1.50272
$604$	29.8127	1.21306
$605$	9.98583	0.405982
$606$	7.51769	0.305385
$607$	−6.97732	−0.283201	−0.141600	−	0.989924i	$-0.545225\pi$
$607$	−6.97732	−0.283201	−0.141600	+	0.989924i	$0.545225\pi$
$608$	0	0
$609$	28.4135	1.15137
$610$	4.23710	0.171555
$611$	34.5830	1.39908
$612$	−19.4223	−0.785099
$613$	32.9530	1.33096	0.665480	−	0.746416i	$-0.268227\pi$
$613$	32.9530	1.33096	0.665480	+	0.746416i	$0.268227\pi$
$614$	−5.24597	−0.211710
$615$	9.11587	0.367587
$616$	21.5161	0.866909
$617$	−23.5354	−0.947501	−0.473750	−	0.880659i	$-0.657100\pi$
$617$	−23.5354	−0.947501	−0.473750	+	0.880659i	$0.657100\pi$
$618$	5.90190	0.237409
$619$	13.9820	0.561985	0.280992	−	0.959710i	$-0.409336\pi$
$619$	13.9820	0.561985	0.280992	+	0.959710i	$0.409336\pi$
$620$	−14.1450	−0.568078
$621$	−1.16119	−0.0465968
$622$	−9.54664	−0.382786
$623$	−36.4009	−1.45837
$624$	−46.4107	−1.85791
$625$	1.00000	0.0400000
$626$	−1.01144	−0.0404254
$627$	0	0
$628$	−36.5179	−1.45722
$629$	−2.64198	−0.105343
$630$	−7.59956	−0.302774
$631$	−13.9729	−0.556253	−0.278126	−	0.960544i	$-0.589713\pi$
$631$	−13.9729	−0.556253	−0.278126	+	0.960544i	$0.589713\pi$
$632$	9.87328	0.392738
$633$	−74.9547	−2.97918
$634$	−5.99963	−0.238276
$635$	−3.53948	−0.140460
$636$	48.6152	1.92772
$637$	−4.85833	−0.192494
$638$	8.74506	0.346220
$639$	63.0801	2.49541
$640$	11.3866	0.450094
$641$	15.2748	0.603319	0.301659	−	0.953416i	$-0.402459\pi$
$641$	15.2748	0.603319	0.301659	+	0.953416i	$0.402459\pi$
$642$	−15.0768	−0.595032
$643$	−1.76672	−0.0696727	−0.0348364	−	0.999393i	$-0.511091\pi$
$643$	−1.76672	−0.0696727	−0.0348364	+	0.999393i	$0.511091\pi$
$644$	−0.547783	−0.0215857
$645$	−26.4480	−1.04139
$646$	0	0
$647$	−6.04239	−0.237551	−0.118776	−	0.992921i	$-0.537897\pi$
$647$	−6.04239	−0.237551	−0.118776	+	0.992921i	$0.537897\pi$
$648$	18.0362	0.708529
$649$	−32.3561	−1.27009
$650$	−3.05279	−0.119740
$651$	−60.7023	−2.37911
$652$	28.8691	1.13060
$653$	−44.5755	−1.74437	−0.872187	−	0.489172i	$-0.837299\pi$
$653$	−44.5755	−1.74437	−0.872187	+	0.489172i	$0.837299\pi$
$654$	2.01252	0.0786958
$655$	−0.000573902 0	−2.24242e−5 0
$656$	−7.70074	−0.300664
$657$	−65.9365	−2.57243
$658$	−7.15119	−0.278782
$659$	10.4177	0.405815	0.202907	−	0.979198i	$-0.434961\pi$
$659$	10.4177	0.405815	0.202907	+	0.979198i	$0.434961\pi$
$660$	24.0840	0.937468
$661$	−12.5048	−0.486379	−0.243190	−	0.969979i	$-0.578194\pi$
$661$	−12.5048	−0.486379	−0.243190	+	0.969979i	$0.578194\pi$
$662$	−1.89246	−0.0735524
$663$	−33.4819	−1.30033
$664$	9.49254	0.368382
$665$	0	0
$666$	4.39574	0.170332
$667$	−0.477608	−0.0184930
$668$	−32.5287	−1.25857
$669$	−25.8796	−1.00056
$670$	−3.06522	−0.118420
$671$	−38.5478	−1.48812
$672$	37.8744	1.46104
$673$	7.51429	0.289655	0.144827	−	0.989457i	$-0.453737\pi$
$673$	7.51429	0.289655	0.144827	+	0.989457i	$0.453737\pi$
$674$	−3.74443	−0.144230
$675$	−9.21717	−0.354769
$676$	−41.4889	−1.59573
$677$	1.23331	0.0473999	0.0236999	−	0.999719i	$-0.492455\pi$
$677$	1.23331	0.0473999	0.0236999	+	0.999719i	$0.492455\pi$
$678$	−9.41360	−0.361527
$679$	−6.21746	−0.238604
$680$	3.46090	0.132719
$681$	−5.63833	−0.216061
$682$	−18.6828	−0.715403
$683$	8.16553	0.312445	0.156223	−	0.987722i	$-0.450068\pi$
$683$	8.16553	0.312445	0.156223	+	0.987722i	$0.450068\pi$
$684$	0	0
$685$	−3.90623	−0.149249
$686$	9.78026	0.373412
$687$	69.4044	2.64794
$688$	22.3423	0.851792
$689$	56.0624	2.13581
$690$	0.190961	0.00726977
$691$	21.6525	0.823699	0.411849	−	0.911252i	$-0.364883\pi$
$691$	21.6525	0.823699	0.411849	+	0.911252i	$0.364883\pi$
$692$	−13.0901	−0.497610
$693$	69.1384	2.62635
$694$	13.7611	0.522363
$695$	−16.6201	−0.630438
$696$	21.5292	0.816064
$697$	−5.55553	−0.210431
$698$	10.2938	0.389626
$699$	39.7826	1.50472
$700$	−4.34815	−0.164345
$701$	24.2137	0.914537	0.457269	−	0.889329i	$-0.348828\pi$
$701$	24.2137	0.914537	0.457269	+	0.889329i	$0.348828\pi$
$702$	28.1381	1.06200
$703$	0	0
$704$	−11.6421	−0.438777
$705$	−17.1714	−0.646714
$706$	3.33487	0.125510
$707$	12.3479	0.464389
$708$	−37.1329	−1.39554
$709$	49.8254	1.87123	0.935616	−	0.353020i	$-0.114845\pi$
$709$	49.8254	1.87123	0.935616	+	0.353020i	$0.114845\pi$
$710$	−5.23983	−0.196647
$711$	31.7261	1.18982
$712$	−27.5813	−1.03365
$713$	1.02036	0.0382126
$714$	6.92352	0.259106
$715$	27.7733	1.03866
$716$	−5.84642	−0.218491
$717$	−27.5626	−1.02934
$718$	−0.427259	−0.0159452
$719$	−33.1389	−1.23587	−0.617936	−	0.786229i	$-0.712031\pi$
$719$	−33.1389	−1.23587	−0.617936	+	0.786229i	$0.712031\pi$
$720$	15.4153	0.574493
$721$	9.69391	0.361020
$722$	0	0
$723$	−43.3439	−1.61198
$724$	2.01206	0.0747776
$725$	−3.79112	−0.140799
$726$	15.1365	0.561768
$727$	19.4204	0.720262	0.360131	−	0.932902i	$-0.382732\pi$
$727$	19.4204	0.720262	0.360131	+	0.932902i	$0.382732\pi$
$728$	28.4751	1.05536
$729$	−25.2830	−0.936407
$730$	5.47710	0.202716
$731$	16.1183	0.596159
$732$	−44.2386	−1.63511
$733$	22.3126	0.824136	0.412068	−	0.911153i	$-0.364807\pi$
$733$	22.3126	0.824136	0.412068	+	0.911153i	$0.364807\pi$
$734$	18.9091	0.697946
$735$	2.41230	0.0889789
$736$	−0.636637	−0.0234668
$737$	27.8864	1.02721
$738$	9.24334	0.340252
$739$	−0.723124	−0.0266006	−0.0133003	−	0.999912i	$-0.504234\pi$
$739$	−0.723124	−0.0266006	−0.0133003	+	0.999912i	$0.504234\pi$
$740$	2.51506	0.0924555
$741$	0	0
$742$	−11.5928	−0.425584
$743$	−24.8856	−0.912965	−0.456482	−	0.889732i	$-0.650891\pi$
$743$	−24.8856	−0.912965	−0.456482	+	0.889732i	$0.650891\pi$
$744$	−45.9948	−1.68625
$745$	−15.7959	−0.578717
$746$	4.43989	0.162556
$747$	30.5027	1.11603
$748$	−14.6776	−0.536667
$749$	−24.7637	−0.904845
$750$	1.51580	0.0553491
$751$	−1.74001	−0.0634938	−0.0317469	−	0.999496i	$-0.510107\pi$
$751$	−1.74001	−0.0634938	−0.0317469	+	0.999496i	$0.510107\pi$
$752$	14.5058	0.528971
$753$	85.5094	3.11614
$754$	11.5735	0.421482
$755$	−17.0704	−0.621257
$756$	40.0777	1.45761
$757$	4.79489	0.174273	0.0871367	−	0.996196i	$-0.472228\pi$
$757$	4.79489	0.174273	0.0871367	+	0.996196i	$0.472228\pi$
$758$	−5.09747	−0.185149
$759$	−1.73731	−0.0630602
$760$	0	0
$761$	−12.1999	−0.442248	−0.221124	−	0.975246i	$-0.570972\pi$
$761$	−12.1999	−0.442248	−0.221124	+	0.975246i	$0.570972\pi$
$762$	−5.36514	−0.194358
$763$	3.30558	0.119670
$764$	33.6337	1.21682
$765$	11.1210	0.402081
$766$	10.9179	0.394478
$767$	−42.8212	−1.54618
$768$	1.95922	0.0706974
$769$	−30.9548	−1.11626	−0.558130	−	0.829754i	$-0.688481\pi$
$769$	−30.9548	−1.11626	−0.558130	+	0.829754i	$0.688481\pi$
$770$	−5.74307	−0.206966
$771$	67.5629	2.43322
$772$	−5.68335	−0.204548
$773$	−36.9748	−1.32989	−0.664946	−	0.746892i	$-0.731545\pi$
$773$	−36.9748	−1.32989	−0.664946	+	0.746892i	$0.731545\pi$
$774$	−26.8178	−0.963947
$775$	8.09930	0.290935
$776$	−4.71104	−0.169116
$777$	10.7932	0.387204
$778$	−12.3691	−0.443454
$779$	0	0
$780$	31.8735	1.14126
$781$	47.6703	1.70578
$782$	−0.116379	−0.00416169
$783$	34.9434	1.24878
$784$	−2.03782	−0.0727792
$785$	20.9098	0.746303
$786$	−0.000869920 0	−3.10290e−5 0
$787$	−3.52509	−0.125656	−0.0628279	−	0.998024i	$-0.520012\pi$
$787$	−3.52509	−0.125656	−0.0628279	+	0.998024i	$0.520012\pi$
$788$	−18.9765	−0.676009
$789$	−9.63610	−0.343054
$790$	−2.63537	−0.0937622
$791$	−15.4619	−0.549762
$792$	52.3869	1.86149
$793$	−51.0154	−1.81161
$794$	−15.8793	−0.563536
$795$	−27.8366	−0.987262
$796$	−4.46263	−0.158174
$797$	25.1503	0.890870	0.445435	−	0.895314i	$-0.353049\pi$
$797$	25.1503	0.890870	0.445435	+	0.895314i	$0.353049\pi$
$798$	0	0
$799$	10.4649	0.370221
$800$	−5.05345	−0.178666
$801$	−88.6280	−3.13152
$802$	17.3151	0.611416
$803$	−49.8289	−1.75842
$804$	32.0033	1.12867
$805$	0.313655	0.0110549
$806$	−24.7255	−0.870918
$807$	12.4700	0.438964
$808$	9.35611	0.329147
$809$	23.3168	0.819775	0.409887	−	0.912136i	$-0.365568\pi$
$809$	23.3168	0.819775	0.409887	+	0.912136i	$0.365568\pi$
$810$	−4.81421	−0.169154
$811$	43.7384	1.53586	0.767932	−	0.640531i	$-0.221286\pi$
$811$	43.7384	1.53586	0.767932	+	0.640531i	$0.221286\pi$
$812$	16.4844	0.578488
$813$	1.37102	0.0480837
$814$	3.32191	0.116433
$815$	−16.5302	−0.579027
$816$	−14.0440	−0.491637
$817$	0	0
$818$	−1.86502	−0.0652088
$819$	91.5000	3.19727
$820$	5.28865	0.184688
$821$	6.31396	0.220359	0.110179	−	0.993912i	$-0.464857\pi$
$821$	6.31396	0.220359	0.110179	+	0.993912i	$0.464857\pi$
$822$	−5.92105	−0.206520
$823$	2.66438	0.0928745	0.0464373	−	0.998921i	$-0.485213\pi$
$823$	2.66438	0.0928745	0.0464373	+	0.998921i	$0.485213\pi$
$824$	7.34518	0.255881
$825$	−13.7903	−0.480115
$826$	8.85471	0.308095
$827$	14.3459	0.498854	0.249427	−	0.968394i	$-0.419758\pi$
$827$	14.3459	0.498854	0.249427	+	0.968394i	$0.419758\pi$
$828$	−1.33373	−0.0463503
$829$	−42.4180	−1.47324	−0.736619	−	0.676308i	$-0.763579\pi$
$829$	−42.4180	−1.47324	−0.736619	+	0.676308i	$0.763579\pi$
$830$	−2.53374	−0.0879475
$831$	−51.7733	−1.79599
$832$	−15.4075	−0.534159
$833$	−1.47014	−0.0509373
$834$	−25.1928	−0.872354
$835$	18.6256	0.644566
$836$	0	0
$837$	−74.6526	−2.58037
$838$	−16.7761	−0.579519
$839$	−17.5099	−0.604508	−0.302254	−	0.953227i	$-0.597739\pi$
$839$	−17.5099	−0.604508	−0.302254	+	0.953227i	$0.597739\pi$
$840$	−14.1387	−0.487832
$841$	−14.6274	−0.504394
$842$	4.49215	0.154810
$843$	83.6582	2.88134
$844$	−43.4856	−1.49684
$845$	23.7561	0.817236
$846$	−17.4115	−0.598621
$847$	24.8618	0.854262
$848$	23.5153	0.807518
$849$	−32.5311	−1.11646
$850$	−0.923781	−0.0316854
$851$	−0.181425	−0.00621916
$852$	54.7079	1.87426
$853$	−10.2019	−0.349305	−0.174652	−	0.984630i	$-0.555880\pi$
$853$	−10.2019	−0.349305	−0.174652	+	0.984630i	$0.555880\pi$
$854$	10.5492	0.360984
$855$	0	0
$856$	−18.7637	−0.641330
$857$	−55.9047	−1.90967	−0.954835	−	0.297138i	$-0.903968\pi$
$857$	−55.9047	−1.90967	−0.954835	+	0.297138i	$0.903968\pi$
$858$	42.0988	1.43723
$859$	−15.4688	−0.527789	−0.263895	−	0.964552i	$-0.585007\pi$
$859$	−15.4688	−0.527789	−0.263895	+	0.964552i	$0.585007\pi$
$860$	−15.3441	−0.523228
$861$	22.6959	0.773473
$862$	1.75977	0.0599380
$863$	−30.1692	−1.02697	−0.513485	−	0.858098i	$-0.671646\pi$
$863$	−30.1692	−1.02697	−0.513485	+	0.858098i	$0.671646\pi$
$864$	46.5785	1.58463
$865$	7.49526	0.254846
$866$	−7.70926	−0.261971
$867$	41.0433	1.39390
$868$	−35.2170	−1.19534
$869$	23.9758	0.813322
$870$	−5.74657	−0.194827
$871$	36.9058	1.25050
$872$	2.50467	0.0848190
$873$	−15.1381	−0.512348
$874$	0	0
$875$	2.48971	0.0841675
$876$	−57.1852	−1.93211
$877$	−40.7303	−1.37537	−0.687683	−	0.726011i	$-0.741372\pi$
$877$	−40.7303	−1.37537	−0.687683	+	0.726011i	$0.741372\pi$
$878$	−11.4835	−0.387548
$879$	−19.3351	−0.652157
$880$	11.6495	0.392704
$881$	−0.768167	−0.0258802	−0.0129401	−	0.999916i	$-0.504119\pi$
$881$	−0.768167	−0.0258802	−0.0129401	+	0.999916i	$0.504119\pi$
$882$	2.44603	0.0823621
$883$	18.3637	0.617989	0.308994	−	0.951064i	$-0.400008\pi$
$883$	18.3637	0.617989	0.308994	+	0.951064i	$0.400008\pi$
$884$	−19.4248	−0.653328
$885$	21.2619	0.714712
$886$	3.38371	0.113678
$887$	−16.6688	−0.559683	−0.279841	−	0.960046i	$-0.590282\pi$
$887$	−16.6688	−0.559683	−0.279841	+	0.960046i	$0.590282\pi$
$888$	8.17813	0.274440
$889$	−8.81227	−0.295554
$890$	7.36200	0.246775
$891$	43.7982	1.46729
$892$	−15.0143	−0.502715
$893$	0	0
$894$	−23.9434	−0.800787
$895$	3.34760	0.111898
$896$	28.3493	0.947082
$897$	−2.29921	−0.0767683
$898$	−16.6317	−0.555008
$899$	−30.7054	−1.02408
$900$	−10.5868	−0.352892
$901$	16.9646	0.565172
$902$	6.98529	0.232585
$903$	−65.8479	−2.19128
$904$	−11.7156	−0.389657
$905$	−1.15209	−0.0382966
$906$	−25.8753	−0.859651
$907$	−35.5645	−1.18090	−0.590451	−	0.807074i	$-0.701050\pi$
$907$	−35.5645	−1.18090	−0.590451	+	0.807074i	$0.701050\pi$
$908$	−3.27112	−0.108556
$909$	30.0643	0.997169
$910$	−7.60056	−0.251956
$911$	−44.2963	−1.46760	−0.733800	−	0.679365i	$-0.762255\pi$
$911$	−44.2963	−1.46760	−0.733800	+	0.679365i	$0.762255\pi$
$912$	0	0
$913$	23.0512	0.762883
$914$	−16.4561	−0.544321
$915$	25.3306	0.837404
$916$	40.2656	1.33041
$917$	−0.00142885	−4.71847e−5 0
$918$	8.51465	0.281025
$919$	46.0213	1.51810	0.759051	−	0.651032i	$-0.225663\pi$
$919$	46.0213	1.51810	0.759051	+	0.651032i	$0.225663\pi$
$920$	0.237660	0.00783542
$921$	−31.3619	−1.03341
$922$	15.2303	0.501584
$923$	63.0884	2.07658
$924$	59.9621	1.97261
$925$	−1.44010	−0.0473502
$926$	−12.2438	−0.402355
$927$	23.6025	0.775207
$928$	19.1582	0.628900
$929$	−55.8815	−1.83341	−0.916706	−	0.399562i	$-0.869162\pi$
$929$	−55.8815	−1.83341	−0.916706	+	0.399562i	$0.869162\pi$
$930$	12.2769	0.402576
$931$	0	0
$932$	23.0802	0.756019
$933$	−57.0726	−1.86847
$934$	14.0085	0.458374
$935$	8.40426	0.274849
$936$	69.3305	2.26614
$937$	36.4904	1.19209	0.596045	−	0.802951i	$-0.296738\pi$
$937$	36.4904	1.19209	0.596045	+	0.802951i	$0.296738\pi$
$938$	−7.63151	−0.249178
$939$	−6.04670	−0.197327
$940$	−9.96216	−0.324930
$941$	−26.3199	−0.858004	−0.429002	−	0.903304i	$-0.641135\pi$
$941$	−26.3199	−0.858004	−0.429002	+	0.903304i	$0.641135\pi$
$942$	31.6951	1.03268
$943$	−0.381499	−0.0124233
$944$	−17.9613	−0.584590
$945$	−22.9481	−0.746501
$946$	−20.2665	−0.658922
$947$	−22.6635	−0.736464	−0.368232	−	0.929734i	$-0.620037\pi$
$947$	−22.6635	−0.736464	−0.368232	+	0.929734i	$0.620037\pi$
$948$	27.5153	0.893656
$949$	−65.9452	−2.14067
$950$	0	0
$951$	−35.8675	−1.16308
$952$	8.61663	0.279266
$953$	−3.56262	−0.115405	−0.0577023	−	0.998334i	$-0.518377\pi$
$953$	−3.56262	−0.115405	−0.0577023	+	0.998334i	$0.518377\pi$
$954$	−28.2258	−0.913844
$955$	−19.2583	−0.623184
$956$	−15.9907	−0.517176
$957$	52.2805	1.68999
$958$	−0.638228	−0.0206202
$959$	−9.72537	−0.314049
$960$	7.65026	0.246911
$961$	34.5987	1.11609
$962$	4.39633	0.141743
$963$	−60.2940	−1.94295
$964$	−25.1463	−0.809908
$965$	3.25423	0.104757
$966$	0.475438	0.0152970
$967$	55.4727	1.78388	0.891940	−	0.452153i	$-0.149344\pi$
$967$	55.4727	1.78388	0.891940	+	0.452153i	$0.149344\pi$
$968$	18.8381	0.605478
$969$	0	0
$970$	1.25747	0.0403749
$971$	34.3074	1.10098	0.550488	−	0.834843i	$-0.314442\pi$
$971$	34.3074	1.10098	0.550488	+	0.834843i	$0.314442\pi$
$972$	1.97215	0.0632569
$973$	−41.3793	−1.32656
$974$	0.688038	0.0220462
$975$	−18.2505	−0.584483
$976$	−21.3984	−0.684945
$977$	36.5074	1.16797	0.583987	−	0.811763i	$-0.301492\pi$
$977$	36.5074	1.16797	0.583987	+	0.811763i	$0.301492\pi$
$978$	−25.0564	−0.801216
$979$	−66.9771	−2.14060
$980$	1.39952	0.0447059
$981$	8.04835	0.256964
$982$	−5.74001	−0.183171
$983$	−8.58556	−0.273837	−0.136918	−	0.990582i	$-0.543720\pi$
$983$	−8.58556	−0.273837	−0.136918	+	0.990582i	$0.543720\pi$
$984$	17.1969	0.548217
$985$	10.8657	0.346211
$986$	3.50216	0.111532
$987$	−42.7519	−1.36081
$988$	0	0
$989$	1.10685	0.0351957
$990$	−13.9831	−0.444411
$991$	14.2243	0.451850	0.225925	−	0.974145i	$-0.427460\pi$
$991$	14.2243	0.451850	0.225925	+	0.974145i	$0.427460\pi$
$992$	−40.9294	−1.29951
$993$	−11.3137	−0.359028
$994$	−13.0456	−0.413783
$995$	2.55526	0.0810071
$996$	26.4543	0.838235
$997$	33.0749	1.04749	0.523746	−	0.851875i	$-0.324534\pi$
$997$	33.0749	1.04749	0.523746	+	0.851875i	$0.324534\pi$
$998$	−12.1621	−0.384986
$999$	13.2737	0.419960

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1805.2.a.w.1.7	✓	16
5.4	even	2		9025.2.a.cm.1.10		16
19.18	odd	2	inner	1805.2.a.w.1.10	yes	16
95.94	odd	2		9025.2.a.cm.1.7		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1805.2.a.w.1.7	✓	16	1.1	even	1	trivial
1805.2.a.w.1.10	yes	16	19.18	odd	2	inner
9025.2.a.cm.1.7		16	95.94	odd	2
9025.2.a.cm.1.10		16	5.4	even	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:	\( N \)	\(=\)	\( 1805 = 5 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1805.a (trivial)

\(f(q)\)	\(=\)	\(q-0.503538 q^{2} -3.01030 q^{3} -1.74645 q^{4} +1.00000 q^{5} +1.51580 q^{6} +2.48971 q^{7} +1.88648 q^{8} +6.06188 q^{9} +O(q^{10})\)	\(q-0.503538 q^{2} -3.01030 q^{3} -1.74645 q^{4} +1.00000 q^{5} +1.51580 q^{6} +2.48971 q^{7} +1.88648 q^{8} +6.06188 q^{9} -0.503538 q^{10} +4.58103 q^{11} +5.25733 q^{12} +6.06268 q^{13} -1.25366 q^{14} -3.01030 q^{15} +2.54298 q^{16} +1.83458 q^{17} -3.05239 q^{18} -1.74645 q^{20} -7.49476 q^{21} -2.30672 q^{22} +0.125981 q^{23} -5.67886 q^{24} +1.00000 q^{25} -3.05279 q^{26} -9.21717 q^{27} -4.34815 q^{28} -3.79112 q^{29} +1.51580 q^{30} +8.09930 q^{31} -5.05345 q^{32} -13.7903 q^{33} -0.923781 q^{34} +2.48971 q^{35} -10.5868 q^{36} -1.44010 q^{37} -18.2505 q^{39} +1.88648 q^{40} -3.02823 q^{41} +3.77390 q^{42} +8.78585 q^{43} -8.00054 q^{44} +6.06188 q^{45} -0.0634361 q^{46} +5.70424 q^{47} -7.65514 q^{48} -0.801349 q^{49} -0.503538 q^{50} -5.52263 q^{51} -10.5882 q^{52} +9.24712 q^{53} +4.64120 q^{54} +4.58103 q^{55} +4.69679 q^{56} +1.90897 q^{58} -7.06307 q^{59} +5.25733 q^{60} -8.41466 q^{61} -4.07831 q^{62} +15.0923 q^{63} -2.54137 q^{64} +6.06268 q^{65} +6.94392 q^{66} +6.08737 q^{67} -3.20400 q^{68} -0.379239 q^{69} -1.25366 q^{70} +10.4060 q^{71} +11.4356 q^{72} -10.8772 q^{73} +0.725145 q^{74} -3.01030 q^{75} +11.4054 q^{77} +9.18981 q^{78} +5.23370 q^{79} +2.54298 q^{80} +9.56077 q^{81} +1.52483 q^{82} +5.03188 q^{83} +13.0892 q^{84} +1.83458 q^{85} -4.42401 q^{86} +11.4124 q^{87} +8.64202 q^{88} -14.6205 q^{89} -3.05239 q^{90} +15.0943 q^{91} -0.220019 q^{92} -24.3813 q^{93} -2.87230 q^{94} +15.2124 q^{96} -2.49726 q^{97} +0.403510 q^{98} +27.7697 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 26 q^{4} + 16 q^{5} - 2 q^{6} + 22 q^{7} + 18 q^{9}+O(q^{10}) \) 16 * q + 26 * q^4 + 16 * q^5 - 2 * q^6 + 22 * q^7 + 18 * q^9	\( 16 q + 26 q^{4} + 16 q^{5} - 2 q^{6} + 22 q^{7} + 18 q^{9} + 12 q^{11} + 42 q^{16} + 22 q^{17} + 26 q^{20} + 42 q^{23} - 14 q^{24} + 16 q^{25} - 26 q^{26} + 46 q^{28} - 2 q^{30} + 22 q^{35} - 8 q^{36} - 38 q^{39} + 74 q^{42} + 88 q^{43} - 48 q^{44} + 18 q^{45} + 32 q^{47} + 30 q^{49} - 22 q^{54} + 12 q^{55} - 2 q^{58} + 20 q^{61} + 6 q^{62} - 6 q^{63} + 24 q^{64} - 24 q^{66} + 84 q^{68} + 44 q^{73} - 122 q^{74} + 4 q^{77} + 42 q^{80} - 36 q^{81} - 50 q^{82} + 56 q^{83} + 22 q^{85} + 34 q^{87} + 6 q^{92} - 58 q^{93} - 96 q^{96} + 6 q^{99}+O(q^{100}) \) 16 * q + 26 * q^4 + 16 * q^5 - 2 * q^6 + 22 * q^7 + 18 * q^9 + 12 * q^11 + 42 * q^16 + 22 * q^17 + 26 * q^20 + 42 * q^23 - 14 * q^24 + 16 * q^25 - 26 * q^26 + 46 * q^28 - 2 * q^30 + 22 * q^35 - 8 * q^36 - 38 * q^39 + 74 * q^42 + 88 * q^43 - 48 * q^44 + 18 * q^45 + 32 * q^47 + 30 * q^49 - 22 * q^54 + 12 * q^55 - 2 * q^58 + 20 * q^61 + 6 * q^62 - 6 * q^63 + 24 * q^64 - 24 * q^66 + 84 * q^68 + 44 * q^73 - 122 * q^74 + 4 * q^77 + 42 * q^80 - 36 * q^81 - 50 * q^82 + 56 * q^83 + 22 * q^85 + 34 * q^87 + 6 * q^92 - 58 * q^93 - 96 * q^96 + 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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