LMFDB - Embedded newform 8027.2.a.c.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8027,2,Mod(1,8027)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8027, 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("8027.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8027 = 23 \cdot 349 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8027.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:	$64.0959177025$
Analytic rank:	$1$
Dimension:	$143$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Character	$\chi$	$=$	8027.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.53769 q^{2} +0.0556295 q^{3} +4.43986 q^{4} +2.89276 q^{5} -0.141170 q^{6} -5.18186 q^{7} -6.19160 q^{8} -2.99691 q^{9} +O(q^{10})$	\(q-2.53769 q^{2} +0.0556295 q^{3} +4.43986 q^{4} +2.89276 q^{5} -0.141170 q^{6} -5.18186 q^{7} -6.19160 q^{8} -2.99691 q^{9} -7.34093 q^{10} -6.09467 q^{11} +0.246987 q^{12} -2.15876 q^{13} +13.1499 q^{14} +0.160923 q^{15} +6.83264 q^{16} -1.34258 q^{17} +7.60521 q^{18} +8.42651 q^{19} +12.8435 q^{20} -0.288264 q^{21} +15.4664 q^{22} +1.00000 q^{23} -0.344436 q^{24} +3.36809 q^{25} +5.47827 q^{26} -0.333605 q^{27} -23.0067 q^{28} +9.63839 q^{29} -0.408373 q^{30} +1.85364 q^{31} -4.95590 q^{32} -0.339043 q^{33} +3.40706 q^{34} -14.9899 q^{35} -13.3058 q^{36} -9.35060 q^{37} -21.3838 q^{38} -0.120091 q^{39} -17.9109 q^{40} +2.14036 q^{41} +0.731525 q^{42} +8.31941 q^{43} -27.0595 q^{44} -8.66934 q^{45} -2.53769 q^{46} +0.302830 q^{47} +0.380097 q^{48} +19.8516 q^{49} -8.54715 q^{50} -0.0746873 q^{51} -9.58461 q^{52} +7.07879 q^{53} +0.846586 q^{54} -17.6304 q^{55} +32.0840 q^{56} +0.468763 q^{57} -24.4592 q^{58} -6.46397 q^{59} +0.714476 q^{60} -0.0116285 q^{61} -4.70395 q^{62} +15.5295 q^{63} -1.08876 q^{64} -6.24479 q^{65} +0.860387 q^{66} +3.52319 q^{67} -5.96088 q^{68} +0.0556295 q^{69} +38.0397 q^{70} -1.74591 q^{71} +18.5557 q^{72} -13.7726 q^{73} +23.7289 q^{74} +0.187365 q^{75} +37.4125 q^{76} +31.5817 q^{77} +0.304753 q^{78} +7.35757 q^{79} +19.7652 q^{80} +8.97216 q^{81} -5.43158 q^{82} +4.36581 q^{83} -1.27985 q^{84} -3.88378 q^{85} -21.1121 q^{86} +0.536179 q^{87} +37.7358 q^{88} +6.57968 q^{89} +22.0001 q^{90} +11.1864 q^{91} +4.43986 q^{92} +0.103117 q^{93} -0.768488 q^{94} +24.3759 q^{95} -0.275694 q^{96} +0.940121 q^{97} -50.3773 q^{98} +18.2651 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 143 q - 17 q^{2} - 17 q^{3} + 121 q^{4} - 22 q^{5} - 11 q^{6} - 33 q^{7} - 45 q^{8} + 104 q^{9}+O(q^{10}) $ 143 * q - 17 * q^2 - 17 * q^3 + 121 * q^4 - 22 * q^5 - 11 * q^6 - 33 * q^7 - 45 * q^8 + 104 * q^9	\( 143 q - 17 q^{2} - 17 q^{3} + 121 q^{4} - 22 q^{5} - 11 q^{6} - 33 q^{7} - 45 q^{8} + 104 q^{9} - 22 q^{10} - 14 q^{11} - 36 q^{12} - 87 q^{13} - 18 q^{14} - 19 q^{15} + 81 q^{16} - 14 q^{17} - 60 q^{18} - 18 q^{19} - 25 q^{20} - 26 q^{21} - 62 q^{22} + 143 q^{23} - 21 q^{24} + 67 q^{25} - 5 q^{26} - 47 q^{27} - 76 q^{28} - 54 q^{29} - 22 q^{30} - 62 q^{31} - 117 q^{32} - 59 q^{33} - 35 q^{34} - 52 q^{35} + 52 q^{36} - 190 q^{37} - 19 q^{38} - 43 q^{39} - 41 q^{40} - 50 q^{41} + 8 q^{42} - 50 q^{43} - 18 q^{44} - 75 q^{45} - 17 q^{46} - 63 q^{47} - 35 q^{48} + 74 q^{49} - 53 q^{50} - 33 q^{51} - 124 q^{52} - 100 q^{53} - 46 q^{54} - 61 q^{55} - 3 q^{56} - 80 q^{57} - 112 q^{58} - 109 q^{59} - 55 q^{60} - 76 q^{61} - 6 q^{62} - 93 q^{63} + 57 q^{64} - 17 q^{65} + 50 q^{66} - 120 q^{67} + 26 q^{68} - 17 q^{69} - 109 q^{71} - 153 q^{72} - 94 q^{73} + 35 q^{74} - 105 q^{75} - 16 q^{76} - 52 q^{77} - 59 q^{78} - 29 q^{79} - 30 q^{80} + 39 q^{81} - 65 q^{82} + 8 q^{83} + 11 q^{84} - 155 q^{85} - 15 q^{86} - 25 q^{87} - 139 q^{88} + 6 q^{89} + 82 q^{90} - 34 q^{91} + 121 q^{92} - 151 q^{93} - 3 q^{94} - 70 q^{95} - 23 q^{96} - 203 q^{97} - 18 q^{98} - 49 q^{99}+O(q^{100}) \) 143 * q - 17 * q^2 - 17 * q^3 + 121 * q^4 - 22 * q^5 - 11 * q^6 - 33 * q^7 - 45 * q^8 + 104 * q^9 - 22 * q^10 - 14 * q^11 - 36 * q^12 - 87 * q^13 - 18 * q^14 - 19 * q^15 + 81 * q^16 - 14 * q^17 - 60 * q^18 - 18 * q^19 - 25 * q^20 - 26 * q^21 - 62 * q^22 + 143 * q^23 - 21 * q^24 + 67 * q^25 - 5 * q^26 - 47 * q^27 - 76 * q^28 - 54 * q^29 - 22 * q^30 - 62 * q^31 - 117 * q^32 - 59 * q^33 - 35 * q^34 - 52 * q^35 + 52 * q^36 - 190 * q^37 - 19 * q^38 - 43 * q^39 - 41 * q^40 - 50 * q^41 + 8 * q^42 - 50 * q^43 - 18 * q^44 - 75 * q^45 - 17 * q^46 - 63 * q^47 - 35 * q^48 + 74 * q^49 - 53 * q^50 - 33 * q^51 - 124 * q^52 - 100 * q^53 - 46 * q^54 - 61 * q^55 - 3 * q^56 - 80 * q^57 - 112 * q^58 - 109 * q^59 - 55 * q^60 - 76 * q^61 - 6 * q^62 - 93 * q^63 + 57 * q^64 - 17 * q^65 + 50 * q^66 - 120 * q^67 + 26 * q^68 - 17 * q^69 - 109 * q^71 - 153 * q^72 - 94 * q^73 + 35 * q^74 - 105 * q^75 - 16 * q^76 - 52 * q^77 - 59 * q^78 - 29 * q^79 - 30 * q^80 + 39 * q^81 - 65 * q^82 + 8 * q^83 + 11 * q^84 - 155 * q^85 - 15 * q^86 - 25 * q^87 - 139 * q^88 + 6 * q^89 + 82 * q^90 - 34 * q^91 + 121 * q^92 - 151 * q^93 - 3 * q^94 - 70 * q^95 - 23 * q^96 - 203 * q^97 - 18 * q^98 - 49 * 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 $

$2$	−2.53769	−1.79442	−0.897208	−	0.441608i	$-0.854408\pi$
$2$	−2.53769	−1.79442	−0.897208	+	0.441608i	$0.854408\pi$
$3$	0.0556295	0.0321177	0.0160589	−	0.999871i	$-0.494888\pi$
$3$	0.0556295	0.0321177	0.0160589	+	0.999871i	$0.494888\pi$
$4$	4.43986	2.21993
$5$	2.89276	1.29368	0.646842	−	0.762624i	$-0.276089\pi$
$5$	2.89276	1.29368	0.646842	+	0.762624i	$0.276089\pi$
$6$	−0.141170	−0.0576326
$7$	−5.18186	−1.95856	−0.979279	−	0.202517i	$-0.935088\pi$
$7$	−5.18186	−1.95856	−0.979279	+	0.202517i	$0.935088\pi$
$8$	−6.19160	−2.18906
$9$	−2.99691	−0.998968
$10$	−7.34093	−2.32141
$11$	−6.09467	−1.83761	−0.918805	−	0.394711i	$-0.870845\pi$
$11$	−6.09467	−1.83761	−0.918805	+	0.394711i	$0.870845\pi$
$12$	0.246987	0.0712991
$13$	−2.15876	−0.598733	−0.299367	−	0.954138i	$-0.596775\pi$
$13$	−2.15876	−0.598733	−0.299367	+	0.954138i	$0.596775\pi$
$14$	13.1499	3.51447
$15$	0.160923	0.0415502
$16$	6.83264	1.70816
$17$	−1.34258	−0.325624	−0.162812	−	0.986657i	$-0.552056\pi$
$17$	−1.34258	−0.325624	−0.162812	+	0.986657i	$0.552056\pi$
$18$	7.60521	1.79257
$19$	8.42651	1.93317	0.966587	−	0.256340i	$-0.0825167\pi$
$19$	8.42651	1.93317	0.966587	+	0.256340i	$0.0825167\pi$
$20$	12.8435	2.87189
$21$	−0.288264	−0.0629044
$22$	15.4664	3.29744
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	−0.344436	−0.0703077
$25$	3.36809	0.673617
$26$	5.47827	1.07438
$27$	−0.333605	−0.0642023
$28$	−23.0067	−4.34786
$29$	9.63839	1.78980	0.894902	−	0.446263i	$-0.147245\pi$
$29$	9.63839	1.78980	0.894902	+	0.446263i	$0.147245\pi$
$30$	−0.408373	−0.0745583
$31$	1.85364	0.332923	0.166462	−	0.986048i	$-0.446766\pi$
$31$	1.85364	0.332923	0.166462	+	0.986048i	$0.446766\pi$
$32$	−4.95590	−0.876087
$33$	−0.339043	−0.0590199
$34$	3.40706	0.584306
$35$	−14.9899	−2.53375
$36$	−13.3058	−2.21764
$37$	−9.35060	−1.53723	−0.768615	−	0.639712i	$-0.779054\pi$
$37$	−9.35060	−1.53723	−0.768615	+	0.639712i	$0.779054\pi$
$38$	−21.3838	−3.46892
$39$	−0.120091	−0.0192300
$40$	−17.9109	−2.83195
$41$	2.14036	0.334269	0.167134	−	0.985934i	$-0.446549\pi$
$41$	2.14036	0.334269	0.167134	+	0.985934i	$0.446549\pi$
$42$	0.731525	0.112877
$43$	8.31941	1.26870	0.634349	−	0.773046i	$-0.281268\pi$
$43$	8.31941	1.26870	0.634349	+	0.773046i	$0.281268\pi$
$44$	−27.0595	−4.07937
$45$	−8.66934	−1.29235
$46$	−2.53769	−0.374162
$47$	0.302830	0.0441723	0.0220861	−	0.999756i	$-0.492969\pi$
$47$	0.302830	0.0441723	0.0220861	+	0.999756i	$0.492969\pi$
$48$	0.380097	0.0548622
$49$	19.8516	2.83595
$50$	−8.54715	−1.20875
$51$	−0.0746873	−0.0104583
$52$	−9.58461	−1.32915
$53$	7.07879	0.972346	0.486173	−	0.873863i	$-0.338392\pi$
$53$	7.07879	0.972346	0.486173	+	0.873863i	$0.338392\pi$
$54$	0.846586	0.115206
$55$	−17.6304	−2.37729
$56$	32.0840	4.28741
$57$	0.468763	0.0620891
$58$	−24.4592	−3.21165
$59$	−6.46397	−0.841537	−0.420768	−	0.907168i	$-0.638240\pi$
$59$	−6.46397	−0.841537	−0.420768	+	0.907168i	$0.638240\pi$
$60$	0.714476	0.0922385
$61$	−0.0116285	−0.00148887	−0.000744436	−	1.00000i	$-0.500237\pi$
$61$	−0.0116285	−0.00148887	−0.000744436		1.00000i	$0.500237\pi$
$62$	−4.70395	−0.597403
$63$	15.5295	1.95654
$64$	−1.08876	−0.136095
$65$	−6.24479	−0.774571
$66$	0.860387	0.105906
$67$	3.52319	0.430426	0.215213	−	0.976567i	$-0.430955\pi$
$67$	3.52319	0.430426	0.215213	+	0.976567i	$0.430955\pi$
$68$	−5.96088	−0.722863
$69$	0.0556295	0.00669701
$70$	38.0397	4.54661
$71$	−1.74591	−0.207201	−0.103601	−	0.994619i	$-0.533036\pi$
$71$	−1.74591	−0.207201	−0.103601	+	0.994619i	$0.533036\pi$
$72$	18.5557	2.18680
$73$	−13.7726	−1.61196	−0.805982	−	0.591940i	$-0.798362\pi$
$73$	−13.7726	−1.61196	−0.805982	+	0.591940i	$0.798362\pi$
$74$	23.7289	2.75843
$75$	0.187365	0.0216351
$76$	37.4125	4.29151
$77$	31.5817	3.59907
$78$	0.304753	0.0345065
$79$	7.35757	0.827791	0.413896	−	0.910324i	$-0.364168\pi$
$79$	7.35757	0.827791	0.413896	+	0.910324i	$0.364168\pi$
$80$	19.7652	2.20982
$81$	8.97216	0.996906
$82$	−5.43158	−0.599817
$83$	4.36581	0.479210	0.239605	−	0.970871i	$-0.422982\pi$
$83$	4.36581	0.479210	0.239605	+	0.970871i	$0.422982\pi$
$84$	−1.27985	−0.139643
$85$	−3.88378	−0.421255
$86$	−21.1121	−2.27657
$87$	0.536179	0.0574844
$88$	37.7358	4.02265
$89$	6.57968	0.697445	0.348722	−	0.937226i	$-0.386616\pi$
$89$	6.57968	0.697445	0.348722	+	0.937226i	$0.386616\pi$
$90$	22.0001	2.31901
$91$	11.1864	1.17265
$92$	4.43986	0.462887
$93$	0.103117	0.0106927
$94$	−0.768488	−0.0792634
$95$	24.3759	2.50091
$96$	−0.275694	−0.0281379
$97$	0.940121	0.0954548	0.0477274	−	0.998860i	$-0.484802\pi$
$97$	0.940121	0.0954548	0.0477274	+	0.998860i	$0.484802\pi$
$98$	−50.3773	−5.08887
$99$	18.2651	1.83572
$100$	14.9538	1.49538
$101$	−6.90127	−0.686702	−0.343351	−	0.939207i	$-0.611562\pi$
$101$	−6.90127	−0.686702	−0.343351	+	0.939207i	$0.611562\pi$
$102$	0.189533	0.0187666
$103$	5.22835	0.515164	0.257582	−	0.966256i	$-0.417074\pi$
$103$	5.22835	0.515164	0.257582	+	0.966256i	$0.417074\pi$
$104$	13.3662	1.31066
$105$	−0.833881	−0.0813784
$106$	−17.9638	−1.74479
$107$	−6.38886	−0.617634	−0.308817	−	0.951121i	$-0.599933\pi$
$107$	−6.38886	−0.617634	−0.308817	+	0.951121i	$0.599933\pi$
$108$	−1.48116	−0.142525
$109$	−11.0930	−1.06251	−0.531257	−	0.847211i	$-0.678280\pi$
$109$	−11.0930	−1.06251	−0.531257	+	0.847211i	$0.678280\pi$
$110$	44.7405	4.26584
$111$	−0.520170	−0.0493723
$112$	−35.4057	−3.34553
$113$	1.01634	0.0956091	0.0478045	−	0.998857i	$-0.484778\pi$
$113$	1.01634	0.0956091	0.0478045	+	0.998857i	$0.484778\pi$
$114$	−1.18957	−0.111414
$115$	2.89276	0.269752
$116$	42.7931	3.97324
$117$	6.46961	0.598116
$118$	16.4035	1.51007
$119$	6.95708	0.637754
$120$	−0.996372	−0.0909559
$121$	26.1450	2.37681
$122$	0.0295094	0.00267166
$123$	0.119068	0.0107360
$124$	8.22989	0.739066
$125$	−4.72074	−0.422236
$126$	−39.4091	−3.51084
$127$	−4.73535	−0.420195	−0.210097	−	0.977680i	$-0.567378\pi$
$127$	−4.73535	−0.420195	−0.210097	+	0.977680i	$0.567378\pi$
$128$	12.6747	1.12030
$129$	0.462805	0.0407477
$130$	15.8473	1.38990
$131$	16.0370	1.40116	0.700580	−	0.713574i	$-0.252925\pi$
$131$	16.0370	1.40116	0.700580	+	0.713574i	$0.252925\pi$
$132$	−1.50531	−0.131020
$133$	−43.6649	−3.78623
$134$	−8.94075	−0.772363
$135$	−0.965041	−0.0830575
$136$	8.31275	0.712812
$137$	−16.0144	−1.36821	−0.684103	−	0.729385i	$-0.739806\pi$
$137$	−16.0144	−1.36821	−0.684103	+	0.729385i	$0.739806\pi$
$138$	−0.141170	−0.0120172
$139$	7.49032	0.635320	0.317660	−	0.948205i	$-0.397103\pi$
$139$	7.49032	0.635320	0.317660	+	0.948205i	$0.397103\pi$
$140$	−66.5530	−5.62476
$141$	0.0168463	0.00141871
$142$	4.43057	0.371806
$143$	13.1569	1.10024
$144$	−20.4768	−1.70640
$145$	27.8816	2.31544
$146$	34.9506	2.89253
$147$	1.10434	0.0910842
$148$	−41.5154	−3.41254
$149$	−3.70836	−0.303801	−0.151900	−	0.988396i	$-0.548539\pi$
$149$	−3.70836	−0.303801	−0.151900	+	0.988396i	$0.548539\pi$
$150$	−0.475474	−0.0388223
$151$	5.82738	0.474225	0.237113	−	0.971482i	$-0.423799\pi$
$151$	5.82738	0.474225	0.237113	+	0.971482i	$0.423799\pi$
$152$	−52.1736	−4.23184
$153$	4.02360	0.325289
$154$	−80.1445	−6.45822
$155$	5.36214	0.430697
$156$	−0.533187	−0.0426891
$157$	2.19327	0.175042	0.0875210	−	0.996163i	$-0.472106\pi$
$157$	2.19327	0.175042	0.0875210	+	0.996163i	$0.472106\pi$
$158$	−18.6712	−1.48540
$159$	0.393790	0.0312296
$160$	−14.3362	−1.13338
$161$	−5.18186	−0.408388
$162$	−22.7685	−1.78887
$163$	10.2280	0.801115	0.400557	−	0.916272i	$-0.368816\pi$
$163$	10.2280	0.801115	0.400557	+	0.916272i	$0.368816\pi$
$164$	9.50292	0.742053
$165$	−0.980773	−0.0763531
$166$	−11.0791	−0.859901
$167$	17.5843	1.36071	0.680356	−	0.732882i	$-0.261825\pi$
$167$	17.5843	1.36071	0.680356	+	0.732882i	$0.261825\pi$
$168$	1.78482	0.137702
$169$	−8.33974	−0.641519
$170$	9.85582	0.755907
$171$	−25.2534	−1.93118
$172$	36.9370	2.81642
$173$	−20.4280	−1.55311	−0.776556	−	0.630048i	$-0.783035\pi$
$173$	−20.4280	−1.55311	−0.776556	+	0.630048i	$0.783035\pi$
$174$	−1.36066	−0.103151
$175$	−17.4529	−1.31932
$176$	−41.6426	−3.13893
$177$	−0.359588	−0.0270283
$178$	−16.6972	−1.25151
$179$	−25.1172	−1.87735	−0.938673	−	0.344809i	$-0.887944\pi$
$179$	−25.1172	−1.87735	−0.938673	+	0.344809i	$0.887944\pi$
$180$	−38.4907	−2.86892
$181$	13.0139	0.967316	0.483658	−	0.875257i	$-0.339308\pi$
$181$	13.0139	0.967316	0.483658	+	0.875257i	$0.339308\pi$
$182$	−28.3876	−2.10423
$183$	−0.000646886 0	−4.78192e−5 0
$184$	−6.19160	−0.456451
$185$	−27.0491	−1.98869
$186$	−0.261679	−0.0191872
$187$	8.18260	0.598371
$188$	1.34452	0.0980593
$189$	1.72869	0.125744
$190$	−61.8584	−4.48768
$191$	−6.08061	−0.439977	−0.219989	−	0.975502i	$-0.570602\pi$
$191$	−6.08061	−0.439977	−0.219989	+	0.975502i	$0.570602\pi$
$192$	−0.0605672	−0.00437106
$193$	−23.2744	−1.67533	−0.837665	−	0.546184i	$-0.816080\pi$
$193$	−23.2744	−1.67533	−0.837665	+	0.546184i	$0.816080\pi$
$194$	−2.38573	−0.171286
$195$	−0.347395	−0.0248775
$196$	88.1385	6.29561
$197$	−17.9055	−1.27572	−0.637859	−	0.770153i	$-0.720180\pi$
$197$	−17.9055	−1.27572	−0.637859	+	0.770153i	$0.720180\pi$
$198$	−46.3512	−3.29404
$199$	8.10108	0.574270	0.287135	−	0.957890i	$-0.407297\pi$
$199$	8.10108	0.574270	0.287135	+	0.957890i	$0.407297\pi$
$200$	−20.8539	−1.47459
$201$	0.195993	0.0138243
$202$	17.5133	1.23223
$203$	−49.9447	−3.50543
$204$	−0.331601	−0.0232167
$205$	6.19157	0.432438
$206$	−13.2679	−0.924419
$207$	−2.99691	−0.208299
$208$	−14.7500	−1.02273
$209$	−51.3567	−3.55242
$210$	2.11613	0.146027
$211$	−5.67692	−0.390815	−0.195408	−	0.980722i	$-0.562603\pi$
$211$	−5.67692	−0.390815	−0.195408	+	0.980722i	$0.562603\pi$
$212$	31.4288	2.15854
$213$	−0.0971242	−0.00665484
$214$	16.2129	1.10829
$215$	24.0661	1.64129
$216$	2.06555	0.140543
$217$	−9.60528	−0.652049
$218$	28.1505	1.90659
$219$	−0.766165	−0.0517726
$220$	−78.2767	−5.27741
$221$	2.89832	0.194962
$222$	1.32003	0.0885945
$223$	12.6452	0.846784	0.423392	−	0.905947i	$-0.360839\pi$
$223$	12.6452	0.846784	0.423392	+	0.905947i	$0.360839\pi$
$224$	25.6807	1.71587
$225$	−10.0938	−0.672922
$226$	−2.57915	−0.171562
$227$	22.4073	1.48723	0.743613	−	0.668611i	$-0.233111\pi$
$227$	22.4073	1.48723	0.743613	+	0.668611i	$0.233111\pi$
$228$	2.08124	0.137834
$229$	−13.9830	−0.924024	−0.462012	−	0.886874i	$-0.652872\pi$
$229$	−13.9830	−0.924024	−0.462012	+	0.886874i	$0.652872\pi$
$230$	−7.34093	−0.484047
$231$	1.75687	0.115594
$232$	−59.6771	−3.91799
$233$	20.8109	1.36336	0.681682	−	0.731648i	$-0.261249\pi$
$233$	20.8109	1.36336	0.681682	+	0.731648i	$0.261249\pi$
$234$	−16.4178	−1.07327
$235$	0.876015	0.0571449
$236$	−28.6991	−1.86815
$237$	0.409298	0.0265868
$238$	−17.6549	−1.14440
$239$	18.1435	1.17361	0.586803	−	0.809730i	$-0.300386\pi$
$239$	18.1435	1.17361	0.586803	+	0.809730i	$0.300386\pi$
$240$	1.09953	0.0709743
$241$	−25.8351	−1.66418	−0.832092	−	0.554638i	$-0.812857\pi$
$241$	−25.8351	−1.66418	−0.832092	+	0.554638i	$0.812857\pi$
$242$	−66.3477	−4.26499
$243$	1.49993	0.0962207
$244$	−0.0516288	−0.00330519
$245$	57.4261	3.66882
$246$	−0.302156	−0.0192648
$247$	−18.1908	−1.15745
$248$	−11.4770	−0.728789
$249$	0.242868	0.0153911
$250$	11.9798	0.757667
$251$	11.1896	0.706280	0.353140	−	0.935571i	$-0.385114\pi$
$251$	11.1896	0.706280	0.353140	+	0.935571i	$0.385114\pi$
$252$	68.9490	4.34338
$253$	−6.09467	−0.383168
$254$	12.0168	0.754004
$255$	−0.216053	−0.0135298
$256$	−29.9870	−1.87419
$257$	−2.39005	−0.149087	−0.0745437	−	0.997218i	$-0.523750\pi$
$257$	−2.39005	−0.149087	−0.0745437	+	0.997218i	$0.523750\pi$
$258$	−1.17446	−0.0731184
$259$	48.4535	3.01075
$260$	−27.7260	−1.71949
$261$	−28.8853	−1.78796
$262$	−40.6969	−2.51426
$263$	16.2515	1.00211	0.501054	−	0.865416i	$-0.332946\pi$
$263$	16.2515	1.00211	0.501054	+	0.865416i	$0.332946\pi$
$264$	2.09922	0.129198
$265$	20.4773	1.25791
$266$	110.808	6.79408
$267$	0.366025	0.0224003
$268$	15.6425	0.955515
$269$	−15.1625	−0.924473	−0.462237	−	0.886757i	$-0.652953\pi$
$269$	−15.1625	−0.924473	−0.462237	+	0.886757i	$0.652953\pi$
$270$	2.44897	0.149040
$271$	−2.64348	−0.160580	−0.0802900	−	0.996772i	$-0.525585\pi$
$271$	−2.64348	−0.160580	−0.0802900	+	0.996772i	$0.525585\pi$
$272$	−9.17339	−0.556218
$273$	0.622294	0.0376630
$274$	40.6397	2.45513
$275$	−20.5274	−1.23785
$276$	0.246987	0.0148669
$277$	−3.57695	−0.214918	−0.107459	−	0.994210i	$-0.534271\pi$
$277$	−3.57695	−0.214918	−0.107459	+	0.994210i	$0.534271\pi$
$278$	−19.0081	−1.14003
$279$	−5.55518	−0.332580
$280$	92.8115	5.54655
$281$	16.1337	0.962456	0.481228	−	0.876595i	$-0.340191\pi$
$281$	16.1337	0.962456	0.481228	+	0.876595i	$0.340191\pi$
$282$	−0.0427506	−0.00254576
$283$	−29.3220	−1.74301	−0.871506	−	0.490385i	$-0.836856\pi$
$283$	−29.3220	−1.74301	−0.871506	+	0.490385i	$0.836856\pi$
$284$	−7.75160	−0.459973
$285$	1.35602	0.0803237
$286$	−33.3882	−1.97429
$287$	−11.0911	−0.654685
$288$	14.8523	0.875183
$289$	−15.1975	−0.893969
$290$	−70.7548	−4.15486
$291$	0.0522985	0.00306579
$292$	−61.1485	−3.57845
$293$	−25.9795	−1.51774	−0.758871	−	0.651241i	$-0.774249\pi$
$293$	−25.9795	−1.51774	−0.758871	+	0.651241i	$0.774249\pi$
$294$	−2.80246	−0.163443
$295$	−18.6987	−1.08868
$296$	57.8952	3.36509
$297$	2.03321	0.117979
$298$	9.41066	0.545145
$299$	−2.15876	−0.124844
$300$	0.831875	0.0480283
$301$	−43.1100	−2.48482
$302$	−14.7881	−0.850958
$303$	−0.383915	−0.0220553
$304$	57.5753	3.30217
$305$	−0.0336384	−0.00192613
$306$	−10.2106	−0.583703
$307$	16.5771	0.946107	0.473054	−	0.881034i	$-0.343152\pi$
$307$	16.5771	0.946107	0.473054	+	0.881034i	$0.343152\pi$
$308$	140.218	7.98968
$309$	0.290850	0.0165459
$310$	−13.6074	−0.772850
$311$	−4.98819	−0.282854	−0.141427	−	0.989949i	$-0.545169\pi$
$311$	−4.98819	−0.282854	−0.141427	+	0.989949i	$0.545169\pi$
$312$	0.743556	0.0420956
$313$	−24.1980	−1.36775	−0.683875	−	0.729599i	$-0.739707\pi$
$313$	−24.1980	−1.36775	−0.683875	+	0.729599i	$0.739707\pi$
$314$	−5.56584	−0.314098
$315$	44.9233	2.53114
$316$	32.6666	1.83764
$317$	18.6004	1.04470	0.522351	−	0.852731i	$-0.325055\pi$
$317$	18.6004	1.04470	0.522351	+	0.852731i	$0.325055\pi$
$318$	−0.999315	−0.0560388
$319$	−58.7427	−3.28896
$320$	−3.14953	−0.176064
$321$	−0.355409	−0.0198370
$322$	13.1499	0.732817
$323$	−11.3133	−0.629488
$324$	39.8351	2.21306
$325$	−7.27090	−0.403317
$326$	−25.9553	−1.43753
$327$	−0.617097	−0.0341256
$328$	−13.2523	−0.731735
$329$	−1.56922	−0.0865139
$330$	2.48890	0.137009
$331$	31.9020	1.75349	0.876747	−	0.480952i	$-0.159709\pi$
$331$	31.9020	1.75349	0.876747	+	0.480952i	$0.159709\pi$
$332$	19.3836	1.06381
$333$	28.0229	1.53564
$334$	−44.6234	−2.44168
$335$	10.1918	0.556835
$336$	−1.96961	−0.107451
$337$	26.6155	1.44984	0.724920	−	0.688833i	$-0.241877\pi$
$337$	26.6155	1.44984	0.724920	+	0.688833i	$0.241877\pi$
$338$	21.1637	1.15115
$339$	0.0565384	0.00307075
$340$	−17.2434	−0.935157
$341$	−11.2973	−0.611783
$342$	64.0854	3.46534
$343$	−66.5953	−3.59581
$344$	−51.5105	−2.77726
$345$	0.160923	0.00866381
$346$	51.8399	2.78693
$347$	1.94628	0.104482	0.0522410	−	0.998635i	$-0.483364\pi$
$347$	1.94628	0.104482	0.0522410	+	0.998635i	$0.483364\pi$
$348$	2.38056	0.127611
$349$	1.00000	0.0535288
$349$	1.00000	0.0535288
$350$	44.2901	2.36741
$351$	0.720174	0.0384401
$352$	30.2045	1.60991
$353$	−4.31599	−0.229717	−0.114858	−	0.993382i	$-0.536641\pi$
$353$	−4.31599	−0.229717	−0.114858	+	0.993382i	$0.536641\pi$
$354$	0.912521	0.0484999
$355$	−5.05051	−0.268053
$356$	29.2129	1.54828
$357$	0.387019	0.0204832
$358$	63.7395	3.36874
$359$	15.1398	0.799050	0.399525	−	0.916722i	$-0.369175\pi$
$359$	15.1398	0.799050	0.399525	+	0.916722i	$0.369175\pi$
$360$	53.6771	2.82903
$361$	52.0060	2.73716
$362$	−33.0252	−1.73577
$363$	1.45443	0.0763379
$364$	49.6661	2.60321
$365$	−39.8410	−2.08537
$366$	0.00164160	8.58076e−5 0
$367$	−22.7954	−1.18991	−0.594956	−	0.803758i	$-0.702831\pi$
$367$	−22.7954	−1.18991	−0.594956	+	0.803758i	$0.702831\pi$
$368$	6.83264	0.356176
$369$	−6.41447	−0.333924
$370$	68.6421	3.56853
$371$	−36.6813	−1.90440
$372$	0.457825	0.0237371
$373$	9.24360	0.478616	0.239308	−	0.970944i	$-0.423080\pi$
$373$	9.24360	0.478616	0.239308	+	0.970944i	$0.423080\pi$
$374$	−20.7649	−1.07373
$375$	−0.262613	−0.0135613
$376$	−1.87500	−0.0966959
$377$	−20.8070	−1.07161
$378$	−4.38689	−0.225637
$379$	−8.78228	−0.451116	−0.225558	−	0.974230i	$-0.572420\pi$
$379$	−8.78228	−0.451116	−0.225558	+	0.974230i	$0.572420\pi$
$380$	108.226	5.55186
$381$	−0.263425	−0.0134957
$382$	15.4307	0.789502
$383$	−16.5867	−0.847543	−0.423771	−	0.905769i	$-0.639294\pi$
$383$	−16.5867	−0.847543	−0.423771	+	0.905769i	$0.639294\pi$
$384$	0.705089	0.0359814
$385$	91.3584	4.65605
$386$	59.0633	3.00624
$387$	−24.9325	−1.26739
$388$	4.17401	0.211903
$389$	−23.1330	−1.17289	−0.586444	−	0.809990i	$-0.699473\pi$
$389$	−23.1330	−1.17289	−0.586444	+	0.809990i	$0.699473\pi$
$390$	0.881580	0.0446405
$391$	−1.34258	−0.0678974
$392$	−122.913	−6.20807
$393$	0.892131	0.0450021
$394$	45.4387	2.28917
$395$	21.2837	1.07090
$396$	81.0947	4.07516
$397$	−11.4924	−0.576789	−0.288394	−	0.957512i	$-0.593121\pi$
$397$	−11.4924	−0.576789	−0.288394	+	0.957512i	$0.593121\pi$
$398$	−20.5580	−1.03048
$399$	−2.42906	−0.121605
$400$	23.0129	1.15065
$401$	−9.25173	−0.462009	−0.231005	−	0.972953i	$-0.574201\pi$
$401$	−9.25173	−0.462009	−0.231005	+	0.972953i	$0.574201\pi$
$402$	−0.497370	−0.0248066
$403$	−4.00156	−0.199332
$404$	−30.6407	−1.52443
$405$	25.9543	1.28968
$406$	126.744	6.29021
$407$	56.9888	2.82483
$408$	0.462434	0.0228939
$409$	4.38107	0.216630	0.108315	−	0.994117i	$-0.465454\pi$
$409$	4.38107	0.216630	0.108315	+	0.994117i	$0.465454\pi$
$410$	−15.7123	−0.775974
$411$	−0.890876	−0.0439437
$412$	23.2131	1.14363
$413$	33.4953	1.64820
$414$	7.60521	0.373776
$415$	12.6292	0.619945
$416$	10.6986	0.524542
$417$	0.416683	0.0204050
$418$	130.327	6.37452
$419$	31.4882	1.53830	0.769148	−	0.639070i	$-0.220681\pi$
$419$	31.4882	1.53830	0.769148	+	0.639070i	$0.220681\pi$
$420$	−3.70231	−0.180654
$421$	−15.2705	−0.744239	−0.372120	−	0.928185i	$-0.621369\pi$
$421$	−15.2705	−0.744239	−0.372120	+	0.928185i	$0.621369\pi$
$422$	14.4063	0.701285
$423$	−0.907552	−0.0441267
$424$	−43.8290	−2.12853
$425$	−4.52194	−0.219346
$426$	0.246471	0.0119416
$427$	0.0602570	0.00291604
$428$	−28.3656	−1.37110
$429$	0.731915	0.0353372
$430$	−61.0723	−2.94517
$431$	4.89455	0.235762	0.117881	−	0.993028i	$-0.462390\pi$
$431$	4.89455	0.235762	0.117881	+	0.993028i	$0.462390\pi$
$432$	−2.27940	−0.109668
$433$	9.49230	0.456171	0.228085	−	0.973641i	$-0.426753\pi$
$433$	9.49230	0.456171	0.228085	+	0.973641i	$0.426753\pi$
$434$	24.3752	1.17005
$435$	1.55104	0.0743667
$436$	−49.2513	−2.35871
$437$	8.42651	0.403094
$438$	1.94429	0.0929016
$439$	−10.5377	−0.502938	−0.251469	−	0.967865i	$-0.580914\pi$
$439$	−10.5377	−0.502938	−0.251469	+	0.967865i	$0.580914\pi$
$440$	109.161	5.20403
$441$	−59.4935	−2.83302
$442$	−7.35503	−0.349843
$443$	−33.2575	−1.58011	−0.790057	−	0.613034i	$-0.789949\pi$
$443$	−33.2575	−1.58011	−0.790057	+	0.613034i	$0.789949\pi$
$444$	−2.30948	−0.109603
$445$	19.0335	0.902273
$446$	−32.0895	−1.51948
$447$	−0.206294	−0.00975739
$448$	5.64180	0.266550
$449$	−33.9374	−1.60161	−0.800803	−	0.598928i	$-0.795594\pi$
$449$	−33.9374	−1.60161	−0.800803	+	0.598928i	$0.795594\pi$
$450$	25.6150	1.20750
$451$	−13.0448	−0.614256
$452$	4.51240	0.212245
$453$	0.324174	0.0152310
$454$	−56.8628	−2.66870
$455$	32.3596	1.51704
$456$	−2.90239	−0.135917
$457$	−30.2102	−1.41317	−0.706586	−	0.707627i	$-0.749766\pi$
$457$	−30.2102	−1.41317	−0.706586	+	0.707627i	$0.749766\pi$
$458$	35.4845	1.65808
$459$	0.447893	0.0209058
$460$	12.8435	0.598830
$461$	28.9176	1.34683	0.673413	−	0.739267i	$-0.264828\pi$
$461$	28.9176	1.34683	0.673413	+	0.739267i	$0.264828\pi$
$462$	−4.45840	−0.207424
$463$	−18.4531	−0.857587	−0.428794	−	0.903402i	$-0.641061\pi$
$463$	−18.4531	−0.857587	−0.428794	+	0.903402i	$0.641061\pi$
$464$	65.8556	3.05727
$465$	0.298293	0.0138330
$466$	−52.8115	−2.44644
$467$	−23.7252	−1.09787	−0.548936	−	0.835865i	$-0.684967\pi$
$467$	−23.7252	−1.09787	−0.548936	+	0.835865i	$0.684967\pi$
$468$	28.7242	1.32777
$469$	−18.2567	−0.843014
$470$	−2.22305	−0.102542
$471$	0.122011	0.00562195
$472$	40.0223	1.84218
$473$	−50.7041	−2.33137
$474$	−1.03867	−0.0477077
$475$	28.3812	1.30222
$476$	30.8884	1.41577
$477$	−21.2145	−0.971343
$478$	−46.0425	−2.10594
$479$	−3.28099	−0.149912	−0.0749560	−	0.997187i	$-0.523882\pi$
$479$	−3.28099	−0.149912	−0.0749560	+	0.997187i	$0.523882\pi$
$480$	−0.797518	−0.0364016
$481$	20.1857	0.920390
$482$	65.5613	2.98624
$483$	−0.288264	−0.0131165
$484$	116.080	5.27636
$485$	2.71955	0.123488
$486$	−3.80636	−0.172660
$487$	−7.70770	−0.349269	−0.174635	−	0.984633i	$-0.555874\pi$
$487$	−7.70770	−0.349269	−0.174635	+	0.984633i	$0.555874\pi$
$488$	0.0719989	0.00325923
$489$	0.568976	0.0257300
$490$	−145.730	−6.58339
$491$	−26.3132	−1.18750	−0.593748	−	0.804651i	$-0.702353\pi$
$491$	−26.3132	−1.18750	−0.593748	+	0.804651i	$0.702353\pi$
$492$	0.528643	0.0238331
$493$	−12.9403	−0.582804
$494$	46.1627	2.07696
$495$	52.8367	2.37483
$496$	12.6652	0.568686
$497$	9.04705	0.405816
$498$	−0.616323	−0.0276181
$499$	−28.6264	−1.28149	−0.640747	−	0.767752i	$-0.721375\pi$
$499$	−28.6264	−1.28149	−0.640747	+	0.767752i	$0.721375\pi$
$500$	−20.9594	−0.937335
$501$	0.978205	0.0437030
$502$	−28.3956	−1.26736
$503$	−1.61194	−0.0718727	−0.0359364	−	0.999354i	$-0.511441\pi$
$503$	−1.61194	−0.0718727	−0.0359364	+	0.999354i	$0.511441\pi$
$504$	−96.1527	−4.28298
$505$	−19.9638	−0.888375
$506$	15.4664	0.687564
$507$	−0.463936	−0.0206041
$508$	−21.0243	−0.932802
$509$	−10.0500	−0.445459	−0.222729	−	0.974880i	$-0.571497\pi$
$509$	−10.0500	−0.445459	−0.222729	+	0.974880i	$0.571497\pi$
$510$	0.548275	0.0242780
$511$	71.3678	3.15712
$512$	50.7481	2.24277
$513$	−2.81113	−0.124114
$514$	6.06521	0.267525
$515$	15.1244	0.666459
$516$	2.05479	0.0904571
$517$	−1.84565	−0.0811714
$518$	−122.960	−5.40254
$519$	−1.13640	−0.0498824
$520$	38.6653	1.69558
$521$	14.2721	0.625270	0.312635	−	0.949873i	$-0.398788\pi$
$521$	14.2721	0.625270	0.312635	+	0.949873i	$0.398788\pi$
$522$	73.3020	3.20834
$523$	5.93085	0.259338	0.129669	−	0.991557i	$-0.458609\pi$
$523$	5.93085	0.259338	0.129669	+	0.991557i	$0.458609\pi$
$524$	71.2020	3.11048
$525$	−0.970899	−0.0423735
$526$	−41.2411	−1.79820
$527$	−2.48866	−0.108408
$528$	−2.31656	−0.100815
$529$	1.00000	0.0434783
$530$	−51.9649	−2.25721
$531$	19.3719	0.840669
$532$	−193.866	−8.40517
$533$	−4.62054	−0.200138
$534$	−0.928856	−0.0401955
$535$	−18.4815	−0.799023
$536$	−21.8142	−0.942229
$537$	−1.39726	−0.0602961
$538$	38.4777	1.65889
$539$	−120.989	−5.21137
$540$	−4.28465	−0.184382
$541$	−37.9043	−1.62963	−0.814816	−	0.579720i	$-0.803162\pi$
$541$	−37.9043	−1.62963	−0.814816	+	0.579720i	$0.803162\pi$
$542$	6.70833	0.288147
$543$	0.723958	0.0310680
$544$	6.65371	0.285275
$545$	−32.0894	−1.37456
$546$	−1.57919	−0.0675830
$547$	−7.24687	−0.309854	−0.154927	−	0.987926i	$-0.549514\pi$
$547$	−7.24687	−0.309854	−0.154927	+	0.987926i	$0.549514\pi$
$548$	−71.1019	−3.03732
$549$	0.0348494	0.00148734
$550$	52.0920	2.22121
$551$	81.2179	3.46000
$552$	−0.344436	−0.0146602
$553$	−38.1259	−1.62128
$554$	9.07718	0.385652
$555$	−1.50473	−0.0638722
$556$	33.2560	1.41037
$557$	−8.02792	−0.340154	−0.170077	−	0.985431i	$-0.554402\pi$
$557$	−8.02792	−0.340154	−0.170077	+	0.985431i	$0.554402\pi$
$558$	14.0973	0.596786
$559$	−17.9596	−0.759612
$560$	−102.420	−4.32806
$561$	0.455194	0.0192183
$562$	−40.9423	−1.72705
$563$	−18.2523	−0.769243	−0.384622	−	0.923074i	$-0.625668\pi$
$563$	−18.2523	−0.769243	−0.384622	+	0.923074i	$0.625668\pi$
$564$	0.0747951	0.00314944
$565$	2.94003	0.123688
$566$	74.4101	3.12769
$567$	−46.4924	−1.95250
$568$	10.8100	0.453577
$569$	36.0591	1.51167	0.755837	−	0.654760i	$-0.227230\pi$
$569$	36.0591	1.51167	0.755837	+	0.654760i	$0.227230\pi$
$570$	−3.44116	−0.144134
$571$	43.7722	1.83181	0.915904	−	0.401397i	$-0.131475\pi$
$571$	43.7722	1.83181	0.915904	+	0.401397i	$0.131475\pi$
$572$	58.4150	2.44245
$573$	−0.338261	−0.0141311
$574$	28.1457	1.17478
$575$	3.36809	0.140459
$576$	3.26291	0.135955
$577$	−4.61544	−0.192143	−0.0960716	−	0.995374i	$-0.530628\pi$
$577$	−4.61544	−0.192143	−0.0960716	+	0.995374i	$0.530628\pi$
$578$	38.5664	1.60415
$579$	−1.29475	−0.0538078
$580$	123.790	5.14011
$581$	−22.6230	−0.938559
$582$	−0.132717	−0.00550131
$583$	−43.1428	−1.78679
$584$	85.2746	3.52869
$585$	18.7151	0.773772
$586$	65.9280	2.72346
$587$	13.4105	0.553511	0.276755	−	0.960940i	$-0.410741\pi$
$587$	13.4105	0.553511	0.276755	+	0.960940i	$0.410741\pi$
$588$	4.90310	0.202201
$589$	15.6197	0.643598
$590$	47.4516	1.95355
$591$	−0.996077	−0.0409732
$592$	−63.8893	−2.62583
$593$	25.5983	1.05120	0.525599	−	0.850732i	$-0.323841\pi$
$593$	25.5983	1.05120	0.525599	+	0.850732i	$0.323841\pi$
$594$	−5.15966	−0.211703
$595$	20.1252	0.825052
$596$	−16.4646	−0.674416
$597$	0.450659	0.0184443
$598$	5.47827	0.224023
$599$	−12.1275	−0.495516	−0.247758	−	0.968822i	$-0.579694\pi$
$599$	−12.1275	−0.495516	−0.247758	+	0.968822i	$0.579694\pi$
$600$	−1.16009	−0.0473605
$601$	21.5884	0.880609	0.440304	−	0.897849i	$-0.354871\pi$
$601$	21.5884	0.880609	0.440304	+	0.897849i	$0.354871\pi$
$602$	109.400	4.45880
$603$	−10.5587	−0.429982
$604$	25.8727	1.05275
$605$	75.6312	3.07484
$606$	0.974256	0.0395764
$607$	12.3642	0.501846	0.250923	−	0.968007i	$-0.419266\pi$
$607$	12.3642	0.501846	0.250923	+	0.968007i	$0.419266\pi$
$608$	−41.7609	−1.69363
$609$	−2.77840	−0.112587
$610$	0.0853638	0.00345628
$611$	−0.653738	−0.0264474
$612$	17.8642	0.722118
$613$	−22.1323	−0.893914	−0.446957	−	0.894555i	$-0.647492\pi$
$613$	−22.1323	−0.893914	−0.446957	+	0.894555i	$0.647492\pi$
$614$	−42.0676	−1.69771
$615$	0.344434	0.0138889
$616$	−195.541	−7.87858
$617$	24.0671	0.968903	0.484452	−	0.874818i	$-0.339019\pi$
$617$	24.0671	0.968903	0.484452	+	0.874818i	$0.339019\pi$
$618$	−0.738088	−0.0296902
$619$	−42.1103	−1.69255	−0.846277	−	0.532743i	$-0.821161\pi$
$619$	−42.1103	−1.69255	−0.846277	+	0.532743i	$0.821161\pi$
$620$	23.8071	0.956117
$621$	−0.333605	−0.0133871
$622$	12.6585	0.507558
$623$	−34.0950	−1.36599
$624$	−0.820538	−0.0328478
$625$	−30.4964	−1.21986
$626$	61.4069	2.45431
$627$	−2.85695	−0.114096
$628$	9.73781	0.388581
$629$	12.5540	0.500559
$630$	−114.001	−4.54192
$631$	−21.5727	−0.858796	−0.429398	−	0.903115i	$-0.641274\pi$
$631$	−21.5727	−0.858796	−0.429398	+	0.903115i	$0.641274\pi$
$632$	−45.5551	−1.81209
$633$	−0.315804	−0.0125521
$634$	−47.2019	−1.87463
$635$	−13.6983	−0.543599
$636$	1.74837	0.0693274
$637$	−42.8550	−1.69798
$638$	149.071	5.90177
$639$	5.23233	0.206988
$640$	36.6650	1.44931
$641$	46.2252	1.82579	0.912893	−	0.408198i	$-0.133843\pi$
$641$	46.2252	1.82579	0.912893	+	0.408198i	$0.133843\pi$
$642$	0.901918	0.0355958
$643$	−35.7105	−1.40829	−0.704143	−	0.710058i	$-0.748669\pi$
$643$	−35.7105	−1.40829	−0.704143	+	0.710058i	$0.748669\pi$
$644$	−23.0067	−0.906592
$645$	1.33879	0.0527147
$646$	28.7096	1.12956
$647$	25.3087	0.994988	0.497494	−	0.867467i	$-0.334254\pi$
$647$	25.3087	0.994988	0.497494	+	0.867467i	$0.334254\pi$
$648$	−55.5520	−2.18229
$649$	39.3957	1.54642
$650$	18.4513	0.723719
$651$	−0.534337	−0.0209423
$652$	45.4107	1.77842
$653$	−33.8740	−1.32559	−0.662797	−	0.748799i	$-0.730631\pi$
$653$	−33.8740	−1.32559	−0.662797	+	0.748799i	$0.730631\pi$
$654$	1.56600	0.0612354
$655$	46.3913	1.81266
$656$	14.6243	0.570984
$657$	41.2753	1.61030
$658$	3.98219	0.155242
$659$	18.0234	0.702092	0.351046	−	0.936358i	$-0.385826\pi$
$659$	18.0234	0.702092	0.351046	+	0.936358i	$0.385826\pi$
$660$	−4.35449	−0.169498
$661$	−4.48741	−0.174540	−0.0872699	−	0.996185i	$-0.527814\pi$
$661$	−4.48741	−0.174540	−0.0872699	+	0.996185i	$0.527814\pi$
$662$	−80.9574	−3.14650
$663$	0.161232	0.00626174
$664$	−27.0313	−1.04902
$665$	−126.312	−4.89819
$666$	−71.1133	−2.75558
$667$	9.63839	0.373200
$668$	78.0717	3.02068
$669$	0.703445	0.0271968
$670$	−25.8635	−0.999194
$671$	0.0708716	0.00273597
$672$	1.42861	0.0551097
$673$	−8.43724	−0.325232	−0.162616	−	0.986689i	$-0.551993\pi$
$673$	−8.43724	−0.325232	−0.162616	+	0.986689i	$0.551993\pi$
$674$	−67.5419	−2.60162
$675$	−1.12361	−0.0432478
$676$	−37.0273	−1.42413
$677$	24.8750	0.956024	0.478012	−	0.878353i	$-0.341357\pi$
$677$	24.8750	0.956024	0.478012	+	0.878353i	$0.341357\pi$
$678$	−0.143477	−0.00551020
$679$	−4.87157	−0.186954
$680$	24.0468	0.922153
$681$	1.24651	0.0477663
$682$	28.6690	1.09779
$683$	21.5381	0.824133	0.412067	−	0.911154i	$-0.364807\pi$
$683$	21.5381	0.824133	0.412067	+	0.911154i	$0.364807\pi$
$684$	−112.122	−4.28708
$685$	−46.3260	−1.77003
$686$	168.998	6.45238
$687$	−0.777869	−0.0296775
$688$	56.8435	2.16714
$689$	−15.2814	−0.582176
$690$	−0.408373	−0.0155465
$691$	−9.42634	−0.358595	−0.179297	−	0.983795i	$-0.557382\pi$
$691$	−9.42634	−0.358595	−0.179297	+	0.983795i	$0.557382\pi$
$692$	−90.6975	−3.44780
$693$	−94.6473	−3.59535
$694$	−4.93906	−0.187484
$695$	21.6677	0.821903
$696$	−3.31981	−0.125837
$697$	−2.87362	−0.108846
$698$	−2.53769	−0.0960529
$699$	1.15770	0.0437882
$700$	−77.4886	−2.92879
$701$	39.5630	1.49428	0.747138	−	0.664669i	$-0.231427\pi$
$701$	39.5630	1.49428	0.747138	+	0.664669i	$0.231427\pi$
$702$	−1.82758	−0.0689775
$703$	−78.7929	−2.97173
$704$	6.63563	0.250090
$705$	0.0487323	0.00183537
$706$	10.9526	0.412207
$707$	35.7614	1.34495
$708$	−1.59652	−0.0600008
$709$	−32.0129	−1.20227	−0.601136	−	0.799147i	$-0.705285\pi$
$709$	−32.0129	−1.20227	−0.601136	+	0.799147i	$0.705285\pi$
$710$	12.8166	0.480999
$711$	−22.0499	−0.826937
$712$	−40.7388	−1.52675
$713$	1.85364	0.0694193
$714$	−0.982133	−0.0367554
$715$	38.0599	1.42336
$716$	−111.517	−4.16758
$717$	1.00931	0.0376935
$718$	−38.4202	−1.43383
$719$	4.91504	0.183300	0.0916501	−	0.995791i	$-0.470786\pi$
$719$	4.91504	0.183300	0.0916501	+	0.995791i	$0.470786\pi$
$720$	−59.2345	−2.20754
$721$	−27.0925	−1.00898
$722$	−131.975	−4.91160
$723$	−1.43719	−0.0534498
$724$	57.7799	2.14737
$725$	32.4629	1.20564
$726$	−3.69089	−0.136982
$727$	−32.3412	−1.19947	−0.599735	−	0.800199i	$-0.704727\pi$
$727$	−32.3412	−1.19947	−0.599735	+	0.800199i	$0.704727\pi$
$728$	−69.2618	−2.56701
$729$	−26.8330	−0.993816
$730$	101.104	3.74202
$731$	−11.1695	−0.413119
$732$	−0.00287208	−0.000106155 0
$733$	−3.94804	−0.145824	−0.0729121	−	0.997338i	$-0.523229\pi$
$733$	−3.94804	−0.145824	−0.0729121	+	0.997338i	$0.523229\pi$
$734$	57.8477	2.13520
$735$	3.19459	0.117834
$736$	−4.95590	−0.182677
$737$	−21.4727	−0.790955
$738$	16.2779	0.599199
$739$	−34.1166	−1.25500	−0.627500	−	0.778616i	$-0.715922\pi$
$739$	−34.1166	−1.25500	−0.627500	+	0.778616i	$0.715922\pi$
$740$	−120.094	−4.41475
$741$	−1.01195	−0.0371748
$742$	93.0856	3.41728
$743$	34.8045	1.27685	0.638426	−	0.769683i	$-0.279586\pi$
$743$	34.8045	1.27685	0.638426	+	0.769683i	$0.279586\pi$
$744$	−0.638460	−0.0234071
$745$	−10.7274	−0.393022
$746$	−23.4574	−0.858836
$747$	−13.0839	−0.478715
$748$	36.3296	1.32834
$749$	33.1061	1.20967
$750$	0.666429	0.0243346
$751$	−43.5045	−1.58750	−0.793752	−	0.608242i	$-0.791875\pi$
$751$	−43.5045	−1.58750	−0.793752	+	0.608242i	$0.791875\pi$
$752$	2.06913	0.0754533
$753$	0.622471	0.0226841
$754$	52.8017	1.92292
$755$	16.8572	0.613498
$756$	7.67516	0.279143
$757$	11.3020	0.410778	0.205389	−	0.978680i	$-0.434154\pi$
$757$	11.3020	0.410778	0.205389	+	0.978680i	$0.434154\pi$
$758$	22.2867	0.809489
$759$	−0.339043	−0.0123065
$760$	−150.926	−5.47466
$761$	1.35297	0.0490451	0.0245225	−	0.999699i	$-0.492193\pi$
$761$	1.35297	0.0490451	0.0245225	+	0.999699i	$0.492193\pi$
$762$	0.668492	0.0242169
$763$	57.4822	2.08100
$764$	−26.9970	−0.976719
$765$	11.6393	0.420820
$766$	42.0920	1.52084
$767$	13.9542	0.503856
$768$	−1.66816	−0.0601946
$769$	−4.70106	−0.169524	−0.0847622	−	0.996401i	$-0.527013\pi$
$769$	−4.70106	−0.169524	−0.0847622	+	0.996401i	$0.527013\pi$
$770$	−231.839	−8.35490
$771$	−0.132958	−0.00478835
$772$	−103.335	−3.71912
$773$	29.2832	1.05324	0.526622	−	0.850100i	$-0.323458\pi$
$773$	29.2832	1.05324	0.526622	+	0.850100i	$0.323458\pi$
$774$	63.2709	2.27423
$775$	6.24321	0.224263
$776$	−5.82086	−0.208957
$777$	2.69544	0.0966985
$778$	58.7042	2.10465
$779$	18.0358	0.646200
$780$	−1.54239	−0.0552262
$781$	10.6407	0.380756
$782$	3.40706	0.121836
$783$	−3.21541	−0.114910
$784$	135.639	4.84425
$785$	6.34461	0.226449
$786$	−2.26395	−0.0807524
$787$	0.167260	0.00596218	0.00298109	−	0.999996i	$-0.499051\pi$
$787$	0.167260	0.00596218	0.00298109	+	0.999996i	$0.499051\pi$
$788$	−79.4981	−2.83200
$789$	0.904061	0.0321854
$790$	−54.0114	−1.92164
$791$	−5.26652	−0.187256
$792$	−113.090	−4.01850
$793$	0.0251031	0.000891437 0
$794$	29.1642	1.03500
$795$	1.13914	0.0404012
$796$	35.9676	1.27484
$797$	16.8762	0.597785	0.298892	−	0.954287i	$-0.403383\pi$
$797$	16.8762	0.597785	0.298892	+	0.954287i	$0.403383\pi$
$798$	6.16420	0.218210
$799$	−0.406574	−0.0143836
$800$	−16.6919	−0.590147
$801$	−19.7187	−0.696725
$802$	23.4780	0.829037
$803$	83.9396	2.96216
$804$	0.870183	0.0306890
$805$	−14.9899	−0.528324
$806$	10.1547	0.357685
$807$	−0.843482	−0.0296920
$808$	42.7299	1.50323
$809$	12.2916	0.432150	0.216075	−	0.976377i	$-0.430675\pi$
$809$	12.2916	0.432150	0.216075	+	0.976377i	$0.430675\pi$
$810$	−65.8640	−2.31423
$811$	−7.45954	−0.261940	−0.130970	−	0.991386i	$-0.541809\pi$
$811$	−7.45954	−0.261940	−0.130970	+	0.991386i	$0.541809\pi$
$812$	−221.748	−7.78182
$813$	−0.147056	−0.00515747
$814$	−144.620	−5.06892
$815$	29.5871	1.03639
$816$	−0.510311	−0.0178645
$817$	70.1036	2.45261
$818$	−11.1178	−0.388724
$819$	−33.5246	−1.17144
$820$	27.4897	0.959982
$821$	11.7737	0.410904	0.205452	−	0.978667i	$-0.434134\pi$
$821$	11.7737	0.410904	0.205452	+	0.978667i	$0.434134\pi$
$822$	2.26077	0.0788533
$823$	−7.34358	−0.255981	−0.127991	−	0.991775i	$-0.540853\pi$
$823$	−7.34358	−0.255981	−0.127991	+	0.991775i	$0.540853\pi$
$824$	−32.3718	−1.12773
$825$	−1.14193	−0.0397568
$826$	−85.0007	−2.95755
$827$	−5.15809	−0.179364	−0.0896821	−	0.995970i	$-0.528585\pi$
$827$	−5.15809	−0.179364	−0.0896821	+	0.995970i	$0.528585\pi$
$828$	−13.3058	−0.462410
$829$	41.2506	1.43269	0.716346	−	0.697745i	$-0.245813\pi$
$829$	41.2506	1.43269	0.716346	+	0.697745i	$0.245813\pi$
$830$	−32.0491	−1.11244
$831$	−0.198984	−0.00690268
$832$	2.35038	0.0814846
$833$	−26.6525	−0.923454
$834$	−1.05741	−0.0366152
$835$	50.8671	1.76033
$836$	−228.017	−7.88612
$837$	−0.618383	−0.0213744
$838$	−79.9071	−2.76035
$839$	−49.1900	−1.69823	−0.849113	−	0.528211i	$-0.822863\pi$
$839$	−49.1900	−1.69823	−0.849113	+	0.528211i	$0.822863\pi$
$840$	5.16306	0.178142
$841$	63.8985	2.20340
$842$	38.7518	1.33548
$843$	0.897511	0.0309119
$844$	−25.2047	−0.867583
$845$	−24.1249	−0.829922
$846$	2.30308	0.0791817
$847$	−135.479	−4.65513
$848$	48.3668	1.66092
$849$	−1.63117	−0.0559816
$850$	11.4753	0.393598
$851$	−9.35060	−0.320534
$852$	−0.431218	−0.0147733
$853$	24.5070	0.839105	0.419552	−	0.907731i	$-0.362187\pi$
$853$	24.5070	0.839105	0.419552	+	0.907731i	$0.362187\pi$
$854$	−0.152914	−0.00523259
$855$	−73.0523	−2.49833
$856$	39.5573	1.35204
$857$	7.91532	0.270382	0.135191	−	0.990820i	$-0.456835\pi$
$857$	7.91532	0.270382	0.135191	+	0.990820i	$0.456835\pi$
$858$	−1.85737	−0.0634096
$859$	−7.75012	−0.264431	−0.132215	−	0.991221i	$-0.542209\pi$
$859$	−7.75012	−0.264431	−0.132215	+	0.991221i	$0.542209\pi$
$860$	106.850	3.64356
$861$	−0.616991	−0.0210270
$862$	−12.4208	−0.423055
$863$	40.3212	1.37255	0.686274	−	0.727343i	$-0.259245\pi$
$863$	40.3212	1.37255	0.686274	+	0.727343i	$0.259245\pi$
$864$	1.65331	0.0562468
$865$	−59.0934	−2.00924
$866$	−24.0885	−0.818560
$867$	−0.845428	−0.0287122
$868$	−42.6461	−1.44750
$869$	−44.8419	−1.52116
$870$	−3.93605	−0.133445
$871$	−7.60573	−0.257710
$872$	68.6833	2.32591
$873$	−2.81745	−0.0953564
$874$	−21.3838	−0.723319
$875$	24.4622	0.826974
$876$	−3.40166	−0.114932
$877$	−4.49438	−0.151765	−0.0758823	−	0.997117i	$-0.524177\pi$
$877$	−4.49438	−0.151765	−0.0758823	+	0.997117i	$0.524177\pi$
$878$	26.7415	0.902481
$879$	−1.44523	−0.0487464
$880$	−120.462	−4.06079
$881$	−40.0005	−1.34765	−0.673825	−	0.738891i	$-0.735350\pi$
$881$	−40.0005	−1.34765	−0.673825	+	0.738891i	$0.735350\pi$
$882$	150.976	5.08362
$883$	−53.8400	−1.81186	−0.905931	−	0.423426i	$-0.860827\pi$
$883$	−53.8400	−1.81186	−0.905931	+	0.423426i	$0.860827\pi$
$884$	12.8681	0.432802
$885$	−1.04020	−0.0349660
$886$	84.3973	2.83538
$887$	−22.8110	−0.765918	−0.382959	−	0.923765i	$-0.625095\pi$
$887$	−22.8110	−0.765918	−0.382959	+	0.923765i	$0.625095\pi$
$888$	3.22068	0.108079
$889$	24.5379	0.822975
$890$	−48.3010	−1.61905
$891$	−54.6823	−1.83193
$892$	56.1428	1.87980
$893$	2.55180	0.0853927
$894$	0.523511	0.0175088
$895$	−72.6581	−2.42869
$896$	−65.6786	−2.19417
$897$	−0.120091	−0.00400972
$898$	86.1226	2.87395
$899$	17.8661	0.595867
$900$	−44.8152	−1.49384
$901$	−9.50387	−0.316620
$902$	33.1037	1.10223
$903$	−2.39819	−0.0798068
$904$	−6.29276	−0.209294
$905$	37.6462	1.25140
$906$	−0.822653	−0.0273308
$907$	−6.02234	−0.199969	−0.0999843	−	0.994989i	$-0.531879\pi$
$907$	−6.02234	−0.199969	−0.0999843	+	0.994989i	$0.531879\pi$
$908$	99.4853	3.30154
$909$	20.6825	0.685994
$910$	−82.1186	−2.72221
$911$	−0.855891	−0.0283569	−0.0141785	−	0.999899i	$-0.504513\pi$
$911$	−0.855891	−0.0283569	−0.0141785	+	0.999899i	$0.504513\pi$
$912$	3.20289	0.106058
$913$	−26.6081	−0.880601
$914$	76.6640	2.53582
$915$	−0.00187129	−6.18629e−5 0
$916$	−62.0826	−2.05127
$917$	−83.1014	−2.74425
$918$	−1.13661	−0.0375138
$919$	−38.8088	−1.28018	−0.640092	−	0.768298i	$-0.721104\pi$
$919$	−38.8088	−1.28018	−0.640092	+	0.768298i	$0.721104\pi$
$920$	−17.9109	−0.590503
$921$	0.922179	0.0303868
$922$	−73.3838	−2.41677
$923$	3.76901	0.124058
$924$	7.80028	0.256610
$925$	−31.4936	−1.03550
$926$	46.8282	1.53887
$927$	−15.6689	−0.514633
$928$	−47.7668	−1.56802
$929$	0.729164	0.0239231	0.0119615	−	0.999928i	$-0.496192\pi$
$929$	0.729164	0.0239231	0.0119615	+	0.999928i	$0.496192\pi$
$930$	−0.756975	−0.0248222
$931$	167.280	5.48238
$932$	92.3973	3.02657
$933$	−0.277491	−0.00908464
$934$	60.2072	1.97004
$935$	23.6703	0.774103
$936$	−40.0573	−1.30931
$937$	−11.6748	−0.381398	−0.190699	−	0.981649i	$-0.561075\pi$
$937$	−11.6748	−0.381398	−0.190699	+	0.981649i	$0.561075\pi$
$938$	46.3297	1.51272
$939$	−1.34612	−0.0439290
$940$	3.88939	0.126858
$941$	54.2165	1.76741	0.883703	−	0.468048i	$-0.155042\pi$
$941$	54.2165	1.76741	0.883703	+	0.468048i	$0.155042\pi$
$942$	−0.309625	−0.0100881
$943$	2.14036	0.0696999
$944$	−44.1659	−1.43748
$945$	5.00070	0.162673
$946$	128.671	4.18346
$947$	13.9478	0.453242	0.226621	−	0.973983i	$-0.427232\pi$
$947$	13.9478	0.453242	0.226621	+	0.973983i	$0.427232\pi$
$948$	1.81723	0.0590208
$949$	29.7318	0.965136
$950$	−72.0226	−2.33672
$951$	1.03473	0.0335534
$952$	−43.0755	−1.39608
$953$	−28.4471	−0.921492	−0.460746	−	0.887532i	$-0.652418\pi$
$953$	−28.4471	−0.921492	−0.460746	+	0.887532i	$0.652418\pi$
$954$	53.8357	1.74299
$955$	−17.5898	−0.569191
$956$	80.5546	2.60532
$957$	−3.26783	−0.105634
$958$	8.32612	0.269005
$959$	82.9846	2.67971
$960$	−0.175207	−0.00565477
$961$	−27.5640	−0.889162
$962$	−51.2251	−1.65156
$963$	19.1468	0.616997
$964$	−114.704	−3.69437
$965$	−67.3275	−2.16735
$966$	0.731525	0.0235364
$967$	7.54669	0.242685	0.121343	−	0.992611i	$-0.461280\pi$
$967$	7.54669	0.242685	0.121343	+	0.992611i	$0.461280\pi$
$968$	−161.879	−5.20299
$969$	−0.629353	−0.0202177
$970$	−6.90137	−0.221589
$971$	20.4416	0.656003	0.328001	−	0.944677i	$-0.393625\pi$
$971$	20.4416	0.656003	0.328001	+	0.944677i	$0.393625\pi$
$972$	6.65949	0.213603
$973$	−38.8137	−1.24431
$974$	19.5597	0.626734
$975$	−0.404477	−0.0129536
$976$	−0.0794531	−0.00254323
$977$	−46.4089	−1.48475	−0.742376	−	0.669983i	$-0.766301\pi$
$977$	−46.4089	−1.48475	−0.742376	+	0.669983i	$0.766301\pi$
$978$	−1.44388	−0.0461703
$979$	−40.1010	−1.28163
$980$	254.964	8.14452
$981$	33.2446	1.06142
$982$	66.7746	2.13086
$983$	13.6971	0.436869	0.218435	−	0.975852i	$-0.429905\pi$
$983$	13.6971	0.436869	0.218435	+	0.975852i	$0.429905\pi$
$984$	−0.737219	−0.0235017
$985$	−51.7965	−1.65037
$986$	32.8386	1.04579
$987$	−0.0872950	−0.00277863
$988$	−80.7648	−2.56947
$989$	8.31941	0.264542
$990$	−134.083	−4.26144
$991$	1.70337	0.0541092	0.0270546	−	0.999634i	$-0.491387\pi$
$991$	1.70337	0.0541092	0.0270546	+	0.999634i	$0.491387\pi$
$992$	−9.18643	−0.291669
$993$	1.77469	0.0563182
$994$	−22.9586	−0.728203
$995$	23.4345	0.742924
$996$	1.07830	0.0341672
$997$	6.59685	0.208924	0.104462	−	0.994529i	$-0.466688\pi$
$997$	6.59685	0.208924	0.104462	+	0.994529i	$0.466688\pi$
$998$	72.6449	2.29953
$999$	3.11941	0.0986937

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8027.2.a.c.1.12	✓	143

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8027.2.a.c.1.12	✓	143	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 8027 = 23 \cdot 349 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8027.a (trivial)

\(f(q)\)	\(=\)	\(q-2.53769 q^{2} +0.0556295 q^{3} +4.43986 q^{4} +2.89276 q^{5} -0.141170 q^{6} -5.18186 q^{7} -6.19160 q^{8} -2.99691 q^{9} +O(q^{10})\)	\(q-2.53769 q^{2} +0.0556295 q^{3} +4.43986 q^{4} +2.89276 q^{5} -0.141170 q^{6} -5.18186 q^{7} -6.19160 q^{8} -2.99691 q^{9} -7.34093 q^{10} -6.09467 q^{11} +0.246987 q^{12} -2.15876 q^{13} +13.1499 q^{14} +0.160923 q^{15} +6.83264 q^{16} -1.34258 q^{17} +7.60521 q^{18} +8.42651 q^{19} +12.8435 q^{20} -0.288264 q^{21} +15.4664 q^{22} +1.00000 q^{23} -0.344436 q^{24} +3.36809 q^{25} +5.47827 q^{26} -0.333605 q^{27} -23.0067 q^{28} +9.63839 q^{29} -0.408373 q^{30} +1.85364 q^{31} -4.95590 q^{32} -0.339043 q^{33} +3.40706 q^{34} -14.9899 q^{35} -13.3058 q^{36} -9.35060 q^{37} -21.3838 q^{38} -0.120091 q^{39} -17.9109 q^{40} +2.14036 q^{41} +0.731525 q^{42} +8.31941 q^{43} -27.0595 q^{44} -8.66934 q^{45} -2.53769 q^{46} +0.302830 q^{47} +0.380097 q^{48} +19.8516 q^{49} -8.54715 q^{50} -0.0746873 q^{51} -9.58461 q^{52} +7.07879 q^{53} +0.846586 q^{54} -17.6304 q^{55} +32.0840 q^{56} +0.468763 q^{57} -24.4592 q^{58} -6.46397 q^{59} +0.714476 q^{60} -0.0116285 q^{61} -4.70395 q^{62} +15.5295 q^{63} -1.08876 q^{64} -6.24479 q^{65} +0.860387 q^{66} +3.52319 q^{67} -5.96088 q^{68} +0.0556295 q^{69} +38.0397 q^{70} -1.74591 q^{71} +18.5557 q^{72} -13.7726 q^{73} +23.7289 q^{74} +0.187365 q^{75} +37.4125 q^{76} +31.5817 q^{77} +0.304753 q^{78} +7.35757 q^{79} +19.7652 q^{80} +8.97216 q^{81} -5.43158 q^{82} +4.36581 q^{83} -1.27985 q^{84} -3.88378 q^{85} -21.1121 q^{86} +0.536179 q^{87} +37.7358 q^{88} +6.57968 q^{89} +22.0001 q^{90} +11.1864 q^{91} +4.43986 q^{92} +0.103117 q^{93} -0.768488 q^{94} +24.3759 q^{95} -0.275694 q^{96} +0.940121 q^{97} -50.3773 q^{98} +18.2651 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 143 q - 17 q^{2} - 17 q^{3} + 121 q^{4} - 22 q^{5} - 11 q^{6} - 33 q^{7} - 45 q^{8} + 104 q^{9}+O(q^{10}) \) 143 * q - 17 * q^2 - 17 * q^3 + 121 * q^4 - 22 * q^5 - 11 * q^6 - 33 * q^7 - 45 * q^8 + 104 * q^9	\( 143 q - 17 q^{2} - 17 q^{3} + 121 q^{4} - 22 q^{5} - 11 q^{6} - 33 q^{7} - 45 q^{8} + 104 q^{9} - 22 q^{10} - 14 q^{11} - 36 q^{12} - 87 q^{13} - 18 q^{14} - 19 q^{15} + 81 q^{16} - 14 q^{17} - 60 q^{18} - 18 q^{19} - 25 q^{20} - 26 q^{21} - 62 q^{22} + 143 q^{23} - 21 q^{24} + 67 q^{25} - 5 q^{26} - 47 q^{27} - 76 q^{28} - 54 q^{29} - 22 q^{30} - 62 q^{31} - 117 q^{32} - 59 q^{33} - 35 q^{34} - 52 q^{35} + 52 q^{36} - 190 q^{37} - 19 q^{38} - 43 q^{39} - 41 q^{40} - 50 q^{41} + 8 q^{42} - 50 q^{43} - 18 q^{44} - 75 q^{45} - 17 q^{46} - 63 q^{47} - 35 q^{48} + 74 q^{49} - 53 q^{50} - 33 q^{51} - 124 q^{52} - 100 q^{53} - 46 q^{54} - 61 q^{55} - 3 q^{56} - 80 q^{57} - 112 q^{58} - 109 q^{59} - 55 q^{60} - 76 q^{61} - 6 q^{62} - 93 q^{63} + 57 q^{64} - 17 q^{65} + 50 q^{66} - 120 q^{67} + 26 q^{68} - 17 q^{69} - 109 q^{71} - 153 q^{72} - 94 q^{73} + 35 q^{74} - 105 q^{75} - 16 q^{76} - 52 q^{77} - 59 q^{78} - 29 q^{79} - 30 q^{80} + 39 q^{81} - 65 q^{82} + 8 q^{83} + 11 q^{84} - 155 q^{85} - 15 q^{86} - 25 q^{87} - 139 q^{88} + 6 q^{89} + 82 q^{90} - 34 q^{91} + 121 q^{92} - 151 q^{93} - 3 q^{94} - 70 q^{95} - 23 q^{96} - 203 q^{97} - 18 q^{98} - 49 q^{99}+O(q^{100}) \) 143 * q - 17 * q^2 - 17 * q^3 + 121 * q^4 - 22 * q^5 - 11 * q^6 - 33 * q^7 - 45 * q^8 + 104 * q^9 - 22 * q^10 - 14 * q^11 - 36 * q^12 - 87 * q^13 - 18 * q^14 - 19 * q^15 + 81 * q^16 - 14 * q^17 - 60 * q^18 - 18 * q^19 - 25 * q^20 - 26 * q^21 - 62 * q^22 + 143 * q^23 - 21 * q^24 + 67 * q^25 - 5 * q^26 - 47 * q^27 - 76 * q^28 - 54 * q^29 - 22 * q^30 - 62 * q^31 - 117 * q^32 - 59 * q^33 - 35 * q^34 - 52 * q^35 + 52 * q^36 - 190 * q^37 - 19 * q^38 - 43 * q^39 - 41 * q^40 - 50 * q^41 + 8 * q^42 - 50 * q^43 - 18 * q^44 - 75 * q^45 - 17 * q^46 - 63 * q^47 - 35 * q^48 + 74 * q^49 - 53 * q^50 - 33 * q^51 - 124 * q^52 - 100 * q^53 - 46 * q^54 - 61 * q^55 - 3 * q^56 - 80 * q^57 - 112 * q^58 - 109 * q^59 - 55 * q^60 - 76 * q^61 - 6 * q^62 - 93 * q^63 + 57 * q^64 - 17 * q^65 + 50 * q^66 - 120 * q^67 + 26 * q^68 - 17 * q^69 - 109 * q^71 - 153 * q^72 - 94 * q^73 + 35 * q^74 - 105 * q^75 - 16 * q^76 - 52 * q^77 - 59 * q^78 - 29 * q^79 - 30 * q^80 + 39 * q^81 - 65 * q^82 + 8 * q^83 + 11 * q^84 - 155 * q^85 - 15 * q^86 - 25 * q^87 - 139 * q^88 + 6 * q^89 + 82 * q^90 - 34 * q^91 + 121 * q^92 - 151 * q^93 - 3 * q^94 - 70 * q^95 - 23 * q^96 - 203 * q^97 - 18 * q^98 - 49 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more