LMFDB - Embedded newform 6023.2.a.a.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6023,2,Mod(1,6023)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6023, 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("6023.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6023 = 19 \cdot 317 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6023.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:	$48.0938971374$
Analytic rank:	$1$
Dimension:	$98$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Character	$\chi$	$=$	6023.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.36387 q^{2} -1.85446 q^{3} +3.58790 q^{4} -2.76467 q^{5} +4.38371 q^{6} +3.05083 q^{7} -3.75360 q^{8} +0.439017 q^{9} +O(q^{10})$	\(q-2.36387 q^{2} -1.85446 q^{3} +3.58790 q^{4} -2.76467 q^{5} +4.38371 q^{6} +3.05083 q^{7} -3.75360 q^{8} +0.439017 q^{9} +6.53534 q^{10} +5.93671 q^{11} -6.65362 q^{12} +0.978971 q^{13} -7.21177 q^{14} +5.12697 q^{15} +1.69724 q^{16} -0.501279 q^{17} -1.03778 q^{18} +1.00000 q^{19} -9.91937 q^{20} -5.65763 q^{21} -14.0336 q^{22} +6.14999 q^{23} +6.96090 q^{24} +2.64341 q^{25} -2.31416 q^{26} +4.74924 q^{27} +10.9461 q^{28} -1.31718 q^{29} -12.1195 q^{30} -0.656535 q^{31} +3.49514 q^{32} -11.0094 q^{33} +1.18496 q^{34} -8.43453 q^{35} +1.57515 q^{36} -5.94413 q^{37} -2.36387 q^{38} -1.81546 q^{39} +10.3775 q^{40} +10.1898 q^{41} +13.3739 q^{42} -9.76337 q^{43} +21.3003 q^{44} -1.21374 q^{45} -14.5378 q^{46} -3.27444 q^{47} -3.14746 q^{48} +2.30754 q^{49} -6.24870 q^{50} +0.929602 q^{51} +3.51245 q^{52} -1.46286 q^{53} -11.2266 q^{54} -16.4130 q^{55} -11.4516 q^{56} -1.85446 q^{57} +3.11365 q^{58} -8.28856 q^{59} +18.3951 q^{60} -0.867113 q^{61} +1.55197 q^{62} +1.33936 q^{63} -11.6566 q^{64} -2.70653 q^{65} +26.0248 q^{66} -0.673800 q^{67} -1.79854 q^{68} -11.4049 q^{69} +19.9382 q^{70} +5.36676 q^{71} -1.64790 q^{72} -12.6270 q^{73} +14.0512 q^{74} -4.90210 q^{75} +3.58790 q^{76} +18.1119 q^{77} +4.29152 q^{78} -15.1142 q^{79} -4.69231 q^{80} -10.1243 q^{81} -24.0875 q^{82} +8.42572 q^{83} -20.2990 q^{84} +1.38587 q^{85} +23.0794 q^{86} +2.44266 q^{87} -22.2840 q^{88} -6.04770 q^{89} +2.86913 q^{90} +2.98667 q^{91} +22.0656 q^{92} +1.21752 q^{93} +7.74036 q^{94} -2.76467 q^{95} -6.48160 q^{96} -7.00252 q^{97} -5.45473 q^{98} +2.60632 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 98 q - 8 q^{2} - 25 q^{3} + 82 q^{4} - 10 q^{5} - 4 q^{6} - 18 q^{7} - 18 q^{8} + 61 q^{9}+O(q^{10}) $ 98 * q - 8 * q^2 - 25 * q^3 + 82 * q^4 - 10 * q^5 - 4 * q^6 - 18 * q^7 - 18 * q^8 + 61 * q^9	\( 98 q - 8 q^{2} - 25 q^{3} + 82 q^{4} - 10 q^{5} - 4 q^{6} - 18 q^{7} - 18 q^{8} + 61 q^{9} - 24 q^{10} - 12 q^{11} - 51 q^{12} - 58 q^{13} - 15 q^{14} - 18 q^{15} + 58 q^{16} - 25 q^{17} - 40 q^{18} + 98 q^{19} - 12 q^{20} - 24 q^{21} - 59 q^{22} - 38 q^{23} - 9 q^{24} - 12 q^{25} - 3 q^{26} - 85 q^{27} - 33 q^{28} - 24 q^{29} - 22 q^{30} - 56 q^{31} - 29 q^{32} - 51 q^{33} - 38 q^{34} - 10 q^{35} + 50 q^{36} - 124 q^{37} - 8 q^{38} - 4 q^{39} - 80 q^{40} - 28 q^{41} - 37 q^{42} - 63 q^{43} - 7 q^{44} - 32 q^{45} - 47 q^{46} - 10 q^{47} - 88 q^{48} + 6 q^{49} - 17 q^{50} - 22 q^{51} - 119 q^{52} - 65 q^{53} + 24 q^{54} - 30 q^{55} - 39 q^{56} - 25 q^{57} - 91 q^{58} - 26 q^{59} - 60 q^{60} - 60 q^{61} + 6 q^{62} - 26 q^{63} + 50 q^{64} - 40 q^{65} + 57 q^{66} - 108 q^{67} - 41 q^{68} - 15 q^{69} - 36 q^{70} - 19 q^{71} - 47 q^{72} - 136 q^{73} + 22 q^{74} - 48 q^{75} + 82 q^{76} - 35 q^{77} - 56 q^{78} - 98 q^{79} - 42 q^{80} + 6 q^{81} - 37 q^{82} - 31 q^{83} - 24 q^{84} - 71 q^{85} - 24 q^{86} + 7 q^{87} - 166 q^{88} - 38 q^{89} + 26 q^{90} - 100 q^{91} - 59 q^{92} - 21 q^{93} - 48 q^{94} - 10 q^{95} - 16 q^{96} - 190 q^{97} - 80 q^{98} - 17 q^{99}+O(q^{100}) \) 98 * q - 8 * q^2 - 25 * q^3 + 82 * q^4 - 10 * q^5 - 4 * q^6 - 18 * q^7 - 18 * q^8 + 61 * q^9 - 24 * q^10 - 12 * q^11 - 51 * q^12 - 58 * q^13 - 15 * q^14 - 18 * q^15 + 58 * q^16 - 25 * q^17 - 40 * q^18 + 98 * q^19 - 12 * q^20 - 24 * q^21 - 59 * q^22 - 38 * q^23 - 9 * q^24 - 12 * q^25 - 3 * q^26 - 85 * q^27 - 33 * q^28 - 24 * q^29 - 22 * q^30 - 56 * q^31 - 29 * q^32 - 51 * q^33 - 38 * q^34 - 10 * q^35 + 50 * q^36 - 124 * q^37 - 8 * q^38 - 4 * q^39 - 80 * q^40 - 28 * q^41 - 37 * q^42 - 63 * q^43 - 7 * q^44 - 32 * q^45 - 47 * q^46 - 10 * q^47 - 88 * q^48 + 6 * q^49 - 17 * q^50 - 22 * q^51 - 119 * q^52 - 65 * q^53 + 24 * q^54 - 30 * q^55 - 39 * q^56 - 25 * q^57 - 91 * q^58 - 26 * q^59 - 60 * q^60 - 60 * q^61 + 6 * q^62 - 26 * q^63 + 50 * q^64 - 40 * q^65 + 57 * q^66 - 108 * q^67 - 41 * q^68 - 15 * q^69 - 36 * q^70 - 19 * q^71 - 47 * q^72 - 136 * q^73 + 22 * q^74 - 48 * q^75 + 82 * q^76 - 35 * q^77 - 56 * q^78 - 98 * q^79 - 42 * q^80 + 6 * q^81 - 37 * q^82 - 31 * q^83 - 24 * q^84 - 71 * q^85 - 24 * q^86 + 7 * q^87 - 166 * q^88 - 38 * q^89 + 26 * q^90 - 100 * q^91 - 59 * q^92 - 21 * q^93 - 48 * q^94 - 10 * q^95 - 16 * q^96 - 190 * q^97 - 80 * q^98 - 17 * 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 $

$2$	−2.36387	−1.67151	−0.835756	−	0.549101i	$-0.814970\pi$
$2$	−2.36387	−1.67151	−0.835756	+	0.549101i	$0.814970\pi$
$3$	−1.85446	−1.07067	−0.535336	−	0.844639i	$-0.679815\pi$
$3$	−1.85446	−1.07067	−0.535336	+	0.844639i	$0.679815\pi$
$4$	3.58790	1.79395
$5$	−2.76467	−1.23640	−0.618200	−	0.786021i	$-0.712138\pi$
$5$	−2.76467	−1.23640	−0.618200	+	0.786021i	$0.712138\pi$
$6$	4.38371	1.78964
$7$	3.05083	1.15310	0.576552	−	0.817061i	$-0.304398\pi$
$7$	3.05083	1.15310	0.576552	+	0.817061i	$0.304398\pi$
$8$	−3.75360	−1.32710
$9$	0.439017	0.146339
$10$	6.53534	2.06666
$11$	5.93671	1.78998	0.894992	−	0.446082i	$-0.147181\pi$
$11$	5.93671	1.78998	0.894992	+	0.446082i	$0.147181\pi$
$12$	−6.65362	−1.92073
$13$	0.978971	0.271518	0.135759	−	0.990742i	$-0.456653\pi$
$13$	0.978971	0.271518	0.135759	+	0.990742i	$0.456653\pi$
$14$	−7.21177	−1.92743
$15$	5.12697	1.32378
$16$	1.69724	0.424310
$17$	−0.501279	−0.121578	−0.0607890	−	0.998151i	$-0.519362\pi$
$17$	−0.501279	−0.121578	−0.0607890	+	0.998151i	$0.519362\pi$
$18$	−1.03778	−0.244607
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	−9.91937	−2.21804
$21$	−5.65763	−1.23460
$22$	−14.0336	−2.99198
$23$	6.14999	1.28236	0.641181	−	0.767390i	$-0.278445\pi$
$23$	6.14999	1.28236	0.641181	+	0.767390i	$0.278445\pi$
$24$	6.96090	1.42089
$25$	2.64341	0.528683
$26$	−2.31416	−0.453845
$27$	4.74924	0.913991
$28$	10.9461	2.06861
$29$	−1.31718	−0.244594	−0.122297	−	0.992494i	$-0.539026\pi$
$29$	−1.31718	−0.244594	−0.122297	+	0.992494i	$0.539026\pi$
$30$	−12.1195	−2.21271
$31$	−0.656535	−0.117917	−0.0589586	−	0.998260i	$-0.518778\pi$
$31$	−0.656535	−0.117917	−0.0589586	+	0.998260i	$0.518778\pi$
$32$	3.49514	0.617860
$33$	−11.0094	−1.91649
$34$	1.18496	0.203219
$35$	−8.43453	−1.42570
$36$	1.57515	0.262525
$37$	−5.94413	−0.977209	−0.488604	−	0.872505i	$-0.662494\pi$
$37$	−5.94413	−0.977209	−0.488604	+	0.872505i	$0.662494\pi$
$38$	−2.36387	−0.383471
$39$	−1.81546	−0.290706
$40$	10.3775	1.64082
$41$	10.1898	1.59138	0.795692	−	0.605701i	$-0.207107\pi$
$41$	10.1898	1.59138	0.795692	+	0.605701i	$0.207107\pi$
$42$	13.3739	2.06364
$43$	−9.76337	−1.48890	−0.744450	−	0.667678i	$-0.767288\pi$
$43$	−9.76337	−1.48890	−0.744450	+	0.667678i	$0.767288\pi$
$44$	21.3003	3.21114
$45$	−1.21374	−0.180933
$46$	−14.5378	−2.14348
$47$	−3.27444	−0.477626	−0.238813	−	0.971066i	$-0.576758\pi$
$47$	−3.27444	−0.477626	−0.238813	+	0.971066i	$0.576758\pi$
$48$	−3.14746	−0.454297
$49$	2.30754	0.329648
$50$	−6.24870	−0.883699
$51$	0.929602	0.130170
$52$	3.51245	0.487090
$53$	−1.46286	−0.200940	−0.100470	−	0.994940i	$-0.532035\pi$
$53$	−1.46286	−0.200940	−0.100470	+	0.994940i	$0.532035\pi$
$54$	−11.2266	−1.52775
$55$	−16.4130	−2.21313
$56$	−11.4516	−1.53028
$57$	−1.85446	−0.245629
$58$	3.11365	0.408842
$59$	−8.28856	−1.07908	−0.539540	−	0.841960i	$-0.681402\pi$
$59$	−8.28856	−1.07908	−0.539540	+	0.841960i	$0.681402\pi$
$60$	18.3951	2.37479
$61$	−0.867113	−0.111023	−0.0555113	−	0.998458i	$-0.517679\pi$
$61$	−0.867113	−0.111023	−0.0555113	+	0.998458i	$0.517679\pi$
$62$	1.55197	0.197100
$63$	1.33936	0.168744
$64$	−11.6566	−1.45707
$65$	−2.70653	−0.335704
$66$	26.0248	3.20343
$67$	−0.673800	−0.0823178	−0.0411589	−	0.999153i	$-0.513105\pi$
$67$	−0.673800	−0.0823178	−0.0411589	+	0.999153i	$0.513105\pi$
$68$	−1.79854	−0.218105
$69$	−11.4049	−1.37299
$70$	19.9382	2.38307
$71$	5.36676	0.636918	0.318459	−	0.947937i	$-0.396835\pi$
$71$	5.36676	0.636918	0.318459	+	0.947937i	$0.396835\pi$
$72$	−1.64790	−0.194206
$73$	−12.6270	−1.47788	−0.738941	−	0.673771i	$-0.764674\pi$
$73$	−12.6270	−1.47788	−0.738941	+	0.673771i	$0.764674\pi$
$74$	14.0512	1.63342
$75$	−4.90210	−0.566046
$76$	3.58790	0.411561
$77$	18.1119	2.06404
$78$	4.29152	0.485919
$79$	−15.1142	−1.70048	−0.850240	−	0.526395i	$-0.823544\pi$
$79$	−15.1142	−1.70048	−0.850240	+	0.526395i	$0.823544\pi$
$80$	−4.69231	−0.524616
$81$	−10.1243	−1.12492
$82$	−24.0875	−2.66002
$83$	8.42572	0.924843	0.462422	−	0.886660i	$-0.346981\pi$
$83$	8.42572	0.924843	0.462422	+	0.886660i	$0.346981\pi$
$84$	−20.2990	−2.21481
$85$	1.38587	0.150319
$86$	23.0794	2.48871
$87$	2.44266	0.261880
$88$	−22.2840	−2.37549
$89$	−6.04770	−0.641055	−0.320527	−	0.947239i	$-0.603860\pi$
$89$	−6.04770	−0.641055	−0.320527	+	0.947239i	$0.603860\pi$
$90$	2.86913	0.302432
$91$	2.98667	0.313088
$92$	22.0656	2.30049
$93$	1.21752	0.126251
$94$	7.74036	0.798357
$95$	−2.76467	−0.283649
$96$	−6.48160	−0.661525
$97$	−7.00252	−0.710998	−0.355499	−	0.934677i	$-0.615689\pi$
$97$	−7.00252	−0.710998	−0.355499	+	0.934677i	$0.615689\pi$
$98$	−5.45473	−0.551011
$99$	2.60632	0.261945
$100$	9.48431	0.948431
$101$	−4.19027	−0.416947	−0.208474	−	0.978028i	$-0.566850\pi$
$101$	−4.19027	−0.416947	−0.208474	+	0.978028i	$0.566850\pi$
$102$	−2.19746	−0.217581
$103$	−6.58044	−0.648390	−0.324195	−	0.945990i	$-0.605093\pi$
$103$	−6.58044	−0.648390	−0.324195	+	0.945990i	$0.605093\pi$
$104$	−3.67467	−0.360331
$105$	15.6415	1.52645
$106$	3.45803	0.335873
$107$	−7.88282	−0.762061	−0.381031	−	0.924562i	$-0.624431\pi$
$107$	−7.88282	−0.762061	−0.381031	+	0.924562i	$0.624431\pi$
$108$	17.0398	1.63966
$109$	−12.8072	−1.22671	−0.613353	−	0.789809i	$-0.710180\pi$
$109$	−12.8072	−1.22671	−0.613353	+	0.789809i	$0.710180\pi$
$110$	38.7984	3.69928
$111$	11.0231	1.04627
$112$	5.17798	0.489273
$113$	−5.64464	−0.531003	−0.265501	−	0.964110i	$-0.585537\pi$
$113$	−5.64464	−0.531003	−0.265501	+	0.964110i	$0.585537\pi$
$114$	4.38371	0.410572
$115$	−17.0027	−1.58551
$116$	−4.72591	−0.438790
$117$	0.429785	0.0397336
$118$	19.5931	1.80369
$119$	−1.52932	−0.140192
$120$	−19.2446	−1.75678
$121$	24.2445	2.20404
$122$	2.04975	0.185575
$123$	−18.8966	−1.70385
$124$	−2.35558	−0.211538
$125$	6.51519	0.582736
$126$	−3.16609	−0.282058
$127$	−4.76793	−0.423086	−0.211543	−	0.977369i	$-0.567849\pi$
$127$	−4.76793	−0.423086	−0.211543	+	0.977369i	$0.567849\pi$
$128$	20.5644	1.81765
$129$	18.1058	1.59412
$130$	6.39791	0.561134
$131$	5.10890	0.446367	0.223183	−	0.974776i	$-0.428355\pi$
$131$	5.10890	0.446367	0.223183	+	0.974776i	$0.428355\pi$
$132$	−39.5006	−3.43808
$133$	3.05083	0.264540
$134$	1.59278	0.137595
$135$	−13.1301	−1.13006
$136$	1.88160	0.161346
$137$	6.33485	0.541223	0.270611	−	0.962689i	$-0.412774\pi$
$137$	6.33485	0.541223	0.270611	+	0.962689i	$0.412774\pi$
$138$	26.9598	2.29497
$139$	23.3601	1.98137	0.990687	−	0.136160i	$-0.0434761\pi$
$139$	23.3601	1.98137	0.990687	+	0.136160i	$0.0434761\pi$
$140$	−30.2623	−2.55763
$141$	6.07231	0.511381
$142$	−12.6864	−1.06462
$143$	5.81186	0.486012
$144$	0.745117	0.0620931
$145$	3.64157	0.302416
$146$	29.8487	2.47030
$147$	−4.27923	−0.352945
$148$	−21.3270	−1.75307
$149$	23.4474	1.92088	0.960442	−	0.278481i	$-0.0898310\pi$
$149$	23.4474	1.92088	0.960442	+	0.278481i	$0.0898310\pi$
$150$	11.5879	0.946152
$151$	−2.13880	−0.174053	−0.0870267	−	0.996206i	$-0.527737\pi$
$151$	−2.13880	−0.174053	−0.0870267	+	0.996206i	$0.527737\pi$
$152$	−3.75360	−0.304457
$153$	−0.220070	−0.0177916
$154$	−42.8142	−3.45006
$155$	1.81510	0.145793
$156$	−6.51370	−0.521513
$157$	13.8519	1.10551	0.552753	−	0.833345i	$-0.313577\pi$
$157$	13.8519	1.10551	0.552753	+	0.833345i	$0.313577\pi$
$158$	35.7281	2.84237
$159$	2.71282	0.215141
$160$	−9.66293	−0.763921
$161$	18.7625	1.47870
$162$	23.9326	1.88032
$163$	−14.6394	−1.14664	−0.573322	−	0.819330i	$-0.694346\pi$
$163$	−14.6394	−1.14664	−0.573322	+	0.819330i	$0.694346\pi$
$164$	36.5601	2.85487
$165$	30.4373	2.36954
$166$	−19.9174	−1.54589
$167$	−24.5881	−1.90268	−0.951341	−	0.308140i	$-0.900293\pi$
$167$	−24.5881	−1.90268	−0.951341	+	0.308140i	$0.900293\pi$
$168$	21.2365	1.63843
$169$	−12.0416	−0.926278
$170$	−3.27603	−0.251260
$171$	0.439017	0.0335725
$172$	−35.0300	−2.67101
$173$	−3.96780	−0.301666	−0.150833	−	0.988559i	$-0.548196\pi$
$173$	−3.96780	−0.301666	−0.150833	+	0.988559i	$0.548196\pi$
$174$	−5.77413	−0.437736
$175$	8.06459	0.609626
$176$	10.0760	0.759508
$177$	15.3708	1.15534
$178$	14.2960	1.07153
$179$	−5.26036	−0.393178	−0.196589	−	0.980486i	$-0.562986\pi$
$179$	−5.26036	−0.393178	−0.196589	+	0.980486i	$0.562986\pi$
$180$	−4.35477	−0.324586
$181$	−1.11371	−0.0827812	−0.0413906	−	0.999143i	$-0.513179\pi$
$181$	−1.11371	−0.0827812	−0.0413906	+	0.999143i	$0.513179\pi$
$182$	−7.06011	−0.523330
$183$	1.60803	0.118869
$184$	−23.0846	−1.70182
$185$	16.4336	1.20822
$186$	−2.87806	−0.211030
$187$	−2.97595	−0.217623
$188$	−11.7484	−0.856837
$189$	14.4891	1.05393
$190$	6.53534	0.474123
$191$	−6.68373	−0.483618	−0.241809	−	0.970324i	$-0.577741\pi$
$191$	−6.68373	−0.483618	−0.241809	+	0.970324i	$0.577741\pi$
$192$	21.6166	1.56004
$193$	17.7358	1.27665	0.638327	−	0.769766i	$-0.279627\pi$
$193$	17.7358	1.27665	0.638327	+	0.769766i	$0.279627\pi$
$194$	16.5531	1.18844
$195$	5.01916	0.359429
$196$	8.27922	0.591373
$197$	10.5766	0.753551	0.376775	−	0.926305i	$-0.377033\pi$
$197$	10.5766	0.753551	0.376775	+	0.926305i	$0.377033\pi$
$198$	−6.16100	−0.437843
$199$	8.31750	0.589612	0.294806	−	0.955557i	$-0.404745\pi$
$199$	8.31750	0.589612	0.294806	+	0.955557i	$0.404745\pi$
$200$	−9.92232	−0.701614
$201$	1.24953	0.0881354
$202$	9.90527	0.696932
$203$	−4.01849	−0.282042
$204$	3.33532	0.233519
$205$	−28.1715	−1.96759
$206$	15.5553	1.08379
$207$	2.69995	0.187660
$208$	1.66155	0.115208
$209$	5.93671	0.410651
$210$	−36.9745	−2.55148
$211$	15.0922	1.03899	0.519494	−	0.854474i	$-0.326121\pi$
$211$	15.0922	1.03899	0.519494	+	0.854474i	$0.326121\pi$
$212$	−5.24861	−0.360476
$213$	−9.95244	−0.681930
$214$	18.6340	1.27379
$215$	26.9925	1.84087
$216$	−17.8267	−1.21296
$217$	−2.00297	−0.135971
$218$	30.2746	2.05045
$219$	23.4163	1.58233
$220$	−58.8884	−3.97026
$221$	−0.490738	−0.0330106
$222$	−26.0573	−1.74885
$223$	−17.6774	−1.18377	−0.591883	−	0.806024i	$-0.701615\pi$
$223$	−17.6774	−1.18377	−0.591883	+	0.806024i	$0.701615\pi$
$224$	10.6631	0.712457
$225$	1.16050	0.0773669
$226$	13.3432	0.887577
$227$	1.65254	0.109683	0.0548416	−	0.998495i	$-0.482535\pi$
$227$	1.65254	0.109683	0.0548416	+	0.998495i	$0.482535\pi$
$228$	−6.65362	−0.440647
$229$	15.0628	0.995381	0.497691	−	0.867355i	$-0.334182\pi$
$229$	15.0628	0.995381	0.497691	+	0.867355i	$0.334182\pi$
$230$	40.1923	2.65020
$231$	−33.5877	−2.20991
$232$	4.94417	0.324601
$233$	−11.7727	−0.771256	−0.385628	−	0.922654i	$-0.626015\pi$
$233$	−11.7727	−0.771256	−0.385628	+	0.922654i	$0.626015\pi$
$234$	−1.01596	−0.0664152
$235$	9.05275	0.590536
$236$	−29.7386	−1.93582
$237$	28.0287	1.82066
$238$	3.61511	0.234333
$239$	−21.5698	−1.39523	−0.697616	−	0.716472i	$-0.745756\pi$
$239$	−21.5698	−1.39523	−0.697616	+	0.716472i	$0.745756\pi$
$240$	8.70170	0.561692
$241$	−2.80051	−0.180397	−0.0901983	−	0.995924i	$-0.528750\pi$
$241$	−2.80051	−0.180397	−0.0901983	+	0.995924i	$0.528750\pi$
$242$	−57.3109	−3.68409
$243$	4.52741	0.290434
$244$	−3.11112	−0.199169
$245$	−6.37959	−0.407577
$246$	44.6692	2.84801
$247$	0.978971	0.0622904
$248$	2.46437	0.156488
$249$	−15.6252	−0.990204
$250$	−15.4011	−0.974051
$251$	−13.5889	−0.857723	−0.428862	−	0.903370i	$-0.641085\pi$
$251$	−13.5889	−0.857723	−0.428862	+	0.903370i	$0.641085\pi$
$252$	4.80551	0.302719
$253$	36.5107	2.29541
$254$	11.2708	0.707192
$255$	−2.57004	−0.160942
$256$	−25.2984	−1.58115
$257$	−25.3563	−1.58168	−0.790841	−	0.612022i	$-0.790356\pi$
$257$	−25.3563	−1.58168	−0.790841	+	0.612022i	$0.790356\pi$
$258$	−42.7998	−2.66460
$259$	−18.1345	−1.12682
$260$	−9.71078	−0.602237
$261$	−0.578264	−0.0357937
$262$	−12.0768	−0.746107
$263$	0.342820	0.0211392	0.0105696	−	0.999944i	$-0.496636\pi$
$263$	0.342820	0.0211392	0.0105696	+	0.999944i	$0.496636\pi$
$264$	41.3248	2.54337
$265$	4.04434	0.248442
$266$	−7.21177	−0.442182
$267$	11.2152	0.686360
$268$	−2.41753	−0.147674
$269$	20.6849	1.26118	0.630591	−	0.776115i	$-0.282813\pi$
$269$	20.6849	1.26118	0.630591	+	0.776115i	$0.282813\pi$
$270$	31.0379	1.88890
$271$	−1.30957	−0.0795504	−0.0397752	−	0.999209i	$-0.512664\pi$
$271$	−1.30957	−0.0795504	−0.0397752	+	0.999209i	$0.512664\pi$
$272$	−0.850791	−0.0515868
$273$	−5.53866	−0.335215
$274$	−14.9748	−0.904661
$275$	15.6932	0.946334
$276$	−40.9197	−2.46308
$277$	23.2153	1.39487	0.697435	−	0.716648i	$-0.254325\pi$
$277$	23.2153	1.39487	0.697435	+	0.716648i	$0.254325\pi$
$278$	−55.2202	−3.31189
$279$	−0.288230	−0.0172559
$280$	31.6599	1.89204
$281$	−18.7186	−1.11666	−0.558328	−	0.829620i	$-0.688557\pi$
$281$	−18.7186	−1.11666	−0.558328	+	0.829620i	$0.688557\pi$
$282$	−14.3542	−0.854779
$283$	−15.5055	−0.921706	−0.460853	−	0.887476i	$-0.652456\pi$
$283$	−15.5055	−0.921706	−0.460853	+	0.887476i	$0.652456\pi$
$284$	19.2554	1.14260
$285$	5.12697	0.303696
$286$	−13.7385	−0.812376
$287$	31.0874	1.83503
$288$	1.53443	0.0904170
$289$	−16.7487	−0.985219
$290$	−8.60822	−0.505492
$291$	12.9859	0.761246
$292$	−45.3045	−2.65125
$293$	−20.5692	−1.20166	−0.600832	−	0.799376i	$-0.705164\pi$
$293$	−20.5692	−1.20166	−0.600832	+	0.799376i	$0.705164\pi$
$294$	10.1156	0.589952
$295$	22.9152	1.33417
$296$	22.3119	1.29685
$297$	28.1948	1.63603
$298$	−55.4266	−3.21078
$299$	6.02066	0.348184
$300$	−17.5883	−1.01546
$301$	−29.7863	−1.71686
$302$	5.05586	0.290932
$303$	7.77068	0.446414
$304$	1.69724	0.0973433
$305$	2.39728	0.137268
$306$	0.520218	0.0297389
$307$	−7.20339	−0.411119	−0.205560	−	0.978645i	$-0.565901\pi$
$307$	−7.20339	−0.411119	−0.205560	+	0.978645i	$0.565901\pi$
$308$	64.9836	3.70278
$309$	12.2031	0.694213
$310$	−4.29068	−0.243694
$311$	27.8676	1.58023	0.790113	−	0.612961i	$-0.210022\pi$
$311$	27.8676	1.58023	0.790113	+	0.612961i	$0.210022\pi$
$312$	6.81452	0.385796
$313$	−8.32434	−0.470519	−0.235260	−	0.971933i	$-0.575594\pi$
$313$	−8.32434	−0.470519	−0.235260	+	0.971933i	$0.575594\pi$
$314$	−32.7443	−1.84787
$315$	−3.70290	−0.208635
$316$	−54.2283	−3.05058
$317$	1.00000	0.0561656
$317$	1.00000	0.0561656
$318$	−6.41277	−0.359610
$319$	−7.81971	−0.437820
$320$	32.2266	1.80152
$321$	14.6184	0.815918
$322$	−44.3523	−2.47166
$323$	−0.501279	−0.0278919
$324$	−36.3251	−2.01806
$325$	2.58782	0.143547
$326$	34.6056	1.91663
$327$	23.7504	1.31340
$328$	−38.2486	−2.11192
$329$	−9.98974	−0.550752
$330$	−71.9500	−3.96072
$331$	18.6100	1.02290	0.511450	−	0.859313i	$-0.329108\pi$
$331$	18.6100	1.02290	0.511450	+	0.859313i	$0.329108\pi$
$332$	30.2307	1.65912
$333$	−2.60957	−0.143004
$334$	58.1231	3.18036
$335$	1.86284	0.101778
$336$	−9.60235	−0.523851
$337$	−4.48937	−0.244552	−0.122276	−	0.992496i	$-0.539019\pi$
$337$	−4.48937	−0.244552	−0.122276	+	0.992496i	$0.539019\pi$
$338$	28.4649	1.54828
$339$	10.4677	0.568530
$340$	4.97238	0.269665
$341$	−3.89766	−0.211070
$342$	−1.03778	−0.0561168
$343$	−14.3159	−0.772985
$344$	36.6478	1.97592
$345$	31.5308	1.69756
$346$	9.37937	0.504238
$347$	11.6188	0.623732	0.311866	−	0.950126i	$-0.399046\pi$
$347$	11.6188	0.623732	0.311866	+	0.950126i	$0.399046\pi$
$348$	8.76401	0.469800
$349$	−1.08540	−0.0581001	−0.0290500	−	0.999578i	$-0.509248\pi$
$349$	−1.08540	−0.0581001	−0.0290500	+	0.999578i	$0.509248\pi$
$350$	−19.0637	−1.01900
$351$	4.64937	0.248165
$352$	20.7496	1.10596
$353$	32.0558	1.70616	0.853078	−	0.521783i	$-0.174733\pi$
$353$	32.0558	1.70616	0.853078	+	0.521783i	$0.174733\pi$
$354$	−36.3346	−1.93116
$355$	−14.8373	−0.787484
$356$	−21.6986	−1.15002
$357$	2.83605	0.150100
$358$	12.4348	0.657201
$359$	−20.8795	−1.10198	−0.550988	−	0.834513i	$-0.685749\pi$
$359$	−20.8795	−1.10198	−0.550988	+	0.834513i	$0.685749\pi$
$360$	4.55589	0.240117
$361$	1.00000	0.0526316
$362$	2.63266	0.138370
$363$	−44.9604	−2.35981
$364$	10.7159	0.561665
$365$	34.9096	1.82725
$366$	−3.80117	−0.198690
$367$	32.6444	1.70402	0.852012	−	0.523522i	$-0.175382\pi$
$367$	32.6444	1.70402	0.852012	+	0.523522i	$0.175382\pi$
$368$	10.4380	0.544119
$369$	4.47351	0.232882
$370$	−38.8469	−2.01955
$371$	−4.46294	−0.231704
$372$	4.36833	0.226488
$373$	9.50394	0.492095	0.246048	−	0.969258i	$-0.420868\pi$
$373$	9.50394	0.492095	0.246048	+	0.969258i	$0.420868\pi$
$374$	7.03477	0.363759
$375$	−12.0822	−0.623920
$376$	12.2909	0.633857
$377$	−1.28948	−0.0664116
$378$	−34.2504	−1.76165
$379$	10.6300	0.546026	0.273013	−	0.962010i	$-0.411980\pi$
$379$	10.6300	0.546026	0.273013	+	0.962010i	$0.411980\pi$
$380$	−9.91937	−0.508853
$381$	8.84193	0.452986
$382$	15.7995	0.808373
$383$	−36.6791	−1.87421	−0.937106	−	0.349044i	$-0.886506\pi$
$383$	−36.6791	−1.87421	−0.937106	+	0.349044i	$0.886506\pi$
$384$	−38.1357	−1.94611
$385$	−50.0734	−2.55197
$386$	−41.9253	−2.13394
$387$	−4.28629	−0.217884
$388$	−25.1244	−1.27550
$389$	−10.1569	−0.514973	−0.257486	−	0.966282i	$-0.582894\pi$
$389$	−10.1569	−0.514973	−0.257486	+	0.966282i	$0.582894\pi$
$390$	−11.8647	−0.600790
$391$	−3.08286	−0.155907
$392$	−8.66158	−0.437476
$393$	−9.47425	−0.477913
$394$	−25.0017	−1.25957
$395$	41.7858	2.10247
$396$	9.35121	0.469916
$397$	−21.4034	−1.07421	−0.537103	−	0.843517i	$-0.680481\pi$
$397$	−21.4034	−1.07421	−0.537103	+	0.843517i	$0.680481\pi$
$398$	−19.6615	−0.985543
$399$	−5.65763	−0.283236
$400$	4.48650	0.224325
$401$	27.1733	1.35697	0.678484	−	0.734615i	$-0.262637\pi$
$401$	27.1733	1.35697	0.678484	+	0.734615i	$0.262637\pi$
$402$	−2.95374	−0.147319
$403$	−0.642729	−0.0320166
$404$	−15.0343	−0.747983
$405$	27.9904	1.39085
$406$	9.49920	0.471437
$407$	−35.2886	−1.74919
$408$	−3.48935	−0.172749
$409$	20.2088	0.999263	0.499631	−	0.866238i	$-0.333469\pi$
$409$	20.2088	0.999263	0.499631	+	0.866238i	$0.333469\pi$
$410$	66.5940	3.28884
$411$	−11.7477	−0.579472
$412$	−23.6100	−1.16318
$413$	−25.2870	−1.24429
$414$	−6.38234	−0.313675
$415$	−23.2944	−1.14348
$416$	3.42164	0.167760
$417$	−43.3203	−2.12140
$418$	−14.0336	−0.686407
$419$	−15.2907	−0.746998	−0.373499	−	0.927631i	$-0.621842\pi$
$419$	−15.2907	−0.746998	−0.373499	+	0.927631i	$0.621842\pi$
$420$	56.1202	2.73838
$421$	−33.4439	−1.62996	−0.814978	−	0.579492i	$-0.803251\pi$
$421$	−33.4439	−1.62996	−0.814978	+	0.579492i	$0.803251\pi$
$422$	−35.6760	−1.73668
$423$	−1.43753	−0.0698953
$424$	5.49101	0.266667
$425$	−1.32509	−0.0642762
$426$	23.5263	1.13985
$427$	−2.64541	−0.128020
$428$	−28.2828	−1.36710
$429$	−10.7779	−0.520360
$430$	−63.8069	−3.07704
$431$	10.8804	0.524092	0.262046	−	0.965055i	$-0.415603\pi$
$431$	10.8804	0.524092	0.262046	+	0.965055i	$0.415603\pi$
$432$	8.06059	0.387815
$433$	29.7553	1.42995	0.714973	−	0.699152i	$-0.246439\pi$
$433$	29.7553	1.42995	0.714973	+	0.699152i	$0.246439\pi$
$434$	4.73478	0.227277
$435$	−6.75314	−0.323788
$436$	−45.9509	−2.20065
$437$	6.14999	0.294194
$438$	−55.3532	−2.64488
$439$	25.1943	1.20246	0.601229	−	0.799077i	$-0.294678\pi$
$439$	25.1943	1.20246	0.601229	+	0.799077i	$0.294678\pi$
$440$	61.6081	2.93705
$441$	1.01305	0.0482404
$442$	1.16004	0.0551776
$443$	−20.2305	−0.961180	−0.480590	−	0.876945i	$-0.659577\pi$
$443$	−20.2305	−0.961180	−0.480590	+	0.876945i	$0.659577\pi$
$444$	39.5500	1.87696
$445$	16.7199	0.792599
$446$	41.7871	1.97868
$447$	−43.4822	−2.05664
$448$	−35.5621	−1.68015
$449$	−39.8022	−1.87838	−0.939191	−	0.343396i	$-0.888423\pi$
$449$	−39.8022	−1.87838	−0.939191	+	0.343396i	$0.888423\pi$
$450$	−2.74328	−0.129320
$451$	60.4940	2.84855
$452$	−20.2524	−0.952593
$453$	3.96632	0.186354
$454$	−3.90641	−0.183337
$455$	−8.25716	−0.387102
$456$	6.96090	0.325974
$457$	−0.807512	−0.0377738	−0.0188869	−	0.999822i	$-0.506012\pi$
$457$	−0.807512	−0.0377738	−0.0188869	+	0.999822i	$0.506012\pi$
$458$	−35.6067	−1.66379
$459$	−2.38069	−0.111121
$460$	−61.0041	−2.84433
$461$	23.0488	1.07349	0.536745	−	0.843745i	$-0.319654\pi$
$461$	23.0488	1.07349	0.536745	+	0.843745i	$0.319654\pi$
$462$	79.3971	3.69389
$463$	−9.06342	−0.421213	−0.210606	−	0.977571i	$-0.567544\pi$
$463$	−9.06342	−0.421213	−0.210606	+	0.977571i	$0.567544\pi$
$464$	−2.23557	−0.103784
$465$	−3.36604	−0.156096
$466$	27.8292	1.28916
$467$	−30.7853	−1.42458	−0.712288	−	0.701888i	$-0.752341\pi$
$467$	−30.7853	−1.42458	−0.712288	+	0.701888i	$0.752341\pi$
$468$	1.54203	0.0712802
$469$	−2.05565	−0.0949209
$470$	−21.3996	−0.987088
$471$	−25.6879	−1.18363
$472$	31.1120	1.43204
$473$	−57.9623	−2.66511
$474$	−66.2563	−3.04325
$475$	2.64341	0.121288
$476$	−5.48704	−0.251498
$477$	−0.642222	−0.0294053
$478$	50.9882	2.33215
$479$	−4.91752	−0.224687	−0.112344	−	0.993669i	$-0.535836\pi$
$479$	−4.91752	−0.224687	−0.112344	+	0.993669i	$0.535836\pi$
$480$	17.9195	0.817909
$481$	−5.81913	−0.265330
$482$	6.62005	0.301535
$483$	−34.7944	−1.58320
$484$	86.9868	3.95395
$485$	19.3597	0.879078
$486$	−10.7022	−0.485463
$487$	−13.1416	−0.595501	−0.297750	−	0.954644i	$-0.596236\pi$
$487$	−13.1416	−0.595501	−0.297750	+	0.954644i	$0.596236\pi$
$488$	3.25480	0.147338
$489$	27.1481	1.22768
$490$	15.0805	0.681269
$491$	−0.436884	−0.0197163	−0.00985814	−	0.999951i	$-0.503138\pi$
$491$	−0.436884	−0.0197163	−0.00985814	+	0.999951i	$0.503138\pi$
$492$	−67.7992	−3.05663
$493$	0.660275	0.0297373
$494$	−2.31416	−0.104119
$495$	−7.20561	−0.323868
$496$	−1.11430	−0.0500334
$497$	16.3731	0.734432
$498$	36.9359	1.65514
$499$	−1.39387	−0.0623983	−0.0311992	−	0.999513i	$-0.509933\pi$
$499$	−1.39387	−0.0623983	−0.0311992	+	0.999513i	$0.509933\pi$
$500$	23.3759	1.04540
$501$	45.5976	2.03715
$502$	32.1224	1.43369
$503$	31.6107	1.40945	0.704725	−	0.709481i	$-0.251070\pi$
$503$	31.6107	1.40945	0.704725	+	0.709481i	$0.251070\pi$
$504$	−5.02744	−0.223940
$505$	11.5847	0.515513
$506$	−86.3067	−3.83680
$507$	22.3307	0.991740
$508$	−17.1069	−0.758995
$509$	−1.26547	−0.0560908	−0.0280454	−	0.999607i	$-0.508928\pi$
$509$	−1.26547	−0.0560908	−0.0280454	+	0.999607i	$0.508928\pi$
$510$	6.07526	0.269017
$511$	−38.5228	−1.70415
$512$	18.6736	0.825265
$513$	4.74924	0.209684
$514$	59.9391	2.64380
$515$	18.1928	0.801668
$516$	64.9617	2.85978
$517$	−19.4394	−0.854943
$518$	42.8677	1.88350
$519$	7.35811	0.322985
$520$	10.1593	0.445513
$521$	27.9515	1.22458	0.612288	−	0.790635i	$-0.290249\pi$
$521$	27.9515	1.22458	0.612288	+	0.790635i	$0.290249\pi$
$522$	1.36694	0.0598295
$523$	−39.5557	−1.72965	−0.864826	−	0.502072i	$-0.832571\pi$
$523$	−39.5557	−1.72965	−0.864826	+	0.502072i	$0.832571\pi$
$524$	18.3302	0.800760
$525$	−14.9555	−0.652710
$526$	−0.810384	−0.0353344
$527$	0.329108	0.0143361
$528$	−18.6855	−0.813184
$529$	14.8224	0.644451
$530$	−9.56031	−0.415273
$531$	−3.63882	−0.157911
$532$	10.9461	0.474572
$533$	9.97555	0.432089
$534$	−26.5113	−1.14726
$535$	21.7934	0.942212
$536$	2.52918	0.109244
$537$	9.75512	0.420965
$538$	−48.8966	−2.10808
$539$	13.6992	0.590065
$540$	−47.1095	−2.02727
$541$	0.339837	0.0146107	0.00730537	−	0.999973i	$-0.497675\pi$
$541$	0.339837	0.0146107	0.00730537	+	0.999973i	$0.497675\pi$
$542$	3.09565	0.132969
$543$	2.06532	0.0886315
$544$	−1.75204	−0.0751182
$545$	35.4077	1.51670
$546$	13.0927	0.560315
$547$	−32.2038	−1.37693	−0.688467	−	0.725268i	$-0.741716\pi$
$547$	−32.2038	−1.37693	−0.688467	+	0.725268i	$0.741716\pi$
$548$	22.7288	0.970928
$549$	−0.380678	−0.0162469
$550$	−37.0967	−1.58181
$551$	−1.31718	−0.0561138
$552$	42.8095	1.82209
$553$	−46.1108	−1.96083
$554$	−54.8780	−2.33154
$555$	−30.4754	−1.29361
$556$	83.8136	3.55449
$557$	−26.4900	−1.12242	−0.561209	−	0.827674i	$-0.689664\pi$
$557$	−26.4900	−1.12242	−0.561209	+	0.827674i	$0.689664\pi$
$558$	0.681340	0.0288434
$559$	−9.55806	−0.404263
$560$	−14.3154	−0.604937
$561$	5.51877	0.233003
$562$	44.2483	1.86650
$563$	−33.0983	−1.39493	−0.697463	−	0.716621i	$-0.745688\pi$
$563$	−33.0983	−1.39493	−0.697463	+	0.716621i	$0.745688\pi$
$564$	21.7869	0.917392
$565$	15.6056	0.656531
$566$	36.6530	1.54064
$567$	−30.8875	−1.29715
$568$	−20.1447	−0.845253
$569$	33.4999	1.40439	0.702195	−	0.711985i	$-0.252203\pi$
$569$	33.4999	1.40439	0.702195	+	0.711985i	$0.252203\pi$
$570$	−12.1195	−0.507631
$571$	21.2927	0.891073	0.445537	−	0.895264i	$-0.353013\pi$
$571$	21.2927	0.891073	0.445537	+	0.895264i	$0.353013\pi$
$572$	20.8524	0.871883
$573$	12.3947	0.517796
$574$	−73.4867	−3.06728
$575$	16.2570	0.677962
$576$	−5.11743	−0.213226
$577$	30.1448	1.25494	0.627472	−	0.778639i	$-0.284090\pi$
$577$	30.1448	1.25494	0.627472	+	0.778639i	$0.284090\pi$
$578$	39.5919	1.64680
$579$	−32.8904	−1.36688
$580$	13.0656	0.542520
$581$	25.7054	1.06644
$582$	−30.6970	−1.27243
$583$	−8.68459	−0.359679
$584$	47.3968	1.96129
$585$	−1.18821	−0.0491266
$586$	48.6229	2.00859
$587$	34.4979	1.42388	0.711940	−	0.702241i	$-0.247817\pi$
$587$	34.4979	1.42388	0.711940	+	0.702241i	$0.247817\pi$
$588$	−15.3535	−0.633167
$589$	−0.656535	−0.0270521
$590$	−54.1686	−2.23008
$591$	−19.6138	−0.806806
$592$	−10.0886	−0.414639
$593$	−15.3627	−0.630868	−0.315434	−	0.948947i	$-0.602150\pi$
$593$	−15.3627	−0.630868	−0.315434	+	0.948947i	$0.602150\pi$
$594$	−66.6490	−2.73464
$595$	4.22806	0.173333
$596$	84.1269	3.44597
$597$	−15.4245	−0.631281
$598$	−14.2321	−0.581993
$599$	−32.4520	−1.32595	−0.662975	−	0.748641i	$-0.730707\pi$
$599$	−32.4520	−1.32595	−0.662975	+	0.748641i	$0.730707\pi$
$600$	18.4005	0.751199
$601$	−24.2101	−0.987551	−0.493775	−	0.869590i	$-0.664383\pi$
$601$	−24.2101	−0.987551	−0.493775	+	0.869590i	$0.664383\pi$
$602$	70.4112	2.86975
$603$	−0.295810	−0.0120463
$604$	−7.67382	−0.312243
$605$	−67.0281	−2.72508
$606$	−18.3689	−0.746186
$607$	−32.7223	−1.32816	−0.664078	−	0.747663i	$-0.731176\pi$
$607$	−32.7223	−1.32816	−0.664078	+	0.747663i	$0.731176\pi$
$608$	3.49514	0.141747
$609$	7.45212	0.301975
$610$	−5.66688	−0.229445
$611$	−3.20558	−0.129684
$612$	−0.789590	−0.0319173
$613$	27.0576	1.09285	0.546423	−	0.837509i	$-0.315989\pi$
$613$	27.0576	1.09285	0.546423	+	0.837509i	$0.315989\pi$
$614$	17.0279	0.687190
$615$	52.2430	2.10664
$616$	−67.9847	−2.73918
$617$	−38.2948	−1.54169	−0.770845	−	0.637023i	$-0.780166\pi$
$617$	−38.2948	−1.54169	−0.770845	+	0.637023i	$0.780166\pi$
$618$	−28.8467	−1.16038
$619$	−6.50787	−0.261573	−0.130787	−	0.991411i	$-0.541750\pi$
$619$	−6.50787	−0.261573	−0.130787	+	0.991411i	$0.541750\pi$
$620$	6.51242	0.261545
$621$	29.2078	1.17207
$622$	−65.8755	−2.64137
$623$	−18.4505	−0.739203
$624$	−3.08127	−0.123350
$625$	−31.2294	−1.24918
$626$	19.6777	0.786478
$627$	−11.0094	−0.439672
$628$	49.6994	1.98322
$629$	2.97967	0.118807
$630$	8.75320	0.348736
$631$	1.24572	0.0495913	0.0247957	−	0.999693i	$-0.492106\pi$
$631$	1.24572	0.0495913	0.0247957	+	0.999693i	$0.492106\pi$
$632$	56.7327	2.25671
$633$	−27.9878	−1.11241
$634$	−2.36387	−0.0938814
$635$	13.1818	0.523103
$636$	9.73334	0.385952
$637$	2.25901	0.0895054
$638$	18.4848	0.731821
$639$	2.35610	0.0932059
$640$	−56.8537	−2.24734
$641$	−8.05730	−0.318244	−0.159122	−	0.987259i	$-0.550866\pi$
$641$	−8.05730	−0.318244	−0.159122	+	0.987259i	$0.550866\pi$
$642$	−34.5560	−1.36382
$643$	−26.9536	−1.06294	−0.531472	−	0.847076i	$-0.678361\pi$
$643$	−26.9536	−1.06294	−0.531472	+	0.847076i	$0.678361\pi$
$644$	67.3182	2.65271
$645$	−50.0565	−1.97097
$646$	1.18496	0.0466217
$647$	−42.3924	−1.66662	−0.833309	−	0.552807i	$-0.813557\pi$
$647$	−42.3924	−1.66662	−0.833309	+	0.552807i	$0.813557\pi$
$648$	38.0027	1.49289
$649$	−49.2068	−1.93153
$650$	−6.11729	−0.239940
$651$	3.71443	0.145580
$652$	−52.5246	−2.05702
$653$	−42.8589	−1.67720	−0.838598	−	0.544750i	$-0.816624\pi$
$653$	−42.8589	−1.67720	−0.838598	+	0.544750i	$0.816624\pi$
$654$	−56.1429	−2.19536
$655$	−14.1244	−0.551888
$656$	17.2946	0.675240
$657$	−5.54348	−0.216272
$658$	23.6145	0.920589
$659$	−2.37534	−0.0925302	−0.0462651	−	0.998929i	$-0.514732\pi$
$659$	−2.37534	−0.0925302	−0.0462651	+	0.998929i	$0.514732\pi$
$660$	109.206	4.25084
$661$	−36.5534	−1.42176	−0.710881	−	0.703312i	$-0.751704\pi$
$661$	−36.5534	−1.42176	−0.710881	+	0.703312i	$0.751704\pi$
$662$	−43.9918	−1.70979
$663$	0.910053	0.0353435
$664$	−31.6268	−1.22736
$665$	−8.43453	−0.327077
$666$	6.16871	0.239033
$667$	−8.10064	−0.313658
$668$	−88.2196	−3.41332
$669$	32.7820	1.26743
$670$	−4.40351	−0.170122
$671$	−5.14780	−0.198729
$672$	−19.7742	−0.762808
$673$	−9.61525	−0.370640	−0.185320	−	0.982678i	$-0.559332\pi$
$673$	−9.61525	−0.370640	−0.185320	+	0.982678i	$0.559332\pi$
$674$	10.6123	0.408771
$675$	12.5542	0.483211
$676$	−43.2041	−1.66170
$677$	7.52934	0.289376	0.144688	−	0.989477i	$-0.453782\pi$
$677$	7.52934	0.289376	0.144688	+	0.989477i	$0.453782\pi$
$678$	−24.7444	−0.950304
$679$	−21.3635	−0.819855
$680$	−5.20202	−0.199488
$681$	−3.06457	−0.117435
$682$	9.21357	0.352806
$683$	30.2065	1.15582	0.577909	−	0.816101i	$-0.303869\pi$
$683$	30.2065	1.15582	0.577909	+	0.816101i	$0.303869\pi$
$684$	1.57515	0.0602274
$685$	−17.5138	−0.669168
$686$	33.8410	1.29205
$687$	−27.9334	−1.06573
$688$	−16.5708	−0.631755
$689$	−1.43210	−0.0545587
$690$	−74.5349	−2.83750
$691$	7.67342	0.291911	0.145955	−	0.989291i	$-0.453374\pi$
$691$	7.67342	0.291911	0.145955	+	0.989291i	$0.453374\pi$
$692$	−14.2361	−0.541174
$693$	7.95141	0.302049
$694$	−27.4655	−1.04258
$695$	−64.5829	−2.44977
$696$	−9.16876	−0.347541
$697$	−5.10795	−0.193477
$698$	2.56575	0.0971149
$699$	21.8320	0.825762
$700$	28.9350	1.09364
$701$	4.15632	0.156982	0.0784911	−	0.996915i	$-0.474990\pi$
$701$	4.15632	0.156982	0.0784911	+	0.996915i	$0.474990\pi$
$702$	−10.9905	−0.414810
$703$	−5.94413	−0.224187
$704$	−69.2016	−2.60813
$705$	−16.7879	−0.632271
$706$	−75.7758	−2.85186
$707$	−12.7838	−0.480784
$708$	55.1489	2.07262
$709$	−2.69593	−0.101248	−0.0506239	−	0.998718i	$-0.516121\pi$
$709$	−2.69593	−0.101248	−0.0506239	+	0.998718i	$0.516121\pi$
$710$	35.0736	1.31629
$711$	−6.63539	−0.248847
$712$	22.7007	0.850743
$713$	−4.03769	−0.151213
$714$	−6.70407	−0.250894
$715$	−16.0679	−0.600905
$716$	−18.8737	−0.705342
$717$	40.0003	1.49384
$718$	49.3564	1.84197
$719$	28.1390	1.04941	0.524703	−	0.851285i	$-0.324176\pi$
$719$	28.1390	1.04941	0.524703	+	0.851285i	$0.324176\pi$
$720$	−2.06000	−0.0767718
$721$	−20.0758	−0.747661
$722$	−2.36387	−0.0879743
$723$	5.19343	0.193146
$724$	−3.99587	−0.148505
$725$	−3.48185	−0.129313
$726$	106.281	3.94445
$727$	−1.87869	−0.0696767	−0.0348384	−	0.999393i	$-0.511092\pi$
$727$	−1.87869	−0.0696767	−0.0348384	+	0.999393i	$0.511092\pi$
$728$	−11.2108	−0.415499
$729$	21.9770	0.813965
$730$	−82.5219	−3.05427
$731$	4.89418	0.181018
$732$	5.76944	0.213245
$733$	−16.6505	−0.615000	−0.307500	−	0.951548i	$-0.599492\pi$
$733$	−16.6505	−0.615000	−0.307500	+	0.951548i	$0.599492\pi$
$734$	−77.1673	−2.84830
$735$	11.8307	0.436381
$736$	21.4951	0.792320
$737$	−4.00015	−0.147348
$738$	−10.5748	−0.389264
$739$	−39.9821	−1.47076	−0.735382	−	0.677653i	$-0.762997\pi$
$739$	−39.9821	−1.47076	−0.735382	+	0.677653i	$0.762997\pi$
$740$	58.9621	2.16749
$741$	−1.81546	−0.0666926
$742$	10.5498	0.387297
$743$	31.5821	1.15864	0.579318	−	0.815102i	$-0.303319\pi$
$743$	31.5821	1.15864	0.579318	+	0.815102i	$0.303319\pi$
$744$	−4.57008	−0.167547
$745$	−64.8243	−2.37498
$746$	−22.4661	−0.822543
$747$	3.69904	0.135341
$748$	−10.6774	−0.390405
$749$	−24.0491	−0.878736
$750$	28.5607	1.04289
$751$	−33.6630	−1.22838	−0.614191	−	0.789158i	$-0.710517\pi$
$751$	−33.6630	−1.22838	−0.614191	+	0.789158i	$0.710517\pi$
$752$	−5.55750	−0.202661
$753$	25.2000	0.918340
$754$	3.04817	0.111008
$755$	5.91309	0.215199
$756$	51.9855	1.89069
$757$	−21.6237	−0.785926	−0.392963	−	0.919554i	$-0.628550\pi$
$757$	−21.6237	−0.785926	−0.392963	+	0.919554i	$0.628550\pi$
$758$	−25.1279	−0.912688
$759$	−67.7076	−2.45763
$760$	10.3775	0.376431
$761$	−18.0533	−0.654431	−0.327215	−	0.944950i	$-0.606110\pi$
$761$	−18.0533	−0.654431	−0.327215	+	0.944950i	$0.606110\pi$
$762$	−20.9012	−0.757171
$763$	−39.0725	−1.41452
$764$	−23.9806	−0.867587
$765$	0.608422	0.0219975
$766$	86.7047	3.13277
$767$	−8.11426	−0.292989
$768$	46.9149	1.69290
$769$	6.10801	0.220260	0.110130	−	0.993917i	$-0.464873\pi$
$769$	6.10801	0.220260	0.110130	+	0.993917i	$0.464873\pi$
$770$	118.367	4.26565
$771$	47.0222	1.69346
$772$	63.6344	2.29025
$773$	−0.478470	−0.0172094	−0.00860468	−	0.999963i	$-0.502739\pi$
$773$	−0.478470	−0.0172094	−0.00860468	+	0.999963i	$0.502739\pi$
$774$	10.1322	0.364196
$775$	−1.73549	−0.0623408
$776$	26.2847	0.943565
$777$	33.6297	1.20646
$778$	24.0095	0.860783
$779$	10.1898	0.365089
$780$	18.0082	0.644798
$781$	31.8609	1.14007
$782$	7.28750	0.260600
$783$	−6.25560	−0.223557
$784$	3.91644	0.139873
$785$	−38.2961	−1.36685
$786$	22.3959	0.798837
$787$	−24.7188	−0.881129	−0.440564	−	0.897721i	$-0.645222\pi$
$787$	−24.7188	−0.881129	−0.440564	+	0.897721i	$0.645222\pi$
$788$	37.9478	1.35183
$789$	−0.635746	−0.0226331
$790$	−98.7764	−3.51431
$791$	−17.2208	−0.612301
$792$	−9.78307	−0.347626
$793$	−0.848879	−0.0301446
$794$	50.5949	1.79555
$795$	−7.50006	−0.266000
$796$	29.8424	1.05773
$797$	19.7925	0.701087	0.350544	−	0.936546i	$-0.385997\pi$
$797$	19.7925	0.701087	0.350544	+	0.936546i	$0.385997\pi$
$798$	13.3739	0.473432
$799$	1.64141	0.0580688
$800$	9.23911	0.326652
$801$	−2.65504	−0.0938113
$802$	−64.2342	−2.26819
$803$	−74.9629	−2.64538
$804$	4.48321	0.158111
$805$	−51.8723	−1.82826
$806$	1.51933	0.0535161
$807$	−38.3593	−1.35031
$808$	15.7286	0.553330
$809$	11.4220	0.401577	0.200788	−	0.979635i	$-0.435650\pi$
$809$	11.4220	0.401577	0.200788	+	0.979635i	$0.435650\pi$
$810$	−66.1658	−2.32483
$811$	19.4829	0.684138	0.342069	−	0.939675i	$-0.388872\pi$
$811$	19.4829	0.684138	0.342069	+	0.939675i	$0.388872\pi$
$812$	−14.4179	−0.505970
$813$	2.42854	0.0851724
$814$	83.4177	2.92379
$815$	40.4731	1.41771
$816$	1.57776	0.0552325
$817$	−9.76337	−0.341577
$818$	−47.7712	−1.67028
$819$	1.31120	0.0458170
$820$	−101.077	−3.52975
$821$	11.5155	0.401892	0.200946	−	0.979602i	$-0.435598\pi$
$821$	11.5155	0.401892	0.200946	+	0.979602i	$0.435598\pi$
$822$	27.7701	0.968595
$823$	40.4739	1.41083	0.705415	−	0.708795i	$-0.250761\pi$
$823$	40.4739	1.41083	0.705415	+	0.708795i	$0.250761\pi$
$824$	24.7003	0.860477
$825$	−29.1023	−1.01321
$826$	59.7752	2.07985
$827$	−7.85747	−0.273231	−0.136615	−	0.990624i	$-0.543622\pi$
$827$	−7.85747	−0.273231	−0.136615	+	0.990624i	$0.543622\pi$
$828$	9.68716	0.336652
$829$	39.4279	1.36939	0.684694	−	0.728830i	$-0.259936\pi$
$829$	39.4279	1.36939	0.684694	+	0.728830i	$0.259936\pi$
$830$	55.0650	1.91133
$831$	−43.0517	−1.49345
$832$	−11.4114	−0.395620
$833$	−1.15672	−0.0400780
$834$	102.404	3.54595
$835$	67.9780	2.35247
$836$	21.3003	0.736687
$837$	−3.11804	−0.107775
$838$	36.1452	1.24862
$839$	−7.01971	−0.242347	−0.121174	−	0.992631i	$-0.538666\pi$
$839$	−7.01971	−0.242347	−0.121174	+	0.992631i	$0.538666\pi$
$840$	−58.7119	−2.02575
$841$	−27.2650	−0.940174
$842$	79.0572	2.72449
$843$	34.7128	1.19557
$844$	54.1492	1.86389
$845$	33.2911	1.14525
$846$	3.39815	0.116831
$847$	73.9657	2.54149
$848$	−2.48283	−0.0852607
$849$	28.7543	0.986845
$850$	3.13234	0.107438
$851$	−36.5563	−1.25314
$852$	−35.7084	−1.22335
$853$	−13.8521	−0.474287	−0.237143	−	0.971475i	$-0.576211\pi$
$853$	−13.8521	−0.474287	−0.237143	+	0.971475i	$0.576211\pi$
$854$	6.25342	0.213988
$855$	−1.21374	−0.0415090
$856$	29.5890	1.01133
$857$	−31.4555	−1.07450	−0.537250	−	0.843423i	$-0.680537\pi$
$857$	−31.4555	−1.07450	−0.537250	+	0.843423i	$0.680537\pi$
$858$	25.4775	0.869788
$859$	28.4563	0.970917	0.485459	−	0.874260i	$-0.338653\pi$
$859$	28.4563	0.970917	0.485459	+	0.874260i	$0.338653\pi$
$860$	96.8465	3.30244
$861$	−57.6503	−1.96472
$862$	−25.7200	−0.876025
$863$	28.7050	0.977130	0.488565	−	0.872527i	$-0.337521\pi$
$863$	28.7050	0.977130	0.488565	+	0.872527i	$0.337521\pi$
$864$	16.5993	0.564718
$865$	10.9697	0.372979
$866$	−70.3377	−2.39017
$867$	31.0598	1.05485
$868$	−7.18648	−0.243925
$869$	−89.7286	−3.04383
$870$	15.9636	0.541216
$871$	−0.659631	−0.0223507
$872$	48.0731	1.62796
$873$	−3.07423	−0.104047
$874$	−14.5378	−0.491749
$875$	19.8767	0.671956
$876$	84.0154	2.83862
$877$	−36.2973	−1.22567	−0.612836	−	0.790210i	$-0.709971\pi$
$877$	−36.2973	−1.22567	−0.612836	+	0.790210i	$0.709971\pi$
$878$	−59.5561	−2.00992
$879$	38.1447	1.28659
$880$	−27.8569	−0.939055
$881$	−5.65536	−0.190534	−0.0952670	−	0.995452i	$-0.530370\pi$
$881$	−5.65536	−0.190534	−0.0952670	+	0.995452i	$0.530370\pi$
$882$	−2.39472	−0.0806344
$883$	−58.4843	−1.96815	−0.984077	−	0.177744i	$-0.943120\pi$
$883$	−58.4843	−1.96815	−0.984077	+	0.177744i	$0.943120\pi$
$884$	−1.76072	−0.0592194
$885$	−42.4952	−1.42846
$886$	47.8224	1.60662
$887$	6.85195	0.230066	0.115033	−	0.993362i	$-0.463303\pi$
$887$	6.85195	0.230066	0.115033	+	0.993362i	$0.463303\pi$
$888$	−41.3765	−1.38850
$889$	−14.5461	−0.487862
$890$	−39.5238	−1.32484
$891$	−60.1051	−2.01360
$892$	−63.4248	−2.12362
$893$	−3.27444	−0.109575
$894$	102.786	3.43769
$895$	14.5432	0.486125
$896$	62.7383	2.09594
$897$	−11.1651	−0.372791
$898$	94.0874	3.13974
$899$	0.864775	0.0288419
$900$	4.16377	0.138792
$901$	0.733303	0.0244299
$902$	−143.000	−4.76139
$903$	55.2375	1.83819
$904$	21.1877	0.704693
$905$	3.07903	0.102351
$906$	−9.37589	−0.311493
$907$	42.9004	1.42448	0.712242	−	0.701934i	$-0.247680\pi$
$907$	42.9004	1.42448	0.712242	+	0.701934i	$0.247680\pi$
$908$	5.92916	0.196766
$909$	−1.83960	−0.0610157
$910$	19.5189	0.647045
$911$	−22.0432	−0.730324	−0.365162	−	0.930944i	$-0.618986\pi$
$911$	−22.0432	−0.730324	−0.365162	+	0.930944i	$0.618986\pi$
$912$	−3.14746	−0.104223
$913$	50.0210	1.65546
$914$	1.90886	0.0631394
$915$	−4.44567	−0.146969
$916$	54.0440	1.78567
$917$	15.5864	0.514707
$918$	5.62766	0.185741
$919$	41.0122	1.35287	0.676434	−	0.736503i	$-0.263524\pi$
$919$	41.0122	1.35287	0.676434	+	0.736503i	$0.263524\pi$
$920$	63.8214	2.10413
$921$	13.3584	0.440174
$922$	−54.4845	−1.79435
$923$	5.25391	0.172934
$924$	−120.509	−3.96447
$925$	−15.7128	−0.516633
$926$	21.4248	0.704062
$927$	−2.88892	−0.0948847
$928$	−4.60373	−0.151125
$929$	1.76477	0.0579003	0.0289502	−	0.999581i	$-0.490784\pi$
$929$	1.76477	0.0579003	0.0289502	+	0.999581i	$0.490784\pi$
$930$	7.95689	0.260917
$931$	2.30754	0.0756265
$932$	−42.2393	−1.38359
$933$	−51.6793	−1.69190
$934$	72.7727	2.38119
$935$	8.22752	0.269069
$936$	−1.61324	−0.0527305
$937$	−48.6194	−1.58833	−0.794164	−	0.607703i	$-0.792091\pi$
$937$	−48.6194	−1.58833	−0.794164	+	0.607703i	$0.792091\pi$
$938$	4.85929	0.158661
$939$	15.4371	0.503772
$940$	32.4804	1.05939
$941$	4.19810	0.136854	0.0684270	−	0.997656i	$-0.478202\pi$
$941$	4.19810	0.136854	0.0684270	+	0.997656i	$0.478202\pi$
$942$	60.7229	1.97846
$943$	62.6674	2.04073
$944$	−14.0677	−0.457864
$945$	−40.0576	−1.30307
$946$	137.016	4.45476
$947$	31.5502	1.02525	0.512623	−	0.858614i	$-0.328674\pi$
$947$	31.5502	1.02525	0.512623	+	0.858614i	$0.328674\pi$
$948$	100.564	3.26617
$949$	−12.3615	−0.401271
$950$	−6.24870	−0.202734
$951$	−1.85446	−0.0601349
$952$	5.74044	0.186049
$953$	51.9163	1.68173	0.840867	−	0.541241i	$-0.182045\pi$
$953$	51.9163	1.68173	0.840867	+	0.541241i	$0.182045\pi$
$954$	1.51813	0.0491514
$955$	18.4783	0.597945
$956$	−77.3902	−2.50298
$957$	14.5013	0.468761
$958$	11.6244	0.375568
$959$	19.3265	0.624086
$960$	−59.7628	−1.92884
$961$	−30.5690	−0.986096
$962$	13.7557	0.443501
$963$	−3.46069	−0.111519
$964$	−10.0480	−0.323623
$965$	−49.0338	−1.57845
$966$	82.2495	2.64634
$967$	−37.5886	−1.20877	−0.604384	−	0.796693i	$-0.706581\pi$
$967$	−37.5886	−1.20877	−0.604384	+	0.796693i	$0.706581\pi$
$968$	−91.0042	−2.92498
$969$	0.929602	0.0298631
$970$	−45.7638	−1.46939
$971$	61.0150	1.95807	0.979033	−	0.203703i	$-0.0652978\pi$
$971$	61.0150	1.95807	0.979033	+	0.203703i	$0.0652978\pi$
$972$	16.2439	0.521024
$973$	71.2674	2.28473
$974$	31.0650	0.995387
$975$	−4.79901	−0.153691
$976$	−1.47170	−0.0471079
$977$	−29.4839	−0.943275	−0.471637	−	0.881793i	$-0.656337\pi$
$977$	−29.4839	−0.943275	−0.471637	+	0.881793i	$0.656337\pi$
$978$	−64.1747	−2.05208
$979$	−35.9034	−1.14748
$980$	−22.8893	−0.731173
$981$	−5.62257	−0.179515
$982$	1.03274	0.0329560
$983$	−8.40509	−0.268081	−0.134040	−	0.990976i	$-0.542795\pi$
$983$	−8.40509	−0.268081	−0.134040	+	0.990976i	$0.542795\pi$
$984$	70.9304	2.26118
$985$	−29.2408	−0.931689
$986$	−1.56081	−0.0497062
$987$	18.5256	0.589675
$988$	3.51245	0.111746
$989$	−60.0446	−1.90931
$990$	17.0332	0.541349
$991$	38.7083	1.22961	0.614805	−	0.788679i	$-0.289235\pi$
$991$	38.7083	1.22961	0.614805	+	0.788679i	$0.289235\pi$
$992$	−2.29469	−0.0728563
$993$	−34.5116	−1.09519
$994$	−38.7039	−1.22761
$995$	−22.9952	−0.728995
$996$	−56.0615	−1.77638
$997$	−13.0936	−0.414678	−0.207339	−	0.978269i	$-0.566480\pi$
$997$	−13.0936	−0.414678	−0.207339	+	0.978269i	$0.566480\pi$
$998$	3.29494	0.104300
$999$	−28.2301	−0.893160

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6023.2.a.a.1.10	✓	98

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6023.2.a.a.1.10	✓	98	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:	\( N \)	\(=\)	\( 6023 = 19 \cdot 317 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6023.a (trivial)

\(f(q)\)	\(=\)	\(q-2.36387 q^{2} -1.85446 q^{3} +3.58790 q^{4} -2.76467 q^{5} +4.38371 q^{6} +3.05083 q^{7} -3.75360 q^{8} +0.439017 q^{9} +O(q^{10})\)	\(q-2.36387 q^{2} -1.85446 q^{3} +3.58790 q^{4} -2.76467 q^{5} +4.38371 q^{6} +3.05083 q^{7} -3.75360 q^{8} +0.439017 q^{9} +6.53534 q^{10} +5.93671 q^{11} -6.65362 q^{12} +0.978971 q^{13} -7.21177 q^{14} +5.12697 q^{15} +1.69724 q^{16} -0.501279 q^{17} -1.03778 q^{18} +1.00000 q^{19} -9.91937 q^{20} -5.65763 q^{21} -14.0336 q^{22} +6.14999 q^{23} +6.96090 q^{24} +2.64341 q^{25} -2.31416 q^{26} +4.74924 q^{27} +10.9461 q^{28} -1.31718 q^{29} -12.1195 q^{30} -0.656535 q^{31} +3.49514 q^{32} -11.0094 q^{33} +1.18496 q^{34} -8.43453 q^{35} +1.57515 q^{36} -5.94413 q^{37} -2.36387 q^{38} -1.81546 q^{39} +10.3775 q^{40} +10.1898 q^{41} +13.3739 q^{42} -9.76337 q^{43} +21.3003 q^{44} -1.21374 q^{45} -14.5378 q^{46} -3.27444 q^{47} -3.14746 q^{48} +2.30754 q^{49} -6.24870 q^{50} +0.929602 q^{51} +3.51245 q^{52} -1.46286 q^{53} -11.2266 q^{54} -16.4130 q^{55} -11.4516 q^{56} -1.85446 q^{57} +3.11365 q^{58} -8.28856 q^{59} +18.3951 q^{60} -0.867113 q^{61} +1.55197 q^{62} +1.33936 q^{63} -11.6566 q^{64} -2.70653 q^{65} +26.0248 q^{66} -0.673800 q^{67} -1.79854 q^{68} -11.4049 q^{69} +19.9382 q^{70} +5.36676 q^{71} -1.64790 q^{72} -12.6270 q^{73} +14.0512 q^{74} -4.90210 q^{75} +3.58790 q^{76} +18.1119 q^{77} +4.29152 q^{78} -15.1142 q^{79} -4.69231 q^{80} -10.1243 q^{81} -24.0875 q^{82} +8.42572 q^{83} -20.2990 q^{84} +1.38587 q^{85} +23.0794 q^{86} +2.44266 q^{87} -22.2840 q^{88} -6.04770 q^{89} +2.86913 q^{90} +2.98667 q^{91} +22.0656 q^{92} +1.21752 q^{93} +7.74036 q^{94} -2.76467 q^{95} -6.48160 q^{96} -7.00252 q^{97} -5.45473 q^{98} +2.60632 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 98 q - 8 q^{2} - 25 q^{3} + 82 q^{4} - 10 q^{5} - 4 q^{6} - 18 q^{7} - 18 q^{8} + 61 q^{9}+O(q^{10}) \) 98 * q - 8 * q^2 - 25 * q^3 + 82 * q^4 - 10 * q^5 - 4 * q^6 - 18 * q^7 - 18 * q^8 + 61 * q^9	\( 98 q - 8 q^{2} - 25 q^{3} + 82 q^{4} - 10 q^{5} - 4 q^{6} - 18 q^{7} - 18 q^{8} + 61 q^{9} - 24 q^{10} - 12 q^{11} - 51 q^{12} - 58 q^{13} - 15 q^{14} - 18 q^{15} + 58 q^{16} - 25 q^{17} - 40 q^{18} + 98 q^{19} - 12 q^{20} - 24 q^{21} - 59 q^{22} - 38 q^{23} - 9 q^{24} - 12 q^{25} - 3 q^{26} - 85 q^{27} - 33 q^{28} - 24 q^{29} - 22 q^{30} - 56 q^{31} - 29 q^{32} - 51 q^{33} - 38 q^{34} - 10 q^{35} + 50 q^{36} - 124 q^{37} - 8 q^{38} - 4 q^{39} - 80 q^{40} - 28 q^{41} - 37 q^{42} - 63 q^{43} - 7 q^{44} - 32 q^{45} - 47 q^{46} - 10 q^{47} - 88 q^{48} + 6 q^{49} - 17 q^{50} - 22 q^{51} - 119 q^{52} - 65 q^{53} + 24 q^{54} - 30 q^{55} - 39 q^{56} - 25 q^{57} - 91 q^{58} - 26 q^{59} - 60 q^{60} - 60 q^{61} + 6 q^{62} - 26 q^{63} + 50 q^{64} - 40 q^{65} + 57 q^{66} - 108 q^{67} - 41 q^{68} - 15 q^{69} - 36 q^{70} - 19 q^{71} - 47 q^{72} - 136 q^{73} + 22 q^{74} - 48 q^{75} + 82 q^{76} - 35 q^{77} - 56 q^{78} - 98 q^{79} - 42 q^{80} + 6 q^{81} - 37 q^{82} - 31 q^{83} - 24 q^{84} - 71 q^{85} - 24 q^{86} + 7 q^{87} - 166 q^{88} - 38 q^{89} + 26 q^{90} - 100 q^{91} - 59 q^{92} - 21 q^{93} - 48 q^{94} - 10 q^{95} - 16 q^{96} - 190 q^{97} - 80 q^{98} - 17 q^{99}+O(q^{100}) \) 98 * q - 8 * q^2 - 25 * q^3 + 82 * q^4 - 10 * q^5 - 4 * q^6 - 18 * q^7 - 18 * q^8 + 61 * q^9 - 24 * q^10 - 12 * q^11 - 51 * q^12 - 58 * q^13 - 15 * q^14 - 18 * q^15 + 58 * q^16 - 25 * q^17 - 40 * q^18 + 98 * q^19 - 12 * q^20 - 24 * q^21 - 59 * q^22 - 38 * q^23 - 9 * q^24 - 12 * q^25 - 3 * q^26 - 85 * q^27 - 33 * q^28 - 24 * q^29 - 22 * q^30 - 56 * q^31 - 29 * q^32 - 51 * q^33 - 38 * q^34 - 10 * q^35 + 50 * q^36 - 124 * q^37 - 8 * q^38 - 4 * q^39 - 80 * q^40 - 28 * q^41 - 37 * q^42 - 63 * q^43 - 7 * q^44 - 32 * q^45 - 47 * q^46 - 10 * q^47 - 88 * q^48 + 6 * q^49 - 17 * q^50 - 22 * q^51 - 119 * q^52 - 65 * q^53 + 24 * q^54 - 30 * q^55 - 39 * q^56 - 25 * q^57 - 91 * q^58 - 26 * q^59 - 60 * q^60 - 60 * q^61 + 6 * q^62 - 26 * q^63 + 50 * q^64 - 40 * q^65 + 57 * q^66 - 108 * q^67 - 41 * q^68 - 15 * q^69 - 36 * q^70 - 19 * q^71 - 47 * q^72 - 136 * q^73 + 22 * q^74 - 48 * q^75 + 82 * q^76 - 35 * q^77 - 56 * q^78 - 98 * q^79 - 42 * q^80 + 6 * q^81 - 37 * q^82 - 31 * q^83 - 24 * q^84 - 71 * q^85 - 24 * q^86 + 7 * q^87 - 166 * q^88 - 38 * q^89 + 26 * q^90 - 100 * q^91 - 59 * q^92 - 21 * q^93 - 48 * q^94 - 10 * q^95 - 16 * q^96 - 190 * q^97 - 80 * q^98 - 17 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more